LMFDB - Embedded newform 950.2.l.m.351.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.4
Character	$\chi$	$=$	950.351
Dual form			950.2.l.m.701.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(1.28288 - 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(1.16183 - 2.01234i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(1.28288 - 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(1.16183 - 2.01234i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +(1.54750 + 2.68035i) q^{11} +(-0.837341 + 1.45032i) q^{12} +(5.18492 + 4.35067i) q^{13} +(2.18352 + 0.794737i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.818439 - 4.64160i) q^{17} -0.195441 q^{18} +(-0.846315 - 4.27595i) q^{19} +(-0.675731 - 3.83226i) q^{21} +(-2.37091 + 1.98943i) q^{22} +(-2.99540 + 1.09024i) q^{23} +(-1.57369 - 0.572775i) q^{24} +(-3.38422 + 5.86164i) q^{26} +(2.67567 + 4.63440i) q^{27} +(-0.403498 + 2.28835i) q^{28} +(0.115201 - 0.653337i) q^{29} +(2.25407 - 3.90416i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.87056 + 1.77274i) q^{33} +(4.42896 - 1.61201i) q^{34} +(-0.0339381 - 0.192472i) q^{36} +9.57421 q^{37} +(4.06403 - 1.57597i) q^{38} +11.3350 q^{39} +(1.86510 - 1.56501i) q^{41} +(3.65670 - 1.33093i) q^{42} +(2.05525 + 0.748052i) q^{43} +(-2.37091 - 1.98943i) q^{44} +(-1.59382 - 2.76058i) q^{46} +(-1.08992 + 6.18124i) q^{47} +(0.290805 - 1.64924i) q^{48} +(0.800316 + 1.38619i) q^{49} +(-6.04648 - 5.07360i) q^{51} +(-6.36025 - 2.31494i) q^{52} +(9.43800 - 3.43515i) q^{53} +(-4.09937 + 3.43978i) q^{54} -2.32365 q^{56} +(-5.68863 - 4.57451i) q^{57} +0.663415 q^{58} +(-1.77002 - 10.0383i) q^{59} +(-3.49881 + 1.27346i) q^{61} +(4.23626 + 1.54187i) q^{62} +(0.347890 + 0.291915i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.900044 + 5.10440i) q^{66} +(-0.920817 + 5.22221i) q^{67} +(2.35660 + 4.08175i) q^{68} +(-2.66914 + 4.62309i) q^{69} +(-11.0982 - 4.03942i) q^{71} +(0.183655 - 0.0668449i) q^{72} +(-1.96449 + 1.64840i) q^{73} +(1.66254 + 9.42875i) q^{74} +(2.25774 + 3.72862i) q^{76} +7.19172 q^{77} +(1.96830 + 11.1628i) q^{78} +(-12.6337 + 10.6009i) q^{79} +(7.87038 + 2.86458i) q^{81} +(1.86510 + 1.56501i) q^{82} +(-3.21477 + 5.56814i) q^{83} +(1.94569 + 3.37003i) q^{84} +(-0.379796 + 2.15393i) q^{86} +(-0.555505 - 0.962162i) q^{87} +(1.54750 - 2.68035i) q^{88} +(-6.47935 - 5.43682i) q^{89} +(14.7790 - 5.37912i) q^{91} +(2.44187 - 2.04898i) q^{92} +(-1.31099 - 7.43499i) q^{93} -6.27659 q^{94} +1.67468 q^{96} +(-0.923151 - 5.23545i) q^{97} +(-1.22615 + 1.02887i) q^{98} +(-0.568413 + 0.206885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) $ 30 * q + 12 * q^7 - 15 * q^8	$ 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.28288	−	1.07646i	0.740671	−	0.621497i	−0.192346	−	0.981327i	$-0.561610\pi$
$3$	1.28288	−	1.07646i	0.740671	−	0.621497i	0.933018	+	0.359830i	$0.117165\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	1.28288	+	1.07646i	0.523734	+	0.439465i
$7$	1.16183	−	2.01234i	0.439129	−	0.760594i	−0.558493	−	0.829509i	$-0.688620\pi$
$7$	1.16183	−	2.01234i	0.439129	−	0.760594i	0.997623	+	0.0689147i	$0.0219536\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.0339381	+	0.192472i	−0.0113127	+	0.0641574i
$10$		0			0
$11$	1.54750	+	2.68035i	0.466589	+	0.808156i	0.999272	−	0.0381589i	$-0.0121493\pi$
$11$	1.54750	+	2.68035i	0.466589	+	0.808156i	−0.532682	+	0.846315i	$0.678816\pi$
$12$	−0.837341	+	1.45032i	−0.241719	+	0.418670i
$13$	5.18492	+	4.35067i	1.43804	+	1.20666i	0.940763	+	0.339065i	$0.110111\pi$
$13$	5.18492	+	4.35067i	1.43804	+	1.20666i	0.497275	+	0.867593i	$0.334334\pi$
$14$	2.18352	+	0.794737i	0.583570	+	0.212402i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.818439	−	4.64160i	−0.198501	−	1.12575i	−0.907345	−	0.420388i	$-0.861894\pi$
$17$	−0.818439	−	4.64160i	−0.198501	−	1.12575i	0.708844	−	0.705365i	$-0.249217\pi$
$18$	−0.195441			−0.0460660
$19$	−0.846315	−	4.27595i	−0.194158	−	0.980970i
$19$	−0.846315	−	4.27595i	−0.194158	−	0.980970i
$20$		0			0
$21$	−0.675731	−	3.83226i	−0.147457	−	0.836268i
$22$	−2.37091	+	1.98943i	−0.505480	+	0.424148i
$23$	−2.99540	+	1.09024i	−0.624585	+	0.227330i	−0.634873	−	0.772617i	$-0.718947\pi$
$23$	−2.99540	+	1.09024i	−0.624585	+	0.227330i	0.0102880	+	0.999947i	$0.496725\pi$
$24$	−1.57369	−	0.572775i	−0.321227	−	0.116917i
$25$		0			0
$26$	−3.38422	+	5.86164i	−0.663700	+	1.14956i
$27$	2.67567	+	4.63440i	0.514934	+	0.891891i
$28$	−0.403498	+	2.28835i	−0.0762540	+	0.432458i
$29$	0.115201	−	0.653337i	0.0213923	−	0.121322i	−0.972242	−	0.233979i	$-0.924825\pi$
$29$	0.115201	−	0.653337i	0.0213923	−	0.121322i	0.993634	+	0.112658i	$0.0359363\pi$
$30$		0			0
$31$	2.25407	−	3.90416i	0.404842	−	0.701207i	−0.589461	−	0.807797i	$-0.700660\pi$
$31$	2.25407	−	3.90416i	0.404842	−	0.701207i	0.994303	+	0.106590i	$0.0339932\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	4.87056	+	1.77274i	0.847856	+	0.308594i
$34$	4.42896	−	1.61201i	0.759561	−	0.276458i
$35$		0			0
$36$	−0.0339381	−	0.192472i	−0.00565634	−	0.0320787i
$37$	9.57421			1.57399			0.786995	−	0.616959i	$-0.211636\pi$
$37$	9.57421			1.57399			0.786995	+	0.616959i	$0.211636\pi$
$38$	4.06403	−	1.57597i	0.659272	−	0.255656i
$39$	11.3350			1.81505
$40$		0			0
$41$	1.86510	−	1.56501i	0.291280	−	0.244413i	−0.485424	−	0.874279i	$-0.661335\pi$
$41$	1.86510	−	1.56501i	0.291280	−	0.244413i	0.776704	+	0.629866i	$0.216890\pi$
$42$	3.65670	−	1.33093i	0.564241	−	0.205367i
$43$	2.05525	+	0.748052i	0.313423	+	0.114077i	0.493942	−	0.869495i	$-0.335555\pi$
$43$	2.05525	+	0.748052i	0.313423	+	0.114077i	−0.180519	+	0.983572i	$0.557778\pi$
$44$	−2.37091	−	1.98943i	−0.357428	−	0.299918i
$45$		0			0
$46$	−1.59382	−	2.76058i	−0.234996	−	0.407025i
$47$	−1.08992	+	6.18124i	−0.158981	+	0.901626i	0.796074	+	0.605199i	$0.206906\pi$
$47$	−1.08992	+	6.18124i	−0.158981	+	0.901626i	−0.955055	+	0.296427i	$0.904205\pi$
$48$	0.290805	−	1.64924i	0.0419741	−	0.238047i
$49$	0.800316	+	1.38619i	0.114331	+	0.198027i
$50$		0			0
$51$	−6.04648	−	5.07360i	−0.846676	−	0.710446i
$52$	−6.36025	−	2.31494i	−0.882008	−	0.321025i
$53$	9.43800	−	3.43515i	1.29641	−	0.471854i	0.400583	−	0.916260i	$-0.368807\pi$
$53$	9.43800	−	3.43515i	1.29641	−	0.471854i	0.895825	+	0.444406i	$0.146585\pi$
$54$	−4.09937	+	3.43978i	−0.557854	+	0.468095i
$55$		0			0
$56$	−2.32365			−0.310511
$57$	−5.68863	−	4.57451i	−0.753477	−	0.605908i
$58$	0.663415			0.0871107
$59$	−1.77002	−	10.0383i	−0.230437	−	1.30687i	−0.852014	−	0.523519i	$-0.824619\pi$
$59$	−1.77002	−	10.0383i	−0.230437	−	1.30687i	0.621577	−	0.783353i	$-0.286492\pi$
$60$		0			0
$61$	−3.49881	+	1.27346i	−0.447976	+	0.163050i	−0.556150	−	0.831082i	$-0.687722\pi$
$61$	−3.49881	+	1.27346i	−0.447976	+	0.163050i	0.108174	+	0.994132i	$0.465500\pi$
$62$	4.23626	+	1.54187i	0.538005	+	0.195818i
$63$	0.347890	+	0.291915i	0.0438300	+	0.0367778i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−0.900044	+	5.10440i	−0.110788	+	0.628308i
$67$	−0.920817	+	5.22221i	−0.112496	+	0.637995i	0.875464	+	0.483283i	$0.160556\pi$
$67$	−0.920817	+	5.22221i	−0.112496	+	0.637995i	−0.987960	+	0.154711i	$0.950555\pi$
$68$	2.35660	+	4.08175i	0.285780	+	0.494985i
$69$	−2.66914	+	4.62309i	−0.321327	+	0.556554i
$70$		0			0
$71$	−11.0982	−	4.03942i	−1.31711	−	0.479390i	−0.414582	−	0.910012i	$-0.636072\pi$
$71$	−11.0982	−	4.03942i	−1.31711	−	0.479390i	−0.902533	+	0.430621i	$0.858294\pi$
$72$	0.183655	−	0.0668449i	0.0216439	−	0.00787775i
$73$	−1.96449	+	1.64840i	−0.229926	+	0.192931i	−0.750471	−	0.660903i	$-0.770173\pi$
$73$	−1.96449	+	1.64840i	−0.229926	+	0.192931i	0.520545	+	0.853834i	$0.325729\pi$
$74$	1.66254	+	9.42875i	0.193267	+	1.09607i
$75$		0			0
$76$	2.25774	+	3.72862i	0.258980	+	0.427702i
$77$	7.19172			0.819572
$78$	1.96830	+	11.1628i	0.222866	+	1.26393i
$79$	−12.6337	+	10.6009i	−1.42140	+	1.19270i	−0.470821	+	0.882229i	$0.656042\pi$
$79$	−12.6337	+	10.6009i	−1.42140	+	1.19270i	−0.950583	+	0.310470i	$0.899513\pi$
$80$		0			0
$81$	7.87038	+	2.86458i	0.874486	+	0.318287i
$82$	1.86510	+	1.56501i	0.205966	+	0.172826i
$83$	−3.21477	+	5.56814i	−0.352866	+	0.611183i	−0.986750	−	0.162246i	$-0.948126\pi$
$83$	−3.21477	+	5.56814i	−0.352866	+	0.611183i	0.633884	+	0.773428i	$0.281460\pi$
$84$	1.94569	+	3.37003i	0.212292	+	0.367701i
$85$		0			0
$86$	−0.379796	+	2.15393i	−0.0409544	+	0.232264i
$87$	−0.555505	−	0.962162i	−0.0595564	−	0.103155i
$88$	1.54750	−	2.68035i	0.164964	−	0.285726i
$89$	−6.47935	−	5.43682i	−0.686810	−	0.576302i	0.231178	−	0.972912i	$-0.425742\pi$
$89$	−6.47935	−	5.43682i	−0.686810	−	0.576302i	−0.917987	+	0.396610i	$0.870187\pi$
$90$		0			0
$91$	14.7790	−	5.37912i	1.54926	−	0.563885i
$92$	2.44187	−	2.04898i	0.254583	−	0.213620i
$93$	−1.31099	−	7.43499i	−0.135943	−	0.770972i
$94$	−6.27659			−0.647381
$95$		0			0
$96$	1.67468			0.170921
$97$	−0.923151	−	5.23545i	−0.0937318	−	0.531579i	−0.995129	−	0.0985853i	$-0.968568\pi$
$97$	−0.923151	−	5.23545i	−0.0937318	−	0.531579i	0.901397	−	0.432994i	$-0.142543\pi$
$98$	−1.22615	+	1.02887i	−0.123860	+	0.103931i
$99$	−0.568413	+	0.206885i	−0.0571276	+	0.0207927i
$100$		0			0
$101$	−9.73383	−	8.16765i	−0.968552	−	0.812712i	0.0137710	−	0.999905i	$-0.495616\pi$
$101$	−9.73383	−	8.16765i	−0.968552	−	0.812712i	−0.982323	+	0.187193i	$0.940061\pi$
$102$	3.94656	−	6.83564i	0.390767	−	0.676829i
$103$	−4.56327	−	7.90381i	−0.449632	−	0.778785i	0.548730	−	0.836000i	$-0.315112\pi$
$103$	−4.56327	−	7.90381i	−0.449632	−	0.778785i	−0.998362	+	0.0572143i	$0.981778\pi$
$104$	1.17533	−	6.66561i	0.115250	−	0.653616i
$105$		0			0
$106$	5.02185	+	8.69811i	0.487766	+	0.844835i
$107$	−4.47737	+	7.75503i	−0.432843	+	0.749707i	−0.997117	−	0.0758813i	$-0.975823\pi$
$107$	−4.47737	+	7.75503i	−0.432843	+	0.749707i	0.564274	+	0.825588i	$0.309156\pi$
$108$	−4.09937	−	3.43978i	−0.394462	−	0.330993i
$109$	9.01456	+	3.28103i	0.863439	+	0.314266i	0.735507	−	0.677517i	$-0.236944\pi$
$109$	9.01456	+	3.28103i	0.863439	+	0.314266i	0.127932	+	0.991783i	$0.459166\pi$
$110$		0			0
$111$	12.2826	−	10.3063i	1.16581	−	0.978230i
$112$	−0.403498	−	2.28835i	−0.0381270	−	0.216229i
$113$	3.77955			0.355551			0.177775	−	0.984071i	$-0.443110\pi$
$113$	3.77955			0.355551			0.177775	+	0.984071i	$0.443110\pi$
$114$	3.51719	−	6.39656i	0.329415	−	0.599093i
$115$		0			0
$116$	0.115201	+	0.653337i	0.0106961	+	0.0606608i
$117$	−1.01335	+	0.850300i	−0.0936841	+	0.0786103i
$118$	9.57841	−	3.48626i	0.881764	−	0.320936i
$119$	−10.2914	−	3.74575i	−0.943409	−	0.343373i
$120$		0			0
$121$	0.710478	−	1.23058i	0.0645889	−	0.111871i
$122$	−1.86168	−	3.22452i	−0.168548	−	0.291934i
$123$	0.708029	−	4.01543i	0.0638408	−	0.362059i
$124$	−0.782829	+	4.43964i	−0.0703001	+	0.398692i
$125$		0			0
$126$	−0.227069	+	0.393295i	−0.0202289	+	0.0350375i
$127$	−1.37966	−	1.15767i	−0.122425	−	0.102727i	0.579520	−	0.814958i	$-0.303240\pi$
$127$	−1.37966	−	1.15767i	−0.122425	−	0.102727i	−0.701945	+	0.712231i	$0.747685\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	3.44190	−	1.25275i	0.303042	−	0.110298i
$130$		0			0
$131$	1.39065	+	7.88678i	0.121502	+	0.689072i	0.983324	+	0.181861i	$0.0582122\pi$
$131$	1.39065	+	7.88678i	0.121502	+	0.689072i	−0.861822	+	0.507210i	$0.830677\pi$
$132$	−5.18314			−0.451135
$133$	−9.58795	−	3.26484i	−0.831381	−	0.283097i
$134$	−5.30277			−0.458090
$135$		0			0
$136$	−3.61052	+	3.02959i	−0.309600	+	0.259785i
$137$	−18.0566	+	6.57208i	−1.54268	+	0.561491i	−0.966687	−	0.255961i	$-0.917608\pi$
$137$	−18.0566	+	6.57208i	−1.54268	+	0.561491i	−0.575996	+	0.817452i	$0.695386\pi$
$138$	−5.01634	−	1.82580i	−0.427020	−	0.155422i
$139$	−0.826741	−	0.693718i	−0.0701233	−	0.0588404i	0.607052	−	0.794662i	$-0.292352\pi$
$139$	−0.826741	−	0.693718i	−0.0701233	−	0.0588404i	−0.677176	+	0.735821i	$0.736796\pi$
$140$		0			0
$141$	5.25565	+	9.10305i	0.442605	+	0.766615i
$142$	2.05087	−	11.6310i	0.172105	−	0.976055i
$143$	−3.63764	+	20.6301i	−0.304195	+	1.72517i
$144$	0.0977207	+	0.169257i	0.00814339	+	0.0141048i
$145$		0			0
$146$	−1.96449	−	1.64840i	−0.162582	−	0.136423i
$147$	2.51889	+	0.916801i	0.207755	+	0.0756165i
$148$	−8.99681	+	3.27457i	−0.739533	+	0.269168i
$149$	−2.12048	+	1.77929i	−0.173716	+	0.145765i	−0.725501	−	0.688222i	$-0.758392\pi$
$149$	−2.12048	+	1.77929i	−0.173716	+	0.145765i	0.551784	+	0.833987i	$0.313947\pi$
$150$		0			0
$151$	−10.2734			−0.836034			−0.418017	−	0.908439i	$-0.637275\pi$
$151$	−10.2734			−0.836034			−0.418017	+	0.908439i	$0.637275\pi$
$152$	−3.27992	+	2.87091i	−0.266037	+	0.232861i
$153$	0.921155			0.0744710
$154$	1.24883	+	7.08246i	0.100633	+	0.570721i
$155$		0			0
$156$	−10.6514	+	3.87679i	−0.852794	+	0.310392i
$157$	6.55116	+	2.38443i	0.522840	+	0.190298i	0.589938	−	0.807448i	$-0.299152\pi$
$157$	6.55116	+	2.38443i	0.522840	+	0.190298i	−0.0670986	+	0.997746i	$0.521374\pi$
$158$	−12.6337	−	10.6009i	−1.00508	−	0.843366i
$159$	8.41001	−	14.5666i	0.666957	−	1.15520i
$160$		0			0
$161$	−1.28621	+	7.29445i	−0.101367	+	0.574883i
$162$	−1.45439	+	8.24824i	−0.114267	+	0.648043i
$163$	−2.51501	−	4.35612i	−0.196991	−	0.341198i	0.750561	−	0.660802i	$-0.229784\pi$
$163$	−2.51501	−	4.35612i	−0.196991	−	0.341198i	−0.947551	+	0.319604i	$0.896450\pi$
$164$	−1.21736	+	2.10853i	−0.0950598	+	0.164648i
$165$		0			0
$166$	−6.04178	−	2.19903i	−0.468933	−	0.170678i
$167$	−5.55242	+	2.02091i	−0.429659	+	0.156383i	−0.547792	−	0.836615i	$-0.684531\pi$
$167$	−5.55242	+	2.02091i	−0.429659	+	0.156383i	0.118133	+	0.992998i	$0.462309\pi$
$168$	−2.98097	+	2.50133i	−0.229987	+	0.192982i
$169$	5.69769	+	32.3132i	0.438284	+	2.48563i
$170$		0			0
$171$	0.851724	−	0.0177748i	0.0651330	−	0.00135927i
$172$	−2.18716			−0.166769
$173$	−3.35907	−	19.0502i	−0.255386	−	1.44836i	−0.795081	−	0.606503i	$-0.792572\pi$
$173$	−3.35907	−	19.0502i	−0.255386	−	1.44836i	0.539695	−	0.841860i	$-0.318539\pi$
$174$	0.851083	−	0.714143i	0.0645204	−	0.0541391i
$175$		0			0
$176$	2.90835	+	1.05855i	0.219225	+	0.0797915i
$177$	−13.0766	−	10.9725i	−0.982895	−	0.824747i
$178$	4.22909	−	7.32501i	0.316984	−	0.549032i
$179$	3.95499	+	6.85025i	0.295610	+	0.512012i	0.975127	−	0.221648i	$-0.0711437\pi$
$179$	3.95499	+	6.85025i	0.295610	+	0.512012i	−0.679517	+	0.733660i	$0.737810\pi$
$180$		0			0
$181$	−2.41624	+	13.7032i	−0.179597	+	1.01855i	0.753105	+	0.657900i	$0.228555\pi$
$181$	−2.41624	+	13.7032i	−0.179597	+	1.01855i	−0.932702	+	0.360647i	$0.882556\pi$
$182$	7.86375	+	13.6204i	0.582900	+	1.00961i
$183$	−3.11772	+	5.40004i	−0.230468	+	0.399183i
$184$	2.44187	+	2.04898i	0.180017	+	0.151052i
$185$		0			0
$186$	7.09438	−	2.58214i	0.520185	−	0.189332i
$187$	11.1746	−	9.37659i	0.817166	−	0.685684i
$188$	−1.08992	−	6.18124i	−0.0794905	−	0.450813i
$189$	12.4347			0.904490
$190$		0			0
$191$	−20.3770			−1.47442			−0.737212	−	0.675661i	$-0.763858\pi$
$191$	−20.3770			−1.47442			−0.737212	+	0.675661i	$0.763858\pi$
$192$	0.290805	+	1.64924i	0.0209871	+	0.119024i
$193$	−14.1218	+	11.8496i	−1.01651	+	0.852955i	−0.989185	−	0.146671i	$-0.953144\pi$
$193$	−14.1218	+	11.8496i	−1.01651	+	0.852955i	−0.0273270	+	0.999627i	$0.508700\pi$
$194$	4.99561	−	1.81825i	0.358664	−	0.130543i
$195$		0			0
$196$	−1.22615	−	1.02887i	−0.0875825	−	0.0734904i
$197$	4.44834	−	7.70476i	0.316931	−	0.548941i	−0.662915	−	0.748695i	$-0.730681\pi$
$197$	4.44834	−	7.70476i	0.316931	−	0.548941i	0.979846	+	0.199754i	$0.0640142\pi$
$198$	−0.302446	−	0.523852i	−0.0214939	−	0.0372285i
$199$	4.19553	−	23.7940i	0.297413	−	1.68671i	−0.359817	−	0.933023i	$-0.617161\pi$
$199$	4.19553	−	23.7940i	0.297413	−	1.68671i	0.657230	−	0.753690i	$-0.271728\pi$
$200$		0			0
$201$	4.44023	+	7.69070i	0.313190	+	0.542460i
$202$	6.35330	−	11.0042i	0.447017	−	0.774256i
$203$	−1.18089	−	0.990888i	−0.0828825	−	0.0695467i
$204$	7.41710	+	2.69960i	0.519301	+	0.189010i
$205$		0			0
$206$	6.99133	−	5.86642i	0.487109	−	0.408733i
$207$	−0.108182	−	0.613532i	−0.00751919	−	0.0426435i
$208$	6.76843			0.469306
$209$	10.1514	−	8.88546i	0.702185	−	0.614620i
$210$		0			0
$211$	0.876981	+	4.97361i	0.0603739	+	0.342397i	1.00000		0.000194382i	$6.18739e-5\pi$
$211$	0.876981	+	4.97361i	0.0603739	+	0.342397i	−0.939626	+	0.342203i	$0.888827\pi$
$212$	−7.69393	+	6.45597i	−0.528421	+	0.443398i
$213$	−18.5860	+	6.76474i	−1.27349	+	0.463512i
$214$	−8.41470	−	3.06270i	−0.575217	−	0.209362i
$215$		0			0
$216$	2.67567	−	4.63440i	0.182057	−	0.315331i
$217$	−5.23767	−	9.07191i	−0.355556	−	0.615841i
$218$	−1.66582	+	9.44736i	−0.112824	+	0.639856i
$219$	−0.745759	+	4.22941i	−0.0503937	+	0.285797i
$220$		0			0
$221$	15.9505	−	27.6271i	1.07295	−	1.85840i
$222$	12.2826	+	10.3063i	0.824352	+	0.691713i
$223$	−2.60238	−	0.947189i	−0.174268	−	0.0634285i	0.253412	−	0.967358i	$-0.418447\pi$
$223$	−2.60238	−	0.947189i	−0.174268	−	0.0634285i	−0.427681	+	0.903930i	$0.640669\pi$
$224$	2.18352	−	0.794737i	0.145893	−	0.0531006i
$225$		0			0
$226$	0.656313	+	3.72213i	0.0436573	+	0.247593i
$227$	−11.4199			−0.757967			−0.378984	−	0.925403i	$-0.623726\pi$
$227$	−11.4199			−0.757967			−0.378984	+	0.925403i	$0.623726\pi$
$228$	6.91014	+	2.35300i	0.457635	+	0.155831i
$229$	−15.0259			−0.992937			−0.496469	−	0.868055i	$-0.665370\pi$
$229$	−15.0259			−0.992937			−0.496469	+	0.868055i	$0.665370\pi$
$230$		0			0
$231$	9.22611	−	7.74163i	0.607034	−	0.509362i
$232$	−0.623407	+	0.226901i	−0.0409286	+	0.0148968i
$233$	7.44632	+	2.71024i	0.487825	+	0.177554i	0.574210	−	0.818708i	$-0.305309\pi$
$233$	7.44632	+	2.71024i	0.487825	+	0.177554i	−0.0863852	+	0.996262i	$0.527532\pi$
$234$	−1.01335	−	0.850300i	−0.0662447	−	0.0555859i
$235$		0			0
$236$	5.09657	+	8.82751i	0.331758	+	0.574622i
$237$	−4.79600	+	27.1995i	−0.311534	+	1.76680i
$238$	1.90177	−	10.7855i	0.123273	−	0.699118i
$239$	−7.40667	−	12.8287i	−0.479097	−	0.829821i	0.520615	−	0.853791i	$-0.325703\pi$
$239$	−7.40667	−	12.8287i	−0.479097	−	0.829821i	−0.999713	+	0.0239703i	$0.992369\pi$
$240$		0			0
$241$	−6.26586	−	5.25768i	−0.403620	−	0.338677i	0.418271	−	0.908322i	$-0.362636\pi$
$241$	−6.26586	−	5.25768i	−0.403620	−	0.338677i	−0.821891	+	0.569645i	$0.807081\pi$
$242$	1.33526	+	0.485995i	0.0858338	+	0.0312410i
$243$	−1.90549	+	0.693542i	−0.122237	+	0.0444908i
$244$	2.85225	−	2.39333i	0.182597	−	0.153217i
$245$		0			0
$246$	4.07738			0.259964
$247$	14.2152	−	25.8525i	0.904488	−	1.64496i
$248$	−4.50813			−0.286267
$249$	1.86974	+	10.6038i	0.118490	+	0.671991i
$250$		0			0
$251$	−0.806527	+	0.293552i	−0.0509075	+	0.0185288i	−0.367348	−	0.930083i	$-0.619734\pi$
$251$	−0.806527	+	0.293552i	−0.0509075	+	0.0185288i	0.316441	+	0.948612i	$0.397512\pi$
$252$	−0.426751	−	0.155324i	−0.0268828	−	0.00978452i
$253$	−7.55761	−	6.34159i	−0.475143	−	0.398692i
$254$	0.900509	−	1.55973i	0.0565030	−	0.0978660i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.97617	−	11.2074i	0.123270	−	0.699101i	−0.859050	−	0.511892i	$-0.828945\pi$
$257$	1.97617	−	11.2074i	0.123270	−	0.699101i	0.982320	−	0.187209i	$-0.0599441\pi$
$258$	1.83140	+	3.17207i	0.114018	+	0.197484i
$259$	11.1236	−	19.2666i	0.691185	−	1.19717i
$260$		0			0
$261$	0.121839	+	0.0443459i	0.00754168	+	0.00274495i
$262$	−7.52548	+	2.73905i	−0.464926	+	0.169219i
$263$	9.72539	−	8.16057i	0.599693	−	0.503202i	−0.291654	−	0.956524i	$-0.594206\pi$
$263$	9.72539	−	8.16057i	0.599693	−	0.503202i	0.891347	+	0.453322i	$0.149761\pi$
$264$	−0.900044	−	5.10440i	−0.0553939	−	0.314154i
$265$		0			0
$266$	1.55031	−	10.0092i	0.0950554	−	0.613705i
$267$	−14.1648			−0.866870
$268$	−0.920817	−	5.22221i	−0.0562478	−	0.318997i
$269$	−16.7636	+	14.0663i	−1.02209	+	0.857639i	−0.989889	−	0.141842i	$-0.954698\pi$
$269$	−16.7636	+	14.0663i	−1.02209	+	0.857639i	−0.0322055	+	0.999481i	$0.510253\pi$
$270$		0			0
$271$	13.2666	+	4.82863i	0.805886	+	0.293319i	0.711924	−	0.702257i	$-0.247824\pi$
$271$	13.2666	+	4.82863i	0.805886	+	0.293319i	0.0939629	+	0.995576i	$0.470046\pi$
$272$	−3.61052	−	3.02959i	−0.218920	−	0.183696i
$273$	13.1693	−	22.8099i	0.797041	−	1.38052i
$274$	−9.60774	−	16.6411i	−0.580425	−	1.00533i
$275$		0			0
$276$	0.926983	−	5.25718i	0.0557978	−	0.316445i
$277$	9.12112	+	15.7982i	0.548035	+	0.949225i	0.998409	+	0.0563847i	$0.0179573\pi$
$277$	9.12112	+	15.7982i	0.548035	+	0.949225i	−0.450374	+	0.892840i	$0.648709\pi$
$278$	0.539617	−	0.934644i	0.0323641	−	0.0560562i
$279$	0.674943	+	0.566344i	0.0404078	+	0.0339062i
$280$		0			0
$281$	−12.2228	+	4.44872i	−0.729149	+	0.265389i	−0.679805	−	0.733393i	$-0.737935\pi$
$281$	−12.2228	+	4.44872i	−0.729149	+	0.265389i	−0.0493445	+	0.998782i	$0.515713\pi$
$282$	−8.05212	+	6.75653i	−0.479497	+	0.402346i
$283$	−0.505725	−	2.86811i	−0.0300622	−	0.170491i	0.966080	−	0.258242i	$-0.0831432\pi$
$283$	−0.505725	−	2.86811i	−0.0300622	−	0.170491i	−0.996142	+	0.0877507i	$0.972032\pi$
$284$	11.8105			0.700822
$285$		0			0
$286$	−20.9483			−1.23870
$287$	−0.982405	−	5.57149i	−0.0579895	−	0.328875i
$288$	−0.149717	+	0.125627i	−0.00882215	+	0.00740266i
$289$	−4.89983	+	1.78339i	−0.288225	+	0.104905i
$290$		0			0
$291$	−6.82007	−	5.72272i	−0.399799	−	0.335472i
$292$	1.28223	−	2.22089i	0.0750368	−	0.129968i
$293$	0.680540	+	1.17873i	0.0397575	+	0.0688621i	0.885219	−	0.465174i	$-0.154008\pi$
$293$	0.680540	+	1.17873i	0.0397575	+	0.0688621i	−0.845462	+	0.534036i	$0.820675\pi$
$294$	−0.465472	+	2.63982i	−0.0271469	+	0.153958i
$295$		0			0
$296$	−4.78710	−	8.29151i	−0.278245	−	0.481934i
$297$	−8.28122	+	14.3435i	−0.480525	+	0.832294i
$298$	−2.12048	−	1.77929i	−0.122836	−	0.103072i
$299$	−20.2742	−	7.37920i	−1.17249	−	0.426750i
$300$		0			0
$301$	3.89319	−	3.26677i	0.224400	−	0.188294i
$302$	−1.78395	−	10.1173i	−0.102655	−	0.582184i
$303$	−21.2795			−1.22248
$304$	−3.39684	−	2.73157i	−0.194822	−	0.156666i
$305$		0			0
$306$	0.159957	+	0.907161i	0.00914413	+	0.0518589i
$307$	1.00946	−	0.847040i	0.0576131	−	0.0483431i	−0.613526	−	0.789674i	$-0.710250\pi$
$307$	1.00946	−	0.847040i	0.0576131	−	0.0483431i	0.671140	+	0.741331i	$0.265805\pi$
$308$	−6.75800	+	2.45971i	−0.385073	+	0.140155i
$309$	−14.3623	−	5.22745i	−0.817042	−	0.297379i
$310$		0			0
$311$	2.94243	−	5.09644i	0.166850	−	0.288993i	−0.770461	−	0.637487i	$-0.779974\pi$
$311$	2.94243	−	5.09644i	0.166850	−	0.288993i	0.937311	+	0.348495i	$0.113307\pi$
$312$	−5.66749	−	9.81637i	−0.320858	−	0.555743i
$313$	−1.08099	+	6.13058i	−0.0611010	+	0.346521i	0.938896	+	0.344200i	$0.111850\pi$
$313$	−1.08099	+	6.13058i	−0.0611010	+	0.346521i	−0.999997	+	0.00232080i	$0.999261\pi$
$314$	−1.21061	+	6.86569i	−0.0683185	+	0.387453i
$315$		0			0
$316$	8.24607	−	14.2826i	0.463878	−	0.803460i
$317$	16.4488	+	13.8022i	0.923856	+	0.775207i	0.974704	−	0.223500i	$-0.0717481\pi$
$317$	16.4488	+	13.8022i	0.923856	+	0.775207i	−0.0508485	+	0.998706i	$0.516193\pi$
$318$	15.8056	+	5.75278i	0.886337	+	0.322600i
$319$	1.92945	−	0.702261i	0.108028	−	0.0393190i
$320$		0			0
$321$	2.60408	+	14.7685i	0.145346	+	0.824297i
$322$	−7.40697			−0.412775
$323$	−19.1546	+	7.42786i	−1.06579	+	0.413297i
$324$	−8.37548			−0.465304
$325$		0			0
$326$	3.85322	−	3.23323i	0.213410	−	0.179072i
$327$	15.0965	−	5.49469i	0.834840	−	0.303857i
$328$	−2.28789	−	0.832723i	−0.126327	−	0.0459794i
$329$	11.1725	+	9.37482i	0.615959	+	0.516851i
$330$		0			0
$331$	−10.2669	−	17.7827i	−0.564318	−	0.977427i	−0.997113	−	0.0759348i	$-0.975806\pi$
$331$	−10.2669	−	17.7827i	−0.564318	−	0.977427i	0.432795	−	0.901492i	$-0.357527\pi$
$332$	1.11648	−	6.33185i	0.0612746	−	0.347506i
$333$	−0.324930	+	1.84277i	−0.0178061	+	0.100983i
$334$	−2.95438	−	5.11713i	−0.161656	−	0.279997i
$335$		0			0
$336$	−2.98097	−	2.50133i	−0.162625	−	0.136459i
$337$	30.5745	+	11.1282i	1.66550	+	0.606192i	0.991213	−	0.132277i	$-0.0422288\pi$
$337$	30.5745	+	11.1282i	1.66550	+	0.606192i	0.674287	+	0.738469i	$0.264451\pi$
$338$	−30.8329	+	11.2223i	−1.67709	+	0.610411i
$339$	4.84872	−	4.06856i	0.263346	−	0.220974i
$340$		0			0
$341$	13.9527			0.755580
$342$	0.165405	+	0.835698i	0.00894408	+	0.0451894i
$343$	19.9849			1.07908
$344$	−0.379796	−	2.15393i	−0.0204772	−	0.116132i
$345$		0			0
$346$	18.1775	−	6.61608i	0.977230	−	0.355683i
$347$	−0.243254	−	0.0885371i	−0.0130585	−	0.00475292i	0.335483	−	0.942046i	$-0.391101\pi$
$347$	−0.243254	−	0.0885371i	−0.0130585	−	0.00475292i	−0.348541	+	0.937293i	$0.613323\pi$
$348$	0.851083	+	0.714143i	0.0456228	+	0.0382821i
$349$	15.5129	−	26.8692i	0.830387	−	1.43827i	−0.0673443	−	0.997730i	$-0.521453\pi$
$349$	15.5129	−	26.8692i	0.830387	−	1.43827i	0.897732	−	0.440543i	$-0.145214\pi$
$350$		0			0
$351$	−6.28958	+	35.6700i	−0.335713	+	1.90392i
$352$	−0.537442	+	3.04798i	−0.0286457	+	0.162458i
$353$	5.19728	+	9.00195i	0.276623	+	0.479125i	0.970543	−	0.240927i	$-0.0774513\pi$
$353$	5.19728	+	9.00195i	0.276623	+	0.479125i	−0.693920	+	0.720052i	$0.744118\pi$
$354$	8.53513	−	14.7833i	0.453637	−	0.785722i
$355$		0			0
$356$	7.94810	+	2.89287i	0.421248	+	0.153322i
$357$	−17.2348	+	6.27295i	−0.912161	+	0.332000i
$358$	−6.05940	+	5.08444i	−0.320249	+	0.268721i
$359$	4.15028	+	23.5374i	0.219044	+	1.24226i	0.873750	+	0.486375i	$0.161681\pi$
$359$	4.15028	+	23.5374i	0.219044	+	1.24226i	−0.654707	+	0.755883i	$0.727208\pi$
$360$		0			0
$361$	−17.5675	+	7.23760i	−0.924605	+	0.380926i
$362$	−13.9145			−0.731332
$363$	−0.413222	−	2.34350i	−0.0216885	−	0.123002i
$364$	−12.0480	+	10.1094i	−0.631485	+	0.529879i
$365$		0			0
$366$	−5.85939	−	2.13264i	−0.306275	−	0.111475i
$367$	−28.5180	−	23.9294i	−1.48863	−	1.24911i	−0.896331	−	0.443385i	$-0.853778\pi$
$367$	−28.5180	−	23.9294i	−1.48863	−	1.24911i	−0.592295	−	0.805721i	$-0.701778\pi$
$368$	−1.59382	+	2.76058i	−0.0830836	+	0.143905i
$369$	0.237922	+	0.412094i	0.0123857	+	0.0214527i
$370$		0			0
$371$	4.05262	−	22.9835i	0.210402	−	1.19325i
$372$	3.77484	+	6.53822i	0.195716	+	0.338991i
$373$	3.31321	−	5.73866i	0.171552	−	0.297136i	−0.767411	−	0.641156i	$-0.778455\pi$
$373$	3.31321	−	5.73866i	0.171552	−	0.297136i	0.938963	+	0.344019i	$0.111789\pi$
$374$	11.1746	+	9.37659i	0.577824	+	0.484852i
$375$		0			0
$376$	5.89807	−	2.14672i	0.304170	−	0.110709i
$377$	3.43976	−	2.88630i	0.177156	−	0.148652i
$378$	2.15926	+	12.2458i	0.111060	+	0.629854i
$379$	24.9336			1.28075			0.640377	−	0.768060i	$-0.278778\pi$
$379$	24.9336			1.28075			0.640377	+	0.768060i	$0.278778\pi$
$380$		0			0
$381$	−3.01613			−0.154521
$382$	−3.53842	−	20.0674i	−0.181041	−	1.02674i
$383$	13.1589	−	11.0417i	0.672390	−	0.564203i	−0.241381	−	0.970430i	$-0.577600\pi$
$383$	13.1589	−	11.0417i	0.672390	−	0.564203i	0.913772	+	0.406228i	$0.133156\pi$
$384$	−1.57369	+	0.572775i	−0.0803068	+	0.0292293i
$385$		0			0
$386$	−14.1218	−	11.8496i	−0.718783	−	0.603130i
$387$	−0.213731	+	0.370192i	−0.0108645	+	0.0188179i
$388$	2.65811	+	4.60398i	0.134945	+	0.233731i
$389$	−3.89323	+	22.0796i	−0.197394	+	1.11948i	0.711573	+	0.702612i	$0.247983\pi$
$389$	−3.89323	+	22.0796i	−0.197394	+	1.11948i	−0.908967	+	0.416867i	$0.863128\pi$
$390$		0			0
$391$	7.51200	+	13.0112i	0.379898	+	0.658003i
$392$	0.800316	−	1.38619i	0.0404220	−	0.0700130i
$393$	10.2739	+	8.62081i	0.518249	+	0.434862i
$394$	8.36015	+	3.04285i	0.421178	+	0.153296i
$395$		0			0
$396$	0.463374	−	0.388817i	0.0232854	−	0.0195388i
$397$	−6.53610	−	37.0681i	−0.328038	−	1.86039i	−0.487408	−	0.873175i	$-0.662057\pi$
$397$	−6.53610	−	37.0681i	−0.328038	−	1.86039i	0.159370	−	0.987219i	$-0.449054\pi$
$398$	24.1611			1.21108
$399$	−15.8147	+	6.13269i	−0.791724	+	0.307019i
$400$		0			0
$401$	3.13998	+	17.8077i	0.156803	+	0.889273i	0.957119	+	0.289695i	$0.0935539\pi$
$401$	3.13998	+	17.8077i	0.156803	+	0.889273i	−0.800316	+	0.599578i	$0.795335\pi$
$402$	−6.80282	+	5.70825i	−0.339294	+	0.284702i
$403$	28.6728	−	10.4361i	1.42830	−	0.519857i
$404$	11.9403	+	4.34592i	0.594053	+	0.216217i
$405$		0			0
$406$	0.770774	−	1.33502i	0.0382529	−	0.0662559i
$407$	14.8161	+	25.6622i	0.734407	+	1.27203i
$408$	−1.37063	+	7.77320i	−0.0678561	+	0.384831i
$409$	−2.43421	+	13.8051i	−0.120364	+	0.682618i	0.863590	+	0.504195i	$0.168211\pi$
$409$	−2.43421	+	13.8051i	−0.120364	+	0.682618i	−0.983954	+	0.178423i	$0.942900\pi$
$410$		0			0
$411$	−16.0899	+	27.8685i	−0.793657	+	1.37465i
$412$	6.99133	+	5.86642i	0.344438	+	0.289018i
$413$	−22.2569	−	8.10085i	−1.09519	−	0.398617i
$414$	0.585426	−	0.213078i	0.0287721	−	0.0104722i
$415$		0			0
$416$	1.17533	+	6.66561i	0.0576251	+	0.326808i
$417$	−1.80737			−0.0885075
$418$	10.5132	+	8.45421i	0.514219	+	0.413509i
$419$	−24.5099			−1.19739			−0.598693	−	0.800978i	$-0.704313\pi$
$419$	−24.5099			−1.19739			−0.598693	+	0.800978i	$0.704313\pi$
$420$		0			0
$421$	−28.5396	+	23.9475i	−1.39093	+	1.16713i	−0.425974	+	0.904736i	$0.640068\pi$
$421$	−28.5396	+	23.9475i	−1.39093	+	1.16713i	−0.964960	+	0.262396i	$0.915487\pi$
$422$	−4.74576	+	1.72732i	−0.231020	+	0.0840844i
$423$	−1.15273	−	0.419558i	−0.0560475	−	0.0203996i
$424$	−7.69393	−	6.45597i	−0.373650	−	0.313530i
$425$		0			0
$426$	−9.88938	−	17.1289i	−0.479142	−	0.829899i
$427$	−1.50237	+	8.52035i	−0.0727046	+	0.412328i
$428$	1.55497	−	8.81869i	0.0751625	−	0.426267i
$429$	17.5409	+	30.3817i	0.846882	+	1.46684i
$430$		0			0
$431$	−3.57632	−	3.00089i	−0.172265	−	0.144548i	0.552579	−	0.833461i	$-0.313644\pi$
$431$	−3.57632	−	3.00089i	−0.172265	−	0.144548i	−0.724844	+	0.688913i	$0.758088\pi$
$432$	5.02862	+	1.83027i	0.241940	+	0.0880588i
$433$	25.9265	−	9.43648i	1.24595	−	0.453488i	0.366918	−	0.930253i	$-0.380413\pi$
$433$	25.9265	−	9.43648i	1.24595	−	0.453488i	0.879031	+	0.476765i	$0.158191\pi$
$434$	8.02457	−	6.73342i	0.385192	−	0.323214i
$435$		0			0
$436$	−9.59310			−0.459426
$437$	7.19685	+	11.8855i	0.344272	+	0.568561i
$438$	−4.29465			−0.205206
$439$	1.01404	+	5.75093i	0.0483977	+	0.274477i	0.999397	−	0.0347154i	$-0.0110525\pi$
$439$	1.01404	+	5.75093i	0.0483977	+	0.274477i	−0.951000	+	0.309192i	$0.899941\pi$
$440$		0			0
$441$	−0.293964	+	0.106994i	−0.0139983	+	0.00509496i
$442$	29.9771	+	10.9108i	1.42587	+	0.518973i
$443$	28.0241	+	23.5150i	1.33146	+	1.11723i	0.983733	+	0.179635i	$0.0574918\pi$
$443$	28.0241	+	23.5150i	1.33146	+	1.11723i	0.347730	+	0.937595i	$0.386953\pi$
$444$	−8.01688	+	13.8856i	−0.380464	+	0.658983i
$445$		0			0
$446$	0.480901	−	2.72732i	0.0227713	−	0.129143i
$447$	−0.804975	+	4.56524i	−0.0380740	+	0.215929i
$448$	1.16183	+	2.01234i	0.0548912	+	0.0950743i
$449$	−8.87052	+	15.3642i	−0.418626	+	0.725081i	−0.995802	−	0.0915387i	$-0.970821\pi$
$449$	−8.87052	+	15.3642i	−0.418626	+	0.725081i	0.577176	+	0.816620i	$0.304155\pi$
$450$		0			0
$451$	7.08102	+	2.57728i	0.333432	+	0.121359i
$452$	−3.55162	+	1.29268i	−0.167054	+	0.0608027i
$453$	−13.1795	+	11.0589i	−0.619227	+	0.519593i
$454$	−1.98305	−	11.2464i	−0.0930692	−	0.527821i
$455$		0			0
$456$	−1.11732	+	7.21375i	−0.0523234	+	0.337815i
$457$	35.9758			1.68288			0.841438	−	0.540354i	$-0.181710\pi$
$457$	35.9758			1.68288			0.841438	+	0.540354i	$0.181710\pi$
$458$	−2.60921	−	14.7976i	−0.121921	−	0.691446i
$459$	19.3212	−	16.2124i	0.901835	−	0.756729i
$460$		0			0
$461$	−35.7175	−	13.0001i	−1.66353	−	0.605476i	−0.672620	−	0.739988i	$-0.734831\pi$
$461$	−35.7175	−	13.0001i	−1.66353	−	0.605476i	−0.990912	+	0.134512i	$0.957053\pi$
$462$	9.22611	+	7.74163i	0.429238	+	0.360173i
$463$	10.1192	−	17.5270i	0.470281	−	0.814551i	−0.529141	−	0.848534i	$-0.677486\pi$
$463$	10.1192	−	17.5270i	0.470281	−	0.814551i	0.999422	+	0.0339831i	$0.0108192\pi$
$464$	−0.331708	−	0.574535i	−0.0153991	−	0.0266721i
$465$		0			0
$466$	−1.37602	+	7.80382i	−0.0637431	+	0.361505i
$467$	−9.70916	−	16.8168i	−0.449286	−	0.778186i	0.549054	−	0.835787i	$-0.314988\pi$
$467$	−9.70916	−	16.8168i	−0.449286	−	0.778186i	−0.998340	+	0.0576007i	$0.981655\pi$
$468$	0.661416	−	1.14561i	0.0305740	−	0.0529557i
$469$	9.43905	+	7.92031i	0.435855	+	0.365726i
$470$		0			0
$471$	10.9711	−	3.99316i	0.505522	−	0.183995i
$472$	−7.80839	+	6.55202i	−0.359410	+	0.301581i
$473$	1.17547	+	6.66642i	0.0540481	+	0.306522i
$474$	−27.6191			−1.26859
$475$		0			0
$476$	10.9519			0.501977
$477$	0.340864	+	1.93314i	0.0156071	+	0.0885122i
$478$	11.3477	−	9.52183i	0.519030	−	0.435518i
$479$	6.88996	−	2.50774i	0.314810	−	0.114582i	−0.179782	−	0.983706i	$-0.557539\pi$
$479$	6.88996	−	2.50774i	0.314810	−	0.114582i	0.494593	+	0.869125i	$0.335317\pi$
$480$		0			0
$481$	49.6415	+	41.6542i	2.26346	+	1.89927i
$482$	4.08975	−	7.08366i	0.186283	−	0.322652i
$483$	6.20216	+	10.7425i	0.282208	+	0.488799i
$484$	−0.246746	+	1.39937i	−0.0112157	+	0.0636076i
$485$		0			0
$486$	−1.01389	−	1.75611i	−0.0459910	−	0.0796588i
$487$	11.5058	−	19.9286i	0.521376	−	0.903049i	−0.478315	−	0.878188i	$-0.658752\pi$
$487$	11.5058	−	19.9286i	0.521376	−	0.903049i	0.999691	−	0.0248610i	$-0.00791432\pi$
$488$	2.85225	+	2.39333i	0.129115	+	0.108341i
$489$	−7.91567	−	2.88107i	−0.357959	−	0.130286i
$490$		0			0
$491$	16.1944	−	13.5887i	0.730842	−	0.613249i	−0.199519	−	0.979894i	$-0.563938\pi$
$491$	16.1944	−	13.5887i	0.730842	−	0.613249i	0.930361	+	0.366645i	$0.119494\pi$
$492$	0.708029	+	4.01543i	0.0319204	+	0.181030i
$493$	−3.12681			−0.140825
$494$	27.9282	+	9.50995i	1.25655	+	0.427873i
$495$		0			0
$496$	−0.782829	−	4.43964i	−0.0351500	−	0.199346i
$497$	−21.0229	+	17.6403i	−0.943005	+	0.791275i
$498$	−10.1181	+	3.68267i	−0.453401	+	0.165025i
$499$	−12.7827	−	4.65252i	−0.572232	−	0.208275i	0.0396647	−	0.999213i	$-0.487371\pi$
$499$	−12.7827	−	4.65252i	−0.572232	−	0.208275i	−0.611897	+	0.790938i	$0.709593\pi$
$500$		0			0
$501$	−4.94764	+	8.56957i	−0.221044	+	0.382860i
$502$	−0.429144	−	0.743299i	−0.0191536	−	0.0331751i
$503$	−1.42656	+	8.09040i	−0.0636070	+	0.360733i	0.936346	+	0.351078i	$0.114185\pi$
$503$	−1.42656	+	8.09040i	−0.0636070	+	0.360733i	−0.999953	+	0.00965567i	$0.996926\pi$
$504$	0.0788603	−	0.447239i	0.00351272	−	0.0199216i
$505$		0			0
$506$	4.93288	−	8.54400i	0.219293	−	0.379827i
$507$	42.0935	+	35.3206i	1.86944	+	1.56864i
$508$	1.69240	+	0.615985i	0.0750883	+	0.0273299i
$509$	5.81193	−	2.11537i	0.257609	−	0.0937621i	−0.209987	−	0.977704i	$-0.567342\pi$
$509$	5.81193	−	2.11537i	0.257609	−	0.0937621i	0.467597	+	0.883942i	$0.345120\pi$
$510$		0			0
$511$	1.03476	+	5.86839i	0.0457749	+	0.259602i
$512$	1.00000			0.0441942
$513$	17.5520	−	15.3632i	0.774940	−	0.678302i
$514$	11.3803			0.501965
$515$		0			0
$516$	−2.80586	+	2.35440i	−0.123521	+	0.103647i
$517$	−18.2545	+	6.64411i	−0.802834	+	0.292208i
$518$	20.9055	+	7.60897i	0.918534	+	0.334319i
$519$	−24.8162	−	20.8233i	−1.08931	−	0.914040i
$520$		0			0
$521$	8.76833	+	15.1872i	0.384148	+	0.665363i	0.991651	−	0.128954i	$-0.0411620\pi$
$521$	8.76833	+	15.1872i	0.384148	+	0.665363i	−0.607503	+	0.794317i	$0.707829\pi$
$522$	−0.0225150	+	0.127689i	−0.000985456	+	0.00558880i
$523$	0.0595191	−	0.337550i	0.00260259	−	0.0147600i	−0.983479	−	0.181023i	$-0.942059\pi$
$523$	0.0595191	−	0.337550i	0.00260259	−	0.0147600i	0.986081	+	0.166263i	$0.0531702\pi$
$524$	−4.00423	−	6.93552i	−0.174925	−	0.302980i
$525$		0			0
$526$	9.72539	+	8.16057i	0.424047	+	0.355818i
$527$	−19.9663	−	7.26715i	−0.869747	−	0.316562i
$528$	4.87056	−	1.77274i	0.211964	−	0.0771486i
$529$	−9.83521	+	8.25272i	−0.427618	+	0.358814i
$530$		0			0
$531$	1.99216			0.0864524
$532$	10.1264	−	0.211329i	0.439034	−	0.00916227i
$533$	16.4792			0.713795
$534$	−2.45969	−	13.9496i	−0.106441	−	0.603657i
$535$		0			0
$536$	4.98298	−	1.81366i	0.215232	−	0.0783380i
$537$	12.4478	+	4.53064i	0.537164	+	0.195512i
$538$	−16.7636	−	14.0663i	−0.722730	−	0.606443i
$539$	−2.47698	+	4.29025i	−0.106691	+	0.184794i
$540$		0			0
$541$	5.40498	−	30.6532i	0.232378	−	1.31788i	−0.615687	−	0.787991i	$-0.711121\pi$
$541$	5.40498	−	30.6532i	0.232378	−	1.31788i	0.848065	−	0.529892i	$-0.177767\pi$
$542$	−2.45156	+	13.9035i	−0.105304	+	0.597206i
$543$	11.6512	+	20.1805i	0.500002	+	0.866028i
$544$	2.35660	−	4.08175i	0.101038	−	0.175004i
$545$		0			0
$546$	24.7501	+	9.00832i	1.05921	+	0.385520i
$547$	−20.5259	+	7.47082i	−0.877625	+	0.319429i	−0.741251	−	0.671228i	$-0.765767\pi$
$547$	−20.5259	+	7.47082i	−0.877625	+	0.319429i	−0.136374	+	0.990657i	$0.543545\pi$
$548$	14.7199	−	12.3515i	0.628804	−	0.527629i
$549$	−0.126363	−	0.716642i	−0.00539306	−	0.0305855i
$550$		0			0
$551$	−2.89113	+	0.0603355i	−0.123166	+	0.00257038i
$552$	5.33828			0.227212
$553$	6.65455	+	37.7398i	0.282980	+	1.60486i
$554$	−13.9744	+	11.7259i	−0.593714	+	0.498185i
$555$		0			0
$556$	1.01415	+	0.369120i	0.0430095	+	0.0156542i
$557$	−5.09607	−	4.27611i	−0.215928	−	0.181185i	0.528408	−	0.848991i	$-0.322789\pi$
$557$	−5.09607	−	4.27611i	−0.215928	−	0.181185i	−0.744335	+	0.667806i	$0.767234\pi$
$558$	−0.440538	+	0.763034i	−0.0186495	+	0.0323018i
$559$	7.40181	+	12.8203i	0.313063	+	0.542242i
$560$		0			0
$561$	4.24209	−	24.0581i	0.179101	−	1.01573i
$562$	−6.50360	−	11.2646i	−0.274338	−	0.475167i
$563$	−3.63425	+	6.29471i	−0.153165	+	0.265290i	−0.932390	−	0.361455i	$-0.882280\pi$
$563$	−3.63425	+	6.29471i	−0.153165	+	0.265290i	0.779224	+	0.626745i	$0.215613\pi$
$564$	−8.05212	−	6.75653i	−0.339055	−	0.284501i
$565$		0			0
$566$	2.73672	−	0.996084i	0.115033	−	0.0418685i
$567$	14.9085	−	12.5097i	0.626100	−	0.525360i
$568$	2.05087	+	11.6310i	0.0860524	+	0.488027i
$569$	−17.9593			−0.752892			−0.376446	−	0.926438i	$-0.622854\pi$
$569$	−17.9593			−0.752892			−0.376446	+	0.926438i	$0.622854\pi$
$570$		0			0
$571$	−0.175164			−0.00733040			−0.00366520	−	0.999993i	$-0.501167\pi$
$571$	−0.175164			−0.00733040			−0.00366520	+	0.999993i	$0.501167\pi$
$572$	−3.63764	−	20.6301i	−0.152097	−	0.862587i
$573$	−26.1412	+	21.9351i	−1.09206	+	0.916351i
$574$	5.31626	−	1.93496i	0.221896	−	0.0807636i
$575$		0			0
$576$	−0.149717	−	0.125627i	−0.00623820	−	0.00523447i
$577$	21.4197	−	37.0999i	0.891712	−	1.54449i	0.0538907	−	0.998547i	$-0.482838\pi$
$577$	21.4197	−	37.0999i	0.891712	−	1.54449i	0.837822	−	0.545944i	$-0.183829\pi$
$578$	−2.60714	−	4.51570i	−0.108443	−	0.187829i
$579$	−5.36093	+	30.4033i	−0.222792	+	1.26352i
$580$		0			0
$581$	7.47001	+	12.9384i	0.309908	+	0.536776i
$582$	4.45148	−	7.71019i	0.184520	−	0.319598i
$583$	23.8127	+	19.9813i	0.986223	+	0.827539i
$584$	2.40980	+	0.877097i	0.0997184	+	0.0362945i
$585$		0			0
$586$	−1.04265	+	0.874885i	−0.0430714	+	0.0361412i
$587$	6.74126	+	38.2316i	0.278242	+	1.57799i	0.728472	+	0.685075i	$0.240231\pi$
$587$	6.74126	+	38.2316i	0.278242	+	1.57799i	−0.450231	+	0.892912i	$0.648658\pi$
$588$	−2.68055			−0.110544
$589$	−18.6016	−	6.33412i	−0.766467	−	0.260993i
$590$		0			0
$591$	−2.58721	−	14.6728i	−0.106423	−	0.603557i
$592$	7.33427	−	6.15418i	0.301437	−	0.252935i
$593$	−35.1745	+	12.8025i	−1.44444	+	0.525735i	−0.941034	−	0.338312i	$-0.890144\pi$
$593$	−35.1745	+	12.8025i	−1.44444	+	0.525735i	−0.503411	+	0.864047i	$0.667922\pi$
$594$	−15.5636	−	5.66469i	−0.638582	−	0.232425i
$595$		0			0
$596$	1.38404	−	2.39724i	0.0566927	−	0.0981946i
$597$	−20.2310	−	35.0412i	−0.828002	−	1.43414i
$598$	3.74652	−	21.2476i	0.153206	−	0.868877i
$599$	7.72566	−	43.8144i	0.315662	−	1.79021i	−0.252822	−	0.967513i	$-0.581359\pi$
$599$	7.72566	−	43.8144i	0.315662	−	1.79021i	0.568484	−	0.822694i	$-0.307530\pi$
$600$		0			0
$601$	−2.34958	+	4.06960i	−0.0958415	+	0.166002i	−0.909959	−	0.414697i	$-0.863888\pi$
$601$	−2.34958	+	4.06960i	−0.0958415	+	0.166002i	0.814118	+	0.580699i	$0.197221\pi$
$602$	3.89319	+	3.26677i	0.158674	+	0.133144i
$603$	−0.973880	−	0.354463i	−0.0396595	−	0.0144349i
$604$	9.65380	−	3.51370i	0.392808	−	0.142970i
$605$		0			0
$606$	−3.69515	−	20.9562i	−0.150105	−	0.851289i
$607$	−35.6234			−1.44591			−0.722954	−	0.690896i	$-0.757216\pi$
$607$	−35.6234			−1.44591			−0.722954	+	0.690896i	$0.757216\pi$
$608$	2.10021	−	3.81957i	0.0851749	−	0.154904i
$609$	−2.58160			−0.104612
$610$		0			0
$611$	−32.5436	+	27.3074i	−1.31657	+	1.10474i
$612$	−0.865603	+	0.315054i	−0.0349899	+	0.0127353i
$613$	7.63724	+	2.77973i	0.308465	+	0.112272i	0.491615	−	0.870813i	$-0.336407\pi$
$613$	7.63724	+	2.77973i	0.308465	+	0.112272i	−0.183149	+	0.983085i	$0.558629\pi$
$614$	1.00946	+	0.847040i	0.0407386	+	0.0341837i
$615$		0			0
$616$	−3.59586	−	6.22821i	−0.144881	−	0.250942i
$617$	−7.17684	+	40.7019i	−0.288929	+	1.63860i	0.401975	+	0.915651i	$0.368324\pi$
$617$	−7.17684	+	40.7019i	−0.288929	+	1.63860i	−0.690904	+	0.722946i	$0.742787\pi$
$618$	2.65404	−	15.0518i	0.106761	−	0.605474i
$619$	17.2816	+	29.9327i	0.694608	+	1.20310i	0.970313	+	0.241854i	$0.0777555\pi$
$619$	17.2816	+	29.9327i	0.694608	+	1.20310i	−0.275705	+	0.961242i	$0.588911\pi$
$620$		0			0
$621$	−13.0673	−	10.9648i	−0.524373	−	0.440001i
$622$	5.52996	+	2.01274i	0.221731	+	0.0807036i
$623$	−18.4686	+	6.72203i	−0.739930	+	0.269313i
$624$	8.68309	−	7.28598i	0.347602	−	0.291673i
$625$		0			0
$626$	−6.22515			−0.248807
$627$	3.45812	−	22.3266i	0.138104	−	0.891638i
$628$	−6.97160			−0.278197
$629$	−7.83591	−	44.4396i	−0.312438	−	1.77192i
$630$		0			0
$631$	0.914627	−	0.332897i	0.0364107	−	0.0132524i	−0.323751	−	0.946142i	$-0.604944\pi$
$631$	0.914627	−	0.332897i	0.0364107	−	0.0132524i	0.360161	+	0.932890i	$0.382722\pi$
$632$	15.4975	+	5.64064i	0.616459	+	0.224373i
$633$	6.47897	+	5.43650i	0.257516	+	0.216082i
$634$	−10.7362	+	18.5956i	−0.426388	+	0.738526i
$635$		0			0
$636$	−2.92077	+	16.5645i	−0.115816	+	0.656824i
$637$	−1.88126	+	10.6692i	−0.0745384	+	0.422728i
$638$	1.02664	+	1.77819i	0.0406449	+	0.0703991i
$639$	1.15413	−	1.99901i	0.0456566	−	0.0790795i
$640$		0			0
$641$	30.0851	+	10.9501i	1.18829	+	0.432502i	0.859123	−	0.511770i	$-0.171010\pi$
$641$	30.0851	+	10.9501i	1.18829	+	0.432502i	0.329167	+	0.944272i	$0.393232\pi$
$642$	−14.0919	+	5.12905i	−0.556164	+	0.202427i
$643$	15.2535	−	12.7992i	0.601540	−	0.504752i	−0.290400	−	0.956905i	$-0.593788\pi$
$643$	15.2535	−	12.7992i	0.601540	−	0.504752i	0.891940	+	0.452153i	$0.149344\pi$
$644$	−1.28621	−	7.29445i	−0.0506837	−	0.287441i
$645$		0			0
$646$	−10.6412	−	17.5738i	−0.418671	−	0.691430i
$647$	30.2057			1.18751			0.593753	−	0.804647i	$-0.297645\pi$
$647$	30.2057			1.18751			0.593753	+	0.804647i	$0.297645\pi$
$648$	−1.45439	−	8.24824i	−0.0571337	−	0.324021i
$649$	24.1670	−	20.2785i	0.948638	−	0.796001i
$650$		0			0
$651$	−16.4849	−	6.00001i	−0.646094	−	0.235159i
$652$	3.85322	+	3.23323i	0.150904	+	0.126623i
$653$	3.44070	−	5.95947i	0.134645	−	0.233212i	−0.790817	−	0.612053i	$-0.790344\pi$
$653$	3.44070	−	5.95947i	0.134645	−	0.233212i	0.925462	+	0.378841i	$0.123677\pi$
$654$	8.03269	+	13.9130i	0.314103	+	0.544043i
$655$		0			0
$656$	0.422784	−	2.39773i	0.0165070	−	0.0936156i
$657$	−0.250601	−	0.434053i	−0.00977687	−	0.0169340i
$658$	−7.29232	+	12.6307i	−0.284284	+	0.492395i
$659$	−26.2163	−	21.9981i	−1.02124	−	0.856925i	−0.0314603	−	0.999505i	$-0.510016\pi$
$659$	−26.2163	−	21.9981i	−1.02124	−	0.856925i	−0.989783	+	0.142580i	$0.954460\pi$
$660$		0			0
$661$	15.7427	−	5.72986i	0.612319	−	0.222866i	−0.0171986	−	0.999852i	$-0.505475\pi$
$661$	15.7427	−	5.72986i	0.612319	−	0.222866i	0.629518	+	0.776986i	$0.283253\pi$
$662$	15.7297	−	13.1988i	0.611354	−	0.512987i
$663$	−9.27698	−	52.6124i	−0.360288	−	2.04330i
$664$	6.42953			0.249514
$665$		0			0
$666$	−1.87120			−0.0725074
$667$	0.367219	+	2.08260i	0.0142188	+	0.0806387i
$668$	4.52637	−	3.79808i	0.175131	−	0.146952i
$669$	−4.35816	+	1.58624i	−0.168496	+	0.0613276i
$670$		0			0
$671$	−8.82774	−	7.40735i	−0.340791	−	0.285958i
$672$	1.94569	−	3.37003i	0.0750566	−	0.130002i
$673$	−4.89013	−	8.46996i	−0.188501	−	0.326493i	0.756250	−	0.654283i	$-0.227029\pi$
$673$	−4.89013	−	8.46996i	−0.188501	−	0.326493i	−0.944751	+	0.327790i	$0.893696\pi$
$674$	−5.64994	+	32.0424i	−0.217628	+	1.23423i
$675$		0			0
$676$	−16.4058	−	28.4158i	−0.630994	−	1.09291i
$677$	2.90819	−	5.03714i	0.111771	−	0.193593i	−0.804713	−	0.593663i	$-0.797681\pi$
$677$	2.90819	−	5.03714i	0.111771	−	0.193593i	0.916484	+	0.400071i	$0.131014\pi$
$678$	4.84872	+	4.06856i	0.186214	+	0.156252i
$679$	−11.6081	−	4.22499i	−0.445477	−	0.162140i
$680$		0			0
$681$	−14.6504	+	12.2932i	−0.561405	+	0.471075i
$682$	2.42286	+	13.7407i	0.0927760	+	0.526159i
$683$	−28.5207			−1.09131			−0.545657	−	0.838008i	$-0.683720\pi$
$683$	−28.5207			−1.09131			−0.545657	+	0.838008i	$0.683720\pi$
$684$	−0.794280	+	0.308010i	−0.0303700	+	0.0117770i
$685$		0			0
$686$	3.47034	+	19.6813i	0.132498	+	0.751435i
$687$	−19.2764	+	16.1748i	−0.735440	+	0.617108i
$688$	2.05525	−	0.748052i	0.0783559	−	0.0285192i
$689$	63.8805	+	23.2506i	2.43365	+	0.885777i
$690$		0			0
$691$	16.1503	−	27.9731i	0.614385	−	1.06415i	−0.376107	−	0.926576i	$-0.622738\pi$
$691$	16.1503	−	27.9731i	0.614385	−	1.06415i	0.990492	−	0.137570i	$-0.0439291\pi$
$692$	9.67206	+	16.7525i	0.367677	+	0.636835i
$693$	−0.244073	+	1.38421i	−0.00927156	+	0.0525816i
$694$	0.0449515	−	0.254933i	0.00170633	−	0.00967711i
$695$		0			0
$696$	−0.555505	+	0.962162i	−0.0210564	+	0.0364707i
$697$	−8.79061	−	7.37619i	−0.332968	−	0.279393i
$698$	29.1547	+	10.6115i	1.10352	+	0.401650i
$699$	12.4702	−	4.53879i	0.471667	−	0.171673i
$700$		0			0
$701$	1.97675	+	11.2107i	0.0746609	+	0.423423i	0.999112	+	0.0421235i	$0.0134123\pi$
$701$	1.97675	+	11.2107i	0.0746609	+	0.423423i	−0.924451	+	0.381300i	$0.875477\pi$
$702$	−36.2202			−1.36704
$703$	−8.10280	−	40.9388i	−0.305603	−	1.54404i
$704$	−3.09500			−0.116647
$705$		0			0
$706$	−7.96269	+	6.68149i	−0.299680	+	0.251461i
$707$	−27.7451	+	10.0984i	−1.04346	+	0.379790i
$708$	16.0408	+	5.83837i	0.602850	+	0.219419i
$709$	26.4481	+	22.1926i	0.993278	+	0.833459i	0.986039	−	0.166515i	$-0.0532513\pi$
$709$	26.4481	+	22.1926i	0.993278	+	0.833459i	0.00723886	+	0.999974i	$0.497696\pi$
$710$		0			0
$711$	−1.61162	−	2.79141i	−0.0604406	−	0.104686i
$712$	−1.46875	+	8.32969i	−0.0550437	+	0.312168i
$713$	−2.49538	+	14.1520i	−0.0934526	+	0.529996i
$714$	−9.17043	−	15.8837i	−0.343195	−	0.594431i
$715$		0			0
$716$	−6.05940	−	5.08444i	−0.226450	−	0.190015i
$717$	−23.3115	−	8.48470i	−0.870585	−	0.316867i
$718$	−22.4592	+	8.17446i	−0.838168	+	0.305068i
$719$	19.8549	−	16.6603i	0.740464	−	0.621323i	−0.192498	−	0.981297i	$-0.561659\pi$
$719$	19.8549	−	16.6603i	0.740464	−	0.621323i	0.932962	+	0.359974i	$0.117215\pi$
$720$		0			0
$721$	−21.2069			−0.789786
$722$	−10.1782	−	16.0438i	−0.378794	−	0.597089i
$723$	−13.6981			−0.509437
$724$	−2.41624	−	13.7032i	−0.0897987	−	0.509274i
$725$		0			0
$726$	2.23614	−	0.813887i	0.0829908	−	0.0302062i
$727$	9.38104	+	3.41442i	0.347923	+	0.126634i	0.510070	−	0.860133i	$-0.329620\pi$
$727$	9.38104	+	3.41442i	0.347923	+	0.126634i	−0.162147	+	0.986767i	$0.551842\pi$
$728$	−12.0480	−	10.1094i	−0.446527	−	0.374681i
$729$	−14.2612	+	24.7011i	−0.528191	+	0.914854i
$730$		0			0
$731$	1.79005	−	10.1519i	0.0662076	−	0.375482i
$732$	1.08277	−	6.14070i	0.0400204	−	0.226967i
$733$	−1.03498	−	1.79264i	−0.0382279	−	0.0662126i	0.846278	−	0.532741i	$-0.178838\pi$
$733$	−1.03498	−	1.79264i	−0.0382279	−	0.0662126i	−0.884506	+	0.466528i	$0.845505\pi$
$734$	18.6138	−	32.2400i	0.687048	−	1.19000i
$735$		0			0
$736$	−2.99540	−	1.09024i	−0.110412	−	0.0401867i
$737$	−15.4223	+	5.61327i	−0.568089	+	0.206767i
$738$	−0.364518	+	0.305867i	−0.0134181	+	0.0112591i
$739$	−4.32655	−	24.5371i	−0.159155	−	0.902612i	−0.954888	−	0.296965i	$-0.904025\pi$
$739$	−4.32655	−	24.5371i	−0.159155	−	0.902612i	0.795733	−	0.605647i	$-0.207086\pi$
$740$		0			0
$741$	−9.59296	−	48.4678i	−0.352406	−	1.78051i
$742$	23.3381			0.856769
$743$	−0.202822	−	1.15026i	−0.00744080	−	0.0421989i	0.980861	−	0.194708i	$-0.0623758\pi$
$743$	−0.202822	−	1.15026i	−0.00744080	−	0.0421989i	−0.988302	+	0.152509i	$0.951265\pi$
$744$	−5.78339	+	4.85284i	−0.212029	+	0.177914i
$745$		0			0
$746$	6.22681	+	2.26637i	0.227980	+	0.0829778i
$747$	−0.962609	−	0.807725i	−0.0352200	−	0.0295531i
$748$	−7.29369	+	12.6330i	−0.266684	+	0.461910i
$749$	10.4039	+	18.0200i	0.380148	+	0.658436i
$750$		0			0
$751$	2.41878	−	13.7176i	0.0882625	−	0.500562i	−0.908342	−	0.418228i	$-0.862651\pi$
$751$	2.41878	−	13.7176i	0.0882625	−	0.500562i	0.996605	−	0.0823341i	$-0.0262374\pi$
$752$	3.13830	+	5.43569i	0.114442	+	0.198219i
$753$	−0.718680	+	1.24479i	−0.0261901	+	0.0453627i
$754$	3.43976	+	2.88630i	0.125269	+	0.105113i
$755$		0			0
$756$	−11.6848	+	4.25291i	−0.424971	+	0.154677i
$757$	6.79067	−	5.69805i	0.246811	−	0.207099i	−0.510987	−	0.859589i	$-0.670720\pi$
$757$	6.79067	−	5.69805i	0.246811	−	0.207099i	0.757798	+	0.652490i	$0.226275\pi$
$758$	4.32968	+	24.5548i	0.157261	+	0.891872i
$759$	−16.5220			−0.599711
$760$		0			0
$761$	8.72950			0.316444			0.158222	−	0.987404i	$-0.449424\pi$
$761$	8.72950			0.316444			0.158222	+	0.987404i	$0.449424\pi$
$762$	−0.523746	−	2.97031i	−0.0189733	−	0.107603i
$763$	17.0759	−	14.3284i	0.618190	−	0.518723i
$764$	19.1481	−	6.96933i	0.692753	−	0.252141i
$765$		0			0
$766$	13.1589	+	11.0417i	0.475452	+	0.398951i
$767$	34.4958	−	59.7484i	1.24557	−	2.15739i
$768$	−0.837341	−	1.45032i	−0.0302149	−	0.0523338i
$769$	3.03165	−	17.1933i	0.109324	−	0.620008i	−0.880081	−	0.474824i	$-0.842512\pi$
$769$	3.03165	−	17.1933i	0.109324	−	0.620008i	0.989405	−	0.145183i	$-0.0463772\pi$
$770$		0			0
$771$	−9.52921	−	16.5051i	−0.343186	−	0.594416i
$772$	9.21738	−	15.9650i	0.331741	−	0.574592i
$773$	10.3498	+	8.68454i	0.372258	+	0.312361i	0.809654	−	0.586908i	$-0.199655\pi$
$773$	10.3498	+	8.68454i	0.372258	+	0.312361i	−0.437396	+	0.899269i	$0.644099\pi$
$774$	−0.401682	−	0.146200i	−0.0144382	−	0.00525506i
$775$		0			0
$776$	−4.07246	+	3.41720i	−0.146193	+	0.122670i
$777$	−6.46959	−	36.6909i	−0.232095	−	1.31628i
$778$	−22.4202			−0.803803
$779$	−8.27035	−	6.65059i	−0.296316	−	0.238282i
$780$		0			0
$781$	−6.34743	−	35.9981i	−0.227129	−	1.28811i
$782$	−11.5090	+	9.65724i	−0.411563	+	0.345342i
$783$	3.33606	−	1.21423i	0.119221	−	0.0433930i
$784$	1.50410	+	0.547448i	0.0537179	+	0.0195517i
$785$		0			0
$786$	−6.70580	+	11.6148i	−0.239188	+	0.414286i
$787$	17.6119	+	30.5047i	0.627797	+	1.08738i	0.987993	+	0.154500i	$0.0493765\pi$
$787$	17.6119	+	30.5047i	0.627797	+	1.08738i	−0.360196	+	0.932877i	$0.617290\pi$
$788$	−1.54489	+	8.76153i	−0.0550346	+	0.312117i
$789$	3.69195	−	20.9381i	0.131437	−	0.745415i
$790$		0			0
$791$	4.39119	−	7.60576i	0.156133	−	0.270430i
$792$	0.463374	+	0.388817i	0.0164653	+	0.0138160i
$793$	−23.6814	−	8.61934i	−0.840953	−	0.306082i
$794$	35.3699	−	12.8736i	1.25523	−	0.456867i
$795$		0			0
$796$	4.19553	+	23.7940i	0.148706	+	0.843356i
$797$	−19.1074			−0.676818			−0.338409	−	0.940999i	$-0.609889\pi$
$797$	−19.1074			−0.676818			−0.338409	+	0.940999i	$0.609889\pi$
$798$	−8.78572	−	14.5095i	−0.311011	−	0.513630i
$799$	29.5829			1.04657
$800$		0			0
$801$	1.26633	−	1.06258i	0.0447437	−	0.0375444i
$802$	−16.9919	+	6.18454i	−0.600005	+	0.218384i
$803$	−7.45835	−	2.71462i	−0.263199	−	0.0957968i
$804$	−6.80282	−	5.70825i	−0.239917	−	0.201314i
$805$		0			0
$806$	15.2565	+	26.4250i	0.537387	+	0.930782i
$807$	−6.36379	+	36.0908i	−0.224016	+	1.27046i
$808$	−2.20648	+	12.5136i	−0.0776237	+	0.440226i
$809$	−5.22079	−	9.04268i	−0.183553	−	0.317924i	0.759535	−	0.650467i	$-0.225427\pi$
$809$	−5.22079	−	9.04268i	−0.183553	−	0.317924i	−0.943088	+	0.332543i	$0.892093\pi$
$810$		0			0
$811$	7.03037	+	5.89918i	0.246870	+	0.207148i	0.757823	−	0.652460i	$-0.226263\pi$
$811$	7.03037	+	5.89918i	0.246870	+	0.207148i	−0.510953	+	0.859609i	$0.670707\pi$
$812$	1.44858	+	0.527240i	0.0508352	+	0.0185025i
$813$	22.2173	−	8.08643i	0.779194	−	0.283603i
$814$	−22.6996	+	19.0472i	−0.795620	+	0.667604i
$815$		0			0
$816$	−7.89312			−0.276314
$817$	1.45924	−	9.42125i	0.0510523	−	0.329608i
$818$	−14.0181			−0.490130
$819$	0.533761	+	3.02711i	0.0186511	+	0.105776i
$820$		0			0
$821$	−8.43841	+	3.07133i	−0.294503	+	0.107190i	−0.485046	−	0.874489i	$-0.661197\pi$
$821$	−8.43841	+	3.07133i	−0.294503	+	0.107190i	0.190544	+	0.981679i	$0.438975\pi$
$822$	−30.2391	−	11.0061i	−1.05471	−	0.383883i
$823$	−27.6581	−	23.2079i	−0.964101	−	0.808977i	0.0175145	−	0.999847i	$-0.494425\pi$
$823$	−27.6581	−	23.2079i	−0.964101	−	0.808977i	−0.981615	+	0.190870i	$0.938869\pi$
$824$	−4.56327	+	7.90381i	−0.158969	+	0.275342i
$825$		0			0
$826$	4.11291	−	23.3255i	0.143106	−	0.811597i
$827$	−0.988578	+	5.60650i	−0.0343762	+	0.194957i	−0.997160	−	0.0753168i	$-0.976003\pi$
$827$	−0.988578	+	5.60650i	−0.0343762	+	0.194957i	0.962783	+	0.270274i	$0.0871143\pi$
$828$	0.311499	+	0.539531i	0.0108253	+	0.0187500i
$829$	−6.25554	+	10.8349i	−0.217264	+	0.376312i	−0.953970	−	0.299901i	$-0.903047\pi$
$829$	−6.25554	+	10.8349i	−0.217264	+	0.376312i	0.736707	+	0.676212i	$0.236380\pi$
$830$		0			0
$831$	28.7076	+	10.4487i	0.995854	+	0.362461i
$832$	−6.36025	+	2.31494i	−0.220502	+	0.0802561i
$833$	5.77912	−	4.84925i	0.200234	−	0.168017i
$834$	−0.313847	−	1.77992i	−0.0108676	−	0.0616334i
$835$		0			0
$836$	−6.50017	+	11.8216i	−0.224813	+	0.408858i
$837$	24.1246			0.833867
$838$	−4.25610	−	24.1375i	−0.147025	−	0.833817i
$839$	25.8961	−	21.7294i	0.894033	−	0.750183i	−0.0749821	−	0.997185i	$-0.523890\pi$
$839$	25.8961	−	21.7294i	0.894033	−	0.750183i	0.969015	+	0.247002i	$0.0794455\pi$
$840$		0			0
$841$	26.8375	+	9.76805i	0.925431	+	0.336829i
$842$	−28.5396	−	23.9475i	−0.983539	−	0.825287i
$843$	−10.8915	+	18.8646i	−0.375122	+	0.649730i
$844$	−2.52517	−	4.37372i	−0.0869198	−	0.150550i
$845$		0			0
$846$	0.213015	−	1.20807i	0.00732362	−	0.0415343i
$847$	−1.65090	−	2.85945i	−0.0567257	−	0.0982519i
$848$	5.02185	−	8.69811i	0.172451	−	0.298694i
$849$	−3.73620	−	3.13505i	−0.128226	−	0.107594i
$850$		0			0
$851$	−28.6786	+	10.4382i	−0.983090	+	0.357815i
$852$	15.1514	−	12.7135i	0.519079	−	0.435559i
$853$	1.99098	+	11.2914i	0.0681697	+	0.386610i	0.999735	+	0.0230347i	$0.00733283\pi$
$853$	1.99098	+	11.2914i	0.0681697	+	0.386610i	−0.931565	+	0.363575i	$0.881556\pi$
$854$	−8.65179			−0.296058
$855$		0			0
$856$	8.95473			0.306066
$857$	2.49949	+	14.1753i	0.0853810	+	0.484220i	0.997274	+	0.0737912i	$0.0235098\pi$
$857$	2.49949	+	14.1753i	0.0853810	+	0.484220i	−0.911893	+	0.410429i	$0.865379\pi$
$858$	−26.8742	+	22.5501i	−0.917470	+	0.769849i
$859$	−32.3900	+	11.7890i	−1.10513	+	0.402236i	−0.829206	−	0.558943i	$-0.811207\pi$
$859$	−32.3900	+	11.7890i	−1.10513	+	0.402236i	−0.275927	+	0.961179i	$0.588985\pi$
$860$		0			0
$861$	−7.25782	−	6.09004i	−0.247346	−	0.207548i
$862$	2.33428	−	4.04309i	0.0795059	−	0.137708i
$863$	−13.3344	−	23.0958i	−0.453907	−	0.786191i	0.544717	−	0.838620i	$-0.316637\pi$
$863$	−13.3344	−	23.0958i	−0.453907	−	0.786191i	−0.998625	+	0.0524291i	$0.983304\pi$
$864$	−0.929252	+	5.27005i	−0.0316138	+	0.179291i
$865$		0			0
$866$	13.7952	+	23.8940i	0.468780	+	0.811951i
$867$	−4.36613	+	7.56237i	−0.148282	+	0.256831i
$868$	8.02457	+	6.73342i	0.272372	+	0.228547i
$869$	−47.9649	−	17.4578i	−1.62710	−	0.592216i
$870$		0			0
$871$	−27.4945	+	23.0706i	−0.931614	+	0.781717i
$872$	−1.66582	−	9.44736i	−0.0564119	−	0.319928i
$873$	1.03901			0.0351651
$874$	−10.4552	+	9.15141i	−0.353653	+	0.309551i
$875$		0			0
$876$	−0.745759	−	4.22941i	−0.0251969	−	0.142898i
$877$	3.91536	−	3.28538i	0.132212	−	0.110939i	−0.574284	−	0.818656i	$-0.694719\pi$
$877$	3.91536	−	3.28538i	0.132212	−	0.110939i	0.706496	+	0.707717i	$0.250275\pi$
$878$	−5.48747	+	1.99728i	−0.185193	+	0.0674048i
$879$	2.14191	+	0.779592i	0.0722449	+	0.0262950i
$880$		0			0
$881$	9.23774	−	16.0002i	0.311227	−	0.539062i	−0.667401	−	0.744699i	$-0.732593\pi$
$881$	9.23774	−	16.0002i	0.311227	−	0.539062i	0.978628	+	0.205637i	$0.0659266\pi$
$882$	−0.156415	−	0.270918i	−0.00526676	−	0.00912230i
$883$	−3.77236	+	21.3941i	−0.126950	+	0.719969i	0.853181	+	0.521616i	$0.174671\pi$
$883$	−3.77236	+	21.3941i	−0.126950	+	0.719969i	−0.980131	+	0.198354i	$0.936441\pi$
$884$	−5.53955	+	31.4164i	−0.186315	+	1.05665i
$885$		0			0
$886$	−18.2914	+	31.6816i	−0.614512	+	1.06437i
$887$	29.7825	+	24.9905i	1.00000	+	0.839099i	0.986984	−	0.160816i	$-0.0514126\pi$
$887$	29.7825	+	24.9905i	1.00000	+	0.839099i	0.0130151	+	0.999915i	$0.495857\pi$
$888$	−15.0668	−	5.48387i	−0.505609	−	0.184026i
$889$	−3.93256	+	1.43134i	−0.131894	+	0.0480054i
$890$		0			0
$891$	4.50133	+	25.5283i	0.150800	+	0.855231i
$892$	2.76940			0.0927263
$893$	27.3531	−	0.570836i	0.915336	−	0.0191023i
$894$	−4.63567			−0.155040
$895$		0			0
$896$	−1.78002	+	1.49362i	−0.0594664	+	0.0498982i
$897$	−33.9528	+	12.3578i	−1.13365	+	0.412615i
$898$	−16.6711	−	6.06780i	−0.556323	−	0.202485i
$899$	−2.29106	−	1.92243i	−0.0764110	−	0.0641165i
$900$		0			0
$901$	−23.6690	−	40.9959i	−0.788529	−	1.36577i
$902$	−1.30852	+	7.42098i	−0.0435689	+	0.247092i
$903$	1.47793	−	8.38176i	0.0491824	−	0.278927i
$904$	−1.88978	−	3.27319i	−0.0628530	−	0.108865i
$905$		0			0
$906$	−13.1795	−	11.0589i	−0.437859	−	0.367408i
$907$	1.45333	+	0.528970i	0.0482572	+	0.0175642i	0.366036	−	0.930601i	$-0.380715\pi$
$907$	1.45333	+	0.528970i	0.0482572	+	0.0175642i	−0.317779	+	0.948165i	$0.602937\pi$
$908$	10.7312	−	3.90585i	0.356128	−	0.129620i
$909$	1.90239	−	1.59630i	0.0630984	−	0.0529459i
$910$		0			0
$911$	34.1846			1.13259			0.566294	−	0.824204i	$-0.308377\pi$
$911$	34.1846			1.13259			0.566294	+	0.824204i	$0.308377\pi$
$912$	−7.29818	+	0.152307i	−0.241667	+	0.00504339i
$913$	−19.8994			−0.658575
$914$	6.24713	+	35.4292i	0.206637	+	1.17189i
$915$		0			0
$916$	14.1197	−	5.13915i	0.466528	−	0.169802i
$917$	17.4866	+	6.36461i	0.577459	+	0.210178i
$918$	19.3212	+	16.2124i	0.637693	+	0.535088i
$919$	−1.47826	+	2.56043i	−0.0487634	+	0.0844606i	−0.889377	−	0.457175i	$-0.848861\pi$
$919$	−1.47826	+	2.56043i	−0.0487634	+	0.0844606i	0.840613	+	0.541635i	$0.182195\pi$
$920$		0			0
$921$	0.383212	−	2.17330i	0.0126273	−	0.0716127i
$922$	6.60033	−	37.4324i	0.217370	−	1.23277i
$923$	−39.9692	−	69.2286i	−1.31560	−	2.27869i
$924$	−6.02192	+	10.4303i	−0.198107	+	0.343131i
$925$		0			0
$926$	19.0180	+	6.92197i	0.624969	+	0.227470i
$927$	1.67613	−	0.610062i	0.0550514	−	0.0200371i
$928$	0.508206	−	0.426435i	0.0166827	−	0.0139984i
$929$	−5.79901	−	32.8878i	−0.190259	−	1.07901i	−0.919010	−	0.394235i	$-0.871010\pi$
$929$	−5.79901	−	32.8878i	−0.190259	−	1.07901i	0.728750	−	0.684779i	$-0.240101\pi$
$930$		0			0
$931$	5.24995	−	4.59526i	0.172060	−	0.150604i
$932$	−7.92421			−0.259566
$933$	−1.71135	−	9.70555i	−0.0560271	−	0.317745i
$934$	14.8753	−	12.4818i	0.486734	−	0.408419i
$935$		0			0
$936$	1.24306	+	0.452435i	0.0406306	+	0.0147883i
$937$	30.6304	+	25.7020i	1.00065	+	0.839647i	0.987075	−	0.160261i	$-0.0512334\pi$
$937$	30.6304	+	25.7020i	1.00065	+	0.839647i	0.0135779	+	0.999908i	$0.495678\pi$
$938$	−6.16091	+	10.6710i	−0.201161	+	0.348421i
$939$	5.21258	+	9.02845i	0.170106	+	0.294632i
$940$		0			0
$941$	−6.18958	+	35.1028i	−0.201774	+	1.14432i	0.700661	+	0.713494i	$0.252889\pi$
$941$	−6.18958	+	35.1028i	−0.201774	+	1.14432i	−0.902435	+	0.430825i	$0.858223\pi$
$942$	5.83761	+	10.1110i	0.190200	+	0.329435i
$943$	−3.88050	+	6.72123i	−0.126367	+	0.218873i
$944$	−7.80839	−	6.55202i	−0.254142	−	0.213250i
$945$		0			0
$946$	−6.36102	+	2.31522i	−0.206815	+	0.0752744i
$947$	12.9277	−	10.8476i	0.420094	−	0.352500i	−0.408105	−	0.912935i	$-0.633810\pi$
$947$	12.9277	−	10.8476i	0.420094	−	0.352500i	0.828199	+	0.560435i	$0.189366\pi$
$948$	−4.79600	−	27.1995i	−0.155767	−	0.883398i
$949$	−17.3574			−0.563444
$950$		0			0
$951$	35.9594			1.16606
$952$	1.90177	+	10.7855i	0.0616367	+	0.349559i
$953$	−18.1350	+	15.2171i	−0.587450	+	0.492929i	−0.887384	−	0.461031i	$-0.847480\pi$
$953$	−18.1350	+	15.2171i	−0.587450	+	0.492929i	0.299934	+	0.953960i	$0.403035\pi$
$954$	−1.84458	+	0.671371i	−0.0597204	+	0.0217364i
$955$		0			0
$956$	11.3477	+	9.52183i	0.367010	+	0.307958i
$957$	1.71929	−	2.97790i	0.0555767	−	0.0962617i
$958$	3.66607	+	6.34982i	0.118445	+	0.205154i
$959$	−7.75341	+	43.9718i	−0.250371	+	1.41992i
$960$		0			0
$961$	5.33838	+	9.24635i	0.172206	+	0.298269i
$962$	−32.4012	+	56.1205i	−1.04466	+	1.80940i
$963$	−1.34067	−	1.12496i	−0.0432026	−	0.0362513i
$964$	7.68622	+	2.79756i	0.247556	+	0.0901032i
$965$		0			0
$966$	−9.50226	+	7.97335i	−0.305730	+	0.256538i
$967$	0.149858	+	0.849889i	0.00481912	+	0.0273306i	0.987122	−	0.159966i	$-0.0511385\pi$
$967$	0.149858	+	0.849889i	0.00481912	+	0.0273306i	−0.982303	+	0.187297i	$0.940027\pi$
$968$	−1.42096			−0.0456712
$969$	−16.5772	+	30.1483i	−0.532537	+	0.968503i
$970$		0			0
$971$	7.54276	+	42.7771i	0.242059	+	1.37278i	0.827226	+	0.561870i	$0.189918\pi$
$971$	7.54276	+	42.7771i	0.242059	+	1.37278i	−0.585167	+	0.810913i	$0.698971\pi$
$972$	1.55337	−	1.30343i	0.0498244	−	0.0418076i
$973$	−2.35653	+	0.857707i	−0.0755469	+	0.0274968i
$974$	21.6238	+	7.87040i	0.692870	+	0.252184i
$975$		0			0
$976$	−1.86168	+	3.22452i	−0.0595908	+	0.103214i
$977$	−22.2280	−	38.5001i	−0.711138	−	1.23173i	−0.964430	−	0.264338i	$-0.914847\pi$
$977$	−22.2280	−	38.5001i	−0.711138	−	1.23173i	0.253292	−	0.967390i	$-0.418487\pi$
$978$	1.46276	−	8.29570i	0.0467738	−	0.265267i
$979$	4.54578	−	25.7804i	0.145284	−	0.823946i
$980$		0			0
$981$	−0.937445	+	1.62370i	−0.0299303	+	0.0518408i
$982$	16.1944	+	13.5887i	0.516783	+	0.433633i
$983$	12.2338	+	4.45274i	0.390198	+	0.142020i	0.529666	−	0.848206i	$-0.322317\pi$
$983$	12.2338	+	4.45274i	0.390198	+	0.142020i	−0.139469	+	0.990226i	$0.544539\pi$
$984$	−3.83148	+	1.39455i	−0.122143	+	0.0444565i
$985$		0			0
$986$	−0.542965	−	3.07931i	−0.0172915	−	0.0980652i
$987$	24.4246			0.777444
$988$	−4.51580	+	29.1553i	−0.143667	+	0.927553i
$989$	−6.97187			−0.221693
$990$		0			0
$991$	20.8851	−	17.5247i	0.663436	−	0.556689i	−0.247678	−	0.968842i	$-0.579668\pi$
$991$	20.8851	−	17.5247i	0.663436	−	0.556689i	0.911115	+	0.412153i	$0.135223\pi$
$992$	4.23626	−	1.54187i	0.134501	−	0.0489545i
$993$	−32.3136	−	11.7612i	−1.02544	−	0.373230i
$994$	−21.0229	−	17.6403i	−0.666806	−	0.559516i
$995$		0			0
$996$	−5.38371	−	9.32486i	−0.170589	−	0.295469i
$997$	3.46311	−	19.6403i	0.109678	−	0.622014i	−0.879570	−	0.475769i	$-0.842170\pi$
$997$	3.46311	−	19.6403i	0.109678	−	0.622014i	0.989248	−	0.146246i	$-0.0467190\pi$
$998$	2.36215	−	13.3964i	0.0747725	−	0.424056i
$999$	25.6175	+	44.3707i	0.810500	+	1.40383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.m.351.4		30
5.2	odd	4		190.2.p.a.9.2	✓	60
5.3	odd	4		190.2.p.a.9.9	yes	60
5.4	even	2		950.2.l.l.351.2		30
19.17	even	9	inner	950.2.l.m.701.4		30
95.17	odd	36		190.2.p.a.169.9	yes	60
95.74	even	18		950.2.l.l.701.2		30
95.93	odd	36		190.2.p.a.169.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.9.2	✓	60	5.2	odd	4
190.2.p.a.9.9	yes	60	5.3	odd	4
190.2.p.a.169.2	yes	60	95.93	odd	36
190.2.p.a.169.9	yes	60	95.17	odd	36
950.2.l.l.351.2		30	5.4	even	2
950.2.l.l.701.2		30	95.74	even	18
950.2.l.m.351.4		30	1.1	even	1	trivial
950.2.l.m.701.4		30	19.17	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.28288 - 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(1.16183 - 2.01234i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.28288 - 1.07646i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28288 + 1.07646i) q^{6} +(1.16183 - 2.01234i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0339381 + 0.192472i) q^{9} +(1.54750 + 2.68035i) q^{11} +(-0.837341 + 1.45032i) q^{12} +(5.18492 + 4.35067i) q^{13} +(2.18352 + 0.794737i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.818439 - 4.64160i) q^{17} -0.195441 q^{18} +(-0.846315 - 4.27595i) q^{19} +(-0.675731 - 3.83226i) q^{21} +(-2.37091 + 1.98943i) q^{22} +(-2.99540 + 1.09024i) q^{23} +(-1.57369 - 0.572775i) q^{24} +(-3.38422 + 5.86164i) q^{26} +(2.67567 + 4.63440i) q^{27} +(-0.403498 + 2.28835i) q^{28} +(0.115201 - 0.653337i) q^{29} +(2.25407 - 3.90416i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.87056 + 1.77274i) q^{33} +(4.42896 - 1.61201i) q^{34} +(-0.0339381 - 0.192472i) q^{36} +9.57421 q^{37} +(4.06403 - 1.57597i) q^{38} +11.3350 q^{39} +(1.86510 - 1.56501i) q^{41} +(3.65670 - 1.33093i) q^{42} +(2.05525 + 0.748052i) q^{43} +(-2.37091 - 1.98943i) q^{44} +(-1.59382 - 2.76058i) q^{46} +(-1.08992 + 6.18124i) q^{47} +(0.290805 - 1.64924i) q^{48} +(0.800316 + 1.38619i) q^{49} +(-6.04648 - 5.07360i) q^{51} +(-6.36025 - 2.31494i) q^{52} +(9.43800 - 3.43515i) q^{53} +(-4.09937 + 3.43978i) q^{54} -2.32365 q^{56} +(-5.68863 - 4.57451i) q^{57} +0.663415 q^{58} +(-1.77002 - 10.0383i) q^{59} +(-3.49881 + 1.27346i) q^{61} +(4.23626 + 1.54187i) q^{62} +(0.347890 + 0.291915i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.900044 + 5.10440i) q^{66} +(-0.920817 + 5.22221i) q^{67} +(2.35660 + 4.08175i) q^{68} +(-2.66914 + 4.62309i) q^{69} +(-11.0982 - 4.03942i) q^{71} +(0.183655 - 0.0668449i) q^{72} +(-1.96449 + 1.64840i) q^{73} +(1.66254 + 9.42875i) q^{74} +(2.25774 + 3.72862i) q^{76} +7.19172 q^{77} +(1.96830 + 11.1628i) q^{78} +(-12.6337 + 10.6009i) q^{79} +(7.87038 + 2.86458i) q^{81} +(1.86510 + 1.56501i) q^{82} +(-3.21477 + 5.56814i) q^{83} +(1.94569 + 3.37003i) q^{84} +(-0.379796 + 2.15393i) q^{86} +(-0.555505 - 0.962162i) q^{87} +(1.54750 - 2.68035i) q^{88} +(-6.47935 - 5.43682i) q^{89} +(14.7790 - 5.37912i) q^{91} +(2.44187 - 2.04898i) q^{92} +(-1.31099 - 7.43499i) q^{93} -6.27659 q^{94} +1.67468 q^{96} +(-0.923151 - 5.23545i) q^{97} +(-1.22615 + 1.02887i) q^{98} +(-0.568413 + 0.206885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) \) 30 * q + 12 * q^7 - 15 * q^8	\( 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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