LMFDB - Embedded newform 225.2.q.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30960 + 1.45446i) q^{2} +(-1.67467 - 0.442133i) q^{3} +(-0.191342 - 1.82050i) q^{4} +(-1.40249 - 1.74155i) q^{5} +(2.83622 - 1.85672i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 - 0.194964i) q^{8} +(2.60904 + 1.48085i) q^{9} +O(q^{10})$	\(q+(-1.30960 + 1.45446i) q^{2} +(-1.67467 - 0.442133i) q^{3} +(-0.191342 - 1.82050i) q^{4} +(-1.40249 - 1.74155i) q^{5} +(2.83622 - 1.85672i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 - 0.194964i) q^{8} +(2.60904 + 1.48085i) q^{9} +(4.36974 + 0.240869i) q^{10} +(1.65278 - 1.83560i) q^{11} +(-0.484468 + 3.13333i) q^{12} +(2.15209 + 2.39014i) q^{13} +(-2.64193 - 0.561560i) q^{14} +(1.57872 + 3.53662i) q^{15} +(4.21604 - 0.896147i) q^{16} +(3.02773 + 2.19977i) q^{17} +(-5.57065 + 1.85541i) q^{18} +(0.234784 + 0.170581i) q^{19} +(-2.90214 + 2.88647i) q^{20} +(-0.627134 - 2.30654i) q^{21} +(0.505323 + 4.80783i) q^{22} +(-0.569918 - 0.121140i) q^{23} +(0.363189 + 0.445145i) q^{24} +(-1.06602 + 4.88504i) q^{25} -6.29476 q^{26} +(-3.71454 - 3.63348i) q^{27} +(2.04372 - 1.48485i) q^{28} +(3.40818 + 1.51742i) q^{29} +(-7.21137 - 2.33538i) q^{30} +(7.82432 - 3.48361i) q^{31} +(-3.88624 + 6.73116i) q^{32} +(-3.57945 + 2.34328i) q^{33} +(-7.16461 + 1.52289i) q^{34} +(1.11366 - 2.87787i) q^{35} +(2.19667 - 5.03309i) q^{36} +(2.37815 - 7.31918i) q^{37} +(-0.555578 + 0.118092i) q^{38} +(-2.54728 - 4.95421i) q^{39} +(0.0368121 + 0.740773i) q^{40} +(4.25243 + 4.72280i) q^{41} +(4.17608 + 2.10851i) q^{42} +(-3.20269 - 5.54723i) q^{43} +(-3.65796 - 2.65766i) q^{44} +(-1.08017 - 6.62067i) q^{45} +(0.922560 - 0.670279i) q^{46} +(6.56303 + 2.92205i) q^{47} +(-7.45669 - 0.363302i) q^{48} +(2.54776 - 4.41285i) q^{49} +(-5.70905 - 7.94795i) q^{50} +(-4.09785 - 5.02255i) q^{51} +(3.93946 - 4.37521i) q^{52} +(6.69073 - 4.86110i) q^{53} +(10.1493 - 0.644232i) q^{54} +(-5.51482 - 0.303989i) q^{55} +(0.0478474 - 0.455238i) q^{56} +(-0.317767 - 0.389473i) q^{57} +(-6.67040 + 2.96985i) q^{58} +(-1.30177 - 1.44576i) q^{59} +(6.13632 - 3.55075i) q^{60} +(-8.77365 + 9.74413i) q^{61} +(-5.17998 + 15.9423i) q^{62} +(0.0304439 + 4.13997i) q^{63} +(-2.03692 - 6.26900i) q^{64} +(1.14426 - 7.10014i) q^{65} +(1.27945 - 8.27494i) q^{66} +(9.24473 - 4.11602i) q^{67} +(3.42535 - 5.93288i) q^{68} +(0.900864 + 0.454849i) q^{69} +(2.72731 + 5.38865i) q^{70} +(-10.4571 + 7.59752i) q^{71} +(-0.411408 - 0.906048i) q^{72} +(1.44065 + 4.43387i) q^{73} +(7.53104 + 13.0442i) q^{74} +(3.94507 - 7.70950i) q^{75} +(0.265618 - 0.460064i) q^{76} +(3.33424 + 0.708716i) q^{77} +(10.5416 + 2.78312i) q^{78} +(-14.5537 - 6.47975i) q^{79} +(-7.47366 - 6.08562i) q^{80} +(4.61414 + 7.72721i) q^{81} -12.4381 q^{82} +(-0.0211178 + 0.200922i) q^{83} +(-4.07905 + 1.58303i) q^{84} +(-0.415350 - 8.35812i) q^{85} +(12.2625 + 2.60647i) q^{86} +(-5.03668 - 4.04805i) q^{87} +(-0.801393 + 0.170341i) q^{88} +(-3.30633 - 10.1758i) q^{89} +(11.0441 + 7.09938i) q^{90} +(-1.37158 + 4.22128i) q^{91} +(-0.111485 + 1.06071i) q^{92} +(-14.6434 + 2.37450i) q^{93} +(-12.8450 + 5.71895i) q^{94} +(-0.0322082 - 0.648128i) q^{95} +(9.48424 - 9.55424i) q^{96} +(10.0866 + 4.49085i) q^{97} +(3.08177 + 9.48471i) q^{98} +(7.03043 - 2.34162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.30960	+	1.45446i	−0.926030	+	1.02846i	0.0734844	+	0.997296i	$0.476588\pi$
$2$	−1.30960	+	1.45446i	−0.926030	+	1.02846i	−0.999514	+	0.0311641i	$0.990079\pi$
$3$	−1.67467	−	0.442133i	−0.966871	−	0.255266i
$3$	−1.67467	−	0.442133i	−0.966871	−	0.255266i
$4$	−0.191342	−	1.82050i	−0.0956710	−	0.910248i
$5$	−1.40249	−	1.74155i	−0.627215	−	0.778846i
$5$	−1.40249	−	1.74155i	−0.627215	−	0.778846i
$6$	2.83622	−	1.85672i	1.15788	−	0.758005i
$7$	0.690014	+	1.19514i	0.260801	+	0.451720i	0.966455	−	0.256836i	$-0.0826801\pi$
$7$	0.690014	+	1.19514i	0.260801	+	0.451720i	−0.705654	+	0.708556i	$0.749347\pi$
$8$	−0.268345	−	0.194964i	−0.0948743	−	0.0689302i
$9$	2.60904	+	1.48085i	0.869679	+	0.493618i
$10$	4.36974	+	0.240869i	1.38183	+	0.0761696i
$11$	1.65278	−	1.83560i	0.498333	−	0.553455i	−0.440533	−	0.897736i	$-0.645211\pi$
$11$	1.65278	−	1.83560i	0.498333	−	0.553455i	0.938867	+	0.344281i	$0.111877\pi$
$12$	−0.484468	+	3.13333i	−0.139854	+	0.904514i
$13$	2.15209	+	2.39014i	0.596883	+	0.662906i	0.963576	−	0.267436i	$-0.0861765\pi$
$13$	2.15209	+	2.39014i	0.596883	+	0.662906i	−0.366692	+	0.930342i	$0.619510\pi$
$14$	−2.64193	−	0.561560i	−0.706086	−	0.150083i
$15$	1.57872	+	3.53662i	0.407623	+	0.913150i
$16$	4.21604	−	0.896147i	1.05401	−	0.224037i
$17$	3.02773	+	2.19977i	0.734332	+	0.533523i	0.890931	−	0.454139i	$-0.150053\pi$
$17$	3.02773	+	2.19977i	0.734332	+	0.533523i	−0.156599	+	0.987662i	$0.550053\pi$
$18$	−5.57065	+	1.85541i	−1.31302	+	0.437325i
$19$	0.234784	+	0.170581i	0.0538632	+	0.0391339i	0.614391	−	0.789002i	$-0.289402\pi$
$19$	0.234784	+	0.170581i	0.0538632	+	0.0391339i	−0.560528	+	0.828136i	$0.689402\pi$
$20$	−2.90214	+	2.88647i	−0.648937	+	0.645434i
$21$	−0.627134	−	2.30654i	−0.136852	−	0.503329i
$22$	0.505323	+	4.80783i	0.107735	+	1.02503i
$23$	−0.569918	−	0.121140i	−0.118836	−	0.0252594i	0.148110	−	0.988971i	$-0.452681\pi$
$23$	−0.569918	−	0.121140i	−0.118836	−	0.0252594i	−0.266946	+	0.963712i	$0.586014\pi$
$24$	0.363189	+	0.445145i	0.0741357	+	0.0908648i
$25$	−1.06602	+	4.88504i	−0.213203	+	0.977008i
$26$	−6.29476			−1.23450
$27$	−3.71454	−	3.63348i	−0.714863	−	0.699264i
$28$	2.04372	−	1.48485i	0.386227	−	0.280610i
$29$	3.40818	+	1.51742i	0.632884	+	0.281778i	0.697998	−	0.716100i	$-0.254075\pi$
$29$	3.40818	+	1.51742i	0.632884	+	0.281778i	−0.0651142	+	0.997878i	$0.520741\pi$
$30$	−7.21137	−	2.33538i	−1.31661	−	0.426381i
$31$	7.82432	−	3.48361i	1.40529	−	0.625675i	0.442707	−	0.896666i	$-0.354018\pi$
$31$	7.82432	−	3.48361i	1.40529	−	0.625675i	0.962582	+	0.270991i	$0.0873515\pi$
$32$	−3.88624	+	6.73116i	−0.686996	+	1.18991i
$33$	−3.57945	+	2.34328i	−0.623102	+	0.407912i
$34$	−7.16461	+	1.52289i	−1.22872	+	0.261173i
$35$	1.11366	−	2.87787i	0.188243	−	0.486449i
$36$	2.19667	−	5.03309i	0.366112	−	0.838849i
$37$	2.37815	−	7.31918i	0.390965	−	1.20327i	−0.541095	−	0.840961i	$-0.681990\pi$
$37$	2.37815	−	7.31918i	0.390965	−	1.20327i	0.932060	−	0.362304i	$-0.118010\pi$
$38$	−0.555578	+	0.118092i	−0.0901267	+	0.0191570i
$39$	−2.54728	−	4.95421i	−0.407892	−	0.793308i
$40$	0.0368121	+	0.740773i	0.00582050	+	0.117127i
$41$	4.25243	+	4.72280i	0.664118	+	0.737578i	0.977240	−	0.212135i	$-0.0680416\pi$
$41$	4.25243	+	4.72280i	0.664118	+	0.737578i	−0.313122	+	0.949713i	$0.601375\pi$
$42$	4.17608	+	2.10851i	0.644383	+	0.325351i
$43$	−3.20269	−	5.54723i	−0.488406	−	0.845944i	0.511505	−	0.859280i	$-0.329088\pi$
$43$	−3.20269	−	5.54723i	−0.488406	−	0.845944i	−0.999911	+	0.0133363i	$0.995755\pi$
$44$	−3.65796	−	2.65766i	−0.551458	−	0.400657i
$45$	−1.08017	−	6.62067i	−0.161023	−	0.986951i
$46$	0.922560	−	0.670279i	0.136024	−	0.0988273i
$47$	6.56303	+	2.92205i	0.957316	+	0.426225i	0.825094	−	0.564996i	$-0.191122\pi$
$47$	6.56303	+	2.92205i	0.957316	+	0.426225i	0.132222	+	0.991220i	$0.457789\pi$
$48$	−7.45669	−	0.363302i	−1.07628	−	0.0524381i
$49$	2.54776	−	4.41285i	0.363966	−	0.630407i
$50$	−5.70905	−	7.94795i	−0.807381	−	1.12401i
$51$	−4.09785	−	5.02255i	−0.573814	−	0.703298i
$52$	3.93946	−	4.37521i	0.546305	−	0.606733i
$53$	6.69073	−	4.86110i	0.919043	−	0.667724i	−0.0242428	−	0.999706i	$-0.507717\pi$
$53$	6.69073	−	4.86110i	0.919043	−	0.667724i	0.943286	+	0.331982i	$0.107717\pi$
$54$	10.1493	−	0.644232i	1.38115	−	0.0876688i
$55$	−5.51482	−	0.303989i	−0.743618	−	0.0409899i
$56$	0.0478474	−	0.455238i	0.00639388	−	0.0608337i
$57$	−0.317767	−	0.389473i	−0.0420892	−	0.0515869i
$58$	−6.67040	+	2.96985i	−0.875867	+	0.389961i
$59$	−1.30177	−	1.44576i	−0.169476	−	0.188222i	0.652424	−	0.757854i	$-0.273752\pi$
$59$	−1.30177	−	1.44576i	−0.169476	−	0.188222i	−0.821900	+	0.569632i	$0.807086\pi$
$60$	6.13632	−	3.55075i	0.792196	−	0.458400i
$61$	−8.77365	+	9.74413i	−1.12335	+	1.24761i	−0.157778	+	0.987475i	$0.550433\pi$
$61$	−8.77365	+	9.74413i	−1.12335	+	1.24761i	−0.965573	+	0.260133i	$0.916234\pi$
$62$	−5.17998	+	15.9423i	−0.657858	+	2.02468i
$63$	0.0304439	+	4.13997i	0.00383557	+	0.521587i
$64$	−2.03692	−	6.26900i	−0.254615	−	0.783625i
$65$	1.14426	−	7.10014i	0.141928	−	0.880665i
$66$	1.27945	−	8.27494i	0.157490	−	1.01857i
$67$	9.24473	−	4.11602i	1.12942	−	0.502852i	0.244994	−	0.969525i	$-0.421214\pi$
$67$	9.24473	−	4.11602i	1.12942	−	0.502852i	0.884430	+	0.466673i	$0.154547\pi$
$68$	3.42535	−	5.93288i	0.415385	−	0.719467i
$69$	0.900864	+	0.454849i	0.108451	+	0.0547574i
$70$	2.72731	+	5.38865i	0.325976	+	0.644067i
$71$	−10.4571	+	7.59752i	−1.24103	+	0.901659i	−0.997666	−	0.0682765i	$-0.978250\pi$
$71$	−10.4571	+	7.59752i	−1.24103	+	0.901659i	−0.243361	+	0.969936i	$0.578250\pi$
$72$	−0.411408	−	0.906048i	−0.0484849	−	0.106779i
$73$	1.44065	+	4.43387i	0.168615	+	0.518945i	0.999285	−	0.0378214i	$-0.0120418\pi$
$73$	1.44065	+	4.43387i	0.168615	+	0.518945i	−0.830669	+	0.556767i	$0.812042\pi$
$74$	7.53104	+	13.0442i	0.875466	+	1.51635i
$75$	3.94507	−	7.70950i	0.455537	−	0.890217i
$76$	0.265618	−	0.460064i	0.0304685	−	0.0527729i
$77$	3.33424	+	0.708716i	0.379972	+	0.0807656i
$78$	10.5416	+	2.78312i	1.19361	+	0.315127i
$79$	−14.5537	−	6.47975i	−1.63742	−	0.729028i	−0.638257	−	0.769824i	$-0.720344\pi$
$79$	−14.5537	−	6.47975i	−1.63742	−	0.729028i	−0.999168	+	0.0407952i	$0.987011\pi$
$80$	−7.47366	−	6.08562i	−0.835581	−	0.680393i
$81$	4.61414	+	7.72721i	0.512682	+	0.858578i
$82$	−12.4381			−1.37356
$83$	−0.0211178	+	0.200922i	−0.00231797	+	0.0220541i	−0.995620	−	0.0934950i	$-0.970196\pi$
$83$	−0.0211178	+	0.200922i	−0.00231797	+	0.0220541i	0.993302	+	0.115549i	$0.0368628\pi$
$84$	−4.07905	+	1.58303i	−0.445061	+	0.172723i
$85$	−0.415350	−	8.35812i	−0.0450510	−	0.906565i
$86$	12.2625	+	2.60647i	1.32230	+	0.281063i
$87$	−5.03668	−	4.04805i	−0.539988	−	0.433996i
$88$	−0.801393	+	0.170341i	−0.0854288	+	0.0181584i
$89$	−3.30633	−	10.1758i	−0.350471	−	1.07864i	−0.958589	−	0.284792i	$-0.908076\pi$
$89$	−3.30633	−	10.1758i	−0.350471	−	1.07864i	0.608119	−	0.793846i	$-0.291924\pi$
$90$	11.0441	+	7.09938i	1.16415	+	0.748341i
$91$	−1.37158	+	4.22128i	−0.143780	+	0.442510i
$92$	−0.111485	+	1.06071i	−0.0116232	+	0.110587i
$93$	−14.6434	+	2.37450i	−1.51845	+	0.246225i
$94$	−12.8450	+	5.71895i	−1.32486	+	0.589865i
$95$	−0.0322082	−	0.648128i	−0.00330449	−	0.0664966i
$96$	9.48424	−	9.55424i	0.967981	−	0.975125i
$97$	10.0866	+	4.49085i	1.02414	+	0.455977i	0.848903	−	0.528549i	$-0.177264\pi$
$97$	10.0866	+	4.49085i	1.02414	+	0.455977i	0.175238	+	0.984526i	$0.443930\pi$
$98$	3.08177	+	9.48471i	0.311306	+	0.958101i
$99$	7.03043	−	2.34162i	0.706585	−	0.235342i
$100$	9.09717	+	1.00597i	0.909717	+	0.100597i
$101$	7.27293	+	12.5971i	0.723684	+	1.25346i	0.959513	+	0.281663i	$0.0908859\pi$
$101$	7.27293	+	12.5971i	0.723684	+	1.25346i	−0.235830	+	0.971794i	$0.575781\pi$
$102$	12.6717	+	0.617385i	1.25468	+	0.0611302i
$103$	0.606222	+	5.76782i	0.0597328	+	0.568320i	0.982928	+	0.183989i	$0.0589011\pi$
$103$	0.606222	+	5.76782i	0.0597328	+	0.568320i	−0.923195	+	0.384331i	$0.874432\pi$
$104$	−0.111512	−	1.06096i	−0.0109346	−	0.104036i
$105$	−3.13741	+	4.32710i	−0.306180	+	0.422282i
$106$	−1.69192	+	16.0975i	−0.164334	+	1.56353i
$107$	−12.8622			−1.24344			−0.621718	−	0.783241i	$-0.713565\pi$
$107$	−12.8622			−1.24344			−0.621718	+	0.783241i	$0.713565\pi$
$108$	−5.90400	+	7.45754i	−0.568113	+	0.717602i
$109$	−4.92848	+	15.1683i	−0.472063	+	1.45286i	0.377816	+	0.925881i	$0.376675\pi$
$109$	−4.92848	+	15.1683i	−0.472063	+	1.45286i	−0.849878	+	0.526979i	$0.823325\pi$
$110$	7.66437	−	7.62300i	0.730769	−	0.726824i
$111$	−7.21866	+	11.2057i	−0.685165	+	1.06360i
$112$	3.98015	+	4.42040i	0.376089	+	0.417689i
$113$	4.94877	+	5.49617i	0.465542	+	0.517036i	0.929501	−	0.368820i	$-0.120238\pi$
$113$	4.94877	+	5.49617i	0.465542	+	0.517036i	−0.463959	+	0.885857i	$0.653572\pi$
$114$	0.982622	+	0.0478749i	0.0920310	+	0.00448390i
$115$	0.588335	+	1.16244i	0.0548626	+	0.108398i
$116$	2.11033	−	6.49493i	0.195939	−	0.603039i
$117$	2.07544	+	9.42290i	0.191874	+	0.871147i
$118$	3.80761			0.350519
$119$	−0.539861	+	5.13643i	−0.0494889	+	0.470856i
$120$	0.265872	−	1.25683i	0.0242707	−	0.114732i
$121$	0.512071	+	4.87203i	0.0465519	+	0.442912i
$122$	−2.68246	−	25.5219i	−0.242858	−	2.31064i
$123$	−5.03331	−	9.78928i	−0.453838	−	0.882669i
$124$	−7.83902	−	13.5776i	−0.703965	−	1.21930i
$125$	10.0026	−	4.99472i	0.894663	−	0.446741i
$126$	−6.06130	−	5.37744i	−0.539984	−	0.479061i
$127$	−4.27237	−	13.1490i	−0.379112	−	1.16679i	−0.940663	−	0.339343i	$-0.889795\pi$
$127$	−4.27237	−	13.1490i	−0.379112	−	1.16679i	0.561551	−	0.827442i	$-0.310205\pi$
$128$	−2.41543	−	1.07542i	−0.213496	−	0.0950544i
$129$	2.91084	+	10.7058i	0.256285	+	0.942592i
$130$	8.82837	+	10.9627i	0.774299	+	0.961489i
$131$	6.74268	−	3.00204i	0.589111	−	0.262289i	−0.0904585	−	0.995900i	$-0.528833\pi$
$131$	6.74268	−	3.00204i	0.589111	−	0.262289i	0.679570	+	0.733611i	$0.262167\pi$
$132$	4.95083	+	6.06801i	0.430914	+	0.528152i
$133$	−0.0418634	+	0.398303i	−0.00363001	+	0.0345373i
$134$	−6.12034	+	18.8365i	−0.528717	+	1.62722i
$135$	−1.11829	+	11.5650i	−0.0962468	+	0.995357i
$136$	−0.383599	−	1.18060i	−0.0328933	−	0.101235i
$137$	4.12212	−	0.876184i	0.352177	−	0.0748574i	−0.0284267	−	0.999596i	$-0.509050\pi$
$137$	4.12212	−	0.876184i	0.352177	−	0.0748574i	0.380603	+	0.924738i	$0.375716\pi$
$138$	−1.84134	+	0.714601i	−0.156745	+	0.0608309i
$139$	0.349017	+	0.0741858i	0.0296032	+	0.00629236i	0.222689	−	0.974889i	$-0.428516\pi$
$139$	0.349017	+	0.0741858i	0.0296032	+	0.00629236i	−0.193086	+	0.981182i	$0.561850\pi$
$140$	−5.45225	−	1.47675i	−0.460799	−	0.124808i
$141$	−9.69897	−	7.79520i	−0.816800	−	0.656474i
$142$	2.64434	−	25.1592i	0.221908	−	2.11131i
$143$	7.94429			0.664335
$144$	12.3269	+	3.90526i	1.02724	+	0.325439i
$145$	−2.13729	−	8.06371i	−0.177492	−	0.669654i
$146$	−8.33558	−	3.71124i	−0.689858	−	0.307144i
$147$	−6.21773	+	6.26362i	−0.512830	+	0.516615i
$148$	−13.7796	−	2.92894i	−1.13267	−	0.240757i
$149$	11.6755	−	20.2226i	0.956497	−	1.65670i	0.225591	−	0.974222i	$-0.427569\pi$
$149$	11.6755	−	20.2226i	0.956497	−	1.65670i	0.730905	−	0.682479i	$-0.239098\pi$
$150$	6.04671	+	15.8343i	0.493712	+	1.29287i
$151$	4.03983	+	6.99720i	0.328757	+	0.569424i	0.982265	−	0.187495i	$-0.0600369\pi$
$151$	4.03983	+	6.99720i	0.328757	+	0.569424i	−0.653508	+	0.756919i	$0.726704\pi$
$152$	−0.0297461	−	0.0915490i	−0.00241273	−	0.00742561i
$153$	4.64191	+	10.2229i	0.375276	+	0.826473i
$154$	−5.39734	+	3.92140i	−0.434930	+	0.315995i
$155$	−17.0405	−	8.74072i	−1.36872	−	0.702072i
$156$	−8.53172	+	5.58527i	−0.683084	+	0.447179i
$157$	8.40415	−	14.5564i	0.670724	−	1.16173i	−0.306975	−	0.951718i	$-0.599317\pi$
$157$	8.40415	−	14.5564i	0.670724	−	1.16173i	0.977699	−	0.210011i	$-0.0673500\pi$
$158$	28.4842	−	12.6820i	2.26608	−	1.00892i
$159$	−13.3540	+	5.18254i	−1.05904	+	0.411002i
$160$	17.1731	−	2.67233i	1.35765	−	0.211266i
$161$	−0.248472	−	0.764719i	−0.0195824	−	0.0602683i
$162$	−17.2816	−	3.40849i	−1.35777	−	0.267796i
$163$	1.89571	−	5.83439i	0.148483	−	0.456985i	−0.848959	−	0.528459i	$-0.822770\pi$
$163$	1.89571	−	5.83439i	0.148483	−	0.456985i	0.997442	+	0.0714737i	$0.0227702\pi$
$164$	7.78418	−	8.64521i	0.607842	−	0.675077i
$165$	9.10110	+	2.94737i	0.708520	+	0.229452i
$166$	−0.264578	−	0.293843i	−0.0205352	−	0.0228067i
$167$	−18.6016	+	8.28195i	−1.43943	+	0.640876i	−0.970224	−	0.242211i	$-0.922127\pi$
$167$	−18.6016	+	8.28195i	−1.43943	+	0.640876i	−0.469208	+	0.883088i	$0.655461\pi$
$168$	−0.281404	+	0.741218i	−0.0217108	+	0.0571862i
$169$	0.277599	−	2.64118i	0.0213538	−	0.203167i
$170$	12.7005	+	10.3417i	0.974085	+	0.793174i
$171$	0.359956	+	0.792733i	0.0275265	+	0.0606218i
$172$	−9.48590	+	6.89191i	−0.723293	+	0.525503i
$173$	−8.79105	+	9.76345i	−0.668371	+	0.742301i	−0.978011	−	0.208553i	$-0.933125\pi$
$173$	−8.79105	+	9.76345i	−0.668371	+	0.742301i	0.309640	+	0.950854i	$0.399791\pi$
$174$	12.4838	−	2.02432i	0.946394	−	0.153463i
$175$	−6.57387	+	2.09671i	−0.496938	+	0.158496i
$176$	5.32323	−	9.22011i	0.401254	−	0.694992i
$177$	1.54082	+	2.99673i	0.115815	+	0.225248i
$178$	19.1304	+	8.51739i	1.43388	+	0.638406i
$179$	4.14235	−	3.00959i	0.309614	−	0.224947i	−0.422117	−	0.906541i	$-0.638713\pi$
$179$	4.14235	−	3.00959i	0.309614	−	0.224947i	0.731731	+	0.681594i	$0.238713\pi$
$180$	−11.8462	+	3.23326i	−0.882965	+	0.240993i
$181$	−7.20858	−	5.23734i	−0.535810	−	0.389289i	0.286717	−	0.958015i	$-0.407436\pi$
$181$	−7.20858	−	5.23734i	−0.535810	−	0.389289i	−0.822526	+	0.568727i	$0.807436\pi$
$182$	−4.34347	−	7.52312i	−0.321960	−	0.557650i
$183$	19.0012	−	12.4391i	1.40461	−	0.919522i
$184$	0.129317	+	0.143621i	0.00953335	+	0.0105879i
$185$	−16.0821	+	6.12344i	−1.18238	+	0.450204i
$186$	15.7234	−	24.4079i	1.15289	−	1.78967i
$187$	9.04209	−	1.92196i	0.661223	−	0.140547i
$188$	4.06380	−	12.5071i	0.296383	−	0.912173i
$189$	1.77944	−	6.94655i	0.129435	−	0.505287i
$190$	0.984859	+	0.801946i	0.0714492	+	0.0581793i
$191$	1.84219	−	0.391569i	0.133296	−	0.0283329i	−0.140781	−	0.990041i	$-0.544961\pi$
$191$	1.84219	−	0.391569i	0.133296	−	0.0283329i	0.274076	+	0.961708i	$0.411628\pi$
$192$	0.639437	+	11.3991i	0.0461474	+	0.822659i
$193$	−0.740550	+	1.28267i	−0.0533060	+	0.0923286i	−0.891447	−	0.453125i	$-0.850309\pi$
$193$	−0.740550	+	1.28267i	−0.0533060	+	0.0923286i	0.838141	+	0.545453i	$0.183643\pi$
$194$	−19.7412	+	8.78937i	−1.41734	+	0.631040i
$195$	−5.05547	+	11.3845i	−0.362030	+	0.815260i
$196$	−8.52108	−	3.79383i	−0.608648	−	0.270988i
$197$	15.6165	−	11.3460i	1.11263	−	0.808372i	0.129553	−	0.991572i	$-0.458646\pi$
$197$	15.6165	−	11.3460i	1.11263	−	0.808372i	0.983076	+	0.183200i	$0.0586457\pi$
$198$	−5.80128	+	13.2921i	−0.412279	+	0.944628i
$199$	6.17381			0.437650			0.218825	−	0.975764i	$-0.429778\pi$
$199$	6.17381			0.437650			0.218825	+	0.975764i	$0.429778\pi$
$200$	1.23847	−	1.10304i	0.0875729	−	0.0779968i
$201$	−17.3017	+	2.80557i	−1.22037	+	0.197889i
$202$	−27.8467	−	5.91899i	−1.95928	−	0.416459i
$203$	0.538165	+	5.12029i	0.0377718	+	0.359374i
$204$	−8.35945	+	8.42115i	−0.585279	+	0.589598i
$205$	2.26100	−	14.0295i	0.157915	−	0.979866i
$206$	−9.18299	−	6.67183i	−0.639809	−	0.464848i
$207$	−1.30755	−	1.16002i	−0.0908807	−	0.0806272i
$208$	11.2152	+	8.14834i	0.777636	+	0.564986i
$209$	0.701167	−	0.149038i	0.0485007	−	0.0103091i
$210$	−2.18484	−	10.2300i	−0.150768	−	0.705940i
$211$	−27.6930	−	5.88633i	−1.90647	−	0.405232i	−0.906606	−	0.421977i	$-0.861336\pi$
$211$	−27.6930	−	5.88633i	−1.90647	−	0.405232i	−0.999860	+	0.0167456i	$0.994669\pi$
$212$	−10.1298	−	11.2503i	−0.695720	−	0.772675i
$213$	20.8713	−	8.09990i	1.43008	−	0.554996i
$214$	16.8444	−	18.7076i	1.15146	−	1.27883i
$215$	−5.16903	+	13.3576i	−0.352525	+	0.910982i
$216$	0.288379	+	1.69923i	0.0196217	+	0.115618i
$217$	9.56229	+	6.94741i	0.649130	+	0.471621i
$218$	−15.6074	−	27.0328i	−1.05706	−	1.83089i
$219$	−0.452254	−	8.06223i	−0.0305605	−	0.544795i
$220$	0.501806	+	10.0979i	0.0338317	+	0.680799i
$221$	1.25818	+	11.9708i	0.0846345	+	0.805244i
$222$	−6.84476	−	25.1744i	−0.459390	−	1.68959i
$223$	0.0705652	−	0.0783706i	0.00472540	−	0.00524809i	−0.740777	−	0.671750i	$-0.765543\pi$
$223$	0.0705652	−	0.0783706i	0.00472540	−	0.00524809i	0.745503	+	0.666502i	$0.232209\pi$
$224$	−10.7262			−0.716677
$225$	−10.0153	+	11.1666i	−0.667687	+	0.744442i
$226$	−14.4749			−0.962857
$227$	−6.70838	+	7.45041i	−0.445251	+	0.494501i	−0.923433	−	0.383760i	$-0.874629\pi$
$227$	−6.70838	+	7.45041i	−0.445251	+	0.494501i	0.478182	+	0.878261i	$0.341296\pi$
$228$	−0.648232	+	0.653016i	−0.0429302	+	0.0432470i
$229$	1.83314	+	17.4412i	0.121137	+	1.15255i	0.871114	+	0.491081i	$0.163398\pi$
$229$	1.83314	+	17.4412i	0.121137	+	1.15255i	−0.749977	+	0.661464i	$0.769935\pi$
$230$	−2.46121	−	0.666625i	−0.162288	−	0.0439559i
$231$	−5.27041	−	2.66105i	−0.346768	−	0.175084i
$232$	−0.618726	−	1.07167i	−0.0406214	−	0.0703583i
$233$	−7.01516	−	5.09682i	−0.459579	−	0.333903i	0.333787	−	0.942648i	$-0.391673\pi$
$233$	−7.01516	−	5.09682i	−0.459579	−	0.333903i	−0.793366	+	0.608745i	$0.791673\pi$
$234$	−16.4233	−	9.32162i	−1.07362	−	0.609374i
$235$	−4.11571	−	15.5280i	−0.268479	−	1.01294i
$236$	−2.38292	+	2.64650i	−0.155115	+	0.172273i
$237$	21.5078	+	17.2861i	1.39708	+	1.12285i
$238$	−6.76374	−	7.51190i	−0.438428	−	0.486924i
$239$	9.90950	+	2.10633i	0.640992	+	0.136247i	0.516930	−	0.856027i	$-0.327075\pi$
$239$	9.90950	+	2.10633i	0.640992	+	0.136247i	0.124062	+	0.992275i	$0.460408\pi$
$240$	9.82526	+	13.4958i	0.634218	+	0.871147i
$241$	7.96968	−	1.69401i	0.513372	−	0.109121i	0.0560610	−	0.998427i	$-0.482146\pi$
$241$	7.96968	−	1.69401i	0.513372	−	0.109121i	0.457311	+	0.889307i	$0.348813\pi$
$242$	−7.75680	−	5.63564i	−0.498626	−	0.362273i
$243$	−4.31070	−	14.9806i	−0.276532	−	0.961005i
$244$	19.4179	+	14.1079i	1.24310	+	0.903168i
$245$	−11.2584	+	1.75194i	−0.719275	+	0.111927i
$246$	20.8298	+	5.49932i	1.32806	+	0.350624i
$247$	0.0975655	+	0.928274i	0.00620794	+	0.0590646i
$248$	−2.77880	−	0.590651i	−0.176454	−	0.0375064i
$249$	0.124200	−	0.327141i	0.00787083	−	0.0207317i
$250$	−5.83487	+	21.0896i	−0.369030	+	1.33382i
$251$	23.5790			1.48829			0.744146	−	0.668017i	$-0.232857\pi$
$251$	23.5790			1.48829			0.744146	+	0.668017i	$0.232857\pi$
$252$	7.53098	−	0.847573i	0.474407	−	0.0533921i
$253$	−1.16432	+	0.845925i	−0.0731999	+	0.0531828i
$254$	24.7199	+	11.0060i	1.55106	+	0.690577i
$255$	−2.99983	+	14.1807i	−0.187857	+	0.888032i
$256$	16.7709	−	7.46688i	1.04818	−	0.466680i
$257$	−6.51124	+	11.2778i	−0.406160	+	0.703490i	−0.994456	−	0.105156i	$-0.966466\pi$
$257$	−6.51124	+	11.2778i	−0.406160	+	0.703490i	0.588296	+	0.808646i	$0.299799\pi$
$258$	−19.3832	−	9.78664i	−1.20675	−	0.609289i
$259$	10.3884	−	2.20812i	0.645503	−	0.137206i
$260$	−13.1447	−	0.724566i	−0.815202	−	0.0449357i
$261$	6.64499	+	9.00603i	0.411315	+	0.557459i
$262$	−4.46390	+	13.7385i	−0.275780	+	0.848765i
$263$	11.0211	−	2.34260i	0.679589	−	0.144451i	0.144831	−	0.989456i	$-0.453736\pi$
$263$	11.0211	−	2.34260i	0.679589	−	0.144451i	0.534758	+	0.845005i	$0.320403\pi$
$264$	1.41738	+	0.0690571i	0.0872338	+	0.00425017i
$265$	−17.8496	−	4.83460i	−1.09649	−	0.296987i
$266$	−0.524493	−	0.582508i	−0.0321587	−	0.0357159i
$267$	1.03793	+	18.5030i	0.0635205	+	1.13237i
$268$	−9.26210	−	16.0424i	−0.565773	−	0.979948i
$269$	−17.7014	−	12.8608i	−1.07927	−	0.784136i	−0.101715	−	0.994814i	$-0.532433\pi$
$269$	−17.7014	−	12.8608i	−1.07927	−	0.784136i	−0.977556	+	0.210677i	$0.932433\pi$
$270$	−15.3564	−	16.7721i	−0.934558	−	1.02072i
$271$	−9.50877	+	6.90853i	−0.577617	+	0.419663i	−0.837864	−	0.545879i	$-0.816196\pi$
$271$	−9.50877	+	6.90853i	−0.577617	+	0.419663i	0.260247	+	0.965542i	$0.416196\pi$
$272$	14.7363	+	6.56104i	0.893522	+	0.397822i
$273$	4.16331	−	6.46283i	0.251975	−	0.391148i
$274$	−4.12397	+	7.14292i	−0.249138	+	0.431520i
$275$	7.20509	+	10.0307i	0.434484	+	0.604874i
$276$	0.655678	−	1.72705i	0.0394672	−	0.103956i
$277$	−14.7246	+	16.3533i	−0.884714	+	0.982575i	−0.999942	−	0.0107642i	$-0.996574\pi$
$277$	−14.7246	+	16.3533i	−0.884714	+	0.982575i	0.115228	+	0.993339i	$0.463240\pi$
$278$	−0.564974	+	0.410478i	−0.0338849	+	0.0246188i
$279$	25.5726	+	2.49781i	1.53099	+	0.149540i
$280$	−0.859926	+	0.555139i	−0.0513904	+	0.0331759i
$281$	−0.134587	+	1.28051i	−0.00802878	+	0.0763888i	−0.997803	−	0.0662570i	$-0.978894\pi$
$281$	−0.134587	+	1.28051i	−0.00802878	+	0.0763888i	0.989774	+	0.142646i	$0.0455610\pi$
$282$	24.0396	−	3.89816i	1.43154	−	0.232132i
$283$	7.02505	−	3.12775i	0.417596	−	0.185926i	−0.187173	−	0.982327i	$-0.559932\pi$
$283$	7.02505	−	3.12775i	0.417596	−	0.185926i	0.604768	+	0.796401i	$0.293266\pi$
$284$	15.8321	+	17.5834i	0.939464	+	1.04338i
$285$	−0.232621	+	1.09964i	−0.0137793	+	0.0651371i
$286$	−10.4039	+	11.5547i	−0.615194	+	0.683242i
$287$	−2.71017	+	8.34105i	−0.159976	+	0.492356i
$288$	−20.1072	+	11.8069i	−1.18483	+	0.695728i
$289$	−0.925154	−	2.84733i	−0.0544209	−	0.167490i
$290$	14.5274	+	7.45166i	0.853076	+	0.437576i
$291$	−14.9062	−	11.9803i	−0.873817	−	0.702299i
$292$	7.79619	−	3.47109i	0.456237	−	0.203130i
$293$	−5.62660	+	9.74556i	−0.328710	+	0.569342i	−0.982256	−	0.187545i	$-0.939947\pi$
$293$	−5.62660	+	9.74556i	−0.328710	+	0.569342i	0.653546	+	0.756886i	$0.273280\pi$
$294$	−0.967438	−	17.2463i	−0.0564221	−	1.00583i
$295$	−0.692147	+	4.29478i	−0.0402983	+	0.250052i
$296$	−2.06514	+	1.50041i	−0.120034	+	0.0872097i
$297$	−12.8090	+	0.813051i	−0.743251	+	0.0471780i
$298$	14.1227	+	43.4652i	0.818107	+	2.51787i
$299$	−0.936975	−	1.62289i	−0.0541867	−	0.0938540i
$300$	−14.7900	−	5.70683i	−0.853900	−	0.329484i
$301$	4.41980	−	7.65533i	0.254753	−	0.441246i
$302$	−15.4677	−	3.28777i	−0.890069	−	0.189190i
$303$	−6.61016	−	24.3116i	−0.379744	−	1.39666i
$304$	1.14273	+	0.508774i	0.0655398	+	0.0291802i
$305$	29.2749	+	1.61370i	1.67628	+	0.0924000i
$306$	−20.9479	−	6.63649i	−1.19751	−	0.379383i
$307$	22.3350			1.27473			0.637363	−	0.770563i	$-0.280025\pi$
$307$	22.3350			1.27473			0.637363	+	0.770563i	$0.280025\pi$
$308$	0.652234	−	6.20559i	0.0371645	−	0.353596i
$309$	1.53492	−	9.92722i	0.0873187	−	0.564740i
$310$	35.0293	−	13.3378i	1.98953	−	0.757537i
$311$	16.3623	+	3.47792i	0.927823	+	0.197215i	0.646952	−	0.762531i	$-0.276043\pi$
$311$	16.3623	+	3.47792i	0.927823	+	0.197215i	0.280871	+	0.959746i	$0.409377\pi$
$312$	−0.282342	+	1.82607i	−0.0159845	+	0.103381i
$313$	−14.3725	+	3.05496i	−0.812380	+	0.172677i	−0.595327	−	0.803483i	$-0.702978\pi$
$313$	−14.3725	+	3.05496i	−0.812380	+	0.172677i	−0.217053	+	0.976160i	$0.569644\pi$
$314$	10.1657	+	31.2867i	0.573681	+	1.76561i
$315$	7.16729	−	5.85931i	0.403831	−	0.330135i
$316$	−9.01161	+	27.7349i	−0.506943	+	1.56021i
$317$	−0.308856	+	2.93857i	−0.0173471	+	0.165047i	−0.999766	−	0.0216446i	$-0.993110\pi$
$317$	−0.308856	+	2.93857i	−0.0173471	+	0.165047i	0.982419	+	0.186691i	$0.0597764\pi$
$318$	9.95067	−	26.2100i	0.558006	−	1.46978i
$319$	8.41837	−	3.74810i	0.471338	−	0.209853i
$320$	−8.06103	+	12.3397i	−0.450625	+	0.689808i
$321$	21.5400	+	5.68681i	1.20224	+	0.317407i
$322$	1.43766	+	0.640086i	0.0801174	+	0.0356706i
$323$	0.335624	+	1.03294i	0.0186746	+	0.0574746i
$324$	13.1845	−	9.87856i	0.732471	−	0.548809i
$325$	−13.9701	+	7.96512i	−0.774922	+	0.441826i
$326$	6.00328	+	10.3980i	0.332491	+	0.575891i
$327$	14.9600	−	23.2228i	0.827289	−	1.28423i
$328$	−0.220342	−	2.09641i	−0.0121663	−	0.115755i
$329$	1.03633	+	9.85999i	0.0571345	+	0.543599i
$330$	−16.2057	+	9.37732i	−0.892093	+	0.516205i
$331$	1.21002	−	11.5126i	0.0665087	−	0.632788i	−0.909597	−	0.415492i	$-0.863610\pi$
$331$	1.21002	−	11.5126i	0.0665087	−	0.632788i	0.976106	−	0.217296i	$-0.0697238\pi$
$332$	0.369819			0.0202964
$333$	17.0433	−	15.5743i	0.933968	−	0.853467i
$334$	12.3149	−	37.9013i	0.673841	−	2.07387i
$335$	−20.1340	−	10.3275i	−1.10004	−	0.564251i
$336$	−4.71102	−	9.16247i	−0.257007	−	0.499854i
$337$	−13.5141	−	15.0089i	−0.736158	−	0.817586i	0.252528	−	0.967590i	$-0.418738\pi$
$337$	−13.5141	−	15.0089i	−0.736158	−	0.817586i	−0.988685	+	0.150004i	$0.952071\pi$
$338$	3.47795	+	3.86265i	0.189175	+	0.210101i
$339$	−5.85752	−	11.3923i	−0.318137	−	0.618744i
$340$	−15.1365	+	2.35540i	−0.820890	+	0.127740i
$341$	6.53738	−	20.1200i	0.354019	−	1.08956i
$342$	−1.62440	−	0.514625i	−0.0878375	−	0.0278277i
$343$	16.6922			0.901292
$344$	−0.222083	+	2.11298i	−0.0119739	+	0.113924i
$345$	−0.471314	−	2.20683i	−0.0253747	−	0.118812i
$346$	−2.68778	−	25.5725i	−0.144496	−	1.37479i
$347$	−0.262376	−	2.49634i	−0.0140851	−	0.134010i	0.985220	−	0.171296i	$-0.0547955\pi$
$347$	−0.262376	−	2.49634i	−0.0140851	−	0.134010i	−0.999305	+	0.0372857i	$0.988129\pi$
$348$	−6.40573	+	9.94382i	−0.343383	+	0.533045i
$349$	−4.09655	−	7.09543i	−0.219283	−	0.379810i	0.735306	−	0.677735i	$-0.237039\pi$
$349$	−4.09655	−	7.09543i	−0.219283	−	0.379810i	−0.954589	+	0.297926i	$0.903705\pi$
$350$	5.55958	−	12.3073i	0.297172	−	0.657853i
$351$	0.690509	−	16.6979i	0.0368566	−	0.891266i
$352$	5.93263	+	18.2587i	0.316210	+	0.973194i
$353$	−17.6248	−	7.84707i	−0.938074	−	0.417658i	−0.120002	−	0.992774i	$-0.538290\pi$
$353$	−17.6248	−	7.84707i	−0.938074	−	0.417658i	−0.818072	+	0.575116i	$0.804957\pi$
$354$	−6.37649	−	1.68347i	−0.338907	−	0.0894755i
$355$	27.8975	+	7.55609i	1.48064	+	0.401036i
$356$	−17.8925	+	7.96624i	−0.948298	+	0.422210i
$357$	3.17508	−	8.36313i	0.168043	−	0.442624i
$358$	−1.04750	+	9.96626i	−0.0553619	+	0.526733i
$359$	−8.64746	+	26.6141i	−0.456395	+	1.40464i	0.413094	+	0.910688i	$0.364448\pi$
$359$	−8.64746	+	26.6141i	−0.456395	+	1.40464i	−0.869489	+	0.493952i	$0.835552\pi$
$360$	−1.00093	+	1.98722i	−0.0527538	+	0.104736i
$361$	−5.84530	−	17.9900i	−0.307647	−	0.946841i
$362$	17.0579	−	3.62577i	0.896544	−	0.190566i
$363$	1.29654	−	8.38545i	0.0680506	−	0.440122i
$364$	7.94727	+	1.68924i	0.416550	+	0.0885405i
$365$	5.70131	−	8.72745i	0.298420	−	0.456816i
$366$	−6.79185	+	43.9267i	−0.355016	+	2.29609i
$367$	−0.335149	+	3.18873i	−0.0174947	+	0.166450i	−0.999781	−	0.0209366i	$-0.993335\pi$
$367$	−0.335149	+	3.18873i	−0.0174947	+	0.166450i	0.982286	+	0.187387i	$0.0600019\pi$
$368$	−2.51136			−0.130913
$369$	4.10096	+	18.6192i	0.213488	+	0.969277i
$370$	12.1548	−	31.4101i	0.631900	−	1.63293i
$371$	10.4264	+	4.64213i	0.541311	+	0.241007i
$372$	7.12467	+	26.2039i	0.369397	+	1.35861i
$373$	−14.9713	−	3.18225i	−0.775186	−	0.164771i	−0.196700	−	0.980464i	$-0.563023\pi$
$373$	−14.9713	−	3.18225i	−0.775186	−	0.164771i	−0.578485	+	0.815693i	$0.696356\pi$
$374$	−9.04614	+	15.6684i	−0.467765	+	0.810193i
$375$	−18.9594	+	3.94200i	−0.979062	+	0.203564i
$376$	−1.19146	−	2.06367i	−0.0614449	−	0.106426i
$377$	3.70788	+	11.4117i	0.190965	+	0.587731i
$378$	7.77313	+	11.6853i	0.399807	+	0.601029i
$379$	5.89428	−	4.28245i	0.302769	−	0.219975i	−0.426019	−	0.904714i	$-0.640084\pi$
$379$	5.89428	−	4.28245i	0.302769	−	0.219975i	0.728788	+	0.684740i	$0.240084\pi$
$380$	−1.17375	+	0.182649i	−0.0602123	+	0.00936970i
$381$	1.34120	+	23.9092i	0.0687115	+	1.22491i
$382$	−1.84301	+	3.19219i	−0.0942968	+	0.163327i
$383$	−27.1725	+	12.0980i	−1.38845	+	0.618178i	−0.958609	−	0.284726i	$-0.908097\pi$
$383$	−27.1725	+	12.0980i	−1.38845	+	0.618178i	−0.429842	+	0.902904i	$0.641431\pi$
$384$	3.56956	+	2.86891i	0.182159	+	0.146403i
$385$	−3.44199	−	6.80074i	−0.175420	−	0.346598i
$386$	−0.895769	−	2.75689i	−0.0455934	−	0.140322i
$387$	−0.141305	−	19.2156i	−0.00718294	−	0.976786i
$388$	6.24559	−	19.2219i	0.317072	−	0.975846i
$389$	−3.01469	+	3.34816i	−0.152851	+	0.169758i	−0.814707	−	0.579873i	$-0.803102\pi$
$389$	−3.01469	+	3.34816i	−0.152851	+	0.169758i	0.661856	+	0.749631i	$0.269769\pi$
$390$	−9.93764	−	22.2622i	−0.503212	−	1.12729i
$391$	−1.45908	−	1.62047i	−0.0737886	−	0.0819506i
$392$	−1.54403	+	0.687445i	−0.0779851	+	0.0347212i
$393$	−12.6191	+	2.04625i	−0.636548	+	0.103220i
$394$	−3.94902	+	37.5724i	−0.198949	+	1.89287i
$395$	9.12673	+	34.4339i	0.459216	+	1.73256i
$396$	−5.60813	−	12.3508i	−0.281819	−	0.620653i
$397$	−20.0082	+	14.5368i	−1.00418	+	0.729582i	−0.962981	−	0.269569i	$-0.913119\pi$
$397$	−20.0082	+	14.5368i	−1.00418	+	0.729582i	−0.0412026	+	0.999151i	$0.513119\pi$
$398$	−8.08525	+	8.97958i	−0.405277	+	0.450106i
$399$	0.246210	−	0.648517i	0.0123259	−	0.0324665i
$400$	−0.116659	+	21.5508i	−0.00583293	+	1.07754i
$401$	7.15907	−	12.3999i	0.357507	−	0.619220i	−0.630037	−	0.776565i	$-0.716960\pi$
$401$	7.15907	−	12.3999i	0.357507	−	0.619220i	0.987544	+	0.157345i	$0.0502935\pi$
$402$	18.5778	−	28.8389i	0.926575	−	1.43835i
$403$	25.1650	+	11.2042i	1.25356	+	0.558119i
$404$	21.5413	−	15.6507i	1.07172	−	0.778651i
$405$	6.98604	−	18.8731i	0.347139	−	0.937814i
$406$	−8.15206	−	5.92282i	−0.404580	−	0.293945i
$407$	−9.50454	−	16.4624i	−0.471123	−	0.816009i
$408$	0.120420	+	2.14671i	0.00596170	+	0.106278i
$409$	14.6532	+	16.2740i	0.724552	+	0.804697i	0.987080	−	0.160227i	$-0.0512228\pi$
$409$	14.6532	+	16.2740i	0.724552	+	0.804697i	−0.262528	+	0.964924i	$0.584556\pi$
$410$	17.4444	+	21.6617i	0.861519	+	1.06979i
$411$	−7.29058	−	0.355209i	−0.359618	−	0.0175212i
$412$	10.3843	−	2.20725i	0.511598	−	0.108743i
$413$	0.829648	−	2.55339i	0.0408243	−	0.125644i
$414$	3.39958	−	0.382605i	0.167080	−	0.0188040i
$415$	0.379534	−	0.245014i	0.0186306	−	0.0120273i
$416$	−24.4520	+	5.19743i	−1.19886	+	0.254825i
$417$	−0.551688	−	0.278549i	−0.0270163	−	0.0136406i
$418$	−0.701481	+	1.21500i	−0.0343106	+	0.0594276i
$419$	−1.08241	+	0.481918i	−0.0528790	+	0.0235432i	−0.433006	−	0.901391i	$-0.642547\pi$
$419$	−1.08241	+	0.481918i	−0.0528790	+	0.0235432i	0.380127	+	0.924934i	$0.375880\pi$
$420$	8.47779	+	4.88369i	0.413674	+	0.238300i
$421$	−10.8468	−	4.82933i	−0.528643	−	0.235367i	0.125018	−	0.992154i	$-0.460101\pi$
$421$	−10.8468	−	4.82933i	−0.528643	−	0.235367i	−0.653661	+	0.756787i	$0.726768\pi$
$422$	44.8283	−	32.5697i	2.18221	−	1.58547i
$423$	12.7960	+	17.3426i	0.622165	+	0.843227i
$424$	−2.74316			−0.133220
$425$	−13.9736	+	12.4456i	−0.677819	+	0.603699i
$426$	−15.5521	+	40.9642i	−0.753502	+	1.98472i
$427$	−17.6995	−	3.76215i	−0.856540	−	0.182063i
$428$	2.46108	+	23.4156i	0.118961	+	1.13184i
$429$	−13.3041	−	3.51244i	−0.642326	−	0.169582i
$430$	−12.6588	−	25.0113i	−0.610460	−	1.20615i
$431$	−16.7241	−	12.1508i	−0.805573	−	0.585283i	0.106971	−	0.994262i	$-0.465885\pi$
$431$	−16.7241	−	12.1508i	−0.805573	−	0.585283i	−0.912544	+	0.408979i	$0.865885\pi$
$432$	−18.9168	−	11.9901i	−0.910134	−	0.576876i
$433$	−10.6992	−	7.77342i	−0.514170	−	0.373566i	0.300233	−	0.953866i	$-0.402936\pi$
$433$	−10.6992	−	7.77342i	−0.514170	−	0.373566i	−0.814403	+	0.580299i	$0.802936\pi$
$434$	−22.6276	+	4.80964i	−1.08616	+	0.230870i
$435$	0.0140184	+	14.4490i	0.000672129	+	0.692777i
$436$	28.5569	+	6.06995i	1.36763	+	0.290698i
$437$	−0.113144	−	0.125659i	−0.00541240	−	0.00601108i
$438$	12.3185	+	9.90054i	0.588600	+	0.473066i
$439$	−9.35778	+	10.3929i	−0.446623	+	0.496025i	−0.923850	−	0.382755i	$-0.874975\pi$
$439$	−9.35778	+	10.3929i	−0.446623	+	0.496025i	0.477227	+	0.878780i	$0.341642\pi$
$440$	1.42061	+	1.15677i	0.0677248	+	0.0551466i
$441$	13.1820	−	7.74043i	0.627714	−	0.368592i
$442$	−19.0588	−	13.8470i	−0.906536	−	0.658637i
$443$	0.0129892	+	0.0224980i	0.000617136	+	0.00106891i	0.866334	−	0.499465i	$-0.166470\pi$
$443$	0.0129892	+	0.0224980i	0.000617136	+	0.00106891i	−0.865717	+	0.500534i	$0.833137\pi$
$444$	21.7813	+	10.9974i	1.03369	+	0.521914i
$445$	−13.0847	+	20.0297i	−0.620273	+	0.949500i
$446$	0.0215746	+	0.205269i	0.00102159	+	0.00971977i
$447$	−28.4937	+	28.7041i	−1.34771	+	1.35765i
$448$	6.08683	−	6.76011i	0.287576	−	0.319385i
$449$	−32.1952			−1.51939			−0.759693	−	0.650282i	$-0.774651\pi$
$449$	−32.1952			−1.51939			−0.759693	+	0.650282i	$0.774651\pi$
$450$	−3.12535	−	29.1908i	−0.147330	−	1.37607i
$451$	15.6975			0.739168
$452$	9.05885	−	10.0609i	0.426093	−	0.473224i
$453$	−3.67169	−	13.5041i	−0.172511	−	0.634480i
$454$	−2.05102	−	19.5142i	−0.0962592	−	0.915845i
$455$	9.27522	−	3.53165i	0.434829	−	0.165566i
$456$	0.00933798	+	0.166466i	0.000437291	+	0.00779549i
$457$	5.72265	+	9.91192i	0.267694	+	0.463660i	0.968266	−	0.249922i	$-0.0804050\pi$
$457$	5.72265	+	9.91192i	0.267694	+	0.463660i	−0.700572	+	0.713582i	$0.747072\pi$
$458$	−27.7682	−	20.1748i	−1.29752	−	0.942707i
$459$	−3.25377	−	19.1723i	−0.151873	−	0.894888i
$460$	2.00365	−	1.29349i	0.0934205	−	0.0603091i
$461$	1.73257	−	1.92422i	0.0806940	−	0.0896197i	−0.701446	−	0.712723i	$-0.747462\pi$
$461$	1.73257	−	1.92422i	0.0806940	−	0.0896197i	0.782140	+	0.623103i	$0.214128\pi$
$462$	10.7725	−	4.18070i	0.501184	−	0.194504i
$463$	19.0782	+	21.1885i	0.886641	+	0.984714i	0.999961	−	0.00884437i	$-0.00281529\pi$
$463$	19.0782	+	21.1885i	0.886641	+	0.984714i	−0.113320	+	0.993559i	$0.536149\pi$
$464$	15.7289	+	3.34327i	0.730194	+	0.155208i
$465$	24.6726	+	22.1720i	1.14416	+	1.02820i
$466$	16.6002	−	3.52848i	0.768990	−	0.163454i
$467$	−19.1318	−	13.9001i	−0.885316	−	0.643220i	0.0493364	−	0.998782i	$-0.484289\pi$
$467$	−19.1318	−	13.9001i	−0.885316	−	0.643220i	−0.934653	+	0.355562i	$0.884289\pi$
$468$	16.7572	−	5.58132i	0.774604	−	0.257997i
$469$	11.2982	+	8.20863i	0.521703	+	0.379039i
$470$	27.9749	+	14.3494i	1.29038	+	0.661889i
$471$	−20.5101	+	20.6614i	−0.945054	+	0.952029i
$472$	0.0674518	+	0.641761i	0.00310472	+	0.0295395i
$473$	−15.4759	−	3.28950i	−0.711581	−	0.151251i
$474$	−53.3087	+	8.64431i	−2.44855	+	0.397046i
$475$	−1.08358	+	0.965089i	−0.0497180	+	0.0442813i
$476$	9.45415			0.433330
$477$	24.6549	−	2.77479i	1.12887	−	0.127049i
$478$	−16.0411	+	11.6545i	−0.733703	+	0.533066i
$479$	−24.7354	−	11.0129i	−1.13019	−	0.503192i	−0.245510	−	0.969394i	$-0.578955\pi$
$479$	−24.7354	−	11.0129i	−1.13019	−	0.503192i	−0.884678	+	0.466202i	$0.845622\pi$
$480$	−29.9408	−	3.11754i	−1.36660	−	0.142296i
$481$	22.6119	−	10.0674i	1.03101	−	0.459036i
$482$	−7.97326	+	13.8101i	−0.363172	+	0.629032i
$483$	0.0780012	+	1.39051i	0.00354918	+	0.0632704i
$484$	8.77154	−	1.86445i	0.398706	−	0.0847476i
$485$	−6.32537	−	23.8648i	−0.287220	−	1.08364i
$486$	27.4340	+	13.3489i	1.24443	+	0.605517i
$487$	1.88824	−	5.81140i	0.0855643	−	0.263340i	−0.899116	−	0.437711i	$-0.855789\pi$
$487$	1.88824	−	5.81140i	0.0855643	−	0.263340i	0.984680	+	0.174371i	$0.0557893\pi$
$488$	4.25412	−	0.904241i	0.192575	−	0.0409331i
$489$	−5.75427	+	8.93252i	−0.260217	+	0.403943i
$490$	12.1960	−	18.6693i	0.550958	−	0.843394i
$491$	−16.1290	−	17.9131i	−0.727894	−	0.808408i	0.259658	−	0.965701i	$-0.416390\pi$
$491$	−16.1290	−	17.9131i	−0.727894	−	0.808408i	−0.987552	+	0.157293i	$0.949723\pi$
$492$	−16.8583	+	11.0362i	−0.760029	+	0.497551i
$493$	6.98107	+	12.0916i	0.314411	+	0.544577i
$494$	−1.47791	−	1.07377i	−0.0664944	−	0.0483110i
$495$	−13.9382	−	8.95977i	−0.626476	−	0.402712i
$496$	29.8658	−	21.6988i	1.34101	−	0.974304i
$497$	−16.2956	−	7.25528i	−0.730959	−	0.325444i
$498$	0.313162	+	0.609069i	0.0140331	+	0.0272930i
$499$	−4.18052	+	7.24087i	−0.187146	+	0.324146i	−0.944298	−	0.329093i	$-0.893257\pi$
$499$	−4.18052	+	7.24087i	−0.187146	+	0.324146i	0.757152	+	0.653239i	$0.226590\pi$
$500$	−11.0068	−	17.2541i	−0.492238	−	0.771626i
$501$	34.8132	−	5.64516i	1.55534	−	0.252207i
$502$	−30.8791	+	34.2947i	−1.37820	+	1.53065i
$503$	21.1533	−	15.3688i	0.943178	−	0.685259i	−0.00600579	−	0.999982i	$-0.501912\pi$
$503$	21.1533	−	15.3688i	0.943178	−	0.685259i	0.949183	+	0.314723i	$0.101912\pi$
$504$	0.798976	−	1.11688i	0.0355892	−	0.0497496i
$505$	11.7383	−	30.3335i	0.522345	−	1.34983i
$506$	0.294426	−	2.80128i	0.0130888	−	0.124532i
$507$	−1.63264	+	4.30036i	−0.0725080	+	0.190986i
$508$	−23.1202	+	10.2938i	−1.02579	+	0.456713i
$509$	−21.7833	−	24.1929i	−0.965530	−	1.07233i	−0.997344	−	0.0728357i	$-0.976795\pi$
$509$	−21.7833	−	24.1929i	−0.965530	−	1.07233i	0.0318141	−	0.999494i	$-0.489872\pi$
$510$	−16.6968	−	22.9343i	−0.739345	−	1.01555i
$511$	−4.30502	+	4.78121i	−0.190443	+	0.211508i
$512$	−9.46884	+	29.1421i	−0.418468	+	1.28791i
$513$	−0.252313	−	1.48671i	−0.0111399	−	0.0656401i
$514$	−7.87599	−	24.2398i	−0.347395	−	1.06917i
$515$	9.19474	−	9.14510i	0.405169	−	0.402981i
$516$	18.9329	−	7.34764i	0.833474	−	0.323462i
$517$	16.2110	−	7.21760i	0.712958	−	0.317430i
$518$	−10.3931	+	18.0013i	−0.456645	+	0.790931i
$519$	19.0388	−	12.4637i	0.835713	−	0.547097i
$520$	−1.69133	+	1.68220i	−0.0741697	+	0.0737693i
$521$	12.7402	−	9.25627i	0.558157	−	0.405525i	−0.272627	−	0.962120i	$-0.587893\pi$
$521$	12.7402	−	9.25627i	0.558157	−	0.405525i	0.830784	+	0.556595i	$0.187893\pi$
$522$	−21.8012	−	2.12944i	−0.954214	−	0.0932030i
$523$	−4.06035	−	12.4965i	−0.177547	−	0.546432i	0.822194	−	0.569207i	$-0.192750\pi$
$523$	−4.06035	−	12.4965i	−0.177547	−	0.546432i	−0.999741	+	0.0227752i	$0.992750\pi$
$524$	−6.75536	−	11.7006i	−0.295109	−	0.511144i
$525$	11.9361	−	0.604763i	0.520933	−	0.0263940i
$526$	−11.0260	+	19.0976i	−0.480757	+	0.832696i
$527$	31.3531	+	6.66430i	1.36576	+	0.290301i
$528$	−12.9912	+	13.0871i	−0.565368	+	0.569541i
$529$	−20.7014	−	9.21686i	−0.900061	−	0.400733i
$530$	30.4076	−	19.6301i	1.32082	−	0.852679i
$531$	−1.25540	−	5.69978i	−0.0544798	−	0.247349i
$532$	0.733120			0.0317848
$533$	−2.13654	+	20.3278i	−0.0925438	+	0.880496i
$534$	−28.2712	−	22.7220i	−1.22342	−	0.983277i
$535$	18.0392	+	22.4002i	0.779902	+	0.968446i
$536$	−3.28325	−	0.697877i	−0.141815	−	0.0301437i
$537$	−8.26770	+	3.20860i	−0.356778	+	0.138461i
$538$	41.8873	−	8.90342i	1.80589	−	0.383854i
$539$	−3.88934	−	11.9702i	−0.167526	−	0.515592i
$540$	21.2680	−	0.177033i	0.915231	−	0.00761830i
$541$	−10.0048	+	30.7916i	−0.430139	+	1.32383i	0.467847	+	0.883809i	$0.345030\pi$
$541$	−10.0048	+	30.7916i	−0.430139	+	1.32383i	−0.897987	+	0.440023i	$0.854970\pi$
$542$	2.40453	−	22.8776i	0.103283	−	0.982677i
$543$	9.75639	+	11.9580i	0.418687	+	0.513166i
$544$	−26.5735	+	11.8313i	−1.13933	+	0.507262i
$545$	33.3286	−	12.6902i	1.42764	−	0.543591i
$546$	3.94766	+	14.5191i	0.168944	+	0.621361i
$547$	12.8061	+	5.70165i	0.547550	+	0.243785i	0.661818	−	0.749665i	$-0.269785\pi$
$547$	12.8061	+	5.70165i	0.547550	+	0.243785i	−0.114267	+	0.993450i	$0.536452\pi$
$548$	−2.38382	−	7.33666i	−0.101832	−	0.313406i
$549$	−37.3204	+	12.4303i	−1.59280	+	0.530511i
$550$	−24.0251	−	2.65670i	−1.02443	−	0.113282i
$551$	0.541345	+	0.937637i	0.0230621	+	0.0399447i
$552$	−0.153063	−	0.297692i	−0.00651480	−	0.0126706i
$553$	−2.29809	−	21.8649i	−0.0977247	−	0.929789i
$554$	−4.50190	−	42.8327i	−0.191267	−	1.81979i
$555$	29.6395	−	3.14432i	1.25813	−	0.133469i
$556$	0.0682735	−	0.649579i	0.00289544	−	0.0275483i
$557$	−4.26938			−0.180900			−0.0904498	−	0.995901i	$-0.528830\pi$
$557$	−4.26938			−0.180900			−0.0904498	+	0.995901i	$0.528830\pi$
$558$	−37.1230	+	33.9233i	−1.57154	+	1.43609i
$559$	6.36616	−	19.5930i	0.269260	−	0.828697i
$560$	2.11623	−	13.1312i	0.0894270	−	0.554896i
$561$	−15.9923	−	0.779169i	−0.675194	−	0.0328966i
$562$	−1.68620	−	1.87271i	−0.0711279	−	0.0789956i
$563$	−8.16098	−	9.06369i	−0.343944	−	0.381989i	0.546210	−	0.837648i	$-0.316070\pi$
$563$	−8.16098	−	9.06369i	−0.343944	−	0.381989i	−0.890154	+	0.455660i	$0.849403\pi$
$564$	−12.3353	+	19.1485i	−0.519411	+	0.806297i
$565$	2.63125	−	16.3269i	0.110697	−	0.686878i
$566$	−4.65083	+	14.3138i	−0.195489	+	0.601654i
$567$	−6.05127	+	10.8464i	−0.254129	+	0.455507i
$568$	4.28735			0.179893
$569$	1.73671	−	16.5237i	0.0728068	−	0.692711i	−0.895858	−	0.444340i	$-0.853438\pi$
$569$	1.73671	−	16.5237i	0.0728068	−	0.692711i	0.968665	−	0.248371i	$-0.0798951\pi$
$570$	−1.29475	−	1.77843i	−0.0542309	−	0.0744904i
$571$	1.74493	+	16.6019i	0.0730232	+	0.694769i	0.968390	+	0.249440i	$0.0802466\pi$
$571$	1.74493	+	16.6019i	0.0730232	+	0.694769i	−0.895367	+	0.445329i	$0.853087\pi$
$572$	−1.52008	−	14.4626i	−0.0635576	−	0.604710i
$573$	−3.25818	−	0.158744i	−0.136112	−	0.00663162i
$574$	−8.58249	−	14.8653i	−0.358226	−	0.620466i
$575$	1.19931	−	2.65493i	0.0500149	−	0.110718i
$576$	3.96908	−	19.3724i	0.165378	−	0.807185i
$577$	9.92545	+	30.5474i	0.413202	+	1.27171i	0.913849	+	0.406054i	$0.133095\pi$
$577$	9.92545	+	30.5474i	0.413202	+	1.27171i	−0.500647	+	0.865651i	$0.666905\pi$
$578$	5.35293	+	2.38328i	0.222652	+	0.0991312i
$579$	1.80729	−	1.82063i	0.0751083	−	0.0756627i
$580$	−14.2710	+	5.43385i	−0.592571	+	0.225628i
$581$	−0.254701	+	0.113400i	−0.0105668	+	0.00470464i
$582$	36.9461	−	5.99103i	1.53147	−	0.248336i
$583$	2.13528	−	20.3159i	0.0884344	−	0.841398i
$584$	0.477853	−	1.47068i	0.0197737	−	0.0608572i
$585$	13.4997	−	16.8301i	0.558144	−	0.695837i
$586$	−6.80594	−	20.9465i	−0.281151	−	0.865293i
$587$	−10.5912	+	2.25124i	−0.437147	+	0.0929185i	−0.421228	−	0.906955i	$-0.638401\pi$
$587$	−10.5912	+	2.25124i	−0.437147	+	0.0929185i	−0.0159191	+	0.999873i	$0.505067\pi$
$588$	12.5926	+	10.1209i	0.519310	+	0.417377i
$589$	2.43127	+	0.516781i	0.100179	+	0.0212936i
$590$	−5.34015	−	6.63116i	−0.219851	−	0.273000i
$591$	−31.1689	+	12.0963i	−1.28212	+	0.497575i
$592$	3.46730	−	32.9891i	0.142505	−	1.35584i
$593$	8.57810			0.352260			0.176130	−	0.984367i	$-0.443642\pi$
$593$	8.57810			0.352260			0.176130	+	0.984367i	$0.443642\pi$
$594$	15.5921	−	19.6949i	0.639752	−	0.808093i
$595$	9.70252	−	6.26362i	0.397765	−	0.256783i
$596$	−39.0492	−	17.3858i	−1.59952	−	0.712151i
$597$	−10.3391	−	2.72965i	−0.423151	−	0.111717i
$598$	3.58750	+	0.762546i	0.146704	+	0.0311828i
$599$	6.67217	−	11.5565i	0.272617	−	0.472187i	−0.696914	−	0.717155i	$-0.745444\pi$
$599$	6.67217	−	11.5565i	0.272617	−	0.472187i	0.969531	+	0.244968i	$0.0787774\pi$
$600$	−2.56171	+	1.29966i	−0.104582	+	0.0530584i
$601$	−3.48996	−	6.04478i	−0.142358	−	0.246572i	0.786026	−	0.618194i	$-0.212135\pi$
$601$	−3.48996	−	6.04478i	−0.142358	−	0.246572i	−0.928384	+	0.371622i	$0.878802\pi$
$602$	5.34619	+	16.4539i	0.217895	+	0.670610i
$603$	30.2151	+	2.95126i	1.23045	+	0.120185i
$604$	11.9654	−	8.69336i	0.486865	−	0.353728i
$605$	7.76673	−	7.72480i	0.315762	−	0.314058i
$606$	44.0170	+	22.2243i	1.78807	+	0.902800i
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	−0.822510	−	0.568751i	$-0.807427\pi$
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	0.903807	+	0.427939i	$0.140760\pi$
$608$	−2.06064	+	0.917454i	−0.0835698	+	0.0372077i
$609$	1.36261	−	8.81274i	0.0552155	−	0.357110i
$610$	−40.6856	+	40.4660i	−1.64731	+	1.63842i
$611$	7.14014	+	21.9751i	0.288859	+	0.889017i
$612$	17.7226	−	10.4066i	0.716393	−	0.420664i
$613$	−11.1550	+	34.3317i	−0.450548	+	1.38664i	0.425735	+	0.904848i	$0.360015\pi$
$613$	−11.1550	+	34.3317i	−0.450548	+	1.38664i	−0.876283	+	0.481796i	$0.839985\pi$
$614$	−29.2500	+	32.4855i	−1.18044	+	1.31101i
$615$	−9.98936	+	22.4952i	−0.402810	+	0.907093i
$616$	−0.756554	−	0.840238i	−0.0304824	−	0.0338542i
$617$	41.2361	−	18.3595i	1.66010	−	0.739126i	0.660176	−	0.751111i	$-0.270482\pi$
$617$	41.2361	−	18.3595i	1.66010	−	0.739126i	0.999928	+	0.0119846i	$0.00381490\pi$
$618$	12.4286	+	15.2332i	0.499953	+	0.612770i
$619$	−1.22908	+	11.6939i	−0.0494010	+	0.470019i	0.941656	+	0.336578i	$0.109269\pi$
$619$	−1.22908	+	11.6939i	−0.0494010	+	0.470019i	−0.991057	+	0.133441i	$0.957397\pi$
$620$	−12.6519	+	32.6946i	−0.508113	+	1.31305i
$621$	1.67682	+	2.52077i	0.0672886	+	0.101155i
$622$	−26.4867	+	19.2437i	−1.06202	+	0.771602i
$623$	9.88014	−	10.9730i	0.395839	−	0.439624i
$624$	−15.1791	−	18.6044i	−0.607652	−	0.744772i
$625$	−22.7272	−	10.4151i	−0.909089	−	0.416603i
$626$	14.3789	−	24.9050i	0.574697	−	0.995405i
$627$	−1.24012	−	0.0604205i	−0.0495255	−	0.00241296i
$628$	−28.1080	−	12.5145i	−1.12163	−	0.499382i
$629$	23.3009	−	16.9291i	0.929068	−	0.675008i
$630$	−0.864161	+	18.0979i	−0.0344290	+	0.721039i
$631$	−28.9418	−	21.0275i	−1.15216	−	0.837090i	−0.163390	−	0.986562i	$-0.552243\pi$
$631$	−28.9418	−	21.0275i	−1.15216	−	0.837090i	−0.988766	+	0.149472i	$0.952243\pi$
$632$	2.64211	+	4.57626i	0.105097	+	0.182034i
$633$	43.7741	+	22.1017i	1.73986	+	0.878463i
$634$	−3.86956	−	4.29759i	−0.153680	−	0.170679i
$635$	−16.9077	+	25.8820i	−0.670962	+	1.02709i
$636$	11.9900	+	23.3193i	0.475434	+	0.924671i
$637$	16.0304	−	3.40736i	0.635146	−	0.135004i
$638$	−5.57326	+	17.1527i	−0.220648	+	0.679083i
$639$	−38.5337	+	4.33677i	−1.52437	+	0.171560i
$640$	1.51473	+	5.71486i	0.0598748	+	0.225900i
$641$	38.8290	−	8.25337i	1.53365	−	0.325988i	0.637753	−	0.770241i	$-0.279864\pi$
$641$	38.8290	−	8.25337i	1.53365	−	0.325988i	0.895902	+	0.444252i	$0.146531\pi$
$642$	−36.4801	+	23.8816i	−1.43975	+	0.942531i
$643$	−16.4497	+	28.4917i	−0.648712	+	1.12360i	0.334718	+	0.942318i	$0.391359\pi$
$643$	−16.4497	+	28.4917i	−0.648712	+	1.12360i	−0.983431	+	0.181284i	$0.941975\pi$
$644$	−1.34463	+	0.598666i	−0.0529857	+	0.0235907i
$645$	14.5623	−	20.0842i	0.573389	−	0.790814i
$646$	−1.94191	−	0.864596i	−0.0764036	−	0.0340171i
$647$	−25.9334	+	18.8417i	−1.01955	+	0.740745i	−0.966190	−	0.257831i	$-0.916992\pi$
$647$	−25.9334	+	18.8417i	−1.01955	+	0.740745i	−0.0533576	+	0.998575i	$0.516992\pi$
$648$	0.268346	−	2.97315i	0.0105416	−	0.116796i
$649$	−4.80539			−0.188628
$650$	6.71032	−	30.7501i	0.263201	−	1.20612i
$651$	−12.9420	−	15.8624i	−0.507237	−	0.621697i
$652$	−10.9842	−	2.33477i	−0.430175	−	0.0914366i
$653$	2.94310	+	28.0017i	0.115172	+	1.09579i	0.887576	+	0.460661i	$0.152387\pi$
$653$	2.94310	+	28.0017i	0.115172	+	1.09579i	−0.772404	+	0.635132i	$0.780946\pi$
$654$	14.1851	+	52.1715i	0.554681	+	2.04007i
$655$	−14.6848	−	7.53241i	−0.573782	−	0.294315i
$656$	22.1607	+	16.1007i	0.865232	+	0.628628i
$657$	−2.80720	+	13.7015i	−0.109519	+	0.534547i
$658$	−15.6982	−	11.4054i	−0.611978	−	0.444628i
$659$	26.4346	−	5.61884i	1.02974	−	0.218879i	0.338094	−	0.941112i	$-0.390218\pi$
$659$	26.4346	−	5.61884i	1.02974	−	0.218879i	0.691649	+	0.722233i	$0.256884\pi$
$660$	3.62425	−	17.1325i	0.141074	−	0.666881i
$661$	9.57615	+	2.03547i	0.372469	+	0.0791707i	0.390343	−	0.920669i	$-0.372356\pi$
$661$	9.57615	+	2.03547i	0.372469	+	0.0791707i	−0.0178739	+	0.999840i	$0.505690\pi$
$662$	15.1600	+	16.8368i	0.589208	+	0.654382i
$663$	3.18565	−	20.6034i	0.123721	−	0.800171i
$664$	0.0448394	−	0.0497992i	0.00174011	−	0.00193258i
$665$	0.752380	−	0.485711i	0.0291760	−	0.0188351i
$666$	0.332275	+	45.1850i	0.0128754	+	1.75088i
$667$	−1.75856	−	1.27767i	−0.0680919	−	0.0494716i
$668$	18.6365	+	32.2794i	0.721068	+	1.24893i
$669$	−0.152824	+	0.100046i	−0.00590851	+	0.00386799i
$670$	41.3885	−	15.7591i	1.59898	−	0.608829i
$671$	3.38539	+	32.2099i	0.130692	+	1.24345i
$672$	17.9629	+	4.74243i	0.692934	+	0.182943i
$673$	−2.93780	+	3.26275i	−0.113244	+	0.125770i	−0.797101	−	0.603846i	$-0.793634\pi$
$673$	−2.93780	+	3.26275i	−0.113244	+	0.125770i	0.683857	+	0.729616i	$0.260301\pi$
$674$	39.5279			1.52256
$675$	21.7095	−	14.2723i	0.835598	−	0.549341i
$676$	−4.86137			−0.186976
$677$	−4.50954	+	5.00836i	−0.173316	+	0.192487i	−0.823544	−	0.567252i	$-0.808007\pi$
$677$	−4.50954	+	5.00836i	−0.173316	+	0.192487i	0.650228	+	0.759739i	$0.274673\pi$
$678$	24.2407	+	6.39984i	0.930958	+	0.245784i
$679$	1.59271	+	15.1537i	0.0611228	+	0.581544i
$680$	−1.51808	+	2.32384i	−0.0582156	+	0.0891151i
$681$	14.5284	−	9.51097i	0.556729	−	0.364461i
$682$	20.7024	+	35.8576i	0.792736	+	1.37306i
$683$	14.2153	+	10.3280i	0.543933	+	0.395191i	0.825544	−	0.564338i	$-0.190869\pi$
$683$	14.2153	+	10.3280i	0.543933	+	0.395191i	−0.281611	+	0.959529i	$0.590869\pi$
$684$	1.37429	−	0.806981i	0.0525474	−	0.0308557i
$685$	−7.30717	−	5.95005i	−0.279193	−	0.227340i
$686$	−21.8601	+	24.2781i	−0.834623	+	0.926943i
$687$	4.64142	−	30.0187i	0.177081	−	1.14528i
$688$	−18.4738	−	20.5172i	−0.704307	−	0.782213i
$689$	26.0178	+	5.53025i	0.991199	+	0.210686i
$690$	3.82698	+	2.20456i	0.145691	+	0.0839262i
$691$	40.1370	−	8.53139i	1.52688	−	0.324549i	0.633465	−	0.773772i	$-0.281632\pi$
$691$	40.1370	−	8.53139i	1.52688	−	0.324549i	0.893420	+	0.449222i	$0.148299\pi$
$692$	19.4564	+	14.1359i	0.739622	+	0.537367i
$693$	7.64966	+	6.78660i	0.290587	+	0.257801i
$694$	3.97444	+	2.88760i	0.150868	+	0.109612i
$695$	−0.360296	−	0.711877i	−0.0136668	−	0.0270030i
$696$	0.562343	+	2.06824i	0.0213156	+	0.0783966i
$697$	2.48611	+	23.6537i	0.0941681	+	0.895949i
$698$	15.6849	+	3.33393i	0.593682	+	0.126191i
$699$	9.49461	+	11.6371i	0.359119	+	0.440156i
$700$	5.07490	+	11.5665i	0.191813	+	0.437173i
$701$	−30.2765			−1.14353			−0.571763	−	0.820419i	$-0.693740\pi$
$701$	−30.2765			−1.14353			−0.571763	+	0.820419i	$0.693740\pi$
$702$	23.3821	+	22.8719i	0.882501	+	0.863245i
$703$	1.80686	−	1.31276i	0.0681472	−	0.0495118i
$704$	−14.8740	−	6.62233i	−0.560585	−	0.249588i
$705$	0.0269947	+	27.8240i	0.00101668	+	1.04791i
$706$	34.4948	−	15.3581i	1.29823	−	0.578009i
$707$	−10.0368	+	17.3843i	−0.377475	+	0.653805i
$708$	5.16071	−	3.37845i	0.193952	−	0.126970i
$709$	10.8221	−	2.30030i	0.406431	−	0.0863896i	−0.000159608	−	1.00000i	$-0.500051\pi$
$709$	10.8221	−	2.30030i	0.406431	−	0.0863896i	0.406591	+	0.913610i	$0.366717\pi$
$710$	−47.5247	+	30.6804i	−1.78357	+	1.15141i
$711$	−28.3757	−	38.4579i	−1.06417	−	1.44228i
$712$	−1.09669	+	3.37525i	−0.0411001	+	0.126493i
$713$	−4.88122	+	1.03754i	−0.182803	+	0.0388560i
$714$	8.00577	+	15.5704i	0.299609	+	0.582708i
$715$	−11.1418	−	13.8354i	−0.416681	−	0.517415i
$716$	−6.27156	−	6.96527i	−0.234379	−	0.260304i
$717$	−15.6639	−	7.90872i	−0.584977	−	0.295357i
$718$	−27.3845	−	47.4314i	−1.02198	−	1.77012i
$719$	1.95143	+	1.41780i	0.0727761	+	0.0528749i	0.623578	−	0.781761i	$-0.285678\pi$
$719$	1.95143	+	1.41780i	0.0727761	+	0.0528749i	−0.550802	+	0.834636i	$0.685678\pi$
$720$	−10.4871	−	26.9450i	−0.390833	−	1.00418i
$721$	−6.47504	+	4.70439i	−0.241143	+	0.175201i
$722$	33.8208	+	15.0580i	1.25868	+	0.560400i
$723$	−14.0956	−	0.686758i	−0.524220	−	0.0255408i
$724$	−8.15526	+	14.1253i	−0.303088	+	0.524964i
$725$	−11.0458	+	15.0315i	−0.410232	+	0.558256i
$726$	10.4984	+	12.8674i	0.389631	+	0.477553i
$727$	14.5405	−	16.1489i	0.539279	−	0.598930i	−0.410497	−	0.911862i	$-0.634645\pi$
$727$	14.5405	−	16.1489i	0.539279	−	0.598930i	0.949775	+	0.312932i	$0.101311\pi$
$728$	1.19105	−	0.865351i	0.0441434	−	0.0320721i
$729$	0.595587	+	26.9934i	0.0220588	+	0.999757i
$730$	5.22729	+	19.7219i	0.193470	+	0.729939i
$731$	2.50576	−	23.8407i	0.0926788	−	0.881780i
$732$	−26.2810	−	32.2115i	−0.971374	−	1.19057i
$733$	27.8246	−	12.3883i	1.02772	−	0.457572i	0.177571	−	0.984108i	$-0.443176\pi$
$733$	27.8246	−	12.3883i	1.02772	−	0.457572i	0.850153	+	0.526536i	$0.176509\pi$
$734$	−4.19898	−	4.66344i	−0.154987	−	0.172131i
$735$	19.6288	+	2.04381i	0.724018	+	0.0753872i
$736$	3.03025	−	3.36543i	0.111696	−	0.124051i
$737$	7.72417	−	23.7725i	0.284523	−	0.875673i
$738$	−32.4516	−	18.4191i	−1.19456	−	0.678016i
$739$	13.7160	+	42.2135i	0.504551	+	1.55285i	0.801524	+	0.597962i	$0.204023\pi$
$739$	13.7160	+	42.2135i	0.504551	+	1.55285i	−0.296973	+	0.954886i	$0.595977\pi$
$740$	14.2249	+	28.1057i	0.522917	+	1.03319i
$741$	0.247031	−	1.59769i	0.00907490	−	0.0586926i
$742$	−20.4062	+	9.08545i	−0.749137	+	0.333537i
$743$	12.5838	−	21.7958i	0.461655	−	0.799609i	−0.537389	−	0.843335i	$-0.680589\pi$
$743$	12.5838	−	21.7958i	0.461655	−	0.799609i	0.999044	+	0.0437252i	$0.0139226\pi$
$744$	4.39242	+	2.21774i	0.161034	+	0.0813064i
$745$	−51.5936	+	8.02854i	−1.89024	+	0.294143i
$746$	24.2350	−	17.6077i	0.887305	−	0.644665i
$747$	−0.352633	+	0.492941i	−0.0129022	+	0.0180358i
$748$	−5.22904	−	16.0933i	−0.191193	−	0.588431i
$749$	−8.87511	−	15.3721i	−0.324289	−	0.561686i
$750$	19.0959	−	32.7383i	0.697283	−	1.19543i
$751$	−25.2077	+	43.6611i	−0.919844	+	1.59322i	−0.120193	+	0.992751i	$0.538351\pi$
$751$	−25.2077	+	43.6611i	−0.919844	+	1.59322i	−0.799651	+	0.600465i	$0.794982\pi$
$752$	30.2886	+	6.43804i	1.10451	+	0.234771i
$753$	−39.4870	−	10.4251i	−1.43899	−	0.379910i
$754$	−21.4537	−	9.55180i	−0.781297	−	0.347856i
$755$	6.52015	−	16.8491i	0.237293	−	0.613202i
$756$	−12.9866	−	1.91029i	−0.472320	−	0.0694767i
$757$	8.34393			0.303265			0.151633	−	0.988437i	$-0.451547\pi$
$757$	8.34393			0.303265			0.151633	+	0.988437i	$0.451547\pi$
$758$	−1.49052	+	14.1813i	−0.0541380	+	0.515089i
$759$	2.32386	−	0.901862i	0.0843506	−	0.0327355i
$760$	−0.117719	+	0.180201i	−0.00427011	+	0.00653659i
$761$	−7.20785	−	1.53207i	−0.261284	−	0.0555377i	0.0754068	−	0.997153i	$-0.475974\pi$
$761$	−7.20785	−	1.53207i	−0.261284	−	0.0555377i	−0.336691	+	0.941615i	$0.609308\pi$
$762$	−36.5315	−	29.3609i	−1.32340	−	1.06363i
$763$	−21.5290	+	4.57612i	−0.779400	+	0.165667i
$764$	−1.06534	−	3.27877i	−0.0385426	−	0.118622i
$765$	11.2935	−	22.4217i	0.408317	−	0.810659i
$766$	17.9892	−	55.3650i	0.649975	−	2.00042i
$767$	0.654046	−	6.22283i	0.0236162	−	0.224693i
$768$	−31.3871	+	5.08959i	−1.13258	+	0.183655i
$769$	−12.7161	+	5.66158i	−0.458555	+	0.204162i	−0.622996	−	0.782225i	$-0.714085\pi$
$769$	−12.7161	+	5.66158i	−0.458555	+	0.204162i	0.164441	+	0.986387i	$0.447418\pi$
$770$	14.3991	+	3.90002i	0.518906	+	0.140547i
$771$	15.8905	−	16.0078i	0.572281	−	0.576505i
$772$	2.47680	+	1.10274i	0.0891418	+	0.0396885i
$773$	7.27997	+	22.4054i	0.261842	+	0.805867i	0.992404	+	0.123021i	$0.0392582\pi$
$773$	7.27997	+	22.4054i	0.261842	+	0.805867i	−0.730562	+	0.682847i	$0.760742\pi$
$774$	28.1335	+	24.9593i	1.01124	+	0.897145i
$775$	8.67672	+	41.9357i	0.311677	+	1.50637i
$776$	−1.83114	−	3.17162i	−0.0657340	−	0.113855i
$777$	−18.3734	−	0.895182i	−0.659142	−	0.0321145i
$778$	−0.921714	−	8.76952i	−0.0330450	−	0.314403i
$779$	0.192785	+	1.83422i	0.00690723	+	0.0657179i
$780$	21.6927	+	7.02514i	0.776724	+	0.251540i
$781$	−3.33728	+	31.7521i	−0.119417	+	1.13618i
$782$	4.26772			0.152613
$783$	−7.14630	−	18.0201i	−0.255388	−	0.643986i
$784$	6.78690	−	20.8879i	0.242389	−	0.745998i
$785$	−37.1376	+	5.77902i	−1.32550	+	0.206262i
$786$	13.5498	−	21.0337i	0.483305	−	0.750249i
$787$	−19.0981	−	21.2106i	−0.680776	−	0.756078i	0.299418	−	0.954122i	$-0.403208\pi$
$787$	−19.0981	−	21.2106i	−0.680776	−	0.756078i	−0.980193	+	0.198044i	$0.936541\pi$
$788$	−23.6435	−	26.2588i	−0.842266	−	0.935431i
$789$	−19.4924	−	0.949701i	−0.693948	−	0.0338103i
$790$	−62.0353	−	31.8203i	−2.20712	−	1.13212i
$791$	−3.15397	+	9.70691i	−0.112142	+	0.345138i
$792$	−2.34311	−	0.742320i	−0.0832589	−	0.0263772i
$793$	−42.1715			−1.49756
$794$	5.05958	−	48.1387i	0.179558	−	1.70838i
$795$	27.7546	+	15.9883i	0.984355	+	0.567045i
$796$	−1.18131	−	11.2394i	−0.0418704	−	0.398370i
$797$	0.874613	+	8.32139i	0.0309804	+	0.294759i	0.999031	+	0.0440050i	$0.0140117\pi$
$797$	0.874613	+	8.32139i	0.0309804	+	0.294759i	−0.968051	+	0.250754i	$0.919322\pi$
$798$	0.620806	+	1.20740i	0.0219763	+	0.0427417i
$799$	13.4432	+	23.2843i	0.475587	+	0.823741i
$800$	−28.7392	−	26.1600i	−1.01608	−	0.924894i
$801$	6.44261	−	31.4454i	0.227638	−	1.11107i
$802$	8.65961	+	26.6515i	0.305781	+	0.941098i
$803$	10.5199	+	4.68376i	0.371239	+	0.165286i
$804$	8.41807	+	30.9609i	0.296882	+	1.09191i
$805$	−0.983318	+	1.50524i	−0.0346574	+	0.0530528i
$806$	−49.2522	+	21.9285i	−1.73483	+	0.772398i
$807$	23.9577	+	29.3639i	0.843352	+	1.03366i
$808$	0.504324	−	4.79833i	0.0177421	−	0.168805i
$809$	12.4306	−	38.2574i	0.437036	−	1.34506i	−0.453951	−	0.891027i	$-0.649986\pi$
$809$	12.4306	−	38.2574i	0.437036	−	1.34506i	0.890986	−	0.454030i	$-0.150014\pi$
$810$	18.3013	+	34.8773i	0.643043	+	1.22546i
$811$	3.05198	+	9.39304i	0.107170	+	0.329834i	0.990234	−	0.139418i	$-0.0445233\pi$
$811$	3.05198	+	9.39304i	0.107170	+	0.329834i	−0.883064	+	0.469253i	$0.844523\pi$
$812$	9.21851	−	1.95945i	0.323506	−	0.0687634i
$813$	18.9785	−	7.36536i	0.665607	−	0.258314i
$814$	36.3911	+	7.73516i	1.27551	+	0.271117i
$815$	−12.8196	+	4.88123i	−0.449052	+	0.170982i
$816$	−21.7776	−	17.5030i	−0.762370	−	0.612728i
$817$	0.194308	−	1.84872i	0.00679799	−	0.0646785i
$818$	−42.8598			−1.49856
$819$	−9.82960	+	8.98237i	−0.343474	+	0.313869i
$820$	−25.9734	−	1.43171i	−0.907029	−	0.0499974i
$821$	−15.3567	−	6.83725i	−0.535953	−	0.238622i	0.120867	−	0.992669i	$-0.461432\pi$
$821$	−15.3567	−	6.83725i	−0.535953	−	0.238622i	−0.656820	+	0.754047i	$0.728099\pi$
$822$	10.0644	−	10.1387i	0.351037	−	0.353628i
$823$	−30.3417	−	6.44934i	−1.05765	−	0.224810i	−0.353917	−	0.935277i	$-0.615150\pi$
$823$	−30.3417	−	6.44934i	−1.05765	−	0.224810i	−0.703730	+	0.710467i	$0.748484\pi$
$824$	0.961840	−	1.66596i	0.0335073	−	0.0580363i
$825$	−7.63124	−	19.9837i	−0.265686	−	0.695744i
$826$	2.62730	+	4.55063i	0.0914156	+	0.158337i
$827$	−12.1795	−	37.4846i	−0.423522	−	1.30347i	−0.904402	−	0.426681i	$-0.859683\pi$
$827$	−12.1795	−	37.4846i	−0.423522	−	1.30347i	0.480880	−	0.876787i	$-0.340317\pi$
$828$	−1.86163	+	2.60234i	−0.0646961	+	0.0904377i
$829$	−19.1615	+	13.9216i	−0.665505	+	0.483518i	−0.868518	−	0.495658i	$-0.834927\pi$
$829$	−19.1615	+	13.9216i	−0.665505	+	0.483518i	0.203012	+	0.979176i	$0.434927\pi$
$830$	−0.140675	+	0.872890i	−0.00488290	+	0.0302985i
$831$	31.8892	−	20.8762i	1.10622	−	0.724186i
$832$	10.6002	−	18.3600i	0.367494	−	0.636519i
$833$	17.4212	−	7.75642i	0.603609	−	0.268744i
$834$	1.12763	−	0.437621i	0.0390467	−	0.0151536i
$835$	40.5120	+	20.7802i	1.40198	+	0.719129i
$836$	−0.405485	−	1.24795i	−0.0140240	−	0.0431614i
$837$	−41.7214	−	15.4895i	−1.44210	−	0.535396i
$838$	0.716591	−	2.20544i	0.0247542	−	0.0761856i
$839$	−1.39459	+	1.54884i	−0.0481465	+	0.0534721i	−0.766737	−	0.641961i	$-0.778121\pi$
$839$	−1.39459	+	1.54884i	−0.0481465	+	0.0534721i	0.718591	+	0.695433i	$0.244788\pi$
$840$	1.68554	−	0.549473i	0.0581566	−	0.0189586i
$841$	−10.0916	−	11.2079i	−0.347988	−	0.386480i
$842$	21.2291	−	9.45183i	0.731605	−	0.325731i
$843$	0.791544	−	2.08492i	0.0272622	−	0.0718086i
$844$	−5.41721	+	51.5414i	−0.186468	+	1.77413i
$845$	−4.98908	+	3.22078i	−0.171630	+	0.110798i
$846$	−41.9820	−	4.10059i	−1.44337	−	0.140981i
$847$	−5.46942	+	3.97377i	−0.187932	+	0.136540i
$848$	23.8521	−	26.4905i	0.819086	−	0.909687i
$849$	−13.1475	+	2.13194i	−0.451222	+	0.0731682i
$850$	0.198246	−	36.6228i	0.00679979	−	1.25615i
$851$	−2.24199	+	3.88324i	−0.0768545	+	0.133116i
$852$	−18.7394	−	36.4462i	−0.642001	−	1.24863i
$853$	−39.5591	−	17.6129i	−1.35448	−	0.603053i	−0.404262	−	0.914643i	$-0.632472\pi$
$853$	−39.5591	−	17.6129i	−1.35448	−	0.603053i	−0.950217	+	0.311590i	$0.899138\pi$
$854$	28.6513	−	20.8164i	0.980427	−	0.712322i
$855$	0.875752	−	1.73869i	0.0299501	−	0.0594618i
$856$	3.45151	+	2.50767i	0.117970	+	0.0857103i
$857$	−7.87916	−	13.6471i	−0.269147	−	0.466176i	0.699495	−	0.714638i	$-0.253408\pi$
$857$	−7.87916	−	13.6471i	−0.269147	−	0.466176i	−0.968642	+	0.248462i	$0.920075\pi$
$858$	22.5318	−	14.7504i	0.769222	−	0.503569i
$859$	0.341216	+	0.378959i	0.0116422	+	0.0129299i	0.748938	−	0.662640i	$-0.230564\pi$
$859$	0.341216	+	0.378959i	0.0116422	+	0.0129299i	−0.737296	+	0.675570i	$0.763898\pi$
$860$	25.3065	+	6.85433i	0.862946	+	0.233731i
$861$	8.22650	−	12.7702i	0.280358	−	0.435209i
$862$	39.5749	−	8.41190i	1.34793	−	0.286510i
$863$	−17.2401	+	53.0596i	−0.586860	+	1.80617i	0.00480758	+	0.999988i	$0.498470\pi$
$863$	−17.2401	+	53.0596i	−0.586860	+	1.80617i	−0.591668	+	0.806182i	$0.701530\pi$
$864$	38.8932	−	10.8826i	1.32317	−	0.370233i
$865$	29.3330	+	1.61690i	0.997351	+	0.0549761i
$866$	25.3178	−	5.38147i	0.860335	−	0.182870i
$867$	0.290427	+	5.17738i	0.00986342	+	0.175833i
$868$	10.8181	−	18.7374i	0.367189	−	0.635990i
$869$	−35.9484	+	16.0053i	−1.21947	+	0.542942i
$870$	−21.0339	−	18.9021i	−0.713116	−	0.640841i
$871$	29.7334	+	13.2382i	1.00748	+	0.448558i
$872$	4.27981	−	3.10946i	0.144933	−	0.105300i
$873$	19.6660	+	26.6536i	0.665595	+	0.902088i
$874$	0.330940			0.0111942
$875$	12.8713	+	8.50813i	0.435131	+	0.287627i
$876$	−14.5907	+	2.36597i	−0.492975	+	0.0799386i
$877$	−0.609512	−	0.129556i	−0.0205818	−	0.00437479i	0.197609	−	0.980281i	$-0.436682\pi$
$877$	−0.609512	−	0.129556i	−0.0205818	−	0.00437479i	−0.218191	+	0.975906i	$0.570016\pi$
$878$	−2.86105	−	27.2211i	−0.0965559	−	0.918668i
$879$	13.7315	−	13.8329i	0.463153	−	0.466572i
$880$	−23.5231	+	3.66046i	−0.792964	+	0.123394i
$881$	0.224011	+	0.162753i	0.00754711	+	0.00548330i	0.591552	−	0.806267i	$-0.298515\pi$
$881$	0.224011	+	0.162753i	0.00754711	+	0.00548330i	−0.584005	+	0.811750i	$0.698515\pi$
$882$	−6.00503	+	29.3096i	−0.202200	+	0.986906i
$883$	−11.9127	−	8.65510i	−0.400895	−	0.291267i	0.369010	−	0.929425i	$-0.379697\pi$
$883$	−11.9127	−	8.65510i	−0.400895	−	0.291267i	−0.769906	+	0.638158i	$0.779697\pi$
$884$	21.5521	−	4.58104i	0.724875	−	0.154077i
$885$	3.05798	−	6.88631i	0.102793	−	0.231481i
$886$	−0.0497331	−	0.0105711i	−0.00167082	−	0.000355143i
$887$	9.05574	+	10.0574i	0.304062	+	0.337695i	0.875740	−	0.482783i	$-0.160374\pi$
$887$	9.05574	+	10.0574i	0.304062	+	0.337695i	−0.571678	+	0.820478i	$0.693707\pi$
$888$	4.12181	−	1.59963i	0.138319	−	0.0536800i
$889$	12.7669	−	14.1791i	0.428188	−	0.475551i
$890$	−11.9968	−	45.2622i	−0.402132	−	1.51719i
$891$	21.8103	+	4.30168i	0.730671	+	0.144112i
$892$	−0.156176	−	0.113468i	−0.00522915	−	0.00379920i
$893$	1.04245	+	1.80558i	0.0348843	+	0.0604214i
$894$	−4.43344	−	79.0340i	−0.148277	−	2.64329i
$895$	−11.0510	−	2.99318i	−0.369394	−	0.100051i
$896$	−0.381405	−	3.62883i	−0.0127418	−	0.121231i
$897$	0.851590	+	3.13207i	0.0284338	+	0.104577i
$898$	42.1630	−	46.8268i	1.40700	−	1.56263i
$899$	31.9528			1.06569
$900$	22.2452	+	16.0962i	0.741505	+	0.536540i
$901$	30.9510			1.03113
$902$	−20.5576	+	22.8315i	−0.684492	+	0.760205i
$903$	−10.7864	+	10.8660i	−0.358949	+	0.361598i
$904$	−0.256423	−	2.43970i	−0.00852851	−	0.0811433i
$905$	0.988888	+	19.8995i	0.0328717	+	0.661481i
$906$	24.4497	+	12.3447i	0.812288	+	0.410126i
$907$	3.57179	+	6.18652i	0.118599	+	0.205420i	0.919213	−	0.393761i	$-0.128826\pi$
$907$	3.57179	+	6.18652i	0.118599	+	0.205420i	−0.800614	+	0.599181i	$0.795493\pi$
$908$	14.8470	+	10.7870i	0.492716	+	0.357979i
$909$	0.320887	+	43.6364i	0.0106432	+	1.44733i
$910$	−7.01021	+	18.1155i	−0.232386	+	0.600524i
$911$	−8.43433	+	9.36728i	−0.279442	+	0.310352i	−0.866484	−	0.499205i	$-0.833626\pi$
$911$	−8.43433	+	9.36728i	−0.279442	+	0.310352i	0.587042	+	0.809556i	$0.300292\pi$
$912$	−1.68874	−	1.35727i	−0.0559198	−	0.0449436i
$913$	0.333910	+	0.370845i	0.0110508	+	0.0122732i
$914$	−21.9109	−	4.65731i	−0.724749	−	0.154050i
$915$	−48.3123	−	15.6458i	−1.59716	−	0.517235i
$916$	31.4009	−	6.67446i	1.03751	−	0.220530i
$917$	8.24040	+	5.98700i	0.272122	+	0.197708i
$918$	32.1466	+	20.3757i	1.06100	+	0.672498i
$919$	32.7101	+	23.7653i	1.07901	+	0.783945i	0.977510	−	0.210891i	$-0.0676365\pi$
$919$	32.7101	+	23.7653i	1.07901	+	0.783945i	0.101498	+	0.994836i	$0.467637\pi$
$920$	0.0687572	−	0.426639i	0.00226686	−	0.0140659i
$921$	−37.4038	−	9.87506i	−1.23250	−	0.325394i
$922$	0.529717	+	5.03992i	0.0174453	+	0.165981i
$923$	−40.6637	−	8.64335i	−1.33846	−	0.284499i
$924$	−3.83597	+	10.1039i	−0.126194	+	0.332395i
$925$	33.2193	+	19.4197i	1.09224	+	0.638516i
$926$	−55.8028			−1.83380
$927$	−6.95964	+	15.9462i	−0.228585	+	0.523741i
$928$	−23.4590	+	17.0440i	−0.770080	+	0.559496i
$929$	39.4258	+	17.5535i	1.29352	+	0.575912i	0.934016	−	0.357232i	$-0.116279\pi$
$929$	39.4258	+	17.5535i	1.29352	+	0.575912i	0.359503	+	0.933144i	$0.382946\pi$
$930$	−64.5596	+	6.84882i	−2.11699	+	0.224582i
$931$	1.35092	−	0.601470i	0.0442747	−	0.0197124i
$932$	−7.93644	+	13.7463i	−0.259967	+	0.450276i
$933$	−25.8638	−	13.0587i	−0.846743	−	0.427523i
$934$	45.2723	−	9.62293i	1.48136	−	0.314872i
$935$	−16.0287	−	13.0517i	−0.524194	−	0.426838i
$936$	1.28019	−	2.93322i	0.0418444	−	0.0958754i
$937$	4.03157	−	12.4079i	0.131706	−	0.405348i	−0.863357	−	0.504593i	$-0.831643\pi$
$937$	4.03157	−	12.4079i	0.131706	−	0.405348i	0.995063	+	0.0992446i	$0.0316426\pi$
$938$	−26.7353	+	5.68277i	−0.872939	+	0.185549i
$939$	25.4198	+	1.23850i	0.829545	+	0.0404168i
$940$	−27.4812	+	10.4638i	−0.896338	+	0.341291i
$941$	−37.1901	−	41.3038i	−1.21236	−	1.34647i	−0.920858	−	0.389898i	$-0.872510\pi$
$941$	−37.1901	−	41.3038i	−1.21236	−	1.34647i	−0.291506	−	0.956569i	$-0.594156\pi$
$942$	−3.19123	−	56.8894i	−0.103976	−	1.85356i
$943$	−1.85142	−	3.20675i	−0.0602904	−	0.104426i
$944$	−6.78393	−	4.92881i	−0.220798	−	0.160419i
$945$	−14.5934	+	6.64351i	−0.474724	+	0.216113i
$946$	25.0517	−	18.2011i	0.814501	−	0.591770i
$947$	−17.1941	−	7.65530i	−0.558732	−	0.248764i	0.107885	−	0.994163i	$-0.465592\pi$
$947$	−17.1941	−	7.65530i	−0.558732	−	0.248764i	−0.666618	+	0.745400i	$0.732259\pi$
$948$	27.3540	−	42.4624i	0.888417	−	1.37912i
$949$	−7.49716	+	12.9855i	−0.243368	+	0.421526i
$950$	0.0153730	−	2.83991i	0.000498764	−	0.0921388i
$951$	1.81647	−	4.78458i	0.0589032	−	0.155151i
$952$	1.14629	−	1.27308i	0.0371514	−	0.0412608i
$953$	−24.1648	+	17.5568i	−0.782775	+	0.568720i	−0.905811	−	0.423683i	$-0.860737\pi$
$953$	−24.1648	+	17.5568i	−0.782775	+	0.568720i	0.123035	+	0.992402i	$0.460737\pi$
$954$	−28.2524	+	39.4936i	−0.914705	+	1.27865i
$955$	−3.26560	−	2.65909i	−0.105672	−	0.0860463i
$956$	1.93846	−	18.4432i	0.0626944	−	0.596497i
$957$	−15.7551	+	2.55479i	−0.509292	+	0.0825845i
$958$	48.4114	−	21.5541i	1.56410	−	0.696383i
$959$	3.89148	+	4.32193i	0.125663	+	0.139562i
$960$	18.9553	−	17.1008i	0.611781	−	0.551926i
$961$	28.3413	−	31.4763i	0.914237	−	1.01536i
$962$	−14.9699	+	46.0725i	−0.482648	+	1.48544i
$963$	−33.5580	−	19.0471i	−1.08139	−	0.613783i
$964$	−4.60887	−	14.1846i	−0.148442	−	0.456857i
$965$	3.27246	−	0.509231i	0.105344	−	0.0163927i
$966$	−2.12460	−	1.70757i	−0.0683577	−	0.0549401i
$967$	35.2090	−	15.6761i	1.13225	−	0.504108i	0.246900	−	0.969041i	$-0.420588\pi$
$967$	35.2090	−	15.6761i	1.13225	−	0.504108i	0.885346	+	0.464933i	$0.153922\pi$
$968$	0.812459	−	1.40722i	0.0261134	−	0.0452298i
$969$	−0.105360	−	1.87823i	−0.00338465	−	0.0603375i
$970$	42.9942	+	22.0534i	1.38046	+	0.708092i
$971$	−22.5194	+	16.3613i	−0.722682	+	0.525059i	−0.887240	−	0.461308i	$-0.847380\pi$
$971$	−22.5194	+	16.3613i	−0.722682	+	0.525059i	0.164558	+	0.986367i	$0.447380\pi$
$972$	−26.4473	+	10.7140i	−0.848297	+	0.343653i
$973$	0.152164	+	0.468313i	0.00487816	+	0.0150134i
$974$	5.97962	+	10.3570i	0.191599	+	0.331860i
$975$	26.9169	−	7.16230i	0.862032	−	0.229377i
$976$	−28.2579	+	48.9441i	−0.904513	+	1.56666i
$977$	1.23727	+	0.262990i	0.0395838	+	0.00841380i	0.227661	−	0.973740i	$-0.426892\pi$
$977$	1.23727	+	0.262990i	0.0395838	+	0.00841380i	−0.188077	+	0.982154i	$0.560226\pi$
$978$	−5.45621	−	20.0674i	−0.174470	−	0.641686i
$979$	−24.1435	−	10.7494i	−0.771629	−	0.343551i
$980$	5.34361	+	20.1607i	0.170695	+	0.644011i
$981$	−35.3206	+	32.2763i	−1.12770	+	1.03050i
$982$	47.1766			1.50547
$983$	−5.12307	+	48.7427i	−0.163401	+	1.55465i	0.538653	+	0.842528i	$0.318933\pi$
$983$	−5.12307	+	48.7427i	−0.163401	+	1.55465i	−0.702053	+	0.712124i	$0.747733\pi$
$984$	−0.557894	+	3.60822i	−0.0177850	+	0.115026i
$985$	−41.6618	−	11.2842i	−1.32745	−	0.359544i
$986$	−26.7292	−	5.68146i	−0.851230	−	0.180935i
$987$	2.62393	−	16.9704i	0.0835205	−	0.540174i
$988$	1.67125	−	0.355235i	0.0531696	−	0.0113015i
$989$	1.15328	+	3.54944i	0.0366722	+	0.112866i
$990$	31.2852	−	8.53885i	0.994308	−	0.271382i
$991$	−16.1594	+	49.7336i	−0.513321	+	1.57984i	0.272995	+	0.962015i	$0.411986\pi$
$991$	−16.1594	+	49.7336i	−0.513321	+	1.57984i	−0.786316	+	0.617824i	$0.788014\pi$
$992$	−6.95841	+	66.2049i	−0.220930	+	2.10201i
$993$	−7.11647	+	18.7448i	−0.225834	+	0.594847i
$994$	31.8933	−	14.1998i	1.01160	−	0.450391i
$995$	−8.65874	−	10.7520i	−0.274500	−	0.340862i
$996$	−0.619324	−	0.163509i	−0.0196240	−	0.00518099i
$997$	−16.6365	−	7.40706i	−0.526884	−	0.234584i	0.126016	−	0.992028i	$-0.459781\pi$
$997$	−16.6365	−	7.40706i	−0.526884	−	0.234584i	−0.652900	+	0.757444i	$0.726448\pi$
$998$	−5.05675	−	15.5631i	−0.160069	−	0.492641i
$999$	−35.4278	+	18.5464i	−1.12089	+	0.586783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.5	✓	224
3.2	odd	2		675.2.r.a.631.24		224
9.2	odd	6		675.2.r.a.181.5		224
9.7	even	3	inner	225.2.q.a.106.24	yes	224
25.21	even	5	inner	225.2.q.a.121.24	yes	224
75.71	odd	10		675.2.r.a.496.5		224
225.146	odd	30		675.2.r.a.46.24		224
225.196	even	15	inner	225.2.q.a.196.5	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.5	✓	224	1.1	even	1	trivial
225.2.q.a.106.24	yes	224	9.7	even	3	inner
225.2.q.a.121.24	yes	224	25.21	even	5	inner
225.2.q.a.196.5	yes	224	225.196	even	15	inner
675.2.r.a.46.24		224	225.146	odd	30
675.2.r.a.181.5		224	9.2	odd	6
675.2.r.a.496.5		224	75.71	odd	10
675.2.r.a.631.24		224	3.2	odd	2

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30960 + 1.45446i) q^{2} +(-1.67467 - 0.442133i) q^{3} +(-0.191342 - 1.82050i) q^{4} +(-1.40249 - 1.74155i) q^{5} +(2.83622 - 1.85672i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 - 0.194964i) q^{8} +(2.60904 + 1.48085i) q^{9} +O(q^{10})\)	\(q+(-1.30960 + 1.45446i) q^{2} +(-1.67467 - 0.442133i) q^{3} +(-0.191342 - 1.82050i) q^{4} +(-1.40249 - 1.74155i) q^{5} +(2.83622 - 1.85672i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 - 0.194964i) q^{8} +(2.60904 + 1.48085i) q^{9} +(4.36974 + 0.240869i) q^{10} +(1.65278 - 1.83560i) q^{11} +(-0.484468 + 3.13333i) q^{12} +(2.15209 + 2.39014i) q^{13} +(-2.64193 - 0.561560i) q^{14} +(1.57872 + 3.53662i) q^{15} +(4.21604 - 0.896147i) q^{16} +(3.02773 + 2.19977i) q^{17} +(-5.57065 + 1.85541i) q^{18} +(0.234784 + 0.170581i) q^{19} +(-2.90214 + 2.88647i) q^{20} +(-0.627134 - 2.30654i) q^{21} +(0.505323 + 4.80783i) q^{22} +(-0.569918 - 0.121140i) q^{23} +(0.363189 + 0.445145i) q^{24} +(-1.06602 + 4.88504i) q^{25} -6.29476 q^{26} +(-3.71454 - 3.63348i) q^{27} +(2.04372 - 1.48485i) q^{28} +(3.40818 + 1.51742i) q^{29} +(-7.21137 - 2.33538i) q^{30} +(7.82432 - 3.48361i) q^{31} +(-3.88624 + 6.73116i) q^{32} +(-3.57945 + 2.34328i) q^{33} +(-7.16461 + 1.52289i) q^{34} +(1.11366 - 2.87787i) q^{35} +(2.19667 - 5.03309i) q^{36} +(2.37815 - 7.31918i) q^{37} +(-0.555578 + 0.118092i) q^{38} +(-2.54728 - 4.95421i) q^{39} +(0.0368121 + 0.740773i) q^{40} +(4.25243 + 4.72280i) q^{41} +(4.17608 + 2.10851i) q^{42} +(-3.20269 - 5.54723i) q^{43} +(-3.65796 - 2.65766i) q^{44} +(-1.08017 - 6.62067i) q^{45} +(0.922560 - 0.670279i) q^{46} +(6.56303 + 2.92205i) q^{47} +(-7.45669 - 0.363302i) q^{48} +(2.54776 - 4.41285i) q^{49} +(-5.70905 - 7.94795i) q^{50} +(-4.09785 - 5.02255i) q^{51} +(3.93946 - 4.37521i) q^{52} +(6.69073 - 4.86110i) q^{53} +(10.1493 - 0.644232i) q^{54} +(-5.51482 - 0.303989i) q^{55} +(0.0478474 - 0.455238i) q^{56} +(-0.317767 - 0.389473i) q^{57} +(-6.67040 + 2.96985i) q^{58} +(-1.30177 - 1.44576i) q^{59} +(6.13632 - 3.55075i) q^{60} +(-8.77365 + 9.74413i) q^{61} +(-5.17998 + 15.9423i) q^{62} +(0.0304439 + 4.13997i) q^{63} +(-2.03692 - 6.26900i) q^{64} +(1.14426 - 7.10014i) q^{65} +(1.27945 - 8.27494i) q^{66} +(9.24473 - 4.11602i) q^{67} +(3.42535 - 5.93288i) q^{68} +(0.900864 + 0.454849i) q^{69} +(2.72731 + 5.38865i) q^{70} +(-10.4571 + 7.59752i) q^{71} +(-0.411408 - 0.906048i) q^{72} +(1.44065 + 4.43387i) q^{73} +(7.53104 + 13.0442i) q^{74} +(3.94507 - 7.70950i) q^{75} +(0.265618 - 0.460064i) q^{76} +(3.33424 + 0.708716i) q^{77} +(10.5416 + 2.78312i) q^{78} +(-14.5537 - 6.47975i) q^{79} +(-7.47366 - 6.08562i) q^{80} +(4.61414 + 7.72721i) q^{81} -12.4381 q^{82} +(-0.0211178 + 0.200922i) q^{83} +(-4.07905 + 1.58303i) q^{84} +(-0.415350 - 8.35812i) q^{85} +(12.2625 + 2.60647i) q^{86} +(-5.03668 - 4.04805i) q^{87} +(-0.801393 + 0.170341i) q^{88} +(-3.30633 - 10.1758i) q^{89} +(11.0441 + 7.09938i) q^{90} +(-1.37158 + 4.22128i) q^{91} +(-0.111485 + 1.06071i) q^{92} +(-14.6434 + 2.37450i) q^{93} +(-12.8450 + 5.71895i) q^{94} +(-0.0322082 - 0.648128i) q^{95} +(9.48424 - 9.55424i) q^{96} +(10.0866 + 4.49085i) q^{97} +(3.08177 + 9.48471i) q^{98} +(7.03043 - 2.34162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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