LMFDB - Embedded newform 450.2.q.b.331.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(31,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("450.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			331.9
Character	$\chi$	$=$	450.331
Dual form			450.2.q.b.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(0.381143 + 1.68959i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.24818 + 1.85528i) q^{5} +(-0.0215278 - 1.73192i) q^{6} +(-0.565275 + 0.979085i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.70946 + 1.28795i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(0.381143 + 1.68959i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.24818 + 1.85528i) q^{5} +(-0.0215278 - 1.73192i) q^{6} +(-0.565275 + 0.979085i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.70946 + 1.28795i) q^{9} +(1.60663 - 1.55522i) q^{10} +(-5.20053 - 1.10541i) q^{11} +(-0.339028 + 1.69855i) q^{12} +(1.93293 - 0.410857i) q^{13} +(0.756486 - 0.840163i) q^{14} +(-3.61040 - 1.40179i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.0340369 - 0.0247293i) q^{17} +(2.91803 - 0.696481i) q^{18} +(-1.40280 - 1.01919i) q^{19} +(-1.89488 + 1.18720i) q^{20} +(-1.86971 - 0.581914i) q^{21} +(4.85706 + 2.16250i) q^{22} +(3.44594 - 3.82710i) q^{23} +(0.684768 - 1.59094i) q^{24} +(-1.88411 - 4.63143i) q^{25} -1.97611 q^{26} +(-3.20881 - 4.08699i) q^{27} +(-0.914634 + 0.664521i) q^{28} +(0.563239 + 5.35886i) q^{29} +(3.24006 + 2.12180i) q^{30} +(-0.272925 + 2.59671i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.114457 - 9.20811i) q^{33} +(0.0281516 + 0.0312656i) q^{34} +(-1.11091 - 2.27081i) q^{35} +(-2.99907 + 0.0745686i) q^{36} +(-0.159708 + 0.491532i) q^{37} +(1.16024 + 1.28858i) q^{38} +(1.43090 + 3.10927i) q^{39} +(2.10030 - 0.767291i) q^{40} +(-10.9834 + 2.33458i) q^{41} +(1.70786 + 0.957932i) q^{42} +(0.855780 - 1.48225i) q^{43} +(-4.30131 - 3.12509i) q^{44} +(0.992370 - 6.63440i) q^{45} +(-4.16634 + 3.02702i) q^{46} +(0.128062 + 1.21843i) q^{47} +(-1.00058 + 1.41380i) q^{48} +(2.86093 + 4.95527i) q^{49} +(0.880010 + 4.92195i) q^{50} +(0.0288095 - 0.0669340i) q^{51} +(1.93293 + 0.410857i) q^{52} +(-6.58990 + 4.78785i) q^{53} +(2.28896 + 4.66483i) q^{54} +(8.54202 - 8.26869i) q^{55} +(1.03281 - 0.459836i) q^{56} +(1.18735 - 2.75862i) q^{57} +(0.563239 - 5.35886i) q^{58} +(-2.87829 + 0.611800i) q^{59} +(-2.72811 - 2.74908i) q^{60} +(-9.21597 - 1.95892i) q^{61} +(0.806847 - 2.48322i) q^{62} +(0.270573 - 3.38084i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.65038 + 4.09894i) q^{65} +(-1.80252 + 9.03069i) q^{66} +(-1.34989 + 12.8434i) q^{67} +(-0.0210360 - 0.0364354i) q^{68} +(7.77965 + 4.36357i) q^{69} +(0.614507 + 2.45216i) q^{70} +(-3.96352 + 2.87967i) q^{71} +(2.94904 + 0.550603i) q^{72} +(3.77264 + 11.6110i) q^{73} +(0.258414 - 0.447586i) q^{74} +(7.10712 - 4.94862i) q^{75} +(-0.866977 - 1.50165i) q^{76} +(4.02202 - 4.46691i) q^{77} +(-0.753181 - 3.33883i) q^{78} +(-0.853496 - 8.12047i) q^{79} +(-2.21393 + 0.313847i) q^{80} +(5.68235 - 6.97932i) q^{81} +11.2287 q^{82} +(-1.44766 + 0.644540i) q^{83} +(-1.47138 - 1.29208i) q^{84} +(0.0883638 - 0.0322815i) q^{85} +(-1.14526 + 1.27194i) q^{86} +(-8.83963 + 2.99414i) q^{87} +(3.55758 + 3.95109i) q^{88} +(4.99075 + 15.3599i) q^{89} +(-2.35005 + 6.28309i) q^{90} +(-0.690373 + 2.12475i) q^{91} +(4.70464 - 2.09464i) q^{92} +(-4.49141 + 0.528585i) q^{93} +(0.128062 - 1.21843i) q^{94} +(3.64182 - 1.33045i) q^{95} +(1.27266 - 1.17488i) q^{96} +(-1.16521 - 11.0862i) q^{97} +(-1.76815 - 5.44181i) q^{98} +(15.5144 - 3.70299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9}+O(q^{10}) $ 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9	\( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21} + 2 q^{22} - 5 q^{23} + 2 q^{24} + 21 q^{25} + 20 q^{26} - 16 q^{27} - 14 q^{28} + 18 q^{29} + 3 q^{30} - 27 q^{31} - 56 q^{32} - 25 q^{33} - 15 q^{34} - 12 q^{35} - 7 q^{36} + 16 q^{37} - 9 q^{38} + 12 q^{39} - q^{40} + 16 q^{41} - 13 q^{42} - 44 q^{43} - 4 q^{44} + 69 q^{45} - 10 q^{46} + 27 q^{47} + 3 q^{48} - 64 q^{49} + 11 q^{50} + 138 q^{51} - 14 q^{53} - 30 q^{54} - 8 q^{55} + 7 q^{56} - 50 q^{57} + 18 q^{58} + 14 q^{59} - 20 q^{60} - 5 q^{61} - 66 q^{62} - 12 q^{63} - 28 q^{64} - 102 q^{65} + 18 q^{66} + 11 q^{67} + 40 q^{68} - 78 q^{69} + 6 q^{70} + 38 q^{71} - 17 q^{72} - 44 q^{73} + 12 q^{74} + 10 q^{75} - 14 q^{76} - 3 q^{77} - 55 q^{78} + 16 q^{79} + 12 q^{80} + 72 q^{81} + 28 q^{82} - 56 q^{83} - 30 q^{84} + 35 q^{85} + 21 q^{86} - 44 q^{87} - 3 q^{88} - 64 q^{89} + 38 q^{90} - 40 q^{91} + 5 q^{92} - 22 q^{93} + 27 q^{94} + 24 q^{95} + 5 q^{96} + 34 q^{97} + 38 q^{98} + 68 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9 - 8 * q^10 - 3 * q^11 - 3 * q^14 + 32 * q^15 + 14 * q^16 + 10 * q^17 - 6 * q^18 - 32 * q^19 - 6 * q^20 - 7 * q^21 + 2 * q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 20 * q^26 - 16 * q^27 - 14 * q^28 + 18 * q^29 + 3 * q^30 - 27 * q^31 - 56 * q^32 - 25 * q^33 - 15 * q^34 - 12 * q^35 - 7 * q^36 + 16 * q^37 - 9 * q^38 + 12 * q^39 - q^40 + 16 * q^41 - 13 * q^42 - 44 * q^43 - 4 * q^44 + 69 * q^45 - 10 * q^46 + 27 * q^47 + 3 * q^48 - 64 * q^49 + 11 * q^50 + 138 * q^51 - 14 * q^53 - 30 * q^54 - 8 * q^55 + 7 * q^56 - 50 * q^57 + 18 * q^58 + 14 * q^59 - 20 * q^60 - 5 * q^61 - 66 * q^62 - 12 * q^63 - 28 * q^64 - 102 * q^65 + 18 * q^66 + 11 * q^67 + 40 * q^68 - 78 * q^69 + 6 * q^70 + 38 * q^71 - 17 * q^72 - 44 * q^73 + 12 * q^74 + 10 * q^75 - 14 * q^76 - 3 * q^77 - 55 * q^78 + 16 * q^79 + 12 * q^80 + 72 * q^81 + 28 * q^82 - 56 * q^83 - 30 * q^84 + 35 * q^85 + 21 * q^86 - 44 * q^87 - 3 * q^88 - 64 * q^89 + 38 * q^90 - 40 * q^91 + 5 * q^92 - 22 * q^93 + 27 * q^94 + 24 * q^95 + 5 * q^96 + 34 * q^97 + 38 * q^98 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	0.381143	+	1.68959i	0.220053	+	0.975488i
$3$	0.381143	+	1.68959i	0.220053	+	0.975488i
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−1.24818	+	1.85528i	−0.558202	+	0.829705i
$5$	−1.24818	+	1.85528i	−0.558202	+	0.829705i
$6$	−0.0215278	−	1.73192i	−0.00878867	−	0.707052i
$7$	−0.565275	+	0.979085i	−0.213654	+	0.370059i	−0.952855	−	0.303425i	$-0.901870\pi$
$7$	−0.565275	+	0.979085i	−0.213654	+	0.370059i	0.739201	+	0.673484i	$0.235203\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−2.70946	+	1.28795i	−0.903153	+	0.429318i
$10$	1.60663	−	1.55522i	0.508063	−	0.491805i
$11$	−5.20053	−	1.10541i	−1.56802	−	0.333293i	−0.659687	−	0.751541i	$-0.729311\pi$
$11$	−5.20053	−	1.10541i	−1.56802	−	0.333293i	−0.908333	+	0.418248i	$0.862644\pi$
$12$	−0.339028	+	1.69855i	−0.0978691	+	0.490328i
$13$	1.93293	−	0.410857i	0.536098	−	0.113951i	0.0680963	−	0.997679i	$-0.478307\pi$
$13$	1.93293	−	0.410857i	0.536098	−	0.113951i	0.468002	+	0.883728i	$0.344974\pi$
$14$	0.756486	−	0.840163i	0.202179	−	0.224543i
$15$	−3.61040	−	1.40179i	−0.932202	−	0.361940i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.0340369	−	0.0247293i	−0.00825517	−	0.00599773i	0.583650	−	0.812005i	$-0.301624\pi$
$17$	−0.0340369	−	0.0247293i	−0.00825517	−	0.00599773i	−0.591905	+	0.806008i	$0.701624\pi$
$18$	2.91803	−	0.696481i	0.687787	−	0.164162i
$19$	−1.40280	−	1.01919i	−0.321824	−	0.233819i	0.415129	−	0.909762i	$-0.363736\pi$
$19$	−1.40280	−	1.01919i	−0.321824	−	0.233819i	−0.736953	+	0.675944i	$0.763736\pi$
$20$	−1.89488	+	1.18720i	−0.423707	+	0.265466i
$21$	−1.86971	−	0.581914i	−0.408004	−	0.126984i
$22$	4.85706	+	2.16250i	1.03553	+	0.461047i
$23$	3.44594	−	3.82710i	0.718528	−	0.798006i	−0.267682	−	0.963507i	$-0.586258\pi$
$23$	3.44594	−	3.82710i	0.718528	−	0.798006i	0.986210	+	0.165501i	$0.0529242\pi$
$24$	0.684768	−	1.59094i	0.139778	−	0.324749i
$25$	−1.88411	−	4.63143i	−0.376822	−	0.926286i
$26$	−1.97611			−0.387547
$27$	−3.20881	−	4.08699i	−0.617536	−	0.786542i
$28$	−0.914634	+	0.664521i	−0.172850	+	0.125583i
$29$	0.563239	+	5.35886i	0.104591	+	0.995115i	0.913405	+	0.407051i	$0.133443\pi$
$29$	0.563239	+	5.35886i	0.104591	+	0.995115i	−0.808814	+	0.588064i	$0.799890\pi$
$30$	3.24006	+	2.12180i	0.591551	+	0.387386i
$31$	−0.272925	+	2.59671i	−0.0490188	+	0.466383i	0.942287	+	0.334806i	$0.108671\pi$
$31$	−0.272925	+	2.59671i	−0.0490188	+	0.466383i	−0.991306	+	0.131577i	$0.957996\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.114457	−	9.20811i	−0.0199244	−	1.60293i
$34$	0.0281516	+	0.0312656i	0.00482797	+	0.00536200i
$35$	−1.11091	−	2.27081i	−0.187778	−	0.383838i
$36$	−2.99907	+	0.0745686i	−0.499846	+	0.0124281i
$37$	−0.159708	+	0.491532i	−0.0262559	+	0.0808074i	−0.963326	−	0.268334i	$-0.913527\pi$
$37$	−0.159708	+	0.491532i	−0.0262559	+	0.0808074i	0.937070	+	0.349142i	$0.113527\pi$
$38$	1.16024	+	1.28858i	0.188216	+	0.209035i
$39$	1.43090	+	3.10927i	0.229128	+	0.497882i
$40$	2.10030	−	0.767291i	0.332087	−	0.121319i
$41$	−10.9834	+	2.33458i	−1.71531	+	0.364601i	−0.957625	−	0.288018i	$-0.907004\pi$
$41$	−10.9834	+	2.33458i	−1.71531	+	0.364601i	−0.757687	+	0.652618i	$0.773671\pi$
$42$	1.70786	+	0.957932i	0.263529	+	0.147812i
$43$	0.855780	−	1.48225i	0.130505	−	0.226042i	−0.793366	−	0.608745i	$-0.791673\pi$
$43$	0.855780	−	1.48225i	0.130505	−	0.226042i	0.923871	+	0.382703i	$0.125007\pi$
$44$	−4.30131	−	3.12509i	−0.648447	−	0.471125i
$45$	0.992370	−	6.63440i	0.147934	−	0.988997i
$46$	−4.16634	+	3.02702i	−0.614293	+	0.446310i
$47$	0.128062	+	1.21843i	0.0186798	+	0.177726i	0.999884	−	0.0152473i	$-0.00485354\pi$
$47$	0.128062	+	1.21843i	0.0186798	+	0.177726i	−0.981204	+	0.192973i	$0.938187\pi$
$48$	−1.00058	+	1.41380i	−0.144421	+	0.204065i
$49$	2.86093	+	4.95527i	0.408704	+	0.707896i
$50$	0.880010	+	4.92195i	0.124452	+	0.696069i
$51$	0.0288095	−	0.0669340i	0.00403414	−	0.00937264i
$52$	1.93293	+	0.410857i	0.268049	+	0.0569756i
$53$	−6.58990	+	4.78785i	−0.905193	+	0.657661i	−0.939795	−	0.341740i	$-0.888984\pi$
$53$	−6.58990	+	4.78785i	−0.905193	+	0.657661i	0.0346016	+	0.999401i	$0.488984\pi$
$54$	2.28896	+	4.66483i	0.311488	+	0.634803i
$55$	8.54202	−	8.26869i	1.15181	−	1.11495i
$56$	1.03281	−	0.459836i	0.138015	−	0.0614482i
$57$	1.18735	−	2.75862i	0.157269	−	0.365388i
$58$	0.563239	−	5.35886i	0.0739569	−	0.703653i
$59$	−2.87829	+	0.611800i	−0.374722	+	0.0796495i	−0.391423	−	0.920211i	$-0.628017\pi$
$59$	−2.87829	+	0.611800i	−0.374722	+	0.0796495i	0.0167011	+	0.999861i	$0.494684\pi$
$60$	−2.72811	−	2.74908i	−0.352197	−	0.354904i
$61$	−9.21597	−	1.95892i	−1.17998	−	0.250813i	−0.424160	−	0.905587i	$-0.639431\pi$
$61$	−9.21597	−	1.95892i	−1.17998	−	0.250813i	−0.755825	+	0.654774i	$0.772764\pi$
$62$	0.806847	−	2.48322i	0.102470	−	0.315369i
$63$	0.270573	−	3.38084i	0.0340890	−	0.425946i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.65038	+	4.09894i	−0.204705	+	0.508411i
$66$	−1.80252	+	9.03069i	−0.221875	+	1.11160i
$67$	−1.34989	+	12.8434i	−0.164916	+	1.56907i	0.528754	+	0.848775i	$0.322659\pi$
$67$	−1.34989	+	12.8434i	−0.164916	+	1.56907i	−0.693670	+	0.720293i	$0.744007\pi$
$68$	−0.0210360	−	0.0364354i	−0.00255099	−	0.00441844i
$69$	7.77965	+	4.36357i	0.936559	+	0.525312i
$70$	0.614507	+	2.45216i	0.0734476	+	0.293089i
$71$	−3.96352	+	2.87967i	−0.470383	+	0.341754i	−0.797591	−	0.603199i	$-0.793892\pi$
$71$	−3.96352	+	2.87967i	−0.470383	+	0.341754i	0.327207	+	0.944953i	$0.393892\pi$
$72$	2.94904	+	0.550603i	0.347548	+	0.0648892i
$73$	3.77264	+	11.6110i	0.441554	+	1.35896i	0.886219	+	0.463267i	$0.153323\pi$
$73$	3.77264	+	11.6110i	0.441554	+	1.35896i	−0.444664	+	0.895697i	$0.646677\pi$
$74$	0.258414	−	0.447586i	0.0300400	−	0.0520308i
$75$	7.10712	−	4.94862i	0.820660	−	0.571417i
$76$	−0.866977	−	1.50165i	−0.0994490	−	0.172251i
$77$	4.02202	−	4.46691i	0.458352	−	0.509051i
$78$	−0.753181	−	3.33883i	−0.0852810	−	0.378048i
$79$	−0.853496	−	8.12047i	−0.0960258	−	0.913624i	−0.931413	−	0.363963i	$-0.881423\pi$
$79$	−0.853496	−	8.12047i	−0.0960258	−	0.913624i	0.835388	−	0.549661i	$-0.185243\pi$
$80$	−2.21393	+	0.313847i	−0.247525	+	0.0350892i
$81$	5.68235	−	6.97932i	0.631372	−	0.775480i
$82$	11.2287			1.24001
$83$	−1.44766	+	0.644540i	−0.158901	+	0.0707474i	−0.484646	−	0.874710i	$-0.661052\pi$
$83$	−1.44766	+	0.644540i	−0.158901	+	0.0707474i	0.325745	+	0.945458i	$0.394385\pi$
$84$	−1.47138	−	1.29208i	−0.160540	−	0.140978i
$85$	0.0883638	−	0.0322815i	0.00958440	−	0.00350142i
$86$	−1.14526	+	1.27194i	−0.123496	+	0.137156i
$87$	−8.83963	+	2.99414i	−0.947707	+	0.321005i
$88$	3.55758	+	3.95109i	0.379239	+	0.421188i
$89$	4.99075	+	15.3599i	0.529018	+	1.62815i	0.756231	+	0.654305i	$0.227039\pi$
$89$	4.99075	+	15.3599i	0.529018	+	1.62815i	−0.227212	+	0.973845i	$0.572961\pi$
$90$	−2.35005	+	6.28309i	−0.247717	+	0.662296i
$91$	−0.690373	+	2.12475i	−0.0723707	+	0.222734i
$92$	4.70464	−	2.09464i	0.490493	−	0.218382i
$93$	−4.49141	+	0.528585i	−0.465737	+	0.0548117i
$94$	0.128062	−	1.21843i	0.0132086	−	0.125671i
$95$	3.64182	−	1.33045i	0.373643	−	0.136501i
$96$	1.27266	−	1.17488i	0.129890	−	0.119910i
$97$	−1.16521	−	11.0862i	−0.118309	−	1.12564i	−0.879100	−	0.476638i	$-0.841855\pi$
$97$	−1.16521	−	11.0862i	−0.118309	−	1.12564i	0.760791	−	0.648997i	$-0.224811\pi$
$98$	−1.76815	−	5.44181i	−0.178610	−	0.549706i
$99$	15.5144	−	3.70299i	1.55925	−	0.372165i
$100$	0.162551	−	4.99736i	0.0162551	−	0.499736i
$101$	3.14438	−	5.44622i	0.312877	−	0.541919i	−0.666107	−	0.745856i	$-0.732041\pi$
$101$	3.14438	−	5.44622i	0.312877	−	0.541919i	0.978984	+	0.203937i	$0.0653739\pi$
$102$	−0.0420963	+	0.0594815i	−0.00416816	+	0.00588955i
$103$	−4.83090	−	2.15086i	−0.476003	−	0.211930i	0.154689	−	0.987963i	$-0.450562\pi$
$103$	−4.83090	−	2.15086i	−0.476003	−	0.211930i	−0.630692	+	0.776033i	$0.717229\pi$
$104$	−1.80527	−	0.803757i	−0.177021	−	0.0788148i
$105$	3.41334	−	2.74250i	0.333108	−	0.267640i
$106$	7.44135	−	3.31310i	0.722768	−	0.321797i
$107$	12.5207			1.21042			0.605212	−	0.796064i	$-0.293088\pi$
$107$	12.5207			1.21042			0.605212	+	0.796064i	$0.293088\pi$
$108$	−1.26907	−	5.03880i	−0.122116	−	0.484858i
$109$	−5.14376	+	15.8309i	−0.492683	+	1.51632i	0.327853	+	0.944729i	$0.393675\pi$
$109$	−5.14376	+	15.8309i	−0.492683	+	1.51632i	−0.820537	+	0.571594i	$0.806325\pi$
$110$	−10.0745	+	6.31201i	−0.960567	+	0.601827i
$111$	−0.891362	−	0.0824985i	−0.0846043	−	0.00783041i
$112$	−1.10584	+	0.235055i	−0.104493	+	0.0222106i
$113$	17.5900	−	3.73886i	1.65472	−	0.351722i	0.716456	−	0.697632i	$-0.245763\pi$
$113$	17.5900	−	3.73886i	1.65472	−	0.351722i	0.938268	+	0.345910i	$0.112430\pi$
$114$	−1.73496	+	2.45147i	−0.162494	+	0.229601i
$115$	2.79920	+	11.1701i	0.261027	+	1.04161i
$116$	−1.66510	+	5.12465i	−0.154601	+	0.475812i
$117$	−4.70803	+	3.60272i	−0.435257	+	0.333072i
$118$	2.94259			0.270888
$119$	0.0434523	−	0.0193462i	0.00398327	−	0.00177346i
$120$	2.09693	+	3.25621i	0.191422	+	0.297250i
$121$	15.7746	+	7.02331i	1.43406	+	0.638483i
$122$	8.60730	+	3.83222i	0.779268	+	0.346953i
$123$	−8.13073	−	17.6676i	−0.733123	−	1.59303i
$124$	−1.30551	+	2.26120i	−0.117238	+	0.203062i
$125$	10.9443	+	2.28529i	0.978887	+	0.204403i
$126$	−0.967576	+	3.25071i	−0.0861986	+	0.289596i
$127$	−1.65916	−	5.10636i	−0.147226	−	0.453116i	0.850064	−	0.526679i	$-0.176563\pi$
$127$	−1.65916	−	5.10636i	−0.147226	−	0.453116i	−0.997291	+	0.0735630i	$0.976563\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	2.83058	+	0.880970i	0.249219	+	0.0775651i
$130$	2.46654	−	3.66624i	0.216329	−	0.321550i
$131$	1.62938	−	15.5025i	0.142359	−	1.35446i	−0.657130	−	0.753777i	$-0.728230\pi$
$131$	1.62938	−	15.5025i	0.142359	−	1.35446i	0.799490	−	0.600680i	$-0.205103\pi$
$132$	3.64071	−	8.45858i	0.316884	−	0.736225i
$133$	1.79084	−	0.797335i	0.155286	−	0.0691377i
$134$	3.99068	−	12.2821i	0.344742	−	1.06101i
$135$	11.5877	−	0.851950i	0.997308	−	0.0733242i
$136$	0.0130010	+	0.0400128i	0.00111482	+	0.00343107i
$137$	14.1669	+	15.7339i	1.21036	+	1.34424i	0.922229	+	0.386644i	$0.126366\pi$
$137$	14.1669	+	15.7339i	1.21036	+	1.34424i	0.288127	+	0.957592i	$0.406968\pi$
$138$	−6.70241	−	5.88569i	−0.570547	−	0.501023i
$139$	1.25269	−	1.39126i	0.106252	−	0.118005i	−0.687673	−	0.726021i	$-0.741368\pi$
$139$	1.25269	−	1.39126i	0.106252	−	0.118005i	0.793925	+	0.608016i	$0.208034\pi$
$140$	−0.0912454	−	2.52634i	−0.00771165	−	0.213515i
$141$	−2.00984	+	0.680769i	−0.169259	+	0.0573311i
$142$	4.47562	−	1.99268i	0.375586	−	0.167222i
$143$	−10.5064			−0.878591
$144$	−2.77012	−	1.15171i	−0.230843	−	0.0959759i
$145$	−10.6452	−	5.64384i	−0.884035	−	0.468695i
$146$	−1.27614	−	12.1416i	−0.105614	−	1.00485i
$147$	−7.28198	+	6.72248i	−0.600608	+	0.554461i
$148$	−0.345825	+	0.384078i	−0.0284266	+	0.0315710i
$149$	7.31377	+	12.6678i	0.599167	+	1.03779i	0.992944	+	0.118582i	$0.0378348\pi$
$149$	7.31377	+	12.6678i	0.599167	+	1.03779i	−0.393777	+	0.919206i	$0.628832\pi$
$150$	−7.98069	+	3.36283i	−0.651620	+	0.274574i
$151$	2.57050	−	4.45223i	0.209184	−	0.362317i	−0.742274	−	0.670097i	$-0.766253\pi$
$151$	2.57050	−	4.45223i	0.209184	−	0.362317i	0.951458	+	0.307780i	$0.0995859\pi$
$152$	0.535821	+	1.64909i	0.0434608	+	0.133759i
$153$	0.124072	+	0.0231650i	0.0100306	+	0.00187278i
$154$	−4.86285	+	3.53307i	−0.391860	+	0.284703i
$155$	−4.47696	−	3.74750i	−0.359598	−	0.301007i
$156$	0.0425412	+	3.42246i	0.00340603	+	0.274016i
$157$	5.02573	+	8.70482i	0.401097	+	0.694720i	0.993859	−	0.110658i	$-0.0352957\pi$
$157$	5.02573	+	8.70482i	0.401097	+	0.694720i	−0.592762	+	0.805378i	$0.701962\pi$
$158$	−0.853496	+	8.12047i	−0.0679005	+	0.646030i
$159$	−10.6012	−	9.30941i	−0.840731	−	0.738284i
$160$	2.23081	+	0.153314i	0.176361	+	0.0121205i
$161$	1.79916	+	5.53723i	0.141793	+	0.436395i
$162$	−7.00926	+	5.64538i	−0.550699	+	0.443543i
$163$	−6.71143	+	20.6556i	−0.525679	+	1.61787i	0.237289	+	0.971439i	$0.423741\pi$
$163$	−6.71143	+	20.6556i	−0.525679	+	1.61787i	−0.762968	+	0.646436i	$0.776259\pi$
$164$	−10.9834	−	2.33458i	−0.857656	−	0.182300i
$165$	17.2265	+	11.2810i	1.34108	+	0.878225i
$166$	1.55003	−	0.329469i	0.120306	−	0.0255718i
$167$	1.34554	−	12.8019i	0.104121	−	0.990644i	−0.810337	−	0.585964i	$-0.800716\pi$
$167$	1.34554	−	12.8019i	0.104121	−	0.990644i	0.914458	−	0.404680i	$-0.132617\pi$
$168$	1.17058	+	1.56977i	0.0903126	+	0.121110i
$169$	−8.30868	+	3.69926i	−0.639129	+	0.284559i
$170$	−0.0931445	+	0.0132042i	−0.00714386	+	0.00101271i
$171$	5.11350	+	0.954720i	0.391039	+	0.0730093i
$172$	1.38468	−	1.00603i	0.105581	−	0.0767090i
$173$	−21.2219	−	4.51085i	−1.61347	−	0.342954i	−0.689164	−	0.724605i	$-0.742022\pi$
$173$	−21.2219	−	4.51085i	−1.61347	−	0.342954i	−0.924306	+	0.381651i	$0.875355\pi$
$174$	9.26898	−	1.09085i	0.702679	−	0.0826969i
$175$	5.59960	+	0.773326i	0.423290	+	0.0584580i
$176$	−2.65836	−	4.60441i	−0.200381	−	0.347071i
$177$	−2.13073	−	4.62996i	−0.160156	−	0.348009i
$178$	−1.68818	−	16.0619i	−0.126534	−	1.20389i
$179$	−11.9432	+	8.67724i	−0.892676	+	0.648567i	−0.936574	−	0.350469i	$-0.886022\pi$
$179$	−11.9432	+	8.67724i	−0.892676	+	0.648567i	0.0438984	+	0.999036i	$0.486022\pi$
$180$	3.60503	−	5.65719i	0.268703	−	0.421662i
$181$	−5.63519	−	4.09421i	−0.418861	−	0.304320i	0.358319	−	0.933599i	$-0.383350\pi$
$181$	−5.63519	−	4.09421i	−0.418861	−	0.304320i	−0.777179	+	0.629279i	$0.783350\pi$
$182$	1.11705	−	1.93478i	0.0828010	−	0.143416i
$183$	−0.202832	−	16.3179i	−0.0149937	−	1.20625i
$184$	−5.03734	+	1.07072i	−0.371357	+	0.0789345i
$185$	−0.712584	−	0.909822i	−0.0523902	−	0.0668915i
$186$	4.50316	+	0.416782i	0.330188	+	0.0305600i
$187$	0.149674	+	0.166230i	0.0109453	+	0.0121559i
$188$	−0.378589	+	1.16518i	−0.0276115	+	0.0849794i
$189$	5.81538	−	0.831426i	0.423006	−	0.0604773i
$190$	−3.83886	+	0.544196i	−0.278500	+	0.0394802i
$191$	−7.55461	−	8.39025i	−0.546633	−	0.607097i	0.405007	−	0.914314i	$-0.367269\pi$
$191$	−7.55461	−	8.39025i	−0.546633	−	0.607097i	−0.951640	+	0.307216i	$0.900602\pi$
$192$	−1.48912	+	0.884602i	−0.107468	+	0.0638407i
$193$	0.949009	+	1.64373i	0.0683111	+	0.118318i	0.898158	−	0.439673i	$-0.144906\pi$
$193$	0.949009	+	1.64373i	0.0683111	+	0.118318i	−0.829847	+	0.557991i	$0.811572\pi$
$194$	−1.16521	+	11.0862i	−0.0836571	+	0.795945i
$195$	−7.55458	−	1.22619i	−0.540995	−	0.0878096i
$196$	0.598097	+	5.69051i	0.0427212	+	0.406465i
$197$	6.94267	−	5.04415i	0.494645	−	0.359381i	−0.312323	−	0.949976i	$-0.601107\pi$
$197$	6.94267	−	5.04415i	0.494645	−	0.359381i	0.806968	+	0.590595i	$0.201107\pi$
$198$	−15.9452	+	0.396460i	−1.13318	+	0.0281752i
$199$	−14.9037			−1.05650			−0.528248	−	0.849090i	$-0.677151\pi$
$199$	−14.9037			−1.05650			−0.528248	+	0.849090i	$0.677151\pi$
$200$	−1.19801	+	4.85436i	−0.0847119	+	0.343255i
$201$	−22.2146	+	2.61439i	−1.56690	+	0.184405i
$202$	−4.20800	+	4.67345i	−0.296074	+	0.328823i
$203$	−5.56517	−	2.47777i	−0.390598	−	0.173905i
$204$	0.0535433	−	0.0494294i	0.00374878	−	0.00346075i
$205$	9.37786	−	23.2911i	0.654978	−	1.62672i
$206$	4.27815	+	3.10826i	0.298073	+	0.216562i
$207$	−4.40750	+	14.8076i	−0.306342	+	1.02920i
$208$	1.59871	+	1.16153i	0.110850	+	0.0805375i
$209$	6.16867	+	6.85101i	0.426696	+	0.473894i
$210$	−3.90895	+	1.97289i	−0.269743	+	0.136143i
$211$	−3.30852	+	3.67449i	−0.227768	+	0.252962i	−0.846186	−	0.532887i	$-0.821107\pi$
$211$	−3.30852	+	3.67449i	−0.227768	+	0.252962i	0.618418	+	0.785849i	$0.287774\pi$
$212$	−7.96757	+	1.69356i	−0.547215	+	0.116314i
$213$	−6.37614	−	5.59918i	−0.436886	−	0.383649i
$214$	−12.2471	−	2.60320i	−0.837195	−	0.177951i
$215$	1.68183	+	3.43782i	0.114700	+	0.234458i
$216$	0.193710	+	5.19254i	0.0131803	+	0.353308i
$217$	−2.38812	−	1.73507i	−0.162116	−	0.117784i
$218$	8.32278	−	14.4155i	0.563690	−	0.976340i
$219$	−18.1800	+	10.7997i	−1.22849	+	0.729775i
$220$	11.1667	−	4.07947i	0.752859	−	0.275038i
$221$	−0.0759511	−	0.0338156i	−0.00510903	−	0.00227469i
$222$	0.854731	+	0.266020i	0.0573658	+	0.0178541i
$223$	−8.10767	−	1.72334i	−0.542929	−	0.115403i	−0.0717204	−	0.997425i	$-0.522849\pi$
$223$	−8.10767	−	1.72334i	−0.542929	−	0.115403i	−0.471209	+	0.882022i	$0.656182\pi$
$224$	1.13055			0.0755381
$225$	11.0700	+	10.1220i	0.737999	+	0.674801i
$226$	−17.9829			−1.19621
$227$	−0.0957178	−	0.0203454i	−0.00635301	−	0.00135037i	0.204734	−	0.978818i	$-0.434367\pi$
$227$	−0.0957178	−	0.0203454i	−0.00635301	−	0.00135037i	−0.211087	+	0.977467i	$0.567700\pi$
$228$	2.20673	−	2.03718i	0.146145	−	0.134916i
$229$	−11.0244	−	4.90836i	−0.728510	−	0.324353i	0.00875095	−	0.999962i	$-0.497214\pi$
$229$	−11.0244	−	4.90836i	−0.728510	−	0.324353i	−0.737261	+	0.675608i	$0.763881\pi$
$230$	−0.415640	−	11.5080i	−0.0274065	−	0.758813i
$231$	9.08023	+	5.09305i	0.597435	+	0.335098i
$232$	2.69419	−	4.66647i	0.176882	−	0.306369i
$233$	16.1874	+	11.7608i	1.06047	+	0.770476i	0.974175	−	0.225793i	$-0.0724974\pi$
$233$	16.1874	+	11.7608i	1.06047	+	0.770476i	0.0862946	+	0.996270i	$0.472497\pi$
$234$	5.35419	−	2.54514i	0.350015	−	0.166381i
$235$	−2.42037	−	1.28322i	−0.157887	−	0.0837083i
$236$	−2.87829	−	0.611800i	−0.187361	−	0.0398248i
$237$	13.3950	−	4.53712i	0.870099	−	0.294718i
$238$	−0.0465251	+	0.00988921i	−0.00301577	+	0.000641022i
$239$	15.1370	−	16.8113i	0.979129	−	1.08743i	−0.0170285	−	0.999855i	$-0.505421\pi$
$239$	15.1370	−	16.8113i	0.979129	−	1.08743i	0.996158	−	0.0875780i	$-0.0279127\pi$
$240$	−1.37410	−	3.62103i	−0.0886978	−	0.233736i
$241$	6.92080	+	7.68632i	0.445808	+	0.495120i	0.923602	−	0.383352i	$-0.125230\pi$
$241$	6.92080	+	7.68632i	0.445808	+	0.495120i	−0.477795	+	0.878472i	$0.658564\pi$
$242$	−13.9697	−	10.1496i	−0.898005	−	0.652439i
$243$	13.9580	+	6.94074i	0.895407	+	0.445249i
$244$	−7.62245	−	5.53803i	−0.487977	−	0.354536i
$245$	−12.7644	−	0.877239i	−0.815484	−	0.0560447i
$246$	4.27975	+	18.9720i	0.272867	+	1.20961i
$247$	−3.13025	−	1.39368i	−0.199173	−	0.0886775i
$248$	1.74711	−	1.94036i	0.110941	−	0.123213i
$249$	−1.64078	−	2.20030i	−0.103980	−	0.139438i
$250$	−10.2300	−	4.51080i	−0.647001	−	0.285288i
$251$	−9.73173			−0.614262			−0.307131	−	0.951667i	$-0.599369\pi$
$251$	−9.73173			−0.614262			−0.307131	+	0.951667i	$0.599369\pi$
$252$	1.62229	−	2.97850i	0.102195	−	0.187628i
$253$	−22.1512	+	16.0938i	−1.39264	+	1.01181i
$254$	0.561228	+	5.33973i	0.0352146	+	0.335044i
$255$	0.0882218	+	0.136995i	0.00552466	+	0.00857897i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−7.76487	−	13.4491i	−0.484359	−	0.838934i	0.515480	−	0.856902i	$-0.327614\pi$
$257$	−7.76487	−	13.4491i	−0.484359	−	0.838934i	−0.999839	+	0.0179674i	$0.994280\pi$
$258$	−2.58556	−	1.45023i	−0.160970	−	0.0902874i
$259$	−0.390973	−	0.434219i	−0.0242939	−	0.0269811i
$260$	−3.17489	+	3.07330i	−0.196898	+	0.190598i
$261$	−8.42804	−	13.7942i	−0.521683	−	0.853839i
$262$	−4.81691	+	14.8249i	−0.297590	+	0.915888i
$263$	19.6953	+	21.8738i	1.21446	+	1.34880i	0.919403	+	0.393318i	$0.128673\pi$
$263$	19.6953	+	21.8738i	1.21446	+	1.34880i	0.295060	+	0.955479i	$0.404660\pi$
$264$	−5.31979	+	7.51679i	−0.327411	+	0.462627i
$265$	−0.657420	−	18.2022i	−0.0403850	−	1.11815i
$266$	−1.91748	+	0.407574i	−0.117568	+	0.0249899i
$267$	−24.0499	+	14.2867i	−1.47183	+	0.874330i
$268$	−6.45706	+	11.1840i	−0.394428	+	0.683169i
$269$	15.0411	+	10.9280i	0.917071	+	0.666291i	0.942793	−	0.333378i	$-0.108189\pi$
$269$	15.0411	+	10.9280i	0.917071	+	0.666291i	−0.0257224	+	0.999669i	$0.508189\pi$
$270$	−11.5116	−	1.57588i	−0.700573	−	0.0959050i
$271$	14.5109	−	10.5428i	0.881473	−	0.640428i	−0.0521678	−	0.998638i	$-0.516613\pi$
$271$	14.5109	−	10.5428i	0.881473	−	0.640428i	0.933641	+	0.358211i	$0.116613\pi$
$272$	−0.00439772	−	0.0418415i	−0.000266651	−	0.00253701i
$273$	−3.85309	−	0.356617i	−0.233200	−	0.0215834i
$274$	−10.5860	−	18.3355i	−0.639524	−	1.10769i
$275$	4.67877	+	26.1686i	0.282140	+	1.57803i
$276$	5.33224	+	7.15058i	0.320963	+	0.430415i
$277$	−17.8600	−	3.79625i	−1.07310	−	0.228095i	−0.362710	−	0.931902i	$-0.618149\pi$
$277$	−17.8600	−	3.79625i	−1.07310	−	0.228095i	−0.710391	+	0.703807i	$0.751482\pi$
$278$	−1.51458	+	1.10040i	−0.0908382	+	0.0659978i
$279$	−2.60496	−	7.38719i	−0.155955	−	0.442260i
$280$	−0.436004	+	2.49010i	−0.0260562	+	0.148812i
$281$	13.2998	−	5.92145i	0.793399	−	0.353244i	0.0303128	−	0.999540i	$-0.490350\pi$
$281$	13.2998	−	5.92145i	0.793399	−	0.353244i	0.763087	+	0.646296i	$0.223683\pi$
$282$	2.10746	−	0.248023i	0.125498	−	0.0147696i
$283$	−1.07718	+	10.2487i	−0.0640316	+	0.609220i	0.914708	+	0.404115i	$0.132420\pi$
$283$	−1.07718	+	10.2487i	−0.0640316	+	0.609220i	−0.978740	+	0.205105i	$0.934246\pi$
$284$	−4.79212	+	1.01860i	−0.284360	+	0.0604426i
$285$	3.63597	+	5.64611i	0.215376	+	0.334447i
$286$	10.2768	+	2.18441i	0.607682	+	0.129167i
$287$	3.92286	−	12.0733i	0.231559	−	0.712666i
$288$	2.47013	+	1.70248i	0.145554	+	0.100320i
$289$	−5.25274	−	16.1663i	−0.308985	−	0.950957i
$290$	9.23915	+	7.73377i	0.542542	+	0.454142i
$291$	18.2871	−	6.19417i	1.07201	−	0.363109i
$292$	−1.27614	+	12.1416i	−0.0746804	+	0.710536i
$293$	9.04993	+	15.6749i	0.528702	+	0.915740i	0.999440	+	0.0334662i	$0.0106546\pi$
$293$	9.04993	+	15.6749i	0.528702	+	0.915740i	−0.470737	+	0.882273i	$0.656012\pi$
$294$	8.52053	−	5.06157i	0.496928	−	0.295197i
$295$	2.45756	−	6.10366i	0.143084	−	0.355369i
$296$	0.418122	−	0.303783i	0.0243029	−	0.0176571i
$297$	12.1697	+	24.8016i	0.706160	+	1.43913i
$298$	−4.52016	−	13.9116i	−0.261846	−	0.805878i
$299$	5.08836	−	8.81330i	0.294268	−	0.509686i
$300$	8.50546	−	1.63006i	0.491063	−	0.0941118i
$301$	0.967502	+	1.67576i	0.0557659	+	0.0965894i
$302$	−3.43999	+	3.82050i	−0.197949	+	0.219845i
$303$	10.4004	+	3.23693i	0.597485	+	0.185957i
$304$	−0.181247	−	1.72445i	−0.0103953	−	0.0989043i
$305$	15.1375	−	14.6531i	0.866770	−	0.839035i
$306$	−0.116544	−	0.0484547i	−0.00666240	−	0.00276997i
$307$	−0.314423			−0.0179450			−0.00897252	−	0.999960i	$-0.502856\pi$
$307$	−0.314423			−0.0179450			−0.00897252	+	0.999960i	$0.502856\pi$
$308$	5.49115	−	2.44482i	0.312887	−	0.139306i
$309$	1.79281	−	8.98205i	0.101989	−	0.510971i
$310$	3.59997	+	4.59642i	0.204465	+	0.261059i
$311$	−15.3991	+	17.1024i	−0.873202	+	0.969789i	−0.999754	−	0.0221707i	$-0.992942\pi$
$311$	−15.3991	+	17.1024i	−0.873202	+	0.969789i	0.126552	+	0.991960i	$0.459609\pi$
$312$	0.669958	−	3.35652i	0.0379289	−	0.190025i
$313$	−6.22761	−	6.91646i	−0.352005	−	0.390941i	0.540974	−	0.841039i	$-0.318056\pi$
$313$	−6.22761	−	6.91646i	−0.352005	−	0.390941i	−0.892979	+	0.450098i	$0.851389\pi$
$314$	−3.10607	−	9.55951i	−0.175286	−	0.539474i
$315$	5.93468	+	4.72187i	0.334381	+	0.266047i
$316$	2.52319	−	7.76557i	0.141940	−	0.436847i
$317$	15.9258	−	7.09062i	0.894482	−	0.398249i	0.0925804	−	0.995705i	$-0.470488\pi$
$317$	15.9258	−	7.09062i	0.894482	−	0.398249i	0.801902	+	0.597456i	$0.203822\pi$
$318$	8.43402	+	11.3101i	0.472956	+	0.634239i
$319$	2.99458	−	28.4915i	0.167664	−	1.59522i
$320$	−2.15018	−	0.613774i	−0.120199	−	0.0343110i
$321$	4.77219	+	21.1549i	0.266357	+	1.18075i
$322$	−0.608585	−	5.79030i	−0.0339151	−	0.322681i
$323$	0.0225430	+	0.0693804i	0.00125433	+	0.00386043i
$324$	8.02983	−	4.06471i	0.446102	−	0.225817i
$325$	−5.54470	−	8.17812i	−0.307565	−	0.453640i
$326$	10.8593	−	18.8089i	0.601442	−	1.04173i
$327$	−28.7083	−	2.65704i	−1.58757	−	0.146935i
$328$	10.2580	+	4.56714i	0.566401	+	0.252178i
$329$	−1.26534	−	0.563364i	−0.0697603	−	0.0310593i
$330$	−14.5046	−	14.6161i	−0.798451	−	0.804588i
$331$	13.7377	−	6.11643i	0.755093	−	0.336189i	0.00716996	−	0.999974i	$-0.497718\pi$
$331$	13.7377	−	6.11643i	0.755093	−	0.336189i	0.747923	+	0.663785i	$0.231051\pi$
$332$	−1.58466			−0.0869695
$333$	−0.200347	−	1.53748i	−0.0109790	−	0.0842536i
$334$	−3.97781	+	12.2424i	−0.217656	+	0.669876i
$335$	−22.1431	−	18.5352i	−1.20981	−	1.01269i
$336$	−0.818632	−	1.77884i	−0.0446600	−	0.0970437i
$337$	23.6809	−	5.03353i	1.28998	−	0.274194i	0.488684	−	0.872461i	$-0.337477\pi$
$337$	23.6809	−	5.03353i	1.28998	−	0.274194i	0.801297	+	0.598267i	$0.204144\pi$
$338$	8.89624	−	1.89095i	0.483892	−	0.102854i
$339$	13.0215	+	28.2949i	0.707228	+	1.53677i
$340$	0.0938544	+	0.00645021i	0.00508997	+	0.000349812i
$341$	4.28978	−	13.2026i	0.232304	−	0.714959i
$342$	−4.80326	−	1.99701i	−0.259730	−	0.107986i
$343$	−14.3827			−0.776593
$344$	−1.56359	+	0.696154i	−0.0843030	+	0.0375341i
$345$	−17.8060	+	8.98691i	−0.958643	+	0.483839i
$346$	19.8203	+	8.82456i	1.06555	+	0.474411i
$347$	−26.8688	−	11.9628i	−1.44239	−	0.642195i	−0.471534	−	0.881848i	$-0.656300\pi$
$347$	−26.8688	−	11.9628i	−1.44239	−	0.642195i	−0.970859	+	0.239653i	$0.922966\pi$
$348$	−9.29323	−	0.860119i	−0.498169	−	0.0461072i
$349$	−5.51207	+	9.54718i	−0.295054	+	0.511049i	−0.974998	−	0.222216i	$-0.928671\pi$
$349$	−5.51207	+	9.54718i	−0.295054	+	0.511049i	0.679943	+	0.733265i	$0.262004\pi$
$350$	−5.31646	−	1.92065i	−0.284176	−	0.102663i
$351$	−7.88157	−	6.58150i	−0.420687	−	0.351295i
$352$	1.64296	+	5.05650i	0.0875698	+	0.269512i
$353$	−2.15587	−	20.5117i	−0.114745	−	1.09173i	−0.888701	−	0.458488i	$-0.848391\pi$
$353$	−2.15587	−	20.5117i	−0.114745	−	1.09173i	0.773955	−	0.633240i	$-0.218275\pi$
$354$	1.12155	+	4.97179i	0.0596097	+	0.264248i
$355$	−0.395407	−	10.9478i	−0.0209860	−	0.581047i
$356$	−1.68818	+	16.0619i	−0.0894732	+	0.851280i
$357$	0.0492488	+	0.0660431i	0.00260652	+	0.00349537i
$358$	13.4863	−	6.00449i	0.712773	−	0.317347i
$359$	11.4218	−	35.1526i	0.602817	−	1.85528i	0.0916672	−	0.995790i	$-0.470780\pi$
$359$	11.4218	−	35.1526i	0.602817	−	1.85528i	0.511150	−	0.859491i	$-0.329220\pi$
$360$	−4.70244	+	4.78404i	−0.247841	+	0.252141i
$361$	−4.94223	−	15.2106i	−0.260118	−	0.800560i
$362$	4.66082	+	5.17636i	0.244967	+	0.272063i
$363$	−5.85416	+	29.3296i	−0.307264	+	1.53940i
$364$	−1.49490	+	1.66025i	−0.0783540	+	0.0870210i
$365$	−26.2506	−	7.49328i	−1.37402	−	0.392216i
$366$	−3.19428	+	16.0035i	−0.166968	+	0.836515i
$367$	10.3076	−	4.58925i	0.538054	−	0.239557i	−0.119673	−	0.992813i	$-0.538185\pi$
$367$	10.3076	−	4.58925i	0.538054	−	0.239557i	0.657727	+	0.753256i	$0.271518\pi$
$368$	5.14987			0.268456
$369$	26.7521	−	20.4715i	1.39266	−	1.06571i
$370$	0.507850	+	1.03809i	0.0264019	+	0.0539680i
$371$	−0.962600	−	9.15853i	−0.0499757	−	0.475487i
$372$	−4.31810	−	1.34393i	−0.223883	−	0.0696797i
$373$	−10.9344	+	12.1438i	−0.566160	+	0.628784i	−0.956446	−	0.291910i	$-0.905709\pi$
$373$	−10.9344	+	12.1438i	−0.566160	+	0.628784i	0.390286	+	0.920694i	$0.372376\pi$
$374$	−0.111842	−	0.193717i	−0.00578323	−	0.0100168i
$375$	0.310125	+	19.3624i	0.0160148	+	0.999872i
$376$	0.612570	−	1.06100i	0.0315909	−	0.0547171i
$377$	3.29042	+	10.1269i	0.169465	+	0.521561i
$378$	−5.86116	−	0.395828i	−0.301466	−	0.0203592i
$379$	10.6333	−	7.72552i	0.546194	−	0.396833i	−0.280186	−	0.959946i	$-0.590396\pi$
$379$	10.6333	−	7.72552i	0.546194	−	0.396833i	0.826380	+	0.563112i	$0.190396\pi$
$380$	3.86811	+	0.265839i	0.198430	+	0.0136372i
$381$	7.99530	−	4.74955i	0.409612	−	0.243327i
$382$	5.64510	+	9.77760i	0.288828	+	0.500265i
$383$	2.00062	−	19.0346i	0.102227	−	0.972622i	−0.816398	−	0.577490i	$-0.804032\pi$
$383$	2.00062	−	19.0346i	0.102227	−	0.972622i	0.918624	−	0.395132i	$-0.129301\pi$
$384$	1.64050	−	0.555666i	0.0837163	−	0.0283562i
$385$	3.26716	+	13.0375i	0.166510	+	0.664450i
$386$	−0.586520	−	1.80512i	−0.0298531	−	0.0918783i
$387$	−0.409625	+	5.11831i	−0.0208224	+	0.260178i
$388$	3.44470	−	10.6017i	0.174878	−	0.538220i
$389$	27.8315	+	5.91576i	1.41111	+	0.299941i	0.849556	−	0.527498i	$-0.176870\pi$
$389$	27.8315	+	5.91576i	1.41111	+	0.299941i	0.561556	+	0.827439i	$0.310203\pi$
$390$	7.13455	+	2.77008i	0.361272	+	0.140269i
$391$	−0.211931	+	0.0450473i	−0.0107178	+	0.00227814i
$392$	0.598097	−	5.69051i	0.0302085	−	0.287414i
$393$	26.8139	−	3.15568i	1.35258	−	0.159183i
$394$	−7.83969	+	3.49046i	−0.394958	+	0.175847i
$395$	16.1310	+	8.55231i	0.811641	+	0.430313i
$396$	15.6792	+	2.92740i	0.787910	+	0.147107i
$397$	−14.4618	+	10.5071i	−0.725818	+	0.527337i	−0.888238	−	0.459384i	$-0.848070\pi$
$397$	−14.4618	+	10.5071i	−0.725818	+	0.527337i	0.162420	+	0.986722i	$0.448070\pi$
$398$	14.5780	+	3.09866i	0.730731	+	0.155322i
$399$	2.02974	+	2.72190i	0.101614	+	0.136265i
$400$	2.18111	−	4.49920i	0.109055	−	0.224960i
$401$	0.286898	+	0.496922i	0.0143270	+	0.0248151i	0.873100	−	0.487541i	$-0.162106\pi$
$401$	0.286898	+	0.496922i	0.0143270	+	0.0248151i	−0.858773	+	0.512356i	$0.828773\pi$
$402$	22.2727	+	2.06141i	1.11086	+	0.102814i
$403$	0.539330	+	5.13138i	0.0268660	+	0.255612i
$404$	5.08771	−	3.69644i	0.253123	−	0.183905i
$405$	5.85601	+	19.2538i	0.290988	+	0.956727i
$406$	4.92840	+	3.58069i	0.244592	+	0.177707i
$407$	1.37391	−	2.37969i	0.0681023	−	0.117957i
$408$	−0.0626502	+	0.0372169i	−0.00310165	+	0.00184251i
$409$	16.7016	−	3.55003i	0.825839	−	0.175538i	0.224442	−	0.974488i	$-0.427944\pi$
$409$	16.7016	−	3.55003i	0.825839	−	0.175538i	0.601397	+	0.798950i	$0.294611\pi$
$410$	−14.0154	+	20.8324i	−0.692173	+	1.02884i
$411$	−21.1843	+	29.9331i	−1.04494	+	1.47649i
$412$	−3.53842	−	3.92981i	−0.174325	−	0.193608i
$413$	1.02802	−	3.16393i	0.0505857	−	0.155687i
$414$	7.38985	−	13.5676i	0.363192	−	0.666813i
$415$	0.611135	−	3.49031i	0.0299994	−	0.171333i
$416$	−1.32228	−	1.46854i	−0.0648299	−	0.0720009i
$417$	2.82811	+	1.58627i	0.138493	+	0.0776802i
$418$	−4.60947	−	7.98383i	−0.225456	−	0.390502i
$419$	−3.14813	+	29.9525i	−0.153796	+	1.46327i	0.596735	+	0.802438i	$0.296464\pi$
$419$	−3.14813	+	29.9525i	−0.153796	+	1.46327i	−0.750531	+	0.660835i	$0.770202\pi$
$420$	4.23371	−	1.11706i	0.206584	−	0.0545072i
$421$	1.93944	+	18.4525i	0.0945226	+	0.899322i	0.934323	+	0.356427i	$0.116005\pi$
$421$	1.93944	+	18.4525i	0.0945226	+	0.899322i	−0.839801	+	0.542895i	$0.817328\pi$
$422$	4.00019	−	2.90631i	0.194726	−	0.141477i
$423$	−1.91626	−	3.13635i	−0.0931718	−	0.152494i
$424$	8.14557			0.395584
$425$	−0.0504025	+	0.204232i	−0.00244488	+	0.00990672i
$426$	5.07267	+	6.80250i	0.245772	+	0.329582i
$427$	7.12751	−	7.91590i	0.344924	−	0.383077i
$428$	11.4382	+	5.09264i	0.552889	+	0.246162i
$429$	−4.00445	−	17.7516i	−0.193337	−	0.857055i
$430$	−0.930313	−	3.71237i	−0.0448637	−	0.179026i
$431$	−19.4458	−	14.1282i	−0.936669	−	0.680530i	0.0109476	−	0.999940i	$-0.496515\pi$
$431$	−19.4458	−	14.1282i	−0.936669	−	0.680530i	−0.947617	+	0.319410i	$0.896515\pi$
$432$	0.890113	−	5.11935i	0.0428256	−	0.246305i
$433$	29.8445	+	21.6833i	1.43424	+	1.04203i	0.989208	+	0.146516i	$0.0468060\pi$
$433$	29.8445	+	21.6833i	1.43424	+	1.04203i	0.445027	+	0.895517i	$0.353194\pi$
$434$	1.97519	+	2.19367i	0.0948123	+	0.105300i
$435$	5.47846	−	20.1372i	0.262672	−	0.965504i
$436$	−11.1381	+	12.3701i	−0.533416	+	0.592419i
$437$	−8.73451	+	1.85658i	−0.417828	+	0.0888121i
$438$	20.0281	−	6.78386i	0.956978	−	0.324145i
$439$	22.2912	+	4.73814i	1.06390	+	0.226139i	0.706428	−	0.707785i	$-0.250305\pi$
$439$	22.2912	+	4.73814i	1.06390	+	0.226139i	0.357473	+	0.933924i	$0.383639\pi$
$440$	−11.7709	+	1.66864i	−0.561153	+	0.0795491i
$441$	−14.1337	−	9.74137i	−0.673035	−	0.463875i
$442$	0.0672608	+	0.0488678i	0.00319927	+	0.00232440i
$443$	−5.31471	+	9.20535i	−0.252510	+	0.437359i	−0.964216	−	0.265118i	$-0.914589\pi$
$443$	−5.31471	+	9.20535i	−0.252510	+	0.437359i	0.711707	+	0.702477i	$0.247923\pi$
$444$	−0.780744	−	0.437916i	−0.0370525	−	0.0207826i
$445$	−34.7263	−	9.91270i	−1.64618	−	0.469907i
$446$	7.57219	+	3.37136i	0.358554	+	0.159638i
$447$	−18.6159	+	17.1855i	−0.880501	+	0.812849i
$448$	−1.10584	−	0.235055i	−0.0522463	−	0.0111053i
$449$	−20.6291			−0.973546			−0.486773	−	0.873528i	$-0.661826\pi$
$449$	−20.6291			−0.973546			−0.486773	+	0.873528i	$0.661826\pi$
$450$	−8.72360	−	12.2024i	−0.411234	−	0.575227i
$451$	59.7000			2.81116
$452$	17.5900	+	3.73886i	0.827362	+	0.175861i
$453$	8.50219	+	2.64616i	0.399468	+	0.124327i
$454$	0.0893960	+	0.0398017i	0.00419556	+	0.00186799i
$455$	−3.08029	−	3.93289i	−0.144406	−	0.184377i
$456$	−2.58207	+	1.53386i	−0.120916	+	0.0718295i
$457$	−8.38678	+	14.5263i	−0.392317	+	0.679513i	−0.992755	−	0.120158i	$-0.961660\pi$
$457$	−8.38678	+	14.5263i	−0.392317	+	0.679513i	0.600438	+	0.799672i	$0.294993\pi$
$458$	9.76294	+	7.09319i	0.456192	+	0.331443i
$459$	0.00814976	+	0.218460i	0.000380398	+	0.0101969i
$460$	−1.98608	+	11.3429i	−0.0926016	+	0.528866i
$461$	−35.6970	−	7.58764i	−1.66258	−	0.353392i	−0.721717	−	0.692188i	$-0.756647\pi$
$461$	−35.6970	−	7.58764i	−1.66258	−	0.353392i	−0.940860	+	0.338797i	$0.889980\pi$
$462$	−7.82290	−	6.86964i	−0.363954	−	0.319605i
$463$	−12.9332	+	2.74904i	−0.601058	+	0.127759i	−0.498384	−	0.866956i	$-0.666073\pi$
$463$	−12.9332	+	2.74904i	−0.601058	+	0.127759i	−0.102674	+	0.994715i	$0.532740\pi$
$464$	−3.60553	+	4.00435i	−0.167382	+	0.185897i
$465$	4.62540	−	8.99258i	0.214498	−	0.417021i
$466$	−13.3884	−	14.8694i	−0.620207	−	0.688810i
$467$	7.38314	+	5.36417i	0.341651	+	0.248224i	0.745358	−	0.666664i	$-0.232278\pi$
$467$	7.38314	+	5.36417i	0.341651	+	0.248224i	−0.403707	+	0.914888i	$0.632278\pi$
$468$	−5.76636	+	1.37632i	−0.266550	+	0.0636206i
$469$	−11.8117	−	8.58170i	−0.545413	−	0.396266i
$470$	2.10068	+	1.75841i	0.0968972	+	0.0811092i
$471$	−12.7921	+	11.8092i	−0.589429	+	0.544141i
$472$	2.68819	+	1.19686i	0.123734	+	0.0550900i
$473$	−6.08901	+	6.76253i	−0.279973	+	0.310941i
$474$	−14.0456	+	1.65300i	−0.645136	+	0.0759248i
$475$	−2.07729	+	8.41723i	−0.0953126	+	0.386209i
$476$	0.0475645			0.00218011
$477$	11.6886	−	21.4600i	0.535182	−	0.982585i
$478$	−18.3015	+	13.2968i	−0.837089	+	0.608181i
$479$	3.54514	+	33.7297i	0.161982	+	1.54115i	0.709709	+	0.704495i	$0.248826\pi$
$479$	3.54514	+	33.7297i	0.161982	+	1.54115i	−0.547728	+	0.836657i	$0.684507\pi$
$480$	0.591218	+	3.82759i	0.0269853	+	0.174705i
$481$	−0.106756	+	1.01571i	−0.00486764	+	0.0463125i
$482$	−5.17149	−	8.95727i	−0.235555	−	0.407993i
$483$	−8.66994	+	5.15032i	−0.394496	+	0.234348i
$484$	11.5542	+	12.8322i	0.525191	+	0.583283i
$485$	22.0224	+	11.6758i	0.999986	+	0.530170i
$486$	−12.2099	−	9.69110i	−0.553854	−	0.439597i
$487$	−4.99429	+	15.3708i	−0.226313	+	0.696519i	0.771843	+	0.635813i	$0.219335\pi$
$487$	−4.99429	+	15.3708i	−0.226313	+	0.696519i	−0.998156	+	0.0607060i	$0.980665\pi$
$488$	6.30446	+	7.00181i	0.285389	+	0.316957i
$489$	−37.4577	−	3.46683i	−1.69389	−	0.156776i
$490$	12.3030	+	3.51193i	0.555794	+	0.158653i
$491$	22.5890	−	4.80145i	1.01943	−	0.216686i	0.332263	−	0.943187i	$-0.392188\pi$
$491$	22.5890	−	4.80145i	1.01943	−	0.216686i	0.687166	+	0.726501i	$0.258855\pi$
$492$	−0.241729	−	19.4472i	−0.0108980	−	0.876749i
$493$	0.113350	−	0.196328i	0.00510502	−	0.00884215i
$494$	2.77208	+	2.01404i	0.124722	+	0.0906158i
$495$	−12.4946	+	33.4054i	−0.561589	+	1.50146i
$496$	−2.11235	+	1.53471i	−0.0948474	+	0.0689107i
$497$	−0.578959	−	5.50843i	−0.0259699	−	0.247087i
$498$	1.14745	+	2.49335i	0.0514186	+	0.111730i
$499$	−9.74981	−	16.8872i	−0.436461	−	0.755973i	0.560952	−	0.827848i	$-0.310435\pi$
$499$	−9.74981	−	16.8872i	−0.436461	−	0.755973i	−0.997414	+	0.0718748i	$0.977102\pi$
$500$	9.06859	+	6.53916i	0.405560	+	0.292440i
$501$	22.1429	−	2.60596i	0.989273	−	0.116426i
$502$	9.51907	+	2.02334i	0.424857	+	0.0903061i
$503$	−10.9747	+	7.97356i	−0.489336	+	0.355524i	−0.804929	−	0.593371i	$-0.797797\pi$
$503$	−10.9747	+	7.97356i	−0.489336	+	0.355524i	0.315593	+	0.948895i	$0.397797\pi$
$504$	−2.20611	+	2.57612i	−0.0982678	+	0.114749i
$505$	6.17951	+	12.6315i	0.274985	+	0.562096i
$506$	25.0133	−	11.1366i	1.11197	−	0.495083i
$507$	−9.41705	−	12.6284i	−0.418226	−	0.560845i
$508$	0.561228	−	5.33973i	0.0249005	−	0.236912i
$509$	−16.0511	+	3.41176i	−0.711450	+	0.151223i	−0.549401	−	0.835559i	$-0.685144\pi$
$509$	−16.0511	+	3.41176i	−0.711450	+	0.151223i	−0.162050	+	0.986783i	$0.551811\pi$
$510$	−0.0578111	−	0.152344i	−0.00255992	−	0.00674590i
$511$	−13.5007	−	2.86967i	−0.597238	−	0.126947i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	0.335884	+	9.00362i	0.0148296	+	0.397520i
$514$	4.79895	+	14.7697i	0.211673	+	0.651461i
$515$	10.0203	−	6.27802i	0.441545	−	0.276642i
$516$	2.22754	+	1.95611i	0.0980621	+	0.0861128i
$517$	0.680870	−	6.47804i	0.0299446	−	0.284904i
$518$	0.292150	+	0.506018i	0.0128363	+	0.0222332i
$519$	−0.467066	−	37.5757i	−0.0205019	−	1.64939i
$520$	3.74448	−	2.34604i	0.164207	−	0.102881i
$521$	−25.0547	+	18.2033i	−1.09766	+	0.797500i	−0.980677	−	0.195634i	$-0.937324\pi$
$521$	−25.0547	+	18.2033i	−1.09766	+	0.797500i	−0.116987	+	0.993133i	$0.537324\pi$
$522$	5.37590	+	15.2450i	0.235297	+	0.667257i
$523$	6.86175	+	21.1183i	0.300043	+	0.923438i	0.981481	+	0.191562i	$0.0613552\pi$
$523$	6.86175	+	21.1183i	0.300043	+	0.923438i	−0.681437	+	0.731877i	$0.738645\pi$
$524$	7.79393	−	13.4995i	0.340479	−	0.589728i
$525$	0.827643	+	9.75581i	0.0361213	+	0.425778i
$526$	−14.7171	−	25.4907i	−0.641694	−	1.11145i
$527$	0.0735043	−	0.0816347i	0.00320190	−	0.00355607i
$528$	6.76637	−	6.24649i	0.294469	−	0.271843i
$529$	−0.368066	−	3.50191i	−0.0160029	−	0.152257i
$530$	−3.14139	+	17.9411i	−0.136453	+	0.779312i
$531$	7.01064	−	5.36475i	0.304236	−	0.232810i
$532$	1.96032			0.0849907
$533$	−20.2709	+	9.02517i	−0.878028	+	0.390923i
$534$	26.4947	−	8.97423i	1.14654	−	0.388353i
$535$	−15.6281	+	23.2294i	−0.675660	+	1.00430i
$536$	8.64123	−	9.59706i	0.373244	−	0.414530i
$537$	−19.2131	−	16.8719i	−0.829105	−	0.728075i
$538$	−12.4403	−	13.8164i	−0.536341	−	0.595667i
$539$	−9.40076	−	28.9326i	−0.404919	−	1.24621i
$540$	10.9324	+	3.93484i	0.470455	+	0.169328i
$541$	11.3235	−	34.8502i	0.486835	−	1.49833i	−0.342470	−	0.939529i	$-0.611263\pi$
$541$	11.3235	−	34.8502i	0.486835	−	1.49833i	0.829305	−	0.558796i	$-0.188737\pi$
$542$	−16.3857	+	7.29540i	−0.703828	+	0.313364i
$543$	4.76974	−	11.0817i	0.204689	−	0.475560i
$544$	−0.00439772	+	0.0418415i	−0.000188551	+	0.00179394i
$545$	−22.9503	−	29.3028i	−0.983085	−	1.25520i
$546$	3.69475	+	1.14993i	0.158121	+	0.0492123i
$547$	−3.44671	−	32.7933i	−0.147371	−	1.40214i	−0.779075	−	0.626930i	$-0.784311\pi$
$547$	−3.44671	−	32.7933i	−0.147371	−	1.40214i	0.631704	−	0.775209i	$-0.282356\pi$
$548$	6.54252	+	20.1358i	0.279482	+	0.860159i
$549$	27.4933	−	6.56215i	1.17339	−	0.280066i
$550$	0.864236	−	26.5695i	0.0368511	−	1.13293i
$551$	4.67160	−	8.09145i	0.199017	−	0.344707i
$552$	−3.72903	−	8.10296i	−0.158718	−	0.344885i
$553$	8.43309	+	3.75465i	0.358612	+	0.159664i
$554$	16.6804	+	7.42659i	0.708682	+	0.315526i
$555$	1.26563	−	1.55075i	0.0537232	−	0.0658257i
$556$	1.71027	−	0.761459i	0.0725314	−	0.0322931i
$557$	−4.67329			−0.198014			−0.0990069	−	0.995087i	$-0.531567\pi$
$557$	−4.67329			−0.198014			−0.0990069	+	0.995087i	$0.531567\pi$
$558$	1.01216	+	7.76737i	0.0428479	+	0.328819i
$559$	1.04517	−	3.21669i	0.0442059	−	0.136052i
$560$	0.944198	−	2.34504i	0.0398997	−	0.0990960i
$561$	−0.223814	+	0.316246i	−0.00944944	+	0.0133519i
$562$	−14.2403	+	3.02687i	−0.600691	+	0.127681i
$563$	35.9929	−	7.65052i	1.51692	−	0.322431i	0.627170	−	0.778882i	$-0.284213\pi$
$563$	35.9929	−	7.65052i	1.51692	−	0.322431i	0.889749	+	0.456451i	$0.150880\pi$
$564$	−2.11298	−	0.195563i	−0.0889723	−	0.00823468i
$565$	−15.0187	+	37.3010i	−0.631843	+	1.56927i
$566$	3.18446	−	9.80075i	0.133853	−	0.411956i
$567$	3.62126	+	9.50874i	0.152079	+	0.399329i
$568$	4.89918			0.205565
$569$	−38.0087	+	16.9226i	−1.59341	+	0.709430i	−0.995731	−	0.0923072i	$-0.970576\pi$
$569$	−38.0087	+	16.9226i	−1.59341	+	0.709430i	−0.597676	+	0.801738i	$0.703909\pi$
$570$	−2.38263	−	6.27870i	−0.0997972	−	0.262986i
$571$	17.0724	+	7.60113i	0.714458	+	0.318097i	0.731580	−	0.681756i	$-0.238783\pi$
$571$	17.0724	+	7.60113i	0.714458	+	0.318097i	−0.0171213	+	0.999853i	$0.505450\pi$
$572$	−9.59809	−	4.27335i	−0.401316	−	0.178678i
$573$	11.2967	−	15.9621i	0.471928	−	0.666827i
$574$	−6.34732	+	10.9939i	−0.264932	+	0.458876i
$575$	−24.2175	−	8.74893i	−1.00994	−	0.364856i
$576$	−2.06219	−	2.17885i	−0.0859245	−	0.0907854i
$577$	2.31822	+	7.13476i	0.0965089	+	0.297024i	0.987644	−	0.156714i	$-0.0500902\pi$
$577$	2.31822	+	7.13476i	0.0965089	+	0.297024i	−0.891135	+	0.453738i	$0.850090\pi$
$578$	1.77680	+	16.9051i	0.0739051	+	0.703160i
$579$	−2.41553	+	2.22994i	−0.100386	+	0.0926730i
$580$	−7.42931	−	9.48569i	−0.308485	−	0.393872i
$581$	0.187267	−	1.78172i	0.00776913	−	0.0739184i
$582$	−19.1753	+	2.25671i	−0.794843	+	0.0935435i
$583$	39.5635	−	17.6148i	1.63855	−	0.729531i
$584$	3.77264	−	11.6110i	0.156113	−	0.480467i
$585$	−0.807604	−	13.2315i	−0.0333903	−	0.547057i
$586$	−5.59316	−	17.2140i	−0.231051	−	0.711103i
$587$	4.52056	+	5.02059i	0.186583	+	0.207222i	0.829178	−	0.558984i	$-0.188809\pi$
$587$	4.52056	+	5.02059i	0.186583	+	0.207222i	−0.642595	+	0.766206i	$0.722142\pi$
$588$	−9.38670	+	3.17944i	−0.387101	+	0.131118i
$589$	3.02940	−	3.36449i	0.124824	−	0.138632i
$590$	−3.67288	+	5.45933i	−0.151210	+	0.224757i
$591$	11.1687	+	9.80776i	0.459419	+	0.403437i
$592$	−0.472145	+	0.210213i	−0.0194051	+	0.00863969i
$593$	24.3330			0.999235			0.499617	−	0.866246i	$-0.333474\pi$
$593$	24.3330			0.999235			0.499617	+	0.866246i	$0.333474\pi$
$594$	−6.74727	−	26.7899i	−0.276844	−	1.09920i
$595$	−0.0183435	+	0.104764i	−0.000752012	+	0.00429489i
$596$	1.52899	+	14.5474i	0.0626300	+	0.595885i
$597$	−5.68045	−	25.1812i	−0.232485	−	1.03060i
$598$	−6.80956	+	7.56278i	−0.278464	+	0.309265i
$599$	−2.11060	−	3.65567i	−0.0862369	−	0.149367i	0.819681	−	0.572821i	$-0.194151\pi$
$599$	−2.11060	−	3.65567i	−0.0862369	−	0.149367i	−0.905918	+	0.423454i	$0.860818\pi$
$600$	−8.65851	−	0.173942i	−0.353482	−	0.00710117i
$601$	3.24764	−	5.62507i	0.132474	−	0.229451i	−0.792156	−	0.610319i	$-0.791041\pi$
$601$	3.24764	−	5.62507i	0.132474	−	0.229451i	0.924630	+	0.380868i	$0.124375\pi$
$602$	−0.597949	−	1.84030i	−0.0243706	−	0.0750050i
$603$	−12.8842	−	36.5372i	−0.524685	−	1.48791i
$604$	4.15915	−	3.02180i	0.169233	−	0.122955i
$605$	−32.7197	+	20.5000i	−1.33025	+	0.833442i
$606$	−9.50009	−	5.32855i	−0.385915	−	0.216458i
$607$	−12.1186	−	20.9900i	−0.491879	−	0.851960i	0.508077	−	0.861312i	$-0.330356\pi$
$607$	−12.1186	−	20.9900i	−0.491879	−	0.851960i	−0.999956	+	0.00935199i	$0.997023\pi$
$608$	−0.181247	+	1.72445i	−0.00735056	+	0.0699359i
$609$	2.06530	−	10.3473i	0.0836904	−	0.419292i
$610$	−17.8533	+	11.1857i	−0.722857	+	0.452894i
$611$	0.748135	+	2.30252i	0.0302663	+	0.0931501i
$612$	0.103923	+	0.0716268i	0.00420085	+	0.00289534i
$613$	10.7648	−	33.1306i	0.434785	−	1.33813i	−0.458521	−	0.888684i	$-0.651621\pi$
$613$	10.7648	−	33.1306i	0.434785	−	1.33813i	0.893306	−	0.449448i	$-0.148379\pi$
$614$	0.307552	+	0.0653721i	0.0124118	+	0.00263820i
$615$	42.9269	+	6.96753i	1.73098	+	0.280958i
$616$	−5.87946	+	1.24972i	−0.236890	+	0.0503526i
$617$	2.21077	−	21.0340i	0.0890021	−	0.846799i	−0.855392	−	0.517982i	$-0.826683\pi$
$617$	2.21077	−	21.0340i	0.0890021	−	0.846799i	0.944394	−	0.328817i	$-0.106650\pi$
$618$	−3.62111	+	8.41303i	−0.145662	+	0.338422i
$619$	−11.2468	+	5.00738i	−0.452046	+	0.201264i	−0.620114	−	0.784512i	$-0.712914\pi$
$619$	−11.2468	+	5.00738i	−0.452046	+	0.201264i	0.168068	+	0.985775i	$0.446247\pi$
$620$	−2.56566	−	5.24446i	−0.103039	−	0.210622i
$621$	−26.6987	−	1.80307i	−1.07138	−	0.0723548i
$622$	18.6184	−	13.5270i	0.746529	−	0.542385i
$623$	−17.8598	−	3.79623i	−0.715539	−	0.152093i
$624$	−1.35318	+	3.14388i	−0.0541704	+	0.125856i
$625$	−17.9003	+	17.4522i	−0.716010	+	0.698090i
$626$	4.65351	+	8.06011i	0.185992	+	0.322147i
$627$	−9.22428	+	13.0338i	−0.368382	+	0.520519i
$628$	1.05066	+	9.99640i	0.0419260	+	0.398900i
$629$	0.0175912	−	0.0127808i	0.000701408	−	0.000509603i
$630$	−4.82326	−	5.85258i	−0.192163	−	0.233172i
$631$	−11.4883	−	8.34671i	−0.457341	−	0.332277i	0.335147	−	0.942166i	$-0.391214\pi$
$631$	−11.4883	−	8.34671i	−0.457341	−	0.332277i	−0.792487	+	0.609889i	$0.791214\pi$
$632$	−4.08260	+	7.07127i	−0.162397	+	0.281280i
$633$	−7.46941	−	4.18956i	−0.296883	−	0.166520i
$634$	−17.0520	+	3.62452i	−0.677222	+	0.143948i
$635$	11.5446	+	3.29544i	0.458135	+	0.130776i
$636$	−5.89821	−	12.8165i	−0.233879	−	0.508206i
$637$	7.56588	+	8.40276i	0.299771	+	0.332929i
$638$	−8.85287	+	27.2463i	−0.350488	+	1.07869i
$639$	7.03012	−	12.9072i	0.278107	−	0.510600i
$640$	1.97558	+	1.04741i	0.0780918	+	0.0414025i
$641$	4.51572	+	5.01522i	0.178360	+	0.198089i	0.825695	−	0.564116i	$-0.190783\pi$
$641$	4.51572	+	5.01522i	0.178360	+	0.198089i	−0.647335	+	0.762206i	$0.724116\pi$
$642$	−0.269543	−	21.6848i	−0.0106380	−	0.855833i
$643$	18.6988	+	32.3872i	0.737407	+	1.27723i	0.953659	+	0.300889i	$0.0972833\pi$
$643$	18.6988	+	32.3872i	0.737407	+	1.27723i	−0.216252	+	0.976338i	$0.569383\pi$
$644$	−0.608585	+	5.79030i	−0.0239816	+	0.228170i
$645$	−5.16751	+	4.15191i	−0.203471	+	0.163481i
$646$	−0.00762544	−	0.0725512i	−0.000300019	−	0.00285449i
$647$	−17.7235	+	12.8769i	−0.696784	+	0.506243i	−0.878883	−	0.477037i	$-0.841711\pi$
$647$	−17.7235	+	12.8769i	−0.696784	+	0.506243i	0.182099	+	0.983280i	$0.441711\pi$
$648$	−8.69946	+	2.30639i	−0.341747	+	0.0906036i
$649$	15.6449			0.614117
$650$	3.72321	+	9.15222i	0.146036	+	0.358979i
$651$	2.02135	−	4.69627i	0.0792230	−	0.184061i
$652$	−14.5326	+	16.1401i	−0.569141	+	0.632095i
$653$	25.8109	+	11.4918i	1.01006	+	0.449707i	0.843963	−	0.536402i	$-0.180217\pi$
$653$	25.8109	+	11.4918i	1.01006	+	0.449707i	0.166097	+	0.986109i	$0.446884\pi$
$654$	27.5285	+	8.56777i	1.07645	+	0.335026i
$655$	26.7276	+	22.3728i	1.04434	+	0.874176i
$656$	−9.08423	−	6.60008i	−0.354680	−	0.257690i
$657$	−25.1763	−	26.6005i	−0.982220	−	1.03779i
$658$	1.12056	+	0.814132i	0.0436838	+	0.0317382i
$659$	11.3500	+	12.6055i	0.442134	+	0.491040i	0.922483	−	0.386038i	$-0.126157\pi$
$659$	11.3500	+	12.6055i	0.442134	+	0.491040i	−0.480349	+	0.877078i	$0.659490\pi$
$660$	11.1488	+	17.3123i	0.433965	+	0.673882i
$661$	4.51795	−	5.01769i	0.175728	−	0.195165i	−0.648846	−	0.760920i	$-0.724748\pi$
$661$	4.51795	−	5.01769i	0.175728	−	0.195165i	0.824574	+	0.565754i	$0.191415\pi$
$662$	−14.7092	+	3.12654i	−0.571689	+	0.121516i
$663$	0.0281864	−	0.141215i	0.00109467	−	0.00548435i
$664$	1.55003	+	0.329469i	0.0601529	+	0.0127859i
$665$	−0.756011	+	4.31772i	−0.0293168	+	0.167434i
$666$	−0.123691	+	1.54554i	−0.00479295	+	0.0598885i
$667$	22.4498	+	16.3107i	0.869259	+	0.631554i
$668$	6.43623	−	11.1479i	0.249025	−	0.431324i
$669$	−0.178439	−	14.3555i	−0.00689886	−	0.555016i
$670$	17.8055	+	22.7340i	0.687888	+	0.878291i
$671$	45.7626	+	20.3748i	1.76664	+	0.786561i
$672$	0.430901	+	1.91017i	0.0166224	+	0.0736865i
$673$	−34.2638	−	7.28300i	−1.32077	−	0.280739i	−0.507012	−	0.861939i	$-0.669250\pi$
$673$	−34.2638	−	7.28300i	−1.32077	−	0.280739i	−0.813761	+	0.581200i	$0.802583\pi$
$674$	−24.2099			−0.932532
$675$	−12.8829	+	22.5617i	−0.495861	+	0.868402i
$676$	−9.09498			−0.349807
$677$	−6.28726	−	1.33640i	−0.241639	−	0.0513620i	0.0855000	−	0.996338i	$-0.472751\pi$
$677$	−6.28726	−	1.33640i	−0.241639	−	0.0513620i	−0.327139	+	0.944976i	$0.606085\pi$
$678$	−6.85407	−	30.3839i	−0.263229	−	1.16689i
$679$	11.5130	+	5.12593i	0.441829	+	0.196715i
$680$	−0.0904624	−	0.0258227i	−0.00346907	−	0.000990255i
$681$	−0.00210662	−	0.169479i	−8.07260e−5	−	0.00649444i
$682$	−6.94100	+	12.0222i	−0.265785	+	0.460353i
$683$	−38.0244	−	27.6263i	−1.45496	−	1.05709i	−0.984640	−	0.174596i	$-0.944138\pi$
$683$	−38.0244	−	27.6263i	−1.45496	−	1.05709i	−0.470321	−	0.882495i	$-0.655862\pi$
$684$	4.28309	+	2.95203i	0.163768	+	0.112874i
$685$	−46.8735	+	6.64478i	−1.79094	+	0.253884i
$686$	14.0684	+	2.99033i	0.537134	+	0.114171i
$687$	4.09128	−	20.4975i	0.156092	−	0.782028i
$688$	1.67416	−	0.355853i	0.0638267	−	0.0135668i
$689$	−10.7707	+	11.9621i	−0.410331	+	0.455718i
$690$	19.2854	−	5.08845i	0.734182	−	0.193714i
$691$	−5.99933	−	6.66293i	−0.228225	−	0.253470i	0.618146	−	0.786063i	$-0.287884\pi$
$691$	−5.99933	−	6.66293i	−0.228225	−	0.253470i	−0.846371	+	0.532594i	$0.821217\pi$
$692$	−17.5524	−	12.7526i	−0.667243	−	0.484781i
$693$	−5.14433	+	17.2831i	−0.195417	+	0.656530i
$694$	23.7945	+	17.2877i	0.903225	+	0.656231i
$695$	1.01758	+	4.06062i	0.0385992	+	0.154028i
$696$	8.91132	+	2.77349i	0.337783	+	0.105129i
$697$	0.431572	+	0.192148i	0.0163470	+	0.00727814i
$698$	7.37659	−	8.19253i	0.279208	−	0.310092i
$699$	−13.7013	+	31.8326i	−0.518231	+	1.20402i
$700$	4.80095	+	2.98403i	0.181459	+	0.112786i
$701$	0.496017			0.0187343			0.00936715	−	0.999956i	$-0.497018\pi$
$701$	0.496017			0.0187343			0.00936715	+	0.999956i	$0.497018\pi$
$702$	6.34097	+	8.07635i	0.239325	+	0.304822i
$703$	0.725004	−	0.526746i	0.0273441	−	0.0198666i
$704$	−0.555748	−	5.28759i	−0.0209455	−	0.199284i
$705$	1.24562	−	4.57853i	0.0469128	−	0.172438i
$706$	−2.15587	+	20.5117i	−0.0811371	+	0.771968i
$707$	3.55487	+	6.15722i	0.133695	+	0.231566i
$708$	−0.0633474	−	5.09633i	−0.00238074	−	0.191532i
$709$	12.0364	+	13.3678i	0.452038	+	0.502039i	0.925485	−	0.378783i	$-0.123657\pi$
$709$	12.0364	+	13.3678i	0.452038	+	0.502039i	−0.473448	+	0.880822i	$0.656991\pi$
$710$	−1.88940	+	10.7907i	−0.0709080	+	0.404969i
$711$	12.7713	+	20.9028i	0.478962	+	0.783917i
$712$	4.99075	−	15.3599i	0.187036	−	0.575638i
$713$	8.99739	+	9.99261i	0.336955	+	0.374226i
$714$	−0.0344415	−	0.0748393i	−0.00128894	−	0.00280079i
$715$	13.1139	−	19.4923i	0.490431	−	0.728972i
$716$	−14.4400	+	3.06932i	−0.539648	+	0.114706i
$717$	34.1736	+	19.1678i	1.27624	+	0.715836i
$718$	−18.4808	+	32.0097i	−0.689697	+	1.19459i
$719$	−3.43978	−	2.49915i	−0.128282	−	0.0932025i	0.521794	−	0.853072i	$-0.325263\pi$
$719$	−3.43978	−	2.49915i	−0.128282	−	0.0932025i	−0.650076	+	0.759869i	$0.725263\pi$
$720$	5.59434	−	3.70180i	0.208489	−	0.137958i
$721$	4.83666	−	3.51404i	0.180127	−	0.130870i
$722$	1.67177	+	15.9058i	0.0622167	+	0.591952i
$723$	−10.3490	+	14.6229i	−0.384882	+	0.543833i
$724$	−3.48274	−	6.03228i	−0.129435	−	0.224188i
$725$	23.7580	−	12.7053i	0.882349	−	0.471862i
$726$	11.8242	−	27.4715i	0.438837	−	1.01956i
$727$	38.7956	+	8.24625i	1.43885	+	0.305837i	0.860290	−	0.509805i	$-0.170282\pi$
$727$	38.7956	+	8.24625i	1.43885	+	0.305837i	0.578558	+	0.815641i	$0.303616\pi$
$728$	1.80742	−	1.31317i	0.0669874	−	0.0486692i
$729$	−6.40703	+	26.2288i	−0.237298	+	0.971437i
$730$	24.1190	+	12.7873i	0.892683	+	0.473280i
$731$	−0.0657832	+	0.0292886i	−0.00243308	+	0.00108328i
$732$	6.45179	−	14.9896i	0.238465	−	0.554033i
$733$	0.235100	−	2.23683i	0.00868361	−	0.0826190i	−0.989322	−	0.145748i	$-0.953441\pi$
$733$	0.235100	−	2.23683i	0.00868361	−	0.0826190i	0.998005	+	0.0631287i	$0.0201079\pi$
$734$	−11.0365	+	2.34589i	−0.407366	+	0.0865884i
$735$	−3.38287	−	21.9009i	−0.124779	−	0.807828i
$736$	−5.03734	−	1.07072i	−0.185679	−	0.0394672i
$737$	21.2173	−	65.3002i	0.781550	−	2.40536i
$738$	−30.4238	+	14.4621i	−1.11992	+	0.532357i
$739$	−3.00386	−	9.24492i	−0.110499	−	0.340080i	0.880483	−	0.474078i	$-0.157218\pi$
$739$	−3.00386	−	9.24492i	−0.110499	−	0.340080i	−0.990982	+	0.133998i	$0.957218\pi$
$740$	−0.280920	−	1.12100i	−0.0103268	−	0.0412087i
$741$	1.16168	−	5.82004i	0.0426752	−	0.213805i
$742$	−0.962600	+	9.15853i	−0.0353382	+	0.336220i
$743$	−21.8268	−	37.8051i	−0.800747	−	1.38693i	−0.919125	−	0.393966i	$-0.871103\pi$
$743$	−21.8268	−	37.8051i	−0.800747	−	1.38693i	0.118378	−	0.992969i	$-0.462230\pi$
$744$	3.94432	+	2.21235i	0.144606	+	0.0811087i
$745$	−32.6312	−	2.24260i	−1.19551	−	0.0821625i
$746$	13.2203	−	9.60508i	0.484028	−	0.351667i
$747$	3.09224	−	3.61087i	0.113139	−	0.132115i
$748$	0.0691224	+	0.212737i	0.00252736	+	0.00777843i
$749$	−7.07765	+	12.2589i	−0.258612	+	0.447929i
$750$	3.72233	−	19.0038i	0.135920	−	0.693921i
$751$	15.7858	+	27.3418i	0.576031	+	0.997715i	0.995929	+	0.0901433i	$0.0287325\pi$
$751$	15.7858	+	27.3418i	0.576031	+	0.997715i	−0.419898	+	0.907571i	$0.637934\pi$
$752$	−0.819779	+	0.910457i	−0.0298943	+	0.0332010i
$753$	−3.70918	−	16.4427i	−0.135170	−	0.599205i
$754$	−1.11302	−	10.5897i	−0.0405339	−	0.385654i
$755$	5.05169	+	10.3262i	0.183850	+	0.375807i
$756$	5.65078	+	1.60578i	0.205517	+	0.0584017i
$757$	−22.8585			−0.830807			−0.415403	−	0.909637i	$-0.636360\pi$
$757$	−22.8585			−0.830807			−0.415403	+	0.909637i	$0.636360\pi$
$758$	−12.0071	+	5.34592i	−0.436118	+	0.194172i
$759$	−35.6348	−	31.2925i	−1.29346	−	1.13585i
$760$	−3.72831	−	1.06426i	−0.135240	−	0.0386046i
$761$	−18.3503	+	20.3801i	−0.665197	+	0.738776i	−0.977437	−	0.211227i	$-0.932254\pi$
$761$	−18.3503	+	20.3801i	−0.665197	+	0.738776i	0.312240	+	0.950003i	$0.398921\pi$
$762$	−8.80807	+	2.98345i	−0.319083	+	0.108079i
$763$	−12.5921	−	13.9850i	−0.455866	−	0.506290i
$764$	−3.48886	−	10.7376i	−0.126223	−	0.388473i
$765$	−0.197841	+	0.201274i	−0.00715296	+	0.00727707i
$766$	−5.91441	+	18.2027i	−0.213696	+	0.657689i
$767$	−5.31217	+	2.36513i	−0.191811	+	0.0853999i
$768$	−1.72018	+	0.202444i	−0.0620716	+	0.00730508i
$769$	−1.27911	+	12.1699i	−0.0461259	+	0.438858i	0.946950	+	0.321382i	$0.104147\pi$
$769$	−1.27911	+	12.1699i	−0.0461259	+	0.438858i	−0.993076	+	0.117477i	$0.962519\pi$
$770$	−0.485126	−	13.4318i	−0.0174827	−	0.484050i
$771$	19.7641	−	18.2455i	0.711786	−	0.657097i
$772$	0.198397	+	1.88762i	0.00714046	+	0.0679369i
$773$	3.41092	+	10.4977i	0.122682	+	0.377577i	0.993472	−	0.114079i	$-0.0363917\pi$
$773$	3.41092	+	10.4977i	0.122682	+	0.377577i	−0.870789	+	0.491656i	$0.836392\pi$
$774$	1.46483	−	4.92130i	0.0526523	−	0.176892i
$775$	12.5407	−	3.62845i	0.450475	−	0.130338i
$776$	−5.57365	+	9.65384i	−0.200082	+	0.346553i
$777$	0.584638	−	0.826085i	0.0209738	−	0.0296356i
$778$	−25.9933	−	11.5730i	−0.931906	−	0.414911i
$779$	17.7868	+	7.91920i	0.637279	+	0.283735i
$780$	−6.40271	−	4.19291i	−0.229254	−	0.150130i
$781$	23.7956	−	10.5945i	0.851474	−	0.379101i
$782$	0.216665			0.00774794
$783$	20.0943	−	19.4975i	0.718112	−	0.696785i
$784$	−1.76815	+	5.44181i	−0.0631482	+	0.194350i
$785$	−22.4229	−	1.54103i	−0.800306	−	0.0550016i
$786$	−26.8841	−	2.48821i	−0.958923	−	0.0887515i
$787$	−25.3824	+	5.39520i	−0.904786	+	0.192318i	−0.636732	−	0.771086i	$-0.719714\pi$
$787$	−25.3824	+	5.39520i	−0.904786	+	0.192318i	−0.268054	+	0.963404i	$0.586381\pi$
$788$	8.39409	−	1.78422i	0.299027	−	0.0635601i
$789$	−29.4512	+	41.6141i	−1.04849	+	1.48150i
$790$	−14.0004	−	11.7193i	−0.498112	−	0.416952i
$791$	−6.28250	+	19.3356i	−0.223380	+	0.687493i
$792$	−14.7279	−	6.12332i	−0.523335	−	0.217583i
$793$	−18.6187			−0.661168
$794$	16.3303	−	7.27074i	0.579542	−	0.258029i
$795$	30.5037	−	8.04841i	1.08186	−	0.285448i
$796$	−13.6152	−	6.06189i	−0.482579	−	0.214858i
$797$	−13.1658	−	5.86180i	−0.466357	−	0.207636i	0.160085	−	0.987103i	$-0.448823\pi$
$797$	−13.1658	−	5.86180i	−0.466357	−	0.207636i	−0.626443	+	0.779468i	$0.715490\pi$
$798$	−1.41947	−	3.08443i	−0.0502487	−	0.109187i
$799$	0.0257720	−	0.0446385i	0.000911749	−	0.00157920i
$800$	−3.06888	+	3.94740i	−0.108501	+	0.139562i
$801$	−33.3051	−	35.1893i	−1.17678	−	1.24335i
$802$	−0.177313	−	0.545713i	−0.00626114	−	0.0192698i
$803$	−6.78487	−	64.5537i	−0.239433	−	2.27805i
$804$	−21.3574	−	6.64712i	−0.753218	−	0.234426i
$805$	−12.5188	−	3.57351i	−0.441229	−	0.125950i
$806$	0.539330	−	5.13138i	0.0189971	−	0.180745i
$807$	−12.7311	+	29.5784i	−0.448154	+	1.04121i
$808$	−5.74506	+	2.55787i	−0.202111	+	0.0899854i
$809$	−3.76821	+	11.5974i	−0.132483	+	0.407742i	−0.995190	−	0.0979629i	$-0.968767\pi$
$809$	−3.76821	+	11.5974i	−0.132483	+	0.407742i	0.862707	+	0.505704i	$0.168767\pi$
$810$	−1.72496	−	20.0505i	−0.0606091	−	0.704504i
$811$	11.2493	+	34.6219i	0.395017	+	1.21574i	0.928948	+	0.370210i	$0.120714\pi$
$811$	11.2493	+	34.6219i	0.395017	+	1.21574i	−0.533931	+	0.845528i	$0.679286\pi$
$812$	−4.07623	−	4.52711i	−0.143048	−	0.158871i
$813$	23.3437	+	20.4992i	0.818700	+	0.718938i
$814$	−1.83865	+	2.04203i	−0.0644448	+	0.0715732i
$815$	−29.9449	−	38.2335i	−1.04892	−	1.33926i
$816$	0.0690190	−	0.0233780i	0.00241615	−	0.000818392i
$817$	−2.71119	+	1.20710i	−0.0948525	+	0.0422310i
$818$	−17.0747			−0.597002
$819$	−0.866043	−	6.64609i	−0.0302620	−	0.232233i
$820$	18.0405	−	17.4632i	0.630000	−	0.609841i
$821$	4.84739	+	46.1198i	0.169175	+	1.60959i	0.668863	+	0.743386i	$0.266781\pi$
$821$	4.84739	+	46.1198i	0.169175	+	1.60959i	−0.499688	+	0.866206i	$0.666552\pi$
$822$	26.9448	−	24.8745i	0.939808	−	0.867599i
$823$	20.9912	−	23.3131i	0.731708	−	0.812645i	−0.256373	−	0.966578i	$-0.582527\pi$
$823$	20.9912	−	23.3131i	0.731708	−	0.812645i	0.988081	+	0.153933i	$0.0491941\pi$
$824$	2.64404	+	4.57961i	0.0921095	+	0.159538i
$825$	−42.4311	+	17.8792i	−1.47726	+	0.622474i
$826$	−1.66337	+	2.88105i	−0.0578762	+	0.100245i
$827$	16.5710	+	51.0003i	0.576231	+	1.77346i	0.631950	+	0.775009i	$0.282255\pi$
$827$	16.5710	+	51.0003i	0.576231	+	1.77346i	−0.0557197	+	0.998446i	$0.517745\pi$
$828$	−10.0492	+	11.7347i	−0.349235	+	0.407810i
$829$	32.0997	−	23.3218i	1.11487	−	0.810001i	0.131447	−	0.991323i	$-0.458038\pi$
$829$	32.0997	−	23.3218i	1.11487	−	0.810001i	0.983424	+	0.181323i	$0.0580378\pi$
$830$	−1.32346	+	3.28698i	−0.0459378	+	0.114093i
$831$	−0.393075	−	31.6230i	−0.0136356	−	1.09699i
$832$	0.988056	+	1.71136i	0.0342547	+	0.0593308i
$833$	0.0251631	−	0.239411i	0.000871850	−	0.00829510i
$834$	−2.43651	−	2.13961i	−0.0843693	−	0.0740885i
$835$	22.0717	+	18.4754i	0.763822	+	0.639369i
$836$	2.84881	+	8.76773i	0.0985281	+	0.303238i
$837$	11.4885	−	7.21691i	0.397101	−	0.249453i
$838$	9.30680	−	28.6434i	0.321498	−	0.989470i
$839$	17.9158	+	3.80811i	0.618521	+	0.131471i	0.506507	−	0.862236i	$-0.330937\pi$
$839$	17.9158	+	3.80811i	0.618521	+	0.131471i	0.112014	+	0.993707i	$0.464270\pi$
$840$	−4.37345	+	0.212416i	−0.150898	+	0.00732905i
$841$	−0.0338623	+	0.00719766i	−0.00116767	+	0.000248195i
$842$	1.93944	−	18.4525i	0.0668376	−	0.635917i
$843$	15.0740	+	20.2143i	0.519175	+	0.696219i
$844$	−4.51703	+	2.01111i	−0.155483	+	0.0692254i
$845$	3.50754	−	20.0322i	0.120663	−	0.689130i
$846$	1.22230	+	3.46622i	0.0420236	+	0.119171i
$847$	−15.7934	+	11.4746i	−0.542668	+	0.394272i
$848$	−7.96757	−	1.69356i	−0.273607	−	0.0581571i
$849$	−17.7267	+	2.08621i	−0.608377	+	0.0715987i
$850$	0.0917634	−	0.189290i	0.00314746	−	0.00649260i
$851$	1.33080	+	2.30501i	0.0456192	+	0.0790147i
$852$	−3.54750	−	7.70851i	−0.121535	−	0.264089i
$853$	−0.374287	−	3.56111i	−0.0128154	−	0.121930i	0.986244	−	0.165297i	$-0.0528582\pi$
$853$	−0.374287	−	3.56111i	−0.0128154	−	0.121930i	−0.999059	+	0.0433669i	$0.986192\pi$
$854$	−8.61756	+	6.26102i	−0.294887	+	0.214248i
$855$	−8.15382	+	8.29530i	−0.278855	+	0.283693i
$856$	−10.1295	−	7.35949i	−0.346218	−	0.251542i
$857$	0.377058	−	0.653084i	0.0128801	−	0.0223089i	−0.859514	−	0.511113i	$-0.829233\pi$
$857$	0.377058	−	0.653084i	0.0128801	−	0.0223089i	0.872394	+	0.488804i	$0.162567\pi$
$858$	0.226180	+	18.1963i	0.00772165	+	0.621210i
$859$	23.3223	−	4.95731i	0.795746	−	0.169141i	0.207939	−	0.978142i	$-0.433325\pi$
$859$	23.3223	−	4.95731i	0.795746	−	0.169141i	0.587808	+	0.809001i	$0.299991\pi$
$860$	0.138138	+	3.82467i	0.00471047	+	0.130420i
$861$	21.8942	+	2.02638i	0.746152	+	0.0690588i
$862$	16.0834	+	17.8624i	0.547803	+	0.608397i
$863$	−2.28766	+	7.04069i	−0.0778728	+	0.239668i	−0.982413	−	0.186720i	$-0.940214\pi$
$863$	−2.28766	+	7.04069i	−0.0778728	+	0.239668i	0.904540	+	0.426388i	$0.140214\pi$
$864$	−1.93503	+	4.82241i	−0.0658312	+	0.164062i
$865$	34.8576	−	33.7422i	1.18519	−	1.14727i
$866$	−24.6841	−	27.4145i	−0.838801	−	0.931582i
$867$	25.3124	−	15.0367i	0.859654	−	0.510672i
$868$	−1.47594	−	2.55640i	−0.0500967	−	0.0867700i
$869$	−4.53780	+	43.1742i	−0.153934	+	1.46459i
$870$	−9.54549	+	18.5581i	−0.323623	+	0.629178i
$871$	2.66754	+	25.3799i	0.0903861	+	0.859966i
$872$	13.4665	−	9.78402i	0.456035	−	0.331329i
$873$	17.4356	+	28.5369i	0.590107	+	0.965829i
$874$	8.92964			0.302050
$875$	−8.42403	+	9.42357i	−0.284784	+	0.318575i
$876$	−21.0009	+	2.47155i	−0.709553	+	0.0835059i
$877$	14.0282	−	15.5799i	0.473699	−	0.526096i	−0.458183	−	0.888858i	$-0.651500\pi$
$877$	14.0282	−	15.5799i	0.473699	−	0.526096i	0.931882	+	0.362762i	$0.118166\pi$
$878$	−20.8190	−	9.26920i	−0.702606	−	0.312820i
$879$	−23.0350	+	21.2651i	−0.776950	+	0.717254i
$880$	11.8606	+	0.815125i	0.399819	+	0.0274779i
$881$	−8.04244	−	5.84318i	−0.270957	−	0.196862i	0.444007	−	0.896024i	$-0.353557\pi$
$881$	−8.04244	−	5.84318i	−0.270957	−	0.196862i	−0.714963	+	0.699162i	$0.753557\pi$
$882$	11.7995	+	12.4671i	0.397311	+	0.419788i
$883$	26.0893	+	18.9550i	0.877973	+	0.637885i	0.932715	−	0.360616i	$-0.117433\pi$
$883$	26.0893	+	18.9550i	0.877973	+	0.637885i	−0.0547412	+	0.998501i	$0.517433\pi$
$884$	−0.0556308	−	0.0617842i	−0.00187107	−	0.00207803i
$885$	11.2494	+	1.82591i	0.378144	+	0.0613771i
$886$	7.11247	−	7.89920i	0.238948	−	0.265379i
$887$	−7.07675	+	1.50421i	−0.237614	+	0.0505064i	−0.325179	−	0.945652i	$-0.605425\pi$
$887$	−7.07675	+	1.50421i	−0.237614	+	0.0505064i	0.0875653	+	0.996159i	$0.472091\pi$
$888$	0.672635	+	0.590672i	0.0225722	+	0.0198217i
$889$	5.93744	+	1.26204i	0.199135	+	0.0423275i
$890$	31.9065	+	16.9161i	1.06951	+	0.567028i
$891$	−37.2662	+	30.0149i	−1.24847	+	1.00554i
$892$	−6.70578	−	4.87203i	−0.224526	−	0.163128i
$893$	1.06217	−	1.83973i	0.0355441	−	0.0615642i
$894$	21.7822	−	12.9395i	0.728504	−	0.432763i
$895$	−1.19147	−	32.9887i	−0.0398265	−	1.10269i
$896$	1.03281	+	0.459836i	0.0345037	+	0.0153620i
$897$	16.8303	+	5.23814i	0.561947	+	0.174896i
$898$	20.1783	+	4.28903i	0.673358	+	0.143127i
$899$	−14.0691			−0.469231
$900$	5.99595	+	13.7495i	0.199865	+	0.458317i
$901$	0.342700			0.0114170
$902$	−58.3954	−	12.4123i	−1.94435	−	0.413285i
$903$	−2.46260	+	2.27339i	−0.0819503	+	0.0756537i
$904$	−16.4282	−	7.31432i	−0.546395	−	0.243271i
$905$	14.6296	−	5.34455i	0.486305	−	0.177659i
$906$	−7.76623	−	4.35604i	−0.258016	−	0.144720i
$907$	−8.73360	+	15.1270i	−0.289994	+	0.502285i	−0.973808	−	0.227372i	$-0.926987\pi$
$907$	−8.73360	+	15.1270i	−0.289994	+	0.502285i	0.683814	+	0.729657i	$0.260320\pi$
$908$	−0.0791673	−	0.0575184i	−0.00262726	−	0.00190882i
$909$	−1.50508	+	18.8061i	−0.0499202	+	0.623760i
$910$	2.19529	+	4.48738i	0.0727730	+	0.148755i
$911$	3.55127	+	0.754845i	0.117659	+	0.0250091i	0.266365	−	0.963872i	$-0.414177\pi$
$911$	3.55127	+	0.754845i	0.117659	+	0.0250091i	−0.148706	+	0.988881i	$0.547511\pi$
$912$	2.84455	−	0.963499i	0.0941924	−	0.0319046i
$913$	8.24108	−	1.75170i	0.272740	−	0.0579727i
$914$	11.2237	−	12.4652i	0.371247	−	0.412312i
$915$	30.5274	+	19.9913i	1.00920	+	0.660892i
$916$	−8.07484	−	8.96802i	−0.266800	−	0.296312i
$917$	14.2572	+	10.3585i	0.470814	+	0.342066i
$918$	0.0374488	−	0.215381i	0.00123599	−	0.00710863i
$919$	11.2981	+	8.20852i	0.372688	+	0.270774i	0.758325	−	0.651877i	$-0.226018\pi$
$919$	11.2981	+	8.20852i	0.372688	+	0.270774i	−0.385636	+	0.922651i	$0.626018\pi$
$920$	4.30100	−	10.6821i	0.141800	−	0.352179i
$921$	−0.119840	−	0.531247i	−0.00394886	−	0.0175052i
$922$	33.3394	+	14.8437i	1.09798	+	0.488850i
$923$	−6.47807	+	7.19463i	−0.213228	+	0.236814i
$924$	6.22367	+	8.34600i	0.204744	+	0.274563i
$925$	2.57740	−	0.186423i	0.0847445	−	0.00612954i
$926$	13.2222			0.434507
$927$	15.8593	−	0.394325i	0.520889	−	0.0129513i
$928$	4.35929	−	3.16721i	0.143101	−	0.103969i
$929$	−1.04497	−	9.94222i	−0.0342843	−	0.326194i	−0.998199	−	0.0599836i	$-0.980895\pi$
$929$	−1.04497	−	9.94222i	−0.0342843	−	0.326194i	0.963915	−	0.266210i	$-0.0857715\pi$
$930$	−6.39398	+	7.83439i	−0.209667	+	0.256900i
$931$	1.03707	−	9.86708i	0.0339887	−	0.323381i
$932$	10.0043	+	17.3280i	0.327703	+	0.567599i
$933$	−34.7654	−	19.4997i	−1.13817	−	0.638393i
$934$	−6.10653	−	6.78199i	−0.199812	−	0.221914i
$935$	−0.495223	+	0.0702028i	−0.0161955	+	0.00229588i
$936$	5.92650	−	0.147356i	0.193714	−	0.00481648i
$937$	11.8262	−	36.3974i	0.386346	−	1.18905i	−0.549154	−	0.835721i	$-0.685050\pi$
$937$	11.8262	−	36.3974i	0.386346	−	1.18905i	0.935499	−	0.353329i	$-0.114950\pi$
$938$	9.76935	+	10.8500i	0.318980	+	0.354264i
$939$	9.31240	−	13.1583i	0.303899	−	0.429405i
$940$	−1.68918	−	2.15674i	−0.0550951	−	0.0703450i
$941$	27.4442	−	5.83345i	0.894656	−	0.190165i	0.262432	−	0.964950i	$-0.415475\pi$
$941$	27.4442	−	5.83345i	0.894656	−	0.190165i	0.632224	+	0.774785i	$0.282142\pi$
$942$	14.9678	−	8.89154i	0.487678	−	0.289702i
$943$	−28.9133	+	50.0793i	−0.941546	+	1.63080i
$944$	−2.38061	−	1.72961i	−0.0774822	−	0.0562941i
$945$	−5.71609	+	11.8269i	−0.185944	+	0.384729i
$946$	7.36195	−	5.34877i	0.239358	−	0.173904i
$947$	0.441171	+	4.19746i	0.0143361	+	0.136399i	0.999349	−	0.0360829i	$-0.0114880\pi$
$947$	0.441171	+	4.19746i	0.0143361	+	0.136399i	−0.985013	+	0.172482i	$0.944821\pi$
$948$	14.0824	+	1.30337i	0.457374	+	0.0423314i
$949$	12.0627	+	20.8932i	0.391572	+	0.678222i
$950$	3.78194	−	7.80140i	0.122702	−	0.253111i
$951$	18.0503	+	24.2056i	0.585321	+	0.784920i
$952$	−0.0465251	−	0.00988921i	−0.00150789	−	0.000320511i
$953$	13.3923	−	9.73008i	0.433820	−	0.315188i	−0.349355	−	0.936991i	$-0.613599\pi$
$953$	13.3923	−	9.73008i	0.433820	−	0.315188i	0.783174	+	0.621802i	$0.213599\pi$
$954$	−15.8949	+	18.5608i	−0.514617	+	0.600929i
$955$	24.9957	−	3.54340i	0.808843	−	0.114662i
$956$	20.6661	−	9.20113i	0.668389	−	0.297586i
$957$	49.2805	−	5.79973i	1.59301	−	0.187478i
$958$	3.54514	−	33.7297i	0.114538	−	1.08976i
$959$	−23.4130	+	4.97658i	−0.756045	+	0.160702i
$960$	0.217502	−	3.86687i	0.00701986	−	0.124803i
$961$	23.6542	+	5.02785i	0.763038	+	0.162189i
$962$	0.315602	−	0.971322i	0.0101754	−	0.0313167i
$963$	−33.9244	+	16.1261i	−1.09320	+	0.519657i
$964$	3.19615	+	9.83675i	0.102941	+	0.316820i
$965$	−4.23411	−	0.290992i	−0.136301	−	0.00936737i
$966$	9.55130	−	3.23519i	0.307308	−	0.104091i
$967$	0.652148	−	6.20477i	0.0209717	−	0.199532i	−0.979019	−	0.203767i	$-0.934681\pi$
$967$	0.652148	−	6.20477i	0.0209717	−	0.199532i	0.999991	+	0.00423523i	$0.00134812\pi$
$968$	−8.63374	−	14.9541i	−0.277499	−	0.480642i
$969$	−0.108633	+	0.0645324i	−0.00348978	+	0.00207308i
$970$	−19.1136	−	15.9994i	−0.613702	−	0.513708i
$971$	−30.8722	+	22.4299i	−0.990735	+	0.719811i	−0.960082	−	0.279719i	$-0.909759\pi$
$971$	−30.8722	+	22.4299i	−0.990735	+	0.719811i	−0.0306531	+	0.999530i	$0.509759\pi$
$972$	9.92823	+	12.0179i	0.318448	+	0.385475i
$973$	0.654042	+	2.01293i	0.0209676	+	0.0645317i
$974$	8.08093	−	13.9966i	0.258930	−	0.448479i
$975$	11.7044	−	12.4853i	0.374840	−	0.399851i
$976$	−4.71093	−	8.15957i	−0.150793	−	0.261182i
$977$	−9.59824	+	10.6599i	−0.307075	+	0.341041i	−0.876854	−	0.480757i	$-0.840362\pi$
$977$	−9.59824	+	10.6599i	−0.307075	+	0.341041i	0.569779	+	0.821798i	$0.307029\pi$
$978$	35.9183	+	11.1790i	1.14854	+	0.357464i
$979$	−8.97555	−	85.3967i	−0.286860	−	2.72929i
$980$	−11.3040	−	5.99313i	−0.361093	−	0.191443i
$981$	−6.45263	−	49.5180i	−0.206017	−	1.58099i
$982$	−23.0937			−0.736949
$983$	−18.0106	+	8.01884i	−0.574449	+	0.255761i	−0.673335	−	0.739338i	$-0.735139\pi$
$983$	−18.0106	+	8.01884i	−0.574449	+	0.255761i	0.0988858	+	0.995099i	$0.468472\pi$
$984$	−3.80686	+	19.0725i	−0.121358	+	0.608010i
$985$	0.692612	+	19.1766i	0.0220685	+	0.611016i
$986$	−0.151692	+	0.168471i	−0.00483085	+	0.00536520i
$987$	0.469583	−	2.35263i	0.0149470	−	0.0748850i
$988$	−2.29277	−	2.54637i	−0.0729426	−	0.0810110i
$989$	−2.72377	−	8.38291i	−0.0866110	−	0.266561i
$990$	19.1669	−	30.0777i	0.609164	−	0.955931i
$991$	−8.10052	+	24.9308i	−0.257322	+	0.791955i	0.736042	+	0.676936i	$0.236693\pi$
$991$	−8.10052	+	24.9308i	−0.257322	+	0.791955i	−0.993363	+	0.115018i	$0.963307\pi$
$992$	2.38528	−	1.06199i	0.0757326	−	0.0337183i
$993$	15.5703	+	20.8799i	0.494109	+	0.662605i
$994$	−0.578959	+	5.50843i	−0.0183635	+	0.174717i
$995$	18.6025	−	27.6505i	0.589738	−	0.876581i
$996$	−0.603982	−	2.67743i	−0.0191379	−	0.0848377i
$997$	1.45076	+	13.8030i	0.0459459	+	0.437146i	0.993179	+	0.116600i	$0.0371997\pi$
$997$	1.45076	+	13.8030i	0.0459459	+	0.437146i	−0.947233	+	0.320546i	$0.896134\pi$
$998$	6.02571	+	18.5452i	0.190741	+	0.587039i
$999$	2.52136	−	0.924507i	0.0797724	−	0.0292501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.q.b.331.9	yes	112
9.4	even	3	inner	450.2.q.b.31.4	✓	112
25.21	even	5	inner	450.2.q.b.421.4	yes	112
225.121	even	15	inner	450.2.q.b.121.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.q.b.31.4	✓	112	9.4	even	3	inner
450.2.q.b.121.9	yes	112	225.121	even	15	inner
450.2.q.b.331.9	yes	112	1.1	even	1	trivial
450.2.q.b.421.4	yes	112	25.21	even	5	inner

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(0.381143 + 1.68959i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.24818 + 1.85528i) q^{5} +(-0.0215278 - 1.73192i) q^{6} +(-0.565275 + 0.979085i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.70946 + 1.28795i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(0.381143 + 1.68959i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.24818 + 1.85528i) q^{5} +(-0.0215278 - 1.73192i) q^{6} +(-0.565275 + 0.979085i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.70946 + 1.28795i) q^{9} +(1.60663 - 1.55522i) q^{10} +(-5.20053 - 1.10541i) q^{11} +(-0.339028 + 1.69855i) q^{12} +(1.93293 - 0.410857i) q^{13} +(0.756486 - 0.840163i) q^{14} +(-3.61040 - 1.40179i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.0340369 - 0.0247293i) q^{17} +(2.91803 - 0.696481i) q^{18} +(-1.40280 - 1.01919i) q^{19} +(-1.89488 + 1.18720i) q^{20} +(-1.86971 - 0.581914i) q^{21} +(4.85706 + 2.16250i) q^{22} +(3.44594 - 3.82710i) q^{23} +(0.684768 - 1.59094i) q^{24} +(-1.88411 - 4.63143i) q^{25} -1.97611 q^{26} +(-3.20881 - 4.08699i) q^{27} +(-0.914634 + 0.664521i) q^{28} +(0.563239 + 5.35886i) q^{29} +(3.24006 + 2.12180i) q^{30} +(-0.272925 + 2.59671i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.114457 - 9.20811i) q^{33} +(0.0281516 + 0.0312656i) q^{34} +(-1.11091 - 2.27081i) q^{35} +(-2.99907 + 0.0745686i) q^{36} +(-0.159708 + 0.491532i) q^{37} +(1.16024 + 1.28858i) q^{38} +(1.43090 + 3.10927i) q^{39} +(2.10030 - 0.767291i) q^{40} +(-10.9834 + 2.33458i) q^{41} +(1.70786 + 0.957932i) q^{42} +(0.855780 - 1.48225i) q^{43} +(-4.30131 - 3.12509i) q^{44} +(0.992370 - 6.63440i) q^{45} +(-4.16634 + 3.02702i) q^{46} +(0.128062 + 1.21843i) q^{47} +(-1.00058 + 1.41380i) q^{48} +(2.86093 + 4.95527i) q^{49} +(0.880010 + 4.92195i) q^{50} +(0.0288095 - 0.0669340i) q^{51} +(1.93293 + 0.410857i) q^{52} +(-6.58990 + 4.78785i) q^{53} +(2.28896 + 4.66483i) q^{54} +(8.54202 - 8.26869i) q^{55} +(1.03281 - 0.459836i) q^{56} +(1.18735 - 2.75862i) q^{57} +(0.563239 - 5.35886i) q^{58} +(-2.87829 + 0.611800i) q^{59} +(-2.72811 - 2.74908i) q^{60} +(-9.21597 - 1.95892i) q^{61} +(0.806847 - 2.48322i) q^{62} +(0.270573 - 3.38084i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.65038 + 4.09894i) q^{65} +(-1.80252 + 9.03069i) q^{66} +(-1.34989 + 12.8434i) q^{67} +(-0.0210360 - 0.0364354i) q^{68} +(7.77965 + 4.36357i) q^{69} +(0.614507 + 2.45216i) q^{70} +(-3.96352 + 2.87967i) q^{71} +(2.94904 + 0.550603i) q^{72} +(3.77264 + 11.6110i) q^{73} +(0.258414 - 0.447586i) q^{74} +(7.10712 - 4.94862i) q^{75} +(-0.866977 - 1.50165i) q^{76} +(4.02202 - 4.46691i) q^{77} +(-0.753181 - 3.33883i) q^{78} +(-0.853496 - 8.12047i) q^{79} +(-2.21393 + 0.313847i) q^{80} +(5.68235 - 6.97932i) q^{81} +11.2287 q^{82} +(-1.44766 + 0.644540i) q^{83} +(-1.47138 - 1.29208i) q^{84} +(0.0883638 - 0.0322815i) q^{85} +(-1.14526 + 1.27194i) q^{86} +(-8.83963 + 2.99414i) q^{87} +(3.55758 + 3.95109i) q^{88} +(4.99075 + 15.3599i) q^{89} +(-2.35005 + 6.28309i) q^{90} +(-0.690373 + 2.12475i) q^{91} +(4.70464 - 2.09464i) q^{92} +(-4.49141 + 0.528585i) q^{93} +(0.128062 - 1.21843i) q^{94} +(3.64182 - 1.33045i) q^{95} +(1.27266 - 1.17488i) q^{96} +(-1.16521 - 11.0862i) q^{97} +(-1.76815 - 5.44181i) q^{98} +(15.5144 - 3.70299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9}+O(q^{10}) \) 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9	\( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21} + 2 q^{22} - 5 q^{23} + 2 q^{24} + 21 q^{25} + 20 q^{26} - 16 q^{27} - 14 q^{28} + 18 q^{29} + 3 q^{30} - 27 q^{31} - 56 q^{32} - 25 q^{33} - 15 q^{34} - 12 q^{35} - 7 q^{36} + 16 q^{37} - 9 q^{38} + 12 q^{39} - q^{40} + 16 q^{41} - 13 q^{42} - 44 q^{43} - 4 q^{44} + 69 q^{45} - 10 q^{46} + 27 q^{47} + 3 q^{48} - 64 q^{49} + 11 q^{50} + 138 q^{51} - 14 q^{53} - 30 q^{54} - 8 q^{55} + 7 q^{56} - 50 q^{57} + 18 q^{58} + 14 q^{59} - 20 q^{60} - 5 q^{61} - 66 q^{62} - 12 q^{63} - 28 q^{64} - 102 q^{65} + 18 q^{66} + 11 q^{67} + 40 q^{68} - 78 q^{69} + 6 q^{70} + 38 q^{71} - 17 q^{72} - 44 q^{73} + 12 q^{74} + 10 q^{75} - 14 q^{76} - 3 q^{77} - 55 q^{78} + 16 q^{79} + 12 q^{80} + 72 q^{81} + 28 q^{82} - 56 q^{83} - 30 q^{84} + 35 q^{85} + 21 q^{86} - 44 q^{87} - 3 q^{88} - 64 q^{89} + 38 q^{90} - 40 q^{91} + 5 q^{92} - 22 q^{93} + 27 q^{94} + 24 q^{95} + 5 q^{96} + 34 q^{97} + 38 q^{98} + 68 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9 - 8 * q^10 - 3 * q^11 - 3 * q^14 + 32 * q^15 + 14 * q^16 + 10 * q^17 - 6 * q^18 - 32 * q^19 - 6 * q^20 - 7 * q^21 + 2 * q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 20 * q^26 - 16 * q^27 - 14 * q^28 + 18 * q^29 + 3 * q^30 - 27 * q^31 - 56 * q^32 - 25 * q^33 - 15 * q^34 - 12 * q^35 - 7 * q^36 + 16 * q^37 - 9 * q^38 + 12 * q^39 - q^40 + 16 * q^41 - 13 * q^42 - 44 * q^43 - 4 * q^44 + 69 * q^45 - 10 * q^46 + 27 * q^47 + 3 * q^48 - 64 * q^49 + 11 * q^50 + 138 * q^51 - 14 * q^53 - 30 * q^54 - 8 * q^55 + 7 * q^56 - 50 * q^57 + 18 * q^58 + 14 * q^59 - 20 * q^60 - 5 * q^61 - 66 * q^62 - 12 * q^63 - 28 * q^64 - 102 * q^65 + 18 * q^66 + 11 * q^67 + 40 * q^68 - 78 * q^69 + 6 * q^70 + 38 * q^71 - 17 * q^72 - 44 * q^73 + 12 * q^74 + 10 * q^75 - 14 * q^76 - 3 * q^77 - 55 * q^78 + 16 * q^79 + 12 * q^80 + 72 * q^81 + 28 * q^82 - 56 * q^83 - 30 * q^84 + 35 * q^85 + 21 * q^86 - 44 * q^87 - 3 * q^88 - 64 * q^89 + 38 * q^90 - 40 * q^91 + 5 * q^92 - 22 * q^93 + 27 * q^94 + 24 * q^95 + 5 * q^96 + 34 * q^97 + 38 * q^98 + 68 * q^99

Introduction

L-functions

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