LMFDB - Embedded newform 805.2.c.b.484.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(484,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("805.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.c (of order $2$, degree $1$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			484.9
Character	$\chi$	$=$	805.484
Dual form			805.2.c.b.484.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.11343i q^{2} -2.87976i q^{3} +0.760266 q^{4} +(-1.36689 - 1.76964i) q^{5} -3.20642 q^{6} -1.00000i q^{7} -3.07337i q^{8} -5.29300 q^{9} +O(q^{10})$	\(q-1.11343i q^{2} -2.87976i q^{3} +0.760266 q^{4} +(-1.36689 - 1.76964i) q^{5} -3.20642 q^{6} -1.00000i q^{7} -3.07337i q^{8} -5.29300 q^{9} +(-1.97037 + 1.52194i) q^{10} -1.44843 q^{11} -2.18938i q^{12} +2.99328i q^{13} -1.11343 q^{14} +(-5.09612 + 3.93631i) q^{15} -1.90146 q^{16} -0.663092i q^{17} +5.89340i q^{18} +6.91587 q^{19} +(-1.03920 - 1.34539i) q^{20} -2.87976 q^{21} +1.61273i q^{22} -1.00000i q^{23} -8.85056 q^{24} +(-1.26323 + 4.83780i) q^{25} +3.33282 q^{26} +6.60327i q^{27} -0.760266i q^{28} -2.85250 q^{29} +(4.38282 + 5.67419i) q^{30} +5.80140 q^{31} -4.02959i q^{32} +4.17113i q^{33} -0.738309 q^{34} +(-1.76964 + 1.36689i) q^{35} -4.02409 q^{36} -1.45671i q^{37} -7.70036i q^{38} +8.61991 q^{39} +(-5.43875 + 4.20096i) q^{40} +1.31097 q^{41} +3.20642i q^{42} -6.04918i q^{43} -1.10119 q^{44} +(7.23494 + 9.36668i) q^{45} -1.11343 q^{46} -7.26934i q^{47} +5.47575i q^{48} -1.00000 q^{49} +(5.38656 + 1.40652i) q^{50} -1.90954 q^{51} +2.27569i q^{52} +7.52908i q^{53} +7.35230 q^{54} +(1.97985 + 2.56320i) q^{55} -3.07337 q^{56} -19.9160i q^{57} +3.17607i q^{58} +1.21914 q^{59} +(-3.87441 + 2.99264i) q^{60} +1.29657 q^{61} -6.45948i q^{62} +5.29300i q^{63} -8.28961 q^{64} +(5.29702 - 4.09148i) q^{65} +4.64428 q^{66} -6.72336i q^{67} -0.504126i q^{68} -2.87976 q^{69} +(1.52194 + 1.97037i) q^{70} -15.4619 q^{71} +16.2673i q^{72} +12.0554i q^{73} -1.62195 q^{74} +(13.9317 + 3.63778i) q^{75} +5.25790 q^{76} +1.44843i q^{77} -9.59770i q^{78} +12.1005 q^{79} +(2.59909 + 3.36490i) q^{80} +3.13682 q^{81} -1.45968i q^{82} +12.8092i q^{83} -2.18938 q^{84} +(-1.17343 + 0.906374i) q^{85} -6.73536 q^{86} +8.21450i q^{87} +4.45157i q^{88} +17.4986 q^{89} +(10.4292 - 8.05563i) q^{90} +2.99328 q^{91} -0.760266i q^{92} -16.7066i q^{93} -8.09393 q^{94} +(-9.45323 - 12.2386i) q^{95} -11.6042 q^{96} +2.17861i q^{97} +1.11343i q^{98} +7.66654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9}+O(q^{10}) $ 24 * q - 16 * q^4 - 2 * q^5 - 12 * q^6 - 16 * q^9	$ 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9} - 4 q^{10} - 16 q^{11} + 4 q^{14} - 2 q^{15} - 8 q^{16} + 52 q^{19} + 2 q^{20} + 24 q^{24} - 8 q^{25} - 44 q^{26} + 24 q^{29} + 8 q^{30} - 100 q^{31} + 56 q^{34} - 2 q^{35} - 36 q^{36} + 52 q^{39} + 10 q^{40} - 8 q^{41} + 20 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{49} + 28 q^{50} - 64 q^{51} + 20 q^{54} + 28 q^{55} - 12 q^{56} + 36 q^{59} + 42 q^{60} + 16 q^{61} - 24 q^{64} + 30 q^{65} - 4 q^{66} + 12 q^{70} - 48 q^{71} - 72 q^{74} - 16 q^{75} - 112 q^{76} + 88 q^{79} + 8 q^{80} - 32 q^{81} - 24 q^{84} - 12 q^{85} - 64 q^{86} + 20 q^{89} + 108 q^{90} - 4 q^{91} - 36 q^{94} + 48 q^{95} - 76 q^{96} + 112 q^{99}+O(q^{100}) $ 24 * q - 16 * q^4 - 2 * q^5 - 12 * q^6 - 16 * q^9 - 4 * q^10 - 16 * q^11 + 4 * q^14 - 2 * q^15 - 8 * q^16 + 52 * q^19 + 2 * q^20 + 24 * q^24 - 8 * q^25 - 44 * q^26 + 24 * q^29 + 8 * q^30 - 100 * q^31 + 56 * q^34 - 2 * q^35 - 36 * q^36 + 52 * q^39 + 10 * q^40 - 8 * q^41 + 20 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^49 + 28 * q^50 - 64 * q^51 + 20 * q^54 + 28 * q^55 - 12 * q^56 + 36 * q^59 + 42 * q^60 + 16 * q^61 - 24 * q^64 + 30 * q^65 - 4 * q^66 + 12 * q^70 - 48 * q^71 - 72 * q^74 - 16 * q^75 - 112 * q^76 + 88 * q^79 + 8 * q^80 - 32 * q^81 - 24 * q^84 - 12 * q^85 - 64 * q^86 + 20 * q^89 + 108 * q^90 - 4 * q^91 - 36 * q^94 + 48 * q^95 - 76 * q^96 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.11343i		−	0.787316i	−0.919257	−	0.393658i	$-0.871209\pi$
$2$		−	1.11343i		−	0.787316i	0.919257	−	0.393658i	$-0.128791\pi$
$3$		−	2.87976i		−	1.66263i	−0.555803	−	0.831314i	$-0.687589\pi$
$3$		−	2.87976i		−	1.66263i	0.555803	−	0.831314i	$-0.312411\pi$
$4$	0.760266			0.380133
$5$	−1.36689	−	1.76964i	−0.611292	−	0.791405i
$5$	−1.36689	−	1.76964i	−0.611292	−	0.791405i
$6$	−3.20642			−1.30901
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	3.07337i		−	1.08660i
$9$	−5.29300			−1.76433
$10$	−1.97037	+	1.52194i	−0.623086	+	0.481280i
$11$	−1.44843			−0.436719			−0.218359	−	0.975868i	$-0.570070\pi$
$11$	−1.44843			−0.436719			−0.218359	+	0.975868i	$0.570070\pi$
$12$		−	2.18938i		−	0.632020i
$13$			2.99328i			0.830186i	0.909779	+	0.415093i	$0.136251\pi$
$13$			2.99328i			0.830186i	−0.909779	+	0.415093i	$0.863749\pi$
$14$	−1.11343			−0.297578
$15$	−5.09612	+	3.93631i	−1.31581	+	1.01635i
$16$	−1.90146			−0.475366
$17$		−	0.663092i		−	0.160823i	−0.996762	−	0.0804117i	$-0.974376\pi$
$17$		−	0.663092i		−	0.160823i	0.996762	−	0.0804117i	$-0.0256235\pi$
$18$			5.89340i			1.38909i
$19$	6.91587			1.58661			0.793304	−	0.608825i	$-0.208359\pi$
$19$	6.91587			1.58661			0.793304	+	0.608825i	$0.208359\pi$
$20$	−1.03920	−	1.34539i	−0.232372	−	0.300839i
$21$	−2.87976			−0.628414
$22$			1.61273i			0.343836i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−8.85056			−1.80661
$25$	−1.26323	+	4.83780i	−0.252645	+	0.967559i
$26$	3.33282			0.653619
$27$			6.60327i			1.27080i
$28$		−	0.760266i		−	0.143677i
$29$	−2.85250			−0.529696			−0.264848	−	0.964290i	$-0.585322\pi$
$29$	−2.85250			−0.529696			−0.264848	+	0.964290i	$0.585322\pi$
$30$	4.38282	+	5.67419i	0.800189	+	1.03596i
$31$	5.80140			1.04196			0.520981	−	0.853568i	$-0.325566\pi$
$31$	5.80140			1.04196			0.520981	+	0.853568i	$0.325566\pi$
$32$		−	4.02959i		−	0.712338i
$33$			4.17113i			0.726100i
$34$	−0.738309			−0.126619
$35$	−1.76964	+	1.36689i	−0.299123	+	0.231047i
$36$	−4.02409			−0.670681
$37$		−	1.45671i		−	0.239482i	−0.992805	−	0.119741i	$-0.961794\pi$
$37$		−	1.45671i		−	0.239482i	0.992805	−	0.119741i	$-0.0382064\pi$
$38$		−	7.70036i		−	1.24916i
$39$	8.61991			1.38029
$40$	−5.43875	+	4.20096i	−0.859942	+	0.664230i
$41$	1.31097			0.204740			0.102370	−	0.994746i	$-0.467357\pi$
$41$	1.31097			0.204740			0.102370	+	0.994746i	$0.467357\pi$
$42$			3.20642i			0.494761i
$43$		−	6.04918i		−	0.922491i	−0.887272	−	0.461246i	$-0.847403\pi$
$43$		−	6.04918i		−	0.922491i	0.887272	−	0.461246i	$-0.152597\pi$
$44$	−1.10119			−0.166011
$45$	7.23494	+	9.36668i	1.07852	+	1.39630i
$46$	−1.11343			−0.164167
$47$		−	7.26934i		−	1.06034i	−0.847891	−	0.530171i	$-0.822128\pi$
$47$		−	7.26934i		−	1.06034i	0.847891	−	0.530171i	$-0.177872\pi$
$48$			5.47575i			0.790357i
$49$	−1.00000			−0.142857
$50$	5.38656	+	1.40652i	0.761775	+	0.198912i
$51$	−1.90954			−0.267390
$52$			2.27569i			0.315581i
$53$			7.52908i			1.03420i	0.855925	+	0.517099i	$0.172988\pi$
$53$			7.52908i			1.03420i	−0.855925	+	0.517099i	$0.827012\pi$
$54$	7.35230			1.00052
$55$	1.97985	+	2.56320i	0.266962	+	0.345621i
$56$	−3.07337			−0.410697
$57$		−	19.9160i		−	2.63794i
$58$			3.17607i			0.417038i
$59$	1.21914			0.158719			0.0793594	−	0.996846i	$-0.474713\pi$
$59$	1.21914			0.158719			0.0793594	+	0.996846i	$0.474713\pi$
$60$	−3.87441	+	2.99264i	−0.500184	+	0.386348i
$61$	1.29657			0.166009			0.0830045	−	0.996549i	$-0.473548\pi$
$61$	1.29657			0.166009			0.0830045	+	0.996549i	$0.473548\pi$
$62$		−	6.45948i		−	0.820354i
$63$			5.29300i			0.666855i
$64$	−8.28961			−1.03620
$65$	5.29702	−	4.09148i	0.657014	−	0.507486i
$66$	4.64428			0.571671
$67$		−	6.72336i		−	0.821389i	−0.911773	−	0.410694i	$-0.865286\pi$
$67$		−	6.72336i		−	0.821389i	0.911773	−	0.410694i	$-0.134714\pi$
$68$		−	0.504126i		−	0.0611343i
$69$	−2.87976			−0.346682
$70$	1.52194	+	1.97037i	0.181907	+	0.235505i
$71$	−15.4619			−1.83499			−0.917497	−	0.397742i	$-0.869794\pi$
$71$	−15.4619			−1.83499			−0.917497	+	0.397742i	$0.869794\pi$
$72$			16.2673i			1.91713i
$73$			12.0554i			1.41098i	0.708719	+	0.705491i	$0.249273\pi$
$73$			12.0554i			1.41098i	−0.708719	+	0.705491i	$0.750727\pi$
$74$	−1.62195			−0.188548
$75$	13.9317	+	3.63778i	1.60869	+	0.420055i
$76$	5.25790			0.603122
$77$			1.44843i			0.165064i
$78$		−	9.59770i		−	1.08673i
$79$	12.1005			1.36141			0.680706	−	0.732557i	$-0.261673\pi$
$79$	12.1005			1.36141			0.680706	+	0.732557i	$0.261673\pi$
$80$	2.59909	+	3.36490i	0.290587	+	0.376207i
$81$	3.13682			0.348536
$82$		−	1.45968i		−	0.161195i
$83$			12.8092i			1.40599i	0.711194	+	0.702995i	$0.248155\pi$
$83$			12.8092i			1.40599i	−0.711194	+	0.702995i	$0.751845\pi$
$84$	−2.18938			−0.238881
$85$	−1.17343	+	0.906374i	−0.127277	+	0.0983100i
$86$	−6.73536			−0.726293
$87$			8.21450i			0.880687i
$88$			4.45157i			0.474539i
$89$	17.4986			1.85485			0.927423	−	0.374013i	$-0.122019\pi$
$89$	17.4986			1.85485			0.927423	+	0.374013i	$0.122019\pi$
$90$	10.4292	−	8.05563i	1.09933	−	0.849138i
$91$	2.99328			0.313781
$92$		−	0.760266i		−	0.0792632i
$93$		−	16.7066i		−	1.73240i
$94$	−8.09393			−0.834825
$95$	−9.45323	−	12.2386i	−0.969881	−	1.25565i
$96$	−11.6042			−1.18435
$97$			2.17861i			0.221204i	0.993865	+	0.110602i	$0.0352780\pi$
$97$			2.17861i			0.221204i	−0.993865	+	0.110602i	$0.964722\pi$
$98$			1.11343i			0.112474i
$99$	7.66654			0.770517
$100$	−0.960387	+	3.67801i	−0.0960387	+	0.367801i
$101$	−2.86707			−0.285285			−0.142642	−	0.989774i	$-0.545560\pi$
$101$	−2.86707			−0.285285			−0.142642	+	0.989774i	$0.545560\pi$
$102$			2.12615i			0.210520i
$103$		−	13.7697i		−	1.35677i	−0.734706	−	0.678386i	$-0.762680\pi$
$103$		−	13.7697i		−	1.35677i	0.734706	−	0.678386i	$-0.237320\pi$
$104$	9.19946			0.902081
$105$	3.93631	+	5.09612i	0.384144	+	0.497331i
$106$	8.38313			0.814241
$107$			7.16382i			0.692552i	0.938133	+	0.346276i	$0.112554\pi$
$107$			7.16382i			0.692552i	−0.938133	+	0.346276i	$0.887446\pi$
$108$			5.02024i			0.483073i
$109$	−10.5009			−1.00580			−0.502902	−	0.864343i	$-0.667735\pi$
$109$	−10.5009			−1.00580			−0.502902	+	0.864343i	$0.667735\pi$
$110$	2.85395	−	2.20443i	0.272113	−	0.210184i
$111$	−4.19498			−0.398170
$112$			1.90146i			0.179671i
$113$		−	13.7108i		−	1.28980i	−0.764266	−	0.644901i	$-0.776898\pi$
$113$		−	13.7108i		−	1.28980i	0.764266	−	0.644901i	$-0.223102\pi$
$114$	−22.1751			−2.07689
$115$	−1.76964	+	1.36689i	−0.165019	+	0.127463i
$116$	−2.16866			−0.201355
$117$		−	15.8434i		−	1.46472i
$118$		−	1.35743i		−	0.124962i
$119$	−0.663092			−0.0607855
$120$	12.0977	+	15.6623i	1.10437	+	1.42976i
$121$	−8.90205			−0.809277
$122$		−	1.44365i		−	0.130702i
$123$		−	3.77529i		−	0.340406i
$124$	4.41061			0.396084
$125$	10.2878	−	4.37728i	0.920171	−	0.391516i
$126$	5.89340			0.525026
$127$			17.5841i			1.56033i	0.625572	+	0.780166i	$0.284866\pi$
$127$			17.5841i			1.56033i	−0.625572	+	0.780166i	$0.715134\pi$
$128$			1.17074i			0.103480i
$129$	−17.4202			−1.53376
$130$	−4.55559	−	5.89787i	−0.399552	−	0.517278i
$131$	−2.10117			−0.183580			−0.0917901	−	0.995778i	$-0.529259\pi$
$131$	−2.10117			−0.183580			−0.0917901	+	0.995778i	$0.529259\pi$
$132$			3.17117i			0.276015i
$133$		−	6.91587i		−	0.599682i
$134$	−7.48601			−0.646693
$135$	11.6854	−	9.02594i	1.00572	−	0.776830i
$136$	−2.03793			−0.174751
$137$		−	3.72916i		−	0.318604i	−0.987230	−	0.159302i	$-0.949076\pi$
$137$		−	3.72916i		−	0.318604i	0.987230	−	0.159302i	$-0.0509243\pi$
$138$			3.20642i			0.272948i
$139$	−7.08538			−0.600974			−0.300487	−	0.953786i	$-0.597149\pi$
$139$	−7.08538			−0.600974			−0.300487	+	0.953786i	$0.597149\pi$
$140$	−1.34539	+	1.03920i	−0.113707	+	0.0878284i
$141$	−20.9339			−1.76296
$142$			17.2158i			1.44472i
$143$		−	4.33556i		−	0.362558i
$144$	10.0644			0.838703
$145$	3.89905	+	5.04789i	0.323799	+	0.419204i
$146$	13.4229			1.11089
$147$			2.87976i			0.237518i
$148$		−	1.10749i		−	0.0910350i
$149$	−1.47690			−0.120992			−0.0604960	−	0.998168i	$-0.519268\pi$
$149$	−1.47690			−0.120992			−0.0604960	+	0.998168i	$0.519268\pi$
$150$	4.05043	−	15.5120i	0.330716	−	1.26655i
$151$	−7.10228			−0.577975			−0.288988	−	0.957333i	$-0.593319\pi$
$151$	−7.10228			−0.577975			−0.288988	+	0.957333i	$0.593319\pi$
$152$		−	21.2550i		−	1.72401i
$153$			3.50974i			0.283746i
$154$	1.61273			0.129958
$155$	−7.92988	−	10.2664i	−0.636943	−	0.824615i
$156$	6.55343			0.524694
$157$		−	18.6138i		−	1.48554i	−0.669547	−	0.742770i	$-0.733512\pi$
$157$		−	18.6138i		−	1.48554i	0.669547	−	0.742770i	$-0.266488\pi$
$158$		−	13.4731i		−	1.07186i
$159$	21.6819			1.71949
$160$	−7.13091	+	5.50801i	−0.563748	+	0.435446i
$161$	−1.00000			−0.0788110
$162$		−	3.49264i		−	0.274408i
$163$		−	0.205611i		−	0.0161047i	−0.999968	−	0.00805233i	$-0.997437\pi$
$163$		−	0.205611i		−	0.0161047i	0.999968	−	0.00805233i	$-0.00256317\pi$
$164$	0.996689			0.0778284
$165$	7.38138	−	5.70147i	0.574640	−	0.443859i
$166$	14.2622			1.10696
$167$			1.27677i			0.0987995i	0.998779	+	0.0493997i	$0.0157308\pi$
$167$			1.27677i			0.0987995i	−0.998779	+	0.0493997i	$0.984269\pi$
$168$			8.85056i			0.682836i
$169$	4.04028			0.310791
$170$	1.00919	+	1.30654i	0.0774011	+	0.100207i
$171$	−36.6057			−2.79930
$172$		−	4.59899i		−	0.350669i
$173$		−	18.0714i		−	1.37395i	−0.726683	−	0.686973i	$-0.758939\pi$
$173$		−	18.0714i		−	1.37395i	0.726683	−	0.686973i	$-0.241061\pi$
$174$	9.14630			0.693379
$175$	4.83780	+	1.26323i	0.365703	+	0.0954908i
$176$	2.75414			0.207601
$177$		−	3.51083i		−	0.263890i
$178$		−	19.4835i		−	1.46035i
$179$	8.27553			0.618542			0.309271	−	0.950974i	$-0.399915\pi$
$179$	8.27553			0.618542			0.309271	+	0.950974i	$0.399915\pi$
$180$	5.50048	+	7.12117i	0.409982	+	0.530781i
$181$	−21.5703			−1.60331			−0.801653	−	0.597790i	$-0.796046\pi$
$181$	−21.5703			−1.60331			−0.801653	+	0.597790i	$0.796046\pi$
$182$		−	3.33282i		−	0.247045i
$183$		−	3.73381i		−	0.276011i
$184$	−3.07337			−0.226572
$185$	−2.57785	+	1.99116i	−0.189527	+	0.146393i
$186$	−18.6017			−1.36394
$187$			0.960443i			0.0702346i
$188$		−	5.52664i		−	0.403071i
$189$	6.60327			0.480317
$190$	−13.6268	+	10.5255i	−0.988594	+	0.763603i
$191$	12.6588			0.915959			0.457980	−	0.888963i	$-0.348573\pi$
$191$	12.6588			0.915959			0.457980	+	0.888963i	$0.348573\pi$
$192$			23.8721i			1.72282i
$193$		−	14.0594i		−	1.01201i	−0.862529	−	0.506007i	$-0.831121\pi$
$193$		−	14.0594i		−	1.01201i	0.862529	−	0.506007i	$-0.168879\pi$
$194$	2.42574			0.174158
$195$	−11.7825	−	15.2541i	−0.843760	−	1.09237i
$196$	−0.760266			−0.0543047
$197$			4.16293i			0.296596i	0.988943	+	0.148298i	$0.0473795\pi$
$197$			4.16293i			0.296596i	−0.988943	+	0.148298i	$0.952620\pi$
$198$		−	8.53618i		−	0.606640i
$199$	26.7246			1.89446			0.947228	−	0.320561i	$-0.103871\pi$
$199$	26.7246			1.89446			0.947228	+	0.320561i	$0.103871\pi$
$200$	14.8683	+	3.88236i	1.05135	+	0.274524i
$201$	−19.3616			−1.36566
$202$			3.19230i			0.224609i
$203$			2.85250i			0.200206i
$204$	−1.45176			−0.101644
$205$	−1.79196	−	2.31995i	−0.125156	−	0.162032i
$206$	−15.3317			−1.06821
$207$			5.29300i			0.367889i
$208$		−	5.69161i		−	0.394642i
$209$	−10.0172			−0.692901
$210$	5.67419	−	4.38282i	0.391556	−	0.302443i
$211$	−5.22635			−0.359796			−0.179898	−	0.983685i	$-0.557577\pi$
$211$	−5.22635			−0.359796			−0.179898	+	0.983685i	$0.557577\pi$
$212$			5.72410i			0.393133i
$213$			44.5266i			3.05091i
$214$	7.97643			0.545258
$215$	−10.7049	+	8.26856i	−0.730065	+	0.563911i
$216$	20.2943			1.38085
$217$		−	5.80140i		−	0.393825i
$218$			11.6921i			0.791887i
$219$	34.7167			2.34594
$220$	1.50521	+	1.94871i	0.101481	+	0.131382i
$221$	1.98482			0.133513
$222$			4.67083i			0.313485i
$223$		−	4.66532i		−	0.312413i	−0.987724	−	0.156206i	$-0.950073\pi$
$223$		−	4.66532i		−	0.312413i	0.987724	−	0.156206i	$-0.0499265\pi$
$224$	−4.02959			−0.269238
$225$	6.68625	−	25.6064i	0.445750	−	1.70710i
$226$	−15.2661			−1.01548
$227$		−	25.0909i		−	1.66534i	−0.553767	−	0.832672i	$-0.686810\pi$
$227$		−	25.0909i		−	1.66534i	0.553767	−	0.832672i	$-0.313190\pi$
$228$		−	15.1415i		−	1.00277i
$229$	18.2807			1.20802			0.604011	−	0.796976i	$-0.293568\pi$
$229$	18.2807			1.20802			0.604011	+	0.796976i	$0.293568\pi$
$230$	1.52194	+	1.97037i	0.100354	+	0.129922i
$231$	4.17113			0.274440
$232$			8.76679i			0.575568i
$233$		−	18.7459i		−	1.22809i	−0.789272	−	0.614044i	$-0.789542\pi$
$233$		−	18.7459i		−	1.22809i	0.789272	−	0.614044i	$-0.210458\pi$
$234$	−17.6406			−1.15320
$235$	−12.8641	+	9.93639i	−0.839161	+	0.648179i
$236$	0.926872			0.0603342
$237$		−	34.8465i		−	2.26352i
$238$			0.738309i			0.0478575i
$239$	18.2568			1.18094			0.590468	−	0.807061i	$-0.298943\pi$
$239$	18.2568			1.18094			0.590468	+	0.807061i	$0.298943\pi$
$240$	9.69009	−	7.48475i	0.625492	−	0.483138i
$241$	18.4641			1.18937			0.594687	−	0.803957i	$-0.297276\pi$
$241$	18.4641			1.18937			0.594687	+	0.803957i	$0.297276\pi$
$242$			9.91184i			0.637157i
$243$			10.7765i			0.691315i
$244$	0.985740			0.0631055
$245$	1.36689	+	1.76964i	0.0873274	+	0.113058i
$246$	−4.20353			−0.268007
$247$			20.7011i			1.31718i
$248$		−	17.8299i		−	1.13220i
$249$	36.8873			2.33764
$250$	−4.87381	−	11.4548i	−0.308247	−	0.724466i
$251$	14.5229			0.916679			0.458339	−	0.888777i	$-0.348444\pi$
$251$	14.5229			0.916679			0.458339	+	0.888777i	$0.348444\pi$
$252$			4.02409i			0.253494i
$253$			1.44843i			0.0910621i
$254$	19.5787			1.22848
$255$	2.61014	+	3.37920i	0.163453	+	0.211614i
$256$	−15.2757			−0.954730
$257$			12.9024i			0.804828i	0.915458	+	0.402414i	$0.131829\pi$
$257$			12.9024i			0.804828i	−0.915458	+	0.402414i	$0.868171\pi$
$258$			19.3962i			1.20755i
$259$	−1.45671			−0.0905157
$260$	4.02714	−	3.11062i	0.249753	−	0.192912i
$261$	15.0983			0.934559
$262$			2.33951i			0.144536i
$263$			8.31789i			0.512903i	0.966557	+	0.256452i	$0.0825534\pi$
$263$			8.31789i			0.512903i	−0.966557	+	0.256452i	$0.917447\pi$
$264$	12.8194			0.788982
$265$	13.3237	−	10.2914i	0.818470	−	0.632197i
$266$	−7.70036			−0.472139
$267$		−	50.3917i		−	3.08392i
$268$		−	5.11154i		−	0.312237i
$269$	−12.4137			−0.756877			−0.378439	−	0.925626i	$-0.623539\pi$
$269$	−12.4137			−0.756877			−0.378439	+	0.925626i	$0.623539\pi$
$270$	−10.0498	−	13.0109i	−0.611611	−	0.791818i
$271$	−7.28170			−0.442331			−0.221166	−	0.975236i	$-0.570986\pi$
$271$	−7.28170			−0.442331			−0.221166	+	0.975236i	$0.570986\pi$
$272$			1.26085i			0.0764500i
$273$		−	8.61991i		−	0.521701i
$274$	−4.15217			−0.250842
$275$	1.82969	−	7.00721i	0.110335	−	0.422551i
$276$	−2.18938			−0.131785
$277$		−	4.12299i		−	0.247726i	−0.992299	−	0.123863i	$-0.960472\pi$
$277$		−	4.12299i		−	0.247726i	0.992299	−	0.123863i	$-0.0395284\pi$
$278$			7.88910i			0.473157i
$279$	−30.7068			−1.83837
$280$	4.20096	+	5.43875i	0.251055	+	0.325028i
$281$	13.3317			0.795305			0.397653	−	0.917536i	$-0.369825\pi$
$281$	13.3317			0.795305			0.397653	+	0.917536i	$0.369825\pi$
$282$			23.3085i			1.38800i
$283$			6.86438i			0.408045i	0.978966	+	0.204023i	$0.0654016\pi$
$283$			6.86438i			0.408045i	−0.978966	+	0.204023i	$0.934598\pi$
$284$	−11.7552			−0.697542
$285$	−35.2441	+	27.2230i	−2.08768	+	1.61255i
$286$	−4.82736			−0.285448
$287$		−	1.31097i		−	0.0773844i
$288$			21.3286i			1.25680i
$289$	16.5603			0.974136
$290$	5.62049	−	4.34133i	0.330046	−	0.254932i
$291$	6.27387			0.367781
$292$			9.16533i			0.536361i
$293$			31.1708i			1.82102i	0.413492	+	0.910508i	$0.364309\pi$
$293$			31.1708i			1.82102i	−0.413492	+	0.910508i	$0.635691\pi$
$294$	3.20642			0.187002
$295$	−1.66643	−	2.15744i	−0.0970234	−	0.125611i
$296$	−4.47702			−0.260221
$297$		−	9.56439i		−	0.554982i
$298$			1.64442i			0.0952590i
$299$	2.99328			0.173106
$300$	10.5918	+	2.76568i	0.611517	+	0.159677i
$301$	−6.04918			−0.348669
$302$			7.90792i			0.455049i
$303$			8.25648i			0.474322i
$304$	−13.1503			−0.754219
$305$	−1.77227	−	2.29446i	−0.101480	−	0.131380i
$306$	3.90787			0.223398
$307$			30.3088i			1.72981i	0.501933	+	0.864907i	$0.332622\pi$
$307$			30.3088i			1.72981i	−0.501933	+	0.864907i	$0.667378\pi$
$308$			1.10119i			0.0627463i
$309$	−39.6535			−2.25581
$310$	−11.4309	+	8.82939i	−0.649233	+	0.501476i
$311$	−11.7717			−0.667514			−0.333757	−	0.942659i	$-0.608317\pi$
$311$	−11.7717			−0.667514			−0.333757	+	0.942659i	$0.608317\pi$
$312$		−	26.4922i		−	1.49983i
$313$			24.4892i			1.38421i	0.721795	+	0.692106i	$0.243317\pi$
$313$			24.4892i			1.38421i	−0.721795	+	0.692106i	$0.756683\pi$
$314$	−20.7252			−1.16959
$315$	9.36668	−	7.23494i	0.527753	−	0.407643i
$316$	9.19959			0.517517
$317$		−	4.07739i		−	0.229009i	−0.993423	−	0.114505i	$-0.963472\pi$
$317$		−	4.07739i		−	0.229009i	0.993423	−	0.114505i	$-0.0365281\pi$
$318$		−	24.1414i		−	1.35378i
$319$	4.13165			0.231328
$320$	11.3310	+	14.6696i	0.633421	+	0.820055i
$321$	20.6301			1.15146
$322$			1.11343i			0.0620492i
$323$		−	4.58586i		−	0.255164i
$324$	2.38482			0.132490
$325$	−14.4809	−	3.78119i	−0.803254	−	0.209742i
$326$	−0.228934			−0.0126795
$327$			30.2401i			1.67228i
$328$		−	4.02911i		−	0.222470i
$329$	−7.26934			−0.400772
$330$	−6.34821	−	8.21868i	−0.349458	−	0.452423i
$331$	4.69263			0.257930			0.128965	−	0.991649i	$-0.458835\pi$
$331$	4.69263			0.257930			0.128965	+	0.991649i	$0.458835\pi$
$332$			9.73839i			0.534464i
$333$			7.71037i			0.422526i
$334$	1.42160			0.0777864
$335$	−11.8979	+	9.19009i	−0.650052	+	0.502108i
$336$	5.47575			0.298727
$337$			21.4035i			1.16592i	0.812501	+	0.582960i	$0.198106\pi$
$337$			21.4035i			1.16592i	−0.812501	+	0.582960i	$0.801894\pi$
$338$		−	4.49858i		−	0.244691i
$339$	−39.4837			−2.14446
$340$	−0.892120	+	0.689085i	−0.0483820	+	0.0373709i
$341$	−8.40293			−0.455044
$342$			40.7580i			2.20394i
$343$			1.00000i			0.0539949i
$344$	−18.5914			−1.00238
$345$	3.93631	+	5.09612i	0.211924	+	0.274366i
$346$	−20.1214			−1.08173
$347$			28.5572i			1.53303i	0.642226	+	0.766515i	$0.278011\pi$
$347$			28.5572i			1.53303i	−0.642226	+	0.766515i	$0.721989\pi$
$348$			6.24521i			0.334778i
$349$	−9.75879			−0.522376			−0.261188	−	0.965288i	$-0.584114\pi$
$349$	−9.75879			−0.522376			−0.261188	+	0.965288i	$0.584114\pi$
$350$	1.40652	−	5.38656i	0.0751815	−	0.287924i
$351$	−19.7654			−1.05500
$352$			5.83659i			0.311091i
$353$		−	37.2666i		−	1.98350i	−0.128191	−	0.991750i	$-0.540917\pi$
$353$		−	37.2666i		−	1.98350i	0.128191	−	0.991750i	$-0.459083\pi$
$354$	−3.90908			−0.207765
$355$	21.1348	+	27.3620i	1.12172	+	1.45222i
$356$	13.3036			0.705089
$357$			1.90954i			0.101064i
$358$		−	9.21425i		−	0.486988i
$359$	5.15223			0.271924			0.135962	−	0.990714i	$-0.456587\pi$
$359$	5.15223			0.271924			0.135962	+	0.990714i	$0.456587\pi$
$360$	28.7873	−	22.2357i	1.51722	−	1.17192i
$361$	28.8292			1.51733
$362$			24.0171i			1.26231i
$363$			25.6357i			1.34553i
$364$	2.27569			0.119278
$365$	21.3337	−	16.4784i	1.11666	−	0.862521i
$366$	−4.15735			−0.217308
$367$		−	23.3715i		−	1.21998i	−0.792409	−	0.609990i	$-0.791173\pi$
$367$		−	23.3715i		−	1.21998i	0.792409	−	0.609990i	$-0.208827\pi$
$368$			1.90146i			0.0991206i
$369$	−6.93898			−0.361229
$370$	2.21703	+	2.87027i	0.115258	+	0.149218i
$371$	7.52908			0.390890
$372$		−	12.7015i		−	0.658541i
$373$		−	31.2466i		−	1.61789i	−0.587888	−	0.808943i	$-0.700040\pi$
$373$		−	31.2466i		−	1.61789i	0.587888	−	0.808943i	$-0.299960\pi$
$374$	1.06939			0.0552968
$375$	−12.6055	−	29.6264i	−0.650946	−	1.52990i
$376$	−22.3414			−1.15217
$377$		−	8.53833i		−	0.439746i
$378$		−	7.35230i		−	0.378162i
$379$	−20.5672			−1.05647			−0.528233	−	0.849099i	$-0.677145\pi$
$379$	−20.5672			−1.05647			−0.528233	+	0.849099i	$0.677145\pi$
$380$	−7.18697	−	9.30457i	−0.368684	−	0.477314i
$381$	50.6378			2.59425
$382$		−	14.0947i		−	0.721150i
$383$			21.5957i			1.10349i	0.834014	+	0.551743i	$0.186037\pi$
$383$			21.5957i			1.10349i	−0.834014	+	0.551743i	$0.813963\pi$
$384$	3.37145			0.172049
$385$	2.56320	−	1.97985i	0.130633	−	0.100902i
$386$	−15.6542			−0.796775
$387$			32.0183i			1.62758i
$388$			1.65632i			0.0840871i
$389$	19.3475			0.980957			0.490478	−	0.871453i	$-0.336822\pi$
$389$	19.3475			0.980957			0.490478	+	0.871453i	$0.336822\pi$
$390$	−16.9844	+	13.1190i	−0.860040	+	0.664306i
$391$	−0.663092			−0.0335340
$392$			3.07337i			0.155229i
$393$			6.05086i			0.305226i
$394$	4.63514			0.233515
$395$	−16.5400	−	21.4135i	−0.832219	−	1.07743i
$396$	5.82861			0.292899
$397$		−	32.1676i		−	1.61445i	−0.590247	−	0.807223i	$-0.700970\pi$
$397$		−	32.1676i		−	1.61445i	0.590247	−	0.807223i	$-0.299030\pi$
$398$		−	29.7560i		−	1.49154i
$399$	−19.9160			−0.997048
$400$	2.40198	−	9.19889i	0.120099	−	0.459944i
$401$	−23.7719			−1.18711			−0.593556	−	0.804793i	$-0.702276\pi$
$401$	−23.7719			−1.18711			−0.593556	+	0.804793i	$0.702276\pi$
$402$			21.5579i			1.07521i
$403$			17.3652i			0.865023i
$404$	−2.17974			−0.108446
$405$	−4.28769	−	5.55104i	−0.213057	−	0.275833i
$406$	3.17607			0.157626
$407$			2.10995i			0.104586i
$408$			5.86874i			0.290546i
$409$	9.99727			0.494333			0.247166	−	0.968973i	$-0.420501\pi$
$409$	9.99727			0.494333			0.247166	+	0.968973i	$0.420501\pi$
$410$	−2.58311	+	1.99522i	−0.127571	+	0.0985371i
$411$	−10.7391			−0.529719
$412$		−	10.4687i		−	0.515754i
$413$		−	1.21914i		−	0.0599900i
$414$	5.89340			0.289645
$415$	22.6676	−	17.5087i	1.11271	−	0.859470i
$416$	12.0617			0.591373
$417$			20.4042i			0.999196i
$418$			11.1534i			0.545532i
$419$	16.2626			0.794482			0.397241	−	0.917714i	$-0.369968\pi$
$419$	16.2626			0.794482			0.397241	+	0.917714i	$0.369968\pi$
$420$	2.99264	+	3.87441i	0.146026	+	0.189052i
$421$	−6.62211			−0.322742			−0.161371	−	0.986894i	$-0.551592\pi$
$421$	−6.62211			−0.322742			−0.161371	+	0.986894i	$0.551592\pi$
$422$			5.81919i			0.283274i
$423$			38.4766i			1.87080i
$424$	23.1397			1.12376
$425$	3.20790	+	0.837634i	0.155606	+	0.0406312i
$426$	49.5774			2.40203
$427$		−	1.29657i		−	0.0627455i
$428$			5.44641i			0.263262i
$429$	−12.4854			−0.602799
$430$	9.20649	+	11.9191i	0.443977	+	0.574792i
$431$	16.1629			0.778540			0.389270	−	0.921124i	$-0.372727\pi$
$431$	16.1629			0.778540			0.389270	+	0.921124i	$0.372727\pi$
$432$		−	12.5559i		−	0.604095i
$433$		−	2.34223i		−	0.112561i	−0.998415	−	0.0562803i	$-0.982076\pi$
$433$		−	2.34223i		−	0.112561i	0.998415	−	0.0562803i	$-0.0179240\pi$
$434$	−6.45948			−0.310065
$435$	14.5367	−	11.2283i	0.696981	−	0.538357i
$436$	−7.98349			−0.382340
$437$		−	6.91587i		−	0.330831i
$438$		−	38.6547i		−	1.84699i
$439$	28.8480			1.37684			0.688421	−	0.725311i	$-0.258304\pi$
$439$	28.8480			1.37684			0.688421	+	0.725311i	$0.258304\pi$
$440$	7.87766	−	6.08480i	0.375553	−	0.290082i
$441$	5.29300			0.252047
$442$		−	2.20996i		−	0.105117i
$443$			27.5171i			1.30737i	0.756765	+	0.653687i	$0.226779\pi$
$443$			27.5171i			1.30737i	−0.756765	+	0.653687i	$0.773221\pi$
$444$	−3.18930			−0.151357
$445$	−23.9186	−	30.9661i	−1.13385	−	1.46794i
$446$	−5.19452			−0.245968
$447$			4.25310i			0.201165i
$448$			8.28961i			0.391647i
$449$	0.919843			0.0434101			0.0217050	−	0.999764i	$-0.493091\pi$
$449$	0.919843			0.0434101			0.0217050	+	0.999764i	$0.493091\pi$
$450$	−28.5111	−	7.44469i	−1.34402	−	0.350946i
$451$	−1.89886			−0.0894137
$452$		−	10.4239i		−	0.490297i
$453$			20.4528i			0.960958i
$454$	−27.9371			−1.31115
$455$	−4.09148	−	5.29702i	−0.191812	−	0.248328i
$456$	−61.2093			−2.86639
$457$		−	1.00887i		−	0.0471930i	−0.999722	−	0.0235965i	$-0.992488\pi$
$457$		−	1.00887i		−	0.0471930i	0.999722	−	0.0235965i	$-0.00751169\pi$
$458$		−	20.3543i		−	0.951096i
$459$	4.37858			0.204374
$460$	−1.34539	+	1.03920i	−0.0627293	+	0.0484529i
$461$	15.4967			0.721754			0.360877	−	0.932613i	$-0.382477\pi$
$461$	15.4967			0.721754			0.360877	+	0.932613i	$0.382477\pi$
$462$		−	4.64428i		−	0.216071i
$463$			41.6691i			1.93653i	0.249927	+	0.968265i	$0.419593\pi$
$463$			41.6691i			1.93653i	−0.249927	+	0.968265i	$0.580407\pi$
$464$	5.42392			0.251799
$465$	−29.5646	+	22.8361i	−1.37103	+	1.05900i
$466$	−20.8724			−0.966894
$467$			4.55326i			0.210700i	0.994435	+	0.105350i	$0.0335962\pi$
$467$			4.55326i			0.210700i	−0.994435	+	0.105350i	$0.966404\pi$
$468$		−	12.0452i		−	0.556790i
$469$	−6.72336			−0.310456
$470$	11.0635	+	14.3233i	0.510322	+	0.660685i
$471$	−53.6031			−2.46990
$472$		−	3.74688i		−	0.172464i
$473$			8.76182i			0.402869i
$474$	−38.7992			−1.78211
$475$	−8.73630	+	33.4575i	−0.400849	+	1.53514i
$476$	−0.504126			−0.0231066
$477$		−	39.8514i		−	1.82467i
$478$		−	20.3278i		−	0.929771i
$479$	−10.1748			−0.464899			−0.232450	−	0.972608i	$-0.574674\pi$
$479$	−10.1748			−0.464899			−0.232450	+	0.972608i	$0.574674\pi$
$480$	15.8617	+	20.5353i	0.723985	+	0.937303i
$481$	4.36035			0.198815
$482$		−	20.5585i		−	0.936414i
$483$			2.87976i			0.131033i
$484$	−6.76792			−0.307633
$485$	3.85535	−	2.97792i	0.175062	−	0.135220i
$486$	11.9989			0.544283
$487$			31.1690i			1.41240i	0.708010	+	0.706202i	$0.249593\pi$
$487$			31.1690i			1.41240i	−0.708010	+	0.706202i	$0.750407\pi$
$488$		−	3.98485i		−	0.180386i
$489$	−0.592109			−0.0267761
$490$	1.97037	−	1.52194i	0.0890123	−	0.0687543i
$491$	13.3052			0.600456			0.300228	−	0.953867i	$-0.402937\pi$
$491$	13.3052			0.600456			0.300228	+	0.953867i	$0.402937\pi$
$492$		−	2.87022i		−	0.129400i
$493$			1.89147i			0.0851875i
$494$	23.0493			1.03704
$495$	−10.4793	−	13.5670i	−0.471010	−	0.609791i
$496$	−11.0312			−0.495313
$497$			15.4619i			0.693563i
$498$		−	41.0716i		−	1.84046i
$499$	39.3655			1.76224			0.881121	−	0.472890i	$-0.156789\pi$
$499$	39.3655			1.76224			0.881121	+	0.472890i	$0.156789\pi$
$500$	7.82149	−	3.32790i	0.349787	−	0.148828i
$501$	3.67679			0.164267
$502$		−	16.1703i		−	0.721716i
$503$		−	6.98352i		−	0.311380i	−0.987806	−	0.155690i	$-0.950240\pi$
$503$		−	6.98352i		−	0.311380i	0.987806	−	0.155690i	$-0.0497600\pi$
$504$	16.2673			0.724605
$505$	3.91897	+	5.07368i	0.174392	+	0.225776i
$506$	1.61273			0.0716947
$507$		−	11.6350i		−	0.516729i
$508$			13.3686i			0.593134i
$509$	−30.8880			−1.36908			−0.684542	−	0.728973i	$-0.739998\pi$
$509$	−30.8880			−1.36908			−0.684542	+	0.728973i	$0.739998\pi$
$510$	3.76251	−	2.90621i	0.166607	−	0.128689i
$511$	12.0554			0.533301
$512$			19.3499i			0.855154i
$513$			45.6673i			2.01626i
$514$	14.3659			0.633654
$515$	−24.3674	+	18.8217i	−1.07376	+	0.829383i
$516$	−13.2440			−0.583033
$517$			10.5291i			0.463071i
$518$			1.62195i			0.0712645i
$519$	−52.0414			−2.28436
$520$	−12.5746	−	16.2797i	−0.551435	−	0.713912i
$521$	38.1013			1.66925			0.834623	−	0.550821i	$-0.185685\pi$
$521$	38.1013			1.66925			0.834623	+	0.550821i	$0.185685\pi$
$522$		−	16.8109i		−	0.735794i
$523$		−	13.0908i		−	0.572421i	−0.958167	−	0.286210i	$-0.907604\pi$
$523$		−	13.0908i		−	0.572421i	0.958167	−	0.286210i	$-0.0923956\pi$
$524$	−1.59745			−0.0697849
$525$	3.63778	−	13.9317i	0.158766	−	0.608028i
$526$	9.26142			0.403817
$527$		−	3.84686i		−	0.167572i
$528$		−	7.93125i		−	0.345163i
$529$	−1.00000			−0.0434783
$530$	−11.4588	−	14.8351i	−0.497739	−	0.644395i
$531$	−6.45291			−0.280033
$532$		−	5.25790i		−	0.227959i
$533$			3.92411i			0.169972i
$534$	−56.1078			−2.42802
$535$	12.6774	−	9.79215i	0.548090	−	0.423352i
$536$	−20.6634			−0.892522
$537$		−	23.8315i		−	1.02841i
$538$			13.8218i			0.595902i
$539$	1.44843			0.0623884
$540$	8.88400	−	6.86212i	0.382307	−	0.295299i
$541$	19.8575			0.853742			0.426871	−	0.904312i	$-0.359616\pi$
$541$	19.8575			0.853742			0.426871	+	0.904312i	$0.359616\pi$
$542$			8.10768i			0.348255i
$543$			62.1171i			2.66570i
$544$	−2.67199			−0.114561
$545$	14.3536	+	18.5828i	0.614840	+	0.795999i
$546$	−9.59770			−0.410744
$547$		−	2.33451i		−	0.0998163i	−0.998754	−	0.0499081i	$-0.984107\pi$
$547$		−	2.33451i		−	0.0998163i	0.998754	−	0.0499081i	$-0.0158929\pi$
$548$		−	2.83515i		−	0.121112i
$549$	−6.86275			−0.292895
$550$	−7.80207	−	2.03724i	−0.332681	−	0.0868683i
$551$	−19.7275			−0.840420
$552$			8.85056i			0.376705i
$553$		−	12.1005i		−	0.514565i
$554$	−4.59067			−0.195039
$555$	5.73407	+	7.42358i	0.243398	+	0.315114i
$556$	−5.38677			−0.228450
$557$			3.11889i			0.132152i	0.997815	+	0.0660759i	$0.0210479\pi$
$557$			3.11889i			0.132152i	−0.997815	+	0.0660759i	$0.978952\pi$
$558$			34.1900i			1.44738i
$559$	18.1069			0.765840
$560$	3.36490	−	2.59909i	0.142193	−	0.109832i
$561$	2.76584			0.116774
$562$		−	14.8440i		−	0.626157i
$563$		−	33.1239i		−	1.39601i	−0.716094	−	0.698003i	$-0.754072\pi$
$563$		−	33.1239i		−	1.39601i	0.716094	−	0.698003i	$-0.245928\pi$
$564$	−15.9154			−0.670158
$565$	−24.2631	+	18.7411i	−1.02076	+	0.788446i
$566$	7.64304			0.321261
$567$		−	3.13682i		−	0.131734i
$568$			47.5203i			1.99391i
$569$	36.2581			1.52002			0.760008	−	0.649913i	$-0.225195\pi$
$569$	36.2581			1.52002			0.760008	+	0.649913i	$0.225195\pi$
$570$	30.3110	+	39.2419i	1.26959	+	1.64366i
$571$	−24.4478			−1.02311			−0.511554	−	0.859251i	$-0.670930\pi$
$571$	−24.4478			−1.02311			−0.511554	+	0.859251i	$0.670930\pi$
$572$		−	3.29618i		−	0.137820i
$573$		−	36.4543i		−	1.52290i
$574$	−1.45968			−0.0609260
$575$	4.83780	+	1.26323i	0.201750	+	0.0526801i
$576$	43.8769			1.82820
$577$			41.1613i			1.71357i	0.515675	+	0.856784i	$0.327541\pi$
$577$			41.1613i			1.71357i	−0.515675	+	0.856784i	$0.672459\pi$
$578$		−	18.4388i		−	0.766953i
$579$	−40.4875			−1.68260
$580$	2.96432	+	3.83774i	0.123087	+	0.159353i
$581$	12.8092			0.531415
$582$		−	6.98554i		−	0.289560i
$583$		−	10.9054i		−	0.451654i
$584$	37.0508			1.53317
$585$	−28.0371	+	21.6562i	−1.15919	+	0.895374i
$586$	34.7066			1.43372
$587$			44.9204i			1.85406i	0.374984	+	0.927031i	$0.377648\pi$
$587$			44.9204i			1.85406i	−0.374984	+	0.927031i	$0.622352\pi$
$588$			2.18938i			0.0902886i
$589$	40.1217			1.65319
$590$	−2.40216	+	1.85546i	−0.0988955	+	0.0763881i
$591$	11.9882			0.493130
$592$			2.76988i			0.113842i
$593$			32.4937i			1.33436i	0.744898	+	0.667178i	$0.232498\pi$
$593$			32.4937i			1.33436i	−0.744898	+	0.667178i	$0.767502\pi$
$594$	−10.6493			−0.436946
$595$	0.906374	+	1.17343i	0.0371577	+	0.0481060i
$596$	−1.12283			−0.0459931
$597$		−	76.9603i		−	3.14978i
$598$		−	3.33282i		−	0.136289i
$599$	−27.3234			−1.11640			−0.558201	−	0.829706i	$-0.688508\pi$
$599$	−27.3234			−1.11640			−0.558201	+	0.829706i	$0.688508\pi$
$600$	11.1803	−	42.8172i	0.456432	−	1.74801i
$601$	5.51397			0.224920			0.112460	−	0.993656i	$-0.464127\pi$
$601$	5.51397			0.224920			0.112460	+	0.993656i	$0.464127\pi$
$602$			6.73536i			0.274513i
$603$			35.5867i			1.44920i
$604$	−5.39962			−0.219708
$605$	12.1681	+	15.7534i	0.494704	+	0.640466i
$606$	9.19303			0.373442
$607$			7.96719i			0.323378i	0.986842	+	0.161689i	$0.0516942\pi$
$607$			7.96719i			0.323378i	−0.986842	+	0.161689i	$0.948306\pi$
$608$		−	27.8681i		−	1.13020i
$609$	8.21450			0.332868
$610$	−2.55473	+	1.97331i	−0.103438	+	0.0798968i
$611$	21.7592			0.880282
$612$			2.66834i			0.107861i
$613$		−	6.29976i		−	0.254445i	−0.991874	−	0.127222i	$-0.959394\pi$
$613$		−	6.29976i		−	0.254445i	0.991874	−	0.127222i	$-0.0406062\pi$
$614$	33.7468			1.36191
$615$	−6.68088	+	5.16040i	−0.269399	+	0.208087i
$616$	4.45157			0.179359
$617$			22.2397i			0.895336i	0.894200	+	0.447668i	$0.147745\pi$
$617$			22.2397i			0.895336i	−0.894200	+	0.447668i	$0.852255\pi$
$618$			44.1515i			1.77603i
$619$	−6.07253			−0.244076			−0.122038	−	0.992525i	$-0.538943\pi$
$619$	−6.07253			−0.244076			−0.122038	+	0.992525i	$0.538943\pi$
$620$	−6.02882	−	7.80517i	−0.242123	−	0.313463i
$621$	6.60327			0.264980
$622$			13.1071i			0.525545i
$623$		−	17.4986i		−	0.701066i
$624$	−16.3905			−0.656143
$625$	−21.8085	−	12.2224i	−0.872341	−	0.488898i
$626$	27.2671			1.08981
$627$			28.8470i			1.15204i
$628$		−	14.1514i		−	0.564703i
$629$	−0.965934			−0.0385143
$630$	−8.05563	−	10.4292i	−0.320944	−	0.415508i
$631$	−48.3297			−1.92398			−0.961988	−	0.273093i	$-0.911953\pi$
$631$	−48.3297			−1.92398			−0.961988	+	0.273093i	$0.911953\pi$
$632$		−	37.1893i		−	1.47931i
$633$			15.0506i			0.598208i
$634$	−4.53990			−0.180303
$635$	31.1174	−	24.0355i	1.23486	−	0.953818i
$636$	16.4840			0.653634
$637$		−	2.99328i		−	0.118598i
$638$		−	4.60032i		−	0.182128i
$639$	81.8400			3.23754
$640$	2.07179	−	1.60028i	0.0818947	−	0.0632565i
$641$	17.7883			0.702595			0.351297	−	0.936264i	$-0.385741\pi$
$641$	17.7883			0.702595			0.351297	+	0.936264i	$0.385741\pi$
$642$		−	22.9702i		−	0.906561i
$643$		−	29.4888i		−	1.16292i	−0.813573	−	0.581462i	$-0.802481\pi$
$643$		−	29.4888i		−	1.16292i	0.813573	−	0.581462i	$-0.197519\pi$
$644$	−0.760266			−0.0299587
$645$	23.8114	+	30.8274i	0.937575	+	1.21383i
$646$	−5.10604			−0.200895
$647$		−	2.00709i		−	0.0789067i	−0.999221	−	0.0394534i	$-0.987438\pi$
$647$		−	2.00709i		−	0.0789067i	0.999221	−	0.0394534i	$-0.0125617\pi$
$648$		−	9.64063i		−	0.378720i
$649$	−1.76584			−0.0693154
$650$	−4.21010	+	16.1235i	−0.165134	+	0.632415i
$651$	−16.7066			−0.654784
$652$		−	0.156319i		−	0.00612192i
$653$		−	5.44963i		−	0.213260i	−0.994299	−	0.106630i	$-0.965994\pi$
$653$		−	5.44963i		−	0.213260i	0.994299	−	0.106630i	$-0.0340061\pi$
$654$	33.6703			1.31661
$655$	2.87207	+	3.71831i	0.112221	+	0.145286i
$656$	−2.49277			−0.0973263
$657$		−	63.8094i		−	2.48944i
$658$			8.09393i			0.315534i
$659$	−5.72411			−0.222980			−0.111490	−	0.993766i	$-0.535562\pi$
$659$	−5.72411			−0.222980			−0.111490	+	0.993766i	$0.535562\pi$
$660$	5.61181	−	4.33464i	0.218440	−	0.168726i
$661$	−0.634951			−0.0246967			−0.0123484	−	0.999924i	$-0.503931\pi$
$661$	−0.634951			−0.0246967			−0.0123484	+	0.999924i	$0.503931\pi$
$662$		−	5.22493i		−	0.203073i
$663$		−	5.71580i		−	0.221983i
$664$	39.3674			1.52775
$665$	−12.2386	+	9.45323i	−0.474591	+	0.366580i
$666$	8.58499			0.332661
$667$			2.85250i			0.110449i
$668$			0.970685i			0.0375569i
$669$	−13.4350			−0.519426
$670$	10.2326	+	13.2475i	0.395318	+	0.511796i
$671$	−1.87800			−0.0724992
$672$			11.6042i			0.447643i
$673$		−	27.6288i		−	1.06501i	−0.846426	−	0.532506i	$-0.821250\pi$
$673$		−	27.6288i		−	1.06501i	0.846426	−	0.532506i	$-0.178750\pi$
$674$	23.8313			0.917948
$675$	−31.9453	−	8.34142i	−1.22957	−	0.321061i
$676$	3.07169			0.118142
$677$		−	13.9294i		−	0.535351i	−0.963509	−	0.267676i	$-0.913744\pi$
$677$		−	13.9294i		−	0.535351i	0.963509	−	0.267676i	$-0.0862556\pi$
$678$			43.9625i			1.68837i
$679$	2.17861			0.0836074
$680$	2.78562	+	3.60639i	0.106824	+	0.138299i
$681$	−72.2557			−2.76885
$682$			9.35611i			0.358264i
$683$		−	22.8605i		−	0.874732i	−0.899284	−	0.437366i	$-0.855911\pi$
$683$		−	22.8605i		−	0.874732i	0.899284	−	0.437366i	$-0.144089\pi$
$684$	−27.8300			−1.06411
$685$	−6.59926	+	5.09735i	−0.252145	+	0.194760i
$686$	1.11343			0.0425111
$687$		−	52.6440i		−	2.00849i
$688$			11.5023i			0.438521i
$689$	−22.5366			−0.858577
$690$	5.67419	−	4.38282i	0.216013	−	0.166851i
$691$	24.1913			0.920282			0.460141	−	0.887846i	$-0.347799\pi$
$691$	24.1913			0.920282			0.460141	+	0.887846i	$0.347799\pi$
$692$		−	13.7391i		−	0.522283i
$693$		−	7.66654i		−	0.291228i
$694$	31.7965			1.20698
$695$	9.68493	+	12.5385i	0.367370	+	0.475614i
$696$	25.2462			0.956956
$697$		−	0.869297i		−	0.0329270i
$698$			10.8658i			0.411275i
$699$	−53.9838			−2.04185
$700$	3.67801	+	0.960387i	0.139016	+	0.0362992i
$701$	27.5742			1.04146			0.520731	−	0.853721i	$-0.325659\pi$
$701$	27.5742			1.04146			0.520731	+	0.853721i	$0.325659\pi$
$702$			22.0075i			0.830619i
$703$		−	10.0744i		−	0.379964i
$704$	12.0069			0.452528
$705$	28.6144	+	37.0455i	1.07768	+	1.39521i
$706$	−41.4938			−1.56164
$707$			2.86707i			0.107827i
$708$		−	2.66917i		−	0.100313i
$709$	−37.7172			−1.41650			−0.708249	−	0.705963i	$-0.750515\pi$
$709$	−37.7172			−1.41650			−0.708249	+	0.705963i	$0.750515\pi$
$710$	30.4658	−	23.5322i	1.14336	−	0.883146i
$711$	−64.0479			−2.40198
$712$		−	53.7797i		−	2.01548i
$713$		−	5.80140i		−	0.217264i
$714$	2.12615			0.0795691
$715$	−7.67236	+	5.92623i	−0.286930	+	0.221629i
$716$	6.29161			0.235128
$717$		−	52.5752i		−	1.96346i
$718$		−	5.73667i		−	0.214091i
$719$	28.5538			1.06488			0.532438	−	0.846469i	$-0.321276\pi$
$719$	28.5538			1.06488			0.532438	+	0.846469i	$0.321276\pi$
$720$	−13.7570	−	17.8104i	−0.512692	−	0.663754i
$721$	−13.7697			−0.512811
$722$		−	32.0994i		−	1.19462i
$723$		−	53.1720i		−	1.97749i
$724$	−16.3991			−0.609469
$725$	3.60335	−	13.7998i	0.133825	−	0.512512i
$726$	28.5437			1.05935
$727$		−	2.95773i		−	0.109696i	−0.998495	−	0.0548480i	$-0.982533\pi$
$727$		−	2.95773i		−	0.109696i	0.998495	−	0.0548480i	$-0.0174674\pi$
$728$		−	9.19946i		−	0.340955i
$729$	40.4442			1.49793
$730$	−18.3476	−	23.7537i	−0.679077	−	0.879163i
$731$	−4.01116			−0.148358
$732$		−	2.83869i		−	0.104921i
$733$			29.3085i			1.08254i	0.840850	+	0.541268i	$0.182055\pi$
$733$			29.3085i			1.08254i	−0.840850	+	0.541268i	$0.817945\pi$
$734$	−26.0226			−0.960510
$735$	5.09612	−	3.93631i	0.187973	−	0.145193i
$736$	−4.02959			−0.148533
$737$			9.73832i			0.358716i
$738$			7.72609i			0.284401i
$739$	−15.4678			−0.568993			−0.284497	−	0.958677i	$-0.591826\pi$
$739$	−15.4678			−0.568993			−0.284497	+	0.958677i	$0.591826\pi$
$740$	−1.95985	+	1.51382i	−0.0720456	+	0.0556490i
$741$	59.6142			2.18998
$742$		−	8.38313i		−	0.307754i
$743$		−	7.62875i		−	0.279872i	−0.990161	−	0.139936i	$-0.955310\pi$
$743$		−	7.62875i		−	0.279872i	0.990161	−	0.139936i	$-0.0446896\pi$
$744$	−51.3457			−1.88242
$745$	2.01875	+	2.61357i	0.0739614	+	0.0957537i
$746$	−34.7910			−1.27379
$747$		−	67.7990i		−	2.48063i
$748$			0.730193i			0.0266985i
$749$	7.16382			0.261760
$750$	−32.9871	+	14.0354i	−1.20452	+	0.512500i
$751$	−4.82336			−0.176007			−0.0880034	−	0.996120i	$-0.528049\pi$
$751$	−4.82336			−0.176007			−0.0880034	+	0.996120i	$0.528049\pi$
$752$			13.8224i			0.504051i
$753$		−	41.8225i		−	1.52410i
$754$	−9.50686			−0.346219
$755$	9.70803	+	12.5685i	0.353312	+	0.457413i
$756$	5.02024			0.182584
$757$		−	4.81593i		−	0.175038i	−0.996163	−	0.0875190i	$-0.972106\pi$
$757$		−	4.81593i		−	0.175038i	0.996163	−	0.0875190i	$-0.0278939\pi$
$758$			22.9002i			0.831773i
$759$	4.17113			0.151402
$760$	−37.6137	+	29.0533i	−1.36439	+	1.05387i
$761$	21.0293			0.762311			0.381156	−	0.924511i	$-0.375526\pi$
$761$	21.0293			0.762311			0.381156	+	0.924511i	$0.375526\pi$
$762$		−	56.3818i		−	2.04250i
$763$			10.5009i			0.380159i
$764$	9.62406			0.348186
$765$	6.21097	−	4.79743i	0.224558	−	0.173452i
$766$	24.0453			0.868793
$767$			3.64923i			0.131766i
$768$			43.9902i			1.58736i
$769$	26.7473			0.964533			0.482267	−	0.876024i	$-0.339814\pi$
$769$	26.7473			0.964533			0.482267	+	0.876024i	$0.339814\pi$
$770$	−2.20443	−	2.85395i	−0.0794420	−	0.102849i
$771$	37.1557			1.33813
$772$		−	10.6888i		−	0.384700i
$773$			18.0588i			0.649530i	0.945795	+	0.324765i	$0.105285\pi$
$773$			18.0588i			0.649530i	−0.945795	+	0.324765i	$0.894715\pi$
$774$	35.6502			1.28142
$775$	−7.32848	+	28.0660i	−0.263247	+	1.00816i
$776$	6.69568			0.240361
$777$			4.19498i			0.150494i
$778$		−	21.5421i		−	0.772323i
$779$	9.06652			0.324842
$780$	−8.95781	−	11.5972i	−0.320741	−	0.415246i
$781$	22.3956			0.801376
$782$			0.738309i			0.0264019i
$783$		−	18.8358i		−	0.673138i
$784$	1.90146			0.0679094
$785$	−32.9396	+	25.4430i	−1.17566	+	0.908098i
$786$	6.73723			0.240309
$787$		−	30.6722i		−	1.09335i	−0.837346	−	0.546674i	$-0.815894\pi$
$787$		−	30.6722i		−	1.09335i	0.837346	−	0.546674i	$-0.184106\pi$
$788$			3.16493i			0.112746i
$789$	23.9535			0.852767
$790$	−23.8425	+	18.4162i	−0.848277	+	0.655220i
$791$	−13.7108			−0.487500
$792$		−	23.5621i		−	0.837244i
$793$			3.88100i			0.137818i
$794$	−35.8165			−1.27108
$795$	−29.6368	−	38.3691i	−1.05111	−	1.36081i
$796$	20.3178			0.720145
$797$		−	8.87753i		−	0.314458i	−0.987562	−	0.157229i	$-0.949744\pi$
$797$		−	8.87753i		−	0.314458i	0.987562	−	0.157229i	$-0.0502561\pi$
$798$			22.1751i			0.784992i
$799$	−4.82024			−0.170528
$800$	19.4943	+	5.09028i	0.689229	+	0.179969i
$801$	−92.6200			−3.27257
$802$			26.4684i			0.934633i
$803$		−	17.4615i		−	0.616202i
$804$	−14.7200			−0.519134
$805$	1.36689	+	1.76964i	0.0481765	+	0.0623715i
$806$	19.3350			0.681047
$807$			35.7485i			1.25841i
$808$			8.81159i			0.309991i
$809$	45.1721			1.58817			0.794083	−	0.607810i	$-0.207952\pi$
$809$	45.1721			1.58817			0.794083	+	0.607810i	$0.207952\pi$
$810$	−6.18071	+	4.77406i	−0.217168	+	0.167743i
$811$	46.7969			1.64326			0.821630	−	0.570021i	$-0.193065\pi$
$811$	46.7969			1.64326			0.821630	+	0.570021i	$0.193065\pi$
$812$			2.16866i			0.0761050i
$813$			20.9695i			0.735433i
$814$	2.34929			0.0823424
$815$	−0.363856	+	0.281047i	−0.0127453	+	0.00984465i
$816$	3.63093			0.127108
$817$		−	41.8353i		−	1.46363i
$818$		−	11.1313i		−	0.389196i
$819$	−15.8434			−0.553614
$820$	−1.36236	−	1.76378i	−0.0475758	−	0.0615938i
$821$	−37.9685			−1.32511			−0.662555	−	0.749013i	$-0.730528\pi$
$821$	−37.9685			−1.32511			−0.662555	+	0.749013i	$0.730528\pi$
$822$			11.9572i			0.417057i
$823$			48.8194i			1.70174i	0.525378	+	0.850869i	$0.323924\pi$
$823$			48.8194i			1.70174i	−0.525378	+	0.850869i	$0.676076\pi$
$824$	−42.3195			−1.47427
$825$	−20.1791	−	5.26908i	−0.702545	−	0.183446i
$826$	−1.35743			−0.0472311
$827$			30.1297i			1.04771i	0.851807	+	0.523855i	$0.175507\pi$
$827$			30.1297i			1.04771i	−0.851807	+	0.523855i	$0.824493\pi$
$828$			4.02409i			0.139847i
$829$	−13.5220			−0.469638			−0.234819	−	0.972039i	$-0.575450\pi$
$829$	−13.5220			−0.469638			−0.234819	+	0.972039i	$0.575450\pi$
$830$	−19.4948	−	25.2389i	−0.676675	−	0.876054i
$831$	−11.8732			−0.411877
$832$		−	24.8131i		−	0.860240i
$833$			0.663092i			0.0229748i
$834$	22.7187			0.786683
$835$	2.25942	−	1.74520i	0.0781904	−	0.0603953i
$836$	−7.61571			−0.263395
$837$			38.3082i			1.32413i
$838$		−	18.1074i		−	0.625508i
$839$	−34.4251			−1.18849			−0.594243	−	0.804285i	$-0.702548\pi$
$839$	−34.4251			−1.18849			−0.594243	+	0.804285i	$0.702548\pi$
$840$	15.6623	−	12.0977i	0.540400	−	0.417412i
$841$	−20.8632			−0.719422
$842$			7.37328i			0.254100i
$843$		−	38.3922i		−	1.32230i
$844$	−3.97341			−0.136771
$845$	−5.52262	−	7.14983i	−0.189984	−	0.245962i
$846$	42.8411			1.47291
$847$			8.90205i			0.305878i
$848$		−	14.3163i		−	0.491623i
$849$	19.7678			0.678428
$850$	0.932650	−	3.57179i	0.0319896	−	0.122511i
$851$	−1.45671			−0.0499355
$852$			33.8521i			1.15975i
$853$		−	31.0886i		−	1.06445i	−0.846602	−	0.532226i	$-0.821356\pi$
$853$		−	31.0886i		−	1.06445i	0.846602	−	0.532226i	$-0.178644\pi$
$854$	−1.44365			−0.0494006
$855$	50.0359	+	64.7787i	1.71119	+	2.21538i
$856$	22.0171			0.752528
$857$			23.5785i			0.805427i	0.915326	+	0.402714i	$0.131933\pi$
$857$			23.5785i			0.805427i	−0.915326	+	0.402714i	$0.868067\pi$
$858$			13.9016i			0.474593i
$859$	31.9744			1.09095			0.545476	−	0.838126i	$-0.316349\pi$
$859$	31.9744			1.09095			0.545476	+	0.838126i	$0.316349\pi$
$860$	−8.13853	+	6.28631i	−0.277522	+	0.214361i
$861$	−3.77529			−0.128661
$862$		−	17.9963i		−	0.612957i
$863$			27.5084i			0.936397i	0.883623	+	0.468198i	$0.155097\pi$
$863$			27.5084i			0.936397i	−0.883623	+	0.468198i	$0.844903\pi$
$864$	26.6085			0.905239
$865$	−31.9799	+	24.7017i	−1.08735	+	0.839882i
$866$	−2.60792			−0.0886208
$867$		−	47.6897i		−	1.61963i
$868$		−	4.41061i		−	0.149706i
$869$	−17.5267			−0.594554
$870$	−12.5020	−	16.1856i	−0.423857	−	0.548744i
$871$	20.1249			0.681906
$872$			32.2732i			1.09291i
$873$		−	11.5314i		−	0.390278i
$874$	−7.70036			−0.260468
$875$	−4.37728	−	10.2878i	−0.147979	−	0.347792i
$876$	26.3939			0.891768
$877$		−	36.4417i		−	1.23055i	−0.788314	−	0.615274i	$-0.789045\pi$
$877$		−	36.4417i		−	1.23055i	0.788314	−	0.615274i	$-0.210955\pi$
$878$		−	32.1204i		−	1.08401i
$879$	89.7642			3.02767
$880$	−3.76460	−	4.87382i	−0.126905	−	0.164297i
$881$	−39.9049			−1.34443			−0.672216	−	0.740355i	$-0.734657\pi$
$881$	−39.9049			−1.34443			−0.672216	+	0.740355i	$0.734657\pi$
$882$		−	5.89340i		−	0.198441i
$883$		−	52.5102i		−	1.76711i	−0.468327	−	0.883555i	$-0.655143\pi$
$883$		−	52.5102i		−	1.76711i	0.468327	−	0.883555i	$-0.344857\pi$
$884$	1.50899			0.0507529
$885$	−6.21289	+	4.79892i	−0.208844	+	0.161314i
$886$	30.6384			1.02932
$887$			2.24783i			0.0754748i	0.999288	+	0.0377374i	$0.0120150\pi$
$887$			2.24783i			0.0754748i	−0.999288	+	0.0377374i	$0.987985\pi$
$888$			12.8927i			0.432651i
$889$	17.5841			0.589750
$890$	−34.4787	+	26.6318i	−1.15573	+	0.892700i
$891$	−4.54347			−0.152212
$892$		−	3.54688i		−	0.118758i
$893$		−	50.2738i		−	1.68235i
$894$	4.73554			0.158380
$895$	−11.3117	−	14.6447i	−0.378110	−	0.489518i
$896$	1.17074			0.0391118
$897$		−	8.61991i		−	0.287811i
$898$		−	1.02418i		−	0.0341774i
$899$	−16.5485			−0.551923
$900$	5.08333	−	19.4677i	0.169444	−	0.648923i
$901$	4.99247			0.166323
$902$			2.11425i			0.0703968i
$903$			17.4202i			0.579707i
$904$	−42.1384			−1.40150
$905$	29.4842	+	38.1715i	0.980087	+	1.26886i
$906$	22.7729			0.756578
$907$			19.1127i			0.634625i	0.948321	+	0.317313i	$0.102780\pi$
$907$			19.1127i			0.634625i	−0.948321	+	0.317313i	$0.897220\pi$
$908$		−	19.0758i		−	0.633052i
$909$	15.1754			0.503337
$910$	−5.89787	+	4.55559i	−0.195513	+	0.151016i
$911$	40.7484			1.35006			0.675028	−	0.737792i	$-0.264131\pi$
$911$	40.7484			1.35006			0.675028	+	0.737792i	$0.264131\pi$
$912$			37.8696i			1.25399i
$913$		−	18.5532i		−	0.614022i
$914$	−1.12331			−0.0371558
$915$	−6.60749	+	5.10371i	−0.218437	+	0.168723i
$916$	13.8982			0.459209
$917$			2.10117i			0.0693868i
$918$		−	4.87525i		−	0.160907i
$919$	−38.7070			−1.27683			−0.638414	−	0.769693i	$-0.720409\pi$
$919$	−38.7070			−1.27683			−0.638414	+	0.769693i	$0.720409\pi$
$920$	4.20096	+	5.43875i	0.138502	+	0.179310i
$921$	87.2819			2.87604
$922$		−	17.2546i		−	0.568249i
$923$		−	46.2819i		−	1.52339i
$924$	3.17117			0.104324
$925$	7.04728	+	1.84016i	0.231713	+	0.0605039i
$926$	46.3958			1.52466
$927$			72.8831i			2.39380i
$928$			11.4944i			0.377322i
$929$	−49.9855			−1.63997			−0.819986	−	0.572384i	$-0.806019\pi$
$929$	−49.9855			−1.63997			−0.819986	+	0.572384i	$0.806019\pi$
$930$	25.4265	+	32.9183i	0.833768	+	1.07943i
$931$	−6.91587			−0.226658
$932$		−	14.2519i		−	0.466837i
$933$			33.8998i			1.10983i
$934$	5.06975			0.165887
$935$	1.69964	−	1.31282i	0.0555840	−	0.0429338i
$936$	−48.6927			−1.59157
$937$		−	12.5826i		−	0.411056i	−0.978651	−	0.205528i	$-0.934109\pi$
$937$		−	12.5826i		−	0.411056i	0.978651	−	0.205528i	$-0.0658911\pi$
$938$			7.48601i			0.244427i
$939$	70.5230			2.30143
$940$	−9.78013	+	7.55430i	−0.318993	+	0.246394i
$941$	0.761460			0.0248229			0.0124114	−	0.999923i	$-0.496049\pi$
$941$	0.761460			0.0248229			0.0124114	+	0.999923i	$0.496049\pi$
$942$			59.6835i			1.94459i
$943$		−	1.31097i		−	0.0426912i
$944$	−2.31815			−0.0754495
$945$	−9.02594	−	11.6854i	−0.293614	−	0.380126i
$946$	9.75571			0.317185
$947$		−	50.8324i		−	1.65183i	−0.563795	−	0.825915i	$-0.690659\pi$
$947$		−	50.8324i		−	1.65183i	0.563795	−	0.825915i	$-0.309341\pi$
$948$		−	26.4926i		−	0.860439i
$949$	−36.0853			−1.17138
$950$	37.2527	+	9.72728i	1.20864	+	0.315595i
$951$	−11.7419			−0.380757
$952$			2.03793i			0.0660496i
$953$			10.3471i			0.335174i	0.985857	+	0.167587i	$0.0535975\pi$
$953$			10.3471i			0.335174i	−0.985857	+	0.167587i	$0.946403\pi$
$954$	−44.3719			−1.43659
$955$	−17.3032	−	22.4015i	−0.559918	−	0.724895i
$956$	13.8801			0.448913
$957$		−	11.8981i		−	0.384612i
$958$			11.3290i			0.366023i
$959$	−3.72916			−0.120421
$960$	42.2449	−	32.6305i	1.36345	−	1.05314i
$961$	2.65627			0.0856861
$962$		−	4.85496i		−	0.156530i
$963$		−	37.9181i		−	1.22189i
$964$	14.0376			0.452121
$965$	−24.8799	+	19.2176i	−0.800914	+	0.618636i
$966$	3.20642			0.103165
$967$			15.7145i			0.505345i	0.967552	+	0.252673i	$0.0813096\pi$
$967$			15.7145i			0.505345i	−0.967552	+	0.252673i	$0.918690\pi$
$968$			27.3593i			0.879361i
$969$	−13.2061			−0.424243
$970$	−3.31572	−	4.29267i	−0.106461	−	0.137829i
$971$	−21.1348			−0.678248			−0.339124	−	0.940742i	$-0.610131\pi$
$971$	−21.1348			−0.678248			−0.339124	+	0.940742i	$0.610131\pi$
$972$			8.19303i			0.262792i
$973$			7.08538i			0.227147i
$974$	34.7046			1.11201
$975$	−10.8889	+	41.7014i	−0.348724	+	1.33551i
$976$	−2.46538			−0.0789150
$977$			42.8162i			1.36981i	0.728632	+	0.684906i	$0.240157\pi$
$977$			42.8162i			1.36981i	−0.728632	+	0.684906i	$0.759843\pi$
$978$			0.659273i			0.0210812i
$979$	−25.3455			−0.810046
$980$	1.03920	+	1.34539i	0.0331960	+	0.0429770i
$981$	55.5813			1.77457
$982$		−	14.8145i		−	0.472749i
$983$		−	17.9746i		−	0.573300i	−0.958035	−	0.286650i	$-0.907458\pi$
$983$		−	17.9746i		−	0.573300i	0.958035	−	0.286650i	$-0.0925417\pi$
$984$	−11.6029			−0.369886
$985$	7.36687	−	5.69027i	0.234728	−	0.181307i
$986$	2.10603			0.0670695
$987$			20.9339i			0.666335i
$988$			15.7384i			0.500704i
$989$	−6.04918			−0.192353
$990$	−15.1059	+	11.6680i	−0.480098	+	0.370834i
$991$	−23.0706			−0.732862			−0.366431	−	0.930445i	$-0.619420\pi$
$991$	−23.0706			−0.732862			−0.366431	+	0.930445i	$0.619420\pi$
$992$		−	23.3773i		−	0.742230i
$993$		−	13.5136i		−	0.428842i
$994$	17.2158			0.546053
$995$	−36.5296	−	47.2928i	−1.15806	−	1.49928i
$996$	28.0442			0.888614
$997$			33.9230i			1.07435i	0.843470	+	0.537176i	$0.180509\pi$
$997$			33.9230i			1.07435i	−0.843470	+	0.537176i	$0.819491\pi$
$998$		−	43.8309i		−	1.38744i
$999$	9.61907			0.304334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.c.b.484.9	✓	24
5.2	odd	4		4025.2.a.x.1.9		12
5.3	odd	4		4025.2.a.y.1.4		12
5.4	even	2	inner	805.2.c.b.484.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.9	✓	24	1.1	even	1	trivial
805.2.c.b.484.16	yes	24	5.4	even	2	inner
4025.2.a.x.1.9		12	5.2	odd	4
4025.2.a.y.1.4		12	5.3	odd	4

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.11343i q^{2} -2.87976i q^{3} +0.760266 q^{4} +(-1.36689 - 1.76964i) q^{5} -3.20642 q^{6} -1.00000i q^{7} -3.07337i q^{8} -5.29300 q^{9} +O(q^{10})\)	\(q-1.11343i q^{2} -2.87976i q^{3} +0.760266 q^{4} +(-1.36689 - 1.76964i) q^{5} -3.20642 q^{6} -1.00000i q^{7} -3.07337i q^{8} -5.29300 q^{9} +(-1.97037 + 1.52194i) q^{10} -1.44843 q^{11} -2.18938i q^{12} +2.99328i q^{13} -1.11343 q^{14} +(-5.09612 + 3.93631i) q^{15} -1.90146 q^{16} -0.663092i q^{17} +5.89340i q^{18} +6.91587 q^{19} +(-1.03920 - 1.34539i) q^{20} -2.87976 q^{21} +1.61273i q^{22} -1.00000i q^{23} -8.85056 q^{24} +(-1.26323 + 4.83780i) q^{25} +3.33282 q^{26} +6.60327i q^{27} -0.760266i q^{28} -2.85250 q^{29} +(4.38282 + 5.67419i) q^{30} +5.80140 q^{31} -4.02959i q^{32} +4.17113i q^{33} -0.738309 q^{34} +(-1.76964 + 1.36689i) q^{35} -4.02409 q^{36} -1.45671i q^{37} -7.70036i q^{38} +8.61991 q^{39} +(-5.43875 + 4.20096i) q^{40} +1.31097 q^{41} +3.20642i q^{42} -6.04918i q^{43} -1.10119 q^{44} +(7.23494 + 9.36668i) q^{45} -1.11343 q^{46} -7.26934i q^{47} +5.47575i q^{48} -1.00000 q^{49} +(5.38656 + 1.40652i) q^{50} -1.90954 q^{51} +2.27569i q^{52} +7.52908i q^{53} +7.35230 q^{54} +(1.97985 + 2.56320i) q^{55} -3.07337 q^{56} -19.9160i q^{57} +3.17607i q^{58} +1.21914 q^{59} +(-3.87441 + 2.99264i) q^{60} +1.29657 q^{61} -6.45948i q^{62} +5.29300i q^{63} -8.28961 q^{64} +(5.29702 - 4.09148i) q^{65} +4.64428 q^{66} -6.72336i q^{67} -0.504126i q^{68} -2.87976 q^{69} +(1.52194 + 1.97037i) q^{70} -15.4619 q^{71} +16.2673i q^{72} +12.0554i q^{73} -1.62195 q^{74} +(13.9317 + 3.63778i) q^{75} +5.25790 q^{76} +1.44843i q^{77} -9.59770i q^{78} +12.1005 q^{79} +(2.59909 + 3.36490i) q^{80} +3.13682 q^{81} -1.45968i q^{82} +12.8092i q^{83} -2.18938 q^{84} +(-1.17343 + 0.906374i) q^{85} -6.73536 q^{86} +8.21450i q^{87} +4.45157i q^{88} +17.4986 q^{89} +(10.4292 - 8.05563i) q^{90} +2.99328 q^{91} -0.760266i q^{92} -16.7066i q^{93} -8.09393 q^{94} +(-9.45323 - 12.2386i) q^{95} -11.6042 q^{96} +2.17861i q^{97} +1.11343i q^{98} +7.66654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9}+O(q^{10}) \) 24 * q - 16 * q^4 - 2 * q^5 - 12 * q^6 - 16 * q^9	\( 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9} - 4 q^{10} - 16 q^{11} + 4 q^{14} - 2 q^{15} - 8 q^{16} + 52 q^{19} + 2 q^{20} + 24 q^{24} - 8 q^{25} - 44 q^{26} + 24 q^{29} + 8 q^{30} - 100 q^{31} + 56 q^{34} - 2 q^{35} - 36 q^{36} + 52 q^{39} + 10 q^{40} - 8 q^{41} + 20 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{49} + 28 q^{50} - 64 q^{51} + 20 q^{54} + 28 q^{55} - 12 q^{56} + 36 q^{59} + 42 q^{60} + 16 q^{61} - 24 q^{64} + 30 q^{65} - 4 q^{66} + 12 q^{70} - 48 q^{71} - 72 q^{74} - 16 q^{75} - 112 q^{76} + 88 q^{79} + 8 q^{80} - 32 q^{81} - 24 q^{84} - 12 q^{85} - 64 q^{86} + 20 q^{89} + 108 q^{90} - 4 q^{91} - 36 q^{94} + 48 q^{95} - 76 q^{96} + 112 q^{99}+O(q^{100}) \) 24 * q - 16 * q^4 - 2 * q^5 - 12 * q^6 - 16 * q^9 - 4 * q^10 - 16 * q^11 + 4 * q^14 - 2 * q^15 - 8 * q^16 + 52 * q^19 + 2 * q^20 + 24 * q^24 - 8 * q^25 - 44 * q^26 + 24 * q^29 + 8 * q^30 - 100 * q^31 + 56 * q^34 - 2 * q^35 - 36 * q^36 + 52 * q^39 + 10 * q^40 - 8 * q^41 + 20 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^49 + 28 * q^50 - 64 * q^51 + 20 * q^54 + 28 * q^55 - 12 * q^56 + 36 * q^59 + 42 * q^60 + 16 * q^61 - 24 * q^64 + 30 * q^65 - 4 * q^66 + 12 * q^70 - 48 * q^71 - 72 * q^74 - 16 * q^75 - 112 * q^76 + 88 * q^79 + 8 * q^80 - 32 * q^81 - 24 * q^84 - 12 * q^85 - 64 * q^86 + 20 * q^89 + 108 * q^90 - 4 * q^91 - 36 * q^94 + 48 * q^95 - 76 * q^96 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more