LMFDB - Embedded newform 450.2.q.b.331.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(31,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
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			331.13
Character	$\chi$	$=$	450.331
Dual form			450.2.q.b.121.13

$q$-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} +(1.67356 - 0.446298i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.23598 + 0.0195000i) q^{5} +(-1.72978 + 0.0885921i) q^{6} +(2.28460 - 3.95705i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.60164 - 1.49382i) q^{9} +(2.19118 + 0.445813i) q^{10} +(-3.20642 - 0.681545i) q^{11} +(1.71040 + 0.272986i) q^{12} +(-0.940327 + 0.199873i) q^{13} +(-3.05739 + 3.39558i) q^{14} +(-3.73336 + 1.03055i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.23251 + 0.895472i) q^{17} +(-2.85537 + 0.920264i) q^{18} +(-4.38425 - 3.18534i) q^{19} +(-2.05060 - 0.891642i) q^{20} +(2.05741 - 7.64199i) q^{21} +(2.99465 + 1.33330i) q^{22} +(1.90079 - 2.11104i) q^{23} +(-1.61627 - 0.622633i) q^{24} +(4.99924 - 0.0872036i) q^{25} +0.961334 q^{26} +(3.68732 - 3.66111i) q^{27} +(3.69656 - 2.68571i) q^{28} +(-0.0431950 - 0.410973i) q^{29} +(3.86604 - 0.231821i) q^{30} +(0.354070 - 3.36875i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.67032 + 0.290409i) q^{33} +(-1.01940 - 1.13216i) q^{34} +(-5.03117 + 8.89244i) q^{35} +(2.98430 - 0.306490i) q^{36} +(-0.111309 + 0.342575i) q^{37} +(3.62617 + 4.02727i) q^{38} +(-1.48449 + 0.754166i) q^{39} +(1.82041 + 1.29850i) q^{40} +(9.84715 - 2.09308i) q^{41} +(-3.60130 + 7.04723i) q^{42} +(-4.32764 + 7.49568i) q^{43} +(-2.65200 - 1.92679i) q^{44} +(-5.78808 + 3.39088i) q^{45} +(-2.29816 + 1.66971i) q^{46} +(-0.0278907 - 0.265363i) q^{47} +(1.45150 + 0.945069i) q^{48} +(-6.93882 - 12.0184i) q^{49} +(-4.90812 - 0.954102i) q^{50} +(2.46234 + 0.948562i) q^{51} +(-0.940327 - 0.199873i) q^{52} +(8.22454 - 5.97548i) q^{53} +(-4.36793 + 2.81447i) q^{54} +(7.18278 + 1.46140i) q^{55} +(-4.17418 + 1.85846i) q^{56} +(-8.75893 - 3.37419i) q^{57} +(-0.0431950 + 0.410973i) q^{58} +(-12.6043 + 2.67912i) q^{59} +(-3.82976 - 0.577039i) q^{60} +(12.5346 + 2.66432i) q^{61} +(-1.04674 + 3.22152i) q^{62} +(0.0325932 - 13.7076i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.09866 - 0.465248i) q^{65} +(5.60679 + 0.894862i) q^{66} +(-0.0195394 + 0.185905i) q^{67} +(0.761734 + 1.31936i) q^{68} +(2.23894 - 4.38128i) q^{69} +(6.77007 - 7.65208i) q^{70} +(2.90137 - 2.10797i) q^{71} +(-2.98281 - 0.320679i) q^{72} +(4.34161 + 13.3621i) q^{73} +(0.180102 - 0.311946i) q^{74} +(8.32763 - 2.37709i) q^{75} +(-2.70961 - 4.69319i) q^{76} +(-10.0223 + 11.1309i) q^{77} +(1.60885 - 0.429042i) q^{78} +(-0.548013 - 5.21399i) q^{79} +(-1.51066 - 1.64861i) q^{80} +(4.53701 - 7.77274i) q^{81} -10.0671 q^{82} +(-10.2949 + 4.58357i) q^{83} +(4.98781 - 6.14448i) q^{84} +(-2.77334 - 1.97823i) q^{85} +(5.79151 - 6.43212i) q^{86} +(-0.255706 - 0.668511i) q^{87} +(2.19344 + 2.43607i) q^{88} +(-0.871515 - 2.68225i) q^{89} +(6.36660 - 2.11337i) q^{90} +(-1.35737 + 4.17755i) q^{91} +(2.59509 - 1.15541i) q^{92} +(-0.910910 - 5.79585i) q^{93} +(-0.0278907 + 0.265363i) q^{94} +(9.86522 + 7.03688i) q^{95} +(-1.22329 - 1.22620i) q^{96} +(1.61359 + 15.3523i) q^{97} +(4.28842 + 13.1984i) q^{98} +(-9.36003 + 3.01667i) 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} - 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}+ \cdots + 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

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
$3$	1.67356	−	0.446298i	0.966233	−	0.257670i
$3$	1.67356	−	0.446298i	0.966233	−	0.257670i
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−2.23598	+	0.0195000i	−0.999962	+	0.00872069i
$5$	−2.23598	+	0.0195000i	−0.999962	+	0.00872069i
$6$	−1.72978	+	0.0885921i	−0.706181	+	0.0361676i
$7$	2.28460	−	3.95705i	0.863499	−	1.49562i	−0.00503171	−	0.999987i	$-0.501602\pi$
$7$	2.28460	−	3.95705i	0.863499	−	1.49562i	0.868530	−	0.495636i	$-0.165065\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.60164	−	1.49382i	0.867212	−	0.497939i
$10$	2.19118	+	0.445813i	0.692911	+	0.140978i
$11$	−3.20642	−	0.681545i	−0.966771	−	0.205494i	−0.302636	−	0.953106i	$-0.597867\pi$
$11$	−3.20642	−	0.681545i	−0.966771	−	0.205494i	−0.664135	+	0.747613i	$0.731200\pi$
$12$	1.71040	+	0.272986i	0.493751	+	0.0788043i
$13$	−0.940327	+	0.199873i	−0.260800	+	0.0554347i	−0.336456	−	0.941699i	$-0.609228\pi$
$13$	−0.940327	+	0.199873i	−0.260800	+	0.0554347i	0.0756560	+	0.997134i	$0.475895\pi$
$14$	−3.05739	+	3.39558i	−0.817123	+	0.907507i
$15$	−3.73336	+	1.03055i	−0.963949	+	0.266087i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	1.23251	+	0.895472i	0.298928	+	0.217184i	0.727131	−	0.686499i	$-0.240853\pi$
$17$	1.23251	+	0.895472i	0.298928	+	0.217184i	−0.428203	+	0.903683i	$0.640853\pi$
$18$	−2.85537	+	0.920264i	−0.673016	+	0.216908i
$19$	−4.38425	−	3.18534i	−1.00582	−	0.730768i	−0.0424881	−	0.999097i	$-0.513528\pi$
$19$	−4.38425	−	3.18534i	−1.00582	−	0.730768i	−0.963327	+	0.268329i	$0.913528\pi$
$20$	−2.05060	−	0.891642i	−0.458529	−	0.199377i
$21$	2.05741	−	7.64199i	0.448963	−	1.66762i
$22$	2.99465	+	1.33330i	0.638461	+	0.284261i
$23$	1.90079	−	2.11104i	0.396341	−	0.440182i	−0.511635	−	0.859203i	$-0.670960\pi$
$23$	1.90079	−	2.11104i	0.396341	−	0.440182i	0.907977	+	0.419021i	$0.137627\pi$
$24$	−1.61627	−	0.622633i	−0.329920	−	0.127095i
$25$	4.99924	−	0.0872036i	0.999848	−	0.0174407i
$26$	0.961334			0.188533
$27$	3.68732	−	3.66111i	0.709624	−	0.704580i
$28$	3.69656	−	2.68571i	0.698585	−	0.507552i
$29$	−0.0431950	−	0.410973i	−0.00802110	−	0.0763157i	0.989779	−	0.142609i	$-0.0455493\pi$
$29$	−0.0431950	−	0.410973i	−0.00802110	−	0.0763157i	−0.997800	+	0.0662937i	$0.978883\pi$
$30$	3.86604	−	0.231821i	0.705839	−	0.0423246i
$31$	0.354070	−	3.36875i	0.0635929	−	0.605046i	−0.915597	−	0.402098i	$-0.868281\pi$
$31$	0.354070	−	3.36875i	0.0635929	−	0.605046i	0.979190	−	0.202948i	$-0.0650523\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−5.67032	+	0.290409i	−0.987075	+	0.0505538i
$34$	−1.01940	−	1.13216i	−0.174826	−	0.194163i
$35$	−5.03117	+	8.89244i	−0.850423	+	1.50310i
$36$	2.98430	−	0.306490i	0.497384	−	0.0510817i
$37$	−0.111309	+	0.342575i	−0.0182992	+	0.0563190i	−0.959789	−	0.280722i	$-0.909426\pi$
$37$	−0.111309	+	0.342575i	−0.0182992	+	0.0563190i	0.941490	+	0.337041i	$0.109426\pi$
$38$	3.62617	+	4.02727i	0.588243	+	0.653310i
$39$	−1.48449	+	0.754166i	−0.237709	+	0.120763i
$40$	1.82041	+	1.29850i	0.287832	+	0.205311i
$41$	9.84715	−	2.09308i	1.53787	−	0.326884i	0.640426	−	0.768020i	$-0.278758\pi$
$41$	9.84715	−	2.09308i	1.53787	−	0.326884i	0.897440	+	0.441136i	$0.145424\pi$
$42$	−3.60130	+	7.04723i	−0.555693	+	1.08741i
$43$	−4.32764	+	7.49568i	−0.659958	+	1.14308i	0.320668	+	0.947192i	$0.396093\pi$
$43$	−4.32764	+	7.49568i	−0.659958	+	1.14308i	−0.980626	+	0.195889i	$0.937241\pi$
$44$	−2.65200	−	1.92679i	−0.399804	−	0.290474i
$45$	−5.78808	+	3.39088i	−0.862836	+	0.505483i
$46$	−2.29816	+	1.66971i	−0.338845	+	0.246185i
$47$	−0.0278907	−	0.265363i	−0.00406828	−	0.0387071i	0.992299	−	0.123862i	$-0.0395281\pi$
$47$	−0.0278907	−	0.265363i	−0.00406828	−	0.0387071i	−0.996368	+	0.0851551i	$0.972861\pi$
$48$	1.45150	+	0.945069i	0.209506	+	0.136409i
$49$	−6.93882	−	12.0184i	−0.991260	−	1.71691i
$50$	−4.90812	−	0.954102i	−0.694114	−	0.134930i
$51$	2.46234	+	0.948562i	0.344796	+	0.132825i
$52$	−0.940327	−	0.199873i	−0.130400	−	0.0277173i
$53$	8.22454	−	5.97548i	1.12973	−	0.820795i	0.144072	−	0.989567i	$-0.453980\pi$
$53$	8.22454	−	5.97548i	1.12973	−	0.820795i	0.985655	+	0.168772i	$0.0539802\pi$
$54$	−4.36793	+	2.81447i	−0.594399	+	0.383000i
$55$	7.18278	+	1.46140i	0.968526	+	0.197055i
$56$	−4.17418	+	1.85846i	−0.557798	+	0.248348i
$57$	−8.75893	−	3.37419i	−1.16015	−	0.446923i
$58$	−0.0431950	+	0.410973i	−0.00567178	+	0.0539633i
$59$	−12.6043	+	2.67912i	−1.64094	+	0.348792i	−0.933664	−	0.358150i	$-0.883408\pi$
$59$	−12.6043	+	2.67912i	−1.64094	+	0.348792i	−0.707272	+	0.706941i	$0.750074\pi$
$60$	−3.82976	−	0.577039i	−0.494419	−	0.0744955i
$61$	12.5346	+	2.66432i	1.60489	+	0.341131i	0.921337	−	0.388765i	$-0.127098\pi$
$61$	12.5346	+	2.66432i	1.60489	+	0.341131i	0.683558	+	0.729896i	$0.260432\pi$
$62$	−1.04674	+	3.22152i	−0.132936	+	0.409134i
$63$	0.0325932	−	13.7076i	0.00410636	−	1.72699i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.09866	−	0.465248i	0.260306	−	0.0577069i
$66$	5.60679	+	0.894862i	0.690148	+	0.110150i
$67$	−0.0195394	+	0.185905i	−0.00238712	+	0.0227119i	−0.995651	−	0.0931657i	$-0.970301\pi$
$67$	−0.0195394	+	0.185905i	−0.00238712	+	0.0227119i	0.993264	+	0.115878i	$0.0369680\pi$
$68$	0.761734	+	1.31936i	0.0923738	+	0.159996i
$69$	2.23894	−	4.38128i	0.269536	−	0.527444i
$70$	6.77007	−	7.65208i	0.809178	−	0.914599i
$71$	2.90137	−	2.10797i	0.344329	−	0.250170i	−0.402157	−	0.915571i	$-0.631739\pi$
$71$	2.90137	−	2.10797i	0.344329	−	0.250170i	0.746486	+	0.665401i	$0.231739\pi$
$72$	−2.98281	−	0.320679i	−0.351528	−	0.0377923i
$73$	4.34161	+	13.3621i	0.508147	+	1.56392i	0.795415	+	0.606065i	$0.207253\pi$
$73$	4.34161	+	13.3621i	0.508147	+	1.56392i	−0.287268	+	0.957850i	$0.592747\pi$
$74$	0.180102	−	0.311946i	0.0209365	−	0.0362630i
$75$	8.32763	−	2.37709i	0.961592	−	0.274483i
$76$	−2.70961	−	4.69319i	−0.310814	−	0.538346i
$77$	−10.0223	+	11.1309i	−1.14215	+	1.26848i
$78$	1.60885	−	0.429042i	0.182167	−	0.0485794i
$79$	−0.548013	−	5.21399i	−0.0616563	−	0.586620i	−0.981114	−	0.193431i	$-0.938038\pi$
$79$	−0.548013	−	5.21399i	−0.0616563	−	0.586620i	0.919458	−	0.393189i	$-0.128628\pi$
$80$	−1.51066	−	1.64861i	−0.168896	−	0.184320i
$81$	4.53701	−	7.77274i	0.504113	−	0.863638i
$82$	−10.0671			−1.11173
$83$	−10.2949	+	4.58357i	−1.13001	+	0.503113i	−0.884620	−	0.466312i	$-0.845582\pi$
$83$	−10.2949	+	4.58357i	−1.13001	+	0.503113i	−0.245389	+	0.969425i	$0.578916\pi$
$84$	4.98781	−	6.14448i	0.544215	−	0.670418i
$85$	−2.77334	−	1.97823i	−0.300811	−	0.214569i
$86$	5.79151	−	6.43212i	0.624514	−	0.693593i
$87$	−0.255706	−	0.668511i	−0.0274146	−	0.0716719i
$88$	2.19344	+	2.43607i	0.233822	+	0.259685i
$89$	−0.871515	−	2.68225i	−0.0923804	−	0.284317i	0.894182	−	0.447704i	$-0.147758\pi$
$89$	−0.871515	−	2.68225i	−0.0923804	−	0.284317i	−0.986562	+	0.163387i	$0.947758\pi$
$90$	6.36660	−	2.11337i	0.671099	−	0.222769i
$91$	−1.35737	+	4.17755i	−0.142291	+	0.437926i
$92$	2.59509	−	1.15541i	0.270557	−	0.120460i
$93$	−0.910910	−	5.79585i	−0.0944570	−	0.601001i
$94$	−0.0278907	+	0.265363i	−0.00287671	+	0.0273701i
$95$	9.86522	+	7.03688i	1.01215	+	0.721968i
$96$	−1.22329	−	1.22620i	−0.124851	−	0.125149i
$97$	1.61359	+	15.3523i	0.163836	+	1.55879i	0.699668	+	0.714468i	$0.253331\pi$
$97$	1.61359	+	15.3523i	0.163836	+	1.55879i	−0.535833	+	0.844324i	$0.680002\pi$
$98$	4.28842	+	13.1984i	0.433196	+	1.33324i
$99$	−9.36003	+	3.01667i	−0.940719	+	0.303187i
$100$	4.60250	+	1.95371i	0.460250	+	0.195371i
$101$	−3.17850	+	5.50532i	−0.316272	+	0.547800i	−0.979707	−	0.200434i	$-0.935765\pi$
$101$	−3.17850	+	5.50532i	−0.316272	+	0.547800i	0.663435	+	0.748234i	$0.269098\pi$
$102$	−2.21131	−	1.43978i	−0.218952	−	0.142560i
$103$	13.1302	+	5.84593i	1.29375	+	0.576016i	0.934081	−	0.357062i	$-0.116221\pi$
$103$	13.1302	+	5.84593i	1.29375	+	0.576016i	0.359673	+	0.933078i	$0.382888\pi$
$104$	0.878223	+	0.391010i	0.0861168	+	0.0383417i
$105$	−4.45130	+	17.1275i	−0.434403	+	1.67147i
$106$	−9.28719	+	4.13492i	−0.902051	+	0.401619i
$107$	17.7786			1.71872			0.859362	−	0.511369i	$-0.170861\pi$
$107$	17.7786			1.71872			0.859362	+	0.511369i	$0.170861\pi$
$108$	4.85764	−	1.84482i	0.467426	−	0.177518i
$109$	−2.87983	+	8.86322i	−0.275838	+	0.848942i	0.713158	+	0.701003i	$0.247264\pi$
$109$	−2.87983	+	8.86322i	−0.275838	+	0.848942i	−0.988996	+	0.147939i	$0.952736\pi$
$110$	−6.72198	−	2.92285i	−0.640916	−	0.278683i
$111$	−0.0333927	+	0.622999i	−0.00316950	+	0.0591324i
$112$	4.46936	−	0.949991i	0.422315	−	0.0897657i
$113$	−10.5956	+	2.25217i	−0.996752	+	0.211866i	−0.677277	−	0.735728i	$-0.736840\pi$
$113$	−10.5956	+	2.25217i	−0.996752	+	0.211866i	−0.319475	+	0.947595i	$0.603507\pi$
$114$	7.86600	+	5.12154i	0.736718	+	0.479676i
$115$	−4.20896	+	4.75731i	−0.392488	+	0.443621i
$116$	0.127697	−	0.393011i	0.0118564	−	0.0364902i
$117$	−2.14781	+	1.92467i	−0.198565	+	0.177936i
$118$	12.8859			1.18624
$119$	6.35923	−	2.83131i	0.582949	−	0.259546i
$120$	3.62609	+	1.36068i	0.331015	+	0.124213i
$121$	−0.232397	−	0.103470i	−0.0211270	−	0.00940633i
$122$	−11.7068	−	5.21219i	−1.05988	−	0.471890i
$123$	15.5457	−	7.89767i	1.40171	−	0.712109i
$124$	1.69366	−	2.93350i	0.152095	−	0.263436i
$125$	−11.1765	+	0.292471i	−0.999658	+	0.0261594i
$126$	−2.88185	+	13.4013i	−0.256735	+	1.19388i
$127$	5.65028	+	17.3898i	0.501381	+	1.54309i	0.806771	+	0.590865i	$0.201213\pi$
$127$	5.65028	+	17.3898i	0.501381	+	1.54309i	−0.305389	+	0.952228i	$0.598787\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	−3.89726	+	14.4759i	−0.343135	+	1.27453i
$130$	−2.14953	+	0.0187461i	−0.188526	+	0.00164414i
$131$	0.735556	−	6.99835i	0.0642658	−	0.611449i	−0.914232	−	0.405191i	$-0.867205\pi$
$131$	0.735556	−	6.99835i	0.0642658	−	0.611449i	0.978498	−	0.206257i	$-0.0661284\pi$
$132$	−5.29821	−	2.04102i	−0.461150	−	0.177648i
$133$	−22.6208	+	10.0714i	−1.96147	+	0.873304i
$134$	0.0577642	−	0.177780i	0.00499007	−	0.0153579i
$135$	−8.17338	+	8.25807i	−0.703453	+	0.710742i
$136$	−0.470778	−	1.44890i	−0.0403688	−	0.124243i
$137$	13.0396	+	14.4819i	1.11405	+	1.23727i	0.968791	+	0.247880i	$0.0797339\pi$
$137$	13.0396	+	14.4819i	1.11405	+	1.23727i	0.145256	+	0.989394i	$0.453599\pi$
$138$	−3.10093	+	3.82003i	−0.263969	+	0.325183i
$139$	1.06526	−	1.18310i	0.0903546	−	0.100349i	−0.696272	−	0.717778i	$-0.745159\pi$
$139$	1.06526	−	1.18310i	0.0903546	−	0.100349i	0.786626	+	0.617429i	$0.211826\pi$
$140$	−8.21308	+	6.07729i	−0.694132	+	0.513625i
$141$	−0.165108	−	0.431654i	−0.0139046	−	0.0363518i
$142$	−3.27624	+	1.45868i	−0.274936	+	0.122409i
$143$	3.15130			0.263525
$144$	2.85096	+	0.933832i	0.237580	+	0.0778194i
$145$	0.104597	+	0.918085i	0.00868632	+	0.0762428i
$146$	−1.46860	−	13.9728i	−0.121542	−	1.15640i
$147$	−16.9763	−	17.0168i	−1.40019	−	1.40352i
$148$	−0.241024	+	0.267684i	−0.0198121	+	0.0220035i
$149$	6.00775	+	10.4057i	0.492174	+	0.852470i	0.999959	−	0.00901334i	$-0.00286907\pi$
$149$	6.00775	+	10.4057i	0.492174	+	0.852470i	−0.507785	+	0.861484i	$0.669536\pi$
$150$	−8.63988	+	0.593736i	−0.705443	+	0.0484784i
$151$	0.642956	−	1.11363i	0.0523230	−	0.0906261i	−0.838678	−	0.544628i	$-0.816671\pi$
$151$	0.642956	−	1.11363i	0.0523230	−	0.0906261i	0.891001	+	0.454002i	$0.150004\pi$
$152$	1.67463	+	5.15399i	0.135831	+	0.418044i
$153$	4.54422	+	0.488544i	0.367378	+	0.0394964i
$154$	12.1175	−	8.80390i	0.976458	−	0.709438i
$155$	−0.726004	+	7.53938i	−0.0583141	+	0.605578i
$156$	−1.66290	+	0.0851666i	−0.133139	+	0.00681879i
$157$	−7.18577	−	12.4461i	−0.573487	−	0.993309i	−0.996204	−	0.0870472i	$-0.972257\pi$
$157$	−7.18577	−	12.4461i	−0.573487	−	0.993309i	0.422717	−	0.906262i	$-0.361076\pi$
$158$	−0.548013	+	5.21399i	−0.0435976	+	0.414803i
$159$	11.0974	−	13.6709i	0.880085	−	1.08418i
$160$	1.13488	+	1.92667i	0.0897201	+	0.152316i
$161$	−4.01093	−	12.3444i	−0.316106	−	0.972874i
$162$	−6.05391	+	6.65959i	−0.475640	+	0.523227i
$163$	6.51096	−	20.0387i	0.509978	−	1.56955i	−0.282260	−	0.959338i	$-0.591084\pi$
$163$	6.51096	−	20.0387i	0.509978	−	1.56955i	0.792238	−	0.610213i	$-0.208916\pi$
$164$	9.84715	+	2.09308i	0.768933	+	0.163442i
$165$	12.6731	−	0.759922i	0.986597	−	0.0591598i
$166$	11.0229	−	2.34299i	0.855542	−	0.181851i
$167$	0.863954	−	8.21997i	0.0668548	−	0.636081i	−0.908870	−	0.417080i	$-0.863054\pi$
$167$	0.863954	−	8.21997i	0.0668548	−	0.636081i	0.975725	−	0.219001i	$-0.0702798\pi$
$168$	−6.15632	+	4.97319i	−0.474971	+	0.383690i
$169$	−11.0318	+	4.91169i	−0.848602	+	0.377822i
$170$	2.30144	+	2.51161i	0.176512	+	0.192631i
$171$	−16.1645	−	1.73783i	−1.23613	−	0.132895i
$172$	−7.00226	+	5.08744i	−0.533917	+	0.387914i
$173$	18.1182	+	3.85113i	1.37750	+	0.292796i	0.836380	−	0.548151i	$-0.184668\pi$
$173$	18.1182	+	3.85113i	1.37750	+	0.292796i	0.541118	+	0.840947i	$0.318001\pi$
$174$	0.111127	+	0.707067i	0.00842450	+	0.0536026i
$175$	11.0762	−	19.9815i	0.837283	−	1.51046i
$176$	−1.63902	−	2.83887i	−0.123546	−	0.213988i
$177$	−19.8984	+	10.1089i	−1.49565	+	0.759835i
$178$	0.294800	+	2.80483i	0.0220962	+	0.210231i
$179$	−4.44525	+	3.22966i	−0.332254	+	0.241396i	−0.741386	−	0.671079i	$-0.765831\pi$
$179$	−4.44525	+	3.22966i	−0.332254	+	0.241396i	0.409133	+	0.912475i	$0.365831\pi$
$180$	−6.66687	+	0.743501i	−0.496919	+	0.0554173i
$181$	6.19392	+	4.50015i	0.460391	+	0.334493i	0.793684	−	0.608330i	$-0.208160\pi$
$181$	6.19392	+	4.50015i	0.460391	+	0.334493i	−0.333294	+	0.942823i	$0.608160\pi$
$182$	2.19627	−	3.80405i	0.162798	−	0.281975i
$183$	22.1666	−	1.13528i	1.63860	−	0.0839221i
$184$	−2.77861	+	0.590611i	−0.204842	+	0.0435404i
$185$	0.242206	−	0.768163i	0.0178073	−	0.0564764i
$186$	−0.314020	+	5.85858i	−0.0230251	+	0.429572i
$187$	−3.34164	−	3.71127i	−0.244365	−	0.271395i
$188$	0.0824532	−	0.253765i	0.00601352	−	0.0185077i
$189$	−6.06312	−	22.9551i	−0.441027	−	1.66973i
$190$	−8.18659	−	8.93420i	−0.593918	−	0.648155i
$191$	−8.58720	−	9.53705i	−0.621348	−	0.690077i	0.347515	−	0.937674i	$-0.387026\pi$
$191$	−8.58720	−	9.53705i	−0.621348	−	0.690077i	−0.968863	+	0.247598i	$0.920359\pi$
$192$	0.941615	+	1.45374i	0.0679552	+	0.104915i
$193$	−4.43483	−	7.68136i	−0.319226	−	0.552916i	0.661101	−	0.750297i	$-0.270090\pi$
$193$	−4.43483	−	7.68136i	−0.319226	−	0.552916i	−0.980327	+	0.197381i	$0.936756\pi$
$194$	1.61359	−	15.3523i	0.115849	−	1.10223i
$195$	3.30460	−	1.71525i	0.236647	−	0.122832i
$196$	−1.45061	−	13.8016i	−0.103615	−	0.985829i
$197$	14.7880	−	10.7441i	1.05360	−	0.765485i	0.0807055	−	0.996738i	$-0.474283\pi$
$197$	14.7880	−	10.7441i	1.05360	−	0.765485i	0.972894	+	0.231253i	$0.0742827\pi$
$198$	9.78269	−	1.00469i	0.695226	−	0.0714003i
$199$	9.13326			0.647440			0.323720	−	0.946153i	$-0.395066\pi$
$199$	9.13326			0.647440			0.323720	+	0.946153i	$0.395066\pi$
$200$	−4.09573	−	2.86793i	−0.289612	−	0.202793i
$201$	0.0502686	+	0.319844i	0.00354568	+	0.0225601i
$202$	4.25366	−	4.72417i	0.299286	−	0.332391i
$203$	−1.72492	−	0.767984i	−0.121066	−	0.0539019i
$204$	1.86364	+	1.86808i	0.130481	+	0.130792i
$205$	−21.9772	+	4.87210i	−1.53496	+	0.340282i
$206$	−11.6278	−	8.44810i	−0.810148	−	0.588607i
$207$	1.79165	−	8.33158i	0.124528	−	0.579085i
$208$	−0.777736	−	0.565058i	−0.0539263	−	0.0391797i
$209$	11.8868	+	13.2016i	0.822225	+	0.913173i
$210$	7.91503	−	15.8277i	0.546189	−	1.09222i
$211$	2.83614	−	3.14985i	0.195248	−	0.216844i	−0.637569	−	0.770393i	$-0.720060\pi$
$211$	2.83614	−	3.14985i	0.195248	−	0.216844i	0.832817	+	0.553549i	$0.186727\pi$
$212$	9.94394	−	2.11365i	0.682952	−	0.145166i
$213$	3.91485	−	4.82270i	0.268241	−	0.330446i
$214$	−17.3901	−	3.69638i	−1.18876	−	0.252679i
$215$	9.53035	−	16.8446i	0.649965	−	1.14879i
$216$	−5.13505	+	0.794548i	−0.349396	+	0.0540621i
$217$	−12.5214	−	9.09734i	−0.850009	−	0.617568i
$218$	4.65967	−	8.07079i	0.315593	−	0.546623i
$219$	13.2294	+	20.4247i	0.893963	+	1.38017i
$220$	5.96739	+	4.25655i	0.402322	+	0.286977i
$221$	−1.33794	−	0.595691i	−0.0899999	−	0.0400705i
$222$	0.162192	−	0.602442i	0.0108856	−	0.0404333i
$223$	−17.3733	−	3.69280i	−1.16340	−	0.247288i	−0.414550	−	0.910027i	$-0.636061\pi$
$223$	−17.3733	−	3.69280i	−1.16340	−	0.247288i	−0.748851	+	0.662738i	$0.769394\pi$
$224$	−4.56921			−0.305293
$225$	12.8759	−	7.69483i	0.858396	−	0.512988i
$226$	10.8323			0.720556
$227$	−14.0942	−	2.99581i	−0.935463	−	0.198839i	−0.285131	−	0.958489i	$-0.592037\pi$
$227$	−14.0942	−	2.99581i	−0.935463	−	0.198839i	−0.650332	+	0.759650i	$0.725370\pi$
$228$	−6.62928	−	6.64506i	−0.439035	−	0.440080i
$229$	−13.1449	−	5.85247i	−0.868637	−	0.386742i	−0.0764884	−	0.997070i	$-0.524371\pi$
$229$	−13.1449	−	5.85247i	−0.868637	−	0.386742i	−0.792148	+	0.610328i	$0.791037\pi$
$230$	5.10609	−	3.77826i	0.336685	−	0.249131i
$231$	−11.8053	+	23.1012i	−0.776729	+	1.51995i
$232$	−0.206618	+	0.357873i	−0.0135651	+	0.0234955i
$233$	7.08259	+	5.14580i	0.463996	+	0.337113i	0.795097	−	0.606483i	$-0.207420\pi$
$233$	7.08259	+	5.14580i	0.463996	+	0.337113i	−0.331101	+	0.943595i	$0.607420\pi$
$234$	2.50104	−	1.43606i	0.163498	−	0.0938781i
$235$	0.0675378	+	0.592802i	0.00440568	+	0.0386702i
$236$	−12.6043	−	2.67912i	−0.820468	−	0.174396i
$237$	−3.24413	−	8.48138i	−0.210729	−	0.550925i
$238$	−6.80892	+	1.44728i	−0.441357	+	0.0938133i
$239$	6.04077	−	6.70895i	0.390745	−	0.433966i	−0.515390	−	0.856956i	$-0.672353\pi$
$239$	6.04077	−	6.70895i	0.390745	−	0.433966i	0.906134	+	0.422990i	$0.139019\pi$
$240$	−3.26395	−	2.08485i	−0.210687	−	0.134577i
$241$	5.17258	+	5.74473i	0.333195	+	0.370051i	0.886340	−	0.463034i	$-0.153239\pi$
$241$	5.17258	+	5.74473i	0.333195	+	0.370051i	−0.553145	+	0.833085i	$0.686573\pi$
$242$	0.205806	+	0.149527i	0.0132297	+	0.00961193i
$243$	4.12402	−	15.0330i	0.264556	−	0.964370i
$244$	10.3673	+	7.53227i	0.663697	+	0.482204i
$245$	15.7494	+	26.7376i	1.00619	+	1.70820i
$246$	−16.8480	+	4.49295i	−1.07419	+	0.286460i
$247$	4.75929	+	2.11897i	0.302826	+	0.134827i
$248$	−2.26655	+	2.51726i	−0.143926	+	0.159846i
$249$	−15.1835	+	12.2655i	−0.962215	+	0.777294i
$250$	10.9931	+	2.03765i	0.695264	+	0.128872i
$251$	−2.07489			−0.130966			−0.0654829	−	0.997854i	$-0.520859\pi$
$251$	−2.07489			−0.130966			−0.0654829	+	0.997854i	$0.520859\pi$
$252$	5.60515	−	12.5092i	0.353091	−	0.788008i
$253$	−7.53348	+	5.47340i	−0.473626	+	0.344109i
$254$	−1.91127	−	18.1845i	−0.119924	−	1.14100i
$255$	−5.52424	−	2.07295i	−0.345941	−	0.129813i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	7.72798	+	13.3853i	0.482058	+	0.834949i	0.999788	−	0.0205952i	$-0.00655611\pi$
$257$	7.72798	+	13.3853i	0.482058	+	0.834949i	−0.517730	+	0.855544i	$0.673223\pi$
$258$	6.82181	−	13.3493i	0.424708	−	0.831091i
$259$	1.10129	+	1.22310i	0.0684307	+	0.0760000i
$260$	2.10645	+	0.428575i	0.130637	+	0.0265791i
$261$	−0.726296	−	1.00468i	−0.0449566	−	0.0621878i
$262$	−2.17452	+	6.69249i	−0.134342	+	0.413463i
$263$	−5.43795	−	6.03946i	−0.335319	−	0.372409i	0.551779	−	0.833990i	$-0.313949\pi$
$263$	−5.43795	−	6.03946i	−0.335319	−	0.372409i	−0.887098	+	0.461581i	$0.847282\pi$
$264$	4.75808	+	3.09798i	0.292840	+	0.190668i
$265$	−18.2734	+	13.5214i	−1.12253	+	0.830616i
$266$	24.2205	−	5.14822i	1.48505	−	0.315658i
$267$	−2.65562	−	4.09996i	−0.162521	−	0.250913i
$268$	−0.0934645	+	0.161885i	−0.00570925	+	0.00988872i
$269$	−12.3392	−	8.96497i	−0.752336	−	0.546604i	0.144214	−	0.989546i	$-0.453935\pi$
$269$	−12.3392	−	8.96497i	−0.752336	−	0.546604i	−0.896550	+	0.442943i	$0.853935\pi$
$270$	9.71173	−	6.37827i	0.591037	−	0.388169i
$271$	−11.5578	+	8.39723i	−0.702086	+	0.510096i	−0.880611	−	0.473840i	$-0.842868\pi$
$271$	−11.5578	+	8.39723i	−0.702086	+	0.510096i	0.178525	+	0.983935i	$0.442868\pi$
$272$	0.159246	+	1.51512i	0.00965569	+	0.0918678i
$273$	−0.407209	+	7.59719i	−0.0246454	+	0.459803i
$274$	−9.74368	−	16.8765i	−0.588637	−	1.01955i
$275$	−16.0891	−	3.12760i	−0.970208	−	0.188601i
$276$	3.82740	−	3.09184i	0.230382	−	0.186107i
$277$	−9.60679	−	2.04199i	−0.577216	−	0.122691i	−0.0899526	−	0.995946i	$-0.528672\pi$
$277$	−9.60679	−	2.04199i	−0.577216	−	0.122691i	−0.487264	+	0.873255i	$0.662005\pi$
$278$	−1.28797	+	0.935762i	−0.0772471	+	0.0561233i
$279$	−4.11114	−	9.29319i	−0.246128	−	0.556369i
$280$	9.29715	−	4.23689i	0.555611	−	0.253203i
$281$	−6.48373	+	2.88674i	−0.386787	+	0.172209i	−0.590912	−	0.806736i	$-0.701232\pi$
$281$	−6.48373	+	2.88674i	−0.386787	+	0.172209i	0.204125	+	0.978945i	$0.434565\pi$
$282$	0.0717540	+	0.456549i	0.00427289	+	0.0271871i
$283$	−2.00944	+	19.1186i	−0.119449	+	1.13648i	0.756472	+	0.654026i	$0.226921\pi$
$283$	−2.00944	+	19.1186i	−0.119449	+	1.13648i	−0.875921	+	0.482455i	$0.839745\pi$
$284$	3.50792	−	0.745632i	0.208157	−	0.0442451i
$285$	19.6506	+	7.37384i	1.16400	+	0.436788i
$286$	−3.08244	−	0.655192i	−0.182268	−	0.0387423i
$287$	14.2144	−	43.7475i	0.839051	−	2.58233i
$288$	−2.59450	−	1.50617i	−0.152883	−	0.0887521i
$289$	−4.53607	−	13.9606i	−0.266828	−	0.821212i
$290$	0.0885692	−	0.919770i	0.00520096	−	0.0540107i
$291$	9.55217	+	24.9729i	0.559958	+	1.46394i
$292$	−1.46860	+	13.9728i	−0.0859432	+	0.817695i
$293$	−0.547862	−	0.948925i	−0.0320064	−	0.0554368i	0.849578	−	0.527462i	$-0.176856\pi$
$293$	−0.547862	−	0.948925i	−0.0320064	−	0.0554368i	−0.881585	+	0.472025i	$0.843523\pi$
$294$	13.0674	+	20.1745i	0.762105	+	1.17660i
$295$	28.1307	−	6.23625i	1.63783	−	0.363089i
$296$	0.291412	−	0.211723i	0.0169380	−	0.0123062i
$297$	−14.3183	+	9.22596i	−0.830831	+	0.535345i
$298$	−3.71299	−	11.4274i	−0.215088	−	0.661972i
$299$	−1.36542	+	2.36498i	−0.0789644	+	0.136770i
$300$	8.57452	+	1.21557i	0.495050	+	0.0701809i
$301$	19.7739	+	34.2493i	1.13975	+	1.97410i
$302$	−0.860443	+	0.955619i	−0.0495129	+	0.0549897i
$303$	−2.86240	+	10.6321i	−0.164441	+	0.610796i
$304$	−0.566464	−	5.38954i	−0.0324889	−	0.309111i
$305$	−28.0792	−	5.71294i	−1.60781	−	0.327122i
$306$	−4.34334	−	1.42266i	−0.248292	−	0.0813283i
$307$	6.92252			0.395089			0.197545	−	0.980294i	$-0.436703\pi$
$307$	6.92252			0.395089			0.197545	+	0.980294i	$0.436703\pi$
$308$	−13.6832	+	6.09213i	−0.779670	+	0.347132i
$309$	24.5832	+	3.92356i	1.39849	+	0.223204i
$310$	2.27767	−	7.22368i	0.129363	−	0.410278i
$311$	4.95267	−	5.50050i	0.280840	−	0.311905i	−0.586177	−	0.810183i	$-0.699368\pi$
$311$	4.95267	−	5.50050i	0.280840	−	0.311905i	0.867017	+	0.498279i	$0.166034\pi$
$312$	1.64427	+	0.262431i	0.0930884	+	0.0148572i
$313$	−20.2911	−	22.5356i	−1.14692	−	1.27379i	−0.956386	−	0.292105i	$-0.905644\pi$
$313$	−20.2911	−	22.5356i	−1.14692	−	1.27379i	−0.190535	−	0.981680i	$-0.561022\pi$
$314$	4.44105	+	13.6682i	0.250623	+	0.771339i
$315$	0.194421	+	30.6505i	0.0109544	+	1.72696i
$316$	1.62009	−	4.98612i	0.0911370	−	0.280491i
$317$	28.9611	−	12.8943i	1.62662	−	0.724218i	0.628075	−	0.778153i	$-0.283843\pi$
$317$	28.9611	−	12.8943i	1.62662	−	0.724218i	0.998544	+	0.0539348i	$0.0171763\pi$
$318$	−13.6973	+	11.0649i	−0.768106	+	0.620489i
$319$	−0.141595	+	1.34719i	−0.00792781	+	0.0754281i
$320$	−0.709502	−	2.12052i	−0.0396624	−	0.118541i
$321$	29.7536	−	7.93456i	1.66069	−	0.442864i
$322$	1.35674	+	12.9086i	0.0756084	+	0.719366i
$323$	−2.55125	−	7.85194i	−0.141955	−	0.436894i
$324$	7.30623	−	5.25538i	0.405902	−	0.291966i
$325$	−4.68349	+	1.08121i	−0.259793	+	0.0599748i
$326$	−10.5350	+	18.2471i	−0.583477	+	1.01061i
$327$	−0.863948	+	16.1184i	−0.0477764	+	0.891351i
$328$	−9.19679	−	4.09468i	−0.507808	−	0.226091i
$329$	−1.11377	−	0.495883i	−0.0614042	−	0.0273389i
$330$	−12.5541	−	1.89156i	−0.691082	−	0.104127i
$331$	6.08414	−	2.70883i	0.334415	−	0.148891i	−0.232658	−	0.972559i	$-0.574742\pi$
$331$	6.08414	−	2.70883i	0.334415	−	0.148891i	0.567073	+	0.823668i	$0.308076\pi$
$332$	−11.2691			−0.618475
$333$	0.222158	+	1.05753i	0.0121742	+	0.0579524i
$334$	−2.55410	+	7.86072i	−0.139754	+	0.430120i
$335$	0.0400646	−	0.416061i	0.00218896	−	0.0227319i
$336$	7.05578	−	3.58454i	0.384924	−	0.195553i
$337$	−9.76854	+	2.07637i	−0.532127	+	0.113107i	−0.466136	−	0.884713i	$-0.654354\pi$
$337$	−9.76854	+	2.07637i	−0.532127	+	0.113107i	−0.0659908	+	0.997820i	$0.521021\pi$
$338$	11.8120	−	2.51071i	0.642485	−	0.136564i
$339$	−16.7273	+	8.49796i	−0.908503	+	0.461546i
$340$	−1.72895	−	2.93522i	−0.0937656	−	0.159185i
$341$	−3.43125	+	10.5603i	−0.185813	+	0.571873i
$342$	15.4500	+	5.06065i	0.835440	+	0.273649i
$343$	−31.4253			−1.69681
$344$	7.90698	−	3.52042i	0.426316	−	0.189808i
$345$	−4.92079	+	9.84012i	−0.264926	+	0.529774i
$346$	−16.9215	−	7.53395i	−0.909707	−	0.405028i
$347$	16.9085	+	7.52817i	0.907698	+	0.404133i	0.806842	−	0.590768i	$-0.201175\pi$
$347$	16.9085	+	7.52817i	0.907698	+	0.404133i	0.100856	+	0.994901i	$0.467842\pi$
$348$	0.0383090	−	0.714720i	0.00205358	−	0.0383130i
$349$	10.4982	−	18.1835i	0.561958	−	0.973340i	−0.435367	−	0.900253i	$-0.643381\pi$
$349$	10.4982	−	18.1835i	0.561958	−	0.973340i	0.997326	−	0.0730873i	$-0.0232852\pi$
$350$	−14.9885	+	17.2419i	−0.801171	+	0.921620i
$351$	−2.73553	+	4.17963i	−0.146012	+	0.223092i
$352$	1.01297	+	3.11761i	0.0539916	+	0.166169i
$353$	0.508592	+	4.83893i	0.0270696	+	0.257550i	0.999684	+	0.0251267i	$0.00799891\pi$
$353$	0.508592	+	4.83893i	0.0270696	+	0.257550i	−0.972615	+	0.232424i	$0.925334\pi$
$354$	21.5653	−	5.75094i	1.14618	−	0.305659i
$355$	−6.44631	+	4.76996i	−0.342135	+	0.253163i
$356$	0.294800	−	2.80483i	0.0156243	−	0.148656i
$357$	9.37896	−	7.57649i	0.496387	−	0.400990i
$358$	5.01959	−	2.23487i	0.265294	−	0.118116i
$359$	−7.12989	+	21.9435i	−0.376301	+	1.15814i	0.566296	+	0.824202i	$0.308376\pi$
$359$	−7.12989	+	21.9435i	−0.376301	+	1.15814i	−0.942597	+	0.333933i	$0.891624\pi$
$360$	6.67577	+	0.658867i	0.351844	+	0.0347253i
$361$	3.20390	+	9.86058i	0.168626	+	0.518978i
$362$	−5.12294	−	5.68960i	−0.269256	−	0.299039i
$363$	−0.435109	−	0.0694449i	−0.0228373	−	0.00364491i
$364$	−2.93918	+	3.26429i	−0.154055	+	0.171095i
$365$	−9.96833	−	29.7928i	−0.521766	−	1.55942i
$366$	−21.9182	−	3.49822i	−1.14568	−	0.182855i
$367$	−23.1052	+	10.2871i	−1.20608	+	0.536983i	−0.908569	−	0.417735i	$-0.862824\pi$
$367$	−23.1052	+	10.2871i	−1.20608	+	0.536983i	−0.297514	+	0.954717i	$0.596157\pi$
$368$	2.84068			0.148081
$369$	22.4920	−	20.1553i	1.17089	−	1.04924i
$370$	−0.396623	+	0.701019i	−0.0206194	+	0.0364442i
$371$	−4.85545	−	46.1965i	−0.252082	−	2.39840i
$372$	1.52523	−	5.66527i	0.0790793	−	0.293731i
$373$	9.49332	−	10.5434i	0.491546	−	0.545917i	−0.445428	−	0.895318i	$-0.646948\pi$
$373$	9.49332	−	10.5434i	0.491546	−	0.545917i	0.936973	+	0.349401i	$0.113615\pi$
$374$	2.49700	+	4.32493i	0.129117	+	0.223637i
$375$	−18.5741	+	5.47753i	−0.959162	+	0.282858i
$376$	−0.133412	+	0.231077i	−0.00688021	+	0.0119169i
$377$	0.122760	+	0.377815i	0.00632244	+	0.0194585i
$378$	1.15800	+	23.7140i	0.0595613	+	1.21972i
$379$	18.6361	−	13.5400i	0.957275	−	0.695501i	0.00475837	−	0.999989i	$-0.498485\pi$
$379$	18.6361	−	13.5400i	0.957275	−	0.695501i	0.952516	+	0.304488i	$0.0984854\pi$
$380$	6.15017	+	10.4411i	0.315497	+	0.535615i
$381$	17.2171	+	26.5812i	0.882060	+	1.36180i
$382$	6.41668	+	11.1140i	0.328306	+	0.568643i
$383$	3.25571	−	30.9760i	0.166359	−	1.58280i	−0.519117	−	0.854703i	$-0.673739\pi$
$383$	3.25571	−	30.9760i	0.166359	−	1.58280i	0.685476	−	0.728095i	$-0.259594\pi$
$384$	−0.618789	−	1.61775i	−0.0315774	−	0.0825552i
$385$	22.1926	−	25.0839i	1.13104	−	1.27839i
$386$	2.74088	+	8.43555i	0.139507	+	0.429358i
$387$	−0.0617401	+	25.9657i	−0.00313843	+	1.31991i
$388$	−4.77026	+	14.6813i	−0.242173	+	0.745333i
$389$	−4.38897	−	0.932905i	−0.222530	−	0.0473001i	0.0952974	−	0.995449i	$-0.469620\pi$
$389$	−4.38897	−	0.932905i	−0.222530	−	0.0473001i	−0.317827	+	0.948149i	$0.602953\pi$
$390$	−3.58901	+	0.990703i	−0.181736	+	0.0501662i
$391$	4.23312	−	0.899777i	0.214078	−	0.0455037i
$392$	−1.45061	+	13.8016i	−0.0732668	+	0.697087i
$393$	−1.89235	−	12.0405i	−0.0954565	−	0.607361i
$394$	−16.6986	+	7.43471i	−0.841265	+	0.374555i
$395$	1.32702	+	11.6477i	0.0667696	+	0.586060i
$396$	−9.77780	−	1.05120i	−0.491353	−	0.0528248i
$397$	28.4452	−	20.6667i	1.42763	−	1.03723i	0.437173	−	0.899378i	$-0.355980\pi$
$397$	28.4452	−	20.6667i	1.42763	−	1.03723i	0.990453	−	0.137853i	$-0.0440201\pi$
$398$	−8.93368	−	1.89891i	−0.447805	−	0.0951839i
$399$	−33.3625	+	26.9508i	−1.67022	+	1.34923i
$400$	3.40995	+	3.65681i	0.170497	+	0.182840i
$401$	−3.04614	−	5.27607i	−0.152117	−	0.263474i	0.779889	−	0.625918i	$-0.215276\pi$
$401$	−3.04614	−	5.27607i	−0.152117	−	0.263474i	−0.932005	+	0.362444i	$0.881942\pi$
$402$	0.0173292	−	0.323306i	0.000864303	−	0.0161251i
$403$	0.340380	+	3.23850i	0.0169555	+	0.161321i
$404$	−5.14292	+	3.73655i	−0.255870	+	0.185900i
$405$	−9.99312	+	17.4682i	−0.496562	+	0.868001i
$406$	1.52755	+	1.10983i	0.0758113	+	0.0550801i
$407$	0.590385	−	1.02258i	0.0292643	−	0.0506872i
$408$	−1.43452	−	2.21473i	−0.0710193	−	0.109645i
$409$	−28.9210	+	6.14734i	−1.43005	+	0.303966i	−0.856899	−	0.515484i	$-0.827612\pi$
$409$	−28.9210	+	6.14734i	−1.43005	+	0.303966i	−0.573150	+	0.819450i	$0.694279\pi$
$410$	22.5100	−	0.196310i	1.11169	−	0.00969505i
$411$	28.2858	+	18.4169i	1.39524	+	0.908438i
$412$	9.61725	+	10.6810i	0.473808	+	0.526217i
$413$	−18.1943	+	55.9964i	−0.895285	+	2.75540i
$414$	−3.48473	+	7.77701i	−0.171265	+	0.382219i
$415$	22.9298	−	10.4495i	1.12558	−	0.512948i
$416$	0.643258	+	0.714411i	0.0315383	+	0.0350269i
$417$	1.25478	−	2.45541i	0.0614466	−	0.120242i
$418$	−8.88225	−	15.3845i	−0.434445	−	0.752481i
$419$	−3.85081	+	36.6380i	−0.188124	+	1.78988i	0.339704	+	0.940532i	$0.389673\pi$
$419$	−3.85081	+	36.6380i	−0.188124	+	1.78988i	−0.527828	+	0.849351i	$0.676994\pi$
$420$	−11.0328	+	13.8362i	−0.538347	+	0.675138i
$421$	0.723035	+	6.87922i	0.0352386	+	0.335273i	0.997911	+	0.0646036i	$0.0205783\pi$
$421$	0.723035	+	6.87922i	0.0352386	+	0.335273i	−0.962672	+	0.270669i	$0.912755\pi$
$422$	−3.42905	+	2.49135i	−0.166924	+	0.121277i
$423$	−0.468965	−	0.648713i	−0.0228019	−	0.0315415i
$424$	−10.1661			−0.493709
$425$	6.23971	+	4.36920i	0.302670	+	0.211937i
$426$	−4.83200	+	3.90337i	−0.234111	+	0.189119i
$427$	39.1795	−	43.5132i	1.89603	−	2.10575i
$428$	16.2416	+	7.23121i	0.785066	+	0.349534i
$429$	5.27391	−	1.40642i	0.254627	−	0.0679026i
$430$	−12.8243	+	14.4950i	−0.618442	+	0.699013i
$431$	4.12148	+	2.99443i	0.198525	+	0.144237i	0.682607	−	0.730786i	$-0.260846\pi$
$431$	4.12148	+	2.99443i	0.198525	+	0.144237i	−0.484082	+	0.875023i	$0.660846\pi$
$432$	5.18803	+	0.290451i	0.249609	+	0.0139743i
$433$	3.96155	+	2.87824i	0.190380	+	0.138319i	0.678892	−	0.734238i	$-0.262460\pi$
$433$	3.96155	+	2.87824i	0.190380	+	0.138319i	−0.488512	+	0.872557i	$0.662460\pi$
$434$	10.3563	+	11.5019i	0.497121	+	0.552108i
$435$	0.584790	+	1.48979i	0.0280385	+	0.0714301i
$436$	−6.23586	+	6.92562i	−0.298643	+	0.331677i
$437$	−15.0579	+	3.20066i	−0.720317	+	0.153108i
$438$	−8.69382	−	22.7289i	−0.415407	−	1.08603i
$439$	−0.404801	−	0.0860432i	−0.0193201	−	0.00410662i	0.198241	−	0.980153i	$-0.436477\pi$
$439$	−0.404801	−	0.0860432i	−0.0193201	−	0.00410662i	−0.217562	+	0.976047i	$0.569810\pi$
$440$	−4.95201	−	5.40423i	−0.236078	−	0.257637i
$441$	−36.0056	−	20.9021i	−1.71455	−	0.995339i
$442$	1.18486	+	0.860848i	0.0563578	+	0.0409464i
$443$	6.30809	−	10.9259i	0.299706	−	0.519107i	−0.676362	−	0.736569i	$-0.736445\pi$
$443$	6.30809	−	10.9259i	0.299706	−	0.519107i	0.976069	+	0.217462i	$0.0697779\pi$
$444$	−0.283902	+	0.555556i	−0.0134734	+	0.0263655i
$445$	2.00100	+	5.98046i	0.0948563	+	0.283501i
$446$	16.2259	+	7.22422i	0.768316	+	0.342077i
$447$	14.6984	+	14.7334i	0.695211	+	0.696866i
$448$	4.46936	+	0.949991i	0.211157	+	0.0448829i
$449$	−9.41821			−0.444473			−0.222237	−	0.974993i	$-0.571336\pi$
$449$	−9.41821			−0.444473			−0.222237	+	0.974993i	$0.571336\pi$
$450$	−14.1944	+	4.84962i	−0.669131	+	0.228613i
$451$	−33.0006			−1.55394
$452$	−10.5956	−	2.25217i	−0.498376	−	0.105933i
$453$	0.579016	−	2.15069i	0.0272045	−	0.101048i
$454$	13.1633	+	5.86069i	0.617785	+	0.275056i
$455$	2.95359	−	9.36739i	0.138466	−	0.439150i
$456$	5.10283	+	7.87815i	0.238962	+	0.368928i
$457$	−0.708042	+	1.22637i	−0.0331208	+	0.0573669i	−0.882111	−	0.471042i	$-0.843878\pi$
$457$	−0.708042	+	1.22637i	−0.0331208	+	0.0573669i	0.848990	+	0.528409i	$0.177211\pi$
$458$	11.6408	+	8.45755i	0.543940	+	0.395195i
$459$	7.82308	−	1.21047i	0.365150	−	0.0564998i
$460$	−5.78005	+	2.63408i	−0.269496	+	0.122815i
$461$	20.8724	+	4.43657i	0.972127	+	0.206632i	0.666488	−	0.745516i	$-0.267797\pi$
$461$	20.8724	+	4.43657i	0.972127	+	0.206632i	0.305639	+	0.952148i	$0.401130\pi$
$462$	16.3503	−	20.1419i	0.760684	−	0.937087i
$463$	29.5811	−	6.28765i	1.37475	−	0.292212i	0.539454	−	0.842015i	$-0.318631\pi$
$463$	29.5811	−	6.28765i	1.37475	−	0.292212i	0.835294	+	0.549803i	$0.185297\pi$
$464$	0.276509	−	0.307094i	0.0128366	−	0.0142565i
$465$	2.14980	+	12.9417i	0.0996945	+	0.600155i
$466$	−5.85795	−	6.50591i	−0.271364	−	0.301380i
$467$	−10.2863	−	7.47341i	−0.475992	−	0.345828i	0.323780	−	0.946132i	$-0.395046\pi$
$467$	−10.2863	−	7.47341i	−0.475992	−	0.345828i	−0.799772	+	0.600304i	$0.795046\pi$
$468$	−2.74496	+	0.884682i	−0.126886	+	0.0408944i
$469$	0.690995	+	0.502037i	0.0319072	+	0.0231819i
$470$	0.0571886	−	0.593890i	0.00263791	−	0.0273941i
$471$	−17.5805	−	17.6224i	−0.810069	−	0.811997i
$472$	11.7718	+	5.24115i	0.541842	+	0.241244i
$473$	18.9848	−	21.0848i	0.872924	−	0.969480i
$474$	1.40986	+	8.97053i	0.0647571	+	0.412030i
$475$	−22.1957	−	15.5420i	−1.01841	−	0.713114i
$476$	6.96104			0.319059
$477$	12.4710	−	27.8320i	0.571007	−	1.27434i
$478$	−7.30363	+	5.30640i	−0.334060	+	0.242709i
$479$	1.49506	+	14.2245i	0.0683108	+	0.649934i	0.974086	+	0.226176i	$0.0726226\pi$
$479$	1.49506	+	14.2245i	0.0683108	+	0.649934i	−0.905776	+	0.423758i	$0.860711\pi$
$480$	2.75916	+	2.71791i	0.125938	+	0.124055i
$481$	0.0361958	−	0.344380i	0.00165039	−	0.0157024i
$482$	−3.86515	−	6.69463i	−0.176053	−	0.304932i
$483$	−12.2218	−	18.8691i	−0.556113	−	0.858572i
$484$	−0.170220	−	0.189048i	−0.00773727	−	0.00859311i
$485$	−3.90734	−	34.2961i	−0.177423	−	1.55730i
$486$	−7.15945	+	13.8471i	−0.324759	+	0.628117i
$487$	4.68997	−	14.4343i	0.212523	−	0.654078i	−0.786797	−	0.617212i	$-0.788262\pi$
$487$	4.68997	−	14.4343i	0.212523	−	0.654078i	0.999320	−	0.0368668i	$-0.0117377\pi$
$488$	−8.57468	−	9.52315i	−0.388158	−	0.431093i
$489$	1.95328	−	36.4419i	0.0883305	−	1.64796i
$490$	−9.84621	−	29.4278i	−0.444807	−	1.32941i
$491$	−5.59930	+	1.19017i	−0.252693	+	0.0537116i	−0.332516	−	0.943097i	$-0.607898\pi$
$491$	−5.59930	+	1.19017i	−0.252693	+	0.0537116i	0.0798234	+	0.996809i	$0.474564\pi$
$492$	17.4140	−	0.891869i	0.785083	−	0.0402086i
$493$	0.314776	−	0.545208i	0.0141768	−	0.0245549i
$494$	−4.21473	−	3.06218i	−0.189630	−	0.137774i
$495$	20.8700	−	6.92775i	0.938039	−	0.311379i
$496$	2.74039	−	1.99101i	0.123047	−	0.0893990i
$497$	−1.71286	−	16.2967i	−0.0768321	−	0.731009i
$498$	17.4018	−	8.84064i	0.779795	−	0.396158i
$499$	6.24424	+	10.8153i	0.279530	+	0.484161i	0.971268	−	0.237988i	$-0.0764879\pi$
$499$	6.24424	+	10.8153i	0.279530	+	0.484161i	−0.691738	+	0.722149i	$0.743155\pi$
$500$	−10.3292	−	4.27871i	−0.461936	−	0.191350i
$501$	−2.22268	−	14.1422i	−0.0993019	−	0.631829i
$502$	2.02955	+	0.431393i	0.0905831	+	0.0192540i
$503$	2.14050	−	1.55517i	0.0954403	−	0.0693414i	−0.539042	−	0.842279i	$-0.681213\pi$
$503$	2.14050	−	1.55517i	0.0954403	−	0.0693414i	0.634482	+	0.772938i	$0.281213\pi$
$504$	−8.08348	+	11.0705i	−0.360067	+	0.493119i
$505$	6.99971	−	12.3718i	0.311483	−	0.550537i
$506$	8.50684	−	3.78749i	0.378175	−	0.168374i
$507$	−16.2704	+	13.1435i	−0.722594	+	0.583724i
$508$	−1.91127	+	18.1845i	−0.0847989	+	0.806808i
$509$	−28.4230	+	6.04149i	−1.25983	+	0.267784i	−0.788973	−	0.614428i	$-0.789387\pi$
$509$	−28.4230	+	6.04149i	−1.25983	+	0.267784i	−0.470852	+	0.882212i	$0.656054\pi$
$510$	4.97253	+	3.17621i	0.220187	+	0.140645i
$511$	62.7933	+	13.3471i	2.77781	+	0.590442i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−27.8280	+	4.30583i	−1.22864	+	0.190107i
$514$	−4.77615	−	14.6995i	−0.210667	−	0.648367i
$515$	−29.4728	−	12.8154i	−1.29873	−	0.564712i
$516$	−9.44822	+	11.6393i	−0.415935	+	0.512390i
$517$	−0.0914272	+	0.869872i	−0.00402096	+	0.0382569i
$518$	−0.822925	−	1.42535i	−0.0361572	−	0.0626262i
$519$	32.0406	−	1.64098i	1.40643	−	0.0720312i
$520$	−1.97132	−	0.857166i	−0.0864479	−	0.0375892i
$521$	−10.4665	+	7.60434i	−0.458545	+	0.333152i	−0.792960	−	0.609274i	$-0.791461\pi$
$521$	−10.4665	+	7.60434i	−0.458545	+	0.333152i	0.334415	+	0.942426i	$0.391461\pi$
$522$	0.501541	+	1.13373i	0.0219518	+	0.0496218i
$523$	10.0371	+	30.8910i	0.438891	+	1.35077i	0.889046	+	0.457818i	$0.151369\pi$
$523$	10.0371	+	30.8910i	0.438891	+	1.35077i	−0.450155	+	0.892950i	$0.648631\pi$
$524$	3.51845	−	6.09413i	0.153704	−	0.266223i
$525$	9.61905	−	38.3835i	0.419810	−	1.67520i
$526$	4.06345	+	7.03810i	0.177175	+	0.306876i
$527$	3.45302	−	3.83497i	0.150416	−	0.167054i
$528$	−4.01000	−	4.01954i	−0.174513	−	0.174928i
$529$	1.56067	+	14.8487i	0.0678550	+	0.645597i
$530$	20.6854	−	9.42671i	0.898514	−	0.409470i
$531$	−28.7896	+	25.7986i	−1.24936	+	1.11956i
$532$	−24.7616			−1.07355
$533$	−8.84119	+	3.93635i	−0.382954	+	0.170502i
$534$	1.74516	+	4.56250i	0.0755203	+	0.197438i
$535$	−39.7527	+	0.346684i	−1.71866	+	0.0149884i
$536$	0.125080	−	0.138915i	0.00540263	−	0.00600023i
$537$	−5.99802	+	7.38896i	−0.258834	+	0.318857i
$538$	10.2057	+	11.3345i	0.439997	+	0.488666i
$539$	14.0577	+	43.2651i	0.605507	+	1.86356i
$540$	−10.8256	+	4.21971i	−0.465860	+	0.181588i
$541$	−7.79036	+	23.9762i	−0.334934	+	1.03082i	0.631821	+	0.775114i	$0.282308\pi$
$541$	−7.79036	+	23.9762i	−0.334934	+	1.03082i	−0.966755	+	0.255705i	$0.917692\pi$
$542$	13.0511	−	5.81073i	0.560593	−	0.249592i
$543$	12.3743	+	4.76695i	0.531033	+	0.204569i
$544$	0.159246	−	1.51512i	0.00682761	−	0.0649603i
$545$	6.26643	−	19.8742i	0.268424	−	0.851316i
$546$	1.97785	−	7.34651i	0.0846443	−	0.314401i
$547$	−1.05963	−	10.0817i	−0.0453064	−	0.431061i	−0.993540	−	0.113486i	$-0.963798\pi$
$547$	−1.05963	−	10.0817i	−0.0453064	−	0.431061i	0.948233	−	0.317575i	$-0.102869\pi$
$548$	6.02192	+	18.5336i	0.257244	+	0.791715i
$549$	36.5905	−	11.7929i	1.56165	−	0.503308i
$550$	15.0872	+	6.40436i	0.643322	+	0.273083i
$551$	−1.11971	+	1.93940i	−0.0477013	+	0.0826210i
$552$	−4.38659	+	2.22851i	−0.186706	+	0.0948518i
$553$	−21.8840	−	9.74339i	−0.930603	−	0.414331i
$554$	8.97231	+	3.99473i	0.381197	+	0.169720i
$555$	0.0625171	−	1.39367i	0.00265370	−	0.0591578i
$556$	1.45438	−	0.647530i	0.0616793	−	0.0274614i
$557$	−5.51844			−0.233824			−0.116912	−	0.993142i	$-0.537300\pi$
$557$	−5.51844			−0.233824			−0.116912	+	0.993142i	$0.537300\pi$
$558$	2.08914	+	9.94486i	0.0884405	+	0.421000i
$559$	2.57121	−	7.91337i	0.108751	−	0.334700i
$560$	−9.97488	+	2.21132i	−0.421516	+	0.0934452i
$561$	−7.24879	−	4.71968i	−0.306044	−	0.199265i
$562$	6.94224	−	1.47562i	0.292841	−	0.0622452i
$563$	−24.7910	+	5.26948i	−1.04482	+	0.222082i	−0.698183	−	0.715919i	$-0.746008\pi$
$563$	−24.7910	+	5.26948i	−1.04482	+	0.222082i	−0.346632	+	0.938001i	$0.612675\pi$
$564$	0.0247359	−	0.461491i	0.00104157	−	0.0194323i
$565$	23.6477	−	5.24243i	0.994867	−	0.220550i
$566$	5.94050	−	18.2830i	0.249698	−	0.768491i
$567$	−20.3918	−	35.7108i	−0.856376	−	1.49971i
$568$	−3.58629			−0.150477
$569$	−35.0462	+	15.6036i	−1.46921	+	0.654136i	−0.976394	−	0.215996i	$-0.930700\pi$
$569$	−35.0462	+	15.6036i	−1.46921	+	0.654136i	−0.492819	+	0.870132i	$0.664034\pi$
$570$	−17.6881	−	11.2983i	−0.740873	−	0.473234i
$571$	−23.6399	−	10.5252i	−0.989299	−	0.440464i	−0.152696	−	0.988273i	$-0.548795\pi$
$571$	−23.6399	−	10.5252i	−0.989299	−	0.440464i	−0.836604	+	0.547809i	$0.815462\pi$
$572$	2.87886	+	1.28175i	0.120371	+	0.0535927i
$573$	−18.6276	−	12.1284i	−0.778179	−	0.506672i
$574$	−22.9994	+	39.8362i	−0.959977	+	1.66273i
$575$	9.31840	−	10.7193i	0.388604	−	0.447027i
$576$	2.22466	+	2.01269i	0.0926940	+	0.0838620i
$577$	10.6135	+	32.6650i	0.441846	+	1.35986i	0.885906	+	0.463865i	$0.153538\pi$
$577$	10.6135	+	32.6650i	0.441846	+	1.35986i	−0.444060	+	0.895997i	$0.646462\pi$
$578$	1.53438	+	14.5986i	0.0638217	+	0.607223i
$579$	−10.8502	−	10.8760i	−0.450917	−	0.451991i
$580$	−0.277865	+	0.881256i	−0.0115377	+	0.0365922i
$581$	−5.38228	+	51.2090i	−0.223295	+	2.12451i
$582$	−4.15126	−	26.4132i	−0.172075	−	1.09486i
$583$	−30.4439	+	13.5545i	−1.26086	+	0.561369i
$584$	4.34161	−	13.3621i	0.179657	−	0.552928i
$585$	4.76494	−	4.34542i	0.197006	−	0.179661i
$586$	0.338597	+	1.04210i	0.0139873	+	0.0430486i
$587$	19.7927	+	21.9821i	0.816933	+	0.907296i	0.997082	−	0.0763431i	$-0.0243244\pi$
$587$	19.7927	+	21.9821i	0.816933	+	0.907296i	−0.180148	+	0.983639i	$0.557658\pi$
$588$	−8.58732	−	22.4505i	−0.354135	−	0.925842i
$589$	−12.2830	+	13.6416i	−0.506111	+	0.562093i
$590$	−28.8126	+	0.251275i	−1.18619	+	0.0103448i
$591$	19.9535	−	24.5808i	0.820779	−	1.01112i
$592$	−0.329063	+	0.146508i	−0.0135244	+	0.00602146i
$593$	24.5441			1.00791			0.503953	−	0.863731i	$-0.331879\pi$
$593$	24.5441			1.00791			0.503953	+	0.863731i	$0.331879\pi$
$594$	15.9236	−	6.04741i	0.653352	−	0.248128i
$595$	−14.1639	+	6.45476i	−0.580664	+	0.264620i
$596$	1.25596	+	11.9497i	0.0514462	+	0.489478i
$597$	15.2851	−	4.07616i	0.625578	−	0.166826i
$598$	1.82729	−	2.02941i	0.0747235	−	0.0829889i
$599$	21.0600	+	36.4769i	0.860487	+	1.49041i	0.871460	+	0.490467i	$0.163174\pi$
$599$	21.0600	+	36.4769i	0.860487	+	1.49041i	−0.0109726	+	0.999940i	$0.503493\pi$
$600$	−8.13441	−	2.97175i	−0.332086	−	0.121321i
$601$	−0.640476	+	1.10934i	−0.0261256	+	0.0452508i	−0.878793	−	0.477204i	$-0.841650\pi$
$601$	−0.640476	+	1.10934i	−0.0261256	+	0.0452508i	0.852667	+	0.522455i	$0.174984\pi$
$602$	−12.2209	−	37.6121i	−0.498087	−	1.53295i
$603$	0.226874	+	0.512845i	0.00923902	+	0.0208847i
$604$	1.04032	−	0.755840i	0.0423302	−	0.0307547i
$605$	0.521652	+	0.226825i	0.0212082	+	0.00922173i
$606$	5.01038	−	9.80460i	0.203533	−	0.398285i
$607$	18.6357	+	32.2780i	0.756399	+	1.31012i	0.944676	+	0.328006i	$0.106377\pi$
$607$	18.6357	+	32.2780i	0.756399	+	1.31012i	−0.188277	+	0.982116i	$0.560290\pi$
$608$	−0.566464	+	5.38954i	−0.0229731	+	0.218575i
$609$	−3.22952	−	0.515442i	−0.130867	−	0.0208868i
$610$	26.2778	+	11.4261i	1.06396	+	0.462629i
$611$	0.0792651	+	0.243953i	0.00320672	+	0.00986928i
$612$	3.95264	+	2.29461i	0.159776	+	0.0927540i
$613$	2.79492	−	8.60189i	0.112886	−	0.347427i	−0.878614	−	0.477532i	$-0.841531\pi$
$613$	2.79492	−	8.60189i	0.112886	−	0.347427i	0.991500	+	0.130105i	$0.0415314\pi$
$614$	−6.77125	−	1.43927i	−0.273265	−	0.0580844i
$615$	−34.6059	+	17.9622i	−1.39545	+	0.724305i
$616$	14.6508	−	3.11412i	0.590297	−	0.125471i
$617$	−3.17655	+	30.2229i	−0.127883	+	1.21673i	0.722803	+	0.691054i	$0.242853\pi$
$617$	−3.17655	+	30.2229i	−0.127883	+	1.21673i	−0.850687	+	0.525673i	$0.823813\pi$
$618$	−23.2303	−	8.94896i	−0.934458	−	0.359980i
$619$	35.2090	−	15.6761i	1.41517	−	0.630074i	0.450317	−	0.892869i	$-0.351311\pi$
$619$	35.2090	−	15.6761i	1.41517	−	0.630074i	0.964852	+	0.262795i	$0.0846443\pi$
$620$	−3.72978	+	6.59228i	−0.149792	+	0.264752i
$621$	−0.719933	−	14.7430i	−0.0288899	−	0.591618i
$622$	−5.98806	+	4.35058i	−0.240099	+	0.174442i
$623$	−12.6048	−	2.67924i	−0.505002	−	0.107342i
$624$	−1.55378	−	0.598559i	−0.0622008	−	0.0239615i
$625$	24.9848	−	0.871903i	0.999392	−	0.0348761i
$626$	15.1623	+	26.2619i	0.606007	+	1.04964i
$627$	25.7851	+	16.7887i	1.02976	+	0.670475i
$628$	−1.50224	−	14.2928i	−0.0599457	−	0.570346i
$629$	−0.443957	+	0.322553i	−0.0177017	+	0.0128610i
$630$	6.18243	−	30.0212i	0.246314	−	1.19607i
$631$	−10.0425	−	7.29632i	−0.399786	−	0.290462i	0.369668	−	0.929164i	$-0.379472\pi$
$631$	−10.0425	−	7.29632i	−0.399786	−	0.290462i	−0.769454	+	0.638702i	$0.779472\pi$
$632$	−2.62136	+	4.54032i	−0.104272	+	0.180604i
$633$	3.34068	−	6.53724i	0.132780	−	0.259832i
$634$	−31.0092	+	6.59120i	−1.23153	+	0.261770i
$635$	−12.9730	−	38.7730i	−0.514819	−	1.53866i
$636$	15.6985	−	7.97529i	0.622486	−	0.316241i
$637$	8.92690	+	9.91433i	0.353697	+	0.392820i
$638$	0.418597	−	1.28831i	0.0165724	−	0.0510047i
$639$	4.39939	−	9.81829i	0.174037	−	0.388406i
$640$	0.253117	+	2.22170i	0.0100053	+	0.0878202i
$641$	−12.2750	−	13.6327i	−0.484832	−	0.538461i	0.450245	−	0.892905i	$-0.351337\pi$
$641$	−12.2750	−	13.6327i	−0.484832	−	0.538461i	−0.935077	+	0.354444i	$0.884670\pi$
$642$	−30.7531	+	1.57504i	−1.21373	+	0.0621620i
$643$	−12.9684	−	22.4619i	−0.511422	−	0.885809i	−0.999912	−	0.0132398i	$-0.995786\pi$
$643$	−12.9684	−	22.4619i	−0.511422	−	0.885809i	0.488490	−	0.872569i	$-0.337548\pi$
$644$	1.35674	−	12.9086i	0.0534632	−	0.508668i
$645$	8.43194	−	32.4439i	0.332007	−	1.27748i
$646$	0.862989	+	8.21079i	0.0339539	+	0.323049i
$647$	−11.0821	+	8.05165i	−0.435684	+	0.316543i	−0.783918	−	0.620865i	$-0.786782\pi$
$647$	−11.0821	+	8.05165i	−0.435684	+	0.316543i	0.348234	+	0.937408i	$0.386782\pi$
$648$	−8.23922	+	3.62149i	−0.323667	+	0.142266i
$649$	42.2405			1.65808
$650$	4.80594	−	0.0838318i	0.188504	−	0.00328815i
$651$	−25.0155	−	9.63670i	−0.980435	−	0.377692i
$652$	14.0985	−	15.6580i	0.552141	−	0.613215i
$653$	16.4441	+	7.32137i	0.643506	+	0.286507i	0.702428	−	0.711755i	$-0.252099\pi$
$653$	16.4441	+	7.32137i	0.643506	+	0.286507i	−0.0589214	+	0.998263i	$0.518766\pi$
$654$	4.19628	−	15.5866i	0.164088	−	0.609484i
$655$	−1.50822	+	15.6625i	−0.0589312	+	0.611986i
$656$	8.14449	+	5.91732i	0.317989	+	0.231032i
$657$	31.2558	+	28.2777i	1.21941	+	1.10322i
$658$	0.986333	+	0.716613i	0.0384513	+	0.0279365i
$659$	−14.3840	−	15.9750i	−0.560320	−	0.622298i	0.394711	−	0.918805i	$-0.370845\pi$
$659$	−14.3840	−	15.9750i	−0.560320	−	0.622298i	−0.955031	+	0.296507i	$0.904178\pi$
$660$	11.8865	+	4.46038i	0.462682	+	0.173620i
$661$	11.4053	−	12.6669i	0.443616	−	0.492685i	−0.479319	−	0.877641i	$-0.659116\pi$
$661$	11.4053	−	12.6669i	0.443616	−	0.492685i	0.922935	+	0.384955i	$0.125783\pi$
$662$	−6.51439	+	1.38468i	−0.253189	+	0.0538169i
$663$	−2.50499	−	0.399805i	−0.0972858	−	0.0155271i
$664$	11.0229	+	2.34299i	0.427771	+	0.0909255i
$665$	50.3834	−	22.9607i	1.95378	−	0.890376i
$666$	0.00256943	−	1.08061i	9.95633e−5	−	0.0418728i
$667$	−0.949683	−	0.689985i	−0.0367719	−	0.0267163i
$668$	4.13263	−	7.15792i	0.159896	−	0.276948i
$669$	−30.7234	+	1.57352i	−1.18784	+	0.0608358i
$670$	−0.125693	+	0.398640i	−0.00485595	+	0.0154008i
$671$	−38.3754	−	17.0858i	−1.48147	−	0.659591i
$672$	−7.64686	+	2.03923i	−0.294984	+	0.0786650i
$673$	−7.31045	−	1.55388i	−0.281797	−	0.0598978i	0.0648449	−	0.997895i	$-0.479345\pi$
$673$	−7.31045	−	1.55388i	−0.281797	−	0.0598978i	−0.346642	+	0.937998i	$0.612678\pi$
$674$	9.98678			0.384676
$675$	18.1145	−	18.6243i	0.697228	−	0.716849i
$676$	−12.0758			−0.464455
$677$	3.55132	+	0.754856i	0.136488	+	0.0290115i	0.275649	−	0.961258i	$-0.411107\pi$
$677$	3.55132	+	0.754856i	0.136488	+	0.0290115i	−0.139161	+	0.990270i	$0.544441\pi$
$678$	18.1286	−	4.83445i	0.696225	−	0.185666i
$679$	64.4363	+	28.6889i	2.47284	+	1.10098i
$680$	1.08090	+	3.23055i	0.0414508	+	0.123886i
$681$	−24.9245	+	1.27653i	−0.955110	+	0.0489166i
$682$	5.55189	−	9.61615i	0.212593	−	0.368221i
$683$	−0.656658	−	0.477090i	−0.0251263	−	0.0182553i	0.575151	−	0.818047i	$-0.304943\pi$
$683$	−0.656658	−	0.477090i	−0.0251263	−	0.0182553i	−0.600278	+	0.799792i	$0.704943\pi$
$684$	−14.0602	−	8.16230i	−0.537605	−	0.312093i
$685$	−29.4387	−	32.1271i	−1.12479	−	1.22751i
$686$	30.7386	+	6.53369i	1.17361	+	0.249458i
$687$	−24.6107	−	3.92795i	−0.938957	−	0.149861i
$688$	−8.46613	+	1.79953i	−0.322768	+	0.0686065i
$689$	−6.53942	+	7.26276i	−0.249132	+	0.276689i
$690$	6.85913	−	8.60200i	0.261123	−	0.327472i
$691$	5.49260	+	6.10015i	0.208948	+	0.232061i	0.838505	−	0.544894i	$-0.183430\pi$
$691$	5.49260	+	6.10015i	0.208948	+	0.232061i	−0.629557	+	0.776955i	$0.716763\pi$
$692$	14.9854	+	10.8875i	0.569658	+	0.413881i
$693$	−9.44684	+	43.9300i	−0.358856	+	1.66876i
$694$	−14.9739	−	10.8791i	−0.568400	−	0.412967i
$695$	−2.35884	+	2.66616i	−0.0894760	+	0.101133i
$696$	−0.186071	+	0.691137i	−0.00705299	+	0.0261975i
$697$	14.0110	+	6.23811i	0.530705	+	0.236285i
$698$	−14.0494	+	15.6034i	−0.531777	+	0.590599i
$699$	14.1497	+	5.45089i	0.535192	+	0.206171i
$700$	18.2458	−	13.7489i	0.689627	−	0.519658i
$701$	4.74278			0.179132			0.0895662	−	0.995981i	$-0.471452\pi$
$701$	4.74278			0.179132			0.0895662	+	0.995981i	$0.471452\pi$
$702$	3.54474	−	3.51955i	0.133788	−	0.132837i
$703$	1.57923	−	1.14738i	0.0595617	−	0.0432741i
$704$	−0.342650	−	3.26009i	−0.0129141	−	0.122869i
$705$	0.377596	+	0.961951i	0.0142211	+	0.0362292i
$706$	0.508592	−	4.83893i	0.0191411	−	0.182116i
$707$	14.5232	+	25.1549i	0.546201	+	0.946048i
$708$	−22.2897	+	1.14159i	−0.837700	+	0.0429034i
$709$	−23.8646	−	26.5043i	−0.896255	−	0.995391i	−1.00000		0.000787562i	$-0.999749\pi$
$709$	−23.8646	−	26.5043i	−0.896255	−	0.995391i	0.103745	−	0.994604i	$-0.466917\pi$
$710$	7.29717	−	3.32546i	0.273858	−	0.124802i
$711$	−9.21449	−	12.7463i	−0.345570	−	0.478023i
$712$	−0.871515	+	2.68225i	−0.0326614	+	0.100521i
$713$	−6.43856	−	7.15074i	−0.241126	−	0.267797i
$714$	−10.7493	+	5.46093i	−0.402281	+	0.204370i
$715$	−7.04626	+	0.0614505i	−0.263515	+	0.00229812i
$716$	−5.37456	+	1.14240i	−0.200857	+	0.0426934i
$717$	7.11542	−	13.9239i	0.265730	−	0.519996i
$718$	11.5364	−	19.9816i	0.430535	−	0.745708i
$719$	−22.9613	−	16.6823i	−0.856311	−	0.622146i	0.0705681	−	0.997507i	$-0.477519\pi$
$719$	−22.9613	−	16.6823i	−0.856311	−	0.622146i	−0.926879	+	0.375361i	$0.877519\pi$
$720$	−6.39290	−	2.03244i	−0.238249	−	0.0757446i
$721$	53.1298	−	38.6011i	1.97866	−	1.43758i
$722$	−1.08375	−	10.3112i	−0.0403332	−	0.383744i
$723$	11.2205	+	7.30566i	0.417295	+	0.271700i
$724$	3.82805	+	6.63038i	0.142268	+	0.246416i
$725$	−0.251780	−	2.05078i	−0.00935088	−	0.0761642i
$726$	0.411162	+	0.158392i	0.0152597	+	0.00587846i
$727$	−22.5937	−	4.80244i	−0.837953	−	0.178112i	−0.231104	−	0.972929i	$-0.574234\pi$
$727$	−22.5937	−	4.80244i	−0.837953	−	0.178112i	−0.606850	+	0.794817i	$0.707567\pi$
$728$	3.55363	−	2.58187i	0.131706	−	0.0956903i
$729$	0.192596	−	26.9993i	0.00713318	−	0.999975i
$730$	3.55623	+	31.2143i	0.131622	+	1.15529i
$731$	−12.0460	+	5.36324i	−0.445539	+	0.198367i
$732$	20.7119	+	7.97884i	0.765535	+	0.294906i
$733$	−4.09955	+	39.0046i	−0.151420	+	1.44067i	0.609997	+	0.792404i	$0.291171\pi$
$733$	−4.09955	+	39.0046i	−0.151420	+	1.44067i	−0.761417	+	0.648263i	$0.775496\pi$
$734$	24.7391	−	5.25846i	0.913138	−	0.194093i
$735$	38.2906	+	37.7181i	1.41237	+	1.39125i
$736$	−2.77861	−	0.590611i	−0.102421	−	0.0217702i
$737$	0.189354	−	0.582772i	0.00697495	−	0.0214667i
$738$	−26.1910	+	15.0385i	−0.964105	+	0.553574i
$739$	−0.371951	−	1.14475i	−0.0136824	−	0.0421102i	0.943982	−	0.329996i	$-0.107048\pi$
$739$	−0.371951	−	1.14475i	−0.0136824	−	0.0421102i	−0.957665	+	0.287886i	$0.907048\pi$
$740$	0.533706	−	0.603238i	0.0196194	−	0.0221755i
$741$	8.91067	+	1.42217i	0.327342	+	0.0522448i
$742$	−4.85545	+	46.1965i	−0.178249	+	1.69593i
$743$	1.10029	+	1.90576i	0.0403658	+	0.0699156i	0.885502	−	0.464635i	$-0.153814\pi$
$743$	1.10029	+	1.90576i	0.0403658	+	0.0699156i	−0.845137	+	0.534550i	$0.820481\pi$
$744$	−2.66977	+	5.22436i	−0.0978786	+	0.191534i
$745$	−13.6361	−	23.1499i	−0.499589	−	0.848146i
$746$	−11.4780	+	8.33923i	−0.420238	+	0.305321i
$747$	−19.9365	+	27.3035i	−0.729438	+	0.998981i
$748$	−1.54323	−	4.74958i	−0.0564262	−	0.173662i
$749$	40.6171	−	70.3508i	1.48411	−	2.57056i
$750$	19.3070	−	1.49606i	0.704993	−	0.0546285i
$751$	−13.9521	−	24.1657i	−0.509119	−	0.881819i	−0.999944	−	0.0105615i	$-0.996638\pi$
$751$	−13.9521	−	24.1657i	−0.509119	−	0.881819i	0.490826	−	0.871258i	$-0.336695\pi$
$752$	0.178540	−	0.198289i	0.00651069	−	0.00723086i
$753$	−3.47246	+	0.926019i	−0.126543	+	0.0337460i
$754$	−0.0415248	−	0.395082i	−0.00151224	−	0.0143880i
$755$	−1.41592	+	2.50260i	−0.0515307	+	0.0910790i
$756$	3.79773	−	23.4366i	0.138122	−	0.852380i
$757$	−36.2996			−1.31933			−0.659666	−	0.751559i	$-0.729302\pi$
$757$	−36.2996			−1.31933			−0.659666	+	0.751559i	$0.729302\pi$
$758$	−21.0440	+	9.36940i	−0.764353	+	0.340312i
$759$	−10.1650	+	12.5223i	−0.368966	+	0.454529i
$760$	−3.84496	−	11.4916i	−0.139471	−	0.416844i
$761$	11.9163	−	13.2344i	0.431966	−	0.479747i	−0.487384	−	0.873188i	$-0.662049\pi$
$761$	11.9163	−	13.2344i	0.431966	−	0.479747i	0.919350	+	0.393441i	$0.128715\pi$
$762$	−11.3144	−	29.5800i	−0.409876	−	1.07157i
$763$	28.4929	+	31.6446i	1.03151	+	1.14561i
$764$	−3.96573	−	12.2053i	−0.143475	−	0.441571i
$765$	−10.1703	−	1.00376i	−0.367709	−	0.0362911i
$766$	−9.62483	+	29.6222i	−0.347759	+	1.07029i
$767$	11.3167	−	5.03850i	0.408621	−	0.181930i
$768$	0.268918	+	1.71105i	0.00970376	+	0.0617421i
$769$	2.75309	−	26.1939i	0.0992789	−	0.944575i	−0.825585	−	0.564277i	$-0.809155\pi$
$769$	2.75309	−	26.1939i	0.0992789	−	0.944575i	0.924864	−	0.380298i	$-0.124178\pi$
$770$	−26.9229	+	19.9217i	−0.970234	+	0.717927i
$771$	18.9071	+	18.9521i	0.680922	+	0.682543i
$772$	−0.927133	−	8.82108i	−0.0333682	−	0.317478i
$773$	6.95554	+	21.4070i	0.250174	+	0.769955i	0.994742	+	0.102409i	$0.0326551\pi$
$773$	6.95554	+	21.4070i	0.250174	+	0.769955i	−0.744569	+	0.667546i	$0.767345\pi$
$774$	5.45897	−	25.3855i	0.196219	−	0.912463i
$775$	1.47632	−	16.8721i	0.0530308	−	0.606063i
$776$	7.71844	−	13.3687i	0.277076	−	0.479910i
$777$	2.38895	+	1.55544i	0.0857030	+	0.0558011i
$778$	4.09910	+	1.82504i	0.146960	+	0.0654307i
$779$	−49.8395	−	22.1900i	−1.78569	−	0.795039i
$780$	3.71656	−	0.222858i	0.133074	−	0.00797959i
$781$	−10.7397	+	4.78161i	−0.384296	+	0.171100i
$782$	−4.32769			−0.154758
$783$	−1.66389	−	1.35724i	−0.0594625	−	0.0485039i
$784$	4.28842	−	13.1984i	0.153158	−	0.471372i
$785$	16.3100	+	27.6892i	0.582128	+	0.988270i
$786$	−0.652355	+	12.1708i	−0.0232687	+	0.434118i
$787$	−45.1930	+	9.60608i	−1.61096	+	0.342420i	−0.923439	−	0.383746i	$-0.874634\pi$
$787$	−45.1930	+	9.60608i	−1.61096	+	0.342420i	−0.687519	+	0.726166i	$0.741300\pi$
$788$	17.8795	−	3.80040i	0.636931	−	0.135384i
$789$	−11.7962	−	7.68047i	−0.419955	−	0.273432i
$790$	1.12367	−	11.6691i	0.0399785	−	0.415167i
$791$	−15.2948	+	47.0727i	−0.543822	+	1.67371i
$792$	9.34558	+	3.06115i	0.332081	+	0.108773i
$793$	−12.3192			−0.437467
$794$	−32.1205	+	14.3010i	−1.13991	+	0.507522i
$795$	−24.5471	+	30.7844i	−0.870597	+	1.09181i
$796$	8.34365	+	3.71483i	0.295733	+	0.131669i
$797$	13.6427	+	6.07412i	0.483249	+	0.215156i	0.633877	−	0.773434i	$-0.281463\pi$
$797$	13.6427	+	6.07412i	0.483249	+	0.215156i	−0.150627	+	0.988591i	$0.548129\pi$
$798$	38.2369	−	19.4254i	1.35357	−	0.687653i
$799$	0.203249	−	0.352038i	0.00719044	−	0.0124542i
$800$	−2.57514	−	4.28587i	−0.0910450	−	0.151528i
$801$	−6.27415	−	5.67634i	−0.221686	−	0.200564i
$802$	1.88262	+	5.79410i	0.0664775	+	0.204597i
$803$	−4.81414	−	45.8035i	−0.169887	−	1.61637i
$804$	−0.0841697	+	0.312638i	−0.00296844	+	0.0110259i
$805$	9.20910	+	27.5236i	0.324578	+	0.970080i
$806$	0.340380	−	3.23850i	0.0119894	−	0.114071i
$807$	−24.6515	−	9.49648i	−0.867775	−	0.334292i
$808$	5.80740	−	2.58562i	0.204304	−	0.0909619i
$809$	8.46830	−	26.0627i	0.297730	−	0.916317i	−0.684561	−	0.728955i	$-0.740006\pi$
$809$	8.46830	−	26.0627i	0.297730	−	0.916317i	0.982291	−	0.187362i	$-0.0599938\pi$
$810$	13.4066	−	15.0088i	0.471059	−	0.527355i
$811$	−13.6879	−	42.1270i	−0.480647	−	1.47928i	−0.838188	−	0.545381i	$-0.816385\pi$
$811$	−13.6879	−	42.1270i	−0.480647	−	1.47928i	0.357541	−	0.933897i	$-0.383615\pi$
$812$	−1.26343	−	1.40318i	−0.0443376	−	0.0492419i
$813$	−15.5950	+	19.2115i	−0.546942	+	0.673778i
$814$	−0.790089	+	0.877483i	−0.0276926	+	0.0307557i
$815$	−14.1676	+	44.9331i	−0.496271	+	1.57394i
$816$	0.942705	+	2.46458i	0.0330013	+	0.0862777i
$817$	42.8497	−	19.0779i	1.49912	−	0.667452i
$818$	29.5671			1.03379
$819$	2.70912	+	12.8961i	0.0946644	+	0.450627i
$820$	−22.0589	−	4.48806i	−0.770329	−	0.156730i
$821$	1.53561	+	14.6103i	0.0535930	+	0.509904i	0.988084	+	0.153916i	$0.0491887\pi$
$821$	1.53561	+	14.6103i	0.0535930	+	0.509904i	−0.934491	+	0.355987i	$0.884145\pi$
$822$	−23.8386	−	23.8954i	−0.831468	−	0.833448i
$823$	11.4774	−	12.7469i	0.400076	−	0.444329i	−0.509122	−	0.860695i	$-0.670030\pi$
$823$	11.4774	−	12.7469i	0.400076	−	0.444329i	0.909197	+	0.416366i	$0.136696\pi$
$824$	−7.18638	−	12.4472i	−0.250349	−	0.433618i
$825$	−28.3219	+	1.94630i	−0.986044	+	0.0677614i
$826$	29.4391	−	50.9900i	1.02432	−	1.77417i
$827$	−4.77057	−	14.6823i	−0.165889	−	0.510554i	0.833212	−	0.552954i	$-0.186500\pi$
$827$	−4.77057	−	14.6823i	−0.165889	−	0.510554i	−0.999101	+	0.0424003i	$0.986500\pi$
$828$	5.02551	−	6.88255i	0.174649	−	0.239185i
$829$	−22.5656	+	16.3949i	−0.783735	+	0.569417i	−0.906098	−	0.423069i	$-0.860953\pi$
$829$	−22.5656	+	16.3949i	−0.783735	+	0.569417i	0.122363	+	0.992485i	$0.460953\pi$
$830$	−24.6013	+	5.45383i	−0.853924	+	0.189305i
$831$	−16.9889	+	0.870100i	−0.589339	+	0.0301834i
$832$	−0.480667	−	0.832540i	−0.0166641	−	0.0288631i
$833$	2.20995	−	21.0263i	0.0765704	−	0.728519i
$834$	−1.73786	+	2.14087i	−0.0601773	+	0.0741324i
$835$	−1.77150	+	18.3966i	−0.0613052	+	0.636639i
$836$	5.48953	+	16.8950i	0.189859	+	0.584327i
$837$	−11.0278	−	13.7180i	−0.381177	−	0.474162i
$838$	11.3841	−	35.0367i	0.393258	−	1.21032i
$839$	36.5050	+	7.75938i	1.26029	+	0.267883i	0.789165	−	0.614182i	$-0.210514\pi$
$839$	36.5050	+	7.75938i	1.26029	+	0.267883i	0.471128	+	0.882065i	$0.343847\pi$
$840$	13.6685	−	11.2400i	0.471607	−	0.387817i
$841$	28.1992	−	5.99394i	0.972388	−	0.206687i
$842$	0.723035	−	6.87922i	0.0249174	−	0.237074i
$843$	−9.56260	+	7.72483i	−0.329353	+	0.266057i
$844$	3.87210	−	1.72397i	0.133283	−	0.0593415i
$845$	24.5712	−	11.1976i	0.845275	−	0.385208i
$846$	0.323842	+	0.732040i	0.0111339	+	0.0251681i
$847$	−0.940368	+	0.683217i	−0.0323114	+	0.0234756i
$848$	9.94394	+	2.11365i	0.341476	+	0.0725830i
$849$	5.16965	+	32.8930i	0.177422	+	1.12888i
$850$	−5.19495	−	5.57103i	−0.178185	−	0.191085i
$851$	0.511614	+	0.886141i	0.0175379	+	0.0303765i
$852$	5.53796	−	2.81344i	0.189727	−	0.0963870i
$853$	1.99980	+	19.0268i	0.0684718	+	0.651465i	0.973902	+	0.226970i	$0.0728819\pi$
$853$	1.99980	+	19.0268i	0.0684718	+	0.651465i	−0.905430	+	0.424495i	$0.860451\pi$
$854$	−47.3702	+	34.4165i	−1.62098	+	1.17771i
$855$	36.1775	+	3.57055i	1.23724	+	0.122110i
$856$	−14.3832	−	10.4500i	−0.491608	−	0.357174i
$857$	−1.12404	+	1.94689i	−0.0383964	+	0.0665045i	−0.884585	−	0.466379i	$-0.845558\pi$
$857$	−1.12404	+	1.94689i	−0.0383964	+	0.0665045i	0.846189	+	0.532884i	$0.178892\pi$
$858$	−5.45107	+	0.279180i	−0.186096	+	0.00953106i
$859$	20.9509	−	4.45326i	0.714836	−	0.151943i	0.163884	−	0.986480i	$-0.447598\pi$
$859$	20.9509	−	4.45326i	0.714836	−	0.151943i	0.550953	+	0.834536i	$0.314264\pi$
$860$	15.5577	−	11.5120i	0.530514	−	0.392555i
$861$	4.26431	−	79.5581i	0.145327	−	2.71133i
$862$	−3.40884	−	3.78590i	−0.116105	−	0.128948i
$863$	−3.82285	+	11.7655i	−0.130131	+	0.400503i	−0.994801	−	0.101838i	$-0.967528\pi$
$863$	−3.82285	+	11.7655i	−0.130131	+	0.400503i	0.864670	+	0.502341i	$0.167528\pi$
$864$	−5.01427	−	1.36276i	−0.170589	−	0.0463619i
$865$	−40.5870	−	8.25776i	−1.38000	−	0.280772i
$866$	−3.27656	−	3.63899i	−0.111342	−	0.123658i
$867$	−13.8220	−	21.3395i	−0.469420	−	0.724728i
$868$	−7.73866	−	13.4037i	−0.262667	−	0.454953i
$869$	−1.79641	+	17.0917i	−0.0609391	+	0.579797i
$870$	−0.262266	−	1.57882i	−0.00889164	−	0.0535271i
$871$	−0.0187839	−	0.178717i	−0.000636468	−	0.00605559i
$872$	7.53950	−	5.47777i	0.255320	−	0.185501i
$873$	27.1316	+	37.5307i	0.918264	+	1.27022i
$874$	15.3943			0.520720
$875$	−24.3766	+	44.8942i	−0.824078	+	1.51770i
$876$	3.77823	+	24.0398i	0.127655	+	0.812229i
$877$	−31.0134	+	34.4439i	−1.04725	+	1.16309i	−0.0609449	+	0.998141i	$0.519411\pi$
$877$	−31.0134	+	34.4439i	−1.04725	+	1.16309i	−0.986303	+	0.164945i	$0.947255\pi$
$878$	0.378066	+	0.168326i	0.0127591	+	0.00568072i
$879$	−1.34039	−	1.34358i	−0.0452101	−	0.0453177i
$880$	3.72019	+	6.31571i	0.125408	+	0.212903i
$881$	−36.6878	−	26.6552i	−1.23604	−	0.898038i	−0.238715	−	0.971090i	$-0.576726\pi$
$881$	−36.6878	−	26.6552i	−1.23604	−	0.898038i	−0.997328	+	0.0730516i	$0.976726\pi$
$882$	30.8730	+	27.9313i	1.03955	+	0.940497i
$883$	12.5292	+	9.10302i	0.421642	+	0.306341i	0.778298	−	0.627895i	$-0.216083\pi$
$883$	12.5292	+	9.10302i	0.421642	+	0.306341i	−0.356656	+	0.934236i	$0.616083\pi$
$884$	−0.979983	−	1.08838i	−0.0329604	−	0.0366062i
$885$	44.2953	−	22.9915i	1.48897	−	0.772849i
$886$	−8.44187	+	9.37565i	−0.283610	+	0.314981i
$887$	−52.4198	+	11.1422i	−1.76009	+	0.374118i	−0.970796	−	0.239905i	$-0.922884\pi$
$887$	−52.4198	+	11.1422i	−1.76009	+	0.374118i	−0.789289	+	0.614022i	$0.789550\pi$
$888$	0.393205	−	0.484389i	0.0131951	−	0.0162550i
$889$	81.7208	+	17.3703i	2.74083	+	0.582581i
$890$	−0.713861	−	6.26580i	−0.0239287	−	0.210030i
$891$	−19.8450	+	21.8305i	−0.664834	+	0.731348i
$892$	−14.3693	−	10.4399i	−0.481119	−	0.349554i
$893$	−0.722991	+	1.25226i	−0.0241940	+	0.0419052i
$894$	−11.3140	−	17.4674i	−0.378396	−	0.584198i
$895$	9.87652	−	7.30815i	0.330136	−	0.244285i
$896$	−4.17418	−	1.85846i	−0.139449	−	0.0620869i
$897$	−1.22963	+	4.56733i	−0.0410563	+	0.152499i
$898$	9.21240	+	1.95816i	0.307422	+	0.0653445i
$899$	−1.39976			−0.0466846
$900$	14.8925	−	1.79246i	0.496417	−	0.0597487i
$901$	15.4877			0.515971
$902$	32.2794	+	6.86121i	1.07479	+	0.228453i
$903$	48.3782	+	48.4934i	1.60993	+	1.61376i
$904$	9.89583	+	4.40591i	0.329130	+	0.146538i
$905$	−13.9373	−	9.94147i	−0.463290	−	0.330466i
$906$	−1.01352	+	1.98330i	−0.0336718	+	0.0658909i
$907$	17.0842	−	29.5907i	0.567272	−	0.982544i	−0.429562	−	0.903037i	$-0.641332\pi$
$907$	17.0842	−	29.5907i	0.567272	−	0.982544i	0.996834	−	0.0795069i	$-0.0253346\pi$
$908$	−11.6572	−	8.46942i	−0.386857	−	0.281068i
$909$	−0.0453459	+	19.0709i	−0.00150403	+	0.632543i
$910$	−4.83664	+	8.54861i	−0.160333	+	0.283384i
$911$	−31.7933	−	6.75787i	−1.05336	−	0.223898i	−0.351480	−	0.936195i	$-0.614322\pi$
$911$	−31.7933	−	6.75787i	−1.05336	−	0.223898i	−0.701878	+	0.712297i	$0.747655\pi$
$912$	−3.35336	−	8.76693i	−0.111041	−	0.290302i
$913$	36.1336	−	7.68043i	1.19585	−	0.254185i
$914$	0.947546	−	1.05236i	0.0313420	−	0.0348088i
$915$	−49.5420	+	2.97071i	−1.63781	+	0.0982087i
$916$	−9.62801	−	10.6930i	−0.318119	−	0.353306i
$917$	−26.0124	−	18.8991i	−0.859004	−	0.624103i
$918$	−7.90380	−	0.442493i	−0.260864	−	0.0146044i
$919$	5.26515	+	3.82536i	0.173681	+	0.126187i	0.671230	−	0.741249i	$-0.265766\pi$
$919$	5.26515	+	3.82536i	0.173681	+	0.126187i	−0.497548	+	0.867436i	$0.665766\pi$
$920$	6.20140	−	1.37478i	0.204454	−	0.0453251i
$921$	11.5853	−	3.08951i	0.381748	−	0.101803i
$922$	−19.4939	−	8.67925i	−0.641998	−	0.285836i
$923$	−2.30691	+	2.56209i	−0.0759329	+	0.0843321i
$924$	−20.1807	+	16.3024i	−0.663897	+	0.536308i
$925$	−0.526589	+	1.72232i	−0.0173141	+	0.0566296i
$926$	−30.2419			−0.993811
$927$	42.8927	−	4.40511i	1.40878	−	0.144683i
$928$	−0.334315	+	0.242894i	−0.0109744	+	0.00797339i
$929$	1.09261	+	10.3955i	0.0358473	+	0.341065i	0.997716	+	0.0675520i	$0.0215189\pi$
$929$	1.09261	+	10.3955i	0.0358473	+	0.341065i	−0.961868	+	0.273513i	$0.911814\pi$
$930$	0.587901	−	13.1058i	0.0192780	−	0.429757i
$931$	−7.86117	+	74.7941i	−0.257640	+	2.45128i
$932$	4.37728	+	7.58168i	0.143383	+	0.248346i
$933$	5.83375	−	11.4158i	0.190988	−	0.373737i
$934$	8.50768	+	9.44873i	0.278380	+	0.309172i
$935$	7.54422	+	8.23317i	0.246722	+	0.269253i
$936$	2.86891	−	0.294640i	0.0937733	−	0.00963060i
$937$	−15.6913	+	48.2929i	−0.512613	+	1.57766i	0.274970	+	0.961453i	$0.411332\pi$
$937$	−15.6913	+	48.2929i	−0.512613	+	1.57766i	−0.787583	+	0.616208i	$0.788668\pi$
$938$	−0.571516	−	0.634733i	−0.0186606	−	0.0207248i
$939$	−44.0161	−	28.6588i	−1.43641	−	0.935245i
$940$	−0.179416	+	0.569022i	−0.00585189	+	0.0185595i
$941$	−29.2068	+	6.20810i	−0.952115	+	0.202378i	−0.657684	−	0.753294i	$-0.728464\pi$
$941$	−29.2068	+	6.20810i	−0.952115	+	0.202378i	−0.294431	+	0.955673i	$0.595130\pi$
$942$	13.5325	+	20.8925i	0.440911	+	0.680714i
$943$	14.2988	−	24.7662i	0.465632	−	0.806498i
$944$	−10.4249	−	7.57412i	−0.339301	−	0.246517i
$945$	14.0047	+	51.2089i	0.455572	+	1.66583i
$946$	−22.9538	+	16.6769i	−0.746291	+	0.542212i
$947$	5.96376	+	56.7414i	0.193796	+	1.84385i	0.469900	+	0.882720i	$0.344290\pi$
$947$	5.96376	+	56.7414i	0.193796	+	1.84385i	−0.276104	+	0.961128i	$0.589043\pi$
$948$	0.486025	−	9.06763i	0.0157854	−	0.294503i
$949$	−6.75325	−	11.6970i	−0.219220	−	0.379700i
$950$	18.4793	+	19.8171i	0.599547	+	0.642951i
$951$	42.7136	−	34.5048i	1.38508	−	1.11889i
$952$	−6.80892	−	1.44728i	−0.220678	−	0.0469067i
$953$	−6.03466	+	4.38444i	−0.195482	+	0.142026i	−0.681221	−	0.732078i	$-0.738551\pi$
$953$	−6.03466	+	4.38444i	−0.195482	+	0.142026i	0.485739	+	0.874104i	$0.338551\pi$
$954$	−17.9850	+	24.6309i	−0.582287	+	0.797456i
$955$	19.3868	+	21.1572i	0.627342	+	0.684632i
$956$	8.24730	−	3.67193i	0.266737	−	0.118759i
$957$	0.364279	+	2.31780i	0.0117755	+	0.0749238i
$958$	1.49506	−	14.2245i	0.0483031	−	0.459573i
$959$	87.0959	−	18.5128i	2.81247	−	0.597810i
$960$	−2.13378	−	3.23218i	−0.0688675	−	0.104318i
$961$	19.0994	+	4.05971i	0.616111	+	0.130958i
$962$	−0.107006	+	0.329329i	−0.00345000	+	0.0106180i
$963$	46.2535	−	26.5580i	1.49050	−	0.855820i
$964$	2.38879	+	7.35195i	0.0769378	+	0.236790i
$965$	10.0660	+	17.0889i	0.324036	+	0.550111i
$966$	8.03166	+	20.9978i	0.258415	+	0.675593i
$967$	1.80450	−	17.1687i	0.0580288	−	0.552107i	−0.926427	−	0.376475i	$-0.877136\pi$
$967$	1.80450	−	17.1687i	0.0580288	−	0.552107i	0.984456	−	0.175633i	$-0.0561971\pi$
$968$	0.127195	+	0.220308i	0.00408820	+	0.00708097i
$969$	−7.77399	−	12.0021i	−0.249737	−	0.385563i
$970$	−3.30860	+	34.3590i	−0.106233	+	1.10320i
$971$	−12.9500	+	9.40872i	−0.415585	+	0.301940i	−0.775859	−	0.630906i	$-0.782683\pi$
$971$	−12.9500	+	9.40872i	−0.415585	+	0.301940i	0.360274	+	0.932846i	$0.382683\pi$
$972$	9.88197	−	12.0560i	0.316964	−	0.386696i
$973$	−2.24786	−	6.91821i	−0.0720632	−	0.221788i
$974$	−7.58854	+	13.1437i	−0.243152	+	0.421152i
$975$	−7.35558	+	3.89971i	−0.235567	+	0.124891i
$976$	6.40733	+	11.0978i	0.205094	+	0.355233i
$977$	16.8223	−	18.6831i	0.538194	−	0.597725i	−0.411304	−	0.911498i	$-0.634926\pi$
$977$	16.8223	−	18.6831i	0.538194	−	0.597725i	0.949498	+	0.313773i	$0.101593\pi$
$978$	−9.48729	+	35.2394i	−0.303370	+	1.12683i
$979$	0.966368	+	9.19437i	0.0308852	+	0.293853i
$980$	3.51267	+	30.8319i	0.112208	+	0.984888i
$981$	5.74776	+	27.3608i	0.183512	+	0.873564i
$982$	5.72439			0.182673
$983$	−26.7520	+	11.9108i	−0.853256	+	0.379894i	−0.786287	−	0.617861i	$-0.788000\pi$
$983$	−26.7520	+	11.9108i	−0.853256	+	0.379894i	−0.0669690	+	0.997755i	$0.521333\pi$
$984$	−17.2189	−	2.74819i	−0.548918	−	0.0876091i
$985$	−32.8561	+	24.3120i	−1.04688	+	0.774644i
$986$	−0.421253	+	0.467849i	−0.0134154	+	0.0148993i
$987$	−2.08528	−	0.332818i	−0.0663752	−	0.0105937i
$988$	3.48596	+	3.87155i	0.110903	+	0.123171i
$989$	7.59776	+	23.3835i	0.241595	+	0.743552i
$990$	−21.8543	+	2.43723i	−0.694577	+	0.0774604i
$991$	7.31313	−	22.5075i	0.232309	−	0.714975i	−0.765158	−	0.643843i	$-0.777339\pi$
$991$	7.31313	−	22.5075i	0.232309	−	0.714975i	0.997467	−	0.0711316i	$-0.0226610\pi$
$992$	−3.09446	+	1.37774i	−0.0982493	+	0.0437434i
$993$	8.97325	−	7.24875i	0.284758	−	0.230032i
$994$	−1.71286	+	16.2967i	−0.0543285	+	0.516901i
$995$	−20.4218	+	0.178099i	−0.647415	+	0.00564612i
$996$	−18.8596	+	5.02940i	−0.597591	+	0.159363i
$997$	−1.67722	−	15.9577i	−0.0531182	−	0.505386i	−0.988443	−	0.151595i	$-0.951559\pi$
$997$	−1.67722	−	15.9577i	−0.0531182	−	0.505386i	0.935325	−	0.353791i	$-0.115108\pi$
$998$	−3.85915	−	11.8772i	−0.122159	−	0.375967i
$999$	0.843771	+	1.67070i	0.0266957	+	0.0528586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.q.b.331.13	yes	112
9.4	even	3	inner	450.2.q.b.31.10	✓	112
25.21	even	5	inner	450.2.q.b.421.10	yes	112
225.121	even	15	inner	450.2.q.b.121.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.q.b.31.10	✓	112	9.4	even	3	inner
450.2.q.b.121.13	yes	112	225.121	even	15	inner
450.2.q.b.331.13	yes	112	1.1	even	1	trivial
450.2.q.b.421.10	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 $\F_{q}$
Belyi maps

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} +(1.67356 - 0.446298i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.23598 + 0.0195000i) q^{5} +(-1.72978 + 0.0885921i) q^{6} +(2.28460 - 3.95705i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.60164 - 1.49382i) q^{9} +(2.19118 + 0.445813i) q^{10} +(-3.20642 - 0.681545i) q^{11} +(1.71040 + 0.272986i) q^{12} +(-0.940327 + 0.199873i) q^{13} +(-3.05739 + 3.39558i) q^{14} +(-3.73336 + 1.03055i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.23251 + 0.895472i) q^{17} +(-2.85537 + 0.920264i) q^{18} +(-4.38425 - 3.18534i) q^{19} +(-2.05060 - 0.891642i) q^{20} +(2.05741 - 7.64199i) q^{21} +(2.99465 + 1.33330i) q^{22} +(1.90079 - 2.11104i) q^{23} +(-1.61627 - 0.622633i) q^{24} +(4.99924 - 0.0872036i) q^{25} +0.961334 q^{26} +(3.68732 - 3.66111i) q^{27} +(3.69656 - 2.68571i) q^{28} +(-0.0431950 - 0.410973i) q^{29} +(3.86604 - 0.231821i) q^{30} +(0.354070 - 3.36875i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.67032 + 0.290409i) q^{33} +(-1.01940 - 1.13216i) q^{34} +(-5.03117 + 8.89244i) q^{35} +(2.98430 - 0.306490i) q^{36} +(-0.111309 + 0.342575i) q^{37} +(3.62617 + 4.02727i) q^{38} +(-1.48449 + 0.754166i) q^{39} +(1.82041 + 1.29850i) q^{40} +(9.84715 - 2.09308i) q^{41} +(-3.60130 + 7.04723i) q^{42} +(-4.32764 + 7.49568i) q^{43} +(-2.65200 - 1.92679i) q^{44} +(-5.78808 + 3.39088i) q^{45} +(-2.29816 + 1.66971i) q^{46} +(-0.0278907 - 0.265363i) q^{47} +(1.45150 + 0.945069i) q^{48} +(-6.93882 - 12.0184i) q^{49} +(-4.90812 - 0.954102i) q^{50} +(2.46234 + 0.948562i) q^{51} +(-0.940327 - 0.199873i) q^{52} +(8.22454 - 5.97548i) q^{53} +(-4.36793 + 2.81447i) q^{54} +(7.18278 + 1.46140i) q^{55} +(-4.17418 + 1.85846i) q^{56} +(-8.75893 - 3.37419i) q^{57} +(-0.0431950 + 0.410973i) q^{58} +(-12.6043 + 2.67912i) q^{59} +(-3.82976 - 0.577039i) q^{60} +(12.5346 + 2.66432i) q^{61} +(-1.04674 + 3.22152i) q^{62} +(0.0325932 - 13.7076i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.09866 - 0.465248i) q^{65} +(5.60679 + 0.894862i) q^{66} +(-0.0195394 + 0.185905i) q^{67} +(0.761734 + 1.31936i) q^{68} +(2.23894 - 4.38128i) q^{69} +(6.77007 - 7.65208i) q^{70} +(2.90137 - 2.10797i) q^{71} +(-2.98281 - 0.320679i) q^{72} +(4.34161 + 13.3621i) q^{73} +(0.180102 - 0.311946i) q^{74} +(8.32763 - 2.37709i) q^{75} +(-2.70961 - 4.69319i) q^{76} +(-10.0223 + 11.1309i) q^{77} +(1.60885 - 0.429042i) q^{78} +(-0.548013 - 5.21399i) q^{79} +(-1.51066 - 1.64861i) q^{80} +(4.53701 - 7.77274i) q^{81} -10.0671 q^{82} +(-10.2949 + 4.58357i) q^{83} +(4.98781 - 6.14448i) q^{84} +(-2.77334 - 1.97823i) q^{85} +(5.79151 - 6.43212i) q^{86} +(-0.255706 - 0.668511i) q^{87} +(2.19344 + 2.43607i) q^{88} +(-0.871515 - 2.68225i) q^{89} +(6.36660 - 2.11337i) q^{90} +(-1.35737 + 4.17755i) q^{91} +(2.59509 - 1.15541i) q^{92} +(-0.910910 - 5.79585i) q^{93} +(-0.0278907 + 0.265363i) q^{94} +(9.86522 + 7.03688i) q^{95} +(-1.22329 - 1.22620i) q^{96} +(1.61359 + 15.3523i) q^{97} +(4.28842 + 13.1984i) q^{98} +(-9.36003 + 3.01667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21}+ \cdots + 68 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

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