LMFDB - Embedded newform 1045.2.b.e.419.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1045,2,Mod(419,1045)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.21
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.45151i q^{2} +0.0791235i q^{3} -0.106883 q^{4} +(-2.19310 - 0.436262i) q^{5} -0.114849 q^{6} +2.96150i q^{7} +2.74788i q^{8} +2.99374 q^{9} +(0.633239 - 3.18330i) q^{10} +1.00000 q^{11} -0.00845698i q^{12} -3.94825i q^{13} -4.29865 q^{14} +(0.0345186 - 0.173526i) q^{15} -4.20234 q^{16} +4.79134i q^{17} +4.34544i q^{18} -1.00000 q^{19} +(0.234405 + 0.0466291i) q^{20} -0.234324 q^{21} +1.45151i q^{22} +5.69554i q^{23} -0.217422 q^{24} +(4.61935 + 1.91353i) q^{25} +5.73093 q^{26} +0.474246i q^{27} -0.316535i q^{28} -2.19295 q^{29} +(0.251874 + 0.0501041i) q^{30} -8.56978 q^{31} -0.603987i q^{32} +0.0791235i q^{33} -6.95468 q^{34} +(1.29199 - 6.49486i) q^{35} -0.319981 q^{36} +6.70306i q^{37} -1.45151i q^{38} +0.312399 q^{39} +(1.19879 - 6.02637i) q^{40} +5.78933 q^{41} -0.340124i q^{42} -11.8680i q^{43} -0.106883 q^{44} +(-6.56556 - 1.30605i) q^{45} -8.26713 q^{46} +3.44076i q^{47} -0.332504i q^{48} -1.77048 q^{49} +(-2.77751 + 6.70504i) q^{50} -0.379107 q^{51} +0.422002i q^{52} +2.73870i q^{53} -0.688373 q^{54} +(-2.19310 - 0.436262i) q^{55} -8.13784 q^{56} -0.0791235i q^{57} -3.18309i q^{58} +1.87690 q^{59} +(-0.00368946 + 0.0185470i) q^{60} -13.7308 q^{61} -12.4391i q^{62} +8.86596i q^{63} -7.52799 q^{64} +(-1.72247 + 8.65890i) q^{65} -0.114849 q^{66} +10.1502i q^{67} -0.512114i q^{68} -0.450651 q^{69} +(9.42735 + 1.87534i) q^{70} -5.59507 q^{71} +8.22643i q^{72} +3.73181i q^{73} -9.72957 q^{74} +(-0.151405 + 0.365499i) q^{75} +0.106883 q^{76} +2.96150i q^{77} +0.453451i q^{78} -16.6160 q^{79} +(9.21615 + 1.83332i) q^{80} +8.94369 q^{81} +8.40327i q^{82} -9.90171i q^{83} +0.0250453 q^{84} +(2.09028 - 10.5079i) q^{85} +17.2266 q^{86} -0.173514i q^{87} +2.74788i q^{88} +1.30858 q^{89} +(1.89575 - 9.52998i) q^{90} +11.6927 q^{91} -0.608757i q^{92} -0.678071i q^{93} -4.99431 q^{94} +(2.19310 + 0.436262i) q^{95} +0.0477895 q^{96} +9.85288i q^{97} -2.56986i q^{98} +2.99374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34}+ \cdots - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

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 $

$2$			1.45151i			1.02637i	0.858277	+	0.513187i	$0.171535\pi$
$2$			1.45151i			1.02637i	−0.858277	+	0.513187i	$0.828465\pi$
$3$			0.0791235i			0.0456820i	0.999739	+	0.0228410i	$0.00727115\pi$
$3$			0.0791235i			0.0456820i	−0.999739	+	0.0228410i	$0.992729\pi$
$4$	−0.106883			−0.0534416
$5$	−2.19310	−	0.436262i	−0.980783	−	0.195102i
$5$	−2.19310	−	0.436262i	−0.980783	−	0.195102i
$6$	−0.114849			−0.0468868
$7$			2.96150i			1.11934i	0.828715	+	0.559671i	$0.189072\pi$
$7$			2.96150i			1.11934i	−0.828715	+	0.559671i	$0.810928\pi$
$8$			2.74788i			0.971522i
$9$	2.99374			0.997913
$10$	0.633239	−	3.18330i	0.200248	−	1.00665i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.00845698i		−	0.00244132i
$13$		−	3.94825i		−	1.09505i	−0.836790	−	0.547524i	$-0.815571\pi$
$13$		−	3.94825i		−	1.09505i	0.836790	−	0.547524i	$-0.184429\pi$
$14$	−4.29865			−1.14886
$15$	0.0345186	−	0.173526i	0.00891265	−	0.0448041i
$16$	−4.20234			−1.05059
$17$			4.79134i			1.16207i	0.813879	+	0.581035i	$0.197352\pi$
$17$			4.79134i			1.16207i	−0.813879	+	0.581035i	$0.802648\pi$
$18$			4.34544i			1.02423i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.234405	+	0.0466291i	0.0524146	+	0.0104266i
$21$	−0.234324			−0.0511337
$22$			1.45151i			0.309463i
$23$			5.69554i			1.18760i	0.804612	+	0.593801i	$0.202373\pi$
$23$			5.69554i			1.18760i	−0.804612	+	0.593801i	$0.797627\pi$
$24$	−0.217422			−0.0443811
$25$	4.61935	+	1.91353i	0.923870	+	0.382706i
$26$	5.73093			1.12393
$27$			0.474246i			0.0912686i
$28$		−	0.316535i		−	0.0598194i
$29$	−2.19295			−0.407221			−0.203611	−	0.979052i	$-0.565268\pi$
$29$	−2.19295			−0.407221			−0.203611	+	0.979052i	$0.565268\pi$
$30$	0.251874	+	0.0501041i	0.0459857	+	0.00914771i
$31$	−8.56978			−1.53918			−0.769589	−	0.638539i	$-0.779539\pi$
$31$	−8.56978			−1.53918			−0.769589	+	0.638539i	$0.779539\pi$
$32$		−	0.603987i		−	0.106771i
$33$			0.0791235i			0.0137736i
$34$	−6.95468			−1.19272
$35$	1.29199	−	6.49486i	0.218386	−	1.09783i
$36$	−0.319981			−0.0533301
$37$			6.70306i			1.10198i	0.834513	+	0.550988i	$0.185749\pi$
$37$			6.70306i			1.10198i	−0.834513	+	0.550988i	$0.814251\pi$
$38$		−	1.45151i		−	0.235466i
$39$	0.312399			0.0500239
$40$	1.19879	−	6.02637i	0.189546	−	0.952852i
$41$	5.78933			0.904141			0.452071	−	0.891982i	$-0.350686\pi$
$41$	5.78933			0.904141			0.452071	+	0.891982i	$0.350686\pi$
$42$		−	0.340124i		−	0.0524823i
$43$		−	11.8680i		−	1.80986i	−0.425560	−	0.904930i	$-0.639923\pi$
$43$		−	11.8680i		−	1.80986i	0.425560	−	0.904930i	$-0.360077\pi$
$44$	−0.106883			−0.0161133
$45$	−6.56556	−	1.30605i	−0.978736	−	0.194695i
$46$	−8.26713			−1.21892
$47$			3.44076i			0.501887i	0.968002	+	0.250944i	$0.0807408\pi$
$47$			3.44076i			0.501887i	−0.968002	+	0.250944i	$0.919259\pi$
$48$		−	0.332504i		−	0.0479928i
$49$	−1.77048			−0.252925
$50$	−2.77751	+	6.70504i	−0.392799	+	0.948236i
$51$	−0.379107			−0.0530857
$52$			0.422002i			0.0585211i
$53$			2.73870i			0.376190i	0.982151	+	0.188095i	$0.0602313\pi$
$53$			2.73870i			0.376190i	−0.982151	+	0.188095i	$0.939769\pi$
$54$	−0.688373			−0.0936757
$55$	−2.19310	−	0.436262i	−0.295717	−	0.0588255i
$56$	−8.13784			−1.08746
$57$		−	0.0791235i		−	0.0104802i
$58$		−	3.18309i		−	0.417961i
$59$	1.87690			0.244351			0.122176	−	0.992508i	$-0.461013\pi$
$59$	1.87690			0.244351			0.122176	+	0.992508i	$0.461013\pi$
$60$	−0.00368946	+	0.0185470i	−0.000476307	+	0.00239440i
$61$	−13.7308			−1.75804			−0.879021	−	0.476782i	$-0.841803\pi$
$61$	−13.7308			−1.75804			−0.879021	+	0.476782i	$0.841803\pi$
$62$		−	12.4391i		−	1.57977i
$63$			8.86596i			1.11701i
$64$	−7.52799			−0.940999
$65$	−1.72247	+	8.65890i	−0.213646	+	1.07400i
$66$	−0.114849			−0.0141369
$67$			10.1502i			1.24005i	0.784582	+	0.620025i	$0.212877\pi$
$67$			10.1502i			1.24005i	−0.784582	+	0.620025i	$0.787123\pi$
$68$		−	0.512114i		−	0.0621029i
$69$	−0.450651			−0.0542520
$70$	9.42735	+	1.87534i	1.12678	+	0.224145i
$71$	−5.59507			−0.664013			−0.332006	−	0.943277i	$-0.607726\pi$
$71$	−5.59507			−0.664013			−0.332006	+	0.943277i	$0.607726\pi$
$72$			8.22643i			0.969495i
$73$			3.73181i			0.436775i	0.975862	+	0.218388i	$0.0700797\pi$
$73$			3.73181i			0.436775i	−0.975862	+	0.218388i	$0.929920\pi$
$74$	−9.72957			−1.13104
$75$	−0.151405	+	0.365499i	−0.0174828	+	0.0422042i
$76$	0.106883			0.0122603
$77$			2.96150i			0.337494i
$78$			0.453451i			0.0513432i
$79$	−16.6160			−1.86944			−0.934722	−	0.355379i	$-0.884352\pi$
$79$	−16.6160			−1.86944			−0.934722	+	0.355379i	$0.884352\pi$
$80$	9.21615	+	1.83332i	1.03040	+	0.204972i
$81$	8.94369			0.993744
$82$			8.40327i			0.927986i
$83$		−	9.90171i		−	1.08685i	−0.839456	−	0.543427i	$-0.817126\pi$
$83$		−	9.90171i		−	1.08685i	0.839456	−	0.543427i	$-0.182874\pi$
$84$	0.0250453			0.00273267
$85$	2.09028	−	10.5079i	0.226722	−	1.13974i
$86$	17.2266			1.85759
$87$		−	0.173514i		−	0.0186027i
$88$			2.74788i			0.292925i
$89$	1.30858			0.138709			0.0693546	−	0.997592i	$-0.477906\pi$
$89$	1.30858			0.138709			0.0693546	+	0.997592i	$0.477906\pi$
$90$	1.89575	−	9.52998i	0.199830	−	1.00455i
$91$	11.6927			1.22573
$92$		−	0.608757i		−	0.0634674i
$93$		−	0.678071i		−	0.0703127i
$94$	−4.99431			−0.515123
$95$	2.19310	+	0.436262i	0.225007	+	0.0447595i
$96$	0.0477895			0.00487750
$97$			9.85288i			1.00041i	0.865908	+	0.500204i	$0.166742\pi$
$97$			9.85288i			1.00041i	−0.865908	+	0.500204i	$0.833258\pi$
$98$		−	2.56986i		−	0.259595i
$99$	2.99374			0.300882
$100$	−0.493731	−	0.204524i	−0.0493731	−	0.0204524i
$101$	18.1171			1.80272			0.901358	−	0.433076i	$-0.142572\pi$
$101$	18.1171			1.80272			0.901358	+	0.433076i	$0.142572\pi$
$102$		−	0.550279i		−	0.0544857i
$103$		−	14.2177i		−	1.40091i	−0.713696	−	0.700455i	$-0.752980\pi$
$103$		−	14.2177i		−	1.40091i	0.713696	−	0.700455i	$-0.247020\pi$
$104$	10.8493			1.06386
$105$	0.513896	+	0.102227i	0.0501511	+	0.00997630i
$106$	−3.97526			−0.386111
$107$		−	1.93848i		−	0.187400i	−0.995600	−	0.0937001i	$-0.970131\pi$
$107$		−	1.93848i		−	0.187400i	0.995600	−	0.0937001i	$-0.0298695\pi$
$108$		−	0.0506889i		−	0.00487754i
$109$	10.8606			1.04026			0.520130	−	0.854087i	$-0.325883\pi$
$109$	10.8606			1.04026			0.520130	+	0.854087i	$0.325883\pi$
$110$	0.633239	−	3.18330i	0.0603769	−	0.303516i
$111$	−0.530370			−0.0503405
$112$		−	12.4452i		−	1.17596i
$113$			16.1744i			1.52156i	0.649008	+	0.760782i	$0.275184\pi$
$113$			16.1744i			1.52156i	−0.649008	+	0.760782i	$0.724816\pi$
$114$	0.114849			0.0107566
$115$	2.48474	−	12.4909i	0.231704	−	1.16478i
$116$	0.234390			0.0217626
$117$		−	11.8200i		−	1.09276i
$118$			2.72434i			0.250796i
$119$	−14.1895			−1.30075
$120$	0.476827	+	0.0948528i	0.0435282	+	0.00865884i
$121$	1.00000			0.0909091
$122$		−	19.9303i		−	1.80441i
$123$			0.458072i			0.0413030i
$124$	0.915966			0.0822562
$125$	−9.29589	−	6.21180i	−0.831449	−	0.555600i
$126$	−12.8690			−1.14646
$127$		−	13.0331i		−	1.15650i	−0.815859	−	0.578251i	$-0.803736\pi$
$127$		−	13.0331i		−	1.15650i	0.815859	−	0.578251i	$-0.196264\pi$
$128$		−	12.1349i		−	1.07259i
$129$	0.939042			0.0826780
$130$	−12.5685	−	2.50018i	−1.10233	−	0.219281i
$131$	13.8516			1.21022			0.605111	−	0.796141i	$-0.293129\pi$
$131$	13.8516			1.21022			0.605111	+	0.796141i	$0.293129\pi$
$132$		−	0.00845698i		−	0.000736085i
$133$		−	2.96150i		−	0.256795i
$134$	−14.7332			−1.27275
$135$	0.206895	−	1.04007i	0.0178067	−	0.0895147i
$136$	−13.1660			−1.12898
$137$			7.87545i			0.672845i	0.941711	+	0.336422i	$0.109217\pi$
$137$			7.87545i			0.672845i	−0.941711	+	0.336422i	$0.890783\pi$
$138$		−	0.654125i		−	0.0556828i
$139$	18.7282			1.58850			0.794251	−	0.607590i	$-0.207864\pi$
$139$	18.7282			1.58850			0.794251	+	0.607590i	$0.207864\pi$
$140$	−0.138092	+	0.694191i	−0.0116709	+	0.0586699i
$141$	−0.272245			−0.0229272
$142$		−	8.12131i		−	0.681525i
$143$		−	3.94825i		−	0.330169i
$144$	−12.5807			−1.04839
$145$	4.80936	+	0.956701i	0.399396	+	0.0794497i
$146$	−5.41676			−0.448294
$147$		−	0.140086i		−	0.0115541i
$148$		−	0.716445i		−	0.0588914i
$149$	5.28231			0.432744			0.216372	−	0.976311i	$-0.430578\pi$
$149$	5.28231			0.432744			0.216372	+	0.976311i	$0.430578\pi$
$150$	−0.530526	−	0.219766i	−0.0433173	−	0.0179438i
$151$	15.4741			1.25926			0.629631	−	0.776895i	$-0.283206\pi$
$151$	15.4741			1.25926			0.629631	+	0.776895i	$0.283206\pi$
$152$		−	2.74788i		−	0.222882i
$153$			14.3440i			1.15964i
$154$	−4.29865			−0.346395
$155$	18.7944	+	3.73867i	1.50960	+	0.300297i
$156$	−0.0333903			−0.00267336
$157$			19.8551i			1.58461i	0.610128	+	0.792303i	$0.291118\pi$
$157$			19.8551i			1.58461i	−0.610128	+	0.792303i	$0.708882\pi$
$158$		−	24.1183i		−	1.91875i
$159$	−0.216696			−0.0171851
$160$	−0.263496	+	1.32460i	−0.0208312	+	0.104719i
$161$	−16.8673			−1.32933
$162$			12.9819i			1.01995i
$163$		−	0.0217138i		−	0.00170076i	−1.00000		0.000850380i	$-0.999729\pi$
$163$		−	0.0217138i		−	0.00170076i	1.00000		0.000850380i	$-0.000270684\pi$
$164$	−0.618782			−0.0483188
$165$	0.0345186	−	0.173526i	0.00268727	−	0.0135089i
$166$	14.3724			1.11552
$167$		−	1.69054i		−	0.130818i	−0.997859	−	0.0654088i	$-0.979165\pi$
$167$		−	1.69054i		−	0.130818i	0.997859	−	0.0654088i	$-0.0208351\pi$
$168$		−	0.643895i		−	0.0496775i
$169$	−2.58868			−0.199129
$170$	15.2523	+	3.03406i	1.16980	+	0.232702i
$171$	−2.99374			−0.228937
$172$			1.26850i			0.0967219i
$173$		−	24.1483i		−	1.83596i	−0.396623	−	0.917982i	$-0.629818\pi$
$173$		−	24.1483i		−	1.83596i	0.396623	−	0.917982i	$-0.370182\pi$
$174$	0.251858			0.0190933
$175$	−5.66691	+	13.6802i	−0.428378	+	1.03413i
$176$	−4.20234			−0.316763
$177$			0.148507i			0.0111625i
$178$			1.89942i			0.142367i
$179$	−4.79370			−0.358298			−0.179149	−	0.983822i	$-0.557334\pi$
$179$	−4.79370			−0.358298			−0.179149	+	0.983822i	$0.557334\pi$
$180$	0.701749	+	0.139595i	0.0523052	+	0.0104048i
$181$	14.6891			1.09183			0.545917	−	0.837839i	$-0.316181\pi$
$181$	14.6891			1.09183			0.545917	+	0.837839i	$0.316181\pi$
$182$			16.9721i			1.25806i
$183$		−	1.08643i		−	0.0803109i
$184$	−15.6506			−1.15378
$185$	2.92429	−	14.7005i	0.214998	−	1.08080i
$186$	0.984228			0.0721671
$187$			4.79134i			0.350377i
$188$		−	0.367760i		−	0.0268217i
$189$	−1.40448			−0.102161
$190$	−0.633239	+	3.18330i	−0.0459400	+	0.230941i
$191$	25.2511			1.82711			0.913553	−	0.406719i	$-0.133327\pi$
$191$	25.2511			1.82711			0.913553	+	0.406719i	$0.133327\pi$
$192$		−	0.595641i		−	0.0429867i
$193$			3.62179i			0.260702i	0.991468	+	0.130351i	$0.0416104\pi$
$193$			3.62179i			0.260702i	−0.991468	+	0.130351i	$0.958390\pi$
$194$	−14.3016			−1.02679
$195$	−0.685122	−	0.136288i	−0.0490626	−	0.00975978i
$196$	0.189234			0.0135167
$197$			7.51197i			0.535206i	0.963529	+	0.267603i	$0.0862315\pi$
$197$			7.51197i			0.535206i	−0.963529	+	0.267603i	$0.913768\pi$
$198$			4.34544i			0.308817i
$199$	−3.89016			−0.275766			−0.137883	−	0.990448i	$-0.544030\pi$
$199$	−3.89016			−0.275766			−0.137883	+	0.990448i	$0.544030\pi$
$200$	−5.25815	+	12.6934i	−0.371807	+	0.897560i
$201$	−0.803123			−0.0566479
$202$			26.2971i			1.85026i
$203$		−	6.49443i		−	0.455819i
$204$	0.0405202			0.00283698
$205$	−12.6966	−	2.52566i	−0.886766	−	0.176400i
$206$	20.6371			1.43786
$207$			17.0510i			1.18512i
$208$			16.5919i			1.15044i
$209$	−1.00000			−0.0691714
$210$	−0.148383	+	0.745925i	−0.0102394	+	0.0514737i
$211$	3.21646			0.221430			0.110715	−	0.993852i	$-0.464686\pi$
$211$	3.21646			0.221430			0.110715	+	0.993852i	$0.464686\pi$
$212$		−	0.292722i		−	0.0201042i
$213$		−	0.442702i		−	0.0303334i
$214$	2.81373			0.192343
$215$	−5.17758	+	26.0278i	−0.353108	+	1.77508i
$216$	−1.30317			−0.0886695
$217$		−	25.3794i		−	1.72287i
$218$			15.7643i			1.06770i
$219$	−0.295274			−0.0199528
$220$	0.234405	+	0.0466291i	0.0158036	+	0.00314373i
$221$	18.9174			1.27252
$222$		−	0.769838i		−	0.0516681i
$223$		−	10.4914i		−	0.702553i	−0.936272	−	0.351277i	$-0.885748\pi$
$223$		−	10.4914i		−	0.702553i	0.936272	−	0.351277i	$-0.114252\pi$
$224$	1.78871			0.119513
$225$	13.8291	+	5.72861i	0.921942	+	0.381907i
$226$	−23.4774			−1.56169
$227$		−	0.798523i		−	0.0529999i	−0.999649	−	0.0264999i	$-0.991564\pi$
$227$		−	0.798523i		−	0.0529999i	0.999649	−	0.0264999i	$-0.00843618\pi$
$228$			0.00845698i			0.000560077i
$229$	16.3354			1.07947			0.539735	−	0.841835i	$-0.318524\pi$
$229$	16.3354			1.07947			0.539735	+	0.841835i	$0.318524\pi$
$230$	18.1306	+	3.60663i	1.19550	+	0.237814i
$231$	−0.234324			−0.0154174
$232$		−	6.02597i		−	0.395624i
$233$			14.9185i			0.977340i	0.872469	+	0.488670i	$0.162518\pi$
$233$			14.9185i			0.977340i	−0.872469	+	0.488670i	$0.837482\pi$
$234$	17.1569			1.12158
$235$	1.50107	−	7.54593i	0.0979192	−	0.492242i
$236$	−0.200609			−0.0130585
$237$		−	1.31472i		−	0.0853999i
$238$		−	20.5963i		−	1.33506i
$239$	23.5350			1.52235			0.761177	−	0.648544i	$-0.224622\pi$
$239$	23.5350			1.52235			0.761177	+	0.648544i	$0.224622\pi$
$240$	−0.145059	+	0.729214i	−0.00936351	+	0.0470706i
$241$	24.7890			1.59680			0.798399	−	0.602129i	$-0.205681\pi$
$241$	24.7890			1.59680			0.798399	+	0.602129i	$0.205681\pi$
$242$			1.45151i			0.0933066i
$243$			2.13039i			0.136665i
$244$	1.46759			0.0939527
$245$	3.88282	+	0.772391i	0.248065	+	0.0493462i
$246$	−0.664896			−0.0423922
$247$			3.94825i			0.251221i
$248$		−	23.5487i		−	1.49535i
$249$	0.783458			0.0496497
$250$	9.01650	−	13.4931i	0.570253	−	0.853377i
$251$	−5.81152			−0.366820			−0.183410	−	0.983036i	$-0.558714\pi$
$251$	−5.81152			−0.366820			−0.183410	+	0.983036i	$0.558714\pi$
$252$		−	0.947622i		−	0.0596946i
$253$			5.69554i			0.358075i
$254$	18.9177			1.18700
$255$	0.831420	+	0.165390i	0.0520655	+	0.0103571i
$256$	2.55800			0.159875
$257$		−	26.8322i		−	1.67375i	−0.547397	−	0.836873i	$-0.684381\pi$
$257$		−	26.8322i		−	1.67375i	0.547397	−	0.836873i	$-0.315619\pi$
$258$			1.36303i			0.0848585i
$259$	−19.8511			−1.23349
$260$	0.184103	−	0.925491i	0.0114176	−	0.0573965i
$261$	−6.56513			−0.406371
$262$			20.1058i			1.24214i
$263$			24.5162i			1.51173i	0.654727	+	0.755865i	$0.272784\pi$
$263$			24.5162i			1.51173i	−0.654727	+	0.755865i	$0.727216\pi$
$264$	−0.217422			−0.0133814
$265$	1.19479	−	6.00625i	0.0733955	−	0.368961i
$266$	4.29865			0.263567
$267$			0.103539i			0.00633651i
$268$		−	1.08489i		−	0.0662702i
$269$	−15.0720			−0.918956			−0.459478	−	0.888189i	$-0.651963\pi$
$269$	−15.0720			−0.918956			−0.459478	+	0.888189i	$0.651963\pi$
$270$	1.50967	+	0.300311i	0.0918755	+	0.0182763i
$271$	−18.3558			−1.11503			−0.557517	−	0.830165i	$-0.688246\pi$
$271$	−18.3558			−1.11503			−0.557517	+	0.830165i	$0.688246\pi$
$272$		−	20.1348i		−	1.22085i
$273$			0.925171i			0.0559939i
$274$	−11.4313			−0.690590
$275$	4.61935	+	1.91353i	0.278557	+	0.115390i
$276$	0.0481670			0.00289931
$277$		−	11.1338i		−	0.668964i	−0.942402	−	0.334482i	$-0.891439\pi$
$277$		−	11.1338i		−	0.668964i	0.942402	−	0.334482i	$-0.108561\pi$
$278$			27.1841i			1.63040i
$279$	−25.6557			−1.53597
$280$	17.8471	+	3.55023i	1.06657	+	0.212167i
$281$	3.26607			0.194837			0.0974187	−	0.995243i	$-0.468941\pi$
$281$	3.26607			0.194837			0.0974187	+	0.995243i	$0.468941\pi$
$282$		−	0.395167i		−	0.0235319i
$283$		−	25.0622i		−	1.48979i	−0.667180	−	0.744897i	$-0.732499\pi$
$283$		−	25.0622i		−	1.48979i	0.667180	−	0.744897i	$-0.267501\pi$
$284$	0.598020			0.0354859
$285$	−0.0345186	+	0.173526i	−0.00204470	+	0.0102788i
$286$	5.73093			0.338877
$287$			17.1451i			1.01204i
$288$		−	1.80818i		−	0.106548i
$289$	−5.95691			−0.350407
$290$	−1.38866	+	6.98084i	−0.0815451	+	0.409929i
$291$	−0.779594			−0.0457006
$292$		−	0.398868i		−	0.0233420i
$293$			21.9171i			1.28041i	0.768204	+	0.640205i	$0.221151\pi$
$293$			21.9171i			1.28041i	−0.768204	+	0.640205i	$0.778849\pi$
$294$	0.203337			0.0118588
$295$	−4.11622	−	0.818819i	−0.239656	−	0.0476735i
$296$	−18.4192			−1.07059
$297$			0.474246i			0.0275185i
$298$			7.66733i			0.444157i
$299$	22.4874			1.30048
$300$	0.0161827	−	0.0390658i	0.000934307	−	0.00225546i
$301$	35.1472			2.02585
$302$			22.4608i			1.29247i
$303$			1.43349i			0.0823516i
$304$	4.20234			0.241021
$305$	30.1129	+	5.99020i	1.72426	+	0.342998i
$306$	−20.8205			−1.19023
$307$		−	16.0425i		−	0.915593i	−0.889057	−	0.457796i	$-0.848639\pi$
$307$		−	16.0425i		−	0.915593i	0.889057	−	0.457796i	$-0.151361\pi$
$308$		−	0.316535i		−	0.0180362i
$309$	1.12495			0.0639964
$310$	−5.42672	+	27.2802i	−0.308217	+	1.54941i
$311$	14.9546			0.847999			0.424000	−	0.905662i	$-0.360626\pi$
$311$	14.9546			0.847999			0.424000	+	0.905662i	$0.360626\pi$
$312$			0.858436i			0.0485994i
$313$		−	34.3903i		−	1.94385i	−0.235282	−	0.971927i	$-0.575601\pi$
$313$		−	34.3903i		−	1.94385i	0.235282	−	0.971927i	$-0.424399\pi$
$314$	−28.8198			−1.62640
$315$	3.86788	−	19.4439i	0.217930	−	1.09554i
$316$	1.77597			0.0999061
$317$		−	7.59079i		−	0.426341i	−0.977015	−	0.213171i	$-0.931621\pi$
$317$		−	7.59079i		−	0.426341i	0.977015	−	0.213171i	$-0.0683790\pi$
$318$		−	0.314536i		−	0.0176383i
$319$	−2.19295			−0.122782
$320$	16.5096	+	3.28417i	0.922916	+	0.183591i
$321$	0.153380			0.00856081
$322$		−	24.4831i		−	1.36439i
$323$		−	4.79134i		−	0.266597i
$324$	−0.955931			−0.0531073
$325$	7.55509	−	18.2384i	0.419081	−	1.01168i
$326$	0.0315179			0.00174561
$327$			0.859332i			0.0475212i
$328$			15.9084i			0.878393i
$329$	−10.1898			−0.561783
$330$	0.251874	+	0.0501041i	0.0138652	+	0.00275814i
$331$	−28.0896			−1.54395			−0.771973	−	0.635655i	$-0.780730\pi$
$331$	−28.0896			−1.54395			−0.771973	+	0.635655i	$0.780730\pi$
$332$			1.05833i			0.0580832i
$333$			20.0672i			1.09968i
$334$	2.45383			0.134268
$335$	4.42816	−	22.2605i	0.241936	−	1.21622i
$336$	0.984711			0.0537204
$337$		−	20.8306i		−	1.13472i	−0.823472	−	0.567358i	$-0.807966\pi$
$337$		−	20.8306i		−	1.13472i	0.823472	−	0.567358i	$-0.192034\pi$
$338$		−	3.75750i		−	0.204381i
$339$	−1.27978			−0.0695081
$340$	−0.223416	+	1.12312i	−0.0121164	+	0.0609095i
$341$	−8.56978			−0.464080
$342$		−	4.34544i		−	0.234975i
$343$			15.4872i			0.836232i
$344$	32.6120			1.75832
$345$	0.988321	+	0.196602i	0.0532094	+	0.0105847i
$346$	35.0516			1.88438
$347$			14.9351i			0.801760i	0.916130	+	0.400880i	$0.131296\pi$
$347$			14.9351i			0.801760i	−0.916130	+	0.400880i	$0.868704\pi$
$348$			0.0185458i			0.000994157i
$349$	−36.0679			−1.93067			−0.965335	−	0.261013i	$-0.915943\pi$
$349$	−36.0679			−1.93067			−0.965335	+	0.261013i	$0.915943\pi$
$350$	−19.8570	−	8.22559i	−1.06140	−	0.439676i
$351$	1.87244			0.0999435
$352$		−	0.603987i		−	0.0321926i
$353$			28.0400i			1.49242i	0.665713	+	0.746208i	$0.268128\pi$
$353$			28.0400i			1.49242i	−0.665713	+	0.746208i	$0.731872\pi$
$354$	−0.215559			−0.0114568
$355$	12.2705	+	2.44092i	0.651253	+	0.129550i
$356$	−0.139865			−0.00741284
$357$		−	1.12273i		−	0.0594210i
$358$		−	6.95811i		−	0.367747i
$359$	−1.28132			−0.0676256			−0.0338128	−	0.999428i	$-0.510765\pi$
$359$	−1.28132			−0.0676256			−0.0338128	+	0.999428i	$0.510765\pi$
$360$	3.58888	−	18.0414i	0.189150	−	0.950864i
$361$	1.00000			0.0526316
$362$			21.3214i			1.12063i
$363$			0.0791235i			0.00415291i
$364$	−1.24976			−0.0655051
$365$	1.62805	−	8.18422i	0.0852158	−	0.428382i
$366$	1.57696			0.0824289
$367$		−	2.01037i		−	0.104940i	−0.998622	−	0.0524702i	$-0.983291\pi$
$367$		−	2.01037i		−	0.104940i	0.998622	−	0.0524702i	$-0.0167095\pi$
$368$		−	23.9346i		−	1.24768i
$369$	17.3317			0.902254
$370$	21.3379	+	4.24464i	1.10930	+	0.220668i
$371$	−8.11067			−0.421085
$372$			0.0724745i			0.00375763i
$373$		−	2.59241i		−	0.134230i	−0.997745	−	0.0671150i	$-0.978621\pi$
$373$		−	2.59241i		−	0.134230i	0.997745	−	0.0671150i	$-0.0213794\pi$
$374$	−6.95468			−0.359618
$375$	0.491500	−	0.735523i	0.0253809	−	0.0379823i
$376$	−9.45480			−0.487594
$377$			8.65833i			0.445926i
$378$		−	2.03862i		−	0.104855i
$379$	−14.3543			−0.737330			−0.368665	−	0.929562i	$-0.620185\pi$
$379$	−14.3543			−0.737330			−0.368665	+	0.929562i	$0.620185\pi$
$380$	−0.234405	−	0.0466291i	−0.0120247	−	0.00239202i
$381$	1.03123			0.0528313
$382$			36.6523i			1.87529i
$383$		−	8.17879i		−	0.417917i	−0.977925	−	0.208958i	$-0.932993\pi$
$383$		−	8.17879i		−	0.417917i	0.977925	−	0.208958i	$-0.0670073\pi$
$384$	0.960159			0.0489979
$385$	1.29199	−	6.49486i	0.0658458	−	0.331008i
$386$	−5.25706			−0.267577
$387$		−	35.5298i		−	1.80608i
$388$		−	1.05311i		−	0.0534634i
$389$	19.7560			1.00167			0.500833	−	0.865544i	$-0.333027\pi$
$389$	19.7560			1.00167			0.500833	+	0.865544i	$0.333027\pi$
$390$	0.197823	−	0.994462i	0.0100172	−	0.0503566i
$391$	−27.2892			−1.38008
$392$		−	4.86505i		−	0.245722i
$393$			1.09599i			0.0552854i
$394$	−10.9037			−0.549321
$395$	36.4405	+	7.24892i	1.83352	+	0.364733i
$396$	−0.319981			−0.0160796
$397$			12.6658i			0.635678i	0.948145	+	0.317839i	$0.102957\pi$
$397$			12.6658i			0.635678i	−0.948145	+	0.317839i	$0.897043\pi$
$398$		−	5.64661i		−	0.283039i
$399$	0.234324			0.0117309
$400$	−19.4121	−	8.04130i	−0.970605	−	0.402065i
$401$	−36.6271			−1.82907			−0.914534	−	0.404509i	$-0.867442\pi$
$401$	−36.6271			−1.82907			−0.914534	+	0.404509i	$0.867442\pi$
$402$		−	1.16574i		−	0.0581419i
$403$			33.8357i			1.68547i
$404$	−1.93641			−0.0963400
$405$	−19.6144	−	3.90179i	−0.974647	−	0.193882i
$406$	9.42673			0.467841
$407$			6.70306i			0.332258i
$408$		−	1.04174i		−	0.0515739i
$409$	8.99494			0.444771			0.222386	−	0.974959i	$-0.428616\pi$
$409$	8.99494			0.444771			0.222386	+	0.974959i	$0.428616\pi$
$410$	3.66603	−	18.4292i	0.181052	−	0.910153i
$411$	−0.623133			−0.0307369
$412$			1.51963i			0.0748669i
$413$			5.55843i			0.273513i
$414$	−24.7496			−1.21638
$415$	−4.31974	+	21.7154i	−0.212048	+	1.06597i
$416$	−2.38469			−0.116919
$417$			1.48184i			0.0725659i
$418$		−	1.45151i		−	0.0709957i
$419$	−27.2758			−1.33251			−0.666254	−	0.745725i	$-0.732103\pi$
$419$	−27.2758			−1.33251			−0.666254	+	0.745725i	$0.732103\pi$
$420$	−0.0549268	−	0.0109263i	−0.00268016	−	0.000533150i
$421$	33.0585			1.61117			0.805587	−	0.592477i	$-0.201850\pi$
$421$	33.0585			1.61117			0.805587	+	0.592477i	$0.201850\pi$
$422$			4.66873i			0.227270i
$423$			10.3008i			0.500840i
$424$	−7.52563			−0.365477
$425$	−9.16836	+	22.1329i	−0.444731	+	1.07360i
$426$	0.642586			0.0311334
$427$		−	40.6636i		−	1.96785i
$428$			0.207191i			0.0100150i
$429$	0.312399			0.0150828
$430$	−37.7796	−	7.51531i	−1.82189	−	0.362420i
$431$	−13.7567			−0.662635			−0.331317	−	0.943519i	$-0.607493\pi$
$431$	−13.7567			−0.662635			−0.331317	+	0.943519i	$0.607493\pi$
$432$		−	1.99294i		−	0.0958855i
$433$			16.8098i			0.807828i	0.914797	+	0.403914i	$0.132350\pi$
$433$			16.8098i			0.807828i	−0.914797	+	0.403914i	$0.867650\pi$
$434$	36.8385			1.76830
$435$	−0.0756976	+	0.380533i	−0.00362942	+	0.0182452i
$436$	−1.16082			−0.0555932
$437$		−	5.69554i		−	0.272454i
$438$		−	0.428593i		−	0.0204790i
$439$	6.24019			0.297828			0.148914	−	0.988850i	$-0.452422\pi$
$439$	6.24019			0.297828			0.148914	+	0.988850i	$0.452422\pi$
$440$	1.19879	−	6.02637i	0.0571503	−	0.287296i
$441$	−5.30034			−0.252397
$442$			27.4588i			1.30608i
$443$			24.8505i			1.18068i	0.807154	+	0.590341i	$0.201007\pi$
$443$			24.8505i			1.18068i	−0.807154	+	0.590341i	$0.798993\pi$
$444$	0.0566877			0.00269028
$445$	−2.86984	−	0.570883i	−0.136044	−	0.0270624i
$446$	15.2283			0.721081
$447$			0.417955i			0.0197686i
$448$		−	22.2941i		−	1.05330i
$449$	0.426567			0.0201309			0.0100655	−	0.999949i	$-0.496796\pi$
$449$	0.426567			0.0201309			0.0100655	+	0.999949i	$0.496796\pi$
$450$	−8.31513	+	20.0731i	−0.391979	+	0.946257i
$451$	5.78933			0.272609
$452$		−	1.72878i		−	0.0813148i
$453$			1.22436i			0.0575255i
$454$	1.15907			0.0543976
$455$	−25.6433	−	5.10109i	−1.20218	−	0.239143i
$456$	0.217422			0.0101817
$457$		−	17.3831i		−	0.813146i	−0.913618	−	0.406573i	$-0.866724\pi$
$457$		−	17.3831i		−	0.813146i	0.913618	−	0.406573i	$-0.133276\pi$
$458$			23.7109i			1.10794i
$459$	−2.27227			−0.106061
$460$	−0.265578	+	1.33506i	−0.0123826	+	0.0622477i
$461$	−24.8094			−1.15549			−0.577745	−	0.816218i	$-0.696067\pi$
$461$	−24.8094			−1.15549			−0.577745	+	0.816218i	$0.696067\pi$
$462$		−	0.340124i		−	0.0158240i
$463$		−	7.55986i		−	0.351337i	−0.984449	−	0.175668i	$-0.943791\pi$
$463$		−	7.55986i		−	0.351337i	0.984449	−	0.175668i	$-0.0562086\pi$
$464$	9.21554			0.427821
$465$	−0.295817	+	1.48708i	−0.0137182	+	0.0689615i
$466$	−21.6543			−1.00312
$467$		−	11.6238i		−	0.537884i	−0.963156	−	0.268942i	$-0.913326\pi$
$467$		−	11.6238i		−	0.537884i	0.963156	−	0.268942i	$-0.0866740\pi$
$468$			1.26336i			0.0583990i
$469$	−30.0599			−1.38804
$470$	10.9530	+	2.17882i	0.505224	+	0.100502i
$471$	−1.57100			−0.0723879
$472$			5.15749i			0.237393i
$473$		−	11.8680i		−	0.545694i
$474$	1.90832			0.0876522
$475$	−4.61935	−	1.91353i	−0.211950	−	0.0877987i
$476$	1.51662			0.0695143
$477$			8.19897i			0.375405i
$478$			34.1614i			1.56250i
$479$	−25.9454			−1.18548			−0.592739	−	0.805395i	$-0.701953\pi$
$479$	−25.9454			−1.18548			−0.592739	+	0.805395i	$0.701953\pi$
$480$	−0.104807	−	0.0208487i	−0.00478377	−	0.000951611i
$481$	26.4654			1.20672
$482$			35.9815i			1.63891i
$483$		−	1.33460i		−	0.0607265i
$484$	−0.106883			−0.00485833
$485$	4.29843	−	21.6083i	0.195182	−	0.981183i
$486$	−3.09229			−0.140269
$487$		−	8.22122i		−	0.372539i	−0.982499	−	0.186270i	$-0.940360\pi$
$487$		−	8.22122i		−	0.372539i	0.982499	−	0.186270i	$-0.0596398\pi$
$488$		−	37.7305i		−	1.70798i
$489$	0.00171808			7.76941e−5
$490$	−1.12113	+	5.63596i	−0.0506476	+	0.254607i
$491$	8.68356			0.391884			0.195942	−	0.980616i	$-0.437224\pi$
$491$	8.68356			0.391884			0.195942	+	0.980616i	$0.437224\pi$
$492$		−	0.0489602i		−	0.00220730i
$493$		−	10.5072i		−	0.473219i
$494$	−5.73093			−0.257847
$495$	−6.56556	−	1.30605i	−0.295100	−	0.0587028i
$496$	36.0132			1.61704
$497$		−	16.5698i		−	0.743257i
$498$			1.13720i			0.0509591i
$499$	22.3175			0.999068			0.499534	−	0.866294i	$-0.333505\pi$
$499$	22.3175			0.999068			0.499534	+	0.866294i	$0.333505\pi$
$500$	0.993575	+	0.663937i	0.0444340	+	0.0296922i
$501$	0.133761			0.00597601
$502$		−	8.43549i		−	0.376494i
$503$			18.6767i			0.832754i	0.909192	+	0.416377i	$0.136700\pi$
$503$			18.6767i			0.832754i	−0.909192	+	0.416377i	$0.863300\pi$
$504$	−24.3626			−1.08520
$505$	−39.7325	−	7.90378i	−1.76807	−	0.351714i
$506$	−8.26713			−0.367519
$507$		−	0.204826i		−	0.00909662i
$508$			1.39302i			0.0618053i
$509$	27.7521			1.23009			0.615045	−	0.788492i	$-0.289138\pi$
$509$	27.7521			1.23009			0.615045	+	0.788492i	$0.289138\pi$
$510$	−0.240065	+	1.20681i	−0.0106303	+	0.0534386i
$511$	−11.0518			−0.488901
$512$		−	20.5569i		−	0.908495i
$513$		−	0.474246i		−	0.0209385i
$514$	38.9472			1.71789
$515$	−6.20263	+	31.1808i	−0.273321	+	1.37399i
$516$	−0.100368			−0.00441845
$517$			3.44076i			0.151325i
$518$		−	28.8141i		−	1.26602i
$519$	1.91070			0.0838704
$520$	−23.7936	−	4.73314i	−1.04342	−	0.207562i
$521$	−10.3834			−0.454905			−0.227452	−	0.973789i	$-0.573040\pi$
$521$	−10.3834			−0.454905			−0.227452	+	0.973789i	$0.573040\pi$
$522$		−	9.52936i		−	0.417089i
$523$		−	22.1998i		−	0.970729i	−0.874312	−	0.485365i	$-0.838687\pi$
$523$		−	22.1998i		−	0.970729i	0.874312	−	0.485365i	$-0.161313\pi$
$524$	−1.48051			−0.0646763
$525$	−1.08243	−	0.448386i	−0.0472409	−	0.0195692i
$526$	−35.5855			−1.55160
$527$		−	41.0607i		−	1.78863i
$528$		−	0.332504i		−	0.0144704i
$529$	−9.43914			−0.410398
$530$	8.71813	+	1.73425i	0.378691	+	0.0753311i
$531$	5.61895			0.243842
$532$			0.316535i			0.0137235i
$533$		−	22.8577i		−	0.990078i
$534$	−0.150289			−0.00650362
$535$	−0.845686	+	4.25128i	−0.0365622	+	0.183799i
$536$	−27.8916			−1.20474
$537$		−	0.379294i		−	0.0163678i
$538$		−	21.8772i		−	0.943191i
$539$	−1.77048			−0.0762598
$540$	−0.0221136	+	0.111166i	−0.000951619	+	0.00478381i
$541$	37.8116			1.62565			0.812824	−	0.582510i	$-0.197929\pi$
$541$	37.8116			1.62565			0.812824	+	0.582510i	$0.197929\pi$
$542$		−	26.6436i		−	1.14444i
$543$			1.16226i			0.0498772i
$544$	2.89390			0.124075
$545$	−23.8184	−	4.73808i	−1.02027	−	0.202957i
$546$	−1.34290			−0.0574706
$547$			11.2780i			0.482212i	0.970499	+	0.241106i	$0.0775101\pi$
$547$			11.2780i			0.482212i	−0.970499	+	0.241106i	$0.922490\pi$
$548$		−	0.841753i		−	0.0359579i
$549$	−41.1063			−1.75437
$550$	−2.77751	+	6.70504i	−0.118433	+	0.285904i
$551$	2.19295			0.0934229
$552$		−	1.23833i		−	0.0527070i
$553$		−	49.2082i		−	2.09255i
$554$	16.1608			0.686606
$555$	1.16315	+	0.231380i	0.0493731	+	0.00982154i
$556$	−2.00173			−0.0848921
$557$		−	7.20468i		−	0.305272i	−0.988282	−	0.152636i	$-0.951224\pi$
$557$		−	7.20468i		−	0.305272i	0.988282	−	0.152636i	$-0.0487763\pi$
$558$		−	37.2395i		−	1.57647i
$559$	−46.8580			−1.98188
$560$	−5.42938	+	27.2936i	−0.229433	+	1.15337i
$561$	−0.379107			−0.0160059
$562$			4.74073i			0.199976i
$563$		−	1.81101i		−	0.0763248i	−0.999272	−	0.0381624i	$-0.987850\pi$
$563$		−	1.81101i		−	0.0763248i	0.999272	−	0.0381624i	$-0.0121504\pi$
$564$	0.0290985			0.00122527
$565$	7.05629	−	35.4721i	0.296860	−	1.49232i
$566$	36.3781			1.52908
$567$			26.4867i			1.11234i
$568$		−	15.3746i		−	0.645103i
$569$	−12.4854			−0.523415			−0.261707	−	0.965147i	$-0.584286\pi$
$569$	−12.4854			−0.523415			−0.261707	+	0.965147i	$0.584286\pi$
$570$	−0.251874	−	0.0501041i	−0.0105498	−	0.00209863i
$571$	−37.5830			−1.57280			−0.786400	−	0.617718i	$-0.788057\pi$
$571$	−37.5830			−1.57280			−0.786400	+	0.617718i	$0.788057\pi$
$572$			0.422002i			0.0176448i
$573$			1.99796i			0.0834659i
$574$	−24.8863			−1.03873
$575$	−10.8986	+	26.3097i	−0.454502	+	1.09719i
$576$	−22.5368			−0.939035
$577$		−	7.68994i		−	0.320136i	−0.987106	−	0.160068i	$-0.948829\pi$
$577$		−	7.68994i		−	0.320136i	0.987106	−	0.160068i	$-0.0511714\pi$
$578$		−	8.64652i		−	0.359648i
$579$	−0.286568			−0.0119094
$580$	−0.514040	−	0.102255i	−0.0213443	−	0.00424592i
$581$	29.3239			1.21656
$582$		−	1.13159i		−	0.0469059i
$583$			2.73870i			0.113426i
$584$	−10.2546			−0.424337
$585$	−5.15663	+	25.9225i	−0.213200	+	1.07176i
$586$	−31.8129			−1.31418
$587$		−	8.55695i		−	0.353183i	−0.984284	−	0.176592i	$-0.943493\pi$
$587$		−	8.55695i		−	0.353183i	0.984284	−	0.176592i	$-0.0565072\pi$
$588$			0.0149729i			0.000617471i
$589$	8.56978			0.353112
$590$	1.18852	−	5.97474i	0.0489308	−	0.245976i
$591$	−0.594374			−0.0244493
$592$		−	28.1686i		−	1.15772i
$593$			17.3812i			0.713761i	0.934150	+	0.356881i	$0.116160\pi$
$593$			17.3812i			0.713761i	−0.934150	+	0.356881i	$0.883840\pi$
$594$	−0.688373			−0.0282443
$595$	31.1190	+	6.19035i	1.27576	+	0.253780i
$596$	−0.564591			−0.0231265
$597$		−	0.307803i		−	0.0125976i
$598$			32.6407i			1.33478i
$599$	15.2377			0.622594			0.311297	−	0.950313i	$-0.399237\pi$
$599$	15.2377			0.622594			0.311297	+	0.950313i	$0.399237\pi$
$600$	−1.00435	−	0.416043i	−0.0410023	−	0.0169849i
$601$	7.32582			0.298826			0.149413	−	0.988775i	$-0.452262\pi$
$601$	7.32582			0.298826			0.149413	+	0.988775i	$0.452262\pi$
$602$			51.0166i			2.07928i
$603$			30.3872i			1.23746i
$604$	−1.65392			−0.0672970
$605$	−2.19310	−	0.436262i	−0.0891621	−	0.0177366i
$606$	−2.08072			−0.0845235
$607$		−	46.8213i		−	1.90042i	−0.311615	−	0.950208i	$-0.600870\pi$
$607$		−	46.8213i		−	1.90042i	0.311615	−	0.950208i	$-0.399130\pi$
$608$			0.603987i			0.0244949i
$609$	0.513862			0.0208227
$610$	−8.69484	+	43.7092i	−0.352044	+	1.76973i
$611$	13.5850			0.549590
$612$		−	1.53313i		−	0.0619733i
$613$		−	0.581511i		−	0.0234870i	−0.999931	−	0.0117435i	$-0.996262\pi$
$613$		−	0.581511i		−	0.0234870i	0.999931	−	0.0117435i	$-0.00373816\pi$
$614$	23.2858			0.939740
$615$	0.199839	−	1.00460i	0.00805830	−	0.0405092i
$616$	−8.13784			−0.327883
$617$		−	31.3211i		−	1.26094i	−0.776214	−	0.630470i	$-0.782862\pi$
$617$		−	31.3211i		−	1.26094i	0.776214	−	0.630470i	$-0.217138\pi$
$618$			1.63288i			0.0656841i
$619$	−4.35588			−0.175078			−0.0875388	−	0.996161i	$-0.527900\pi$
$619$	−4.35588			−0.175078			−0.0875388	+	0.996161i	$0.527900\pi$
$620$	−2.00880	−	0.399601i	−0.0806755	−	0.0160484i
$621$	−2.70108			−0.108391
$622$			21.7068i			0.870364i
$623$			3.87536i			0.155263i
$624$	−1.31281			−0.0525544
$625$	17.6768	+	17.6785i	0.707073	+	0.707141i
$626$	49.9179			1.99512
$627$		−	0.0791235i		−	0.00315989i
$628$		−	2.12217i		−	0.0846839i
$629$	−32.1166			−1.28057
$630$	28.2230	+	5.61426i	1.12443	+	0.223678i
$631$	9.65769			0.384467			0.192233	−	0.981349i	$-0.438427\pi$
$631$	9.65769			0.384467			0.192233	+	0.981349i	$0.438427\pi$
$632$		−	45.6587i		−	1.81621i
$633$			0.254498i			0.0101154i
$634$	11.0181			0.437585
$635$	−5.68585	+	28.5829i	−0.225636	+	1.13428i
$636$	0.0231612			0.000918400
$637$			6.99028i			0.276965i
$638$		−	3.18309i		−	0.126020i
$639$	−16.7502			−0.662627
$640$	−5.29401	+	26.6131i	−0.209264	+	1.05197i
$641$	33.4025			1.31932			0.659661	−	0.751564i	$-0.270700\pi$
$641$	33.4025			1.31932			0.659661	+	0.751564i	$0.270700\pi$
$642$			0.222632i			0.00878659i
$643$			23.3959i			0.922646i	0.887232	+	0.461323i	$0.152625\pi$
$643$			23.3959i			0.922646i	−0.887232	+	0.461323i	$0.847375\pi$
$644$	1.80283			0.0710416
$645$	−2.05941	−	0.409668i	−0.0810892	−	0.0161307i
$646$	6.95468			0.273628
$647$			25.8707i			1.01708i	0.861038	+	0.508540i	$0.169815\pi$
$647$			25.8707i			1.01708i	−0.861038	+	0.508540i	$0.830185\pi$
$648$			24.5762i			0.965444i
$649$	1.87690			0.0736747
$650$	26.4732	+	10.9663i	1.03836	+	0.430133i
$651$	2.00811			0.0787039
$652$			0.00232085i			9.08914e-5i
$653$			9.99941i			0.391307i	0.980673	+	0.195654i	$0.0626828\pi$
$653$			9.99941i			0.391307i	−0.980673	+	0.195654i	$0.937317\pi$
$654$	−1.24733			−0.0487744
$655$	−30.3780	−	6.04294i	−1.18697	−	0.236117i
$656$	−24.3287			−0.949878
$657$			11.1721i			0.435864i
$658$		−	14.7906i		−	0.576599i
$659$	−15.8834			−0.618729			−0.309365	−	0.950944i	$-0.600116\pi$
$659$	−15.8834			−0.618729			−0.309365	+	0.950944i	$0.600116\pi$
$660$	−0.00368946	+	0.0185470i	−0.000143612	+	0.000721940i
$661$	20.4289			0.794590			0.397295	−	0.917691i	$-0.369949\pi$
$661$	20.4289			0.794590			0.397295	+	0.917691i	$0.369949\pi$
$662$		−	40.7724i		−	1.58466i
$663$			1.49681i			0.0581313i
$664$	27.2087			1.05590
$665$	−1.29199	+	6.49486i	−0.0501012	+	0.251860i
$666$	−29.1278			−1.12868
$667$		−	12.4900i		−	0.483616i
$668$			0.180690i			0.00699111i
$669$	0.830113			0.0320940
$670$	32.3113	+	6.42752i	1.24829	+	0.248317i
$671$	−13.7308			−0.530070
$672$			0.141529i			0.00545959i
$673$			8.43312i			0.325073i	0.986703	+	0.162536i	$0.0519675\pi$
$673$			8.43312i			0.325073i	−0.986703	+	0.162536i	$0.948032\pi$
$674$	30.2358			1.16464
$675$	−0.907483	+	2.19071i	−0.0349290	+	0.0843204i
$676$	0.276687			0.0106418
$677$			0.570325i			0.0219194i	0.999940	+	0.0109597i	$0.00348865\pi$
$677$			0.570325i			0.0219194i	−0.999940	+	0.0109597i	$0.996511\pi$
$678$		−	1.85761i		−	0.0713412i
$679$	−29.1793			−1.11980
$680$	28.8744	+	5.74383i	1.10728	+	0.220266i
$681$	0.0631820			0.00242114
$682$		−	12.4391i		−	0.476319i
$683$		−	15.1949i		−	0.581415i	−0.956812	−	0.290708i	$-0.906109\pi$
$683$		−	15.1949i		−	0.581415i	0.956812	−	0.290708i	$-0.0938907\pi$
$684$	0.319981			0.0122348
$685$	3.43576	−	17.2716i	0.131273	−	0.659915i
$686$	−22.4799			−0.858286
$687$			1.29251i			0.0493123i
$688$			49.8736i			1.90141i
$689$	10.8131			0.411946
$690$	−0.285370	+	1.43456i	−0.0108638	+	0.0546127i
$691$	3.49109			0.132807			0.0664036	−	0.997793i	$-0.478848\pi$
$691$	3.49109			0.132807			0.0664036	+	0.997793i	$0.478848\pi$
$692$			2.58105i			0.0981169i
$693$			8.86596i			0.336790i
$694$	−21.6785			−0.822905
$695$	−41.0727	−	8.17038i	−1.55798	−	0.309920i
$696$	0.476796			0.0180729
$697$			27.7386i			1.05068i
$698$		−	52.3529i		−	1.98159i
$699$	−1.18040			−0.0446468
$700$	0.605698	−	1.46218i	0.0228932	−	0.0552654i
$701$	2.17137			0.0820116			0.0410058	−	0.999159i	$-0.486944\pi$
$701$	2.17137			0.0820116			0.0410058	+	0.999159i	$0.486944\pi$
$702$			2.71787i			0.102579i
$703$		−	6.70306i		−	0.252811i
$704$	−7.52799			−0.283722
$705$	0.597061	+	0.118770i	0.0224866	+	0.00447315i
$706$	−40.7003			−1.53178
$707$			53.6537i			2.01785i
$708$		−	0.0158729i		−	0.000596540i
$709$	3.77213			0.141665			0.0708326	−	0.997488i	$-0.477434\pi$
$709$	3.77213			0.141665			0.0708326	+	0.997488i	$0.477434\pi$
$710$	−3.54302	+	17.8108i	−0.132967	+	0.668428i
$711$	−49.7439			−1.86554
$712$			3.59582i			0.134759i
$713$		−	48.8095i		−	1.82793i
$714$	1.62965			0.0609881
$715$	−1.72247	+	8.65890i	−0.0644167	+	0.323824i
$716$	0.512366			0.0191480
$717$			1.86217i			0.0695442i
$718$		−	1.85985i		−	0.0694091i
$719$	13.6203			0.507952			0.253976	−	0.967211i	$-0.418262\pi$
$719$	13.6203			0.507952			0.253976	+	0.967211i	$0.418262\pi$
$720$	27.5907	+	5.48849i	1.02825	+	0.204544i
$721$	42.1057			1.56810
$722$			1.45151i			0.0540196i
$723$			1.96139i			0.0729449i
$724$	−1.57002			−0.0583494
$725$	−10.1300	−	4.19628i	−0.376219	−	0.155846i
$726$	−0.114849			−0.00426243
$727$		−	1.60527i		−	0.0595361i	−0.999557	−	0.0297681i	$-0.990523\pi$
$727$		−	1.60527i		−	0.0595361i	0.999557	−	0.0297681i	$-0.00947687\pi$
$728$			32.1302i			1.19083i
$729$	26.6625			0.987501
$730$	11.8795	+	2.36313i	0.439680	+	0.0874632i
$731$	56.8638			2.10318
$732$			0.116121i			0.00429194i
$733$			21.6583i			0.799968i	0.916522	+	0.399984i	$0.130984\pi$
$733$			21.6583i			0.799968i	−0.916522	+	0.399984i	$0.869016\pi$
$734$	2.91807			0.107708
$735$	−0.0611143	+	0.307223i	−0.00225423	+	0.0113321i
$736$	3.44003			0.126801
$737$			10.1502i			0.373889i
$738$			25.1572i			0.926050i
$739$	6.77955			0.249390			0.124695	−	0.992195i	$-0.460205\pi$
$739$	6.77955			0.249390			0.124695	+	0.992195i	$0.460205\pi$
$740$	−0.312558	+	1.57123i	−0.0114898	+	0.0577597i
$741$	−0.312399			−0.0114763
$742$		−	11.7727i		−	0.432190i
$743$			26.6272i			0.976857i	0.872604	+	0.488429i	$0.162430\pi$
$743$			26.6272i			0.976857i	−0.872604	+	0.488429i	$0.837570\pi$
$744$	1.86326			0.0683104
$745$	−11.5846	−	2.30447i	−0.424428	−	0.0844293i
$746$	3.76291			0.137770
$747$		−	29.6431i		−	1.08459i
$748$		−	0.512114i		−	0.0187247i
$749$	5.74082			0.209765
$750$	1.06762	+	0.713417i	0.0389840	+	0.0260503i
$751$	32.6441			1.19120			0.595600	−	0.803281i	$-0.296914\pi$
$751$	32.6441			1.19120			0.595600	+	0.803281i	$0.296914\pi$
$752$		−	14.4593i		−	0.527275i
$753$		−	0.459828i		−	0.0167571i
$754$	−12.5677			−0.457687
$755$	−33.9361	−	6.75074i	−1.23506	−	0.245685i
$756$	0.150115			0.00545964
$757$			0.751499i			0.0273137i	0.999907	+	0.0136569i	$0.00434725\pi$
$757$			0.751499i			0.0273137i	−0.999907	+	0.0136569i	$0.995653\pi$
$758$		−	20.8354i		−	0.756775i
$759$	−0.450651			−0.0163576
$760$	−1.19879	+	6.02637i	−0.0434848	+	0.218599i
$761$	−17.5654			−0.636746			−0.318373	−	0.947966i	$-0.603136\pi$
$761$	−17.5654			−0.636746			−0.318373	+	0.947966i	$0.603136\pi$
$762$			1.49683i			0.0542246i
$763$			32.1638i			1.16441i
$764$	−2.69892			−0.0976435
$765$	6.25774	−	31.4578i	0.226249	−	1.13736i
$766$	11.8716			0.428938
$767$		−	7.41047i		−	0.267576i
$768$			0.202398i			0.00730341i
$769$	35.7457			1.28902			0.644512	−	0.764595i	$-0.277061\pi$
$769$	35.7457			1.28902			0.644512	+	0.764595i	$0.277061\pi$
$770$	9.42735	+	1.87534i	0.339738	+	0.0675824i
$771$	2.12306			0.0764600
$772$		−	0.387108i		−	0.0139323i
$773$		−	14.7295i		−	0.529783i	−0.964278	−	0.264891i	$-0.914664\pi$
$773$		−	14.7295i		−	0.529783i	0.964278	−	0.264891i	$-0.0853361\pi$
$774$	51.5720			1.85372
$775$	−39.5868	−	16.3985i	−1.42200	−	0.589052i
$776$	−27.0745			−0.971919
$777$		−	1.57069i		−	0.0563482i
$778$			28.6760i			1.02808i
$779$	−5.78933			−0.207424
$780$	0.0732281	+	0.0145669i	0.00262199	+	0.000521578i
$781$	−5.59507			−0.200207
$782$		−	39.6106i		−	1.41647i
$783$		−	1.04000i		−	0.0371665i
$784$	7.44014			0.265719
$785$	8.66200	−	43.5441i	0.309160	−	1.55415i
$786$	−1.59084			−0.0567434
$787$			40.2297i			1.43403i	0.697056	+	0.717016i	$0.254493\pi$
$787$			40.2297i			1.43403i	−0.697056	+	0.717016i	$0.745507\pi$
$788$		−	0.802904i		−	0.0286023i
$789$	−1.93980			−0.0690589
$790$	−10.5219	+	52.8937i	−0.374352	+	1.88187i
$791$	−47.9006			−1.70315
$792$			8.22643i			0.292314i
$793$			54.2125i			1.92514i
$794$	−18.3845			−0.652442
$795$	0.475235	+	0.0945361i	0.0168549	+	0.00335285i
$796$	0.415793			0.0147374
$797$		−	4.53756i		−	0.160729i	−0.996766	−	0.0803643i	$-0.974392\pi$
$797$		−	4.53756i		−	0.160729i	0.996766	−	0.0803643i	$-0.0256084\pi$
$798$			0.340124i			0.0120403i
$799$	−16.4859			−0.583228
$800$	1.15575	−	2.79003i	0.0408618	−	0.0986423i
$801$	3.91755			0.138420
$802$		−	53.1646i		−	1.87731i
$803$			3.73181i			0.131693i
$804$	0.0858404			0.00302736
$805$	36.9917	+	7.35857i	1.30379	+	0.259355i
$806$	−49.1128			−1.72992
$807$		−	1.19255i		−	0.0419797i
$808$			49.7835i			1.75138i
$809$	−1.86885			−0.0657052			−0.0328526	−	0.999460i	$-0.510459\pi$
$809$	−1.86885			−0.0657052			−0.0328526	+	0.999460i	$0.510459\pi$
$810$	5.66349	−	28.4705i	0.198995	−	1.00035i
$811$	26.5983			0.933994			0.466997	−	0.884259i	$-0.345336\pi$
$811$	26.5983			0.933994			0.466997	+	0.884259i	$0.345336\pi$
$812$			0.694145i			0.0243597i
$813$		−	1.45237i		−	0.0509370i
$814$	−9.72957			−0.341021
$815$	−0.00947292	+	0.0476206i	−0.000331822	+	0.00166808i
$816$	1.59314			0.0557710
$817$			11.8680i			0.415211i
$818$			13.0563i			0.456501i
$819$	35.0050			1.22317
$820$	1.35705	+	0.269951i	0.0473902	+	0.00942710i
$821$	11.4661			0.400171			0.200086	−	0.979778i	$-0.435878\pi$
$821$	11.4661			0.400171			0.200086	+	0.979778i	$0.435878\pi$
$822$		−	0.904484i		−	0.0315475i
$823$			13.8917i			0.484233i	0.970247	+	0.242117i	$0.0778417\pi$
$823$			13.8917i			0.484233i	−0.970247	+	0.242117i	$0.922158\pi$
$824$	39.0685			1.36102
$825$	−0.151405	+	0.365499i	−0.00527125	+	0.0127251i
$826$	−8.06813			−0.280726
$827$		−	53.0943i		−	1.84627i	−0.384478	−	0.923134i	$-0.625618\pi$
$827$		−	53.0943i		−	1.84627i	0.384478	−	0.923134i	$-0.374382\pi$
$828$		−	1.82246i		−	0.0633349i
$829$	0.910926			0.0316378			0.0158189	−	0.999875i	$-0.494964\pi$
$829$	0.910926			0.0316378			0.0158189	+	0.999875i	$0.494964\pi$
$830$	−31.5202	−	6.27015i	−1.09408	−	0.217640i
$831$	0.880944			0.0305596
$832$			29.7224i			1.03044i
$833$		−	8.48294i		−	0.293917i
$834$	−2.15090			−0.0744797
$835$	−0.737516	+	3.70751i	−0.0255228	+	0.128304i
$836$	0.106883			0.00369663
$837$		−	4.06418i		−	0.140479i
$838$		−	39.5911i		−	1.36765i
$839$	45.6602			1.57636			0.788182	−	0.615442i	$-0.211023\pi$
$839$	45.6602			1.57636			0.788182	+	0.615442i	$0.211023\pi$
$840$	−0.280907	+	1.41212i	−0.00969220	+	0.0487229i
$841$	−24.1910			−0.834171
$842$			47.9848i			1.65367i
$843$			0.258423i			0.00890056i
$844$	−0.343786			−0.0118336
$845$	5.67723	+	1.12934i	0.195303	+	0.0388506i
$846$	−14.9517			−0.514048
$847$			2.96150i			0.101758i
$848$		−	11.5090i		−	0.395220i
$849$	1.98301			0.0680567
$850$	−32.1261	−	13.3080i	−1.10192	−	0.456460i
$851$	−38.1775			−1.30871
$852$			0.0473174i			0.00162107i
$853$		−	15.5961i		−	0.534001i	−0.963696	−	0.267000i	$-0.913967\pi$
$853$		−	15.5961i		−	0.534001i	0.963696	−	0.267000i	$-0.0860325\pi$
$854$	59.0237			2.01975
$855$	6.56556	+	1.30605i	0.224537	+	0.0446661i
$856$	5.32672			0.182063
$857$			3.21516i			0.109828i	0.998491	+	0.0549138i	$0.0174884\pi$
$857$			3.21516i			0.109828i	−0.998491	+	0.0549138i	$0.982512\pi$
$858$			0.453451i			0.0154806i
$859$	−20.1995			−0.689198			−0.344599	−	0.938750i	$-0.611985\pi$
$859$	−20.1995			−0.689198			−0.344599	+	0.938750i	$0.611985\pi$
$860$	0.553396	−	2.78193i	0.0188706	−	0.0948632i
$861$	−1.35658			−0.0462321
$862$		−	19.9679i		−	0.680111i
$863$		−	3.58013i		−	0.121869i	−0.998142	−	0.0609345i	$-0.980592\pi$
$863$		−	3.58013i		−	0.121869i	0.998142	−	0.0609345i	$-0.0194081\pi$
$864$	0.286438			0.00974482
$865$	−10.5350	+	52.9596i	−0.358200	+	1.80068i
$866$	−24.3996			−0.829133
$867$		−	0.471332i		−	0.0160073i
$868$			2.71263i			0.0920728i
$869$	−16.6160			−0.563659
$870$	−0.552348	−	0.109876i	−0.0187264	−	0.00372514i
$871$	40.0757			1.35791
$872$			29.8437i			1.01064i
$873$			29.4970i			0.998321i
$874$	8.26713			0.279640
$875$	18.3962	−	27.5298i	0.621906	−	0.930676i
$876$	0.0315598			0.00106631
$877$		−	1.12880i		−	0.0381169i	−0.999818	−	0.0190585i	$-0.993933\pi$
$877$		−	1.12880i		−	0.0381169i	0.999818	−	0.0190585i	$-0.00606686\pi$
$878$			9.05771i			0.305683i
$879$	−1.73416			−0.0584917
$880$	9.21615	+	1.83332i	0.310676	+	0.0618012i
$881$	−9.42205			−0.317437			−0.158719	−	0.987324i	$-0.550736\pi$
$881$	−9.42205			−0.317437			−0.158719	+	0.987324i	$0.550736\pi$
$882$		−	7.69350i		−	0.259054i
$883$		−	33.9568i		−	1.14274i	−0.820694	−	0.571368i	$-0.806413\pi$
$883$		−	33.9568i		−	1.14274i	0.820694	−	0.571368i	$-0.193587\pi$
$884$	−2.02195			−0.0680056
$885$	0.0647879	−	0.325690i	0.00217782	−	0.0109479i
$886$	−36.0708			−1.21182
$887$		−	23.9547i		−	0.804321i	−0.915569	−	0.402161i	$-0.868259\pi$
$887$		−	23.9547i		−	0.804321i	0.915569	−	0.402161i	$-0.131741\pi$
$888$		−	1.45739i		−	0.0489069i
$889$	38.5975			1.29452
$890$	0.828643	−	4.16561i	0.0277762	−	0.139631i
$891$	8.94369			0.299625
$892$			1.12135i			0.0375456i
$893$		−	3.44076i		−	0.115141i
$894$	−0.606666			−0.0202900
$895$	10.5130	+	2.09131i	0.351412	+	0.0699047i
$896$	35.9376			1.20059
$897$			1.77928i			0.0594085i
$898$			0.619167i			0.0206619i
$899$	18.7931			0.626786
$900$	−1.47810	−	0.612292i	−0.0492701	−	0.0204097i
$901$	−13.1221			−0.437159
$902$			8.40327i			0.279798i
$903$			2.78097i			0.0925449i
$904$	−44.4454			−1.47823
$905$	−32.2147	−	6.40831i	−1.07085	−	0.213019i
$906$	−1.77717			−0.0590427
$907$			20.1340i			0.668538i	0.942478	+	0.334269i	$0.108489\pi$
$907$			20.1340i			0.668538i	−0.942478	+	0.334269i	$0.891511\pi$
$908$			0.0853488i			0.00283240i
$909$	54.2378			1.79895
$910$	7.40429	−	37.2215i	0.245450	−	1.23388i
$911$	−51.7375			−1.71414			−0.857070	−	0.515201i	$-0.827717\pi$
$911$	−51.7375			−1.71414			−0.857070	+	0.515201i	$0.827717\pi$
$912$			0.332504i			0.0110103i
$913$		−	9.90171i		−	0.327699i
$914$	25.2317			0.834591
$915$	−0.473966	+	2.38264i	−0.0156688	+	0.0787675i
$916$	−1.74598			−0.0576886
$917$			41.0216i			1.35465i
$918$		−	3.29823i		−	0.108858i
$919$	−19.5840			−0.646017			−0.323009	−	0.946396i	$-0.604694\pi$
$919$	−19.5840			−0.646017			−0.323009	+	0.946396i	$0.604694\pi$
$920$	34.3234	+	6.82778i	1.13161	+	0.225105i
$921$	1.26934			0.0418261
$922$		−	36.0111i		−	1.18596i
$923$			22.0907i			0.727126i
$924$	0.0250453			0.000823931
$925$	−12.8265	+	30.9638i	−0.421733	+	1.01808i
$926$	10.9732			0.360602
$927$		−	42.5640i		−	1.39799i
$928$			1.32451i			0.0434793i
$929$	26.0616			0.855055			0.427527	−	0.904002i	$-0.359385\pi$
$929$	26.0616			0.855055			0.427527	+	0.904002i	$0.359385\pi$
$930$	−2.15851	−	0.429381i	−0.0707802	−	0.0140800i
$931$	1.77048			0.0580250
$932$		−	1.59453i		−	0.0522307i
$933$			1.18326i			0.0387383i
$934$	16.8720			0.552069
$935$	2.09028	−	10.5079i	0.0683594	−	0.343644i
$936$	32.4800			1.06164
$937$			37.3846i			1.22130i	0.791900	+	0.610650i	$0.209092\pi$
$937$			37.3846i			1.22130i	−0.791900	+	0.610650i	$0.790908\pi$
$938$		−	43.6323i		−	1.42465i
$939$	2.72108			0.0887991
$940$	−0.160440	+	0.806534i	−0.00523296	+	0.0263062i
$941$	−33.0380			−1.07701			−0.538504	−	0.842623i	$-0.681010\pi$
$941$	−33.0380			−1.07701			−0.538504	+	0.842623i	$0.681010\pi$
$942$		−	2.28033i		−	0.0742970i
$943$			32.9733i			1.07376i
$944$	−7.88737			−0.256712
$945$	3.08016	+	0.612720i	0.100198	+	0.0199318i
$946$	17.2266			0.560085
$947$			47.6863i			1.54960i	0.632208	+	0.774799i	$0.282149\pi$
$947$			47.6863i			1.54960i	−0.632208	+	0.774799i	$0.717851\pi$
$948$			0.140521i			0.00456391i
$949$	14.7341			0.478290
$950$	2.77751	−	6.70504i	0.0901142	−	0.217540i
$951$	0.600610			0.0194761
$952$		−	38.9911i		−	1.26371i
$953$		−	22.0635i		−	0.714708i	−0.933969	−	0.357354i	$-0.883679\pi$
$953$		−	22.0635i		−	0.714708i	0.933969	−	0.357354i	$-0.116321\pi$
$954$	−11.9009			−0.385306
$955$	−55.3782	−	11.0161i	−1.79199	−	0.356472i
$956$	−2.51550			−0.0813571
$957$		−	0.173514i		−	0.00560892i
$958$		−	37.6601i		−	1.21674i
$959$	−23.3231			−0.753143
$960$	−0.259855	+	1.30630i	−0.00838680	+	0.0421606i
$961$	42.4412			1.36907
$962$			38.4148i			1.23854i
$963$		−	5.80331i		−	0.187009i
$964$	−2.64953			−0.0853355
$965$	1.58005	−	7.94293i	0.0508635	−	0.255692i
$966$	1.93719			0.0623280
$967$		−	53.0016i		−	1.70442i	−0.523201	−	0.852209i	$-0.675262\pi$
$967$		−	53.0016i		−	1.70442i	0.523201	−	0.852209i	$-0.324738\pi$
$968$			2.74788i			0.0883202i
$969$	0.379107			0.0121787
$970$	31.3647	+	6.23922i	1.00706	+	0.200329i
$971$	−10.0046			−0.321062			−0.160531	−	0.987031i	$-0.551321\pi$
$971$	−10.0046			−0.321062			−0.160531	+	0.987031i	$0.551321\pi$
$972$		−	0.227703i		−	0.00730359i
$973$			55.4634i			1.77808i
$974$	11.9332			0.382364
$975$	1.44308	+	0.597785i	0.0462156	+	0.0191445i
$976$	57.7013			1.84697
$977$			0.508472i			0.0162675i	0.999967	+	0.00813373i	$0.00258908\pi$
$977$			0.508472i			0.0162675i	−0.999967	+	0.00813373i	$0.997411\pi$
$978$			0.00249381i			7.97431e-5i
$979$	1.30858			0.0418224
$980$	−0.415009	−	0.0825556i	−0.0132570	−	0.00263714i
$981$	32.5139			1.03809
$982$			12.6043i			0.402219i
$983$		−	22.0873i		−	0.704476i	−0.935910	−	0.352238i	$-0.885421\pi$
$983$		−	22.0873i		−	0.704476i	0.935910	−	0.352238i	$-0.114579\pi$
$984$	−1.25873			−0.0401267
$985$	3.27719	−	16.4745i	0.104420	−	0.524921i
$986$	15.2513			0.485700
$987$		−	0.806254i		−	0.0256634i
$988$		−	0.422002i		−	0.0134257i
$989$	67.5949			2.14939
$990$	1.89575	−	9.52998i	0.0602509	−	0.302883i
$991$	−48.5368			−1.54182			−0.770911	−	0.636943i	$-0.780199\pi$
$991$	−48.5368			−1.54182			−0.770911	+	0.636943i	$0.780199\pi$
$992$			5.17603i			0.164339i
$993$		−	2.22255i		−	0.0705305i
$994$	24.0512			0.762859
$995$	8.53151	+	1.69713i	0.270467	+	0.0538026i
$996$	−0.0837386			−0.00265336
$997$			20.4836i			0.648723i	0.945933	+	0.324362i	$0.105149\pi$
$997$			20.4836i			0.648723i	−0.945933	+	0.324362i	$0.894851\pi$
$998$			32.3941i			1.02542i
$999$	−3.17890			−0.100576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.21	yes	30
5.2	odd	4		5225.2.a.bc.1.10		30
5.3	odd	4		5225.2.a.bc.1.21		30
5.4	even	2	inner	1045.2.b.e.419.10	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.10	✓	30	5.4	even	2	inner
1045.2.b.e.419.21	yes	30	1.1	even	1	trivial
5225.2.a.bc.1.10		30	5.2	odd	4
5225.2.a.bc.1.21		30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.45151i q^{2} +0.0791235i q^{3} -0.106883 q^{4} +(-2.19310 - 0.436262i) q^{5} -0.114849 q^{6} +2.96150i q^{7} +2.74788i q^{8} +2.99374 q^{9} +(0.633239 - 3.18330i) q^{10} +1.00000 q^{11} -0.00845698i q^{12} -3.94825i q^{13} -4.29865 q^{14} +(0.0345186 - 0.173526i) q^{15} -4.20234 q^{16} +4.79134i q^{17} +4.34544i q^{18} -1.00000 q^{19} +(0.234405 + 0.0466291i) q^{20} -0.234324 q^{21} +1.45151i q^{22} +5.69554i q^{23} -0.217422 q^{24} +(4.61935 + 1.91353i) q^{25} +5.73093 q^{26} +0.474246i q^{27} -0.316535i q^{28} -2.19295 q^{29} +(0.251874 + 0.0501041i) q^{30} -8.56978 q^{31} -0.603987i q^{32} +0.0791235i q^{33} -6.95468 q^{34} +(1.29199 - 6.49486i) q^{35} -0.319981 q^{36} +6.70306i q^{37} -1.45151i q^{38} +0.312399 q^{39} +(1.19879 - 6.02637i) q^{40} +5.78933 q^{41} -0.340124i q^{42} -11.8680i q^{43} -0.106883 q^{44} +(-6.56556 - 1.30605i) q^{45} -8.26713 q^{46} +3.44076i q^{47} -0.332504i q^{48} -1.77048 q^{49} +(-2.77751 + 6.70504i) q^{50} -0.379107 q^{51} +0.422002i q^{52} +2.73870i q^{53} -0.688373 q^{54} +(-2.19310 - 0.436262i) q^{55} -8.13784 q^{56} -0.0791235i q^{57} -3.18309i q^{58} +1.87690 q^{59} +(-0.00368946 + 0.0185470i) q^{60} -13.7308 q^{61} -12.4391i q^{62} +8.86596i q^{63} -7.52799 q^{64} +(-1.72247 + 8.65890i) q^{65} -0.114849 q^{66} +10.1502i q^{67} -0.512114i q^{68} -0.450651 q^{69} +(9.42735 + 1.87534i) q^{70} -5.59507 q^{71} +8.22643i q^{72} +3.73181i q^{73} -9.72957 q^{74} +(-0.151405 + 0.365499i) q^{75} +0.106883 q^{76} +2.96150i q^{77} +0.453451i q^{78} -16.6160 q^{79} +(9.21615 + 1.83332i) q^{80} +8.94369 q^{81} +8.40327i q^{82} -9.90171i q^{83} +0.0250453 q^{84} +(2.09028 - 10.5079i) q^{85} +17.2266 q^{86} -0.173514i q^{87} +2.74788i q^{88} +1.30858 q^{89} +(1.89575 - 9.52998i) q^{90} +11.6927 q^{91} -0.608757i q^{92} -0.678071i q^{93} -4.99431 q^{94} +(2.19310 + 0.436262i) q^{95} +0.0477895 q^{96} +9.85288i q^{97} -2.56986i q^{98} +2.99374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34}+ \cdots - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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