LMFDB - Embedded newform 273.2.n.c.8.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.n (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.12
Character	$\chi$	$=$	273.8
Dual form			273.2.n.c.239.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0762157 + 0.0762157i) q^{2} +(1.58361 - 0.701549i) q^{3} +1.98838i q^{4} +(-2.41817 + 2.41817i) q^{5} +(-0.0672271 + 0.174165i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.303978 - 0.303978i) q^{8} +(2.01566 - 2.22196i) q^{9} +O(q^{10})$	\(q+(-0.0762157 + 0.0762157i) q^{2} +(1.58361 - 0.701549i) q^{3} +1.98838i q^{4} +(-2.41817 + 2.41817i) q^{5} +(-0.0672271 + 0.174165i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.303978 - 0.303978i) q^{8} +(2.01566 - 2.22196i) q^{9} -0.368606i q^{10} +(3.75644 + 3.75644i) q^{11} +(1.39495 + 3.14883i) q^{12} +(-3.50109 + 0.861588i) q^{13} +0.107785i q^{14} +(-2.13298 + 5.52592i) q^{15} -3.93043 q^{16} -0.501131 q^{17} +(0.0157237 + 0.322973i) q^{18} +(3.52276 + 3.52276i) q^{19} +(-4.80825 - 4.80825i) q^{20} +(0.623713 - 1.61585i) q^{21} -0.572600 q^{22} +4.77125 q^{23} +(-0.694638 - 0.268128i) q^{24} -6.69513i q^{25} +(0.201172 - 0.332505i) q^{26} +(1.63320 - 4.93281i) q^{27} +(1.40600 + 1.40600i) q^{28} -6.76629i q^{29} +(-0.258595 - 0.583729i) q^{30} +(-3.11290 - 3.11290i) q^{31} +(0.907516 - 0.907516i) q^{32} +(8.58408 + 3.31342i) q^{33} +(0.0381941 - 0.0381941i) q^{34} +3.41981i q^{35} +(4.41811 + 4.00790i) q^{36} +(2.59939 - 2.59939i) q^{37} -0.536979 q^{38} +(-4.93993 + 3.82061i) q^{39} +1.47014 q^{40} +(1.35341 - 1.35341i) q^{41} +(0.0756167 + 0.170690i) q^{42} -5.63601i q^{43} +(-7.46925 + 7.46925i) q^{44} +(0.498883 + 10.2473i) q^{45} +(-0.363645 + 0.363645i) q^{46} +(-4.05418 - 4.05418i) q^{47} +(-6.22428 + 2.75739i) q^{48} -1.00000i q^{49} +(0.510274 + 0.510274i) q^{50} +(-0.793597 + 0.351568i) q^{51} +(-1.71317 - 6.96152i) q^{52} -4.05654i q^{53} +(0.251482 + 0.500434i) q^{54} -18.1675 q^{55} -0.429889 q^{56} +(8.05007 + 3.10730i) q^{57} +(0.515698 + 0.515698i) q^{58} +(9.92175 + 9.92175i) q^{59} +(-10.9876 - 4.24119i) q^{60} +0.198691 q^{61} +0.474504 q^{62} +(-0.145880 - 2.99645i) q^{63} -7.72252i q^{64} +(6.38278 - 10.5497i) q^{65} +(-0.906777 + 0.401707i) q^{66} +(-2.62400 - 2.62400i) q^{67} -0.996440i q^{68} +(7.55582 - 3.34727i) q^{69} +(-0.260644 - 0.260644i) q^{70} +(-5.51972 + 5.51972i) q^{71} +(-1.28814 + 0.0627123i) q^{72} +(-5.30667 + 5.30667i) q^{73} +0.396228i q^{74} +(-4.69696 - 10.6025i) q^{75} +(-7.00459 + 7.00459i) q^{76} +5.31241 q^{77} +(0.0853098 - 0.667691i) q^{78} +13.0695 q^{79} +(9.50446 - 9.50446i) q^{80} +(-0.874246 - 8.95744i) q^{81} +0.206302i q^{82} +(4.32106 - 4.32106i) q^{83} +(3.21293 + 1.24018i) q^{84} +(1.21182 - 1.21182i) q^{85} +(0.429553 + 0.429553i) q^{86} +(-4.74689 - 10.7152i) q^{87} -2.28375i q^{88} +(-1.57446 - 1.57446i) q^{89} +(-0.819029 - 0.742983i) q^{90} +(-1.86641 + 3.08488i) q^{91} +9.48708i q^{92} +(-7.11349 - 2.74578i) q^{93} +0.617985 q^{94} -17.0373 q^{95} +(0.800486 - 2.07382i) q^{96} +(-4.63648 - 4.63648i) q^{97} +(0.0762157 + 0.0762157i) q^{98} +(15.9184 - 0.774976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) $ 48 * q + 8 * q^3 + 4 * q^6	$ 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) $ 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0762157	+	0.0762157i	−0.0538927	+	0.0538927i	−0.733539	−	0.679647i	$-0.762133\pi$
$2$	−0.0762157	+	0.0762157i	−0.0538927	+	0.0538927i	0.679647	+	0.733539i	$0.262133\pi$
$3$	1.58361	−	0.701549i	0.914299	−	0.405040i
$3$	1.58361	−	0.701549i	0.914299	−	0.405040i
$4$			1.98838i			0.994191i
$5$	−2.41817	+	2.41817i	−1.08144	+	1.08144i	−0.0850646	+	0.996375i	$0.527110\pi$
$5$	−2.41817	+	2.41817i	−1.08144	+	1.08144i	−0.996375	+	0.0850646i	$0.972890\pi$
$6$	−0.0672271	+	0.174165i	−0.0274454	+	0.0711027i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−0.303978	−	0.303978i	−0.107472	−	0.107472i
$9$	2.01566	−	2.22196i	0.671886	−	0.740655i
$10$		−	0.368606i		−	0.116563i
$11$	3.75644	+	3.75644i	1.13261	+	1.13261i	0.989742	+	0.142869i	$0.0456328\pi$
$11$	3.75644	+	3.75644i	1.13261	+	1.13261i	0.142869	+	0.989742i	$0.454367\pi$
$12$	1.39495	+	3.14883i	0.402687	+	0.908988i
$13$	−3.50109	+	0.861588i	−0.971029	+	0.238962i
$13$	−3.50109	+	0.861588i	−0.971029	+	0.238962i
$14$			0.107785i			0.0288068i
$15$	−2.13298	+	5.52592i	−0.550734	+	1.42679i
$16$	−3.93043			−0.982607
$17$	−0.501131			−0.121542			−0.0607710	−	0.998152i	$-0.519356\pi$
$17$	−0.501131			−0.121542			−0.0607710	+	0.998152i	$0.519356\pi$
$18$	0.0157237	+	0.322973i	0.00370612	+	0.0761256i
$19$	3.52276	+	3.52276i	0.808176	+	0.808176i	0.984358	−	0.176182i	$-0.0563747\pi$
$19$	3.52276	+	3.52276i	0.808176	+	0.808176i	−0.176182	+	0.984358i	$0.556375\pi$
$20$	−4.80825	−	4.80825i	−1.07516	−	1.07516i
$21$	0.623713	−	1.61585i	0.136105	−	0.352608i
$22$	−0.572600			−0.122079
$23$	4.77125			0.994875			0.497438	−	0.867500i	$-0.334274\pi$
$23$	4.77125			0.994875			0.497438	+	0.867500i	$0.334274\pi$
$24$	−0.694638	−	0.268128i	−0.141792	−	0.0547313i
$25$		−	6.69513i		−	1.33903i
$26$	0.201172	−	0.332505i	0.0394531	−	0.0652096i
$27$	1.63320	−	4.93281i	0.314310	−	0.949320i
$28$	1.40600	+	1.40600i	0.265709	+	0.265709i
$29$		−	6.76629i		−	1.25647i	−0.778024	−	0.628235i	$-0.783778\pi$
$29$		−	6.76629i		−	1.25647i	0.778024	−	0.628235i	$-0.216222\pi$
$30$	−0.258595	−	0.583729i	−0.0472128	−	0.106574i
$31$	−3.11290	−	3.11290i	−0.559094	−	0.559094i	0.369956	−	0.929049i	$-0.379373\pi$
$31$	−3.11290	−	3.11290i	−0.559094	−	0.559094i	−0.929049	+	0.369956i	$0.879373\pi$
$32$	0.907516	−	0.907516i	0.160428	−	0.160428i
$33$	8.58408	+	3.31342i	1.49430	+	0.576793i
$34$	0.0381941	−	0.0381941i	0.00655023	−	0.00655023i
$35$			3.41981i			0.578054i
$36$	4.41811	+	4.00790i	0.736352	+	0.667983i
$37$	2.59939	−	2.59939i	0.427337	−	0.427337i	−0.460384	−	0.887720i	$-0.652288\pi$
$37$	2.59939	−	2.59939i	0.427337	−	0.427337i	0.887720	+	0.460384i	$0.152288\pi$
$38$	−0.536979			−0.0871095
$39$	−4.93993	+	3.82061i	−0.791022	+	0.611788i
$40$	1.47014			0.232450
$41$	1.35341	−	1.35341i	0.211367	−	0.211367i	−0.593481	−	0.804848i	$-0.702247\pi$
$41$	1.35341	−	1.35341i	0.211367	−	0.211367i	0.804848	+	0.593481i	$0.202247\pi$
$42$	0.0756167	+	0.170690i	0.0116679	+	0.0263381i
$43$		−	5.63601i		−	0.859484i	−0.902952	−	0.429742i	$-0.858605\pi$
$43$		−	5.63601i		−	0.859484i	0.902952	−	0.429742i	$-0.141395\pi$
$44$	−7.46925	+	7.46925i	−1.12603	+	1.12603i
$45$	0.498883	+	10.2473i	0.0743691	+	1.52758i
$46$	−0.363645	+	0.363645i	−0.0536165	+	0.0536165i
$47$	−4.05418	−	4.05418i	−0.591364	−	0.591364i	0.346636	−	0.938000i	$-0.387324\pi$
$47$	−4.05418	−	4.05418i	−0.591364	−	0.591364i	−0.938000	+	0.346636i	$0.887324\pi$
$48$	−6.22428	+	2.75739i	−0.898397	+	0.397995i
$49$		−	1.00000i		−	0.142857i
$50$	0.510274	+	0.510274i	0.0721636	+	0.0721636i
$51$	−0.793597	+	0.351568i	−0.111126	+	0.0492293i
$52$	−1.71317	−	6.96152i	−0.237574	−	0.965388i
$53$		−	4.05654i		−	0.557209i	−0.960406	−	0.278604i	$-0.910128\pi$
$53$		−	4.05654i		−	0.557209i	0.960406	−	0.278604i	$-0.0898718\pi$
$54$	0.251482	+	0.500434i	0.0342224	+	0.0681004i
$55$	−18.1675			−2.44970
$56$	−0.429889			−0.0574463
$57$	8.05007	+	3.10730i	1.06626	+	0.411571i
$58$	0.515698	+	0.515698i	0.0677145	+	0.0677145i
$59$	9.92175	+	9.92175i	1.29170	+	1.29170i	0.933734	+	0.357967i	$0.116530\pi$
$59$	9.92175	+	9.92175i	1.29170	+	1.29170i	0.357967	+	0.933734i	$0.383470\pi$
$60$	−10.9876	−	4.24119i	−1.41850	−	0.547535i
$61$	0.198691			0.0254398			0.0127199	−	0.999919i	$-0.495951\pi$
$61$	0.198691			0.0254398			0.0127199	+	0.999919i	$0.495951\pi$
$62$	0.474504			0.0602621
$63$	−0.145880	−	2.99645i	−0.0183792	−	0.377517i
$64$		−	7.72252i		−	0.965315i
$65$	6.38278	−	10.5497i	0.791687	−	1.30853i
$66$	−0.906777	+	0.401707i	−0.111617	+	0.0494467i
$67$	−2.62400	−	2.62400i	−0.320573	−	0.320573i	0.528414	−	0.848987i	$-0.322787\pi$
$67$	−2.62400	−	2.62400i	−0.320573	−	0.320573i	−0.848987	+	0.528414i	$0.822787\pi$
$68$		−	0.996440i		−	0.120836i
$69$	7.55582	−	3.34727i	0.909614	−	0.402964i
$70$	−0.260644	−	0.260644i	−0.0311529	−	0.0311529i
$71$	−5.51972	+	5.51972i	−0.655071	+	0.655071i	−0.954210	−	0.299139i	$-0.903301\pi$
$71$	−5.51972	+	5.51972i	−0.655071	+	0.655071i	0.299139	+	0.954210i	$0.403301\pi$
$72$	−1.28814	+	0.0627123i	−0.151809	+	0.00739072i
$73$	−5.30667	+	5.30667i	−0.621099	+	0.621099i	−0.945812	−	0.324713i	$-0.894732\pi$
$73$	−5.30667	+	5.30667i	−0.621099	+	0.621099i	0.324713	+	0.945812i	$0.394732\pi$
$74$			0.396228i			0.0460606i
$75$	−4.69696	−	10.6025i	−0.542358	−	1.22427i
$76$	−7.00459	+	7.00459i	−0.803481	+	0.803481i
$77$	5.31241			0.605406
$78$	0.0853098	−	0.667691i	0.00965943	−	0.0756012i
$79$	13.0695			1.47043			0.735216	−	0.677833i	$-0.237081\pi$
$79$	13.0695			1.47043			0.735216	+	0.677833i	$0.237081\pi$
$80$	9.50446	−	9.50446i	1.06263	−	1.06263i
$81$	−0.874246	−	8.95744i	−0.0971384	−	0.995271i
$82$			0.206302i			0.0227823i
$83$	4.32106	−	4.32106i	0.474298	−	0.474298i	−0.429004	−	0.903302i	$-0.641136\pi$
$83$	4.32106	−	4.32106i	0.474298	−	0.474298i	0.903302	+	0.429004i	$0.141136\pi$
$84$	3.21293	+	1.24018i	0.350560	+	0.135315i
$85$	1.21182	−	1.21182i	0.131440	−	0.131440i
$86$	0.429553	+	0.429553i	0.0463199	+	0.0463199i
$87$	−4.74689	−	10.7152i	−0.508920	−	1.14879i
$88$		−	2.28375i		−	0.243448i
$89$	−1.57446	−	1.57446i	−0.166892	−	0.166892i	0.618720	−	0.785612i	$-0.287652\pi$
$89$	−1.57446	−	1.57446i	−0.166892	−	0.166892i	−0.785612	+	0.618720i	$0.787652\pi$
$90$	−0.819029	−	0.742983i	−0.0863332	−	0.0783173i
$91$	−1.86641	+	3.08488i	−0.195653	+	0.323384i
$92$			9.48708i			0.989096i
$93$	−7.11349	−	2.74578i	−0.737634	−	0.284724i
$94$	0.617985			0.0637403
$95$	−17.0373			−1.74799
$96$	0.800486	−	2.07382i	0.0816993	−	0.211658i
$97$	−4.63648	−	4.63648i	−0.470763	−	0.470763i	0.431398	−	0.902162i	$-0.358020\pi$
$97$	−4.63648	−	4.63648i	−0.470763	−	0.470763i	−0.902162	+	0.431398i	$0.858020\pi$
$98$	0.0762157	+	0.0762157i	0.00769895	+	0.00769895i
$99$	15.9184	−	0.774976i	1.59986	−	0.0778880i
$100$	13.3125			1.33125
$101$	−15.4221			−1.53456			−0.767278	−	0.641314i	$-0.778390\pi$
$101$	−15.4221			−1.53456			−0.767278	+	0.641314i	$0.778390\pi$
$102$	0.0336896	−	0.0872796i	0.00333577	−	0.00864197i
$103$		−	9.63304i		−	0.949171i	−0.880209	−	0.474586i	$-0.842598\pi$
$103$		−	9.63304i		−	0.949171i	0.880209	−	0.474586i	$-0.157402\pi$
$104$	1.32616	+	0.802351i	0.130040	+	0.0786770i
$105$	2.39917	+	5.41566i	0.234135	+	0.528514i
$106$	0.309172	+	0.309172i	0.0300295	+	0.0300295i
$107$			13.0585i			1.26241i	0.775617	+	0.631204i	$0.217439\pi$
$107$			13.0585i			1.26241i	−0.775617	+	0.631204i	$0.782561\pi$
$108$	9.80832	+	3.24744i	0.943806	+	0.312485i
$109$	10.6979	+	10.6979i	1.02468	+	1.02468i	0.999688	+	0.0249883i	$0.00795486\pi$
$109$	10.6979	+	10.6979i	1.02468	+	1.02468i	0.0249883	+	0.999688i	$0.492045\pi$
$110$	1.38465	−	1.38465i	0.132021	−	0.132021i
$111$	2.29282	−	5.94002i	0.217625	−	0.563802i
$112$	−2.77923	+	2.77923i	−0.262613	+	0.262613i
$113$			6.43322i			0.605186i	0.953120	+	0.302593i	$0.0978523\pi$
$113$			6.43322i			0.605186i	−0.953120	+	0.302593i	$0.902148\pi$
$114$	−0.850367	+	0.376717i	−0.0796441	+	0.0352828i
$115$	−11.5377	+	11.5377i	−1.07590	+	1.07590i
$116$	13.4540			1.24917
$117$	−5.14259	+	9.51597i	−0.475433	+	0.879752i
$118$	−1.51239			−0.139226
$119$	−0.354353	+	0.354353i	−0.0324835	+	0.0324835i
$120$	2.32813	−	1.03138i	0.212529	−	0.0941513i
$121$			17.2218i			1.56561i
$122$	−0.0151434	+	0.0151434i	−0.00137102	+	0.00137102i
$123$	1.19379	−	3.09276i	0.107641	−	0.278865i
$124$	6.18964	−	6.18964i	0.555846	−	0.555846i
$125$	4.09911	+	4.09911i	0.366635	+	0.366635i
$126$	0.239495	+	0.217258i	0.0213359	+	0.0193549i
$127$			9.34163i			0.828936i	0.910064	+	0.414468i	$0.136032\pi$
$127$			9.34163i			0.828936i	−0.910064	+	0.414468i	$0.863968\pi$
$128$	2.40361	+	2.40361i	0.212451	+	0.212451i
$129$	−3.95394	−	8.92526i	−0.348125	−	0.785825i
$130$	0.317586	+	1.29052i	0.0278542	+	0.113186i
$131$		−	0.986069i		−	0.0861533i	−0.999072	−	0.0430766i	$-0.986284\pi$
$131$		−	0.986069i		−	0.0861533i	0.999072	−	0.0430766i	$-0.0137160\pi$
$132$	−6.58835	+	17.0684i	−0.573442	+	1.48562i
$133$	4.98193			0.431988
$134$	0.399980			0.0345530
$135$	7.97902	+	15.8778i	0.686725	+	1.36654i
$136$	0.152333	+	0.152333i	0.0130624	+	0.0130624i
$137$	−7.92834	−	7.92834i	−0.677363	−	0.677363i	0.282039	−	0.959403i	$-0.408989\pi$
$137$	−7.92834	−	7.92834i	−0.677363	−	0.677363i	−0.959403	+	0.282039i	$0.908989\pi$
$138$	−0.320758	+	0.830987i	−0.0273047	+	0.0707383i
$139$	4.55442			0.386301			0.193150	−	0.981169i	$-0.438129\pi$
$139$	4.55442			0.386301			0.193150	+	0.981169i	$0.438129\pi$
$140$	−6.79990			−0.574696
$141$	−9.26447	−	3.57605i	−0.780209	−	0.301158i
$142$		−	0.841379i		−	0.0706070i
$143$	−16.3882	−	9.91516i	−1.37045	−	0.829147i
$144$	−7.92240	+	8.73327i	−0.660200	+	0.727773i
$145$	16.3621	+	16.3621i	1.35880	+	1.35880i
$146$		−	0.808904i		−	0.0669454i
$147$	−0.701549	−	1.58361i	−0.0578628	−	0.130614i
$148$	5.16857	+	5.16857i	0.424854	+	0.424854i
$149$	−7.78532	+	7.78532i	−0.637798	+	0.637798i	−0.950012	−	0.312214i	$-0.898930\pi$
$149$	−7.78532	+	7.78532i	−0.637798	+	0.637798i	0.312214	+	0.950012i	$0.398930\pi$
$150$	1.16606	+	0.450094i	0.0952083	+	0.0367500i
$151$	−3.48647	+	3.48647i	−0.283725	+	0.283725i	−0.834593	−	0.550868i	$-0.814297\pi$
$151$	−3.48647	+	3.48647i	−0.283725	+	0.283725i	0.550868	+	0.834593i	$0.314297\pi$
$152$		−	2.14168i		−	0.173713i
$153$	−1.01011	+	1.11349i	−0.0816624	+	0.0900207i
$154$	−0.404890	+	0.404890i	−0.0326269	+	0.0326269i
$155$	15.0551			1.20925
$156$	−7.59684	−	9.82247i	−0.608234	−	0.786427i
$157$	3.46210			0.276306			0.138153	−	0.990411i	$-0.455883\pi$
$157$	3.46210			0.276306			0.138153	+	0.990411i	$0.455883\pi$
$158$	−0.996100	+	0.996100i	−0.0792455	+	0.0792455i
$159$	−2.84586	−	6.42399i	−0.225691	−	0.509455i
$160$			4.38906i			0.346986i
$161$	3.37379	−	3.37379i	0.265892	−	0.265892i
$162$	0.749329	+	0.616066i	0.0588728	+	0.0484028i
$163$	10.9583	−	10.9583i	0.858318	−	0.858318i	−0.132822	−	0.991140i	$-0.542404\pi$
$163$	10.9583	−	10.9583i	0.858318	−	0.858318i	0.991140	+	0.132822i	$0.0424039\pi$
$164$	2.69109	+	2.69109i	0.210139	+	0.210139i
$165$	−28.7702	+	12.7454i	−2.23976	+	0.992226i
$166$			0.658666i			0.0511224i
$167$	−14.1220	−	14.1220i	−1.09280	−	1.09280i	−0.995229	−	0.0975680i	$-0.968894\pi$
$167$	−14.1220	−	14.1220i	−1.09280	−	1.09280i	−0.0975680	−	0.995229i	$-0.531106\pi$
$168$	−0.680778	+	0.301588i	−0.0525232	+	0.0232680i
$169$	11.5153	−	6.03300i	0.885795	−	0.464077i
$170$			0.184720i			0.0141674i
$171$	14.9281	−	0.726765i	1.14158	−	0.0555771i
$172$	11.2065			0.854491
$173$	18.6189			1.41557			0.707786	−	0.706427i	$-0.249694\pi$
$173$	18.6189			1.41557			0.707786	+	0.706427i	$0.249694\pi$
$174$	1.17845	+	0.454879i	0.0893383	+	0.0344843i
$175$	−4.73417	−	4.73417i	−0.357870	−	0.357870i
$176$	−14.7644	−	14.7644i	−1.11291	−	1.11291i
$177$	22.6728	+	8.75161i	1.70419	+	0.657812i
$178$	0.239997			0.0179885
$179$	18.3518			1.37168			0.685841	−	0.727752i	$-0.259435\pi$
$179$	18.3518			1.37168			0.685841	+	0.727752i	$0.259435\pi$
$180$	−20.3756	+	0.991970i	−1.51870	+	0.0739371i
$181$			7.60589i			0.565342i	0.959217	+	0.282671i	$0.0912204\pi$
$181$			7.60589i			0.565342i	−0.959217	+	0.282671i	$0.908780\pi$
$182$	−0.0928666	−	0.377367i	−0.00688373	−	0.0279723i
$183$	0.314649	−	0.139391i	0.0232595	−	0.0103041i
$184$	−1.45035	−	1.45035i	−0.106922	−	0.106922i
$185$			12.5715i			0.924278i
$186$	0.751431	−	0.332888i	0.0550976	−	0.0244085i
$187$	−1.88247	−	1.88247i	−0.137660	−	0.137660i
$188$	8.06127	−	8.06127i	0.587929	−	0.587929i
$189$	−2.33318	−	4.64288i	−0.169714	−	0.337720i
$190$	1.29851	−	1.29851i	0.0942037	−	0.0942037i
$191$		−	9.11788i		−	0.659746i	−0.944025	−	0.329873i	$-0.892994\pi$
$191$		−	9.11788i		−	0.659746i	0.944025	−	0.329873i	$-0.107006\pi$
$192$	−5.41773	−	12.2295i	−0.390991	−	0.882587i
$193$	1.65201	−	1.65201i	0.118914	−	0.118914i	−0.645145	−	0.764060i	$-0.723203\pi$
$193$	1.65201	−	1.65201i	0.118914	−	0.118914i	0.764060	+	0.645145i	$0.223203\pi$
$194$	0.706745			0.0507414
$195$	2.70671	−	21.1845i	0.193832	−	1.51705i
$196$	1.98838			0.142027
$197$	−5.88344	+	5.88344i	−0.419177	+	0.419177i	−0.884920	−	0.465743i	$-0.845787\pi$
$197$	−5.88344	+	5.88344i	−0.419177	+	0.419177i	0.465743	+	0.884920i	$0.345787\pi$
$198$	−1.15417	+	1.27230i	−0.0820230	+	0.0904182i
$199$			9.84621i			0.697980i	0.937127	+	0.348990i	$0.113475\pi$
$199$			9.84621i			0.697980i	−0.937127	+	0.348990i	$0.886525\pi$
$200$	−2.03517	+	2.03517i	−0.143908	+	0.143908i
$201$	−5.99627	−	2.31454i	−0.422944	−	0.163255i
$202$	1.17541	−	1.17541i	0.0827014	−	0.0827014i
$203$	−4.78449	−	4.78449i	−0.335806	−	0.335806i
$204$	−0.699051	−	1.57797i	−0.0489434	−	0.110480i
$205$			6.54556i			0.457161i
$206$	0.734189	+	0.734189i	0.0511534	+	0.0511534i
$207$	9.61722	−	10.6016i	0.668443	−	0.736859i
$208$	13.7608	−	3.38641i	0.954140	−	0.234805i
$209$			26.4661i			1.83070i
$210$	−0.595613	−	0.229904i	−0.0411012	−	0.0158649i
$211$	−20.9352			−1.44124			−0.720620	−	0.693330i	$-0.756143\pi$
$211$	−20.9352			−1.44124			−0.720620	+	0.693330i	$0.756143\pi$
$212$	8.06595			0.553972
$213$	−4.86875	+	12.6135i	−0.333601	+	0.864260i
$214$	−0.995260	−	0.995260i	−0.0680345	−	0.0680345i
$215$	13.6289	+	13.6289i	0.929480	+	0.929480i
$216$	−1.99592	+	1.00301i	−0.135805	+	0.0682460i
$217$	−4.40231			−0.298848
$218$	−1.63070			−0.110445
$219$	−4.68082	+	12.1266i	−0.316301	+	0.819440i
$220$		−	36.1239i		−	2.43547i
$221$	1.75451	−	0.431768i	0.118021	−	0.0290439i
$222$	0.277974	+	0.627472i	0.0186564	+	0.0421132i
$223$	−18.2346	−	18.2346i	−1.22108	−	1.22108i	−0.967248	−	0.253835i	$-0.918308\pi$
$223$	−18.2346	−	18.2346i	−1.22108	−	1.22108i	−0.253835	−	0.967248i	$-0.581692\pi$
$224$		−	1.28342i		−	0.0857522i
$225$	−14.8763	−	13.4951i	−0.991755	−	0.899672i
$226$	−0.490312	−	0.490312i	−0.0326151	−	0.0326151i
$227$	7.91163	−	7.91163i	0.525113	−	0.525113i	−0.393998	−	0.919111i	$-0.628908\pi$
$227$	7.91163	−	7.91163i	0.525113	−	0.525113i	0.919111	+	0.393998i	$0.128908\pi$
$228$	−6.17849	+	16.0066i	−0.409181	+	1.06006i
$229$	−7.34584	+	7.34584i	−0.485427	+	0.485427i	−0.906860	−	0.421433i	$-0.861527\pi$
$229$	−7.34584	+	7.34584i	−0.485427	+	0.485427i	0.421433	+	0.906860i	$0.361527\pi$
$230$		−	1.75871i		−	0.115966i
$231$	8.41281	−	3.72692i	0.553522	−	0.245213i
$232$	−2.05680	+	2.05680i	−0.135036	+	0.135036i
$233$	−25.0497			−1.64106			−0.820531	−	0.571602i	$-0.806322\pi$
$233$	−25.0497			−1.64106			−0.820531	+	0.571602i	$0.806322\pi$
$234$	−0.333320	−	1.11721i	−0.0217898	−	0.0730345i
$235$	19.6074			1.27905
$236$	−19.7282	+	19.7282i	−1.28420	+	1.28420i
$237$	20.6970	−	9.16888i	1.34441	−	0.595583i
$238$		−	0.0540146i		−	0.00350124i
$239$	8.87266	−	8.87266i	0.573924	−	0.573924i	−0.359298	−	0.933223i	$-0.616984\pi$
$239$	8.87266	−	8.87266i	0.573924	−	0.573924i	0.933223	+	0.359298i	$0.116984\pi$
$240$	8.38354	−	21.7192i	0.541155	−	1.40197i
$241$	−10.1362	+	10.1362i	−0.652931	+	0.652931i	−0.953698	−	0.300767i	$-0.902758\pi$
$241$	−10.1362	+	10.1362i	−0.652931	+	0.652931i	0.300767	+	0.953698i	$0.402758\pi$
$242$	−1.31257	−	1.31257i	−0.0843751	−	0.0843751i
$243$	−7.66855	−	13.5718i	−0.491938	−	0.870630i
$244$			0.395073i			0.0252920i
$245$	2.41817	+	2.41817i	0.154491	+	0.154491i
$246$	0.144731	+	0.326703i	0.00922772	+	0.0208298i
$247$	−15.3687	−	9.29834i	−0.977885	−	0.591639i
$248$			1.89251i			0.120174i
$249$	3.81145	−	9.87432i	0.241541	−	0.625760i
$250$	−0.624833			−0.0395179
$251$	−20.3901			−1.28701			−0.643505	−	0.765441i	$-0.722521\pi$
$251$	−20.3901			−1.28701			−0.643505	+	0.765441i	$0.722521\pi$
$252$	5.95809	−	0.290066i	0.375324	−	0.0182724i
$253$	17.9230	+	17.9230i	1.12681	+	1.12681i
$254$	−0.711979	−	0.711979i	−0.0446736	−	0.0446736i
$255$	1.06890	−	2.76921i	0.0669373	−	0.173415i
$256$	15.0787			0.942416
$257$	2.53131			0.157899			0.0789493	−	0.996879i	$-0.474843\pi$
$257$	2.53131			0.157899			0.0789493	+	0.996879i	$0.474843\pi$
$258$	0.981598	+	0.378893i	0.0611116	+	0.0235888i
$259$		−	3.67609i		−	0.228421i
$260$	20.9769	+	12.6914i	1.30093	+	0.787088i
$261$	−15.0345	−	13.6385i	−0.930610	−	0.844204i
$262$	0.0751540	+	0.0751540i	0.00464303	+	0.00464303i
$263$			13.0477i			0.804558i	0.915517	+	0.402279i	$0.131782\pi$
$263$			13.0477i			0.804558i	−0.915517	+	0.402279i	$0.868218\pi$
$264$	−1.60216	−	3.61657i	−0.0986063	−	0.222585i
$265$	9.80942	+	9.80942i	0.602588	+	0.602588i
$266$	−0.379702	+	0.379702i	−0.0232810	+	0.0232810i
$267$	−3.59789	−	1.38877i	−0.220187	−	0.0849914i
$268$	5.21752	−	5.21752i	0.318711	−	0.318711i
$269$		−	31.5128i		−	1.92137i	−0.277637	−	0.960686i	$-0.589551\pi$
$269$		−	31.5128i		−	1.92137i	0.277637	−	0.960686i	$-0.410449\pi$
$270$	−1.81826	−	0.602009i	−0.110656	−	0.0366371i
$271$	−16.2599	+	16.2599i	−0.987720	+	0.987720i	−0.999926	−	0.0122053i	$-0.996115\pi$
$271$	−16.2599	+	16.2599i	−0.987720	+	0.987720i	0.0122053	+	0.999926i	$0.496115\pi$
$272$	1.96966			0.119428
$273$	−0.791479	+	6.19464i	−0.0479025	+	0.374917i
$274$	1.20853			0.0730098
$275$	25.1499	−	25.1499i	1.51659	−	1.51659i
$276$	6.65565	+	15.0239i	0.400623	+	0.904330i
$277$			1.90282i			0.114329i	0.998365	+	0.0571646i	$0.0182060\pi$
$277$			1.90282i			0.114329i	−0.998365	+	0.0571646i	$0.981794\pi$
$278$	−0.347118	+	0.347118i	−0.0208188	+	0.0208188i
$279$	−13.1913	+	0.642210i	−0.789743	+	0.0384481i
$280$	1.03955	−	1.03955i	0.0621248	−	0.0621248i
$281$	−2.68945	−	2.68945i	−0.160439	−	0.160439i	0.622322	−	0.782761i	$-0.286189\pi$
$281$	−2.68945	−	2.68945i	−0.160439	−	0.160439i	−0.782761	+	0.622322i	$0.786189\pi$
$282$	0.978649	−	0.433547i	0.0582777	−	0.0258174i
$283$			13.8911i			0.825738i	0.910790	+	0.412869i	$0.135473\pi$
$283$			13.8911i			0.825738i	−0.910790	+	0.412869i	$0.864527\pi$
$284$	−10.9753	−	10.9753i	−0.651265	−	0.651265i
$285$	−26.9804	+	11.9525i	−1.59818	+	0.708004i
$286$	2.00473	−	0.493346i	0.118542	−	0.0291721i
$287$		−	1.91401i		−	0.112980i
$288$	−0.187226	−	3.84571i	−0.0110324	−	0.226610i
$289$	−16.7489			−0.985228
$290$	−2.49409			−0.146458
$291$	−10.5951	−	4.08967i	−0.621096	−	0.239741i
$292$	−10.5517	−	10.5517i	−0.617491	−	0.617491i
$293$	11.0121	+	11.0121i	0.643335	+	0.643335i	0.951374	−	0.308039i	$-0.0996726\pi$
$293$	11.0121	+	11.0121i	0.643335	+	0.643335i	−0.308039	+	0.951374i	$0.599673\pi$
$294$	0.174165	+	0.0672271i	0.0101575	+	0.00392077i
$295$	−47.9850			−2.79380
$296$	−1.58031			−0.0918537
$297$	24.6649	−	12.3948i	1.43120	−	0.719219i
$298$		−	1.18673i		−	0.0687453i
$299$	−16.7046	+	4.11086i	−0.966053	+	0.237737i
$300$	21.0818	−	9.33935i	1.21716	−	0.539208i
$301$	−3.98526	−	3.98526i	−0.229707	−	0.229707i
$302$		−	0.531448i		−	0.0305814i
$303$	−24.4226	+	10.8194i	−1.40304	+	0.621556i
$304$	−13.8459	−	13.8459i	−0.794119	−	0.794119i
$305$	−0.480469	+	0.480469i	−0.0275116	+	0.0275116i
$306$	−0.00787965	−	0.161852i	−0.000450450	−	0.00925246i
$307$	10.7862	−	10.7862i	0.615604	−	0.615604i	−0.328797	−	0.944401i	$-0.606643\pi$
$307$	10.7862	−	10.7862i	0.615604	−	0.615604i	0.944401	+	0.328797i	$0.106643\pi$
$308$			10.5631i			0.601889i
$309$	−6.75805	−	15.2550i	−0.384452	−	0.867827i
$310$	−1.14743	+	1.14743i	−0.0651699	+	0.0651699i
$311$	18.5793			1.05353			0.526767	−	0.850010i	$-0.323404\pi$
$311$	18.5793			1.05353			0.526767	+	0.850010i	$0.323404\pi$
$312$	2.66301	+	0.340248i	0.150763	+	0.0192628i
$313$	15.0945			0.853193			0.426596	−	0.904442i	$-0.359712\pi$
$313$	15.0945			0.853193			0.426596	+	0.904442i	$0.359712\pi$
$314$	−0.263866	+	0.263866i	−0.0148908	+	0.0148908i
$315$	7.59870	+	6.89317i	0.428138	+	0.388386i
$316$			25.9871i			1.46189i
$317$	−5.43020	+	5.43020i	−0.304991	+	0.304991i	−0.842963	−	0.537972i	$-0.819191\pi$
$317$	−5.43020	+	5.43020i	−0.304991	+	0.304991i	0.537972	+	0.842963i	$0.319191\pi$
$318$	0.706508	+	0.272710i	0.0396190	+	0.0152928i
$319$	25.4172	−	25.4172i	1.42309	−	1.42309i
$320$	18.6744	+	18.6744i	1.04393	+	1.04393i
$321$	9.16114	+	20.6795i	0.511325	+	1.15422i
$322$			0.514271i			0.0286592i
$323$	−1.76536	−	1.76536i	−0.0982274	−	0.0982274i
$324$	17.8108	−	1.73833i	0.989490	−	0.0965742i
$325$	5.76844	+	23.4403i	0.319976	+	1.30023i
$326$			1.67038i			0.0925141i
$327$	24.4465	+	9.43626i	1.35189	+	0.521826i
$328$	−0.822812			−0.0454322
$329$	−5.73348			−0.316097
$330$	1.22135	−	3.16414i	0.0672329	−	0.174180i
$331$	−22.0803	−	22.0803i	−1.21364	−	1.21364i	−0.969819	−	0.243826i	$-0.921597\pi$
$331$	−22.0803	−	22.0803i	−1.21364	−	1.21364i	−0.243826	−	0.969819i	$-0.578403\pi$
$332$	8.59192	+	8.59192i	0.471543	+	0.471543i
$333$	−0.536268	−	11.0152i	−0.0293873	−	0.603630i
$334$	2.15264			0.117787
$335$	12.6906			0.693360
$336$	−2.45146	+	6.35100i	−0.133738	+	0.346475i
$337$		−	7.71489i		−	0.420257i	−0.977674	−	0.210128i	$-0.932612\pi$
$337$		−	7.71489i		−	0.420257i	0.977674	−	0.210128i	$-0.0673882\pi$
$338$	−0.417840	+	1.33746i	−0.0227275	+	0.0727482i
$339$	4.51322	+	10.1877i	0.245124	+	0.553321i
$340$	2.40956	+	2.40956i	0.130677	+	0.130677i
$341$		−	23.3869i		−	1.26647i
$342$	−1.08237	+	1.19315i	−0.0585277	+	0.0645181i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.71322	+	1.71322i	−0.0923707	+	0.0923707i
$345$	−10.1770	+	26.3656i	−0.547911	+	1.41947i
$346$	−1.41906	+	1.41906i	−0.0762889	+	0.0762889i
$347$		−	4.79422i		−	0.257367i	−0.991686	−	0.128684i	$-0.958925\pi$
$347$		−	4.79422i		−	0.257367i	0.991686	−	0.128684i	$-0.0410752\pi$
$348$	21.3059	−	9.43863i	1.14212	−	0.505963i
$349$	−8.06409	+	8.06409i	−0.431661	+	0.431661i	−0.889193	−	0.457532i	$-0.848733\pi$
$349$	−8.06409	+	8.06409i	−0.431661	+	0.431661i	0.457532	+	0.889193i	$0.348733\pi$
$350$	0.721636			0.0385731
$351$	−1.46795	+	18.6774i	−0.0783535	+	0.996926i
$352$	6.81806			0.363404
$353$	−12.1942	+	12.1942i	−0.649030	+	0.649030i	−0.952759	−	0.303728i	$-0.901769\pi$
$353$	−12.1942	+	12.1942i	−0.649030	+	0.649030i	0.303728	+	0.952759i	$0.401769\pi$
$354$	−2.39503	+	1.06101i	−0.127295	+	0.0563922i
$355$		−	26.6953i		−	1.41684i
$356$	3.13062	−	3.13062i	0.165923	−	0.165923i
$357$	−0.312562	+	0.809754i	−0.0165425	+	0.0428567i
$358$	−1.39870	+	1.39870i	−0.0739235	+	0.0739235i
$359$	−23.9855	−	23.9855i	−1.26591	−	1.26591i	−0.948183	−	0.317726i	$-0.897081\pi$
$359$	−23.9855	−	23.9855i	−1.26591	−	1.26591i	−0.317726	−	0.948183i	$-0.602919\pi$
$360$	2.96330	−	3.26660i	0.156180	−	0.172165i
$361$			5.81963i			0.306296i
$362$	−0.579689	−	0.579689i	−0.0304678	−	0.0304678i
$363$	12.0819	+	27.2726i	0.634135	+	1.43144i
$364$	−6.13393	−	3.71114i	−0.321505	−	0.194517i
$365$		−	25.6649i		−	1.34336i
$366$	−0.0133574	+	0.0346050i	−0.000698203	+	0.00180883i
$367$	−2.28417			−0.119233			−0.0596165	−	0.998221i	$-0.518988\pi$
$367$	−2.28417			−0.119233			−0.0596165	+	0.998221i	$0.518988\pi$
$368$	−18.7531			−0.977572
$369$	−0.279216	−	5.73524i	−0.0145354	−	0.298564i
$370$	−0.958149	−	0.958149i	−0.0498118	−	0.0498118i
$371$	−2.86841	−	2.86841i	−0.148920	−	0.148920i
$372$	5.45966	−	14.1443i	0.283070	−	0.733349i
$373$	11.8342			0.612749			0.306375	−	0.951911i	$-0.400884\pi$
$373$	11.8342			0.612749			0.306375	+	0.951911i	$0.400884\pi$
$374$	0.286948			0.0148377
$375$	9.36712	+	3.61567i	0.483716	+	0.186713i
$376$			2.46476i			0.127110i
$377$	5.82976	+	23.6894i	0.300248	+	1.22007i
$378$	0.531685	+	0.176036i	0.0273469	+	0.00905429i
$379$	−19.4424	−	19.4424i	−0.998690	−	0.998690i	0.00130884	−	0.999999i	$-0.499583\pi$
$379$	−19.4424	−	19.4424i	−0.998690	−	0.998690i	−0.999999	+	0.00130884i	$0.999583\pi$
$380$		−	33.8766i		−	1.73783i
$381$	6.55361	+	14.7935i	0.335752	+	0.757895i
$382$	0.694926	+	0.694926i	0.0355555	+	0.0355555i
$383$	2.79878	−	2.79878i	0.143011	−	0.143011i	−0.631976	−	0.774988i	$-0.717756\pi$
$383$	2.79878	−	2.79878i	0.143011	−	0.143011i	0.774988	+	0.631976i	$0.217756\pi$
$384$	5.49264	+	2.12014i	0.280295	+	0.108193i
$385$	−12.8463	+	12.8463i	−0.654710	+	0.654710i
$386$			0.251819i			0.0128172i
$387$	−12.5230	−	11.3603i	−0.636581	−	0.577475i
$388$	9.21909	−	9.21909i	0.468029	−	0.468029i
$389$	−0.726856			−0.0368530			−0.0184265	−	0.999830i	$-0.505866\pi$
$389$	−0.726856			−0.0368530			−0.0184265	+	0.999830i	$0.505866\pi$
$390$	1.40830	+	1.82089i	0.0713120	+	0.0922042i
$391$	−2.39102			−0.120919
$392$	−0.303978	+	0.303978i	−0.0153532	+	0.0153532i
$393$	−0.691776	−	1.56155i	−0.0348955	−	0.0787699i
$394$		−	0.896821i		−	0.0451812i
$395$	−31.6043	+	31.6043i	−1.59018	+	1.59018i
$396$	1.54095	+	31.6518i	0.0774356	+	1.59057i
$397$	24.2351	−	24.2351i	1.21632	−	1.21632i	0.247413	−	0.968910i	$-0.420420\pi$
$397$	24.2351	−	24.2351i	1.21632	−	1.21632i	0.968910	−	0.247413i	$-0.0795805\pi$
$398$	−0.750436	−	0.750436i	−0.0376160	−	0.0376160i
$399$	7.88945	−	3.49507i	0.394966	−	0.174972i
$400$			26.3147i			1.31574i
$401$	1.28813	+	1.28813i	0.0643260	+	0.0643260i	0.738538	−	0.674212i	$-0.235517\pi$
$401$	1.28813	+	1.28813i	0.0643260	+	0.0643260i	−0.674212	+	0.738538i	$0.735517\pi$
$402$	0.633414	−	0.280606i	0.0315918	−	0.0139953i
$403$	13.5806	+	8.21653i	0.676498	+	0.409294i
$404$		−	30.6650i		−	1.52564i
$405$	23.7747	+	19.5466i	1.18138	+	0.971276i
$406$	0.729307			0.0361949
$407$	19.5289			0.968012
$408$	0.348104	+	0.134367i	0.0172337	+	0.00665216i
$409$	16.8469	+	16.8469i	0.833026	+	0.833026i	0.987930	−	0.154903i	$-0.0495066\pi$
$409$	16.8469	+	16.8469i	0.833026	+	0.833026i	−0.154903	+	0.987930i	$0.549507\pi$
$410$	−0.498874	−	0.498874i	−0.0246376	−	0.0246376i
$411$	−18.1175	−	6.99330i	−0.893672	−	0.344954i
$412$	19.1542			0.943658
$413$	14.0315			0.690444
$414$	0.0750220	+	1.54099i	0.00368713	+	0.0757355i
$415$			20.8981i			1.02585i
$416$	−2.39539	+	3.95920i	−0.117444	+	0.194116i
$417$	7.21243	−	3.19515i	0.353194	−	0.156467i
$418$	−2.01713	−	2.01713i	−0.0986611	−	0.0986611i
$419$		−	11.4113i		−	0.557480i	−0.960367	−	0.278740i	$-0.910083\pi$
$419$		−	11.4113i		−	0.557480i	0.960367	−	0.278740i	$-0.0899168\pi$
$420$	−10.7684	+	4.77046i	−0.525444	+	0.232775i
$421$	−4.62592	−	4.62592i	−0.225454	−	0.225454i	0.585337	−	0.810790i	$-0.300962\pi$
$421$	−4.62592	−	4.62592i	−0.225454	−	0.225454i	−0.810790	+	0.585337i	$0.800962\pi$
$422$	1.59559	−	1.59559i	0.0776723	−	0.0776723i
$423$	−17.1801	+	0.836402i	−0.835325	+	0.0406672i
$424$	−1.23310	+	1.23310i	−0.0598845	+	0.0598845i
$425$			3.35513i			0.162748i
$426$	−0.590269	−	1.33242i	−0.0285986	−	0.0645559i
$427$	0.140496	−	0.140496i	0.00679906	−	0.00679906i
$428$	−25.9652			−1.25508
$429$	−32.9085	−	4.20466i	−1.58884	−	0.203003i
$430$	−2.07747			−0.100184
$431$	−13.4869	+	13.4869i	−0.649642	+	0.649642i	−0.952907	−	0.303264i	$-0.901924\pi$
$431$	−13.4869	+	13.4869i	−0.649642	+	0.649642i	0.303264	+	0.952907i	$0.401924\pi$
$432$	−6.41920	+	19.3881i	−0.308844	+	0.932809i
$433$		−	15.1964i		−	0.730291i	−0.930950	−	0.365145i	$-0.881019\pi$
$433$		−	15.1964i		−	0.730291i	0.930950	−	0.365145i	$-0.118981\pi$
$434$	0.335525	−	0.335525i	0.0161057	−	0.0161057i
$435$	37.3900	+	14.4324i	1.79271	+	0.691980i
$436$	−21.2716	+	21.2716i	−1.01872	+	1.01872i
$437$	16.8080	+	16.8080i	0.804034	+	0.804034i
$438$	−0.567486	−	1.28099i	−0.0271155	−	0.0612081i
$439$			16.7674i			0.800264i	0.916458	+	0.400132i	$0.131036\pi$
$439$			16.7674i			0.800264i	−0.916458	+	0.400132i	$0.868964\pi$
$440$	5.52250	+	5.52250i	0.263275	+	0.263275i
$441$	−2.22196	−	2.01566i	−0.105808	−	0.0959837i
$442$	−0.100813	+	0.166629i	−0.00479521	+	0.00792571i
$443$			39.9481i			1.89799i	0.315290	+	0.948995i	$0.397898\pi$
$443$			39.9481i			1.89799i	−0.315290	+	0.948995i	$0.602102\pi$
$444$	11.8110	+	4.55901i	0.560527	+	0.216361i
$445$	7.61462			0.360967
$446$	2.77953			0.131615
$447$	−6.86715	+	17.7907i	−0.324805	+	0.841472i
$448$	−5.46065	−	5.46065i	−0.257991	−	0.257991i
$449$	14.9022	+	14.9022i	0.703279	+	0.703279i	0.965113	−	0.261834i	$-0.0843274\pi$
$449$	14.9022	+	14.9022i	0.703279	+	0.703279i	−0.261834	+	0.965113i	$0.584327\pi$
$450$	2.16235	−	0.105272i	0.101934	−	0.00496259i
$451$	10.1680			0.478793
$452$	−12.7917			−0.601671
$453$	−3.07529	+	7.96715i	−0.144490	+	0.374329i
$454$			1.20598i			0.0565995i
$455$	−2.94647	−	11.9731i	−0.138133	−	0.561307i
$456$	−1.50249	−	3.39159i	−0.0703606	−	0.158826i
$457$	−11.6398	−	11.6398i	−0.544485	−	0.544485i	0.380355	−	0.924841i	$-0.375802\pi$
$457$	−11.6398	−	11.6398i	−0.544485	−	0.544485i	−0.924841	+	0.380355i	$0.875802\pi$
$458$		−	1.11974i		−	0.0523219i
$459$	−0.818449	+	2.47198i	−0.0382019	+	0.115382i
$460$	−22.9414	−	22.9414i	−1.06965	−	1.06965i
$461$	3.58435	−	3.58435i	0.166940	−	0.166940i	−0.618693	−	0.785633i	$-0.712337\pi$
$461$	3.58435	−	3.58435i	0.166940	−	0.166940i	0.785633	+	0.618693i	$0.212337\pi$
$462$	−0.357138	+	0.925238i	−0.0166156	+	0.0430460i
$463$	11.1773	−	11.1773i	0.519453	−	0.519453i	−0.397953	−	0.917406i	$-0.630279\pi$
$463$	11.1773	−	11.1773i	0.519453	−	0.519453i	0.917406	+	0.397953i	$0.130279\pi$
$464$			26.5944i			1.23462i
$465$	23.8414	−	10.5619i	1.10562	−	0.489795i
$466$	1.90918	−	1.90918i	0.0884412	−	0.0884412i
$467$	−8.54855			−0.395580			−0.197790	−	0.980244i	$-0.563376\pi$
$467$	−8.54855			−0.395580			−0.197790	+	0.980244i	$0.563376\pi$
$468$	−18.9214	−	10.2254i	−0.874642	−	0.472671i
$469$	−3.71090			−0.171353
$470$	−1.49440	+	1.49440i	−0.0689313	+	0.0689313i
$471$	5.48263	−	2.42883i	0.252626	−	0.111915i
$472$		−	6.03198i		−	0.277644i
$473$	21.1714	−	21.1714i	0.973460	−	0.973460i
$474$	−0.878624	+	2.27625i	−0.0403565	+	0.104552i
$475$	23.5853	−	23.5853i	1.08217	−	1.08217i
$476$	−0.704589	−	0.704589i	−0.0322948	−	0.0322948i
$477$	−9.01348	−	8.17660i	−0.412699	−	0.374381i
$478$			1.35247i			0.0618606i
$479$	8.43892	+	8.43892i	0.385584	+	0.385584i	0.873109	−	0.487525i	$-0.162100\pi$
$479$	8.43892	+	8.43892i	0.385584	+	0.385584i	−0.487525	+	0.873109i	$0.662100\pi$
$480$	3.07914	+	6.95057i	0.140543	+	0.317249i
$481$	−6.86110	+	11.3403i	−0.312839	+	0.517073i
$482$		−	1.54508i		−	0.0703764i
$483$	2.97589	−	7.70965i	0.135408	−	0.350801i
$484$	−34.2434			−1.55652
$485$	22.4236			1.01820
$486$	1.61885	+	0.449920i	0.0734324	+	0.0204088i
$487$	19.8189	+	19.8189i	0.898079	+	0.898079i	0.995266	−	0.0971868i	$-0.0309844\pi$
$487$	19.8189	+	19.8189i	0.898079	+	0.898079i	−0.0971868	+	0.995266i	$0.530984\pi$
$488$	−0.0603975	−	0.0603975i	−0.00273407	−	0.00273407i
$489$	9.66589	−	25.0414i	0.437107	−	1.13241i
$490$	−0.368606			−0.0166519
$491$	−19.7592			−0.891722			−0.445861	−	0.895102i	$-0.647102\pi$
$491$	−19.7592			−0.891722			−0.445861	+	0.895102i	$0.647102\pi$
$492$	6.14959	+	2.37372i	0.277245	+	0.107015i
$493$			3.39080i			0.152714i
$494$	1.88001	−	0.462655i	0.0845859	−	0.0208158i
$495$	−36.6194	+	40.3675i	−1.64592	+	1.81438i
$496$	12.2350	+	12.2350i	0.549370	+	0.549370i
$497$			7.80607i			0.350150i
$498$	0.462086	+	1.04307i	0.0207066	+	0.0467411i
$499$	4.18799	+	4.18799i	0.187480	+	0.187480i	0.794606	−	0.607126i	$-0.207678\pi$
$499$	4.18799	+	4.18799i	0.187480	+	0.187480i	−0.607126	+	0.794606i	$0.707678\pi$
$500$	−8.15059	+	8.15059i	−0.364506	+	0.364506i
$501$	−32.2712	−	12.4565i	−1.44177	−	0.556517i
$502$	1.55405	−	1.55405i	0.0693605	−	0.0693605i
$503$			5.88524i			0.262410i	0.991355	+	0.131205i	$0.0418846\pi$
$503$			5.88524i			0.262410i	−0.991355	+	0.131205i	$0.958115\pi$
$504$	−0.866509	+	0.955198i	−0.0385974	+	0.0425479i
$505$	37.2933	−	37.2933i	1.65953	−	1.65953i
$506$	−2.73202			−0.121453
$507$	14.0034	−	17.6325i	0.621912	−	0.783087i
$508$	−18.5747			−0.824121
$509$	−25.8430	+	25.8430i	−1.14547	+	1.14547i	−0.158038	+	0.987433i	$0.550517\pi$
$509$	−25.8430	+	25.8430i	−1.14547	+	1.14547i	−0.987433	+	0.158038i	$0.949483\pi$
$510$	0.129590	+	0.292524i	0.00573834	+	0.0129532i
$511$			7.50477i			0.331991i
$512$	−5.95645	+	5.95645i	−0.263240	+	0.263240i
$513$	23.1305	−	11.6237i	1.02124	−	0.513200i
$514$	−0.192926	+	0.192926i	−0.00850958	+	0.00850958i
$515$	23.2944	+	23.2944i	1.02647	+	1.02647i
$516$	17.7468	−	7.86194i	0.781261	−	0.346103i
$517$		−	30.4586i		−	1.33957i
$518$	0.280176	+	0.280176i	0.0123102	+	0.0123102i
$519$	29.4852	−	13.0621i	1.29426	−	0.573363i
$520$	−5.14710	+	1.26666i	−0.225715	+	0.0555465i
$521$		−	37.6849i		−	1.65100i	−0.564399	−	0.825502i	$-0.690892\pi$
$521$		−	37.6849i		−	1.65100i	0.564399	−	0.825502i	$-0.309108\pi$
$522$	2.18533	−	0.106391i	0.0956494	−	0.00465663i
$523$	−5.99895			−0.262316			−0.131158	−	0.991361i	$-0.541870\pi$
$523$	−5.99895			−0.262316			−0.131158	+	0.991361i	$0.541870\pi$
$524$	1.96068			0.0856528
$525$	−10.8183	−	4.17584i	−0.472151	−	0.182249i
$526$	−0.994443	−	0.994443i	−0.0433598	−	0.0433598i
$527$	1.55997	+	1.55997i	0.0679534	+	0.0679534i
$528$	−33.7391	−	13.0232i	−1.46831	−	0.566761i
$529$	−0.235131			−0.0102231
$530$	−1.49526			−0.0649501
$531$	42.0446	−	2.04691i	1.82458	−	0.0888285i
$532$			9.90598i			0.429479i
$533$	−3.57233	+	5.90450i	−0.154735	+	0.255752i
$534$	0.380062	−	0.168369i	0.0164469	−	0.00728606i
$535$	−31.5776	−	31.5776i	−1.36522	−	1.36522i
$536$			1.59527i			0.0689054i
$537$	29.0622	−	12.8747i	1.25413	−	0.555585i
$538$	2.40177	+	2.40177i	0.103548	+	0.103548i
$539$	3.75644	−	3.75644i	0.161802	−	0.161802i
$540$	−31.5711	+	15.8653i	−1.35860	+	0.682736i
$541$	−7.87500	+	7.87500i	−0.338573	+	0.338573i	−0.855830	−	0.517257i	$-0.826953\pi$
$541$	−7.87500	+	7.87500i	−0.338573	+	0.338573i	0.517257	+	0.855830i	$0.326953\pi$
$542$		−	2.47852i		−	0.106462i
$543$	5.33591	+	12.0448i	0.228986	+	0.516891i
$544$	−0.454784	+	0.454784i	−0.0194987	+	0.0194987i
$545$	−51.7389			−2.21625
$546$	−0.411806	−	0.532452i	−0.0176237	−	0.0227868i
$547$	−43.8530			−1.87502			−0.937510	−	0.347959i	$-0.886875\pi$
$547$	−43.8530			−1.87502			−0.937510	+	0.347959i	$0.886875\pi$
$548$	15.7646	−	15.7646i	0.673429	−	0.673429i
$549$	0.400493	−	0.441484i	0.0170926	−	0.0188421i
$550$			3.83363i			0.163467i
$551$	23.8360	−	23.8360i	1.01545	−	1.01545i
$552$	−3.31429	−	1.27930i	−0.141066	−	0.0544508i
$553$	9.24152	−	9.24152i	0.392989	−	0.392989i
$554$	−0.145025	−	0.145025i	−0.00616151	−	0.00616151i
$555$	8.81955	+	19.9084i	0.374369	+	0.845066i
$556$			9.05592i			0.384057i
$557$	22.1841	+	22.1841i	0.939971	+	0.939971i	0.998298	−	0.0583261i	$-0.0185763\pi$
$557$	22.1841	+	22.1841i	0.939971	+	0.939971i	−0.0583261	+	0.998298i	$0.518576\pi$
$558$	0.956439	−	1.05433i	0.0404893	−	0.0446334i
$559$	4.85592	+	19.7322i	0.205384	+	0.834584i
$560$		−	13.4413i		−	0.568000i
$561$	−4.30175	−	1.66046i	−0.181620	−	0.0701046i
$562$	0.409957			0.0172930
$563$	21.3528			0.899912			0.449956	−	0.893051i	$-0.351440\pi$
$563$	21.3528			0.899912			0.449956	+	0.893051i	$0.351440\pi$
$564$	7.11055	−	18.4213i	0.299408	−	0.775677i
$565$	−15.5566	−	15.5566i	−0.654473	−	0.654473i
$566$	−1.05872	−	1.05872i	−0.0445012	−	0.0445012i
$567$	−6.95205	−	5.71568i	−0.291959	−	0.240036i
$568$	3.35574			0.140804
$569$	−0.257521			−0.0107959			−0.00539793	−	0.999985i	$-0.501718\pi$
$569$	−0.257521			−0.0107959			−0.00539793	+	0.999985i	$0.501718\pi$
$570$	1.14537	−	2.96730i	0.0479741	−	0.124287i
$571$		−	19.1071i		−	0.799608i	−0.916601	−	0.399804i	$-0.869078\pi$
$571$		−	19.1071i		−	0.799608i	0.916601	−	0.399804i	$-0.130922\pi$
$572$	19.7151	−	32.5860i	0.824331	−	1.36249i
$573$	−6.39664	−	14.4392i	−0.267223	−	0.603205i
$574$	0.145878	+	0.145878i	0.00608882	+	0.00608882i
$575$		−	31.9441i		−	1.33216i
$576$	−17.1592	−	15.5660i	−0.714965	−	0.648582i
$577$	−1.97056	−	1.97056i	−0.0820354	−	0.0820354i	0.664898	−	0.746934i	$-0.268475\pi$
$577$	−1.97056	−	1.97056i	−0.0820354	−	0.0820354i	−0.746934	+	0.664898i	$0.768475\pi$
$578$	1.27653	−	1.27653i	0.0530965	−	0.0530965i
$579$	1.45718	−	3.77511i	0.0605583	−	0.156888i
$580$	−32.5341	+	32.5341i	−1.35090	+	1.35090i
$581$		−	6.11090i		−	0.253523i
$582$	1.11921	−	0.495817i	0.0463928	−	0.0205523i
$583$	15.2382	−	15.2382i	0.631100	−	0.631100i
$584$	3.22622			0.133502
$585$	−10.5756	−	35.4470i	−0.437247	−	1.46555i
$586$	−1.67859			−0.0693421
$587$	13.5995	−	13.5995i	0.561312	−	0.561312i	−0.368368	−	0.929680i	$-0.620083\pi$
$587$	13.5995	−	13.5995i	0.561312	−	0.561312i	0.929680	+	0.368368i	$0.120083\pi$
$588$	3.14883	−	1.39495i	0.129855	−	0.0575267i
$589$		−	21.9320i		−	0.903692i
$590$	3.65721	−	3.65721i	0.150565	−	0.150565i
$591$	−5.18956	+	13.4446i	−0.213470	+	0.553037i
$592$	−10.2167	+	10.2167i	−0.419904	+	0.419904i
$593$	−7.34318	−	7.34318i	−0.301548	−	0.301548i	0.540071	−	0.841619i	$-0.318397\pi$
$593$	−7.34318	−	7.34318i	−0.301548	−	0.301548i	−0.841619	+	0.540071i	$0.818397\pi$
$594$	−0.935174	+	2.82453i	−0.0383706	+	0.115892i
$595$		−	1.71377i		−	0.0702579i
$596$	−15.4802	−	15.4802i	−0.634094	−	0.634094i
$597$	6.90760	+	15.5926i	0.282709	+	0.638162i
$598$	0.959843	−	1.58647i	0.0392509	−	0.0648754i
$599$			6.49210i			0.265260i	0.991166	+	0.132630i	$0.0423422\pi$
$599$			6.49210i			0.265260i	−0.991166	+	0.132630i	$0.957658\pi$
$600$	−1.79515	+	4.65069i	−0.0732866	+	0.189863i
$601$	18.1602			0.740770			0.370385	−	0.928878i	$-0.379226\pi$
$601$	18.1602			0.740770			0.370385	+	0.928878i	$0.379226\pi$
$602$	0.607479			0.0247590
$603$	−11.1195	+	0.541347i	−0.452822	+	0.0220453i
$604$	−6.93244	−	6.93244i	−0.282077	−	0.282077i
$605$	−41.6452	−	41.6452i	−1.69312	−	1.69312i
$606$	1.03678	−	2.68600i	0.0421165	−	0.109111i
$607$	−5.36955			−0.217943			−0.108972	−	0.994045i	$-0.534756\pi$
$607$	−5.36955			−0.217943			−0.108972	+	0.994045i	$0.534756\pi$
$608$	6.39391			0.259307
$609$	−10.9333	−	4.22023i	−0.443041	−	0.171012i
$610$		−	0.0732386i		−	0.00296534i
$611$	17.6871	+	10.7010i	0.715544	+	0.432918i
$612$	−2.21405	−	2.00848i	−0.0894978	−	0.0811881i
$613$	−33.3385	−	33.3385i	−1.34653	−	1.34653i	−0.889398	−	0.457133i	$-0.848876\pi$
$613$	−33.3385	−	33.3385i	−1.34653	−	1.34653i	−0.457133	−	0.889398i	$-0.651124\pi$
$614$			1.64416i			0.0663530i
$615$	4.59203	+	10.3656i	0.185168	+	0.417982i
$616$	−1.61485	−	1.61485i	−0.0650643	−	0.0650643i
$617$	−24.3339	+	24.3339i	−0.979648	+	0.979648i	−0.999797	−	0.0201491i	$-0.993586\pi$
$617$	−24.3339	+	24.3339i	−0.979648	+	0.979648i	0.0201491	+	0.999797i	$0.493586\pi$
$618$	1.67774	+	0.647602i	0.0674886	+	0.0260504i
$619$	−1.81623	+	1.81623i	−0.0730002	+	0.0730002i	−0.742664	−	0.669664i	$-0.766438\pi$
$619$	−1.81623	+	1.81623i	−0.0730002	+	0.0730002i	0.669664	+	0.742664i	$0.266438\pi$
$620$			29.9353i			1.20223i
$621$	7.79244	−	23.5357i	0.312700	−	0.944455i
$622$	−1.41603	+	1.41603i	−0.0567777	+	0.0567777i
$623$	−2.22662			−0.0892075
$624$	19.4161	−	15.0166i	0.777264	−	0.601147i
$625$	13.6509			0.546037
$626$	−1.15044	+	1.15044i	−0.0459808	+	0.0459808i
$627$	18.5673	+	41.9120i	0.741505	+	1.67380i
$628$			6.88398i			0.274701i
$629$	−1.30263	+	1.30263i	−0.0519394	+	0.0519394i
$630$	−1.10451	+	0.0537723i	−0.0440047	+	0.00214234i
$631$	−11.6645	+	11.6645i	−0.464356	+	0.464356i	−0.900080	−	0.435725i	$-0.856492\pi$
$631$	−11.6645	+	11.6645i	−0.464356	+	0.464356i	0.435725	+	0.900080i	$0.356492\pi$
$632$	−3.97283	−	3.97283i	−0.158031	−	0.158031i
$633$	−33.1533	+	14.6871i	−1.31772	+	0.583759i
$634$		−	0.827734i		−	0.0328735i
$635$	−22.5897	−	22.5897i	−0.896444	−	0.896444i
$636$	12.7733	−	5.65866i	0.506496	−	0.224380i
$637$	0.861588	+	3.50109i	0.0341374	+	0.138718i
$638$			3.87438i			0.153388i
$639$	1.13875	+	23.3905i	0.0450483	+	0.925314i
$640$	−11.6247			−0.459506
$641$	32.9439			1.30121			0.650603	−	0.759418i	$-0.274516\pi$
$641$	32.9439			1.30121			0.650603	+	0.759418i	$0.274516\pi$
$642$	−2.27433	−	0.877882i	−0.0897606	−	0.0346473i
$643$	−10.4149	−	10.4149i	−0.410724	−	0.410724i	0.471267	−	0.881991i	$-0.343797\pi$
$643$	−10.4149	−	10.4149i	−0.410724	−	0.410724i	−0.881991	+	0.471267i	$0.843797\pi$
$644$	6.70838	+	6.70838i	0.264347	+	0.264347i
$645$	31.1441	+	12.0215i	1.22630	+	0.473347i
$646$	0.269097			0.0105875
$647$	6.47112			0.254406			0.127203	−	0.991877i	$-0.459400\pi$
$647$	6.47112			0.254406			0.127203	+	0.991877i	$0.459400\pi$
$648$	−2.45711	+	2.98861i	−0.0965243	+	0.117404i
$649$			74.5410i			2.92599i
$650$	−2.22616	−	1.34687i	−0.0873173	−	0.0528286i
$651$	−6.97155	+	3.08844i	−0.273237	+	0.121045i
$652$	21.7892	+	21.7892i	0.853332	+	0.853332i
$653$			21.2554i			0.831789i	0.909413	+	0.415894i	$0.136531\pi$
$653$			21.2554i			0.831789i	−0.909413	+	0.415894i	$0.863469\pi$
$654$	−2.58240	+	1.14402i	−0.100980	+	0.0447346i
$655$	2.38449	+	2.38449i	0.0931696	+	0.0931696i
$656$	−5.31948	+	5.31948i	−0.207691	+	0.207691i
$657$	1.09480	+	22.4877i	0.0427121	+	0.877328i
$658$	0.436982	−	0.436982i	0.0170353	−	0.0170353i
$659$		−	7.13030i		−	0.277757i	−0.990309	−	0.138878i	$-0.955650\pi$
$659$		−	7.13030i		−	0.277757i	0.990309	−	0.138878i	$-0.0443497\pi$
$660$	−25.3427	−	57.2062i	−0.986462	−	2.22675i
$661$	2.74264	−	2.74264i	0.106676	−	0.106676i	−0.651754	−	0.758430i	$-0.725967\pi$
$661$	2.74264	−	2.74264i	0.106676	−	0.106676i	0.758430	+	0.651754i	$0.225967\pi$
$662$	3.36574			0.130813
$663$	2.47555	−	1.91463i	0.0961425	−	0.0743579i
$664$	−2.62701			−0.101948
$665$	−12.0472	+	12.0472i	−0.467169	+	0.467169i
$666$	0.880405	+	0.798661i	0.0341150	+	0.0309475i
$667$		−	32.2837i		−	1.25003i
$668$	28.0800	−	28.0800i	1.08645	−	1.08645i
$669$	−41.6691	−	16.0841i	−1.61102	−	0.621848i
$670$	−0.967222	+	0.967222i	−0.0373670	+	0.0373670i
$671$	0.746371	+	0.746371i	0.0288133	+	0.0288133i
$672$	−0.900383	−	2.03244i	−0.0347330	−	0.0784031i
$673$			27.9879i			1.07885i	0.842033	+	0.539427i	$0.181359\pi$
$673$			27.9879i			1.07885i	−0.842033	+	0.539427i	$0.818641\pi$
$674$	0.587996	+	0.587996i	0.0226488	+	0.0226488i
$675$	−33.0258	−	10.9345i	−1.27116	−	0.420870i
$676$	11.9959	+	22.8969i	0.461382	+	0.880649i
$677$			0.255809i			0.00983153i	0.999988	+	0.00491576i	$0.00156474\pi$
$677$			0.255809i			0.00983153i	−0.999988	+	0.00491576i	$0.998435\pi$
$678$	−1.12044	−	0.432487i	−0.0430304	−	0.0166096i
$679$	−6.55697			−0.251633
$680$	−0.736733			−0.0282524
$681$	6.97856	−	18.0793i	0.267419	−	0.692802i
$682$	1.78245	+	1.78245i	0.0682535	+	0.0682535i
$683$	−2.86120	−	2.86120i	−0.109481	−	0.109481i	0.650244	−	0.759725i	$-0.274666\pi$
$683$	−2.86120	−	2.86120i	−0.109481	−	0.109481i	−0.759725	+	0.650244i	$0.774666\pi$
$684$	1.44509	+	29.6828i	0.0552543	+	1.13495i
$685$	38.3442			1.46506
$686$	0.107785			0.00411526
$687$	−6.47950	+	16.7864i	−0.247208	+	0.640442i
$688$			22.1519i			0.844535i
$689$	3.49507	+	14.2023i	0.133151	+	0.541066i
$690$	−1.23382	−	2.78512i	−0.0469708	−	0.106028i
$691$	10.8229	+	10.8229i	0.411723	+	0.411723i	0.882338	−	0.470616i	$-0.155968\pi$
$691$	10.8229	+	10.8229i	0.411723	+	0.411723i	−0.470616	+	0.882338i	$0.655968\pi$
$692$			37.0216i			1.40735i
$693$	10.7080	−	11.8040i	0.406764	−	0.448397i
$694$	0.365395	+	0.365395i	0.0138702	+	0.0138702i
$695$	−11.0134	+	11.0134i	−0.417761	+	0.417761i
$696$	−1.81423	+	4.70012i	−0.0687682	+	0.178158i
$697$	−0.678235	+	0.678235i	−0.0256900	+	0.0256900i
$698$		−	1.22922i		−	0.0465267i
$699$	−39.6691	+	17.5736i	−1.50042	+	0.664695i
$700$	9.41334	−	9.41334i	0.355791	−	0.355791i
$701$	25.3131			0.956063			0.478031	−	0.878343i	$-0.341350\pi$
$701$	25.3131			0.956063			0.478031	+	0.878343i	$0.341350\pi$
$702$	−1.31163	−	1.53539i	−0.0495043	−	0.0579497i
$703$	18.3140			0.690726
$704$	29.0092	−	29.0092i	1.09333	−	1.09333i
$705$	31.0506	−	13.7556i	1.16943	−	0.518065i
$706$		−	1.85878i		−	0.0699560i
$707$	−10.9051	+	10.9051i	−0.410128	+	0.410128i
$708$	−17.4016	+	45.0822i	−0.653990	+	1.69429i
$709$	15.2862	−	15.2862i	0.574087	−	0.574087i	−0.359181	−	0.933268i	$-0.616944\pi$
$709$	15.2862	−	15.2862i	0.574087	−	0.574087i	0.933268	+	0.359181i	$0.116944\pi$
$710$	2.03460	+	2.03460i	0.0763572	+	0.0763572i
$711$	26.3436	−	29.0399i	0.987963	−	1.08908i
$712$			0.957198i			0.0358725i
$713$	−14.8525	−	14.8525i	−0.556229	−	0.556229i
$714$	−0.0378939	−	0.0855381i	−0.00141814	−	0.00320118i
$715$	63.6060	−	15.6529i	2.37873	−	0.585384i
$716$			36.4905i			1.36371i
$717$	7.82625	−	20.2755i	0.292277	−	0.757201i
$718$	3.65615			0.136446
$719$	−5.98364			−0.223152			−0.111576	−	0.993756i	$-0.535590\pi$
$719$	−5.98364			−0.223152			−0.111576	+	0.993756i	$0.535590\pi$
$720$	−1.96082	−	40.2763i	−0.0730756	−	1.50101i
$721$	−6.81159	−	6.81159i	−0.253677	−	0.253677i
$722$	−0.443548	−	0.443548i	−0.0165071	−	0.0165071i
$723$	−8.94079	+	23.1629i	−0.332512	+	0.861437i
$724$	−15.1234			−0.562058
$725$	−45.3012			−1.68244
$726$	−2.99943	−	1.15777i	−0.111319	−	0.0429688i
$727$			32.6607i			1.21132i	0.795724	+	0.605660i	$0.207091\pi$
$727$			32.6607i			1.21132i	−0.795724	+	0.605660i	$0.792909\pi$
$728$	1.50508	−	0.370387i	0.0557821	−	0.0137275i
$729$	−21.6653	−	16.1126i	−0.802418	−	0.596763i
$730$	1.95607	+	1.95607i	0.0723974	+	0.0723974i
$731$			2.82438i			0.104463i
$732$	0.277163	+	0.625643i	0.0102442	+	0.0231244i
$733$	4.27208	+	4.27208i	0.157793	+	0.157793i	0.781588	−	0.623795i	$-0.214410\pi$
$733$	4.27208	+	4.27208i	0.157793	+	0.157793i	−0.623795	+	0.781588i	$0.714410\pi$
$734$	0.174090	−	0.174090i	0.00642578	−	0.00642578i
$735$	5.52592	+	2.13298i	0.203827	+	0.0786763i
$736$	4.32999	−	4.32999i	0.159605	−	0.159605i
$737$		−	19.7138i		−	0.726168i
$738$	0.458396	+	0.415835i	0.0168738	+	0.0153071i
$739$	29.0152	−	29.0152i	1.06734	−	1.06734i	0.0697770	−	0.997563i	$-0.477771\pi$
$739$	29.0152	−	29.0152i	1.06734	−	1.06734i	0.997563	−	0.0697770i	$-0.0222288\pi$
$740$	−24.9970			−0.918909
$741$	−30.8613	−	3.94309i	−1.13372	−	0.144853i
$742$	0.437235			0.0160514
$743$	17.8103	−	17.8103i	0.653395	−	0.653395i	−0.300414	−	0.953809i	$-0.597125\pi$
$743$	17.8103	−	17.8103i	0.653395	−	0.653395i	0.953809	+	0.300414i	$0.0971248\pi$
$744$	1.32769	+	2.99700i	0.0486753	+	0.109875i
$745$		−	37.6525i		−	1.37948i
$746$	−0.901949	+	0.901949i	−0.0330227	+	0.0330227i
$747$	−0.891460	−	18.3110i	−0.0326168	−	0.669965i
$748$	3.74307	−	3.74307i	0.136860	−	0.136860i
$749$	9.23372	+	9.23372i	0.337393	+	0.337393i
$750$	−0.989493	+	0.438351i	−0.0361312	+	0.0160063i
$751$			42.7282i			1.55917i	0.626294	+	0.779587i	$0.284571\pi$
$751$			42.7282i			1.55917i	−0.626294	+	0.779587i	$0.715429\pi$
$752$	15.9347	+	15.9347i	0.581078	+	0.581078i
$753$	−32.2900	+	14.3046i	−1.17671	+	0.521290i
$754$	−2.24983	−	1.36119i	−0.0819339	−	0.0495716i
$755$		−	16.8618i		−	0.613663i
$756$	9.23181	−	4.63924i	0.335758	−	0.168728i
$757$	37.7081			1.37052			0.685262	−	0.728297i	$-0.259688\pi$
$757$	37.7081			1.37052			0.685262	+	0.728297i	$0.259688\pi$
$758$	2.96364			0.107644
$759$	40.9568	+	15.8092i	1.48664	+	0.573837i
$760$	5.17895	+	5.17895i	0.187860	+	0.187860i
$761$	7.63106	+	7.63106i	0.276626	+	0.276626i	0.831760	−	0.555135i	$-0.187333\pi$
$761$	7.63106	+	7.63106i	0.276626	+	0.276626i	−0.555135	+	0.831760i	$0.687333\pi$
$762$	−1.62699	−	0.628011i	−0.0589396	−	0.0227504i
$763$	15.1292			0.547712
$764$	18.1298			0.655914
$765$	−0.250006	−	5.13524i	−0.00903898	−	0.185665i
$766$			0.426623i			0.0154145i
$767$	−43.2854	−	26.1885i	−1.56295	−	0.945613i
$768$	23.8788	−	10.5784i	0.861651	−	0.381716i
$769$	−3.70390	−	3.70390i	−0.133566	−	0.133566i	0.637163	−	0.770729i	$-0.280108\pi$
$769$	−3.70390	−	3.70390i	−0.133566	−	0.133566i	−0.770729	+	0.637163i	$0.780108\pi$
$770$		−	1.95819i		−	0.0705681i
$771$	4.00861	−	1.77584i	0.144367	−	0.0639552i
$772$	3.28483	+	3.28483i	0.118224	+	0.118224i
$773$	−0.164003	+	0.164003i	−0.00589878	+	0.00589878i	−0.710050	−	0.704151i	$-0.751328\pi$
$773$	−0.164003	+	0.164003i	−0.00589878	+	0.00589878i	0.704151	+	0.710050i	$0.251328\pi$
$774$	1.82028	−	0.0886192i	0.0654287	−	0.00318535i
$775$	−20.8413	+	20.8413i	−0.748641	+	0.748641i
$776$			2.81877i			0.101188i
$777$	−2.57896	−	5.82150i	−0.0925195	−	0.208845i
$778$	0.0553978	−	0.0553978i	0.00198611	−	0.00198611i
$779$	9.53546			0.341643
$780$	42.1229	+	5.38197i	1.50824	+	0.192706i
$781$	−41.4691			−1.48388
$782$	0.182234	−	0.182234i	0.00651666	−	0.00651666i
$783$	−33.3769	−	11.0507i	−1.19279	−	0.394921i
$784$			3.93043i			0.140372i
$785$	−8.37196	+	8.37196i	−0.298808	+	0.298808i
$786$	0.171739	+	0.0662906i	0.00612573	+	0.00236451i
$787$	0.0454837	−	0.0454837i	0.00162132	−	0.00162132i	−0.706296	−	0.707917i	$-0.749635\pi$
$787$	0.0454837	−	0.0454837i	0.00162132	−	0.00162132i	0.707917	+	0.706296i	$0.249635\pi$
$788$	−11.6985	−	11.6985i	−0.416743	−	0.416743i
$789$	9.15363	+	20.6626i	0.325878	+	0.735607i
$790$		−	4.81749i		−	0.171398i
$791$	4.54897	+	4.54897i	0.161743	+	0.161743i
$792$	−5.07441	−	4.60326i	−0.180311	−	0.163570i
$793$	−0.695635	+	0.171190i	−0.0247027	+	0.00607912i
$794$			3.69419i			0.131102i
$795$	22.4161	+	8.65253i	0.795017	+	0.306874i
$796$	−19.5780			−0.693925
$797$	42.6814			1.51185			0.755927	−	0.654656i	$-0.227187\pi$
$797$	42.6814			1.51185			0.755927	+	0.654656i	$0.227187\pi$
$798$	−0.334921	+	0.867679i	−0.0118561	+	0.0307155i
$799$	2.03168	+	2.03168i	0.0718756	+	0.0718756i
$800$	−6.07593	−	6.07593i	−0.214817	−	0.214817i
$801$	−6.67195	+	0.324819i	−0.235742	+	0.0114769i
$802$	−0.196351			−0.00693340
$803$	−39.8685			−1.40693
$804$	4.60218	−	11.9229i	0.162306	−	0.420487i
$805$			16.3168i			0.575092i
$806$	−1.66129	+	0.408827i	−0.0585163	+	0.0144003i
$807$	−22.1078	−	49.9041i	−0.778232	−	1.75671i
$808$	4.68797	+	4.68797i	0.164922	+	0.164922i
$809$		−	10.1993i		−	0.358588i	−0.983796	−	0.179294i	$-0.942619\pi$
$809$		−	10.1993i		−	0.358588i	0.983796	−	0.179294i	$-0.0573813\pi$
$810$	−3.30176	+	0.322252i	−0.116012	+	0.0113228i
$811$	−0.875146	−	0.875146i	−0.0307305	−	0.0307305i	0.691575	−	0.722305i	$-0.256917\pi$
$811$	−0.875146	−	0.875146i	−0.0307305	−	0.0307305i	−0.722305	+	0.691575i	$0.756917\pi$
$812$	9.51340	−	9.51340i	0.333855	−	0.333855i
$813$	−14.3423	+	37.1566i	−0.503006	+	1.30314i
$814$	−1.48841	+	1.48841i	−0.0521687	+	0.0521687i
$815$			52.9980i			1.85644i
$816$	3.11918	−	1.38181i	0.109193	−	0.0483731i
$817$	19.8543	−	19.8543i	0.694614	−	0.694614i
$818$	−2.56800			−0.0897880
$819$	3.09245	+	10.3652i	0.108059	+	0.362188i
$820$	−13.0151			−0.454506
$821$	−6.81319	+	6.81319i	−0.237782	+	0.237782i	−0.815931	−	0.578149i	$-0.803775\pi$
$821$	−6.81319	+	6.81319i	−0.237782	+	0.237782i	0.578149	+	0.815931i	$0.303775\pi$
$822$	1.91384	−	0.847842i	0.0667528	−	0.0295719i
$823$			4.17913i			0.145675i	0.997344	+	0.0728376i	$0.0232055\pi$
$823$			4.17913i			0.145675i	−0.997344	+	0.0728376i	$0.976795\pi$
$824$	−2.92823	+	2.92823i	−0.102010	+	0.102010i
$825$	22.1838	−	57.4715i	0.772340	−	2.00090i
$826$	−1.06942	+	1.06942i	−0.0372098	+	0.0372098i
$827$	−10.0858	−	10.0858i	−0.350718	−	0.350718i	0.509659	−	0.860377i	$-0.329772\pi$
$827$	−10.0858	−	10.0858i	−0.350718	−	0.350718i	−0.860377	+	0.509659i	$0.829772\pi$
$828$	21.0799	+	19.1227i	0.732579	+	0.664560i
$829$			52.7813i			1.83317i	0.399839	+	0.916585i	$0.369066\pi$
$829$			52.7813i			1.83317i	−0.399839	+	0.916585i	$0.630934\pi$
$830$	−1.59277	−	1.59277i	−0.0552858	−	0.0552858i
$831$	1.33492	+	3.01333i	0.0463078	+	0.104531i
$832$	6.65364	+	27.0373i	0.230673	+	0.937349i
$833$			0.501131i			0.0173632i
$834$	−0.306180	+	0.793221i	−0.0106022	+	0.0274670i
$835$	68.2991			2.36359
$836$	−52.6247			−1.82006
$837$	−20.4394	+	10.2714i	−0.706488	+	0.355030i
$838$	0.869723	+	0.869723i	0.0300441	+	0.0300441i
$839$	−0.873967	−	0.873967i	−0.0301727	−	0.0301727i	0.691859	−	0.722032i	$-0.256792\pi$
$839$	−0.873967	−	0.873967i	−0.0301727	−	0.0301727i	−0.722032	+	0.691859i	$0.756792\pi$
$840$	0.916946	−	2.37553i	0.0316376	−	0.0819636i
$841$	−16.7827			−0.578715
$842$	0.705136			0.0243006
$843$	−6.14583	−	2.37227i	−0.211674	−	0.0817052i
$844$		−	41.6272i		−	1.43287i
$845$	−13.2572	+	42.4349i	−0.456062	+	1.45981i
$846$	1.24565	−	1.37314i	0.0428262	−	0.0472096i
$847$	12.1776	+	12.1776i	0.418428	+	0.418428i
$848$			15.9439i			0.547517i
$849$	9.74526	+	21.9981i	0.334456	+	0.754971i
$850$	−0.255714	−	0.255714i	−0.00877092	−	0.00877092i
$851$	12.4023	−	12.4023i	0.425147	−	0.425147i
$852$	−25.0804	−	9.68093i	−0.859240	−	0.331663i
$853$	−8.36431	+	8.36431i	−0.286388	+	0.286388i	−0.835650	−	0.549262i	$-0.814909\pi$
$853$	−8.36431	+	8.36431i	−0.286388	+	0.286388i	0.549262	+	0.835650i	$0.314909\pi$
$854$			0.0214160i			0.000732839i
$855$	−34.3413	+	37.8562i	−1.17445	+	1.29465i
$856$	3.96948	−	3.96948i	0.135674	−	0.135674i
$857$	36.9543			1.26234			0.631168	−	0.775646i	$-0.282576\pi$
$857$	36.9543			1.26234			0.631168	+	0.775646i	$0.282576\pi$
$858$	2.82861	−	2.18768i	0.0965670	−	0.0746863i
$859$	38.8763			1.32644			0.663220	−	0.748424i	$-0.269189\pi$
$859$	38.8763			1.32644			0.663220	+	0.748424i	$0.269189\pi$
$860$	−27.0994	+	27.0994i	−0.924081	+	0.924081i
$861$	−1.34277	−	3.03105i	−0.0457615	−	0.103298i
$862$		−	2.05583i		−	0.0700219i
$863$	2.77181	−	2.77181i	0.0943535	−	0.0943535i	−0.658355	−	0.752708i	$-0.728747\pi$
$863$	2.77181	−	2.77181i	0.0943535	−	0.0943535i	0.752708	+	0.658355i	$0.228747\pi$
$864$	−2.99445	−	5.95876i	−0.101873	−	0.202721i
$865$	−45.0238	+	45.0238i	−1.53086	+	1.53086i
$866$	1.15820	+	1.15820i	0.0393573	+	0.0393573i
$867$	−26.5237	+	11.7502i	−0.900793	+	0.399056i
$868$		−	8.75348i		−	0.297112i
$869$	49.0948	+	49.0948i	1.66543	+	1.66543i
$870$	−3.94968	+	1.74973i	−0.133907	+	0.0593214i
$871$	11.4477	+	6.92607i	0.387890	+	0.234681i
$872$		−	6.50386i		−	0.220249i
$873$	−19.6476	+	0.956532i	−0.664972	+	0.0323737i
$874$	−2.56206			−0.0866631
$875$	5.79701			0.195975
$876$	−24.1123	−	9.30727i	−0.814680	−	0.314463i
$877$	−4.98129	−	4.98129i	−0.168206	−	0.168206i	0.617984	−	0.786190i	$-0.287950\pi$
$877$	−4.98129	−	4.98129i	−0.168206	−	0.168206i	−0.786190	+	0.617984i	$0.787950\pi$
$878$	−1.27794	−	1.27794i	−0.0431283	−	0.0431283i
$879$	25.1645	+	9.71339i	0.848777	+	0.327625i
$880$	71.4059			2.40709
$881$	24.6836			0.831610			0.415805	−	0.909454i	$-0.363500\pi$
$881$	24.6836			0.831610			0.415805	+	0.909454i	$0.363500\pi$
$882$	0.322973	−	0.0157237i	0.0108751	−	0.000529446i
$883$		−	42.4570i		−	1.42879i	−0.699741	−	0.714397i	$-0.746701\pi$
$883$		−	42.4570i		−	1.42879i	0.699741	−	0.714397i	$-0.253299\pi$
$884$	0.858521	+	3.48863i	0.0288752	+	0.117335i
$885$	−75.9897	+	33.6638i	−2.55436	+	1.13160i
$886$	−3.04467	−	3.04467i	−0.102288	−	0.102288i
$887$			32.9418i			1.10608i	0.833155	+	0.553039i	$0.186532\pi$
$887$			32.9418i			1.10608i	−0.833155	+	0.553039i	$0.813468\pi$
$888$	−2.50260	+	1.10867i	−0.0839817	+	0.0372044i
$889$	6.60553	+	6.60553i	0.221542	+	0.221542i
$890$	−0.580354	+	0.580354i	−0.0194535	+	0.0194535i
$891$	30.3641	−	36.9322i	1.01723	−	1.23727i
$892$	36.2575	−	36.2575i	1.21399	−	1.21399i
$893$		−	28.5638i		−	0.955852i
$894$	−0.832548	−	1.87932i	−0.0278446	−	0.0628538i
$895$	−44.3779	+	44.3779i	−1.48339	+	1.48339i
$896$	3.39922			0.113560
$897$	−23.5697	+	18.2291i	−0.786968	+	0.608652i
$898$	−2.27157			−0.0758031
$899$	−21.0628	+	21.0628i	−0.702484	+	0.702484i
$900$	26.8334	−	29.5798i	0.894446	−	0.985994i
$901$			2.03286i			0.0677243i
$902$	−0.774963	+	0.774963i	−0.0258034	+	0.0258034i
$903$	−9.10697	−	3.51525i	−0.303061	−	0.116980i
$904$	1.95555	−	1.95555i	0.0650407	−	0.0650407i
$905$	−18.3924	−	18.3924i	−0.611383	−	0.611383i
$906$	−0.372837	−	0.841608i	−0.0123867	−	0.0279605i
$907$			37.1213i			1.23259i	0.787514	+	0.616297i	$0.211368\pi$
$907$			37.1213i			1.23259i	−0.787514	+	0.616297i	$0.788632\pi$
$908$	15.7313	+	15.7313i	0.522063	+	0.522063i
$909$	−31.0857	+	34.2674i	−1.03105	+	1.13658i
$910$	1.13711	+	0.687971i	0.0376947	+	0.0228060i
$911$			5.99621i			0.198663i	0.995054	+	0.0993316i	$0.0316705\pi$
$911$			5.99621i			0.198663i	−0.995054	+	0.0993316i	$0.968330\pi$
$912$	−31.6402	−	12.2130i	−1.04771	−	0.404413i
$913$	32.4637			1.07439
$914$	1.77427			0.0586875
$915$	−0.423804	+	1.09795i	−0.0140105	+	0.0362971i
$916$	−14.6063	−	14.6063i	−0.482607	−	0.482607i
$917$	−0.697256	−	0.697256i	−0.0230254	−	0.0230254i
$918$	−0.126025	−	0.250783i	−0.00415946	−	0.00827707i
$919$	−8.82388			−0.291073			−0.145536	−	0.989353i	$-0.546491\pi$
$919$	−8.82388			−0.291073			−0.145536	+	0.989353i	$0.546491\pi$
$920$	7.01442			0.231258
$921$	9.51416	−	24.6483i	0.313502	−	0.812190i
$922$			0.546368i			0.0179937i
$923$	14.5693	−	24.0808i	0.479556	−	0.792629i
$924$	7.41054	+	16.7279i	0.243789	+	0.550307i
$925$	−17.4032	−	17.4032i	−0.572214	−	0.572214i
$926$			1.70377i			0.0559894i
$927$	−21.4043	−	19.4169i	−0.703008	−	0.637735i
$928$	−6.14052	−	6.14052i	−0.201572	−	0.201572i
$929$	30.5160	−	30.5160i	1.00120	−	1.00120i	0.00119660	−	0.999999i	$-0.499619\pi$
$929$	30.5160	−	30.5160i	1.00120	−	1.00120i	0.999999	−	0.00119660i	$-0.000380889\pi$
$930$	−1.01211	+	2.62207i	−0.0331884	+	0.0859811i
$931$	3.52276	−	3.52276i	0.115454	−	0.115454i
$932$		−	49.8084i		−	1.63153i
$933$	29.4224	−	13.0343i	0.963245	−	0.426723i
$934$	0.651534	−	0.651534i	0.0213188	−	0.0213188i
$935$	9.10428			0.297742
$936$	4.45587	−	1.32941i	0.145645	−	0.0434531i
$937$	−48.0385			−1.56935			−0.784675	−	0.619908i	$-0.787170\pi$
$937$	−48.0385			−1.56935			−0.784675	+	0.619908i	$0.787170\pi$
$938$	0.282829	−	0.282829i	0.00923469	−	0.00923469i
$939$	23.9039	−	10.5895i	0.780074	−	0.345577i
$940$			38.9871i			1.27162i
$941$	21.9053	−	21.9053i	0.714093	−	0.714093i	−0.253296	−	0.967389i	$-0.581515\pi$
$941$	21.9053	−	21.9053i	0.714093	−	0.714093i	0.967389	+	0.253296i	$0.0815147\pi$
$942$	−0.232747	+	0.602978i	−0.00758331	+	0.0196461i
$943$	6.45746	−	6.45746i	0.210284	−	0.210284i
$944$	−38.9967	−	38.9967i	−1.26924	−	1.26924i
$945$	16.8693	+	5.58526i	0.548758	+	0.181688i
$946$			3.22718i			0.104925i
$947$	−22.3201	−	22.3201i	−0.725306	−	0.725306i	0.244375	−	0.969681i	$-0.421417\pi$
$947$	−22.3201	−	22.3201i	−0.725306	−	0.725306i	−0.969681	+	0.244375i	$0.921417\pi$
$948$	18.2312	+	41.1535i	0.592123	+	1.33661i
$949$	14.0070	−	23.1513i	0.454686	−	0.751524i
$950$			3.59514i			0.116642i
$951$	−4.78978	+	12.4089i	−0.155319	+	0.402386i
$952$	0.215431			0.00698215
$953$	−8.90539			−0.288474			−0.144237	−	0.989543i	$-0.546073\pi$
$953$	−8.90539			−0.288474			−0.144237	+	0.989543i	$0.546073\pi$
$954$	1.31015	−	0.0637840i	0.0424178	−	0.00206508i
$955$	22.0486	+	22.0486i	0.713476	+	0.713476i
$956$	17.6422	+	17.6422i	0.570591	+	0.570591i
$957$	22.4196	−	58.0824i	0.724723	−	1.87754i
$958$	−1.28636			−0.0415603
$959$	−11.2124			−0.362066
$960$	42.6740	+	16.4720i	1.37730	+	0.531632i
$961$		−	11.6197i		−	0.374828i
$962$	−0.341386	−	1.38723i	−0.0110067	−	0.0447262i
$963$	29.0154	+	26.3214i	0.935008	+	0.848194i
$964$	−20.1547	−	20.1547i	−0.649138	−	0.649138i
$965$			7.98970i			0.257198i
$966$	0.360786	+	0.814406i	0.0116081	+	0.0262031i
$967$	28.2133	+	28.2133i	0.907278	+	0.907278i	0.996052	−	0.0887740i	$-0.0282949\pi$
$967$	28.2133	+	28.2133i	0.907278	+	0.907278i	−0.0887740	+	0.996052i	$0.528295\pi$
$968$	5.23503	−	5.23503i	0.168260	−	0.168260i
$969$	−4.03414	−	1.55716i	−0.129595	−	0.0500232i
$970$	−1.70903	+	1.70903i	−0.0548737	+	0.0548737i
$971$			50.5527i			1.62231i	0.584828	+	0.811157i	$0.301162\pi$
$971$			50.5527i			1.62231i	−0.584828	+	0.811157i	$0.698838\pi$
$972$	26.9859	−	15.2480i	0.865573	−	0.489080i
$973$	3.22046	−	3.22046i	0.103243	−	0.103243i
$974$	−3.02102			−0.0967998
$975$	25.5795	+	33.0735i	0.819199	+	1.05920i
$976$	−0.780940			−0.0249973
$977$	8.22638	−	8.22638i	0.263185	−	0.263185i	−0.563162	−	0.826347i	$-0.690415\pi$
$977$	8.22638	−	8.22638i	0.263185	−	0.263185i	0.826347	+	0.563162i	$0.190415\pi$
$978$	1.17186	+	2.64524i	0.0374718	+	0.0845855i
$979$		−	11.8287i		−	0.378047i
$980$	−4.80825	+	4.80825i	−0.153594	+	0.153594i
$981$	45.3338	−	2.20705i	1.44740	−	0.0704655i
$982$	1.50596	−	1.50596i	0.0480573	−	0.0480573i
$983$	−6.08660	−	6.08660i	−0.194132	−	0.194132i	0.603347	−	0.797479i	$-0.293834\pi$
$983$	−6.08660	−	6.08660i	−0.194132	−	0.194132i	−0.797479	+	0.603347i	$0.793834\pi$
$984$	−1.30302	+	0.577243i	−0.0415386	+	0.0184018i
$985$		−	28.4543i		−	0.906631i
$986$	−0.258432	−	0.258432i	−0.00823016	−	0.00823016i
$987$	−9.07962	+	4.02232i	−0.289007	+	0.128032i
$988$	18.4887	−	30.5588i	0.588202	−	0.972205i
$989$		−	26.8908i		−	0.855079i
$990$	−0.285661	−	5.86761i	−0.00907889	−	0.186485i
$991$	−51.0667			−1.62219			−0.811094	−	0.584916i	$-0.801128\pi$
$991$	−51.0667			−1.62219			−0.811094	+	0.584916i	$0.801128\pi$
$992$	−5.65002			−0.179388
$993$	−50.4571	−	19.4763i	−1.60121	−	0.618060i
$994$	−0.594945	−	0.594945i	−0.0188705	−	0.0188705i
$995$	−23.8098	−	23.8098i	−0.754823	−	0.754823i
$996$	19.6339	+	7.57862i	0.622125	+	0.240138i
$997$	−27.4732			−0.870086			−0.435043	−	0.900410i	$-0.643267\pi$
$997$	−27.4732			−0.870086			−0.435043	+	0.900410i	$0.643267\pi$
$998$	−0.638381			−0.0202076
$999$	−8.57696	−	17.0676i	−0.271363	−	0.539996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.c.8.12	✓	48
3.2	odd	2	inner	273.2.n.c.8.13	yes	48
13.5	odd	4	inner	273.2.n.c.239.13	yes	48
39.5	even	4	inner	273.2.n.c.239.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.c.8.12	✓	48	1.1	even	1	trivial
273.2.n.c.8.13	yes	48	3.2	odd	2	inner
273.2.n.c.239.12	yes	48	39.5	even	4	inner
273.2.n.c.239.13	yes	48	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0762157 + 0.0762157i) q^{2} +(1.58361 - 0.701549i) q^{3} +1.98838i q^{4} +(-2.41817 + 2.41817i) q^{5} +(-0.0672271 + 0.174165i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.303978 - 0.303978i) q^{8} +(2.01566 - 2.22196i) q^{9} +O(q^{10})\)	\(q+(-0.0762157 + 0.0762157i) q^{2} +(1.58361 - 0.701549i) q^{3} +1.98838i q^{4} +(-2.41817 + 2.41817i) q^{5} +(-0.0672271 + 0.174165i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.303978 - 0.303978i) q^{8} +(2.01566 - 2.22196i) q^{9} -0.368606i q^{10} +(3.75644 + 3.75644i) q^{11} +(1.39495 + 3.14883i) q^{12} +(-3.50109 + 0.861588i) q^{13} +0.107785i q^{14} +(-2.13298 + 5.52592i) q^{15} -3.93043 q^{16} -0.501131 q^{17} +(0.0157237 + 0.322973i) q^{18} +(3.52276 + 3.52276i) q^{19} +(-4.80825 - 4.80825i) q^{20} +(0.623713 - 1.61585i) q^{21} -0.572600 q^{22} +4.77125 q^{23} +(-0.694638 - 0.268128i) q^{24} -6.69513i q^{25} +(0.201172 - 0.332505i) q^{26} +(1.63320 - 4.93281i) q^{27} +(1.40600 + 1.40600i) q^{28} -6.76629i q^{29} +(-0.258595 - 0.583729i) q^{30} +(-3.11290 - 3.11290i) q^{31} +(0.907516 - 0.907516i) q^{32} +(8.58408 + 3.31342i) q^{33} +(0.0381941 - 0.0381941i) q^{34} +3.41981i q^{35} +(4.41811 + 4.00790i) q^{36} +(2.59939 - 2.59939i) q^{37} -0.536979 q^{38} +(-4.93993 + 3.82061i) q^{39} +1.47014 q^{40} +(1.35341 - 1.35341i) q^{41} +(0.0756167 + 0.170690i) q^{42} -5.63601i q^{43} +(-7.46925 + 7.46925i) q^{44} +(0.498883 + 10.2473i) q^{45} +(-0.363645 + 0.363645i) q^{46} +(-4.05418 - 4.05418i) q^{47} +(-6.22428 + 2.75739i) q^{48} -1.00000i q^{49} +(0.510274 + 0.510274i) q^{50} +(-0.793597 + 0.351568i) q^{51} +(-1.71317 - 6.96152i) q^{52} -4.05654i q^{53} +(0.251482 + 0.500434i) q^{54} -18.1675 q^{55} -0.429889 q^{56} +(8.05007 + 3.10730i) q^{57} +(0.515698 + 0.515698i) q^{58} +(9.92175 + 9.92175i) q^{59} +(-10.9876 - 4.24119i) q^{60} +0.198691 q^{61} +0.474504 q^{62} +(-0.145880 - 2.99645i) q^{63} -7.72252i q^{64} +(6.38278 - 10.5497i) q^{65} +(-0.906777 + 0.401707i) q^{66} +(-2.62400 - 2.62400i) q^{67} -0.996440i q^{68} +(7.55582 - 3.34727i) q^{69} +(-0.260644 - 0.260644i) q^{70} +(-5.51972 + 5.51972i) q^{71} +(-1.28814 + 0.0627123i) q^{72} +(-5.30667 + 5.30667i) q^{73} +0.396228i q^{74} +(-4.69696 - 10.6025i) q^{75} +(-7.00459 + 7.00459i) q^{76} +5.31241 q^{77} +(0.0853098 - 0.667691i) q^{78} +13.0695 q^{79} +(9.50446 - 9.50446i) q^{80} +(-0.874246 - 8.95744i) q^{81} +0.206302i q^{82} +(4.32106 - 4.32106i) q^{83} +(3.21293 + 1.24018i) q^{84} +(1.21182 - 1.21182i) q^{85} +(0.429553 + 0.429553i) q^{86} +(-4.74689 - 10.7152i) q^{87} -2.28375i q^{88} +(-1.57446 - 1.57446i) q^{89} +(-0.819029 - 0.742983i) q^{90} +(-1.86641 + 3.08488i) q^{91} +9.48708i q^{92} +(-7.11349 - 2.74578i) q^{93} +0.617985 q^{94} -17.0373 q^{95} +(0.800486 - 2.07382i) q^{96} +(-4.63648 - 4.63648i) q^{97} +(0.0762157 + 0.0762157i) q^{98} +(15.9184 - 0.774976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) \) 48 * q + 8 * q^3 + 4 * q^6	\( 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) \) 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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