LMFDB - Embedded newform 700.2.bj.a.323.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(127,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			323.30
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.719657 + 1.21741i) q^{2} +(-1.27690 - 2.50605i) q^{3} +(-0.964187 - 1.75224i) q^{4} +(-1.94714 + 1.09938i) q^{5} +(3.96983 + 0.248987i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.82708 + 0.0871975i) q^{8} +(-2.88647 + 3.97289i) q^{9} +(0.0628736 - 3.16165i) q^{10} +(0.113598 + 0.156355i) q^{11} +(-3.16003 + 4.65373i) q^{12} +(0.311602 + 1.96738i) q^{13} +(-1.36972 + 0.351966i) q^{14} +(5.24141 + 3.47584i) q^{15} +(-2.14069 + 3.37897i) q^{16} +(2.57778 + 1.31344i) q^{17} +(-2.75938 - 6.37315i) q^{18} +(1.09308 + 3.36414i) q^{19} +(3.80379 + 2.35185i) q^{20} +(0.869144 - 2.67495i) q^{21} +(-0.272100 + 0.0257743i) q^{22} +(1.18219 - 7.46403i) q^{23} +(-3.39137 - 7.19616i) q^{24} +(2.58272 - 4.28130i) q^{25} +(-2.61936 - 1.03649i) q^{26} +(5.30806 + 0.840714i) q^{27} +(0.557237 - 1.92080i) q^{28} +(-6.16617 - 2.00351i) q^{29} +(-8.00355 + 3.87954i) q^{30} +(1.24769 - 0.405398i) q^{31} +(-2.57305 - 5.03780i) q^{32} +(0.246780 - 0.484333i) q^{33} +(-3.45412 + 2.19299i) q^{34} +(-2.15422 - 0.599457i) q^{35} +(9.74455 + 1.22718i) q^{36} +(6.90220 - 1.09320i) q^{37} +(-4.88219 - 1.09030i) q^{38} +(4.53247 - 3.29303i) q^{39} +(-5.60059 + 2.93826i) q^{40} +(0.540341 + 0.392581i) q^{41} +(2.63103 + 2.98315i) q^{42} +(8.00342 - 8.00342i) q^{43} +(0.164441 - 0.349807i) q^{44} +(1.25265 - 10.9091i) q^{45} +(8.23603 + 6.81075i) q^{46} +(2.53580 - 1.29205i) q^{47} +(11.2013 + 1.05007i) q^{48} +1.00000i q^{49} +(3.35344 + 6.22531i) q^{50} -8.13717i q^{51} +(3.14688 - 2.44292i) q^{52} +(-2.57372 + 1.31138i) q^{53} +(-4.84348 + 5.85707i) q^{54} +(-0.393086 - 0.179557i) q^{55} +(1.93739 + 2.06071i) q^{56} +(7.03497 - 7.03497i) q^{57} +(6.87662 - 6.06493i) q^{58} +(-3.06178 - 2.22451i) q^{59} +(1.03681 - 12.5356i) q^{60} +(3.48795 - 2.53414i) q^{61} +(-0.404370 + 1.81070i) q^{62} +(-4.85030 + 0.768212i) q^{63} +(7.98479 + 0.493029i) q^{64} +(-2.76963 - 3.48820i) q^{65} +(0.412036 + 0.648986i) q^{66} +(2.15173 - 4.22302i) q^{67} +(-0.183994 - 5.78329i) q^{68} +(-20.2148 + 6.56818i) q^{69} +(2.28008 - 2.19117i) q^{70} +(4.27870 + 1.39024i) q^{71} +(-8.50672 + 10.9800i) q^{72} +(13.6037 + 2.15462i) q^{73} +(-3.63634 + 9.18956i) q^{74} +(-14.0270 - 1.00565i) q^{75} +(4.84085 - 5.15900i) q^{76} +(-0.0302333 + 0.190886i) q^{77} +(0.747155 + 7.88774i) q^{78} +(2.57602 - 7.92819i) q^{79} +(0.453437 - 8.93277i) q^{80} +(-0.118444 - 0.364533i) q^{81} +(-0.866793 + 0.375295i) q^{82} +(3.53662 + 1.80200i) q^{83} +(-5.52517 + 1.05620i) q^{84} +(-6.46327 + 0.276500i) q^{85} +(3.98375 + 15.5032i) q^{86} +(2.85266 + 18.0110i) q^{87} +(0.307519 + 0.451934i) q^{88} +(10.8971 + 14.9986i) q^{89} +(12.3794 + 9.37582i) q^{90} +(-1.17081 + 1.61148i) q^{91} +(-14.2186 + 5.12525i) q^{92} +(-2.60912 - 2.60912i) q^{93} +(-0.251942 + 4.01695i) q^{94} +(-5.82685 - 5.34876i) q^{95} +(-9.33947 + 12.8809i) q^{96} +(-6.65984 - 13.0707i) q^{97} +(-1.21741 - 0.719657i) q^{98} -0.949080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.719657	+	1.21741i	−0.508874	+	0.860841i
$2$	−0.719657	+	1.21741i	−0.508874	+	0.860841i
$3$	−1.27690	−	2.50605i	−0.737217	−	1.44687i	−0.888738	−	0.458416i	$-0.848417\pi$
$3$	−1.27690	−	2.50605i	−0.737217	−	1.44687i	0.151521	−	0.988454i	$-0.451583\pi$
$4$	−0.964187	−	1.75224i	−0.482094	−	0.876120i
$5$	−1.94714	+	1.09938i	−0.870788	+	0.491658i
$5$	−1.94714	+	1.09938i	−0.870788	+	0.491658i
$6$	3.96983	+	0.248987i	1.62068	+	0.101649i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.82708	+	0.0871975i	0.999525	+	0.0308290i
$9$	−2.88647	+	3.97289i	−0.962158	+	1.32430i
$10$	0.0628736	−	3.16165i	0.0198824	−	0.999802i
$11$	0.113598	+	0.156355i	0.0342512	+	0.0471428i	0.825799	−	0.563964i	$-0.190724\pi$
$11$	0.113598	+	0.156355i	0.0342512	+	0.0471428i	−0.791548	+	0.611107i	$0.790724\pi$
$12$	−3.16003	+	4.65373i	−0.912223	+	1.34342i
$13$	0.311602	+	1.96738i	0.0864229	+	0.545653i	0.992471	+	0.122478i	$0.0390842\pi$
$13$	0.311602	+	1.96738i	0.0864229	+	0.545653i	−0.906048	+	0.423174i	$0.860916\pi$
$14$	−1.36972	+	0.351966i	−0.366072	+	0.0940670i
$15$	5.24141	+	3.47584i	1.35333	+	0.897458i
$16$	−2.14069	+	3.37897i	−0.535171	+	0.844744i
$17$	2.57778	+	1.31344i	0.625203	+	0.318557i	0.737734	−	0.675092i	$-0.235896\pi$
$17$	2.57778	+	1.31344i	0.625203	+	0.318557i	−0.112531	+	0.993648i	$0.535896\pi$
$18$	−2.75938	−	6.37315i	−0.650391	−	1.50217i
$19$	1.09308	+	3.36414i	0.250769	+	0.771787i	0.994634	+	0.103457i	$0.0329906\pi$
$19$	1.09308	+	3.36414i	0.250769	+	0.771787i	−0.743865	+	0.668330i	$0.767009\pi$
$20$	3.80379	+	2.35185i	0.850553	+	0.525889i
$21$	0.869144	−	2.67495i	0.189663	−	0.583722i
$22$	−0.272100	+	0.0257743i	−0.0580120	+	0.00549510i
$23$	1.18219	−	7.46403i	0.246503	−	1.55636i	−0.484997	−	0.874516i	$-0.661179\pi$
$23$	1.18219	−	7.46403i	0.246503	−	1.55636i	0.731500	−	0.681841i	$-0.238821\pi$
$24$	−3.39137	−	7.19616i	−0.692261	−	1.46891i
$25$	2.58272	−	4.28130i	0.516544	−	0.856260i
$26$	−2.61936	−	1.03649i	−0.513699	−	0.203272i
$27$	5.30806	+	0.840714i	1.02154	+	0.161795i
$28$	0.557237	−	1.92080i	0.105308	−	0.362998i
$29$	−6.16617	−	2.00351i	−1.14503	−	0.372042i	−0.325760	−	0.945453i	$-0.605620\pi$
$29$	−6.16617	−	2.00351i	−1.14503	−	0.372042i	−0.819268	+	0.573410i	$0.805620\pi$
$30$	−8.00355	+	3.87954i	−1.46124	+	0.708304i
$31$	1.24769	−	0.405398i	0.224091	−	0.0728117i	−0.194819	−	0.980839i	$-0.562412\pi$
$31$	1.24769	−	0.405398i	0.224091	−	0.0728117i	0.418911	+	0.908027i	$0.362412\pi$
$32$	−2.57305	−	5.03780i	−0.454855	−	0.890566i
$33$	0.246780	−	0.484333i	0.0429589	−	0.0843115i
$34$	−3.45412	+	2.19299i	−0.592376	+	0.376095i
$35$	−2.15422	−	0.599457i	−0.364129	−	0.101327i
$36$	9.74455	+	1.22718i	1.62409	+	0.204530i
$37$	6.90220	−	1.09320i	1.13472	−	0.179721i	0.439308	−	0.898337i	$-0.355224\pi$
$37$	6.90220	−	1.09320i	1.13472	−	0.179721i	0.695408	+	0.718615i	$0.255224\pi$
$38$	−4.88219	−	1.09030i	−0.791996	−	0.176871i
$39$	4.53247	−	3.29303i	0.725776	−	0.527307i
$40$	−5.60059	+	2.93826i	−0.885532	+	0.464579i
$41$	0.540341	+	0.392581i	0.0843871	+	0.0613108i	0.629179	−	0.777261i	$-0.283391\pi$
$41$	0.540341	+	0.392581i	0.0843871	+	0.0613108i	−0.544792	+	0.838571i	$0.683391\pi$
$42$	2.63103	+	2.98315i	0.405977	+	0.460310i
$43$	8.00342	−	8.00342i	1.22051	−	1.22051i	0.253058	−	0.967451i	$-0.418563\pi$
$43$	8.00342	−	8.00342i	1.22051	−	1.22051i	0.967451	−	0.253058i	$-0.0814365\pi$
$44$	0.164441	−	0.349807i	0.0247904	−	0.0527354i
$45$	1.25265	−	10.9091i	0.186734	−	1.62623i
$46$	8.23603	+	6.81075i	1.21434	+	1.00419i
$47$	2.53580	−	1.29205i	0.369884	−	0.188465i	−0.259161	−	0.965834i	$-0.583446\pi$
$47$	2.53580	−	1.29205i	0.369884	−	0.188465i	0.629045	+	0.777369i	$0.283446\pi$
$48$	11.2013	+	1.05007i	1.61677	+	0.151564i
$49$			1.00000i			0.142857i
$50$	3.35344	+	6.22531i	0.474248	+	0.880391i
$51$		−	8.13717i		−	1.13943i
$52$	3.14688	−	2.44292i	0.436393	−	0.338773i
$53$	−2.57372	+	1.31138i	−0.353528	+	0.180131i	−0.621731	−	0.783231i	$-0.713570\pi$
$53$	−2.57372	+	1.31138i	−0.353528	+	0.180131i	0.268203	+	0.963362i	$0.413570\pi$
$54$	−4.84348	+	5.85707i	−0.659114	+	0.797046i
$55$	−0.393086	−	0.179557i	−0.0530037	−	0.0242115i
$56$	1.93739	+	2.06071i	0.258895	+	0.275374i
$57$	7.03497	−	7.03497i	0.931805	−	0.931805i
$58$	6.87662	−	6.06493i	0.902945	−	0.796364i
$59$	−3.06178	−	2.22451i	−0.398610	−	0.289607i	0.370365	−	0.928886i	$-0.379233\pi$
$59$	−3.06178	−	2.22451i	−0.398610	−	0.289607i	−0.768974	+	0.639279i	$0.779233\pi$
$60$	1.03681	−	12.5356i	0.133851	−	1.61833i
$61$	3.48795	−	2.53414i	0.446586	−	0.324463i	−0.341661	−	0.939823i	$-0.610989\pi$
$61$	3.48795	−	2.53414i	0.446586	−	0.324463i	0.788246	+	0.615360i	$0.210989\pi$
$62$	−0.404370	+	1.81070i	−0.0513551	+	0.229959i
$63$	−4.85030	+	0.768212i	−0.611081	+	0.0967857i
$64$	7.98479	+	0.493029i	0.998099	+	0.0616286i
$65$	−2.76963	−	3.48820i	−0.343531	−	0.432658i
$66$	0.412036	+	0.648986i	0.0507181	+	0.0798847i
$67$	2.15173	−	4.22302i	0.262876	−	0.515924i	−0.721409	−	0.692509i	$-0.756505\pi$
$67$	2.15173	−	4.22302i	0.262876	−	0.515924i	0.984285	+	0.176586i	$0.0565052\pi$
$68$	−0.183994	−	5.78329i	−0.0223125	−	0.701326i
$69$	−20.2148	+	6.56818i	−2.43357	+	0.790715i
$70$	2.28008	−	2.19117i	0.272522	−	0.261895i
$71$	4.27870	+	1.39024i	0.507789	+	0.164991i	0.551696	−	0.834045i	$-0.313981\pi$
$71$	4.27870	+	1.39024i	0.507789	+	0.164991i	−0.0439076	+	0.999036i	$0.513981\pi$
$72$	−8.50672	+	10.9800i	−1.00253	+	1.29400i
$73$	13.6037	+	2.15462i	1.59219	+	0.252179i	0.888689	−	0.458511i	$-0.151617\pi$
$73$	13.6037	+	2.15462i	1.59219	+	0.252179i	0.703506	+	0.710689i	$0.251617\pi$
$74$	−3.63634	+	9.18956i	−0.422716	+	1.06826i
$75$	−14.0270	−	1.00565i	−1.61970	−	0.116123i
$76$	4.84085	−	5.15900i	0.555284	−	0.591777i
$77$	−0.0302333	+	0.190886i	−0.00344541	+	0.0217535i
$78$	0.747155	+	7.88774i	0.0845987	+	0.893111i
$79$	2.57602	−	7.92819i	0.289825	−	0.891991i	−0.695085	−	0.718927i	$-0.744633\pi$
$79$	2.57602	−	7.92819i	0.289825	−	0.891991i	0.984911	−	0.173063i	$-0.0553666\pi$
$80$	0.453437	−	8.93277i	0.0506958	−	0.998714i
$81$	−0.118444	−	0.364533i	−0.0131605	−	0.0405037i
$82$	−0.866793	+	0.375295i	−0.0957213	+	0.0414444i
$83$	3.53662	+	1.80200i	0.388195	+	0.197795i	0.637185	−	0.770711i	$-0.280099\pi$
$83$	3.53662	+	1.80200i	0.388195	+	0.197795i	−0.248990	+	0.968506i	$0.580099\pi$
$84$	−5.52517	+	1.05620i	−0.602845	+	0.115241i
$85$	−6.46327	+	0.276500i	−0.701040	+	0.0299906i
$86$	3.98375	+	15.5032i	0.429578	+	1.67175i
$87$	2.85266	+	18.0110i	0.305838	+	1.93098i
$88$	0.307519	+	0.451934i	0.0327816	+	0.0481763i
$89$	10.8971	+	14.9986i	1.15509	+	1.58985i	0.727898	+	0.685686i	$0.240497\pi$
$89$	10.8971	+	14.9986i	1.15509	+	1.58985i	0.427193	+	0.904160i	$0.359503\pi$
$90$	12.3794	+	9.37582i	1.30490	+	0.988298i
$91$	−1.17081	+	1.61148i	−0.122734	+	0.168929i
$92$	−14.2186	+	5.12525i	−1.48239	+	0.534344i
$93$	−2.60912	−	2.60912i	−0.270553	−	0.270553i
$94$	−0.251942	+	4.01695i	−0.0259859	+	0.414316i
$95$	−5.82685	−	5.34876i	−0.597822	−	0.548771i
$96$	−9.33947	+	12.8809i	−0.953206	+	1.31466i
$97$	−6.65984	−	13.0707i	−0.676204	−	1.32713i	−0.932726	−	0.360587i	$-0.882576\pi$
$97$	−6.65984	−	13.0707i	−0.676204	−	1.32713i	0.256521	−	0.966539i	$-0.417424\pi$
$98$	−1.21741	−	0.719657i	−0.122977	−	0.0726963i
$99$	−0.949080			−0.0953861
$100$	−9.99209	−	0.397569i	−0.999209	−	0.0397569i
$101$	−9.70759			−0.965942			−0.482971	−	0.875636i	$-0.660442\pi$
$101$	−9.70759			−0.965942			−0.482971	+	0.875636i	$0.660442\pi$
$102$	9.90630	+	5.85597i	0.980870	+	0.579828i
$103$	7.18473	+	14.1008i	0.707933	+	1.38940i	0.911897	+	0.410418i	$0.134617\pi$
$103$	7.18473	+	14.1008i	0.707933	+	1.38940i	−0.203964	+	0.978978i	$0.565383\pi$
$104$	0.709375	+	5.58911i	0.0695599	+	0.548058i
$105$	1.24844	+	6.16402i	0.121836	+	0.601547i
$106$	0.255710	−	4.07702i	0.0248368	−	0.395995i
$107$	−7.41609	−	7.41609i	−0.716940	−	0.716940i	0.251037	−	0.967977i	$-0.419228\pi$
$107$	−7.41609	−	7.41609i	−0.716940	−	0.716940i	−0.967977	+	0.251037i	$0.919228\pi$
$108$	−3.64483	−	10.1116i	−0.350724	−	0.972988i
$109$	−8.38062	+	11.5349i	−0.802718	+	1.10485i	0.189689	+	0.981844i	$0.439252\pi$
$109$	−8.38062	+	11.5349i	−0.802718	+	1.10485i	−0.992406	+	0.123002i	$0.960748\pi$
$110$	0.501482	−	0.349328i	0.0478145	−	0.0333071i
$111$	−11.5530	−	15.9014i	−1.09656	−	1.50929i
$112$	−3.90299	+	0.875602i	−0.368798	+	0.0827366i
$113$	−0.791630	−	4.99816i	−0.0744703	−	0.470187i	−0.996537	−	0.0831551i	$-0.973500\pi$
$113$	−0.791630	−	4.99816i	−0.0744703	−	0.470187i	0.922066	−	0.387032i	$-0.126500\pi$
$114$	3.50170	+	13.6272i	0.327964	+	1.27631i
$115$	5.90393	+	15.8332i	0.550544	+	1.47645i
$116$	2.43471	+	12.7364i	0.226057	+	1.18254i
$117$	−8.71561	−	4.44083i	−0.805759	−	0.410555i
$118$	4.91158	−	2.12656i	0.452148	−	0.195766i
$119$	0.894019	+	2.75151i	0.0819546	+	0.252230i
$120$	14.5148	+	10.2835i	1.32501	+	0.938753i
$121$	3.38764	−	10.4261i	0.307968	−	0.947827i
$122$	0.574970	+	6.06998i	0.0520554	+	0.549550i
$123$	0.293868	−	1.85541i	0.0264972	−	0.167297i
$124$	−1.91336	−	1.79537i	−0.171825	−	0.161229i
$125$	−0.322142	+	11.1757i	−0.0288133	+	0.999585i
$126$	2.55532	−	6.45767i	0.227646	−	0.575295i
$127$	2.35896	+	0.373623i	0.209324	+	0.0331537i	0.260216	−	0.965551i	$-0.416206\pi$
$127$	2.35896	+	0.373623i	0.209324	+	0.0331537i	−0.0508916	+	0.998704i	$0.516206\pi$
$128$	−6.34653	+	9.36598i	−0.560960	+	0.827843i
$129$	−30.2765	−	9.83744i	−2.66570	−	0.866138i
$130$	6.23976	−	0.861482i	0.547263	−	0.0755570i
$131$	−11.7003	+	3.80166i	−1.02226	+	0.332152i	−0.771726	−	0.635955i	$-0.780606\pi$
$131$	−11.7003	+	3.80166i	−1.02226	+	0.332152i	−0.250534	+	0.968108i	$0.580606\pi$
$132$	−1.08661	+	0.0345701i	−0.0945772	+	0.00300894i
$133$	−1.60589	+	3.15173i	−0.139248	+	0.273290i
$134$	3.59264	+	5.65867i	0.310357	+	0.488835i
$135$	−11.2598	+	4.19859i	−0.969090	+	0.361357i
$136$	7.17306	+	3.93799i	0.615085	+	0.337680i
$137$	22.7031	−	3.59582i	1.93966	−	0.307212i	0.940217	−	0.340577i	$-0.110622\pi$
$137$	22.7031	−	3.59582i	1.93966	−	0.307212i	0.999443	+	0.0333652i	$0.0106225\pi$
$138$	6.55152	−	29.3365i	0.557702	−	2.49729i
$139$	13.8016	−	10.0275i	1.17064	−	0.850518i	0.179552	−	0.983748i	$-0.442535\pi$
$139$	13.8016	−	10.0275i	1.17064	−	0.850518i	0.991085	+	0.133231i	$0.0425351\pi$
$140$	1.02668	+	4.35269i	0.0867700	+	0.367870i
$141$	−6.47590	−	4.70502i	−0.545369	−	0.396234i
$142$	−4.77169	+	4.20846i	−0.400431	+	0.353166i
$143$	−0.272212	+	0.272212i	−0.0227635	+	0.0227635i
$144$	−7.24526	−	18.2580i	−0.603772	−	1.52150i
$145$	14.2090	−	2.87785i	1.17999	−	0.238993i
$146$	−12.4131	+	15.0108i	−1.02731	+	1.24230i
$147$	2.50605	−	1.27690i	0.206696	−	0.105317i
$148$	−8.57057	−	11.0403i	−0.704496	−	0.907504i
$149$		−	3.56283i		−	0.291879i	−0.989294	−	0.145939i	$-0.953380\pi$
$149$		−	3.56283i		−	0.291879i	0.989294	−	0.145939i	$-0.0466204\pi$
$150$	11.3189	−	16.3530i	0.924188	−	1.33521i
$151$			13.3471i			1.08618i	0.839676	+	0.543088i	$0.182745\pi$
$151$			13.3471i			1.08618i	−0.839676	+	0.543088i	$0.817255\pi$
$152$	2.79687	+	9.60603i	0.226856	+	0.779152i
$153$	−12.6588	+	6.45000i	−1.02341	+	0.521452i
$154$	−0.210629	−	0.174179i	−0.0169730	−	0.0140357i
$155$	−1.98374	+	2.16105i	−0.159338	+	0.173580i
$156$	−10.1403	−	4.76687i	−0.811876	−	0.381655i
$157$	6.33245	−	6.33245i	0.505385	−	0.505385i	−0.407722	−	0.913106i	$-0.633677\pi$
$157$	6.33245	−	6.33245i	0.505385	−	0.505385i	0.913106	+	0.407722i	$0.133677\pi$
$158$	7.79802	+	8.84166i	0.620377	+	0.703405i
$159$	6.57275	+	4.77538i	0.521253	+	0.378712i
$160$	10.5485	+	6.98055i	0.833936	+	0.551861i
$161$	6.11379	−	4.44193i	0.481835	−	0.350073i
$162$	0.529027	+	0.118144i	0.0415643	+	0.00928225i
$163$	−3.95921	+	0.627078i	−0.310109	+	0.0491165i	−0.309549	−	0.950883i	$-0.600178\pi$
$163$	−3.95921	+	0.627078i	−0.310109	+	0.0491165i	−0.000559940		1.00000i	$0.500178\pi$
$164$	0.166905	−	1.32533i	0.0130331	−	0.103491i
$165$	0.0519510	+	1.21437i	0.00404438	+	0.0945386i
$166$	−4.73893	+	3.00871i	−0.367813	+	0.233521i
$167$	7.00196	−	13.7421i	0.541828	−	1.06340i	−0.444061	−	0.895996i	$-0.646463\pi$
$167$	7.00196	−	13.7421i	0.541828	−	1.06340i	0.985889	−	0.167400i	$-0.0535372\pi$
$168$	2.69039	−	7.48651i	0.207568	−	0.577597i
$169$	8.59025	−	2.79114i	0.660788	−	0.214703i
$170$	4.31472	−	8.06745i	0.330924	−	0.618745i
$171$	−16.5205	−	5.36784i	−1.26335	−	0.410489i
$172$	−21.7407	−	6.30711i	−1.65771	−	0.480912i
$173$	−6.09575	−	0.965472i	−0.463451	−	0.0734035i	−0.0796576	−	0.996822i	$-0.525383\pi$
$173$	−6.09575	−	0.965472i	−0.463451	−	0.0734035i	−0.383794	+	0.923419i	$0.625383\pi$
$174$	−23.9798	−	9.48888i	−1.81790	−	0.719350i
$175$	4.85360	−	1.20108i	0.366898	−	0.0907929i
$176$	−0.771498	+	0.0491397i	−0.0581538	+	0.00370404i
$177$	−1.66517	+	10.5135i	−0.125162	+	0.790240i
$178$	−26.1016	+	2.47244i	−1.95640	+	0.185317i
$179$	7.00479	−	21.5585i	0.523563	−	1.61136i	−0.243578	−	0.969881i	$-0.578321\pi$
$179$	7.00479	−	21.5585i	0.523563	−	1.61136i	0.767141	−	0.641479i	$-0.221679\pi$
$180$	−20.3232	+	8.32348i	−1.51480	+	0.620396i
$181$	1.85746	+	5.71666i	0.138064	+	0.424916i	0.996054	−	0.0887498i	$-0.0282872\pi$
$181$	1.85746	+	5.71666i	0.138064	+	0.424916i	−0.857990	+	0.513666i	$0.828287\pi$
$182$	−1.11926	−	2.58508i	−0.0829649	−	0.191619i
$183$	−10.8044	−	5.50513i	−0.798687	−	0.406951i
$184$	3.99298	−	20.9983i	0.294366	−	1.54802i
$185$	−12.2377	+	9.71677i	−0.899735	+	0.714391i
$186$	5.05404	−	1.29870i	0.370580	−	0.0952255i
$187$	0.0874683	+	0.552253i	0.00639631	+	0.0403847i
$188$	−4.70897	−	3.19754i	−0.343437	−	0.233205i
$189$	3.15889	+	4.34784i	0.229775	+	0.316259i
$190$	10.7050	−	3.24441i	0.776621	−	0.235374i
$191$	10.1003	−	13.9019i	0.730834	−	1.00591i	−0.268260	−	0.963347i	$-0.586449\pi$
$191$	10.1003	−	13.9019i	0.730834	−	1.00591i	0.999094	−	0.0425601i	$-0.0135514\pi$
$192$	−8.96020	−	20.6399i	−0.646647	−	1.48955i
$193$	15.4272	+	15.4272i	1.11048	+	1.11048i	0.993086	+	0.117392i	$0.0374533\pi$
$193$	15.4272	+	15.4272i	1.11048	+	1.11048i	0.117392	+	0.993086i	$0.462547\pi$
$194$	20.7052	+	1.29863i	1.48655	+	0.0932360i
$195$	−5.20506	+	11.3949i	−0.372742	+	0.816007i
$196$	1.75224	−	0.964187i	0.125160	−	0.0688705i
$197$	12.1297	+	23.8058i	0.864202	+	1.69609i	0.705433	+	0.708776i	$0.250752\pi$
$197$	12.1297	+	23.8058i	0.864202	+	1.69609i	0.158769	+	0.987316i	$0.449248\pi$
$198$	0.683012	−	1.15542i	0.0485395	−	0.0821122i
$199$	−19.0703			−1.35185			−0.675927	−	0.736968i	$-0.736257\pi$
$199$	−19.0703			−1.35185			−0.675927	+	0.736968i	$0.736257\pi$
$200$	7.67489	−	11.8784i	0.542696	−	0.839929i
$201$	−13.3306			−0.940271
$202$	6.98614	−	11.8181i	0.491543	−	0.831522i
$203$	−2.94344	−	5.77683i	−0.206589	−	0.405454i
$204$	−14.2583	+	7.84576i	−0.998279	+	0.549313i
$205$	−1.48372	−	0.170370i	−0.103627	−	0.0118991i
$206$	−22.3371	−	1.40098i	−1.55630	−	0.0976108i
$207$	26.2414	+	26.2414i	1.82390	+	1.82390i
$208$	−7.31477	−	3.15864i	−0.507188	−	0.219013i
$209$	−0.401828	+	0.553069i	−0.0277951	+	0.0382566i
$210$	−8.40261	−	2.91611i	−0.579835	−	0.201231i
$211$	−1.68155	−	2.31445i	−0.115762	−	0.159333i	0.747204	−	0.664595i	$-0.231396\pi$
$211$	−1.68155	−	2.31445i	−0.115762	−	0.159333i	−0.862966	+	0.505262i	$0.831396\pi$
$212$	4.77939	+	3.24536i	0.328250	+	0.222892i
$213$	−1.97946	−	12.4978i	−0.135631	−	0.856338i
$214$	14.3655	−	3.69140i	0.982004	−	0.252339i
$215$	−6.78498	+	24.3826i	−0.462732	+	1.66288i
$216$	14.9330	+	2.83962i	1.01606	+	0.193211i
$217$	1.16891	+	0.595588i	0.0793507	+	0.0404312i
$218$	−8.01160	−	18.5039i	−0.542614	−	1.25324i
$219$	−11.9710	−	36.8428i	−0.808923	−	2.48961i
$220$	0.0643815	+	0.861907i	0.00434060	+	0.0581098i
$221$	−1.78080	+	5.48074i	−0.119789	+	0.368674i
$222$	27.6727	−	2.62126i	1.85727	−	0.175928i
$223$	−2.68090	+	16.9265i	−0.179526	+	1.13348i	0.719145	+	0.694860i	$0.244534\pi$
$223$	−2.68090	+	16.9265i	−0.179526	+	1.13348i	−0.898671	+	0.438624i	$0.855466\pi$
$224$	1.74284	−	5.38168i	0.116449	−	0.359579i
$225$	9.55418	+	22.6187i	0.636946	+	1.50792i
$226$	6.65452	+	2.63322i	0.442652	+	0.175159i
$227$	−23.4230	−	3.70984i	−1.55464	−	0.246231i	−0.680809	−	0.732461i	$-0.738371\pi$
$227$	−23.4230	−	3.70984i	−1.55464	−	0.246231i	−0.873830	+	0.486231i	$0.838371\pi$
$228$	−19.1100	−	5.54392i	−1.26559	−	0.367155i
$229$	16.6630	+	5.41413i	1.10112	+	0.357776i	0.802534	−	0.596606i	$-0.203485\pi$
$229$	16.6630	+	5.41413i	1.10112	+	0.357776i	0.298587	+	0.954382i	$0.403485\pi$
$230$	−23.5243	−	4.20695i	−1.55115	−	0.277398i
$231$	0.516975	−	0.167975i	0.0340144	−	0.0110520i
$232$	−17.2576	−	6.20176i	−1.13301	−	0.407165i
$233$	−1.42880	+	2.80418i	−0.0936040	+	0.183708i	−0.933061	−	0.359718i	$-0.882873\pi$
$233$	−1.42880	+	2.80418i	−0.0936040	+	0.183708i	0.839457	+	0.543426i	$0.182873\pi$
$234$	11.6786	−	7.41462i	0.763452	−	0.484709i
$235$	−3.51710	+	5.30362i	−0.229430	+	0.345970i
$236$	−0.945750	+	7.50982i	−0.0615631	+	0.488848i
$237$	−23.1578	+	3.66783i	−1.50426	+	0.238251i
$238$	−3.99311	−	0.891752i	−0.258835	−	0.0578037i
$239$	−0.302941	+	0.220100i	−0.0195957	+	0.0142371i	−0.597540	−	0.801839i	$-0.703855\pi$
$239$	−0.302941	+	0.220100i	−0.0195957	+	0.0142371i	0.577944	+	0.816076i	$0.303855\pi$
$240$	−22.9650	+	10.2699i	−1.48238	+	0.662919i
$241$	−6.61994	−	4.80967i	−0.426428	−	0.309818i	0.353791	−	0.935325i	$-0.384892\pi$
$241$	−6.61994	−	4.80967i	−0.426428	−	0.309818i	−0.780219	+	0.625506i	$0.784892\pi$
$242$	10.2549	+	11.6274i	0.659211	+	0.747436i
$243$	10.6381	−	10.6381i	0.682437	−	0.682437i
$244$	−7.80345	−	3.66833i	−0.499565	−	0.234841i
$245$	−1.09938	−	1.94714i	−0.0702369	−	0.124398i
$246$	2.04731	+	1.69302i	0.130532	+	0.107943i
$247$	−6.27794	+	3.19877i	−0.399456	+	0.203533i
$248$	3.56267	−	1.03730i	0.226229	−	0.0658686i
$249$		−	11.1639i		−	0.707485i
$250$	−13.3736	−	8.43485i	−0.845821	−	0.533467i
$251$			11.5932i			0.731756i	0.930663	+	0.365878i	$0.119231\pi$
$251$			11.5932i			0.731756i	−0.930663	+	0.365878i	$0.880769\pi$
$252$	6.02269	+	7.75819i	0.379394	+	0.488720i
$253$	1.30133	−	0.663062i	0.0818140	−	0.0416863i
$254$	−2.15250	+	2.60295i	−0.135060	+	0.163324i
$255$	8.94585	+	15.8442i	0.560211	+	0.992204i
$256$	−6.83493	−	14.4666i	−0.427183	−	0.904165i
$257$	15.5607	−	15.5607i	0.970648	−	0.970648i	−0.0289336	−	0.999581i	$-0.509211\pi$
$257$	15.5607	−	15.5607i	0.970648	−	0.970648i	0.999581	+	0.0289336i	$0.00921113\pi$
$258$	33.7649	−	29.7794i	2.10211	−	1.85399i
$259$	5.65361	+	4.10758i	0.351298	+	0.255233i
$260$	−3.44171	+	8.21634i	−0.213446	+	0.509556i
$261$	25.7582	−	18.7144i	1.59439	−	1.15839i
$262$	3.79202	−	16.9800i	0.234272	−	1.04903i
$263$	−26.3450	+	4.17263i	−1.62450	+	0.257296i	−0.901253	−	0.433293i	$-0.857352\pi$
$263$	−26.3450	+	4.17263i	−1.62450	+	0.257296i	−0.723248	+	0.690589i	$0.757352\pi$
$264$	0.739900	−	1.34773i	0.0455377	−	0.0829471i
$265$	3.56969	−	5.38293i	0.219285	−	0.330671i
$266$	−2.68127	−	4.22319i	−0.164399	−	0.258941i
$267$	23.6727	−	46.4603i	1.44875	−	2.84333i
$268$	−9.47441	+	0.301426i	−0.578742	+	0.0184125i
$269$	11.8026	−	3.83490i	0.719618	−	0.233818i	0.0737606	−	0.997276i	$-0.476500\pi$
$269$	11.8026	−	3.83490i	0.719618	−	0.233818i	0.645858	+	0.763458i	$0.276500\pi$
$270$	2.99178	−	16.7294i	0.182074	−	1.01812i
$271$	−2.15035	−	0.698692i	−0.130625	−	0.0424425i	0.242975	−	0.970033i	$-0.421877\pi$
$271$	−2.15035	−	0.698692i	−0.130625	−	0.0424425i	−0.373600	+	0.927590i	$0.621877\pi$
$272$	−9.95630	+	5.89857i	−0.603689	+	0.357653i
$273$	5.53347	+	0.876415i	0.334901	+	0.0530430i
$274$	−11.9609	+	30.2268i	−0.722583	+	1.82607i
$275$	0.962796	−	0.0825282i	0.0580588	−	0.00497664i
$276$	30.9998	+	29.0882i	1.86597	+	1.75090i
$277$	−1.05832	+	6.68197i	−0.0635883	+	0.401480i	0.935280	+	0.353910i	$0.115148\pi$
$277$	−1.05832	+	6.68197i	−0.0635883	+	0.401480i	−0.998868	+	0.0475708i	$0.984852\pi$
$278$	2.27513	+	24.0186i	0.136453	+	1.44054i
$279$	−1.99081	+	6.12710i	−0.119187	+	0.366820i
$280$	−6.03788	−	1.88256i	−0.360832	−	0.112504i
$281$	10.0650	+	30.9770i	0.600430	+	1.84793i	0.525590	+	0.850738i	$0.323845\pi$
$281$	10.0650	+	30.9770i	0.600430	+	1.84793i	0.0748397	+	0.997196i	$0.476155\pi$
$282$	10.3884	−	4.49785i	0.618619	−	0.267843i
$283$	−8.49665	−	4.32926i	−0.505073	−	0.257348i	0.182837	−	0.983143i	$-0.441472\pi$
$283$	−8.49665	−	4.32926i	−0.505073	−	0.257348i	−0.687911	+	0.725795i	$0.741472\pi$
$284$	−1.68945	−	8.83776i	−0.100250	−	0.524425i
$285$	−5.96397	+	21.4322i	−0.353275	+	1.26953i
$286$	−0.135495	−	0.527293i	−0.00801199	−	0.0311795i
$287$	0.104482	+	0.659675i	0.00616740	+	0.0389394i
$288$	27.4417	+	4.31905i	1.61701	+	0.254502i
$289$	−5.07255	−	6.98177i	−0.298385	−	0.410692i
$290$	−6.72209	+	19.3693i	−0.394735	+	1.13740i
$291$	−24.2518	+	33.3798i	−1.42167	+	1.95676i
$292$	−9.34113	−	25.9144i	−0.546648	−	1.51653i
$293$	3.82305	+	3.82305i	0.223345	+	0.223345i	0.809905	−	0.586560i	$-0.199518\pi$
$293$	3.82305	+	3.82305i	0.223345	+	0.223345i	−0.586560	+	0.809905i	$0.699518\pi$
$294$	−0.248987	+	3.96983i	−0.0145212	+	0.231525i
$295$	8.40731	+	0.965379i	0.489492	+	0.0562066i
$296$	19.6084	−	2.48872i	1.13972	−	0.144654i
$297$	0.471537	+	0.925444i	0.0273614	+	0.0536997i
$298$	4.33744	+	2.56402i	0.251261	+	0.148530i
$299$	15.0529			0.870534
$300$	11.7625	+	25.5484i	0.679111	+	1.47504i
$301$	11.3185			0.652390
$302$	−16.2490	−	9.60537i	−0.935024	−	0.552727i
$303$	12.3956	+	24.3277i	0.712109	+	1.39759i
$304$	−13.7073	−	3.50810i	−0.786167	−	0.201203i
$305$	−4.00554	+	8.76891i	−0.229356	+	0.502106i
$306$	1.25771	−	20.0528i	0.0718985	−	1.14634i
$307$	19.2149	+	19.2149i	1.09665	+	1.09665i	0.994799	+	0.101856i	$0.0324780\pi$
$307$	19.2149	+	19.2149i	1.09665	+	1.09665i	0.101856	+	0.994799i	$0.467522\pi$
$308$	0.363628	−	0.131074i	0.0207196	−	0.00746862i
$309$	26.1633	−	36.0106i	1.48838	−	2.04857i
$310$	−1.20328	−	3.97024i	−0.0683418	−	0.225495i
$311$	8.08637	+	11.1299i	0.458536	+	0.631121i	0.974204	−	0.225668i	$-0.0724563\pi$
$311$	8.08637	+	11.1299i	0.458536	+	0.631121i	−0.515668	+	0.856788i	$0.672456\pi$
$312$	13.1008	−	8.91445i	0.741687	−	0.504682i
$313$	−4.10087	−	25.8919i	−0.231795	−	1.46350i	−0.779278	−	0.626679i	$-0.784414\pi$
$313$	−4.10087	−	25.8919i	−0.231795	−	1.46350i	0.547483	−	0.836817i	$-0.315586\pi$
$314$	3.15201	+	12.2664i	0.177878	+	0.692233i
$315$	8.59967	−	6.82815i	0.484536	−	0.384723i
$316$	−16.3759	+	3.13045i	−0.921214	+	0.176101i
$317$	−9.51074	−	4.84596i	−0.534176	−	0.272176i	0.166025	−	0.986121i	$-0.446907\pi$
$317$	−9.51074	−	4.84596i	−0.534176	−	0.272176i	−0.700202	+	0.713945i	$0.746907\pi$
$318$	−10.5437	+	4.56511i	−0.591263	+	0.255999i
$319$	−0.387209	−	1.19171i	−0.0216795	−	0.0667227i
$320$	−16.0896	+	7.81833i	−0.899433	+	0.437058i
$321$	−9.11552	+	28.0547i	−0.508779	+	1.56586i
$322$	1.00783	+	10.6397i	0.0561641	+	0.592926i
$323$	−1.60090	+	10.1077i	−0.0890766	+	0.562408i
$324$	−0.524548	+	0.559021i	−0.0291415	+	0.0310567i
$325$	9.22773	+	3.74713i	0.511862	+	0.207853i
$326$	2.08586	−	5.27128i	0.115525	−	0.291949i
$327$	39.6083	+	6.27334i	2.19035	+	0.346917i
$328$	1.49336	+	1.15697i	0.0824569	+	0.0638833i
$329$	2.70670	+	0.879460i	0.149225	+	0.0484862i
$330$	−1.51578	−	0.810684i	−0.0834407	−	0.0446267i
$331$	19.6171	−	6.37399i	1.07825	−	0.350346i	0.284557	−	0.958659i	$-0.408154\pi$
$331$	19.6171	−	6.37399i	1.07825	−	0.350346i	0.793697	+	0.608313i	$0.208154\pi$
$332$	−0.252433	−	7.93448i	−0.0138541	−	0.435461i
$333$	−15.5799	+	30.5772i	−0.853771	+	1.67562i
$334$	11.6908	+	18.4139i	0.639693	+	1.00756i
$335$	0.452973	+	10.5884i	0.0247486	+	0.578506i
$336$	7.17802	+	8.66304i	0.391593	+	0.472607i
$337$	18.2755	−	2.89455i	0.995530	−	0.157676i	0.362649	−	0.931926i	$-0.381872\pi$
$337$	18.2755	−	2.89455i	0.995530	−	0.157676i	0.632881	+	0.774249i	$0.281872\pi$
$338$	−2.78406	+	12.4665i	−0.151433	+	0.678091i
$339$	−11.5148	+	8.36600i	−0.625398	+	0.454379i
$340$	6.71630	+	11.0586i	0.364242	+	0.599737i
$341$	0.205121	+	0.149029i	0.0111079	+	0.00807040i
$342$	18.4240	−	16.2493i	0.996254	−	0.878660i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	23.3242	−	21.9284i	1.25756	−	1.18230i
$345$	32.1401	−	35.0129i	1.73036	−	1.88503i
$346$	5.56223	−	6.72624i	0.299027	−	0.361605i
$347$	7.18732	−	3.66212i	0.385836	−	0.196593i	−0.250303	−	0.968167i	$-0.580530\pi$
$347$	7.18732	−	3.66212i	0.385836	−	0.196593i	0.636139	+	0.771574i	$0.280530\pi$
$348$	28.8091	−	22.3645i	1.54433	−	1.19886i
$349$		−	8.72892i		−	0.467248i	−0.972327	−	0.233624i	$-0.924942\pi$
$349$		−	8.72892i		−	0.467248i	0.972327	−	0.233624i	$-0.0750585\pi$
$350$	−2.03072	+	6.77320i	−0.108546	+	0.362043i
$351$			10.7049i			0.571387i
$352$	0.495391	−	0.974595i	0.0264044	−	0.0519461i
$353$	−4.29662	+	2.18924i	−0.228686	+	0.116521i	−0.564580	−	0.825379i	$-0.690962\pi$
$353$	−4.29662	+	2.18924i	−0.228686	+	0.116521i	0.335894	+	0.941900i	$0.390962\pi$
$354$	−11.6009	−	9.59328i	−0.616579	−	0.509877i
$355$	−9.85964	+	1.99694i	−0.523295	+	0.105987i
$356$	15.7742	−	33.5558i	0.836033	−	1.77845i
$357$	5.75385	−	5.75385i	0.304526	−	0.304526i
$358$	21.2046	+	24.0425i	1.12070	+	1.27068i
$359$	−11.3025	−	8.21177i	−0.596525	−	0.433400i	0.248119	−	0.968730i	$-0.420188\pi$
$359$	−11.3025	−	8.21177i	−0.596525	−	0.433400i	−0.844644	+	0.535329i	$0.820188\pi$
$360$	4.49260	−	30.7317i	0.236781	−	1.61970i
$361$	5.24868	−	3.81339i	0.276246	−	0.200705i
$362$	−8.29626	−	1.85274i	−0.436042	−	0.0973781i
$363$	−30.4540	+	4.82344i	−1.59842	+	0.253165i
$364$	3.95259	+	0.497769i	0.207172	+	0.0260902i
$365$	−28.8571	+	10.7603i	−1.51045	+	0.563221i
$366$	14.4775	−	9.19165i	0.756751	−	0.480455i
$367$	−3.13448	+	6.15176i	−0.163618	+	0.321119i	−0.958230	−	0.285999i	$-0.907675\pi$
$367$	−3.13448	+	6.15176i	−0.163618	+	0.321119i	0.794611	+	0.607118i	$0.207675\pi$
$368$	22.6901	+	19.9727i	1.18280	+	1.04115i
$369$	−3.11936	+	1.01354i	−0.162387	+	0.0527629i
$370$	−3.02236	−	21.8911i	−0.157125	−	1.13806i
$371$	−2.74718	−	0.892612i	−0.142626	−	0.0463421i
$372$	−2.05612	+	7.08748i	−0.106605	+	0.367469i
$373$	−33.3777	−	5.28651i	−1.72823	−	0.273725i	−0.788351	−	0.615226i	$-0.789065\pi$
$373$	−33.3777	−	5.28651i	−1.72823	−	0.273725i	−0.939882	+	0.341501i	$0.889065\pi$
$374$	−0.735267	−	0.290948i	−0.0380198	−	0.0150446i
$375$	28.4182	−	13.4629i	1.46751	−	0.695222i
$376$	7.28157	−	3.43163i	0.375518	−	0.176973i
$377$	2.02027	−	12.7555i	0.104049	−	0.656941i
$378$	−7.56643	+	0.716719i	−0.389175	+	0.0368641i
$379$	−3.01033	+	9.26483i	−0.154630	+	0.475903i	−0.998123	−	0.0612375i	$-0.980495\pi$
$379$	−3.01033	+	9.26483i	−0.154630	+	0.475903i	0.843493	+	0.537140i	$0.180495\pi$
$380$	−3.75413	+	15.3672i	−0.192583	+	0.788323i
$381$	−2.07583	−	6.38876i	−0.106348	−	0.327306i
$382$	9.65559	+	22.3009i	0.494023	+	1.14101i
$383$	−13.0952	−	6.67234i	−0.669134	−	0.340941i	0.0862030	−	0.996278i	$-0.472527\pi$
$383$	−13.0952	−	6.67234i	−0.669134	−	0.340941i	−0.755337	+	0.655337i	$0.772527\pi$
$384$	31.5755	+	3.94535i	1.61133	+	0.201335i
$385$	−0.150988	−	0.404920i	−0.00769505	−	0.0206366i
$386$	−29.8836	+	7.67900i	−1.52104	+	0.390851i
$387$	8.69504	+	54.8983i	0.441994	+	2.79064i
$388$	−16.4816	+	24.2722i	−0.836727	+	1.23223i
$389$	−2.16236	−	2.97623i	−0.109636	−	0.150901i	0.750673	−	0.660674i	$-0.229729\pi$
$389$	−2.16236	−	2.97623i	−0.109636	−	0.150901i	−0.860309	+	0.509773i	$0.829729\pi$
$390$	−10.1265	−	14.5371i	−0.512773	−	0.736117i
$391$	12.8510	−	17.6879i	0.649902	−	0.894513i
$392$	−0.0871975	+	2.82708i	−0.00440414	+	0.142789i
$393$	24.4672	+	24.4672i	1.23421	+	1.23421i
$394$	−37.7107	−	2.36521i	−1.89984	−	0.119157i
$395$	3.70022	+	18.2693i	0.186178	+	0.919230i
$396$	0.915091	+	1.66301i	0.0459850	+	0.0835696i
$397$	−12.7621	−	25.0470i	−0.640510	−	1.25707i	−0.951789	−	0.306754i	$-0.900757\pi$
$397$	−12.7621	−	25.0470i	−0.640510	−	1.25707i	0.311279	−	0.950319i	$-0.399243\pi$
$398$	13.7240	−	23.2164i	0.687924	−	1.16373i
$399$	9.94895			0.498071
$400$	8.93761	+	17.8919i	0.446881	+	0.894594i
$401$	−5.31994			−0.265665			−0.132833	−	0.991138i	$-0.542407\pi$
$401$	−5.31994			−0.265665			−0.132833	+	0.991138i	$0.542407\pi$
$402$	9.59349	−	16.2289i	0.478480	−	0.809424i
$403$	1.18635	+	2.32835i	0.0590965	+	0.115983i
$404$	9.35994	+	17.0100i	0.465674	+	0.846280i
$405$	0.631389	+	0.579583i	0.0313740	+	0.0287997i
$406$	9.15106	+	0.573953i	0.454159	+	0.0284848i
$407$	0.955007	+	0.955007i	0.0473380	+	0.0473380i
$408$	0.709541	−	23.0045i	0.0351275	−	1.13889i
$409$	−13.4972	+	18.5773i	−0.667394	+	0.918589i	−0.999698	−	0.0245833i	$-0.992174\pi$
$409$	−13.4972	+	18.5773i	−0.667394	+	0.918589i	0.332304	+	0.943172i	$0.392174\pi$
$410$	1.27518	−	1.68369i	0.0629765	−	0.0831514i
$411$	−38.0009	−	52.3037i	−1.87445	−	2.57995i
$412$	17.7806	−	26.1852i	0.875988	−	1.29005i
$413$	−0.592037	−	3.73797i	−0.0291322	−	0.183934i
$414$	−50.8314	+	13.0618i	−2.49823	+	0.641953i
$415$	−8.86739	+	0.379349i	−0.435283	+	0.0186215i
$416$	9.10950	−	6.63195i	0.446630	−	0.325158i
$417$	−42.7526	−	21.7835i	−2.09360	−	1.06674i
$418$	−0.384135	−	0.887211i	−0.0187887	−	0.0433949i
$419$	6.34079	+	19.5149i	0.309768	+	0.953367i	0.977855	+	0.209284i	$0.0671133\pi$
$419$	6.34079	+	19.5149i	0.309768	+	0.953367i	−0.668087	+	0.744083i	$0.732887\pi$
$420$	9.59711	−	8.13085i	0.468291	−	0.396745i
$421$	−7.91193	+	24.3504i	−0.385604	+	1.18677i	0.550437	+	0.834877i	$0.314461\pi$
$421$	−7.91193	+	24.3504i	−0.385604	+	1.18677i	−0.936041	+	0.351891i	$0.885539\pi$
$422$	4.02778	−	0.381525i	0.196069	−	0.0185724i
$423$	−2.18633	+	13.8039i	−0.106303	+	0.671169i
$424$	−7.39047	+	3.48294i	−0.358913	+	0.169147i
$425$	12.2809	−	7.64398i	0.595712	−	0.370788i
$426$	16.6396	+	6.58434i	0.806190	+	0.319012i
$427$	4.25826	+	0.674442i	0.206072	+	0.0326385i
$428$	−5.84426	+	20.1453i	−0.282493	+	0.973758i
$429$	1.02976	+	0.334590i	0.0497174	+	0.0161542i
$430$	−24.8008	−	25.8072i	−1.19600	−	1.24453i
$431$	−13.7894	+	4.48044i	−0.664211	+	0.215815i	−0.621670	−	0.783279i	$-0.713545\pi$
$431$	−13.7894	+	4.48044i	−0.664211	+	0.215815i	−0.0425414	+	0.999095i	$0.513545\pi$
$432$	−14.2036	+	16.1361i	−0.683372	+	0.776348i
$433$	1.84854	−	3.62796i	0.0888351	−	0.174349i	−0.842314	−	0.538987i	$-0.818807\pi$
$433$	1.84854	−	3.62796i	0.0888351	−	0.174349i	0.931149	+	0.364638i	$0.118807\pi$
$434$	−1.56629	+	0.994424i	−0.0751843	+	0.0477339i
$435$	−25.3555	−	31.9338i	−1.21570	−	1.53111i
$436$	28.2924	+	3.56301i	1.35496	+	0.170637i
$437$	26.4023	−	4.18171i	1.26299	−	0.200038i
$438$	53.4679	+	11.9406i	2.55480	+	0.570544i
$439$	−13.7298	+	9.97530i	−0.655288	+	0.476095i	−0.865069	−	0.501654i	$-0.832725\pi$
$439$	−13.7298	+	9.97530i	−0.655288	+	0.476095i	0.209780	+	0.977749i	$0.432725\pi$
$440$	−1.09563	−	0.541899i	−0.0522321	−	0.0258340i
$441$	−3.97289	−	2.88647i	−0.189185	−	0.137451i
$442$	−5.39075	−	6.11222i	−0.256412	−	0.290729i
$443$	7.82885	−	7.82885i	0.371960	−	0.371960i	−0.496231	−	0.868191i	$-0.665283\pi$
$443$	7.82885	−	7.82885i	0.371960	−	0.371960i	0.868191	+	0.496231i	$0.165283\pi$
$444$	−16.7237	+	35.5756i	−0.793673	+	1.68834i
$445$	−37.7074	−	17.2243i	−1.78750	−	0.816509i
$446$	−18.6772	−	15.4451i	−0.884393	−	0.731345i
$447$	−8.92864	+	4.54937i	−0.422310	+	0.215178i
$448$	5.29748	+	5.99473i	0.250282	+	0.283224i
$449$		−	30.6183i		−	1.44497i	−0.691389	−	0.722483i	$-0.743001\pi$
$449$		−	30.6183i		−	1.44497i	0.691389	−	0.722483i	$-0.256999\pi$
$450$	−34.4121	−	4.64635i	−1.62220	−	0.219031i
$451$			0.129082i			0.00607821i
$452$	−7.99469	+	6.20628i	−0.376038	+	0.291919i
$453$	33.4486	−	17.0429i	1.57155	−	0.800747i
$454$	21.3729	−	25.8456i	1.00308	−	1.21300i
$455$	0.508101	−	4.42495i	0.0238201	−	0.207445i
$456$	20.5019	−	19.2750i	0.960088	−	0.902635i
$457$	−1.35049	+	1.35049i	−0.0631734	+	0.0631734i	−0.737988	−	0.674814i	$-0.764224\pi$
$457$	−1.35049	+	1.35049i	−0.0631734	+	0.0631734i	0.674814	+	0.737988i	$0.264224\pi$
$458$	−18.5829	+	16.3894i	−0.868321	+	0.765827i
$459$	12.5788	+	9.13900i	0.587126	+	0.426572i
$460$	22.0510	−	25.6113i	1.02814	−	1.19413i
$461$	14.5967	−	10.6051i	0.679837	−	0.493931i	−0.193467	−	0.981107i	$-0.561973\pi$
$461$	14.5967	−	10.6051i	0.679837	−	0.493931i	0.873304	+	0.487176i	$0.161973\pi$
$462$	−0.167549	+	0.750256i	−0.00779510	+	0.0349051i
$463$	−33.0145	+	5.22898i	−1.53431	+	0.243011i	−0.865687	−	0.500586i	$-0.833118\pi$
$463$	−33.0145	+	5.22898i	−1.53431	+	0.243011i	−0.668627	+	0.743598i	$0.733118\pi$
$464$	19.9696	−	16.5464i	0.927067	−	0.768149i
$465$	7.94874	+	2.21191i	0.368614	+	0.102575i
$466$	−2.38560	−	3.75749i	−0.110511	−	0.174062i
$467$	−11.1914	+	21.9643i	−0.517875	+	1.01639i	0.472931	+	0.881099i	$0.343196\pi$
$467$	−11.1914	+	21.9643i	−0.517875	+	1.01639i	−0.990806	+	0.135288i	$0.956804\pi$
$468$	0.622093	+	19.5536i	0.0287563	+	0.903867i
$469$	4.50763	−	1.46462i	0.208143	−	0.0676298i
$470$	−3.92559	−	8.09854i	−0.181074	−	0.373558i
$471$	−23.9553	−	7.78356i	−1.10380	−	0.358648i
$472$	−8.46193	−	6.55586i	−0.389492	−	0.301758i
$473$	2.16055	+	0.342197i	0.0993422	+	0.0157343i
$474$	12.2004	−	30.8321i	0.560382	−	1.41617i
$475$	17.2260	+	4.00886i	0.790384	+	0.183939i
$476$	3.95930	−	4.21950i	0.181474	−	0.193401i
$477$	2.21902	−	14.0104i	0.101602	−	0.641490i
$478$	−0.0499384	−	0.527201i	−0.00228413	−	0.0241136i
$479$	4.66904	−	14.3698i	0.213334	−	0.656574i	−0.785934	−	0.618311i	$-0.787817\pi$
$479$	4.66904	−	14.3698i	0.213334	−	0.656574i	0.999268	−	0.0382635i	$-0.0121826\pi$
$480$	4.02421	−	35.3487i	0.183679	−	1.61344i
$481$	4.30148	+	13.2386i	0.196131	+	0.603629i
$482$	10.6194	−	4.59789i	0.483702	−	0.209428i
$483$	−18.9384	−	9.64960i	−0.861727	−	0.439072i
$484$	−21.5353	+	4.11675i	−0.978879	+	0.187125i
$485$	27.3373	+	18.1287i	1.24132	+	0.823184i
$486$	5.29520	+	20.6068i	0.240195	+	0.934745i
$487$	1.22289	+	7.72102i	0.0554144	+	0.349873i	0.999780	+	0.0209753i	$0.00667713\pi$
$487$	1.22289	+	7.72102i	0.0554144	+	0.349873i	−0.944366	+	0.328898i	$0.893323\pi$
$488$	10.0817	−	6.86008i	0.456376	−	0.310541i
$489$	6.62700	+	9.12128i	0.299683	+	0.412478i
$490$	3.16165	+	0.0628736i	0.142829	+	0.00284034i
$491$	−17.6441	+	24.2850i	−0.796267	+	1.09597i	0.197032	+	0.980397i	$0.436870\pi$
$491$	−17.6441	+	24.2850i	−0.796267	+	1.09597i	−0.993299	+	0.115571i	$0.963130\pi$
$492$	−3.53446	+	1.27403i	−0.159346	+	0.0574379i
$493$	−13.2635	−	13.2635i	−0.597358	−	0.597358i
$494$	0.623741	−	9.94486i	0.0280634	−	0.447441i
$495$	1.84799	−	1.04340i	0.0830611	−	0.0468974i
$496$	−1.30108	+	5.08373i	−0.0584200	+	0.228266i
$497$	2.04246	+	4.00855i	0.0916167	+	0.179808i
$498$	13.5911	+	8.03420i	0.609032	+	0.360021i
$499$	9.66277			0.432565			0.216283	−	0.976331i	$-0.430607\pi$
$499$	9.66277			0.432565			0.216283	+	0.976331i	$0.430607\pi$
$500$	19.8931	−	10.2110i	0.889647	−	0.456650i
$501$	−43.3792			−1.93804
$502$	−14.1137	−	8.34313i	−0.629926	−	0.372372i
$503$	−5.32908	−	10.4589i	−0.237612	−	0.466340i	0.741150	−	0.671339i	$-0.234281\pi$
$503$	−5.32908	−	10.4589i	−0.237612	−	0.466340i	−0.978762	+	0.205000i	$0.934281\pi$
$504$	−13.7792	+	1.74887i	−0.613774	+	0.0779007i
$505$	18.9021	−	10.6723i	0.841131	−	0.474913i
$506$	−0.129293	+	2.06143i	−0.00574777	+	0.0916419i
$507$	−17.9636	−	17.9636i	−0.797792	−	0.797792i
$508$	−1.61981	−	4.49371i	−0.0718672	−	0.199376i
$509$	16.2315	−	22.3408i	0.719449	−	0.990237i	−0.280093	−	0.959973i	$-0.590365\pi$
$509$	16.2315	−	22.3408i	0.719449	−	0.990237i	0.999542	−	0.0302641i	$-0.00963483\pi$
$510$	−25.7269	−	0.511614i	−1.13921	−	0.0226546i
$511$	8.09574	+	11.1428i	0.358134	+	0.492930i
$512$	22.5307	+	2.09009i	0.995725	+	0.0923697i
$513$	2.97383	+	18.7760i	0.131298	+	0.828982i
$514$	7.74541	+	30.1421i	0.341635	+	1.32951i
$515$	−29.4919	−	19.5576i	−1.29957	−	0.861809i
$516$	11.9547	+	62.5368i	0.526276	+	2.75303i
$517$	0.490081	+	0.249709i	0.0215538	+	0.0109822i
$518$	−9.06928	+	3.92672i	−0.398481	+	0.172530i
$519$	5.36413	+	16.5091i	0.235459	+	0.724668i
$520$	−7.52582	−	10.1029i	−0.330029	−	0.443043i
$521$	−5.38376	+	16.5695i	−0.235867	+	0.725923i	0.761139	+	0.648589i	$0.224641\pi$
$521$	−5.38376	+	16.5695i	−0.235867	+	0.725923i	−0.997005	+	0.0773338i	$0.975359\pi$
$522$	4.24611	+	44.8263i	0.185847	+	1.96199i
$523$	3.45463	−	21.8117i	0.151061	−	0.953759i	−0.789406	−	0.613872i	$-0.789611\pi$
$523$	3.45463	−	21.8117i	0.151061	−	0.953759i	0.940466	−	0.339887i	$-0.110389\pi$
$524$	17.9427	+	16.8362i	0.783830	+	0.735494i
$525$	−9.20751	−	10.6297i	−0.401849	−	0.463919i
$526$	13.8795	−	35.0756i	0.605176	−	1.52937i
$527$	3.74873	+	0.593740i	0.163297	+	0.0258637i
$528$	1.10827	+	1.87067i	0.0482313	+	0.0814103i
$529$	−32.4398	−	10.5403i	−1.41043	−	0.458276i
$530$	3.98429	+	8.21966i	0.173067	+	0.357039i
$531$	17.6755	−	5.74312i	0.767051	−	0.249230i
$532$	7.07096	−	0.224961i	0.306565	−	0.00975328i
$533$	−0.603984	+	1.18539i	−0.0261614	+	0.0513447i
$534$	39.5252	+	62.2550i	1.71042	+	2.69404i
$535$	22.5933	+	6.28707i	0.976793	+	0.271814i
$536$	6.45137	−	11.7512i	0.278657	−	0.507574i
$537$	−62.9712	+	9.97366i	−2.71741	+	0.430395i
$538$	−3.82518	+	17.1285i	−0.164915	+	0.738461i
$539$	−0.156355	+	0.113598i	−0.00673468	+	0.00489303i
$540$	18.2135	+	15.6816i	0.783784	+	0.674830i
$541$	18.3679	+	13.3451i	0.789700	+	0.573750i	0.907874	−	0.419242i	$-0.137704\pi$
$541$	18.3679	+	13.3451i	0.789700	+	0.573750i	−0.118175	+	0.992993i	$0.537704\pi$
$542$	2.39811	−	2.11505i	0.103008	−	0.0908491i
$543$	11.9545	−	11.9545i	0.513015	−	0.513015i
$544$	−0.0158771	−	16.3659i	−0.000680724	−	0.701681i
$545$	3.63696	−	31.6736i	0.155790	−	1.35675i
$546$	−5.04916	+	6.10579i	−0.216084	+	0.261304i
$547$	−6.08024	+	3.09804i	−0.259972	+	0.132463i	−0.579120	−	0.815243i	$-0.696604\pi$
$547$	−6.08024	+	3.09804i	−0.259972	+	0.132463i	0.319147	+	0.947705i	$0.396604\pi$
$548$	−28.1908	−	36.3143i	−1.20425	−	1.55127i
$549$			21.1719i			0.903597i
$550$	−0.592412	+	1.23151i	−0.0252605	+	0.0525118i
$551$		−	22.9339i		−	0.977015i
$552$	−57.7215	+	16.8061i	−2.45679	+	0.715315i
$553$	7.42760	−	3.78455i	0.315854	−	0.160935i
$554$	−7.37308	−	6.09714i	−0.313252	−	0.259042i
$555$	39.9770	+	18.2610i	1.69693	+	0.775138i
$556$	−30.8778	−	14.5154i	−1.30951	−	0.615589i
$557$	−24.2714	+	24.2714i	−1.02841	+	1.02841i	−0.0288284	+	0.999584i	$0.509178\pi$
$557$	−24.2714	+	24.2714i	−1.02841	+	1.02841i	−0.999584	+	0.0288284i	$0.990822\pi$
$558$	−6.02650	−	6.83305i	−0.255122	−	0.289266i
$559$	18.2396	+	13.2519i	0.771454	+	0.560494i
$560$	6.63705	−	5.99579i	0.280467	−	0.253369i
$561$	1.27229	−	0.924370i	0.0537160	−	0.0390269i
$562$	−44.9552	−	10.0395i	−1.89632	−	0.423491i
$563$	7.26737	−	1.15104i	0.306283	−	0.0485105i	−0.00140101	−	0.999999i	$-0.500446\pi$
$563$	7.26737	−	1.15104i	0.306283	−	0.0485105i	0.307684	+	0.951489i	$0.400446\pi$
$564$	−2.00034	+	15.8839i	−0.0842293	+	0.668831i
$565$	7.03629	+	8.86181i	0.296019	+	0.372819i
$566$	11.3852	−	7.22835i	0.478554	−	0.303830i
$567$	0.174011	−	0.341517i	0.00730779	−	0.0143424i
$568$	11.9750	+	4.30340i	0.502461	+	0.180567i
$569$	0.705433	−	0.229209i	0.0295733	−	0.00960895i	−0.294193	−	0.955746i	$-0.595051\pi$
$569$	0.705433	−	0.229209i	0.0295733	−	0.00960895i	0.323766	+	0.946137i	$0.395051\pi$
$570$	−21.7998	−	22.6845i	−0.913094	−	0.950147i
$571$	14.1569	+	4.59986i	0.592448	+	0.192498i	0.589869	−	0.807499i	$-0.299179\pi$
$571$	14.1569	+	4.59986i	0.592448	+	0.192498i	0.00257852	+	0.999997i	$0.499179\pi$
$572$	0.739443	+	0.214517i	0.0309177	+	0.00896941i
$573$	−47.7360	−	7.56064i	−1.99420	−	0.315850i
$574$	−0.878289	−	0.347542i	−0.0366591	−	0.0145061i
$575$	−28.9025	−	24.3388i	−1.20532	−	1.01500i
$576$	−25.0066	+	30.2996i	−1.04194	+	1.26248i
$577$	2.34744	−	14.8211i	0.0977252	−	0.617012i	−0.889408	−	0.457114i	$-0.848883\pi$
$577$	2.34744	−	14.8211i	0.0977252	−	0.617012i	0.987133	−	0.159899i	$-0.0511168\pi$
$578$	12.1502	−	1.15091i	0.505381	−	0.0478715i
$579$	18.9625	−	58.3605i	0.788053	−	2.42538i
$580$	−18.7428	−	22.1228i	−0.778254	−	0.918600i
$581$	1.22656	+	3.77498i	0.0508865	+	0.156612i
$582$	−23.1840	−	53.5465i	−0.961007	−	2.21957i
$583$	−0.497411	−	0.253443i	−0.0206006	−	0.0104965i
$584$	38.2710	+	7.27749i	1.58366	+	0.301145i
$585$	21.8527	−	0.934862i	0.903498	−	0.0386518i
$586$	−7.40552	+	1.90295i	−0.305919	+	0.0786099i
$587$	−5.38898	−	34.0247i	−0.222427	−	1.40435i	−0.805820	−	0.592160i	$-0.798275\pi$
$587$	−5.38898	−	34.0247i	−0.222427	−	1.40435i	0.583393	−	0.812190i	$-0.301725\pi$
$588$	−4.65373	−	3.16003i	−0.191917	−	0.130318i
$589$	2.72764	+	3.75427i	0.112390	+	0.154692i
$590$	−7.22564	+	9.54042i	−0.297475	+	0.392773i
$591$	44.1702	−	60.7951i	1.81692	−	2.50078i
$592$	−11.0815	+	25.6626i	−0.455449	+	1.05473i
$593$	−2.66144	−	2.66144i	−0.109292	−	0.109292i	0.650346	−	0.759638i	$-0.274624\pi$
$593$	−2.66144	−	2.66144i	−0.109292	−	0.109292i	−0.759638	+	0.650346i	$0.774624\pi$
$594$	−1.46599	−	0.0919469i	−0.0601504	−	0.00377263i
$595$	−4.76574	−	4.37471i	−0.195376	−	0.179346i
$596$	−6.24293	+	3.43524i	−0.255721	+	0.140713i
$597$	24.3508	+	47.7910i	0.996610	+	1.95596i
$598$	−10.8330	+	18.3256i	−0.442993	+	0.749391i
$599$	22.6799			0.926676			0.463338	−	0.886182i	$-0.346652\pi$
$599$	22.6799			0.926676			0.463338	+	0.886182i	$0.346652\pi$
$600$	−39.5679	−	4.06618i	−1.61535	−	0.166001i
$601$	−10.1159			−0.412635			−0.206317	−	0.978485i	$-0.566148\pi$
$601$	−10.1159			−0.412635			−0.206317	+	0.978485i	$0.566148\pi$
$602$	−8.14547	+	13.7793i	−0.331984	+	0.561604i
$603$	10.5667	+	20.7382i	0.430308	+	0.844526i
$604$	23.3874	−	12.8692i	0.951620	−	0.523638i
$605$	4.86603	+	24.0254i	0.197832	+	0.976772i
$606$	−38.5375	−	2.41707i	−1.56548	−	0.0981866i
$607$	−18.3845	−	18.3845i	−0.746206	−	0.746206i	0.227559	−	0.973764i	$-0.426926\pi$
$607$	−18.3845	−	18.3845i	−0.746206	−	0.746206i	−0.973764	+	0.227559i	$0.926926\pi$
$608$	14.1353	−	14.1628i	0.573264	−	0.574377i
$609$	−10.7186	+	14.7528i	−0.434338	+	0.597815i
$610$	−7.79277	−	11.1870i	−0.315520	−	0.452948i
$611$	3.33212	+	4.58627i	0.134803	+	0.185541i
$612$	23.5074	+	15.9623i	0.950232	+	0.645238i
$613$	0.273273	+	1.72538i	0.0110374	+	0.0696874i	0.992592	−	0.121493i	$-0.0387683\pi$
$613$	0.273273	+	1.72538i	0.0110374	+	0.0696874i	−0.981555	+	0.191181i	$0.938768\pi$
$614$	−37.2207	+	9.56435i	−1.50210	+	0.385986i
$615$	1.46760	+	3.93582i	0.0591793	+	0.158707i
$616$	−0.102117	+	0.537014i	−0.00411441	+	0.0216369i
$617$	−41.2822	−	21.0344i	−1.66196	−	0.846811i	−0.994794	−	0.101902i	$-0.967507\pi$
$617$	−41.2822	−	21.0344i	−1.66196	−	0.846811i	−0.667166	−	0.744909i	$-0.732493\pi$
$618$	25.0112	+	57.7668i	1.00610	+	2.32372i
$619$	−13.8374	−	42.5873i	−0.556174	−	1.71173i	−0.692823	−	0.721108i	$-0.743633\pi$
$619$	−13.8374	−	42.5873i	−0.556174	−	1.71173i	0.136649	−	0.990620i	$-0.456367\pi$
$620$	5.69937	+	1.39232i	0.228892	+	0.0559170i
$621$	12.5502	−	38.6256i	0.503623	−	1.54999i
$622$	−19.3691	+	1.83471i	−0.776632	+	0.0735653i
$623$	−2.90018	+	18.3110i	−0.116193	+	0.733615i
$624$	1.42448	+	22.3644i	0.0570248	+	0.895294i
$625$	−11.6591	−	22.1148i	−0.466364	−	0.884593i
$626$	34.4723	+	13.6408i	1.37779	+	0.545197i
$627$	1.89911	+	0.300790i	0.0758433	+	0.0120124i
$628$	−17.2016	−	4.99030i	−0.686420	−	0.199135i
$629$	19.2282	+	6.24762i	0.766678	+	0.249109i
$630$	2.12386	+	15.3833i	0.0846168	+	0.612884i
$631$	33.8162	−	10.9875i	1.34620	−	0.437407i	0.454788	−	0.890600i	$-0.349715\pi$
$631$	33.8162	−	10.9875i	1.34620	−	0.437407i	0.891413	+	0.453192i	$0.149715\pi$
$632$	7.97395	−	22.1890i	0.317187	−	0.882632i
$633$	−3.65297	+	7.16936i	−0.145192	+	0.284956i
$634$	12.7440	−	8.09106i	0.506129	−	0.321337i
$635$	−5.00399	+	1.86590i	−0.198577	+	0.0740461i
$636$	2.03025	−	16.1214i	0.0805046	−	0.639255i
$637$	−1.96738	+	0.311602i	−0.0779504	+	0.0123461i
$638$	1.72946	+	0.386227i	0.0684698	+	0.0152909i
$639$	−17.8736	+	12.9859i	−0.707069	+	0.513716i
$640$	2.06082	−	25.2141i	0.0814610	−	0.996677i
$641$	1.48461	+	1.07863i	0.0586386	+	0.0426034i	0.616718	−	0.787184i	$-0.288462\pi$
$641$	1.48461	+	1.07863i	0.0586386	+	0.0426034i	−0.558080	+	0.829787i	$0.688462\pi$
$642$	−27.5941	−	31.2871i	−1.08905	−	1.23480i
$643$	−12.1829	+	12.1829i	−0.480447	+	0.480447i	−0.905274	−	0.424828i	$-0.860335\pi$
$643$	−12.1829	+	12.1829i	−0.480447	+	0.480447i	0.424828	+	0.905274i	$0.360335\pi$
$644$	−13.6782	−	6.42998i	−0.538995	−	0.253377i
$645$	69.7678	−	14.1305i	2.74710	−	0.556390i
$646$	−11.1531	−	9.22304i	−0.438815	−	0.362876i
$647$	0.362239	−	0.184570i	0.0142411	−	0.00725620i	−0.446855	−	0.894606i	$-0.647456\pi$
$647$	0.362239	−	0.184570i	0.0142411	−	0.00725620i	0.461097	+	0.887350i	$0.347456\pi$
$648$	−0.303065	−	1.04089i	−0.0119055	−	0.0408902i
$649$		−	0.731426i		−	0.0287110i
$650$	−11.2026	+	8.53730i	−0.439402	+	0.334861i
$651$		−	3.68985i		−	0.144617i
$652$	4.91621	+	6.33287i	0.192534	+	0.248014i
$653$	20.8669	−	10.6322i	0.816585	−	0.416071i	0.00477225	−	0.999989i	$-0.498481\pi$
$653$	20.8669	−	10.6322i	0.816585	−	0.416071i	0.811813	+	0.583918i	$0.198481\pi$
$654$	−36.1417	+	43.7050i	−1.41325	+	1.70900i
$655$	18.6027	−	20.2655i	0.726867	−	0.791837i
$656$	−2.48322	+	0.985407i	−0.0969535	+	0.0384737i
$657$	−47.8268	+	47.8268i	−1.86590	+	1.86590i
$658$	−3.01856	+	2.66226i	−0.117676	+	0.103786i
$659$	25.6127	+	18.6087i	0.997730	+	0.724893i	0.961600	−	0.274454i	$-0.0884972\pi$
$659$	25.6127	+	18.6087i	0.997730	+	0.724893i	0.0361293	+	0.999347i	$0.488497\pi$
$660$	2.07778	−	1.26191i	0.0808773	−	0.0491198i
$661$	6.80975	−	4.94758i	0.264869	−	0.192438i	−0.447422	−	0.894323i	$-0.647658\pi$
$661$	6.80975	−	4.94758i	0.264869	−	0.192438i	0.712291	+	0.701885i	$0.247658\pi$
$662$	−6.35782	+	28.4692i	−0.247104	+	1.10649i
$663$	16.0089	−	2.53556i	0.621734	−	0.0984730i
$664$	9.84120	+	5.40279i	0.381913	+	0.209669i
$665$	−0.338064	−	7.90235i	−0.0131096	−	0.306440i
$666$	−26.0129	−	40.9722i	−1.00798	−	1.58764i
$667$	−22.2438	+	43.6559i	−0.861283	+	1.69036i
$668$	−30.8307	+	0.980869i	−1.19287	+	0.0379510i
$669$	45.8420	−	14.8950i	1.77235	−	0.575873i
$670$	−13.2164	−	7.06855i	−0.510595	−	0.273082i
$671$	0.792450	+	0.257483i	0.0305922	+	0.00994001i
$672$	−15.7122	+	2.50420i	−0.606111	+	0.0966015i
$673$	1.44077	+	0.228196i	0.0555377	+	0.00879630i	0.184141	−	0.982900i	$-0.441050\pi$
$673$	1.44077	+	0.228196i	0.0555377	+	0.00879630i	−0.128604	+	0.991696i	$0.541050\pi$
$674$	−9.62823	+	24.3319i	−0.370865	+	0.937230i
$675$	17.3086	−	20.5541i	0.666208	−	0.791126i
$676$	−13.1734	−	12.3610i	−0.506668	−	0.475423i
$677$	−3.50309	+	22.1176i	−0.134635	+	0.850050i	0.824244	+	0.566235i	$0.191600\pi$
$677$	−3.50309	+	22.1176i	−0.134635	+	0.850050i	−0.958879	+	0.283816i	$0.908400\pi$
$678$	−1.89816	−	20.0389i	−0.0728983	−	0.769590i
$679$	4.53314	−	13.9516i	0.173966	−	0.535412i
$680$	−18.2963	+	0.218107i	−0.701631	+	0.00836404i
$681$	20.6117	+	63.4363i	0.789843	+	2.43089i
$682$	−0.329047	+	0.142467i	−0.0125999	+	0.00545536i
$683$	−22.9567	−	11.6970i	−0.878413	−	0.447574i	−0.0442041	−	0.999023i	$-0.514075\pi$
$683$	−22.9567	−	11.6970i	−0.878413	−	0.447574i	−0.834209	+	0.551449i	$0.814075\pi$
$684$	6.52313	+	34.1235i	0.249418	+	1.30474i
$685$	−40.2530	+	31.9610i	−1.53799	+	1.22117i
$686$	−0.351966	−	1.36972i	−0.0134381	−	0.0522960i
$687$	−7.70883	−	48.6716i	−0.294110	−	1.85694i
$688$	9.91054	+	44.1761i	0.377836	+	1.68420i
$689$	−3.38195	−	4.65485i	−0.128842	−	0.177336i
$690$	19.4953	+	64.3250i	0.742174	+	2.44881i
$691$	−6.73585	+	9.27110i	−0.256244	+	0.352689i	−0.917686	−	0.397307i	$-0.869945\pi$
$691$	−6.73585	+	9.27110i	−0.256244	+	0.352689i	0.661442	+	0.749996i	$0.269945\pi$
$692$	4.18571	+	11.6121i	0.159117	+	0.441426i
$693$	−0.671101	−	0.671101i	−0.0254930	−	0.0254930i
$694$	−0.714092	+	11.3854i	−0.0271065	+	0.432184i
$695$	−15.8497	+	34.6981i	−0.601213	+	1.31617i
$696$	6.49420	+	51.1673i	0.246162	+	1.93949i
$697$	0.877246	+	1.72169i	0.0332281	+	0.0652138i
$698$	10.6267	+	6.28183i	0.402226	+	0.237771i
$699$	8.85186			0.334808
$700$	−6.78435	−	7.34660i	−0.256424	−	0.277675i
$701$	−24.2625			−0.916383			−0.458192	−	0.888853i	$-0.651503\pi$
$701$	−24.2625			−0.916383			−0.458192	+	0.888853i	$0.651503\pi$
$702$	−13.0323	−	7.70388i	−0.491873	−	0.290764i
$703$	11.2223	+	22.0251i	0.423258	+	0.830691i
$704$	0.829973	+	1.30447i	0.0312808	+	0.0491640i
$705$	17.7821	+	2.04185i	0.669713	+	0.0769006i
$706$	0.426888	−	6.80626i	0.0160661	−	0.256157i
$707$	−6.86431	−	6.86431i	−0.258159	−	0.258159i
$708$	20.0276	−	7.21917i	0.752684	−	0.271313i
$709$	10.3520	−	14.2483i	0.388777	−	0.535106i	−0.569106	−	0.822264i	$-0.692711\pi$
$709$	10.3520	−	14.2483i	0.388777	−	0.535106i	0.957883	+	0.287158i	$0.0927106\pi$
$710$	4.66446	−	13.4404i	0.175054	−	0.504408i
$711$	24.0622	+	33.1188i	0.902402	+	1.24205i
$712$	29.4992	+	43.3524i	1.10553	+	1.62470i
$713$	−1.55090	−	9.79203i	−0.0580818	−	0.366714i
$714$	2.86401	+	11.1456i	0.107183	+	0.417114i
$715$	0.230770	−	0.829300i	0.00863032	−	0.0310140i
$716$	−44.5296	+	8.51239i	−1.66415	+	0.318123i
$717$	0.938407	+	0.478142i	0.0350454	+	0.0178565i
$718$	18.1311	−	7.85018i	0.676645	−	0.292966i
$719$	6.66074	+	20.4996i	0.248404	+	0.764507i	0.995058	+	0.0992954i	$0.0316589\pi$
$719$	6.66074	+	20.4996i	0.248404	+	0.764507i	−0.746654	+	0.665212i	$0.768341\pi$
$720$	34.1801	+	27.5857i	1.27382	+	1.02806i
$721$	−4.89042	+	15.0512i	−0.182129	+	0.560535i
$722$	0.865218	+	9.13414i	0.0322001	+	0.339937i
$723$	−3.60030	+	22.7314i	−0.133896	+	0.845389i
$724$	8.22602	−	8.76664i	0.305718	−	0.325809i
$725$	−24.5031	+	21.2247i	−0.910023	+	0.788266i
$726$	16.0443	−	40.5463i	0.595461	−	1.50482i
$727$	14.8929	+	2.35880i	0.552346	+	0.0874830i	0.426368	−	0.904550i	$-0.359793\pi$
$727$	14.8929	+	2.35880i	0.552346	+	0.0874830i	0.125978	+	0.992033i	$0.459793\pi$
$728$	−3.45050	+	4.45370i	−0.127884	+	0.165065i
$729$	−41.3372	−	13.4313i	−1.53101	−	0.497454i
$730$	7.66747	−	42.8748i	0.283786	−	1.58687i
$731$	31.1430	−	10.1190i	1.15187	−	0.374264i
$732$	0.771186	+	24.2399i	0.0285039	+	0.895934i
$733$	−5.41443	+	10.6264i	−0.199987	+	0.392496i	−0.969119	−	0.246594i	$-0.920689\pi$
$733$	−5.41443	+	10.6264i	−0.199987	+	0.392496i	0.769132	+	0.639090i	$0.220689\pi$
$734$	−5.23348	−	8.24311i	−0.193171	−	0.304259i
$735$	−3.47584	+	5.24141i	−0.128208	+	0.193332i
$736$	−40.6441	+	13.2497i	−1.49816	+	0.488389i
$737$	0.904723	−	0.143294i	0.0333259	−	0.00527831i
$738$	1.01097	−	4.52695i	0.0372144	−	0.166639i
$739$	−18.6634	+	13.5598i	−0.686546	+	0.498805i	−0.875523	−	0.483177i	$-0.839483\pi$
$739$	−18.6634	+	13.5598i	−0.686546	+	0.498805i	0.188977	+	0.981982i	$0.439483\pi$
$740$	28.8256	+	12.0746i	1.05965	+	0.443872i
$741$	16.0326	+	11.6483i	0.588971	+	0.427913i
$742$	3.06370	−	2.70207i	0.112472	−	0.0991962i
$743$	−7.92175	+	7.92175i	−0.290621	+	0.290621i	−0.837326	−	0.546705i	$-0.815882\pi$
$743$	−7.92175	+	7.92175i	−0.290621	+	0.290621i	0.546705	+	0.837326i	$0.315882\pi$
$744$	−7.14868	−	7.60370i	−0.262083	−	0.278765i
$745$	3.91691	+	6.93734i	0.143504	+	0.254164i
$746$	30.4564	−	36.8300i	1.11509	−	1.34844i
$747$	−17.3675	+	8.84919i	−0.635444	+	0.323775i
$748$	0.883344	−	0.685741i	0.0322982	−	0.0250732i
$749$		−	10.4879i		−	0.383221i
$750$	−4.06145	+	44.2854i	−0.148303	+	1.61707i
$751$		−	30.6572i		−	1.11870i	−0.828933	−	0.559348i	$-0.811052\pi$
$751$		−	30.6572i		−	1.11870i	0.828933	−	0.559348i	$-0.188948\pi$
$752$	−1.06253	+	11.3343i	−0.0387465	+	0.413318i
$753$	29.0532	−	14.8033i	1.05876	−	0.539463i
$754$	14.0748	+	11.6391i	0.512573	+	0.423870i
$755$	−14.6736	−	25.9888i	−0.534027	−	0.945829i
$756$	4.57269	−	9.72726i	0.166307	−	0.353777i
$757$	28.3634	−	28.3634i	1.03088	−	1.03088i	0.0313771	−	0.999508i	$-0.490011\pi$
$757$	28.3634	−	28.3634i	1.03088	−	1.03088i	0.999508	−	0.0313771i	$-0.00998929\pi$
$758$	−9.11272	−	10.3323i	−0.330989	−	0.375286i
$759$	−3.32333	−	2.41454i	−0.120629	−	0.0876423i
$760$	−16.0066	−	15.6295i	−0.580620	−	0.566940i
$761$	−35.2076	+	25.5798i	−1.27628	+	0.927269i	−0.999434	−	0.0336470i	$-0.989288\pi$
$761$	−35.2076	+	25.5798i	−1.27628	+	0.927269i	−0.276842	+	0.960916i	$0.589288\pi$
$762$	9.27165	+	2.07057i	0.335876	+	0.0750088i
$763$	−14.0824	+	2.23044i	−0.509818	+	0.0807472i
$764$	−34.0981	−	4.29415i	−1.23362	−	0.155357i
$765$	17.5576	−	26.4760i	0.634795	−	0.957241i
$766$	17.5470	−	11.1405i	0.634001	−	0.402522i
$767$	3.42240	−	6.71685i	0.123576	−	0.242531i
$768$	−27.5266	+	35.6011i	−0.993282	+	1.28464i
$769$	−38.5208	+	12.5162i	−1.38910	+	0.451344i	−0.905648	−	0.424029i	$-0.860615\pi$
$769$	−38.5208	+	12.5162i	−1.38910	+	0.451344i	−0.483447	+	0.875374i	$0.660615\pi$
$770$	0.601614	+	0.107589i	0.0216807	+	0.00387724i
$771$	−58.8652	−	19.1265i	−2.11998	−	0.688823i
$772$	12.1575	−	41.9070i	0.437557	−	1.50827i
$773$	10.2381	+	1.62155i	0.368238	+	0.0583232i	0.337812	−	0.941214i	$-0.390313\pi$
$773$	10.2381	+	1.62155i	0.368238	+	0.0583232i	0.0304268	+	0.999537i	$0.490313\pi$
$774$	−73.0914	−	28.9225i	−2.62722	−	1.03960i
$775$	1.48680	−	6.38876i	0.0534073	−	0.229491i
$776$	−17.6882	−	37.5326i	−0.634969	−	1.34734i
$777$	3.07475	−	19.4132i	0.110306	−	0.696444i
$778$	5.17946	−	0.490617i	0.185693	−	0.0175895i
$779$	−0.730064	+	2.24691i	−0.0261573	+	0.0805038i
$780$	24.9853	−	1.86631i	0.894616	−	0.0668248i
$781$	0.268684	+	0.826925i	0.00961428	+	0.0295897i
$782$	12.2851	+	28.3741i	0.439315	+	1.01466i
$783$	−31.0460	−	15.8187i	−1.10949	−	0.565315i
$784$	−3.37897	−	2.14069i	−0.120678	−	0.0764530i
$785$	−5.36840	+	19.2920i	−0.191607	+	0.688560i
$786$	−47.3947	+	12.1787i	−1.69051	+	0.434400i
$787$	1.60038	+	10.1044i	0.0570473	+	0.360183i	0.999655	+	0.0262793i	$0.00836592\pi$
$787$	1.60038	+	10.1044i	0.0570473	+	0.360183i	−0.942607	+	0.333903i	$0.891634\pi$
$788$	30.0182	−	44.2073i	1.06935	−	1.57482i
$789$	44.0967	+	60.6938i	1.56988	+	2.16076i
$790$	−24.9042	−	8.64297i	−0.886052	−	0.307503i
$791$	2.97446	−	4.09400i	0.105760	−	0.145566i
$792$	−2.68313	−	0.0827573i	−0.0953408	−	0.00294065i
$793$	6.07247	+	6.07247i	0.215640	+	0.215640i
$794$	39.6768	+	2.48853i	1.40808	+	0.0883145i
$795$	−18.0480	−	2.07239i	−0.640098	−	0.0735000i
$796$	18.3873	+	33.4157i	0.651721	+	1.18439i
$797$	12.7550	+	25.0331i	0.451806	+	0.886719i	0.998771	+	0.0495637i	$0.0157831\pi$
$797$	12.7550	+	25.0331i	0.451806	+	0.886719i	−0.546965	+	0.837156i	$0.684217\pi$
$798$	−7.15983	+	12.1120i	−0.253455	+	0.428759i
$799$	8.23375			0.291289
$800$	−28.2138	−	1.99525i	−0.997509	−	0.0705426i
$801$	−91.0419			−3.21681
$802$	3.82853	−	6.47656i	0.135190	−	0.228695i
$803$	1.20848	+	2.37177i	0.0426462	+	0.0836979i
$804$	12.8532	+	23.3585i	0.453299	+	0.823790i
$805$	−7.02105	+	15.3705i	−0.247459	+	0.541738i
$806$	−3.68833	−	0.231332i	−0.129916	−	0.00814831i
$807$	−24.6812	−	24.6812i	−0.868819	−	0.868819i
$808$	−27.4442	−	0.846478i	−0.965483	−	0.0297790i
$809$	7.89972	−	10.8730i	0.277739	−	0.382275i	−0.647244	−	0.762283i	$-0.724079\pi$
$809$	7.89972	−	10.8730i	0.277739	−	0.382275i	0.924983	+	0.380007i	$0.124079\pi$
$810$	−1.15998	+	0.351560i	−0.0407574	+	0.0123525i
$811$	4.59656	+	6.32663i	0.161407	+	0.222158i	0.882059	−	0.471140i	$-0.156157\pi$
$811$	4.59656	+	6.32663i	0.161407	+	0.222158i	−0.720652	+	0.693297i	$0.756157\pi$
$812$	−7.28436	+	10.7276i	−0.255631	+	0.376464i
$813$	0.994821	+	6.28105i	0.0348899	+	0.220286i
$814$	−1.84992	+	0.475360i	−0.0648395	+	0.0166614i
$815$	7.01975	−	5.57369i	0.245891	−	0.195238i
$816$	27.4953	+	17.4191i	0.962528	+	0.609791i
$817$	35.6730	+	18.1763i	1.24804	+	0.635908i
$818$	−12.9029	−	29.8010i	−0.451139	−	1.04197i
$819$	−3.02273	−	9.30301i	−0.105623	−	0.325073i
$820$	1.13205	+	2.76410i	0.0395330	+	0.0965264i
$821$	12.3714	−	38.0751i	0.431763	−	1.32883i	−0.464604	−	0.885519i	$-0.653803\pi$
$821$	12.3714	−	38.0751i	0.431763	−	1.32883i	0.896367	−	0.443312i	$-0.146197\pi$
$822$	91.0228	−	8.62201i	3.17479	−	0.300727i
$823$	−0.0415403	+	0.262275i	−0.00144801	+	0.00914234i	−0.988402	−	0.151862i	$-0.951473\pi$
$823$	−0.0415403	+	0.262275i	−0.00144801	+	0.00914234i	0.986954	+	0.161004i	$0.0514732\pi$
$824$	19.0823	+	40.4907i	0.664763	+	1.41056i
$825$	−1.43621	−	2.30744i	−0.0500025	−	0.0803346i
$826$	4.97672	+	1.96931i	0.173162	+	0.0685209i
$827$	20.4902	+	3.24533i	0.712515	+	0.112851i	0.502161	−	0.864774i	$-0.332538\pi$
$827$	20.4902	+	3.24533i	0.712515	+	0.112851i	0.210354	+	0.977625i	$0.432538\pi$
$828$	20.6796	−	71.2828i	0.718665	−	2.47725i
$829$	11.4737	+	3.72804i	0.398499	+	0.129480i	0.501409	−	0.865211i	$-0.332815\pi$
$829$	11.4737	+	3.72804i	0.398499	+	0.129480i	−0.102910	+	0.994691i	$0.532815\pi$
$830$	5.91966	−	11.0683i	0.205474	−	0.384186i
$831$	18.0967	−	5.87998i	0.627768	−	0.203974i
$832$	1.51810	+	15.8627i	0.0526308	+	0.549942i
$833$	−1.31344	+	2.57778i	−0.0455081	+	0.0893147i
$834$	57.2867	−	36.3708i	1.98368	−	1.25942i
$835$	1.47402	+	34.4557i	0.0510106	+	1.19239i
$836$	1.35655	+	0.170837i	0.0469172	+	0.00590852i
$837$	6.96362	−	1.10293i	0.240698	−	0.0381228i
$838$	−28.3209	−	6.32471i	−0.978330	−	0.218483i
$839$	−13.9071	+	10.1041i	−0.480126	+	0.348832i	−0.801374	−	0.598163i	$-0.795897\pi$
$839$	−13.9071	+	10.1041i	−0.480126	+	0.348832i	0.321249	+	0.946995i	$0.395897\pi$
$840$	2.99196	+	17.5351i	0.103233	+	0.605017i
$841$	10.5461	+	7.66216i	0.363657	+	0.264212i
$842$	−23.9506	−	27.1560i	−0.825394	−	0.935859i
$843$	64.7780	−	64.7780i	2.23107	−	2.23107i
$844$	−2.43414	+	5.17803i	−0.0837867	+	0.178235i
$845$	−13.6579	+	14.8787i	−0.469846	+	0.511843i
$846$	−15.2317	−	12.5957i	−0.523675	−	0.433051i
$847$	9.76779	−	4.97694i	0.335625	−	0.171010i
$848$	1.07842	−	11.5038i	0.0370331	−	0.395041i
$849$			26.8211i			0.920496i
$850$	0.467827	+	20.4520i	0.0160463	+	0.701498i
$851$		−	52.8106i		−	1.81032i
$852$	−19.9906	+	15.5188i	−0.684868	+	0.531664i
$853$	19.8128	−	10.0951i	0.678377	−	0.345651i	−0.0806193	−	0.996745i	$-0.525690\pi$
$853$	19.8128	−	10.0951i	0.678377	−	0.345651i	0.758997	+	0.651094i	$0.225690\pi$
$854$	−3.88556	+	4.69869i	−0.132961	+	0.160786i
$855$	38.0691	−	7.71039i	1.30193	−	0.263690i
$856$	−20.3192	−	21.6126i	−0.694497	−	0.738702i
$857$	−7.17153	+	7.17153i	−0.244975	+	0.244975i	−0.818905	−	0.573930i	$-0.805418\pi$
$857$	−7.17153	+	7.17153i	−0.244975	+	0.244975i	0.573930	+	0.818905i	$0.305418\pi$
$858$	−1.14841	+	1.01286i	−0.0392061	+	0.0345784i
$859$	−41.7760	−	30.3520i	−1.42538	−	1.03560i	−0.990854	−	0.134936i	$-0.956917\pi$
$859$	−41.7760	−	30.3520i	−1.42538	−	1.03560i	−0.434523	−	0.900661i	$-0.643083\pi$
$860$	49.2661	−	11.6205i	1.67996	−	0.396255i
$861$	1.51977	−	1.10418i	0.0517935	−	0.0376302i
$862$	4.46908	−	20.0118i	0.152217	−	0.681603i
$863$	−13.9914	+	2.21601i	−0.476271	+	0.0754340i	−0.389955	−	0.920834i	$-0.627510\pi$
$863$	−13.9914	+	2.21601i	−0.476271	+	0.0754340i	−0.0863162	+	0.996268i	$0.527510\pi$
$864$	−9.42253	−	28.9041i	−0.320561	−	0.983338i
$865$	12.9307	−	4.82164i	0.439658	−	0.163941i
$866$	3.08641	+	4.86132i	0.104881	+	0.165194i
$867$	−11.0195	+	21.6271i	−0.374243	+	0.734494i
$868$	−0.0834330	−	2.62247i	−0.00283190	−	0.0890123i
$869$	1.53224	−	0.497856i	0.0519778	−	0.0168886i
$870$	57.1239	−	7.88671i	1.93668	−	0.267385i
$871$	8.97876	+	2.91738i	0.304234	+	0.0988515i
$872$	−24.6985	+	31.8794i	−0.836397	+	1.07957i
$873$	71.1518	+	11.2693i	2.40812	+	0.381409i
$874$	−13.9097	+	35.1519i	−0.470503	+	1.18903i
$875$	−8.13020	+	7.67462i	−0.274851	+	0.259450i
$876$	−53.0152	+	56.4994i	−1.79122	+	1.90894i
$877$	−4.10685	+	25.9296i	−0.138679	+	0.875582i	0.816024	+	0.578019i	$0.196174\pi$
$877$	−4.10685	+	25.9296i	−0.138679	+	0.875582i	−0.954702	+	0.297563i	$0.903826\pi$
$878$	−2.26329	−	23.8936i	−0.0763824	−	0.806372i
$879$	4.69912	−	14.4624i	0.158497	−	0.487805i
$880$	1.44819	−	0.943852i	0.0488185	−	0.0318172i
$881$	2.56635	+	7.89842i	0.0864626	+	0.266105i	0.984935	−	0.172926i	$-0.0553221\pi$
$881$	2.56635	+	7.89842i	0.0864626	+	0.266105i	−0.898472	+	0.439030i	$0.855322\pi$
$882$	6.37315	−	2.75938i	0.214595	−	0.0929130i
$883$	36.5369	+	18.6165i	1.22957	+	0.626495i	0.943391	−	0.331683i	$-0.107616\pi$
$883$	36.5369	+	18.6165i	1.22957	+	0.626495i	0.286174	+	0.958178i	$0.407616\pi$
$884$	11.3206	−	2.16407i	0.380752	−	0.0727856i
$885$	−8.31598	−	22.3018i	−0.279538	−	0.749668i
$886$	3.89686	+	15.1650i	0.130917	+	0.509479i
$887$	−1.33985	−	8.45945i	−0.0449876	−	0.284041i	0.954931	−	0.296829i	$-0.0959292\pi$
$887$	−1.33985	−	8.45945i	−0.0449876	−	0.284041i	−0.999918	+	0.0127885i	$0.995929\pi$
$888$	−31.2748	−	45.9619i	−1.04951	−	1.54238i
$889$	1.40385	+	1.93223i	0.0470835	+	0.0648049i
$890$	48.1054	−	33.5098i	1.61250	−	1.12325i
$891$	0.0435415	−	0.0599298i	0.00145870	−	0.00200772i
$892$	32.2442	−	11.6228i	1.07962	−	0.389159i
$893$	7.11847	+	7.11847i	0.238211	+	0.238211i
$894$	0.887099	−	14.1438i	0.0296690	−	0.473040i
$895$	10.0617	+	49.6784i	0.336326	+	1.66057i
$896$	−11.1104	+	2.13507i	−0.371173	+	0.0713277i
$897$	−19.2211	−	37.7235i	−0.641772	−	1.25955i
$898$	37.2751	+	22.0347i	1.24389	+	0.735306i
$899$	−8.50567			−0.283680
$900$	30.4214	−	38.5499i	1.01405	−	1.28500i
$901$	−8.35689			−0.278408
$902$	−0.157146	−	0.0928945i	−0.00523237	−	0.00309305i
$903$	−14.4526	−	28.3648i	−0.480953	−	0.943923i
$904$	−1.80218	−	14.1992i	−0.0599395	−	0.472259i
$905$	−9.90152	−	9.08909i	−0.329138	−	0.302132i
$906$	−3.32327	+	52.9859i	−0.110408	+	1.76034i
$907$	5.25117	+	5.25117i	0.174362	+	0.174362i	0.788893	−	0.614531i	$-0.210655\pi$
$907$	5.25117	+	5.25117i	0.174362	+	0.174362i	−0.614531	+	0.788893i	$0.710655\pi$
$908$	16.0836	+	44.6197i	0.533754	+	1.48076i
$909$	28.0207	−	38.5672i	0.929388	−	1.27919i
$910$	5.02134	+	3.80302i	0.166456	+	0.126069i
$911$	32.2540	+	44.3938i	1.06862	+	1.47083i	0.871463	+	0.490462i	$0.163172\pi$
$911$	32.2540	+	44.3938i	1.06862	+	1.47083i	0.197160	+	0.980371i	$0.436828\pi$
$912$	8.71133	+	38.8306i	0.288461	+	1.28581i
$913$	0.120004	+	0.757673i	0.00397154	+	0.0250753i
$914$	−0.672216	−	2.61600i	−0.0222349	−	0.0865296i
$915$	27.0900	−	1.15892i	0.895568	−	0.0383126i
$916$	−6.57939	−	34.4178i	−0.217389	−	1.13720i
$917$	−10.9615	−	5.58518i	−0.361982	−	0.184439i
$918$	−20.1783	+	8.73659i	−0.665984	+	0.288350i
$919$	−3.08011	−	9.47960i	−0.101603	−	0.312703i	0.887315	−	0.461164i	$-0.152568\pi$
$919$	−3.08011	−	9.47960i	−0.101603	−	0.312703i	−0.988918	+	0.148461i	$0.952568\pi$
$920$	15.3103	+	45.2765i	0.504765	+	1.49272i
$921$	23.6181	−	72.6891i	0.778244	−	2.39519i
$922$	2.40620	+	25.4023i	0.0792439	+	0.836580i
$923$	−1.40187	+	8.85103i	−0.0461430	+	0.291335i
$924$	−0.792793	−	0.743904i	−0.0260810	−	0.0244726i
$925$	13.1461	−	32.3739i	0.432243	−	1.06445i
$926$	17.3933	−	43.9554i	0.571579	−	1.44446i
$927$	−76.7596	−	12.1575i	−2.52112	−	0.399306i
$928$	5.77256	+	36.2190i	0.189493	+	1.18895i
$929$	−18.5116	−	6.01477i	−0.607344	−	0.197338i	−0.0108310	−	0.999941i	$-0.503448\pi$
$929$	−18.5116	−	6.01477i	−0.607344	−	0.197338i	−0.596513	+	0.802603i	$0.703448\pi$
$930$	−8.41317	+	8.08508i	−0.275879	+	0.265120i
$931$	−3.36414	+	1.09308i	−0.110255	+	0.0358241i
$932$	6.29123	−	0.200154i	0.206076	−	0.00655625i
$933$	17.5667	−	34.4766i	0.575109	−	1.12871i
$934$	−18.6857	−	29.4313i	−0.611414	−	0.963021i
$935$	−0.777450	−	0.979154i	−0.0254253	−	0.0320218i
$936$	−24.2525	−	13.3146i	−0.792719	−	0.435200i
$937$	32.4747	−	5.14349i	1.06090	−	0.168030i	0.398492	−	0.917172i	$-0.369534\pi$
$937$	32.4747	−	5.14349i	1.06090	−	0.168030i	0.662410	+	0.749141i	$0.269534\pi$
$938$	−1.46090	+	6.54167i	−0.0477002	+	0.213593i
$939$	−59.6500	+	43.3383i	−1.94660	+	1.41429i
$940$	12.6843	+	1.04911i	0.413718	+	0.0342183i
$941$	−36.5383	−	26.5466i	−1.19111	−	0.865395i	−0.197732	−	0.980256i	$-0.563358\pi$
$941$	−36.5383	−	26.5466i	−1.19111	−	0.865395i	−0.993382	+	0.114861i	$0.963358\pi$
$942$	26.7154	−	23.5620i	0.870436	−	0.767693i
$943$	3.56902	−	3.56902i	0.116223	−	0.116223i
$944$	14.0709	−	5.58369i	0.457968	−	0.181734i
$945$	−10.9307	−	4.99303i	−0.355577	−	0.162423i
$946$	−1.97145	+	2.38402i	−0.0640974	+	0.0775110i
$947$	36.6520	−	18.6751i	1.19103	−	0.606861i	0.257822	−	0.966193i	$-0.416995\pi$
$947$	36.6520	−	18.6751i	1.19103	−	0.606861i	0.933210	+	0.359332i	$0.116995\pi$
$948$	28.7553	+	37.0415i	0.933930	+	1.20305i
$949$			27.4351i			0.890580i
$950$	−17.2773	+	18.0862i	−0.560549	+	0.586793i
$951$			30.0222i			0.973536i
$952$	2.28754	+	7.85670i	0.0741396	+	0.254637i
$953$	−22.3747	+	11.4005i	−0.724788	+	0.369298i	−0.777137	−	0.629331i	$-0.783329\pi$
$953$	−22.3747	+	11.4005i	−0.724788	+	0.369298i	0.0523496	+	0.998629i	$0.483329\pi$
$954$	15.4594	+	12.7841i	0.500518	+	0.413901i
$955$	−4.38327	+	38.1731i	−0.141839	+	1.23525i
$956$	0.677760	+	0.318608i	0.0219203	+	0.0103045i
$957$	−2.49205	+	2.49205i	−0.0805565	+	0.0805565i
$958$	14.1339	+	16.0255i	0.456646	+	0.517760i
$959$	18.5962	+	13.5109i	0.600502	+	0.436290i
$960$	40.1379	+	30.3380i	1.29544	+	0.979156i
$961$	−23.6872	+	17.2097i	−0.764102	+	0.555152i
$962$	−19.2124	−	4.29058i	−0.619434	−	0.138334i
$963$	50.8696	−	8.05696i	1.63925	−	0.259632i
$964$	−2.04483	+	16.2371i	−0.0658595	+	0.522963i
$965$	−46.9995	−	13.0786i	−1.51297	−	0.421015i
$966$	25.3767	−	16.1114i	0.816482	−	0.518377i
$967$	15.3189	−	30.0651i	0.492623	−	0.966827i	−0.502156	−	0.864777i	$-0.667460\pi$
$967$	15.3189	−	30.0651i	0.492623	−	0.966827i	0.994779	−	0.102050i	$-0.0325402\pi$
$968$	10.4863	−	29.1800i	0.337042	−	0.937882i
$969$	27.3746	−	8.89455i	0.879399	−	0.285734i
$970$	−41.7437	+	20.2343i	−1.34031	+	0.649684i
$971$	21.6943	+	7.04889i	0.696202	+	0.226210i	0.635675	−	0.771957i	$-0.280722\pi$
$971$	21.6943	+	7.04889i	0.696202	+	0.226210i	0.0605271	+	0.998167i	$0.480722\pi$
$972$	−28.8977	−	8.38341i	−0.926896	−	0.268898i
$973$	16.8497	+	2.66873i	0.540176	+	0.0855555i
$974$	−10.2797	−	4.06773i	−0.329384	−	0.130338i
$975$	−2.39236	−	27.9099i	−0.0766167	−	0.893831i
$976$	1.09620	+	17.2105i	0.0350886	+	0.550894i
$977$	6.41792	−	40.5211i	0.205327	−	1.29639i	−0.642571	−	0.766226i	$-0.722132\pi$
$977$	6.41792	−	40.5211i	0.205327	−	1.29639i	0.847898	−	0.530159i	$-0.177868\pi$
$978$	−15.8735	+	1.50360i	−0.507579	+	0.0480797i
$979$	−1.10721	+	3.40763i	−0.0353865	+	0.108908i
$980$	−2.35185	+	3.80379i	−0.0751271	+	0.121508i
$981$	−21.6366	−	66.5905i	−0.690803	−	2.12607i
$982$	−16.8672	−	38.9571i	−0.538254	−	1.24317i
$983$	43.4202	+	22.1237i	1.38489	+	0.705636i	0.978148	−	0.207908i	$-0.0666654\pi$
$983$	43.4202	+	22.1237i	1.38489	+	0.705636i	0.406740	+	0.913544i	$0.366665\pi$
$984$	0.992575	−	5.21977i	0.0316422	−	0.166400i
$985$	−49.7898	−	33.0181i	−1.58643	−	1.05205i
$986$	25.6923	−	6.60198i	0.818210	−	0.210250i
$987$	−1.25220	−	7.90611i	−0.0398581	−	0.251654i
$988$	11.6581	+	7.91624i	0.370894	+	0.251849i
$989$	−50.2762	−	69.1992i	−1.59869	−	2.20041i
$990$	−0.0596721	+	3.00066i	−0.00189650	+	0.0953672i
$991$	−34.1756	+	47.0387i	−1.08562	+	1.49423i	−0.232449	+	0.972609i	$0.574674\pi$
$991$	−34.1756	+	47.0387i	−1.08562	+	1.49423i	−0.853175	+	0.521625i	$0.825326\pi$
$992$	−5.25267	−	5.24249i	−0.166773	−	0.166449i
$993$	−41.0226	−	41.0226i	−1.30181	−	1.30181i
$994$	−6.34992	−	0.398266i	−0.201407	−	0.0126322i
$995$	37.1325	−	20.9655i	1.17718	−	0.664650i
$996$	−19.5619	+	10.7641i	−0.619842	+	0.341074i
$997$	17.6773	+	34.6937i	0.559847	+	1.09876i	0.981403	+	0.191959i	$0.0614841\pi$
$997$	17.6773	+	34.6937i	0.559847	+	1.09876i	−0.421556	+	0.906802i	$0.638516\pi$
$998$	−6.95388	+	11.7636i	−0.220121	+	0.372370i
$999$	37.5564			1.18823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.323.30	✓	720
4.3	odd	2	inner	700.2.bj.a.323.53	yes	720
25.12	odd	20	inner	700.2.bj.a.687.53	yes	720
100.87	even	20	inner	700.2.bj.a.687.30	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.30	✓	720	1.1	even	1	trivial
700.2.bj.a.323.53	yes	720	4.3	odd	2	inner
700.2.bj.a.687.30	yes	720	100.87	even	20	inner
700.2.bj.a.687.53	yes	720	25.12	odd	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719657 + 1.21741i) q^{2} +(-1.27690 - 2.50605i) q^{3} +(-0.964187 - 1.75224i) q^{4} +(-1.94714 + 1.09938i) q^{5} +(3.96983 + 0.248987i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.82708 + 0.0871975i) q^{8} +(-2.88647 + 3.97289i) q^{9} +(0.0628736 - 3.16165i) q^{10} +(0.113598 + 0.156355i) q^{11} +(-3.16003 + 4.65373i) q^{12} +(0.311602 + 1.96738i) q^{13} +(-1.36972 + 0.351966i) q^{14} +(5.24141 + 3.47584i) q^{15} +(-2.14069 + 3.37897i) q^{16} +(2.57778 + 1.31344i) q^{17} +(-2.75938 - 6.37315i) q^{18} +(1.09308 + 3.36414i) q^{19} +(3.80379 + 2.35185i) q^{20} +(0.869144 - 2.67495i) q^{21} +(-0.272100 + 0.0257743i) q^{22} +(1.18219 - 7.46403i) q^{23} +(-3.39137 - 7.19616i) q^{24} +(2.58272 - 4.28130i) q^{25} +(-2.61936 - 1.03649i) q^{26} +(5.30806 + 0.840714i) q^{27} +(0.557237 - 1.92080i) q^{28} +(-6.16617 - 2.00351i) q^{29} +(-8.00355 + 3.87954i) q^{30} +(1.24769 - 0.405398i) q^{31} +(-2.57305 - 5.03780i) q^{32} +(0.246780 - 0.484333i) q^{33} +(-3.45412 + 2.19299i) q^{34} +(-2.15422 - 0.599457i) q^{35} +(9.74455 + 1.22718i) q^{36} +(6.90220 - 1.09320i) q^{37} +(-4.88219 - 1.09030i) q^{38} +(4.53247 - 3.29303i) q^{39} +(-5.60059 + 2.93826i) q^{40} +(0.540341 + 0.392581i) q^{41} +(2.63103 + 2.98315i) q^{42} +(8.00342 - 8.00342i) q^{43} +(0.164441 - 0.349807i) q^{44} +(1.25265 - 10.9091i) q^{45} +(8.23603 + 6.81075i) q^{46} +(2.53580 - 1.29205i) q^{47} +(11.2013 + 1.05007i) q^{48} +1.00000i q^{49} +(3.35344 + 6.22531i) q^{50} -8.13717i q^{51} +(3.14688 - 2.44292i) q^{52} +(-2.57372 + 1.31138i) q^{53} +(-4.84348 + 5.85707i) q^{54} +(-0.393086 - 0.179557i) q^{55} +(1.93739 + 2.06071i) q^{56} +(7.03497 - 7.03497i) q^{57} +(6.87662 - 6.06493i) q^{58} +(-3.06178 - 2.22451i) q^{59} +(1.03681 - 12.5356i) q^{60} +(3.48795 - 2.53414i) q^{61} +(-0.404370 + 1.81070i) q^{62} +(-4.85030 + 0.768212i) q^{63} +(7.98479 + 0.493029i) q^{64} +(-2.76963 - 3.48820i) q^{65} +(0.412036 + 0.648986i) q^{66} +(2.15173 - 4.22302i) q^{67} +(-0.183994 - 5.78329i) q^{68} +(-20.2148 + 6.56818i) q^{69} +(2.28008 - 2.19117i) q^{70} +(4.27870 + 1.39024i) q^{71} +(-8.50672 + 10.9800i) q^{72} +(13.6037 + 2.15462i) q^{73} +(-3.63634 + 9.18956i) q^{74} +(-14.0270 - 1.00565i) q^{75} +(4.84085 - 5.15900i) q^{76} +(-0.0302333 + 0.190886i) q^{77} +(0.747155 + 7.88774i) q^{78} +(2.57602 - 7.92819i) q^{79} +(0.453437 - 8.93277i) q^{80} +(-0.118444 - 0.364533i) q^{81} +(-0.866793 + 0.375295i) q^{82} +(3.53662 + 1.80200i) q^{83} +(-5.52517 + 1.05620i) q^{84} +(-6.46327 + 0.276500i) q^{85} +(3.98375 + 15.5032i) q^{86} +(2.85266 + 18.0110i) q^{87} +(0.307519 + 0.451934i) q^{88} +(10.8971 + 14.9986i) q^{89} +(12.3794 + 9.37582i) q^{90} +(-1.17081 + 1.61148i) q^{91} +(-14.2186 + 5.12525i) q^{92} +(-2.60912 - 2.60912i) q^{93} +(-0.251942 + 4.01695i) q^{94} +(-5.82685 - 5.34876i) q^{95} +(-9.33947 + 12.8809i) q^{96} +(-6.65984 - 13.0707i) q^{97} +(-1.21741 - 0.719657i) q^{98} -0.949080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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