LMFDB - Embedded newform 1045.2.b.d.419.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.11
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.104144i q^{2} +0.696995i q^{3} +1.98915 q^{4} +(2.09312 - 0.786662i) q^{5} +0.0725876 q^{6} +3.21657i q^{7} -0.415445i q^{8} +2.51420 q^{9} +O(q^{10})$	\(q-0.104144i q^{2} +0.696995i q^{3} +1.98915 q^{4} +(2.09312 - 0.786662i) q^{5} +0.0725876 q^{6} +3.21657i q^{7} -0.415445i q^{8} +2.51420 q^{9} +(-0.0819259 - 0.217986i) q^{10} -1.00000 q^{11} +1.38643i q^{12} -4.65405i q^{13} +0.334986 q^{14} +(0.548300 + 1.45890i) q^{15} +3.93504 q^{16} -0.00602394i q^{17} -0.261838i q^{18} +1.00000 q^{19} +(4.16354 - 1.56479i) q^{20} -2.24194 q^{21} +0.104144i q^{22} +1.65858i q^{23} +0.289563 q^{24} +(3.76233 - 3.29316i) q^{25} -0.484690 q^{26} +3.84337i q^{27} +6.39826i q^{28} -3.49988 q^{29} +(0.151935 - 0.0571020i) q^{30} -3.34225 q^{31} -1.24070i q^{32} -0.696995i q^{33} -0.000627356 q^{34} +(2.53036 + 6.73268i) q^{35} +5.00113 q^{36} +6.13742i q^{37} -0.104144i q^{38} +3.24385 q^{39} +(-0.326815 - 0.869578i) q^{40} -9.38032 q^{41} +0.233483i q^{42} -8.61740i q^{43} -1.98915 q^{44} +(5.26252 - 1.97782i) q^{45} +0.172731 q^{46} +0.893231i q^{47} +2.74270i q^{48} -3.34635 q^{49} +(-0.342962 - 0.391822i) q^{50} +0.00419866 q^{51} -9.25763i q^{52} -1.78431i q^{53} +0.400263 q^{54} +(-2.09312 + 0.786662i) q^{55} +1.33631 q^{56} +0.696995i q^{57} +0.364491i q^{58} -2.57022 q^{59} +(1.09065 + 2.90197i) q^{60} -3.68861 q^{61} +0.348074i q^{62} +8.08710i q^{63} +7.74087 q^{64} +(-3.66117 - 9.74151i) q^{65} -0.0725876 q^{66} +5.98644i q^{67} -0.0119826i q^{68} -1.15602 q^{69} +(0.701167 - 0.263521i) q^{70} +0.852858 q^{71} -1.04451i q^{72} -4.72786i q^{73} +0.639174 q^{74} +(2.29532 + 2.62232i) q^{75} +1.98915 q^{76} -3.21657i q^{77} -0.337827i q^{78} +4.94098 q^{79} +(8.23653 - 3.09555i) q^{80} +4.86379 q^{81} +0.976902i q^{82} +15.0339i q^{83} -4.45956 q^{84} +(-0.00473881 - 0.0126089i) q^{85} -0.897448 q^{86} -2.43940i q^{87} +0.415445i q^{88} -5.11449 q^{89} +(-0.205978 - 0.548059i) q^{90} +14.9701 q^{91} +3.29917i q^{92} -2.32953i q^{93} +0.0930244 q^{94} +(2.09312 - 0.786662i) q^{95} +0.864762 q^{96} -16.5462i q^{97} +0.348501i q^{98} -2.51420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	0.104144i		−	0.0736407i	−0.999322	−	0.0368204i	$-0.988277\pi$
$2$		−	0.104144i		−	0.0736407i	0.999322	−	0.0368204i	$-0.0117229\pi$
$3$			0.696995i			0.402410i	0.979549	+	0.201205i	$0.0644858\pi$
$3$			0.696995i			0.402410i	−0.979549	+	0.201205i	$0.935514\pi$
$4$	1.98915			0.994577
$5$	2.09312	−	0.786662i	0.936073	−	0.351806i
$5$	2.09312	−	0.786662i	0.936073	−	0.351806i
$6$	0.0725876			0.0296338
$7$			3.21657i			1.21575i	0.794033	+	0.607875i	$0.207978\pi$
$7$			3.21657i			1.21575i	−0.794033	+	0.607875i	$0.792022\pi$
$8$		−	0.415445i		−	0.146882i
$9$	2.51420			0.838066
$10$	−0.0819259	−	0.217986i	−0.0259072	−	0.0689331i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			1.38643i			0.400228i
$13$		−	4.65405i		−	1.29080i	−0.763844	−	0.645401i	$-0.776690\pi$
$13$		−	4.65405i		−	1.29080i	0.763844	−	0.645401i	$-0.223310\pi$
$14$	0.334986			0.0895287
$15$	0.548300	+	1.45890i	0.141570	+	0.376685i
$16$	3.93504			0.983761
$17$		−	0.00602394i		−	0.00146102i	−1.00000		0.000730510i	$-0.999767\pi$
$17$		−	0.00602394i		−	0.00146102i	1.00000		0.000730510i	$-0.000232529\pi$
$18$		−	0.261838i		−	0.0617158i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	4.16354	−	1.56479i	0.930997	−	0.349898i
$21$	−2.24194			−0.489230
$22$			0.104144i			0.0222035i
$23$			1.65858i			0.345838i	0.984936	+	0.172919i	$0.0553198\pi$
$23$			1.65858i			0.345838i	−0.984936	+	0.172919i	$0.944680\pi$
$24$	0.289563			0.0591069
$25$	3.76233	−	3.29316i	0.752465	−	0.658632i
$26$	−0.484690			−0.0950556
$27$			3.84337i			0.739657i
$28$			6.39826i			1.20916i
$29$	−3.49988			−0.649912			−0.324956	−	0.945729i	$-0.605350\pi$
$29$	−3.49988			−0.649912			−0.324956	+	0.945729i	$0.605350\pi$
$30$	0.151935	−	0.0571020i	0.0277394	−	0.0104253i
$31$	−3.34225			−0.600285			−0.300143	−	0.953894i	$-0.597034\pi$
$31$	−3.34225			−0.600285			−0.300143	+	0.953894i	$0.597034\pi$
$32$		−	1.24070i		−	0.219327i
$33$		−	0.696995i		−	0.121331i
$34$	−0.000627356	0		−0.000107591	0
$35$	2.53036	+	6.73268i	0.427708	+	1.13803i
$36$	5.00113			0.833521
$37$			6.13742i			1.00899i	0.863416	+	0.504493i	$0.168320\pi$
$37$			6.13742i			1.00899i	−0.863416	+	0.504493i	$0.831680\pi$
$38$		−	0.104144i		−	0.0168943i
$39$	3.24385			0.519432
$40$	−0.326815	−	0.869578i	−0.0516740	−	0.137492i
$41$	−9.38032			−1.46496			−0.732480	−	0.680788i	$-0.761637\pi$
$41$	−9.38032			−1.46496			−0.732480	+	0.680788i	$0.761637\pi$
$42$			0.233483i			0.0360273i
$43$		−	8.61740i		−	1.31414i	−0.753829	−	0.657071i	$-0.771795\pi$
$43$		−	8.61740i		−	1.31414i	0.753829	−	0.657071i	$-0.228205\pi$
$44$	−1.98915			−0.299876
$45$	5.26252	−	1.97782i	0.784491	−	0.294837i
$46$	0.172731			0.0254677
$47$			0.893231i			0.130291i	0.997876	+	0.0651456i	$0.0207512\pi$
$47$			0.893231i			0.130291i	−0.997876	+	0.0651456i	$0.979249\pi$
$48$			2.74270i			0.395875i
$49$	−3.34635			−0.478049
$50$	−0.342962	−	0.391822i	−0.0485021	−	0.0554121i
$51$	0.00419866			0.000587930
$52$		−	9.25763i		−	1.28380i
$53$		−	1.78431i		−	0.245093i	−0.992463	−	0.122547i	$-0.960894\pi$
$53$		−	1.78431i		−	0.245093i	0.992463	−	0.122547i	$-0.0391061\pi$
$54$	0.400263			0.0544688
$55$	−2.09312	+	0.786662i	−0.282237	+	0.106074i
$56$	1.33631			0.178572
$57$			0.696995i			0.0923192i
$58$			0.364491i			0.0478600i
$59$	−2.57022			−0.334614			−0.167307	−	0.985905i	$-0.553507\pi$
$59$	−2.57022			−0.334614			−0.167307	+	0.985905i	$0.553507\pi$
$60$	1.09065	+	2.90197i	0.140803	+	0.374643i
$61$	−3.68861			−0.472278			−0.236139	−	0.971719i	$-0.575882\pi$
$61$	−3.68861			−0.472278			−0.236139	+	0.971719i	$0.575882\pi$
$62$			0.348074i			0.0442054i
$63$			8.08710i			1.01888i
$64$	7.74087			0.967609
$65$	−3.66117	−	9.74151i	−0.454112	−	1.20829i
$66$	−0.0725876			−0.00893492
$67$			5.98644i			0.731361i	0.930741	+	0.365680i	$0.119164\pi$
$67$			5.98644i			0.731361i	−0.930741	+	0.365680i	$0.880836\pi$
$68$		−	0.0119826i		−	0.00145310i
$69$	−1.15602			−0.139169
$70$	0.701167	−	0.263521i	0.0838054	−	0.0314968i
$71$	0.852858			0.101216			0.0506078	−	0.998719i	$-0.483884\pi$
$71$	0.852858			0.101216			0.0506078	+	0.998719i	$0.483884\pi$
$72$		−	1.04451i		−	0.123097i
$73$		−	4.72786i		−	0.553354i	−0.960963	−	0.276677i	$-0.910767\pi$
$73$		−	4.72786i		−	0.553354i	0.960963	−	0.276677i	$-0.0892331\pi$
$74$	0.639174			0.0743024
$75$	2.29532	+	2.62232i	0.265040	+	0.302800i
$76$	1.98915			0.228172
$77$		−	3.21657i		−	0.366563i
$78$		−	0.337827i		−	0.0382513i
$79$	4.94098			0.555903			0.277952	−	0.960595i	$-0.410344\pi$
$79$	4.94098			0.555903			0.277952	+	0.960595i	$0.410344\pi$
$80$	8.23653	−	3.09555i	0.920872	−	0.346093i
$81$	4.86379			0.540421
$82$			0.976902i			0.107881i
$83$			15.0339i			1.65019i	0.564997	+	0.825093i	$0.308877\pi$
$83$			15.0339i			1.65019i	−0.564997	+	0.825093i	$0.691123\pi$
$84$	−4.45956			−0.486577
$85$	−0.00473881	−	0.0126089i	−0.000513996	−	0.00136762i
$86$	−0.897448			−0.0967743
$87$		−	2.43940i		−	0.261531i
$88$			0.415445i			0.0442866i
$89$	−5.11449			−0.542135			−0.271067	−	0.962560i	$-0.587377\pi$
$89$	−5.11449			−0.542135			−0.271067	+	0.962560i	$0.587377\pi$
$90$	−0.205978	−	0.548059i	−0.0217120	−	0.0577705i
$91$	14.9701			1.56929
$92$			3.29917i			0.343962i
$93$		−	2.32953i		−	0.241561i
$94$	0.0930244			0.00959474
$95$	2.09312	−	0.786662i	0.214750	−	0.0807098i
$96$	0.864762			0.0882594
$97$		−	16.5462i		−	1.68001i	−0.542578	−	0.840005i	$-0.682552\pi$
$97$		−	16.5462i		−	1.68001i	0.542578	−	0.840005i	$-0.317448\pi$
$98$			0.348501i			0.0352039i
$99$	−2.51420			−0.252686
$100$	7.48384	−	6.55060i	0.748384	−	0.655060i
$101$	5.62840			0.560047			0.280023	−	0.959993i	$-0.409658\pi$
$101$	5.62840			0.560047			0.280023	+	0.959993i	$0.409658\pi$
$102$		0	0.000437264i		0	4.32956e-5i
$103$			7.56366i			0.745270i	0.927978	+	0.372635i	$0.121546\pi$
$103$			7.56366i			0.745270i	−0.927978	+	0.372635i	$0.878454\pi$
$104$	−1.93350			−0.189596
$105$	−4.69265	+	1.76365i	−0.457955	+	0.172114i
$106$	−0.185824			−0.0180488
$107$			5.01113i			0.484444i	0.970221	+	0.242222i	$0.0778762\pi$
$107$			5.01113i			0.484444i	−0.970221	+	0.242222i	$0.922124\pi$
$108$			7.64505i			0.735645i
$109$	−3.73155			−0.357418			−0.178709	−	0.983902i	$-0.557192\pi$
$109$	−3.73155			−0.357418			−0.178709	+	0.983902i	$0.557192\pi$
$110$	0.0819259	+	0.217986i	0.00781133	+	0.0207841i
$111$	−4.27775			−0.406026
$112$			12.6574i			1.19601i
$113$			16.9702i			1.59642i	0.602380	+	0.798209i	$0.294219\pi$
$113$			16.9702i			1.59642i	−0.602380	+	0.798209i	$0.705781\pi$
$114$	0.0725876			0.00679846
$115$	1.30474	+	3.47161i	0.121668	+	0.323729i
$116$	−6.96181			−0.646388
$117$		−	11.7012i		−	1.08178i
$118$			0.267672i			0.0246412i
$119$	0.0193765			0.00177624
$120$	0.606091	−	0.227788i	0.0553283	−	0.0207941i
$121$	1.00000			0.0909091
$122$			0.384146i			0.0347789i
$123$		−	6.53804i		−	0.589515i
$124$	−6.64824			−0.597030
$125$	5.28440	−	9.85267i	0.472651	−	0.881250i
$126$	0.842221			0.0750310
$127$			0.870581i			0.0772516i	0.999254	+	0.0386258i	$0.0122980\pi$
$127$			0.870581i			0.0772516i	−0.999254	+	0.0386258i	$0.987702\pi$
$128$		−	3.28756i		−	0.290582i
$129$	6.00628			0.528824
$130$	−1.01452	+	0.381288i	−0.0889790	+	0.0334411i
$131$	−0.332706			−0.0290687			−0.0145343	−	0.999894i	$-0.504627\pi$
$131$	−0.332706			−0.0290687			−0.0145343	+	0.999894i	$0.504627\pi$
$132$		−	1.38643i		−	0.120673i
$133$			3.21657i			0.278912i
$134$	0.623450			0.0538579
$135$	3.02343	+	8.04464i	0.260216	+	0.692372i
$136$	−0.00250262			−0.000214598
$137$		−	13.0314i		−	1.11335i	−0.830732	−	0.556673i	$-0.812078\pi$
$137$		−	13.0314i		−	1.11335i	0.830732	−	0.556673i	$-0.187922\pi$
$138$			0.120392i			0.0102485i
$139$	−12.6827			−1.07573			−0.537867	−	0.843030i	$-0.680770\pi$
$139$	−12.6827			−1.07573			−0.537867	+	0.843030i	$0.680770\pi$
$140$	5.03327	+	13.3923i	0.425389	+	1.13186i
$141$	−0.622578			−0.0524305
$142$		−	0.0888197i		−	0.00745359i
$143$			4.65405i			0.389192i
$144$	9.89348			0.824456
$145$	−7.32569	+	2.75323i	−0.608365	+	0.228643i
$146$	−0.492376			−0.0407494
$147$		−	2.33239i		−	0.192372i
$148$			12.2083i			1.00351i
$149$	−17.2444			−1.41272			−0.706358	−	0.707855i	$-0.749663\pi$
$149$	−17.2444			−1.41272			−0.706358	+	0.707855i	$0.749663\pi$
$150$	0.273098	−	0.239043i	0.0222984	−	0.0195178i
$151$	22.5478			1.83491			0.917456	−	0.397836i	$-0.130239\pi$
$151$	22.5478			1.83491			0.917456	+	0.397836i	$0.130239\pi$
$152$		−	0.415445i		−	0.0336971i
$153$		−	0.0151454i		−	0.00122443i
$154$	−0.334986			−0.0269939
$155$	−6.99573	+	2.62922i	−0.561911	+	0.211184i
$156$	6.45252			0.516615
$157$			12.1662i			0.970972i	0.874244	+	0.485486i	$0.161357\pi$
$157$			12.1662i			0.970972i	−0.874244	+	0.485486i	$0.838643\pi$
$158$		−	0.514572i		−	0.0409371i
$159$	1.24365			0.0986280
$160$	−0.976012	−	2.59694i	−0.0771605	−	0.205306i
$161$	−5.33494			−0.420452
$162$		−	0.506533i		−	0.0397970i
$163$		−	21.8086i		−	1.70818i	−0.520125	−	0.854090i	$-0.674115\pi$
$163$		−	21.8086i		−	1.70818i	0.520125	−	0.854090i	$-0.325885\pi$
$164$	−18.6589			−1.45702
$165$	−0.548300	−	1.45890i	−0.0426851	−	0.113575i
$166$	1.56569			0.121521
$167$		−	15.5829i		−	1.20584i	−0.797802	−	0.602919i	$-0.794004\pi$
$167$		−	15.5829i		−	1.20584i	0.797802	−	0.602919i	$-0.205996\pi$
$168$			0.931402i			0.0718592i
$169$	−8.66022			−0.666170
$170$	−0.00131313		0.000493517i	−0.000100713		3.78510e-5i
$171$	2.51420			0.192266
$172$		−	17.1413i		−	1.30701i
$173$		−	10.4213i		−	0.792315i	−0.918183	−	0.396157i	$-0.870344\pi$
$173$		−	10.4213i		−	0.792315i	0.918183	−	0.396157i	$-0.129656\pi$
$174$	−0.254048			−0.0192594
$175$	10.5927	+	12.1018i	0.800732	+	0.914810i
$176$	−3.93504			−0.296615
$177$		−	1.79143i		−	0.134652i
$178$			0.532642i			0.0399232i
$179$	−20.5356			−1.53490			−0.767452	−	0.641107i	$-0.778476\pi$
$179$	−20.5356			−1.53490			−0.767452	+	0.641107i	$0.778476\pi$
$180$	10.4680	−	3.93420i	0.780237	−	0.293238i
$181$	0.0667973			0.00496500			0.00248250	−	0.999997i	$-0.499210\pi$
$181$	0.0667973			0.00496500			0.00248250	+	0.999997i	$0.499210\pi$
$182$		−	1.55904i		−	0.115564i
$183$		−	2.57094i		−	0.190050i
$184$	0.689049			0.0507974
$185$	4.82808	+	12.8464i	0.354967	+	0.944484i
$186$	−0.242606			−0.0177887
$187$			0.00602394i			0.000440514i
$188$			1.77677i			0.129585i
$189$	−12.3625			−0.899238
$190$	−0.0819259	−	0.217986i	−0.00594353	−	0.0158143i
$191$	−2.09641			−0.151691			−0.0758456	−	0.997120i	$-0.524166\pi$
$191$	−2.09641			−0.151691			−0.0758456	+	0.997120i	$0.524166\pi$
$192$			5.39535i			0.389376i
$193$		−	25.1960i		−	1.81365i	−0.421507	−	0.906825i	$-0.638499\pi$
$193$		−	25.1960i		−	1.81365i	0.421507	−	0.906825i	$-0.361501\pi$
$194$	−1.72318			−0.123717
$195$	6.78978	−	2.55182i	0.486226	−	0.182739i
$196$	−6.65640			−0.475457
$197$			5.70885i			0.406739i	0.979102	+	0.203369i	$0.0651892\pi$
$197$			5.70885i			0.406739i	−0.979102	+	0.203369i	$0.934811\pi$
$198$			0.261838i			0.0186080i
$199$	10.2003			0.723081			0.361541	−	0.932356i	$-0.382251\pi$
$199$	10.2003			0.723081			0.361541	+	0.932356i	$0.382251\pi$
$200$	−1.36813	−	1.56304i	−0.0967413	−	0.110524i
$201$	−4.17252			−0.294307
$202$		−	0.586162i		−	0.0412422i
$203$		−	11.2576i		−	0.790131i
$204$	0.00835178			0.000584741
$205$	−19.6342	+	7.37915i	−1.37131	+	0.515382i
$206$	0.787708			0.0548822
$207$			4.17000i			0.289835i
$208$		−	18.3139i		−	1.26984i
$209$	−1.00000			−0.0691714
$210$	0.183673	+	0.488710i	0.0126746	+	0.0337242i
$211$	1.03962			0.0715706			0.0357853	−	0.999360i	$-0.488607\pi$
$211$	1.03962			0.0715706			0.0357853	+	0.999360i	$0.488607\pi$
$212$		−	3.54926i		−	0.243764i
$213$			0.594437i			0.0407302i
$214$	0.521877			0.0356748
$215$	−6.77898	−	18.0373i	−0.462323	−	1.23013i
$216$	1.59671			0.108642
$217$		−	10.7506i		−	0.729797i
$218$			0.388618i			0.0263205i
$219$	3.29529			0.222675
$220$	−4.16354	+	1.56479i	−0.280706	+	0.105498i
$221$	−0.0280358			−0.00188589
$222$			0.445501i			0.0299001i
$223$		−	6.42634i		−	0.430339i	−0.976577	−	0.215170i	$-0.930970\pi$
$223$		−	6.42634i		−	0.430339i	0.976577	−	0.215170i	$-0.0690305\pi$
$224$	3.99080			0.266647
$225$	9.45923	−	8.27966i	0.630615	−	0.551977i
$226$	1.76734			0.117561
$227$			6.25815i			0.415368i	0.978196	+	0.207684i	$0.0665926\pi$
$227$			6.25815i			0.415368i	−0.978196	+	0.207684i	$0.933407\pi$
$228$			1.38643i			0.0918186i
$229$	−26.2671			−1.73578			−0.867890	−	0.496757i	$-0.834524\pi$
$229$	−26.2671			−1.73578			−0.867890	+	0.496757i	$0.834524\pi$
$230$	0.361546	−	0.135881i	0.0238397	−	0.00895970i
$231$	2.24194			0.147509
$232$			1.45401i			0.0954605i
$233$		−	2.94990i		−	0.193255i	−0.995321	−	0.0966273i	$-0.969195\pi$
$233$		−	2.94990i		−	0.193255i	0.995321	−	0.0966273i	$-0.0308055\pi$
$234$	−1.21861			−0.0796629
$235$	0.702671	+	1.86964i	0.0458372	+	0.121962i
$236$	−5.11257			−0.332800
$237$			3.44384i			0.223701i
$238$		−	0.00201794i		−	0.000130803i
$239$	−18.5942			−1.20276			−0.601378	−	0.798965i	$-0.705381\pi$
$239$	−18.5942			−1.20276			−0.601378	+	0.798965i	$0.705381\pi$
$240$	2.15758	+	5.74082i	0.139271	+	0.370568i
$241$	−8.68183			−0.559246			−0.279623	−	0.960110i	$-0.590209\pi$
$241$	−8.68183			−0.559246			−0.279623	+	0.960110i	$0.590209\pi$
$242$		−	0.104144i		−	0.00669461i
$243$			14.9201i			0.957127i
$244$	−7.33722			−0.469717
$245$	−7.00431	+	2.63244i	−0.447489	+	0.168181i
$246$	−0.680896			−0.0434123
$247$		−	4.65405i		−	0.296130i
$248$			1.38852i			0.0881711i
$249$	−10.4786			−0.664052
$250$	−1.02609	−	0.550337i	−0.0648958	−	0.0348064i
$251$	−27.7431			−1.75113			−0.875565	−	0.483100i	$-0.839511\pi$
$251$	−27.7431			−1.75113			−0.875565	+	0.483100i	$0.839511\pi$
$252$			16.0865i			1.01335i
$253$		−	1.65858i		−	0.104274i
$254$	0.0906655			0.00568886
$255$	0.00878831	−	0.00330293i	0.000550345	−	0.000206837i
$256$	15.1394			0.946210
$257$		−	17.7003i		−	1.10412i	−0.833805	−	0.552059i	$-0.813842\pi$
$257$		−	17.7003i		−	1.10412i	0.833805	−	0.552059i	$-0.186158\pi$
$258$		−	0.625517i		−	0.0389430i
$259$	−19.7415			−1.22667
$260$	−7.28263	−	19.3774i	−0.451649	−	1.20173i
$261$	−8.79940			−0.544669
$262$			0.0346492i			0.00214064i
$263$		−	22.4026i		−	1.38140i	−0.723139	−	0.690702i	$-0.757302\pi$
$263$		−	22.4026i		−	1.38140i	0.723139	−	0.690702i	$-0.242698\pi$
$264$	−0.289563			−0.0178214
$265$	−1.40365	−	3.73477i	−0.0862253	−	0.229425i
$266$	0.334986			0.0205393
$267$		−	3.56477i		−	0.218161i
$268$			11.9080i			0.727394i
$269$	−16.1724			−0.986046			−0.493023	−	0.870016i	$-0.664108\pi$
$269$	−16.1724			−0.986046			−0.493023	+	0.870016i	$0.664108\pi$
$270$	0.837799	−	0.314871i	0.0509868	−	0.0191625i
$271$	2.09973			0.127550			0.0637748	−	0.997964i	$-0.479686\pi$
$271$	2.09973			0.127550			0.0637748	+	0.997964i	$0.479686\pi$
$272$		−	0.0237045i		−	0.00143729i
$273$			10.4341i			0.631500i
$274$	−1.35714			−0.0819876
$275$	−3.76233	+	3.29316i	−0.226877	+	0.198585i
$276$	−2.29950			−0.138414
$277$			29.9790i			1.80127i	0.434580	+	0.900633i	$0.356897\pi$
$277$			29.9790i			1.80127i	−0.434580	+	0.900633i	$0.643103\pi$
$278$			1.32082i			0.0792178i
$279$	−8.40307			−0.503078
$280$	2.79706	−	1.05122i	0.167156	−	0.0628227i
$281$	−0.469805			−0.0280262			−0.0140131	−	0.999902i	$-0.504461\pi$
$281$	−0.469805			−0.0280262			−0.0140131	+	0.999902i	$0.504461\pi$
$282$			0.0648376i			0.00386102i
$283$			13.2122i			0.785386i	0.919670	+	0.392693i	$0.128457\pi$
$283$			13.2122i			0.785386i	−0.919670	+	0.392693i	$0.871543\pi$
$284$	1.69647			0.100667
$285$	0.548300	+	1.45890i	0.0324785	+	0.0864175i
$286$	0.484690			0.0286603
$287$		−	30.1725i		−	1.78103i
$288$		−	3.11937i		−	0.183810i
$289$	17.0000			0.999998
$290$	0.286731	+	0.762924i	0.0168374	+	0.0448005i
$291$	11.5326			0.676054
$292$		−	9.40443i		−	0.550353i
$293$		−	5.47146i		−	0.319646i	−0.987146	−	0.159823i	$-0.948908\pi$
$293$		−	5.47146i		−	0.319646i	0.987146	−	0.159823i	$-0.0510924\pi$
$294$	−0.242903			−0.0141664
$295$	−5.37979	+	2.02190i	−0.313223	+	0.117719i
$296$	2.54976			0.148202
$297$		−	3.84337i		−	0.223015i
$298$			1.79590i			0.104033i
$299$	7.71912			0.446408
$300$	4.56574	+	5.21620i	0.263603	+	0.301158i
$301$	27.7185			1.59767
$302$		−	2.34821i		−	0.135124i
$303$			3.92297i			0.225369i
$304$	3.93504			0.225690
$305$	−7.72072	+	2.90169i	−0.442087	+	0.166150i
$306$	−0.00157730			−9.01681e−5
$307$			30.8787i			1.76234i	0.472801	+	0.881169i	$0.343243\pi$
$307$			30.8787i			1.76234i	−0.472801	+	0.881169i	$0.656757\pi$
$308$		−	6.39826i		−	0.364575i
$309$	−5.27183			−0.299904
$310$	0.273817	+	0.728561i	0.0155517	+	0.0413795i
$311$	24.2528			1.37525			0.687625	−	0.726066i	$-0.258653\pi$
$311$	24.2528			1.37525			0.687625	+	0.726066i	$0.258653\pi$
$312$		−	1.34764i		−	0.0762953i
$313$			12.2922i			0.694796i	0.937718	+	0.347398i	$0.112935\pi$
$313$			12.2922i			0.694796i	−0.937718	+	0.347398i	$0.887065\pi$
$314$	1.26704			0.0715031
$315$	6.36182	+	16.9273i	0.358448	+	0.953745i
$316$	9.82837			0.552889
$317$		−	20.0634i		−	1.12687i	−0.826160	−	0.563436i	$-0.809479\pi$
$317$		−	20.0634i		−	1.12687i	0.826160	−	0.563436i	$-0.190521\pi$
$318$		−	0.129519i		−	0.00726304i
$319$	3.49988			0.195956
$320$	16.2026	−	6.08945i	0.905753	−	0.340411i
$321$	−3.49273			−0.194945
$322$			0.555601i			0.0309624i
$323$		−	0.00602394i		−	0.000335181i
$324$	9.67482			0.537490
$325$	−15.3265	−	17.5101i	−0.850164	−	0.971284i
$326$	−2.27123			−0.125792
$327$		−	2.60087i		−	0.143829i
$328$			3.89701i			0.215176i
$329$	−2.87314			−0.158402
$330$	−0.151935	+	0.0571020i	−0.00836374	+	0.00314336i
$331$	−28.3147			−1.55632			−0.778159	−	0.628067i	$-0.783846\pi$
$331$	−28.3147			−1.55632			−0.778159	+	0.628067i	$0.783846\pi$
$332$			29.9048i			1.64124i
$333$			15.4307i			0.845596i
$334$	−1.62286			−0.0887988
$335$	4.70931	+	12.5304i	0.257297	+	0.684607i
$336$	−8.82211			−0.481286
$337$			35.6067i			1.93962i	0.243863	+	0.969810i	$0.421585\pi$
$337$			35.6067i			1.93962i	−0.243863	+	0.969810i	$0.578415\pi$
$338$			0.901907i			0.0490573i
$339$	−11.8281			−0.642415
$340$	−0.00942622	−	0.0250810i	−0.000511209	−	0.00136021i
$341$	3.34225			0.180993
$342$		−	0.261838i		−	0.0141586i
$343$			11.7522i			0.634562i
$344$	−3.58006			−0.193024
$345$	−2.41969	+	0.909398i	−0.130272	+	0.0489604i
$346$	−1.08531			−0.0583466
$347$			8.36165i			0.448877i	0.974488	+	0.224438i	$0.0720548\pi$
$347$			8.36165i			0.448877i	−0.974488	+	0.224438i	$0.927945\pi$
$348$		−	4.85235i		−	0.260113i
$349$	26.3753			1.41184			0.705919	−	0.708293i	$-0.250534\pi$
$349$	26.3753			1.41184			0.705919	+	0.708293i	$0.250534\pi$
$350$	1.26033	−	1.10316i	0.0673672	−	0.0589665i
$351$	17.8872			0.954750
$352$			1.24070i			0.0661296i
$353$		−	13.3537i		−	0.710745i	−0.934725	−	0.355372i	$-0.884354\pi$
$353$		−	13.3537i		−	0.710745i	0.934725	−	0.355372i	$-0.115646\pi$
$354$	−0.186566			−0.00991589
$355$	1.78514	−	0.670911i	0.0947452	−	0.0356082i
$356$	−10.1735			−0.539195
$357$			0.0135053i			0.000714776i
$358$			2.13865i			0.113031i
$359$	−14.7872			−0.780439			−0.390220	−	0.920722i	$-0.627601\pi$
$359$	−14.7872			−0.780439			−0.390220	+	0.920722i	$0.627601\pi$
$360$	−0.821678	−	2.18629i	−0.0433062	−	0.115228i
$361$	1.00000			0.0526316
$362$		−	0.00695651i		−	0.000365626i
$363$			0.696995i			0.0365827i
$364$	29.7778			1.56078
$365$	−3.71923	−	9.89598i	−0.194673	−	0.517979i
$366$	−0.267748			−0.0139954
$367$			26.2183i			1.36858i	0.729209	+	0.684291i	$0.239888\pi$
$367$			26.2183i			1.36858i	−0.729209	+	0.684291i	$0.760112\pi$
$368$			6.52658i			0.340221i
$369$	−23.5840			−1.22773
$370$	1.33787	−	0.502814i	0.0695525	−	0.0261400i
$371$	5.73935			0.297972
$372$		−	4.63379i		−	0.240251i
$373$			1.30489i			0.0675648i	0.999429	+	0.0337824i	$0.0107553\pi$
$373$			1.30489i			0.0675648i	−0.999429	+	0.0337824i	$0.989245\pi$
$374$	0.000627356	0		3.24398e−5	0
$375$	6.86726	+	3.68320i	0.354624	+	0.190200i
$376$	0.371089			0.0191374
$377$			16.2887i			0.838908i
$378$			1.28747i			0.0662205i
$379$	10.0189			0.514634			0.257317	−	0.966327i	$-0.417162\pi$
$379$	10.0189			0.514634			0.257317	+	0.966327i	$0.417162\pi$
$380$	4.16354	−	1.56479i	0.213585	−	0.0802722i
$381$	−0.606791			−0.0310868
$382$			0.218328i			0.0111706i
$383$		−	5.44686i		−	0.278322i	−0.990270	−	0.139161i	$-0.955560\pi$
$383$		−	5.44686i		−	0.278322i	0.990270	−	0.139161i	$-0.0444405\pi$
$384$	2.29142			0.116933
$385$	−2.53036	−	6.73268i	−0.128959	−	0.343129i
$386$	−2.62401			−0.133559
$387$		−	21.6659i		−	1.10134i
$388$		−	32.9129i		−	1.67090i
$389$	7.59394			0.385028			0.192514	−	0.981294i	$-0.438336\pi$
$389$	7.59394			0.385028			0.192514	+	0.981294i	$0.438336\pi$
$390$	−0.265756	−	0.707113i	−0.0134571	−	0.0358061i
$391$	0.00999119			0.000505276
$392$			1.39022i			0.0702169i
$393$		−	0.231894i		−	0.0116975i
$394$	0.594541			0.0299525
$395$	10.3421	−	3.88688i	0.520366	−	0.195570i
$396$	−5.00113			−0.251316
$397$		−	6.27453i		−	0.314910i	−0.987526	−	0.157455i	$-0.949671\pi$
$397$		−	6.27453i		−	0.314910i	0.987526	−	0.157455i	$-0.0503289\pi$
$398$		−	1.06230i		−	0.0532482i
$399$	−2.24194			−0.112237
$400$	14.8049	−	12.9587i	0.740245	−	0.647936i
$401$	17.8048			0.889131			0.444565	−	0.895746i	$-0.353358\pi$
$401$	17.8048			0.889131			0.444565	+	0.895746i	$0.353358\pi$
$402$			0.434542i			0.0216730i
$403$			15.5550i			0.774849i
$404$	11.1958			0.557010
$405$	10.1805	−	3.82616i	0.505873	−	0.190123i
$406$	−1.17241			−0.0581858
$407$		−	6.13742i		−	0.304221i
$408$		−	0.00174431i		−	8.63564e-5i
$409$	−8.47192			−0.418909			−0.209455	−	0.977818i	$-0.567169\pi$
$409$	−8.47192			−0.418909			−0.209455	+	0.977818i	$0.567169\pi$
$410$	0.768492	+	2.04478i	0.0379531	+	0.100984i
$411$	9.08281			0.448022
$412$			15.0453i			0.741228i
$413$		−	8.26731i		−	0.406807i
$414$	0.434279			0.0213436
$415$	11.8266	+	31.4678i	0.580545	+	1.54469i
$416$	−5.77429			−0.283108
$417$		−	8.83978i		−	0.432886i
$418$			0.104144i			0.00509384i
$419$	−10.4558			−0.510799			−0.255399	−	0.966836i	$-0.582207\pi$
$419$	−10.4558			−0.510799			−0.255399	+	0.966836i	$0.582207\pi$
$420$	−9.33440	+	3.50816i	−0.455472	+	0.171181i
$421$	32.4814			1.58305			0.791523	−	0.611139i	$-0.209288\pi$
$421$	32.4814			1.58305			0.791523	+	0.611139i	$0.209288\pi$
$422$		−	0.108270i		−	0.00527051i
$423$			2.24576i			0.109193i
$424$	−0.741281			−0.0359998
$425$	−0.0198378	−	0.0226640i	−0.000962275	−	0.00109937i
$426$	0.0619069			0.00299940
$427$		−	11.8647i		−	0.574173i
$428$			9.96790i			0.481817i
$429$	−3.24385			−0.156615
$430$	−1.87847	+	0.705988i	−0.0905878	+	0.0340458i
$431$	−2.28726			−0.110174			−0.0550868	−	0.998482i	$-0.517544\pi$
$431$	−2.28726			−0.110174			−0.0550868	+	0.998482i	$0.517544\pi$
$432$			15.1238i			0.727645i
$433$		−	36.5224i		−	1.75515i	−0.479437	−	0.877576i	$-0.659159\pi$
$433$		−	36.5224i		−	1.75515i	0.479437	−	0.877576i	$-0.340841\pi$
$434$	−1.11961			−0.0537428
$435$	−1.91899	−	5.10597i	−0.0920083	−	0.244812i
$436$	−7.42264			−0.355480
$437$			1.65858i			0.0793406i
$438$		−	0.343184i		−	0.0163980i
$439$	23.0323			1.09927			0.549636	−	0.835404i	$-0.314767\pi$
$439$	23.0323			1.09927			0.549636	+	0.835404i	$0.314767\pi$
$440$	0.326815	+	0.869578i	0.0155803	+	0.0414555i
$441$	−8.41338			−0.400637
$442$			0.00291975i			0.000138878i
$443$		−	3.63563i		−	0.172734i	−0.996263	−	0.0863671i	$-0.972474\pi$
$443$		−	3.63563i		−	0.172734i	0.996263	−	0.0863671i	$-0.0275258\pi$
$444$	−8.50910			−0.403824
$445$	−10.7053	+	4.02337i	−0.507478	+	0.190726i
$446$	−0.669263			−0.0316905
$447$		−	12.0193i		−	0.568492i
$448$			24.8991i			1.17637i
$449$	−25.5726			−1.20685			−0.603423	−	0.797422i	$-0.706197\pi$
$449$	−25.5726			−1.20685			−0.603423	+	0.797422i	$0.706197\pi$
$450$	−0.862274	−	0.985119i	−0.0406480	−	0.0464390i
$451$	9.38032			0.441702
$452$			33.7563i			1.58776i
$453$			15.7157i			0.738388i
$454$	0.651747			0.0305880
$455$	31.3343	−	11.7764i	1.46897	−	0.552087i
$456$	0.289563			0.0135600
$457$			6.45150i			0.301789i	0.988550	+	0.150894i	$0.0482153\pi$
$457$			6.45150i			0.301789i	−0.988550	+	0.150894i	$0.951785\pi$
$458$			2.73555i			0.127824i
$459$	0.0231522			0.00108065
$460$	2.59533	+	6.90557i	0.121008	+	0.321974i
$461$	−23.1293			−1.07724			−0.538619	−	0.842550i	$-0.681054\pi$
$461$	−23.1293			−1.07724			−0.538619	+	0.842550i	$0.681054\pi$
$462$		−	0.233483i		−	0.0108626i
$463$		−	36.4434i		−	1.69367i	−0.531858	−	0.846834i	$-0.678506\pi$
$463$		−	36.4434i		−	1.69367i	0.531858	−	0.846834i	$-0.321494\pi$
$464$	−13.7722			−0.639358
$465$	−1.83255	−	4.87599i	−0.0849826	−	0.226119i
$466$	−0.307214			−0.0142314
$467$		−	36.0540i		−	1.66838i	−0.551476	−	0.834191i	$-0.685935\pi$
$467$		−	36.0540i		−	1.66838i	0.551476	−	0.834191i	$-0.314065\pi$
$468$		−	23.2755i		−	1.07591i
$469$	−19.2558			−0.889152
$470$	0.194712	−	0.0731788i	0.00898137	−	0.00337549i
$471$	−8.47981			−0.390729
$472$			1.06779i			0.0491488i
$473$			8.61740i			0.396228i
$474$	0.358654			0.0164735
$475$	3.76233	−	3.29316i	0.172627	−	0.151101i
$476$	0.0385428			0.00176660
$477$		−	4.48610i		−	0.205404i
$478$			1.93646i			0.0885718i
$479$	−17.2250			−0.787032			−0.393516	−	0.919318i	$-0.628741\pi$
$479$	−17.2250			−0.787032			−0.393516	+	0.919318i	$0.628741\pi$
$480$	1.81005	−	0.680276i	0.0826172	−	0.0310502i
$481$	28.5639			1.30240
$482$			0.904158i			0.0411832i
$483$		−	3.71843i		−	0.169194i
$484$	1.98915			0.0904161
$485$	−13.0163	−	34.6332i	−0.591038	−	1.57261i
$486$	1.55384			0.0704835
$487$		−	31.6437i		−	1.43391i	−0.697117	−	0.716957i	$-0.745534\pi$
$487$		−	31.6437i		−	1.43391i	0.697117	−	0.716957i	$-0.254466\pi$
$488$			1.53242i			0.0693692i
$489$	15.2005			0.687389
$490$	0.274152	+	0.729455i	0.0123849	+	0.0329534i
$491$	38.9066			1.75583			0.877916	−	0.478814i	$-0.158933\pi$
$491$	38.9066			1.75583			0.877916	+	0.478814i	$0.158933\pi$
$492$		−	13.0052i		−	0.586318i
$493$			0.0210831i			0.000949536i
$494$	−0.484690			−0.0218073
$495$	−5.26252	+	1.97782i	−0.236533	+	0.0888966i
$496$	−13.1519			−0.590537
$497$			2.74328i			0.123053i
$498$			1.09128i			0.0489013i
$499$	−16.4194			−0.735033			−0.367516	−	0.930017i	$-0.619792\pi$
$499$	−16.4194			−0.735033			−0.367516	+	0.930017i	$0.619792\pi$
$500$	10.5115	−	19.5985i	0.470088	−	0.876471i
$501$	10.8612			0.485242
$502$			2.88927i			0.128954i
$503$		−	4.73308i		−	0.211038i	−0.994417	−	0.105519i	$-0.966350\pi$
$503$		−	4.73308i		−	0.211038i	0.994417	−	0.105519i	$-0.0336503\pi$
$504$	3.35975			0.149655
$505$	11.7809	−	4.42765i	0.524245	−	0.197028i
$506$	−0.172731			−0.00767881
$507$		−	6.03613i		−	0.268074i
$508$			1.73172i			0.0768326i
$509$	32.8750			1.45716			0.728580	−	0.684961i	$-0.240181\pi$
$509$	32.8750			1.45716			0.728580	+	0.684961i	$0.240181\pi$
$510$	−0.000343979	0	0.000915247i	−1.52316e−5	0	4.05278e-5i
$511$	15.2075			0.672740
$512$		−	8.15180i		−	0.360262i
$513$			3.84337i			0.169689i
$514$	−1.84338			−0.0813080
$515$	5.95005	+	15.8317i	0.262190	+	0.697627i
$516$	11.9474			0.525956
$517$		−	0.893231i		−	0.0392843i
$518$			2.05595i			0.0903332i
$519$	7.26357			0.318835
$520$	−4.04706	+	1.52102i	−0.177475	+	0.0667009i
$521$	7.50334			0.328727			0.164364	−	0.986400i	$-0.447443\pi$
$521$	7.50334			0.328727			0.164364	+	0.986400i	$0.447443\pi$
$522$			0.916402i			0.0401098i
$523$		−	11.7845i		−	0.515300i	−0.966238	−	0.257650i	$-0.917052\pi$
$523$		−	11.7845i		−	0.515300i	0.966238	−	0.257650i	$-0.0829481\pi$
$524$	−0.661803			−0.0289110
$525$	−8.43489	+	7.38305i	−0.368129	+	0.322223i
$526$	−2.33309			−0.101728
$527$			0.0201335i			0.000877029i
$528$		−	2.74270i		−	0.119361i
$529$	20.2491			0.880396
$530$	−0.388953	+	0.146181i	−0.0168950	+	0.00634969i
$531$	−6.46204			−0.280429
$532$			6.39826i			0.277400i
$533$			43.6565i			1.89097i
$534$	−0.371249			−0.0160655
$535$	3.94206	+	10.4889i	0.170430	+	0.453475i
$536$	2.48704			0.107424
$537$		−	14.3132i		−	0.617661i
$538$			1.68425i			0.0726131i
$539$	3.34635			0.144137
$540$	6.01407	+	16.0020i	0.258805	+	0.688618i
$541$	18.8061			0.808535			0.404268	−	0.914641i	$-0.367526\pi$
$541$	18.8061			0.808535			0.404268	+	0.914641i	$0.367526\pi$
$542$		−	0.218674i		−	0.00939285i
$543$			0.0465574i			0.00199797i
$544$	−0.00747391			−0.000320441
$545$	−7.81060	+	2.93547i	−0.334569	+	0.125742i
$546$	1.08664			0.0465041
$547$			11.1690i			0.477550i	0.971075	+	0.238775i	$0.0767459\pi$
$547$			11.1690i			0.477550i	−0.971075	+	0.238775i	$0.923254\pi$
$548$		−	25.9214i		−	1.10731i
$549$	−9.27390			−0.395800
$550$	0.342962	+	0.391822i	0.0146239	+	0.0167074i
$551$	−3.49988			−0.149100
$552$			0.480264i			0.0204414i
$553$			15.8930i			0.675840i
$554$	3.12213			0.132647
$555$	−8.95386	+	3.36514i	−0.380070	+	0.142842i
$556$	−25.2279			−1.06990
$557$			26.3044i			1.11455i	0.830327	+	0.557276i	$0.188154\pi$
$557$			26.3044i			1.11455i	−0.830327	+	0.557276i	$0.811846\pi$
$558$			0.875127i			0.0370471i
$559$	−40.1058			−1.69630
$560$	9.95706	+	26.4934i	0.420763	+	1.11955i
$561$	−0.00419866			−0.000177267
$562$			0.0489273i			0.00206387i
$563$		−	27.3566i		−	1.15294i	−0.817117	−	0.576472i	$-0.804429\pi$
$563$		−	27.3566i		−	1.15294i	0.817117	−	0.576472i	$-0.195571\pi$
$564$	−1.23840			−0.0521462
$565$	13.3498	+	35.5206i	0.561630	+	1.49436i
$566$	1.37597			0.0578364
$567$			15.6447i			0.657017i
$568$		−	0.354316i		−	0.0148668i
$569$	17.7921			0.745882			0.372941	−	0.927855i	$-0.378349\pi$
$569$	17.7921			0.745882			0.372941	+	0.927855i	$0.378349\pi$
$570$	0.151935	−	0.0571020i	0.00636385	−	0.00239174i
$571$	25.9440			1.08572			0.542862	−	0.839822i	$-0.317341\pi$
$571$	25.9440			1.08572			0.542862	+	0.839822i	$0.317341\pi$
$572$			9.25763i			0.387081i
$573$		−	1.46119i		−	0.0610421i
$574$	−3.14228			−0.131156
$575$	5.46197	+	6.24011i	0.227780	+	0.260231i
$576$	19.4621			0.810920
$577$		−	13.7994i		−	0.574476i	−0.957859	−	0.287238i	$-0.907263\pi$
$577$		−	13.7994i		−	0.574476i	0.957859	−	0.287238i	$-0.0927370\pi$
$578$		−	1.77044i		−	0.0736406i
$579$	17.5615			0.729831
$580$	−14.5719	+	5.47659i	−0.605066	+	0.227403i
$581$	−48.3577			−2.00621
$582$		−	1.20105i		−	0.0497851i
$583$			1.78431i			0.0738984i
$584$	−1.96417			−0.0812777
$585$	−9.20490	−	24.4921i	−0.380576	−	1.01262i
$586$	−0.569818			−0.0235390
$587$			31.3230i			1.29284i	0.762982	+	0.646420i	$0.223734\pi$
$587$			31.3230i			1.29284i	−0.762982	+	0.646420i	$0.776266\pi$
$588$		−	4.63947i		−	0.191329i
$589$	−3.34225			−0.137715
$590$	0.210568	+	0.560271i	0.00866894	+	0.0230660i
$591$	−3.97904			−0.163676
$592$			24.1510i			0.992600i
$593$			33.8912i			1.39174i	0.718166	+	0.695872i	$0.244982\pi$
$593$			33.8912i			1.39174i	−0.718166	+	0.695872i	$0.755018\pi$
$594$	−0.400263			−0.0164230
$595$	0.0405573	−	0.0152427i	0.00166269	−	0.000624891i
$596$	−34.3018			−1.40506
$597$			7.10957i			0.290975i
$598$		−	0.803897i		−	0.0328738i
$599$	20.5165			0.838280			0.419140	−	0.907922i	$-0.362332\pi$
$599$	20.5165			0.838280			0.419140	+	0.907922i	$0.362332\pi$
$600$	1.08943	−	0.953578i	0.0444758	−	0.0389297i
$601$	23.2037			0.946501			0.473250	−	0.880928i	$-0.343081\pi$
$601$	23.2037			0.946501			0.473250	+	0.880928i	$0.343081\pi$
$602$		−	2.88671i		−	0.117653i
$603$			15.0511i			0.612928i
$604$	44.8510			1.82496
$605$	2.09312	−	0.786662i	0.0850975	−	0.0319824i
$606$	0.408552			0.0165963
$607$			2.28113i			0.0925881i	0.998928	+	0.0462941i	$0.0147411\pi$
$607$			2.28113i			0.0925881i	−0.998928	+	0.0462941i	$0.985259\pi$
$608$		−	1.24070i		−	0.0503170i
$609$	7.84652			0.317957
$610$	0.302193	+	0.804064i	0.0122354	+	0.0325556i
$611$	4.15715			0.168180
$612$		−	0.0301265i		−	0.00121779i
$613$		−	2.06670i		−	0.0834732i	−0.999129	−	0.0417366i	$-0.986711\pi$
$613$		−	2.06670i		−	0.0834732i	0.999129	−	0.0417366i	$-0.0132890\pi$
$614$	3.21582			0.129780
$615$	−5.14323	−	13.6849i	−0.207395	−	0.551829i
$616$	−1.33631			−0.0538415
$617$			39.7201i			1.59907i	0.600618	+	0.799536i	$0.294921\pi$
$617$			39.7201i			1.59907i	−0.600618	+	0.799536i	$0.705079\pi$
$618$			0.549028i			0.0220852i
$619$	−3.94724			−0.158653			−0.0793266	−	0.996849i	$-0.525277\pi$
$619$	−3.94724			−0.158653			−0.0793266	+	0.996849i	$0.525277\pi$
$620$	−13.9156	+	5.22992i	−0.558863	+	0.210039i
$621$	−6.37453			−0.255801
$622$		−	2.52578i		−	0.101274i
$623$		−	16.4511i		−	0.659101i
$624$	12.7647			0.510997
$625$	3.31018	−	24.7799i	0.132407	−	0.991195i
$626$	1.28016			0.0511653
$627$		−	0.696995i		−	0.0278353i
$628$			24.2005i			0.965707i
$629$	0.0369715			0.00147415
$630$	1.76287	−	0.662543i	0.0702345	−	0.0263964i
$631$	−12.3504			−0.491663			−0.245832	−	0.969313i	$-0.579061\pi$
$631$	−12.3504			−0.491663			−0.245832	+	0.969313i	$0.579061\pi$
$632$		−	2.05271i		−	0.0816523i
$633$			0.724612i			0.0288007i
$634$	−2.08947			−0.0829836
$635$	0.684853	+	1.82223i	0.0271776	+	0.0723131i
$636$	2.47382			0.0980932
$637$			15.5741i			0.617067i
$638$		−	0.364491i		−	0.0144303i
$639$	2.14425			0.0848253
$640$	−2.58620	−	6.88127i	−0.102229	−	0.272006i
$641$	44.1646			1.74440			0.872198	−	0.489153i	$-0.162694\pi$
$641$	44.1646			1.74440			0.872198	+	0.489153i	$0.162694\pi$
$642$			0.363746i			0.0143559i
$643$			7.27326i			0.286829i	0.989663	+	0.143415i	$0.0458082\pi$
$643$			7.27326i			0.286829i	−0.989663	+	0.143415i	$0.954192\pi$
$644$	−10.6120			−0.418172
$645$	12.5719	−	4.72492i	0.495018	−	0.186043i
$646$	−0.000627356	0		−2.46830e−5	0
$647$		−	11.7738i		−	0.462878i	−0.972849	−	0.231439i	$-0.925657\pi$
$647$		−	11.7738i		−	0.462878i	0.972849	−	0.231439i	$-0.0743433\pi$
$648$		−	2.02064i		−	0.0793781i
$649$	2.57022			0.100890
$650$	−1.82356	+	1.59616i	−0.0715260	+	0.0626067i
$651$	7.49310			0.293678
$652$		−	43.3806i		−	1.69892i
$653$			31.7958i			1.24427i	0.782911	+	0.622134i	$0.213734\pi$
$653$			31.7958i			1.24427i	−0.782911	+	0.622134i	$0.786266\pi$
$654$	−0.270865			−0.0105916
$655$	−0.696394	+	0.261727i	−0.0272104	+	0.0102265i
$656$	−36.9120			−1.44117
$657$		−	11.8868i		−	0.463747i
$658$			0.299220i			0.0116648i
$659$	23.9090			0.931361			0.465680	−	0.884953i	$-0.345810\pi$
$659$	23.9090			0.931361			0.465680	+	0.884953i	$0.345810\pi$
$660$	−1.09065	−	2.90197i	−0.0424536	−	0.112959i
$661$	−39.9343			−1.55327			−0.776633	−	0.629953i	$-0.783074\pi$
$661$	−39.9343			−1.55327			−0.776633	+	0.629953i	$0.783074\pi$
$662$			2.94880i			0.114608i
$663$		−	0.0195408i		−	0.000758901i
$664$	6.24577			0.242383
$665$	2.53036	+	6.73268i	0.0981230	+	0.261082i
$666$	1.60701			0.0622703
$667$		−	5.80484i		−	0.224764i
$668$		−	30.9967i		−	1.19930i
$669$	4.47913			0.173173
$670$	1.30496	−	0.490445i	0.0504149	−	0.0189475i
$671$	3.68861			0.142397
$672$			2.78157i			0.107301i
$673$			15.3378i			0.591228i	0.955308	+	0.295614i	$0.0955241\pi$
$673$			15.3378i			0.591228i	−0.955308	+	0.295614i	$0.904476\pi$
$674$	3.70821			0.142835
$675$	12.6568	+	14.4600i	0.487162	+	0.556566i
$676$	−17.2265			−0.662558
$677$		−	20.2183i		−	0.777054i	−0.921437	−	0.388527i	$-0.872984\pi$
$677$		−	20.2183i		−	0.777054i	0.921437	−	0.388527i	$-0.127016\pi$
$678$			1.23182i			0.0473079i
$679$	53.2220			2.04247
$680$	−0.00523829	+	0.00196872i	−0.000200879	+	7.54968e-5i
$681$	−4.36190			−0.167148
$682$		−	0.348074i		−	0.0133284i
$683$			9.75882i			0.373411i	0.982416	+	0.186705i	$0.0597810\pi$
$683$			9.75882i			0.373411i	−0.982416	+	0.186705i	$0.940219\pi$
$684$	5.00113			0.191223
$685$	−10.2513	−	27.2763i	−0.391682	−	1.04217i
$686$	1.22392			0.0467296
$687$		−	18.3080i		−	0.698495i
$688$		−	33.9098i		−	1.29280i
$689$	−8.30425			−0.316367
$690$	0.0947081	+	0.251996i	0.00360548	+	0.00959332i
$691$	−3.10119			−0.117975			−0.0589873	−	0.998259i	$-0.518787\pi$
$691$	−3.10119			−0.117975			−0.0589873	+	0.998259i	$0.518787\pi$
$692$		−	20.7295i		−	0.788018i
$693$		−	8.08710i		−	0.307204i
$694$	0.870813			0.0330556
$695$	−26.5465	+	9.97701i	−1.00696	+	0.378449i
$696$	−1.01344			−0.0384143
$697$			0.0565066i			0.00214034i
$698$		−	2.74682i		−	0.103969i
$699$	2.05607			0.0777676
$700$	21.0705	+	24.0723i	0.796390	+	0.909849i
$701$	1.49983			0.0566478			0.0283239	−	0.999599i	$-0.490983\pi$
$701$	1.49983			0.0566478			0.0283239	+	0.999599i	$0.490983\pi$
$702$		−	1.86284i		−	0.0703085i
$703$			6.13742i			0.231477i
$704$	−7.74087			−0.291745
$705$	−1.30313	+	0.489758i	−0.0490788	+	0.0184454i
$706$	−1.39070			−0.0523397
$707$			18.1042i			0.680877i
$708$		−	3.56343i		−	0.133922i
$709$	33.3647			1.25304			0.626518	−	0.779407i	$-0.284480\pi$
$709$	33.3647			1.25304			0.626518	+	0.779407i	$0.284480\pi$
$710$	−0.0698711	−	0.185911i	−0.00262222	−	0.00697710i
$711$	12.4226			0.465884
$712$			2.12479i			0.0796299i
$713$		−	5.54338i		−	0.207601i
$714$	0.00140649			5.26366e−5
$715$	3.66117	+	9.74151i	0.136920	+	0.364312i
$716$	−40.8485			−1.52658
$717$		−	12.9600i		−	0.484001i
$718$			1.53999i			0.0574721i
$719$	11.9782			0.446711			0.223355	−	0.974737i	$-0.428299\pi$
$719$	11.9782			0.446711			0.223355	+	0.974737i	$0.428299\pi$
$720$	20.7083	−	7.78282i	0.771751	−	0.290049i
$721$	−24.3291			−0.906062
$722$		−	0.104144i		−	0.00387583i
$723$		−	6.05119i		−	0.225046i
$724$	0.132870			0.00493808
$725$	−13.1677	+	11.5257i	−0.489036	+	0.428053i
$726$	0.0725876			0.00269398
$727$		−	4.56220i		−	0.169203i	−0.996415	−	0.0846014i	$-0.973038\pi$
$727$		−	4.56220i		−	0.169203i	0.996415	−	0.0846014i	$-0.0269617\pi$
$728$		−	6.21926i		−	0.230501i
$729$	4.19210			0.155263
$730$	−1.03060	+	0.387334i	−0.0381444	+	0.0143359i
$731$	−0.0519107			−0.00191999
$732$		−	5.11400i		−	0.189019i
$733$		−	22.2267i		−	0.820963i	−0.911869	−	0.410482i	$-0.865361\pi$
$733$		−	22.2267i		−	0.820963i	0.911869	−	0.410482i	$-0.134639\pi$
$734$	2.73047			0.100783
$735$	−1.83480	−	4.88197i	−0.0676776	−	0.180074i
$736$	2.05780			0.0758515
$737$		−	5.98644i		−	0.220513i
$738$			2.45612i			0.0904112i
$739$	−14.4390			−0.531149			−0.265574	−	0.964090i	$-0.585562\pi$
$739$	−14.4390			−0.531149			−0.265574	+	0.964090i	$0.585562\pi$
$740$	9.60379	+	25.5534i	0.353042	+	0.939362i
$741$	3.24385			0.119166
$742$		−	0.597717i		−	0.0219429i
$743$			43.0239i			1.57839i	0.614141	+	0.789197i	$0.289503\pi$
$743$			43.0239i			1.57839i	−0.614141	+	0.789197i	$0.710497\pi$
$744$	−0.967792			−0.0354810
$745$	−36.0946	+	13.5655i	−1.32241	+	0.497002i
$746$	0.135896			0.00497552
$747$			37.7982i			1.38297i
$748$			0.0119826i			0.000438126i
$749$	−16.1187			−0.588963
$750$	0.383582	−	0.715182i	0.0140064	−	0.0261148i
$751$	8.50342			0.310294			0.155147	−	0.987891i	$-0.450415\pi$
$751$	8.50342			0.310294			0.155147	+	0.987891i	$0.450415\pi$
$752$			3.51490i			0.128175i
$753$		−	19.3368i		−	0.704673i
$754$	1.69636			0.0617778
$755$	47.1953	−	17.7375i	1.71761	−	0.645533i
$756$	−24.5909			−0.894361
$757$		−	18.2012i		−	0.661533i	−0.943713	−	0.330766i	$-0.892693\pi$
$757$		−	18.2012i		−	0.661533i	0.943713	−	0.330766i	$-0.107307\pi$
$758$		−	1.04340i		−	0.0378980i
$759$	1.15602			0.0419609
$760$	−0.326815	−	0.869578i	−0.0118548	−	0.0315429i
$761$	45.3295			1.64319			0.821597	−	0.570069i	$-0.193083\pi$
$761$	45.3295			1.64319			0.821597	+	0.570069i	$0.193083\pi$
$762$			0.0631934i			0.00228926i
$763$		−	12.0028i		−	0.434531i
$764$	−4.17009			−0.150869
$765$	−0.0119143	−	0.0317012i	−0.000430763	−	0.00114616i
$766$	−0.567256			−0.0204958
$767$			11.9619i			0.431921i
$768$			10.5521i			0.380765i
$769$	27.6341			0.996510			0.498255	−	0.867031i	$-0.333974\pi$
$769$	27.6341			0.996510			0.498255	+	0.867031i	$0.333974\pi$
$770$	−0.701167	+	0.263521i	−0.0252683	+	0.00949663i
$771$	12.3371			0.444308
$772$		−	50.1188i		−	1.80382i
$773$			27.7758i			0.999027i	0.866306	+	0.499513i	$0.166488\pi$
$773$			27.7758i			0.999027i	−0.866306	+	0.499513i	$0.833512\pi$
$774$	−2.25636			−0.0811033
$775$	−12.5746	+	11.0066i	−0.451693	+	0.395367i
$776$	−6.87404			−0.246764
$777$		−	13.7597i		−	0.493626i
$778$		−	0.790861i		−	0.0283538i
$779$	−9.38032			−0.336085
$780$	13.5059	−	5.07595i	0.483589	−	0.181748i
$781$	−0.852858			−0.0305176
$782$		−	0.00104052i		−	3.72089e-5i
$783$		−	13.4513i		−	0.480712i
$784$	−13.1680			−0.470286
$785$	9.57073	+	25.4655i	0.341594	+	0.908901i
$786$	−0.0241503			−0.000861414
$787$			1.98342i			0.0707012i	0.999375	+	0.0353506i	$0.0112548\pi$
$787$			1.98342i			0.0707012i	−0.999375	+	0.0353506i	$0.988745\pi$
$788$			11.3558i			0.404533i
$789$	15.6145			0.555891
$790$	−0.404794	−	1.07706i	−0.0144019	−	0.0383201i
$791$	−54.5858			−1.94085
$792$			1.04451i			0.0371151i
$793$			17.1670i			0.609618i
$794$	−0.653453			−0.0231902
$795$	2.60312	−	0.978334i	0.0923230	−	0.0346979i
$796$	20.2900			0.719160
$797$			30.9790i			1.09733i	0.836041	+	0.548666i	$0.184864\pi$
$797$			30.9790i			1.09733i	−0.836041	+	0.548666i	$0.815136\pi$
$798$			0.233483i			0.00826523i
$799$	0.00538078			0.000190358
$800$	−4.08583	−	4.66792i	−0.144456	−	0.165036i
$801$	−12.8588			−0.454345
$802$		−	1.85426i		−	0.0654762i
$803$			4.72786i			0.166842i
$804$	−8.29979			−0.292711
$805$	−11.1667	+	4.19680i	−0.393574	+	0.147918i
$806$	1.61995			0.0570605
$807$		−	11.2721i		−	0.396795i
$808$		−	2.33829i		−	0.0822608i
$809$	−33.4595			−1.17637			−0.588186	−	0.808725i	$-0.700158\pi$
$809$	−33.4595			−1.17637			−0.588186	+	0.808725i	$0.700158\pi$
$810$	−0.398470	−	1.06024i	−0.0140008	−	0.0372529i
$811$	−33.7987			−1.18683			−0.593416	−	0.804896i	$-0.702221\pi$
$811$	−33.7987			−1.18683			−0.593416	+	0.804896i	$0.702221\pi$
$812$		−	22.3932i		−	0.785846i
$813$			1.46350i			0.0513273i
$814$	−0.639174			−0.0224030
$815$	−17.1560	−	45.6481i	−0.600948	−	1.59898i
$816$	0.0165219			0.000578382
$817$		−	8.61740i		−	0.301485i
$818$			0.882297i			0.0308488i
$819$	37.6378			1.31517
$820$	−39.0554	+	14.6783i	−1.36387	+	0.512587i
$821$	−17.6687			−0.616641			−0.308320	−	0.951283i	$-0.599767\pi$
$821$	−17.6687			−0.616641			−0.308320	+	0.951283i	$0.599767\pi$
$822$		−	0.945917i		−	0.0329927i
$823$			46.0491i			1.60517i	0.596538	+	0.802585i	$0.296543\pi$
$823$			46.0491i			1.60517i	−0.596538	+	0.802585i	$0.703457\pi$
$824$	3.14229			0.109467
$825$	−2.29532	−	2.62232i	−0.0799127	−	0.0912975i
$826$	−0.860988			−0.0299576
$827$		−	23.9121i		−	0.831503i	−0.909478	−	0.415752i	$-0.863519\pi$
$827$		−	23.9121i		−	0.831503i	0.909478	−	0.415752i	$-0.136481\pi$
$828$			8.29476i			0.288263i
$829$	10.2688			0.356649			0.178324	−	0.983972i	$-0.442932\pi$
$829$	10.2688			0.356649			0.178324	+	0.983972i	$0.442932\pi$
$830$	3.27718	−	1.23167i	0.113752	−	0.0427518i
$831$	−20.8952			−0.724848
$832$		−	36.0264i		−	1.24899i
$833$			0.0201582i			0.000698440i
$834$	−0.920608			−0.0318780
$835$	−12.2584	−	32.6168i	−0.424221	−	1.12875i
$836$	−1.98915			−0.0687963
$837$		−	12.8455i		−	0.444005i
$838$			1.08890i			0.0376156i
$839$	40.5454			1.39978			0.699890	−	0.714250i	$-0.253232\pi$
$839$	40.5454			1.39978			0.699890	+	0.714250i	$0.253232\pi$
$840$	0.732698	+	1.94954i	0.0252805	+	0.0672654i
$841$	−16.7508			−0.577614
$842$		−	3.38273i		−	0.116577i
$843$		−	0.327452i		−	0.0112780i
$844$	2.06797			0.0711825
$845$	−18.1269	+	6.81267i	−0.623584	+	0.234363i
$846$	0.233882			0.00804102
$847$			3.21657i			0.110523i
$848$		−	7.02132i		−	0.241113i
$849$	−9.20886			−0.316047
$850$	−0.00236032	+	0.00206598i	−8.09582e−5	+	7.08627e-5i
$851$	−10.1794			−0.348945
$852$			1.18243i			0.0405093i
$853$			1.99694i			0.0683740i	0.999415	+	0.0341870i	$0.0108842\pi$
$853$			1.99694i			0.0683740i	−0.999415	+	0.0341870i	$0.989116\pi$
$854$	−1.23563			−0.0422825
$855$	5.26252	−	1.97782i	0.179975	−	0.0676402i
$856$	2.08185			0.0711561
$857$			25.1830i			0.860235i	0.902773	+	0.430118i	$0.141528\pi$
$857$			25.1830i			0.860235i	−0.902773	+	0.430118i	$0.858472\pi$
$858$			0.337827i			0.0115332i
$859$	0.915472			0.0312355			0.0156178	−	0.999878i	$-0.495029\pi$
$859$	0.915472			0.0312355			0.0156178	+	0.999878i	$0.495029\pi$
$860$	−13.4844	−	35.8789i	−0.459816	−	1.22346i
$861$	21.0301			0.716703
$862$			0.238204i			0.00811326i
$863$			49.8812i			1.69797i	0.528413	+	0.848987i	$0.322787\pi$
$863$			49.8812i			1.69797i	−0.528413	+	0.848987i	$0.677213\pi$
$864$	4.76847			0.162227
$865$	−8.19802	−	21.8130i	−0.278741	−	0.741664i
$866$	−3.80357			−0.129251
$867$			11.8489i			0.402409i
$868$		−	21.3846i		−	0.725839i
$869$	−4.94098			−0.167611
$870$	−0.531754	+	0.199850i	−0.0180282	+	0.00677556i
$871$	27.8612			0.944042
$872$			1.55026i			0.0524983i
$873$		−	41.6004i		−	1.40796i
$874$	0.172731			0.00584270
$875$	31.6918	+	16.9977i	1.07138	+	0.574626i
$876$	6.55484			0.221468
$877$			18.6769i			0.630673i	0.948980	+	0.315337i	$0.102117\pi$
$877$			18.6769i			0.630673i	−0.948980	+	0.315337i	$0.897883\pi$
$878$		−	2.39867i		−	0.0809511i
$879$	3.81358			0.128629
$880$	−8.23653	+	3.09555i	−0.277653	+	0.104351i
$881$	−46.9216			−1.58083			−0.790414	−	0.612573i	$-0.790134\pi$
$881$	−46.9216			−1.58083			−0.790414	+	0.612573i	$0.790134\pi$
$882$			0.876200i			0.0295032i
$883$			44.8499i			1.50932i	0.656117	+	0.754659i	$0.272198\pi$
$883$			44.8499i			1.50932i	−0.656117	+	0.754659i	$0.727802\pi$
$884$	−0.0557674			−0.00187566
$885$	−1.40925	−	3.74969i	−0.0473715	−	0.126044i
$886$	−0.378628			−0.0127203
$887$			14.5451i			0.488376i	0.969728	+	0.244188i	$0.0785214\pi$
$887$			14.5451i			0.488376i	−0.969728	+	0.244188i	$0.921479\pi$
$888$			1.77717i			0.0596380i
$889$	−2.80029			−0.0939186
$890$	0.419009	+	1.11488i	0.0140452	+	0.0373710i
$891$	−4.86379			−0.162943
$892$		−	12.7830i		−	0.428006i
$893$			0.893231i			0.0298908i
$894$	−1.25173			−0.0418641
$895$	−42.9835	+	16.1546i	−1.43678	+	0.539988i
$896$	10.5747			0.353276
$897$			5.38018i			0.179639i
$898$			2.66322i			0.0888730i
$899$	11.6975			0.390133
$900$	18.8159	−	16.4695i	0.627196	−	0.548984i
$901$	−0.0107486			−0.000358086
$902$		−	0.976902i		−	0.0325273i
$903$			19.3197i			0.642918i
$904$	7.05017			0.234485
$905$	0.139815	−	0.0525469i	0.00464760	−	0.00174672i
$906$	1.63669			0.0543754
$907$			56.2751i			1.86858i	0.356510	+	0.934292i	$0.383967\pi$
$907$			56.2751i			1.86858i	−0.356510	+	0.934292i	$0.616033\pi$
$908$			12.4484i			0.413115i
$909$	14.1509			0.469356
$910$	−1.22644	−	3.26327i	−0.0406561	−	0.108176i
$911$	11.8656			0.393123			0.196562	−	0.980491i	$-0.437022\pi$
$911$	11.8656			0.393123			0.196562	+	0.980491i	$0.437022\pi$
$912$			2.74270i			0.0908200i
$913$		−	15.0339i		−	0.497550i
$914$	0.671883			0.0222239
$915$	−2.02246	−	5.38130i	−0.0668606	−	0.177900i
$916$	−52.2493			−1.72637
$917$		−	1.07017i		−	0.0353402i
$918$		−	0.00241116i		−	7.95801e-5i
$919$	−17.4567			−0.575844			−0.287922	−	0.957654i	$-0.592964\pi$
$919$	−17.4567			−0.575844			−0.287922	+	0.957654i	$0.592964\pi$
$920$	1.44226	−	0.542049i	0.0475500	−	0.0178708i
$921$	−21.5223			−0.709183
$922$			2.40877i			0.0793286i
$923$		−	3.96924i		−	0.130649i
$924$	4.45956			0.146709
$925$	20.2115	+	23.0910i	0.664550	+	0.759226i
$926$	−3.79535			−0.124723
$927$			19.0165i			0.624585i
$928$			4.34231i			0.142543i
$929$	−6.75452			−0.221609			−0.110804	−	0.993842i	$-0.535343\pi$
$929$	−6.75452			−0.221609			−0.110804	+	0.993842i	$0.535343\pi$
$930$	−0.507804	+	0.190849i	−0.0166515	+	0.00625818i
$931$	−3.34635			−0.109672
$932$		−	5.86781i		−	0.192206i
$933$			16.9041i			0.553415i
$934$	−3.75480			−0.122861
$935$	0.00473881	+	0.0126089i	0.000154976	+	0.000412354i
$936$	−4.86121			−0.158894
$937$		−	45.1286i		−	1.47429i	−0.675736	−	0.737143i	$-0.736174\pi$
$937$		−	45.1286i		−	1.47429i	0.675736	−	0.737143i	$-0.263826\pi$
$938$			2.00537i			0.0654778i
$939$	−8.56760			−0.279593
$940$	1.39772	+	3.71901i	0.0455887	+	0.121301i
$941$	26.7484			0.871972			0.435986	−	0.899954i	$-0.356400\pi$
$941$	26.7484			0.871972			0.435986	+	0.899954i	$0.356400\pi$
$942$			0.883119i			0.0287736i
$943$		−	15.5580i		−	0.506639i
$944$	−10.1139			−0.329180
$945$	−25.8762	+	9.72509i	−0.841752	+	0.316357i
$946$	0.897448			0.0291786
$947$		−	16.2900i		−	0.529355i	−0.964337	−	0.264677i	$-0.914735\pi$
$947$		−	16.2900i		−	0.529355i	0.964337	−	0.264677i	$-0.0852655\pi$
$948$			6.85032i			0.222488i
$949$	−22.0037			−0.714270
$950$	−0.342962	−	0.391822i	−0.0111272	−	0.0127124i
$951$	13.9841			0.453465
$952$		−	0.00804986i		−	0.000260897i
$953$		−	4.10009i		−	0.132815i	−0.997793	−	0.0664075i	$-0.978846\pi$
$953$		−	4.10009i		−	0.132815i	0.997793	−	0.0664075i	$-0.0211537\pi$
$954$	−0.467199			−0.0151261
$955$	−4.38805	+	1.64917i	−0.141994	+	0.0533659i
$956$	−36.9866			−1.19623
$957$			2.43940i			0.0788547i
$958$			1.79388i			0.0579576i
$959$	41.9164			1.35355
$960$	4.24432	+	11.2931i	0.136985	+	0.364484i
$961$	−19.8294			−0.639658
$962$		−	2.97475i		−	0.0959097i
$963$			12.5990i			0.405996i
$964$	−17.2695			−0.556213
$965$	−19.8208	−	52.7384i	−0.638053	−	1.69771i
$966$	−0.387251			−0.0124596
$967$		−	34.0890i		−	1.09623i	−0.836403	−	0.548115i	$-0.815346\pi$
$967$		−	34.0890i		−	1.09623i	0.836403	−	0.548115i	$-0.184654\pi$
$968$		−	0.415445i		−	0.0133529i
$969$	0.00419866			0.000134880
$970$	−3.60683	+	1.35556i	−0.115808	+	0.0435245i
$971$	40.8253			1.31015			0.655073	−	0.755565i	$-0.272638\pi$
$971$	40.8253			1.31015			0.655073	+	0.755565i	$0.272638\pi$
$972$			29.6785i			0.951937i
$973$		−	40.7949i		−	1.30782i
$974$	−3.29550			−0.105594
$975$	12.2044	−	10.6825i	0.390854	−	0.342115i
$976$	−14.5148			−0.464609
$977$		−	14.7093i		−	0.470591i	−0.971924	−	0.235296i	$-0.924394\pi$
$977$		−	14.7093i		−	0.470591i	0.971924	−	0.235296i	$-0.0756058\pi$
$978$		−	1.58303i		−	0.0506198i
$979$	5.11449			0.163460
$980$	−13.9327	+	5.23634i	−0.445062	+	0.167269i
$981$	−9.38187			−0.299540
$982$		−	4.05188i		−	0.129301i
$983$		−	31.0823i		−	0.991372i	−0.868502	−	0.495686i	$-0.834917\pi$
$983$		−	31.0823i		−	0.991372i	0.868502	−	0.495686i	$-0.165083\pi$
$984$	−2.71620			−0.0865892
$985$	4.49094	+	11.9493i	0.143093	+	0.380737i
$986$	0.00219567			6.99245e−5
$987$		−	2.00257i		−	0.0637424i
$988$		−	9.25763i		−	0.294524i
$989$	14.2926			0.454479
$990$	0.205978	+	0.548059i	0.00654641	+	0.0174185i
$991$	45.1569			1.43446			0.717228	−	0.696838i	$-0.245411\pi$
$991$	45.1569			1.43446			0.717228	+	0.696838i	$0.245411\pi$
$992$			4.14673i			0.131659i
$993$		−	19.7352i		−	0.626279i
$994$	0.285695			0.00906170
$995$	21.3505	−	8.02421i	0.676857	−	0.254384i
$996$	−20.8435			−0.660451
$997$		−	46.8604i		−	1.48409i	−0.670353	−	0.742043i	$-0.733857\pi$
$997$		−	46.8604i		−	1.48409i	0.670353	−	0.742043i	$-0.266143\pi$
$998$			1.70998i			0.0541283i
$999$	−23.5884			−0.746303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.11	✓	22
5.2	odd	4		5225.2.a.bb.1.12		22
5.3	odd	4		5225.2.a.bb.1.11		22
5.4	even	2	inner	1045.2.b.d.419.12	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.11	✓	22	1.1	even	1	trivial
1045.2.b.d.419.12	yes	22	5.4	even	2	inner
5225.2.a.bb.1.11		22	5.3	odd	4
5225.2.a.bb.1.12		22	5.2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.104144i q^{2} +0.696995i q^{3} +1.98915 q^{4} +(2.09312 - 0.786662i) q^{5} +0.0725876 q^{6} +3.21657i q^{7} -0.415445i q^{8} +2.51420 q^{9} +O(q^{10})\)	\(q-0.104144i q^{2} +0.696995i q^{3} +1.98915 q^{4} +(2.09312 - 0.786662i) q^{5} +0.0725876 q^{6} +3.21657i q^{7} -0.415445i q^{8} +2.51420 q^{9} +(-0.0819259 - 0.217986i) q^{10} -1.00000 q^{11} +1.38643i q^{12} -4.65405i q^{13} +0.334986 q^{14} +(0.548300 + 1.45890i) q^{15} +3.93504 q^{16} -0.00602394i q^{17} -0.261838i q^{18} +1.00000 q^{19} +(4.16354 - 1.56479i) q^{20} -2.24194 q^{21} +0.104144i q^{22} +1.65858i q^{23} +0.289563 q^{24} +(3.76233 - 3.29316i) q^{25} -0.484690 q^{26} +3.84337i q^{27} +6.39826i q^{28} -3.49988 q^{29} +(0.151935 - 0.0571020i) q^{30} -3.34225 q^{31} -1.24070i q^{32} -0.696995i q^{33} -0.000627356 q^{34} +(2.53036 + 6.73268i) q^{35} +5.00113 q^{36} +6.13742i q^{37} -0.104144i q^{38} +3.24385 q^{39} +(-0.326815 - 0.869578i) q^{40} -9.38032 q^{41} +0.233483i q^{42} -8.61740i q^{43} -1.98915 q^{44} +(5.26252 - 1.97782i) q^{45} +0.172731 q^{46} +0.893231i q^{47} +2.74270i q^{48} -3.34635 q^{49} +(-0.342962 - 0.391822i) q^{50} +0.00419866 q^{51} -9.25763i q^{52} -1.78431i q^{53} +0.400263 q^{54} +(-2.09312 + 0.786662i) q^{55} +1.33631 q^{56} +0.696995i q^{57} +0.364491i q^{58} -2.57022 q^{59} +(1.09065 + 2.90197i) q^{60} -3.68861 q^{61} +0.348074i q^{62} +8.08710i q^{63} +7.74087 q^{64} +(-3.66117 - 9.74151i) q^{65} -0.0725876 q^{66} +5.98644i q^{67} -0.0119826i q^{68} -1.15602 q^{69} +(0.701167 - 0.263521i) q^{70} +0.852858 q^{71} -1.04451i q^{72} -4.72786i q^{73} +0.639174 q^{74} +(2.29532 + 2.62232i) q^{75} +1.98915 q^{76} -3.21657i q^{77} -0.337827i q^{78} +4.94098 q^{79} +(8.23653 - 3.09555i) q^{80} +4.86379 q^{81} +0.976902i q^{82} +15.0339i q^{83} -4.45956 q^{84} +(-0.00473881 - 0.0126089i) q^{85} -0.897448 q^{86} -2.43940i q^{87} +0.415445i q^{88} -5.11449 q^{89} +(-0.205978 - 0.548059i) q^{90} +14.9701 q^{91} +3.29917i q^{92} -2.32953i q^{93} +0.0930244 q^{94} +(2.09312 - 0.786662i) q^{95} +0.864762 q^{96} -16.5462i q^{97} +0.348501i q^{98} -2.51420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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