LMFDB - Embedded newform 336.2.u.a.139.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.19
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0748365 - 1.41223i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98880 - 0.211373i) q^{4} +(-0.353074 + 0.353074i) q^{5} +(0.945681 + 1.05152i) q^{6} +(2.14763 + 1.54521i) q^{7} +(-0.447343 + 2.79283i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.0748365 - 1.41223i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98880 - 0.211373i) q^{4} +(-0.353074 + 0.353074i) q^{5} +(0.945681 + 1.05152i) q^{6} +(2.14763 + 1.54521i) q^{7} +(-0.447343 + 2.79283i) q^{8} -1.00000i q^{9} +(0.472200 + 0.525045i) q^{10} +(2.06639 - 2.06639i) q^{11} +(1.55576 - 1.25683i) q^{12} +(2.73784 + 2.73784i) q^{13} +(2.34292 - 2.91732i) q^{14} -0.499322i q^{15} +(3.91064 + 0.840757i) q^{16} +3.57407i q^{17} +(-1.41223 - 0.0748365i) q^{18} +(5.95882 - 5.95882i) q^{19} +(0.776824 - 0.627563i) q^{20} +(-2.61123 + 0.425977i) q^{21} +(-2.76359 - 3.07287i) q^{22} -1.74465 q^{23} +(-1.65851 - 2.29115i) q^{24} +4.75068i q^{25} +(4.07136 - 3.66158i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.94459 - 3.52706i) q^{28} +(4.96403 - 4.96403i) q^{29} +(-0.705159 - 0.0373675i) q^{30} -3.65022 q^{31} +(1.48000 - 5.45982i) q^{32} +2.92232i q^{33} +(5.04742 + 0.267471i) q^{34} +(-1.30385 + 0.212700i) q^{35} +(-0.211373 + 1.98880i) q^{36} +(6.34670 + 6.34670i) q^{37} +(-7.96931 - 8.86118i) q^{38} -3.87190 q^{39} +(-0.828130 - 1.14402i) q^{40} -6.29768 q^{41} +(0.406163 + 3.71955i) q^{42} +(-4.71295 + 4.71295i) q^{43} +(-4.54642 + 3.67286i) q^{44} +(0.353074 + 0.353074i) q^{45} +(-0.130564 + 2.46386i) q^{46} +0.538446 q^{47} +(-3.35975 + 2.17074i) q^{48} +(2.22465 + 6.63709i) q^{49} +(6.70906 + 0.355524i) q^{50} +(-2.52725 - 2.52725i) q^{51} +(-4.86632 - 6.02373i) q^{52} +(-1.52324 - 1.52324i) q^{53} +(1.05152 - 0.945681i) q^{54} +1.45918i q^{55} +(-5.27623 + 5.30673i) q^{56} +8.42705i q^{57} +(-6.63887 - 7.38186i) q^{58} +(-7.32765 - 7.32765i) q^{59} +(-0.105543 + 0.993051i) q^{60} +(4.15611 + 4.15611i) q^{61} +(-0.273170 + 5.15496i) q^{62} +(1.54521 - 2.14763i) q^{63} +(-7.59977 - 2.49870i) q^{64} -1.93332 q^{65} +(4.12700 + 0.218697i) q^{66} +(-1.75078 - 1.75078i) q^{67} +(0.755463 - 7.10811i) q^{68} +(1.23366 - 1.23366i) q^{69} +(0.202806 + 1.85725i) q^{70} +9.51053 q^{71} +(2.79283 + 0.447343i) q^{72} -8.67488 q^{73} +(9.43798 - 8.48805i) q^{74} +(-3.35924 - 3.35924i) q^{75} +(-13.1104 + 10.5914i) q^{76} +(7.63087 - 1.24484i) q^{77} +(-0.289759 + 5.46802i) q^{78} +1.66646i q^{79} +(-1.67760 + 1.08390i) q^{80} -1.00000 q^{81} +(-0.471297 + 8.89379i) q^{82} +(7.80102 - 7.80102i) q^{83} +(5.28326 - 0.295238i) q^{84} +(-1.26191 - 1.26191i) q^{85} +(6.30308 + 7.00848i) q^{86} +7.02020i q^{87} +(4.84670 + 6.69547i) q^{88} -5.38478 q^{89} +(0.525045 - 0.472200i) q^{90} +(1.64934 + 10.1104i) q^{91} +(3.46977 + 0.368773i) q^{92} +(2.58110 - 2.58110i) q^{93} +(0.0402954 - 0.760410i) q^{94} +4.20781i q^{95} +(2.81415 + 4.90719i) q^{96} -15.5590i q^{97} +(9.53959 - 2.64503i) q^{98} +(-2.06639 - 2.06639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.0748365	−	1.41223i	0.0529174	−	0.998599i
$2$	0.0748365	−	1.41223i	0.0529174	−	0.998599i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.98880	−	0.211373i	−0.994399	−	0.105687i
$5$	−0.353074	+	0.353074i	−0.157900	+	0.157900i	−0.781635	−	0.623736i	$-0.785614\pi$
$5$	−0.353074	+	0.353074i	−0.157900	+	0.157900i	0.623736	+	0.781635i	$0.285614\pi$
$6$	0.945681	+	1.05152i	0.386073	+	0.429280i
$7$	2.14763	+	1.54521i	0.811729	+	0.584035i
$7$	2.14763	+	1.54521i	0.811729	+	0.584035i
$8$	−0.447343	+	2.79283i	−0.158160	+	0.987414i
$9$		−	1.00000i		−	0.333333i
$10$	0.472200	+	0.525045i	0.149323	+	0.166034i
$11$	2.06639	−	2.06639i	0.623041	−	0.623041i	−0.323267	−	0.946308i	$-0.604781\pi$
$11$	2.06639	−	2.06639i	0.623041	−	0.623041i	0.946308	+	0.323267i	$0.104781\pi$
$12$	1.55576	−	1.25683i	0.449108	−	0.362816i
$13$	2.73784	+	2.73784i	0.759342	+	0.759342i	0.976202	−	0.216861i	$-0.0695818\pi$
$13$	2.73784	+	2.73784i	0.759342	+	0.759342i	−0.216861	+	0.976202i	$0.569582\pi$
$14$	2.34292	−	2.91732i	0.626171	−	0.779686i
$15$		−	0.499322i		−	0.128924i
$16$	3.91064	+	0.840757i	0.977661	+	0.210189i
$17$			3.57407i			0.866840i	0.901192	+	0.433420i	$0.142693\pi$
$17$			3.57407i			0.866840i	−0.901192	+	0.433420i	$0.857307\pi$
$18$	−1.41223	−	0.0748365i	−0.332866	−	0.0176391i
$19$	5.95882	−	5.95882i	1.36705	−	1.36705i	0.502430	−	0.864618i	$-0.332439\pi$
$19$	5.95882	−	5.95882i	1.36705	−	1.36705i	0.864618	−	0.502430i	$-0.167561\pi$
$20$	0.776824	−	0.627563i	0.173703	−	0.140327i
$21$	−2.61123	+	0.425977i	−0.569818	+	0.0929558i
$22$	−2.76359	−	3.07287i	−0.589199	−	0.655138i
$23$	−1.74465			−0.363786			−0.181893	−	0.983318i	$-0.558222\pi$
$23$	−1.74465			−0.363786			−0.181893	+	0.983318i	$0.558222\pi$
$24$	−1.65851	−	2.29115i	−0.338542	−	0.467678i
$25$			4.75068i			0.950135i
$26$	4.07136	−	3.66158i	0.798460	−	0.718095i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−3.94459	−	3.52706i	−0.745458	−	0.666552i
$29$	4.96403	−	4.96403i	0.921797	−	0.921797i	−0.0753590	−	0.997156i	$-0.524010\pi$
$29$	4.96403	−	4.96403i	0.921797	−	0.921797i	0.997156	+	0.0753590i	$0.0240103\pi$
$30$	−0.705159	−	0.0373675i	−0.128744	−	0.00682235i
$31$	−3.65022			−0.655599			−0.327800	−	0.944747i	$-0.606307\pi$
$31$	−3.65022			−0.655599			−0.327800	+	0.944747i	$0.606307\pi$
$32$	1.48000	−	5.45982i	0.261630	−	0.965168i
$33$			2.92232i			0.508711i
$34$	5.04742	+	0.267471i	0.865625	+	0.0458709i
$35$	−1.30385	+	0.212700i	−0.220390	+	0.0359528i
$36$	−0.211373	+	1.98880i	−0.0352288	+	0.331466i
$37$	6.34670	+	6.34670i	1.04339	+	1.04339i	0.999015	+	0.0443760i	$0.0141300\pi$
$37$	6.34670	+	6.34670i	1.04339	+	1.04339i	0.0443760	+	0.999015i	$0.485870\pi$
$38$	−7.96931	−	8.86118i	−1.29279	−	1.43747i
$39$	−3.87190			−0.620000
$40$	−0.828130	−	1.14402i	−0.130939	−	0.180885i
$41$	−6.29768			−0.983533			−0.491766	−	0.870727i	$-0.663649\pi$
$41$	−6.29768			−0.983533			−0.491766	+	0.870727i	$0.663649\pi$
$42$	0.406163	+	3.71955i	0.0626723	+	0.573939i
$43$	−4.71295	+	4.71295i	−0.718719	+	0.718719i	−0.968343	−	0.249624i	$-0.919693\pi$
$43$	−4.71295	+	4.71295i	−0.718719	+	0.718719i	0.249624	+	0.968343i	$0.419693\pi$
$44$	−4.54642	+	3.67286i	−0.685399	+	0.553705i
$45$	0.353074	+	0.353074i	0.0526332	+	0.0526332i
$46$	−0.130564	+	2.46386i	−0.0192506	+	0.363276i
$47$	0.538446			0.0785404			0.0392702	−	0.999229i	$-0.487497\pi$
$47$	0.538446			0.0785404			0.0392702	+	0.999229i	$0.487497\pi$
$48$	−3.35975	+	2.17074i	−0.484938	+	0.313319i
$49$	2.22465	+	6.63709i	0.317807	+	0.948155i
$50$	6.70906	+	0.355524i	0.948804	+	0.0502787i
$51$	−2.52725	−	2.52725i	−0.353886	−	0.353886i
$52$	−4.86632	−	6.02373i	−0.674837	−	0.835341i
$53$	−1.52324	−	1.52324i	−0.209233	−	0.209233i	0.594709	−	0.803941i	$-0.297267\pi$
$53$	−1.52324	−	1.52324i	−0.209233	−	0.209233i	−0.803941	+	0.594709i	$0.797267\pi$
$54$	1.05152	−	0.945681i	0.143093	−	0.128691i
$55$			1.45918i			0.196756i
$56$	−5.27623	+	5.30673i	−0.705066	+	0.709141i
$57$			8.42705i			1.11619i
$58$	−6.63887	−	7.38186i	−0.871727	−	0.969285i
$59$	−7.32765	−	7.32765i	−0.953979	−	0.953979i	0.0450080	−	0.998987i	$-0.485669\pi$
$59$	−7.32765	−	7.32765i	−0.953979	−	0.953979i	−0.998987	+	0.0450080i	$0.985669\pi$
$60$	−0.105543	+	0.993051i	−0.0136256	+	0.128202i
$61$	4.15611	+	4.15611i	0.532135	+	0.532135i	0.921207	−	0.389072i	$-0.127204\pi$
$61$	4.15611	+	4.15611i	0.532135	+	0.532135i	−0.389072	+	0.921207i	$0.627204\pi$
$62$	−0.273170	+	5.15496i	−0.0346926	+	0.654681i
$63$	1.54521	−	2.14763i	0.194678	−	0.270576i
$64$	−7.59977	−	2.49870i	−0.949971	−	0.312338i
$65$	−1.93332			−0.239799
$66$	4.12700	+	0.218697i	0.507998	+	0.0269197i
$67$	−1.75078	−	1.75078i	−0.213892	−	0.213892i	0.592026	−	0.805919i	$-0.298328\pi$
$67$	−1.75078	−	1.75078i	−0.213892	−	0.213892i	−0.805919	+	0.592026i	$0.798328\pi$
$68$	0.755463	−	7.10811i	0.0916133	−	0.861985i
$69$	1.23366	−	1.23366i	0.148515	−	0.148515i
$70$	0.202806	+	1.85725i	0.0242400	+	0.221984i
$71$	9.51053			1.12869			0.564346	−	0.825538i	$-0.309128\pi$
$71$	9.51053			1.12869			0.564346	+	0.825538i	$0.309128\pi$
$72$	2.79283	+	0.447343i	0.329138	+	0.0527198i
$73$	−8.67488			−1.01532			−0.507659	−	0.861558i	$-0.669489\pi$
$73$	−8.67488			−1.01532			−0.507659	+	0.861558i	$0.669489\pi$
$74$	9.43798	−	8.48805i	1.09714	−	0.986715i
$75$	−3.35924	−	3.35924i	−0.387891	−	0.387891i
$76$	−13.1104	+	10.5914i	−1.50387	+	1.21491i
$77$	7.63087	−	1.24484i	0.869618	−	0.141863i
$78$	−0.289759	+	5.46802i	−0.0328088	+	0.619131i
$79$			1.66646i			0.187491i	0.995596	+	0.0937457i	$0.0298841\pi$
$79$			1.66646i			0.187491i	−0.995596	+	0.0937457i	$0.970116\pi$
$80$	−1.67760	+	1.08390i	−0.187561	+	0.121183i
$81$	−1.00000			−0.111111
$82$	−0.471297	+	8.89379i	−0.0520460	+	0.982155i
$83$	7.80102	−	7.80102i	0.856273	−	0.856273i	−0.134624	−	0.990897i	$-0.542983\pi$
$83$	7.80102	−	7.80102i	0.856273	−	0.856273i	0.990897	+	0.134624i	$0.0429825\pi$
$84$	5.28326	−	0.295238i	0.576451	−	0.0322131i
$85$	−1.26191	−	1.26191i	−0.136874	−	0.136874i
$86$	6.30308	+	7.00848i	0.679679	+	0.755744i
$87$			7.02020i			0.752645i
$88$	4.84670	+	6.69547i	0.516660	+	0.713739i
$89$	−5.38478			−0.570786			−0.285393	−	0.958411i	$-0.592124\pi$
$89$	−5.38478			−0.570786			−0.285393	+	0.958411i	$0.592124\pi$
$90$	0.525045	−	0.472200i	0.0553446	−	0.0497742i
$91$	1.64934	+	10.1104i	0.172898	+	1.05986i
$92$	3.46977	+	0.368773i	0.361748	+	0.0384473i
$93$	2.58110	−	2.58110i	0.267647	−	0.267647i
$94$	0.0402954	−	0.760410i	0.00415615	−	0.0784303i
$95$			4.20781i			0.431712i
$96$	2.81415	+	4.90719i	0.287218	+	0.500838i
$97$		−	15.5590i		−	1.57978i	−0.613248	−	0.789891i	$-0.710137\pi$
$97$		−	15.5590i		−	1.57978i	0.613248	−	0.789891i	$-0.289863\pi$
$98$	9.53959	−	2.64503i	0.963644	−	0.267188i
$99$	−2.06639	−	2.06639i	−0.207680	−	0.207680i
$100$	1.00417	−	9.44814i	0.100417	−	0.944814i
$101$	−10.8391	+	10.8391i	−1.07853	+	1.07853i	−0.0818847	+	0.996642i	$0.526094\pi$
$101$	−10.8391	+	10.8391i	−1.07853	+	1.07853i	−0.996642	+	0.0818847i	$0.973906\pi$
$102$	−3.75819	+	3.37993i	−0.372117	+	0.334663i
$103$		−	8.56545i		−	0.843978i	−0.906601	−	0.421989i	$-0.861332\pi$
$103$		−	8.56545i		−	0.843978i	0.906601	−	0.421989i	$-0.138668\pi$
$104$	−8.87108	+	6.42157i	−0.869881	+	0.629687i
$105$	0.771558	−	1.07236i	0.0752963	−	0.104652i
$106$	−2.26516	+	2.03717i	−0.220012	+	0.197868i
$107$	−10.4598	+	10.4598i	−1.01118	+	1.01118i	−0.0112477	+	0.999937i	$0.503580\pi$
$107$	−10.4598	+	10.4598i	−1.01118	+	1.01118i	−0.999937	+	0.0112477i	$0.996420\pi$
$108$	−1.25683	−	1.55576i	−0.120939	−	0.149703i
$109$	0.746037	−	0.746037i	0.0714574	−	0.0714574i	−0.670475	−	0.741932i	$-0.733910\pi$
$109$	0.746037	−	0.746037i	0.0714574	−	0.0714574i	0.741932	+	0.670475i	$0.233910\pi$
$110$	2.06070	+	0.109200i	0.196480	+	0.0104118i
$111$	−8.97559			−0.851925
$112$	7.09948	+	7.84840i	0.670838	+	0.741604i
$113$	−1.23013			−0.115721			−0.0578606	−	0.998325i	$-0.518428\pi$
$113$	−1.23013			−0.115721			−0.0578606	+	0.998325i	$0.518428\pi$
$114$	11.9010	+	0.630651i	1.11463	+	0.0590659i
$115$	0.615992	−	0.615992i	0.0574416	−	0.0574416i
$116$	−10.9217	+	8.82320i	−1.01406	+	0.819213i
$117$	2.73784	−	2.73784i	0.253114	−	0.253114i
$118$	−10.8967	+	9.79997i	−1.00312	+	0.902160i
$119$	−5.52269	+	7.67579i	−0.506264	+	0.703639i
$120$	1.39452	+	0.223368i	0.127302	+	0.0203906i
$121$			2.46003i			0.223639i
$122$	6.18042	−	5.55836i	0.559549	−	0.503230i
$123$	4.45313	−	4.45313i	0.401526	−	0.401526i
$124$	7.25956	+	0.771559i	0.651928	+	0.0692880i
$125$	−3.44271	−	3.44271i	−0.307925	−	0.307925i
$126$	−2.91732	−	2.34292i	−0.259895	−	0.208724i
$127$		−	11.6177i		−	1.03090i	−0.856919	−	0.515451i	$-0.827624\pi$
$127$		−	11.6177i		−	1.03090i	0.856919	−	0.515451i	$-0.172376\pi$
$128$	−4.09749	+	10.5456i	−0.362170	+	0.932112i
$129$		−	6.66512i		−	0.586831i
$130$	−0.144683	+	2.73030i	−0.0126896	+	0.239463i
$131$	14.1444	−	14.1444i	1.23580	−	1.23580i	0.274102	−	0.961701i	$-0.411619\pi$
$131$	14.1444	−	14.1444i	1.23580	−	1.23580i	0.961701	−	0.274102i	$-0.0883806\pi$
$132$	0.617700	−	5.81191i	0.0537639	−	0.505862i
$133$	22.0050	−	3.58973i	1.90808	−	0.311269i
$134$	−2.60353	+	2.34149i	−0.224911	+	0.202274i
$135$	−0.499322			−0.0429748
$136$	−9.98177	−	1.59883i	−0.855929	−	0.137099i
$137$		−	2.58160i		−	0.220561i	−0.993901	−	0.110281i	$-0.964825\pi$
$137$		−	2.58160i		−	0.220561i	0.993901	−	0.110281i	$-0.0351749\pi$
$138$	−1.64989	−	1.83453i	−0.140448	−	0.156166i
$139$	−10.2454	−	10.2454i	−0.869002	−	0.869002i	0.123360	−	0.992362i	$-0.460633\pi$
$139$	−10.2454	−	10.2454i	−0.869002	−	0.869002i	−0.992362	+	0.123360i	$0.960633\pi$
$140$	2.63805	−	0.147419i	0.222956	−	0.0124592i
$141$	−0.380739	+	0.380739i	−0.0320640	+	0.0320640i
$142$	0.711735	−	13.4311i	0.0597275	−	1.12711i
$143$	11.3149			0.946202
$144$	0.840757	−	3.91064i	0.0700631	−	0.325887i
$145$			3.50534i			0.291103i
$146$	−0.649198	+	12.2509i	−0.0537280	+	1.01390i
$147$	−6.26620	−	3.12006i	−0.516827	−	0.257338i
$148$	−11.2808	−	13.9638i	−0.927275	−	1.14782i
$149$	−16.4288	−	16.4288i	−1.34590	−	1.34590i	−0.890064	−	0.455836i	$-0.849341\pi$
$149$	−16.4288	−	16.4288i	−1.34590	−	1.34590i	−0.455836	−	0.890064i	$-0.650659\pi$
$150$	−4.99541	+	4.49263i	−0.407874	+	0.366822i
$151$	10.6869			0.869686			0.434843	−	0.900506i	$-0.356804\pi$
$151$	10.6869			0.869686			0.434843	+	0.900506i	$0.356804\pi$
$152$	13.9763	+	19.3076i	1.13363	+	1.56605i
$153$	3.57407			0.288947
$154$	−1.18694	−	10.8697i	−0.0956463	−	0.875907i
$155$	1.28880	−	1.28880i	0.103519	−	0.103519i
$156$	7.70043	+	0.818415i	0.616527	+	0.0655256i
$157$	7.53988	+	7.53988i	0.601748	+	0.601748i	0.940776	−	0.339028i	$-0.110098\pi$
$157$	7.53988	+	7.53988i	0.601748	+	0.601748i	−0.339028	+	0.940776i	$0.610098\pi$
$158$	2.35343	+	0.124712i	0.187229	+	0.00992156i
$159$	2.15418			0.170838
$160$	1.40517	+	2.45027i	0.111088	+	0.193711i
$161$	−3.74688	−	2.69586i	−0.295295	−	0.212463i
$162$	−0.0748365	+	1.41223i	−0.00587971	+	0.110955i
$163$	−10.2545	−	10.2545i	−0.803198	−	0.803198i	0.180396	−	0.983594i	$-0.442262\pi$
$163$	−10.2545	−	10.2545i	−0.803198	−	0.803198i	−0.983594	+	0.180396i	$0.942262\pi$
$164$	12.5248	+	1.33116i	0.978025	+	0.103946i
$165$	−1.03180	−	1.03180i	−0.0803252	−	0.0803252i
$166$	−10.4331	−	11.6007i	−0.809762	−	0.900385i
$167$			2.17484i			0.168294i	0.996453	+	0.0841472i	$0.0268166\pi$
$167$			2.17484i			0.168294i	−0.996453	+	0.0841472i	$0.973183\pi$
$168$	−0.0215640	−	7.48328i	−0.00166370	−	0.577348i
$169$			1.99159i			0.153199i
$170$	−1.87655	+	1.68768i	−0.143925	+	0.129439i
$171$	−5.95882	−	5.95882i	−0.455683	−	0.455683i
$172$	10.3693	−	8.37692i	0.790652	−	0.638734i
$173$	5.40669	+	5.40669i	0.411063	+	0.411063i	0.882109	−	0.471046i	$-0.156123\pi$
$173$	5.40669	+	5.40669i	0.411063	+	0.411063i	−0.471046	+	0.882109i	$0.656123\pi$
$174$	9.91415	+	0.525367i	0.751590	+	0.0398280i
$175$	−7.34079	+	10.2027i	−0.554912	+	0.771252i
$176$	9.81827	−	6.34359i	0.740080	−	0.478166i
$177$	10.3629			0.778920
$178$	−0.402979	+	7.60457i	−0.0302045	+	0.569986i
$179$	−1.42198	−	1.42198i	−0.106284	−	0.106284i	0.651965	−	0.758249i	$-0.273945\pi$
$179$	−1.42198	−	1.42198i	−0.106284	−	0.106284i	−0.758249	+	0.651965i	$0.773945\pi$
$180$	−0.627563	−	0.776824i	−0.0467758	−	0.0579010i
$181$	14.2278	−	14.2278i	1.05754	−	1.05754i	0.0593014	−	0.998240i	$-0.481113\pi$
$181$	14.2278	−	14.2278i	1.05754	−	1.05754i	0.998240	−	0.0593014i	$-0.0188873\pi$
$182$	14.4017	−	1.57262i	1.06753	−	0.116570i
$183$	−5.87762			−0.434486
$184$	0.780459	−	4.87252i	0.0575362	−	0.359207i
$185$	−4.48171			−0.329502
$186$	−3.45195	−	3.83827i	−0.253109	−	0.281435i
$187$	7.38544	+	7.38544i	0.540077	+	0.540077i
$188$	−1.07086	−	0.113813i	−0.0781005	−	0.00830066i
$189$	0.425977	+	2.61123i	0.0309853	+	0.189939i
$190$	5.94241	+	0.314898i	0.431108	+	0.0228451i
$191$			11.5354i			0.834673i	0.908752	+	0.417336i	$0.137036\pi$
$191$			11.5354i			0.834673i	−0.908752	+	0.417336i	$0.862964\pi$
$192$	7.14070	−	3.60700i	0.515335	−	0.260313i
$193$	−12.7812			−0.920013			−0.460006	−	0.887916i	$-0.652153\pi$
$193$	−12.7812			−0.920013			−0.460006	+	0.887916i	$0.652153\pi$
$194$	−21.9730	−	1.16438i	−1.57757	−	0.0835979i
$195$	1.36707	−	1.36707i	0.0978977	−	0.0978977i
$196$	−3.02148	−	13.6701i	−0.215820	−	0.976433i
$197$	−11.5499	−	11.5499i	−0.822894	−	0.822894i	0.163628	−	0.986522i	$-0.447680\pi$
$197$	−11.5499	−	11.5499i	−0.822894	−	0.822894i	−0.986522	+	0.163628i	$0.947680\pi$
$198$	−3.07287	+	2.76359i	−0.218379	+	0.196400i
$199$			2.69165i			0.190806i	0.995439	+	0.0954030i	$0.0304140\pi$
$199$			2.69165i			0.190806i	−0.995439	+	0.0954030i	$0.969586\pi$
$200$	−13.2678	−	2.12518i	−0.938177	−	0.150273i
$201$	2.47598			0.174642
$202$	14.4961	+	16.1184i	1.01994	+	1.13409i
$203$	18.3314	−	2.99044i	1.28661	−	0.209888i
$204$	4.49200	+	5.56039i	0.314503	+	0.389305i
$205$	2.22355	−	2.22355i	0.155299	−	0.155299i
$206$	−12.0964	−	0.641008i	−0.842796	−	0.0446612i
$207$			1.74465i			0.121262i
$208$	8.40487	+	13.0086i	0.582773	+	0.901984i
$209$		−	24.6266i		−	1.70345i
$210$	−1.45668	−	1.16987i	−0.100521	−	0.0807287i
$211$	−12.4646	−	12.4646i	−0.858099	−	0.858099i	0.133015	−	0.991114i	$-0.457534\pi$
$211$	−12.4646	−	12.4646i	−0.858099	−	0.858099i	−0.991114	+	0.133015i	$0.957534\pi$
$212$	2.70744	+	3.35138i	0.185948	+	0.230174i
$213$	−6.72496	+	6.72496i	−0.460787	+	0.460787i
$214$	13.9889	+	15.5544i	0.956258	+	1.06328i
$215$		−	3.32804i		−	0.226971i
$216$	−2.29115	+	1.65851i	−0.155893	+	0.112847i
$217$	−7.83934	−	5.64036i	−0.532169	−	0.382893i
$218$	−0.997747	−	1.10941i	−0.0675760	−	0.0751386i
$219$	6.13407	−	6.13407i	0.414502	−	0.414502i
$220$	0.308432	−	2.90202i	0.0207944	−	0.195654i
$221$	−9.78525	+	9.78525i	−0.658227	+	0.658227i
$222$	−0.671702	+	12.6756i	−0.0450817	+	0.850731i
$223$	12.7117			0.851237			0.425618	−	0.904903i	$-0.360057\pi$
$223$	12.7117			0.851237			0.425618	+	0.904903i	$0.360057\pi$
$224$	11.6151	−	9.43876i	0.776064	−	0.630654i
$225$	4.75068			0.316712
$226$	−0.0920589	+	1.73723i	−0.00612367	+	0.115559i
$227$	−10.9992	+	10.9992i	−0.730040	+	0.730040i	−0.970627	−	0.240587i	$-0.922660\pi$
$227$	−10.9992	+	10.9992i	−0.730040	+	0.730040i	0.240587	+	0.970627i	$0.422660\pi$
$228$	1.78125	−	16.7597i	0.117966	−	1.10994i
$229$	2.73573	−	2.73573i	0.180782	−	0.180782i	−0.610914	−	0.791697i	$-0.709198\pi$
$229$	2.73573	−	2.73573i	0.180782	−	0.180782i	0.791697	+	0.610914i	$0.209198\pi$
$230$	−0.823825	−	0.916023i	−0.0543214	−	0.0604008i
$231$	−4.51560	+	6.27608i	−0.297105	+	0.412935i
$232$	11.6431	+	16.0843i	0.764404	+	1.05599i
$233$			8.97538i			0.587996i	0.955806	+	0.293998i	$0.0949860\pi$
$233$			8.97538i			0.587996i	−0.955806	+	0.293998i	$0.905014\pi$
$234$	−3.66158	−	4.07136i	−0.239365	−	0.266153i
$235$	−0.190111	+	0.190111i	−0.0124015	+	0.0124015i
$236$	13.0244	+	16.1221i	0.847813	+	1.04946i
$237$	−1.17836	−	1.17836i	−0.0765430	−	0.0765430i
$238$	10.4267	+	8.37375i	0.675863	+	0.542790i
$239$			20.5737i			1.33080i	0.746487	+	0.665400i	$0.231739\pi$
$239$			20.5737i			1.33080i	−0.746487	+	0.665400i	$0.768261\pi$
$240$	0.419809	−	1.95267i	0.0270985	−	0.126044i
$241$			2.73898i			0.176434i	0.996101	+	0.0882168i	$0.0281168\pi$
$241$			2.73898i			0.176434i	−0.996101	+	0.0882168i	$0.971883\pi$
$242$	3.47413	+	0.184100i	0.223326	+	0.0118344i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−7.38717	−	9.14415i	−0.472915	−	0.585394i
$245$	−3.12885	−	1.55792i	−0.199895	−	0.0995316i
$246$	−5.95560	−	6.62212i	−0.379715	−	0.422211i
$247$	32.6287			2.07611
$248$	1.63290	−	10.1944i	0.103689	−	0.647348i
$249$			11.0323i			0.699144i
$250$	−5.11955	+	4.60427i	−0.323789	+	0.291199i
$251$	1.27628	+	1.27628i	0.0805580	+	0.0805580i	0.746238	−	0.665680i	$-0.231858\pi$
$251$	1.27628	+	1.27628i	0.0805580	+	0.0805580i	−0.665680	+	0.746238i	$0.731858\pi$
$252$	−3.52706	+	3.94459i	−0.222184	+	0.248486i
$253$	−3.60514	+	3.60514i	−0.226654	+	0.226654i
$254$	−16.4069	−	0.869427i	−1.02946	−	0.0545527i
$255$	1.78461			0.111757
$256$	14.5863	+	6.57580i	0.911641	+	0.410988i
$257$			30.4875i			1.90176i	0.309560	+	0.950880i	$0.399818\pi$
$257$			30.4875i			1.90176i	−0.309560	+	0.950880i	$0.600182\pi$
$258$	−9.41270	−	0.498795i	−0.586009	−	0.0310536i
$259$	3.82339	+	23.4374i	0.237574	+	1.45633i
$260$	3.84499	+	0.408653i	0.238456	+	0.0253436i
$261$	−4.96403	−	4.96403i	−0.307266	−	0.307266i
$262$	−18.9167	−	21.0337i	−1.16868	−	1.29947i
$263$	6.42214			0.396006			0.198003	−	0.980201i	$-0.436554\pi$
$263$	6.42214			0.396006			0.198003	+	0.980201i	$0.436554\pi$
$264$	−8.16154	−	1.30728i	−0.502308	−	0.0804575i
$265$	1.07563			0.0660755
$266$	−3.42275	−	31.3448i	−0.209863	−	1.92187i
$267$	3.80762	−	3.80762i	0.233022	−	0.233022i
$268$	3.11189	+	3.85202i	0.190089	+	0.235300i
$269$	4.61296	+	4.61296i	0.281257	+	0.281257i	0.833610	−	0.552353i	$-0.186270\pi$
$269$	4.61296	+	4.61296i	0.281257	+	0.281257i	−0.552353	+	0.833610i	$0.686270\pi$
$270$	−0.0373675	+	0.705159i	−0.00227412	+	0.0429146i
$271$	−19.5070			−1.18496			−0.592482	−	0.805584i	$-0.701852\pi$
$271$	−19.5070			−1.18496			−0.592482	+	0.805584i	$0.701852\pi$
$272$	−3.00493	+	13.9769i	−0.182200	+	0.847475i
$273$	−8.31541	−	5.98289i	−0.503272	−	0.362101i
$274$	−3.64582	−	0.193198i	−0.220252	−	0.0116715i
$275$	9.81677	+	9.81677i	0.591974	+	0.591974i
$276$	−2.71426	+	2.19273i	−0.163379	+	0.131987i
$277$	6.01010	+	6.01010i	0.361112	+	0.361112i	0.864222	−	0.503110i	$-0.167811\pi$
$277$	6.01010	+	6.01010i	0.361112	+	0.361112i	−0.503110	+	0.864222i	$0.667811\pi$
$278$	−15.2356	+	13.7021i	−0.913770	+	0.821799i
$279$			3.65022i			0.218533i
$280$	−0.0107674	−	3.73657i	−0.000643475	−	0.223303i
$281$		−	4.75038i		−	0.283384i	−0.989911	−	0.141692i	$-0.954746\pi$
$281$		−	4.75038i		−	0.283384i	0.989911	−	0.141692i	$-0.0452542\pi$
$282$	0.509198	+	0.566184i	0.0303223	+	0.0337158i
$283$	2.71232	+	2.71232i	0.161231	+	0.161231i	0.783112	−	0.621881i	$-0.213631\pi$
$283$	2.71232	+	2.71232i	0.161231	+	0.161231i	−0.621881	+	0.783112i	$0.713631\pi$
$284$	−18.9145	−	2.01027i	−1.12237	−	0.119288i
$285$	−2.97537	−	2.97537i	−0.176246	−	0.176246i
$286$	0.846770	−	15.9793i	0.0500706	−	0.944877i
$287$	−13.5251	−	9.73124i	−0.798362	−	0.574417i
$288$	−5.45982	−	1.48000i	−0.321723	−	0.0872100i
$289$	4.22601			0.248589
$290$	4.95036	+	0.262328i	0.290695	+	0.0154044i
$291$	11.0019	+	11.0019i	0.644943	+	0.644943i
$292$	17.2526	+	1.83364i	1.00963	+	0.107305i
$293$	12.9786	−	12.9786i	0.758217	−	0.758217i	−0.217781	−	0.975998i	$-0.569882\pi$
$293$	12.9786	−	12.9786i	0.758217	−	0.758217i	0.975998	+	0.217781i	$0.0698819\pi$
$294$	−4.87519	+	8.61583i	−0.284327	+	0.502485i
$295$	5.17441			0.301266
$296$	−20.5644	+	14.8861i	−1.19528	+	0.865236i
$297$	2.92232			0.169570
$298$	−24.4307	+	21.9718i	−1.41524	+	1.27279i
$299$	−4.77659	−	4.77659i	−0.276238	−	0.276238i
$300$	5.97079	+	7.39090i	0.344724	+	0.426714i
$301$	−17.4042	+	2.83919i	−1.00316	+	0.163648i
$302$	0.799769	−	15.0924i	0.0460215	−	0.868468i
$303$		−	15.3287i		−	0.880613i
$304$	28.3128	−	18.2929i	1.62385	−	1.04917i
$305$	−2.93483			−0.168048
$306$	0.267471	−	5.04742i	0.0152903	−	0.288542i
$307$	−13.2165	+	13.2165i	−0.754307	+	0.754307i	−0.975280	−	0.220973i	$-0.929077\pi$
$307$	−13.2165	+	13.2165i	−0.754307	+	0.754307i	0.220973	+	0.975280i	$0.429077\pi$
$308$	−15.4394	+	0.862781i	−0.879741	+	0.0491615i
$309$	6.05668	+	6.05668i	0.344553	+	0.344553i
$310$	−1.72363	−	1.91653i	−0.0978958	−	0.108852i
$311$			23.9389i			1.35745i	0.734391	+	0.678726i	$0.237468\pi$
$311$			23.9389i			1.35745i	−0.734391	+	0.678726i	$0.762532\pi$
$312$	1.73206	−	10.8135i	0.0980589	−	0.612196i
$313$	−9.65156			−0.545539			−0.272769	−	0.962079i	$-0.587940\pi$
$313$	−9.65156			−0.545539			−0.272769	+	0.962079i	$0.587940\pi$
$314$	11.2123	−	10.0838i	0.632748	−	0.569062i
$315$	0.212700	+	1.30385i	0.0119843	+	0.0734635i
$316$	0.352245	−	3.31425i	0.0198153	−	0.186441i
$317$	2.04754	−	2.04754i	0.115001	−	0.115001i	−0.647264	−	0.762266i	$-0.724087\pi$
$317$	2.04754	−	2.04754i	0.115001	−	0.115001i	0.762266	+	0.647264i	$0.224087\pi$
$318$	0.161212	−	3.04221i	0.00904030	−	0.170598i
$319$		−	20.5153i		−	1.14864i
$320$	3.56551	−	1.80105i	0.199318	−	0.100682i
$321$		−	14.7924i		−	0.825629i
$322$	−4.08758	+	5.08971i	−0.227792	+	0.283639i
$323$	21.2973	+	21.2973i	1.18501	+	1.18501i
$324$	1.98880	+	0.211373i	0.110489	+	0.0117429i
$325$	−13.0066	+	13.0066i	−0.721477	+	0.721477i
$326$	−15.2492	+	13.7144i	−0.844575	+	0.759569i
$327$			1.05506i			0.0583447i
$328$	2.81722	−	17.5883i	0.155555	−	0.971154i
$329$	1.15638	+	0.832012i	0.0637535	+	0.0458703i
$330$	−1.53435	+	1.37992i	−0.0844633	+	0.0759621i
$331$	−4.46464	+	4.46464i	−0.245399	+	0.245399i	−0.819079	−	0.573680i	$-0.805515\pi$
$331$	−4.46464	+	4.46464i	−0.245399	+	0.245399i	0.573680	+	0.819079i	$0.305515\pi$
$332$	−17.1636	+	13.8657i	−0.941974	+	0.760981i
$333$	6.34670	−	6.34670i	0.347797	−	0.347797i
$334$	3.07138	+	0.162758i	0.168059	+	0.00890570i
$335$	1.23631			0.0675470
$336$	−10.5697	−	0.529570i	−0.576627	−	0.0288904i
$337$	−11.1195			−0.605716			−0.302858	−	0.953036i	$-0.597941\pi$
$337$	−11.1195			−0.605716			−0.302858	+	0.953036i	$0.597941\pi$
$338$	2.81258	+	0.149044i	0.152984	+	0.00810690i
$339$	0.869835	−	0.869835i	0.0472430	−	0.0472430i
$340$	2.24296	+	2.77642i	0.121641	+	0.150573i
$341$	−7.54280	+	7.54280i	−0.408465	+	0.408465i
$342$	−8.86118	+	7.96931i	−0.479158	+	0.430931i
$343$	−5.47796	+	17.6916i	−0.295782	+	0.955255i
$344$	−11.0542	−	15.2708i	−0.596000	−	0.823345i
$345$			0.871145i			0.0469009i
$346$	8.04011	−	7.23088i	0.432239	−	0.388734i
$347$	−2.56028	+	2.56028i	−0.137443	+	0.137443i	−0.772481	−	0.635038i	$-0.780985\pi$
$347$	−2.56028	+	2.56028i	−0.137443	+	0.137443i	0.635038	+	0.772481i	$0.280985\pi$
$348$	1.48388	−	13.9618i	0.0795444	−	0.748429i
$349$	−15.4685	−	15.4685i	−0.828011	−	0.828011i	0.159231	−	0.987241i	$-0.449099\pi$
$349$	−15.4685	−	15.4685i	−0.828011	−	0.828011i	−0.987241	+	0.159231i	$0.949099\pi$
$350$	13.8592	+	11.1304i	0.740807	+	0.594947i
$351$			3.87190i			0.206667i
$352$	−8.22386	−	14.3404i	−0.438333	−	0.764346i
$353$		−	21.5190i		−	1.14534i	−0.819786	−	0.572670i	$-0.805908\pi$
$353$		−	21.5190i		−	1.14534i	0.819786	−	0.572670i	$-0.194092\pi$
$354$	0.775520	−	14.6348i	0.0412184	−	0.777829i
$355$	−3.35792	+	3.35792i	−0.178220	+	0.178220i
$356$	10.7093	+	1.13820i	0.567589	+	0.0603244i
$357$	−1.52247	−	9.33274i	−0.0805778	−	0.493941i
$358$	−2.11459	+	1.90175i	−0.111759	+	0.100511i
$359$	−28.9399			−1.52739			−0.763696	−	0.645576i	$-0.776617\pi$
$359$	−28.9399			−1.52739			−0.763696	+	0.645576i	$0.776617\pi$
$360$	−1.14402	+	0.828130i	−0.0602951	+	0.0436463i
$361$		−	52.0152i		−	2.73764i
$362$	−19.0282	−	21.1577i	−1.00010	−	1.11202i
$363$	−1.73950	−	1.73950i	−0.0913002	−	0.0913002i
$364$	−1.14313	−	20.4562i	−0.0599164	−	1.07220i
$365$	3.06287	−	3.06287i	0.160318	−	0.160318i
$366$	−0.439861	+	8.30057i	−0.0229919	+	0.433878i
$367$	5.65132			0.294996			0.147498	−	0.989062i	$-0.452878\pi$
$367$	5.65132			0.294996			0.147498	+	0.989062i	$0.452878\pi$
$368$	−6.82272	−	1.46683i	−0.355659	−	0.0764639i
$369$			6.29768i			0.327844i
$370$	−0.335396	+	6.32921i	−0.0174364	+	0.329040i
$371$	−0.917633	−	5.62508i	−0.0476411	−	0.292039i
$372$	−5.67886	+	4.58771i	−0.294435	+	0.237862i
$373$	13.3574	+	13.3574i	0.691618	+	0.691618i	0.962588	−	0.270970i	$-0.0873445\pi$
$373$	13.3574	+	13.3574i	0.691618	+	0.691618i	−0.270970	+	0.962588i	$0.587344\pi$
$374$	10.9827	−	9.87726i	0.567900	−	0.510741i
$375$	4.86873			0.251420
$376$	−0.240870	+	1.50379i	−0.0124219	+	0.0775518i
$377$	27.1815			1.39992
$378$	3.71955	−	0.406163i	0.191313	−	0.0208908i
$379$	−12.3344	+	12.3344i	−0.633577	+	0.633577i	−0.948963	−	0.315386i	$-0.897866\pi$
$379$	−12.3344	+	12.3344i	−0.633577	+	0.633577i	0.315386	+	0.948963i	$0.397866\pi$
$380$	0.889418	−	8.36849i	0.0456262	−	0.429295i
$381$	8.21494	+	8.21494i	0.420864	+	0.420864i
$382$	16.2907	+	0.863270i	0.833503	+	0.0441687i
$383$	4.53694			0.231827			0.115913	−	0.993259i	$-0.463021\pi$
$383$	4.53694			0.231827			0.115913	+	0.993259i	$0.463021\pi$
$384$	−4.55954	−	10.3543i	−0.232678	−	0.528388i
$385$	−2.25474	+	3.13378i	−0.114912	+	0.159712i
$386$	−0.956503	+	18.0501i	−0.0486847	+	0.918724i
$387$	4.71295	+	4.71295i	0.239573	+	0.239573i
$388$	−3.28876	+	30.9438i	−0.166962	+	1.57093i
$389$	16.5413	+	16.5413i	0.838679	+	0.838679i	0.988685	−	0.150006i	$-0.0479294\pi$
$389$	16.5413	+	16.5413i	0.838679	+	0.838679i	−0.150006	+	0.988685i	$0.547929\pi$
$390$	−1.82831	−	2.03292i	−0.0925800	−	0.102941i
$391$		−	6.23552i		−	0.315344i
$392$	−19.5314	+	3.24402i	−0.986486	+	0.163848i
$393$			20.0032i			1.00903i
$394$	−17.1755	+	15.4467i	−0.865287	+	0.778196i
$395$	−0.588384	−	0.588384i	−0.0296048	−	0.0296048i
$396$	3.67286	+	4.54642i	0.184568	+	0.228466i
$397$	−2.13420	−	2.13420i	−0.107113	−	0.107113i	0.651519	−	0.758632i	$-0.274132\pi$
$397$	−2.13420	−	2.13420i	−0.107113	−	0.107113i	−0.758632	+	0.651519i	$0.774132\pi$
$398$	3.80124	+	0.201434i	0.190539	+	0.0100970i
$399$	−13.0216	+	18.0982i	−0.651894	+	0.906044i
$400$	−3.99417	+	18.5782i	−0.199708	+	0.928910i
$401$	−8.15672			−0.407327			−0.203663	−	0.979041i	$-0.565285\pi$
$401$	−8.15672			−0.407327			−0.203663	+	0.979041i	$0.565285\pi$
$402$	0.185294	−	3.49666i	0.00924162	−	0.174398i
$403$	−9.99374	−	9.99374i	−0.497824	−	0.497824i
$404$	23.8478	−	19.2656i	1.18647	−	0.958500i
$405$	0.353074	−	0.353074i	0.0175444	−	0.0175444i
$406$	−2.85134	−	26.1120i	−0.141510	−	1.29592i
$407$	26.2296			1.30015
$408$	8.18872	−	5.92763i	0.405402	−	0.293461i
$409$	12.5423			0.620177			0.310089	−	0.950708i	$-0.399641\pi$
$409$	12.5423			0.620177			0.310089	+	0.950708i	$0.399641\pi$
$410$	−2.97376	−	3.30657i	−0.146864	−	0.163300i
$411$	1.82547	+	1.82547i	0.0900437	+	0.0900437i
$412$	−1.81050	+	17.0350i	−0.0891972	+	0.839252i
$413$	−4.41434	−	27.0599i	−0.217216	−	1.33153i
$414$	2.46386	+	0.130564i	0.121092	+	0.00641687i
$415$			5.50868i			0.270410i
$416$	19.0001	−	10.8961i	0.931559	−	0.534226i
$417$	14.4892			0.709537
$418$	−34.7784	−	1.84297i	−1.70107	−	0.0901424i
$419$	−18.0414	+	18.0414i	−0.881378	+	0.881378i	−0.993675	−	0.112296i	$-0.964179\pi$
$419$	−18.0414	+	18.0414i	−0.881378	+	0.881378i	0.112296	+	0.993675i	$0.464179\pi$
$420$	−1.76114	+	1.96962i	−0.0859349	+	0.0961078i
$421$	−0.0605701	−	0.0605701i	−0.00295201	−	0.00295201i	0.705629	−	0.708581i	$-0.250664\pi$
$421$	−0.0605701	−	0.0605701i	−0.00295201	−	0.00295201i	−0.708581	+	0.705629i	$0.750664\pi$
$422$	−18.5357	+	16.6701i	−0.902305	+	0.811488i
$423$		−	0.538446i		−	0.0261801i
$424$	4.93555	−	3.57273i	0.239691	−	0.173507i
$425$	−16.9793			−0.823615
$426$	8.99394	+	10.0005i	0.435758	+	0.484525i
$427$	2.50373	+	15.3478i	0.121164	+	0.742734i
$428$	23.0133	−	18.5915i	1.11239	−	0.898653i
$429$	−8.00087	+	8.00087i	−0.386285	+	0.386285i
$430$	−4.69997	−	0.249059i	−0.226653	−	0.0120107i
$431$			12.8411i			0.618532i	0.950976	+	0.309266i	$0.100083\pi$
$431$			12.8411i			0.618532i	−0.950976	+	0.309266i	$0.899917\pi$
$432$	2.17074	+	3.35975i	0.104440	+	0.161646i
$433$			8.05085i			0.386899i	0.981110	+	0.193449i	$0.0619676\pi$
$433$			8.05085i			0.386899i	−0.981110	+	0.193449i	$0.938032\pi$
$434$	−8.55217	+	10.6489i	−0.410517	+	0.511162i
$435$	−2.47865	−	2.47865i	−0.118842	−	0.118842i
$436$	−1.64141	+	1.32603i	−0.0786093	+	0.0635051i
$437$	−10.3961	+	10.3961i	−0.497312	+	0.497312i
$438$	−8.20367	−	9.12178i	−0.391987	−	0.435855i
$439$		−	36.3698i		−	1.73584i	−0.496708	−	0.867918i	$-0.665458\pi$
$439$		−	36.3698i		−	1.73584i	0.496708	−	0.867918i	$-0.334542\pi$
$440$	−4.07524	−	0.652754i	−0.194279	−	0.0311188i
$441$	6.63709	−	2.22465i	0.316052	−	0.105936i
$442$	13.0868	+	14.5513i	0.622473	+	0.692137i
$443$	27.1483	−	27.1483i	1.28986	−	1.28986i	0.354984	−	0.934873i	$-0.384486\pi$
$443$	27.1483	−	27.1483i	1.28986	−	1.28986i	0.934873	−	0.354984i	$-0.115514\pi$
$444$	17.8506	+	1.89720i	0.847154	+	0.0900370i
$445$	1.90123	−	1.90123i	0.0901268	−	0.0901268i
$446$	0.951298	−	17.9518i	0.0450453	−	0.850044i
$447$	23.2338			1.09892
$448$	−12.4605	−	17.1095i	−0.588703	−	0.808349i
$449$	6.95274			0.328120			0.164060	−	0.986450i	$-0.447541\pi$
$449$	6.95274			0.328120			0.164060	+	0.986450i	$0.447541\pi$
$450$	0.355524	−	6.70906i	0.0167596	−	0.316268i
$451$	−13.0135	+	13.0135i	−0.612782	+	0.612782i
$452$	2.44649	+	0.260017i	0.115073	+	0.0122302i
$453$	−7.55677	+	7.55677i	−0.355048	+	0.355048i
$454$	14.7102	+	16.3565i	0.690385	+	0.767649i
$455$	−4.15207	−	2.98739i	−0.194652	−	0.140051i
$456$	−23.5353	−	3.76978i	−1.10214	−	0.176536i
$457$		−	5.32640i		−	0.249158i	−0.992210	−	0.124579i	$-0.960242\pi$
$457$		−	5.32640i		−	0.249158i	0.992210	−	0.124579i	$-0.0397581\pi$
$458$	−3.65876	−	4.06822i	−0.170962	−	0.190096i
$459$	−2.52725	+	2.52725i	−0.117962	+	0.117962i
$460$	−1.35529	+	1.09488i	−0.0631907	+	0.0510491i
$461$	−7.44077	−	7.44077i	−0.346551	−	0.346551i	0.512272	−	0.858823i	$-0.328804\pi$
$461$	−7.44077	−	7.44077i	−0.346551	−	0.346551i	−0.858823	+	0.512272i	$0.828804\pi$
$462$	8.52534	+	6.84676i	0.396635	+	0.318540i
$463$		−	35.4707i		−	1.64846i	−0.566252	−	0.824232i	$-0.691607\pi$
$463$		−	35.4707i		−	1.64846i	0.566252	−	0.824232i	$-0.308393\pi$
$464$	23.5861	−	15.2390i	1.09496	−	0.707453i
$465$			1.82264i			0.0845228i
$466$	12.6753	+	0.671686i	0.587173	+	0.0311153i
$467$	9.30469	−	9.30469i	0.430570	−	0.430570i	−0.458252	−	0.888822i	$-0.651524\pi$
$467$	9.30469	−	9.30469i	0.430570	−	0.430570i	0.888822	+	0.458252i	$0.151524\pi$
$468$	−6.02373	+	4.86632i	−0.278447	+	0.224946i
$469$	−1.05471	−	6.46537i	−0.0487020	−	0.298543i
$470$	0.254254	+	0.282708i	0.0117279	+	0.0130404i
$471$	−10.6630			−0.491325
$472$	23.7428	−	17.1869i	1.09285	−	0.791091i
$473$			19.4776i			0.895583i
$474$	−1.75231	+	1.57594i	−0.0804862	+	0.0723853i
$475$	28.3085	+	28.3085i	1.29888	+	1.29888i
$476$	12.6060	−	14.0983i	0.577794	−	0.646193i
$477$	−1.52324	+	1.52324i	−0.0697443	+	0.0697443i
$478$	29.0548	+	1.53966i	1.32894	+	0.0704225i
$479$	31.1329			1.42250			0.711250	−	0.702940i	$-0.248130\pi$
$479$	31.1329			1.42250			0.711250	+	0.702940i	$0.248130\pi$
$480$	−2.72621	−	0.738998i	−0.124434	−	0.0337305i
$481$			34.7526i			1.58458i
$482$	3.86808	+	0.204976i	0.176186	+	0.00933641i
$483$	4.55570	−	0.743183i	0.207292	−	0.0338160i
$484$	0.519984	−	4.89250i	0.0236356	−	0.222386i
$485$	5.49349	+	5.49349i	0.249447	+	0.249447i
$486$	−0.945681	−	1.05152i	−0.0428970	−	0.0476977i
$487$	−32.7989			−1.48626			−0.743131	−	0.669146i	$-0.766660\pi$
$487$	−32.7989			−1.48626			−0.743131	+	0.669146i	$0.766660\pi$
$488$	−13.4665	+	9.74809i	−0.609599	+	0.441275i
$489$	14.5021			0.655808
$490$	−2.43429	+	4.30207i	−0.109970	+	0.194348i
$491$	−6.83946	+	6.83946i	−0.308660	+	0.308660i	−0.844390	−	0.535729i	$-0.820037\pi$
$491$	−6.83946	+	6.83946i	−0.308660	+	0.308660i	0.535729	+	0.844390i	$0.320037\pi$
$492$	−9.79766	+	7.91512i	−0.441713	+	0.356841i
$493$	17.7418	+	17.7418i	0.799051	+	0.799051i
$494$	2.44182	−	46.0793i	0.109863	−	2.07320i
$495$	1.45918			0.0655853
$496$	−14.2747	−	3.06895i	−0.640954	−	0.137800i
$497$	20.4251	+	14.6958i	0.916192	+	0.659196i
$498$	15.5802	+	0.825620i	0.698165	+	0.0369969i
$499$	6.96812	+	6.96812i	0.311936	+	0.311936i	0.845659	−	0.533723i	$-0.179208\pi$
$499$	6.96812	+	6.96812i	0.311936	+	0.311936i	−0.533723	+	0.845659i	$0.679208\pi$
$500$	6.11916	+	7.57456i	0.273657	+	0.338744i
$501$	−1.53785	−	1.53785i	−0.0687059	−	0.0687059i
$502$	1.89791	−	1.70689i	0.0847080	−	0.0761822i
$503$			15.3570i			0.684735i	0.939566	+	0.342368i	$0.111229\pi$
$503$			15.3570i			0.684735i	−0.939566	+	0.342368i	$0.888771\pi$
$504$	5.30673	+	5.27623i	0.236380	+	0.235022i
$505$		−	7.65398i		−	0.340598i
$506$	4.82150	+	5.36110i	0.214342	+	0.238330i
$507$	−1.40827	−	1.40827i	−0.0625433	−	0.0625433i
$508$	−2.45567	+	23.1052i	−0.108953	+	1.02513i
$509$	−16.6366	−	16.6366i	−0.737403	−	0.737403i	0.234672	−	0.972075i	$-0.424598\pi$
$509$	−16.6366	−	16.6366i	−0.737403	−	0.737403i	−0.972075	+	0.234672i	$0.924598\pi$
$510$	0.133554	−	2.52029i	0.00591388	−	0.111600i
$511$	−18.6305	−	13.4045i	−0.824163	−	0.592981i
$512$	10.3781	−	20.1071i	0.458653	−	0.888615i
$513$	8.42705			0.372063
$514$	43.0555	+	2.28158i	1.89910	+	0.100636i
$515$	3.02424	+	3.02424i	0.133264	+	0.133264i
$516$	−1.40883	+	13.2556i	−0.0620202	+	0.583545i
$517$	1.11264	−	1.11264i	0.0489339	−	0.0489339i
$518$	33.3851	−	3.64555i	1.46686	−	0.160176i
$519$	−7.64621			−0.335631
$520$	0.864858	−	5.39944i	0.0379265	−	0.236781i
$521$	44.6141			1.95458			0.977290	−	0.211906i	$-0.0679672\pi$
$521$	44.6141			1.95458			0.977290	+	0.211906i	$0.0679672\pi$
$522$	−7.38186	+	6.63887i	−0.323095	+	0.290576i
$523$	9.34118	+	9.34118i	0.408461	+	0.408461i	0.881202	−	0.472741i	$-0.156735\pi$
$523$	9.34118	+	9.34118i	0.408461	+	0.408461i	−0.472741	+	0.881202i	$0.656735\pi$
$524$	−31.1201	+	25.1406i	−1.35949	+	1.09827i
$525$	−2.02368	−	12.4051i	−0.0883206	−	0.541404i
$526$	0.480611	−	9.06956i	0.0209556	−	0.395451i
$527$		−	13.0462i		−	0.568300i
$528$	−2.45696	+	11.4282i	−0.106926	+	0.497347i
$529$	−19.9562			−0.867660
$530$	0.0804965	−	1.51904i	0.00349655	−	0.0659829i
$531$	−7.32765	+	7.32765i	−0.317993	+	0.317993i
$532$	−44.5223	+	2.48799i	−1.93029	+	0.107868i
$533$	−17.2421	−	17.2421i	−0.746837	−	0.746837i
$534$	−5.09229	−	5.66219i	−0.220365	−	0.245027i
$535$		−	7.38615i		−	0.319331i
$536$	5.67284	−	4.10644i	0.245029	−	0.177371i
$537$	2.01099			0.0867805
$538$	6.85978	−	6.16935i	0.295746	−	0.265979i
$539$	18.3118	+	9.11783i	0.788747	+	0.392733i
$540$	0.993051	+	0.105543i	0.0427341	+	0.00454186i
$541$	11.7558	−	11.7558i	0.505423	−	0.505423i	−0.407695	−	0.913118i	$-0.633667\pi$
$541$	11.7558	−	11.7558i	0.505423	−	0.505423i	0.913118	+	0.407695i	$0.133667\pi$
$542$	−1.45983	+	27.5483i	−0.0627052	+	1.18330i
$543$			20.1211i			0.863479i
$544$	19.5138	+	5.28964i	0.836646	+	0.226791i
$545$			0.526813i			0.0225662i
$546$	−9.07153	+	11.2956i	−0.388226	+	0.483405i
$547$	2.81777	+	2.81777i	0.120479	+	0.120479i	0.764776	−	0.644297i	$-0.222850\pi$
$547$	2.81777	+	2.81777i	0.120479	+	0.120479i	−0.644297	+	0.764776i	$0.722850\pi$
$548$	−0.545681	+	5.13428i	−0.0233103	+	0.219326i
$549$	4.15611	−	4.15611i	0.177378	−	0.177378i
$550$	14.5982	−	13.1289i	0.622470	−	0.559819i
$551$		−	59.1596i		−	2.52028i
$552$	2.89352	+	3.99726i	0.123157	+	0.170135i
$553$	−2.57503	+	3.57894i	−0.109501	+	0.152192i
$554$	8.93744	−	8.03789i	0.379715	−	0.341497i
$555$	3.16905	−	3.16905i	0.134519	−	0.134519i
$556$	18.2104	+	22.5416i	0.772294	+	0.955977i
$557$	−4.72518	+	4.72518i	−0.200212	+	0.200212i	−0.800091	−	0.599879i	$-0.795216\pi$
$557$	−4.72518	+	4.72518i	−0.200212	+	0.200212i	0.599879	+	0.800091i	$0.295216\pi$
$558$	5.15496	+	0.273170i	0.218227	+	0.0115642i
$559$	−25.8067			−1.09151
$560$	−5.27771	−	0.264426i	−0.223024	−	0.0111740i
$561$	−10.4446			−0.440971
$562$	−6.70863	−	0.355502i	−0.282987	−	0.0149959i
$563$	15.3342	−	15.3342i	0.646258	−	0.646258i	−0.305829	−	0.952087i	$-0.598933\pi$
$563$	15.3342	−	15.3342i	0.646258	−	0.646258i	0.952087	+	0.305829i	$0.0989335\pi$
$564$	0.837690	−	0.676735i	0.0352731	−	0.0284957i
$565$	0.434328	−	0.434328i	0.0182723	−	0.0182723i
$566$	4.03341	−	3.62745i	0.169537	−	0.152473i
$567$	−2.14763	−	1.54521i	−0.0901921	−	0.0648927i
$568$	−4.25447	+	26.5613i	−0.178514	+	1.11449i
$569$		−	23.2208i		−	0.973465i	−0.873551	−	0.486733i	$-0.838189\pi$
$569$		−	23.2208i		−	0.973465i	0.873551	−	0.486733i	$-0.161811\pi$
$570$	−4.42458	+	3.97925i	−0.185325	+	0.166672i
$571$	8.47744	−	8.47744i	0.354770	−	0.354770i	−0.507111	−	0.861881i	$-0.669287\pi$
$571$	8.47744	−	8.47744i	0.354770	−	0.354770i	0.861881	+	0.507111i	$0.169287\pi$
$572$	−22.5031	−	2.39167i	−0.940903	−	0.100001i
$573$	−8.15676	−	8.15676i	−0.340754	−	0.340754i
$574$	−14.7549	+	18.3723i	−0.615860	+	0.766847i
$575$		−	8.28829i		−	0.345646i
$576$	−2.49870	+	7.59977i	−0.104113	+	0.316657i
$577$		−	24.4767i		−	1.01898i	−0.860477	−	0.509489i	$-0.829834\pi$
$577$		−	24.4767i		−	1.01898i	0.860477	−	0.509489i	$-0.170166\pi$
$578$	0.316260	−	5.96811i	0.0131547	−	0.248241i
$579$	9.03769	−	9.03769i	0.375594	−	0.375594i
$580$	0.740935	−	6.97142i	0.0307656	−	0.289472i
$581$	28.8079	−	4.69951i	1.19515	−	0.194969i
$582$	16.3606	−	14.7139i	0.678168	−	0.609911i
$583$	−6.29522			−0.260721
$584$	3.88064	−	24.2274i	0.160582	−	1.00254i
$585$			1.93332i			0.0799331i
$586$	−17.3575	−	19.3000i	−0.717031	−	0.797277i
$587$	−23.2347	−	23.2347i	−0.958999	−	0.958999i	0.0401932	−	0.999192i	$-0.487203\pi$
$587$	−23.2347	−	23.2347i	−0.958999	−	0.958999i	−0.999192	+	0.0401932i	$0.987203\pi$
$588$	11.8027	+	7.52968i	0.486735	+	0.310519i
$589$	−21.7510	+	21.7510i	−0.896236	+	0.896236i
$590$	0.387235	−	7.30746i	0.0159422	−	0.300843i
$591$	16.3340			0.671890
$592$	19.4836	+	30.1557i	0.800773	+	1.23939i
$593$			9.36212i			0.384456i	0.981350	+	0.192228i	$0.0615714\pi$
$593$			9.36212i			0.384456i	−0.981350	+	0.192228i	$0.938429\pi$
$594$	0.218697	−	4.12700i	0.00897323	−	0.169333i
$595$	−0.760204	−	4.66004i	−0.0311653	−	0.191043i
$596$	29.2010	+	36.1462i	1.19612	+	1.48061i
$597$	−1.90328	−	1.90328i	−0.0778963	−	0.0778963i
$598$	−7.10312	+	6.38820i	−0.290468	+	0.261233i
$599$	−40.1015			−1.63850			−0.819251	−	0.573435i	$-0.805611\pi$
$599$	−40.1015			−1.63850			−0.819251	+	0.573435i	$0.805611\pi$
$600$	10.8845	−	7.87904i	0.444358	−	0.321660i
$601$	−6.55291			−0.267299			−0.133649	−	0.991029i	$-0.542670\pi$
$601$	−6.55291			−0.267299			−0.133649	+	0.991029i	$0.542670\pi$
$602$	2.70712	+	24.7912i	0.110334	+	1.01042i
$603$	−1.75078	+	1.75078i	−0.0712974	+	0.0712974i
$604$	−21.2541	−	2.25892i	−0.864816	−	0.0919141i
$605$	−0.868572	−	0.868572i	−0.0353125	−	0.0353125i
$606$	−21.6477	−	1.14715i	−0.879379	−	0.0465998i
$607$	−8.02925			−0.325897			−0.162949	−	0.986635i	$-0.552100\pi$
$607$	−8.02925			−0.325897			−0.162949	+	0.986635i	$0.552100\pi$
$608$	−23.7150	−	41.3532i	−0.961770	−	1.67709i
$609$	−10.8477	+	15.0768i	−0.439570	+	0.610943i
$610$	−0.219632	+	4.14466i	−0.00889265	+	0.167812i
$611$	1.47418	+	1.47418i	0.0596390	+	0.0596390i
$612$	−7.10811	−	0.755463i	−0.287328	−	0.0305378i
$613$	−25.1899	−	25.1899i	−1.01741	−	1.01741i	−0.999846	−	0.0175663i	$-0.994408\pi$
$613$	−25.1899	−	25.1899i	−1.01741	−	1.01741i	−0.0175663	−	0.999846i	$-0.505592\pi$
$614$	17.6757	+	19.6539i	0.713334	+	0.793166i
$615$			3.14457i			0.126801i
$616$	0.0630170	+	21.8686i	0.00253903	+	0.881110i
$617$		−	4.23466i		−	0.170481i	−0.996360	−	0.0852406i	$-0.972834\pi$
$617$		−	4.23466i		−	0.170481i	0.996360	−	0.0852406i	$-0.0271659\pi$
$618$	9.00671	−	8.10018i	0.362303	−	0.325837i
$619$	−34.1958	−	34.1958i	−1.37445	−	1.37445i	−0.853730	−	0.520716i	$-0.825665\pi$
$619$	−34.1958	−	34.1958i	−1.37445	−	1.37445i	−0.520716	−	0.853730i	$-0.674335\pi$
$620$	−2.83558	+	2.29074i	−0.113880	+	0.0919985i
$621$	−1.23366	−	1.23366i	−0.0495050	−	0.0495050i
$622$	33.8073	+	1.79151i	1.35555	+	0.0718329i
$623$	−11.5645	−	8.32062i	−0.463324	−	0.333359i
$624$	−15.1416	−	3.25533i	−0.606149	−	0.130317i
$625$	−21.3223			−0.852893
$626$	−0.722289	+	13.6302i	−0.0288685	+	0.544774i
$627$	17.4136	+	17.4136i	0.695433	+	0.695433i
$628$	−13.4016	−	16.5890i	−0.534781	−	0.661975i
$629$	−22.6836	+	22.6836i	−0.904453	+	0.904453i
$630$	1.85725	−	0.202806i	0.0739947	−	0.00807999i
$631$	−13.8558			−0.551590			−0.275795	−	0.961216i	$-0.588941\pi$
$631$	−13.8558			−0.551590			−0.275795	+	0.961216i	$0.588941\pi$
$632$	−4.65413	−	0.745478i	−0.185131	−	0.0296535i
$633$	17.6276			0.700635
$634$	−2.73837	−	3.04483i	−0.108754	−	0.120926i
$635$	4.10190	+	4.10190i	0.162779	+	0.162779i
$636$	−4.28424	−	0.455336i	−0.169881	−	0.0180553i
$637$	−12.0806	+	24.2621i	−0.478649	+	0.961298i
$638$	−28.9724	−	1.53529i	−1.14703	−	0.0607828i
$639$		−	9.51053i		−	0.376231i
$640$	−2.27668	−	5.17011i	−0.0899936	−	0.204367i
$641$	46.9366			1.85388			0.926942	−	0.375204i	$-0.122427\pi$
$641$	46.9366			1.85388			0.926942	+	0.375204i	$0.122427\pi$
$642$	−20.8902	−	1.10701i	−0.824472	−	0.0436901i
$643$	2.57173	−	2.57173i	0.101419	−	0.101419i	−0.654577	−	0.755996i	$-0.727153\pi$
$643$	2.57173	−	2.57173i	0.101419	−	0.101419i	0.755996	+	0.654577i	$0.227153\pi$
$644$	6.88195	+	6.15351i	0.271187	+	0.242482i
$645$	2.35328	+	2.35328i	0.0926604	+	0.0926604i
$646$	31.6705	−	28.4829i	1.24606	−	1.12064i
$647$		−	43.5484i		−	1.71206i	−0.516924	−	0.856031i	$-0.672923\pi$
$647$		−	43.5484i		−	1.71206i	0.516924	−	0.856031i	$-0.327077\pi$
$648$	0.447343	−	2.79283i	0.0175733	−	0.109713i
$649$	−30.2836			−1.18874
$650$	17.3950	+	19.3417i	0.682288	+	0.758645i
$651$	9.53158	−	1.55491i	0.373572	−	0.0609418i
$652$	18.2267	+	22.5618i	0.713812	+	0.883587i
$653$	−33.5572	+	33.5572i	−1.31320	+	1.31320i	−0.394150	+	0.919046i	$0.628961\pi$
$653$	−33.5572	+	33.5572i	−1.31320	+	1.31320i	−0.919046	+	0.394150i	$0.871039\pi$
$654$	1.48998	+	0.0789567i	0.0582630	+	0.00308745i
$655$			9.98805i			0.390265i
$656$	−24.6280	−	5.29482i	−0.961561	−	0.206728i
$657$			8.67488i			0.338439i
$658$	1.26153	−	1.57082i	0.0491797	−	0.0612368i
$659$	−7.90569	−	7.90569i	−0.307962	−	0.307962i	0.536157	−	0.844119i	$-0.319876\pi$
$659$	−7.90569	−	7.90569i	−0.307962	−	0.307962i	−0.844119	+	0.536157i	$0.819876\pi$
$660$	1.83394	+	2.27013i	0.0713861	+	0.0883647i
$661$	−17.8307	+	17.8307i	−0.693532	+	0.693532i	−0.963007	−	0.269475i	$-0.913150\pi$
$661$	−17.8307	+	17.8307i	−0.693532	+	0.693532i	0.269475	+	0.963007i	$0.413150\pi$
$662$	5.97099	+	6.63923i	0.232069	+	0.258041i
$663$		−	13.8384i		−	0.537440i
$664$	18.2972	+	25.2766i	0.710068	+	0.980924i
$665$	−6.50195	+	9.03684i	−0.252135	+	0.350433i
$666$	−8.48805	−	9.43798i	−0.328905	−	0.365714i
$667$	−8.66052	+	8.66052i	−0.335337	+	0.335337i
$668$	0.459703	−	4.32532i	0.0177864	−	0.167352i
$669$	−8.98851	+	8.98851i	−0.347516	+	0.347516i
$670$	0.0925213	−	1.74596i	0.00357441	−	0.0674523i
$671$	17.1763			0.663084
$672$	−1.53888	+	14.8873i	−0.0593635	+	0.574290i
$673$	36.1564			1.39373			0.696864	−	0.717203i	$-0.254578\pi$
$673$	36.1564			1.39373			0.696864	+	0.717203i	$0.254578\pi$
$674$	−0.832142	+	15.7033i	−0.0320529	+	0.604867i
$675$	−3.35924	+	3.35924i	−0.129297	+	0.129297i
$676$	0.420968	−	3.96087i	0.0161911	−	0.152341i
$677$	12.4463	−	12.4463i	0.478351	−	0.478351i	−0.426253	−	0.904604i	$-0.640167\pi$
$677$	12.4463	−	12.4463i	0.478351	−	0.478351i	0.904604	+	0.426253i	$0.140167\pi$
$678$	−1.16331	−	1.29351i	−0.0446768	−	0.0496768i
$679$	24.0420	−	33.4151i	0.922647	−	1.28235i
$680$	4.08881	−	2.95980i	0.156799	−	0.113503i
$681$		−	15.5552i		−	0.596075i
$682$	10.0877	+	11.2167i	0.386278	+	0.429508i
$683$	6.11759	−	6.11759i	0.234083	−	0.234083i	−0.580312	−	0.814395i	$-0.697069\pi$
$683$	6.11759	−	6.11759i	0.234083	−	0.234083i	0.814395	+	0.580312i	$0.197069\pi$
$684$	10.5914	+	13.1104i	0.404971	+	0.501290i
$685$	0.911496	+	0.911496i	0.0348265	+	0.0348265i
$686$	24.5747	+	9.06013i	0.938265	+	0.345917i
$687$			3.86891i			0.147608i
$688$	−22.3931	+	14.4682i	−0.853730	+	0.551596i
$689$		−	8.34078i		−	0.317758i
$690$	1.23026	+	0.0651934i	0.0468351	+	0.00248187i
$691$	27.1676	−	27.1676i	1.03350	−	1.03350i	0.0340857	−	0.999419i	$-0.489148\pi$
$691$	27.1676	−	27.1676i	1.03350	−	1.03350i	0.999419	−	0.0340857i	$-0.0108519\pi$
$692$	−9.60998	−	11.8956i	−0.365317	−	0.452204i
$693$	−1.24484	−	7.63087i	−0.0472877	−	0.289873i
$694$	3.42411	+	3.80732i	0.129978	+	0.144524i
$695$	7.23476			0.274430
$696$	−19.6062	−	3.14044i	−0.743171	−	0.119038i
$697$		−	22.5084i		−	0.852565i
$698$	−23.0027	+	20.6875i	−0.870667	+	0.783034i
$699$	−6.34655	−	6.34655i	−0.240049	−	0.240049i
$700$	16.7559	−	18.7395i	0.633315	−	0.708286i
$701$	29.1131	−	29.1131i	1.09959	−	1.09959i	0.105127	−	0.994459i	$-0.466475\pi$
$701$	29.1131	−	29.1131i	1.09959	−	1.09959i	0.994459	−	0.105127i	$-0.0335248\pi$
$702$	5.46802	+	0.289759i	0.206377	+	0.0109363i
$703$	75.6377			2.85273
$704$	−20.8674	+	10.5408i	−0.786471	+	0.397272i
$705$		−	0.268858i		−	0.0101258i
$706$	−30.3898	−	1.61041i	−1.14373	−	0.0606084i
$707$	−40.0269	+	6.52969i	−1.50537	+	0.245574i
$708$	−20.6096	−	2.19043i	−0.774558	−	0.0823214i
$709$	17.0893	+	17.0893i	0.641803	+	0.641803i	0.950998	−	0.309196i	$-0.100060\pi$
$709$	17.0893	+	17.0893i	0.641803	+	0.641803i	−0.309196	+	0.950998i	$0.600060\pi$
$710$	4.49087	+	4.99346i	0.168539	+	0.187401i
$711$	1.66646			0.0624971
$712$	2.40884	−	15.0388i	0.0902752	−	0.563602i
$713$	6.36838			0.238498
$714$	−13.2939	+	1.45166i	−0.497513	+	0.0543268i
$715$	−3.99501	+	3.99501i	−0.149405	+	0.149405i
$716$	2.52747	+	3.12861i	0.0944560	+	0.116922i
$717$	−14.5478	−	14.5478i	−0.543297	−	0.543297i
$718$	−2.16577	+	40.8699i	−0.0808256	+	1.52525i
$719$	−41.2461			−1.53822			−0.769109	−	0.639117i	$-0.779300\pi$
$719$	−41.2461			−1.53822			−0.769109	+	0.639117i	$0.779300\pi$
$720$	1.08390	+	1.67760i	0.0403945	+	0.0625203i
$721$	13.2354	−	18.3954i	0.492913	−	0.685082i
$722$	−73.4575	−	3.89264i	−2.73381	−	0.144869i
$723$	−1.93675	−	1.93675i	−0.0720287	−	0.0720287i
$724$	−31.3035	+	25.2888i	−1.16339	+	0.939851i
$725$	23.5825	+	23.5825i	0.875833	+	0.875833i
$726$	−2.58676	+	2.32640i	−0.0960037	+	0.0863409i
$727$			1.60524i			0.0595352i	0.999557	+	0.0297676i	$0.00947672\pi$
$727$			1.60524i			0.0595352i	−0.999557	+	0.0297676i	$0.990523\pi$
$728$	−28.9745	+	0.0834937i	−1.07387	+	0.00309448i
$729$			1.00000i			0.0370370i
$730$	−4.09628	−	4.55471i	−0.151610	−	0.168577i
$731$	−16.8444	−	16.8444i	−0.623014	−	0.623014i
$732$	11.6894	+	1.24237i	0.432053	+	0.0459194i
$733$	−6.18188	−	6.18188i	−0.228333	−	0.228333i	0.583663	−	0.811996i	$-0.301619\pi$
$733$	−6.18188	−	6.18188i	−0.228333	−	0.228333i	−0.811996	+	0.583663i	$0.801619\pi$
$734$	0.422925	−	7.98097i	0.0156104	−	0.294583i
$735$	3.31404	−	1.11082i	0.122240	−	0.0409731i
$736$	−2.58209	+	9.52549i	−0.0951773	+	0.351114i
$737$	−7.23562			−0.266527
$738$	8.89379	+	0.471297i	0.327385	+	0.0173487i
$739$	−8.69821	−	8.69821i	−0.319969	−	0.319969i	0.528786	−	0.848755i	$-0.322647\pi$
$739$	−8.69821	−	8.69821i	−0.319969	−	0.319969i	−0.848755	+	0.528786i	$0.822647\pi$
$740$	8.91322	+	0.947313i	0.327656	+	0.0348239i
$741$	−23.0720	+	23.0720i	−0.847569	+	0.847569i
$742$	−8.01259	+	0.874949i	−0.294151	+	0.0321204i
$743$	−41.3906			−1.51847			−0.759236	−	0.650815i	$-0.774427\pi$
$743$	−41.3906			−1.51847			−0.759236	+	0.650815i	$0.774427\pi$
$744$	6.05392	+	8.36319i	0.221948	+	0.306610i
$745$	11.6012			0.425034
$746$	19.8633	−	17.8641i	0.727247	−	0.654050i
$747$	−7.80102	−	7.80102i	−0.285424	−	0.285424i
$748$	−13.1271	−	16.2492i	−0.479973	−	0.594131i
$749$	−38.6263	+	6.30120i	−1.41137	+	0.230241i
$750$	0.364359	−	6.87578i	0.0133045	−	0.251068i
$751$			37.5813i			1.37136i	0.727903	+	0.685680i	$0.240495\pi$
$751$			37.5813i			1.37136i	−0.727903	+	0.685680i	$0.759505\pi$
$752$	2.10567	+	0.452702i	0.0767858	+	0.0165083i
$753$	−1.80493			−0.0657753
$754$	2.03417	−	38.3866i	0.0740801	−	1.39796i
$755$	−3.77326	+	3.77326i	−0.137323	+	0.137323i
$756$	−0.295238	−	5.28326i	−0.0107377	−	0.192150i
$757$	35.7246	+	35.7246i	1.29843	+	1.29843i	0.929428	+	0.369002i	$0.120301\pi$
$757$	35.7246	+	35.7246i	1.29843	+	1.29843i	0.369002	+	0.929428i	$0.379699\pi$
$758$	16.4960	+	18.3421i	0.599162	+	0.666216i
$759$		−	5.09844i		−	0.185062i
$760$	−11.7517	−	1.88233i	−0.426279	−	0.0682794i
$761$	45.5380			1.65075			0.825375	−	0.564585i	$-0.190964\pi$
$761$	45.5380			1.65075			0.825375	+	0.564585i	$0.190964\pi$
$762$	12.2162	−	10.9866i	0.442546	−	0.398004i
$763$	2.75500	−	0.449430i	0.0997376	−	0.0162704i
$764$	2.43827	−	22.9416i	0.0882137	−	0.829998i
$765$	−1.26191	+	1.26191i	−0.0456245	+	0.0456245i
$766$	0.339529	−	6.40721i	0.0122677	−	0.231502i
$767$		−	40.1239i		−	1.44879i
$768$	−14.9638	+	5.66425i	−0.539961	+	0.204391i
$769$			6.07515i			0.219075i	0.993983	+	0.109538i	$0.0349370\pi$
$769$			6.07515i			0.219075i	−0.993983	+	0.109538i	$0.965063\pi$
$770$	4.25689	+	3.41874i	0.153408	+	0.123203i
$771$	−21.5579	−	21.5579i	−0.776390	−	0.776390i
$772$	25.4193	+	2.70161i	0.914860	+	0.0972330i
$773$	−26.1824	+	26.1824i	−0.941716	+	0.941716i	−0.998393	−	0.0566766i	$-0.981950\pi$
$773$	−26.1824	+	26.1824i	−0.941716	+	0.941716i	0.0566766	+	0.998393i	$0.481950\pi$
$774$	7.00848	−	6.30308i	0.251915	−	0.226560i
$775$		−	17.3410i		−	0.622908i
$776$	43.4537	+	6.96022i	1.55990	+	0.249857i
$777$	−19.2763	−	13.8692i	−0.691532	−	0.497554i
$778$	24.5981	−	22.1223i	0.881884	−	0.793123i
$779$	−37.5268	+	37.5268i	−1.34454	+	1.34454i
$780$	−3.00778	+	2.42986i	−0.107696	+	0.0870029i
$781$	19.6525	−	19.6525i	0.703222	−	0.703222i
$782$	−8.80600	−	0.466645i	−0.314902	−	0.0166872i
$783$	7.02020			0.250882
$784$	3.11964	+	27.8257i	0.111416	+	0.993774i
$785$	−5.32427			−0.190031
$786$	28.2492	+	1.49697i	1.00761	+	0.0533952i
$787$	−3.92778	+	3.92778i	−0.140010	+	0.140010i	−0.773638	−	0.633628i	$-0.781565\pi$
$787$	−3.92778	+	3.92778i	−0.140010	+	0.140010i	0.633628	+	0.773638i	$0.281565\pi$
$788$	20.5290	+	25.4117i	0.731317	+	0.905255i
$789$	−4.54114	+	4.54114i	−0.161669	+	0.161669i
$790$	−0.874967	+	0.786902i	−0.0311299	+	0.0279967i
$791$	−2.64187	−	1.90081i	−0.0939342	−	0.0675852i
$792$	6.69547	−	4.84670i	0.237913	−	0.172220i
$793$			22.7576i			0.808144i
$794$	−3.17371	+	2.85427i	−0.112631	+	0.101294i
$795$	−0.760586	+	0.760586i	−0.0269752	+	0.0269752i
$796$	0.568943	−	5.35315i	0.0201656	−	0.189737i
$797$	34.0489	+	34.0489i	1.20608	+	1.20608i	0.972288	+	0.233788i	$0.0751122\pi$
$797$	34.0489	+	34.0489i	1.20608	+	1.20608i	0.233788	+	0.972288i	$0.424888\pi$
$798$	24.5844	+	19.7439i	0.870278	+	0.698926i
$799$			1.92444i			0.0680819i
$800$	25.9378	+	7.03102i	0.917041	+	0.248584i
$801$			5.38478i			0.190262i
$802$	−0.610420	+	11.5192i	−0.0215547	+	0.406756i
$803$	−17.9257	+	17.9257i	−0.632585	+	0.632585i
$804$	−4.92423	−	0.523356i	−0.173664	−	0.0184573i
$805$	2.27476	−	0.371088i	0.0801749	−	0.0130791i
$806$	−14.8614	+	13.3656i	−0.523470	+	0.470783i
$807$	−6.52370			−0.229645
$808$	−25.4228	−	35.1204i	−0.894372	−	1.23553i
$809$			53.0107i			1.86376i	0.362772	+	0.931878i	$0.381830\pi$
$809$			53.0107i			1.86376i	−0.362772	+	0.931878i	$0.618170\pi$
$810$	−0.472200	−	0.525045i	−0.0165914	−	0.0184482i
$811$	12.0779	+	12.0779i	0.424114	+	0.424114i	0.886617	−	0.462504i	$-0.153049\pi$
$811$	12.0779	+	12.0779i	0.424114	+	0.424114i	−0.462504	+	0.886617i	$0.653049\pi$
$812$	−37.0895	+	2.07263i	−1.30159	+	0.0727351i
$813$	13.7935	−	13.7935i	0.483759	−	0.483759i
$814$	1.96293	−	37.0422i	0.0688007	−	1.29833i
$815$	7.24123			0.253649
$816$	−7.75837	−	12.0080i	−0.271597	−	0.420363i
$817$			56.1673i			1.96505i
$818$	0.938622	−	17.7126i	0.0328182	−	0.619308i
$819$	10.1104	−	1.64934i	0.353287	−	0.0576326i
$820$	−4.89219	+	3.95219i	−0.170843	+	0.138017i
$821$	−9.63963	−	9.63963i	−0.336425	−	0.336425i	0.518595	−	0.855020i	$-0.326455\pi$
$821$	−9.63963	−	9.63963i	−0.336425	−	0.336425i	−0.855020	+	0.518595i	$0.826455\pi$
$822$	2.71460	−	2.44137i	0.0946824	−	0.0851526i
$823$	9.83217			0.342728			0.171364	−	0.985208i	$-0.445183\pi$
$823$	9.83217			0.342728			0.171364	+	0.985208i	$0.445183\pi$
$824$	23.9218	+	3.83169i	0.833356	+	0.133483i
$825$	−13.8830			−0.483345
$826$	−38.5451	+	4.20901i	−1.34116	+	0.146450i
$827$	22.5314	−	22.5314i	0.783492	−	0.783492i	−0.196926	−	0.980418i	$-0.563096\pi$
$827$	22.5314	−	22.5314i	0.783492	−	0.783492i	0.980418	+	0.196926i	$0.0630959\pi$
$828$	0.368773	−	3.46977i	0.0128158	−	0.120583i
$829$	−16.6214	−	16.6214i	−0.577286	−	0.577286i	0.356869	−	0.934155i	$-0.383844\pi$
$829$	−16.6214	−	16.6214i	−0.577286	−	0.577286i	−0.934155	+	0.356869i	$0.883844\pi$
$830$	7.77953	+	0.412250i	0.270031	+	0.0143094i
$831$	−8.49957			−0.294847
$832$	−13.9659	−	27.6480i	−0.484182	−	0.958524i
$833$	−23.7214	+	7.95107i	−0.821899	+	0.275488i
$834$	1.08432	−	20.4621i	0.0375469	−	0.708543i
$835$	−0.767880	−	0.767880i	−0.0265736	−	0.0265736i
$836$	−5.20539	+	48.9773i	−0.180032	+	1.69391i
$837$	−2.58110	−	2.58110i	−0.0892158	−	0.0892158i
$838$	24.1284	+	26.8287i	0.833503	+	0.926784i
$839$			32.5829i			1.12489i	0.826836	+	0.562444i	$0.190139\pi$
$839$			32.5829i			1.12489i	−0.826836	+	0.562444i	$0.809861\pi$
$840$	2.64977	+	2.63454i	0.0914256	+	0.0909003i
$841$		−	20.2832i		−	0.699421i
$842$	−0.0900719	+	0.0810062i	−0.00310408	+	0.00279166i
$843$	3.35902	+	3.35902i	0.115691	+	0.115691i
$844$	22.1549	+	27.4243i	0.762603	+	0.943982i
$845$	−0.703178	−	0.703178i	−0.0241901	−	0.0241901i
$846$	−0.760410	−	0.0402954i	−0.0261434	−	0.00138538i
$847$	−3.80126	+	5.28324i	−0.130613	+	0.181534i
$848$	−4.67617	−	7.23751i	−0.160580	−	0.248537i
$849$	−3.83581			−0.131645
$850$	−1.27067	+	23.9787i	−0.0435836	+	0.822461i
$851$	−11.0728	−	11.0728i	−0.379571	−	0.379571i
$852$	14.7961	−	11.9531i	0.506905	−	0.409507i
$853$	−7.56835	+	7.56835i	−0.259135	+	0.259135i	−0.824702	−	0.565567i	$-0.808657\pi$
$853$	−7.56835	+	7.56835i	−0.259135	+	0.259135i	0.565567	+	0.824702i	$0.308657\pi$
$854$	21.8621	−	2.38727i	0.748106	−	0.0816908i
$855$	4.20781			0.143904
$856$	−24.5332	−	33.8914i	−0.838529	−	1.15839i
$857$	−31.0643			−1.06114			−0.530568	−	0.847642i	$-0.678021\pi$
$857$	−31.0643			−1.06114			−0.530568	+	0.847642i	$0.678021\pi$
$858$	10.7003	+	11.8978i	0.365303	+	0.406185i
$859$	3.62803	+	3.62803i	0.123787	+	0.123787i	0.766286	−	0.642499i	$-0.222103\pi$
$859$	3.62803	+	3.62803i	0.123787	+	0.123787i	−0.642499	+	0.766286i	$0.722103\pi$
$860$	−0.703459	+	6.61881i	−0.0239877	+	0.225699i
$861$	16.4447	−	2.68267i	0.560435	−	0.0914251i
$862$	18.1345	+	0.960980i	0.617665	+	0.0327311i
$863$		−	41.7045i		−	1.41964i	−0.704384	−	0.709819i	$-0.748777\pi$
$863$		−	41.7045i		−	1.41964i	0.704384	−	0.709819i	$-0.251223\pi$
$864$	4.90719	−	2.81415i	0.166946	−	0.0957394i
$865$	−3.81792			−0.129813
$866$	11.3697	+	0.602497i	0.386357	+	0.0204737i
$867$	−2.98824	+	2.98824i	−0.101486	+	0.101486i
$868$	14.3986	+	12.8746i	0.488722	+	0.436991i
$869$	3.44356	+	3.44356i	0.116815	+	0.116815i
$870$	−3.68592	+	3.31494i	−0.124965	+	0.112387i
$871$		−	9.58675i		−	0.324835i
$872$	1.74982	+	2.41729i	0.0592564	+	0.0818597i
$873$	−15.5590			−0.526594
$874$	13.9037	+	15.4597i	0.470299	+	0.522932i
$875$	−2.07397	−	12.7134i	−0.0701129	−	0.429791i
$876$	−13.4960	+	10.9028i	−0.455988	+	0.368373i
$877$	11.5486	−	11.5486i	0.389968	−	0.389968i	−0.484708	−	0.874676i	$-0.661074\pi$
$877$	11.5486	−	11.5486i	0.389968	−	0.389968i	0.874676	+	0.484708i	$0.161074\pi$
$878$	−51.3626	−	2.72179i	−1.73340	−	0.0918559i
$879$			18.3545i			0.619081i
$880$	−1.22682	+	5.70633i	−0.0413560	+	0.192360i
$881$		−	13.5809i		−	0.457551i	−0.973479	−	0.228775i	$-0.926528\pi$
$881$		−	13.5809i		−	0.457551i	0.973479	−	0.228775i	$-0.0734721\pi$
$882$	−2.64503	−	9.53959i	−0.0890627	−	0.321215i
$883$	26.0931	+	26.0931i	0.878104	+	0.878104i	0.993338	−	0.115234i	$-0.0367619\pi$
$883$	26.0931	+	26.0931i	0.878104	+	0.878104i	−0.115234	+	0.993338i	$0.536762\pi$
$884$	21.5292	−	17.3926i	0.724107	−	0.584975i
$885$	−3.65886	+	3.65886i	−0.122991	+	0.122991i
$886$	−36.3081	−	40.3714i	−1.21979	−	1.35630i
$887$			46.2557i			1.55312i	0.630046	+	0.776558i	$0.283036\pi$
$887$			46.2557i			1.55312i	−0.630046	+	0.776558i	$0.716964\pi$
$888$	4.01516	−	25.0673i	0.134740	−	0.841202i
$889$	17.9518	−	24.9505i	0.602083	−	0.836814i
$890$	−2.54269	−	2.82726i	−0.0852313	−	0.0947698i
$891$	−2.06639	+	2.06639i	−0.0692268	+	0.0692268i
$892$	−25.2810	−	2.68691i	−0.846469	−	0.0899643i
$893$	3.20850	−	3.20850i	0.107368	−	0.107368i
$894$	1.73874	−	32.8116i	0.0581521	−	1.09738i
$895$	1.00413			0.0335644
$896$	−25.0951	+	16.3167i	−0.838369	+	0.545102i
$897$	6.75512			0.225547
$898$	0.520319	−	9.81889i	0.0173633	−	0.327661i
$899$	−18.1198	+	18.1198i	−0.604330	+	0.604330i
$900$	−9.44814	−	1.00417i	−0.314938	−	0.0334722i
$901$	5.44416	−	5.44416i	0.181371	−	0.181371i
$902$	17.4042	+	19.3520i	0.579496	+	0.644350i
$903$	10.2990	−	14.3142i	0.342730	−	0.476348i
$904$	0.550291	−	3.43555i	0.0183024	−	0.114265i
$905$			10.0469i			0.333971i
$906$	10.1064	+	11.2374i	0.335762	+	0.373339i
$907$	−24.3139	+	24.3139i	−0.807329	+	0.807329i	−0.984229	−	0.176900i	$-0.943393\pi$
$907$	−24.3139	+	24.3139i	−0.807329	+	0.807329i	0.176900	+	0.984229i	$0.443393\pi$
$908$	24.2001	−	19.5502i	0.803107	−	0.648796i
$909$	10.8391	+	10.8391i	0.359509	+	0.359509i
$910$	−4.52962	+	5.64012i	−0.150155	+	0.186968i
$911$			57.0504i			1.89017i	0.326832	+	0.945083i	$0.394019\pi$
$911$			57.0504i			1.89017i	−0.326832	+	0.945083i	$0.605981\pi$
$912$	−7.08510	+	32.9552i	−0.234611	+	1.09126i
$913$		−	32.2400i		−	1.06699i
$914$	−7.52211	−	0.398609i	−0.248809	−	0.0131848i
$915$	2.07524	−	2.07524i	0.0686052	−	0.0686052i
$916$	−6.01908	+	4.86256i	−0.198876	+	0.160664i
$917$	52.2331	−	8.52091i	1.72489	−	0.281385i
$918$	3.37993	+	3.75819i	0.111554	+	0.124039i
$919$	29.2687			0.965487			0.482743	−	0.875762i	$-0.339640\pi$
$919$	29.2687			0.965487			0.482743	+	0.875762i	$0.339640\pi$
$920$	1.44480	+	1.99592i	0.0476337	+	0.0658035i
$921$		−	18.6910i		−	0.615889i
$922$	−11.0649	+	9.95125i	−0.364404	+	0.327727i
$923$	26.0384	+	26.0384i	0.857063	+	0.857063i
$924$	10.3072	−	11.5274i	0.339083	−	0.379223i
$925$	−30.1511	+	30.1511i	−0.991363	+	0.991363i
$926$	−50.0929	−	2.65451i	−1.64615	−	0.0872325i
$927$	−8.56545			−0.281326
$928$	−19.7559	−	34.4495i	−0.648520	−	1.13086i
$929$			10.5983i			0.347719i	0.984770	+	0.173860i	$0.0556239\pi$
$929$			10.5983i			0.347719i	−0.984770	+	0.173860i	$0.944376\pi$
$930$	2.57399	+	0.136400i	0.0844043	+	0.00447273i
$931$	52.8055	+	26.2929i	1.73063	+	0.861716i
$932$	1.89715	−	17.8502i	0.0621433	−	0.584703i
$933$	−16.9274	−	16.9274i	−0.554178	−	0.554178i
$934$	−12.4441	−	13.8367i	−0.407182	−	0.452751i
$935$	−5.21522			−0.170556
$936$	6.42157	+	8.87108i	0.209896	+	0.289960i
$937$	22.8293			0.745801			0.372901	−	0.927871i	$-0.378363\pi$
$937$	22.8293			0.745801			0.372901	+	0.927871i	$0.378363\pi$
$938$	−9.20953	+	1.00565i	−0.300702	+	0.0328357i
$939$	6.82469	−	6.82469i	0.222715	−	0.222715i
$940$	0.418277	−	0.337909i	0.0136427	−	0.0110214i
$941$	34.5257	+	34.5257i	1.12551	+	1.12551i	0.990899	+	0.134606i	$0.0429769\pi$
$941$	34.5257	+	34.5257i	1.12551	+	1.12551i	0.134606	+	0.990899i	$0.457023\pi$
$942$	−0.797982	+	15.0586i	−0.0259997	+	0.490637i
$943$	10.9873			0.357795
$944$	−22.4950	−	34.8166i	−0.732151	−	1.13318i
$945$	−1.07236	−	0.771558i	−0.0348839	−	0.0250988i
$946$	27.5069	+	1.45764i	0.894328	+	0.0473919i
$947$	−11.7166	−	11.7166i	−0.380738	−	0.380738i	0.490630	−	0.871368i	$-0.336767\pi$
$947$	−11.7166	−	11.7166i	−0.380738	−	0.380738i	−0.871368	+	0.490630i	$0.836767\pi$
$948$	2.09446	+	2.59260i	0.0680248	+	0.0842039i
$949$	−23.7505	−	23.7505i	−0.770973	−	0.770973i
$950$	42.0966	−	37.8596i	1.36579	−	1.22833i
$951$			2.89565i			0.0938980i
$952$	−18.9666	−	18.8576i	−0.614712	−	0.611179i
$953$		−	44.2619i		−	1.43378i	−0.697185	−	0.716891i	$-0.745564\pi$
$953$		−	44.2619i		−	1.43378i	0.697185	−	0.716891i	$-0.254436\pi$
$954$	2.03717	+	2.26516i	0.0659559	+	0.0733372i
$955$	−4.07285	−	4.07285i	−0.131794	−	0.131794i
$956$	4.34872	−	40.9169i	0.140648	−	1.32335i
$957$	14.5065	+	14.5065i	0.468929	+	0.468929i
$958$	2.32988	−	43.9669i	0.0752750	−	1.42051i
$959$	3.98912	−	5.54433i	0.128815	−	0.179036i
$960$	−1.24766	+	3.79473i	−0.0402680	+	0.122474i
$961$	−17.6759			−0.570190
$962$	49.0787	+	2.60076i	1.58236	+	0.0838519i
$963$	10.4598	+	10.4598i	0.337061	+	0.337061i
$964$	0.578948	−	5.44729i	0.0186466	−	0.175445i
$965$	4.51272	−	4.51272i	0.145270	−	0.145270i
$966$	−0.708614	−	6.48933i	−0.0227993	−	0.208791i
$967$	−20.2806			−0.652179			−0.326089	−	0.945339i	$-0.605731\pi$
$967$	−20.2806			−0.652179			−0.326089	+	0.945339i	$0.605731\pi$
$968$	−6.87043	−	1.10048i	−0.220824	−	0.0353706i
$969$	−30.1189			−0.967558
$970$	8.16920	−	7.34697i	0.262297	−	0.235897i
$971$	22.3463	+	22.3463i	0.717127	+	0.717127i	0.968016	−	0.250889i	$-0.0807230\pi$
$971$	22.3463	+	22.3463i	0.717127	+	0.717127i	−0.250889	+	0.968016i	$0.580723\pi$
$972$	−1.55576	+	1.25683i	−0.0499009	+	0.0403128i
$973$	−6.17205	−	37.8346i	−0.197867	−	1.21292i
$974$	−2.45456	+	46.3197i	−0.0786491	+	1.48418i
$975$		−	18.3941i		−	0.589084i
$976$	12.7588	+	19.7473i	0.408398	+	0.632097i
$977$	21.0247			0.672638			0.336319	−	0.941748i	$-0.390818\pi$
$977$	21.0247			0.672638			0.336319	+	0.941748i	$0.390818\pi$
$978$	1.08529	−	20.4803i	0.0347037	−	0.654889i
$979$	−11.1271	+	11.1271i	−0.355623	+	0.355623i
$980$	5.89335	+	3.75974i	0.188256	+	0.120100i
$981$	−0.746037	−	0.746037i	−0.0238191	−	0.0238191i
$982$	9.14706	+	10.1707i	0.291894	+	0.324561i
$983$			18.7833i			0.599096i	0.954081	+	0.299548i	$0.0968358\pi$
$983$			18.7833i			0.599096i	−0.954081	+	0.299548i	$0.903164\pi$
$984$	10.4448	+	14.4289i	0.332967	+	0.459977i
$985$	8.15592			0.259869
$986$	26.3833	−	23.7278i	0.840215	−	0.755647i
$987$	−1.40601	+	0.229365i	−0.0447537	+	0.00730078i
$988$	−64.8919	−	6.89682i	−2.06449	−	0.219417i
$989$	8.22248	−	8.22248i	0.261460	−	0.261460i
$990$	0.109200	−	2.06070i	0.00347060	−	0.0654934i
$991$			13.2725i			0.421614i	0.977528	+	0.210807i	$0.0676092\pi$
$991$			13.2725i			0.421614i	−0.977528	+	0.210807i	$0.932391\pi$
$992$	−5.40234	+	19.9295i	−0.171524	+	0.632764i
$993$		−	6.31395i		−	0.200367i
$994$	22.2824	−	27.7452i	0.706754	−	0.880026i
$995$	−0.950352	−	0.950352i	−0.0301282	−	0.0301282i
$996$	2.33193	−	21.9410i	0.0738901	−	0.695229i
$997$	−6.05815	+	6.05815i	−0.191864	+	0.191864i	−0.796501	−	0.604637i	$-0.793318\pi$
$997$	−6.05815	+	6.05815i	−0.191864	+	0.191864i	0.604637	+	0.796501i	$0.293318\pi$
$998$	10.3621	−	9.31913i	0.328006	−	0.294992i
$999$			8.97559i			0.283975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.19	✓	64
4.3	odd	2		1344.2.u.a.1231.23		64
7.6	odd	2	inner	336.2.u.a.139.20	yes	64
16.3	odd	4	inner	336.2.u.a.307.20	yes	64
16.13	even	4		1344.2.u.a.559.10		64
28.27	even	2		1344.2.u.a.1231.10		64
112.13	odd	4		1344.2.u.a.559.23		64
112.83	even	4	inner	336.2.u.a.307.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.19	✓	64	1.1	even	1	trivial
336.2.u.a.139.20	yes	64	7.6	odd	2	inner
336.2.u.a.307.19	yes	64	112.83	even	4	inner
336.2.u.a.307.20	yes	64	16.3	odd	4	inner
1344.2.u.a.559.10		64	16.13	even	4
1344.2.u.a.559.23		64	112.13	odd	4
1344.2.u.a.1231.10		64	28.27	even	2
1344.2.u.a.1231.23		64	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0748365 - 1.41223i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98880 - 0.211373i) q^{4} +(-0.353074 + 0.353074i) q^{5} +(0.945681 + 1.05152i) q^{6} +(2.14763 + 1.54521i) q^{7} +(-0.447343 + 2.79283i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.0748365 - 1.41223i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98880 - 0.211373i) q^{4} +(-0.353074 + 0.353074i) q^{5} +(0.945681 + 1.05152i) q^{6} +(2.14763 + 1.54521i) q^{7} +(-0.447343 + 2.79283i) q^{8} -1.00000i q^{9} +(0.472200 + 0.525045i) q^{10} +(2.06639 - 2.06639i) q^{11} +(1.55576 - 1.25683i) q^{12} +(2.73784 + 2.73784i) q^{13} +(2.34292 - 2.91732i) q^{14} -0.499322i q^{15} +(3.91064 + 0.840757i) q^{16} +3.57407i q^{17} +(-1.41223 - 0.0748365i) q^{18} +(5.95882 - 5.95882i) q^{19} +(0.776824 - 0.627563i) q^{20} +(-2.61123 + 0.425977i) q^{21} +(-2.76359 - 3.07287i) q^{22} -1.74465 q^{23} +(-1.65851 - 2.29115i) q^{24} +4.75068i q^{25} +(4.07136 - 3.66158i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.94459 - 3.52706i) q^{28} +(4.96403 - 4.96403i) q^{29} +(-0.705159 - 0.0373675i) q^{30} -3.65022 q^{31} +(1.48000 - 5.45982i) q^{32} +2.92232i q^{33} +(5.04742 + 0.267471i) q^{34} +(-1.30385 + 0.212700i) q^{35} +(-0.211373 + 1.98880i) q^{36} +(6.34670 + 6.34670i) q^{37} +(-7.96931 - 8.86118i) q^{38} -3.87190 q^{39} +(-0.828130 - 1.14402i) q^{40} -6.29768 q^{41} +(0.406163 + 3.71955i) q^{42} +(-4.71295 + 4.71295i) q^{43} +(-4.54642 + 3.67286i) q^{44} +(0.353074 + 0.353074i) q^{45} +(-0.130564 + 2.46386i) q^{46} +0.538446 q^{47} +(-3.35975 + 2.17074i) q^{48} +(2.22465 + 6.63709i) q^{49} +(6.70906 + 0.355524i) q^{50} +(-2.52725 - 2.52725i) q^{51} +(-4.86632 - 6.02373i) q^{52} +(-1.52324 - 1.52324i) q^{53} +(1.05152 - 0.945681i) q^{54} +1.45918i q^{55} +(-5.27623 + 5.30673i) q^{56} +8.42705i q^{57} +(-6.63887 - 7.38186i) q^{58} +(-7.32765 - 7.32765i) q^{59} +(-0.105543 + 0.993051i) q^{60} +(4.15611 + 4.15611i) q^{61} +(-0.273170 + 5.15496i) q^{62} +(1.54521 - 2.14763i) q^{63} +(-7.59977 - 2.49870i) q^{64} -1.93332 q^{65} +(4.12700 + 0.218697i) q^{66} +(-1.75078 - 1.75078i) q^{67} +(0.755463 - 7.10811i) q^{68} +(1.23366 - 1.23366i) q^{69} +(0.202806 + 1.85725i) q^{70} +9.51053 q^{71} +(2.79283 + 0.447343i) q^{72} -8.67488 q^{73} +(9.43798 - 8.48805i) q^{74} +(-3.35924 - 3.35924i) q^{75} +(-13.1104 + 10.5914i) q^{76} +(7.63087 - 1.24484i) q^{77} +(-0.289759 + 5.46802i) q^{78} +1.66646i q^{79} +(-1.67760 + 1.08390i) q^{80} -1.00000 q^{81} +(-0.471297 + 8.89379i) q^{82} +(7.80102 - 7.80102i) q^{83} +(5.28326 - 0.295238i) q^{84} +(-1.26191 - 1.26191i) q^{85} +(6.30308 + 7.00848i) q^{86} +7.02020i q^{87} +(4.84670 + 6.69547i) q^{88} -5.38478 q^{89} +(0.525045 - 0.472200i) q^{90} +(1.64934 + 10.1104i) q^{91} +(3.46977 + 0.368773i) q^{92} +(2.58110 - 2.58110i) q^{93} +(0.0402954 - 0.760410i) q^{94} +4.20781i q^{95} +(2.81415 + 4.90719i) q^{96} -15.5590i q^{97} +(9.53959 - 2.64503i) q^{98} +(-2.06639 - 2.06639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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