LMFDB - Embedded newform 490.2.l.c.117.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, not 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.4
Root			$0.587308 + 2.01725i$ of defining polynomial
Character	$\chi$	$=$	490.117
Dual form			490.2.l.c.423.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} -2.90667i q^{6} +(0.707107 - 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} -2.90667i q^{6} +(0.707107 - 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +(1.79038 + 1.33961i) q^{10} +(-1.83557 - 3.17930i) q^{11} +(-0.752300 - 2.80762i) q^{12} +(0.830578 + 0.830578i) q^{13} +(5.97414 - 2.55992i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.761471 + 0.204036i) q^{17} +(-5.26305 - 1.41023i) q^{18} +(1.09461 - 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-2.59589 - 2.59589i) q^{22} +(1.21791 + 4.54529i) q^{23} +(-1.45333 - 2.51725i) q^{24} +(-1.17653 + 4.85961i) q^{25} +(1.01725 + 0.587308i) q^{26} +(-5.03288 + 5.03288i) q^{27} +2.62236i q^{29} +(5.10802 - 4.01892i) q^{30} +(-0.0359651 + 0.0207644i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-10.3072 + 2.76180i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(-0.248174 + 0.0664979i) q^{37} +(0.566614 - 2.11463i) q^{38} +(2.95680 - 1.70711i) q^{39} +(2.22032 + 0.264946i) q^{40} +8.98026i q^{41} +(-0.474569 + 0.474569i) q^{43} +(-3.17930 - 1.83557i) q^{44} +(-1.73673 - 12.0593i) q^{45} +(2.35282 + 4.07520i) q^{46} +(-1.65648 - 6.18205i) q^{47} +(-2.05532 - 2.05532i) q^{48} +(0.121320 + 4.99853i) q^{50} +(1.14571 - 1.98443i) q^{51} +(1.13459 + 0.304013i) q^{52} +(-7.64413 - 2.04824i) q^{53} +(-3.55879 + 6.16400i) q^{54} +(3.04917 - 7.62161i) q^{55} +(-4.49957 - 4.49957i) q^{57} +(0.678717 + 2.53301i) q^{58} +(5.35616 + 9.27713i) q^{59} +(3.89379 - 5.20403i) q^{60} +(-1.72539 - 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} -1.00000i q^{64} +(-0.311210 + 2.60802i) q^{65} +(-9.24117 + 5.33539i) q^{66} +(-1.71399 + 6.39671i) q^{67} +(0.761471 - 0.204036i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(-5.26305 + 1.41023i) q^{72} +(-2.55331 + 9.52910i) q^{73} +(-0.222506 + 0.128464i) q^{74} +(12.7588 + 6.95913i) q^{75} -2.18923i q^{76} +(2.41421 - 2.41421i) q^{78} +(11.6145 + 6.70563i) q^{79} +(2.21323 - 0.318742i) q^{80} +(2.17114 + 3.76053i) q^{81} +(2.32426 + 8.67427i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(-0.335571 + 0.581226i) q^{86} +(7.36260 + 1.97280i) q^{87} +(-3.54605 - 0.950161i) q^{88} +(0.715130 - 1.23864i) q^{89} +(-4.79872 - 11.1989i) q^{90} +(3.32739 + 3.32739i) q^{92} +(0.0312422 + 0.116597i) q^{93} +(-3.20007 - 5.54268i) q^{94} +(4.84527 - 0.697798i) q^{95} +(-2.51725 - 1.45333i) q^{96} +(-3.16693 + 3.16693i) q^{97} +20.0030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5}+O(q^{10}) $ 16 * q + 12 * q^5	$ 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.752300	−	2.80762i	0.434341	−	1.62098i	−0.308298	−	0.951290i	$-0.599759\pi$
$3$	0.752300	−	2.80762i	0.434341	−	1.62098i	0.742639	−	0.669692i	$-0.233574\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.38266	+	1.75735i	0.618342	+	0.785909i
$5$	1.38266	+	1.75735i	0.618342	+	0.785909i
$6$		−	2.90667i		−	1.18664i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−4.71872	−	2.72435i	−1.57291	−	0.908118i
$10$	1.79038	+	1.33961i	0.566167	+	0.423621i
$11$	−1.83557	−	3.17930i	−0.553445	−	0.958596i	−0.998023	−	0.0628551i	$-0.979979\pi$
$11$	−1.83557	−	3.17930i	−0.553445	−	0.958596i	0.444577	−	0.895741i	$-0.353354\pi$
$12$	−0.752300	−	2.80762i	−0.217170	−	0.810491i
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	0.812843	−	0.582482i	$-0.197918\pi$
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	−0.582482	+	0.812843i	$0.697918\pi$
$14$		0			0
$15$	5.97414	−	2.55992i	1.54252	−	0.660970i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.761471	+	0.204036i	0.184684	+	0.0494859i	0.349976	−	0.936759i	$-0.386190\pi$
$17$	0.761471	+	0.204036i	0.184684	+	0.0494859i	−0.165292	+	0.986245i	$0.552857\pi$
$18$	−5.26305	−	1.41023i	−1.24051	−	0.332394i
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	−0.712713	−	0.701455i	$-0.752534\pi$
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	0.963835	+	0.266500i	$0.0858673\pi$
$20$	2.07609	+	0.830578i	0.464227	+	0.185723i
$21$		0			0
$22$	−2.59589	−	2.59589i	−0.553445	−	0.553445i
$23$	1.21791	+	4.54529i	0.253951	+	0.947759i	0.968671	+	0.248348i	$0.0798877\pi$
$23$	1.21791	+	4.54529i	0.253951	+	0.947759i	−0.714719	+	0.699411i	$0.753446\pi$
$24$	−1.45333	−	2.51725i	−0.296660	−	0.513831i
$25$	−1.17653	+	4.85961i	−0.235306	+	0.971921i
$26$	1.01725	+	0.587308i	0.199498	+	0.115180i
$27$	−5.03288	+	5.03288i	−0.968579	+	0.968579i
$28$		0			0
$29$			2.62236i			0.486960i	0.969906	+	0.243480i	$0.0782891\pi$
$29$			2.62236i			0.486960i	−0.969906	+	0.243480i	$0.921711\pi$
$30$	5.10802	−	4.01892i	0.932592	−	0.733751i
$31$	−0.0359651	+	0.0207644i	−0.00645952	+	0.00372940i	−0.503226	−	0.864155i	$-0.667854\pi$
$31$	−0.0359651	+	0.0207644i	−0.00645952	+	0.00372940i	0.496767	+	0.867884i	$0.334520\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−10.3072	+	2.76180i	−1.79425	+	0.480768i
$34$	0.788333			0.135198
$35$		0			0
$36$	−5.44871			−0.908118
$37$	−0.248174	+	0.0664979i	−0.0407995	+	0.0109322i	−0.279161	−	0.960244i	$-0.590056\pi$
$37$	−0.248174	+	0.0664979i	−0.0407995	+	0.0109322i	0.238362	+	0.971176i	$0.423390\pi$
$38$	0.566614	−	2.11463i	0.0919169	−	0.343038i
$39$	2.95680	−	1.70711i	0.473466	−	0.273356i
$40$	2.22032	+	0.264946i	0.351063	+	0.0418916i
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$		0			0
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	−0.742366	−	0.669995i	$-0.766296\pi$
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	0.669995	+	0.742366i	$0.266296\pi$
$44$	−3.17930	−	1.83557i	−0.479298	−	0.276723i
$45$	−1.73673	−	12.0593i	−0.258897	−	1.79769i
$46$	2.35282	+	4.07520i	0.346904	+	0.600855i
$47$	−1.65648	−	6.18205i	−0.241622	−	0.901745i	−0.975051	−	0.221980i	$-0.928748\pi$
$47$	−1.65648	−	6.18205i	−0.241622	−	0.901745i	0.733429	−	0.679766i	$-0.237919\pi$
$48$	−2.05532	−	2.05532i	−0.296660	−	0.296660i
$49$		0			0
$50$	0.121320	+	4.99853i	0.0171573	+	0.706899i
$51$	1.14571	−	1.98443i	0.160432	−	0.277876i
$52$	1.13459	+	0.304013i	0.157339	+	0.0421590i
$53$	−7.64413	−	2.04824i	−1.05000	−	0.281347i	−0.307749	−	0.951468i	$-0.599576\pi$
$53$	−7.64413	−	2.04824i	−1.05000	−	0.281347i	−0.742252	+	0.670120i	$0.766242\pi$
$54$	−3.55879	+	6.16400i	−0.484289	+	0.838814i
$55$	3.04917	−	7.62161i	0.411150	−	1.02770i
$56$		0			0
$57$	−4.49957	−	4.49957i	−0.595982	−	0.595982i
$58$	0.678717	+	2.53301i	0.0891199	+	0.332600i
$59$	5.35616	+	9.27713i	0.697312	+	1.20778i	0.969395	+	0.245506i	$0.0789541\pi$
$59$	5.35616	+	9.27713i	0.697312	+	1.20778i	−0.272083	+	0.962274i	$0.587713\pi$
$60$	3.89379	−	5.20403i	0.502687	−	0.671837i
$61$	−1.72539	−	0.996157i	−0.220914	−	0.127545i	0.385459	−	0.922725i	$-0.374043\pi$
$61$	−1.72539	−	0.996157i	−0.220914	−	0.127545i	−0.606373	+	0.795180i	$0.707376\pi$
$62$	−0.0293654	+	0.0293654i	−0.00372940	+	0.00372940i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.311210	+	2.60802i	−0.0386008	+	0.323485i
$66$	−9.24117	+	5.33539i	−1.13751	+	0.656741i
$67$	−1.71399	+	6.39671i	−0.209398	+	0.781482i	0.778666	+	0.627438i	$0.215897\pi$
$67$	−1.71399	+	6.39671i	−0.209398	+	0.781482i	−0.988064	+	0.154044i	$0.950770\pi$
$68$	0.761471	−	0.204036i	0.0923420	−	0.0247430i
$69$	13.6777			1.64660
$70$		0			0
$71$	8.11777			0.963402			0.481701	−	0.876336i	$-0.340019\pi$
$71$	8.11777			0.963402			0.481701	+	0.876336i	$0.340019\pi$
$72$	−5.26305	+	1.41023i	−0.620256	+	0.166197i
$73$	−2.55331	+	9.52910i	−0.298843	+	1.11530i	0.639274	+	0.768979i	$0.279235\pi$
$73$	−2.55331	+	9.52910i	−0.298843	+	1.11530i	−0.938117	+	0.346318i	$0.887432\pi$
$74$	−0.222506	+	0.128464i	−0.0258658	+	0.0149336i
$75$	12.7588	+	6.95913i	1.47326	+	0.803571i
$76$		−	2.18923i		−	0.251122i
$77$		0			0
$78$	2.41421	−	2.41421i	0.273356	−	0.273356i
$79$	11.6145	+	6.70563i	1.30673	+	0.754443i	0.981550	−	0.191208i	$-0.0612405\pi$
$79$	11.6145	+	6.70563i	1.30673	+	0.754443i	0.325184	+	0.945651i	$0.394574\pi$
$80$	2.21323	−	0.318742i	0.247447	−	0.0356364i
$81$	2.17114	+	3.76053i	0.241238	+	0.417836i
$82$	2.32426	+	8.67427i	0.256672	+	0.957912i
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.997509	−	0.0705331i	$-0.977530\pi$
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.0705331	−	0.997509i	$-0.522470\pi$
$84$		0			0
$85$	0.694291	+	1.62028i	0.0753065	+	0.175744i
$86$	−0.335571	+	0.581226i	−0.0361855	+	0.0626752i
$87$	7.36260	+	1.97280i	0.789354	+	0.211507i
$88$	−3.54605	−	0.950161i	−0.378010	−	0.101288i
$89$	0.715130	−	1.23864i	0.0758036	−	0.131296i	−0.825632	−	0.564209i	$-0.809181\pi$
$89$	0.715130	−	1.23864i	0.0758036	−	0.131296i	0.901435	+	0.432914i	$0.142514\pi$
$90$	−4.79872	−	11.1989i	−0.505829	−	1.18046i
$91$		0			0
$92$	3.32739	+	3.32739i	0.346904	+	0.346904i
$93$	0.0312422	+	0.116597i	0.00323967	+	0.0120906i
$94$	−3.20007	−	5.54268i	−0.330062	−	0.571684i
$95$	4.84527	−	0.697798i	0.497114	−	0.0715926i
$96$	−2.51725	−	1.45333i	−0.256915	−	0.148330i
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	−0.849363	−	0.527810i	$-0.823013\pi$
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	0.527810	+	0.849363i	$0.323013\pi$
$98$		0			0
$99$			20.0030i			2.01037i
$100$	1.41090	+	4.79681i	0.141090	+	0.479681i
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	−0.496899	−	0.867809i	$-0.665528\pi$
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	0.503095	+	0.864231i	$0.332195\pi$
$102$	0.593063	−	2.21334i	0.0587220	−	0.219154i
$103$	16.0148	−	4.29116i	1.57799	−	0.422820i	0.639685	−	0.768638i	$-0.279065\pi$
$103$	16.0148	−	4.29116i	1.57799	−	0.422820i	0.938302	+	0.345817i	$0.112398\pi$
$104$	1.17462			0.115180
$105$		0			0
$106$	−7.91378			−0.768654
$107$	−4.41372	+	1.18265i	−0.426690	+	0.114331i	−0.465772	−	0.884905i	$-0.654223\pi$
$107$	−4.41372	+	1.18265i	−0.426690	+	0.114331i	0.0390819	+	0.999236i	$0.487557\pi$
$108$	−1.84216	+	6.87505i	−0.177262	+	0.661552i
$109$	15.6773	−	9.05131i	1.50162	−	0.866958i	0.501617	−	0.865090i	$-0.332739\pi$
$109$	15.6773	−	9.05131i	1.50162	−	0.866958i	0.999998	−	0.00186842i	$-0.000594737\pi$
$110$	0.972654	−	8.15110i	0.0927390	−	0.777176i
$111$			0.746804i			0.0708835i
$112$		0			0
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	−0.631955	−	0.775005i	$-0.717747\pi$
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	0.775005	+	0.631955i	$0.217747\pi$
$114$	−5.51082	−	3.18168i	−0.516136	−	0.297991i
$115$	−6.30371	+	8.42486i	−0.587824	+	0.785622i
$116$	1.31118	+	2.27103i	0.121740	+	0.210860i
$117$	−1.65648	−	6.18205i	−0.153141	−	0.571531i
$118$	7.57475	+	7.57475i	0.697312	+	0.697312i
$119$		0			0
$120$	2.41421	−	6.03449i	0.220387	−	0.550871i
$121$	−1.23864	+	2.14539i	−0.112604	+	0.195035i
$122$	−1.92443	−	0.515649i	−0.174229	−	0.0466846i
$123$	25.2132	+	6.75585i	2.27340	+	0.609155i
$124$	−0.0207644	+	0.0359651i	−0.00186470	+	0.00322976i
$125$	−10.1667	+	4.65160i	−0.909341	+	0.416051i
$126$		0			0
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.980757	−	0.195234i	$-0.937453\pi$
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.195234	−	0.980757i	$-0.562547\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.975392	+	1.68943i	0.0858785	+	0.148746i
$130$	0.374399	+	2.59970i	0.0328370	+	0.228009i
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.144755	−	0.989468i	$-0.546239\pi$
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.929281	+	0.369372i	$0.879573\pi$
$132$	−7.54538	+	7.54538i	−0.656741	+	0.656741i
$133$		0			0
$134$			6.62236i			0.572085i
$135$	−15.8033	−	1.88577i	−1.36013	−	0.162301i
$136$	0.682717	−	0.394167i	0.0585425	−	0.0337995i
$137$	−4.90887	+	18.3201i	−0.419393	+	1.56519i	0.356479	+	0.934303i	$0.383977\pi$
$137$	−4.90887	+	18.3201i	−0.419393	+	1.56519i	−0.775871	+	0.630891i	$0.782689\pi$
$138$	13.2117	−	3.54005i	1.12465	−	0.301349i
$139$	8.23706			0.698658			0.349329	−	0.937000i	$-0.386409\pi$
$139$	8.23706			0.698658			0.349329	+	0.937000i	$0.386409\pi$
$140$		0			0
$141$	−18.6030			−1.56666
$142$	7.84116	−	2.10103i	0.658016	−	0.176315i
$143$	1.11607	−	4.16524i	0.0933308	−	0.348315i
$144$	−4.71872	+	2.72435i	−0.393227	+	0.227029i
$145$	−4.60840	+	3.62582i	−0.382706	+	0.301108i
$146$			9.86525i			0.816454i
$147$		0			0
$148$	−0.181676	+	0.181676i	−0.0149336	+	0.0149336i
$149$	−4.19317	−	2.42093i	−0.343518	−	0.198330i	0.318309	−	0.947987i	$-0.396885\pi$
$149$	−4.19317	−	2.42093i	−0.343518	−	0.198330i	−0.661826	+	0.749657i	$0.730218\pi$
$150$	14.1253	+	3.41977i	1.15332	+	0.279223i
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	0.585992	−	0.810317i	$-0.300705\pi$
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	−0.994751	+	0.102325i	$0.967372\pi$
$152$	−0.566614	−	2.11463i	−0.0459584	−	0.171519i
$153$	−3.03730	−	3.03730i	−0.245551	−	0.245551i
$154$		0			0
$155$	−0.0862176	−	0.0344930i	−0.00692516	−	0.00277054i
$156$	1.70711	−	2.95680i	0.136678	−	0.236733i
$157$	−23.6523	−	6.33762i	−1.88766	−	0.505797i	−0.998872	−	0.0474774i	$-0.984882\pi$
$157$	−23.6523	−	6.33762i	−1.88766	−	0.505797i	−0.888788	−	0.458320i	$-0.848452\pi$
$158$	12.9543	+	3.47109i	1.03059	+	0.276145i
$159$	−11.5014	+	19.9209i	−0.912117	+	1.57983i
$160$	2.05532	−	0.880708i	0.162488	−	0.0696261i
$161$		0			0
$162$	3.07046	+	3.07046i	0.241238	+	0.241238i
$163$	−5.68510	−	21.2171i	−0.445291	−	1.66185i	−0.715166	−	0.698954i	$-0.753649\pi$
$163$	−5.68510	−	21.2171i	−0.445291	−	1.66185i	0.269875	−	0.962895i	$-0.413018\pi$
$164$	4.49013	+	7.77713i	0.350620	+	0.607292i
$165$	−19.1047	−	14.2947i	−1.48730	−	1.11284i
$166$	−11.9172	−	6.88038i	−0.924952	−	0.534021i
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	−0.818279	−	0.574821i	$-0.805072\pi$
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	0.574821	+	0.818279i	$0.305072\pi$
$168$		0			0
$169$		−	11.6203i		−	0.893868i
$170$	1.08999	+	1.38537i	0.0835987	+	0.106253i
$171$	−10.3303	+	5.96423i	−0.789981	+	0.456096i
$172$	−0.173704	+	0.648273i	−0.0132448	+	0.0494304i
$173$	5.04844	−	1.35273i	0.383826	−	0.102846i	−0.0617463	−	0.998092i	$-0.519667\pi$
$173$	5.04844	−	1.35273i	0.383826	−	0.102846i	0.445572	+	0.895246i	$0.353000\pi$
$174$	7.62233			0.577847
$175$		0			0
$176$	−3.67114			−0.276723
$177$	30.0761	−	8.05888i	2.26066	−	0.605742i
$178$	0.370178	−	1.38152i	0.0277460	−	0.103550i
$179$	−10.8847	+	6.28428i	−0.813560	+	0.469709i	−0.848191	−	0.529691i	$-0.822308\pi$
$179$	−10.8847	+	6.28428i	−0.813560	+	0.469709i	0.0346308	+	0.999400i	$0.488974\pi$
$180$	−7.53368	−	9.57526i	−0.561528	−	0.713698i
$181$		−	11.6742i		−	0.867740i	−0.900976	−	0.433870i	$-0.857148\pi$
$181$		−	11.6742i		−	0.867740i	0.900976	−	0.433870i	$-0.142852\pi$
$182$		0			0
$183$	−4.09485	+	4.09485i	−0.302700	+	0.302700i
$184$	4.07520	+	2.35282i	0.300428	+	0.173452i
$185$	−0.459998	−	0.344183i	−0.0338197	−	0.0253048i
$186$	0.0603553	+	0.104538i	0.00442546	+	0.00766513i
$187$	−0.749044	−	2.79547i	−0.0547755	−	0.204425i
$188$	−4.52558	−	4.52558i	−0.330062	−	0.330062i
$189$		0			0
$190$	4.49957	−	1.92807i	0.326433	−	0.139877i
$191$	−7.75170	+	13.4263i	−0.560894	+	0.971496i	0.436525	+	0.899692i	$0.356209\pi$
$191$	−7.75170	+	13.4263i	−0.560894	+	0.971496i	−0.997419	+	0.0718040i	$0.977124\pi$
$192$	−2.80762	−	0.752300i	−0.202623	−	0.0542926i
$193$	−8.69132	−	2.32883i	−0.625615	−	0.167633i	−0.0679359	−	0.997690i	$-0.521641\pi$
$193$	−8.69132	−	2.32883i	−0.625615	−	0.167633i	−0.557679	+	0.830057i	$0.688308\pi$
$194$	−2.23936	+	3.87868i	−0.160776	+	0.278473i
$195$	7.08821	+	2.83577i	0.507597	+	0.203074i
$196$		0			0
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	0.992347	−	0.123482i	$-0.0394061\pi$
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	−0.123482	+	0.992347i	$0.539406\pi$
$198$	5.17715	+	19.3214i	0.367924	+	1.37311i
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	0.978246	−	0.207448i	$-0.0665159\pi$
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	−0.668779	+	0.743462i	$0.733183\pi$
$200$	2.60433	+	4.26819i	0.184154	+	0.301807i
$201$	16.6701	+	9.62450i	1.17582	+	0.678860i
$202$	0.0508460	−	0.0508460i	0.00357751	−	0.00357751i
$203$		0			0
$204$		−	2.29142i		−	0.160432i
$205$	−15.7814	+	12.4166i	−1.10222	+	0.867213i
$206$	14.3585	−	8.28988i	1.00040	−	0.577583i
$207$	6.63602	−	24.7660i	0.461235	−	1.72135i
$208$	1.13459	−	0.304013i	0.0786697	−	0.0210795i
$209$	−8.03696			−0.555928
$210$		0			0
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	−7.64413	+	2.04824i	−0.525001	+	0.140674i
$213$	6.10700	−	22.7916i	0.418445	−	1.56166i
$214$	−3.95723	+	2.28471i	−0.270511	+	0.156179i
$215$	−1.49015	−	0.177816i	−0.101627	−	0.0121270i
$216$			7.11757i			0.484289i
$217$		0			0
$218$	12.8005	−	12.8005i	0.866958	−	0.866958i
$219$	24.8333	+	14.3375i	1.67808	+	0.968838i
$220$	−1.17015	−	8.12509i	−0.0788913	−	0.547794i
$221$	0.462994	+	0.801929i	0.0311443	+	0.0539436i
$222$	0.193287	+	0.721358i	0.0129726	+	0.0484143i
$223$	0.746804	+	0.746804i	0.0500097	+	0.0500097i	0.731669	−	0.681660i	$-0.238742\pi$
$223$	0.746804	+	0.746804i	0.0500097	+	0.0500097i	−0.681660	+	0.731669i	$0.738742\pi$
$224$		0			0
$225$	18.7910	−	19.7258i	1.25273	−	1.31506i
$226$	1.07525	−	1.86239i	0.0715247	−	0.123884i
$227$	3.01404	+	0.807609i	0.200049	+	0.0536029i	0.357452	−	0.933932i	$-0.383646\pi$
$227$	3.01404	+	0.807609i	0.200049	+	0.0536029i	−0.157403	+	0.987534i	$0.550312\pi$
$228$	−6.14653	−	1.64696i	−0.407064	−	0.109072i
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	−0.692689	−	0.721236i	$-0.743574\pi$
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	0.970954	+	0.239268i	$0.0769075\pi$
$230$	−3.90840	+	9.76931i	−0.257712	+	0.644169i
$231$		0			0
$232$	1.85429	+	1.85429i	0.121740	+	0.121740i
$233$	−5.90027	−	22.0201i	−0.386540	−	1.44259i	−0.835725	−	0.549148i	$-0.814952\pi$
$233$	−5.90027	−	22.0201i	−0.386540	−	1.44259i	0.449186	−	0.893439i	$-0.351714\pi$
$234$	−3.20007	−	5.54268i	−0.209195	−	0.362336i
$235$	8.57367	−	11.4587i	0.559285	−	0.747480i
$236$	9.27713	+	5.35616i	0.603890	+	0.348656i
$237$	27.5645	−	27.5645i	1.79051	−	1.79051i
$238$		0			0
$239$			23.9971i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$239$			23.9971i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$240$	0.770110	−	6.45372i	0.0497104	−	0.416586i
$241$	21.4666	−	12.3937i	1.38278	−	0.798350i	0.390295	−	0.920690i	$-0.372373\pi$
$241$	21.4666	−	12.3937i	1.38278	−	0.798350i	0.992488	+	0.122340i	$0.0390398\pi$
$242$	−0.641168	+	2.39287i	−0.0412158	+	0.153820i
$243$	−8.43364	+	2.25979i	−0.541018	+	0.144965i
$244$	−1.99231			−0.127545
$245$		0			0
$246$	26.1026			1.66424
$247$	2.48388	−	0.665553i	0.158045	−	0.0423481i
$248$	−0.0107485	+	0.0401138i	−0.000682528	+	0.00254723i
$249$	−34.6392	+	19.9990i	−2.19517	+	1.26738i
$250$	−8.61640	+	7.12444i	−0.544949	+	0.450589i
$251$			11.1158i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$251$			11.1158i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$252$		0			0
$253$	12.2153	−	12.2153i	0.767970	−	0.767970i
$254$	−16.2312	−	9.37110i	−1.01844	−	0.587995i
$255$	5.07145	−	0.730372i	0.317587	−	0.0457377i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.54637	+	24.4314i	0.408351	+	1.52399i	0.797790	+	0.602935i	$0.206002\pi$
$257$	6.54637	+	24.4314i	0.408351	+	1.52399i	−0.389439	+	0.921052i	$0.627331\pi$
$258$	1.37941	+	1.37941i	0.0858785	+	0.0858785i
$259$		0			0
$260$	1.03449	+	2.41421i	0.0641565	+	0.149723i
$261$	7.14424	−	12.3742i	0.442217	−	0.765943i
$262$	−13.7110	−	3.67384i	−0.847066	−	0.226971i
$263$	−10.9595	−	2.93659i	−0.675792	−	0.181078i	−0.0954297	−	0.995436i	$-0.530423\pi$
$263$	−10.9595	−	2.93659i	−0.675792	−	0.181078i	−0.580363	+	0.814358i	$0.697089\pi$
$264$	−5.33539	+	9.24117i	−0.328371	+	0.568755i
$265$	−6.96973	−	16.2654i	−0.428147	−	0.999174i
$266$		0			0
$267$	−2.93964	−	2.93964i	−0.179903	−	0.179903i
$268$	1.71399	+	6.39671i	0.104699	+	0.390741i
$269$	−4.03346	−	6.98616i	−0.245924	−	0.425954i	0.716467	−	0.697621i	$-0.245758\pi$
$269$	−4.03346	−	6.98616i	−0.245924	−	0.425954i	−0.962391	+	0.271668i	$0.912425\pi$
$270$	−15.7529	+	2.26867i	−0.958688	+	0.138067i
$271$	−7.27419	−	4.19976i	−0.441876	−	0.255117i	0.262517	−	0.964927i	$-0.415447\pi$
$271$	−7.27419	−	4.19976i	−0.441876	−	0.255117i	−0.704393	+	0.709810i	$0.748781\pi$
$272$	0.557436	−	0.557436i	0.0337995	−	0.0337995i
$273$		0			0
$274$			18.9664i			1.14580i
$275$	17.6098	−	5.17962i	1.06191	−	0.312343i
$276$	11.8452	−	6.83885i	0.713000	−	0.411651i
$277$	1.47009	−	5.48646i	0.0883293	−	0.329650i	−0.907594	−	0.419848i	$-0.862083\pi$
$277$	1.47009	−	5.48646i	0.0883293	−	0.329650i	0.995924	+	0.0901983i	$0.0287501\pi$
$278$	7.95639	−	2.13191i	0.477193	−	0.127863i
$279$	0.226279			0.0135470
$280$		0			0
$281$	7.27627			0.434066			0.217033	−	0.976164i	$-0.430362\pi$
$281$	7.27627			0.434066			0.217033	+	0.976164i	$0.430362\pi$
$282$	−17.9692	+	4.81482i	−1.07005	+	0.286719i
$283$	1.99550	−	7.44729i	0.118620	−	0.442696i	−0.880912	−	0.473280i	$-0.843070\pi$
$283$	1.99550	−	7.44729i	0.118620	−	0.442696i	0.999532	+	0.0305840i	$0.00973671\pi$
$284$	7.03019	−	4.05888i	0.417165	−	0.240850i
$285$	1.68594	−	14.1287i	0.0998667	−	0.836909i
$286$		−	4.31218i		−	0.254984i
$287$		0			0
$288$	−3.85282	+	3.85282i	−0.227029	+	0.227029i
$289$	−14.1842	−	8.18927i	−0.834366	−	0.481721i
$290$	−3.51294	+	4.69502i	−0.206287	+	0.275701i
$291$	6.50906	+	11.2740i	0.381568	+	0.660895i
$292$	2.55331	+	9.52910i	0.149421	+	0.557648i
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	0.798207	−	0.602383i	$-0.205782\pi$
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	−0.602383	+	0.798207i	$0.705782\pi$
$294$		0			0
$295$	−8.89741	+	22.2397i	−0.518027	+	1.29485i
$296$	−0.128464	+	0.222506i	−0.00746682	+	0.0129329i
$297$	25.2393	+	6.76284i	1.46453	+	0.392420i
$298$	−4.67687	−	1.25316i	−0.270924	−	0.0725938i
$299$	−2.76365	+	4.78679i	−0.159826	+	0.276827i
$300$	14.5291	−	0.352638i	0.838835	−	0.0203595i
$301$		0			0
$302$	−7.10348	−	7.10348i	−0.408759	−	0.408759i
$303$	−0.0540958	−	0.201888i	−0.00310772	−	0.0115982i
$304$	−1.09461	−	1.89593i	−0.0627804	−	0.108739i
$305$	−0.635034	−	4.40946i	−0.0363619	−	0.252485i
$306$	−3.71992	−	2.14770i	−0.212654	−	0.122776i
$307$	−1.06546	+	1.06546i	−0.0608089	+	0.0608089i	−0.736857	−	0.676048i	$-0.763691\pi$
$307$	−1.06546	+	1.06546i	−0.0608089	+	0.0608089i	0.676048	+	0.736857i	$0.263691\pi$
$308$		0			0
$309$		−	48.1918i		−	2.74154i
$310$	−0.0922072	−	0.0110029i	−0.00523702	−	0.000624923i
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	−0.799138	−	0.601148i	$-0.794710\pi$
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	0.121040	+	0.992648i	$0.461377\pi$
$312$	0.883663	−	3.29788i	0.0500276	−	0.186706i
$313$	−22.5515	+	6.04266i	−1.27469	+	0.341551i	−0.831825	−	0.555038i	$-0.812704\pi$
$313$	−22.5515	+	6.04266i	−1.27469	+	0.341551i	−0.442863	+	0.896590i	$0.646037\pi$
$314$	−24.4867			−1.38186
$315$		0			0
$316$	13.4113			0.754443
$317$	−12.7394	+	3.41352i	−0.715518	+	0.191722i	−0.598171	−	0.801369i	$-0.704106\pi$
$317$	−12.7394	+	3.41352i	−0.715518	+	0.191722i	−0.117347	+	0.993091i	$0.537439\pi$
$318$	−5.95354	+	22.2189i	−0.333858	+	1.24598i
$319$	8.33728	−	4.81353i	0.466798	−	0.269506i
$320$	1.75735	−	1.38266i	0.0982386	−	0.0772928i
$321$			13.2818i			0.741316i
$322$		0			0
$323$	1.22035	−	1.22035i	0.0679023	−	0.0679023i
$324$	3.76053	+	2.17114i	0.208918	+	0.120619i
$325$	−5.01348	+	3.05909i	−0.278098	+	0.169688i
$326$	−10.9828	−	19.0227i	−0.608279	−	1.05357i
$327$	−13.6186	−	50.8253i	−0.753111	−	2.81065i
$328$	6.35000	+	6.35000i	0.350620	+	0.350620i
$329$		0			0
$330$	−22.1535	−	8.86292i	−1.21951	−	0.487888i
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	−0.474778	−	0.880106i	$-0.657472\pi$
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	0.999583	−	0.0288830i	$-0.00919501\pi$
$332$	−13.2919	−	3.56155i	−0.729487	−	0.195465i
$333$	1.35222	+	0.362328i	0.0741015	+	0.0198554i
$334$	−2.22467	+	3.85325i	−0.121729	+	0.210840i
$335$	−13.6111	+	5.83237i	−0.743653	+	0.318656i
$336$		0			0
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	0.720279	−	0.693684i	$-0.244014\pi$
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	−0.693684	+	0.720279i	$0.744014\pi$
$338$	−3.00755	−	11.2243i	−0.163589	−	0.610523i
$339$	−3.12540	−	5.41335i	−0.169748	−	0.294013i
$340$	1.41141	+	1.05606i	0.0765447	+	0.0572728i
$341$	0.132033	+	0.0762292i	0.00714998	+	0.00412804i
$342$	−8.43469	+	8.43469i	−0.456096	+	0.456096i
$343$		0			0
$344$			0.671142i			0.0361855i
$345$	18.9116	+	24.0365i	1.01816	+	1.29408i
$346$	4.52631	−	2.61327i	0.243336	−	0.140490i
$347$	0.986094	−	3.68015i	0.0529363	−	0.197561i	−0.934393	−	0.356243i	$-0.884058\pi$
$347$	0.986094	−	3.68015i	0.0529363	−	0.197561i	0.987330	+	0.158682i	$0.0507243\pi$
$348$	7.36260	−	1.97280i	0.394677	−	0.105753i
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$		0			0
$351$	−8.36041			−0.446246
$352$	−3.54605	+	0.950161i	−0.189005	+	0.0506438i
$353$	6.67203	−	24.9004i	0.355116	−	1.32531i	−0.525222	−	0.850965i	$-0.676018\pi$
$353$	6.67203	−	24.9004i	0.355116	−	1.32531i	0.880338	−	0.474347i	$-0.157316\pi$
$354$	26.9655	−	15.5686i	1.43320	−	0.827459i
$355$	11.2241	+	14.2657i	0.595712	+	0.757146i
$356$		−	1.43026i		−	0.0758036i
$357$		0			0
$358$	−8.88731	+	8.88731i	−0.469709	+	0.469709i
$359$	−8.99497	−	5.19325i	−0.474737	−	0.274089i	0.243484	−	0.969905i	$-0.421710\pi$
$359$	−8.99497	−	5.19325i	−0.474737	−	0.274089i	−0.718220	+	0.695816i	$0.755043\pi$
$360$	−9.75524	−	7.29913i	−0.514146	−	0.384698i
$361$	7.10364	+	12.3039i	0.373876	+	0.647572i
$362$	−3.02152	−	11.2765i	−0.158807	−	0.592677i
$363$	5.09161	+	5.09161i	0.267240	+	0.267240i
$364$		0			0
$365$	−20.2763	+	8.68840i	−1.06131	+	0.454772i
$366$	−2.89549	+	5.01514i	−0.151350	+	0.262146i
$367$	8.39004	+	2.24811i	0.437957	+	0.117350i	0.471059	−	0.882102i	$-0.343872\pi$
$367$	8.39004	+	2.24811i	0.437957	+	0.117350i	−0.0331020	+	0.999452i	$0.510539\pi$
$368$	4.54529	+	1.21791i	0.236940	+	0.0634878i
$369$	24.4654	−	42.3753i	1.27362	−	2.20597i
$370$	−0.533405	−	0.213399i	−0.0277304	−	0.0110941i
$371$		0			0
$372$	0.0853553	+	0.0853553i	0.00442546	+	0.00442546i
$373$	3.44476	+	12.8560i	0.178363	+	0.665660i	0.995954	+	0.0898611i	$0.0286423\pi$
$373$	3.44476	+	12.8560i	0.178363	+	0.665660i	−0.817591	+	0.575799i	$0.804691\pi$
$374$	−1.44704	−	2.50635i	−0.0748247	−	0.129600i
$375$	5.41149	+	32.0438i	0.279448	+	1.65473i
$376$	−5.54268	−	3.20007i	−0.285842	−	0.165031i
$377$	−2.17808	+	2.17808i	−0.112177	+	0.112177i
$378$		0			0
$379$		−	25.3453i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$379$		−	25.3453i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$380$	3.84723	−	3.02695i	0.197359	−	0.155279i
$381$	−47.1788	+	27.2387i	−2.41704	+	1.39548i
$382$	−4.01258	+	14.9751i	−0.205301	+	0.766195i
$383$	−17.7739	+	4.76251i	−0.908205	+	0.243353i	−0.682537	−	0.730851i	$-0.739123\pi$
$383$	−17.7739	+	4.76251i	−0.908205	+	0.243353i	−0.225668	+	0.974204i	$0.572457\pi$
$384$	−2.90667			−0.148330
$385$		0			0
$386$	−8.99792			−0.457982
$387$	3.53225	−	0.946464i	0.179554	−	0.0481114i
$388$	−1.15918	+	4.32611i	−0.0588483	+	0.219625i
$389$	19.3621	−	11.1787i	0.981699	−	0.566784i	0.0789164	−	0.996881i	$-0.474854\pi$
$389$	19.3621	−	11.1787i	0.981699	−	0.566784i	0.902783	+	0.430097i	$0.141521\pi$
$390$	7.58063	+	0.904582i	0.383860	+	0.0458053i
$391$			3.70961i			0.187603i
$392$		0			0
$393$	−29.1745	+	29.1745i	−1.47166	+	1.47166i
$394$	14.9359	+	8.62324i	0.752459	+	0.434432i
$395$	4.27473	+	29.6823i	0.215085	+	1.49348i
$396$	10.0015	+	17.3231i	0.502594	+	0.870518i
$397$	4.08518	+	15.2461i	0.205029	+	0.765181i	0.989441	+	0.144939i	$0.0462987\pi$
$397$	4.08518	+	15.2461i	0.205029	+	0.765181i	−0.784411	+	0.620241i	$0.787035\pi$
$398$	6.17385	+	6.17385i	0.309467	+	0.309467i
$399$		0			0
$400$	3.62028	+	3.44871i	0.181014	+	0.172435i
$401$	−6.98528	+	12.0989i	−0.348828	+	0.604188i	−0.986042	−	0.166499i	$-0.946754\pi$
$401$	−6.98528	+	12.0989i	−0.348828	+	0.604188i	0.637213	+	0.770687i	$0.280087\pi$
$402$	18.5931	+	4.98201i	0.927339	+	0.248480i
$403$	−0.0471183	−	0.0126253i	−0.00234713	−	0.000628911i
$404$	0.0359536	−	0.0622734i	0.00178876	−	0.00309822i
$405$	−3.60661	+	9.01496i	−0.179214	+	0.447957i
$406$		0			0
$407$	0.666957	+	0.666957i	0.0330598	+	0.0330598i
$408$	−0.593063	−	2.21334i	−0.0293610	−	0.109577i
$409$	−0.156681	−	0.271379i	−0.00774737	−	0.0134188i	0.862126	−	0.506694i	$-0.169133\pi$
$409$	−0.156681	−	0.271379i	−0.00774737	−	0.0134188i	−0.869873	+	0.493276i	$0.835799\pi$
$410$	−12.0300	+	16.0781i	−0.594121	+	0.794038i
$411$	47.7431	+	27.5645i	2.35499	+	1.35966i
$412$	11.7237	−	11.7237i	0.577583	−	0.577583i
$413$		0			0
$414$		−	25.6396i		−	1.26012i
$415$	3.64586	−	30.5532i	0.178968	−	1.49980i
$416$	1.01725	−	0.587308i	0.0498746	−	0.0287951i
$417$	6.19675	−	23.1266i	0.303456	−	1.13251i
$418$	−7.76311	+	2.08012i	−0.379706	+	0.101742i
$419$	31.6254			1.54500			0.772501	−	0.635014i	$-0.219006\pi$
$419$	31.6254			1.54500			0.772501	+	0.635014i	$0.219006\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	−10.7938	+	2.89219i	−0.525433	+	0.140789i
$423$	−9.02565	+	33.6842i	−0.438842	+	1.63778i
$424$	−6.85354	+	3.95689i	−0.332837	+	0.192164i
$425$	−1.88743	+	3.46040i	−0.0915536	+	0.167854i
$426$		−	23.5956i		−	1.14321i
$427$		0			0
$428$	−3.23107	+	3.23107i	−0.156179	+	0.156179i
$429$	−10.8548	−	6.26703i	−0.524075	−	0.302575i
$430$	−1.48539	+	0.213921i	−0.0716320	+	0.0103162i
$431$	−0.779037	−	1.34933i	−0.0375249	−	0.0649950i	0.846653	−	0.532145i	$-0.178614\pi$
$431$	−0.779037	−	1.34933i	−0.0375249	−	0.0649950i	−0.884178	+	0.467150i	$0.845281\pi$
$432$	1.84216	+	6.87505i	0.0886311	+	0.330776i
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	0.841748	−	0.539871i	$-0.181527\pi$
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	−0.539871	+	0.841748i	$0.681527\pi$
$434$		0			0
$435$	6.71305	+	15.6663i	0.321866	+	0.751144i
$436$	9.05131	−	15.6773i	0.433479	−	0.750808i
$437$	9.95068	+	2.66628i	0.476006	+	0.127545i
$438$	27.6979	+	7.42163i	1.32346	+	0.354619i
$439$	11.9571	−	20.7103i	0.570681	−	0.988449i	−0.425815	−	0.904810i	$-0.640012\pi$
$439$	11.9571	−	20.7103i	0.570681	−	0.988449i	0.996496	−	0.0836389i	$-0.0266542\pi$
$440$	−3.23320	−	7.54538i	−0.154137	−	0.359712i
$441$		0			0
$442$	0.654772	+	0.654772i	0.0311443	+	0.0311443i
$443$	3.32895	+	12.4238i	0.158163	+	0.590272i	0.998814	+	0.0486946i	$0.0155061\pi$
$443$	3.32895	+	12.4238i	0.158163	+	0.590272i	−0.840651	+	0.541578i	$0.817827\pi$
$444$	0.373402	+	0.646751i	0.0177209	+	0.0306935i
$445$	3.16550	−	0.455884i	0.150059	−	0.0216110i
$446$	0.914645	+	0.528070i	0.0433097	+	0.0250049i
$447$	−9.95157	+	9.95157i	−0.470693	+	0.470693i
$448$		0			0
$449$			17.8932i			0.844435i	0.906495	+	0.422217i	$0.138748\pi$
$449$			17.8932i			0.844435i	−0.906495	+	0.422217i	$0.861252\pi$
$450$	13.0453	−	23.9172i	0.614960	−	1.12747i
$451$	28.5510	−	16.4839i	1.34441	−	0.776197i
$452$	0.556592	−	2.07723i	0.0261799	−	0.0977046i
$453$	−28.2049	+	7.55749i	−1.32518	+	0.355082i
$454$	3.12036			0.146446
$455$		0			0
$456$	−6.36335			−0.297991
$457$	−33.0454	+	8.85449i	−1.54580	+	0.414196i	−0.928134	−	0.372246i	$-0.878588\pi$
$457$	−33.0454	+	8.85449i	−1.54580	+	0.414196i	−0.617665	+	0.786442i	$0.711921\pi$
$458$	2.17973	−	8.13485i	0.101852	−	0.380116i
$459$	−4.85928	+	2.80551i	−0.226812	+	0.130950i
$460$	−1.24674	+	10.4480i	−0.0581295	+	0.487140i
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$		0			0
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	−0.608415	−	0.793619i	$-0.708195\pi$
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	0.793619	+	0.608415i	$0.208195\pi$
$464$	2.27103	+	1.31118i	0.105430	+	0.0608700i
$465$	−0.161705	+	0.216117i	−0.00749888	+	0.0100222i
$466$	−11.3985	−	19.7427i	−0.528023	−	0.914563i
$467$	1.26454	+	4.71932i	0.0585159	+	0.218384i	0.988992	−	0.147968i	$-0.0472732\pi$
$467$	1.26454	+	4.71932i	0.0585159	+	0.218384i	−0.930476	+	0.366352i	$0.880607\pi$
$468$	−4.52558	−	4.52558i	−0.209195	−	0.209195i
$469$		0			0
$470$	5.31581	−	13.2872i	0.245200	−	0.612895i
$471$	−35.5873	+	61.6390i	−1.63978	+	2.84017i
$472$	10.3473	+	2.77255i	0.476273	+	0.127617i
$473$	2.37990	+	0.637693i	0.109428	+	0.0293212i
$474$	19.4910	−	33.7595i	0.895253	−	1.55062i
$475$	7.92561	+	7.55000i	0.363652	+	0.346418i
$476$		0			0
$477$	30.4904	+	30.4904i	1.39606	+	1.39606i
$478$	6.21090	+	23.1794i	0.284080	+	1.06020i
$479$	−8.55572	−	14.8189i	−0.390921	−	0.677094i	0.601651	−	0.798759i	$-0.294510\pi$
$479$	−8.55572	−	14.8189i	−0.390921	−	0.677094i	−0.992571	+	0.121665i	$0.961177\pi$
$480$	−0.926476	−	6.43313i	−0.0422877	−	0.293631i
$481$	−0.261359	−	0.150896i	−0.0119170	−	0.00688026i
$482$	17.5274	−	17.5274i	0.798350	−	0.798350i
$483$		0			0
$484$			2.47728i			0.112604i
$485$	−9.94416	−	1.18662i	−0.451541	−	0.0538815i
$486$	−7.56140	+	4.36557i	−0.342992	+	0.198026i
$487$	0.0337240	−	0.125860i	0.00152818	−	0.00570325i	−0.965158	−	0.261670i	$-0.915727\pi$
$487$	0.0337240	−	0.125860i	0.00152818	−	0.00570325i	0.966686	+	0.255966i	$0.0823936\pi$
$488$	−1.92443	+	0.515649i	−0.0871147	+	0.0233423i
$489$	−63.8465			−2.88724
$490$		0			0
$491$	26.9895			1.21802			0.609011	−	0.793162i	$-0.291567\pi$
$491$	26.9895			1.21802			0.609011	+	0.793162i	$0.291567\pi$
$492$	25.2132	−	6.75585i	1.13670	−	0.304577i
$493$	−0.535055	+	1.99685i	−0.0240977	+	0.0899337i
$494$	2.22698	−	1.28575i	0.100197	−	0.0578486i
$495$	−35.1521	+	27.6572i	−1.57997	+	1.24310i
$496$			0.0415289i			0.00186470i
$497$		0			0
$498$	−28.2828	+	28.2828i	−1.26738	+	1.26738i
$499$	0.0833977	+	0.0481497i	0.00373339	+	0.00215548i	0.501866	−	0.864946i	$-0.332647\pi$
$499$	0.0833977	+	0.0481497i	0.00373339	+	0.00215548i	−0.498132	+	0.867101i	$0.665981\pi$
$500$	−6.47886	+	9.11177i	−0.289743	+	0.407491i
$501$	6.46638	+	11.2001i	0.288897	+	0.500384i
$502$	2.87698	+	10.7370i	0.128406	+	0.479217i
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	0.334509	−	0.942392i	$-0.391429\pi$
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	−0.942392	+	0.334509i	$0.891429\pi$
$504$		0			0
$505$	0.149286	+	0.0597245i	0.00664312	+	0.00265771i
$506$	8.63753	−	14.9606i	0.383985	−	0.665081i
$507$	−32.6254	−	8.74194i	−1.44894	−	0.388243i
$508$	−18.1036	−	4.85084i	−0.803217	−	0.215221i
$509$	−6.16366	+	10.6758i	−0.273199	+	0.473195i	−0.969679	−	0.244381i	$-0.921415\pi$
$509$	−6.16366	+	10.6758i	−0.273199	+	0.473195i	0.696480	+	0.717576i	$0.254749\pi$
$510$	4.70961	−	2.01807i	0.208545	−	0.0893618i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.03291	+	15.0510i	0.178057	+	0.664520i
$514$	12.6466	+	21.9046i	0.557818	+	0.966169i
$515$	29.6840	+	22.2104i	1.30803	+	0.978706i
$516$	1.68943	+	0.975392i	0.0743730	+	0.0429393i
$517$	−16.6140	+	16.6140i	−0.730684	+	0.730684i
$518$		0			0
$519$		−	15.1918i		−	0.666845i
$520$	1.62409	+	2.06420i	0.0712210	+	0.0905214i
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	−0.776694	−	0.629878i	$-0.783105\pi$
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	0.157143	+	0.987576i	$0.449772\pi$
$522$	3.69813	−	13.8016i	0.161863	−	0.604080i
$523$	26.4703	−	7.09270i	1.15747	−	0.310142i	0.371512	−	0.928428i	$-0.378839\pi$
$523$	26.4703	−	7.09270i	1.15747	−	0.310142i	0.785953	+	0.618286i	$0.212173\pi$
$524$	−14.1946			−0.620095
$525$		0			0
$526$	−11.3461			−0.494714
$527$	−0.0316231	+	0.00847337i	−0.00137752	+	0.000369106i
$528$	−2.76180	+	10.3072i	−0.120192	+	0.448563i
$529$	0.742186	−	0.428501i	0.0322689	−	0.0186305i
$530$	−10.9420	−	13.9073i	−0.475292	−	0.604092i
$531$		−	58.3682i		−	2.53297i
$532$		0			0
$533$	−7.45881	+	7.45881i	−0.323077	+	0.323077i
$534$	−3.60031	−	2.07864i	−0.155801	−	0.0899517i
$535$	−8.18098	−	6.12123i	−0.353695	−	0.264644i
$536$	3.31118	+	5.73513i	0.143021	+	0.247720i
$537$	9.45533	+	35.2878i	0.408028	+	1.52278i
$538$	−5.70417	−	5.70417i	−0.245924	−	0.245924i
$539$		0			0
$540$	−14.6289	+	6.26850i	−0.629528	+	0.269753i
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.0386200	−	0.999254i	$-0.487704\pi$
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.846069	−	0.533073i	$-0.178963\pi$
$542$	−8.11330	−	2.17395i	−0.348496	−	0.0933793i
$543$	−32.7769	−	8.78254i	−1.40659	−	0.376895i
$544$	0.394167	−	0.682717i	0.0168998	−	0.0292712i
$545$	37.5826	+	15.0356i	1.60986	+	0.644056i
$546$		0			0
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	0.858188	−	0.513336i	$-0.171590\pi$
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	−0.513336	+	0.858188i	$0.671590\pi$
$548$	4.90887	+	18.3201i	0.209696	+	0.782597i
$549$	5.42777	+	9.40117i	0.231651	+	0.401232i
$550$	15.6691	−	9.56087i	0.668134	−	0.407677i
$551$	4.97180	+	2.87047i	0.211806	+	0.122286i
$552$	9.67160	−	9.67160i	0.411651	−	0.411651i
$553$		0			0
$554$		−	5.68000i		−	0.241320i
$555$	−1.31239	+	1.03257i	−0.0557080	+	0.0438303i
$556$	7.13350	−	4.11853i	0.302528	−	0.174665i
$557$	−6.64049	+	24.7826i	−0.281367	+	1.05007i	0.670087	+	0.742282i	$0.266257\pi$
$557$	−6.64049	+	24.7826i	−0.281367	+	1.05007i	−0.951454	+	0.307792i	$0.900410\pi$
$558$	0.218568	−	0.0585652i	0.00925274	−	0.00247926i
$559$	−0.788333			−0.0333429
$560$		0			0
$561$	−8.41213			−0.355160
$562$	7.02834	−	1.88324i	0.296473	−	0.0794396i
$563$	3.31584	−	12.3749i	0.139746	−	0.521539i	−0.860187	−	0.509978i	$-0.829653\pi$
$563$	3.31584	−	12.3749i	0.139746	−	0.521539i	0.999933	−	0.0115606i	$-0.00367993\pi$
$564$	−16.1107	+	9.30152i	−0.678383	+	0.391665i
$565$	4.77480	+	0.569768i	0.200877	+	0.0239703i
$566$		−	7.71000i		−	0.324076i
$567$		0			0
$568$	5.74013	−	5.74013i	0.240850	−	0.240850i
$569$	29.8291	+	17.2218i	1.25050	+	0.721977i	0.971209	−	0.238229i	$-0.0765669\pi$
$569$	29.8291	+	17.2218i	1.25050	+	0.721977i	0.279292	+	0.960206i	$0.409900\pi$
$570$	−2.02827	−	14.0836i	−0.0849547	−	0.589896i
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	0.939262	−	0.343201i	$-0.111511\pi$
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	−0.766852	+	0.641824i	$0.778178\pi$
$572$	−1.11607	−	4.16524i	−0.0466654	−	0.174158i
$573$	31.8645	+	31.8645i	1.33116	+	1.33116i
$574$		0			0
$575$	−23.5212	+	0.570889i	−0.980904	+	0.0238077i
$576$	−2.72435	+	4.71872i	−0.113515	+	0.196613i
$577$	3.39649	+	0.910086i	0.141398	+	0.0378874i	0.328824	−	0.944391i	$-0.393348\pi$
$577$	3.39649	+	0.910086i	0.141398	+	0.0378874i	−0.187426	+	0.982279i	$0.560015\pi$
$578$	−15.8204	−	4.23908i	−0.658044	−	0.176322i
$579$	−13.0770	+	22.6500i	−0.543460	+	0.941301i
$580$	−2.17808	+	5.44425i	−0.0904397	+	0.226060i
$581$		0			0
$582$	9.20520	+	9.20520i	0.381568	+	0.381568i
$583$	7.51937	+	28.0627i	0.311421	+	1.16224i
$584$	4.93262	+	8.54355i	0.204113	+	0.353535i
$585$	8.57367	−	11.4587i	0.354478	−	0.473757i
$586$	4.10531	+	2.37020i	0.169589	+	0.0979122i
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	−0.809275	−	0.587431i	$-0.800139\pi$
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	0.587431	+	0.809275i	$0.300139\pi$
$588$		0			0
$589$			0.0909162i			0.00374613i
$590$	−2.83818	+	23.7847i	−0.116846	+	0.979201i
$591$	43.4136	−	25.0649i	1.78580	−	1.03103i
$592$	−0.0664979	+	0.248174i	−0.00273305	+	0.0101999i
$593$	−0.709668	+	0.190155i	−0.0291426	+	0.00780872i	−0.273361	−	0.961912i	$-0.588135\pi$
$593$	−0.709668	+	0.190155i	−0.0291426	+	0.00780872i	0.244218	+	0.969720i	$0.421469\pi$
$594$	26.1296			1.07211
$595$		0			0
$596$	−4.84185			−0.198330
$597$	24.5138	−	6.56845i	1.00328	−	0.268829i
$598$	−1.43057	+	5.33897i	−0.0585005	+	0.218327i
$599$	−7.23778	+	4.17873i	−0.295727	+	0.170738i	−0.640522	−	0.767940i	$-0.721282\pi$
$599$	−7.23778	+	4.17873i	−0.295727	+	0.170738i	0.344794	+	0.938678i	$0.387949\pi$
$600$	13.9427	−	4.10102i	0.569209	−	0.167423i
$601$			39.9236i			1.62852i	0.580501	+	0.814259i	$0.302857\pi$
$601$			39.9236i			1.62852i	−0.580501	+	0.814259i	$0.697143\pi$
$602$		0			0
$603$	25.5147	−	25.5147i	1.03904	−	1.03904i
$604$	−8.69995	−	5.02292i	−0.353996	−	0.204380i
$605$	−5.48280	+	0.789613i	−0.222908	+	0.0321024i
$606$	−0.104505	−	0.181008i	−0.00424523	−	0.00735295i
$607$	−8.91623	−	33.2758i	−0.361899	−	1.35062i	−0.871577	−	0.490259i	$-0.836902\pi$
$607$	−8.91623	−	33.2758i	−0.361899	−	1.35062i	0.509678	−	0.860365i	$-0.329765\pi$
$608$	−1.54802	−	1.54802i	−0.0627804	−	0.0627804i
$609$		0			0
$610$	−1.75465	−	4.09485i	−0.0710436	−	0.165796i
$611$	3.75885	−	6.51051i	0.152067	−	0.263387i
$612$	−4.14903	−	1.11173i	−0.167715	−	0.0449390i
$613$	31.6042	+	8.46832i	1.27648	+	0.342032i	0.832510	−	0.554009i	$-0.186903\pi$
$613$	31.6042	+	8.46832i	1.27648	+	0.342032i	0.443971	+	0.896041i	$0.353569\pi$
$614$	−0.753393	+	1.30491i	−0.0304044	+	0.0526620i
$615$	22.9888	+	53.6493i	0.926997	+	2.16335i
$616$		0			0
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	0.322533	−	0.946558i	$-0.395466\pi$
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	−0.946558	+	0.322533i	$0.895466\pi$
$618$	−12.4730	−	46.5497i	−0.501736	−	1.87250i
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	0.939568	−	0.342363i	$-0.111227\pi$
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	−0.766279	+	0.642508i	$0.777894\pi$
$620$	−0.0919131	+	0.0132370i	−0.00369132	+	0.000531611i
$621$	−29.0055	−	16.7463i	−1.16395	−	0.672008i
$622$	−9.76397	+	9.76397i	−0.391500	+	0.391500i
$623$		0			0
$624$		−	3.41421i		−	0.136678i
$625$	−22.2316	−	11.4349i	−0.889263	−	0.457397i
$626$	−20.2191	+	11.6735i	−0.808119	+	0.466568i
$627$	−6.04621	+	22.5648i	−0.241462	+	0.901150i
$628$	−23.6523	+	6.33762i	−0.943830	+	0.252898i
$629$	−0.202545			−0.00807600
$630$		0			0
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	12.9543	−	3.47109i	0.515294	−	0.138073i
$633$	−8.40662	+	31.3739i	−0.334133	+	1.24700i
$634$	−11.4219	+	6.59442i	−0.453620	+	0.261898i
$635$	4.96567	−	41.6136i	0.197057	−	1.65139i
$636$			23.0027i			0.912117i
$637$		0			0
$638$	6.80736	−	6.80736i	0.269506	−	0.269506i
$639$	−38.3055	−	22.1157i	−1.51534	−	0.874882i
$640$	1.33961	−	1.79038i	0.0529527	−	0.0707709i
$641$	−5.42807	−	9.40169i	−0.214396	−	0.371345i	0.738690	−	0.674046i	$-0.235445\pi$
$641$	−5.42807	−	9.40169i	−0.214396	−	0.371345i	−0.953086	+	0.302701i	$0.902112\pi$
$642$	3.43757	+	12.8292i	0.135670	+	0.506328i
$643$	−8.06230	−	8.06230i	−0.317946	−	0.317946i	0.530032	−	0.847978i	$-0.322180\pi$
$643$	−8.06230	−	8.06230i	−0.317946	−	0.317946i	−0.847978	+	0.530032i	$0.822180\pi$
$644$		0			0
$645$	−1.62028	+	4.05000i	−0.0637984	+	0.159469i
$646$	0.862920	−	1.49462i	0.0339511	−	0.0588051i
$647$	10.0715	+	2.69865i	0.395951	+	0.106095i	0.451300	−	0.892372i	$-0.350960\pi$
$647$	10.0715	+	2.69865i	0.395951	+	0.106095i	−0.0553490	+	0.998467i	$0.517627\pi$
$648$	4.19432	+	1.12387i	0.164769	+	0.0441496i
$649$	19.6632	−	34.0577i	0.771848	−	1.33688i
$650$	−4.05090	+	4.25243i	−0.158889	+	0.166794i
$651$		0			0
$652$	−15.5320	−	15.5320i	−0.608279	−	0.608279i
$653$	−1.72009	−	6.41946i	−0.0673123	−	0.251213i	0.924068	−	0.382228i	$-0.124843\pi$
$653$	−1.72009	−	6.41946i	−0.0673123	−	0.251213i	−0.991380	+	0.131015i	$0.958176\pi$
$654$	−26.3091	−	45.5687i	−1.02877	−	1.78188i
$655$	−4.52442	−	31.4160i	−0.176784	−	1.22753i
$656$	7.77713	+	4.49013i	0.303646	+	0.175310i
$657$	38.0090	−	38.0090i	1.48287	−	1.48287i
$658$		0			0
$659$		−	22.0345i		−	0.858343i	−0.903223	−	0.429172i	$-0.858806\pi$
$659$		−	22.0345i		−	0.858343i	0.903223	−	0.429172i	$-0.141194\pi$
$660$	−23.6925	−	2.82718i	−0.922230	−	0.110048i
$661$	9.94278	−	5.74047i	0.386729	−	0.223278i	−0.294013	−	0.955802i	$-0.594991\pi$
$661$	9.94278	−	5.74047i	0.386729	−	0.223278i	0.680742	+	0.732523i	$0.261657\pi$
$662$	4.94240	−	18.4453i	0.192092	−	0.716897i
$663$	2.59983	−	0.696621i	0.100969	−	0.0270545i
$664$	−13.7608			−0.534021
$665$		0			0
$666$	1.39993			0.0542460
$667$	−11.9194	+	3.19379i	−0.461521	+	0.123664i
$668$	−1.15158	+	4.29774i	−0.0445558	+	0.166285i
$669$	2.65857	−	1.53492i	0.102786	−	0.0593436i
$670$	−11.6378	+	9.15644i	−0.449607	+	0.353744i
$671$			7.31407i			0.282356i
$672$		0			0
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	−0.936600	−	0.350402i	$-0.886045\pi$
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	0.350402	+	0.936600i	$0.386045\pi$
$674$	0.597952	+	0.345228i	0.0230322	+	0.0132977i
$675$	−18.5365	−	30.3792i	−0.713471	−	1.16929i
$676$	−5.81014	−	10.0635i	−0.223467	−	0.387056i
$677$	1.48523	+	5.54296i	0.0570821	+	0.213033i	0.988576	−	0.150724i	$-0.0481604\pi$
$677$	1.48523	+	5.54296i	0.0570821	+	0.213033i	−0.931494	+	0.363757i	$0.881494\pi$
$678$	−4.41998	−	4.41998i	−0.169748	−	0.169748i
$679$		0			0
$680$	1.63665	+	0.654772i	0.0627626	+	0.0251094i
$681$	4.53492	−	7.85472i	0.173779	−	0.300993i
$682$	0.147264	+	0.0394591i	0.00563901	+	0.00151097i
$683$	−18.7685	−	5.02900i	−0.718157	−	0.192430i	−0.118808	−	0.992917i	$-0.537907\pi$
$683$	−18.7685	−	5.02900i	−0.718157	−	0.192430i	−0.599349	+	0.800488i	$0.704574\pi$
$684$	−5.96423	+	10.3303i	−0.228048	+	0.394991i
$685$	−38.9821	+	16.7039i	−1.48943	+	0.638222i
$686$		0			0
$687$	−17.3095	−	17.3095i	−0.660400	−	0.660400i
$688$	0.173704	+	0.648273i	0.00662241	+	0.0247152i
$689$	−4.64782	−	8.05027i	−0.177068	−	0.306691i
$690$	24.4883	+	18.3228i	0.932252	+	0.697536i
$691$	−19.0914	−	11.0224i	−0.726270	−	0.419312i	0.0907861	−	0.995870i	$-0.471062\pi$
$691$	−19.0914	−	11.0224i	−0.726270	−	0.419312i	−0.817056	+	0.576558i	$0.804395\pi$
$692$	3.69572	−	3.69572i	0.140490	−	0.140490i
$693$		0			0
$694$		−	3.80998i		−	0.144625i
$695$	11.3890	+	14.4754i	0.432010	+	0.549082i
$696$	6.60113	−	3.81116i	0.250215	−	0.144462i
$697$	−1.83229	+	6.83821i	−0.0694031	+	0.259016i
$698$	−7.64340	+	2.04804i	−0.289307	+	0.0775196i
$699$	−66.2630			−2.50630
$700$		0			0
$701$	−18.0270			−0.680870			−0.340435	−	0.940268i	$-0.610574\pi$
$701$	−18.0270			−0.680870			−0.340435	+	0.940268i	$0.610574\pi$
$702$	−8.07553	+	2.16383i	−0.304791	+	0.0816686i
$703$	−0.145579	+	0.543308i	−0.00549062	+	0.0204913i
$704$	−3.17930	+	1.83557i	−0.119824	+	0.0691807i
$705$	−25.7216	−	32.6920i	−0.968732	−	1.23125i
$706$		−	25.7787i		−	0.970196i
$707$		0			0
$708$	22.0173	−	22.0173i	0.827459	−	0.827459i
$709$	37.0614	+	21.3974i	1.39187	+	0.803597i	0.993522	−	0.113637i	$-0.0362500\pi$
$709$	37.0614	+	21.3974i	1.39187	+	0.803597i	0.398349	+	0.917234i	$0.369583\pi$
$710$	14.5339	+	10.8746i	0.545446	+	0.408117i
$711$	−36.5370	−	63.2840i	−1.37025	−	2.37334i
$712$	−0.370178	−	1.38152i	−0.0138730	−	0.0517748i
$713$	−0.138183	−	0.138183i	−0.00517498	−	0.00517498i
$714$		0			0
$715$	8.86292	−	3.79777i	0.331454	−	0.142029i
$716$	−6.28428	+	10.8847i	−0.234854	+	0.406780i
$717$	67.3747	+	18.0530i	2.51615	+	0.674202i
$718$	−10.0326	−	2.68822i	−0.374413	−	0.100324i
$719$	−2.72691	+	4.72315i	−0.101697	+	0.176144i	−0.912384	−	0.409336i	$-0.865760\pi$
$719$	−2.72691	+	4.72315i	−0.101697	+	0.176144i	0.810687	+	0.585480i	$0.199094\pi$
$720$	−11.3120	−	4.52558i	−0.421573	−	0.168658i
$721$		0			0
$722$	10.0461	+	10.0461i	0.373876	+	0.373876i
$723$	−18.6476	−	69.5938i	−0.693512	−	2.58822i
$724$	−5.83712	−	10.1102i	−0.216935	−	0.375742i
$725$	−12.7436	−	3.08528i	−0.473287	−	0.114584i
$726$	6.23593	+	3.60031i	0.231437	+	0.133620i
$727$	16.6781	−	16.6781i	0.618555	−	0.618555i	−0.326606	−	0.945161i	$-0.605905\pi$
$727$	16.6781	−	16.6781i	0.618555	−	0.618555i	0.945161	+	0.326606i	$0.105905\pi$
$728$		0			0
$729$			38.4054i			1.42242i
$730$	−17.3366	+	13.6402i	−0.641658	+	0.504848i
$731$	−0.458200	+	0.264542i	−0.0169471	+	0.00978443i
$732$	−1.49882	+	5.59367i	−0.0553979	+	0.206748i
$733$	32.8405	−	8.79960i	1.21299	−	0.325021i	0.405057	−	0.914291i	$-0.367252\pi$
$733$	32.8405	−	8.79960i	1.21299	−	0.325021i	0.807936	+	0.589271i	$0.200585\pi$
$734$	8.68601			0.320607
$735$		0			0
$736$	4.70563			0.173452
$737$	23.4832	−	6.29231i	0.865016	−	0.231780i
$738$	12.6642	−	47.2635i	0.466177	−	1.73979i
$739$	−25.0733	+	14.4761i	−0.922335	+	0.532510i	−0.884379	−	0.466769i	$-0.845418\pi$
$739$	−25.0733	+	14.4761i	−0.922335	+	0.532510i	−0.0379557	+	0.999279i	$0.512085\pi$
$740$	−0.570462	−	0.0680721i	−0.0209706	−	0.00250238i
$741$		−	7.47449i		−	0.274582i
$742$		0			0
$743$	34.0351	−	34.0351i	1.24863	−	1.24863i	0.292300	−	0.956327i	$-0.405579\pi$
$743$	34.0351	−	34.0351i	1.24863	−	1.24863i	0.956327	−	0.292300i	$-0.0944206\pi$
$744$	0.104538	+	0.0603553i	0.00383257	+	0.00221273i
$745$	−1.54330	−	10.7162i	−0.0565422	−	0.392609i
$746$	6.65477	+	11.5264i	0.243649	+	0.422012i
$747$	19.4058	+	72.4235i	0.710022	+	2.64984i
$748$	−2.04643	−	2.04643i	−0.0748247	−	0.0748247i
$749$		0			0
$750$	13.5206	+	29.5513i	0.493704	+	1.07906i
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	−0.644782	−	0.764366i	$-0.723052\pi$
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	0.984352	+	0.176215i	$0.0563853\pi$
$752$	−6.18205	−	1.65648i	−0.225436	−	0.0604055i
$753$	31.2090	+	8.36242i	1.13732	+	0.304743i
$754$	−1.54013	+	2.66759i	−0.0560883	+	0.0971478i
$755$	8.34385	−	20.8560i	0.303664	−	0.759029i
$756$		0			0
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.996416	+	0.0845825i	$0.0269557\pi$
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.0845825	+	0.996416i	$0.473044\pi$
$758$	−6.55984	−	24.4816i	−0.238264	−	0.889213i
$759$	−25.1064	−	43.4856i	−0.911305	−	1.57843i
$760$	2.93271	−	3.91954i	0.106380	−	0.142177i
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	0.144788	−	0.989463i	$-0.453750\pi$
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	−0.784506	+	0.620122i	$0.787083\pi$
$762$	−38.5213	+	38.5213i	−1.39548	+	1.39548i
$763$		0			0
$764$			15.5034i			0.560894i
$765$	1.13805	−	9.53714i	0.0411462	−	0.344816i
$766$	−15.9357	+	9.20046i	−0.575779	+	0.332426i
$767$	−3.25668	+	12.1541i	−0.117592	+	0.438859i
$768$	−2.80762	+	0.752300i	−0.101311	+	0.0271463i
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$		0			0
$771$	73.5189			2.64772
$772$	−8.69132	+	2.32883i	−0.312808	+	0.0838165i
$773$	−6.39265	+	23.8577i	−0.229928	+	0.858101i	0.750443	+	0.660936i	$0.229840\pi$
$773$	−6.39265	+	23.8577i	−0.229928	+	0.858101i	−0.980370	+	0.197166i	$0.936826\pi$
$774$	3.16693	−	1.82843i	0.113833	−	0.0657215i
$775$	−0.0585931	−	0.199206i	−0.00210473	−	0.00715569i
$776$			4.47871i			0.160776i
$777$		0			0
$778$	15.8091	−	15.8091i	0.566784	−	0.566784i
$779$	17.0259	+	9.82991i	0.610017	+	0.352193i
$780$	7.55645	−	1.08825i	0.270564	−	0.0389657i
$781$	−14.9007	−	25.8088i	−0.533190	−	0.923513i
$782$	0.960117	+	3.58321i	0.0343337	+	0.128135i
$783$	−13.1980	−	13.1980i	−0.471659	−	0.471659i
$784$		0			0
$785$	−21.5656	−	50.3280i	−0.769710	−	1.79628i
$786$	−20.6295	+	35.7314i	−0.735831	+	1.27450i
$787$	−7.92843	−	2.12442i	−0.282618	−	0.0757273i	0.114725	−	0.993397i	$-0.463401\pi$
$787$	−7.92843	−	2.12442i	−0.282618	−	0.0757273i	−0.397343	+	0.917670i	$0.630068\pi$
$788$	16.6588	+	4.46372i	0.593446	+	0.159013i
$789$	−16.4897	+	28.5610i	−0.587048	+	1.01680i
$790$	11.8114	+	27.5645i	0.420231	+	0.980701i
$791$		0			0
$792$	14.1442	+	14.1442i	0.502594	+	0.502594i
$793$	−0.605689	−	2.26046i	−0.0215086	−	0.0802713i
$794$	7.89197	+	13.6693i	0.280076	+	0.485105i
$795$	−50.9104	+	7.33193i	−1.80561	+	0.260037i
$796$	7.56140	+	4.36557i	0.268007	+	0.154734i
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	−0.466696	−	0.884418i	$-0.654556\pi$
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	0.884418	+	0.466696i	$0.154556\pi$
$798$		0			0
$799$		−	5.04544i		−	0.178495i
$800$	4.38951	+	2.39420i	0.155193	+	0.0846477i
$801$	−6.74899	+	3.89653i	−0.238464	+	0.137677i
$802$	−3.61585	+	13.4945i	−0.127680	+	0.476508i
$803$	34.9827	−	9.37358i	1.23451	−	0.330786i
$804$	19.2490			0.678860
$805$		0			0
$806$	−0.0487805			−0.00171822
$807$	−22.6489	+	6.06875i	−0.797278	+	0.213630i
$808$	0.0186109	−	0.0694570i	0.000654730	−	0.00244349i
$809$	28.8498	−	16.6564i	1.01430	−	0.585609i	0.101855	−	0.994799i	$-0.467522\pi$
$809$	28.8498	−	16.6564i	1.01430	−	0.585609i	0.912449	+	0.409191i	$0.134189\pi$
$810$	−1.15047	+	9.64124i	−0.0404234	+	0.338759i
$811$		−	55.2368i		−	1.93963i	−0.243850	−	0.969813i	$-0.578410\pi$
$811$		−	55.2368i		−	1.93963i	0.243850	−	0.969813i	$-0.421590\pi$
$812$		0			0
$813$	−17.2637	+	17.2637i	−0.605465	+	0.605465i
$814$	0.816852	+	0.471610i	0.0286307	+	0.0165299i
$815$	29.4252	−	39.3266i	1.03072	−	1.37755i
$816$	−1.14571	−	1.98443i	−0.0401079	−	0.0694689i
$817$	0.380278	+	1.41922i	0.0133042	+	0.0496521i
$818$	−0.221580	−	0.221580i	−0.00774737	−	0.00774737i
$819$		0			0
$820$	−7.45881	+	18.6438i	−0.260473	+	0.651070i
$821$	−9.31457	+	16.1333i	−0.325081	+	0.563056i	−0.981529	−	0.191315i	$-0.938725\pi$
$821$	−9.31457	+	16.1333i	−0.325081	+	0.563056i	0.656448	+	0.754371i	$0.272058\pi$
$822$	53.2505	+	14.2684i	1.85732	+	0.497669i
$823$	16.3139	+	4.37130i	0.568668	+	0.152374i	0.531685	−	0.846942i	$-0.321559\pi$
$823$	16.3139	+	4.37130i	0.568668	+	0.152374i	0.0369821	+	0.999316i	$0.488226\pi$
$824$	8.28988	−	14.3585i	0.288792	−	0.500202i
$825$	−1.29458	−	53.3382i	−0.0450716	−	1.85700i
$826$		0			0
$827$	−5.62716	−	5.62716i	−0.195675	−	0.195675i	0.602468	−	0.798143i	$-0.294184\pi$
$827$	−5.62716	−	5.62716i	−0.195675	−	0.195675i	−0.798143	+	0.602468i	$0.794184\pi$
$828$	−6.63602	−	24.7660i	−0.230618	−	0.860677i
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	0.917591	−	0.397525i	$-0.130131\pi$
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	−0.803062	+	0.595895i	$0.796797\pi$
$830$	−4.38613	−	30.4558i	−0.152245	−	1.05714i
$831$	−14.2980	−	8.25494i	−0.495991	−	0.286361i
$832$	0.830578	−	0.830578i	0.0287951	−	0.0287951i
$833$		0			0
$834$		−	23.9424i		−	0.829057i
$835$	−9.87896	−	1.17884i	−0.341875	−	0.0407953i
$836$	−6.96021	+	4.01848i	−0.240724	+	0.138982i
$837$	0.0765030	−	0.285513i	0.00264433	−	0.00986877i
$838$	30.5478	−	8.18525i	1.05526	−	0.282755i
$839$	46.0930			1.59131			0.795654	−	0.605752i	$-0.207128\pi$
$839$	46.0930			1.59131			0.795654	+	0.605752i	$0.207128\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$	23.3887	−	6.26698i	0.806027	−	0.215974i
$843$	5.47394	−	20.4290i	0.188533	−	0.703613i
$844$	−9.67744	+	5.58727i	−0.333111	+	0.192322i
$845$	20.4208	−	16.0668i	0.702499	−	0.552716i
$846$			34.8724i			1.19894i
$847$		0			0
$848$	−5.59589	+	5.59589i	−0.192164	+	0.192164i
$849$	−19.4080	−	11.2052i	−0.666080	−	0.384562i
$850$	−0.927496	+	3.83099i	−0.0318128	+	0.131402i
$851$	−0.604505	−	1.04703i	−0.0207222	−	0.0358918i
$852$	−6.10700	−	22.7916i	−0.209222	−	0.780828i
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	0.915200	−	0.403000i	$-0.132032\pi$
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	−0.403000	+	0.915200i	$0.632032\pi$
$854$		0			0
$855$	−24.7645	−	9.90752i	−0.846929	−	0.338830i
$856$	−2.28471	+	3.95723i	−0.0780897	+	0.135255i
$857$	−11.6491	−	3.12136i	−0.397924	−	0.106623i	0.0543068	−	0.998524i	$-0.482705\pi$
$857$	−11.6491	−	3.12136i	−0.397924	−	0.106623i	−0.452231	+	0.891901i	$0.649372\pi$
$858$	−12.1070	−	3.24405i	−0.413325	−	0.110750i
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	−0.911258	−	0.411837i	$-0.864887\pi$
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	0.812290	+	0.583254i	$0.198221\pi$
$860$	−1.37941	+	0.591080i	−0.0470376	+	0.0201557i
$861$		0			0
$862$	−1.10172	−	1.10172i	−0.0375249	−	0.0375249i
$863$	−0.778623	−	2.90586i	−0.0265046	−	0.0989167i	0.951406	−	0.307938i	$-0.0996389\pi$
$863$	−0.778623	−	2.90586i	−0.0265046	−	0.0989167i	−0.977911	+	0.209021i	$0.932972\pi$
$864$	3.55879	+	6.16400i	0.121072	+	0.209703i
$865$	9.35746	+	7.00150i	0.318163	+	0.238058i
$866$	7.69343	+	4.44180i	0.261433	+	0.150939i
$867$	−33.6632	+	33.6632i	−1.14326	+	1.14326i
$868$		0			0
$869$		−	49.2347i		−	1.67017i
$870$	10.5391	+	13.3951i	0.357307	+	0.454135i
$871$	−6.73657	+	3.88936i	−0.228260	+	0.131786i
$872$	4.68530	−	17.4858i	0.158664	−	0.592143i
$873$	23.5717	−	6.31601i	0.797780	−	0.213765i
$874$	10.3017			0.348460
$875$		0			0
$876$	28.6750			0.968838
$877$	−33.8582	+	9.07228i	−1.14331	+	0.306349i	−0.780282	−	0.625428i	$-0.784924\pi$
$877$	−33.8582	+	9.07228i	−1.14331	+	0.306349i	−0.363030	+	0.931778i	$0.618258\pi$
$878$	6.18945	−	23.0994i	0.208884	−	0.779565i
$879$	11.9328	−	6.88939i	0.402483	−	0.232373i
$880$	−5.07592	−	6.45147i	−0.171109	−	0.217479i
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$		0			0
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	−0.828158	−	0.560495i	$-0.810611\pi$
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	0.560495	+	0.828158i	$0.310611\pi$
$884$	0.801929	+	0.462994i	0.0269718	+	0.0155722i
$885$	55.7472	+	41.7115i	1.87392	+	1.40212i
$886$	6.43103	+	11.1389i	0.216055	+	0.374218i
$887$	5.27738	+	19.6954i	0.177197	+	0.661308i	0.996167	+	0.0874718i	$0.0278788\pi$
$887$	5.27738	+	19.6954i	0.177197	+	0.661308i	−0.818970	+	0.573836i	$0.805455\pi$
$888$	0.528070	+	0.528070i	0.0177209	+	0.0177209i
$889$		0			0
$890$	2.93964	−	1.25964i	0.0985371	−	0.0422233i
$891$	7.97057	−	13.8054i	0.267024	−	0.462499i
$892$	1.02015	+	0.273349i	0.0341573	+	0.00915241i
$893$	−13.5339	−	3.62640i	−0.452895	−	0.121353i
$894$	−7.03682	+	12.1881i	−0.235347	+	0.407632i
$895$	−26.0934	−	10.4392i	−0.872207	−	0.348943i
$896$		0			0
$897$	11.3604	+	11.3604i	0.379313	+	0.379313i
$898$	4.63111	+	17.2836i	0.154542	+	0.576760i
$899$	−0.0544519	−	0.0943134i	−0.00181607	−	0.00314553i
$900$	6.41055	−	26.4786i	0.213685	−	0.882619i
$901$	−5.40287	−	3.11935i	−0.179996	−	0.103921i
$902$	23.3118	−	23.3118i	0.776197	−	0.776197i
$903$		0			0
$904$		−	2.15051i		−	0.0715247i
$905$	20.5157	−	16.1415i	0.681964	−	0.536560i
$906$	−25.2878	+	14.5999i	−0.840132	+	0.485051i
$907$	−1.68614	+	6.29276i	−0.0559874	+	0.208948i	−0.988253	−	0.152827i	$-0.951162\pi$
$907$	−1.68614	+	6.29276i	−0.0559874	+	0.208948i	0.932266	+	0.361775i	$0.117829\pi$
$908$	3.01404	−	0.807609i	0.100024	−	0.0268014i
$909$	−0.391801			−0.0129952
$910$		0			0
$911$	−24.2528			−0.803531			−0.401765	−	0.915743i	$-0.631603\pi$
$911$	−24.2528			−0.803531			−0.401765	+	0.915743i	$0.631603\pi$
$912$	−6.14653	+	1.64696i	−0.203532	+	0.0545362i
$913$	−13.0749	+	48.7964i	−0.432718	+	1.61492i
$914$	−29.6277	+	17.1056i	−0.979997	+	0.565802i
$915$	−12.8578	−	1.53430i	−0.425067	−	0.0507224i
$916$		−	8.42181i		−	0.278264i
$917$		0			0
$918$	−3.96759	+	3.96759i	−0.130950	+	0.130950i
$919$	31.2542	+	18.0446i	1.03098	+	0.595236i	0.917265	−	0.398277i	$-0.130392\pi$
$919$	31.2542	+	18.0446i	1.03098	+	0.595236i	0.113714	+	0.993513i	$0.463725\pi$
$920$	1.49988	+	10.4147i	0.0494497	+	0.343361i
$921$	2.18986	+	3.79295i	0.0721583	+	0.124982i
$922$	−6.04266	−	22.5515i	−0.199004	−	0.742695i
$923$	6.74244	+	6.74244i	0.221930	+	0.221930i
$924$		0			0
$925$	−0.0311706	−	1.28426i	−0.00102488	−	0.0422263i
$926$	2.81789	−	4.88073i	0.0926017	−	0.160391i
$927$	−87.2600	−	23.3813i	−2.86600	−	0.767941i
$928$	2.53301	+	0.678717i	0.0831500	+	0.0222800i
$929$	−21.2041	+	36.7266i	−0.695685	+	1.20496i	0.274264	+	0.961654i	$0.411566\pi$
$929$	−21.2041	+	36.7266i	−0.695685	+	1.20496i	−0.969949	+	0.243307i	$0.921768\pi$
$930$	−0.100260	+	0.250606i	−0.00328764	+	0.00821769i
$931$		0			0
$932$	−16.1198	−	16.1198i	−0.528023	−	0.528023i
$933$	10.3880	+	38.7686i	0.340089	+	1.26923i
$934$	2.44290	+	4.23123i	0.0799342	+	0.138450i
$935$	3.87694	−	5.18150i	0.126789	−	0.169453i
$936$	−5.54268	−	3.20007i	−0.181168	−	0.104597i
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	−0.637546	−	0.770412i	$-0.720050\pi$
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	0.770412	+	0.637546i	$0.220050\pi$
$938$		0			0
$939$			67.8621i			2.21460i
$940$	1.69569	−	14.2103i	0.0553073	−	0.463489i
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	−0.188677	−	0.982039i	$-0.560420\pi$
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	0.756132	+	0.654419i	$0.227087\pi$
$942$	−18.4213	+	68.7494i	−0.600200	+	2.23998i
$943$	−40.8179	+	10.9371i	−1.32921	+	0.356162i
$944$	10.7123			0.348656
$945$		0			0
$946$	2.46386			0.0801069
$947$	56.9449	−	15.2583i	1.85046	−	0.495830i	0.850897	−	0.525333i	$-0.176059\pi$
$947$	56.9449	−	15.2583i	1.85046	−	0.495830i	0.999565	+	0.0295030i	$0.00939246\pi$
$948$	10.0893	−	37.6538i	0.327685	−	1.22294i
$949$	−10.0354	+	5.79393i	−0.325762	+	0.188079i
$950$	9.60964	+	5.24144i	0.311778	+	0.170055i
$951$			38.3355i			1.24311i
$952$		0			0
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.00759828	+	0.999971i	$0.502419\pi$
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.999971	+	0.00759828i	$0.997581\pi$
$954$	37.3429	+	21.5599i	1.20902	+	0.698029i
$955$	−34.3127	+	4.94158i	−1.11033	+	0.159906i
$956$	11.9985	+	20.7821i	0.388060	+	0.672140i
$957$	−7.24244	−	27.0292i	−0.234115	−	0.873729i
$958$	−12.0996	−	12.0996i	−0.390921	−	0.390921i
$959$		0			0
$960$	−2.55992	−	5.97414i	−0.0826212	−	0.192814i
$961$	−15.4991	+	26.8453i	−0.499972	+	0.865977i
$962$	−0.291508	−	0.0781094i	−0.00939861	−	0.00251835i
$963$	24.0491	+	6.44392i	0.774970	+	0.207653i
$964$	12.3937	−	21.4666i	0.399175	−	0.691391i
$965$	−7.92454	−	18.4936i	−0.255100	−	0.595331i
$966$		0			0
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	0.271054	−	0.962564i	$-0.412628\pi$
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	−0.962564	+	0.271054i	$0.912628\pi$
$968$	0.641168	+	2.39287i	0.0206079	+	0.0769098i
$969$	−2.50822	−	4.34437i	−0.0805756	−	0.139561i
$970$	−9.91244	+	1.42755i	−0.318269	+	0.0458360i
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.998697	−	0.0510273i	$-0.0162496\pi$
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.455158	+	0.890411i	$0.349583\pi$
$972$	−6.17385	+	6.17385i	−0.198026	+	0.198026i
$973$		0			0
$974$		−	0.130300i		−	0.00417507i
$975$	4.81712	+	16.3773i	0.154271	+	0.524494i
$976$	−1.72539	+	0.996157i	−0.0552285	+	0.0318862i
$977$	14.6477	−	54.6658i	0.468620	−	1.74891i	−0.175979	−	0.984394i	$-0.556309\pi$
$977$	14.6477	−	54.6658i	0.468620	−	1.74891i	0.644599	−	0.764520i	$-0.277024\pi$
$978$	−61.6710	+	16.5247i	−1.97202	+	0.528401i
$979$	−5.25068			−0.167813
$980$		0			0
$981$	−98.6358			−3.14920
$982$	26.0699	−	6.98541i	0.831924	−	0.222913i
$983$	−4.00621	+	14.9514i	−0.127778	+	0.476875i	−0.999923	−	0.0123723i	$-0.996062\pi$
$983$	−4.00621	+	14.9514i	−0.127778	+	0.476875i	0.872145	+	0.489247i	$0.162728\pi$
$984$	22.6055	−	13.0513i	0.720638	−	0.416061i
$985$	−4.56939	+	38.2926i	−0.145593	+	1.22010i
$986$			2.06729i			0.0658361i
$987$		0			0
$988$	1.81832	−	1.81832i	0.0578486	−	0.0578486i
$989$	−2.73504	−	1.57907i	−0.0869691	−	0.0502116i
$990$	−26.7961	+	35.8129i	−0.851637	+	1.13821i
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	0.878133	+	0.478417i	$0.158789\pi$
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	−0.0247453	+	0.999694i	$0.507877\pi$
$992$	0.0107485	+	0.0401138i	0.000341264	+	0.00127362i
$993$	−39.2484	−	39.2484i	−1.24551	−	1.24551i
$994$		0			0
$995$	−7.25190	+	18.1266i	−0.229901	+	0.574653i
$996$	−19.9990	+	34.6392i	−0.633692	+	1.09759i
$997$	−37.2167	−	9.97217i	−1.17866	−	0.315822i	−0.384267	−	0.923222i	$-0.625546\pi$
$997$	−37.2167	−	9.97217i	−1.17866	−	0.315822i	−0.794396	+	0.607400i	$0.792213\pi$
$998$	0.0930180	+	0.0249241i	0.00294443	+	0.000788959i
$999$	0.914352	−	1.58370i	0.0289288	−	0.0501062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.c.117.4		16
5.3	odd	4	inner	490.2.l.c.313.2		16
7.2	even	3		490.2.g.c.97.4		16
7.3	odd	6	inner	490.2.l.c.227.2		16
7.4	even	3		70.2.k.a.17.1	yes	16
7.5	odd	6		490.2.g.c.97.1		16
7.6	odd	2		70.2.k.a.47.3	yes	16
21.11	odd	6		630.2.bv.c.577.4		16
21.20	even	2		630.2.bv.c.397.1		16
28.11	odd	6		560.2.ci.c.17.4		16
28.27	even	2		560.2.ci.c.257.4		16
35.3	even	12	inner	490.2.l.c.423.4		16
35.4	even	6		350.2.o.c.157.4		16
35.13	even	4		70.2.k.a.33.1	yes	16
35.18	odd	12		70.2.k.a.3.3	✓	16
35.23	odd	12		490.2.g.c.293.1		16
35.27	even	4		350.2.o.c.243.4		16
35.32	odd	12		350.2.o.c.143.2		16
35.33	even	12		490.2.g.c.293.4		16
35.34	odd	2		350.2.o.c.257.2		16
105.53	even	12		630.2.bv.c.73.1		16
105.83	odd	4		630.2.bv.c.523.4		16
140.83	odd	4		560.2.ci.c.33.4		16
140.123	even	12		560.2.ci.c.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	35.18	odd	12
70.2.k.a.17.1	yes	16	7.4	even	3
70.2.k.a.33.1	yes	16	35.13	even	4
70.2.k.a.47.3	yes	16	7.6	odd	2
350.2.o.c.143.2		16	35.32	odd	12
350.2.o.c.157.4		16	35.4	even	6
350.2.o.c.243.4		16	35.27	even	4
350.2.o.c.257.2		16	35.34	odd	2
490.2.g.c.97.1		16	7.5	odd	6
490.2.g.c.97.4		16	7.2	even	3
490.2.g.c.293.1		16	35.23	odd	12
490.2.g.c.293.4		16	35.33	even	12
490.2.l.c.117.4		16	1.1	even	1	trivial
490.2.l.c.227.2		16	7.3	odd	6	inner
490.2.l.c.313.2		16	5.3	odd	4	inner
490.2.l.c.423.4		16	35.3	even	12	inner
560.2.ci.c.17.4		16	28.11	odd	6
560.2.ci.c.33.4		16	140.83	odd	4
560.2.ci.c.257.4		16	28.27	even	2
560.2.ci.c.353.4		16	140.123	even	12
630.2.bv.c.73.1		16	105.53	even	12
630.2.bv.c.397.1		16	21.20	even	2
630.2.bv.c.523.4		16	105.83	odd	4
630.2.bv.c.577.4		16	21.11	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} -2.90667i q^{6} +(0.707107 - 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.752300 - 2.80762i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} -2.90667i q^{6} +(0.707107 - 0.707107i) q^{8} +(-4.71872 - 2.72435i) q^{9} +(1.79038 + 1.33961i) q^{10} +(-1.83557 - 3.17930i) q^{11} +(-0.752300 - 2.80762i) q^{12} +(0.830578 + 0.830578i) q^{13} +(5.97414 - 2.55992i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.761471 + 0.204036i) q^{17} +(-5.26305 - 1.41023i) q^{18} +(1.09461 - 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-2.59589 - 2.59589i) q^{22} +(1.21791 + 4.54529i) q^{23} +(-1.45333 - 2.51725i) q^{24} +(-1.17653 + 4.85961i) q^{25} +(1.01725 + 0.587308i) q^{26} +(-5.03288 + 5.03288i) q^{27} +2.62236i q^{29} +(5.10802 - 4.01892i) q^{30} +(-0.0359651 + 0.0207644i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-10.3072 + 2.76180i) q^{33} +0.788333 q^{34} -5.44871 q^{36} +(-0.248174 + 0.0664979i) q^{37} +(0.566614 - 2.11463i) q^{38} +(2.95680 - 1.70711i) q^{39} +(2.22032 + 0.264946i) q^{40} +8.98026i q^{41} +(-0.474569 + 0.474569i) q^{43} +(-3.17930 - 1.83557i) q^{44} +(-1.73673 - 12.0593i) q^{45} +(2.35282 + 4.07520i) q^{46} +(-1.65648 - 6.18205i) q^{47} +(-2.05532 - 2.05532i) q^{48} +(0.121320 + 4.99853i) q^{50} +(1.14571 - 1.98443i) q^{51} +(1.13459 + 0.304013i) q^{52} +(-7.64413 - 2.04824i) q^{53} +(-3.55879 + 6.16400i) q^{54} +(3.04917 - 7.62161i) q^{55} +(-4.49957 - 4.49957i) q^{57} +(0.678717 + 2.53301i) q^{58} +(5.35616 + 9.27713i) q^{59} +(3.89379 - 5.20403i) q^{60} +(-1.72539 - 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} -1.00000i q^{64} +(-0.311210 + 2.60802i) q^{65} +(-9.24117 + 5.33539i) q^{66} +(-1.71399 + 6.39671i) q^{67} +(0.761471 - 0.204036i) q^{68} +13.6777 q^{69} +8.11777 q^{71} +(-5.26305 + 1.41023i) q^{72} +(-2.55331 + 9.52910i) q^{73} +(-0.222506 + 0.128464i) q^{74} +(12.7588 + 6.95913i) q^{75} -2.18923i q^{76} +(2.41421 - 2.41421i) q^{78} +(11.6145 + 6.70563i) q^{79} +(2.21323 - 0.318742i) q^{80} +(2.17114 + 3.76053i) q^{81} +(2.32426 + 8.67427i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(-0.335571 + 0.581226i) q^{86} +(7.36260 + 1.97280i) q^{87} +(-3.54605 - 0.950161i) q^{88} +(0.715130 - 1.23864i) q^{89} +(-4.79872 - 11.1989i) q^{90} +(3.32739 + 3.32739i) q^{92} +(0.0312422 + 0.116597i) q^{93} +(-3.20007 - 5.54268i) q^{94} +(4.84527 - 0.697798i) q^{95} +(-2.51725 - 1.45333i) q^{96} +(-3.16693 + 3.16693i) q^{97} +20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5}+O(q^{10}) \) 16 * q + 12 * q^5	\( 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

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