LMFDB - Embedded newform 798.2.m.b.787.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(145,798)] 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("798.145"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			787.1
Character	$\chi$	$=$	798.787
Dual form			798.2.m.b.145.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} -4.07585i q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.41205 - 2.23744i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -4.07585 q^{10} +(-0.485128 + 0.840267i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.85511 - 3.21315i) q^{13} +(-2.23744 + 1.41205i) q^{14} +(3.52979 - 2.03792i) q^{15} +1.00000 q^{16} +(-6.48478 + 3.74399i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.91461 + 1.91725i) q^{19} +4.07585i q^{20} +(1.23165 - 2.34159i) q^{21} +(0.840267 + 0.485128i) q^{22} +(-1.25748 + 2.17802i) q^{23} +(-0.866025 + 0.500000i) q^{24} -11.6125 q^{25} +(-3.21315 + 1.85511i) q^{26} -1.00000 q^{27} +(1.41205 + 2.23744i) q^{28} +(2.39269 - 1.38142i) q^{29} +(-2.03792 - 3.52979i) q^{30} +(-0.648141 + 1.12261i) q^{31} -1.00000i q^{32} -0.970257 q^{33} +(3.74399 + 6.48478i) q^{34} +(-9.11945 + 5.75528i) q^{35} +(0.500000 - 0.866025i) q^{36} +(8.55440 - 4.93889i) q^{37} +(1.91725 - 3.91461i) q^{38} +(1.85511 - 3.21315i) q^{39} +4.07585 q^{40} +(-5.12688 + 8.88001i) q^{41} +(-2.34159 - 1.23165i) q^{42} +(4.80115 - 8.31583i) q^{43} +(0.485128 - 0.840267i) q^{44} +(3.52979 + 2.03792i) q^{45} +(2.17802 + 1.25748i) q^{46} +(-2.30571 - 1.33120i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.01225 + 6.31873i) q^{49} +11.6125i q^{50} +(-6.48478 - 3.74399i) q^{51} +(1.85511 + 3.21315i) q^{52} -10.7716i q^{53} +1.00000i q^{54} +(3.42480 + 1.97731i) q^{55} +(2.23744 - 1.41205i) q^{56} +(0.296922 + 4.34877i) q^{57} +(-1.38142 - 2.39269i) q^{58} +(-4.75870 - 8.24231i) q^{59} +(-3.52979 + 2.03792i) q^{60} +(-11.9306 - 6.88815i) q^{61} +(1.12261 + 0.648141i) q^{62} +(2.64370 - 0.104149i) q^{63} -1.00000 q^{64} +(-13.0963 + 7.56116i) q^{65} +0.970257i q^{66} +7.12386i q^{67} +(6.48478 - 3.74399i) q^{68} -2.51497 q^{69} +(5.75528 + 9.11945i) q^{70} +(-0.430764 - 0.248702i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.85245 - 1.06951i) q^{73} +(-4.93889 - 8.55440i) q^{74} +(-5.80626 - 10.0567i) q^{75} +(-3.91461 - 1.91725i) q^{76} +(2.56507 - 0.101051i) q^{77} +(-3.21315 - 1.85511i) q^{78} -11.4685i q^{79} -4.07585i q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.88001 + 5.12688i) q^{82} -17.0639i q^{83} +(-1.23165 + 2.34159i) q^{84} +(15.2599 + 26.4310i) q^{85} +(-8.31583 - 4.80115i) q^{86} +(2.39269 + 1.38142i) q^{87} +(-0.840267 - 0.485128i) q^{88} +(-0.360720 + 0.624786i) q^{89} +(2.03792 - 3.52979i) q^{90} +(-4.56972 + 8.68782i) q^{91} +(1.25748 - 2.17802i) q^{92} -1.29628 q^{93} +(-1.33120 + 2.30571i) q^{94} +(7.81440 - 15.9553i) q^{95} +(0.866025 - 0.500000i) q^{96} +(7.84588 - 13.5895i) q^{97} +(6.31873 + 3.01225i) q^{98} +(-0.485128 - 0.840267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9} + 4 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 28 q^{16} - 6 q^{17} + 2 q^{21} - 12 q^{22} - 12 q^{23} - 28 q^{25} + 24 q^{26} - 28 q^{27} + 8 q^{28}+ \cdots + 32 q^{98}+O(q^{100}) $ 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9 + 4 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 28 * q^16 - 6 * q^17 + 2 * q^21 - 12 * q^22 - 12 * q^23 - 28 * q^25 + 24 * q^26 - 28 * q^27 + 8 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 + 4 * q^34 - 4 * q^35 + 14 * q^36 + 24 * q^37 + 18 * q^38 + 2 * q^39 - 4 * q^40 - 4 * q^41 + 4 * q^42 - 14 * q^43 + 6 * q^45 + 12 * q^46 + 24 * q^47 + 14 * q^48 - 24 * q^49 - 6 * q^51 + 2 * q^52 - 18 * q^55 + 4 * q^56 + 12 * q^57 - 2 * q^58 + 22 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 10 * q^63 - 28 * q^64 + 24 * q^65 + 6 * q^68 - 24 * q^69 + 30 * q^70 - 6 * q^71 - 42 * q^73 - 6 * q^74 - 14 * q^75 + 40 * q^77 + 24 * q^78 - 14 * q^81 - 6 * q^82 - 2 * q^84 + 28 * q^85 - 54 * q^86 + 18 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 - 22 * q^91 + 12 * q^92 - 8 * q^93 + 18 * q^94 + 20 * q^95 + 40 * q^97 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000			−0.500000
$5$		−	4.07585i		−	1.82277i	−0.411550	−	0.911387i	$-0.635013\pi$
$5$		−	4.07585i		−	1.82277i	0.411550	−	0.911387i	$-0.364987\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.41205	−	2.23744i	−0.533703	−	0.845672i
$7$	−1.41205	−	2.23744i	−0.533703	−	0.845672i
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.07585			−1.28890
$11$	−0.485128	+	0.840267i	−0.146272	+	0.253350i	−0.929847	−	0.367947i	$-0.880061\pi$
$11$	−0.485128	+	0.840267i	−0.146272	+	0.253350i	0.783575	+	0.621297i	$0.213394\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.85511	−	3.21315i	−0.514516	−	0.891168i	−0.999858	−	0.0168439i	$-0.994638\pi$
$13$	−1.85511	−	3.21315i	−0.514516	−	0.891168i	0.485342	−	0.874324i	$-0.338695\pi$
$14$	−2.23744	+	1.41205i	−0.597980	+	0.377385i
$15$	3.52979	−	2.03792i	0.911387	−	0.526190i
$16$	1.00000			0.250000
$17$	−6.48478	+	3.74399i	−1.57279	+	0.908051i	−0.576966	+	0.816768i	$0.695764\pi$
$17$	−6.48478	+	3.74399i	−1.57279	+	0.908051i	−0.995825	+	0.0912833i	$0.970903\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	3.91461	+	1.91725i	0.898073	+	0.439846i
$19$	3.91461	+	1.91725i	0.898073	+	0.439846i
$20$			4.07585i			0.911387i
$21$	1.23165	−	2.34159i	0.268769	−	0.510976i
$22$	0.840267	+	0.485128i	0.179146	+	0.103430i
$23$	−1.25748	+	2.17802i	−0.262203	+	0.454149i	−0.966827	−	0.255432i	$-0.917782\pi$
$23$	−1.25748	+	2.17802i	−0.262203	+	0.454149i	0.704624	+	0.709581i	$0.251116\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−11.6125			−2.32250
$26$	−3.21315	+	1.85511i	−0.630151	+	0.363818i
$27$	−1.00000			−0.192450
$28$	1.41205	+	2.23744i	0.266852	+	0.422836i
$29$	2.39269	−	1.38142i	0.444312	−	0.256524i	−0.261113	−	0.965308i	$-0.584089\pi$
$29$	2.39269	−	1.38142i	0.444312	−	0.256524i	0.705425	+	0.708785i	$0.250756\pi$
$30$	−2.03792	−	3.52979i	−0.372072	−	0.644448i
$31$	−0.648141	+	1.12261i	−0.116410	+	0.201627i	−0.918342	−	0.395787i	$-0.870472\pi$
$31$	−0.648141	+	1.12261i	−0.116410	+	0.201627i	0.801933	+	0.597414i	$0.203805\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.970257			−0.168900
$34$	3.74399	+	6.48478i	0.642089	+	1.11213i
$35$	−9.11945	+	5.75528i	−1.54147	+	0.972820i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	8.55440	−	4.93889i	1.40633	−	0.811948i	0.411302	−	0.911499i	$-0.365074\pi$
$37$	8.55440	−	4.93889i	1.40633	−	0.811948i	0.995032	+	0.0995513i	$0.0317407\pi$
$38$	1.91725	−	3.91461i	0.311018	−	0.635034i
$39$	1.85511	−	3.21315i	0.297056	−	0.514516i
$40$	4.07585			0.644448
$41$	−5.12688	+	8.88001i	−0.800683	+	1.38682i	0.118484	+	0.992956i	$0.462197\pi$
$41$	−5.12688	+	8.88001i	−0.800683	+	1.38682i	−0.919167	+	0.393868i	$0.871137\pi$
$42$	−2.34159	−	1.23165i	−0.361315	−	0.190048i
$43$	4.80115	−	8.31583i	0.732168	−	1.26815i	−0.223787	−	0.974638i	$-0.571842\pi$
$43$	4.80115	−	8.31583i	0.732168	−	1.26815i	0.955955	−	0.293514i	$-0.0948247\pi$
$44$	0.485128	−	0.840267i	0.0731359	−	0.126675i
$45$	3.52979	+	2.03792i	0.526190	+	0.303796i
$46$	2.17802	+	1.25748i	0.321132	+	0.185406i
$47$	−2.30571	−	1.33120i	−0.336323	−	0.194176i	0.322322	−	0.946630i	$-0.395537\pi$
$47$	−2.30571	−	1.33120i	−0.336323	−	0.194176i	−0.658645	+	0.752454i	$0.728870\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−3.01225	+	6.31873i	−0.430322	+	0.902676i
$50$			11.6125i			1.64226i
$51$	−6.48478	−	3.74399i	−0.908051	−	0.524264i
$52$	1.85511	+	3.21315i	0.257258	+	0.445584i
$53$		−	10.7716i		−	1.47959i	−0.672832	−	0.739795i	$-0.734922\pi$
$53$		−	10.7716i		−	1.47959i	0.672832	−	0.739795i	$-0.265078\pi$
$54$			1.00000i			0.136083i
$55$	3.42480	+	1.97731i	0.461800	+	0.266620i
$56$	2.23744	−	1.41205i	0.298990	−	0.188693i
$57$	0.296922	+	4.34877i	0.0393282	+	0.576009i
$58$	−1.38142	−	2.39269i	−0.181390	−	0.314176i
$59$	−4.75870	−	8.24231i	−0.619530	−	1.07306i	−0.989572	−	0.144042i	$-0.953990\pi$
$59$	−4.75870	−	8.24231i	−0.619530	−	1.07306i	0.370042	−	0.929015i	$-0.379343\pi$
$60$	−3.52979	+	2.03792i	−0.455693	+	0.263095i
$61$	−11.9306	−	6.88815i	−1.52756	−	0.881937i	−0.999464	−	0.0327518i	$-0.989573\pi$
$61$	−11.9306	−	6.88815i	−1.52756	−	0.881937i	−0.528096	−	0.849185i	$-0.677094\pi$
$62$	1.12261	+	0.648141i	0.142572	+	0.0823140i
$63$	2.64370	−	0.104149i	0.333075	−	0.0131215i
$64$	−1.00000			−0.125000
$65$	−13.0963	+	7.56116i	−1.62440	+	0.937847i
$66$			0.970257i			0.119430i
$67$			7.12386i			0.870318i	0.900354	+	0.435159i	$0.143308\pi$
$67$			7.12386i			0.870318i	−0.900354	+	0.435159i	$0.856692\pi$
$68$	6.48478	−	3.74399i	0.786396	−	0.454026i
$69$	−2.51497			−0.302766
$70$	5.75528	+	9.11945i	0.687888	+	1.08998i
$71$	−0.430764	−	0.248702i	−0.0511223	−	0.0295155i	0.474221	−	0.880406i	$-0.342730\pi$
$71$	−0.430764	−	0.248702i	−0.0511223	−	0.0295155i	−0.525343	+	0.850890i	$0.676063\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	1.85245	−	1.06951i	0.216813	−	0.125177i	−0.387661	−	0.921802i	$-0.626717\pi$
$73$	1.85245	−	1.06951i	0.216813	−	0.125177i	0.604474	+	0.796625i	$0.293383\pi$
$74$	−4.93889	−	8.55440i	−0.574134	−	0.994429i
$75$	−5.80626	−	10.0567i	−0.670449	−	1.16125i
$76$	−3.91461	−	1.91725i	−0.449037	−	0.219923i
$77$	2.56507	−	0.101051i	0.292317	−	0.0115159i
$78$	−3.21315	−	1.85511i	−0.363818	−	0.210050i
$79$		−	11.4685i		−	1.29031i	−0.764052	−	0.645155i	$-0.776793\pi$
$79$		−	11.4685i		−	1.29031i	0.764052	−	0.645155i	$-0.223207\pi$
$80$		−	4.07585i		−	0.455693i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.88001	+	5.12688i	0.980633	+	0.566169i
$83$		−	17.0639i		−	1.87301i	−0.350655	−	0.936505i	$-0.614041\pi$
$83$		−	17.0639i		−	1.87301i	0.350655	−	0.936505i	$-0.385959\pi$
$84$	−1.23165	+	2.34159i	−0.134385	+	0.255488i
$85$	15.2599	+	26.4310i	1.65517	+	2.86684i
$86$	−8.31583	−	4.80115i	−0.896719	−	0.517721i
$87$	2.39269	+	1.38142i	0.256524	+	0.148104i
$88$	−0.840267	−	0.485128i	−0.0895728	−	0.0517149i
$89$	−0.360720	+	0.624786i	−0.0382363	+	0.0662271i	−0.884510	−	0.466521i	$-0.845507\pi$
$89$	−0.360720	+	0.624786i	−0.0382363	+	0.0662271i	0.846274	+	0.532748i	$0.178841\pi$
$90$	2.03792	−	3.52979i	0.214816	−	0.372072i
$91$	−4.56972	+	8.68782i	−0.479037	+	0.910731i
$92$	1.25748	−	2.17802i	0.131102	−	0.227075i
$93$	−1.29628			−0.134418
$94$	−1.33120	+	2.30571i	−0.137303	+	0.237816i
$95$	7.81440	−	15.9553i	0.801740	−	1.63698i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	7.84588	−	13.5895i	0.796629	−	1.37980i	−0.125171	−	0.992135i	$-0.539948\pi$
$97$	7.84588	−	13.5895i	0.796629	−	1.37980i	0.921800	−	0.387666i	$-0.126719\pi$
$98$	6.31873	+	3.01225i	0.638288	+	0.304283i
$99$	−0.485128	−	0.840267i	−0.0487572	−	0.0844500i
$100$	11.6125			1.16125
$101$			3.71819i			0.369973i	0.982741	+	0.184987i	$0.0592242\pi$
$101$			3.71819i			0.369973i	−0.982741	+	0.184987i	$0.940776\pi$
$102$	−3.74399	+	6.48478i	−0.370710	+	0.642089i
$103$	−1.12602	−	1.95033i	−0.110950	−	0.192172i	0.805203	−	0.592999i	$-0.202056\pi$
$103$	−1.12602	−	1.95033i	−0.110950	−	0.192172i	−0.916154	+	0.400827i	$0.868723\pi$
$104$	3.21315	−	1.85511i	0.315076	−	0.181909i
$105$	−9.54395	−	5.02004i	−0.931394	−	0.489905i
$106$	−10.7716			−1.04623
$107$	5.70984	−	3.29658i	0.551991	−	0.318692i	−0.197934	−	0.980215i	$-0.563423\pi$
$107$	5.70984	−	3.29658i	0.551991	−	0.318692i	0.749925	+	0.661523i	$0.230090\pi$
$108$	1.00000			0.0962250
$109$	−6.75153	+	3.89800i	−0.646679	+	0.373361i	−0.787183	−	0.616720i	$-0.788461\pi$
$109$	−6.75153	+	3.89800i	−0.646679	+	0.373361i	0.140503	+	0.990080i	$0.455128\pi$
$110$	1.97731	−	3.42480i	0.188529	−	0.326542i
$111$	8.55440	+	4.93889i	0.811948	+	0.468778i
$112$	−1.41205	−	2.23744i	−0.133426	−	0.211418i
$113$			10.2155i			0.960994i	0.876996	+	0.480497i	$0.159544\pi$
$113$			10.2155i			0.960994i	−0.876996	+	0.480497i	$0.840456\pi$
$114$	4.34877	−	0.296922i	0.407300	−	0.0278093i
$115$	8.87729	+	5.12531i	0.827812	+	0.477937i
$116$	−2.39269	+	1.38142i	−0.222156	+	0.128262i
$117$	3.71023			0.343011
$118$	−8.24231	+	4.75870i	−0.758766	+	0.438074i
$119$	17.5338	+	9.22261i	1.60732	+	0.845435i
$120$	2.03792	+	3.52979i	0.186036	+	0.322224i
$121$	5.02930	+	8.71100i	0.457209	+	0.791910i
$122$	−6.88815	+	11.9306i	−0.623623	+	1.08015i
$123$	−10.2538			−0.924550
$124$	0.648141	−	1.12261i	0.0582048	−	0.100814i
$125$			26.9516i			2.41063i
$126$	−0.104149	−	2.64370i	−0.00927833	−	0.235520i
$127$	−4.63310	+	2.67492i	−0.411122	+	0.237361i	−0.691272	−	0.722595i	$-0.742949\pi$
$127$	−4.63310	+	2.67492i	−0.411122	+	0.237361i	0.280150	+	0.959956i	$0.409616\pi$
$128$			1.00000i			0.0883883i
$129$	9.60229			0.845435
$130$	7.56116	+	13.0963i	0.663158	+	1.14862i
$131$		−	1.69994i		−	0.148524i	−0.997239	−	0.0742622i	$-0.976340\pi$
$131$		−	1.69994i		−	0.148524i	0.997239	−	0.0742622i	$-0.0236602\pi$
$132$	0.970257			0.0844500
$133$	−1.23789	−	11.4659i	−0.107339	−	0.994222i
$134$	7.12386			0.615408
$135$			4.07585i			0.350793i
$136$	−3.74399	−	6.48478i	−0.321045	−	0.556066i
$137$	−2.21715			−0.189424			−0.0947120	−	0.995505i	$-0.530193\pi$
$137$	−2.21715			−0.189424			−0.0947120	+	0.995505i	$0.530193\pi$
$138$			2.51497i			0.214088i
$139$	13.6907	−	7.90435i	1.16123	−	0.670438i	0.209634	−	0.977780i	$-0.432773\pi$
$139$	13.6907	−	7.90435i	1.16123	−	0.670438i	0.951599	+	0.307341i	$0.0994394\pi$
$140$	9.11945	−	5.75528i	0.770734	−	0.486410i
$141$		−	2.66241i		−	0.224215i
$142$	−0.248702	+	0.430764i	−0.0208706	+	0.0361489i
$143$	3.59988			0.301037
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.63047	−	9.75225i	−0.467585	−	0.809880i
$146$	−1.06951	−	1.85245i	−0.0885135	−	0.153310i
$147$	−6.97831	+	0.550678i	−0.575561	+	0.0454191i
$148$	−8.55440	+	4.93889i	−0.703167	+	0.405974i
$149$	13.0323			1.06765			0.533824	−	0.845596i	$-0.320754\pi$
$149$	13.0323			1.06765			0.533824	+	0.845596i	$0.320754\pi$
$150$	−10.0567	+	5.80626i	−0.821129	+	0.474079i
$151$	12.1248	+	7.00028i	0.986706	+	0.569675i	0.904288	−	0.426923i	$-0.140402\pi$
$151$	12.1248	+	7.00028i	0.986706	+	0.569675i	0.0824181	+	0.996598i	$0.473736\pi$
$152$	−1.91725	+	3.91461i	−0.155509	+	0.317517i
$153$		−	7.48798i		−	0.605368i
$154$	−0.101051	−	2.56507i	−0.00814294	−	0.206699i
$155$	4.57560	+	2.64172i	0.367521	+	0.212188i
$156$	−1.85511	+	3.21315i	−0.148528	+	0.257258i
$157$	6.88812	−	3.97686i	0.549732	−	0.317388i	−0.199282	−	0.979942i	$-0.563861\pi$
$157$	6.88812	−	3.97686i	0.549732	−	0.317388i	0.749014	+	0.662554i	$0.230528\pi$
$158$	−11.4685			−0.912387
$159$	9.32846	−	5.38579i	0.739795	−	0.427121i
$160$	−4.07585			−0.322224
$161$	6.64882	−	0.261931i	0.524000	−	0.0206431i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	10.8199	+	18.7407i	0.847484	+	1.46789i	0.883447	+	0.468532i	$0.155217\pi$
$163$	10.8199	+	18.7407i	0.847484	+	1.46789i	−0.0359628	+	0.999353i	$0.511450\pi$
$164$	5.12688	−	8.88001i	0.400342	−	0.693412i
$165$			3.95462i			0.307867i
$166$	−17.0639			−1.32442
$167$	−0.0757722	−	0.131241i	−0.00586343	−	0.0101558i	0.863079	−	0.505069i	$-0.168533\pi$
$167$	−0.0757722	−	0.131241i	−0.00586343	−	0.0101558i	−0.868942	+	0.494914i	$0.835200\pi$
$168$	2.34159	+	1.23165i	0.180657	+	0.0950242i
$169$	−0.382903	+	0.663208i	−0.0294541	+	0.0510160i
$170$	26.4310	−	15.2599i	2.02716	−	1.17038i
$171$	−3.61769	+	2.43153i	−0.276652	+	0.185944i
$172$	−4.80115	+	8.31583i	−0.366084	+	0.634076i
$173$	−9.14455			−0.695247			−0.347624	−	0.937634i	$-0.613011\pi$
$173$	−9.14455			−0.695247			−0.347624	+	0.937634i	$0.613011\pi$
$174$	1.38142	−	2.39269i	0.104725	−	0.181390i
$175$	16.3974	+	25.9823i	1.23953	+	1.96408i
$176$	−0.485128	+	0.840267i	−0.0365679	+	0.0633375i
$177$	4.75870	−	8.24231i	0.357686	−	0.619530i
$178$	0.624786	+	0.360720i	0.0468297	+	0.0270371i
$179$	−5.49625	−	3.17326i	−0.410809	−	0.237181i	0.280328	−	0.959904i	$-0.409557\pi$
$179$	−5.49625	−	3.17326i	−0.410809	−	0.237181i	−0.691137	+	0.722723i	$0.742890\pi$
$180$	−3.52979	−	2.03792i	−0.263095	−	0.151898i
$181$	−7.25677	−	12.5691i	−0.539392	−	0.934254i	−0.998937	−	0.0460992i	$-0.985321\pi$
$181$	−7.25677	−	12.5691i	−0.539392	−	0.934254i	0.459545	−	0.888154i	$-0.348012\pi$
$182$	8.68782	+	4.56972i	0.643984	+	0.338730i
$183$		−	13.7763i		−	1.01837i
$184$	−2.17802	−	1.25748i	−0.160566	−	0.0927029i
$185$	−20.1301	−	34.8664i	−1.48000	−	2.56343i
$186$			1.29628i			0.0950480i
$187$		−	7.26527i		−	0.531289i
$188$	2.30571	+	1.33120i	0.168161	+	0.0970880i
$189$	1.41205	+	2.23744i	0.102711	+	0.162750i
$190$	−15.9553	−	7.81440i	−1.15752	−	0.566916i
$191$	−3.41302	−	5.91152i	−0.246957	−	0.427743i	0.715723	−	0.698384i	$-0.246097\pi$
$191$	−3.41302	−	5.91152i	−0.246957	−	0.427743i	−0.962680	+	0.270642i	$0.912764\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	11.4737	−	6.62433i	0.825893	−	0.476830i	−0.0265511	−	0.999647i	$-0.508452\pi$
$193$	11.4737	−	6.62433i	0.825893	−	0.476830i	0.852445	+	0.522818i	$0.175119\pi$
$194$	−13.5895	−	7.84588i	−0.975667	−	0.563302i
$195$	−13.0963	−	7.56116i	−0.937847	−	0.541466i
$196$	3.01225	−	6.31873i	0.215161	−	0.451338i
$197$	−6.85013			−0.488052			−0.244026	−	0.969769i	$-0.578468\pi$
$197$	−6.85013			−0.488052			−0.244026	+	0.969769i	$0.578468\pi$
$198$	−0.840267	+	0.485128i	−0.0597152	+	0.0344766i
$199$			8.47472i			0.600757i	0.953820	+	0.300378i	$0.0971129\pi$
$199$			8.47472i			0.600757i	−0.953820	+	0.300378i	$0.902887\pi$
$200$		−	11.6125i		−	0.821129i
$201$	−6.16944	+	3.56193i	−0.435159	+	0.251239i
$202$	3.71819			0.261611
$203$	−6.46944	−	3.40287i	−0.454066	−	0.238835i
$204$	6.48478	+	3.74399i	0.454026	+	0.262132i
$205$	36.1936	+	20.8964i	2.52787	+	1.45946i
$206$	−1.95033	+	1.12602i	−0.135886	+	0.0784538i
$207$	−1.25748	−	2.17802i	−0.0874011	−	0.151383i
$208$	−1.85511	−	3.21315i	−0.128629	−	0.222792i
$209$	−3.51009	+	2.35921i	−0.242798	+	0.163190i
$210$	−5.02004	+	9.54395i	−0.346415	+	0.658595i
$211$	−1.35940	−	0.784849i	−0.0935848	−	0.0540312i	0.452477	−	0.891776i	$-0.350540\pi$
$211$	−1.35940	−	0.784849i	−0.0935848	−	0.0540312i	−0.546062	+	0.837745i	$0.683874\pi$
$212$			10.7716i			0.739795i
$213$		−	0.497403i		−	0.0340815i
$214$	−3.29658	−	5.70984i	−0.225349	−	0.390317i
$215$	−33.8940	−	19.5687i	−2.31155	−	1.33458i
$216$		−	1.00000i		−	0.0680414i
$217$	3.42698	−	0.135006i	0.232639	−	0.00916484i
$218$	3.89800	+	6.75153i	0.264006	+	0.457271i
$219$	1.85245	+	1.06951i	0.125177	+	0.0722710i
$220$	−3.42480	−	1.97731i	−0.230900	−	0.133310i
$221$	24.0600	+	13.8911i	1.61845	+	0.934415i
$222$	4.93889	−	8.55440i	0.331476	−	0.574134i
$223$	9.83556	−	17.0357i	0.658638	−	1.14079i	−0.322331	−	0.946627i	$-0.604466\pi$
$223$	9.83556	−	17.0357i	0.658638	−	1.14079i	0.980968	−	0.194167i	$-0.0622004\pi$
$224$	−2.23744	+	1.41205i	−0.149495	+	0.0943463i
$225$	5.80626	−	10.0567i	0.387084	−	0.670449i
$226$	10.2155			0.679525
$227$	4.47042	−	7.74299i	0.296712	−	0.513921i	−0.678670	−	0.734444i	$-0.737443\pi$
$227$	4.47042	−	7.74299i	0.296712	−	0.513921i	0.975382	+	0.220523i	$0.0707765\pi$
$228$	−0.296922	−	4.34877i	−0.0196641	−	0.288005i
$229$	7.36441	−	4.25184i	0.486654	−	0.280970i	−0.236531	−	0.971624i	$-0.576011\pi$
$229$	7.36441	−	4.25184i	0.486654	−	0.280970i	0.723185	+	0.690654i	$0.242677\pi$
$230$	5.12531	−	8.87729i	0.337953	−	0.585351i
$231$	1.37005	+	2.17089i	0.0901425	+	0.142834i
$232$	1.38142	+	2.39269i	0.0906948	+	0.157088i
$233$	−0.470178			−0.0308024			−0.0154012	−	0.999881i	$-0.504903\pi$
$233$	−0.470178			−0.0308024			−0.0154012	+	0.999881i	$0.504903\pi$
$234$		−	3.71023i		−	0.242545i
$235$	−5.42578	+	9.39773i	−0.353939	+	0.613040i
$236$	4.75870	+	8.24231i	0.309765	+	0.536529i
$237$	9.93203	−	5.73426i	0.645155	−	0.372480i
$238$	9.22261	−	17.5338i	0.597813	−	1.13654i
$239$	−12.3419			−0.798329			−0.399164	−	0.916879i	$-0.630700\pi$
$239$	−12.3419			−0.798329			−0.399164	+	0.916879i	$0.630700\pi$
$240$	3.52979	−	2.03792i	0.227847	−	0.131547i
$241$	−16.8484			−1.08530			−0.542649	−	0.839959i	$-0.682579\pi$
$241$	−16.8484			−1.08530			−0.542649	+	0.839959i	$0.682579\pi$
$242$	8.71100	−	5.02930i	0.559965	−	0.323296i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.9306	+	6.88815i	0.763780	+	0.440968i
$245$	25.7542	+	12.2775i	1.64537	+	0.784379i
$246$			10.2538i			0.653755i
$247$	−1.10165	−	16.1350i	−0.0700961	−	1.02664i
$248$	−1.12261	−	0.648141i	−0.0712860	−	0.0411570i
$249$	14.7778	−	8.53197i	0.936505	−	0.540691i
$250$	26.9516			1.70457
$251$	−1.39946	+	0.807976i	−0.0883329	+	0.0509990i	−0.543516	−	0.839399i	$-0.682907\pi$
$251$	−1.39946	+	0.807976i	−0.0883329	+	0.0509990i	0.455183	+	0.890398i	$0.349574\pi$
$252$	−2.64370	+	0.104149i	−0.166537	+	0.00656077i
$253$	−1.22008	−	2.11324i	−0.0767058	−	0.132858i
$254$	2.67492	+	4.63310i	0.167840	+	0.290707i
$255$	−15.2599	+	26.4310i	−0.955614	+	1.65517i
$256$	1.00000			0.0625000
$257$	−9.02311	+	15.6285i	−0.562846	+	0.974878i	0.434400	+	0.900720i	$0.356960\pi$
$257$	−9.02311	+	15.6285i	−0.562846	+	0.974878i	−0.997246	+	0.0741582i	$0.976373\pi$
$258$		−	9.60229i		−	0.597813i
$259$	−23.1297	−	12.1660i	−1.43721	−	0.755959i
$260$	13.0963	−	7.56116i	0.812199	−	0.468923i
$261$			2.76284i			0.171016i
$262$	−1.69994			−0.105023
$263$	−10.8038	−	18.7127i	−0.666191	−	1.15388i	−0.978961	−	0.204047i	$-0.934590\pi$
$263$	−10.8038	−	18.7127i	−0.666191	−	1.15388i	0.312770	−	0.949829i	$-0.398743\pi$
$264$		−	0.970257i		−	0.0597152i
$265$	−43.9033			−2.69696
$266$	−11.4659	+	1.23789i	−0.703021	+	0.0759000i
$267$	−0.721440			−0.0441514
$268$		−	7.12386i		−	0.435159i
$269$	5.35097	+	9.26815i	0.326254	+	0.565089i	0.981765	−	0.190096i	$-0.0608801\pi$
$269$	5.35097	+	9.26815i	0.326254	+	0.565089i	−0.655511	+	0.755186i	$0.727547\pi$
$270$	4.07585			0.248048
$271$			6.49782i			0.394714i	0.980332	+	0.197357i	$0.0632359\pi$
$271$			6.49782i			0.394714i	−0.980332	+	0.197357i	$0.936764\pi$
$272$	−6.48478	+	3.74399i	−0.393198	+	0.227013i
$273$	−9.80874	+	0.386417i	−0.593652	+	0.0233870i
$274$			2.21715i			0.133943i
$275$	5.63357	−	9.75762i	0.339717	−	0.588407i
$276$	2.51497			0.151383
$277$	−5.34502	+	9.25785i	−0.321151	+	0.556250i	−0.980726	−	0.195389i	$-0.937403\pi$
$277$	−5.34502	+	9.25785i	−0.321151	+	0.556250i	0.659575	+	0.751639i	$0.270736\pi$
$278$	−7.90435	−	13.6907i	−0.474072	−	0.821116i
$279$	−0.648141	−	1.12261i	−0.0388032	−	0.0672091i
$280$	−5.75528	−	9.11945i	−0.343944	−	0.544991i
$281$	−4.64102	+	2.67950i	−0.276860	+	0.159845i	−0.632001	−	0.774967i	$-0.717766\pi$
$281$	−4.64102	+	2.67950i	−0.276860	+	0.159845i	0.355141	+	0.934813i	$0.384433\pi$
$282$	−2.66241			−0.158544
$283$	11.7540	−	6.78618i	0.698703	−	0.403397i	−0.108161	−	0.994133i	$-0.534496\pi$
$283$	11.7540	−	6.78618i	0.698703	−	0.403397i	0.806864	+	0.590737i	$0.201163\pi$
$284$	0.430764	+	0.248702i	0.0255611	+	0.0147577i
$285$	17.7249	−	1.21021i	1.04993	−	0.0716865i
$286$		−	3.59988i		−	0.212865i
$287$	27.1078	−	1.06792i	1.60013	−	0.0630372i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	19.5349	−	33.8355i	1.14911	−	1.99032i
$290$	−9.75225	+	5.63047i	−0.572672	+	0.330632i
$291$	15.6918			0.919868
$292$	−1.85245	+	1.06951i	−0.108406	+	0.0625885i
$293$	−17.3263			−1.01221			−0.506106	−	0.862471i	$-0.668916\pi$
$293$	−17.3263			−1.01221			−0.506106	+	0.862471i	$0.668916\pi$
$294$	0.550678	+	6.97831i	0.0321162	+	0.406983i
$295$	−33.5944	+	19.3957i	−1.95594	+	1.12926i
$296$	4.93889	+	8.55440i	0.287067	+	0.497214i
$297$	0.485128	−	0.840267i	0.0281500	−	0.0487572i
$298$		−	13.0323i		−	0.754941i
$299$	9.33110			0.539631
$300$	5.80626	+	10.0567i	0.335225	+	0.580626i
$301$	−25.3856	+	1.00007i	−1.46320	+	0.0576430i
$302$	7.00028	−	12.1248i	0.402821	−	0.697707i
$303$	−3.22004	+	1.85909i	−0.184987	+	0.106802i
$304$	3.91461	+	1.91725i	0.224518	+	0.109962i
$305$	−28.0750	+	48.6274i	−1.60757	+	2.78440i
$306$	−7.48798			−0.428060
$307$	−10.4330	+	18.0706i	−0.595446	+	1.03134i	0.398038	+	0.917369i	$0.369691\pi$
$307$	−10.4330	+	18.0706i	−0.595446	+	1.03134i	−0.993484	+	0.113973i	$0.963642\pi$
$308$	−2.56507	+	0.101051i	−0.146158	+	0.00575793i
$309$	1.12602	−	1.95033i	0.0640572	−	0.110950i
$310$	2.64172	−	4.57560i	0.150040	−	0.259877i
$311$	18.1423	+	10.4745i	1.02875	+	0.593952i	0.916628	−	0.399742i	$-0.130900\pi$
$311$	18.1423	+	10.4745i	1.02875	+	0.593952i	0.112127	+	0.993694i	$0.464234\pi$
$312$	3.21315	+	1.85511i	0.181909	+	0.105025i
$313$	−6.00681	−	3.46804i	−0.339525	−	0.196025i	0.320537	−	0.947236i	$-0.396137\pi$
$313$	−6.00681	−	3.46804i	−0.339525	−	0.196025i	−0.660062	+	0.751211i	$0.729470\pi$
$314$	−3.97686	−	6.88812i	−0.224427	−	0.388719i
$315$	−0.424495	−	10.7753i	−0.0239176	−	0.607120i
$316$			11.4685i			0.645155i
$317$	8.13501	+	4.69675i	0.456908	+	0.263796i	0.710743	−	0.703452i	$-0.248359\pi$
$317$	8.13501	+	4.69675i	0.456908	+	0.263796i	−0.253835	+	0.967247i	$0.581692\pi$
$318$	−5.38579	−	9.32846i	−0.302020	−	0.523114i
$319$			2.68067i			0.150089i
$320$			4.07585i			0.227847i
$321$	5.70984	+	3.29658i	0.318692	+	0.183997i
$322$	−0.261931	−	6.64882i	−0.0145969	−	0.370524i
$323$	−32.5636	+	2.22334i	−1.81188	+	0.123710i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	21.5426	+	37.3128i	1.19497	+	2.06974i
$326$	18.7407	−	10.8199i	1.03795	−	0.599262i
$327$	−6.75153	−	3.89800i	−0.373361	−	0.215560i
$328$	−8.88001	−	5.12688i	−0.490316	−	0.283084i
$329$	0.277287	+	7.03861i	0.0152873	+	0.388051i
$330$	3.95462			0.217695
$331$	16.7710	−	9.68272i	0.921816	−	0.532211i	0.0376019	−	0.999293i	$-0.488028\pi$
$331$	16.7710	−	9.68272i	0.921816	−	0.532211i	0.884214	+	0.467082i	$0.154695\pi$
$332$			17.0639i			0.936505i
$333$			9.87777i			0.541298i
$334$	−0.131241	+	0.0757722i	−0.00718120	+	0.00414607i
$335$	29.0357			1.58639
$336$	1.23165	−	2.34159i	0.0671923	−	0.127744i
$337$	19.3232	+	11.1562i	1.05260	+	0.607719i	0.923376	−	0.383897i	$-0.125418\pi$
$337$	19.3232	+	11.1562i	1.05260	+	0.607719i	0.129224	+	0.991615i	$0.458751\pi$
$338$	0.663208	+	0.382903i	0.0360737	+	0.0208272i
$339$	−8.84689	+	5.10775i	−0.480497	+	0.277415i
$340$	−15.2599	−	26.4310i	−0.827586	−	1.43342i
$341$	−0.628863	−	1.08922i	−0.0340549	−	0.0589847i
$342$	2.43153	+	3.61769i	0.131482	+	0.195622i
$343$	18.3912	−	2.18261i	0.993031	−	0.117850i
$344$	8.31583	+	4.80115i	0.448359	+	0.258860i
$345$			10.2506i			0.551874i
$346$			9.14455i			0.491614i
$347$	−1.23494	−	2.13899i	−0.0662953	−	0.114827i	0.830973	−	0.556313i	$-0.187785\pi$
$347$	−1.23494	−	2.13899i	−0.0662953	−	0.114827i	−0.897268	+	0.441487i	$0.854451\pi$
$348$	−2.39269	−	1.38142i	−0.128262	−	0.0740520i
$349$		−	4.96655i		−	0.265853i	−0.991126	−	0.132927i	$-0.957563\pi$
$349$		−	4.96655i		−	0.265853i	0.991126	−	0.132927i	$-0.0424375\pi$
$350$	25.9823	−	16.3974i	1.38881	−	0.876479i
$351$	1.85511	+	3.21315i	0.0990187	+	0.171505i
$352$	0.840267	+	0.485128i	0.0447864	+	0.0258574i
$353$	29.6058	+	17.0929i	1.57576	+	0.909764i	0.995442	+	0.0953725i	$0.0304042\pi$
$353$	29.6058	+	17.0929i	1.57576	+	0.909764i	0.580316	+	0.814391i	$0.302929\pi$
$354$	−8.24231	−	4.75870i	−0.438074	−	0.252922i
$355$	−1.01367	+	1.75573i	−0.0538000	+	0.0931844i
$356$	0.360720	−	0.624786i	0.0191181	−	0.0331136i
$357$	0.779866	+	19.7960i	0.0412749	+	1.04771i
$358$	−3.17326	+	5.49625i	−0.167712	+	0.290486i
$359$	−24.0215			−1.26780			−0.633902	−	0.773413i	$-0.718548\pi$
$359$	−24.0215			−1.26780			−0.633902	+	0.773413i	$0.718548\pi$
$360$	−2.03792	+	3.52979i	−0.107408	+	0.186036i
$361$	11.6483	+	15.0105i	0.613070	+	0.790028i
$362$	−12.5691	+	7.25677i	−0.660617	+	0.381407i
$363$	−5.02930	+	8.71100i	−0.263970	+	0.457209i
$364$	4.56972	−	8.68782i	0.239519	−	0.455366i
$365$	−4.35917	−	7.55030i	−0.228169	−	0.395201i
$366$	−13.7763			−0.720098
$367$		−	21.3328i		−	1.11357i	−0.830658	−	0.556783i	$-0.812036\pi$
$367$		−	21.3328i		−	1.11357i	0.830658	−	0.556783i	$-0.187964\pi$
$368$	−1.25748	+	2.17802i	−0.0655508	+	0.113537i
$369$	−5.12688	−	8.88001i	−0.266894	−	0.462275i
$370$	−34.8664	+	20.1301i	−1.81262	+	1.04652i
$371$	−24.1007	+	15.2100i	−1.25125	+	0.789662i
$372$	1.29628			0.0672091
$373$	−8.29433	+	4.78873i	−0.429464	+	0.247951i	−0.699118	−	0.715006i	$-0.746424\pi$
$373$	−8.29433	+	4.78873i	−0.429464	+	0.247951i	0.269654	+	0.962957i	$0.413091\pi$
$374$	−7.26527			−0.375678
$375$	−23.3408	+	13.4758i	−1.20531	+	0.695888i
$376$	1.33120	−	2.30571i	0.0686516	−	0.118908i
$377$	−8.87744	−	5.12539i	−0.457212	−	0.263971i
$378$	2.23744	−	1.41205i	0.115081	−	0.0726278i
$379$		−	24.4666i		−	1.25676i	−0.777905	−	0.628382i	$-0.783718\pi$
$379$		−	24.4666i		−	1.25676i	0.777905	−	0.628382i	$-0.216282\pi$
$380$	−7.81440	+	15.9553i	−0.400870	+	0.818492i
$381$	−4.63310	−	2.67492i	−0.237361	−	0.137041i
$382$	−5.91152	+	3.41302i	−0.302460	+	0.174625i
$383$	7.12577			0.364110			0.182055	−	0.983288i	$-0.441725\pi$
$383$	7.12577			0.364110			0.182055	+	0.983288i	$0.441725\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−0.411870	−	10.4548i	−0.0209908	−	0.532827i
$386$	−6.62433	−	11.4737i	−0.337170	−	0.583995i
$387$	4.80115	+	8.31583i	0.244056	+	0.422717i
$388$	−7.84588	+	13.5895i	−0.398314	+	0.689901i
$389$	9.22919			0.467939			0.233969	−	0.972244i	$-0.424828\pi$
$389$	9.22919			0.467939			0.233969	+	0.972244i	$0.424828\pi$
$390$	−7.56116	+	13.0963i	−0.382874	+	0.663158i
$391$		−	18.8320i		−	0.952376i
$392$	−6.31873	−	3.01225i	−0.319144	−	0.152142i
$393$	1.47219	−	0.849970i	0.0742622	−	0.0428753i
$394$			6.85013i			0.345105i
$395$	−46.7439			−2.35194
$396$	0.485128	+	0.840267i	0.0243786	+	0.0422250i
$397$			13.3617i			0.670606i	0.942110	+	0.335303i	$0.108839\pi$
$397$			13.3617i			0.670606i	−0.942110	+	0.335303i	$0.891161\pi$
$398$	8.47472			0.424799
$399$	9.31084	−	6.80501i	0.466125	−	0.340677i
$400$	−11.6125			−0.580626
$401$			25.9594i			1.29635i	0.761491	+	0.648176i	$0.224468\pi$
$401$			25.9594i			1.29635i	−0.761491	+	0.648176i	$0.775532\pi$
$402$	3.56193	+	6.16944i	0.177653	+	0.307704i
$403$	4.80950			0.239578
$404$		−	3.71819i		−	0.184987i
$405$	−3.52979	+	2.03792i	−0.175397	+	0.101265i
$406$	−3.40287	+	6.46944i	−0.168882	+	0.321073i
$407$			9.58397i			0.475060i
$408$	3.74399	−	6.48478i	0.185355	−	0.321045i
$409$	−6.20352			−0.306744			−0.153372	−	0.988168i	$-0.549013\pi$
$409$	−6.20352			−0.306744			−0.153372	+	0.988168i	$0.549013\pi$
$410$	20.8964	−	36.1936i	1.03200	−	1.78747i
$411$	−1.10858	−	1.92011i	−0.0546820	−	0.0947120i
$412$	1.12602	+	1.95033i	0.0554752	+	0.0960859i
$413$	−11.7221	+	22.2858i	−0.576809	+	1.09661i
$414$	−2.17802	+	1.25748i	−0.107044	+	0.0618019i
$415$	−69.5500			−3.41407
$416$	−3.21315	+	1.85511i	−0.157538	+	0.0909545i
$417$	13.6907	+	7.90435i	0.670438	+	0.387078i
$418$	2.35921	+	3.51009i	0.115393	+	0.171684i
$419$			7.95386i			0.388571i	0.980945	+	0.194286i	$0.0622389\pi$
$419$			7.95386i			0.388571i	−0.980945	+	0.194286i	$0.937761\pi$
$420$	9.54395	+	5.02004i	0.465697	+	0.244953i
$421$	−12.8689	−	7.42985i	−0.627191	−	0.362109i	0.152472	−	0.988308i	$-0.451276\pi$
$421$	−12.8689	−	7.42985i	−0.627191	−	0.362109i	−0.779663	+	0.626199i	$0.784610\pi$
$422$	−0.784849	+	1.35940i	−0.0382058	+	0.0661745i
$423$	2.30571	−	1.33120i	0.112108	−	0.0647253i
$424$	10.7716			0.523114
$425$	75.3047	−	43.4772i	3.65282	−	2.10895i
$426$	−0.497403			−0.0240993
$427$	1.43479	+	36.4204i	0.0694342	+	1.76251i
$428$	−5.70984	+	3.29658i	−0.275995	+	0.159346i
$429$	1.79994	+	3.11758i	0.0869018	+	0.150518i
$430$	−19.5687	+	33.8940i	−0.943688	+	1.63452i
$431$			7.45630i			0.359157i	0.983744	+	0.179579i	$0.0574734\pi$
$431$			7.45630i			0.359157i	−0.983744	+	0.179579i	$0.942527\pi$
$432$	−1.00000			−0.0481125
$433$	5.01071	+	8.67881i	0.240799	+	0.417077i	0.960942	−	0.276749i	$-0.0892571\pi$
$433$	5.01071	+	8.67881i	0.240799	+	0.417077i	−0.720143	+	0.693826i	$0.755924\pi$
$434$	−0.135006	−	3.42698i	−0.00648052	−	0.164500i
$435$	5.63047	−	9.75225i	0.269960	−	0.467585i
$436$	6.75153	−	3.89800i	0.323340	−	0.186680i
$437$	−9.09836	+	6.11521i	−0.435234	+	0.292530i
$438$	1.06951	−	1.85245i	0.0511033	−	0.0885135i
$439$	−20.8943			−0.997230			−0.498615	−	0.866823i	$-0.666158\pi$
$439$	−20.8943			−0.997230			−0.498615	+	0.866823i	$0.666158\pi$
$440$	−1.97731	+	3.42480i	−0.0942645	+	0.163271i
$441$	−3.96605	−	5.76805i	−0.188860	−	0.274669i
$442$	13.8911	−	24.0600i	0.660731	−	1.14442i
$443$	5.21714	−	9.03634i	0.247874	−	0.429330i	−0.715062	−	0.699061i	$-0.753602\pi$
$443$	5.21714	−	9.03634i	0.247874	−	0.429330i	0.962936	+	0.269731i	$0.0869349\pi$
$444$	−8.55440	−	4.93889i	−0.405974	−	0.234389i
$445$	2.54653	+	1.47024i	0.120717	+	0.0696960i
$446$	−17.0357	−	9.83556i	−0.806663	−	0.465727i
$447$	6.51615	+	11.2863i	0.308203	+	0.533824i
$448$	1.41205	+	2.23744i	0.0667129	+	0.105709i
$449$			19.7533i			0.932214i	0.884728	+	0.466107i	$0.154344\pi$
$449$			19.7533i			0.932214i	−0.884728	+	0.466107i	$0.845656\pi$
$450$	−10.0567	−	5.80626i	−0.474079	−	0.273710i
$451$	−4.97439	−	8.61589i	−0.234235	−	0.405706i
$452$		−	10.2155i		−	0.480497i
$453$			14.0006i			0.657804i
$454$	−7.74299	−	4.47042i	−0.363397	−	0.209807i
$455$	35.4102	+	18.6255i	1.66006	+	0.873176i
$456$	−4.34877	+	0.296922i	−0.203650	+	0.0139046i
$457$	−4.05777	−	7.02827i	−0.189815	−	0.328769i	0.755374	−	0.655294i	$-0.227455\pi$
$457$	−4.05777	−	7.02827i	−0.189815	−	0.328769i	−0.945188	+	0.326526i	$0.894122\pi$
$458$	−4.25184	−	7.36441i	−0.198676	−	0.344116i
$459$	6.48478	−	3.74399i	0.302684	−	0.174755i
$460$	−8.87729	−	5.12531i	−0.413906	−	0.238969i
$461$	−29.0623	−	16.7791i	−1.35357	−	0.781483i	−0.364820	−	0.931078i	$-0.618870\pi$
$461$	−29.0623	−	16.7791i	−1.35357	−	0.781483i	−0.988747	+	0.149596i	$0.952203\pi$
$462$	2.17089	−	1.37005i	0.100999	−	0.0637404i
$463$	14.8883			0.691917			0.345959	−	0.938250i	$-0.387554\pi$
$463$	14.8883			0.691917			0.345959	+	0.938250i	$0.387554\pi$
$464$	2.39269	−	1.38142i	0.111078	−	0.0641309i
$465$			5.28345i			0.245014i
$466$			0.470178i			0.0217806i
$467$	7.71786	−	4.45591i	0.357140	−	0.206195i	−0.310686	−	0.950513i	$-0.600559\pi$
$467$	7.71786	−	4.45591i	0.357140	−	0.206195i	0.667825	+	0.744318i	$0.267225\pi$
$468$	−3.71023			−0.171505
$469$	15.9392	−	10.0592i	0.736003	−	0.464491i
$470$	9.39773	+	5.42578i	0.433485	+	0.250273i
$471$	6.88812	+	3.97686i	0.317388	+	0.183244i
$472$	8.24231	−	4.75870i	0.379383	−	0.219037i
$473$	4.65834	+	8.06849i	0.214191	+	0.370990i
$474$	−5.73426	−	9.93203i	−0.263383	−	0.456193i
$475$	−45.4585	−	22.2641i	−2.08578	−	1.02155i
$476$	−17.5338	−	9.22261i	−0.803659	−	0.422718i
$477$	9.32846	+	5.38579i	0.427121	+	0.246598i
$478$			12.3419i			0.564504i
$479$			17.7340i			0.810289i	0.914253	+	0.405144i	$0.132779\pi$
$479$			17.7340i			0.810289i	−0.914253	+	0.405144i	$0.867221\pi$
$480$	−2.03792	−	3.52979i	−0.0930180	−	0.161112i
$481$	−31.7388	−	18.3244i	−1.44716	−	0.835521i
$482$			16.8484i			0.767422i
$483$	3.55125	+	5.62708i	0.161587	+	0.256041i
$484$	−5.02930	−	8.71100i	−0.228605	−	0.395955i
$485$	−55.3886	−	31.9786i	−2.51507	−	1.45207i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−12.2636	−	7.08040i	−0.555717	−	0.320844i	0.195707	−	0.980662i	$-0.437300\pi$
$487$	−12.2636	−	7.08040i	−0.555717	−	0.320844i	−0.751425	+	0.659819i	$0.770633\pi$
$488$	6.88815	−	11.9306i	0.311812	−	0.540074i
$489$	−10.8199	+	18.7407i	−0.489295	+	0.847484i
$490$	12.2775	−	25.7542i	0.554640	−	1.16345i
$491$	5.82747	−	10.0935i	0.262990	−	0.455512i	−0.704045	−	0.710155i	$-0.748625\pi$
$491$	5.82747	−	10.0935i	0.262990	−	0.455512i	0.967035	+	0.254643i	$0.0819580\pi$
$492$	10.2538			0.462275
$493$	−10.3441	+	17.9165i	−0.465873	+	0.806916i
$494$	−16.1350	+	1.10165i	−0.725946	+	0.0495655i
$495$	−3.42480	+	1.97731i	−0.153933	+	0.0888734i
$496$	−0.648141	+	1.12261i	−0.0291024	+	0.0504068i
$497$	0.0518041	+	1.31499i	0.00232373	+	0.0589852i
$498$	−8.53197	−	14.7778i	−0.382327	−	0.662209i
$499$	7.22272			0.323333			0.161667	−	0.986845i	$-0.448313\pi$
$499$	7.22272			0.323333			0.161667	+	0.986845i	$0.448313\pi$
$500$		−	26.9516i		−	1.20531i
$501$	0.0757722	−	0.131241i	0.00338525	−	0.00586343i
$502$	0.807976	+	1.39946i	0.0360617	+	0.0624608i
$503$	25.1228	−	14.5047i	1.12017	−	0.646731i	0.178726	−	0.983899i	$-0.442803\pi$
$503$	25.1228	−	14.5047i	1.12017	−	0.646731i	0.941444	+	0.337168i	$0.109469\pi$
$504$	0.104149	+	2.64370i	0.00463917	+	0.117760i
$505$	15.1548			0.674378
$506$	−2.11324	+	1.22008i	−0.0939451	+	0.0542392i
$507$	−0.765806			−0.0340106
$508$	4.63310	−	2.67492i	0.205561	−	0.118681i
$509$	13.6875	−	23.7074i	0.606686	−	1.05081i	−0.385097	−	0.922876i	$-0.625832\pi$
$509$	13.6875	−	23.7074i	0.606686	−	1.05081i	0.991783	−	0.127935i	$-0.0408347\pi$
$510$	26.4310	+	15.2599i	1.17038	+	0.675721i
$511$	−5.00871	−	2.63454i	−0.221572	−	0.116545i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.91461	−	1.91725i	−0.172834	−	0.0846485i
$514$	15.6285	+	9.02311i	0.689343	+	0.397992i
$515$	−7.94925	+	4.58950i	−0.350286	+	0.202238i
$516$	−9.60229			−0.422717
$517$	2.23713	−	1.29161i	0.0983890	−	0.0568049i
$518$	−12.1660	+	23.1297i	−0.534543	+	1.01626i
$519$	−4.57227	−	7.91941i	−0.200701	−	0.347624i
$520$	−7.56116	−	13.0963i	−0.331579	−	0.574312i
$521$	12.8508	−	22.2583i	0.563005	−	0.975154i	−0.434227	−	0.900804i	$-0.642978\pi$
$521$	12.8508	−	22.2583i	0.563005	−	0.975154i	0.997232	−	0.0743503i	$-0.0236883\pi$
$522$	2.76284			0.120926
$523$	−3.81566	+	6.60891i	−0.166847	+	0.288987i	−0.937310	−	0.348498i	$-0.886692\pi$
$523$	−3.81566	+	6.60891i	−0.166847	+	0.288987i	0.770463	+	0.637485i	$0.220025\pi$
$524$			1.69994i			0.0742622i
$525$	−14.3026	+	27.1917i	−0.624218	+	1.18674i
$526$	−18.7127	+	10.8038i	−0.815914	+	0.471068i
$527$		−	9.70654i		−	0.422823i
$528$	−0.970257			−0.0422250
$529$	8.33747	+	14.4409i	0.362499	+	0.627867i
$530$			43.9033i			1.90704i
$531$	9.51740			0.413020
$532$	1.23789	+	11.4659i	0.0536694	+	0.497111i
$533$	38.0438			1.64786
$534$			0.721440i			0.0312198i
$535$	−13.4363	−	23.2724i	−0.580904	−	1.00615i
$536$	−7.12386			−0.307704
$537$		−	6.34652i		−	0.273873i
$538$	9.26815	−	5.35097i	0.399578	−	0.230697i
$539$	−3.84809	−	5.59649i	−0.165749	−	0.241058i
$540$		−	4.07585i		−	0.175397i
$541$	13.6481	−	23.6392i	0.586777	−	1.01633i	−0.407874	−	0.913038i	$-0.633730\pi$
$541$	13.6481	−	23.6392i	0.586777	−	1.01633i	0.994651	−	0.103290i	$-0.0329369\pi$
$542$	6.49782			0.279105
$543$	7.25677	−	12.5691i	0.311418	−	0.539392i
$544$	3.74399	+	6.48478i	0.160522	+	0.278033i
$545$	15.8876	+	27.5182i	0.680552	+	1.17875i
$546$	0.386417	+	9.80874i	0.0165371	+	0.419775i
$547$	−16.3761	+	9.45474i	−0.700191	+	0.404256i	−0.807419	−	0.589979i	$-0.799136\pi$
$547$	−16.3761	+	9.45474i	−0.700191	+	0.404256i	0.107227	+	0.994235i	$0.465803\pi$
$548$	2.21715			0.0947120
$549$	11.9306	−	6.88815i	0.509186	−	0.293979i
$550$	−9.75762	−	5.63357i	−0.416066	−	0.240216i
$551$	12.0150	−	0.820348i	0.511856	−	0.0349480i
$552$		−	2.51497i		−	0.107044i
$553$	−25.6601	+	16.1941i	−1.09118	+	0.688642i
$554$	9.25785	+	5.34502i	0.393328	+	0.227088i
$555$	20.1301	−	34.8664i	0.854477	−	1.48000i
$556$	−13.6907	+	7.90435i	−0.580617	+	0.335219i
$557$	−4.14219			−0.175510			−0.0877552	−	0.996142i	$-0.527969\pi$
$557$	−4.14219			−0.175510			−0.0877552	+	0.996142i	$0.527969\pi$
$558$	−1.12261	+	0.648141i	−0.0475240	+	0.0274380i
$559$	−35.6267			−1.50685
$560$	−9.11945	+	5.75528i	−0.385367	+	0.243205i
$561$	6.29191	−	3.63263i	0.265644	−	0.153370i
$562$	2.67950	+	4.64102i	0.113028	+	0.195770i
$563$	3.24552	−	5.62141i	0.136782	−	0.236914i	−0.789494	−	0.613758i	$-0.789657\pi$
$563$	3.24552	−	5.62141i	0.136782	−	0.236914i	0.926277	+	0.376843i	$0.122991\pi$
$564$			2.66241i			0.112108i
$565$	41.6368			1.75167
$566$	−6.78618	−	11.7540i	−0.285244	−	0.494058i
$567$	−1.23165	+	2.34159i	−0.0517246	+	0.0983374i
$568$	0.248702	−	0.430764i	0.0104353	−	0.0180745i
$569$	22.6885	−	13.0992i	0.951152	−	0.549148i	0.0577133	−	0.998333i	$-0.481619\pi$
$569$	22.6885	−	13.0992i	0.951152	−	0.549148i	0.893439	+	0.449185i	$0.148286\pi$
$570$	−1.21021	−	17.7249i	−0.0506900	−	0.742416i
$571$	10.2510	−	17.7552i	0.428991	−	0.743034i	−0.567793	−	0.823171i	$-0.692203\pi$
$571$	10.2510	−	17.7552i	0.428991	−	0.743034i	0.996784	+	0.0801376i	$0.0255360\pi$
$572$	−3.59988			−0.150518
$573$	3.41302	−	5.91152i	0.142581	−	0.246957i
$574$	−1.06792	−	27.1078i	−0.0445740	−	1.13146i
$575$	14.6025	−	25.2924i	0.608968	−	1.05476i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−34.4102	−	19.8667i	−1.43251	−	0.827062i	−0.435201	−	0.900333i	$-0.643323\pi$
$577$	−34.4102	−	19.8667i	−1.43251	−	0.827062i	−0.997312	+	0.0732710i	$0.976656\pi$
$578$	−33.8355	−	19.5349i	−1.40737	−	0.812547i
$579$	11.4737	+	6.62433i	0.476830	+	0.275298i
$580$	5.63047	+	9.75225i	0.233792	+	0.404940i
$581$	−38.1795	+	24.0951i	−1.58395	+	0.999631i
$582$		−	15.6918i		−	0.650445i
$583$	9.05101	+	5.22560i	0.374854	+	0.216422i
$584$	1.06951	+	1.85245i	0.0442568	+	0.0766549i
$585$		−	15.1223i		−	0.625231i
$586$			17.3263i			0.715742i
$587$	15.2614	+	8.81115i	0.629904	+	0.363675i	0.780715	−	0.624887i	$-0.214855\pi$
$587$	15.2614	+	8.81115i	0.629904	+	0.363675i	−0.150811	+	0.988563i	$0.548188\pi$
$588$	6.97831	−	0.550678i	0.287780	−	0.0227096i
$589$	−4.68954	+	3.15195i	−0.193229	+	0.129874i
$590$	19.3957	+	33.5944i	0.798510	+	1.38306i
$591$	−3.42507	−	5.93239i	−0.140888	−	0.244026i
$592$	8.55440	−	4.93889i	0.351584	−	0.202987i
$593$	−13.8171	−	7.97729i	−0.567399	−	0.327588i	0.188711	−	0.982033i	$-0.439569\pi$
$593$	−13.8171	−	7.97729i	−0.567399	−	0.327588i	−0.756110	+	0.654445i	$0.772902\pi$
$594$	−0.840267	−	0.485128i	−0.0344766	−	0.0199051i
$595$	37.5899	−	71.4649i	1.54104	−	2.92978i
$596$	−13.0323			−0.533824
$597$	−7.33932	+	4.23736i	−0.300378	+	0.173424i
$598$		−	9.33110i		−	0.381577i
$599$			8.78304i			0.358865i	0.983770	+	0.179433i	$0.0574262\pi$
$599$			8.78304i			0.358865i	−0.983770	+	0.179433i	$0.942574\pi$
$600$	10.0567	−	5.80626i	0.410565	−	0.237040i
$601$	8.16815			0.333186			0.166593	−	0.986026i	$-0.446723\pi$
$601$	8.16815			0.333186			0.166593	+	0.986026i	$0.446723\pi$
$602$	1.00007	+	25.3856i	0.0407598	+	1.03464i
$603$	−6.16944	−	3.56193i	−0.251239	−	0.145053i
$604$	−12.1248	−	7.00028i	−0.493353	−	0.284838i
$605$	35.5047	−	20.4987i	1.44347	−	0.833389i
$606$	1.85909	+	3.22004i	0.0755205	+	0.130805i
$607$	−7.02409	−	12.1661i	−0.285099	−	0.493806i	0.687534	−	0.726152i	$-0.258693\pi$
$607$	−7.02409	−	12.1661i	−0.285099	−	0.493806i	−0.972633	+	0.232346i	$0.925360\pi$
$608$	1.91725	−	3.91461i	0.0777546	−	0.158758i
$609$	−0.287748	−	7.30413i	−0.0116601	−	0.295978i
$610$	48.6274	+	28.0750i	1.96886	+	1.13672i
$611$			9.87814i			0.399627i
$612$			7.48798i			0.302684i
$613$	7.91814	+	13.7146i	0.319811	+	0.553928i	0.980448	−	0.196777i	$-0.0630473\pi$
$613$	7.91814	+	13.7146i	0.319811	+	0.553928i	−0.660638	+	0.750705i	$0.729714\pi$
$614$	18.0706	+	10.4330i	0.729269	+	0.421044i
$615$			41.7927i			1.68524i
$616$	0.101051	+	2.56507i	0.00407147	+	0.103350i
$617$	−21.5429	−	37.3134i	−0.867285	−	1.50218i	−0.864761	−	0.502184i	$-0.832530\pi$
$617$	−21.5429	−	37.3134i	−0.867285	−	1.50218i	−0.00252400	−	0.999997i	$-0.500803\pi$
$618$	−1.95033	−	1.12602i	−0.0784538	−	0.0452953i
$619$	35.7535	+	20.6423i	1.43705	+	0.829684i	0.997644	−	0.0686028i	$-0.0218541\pi$
$619$	35.7535	+	20.6423i	1.43705	+	0.829684i	0.439410	+	0.898287i	$0.355187\pi$
$620$	−4.57560	−	2.64172i	−0.183760	−	0.106094i
$621$	1.25748	−	2.17802i	0.0504610	−	0.0874011i
$622$	10.4745	−	18.1423i	0.419987	−	0.727440i
$623$	1.90727	−	0.0751373i	0.0764132	−	0.00301031i
$624$	1.85511	−	3.21315i	0.0742640	−	0.128629i
$625$	51.7881			2.07152
$626$	−3.46804	+	6.00681i	−0.138611	+	0.240081i
$627$	−3.79818	−	1.86022i	−0.151685	−	0.0742901i
$628$	−6.88812	+	3.97686i	−0.274866	+	0.158694i
$629$	−36.9823	+	64.0552i	−1.47458	+	2.55405i
$630$	−10.7753	+	0.424495i	−0.429299	+	0.0169123i
$631$	5.05007	+	8.74698i	0.201040	+	0.348212i	0.948864	−	0.315686i	$-0.102235\pi$
$631$	5.05007	+	8.74698i	0.201040	+	0.348212i	−0.747824	+	0.663897i	$0.768901\pi$
$632$	11.4685			0.456193
$633$		−	1.56970i		−	0.0623899i
$634$	4.69675	−	8.13501i	0.186532	−	0.323083i
$635$	10.9026	+	18.8838i	0.432656	+	0.749382i
$636$	−9.32846	+	5.38579i	−0.369898	+	0.213561i
$637$	25.8911	−	2.04314i	1.02584	−	0.0809522i
$638$	2.68067			0.106129
$639$	0.430764	−	0.248702i	0.0170408	−	0.00983849i
$640$	4.07585			0.161112
$641$	−19.7269	+	11.3893i	−0.779164	+	0.449851i	−0.836134	−	0.548525i	$-0.815189\pi$
$641$	−19.7269	+	11.3893i	−0.779164	+	0.449851i	0.0569697	+	0.998376i	$0.481856\pi$
$642$	3.29658	−	5.70984i	0.130106	−	0.225349i
$643$	−6.73718	−	3.88971i	−0.265688	−	0.153395i	0.361238	−	0.932474i	$-0.382354\pi$
$643$	−6.73718	−	3.88971i	−0.265688	−	0.153395i	−0.626927	+	0.779078i	$0.715687\pi$
$644$	−6.64882	+	0.261931i	−0.262000	+	0.0103215i
$645$		−	39.1375i		−	1.54104i
$646$	2.22334	+	32.5636i	0.0874763	+	1.28120i
$647$	36.1528	+	20.8728i	1.42131	+	0.820596i	0.996411	−	0.0846425i	$-0.0269748\pi$
$647$	36.1528	+	20.8728i	1.42131	+	0.820596i	0.424903	+	0.905239i	$0.360308\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	9.23432			0.362479
$650$	37.3128	−	21.5426i	1.46353	−	0.844969i
$651$	1.83041	+	2.90035i	0.0717394	+	0.113674i
$652$	−10.8199	−	18.7407i	−0.423742	−	0.733943i
$653$	−0.316827	−	0.548760i	−0.0123984	−	0.0214746i	0.859760	−	0.510699i	$-0.170613\pi$
$653$	−0.316827	−	0.548760i	−0.0123984	−	0.0214746i	−0.872158	+	0.489224i	$0.837280\pi$
$654$	−3.89800	+	6.75153i	−0.152424	+	0.264006i
$655$	−6.92870			−0.270727
$656$	−5.12688	+	8.88001i	−0.200171	+	0.346706i
$657$			2.13903i			0.0834513i
$658$	7.03861	−	0.277287i	0.274393	−	0.0108098i
$659$	2.65971	−	1.53559i	0.103608	−	0.0598179i	−0.447301	−	0.894384i	$-0.647615\pi$
$659$	2.65971	−	1.53559i	0.103608	−	0.0598179i	0.550909	+	0.834566i	$0.314281\pi$
$660$		−	3.95462i		−	0.153933i
$661$	−32.9715			−1.28244			−0.641221	−	0.767357i	$-0.721572\pi$
$661$	−32.9715			−1.28244			−0.641221	+	0.767357i	$0.721572\pi$
$662$	−9.68272	−	16.7710i	−0.376330	−	0.651822i
$663$			27.7821i			1.07897i
$664$	17.0639			0.662209
$665$	−46.7334	+	5.04546i	−1.81224	+	0.195654i
$666$	9.87777			0.382756
$667$			6.94846i			0.269045i
$668$	0.0757722	+	0.131241i	0.00293171	+	0.00507788i
$669$	19.6711			0.760529
$670$		−	29.0357i		−	1.12175i
$671$	11.5758	−	6.68327i	0.446877	−	0.258005i
$672$	−2.34159	−	1.23165i	−0.0903287	−	0.0475121i
$673$			14.2527i			0.549400i	0.961530	+	0.274700i	$0.0885786\pi$
$673$			14.2527i			0.549400i	−0.961530	+	0.274700i	$0.911421\pi$
$674$	11.1562	−	19.3232i	0.429722	−	0.744301i
$675$	11.6125			0.446966
$676$	0.382903	−	0.663208i	0.0147270	−	0.0255080i
$677$	14.3151	+	24.7946i	0.550176	+	0.952933i	0.998261	+	0.0589419i	$0.0187727\pi$
$677$	14.3151	+	24.7946i	0.550176	+	0.952933i	−0.448086	+	0.893991i	$0.647894\pi$
$678$	5.10775	+	8.84689i	0.196162	+	0.339763i
$679$	−41.4843	+	1.63428i	−1.59202	+	0.0627180i
$680$	−26.4310	+	15.2599i	−1.01358	+	0.585192i
$681$	8.94084			0.342614
$682$	−1.08922	+	0.628863i	−0.0417085	+	0.0240804i
$683$	−2.69797	−	1.55767i	−0.103235	−	0.0596027i	0.447494	−	0.894287i	$-0.352317\pi$
$683$	−2.69797	−	1.55767i	−0.103235	−	0.0596027i	−0.550729	+	0.834684i	$0.685650\pi$
$684$	3.61769	−	2.43153i	0.138326	−	0.0929718i
$685$			9.03677i			0.345277i
$686$	−2.18261	−	18.3912i	−0.0833324	−	0.702179i
$687$	7.36441	+	4.25184i	0.280970	+	0.162218i
$688$	4.80115	−	8.31583i	0.183042	−	0.317038i
$689$	−34.6107	+	19.9825i	−1.31856	+	0.761274i
$690$	10.2506			0.390234
$691$	−27.5558	+	15.9093i	−1.04827	+	0.605219i	−0.922165	−	0.386797i	$-0.873581\pi$
$691$	−27.5558	+	15.9093i	−1.04827	+	0.605219i	−0.126106	+	0.992017i	$0.540248\pi$
$692$	9.14455			0.347624
$693$	−1.19502	+	2.27194i	−0.0453951	+	0.0863039i
$694$	−2.13899	+	1.23494i	−0.0811948	+	0.0468778i
$695$	−32.2169	−	55.8014i	−1.22206	−	2.11667i
$696$	−1.38142	+	2.39269i	−0.0523627	+	0.0906948i
$697$		−	76.7799i		−	2.90825i
$698$	−4.96655			−0.187987
$699$	−0.235089	−	0.407186i	−0.00889188	−	0.0154012i
$700$	−16.3974	−	25.9823i	−0.619764	−	0.982039i
$701$	−4.37494	+	7.57761i	−0.165239	+	0.286203i	−0.936740	−	0.350025i	$-0.886173\pi$
$701$	−4.37494	+	7.57761i	−0.165239	+	0.286203i	0.771501	+	0.636228i	$0.219506\pi$
$702$	3.21315	−	1.85511i	0.121273	−	0.0700168i
$703$	42.9562	−	2.93292i	1.62012	−	0.110617i
$704$	0.485128	−	0.840267i	0.0182840	−	0.0316688i
$705$	−10.8516			−0.408693
$706$	17.0929	−	29.6058i	0.643300	−	1.11423i
$707$	8.31921	−	5.25025i	0.312876	−	0.197456i
$708$	−4.75870	+	8.24231i	−0.178843	+	0.309765i
$709$	−5.88151	+	10.1871i	−0.220885	+	0.382584i	−0.955077	−	0.296358i	$-0.904228\pi$
$709$	−5.88151	+	10.1871i	−0.220885	+	0.382584i	0.734192	+	0.678942i	$0.237561\pi$
$710$	1.75573	+	1.01367i	0.0658913	+	0.0380424i
$711$	9.93203	+	5.73426i	0.372480	+	0.215052i
$712$	−0.624786	−	0.360720i	−0.0234148	−	0.0135186i
$713$	−1.63005	−	2.82333i	−0.0610459	−	0.105735i
$714$	19.7960	−	0.779866i	0.740846	−	0.0291858i
$715$		−	14.6725i		−	0.548722i
$716$	5.49625	+	3.17326i	0.205405	+	0.118590i
$717$	−6.17093	−	10.6884i	−0.230458	−	0.399164i
$718$			24.0215i			0.896473i
$719$			24.8775i			0.927775i	0.885894	+	0.463887i	$0.153546\pi$
$719$			24.8775i			0.927775i	−0.885894	+	0.463887i	$0.846454\pi$
$720$	3.52979	+	2.03792i	0.131547	+	0.0759489i
$721$	−2.77374	+	5.27336i	−0.103300	+	0.196390i
$722$	15.0105	−	11.6483i	0.558634	−	0.433506i
$723$	−8.42418	−	14.5911i	−0.313299	−	0.542649i
$724$	7.25677	+	12.5691i	0.269696	+	0.467127i
$725$	−27.7852	+	16.0418i	−1.03192	+	0.595778i
$726$	8.71100	+	5.02930i	0.323296	+	0.186655i
$727$	−43.3648	−	25.0367i	−1.60831	−	0.928559i	−0.989748	−	0.142825i	$-0.954381\pi$
$727$	−43.3648	−	25.0367i	−1.60831	−	0.928559i	−0.618564	−	0.785734i	$-0.712285\pi$
$728$	−8.68782	−	4.56972i	−0.321992	−	0.169365i
$729$	1.00000			0.0370370
$730$	−7.55030	+	4.35917i	−0.279449	+	0.161340i
$731$			71.9018i			2.65938i
$732$			13.7763i			0.509186i
$733$	19.1045	−	11.0300i	0.705640	−	0.407402i	−0.103804	−	0.994598i	$-0.533102\pi$
$733$	19.1045	−	11.0300i	0.705640	−	0.407402i	0.809445	+	0.587196i	$0.199768\pi$
$734$	−21.3328			−0.787410
$735$	2.24448	+	28.4425i	0.0827888	+	1.04912i
$736$	2.17802	+	1.25748i	0.0802830	+	0.0463514i
$737$	−5.98594	−	3.45599i	−0.220495	−	0.127303i
$738$	−8.88001	+	5.12688i	−0.326878	+	0.188723i
$739$	25.1743	+	43.6032i	0.926052	+	1.60397i	0.789860	+	0.613288i	$0.210153\pi$
$739$	25.1743	+	43.6032i	0.926052	+	1.60397i	0.136193	+	0.990682i	$0.456513\pi$
$740$	20.1301	+	34.8664i	0.739999	+	1.28172i
$741$	13.4225	−	9.02153i	0.493086	−	0.331414i
$742$	15.2100	+	24.1007i	0.558376	+	0.884766i
$743$	18.1811	+	10.4968i	0.666998	+	0.385092i	0.794938	−	0.606690i	$-0.207503\pi$
$743$	18.1811	+	10.4968i	0.666998	+	0.385092i	−0.127940	+	0.991782i	$0.540837\pi$
$744$		−	1.29628i		−	0.0475240i
$745$		−	53.1177i		−	1.94608i
$746$	4.78873	+	8.29433i	0.175328	+	0.303677i
$747$	14.7778	+	8.53197i	0.540691	+	0.312168i
$748$			7.26527i			0.265644i
$749$	−15.4384	−	8.12049i	−0.564108	−	0.296716i
$750$	13.4758	+	23.3408i	0.492067	+	0.852286i
$751$	−30.3419	−	17.5179i	−1.10719	−	0.639237i	−0.169091	−	0.985600i	$-0.554083\pi$
$751$	−30.3419	−	17.5179i	−1.10719	−	0.639237i	−0.938100	+	0.346363i	$0.887416\pi$
$752$	−2.30571	−	1.33120i	−0.0840807	−	0.0485440i
$753$	−1.39946	−	0.807976i	−0.0509990	−	0.0294443i
$754$	−5.12539	+	8.87744i	−0.186656	+	0.323297i
$755$	28.5321	−	49.4190i	1.03839	−	1.79854i
$756$	−1.41205	−	2.23744i	−0.0513556	−	0.0813748i
$757$	9.36580	−	16.2220i	0.340406	−	0.589600i	−0.644102	−	0.764939i	$-0.722769\pi$
$757$	9.36580	−	16.2220i	0.340406	−	0.589600i	0.984508	+	0.175339i	$0.0561023\pi$
$758$	−24.4666			−0.888666
$759$	1.22008	−	2.11324i	0.0442861	−	0.0767058i
$760$	15.9553	+	7.81440i	0.578761	+	0.283458i
$761$	−31.0528	+	17.9284i	−1.12566	+	0.649903i	−0.942841	−	0.333243i	$-0.891857\pi$
$761$	−31.0528	+	17.9284i	−1.12566	+	0.649903i	−0.182824	+	0.983146i	$0.558524\pi$
$762$	−2.67492	+	4.63310i	−0.0969023	+	0.167840i
$763$	18.2550	+	9.60198i	0.660875	+	0.347615i
$764$	3.41302	+	5.91152i	0.123479	+	0.213871i
$765$	−30.5199			−1.10345
$766$		−	7.12577i		−	0.257464i
$767$	−17.6559	+	30.5809i	−0.637517	+	1.10421i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	14.7852	−	8.53622i	0.533167	−	0.307824i	−0.209138	−	0.977886i	$-0.567066\pi$
$769$	14.7852	−	8.53622i	0.533167	−	0.307824i	0.742305	+	0.670062i	$0.233733\pi$
$770$	−10.4548	+	0.411870i	−0.376766	+	0.0148427i
$771$	−18.0462			−0.649919
$772$	−11.4737	+	6.62433i	−0.412947	+	0.238415i
$773$	−6.28142			−0.225927			−0.112963	−	0.993599i	$-0.536034\pi$
$773$	−6.28142			−0.225927			−0.112963	+	0.993599i	$0.536034\pi$
$774$	8.31583	−	4.80115i	0.298906	−	0.172574i
$775$	7.52655	−	13.0364i	0.270362	−	0.468280i
$776$	13.5895	+	7.84588i	0.487833	+	0.281651i
$777$	−1.02876	−	26.1139i	−0.0369066	−	0.936830i
$778$		−	9.22919i		−	0.330883i
$779$	−37.0949	+	24.9323i	−1.32906	+	0.893292i
$780$	13.0963	+	7.56116i	0.468923	+	0.270733i
$781$	0.417952	−	0.241305i	0.0149555	−	0.00863456i
$782$	−18.8320			−0.673432
$783$	−2.39269	+	1.38142i	−0.0855079	+	0.0493680i
$784$	−3.01225	+	6.31873i	−0.107580	+	0.225669i
$785$	−16.2091	−	28.0749i	−0.578527	−	1.00204i
$786$	−0.849970	−	1.47219i	−0.0303174	−	0.0525113i
$787$	12.3838	−	21.4493i	0.441434	−	0.764586i	−0.556362	−	0.830940i	$-0.687803\pi$
$787$	12.3838	−	21.4493i	0.441434	−	0.764586i	0.997796	+	0.0663537i	$0.0211366\pi$
$788$	6.85013			0.244026
$789$	10.8038	−	18.7127i	0.384625	−	0.666191i
$790$			46.7439i			1.66307i
$791$	22.8566	−	14.4248i	0.812685	−	0.512886i
$792$	0.840267	−	0.485128i	0.0298576	−	0.0172383i
$793$			51.1132i			1.81508i
$794$	13.3617			0.474190
$795$	−21.9517	−	38.0214i	−0.778545	−	1.34848i
$796$		−	8.47472i		−	0.300378i
$797$	−15.8875			−0.562764			−0.281382	−	0.959596i	$-0.590793\pi$
$797$	−15.8875			−0.562764			−0.281382	+	0.959596i	$0.590793\pi$
$798$	−6.80501	−	9.31084i	−0.240895	−	0.329600i
$799$	19.9361			0.705287
$800$			11.6125i			0.410565i
$801$	−0.360720	−	0.624786i	−0.0127454	−	0.0220757i
$802$	25.9594			0.916659
$803$			2.07540i			0.0732394i
$804$	6.16944	−	3.56193i	0.217579	−	0.125620i
$805$	−1.06759	−	27.0996i	−0.0376276	−	0.955134i
$806$		−	4.80950i		−	0.169408i
$807$	−5.35097	+	9.26815i	−0.188363	+	0.326254i
$808$	−3.71819			−0.130805
$809$	15.2941	−	26.4902i	0.537713	−	0.931347i	−0.461313	−	0.887237i	$-0.652622\pi$
$809$	15.2941	−	26.4902i	0.537713	−	0.931347i	0.999027	−	0.0441095i	$-0.0140450\pi$
$810$	2.03792	+	3.52979i	0.0716053	+	0.124024i
$811$	−0.304033	−	0.526601i	−0.0106760	−	0.0184915i	0.860638	−	0.509217i	$-0.170065\pi$
$811$	−0.304033	−	0.526601i	−0.0106760	−	0.0184915i	−0.871314	+	0.490726i	$0.836732\pi$
$812$	6.46944	+	3.40287i	0.227033	+	0.119417i
$813$	−5.62728	+	3.24891i	−0.197357	+	0.113944i
$814$	9.58397			0.335918
$815$	76.3842	−	44.1005i	2.67562	−	1.54477i
$816$	−6.48478	−	3.74399i	−0.227013	−	0.131066i
$817$	34.7381	−	23.3482i	1.21533	−	0.816852i
$818$			6.20352i			0.216901i
$819$	−5.23902	−	8.30141i	−0.183066	−	0.290075i
$820$	−36.1936	−	20.8964i	−1.26393	−	0.729732i
$821$	10.7834	−	18.6774i	0.376343	−	0.651845i	−0.614184	−	0.789163i	$-0.710515\pi$
$821$	10.7834	−	18.6774i	0.376343	−	0.651845i	0.990527	+	0.137318i	$0.0438481\pi$
$822$	−1.92011	+	1.10858i	−0.0669715	+	0.0386660i
$823$	23.9544			0.834999			0.417499	−	0.908677i	$-0.362907\pi$
$823$	23.9544			0.834999			0.417499	+	0.908677i	$0.362907\pi$
$824$	1.95033	−	1.12602i	0.0679430	−	0.0392269i
$825$	11.2671			0.392271
$826$	22.2858	+	11.7221i	0.775423	+	0.407866i
$827$	31.9154	−	18.4264i	1.10981	−	0.640748i	0.171029	−	0.985266i	$-0.445291\pi$
$827$	31.9154	−	18.4264i	1.10981	−	0.640748i	0.938780	+	0.344518i	$0.111958\pi$
$828$	1.25748	+	2.17802i	0.0437005	+	0.0756916i
$829$	−11.6590	+	20.1940i	−0.404934	+	0.701366i	−0.994314	−	0.106490i	$-0.966039\pi$
$829$	−11.6590	+	20.1940i	−0.404934	+	0.701366i	0.589380	+	0.807856i	$0.299372\pi$
$830$			69.5500i			2.41411i
$831$	−10.6900			−0.370833
$832$	1.85511	+	3.21315i	0.0643145	+	0.111396i
$833$	−4.12346	−	52.2534i	−0.142870	−	1.81047i
$834$	7.90435	−	13.6907i	0.273705	−	0.474072i
$835$	−0.534919	+	0.308836i	−0.0185116	+	0.0106877i
$836$	3.51009	−	2.35921i	0.121399	−	0.0815949i
$837$	0.648141	−	1.12261i	0.0224030	−	0.0388032i
$838$	7.95386			0.274761
$839$	−7.89487	+	13.6743i	−0.272561	+	0.472090i	−0.969517	−	0.245024i	$-0.921204\pi$
$839$	−7.89487	+	13.6743i	−0.272561	+	0.472090i	0.696956	+	0.717114i	$0.254537\pi$
$840$	5.02004	−	9.54395i	0.173208	−	0.329297i
$841$	−10.6833	+	18.5041i	−0.368391	+	0.638072i
$842$	−7.42985	+	12.8689i	−0.256050	+	0.443491i
$843$	−4.64102	−	2.67950i	−0.159845	−	0.0922867i
$844$	1.35940	+	0.784849i	0.0467924	+	0.0270156i
$845$	2.70313	+	1.56065i	0.0929906	+	0.0536881i
$846$	−1.33120	−	2.30571i	−0.0457677	−	0.0792720i
$847$	12.3887	−	23.5531i	0.425682	−	0.809294i
$848$		−	10.7716i		−	0.369898i
$849$	11.7540	+	6.78618i	0.403397	+	0.232901i
$850$	−43.4772	−	75.3047i	−1.49126	−	2.58293i
$851$			24.8422i			0.851581i
$852$			0.497403i			0.0170408i
$853$	−15.3678	−	8.87262i	−0.526185	−	0.303793i	0.213277	−	0.976992i	$-0.431586\pi$
$853$	−15.3678	−	8.87262i	−0.526185	−	0.303793i	−0.739461	+	0.673199i	$0.764920\pi$
$854$	36.4204	−	1.43479i	1.24628	−	0.0490974i
$855$	9.91054	+	14.7451i	0.338933	+	0.504273i
$856$	3.29658	+	5.70984i	0.112675	+	0.195158i
$857$	11.8316	+	20.4929i	0.404160	+	0.700025i	0.994223	−	0.107332i	$-0.0342307\pi$
$857$	11.8316	+	20.4929i	0.404160	+	0.700025i	−0.590064	+	0.807357i	$0.700897\pi$
$858$	3.11758	−	1.79994i	0.106433	−	0.0614489i
$859$	−23.4022	−	13.5113i	−0.798473	−	0.460999i	0.0444640	−	0.999011i	$-0.485842\pi$
$859$	−23.4022	−	13.5113i	−0.798473	−	0.460999i	−0.842937	+	0.538012i	$0.819175\pi$
$860$	33.8940	+	19.5687i	1.15578	+	0.667288i
$861$	14.4788	+	22.9421i	0.493435	+	0.781866i
$862$	7.45630			0.253963
$863$	24.9978	−	14.4325i	0.850933	−	0.491287i	−0.0100322	−	0.999950i	$-0.503193\pi$
$863$	24.9978	−	14.4325i	0.850933	−	0.491287i	0.860966	+	0.508663i	$0.169860\pi$
$864$			1.00000i			0.0340207i
$865$			37.2718i			1.26728i
$866$	8.67881	−	5.01071i	0.294918	−	0.170271i
$867$	39.0699			1.32688
$868$	−3.42698	+	0.135006i	−0.116319	+	0.00458242i
$869$	9.63662	+	5.56371i	0.326900	+	0.188736i
$870$	−9.75225	−	5.63047i	−0.330632	−	0.190891i
$871$	22.8900	−	13.2156i	0.775600	−	0.447793i
$872$	−3.89800	−	6.75153i	−0.132003	−	0.228636i
$873$	7.84588	+	13.5895i	0.265543	+	0.459934i
$874$	6.11521	+	9.09836i	0.206850	+	0.307757i
$875$	60.3026	−	38.0569i	2.03860	−	1.28656i
$876$	−1.85245	−	1.06951i	−0.0625885	−	0.0361355i
$877$			15.7433i			0.531612i	0.964027	+	0.265806i	$0.0856381\pi$
$877$			15.7433i			0.531612i	−0.964027	+	0.265806i	$0.914362\pi$
$878$			20.8943i			0.705148i
$879$	−8.66314	−	15.0050i	−0.292201	−	0.506106i
$880$	3.42480	+	1.97731i	0.115450	+	0.0666551i
$881$		−	17.0246i		−	0.573575i	−0.957994	−	0.286787i	$-0.907413\pi$
$881$		−	17.0246i		−	0.573575i	0.957994	−	0.286787i	$-0.0925873\pi$
$882$	−5.76805	+	3.96605i	−0.194220	+	0.133544i
$883$	1.18000	+	2.04382i	0.0397102	+	0.0687801i	0.885197	−	0.465216i	$-0.154023\pi$
$883$	1.18000	+	2.04382i	0.0397102	+	0.0687801i	−0.845487	+	0.533996i	$0.820690\pi$
$884$	−24.0600	−	13.8911i	−0.809227	−	0.467207i
$885$	−33.5944	−	19.3957i	−1.12926	−	0.651980i
$886$	−9.03634	−	5.21714i	−0.303582	−	0.175273i
$887$	21.5758	−	37.3703i	0.724443	−	1.25477i	−0.234760	−	0.972053i	$-0.575430\pi$
$887$	21.5758	−	37.3703i	0.724443	−	1.25477i	0.959203	−	0.282719i	$-0.0912363\pi$
$888$	−4.93889	+	8.55440i	−0.165738	+	0.287067i
$889$	12.5271	+	6.58917i	0.420147	+	0.220994i
$890$	1.47024	−	2.54653i	0.0492825	−	0.0853599i
$891$	0.970257			0.0325048
$892$	−9.83556	+	17.0357i	−0.329319	+	0.570397i
$893$	−6.47372	−	9.63176i	−0.216635	−	0.322315i
$894$	11.2863	−	6.51615i	0.377471	−	0.217933i
$895$	−12.9337	+	22.4019i	−0.432327	+	0.748812i
$896$	2.23744	−	1.41205i	0.0747475	−	0.0471731i
$897$	4.66555	+	8.08097i	0.155778	+	0.269816i
$898$	19.7533			0.659175
$899$			3.58143i			0.119447i
$900$	−5.80626	+	10.0567i	−0.193542	+	0.335225i
$901$	40.3287	+	69.8514i	1.34354	+	2.32709i
$902$	−8.61589	+	4.97439i	−0.286878	+	0.165629i
$903$	−13.5589	−	21.4845i	−0.451211	−	0.714960i
$904$	−10.2155			−0.339763
$905$	−51.2297	+	29.5775i	−1.70293	+	0.983189i
$906$	14.0006			0.465138
$907$	46.5100	−	26.8526i	1.54434	−	0.891625i	0.545783	−	0.837926i	$-0.316232\pi$
$907$	46.5100	−	26.8526i	1.54434	−	0.891625i	0.998557	−	0.0536988i	$-0.0171011\pi$
$908$	−4.47042	+	7.74299i	−0.148356	+	0.256960i
$909$	−3.22004	−	1.85909i	−0.106802	−	0.0616622i
$910$	18.6255	−	35.4102i	0.617429	−	1.17384i
$911$			20.9585i			0.694385i	0.937794	+	0.347193i	$0.112865\pi$
$911$			20.9585i			0.694385i	−0.937794	+	0.347193i	$0.887135\pi$
$912$	0.296922	+	4.34877i	0.00983206	+	0.144002i
$913$	14.3383	+	8.27820i	0.474527	+	0.273968i
$914$	−7.02827	+	4.05777i	−0.232474	+	0.134219i
$915$	−56.1500			−1.85626
$916$	−7.36441	+	4.25184i	−0.243327	+	0.140485i
$917$	−3.80351	+	2.40039i	−0.125603	+	0.0792680i
$918$	−3.74399	−	6.48478i	−0.123570	−	0.214030i
$919$	19.3534	+	33.5211i	0.638411	+	1.10576i	0.985781	+	0.168033i	$0.0537414\pi$
$919$	19.3534	+	33.5211i	0.638411	+	1.10576i	−0.347370	+	0.937728i	$0.612925\pi$
$920$	−5.12531	+	8.87729i	−0.168976	+	0.292676i
$921$	−20.8661			−0.687561
$922$	−16.7791	+	29.0623i	−0.552592	+	0.957117i
$923$			1.84548i			0.0607448i
$924$	−1.37005	−	2.17089i	−0.0450712	−	0.0714170i
$925$	−99.3382	+	57.3529i	−3.26622	+	1.88575i
$926$		−	14.8883i		−	0.489259i
$927$	2.25205			0.0739669
$928$	−1.38142	−	2.39269i	−0.0453474	−	0.0785440i
$929$		−	35.2938i		−	1.15795i	−0.815344	−	0.578977i	$-0.803452\pi$
$929$		−	35.2938i		−	1.15795i	0.815344	−	0.578977i	$-0.196548\pi$
$930$	5.28345			0.173251
$931$	−23.9063	+	18.9601i	−0.783499	+	0.621393i
$932$	0.470178			0.0154012
$933$			20.9489i			0.685837i
$934$	−4.45591	−	7.71786i	−0.145802	−	0.252536i
$935$	−29.6121			−0.968420
$936$			3.71023i			0.121273i
$937$	0.638730	−	0.368771i	0.0208664	−	0.0120472i	−0.489531	−	0.871986i	$-0.662832\pi$
$937$	0.638730	−	0.368771i	0.0208664	−	0.0120472i	0.510397	+	0.859939i	$0.329498\pi$
$938$	−10.0592	−	15.9392i	−0.328445	−	0.520433i
$939$		−	6.93607i		−	0.226350i
$940$	5.42578	−	9.39773i	0.176969	−	0.306520i
$941$	−23.9231			−0.779872			−0.389936	−	0.920842i	$-0.627503\pi$
$941$	−23.9231			−0.779872			−0.389936	+	0.920842i	$0.627503\pi$
$942$	3.97686	−	6.88812i	0.129573	−	0.224427i
$943$	−12.8939	−	22.3329i	−0.419884	−	0.727260i
$944$	−4.75870	−	8.24231i	−0.154882	−	0.268264i
$945$	9.11945	−	5.75528i	0.296656	−	0.187219i
$946$	8.06849	−	4.65834i	0.262329	−	0.151456i
$947$	13.7977			0.448364			0.224182	−	0.974547i	$-0.428029\pi$
$947$	13.7977			0.448364			0.224182	+	0.974547i	$0.428029\pi$
$948$	−9.93203	+	5.73426i	−0.322577	+	0.186240i
$949$	−6.87302	−	3.96814i	−0.223108	−	0.128811i
$950$	−22.2641	+	45.4585i	−0.722342	+	1.47487i
$951$			9.39350i			0.304605i
$952$	−9.22261	+	17.5338i	−0.298906	+	0.568272i
$953$	−20.2313	−	11.6806i	−0.655357	−	0.378370i	0.135149	−	0.990825i	$-0.456849\pi$
$953$	−20.2313	−	11.6806i	−0.655357	−	0.378370i	−0.790506	+	0.612455i	$0.790182\pi$
$954$	5.38579	−	9.32846i	0.174371	−	0.302020i
$955$	−24.0944	+	13.9109i	−0.779678	+	0.450147i
$956$	12.3419			0.399164
$957$	−2.32153	+	1.34033i	−0.0750443	+	0.0433269i
$958$	17.7340			0.572961
$959$	3.13072	+	4.96074i	0.101096	+	0.160191i
$960$	−3.52979	+	2.03792i	−0.113923	+	0.0657737i
$961$	14.6598	+	25.3916i	0.472898	+	0.819083i
$962$	−18.3244	+	31.7388i	−0.590802	+	1.02330i
$963$			6.59315i			0.212461i
$964$	16.8484			0.542649
$965$	−26.9998	−	46.7650i	−0.869153	−	1.50542i
$966$	5.62708	−	3.55125i	0.181048	−	0.114259i
$967$	−8.02350	+	13.8971i	−0.258018	+	0.446901i	−0.965711	−	0.259620i	$-0.916403\pi$
$967$	−8.02350	+	13.8971i	−0.258018	+	0.446901i	0.707693	+	0.706520i	$0.249736\pi$
$968$	−8.71100	+	5.02930i	−0.279982	+	0.161648i
$969$	−18.2072	−	27.0892i	−0.584901	−	0.870230i
$970$	−31.9786	+	55.3886i	−1.02677	+	1.77842i
$971$	17.5872			0.564399			0.282199	−	0.959356i	$-0.408936\pi$
$971$	17.5872			0.564399			0.282199	+	0.959356i	$0.408936\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−37.0174	−	19.4709i	−1.18672	−	0.624207i
$974$	−7.08040	+	12.2636i	−0.226871	+	0.392952i
$975$	−21.5426	+	37.3128i	−0.689914	+	1.19497i
$976$	−11.9306	−	6.88815i	−0.381890	−	0.220484i
$977$	40.7937	+	23.5523i	1.30511	+	0.753503i	0.981275	−	0.192611i	$-0.0616957\pi$
$977$	40.7937	+	23.5523i	1.30511	+	0.753503i	0.323831	+	0.946115i	$0.395029\pi$
$978$	18.7407	+	10.8199i	0.599262	+	0.345984i
$979$	−0.349991	−	0.606202i	−0.0111858	−	0.0193743i
$980$	−25.7542	−	12.2775i	−0.822687	−	0.392190i
$981$		−	7.79600i		−	0.248907i
$982$	−10.0935	−	5.82747i	−0.322096	−	0.185962i
$983$	−16.0280	−	27.7613i	−0.511214	−	0.885448i	−0.999916	−	0.0129975i	$-0.995863\pi$
$983$	−16.0280	−	27.7613i	−0.511214	−	0.885448i	0.488702	−	0.872451i	$-0.337471\pi$
$984$		−	10.2538i		−	0.326878i
$985$			27.9201i			0.889608i
$986$	17.9165	+	10.3441i	0.570576	+	0.329422i
$987$	−5.95697	+	3.75944i	−0.189612	+	0.119664i
$988$	1.10165	+	16.1350i	0.0350481	+	0.513321i
$989$	12.0747	+	20.9140i	0.383954	+	0.665027i
$990$	1.97731	+	3.42480i	0.0628430	+	0.108847i
$991$	3.81577	−	2.20303i	0.121212	−	0.0699817i	−0.438168	−	0.898893i	$-0.644373\pi$
$991$	3.81577	−	2.20303i	0.121212	−	0.0699817i	0.559380	+	0.828911i	$0.311039\pi$
$992$	1.12261	+	0.648141i	0.0356430	+	0.0205785i
$993$	16.7710	+	9.68272i	0.532211	+	0.307272i
$994$	1.31499	−	0.0518041i	0.0417088	−	0.00164313i
$995$	34.5416			1.09504
$996$	−14.7778	+	8.53197i	−0.468252	+	0.270346i
$997$			9.96486i			0.315590i	0.987472	+	0.157795i	$0.0504386\pi$
$997$			9.96486i			0.315590i	−0.987472	+	0.157795i	$0.949561\pi$
$998$		−	7.22272i		−	0.228631i
$999$	−8.55440	+	4.93889i	−0.270649	+	0.156259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.m.b.787.1	yes	28
7.5	odd	6		798.2.bc.b.103.7	yes	28
19.12	odd	6		798.2.bc.b.31.7	yes	28
133.12	even	6	inner	798.2.m.b.145.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.14	✓	28	133.12	even	6	inner
798.2.m.b.787.1	yes	28	1.1	even	1	trivial
798.2.bc.b.31.7	yes	28	19.12	odd	6
798.2.bc.b.103.7	yes	28	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} -4.07585i q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.41205 - 2.23744i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -4.07585 q^{10} +(-0.485128 + 0.840267i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.85511 - 3.21315i) q^{13} +(-2.23744 + 1.41205i) q^{14} +(3.52979 - 2.03792i) q^{15} +1.00000 q^{16} +(-6.48478 + 3.74399i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.91461 + 1.91725i) q^{19} +4.07585i q^{20} +(1.23165 - 2.34159i) q^{21} +(0.840267 + 0.485128i) q^{22} +(-1.25748 + 2.17802i) q^{23} +(-0.866025 + 0.500000i) q^{24} -11.6125 q^{25} +(-3.21315 + 1.85511i) q^{26} -1.00000 q^{27} +(1.41205 + 2.23744i) q^{28} +(2.39269 - 1.38142i) q^{29} +(-2.03792 - 3.52979i) q^{30} +(-0.648141 + 1.12261i) q^{31} -1.00000i q^{32} -0.970257 q^{33} +(3.74399 + 6.48478i) q^{34} +(-9.11945 + 5.75528i) q^{35} +(0.500000 - 0.866025i) q^{36} +(8.55440 - 4.93889i) q^{37} +(1.91725 - 3.91461i) q^{38} +(1.85511 - 3.21315i) q^{39} +4.07585 q^{40} +(-5.12688 + 8.88001i) q^{41} +(-2.34159 - 1.23165i) q^{42} +(4.80115 - 8.31583i) q^{43} +(0.485128 - 0.840267i) q^{44} +(3.52979 + 2.03792i) q^{45} +(2.17802 + 1.25748i) q^{46} +(-2.30571 - 1.33120i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.01225 + 6.31873i) q^{49} +11.6125i q^{50} +(-6.48478 - 3.74399i) q^{51} +(1.85511 + 3.21315i) q^{52} -10.7716i q^{53} +1.00000i q^{54} +(3.42480 + 1.97731i) q^{55} +(2.23744 - 1.41205i) q^{56} +(0.296922 + 4.34877i) q^{57} +(-1.38142 - 2.39269i) q^{58} +(-4.75870 - 8.24231i) q^{59} +(-3.52979 + 2.03792i) q^{60} +(-11.9306 - 6.88815i) q^{61} +(1.12261 + 0.648141i) q^{62} +(2.64370 - 0.104149i) q^{63} -1.00000 q^{64} +(-13.0963 + 7.56116i) q^{65} +0.970257i q^{66} +7.12386i q^{67} +(6.48478 - 3.74399i) q^{68} -2.51497 q^{69} +(5.75528 + 9.11945i) q^{70} +(-0.430764 - 0.248702i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.85245 - 1.06951i) q^{73} +(-4.93889 - 8.55440i) q^{74} +(-5.80626 - 10.0567i) q^{75} +(-3.91461 - 1.91725i) q^{76} +(2.56507 - 0.101051i) q^{77} +(-3.21315 - 1.85511i) q^{78} -11.4685i q^{79} -4.07585i q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.88001 + 5.12688i) q^{82} -17.0639i q^{83} +(-1.23165 + 2.34159i) q^{84} +(15.2599 + 26.4310i) q^{85} +(-8.31583 - 4.80115i) q^{86} +(2.39269 + 1.38142i) q^{87} +(-0.840267 - 0.485128i) q^{88} +(-0.360720 + 0.624786i) q^{89} +(2.03792 - 3.52979i) q^{90} +(-4.56972 + 8.68782i) q^{91} +(1.25748 - 2.17802i) q^{92} -1.29628 q^{93} +(-1.33120 + 2.30571i) q^{94} +(7.81440 - 15.9553i) q^{95} +(0.866025 - 0.500000i) q^{96} +(7.84588 - 13.5895i) q^{97} +(6.31873 + 3.01225i) q^{98} +(-0.485128 - 0.840267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{3} - 28 q^{4} - 8 q^{7} - 14 q^{9} + 4 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 28 q^{16} - 6 q^{17} + 2 q^{21} - 12 q^{22} - 12 q^{23} - 28 q^{25} + 24 q^{26} - 28 q^{27} + 8 q^{28}+ \cdots + 32 q^{98}+O(q^{100}) \) 28 * q + 14 * q^3 - 28 * q^4 - 8 * q^7 - 14 * q^9 + 4 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 28 * q^16 - 6 * q^17 + 2 * q^21 - 12 * q^22 - 12 * q^23 - 28 * q^25 + 24 * q^26 - 28 * q^27 + 8 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 + 4 * q^34 - 4 * q^35 + 14 * q^36 + 24 * q^37 + 18 * q^38 + 2 * q^39 - 4 * q^40 - 4 * q^41 + 4 * q^42 - 14 * q^43 + 6 * q^45 + 12 * q^46 + 24 * q^47 + 14 * q^48 - 24 * q^49 - 6 * q^51 + 2 * q^52 - 18 * q^55 + 4 * q^56 + 12 * q^57 - 2 * q^58 + 22 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 10 * q^63 - 28 * q^64 + 24 * q^65 + 6 * q^68 - 24 * q^69 + 30 * q^70 - 6 * q^71 - 42 * q^73 - 6 * q^74 - 14 * q^75 + 40 * q^77 + 24 * q^78 - 14 * q^81 - 6 * q^82 - 2 * q^84 + 28 * q^85 - 54 * q^86 + 18 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 - 22 * q^91 + 12 * q^92 - 8 * q^93 + 18 * q^94 + 20 * q^95 + 40 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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