LMFDB - Embedded newform 1638.2.p.j.991.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.5
Root			$2.07085 - 3.58682i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.j.919.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.07085 + 3.58682i) q^{5} +(2.11344 - 1.59166i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.07085 + 3.58682i) q^{5} +(2.11344 - 1.59166i) q^{7} +1.00000 q^{8} -4.14170 q^{10} -0.523095 q^{11} +(-3.28981 + 1.47551i) q^{13} +(0.321703 + 2.62612i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.26155 - 2.18506i) q^{17} -5.69993 q^{19} +(2.07085 - 3.58682i) q^{20} +(0.261547 - 0.453013i) q^{22} +(-3.69669 + 6.40285i) q^{23} +(-6.07684 + 10.5254i) q^{25} +(0.367074 - 3.58682i) q^{26} +(-2.43514 - 1.03446i) q^{28} +(1.54066 + 2.66851i) q^{29} +(-2.17638 + 3.76959i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.52309 q^{34} +(10.0856 + 4.28441i) q^{35} +(2.83240 - 4.90586i) q^{37} +(2.84997 - 4.93629i) q^{38} +(2.07085 + 3.58682i) q^{40} +(-2.33240 - 4.03983i) q^{41} +(-4.81529 + 8.34033i) q^{43} +(0.261547 + 0.453013i) q^{44} +(-3.69669 - 6.40285i) q^{46} +(5.58154 + 9.66752i) q^{47} +(1.93322 - 6.72775i) q^{49} +(-6.07684 - 10.5254i) q^{50} +(2.92274 + 2.11130i) q^{52} +(0.00192073 - 0.00332680i) q^{53} +(-1.08325 - 1.87624i) q^{55} +(2.11344 - 1.59166i) q^{56} -3.08133 q^{58} +(4.05374 + 7.02129i) q^{59} +6.01198 q^{61} +(-2.17638 - 3.76959i) q^{62} +1.00000 q^{64} +(-12.1051 - 8.74439i) q^{65} +3.23244 q^{67} +(-1.26155 + 2.18506i) q^{68} +(-8.75321 + 6.59219i) q^{70} +(-3.98568 + 6.90340i) q^{71} +(5.99080 - 10.3764i) q^{73} +(2.83240 + 4.90586i) q^{74} +(2.84997 + 4.93629i) q^{76} +(-1.10553 + 0.832590i) q^{77} +(1.15602 + 2.00229i) q^{79} -4.14170 q^{80} +4.66479 q^{82} -3.08133 q^{83} +(5.22495 - 9.04988i) q^{85} +(-4.81529 - 8.34033i) q^{86} -0.523095 q^{88} +(-5.42599 + 9.39808i) q^{89} +(-4.60428 + 8.35467i) q^{91} +7.39337 q^{92} -11.1631 q^{94} +(-11.8037 - 20.4446i) q^{95} +(-1.31892 + 2.28443i) q^{97} +(4.85980 + 5.03809i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8	$ 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8} - 4 q^{10} + 12 q^{11} - 4 q^{13} - 2 q^{14} - 5 q^{16} - 4 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{22} - 6 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 10 q^{31} - 5 q^{32} + 8 q^{34} + 2 q^{35} + q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} - 6 q^{46} + 15 q^{47} - 20 q^{49} - q^{50} + 2 q^{52} + 17 q^{53} + 3 q^{55} + 4 q^{56} - 2 q^{59} - 22 q^{61} - 10 q^{62} + 10 q^{64} - 41 q^{65} + 2 q^{67} - 4 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} + q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} - 4 q^{80} - 8 q^{82} + q^{85} + 3 q^{86} + 12 q^{88} - 7 q^{89} - 4 q^{91} + 12 q^{92} - 30 q^{94} - 24 q^{95} - 6 q^{97} + 16 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8 - 4 * q^10 + 12 * q^11 - 4 * q^13 - 2 * q^14 - 5 * q^16 - 4 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^22 - 6 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 10 * q^31 - 5 * q^32 + 8 * q^34 + 2 * q^35 + q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 - 6 * q^46 + 15 * q^47 - 20 * q^49 - q^50 + 2 * q^52 + 17 * q^53 + 3 * q^55 + 4 * q^56 - 2 * q^59 - 22 * q^61 - 10 * q^62 + 10 * q^64 - 41 * q^65 + 2 * q^67 - 4 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 + q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 - 4 * q^80 - 8 * q^82 + q^85 + 3 * q^86 + 12 * q^88 - 7 * q^89 - 4 * q^91 + 12 * q^92 - 30 * q^94 - 24 * q^95 - 6 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.07085	+	3.58682i	0.926112	+	1.60407i	0.789763	+	0.613413i	$0.210204\pi$
$5$	2.07085	+	3.58682i	0.926112	+	1.60407i	0.136350	+	0.990661i	$0.456463\pi$
$6$		0			0
$7$	2.11344	−	1.59166i	0.798803	−	0.601592i
$7$	2.11344	−	1.59166i	0.798803	−	0.601592i
$8$	1.00000			0.353553
$9$		0			0
$10$	−4.14170			−1.30972
$11$	−0.523095			−0.157719			−0.0788595	−	0.996886i	$-0.525128\pi$
$11$	−0.523095			−0.157719			−0.0788595	+	0.996886i	$0.525128\pi$
$12$		0			0
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$14$	0.321703	+	2.62612i	0.0859787	+	0.701860i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.26155	−	2.18506i	−0.305970	−	0.529956i	0.671507	−	0.740998i	$-0.265647\pi$
$17$	−1.26155	−	2.18506i	−0.305970	−	0.529956i	−0.977477	+	0.211043i	$0.932314\pi$
$18$		0			0
$19$	−5.69993			−1.30765			−0.653827	−	0.756644i	$-0.726838\pi$
$19$	−5.69993			−1.30765			−0.653827	+	0.756644i	$0.726838\pi$
$20$	2.07085	−	3.58682i	0.463056	−	0.802037i
$21$		0			0
$22$	0.261547	−	0.453013i	0.0557621	−	0.0965827i
$23$	−3.69669	+	6.40285i	−0.770812	+	1.33509i	0.166306	+	0.986074i	$0.446816\pi$
$23$	−3.69669	+	6.40285i	−0.770812	+	1.33509i	−0.937118	+	0.349012i	$0.886517\pi$
$24$		0			0
$25$	−6.07684	+	10.5254i	−1.21537	+	2.10508i
$26$	0.367074	−	3.58682i	0.0719891	−	0.703433i
$27$		0			0
$28$	−2.43514	−	1.03446i	−0.460198	−	0.195494i
$29$	1.54066	+	2.66851i	0.286094	+	0.495530i	0.972874	−	0.231336i	$-0.0743096\pi$
$29$	1.54066	+	2.66851i	0.286094	+	0.495530i	−0.686780	+	0.726866i	$0.740976\pi$
$30$		0			0
$31$	−2.17638	+	3.76959i	−0.390889	+	0.677039i	−0.992567	−	0.121699i	$-0.961166\pi$
$31$	−2.17638	+	3.76959i	−0.390889	+	0.677039i	0.601678	+	0.798739i	$0.294499\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.52309			0.432707
$35$	10.0856	+	4.28441i	1.70478	+	0.724198i
$36$		0			0
$37$	2.83240	−	4.90586i	0.465643	−	0.806518i	−0.533587	−	0.845745i	$-0.679156\pi$
$37$	2.83240	−	4.90586i	0.465643	−	0.806518i	0.999230	+	0.0392274i	$0.0124897\pi$
$38$	2.84997	−	4.93629i	0.462326	−	0.800772i
$39$		0			0
$40$	2.07085	+	3.58682i	0.327430	+	0.567126i
$41$	−2.33240	−	4.03983i	−0.364259	−	0.630915i	0.624398	−	0.781107i	$-0.285344\pi$
$41$	−2.33240	−	4.03983i	−0.364259	−	0.630915i	−0.988657	+	0.150191i	$0.952011\pi$
$42$		0			0
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	0.220694	+	0.975343i	$0.429168\pi$
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	−0.955019	+	0.296545i	$0.904166\pi$
$44$	0.261547	+	0.453013i	0.0394297	+	0.0682943i
$45$		0			0
$46$	−3.69669	−	6.40285i	−0.545047	−	0.944048i
$47$	5.58154	+	9.66752i	0.814152	+	1.41015i	0.909935	+	0.414750i	$0.136131\pi$
$47$	5.58154	+	9.66752i	0.814152	+	1.41015i	−0.0957835	+	0.995402i	$0.530536\pi$
$48$		0			0
$49$	1.93322	−	6.72775i	0.276174	−	0.961108i
$50$	−6.07684	−	10.5254i	−0.859395	−	1.48852i
$51$		0			0
$52$	2.92274	+	2.11130i	0.405311	+	0.292785i
$53$	0.00192073	−	0.00332680i	0.000263832	−	0.000456971i	−0.865893	−	0.500228i	$-0.833249\pi$
$53$	0.00192073	−	0.00332680i	0.000263832	−	0.000456971i	0.866157	+	0.499771i	$0.166583\pi$
$54$		0			0
$55$	−1.08325	−	1.87624i	−0.146065	−	0.252993i
$56$	2.11344	−	1.59166i	0.282420	−	0.212695i
$57$		0			0
$58$	−3.08133			−0.404598
$59$	4.05374	+	7.02129i	0.527752	+	0.914094i	0.999477	+	0.0323479i	$0.0102985\pi$
$59$	4.05374	+	7.02129i	0.527752	+	0.914094i	−0.471724	+	0.881746i	$0.656368\pi$
$60$		0			0
$61$	6.01198			0.769755			0.384877	−	0.922968i	$-0.374244\pi$
$61$	6.01198			0.769755			0.384877	+	0.922968i	$0.374244\pi$
$62$	−2.17638	−	3.76959i	−0.276400	−	0.478739i
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.1051	−	8.74439i	−1.50145	−	1.08461i
$66$		0			0
$67$	3.23244			0.394906			0.197453	−	0.980312i	$-0.436733\pi$
$67$	3.23244			0.394906			0.197453	+	0.980312i	$0.436733\pi$
$68$	−1.26155	+	2.18506i	−0.152985	+	0.264978i
$69$		0			0
$70$	−8.75321	+	6.59219i	−1.04621	+	0.787917i
$71$	−3.98568	+	6.90340i	−0.473013	+	0.819283i	−0.999523	−	0.0308864i	$-0.990167\pi$
$71$	−3.98568	+	6.90340i	−0.473013	+	0.819283i	0.526510	+	0.850169i	$0.323500\pi$
$72$		0			0
$73$	5.99080	−	10.3764i	0.701170	−	1.21446i	−0.266886	−	0.963728i	$-0.585995\pi$
$73$	5.99080	−	10.3764i	0.701170	−	1.21446i	0.968056	−	0.250734i	$-0.0806721\pi$
$74$	2.83240	+	4.90586i	0.329259	+	0.570294i
$75$		0			0
$76$	2.84997	+	4.93629i	0.326914	+	0.566231i
$77$	−1.10553	+	0.832590i	−0.125986	+	0.0948825i
$78$		0			0
$79$	1.15602	+	2.00229i	0.130063	+	0.225275i	0.923700	−	0.383115i	$-0.125149\pi$
$79$	1.15602	+	2.00229i	0.130063	+	0.225275i	−0.793638	+	0.608390i	$0.791816\pi$
$80$	−4.14170			−0.463056
$81$		0			0
$82$	4.66479			0.515140
$83$	−3.08133			−0.338220			−0.169110	−	0.985597i	$-0.554089\pi$
$83$	−3.08133			−0.338220			−0.169110	+	0.985597i	$0.554089\pi$
$84$		0			0
$85$	5.22495	−	9.04988i	0.566725	−	0.981597i
$86$	−4.81529	−	8.34033i	−0.519246	−	0.899361i
$87$		0			0
$88$	−0.523095			−0.0557621
$89$	−5.42599	+	9.39808i	−0.575153	+	0.996195i	0.420871	+	0.907120i	$0.361724\pi$
$89$	−5.42599	+	9.39808i	−0.575153	+	0.996195i	−0.996025	+	0.0890747i	$0.971609\pi$
$90$		0			0
$91$	−4.60428	+	8.35467i	−0.482660	+	0.875808i
$92$	7.39337			0.770812
$93$		0			0
$94$	−11.1631			−1.15138
$95$	−11.8037	−	20.4446i	−1.21103	−	2.09757i
$96$		0			0
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	−0.925183	−	0.379522i	$-0.876089\pi$
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	0.791267	+	0.611471i	$0.209422\pi$
$98$	4.85980	+	5.03809i	0.490914	+	0.508924i
$99$		0			0
$100$	12.1537			1.21537
$101$	12.1845			1.21240			0.606200	−	0.795312i	$-0.292693\pi$
$101$	12.1845			1.21240			0.606200	+	0.795312i	$0.292693\pi$
$102$		0			0
$103$	6.81529	+	11.8044i	0.671531	+	1.16313i	0.977470	+	0.211074i	$0.0676961\pi$
$103$	6.81529	+	11.8044i	0.671531	+	1.16313i	−0.305940	+	0.952051i	$0.598971\pi$
$104$	−3.28981	+	1.47551i	−0.322593	+	0.144686i
$105$		0			0
$106$	0.00192073	+	0.00332680i	0.000186558	+	0.000323127i
$107$	2.69861	−	4.67412i	0.260884	−	0.451865i	−0.705593	−	0.708617i	$-0.749319\pi$
$107$	2.69861	−	4.67412i	0.260884	−	0.451865i	0.966477	+	0.256753i	$0.0826526\pi$
$108$		0			0
$109$	5.58133	−	9.66715i	0.534594	−	0.925945i	−0.464588	−	0.885527i	$-0.653798\pi$
$109$	5.58133	−	9.66715i	0.534594	−	0.925945i	0.999183	−	0.0404180i	$-0.0128689\pi$
$110$	2.16650			0.206568
$111$		0			0
$112$	0.321703	+	2.62612i	0.0303981	+	0.248145i
$113$	−2.03617	+	3.52676i	−0.191547	+	0.331769i	−0.945763	−	0.324857i	$-0.894684\pi$
$113$	−2.03617	+	3.52676i	−0.191547	+	0.331769i	0.754216	+	0.656626i	$0.228017\pi$
$114$		0			0
$115$	−30.6211			−2.85543
$116$	1.54066	−	2.66851i	0.143047	−	0.247765i
$117$		0			0
$118$	−8.10749			−0.746355
$119$	−6.14408	−	2.61003i	−0.563227	−	0.239261i
$120$		0			0
$121$	−10.7264			−0.975125
$122$	−3.00599	+	5.20652i	−0.272149	+	0.471377i
$123$		0			0
$124$	4.35275			0.390889
$125$	−29.6284			−2.65004
$126$		0			0
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	0.644237	−	0.764826i	$-0.277175\pi$
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	−0.984477	+	0.175512i	$0.943842\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	13.6254	−	6.11113i	1.19503	−	0.535982i
$131$	5.62392	+	9.74091i	0.491364	+	0.851067i	0.999951	−	0.00994375i	$-0.00316525\pi$
$131$	5.62392	+	9.74091i	0.491364	+	0.851067i	−0.508587	+	0.861011i	$0.669832\pi$
$132$		0			0
$133$	−12.0464	+	9.07238i	−1.04456	+	0.786675i
$134$	−1.61622	+	2.79938i	−0.139620	+	0.241829i
$135$		0			0
$136$	−1.26155	−	2.18506i	−0.108177	−	0.187368i
$137$	−3.51116	−	6.08150i	−0.299978	−	0.519578i	0.676152	−	0.736762i	$-0.263646\pi$
$137$	−3.51116	−	6.08150i	−0.299978	−	0.519578i	−0.976131	+	0.217184i	$0.930313\pi$
$138$		0			0
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	−0.438441	−	0.898760i	$-0.644469\pi$
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	0.997569	−	0.0696786i	$-0.0221974\pi$
$140$	−1.33240	−	10.8766i	−0.112608	−	0.919241i
$141$		0			0
$142$	−3.98568	−	6.90340i	−0.334471	−	0.579320i
$143$	1.72088	−	0.771833i	0.143907	−	0.0645439i
$144$		0			0
$145$	−6.38097	+	11.0522i	−0.529911	+	0.917832i
$146$	5.99080	+	10.3764i	0.495802	+	0.858755i
$147$		0			0
$148$	−5.66479			−0.465643
$149$	−18.1322			−1.48545			−0.742726	−	0.669596i	$-0.766467\pi$
$149$	−18.1322			−1.48545			−0.742726	+	0.669596i	$0.766467\pi$
$150$		0			0
$151$	−2.53343	+	4.38804i	−0.206168	+	0.357093i	−0.950504	−	0.310712i	$-0.899433\pi$
$151$	−2.53343	+	4.38804i	−0.206168	+	0.357093i	0.744336	+	0.667805i	$0.232766\pi$
$152$	−5.69993			−0.462326
$153$		0			0
$154$	−0.168281	−	1.37371i	−0.0135605	−	0.110697i
$155$	−18.0278			−1.44803
$156$		0			0
$157$	5.80481	−	10.0542i	0.463274	−	0.802415i	−0.535847	−	0.844315i	$-0.680008\pi$
$157$	5.80481	−	10.0542i	0.463274	−	0.802415i	0.999122	+	0.0419001i	$0.0133411\pi$
$158$	−2.31204			−0.183936
$159$		0			0
$160$	2.07085	−	3.58682i	0.163715	−	0.283563i
$161$	2.37847	+	19.4159i	0.187450	+	1.53019i
$162$		0			0
$163$	−19.9927			−1.56595			−0.782976	−	0.622051i	$-0.786299\pi$
$163$	−19.9927			−1.56595			−0.782976	+	0.622051i	$0.786299\pi$
$164$	−2.33240	+	4.03983i	−0.182130	+	0.315458i
$165$		0			0
$166$	1.54066	−	2.66851i	0.119579	−	0.207117i
$167$	8.82851	+	15.2914i	0.683171	+	1.18329i	0.974008	+	0.226514i	$0.0727328\pi$
$167$	8.82851	+	15.2914i	0.683171	+	1.18329i	−0.290837	+	0.956772i	$0.593934\pi$
$168$		0			0
$169$	8.64572	−	9.70832i	0.665055	−	0.746794i
$170$	5.22495	+	9.04988i	0.400735	+	0.694094i
$171$		0			0
$172$	9.63058			0.734325
$173$	3.86985			0.294219			0.147110	−	0.989120i	$-0.453003\pi$
$173$	3.86985			0.294219			0.147110	+	0.989120i	$0.453003\pi$
$174$		0			0
$175$	3.90987	+	31.9170i	0.295559	+	2.41270i
$176$	0.261547	−	0.453013i	0.0197149	−	0.0341472i
$177$		0			0
$178$	−5.42599	−	9.39808i	−0.406695	−	0.704416i
$179$	3.51968			0.263073			0.131537	−	0.991311i	$-0.458009\pi$
$179$	3.51968			0.263073			0.131537	+	0.991311i	$0.458009\pi$
$180$		0			0
$181$	8.47129			0.629666			0.314833	−	0.949147i	$-0.398052\pi$
$181$	8.47129			0.629666			0.314833	+	0.949147i	$0.398052\pi$
$182$	−4.93322	−	8.16476i	−0.365674	−	0.605213i
$183$		0			0
$184$	−3.69669	+	6.40285i	−0.272523	+	0.472024i
$185$	23.4619			1.72495
$186$		0			0
$187$	0.659909	+	1.14300i	0.0482573	+	0.0835841i
$188$	5.58154	−	9.66752i	0.407076	−	0.705076i
$189$		0			0
$190$	23.6074			1.71266
$191$	21.9508			1.58830			0.794151	−	0.607721i	$-0.207916\pi$
$191$	21.9508			1.58830			0.794151	+	0.607721i	$0.207916\pi$
$192$		0			0
$193$	12.8592			0.925624			0.462812	−	0.886456i	$-0.346840\pi$
$193$	12.8592			0.925624			0.462812	+	0.886456i	$0.346840\pi$
$194$	−1.31892	−	2.28443i	−0.0946928	−	0.164013i
$195$		0			0
$196$	−6.79301	+	1.68966i	−0.485215	+	0.120690i
$197$	5.27054	+	9.12883i	0.375510	+	0.650403i	0.990403	−	0.138208i	$-0.0441342\pi$
$197$	5.27054	+	9.12883i	0.375510	+	0.650403i	−0.614893	+	0.788610i	$0.710801\pi$
$198$		0			0
$199$	−6.55182	−	11.3481i	−0.464446	−	0.804445i	0.534730	−	0.845023i	$-0.320413\pi$
$199$	−6.55182	−	11.3481i	−0.464446	−	0.804445i	−0.999176	+	0.0405782i	$0.987080\pi$
$200$	−6.07684	+	10.5254i	−0.429697	+	0.744258i
$201$		0			0
$202$	−6.09224	+	10.5521i	−0.428648	+	0.742441i
$203$	7.50346	+	3.18750i	0.526640	+	0.223719i
$204$		0			0
$205$	9.66009	−	16.7318i	0.674690	−	1.16860i
$206$	−13.6306			−0.949688
$207$		0			0
$208$	0.367074	−	3.58682i	0.0254520	−	0.248701i
$209$	2.98160			0.206242
$210$		0			0
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	0.830341	−	0.557255i	$-0.188146\pi$
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	−0.897768	+	0.440469i	$0.854812\pi$
$212$	−0.00384145			−0.000263832
$213$		0			0
$214$	2.69861	+	4.67412i	0.184473	+	0.319516i
$215$	−39.8870			−2.72027
$216$		0			0
$217$	1.40029	+	11.4309i	0.0950581	+	0.775977i
$218$	5.58133	+	9.66715i	0.378015	+	0.654742i
$219$		0			0
$220$	−1.08325	+	1.87624i	−0.0730327	+	0.126496i
$221$	7.37434	+	5.32702i	0.496052	+	0.358334i
$222$		0			0
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	0.995914	−	0.0903050i	$-0.0287842\pi$
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	−0.576164	+	0.817334i	$0.695451\pi$
$224$	−2.43514	−	1.03446i	−0.162705	−	0.0691176i
$225$		0			0
$226$	−2.03617	−	3.52676i	−0.135444	−	0.234596i
$227$	−10.8649	−	18.8186i	−0.721132	−	1.24904i	−0.960547	−	0.278119i	$-0.910289\pi$
$227$	−10.8649	−	18.8186i	−0.721132	−	1.24904i	0.239415	−	0.970917i	$-0.423044\pi$
$228$		0			0
$229$	−7.77570	−	13.4679i	−0.513833	−	0.889985i	−0.999871	−	0.0160474i	$-0.994892\pi$
$229$	−7.77570	−	13.4679i	−0.513833	−	0.889985i	0.486038	−	0.873938i	$-0.338442\pi$
$230$	15.3106	−	26.5187i	1.00955	−	1.74859i
$231$		0			0
$232$	1.54066	+	2.66851i	0.101150	+	0.175196i
$233$	−10.3320	−	17.8955i	−0.676870	−	1.17237i	−0.975919	−	0.218135i	$-0.930003\pi$
$233$	−10.3320	−	17.8955i	−0.676870	−	1.17237i	0.299048	−	0.954238i	$-0.403331\pi$
$234$		0			0
$235$	−23.1171	+	40.0400i	−1.50799	+	2.61192i
$236$	4.05374	−	7.02129i	0.263876	−	0.457047i
$237$		0			0
$238$	5.33240	−	4.01592i	0.345648	−	0.260313i
$239$	30.0971			1.94682			0.973410	−	0.229071i	$-0.0735687\pi$
$239$	30.0971			1.94682			0.973410	+	0.229071i	$0.0735687\pi$
$240$		0			0
$241$	−1.02609	−	1.77725i	−0.0660965	−	0.114483i	0.831083	−	0.556148i	$-0.187721\pi$
$241$	−1.02609	−	1.77725i	−0.0660965	−	0.114483i	−0.897180	+	0.441665i	$0.854388\pi$
$242$	5.36319	−	9.28931i	0.344759	−	0.597140i
$243$		0			0
$244$	−3.00599	−	5.20652i	−0.192439	−	0.333314i
$245$	28.1346	−	6.99807i	1.79746	−	0.447090i
$246$		0			0
$247$	18.7517	−	8.41033i	1.19314	−	0.535136i
$248$	−2.17638	+	3.76959i	−0.138200	+	0.239369i
$249$		0			0
$250$	14.8142	−	25.6589i	0.936932	−	1.62281i
$251$	8.23457	−	14.2627i	0.519761	−	0.900253i	−0.479975	−	0.877282i	$-0.659354\pi$
$251$	8.23457	−	14.2627i	0.519761	−	0.900253i	0.999736	−	0.0229705i	$-0.00731239\pi$
$252$		0			0
$253$	1.93372	−	3.34929i	0.121572	−	0.210568i
$254$	7.66864			0.481173
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.93711	−	10.2834i	0.370346	−	0.641459i	−0.619272	−	0.785176i	$-0.712572\pi$
$257$	5.93711	−	10.2834i	0.370346	−	0.641459i	0.989619	+	0.143717i	$0.0459056\pi$
$258$		0			0
$259$	−1.82238	−	14.8764i	−0.113237	−	0.924376i
$260$	−1.52031	+	14.8555i	−0.0942856	+	0.921300i
$261$		0			0
$262$	−11.2478			−0.694893
$263$	−25.0317			−1.54352			−0.771760	−	0.635914i	$-0.780623\pi$
$263$	−25.0317			−1.54352			−0.771760	+	0.635914i	$0.780623\pi$
$264$		0			0
$265$	0.0159101			0.000977353
$266$	−1.83369	−	14.9687i	−0.112430	−	0.917791i
$267$		0			0
$268$	−1.61622	−	2.79938i	−0.0987264	−	0.170999i
$269$	−7.76501	−	13.4494i	−0.473441	−	0.820024i	0.526097	−	0.850425i	$-0.323655\pi$
$269$	−7.76501	−	13.4494i	−0.473441	−	0.820024i	−0.999538	+	0.0304008i	$0.990322\pi$
$270$		0			0
$271$	2.63845	−	4.56993i	0.160274	−	0.277604i	−0.774693	−	0.632338i	$-0.782095\pi$
$271$	2.63845	−	4.56993i	0.160274	−	0.277604i	0.934967	+	0.354734i	$0.115429\pi$
$272$	2.52309			0.152985
$273$		0			0
$274$	7.02232			0.424234
$275$	3.17876	−	5.50578i	0.191686	−	0.332011i
$276$		0			0
$277$	5.56594	+	9.64049i	0.334425	+	0.579241i	0.983374	−	0.181591i	$-0.0581246\pi$
$277$	5.56594	+	9.64049i	0.334425	+	0.579241i	−0.648949	+	0.760832i	$0.724791\pi$
$278$	6.59202	+	11.4177i	0.395363	+	0.684789i
$279$		0			0
$280$	10.0856	+	4.28441i	0.602731	+	0.256043i
$281$	−19.3908			−1.15676			−0.578379	−	0.815768i	$-0.696314\pi$
$281$	−19.3908			−1.15676			−0.578379	+	0.815768i	$0.696314\pi$
$282$		0			0
$283$	26.0359			1.54768			0.773838	−	0.633384i	$-0.218335\pi$
$283$	26.0359			1.54768			0.773838	+	0.633384i	$0.218335\pi$
$284$	7.97136			0.473013
$285$		0			0
$286$	−0.192014	+	1.87624i	−0.0113540	+	0.110945i
$287$	−11.3594	−	4.82553i	−0.670525	−	0.284842i
$288$		0			0
$289$	5.31700	−	9.20931i	0.312765	−	0.541724i
$290$	−6.38097	−	11.0522i	−0.374703	−	0.649005i
$291$		0			0
$292$	−11.9816			−0.701170
$293$	6.46216	−	11.1928i	0.377523	−	0.653890i	−0.613178	−	0.789945i	$-0.710109\pi$
$293$	6.46216	−	11.1928i	0.377523	−	0.653890i	0.990701	+	0.136055i	$0.0434424\pi$
$294$		0			0
$295$	−16.7894	+	29.0801i	−0.977516	+	1.69311i
$296$	2.83240	−	4.90586i	0.164630	−	0.285147i
$297$		0			0
$298$	9.06612	−	15.7030i	0.525186	−	0.909649i
$299$	2.71391	−	26.5187i	0.156950	−	1.53361i
$300$		0			0
$301$	3.09819	+	25.2911i	0.178577	+	1.45775i
$302$	−2.53343	−	4.38804i	−0.145783	−	0.252503i
$303$		0			0
$304$	2.84997	−	4.93629i	0.163457	−	0.283116i
$305$	12.4499	+	21.5639i	0.712879	+	1.23474i
$306$		0			0
$307$	20.0771			1.14586			0.572931	−	0.819604i	$-0.305806\pi$
$307$	20.0771			1.14586			0.572931	+	0.819604i	$0.305806\pi$
$308$	1.27381	+	0.541119i	0.0725819	+	0.0308331i
$309$		0			0
$310$	9.01390	−	15.6125i	0.511955	−	0.886732i
$311$	−10.4837	+	18.1583i	−0.594475	+	1.02966i	0.399145	+	0.916888i	$0.369307\pi$
$311$	−10.4837	+	18.1583i	−0.594475	+	1.02966i	−0.993621	+	0.112774i	$0.964026\pi$
$312$		0			0
$313$	9.55610	+	16.5517i	0.540143	+	0.935555i	0.998895	+	0.0469909i	$0.0149632\pi$
$313$	9.55610	+	16.5517i	0.540143	+	0.935555i	−0.458752	+	0.888564i	$0.651703\pi$
$314$	5.80481	+	10.0542i	0.327584	+	0.567393i
$315$		0			0
$316$	1.15602	−	2.00229i	0.0650313	−	0.112637i
$317$	−9.13122	−	15.8157i	−0.512860	−	0.888300i	−0.999889	−	0.0149141i	$-0.995253\pi$
$317$	−9.13122	−	15.8157i	−0.512860	−	0.888300i	0.487028	−	0.873386i	$-0.338081\pi$
$318$		0			0
$319$	−0.805913	−	1.39588i	−0.0451225	−	0.0781544i
$320$	2.07085	+	3.58682i	0.115764	+	0.200509i
$321$		0			0
$322$	−18.0039	−	7.64813i	−1.00332	−	0.426213i
$323$	7.19074	+	12.4547i	0.400103	+	0.692999i
$324$		0			0
$325$	4.46130	−	43.5930i	0.247468	−	2.41811i
$326$	9.99637	−	17.3142i	0.553648	−	0.958946i
$327$		0			0
$328$	−2.33240	−	4.03983i	−0.128785	−	0.223062i
$329$	27.1837	+	11.5477i	1.49868	+	0.636647i
$330$		0			0
$331$	−10.2440			−0.563061			−0.281530	−	0.959552i	$-0.590842\pi$
$331$	−10.2440			−0.563061			−0.281530	+	0.959552i	$0.590842\pi$
$332$	1.54066	+	2.66851i	0.0845550	+	0.146453i
$333$		0			0
$334$	−17.6570			−0.966149
$335$	6.69390	+	11.5942i	0.365727	+	0.633457i
$336$		0			0
$337$	−32.6266			−1.77728			−0.888642	−	0.458601i	$-0.848351\pi$
$337$	−32.6266			−1.77728			−0.888642	+	0.458601i	$0.848351\pi$
$338$	4.08479	+	12.3416i	0.222183	+	0.671293i
$339$		0			0
$340$	−10.4499			−0.566725
$341$	1.13845	−	1.97185i	0.0616506	−	0.106782i
$342$		0			0
$343$	−6.62259	−	17.2957i	−0.357586	−	0.933880i
$344$	−4.81529	+	8.34033i	−0.259623	+	0.449680i
$345$		0			0
$346$	−1.93492	+	3.35139i	−0.104022	+	0.180172i
$347$	4.21596	+	7.30226i	0.226325	+	0.392006i	0.956716	−	0.291023i	$-0.0939956\pi$
$347$	4.21596	+	7.30226i	0.226325	+	0.392006i	−0.730391	+	0.683029i	$0.760662\pi$
$348$		0			0
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.662373	+	0.749174i	$0.269549\pi$
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.317617	+	0.948219i	$0.397117\pi$
$350$	−29.5959	−	12.5725i	−1.58197	−	0.672026i
$351$		0			0
$352$	0.261547	+	0.453013i	0.0139405	+	0.0241457i
$353$	5.23894			0.278841			0.139420	−	0.990233i	$-0.455476\pi$
$353$	5.23894			0.278841			0.139420	+	0.990233i	$0.455476\pi$
$354$		0			0
$355$	−33.0150			−1.75225
$356$	10.8520			0.575153
$357$		0			0
$358$	−1.75984	+	3.04813i	−0.0930105	+	0.161099i
$359$	2.54006	+	4.39951i	0.134059	+	0.232197i	0.925238	−	0.379388i	$-0.123865\pi$
$359$	2.54006	+	4.39951i	0.134059	+	0.232197i	−0.791178	+	0.611585i	$0.790532\pi$
$360$		0			0
$361$	13.4893			0.709961
$362$	−4.23564	+	7.33635i	−0.222621	+	0.385590i
$363$		0			0
$364$	9.53750	−	0.189910i	0.499901	−	0.00995398i
$365$	49.6242			2.59745
$366$		0			0
$367$	4.86302			0.253848			0.126924	−	0.991912i	$-0.459490\pi$
$367$	4.86302			0.253848			0.126924	+	0.991912i	$0.459490\pi$
$368$	−3.69669	−	6.40285i	−0.192703	−	0.333771i
$369$		0			0
$370$	−11.7309	+	20.3186i	−0.609862	+	1.05631i
$371$	−0.00123581	−	0.0100881i	−6.41599e−5	−	0.000523749i
$372$		0			0
$373$	28.8122			1.49184			0.745919	−	0.666036i	$-0.232010\pi$
$373$	28.8122			1.49184			0.745919	+	0.666036i	$0.232010\pi$
$374$	−1.31982			−0.0682461
$375$		0			0
$376$	5.58154	+	9.66752i	0.287846	+	0.498564i
$377$	−9.00592	−	6.50562i	−0.463828	−	0.335057i
$378$		0			0
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	−0.958106	−	0.286413i	$-0.907537\pi$
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	0.231013	−	0.972951i	$-0.425796\pi$
$380$	−11.8037	+	20.4446i	−0.605517	+	1.04879i
$381$		0			0
$382$	−10.9754	+	19.0099i	−0.561549	+	0.972632i
$383$	18.7363			0.957380			0.478690	−	0.877984i	$-0.341112\pi$
$383$	18.7363			0.957380			0.478690	+	0.877984i	$0.341112\pi$
$384$		0			0
$385$	−5.27573	−	2.24115i	−0.268876	−	0.114220i
$386$	−6.42959	+	11.1364i	−0.327258	+	0.566827i
$387$		0			0
$388$	2.63784			0.133916
$389$	−3.55307	+	6.15409i	−0.180148	+	0.312025i	−0.941931	−	0.335807i	$-0.890991\pi$
$389$	−3.55307	+	6.15409i	−0.180148	+	0.312025i	0.761783	+	0.647832i	$0.224324\pi$
$390$		0			0
$391$	18.6542			0.943382
$392$	1.93322	−	6.72775i	0.0976422	−	0.339803i
$393$		0			0
$394$	−10.5411			−0.531051
$395$	−4.78789	+	8.29287i	−0.240905	+	0.417260i
$396$		0			0
$397$	39.3266			1.97374			0.986872	−	0.161503i	$-0.0516340\pi$
$397$	39.3266			1.97374			0.986872	+	0.161503i	$0.0516340\pi$
$398$	13.1036			0.656826
$399$		0			0
$400$	−6.07684	−	10.5254i	−0.303842	−	0.526270i
$401$	−4.30153	+	7.45048i	−0.214808	+	0.372059i	−0.953213	−	0.302299i	$-0.902246\pi$
$401$	−4.30153	+	7.45048i	−0.214808	+	0.372059i	0.738405	+	0.674358i	$0.235579\pi$
$402$		0			0
$403$	1.59778	−	15.6125i	0.0795912	−	0.777715i
$404$	−6.09224	−	10.5521i	−0.303100	−	0.524985i
$405$		0			0
$406$	−6.51219	+	4.90444i	−0.323195	+	0.243403i
$407$	−1.48161	+	2.56623i	−0.0734408	+	0.127203i
$408$		0			0
$409$	18.2662	+	31.6381i	0.903208	+	1.56440i	0.823305	+	0.567599i	$0.192128\pi$
$409$	18.2662	+	31.6381i	0.903208	+	1.56440i	0.0799027	+	0.996803i	$0.474539\pi$
$410$	9.66009	+	16.7318i	0.477078	+	0.826323i
$411$		0			0
$412$	6.81529	−	11.8044i	0.335765	−	0.581563i
$413$	19.7429	+	8.38685i	0.971482	+	0.412690i
$414$		0			0
$415$	−6.38097	−	11.0522i	−0.313230	−	0.542529i
$416$	2.92274	+	2.11130i	0.143299	+	0.103515i
$417$		0			0
$418$	−1.49080	+	2.58215i	−0.0729175	+	0.126297i
$419$	−6.77818	−	11.7402i	−0.331136	−	0.573544i	0.651599	−	0.758564i	$-0.274099\pi$
$419$	−6.77818	−	11.7402i	−0.331136	−	0.573544i	−0.982735	+	0.185019i	$0.940765\pi$
$420$		0			0
$421$	4.50209			0.219418			0.109709	−	0.993964i	$-0.465008\pi$
$421$	4.50209			0.219418			0.109709	+	0.993964i	$0.465008\pi$
$422$	1.95886			0.0953558
$423$		0			0
$424$	0.00192073	−	0.00332680i	9.32788e−5	−	0.000161564i
$425$	30.6649			1.48746
$426$		0			0
$427$	12.7059	−	9.56904i	0.614883	−	0.463078i
$428$	−5.39721			−0.260884
$429$		0			0
$430$	19.9435	−	34.5431i	0.961760	−	1.66582i
$431$	0.507706			0.0244553			0.0122277	−	0.999925i	$-0.496108\pi$
$431$	0.507706			0.0244553			0.0122277	+	0.999925i	$0.496108\pi$
$432$		0			0
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	−0.977944	−	0.208865i	$-0.933023\pi$
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	0.669855	+	0.742492i	$0.266356\pi$
$434$	−10.5996	−	4.50274i	−0.508795	−	0.216138i
$435$		0			0
$436$	−11.1627			−0.534594
$437$	21.0709	−	36.4958i	1.00796	−	1.74583i
$438$		0			0
$439$	0.216640	−	0.375232i	0.0103397	−	0.0179088i	−0.860809	−	0.508928i	$-0.830042\pi$
$439$	0.216640	−	0.375232i	0.0103397	−	0.0179088i	0.871149	+	0.491019i	$0.163375\pi$
$440$	−1.08325	−	1.87624i	−0.0516419	−	0.0894464i
$441$		0			0
$442$	−8.30051	+	3.72286i	−0.394815	+	0.177078i
$443$	7.03339	+	12.1822i	0.334166	+	0.578793i	0.983324	−	0.181861i	$-0.0582119\pi$
$443$	7.03339	+	12.1822i	0.334166	+	0.578793i	−0.649158	+	0.760654i	$0.724879\pi$
$444$		0			0
$445$	−44.9456			−2.13063
$446$	−12.5364			−0.593617
$447$		0			0
$448$	2.11344	−	1.59166i	0.0998504	−	0.0751990i
$449$	−15.2892	+	26.4817i	−0.721542	+	1.24975i	0.238840	+	0.971059i	$0.423233\pi$
$449$	−15.2892	+	26.4817i	−0.721542	+	1.24975i	−0.960382	+	0.278688i	$0.910100\pi$
$450$		0			0
$451$	1.22006	+	2.11321i	0.0574506	+	0.0995073i
$452$	4.07235			0.191547
$453$		0			0
$454$	21.7299			1.01983
$455$	−39.5015	+	0.786550i	−1.85186	+	0.0368740i
$456$		0			0
$457$	−1.15513	+	2.00074i	−0.0540346	+	0.0935907i	−0.891778	−	0.452474i	$-0.850541\pi$
$457$	−1.15513	+	2.00074i	−0.0540346	+	0.0935907i	0.837743	+	0.546065i	$0.183875\pi$
$458$	15.5514			0.726670
$459$		0			0
$460$	15.3106	+	26.5187i	0.713859	+	1.23644i
$461$	15.0409	−	26.0516i	0.700524	−	1.21334i	−0.267759	−	0.963486i	$-0.586283\pi$
$461$	15.0409	−	26.0516i	0.700524	−	1.21334i	0.968283	−	0.249857i	$-0.0803835\pi$
$462$		0			0
$463$	29.4727			1.36971			0.684856	−	0.728679i	$-0.259865\pi$
$463$	29.4727			1.36971			0.684856	+	0.728679i	$0.259865\pi$
$464$	−3.08133			−0.143047
$465$		0			0
$466$	20.6639			0.957239
$467$	−2.92442	−	5.06525i	−0.135326	−	0.234392i	0.790396	−	0.612596i	$-0.209875\pi$
$467$	−2.92442	−	5.06525i	−0.135326	−	0.234392i	−0.925722	+	0.378205i	$0.876542\pi$
$468$		0			0
$469$	6.83156	−	5.14496i	0.315452	−	0.237572i
$470$	−23.1171	−	40.0400i	−1.06631	−	1.84691i
$471$		0			0
$472$	4.05374	+	7.02129i	0.186589	+	0.323181i
$473$	2.51885	−	4.36278i	0.115817	−	0.200601i
$474$		0			0
$475$	34.6376	−	59.9940i	1.58928	−	2.75272i
$476$	0.811687	+	6.62595i	0.0372036	+	0.303700i
$477$		0			0
$478$	−15.0486	+	26.0649i	−0.688305	+	1.19218i
$479$	−17.3275			−0.791713			−0.395856	−	0.918312i	$-0.629552\pi$
$479$	−17.3275			−0.791713			−0.395856	+	0.918312i	$0.629552\pi$
$480$		0			0
$481$	−2.07940	+	20.3186i	−0.0948124	+	0.926448i
$482$	2.05219			0.0934746
$483$		0			0
$484$	5.36319	+	9.28931i	0.243781	+	0.422241i
$485$	−10.9251			−0.496084
$486$		0			0
$487$	19.0323	+	32.9648i	0.862434	+	1.49378i	0.869573	+	0.493805i	$0.164394\pi$
$487$	19.0323	+	32.9648i	0.862434	+	1.49378i	−0.00713845	+	0.999975i	$0.502272\pi$
$488$	6.01198			0.272149
$489$		0			0
$490$	−8.00681	+	27.8643i	−0.361711	+	1.25878i
$491$	8.22130	+	14.2397i	0.371022	+	0.642629i	0.989723	−	0.142997i	$-0.0456741\pi$
$491$	8.22130	+	14.2397i	0.371022	+	0.642629i	−0.618701	+	0.785627i	$0.712341\pi$
$492$		0			0
$493$	3.88724	−	6.73290i	0.175073	−	0.303235i
$494$	−2.09230	+	20.4446i	−0.0941369	+	0.919847i
$495$		0			0
$496$	−2.17638	−	3.76959i	−0.0977222	−	0.169260i
$497$	2.56441	+	20.9337i	0.115029	+	0.939007i
$498$		0			0
$499$	−3.74298	−	6.48304i	−0.167559	−	0.290221i	0.770002	−	0.638041i	$-0.220255\pi$
$499$	−3.74298	−	6.48304i	−0.167559	−	0.290221i	−0.937561	+	0.347821i	$0.886922\pi$
$500$	14.8142	+	25.6589i	0.662511	+	1.14750i
$501$		0			0
$502$	8.23457	+	14.2627i	0.367527	+	0.636575i
$503$	−1.27275	+	2.20447i	−0.0567492	+	0.0982925i	−0.893004	−	0.450048i	$-0.851407\pi$
$503$	−1.27275	+	2.20447i	−0.0567492	+	0.0982925i	0.836255	+	0.548340i	$0.184740\pi$
$504$		0			0
$505$	25.2322	+	43.7035i	1.12282	+	1.94478i
$506$	1.93372	+	3.34929i	0.0859642	+	0.148894i
$507$		0			0
$508$	−3.83432	+	6.64123i	−0.170120	+	0.294657i
$509$	−17.2213	+	29.8281i	−0.763320	+	1.32211i	0.177811	+	0.984065i	$0.443099\pi$
$509$	−17.2213	+	29.8281i	−0.763320	+	1.32211i	−0.941130	+	0.338044i	$0.890235\pi$
$510$		0			0
$511$	−3.85452	−	31.4651i	−0.170514	−	1.39194i
$512$	1.00000			0.0441942
$513$		0			0
$514$	5.93711	+	10.2834i	0.261874	+	0.453580i
$515$	−28.2269	+	48.8904i	−1.24383	+	2.15437i
$516$		0			0
$517$	−2.91968	−	5.05703i	−0.128407	−	0.222408i
$518$	13.7946	+	5.85999i	0.606098	+	0.257473i
$519$		0			0
$520$	−12.1051	−	8.74439i	−0.530844	−	0.383467i
$521$	−21.9782	+	38.0673i	−0.962881	+	1.66776i	−0.247677	+	0.968843i	$0.579667\pi$
$521$	−21.9782	+	38.0673i	−0.962881	+	1.66776i	−0.715204	+	0.698916i	$0.753666\pi$
$522$		0			0
$523$	14.2468	−	24.6763i	0.622971	−	1.07902i	−0.365958	−	0.930631i	$-0.619259\pi$
$523$	14.2468	−	24.6763i	0.622971	−	1.07902i	0.988929	−	0.148386i	$-0.0474080\pi$
$524$	5.62392	−	9.74091i	0.245682	−	0.425533i
$525$		0			0
$526$	12.5158	−	21.6781i	0.545717	−	0.945209i
$527$	10.9824			0.478401
$528$		0			0
$529$	−15.8310	−	27.4200i	−0.688303	−	1.19218i
$530$	−0.00795507	+	0.0137786i	−0.000345546	+	0.000598504i
$531$		0			0
$532$	13.8801	+	5.89634i	0.601780	+	0.255639i
$533$	13.6340	+	9.84880i	0.590553	+	0.426599i
$534$		0			0
$535$	22.3536			0.966432
$536$	3.23244			0.139620
$537$		0			0
$538$	15.5300			0.669547
$539$	−1.01126	+	3.51925i	−0.0435579	+	0.151585i
$540$		0			0
$541$	0.327013	+	0.566403i	0.0140594	+	0.0243516i	0.872969	−	0.487775i	$-0.162191\pi$
$541$	0.327013	+	0.566403i	0.0140594	+	0.0243516i	−0.858910	+	0.512126i	$0.828858\pi$
$542$	2.63845	+	4.56993i	0.113331	+	0.196295i
$543$		0			0
$544$	−1.26155	+	2.18506i	−0.0540884	+	0.0936838i
$545$	46.2324			1.98038
$546$		0			0
$547$	4.52174			0.193336			0.0966678	−	0.995317i	$-0.469182\pi$
$547$	4.52174			0.193336			0.0966678	+	0.995317i	$0.469182\pi$
$548$	−3.51116	+	6.08150i	−0.149989	+	0.259789i
$549$		0			0
$550$	3.17876	+	5.50578i	0.135543	+	0.234767i
$551$	−8.78169	−	15.2103i	−0.374113	−	0.647982i
$552$		0			0
$553$	5.63014	+	2.39171i	0.239418	+	0.101706i
$554$	−11.1319			−0.472948
$555$		0			0
$556$	−13.1840			−0.559128
$557$	2.19422			0.0929719			0.0464859	−	0.998919i	$-0.485198\pi$
$557$	2.19422			0.0929719			0.0464859	+	0.998919i	$0.485198\pi$
$558$		0			0
$559$	3.53513	−	34.5431i	0.149520	−	1.46102i
$560$	−8.75321	+	6.59219i	−0.369891	+	0.278571i
$561$		0			0
$562$	9.69540	−	16.7929i	0.408976	−	0.708367i
$563$	−7.51839	−	13.0222i	−0.316862	−	0.548822i	0.662969	−	0.748647i	$-0.269296\pi$
$563$	−7.51839	−	13.0222i	−0.316862	−	0.548822i	−0.979832	+	0.199825i	$0.935963\pi$
$564$		0			0
$565$	−16.8664			−0.709576
$566$	−13.0180	+	22.5478i	−0.547186	+	0.947754i
$567$		0			0
$568$	−3.98568	+	6.90340i	−0.167235	+	0.289660i
$569$	−9.08664	+	15.7385i	−0.380932	+	0.659793i	−0.991196	−	0.132405i	$-0.957730\pi$
$569$	−9.08664	+	15.7385i	−0.380932	+	0.659793i	0.610264	+	0.792198i	$0.291063\pi$
$570$		0			0
$571$	−18.3240	+	31.7382i	−0.766837	+	1.32820i	0.172433	+	0.985021i	$0.444837\pi$
$571$	−18.3240	+	31.7382i	−0.766837	+	1.32820i	−0.939270	+	0.343180i	$0.888496\pi$
$572$	−1.52887	−	1.10441i	−0.0639252	−	0.0461778i
$573$		0			0
$574$	9.85874	−	7.42478i	0.411496	−	0.309904i
$575$	−44.9283	−	77.8181i	−1.87364	−	3.24524i
$576$		0			0
$577$	−14.3809	+	24.9085i	−0.598686	+	1.03695i	0.394330	+	0.918969i	$0.370977\pi$
$577$	−14.3809	+	24.9085i	−0.598686	+	1.03695i	−0.993015	+	0.117985i	$0.962357\pi$
$578$	5.31700	+	9.20931i	0.221158	+	0.383057i
$579$		0			0
$580$	12.7619			0.529911
$581$	−6.51219	+	4.90444i	−0.270171	+	0.203470i
$582$		0			0
$583$	−0.00100472	+	0.00174023i	−4.16113e−5	+	7.20729e-5i
$584$	5.99080	−	10.3764i	0.247901	−	0.429377i
$585$		0			0
$586$	6.46216	+	11.1928i	0.266949	+	0.462370i
$587$	7.20528	+	12.4799i	0.297394	+	0.515101i	0.975539	−	0.219827i	$-0.0705493\pi$
$587$	7.20528	+	12.4799i	0.297394	+	0.515101i	−0.678145	+	0.734928i	$0.737216\pi$
$588$		0			0
$589$	12.4052	−	21.4864i	0.511147	−	0.885333i
$590$	−16.7894	−	29.0801i	−0.691208	−	1.19721i
$591$		0			0
$592$	2.83240	+	4.90586i	0.116411	+	0.201629i
$593$	−9.75838	−	16.9020i	−0.400729	−	0.694083i	0.593085	−	0.805140i	$-0.297910\pi$
$593$	−9.75838	−	16.9020i	−0.400729	−	0.694083i	−0.993814	+	0.111057i	$0.964576\pi$
$594$		0			0
$595$	−3.36176	−	27.4427i	−0.137819	−	1.12504i
$596$	9.06612	+	15.7030i	0.371363	+	0.643219i
$597$		0			0
$598$	21.6089	+	15.6097i	0.883653	+	0.638326i
$599$	−0.837961	+	1.45139i	−0.0342382	+	0.0593022i	−0.882637	−	0.470056i	$-0.844234\pi$
$599$	−0.837961	+	1.45139i	−0.0342382	+	0.0593022i	0.848399	+	0.529358i	$0.177567\pi$
$600$		0			0
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	0.683446	−	0.730001i	$-0.260480\pi$
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	−0.973922	+	0.226882i	$0.927147\pi$
$602$	−23.4518	−	9.96242i	−0.955824	−	0.406038i
$603$		0			0
$604$	5.06687			0.206168
$605$	−22.2127	−	38.4735i	−0.903075	−	1.56417i
$606$		0			0
$607$	−34.3019			−1.39227			−0.696135	−	0.717911i	$-0.745099\pi$
$607$	−34.3019			−1.39227			−0.696135	+	0.717911i	$0.745099\pi$
$608$	2.84997	+	4.93629i	0.115581	+	0.200193i
$609$		0			0
$610$	−24.8998			−1.00816
$611$	−32.6268	−	23.5687i	−1.31994	−	0.953486i
$612$		0			0
$613$	−3.65538			−0.147639			−0.0738197	−	0.997272i	$-0.523519\pi$
$613$	−3.65538			−0.147639			−0.0738197	+	0.997272i	$0.523519\pi$
$614$	−10.0386	+	17.3873i	−0.405123	+	0.701694i
$615$		0			0
$616$	−1.10553	+	0.832590i	−0.0445429	+	0.0335460i
$617$	−2.31545	+	4.01048i	−0.0932167	+	0.161456i	−0.908863	−	0.417095i	$-0.863048\pi$
$617$	−2.31545	+	4.01048i	−0.0932167	+	0.161456i	0.815646	+	0.578551i	$0.196382\pi$
$618$		0			0
$619$	−0.674947	+	1.16904i	−0.0271284	+	0.0469878i	−0.879271	−	0.476322i	$-0.841970\pi$
$619$	−0.674947	+	1.16904i	−0.0271284	+	0.0469878i	0.852142	+	0.523310i	$0.175303\pi$
$620$	9.01390	+	15.6125i	0.362007	+	0.627014i
$621$		0			0
$622$	−10.4837	−	18.1583i	−0.420358	−	0.728081i
$623$	3.49111	+	28.4986i	0.139868	+	1.14177i
$624$		0			0
$625$	−30.9717	−	53.6446i	−1.23887	−	2.14578i
$626$	−19.1122			−0.763877
$627$		0			0
$628$	−11.6096			−0.463274
$629$	−14.2928			−0.569892
$630$		0			0
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	0.0666652	+	0.997775i	$0.478764\pi$
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	−0.897431	+	0.441154i	$0.854569\pi$
$632$	1.15602	+	2.00229i	0.0459840	+	0.0796467i
$633$		0			0
$634$	18.2624			0.725294
$635$	15.8806	−	27.5060i	0.630202	−	1.09154i
$636$		0			0
$637$	3.56697	+	24.9855i	0.141328	+	0.989963i
$638$	1.61183			0.0638128
$639$		0			0
$640$	−4.14170			−0.163715
$641$	−7.90110	−	13.6851i	−0.312075	−	0.540529i	0.666737	−	0.745293i	$-0.267691\pi$
$641$	−7.90110	−	13.6851i	−0.312075	−	0.540529i	−0.978811	+	0.204764i	$0.934357\pi$
$642$		0			0
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	−0.268021	−	0.963413i	$-0.586370\pi$
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	0.968351	−	0.249594i	$-0.0802971\pi$
$644$	15.6254	−	11.7678i	0.615727	−	0.463715i
$645$		0			0
$646$	−14.3815			−0.565832
$647$	7.99092			0.314156			0.157078	−	0.987586i	$-0.449793\pi$
$647$	7.99092			0.314156			0.157078	+	0.987586i	$0.449793\pi$
$648$		0			0
$649$	−2.12049	−	3.67280i	−0.0832366	−	0.144170i
$650$	35.5220	+	25.6601i	1.39329	+	1.00647i
$651$		0			0
$652$	9.99637	+	17.3142i	0.391488	+	0.678077i
$653$	21.7485	−	37.6696i	0.851086	−	1.47412i	−0.0291423	−	0.999575i	$-0.509278\pi$
$653$	21.7485	−	37.6696i	0.851086	−	1.47412i	0.880229	−	0.474550i	$-0.157389\pi$
$654$		0			0
$655$	−23.2926	+	40.3439i	−0.910116	+	1.57637i
$656$	4.66479			0.182130
$657$		0			0
$658$	−23.5925	+	17.7679i	−0.919730	+	0.692664i
$659$	−2.30892	+	3.99917i	−0.0899429	+	0.155786i	−0.907487	−	0.420081i	$-0.862002\pi$
$659$	−2.30892	+	3.99917i	−0.0899429	+	0.155786i	0.817544	+	0.575866i	$0.195335\pi$
$660$		0			0
$661$	25.8552			1.00565			0.502824	−	0.864389i	$-0.332294\pi$
$661$	25.8552			1.00565			0.502824	+	0.864389i	$0.332294\pi$
$662$	5.12199	−	8.87155i	0.199072	−	0.344803i
$663$		0			0
$664$	−3.08133			−0.119579
$665$	−57.4873	−	24.4209i	−2.22926	−	0.947000i
$666$		0			0
$667$	−22.7814			−0.882100
$668$	8.82851	−	15.2914i	0.341585	−	0.591643i
$669$		0			0
$670$	−13.3878			−0.517216
$671$	−3.14483			−0.121405
$672$		0			0
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	0.962281	−	0.272056i	$-0.0877038\pi$
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	−0.716748	+	0.697332i	$0.754370\pi$
$674$	16.3133	−	28.2555i	0.628365	−	1.08836i
$675$		0			0
$676$	−12.7305	−	2.63325i	−0.489635	−	0.101279i
$677$	−12.1455	−	21.0367i	−0.466791	−	0.808505i	0.532490	−	0.846436i	$-0.321256\pi$
$677$	−12.1455	−	21.0367i	−0.466791	−	0.808505i	−0.999280	+	0.0379314i	$0.987923\pi$
$678$		0			0
$679$	0.848599	+	6.92727i	0.0325663	+	0.265844i
$680$	5.22495	−	9.04988i	0.200368	−	0.347047i
$681$		0			0
$682$	1.13845	+	1.97185i	0.0435935	+	0.0755062i
$683$	4.98049	+	8.62645i	0.190573	+	0.330082i	0.945440	−	0.325795i	$-0.105632\pi$
$683$	4.98049	+	8.62645i	0.190573	+	0.330082i	−0.754867	+	0.655878i	$0.772299\pi$
$684$		0			0
$685$	14.5422	−	25.1878i	0.555627	−	0.962375i
$686$	18.2898	+	2.91252i	0.698308	+	0.111201i
$687$		0			0
$688$	−4.81529	−	8.34033i	−0.183581	−	0.317972i
$689$	−0.00141010	+	0.0137786i	−5.37204e−5	+	0.000524923i
$690$		0			0
$691$	14.1115	−	24.4419i	0.536827	−	0.929812i	−0.462245	−	0.886752i	$-0.652956\pi$
$691$	14.1115	−	24.4419i	0.536827	−	0.929812i	0.999072	−	0.0430600i	$-0.0137107\pi$
$692$	−1.93492	−	3.35139i	−0.0735548	−	0.127401i
$693$		0			0
$694$	−8.43192			−0.320071
$695$	54.6044			2.07126
$696$		0			0
$697$	−5.88486	+	10.1929i	−0.222905	+	0.386083i
$698$	−36.6155			−1.38592
$699$		0			0
$700$	25.6860	−	19.3446i	0.970840	−	0.731156i
$701$	1.33647			0.0504778			0.0252389	−	0.999681i	$-0.491965\pi$
$701$	1.33647			0.0504778			0.0252389	+	0.999681i	$0.491965\pi$
$702$		0			0
$703$	−16.1445	+	27.9631i	−0.608901	+	1.05465i
$704$	−0.523095			−0.0197149
$705$		0			0
$706$	−2.61947	+	4.53705i	−0.0985850	+	0.170754i
$707$	25.7511	−	19.3936i	0.968470	−	0.729371i
$708$		0			0
$709$	−33.5104			−1.25851			−0.629254	−	0.777200i	$-0.716639\pi$
$709$	−33.5104			−1.25851			−0.629254	+	0.777200i	$0.716639\pi$
$710$	16.5075	−	28.5918i	0.619515	−	1.07303i
$711$		0			0
$712$	−5.42599	+	9.39808i	−0.203347	+	0.352208i
$713$	−16.0908	−	27.8700i	−0.602604	−	1.04374i
$714$		0			0
$715$	6.33211	+	4.57414i	0.236808	+	0.171063i
$716$	−1.75984	−	3.04813i	−0.0657683	−	0.113914i
$717$		0			0
$718$	−5.08012			−0.189588
$719$	7.06328			0.263416			0.131708	−	0.991289i	$-0.457954\pi$
$719$	7.06328			0.263416			0.131708	+	0.991289i	$0.457954\pi$
$720$		0			0
$721$	33.1924	+	14.1003i	1.23615	+	0.525121i
$722$	−6.74463	+	11.6820i	−0.251009	+	0.434760i
$723$		0			0
$724$	−4.23564	−	7.33635i	−0.157416	−	0.272653i
$725$	−37.4495			−1.39084
$726$		0			0
$727$	−22.2264			−0.824331			−0.412166	−	0.911109i	$-0.635228\pi$
$727$	−22.2264			−0.824331			−0.412166	+	0.911109i	$0.635228\pi$
$728$	−4.60428	+	8.35467i	−0.170646	+	0.309645i
$729$		0			0
$730$	−24.8121	+	42.9758i	−0.918337	+	1.59061i
$731$	24.2989			0.898726
$732$		0			0
$733$	7.77847	+	13.4727i	0.287304	+	0.497626i	0.973165	−	0.230107i	$-0.0739076\pi$
$733$	7.77847	+	13.4727i	0.287304	+	0.497626i	−0.685861	+	0.727732i	$0.740574\pi$
$734$	−2.43151	+	4.21150i	−0.0897487	+	0.155449i
$735$		0			0
$736$	7.39337			0.272523
$737$	−1.69087			−0.0622841
$738$		0			0
$739$	−6.38799			−0.234986			−0.117493	−	0.993074i	$-0.537486\pi$
$739$	−6.38799			−0.234986			−0.117493	+	0.993074i	$0.537486\pi$
$740$	−11.7309	−	20.3186i	−0.431238	−	0.746926i
$741$		0			0
$742$	0.00935447	+	0.00397382i	0.000343413	+	0.000145884i
$743$	5.24875	+	9.09109i	0.192558	+	0.333520i	0.946097	−	0.323883i	$-0.104988\pi$
$743$	5.24875	+	9.09109i	0.192558	+	0.333520i	−0.753539	+	0.657403i	$0.771655\pi$
$744$		0			0
$745$	−37.5491	−	65.0370i	−1.37569	−	2.38277i
$746$	−14.4061	+	24.9521i	−0.527445	+	0.913561i
$747$		0			0
$748$	0.659909	−	1.14300i	0.0241286	−	0.0417920i
$749$	−1.73630	−	14.1737i	−0.0634430	−	0.517897i
$750$		0			0
$751$	−8.28166	+	14.3443i	−0.302202	+	0.523430i	−0.976634	−	0.214907i	$-0.931055\pi$
$751$	−8.28166	+	14.3443i	−0.302202	+	0.523430i	0.674432	+	0.738337i	$0.264388\pi$
$752$	−11.1631			−0.407076
$753$		0			0
$754$	10.1370	−	4.54654i	0.369168	−	0.165575i
$755$	−20.9854			−0.763739
$756$		0			0
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	0.507570	−	0.861610i	$-0.330544\pi$
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	−0.999962	+	0.00876370i	$0.997210\pi$
$758$	28.3100			1.02827
$759$		0			0
$760$	−11.8037	−	20.4446i	−0.428166	−	0.741604i
$761$	2.80358			0.101630			0.0508148	−	0.998708i	$-0.483818\pi$
$761$	2.80358			0.101630			0.0508148	+	0.998708i	$0.483818\pi$
$762$		0			0
$763$	−3.59106	−	29.3145i	−0.130005	−	1.06126i
$764$	−10.9754	−	19.0099i	−0.397075	−	0.687755i
$765$		0			0
$766$	−9.36815	+	16.2261i	−0.338485	+	0.586273i
$767$	−23.6961	−	17.1174i	−0.855615	−	0.618072i
$768$		0			0
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	0.769406	−	0.638761i	$-0.220553\pi$
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	−0.937886	+	0.346945i	$0.887219\pi$
$770$	4.57876	−	3.44834i	0.165007	−	0.124270i
$771$		0			0
$772$	−6.42959	−	11.1364i	−0.231406	−	0.400807i
$773$	25.2786	+	43.7838i	0.909207	+	1.57479i	0.815168	+	0.579225i	$0.196645\pi$
$773$	25.2786	+	43.7838i	0.909207	+	1.57479i	0.0940393	+	0.995568i	$0.470022\pi$
$774$		0			0
$775$	−26.4510	−	45.8144i	−0.950147	−	1.64570i
$776$	−1.31892	+	2.28443i	−0.0473464	+	0.0820063i
$777$		0			0
$778$	−3.55307	−	6.15409i	−0.127384	−	0.220635i
$779$	13.2945	+	23.0268i	0.476325	+	0.825020i
$780$		0			0
$781$	2.08489	−	3.61113i	0.0746031	−	0.129216i
$782$	−9.32709	+	16.1550i	−0.333536	+	0.577701i
$783$		0			0
$784$	4.85980	+	5.03809i	0.173564	+	0.179932i
$785$	48.0836			1.71618
$786$		0			0
$787$	−2.77011	−	4.79796i	−0.0987436	−	0.171029i	0.812421	−	0.583071i	$-0.198149\pi$
$787$	−2.77011	−	4.79796i	−0.0987436	−	0.171029i	−0.911165	+	0.412042i	$0.864816\pi$
$788$	5.27054	−	9.12883i	0.187755	−	0.325201i
$789$		0			0
$790$	−4.78789	−	8.29287i	−0.170346	−	0.295047i
$791$	1.31009	+	10.6945i	0.0465813	+	0.380252i
$792$		0			0
$793$	−19.7783	+	8.87075i	−0.702347	+	0.315010i
$794$	−19.6633	+	34.0578i	−0.697824	+	1.20867i
$795$		0			0
$796$	−6.55182	+	11.3481i	−0.232223	+	0.402222i
$797$	4.90846	−	8.50171i	0.173867	−	0.301146i	−0.765902	−	0.642958i	$-0.777707\pi$
$797$	4.90846	−	8.50171i	0.173867	−	0.301146i	0.939768	+	0.341812i	$0.111040\pi$
$798$		0			0
$799$	14.0828	−	24.3921i	0.498212	−	0.862929i
$800$	12.1537			0.429697
$801$		0			0
$802$	−4.30153	−	7.45048i	−0.151892	−	0.263085i
$803$	−3.13376	+	5.42782i	−0.110588	+	0.191544i
$804$		0			0
$805$	−64.7158	+	48.7385i	−2.28093	+	1.71781i
$806$	12.7220	+	9.18998i	0.448112	+	0.323703i
$807$		0			0
$808$	12.1845			0.428648
$809$	40.7368			1.43223			0.716114	−	0.697983i	$-0.245919\pi$
$809$	40.7368			1.43223			0.716114	+	0.697983i	$0.245919\pi$
$810$		0			0
$811$	−23.9184			−0.839887			−0.419944	−	0.907550i	$-0.637950\pi$
$811$	−23.9184			−0.839887			−0.419944	+	0.907550i	$0.637950\pi$
$812$	−0.991273	−	8.09194i	−0.0347869	−	0.283971i
$813$		0			0
$814$	−1.48161	−	2.56623i	−0.0519305	−	0.0899462i
$815$	−41.4020	−	71.7103i	−1.45025	−	2.51190i
$816$		0			0
$817$	27.4468	−	47.5393i	0.960243	−	1.66319i
$818$	−36.5325			−1.27733
$819$		0			0
$820$	−19.3202			−0.674690
$821$	−10.9625	+	18.9876i	−0.382594	+	0.662672i	−0.991432	−	0.130623i	$-0.958302\pi$
$821$	−10.9625	+	18.9876i	−0.382594	+	0.662672i	0.608839	+	0.793294i	$0.291636\pi$
$822$		0			0
$823$	1.29499	+	2.24299i	0.0451404	+	0.0781856i	0.887713	−	0.460398i	$-0.152293\pi$
$823$	1.29499	+	2.24299i	0.0451404	+	0.0781856i	−0.842572	+	0.538583i	$0.818960\pi$
$824$	6.81529	+	11.8044i	0.237422	+	0.411227i
$825$		0			0
$826$	−17.1346	+	12.9044i	−0.596191	+	0.449001i
$827$	−8.21658			−0.285718			−0.142859	−	0.989743i	$-0.545630\pi$
$827$	−8.21658			−0.285718			−0.142859	+	0.989743i	$0.545630\pi$
$828$		0			0
$829$	−8.62987			−0.299728			−0.149864	−	0.988707i	$-0.547884\pi$
$829$	−8.62987			−0.299728			−0.149864	+	0.988707i	$0.547884\pi$
$830$	12.7619			0.442973
$831$		0			0
$832$	−3.28981	+	1.47551i	−0.114054	+	0.0511542i
$833$	−17.1394	+	4.26318i	−0.593846	+	0.147710i
$834$		0			0
$835$	−36.5650	+	63.3325i	−1.26539	+	2.19171i
$836$	−1.49080	−	2.58215i	−0.0515605	−	0.0893054i
$837$		0			0
$838$	13.5564			0.468297
$839$	−0.656067	+	1.13634i	−0.0226499	+	0.0392309i	−0.877128	−	0.480256i	$-0.840544\pi$
$839$	−0.656067	+	1.13634i	−0.0226499	+	0.0392309i	0.854478	+	0.519487i	$0.173877\pi$
$840$		0			0
$841$	9.75270	−	16.8922i	0.336300	−	0.582489i
$842$	−2.25104	+	3.89892i	−0.0775761	+	0.134366i
$843$		0			0
$844$	−0.979430	+	1.69642i	−0.0337134	+	0.0583933i
$845$	52.7260	+	10.9061i	1.81383	+	0.375183i
$846$		0			0
$847$	−22.6695	+	17.0728i	−0.778933	+	0.586627i
$848$	0.00192073	+	0.00332680i	6.59580e−5	+	0.000114243i
$849$		0			0
$850$	−15.3324	+	26.5566i	−0.525898	+	0.910882i
$851$	20.9410	+	36.2708i	0.717847	+	1.24335i
$852$		0			0
$853$	3.91347			0.133995			0.0669974	−	0.997753i	$-0.478658\pi$
$853$	3.91347			0.133995			0.0669974	+	0.997753i	$0.478658\pi$
$854$	1.93407	+	15.7882i	0.0661825	+	0.540260i
$855$		0			0
$856$	2.69861	−	4.67412i	0.0922365	−	0.159758i
$857$	20.7141	−	35.8779i	0.707580	−	1.22556i	−0.258172	−	0.966099i	$-0.583120\pi$
$857$	20.7141	−	35.8779i	0.707580	−	1.22556i	0.965752	−	0.259466i	$-0.0835464\pi$
$858$		0			0
$859$	−6.13898	−	10.6330i	−0.209459	−	0.362794i	0.742085	−	0.670306i	$-0.233837\pi$
$859$	−6.13898	−	10.6330i	−0.209459	−	0.362794i	−0.951544	+	0.307511i	$0.900504\pi$
$860$	19.9435	+	34.5431i	0.680067	+	1.17791i
$861$		0			0
$862$	−0.253853	+	0.439686i	−0.00864626	+	0.0149758i
$863$	−18.8040	−	32.5694i	−0.640095	−	1.10868i	−0.985411	−	0.170191i	$-0.945562\pi$
$863$	−18.8040	−	32.5694i	−0.640095	−	1.10868i	0.345316	−	0.938486i	$-0.387772\pi$
$864$		0			0
$865$	8.01387	+	13.8804i	0.272480	+	0.471949i
$866$	−6.41093	−	11.1041i	−0.217852	−	0.377331i
$867$		0			0
$868$	9.19926	−	6.92812i	0.312243	−	0.235156i
$869$	−0.604708	−	1.04739i	−0.0205133	−	0.0355301i
$870$		0			0
$871$	−10.6341	+	4.76951i	−0.360323	+	0.161609i
$872$	5.58133	−	9.66715i	0.189008	−	0.327371i
$873$		0			0
$874$	21.0709	+	36.4958i	0.712733	+	1.23449i
$875$	−62.6177	+	47.1584i	−2.11686	+	1.59424i
$876$		0			0
$877$	−23.1321			−0.781114			−0.390557	−	0.920579i	$-0.627718\pi$
$877$	−23.1321			−0.781114			−0.390557	+	0.920579i	$0.627718\pi$
$878$	0.216640	+	0.375232i	0.00731125	+	0.0126635i
$879$		0			0
$880$	2.16650			0.0730327
$881$	25.2659	+	43.7618i	0.851229	+	1.47437i	0.880100	+	0.474788i	$0.157475\pi$
$881$	25.2659	+	43.7618i	0.851229	+	1.47437i	−0.0288713	+	0.999583i	$0.509191\pi$
$882$		0			0
$883$	30.7977			1.03643			0.518213	−	0.855251i	$-0.326597\pi$
$883$	30.7977			1.03643			0.518213	+	0.855251i	$0.326597\pi$
$884$	0.926162	−	9.04988i	0.0311502	−	0.304380i
$885$		0			0
$886$	−14.0668			−0.472583
$887$	10.0158	−	17.3479i	0.336299	−	0.582486i	−0.647435	−	0.762121i	$-0.724158\pi$
$887$	10.0158	−	17.3479i	0.336299	−	0.582486i	0.983733	+	0.179635i	$0.0574915\pi$
$888$		0			0
$889$	−18.6742	−	7.93287i	−0.626312	−	0.266060i
$890$	22.4728	−	38.9240i	0.753290	−	1.30474i
$891$		0			0
$892$	6.26821	−	10.8569i	0.209875	−	0.363515i
$893$	−31.8144	−	55.1042i	−1.06463	−	1.84399i
$894$		0			0
$895$	7.28873	+	12.6245i	0.243635	+	0.421989i
$896$	0.321703	+	2.62612i	0.0107473	+	0.0877325i
$897$		0			0
$898$	−15.2892	−	26.4817i	−0.510207	−	0.883705i
$899$	−13.4123			−0.447324
$900$		0			0
$901$	−0.00969235			−0.000322899
$902$	−2.44013			−0.0812474
$903$		0			0
$904$	−2.03617	+	3.52676i	−0.0677221	+	0.117298i
$905$	17.5428	+	30.3850i	0.583141	+	1.01003i
$906$		0			0
$907$	15.6640			0.520114			0.260057	−	0.965593i	$-0.416259\pi$
$907$	15.6640			0.520114			0.260057	+	0.965593i	$0.416259\pi$
$908$	−10.8649	+	18.8186i	−0.360566	+	0.624518i
$909$		0			0
$910$	19.0696	−	34.6025i	0.632150	−	1.14706i
$911$	−6.84991			−0.226948			−0.113474	−	0.993541i	$-0.536198\pi$
$911$	−6.84991			−0.226948			−0.113474	+	0.993541i	$0.536198\pi$
$912$		0			0
$913$	1.61183			0.0533437
$914$	−1.15513	−	2.00074i	−0.0382082	−	0.0661786i
$915$		0			0
$916$	−7.77570	+	13.4679i	−0.256917	+	0.444992i
$917$	27.3900	+	11.6354i	0.904498	+	0.384235i
$918$		0			0
$919$	9.54874			0.314984			0.157492	−	0.987520i	$-0.449659\pi$
$919$	9.54874			0.314984			0.157492	+	0.987520i	$0.449659\pi$
$920$	−30.6211			−1.00955
$921$		0			0
$922$	15.0409	+	26.0516i	0.495345	+	0.857963i
$923$	2.92608	−	28.5918i	0.0963130	−	0.941111i
$924$		0			0
$925$	34.4240	+	59.6242i	1.13186	+	1.96043i
$926$	−14.7363	+	25.5241i	−0.484266	+	0.838773i
$927$		0			0
$928$	1.54066	−	2.66851i	0.0505748	−	0.0875981i
$929$	39.8657			1.30795			0.653975	−	0.756516i	$-0.273100\pi$
$929$	39.8657			1.30795			0.653975	+	0.756516i	$0.273100\pi$
$930$		0			0
$931$	−11.0192	+	38.3478i	−0.361140	+	1.25680i
$932$	−10.3320	+	17.8955i	−0.338435	+	0.586187i
$933$		0			0
$934$	5.84884			0.191380
$935$	−2.73314	+	4.73394i	−0.0893833	+	0.154816i
$936$		0			0
$937$	−11.4259			−0.373268			−0.186634	−	0.982430i	$-0.559758\pi$
$937$	−11.4259			−0.373268			−0.186634	+	0.982430i	$0.559758\pi$
$938$	1.03989	+	8.48878i	0.0339535	+	0.277168i
$939$		0			0
$940$	46.2342			1.50799
$941$	−19.0547	+	33.0037i	−0.621165	+	1.07589i	0.368105	+	0.929784i	$0.380007\pi$
$941$	−19.0547	+	33.0037i	−0.621165	+	1.07589i	−0.989269	+	0.146104i	$0.953326\pi$
$942$		0			0
$943$	34.4886			1.12310
$944$	−8.10749			−0.263876
$945$		0			0
$946$	2.51885	+	4.36278i	0.0818950	+	0.141846i
$947$	−4.04628	+	7.00835i	−0.131486	+	0.227741i	−0.924250	−	0.381789i	$-0.875308\pi$
$947$	−4.04628	+	7.00835i	−0.131486	+	0.227741i	0.792763	+	0.609529i	$0.208642\pi$
$948$		0			0
$949$	−4.39813	+	42.9758i	−0.142769	+	1.39505i
$950$	34.6376	+	59.9940i	1.12379	+	1.94646i
$951$		0			0
$952$	−6.14408	−	2.61003i	−0.199131	−	0.0845917i
$953$	2.17357	−	3.76473i	0.0704088	−	0.121952i	−0.828672	−	0.559735i	$-0.810903\pi$
$953$	2.17357	−	3.76473i	0.0704088	−	0.121952i	0.899081	+	0.437783i	$0.144236\pi$
$954$		0			0
$955$	45.4567	+	78.7334i	1.47094	+	2.54775i
$956$	−15.0486	−	26.0649i	−0.486705	−	0.842998i
$957$		0			0
$958$	8.66374	−	15.0060i	0.279913	−	0.484823i
$959$	−17.1003	−	7.26428i	−0.552198	−	0.234576i
$960$		0			0
$961$	6.02677	+	10.4387i	0.194412	+	0.336731i
$962$	−16.5567	−	11.9601i	−0.533810	−	0.385609i
$963$		0			0
$964$	−1.02609	+	1.77725i	−0.0330483	+	0.0572413i
$965$	26.6294	+	46.1235i	0.857232	+	1.48477i
$966$		0			0
$967$	−6.10945			−0.196467			−0.0982333	−	0.995163i	$-0.531319\pi$
$967$	−6.10945			−0.196467			−0.0982333	+	0.995163i	$0.531319\pi$
$968$	−10.7264			−0.344759
$969$		0			0
$970$	5.46256	−	9.46143i	0.175392	−	0.303788i
$971$	−7.04259			−0.226007			−0.113004	−	0.993595i	$-0.536047\pi$
$971$	−7.04259			−0.226007			−0.113004	+	0.993595i	$0.536047\pi$
$972$		0			0
$973$	−4.24135	−	34.6229i	−0.135971	−	1.10996i
$974$	−38.0645			−1.21967
$975$		0			0
$976$	−3.00599	+	5.20652i	−0.0962193	+	0.166657i
$977$	−30.9306			−0.989557			−0.494779	−	0.869019i	$-0.664751\pi$
$977$	−30.9306			−0.989557			−0.494779	+	0.869019i	$0.664751\pi$
$978$		0			0
$979$	2.83830	−	4.91609i	0.0907126	−	0.157119i
$980$	−20.1278	−	20.8663i	−0.642960	−	0.666548i
$981$		0			0
$982$	−16.4426			−0.524704
$983$	−14.5237	+	25.1559i	−0.463235	+	0.802347i	−0.999120	−	0.0419441i	$-0.986645\pi$
$983$	−14.5237	+	25.1559i	−0.463235	+	0.802347i	0.535885	+	0.844291i	$0.319978\pi$
$984$		0			0
$985$	−21.8290	+	37.8089i	−0.695529	+	1.20469i
$986$	3.88724	+	6.73290i	0.123795	+	0.214419i
$987$		0			0
$988$	−16.6594	−	12.0343i	−0.530007	−	0.382862i
$989$	−35.6012	−	61.6631i	−1.13205	−	1.96077i
$990$		0			0
$991$	−13.9391			−0.442790			−0.221395	−	0.975184i	$-0.571061\pi$
$991$	−13.9391			−0.442790			−0.221395	+	0.975184i	$0.571061\pi$
$992$	4.35275			0.138200
$993$		0			0
$994$	−19.4114	−	8.24603i	−0.615691	−	0.261548i
$995$	27.1357	−	47.0004i	0.860259	−	1.49001i
$996$		0			0
$997$	18.4125	+	31.8914i	0.583129	+	1.01001i	0.995106	+	0.0988150i	$0.0315052\pi$
$997$	18.4125	+	31.8914i	0.583129	+	1.01001i	−0.411977	+	0.911194i	$0.635161\pi$
$998$	7.48597			0.236964
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.j.991.5		10
3.2	odd	2		546.2.k.e.445.1	yes	10
7.2	even	3		1638.2.m.k.289.5		10
13.9	even	3		1638.2.m.k.1621.5		10
21.2	odd	6		546.2.j.e.289.1	✓	10
39.35	odd	6		546.2.j.e.529.1	yes	10
91.9	even	3	inner	1638.2.p.j.919.5		10
273.191	odd	6		546.2.k.e.373.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.1	✓	10	21.2	odd	6
546.2.j.e.529.1	yes	10	39.35	odd	6
546.2.k.e.373.1	yes	10	273.191	odd	6
546.2.k.e.445.1	yes	10	3.2	odd	2
1638.2.m.k.289.5		10	7.2	even	3
1638.2.m.k.1621.5		10	13.9	even	3
1638.2.p.j.919.5		10	91.9	even	3	inner
1638.2.p.j.991.5		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.07085 + 3.58682i) q^{5} +(2.11344 - 1.59166i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.07085 + 3.58682i) q^{5} +(2.11344 - 1.59166i) q^{7} +1.00000 q^{8} -4.14170 q^{10} -0.523095 q^{11} +(-3.28981 + 1.47551i) q^{13} +(0.321703 + 2.62612i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.26155 - 2.18506i) q^{17} -5.69993 q^{19} +(2.07085 - 3.58682i) q^{20} +(0.261547 - 0.453013i) q^{22} +(-3.69669 + 6.40285i) q^{23} +(-6.07684 + 10.5254i) q^{25} +(0.367074 - 3.58682i) q^{26} +(-2.43514 - 1.03446i) q^{28} +(1.54066 + 2.66851i) q^{29} +(-2.17638 + 3.76959i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.52309 q^{34} +(10.0856 + 4.28441i) q^{35} +(2.83240 - 4.90586i) q^{37} +(2.84997 - 4.93629i) q^{38} +(2.07085 + 3.58682i) q^{40} +(-2.33240 - 4.03983i) q^{41} +(-4.81529 + 8.34033i) q^{43} +(0.261547 + 0.453013i) q^{44} +(-3.69669 - 6.40285i) q^{46} +(5.58154 + 9.66752i) q^{47} +(1.93322 - 6.72775i) q^{49} +(-6.07684 - 10.5254i) q^{50} +(2.92274 + 2.11130i) q^{52} +(0.00192073 - 0.00332680i) q^{53} +(-1.08325 - 1.87624i) q^{55} +(2.11344 - 1.59166i) q^{56} -3.08133 q^{58} +(4.05374 + 7.02129i) q^{59} +6.01198 q^{61} +(-2.17638 - 3.76959i) q^{62} +1.00000 q^{64} +(-12.1051 - 8.74439i) q^{65} +3.23244 q^{67} +(-1.26155 + 2.18506i) q^{68} +(-8.75321 + 6.59219i) q^{70} +(-3.98568 + 6.90340i) q^{71} +(5.99080 - 10.3764i) q^{73} +(2.83240 + 4.90586i) q^{74} +(2.84997 + 4.93629i) q^{76} +(-1.10553 + 0.832590i) q^{77} +(1.15602 + 2.00229i) q^{79} -4.14170 q^{80} +4.66479 q^{82} -3.08133 q^{83} +(5.22495 - 9.04988i) q^{85} +(-4.81529 - 8.34033i) q^{86} -0.523095 q^{88} +(-5.42599 + 9.39808i) q^{89} +(-4.60428 + 8.35467i) q^{91} +7.39337 q^{92} -11.1631 q^{94} +(-11.8037 - 20.4446i) q^{95} +(-1.31892 + 2.28443i) q^{97} +(4.85980 + 5.03809i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8	\( 10 q - 5 q^{2} - 5 q^{4} + 2 q^{5} + 4 q^{7} + 10 q^{8} - 4 q^{10} + 12 q^{11} - 4 q^{13} - 2 q^{14} - 5 q^{16} - 4 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{22} - 6 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 10 q^{31} - 5 q^{32} + 8 q^{34} + 2 q^{35} + q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} - 6 q^{46} + 15 q^{47} - 20 q^{49} - q^{50} + 2 q^{52} + 17 q^{53} + 3 q^{55} + 4 q^{56} - 2 q^{59} - 22 q^{61} - 10 q^{62} + 10 q^{64} - 41 q^{65} + 2 q^{67} - 4 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} + q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} - 4 q^{80} - 8 q^{82} + q^{85} + 3 q^{86} + 12 q^{88} - 7 q^{89} - 4 q^{91} + 12 q^{92} - 30 q^{94} - 24 q^{95} - 6 q^{97} + 16 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + 2 * q^5 + 4 * q^7 + 10 * q^8 - 4 * q^10 + 12 * q^11 - 4 * q^13 - 2 * q^14 - 5 * q^16 - 4 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^22 - 6 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 10 * q^31 - 5 * q^32 + 8 * q^34 + 2 * q^35 + q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 - 6 * q^46 + 15 * q^47 - 20 * q^49 - q^50 + 2 * q^52 + 17 * q^53 + 3 * q^55 + 4 * q^56 - 2 * q^59 - 22 * q^61 - 10 * q^62 + 10 * q^64 - 41 * q^65 + 2 * q^67 - 4 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 + q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 - 4 * q^80 - 8 * q^82 + q^85 + 3 * q^86 + 12 * q^88 - 7 * q^89 - 4 * q^91 + 12 * q^92 - 30 * q^94 - 24 * q^95 - 6 * q^97 + 16 * q^98

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