LMFDB - Embedded newform 420.2.n.b.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(71,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("420.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.n (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09313 + 0.897253i) q^{2} +(-1.62224 - 0.606916i) q^{3} +(0.389874 - 1.96163i) q^{4} -1.00000i q^{5} +(2.31788 - 0.792118i) q^{6} -1.00000i q^{7} +(1.33390 + 2.49414i) q^{8} +(2.26331 + 1.96912i) q^{9} +O(q^{10})$	\(q+(-1.09313 + 0.897253i) q^{2} +(-1.62224 - 0.606916i) q^{3} +(0.389874 - 1.96163i) q^{4} -1.00000i q^{5} +(2.31788 - 0.792118i) q^{6} -1.00000i q^{7} +(1.33390 + 2.49414i) q^{8} +(2.26331 + 1.96912i) q^{9} +(0.897253 + 1.09313i) q^{10} +1.07205 q^{11} +(-1.82301 + 2.94561i) q^{12} -1.72442 q^{13} +(0.897253 + 1.09313i) q^{14} +(-0.606916 + 1.62224i) q^{15} +(-3.69600 - 1.52958i) q^{16} -5.38606i q^{17} +(-4.24089 - 0.121752i) q^{18} +2.00965i q^{19} +(-1.96163 - 0.389874i) q^{20} +(-0.606916 + 1.62224i) q^{21} +(-1.17189 + 0.961896i) q^{22} -8.92300 q^{23} +(-0.650165 - 4.85564i) q^{24} -1.00000 q^{25} +(1.88502 - 1.54725i) q^{26} +(-2.47653 - 4.56802i) q^{27} +(-1.96163 - 0.389874i) q^{28} -1.69137i q^{29} +(-0.792118 - 2.31788i) q^{30} -3.27357i q^{31} +(5.41263 - 1.64421i) q^{32} +(-1.73911 - 0.650641i) q^{33} +(4.83266 + 5.88767i) q^{34} -1.00000 q^{35} +(4.74510 - 3.67206i) q^{36} -8.95056 q^{37} +(-1.80316 - 2.19681i) q^{38} +(2.79743 + 1.04658i) q^{39} +(2.49414 - 1.33390i) q^{40} -11.8213i q^{41} +(-0.792118 - 2.31788i) q^{42} +2.46826i q^{43} +(0.417963 - 2.10296i) q^{44} +(1.96912 - 2.26331i) q^{45} +(9.75401 - 8.00619i) q^{46} +5.04271 q^{47} +(5.06746 + 4.72450i) q^{48} -1.00000 q^{49} +(1.09313 - 0.897253i) q^{50} +(-3.26888 + 8.73746i) q^{51} +(-0.672308 + 3.38269i) q^{52} +4.28200i q^{53} +(6.80584 + 2.77138i) q^{54} -1.07205i q^{55} +(2.49414 - 1.33390i) q^{56} +(1.21969 - 3.26012i) q^{57} +(1.51758 + 1.84889i) q^{58} -12.3591 q^{59} +(2.94561 + 1.82301i) q^{60} -11.1904 q^{61} +(2.93722 + 3.57844i) q^{62} +(1.96912 - 2.26331i) q^{63} +(-4.44144 + 6.65384i) q^{64} +1.72442i q^{65} +(2.48487 - 0.849187i) q^{66} -4.42168i q^{67} +(-10.5655 - 2.09988i) q^{68} +(14.4752 + 5.41551i) q^{69} +(1.09313 - 0.897253i) q^{70} +6.71322 q^{71} +(-1.89225 + 8.27160i) q^{72} +2.20666 q^{73} +(9.78414 - 8.03092i) q^{74} +(1.62224 + 0.606916i) q^{75} +(3.94219 + 0.783509i) q^{76} -1.07205i q^{77} +(-3.99700 + 1.36595i) q^{78} +2.97652i q^{79} +(-1.52958 + 3.69600i) q^{80} +(1.24511 + 8.91346i) q^{81} +(10.6067 + 12.9223i) q^{82} -9.69674 q^{83} +(2.94561 + 1.82301i) q^{84} -5.38606 q^{85} +(-2.21466 - 2.69814i) q^{86} +(-1.02652 + 2.74380i) q^{87} +(1.43000 + 2.67383i) q^{88} -8.62897i q^{89} +(-0.121752 + 4.24089i) q^{90} +1.72442i q^{91} +(-3.47884 + 17.5036i) q^{92} +(-1.98678 + 5.31050i) q^{93} +(-5.51234 + 4.52458i) q^{94} +2.00965 q^{95} +(-9.77847 - 0.617704i) q^{96} +13.7216 q^{97} +(1.09313 - 0.897253i) q^{98} +(2.42637 + 2.11099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.09313	+	0.897253i	−0.772961	+	0.634454i
$2$	−1.09313	+	0.897253i	−0.772961	+	0.634454i
$3$	−1.62224	−	0.606916i	−0.936599	−	0.350403i
$3$	−1.62224	−	0.606916i	−0.936599	−	0.350403i
$4$	0.389874	−	1.96163i	0.194937	−	0.980816i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.31788	−	0.792118i	0.946269	−	0.323381i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.33390	+	2.49414i	0.471604	+	0.881811i
$9$	2.26331	+	1.96912i	0.754435	+	0.656374i
$10$	0.897253	+	1.09313i	0.283736	+	0.345679i
$11$	1.07205			0.323234			0.161617	−	0.986854i	$-0.448329\pi$
$11$	1.07205			0.323234			0.161617	+	0.986854i	$0.448329\pi$
$12$	−1.82301	+	2.94561i	−0.526259	+	0.850325i
$13$	−1.72442			−0.478269			−0.239135	−	0.970986i	$-0.576864\pi$
$13$	−1.72442			−0.478269			−0.239135	+	0.970986i	$0.576864\pi$
$14$	0.897253	+	1.09313i	0.239801	+	0.292152i
$15$	−0.606916	+	1.62224i	−0.156705	+	0.418860i
$16$	−3.69600	−	1.52958i	−0.923999	−	0.382394i
$17$		−	5.38606i		−	1.30631i	−0.757224	−	0.653155i	$-0.773445\pi$
$17$		−	5.38606i		−	1.30631i	0.757224	−	0.653155i	$-0.226555\pi$
$18$	−4.24089	−	0.121752i	−0.999588	−	0.0286971i
$19$			2.00965i			0.461044i	0.973067	+	0.230522i	$0.0740434\pi$
$19$			2.00965i			0.461044i	−0.973067	+	0.230522i	$0.925957\pi$
$20$	−1.96163	−	0.389874i	−0.438634	−	0.0871784i
$21$	−0.606916	+	1.62224i	−0.132440	+	0.354001i
$22$	−1.17189	+	0.961896i	−0.249847	+	0.205077i
$23$	−8.92300			−1.86057			−0.930287	−	0.366833i	$-0.880442\pi$
$23$	−8.92300			−1.86057			−0.930287	+	0.366833i	$0.880442\pi$
$24$	−0.650165	−	4.85564i	−0.132714	−	0.991154i
$25$	−1.00000			−0.200000
$26$	1.88502	−	1.54725i	0.369683	−	0.303440i
$27$	−2.47653	−	4.56802i	−0.476608	−	0.879116i
$28$	−1.96163	−	0.389874i	−0.370714	−	0.0736792i
$29$		−	1.69137i		−	0.314079i	−0.987592	−	0.157039i	$-0.949805\pi$
$29$		−	1.69137i		−	0.314079i	0.987592	−	0.157039i	$-0.0501950\pi$
$30$	−0.792118	−	2.31788i	−0.144620	−	0.423184i
$31$		−	3.27357i		−	0.587950i	−0.955813	−	0.293975i	$-0.905022\pi$
$31$		−	3.27357i		−	0.587950i	0.955813	−	0.293975i	$-0.0949782\pi$
$32$	5.41263	−	1.64421i	0.956827	−	0.290659i
$33$	−1.73911	−	0.650641i	−0.302741	−	0.113262i
$34$	4.83266	+	5.88767i	0.828794	+	1.00973i
$35$	−1.00000			−0.169031
$36$	4.74510	−	3.67206i	0.790849	−	0.612011i
$37$	−8.95056			−1.47146			−0.735732	−	0.677273i	$-0.763161\pi$
$37$	−8.95056			−1.47146			−0.735732	+	0.677273i	$0.763161\pi$
$38$	−1.80316	−	2.19681i	−0.292511	−	0.356369i
$39$	2.79743	+	1.04658i	0.447947	+	0.167587i
$40$	2.49414	−	1.33390i	0.394358	−	0.210908i
$41$		−	11.8213i		−	1.84618i	−0.384584	−	0.923090i	$-0.625655\pi$
$41$		−	11.8213i		−	1.84618i	0.384584	−	0.923090i	$-0.374345\pi$
$42$	−0.792118	−	2.31788i	−0.122227	−	0.357656i
$43$			2.46826i			0.376407i	0.982130	+	0.188203i	$0.0602664\pi$
$43$			2.46826i			0.376407i	−0.982130	+	0.188203i	$0.939734\pi$
$44$	0.417963	−	2.10296i	0.0630102	−	0.317033i
$45$	1.96912	−	2.26331i	0.293539	−	0.337394i
$46$	9.75401	−	8.00619i	1.43815	−	1.18045i
$47$	5.04271			0.735554			0.367777	−	0.929914i	$-0.380119\pi$
$47$	5.04271			0.735554			0.367777	+	0.929914i	$0.380119\pi$
$48$	5.06746	+	4.72450i	0.731425	+	0.681922i
$49$	−1.00000			−0.142857
$50$	1.09313	−	0.897253i	0.154592	−	0.126891i
$51$	−3.26888	+	8.73746i	−0.457735	+	1.22349i
$52$	−0.672308	+	3.38269i	−0.0932323	+	0.469094i
$53$			4.28200i			0.588178i	0.955778	+	0.294089i	$0.0950163\pi$
$53$			4.28200i			0.588178i	−0.955778	+	0.294089i	$0.904984\pi$
$54$	6.80584	+	2.77138i	0.926158	+	0.377136i
$55$		−	1.07205i		−	0.144555i
$56$	2.49414	−	1.33390i	0.333293	−	0.178249i
$57$	1.21969	−	3.26012i	0.161551	−	0.431814i
$58$	1.51758	+	1.84889i	0.199269	+	0.242771i
$59$	−12.3591			−1.60901			−0.804507	−	0.593943i	$-0.797571\pi$
$59$	−12.3591			−1.60901			−0.804507	+	0.593943i	$0.797571\pi$
$60$	2.94561	+	1.82301i	0.380277	+	0.235350i
$61$	−11.1904			−1.43279			−0.716395	−	0.697695i	$-0.754209\pi$
$61$	−11.1904			−1.43279			−0.716395	+	0.697695i	$0.754209\pi$
$62$	2.93722	+	3.57844i	0.373027	+	0.454462i
$63$	1.96912	−	2.26331i	0.248086	−	0.285150i
$64$	−4.44144	+	6.65384i	−0.555180	+	0.831730i
$65$			1.72442i			0.213889i
$66$	2.48487	−	0.849187i	0.305866	−	0.104528i
$67$		−	4.42168i		−	0.540195i	−0.962833	−	0.270097i	$-0.912944\pi$
$67$		−	4.42168i		−	0.540195i	0.962833	−	0.270097i	$-0.0870559\pi$
$68$	−10.5655	−	2.09988i	−1.28125	−	0.254648i
$69$	14.4752	+	5.41551i	1.74261	+	0.651951i
$70$	1.09313	−	0.897253i	0.130654	−	0.107242i
$71$	6.71322			0.796712			0.398356	−	0.917231i	$-0.369581\pi$
$71$	6.71322			0.796712			0.398356	+	0.917231i	$0.369581\pi$
$72$	−1.89225	+	8.27160i	−0.223003	+	0.974818i
$73$	2.20666			0.258270			0.129135	−	0.991627i	$-0.458780\pi$
$73$	2.20666			0.258270			0.129135	+	0.991627i	$0.458780\pi$
$74$	9.78414	−	8.03092i	1.13738	−	0.933575i
$75$	1.62224	+	0.606916i	0.187320	+	0.0700806i
$76$	3.94219	+	0.783509i	0.452200	+	0.0898746i
$77$		−	1.07205i		−	0.122171i
$78$	−3.99700	+	1.36595i	−0.452571	+	0.154663i
$79$			2.97652i			0.334885i	0.985882	+	0.167442i	$0.0535508\pi$
$79$			2.97652i			0.334885i	−0.985882	+	0.167442i	$0.946449\pi$
$80$	−1.52958	+	3.69600i	−0.171012	+	0.413225i
$81$	1.24511	+	8.91346i	0.138346	+	0.990384i
$82$	10.6067	+	12.9223i	1.17132	+	1.42702i
$83$	−9.69674			−1.06436			−0.532178	−	0.846633i	$-0.678626\pi$
$83$	−9.69674			−1.06436			−0.532178	+	0.846633i	$0.678626\pi$
$84$	2.94561	+	1.82301i	0.321393	+	0.198907i
$85$	−5.38606			−0.584200
$86$	−2.21466	−	2.69814i	−0.238813	−	0.290947i
$87$	−1.02652	+	2.74380i	−0.110054	+	0.294166i
$88$	1.43000	+	2.67383i	0.152438	+	0.285031i
$89$		−	8.62897i		−	0.914669i	−0.889295	−	0.457335i	$-0.848804\pi$
$89$		−	8.62897i		−	0.914669i	0.889295	−	0.457335i	$-0.151196\pi$
$90$	−0.121752	+	4.24089i	−0.0128337	+	0.447029i
$91$			1.72442i			0.180769i
$92$	−3.47884	+	17.5036i	−0.362695	+	1.82488i
$93$	−1.98678	+	5.31050i	−0.206019	+	0.550673i
$94$	−5.51234	+	4.52458i	−0.568555	+	0.466675i
$95$	2.00965			0.206185
$96$	−9.77847	−	0.617704i	−0.998011	−	0.0630442i
$97$	13.7216			1.39321			0.696607	−	0.717453i	$-0.254692\pi$
$97$	13.7216			1.39321			0.696607	+	0.717453i	$0.254692\pi$
$98$	1.09313	−	0.897253i	0.110423	−	0.0906362i
$99$	2.42637	+	2.11099i	0.243859	+	0.212162i
$100$	−0.389874	+	1.96163i	−0.0389874	+	0.196163i
$101$			9.27538i			0.922935i	0.887157	+	0.461467i	$0.152677\pi$
$101$			9.27538i			0.922935i	−0.887157	+	0.461467i	$0.847323\pi$
$102$	−4.26640	−	12.4842i	−0.422436	−	1.23612i
$103$		−	0.394121i		−	0.0388339i	−0.999811	−	0.0194169i	$-0.993819\pi$
$103$		−	0.394121i		−	0.0388339i	0.999811	−	0.0194169i	$-0.00618099\pi$
$104$	−2.30020	−	4.30095i	−0.225554	−	0.421743i
$105$	1.62224	+	0.606916i	0.158314	+	0.0592289i
$106$	−3.84204	−	4.68079i	−0.373172	−	0.454639i
$107$	7.92337			0.765981			0.382990	−	0.923752i	$-0.374894\pi$
$107$	7.92337			0.765981			0.382990	+	0.923752i	$0.374894\pi$
$108$	−9.92631	+	3.07708i	−0.955159	+	0.296093i
$109$	4.53839			0.434699			0.217350	−	0.976094i	$-0.430259\pi$
$109$	4.53839			0.434699			0.217350	+	0.976094i	$0.430259\pi$
$110$	0.961896	+	1.17189i	0.0917132	+	0.111735i
$111$	14.5199	+	5.43224i	1.37817	+	0.515605i
$112$	−1.52958	+	3.69600i	−0.144532	+	0.349239i
$113$			5.85865i			0.551135i	0.961282	+	0.275568i	$0.0888658\pi$
$113$			5.85865i			0.551135i	−0.961282	+	0.275568i	$0.911134\pi$
$114$	1.59188	+	4.65811i	0.149093	+	0.436272i
$115$			8.92300i			0.832074i
$116$	−3.31784	−	0.659420i	−0.308054	−	0.0612256i
$117$	−3.90290	−	3.39560i	−0.360823	−	0.313924i
$118$	13.5101	−	11.0892i	1.24371	−	1.02085i
$119$	−5.38606			−0.493739
$120$	−4.85564	+	0.650165i	−0.443258	+	0.0593517i
$121$	−9.85072			−0.895520
$122$	12.2326	−	10.0407i	1.10749	−	0.909038i
$123$	−7.17454	+	19.1770i	−0.646907	+	1.72913i
$124$	−6.42153	−	1.27628i	−0.576670	−	0.114613i
$125$			1.00000i			0.0894427i
$126$	−0.121752	+	4.24089i	−0.0108465	+	0.377809i
$127$		−	21.6673i		−	1.92266i	−0.275402	−	0.961329i	$-0.588811\pi$
$127$		−	21.6673i		−	1.92266i	0.275402	−	0.961329i	$-0.411189\pi$
$128$	−1.11510	−	11.2586i	−0.0985619	−	0.995131i
$129$	1.49803	−	4.00411i	0.131894	−	0.352542i
$130$	−1.54725	−	1.88502i	−0.135702	−	0.165327i
$131$	16.8414			1.47144			0.735718	−	0.677288i	$-0.236845\pi$
$131$	16.8414			1.47144			0.735718	+	0.677288i	$0.236845\pi$
$132$	−1.95435	+	3.15783i	−0.170105	+	0.274854i
$133$	2.00965			0.174258
$134$	3.96737	+	4.83348i	0.342729	+	0.417549i
$135$	−4.56802	+	2.47653i	−0.393153	+	0.213146i
$136$	13.4336	−	7.18444i	1.15192	−	0.616061i
$137$			1.88824i			0.161323i	0.996742	+	0.0806615i	$0.0257033\pi$
$137$			1.88824i			0.161323i	−0.996742	+	0.0806615i	$0.974297\pi$
$138$	−20.6824	+	7.06807i	−1.76060	+	0.601674i
$139$		−	10.8407i		−	0.919495i	−0.888050	−	0.459747i	$-0.847940\pi$
$139$		−	10.8407i		−	0.919495i	0.888050	−	0.459747i	$-0.152060\pi$
$140$	−0.389874	+	1.96163i	−0.0329504	+	0.165788i
$141$	−8.18047	−	3.06050i	−0.688920	−	0.257740i
$142$	−7.33843	+	6.02345i	−0.615827	+	0.505477i
$143$	−1.84866			−0.154593
$144$	−5.35325	−	10.7398i	−0.446104	−	0.894981i
$145$	−1.69137			−0.140460
$146$	−2.41217	+	1.97993i	−0.199633	+	0.163860i
$147$	1.62224	+	0.606916i	0.133800	+	0.0500576i
$148$	−3.48959	+	17.5577i	−0.286842	+	1.44323i
$149$		−	1.96331i		−	0.160840i	−0.996761	−	0.0804202i	$-0.974374\pi$
$149$		−	1.96331i		−	0.160840i	0.996761	−	0.0804202i	$-0.0256262\pi$
$150$	−2.31788	+	0.792118i	−0.189254	+	0.0646762i
$151$			15.7675i			1.28314i	0.767065	+	0.641569i	$0.221716\pi$
$151$			15.7675i			1.28314i	−0.767065	+	0.641569i	$0.778284\pi$
$152$	−5.01233	+	2.68066i	−0.406554	+	0.217430i
$153$	10.6058	−	12.1903i	0.857429	−	0.985527i
$154$	0.961896	+	1.17189i	0.0775118	+	0.0944333i
$155$	−3.27357			−0.262939
$156$	3.14365	−	5.07948i	0.251693	−	0.406684i
$157$	17.3726			1.38649			0.693243	−	0.720704i	$-0.256181\pi$
$157$	17.3726			1.38649			0.693243	+	0.720704i	$0.256181\pi$
$158$	−2.67069	−	3.25373i	−0.212469	−	0.258853i
$159$	2.59882	−	6.94643i	0.206099	−	0.550887i
$160$	−1.64421	−	5.41263i	−0.129987	−	0.427906i
$161$			8.92300i			0.703231i
$162$	−9.35870	−	8.62640i	−0.735289	−	0.677754i
$163$		−	7.80107i		−	0.611027i	−0.952188	−	0.305514i	$-0.901172\pi$
$163$		−	7.80107i		−	0.611027i	0.952188	−	0.305514i	$-0.0988281\pi$
$164$	−23.1891	−	4.60882i	−1.81076	−	0.359889i
$165$	−0.650641	+	1.73911i	−0.0506524	+	0.135390i
$166$	10.5998	−	8.70043i	0.822705	−	0.675284i
$167$	6.05107			0.468246			0.234123	−	0.972207i	$-0.424778\pi$
$167$	6.05107			0.468246			0.234123	+	0.972207i	$0.424778\pi$
$168$	−4.85564	+	0.650165i	−0.374621	+	0.0501613i
$169$	−10.0264			−0.771258
$170$	5.88767	−	4.83266i	0.451564	−	0.370648i
$171$	−3.95724	+	4.54845i	−0.302618	+	0.347828i
$172$	4.84182	+	0.962311i	0.369185	+	0.0733755i
$173$		−	10.6700i		−	0.811223i	−0.914046	−	0.405611i	$-0.867059\pi$
$173$		−	10.6700i		−	0.811223i	0.914046	−	0.405611i	$-0.132941\pi$
$174$	−1.33976	−	3.92038i	−0.101567	−	0.297203i
$175$			1.00000i			0.0755929i
$176$	−3.96228	−	1.63978i	−0.298668	−	0.123603i
$177$	20.0494	+	7.50092i	1.50700	+	0.563804i
$178$	7.74237	+	9.43260i	0.580315	+	0.707004i
$179$	20.2873			1.51634			0.758171	−	0.652055i	$-0.226093\pi$
$179$	20.2873			1.51634			0.758171	+	0.652055i	$0.226093\pi$
$180$	−3.67206	−	4.74510i	−0.273699	−	0.353679i
$181$	−7.09011			−0.527004			−0.263502	−	0.964659i	$-0.584878\pi$
$181$	−7.09011			−0.527004			−0.263502	+	0.964659i	$0.584878\pi$
$182$	−1.54725	−	1.88502i	−0.114689	−	0.139727i
$183$	18.1535	+	6.79166i	1.34195	+	0.502054i
$184$	−11.9024	−	22.2552i	−0.877453	−	1.64067i
$185$			8.95056i			0.658058i
$186$	−2.59305	−	7.58772i	−0.190132	−	0.556359i
$187$		−	5.77410i		−	0.422244i
$188$	1.96602	−	9.89193i	0.143387	−	0.721443i
$189$	−4.56802	+	2.47653i	−0.332275	+	0.180141i
$190$	−2.19681	+	1.80316i	−0.159373	+	0.130815i
$191$	14.9389			1.08094			0.540472	−	0.841362i	$-0.318246\pi$
$191$	14.9389			1.08094			0.540472	+	0.841362i	$0.318246\pi$
$192$	11.2434	−	8.09853i	0.811422	−	0.584461i
$193$	20.0813			1.44549			0.722743	−	0.691117i	$-0.242881\pi$
$193$	20.0813			1.44549			0.722743	+	0.691117i	$0.242881\pi$
$194$	−14.9995	+	12.3117i	−1.07690	+	0.883930i
$195$	1.04658	−	2.79743i	0.0749472	−	0.200328i
$196$	−0.389874	+	1.96163i	−0.0278481	+	0.140117i
$197$		−	0.0667057i		−	0.00475259i	−0.999997	−	0.00237629i	$-0.999244\pi$
$197$		−	0.0667057i		−	0.00475259i	0.999997	−	0.00237629i	$-0.000756398\pi$
$198$	−4.54643	−	0.130523i	−0.323101	−	0.00927589i
$199$		−	21.6877i		−	1.53740i	−0.639609	−	0.768700i	$-0.720904\pi$
$199$		−	21.6877i		−	1.53740i	0.639609	−	0.768700i	$-0.279096\pi$
$200$	−1.33390	−	2.49414i	−0.0943207	−	0.176362i
$201$	−2.68359	+	7.17302i	−0.189286	+	0.505946i
$202$	−8.32236	−	10.1392i	−0.585559	−	0.713392i
$203$	−1.69137			−0.118711
$204$	15.8652	+	9.81885i	1.11079	+	0.687457i
$205$	−11.8213			−0.825637
$206$	0.353626	+	0.430826i	0.0246383	+	0.0300171i
$207$	−20.1955	−	17.5705i	−1.40368	−	1.22123i
$208$	6.37347	+	2.63764i	0.441920	+	0.182888i
$209$			2.15443i			0.149025i
$210$	−2.31788	+	0.792118i	−0.159949	+	0.0546614i
$211$		−	17.8037i		−	1.22566i	−0.790215	−	0.612830i	$-0.790031\pi$
$211$		−	17.8037i		−	1.22566i	0.790215	−	0.612830i	$-0.209969\pi$
$212$	8.39971	+	1.66944i	0.576895	+	0.114658i
$213$	−10.8904	−	4.07436i	−0.746200	−	0.279170i
$214$	−8.66129	+	7.10927i	−0.592073	+	0.485979i
$215$	2.46826			0.168334
$216$	8.08984	−	12.2701i	0.550444	−	0.834872i
$217$	−3.27357			−0.222224
$218$	−4.96106	+	4.07209i	−0.336006	+	0.275797i
$219$	−3.57973	−	1.33926i	−0.241896	−	0.0904986i
$220$	−2.10296	−	0.417963i	−0.141781	−	0.0281790i
$221$			9.28785i			0.624768i
$222$	−20.7463	+	7.08990i	−1.39240	+	0.475843i
$223$		−	13.6045i		−	0.911025i	−0.890229	−	0.455512i	$-0.849456\pi$
$223$		−	13.6045i		−	0.911025i	0.890229	−	0.455512i	$-0.150544\pi$
$224$	−1.64421	−	5.41263i	−0.109859	−	0.361647i
$225$	−2.26331	−	1.96912i	−0.150887	−	0.131275i
$226$	−5.25669	−	6.40427i	−0.349670	−	0.426006i
$227$	6.10415			0.405146			0.202573	−	0.979267i	$-0.435070\pi$
$227$	6.10415			0.405146			0.202573	+	0.979267i	$0.435070\pi$
$228$	−5.91964	−	3.66361i	−0.392037	−	0.242629i
$229$	−18.6048			−1.22944			−0.614718	−	0.788747i	$-0.710730\pi$
$229$	−18.6048			−1.22944			−0.614718	+	0.788747i	$0.710730\pi$
$230$	−8.00619	−	9.75401i	−0.527912	−	0.643161i
$231$	−0.650641	+	1.73911i	−0.0428091	+	0.114425i
$232$	4.21850	−	2.25611i	0.276958	−	0.148121i
$233$			26.9262i			1.76399i	0.471256	+	0.881996i	$0.343801\pi$
$233$			26.9262i			1.76399i	−0.471256	+	0.881996i	$0.656199\pi$
$234$	7.31310	+	0.209951i	0.478072	+	0.0137250i
$235$		−	5.04271i		−	0.328950i
$236$	−4.81848	+	24.2440i	−0.313656	+	1.57815i
$237$	1.80650	−	4.82862i	0.117345	−	0.313653i
$238$	5.88767	−	4.83266i	0.381641	−	0.313255i
$239$	−8.84647			−0.572231			−0.286115	−	0.958195i	$-0.592364\pi$
$239$	−8.84647			−0.572231			−0.286115	+	0.958195i	$0.592364\pi$
$240$	4.72450	−	5.06746i	0.304965	−	0.327103i
$241$	6.96358			0.448564			0.224282	−	0.974524i	$-0.427996\pi$
$241$	6.96358			0.448564			0.224282	+	0.974524i	$0.427996\pi$
$242$	10.7681	−	8.83859i	0.692202	−	0.568166i
$243$	3.38985	−	15.2154i	0.217459	−	0.976069i
$244$	−4.36286	+	21.9515i	−0.279304	+	1.40530i
$245$			1.00000i			0.0638877i
$246$	−9.36388	−	27.4003i	−0.597019	−	1.74698i
$247$		−	3.46548i		−	0.220503i
$248$	8.16472	−	4.36660i	0.518460	−	0.277279i
$249$	15.7304	+	5.88511i	0.996875	+	0.372953i
$250$	−0.897253	−	1.09313i	−0.0567473	−	0.0691357i
$251$	−12.0580			−0.761097			−0.380548	−	0.924761i	$-0.624265\pi$
$251$	−12.0580			−0.761097			−0.380548	+	0.924761i	$0.624265\pi$
$252$	−3.67206	−	4.74510i	−0.231318	−	0.298913i
$253$	−9.56586			−0.601401
$254$	19.4410	+	23.6852i	1.21984	+	1.48614i
$255$	8.73746	+	3.26888i	0.547161	+	0.204705i
$256$	11.3208	+	11.3066i	0.707549	+	0.706664i
$257$		−	15.1550i		−	0.945340i	−0.881240	−	0.472670i	$-0.843290\pi$
$257$		−	15.1550i		−	0.945340i	0.881240	−	0.472670i	$-0.156710\pi$
$258$	1.95516	+	5.72113i	0.121723	+	0.356182i
$259$			8.95056i			0.556161i
$260$	3.38269	+	0.672308i	0.209785	+	0.0416948i
$261$	3.33051	−	3.82808i	0.206153	−	0.236952i
$262$	−18.4098	+	15.1110i	−1.13736	+	0.933558i
$263$	−12.5299			−0.772625			−0.386313	−	0.922368i	$-0.626251\pi$
$263$	−12.5299			−0.772625			−0.386313	+	0.922368i	$0.626251\pi$
$264$	−0.697007	−	5.20547i	−0.0428978	−	0.320375i
$265$	4.28200			0.263041
$266$	−2.19681	+	1.80316i	−0.134695	+	0.110559i
$267$	−5.23706	+	13.9982i	−0.320503	+	0.856678i
$268$	−8.67372	−	1.72390i	−0.529832	−	0.105304i
$269$			25.2977i			1.54243i	0.636575	+	0.771215i	$0.280351\pi$
$269$			25.2977i			1.54243i	−0.636575	+	0.771215i	$0.719649\pi$
$270$	2.77138	−	6.80584i	0.168661	−	0.414190i
$271$			18.7529i			1.13916i	0.821937	+	0.569578i	$0.192893\pi$
$271$			18.7529i			1.13916i	−0.821937	+	0.569578i	$0.807107\pi$
$272$	−8.23839	+	19.9069i	−0.499526	+	1.20703i
$273$	1.04658	−	2.79743i	0.0633419	−	0.169308i
$274$	−1.69423	−	2.06409i	−0.102352	−	0.124696i
$275$	−1.07205			−0.0646468
$276$	16.2667	−	26.2837i	0.979143	−	1.58209i
$277$	−14.3252			−0.860719			−0.430359	−	0.902658i	$-0.641613\pi$
$277$	−14.3252			−0.860719			−0.430359	+	0.902658i	$0.641613\pi$
$278$	9.72684	+	11.8503i	0.583377	+	0.710734i
$279$	6.44605	−	7.40908i	0.385915	−	0.443570i
$280$	−1.33390	−	2.49414i	−0.0797156	−	0.149053i
$281$		−	18.7574i		−	1.11897i	−0.828841	−	0.559485i	$-0.810999\pi$
$281$		−	18.7574i		−	1.11897i	0.828841	−	0.559485i	$-0.189001\pi$
$282$	11.6884	−	3.99442i	0.696032	−	0.237864i
$283$			4.48257i			0.266461i	0.991085	+	0.133231i	$0.0425351\pi$
$283$			4.48257i			0.266461i	−0.991085	+	0.133231i	$0.957465\pi$
$284$	2.61731	−	13.1689i	0.155309	−	0.781428i
$285$	−3.26012	−	1.21969i	−0.193113	−	0.0722480i
$286$	2.02083	−	1.65872i	0.119494	−	0.0980820i
$287$	−11.8213			−0.697790
$288$	15.4881	+	6.93677i	0.912645	+	0.408753i
$289$	−12.0096			−0.706448
$290$	1.84889	−	1.51758i	0.108570	−	0.0891156i
$291$	−22.2596	−	8.32784i	−1.30488	−	0.488186i
$292$	0.860319	−	4.32866i	0.0503464	−	0.253315i
$293$		−	4.84084i		−	0.282805i	−0.989952	−	0.141403i	$-0.954839\pi$
$293$		−	4.84084i		−	0.282805i	0.989952	−	0.141403i	$-0.0451612\pi$
$294$	−2.31788	+	0.792118i	−0.135181	+	0.0461973i
$295$			12.3591i			0.719573i
$296$	−11.9391	−	22.3239i	−0.693947	−	1.29755i
$297$	−2.65495	−	4.89713i	−0.154056	−	0.284160i
$298$	1.76158	+	2.14615i	0.102046	+	0.124323i
$299$	15.3870			0.889855
$300$	1.82301	−	2.94561i	0.105252	−	0.170065i
$301$	2.46826			0.142268
$302$	−14.1474	−	17.2359i	−0.814092	−	0.991816i
$303$	5.62937	−	15.0469i	0.323399	−	0.864420i
$304$	3.07391	−	7.42765i	0.176301	−	0.426005i
$305$			11.1904i			0.640763i
$306$	−0.655761	+	22.8417i	−0.0374874	+	1.30577i
$307$			13.4869i			0.769736i	0.922972	+	0.384868i	$0.125753\pi$
$307$			13.4869i			0.769736i	−0.922972	+	0.384868i	$0.874247\pi$
$308$	−2.10296	−	0.417963i	−0.119827	−	0.0238156i
$309$	−0.239198	+	0.639358i	−0.0136075	+	0.0363718i
$310$	3.57844	−	2.93722i	0.203242	−	0.166823i
$311$	−1.94704			−0.110406			−0.0552032	−	0.998475i	$-0.517581\pi$
$311$	−1.94704			−0.110406			−0.0552032	+	0.998475i	$0.517581\pi$
$312$	1.12116	+	8.37319i	0.0634732	+	0.474039i
$313$	19.9111			1.12544			0.562720	−	0.826647i	$-0.309755\pi$
$313$	19.9111			1.12544			0.562720	+	0.826647i	$0.309755\pi$
$314$	−18.9906	+	15.5876i	−1.07170	+	0.879661i
$315$	−2.26331	−	1.96912i	−0.127523	−	0.110947i
$316$	5.83883	+	1.16047i	0.328460	+	0.0652814i
$317$			33.7879i			1.89772i	0.315701	+	0.948859i	$0.397760\pi$
$317$			33.7879i			1.89772i	−0.315701	+	0.948859i	$0.602240\pi$
$318$	3.39185	+	9.92515i	0.190206	+	0.556575i
$319$		−	1.81322i		−	0.101521i
$320$	6.65384	+	4.44144i	0.371961	+	0.248284i
$321$	−12.8536	−	4.80882i	−0.717417	−	0.268402i
$322$	−8.00619	−	9.75401i	−0.446167	−	0.543570i
$323$	10.8241			0.602267
$324$	17.9704	+	1.03267i	0.998353	+	0.0573706i
$325$	1.72442			0.0956539
$326$	6.99954	+	8.52760i	0.387668	+	0.472300i
$327$	−7.36235	−	2.75442i	−0.407139	−	0.152320i
$328$	29.4840	−	15.7684i	1.62798	−	0.870665i
$329$		−	5.04271i		−	0.278013i
$330$	−0.849187	−	2.48487i	−0.0467462	−	0.136788i
$331$			14.3814i			0.790472i	0.918580	+	0.395236i	$0.129337\pi$
$331$			14.3814i			0.790472i	−0.918580	+	0.395236i	$0.870663\pi$
$332$	−3.78051	+	19.0214i	−0.207482	+	1.04394i
$333$	−20.2579	−	17.6248i	−1.11012	−	0.965830i
$334$	−6.61462	+	5.42934i	−0.361936	+	0.297081i
$335$	−4.42168			−0.241582
$336$	4.72450	−	5.06746i	0.257742	−	0.276453i
$337$	25.1270			1.36875			0.684377	−	0.729128i	$-0.260074\pi$
$337$	25.1270			1.36875			0.684377	+	0.729128i	$0.260074\pi$
$338$	10.9601	−	8.99618i	0.596153	−	0.489328i
$339$	3.55570	−	9.50411i	0.193119	−	0.516193i
$340$	−2.09988	+	10.5655i	−0.113882	+	0.572993i
$341$		−	3.50941i		−	0.190045i
$342$	0.244678	−	8.52270i	0.0132307	−	0.460855i
$343$			1.00000i			0.0539949i
$344$	−6.15619	+	3.29241i	−0.331919	+	0.177515i
$345$	5.41551	−	14.4752i	0.291561	−	0.779320i
$346$	9.57366	+	11.6637i	0.514683	+	0.627043i
$347$	−20.6683			−1.10953			−0.554765	−	0.832007i	$-0.687192\pi$
$347$	−20.6683			−1.10953			−0.554765	+	0.832007i	$0.687192\pi$
$348$	4.98211	+	3.08338i	0.267069	+	0.165287i
$349$	−20.9802			−1.12305			−0.561523	−	0.827461i	$-0.689785\pi$
$349$	−20.9802			−1.12305			−0.561523	+	0.827461i	$0.689785\pi$
$350$	−0.897253	−	1.09313i	−0.0479602	−	0.0584303i
$351$	4.27059	+	7.87721i	0.227947	+	0.420454i
$352$	5.80259	−	1.76267i	0.309279	−	0.0939508i
$353$		−	2.07741i		−	0.110569i	−0.998471	−	0.0552847i	$-0.982393\pi$
$353$		−	2.07741i		−	0.110569i	0.998471	−	0.0552847i	$-0.0176066\pi$
$354$	−28.6468	+	9.78985i	−1.52256	+	0.520325i
$355$		−	6.71322i		−	0.356301i
$356$	−16.9269	−	3.36421i	−0.897122	−	0.178303i
$357$	8.73746	+	3.26888i	0.462436	+	0.173008i
$358$	−22.1767	+	18.2028i	−1.17207	+	0.962049i
$359$	−31.6594			−1.67092			−0.835460	−	0.549551i	$-0.814799\pi$
$359$	−31.6594			−1.67092			−0.835460	+	0.549551i	$0.814799\pi$
$360$	8.27160	+	1.89225i	0.435952	+	0.0997301i
$361$	14.9613			0.787438
$362$	7.75043	−	6.36162i	0.407353	−	0.334360i
$363$	15.9802	+	5.97856i	0.838743	+	0.313793i
$364$	3.38269	+	0.672308i	0.177301	+	0.0352385i
$365$		−	2.20666i		−	0.115502i
$366$	−25.9381	+	8.86415i	−1.35580	+	0.463337i
$367$			20.4298i			1.06643i	0.845981	+	0.533213i	$0.179016\pi$
$367$			20.4298i			1.06643i	−0.845981	+	0.533213i	$0.820984\pi$
$368$	32.9794	+	13.6484i	1.71917	+	0.711473i
$369$	23.2776	−	26.7553i	1.21178	−	1.39282i
$370$	−8.03092	−	9.78414i	−0.417508	−	0.508653i
$371$	4.28200			0.222311
$372$	9.64265	+	5.96775i	0.499948	+	0.309414i
$373$	24.6871			1.27825			0.639126	−	0.769102i	$-0.279296\pi$
$373$	24.6871			1.27825			0.639126	+	0.769102i	$0.279296\pi$
$374$	5.18083	+	6.31185i	0.267894	+	0.326378i
$375$	0.606916	−	1.62224i	0.0313410	−	0.0837720i
$376$	6.72645	+	12.5772i	0.346890	+	0.648620i
$377$			2.91663i			0.150214i
$378$	2.77138	−	6.80584i	0.142544	−	0.350055i
$379$		−	4.33039i		−	0.222437i	−0.993796	−	0.111219i	$-0.964525\pi$
$379$		−	4.33039i		−	0.222437i	0.993796	−	0.111219i	$-0.0354754\pi$
$380$	0.783509	−	3.94219i	0.0401931	−	0.202230i
$381$	−13.1502	+	35.1494i	−0.673705	+	1.80076i
$382$	−16.3302	+	13.4040i	−0.835527	+	0.685809i
$383$	13.4106			0.685250			0.342625	−	0.939472i	$-0.388684\pi$
$383$	13.4106			0.685250			0.342625	+	0.939472i	$0.388684\pi$
$384$	−5.02408	+	18.9409i	−0.256384	+	0.966575i
$385$	−1.07205			−0.0546365
$386$	−21.9515	+	18.0180i	−1.11730	+	0.917093i
$387$	−4.86031	+	5.58643i	−0.247064	+	0.283974i
$388$	5.34968	−	26.9167i	0.271589	−	1.36649i
$389$		−	22.4749i		−	1.13952i	−0.821810	−	0.569761i	$-0.807036\pi$
$389$		−	22.4749i		−	1.13952i	0.821810	−	0.569761i	$-0.192964\pi$
$390$	1.36595	+	3.99700i	0.0691675	+	0.202396i
$391$			48.0598i			2.43049i
$392$	−1.33390	−	2.49414i	−0.0673719	−	0.125973i
$393$	−27.3207	−	10.2213i	−1.37815	−	0.515595i
$394$	0.0598519	+	0.0729181i	0.00301530	+	0.00367356i
$395$	2.97652			0.149765
$396$	5.08696	−	3.93662i	0.255629	−	0.197823i
$397$	−14.6132			−0.733417			−0.366709	−	0.930336i	$-0.619515\pi$
$397$	−14.6132			−0.733417			−0.366709	+	0.930336i	$0.619515\pi$
$398$	19.4594	+	23.7075i	0.975409	+	1.18835i
$399$	−3.26012	−	1.21969i	−0.163210	−	0.0610607i
$400$	3.69600	+	1.52958i	0.184800	+	0.0764789i
$401$		−	38.5750i		−	1.92634i	−0.268889	−	0.963171i	$-0.586656\pi$
$401$		−	38.5750i		−	1.92634i	0.268889	−	0.963171i	$-0.413344\pi$
$402$	−3.50250	−	10.2489i	−0.174689	−	0.511169i
$403$			5.64502i			0.281198i
$404$	18.1949	+	3.61623i	0.905229	+	0.179914i
$405$	8.91346	−	1.24511i	0.442913	−	0.0618701i
$406$	1.84889	−	1.51758i	0.0917587	−	0.0753164i
$407$	−9.59541			−0.475627
$408$	−26.1528	+	3.50183i	−1.29476	+	0.173366i
$409$	−0.134480			−0.00664963			−0.00332481	−	0.999994i	$-0.501058\pi$
$409$	−0.134480			−0.00664963			−0.00332481	+	0.999994i	$0.501058\pi$
$410$	12.9223	−	10.6067i	0.638185	−	0.523828i
$411$	1.14600	−	3.06317i	0.0565281	−	0.151095i
$412$	−0.773120	−	0.153657i	−0.0380889	−	0.00757016i
$413$			12.3591i			0.608150i
$414$	37.8415	+	1.08639i	1.85981	+	0.0533931i
$415$			9.69674i			0.475994i
$416$	−9.33367	+	2.83532i	−0.457621	+	0.139013i
$417$	−6.57938	+	17.5862i	−0.322194	+	0.861198i
$418$	−1.93307	−	2.35508i	−0.0945496	−	0.115191i
$419$	26.3509			1.28732			0.643662	−	0.765310i	$-0.277414\pi$
$419$	26.3509			1.28732			0.643662	+	0.765310i	$0.277414\pi$
$420$	1.82301	−	2.94561i	0.0889539	−	0.143731i
$421$	14.6370			0.713366			0.356683	−	0.934226i	$-0.383908\pi$
$421$	14.6370			0.713366			0.356683	+	0.934226i	$0.383908\pi$
$422$	15.9745	+	19.4618i	0.777624	+	0.947387i
$423$	11.4132	+	9.92971i	0.554928	+	0.482799i
$424$	−10.6799	+	5.71175i	−0.518662	+	0.277387i
$425$			5.38606i			0.261262i
$426$	15.5604	−	5.31766i	0.753904	−	0.257642i
$427$			11.1904i			0.541543i
$428$	3.08911	−	15.5427i	0.149318	−	0.751286i
$429$	2.99897	+	1.12198i	0.144792	+	0.0541698i
$430$	−2.69814	+	2.21466i	−0.130116	+	0.106800i
$431$	−0.863259			−0.0415817			−0.0207909	−	0.999784i	$-0.506618\pi$
$431$	−0.863259			−0.0415817			−0.0207909	+	0.999784i	$0.506618\pi$
$432$	2.16610	+	20.6714i	0.104216	+	0.994555i
$433$	−31.4459			−1.51119			−0.755597	−	0.655037i	$-0.772653\pi$
$433$	−31.4459			−1.51119			−0.755597	+	0.655037i	$0.772653\pi$
$434$	3.57844	−	2.93722i	0.171771	−	0.140991i
$435$	2.74380	+	1.02652i	0.131555	+	0.0492177i
$436$	1.76940	−	8.90266i	0.0847389	−	0.426360i
$437$		−	17.9321i		−	0.857807i
$438$	5.11477	−	1.74794i	0.244393	−	0.0835197i
$439$			25.4002i			1.21228i	0.795357	+	0.606142i	$0.207284\pi$
$439$			25.4002i			1.21228i	−0.795357	+	0.606142i	$0.792716\pi$
$440$	2.67383	−	1.43000i	0.127470	−	0.0681725i
$441$	−2.26331	−	1.96912i	−0.107776	−	0.0937677i
$442$	−8.33355	−	10.1528i	−0.396387	−	0.482921i
$443$	14.4712			0.687546			0.343773	−	0.939053i	$-0.388295\pi$
$443$	14.4712			0.687546			0.343773	+	0.939053i	$0.388295\pi$
$444$	16.3170	−	26.3649i	0.774370	−	1.25122i
$445$	−8.62897			−0.409053
$446$	12.2067	+	14.8715i	0.578003	+	0.704186i
$447$	−1.19156	+	3.18495i	−0.0563589	+	0.150643i
$448$	6.65384	+	4.44144i	0.314364	+	0.209838i
$449$		−	23.0450i		−	1.08756i	−0.839227	−	0.543782i	$-0.816992\pi$
$449$		−	23.0450i		−	1.08756i	0.839227	−	0.543782i	$-0.183008\pi$
$450$	4.24089	+	0.121752i	0.199918	+	0.00573943i
$451$		−	12.6730i		−	0.596748i
$452$	11.4925	+	2.28413i	0.540562	+	0.107437i
$453$	9.56953	−	25.5786i	0.449616	−	1.20179i
$454$	−6.67264	+	5.47696i	−0.313162	+	0.257047i
$455$	1.72442			0.0808423
$456$	9.75813	−	1.30660i	0.456966	−	0.0611872i
$457$	25.5690			1.19607			0.598034	−	0.801471i	$-0.295949\pi$
$457$	25.5690			1.19607			0.598034	+	0.801471i	$0.295949\pi$
$458$	20.3374	−	16.6932i	0.950306	−	0.780021i
$459$	−24.6036	+	13.3387i	−1.14840	+	0.622598i
$460$	17.5036	+	3.47884i	0.816111	+	0.162202i
$461$		−	1.13772i		−	0.0529891i	−0.999649	−	0.0264945i	$-0.991566\pi$
$461$		−	1.13772i		−	0.0529891i	0.999649	−	0.0264945i	$-0.00843446\pi$
$462$	−0.849187	−	2.48487i	−0.0395078	−	0.115607i
$463$			13.5440i			0.629441i	0.949184	+	0.314720i	$0.101911\pi$
$463$			13.5440i			0.629441i	−0.949184	+	0.314720i	$0.898089\pi$
$464$	−2.58708	+	6.25129i	−0.120102	+	0.290209i
$465$	5.31050	+	1.98678i	0.246269	+	0.0921347i
$466$	−24.1596	−	29.4339i	−1.11917	−	1.36350i
$467$	17.0238			0.787769			0.393884	−	0.919160i	$-0.371131\pi$
$467$	17.0238			0.787769			0.393884	+	0.919160i	$0.371131\pi$
$468$	−8.18256	+	6.33220i	−0.378239	+	0.292706i
$469$	−4.42168			−0.204174
$470$	4.52458	+	5.51234i	0.208704	+	0.254265i
$471$	−28.1825	−	10.5437i	−1.29858	−	0.485829i
$472$	−16.4857	−	30.8252i	−0.758817	−	1.41885i
$473$			2.64609i			0.121667i
$474$	2.35776	+	6.89920i	0.108295	+	0.316891i
$475$		−	2.00965i		−	0.0922089i
$476$	−2.09988	+	10.5655i	−0.0962480	+	0.484267i
$477$	−8.43179	+	9.69149i	−0.386065	+	0.443743i
$478$	9.67036	−	7.93752i	0.442312	−	0.363054i
$479$	−8.49209			−0.388014			−0.194007	−	0.981000i	$-0.562148\pi$
$479$	−8.49209			−0.388014			−0.194007	+	0.981000i	$0.562148\pi$
$480$	−0.617704	+	9.77847i	−0.0281942	+	0.446324i
$481$	15.4346			0.703756
$482$	−7.61212	+	6.24810i	−0.346722	+	0.284593i
$483$	5.41551	−	14.4752i	0.246414	−	0.658645i
$484$	−3.84054	+	19.3235i	−0.174570	+	0.878340i
$485$		−	13.7216i		−	0.623064i
$486$	9.94653	+	19.6740i	0.451184	+	0.892431i
$487$		−	26.9280i		−	1.22022i	−0.792316	−	0.610111i	$-0.791125\pi$
$487$		−	26.9280i		−	1.22022i	0.792316	−	0.610111i	$-0.208875\pi$
$488$	−14.9269	−	27.9105i	−0.675709	−	1.26345i
$489$	−4.73459	+	12.6552i	−0.214106	+	0.572287i
$490$	−0.897253	−	1.09313i	−0.0405338	−	0.0493827i
$491$	−17.9651			−0.810753			−0.405377	−	0.914150i	$-0.632860\pi$
$491$	−17.9651			−0.810753			−0.405377	+	0.914150i	$0.632860\pi$
$492$	34.8210	+	21.5504i	1.56985	+	0.971568i
$493$	−9.10980			−0.410285
$494$	3.10942	+	3.78823i	0.139899	+	0.170441i
$495$	2.11099	−	2.42637i	0.0948819	−	0.109057i
$496$	−5.00717	+	12.0991i	−0.224829	+	0.543265i
$497$		−	6.71322i		−	0.301129i
$498$	−22.4758	+	7.68097i	−1.00717	+	0.344192i
$499$			11.1090i			0.497308i	0.968592	+	0.248654i	$0.0799881\pi$
$499$			11.1090i			0.497308i	−0.968592	+	0.248654i	$0.920012\pi$
$500$	1.96163	+	0.389874i	0.0877268	+	0.0174357i
$501$	−9.81628	−	3.67249i	−0.438559	−	0.164075i
$502$	13.1810	−	10.8191i	0.588298	−	0.482881i
$503$	−32.3691			−1.44327			−0.721633	−	0.692275i	$-0.756608\pi$
$503$	−32.3691			−1.44327			−0.721633	+	0.692275i	$0.756608\pi$
$504$	8.27160	+	1.89225i	0.368446	+	0.0842873i
$505$	9.27538			0.412749
$506$	10.4567	−	8.58300i	0.464859	−	0.381561i
$507$	16.2651	+	6.08516i	0.722360	+	0.270251i
$508$	−42.5032	−	8.44750i	−1.88577	−	0.374797i
$509$		−	24.4080i		−	1.08186i	−0.841066	−	0.540932i	$-0.818072\pi$
$509$		−	24.4080i		−	1.08186i	0.841066	−	0.540932i	$-0.181928\pi$
$510$	−12.4842	+	4.26640i	−0.552810	+	0.188919i
$511$		−	2.20666i		−	0.0976169i
$512$	−22.5200	−	2.20203i	−0.995253	−	0.0973167i
$513$	9.18010	−	4.97695i	0.405312	−	0.219738i
$514$	13.5978	+	16.5664i	0.599775	+	0.730711i
$515$	−0.394121			−0.0173670
$516$	−7.27054	−	4.49967i	−0.320068	−	0.198087i
$517$	5.40601			0.237756
$518$	−8.03092	−	9.78414i	−0.352858	−	0.429891i
$519$	−6.47577	+	17.3092i	−0.284255	+	0.759790i
$520$	−4.30095	+	2.30020i	−0.188609	+	0.100871i
$521$		−	7.28172i		−	0.319018i	−0.987196	−	0.159509i	$-0.949009\pi$
$521$		−	7.28172i		−	0.319018i	0.987196	−	0.159509i	$-0.0509911\pi$
$522$	−0.205927	+	7.17291i	−0.00901316	+	0.313950i
$523$		−	25.4602i		−	1.11330i	−0.830748	−	0.556649i	$-0.812087\pi$
$523$		−	25.4602i		−	1.11330i	0.830748	−	0.556649i	$-0.187913\pi$
$524$	6.56600	−	33.0365i	0.286837	−	1.44321i
$525$	0.606916	−	1.62224i	0.0264880	−	0.0708002i
$526$	13.6968	−	11.2425i	0.597209	−	0.490195i
$527$	−17.6316			−0.768045
$528$	5.43255	+	5.06488i	0.236421	+	0.220420i
$529$	56.6199			2.46174
$530$	−4.68079	+	3.84204i	−0.203321	+	0.166888i
$531$	−27.9724	−	24.3365i	−1.21390	−	1.05612i
$532$	0.783509	−	3.94219i	0.0339694	−	0.170915i
$533$			20.3850i			0.882971i
$534$	−6.83517	−	20.0009i	−0.295787	−	0.865523i
$535$		−	7.92337i		−	0.342557i
$536$	11.0283	−	5.89807i	0.476350	−	0.254758i
$537$	−32.9108	−	12.3127i	−1.42021	−	0.531331i
$538$	−22.6985	−	27.6538i	−0.978601	−	1.19224i
$539$	−1.07205			−0.0461763
$540$	3.07708	+	9.92631i	0.132417	+	0.427160i
$541$	−17.1802			−0.738637			−0.369318	−	0.929303i	$-0.620409\pi$
$541$	−17.1802			−0.738637			−0.369318	+	0.929303i	$0.620409\pi$
$542$	−16.8261	−	20.4994i	−0.722742	−	0.880523i
$543$	11.5018	+	4.30310i	0.493591	+	0.184664i
$544$	−8.85583	−	29.1527i	−0.379691	−	1.24991i
$545$		−	4.53839i		−	0.194403i
$546$	1.36595	+	3.99700i	0.0584572	+	0.171056i
$547$		−	15.9895i		−	0.683661i	−0.939762	−	0.341830i	$-0.888953\pi$
$547$		−	15.9895i		−	0.683661i	0.939762	−	0.341830i	$-0.111047\pi$
$548$	3.70403	+	0.736174i	0.158228	+	0.0314478i
$549$	−25.3274	−	22.0354i	−1.08095	−	0.940446i
$550$	1.17189	−	0.961896i	0.0499694	−	0.0410154i
$551$	3.39905			0.144804
$552$	5.80142	+	43.3269i	0.246925	+	1.84412i
$553$	2.97652			0.126574
$554$	15.6593	−	12.8533i	0.665302	−	0.546086i
$555$	5.43224	−	14.5199i	0.230586	−	0.616337i
$556$	−21.2654	−	4.22650i	−0.901855	−	0.179244i
$557$		−	20.8276i		−	0.882494i	−0.897386	−	0.441247i	$-0.854536\pi$
$557$		−	20.8276i		−	0.882494i	0.897386	−	0.441247i	$-0.145464\pi$
$558$	−0.398562	+	13.8828i	−0.0168725	+	0.587708i
$559$		−	4.25633i		−	0.180024i
$560$	3.69600	+	1.52958i	0.156184	+	0.0646365i
$561$	−3.50439	+	9.36696i	−0.147956	+	0.395473i
$562$	16.8301	+	20.5043i	0.709935	+	0.864920i
$563$	−12.1108			−0.510408			−0.255204	−	0.966887i	$-0.582143\pi$
$563$	−12.1108			−0.510408			−0.255204	+	0.966887i	$0.582143\pi$
$564$	−9.19292	+	14.8539i	−0.387092	+	0.625460i
$565$	5.85865			0.246475
$566$	−4.02200	−	4.90004i	−0.169057	−	0.205964i
$567$	8.91346	−	1.24511i	0.374330	−	0.0522898i
$568$	8.95474	+	16.7437i	0.375732	+	0.702549i
$569$			31.9004i			1.33733i	0.743562	+	0.668667i	$0.233135\pi$
$569$			31.9004i			1.33733i	−0.743562	+	0.668667i	$0.766865\pi$
$570$	4.65811	−	1.59188i	0.195107	−	0.0666764i
$571$		−	9.54804i		−	0.399573i	−0.979839	−	0.199786i	$-0.935975\pi$
$571$		−	9.54804i		−	0.399573i	0.979839	−	0.199786i	$-0.0640248\pi$
$572$	−0.720745	+	3.62639i	−0.0301359	+	0.151627i
$573$	−24.2345	−	9.06668i	−1.01241	−	0.378766i
$574$	12.9223	−	10.6067i	0.539365	−	0.442716i
$575$	8.92300			0.372115
$576$	−23.1546	+	6.31394i	−0.964774	+	0.263081i
$577$	−10.0000			−0.416307			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416307			−0.208153	+	0.978096i	$0.566745\pi$
$578$	13.1281	−	10.7757i	0.546057	−	0.448209i
$579$	−32.5767	−	12.1877i	−1.35384	−	0.506502i
$580$	−0.659420	+	3.31784i	−0.0273809	+	0.137766i
$581$			9.69674i			0.402289i
$582$	31.8049	−	10.8691i	1.31836	−	0.450539i
$583$			4.59050i			0.190119i
$584$	2.94346	+	5.50372i	0.121801	+	0.227745i
$585$	−3.39560	+	3.90290i	−0.140391	+	0.161365i
$586$	4.34346	+	5.29168i	0.179427	+	0.218597i
$587$	11.2911			0.466035			0.233018	−	0.972473i	$-0.425140\pi$
$587$	11.2911			0.466035			0.233018	+	0.972473i	$0.425140\pi$
$588$	1.82301	−	2.94561i	0.0751798	−	0.121475i
$589$	6.57871			0.271071
$590$	−11.0892	−	13.5101i	−0.456536	−	0.556202i
$591$	−0.0404848	+	0.108212i	−0.00166532	+	0.00445127i
$592$	33.0812	+	13.6906i	1.35963	+	0.562679i
$593$			20.6062i			0.846196i	0.906084	+	0.423098i	$0.139057\pi$
$593$			20.6062i			0.846196i	−0.906084	+	0.423098i	$0.860943\pi$
$594$	7.29617	+	2.97104i	0.299366	+	0.121903i
$595$			5.38606i			0.220807i
$596$	−3.85128	−	0.765442i	−0.157755	−	0.0313537i
$597$	−13.1626	+	35.1826i	−0.538710	+	1.43993i
$598$	−16.8201	+	13.8061i	−0.687823	+	0.564572i
$599$	16.0663			0.656449			0.328225	−	0.944600i	$-0.393550\pi$
$599$	16.0663			0.656449			0.328225	+	0.944600i	$0.393550\pi$
$600$	0.650165	+	4.85564i	0.0265429	+	0.198231i
$601$	−32.0367			−1.30681			−0.653403	−	0.757010i	$-0.726659\pi$
$601$	−32.0367			−1.30681			−0.653403	+	0.757010i	$0.726659\pi$
$602$	−2.69814	+	2.21466i	−0.109968	+	0.0902626i
$603$	8.70684	−	10.0076i	0.354570	−	0.407542i
$604$	30.9300	+	6.14733i	1.25852	+	0.250131i
$605$			9.85072i			0.400489i
$606$	7.34720	+	21.4992i	0.298459	+	0.873344i
$607$		−	3.95445i		−	0.160506i	−0.996775	−	0.0802532i	$-0.974427\pi$
$607$		−	3.95445i		−	0.160506i	0.996775	−	0.0802532i	$-0.0255729\pi$
$608$	3.30429	+	10.8775i	0.134007	+	0.441140i
$609$	2.74380	+	1.02652i	0.111184	+	0.0415966i
$610$	−10.0407	−	12.2326i	−0.406534	−	0.495285i
$611$	−8.69577			−0.351793
$612$	−19.7779	−	25.5574i	−0.799476	−	1.03310i
$613$	−4.60072			−0.185821			−0.0929106	−	0.995674i	$-0.529617\pi$
$613$	−4.60072			−0.185821			−0.0929106	+	0.995674i	$0.529617\pi$
$614$	−12.1011	−	14.7429i	−0.488362	−	0.594976i
$615$	19.1770	+	7.17454i	0.773291	+	0.289306i
$616$	2.67383	−	1.43000i	0.107732	−	0.0576163i
$617$		−	13.6198i		−	0.548313i	−0.961685	−	0.274157i	$-0.911601\pi$
$617$		−	13.6198i		−	0.548313i	0.961685	−	0.274157i	$-0.0883986\pi$
$618$	−0.312190	−	0.913523i	−0.0125581	−	0.0367473i
$619$			13.0679i			0.525244i	0.964899	+	0.262622i	$0.0845872\pi$
$619$			13.0679i			0.525244i	−0.964899	+	0.262622i	$0.915413\pi$
$620$	−1.27628	+	6.42153i	−0.0512565	+	0.257895i
$621$	22.0981	+	40.7604i	0.886765	+	1.63566i
$622$	2.12837	−	1.74699i	0.0853399	−	0.0700478i
$623$	−8.62897			−0.345713
$624$	−8.73845	−	8.14704i	−0.349818	−	0.326143i
$625$	1.00000			0.0400000
$626$	−21.7654	+	17.8653i	−0.869922	+	0.714040i
$627$	1.30756	−	3.49500i	0.0522189	−	0.139577i
$628$	6.77313	−	34.0787i	0.270277	−	1.35989i
$629$			48.2082i			1.92219i
$630$	4.24089	+	0.121752i	0.168961	+	0.00485070i
$631$		−	39.6858i		−	1.57987i	−0.613191	−	0.789934i	$-0.710115\pi$
$631$		−	39.6858i		−	1.57987i	0.613191	−	0.789934i	$-0.289885\pi$
$632$	−7.42385	+	3.97037i	−0.295305	+	0.157933i
$633$	−10.8054	+	28.8819i	−0.429475	+	1.14795i
$634$	−30.3163	−	36.9346i	−1.20401	−	1.46686i
$635$	−21.6673			−0.859839
$636$	−12.6131	−	7.80615i	−0.500143	−	0.309534i
$637$	1.72442			0.0683242
$638$	1.62692	+	1.98209i	0.0644103	+	0.0784717i
$639$	15.1941	+	13.2191i	0.601068	+	0.522941i
$640$	−11.2586	+	1.11510i	−0.445036	+	0.0440782i
$641$			4.32984i			0.171018i	0.996337	+	0.0855092i	$0.0272517\pi$
$641$			4.32984i			0.171018i	−0.996337	+	0.0855092i	$0.972748\pi$
$642$	18.3654	−	6.27625i	0.724824	−	0.247704i
$643$			15.5792i			0.614385i	0.951647	+	0.307192i	$0.0993895\pi$
$643$			15.5792i			0.614385i	−0.951647	+	0.307192i	$0.900610\pi$
$644$	17.5036	+	3.47884i	0.689740	+	0.137086i
$645$	−4.00411	−	1.49803i	−0.157662	−	0.0589848i
$646$	−11.8321	+	9.71193i	−0.465529	+	0.382111i
$647$	−32.4643			−1.27630			−0.638151	−	0.769911i	$-0.720301\pi$
$647$	−32.4643			−1.27630			−0.638151	+	0.769911i	$0.720301\pi$
$648$	−20.5705	+	14.9951i	−0.808087	+	0.589064i
$649$	−13.2495			−0.520088
$650$	−1.88502	+	1.54725i	−0.0739367	+	0.0606879i
$651$	5.31050	+	1.98678i	0.208135	+	0.0778680i
$652$	−15.3028	−	3.04143i	−0.599305	−	0.119112i
$653$		−	42.3830i		−	1.65857i	−0.558824	−	0.829287i	$-0.688747\pi$
$653$		−	42.3830i		−	1.65857i	0.558824	−	0.829287i	$-0.311253\pi$
$654$	10.5194	−	3.59494i	0.411342	−	0.140573i
$655$		−	16.8414i		−	0.658046i
$656$	−18.0816	+	43.6916i	−0.705969	+	1.70587i
$657$	4.99435	+	4.34519i	0.194848	+	0.169522i
$658$	4.52458	+	5.51234i	0.176387	+	0.214894i
$659$	6.65829			0.259370			0.129685	−	0.991555i	$-0.458603\pi$
$659$	6.65829			0.259370			0.129685	+	0.991555i	$0.458603\pi$
$660$	3.15783	+	1.95435i	0.122918	+	0.0760731i
$661$	36.1742			1.40701			0.703507	−	0.710688i	$-0.251616\pi$
$661$	36.1742			1.40701			0.703507	+	0.710688i	$0.251616\pi$
$662$	−12.9037	−	15.7207i	−0.501518	−	0.611004i
$663$	5.63694	−	15.0671i	0.218921	−	0.585157i
$664$	−12.9345	−	24.1850i	−0.501954	−	0.938560i
$665$		−	2.00965i		−	0.0779307i
$666$	37.9584	+	1.08975i	1.47086	+	0.0422268i
$667$			15.0921i			0.584367i
$668$	2.35916	−	11.8700i	0.0912785	−	0.459263i
$669$	−8.25679	+	22.0697i	−0.319226	+	0.853265i
$670$	4.83348	−	3.96737i	0.186734	−	0.153273i
$671$	−11.9967			−0.463126
$672$	−0.617704	+	9.77847i	−0.0238285	+	0.377213i
$673$	44.0358			1.69746			0.848728	−	0.528830i	$-0.177369\pi$
$673$	44.0358			1.69746			0.848728	+	0.528830i	$0.177369\pi$
$674$	−27.4671	+	22.5453i	−1.05799	+	0.868411i
$675$	2.47653	+	4.56802i	0.0953216	+	0.175823i
$676$	−3.90902	+	19.6680i	−0.150347	+	0.756462i
$677$		−	19.0745i		−	0.733092i	−0.930400	−	0.366546i	$-0.880540\pi$
$677$		−	19.0745i		−	0.733092i	0.930400	−	0.366546i	$-0.119460\pi$
$678$	4.64074	+	13.5796i	0.178227	+	0.521522i
$679$		−	13.7216i		−	0.526586i
$680$	−7.18444	−	13.4336i	−0.275511	−	0.515154i
$681$	−9.90237	−	3.70470i	−0.379460	−	0.141965i
$682$	3.14883	+	3.83625i	0.120575	+	0.146898i
$683$	20.8966			0.799586			0.399793	−	0.916605i	$-0.369082\pi$
$683$	20.8966			0.799586			0.399793	+	0.916605i	$0.369082\pi$
$684$	7.37955	+	9.53597i	0.282164	+	0.364617i
$685$	1.88824			0.0721458
$686$	−0.897253	−	1.09313i	−0.0342573	−	0.0417360i
$687$	30.1813	+	11.2915i	1.15149	+	0.430798i
$688$	3.77540	−	9.12269i	0.143936	−	0.347799i
$689$		−	7.38399i		−	0.281308i
$690$	7.06807	+	20.6824i	0.269077	+	0.787366i
$691$		−	24.9258i		−	0.948221i	−0.880465	−	0.474110i	$-0.842770\pi$
$691$		−	24.9258i		−	0.948221i	0.880465	−	0.474110i	$-0.157230\pi$
$692$	−20.9305	−	4.15994i	−0.795660	−	0.158137i
$693$	2.11099	−	2.42637i	0.0801898	−	0.0921701i
$694$	22.5931	−	18.5447i	0.857624	−	0.703946i
$695$	−10.8407			−0.411211
$696$	−8.21268	+	1.09967i	−0.311301	+	0.0416828i
$697$	−63.6703			−2.41168
$698$	22.9342	−	18.8246i	0.868071	−	0.712521i
$699$	16.3419	−	43.6807i	0.618108	−	1.65215i
$700$	1.96163	+	0.389874i	0.0741427	+	0.0147358i
$701$			3.13952i			0.118578i	0.998241	+	0.0592890i	$0.0188834\pi$
$701$			3.13952i			0.118578i	−0.998241	+	0.0592890i	$0.981117\pi$
$702$	−11.7362	−	4.77903i	−0.442953	−	0.180373i
$703$		−	17.9875i		−	0.678410i
$704$	−4.76143	+	7.13322i	−0.179453	+	0.268843i
$705$	−3.06050	+	8.18047i	−0.115265	+	0.308094i
$706$	1.86396	+	2.27088i	0.0701512	+	0.0854658i
$707$	9.27538			0.348836
$708$	22.5308	−	36.4050i	0.846758	−	1.36819i
$709$	48.0762			1.80554			0.902769	−	0.430126i	$-0.141531\pi$
$709$	48.0762			1.80554			0.902769	+	0.430126i	$0.141531\pi$
$710$	6.02345	+	7.33843i	0.226056	+	0.275406i
$711$	−5.86113	+	6.73677i	−0.219810	+	0.252649i
$712$	21.5218	−	11.5102i	0.806565	−	0.431361i
$713$			29.2100i			1.09392i
$714$	−12.4842	+	4.26640i	−0.467210	+	0.159666i
$715$			1.84866i			0.0691360i
$716$	7.90948	−	39.7962i	0.295591	−	1.48725i
$717$	14.3511	+	5.36906i	0.535951	+	0.200511i
$718$	34.6079	−	28.4065i	1.29156	−	1.06012i
$719$	−1.28393			−0.0478826			−0.0239413	−	0.999713i	$-0.507621\pi$
$719$	−1.28393			−0.0478826			−0.0239413	+	0.999713i	$0.507621\pi$
$720$	−10.7398	+	5.35325i	−0.400248	+	0.199504i
$721$	−0.394121			−0.0146778
$722$	−16.3547	+	13.4241i	−0.608659	+	0.499593i
$723$	−11.2966	−	4.22631i	−0.420125	−	0.157178i
$724$	−2.76425	+	13.9082i	−0.102733	+	0.516894i
$725$			1.69137i			0.0628158i
$726$	−22.8327	+	7.80293i	−0.847403	+	0.289594i
$727$			42.3919i			1.57223i	0.618080	+	0.786115i	$0.287911\pi$
$727$			42.3919i			1.57223i	−0.618080	+	0.786115i	$0.712089\pi$
$728$	−4.30095	+	2.30020i	−0.159404	+	0.0852512i
$729$	−14.7336	+	22.6257i	−0.545689	+	0.837987i
$730$	1.97993	+	2.41217i	0.0732806	+	0.0892785i
$731$	13.2942			0.491704
$732$	20.4003	−	32.9627i	0.754018	−	1.21834i
$733$	−32.0711			−1.18457			−0.592286	−	0.805728i	$-0.701774\pi$
$733$	−32.0711			−1.18457			−0.592286	+	0.805728i	$0.701774\pi$
$734$	−18.3307	−	22.3324i	−0.676598	−	0.824305i
$735$	0.606916	−	1.62224i	0.0223864	−	0.0598371i
$736$	−48.2969	+	14.6713i	−1.78025	+	0.540792i
$737$		−	4.74025i		−	0.174609i
$738$	−1.43926	+	50.1330i	−0.0529801	+	1.84542i
$739$			52.4675i			1.93005i	0.262159	+	0.965025i	$0.415566\pi$
$739$			52.4675i			1.93005i	−0.262159	+	0.965025i	$0.584434\pi$
$740$	17.5577	+	3.48959i	0.645434	+	0.128280i
$741$	−2.10326	+	5.62184i	−0.0772651	+	0.206523i
$742$	−4.68079	+	3.84204i	−0.171837	+	0.141046i
$743$	−10.6740			−0.391591			−0.195796	−	0.980645i	$-0.562729\pi$
$743$	−10.6740			−0.391591			−0.195796	+	0.980645i	$0.562729\pi$
$744$	−15.8953	+	2.12836i	−0.582749	+	0.0780294i
$745$	−1.96331			−0.0719300
$746$	−26.9863	+	22.1506i	−0.988038	+	0.810991i
$747$	−21.9467	−	19.0941i	−0.802988	−	0.698616i
$748$	−11.3267	−	2.25117i	−0.414144	−	0.0823109i
$749$		−	7.92337i		−	0.289514i
$750$	0.792118	+	2.31788i	0.0289241	+	0.0846369i
$751$		−	30.7818i		−	1.12324i	−0.827394	−	0.561622i	$-0.810177\pi$
$751$		−	30.7818i		−	1.12324i	0.827394	−	0.561622i	$-0.189823\pi$
$752$	−18.6378	−	7.71321i	−0.679652	−	0.281272i
$753$	19.5610	+	7.31822i	0.712843	+	0.266691i
$754$	−2.61696	−	3.18827i	−0.0953040	−	0.116110i
$755$	15.7675			0.573837
$756$	3.07708	+	9.92631i	0.111912	+	0.361016i
$757$	42.3345			1.53867			0.769337	−	0.638843i	$-0.220587\pi$
$757$	42.3345			1.53867			0.769337	+	0.638843i	$0.220587\pi$
$758$	3.88546	+	4.73369i	0.141126	+	0.171935i
$759$	15.5181	+	5.80567i	0.563271	+	0.210733i
$760$	2.68066	+	5.01233i	0.0972378	+	0.181816i
$761$			1.49042i			0.0540276i	0.999635	+	0.0270138i	$0.00859981\pi$
$761$			1.49042i			0.0540276i	−0.999635	+	0.0270138i	$0.991400\pi$
$762$	−17.1630	−	50.2220i	−0.621751	−	1.81935i
$763$		−	4.53839i		−	0.164301i
$764$	5.82430	−	29.3047i	0.210716	−	1.06021i
$765$	−12.1903	−	10.6058i	−0.440741	−	0.383454i
$766$	−14.6596	+	12.0327i	−0.529671	+	0.434759i
$767$	21.3123			0.769542
$768$	−11.5028	−	25.2128i	−0.415072	−	0.909788i
$769$	6.98367			0.251838			0.125919	−	0.992041i	$-0.459812\pi$
$769$	6.98367			0.251838			0.125919	+	0.992041i	$0.459812\pi$
$770$	1.17189	−	0.961896i	0.0422319	−	0.0346643i
$771$	−9.19778	+	24.5849i	−0.331250	+	0.885405i
$772$	7.82918	−	39.3922i	0.281778	−	1.41775i
$773$		−	0.726102i		−	0.0261161i	−0.999915	−	0.0130580i	$-0.995843\pi$
$773$		−	0.726102i		−	0.0261161i	0.999915	−	0.0130580i	$-0.00415662\pi$
$774$	0.300515	−	10.4676i	0.0108018	−	0.376251i
$775$			3.27357i			0.117590i
$776$	18.3032	+	34.2235i	0.657045	+	1.22855i
$777$	5.43224	−	14.5199i	0.194880	−	0.520900i
$778$	20.1657	+	24.5680i	0.722975	+	0.880807i
$779$	23.7567			0.851171
$780$	−5.07948	−	3.14365i	−0.181875	−	0.112561i
$781$	7.19687			0.257524
$782$	−43.1218	−	52.5357i	−1.54203	−	1.87867i
$783$	−7.72620	+	4.18872i	−0.276112	+	0.149693i
$784$	3.69600	+	1.52958i	0.132000	+	0.0546278i
$785$		−	17.3726i		−	0.620055i
$786$	39.0362	−	13.3403i	1.39237	−	0.475834i
$787$			15.1694i			0.540730i	0.962758	+	0.270365i	$0.0871444\pi$
$787$			15.1694i			0.540730i	−0.962758	+	0.270365i	$0.912856\pi$
$788$	−0.130852	−	0.0260068i	−0.00466141	−	0.000926454i
$789$	20.3264	+	7.60458i	0.723640	+	0.270730i
$790$	−3.25373	+	2.67069i	−0.115762	+	0.0950189i
$791$	5.85865			0.208309
$792$	−2.02857	+	8.86753i	−0.0720822	+	0.315094i
$793$	19.2971			0.685259
$794$	15.9742	−	13.1118i	0.566903	−	0.465319i
$795$	−6.94643	−	2.59882i	−0.246364	−	0.0921705i
$796$	−42.5433	−	8.45547i	−1.50791	−	0.299696i
$797$			20.5602i			0.728279i	0.931344	+	0.364139i	$0.118637\pi$
$797$			20.5602i			0.728279i	−0.931344	+	0.364139i	$0.881363\pi$
$798$	4.65811	−	1.59188i	0.164895	−	0.0563519i
$799$		−	27.1603i		−	0.960863i
$800$	−5.41263	+	1.64421i	−0.191365	+	0.0581318i
$801$	16.9915	−	19.5300i	0.600365	−	0.690059i
$802$	34.6115	+	42.1675i	1.22218	+	1.48899i
$803$	2.36564			0.0834817
$804$	13.0246	+	8.06079i	0.459341	+	0.284282i
$805$	8.92300			0.314494
$806$	−5.06501	−	6.17075i	−0.178407	−	0.217355i
$807$	15.3536	−	41.0389i	0.540472	−	1.44464i
$808$	−23.1341	+	12.3724i	−0.813853	+	0.435259i
$809$			5.79770i			0.203836i	0.994793	+	0.101918i	$0.0324980\pi$
$809$			5.79770i			0.203836i	−0.994793	+	0.101918i	$0.967502\pi$
$810$	−8.62640	+	9.35870i	−0.303101	+	0.328831i
$811$		−	2.22709i		−	0.0782037i	−0.999235	−	0.0391019i	$-0.987550\pi$
$811$		−	2.22709i		−	0.0782037i	0.999235	−	0.0391019i	$-0.0124497\pi$
$812$	−0.659420	+	3.31784i	−0.0231411	+	0.116433i
$813$	11.3814	−	30.4216i	0.399164	−	1.06693i
$814$	10.4890	−	8.60951i	0.367641	−	0.301763i
$815$	−7.80107			−0.273260
$816$	25.4464	−	27.2936i	0.890802	−	0.955468i
$817$	−4.96033			−0.173540
$818$	0.147005	−	0.120663i	0.00513990	−	0.00421888i
$819$	−3.39560	+	3.90290i	−0.118652	+	0.136378i
$820$	−4.60882	+	23.1891i	−0.160947	+	0.809798i
$821$		−	21.9085i		−	0.764611i	−0.924036	−	0.382305i	$-0.875130\pi$
$821$		−	21.9085i		−	0.764611i	0.924036	−	0.382305i	$-0.124870\pi$
$822$	1.49571	+	4.37670i	0.0521688	+	0.152655i
$823$		−	4.39771i		−	0.153295i	−0.997058	−	0.0766473i	$-0.975578\pi$
$823$		−	4.39771i		−	0.153295i	0.997058	−	0.0766473i	$-0.0244215\pi$
$824$	0.982992	−	0.525716i	0.0342441	−	0.0183142i
$825$	1.73911	+	0.650641i	0.0605481	+	0.0226524i
$826$	−11.0892	−	13.5101i	−0.385843	−	0.470077i
$827$	49.6718			1.72726			0.863629	−	0.504128i	$-0.168186\pi$
$827$	49.6718			1.72726			0.863629	+	0.504128i	$0.168186\pi$
$828$	−42.3405	+	32.7658i	−1.47143	+	1.13869i
$829$	−22.9577			−0.797354			−0.398677	−	0.917091i	$-0.630530\pi$
$829$	−22.9577			−0.797354			−0.398677	+	0.917091i	$0.630530\pi$
$830$	−8.70043	−	10.5998i	−0.301996	−	0.367925i
$831$	23.2389	+	8.69420i	0.806148	+	0.301598i
$832$	7.65893	−	11.4740i	0.265526	−	0.397791i
$833$			5.38606i			0.186616i
$834$	−8.58711	−	25.1274i	−0.297347	−	0.870089i
$835$		−	6.05107i		−	0.209406i
$836$	4.22620	+	0.839957i	0.146166	+	0.0290505i
$837$	−14.9537	+	8.10708i	−0.516876	+	0.280222i
$838$	−28.8050	+	23.6434i	−0.995051	+	0.816748i
$839$	3.71088			0.128114			0.0640570	−	0.997946i	$-0.479596\pi$
$839$	3.71088			0.128114			0.0640570	+	0.997946i	$0.479596\pi$
$840$	0.650165	+	4.85564i	0.0224328	+	0.167536i
$841$	26.1393			0.901354
$842$	−16.0002	+	13.1331i	−0.551404	+	0.452598i
$843$	−11.3841	+	30.4289i	−0.392090	+	1.04803i
$844$	−34.9244	−	6.94121i	−1.20215	−	0.238926i
$845$			10.0264i			0.344917i
$846$	−21.3856	−	0.613958i	−0.735252	−	0.0211083i
$847$			9.85072i			0.338475i
$848$	6.54966	−	15.8263i	0.224916	−	0.543476i
$849$	2.72054	−	7.27180i	0.0933688	−	0.249567i
$850$	−4.83266	−	5.88767i	−0.165759	−	0.201945i
$851$	79.8658			2.73777
$852$	−12.2383	+	19.7745i	−0.419277	+	0.677464i
$853$	1.51334			0.0518158			0.0259079	−	0.999664i	$-0.491752\pi$
$853$	1.51334			0.0518158			0.0259079	+	0.999664i	$0.491752\pi$
$854$	−10.0407	−	12.2326i	−0.343584	−	0.418592i
$855$	4.54845	+	3.95724i	0.155554	+	0.135335i
$856$	10.5690	+	19.7620i	0.361239	+	0.675450i
$857$		−	52.4046i		−	1.79011i	−0.445957	−	0.895054i	$-0.647137\pi$
$857$		−	52.4046i		−	1.79011i	0.445957	−	0.895054i	$-0.352863\pi$
$858$	−4.28497	+	1.46436i	−0.146286	+	0.0499924i
$859$			38.2474i			1.30498i	0.757796	+	0.652492i	$0.226276\pi$
$859$			38.2474i			1.30498i	−0.757796	+	0.652492i	$0.773724\pi$
$860$	0.962311	−	4.84182i	0.0328145	−	0.165105i
$861$	19.1770	+	7.17454i	0.653550	+	0.244508i
$862$	0.943656	−	0.774562i	0.0321411	−	0.0263817i
$863$	35.9301			1.22308			0.611538	−	0.791215i	$-0.290551\pi$
$863$	35.9301			1.22308			0.611538	+	0.791215i	$0.290551\pi$
$864$	−20.9153	−	20.6531i	−0.711554	−	0.702631i
$865$	−10.6700			−0.362790
$866$	34.3745	−	28.2149i	1.16809	−	0.958782i
$867$	19.4824	+	7.28882i	0.661658	+	0.247541i
$868$	−1.27628	+	6.42153i	−0.0433197	+	0.217961i
$869$			3.19096i			0.108246i
$870$	−3.92038	+	1.33976i	−0.132913	+	0.0454222i
$871$			7.62486i			0.258359i
$872$	6.05375	+	11.3194i	0.205006	+	0.383322i
$873$	31.0561	+	27.0195i	1.05109	+	0.914470i
$874$	16.0896	+	19.6021i	0.544239	+	0.663051i
$875$	1.00000			0.0338062
$876$	−4.02277	+	6.49997i	−0.135917	+	0.219613i
$877$	−39.3132			−1.32751			−0.663756	−	0.747949i	$-0.731039\pi$
$877$	−39.3132			−1.32751			−0.663756	+	0.747949i	$0.731039\pi$
$878$	−22.7904	−	27.7657i	−0.769138	−	0.937048i
$879$	−2.93798	+	7.85300i	−0.0990958	+	0.264875i
$880$	−1.63978	+	3.96228i	−0.0552769	+	0.133568i
$881$		−	47.9601i		−	1.61582i	−0.589309	−	0.807908i	$-0.700600\pi$
$881$		−	47.9601i		−	1.61582i	0.589309	−	0.807908i	$-0.299400\pi$
$882$	4.24089	+	0.121752i	0.142798	+	0.00409959i
$883$		−	28.1879i		−	0.948598i	−0.880364	−	0.474299i	$-0.842702\pi$
$883$		−	28.1879i		−	0.948598i	0.880364	−	0.474299i	$-0.157298\pi$
$884$	18.2193	+	3.62109i	0.612783	+	0.121790i
$885$	7.50092	−	20.0494i	0.252141	−	0.673952i
$886$	−15.8189	+	12.9843i	−0.531446	+	0.436216i
$887$	−5.41835			−0.181930			−0.0909651	−	0.995854i	$-0.528995\pi$
$887$	−5.41835			−0.181930			−0.0909651	+	0.995854i	$0.528995\pi$
$888$	5.81934	+	43.4607i	0.195284	+	1.45845i
$889$	−21.6673			−0.726697
$890$	9.43260	−	7.74237i	0.316182	−	0.259525i
$891$	1.33482	+	9.55563i	0.0447181	+	0.320126i
$892$	−26.6870	−	5.30404i	−0.893547	−	0.177592i
$893$			10.1341i			0.339123i
$894$	−1.55517	−	4.55070i	−0.0520127	−	0.152198i
$895$		−	20.2873i		−	0.678129i
$896$	−11.2586	+	1.11510i	−0.376124	+	0.0372529i
$897$	−24.9614	−	9.33864i	−0.833438	−	0.311808i
$898$	20.6772	+	25.1913i	0.690008	+	0.840644i
$899$	−5.53680			−0.184663
$900$	−4.74510	+	3.67206i	−0.158170	+	0.122402i
$901$	23.0631			0.768344
$902$	11.3709	+	13.8532i	0.378609	+	0.461263i
$903$	−4.00411	−	1.49803i	−0.133248	−	0.0498512i
$904$	−14.6123	+	7.81483i	−0.485997	+	0.259917i
$905$			7.09011i			0.235683i
$906$	12.4897	+	36.5470i	0.414943	+	1.21419i
$907$			8.14282i			0.270378i	0.990820	+	0.135189i	$0.0431641\pi$
$907$			8.14282i			0.270378i	−0.990820	+	0.135189i	$0.956836\pi$
$908$	2.37985	−	11.9741i	0.0789780	−	0.397374i
$909$	−18.2644	+	20.9930i	−0.605790	+	0.696295i
$910$	−1.88502	+	1.54725i	−0.0624879	+	0.0512907i
$911$	−9.79076			−0.324382			−0.162191	−	0.986759i	$-0.551856\pi$
$911$	−9.79076			−0.324382			−0.162191	+	0.986759i	$0.551856\pi$
$912$	−9.49457	+	10.1838i	−0.314397	+	0.337219i
$913$	−10.3953			−0.344036
$914$	−27.9503	+	22.9419i	−0.924513	+	0.758849i
$915$	6.79166	−	18.1535i	0.224525	−	0.600138i
$916$	−7.25351	+	36.4957i	−0.239663	+	1.20585i
$917$		−	16.8414i		−	0.556150i
$918$	14.9268	−	36.6567i	0.492657	−	1.20985i
$919$			20.6808i			0.682198i	0.940027	+	0.341099i	$0.110799\pi$
$919$			20.6808i			0.682198i	−0.940027	+	0.341099i	$0.889201\pi$
$920$	−22.2552	+	11.9024i	−0.733732	+	0.392409i
$921$	8.18539	−	21.8789i	0.269718	−	0.720934i
$922$	1.02083	+	1.24368i	0.0336191	+	0.0409585i
$923$	−11.5764			−0.381043
$924$	3.15783	+	1.95435i	0.103885	+	0.0642935i
$925$	8.95056			0.294293
$926$	−12.1524	−	14.8053i	−0.399351	−	0.486533i
$927$	0.776072	−	0.892016i	0.0254896	−	0.0292977i
$928$	−2.78097	−	9.15474i	−0.0912898	−	0.300519i
$929$			46.4088i			1.52262i	0.648386	+	0.761312i	$0.275444\pi$
$929$			46.4088i			1.52262i	−0.648386	+	0.761312i	$0.724556\pi$
$930$	−7.58772	+	2.59305i	−0.248811	+	0.0850295i
$931$		−	2.00965i		−	0.0658635i
$932$	52.8193	+	10.4978i	1.73015	+	0.343867i
$933$	3.15856	+	1.18169i	0.103407	+	0.0386867i
$934$	−18.6093	+	15.2747i	−0.608914	+	0.499803i
$935$	−5.77410			−0.188833
$936$	3.26303	−	14.2638i	0.106656	−	0.466225i
$937$	−29.6584			−0.968898			−0.484449	−	0.874820i	$-0.660980\pi$
$937$	−29.6584			−0.968898			−0.484449	+	0.874820i	$0.660980\pi$
$938$	4.83348	−	3.96737i	0.157819	−	0.129539i
$939$	−32.3005	−	12.0843i	−1.05409	−	0.394358i
$940$	−9.89193	−	1.96602i	−0.322639	−	0.0641245i
$941$			18.0408i			0.588113i	0.955788	+	0.294056i	$0.0950053\pi$
$941$			18.0408i			0.588113i	−0.955788	+	0.294056i	$0.904995\pi$
$942$	40.2676	−	13.7612i	1.31199	−	0.448363i
$943$			105.482i			3.43495i
$944$	45.6791	+	18.9042i	1.48673	+	0.615278i
$945$	2.47653	+	4.56802i	0.0805615	+	0.148598i
$946$	−2.37421	−	2.89252i	−0.0771923	−	0.0940441i
$947$	26.0719			0.847224			0.423612	−	0.905844i	$-0.360762\pi$
$947$	26.0719			0.847224			0.423612	+	0.905844i	$0.360762\pi$
$948$	−8.76767	−	5.42623i	−0.284761	−	0.176236i
$949$	−3.80522			−0.123523
$950$	1.80316	+	2.19681i	0.0585023	+	0.0712739i
$951$	20.5064	−	54.8120i	0.664966	−	1.77740i
$952$	−7.18444	−	13.4336i	−0.232849	−	0.435384i
$953$			57.9429i			1.87695i	0.345343	+	0.938477i	$0.387763\pi$
$953$			57.9429i			1.87695i	−0.345343	+	0.938477i	$0.612237\pi$
$954$	0.521341	−	18.1595i	0.0168790	−	0.587936i
$955$		−	14.9389i		−	0.483413i
$956$	−3.44901	+	17.3535i	−0.111549	+	0.561253i
$957$	−1.10047	+	2.94148i	−0.0355732	+	0.0950844i
$958$	9.28298	−	7.61956i	0.299919	−	0.246177i
$959$	1.88824			0.0609744
$960$	−8.09853	−	11.2434i	−0.261379	−	0.362879i
$961$	20.2838			0.654315
$962$	−16.8720	+	13.8487i	−0.543976	+	0.446500i
$963$	17.9330	+	15.6021i	0.577883	+	0.502770i
$964$	2.71492	−	13.6600i	0.0874417	−	0.439959i
$965$		−	20.0813i		−	0.646441i
$966$	7.06807	+	20.6824i	0.227411	+	0.665445i
$967$			57.5335i			1.85015i	0.379780	+	0.925077i	$0.376000\pi$
$967$			57.5335i			1.85015i	−0.379780	+	0.925077i	$0.624000\pi$
$968$	−13.1398	−	24.5690i	−0.422330	−	0.789679i
$969$	−17.5592	−	6.56930i	−0.564083	−	0.211036i
$970$	12.3117	+	14.9995i	0.395306	+	0.481604i
$971$	−44.3400			−1.42294			−0.711470	−	0.702717i	$-0.751970\pi$
$971$	−44.3400			−1.42294			−0.711470	+	0.702717i	$0.751970\pi$
$972$	−28.5254	−	12.5817i	−0.914954	−	0.403559i
$973$	−10.8407			−0.347536
$974$	24.1612	+	29.4358i	0.774174	+	0.943184i
$975$	−2.79743	−	1.04658i	−0.0895893	−	0.0335174i
$976$	41.3598	+	17.1166i	1.32390	+	0.547891i
$977$			23.4053i			0.748803i	0.927267	+	0.374402i	$0.122152\pi$
$977$			23.4053i			0.748803i	−0.927267	+	0.374402i	$0.877848\pi$
$978$	−6.17937	−	18.0819i	−0.197595	−	0.578196i
$979$		−	9.25065i		−	0.295652i
$980$	1.96163	+	0.389874i	0.0626620	+	0.0124541i
$981$	10.2718	+	8.93665i	0.327953	+	0.285325i
$982$	19.6382	−	16.1192i	0.626681	−	0.514385i
$983$	−40.6833			−1.29760			−0.648798	−	0.760960i	$-0.724728\pi$
$983$	−40.6833			−1.29760			−0.648798	+	0.760960i	$0.724728\pi$
$984$	−57.4001	+	7.68581i	−1.82985	+	0.245015i
$985$	−0.0667057			−0.00212542
$986$	9.95821	−	8.17379i	0.317134	−	0.260307i
$987$	−3.06050	+	8.18047i	−0.0974167	+	0.260387i
$988$	−6.79800	−	1.35110i	−0.216273	−	0.0429843i
$989$		−	22.0243i		−	0.700332i
$990$	−0.130523	+	4.54643i	−0.00414830	+	0.144495i
$991$		−	24.3142i		−	0.772366i	−0.922422	−	0.386183i	$-0.873793\pi$
$991$		−	24.3142i		−	0.772366i	0.922422	−	0.386183i	$-0.126207\pi$
$992$	−5.38245	−	17.7186i	−0.170893	−	0.562566i
$993$	8.72829	−	23.3300i	0.276984	−	0.740356i
$994$	6.02345	+	7.33843i	0.191052	+	0.232761i
$995$	−21.6877			−0.687546
$996$	17.6773	−	28.5628i	0.560126	−	0.905048i
$997$	21.5783			0.683390			0.341695	−	0.939811i	$-0.388999\pi$
$997$	21.5783			0.683390			0.341695	+	0.939811i	$0.388999\pi$
$998$	−9.96759	−	12.1436i	−0.315519	−	0.384399i
$999$	22.1663	+	40.8863i	0.701311	+	1.29359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.6	yes	24
3.2	odd	2		420.2.n.a.71.19	✓	24
4.3	odd	2		420.2.n.a.71.20	yes	24
12.11	even	2	inner	420.2.n.b.71.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.19	✓	24	3.2	odd	2
420.2.n.a.71.20	yes	24	4.3	odd	2
420.2.n.b.71.5	yes	24	12.11	even	2	inner
420.2.n.b.71.6	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09313 + 0.897253i) q^{2} +(-1.62224 - 0.606916i) q^{3} +(0.389874 - 1.96163i) q^{4} -1.00000i q^{5} +(2.31788 - 0.792118i) q^{6} -1.00000i q^{7} +(1.33390 + 2.49414i) q^{8} +(2.26331 + 1.96912i) q^{9} +O(q^{10})\)	\(q+(-1.09313 + 0.897253i) q^{2} +(-1.62224 - 0.606916i) q^{3} +(0.389874 - 1.96163i) q^{4} -1.00000i q^{5} +(2.31788 - 0.792118i) q^{6} -1.00000i q^{7} +(1.33390 + 2.49414i) q^{8} +(2.26331 + 1.96912i) q^{9} +(0.897253 + 1.09313i) q^{10} +1.07205 q^{11} +(-1.82301 + 2.94561i) q^{12} -1.72442 q^{13} +(0.897253 + 1.09313i) q^{14} +(-0.606916 + 1.62224i) q^{15} +(-3.69600 - 1.52958i) q^{16} -5.38606i q^{17} +(-4.24089 - 0.121752i) q^{18} +2.00965i q^{19} +(-1.96163 - 0.389874i) q^{20} +(-0.606916 + 1.62224i) q^{21} +(-1.17189 + 0.961896i) q^{22} -8.92300 q^{23} +(-0.650165 - 4.85564i) q^{24} -1.00000 q^{25} +(1.88502 - 1.54725i) q^{26} +(-2.47653 - 4.56802i) q^{27} +(-1.96163 - 0.389874i) q^{28} -1.69137i q^{29} +(-0.792118 - 2.31788i) q^{30} -3.27357i q^{31} +(5.41263 - 1.64421i) q^{32} +(-1.73911 - 0.650641i) q^{33} +(4.83266 + 5.88767i) q^{34} -1.00000 q^{35} +(4.74510 - 3.67206i) q^{36} -8.95056 q^{37} +(-1.80316 - 2.19681i) q^{38} +(2.79743 + 1.04658i) q^{39} +(2.49414 - 1.33390i) q^{40} -11.8213i q^{41} +(-0.792118 - 2.31788i) q^{42} +2.46826i q^{43} +(0.417963 - 2.10296i) q^{44} +(1.96912 - 2.26331i) q^{45} +(9.75401 - 8.00619i) q^{46} +5.04271 q^{47} +(5.06746 + 4.72450i) q^{48} -1.00000 q^{49} +(1.09313 - 0.897253i) q^{50} +(-3.26888 + 8.73746i) q^{51} +(-0.672308 + 3.38269i) q^{52} +4.28200i q^{53} +(6.80584 + 2.77138i) q^{54} -1.07205i q^{55} +(2.49414 - 1.33390i) q^{56} +(1.21969 - 3.26012i) q^{57} +(1.51758 + 1.84889i) q^{58} -12.3591 q^{59} +(2.94561 + 1.82301i) q^{60} -11.1904 q^{61} +(2.93722 + 3.57844i) q^{62} +(1.96912 - 2.26331i) q^{63} +(-4.44144 + 6.65384i) q^{64} +1.72442i q^{65} +(2.48487 - 0.849187i) q^{66} -4.42168i q^{67} +(-10.5655 - 2.09988i) q^{68} +(14.4752 + 5.41551i) q^{69} +(1.09313 - 0.897253i) q^{70} +6.71322 q^{71} +(-1.89225 + 8.27160i) q^{72} +2.20666 q^{73} +(9.78414 - 8.03092i) q^{74} +(1.62224 + 0.606916i) q^{75} +(3.94219 + 0.783509i) q^{76} -1.07205i q^{77} +(-3.99700 + 1.36595i) q^{78} +2.97652i q^{79} +(-1.52958 + 3.69600i) q^{80} +(1.24511 + 8.91346i) q^{81} +(10.6067 + 12.9223i) q^{82} -9.69674 q^{83} +(2.94561 + 1.82301i) q^{84} -5.38606 q^{85} +(-2.21466 - 2.69814i) q^{86} +(-1.02652 + 2.74380i) q^{87} +(1.43000 + 2.67383i) q^{88} -8.62897i q^{89} +(-0.121752 + 4.24089i) q^{90} +1.72442i q^{91} +(-3.47884 + 17.5036i) q^{92} +(-1.98678 + 5.31050i) q^{93} +(-5.51234 + 4.52458i) q^{94} +2.00965 q^{95} +(-9.77847 - 0.617704i) q^{96} +13.7216 q^{97} +(1.09313 - 0.897253i) q^{98} +(2.42637 + 2.11099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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