LMFDB - Embedded newform 402.2.e.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [402,2,Mod(37,402)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(402, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("402.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 402 = 2 \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	402.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.20998616126$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	402.37
Dual form			402.2.e.c.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -2.69963 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555632 - 0.962383i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -2.69963 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555632 - 0.962383i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +(-1.34981 - 2.33795i) q^{10} +(-0.738550 + 1.27921i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.43818 - 4.22305i) q^{13} +1.11126 q^{14} +2.69963 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.34981 - 2.33795i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.78799 - 6.56099i) q^{19} +(1.34981 - 2.33795i) q^{20} +(-0.555632 + 0.962383i) q^{21} -1.47710 q^{22} +(-0.349814 - 0.605896i) q^{23} +1.00000 q^{24} +2.28799 q^{25} +(2.43818 - 4.22305i) q^{26} -1.00000 q^{27} +(0.555632 + 0.962383i) q^{28} +(-1.08836 + 1.88510i) q^{29} +(1.34981 + 2.33795i) q^{30} +(0.905446 - 1.56828i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.738550 - 1.27921i) q^{33} +(1.34981 - 2.33795i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.64400 + 2.84748i) q^{37} +(3.78799 - 6.56099i) q^{38} +(2.43818 + 4.22305i) q^{39} +2.69963 q^{40} +(-2.89926 + 5.02166i) q^{41} -1.11126 q^{42} -1.36584 q^{43} +(-0.738550 - 1.27921i) q^{44} -2.69963 q^{45} +(0.349814 - 0.605896i) q^{46} +(-2.49381 + 4.31941i) q^{47} +(0.500000 + 0.866025i) q^{48} +(2.88255 + 4.99272i) q^{49} +(1.14400 + 1.98146i) q^{50} +(1.34981 + 2.33795i) q^{51} +4.87636 q^{52} -2.51052 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.99381 - 3.45338i) q^{55} +(-0.555632 + 0.962383i) q^{56} +(3.78799 + 6.56099i) q^{57} -2.17673 q^{58} -7.32141 q^{59} +(-1.34981 + 2.33795i) q^{60} +(2.93818 + 5.08907i) q^{61} +1.81089 q^{62} +(0.555632 - 0.962383i) q^{63} +1.00000 q^{64} +(6.58217 + 11.4007i) q^{65} +1.47710 q^{66} +(-7.74288 - 2.65477i) q^{67} +2.69963 q^{68} +(0.349814 + 0.605896i) q^{69} -3.00000 q^{70} +(0.0716537 - 0.124108i) q^{71} -1.00000 q^{72} +(-5.78799 - 10.0251i) q^{73} +(-1.64400 + 2.84748i) q^{74} -2.28799 q^{75} +7.57598 q^{76} +(0.820724 + 1.42154i) q^{77} +(-2.43818 + 4.22305i) q^{78} +(3.88255 - 6.72477i) q^{79} +(1.34981 + 2.33795i) q^{80} +1.00000 q^{81} -5.79851 q^{82} +(-5.75526 - 9.96840i) q^{83} +(-0.555632 - 0.962383i) q^{84} +(3.64400 + 6.31159i) q^{85} +(-0.682918 - 1.18285i) q^{86} +(1.08836 - 1.88510i) q^{87} +(0.738550 - 1.27921i) q^{88} +5.47710 q^{89} +(-1.34981 - 2.33795i) q^{90} -5.41892 q^{91} +0.699628 q^{92} +(-0.905446 + 1.56828i) q^{93} -4.98762 q^{94} +(10.2262 + 17.7122i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.71634 + 9.90099i) q^{97} +(-2.88255 + 4.99272i) q^{98} +(-0.738550 + 1.27921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 4 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 4 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 4 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 6 q^{9} - 2 q^{10} + q^{11} + 3 q^{12} + 3 q^{13} + 6 q^{14} + 4 q^{15} - 3 q^{16} - 2 q^{17} + 3 q^{18} + q^{19} + 2 q^{20} - 3 q^{21} + 2 q^{22} + 4 q^{23} + 6 q^{24} - 10 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{28} + 5 q^{29} + 2 q^{30} - q^{31} + 3 q^{32} - q^{33} + 2 q^{34} - 9 q^{35} - 3 q^{36} - 2 q^{37} - q^{38} - 3 q^{39} + 4 q^{40} + 7 q^{41} - 6 q^{42} + 2 q^{43} + q^{44} - 4 q^{45} - 4 q^{46} + 3 q^{47} + 3 q^{48} - 5 q^{50} + 2 q^{51} - 6 q^{52} + 10 q^{53} - 3 q^{54} - 6 q^{55} - 3 q^{56} - q^{57} + 10 q^{58} - 6 q^{59} - 2 q^{60} - 2 q^{62} + 3 q^{63} + 6 q^{64} + 10 q^{65} - 2 q^{66} + 2 q^{67} + 4 q^{68} - 4 q^{69} - 18 q^{70} - 4 q^{71} - 6 q^{72} - 11 q^{73} + 2 q^{74} + 10 q^{75} - 2 q^{76} - 30 q^{77} + 3 q^{78} + 6 q^{79} + 2 q^{80} + 6 q^{81} + 14 q^{82} - 22 q^{83} - 3 q^{84} + 10 q^{85} + q^{86} - 5 q^{87} - q^{88} + 22 q^{89} - 2 q^{90} + 36 q^{91} - 8 q^{92} + q^{93} + 6 q^{94} + 20 q^{95} - 3 q^{96} + 15 q^{97} + q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 4 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 6 * q^9 - 2 * q^10 + q^11 + 3 * q^12 + 3 * q^13 + 6 * q^14 + 4 * q^15 - 3 * q^16 - 2 * q^17 + 3 * q^18 + q^19 + 2 * q^20 - 3 * q^21 + 2 * q^22 + 4 * q^23 + 6 * q^24 - 10 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^28 + 5 * q^29 + 2 * q^30 - q^31 + 3 * q^32 - q^33 + 2 * q^34 - 9 * q^35 - 3 * q^36 - 2 * q^37 - q^38 - 3 * q^39 + 4 * q^40 + 7 * q^41 - 6 * q^42 + 2 * q^43 + q^44 - 4 * q^45 - 4 * q^46 + 3 * q^47 + 3 * q^48 - 5 * q^50 + 2 * q^51 - 6 * q^52 + 10 * q^53 - 3 * q^54 - 6 * q^55 - 3 * q^56 - q^57 + 10 * q^58 - 6 * q^59 - 2 * q^60 - 2 * q^62 + 3 * q^63 + 6 * q^64 + 10 * q^65 - 2 * q^66 + 2 * q^67 + 4 * q^68 - 4 * q^69 - 18 * q^70 - 4 * q^71 - 6 * q^72 - 11 * q^73 + 2 * q^74 + 10 * q^75 - 2 * q^76 - 30 * q^77 + 3 * q^78 + 6 * q^79 + 2 * q^80 + 6 * q^81 + 14 * q^82 - 22 * q^83 - 3 * q^84 + 10 * q^85 + q^86 - 5 * q^87 - q^88 + 22 * q^89 - 2 * q^90 + 36 * q^91 - 8 * q^92 + q^93 + 6 * q^94 + 20 * q^95 - 3 * q^96 + 15 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/402\mathbb{Z}\right)^\times$.

$n$	$269$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.69963			−1.20731			−0.603655	−	0.797246i	$-0.706290\pi$
$5$	−2.69963			−1.20731			−0.603655	+	0.797246i	$0.706290\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.555632	−	0.962383i	0.210009	−	0.363747i	−0.741708	−	0.670723i	$-0.765984\pi$
$7$	0.555632	−	0.962383i	0.210009	−	0.363747i	0.951717	+	0.306976i	$0.0993173\pi$
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	−1.34981	−	2.33795i	−0.426849	−	0.739324i
$11$	−0.738550	+	1.27921i	−0.222681	+	0.385695i	−0.955621	−	0.294598i	$-0.904814\pi$
$11$	−0.738550	+	1.27921i	−0.222681	+	0.385695i	0.732940	+	0.680293i	$0.238148\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.43818	−	4.22305i	−0.676229	−	1.17126i	−0.976108	−	0.217286i	$-0.930280\pi$
$13$	−2.43818	−	4.22305i	−0.676229	−	1.17126i	0.299879	−	0.953977i	$-0.403054\pi$
$14$	1.11126			0.296998
$15$	2.69963			0.697041
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.34981	−	2.33795i	−0.327378	−	0.567035i	0.654613	−	0.755964i	$-0.272832\pi$
$17$	−1.34981	−	2.33795i	−0.327378	−	0.567035i	−0.981991	+	0.188929i	$0.939498\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.78799	−	6.56099i	−0.869025	−	1.50520i	−0.862994	−	0.505214i	$-0.831414\pi$
$19$	−3.78799	−	6.56099i	−0.869025	−	1.50520i	−0.00603068	−	0.999982i	$-0.501920\pi$
$20$	1.34981	−	2.33795i	0.301828	−	0.522781i
$21$	−0.555632	+	0.962383i	−0.121249	+	0.210009i
$22$	−1.47710			−0.314919
$23$	−0.349814	−	0.605896i	−0.0729413	−	0.126338i	0.827248	−	0.561837i	$-0.189905\pi$
$23$	−0.349814	−	0.605896i	−0.0729413	−	0.126338i	−0.900189	+	0.435499i	$0.856572\pi$
$24$	1.00000			0.204124
$25$	2.28799			0.457598
$26$	2.43818	−	4.22305i	0.478166	−	0.828208i
$27$	−1.00000			−0.192450
$28$	0.555632	+	0.962383i	0.105005	+	0.181873i
$29$	−1.08836	+	1.88510i	−0.202104	+	0.350055i	−0.949206	−	0.314655i	$-0.898111\pi$
$29$	−1.08836	+	1.88510i	−0.202104	+	0.350055i	0.747102	+	0.664709i	$0.231445\pi$
$30$	1.34981	+	2.33795i	0.246441	+	0.426849i
$31$	0.905446	−	1.56828i	0.162623	−	0.281671i	−0.773186	−	0.634180i	$-0.781338\pi$
$31$	0.905446	−	1.56828i	0.162623	−	0.281671i	0.935809	+	0.352509i	$0.114671\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.738550	−	1.27921i	0.128565	−	0.222681i
$34$	1.34981	−	2.33795i	0.231491	−	0.400955i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.64400	+	2.84748i	0.270271	+	0.468124i	0.968931	−	0.247330i	$-0.0795533\pi$
$37$	1.64400	+	2.84748i	0.270271	+	0.468124i	−0.698660	+	0.715454i	$0.746220\pi$
$38$	3.78799	−	6.56099i	0.614493	−	1.06433i
$39$	2.43818	+	4.22305i	0.390421	+	0.676229i
$40$	2.69963			0.426849
$41$	−2.89926	+	5.02166i	−0.452788	+	0.784251i	−0.998558	−	0.0536835i	$-0.982904\pi$
$41$	−2.89926	+	5.02166i	−0.452788	+	0.784251i	0.545770	+	0.837935i	$0.316237\pi$
$42$	−1.11126			−0.171472
$43$	−1.36584			−0.208288			−0.104144	−	0.994562i	$-0.533210\pi$
$43$	−1.36584			−0.208288			−0.104144	+	0.994562i	$0.533210\pi$
$44$	−0.738550	−	1.27921i	−0.111341	−	0.192848i
$45$	−2.69963			−0.402437
$46$	0.349814	−	0.605896i	0.0515773	−	0.0893345i
$47$	−2.49381	+	4.31941i	−0.363760	+	0.630050i	−0.988576	−	0.150721i	$-0.951840\pi$
$47$	−2.49381	+	4.31941i	−0.363760	+	0.630050i	0.624817	+	0.780771i	$0.285174\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	2.88255	+	4.99272i	0.411792	+	0.713245i
$50$	1.14400	+	1.98146i	0.161785	+	0.280221i
$51$	1.34981	+	2.33795i	0.189012	+	0.327378i
$52$	4.87636			0.676229
$53$	−2.51052			−0.344847			−0.172423	−	0.985023i	$-0.555160\pi$
$53$	−2.51052			−0.344847			−0.172423	+	0.985023i	$0.555160\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.99381	−	3.45338i	0.268845	−	0.465654i
$56$	−0.555632	+	0.962383i	−0.0742495	+	0.128604i
$57$	3.78799	+	6.56099i	0.501732	+	0.869025i
$58$	−2.17673			−0.285818
$59$	−7.32141			−0.953167			−0.476583	−	0.879129i	$-0.658125\pi$
$59$	−7.32141			−0.953167			−0.476583	+	0.879129i	$0.658125\pi$
$60$	−1.34981	+	2.33795i	−0.174260	+	0.301828i
$61$	2.93818	+	5.08907i	0.376195	+	0.651589i	0.990505	−	0.137476i	$-0.0438989\pi$
$61$	2.93818	+	5.08907i	0.376195	+	0.651589i	−0.614310	+	0.789065i	$0.710566\pi$
$62$	1.81089			0.229984
$63$	0.555632	−	0.962383i	0.0700031	−	0.121249i
$64$	1.00000			0.125000
$65$	6.58217	+	11.4007i	0.816418	+	1.41408i
$66$	1.47710			0.181818
$67$	−7.74288	−	2.65477i	−0.945943	−	0.324332i
$67$	−7.74288	−	2.65477i	−0.945943	−	0.324332i
$68$	2.69963			0.327378
$69$	0.349814	+	0.605896i	0.0421127	+	0.0729413i
$70$	−3.00000			−0.358569
$71$	0.0716537	−	0.124108i	0.00850373	−	0.0147289i	−0.861742	−	0.507346i	$-0.830626\pi$
$71$	0.0716537	−	0.124108i	0.00850373	−	0.0147289i	0.870246	+	0.492617i	$0.163960\pi$
$72$	−1.00000			−0.117851
$73$	−5.78799	−	10.0251i	−0.677433	−	1.17335i	−0.975751	−	0.218882i	$-0.929759\pi$
$73$	−5.78799	−	10.0251i	−0.677433	−	1.17335i	0.298318	−	0.954467i	$-0.403574\pi$
$74$	−1.64400	+	2.84748i	−0.191111	+	0.331013i
$75$	−2.28799			−0.264195
$76$	7.57598			0.869025
$77$	0.820724	+	1.42154i	0.0935302	+	0.161999i
$78$	−2.43818	+	4.22305i	−0.276069	+	0.478166i
$79$	3.88255	−	6.72477i	0.436821	−	0.756595i	−0.560622	−	0.828072i	$-0.689438\pi$
$79$	3.88255	−	6.72477i	0.436821	−	0.756595i	0.997442	+	0.0714766i	$0.0227711\pi$
$80$	1.34981	+	2.33795i	0.150914	+	0.261390i
$81$	1.00000			0.111111
$82$	−5.79851			−0.640339
$83$	−5.75526	−	9.96840i	−0.631722	−	1.09417i	−0.987200	−	0.159490i	$-0.949015\pi$
$83$	−5.75526	−	9.96840i	−0.631722	−	1.09417i	0.355478	−	0.934685i	$-0.384318\pi$
$84$	−0.555632	−	0.962383i	−0.0606244	−	0.105005i
$85$	3.64400	+	6.31159i	0.395247	+	0.684588i
$86$	−0.682918	−	1.18285i	−0.0736409	−	0.127550i
$87$	1.08836	−	1.88510i	0.116685	−	0.202104i
$88$	0.738550	−	1.27921i	0.0787297	−	0.136364i
$89$	5.47710			0.580571			0.290286	−	0.956940i	$-0.406250\pi$
$89$	5.47710			0.580571			0.290286	+	0.956940i	$0.406250\pi$
$90$	−1.34981	−	2.33795i	−0.142283	−	0.246441i
$91$	−5.41892			−0.568057
$92$	0.699628			0.0729413
$93$	−0.905446	+	1.56828i	−0.0938904	+	0.162623i
$94$	−4.98762			−0.514434
$95$	10.2262	+	17.7122i	1.04918	+	1.81724i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.71634	+	9.90099i	0.580406	+	1.00529i	0.995431	+	0.0954830i	$0.0304396\pi$
$97$	5.71634	+	9.90099i	0.580406	+	1.00529i	−0.415025	+	0.909810i	$0.636227\pi$
$98$	−2.88255	+	4.99272i	−0.291181	+	0.504340i
$99$	−0.738550	+	1.27921i	−0.0742271	+	0.128565i
$100$	−1.14400	+	1.98146i	−0.114400	+	0.198146i
$101$	2.64400	−	4.57954i	0.263087	−	0.455681i	−0.703973	−	0.710226i	$-0.748593\pi$
$101$	2.64400	−	4.57954i	0.263087	−	0.455681i	0.967061	+	0.254546i	$0.0819259\pi$
$102$	−1.34981	+	2.33795i	−0.133652	+	0.231491i
$103$	7.03706	−	12.1885i	0.693382	−	1.20097i	−0.277341	−	0.960772i	$-0.589453\pi$
$103$	7.03706	−	12.1885i	0.693382	−	1.20097i	0.970723	−	0.240202i	$-0.0772136\pi$
$104$	2.43818	+	4.22305i	0.239083	+	0.414104i
$105$	1.50000	−	2.59808i	0.146385	−	0.253546i
$106$	−1.25526	−	2.17417i	−0.121922	−	0.211174i
$107$	9.57598			0.925745			0.462873	−	0.886425i	$-0.346819\pi$
$107$	9.57598			0.925745			0.462873	+	0.886425i	$0.346819\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−13.3214			−1.27596			−0.637980	−	0.770053i	$-0.720230\pi$
$109$	−13.3214			−1.27596			−0.637980	+	0.770053i	$0.720230\pi$
$110$	3.98762			0.380205
$111$	−1.64400	−	2.84748i	−0.156041	−	0.270271i
$112$	−1.11126			−0.105005
$113$	−7.46108	+	12.9230i	−0.701879	+	1.21569i	0.265927	+	0.963993i	$0.414322\pi$
$113$	−7.46108	+	12.9230i	−0.701879	+	1.21569i	−0.967806	+	0.251697i	$0.919011\pi$
$114$	−3.78799	+	6.56099i	−0.354778	+	0.614493i
$115$	0.944368	+	1.63569i	0.0880628	+	0.152529i
$116$	−1.08836	−	1.88510i	−0.101052	−	0.175027i
$117$	−2.43818	−	4.22305i	−0.225410	−	0.390421i
$118$	−3.66071	−	6.34053i	−0.336995	−	0.583693i
$119$	−3.00000			−0.275010
$120$	−2.69963			−0.246441
$121$	4.40909	+	7.63676i	0.400826	+	0.694251i
$122$	−2.93818	+	5.08907i	−0.266010	+	0.460743i
$123$	2.89926	−	5.02166i	0.261417	−	0.452788i
$124$	0.905446	+	1.56828i	0.0813115	+	0.140836i
$125$	7.32141			0.654847
$126$	1.11126			0.0989993
$127$	5.34981	−	9.26615i	0.474719	−	0.822238i	−0.524862	−	0.851188i	$-0.675883\pi$
$127$	5.34981	−	9.26615i	0.474719	−	0.822238i	0.999581	+	0.0289497i	$0.00921627\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.36584			0.120255
$130$	−6.58217	+	11.4007i	−0.577295	+	0.999904i
$131$	2.41164			0.210706			0.105353	−	0.994435i	$-0.466403\pi$
$131$	2.41164			0.210706			0.105353	+	0.994435i	$0.466403\pi$
$132$	0.738550	+	1.27921i	0.0642825	+	0.111341i
$133$	−8.41892			−0.730013
$134$	−1.57234	−	8.03292i	−0.135830	−	0.693938i
$135$	2.69963			0.232347
$136$	1.34981	+	2.33795i	0.115746	+	0.200477i
$137$	−21.9876			−1.87853			−0.939265	−	0.343194i	$-0.888491\pi$
$137$	−21.9876			−1.87853			−0.939265	+	0.343194i	$0.888491\pi$
$138$	−0.349814	+	0.605896i	−0.0297782	+	0.0515773i
$139$	−17.9418			−1.52181			−0.760903	−	0.648866i	$-0.775244\pi$
$139$	−17.9418			−1.52181			−0.760903	+	0.648866i	$0.775244\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$	2.49381	−	4.31941i	0.210017	−	0.363760i
$142$	0.143307			0.0120261
$143$	7.20286			0.602334
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.93818	−	5.08907i	0.244002	−	0.422625i
$146$	5.78799	−	10.0251i	0.479018	−	0.829683i
$147$	−2.88255	−	4.99272i	−0.237748	−	0.411792i
$148$	−3.28799			−0.270271
$149$	11.9542			0.979326			0.489663	−	0.871912i	$-0.337120\pi$
$149$	11.9542			0.979326			0.489663	+	0.871912i	$0.337120\pi$
$150$	−1.14400	−	1.98146i	−0.0934069	−	0.161785i
$151$	−0.323272	−	0.559924i	−0.0263075	−	0.0455659i	0.852572	−	0.522610i	$-0.175042\pi$
$151$	−0.323272	−	0.559924i	−0.0263075	−	0.0455659i	−0.878879	+	0.477044i	$0.841708\pi$
$152$	3.78799	+	6.56099i	0.307247	+	0.532167i
$153$	−1.34981	−	2.33795i	−0.109126	−	0.189012i
$154$	−0.820724	+	1.42154i	−0.0661358	+	0.114551i
$155$	−2.44437	+	4.23377i	−0.196336	+	0.340065i
$156$	−4.87636			−0.390421
$157$	10.4320	+	18.0687i	0.832563	+	1.44204i	0.895999	+	0.444056i	$0.146461\pi$
$157$	10.4320	+	18.0687i	0.832563	+	1.44204i	−0.0634357	+	0.997986i	$0.520206\pi$
$158$	7.76509			0.617758
$159$	2.51052			0.199097
$160$	−1.34981	+	2.33795i	−0.106712	+	0.184831i
$161$	−0.777472			−0.0612734
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	10.1218	−	17.5314i	0.792799	−	1.37317i	−0.131428	−	0.991326i	$-0.541956\pi$
$163$	10.1218	−	17.5314i	0.792799	−	1.37317i	0.924227	−	0.381843i	$-0.124711\pi$
$164$	−2.89926	−	5.02166i	−0.226394	−	0.392126i
$165$	−1.99381	+	3.45338i	−0.155218	+	0.268845i
$166$	5.75526	−	9.96840i	0.446695	−	0.773698i
$167$	9.20327	−	15.9405i	0.712170	−	1.23352i	−0.251870	−	0.967761i	$-0.581046\pi$
$167$	9.20327	−	15.9405i	0.712170	−	1.23352i	0.964041	−	0.265754i	$-0.0856210\pi$
$168$	0.555632	−	0.962383i	0.0428679	−	0.0742495i
$169$	−5.38942	+	9.33476i	−0.414571	+	0.718058i
$170$	−3.64400	+	6.31159i	−0.279482	+	0.484077i
$171$	−3.78799	−	6.56099i	−0.289675	−	0.501732i
$172$	0.682918	−	1.18285i	0.0520720	−	0.0901913i
$173$	−4.32072	−	7.48371i	−0.328499	−	0.568976i	0.653716	−	0.756740i	$-0.273209\pi$
$173$	−4.32072	−	7.48371i	−0.328499	−	0.568976i	−0.982214	+	0.187764i	$0.939876\pi$
$174$	2.17673			0.165017
$175$	1.27128	−	2.20192i	0.0960999	−	0.166450i
$176$	1.47710			0.111341
$177$	7.32141			0.550311
$178$	2.73855	+	4.74331i	0.205263	+	0.355526i
$179$	−11.9876			−0.895997			−0.447998	−	0.894034i	$-0.647863\pi$
$179$	−11.9876			−0.895997			−0.447998	+	0.894034i	$0.647863\pi$
$180$	1.34981	−	2.33795i	0.100609	−	0.174260i
$181$	−1.11745	+	1.93549i	−0.0830597	+	0.143864i	−0.904563	−	0.426340i	$-0.859803\pi$
$181$	−1.11745	+	1.93549i	−0.0830597	+	0.143864i	0.821503	+	0.570204i	$0.193136\pi$
$182$	−2.70946	−	4.69292i	−0.200839	−	0.347863i
$183$	−2.93818	−	5.08907i	−0.217196	−	0.376195i
$184$	0.349814	+	0.605896i	0.0257886	+	0.0446672i
$185$	−4.43818	−	7.68715i	−0.326301	−	0.565171i
$186$	−1.81089			−0.132781
$187$	3.98762			0.291604
$188$	−2.49381	−	4.31941i	−0.181880	−	0.315025i
$189$	−0.555632	+	0.962383i	−0.0404163	+	0.0700031i
$190$	−10.2262	+	17.7122i	−0.741884	+	1.28498i
$191$	−1.86584	−	3.23172i	−0.135007	−	0.233839i	0.790593	−	0.612342i	$-0.209772\pi$
$191$	−1.86584	−	3.23172i	−0.135007	−	0.233839i	−0.925600	+	0.378503i	$0.876439\pi$
$192$	−1.00000			−0.0721688
$193$	11.1643			0.803627			0.401814	−	0.915721i	$-0.368380\pi$
$193$	11.1643			0.803627			0.401814	+	0.915721i	$0.368380\pi$
$194$	−5.71634	+	9.90099i	−0.410409	+	0.710850i
$195$	−6.58217	−	11.4007i	−0.471359	−	0.816418i
$196$	−5.76509			−0.411792
$197$	11.3374	−	19.6370i	0.807759	−	1.39908i	−0.106654	−	0.994296i	$-0.534014\pi$
$197$	11.3374	−	19.6370i	0.807759	−	1.39908i	0.914413	−	0.404783i	$-0.132653\pi$
$198$	−1.47710			−0.104973
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	0.980279	−	0.197619i	$-0.0633208\pi$
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	−0.661282	+	0.750137i	$0.729987\pi$
$200$	−2.28799			−0.161785
$201$	7.74288	+	2.65477i	0.546141	+	0.187253i
$202$	5.28799			0.372062
$203$	1.20946	+	2.09485i	0.0848874	+	0.147029i
$204$	−2.69963			−0.189012
$205$	7.82691	−	13.5566i	0.546655	−	0.946835i
$206$	14.0741			0.980591
$207$	−0.349814	−	0.605896i	−0.0243138	−	0.0421127i
$208$	−2.43818	+	4.22305i	−0.169057	+	0.292816i
$209$	11.1905			0.774062
$210$	3.00000			0.207020
$211$	−9.98762	−	17.2991i	−0.687576	−	1.19092i	−0.972620	−	0.232402i	$-0.925341\pi$
$211$	−9.98762	−	17.2991i	−0.687576	−	1.19092i	0.285044	−	0.958515i	$-0.407992\pi$
$212$	1.25526	−	2.17417i	0.0862116	−	0.149323i
$213$	−0.0716537	+	0.124108i	−0.00490963	+	0.00850373i
$214$	4.78799	+	8.29305i	0.327300	+	0.566901i
$215$	3.68725			0.251468
$216$	1.00000			0.0680414
$217$	−1.00619	−	1.74277i	−0.0683046	−	0.118307i
$218$	−6.66071	−	11.5367i	−0.451120	−	0.781363i
$219$	5.78799	+	10.0251i	0.391116	+	0.677433i
$220$	1.99381	+	3.45338i	0.134423	+	0.232827i
$221$	−6.58217	+	11.4007i	−0.442765	+	0.766891i
$222$	1.64400	−	2.84748i	0.110338	−	0.191111i
$223$	16.9963			1.13816			0.569078	−	0.822284i	$-0.307300\pi$
$223$	16.9963			1.13816			0.569078	+	0.822284i	$0.307300\pi$
$224$	−0.555632	−	0.962383i	−0.0371247	−	0.0643019i
$225$	2.28799			0.152533
$226$	−14.9222			−0.992607
$227$	5.03342	−	8.71814i	0.334080	−	0.578643i	−0.649228	−	0.760594i	$-0.724908\pi$
$227$	5.03342	−	8.71814i	0.334080	−	0.578643i	0.983308	+	0.181951i	$0.0582411\pi$
$228$	−7.57598			−0.501732
$229$	11.4382	+	19.8115i	0.755856	+	1.30918i	0.944948	+	0.327222i	$0.106112\pi$
$229$	11.4382	+	19.8115i	0.755856	+	1.30918i	−0.189092	+	0.981959i	$0.560554\pi$
$230$	−0.944368	+	1.63569i	−0.0622698	+	0.107854i
$231$	−0.820724	−	1.42154i	−0.0539997	−	0.0935302i
$232$	1.08836	−	1.88510i	0.0714546	−	0.123763i
$233$	11.4425	−	19.8190i	0.749624	−	1.29839i	−0.198379	−	0.980125i	$-0.563568\pi$
$233$	11.4425	−	19.8190i	0.749624	−	1.29839i	0.948003	−	0.318261i	$-0.103099\pi$
$234$	2.43818	−	4.22305i	0.159389	−	0.276069i
$235$	6.73236	−	11.6608i	0.439171	−	0.760666i
$236$	3.66071	−	6.34053i	0.238292	−	0.412733i
$237$	−3.88255	+	6.72477i	−0.252198	+	0.436821i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−9.47524	+	16.4116i	−0.612902	+	1.06158i	0.377846	+	0.925868i	$0.376665\pi$
$239$	−9.47524	+	16.4116i	−0.612902	+	1.06158i	−0.990749	+	0.135710i	$0.956669\pi$
$240$	−1.34981	−	2.33795i	−0.0871301	−	0.150914i
$241$	−11.3745			−0.732696			−0.366348	−	0.930478i	$-0.619392\pi$
$241$	−11.3745			−0.732696			−0.366348	+	0.930478i	$0.619392\pi$
$242$	−4.40909	+	7.63676i	−0.283427	+	0.490910i
$243$	−1.00000			−0.0641500
$244$	−5.87636			−0.376195
$245$	−7.78180	−	13.4785i	−0.497161	−	0.861108i
$246$	5.79851			0.369700
$247$	−18.4716	+	31.9937i	−1.17532	+	2.03571i
$248$	−0.905446	+	1.56828i	−0.0574959	+	0.0995858i
$249$	5.75526	+	9.96840i	0.364725	+	0.631722i
$250$	3.66071	+	6.34053i	0.231523	+	0.401010i
$251$	−6.17742	−	10.6996i	−0.389915	−	0.675353i	0.602523	−	0.798102i	$-0.294162\pi$
$251$	−6.17742	−	10.6996i	−0.389915	−	0.675353i	−0.992438	+	0.122749i	$0.960829\pi$
$252$	0.555632	+	0.962383i	0.0350015	+	0.0606244i
$253$	1.03342			0.0649706
$254$	10.6996			0.671354
$255$	−3.64400	−	6.31159i	−0.228196	−	0.395247i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.117454	+	0.203436i	−0.00732658	+	0.0126900i	−0.869665	−	0.493642i	$-0.835665\pi$
$257$	−0.117454	+	0.203436i	−0.00732658	+	0.0126900i	0.862339	+	0.506332i	$0.168999\pi$
$258$	0.682918	+	1.18285i	0.0425166	+	0.0736409i
$259$	3.65383			0.227038
$260$	−13.1643			−0.816418
$261$	−1.08836	+	1.88510i	−0.0673680	+	0.116685i
$262$	1.20582	+	2.08854i	0.0744957	+	0.129030i
$263$	−12.1185			−0.747262			−0.373631	−	0.927577i	$-0.621887\pi$
$263$	−12.1185			−0.747262			−0.373631	+	0.927577i	$0.621887\pi$
$264$	−0.738550	+	1.27921i	−0.0454546	+	0.0787297i
$265$	6.77747			0.416337
$266$	−4.20946	−	7.29100i	−0.258099	−	0.447040i
$267$	−5.47710			−0.335193
$268$	6.17054	−	5.37815i	0.376926	−	0.328523i
$269$	−18.7861			−1.14541			−0.572705	−	0.819761i	$-0.694106\pi$
$269$	−18.7861			−1.14541			−0.572705	+	0.819761i	$0.694106\pi$
$270$	1.34981	+	2.33795i	0.0821471	+	0.142283i
$271$	−23.0531			−1.40038			−0.700188	−	0.713959i	$-0.746900\pi$
$271$	−23.0531			−1.40038			−0.700188	+	0.713959i	$0.746900\pi$
$272$	−1.34981	+	2.33795i	−0.0818445	+	0.141759i
$273$	5.41892			0.327968
$274$	−10.9938	−	19.0418i	−0.664160	−	1.15036i
$275$	−1.68980	+	2.92681i	−0.101899	+	0.176493i
$276$	−0.699628			−0.0421127
$277$	28.1840			1.69341			0.846707	−	0.532060i	$-0.178582\pi$
$277$	28.1840			1.69341			0.846707	+	0.532060i	$0.178582\pi$
$278$	−8.97091	−	15.5381i	−0.538039	−	0.931912i
$279$	0.905446	−	1.56828i	0.0542076	−	0.0938904i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−4.11559	−	7.12842i	−0.245516	−	0.425246i	0.716761	−	0.697319i	$-0.245624\pi$
$281$	−4.11559	−	7.12842i	−0.245516	−	0.425246i	−0.962277	+	0.272073i	$0.912291\pi$
$282$	4.98762			0.297008
$283$	−4.83922			−0.287662			−0.143831	−	0.989602i	$-0.545942\pi$
$283$	−4.83922			−0.287662			−0.143831	+	0.989602i	$0.545942\pi$
$284$	0.0716537	+	0.124108i	0.00425186	+	0.00736444i
$285$	−10.2262	−	17.7122i	−0.605746	−	1.04918i
$286$	3.60143	+	6.23786i	0.212957	+	0.368853i
$287$	3.22184	+	5.58039i	0.190179	+	0.329400i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	4.85600	−	8.41085i	0.285647	−	0.494756i
$290$	5.87636			0.345072
$291$	−5.71634	−	9.90099i	−0.335098	−	0.580406i
$292$	11.5760			0.677433
$293$	−17.8960			−1.04550			−0.522748	−	0.852487i	$-0.675093\pi$
$293$	−17.8960			−1.04550			−0.522748	+	0.852487i	$0.675093\pi$
$294$	2.88255	−	4.99272i	0.168113	−	0.291181i
$295$	19.7651			1.15077
$296$	−1.64400	−	2.84748i	−0.0955553	−	0.165507i
$297$	0.738550	−	1.27921i	0.0428550	−	0.0742271i
$298$	5.97710	+	10.3526i	0.346244	+	0.599712i
$299$	−1.70582	+	2.95456i	−0.0986500	+	0.170867i
$300$	1.14400	−	1.98146i	0.0660486	−	0.114400i
$301$	−0.758902	+	1.31446i	−0.0437424	+	0.0757640i
$302$	0.323272	−	0.559924i	0.0186022	−	0.0322200i
$303$	−2.64400	+	4.57954i	−0.151894	+	0.263087i
$304$	−3.78799	+	6.56099i	−0.217256	+	0.376299i
$305$	−7.93199	−	13.7386i	−0.454184	−	0.786670i
$306$	1.34981	−	2.33795i	0.0771637	−	0.133652i
$307$	8.51671	+	14.7514i	0.486074	+	0.841905i	0.999872	−	0.0160060i	$-0.00509509\pi$
$307$	8.51671	+	14.7514i	0.486074	+	0.841905i	−0.513798	+	0.857911i	$0.671762\pi$
$308$	−1.64145			−0.0935302
$309$	−7.03706	+	12.1885i	−0.400324	+	0.693382i
$310$	−4.88874			−0.277662
$311$	11.9294			0.676456			0.338228	−	0.941064i	$-0.390172\pi$
$311$	11.9294			0.676456			0.338228	+	0.941064i	$0.390172\pi$
$312$	−2.43818	−	4.22305i	−0.138035	−	0.239083i
$313$	−8.78985			−0.496832			−0.248416	−	0.968653i	$-0.579910\pi$
$313$	−8.78985			−0.496832			−0.248416	+	0.968653i	$0.579910\pi$
$314$	−10.4320	+	18.0687i	−0.588711	+	1.01968i
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$	3.88255	+	6.72477i	0.218410	+	0.378298i
$317$	−14.4462	−	25.0215i	−0.811377	−	1.40535i	−0.911901	−	0.410411i	$-0.865385\pi$
$317$	−14.4462	−	25.0215i	−0.811377	−	1.40535i	0.100524	−	0.994935i	$-0.467948\pi$
$318$	1.25526	+	2.17417i	0.0703915	+	0.121922i
$319$	−1.60762	−	2.78448i	−0.0900096	−	0.155901i
$320$	−2.69963			−0.150914
$321$	−9.57598			−0.534479
$322$	−0.388736	−	0.673310i	−0.0216634	−	0.0375221i
$323$	−10.2262	+	17.7122i	−0.568999	+	0.985536i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−5.57853	−	9.66230i	−0.309441	−	0.535968i
$326$	20.2436			1.12119
$327$	13.3214			0.736676
$328$	2.89926	−	5.02166i	0.160085	−	0.277275i
$329$	2.77128	+	4.80000i	0.152786	+	0.264633i
$330$	−3.98762			−0.219511
$331$	−14.0371	+	24.3129i	−0.771547	+	1.33636i	0.165168	+	0.986265i	$0.447183\pi$
$331$	−14.0371	+	24.3129i	−0.771547	+	1.33636i	−0.936715	+	0.350093i	$0.886150\pi$
$332$	11.5105			0.631722
$333$	1.64400	+	2.84748i	0.0900904	+	0.156041i
$334$	18.4065			1.00716
$335$	20.9029	+	7.16689i	1.14205	+	0.391569i
$336$	1.11126			0.0606244
$337$	−6.25093	−	10.8269i	−0.340510	−	0.589780i	0.644018	−	0.765011i	$-0.277266\pi$
$337$	−6.25093	−	10.8269i	−0.340510	−	0.589780i	−0.984527	+	0.175230i	$0.943933\pi$
$338$	−10.7788			−0.586292
$339$	7.46108	−	12.9230i	0.405230	−	0.701879i
$340$	−7.28799			−0.395247
$341$	1.33743	+	2.31650i	0.0724261	+	0.125446i
$342$	3.78799	−	6.56099i	0.204831	−	0.354778i
$343$	14.1854			0.765939
$344$	1.36584			0.0736409
$345$	−0.944368	−	1.63569i	−0.0508431	−	0.0880628i
$346$	4.32072	−	7.48371i	0.232284	−	0.402327i
$347$	−11.0247	+	19.0953i	−0.591836	+	1.02509i	0.402149	+	0.915574i	$0.368263\pi$
$347$	−11.0247	+	19.0953i	−0.591836	+	1.02509i	−0.993985	+	0.109516i	$0.965070\pi$
$348$	1.08836	+	1.88510i	0.0583424	+	0.101052i
$349$	−7.94692			−0.425389			−0.212694	−	0.977119i	$-0.568224\pi$
$349$	−7.94692			−0.425389			−0.212694	+	0.977119i	$0.568224\pi$
$350$	2.54256			0.135906
$351$	2.43818	+	4.22305i	0.130140	+	0.225410i
$352$	0.738550	+	1.27921i	0.0393648	+	0.0681819i
$353$	−9.64214	−	16.7007i	−0.513199	−	0.888887i	−0.999883	−	0.0153087i	$-0.995127\pi$
$353$	−9.64214	−	16.7007i	−0.513199	−	0.888887i	0.486684	−	0.873578i	$-0.338206\pi$
$354$	3.66071	+	6.34053i	0.194564	+	0.336995i
$355$	−0.193438	+	0.335045i	−0.0102666	+	0.0177823i
$356$	−2.73855	+	4.74331i	−0.145143	+	0.251395i
$357$	3.00000			0.158777
$358$	−5.99381	−	10.3816i	−0.316783	−	0.548684i
$359$	1.64145			0.0866323			0.0433162	−	0.999061i	$-0.486208\pi$
$359$	1.64145			0.0866323			0.0433162	+	0.999061i	$0.486208\pi$
$360$	2.69963			0.142283
$361$	−19.1978	+	33.2515i	−1.01041	+	1.75008i
$362$	−2.23491			−0.117464
$363$	−4.40909	−	7.63676i	−0.231417	−	0.400826i
$364$	2.70946	−	4.69292i	0.142014	−	0.245976i
$365$	15.6254	+	27.0640i	0.817872	+	1.41660i
$366$	2.93818	−	5.08907i	0.153581	−	0.266010i
$367$	−3.11559	+	5.39637i	−0.162633	+	0.281688i	−0.935812	−	0.352499i	$-0.885332\pi$
$367$	−3.11559	+	5.39637i	−0.162633	+	0.281688i	0.773179	+	0.634187i	$0.218665\pi$
$368$	−0.349814	+	0.605896i	−0.0182353	+	0.0315845i
$369$	−2.89926	+	5.02166i	−0.150929	+	0.261417i
$370$	4.43818	−	7.68715i	0.230730	−	0.399636i
$371$	−1.39493	+	2.41608i	−0.0724209	+	0.125437i
$372$	−0.905446	−	1.56828i	−0.0469452	−	0.0813115i
$373$	−10.3214	+	17.8772i	−0.534422	+	0.925647i	0.464769	+	0.885432i	$0.346138\pi$
$373$	−10.3214	+	17.8772i	−0.534422	+	0.925647i	−0.999191	+	0.0402147i	$0.987196\pi$
$374$	1.99381	+	3.45338i	0.103097	+	0.178570i
$375$	−7.32141			−0.378076
$376$	2.49381	−	4.31941i	0.128608	−	0.222756i
$377$	10.6145			0.546675
$378$	−1.11126			−0.0571573
$379$	17.6804	+	30.6233i	0.908180	+	1.57301i	0.816591	+	0.577216i	$0.195861\pi$
$379$	17.6804	+	30.6233i	0.908180	+	1.57301i	0.0915883	+	0.995797i	$0.470806\pi$
$380$	−20.4523			−1.04918
$381$	−5.34981	+	9.26615i	−0.274079	+	0.474719i
$382$	1.86584	−	3.23172i	0.0954645	−	0.165349i
$383$	5.63162	+	9.75425i	0.287762	+	0.498419i	0.973275	−	0.229642i	$-0.0737554\pi$
$383$	5.63162	+	9.75425i	0.287762	+	0.498419i	−0.685513	+	0.728060i	$0.740422\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−2.21565	−	3.83762i	−0.112920	−	0.195583i
$386$	5.58217	+	9.66861i	0.284125	+	0.492119i
$387$	−1.36584			−0.0694293
$388$	−11.4327			−0.580406
$389$	13.2040	+	22.8699i	0.669467	+	1.15955i	0.978053	+	0.208355i	$0.0668109\pi$
$389$	13.2040	+	22.8699i	0.669467	+	1.15955i	−0.308586	+	0.951196i	$0.599856\pi$
$390$	6.58217	−	11.4007i	0.333301	−	0.577295i
$391$	−0.944368	+	1.63569i	−0.0477587	+	0.0827206i
$392$	−2.88255	−	4.99272i	−0.145591	−	0.252170i
$393$	−2.41164			−0.121651
$394$	22.6749			1.14234
$395$	−10.4814	+	18.1544i	−0.527378	+	0.913445i
$396$	−0.738550	−	1.27921i	−0.0371135	−	0.0642825i
$397$	−3.55632			−0.178487			−0.0892433	−	0.996010i	$-0.528445\pi$
$397$	−3.55632			−0.178487			−0.0892433	+	0.996010i	$0.528445\pi$
$398$	−4.50000	+	7.79423i	−0.225565	+	0.390689i
$399$	8.41892			0.421473
$400$	−1.14400	−	1.98146i	−0.0571998	−	0.0990730i
$401$	34.5709			1.72639			0.863194	−	0.504873i	$-0.168461\pi$
$401$	34.5709			1.72639			0.863194	+	0.504873i	$0.168461\pi$
$402$	1.57234	+	8.03292i	0.0784213	+	0.400645i
$403$	−8.83056			−0.439881
$404$	2.64400	+	4.57954i	0.131544	+	0.227840i
$405$	−2.69963			−0.134146
$406$	−1.20946	+	2.09485i	−0.0600245	+	0.103965i
$407$	−4.85669			−0.240737
$408$	−1.34981	−	2.33795i	−0.0668258	−	0.115746i
$409$	−1.87017	+	3.23922i	−0.0924738	+	0.160169i	−0.908551	−	0.417773i	$-0.862811\pi$
$409$	−1.87017	+	3.23922i	−0.0924738	+	0.160169i	0.816078	+	0.577942i	$0.196144\pi$
$410$	15.6538			0.773087
$411$	21.9876			1.08457
$412$	7.03706	+	12.1885i	0.346691	+	0.600487i
$413$	−4.06801	+	7.04600i	−0.200174	+	0.346711i
$414$	0.349814	−	0.605896i	0.0171924	−	0.0297782i
$415$	15.5371	+	26.9110i	0.762684	+	1.32101i
$416$	−4.87636			−0.239083
$417$	17.9418			0.878615
$418$	5.59524	+	9.69124i	0.273672	+	0.474014i
$419$	−1.28985	−	2.23409i	−0.0630134	−	0.109142i	0.832798	−	0.553578i	$-0.186738\pi$
$419$	−1.28985	−	2.23409i	−0.0630134	−	0.109142i	−0.895811	+	0.444435i	$0.853404\pi$
$420$	1.50000	+	2.59808i	0.0731925	+	0.126773i
$421$	−4.74976	−	8.22682i	−0.231489	−	0.400951i	0.726757	−	0.686894i	$-0.241026\pi$
$421$	−4.74976	−	8.22682i	−0.231489	−	0.400951i	−0.958247	+	0.285943i	$0.907693\pi$
$422$	9.98762	−	17.2991i	0.486190	−	0.842105i
$423$	−2.49381	+	4.31941i	−0.121253	+	0.210017i
$424$	2.51052			0.121922
$425$	−3.08836	−	5.34920i	−0.149808	−	0.259474i
$426$	−0.143307			−0.00694326
$427$	6.53018			0.316018
$428$	−4.78799	+	8.29305i	−0.231436	+	0.400859i
$429$	−7.20286			−0.347758
$430$	1.84362	+	3.19325i	0.0889075	+	0.153992i
$431$	0.855315	−	1.48145i	0.0411991	−	0.0713589i	−0.844691	−	0.535255i	$-0.820216\pi$
$431$	0.855315	−	1.48145i	0.0411991	−	0.0713589i	0.885890	+	0.463896i	$0.153549\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	9.91961	−	17.1813i	0.476706	−	0.825679i	−0.522938	−	0.852371i	$-0.675164\pi$
$433$	9.91961	−	17.1813i	0.476706	−	0.825679i	0.999644	+	0.0266919i	$0.00849732\pi$
$434$	1.00619	−	1.74277i	0.0482987	−	0.0836557i
$435$	−2.93818	+	5.08907i	−0.140875	+	0.244002i
$436$	6.66071	−	11.5367i	0.318990	−	0.552507i
$437$	−2.65019	+	4.59026i	−0.126776	+	0.219582i
$438$	−5.78799	+	10.0251i	−0.276561	+	0.479018i
$439$	7.53706	+	13.0546i	0.359724	+	0.623061i	0.987915	−	0.154999i	$-0.0495374\pi$
$439$	7.53706	+	13.0546i	0.359724	+	0.623061i	−0.628190	+	0.778060i	$0.716204\pi$
$440$	−1.99381	+	3.45338i	−0.0950512	+	0.164633i
$441$	2.88255	+	4.99272i	0.137264	+	0.237748i
$442$	−13.1643			−0.626164
$443$	20.7341	−	35.9126i	0.985109	−	1.70626i	0.343657	−	0.939095i	$-0.388334\pi$
$443$	20.7341	−	35.9126i	0.985109	−	1.70626i	0.641452	−	0.767163i	$-0.278332\pi$
$444$	3.28799			0.156041
$445$	−14.7861			−0.700930
$446$	8.49814	+	14.7192i	0.402399	+	0.696975i
$447$	−11.9542			−0.565414
$448$	0.555632	−	0.962383i	0.0262511	−	0.0454683i
$449$	2.11745	−	3.66754i	0.0999288	−	0.173082i	−0.811726	−	0.584038i	$-0.801472\pi$
$449$	2.11745	−	3.66754i	0.0999288	−	0.173082i	0.911655	+	0.410956i	$0.134805\pi$
$450$	1.14400	+	1.98146i	0.0539285	+	0.0934069i
$451$	−4.28249	−	7.41749i	−0.201655	−	0.349276i
$452$	−7.46108	−	12.9230i	−0.350940	−	0.607845i
$453$	0.323272	+	0.559924i	0.0151886	+	0.0263075i
$454$	10.0668			0.472460
$455$	14.6291			0.685821
$456$	−3.78799	−	6.56099i	−0.177389	−	0.307247i
$457$	−7.77197	+	13.4614i	−0.363557	+	0.629700i	−0.988544	−	0.150936i	$-0.951771\pi$
$457$	−7.77197	+	13.4614i	−0.363557	+	0.629700i	0.624986	+	0.780636i	$0.285105\pi$
$458$	−11.4382	+	19.8115i	−0.534471	+	0.925731i
$459$	1.34981	+	2.33795i	0.0630039	+	0.109126i
$460$	−1.88874			−0.0880628
$461$	17.0617			0.794645			0.397322	−	0.917679i	$-0.369939\pi$
$461$	17.0617			0.794645			0.397322	+	0.917679i	$0.369939\pi$
$462$	0.820724	−	1.42154i	0.0381835	−	0.0661358i
$463$	−13.9691	−	24.1951i	−0.649197	−	1.12444i	−0.983315	−	0.181911i	$-0.941772\pi$
$463$	−13.9691	−	24.1951i	−0.649197	−	1.12444i	0.334118	−	0.942531i	$-0.391562\pi$
$464$	2.17673			0.101052
$465$	2.44437	−	4.23377i	0.113355	−	0.196336i
$466$	22.8850			1.06013
$467$	12.0167	+	20.8136i	0.556067	+	0.963136i	0.997820	+	0.0659995i	$0.0210236\pi$
$467$	12.0167	+	20.8136i	0.556067	+	0.963136i	−0.441753	+	0.897137i	$0.645643\pi$
$468$	4.87636			0.225410
$469$	−6.85710	+	5.97654i	−0.316631	+	0.275971i
$470$	13.4647			0.621081
$471$	−10.4320	−	18.0687i	−0.480681	−	0.832563i
$472$	7.32141			0.336995
$473$	1.00874	−	1.74719i	0.0463818	−	0.0803357i
$474$	−7.76509			−0.356662
$475$	−8.66690	−	15.0115i	−0.397664	−	0.688775i
$476$	1.50000	−	2.59808i	0.0687524	−	0.119083i
$477$	−2.51052			−0.114949
$478$	−18.9505			−0.866775
$479$	−18.7942	−	32.5525i	−0.858728	−	1.48736i	−0.873143	−	0.487465i	$-0.837922\pi$
$479$	−18.7942	−	32.5525i	−0.858728	−	1.48736i	0.0144147	−	0.999896i	$-0.495412\pi$
$480$	1.34981	−	2.33795i	0.0616103	−	0.106712i
$481$	8.01671	−	13.8853i	0.365531	−	0.633117i
$482$	−5.68725	−	9.85060i	−0.259047	−	0.448683i
$483$	0.777472			0.0353762
$484$	−8.81818			−0.400826
$485$	−15.4320	−	26.7290i	−0.700730	−	1.21370i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	3.52723	+	6.10934i	0.159834	+	0.276841i	0.934809	−	0.355152i	$-0.115571\pi$
$487$	3.52723	+	6.10934i	0.159834	+	0.276841i	−0.774975	+	0.631992i	$0.782237\pi$
$488$	−2.93818	−	5.08907i	−0.133005	−	0.230372i
$489$	−10.1218	+	17.5314i	−0.457723	+	0.792799i
$490$	7.78180	−	13.4785i	0.351546	−	0.608896i
$491$	−4.21881			−0.190392			−0.0951961	−	0.995459i	$-0.530348\pi$
$491$	−4.21881			−0.190392			−0.0951961	+	0.995459i	$0.530348\pi$
$492$	2.89926	+	5.02166i	0.130709	+	0.226394i
$493$	5.87636			0.264658
$494$	−36.9432			−1.66215
$495$	1.99381	−	3.45338i	0.0896151	−	0.155218i
$496$	−1.81089			−0.0813115
$497$	−0.0796262	−	0.137917i	−0.00357172	−	0.00618640i
$498$	−5.75526	+	9.96840i	−0.257899	+	0.446695i
$499$	−5.03706	−	8.72445i	−0.225490	−	0.390560i	0.730976	−	0.682403i	$-0.239065\pi$
$499$	−5.03706	−	8.72445i	−0.225490	−	0.390560i	−0.956466	+	0.291843i	$0.905732\pi$
$500$	−3.66071	+	6.34053i	−0.163712	+	0.283557i
$501$	−9.20327	+	15.9405i	−0.411172	+	0.712170i
$502$	6.17742	−	10.6996i	0.275712	−	0.477546i
$503$	6.99312	−	12.1124i	0.311808	−	0.540067i	−0.666946	−	0.745106i	$-0.732399\pi$
$503$	6.99312	−	12.1124i	0.311808	−	0.540067i	0.978754	+	0.205039i	$0.0657321\pi$
$504$	−0.555632	+	0.962383i	−0.0247498	+	0.0428679i
$505$	−7.13781	+	12.3630i	−0.317628	+	0.550148i
$506$	0.516710	+	0.894969i	0.0229706	+	0.0397862i
$507$	5.38942	−	9.33476i	0.239353	−	0.414571i
$508$	5.34981	+	9.26615i	0.237360	+	0.411119i
$509$	31.4944			1.39597			0.697983	−	0.716114i	$-0.254081\pi$
$509$	31.4944			1.39597			0.697983	+	0.716114i	$0.254081\pi$
$510$	3.64400	−	6.31159i	0.161359	−	0.279482i
$511$	−12.8640			−0.569069
$512$	−1.00000			−0.0441942
$513$	3.78799	+	6.56099i	0.167244	+	0.289675i
$514$	−0.234908			−0.0103613
$515$	−18.9975	+	32.9046i	−0.837128	+	1.44995i
$516$	−0.682918	+	1.18285i	−0.0300638	+	0.0520720i
$517$	−3.68361	−	6.38019i	−0.162005	−	0.280601i
$518$	1.82691	+	3.16431i	0.0802700	+	0.139032i
$519$	4.32072	+	7.48371i	0.189659	+	0.328499i
$520$	−6.58217	−	11.4007i	−0.288647	−	0.499952i
$521$	−40.6822			−1.78232			−0.891159	−	0.453692i	$-0.850107\pi$
$521$	−40.6822			−1.78232			−0.891159	+	0.453692i	$0.850107\pi$
$522$	−2.17673			−0.0952728
$523$	−18.4010	−	31.8715i	−0.804621	−	1.39364i	−0.916546	−	0.399928i	$-0.869035\pi$
$523$	−18.4010	−	31.8715i	−0.804621	−	1.39364i	0.111925	−	0.993717i	$-0.464298\pi$
$524$	−1.20582	+	2.08854i	−0.0526764	+	0.0912382i
$525$	−1.27128	+	2.20192i	−0.0554833	+	0.0960999i
$526$	−6.05927	−	10.4950i	−0.264197	−	0.457602i
$527$	−4.88874			−0.212957
$528$	−1.47710			−0.0642825
$529$	11.2553	−	19.4947i	0.489359	−	0.847595i
$530$	3.38874	+	5.86946i	0.147197	+	0.254953i
$531$	−7.32141			−0.317722
$532$	4.20946	−	7.29100i	0.182503	−	0.316105i
$533$	28.2756			1.22475
$534$	−2.73855	−	4.74331i	−0.118509	−	0.205263i
$535$	−25.8516			−1.11766
$536$	7.74288	+	2.65477i	0.334441	+	0.114669i
$537$	11.9876			0.517304
$538$	−9.39307	−	16.2693i	−0.404964	−	0.701418i
$539$	−8.51562			−0.366794
$540$	−1.34981	+	2.33795i	−0.0580867	+	0.100609i
$541$	2.65521			0.114156			0.0570781	−	0.998370i	$-0.481822\pi$
$541$	2.65521			0.114156			0.0570781	+	0.998370i	$0.481822\pi$
$542$	−11.5265	−	19.9646i	−0.495107	−	0.857551i
$543$	1.11745	−	1.93549i	0.0479545	−	0.0830597i
$544$	−2.69963			−0.115746
$545$	35.9629			1.54048
$546$	2.70946	+	4.69292i	0.115954	+	0.200839i
$547$	−15.2651	+	26.4399i	−0.652688	+	1.13049i	0.329780	+	0.944058i	$0.393025\pi$
$547$	−15.2651	+	26.4399i	−0.652688	+	1.13049i	−0.982468	+	0.186431i	$0.940308\pi$
$548$	10.9938	−	19.0418i	0.469632	−	0.813427i
$549$	2.93818	+	5.08907i	0.125398	+	0.217196i
$550$	−3.37959			−0.144106
$551$	16.4909			0.702534
$552$	−0.349814	−	0.605896i	−0.0148891	−	0.0257886i
$553$	−4.31453	−	7.47299i	−0.183473	−	0.317784i
$554$	14.0920	+	24.4081i	0.598712	+	1.03700i
$555$	4.43818	+	7.68715i	0.188390	+	0.326301i
$556$	8.97091	−	15.5381i	0.380451	−	0.658961i
$557$	3.90978	−	6.77193i	0.165663	−	0.286936i	−0.771228	−	0.636559i	$-0.780357\pi$
$557$	3.90978	−	6.77193i	0.165663	−	0.286936i	0.936890	+	0.349623i	$0.113690\pi$
$558$	1.81089			0.0766612
$559$	3.33015	+	5.76799i	0.140850	+	0.243960i
$560$	3.00000			0.126773
$561$	−3.98762			−0.168357
$562$	4.11559	−	7.12842i	0.173606	−	0.300694i
$563$	14.3017			0.602747			0.301373	−	0.953506i	$-0.402555\pi$
$563$	14.3017			0.602747			0.301373	+	0.953506i	$0.402555\pi$
$564$	2.49381	+	4.31941i	0.105008	+	0.181880i
$565$	20.1421	−	34.8872i	0.847386	−	1.46772i
$566$	−2.41961	−	4.19088i	−0.101704	−	0.176156i
$567$	0.555632	−	0.962383i	0.0233344	−	0.0404163i
$568$	−0.0716537	+	0.124108i	−0.00300652	+	0.00520745i
$569$	−6.98074	+	12.0910i	−0.292648	+	0.506881i	−0.974435	−	0.224670i	$-0.927870\pi$
$569$	−6.98074	+	12.0910i	−0.292648	+	0.506881i	0.681787	+	0.731551i	$0.261203\pi$
$570$	10.2262	−	17.7122i	0.428327	−	0.741884i
$571$	1.24543	−	2.15715i	0.0521196	−	0.0902737i	−0.838789	−	0.544457i	$-0.816736\pi$
$571$	1.24543	−	2.15715i	0.0521196	−	0.0902737i	0.890908	+	0.454184i	$0.150069\pi$
$572$	−3.60143	+	6.23786i	−0.150583	+	0.260818i
$573$	1.86584	+	3.23172i	0.0779464	+	0.135007i
$574$	−3.22184	+	5.58039i	−0.134477	+	0.232921i
$575$	−0.800372	−	1.38628i	−0.0333778	−	0.0578121i
$576$	1.00000			0.0416667
$577$	−19.1964	+	33.2491i	−0.799156	+	1.38418i	0.121010	+	0.992651i	$0.461387\pi$
$577$	−19.1964	+	33.2491i	−0.799156	+	1.38418i	−0.920166	+	0.391528i	$0.871947\pi$
$578$	9.71201			0.403966
$579$	−11.1643			−0.463974
$580$	2.93818	+	5.08907i	0.122001	+	0.211312i
$581$	−12.7912			−0.530670
$582$	5.71634	−	9.90099i	0.236950	−	0.410409i
$583$	1.85414	−	3.21147i	0.0767908	−	0.133006i
$584$	5.78799	+	10.0251i	0.239509	+	0.414841i
$585$	6.58217	+	11.4007i	0.272139	+	0.471359i
$586$	−8.94801	−	15.4984i	−0.369639	−	0.640233i
$587$	−21.7138	−	37.6094i	−0.896224	−	1.55231i	−0.832282	−	0.554352i	$-0.812966\pi$
$587$	−21.7138	−	37.6094i	−0.896224	−	1.55231i	−0.0639417	−	0.997954i	$-0.520367\pi$
$588$	5.76509			0.237748
$589$	−13.7193			−0.565294
$590$	9.88255	+	17.1171i	0.406858	+	0.704699i
$591$	−11.3374	+	19.6370i	−0.466360	+	0.807759i
$592$	1.64400	−	2.84748i	0.0675678	−	0.117031i
$593$	−16.7101	−	28.9428i	−0.686204	−	1.18854i	−0.973057	−	0.230565i	$-0.925943\pi$
$593$	−16.7101	−	28.9428i	−0.686204	−	1.18854i	0.286853	−	0.957974i	$-0.407391\pi$
$594$	1.47710			0.0606061
$595$	8.09888			0.332022
$596$	−5.97710	+	10.3526i	−0.244832	+	0.424061i
$597$	−4.50000	−	7.79423i	−0.184173	−	0.318997i
$598$	−3.41164			−0.139512
$599$	9.11422	−	15.7863i	0.372397	−	0.645010i	−0.617537	−	0.786542i	$-0.711869\pi$
$599$	9.11422	−	15.7863i	0.372397	−	0.645010i	0.989934	+	0.141532i	$0.0452027\pi$
$600$	2.28799			0.0934069
$601$	−3.21379	−	5.56645i	−0.131093	−	0.227060i	0.793005	−	0.609215i	$-0.208515\pi$
$601$	−3.21379	−	5.56645i	−0.131093	−	0.227060i	−0.924098	+	0.382155i	$0.875182\pi$
$602$	−1.51780			−0.0618611
$603$	−7.74288	−	2.65477i	−0.315314	−	0.108111i
$604$	0.646544			0.0263075
$605$	−11.9029	−	20.6164i	−0.483922	−	0.838177i
$606$	−5.28799			−0.214810
$607$	17.9876	−	31.1555i	0.730095	−	1.26456i	−0.226747	−	0.973954i	$-0.572809\pi$
$607$	17.9876	−	31.1555i	0.730095	−	1.26456i	0.956842	−	0.290608i	$-0.0938575\pi$
$608$	−7.57598			−0.307247
$609$	−1.20946	−	2.09485i	−0.0490098	−	0.0848874i
$610$	7.93199	−	13.7386i	0.321157	−	0.556260i
$611$	24.3214			0.983939
$612$	2.69963			0.109126
$613$	−8.83675	−	15.3057i	−0.356913	−	0.618191i	0.630531	−	0.776164i	$-0.282837\pi$
$613$	−8.83675	−	15.3057i	−0.356913	−	0.618191i	−0.987443	+	0.157973i	$0.949504\pi$
$614$	−8.51671	+	14.7514i	−0.343706	+	0.595317i
$615$	−7.82691	+	13.5566i	−0.315612	+	0.546655i
$616$	−0.820724	−	1.42154i	−0.0330679	−	0.0572753i
$617$	−38.2632			−1.54042			−0.770210	−	0.637791i	$-0.779849\pi$
$617$	−38.2632			−1.54042			−0.770210	+	0.637791i	$0.779849\pi$
$618$	−14.0741			−0.566144
$619$	−12.8709	−	22.2930i	−0.517323	−	0.896030i	−0.999798	−	0.0201201i	$-0.993595\pi$
$619$	−12.8709	−	22.2930i	−0.517323	−	0.896030i	0.482474	−	0.875910i	$-0.339738\pi$
$620$	−2.44437	−	4.23377i	−0.0981682	−	0.170032i
$621$	0.349814	+	0.605896i	0.0140376	+	0.0243138i
$622$	5.96472	+	10.3312i	0.239163	+	0.414243i
$623$	3.04325	−	5.27107i	0.121925	−	0.211181i
$624$	2.43818	−	4.22305i	0.0976052	−	0.169057i
$625$	−31.2051			−1.24820
$626$	−4.39493	−	7.61223i	−0.175657	−	0.304246i
$627$	−11.1905			−0.446905
$628$	−20.8640			−0.832563
$629$	4.43818	−	7.68715i	0.176962	−	0.306507i
$630$	−3.00000			−0.119523
$631$	4.33310	+	7.50516i	0.172498	+	0.298776i	0.939293	−	0.343117i	$-0.111483\pi$
$631$	4.33310	+	7.50516i	0.172498	+	0.298776i	−0.766794	+	0.641893i	$0.778149\pi$
$632$	−3.88255	+	6.72477i	−0.154439	+	0.267497i
$633$	9.98762	+	17.2991i	0.396972	+	0.687576i
$634$	14.4462	−	25.0215i	0.573730	−	0.993729i
$635$	−14.4425	+	25.0152i	−0.573133	+	0.992696i
$636$	−1.25526	+	2.17417i	−0.0497743	+	0.0862116i
$637$	14.0563	−	24.3463i	0.556932	−	0.964634i
$638$	1.60762	−	2.78448i	0.0636464	−	0.110239i
$639$	0.0716537	−	0.124108i	0.00283458	−	0.00490963i
$640$	−1.34981	−	2.33795i	−0.0533561	−	0.0924155i
$641$	8.87450	−	15.3711i	0.350522	−	0.607121i	−0.635819	−	0.771838i	$-0.719338\pi$
$641$	8.87450	−	15.3711i	0.350522	−	0.607121i	0.986341	+	0.164717i	$0.0526710\pi$
$642$	−4.78799	−	8.29305i	−0.188967	−	0.327300i
$643$	13.6181			0.537044			0.268522	−	0.963274i	$-0.413465\pi$
$643$	13.6181			0.537044			0.268522	+	0.963274i	$0.413465\pi$
$644$	0.388736	−	0.673310i	0.0153183	−	0.0265321i
$645$	−3.68725			−0.145185
$646$	−20.4523			−0.804687
$647$	16.7200	+	28.9599i	0.657330	+	1.13853i	0.981304	+	0.192463i	$0.0616477\pi$
$647$	16.7200	+	28.9599i	0.657330	+	1.13853i	−0.323974	+	0.946066i	$0.605019\pi$
$648$	−1.00000			−0.0392837
$649$	5.40723	−	9.36559i	0.212252	−	0.367632i
$650$	5.57853	−	9.66230i	0.218808	−	0.378987i
$651$	1.00619	+	1.74277i	0.0394357	+	0.0683046i
$652$	10.1218	+	17.5314i	0.396400	+	0.686584i
$653$	−2.27059	−	3.93278i	−0.0888552	−	0.153902i	0.818172	−	0.574973i	$-0.194987\pi$
$653$	−2.27059	−	3.93278i	−0.0888552	−	0.153902i	−0.907027	+	0.421071i	$0.861654\pi$
$654$	6.66071	+	11.5367i	0.260454	+	0.451120i
$655$	−6.51052			−0.254387
$656$	5.79851			0.226394
$657$	−5.78799	−	10.0251i	−0.225811	−	0.391116i
$658$	−2.77128	+	4.80000i	−0.108036	+	0.187124i
$659$	−13.6916	+	23.7145i	−0.533348	+	0.923786i	0.465893	+	0.884841i	$0.345733\pi$
$659$	−13.6916	+	23.7145i	−0.533348	+	0.923786i	−0.999241	+	0.0389452i	$0.987600\pi$
$660$	−1.99381	−	3.45338i	−0.0776090	−	0.134423i
$661$	−33.6515			−1.30889			−0.654446	−	0.756109i	$-0.727098\pi$
$661$	−33.6515			−1.30889			−0.654446	+	0.756109i	$0.727098\pi$
$662$	−28.0741			−1.09113
$663$	6.58217	−	11.4007i	0.255630	−	0.442765i
$664$	5.75526	+	9.96840i	0.223347	+	0.386849i
$665$	22.7280			0.881352
$666$	−1.64400	+	2.84748i	−0.0637036	+	0.110338i
$667$	1.52290			0.0589669
$668$	9.20327	+	15.9405i	0.356085	+	0.616758i
$669$	−16.9963			−0.657114
$670$	4.24474	+	21.6859i	0.163989	+	0.837799i
$671$	−8.67996			−0.335086
$672$	0.555632	+	0.962383i	0.0214340	+	0.0371247i
$673$	10.6304			0.409774			0.204887	−	0.978786i	$-0.434317\pi$
$673$	10.6304			0.409774			0.204887	+	0.978786i	$0.434317\pi$
$674$	6.25093	−	10.8269i	0.240777	−	0.417038i
$675$	−2.28799			−0.0880649
$676$	−5.38942	−	9.33476i	−0.207286	−	0.359029i
$677$	5.12543	−	8.87750i	0.196986	−	0.341190i	−0.750564	−	0.660798i	$-0.770218\pi$
$677$	5.12543	−	8.87750i	0.196986	−	0.341190i	0.947550	+	0.319608i	$0.103551\pi$
$678$	14.9222			0.573082
$679$	12.7047			0.487563
$680$	−3.64400	−	6.31159i	−0.139741	−	0.242038i
$681$	−5.03342	+	8.71814i	−0.192881	+	0.334080i
$682$	−1.33743	+	2.31650i	−0.0512130	+	0.0887035i
$683$	9.43749	+	16.3462i	0.361115	+	0.625470i	0.988145	−	0.153525i	$-0.0490627\pi$
$683$	9.43749	+	16.3462i	0.361115	+	0.625470i	−0.627029	+	0.778996i	$0.715729\pi$
$684$	7.57598			0.289675
$685$	59.3584			2.26797
$686$	7.09269	+	12.2849i	0.270800	+	0.469040i
$687$	−11.4382	−	19.8115i	−0.436394	−	0.755856i
$688$	0.682918	+	1.18285i	0.0260360	+	0.0450957i
$689$	6.12110	+	10.6020i	0.233195	+	0.403906i
$690$	0.944368	−	1.63569i	0.0359515	−	0.0622698i
$691$	12.7553	−	22.0928i	0.485233	−	0.840448i	−0.514623	−	0.857417i	$-0.672068\pi$
$691$	12.7553	−	22.0928i	0.485233	−	0.840448i	0.999856	+	0.0169684i	$0.00540146\pi$
$692$	8.64145			0.328499
$693$	0.820724	+	1.42154i	0.0311767	+	0.0539997i
$694$	−22.0494			−0.836982
$695$	48.4362			1.83729
$696$	−1.08836	+	1.88510i	−0.0412543	+	0.0714546i
$697$	15.6538			0.592931
$698$	−3.97346	−	6.88223i	−0.150398	−	0.260496i
$699$	−11.4425	+	19.8190i	−0.432795	+	0.749624i
$700$	1.27128	+	2.20192i	0.0480499	+	0.0832249i
$701$	−16.5247	+	28.6216i	−0.624129	+	1.08102i	0.364580	+	0.931172i	$0.381213\pi$
$701$	−16.5247	+	28.6216i	−0.624129	+	1.08102i	−0.988709	+	0.149850i	$0.952121\pi$
$702$	−2.43818	+	4.22305i	−0.0920231	+	0.159389i
$703$	12.4549	−	21.5725i	0.469745	−	0.813622i
$704$	−0.738550	+	1.27921i	−0.0278351	+	0.0482119i
$705$	−6.73236	+	11.6608i	−0.253555	+	0.439171i
$706$	9.64214	−	16.7007i	0.362887	−	0.628538i
$707$	−2.93818	−	5.08907i	−0.110502	−	0.191394i
$708$	−3.66071	+	6.34053i	−0.137578	+	0.238292i
$709$	8.78180	+	15.2105i	0.329808	+	0.571243i	0.982473	−	0.186402i	$-0.0596828\pi$
$709$	8.78180	+	15.2105i	0.329808	+	0.571243i	−0.652666	+	0.757646i	$0.726349\pi$
$710$	−0.386877			−0.0145192
$711$	3.88255	−	6.72477i	0.145607	−	0.252198i
$712$	−5.47710			−0.205263
$713$	−1.26695			−0.0474477
$714$	1.50000	+	2.59808i	0.0561361	+	0.0972306i
$715$	−19.4451			−0.727204
$716$	5.99381	−	10.3816i	0.223999	−	0.387978i
$717$	9.47524	−	16.4116i	0.353859	−	0.612902i
$718$	0.820724	+	1.42154i	0.0306291	+	0.0530512i
$719$	22.3189	+	38.6574i	0.832353	+	1.44168i	0.896167	+	0.443716i	$0.146340\pi$
$719$	22.3189	+	38.6574i	0.832353	+	1.44168i	−0.0638141	+	0.997962i	$0.520326\pi$
$720$	1.34981	+	2.33795i	0.0503046	+	0.0871301i
$721$	−7.82004	−	13.5447i	−0.291233	−	0.504431i
$722$	−38.3955			−1.42893
$723$	11.3745			0.423022
$724$	−1.11745	−	1.93549i	−0.0415299	−	0.0719318i
$725$	−2.49017	+	4.31310i	−0.0924825	+	0.160184i
$726$	4.40909	−	7.63676i	0.163637	−	0.283427i
$727$	−9.28002	−	16.0735i	−0.344177	−	0.596132i	0.641027	−	0.767518i	$-0.278509\pi$
$727$	−9.28002	−	16.0735i	−0.344177	−	0.596132i	−0.985204	+	0.171386i	$0.945175\pi$
$728$	5.41892			0.200839
$729$	1.00000			0.0370370
$730$	−15.6254	+	27.0640i	−0.578323	+	1.00168i
$731$	1.84362	+	3.19325i	0.0681889	+	0.118107i
$732$	5.87636			0.217196
$733$	6.44251	−	11.1588i	0.237959	−	0.412158i	−0.722169	−	0.691717i	$-0.756855\pi$
$733$	6.44251	−	11.1588i	0.237959	−	0.412158i	0.960129	+	0.279559i	$0.0901881\pi$
$734$	−6.23119			−0.229997
$735$	7.78180	+	13.4785i	0.287036	+	0.497161i
$736$	−0.699628			−0.0257886
$737$	9.11450	−	7.94406i	0.335737	−	0.292623i
$738$	−5.79851			−0.213446
$739$	−14.0488	−	24.3332i	−0.516792	−	0.895110i	−0.999810	−	0.0194992i	$-0.993793\pi$
$739$	−14.0488	−	24.3332i	−0.516792	−	0.895110i	0.483018	−	0.875610i	$-0.339541\pi$
$740$	8.87636			0.326301
$741$	18.4716	−	31.9937i	0.678571	−	1.17532i
$742$	−2.78985			−0.102419
$743$	12.5185	+	21.6827i	0.459259	+	0.795460i	0.998922	−	0.0464213i	$-0.0147817\pi$
$743$	12.5185	+	21.6827i	0.459259	+	0.795460i	−0.539663	+	0.841881i	$0.681448\pi$
$744$	0.905446	−	1.56828i	0.0331953	−	0.0574959i
$745$	−32.2719			−1.18235
$746$	−20.6428			−0.755788
$747$	−5.75526	−	9.96840i	−0.210574	−	0.364725i
$748$	−1.99381	+	3.45338i	−0.0729009	+	0.126268i
$749$	5.32072	−	9.21576i	0.194415	−	0.336737i
$750$	−3.66071	−	6.34053i	−0.133670	−	0.231523i
$751$	−12.4437			−0.454076			−0.227038	−	0.973886i	$-0.572904\pi$
$751$	−12.4437			−0.454076			−0.227038	+	0.973886i	$0.572904\pi$
$752$	4.98762			0.181880
$753$	6.17742	+	10.6996i	0.225118	+	0.389915i
$754$	5.30725	+	9.19243i	0.193279	+	0.334768i
$755$	0.872714	+	1.51159i	0.0317613	+	0.0550122i
$756$	−0.555632	−	0.962383i	−0.0202081	−	0.0350015i
$757$	15.2200	−	26.3618i	0.553180	−	0.958135i	−0.444863	−	0.895599i	$-0.646748\pi$
$757$	15.2200	−	26.3618i	0.553180	−	0.958135i	0.998043	−	0.0625366i	$-0.0199190\pi$
$758$	−17.6804	+	30.6233i	−0.642180	+	1.11229i
$759$	−1.03342			−0.0375108
$760$	−10.2262	−	17.7122i	−0.370942	−	0.642491i
$761$	−29.0865			−1.05438			−0.527192	−	0.849746i	$-0.676755\pi$
$761$	−29.0865			−1.05438			−0.527192	+	0.849746i	$0.676755\pi$
$762$	−10.6996			−0.387607
$763$	−7.40180	+	12.8203i	−0.267963	+	0.464126i
$764$	3.73167			0.135007
$765$	3.64400	+	6.31159i	0.131749	+	0.228196i
$766$	−5.63162	+	9.75425i	−0.203479	+	0.352435i
$767$	17.8509	+	30.9187i	0.644559	+	1.11641i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	8.62041	−	14.9310i	0.310860	−	0.538425i	−0.667689	−	0.744440i	$-0.732716\pi$
$769$	8.62041	−	14.9310i	0.310860	−	0.538425i	0.978549	+	0.206015i	$0.0660497\pi$
$770$	2.21565	−	3.83762i	0.0798465	−	0.138298i
$771$	0.117454	−	0.203436i	0.00423000	−	0.00732658i
$772$	−5.58217	+	9.66861i	−0.200907	+	0.347981i
$773$	−2.66257	+	4.61170i	−0.0957658	+	0.165871i	−0.909928	−	0.414766i	$-0.863863\pi$
$773$	−2.66257	+	4.61170i	−0.0957658	+	0.165871i	0.814162	+	0.580638i	$0.197197\pi$
$774$	−0.682918	−	1.18285i	−0.0245470	−	0.0425166i
$775$	2.07165	−	3.58821i	0.0744160	−	0.128892i
$776$	−5.71634	−	9.90099i	−0.205205	−	0.355425i
$777$	−3.65383			−0.131080
$778$	−13.2040	+	22.8699i	−0.473385	+	0.819927i
$779$	43.9294			1.57394
$780$	13.1643			0.471359
$781$	0.105840	+	0.183320i	0.00378724	+	0.00655969i
$782$	−1.88874			−0.0675411
$783$	1.08836	−	1.88510i	0.0388950	−	0.0673680i
$784$	2.88255	−	4.99272i	0.102948	−	0.178311i
$785$	−28.1625	−	48.7789i	−1.00516	−	1.74099i
$786$	−1.20582	−	2.08854i	−0.0430101	−	0.0744957i
$787$	8.63712	+	14.9599i	0.307880	+	0.533264i	0.977898	−	0.209081i	$-0.0670471\pi$
$787$	8.63712	+	14.9599i	0.307880	+	0.533264i	−0.670018	+	0.742344i	$0.733714\pi$
$788$	11.3374	+	19.6370i	0.403879	+	0.699540i
$789$	12.1185			0.431432
$790$	−20.9629			−0.745825
$791$	8.29123	+	14.3608i	0.294802	+	0.510612i
$792$	0.738550	−	1.27921i	0.0262432	−	0.0454546i
$793$	14.3276	−	24.8161i	0.508788	−	0.881247i
$794$	−1.77816	−	3.07986i	−0.0631046	−	0.109300i
$795$	−6.77747			−0.240372
$796$	−9.00000			−0.318997
$797$	−2.45489	+	4.25199i	−0.0869566	+	0.150613i	−0.906223	−	0.422799i	$-0.861047\pi$
$797$	−2.45489	+	4.25199i	−0.0869566	+	0.150613i	0.819267	+	0.573413i	$0.194381\pi$
$798$	4.20946	+	7.29100i	0.149013	+	0.258099i
$799$	13.4647			0.476348
$800$	1.14400	−	1.98146i	0.0404464	−	0.0700552i
$801$	5.47710			0.193524
$802$	17.2854	+	29.9393i	0.610370	+	1.05719i
$803$	17.0989			0.603407
$804$	−6.17054	+	5.37815i	−0.217618	+	0.189673i
$805$	2.09888			0.0739760
$806$	−4.41528	−	7.64749i	−0.155522	−	0.269371i
$807$	18.7861			0.661303
$808$	−2.64400	+	4.57954i	−0.0930155	+	0.161107i
$809$	10.9666			0.385564			0.192782	−	0.981242i	$-0.438249\pi$
$809$	10.9666			0.385564			0.192782	+	0.981242i	$0.438249\pi$
$810$	−1.34981	−	2.33795i	−0.0474276	−	0.0821471i
$811$	20.1971	−	34.9824i	0.709215	−	1.22840i	−0.255933	−	0.966694i	$-0.582383\pi$
$811$	20.1971	−	34.9824i	0.709215	−	1.22840i	0.965149	−	0.261703i	$-0.0842840\pi$
$812$	−2.41892			−0.0848874
$813$	23.0531			0.808507
$814$	−2.42835	−	4.20602i	−0.0851135	−	0.147421i
$815$	−27.3251	+	47.3284i	−0.957155	+	1.65784i
$816$	1.34981	−	2.33795i	0.0472529	−	0.0818445i
$817$	5.17377	+	8.96124i	0.181007	+	0.313514i
$818$	−3.74033			−0.130778
$819$	−5.41892			−0.189352
$820$	7.82691	+	13.5566i	0.273328	+	0.473417i
$821$	11.3621	+	19.6798i	0.396541	+	0.686829i	0.993297	−	0.115594i	$-0.0368773\pi$
$821$	11.3621	+	19.6798i	0.396541	+	0.686829i	−0.596756	+	0.802423i	$0.703544\pi$
$822$	10.9938	+	19.0418i	0.383453	+	0.664160i
$823$	7.01121	+	12.1438i	0.244395	+	0.423305i	0.961961	−	0.273185i	$-0.0880772\pi$
$823$	7.01121	+	12.1438i	0.244395	+	0.423305i	−0.717566	+	0.696490i	$0.754744\pi$
$824$	−7.03706	+	12.1885i	−0.245148	+	0.424608i
$825$	1.68980	−	2.92681i	0.0588312	−	0.101899i
$826$	−8.13602			−0.283088
$827$	−8.88323	−	15.3862i	−0.308900	−	0.535031i	0.669222	−	0.743063i	$-0.266628\pi$
$827$	−8.88323	−	15.3862i	−0.308900	−	0.535031i	−0.978122	+	0.208032i	$0.933294\pi$
$828$	0.699628			0.0243138
$829$	11.5178			0.400030			0.200015	−	0.979793i	$-0.435901\pi$
$829$	11.5178			0.400030			0.200015	+	0.979793i	$0.435901\pi$
$830$	−15.5371	+	26.9110i	−0.539299	+	0.934094i
$831$	−28.1840			−0.977693
$832$	−2.43818	−	4.22305i	−0.0845286	−	0.146408i
$833$	7.78180	−	13.4785i	0.269623	−	0.467002i
$834$	8.97091	+	15.5381i	0.310637	+	0.538039i
$835$	−24.8454	+	43.0335i	−0.859811	+	1.48924i
$836$	−5.59524	+	9.69124i	−0.193516	+	0.335179i
$837$	−0.905446	+	1.56828i	−0.0312968	+	0.0542076i
$838$	1.28985	−	2.23409i	0.0445572	−	0.0771753i
$839$	24.6396	−	42.6770i	0.850653	−	1.47337i	−0.0299668	−	0.999551i	$-0.509540\pi$
$839$	24.6396	−	42.6770i	0.850653	−	1.47337i	0.880620	−	0.473823i	$-0.157127\pi$
$840$	−1.50000	+	2.59808i	−0.0517549	+	0.0896421i
$841$	12.1309	+	21.0114i	0.418308	+	0.724530i
$842$	4.74976	−	8.22682i	0.163688	−	0.283515i
$843$	4.11559	+	7.12842i	0.141749	+	0.245516i
$844$	19.9752			0.687576
$845$	14.5494	−	25.2004i	0.500516	−	0.866919i
$846$	−4.98762			−0.171478
$847$	9.79932			0.336709
$848$	1.25526	+	2.17417i	0.0431058	+	0.0746615i
$849$	4.83922			0.166081
$850$	3.08836	−	5.34920i	0.105930	−	0.183476i
$851$	1.15019	−	1.99218i	0.0394279	−	0.0682911i
$852$	−0.0716537	−	0.124108i	−0.00245481	−	0.00425186i
$853$	7.50000	+	12.9904i	0.256795	+	0.444782i	0.965382	−	0.260842i	$-0.0840001\pi$
$853$	7.50000	+	12.9904i	0.256795	+	0.444782i	−0.708586	+	0.705624i	$0.750667\pi$
$854$	3.26509	+	5.65531i	0.111729	+	0.193521i
$855$	10.2262	+	17.7122i	0.349728	+	0.605746i
$856$	−9.57598			−0.327300
$857$	−38.0480			−1.29969			−0.649847	−	0.760065i	$-0.725167\pi$
$857$	−38.0480			−1.29969			−0.649847	+	0.760065i	$0.725167\pi$
$858$	−3.60143	−	6.23786i	−0.122951	−	0.212957i
$859$	−20.1964	+	34.9812i	−0.689092	+	1.19354i	0.283040	+	0.959108i	$0.408657\pi$
$859$	−20.1964	+	34.9812i	−0.689092	+	1.19354i	−0.972132	+	0.234434i	$0.924676\pi$
$860$	−1.84362	+	3.19325i	−0.0628671	+	0.108889i
$861$	−3.22184	−	5.58039i	−0.109800	−	0.190179i
$862$	1.71063			0.0582643
$863$	−46.3570			−1.57801			−0.789006	−	0.614386i	$-0.789404\pi$
$863$	−46.3570			−1.57801			−0.789006	+	0.614386i	$0.789404\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	11.6643	+	20.2032i	0.396600	+	0.686931i
$866$	19.8392			0.674164
$867$	−4.85600	+	8.41085i	−0.164919	+	0.285647i
$868$	2.01238			0.0683046
$869$	5.73491	+	9.93315i	0.194543	+	0.336959i
$870$	−5.87636			−0.199227
$871$	7.66730	+	39.1714i	0.259797	+	1.32727i
$872$	13.3214			0.451120
$873$	5.71634	+	9.90099i	0.193469	+	0.335098i
$874$	−5.30037			−0.179288
$875$	4.06801	−	7.04600i	0.137524	−	0.238198i
$876$	−11.5760			−0.391116
$877$	2.78180	+	4.81822i	0.0939348	+	0.162700i	0.909164	−	0.416439i	$-0.136722\pi$
$877$	2.78180	+	4.81822i	0.0939348	+	0.162700i	−0.815229	+	0.579139i	$0.803389\pi$
$878$	−7.53706	+	13.0546i	−0.254364	+	0.440571i
$879$	17.8960			0.603618
$880$	−3.98762			−0.134423
$881$	−11.1342	−	19.2849i	−0.375120	−	0.649726i	0.615225	−	0.788351i	$-0.289065\pi$
$881$	−11.1342	−	19.2849i	−0.375120	−	0.649726i	−0.990345	+	0.138625i	$0.955732\pi$
$882$	−2.88255	+	4.99272i	−0.0970604	+	0.168113i
$883$	18.2687	−	31.6424i	0.614792	−	1.06485i	−0.375629	−	0.926770i	$-0.622573\pi$
$883$	18.2687	−	31.6424i	0.614792	−	1.06485i	0.990421	−	0.138081i	$-0.0440933\pi$
$884$	−6.58217	−	11.4007i	−0.221382	−	0.383446i
$885$	−19.7651			−0.664396
$886$	41.4683			1.39315
$887$	−15.4938	−	26.8361i	−0.520231	−	0.901067i	−0.999723	−	0.0235207i	$-0.992512\pi$
$887$	−15.4938	−	26.8361i	−0.520231	−	0.901067i	0.479492	−	0.877546i	$-0.340821\pi$
$888$	1.64400	+	2.84748i	0.0551689	+	0.0955553i
$889$	−5.94506	−	10.2971i	−0.199391	−	0.345355i
$890$	−7.39307	−	12.8052i	−0.247816	−	0.429230i
$891$	−0.738550	+	1.27921i	−0.0247424	+	0.0428550i
$892$	−8.49814	+	14.7192i	−0.284539	+	0.492836i
$893$	37.7861			1.26446
$894$	−5.97710	−	10.3526i	−0.199904	−	0.346244i
$895$	32.3621			1.08175
$896$	1.11126			0.0371247
$897$	1.70582	−	2.95456i	0.0569556	−	0.0986500i
$898$	4.23491			0.141321
$899$	1.97091	+	3.41372i	0.0657335	+	0.113854i
$900$	−1.14400	+	1.98146i	−0.0381332	+	0.0660486i
$901$	3.38874	+	5.86946i	0.112895	+	0.195540i
$902$	4.28249	−	7.41749i	0.142591	−	0.246975i
$903$	0.758902	−	1.31446i	0.0252547	−	0.0437424i
$904$	7.46108	−	12.9230i	0.248152	−	0.429811i
$905$	3.01671	−	5.22510i	0.100279	−	0.173688i
$906$	−0.323272	+	0.559924i	−0.0107400	+	0.0186022i
$907$	−24.8559	+	43.0517i	−0.825328	+	1.42951i	0.0763412	+	0.997082i	$0.475676\pi$
$907$	−24.8559	+	43.0517i	−0.825328	+	1.42951i	−0.901669	+	0.432427i	$0.857657\pi$
$908$	5.03342	+	8.71814i	0.167040	+	0.289322i
$909$	2.64400	−	4.57954i	0.0876958	−	0.151894i
$910$	7.31453	+	12.6691i	0.242474	+	0.419978i
$911$	−10.6232			−0.351961			−0.175981	−	0.984394i	$-0.556310\pi$
$911$	−10.6232			−0.351961			−0.175981	+	0.984394i	$0.556310\pi$
$912$	3.78799	−	6.56099i	0.125433	−	0.217256i
$913$	17.0022			0.562690
$914$	−15.5439			−0.514148
$915$	7.93199	+	13.7386i	0.262223	+	0.454184i
$916$	−22.8764			−0.755856
$917$	1.33998	−	2.32092i	0.0442501	−	0.0766434i
$918$	−1.34981	+	2.33795i	−0.0445505	+	0.0771637i
$919$	0.644685	+	1.11663i	0.0212662	+	0.0368341i	0.876463	−	0.481470i	$-0.159897\pi$
$919$	0.644685	+	1.11663i	0.0212662	+	0.0368341i	−0.855196	+	0.518304i	$0.826564\pi$
$920$	−0.944368	−	1.63569i	−0.0311349	−	0.0539272i
$921$	−8.51671	−	14.7514i	−0.280635	−	0.486074i
$922$	8.53087	+	14.7759i	0.280949	+	0.486619i
$923$	−0.698818			−0.0230019
$924$	1.64145			0.0539997
$925$	3.76145	+	6.51502i	0.123676	+	0.214213i
$926$	13.9691	−	24.1951i	0.459051	−	0.795101i
$927$	7.03706	−	12.1885i	0.231127	−	0.400324i
$928$	1.08836	+	1.88510i	0.0357273	+	0.0618815i
$929$	−35.6291			−1.16895			−0.584476	−	0.811411i	$-0.698700\pi$
$929$	−35.6291			−1.16895			−0.584476	+	0.811411i	$0.698700\pi$
$930$	4.88874			0.160308
$931$	21.8381	−	37.8247i	0.715716	−	1.23966i
$932$	11.4425	+	19.8190i	0.374812	+	0.649193i
$933$	−11.9294			−0.390552
$934$	−12.0167	+	20.8136i	−0.393199	+	0.681040i
$935$	−10.7651			−0.352056
$936$	2.43818	+	4.22305i	0.0796943	+	0.138035i
$937$	6.07413			0.198433			0.0992165	−	0.995066i	$-0.468366\pi$
$937$	6.07413			0.198433			0.0992165	+	0.995066i	$0.468366\pi$
$938$	−8.60439	−	2.95015i	−0.280943	−	0.0963258i
$939$	8.78985			0.286846
$940$	6.73236	+	11.6608i	0.219585	+	0.380333i
$941$	−40.4582			−1.31890			−0.659451	−	0.751748i	$-0.729211\pi$
$941$	−40.4582			−1.31890			−0.659451	+	0.751748i	$0.729211\pi$
$942$	10.4320	−	18.0687i	0.339893	−	0.588711i
$943$	4.05680			0.132108
$944$	3.66071	+	6.34053i	0.119146	+	0.206367i
$945$	1.50000	−	2.59808i	0.0487950	−	0.0845154i
$946$	2.01748			0.0655938
$947$	2.69606			0.0876103			0.0438051	−	0.999040i	$-0.486052\pi$
$947$	2.69606			0.0876103			0.0438051	+	0.999040i	$0.486052\pi$
$948$	−3.88255	−	6.72477i	−0.126099	−	0.218410i
$949$	−28.2243	+	48.8859i	−0.916200	+	1.58690i
$950$	8.66690	−	15.0115i	0.281191	−	0.487038i
$951$	14.4462	+	25.0215i	0.468449	+	0.811377i
$952$	3.00000			0.0972306
$953$	4.20149			0.136100			0.0680498	−	0.997682i	$-0.478322\pi$
$953$	4.20149			0.136100			0.0680498	+	0.997682i	$0.478322\pi$
$954$	−1.25526	−	2.17417i	−0.0406406	−	0.0703915i
$955$	5.03706	+	8.72445i	0.162996	+	0.282317i
$956$	−9.47524	−	16.4116i	−0.306451	−	0.530789i
$957$	1.60762	+	2.78448i	0.0519670	+	0.0900096i
$958$	18.7942	−	32.5525i	0.607212	−	1.05172i
$959$	−12.2170	+	21.1605i	−0.394508	+	0.683309i
$960$	2.69963			0.0871301
$961$	13.8603	+	24.0068i	0.447108	+	0.774413i
$962$	16.0334			0.516938
$963$	9.57598			0.308582
$964$	5.68725	−	9.85060i	0.183174	−	0.317267i
$965$	−30.1396			−0.970228
$966$	0.388736	+	0.673310i	0.0125074	+	0.0216634i
$967$	−20.3763	+	35.2928i	−0.655257	+	1.13494i	0.326572	+	0.945172i	$0.394106\pi$
$967$	−20.3763	+	35.2928i	−0.655257	+	1.13494i	−0.981829	+	0.189766i	$0.939227\pi$
$968$	−4.40909	−	7.63676i	−0.141713	−	0.245455i
$969$	10.2262	−	17.7122i	0.328512	−	0.568999i
$970$	15.4320	−	26.7290i	0.495491	−	0.858216i
$971$	4.84362	−	8.38940i	0.155439	−	0.269229i	−0.777780	−	0.628537i	$-0.783654\pi$
$971$	4.84362	−	8.38940i	0.155439	−	0.269229i	0.933219	+	0.359308i	$0.116987\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−9.96905	+	17.2669i	−0.319593	+	0.553551i
$974$	−3.52723	+	6.10934i	−0.113020	+	0.195756i
$975$	5.57853	+	9.66230i	0.178656	+	0.309441i
$976$	2.93818	−	5.08907i	0.0940488	−	0.162897i
$977$	−26.5192	−	45.9326i	−0.848424	−	1.46951i	−0.882614	−	0.470098i	$-0.844219\pi$
$977$	−26.5192	−	45.9326i	−0.848424	−	1.46951i	0.0341906	−	0.999415i	$-0.489115\pi$
$978$	−20.2436			−0.647318
$979$	−4.04511	+	7.00634i	−0.129282	+	0.223924i
$980$	15.5636			0.497161
$981$	−13.3214			−0.425320
$982$	−2.10940	−	3.65360i	−0.0673138	−	0.116591i
$983$	−38.8443			−1.23894			−0.619471	−	0.785020i	$-0.712653\pi$
$983$	−38.8443			−1.23894			−0.619471	+	0.785020i	$0.712653\pi$
$984$	−2.89926	+	5.02166i	−0.0924249	+	0.160085i
$985$	−30.6069	+	53.0126i	−0.975216	+	1.68912i
$986$	2.93818	+	5.08907i	0.0935707	+	0.162069i
$987$	−2.77128	−	4.80000i	−0.0882109	−	0.152786i
$988$	−18.4716	−	31.9937i	−0.587660	−	1.01786i
$989$	0.477789	+	0.827554i	0.0151928	+	0.0263147i
$990$	3.98762			0.126735
$991$	18.7280			0.594913			0.297457	−	0.954735i	$-0.403862\pi$
$991$	18.7280			0.594913			0.297457	+	0.954735i	$0.403862\pi$
$992$	−0.905446	−	1.56828i	−0.0287479	−	0.0497929i
$993$	14.0371	−	24.3129i	0.445453	−	0.771547i
$994$	0.0796262	−	0.137917i	0.00252559	−	0.00437445i
$995$	−12.1483	−	21.0415i	−0.385128	−	0.667061i
$996$	−11.5105			−0.364725
$997$	−55.5300			−1.75865			−0.879327	−	0.476219i	$-0.842007\pi$
$997$	−55.5300			−1.75865			−0.879327	+	0.476219i	$0.842007\pi$
$998$	5.03706	−	8.72445i	0.159445	−	0.276168i
$999$	−1.64400	−	2.84748i	−0.0520137	−	0.0900904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	402.2.e.c.37.1	✓	6
3.2	odd	2		1206.2.h.e.37.3		6
67.29	even	3	inner	402.2.e.c.163.1	yes	6
201.29	odd	6		1206.2.h.e.163.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
402.2.e.c.37.1	✓	6	1.1	even	1	trivial
402.2.e.c.163.1	yes	6	67.29	even	3	inner
1206.2.h.e.37.3		6	3.2	odd	2
1206.2.h.e.163.3		6	201.29	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 402 = 2 \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	402.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -2.69963 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555632 - 0.962383i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -2.69963 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555632 - 0.962383i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +(-1.34981 - 2.33795i) q^{10} +(-0.738550 + 1.27921i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.43818 - 4.22305i) q^{13} +1.11126 q^{14} +2.69963 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.34981 - 2.33795i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.78799 - 6.56099i) q^{19} +(1.34981 - 2.33795i) q^{20} +(-0.555632 + 0.962383i) q^{21} -1.47710 q^{22} +(-0.349814 - 0.605896i) q^{23} +1.00000 q^{24} +2.28799 q^{25} +(2.43818 - 4.22305i) q^{26} -1.00000 q^{27} +(0.555632 + 0.962383i) q^{28} +(-1.08836 + 1.88510i) q^{29} +(1.34981 + 2.33795i) q^{30} +(0.905446 - 1.56828i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.738550 - 1.27921i) q^{33} +(1.34981 - 2.33795i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.64400 + 2.84748i) q^{37} +(3.78799 - 6.56099i) q^{38} +(2.43818 + 4.22305i) q^{39} +2.69963 q^{40} +(-2.89926 + 5.02166i) q^{41} -1.11126 q^{42} -1.36584 q^{43} +(-0.738550 - 1.27921i) q^{44} -2.69963 q^{45} +(0.349814 - 0.605896i) q^{46} +(-2.49381 + 4.31941i) q^{47} +(0.500000 + 0.866025i) q^{48} +(2.88255 + 4.99272i) q^{49} +(1.14400 + 1.98146i) q^{50} +(1.34981 + 2.33795i) q^{51} +4.87636 q^{52} -2.51052 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.99381 - 3.45338i) q^{55} +(-0.555632 + 0.962383i) q^{56} +(3.78799 + 6.56099i) q^{57} -2.17673 q^{58} -7.32141 q^{59} +(-1.34981 + 2.33795i) q^{60} +(2.93818 + 5.08907i) q^{61} +1.81089 q^{62} +(0.555632 - 0.962383i) q^{63} +1.00000 q^{64} +(6.58217 + 11.4007i) q^{65} +1.47710 q^{66} +(-7.74288 - 2.65477i) q^{67} +2.69963 q^{68} +(0.349814 + 0.605896i) q^{69} -3.00000 q^{70} +(0.0716537 - 0.124108i) q^{71} -1.00000 q^{72} +(-5.78799 - 10.0251i) q^{73} +(-1.64400 + 2.84748i) q^{74} -2.28799 q^{75} +7.57598 q^{76} +(0.820724 + 1.42154i) q^{77} +(-2.43818 + 4.22305i) q^{78} +(3.88255 - 6.72477i) q^{79} +(1.34981 + 2.33795i) q^{80} +1.00000 q^{81} -5.79851 q^{82} +(-5.75526 - 9.96840i) q^{83} +(-0.555632 - 0.962383i) q^{84} +(3.64400 + 6.31159i) q^{85} +(-0.682918 - 1.18285i) q^{86} +(1.08836 - 1.88510i) q^{87} +(0.738550 - 1.27921i) q^{88} +5.47710 q^{89} +(-1.34981 - 2.33795i) q^{90} -5.41892 q^{91} +0.699628 q^{92} +(-0.905446 + 1.56828i) q^{93} -4.98762 q^{94} +(10.2262 + 17.7122i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.71634 + 9.90099i) q^{97} +(-2.88255 + 4.99272i) q^{98} +(-0.738550 + 1.27921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 4 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 4 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 4 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 6 q^{9} - 2 q^{10} + q^{11} + 3 q^{12} + 3 q^{13} + 6 q^{14} + 4 q^{15} - 3 q^{16} - 2 q^{17} + 3 q^{18} + q^{19} + 2 q^{20} - 3 q^{21} + 2 q^{22} + 4 q^{23} + 6 q^{24} - 10 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{28} + 5 q^{29} + 2 q^{30} - q^{31} + 3 q^{32} - q^{33} + 2 q^{34} - 9 q^{35} - 3 q^{36} - 2 q^{37} - q^{38} - 3 q^{39} + 4 q^{40} + 7 q^{41} - 6 q^{42} + 2 q^{43} + q^{44} - 4 q^{45} - 4 q^{46} + 3 q^{47} + 3 q^{48} - 5 q^{50} + 2 q^{51} - 6 q^{52} + 10 q^{53} - 3 q^{54} - 6 q^{55} - 3 q^{56} - q^{57} + 10 q^{58} - 6 q^{59} - 2 q^{60} - 2 q^{62} + 3 q^{63} + 6 q^{64} + 10 q^{65} - 2 q^{66} + 2 q^{67} + 4 q^{68} - 4 q^{69} - 18 q^{70} - 4 q^{71} - 6 q^{72} - 11 q^{73} + 2 q^{74} + 10 q^{75} - 2 q^{76} - 30 q^{77} + 3 q^{78} + 6 q^{79} + 2 q^{80} + 6 q^{81} + 14 q^{82} - 22 q^{83} - 3 q^{84} + 10 q^{85} + q^{86} - 5 q^{87} - q^{88} + 22 q^{89} - 2 q^{90} + 36 q^{91} - 8 q^{92} + q^{93} + 6 q^{94} + 20 q^{95} - 3 q^{96} + 15 q^{97} + q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 4 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 6 * q^9 - 2 * q^10 + q^11 + 3 * q^12 + 3 * q^13 + 6 * q^14 + 4 * q^15 - 3 * q^16 - 2 * q^17 + 3 * q^18 + q^19 + 2 * q^20 - 3 * q^21 + 2 * q^22 + 4 * q^23 + 6 * q^24 - 10 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^28 + 5 * q^29 + 2 * q^30 - q^31 + 3 * q^32 - q^33 + 2 * q^34 - 9 * q^35 - 3 * q^36 - 2 * q^37 - q^38 - 3 * q^39 + 4 * q^40 + 7 * q^41 - 6 * q^42 + 2 * q^43 + q^44 - 4 * q^45 - 4 * q^46 + 3 * q^47 + 3 * q^48 - 5 * q^50 + 2 * q^51 - 6 * q^52 + 10 * q^53 - 3 * q^54 - 6 * q^55 - 3 * q^56 - q^57 + 10 * q^58 - 6 * q^59 - 2 * q^60 - 2 * q^62 + 3 * q^63 + 6 * q^64 + 10 * q^65 - 2 * q^66 + 2 * q^67 + 4 * q^68 - 4 * q^69 - 18 * q^70 - 4 * q^71 - 6 * q^72 - 11 * q^73 + 2 * q^74 + 10 * q^75 - 2 * q^76 - 30 * q^77 + 3 * q^78 + 6 * q^79 + 2 * q^80 + 6 * q^81 + 14 * q^82 - 22 * q^83 - 3 * q^84 + 10 * q^85 + q^86 - 5 * q^87 - q^88 + 22 * q^89 - 2 * q^90 + 36 * q^91 - 8 * q^92 + q^93 + 6 * q^94 + 20 * q^95 - 3 * q^96 + 15 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

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