LMFDB - Embedded newform 418.2.v.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	418.29
Dual form			418.2.v.a.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.898794i) q^{2} +(-2.91493 + 1.17771i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.450149 + 0.129078i) q^{5} +(0.219304 - 3.13619i) q^{6} +(0.395058 - 1.85860i) q^{7} +(0.978148 - 0.207912i) q^{8} +(4.95179 - 4.78189i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.898794i) q^{2} +(-2.91493 + 1.17771i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.450149 + 0.129078i) q^{5} +(0.219304 - 3.13619i) q^{6} +(0.395058 - 1.85860i) q^{7} +(0.978148 - 0.207912i) q^{8} +(4.95179 - 4.78189i) q^{9} +(0.0813176 - 0.461175i) q^{10} +(2.57721 - 2.08758i) q^{11} +(2.72265 + 1.57193i) q^{12} +(0.751931 + 3.01583i) q^{13} +(1.49732 + 1.16983i) q^{14} +(1.16013 - 0.906397i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-4.71559 + 4.88314i) q^{17} +(2.12721 + 6.54688i) q^{18} +(2.09344 - 3.82328i) q^{19} +(0.378854 + 0.275254i) q^{20} +(1.03732 + 5.88295i) q^{21} +(0.746527 + 3.23152i) q^{22} +(0.359669 - 0.130909i) q^{23} +(-2.60637 + 1.75802i) q^{24} +(-4.05427 + 2.53339i) q^{25} +(-3.04024 - 0.646222i) q^{26} +(-4.96629 + 11.1545i) q^{27} +(-1.70782 + 0.832959i) q^{28} +(6.48660 - 0.911632i) q^{29} +(0.306094 + 1.44006i) q^{30} +(0.445986 + 1.00170i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-5.05383 + 9.12034i) q^{33} +(-2.32176 - 6.37897i) q^{34} +(0.0620698 + 0.887640i) q^{35} +(-6.81680 - 0.958039i) q^{36} +(10.1558 - 3.29982i) q^{37} +(2.51864 + 3.55759i) q^{38} +(-5.74359 - 7.90537i) q^{39} +(-0.413475 + 0.219849i) q^{40} +(4.13359 + 10.2310i) q^{41} +(-5.74229 - 1.64658i) q^{42} +(2.05989 - 5.65949i) q^{43} +(-3.23172 - 0.745629i) q^{44} +(-1.61180 + 2.79173i) q^{45} +(-0.0400085 + 0.380655i) q^{46} +(4.71866 + 2.50896i) q^{47} +(-0.437539 - 3.11325i) q^{48} +(3.09649 + 1.37865i) q^{49} +(-0.499720 - 4.75452i) q^{50} +(7.99470 - 19.7876i) q^{51} +(1.91357 - 2.44926i) q^{52} +(-1.63719 + 5.70956i) q^{53} +(-7.84849 - 9.35346i) q^{54} +(-0.890668 + 1.27238i) q^{55} -1.90012i q^{56} +(-1.59952 + 13.6101i) q^{57} +(-2.02417 + 6.22975i) q^{58} +(4.57399 + 8.60243i) q^{59} +(-1.42850 - 0.356165i) q^{60} +(-1.73327 - 1.16911i) q^{61} +(-1.09583 - 0.0382672i) q^{62} +(-6.93138 - 11.0925i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.727758 - 1.26051i) q^{65} +(-5.98185 - 8.54045i) q^{66} +(6.09645 + 1.07497i) q^{67} +(6.75117 + 0.709577i) q^{68} +(-0.894237 + 0.805175i) q^{69} +(-0.825015 - 0.333328i) q^{70} +(-1.65319 - 5.76537i) q^{71} +(3.84937 - 5.70693i) q^{72} +(3.82558 - 6.12221i) q^{73} +(-1.48615 + 10.5745i) q^{74} +(8.83431 - 12.1594i) q^{75} +(-4.30164 + 0.704193i) q^{76} +(-2.86183 - 5.61472i) q^{77} +(9.62313 - 1.69682i) q^{78} +(-10.3815 + 0.725944i) q^{79} +(-0.0163431 - 0.468004i) q^{80} +(0.618952 - 17.7245i) q^{81} +(-11.0076 - 0.769726i) q^{82} +(1.59395 - 0.167531i) q^{83} +(3.99719 - 4.43933i) q^{84} +(1.49241 - 2.80682i) q^{85} +(4.18372 + 4.33237i) q^{86} +(-17.8343 + 10.2966i) q^{87} +(2.08686 - 2.57779i) q^{88} +(4.29848 - 5.12273i) q^{89} +(-1.80262 - 2.67249i) q^{90} +(5.90228 - 0.206112i) q^{91} +(-0.324592 - 0.202828i) q^{92} +(-2.47973 - 2.39465i) q^{93} +(-4.32356 + 3.14125i) q^{94} +(-0.448858 + 1.99126i) q^{95} +(2.98998 + 0.971503i) q^{96} +(-0.456643 - 0.222720i) q^{97} +(-2.59653 + 2.17875i) q^{98} +(2.77925 - 22.6612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$3$	−2.91493	+	1.17771i	−1.68293	+	0.679950i	−0.998780	−	0.0493876i	$-0.984273\pi$
$3$	−2.91493	+	1.17771i	−1.68293	+	0.679950i	−0.684155	+	0.729337i	$0.739829\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	−0.450149	+	0.129078i	−0.201313	+	0.0577255i	−0.374778	−	0.927114i	$-0.622281\pi$
$5$	−0.450149	+	0.129078i	−0.201313	+	0.0577255i	0.173466	+	0.984840i	$0.444503\pi$
$6$	0.219304	−	3.13619i	0.0895305	−	1.28035i
$7$	0.395058	−	1.85860i	0.149318	−	0.702485i	−0.838249	−	0.545287i	$-0.816421\pi$
$7$	0.395058	−	1.85860i	0.149318	−	0.702485i	0.987567	−	0.157198i	$-0.0502460\pi$
$8$	0.978148	−	0.207912i	0.345827	−	0.0735079i
$9$	4.95179	−	4.78189i	1.65060	−	1.59396i
$10$	0.0813176	−	0.461175i	0.0257149	−	0.145836i
$11$	2.57721	−	2.08758i	0.777059	−	0.629428i
$11$	2.57721	−	2.08758i	0.777059	−	0.629428i
$12$	2.72265	+	1.57193i	0.785963	+	0.453776i
$13$	0.751931	+	3.01583i	0.208548	+	0.836441i	0.979811	+	0.199924i	$0.0640697\pi$
$13$	0.751931	+	3.01583i	0.208548	+	0.836441i	−0.771263	+	0.636516i	$0.780375\pi$
$14$	1.49732	+	1.16983i	0.400175	+	0.312651i
$15$	1.16013	−	0.906397i	0.299545	−	0.234031i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−4.71559	+	4.88314i	−1.14370	+	1.18434i	−0.163454	+	0.986551i	$0.552263\pi$
$17$	−4.71559	+	4.88314i	−1.14370	+	1.18434i	−0.980246	+	0.197784i	$0.936626\pi$
$18$	2.12721	+	6.54688i	0.501388	+	1.54311i
$19$	2.09344	−	3.82328i	0.480269	−	0.877121i
$19$	2.09344	−	3.82328i	0.480269	−	0.877121i
$20$	0.378854	+	0.275254i	0.0847144	+	0.0615486i
$21$	1.03732	+	5.88295i	0.226362	+	1.28376i
$22$	0.746527	+	3.23152i	0.159160	+	0.688962i
$23$	0.359669	−	0.130909i	0.0749962	−	0.0272964i	−0.304250	−	0.952592i	$-0.598406\pi$
$23$	0.359669	−	0.130909i	0.0749962	−	0.0272964i	0.379246	+	0.925296i	$0.376183\pi$
$24$	−2.60637	+	1.75802i	−0.532023	+	0.358854i
$25$	−4.05427	+	2.53339i	−0.810854	+	0.506678i
$26$	−3.04024	−	0.646222i	−0.596239	−	0.126735i
$27$	−4.96629	+	11.1545i	−0.955762	+	2.14668i
$28$	−1.70782	+	0.832959i	−0.322747	+	0.157414i
$29$	6.48660	−	0.911632i	1.20453	−	0.169286i	0.491790	−	0.870714i	$-0.336343\pi$
$29$	6.48660	−	0.911632i	1.20453	−	0.169286i	0.712740	+	0.701428i	$0.247454\pi$
$30$	0.306094	+	1.44006i	0.0558849	+	0.262918i
$31$	0.445986	+	1.00170i	0.0801015	+	0.179911i	0.949157	−	0.314805i	$-0.101939\pi$
$31$	0.445986	+	1.00170i	0.0801015	+	0.179911i	−0.869055	+	0.494715i	$0.835272\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−5.05383	+	9.12034i	−0.879759	+	1.58765i
$34$	−2.32176	−	6.37897i	−0.398178	−	1.09398i
$35$	0.0620698	+	0.887640i	0.0104917	+	0.150039i
$36$	−6.81680	−	0.958039i	−1.13613	−	0.159673i
$37$	10.1558	−	3.29982i	1.66960	−	0.542487i	0.686753	−	0.726891i	$-0.259035\pi$
$37$	10.1558	−	3.29982i	1.66960	−	0.542487i	0.982851	+	0.184404i	$0.0590355\pi$
$38$	2.51864	+	3.55759i	0.408577	+	0.577117i
$39$	−5.74359	−	7.90537i	−0.919710	−	1.26587i
$40$	−0.413475	+	0.219849i	−0.0653761	+	0.0347611i
$41$	4.13359	+	10.2310i	0.645558	+	1.59781i	0.793331	+	0.608790i	$0.208345\pi$
$41$	4.13359	+	10.2310i	0.645558	+	1.59781i	−0.147773	+	0.989021i	$0.547211\pi$
$42$	−5.74229	−	1.64658i	−0.886055	−	0.254072i
$43$	2.05989	−	5.65949i	0.314130	−	0.863064i	−0.677682	−	0.735355i	$-0.737015\pi$
$43$	2.05989	−	5.65949i	0.314130	−	0.863064i	0.991812	−	0.127709i	$-0.0407624\pi$
$44$	−3.23172	−	0.745629i	−0.487201	−	0.112408i
$45$	−1.61180	+	2.79173i	−0.240274	+	0.416166i
$46$	−0.0400085	+	0.380655i	−0.00589893	+	0.0561245i
$47$	4.71866	+	2.50896i	0.688287	+	0.365969i	0.776486	−	0.630134i	$-0.217000\pi$
$47$	4.71866	+	2.50896i	0.688287	+	0.365969i	−0.0881990	+	0.996103i	$0.528111\pi$
$48$	−0.437539	−	3.11325i	−0.0631534	−	0.449360i
$49$	3.09649	+	1.37865i	0.442356	+	0.196950i
$50$	−0.499720	−	4.75452i	−0.0706710	−	0.672390i
$51$	7.99470	−	19.7876i	1.11948	−	2.77082i
$52$	1.91357	−	2.44926i	0.265365	−	0.339651i
$53$	−1.63719	+	5.70956i	−0.224885	+	0.784269i	0.765199	+	0.643794i	$0.222641\pi$
$53$	−1.63719	+	5.70956i	−0.224885	+	0.784269i	−0.990084	+	0.140475i	$0.955137\pi$
$54$	−7.84849	−	9.35346i	−1.06804	−	1.27284i
$55$	−0.890668	+	1.27238i	−0.120098	+	0.171568i
$56$		−	1.90012i		−	0.253915i
$57$	−1.59952	+	13.6101i	−0.211862	+	1.80270i
$58$	−2.02417	+	6.22975i	−0.265786	+	0.818006i
$59$	4.57399	+	8.60243i	0.595483	+	1.11994i	0.980405	+	0.196992i	$0.0631173\pi$
$59$	4.57399	+	8.60243i	0.595483	+	1.11994i	−0.384922	+	0.922949i	$0.625772\pi$
$60$	−1.42850	−	0.356165i	−0.184419	−	0.0459807i
$61$	−1.73327	−	1.16911i	−0.221923	−	0.149689i	0.443200	−	0.896423i	$-0.353843\pi$
$61$	−1.73327	−	1.16911i	−0.221923	−	0.149689i	−0.665123	+	0.746734i	$0.731621\pi$
$62$	−1.09583	−	0.0382672i	−0.139171	−	0.00485994i
$63$	−6.93138	−	11.0925i	−0.873271	−	1.39753i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−0.727758	−	1.26051i	−0.0902673	−	0.156348i
$66$	−5.98185	−	8.54045i	−0.736315	−	1.05126i
$67$	6.09645	+	1.07497i	0.744800	+	0.131328i	0.533154	−	0.846018i	$-0.321007\pi$
$67$	6.09645	+	1.07497i	0.744800	+	0.131328i	0.211646	+	0.977346i	$0.432118\pi$
$68$	6.75117	+	0.709577i	0.818700	+	0.0860489i
$69$	−0.894237	+	0.805175i	−0.107653	+	0.0969316i
$70$	−0.825015	−	0.333328i	−0.0986082	−	0.0398403i
$71$	−1.65319	−	5.76537i	−0.196198	−	0.684224i	−0.996422	−	0.0845220i	$-0.973064\pi$
$71$	−1.65319	−	5.76537i	−0.196198	−	0.684224i	0.800224	−	0.599702i	$-0.204714\pi$
$72$	3.84937	−	5.70693i	0.453653	−	0.672568i
$73$	3.82558	−	6.12221i	0.447750	−	0.716550i	−0.544776	−	0.838582i	$-0.683385\pi$
$73$	3.82558	−	6.12221i	0.447750	−	0.716550i	0.992526	+	0.122031i	$0.0389409\pi$
$74$	−1.48615	+	10.5745i	−0.172762	+	1.22926i
$75$	8.83431	−	12.1594i	1.02010	−	1.40404i
$76$	−4.30164	+	0.704193i	−0.493432	+	0.0807765i
$77$	−2.86183	−	5.61472i	−0.326135	−	0.639857i
$78$	9.62313	−	1.69682i	1.08960	−	0.192127i
$79$	−10.3815	+	0.725944i	−1.16801	+	0.0816750i	−0.640557	−	0.767911i	$-0.721296\pi$
$79$	−10.3815	+	0.725944i	−1.16801	+	0.0816750i	−0.527450	+	0.849586i	$0.676852\pi$
$80$	−0.0163431	−	0.468004i	−0.00182721	−	0.0523245i
$81$	0.618952	−	17.7245i	0.0687724	−	1.96938i
$82$	−11.0076	−	0.769726i	−1.21559	−	0.0850020i
$83$	1.59395	−	0.167531i	0.174958	−	0.0183889i	−0.0166441	−	0.999861i	$-0.505298\pi$
$83$	1.59395	−	0.167531i	0.174958	−	0.0183889i	0.191603	+	0.981473i	$0.438632\pi$
$84$	3.99719	−	4.43933i	0.436129	−	0.484370i
$85$	1.49241	−	2.80682i	0.161875	−	0.304442i
$86$	4.18372	+	4.33237i	0.451142	+	0.467172i
$87$	−17.8343	+	10.2966i	−1.91204	+	1.10392i
$88$	2.08686	−	2.57779i	0.222460	−	0.274794i
$89$	4.29848	−	5.12273i	0.455638	−	0.543008i	−0.488498	−	0.872565i	$-0.662455\pi$
$89$	4.29848	−	5.12273i	0.455638	−	0.543008i	0.944136	+	0.329557i	$0.106899\pi$
$90$	−1.80262	−	2.67249i	−0.190013	−	0.281706i
$91$	5.90228	−	0.206112i	0.618727	−	0.0216064i
$92$	−0.324592	−	0.202828i	−0.0338410	−	0.0211462i
$93$	−2.47973	−	2.39465i	−0.257136	−	0.248313i
$94$	−4.32356	+	3.14125i	−0.445941	+	0.323995i
$95$	−0.448858	+	1.99126i	−0.0460519	+	0.204299i
$96$	2.98998	+	0.971503i	0.305164	+	0.0991536i
$97$	−0.456643	−	0.222720i	−0.0463651	−	0.0226138i	0.415043	−	0.909802i	$-0.363767\pi$
$97$	−0.456643	−	0.222720i	−0.0463651	−	0.0226138i	−0.461408	+	0.887188i	$0.652656\pi$
$98$	−2.59653	+	2.17875i	−0.262289	+	0.220087i
$99$	2.77925	−	22.6612i	0.279325	−	2.27753i
$100$	4.49239	+	1.63510i	0.449239	+	0.163510i
$101$	15.7112	−	3.91725i	1.56333	−	0.389781i	0.638332	−	0.769761i	$-0.279625\pi$
$101$	15.7112	−	3.91725i	1.56333	−	0.389781i	0.924995	+	0.379980i	$0.124069\pi$
$102$	14.2803	+	15.8599i	1.41396	+	1.57036i
$103$	−5.65429	−	5.09115i	−0.557134	−	0.501645i	0.341775	−	0.939782i	$-0.388972\pi$
$103$	−5.65429	−	5.09115i	−0.557134	−	0.501645i	−0.898908	+	0.438136i	$0.855639\pi$
$104$	1.36253	+	2.79359i	0.133607	+	0.273934i
$105$	−1.22631	−	2.51431i	−0.119676	−	0.245371i
$106$	−4.41402	−	3.97441i	−0.428728	−	0.386028i
$107$	8.93719	+	9.92576i	0.863991	+	0.959559i	0.999513	−	0.0312153i	$-0.00993776\pi$
$107$	8.93719	+	9.92576i	0.863991	+	0.959559i	−0.135522	+	0.990774i	$0.543271\pi$
$108$	11.8474	−	2.95388i	1.14002	−	0.284238i
$109$	−3.99295	−	1.45332i	−0.382456	−	0.139202i	0.143635	−	0.989631i	$-0.454121\pi$
$109$	−3.99295	−	1.45332i	−0.382456	−	0.139202i	−0.526091	+	0.850428i	$0.676343\pi$
$110$	−0.753166	−	1.35830i	−0.0718116	−	0.129509i
$111$	−25.7172	+	21.5793i	−2.44097	+	2.04822i
$112$	1.70782	+	0.832959i	0.161374	+	0.0787072i
$113$	−8.39735	−	2.72847i	−0.789957	−	0.256672i	−0.113871	−	0.993496i	$-0.536325\pi$
$113$	−8.39735	−	2.72847i	−0.789957	−	0.256672i	−0.676086	+	0.736823i	$0.736325\pi$
$114$	−11.5315	−	7.40390i	−1.08002	−	0.693439i
$115$	−0.145007	+	0.105354i	−0.0135220	+	0.00982429i
$116$	−4.71192	−	4.55025i	−0.437491	−	0.422480i
$117$	18.1448	+	11.3381i	1.67748	+	1.04821i
$118$	−9.73692	+	0.340021i	−0.896356	+	0.0313015i
$119$	7.21287	+	10.6935i	0.661203	+	0.980274i
$120$	0.946333	−	1.12780i	0.0863879	−	0.102953i
$121$	2.28404	−	10.7603i	0.207640	−	0.978205i
$122$	1.81060	−	1.04535i	0.163924	−	0.0946418i
$123$	−24.0982	−	24.9544i	−2.17286	−	2.25007i
$124$	0.514775	−	0.968151i	0.0462281	−	0.0869425i
$125$	3.06475	−	3.40375i	0.274120	−	0.304441i
$126$	13.0084	−	1.36724i	1.15888	−	0.121803i
$127$	10.1215	+	0.707768i	0.898142	+	0.0628042i	0.511360	−	0.859367i	$-0.329142\pi$
$127$	10.1215	+	0.707768i	0.898142	+	0.0628042i	0.386782	+	0.922171i	$0.373586\pi$
$128$	−0.0348995	+	0.999391i	−0.00308471	+	0.0883345i
$129$	0.660804	+	18.9230i	0.0581806	+	1.66607i
$130$	1.45197	−	0.101532i	0.127346	−	0.00890492i
$131$	3.60657	−	0.635935i	0.315107	−	0.0555619i	−0.0138580	−	0.999904i	$-0.504411\pi$
$131$	3.60657	−	0.635935i	0.315107	−	0.0555619i	0.328965	+	0.944342i	$0.393300\pi$
$132$	10.2984	−	1.63257i	0.896358	−	0.142097i
$133$	−6.27893	−	5.40129i	−0.544452	−	0.468351i
$134$	−3.63868	+	5.00822i	−0.314334	+	0.432644i
$135$	0.795771	−	5.66220i	0.0684891	−	0.487325i
$136$	−3.59728	+	5.75686i	−0.308465	+	0.493646i
$137$	−11.4652	+	16.9979i	−0.979541	+	1.45223i	−0.0896944	+	0.995969i	$0.528589\pi$
$137$	−11.4652	+	16.9979i	−0.979541	+	1.45223i	−0.889847	+	0.456260i	$0.849189\pi$
$138$	−0.331678	−	1.15670i	−0.0282343	−	0.0984649i
$139$	−3.81405	−	1.54098i	−0.323503	−	0.130704i	0.207110	−	0.978318i	$-0.433594\pi$
$139$	−3.81405	−	1.54098i	−0.323503	−	0.130704i	−0.530614	+	0.847614i	$0.678039\pi$
$140$	0.661256	−	0.595397i	0.0558863	−	0.0503203i
$141$	−16.7094	−	1.75623i	−1.40718	−	0.147901i
$142$	5.90659	+	1.04149i	0.495670	+	0.0874001i
$143$	8.23367	+	6.20272i	0.688534	+	0.518697i
$144$	3.44190	+	5.96154i	0.286825	+	0.496795i
$145$	−2.80226	+	1.24765i	−0.232715	+	0.103611i
$146$	3.82558	+	6.12221i	0.316607	+	0.506678i
$147$	−10.6497	−	0.371895i	−0.878372	−	0.0306734i
$148$	−8.85283	−	5.97131i	−0.727698	−	0.490839i
$149$	7.12756	+	1.77710i	0.583912	+	0.145586i	0.522667	−	0.852537i	$-0.324937\pi$
$149$	7.12756	+	1.77710i	0.583912	+	0.145586i	0.0612454	+	0.998123i	$0.480493\pi$
$150$	7.05607	+	13.2705i	0.576126	+	1.08354i
$151$	−3.94217	+	12.1328i	−0.320809	+	0.987350i	0.652487	+	0.757800i	$0.273726\pi$
$151$	−3.94217	+	12.1328i	−0.320809	+	0.987350i	−0.973297	+	0.229550i	$0.926274\pi$
$152$	1.25279	−	4.17499i	0.101615	−	0.338636i
$153$			46.7297i			3.77787i
$154$	6.30102	−	0.110861i	0.507751	−	0.00893339i
$155$	−0.330058	−	0.393347i	−0.0265109	−	0.0315944i
$156$	−2.69341	+	9.39304i	−0.215646	+	0.752045i
$157$	10.9553	−	14.0222i	0.874328	−	1.11909i	−0.117697	−	0.993050i	$-0.537551\pi$
$157$	10.9553	−	14.0222i	0.874328	−	1.11909i	0.992025	−	0.126040i	$-0.0402267\pi$
$158$	3.89847	−	9.64904i	0.310145	−	0.767637i
$159$	−1.95190	−	18.5711i	−0.154796	−	1.47278i
$160$	0.427804	+	0.190470i	0.0338209	+	0.0150580i
$161$	−0.101217	−	0.720198i	−0.00797703	−	0.0567595i
$162$	15.6593	+	8.32620i	1.23031	+	0.654168i
$163$	0.0423948	−	0.403360i	0.00332062	−	0.0315936i	−0.992736	−	0.120312i	$-0.961610\pi$
$163$	0.0423948	−	0.403360i	0.00332062	−	0.0315936i	0.996057	+	0.0887185i	$0.0282772\pi$
$164$	5.51724	−	9.55614i	0.430824	−	0.746209i
$165$	1.09774	−	4.75785i	0.0854589	−	0.370398i
$166$	−0.548165	+	1.50607i	−0.0425458	+	0.116894i
$167$	9.94654	+	2.85212i	0.769686	+	0.220704i	0.637427	−	0.770511i	$-0.279999\pi$
$167$	9.94654	+	2.85212i	0.769686	+	0.220704i	0.132260	+	0.991215i	$0.457777\pi$
$168$	2.23779	+	5.53872i	0.172649	+	0.427322i
$169$	2.94849	−	1.56774i	0.226807	−	0.120595i
$170$	1.86852	+	2.57180i	0.143309	+	0.197248i
$171$	−7.91623	−	28.9427i	−0.605369	−	2.21330i
$172$	−5.72793	+	1.86112i	−0.436751	+	0.141909i
$173$	−15.7548	−	2.21419i	−1.19781	−	0.168342i	−0.488072	−	0.872804i	$-0.662300\pi$
$173$	−15.7548	−	2.21419i	−1.19781	−	0.168342i	−0.709742	+	0.704462i	$0.751188\pi$
$174$	−1.43652	−	20.5431i	−0.108902	−	1.55737i
$175$	3.10689	+	8.53610i	0.234859	+	0.645268i
$176$	1.40208	+	3.00569i	0.105686	+	0.226562i
$177$	−23.4640	−	19.6886i	−1.76366	−	1.47989i
$178$	2.71995	+	6.10910i	0.203869	+	0.457897i
$179$	0.116075	+	0.546088i	0.00867582	+	0.0408165i	0.982273	−	0.187458i	$-0.0600249\pi$
$179$	0.116075	+	0.546088i	0.00867582	+	0.0408165i	−0.973597	+	0.228275i	$0.926692\pi$
$180$	3.19224	−	0.448640i	0.237935	−	0.0334396i
$181$	−10.5359	+	5.13869i	−0.783125	+	0.381955i	−0.786147	−	0.618040i	$-0.787927\pi$
$181$	−10.5359	+	5.13869i	−0.783125	+	0.381955i	0.00302191	+	0.999995i	$0.499038\pi$
$182$	−2.40214	+	5.39529i	−0.178058	+	0.399925i
$183$	6.42923	+	1.36658i	0.475263	+	0.101020i
$184$	0.324592	−	0.202828i	0.0239292	−	0.0149526i
$185$	−4.14569	+	2.79630i	−0.304797	+	0.205588i
$186$	3.23933	−	1.17902i	0.237519	−	0.0864500i
$187$	−1.95915	+	22.4290i	−0.143267	+	1.64017i
$188$	−0.928013	−	5.26302i	−0.0676823	−	0.383845i
$189$	18.7697	+	13.6370i	1.36530	+	0.991946i
$190$	−1.59297	−	1.27634i	−0.115566	−	0.0925957i
$191$	−5.55945	−	17.1102i	−0.402267	−	1.23805i	−0.923155	−	0.384427i	$-0.874399\pi$
$191$	−5.55945	−	17.1102i	−0.402267	−	1.23805i	0.520888	−	0.853625i	$-0.325601\pi$
$192$	−2.18390	+	2.26150i	−0.157610	+	0.163209i
$193$	−0.662666	+	2.65781i	−0.0476998	+	0.191313i	−0.989419	−	0.145087i	$-0.953654\pi$
$193$	−0.662666	+	2.65781i	−0.0476998	+	0.191313i	0.941719	+	0.336400i	$0.109209\pi$
$194$	0.400358	−	0.312794i	0.0287441	−	0.0224573i
$195$	3.60588	+	2.81722i	0.258222	+	0.201745i
$196$	−0.820002	−	3.28885i	−0.0585716	−	0.234918i
$197$	2.40768	+	1.39007i	0.171540	+	0.0990387i	0.583312	−	0.812248i	$-0.301757\pi$
$197$	2.40768	+	1.39007i	0.171540	+	0.0990387i	−0.411772	+	0.911287i	$0.635090\pi$
$198$	19.1494	+	12.4320i	1.36089	+	0.883502i
$199$	0.724118	−	4.10668i	0.0513314	−	0.291115i	−0.948326	−	0.317298i	$-0.897224\pi$
$199$	0.724118	−	4.10668i	0.0513314	−	0.291115i	0.999657	+	0.0261836i	$0.00833544\pi$
$200$	−3.43895	+	3.32096i	−0.243171	+	0.234827i
$201$	−19.0367	+	4.04638i	−1.34275	+	0.285409i
$202$	−3.36655	+	15.8384i	−0.236870	+	1.11438i
$203$	0.868221	−	12.4161i	0.0609372	−	0.871442i
$204$	−20.5149	+	5.88254i	−1.43633	+	0.411860i
$205$	−3.18132	−	4.07191i	−0.222193	−	0.284395i
$206$	7.05457	−	2.85023i	0.491515	−	0.198585i
$207$	1.15501	−	2.36813i	0.0802790	−	0.164596i
$208$	−3.10816			−0.215512
$209$	−2.58616	−	14.2236i	−0.178888	−	0.983869i
$210$	2.79742			0.193040
$211$	−0.425898	+	0.873220i	−0.0293200	+	0.0601149i	−0.912951	−	0.408068i	$-0.866202\pi$
$211$	−0.425898	+	0.873220i	−0.0293200	+	0.0601149i	0.883631	+	0.468183i	$0.155091\pi$
$212$	5.50715	−	2.22503i	0.378233	−	0.152816i
$213$	11.6089	+	14.8587i	0.795426	+	1.01810i
$214$	−12.8390	+	3.68153i	−0.877657	+	0.251664i
$215$	−0.196739	+	2.81350i	−0.0134175	+	0.191879i
$216$	−2.53862	+	11.9433i	−0.172731	+	0.812636i
$217$	2.03795	−	0.433180i	0.138345	−	0.0294062i
$218$	3.05663	−	2.95175i	0.207021	−	0.199918i
$219$	−3.94112	+	22.3512i	−0.266316	+	1.51035i
$220$	1.55100	−	0.0815006i	0.104568	−	0.00549477i
$221$	−18.2725	−	10.5496i	−1.22914	−	0.709646i
$222$	−8.12166	−	32.5742i	−0.545090	−	2.18624i
$223$	−22.9306	−	17.9154i	−1.53555	−	1.19970i	−0.906402	−	0.422415i	$-0.861182\pi$
$223$	−22.9306	−	17.9154i	−1.53555	−	1.19970i	−0.629146	−	0.777287i	$-0.716595\pi$
$224$	−1.49732	+	1.16983i	−0.100044	+	0.0781627i
$225$	−7.96150	+	31.9319i	−0.530767	+	2.12879i
$226$	6.13349	−	6.35141i	0.407993	−	0.422490i
$227$	0.807277	+	2.48454i	0.0535809	+	0.164905i	0.974266	−	0.225401i	$-0.0723692\pi$
$227$	0.807277	+	2.48454i	0.0535809	+	0.164905i	−0.920685	+	0.390306i	$0.872369\pi$
$228$	11.7096	−	7.11875i	0.775490	−	0.471450i
$229$	10.6072	+	7.70661i	0.700946	+	0.509267i	0.880240	−	0.474528i	$-0.157381\pi$
$229$	10.6072	+	7.70661i	0.700946	+	0.509267i	−0.179294	+	0.983796i	$0.557381\pi$
$230$	−0.0311245	−	0.176516i	−0.00205229	−	0.0116391i
$231$	14.9545	+	12.9961i	0.983935	+	0.855081i
$232$	6.15531	−	2.24035i	0.404116	−	0.147086i
$233$	15.4872	−	10.4462i	1.01460	−	0.684355i	0.0650195	−	0.997884i	$-0.479289\pi$
$233$	15.4872	−	10.4462i	1.01460	−	0.684355i	0.949579	+	0.313529i	$0.101511\pi$
$234$	−18.1448	+	11.3381i	−1.18616	+	0.741195i
$235$	−2.44795	−	0.520328i	−0.159687	−	0.0339425i
$236$	3.96278	−	8.90054i	0.257955	−	0.579376i
$237$	29.4063	−	14.3424i	1.91014	−	0.931640i
$238$	−12.7732	+	1.79516i	−0.827963	+	0.116363i
$239$	3.01608	+	14.1895i	0.195094	+	0.917845i	0.961354	+	0.275315i	$0.0887821\pi$
$239$	3.01608	+	14.1895i	0.195094	+	0.917845i	−0.766260	+	0.642530i	$0.777885\pi$
$240$	0.598811	+	1.34495i	0.0386531	+	0.0868162i
$241$	4.30292	+	3.61058i	0.277175	+	0.232578i	0.770769	−	0.637115i	$-0.219872\pi$
$241$	4.30292	+	3.61058i	0.277175	+	0.232578i	−0.493593	+	0.869693i	$0.664317\pi$
$242$	8.67000	+	6.76987i	0.557329	+	0.435184i
$243$	6.54175	+	17.9733i	0.419654	+	1.15299i
$244$	0.145840	+	2.08561i	0.00933646	+	0.133518i
$245$	−1.57184	−	0.220907i	−0.100421	−	0.0141132i
$246$	32.9929	−	10.7200i	2.10355	−	0.683484i
$247$	13.1045	+	3.43862i	0.833819	+	0.218794i
$248$	0.644506	+	0.887086i	0.0409261	+	0.0563300i
$249$	−4.44894	+	2.36554i	−0.281940	+	0.149910i
$250$	1.71577	+	4.24669i	0.108515	+	0.268584i
$251$	−24.6681	−	7.07346i	−1.55704	−	0.446473i	−0.616835	−	0.787092i	$-0.711586\pi$
$251$	−24.6681	−	7.07346i	−1.55704	−	0.446473i	−0.940201	+	0.340619i	$0.889363\pi$
$252$	−4.47364	+	12.2912i	−0.281813	+	0.774275i
$253$	0.653661	−	1.08822i	0.0410953	−	0.0684156i
$254$	−5.07313	+	8.78692i	−0.318317	+	0.551341i
$255$	−1.04466	+	9.93930i	−0.0654193	+	0.622423i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	−1.01303	−	7.20806i	−0.0631909	−	0.449627i	−0.996007	−	0.0892740i	$-0.971545\pi$
$257$	−1.01303	−	7.20806i	−0.0631909	−	0.449627i	0.932816	−	0.360352i	$-0.117344\pi$
$258$	−17.2975	−	7.70135i	−1.07690	−	0.479465i
$259$	−2.12092	−	20.1792i	−0.131788	−	1.25387i
$260$	−0.545246	+	1.34953i	−0.0338147	+	0.0836944i
$261$	27.7609	−	35.5324i	1.71836	−	2.19940i
$262$	−1.00944	+	3.52033i	−0.0623634	+	0.217487i
$263$	18.2447	+	21.7432i	1.12502	+	1.34074i	0.933219	+	0.359309i	$0.116988\pi$
$263$	18.2447	+	21.7432i	1.12502	+	1.34074i	0.191799	+	0.981434i	$0.438568\pi$
$264$	−3.04717	+	9.97179i	−0.187540	+	0.613721i
$265$		−	2.78148i		−	0.170865i
$266$	7.60715	−	3.27569i	0.466424	−	0.200846i
$267$	−6.49668	+	19.9947i	−0.397590	+	1.22366i
$268$	−2.90626	−	5.46588i	−0.177528	−	0.333882i
$269$	20.2552	+	5.05018i	1.23498	+	0.307915i	0.804100	−	0.594494i	$-0.202648\pi$
$269$	20.2552	+	5.05018i	1.23498	+	0.307915i	0.430880	+	0.902409i	$0.358203\pi$
$270$	4.74031	+	3.19738i	0.288486	+	0.194586i
$271$	−2.30258	−	0.0804077i	−0.139872	−	0.00488442i	−0.0351218	−	0.999383i	$-0.511182\pi$
$271$	−2.30258	−	0.0804077i	−0.139872	−	0.00488442i	−0.104750	+	0.994499i	$0.533404\pi$
$272$	−3.59728	−	5.75686i	−0.218117	−	0.349061i
$273$	−16.9620	+	7.55196i	−1.02659	+	0.457065i
$274$	−10.2516	−	17.7563i	−0.619321	−	1.07270i
$275$	−5.16006	+	14.9927i	−0.311163	+	0.904092i
$276$	1.18503	+	0.208953i	0.0713306	+	0.0125775i
$277$	30.9955	+	3.25776i	1.86234	+	0.195740i	0.967881	−	0.251409i	$-0.0808940\pi$
$277$	30.9955	+	3.25776i	1.86234	+	0.195740i	0.894459	+	0.447149i	$0.147561\pi$
$278$	3.05699	−	2.75253i	0.183346	−	0.165086i
$279$	6.99845	+	2.82756i	0.418986	+	0.169281i
$280$	0.245264	+	0.855338i	0.0146573	+	0.0511162i
$281$	−1.09755	+	1.62718i	−0.0654741	+	0.0970694i	−0.860353	−	0.509699i	$-0.829757\pi$
$281$	−1.09755	+	1.62718i	−0.0654741	+	0.0970694i	0.794879	+	0.606768i	$0.207534\pi$
$282$	8.90339	−	14.2484i	0.530189	−	0.848480i
$283$	2.30044	−	16.3685i	0.136747	−	0.973004i	−0.794150	−	0.607722i	$-0.792084\pi$
$283$	2.30044	−	16.3685i	0.136747	−	0.973004i	0.930897	−	0.365282i	$-0.119028\pi$
$284$	−3.52537	+	4.85225i	−0.209192	+	0.287928i
$285$	−1.03674	−	6.33301i	−0.0614109	−	0.375135i
$286$	−9.18437	+	4.68128i	−0.543083	+	0.276810i
$287$	20.6483	−	3.64086i	1.21883	−	0.214913i
$288$	−6.86703	+	0.480189i	−0.404644	+	0.0282954i
$289$	−1.01494	−	29.0641i	−0.0597025	−	1.70966i
$290$	0.107053	−	3.06559i	0.00628635	−	0.180018i
$291$	1.59338	+	0.111420i	0.0934056	+	0.00653156i
$292$	−7.17963	+	0.754609i	−0.420156	+	0.0441602i
$293$	−20.0184	+	22.2326i	−1.16948	+	1.29884i	−0.223474	+	0.974710i	$0.571740\pi$
$293$	−20.0184	+	22.2326i	−1.16948	+	1.29884i	−0.946011	+	0.324135i	$0.894927\pi$
$294$	5.00278	−	9.40885i	0.291768	−	0.548735i
$295$	−3.16936	−	3.28197i	−0.184527	−	0.191084i
$296$	9.24780	−	5.33922i	0.537518	−	0.310336i
$297$	10.4866	+	39.1149i	0.608496	+	2.26968i
$298$	−4.72176	+	5.62718i	−0.273524	+	0.325974i
$299$	0.665245	+	0.986266i	0.0384721	+	0.0570373i
$300$	−15.0207	+	0.524533i	−0.867219	+	0.0302839i
$301$	−9.70496	−	6.06433i	−0.559385	−	0.349542i
$302$	−9.17672	−	8.86185i	−0.528061	−	0.509942i
$303$	−41.1837	+	29.9217i	−2.36594	+	1.71896i
$304$	3.20327	+	2.95619i	0.183720	+	0.169549i
$305$	0.931137	+	0.302545i	0.0533167	+	0.0173237i
$306$	−42.0004	−	20.4850i	−2.40100	−	1.17105i
$307$	−4.36538	+	3.66299i	−0.249146	+	0.209058i	−0.758804	−	0.651319i	$-0.774216\pi$
$307$	−4.36538	+	3.66299i	−0.249146	+	0.209058i	0.509659	+	0.860377i	$0.329772\pi$
$308$	−2.66254	+	5.71192i	−0.151713	+	0.325467i
$309$	22.4777	+	8.18122i	1.27871	+	0.465413i
$310$	0.498226	−	0.124222i	0.0282973	−	0.00705532i
$311$	9.43989	+	10.4841i	0.535287	+	0.594497i	0.948751	−	0.316024i	$-0.102348\pi$
$311$	9.43989	+	10.4841i	0.535287	+	0.594497i	−0.413464	+	0.910520i	$0.635681\pi$
$312$	−7.26170	−	6.53846i	−0.411113	−	0.370168i
$313$	0.243139	+	0.498509i	0.0137430	+	0.0281774i	0.905555	−	0.424229i	$-0.139455\pi$
$313$	0.243139	+	0.498509i	0.0137430	+	0.0281774i	−0.891812	+	0.452406i	$0.850566\pi$
$314$	7.80054	+	15.9935i	0.440210	+	0.902564i
$315$	4.55195	+	4.09859i	0.256473	+	0.230930i
$316$	6.96353	+	7.73378i	0.391729	+	0.435059i
$317$	−13.6213	+	3.39617i	−0.765048	+	0.190748i	−0.604852	−	0.796338i	$-0.706768\pi$
$317$	−13.6213	+	3.39617i	−0.765048	+	0.190748i	−0.160195	+	0.987085i	$0.551212\pi$
$318$	17.5472	+	6.38668i	0.984001	+	0.358147i
$319$	14.8142	−	15.8907i	0.829437	−	0.889711i
$320$	−0.358731	+	0.301011i	−0.0200536	+	0.0168270i
$321$	−37.7409	−	18.4075i	−2.10649	−	1.02740i
$322$	0.691680	+	0.224740i	0.0385458	+	0.0125243i
$323$	8.79780	+	28.2516i	0.489523	+	1.57196i
$324$	−14.3481	+	10.4245i	−0.797118	+	0.579140i
$325$	−10.6888	−	10.3221i	−0.592908	−	0.572564i
$326$	0.343953	+	0.214925i	0.0190498	+	0.0119036i
$327$	13.3508	−	0.466219i	0.738298	−	0.0257819i
$328$	6.17040	+	9.14799i	0.340703	+	0.505113i
$329$	6.52729	−	7.77892i	0.359861	−	0.428866i
$330$	3.79511	+	3.07234i	0.208914	+	0.169127i
$331$	−11.1089	+	6.41373i	−0.610601	+	0.352530i	−0.773200	−	0.634162i	$-0.781345\pi$
$331$	−11.1089	+	6.41373i	−0.610601	+	0.352530i	0.162600	+	0.986692i	$0.448012\pi$
$332$	−1.11335	−	1.15291i	−0.0611029	−	0.0632739i
$333$	34.5100	−	64.9039i	1.89114	−	3.55671i
$334$	−6.92375	+	7.68960i	−0.378851	+	0.420756i
$335$	−2.88306	+	0.303022i	−0.157519	+	0.0165559i
$336$	−5.95915	−	0.416704i	−0.325098	−	0.0227331i
$337$	−0.149607	+	4.28419i	−0.00814962	+	0.233375i	0.988481	+	0.151348i	$0.0483614\pi$
$337$	−0.149607	+	4.28419i	−0.00814962	+	0.233375i	−0.996630	+	0.0820265i	$0.973861\pi$
$338$	0.116542	+	3.33733i	0.00633906	+	0.181527i
$339$	27.6910	−	1.93634i	1.50397	−	0.105168i
$340$	−3.13062	+	0.552013i	−0.169782	+	0.0299371i
$341$	3.24053	+	1.65056i	0.175484	+	0.0893831i
$342$	29.4838	+	5.57259i	1.59430	+	0.301331i
$343$	11.6037	−	15.9711i	0.626541	−	0.862359i
$344$	0.838199	−	5.96409i	0.0451926	−	0.321562i
$345$	0.298609	−	0.477875i	0.0160766	−	0.0257279i
$346$	8.89654	−	13.1897i	0.478281	−	0.709081i
$347$	−4.78959	−	16.7033i	−0.257119	−	0.896679i	−0.978863	−	0.204519i	$-0.934437\pi$
$347$	−4.78959	−	16.7033i	−0.257119	−	0.896679i	0.721744	−	0.692160i	$-0.243341\pi$
$348$	19.0938	+	7.71439i	1.02353	+	0.413534i
$349$	−19.6883	+	17.7274i	−1.05389	+	0.948928i	−0.998772	−	0.0495517i	$-0.984221\pi$
$349$	−19.6883	+	17.7274i	−1.05389	+	0.948928i	−0.0551198	+	0.998480i	$0.517554\pi$
$350$	−9.03416	−	0.949529i	−0.482896	−	0.0507545i
$351$	−37.3743	−	6.59009i	−1.99489	−	0.351753i
$352$	−3.31613	−	0.0574223i	−0.176750	−	0.00306062i
$353$	−16.3401	−	28.3019i	−0.869697	−	1.50636i	−0.862307	−	0.506387i	$-0.830981\pi$
$353$	−16.3401	−	28.3019i	−0.869697	−	1.50636i	−0.00739048	−	0.999973i	$-0.502352\pi$
$354$	27.9820	−	12.4584i	1.48723	−	0.662155i
$355$	1.48837	+	2.38188i	0.0789943	+	0.126417i
$356$	−6.68317	−	0.233381i	−0.354207	−	0.0123692i
$357$	−33.6188	−	22.6762i	−1.77930	−	1.20015i
$358$	−0.541704	−	0.135062i	−0.0286300	−	0.00713825i
$359$	−6.51760	−	12.2578i	−0.343986	−	0.646943i	0.649568	−	0.760303i	$-0.274950\pi$
$359$	−6.51760	−	12.2578i	−0.343986	−	0.646943i	−0.993554	+	0.113360i	$0.963839\pi$
$360$	−0.996150	+	3.06583i	−0.0525017	+	0.161584i
$361$	−10.2350	−	16.0076i	−0.538684	−	0.842508i
$362$		−	11.7222i		−	0.616106i
$363$	6.01463	+	34.0553i	0.315686	+	1.78744i
$364$	−3.79623	−	4.52417i	−0.198976	−	0.237131i
$365$	−0.931837	+	3.24970i	−0.0487746	+	0.170097i
$366$	−4.04666	+	5.17949i	−0.211522	+	0.270736i
$367$	−9.73114	+	24.0854i	−0.507961	+	1.25725i	0.427563	+	0.903986i	$0.359372\pi$
$367$	−9.73114	+	24.0854i	−0.507961	+	1.25725i	−0.935524	+	0.353263i	$0.885072\pi$
$368$	0.0400085	+	0.380655i	0.00208559	+	0.0198430i
$369$	69.3921	+	30.8953i	3.61241	+	1.60835i
$370$	−0.695949	−	4.95194i	−0.0361807	−	0.257439i
$371$	9.96501	+	5.29849i	0.517358	+	0.275084i
$372$	−0.360333	+	3.42834i	−0.0186824	+	0.177751i
$373$	9.55922	−	16.5571i	0.494958	−	0.857292i	−0.505025	−	0.863104i	$-0.668517\pi$
$373$	9.55922	−	16.5571i	0.494958	−	0.857292i	0.999983	+	0.00581260i	$0.00185022\pi$
$374$	−19.3003	−	11.5931i	−0.997993	−	0.599466i
$375$	−4.92491	+	13.5311i	−0.254321	+	0.698742i
$376$	5.13719	+	1.47307i	0.264930	+	0.0759675i
$377$	7.62680	+	18.8770i	0.392800	+	0.972214i
$378$	−20.4850	+	10.8920i	−1.05363	+	0.560226i
$379$	−18.4018	−	25.3278i	−0.945235	−	1.30100i	−0.953612	−	0.301039i	$-0.902667\pi$
$379$	−18.4018	−	25.3278i	−0.945235	−	1.30100i	0.00837729	−	0.999965i	$-0.497333\pi$
$380$	1.84548	−	0.872239i	0.0946712	−	0.0447449i
$381$	−30.3371	+	9.85713i	−1.55422	+	0.504996i
$382$	17.8157	+	2.50383i	0.911528	+	0.128107i
$383$	−2.04997	−	29.3159i	−0.104748	−	1.49797i	−0.711278	−	0.702911i	$-0.751883\pi$
$383$	−2.04997	−	29.3159i	−0.104748	−	1.49797i	0.606529	−	0.795061i	$-0.292561\pi$
$384$	−1.07526	−	2.95425i	−0.0548716	−	0.150759i
$385$	2.01298	+	2.15806i	0.102591	+	0.109985i
$386$	−2.09833	−	1.76071i	−0.106802	−	0.0896176i
$387$	−16.8629	−	37.8748i	−0.857191	−	1.92528i
$388$	0.105632	+	0.496960i	0.00536265	+	0.0252293i
$389$	−28.4741	+	4.00177i	−1.44369	+	0.202898i	−0.817121	−	0.576466i	$-0.804431\pi$
$389$	−28.4741	+	4.00177i	−1.44369	+	0.202898i	−0.626572	+	0.779364i	$0.715543\pi$
$390$	−4.11282	+	2.00595i	−0.208261	+	0.101575i
$391$	−1.05681	+	2.37363i	−0.0534450	+	0.120039i
$392$	3.31546	+	0.704723i	0.167456	+	0.0355939i
$393$	−9.76393	+	6.10118i	−0.492525	+	0.307764i
$394$	−2.30485	+	1.55464i	−0.116117	+	0.0783216i
$395$	4.57950	−	1.66680i	0.230420	−	0.0838660i
$396$	−19.5683	+	11.7615i	−0.983345	+	0.591040i
$397$	−1.13630	−	6.44428i	−0.0570293	−	0.323429i	0.942925	−	0.333006i	$-0.108063\pi$
$397$	−1.13630	−	6.44428i	−0.0570293	−	0.323429i	−0.999954	+	0.00957641i	$0.996952\pi$
$398$	3.37363	+	2.45108i	0.169105	+	0.122862i
$399$	24.6638	+	8.34964i	1.23473	+	0.418005i
$400$	−1.47732	−	4.54672i	−0.0738660	−	0.227336i
$401$	13.5621	−	14.0440i	0.677259	−	0.701323i	−0.289452	−	0.957193i	$-0.593473\pi$
$401$	13.5621	−	14.0440i	0.677259	−	0.701323i	0.966711	+	0.255870i	$0.0823619\pi$
$402$	4.70828	−	18.8839i	0.234828	−	0.941843i
$403$	−2.68561	+	2.09823i	−0.133780	+	0.104520i
$404$	−12.7596	−	9.96892i	−0.634816	−	0.495972i
$405$	2.00922	+	8.05854i	0.0998389	+	0.400432i
$406$	10.7789	+	6.22323i	0.534950	+	0.308854i
$407$	19.2850	−	29.7054i	0.955923	−	1.47244i
$408$	3.70593	−	21.0174i	0.183471	−	1.04051i
$409$	−9.18374	+	8.86864i	−0.454107	+	0.438526i	−0.886200	−	0.463303i	$-0.846664\pi$
$409$	−9.18374	+	8.86864i	−0.454107	+	0.438526i	0.432093	+	0.901829i	$0.357775\pi$
$410$	5.05441	−	1.07435i	0.249619	−	0.0530583i
$411$	13.4018	−	63.0504i	0.661060	−	3.11004i
$412$	−0.530749	+	7.59006i	−0.0261481	+	0.373936i
$413$	17.7955	−	5.10277i	0.875658	−	0.251091i
$414$	1.62214	+	2.07624i	0.0797236	+	0.102042i
$415$	−0.695889	+	0.281157i	−0.0341598	+	0.0138015i
$416$	1.36253	−	2.79359i	0.0668033	−	0.136967i
$417$	12.9325			0.633307
$418$	13.9178	+	3.91081i	0.680743	+	0.191284i
$419$	16.0396			0.783585			0.391793	−	0.920054i	$-0.371855\pi$
$419$	16.0396			0.783585			0.391793	+	0.920054i	$0.371855\pi$
$420$	−1.22631	+	2.51431i	−0.0598378	+	0.122686i
$421$	−2.60240	+	1.05144i	−0.126833	+	0.0512439i	−0.437146	−	0.899391i	$-0.644011\pi$
$421$	−2.60240	+	1.05144i	−0.126833	+	0.0512439i	0.310313	+	0.950635i	$0.399566\pi$
$422$	−0.598144	−	0.765589i	−0.0291172	−	0.0372683i
$423$	35.3634	−	10.1403i	1.71943	−	0.493037i
$424$	−0.414329	+	5.92519i	−0.0201216	+	0.287753i
$425$	6.74739	−	31.7440i	0.327297	−	1.53981i
$426$	−18.4439	+	3.92037i	−0.893608	+	0.189942i
$427$	−2.85765	+	2.75960i	−0.138291	+	0.133546i
$428$	2.31932	−	13.1535i	0.112108	−	0.635799i
$429$	−31.3055	−	8.38363i	−1.51144	−	0.404765i
$430$	−2.44251	−	1.41018i	−0.117788	−	0.0680051i
$431$	−2.62115	−	10.5128i	−0.126256	−	0.506386i	−0.999807	−	0.0196527i	$-0.993744\pi$
$431$	−2.62115	−	10.5128i	−0.126256	−	0.506386i	0.873551	−	0.486733i	$-0.161812\pi$
$432$	−9.62167	−	7.51727i	−0.462923	−	0.361675i
$433$	10.0140	−	7.82382i	0.481244	−	0.375989i	−0.345635	−	0.938369i	$-0.612336\pi$
$433$	10.0140	−	7.82382i	0.481244	−	0.375989i	0.826879	+	0.562380i	$0.190114\pi$
$434$	−0.504040	+	2.02159i	−0.0241947	+	0.0970396i
$435$	6.69902	−	6.93704i	0.321194	−	0.332606i
$436$	1.31308	+	4.04124i	0.0628851	+	0.193540i
$437$	0.252445	−	1.64917i	0.0120761	−	0.0788904i
$438$	−18.3615	−	13.3404i	−0.877344	−	0.637428i
$439$	2.43645	+	13.8178i	0.116286	+	0.659488i	0.986106	+	0.166119i	$0.0531237\pi$
$439$	2.43645	+	13.8178i	0.116286	+	0.659488i	−0.869820	+	0.493369i	$0.835765\pi$
$440$	−0.606662	+	1.42976i	−0.0289215	+	0.0681610i
$441$	21.9257	−	7.98031i	1.04408	−	0.380015i
$442$	17.4921	−	11.7986i	0.832014	−	0.561201i
$443$	−31.1805	+	19.4838i	−1.48143	+	0.925702i	−0.482678	+	0.875798i	$0.660336\pi$
$443$	−31.1805	+	19.4838i	−1.48143	+	0.925702i	−0.998754	+	0.0499039i	$0.984108\pi$
$444$	32.8378	+	6.97989i	1.55841	+	0.331251i
$445$	−1.27372	+	2.86083i	−0.0603802	+	0.135616i
$446$	26.1544	−	12.7563i	1.23844	−	0.604030i
$447$	−22.8692	+	3.21406i	−1.08168	+	0.152020i
$448$	−0.395058	−	1.85860i	−0.0186647	−	0.0878106i
$449$	5.90057	+	13.2529i	0.278465	+	0.625442i	0.997586	−	0.0694423i	$-0.0221220\pi$
$449$	5.90057	+	13.2529i	0.278465	+	0.625442i	−0.719121	+	0.694885i	$0.755455\pi$
$450$	−25.2101	−	21.1538i	−1.18841	−	0.997198i
$451$	32.0111	+	17.7382i	1.50734	+	0.835261i
$452$	3.01987	+	8.29702i	0.142043	+	0.390259i
$453$	−2.79769	−	40.0088i	−0.131447	−	1.87978i
$454$	−2.58698	−	0.363576i	−0.121413	−	0.0170635i
$455$	−2.63030	+	0.854636i	−0.123310	+	0.0400660i
$456$	1.26512	+	13.6452i	0.0592446	+	0.638995i
$457$	−2.37095	−	3.26333i	−0.110908	−	0.152652i	0.749954	−	0.661490i	$-0.230075\pi$
$457$	−2.37095	−	3.26333i	−0.110908	−	0.152652i	−0.860863	+	0.508838i	$0.830075\pi$
$458$	−11.5766	+	6.15537i	−0.540937	+	0.287621i
$459$	−31.0498	−	76.8509i	−1.44928	−	3.58710i
$460$	0.172295	+	0.0494049i	0.00803331	+	0.00230351i
$461$	−6.33606	+	17.4082i	−0.295100	+	0.810779i	0.700201	+	0.713946i	$0.253094\pi$
$461$	−6.33606	+	17.4082i	−0.295100	+	0.810779i	−0.995301	+	0.0968337i	$0.969129\pi$
$462$	−18.2365	+	7.74391i	−0.848437	+	0.360279i
$463$	−13.1713	+	22.8134i	−0.612124	+	1.06023i	0.378757	+	0.925496i	$0.376351\pi$
$463$	−13.1713	+	22.8134i	−0.612124	+	1.06023i	−0.990882	+	0.134735i	$0.956982\pi$
$464$	−0.684697	+	6.51446i	−0.0317863	+	0.302426i
$465$	1.42534	+	0.757868i	0.0660987	+	0.0351453i
$466$	2.59988	+	18.4991i	0.120437	+	0.856954i
$467$	−9.77095	−	4.35031i	−0.452145	−	0.201308i	0.168013	−	0.985785i	$-0.446265\pi$
$467$	−9.77095	−	4.35031i	−0.452145	−	0.201308i	−0.620158	+	0.784477i	$0.712932\pi$
$468$	−2.23648	−	21.2787i	−0.103381	−	0.983608i
$469$	4.40639	−	10.9062i	0.203468	−	0.503601i
$470$	1.54078	−	1.97211i	0.0710708	−	0.0909665i
$471$	−15.4199	+	53.7757i	−0.710513	+	2.47785i
$472$	6.26259	+	7.46346i	0.288259	+	0.343534i
$473$	−6.50587	−	18.8859i	−0.299140	−	0.868374i
$474$			32.7175i			1.50276i
$475$	1.19848	+	20.8041i	0.0549902	+	0.954558i
$476$	3.98592	−	12.2674i	0.182695	−	0.562276i
$477$	19.1955	+	36.1014i	0.878900	+	1.65297i
$478$	−14.0756	−	3.50945i	−0.643805	−	0.160519i
$479$	−18.5532	−	12.5143i	−0.847716	−	0.571792i	0.0567253	−	0.998390i	$-0.481934\pi$
$479$	−18.5532	−	12.5143i	−0.847716	−	0.571792i	−0.904441	+	0.426598i	$0.859712\pi$
$480$	−1.47134	−	0.0513802i	−0.0671570	−	0.00234517i
$481$	17.5882	+	28.1469i	0.801951	+	1.28339i
$482$	−5.13144	+	2.28466i	−0.233731	+	0.104064i
$483$	1.14322	+	1.98012i	0.0520184	+	0.0900986i
$484$	−9.88539	+	4.82483i	−0.449336	+	0.219310i
$485$	0.234306	+	0.0413144i	0.0106393	+	0.00187599i
$486$	−19.0220	−	1.99930i	−0.862856	−	0.0906899i
$487$	−3.01395	+	2.71377i	−0.136575	+	0.122973i	−0.734587	−	0.678514i	$-0.762624\pi$
$487$	−3.01395	+	2.71377i	−0.136575	+	0.122973i	0.598012	+	0.801487i	$0.295957\pi$
$488$	−1.93847	−	0.783192i	−0.0877503	−	0.0354534i
$489$	0.351462	+	1.22569i	0.0158937	+	0.0554277i
$490$	0.887597	−	1.31592i	0.0400975	−	0.0594471i
$491$	−9.40045	+	15.0439i	−0.424236	+	0.678920i	−0.989262	−	0.146153i	$-0.953311\pi$
$491$	−9.40045	+	15.0439i	−0.424236	+	0.678920i	0.565026	+	0.825073i	$0.308866\pi$
$492$	−4.82802	+	34.3531i	−0.217664	+	1.54876i
$493$	−26.1365	+	35.9738i	−1.17713	+	1.62018i
$494$	−8.83525	+	10.2709i	−0.397517	+	0.462108i
$495$	1.67399	+	10.5596i	0.0752401	+	0.474621i
$496$	−1.07984	+	0.190405i	−0.0484863	+	0.00854943i
$497$	−11.3686	+	0.794972i	−0.509953	+	0.0356594i
$498$	−0.175849	−	5.03566i	−0.00787999	−	0.225654i
$499$	0.608111	−	17.4140i	0.0272228	−	0.779559i	−0.906635	−	0.421915i	$-0.861358\pi$
$499$	0.608111	−	17.4140i	0.0272228	−	0.779559i	0.933858	−	0.357644i	$-0.116420\pi$
$500$	−4.56904	−	0.319499i	−0.204334	−	0.0142884i
$501$	−32.3524	+	3.40038i	−1.44540	+	0.151918i
$502$	17.1714	−	19.0707i	0.766396	−	0.851169i
$503$	−16.3378	+	30.7270i	−0.728468	+	1.37005i	0.192846	+	0.981229i	$0.438228\pi$
$503$	−16.3378	+	30.7270i	−0.728468	+	1.37005i	−0.921314	+	0.388820i	$0.872883\pi$
$504$	−9.08617	−	9.40901i	−0.404730	−	0.419111i
$505$	−6.56676	+	3.79132i	−0.292217	+	0.168712i
$506$	0.691537	+	1.06455i	0.0307426	+	0.0473250i
$507$	−6.74829	+	8.04229i	−0.299702	+	0.357171i
$508$	−5.67372	−	8.41163i	−0.251731	−	0.373206i
$509$	8.56542	−	0.299111i	0.379655	−	0.0132579i	0.155564	−	0.987826i	$-0.450281\pi$
$509$	8.56542	−	0.299111i	0.379655	−	0.0132579i	0.224092	+	0.974568i	$0.428058\pi$
$510$	−8.47543	−	5.29604i	−0.375298	−	0.234512i
$511$	−9.86742	−	9.52885i	−0.436509	−	0.421532i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	32.2500	+	42.3387i	1.42387	+	1.86930i
$514$	6.92264	+	2.24930i	0.305345	+	0.0992125i
$515$	3.20243	+	1.56193i	0.141116	+	0.0688268i
$516$	14.5047	−	12.1709i	0.638532	−	0.535792i
$517$	17.3986	−	3.38446i	0.765191	−	0.148848i
$518$	19.0667	+	6.93971i	0.837742	+	0.304913i
$519$	48.5317	−	12.1003i	2.13030	−	0.531145i
$520$	−0.973931	−	1.08166i	−0.0427097	−	0.0474339i
$521$	−13.9649	−	12.5740i	−0.611812	−	0.550878i	0.303905	−	0.952702i	$-0.401709\pi$
$521$	−13.9649	−	12.5740i	−0.611812	−	0.550878i	−0.915717	+	0.401825i	$0.868376\pi$
$522$	19.7667	+	40.5277i	0.865165	+	1.77385i
$523$	17.9433	+	36.7892i	0.784605	+	1.60868i	0.793388	+	0.608717i	$0.208315\pi$
$523$	17.9433	+	36.7892i	0.784605	+	1.60868i	−0.00878313	+	0.999961i	$0.502796\pi$
$524$	−2.72155	−	2.45049i	−0.118891	−	0.107050i
$525$	−19.1094	−	21.2231i	−0.834001	−	0.926252i
$526$	−27.5406	+	6.86665i	−1.20083	+	0.299400i
$527$	−6.99453	−	2.54580i	−0.304687	−	0.110897i
$528$	−7.62679	−	7.11012i	−0.331914	−	0.309428i
$529$	−17.5068	+	14.6899i	−0.761165	+	0.638693i
$530$	2.49998	+	1.21932i	0.108592	+	0.0529639i
$531$	63.7853	+	20.7251i	2.76805	+	0.899393i
$532$	−0.390582	+	8.27323i	−0.0169339	+	0.358690i
$533$	−27.7467	+	20.1592i	−1.20185	+	0.873192i
$534$	−15.1232	−	14.6043i	−0.654444	−	0.631989i
$535$	−5.30426	−	3.31447i	−0.229323	−	0.143297i
$536$	6.18672	−	0.216045i	0.267226	−	0.00933173i
$537$	−0.981481	−	1.45510i	−0.0423540	−	0.0627924i
$538$	−13.4184	+	15.9914i	−0.578507	+	0.689437i
$539$	10.8583	−	2.91110i	0.467702	−	0.125390i
$540$	−4.95180	+	2.85892i	−0.213092	+	0.123029i
$541$	14.9820	+	15.5143i	0.644125	+	0.667011i	0.959419	−	0.281983i	$-0.0909922\pi$
$541$	14.9820	+	15.5143i	0.644125	+	0.667011i	−0.315295	+	0.948994i	$0.602103\pi$
$542$	1.08165	−	2.03429i	0.0464610	−	0.0873804i
$543$	24.6594	−	27.3871i	1.05824	−	1.17529i
$544$	6.75117	−	0.709577i	0.289454	−	0.0304229i
$545$	1.98501	+	0.138806i	0.0850287	+	0.00594578i
$546$	0.647986	−	18.5559i	0.0277312	−	0.794119i
$547$	−0.783783	−	22.4446i	−0.0335121	−	0.959662i	−0.893423	−	0.449217i	$-0.851703\pi$
$547$	−0.783783	−	22.4446i	−0.0335121	−	0.959662i	0.859911	−	0.510445i	$-0.170519\pi$
$548$	20.4532	−	1.43023i	0.873719	−	0.0610964i
$549$	−14.1733	+	2.49914i	−0.604904	+	0.106661i
$550$	−11.2133	−	11.2102i	−0.478137	−	0.478004i
$551$	10.0939	−	26.7085i	0.430014	−	1.13782i
$552$	−0.707291	+	0.973502i	−0.0301043	+	0.0414350i
$553$	−2.75204	+	19.5818i	−0.117029	+	0.832703i
$554$	−16.5156	+	26.4305i	−0.701681	+	1.12292i
$555$	8.79115	−	13.0334i	0.373164	−	0.553238i
$556$	1.13386	+	3.95423i	0.0480863	+	0.167697i
$557$	12.4484	+	5.02949i	0.527457	+	0.213106i	0.622861	−	0.782332i	$-0.285970\pi$
$557$	12.4484	+	5.02949i	0.527457	+	0.213106i	−0.0954045	+	0.995439i	$0.530414\pi$
$558$	−5.60931	+	5.05065i	−0.237461	+	0.213811i
$559$	18.6170	+	1.95672i	0.787414	+	0.0827605i
$560$	−0.876289	−	0.154513i	−0.0370300	−	0.00652939i
$561$	−20.7041	−	67.6863i	−0.874127	−	2.85772i
$562$	−0.981366	−	1.69978i	−0.0413964	−	0.0717007i
$563$	−15.6635	+	6.97386i	−0.660139	+	0.293913i	−0.709330	−	0.704876i	$-0.751002\pi$
$563$	−15.6635	+	6.97386i	−0.660139	+	0.293913i	0.0491907	+	0.998789i	$0.484336\pi$
$564$	8.90339	+	14.2484i	0.374900	+	0.599966i
$565$	4.13224	+	0.144301i	0.173845	+	0.00607079i
$566$	13.7034	+	9.24308i	0.575998	+	0.388516i
$567$	−32.6982	−	8.15257i	−1.37319	−	0.342376i
$568$	−2.81576	−	5.29567i	−0.118146	−	0.222201i
$569$	−7.46493	+	22.9747i	−0.312946	+	0.963149i	0.663646	+	0.748047i	$0.269008\pi$
$569$	−7.46493	+	22.9747i	−0.312946	+	0.963149i	−0.976592	+	0.215102i	$0.930992\pi$
$570$	6.14655	+	1.84440i	0.257451	+	0.0772533i
$571$		−	24.9392i		−	1.04367i	−0.853046	−	0.521836i	$-0.825247\pi$
$571$		−	24.9392i		−	1.04367i	0.853046	−	0.521836i	$-0.174753\pi$
$572$	−0.181342	−	10.3070i	−0.00758228	−	0.430957i
$573$	36.3562	+	43.3276i	1.51880	+	1.81004i
$574$	−5.77925	+	20.1546i	−0.241221	+	0.841238i
$575$	−1.12655	+	1.44192i	−0.0469805	+	0.0601322i
$576$	2.57872	−	6.38255i	0.107446	−	0.265939i
$577$	2.11774	+	20.1490i	0.0881627	+	0.838812i	0.945842	+	0.324627i	$0.105239\pi$
$577$	2.11774	+	20.1490i	0.0881627	+	0.838812i	−0.857679	+	0.514185i	$0.828095\pi$
$578$	26.5676	+	11.8287i	1.10507	+	0.492007i
$579$	−1.19850	−	8.52775i	−0.0498078	−	0.354401i
$580$	2.70840	+	1.44008i	0.112460	+	0.0597962i
$581$	0.318329	−	3.02870i	0.0132065	−	0.125651i
$582$	−0.798636	+	1.38328i	−0.0331045	+	0.0573387i
$583$	7.69977	+	18.1325i	0.318892	+	0.750972i
$584$	2.46910	−	6.78381i	0.102172	−	0.280716i
$585$	−9.63134	−	2.76174i	−0.398207	−	0.114184i
$586$	−11.2071	−	27.7385i	−0.462961	−	1.14587i
$587$	−5.49199	+	2.92014i	−0.226679	+	0.120527i	−0.578927	−	0.815379i	$-0.696528\pi$
$587$	−5.49199	+	2.92014i	−0.226679	+	0.120527i	0.352248	+	0.935907i	$0.385417\pi$
$588$	6.26355	+	8.62103i	0.258304	+	0.355525i
$589$	4.76343	+	0.391872i	0.196274	+	0.0161468i
$590$	4.33917	−	1.40988i	0.178641	−	0.0580440i
$591$	−8.65531	−	1.21643i	−0.356032	−	0.0500370i
$592$	0.744890	+	10.6524i	0.0306148	+	0.437812i
$593$	5.91417	+	16.2491i	0.242866	+	0.667269i	0.999903	+	0.0138973i	$0.00442379\pi$
$593$	5.91417	+	16.2491i	0.242866	+	0.667269i	−0.757037	+	0.653371i	$0.773354\pi$
$594$	−39.7533	−	7.72152i	−1.63110	−	0.316818i
$595$	−4.62717	−	3.88265i	−0.189695	−	0.159173i
$596$	−2.98779	−	6.71068i	−0.122385	−	0.274880i
$597$	2.72571	+	12.8235i	0.111556	+	0.524830i
$598$	−1.17807	+	0.165568i	−0.0481751	+	0.00677056i
$599$	−9.98250	+	4.86879i	−0.407874	+	0.198933i	−0.630875	−	0.775885i	$-0.717304\pi$
$599$	−9.98250	+	4.86879i	−0.407874	+	0.198933i	0.223000	+	0.974818i	$0.428415\pi$
$600$	6.11318	−	13.7304i	0.249570	−	0.560542i
$601$	21.4942	+	4.56872i	0.876765	+	0.186362i	0.624244	−	0.781229i	$-0.285407\pi$
$601$	21.4942	+	4.56872i	0.876765	+	0.186362i	0.252521	+	0.967591i	$0.418740\pi$
$602$	9.70496	−	6.06433i	0.395545	−	0.247164i
$603$	35.3287	−	23.8295i	1.43870	−	0.970412i
$604$	11.9878	−	4.36320i	0.487776	−	0.177536i
$605$	0.360756	+	5.13854i	0.0146668	+	0.208911i
$606$	−8.83972	−	50.1325i	−0.359089	−	2.03649i
$607$	37.3106	+	27.1078i	1.51439	+	1.10027i	0.964181	+	0.265244i	$0.0854524\pi$
$607$	37.3106	+	27.1078i	1.51439	+	1.10027i	0.550210	+	0.835026i	$0.314548\pi$
$608$	−4.06123	+	1.58317i	−0.164705	+	0.0642059i
$609$	12.0918	+	37.2147i	0.489983	+	1.50801i
$610$	−0.680109	+	0.704273i	−0.0275368	+	0.0285152i
$611$	−4.01848	+	16.1172i	−0.162570	+	0.652034i
$612$	36.8235	−	28.7697i	1.48850	−	1.16295i
$613$	23.5869	+	18.4281i	0.952667	+	0.744305i	0.966784	−	0.255595i	$-0.0822714\pi$
$613$	23.5869	+	18.4281i	0.952667	+	0.744305i	−0.0141166	+	0.999900i	$0.504494\pi$
$614$	−1.37862	−	5.52933i	−0.0556365	−	0.223146i
$615$	14.0688	+	8.12265i	0.567311	+	0.327537i
$616$	−3.96665	−	4.89702i	−0.159821	−	0.197307i
$617$	1.74141	−	9.87604i	0.0701066	−	0.397594i	−0.929481	−	0.368871i	$-0.879745\pi$
$617$	1.74141	−	9.87604i	0.0701066	−	0.397594i	0.999587	−	0.0287237i	$-0.00914431\pi$
$618$	−17.2068	+	16.6164i	−0.692160	+	0.668411i
$619$	−2.19093	+	0.465696i	−0.0880608	+	0.0187179i	−0.251731	−	0.967797i	$-0.581000\pi$
$619$	−2.19093	+	0.465696i	−0.0880608	+	0.0187179i	0.163671	+	0.986515i	$0.447667\pi$
$620$	−0.106758	+	0.502258i	−0.00428751	+	0.0201712i
$621$	−0.326002	+	4.66204i	−0.0130820	+	0.187081i
$622$	−13.5612	+	3.88861i	−0.543754	+	0.155919i
$623$	−7.82296	−	10.0129i	−0.313420	−	0.401159i
$624$	9.06005	−	3.66050i	0.362692	−	0.146537i
$625$	9.53837	−	19.5566i	0.381535	−	0.782262i
$626$	−0.554642			−0.0221679
$627$	24.2897	+	38.4151i	0.970039	+	1.53415i
$628$	−17.7944			−0.710072
$629$	−31.7771	+	65.1528i	−1.26704	+	2.59781i
$630$	−5.67924	+	2.29456i	−0.226266	+	0.0914175i
$631$	26.5301	+	33.9570i	1.05615	+	1.35181i	0.933185	+	0.359396i	$0.117017\pi$
$631$	26.5301	+	33.9570i	1.05615	+	1.35181i	0.122963	+	0.992411i	$0.460761\pi$
$632$	−10.0037	+	2.86851i	−0.397925	+	0.114103i
$633$	0.213064	−	3.04696i	0.00846853	−	0.121106i
$634$	2.91872	−	13.7315i	0.115917	−	0.545348i
$635$	−4.64756	+	0.987869i	−0.184433	+	0.0392024i
$636$	−13.4325	+	12.9716i	−0.532634	+	0.514358i
$637$	−1.82942	+	10.3751i	−0.0724842	+	0.411078i
$638$	7.78837	+	20.2810i	0.308345	+	0.802932i
$639$	−35.7556	−	20.6435i	−1.41447	−	0.816645i
$640$	−0.113289	−	0.454379i	−0.00447816	−	0.0179609i
$641$	−22.5524	−	17.6199i	−0.890768	−	0.695944i	0.0625086	−	0.998044i	$-0.480090\pi$
$641$	−22.5524	−	17.6199i	−0.890768	−	0.695944i	−0.953276	+	0.302101i	$0.902312\pi$
$642$	33.0890	−	25.8520i	1.30592	−	1.02030i
$643$	6.55623	−	26.2956i	0.258552	−	1.03700i	−0.690866	−	0.722983i	$-0.742771\pi$
$643$	6.55623	−	26.2956i	0.258552	−	1.03700i	0.949418	−	0.314014i	$-0.101674\pi$
$644$	−0.505208	+	0.523158i	−0.0199080	+	0.0206153i
$645$	−2.74000	−	8.43285i	−0.107887	−	0.332043i
$646$	−29.2491	−	4.47728i	−1.15079	−	0.176156i
$647$	−0.190262	−	0.138234i	−0.00747998	−	0.00543452i	0.584039	−	0.811726i	$-0.301472\pi$
$647$	−0.190262	−	0.138234i	−0.00747998	−	0.00543452i	−0.591519	+	0.806291i	$0.701472\pi$
$648$	−3.07970	−	17.4658i	−0.120982	−	0.686123i
$649$	29.7464	+	12.6217i	1.16765	+	0.495446i
$650$	13.9631	−	5.08214i	0.547676	−	0.199338i
$651$	−5.43032	+	3.66280i	−0.212831	+	0.143556i
$652$	−0.343953	+	0.214925i	−0.0134702	+	0.00841713i
$653$	−15.6290	−	3.32205i	−0.611611	−	0.130002i	−0.108316	−	0.994117i	$-0.534546\pi$
$653$	−15.6290	−	3.32205i	−0.611611	−	0.130002i	−0.503295	+	0.864115i	$0.667879\pi$
$654$	−5.43355	+	12.2040i	−0.212469	+	0.477212i
$655$	−1.54141	+	0.751794i	−0.0602277	+	0.0293750i
$656$	−10.9271	+	1.53570i	−0.426631	+	0.0599591i
$657$	−10.3322	−	48.6094i	−0.403099	−	1.89643i
$658$	4.13027	+	9.27675i	0.161015	+	0.361645i
$659$	−8.66312	−	7.26922i	−0.337467	−	0.283169i	0.458267	−	0.888815i	$-0.348470\pi$
$659$	−8.66312	−	7.26922i	−0.337467	−	0.283169i	−0.795734	+	0.605646i	$0.792915\pi$
$660$	−4.42507	+	2.06419i	−0.172246	+	0.0803486i
$661$	1.67141	+	4.59216i	0.0650103	+	0.178614i	0.967944	−	0.251165i	$-0.0808136\pi$
$661$	1.67141	+	4.59216i	0.0650103	+	0.178614i	−0.902934	+	0.429779i	$0.858591\pi$
$662$	−0.894798	−	12.7962i	−0.0347773	−	0.497339i
$663$	65.6875	+	9.23177i	2.55109	+	0.358532i
$664$	1.52428	−	0.495270i	0.0591537	−	0.0192202i
$665$	3.52364	+	1.62091i	0.136641	+	0.0628563i
$666$	43.2070	+	59.4694i	1.67424	+	2.30439i
$667$	2.21369	−	1.17704i	0.0857143	−	0.0455751i
$668$	−3.87620	−	9.59392i	−0.149975	−	0.371200i
$669$	87.9402	+	25.2164i	3.39996	+	0.974924i
$670$	0.991497	−	2.72412i	0.0383049	−	0.105242i
$671$	−6.90761	+	0.605305i	−0.266666	+	0.0233675i
$672$	2.98685	−	5.17338i	0.115220	−	0.199567i
$673$	2.13326	−	20.2966i	0.0822311	−	0.782377i	−0.873240	−	0.487291i	$-0.837985\pi$
$673$	2.13326	−	20.2966i	0.0822311	−	0.782377i	0.955471	−	0.295086i	$-0.0953482\pi$
$674$	−3.78502	−	2.01253i	−0.145794	−	0.0775198i
$675$	−8.12392	−	57.8047i	−0.312690	−	2.22490i
$676$	−3.05066	−	1.35824i	−0.117333	−	0.0522401i
$677$	−0.407281	−	3.87502i	−0.0156531	−	0.148929i	0.983904	−	0.178700i	$-0.0571891\pi$
$677$	−0.407281	−	3.87502i	−0.0156531	−	0.148929i	−0.999557	+	0.0297704i	$0.990522\pi$
$678$	−10.3986	+	25.7374i	−0.399355	+	0.988437i
$679$	−0.594348	+	0.760730i	−0.0228090	+	0.0291941i
$680$	0.876229	−	3.05577i	0.0336018	−	0.117184i
$681$	−5.27922	−	6.29153i	−0.202300	−	0.241092i
$682$	−2.90407	+	2.18901i	−0.111203	+	0.0838215i
$683$		−	10.9661i		−	0.419607i	−0.977744	−	0.209804i	$-0.932718\pi$
$683$		−	10.9661i		−	0.419607i	0.977744	−	0.209804i	$-0.0672825\pi$
$684$	−17.9334	+	24.0570i	−0.685702	+	0.919841i
$685$	2.96700	−	9.13150i	0.113363	−	0.348897i
$686$	9.26802	+	17.4306i	0.353855	+	0.665504i
$687$	−39.9955	−	9.97199i	−1.52592	−	0.380455i
$688$	4.99305	+	3.36785i	0.190358	+	0.128398i
$689$	−18.4501	−	0.644293i	−0.702894	−	0.0245456i
$690$	0.298609	+	0.477875i	0.0113679	+	0.0181924i
$691$	36.2344	−	16.1326i	1.37842	−	0.613712i	0.422238	−	0.906485i	$-0.361245\pi$
$691$	36.2344	−	16.1326i	1.37842	−	0.613712i	0.956182	+	0.292773i	$0.0945781\pi$
$692$	7.95480	+	13.7781i	0.302396	+	0.523766i
$693$	−41.0201	−	14.1180i	−1.55823	−	0.536298i
$694$	17.1124	+	3.01738i	0.649579	+	0.114538i
$695$	1.91580	+	0.201358i	0.0726703	+	0.00763795i
$696$	−15.3038	+	13.7796i	−0.580089	+	0.522315i
$697$	−69.4516	−	28.0603i	−2.63067	−	1.06286i
$698$	−7.30253	−	25.4669i	−0.276405	−	0.963938i
$699$	−32.8414	+	48.6893i	−1.24218	+	1.84160i
$700$	4.81375	−	7.70361i	0.181943	−	0.291169i
$701$	4.30557	−	30.6357i	0.162619	−	1.15709i	−0.722378	−	0.691498i	$-0.756951\pi$
$701$	4.30557	−	30.6357i	0.162619	−	1.15709i	0.884997	−	0.465596i	$-0.154160\pi$
$702$	22.3069	−	30.7029i	0.841921	−	1.15880i
$703$	8.64444	−	45.7365i	0.326031	−	1.72498i
$704$	1.50531	−	2.95534i	0.0567333	−	0.111384i
$705$	7.74839	−	1.36625i	0.291821	−	0.0514560i
$706$	32.6006	−	2.27966i	1.22694	−	0.0857961i
$707$	−1.07376	−	30.7485i	−0.0403829	−	1.15641i
$708$	−1.06897	+	30.6114i	−0.0401745	+	1.15045i
$709$	37.6597	+	2.63342i	1.41434	+	0.0989002i	0.756369	−	0.654145i	$-0.226971\pi$
$709$	37.6597	+	2.63342i	1.41434	+	0.0989002i	0.657969	+	0.753045i	$0.271416\pi$
$710$	−2.79328	+	0.293586i	−0.104830	+	0.0110181i
$711$	−47.9355	+	53.2378i	−1.79772	+	1.99657i
$712$	3.13947	−	5.90449i	0.117657	−	0.221280i
$713$	0.291539	+	0.301897i	0.0109182	+	0.0113061i
$714$	35.1188	−	20.2758i	1.31429	−	0.758804i
$715$	−4.50701	−	1.72936i	−0.168553	−	0.0646744i
$716$	0.358861	−	0.427673i	0.0134112	−	0.0159829i
$717$	−25.5028	−	37.8094i	−0.952419	−	1.41202i
$718$	13.8744	−	0.484504i	0.517788	−	0.0180815i
$719$	23.3816	+	14.6104i	0.871987	+	0.544878i	0.890517	−	0.454951i	$-0.150343\pi$
$719$	23.3816	+	14.6104i	0.871987	+	0.544878i	−0.0185300	+	0.999828i	$0.505899\pi$
$720$	−2.31887	−	2.23931i	−0.0864192	−	0.0834541i
$721$	−11.6962	+	8.49777i	−0.435588	+	0.316474i
$722$	18.8743	−	2.18186i	0.702429	−	0.0812005i
$723$	−16.7949	−	5.45699i	−0.624609	−	0.202948i
$724$	10.5359	+	5.13869i	0.391562	+	0.190978i
$725$	−23.9889	+	20.1291i	−0.890925	+	0.747575i
$726$	−33.2453	−	9.52295i	−1.23385	−	0.353430i
$727$	−38.3845	−	13.9708i	−1.42360	−	0.518149i	−0.488512	−	0.872557i	$-0.662460\pi$
$727$	−38.3845	−	13.9708i	−1.42360	−	0.518149i	−0.935091	+	0.354408i	$0.884682\pi$
$728$	5.73045	−	1.42876i	0.212385	−	0.0529534i
$729$	−4.63440	−	5.14702i	−0.171644	−	0.190630i
$730$	−2.51232	−	2.26211i	−0.0929852	−	0.0837243i
$731$	17.9225	+	36.7466i	0.662888	+	1.35912i
$732$	−2.88135	−	5.90765i	−0.106498	−	0.218353i
$733$	−13.4173	−	12.0810i	−0.495580	−	0.446222i	0.383048	−	0.923728i	$-0.374874\pi$
$733$	−13.4173	−	12.0810i	−0.495580	−	0.446222i	−0.878629	+	0.477506i	$0.841541\pi$
$734$	−17.3820	−	19.3046i	−0.641581	−	0.712547i
$735$	4.84195	−	1.20723i	0.178598	−	0.0445295i
$736$	−0.359669	−	0.130909i	−0.0132576	−	0.00482536i
$737$	17.9559	−	9.95639i	0.661415	−	0.366748i
$738$	−58.1880	+	48.8256i	−2.14193	+	1.79729i
$739$	19.1524	+	9.34124i	0.704532	+	0.343623i	0.755565	−	0.655074i	$-0.227362\pi$
$739$	19.1524	+	9.34124i	0.704532	+	0.343623i	−0.0510329	+	0.998697i	$0.516251\pi$
$740$	4.75585	+	1.54527i	0.174829	+	0.0568053i
$741$	−42.2484	+	5.40993i	−1.55203	+	0.198739i
$742$	−9.13063	+	6.63379i	−0.335196	+	0.243534i
$743$	−10.8882	−	10.5146i	−0.399450	−	0.385744i	0.467621	−	0.883929i	$-0.345111\pi$
$743$	−10.8882	−	10.5146i	−0.399450	−	0.385744i	−0.867071	+	0.498185i	$0.834000\pi$
$744$	−2.92341	−	1.82675i	−0.107178	−	0.0669720i
$745$	−3.43784	+	0.120052i	−0.125953	+	0.00439837i
$746$	10.6909	+	15.8499i	0.391422	+	0.580306i
$747$	7.09178	−	8.45165i	0.259475	−	0.309230i
$748$	18.8805	−	12.2649i	0.690340	−	0.448448i
$749$	21.9787	−	12.6894i	0.803085	−	0.463661i
$750$	−10.0027	−	10.3581i	−0.365247	−	0.378225i
$751$	−15.8607	+	29.8296i	−0.578765	+	1.08850i	0.405880	+	0.913927i	$0.366965\pi$
$751$	−15.8607	+	29.8296i	−0.578765	+	1.08850i	−0.984644	+	0.174572i	$0.944146\pi$
$752$	−3.57598	+	3.97153i	−0.130402	+	0.144827i
$753$	80.2362	−	8.43316i	2.92397	−	0.307322i
$754$	−20.3099	−	1.42021i	−0.739643	−	0.0517209i
$755$	0.208491	−	5.97039i	0.00758775	−	0.217285i
$756$	−0.809691	−	23.1865i	−0.0294482	−	0.843285i
$757$	43.9978	−	3.07662i	1.59913	−	0.111822i	0.757850	−	0.652428i	$-0.226250\pi$
$757$	43.9978	−	3.07662i	1.59913	−	0.111822i	0.841276	+	0.540607i	$0.181805\pi$
$758$	30.8313	−	5.43639i	1.11984	−	0.197459i
$759$	−0.623773	+	3.94189i	−0.0226415	+	0.143082i
$760$	−0.0250427	+	2.04107i	−0.000908395	+	0.0740375i
$761$	−2.73641	+	3.76634i	−0.0991947	+	0.136530i	−0.855729	−	0.517424i	$-0.826891\pi$
$761$	−2.73641	+	3.76634i	−0.0991947	+	0.136530i	0.756534	+	0.653954i	$0.226891\pi$
$762$	4.43939	−	31.5879i	0.160822	−	1.14431i
$763$	−4.27858	+	6.84716i	−0.154895	+	0.247884i
$764$	−10.0603	+	14.9150i	−0.363969	+	0.539606i
$765$	−6.03178	−	21.0353i	−0.218079	−	0.760533i
$766$	27.2476	+	11.0087i	0.984496	+	0.397762i
$767$	−22.5041	+	20.2628i	−0.812578	+	0.731648i
$768$	3.12663	+	0.328622i	0.112822	+	0.0118581i
$769$	−12.3133	−	2.17116i	−0.444028	−	0.0782941i	−0.0528360	−	0.998603i	$-0.516826\pi$
$769$	−12.3133	−	2.17116i	−0.444028	−	0.0782941i	−0.391192	+	0.920309i	$0.627937\pi$
$770$	−2.82209	+	0.863227i	−0.101701	+	0.0311085i
$771$	11.4419	+	19.8179i	0.412069	+	0.713725i
$772$	2.50236	−	1.11412i	0.0900619	−	0.0400982i
$773$	−8.83992	−	14.1468i	−0.317950	−	0.508826i	0.650012	−	0.759924i	$-0.274764\pi$
$773$	−8.83992	−	14.1468i	−0.317950	−	0.508826i	−0.967962	+	0.251098i	$0.919208\pi$
$774$	41.4338	+	1.44690i	1.48931	+	0.0520078i
$775$	−4.34584	−	2.93131i	−0.156107	−	0.105296i
$776$	−0.492970	−	0.122911i	−0.0176966	−	0.00441226i
$777$	29.9475	+	56.3231i	1.07436	+	2.02058i
$778$	8.88545	−	27.3466i	0.318559	−	0.980423i
$779$	47.7694	+	5.61411i	1.71152	+	0.201146i
$780$		−	4.57593i		−	0.163844i
$781$	−16.2963	−	11.4074i	−0.583127	−	0.408189i
$782$	−1.67013	−	1.99038i	−0.0597237	−	0.0711759i
$783$	−22.0455	+	76.8819i	−0.787843	+	2.74753i
$784$	−2.08680	+	2.67099i	−0.0745287	+	0.0953924i
$785$	−3.12156	+	7.72614i	−0.111413	+	0.275758i
$786$	−1.20348	−	11.4503i	−0.0429267	−	0.408420i
$787$	−6.70752	−	2.98638i	−0.239097	−	0.106453i	0.283690	−	0.958916i	$-0.408441\pi$
$787$	−6.70752	−	2.98638i	−0.239097	−	0.106453i	−0.522788	+	0.852463i	$0.675108\pi$
$788$	−0.386922	−	2.75309i	−0.0137835	−	0.0980749i
$789$	−78.7892	−	41.8929i	−2.80497	−	1.49143i
$790$	−0.509410	+	4.84671i	−0.0181240	+	0.172438i
$791$	−8.38857	+	14.5294i	−0.298263	+	0.516607i
$792$	−1.99301	−	22.7438i	−0.0708185	−	0.808166i
$793$	2.22253	−	6.10635i	0.0789243	−	0.216843i
$794$	6.29020	+	1.80369i	0.223231	+	0.0640104i
$795$	3.27577	+	8.10781i	0.116179	+	0.287554i
$796$	−3.68192	+	1.95771i	−0.130502	+	0.0693892i
$797$	−24.3710	−	33.5438i	−0.863265	−	1.18818i	−0.980781	−	0.195112i	$-0.937493\pi$
$797$	−24.3710	−	33.5438i	−0.863265	−	1.18818i	0.117516	−	0.993071i	$-0.462507\pi$
$798$	−18.3165	+	18.5074i	−0.648396	+	0.655155i
$799$	−34.5029	+	11.2107i	−1.22062	+	0.396605i
$800$	4.73418	+	0.665346i	0.167379	+	0.0235235i
$801$	−3.21114	−	45.9215i	−0.113460	−	1.62256i
$802$	6.67740	+	18.3460i	0.235787	+	0.647820i
$803$	−2.92126	−	23.7644i	−0.103089	−	0.838628i
$804$	14.9087	+	12.5099i	0.525791	+	0.441191i
$805$	0.138525	+	0.311131i	0.00488235	+	0.0109659i
$806$	−0.708581	−	3.33361i	−0.0249587	−	0.117422i
$807$	−64.9900	+	9.13375i	−2.28776	+	0.321523i
$808$	14.5535	−	7.09820i	0.511989	−	0.249714i
$809$	5.56179	−	12.4920i	0.195542	−	0.439194i	−0.788988	−	0.614408i	$-0.789395\pi$
$809$	5.56179	−	12.4920i	0.195542	−	0.439194i	0.984530	+	0.175214i	$0.0560616\pi$
$810$	−8.12375	−	1.72676i	−0.285439	−	0.0606720i
$811$	2.20568	−	1.37826i	0.0774519	−	0.0483973i	−0.490641	−	0.871362i	$-0.663237\pi$
$811$	2.20568	−	1.37826i	0.0774519	−	0.0483973i	0.568092	+	0.822965i	$0.307682\pi$
$812$	−10.3186	+	6.95997i	−0.362111	+	0.244247i
$813$	6.80654	−	2.47738i	0.238716	−	0.0868854i
$814$	18.2450	+	30.3552i	0.639487	+	1.06395i
$815$	0.0329809	+	0.187044i	0.00115527	+	0.00655187i
$816$	17.2657	+	12.5443i	0.604421	+	0.439137i
$817$	−17.3256	−	19.7234i	−0.606146	−	0.690033i
$818$	−3.94519	−	12.1420i	−0.137940	−	0.424537i
$819$	28.2412	−	29.2447i	0.986829	−	1.02189i
$820$	−1.25009	+	5.01384i	−0.0436550	+	0.175091i
$821$	−12.8509	+	10.0402i	−0.448498	+	0.350405i	−0.814455	−	0.580227i	$-0.802964\pi$
$821$	−12.8509	+	10.0402i	−0.448498	+	0.350405i	0.365957	+	0.930632i	$0.380742\pi$
$822$	50.7943	+	39.6849i	1.77166	+	1.38417i
$823$	2.78293	+	11.1617i	0.0970068	+	0.389073i	0.999098	−	0.0424731i	$-0.0135237\pi$
$823$	2.78293	+	11.1617i	0.0970068	+	0.389073i	−0.902091	+	0.431546i	$0.857968\pi$
$824$	−6.58924	−	3.80430i	−0.229547	−	0.132529i
$825$	−2.61577	−	49.7796i	−0.0910696	−	1.73310i
$826$	−3.21468	+	18.2314i	−0.111853	+	0.634351i
$827$	3.66038	−	3.53478i	0.127284	−	0.122916i	−0.628292	−	0.777977i	$-0.716246\pi$
$827$	3.66038	−	3.53478i	0.127284	−	0.122916i	0.755576	+	0.655061i	$0.227357\pi$
$828$	−2.57721	+	0.547803i	−0.0895642	+	0.0190375i
$829$	−11.2459	+	52.9076i	−0.390585	+	1.83756i	0.140295	+	0.990110i	$0.455195\pi$
$829$	−11.2459	+	52.9076i	−0.390585	+	1.83756i	−0.530880	+	0.847447i	$0.678139\pi$
$830$	0.0523550	−	0.748712i	0.00181727	−	0.0259882i
$831$	−94.1864	+	27.0075i	−3.26729	+	0.936880i
$832$	1.91357	+	2.44926i	0.0663412	+	0.0849128i
$833$	−21.3339	+	8.61946i	−0.739177	+	0.298647i
$834$	−5.66923	+	11.6237i	−0.196310	+	0.402494i
$835$	−4.84557			−0.167688
$836$	−9.61618	+	10.7949i	−0.332583	+	0.373348i
$837$	−13.3883			−0.462768
$838$	−7.03129	+	14.4163i	−0.242892	+	0.498002i
$839$	−25.2818	+	10.2145i	−0.872825	+	0.352644i	−0.766928	−	0.641733i	$-0.778216\pi$
$839$	−25.2818	+	10.2145i	−0.872825	+	0.352644i	−0.105897	+	0.994377i	$0.533771\pi$
$840$	−1.72226	−	2.20440i	−0.0594238	−	0.0760590i
$841$	13.3683	−	3.83329i	0.460974	−	0.132182i
$842$	0.195791	−	2.79994i	0.00674739	−	0.0964922i
$843$	1.28293	−	6.03570i	0.0441864	−	0.207880i
$844$	0.950316	−	0.201996i	0.0327112	−	0.00695298i
$845$	−1.12490	+	1.08630i	−0.0386976	+	0.0373699i
$846$	−6.38825	+	36.2296i	−0.219633	+	1.24560i
$847$	−19.0967	−	8.49604i	−0.656170	−	0.291927i
$848$	−5.14389	−	2.96983i	−0.176642	−	0.101984i
$849$	12.5716	+	50.4221i	0.431458	+	1.73048i
$850$	25.5734	+	19.9802i	0.877162	+	0.685314i
$851$	3.22075	−	2.51633i	0.110406	−	0.0862586i
$852$	4.56166	−	18.2958i	0.156280	−	0.626804i
$853$	24.9928	−	25.8808i	0.855736	−	0.886140i	−0.138823	−	0.990317i	$-0.544332\pi$
$853$	24.9928	−	25.8808i	0.855736	−	0.886140i	0.994559	+	0.104177i	$0.0332208\pi$
$854$	−1.22760	−	3.77816i	−0.0420076	−	0.129286i
$855$	7.29935	+	12.0067i	0.249632	+	0.410621i
$856$	10.8056	+	7.85071i	0.369327	+	0.268332i
$857$	−6.52039	−	36.9790i	−0.222732	−	1.26318i	−0.866973	−	0.498355i	$-0.833937\pi$
$857$	−6.52039	−	36.9790i	−0.222732	−	1.26318i	0.644240	−	0.764823i	$-0.277174\pi$
$858$	21.2586	−	24.4621i	0.725756	−	0.835122i
$859$	−12.1414	+	4.41910i	−0.414258	+	0.150778i	−0.540737	−	0.841192i	$-0.681855\pi$
$859$	−12.1414	+	4.41910i	−0.414258	+	0.150778i	0.126479	+	0.991969i	$0.459632\pi$
$860$	2.33819	−	1.57713i	0.0797317	−	0.0537797i
$861$	−55.9005	+	34.9305i	−1.90508	+	1.19043i
$862$	10.5979	+	2.25266i	0.360967	+	0.0767258i
$863$	−11.8829	+	26.6895i	−0.404499	+	0.908520i	0.590350	+	0.807148i	$0.298990\pi$
$863$	−11.8829	+	26.6895i	−0.404499	+	0.908520i	−0.994849	+	0.101372i	$0.967677\pi$
$864$	10.9743	−	5.35255i	0.373355	−	0.182097i
$865$	7.37779	−	1.03688i	0.250853	−	0.0352550i
$866$	2.64214	+	12.4303i	0.0897836	+	0.422399i
$867$	37.1875	+	83.5246i	1.26295	+	2.83664i
$868$	−1.59604	−	1.33924i	−0.0541731	−	0.0454566i
$869$	−25.2398	+	23.5430i	−0.856201	+	0.798643i
$870$	3.29831	+	9.06204i	0.111823	+	0.307232i
$871$	1.34219	+	19.1942i	0.0454782	+	0.650369i
$872$	−4.20786	−	0.591376i	−0.142496	−	0.0200265i
$873$	−3.32622	+	1.08075i	−0.112576	+	0.0365780i
$874$	1.37160	+	0.949843i	0.0463950	+	0.0321289i
$875$	−5.11546	−	7.04083i	−0.172934	−	0.238024i
$876$	20.0394	−	10.6551i	0.677068	−	0.360004i
$877$	−0.467205	−	1.15637i	−0.0157764	−	0.0390479i	0.919090	−	0.394047i	$-0.128925\pi$
$877$	−0.467205	−	1.15637i	−0.0157764	−	0.0390479i	−0.934866	+	0.355000i	$0.884481\pi$
$878$	−13.4874	−	3.86746i	−0.455179	−	0.130520i
$879$	32.1685	−	88.3823i	1.08502	−	2.98106i
$880$	−1.01911	−	1.17203i	−0.0343543	−	0.0395091i
$881$	23.2294	−	40.2345i	0.782618	−	1.35553i	−0.147794	−	0.989018i	$-0.547217\pi$
$881$	23.2294	−	40.2345i	0.782618	−	1.35553i	0.930412	−	0.366516i	$-0.119449\pi$
$882$	−2.43895	+	23.2050i	−0.0821236	+	0.781354i
$883$	−22.9300	−	12.1921i	−0.771655	−	0.410296i	0.0364494	−	0.999336i	$-0.488395\pi$
$883$	−22.9300	−	12.1921i	−0.771655	−	0.410296i	−0.808104	+	0.589039i	$0.799506\pi$
$884$	2.93645	+	20.8940i	0.0987636	+	0.702740i
$885$	13.1037	+	5.83413i	0.440475	+	0.196112i
$886$	−3.84324	−	36.5660i	−0.129116	−	1.22846i
$887$	2.78641	−	6.89660i	0.0935584	−	0.231565i	−0.873147	−	0.487457i	$-0.837925\pi$
$887$	2.78641	−	6.89660i	0.0935584	−	0.231565i	0.966705	+	0.255892i	$0.0823690\pi$
$888$	−20.6686	+	26.4546i	−0.693594	+	0.887760i
$889$	5.31405	−	18.5323i	0.178228	−	0.621554i
$890$	−2.01293	−	2.39892i	−0.0674736	−	0.0804119i
$891$	−35.4060	−	46.9718i	−1.18615	−	1.57361i
$892$			29.0994i			0.974320i
$893$	19.4707	−	12.7884i	0.651562	−	0.427948i
$894$	7.13643	−	21.9637i	0.238678	−	0.734575i
$895$	−0.122739	−	0.230838i	−0.00410271	−	0.00771607i
$896$	1.84368	+	0.459681i	0.0615931	+	0.0153569i
$897$	−3.10067	−	2.09143i	−0.103529	−	0.0698309i
$898$	−14.4983	−	0.506290i	−0.483813	−	0.0168951i
$899$	3.80611	+	6.09105i	0.126941	+	0.203148i
$900$	30.0642	−	13.3855i	1.00214	−	0.446182i
$901$	−20.1603	−	34.9186i	−0.671636	−	1.16331i
$902$	−29.9758	+	20.9955i	−0.998084	+	0.699072i
$903$	35.4313	+	6.24749i	1.17908	+	0.207903i
$904$	−8.78113	−	0.922934i	−0.292056	−	0.0306963i
$905$	4.07941	−	3.67312i	0.135604	−	0.122099i
$906$	37.1861	+	15.0242i	1.23543	+	0.499145i
$907$	5.82211	+	20.3041i	0.193320	+	0.674187i	0.996878	+	0.0789605i	$0.0251601\pi$
$907$	5.82211	+	20.3041i	0.193320	+	0.674187i	−0.803558	+	0.595227i	$0.797062\pi$
$908$	1.46084	−	2.16578i	0.0484796	−	0.0718739i
$909$	59.0669	−	94.5268i	1.95912	−	3.13525i
$910$	0.384906	−	2.73875i	0.0127595	−	0.0907885i
$911$	9.52726	−	13.1132i	0.315652	−	0.434458i	−0.621481	−	0.783429i	$-0.713469\pi$
$911$	9.52726	−	13.1132i	0.315652	−	0.434458i	0.937134	+	0.348971i	$0.113469\pi$
$912$	−12.8188	−	4.84458i	−0.424474	−	0.160420i
$913$	3.75821	−	3.75925i	0.124378	−	0.124413i
$914$	3.97241	−	0.700443i	0.131396	−	0.0231686i
$915$	−3.07051	+	0.214711i	−0.101508	+	0.00709812i
$916$	−0.457577	−	13.1033i	−0.0151188	−	0.432945i
$917$	0.242853	−	6.95440i	0.00801971	−	0.229654i
$918$	82.6845	+	5.78186i	2.72900	+	0.190830i
$919$	−2.06598	+	0.217143i	−0.0681503	+	0.00716289i	−0.138542	−	0.990357i	$-0.544242\pi$
$919$	−2.06598	+	0.217143i	−0.0681503	+	0.00716289i	0.0703919	+	0.997519i	$0.477575\pi$
$920$	−0.119934	+	0.133200i	−0.00395411	+	0.00439148i
$921$	8.41085	−	15.8185i	0.277147	−	0.521237i
$922$	−12.8688	−	13.3261i	−0.423812	−	0.438870i
$923$	16.1443	−	9.32091i	0.531396	−	0.306802i
$924$	1.03416	−	19.7855i	0.0340213	−	0.650896i
$925$	−32.8146	+	39.1069i	−1.07894	+	1.28583i
$926$	−14.7306	−	21.8391i	−0.484079	−	0.717677i
$927$	−52.3441	+	1.82790i	−1.71921	+	0.0600360i
$928$	−5.55501	−	3.47115i	−0.182352	−	0.113946i
$929$	34.7758	+	33.5826i	1.14096	+	1.10181i	0.993627	+	0.112722i	$0.0359568\pi$
$929$	34.7758	+	33.5826i	1.14096	+	1.10181i	0.147330	+	0.989087i	$0.452932\pi$
$930$	−1.30600	+	0.948862i	−0.0428253	+	0.0311144i
$931$	11.7533	−	8.95265i	0.385198	−	0.293411i
$932$	−17.7666	−	5.77272i	−0.581964	−	0.189092i
$933$	−39.8638	−	19.4429i	−1.30508	−	0.636530i
$934$	8.19333	−	6.87502i	0.268094	−	0.224958i
$935$	−2.01319	−	10.3493i	−0.0658384	−	0.338458i
$936$	20.1056	+	7.31783i	0.657172	+	0.239191i
$937$	10.7132	−	2.67110i	0.349985	−	0.0872610i	−0.0629626	−	0.998016i	$-0.520055\pi$
$937$	10.7132	−	2.67110i	0.349985	−	0.0872610i	0.412947	+	0.910755i	$0.364499\pi$
$938$	7.87078	+	8.74139i	0.256990	+	0.285416i
$939$	−1.29583	−	1.16677i	−0.0422878	−	0.0380761i
$940$	1.09708	+	2.24936i	0.0357830	+	0.0733659i
$941$	25.9219	+	53.1477i	0.845029	+	1.73257i	0.662065	+	0.749446i	$0.269680\pi$
$941$	25.9219	+	53.1477i	0.845029	+	1.73257i	0.182964	+	0.983120i	$0.441431\pi$
$942$	−41.5736	−	37.4331i	−1.35454	−	1.21963i
$943$	2.82605	+	3.13865i	0.0920288	+	0.102208i
$944$	−9.45345	+	2.35701i	−0.307684	+	0.0767142i
$945$	−10.2094	−	3.71592i	−0.332112	−	0.120879i
$946$	19.8265	+	2.43159i	0.644615	+	0.0790579i
$947$	13.2758	−	11.1397i	0.431406	−	0.361993i	−0.401076	−	0.916045i	$-0.631364\pi$
$947$	13.2758	−	11.1397i	0.431406	−	0.361993i	0.832482	+	0.554052i	$0.186919\pi$
$948$	−29.4063	−	14.3424i	−0.955072	−	0.465820i
$949$	21.3401	+	6.93382i	0.692729	+	0.225081i
$950$	−19.2240	−	8.04273i	−0.623709	−	0.260941i
$951$	35.7054	−	25.9415i	1.15783	−	0.841210i
$952$	9.27856	+	8.96021i	0.300720	+	0.290402i
$953$	−51.9879	−	32.4856i	−1.68405	−	1.05231i	−0.905066	−	0.425271i	$-0.860179\pi$
$953$	−51.9879	−	32.4856i	−1.68405	−	1.05231i	−0.778986	−	0.627041i	$-0.784266\pi$
$954$	−40.8625	+	1.42695i	−1.32297	+	0.0461992i
$955$	4.71113	+	6.98454i	0.152449	+	0.226014i
$956$	9.32463	−	11.1127i	0.301580	−	0.359409i
$957$	−24.4678	+	63.7672i	−0.790930	+	2.06130i
$958$	19.3809	−	11.1896i	0.626169	−	0.361519i
$959$	27.0629	+	28.0244i	0.873906	+	0.904957i
$960$	0.691171	−	1.29990i	0.0223075	−	0.0419542i
$961$	19.9385	−	22.1440i	0.643179	−	0.714323i
$962$	−33.0084	+	3.46933i	−1.06423	+	0.111856i
$963$	91.7189	+	6.41361i	2.95560	+	0.206676i
$964$	0.196033	−	5.61364i	0.00631378	−	0.180803i
$965$	−0.0447665	−	1.28195i	−0.00144108	−	0.0412673i
$966$	−2.28088	+	0.159494i	−0.0733860	+	0.00513165i
$967$	−1.92700	+	0.339782i	−0.0619682	+	0.0109267i	−0.204546	−	0.978857i	$-0.565572\pi$
$967$	−1.92700	+	0.339782i	−0.0619682	+	0.0109267i	0.142578	+	0.989784i	$0.454461\pi$
$968$	−0.00305693	−	11.0000i	−9.82536e−5	−	0.353553i
$969$	−58.9171	−	71.9902i	−1.89269	−	2.31266i
$970$	−0.139846	+	0.192481i	−0.00449018	+	0.00618021i
$971$	0.850200	−	6.04948i	0.0272842	−	0.194137i	−0.971857	−	0.235571i	$-0.924304\pi$
$971$	0.850200	−	6.04948i	0.0272842	−	0.194137i	0.999141	+	0.0414343i	$0.0131927\pi$
$972$	10.1357	−	16.2204i	0.325101	−	0.520271i
$973$	−4.37083	+	6.48002i	−0.140122	+	0.207740i
$974$	−1.11789	−	3.89856i	−0.0358196	−	0.124918i
$975$	43.3134	+	17.4998i	1.38714	+	0.560441i
$976$	1.55370	−	1.39895i	0.0497326	−	0.0447795i
$977$	−44.0571	−	4.63058i	−1.40951	−	0.148145i	−0.631002	−	0.775781i	$-0.717356\pi$
$977$	−44.0571	−	4.63058i	−1.40951	−	0.148145i	−0.778507	+	0.627635i	$0.784023\pi$
$978$	−1.25572	−	0.221417i	−0.0401534	−	0.00708012i
$979$	0.383997	−	22.1758i	0.0122726	−	0.708740i
$980$	0.793641	+	1.37463i	0.0253519	+	0.0439108i
$981$	−26.7219	+	11.8973i	−0.853163	+	0.379853i
$982$	−9.40045	−	15.0439i	−0.299980	−	0.480069i
$983$	15.0961	+	0.527169i	0.481492	+	0.0168141i	0.274618	−	0.961553i	$-0.411449\pi$
$983$	15.0961	+	0.527169i	0.481492	+	0.0168141i	0.206874	+	0.978368i	$0.433671\pi$
$984$	−28.7599	−	19.3988i	−0.916833	−	0.618412i
$985$	−1.26324	−	0.314962i	−0.0402502	−	0.0100355i
$986$	−20.8756	−	39.2612i	−0.664814	−	1.25033i
$987$	−9.86529	+	30.3622i	−0.314016	+	0.966441i
$988$	−5.35826	−	12.4435i	−0.170469	−	0.395881i
$989$		−	2.30520i		−	0.0733011i
$990$	−10.2248	−	3.12447i	−0.324964	−	0.0993022i
$991$	27.6660	+	32.9710i	0.878839	+	1.04736i	0.998511	+	0.0545462i	$0.0173712\pi$
$991$	27.6660	+	32.9710i	0.878839	+	1.04736i	−0.119672	+	0.992813i	$0.538184\pi$
$992$	0.302236	−	1.05402i	0.00959600	−	0.0334652i
$993$	24.8282	−	31.7786i	0.787898	−	1.00846i
$994$	4.26916	−	10.5666i	0.135410	−	0.335151i
$995$	0.204121	+	1.94208i	0.00647108	+	0.0615682i
$996$	4.60311	+	2.04944i	0.145855	+	0.0649389i
$997$	−5.71047	−	40.6321i	−0.180852	−	1.28683i	−0.843186	−	0.537622i	$-0.819323\pi$
$997$	−5.71047	−	40.6321i	−0.180852	−	1.28683i	0.662333	−	0.749209i	$-0.269566\pi$
$998$	15.3850	+	8.18037i	0.487005	+	0.258945i
$999$	−13.6289	+	129.670i	−0.431199	+	4.10259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.29.1	✓	240
11.8	odd	10		418.2.v.b.371.10	yes	240
19.2	odd	18		418.2.v.b.249.10	yes	240
209.173	even	90	inner	418.2.v.a.173.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.29.1	✓	240	1.1	even	1	trivial
418.2.v.a.173.1	yes	240	209.173	even	90	inner
418.2.v.b.249.10	yes	240	19.2	odd	18
418.2.v.b.371.10	yes	240	11.8	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-2.91493 + 1.17771i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.450149 + 0.129078i) q^{5} +(0.219304 - 3.13619i) q^{6} +(0.395058 - 1.85860i) q^{7} +(0.978148 - 0.207912i) q^{8} +(4.95179 - 4.78189i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-2.91493 + 1.17771i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.450149 + 0.129078i) q^{5} +(0.219304 - 3.13619i) q^{6} +(0.395058 - 1.85860i) q^{7} +(0.978148 - 0.207912i) q^{8} +(4.95179 - 4.78189i) q^{9} +(0.0813176 - 0.461175i) q^{10} +(2.57721 - 2.08758i) q^{11} +(2.72265 + 1.57193i) q^{12} +(0.751931 + 3.01583i) q^{13} +(1.49732 + 1.16983i) q^{14} +(1.16013 - 0.906397i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-4.71559 + 4.88314i) q^{17} +(2.12721 + 6.54688i) q^{18} +(2.09344 - 3.82328i) q^{19} +(0.378854 + 0.275254i) q^{20} +(1.03732 + 5.88295i) q^{21} +(0.746527 + 3.23152i) q^{22} +(0.359669 - 0.130909i) q^{23} +(-2.60637 + 1.75802i) q^{24} +(-4.05427 + 2.53339i) q^{25} +(-3.04024 - 0.646222i) q^{26} +(-4.96629 + 11.1545i) q^{27} +(-1.70782 + 0.832959i) q^{28} +(6.48660 - 0.911632i) q^{29} +(0.306094 + 1.44006i) q^{30} +(0.445986 + 1.00170i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-5.05383 + 9.12034i) q^{33} +(-2.32176 - 6.37897i) q^{34} +(0.0620698 + 0.887640i) q^{35} +(-6.81680 - 0.958039i) q^{36} +(10.1558 - 3.29982i) q^{37} +(2.51864 + 3.55759i) q^{38} +(-5.74359 - 7.90537i) q^{39} +(-0.413475 + 0.219849i) q^{40} +(4.13359 + 10.2310i) q^{41} +(-5.74229 - 1.64658i) q^{42} +(2.05989 - 5.65949i) q^{43} +(-3.23172 - 0.745629i) q^{44} +(-1.61180 + 2.79173i) q^{45} +(-0.0400085 + 0.380655i) q^{46} +(4.71866 + 2.50896i) q^{47} +(-0.437539 - 3.11325i) q^{48} +(3.09649 + 1.37865i) q^{49} +(-0.499720 - 4.75452i) q^{50} +(7.99470 - 19.7876i) q^{51} +(1.91357 - 2.44926i) q^{52} +(-1.63719 + 5.70956i) q^{53} +(-7.84849 - 9.35346i) q^{54} +(-0.890668 + 1.27238i) q^{55} -1.90012i q^{56} +(-1.59952 + 13.6101i) q^{57} +(-2.02417 + 6.22975i) q^{58} +(4.57399 + 8.60243i) q^{59} +(-1.42850 - 0.356165i) q^{60} +(-1.73327 - 1.16911i) q^{61} +(-1.09583 - 0.0382672i) q^{62} +(-6.93138 - 11.0925i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.727758 - 1.26051i) q^{65} +(-5.98185 - 8.54045i) q^{66} +(6.09645 + 1.07497i) q^{67} +(6.75117 + 0.709577i) q^{68} +(-0.894237 + 0.805175i) q^{69} +(-0.825015 - 0.333328i) q^{70} +(-1.65319 - 5.76537i) q^{71} +(3.84937 - 5.70693i) q^{72} +(3.82558 - 6.12221i) q^{73} +(-1.48615 + 10.5745i) q^{74} +(8.83431 - 12.1594i) q^{75} +(-4.30164 + 0.704193i) q^{76} +(-2.86183 - 5.61472i) q^{77} +(9.62313 - 1.69682i) q^{78} +(-10.3815 + 0.725944i) q^{79} +(-0.0163431 - 0.468004i) q^{80} +(0.618952 - 17.7245i) q^{81} +(-11.0076 - 0.769726i) q^{82} +(1.59395 - 0.167531i) q^{83} +(3.99719 - 4.43933i) q^{84} +(1.49241 - 2.80682i) q^{85} +(4.18372 + 4.33237i) q^{86} +(-17.8343 + 10.2966i) q^{87} +(2.08686 - 2.57779i) q^{88} +(4.29848 - 5.12273i) q^{89} +(-1.80262 - 2.67249i) q^{90} +(5.90228 - 0.206112i) q^{91} +(-0.324592 - 0.202828i) q^{92} +(-2.47973 - 2.39465i) q^{93} +(-4.32356 + 3.14125i) q^{94} +(-0.448858 + 1.99126i) q^{95} +(2.98998 + 0.971503i) q^{96} +(-0.456643 - 0.222720i) q^{97} +(-2.59653 + 2.17875i) q^{98} +(2.77925 - 22.6612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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