LMFDB - Embedded newform 385.2.b.c.309.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(309,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, 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("385.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 156x^{6} + 135x^{4} + 26x^{2} + 1 $ x^12 + 14x^10 + 71x^8 + 156x^6 + 135x^4 + 26*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			309.10
Root			$1.68955i$ of defining polynomial
Character	$\chi$	$=$	385.309
Dual form			385.2.b.c.309.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68955i q^{2} +2.93524i q^{3} -0.854580 q^{4} +(-1.80653 - 1.31774i) q^{5} -4.95924 q^{6} +1.00000i q^{7} +1.93524i q^{8} -5.61566 q^{9} +O(q^{10})$	\(q+1.68955i q^{2} +2.93524i q^{3} -0.854580 q^{4} +(-1.80653 - 1.31774i) q^{5} -4.95924 q^{6} +1.00000i q^{7} +1.93524i q^{8} -5.61566 q^{9} +(2.22639 - 3.05223i) q^{10} -1.00000 q^{11} -2.50840i q^{12} -3.59605i q^{13} -1.68955 q^{14} +(3.86789 - 5.30261i) q^{15} -4.97885 q^{16} +1.75150i q^{17} -9.48794i q^{18} +1.84285 q^{19} +(1.54383 + 1.12611i) q^{20} -2.93524 q^{21} -1.68955i q^{22} +8.49424i q^{23} -5.68042 q^{24} +(1.52712 + 4.76108i) q^{25} +6.07571 q^{26} -7.67761i q^{27} -0.854580i q^{28} -4.43102 q^{29} +(8.95903 + 6.53500i) q^{30} +6.61939 q^{31} -4.54153i q^{32} -2.93524i q^{33} -2.95924 q^{34} +(1.31774 - 1.80653i) q^{35} +4.79903 q^{36} -4.91497i q^{37} +3.11359i q^{38} +10.5553 q^{39} +(2.55015 - 3.49608i) q^{40} +5.49965 q^{41} -4.95924i q^{42} +9.93310i q^{43} +0.854580 q^{44} +(10.1449 + 7.39999i) q^{45} -14.3514 q^{46} -4.65189i q^{47} -14.6142i q^{48} -1.00000 q^{49} +(-8.04409 + 2.58014i) q^{50} -5.14108 q^{51} +3.07311i q^{52} +4.76762i q^{53} +12.9717 q^{54} +(1.80653 + 1.31774i) q^{55} -1.93524 q^{56} +5.40921i q^{57} -7.48644i q^{58} +8.72384 q^{59} +(-3.30542 + 4.53151i) q^{60} -7.08196 q^{61} +11.1838i q^{62} -5.61566i q^{63} -2.28456 q^{64} +(-4.73867 + 6.49639i) q^{65} +4.95924 q^{66} -7.30384i q^{67} -1.49679i q^{68} -24.9327 q^{69} +(3.05223 + 2.22639i) q^{70} -7.93402 q^{71} -10.8677i q^{72} +16.7363i q^{73} +8.30409 q^{74} +(-13.9749 + 4.48247i) q^{75} -1.57486 q^{76} -1.00000i q^{77} +17.8337i q^{78} +6.47350 q^{79} +(8.99446 + 6.56084i) q^{80} +5.68868 q^{81} +9.29193i q^{82} +7.82170i q^{83} +2.50840 q^{84} +(2.30802 - 3.16414i) q^{85} -16.7825 q^{86} -13.0061i q^{87} -1.93524i q^{88} -9.03302 q^{89} +(-12.5027 + 17.1403i) q^{90} +3.59605 q^{91} -7.25901i q^{92} +19.4295i q^{93} +7.85959 q^{94} +(-3.32917 - 2.42840i) q^{95} +13.3305 q^{96} -10.8948i q^{97} -1.68955i q^{98} +5.61566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 6 q^{5} - 4 q^{6} - 20 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 + 6 * q^5 - 4 * q^6 - 20 * q^9	$ 12 q - 4 q^{4} + 6 q^{5} - 4 q^{6} - 20 q^{9} + 14 q^{10} - 12 q^{11} - 8 q^{15} - 12 q^{16} + 4 q^{19} - 6 q^{20} - 12 q^{21} - 44 q^{24} - 8 q^{25} + 16 q^{29} + 40 q^{30} + 8 q^{31} + 20 q^{34} + 2 q^{35} + 52 q^{36} + 16 q^{39} - 10 q^{40} + 8 q^{41} + 4 q^{44} - 2 q^{45} - 16 q^{46} - 12 q^{49} + 28 q^{50} - 8 q^{51} - 76 q^{54} - 6 q^{55} - 28 q^{59} + 16 q^{60} + 24 q^{61} + 44 q^{64} + 12 q^{65} + 4 q^{66} - 24 q^{69} + 6 q^{70} + 8 q^{71} + 16 q^{74} - 60 q^{75} - 16 q^{76} + 16 q^{79} + 22 q^{80} + 52 q^{81} + 24 q^{84} - 20 q^{85} + 24 q^{86} - 16 q^{89} - 46 q^{90} - 12 q^{91} + 20 q^{94} - 40 q^{95} - 32 q^{96} + 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 + 6 * q^5 - 4 * q^6 - 20 * q^9 + 14 * q^10 - 12 * q^11 - 8 * q^15 - 12 * q^16 + 4 * q^19 - 6 * q^20 - 12 * q^21 - 44 * q^24 - 8 * q^25 + 16 * q^29 + 40 * q^30 + 8 * q^31 + 20 * q^34 + 2 * q^35 + 52 * q^36 + 16 * q^39 - 10 * q^40 + 8 * q^41 + 4 * q^44 - 2 * q^45 - 16 * q^46 - 12 * q^49 + 28 * q^50 - 8 * q^51 - 76 * q^54 - 6 * q^55 - 28 * q^59 + 16 * q^60 + 24 * q^61 + 44 * q^64 + 12 * q^65 + 4 * q^66 - 24 * q^69 + 6 * q^70 + 8 * q^71 + 16 * q^74 - 60 * q^75 - 16 * q^76 + 16 * q^79 + 22 * q^80 + 52 * q^81 + 24 * q^84 - 20 * q^85 + 24 * q^86 - 16 * q^89 - 46 * q^90 - 12 * q^91 + 20 * q^94 - 40 * q^95 - 32 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.68955i			1.19469i	0.801983	+	0.597346i	$0.203778\pi$
$2$			1.68955i			1.19469i	−0.801983	+	0.597346i	$0.796222\pi$
$3$			2.93524i			1.69466i	0.531063	+	0.847332i	$0.321793\pi$
$3$			2.93524i			1.69466i	−0.531063	+	0.847332i	$0.678207\pi$
$4$	−0.854580			−0.427290
$5$	−1.80653	−	1.31774i	−0.807906	−	0.589312i
$5$	−1.80653	−	1.31774i	−0.807906	−	0.589312i
$6$	−4.95924			−2.02460
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.93524i			0.684212i
$9$	−5.61566			−1.87189
$10$	2.22639	−	3.05223i	0.704046	−	0.965199i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	2.50840i		−	0.724113i
$13$		−	3.59605i		−	0.997366i	−0.866785	−	0.498683i	$-0.833817\pi$
$13$		−	3.59605i		−	0.997366i	0.866785	−	0.498683i	$-0.166183\pi$
$14$	−1.68955			−0.451551
$15$	3.86789	−	5.30261i	0.998685	−	1.36913i
$16$	−4.97885			−1.24471
$17$			1.75150i			0.424801i	0.977183	+	0.212400i	$0.0681281\pi$
$17$			1.75150i			0.424801i	−0.977183	+	0.212400i	$0.931872\pi$
$18$		−	9.48794i		−	2.23633i
$19$	1.84285			0.422779			0.211389	−	0.977402i	$-0.432201\pi$
$19$	1.84285			0.422779			0.211389	+	0.977402i	$0.432201\pi$
$20$	1.54383	+	1.12611i	0.345210	+	0.251807i
$21$	−2.93524			−0.640523
$22$		−	1.68955i		−	0.360213i
$23$			8.49424i			1.77117i	0.464476	+	0.885586i	$0.346243\pi$
$23$			8.49424i			1.77117i	−0.464476	+	0.885586i	$0.653757\pi$
$24$	−5.68042			−1.15951
$25$	1.52712	+	4.76108i	0.305424	+	0.952217i
$26$	6.07571			1.19155
$27$		−	7.67761i		−	1.47756i
$28$		−	0.854580i		−	0.161500i
$29$	−4.43102			−0.822820			−0.411410	−	0.911450i	$-0.634964\pi$
$29$	−4.43102			−0.822820			−0.411410	+	0.911450i	$0.634964\pi$
$30$	8.95903	+	6.53500i	1.63569	+	1.19312i
$31$	6.61939			1.18888			0.594439	−	0.804141i	$-0.297374\pi$
$31$	6.61939			1.18888			0.594439	+	0.804141i	$0.297374\pi$
$32$		−	4.54153i		−	0.802837i
$33$		−	2.93524i		−	0.510961i
$34$	−2.95924			−0.507506
$35$	1.31774	−	1.80653i	0.222739	−	0.305360i
$36$	4.79903			0.799839
$37$		−	4.91497i		−	0.808017i	−0.914755	−	0.404008i	$-0.867617\pi$
$37$		−	4.91497i		−	0.808017i	0.914755	−	0.404008i	$-0.132383\pi$
$38$			3.11359i			0.505090i
$39$	10.5553			1.69020
$40$	2.55015	−	3.49608i	0.403214	−	0.552779i
$41$	5.49965			0.858900			0.429450	−	0.903091i	$-0.358707\pi$
$41$	5.49965			0.858900			0.429450	+	0.903091i	$0.358707\pi$
$42$		−	4.95924i		−	0.765228i
$43$			9.93310i			1.51478i	0.652961	+	0.757392i	$0.273527\pi$
$43$			9.93310i			1.51478i	−0.652961	+	0.757392i	$0.726473\pi$
$44$	0.854580			0.128833
$45$	10.1449	+	7.39999i	1.51231	+	1.10313i
$46$	−14.3514			−2.11601
$47$		−	4.65189i		−	0.678547i	−0.940688	−	0.339274i	$-0.889819\pi$
$47$		−	4.65189i		−	0.678547i	0.940688	−	0.339274i	$-0.110181\pi$
$48$		−	14.6142i		−	2.10937i
$49$	−1.00000			−0.142857
$50$	−8.04409	+	2.58014i	−1.13761	+	0.364887i
$51$	−5.14108			−0.719895
$52$			3.07311i			0.426164i
$53$			4.76762i			0.654883i	0.944872	+	0.327441i	$0.106186\pi$
$53$			4.76762i			0.654883i	−0.944872	+	0.327441i	$0.893814\pi$
$54$	12.9717			1.76523
$55$	1.80653	+	1.31774i	0.243593	+	0.177684i
$56$	−1.93524			−0.258608
$57$			5.40921i			0.716468i
$58$		−	7.48644i		−	0.983017i
$59$	8.72384			1.13575			0.567874	−	0.823116i	$-0.307766\pi$
$59$	8.72384			1.13575			0.567874	+	0.823116i	$0.307766\pi$
$60$	−3.30542	+	4.53151i	−0.426728	+	0.585015i
$61$	−7.08196			−0.906752			−0.453376	−	0.891319i	$-0.649781\pi$
$61$	−7.08196			−0.906752			−0.453376	+	0.891319i	$0.649781\pi$
$62$			11.1838i			1.42034i
$63$		−	5.61566i		−	0.707507i
$64$	−2.28456			−0.285570
$65$	−4.73867	+	6.49639i	−0.587759	+	0.805778i
$66$	4.95924			0.610441
$67$		−	7.30384i		−	0.892306i	−0.894957	−	0.446153i	$-0.852794\pi$
$67$		−	7.30384i		−	0.892306i	0.894957	−	0.446153i	$-0.147206\pi$
$68$		−	1.49679i		−	0.181513i
$69$	−24.9327			−3.00154
$70$	3.05223	+	2.22639i	0.364811	+	0.266104i
$71$	−7.93402			−0.941595			−0.470797	−	0.882241i	$-0.656034\pi$
$71$	−7.93402			−0.941595			−0.470797	+	0.882241i	$0.656034\pi$
$72$		−	10.8677i		−	1.28077i
$73$			16.7363i			1.95883i	0.201853	+	0.979416i	$0.435304\pi$
$73$			16.7363i			1.95883i	−0.201853	+	0.979416i	$0.564696\pi$
$74$	8.30409			0.965331
$75$	−13.9749	+	4.48247i	−1.61369	+	0.517591i
$76$	−1.57486			−0.180649
$77$		−	1.00000i		−	0.113961i
$78$			17.8337i			2.01927i
$79$	6.47350			0.728326			0.364163	−	0.931335i	$-0.381355\pi$
$79$	6.47350			0.728326			0.364163	+	0.931335i	$0.381355\pi$
$80$	8.99446	+	6.56084i	1.00561	+	0.733524i
$81$	5.68868			0.632075
$82$			9.29193i			1.02612i
$83$			7.82170i			0.858543i	0.903175	+	0.429272i	$0.141230\pi$
$83$			7.82170i			0.858543i	−0.903175	+	0.429272i	$0.858770\pi$
$84$	2.50840			0.273689
$85$	2.30802	−	3.16414i	0.250340	−	0.343199i
$86$	−16.7825			−1.80970
$87$		−	13.0061i		−	1.39440i
$88$		−	1.93524i		−	0.206298i
$89$	−9.03302			−0.957499			−0.478749	−	0.877952i	$-0.658910\pi$
$89$	−9.03302			−0.957499			−0.478749	+	0.877952i	$0.658910\pi$
$90$	−12.5027	+	17.1403i	−1.31790	+	1.80674i
$91$	3.59605			0.376969
$92$		−	7.25901i		−	0.756804i
$93$			19.4295i			2.01475i
$94$	7.85959			0.810655
$95$	−3.32917	−	2.42840i	−0.341565	−	0.249148i
$96$	13.3305			1.36054
$97$		−	10.8948i		−	1.10620i	−0.833116	−	0.553098i	$-0.813445\pi$
$97$		−	10.8948i		−	1.10620i	0.833116	−	0.553098i	$-0.186555\pi$
$98$		−	1.68955i		−	0.170670i
$99$	5.61566			0.564395
$100$	−1.30504	−	4.06873i	−0.130504	−	0.406873i
$101$	5.53367			0.550621			0.275310	−	0.961355i	$-0.411219\pi$
$101$	5.53367			0.550621			0.275310	+	0.961355i	$0.411219\pi$
$102$		−	8.68610i		−	0.860053i
$103$		−	11.2110i		−	1.10465i	−0.833627	−	0.552327i	$-0.813740\pi$
$103$		−	11.2110i		−	1.10465i	0.833627	−	0.552327i	$-0.186260\pi$
$104$	6.95924			0.682410
$105$	5.30261	+	3.86789i	0.517482	+	0.377468i
$106$	−8.05513			−0.782383
$107$			6.44910i			0.623458i	0.950171	+	0.311729i	$0.100908\pi$
$107$			6.44910i			0.623458i	−0.950171	+	0.311729i	$0.899092\pi$
$108$			6.56113i			0.631345i
$109$	18.9353			1.81367			0.906836	−	0.421484i	$-0.138491\pi$
$109$	18.9353			1.81367			0.906836	+	0.421484i	$0.138491\pi$
$110$	−2.22639	+	3.05223i	−0.212278	+	0.291018i
$111$	14.4267			1.36932
$112$		−	4.97885i		−	0.470457i
$113$		−	0.0174640i		−	0.00164288i	−1.00000		0.000821438i	$-0.999739\pi$
$113$		−	0.0174640i		−	0.00164288i	1.00000		0.000821438i	$-0.000261472\pi$
$114$	−9.13914			−0.855959
$115$	11.1932	−	15.3451i	1.04377	−	1.43094i
$116$	3.78666			0.351583
$117$			20.1942i			1.86696i
$118$			14.7394i			1.35687i
$119$	−1.75150			−0.160560
$120$	10.2619	+	7.48532i	0.936775	+	0.683313i
$121$	1.00000			0.0909091
$122$		−	11.9653i		−	1.08329i
$123$			16.1428i			1.45555i
$124$	−5.65680			−0.507995
$125$	3.51508	−	10.6134i	0.314399	−	0.949291i
$126$	9.48794			0.845253
$127$		−	3.81559i		−	0.338579i	−0.985566	−	0.169289i	$-0.945853\pi$
$127$		−	3.81559i		−	0.338579i	0.985566	−	0.169289i	$-0.0541473\pi$
$128$		−	12.9429i		−	1.14401i
$129$	−29.1561			−2.56705
$130$	−10.9760	−	8.00621i	−0.962656	−	0.702191i
$131$	2.39529			0.209278			0.104639	−	0.994510i	$-0.466631\pi$
$131$	2.39529			0.209278			0.104639	+	0.994510i	$0.466631\pi$
$132$			2.50840i			0.218328i
$133$			1.84285i			0.159795i
$134$	12.3402			1.06603
$135$	−10.1171	+	13.8699i	−0.870741	+	1.19373i
$136$	−3.38958			−0.290654
$137$			19.4393i			1.66081i	0.557162	+	0.830404i	$0.311890\pi$
$137$			19.4393i			1.66081i	−0.557162	+	0.830404i	$0.688110\pi$
$138$		−	42.1250i		−	3.58592i
$139$	−5.68824			−0.482470			−0.241235	−	0.970467i	$-0.577552\pi$
$139$	−5.68824			−0.482470			−0.241235	+	0.970467i	$0.577552\pi$
$140$	−1.12611	+	1.54383i	−0.0951741	+	0.130477i
$141$	13.6544			1.14991
$142$		−	13.4049i		−	1.12492i
$143$			3.59605i			0.300717i
$144$	27.9596			2.32996
$145$	8.00479	+	5.83894i	0.664761	+	0.484898i
$146$	−28.2768			−2.34020
$147$		−	2.93524i		−	0.242095i
$148$			4.20024i			0.345257i
$149$	17.3898			1.42463			0.712313	−	0.701862i	$-0.247648\pi$
$149$	17.3898			1.42463			0.712313	+	0.701862i	$0.247648\pi$
$150$	−7.57335	−	23.6114i	−0.618362	−	1.92786i
$151$	6.54075			0.532279			0.266140	−	0.963935i	$-0.414252\pi$
$151$	6.54075			0.532279			0.266140	+	0.963935i	$0.414252\pi$
$152$			3.56637i			0.289270i
$153$		−	9.83582i		−	0.795179i
$154$	1.68955			0.136148
$155$	−11.9581	−	8.72264i	−0.960501	−	0.700619i
$156$	−9.02034			−0.722205
$157$		−	23.2280i		−	1.85380i	−0.375310	−	0.926899i	$-0.622464\pi$
$157$		−	23.2280i		−	1.85380i	0.375310	−	0.926899i	$-0.377536\pi$
$158$			10.9373i			0.870125i
$159$	−13.9941			−1.10981
$160$	−5.98456	+	8.20442i	−0.473121	+	0.648617i
$161$	−8.49424			−0.669440
$162$			9.61131i			0.755136i
$163$		−	14.7123i		−	1.15236i	−0.817324	−	0.576179i	$-0.804543\pi$
$163$		−	14.7123i		−	1.15236i	0.817324	−	0.576179i	$-0.195457\pi$
$164$	−4.69989			−0.366999
$165$	−3.86789	+	5.30261i	−0.301115	+	0.412808i
$166$	−13.2152			−1.02570
$167$			21.4503i			1.65987i	0.557860	+	0.829935i	$0.311623\pi$
$167$			21.4503i			1.65987i	−0.557860	+	0.829935i	$0.688377\pi$
$168$		−	5.68042i		−	0.438254i
$169$	0.0684016			0.00526166
$170$	5.34597	+	3.89952i	0.410017	+	0.299079i
$171$	−10.3488			−0.791394
$172$		−	8.48863i		−	0.647252i
$173$		−	10.3341i		−	0.785689i	−0.919605	−	0.392844i	$-0.871491\pi$
$173$		−	10.3341i		−	0.785689i	0.919605	−	0.392844i	$-0.128509\pi$
$174$	21.9745			1.66588
$175$	−4.76108	+	1.52712i	−0.359904	+	0.115439i
$176$	4.97885			0.375295
$177$			25.6066i			1.92471i
$178$		−	15.2617i		−	1.14392i
$179$	5.67740			0.424348			0.212174	−	0.977232i	$-0.431946\pi$
$179$	5.67740			0.424348			0.212174	+	0.977232i	$0.431946\pi$
$180$	−8.66961	−	6.32388i	−0.646194	−	0.471354i
$181$	21.2115			1.57664			0.788318	−	0.615268i	$-0.210952\pi$
$181$	21.2115			1.57664			0.788318	+	0.615268i	$0.210952\pi$
$182$			6.07571i			0.450362i
$183$		−	20.7873i		−	1.53664i
$184$	−16.4384			−1.21186
$185$	−6.47666	+	8.87906i	−0.476174	+	0.652801i
$186$	−32.8272			−2.40700
$187$		−	1.75150i		−	0.128082i
$188$			3.97541i			0.289936i
$189$	7.67761			0.558464
$190$	4.10290	−	5.62480i	0.297656	−	0.408066i
$191$	6.83000			0.494202			0.247101	−	0.968990i	$-0.420522\pi$
$191$	6.83000			0.494202			0.247101	+	0.968990i	$0.420522\pi$
$192$		−	6.70574i		−	0.483945i
$193$			13.4586i			0.968772i	0.874854	+	0.484386i	$0.160957\pi$
$193$			13.4586i			0.968772i	−0.874854	+	0.484386i	$0.839043\pi$
$194$	18.4073			1.32156
$195$	−19.0685	−	13.9091i	−1.36552	−	0.996055i
$196$	0.854580			0.0610414
$197$			13.2385i			0.943202i	0.881812	+	0.471601i	$0.156324\pi$
$197$			13.2385i			0.943202i	−0.881812	+	0.471601i	$0.843676\pi$
$198$			9.48794i			0.674279i
$199$	6.98738			0.495322			0.247661	−	0.968847i	$-0.420338\pi$
$199$	6.98738			0.495322			0.247661	+	0.968847i	$0.420338\pi$
$200$	−9.21386	+	2.95535i	−0.651518	+	0.208975i
$201$	21.4386			1.51216
$202$			9.34941i			0.657822i
$203$		−	4.43102i		−	0.310997i
$204$	4.39346			0.307604
$205$	−9.93529	−	7.24711i	−0.693911	−	0.506160i
$206$	18.9416			1.31972
$207$		−	47.7008i		−	3.31543i
$208$			17.9042i			1.24143i
$209$	−1.84285			−0.127473
$210$	−6.53500	+	8.95903i	−0.450958	+	0.618232i
$211$	14.0484			0.967134			0.483567	−	0.875307i	$-0.339341\pi$
$211$	14.0484			0.967134			0.483567	+	0.875307i	$0.339341\pi$
$212$		−	4.07431i		−	0.279825i
$213$		−	23.2883i		−	1.59569i
$214$	−10.8961			−0.744840
$215$	13.0893	−	17.9445i	0.892679	−	1.22380i
$216$	14.8581			1.01096
$217$			6.61939i			0.449353i
$218$			31.9921i			2.16678i
$219$	−49.1250			−3.31956
$220$	−1.54383	−	1.12611i	−0.104085	−	0.0759226i
$221$	6.29848			0.423682
$222$			24.3746i			1.63591i
$223$			7.68300i			0.514492i	0.966346	+	0.257246i	$0.0828150\pi$
$223$			7.68300i			0.514492i	−0.966346	+	0.257246i	$0.917185\pi$
$224$	4.54153			0.303444
$225$	−8.57578	−	26.7366i	−0.571719	−	1.78244i
$226$	0.0295063			0.00196273
$227$		−	16.2711i		−	1.07995i	−0.841681	−	0.539974i	$-0.818434\pi$
$227$		−	16.2711i		−	1.07995i	0.841681	−	0.539974i	$-0.181566\pi$
$228$		−	4.62261i		−	0.306140i
$229$	13.9687			0.923079			0.461540	−	0.887120i	$-0.347297\pi$
$229$	13.9687			0.923079			0.461540	+	0.887120i	$0.347297\pi$
$230$	25.9264	+	18.9115i	1.70953	+	1.24699i
$231$	2.93524			0.193125
$232$		−	8.57512i		−	0.562984i
$233$		−	20.3722i		−	1.33463i	−0.744777	−	0.667313i	$-0.767444\pi$
$233$		−	20.3722i		−	1.33463i	0.744777	−	0.667313i	$-0.232556\pi$
$234$	−34.1192			−2.23044
$235$	−6.12998	+	8.40378i	−0.399876	+	0.548202i
$236$	−7.45522			−0.485294
$237$			19.0013i			1.23427i
$238$		−	2.95924i		−	0.191819i
$239$	−0.813371			−0.0526126			−0.0263063	−	0.999654i	$-0.508375\pi$
$239$	−0.813371			−0.0526126			−0.0263063	+	0.999654i	$0.508375\pi$
$240$	−19.2577	+	26.4009i	−1.24308	+	1.70417i
$241$	1.94243			0.125123			0.0625615	−	0.998041i	$-0.480073\pi$
$241$	1.94243			0.125123			0.0625615	+	0.998041i	$0.480073\pi$
$242$			1.68955i			0.108608i
$243$		−	6.33517i		−	0.406401i
$244$	6.05210			0.387446
$245$	1.80653	+	1.31774i	0.115415	+	0.0841874i
$246$	−27.2741			−1.73893
$247$		−	6.62698i		−	0.421665i
$248$			12.8101i			0.813445i
$249$	−22.9586			−1.45494
$250$	17.9319	+	5.93891i	1.13411	+	0.375610i
$251$	6.56563			0.414419			0.207209	−	0.978297i	$-0.433562\pi$
$251$	6.56563			0.414419			0.207209	+	0.978297i	$0.433562\pi$
$252$			4.79903i			0.302311i
$253$		−	8.49424i		−	0.534028i
$254$	6.44663			0.404498
$255$	9.28752	+	6.77460i	0.581607	+	0.424242i
$256$	17.2986			1.08116
$257$		−	24.0198i		−	1.49831i	−0.662392	−	0.749157i	$-0.730459\pi$
$257$		−	24.0198i		−	1.49831i	0.662392	−	0.749157i	$-0.269541\pi$
$258$		−	49.2607i		−	3.06683i
$259$	4.91497			0.305402
$260$	4.04957	−	5.55168i	0.251144	−	0.344301i
$261$	24.8831			1.54023
$262$			4.04697i			0.250023i
$263$			8.99713i			0.554787i	0.960756	+	0.277394i	$0.0894706\pi$
$263$			8.99713i			0.554787i	−0.960756	+	0.277394i	$0.910529\pi$
$264$	5.68042			0.349606
$265$	6.28248	−	8.61286i	0.385930	−	0.529083i
$266$	−3.11359			−0.190906
$267$		−	26.5141i		−	1.62264i
$268$			6.24171i			0.381273i
$269$	−22.1504			−1.35053			−0.675266	−	0.737575i	$-0.735971\pi$
$269$	−22.1504			−1.35053			−0.675266	+	0.737575i	$0.735971\pi$
$270$	−23.4338	−	17.0933i	−1.42614	−	1.04027i
$271$	−15.2076			−0.923795			−0.461898	−	0.886933i	$-0.652831\pi$
$271$	−15.2076			−0.923795			−0.461898	+	0.886933i	$0.652831\pi$
$272$		−	8.72045i		−	0.528755i
$273$			10.5553i			0.638836i
$274$	−32.8436			−1.98415
$275$	−1.52712	−	4.76108i	−0.0920887	−	0.287104i
$276$	21.3070			1.28253
$277$		−	11.9060i		−	0.715360i	−0.933844	−	0.357680i	$-0.883568\pi$
$277$		−	11.9060i		−	0.715360i	0.933844	−	0.357680i	$-0.116432\pi$
$278$		−	9.61056i		−	0.576403i
$279$	−37.1723			−2.22544
$280$	3.49608	+	2.55015i	0.208931	+	0.152401i
$281$	−14.8195			−0.884059			−0.442029	−	0.897001i	$-0.645741\pi$
$281$	−14.8195			−0.884059			−0.442029	+	0.897001i	$0.645741\pi$
$282$			23.0698i			1.37379i
$283$			25.1541i			1.49526i	0.664118	+	0.747628i	$0.268807\pi$
$283$			25.1541i			1.49526i	−0.664118	+	0.747628i	$0.731193\pi$
$284$	6.78025			0.402334
$285$	7.12794	−	9.77192i	0.422223	−	0.578839i
$286$	−6.07571			−0.359264
$287$			5.49965i			0.324634i
$288$			25.5037i			1.50282i
$289$	13.9323			0.819544
$290$	−9.86518	+	13.5245i	−0.579303	+	0.794185i
$291$	31.9788			1.87463
$292$		−	14.3025i		−	0.836989i
$293$		−	12.2872i		−	0.717824i	−0.933371	−	0.358912i	$-0.883148\pi$
$293$		−	12.2872i		−	0.717824i	0.933371	−	0.358912i	$-0.116852\pi$
$294$	4.95924			0.289229
$295$	−15.7599	−	11.4958i	−0.917577	−	0.669309i
$296$	9.51168			0.552855
$297$			7.67761i			0.445500i
$298$			29.3809i			1.70199i
$299$	30.5457			1.76651
$300$	11.9427	−	3.83063i	0.689512	−	0.221161i
$301$	−9.93310			−0.572534
$302$			11.0509i			0.635910i
$303$			16.2427i			0.933117i
$304$	−9.17528			−0.526238
$305$	12.7938	+	9.33219i	0.732571	+	0.534360i
$306$	16.6181			0.949994
$307$			6.34340i			0.362037i	0.983480	+	0.181018i	$0.0579394\pi$
$307$			6.34340i			0.362037i	−0.983480	+	0.181018i	$0.942061\pi$
$308$			0.854580i			0.0486942i
$309$	32.9071			1.87202
$310$	14.7373	−	20.2039i	0.837025	−	1.14750i
$311$	−11.8700			−0.673086			−0.336543	−	0.941668i	$-0.609258\pi$
$311$	−11.8700			−0.673086			−0.336543	+	0.941668i	$0.609258\pi$
$312$			20.4271i			1.15646i
$313$			22.5619i			1.27527i	0.770337	+	0.637637i	$0.220088\pi$
$313$			22.5619i			1.27527i	−0.770337	+	0.637637i	$0.779912\pi$
$314$	39.2449			2.21472
$315$	−7.39999	+	10.1449i	−0.416942	+	0.571599i
$316$	−5.53212			−0.311206
$317$		−	5.26577i		−	0.295755i	−0.989006	−	0.147877i	$-0.952756\pi$
$317$		−	5.26577i		−	0.295755i	0.989006	−	0.147877i	$-0.0472441\pi$
$318$		−	23.6438i		−	1.32588i
$319$	4.43102			0.248090
$320$	4.12713	+	3.01046i	0.230714	+	0.168290i
$321$	−18.9297			−1.05655
$322$		−	14.3514i		−	0.799775i
$323$			3.22775i			0.179597i
$324$	−4.86143			−0.270079
$325$	17.1211	−	5.49160i	0.949708	−	0.304619i
$326$	24.8572			1.37671
$327$			55.5797i			3.07357i
$328$			10.6432i			0.587670i
$329$	4.65189			0.256467
$330$	−8.95903	−	6.53500i	−0.493179	−	0.359740i
$331$	−32.1189			−1.76541			−0.882707	−	0.469923i	$-0.844282\pi$
$331$	−32.1189			−1.76541			−0.882707	+	0.469923i	$0.844282\pi$
$332$		−	6.68427i		−	0.366847i
$333$			27.6008i			1.51252i
$334$	−36.2413			−1.98303
$335$	−9.62457	+	13.1946i	−0.525846	+	0.720899i
$336$	14.6142			0.797267
$337$			27.8757i			1.51848i	0.650808	+	0.759242i	$0.274430\pi$
$337$			27.8757i			1.51848i	−0.650808	+	0.759242i	$0.725570\pi$
$338$			0.115568i			0.00628607i
$339$	0.0512612			0.00278413
$340$	−1.97239	+	2.70401i	−0.106968	+	0.146645i
$341$	−6.61939			−0.358460
$342$		−	17.4849i		−	0.945473i
$343$		−	1.00000i		−	0.0539949i
$344$	−19.2230			−1.03643
$345$	45.0417	+	32.8548i	2.42496	+	1.76884i
$346$	17.4600			0.938656
$347$		−	20.0682i		−	1.07732i	−0.842524	−	0.538659i	$-0.818931\pi$
$347$		−	20.0682i		−	1.07732i	0.842524	−	0.538659i	$-0.181069\pi$
$348$			11.1148i			0.595815i
$349$	−17.8094			−0.953316			−0.476658	−	0.879089i	$-0.658152\pi$
$349$	−17.8094			−0.953316			−0.476658	+	0.879089i	$0.658152\pi$
$350$	−2.58014	−	8.04409i	−0.137914	−	0.429975i
$351$	−27.6091			−1.47366
$352$			4.54153i			0.242064i
$353$		−	27.0142i		−	1.43782i	−0.695102	−	0.718911i	$-0.744641\pi$
$353$		−	27.0142i		−	1.43782i	0.695102	−	0.718911i	$-0.255359\pi$
$354$	−43.2637			−2.29944
$355$	14.3331	+	10.4550i	0.760720	+	0.554893i
$356$	7.71944			0.409129
$357$		−	5.14108i		−	0.272095i
$358$			9.59224i			0.506966i
$359$	11.6176			0.613154			0.306577	−	0.951846i	$-0.400816\pi$
$359$	11.6176			0.613154			0.306577	+	0.951846i	$0.400816\pi$
$360$	−14.3208	+	19.6328i	−0.754772	+	1.03474i
$361$	−15.6039			−0.821258
$362$			35.8379i			1.88360i
$363$			2.93524i			0.154060i
$364$	−3.07311			−0.161075
$365$	22.0541	−	30.2346i	1.15436	−	1.58255i
$366$	35.1212			1.83581
$367$		−	0.143655i		−	0.00749874i	−0.999993	−	0.00374937i	$-0.998807\pi$
$367$		−	0.143655i		−	0.00749874i	0.999993	−	0.00374937i	$-0.00119347\pi$
$368$		−	42.2916i		−	2.20460i
$369$	−30.8842			−1.60777
$370$	−15.0016	−	10.9426i	−0.779897	−	0.568881i
$371$	−4.76762			−0.247522
$372$		−	16.6041i		−	0.860882i
$373$			6.97831i			0.361323i	0.983545	+	0.180662i	$0.0578239\pi$
$373$			6.97831i			0.361323i	−0.983545	+	0.180662i	$0.942176\pi$
$374$	2.95924			0.153019
$375$	31.1529	+	10.3176i	1.60873	+	0.532800i
$376$	9.00254			0.464270
$377$			15.9342i			0.820653i
$378$			12.9717i			0.667193i
$379$	−11.7983			−0.606039			−0.303020	−	0.952984i	$-0.597995\pi$
$379$	−11.7983			−0.606039			−0.303020	+	0.952984i	$0.597995\pi$
$380$	2.84504	+	2.07526i	0.145947	+	0.106459i
$381$	11.1997			0.573778
$382$			11.5396i			0.590419i
$383$		−	16.2417i		−	0.829913i	−0.909841	−	0.414956i	$-0.863797\pi$
$383$		−	16.2417i		−	0.829913i	0.909841	−	0.414956i	$-0.136203\pi$
$384$	37.9907			1.93871
$385$	−1.31774	+	1.80653i	−0.0671583	+	0.0920694i
$386$	−22.7390			−1.15738
$387$		−	55.7809i		−	2.83550i
$388$			9.31045i			0.472667i
$389$	−1.46174			−0.0741134			−0.0370567	−	0.999313i	$-0.511798\pi$
$389$	−1.46174			−0.0741134			−0.0370567	+	0.999313i	$0.511798\pi$
$390$	23.5002	−	32.2172i	1.18998	−	1.63138i
$391$	−14.8776			−0.752395
$392$		−	1.93524i		−	0.0977446i
$393$			7.03078i			0.354656i
$394$	−22.3671			−1.12684
$395$	−11.6946	−	8.53040i	−0.588419	−	0.429211i
$396$	−4.79903			−0.241160
$397$			15.4702i			0.776425i	0.921570	+	0.388212i	$0.126907\pi$
$397$			15.4702i			0.776425i	−0.921570	+	0.388212i	$0.873093\pi$
$398$			11.8055i			0.591758i
$399$	−5.40921			−0.270799
$400$	−7.60330	−	23.7047i	−0.380165	−	1.18524i
$401$	21.8408			1.09068			0.545340	−	0.838215i	$-0.316401\pi$
$401$	21.8408			1.09068			0.545340	+	0.838215i	$0.316401\pi$
$402$			36.2215i			1.80657i
$403$		−	23.8037i		−	1.18575i
$404$	−4.72896			−0.235275
$405$	−10.2768	−	7.49620i	−0.510657	−	0.372489i
$406$	7.48644			0.371546
$407$			4.91497i			0.243626i
$408$		−	9.94924i		−	0.492561i
$409$	−20.2574			−1.00166			−0.500832	−	0.865545i	$-0.666973\pi$
$409$	−20.2574			−1.00166			−0.500832	+	0.865545i	$0.666973\pi$
$410$	12.2444	−	16.7862i	0.604705	−	0.829010i
$411$	−57.0590			−2.81451
$412$			9.58071i			0.472008i
$413$			8.72384i			0.429272i
$414$	80.5929			3.96092
$415$	10.3070	−	14.1302i	0.505950	−	0.693622i
$416$	−16.3316			−0.800722
$417$		−	16.6964i		−	0.817625i
$418$		−	3.11359i		−	0.152291i
$419$	0.590485			0.0288471			0.0144235	−	0.999896i	$-0.495409\pi$
$419$	0.590485			0.0288471			0.0144235	+	0.999896i	$0.495409\pi$
$420$	−4.53151	−	3.30542i	−0.221115	−	0.161288i
$421$	28.0174			1.36549			0.682743	−	0.730659i	$-0.260787\pi$
$421$	28.0174			1.36549			0.682743	+	0.730659i	$0.260787\pi$
$422$			23.7355i			1.15543i
$423$			26.1234i			1.27016i
$424$	−9.22651			−0.448079
$425$	−8.33903	+	2.67474i	−0.404502	+	0.129744i
$426$	39.3467			1.90636
$427$		−	7.08196i		−	0.342720i
$428$		−	5.51127i		−	0.266397i
$429$	−10.5553			−0.509615
$430$	30.3181	+	22.1149i	1.46207	+	1.06648i
$431$	−7.56856			−0.364565			−0.182282	−	0.983246i	$-0.558348\pi$
$431$	−7.56856			−0.364565			−0.182282	+	0.983246i	$0.558348\pi$
$432$			38.2257i			1.83913i
$433$		−	10.4631i		−	0.502823i	−0.967880	−	0.251412i	$-0.919105\pi$
$433$		−	10.4631i		−	0.502823i	0.967880	−	0.251412i	$-0.0808947\pi$
$434$	−11.1838			−0.536839
$435$	−17.1387	+	23.4960i	−0.821739	+	1.12655i
$436$	−16.1817			−0.774964
$437$			15.6536i			0.748814i
$438$		−	82.9992i		−	3.96586i
$439$	14.2208			0.678722			0.339361	−	0.940656i	$-0.389789\pi$
$439$	14.2208			0.678722			0.339361	+	0.940656i	$0.389789\pi$
$440$	−2.55015	+	3.49608i	−0.121574	+	0.166669i
$441$	5.61566			0.267413
$442$			10.6416i			0.506169i
$443$		−	0.985249i		−	0.0468106i	−0.999726	−	0.0234053i	$-0.992549\pi$
$443$		−	0.985249i		−	0.0468106i	0.999726	−	0.0234053i	$-0.00745082\pi$
$444$	−12.3287			−0.585095
$445$	16.3185	+	11.9032i	0.773569	+	0.564265i
$446$	−12.9808			−0.614659
$447$			51.0432i			2.41426i
$448$		−	2.28456i		−	0.107935i
$449$	18.3006			0.863657			0.431829	−	0.901956i	$-0.357869\pi$
$449$	18.3006			0.863657			0.431829	+	0.901956i	$0.357869\pi$
$450$	45.1729	−	14.4892i	2.12947	−	0.683028i
$451$	−5.49965			−0.258968
$452$			0.0149244i			0.000701985i
$453$			19.1987i			0.902034i
$454$	27.4908			1.29021
$455$	−6.49639	−	4.73867i	−0.304555	−	0.222152i
$456$	−10.4682			−0.490216
$457$		−	2.97818i		−	0.139313i	−0.997571	−	0.0696566i	$-0.977810\pi$
$457$		−	2.97818i		−	0.139313i	0.997571	−	0.0696566i	$-0.0221904\pi$
$458$			23.6009i			1.10280i
$459$	13.4473			0.627667
$460$	−9.56549	+	13.1136i	−0.445993	+	0.611426i
$461$	−35.6463			−1.66021			−0.830106	−	0.557606i	$-0.811720\pi$
$461$	−35.6463			−1.66021			−0.830106	+	0.557606i	$0.811720\pi$
$462$			4.95924i			0.230725i
$463$		−	28.7121i		−	1.33437i	−0.744894	−	0.667183i	$-0.767500\pi$
$463$		−	28.7121i		−	1.33437i	0.744894	−	0.667183i	$-0.232500\pi$
$464$	22.0614			1.02418
$465$	25.6031	−	35.1001i	1.18731	−	1.62773i
$466$	34.4198			1.59447
$467$		−	6.70656i		−	0.310343i	−0.987888	−	0.155171i	$-0.950407\pi$
$467$		−	6.70656i		−	0.310343i	0.987888	−	0.155171i	$-0.0495930\pi$
$468$		−	17.2576i		−	0.797732i
$469$	7.30384			0.337260
$470$	−14.1986	−	10.3569i	−0.654933	−	0.477729i
$471$	68.1800			3.14157
$472$			16.8828i			0.777093i
$473$		−	9.93310i		−	0.456724i
$474$	−32.1037			−1.47457
$475$	2.81425	+	8.77396i	0.129127	+	0.402577i
$476$	1.49679			0.0686055
$477$		−	26.7733i		−	1.22587i
$478$		−	1.37423i		−	0.0628559i
$479$	8.26047			0.377430			0.188715	−	0.982032i	$-0.439568\pi$
$479$	8.26047			0.377430			0.188715	+	0.982032i	$0.439568\pi$
$480$	−24.0820	−	17.5662i	−1.09919	−	0.801782i
$481$	−17.6745			−0.805888
$482$			3.28183i			0.149483i
$483$		−	24.9327i		−	1.13448i
$484$	−0.854580			−0.0388445
$485$	−14.3565	+	19.6818i	−0.651894	+	0.893703i
$486$	10.7036			0.485524
$487$			35.3962i			1.60396i	0.597354	+	0.801978i	$0.296219\pi$
$487$			35.3962i			1.60396i	−0.597354	+	0.801978i	$0.703781\pi$
$488$		−	13.7053i		−	0.620411i
$489$	43.1842			1.95286
$490$	−2.22639	+	3.05223i	−0.100578	+	0.137886i
$491$	−0.647846			−0.0292369			−0.0146184	−	0.999893i	$-0.504653\pi$
$491$	−0.647846			−0.0292369			−0.0146184	+	0.999893i	$0.504653\pi$
$492$		−	13.7953i		−	0.621941i
$493$		−	7.76093i		−	0.349535i
$494$	11.1966			0.503760
$495$	−10.1449	−	7.39999i	−0.455978	−	0.332605i
$496$	−32.9570			−1.47981
$497$		−	7.93402i		−	0.355889i
$498$		−	38.7897i		−	1.73821i
$499$	−32.0408			−1.43434			−0.717172	−	0.696896i	$-0.754564\pi$
$499$	−32.0408			−1.43434			−0.717172	+	0.696896i	$0.754564\pi$
$500$	−3.00392	+	9.06999i	−0.134339	+	0.405622i
$501$	−62.9617			−2.81292
$502$			11.0930i			0.495103i
$503$			8.97336i			0.400103i	0.979785	+	0.200051i	$0.0641109\pi$
$503$			8.97336i			0.400103i	−0.979785	+	0.200051i	$0.935889\pi$
$504$	10.8677			0.484085
$505$	−9.99675	−	7.29194i	−0.444850	−	0.324487i
$506$	14.3514			0.638000
$507$			0.200776i			0.00891675i
$508$			3.26073i			0.144671i
$509$	−4.79958			−0.212738			−0.106369	−	0.994327i	$-0.533922\pi$
$509$	−4.79958			−0.212738			−0.106369	+	0.994327i	$0.533922\pi$
$510$	−11.4460	+	15.6917i	−0.506839	+	0.694841i
$511$	−16.7363			−0.740369
$512$			3.34102i			0.147654i
$513$		−	14.1487i		−	0.624679i
$514$	40.5827			1.79002
$515$	−14.7732	+	20.2531i	−0.650986	+	0.892457i
$516$	24.9162			1.09687
$517$			4.65189i			0.204590i
$518$			8.30409i			0.364861i
$519$	30.3332			1.33148
$520$	−12.5721	−	9.17048i	−0.551323	−	0.402152i
$521$	0.615141			0.0269498			0.0134749	−	0.999909i	$-0.495711\pi$
$521$	0.615141			0.0269498			0.0134749	+	0.999909i	$0.495711\pi$
$522$			42.0413i			1.84010i
$523$			2.31342i			0.101159i	0.998720	+	0.0505795i	$0.0161068\pi$
$523$			2.31342i			0.101159i	−0.998720	+	0.0505795i	$0.983893\pi$
$524$	−2.04697			−0.0894223
$525$	−4.48247	−	13.9749i	−0.195631	−	0.609917i
$526$	−15.2011			−0.662800
$527$			11.5938i			0.505036i
$528$			14.6142i			0.635999i
$529$	−49.1521			−2.13705
$530$	14.5519	+	10.6146i	0.632092	+	0.461068i
$531$	−48.9902			−2.12599
$532$		−	1.57486i		−	0.0682789i
$533$		−	19.7770i		−	0.856638i
$534$	44.7970			1.93855
$535$	8.49824	−	11.6505i	0.367411	−	0.503695i
$536$	14.1347			0.610527
$537$			16.6645i			0.719128i
$538$		−	37.4241i		−	1.61347i
$539$	1.00000			0.0430730
$540$	8.64587	−	11.8529i	0.372059	−	0.510067i
$541$	−33.4865			−1.43970			−0.719849	−	0.694130i	$-0.755789\pi$
$541$	−33.4865			−1.43970			−0.719849	+	0.694130i	$0.755789\pi$
$542$		−	25.6940i		−	1.10365i
$543$			62.2609i			2.67187i
$544$	7.95448			0.341046
$545$	−34.2072	−	24.9518i	−1.46528	−	1.06882i
$546$	−17.8337			−0.763212
$547$		−	38.4969i		−	1.64601i	−0.568035	−	0.823005i	$-0.692296\pi$
$547$		−	38.4969i		−	1.64601i	0.568035	−	0.823005i	$-0.307704\pi$
$548$		−	16.6124i		−	0.709646i
$549$	39.7699			1.69734
$550$	8.04409	−	2.58014i	0.343001	−	0.110018i
$551$	−8.16571			−0.347871
$552$		−	48.2508i		−	2.05369i
$553$			6.47350i			0.275281i
$554$	20.1157			0.854635
$555$	−26.0622	−	19.0106i	−1.10628	−	0.806954i
$556$	4.86105			0.206155
$557$		−	29.3070i		−	1.24178i	−0.783899	−	0.620889i	$-0.786772\pi$
$557$		−	29.3070i		−	1.24178i	0.783899	−	0.620889i	$-0.213228\pi$
$558$		−	62.8044i		−	2.65872i
$559$	35.7200			1.51079
$560$	−6.56084	+	8.99446i	−0.277246	+	0.380085i
$561$	5.14108			0.217056
$562$		−	25.0383i		−	1.05618i
$563$		−	27.7170i		−	1.16813i	−0.811706	−	0.584066i	$-0.801461\pi$
$563$		−	27.7170i		−	1.16813i	0.811706	−	0.584066i	$-0.198539\pi$
$564$	−11.6688			−0.491345
$565$	−0.0230131	+	0.0315493i	−0.000968166	+	0.00132729i
$566$	−42.4991			−1.78637
$567$			5.68868i			0.238902i
$568$		−	15.3543i		−	0.644251i
$569$	−14.2301			−0.596556			−0.298278	−	0.954479i	$-0.596412\pi$
$569$	−14.2301			−0.596556			−0.298278	+	0.954479i	$0.596412\pi$
$570$	16.5102	+	12.0430i	0.691534	+	0.504426i
$571$	−10.6231			−0.444563			−0.222281	−	0.974983i	$-0.571350\pi$
$571$	−10.6231			−0.444563			−0.222281	+	0.974983i	$0.571350\pi$
$572$		−	3.07311i		−	0.128493i
$573$			20.0477i			0.837506i
$574$	−9.29193			−0.387838
$575$	−40.4418	+	12.9717i	−1.68654	+	0.540958i
$576$	12.8293			0.534555
$577$			35.1789i			1.46452i	0.681027	+	0.732259i	$0.261534\pi$
$577$			35.1789i			1.46452i	−0.681027	+	0.732259i	$0.738466\pi$
$578$			23.5392i			0.979103i
$579$	−39.5043			−1.64174
$580$	−6.84073	−	4.98984i	−0.284046	−	0.207192i
$581$	−7.82170			−0.324499
$582$			54.0298i			2.23961i
$583$		−	4.76762i		−	0.197455i
$584$	−32.3888			−1.34026
$585$	26.6107	−	36.4815i	1.10022	−	1.50832i
$586$	20.7598			0.857579
$587$		−	18.6001i		−	0.767710i	−0.923393	−	0.383855i	$-0.874596\pi$
$587$		−	18.6001i		−	0.767710i	0.923393	−	0.383855i	$-0.125404\pi$
$588$			2.50840i			0.103445i
$589$	12.1985			0.502632
$590$	19.4227	−	26.6272i	0.799619	−	1.09622i
$591$	−38.8581			−1.59841
$592$			24.4709i			1.00575i
$593$		−	16.7486i		−	0.687784i	−0.939009	−	0.343892i	$-0.888255\pi$
$593$		−	16.7486i		−	0.687784i	0.939009	−	0.343892i	$-0.111745\pi$
$594$	−12.9717			−0.532236
$595$	3.16414	+	2.30802i	0.129717	+	0.0946196i
$596$	−14.8609			−0.608728
$597$			20.5097i			0.839405i
$598$			51.6086i			2.11043i
$599$	6.12489			0.250256			0.125128	−	0.992141i	$-0.460066\pi$
$599$	6.12489			0.250256			0.125128	+	0.992141i	$0.460066\pi$
$600$	−8.67467	−	27.0449i	−0.354142	−	1.10411i
$601$	32.8690			1.34075			0.670377	−	0.742021i	$-0.266132\pi$
$601$	32.8690			1.34075			0.670377	+	0.742021i	$0.266132\pi$
$602$		−	16.7825i		−	0.684002i
$603$			41.0159i			1.67030i
$604$	−5.58960			−0.227437
$605$	−1.80653	−	1.31774i	−0.0734460	−	0.0535738i
$606$	−27.4428			−1.11479
$607$		−	2.51883i		−	0.102236i	−0.998693	−	0.0511181i	$-0.983722\pi$
$607$		−	2.51883i		−	0.102236i	0.998693	−	0.0511181i	$-0.0162785\pi$
$608$		−	8.36936i		−	0.339422i
$609$	13.0061			0.527035
$610$	−15.7672	+	21.6158i	−0.638395	+	0.875196i
$611$	−16.7284			−0.676760
$612$			8.40549i			0.339772i
$613$			29.4405i			1.18909i	0.804062	+	0.594546i	$0.202668\pi$
$613$			29.4405i			1.18909i	−0.804062	+	0.594546i	$0.797332\pi$
$614$	−10.7175			−0.432523
$615$	21.2720	−	29.1625i	0.857771	−	1.17595i
$616$	1.93524			0.0779732
$617$			14.2375i			0.573181i	0.958053	+	0.286590i	$0.0925219\pi$
$617$			14.2375i			0.573181i	−0.958053	+	0.286590i	$0.907478\pi$
$618$			55.5982i			2.23649i
$619$	−14.5186			−0.583550			−0.291775	−	0.956487i	$-0.594246\pi$
$619$	−14.5186			−0.583550			−0.291775	+	0.956487i	$0.594246\pi$
$620$	10.2192	+	7.45419i	0.410412	+	0.299368i
$621$	65.2155			2.61701
$622$		−	20.0550i		−	0.804130i
$623$		−	9.03302i		−	0.361900i
$624$	−52.5533			−2.10381
$625$	−20.3358	+	14.5415i	−0.813433	+	0.581659i
$626$	−38.1195			−1.52356
$627$		−	5.40921i		−	0.216023i
$628$			19.8502i			0.792110i
$629$	8.60857			0.343246
$630$	−17.1403	−	12.5027i	−0.682885	−	0.498118i
$631$	11.7388			0.467313			0.233657	−	0.972319i	$-0.424931\pi$
$631$	11.7388			0.467313			0.233657	+	0.972319i	$0.424931\pi$
$632$			12.5278i			0.498330i
$633$			41.2356i			1.63897i
$634$	8.89678			0.353336
$635$	−5.02796	+	6.89299i	−0.199529	+	0.273540i
$636$	11.9591			0.474209
$637$			3.59605i			0.142481i
$638$			7.48644i			0.296391i
$639$	44.5548			1.76256
$640$	−17.0554	+	23.3818i	−0.674176	+	0.924249i
$641$	−35.5107			−1.40259			−0.701293	−	0.712873i	$-0.747394\pi$
$641$	−35.5107			−1.40259			−0.701293	+	0.712873i	$0.747394\pi$
$642$		−	31.9826i		−	1.26225i
$643$			27.4051i			1.08075i	0.841423	+	0.540377i	$0.181718\pi$
$643$			27.4051i			1.08075i	−0.841423	+	0.540377i	$0.818282\pi$
$644$	7.25901			0.286045
$645$	52.6714	+	38.4202i	2.07393	+	1.51279i
$646$	−5.45344			−0.214563
$647$			21.9689i			0.863687i	0.901948	+	0.431844i	$0.142137\pi$
$647$			21.9689i			0.863687i	−0.901948	+	0.431844i	$0.857863\pi$
$648$			11.0090i			0.432474i
$649$	−8.72384			−0.342441
$650$	9.27833	+	28.9270i	0.363926	+	1.13461i
$651$	−19.4295			−0.761503
$652$			12.5728i			0.492391i
$653$		−	24.4212i		−	0.955676i	−0.878448	−	0.477838i	$-0.841421\pi$
$653$		−	24.4212i		−	0.955676i	0.878448	−	0.477838i	$-0.158579\pi$
$654$	−93.9047			−3.67196
$655$	−4.32718	−	3.15638i	−0.169077	−	0.123330i
$656$	−27.3819			−1.06908
$657$		−	93.9852i		−	3.66671i
$658$			7.85959i			0.306399i
$659$	11.1612			0.434779			0.217389	−	0.976085i	$-0.430246\pi$
$659$	11.1612			0.434779			0.217389	+	0.976085i	$0.430246\pi$
$660$	3.30542	−	4.53151i	0.128663	−	0.176389i
$661$	−10.0360			−0.390355			−0.195177	−	0.980768i	$-0.562528\pi$
$661$	−10.0360			−0.390355			−0.195177	+	0.980768i	$0.562528\pi$
$662$		−	54.2665i		−	2.10913i
$663$			18.4876i			0.717998i
$664$	−15.1369			−0.587426
$665$	2.42840	−	3.32917i	0.0941692	−	0.129100i
$666$	−46.6330			−1.80699
$667$		−	37.6382i		−	1.45736i
$668$		−	18.3310i		−	0.709246i
$669$	−22.5515			−0.871891
$670$	−22.2930	−	16.2612i	−0.861253	−	0.628225i
$671$	7.08196			0.273396
$672$			13.3305i			0.514236i
$673$			1.63730i			0.0631131i	0.999502	+	0.0315565i	$0.0100464\pi$
$673$			1.63730i			0.0631131i	−0.999502	+	0.0315565i	$0.989954\pi$
$674$	−47.0973			−1.81412
$675$	36.5537	−	11.7246i	1.40695	−	0.451281i
$676$	−0.0584546			−0.00224826
$677$		−	9.24088i		−	0.355156i	−0.984107	−	0.177578i	$-0.943174\pi$
$677$		−	9.24088i		−	0.355156i	0.984107	−	0.177578i	$-0.0568262\pi$
$678$			0.0866083i			0.00332617i
$679$	10.8948			0.418103
$680$	6.12338	+	4.46658i	0.234821	+	0.171286i
$681$	47.7596			1.83015
$682$		−	11.1838i		−	0.428249i
$683$		−	8.12240i		−	0.310795i	−0.987852	−	0.155398i	$-0.950334\pi$
$683$		−	8.12240i		−	0.310795i	0.987852	−	0.155398i	$-0.0496658\pi$
$684$	8.84389			0.338155
$685$	25.6159	−	35.1177i	0.978733	−	1.34178i
$686$	1.68955			0.0645073
$687$			41.0016i			1.56431i
$688$		−	49.4554i		−	1.88547i
$689$	17.1446			0.653157
$690$	−55.5098	+	76.1002i	−2.11322	+	2.89708i
$691$	40.5364			1.54208			0.771038	−	0.636789i	$-0.219738\pi$
$691$	40.5364			1.54208			0.771038	+	0.636789i	$0.219738\pi$
$692$			8.83133i			0.335717i
$693$			5.61566i			0.213321i
$694$	33.9062			1.28706
$695$	10.2760	+	7.49562i	0.389790	+	0.284325i
$696$	25.1701			0.954069
$697$			9.63262i			0.364861i
$698$		−	30.0899i		−	1.13892i
$699$	59.7974			2.26174
$700$	4.06873	−	1.30504i	0.153783	−	0.0493260i
$701$	39.3047			1.48452			0.742259	−	0.670114i	$-0.233755\pi$
$701$	39.3047			1.48452			0.742259	+	0.670114i	$0.233755\pi$
$702$		−	46.6470i		−	1.76058i
$703$		−	9.05756i		−	0.341612i
$704$	2.28456			0.0861026
$705$	−24.6672	−	17.9930i	−0.929019	−	0.677655i
$706$	45.6419			1.71776
$707$			5.53367i			0.208115i
$708$		−	21.8829i		−	0.822410i
$709$	48.6858			1.82843			0.914217	−	0.405224i	$-0.132806\pi$
$709$	48.6858			1.82843			0.914217	+	0.405224i	$0.132806\pi$
$710$	−17.6642	+	24.2164i	−0.662926	+	0.908826i
$711$	−36.3530			−1.36334
$712$		−	17.4811i		−	0.655132i
$713$			56.2267i			2.10571i
$714$	8.68610			0.325069
$715$	4.73867	−	6.49639i	0.177216	−	0.242951i
$716$	−4.85179			−0.181320
$717$		−	2.38744i		−	0.0891607i
$718$			19.6285i			0.732531i
$719$	35.6720			1.33034			0.665171	−	0.746691i	$-0.268359\pi$
$719$	35.6720			1.33034			0.665171	+	0.746691i	$0.268359\pi$
$720$	−50.5098	−	36.8435i	−1.88239	−	1.37307i
$721$	11.2110			0.417520
$722$		−	26.3636i		−	0.981151i
$723$			5.70151i			0.212041i
$724$	−18.1269			−0.673681
$725$	−6.76670	−	21.0965i	−0.251309	−	0.783503i
$726$	−4.95924			−0.184055
$727$		−	2.10788i		−	0.0781769i	−0.999236	−	0.0390884i	$-0.987555\pi$
$727$		−	2.10788i		−	0.0781769i	0.999236	−	0.0390884i	$-0.0124454\pi$
$728$			6.95924i			0.257927i
$729$	35.6613			1.32079
$730$	51.0829	+	37.2614i	1.89066	+	1.37911i
$731$	−17.3978			−0.643481
$732$			17.7644i			0.656591i
$733$			29.5903i			1.09294i	0.837478	+	0.546472i	$0.184029\pi$
$733$			29.5903i			1.09294i	−0.837478	+	0.546472i	$0.815971\pi$
$734$	0.242713			0.00895869
$735$	−3.86789	+	5.30261i	−0.142669	+	0.195590i
$736$	38.5769			1.42196
$737$			7.30384i			0.269040i
$738$		−	52.1803i		−	1.92078i
$739$	45.2134			1.66320			0.831601	−	0.555374i	$-0.187425\pi$
$739$	45.2134			1.66320			0.831601	+	0.555374i	$0.187425\pi$
$740$	5.53482	−	7.58786i	0.203464	−	0.278935i
$741$	19.4518			0.714581
$742$		−	8.05513i		−	0.295713i
$743$		−	15.6873i		−	0.575512i	−0.957704	−	0.287756i	$-0.907091\pi$
$743$		−	15.6873i		−	0.575512i	0.957704	−	0.287756i	$-0.0929093\pi$
$744$	−37.6009			−1.37852
$745$	−31.4152	−	22.9152i	−1.15096	−	0.839548i
$746$	−11.7902			−0.431670
$747$		−	43.9240i		−	1.60710i
$748$			1.49679i			0.0547282i
$749$	−6.44910			−0.235645
$750$	−17.4322	+	52.6344i	−0.636532	+	1.92194i
$751$	−43.5568			−1.58941			−0.794705	−	0.606996i	$-0.792374\pi$
$751$	−43.5568			−1.58941			−0.794705	+	0.606996i	$0.792374\pi$
$752$			23.1611i			0.844597i
$753$			19.2717i			0.702301i
$754$	−26.9216			−0.980428
$755$	−11.8161	−	8.61902i	−0.430031	−	0.313678i
$756$	−6.56113			−0.238626
$757$		−	3.70349i		−	0.134606i	−0.997733	−	0.0673029i	$-0.978561\pi$
$757$		−	3.70349i		−	0.134606i	0.997733	−	0.0673029i	$-0.0214394\pi$
$758$		−	19.9339i		−	0.724031i
$759$	24.9327			0.904999
$760$	4.69954	−	6.44275i	0.170470	−	0.233703i
$761$	−13.9814			−0.506825			−0.253412	−	0.967358i	$-0.581553\pi$
$761$	−13.9814			−0.506825			−0.253412	+	0.967358i	$0.581553\pi$
$762$			18.9224i			0.685488i
$763$			18.9353i			0.685503i
$764$	−5.83678			−0.211167
$765$	−12.9611	+	17.7687i	−0.468608	+	0.642430i
$766$	27.4412			0.991490
$767$		−	31.3714i		−	1.13276i
$768$			50.7757i			1.83221i
$769$	−19.0164			−0.685750			−0.342875	−	0.939381i	$-0.611401\pi$
$769$	−19.0164			−0.685750			−0.342875	+	0.939381i	$0.611401\pi$
$770$	−3.05223	−	2.22639i	−0.109995	−	0.0802335i
$771$	70.5040			2.53914
$772$		−	11.5015i		−	0.413946i
$773$		−	3.76217i		−	0.135316i	−0.997709	−	0.0676579i	$-0.978447\pi$
$773$		−	3.76217i		−	0.135316i	0.997709	−	0.0676579i	$-0.0215527\pi$
$774$	94.2447			3.38756
$775$	10.1086	+	31.5155i	0.363111	+	1.13207i
$776$	21.0841			0.756873
$777$			14.4267i			0.517553i
$778$		−	2.46969i		−	0.0885427i
$779$	10.1350			0.363125
$780$	16.2955	+	11.8865i	0.583474	+	0.425604i
$781$	7.93402			0.283902
$782$		−	25.1365i		−	0.898880i
$783$			34.0197i			1.21576i
$784$	4.97885			0.177816
$785$	−30.6085	+	41.9622i	−1.09247	+	1.49770i
$786$	−11.8788			−0.423705
$787$		−	17.5146i		−	0.624330i	−0.950028	−	0.312165i	$-0.898946\pi$
$787$		−	17.5146i		−	0.624330i	0.950028	−	0.312165i	$-0.101054\pi$
$788$		−	11.3133i		−	0.403021i
$789$	−26.4088			−0.940178
$790$	14.4125	−	19.7586i	0.512775	−	0.702979i
$791$	0.0174640			0.000620949
$792$			10.8677i			0.386166i
$793$			25.4671i			0.904364i
$794$	−26.1376			−0.927589
$795$	25.2808	+	18.4406i	0.896619	+	0.654022i
$796$	−5.97127			−0.211646
$797$		−	4.71730i		−	0.167095i	−0.996504	−	0.0835477i	$-0.973375\pi$
$797$		−	4.71730i		−	0.167095i	0.996504	−	0.0835477i	$-0.0266251\pi$
$798$		−	9.13914i		−	0.323522i
$799$	8.14777			0.288247
$800$	21.6226	−	6.93546i	0.764475	−	0.245205i
$801$	50.7264			1.79233
$802$			36.9012i			1.30303i
$803$		−	16.7363i		−	0.590610i
$804$	−18.3210			−0.646130
$805$	15.3451	+	11.1932i	0.540844	+	0.394509i
$806$	40.2175			1.41660
$807$		−	65.0167i		−	2.28870i
$808$			10.7090i			0.376742i
$809$	−3.28974			−0.115661			−0.0578306	−	0.998326i	$-0.518418\pi$
$809$	−3.28974			−0.115661			−0.0578306	+	0.998326i	$0.518418\pi$
$810$	12.6652	−	17.3631i	0.445010	−	0.610079i
$811$	37.5502			1.31857			0.659283	−	0.751895i	$-0.270860\pi$
$811$	37.5502			1.31857			0.659283	+	0.751895i	$0.270860\pi$
$812$			3.78666i			0.132886i
$813$		−	44.6380i		−	1.56552i
$814$	−8.30409			−0.291058
$815$	−19.3870	+	26.5783i	−0.679097	+	0.930996i
$816$	25.5967			0.896062
$817$			18.3052i			0.640418i
$818$		−	34.2259i		−	1.19668i
$819$	−20.1942			−0.705643
$820$	8.49050	+	6.19323i	0.296501	+	0.216277i
$821$	−19.7528			−0.689379			−0.344690	−	0.938717i	$-0.612016\pi$
$821$	−19.7528			−0.689379			−0.344690	+	0.938717i	$0.612016\pi$
$822$		−	96.4040i		−	3.36248i
$823$		−	45.8579i		−	1.59851i	−0.600995	−	0.799253i	$-0.705229\pi$
$823$		−	45.8579i		−	1.59851i	0.600995	−	0.799253i	$-0.294771\pi$
$824$	21.6961			0.755819
$825$	13.9749	−	4.48247i	0.486545	−	0.156059i
$826$	−14.7394			−0.512848
$827$			23.9374i			0.832385i	0.909277	+	0.416192i	$0.136636\pi$
$827$			23.9374i			0.832385i	−0.909277	+	0.416192i	$0.863364\pi$
$828$			40.7641i			1.41665i
$829$	22.8596			0.793947			0.396974	−	0.917830i	$-0.370060\pi$
$829$	22.8596			0.793947			0.396974	+	0.917830i	$0.370060\pi$
$830$	23.8736	+	17.4142i	0.828665	+	0.604454i
$831$	34.9469			1.21230
$832$			8.21540i			0.284818i
$833$		−	1.75150i		−	0.0606858i
$834$	28.2094			0.976810
$835$	28.2659	−	38.7506i	0.978181	−	1.34102i
$836$	1.57486			0.0544677
$837$		−	50.8211i		−	1.75663i
$838$			0.997654i			0.0344634i
$839$	29.2730			1.01062			0.505308	−	0.862939i	$-0.331379\pi$
$839$	29.2730			1.01062			0.505308	+	0.862939i	$0.331379\pi$
$840$	−7.48532	+	10.2619i	−0.258268	+	0.354068i
$841$	−9.36603			−0.322967
$842$			47.3368i			1.63133i
$843$		−	43.4989i		−	1.49818i
$844$	−12.0055			−0.413246
$845$	−0.123570	−	0.0901356i	−0.00425093	−	0.00310076i
$846$	−44.1368			−1.51746
$847$			1.00000i			0.0343604i
$848$		−	23.7373i		−	0.815141i
$849$	−73.8335			−2.53396
$850$	−4.51912	−	14.0892i	−0.155004	−	0.483256i
$851$	41.7490			1.43114
$852$			19.9017i			0.681821i
$853$		−	10.3181i		−	0.353286i	−0.984275	−	0.176643i	$-0.943476\pi$
$853$		−	10.3181i		−	0.353286i	0.984275	−	0.176643i	$-0.0565238\pi$
$854$	11.9653			0.409445
$855$	18.6955	+	13.6371i	0.639372	+	0.466378i
$856$	−12.4806			−0.426577
$857$			15.5992i			0.532858i	0.963855	+	0.266429i	$0.0858438\pi$
$857$			15.5992i			0.532858i	−0.963855	+	0.266429i	$0.914156\pi$
$858$		−	17.8337i		−	0.608833i
$859$	−14.6335			−0.499289			−0.249645	−	0.968338i	$-0.580314\pi$
$859$	−14.6335			−0.499289			−0.249645	+	0.968338i	$0.580314\pi$
$860$	−11.1858	+	15.3350i	−0.381433	+	0.522918i
$861$	−16.1428			−0.550145
$862$		−	12.7875i		−	0.435543i
$863$		−	29.5000i		−	1.00419i	−0.864812	−	0.502096i	$-0.832562\pi$
$863$		−	29.5000i		−	1.00419i	0.864812	−	0.502096i	$-0.167438\pi$
$864$	−34.8681			−1.18624
$865$	−13.6177	+	18.6689i	−0.463016	+	0.634763i
$866$	17.6779			0.600719
$867$			40.8946i			1.38885i
$868$		−	5.65680i		−	0.192004i
$869$	−6.47350			−0.219599
$870$	−39.6977	−	28.9567i	−1.34588	−	0.981725i
$871$	−26.2650			−0.889956
$872$			36.6444i			1.24094i
$873$			61.1814i			2.07068i
$874$	−26.4476			−0.894602
$875$	10.6134	+	3.51508i	0.358798	+	0.118832i
$876$	41.9813			1.41842
$877$			36.1858i			1.22191i	0.791666	+	0.610954i	$0.209214\pi$
$877$			36.1858i			1.22191i	−0.791666	+	0.610954i	$0.790786\pi$
$878$			24.0268i			0.810864i
$879$	36.0658			1.21647
$880$	−8.99446	−	6.56084i	−0.303203	−	0.221166i
$881$	−35.9099			−1.20983			−0.604917	−	0.796289i	$-0.706794\pi$
$881$	−35.9099			−1.20983			−0.604917	+	0.796289i	$0.706794\pi$
$882$			9.48794i			0.319476i
$883$			11.7886i			0.396720i	0.980129	+	0.198360i	$0.0635615\pi$
$883$			11.7886i			0.396720i	−0.980129	+	0.198360i	$0.936439\pi$
$884$	−5.38255			−0.181035
$885$	33.7429	−	46.2592i	1.13425	−	1.55499i
$886$	1.66463			0.0559242
$887$			17.6251i			0.591793i	0.955220	+	0.295896i	$0.0956183\pi$
$887$			17.6251i			0.591793i	−0.955220	+	0.295896i	$0.904382\pi$
$888$			27.9191i			0.936904i
$889$	3.81559			0.127971
$890$	−20.1110	+	27.5708i	−0.674123	+	0.924177i
$891$	−5.68868			−0.190578
$892$		−	6.56574i		−	0.219837i
$893$		−	8.57272i		−	0.286875i
$894$	−86.2401			−2.88430
$895$	−10.2564	−	7.48134i	−0.342834	−	0.250073i
$896$	12.9429			0.432393
$897$			89.6592i			2.99363i
$898$			30.9197i			1.03180i
$899$	−29.3307			−0.978233
$900$	7.32869	+	22.8486i	0.244290	+	0.761620i
$901$	−8.35047			−0.278195
$902$		−	9.29193i		−	0.309387i
$903$		−	29.1561i		−	0.970254i
$904$	0.0337972			0.00112408
$905$	−38.3192	−	27.9512i	−1.27377	−	0.929130i
$906$	−32.4372			−1.07765
$907$			4.28322i			0.142222i	0.997468	+	0.0711110i	$0.0226544\pi$
$907$			4.28322i			0.142222i	−0.997468	+	0.0711110i	$0.977346\pi$
$908$			13.9049i			0.461451i
$909$	−31.0752			−1.03070
$910$	8.00621	−	10.9760i	0.265403	−	0.363850i
$911$	53.6814			1.77854			0.889272	−	0.457379i	$-0.151212\pi$
$911$	53.6814			1.77854			0.889272	+	0.457379i	$0.151212\pi$
$912$		−	26.9317i		−	0.891797i
$913$		−	7.82170i		−	0.258861i
$914$	5.03178			0.166436
$915$	−27.3923	+	37.5529i	−0.905560	+	1.24146i
$916$	−11.9374			−0.394422
$917$			2.39529i			0.0790996i
$918$			22.7199i			0.749869i
$919$	−23.0274			−0.759602			−0.379801	−	0.925068i	$-0.624008\pi$
$919$	−23.0274			−0.759602			−0.379801	+	0.925068i	$0.624008\pi$
$920$	29.6966	+	21.6616i	0.979067	+	0.714162i
$921$	−18.6194			−0.613531
$922$		−	60.2261i		−	1.98344i
$923$			28.5312i			0.939114i
$924$	−2.50840			−0.0825203
$925$	23.4006	−	7.50575i	0.769407	−	0.246787i
$926$	48.5106			1.59416
$927$			62.9573i			2.06779i
$928$			20.1236i			0.660591i
$929$	−35.6526			−1.16972			−0.584861	−	0.811133i	$-0.698851\pi$
$929$	−35.6526			−1.16972			−0.584861	+	0.811133i	$0.698851\pi$
$930$	59.3033	+	43.2577i	1.94463	+	1.41848i
$931$	−1.84285			−0.0603970
$932$			17.4097i			0.570272i
$933$		−	34.8413i		−	1.14065i
$934$	11.3311			0.370764
$935$	−2.30802	+	3.16414i	−0.0754803	+	0.103478i
$936$	−39.0808			−1.27739
$937$		−	14.6147i		−	0.477442i	−0.971088	−	0.238721i	$-0.923272\pi$
$937$		−	14.6147i		−	0.477442i	0.971088	−	0.238721i	$-0.0767282\pi$
$938$			12.3402i			0.402922i
$939$	−66.2247			−2.16116
$940$	5.23856	−	7.18170i	0.170863	−	0.234241i
$941$	31.7910			1.03636			0.518178	−	0.855273i	$-0.326610\pi$
$941$	31.7910			1.03636			0.518178	+	0.855273i	$0.326610\pi$
$942$			115.193i			3.75321i
$943$			46.7153i			1.52126i
$944$	−43.4347			−1.41368
$945$	−13.8699	−	10.1171i	−0.451186	−	0.329109i
$946$	16.7825			0.545645
$947$			26.1700i			0.850412i	0.905097	+	0.425206i	$0.139798\pi$
$947$			26.1700i			0.850412i	−0.905097	+	0.425206i	$0.860202\pi$
$948$		−	16.2381i		−	0.527390i
$949$	60.1845			1.95367
$950$	−14.8240	+	4.75482i	−0.480955	+	0.154267i
$951$	15.4563			0.501205
$952$		−	3.38958i		−	0.109857i
$953$			34.9843i			1.13325i	0.823975	+	0.566626i	$0.191752\pi$
$953$			34.9843i			1.13325i	−0.823975	+	0.566626i	$0.808248\pi$
$954$	45.2349			1.46453
$955$	−12.3386	−	9.00017i	−0.399268	−	0.291239i
$956$	0.695090			0.0224808
$957$			13.0061i			0.420429i
$958$			13.9565i			0.450913i
$959$	−19.4393			−0.627726
$960$	−8.83643	+	12.1141i	−0.285195	+	0.390982i
$961$	12.8163			0.413430
$962$		−	29.8620i		−	0.962788i
$963$		−	36.2159i		−	1.16704i
$964$	−1.65996			−0.0534638
$965$	17.7350	−	24.3134i	0.570908	−	0.782676i
$966$	42.1250			1.35535
$967$		−	3.60712i		−	0.115997i	−0.998317	−	0.0579985i	$-0.981528\pi$
$967$		−	3.60712i		−	0.115997i	0.998317	−	0.0579985i	$-0.0184719\pi$
$968$			1.93524i			0.0622011i
$969$	−9.47423			−0.304356
$970$	−33.2533	−	24.2560i	−1.06770	−	0.778813i
$971$	11.0925			0.355974			0.177987	−	0.984033i	$-0.443041\pi$
$971$	11.0925			0.355974			0.177987	+	0.984033i	$0.443041\pi$
$972$			5.41390i			0.173651i
$973$		−	5.68824i		−	0.182357i
$974$	−59.8037			−1.91623
$975$	16.1192	+	50.2546i	0.516227	+	1.60944i
$976$	35.2601			1.12865
$977$			3.14654i			0.100667i	0.998732	+	0.0503334i	$0.0160284\pi$
$977$			3.14654i			0.100667i	−0.998732	+	0.0503334i	$0.983972\pi$
$978$			72.9619i			2.33307i
$979$	9.03302			0.288697
$980$	−1.54383	−	1.12611i	−0.0493157	−	0.0359724i
$981$	−106.334			−3.39499
$982$		−	1.09457i		−	0.0349291i
$983$		−	28.0142i		−	0.893515i	−0.894655	−	0.446758i	$-0.852579\pi$
$983$		−	28.0142i		−	0.893515i	0.894655	−	0.446758i	$-0.147421\pi$
$984$	−31.2403			−0.995904
$985$	17.4449	−	23.9157i	0.555840	−	0.762018i
$986$	13.1125			0.417586
$987$			13.6544i			0.434625i
$988$			5.66329i			0.180173i
$989$	−84.3741			−2.68294
$990$	12.5027	−	17.1403i	0.397360	−	0.544754i
$991$	21.1389			0.671501			0.335750	−	0.941951i	$-0.391010\pi$
$991$	21.1389			0.671501			0.335750	+	0.941951i	$0.391010\pi$
$992$		−	30.0622i		−	0.954475i
$993$		−	94.2768i		−	2.99178i
$994$	13.4049			0.425178
$995$	−12.6229	−	9.20756i	−0.400174	−	0.291899i
$996$	19.6200			0.621682
$997$			20.7522i			0.657228i	0.944464	+	0.328614i	$0.106582\pi$
$997$			20.7522i			0.657228i	−0.944464	+	0.328614i	$0.893418\pi$
$998$		−	54.1346i		−	1.71360i
$999$	−37.7353			−1.19389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.b.c.309.10	yes	12
5.2	odd	4		1925.2.a.z.1.2		6
5.3	odd	4		1925.2.a.y.1.5		6
5.4	even	2	inner	385.2.b.c.309.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.c.309.3	✓	12	5.4	even	2	inner
385.2.b.c.309.10	yes	12	1.1	even	1	trivial
1925.2.a.y.1.5		6	5.3	odd	4
1925.2.a.z.1.2		6	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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.68955i q^{2} +2.93524i q^{3} -0.854580 q^{4} +(-1.80653 - 1.31774i) q^{5} -4.95924 q^{6} +1.00000i q^{7} +1.93524i q^{8} -5.61566 q^{9} +O(q^{10})\)	\(q+1.68955i q^{2} +2.93524i q^{3} -0.854580 q^{4} +(-1.80653 - 1.31774i) q^{5} -4.95924 q^{6} +1.00000i q^{7} +1.93524i q^{8} -5.61566 q^{9} +(2.22639 - 3.05223i) q^{10} -1.00000 q^{11} -2.50840i q^{12} -3.59605i q^{13} -1.68955 q^{14} +(3.86789 - 5.30261i) q^{15} -4.97885 q^{16} +1.75150i q^{17} -9.48794i q^{18} +1.84285 q^{19} +(1.54383 + 1.12611i) q^{20} -2.93524 q^{21} -1.68955i q^{22} +8.49424i q^{23} -5.68042 q^{24} +(1.52712 + 4.76108i) q^{25} +6.07571 q^{26} -7.67761i q^{27} -0.854580i q^{28} -4.43102 q^{29} +(8.95903 + 6.53500i) q^{30} +6.61939 q^{31} -4.54153i q^{32} -2.93524i q^{33} -2.95924 q^{34} +(1.31774 - 1.80653i) q^{35} +4.79903 q^{36} -4.91497i q^{37} +3.11359i q^{38} +10.5553 q^{39} +(2.55015 - 3.49608i) q^{40} +5.49965 q^{41} -4.95924i q^{42} +9.93310i q^{43} +0.854580 q^{44} +(10.1449 + 7.39999i) q^{45} -14.3514 q^{46} -4.65189i q^{47} -14.6142i q^{48} -1.00000 q^{49} +(-8.04409 + 2.58014i) q^{50} -5.14108 q^{51} +3.07311i q^{52} +4.76762i q^{53} +12.9717 q^{54} +(1.80653 + 1.31774i) q^{55} -1.93524 q^{56} +5.40921i q^{57} -7.48644i q^{58} +8.72384 q^{59} +(-3.30542 + 4.53151i) q^{60} -7.08196 q^{61} +11.1838i q^{62} -5.61566i q^{63} -2.28456 q^{64} +(-4.73867 + 6.49639i) q^{65} +4.95924 q^{66} -7.30384i q^{67} -1.49679i q^{68} -24.9327 q^{69} +(3.05223 + 2.22639i) q^{70} -7.93402 q^{71} -10.8677i q^{72} +16.7363i q^{73} +8.30409 q^{74} +(-13.9749 + 4.48247i) q^{75} -1.57486 q^{76} -1.00000i q^{77} +17.8337i q^{78} +6.47350 q^{79} +(8.99446 + 6.56084i) q^{80} +5.68868 q^{81} +9.29193i q^{82} +7.82170i q^{83} +2.50840 q^{84} +(2.30802 - 3.16414i) q^{85} -16.7825 q^{86} -13.0061i q^{87} -1.93524i q^{88} -9.03302 q^{89} +(-12.5027 + 17.1403i) q^{90} +3.59605 q^{91} -7.25901i q^{92} +19.4295i q^{93} +7.85959 q^{94} +(-3.32917 - 2.42840i) q^{95} +13.3305 q^{96} -10.8948i q^{97} -1.68955i q^{98} +5.61566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 6 q^{5} - 4 q^{6} - 20 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 + 6 * q^5 - 4 * q^6 - 20 * q^9	\( 12 q - 4 q^{4} + 6 q^{5} - 4 q^{6} - 20 q^{9} + 14 q^{10} - 12 q^{11} - 8 q^{15} - 12 q^{16} + 4 q^{19} - 6 q^{20} - 12 q^{21} - 44 q^{24} - 8 q^{25} + 16 q^{29} + 40 q^{30} + 8 q^{31} + 20 q^{34} + 2 q^{35} + 52 q^{36} + 16 q^{39} - 10 q^{40} + 8 q^{41} + 4 q^{44} - 2 q^{45} - 16 q^{46} - 12 q^{49} + 28 q^{50} - 8 q^{51} - 76 q^{54} - 6 q^{55} - 28 q^{59} + 16 q^{60} + 24 q^{61} + 44 q^{64} + 12 q^{65} + 4 q^{66} - 24 q^{69} + 6 q^{70} + 8 q^{71} + 16 q^{74} - 60 q^{75} - 16 q^{76} + 16 q^{79} + 22 q^{80} + 52 q^{81} + 24 q^{84} - 20 q^{85} + 24 q^{86} - 16 q^{89} - 46 q^{90} - 12 q^{91} + 20 q^{94} - 40 q^{95} - 32 q^{96} + 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 + 6 * q^5 - 4 * q^6 - 20 * q^9 + 14 * q^10 - 12 * q^11 - 8 * q^15 - 12 * q^16 + 4 * q^19 - 6 * q^20 - 12 * q^21 - 44 * q^24 - 8 * q^25 + 16 * q^29 + 40 * q^30 + 8 * q^31 + 20 * q^34 + 2 * q^35 + 52 * q^36 + 16 * q^39 - 10 * q^40 + 8 * q^41 + 4 * q^44 - 2 * q^45 - 16 * q^46 - 12 * q^49 + 28 * q^50 - 8 * q^51 - 76 * q^54 - 6 * q^55 - 28 * q^59 + 16 * q^60 + 24 * q^61 + 44 * q^64 + 12 * q^65 + 4 * q^66 - 24 * q^69 + 6 * q^70 + 8 * q^71 + 16 * q^74 - 60 * q^75 - 16 * q^76 + 16 * q^79 + 22 * q^80 + 52 * q^81 + 24 * q^84 - 20 * q^85 + 24 * q^86 - 16 * q^89 - 46 * q^90 - 12 * q^91 + 20 * q^94 - 40 * q^95 - 32 * q^96 + 20 * q^99

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