LMFDB - Embedded newform 675.2.l.f.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55121 - 1.30162i) q^{2} +(-1.45868 + 0.933937i) q^{3} +(0.364742 + 2.06856i) q^{4} +(3.47836 + 0.449921i) q^{6} +(0.0652816 - 0.370230i) q^{7} +(0.101721 - 0.176186i) q^{8} +(1.25552 - 2.72464i) q^{9} +O(q^{10})$	\(q+(-1.55121 - 1.30162i) q^{2} +(-1.45868 + 0.933937i) q^{3} +(0.364742 + 2.06856i) q^{4} +(3.47836 + 0.449921i) q^{6} +(0.0652816 - 0.370230i) q^{7} +(0.101721 - 0.176186i) q^{8} +(1.25552 - 2.72464i) q^{9} +(0.272976 - 0.0993552i) q^{11} +(-2.46395 - 2.67673i) q^{12} +(-0.677752 + 0.568702i) q^{13} +(-0.583165 + 0.489333i) q^{14} +(3.56047 - 1.29590i) q^{16} +(-2.32471 - 4.02651i) q^{17} +(-5.49403 + 2.59227i) q^{18} +(-1.75100 + 3.03282i) q^{19} +(0.250547 + 0.601018i) q^{21} +(-0.552766 - 0.201190i) q^{22} +(-0.0948473 - 0.537906i) q^{23} +(0.0161677 + 0.352001i) q^{24} +1.79157 q^{26} +(0.713228 + 5.14697i) q^{27} +0.789653 q^{28} +(-4.65300 - 3.90433i) q^{29} +(0.953291 + 5.40638i) q^{31} +(-7.59216 - 2.76332i) q^{32} +(-0.305395 + 0.399870i) q^{33} +(-1.63488 + 9.27184i) q^{34} +(6.09401 + 1.60333i) q^{36} +(5.47398 + 9.48122i) q^{37} +(6.66375 - 2.42541i) q^{38} +(0.457496 - 1.46253i) q^{39} +(-7.28901 + 6.11620i) q^{41} +(0.393647 - 1.25842i) q^{42} +(9.54330 - 3.47348i) q^{43} +(0.305088 + 0.528427i) q^{44} +(-0.553021 + 0.957860i) q^{46} +(-1.09967 + 6.23654i) q^{47} +(-3.98331 + 5.21557i) q^{48} +(6.44504 + 2.34580i) q^{49} +(7.15152 + 3.70228i) q^{51} +(-1.42360 - 1.19454i) q^{52} +12.2148 q^{53} +(5.59303 - 8.91238i) q^{54} +(-0.0585889 - 0.0491619i) q^{56} +(-0.278306 - 6.05925i) q^{57} +(2.13583 + 12.1129i) q^{58} +(-1.18778 - 0.432318i) q^{59} +(0.499613 - 2.83345i) q^{61} +(5.55830 - 9.62726i) q^{62} +(-0.926782 - 0.642702i) q^{63} +(4.39127 + 7.60590i) q^{64} +(0.994211 - 0.222775i) q^{66} +(-6.78495 + 5.69325i) q^{67} +(7.48114 - 6.27742i) q^{68} +(0.640723 + 0.696054i) q^{69} +(5.36876 + 9.29896i) q^{71} +(-0.352330 - 0.498359i) q^{72} +(0.389512 - 0.674654i) q^{73} +(3.84964 - 21.8324i) q^{74} +(-6.91222 - 2.51584i) q^{76} +(-0.0189640 - 0.107550i) q^{77} +(-2.61334 + 1.67321i) q^{78} +(5.29571 + 4.44363i) q^{79} +(-5.84732 - 6.84170i) q^{81} +19.2678 q^{82} +(6.88221 + 5.77486i) q^{83} +(-1.15186 + 0.737486i) q^{84} +(-19.3248 - 7.03366i) q^{86} +(10.4337 + 1.34958i) q^{87} +(0.0102624 - 0.0582011i) q^{88} +(-3.11061 + 5.38773i) q^{89} +(0.166306 + 0.288050i) q^{91} +(1.07809 - 0.392394i) q^{92} +(-6.43977 - 6.99589i) q^{93} +(9.82342 - 8.24283i) q^{94} +(13.6553 - 3.05978i) q^{96} +(-13.1743 + 4.79504i) q^{97} +(-6.94427 - 12.0278i) q^{98} +(0.0720209 - 0.868504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.55121	−	1.30162i	−1.09687	−	0.920384i	−0.0996605	−	0.995022i	$-0.531776\pi$
$2$	−1.55121	−	1.30162i	−1.09687	−	0.920384i	−0.997211	+	0.0746373i	$0.976220\pi$
$3$	−1.45868	+	0.933937i	−0.842172	+	0.539209i
$3$	−1.45868	+	0.933937i	−0.842172	+	0.539209i
$4$	0.364742	+	2.06856i	0.182371	+	1.03428i
$5$		0			0
$5$		0			0
$6$	3.47836	+	0.449921i	1.42003	+	0.183679i
$7$	0.0652816	−	0.370230i	0.0246741	−	0.139934i	−0.969982	−	0.243176i	$-0.921811\pi$
$7$	0.0652816	−	0.370230i	0.0246741	−	0.139934i	0.994656	+	0.103242i	$0.0329217\pi$
$8$	0.101721	−	0.176186i	0.0359638	−	0.0622912i
$9$	1.25552	−	2.72464i	0.418508	−	0.908213i
$10$		0			0
$11$	0.272976	−	0.0993552i	0.0823054	−	0.0299567i	−0.300539	−	0.953769i	$-0.597167\pi$
$11$	0.272976	−	0.0993552i	0.0823054	−	0.0299567i	0.382845	+	0.923813i	$0.374944\pi$
$12$	−2.46395	−	2.67673i	−0.711280	−	0.772704i
$13$	−0.677752	+	0.568702i	−0.187975	+	0.157729i	−0.731919	−	0.681392i	$-0.761375\pi$
$13$	−0.677752	+	0.568702i	−0.187975	+	0.157729i	0.543944	+	0.839122i	$0.316930\pi$
$14$	−0.583165	+	0.489333i	−0.155857	+	0.130780i
$15$		0			0
$16$	3.56047	−	1.29590i	0.890117	−	0.323976i
$17$	−2.32471	−	4.02651i	−0.563824	−	0.976572i	−0.997158	−	0.0753383i	$-0.975996\pi$
$17$	−2.32471	−	4.02651i	−0.563824	−	0.976572i	0.433334	−	0.901233i	$-0.357337\pi$
$18$	−5.49403	+	2.59227i	−1.29495	+	0.611005i
$19$	−1.75100	+	3.03282i	−0.401707	+	0.695777i	−0.993932	−	0.109996i	$-0.964916\pi$
$19$	−1.75100	+	3.03282i	−0.401707	+	0.695777i	0.592225	+	0.805772i	$0.298250\pi$
$20$		0			0
$21$	0.250547	+	0.601018i	0.0546737	+	0.131153i
$22$	−0.552766	−	0.201190i	−0.117850	−	0.0428939i
$23$	−0.0948473	−	0.537906i	−0.0197770	−	0.112161i	0.973321	−	0.229447i	$-0.0736918\pi$
$23$	−0.0948473	−	0.537906i	−0.0197770	−	0.112161i	−0.993098	+	0.117286i	$0.962581\pi$
$24$	0.0161677	+	0.352001i	0.00330021	+	0.0718519i
$25$		0			0
$26$	1.79157			0.351356
$27$	0.713228	+	5.14697i	0.137261	+	0.990535i
$28$	0.789653			0.149230
$29$	−4.65300	−	3.90433i	−0.864040	−	0.725016i	0.0987944	−	0.995108i	$-0.468501\pi$
$29$	−4.65300	−	3.90433i	−0.864040	−	0.725016i	−0.962834	+	0.270092i	$0.912946\pi$
$30$		0			0
$31$	0.953291	+	5.40638i	0.171216	+	0.971015i	0.942421	+	0.334428i	$0.108543\pi$
$31$	0.953291	+	5.40638i	0.171216	+	0.971015i	−0.771205	+	0.636587i	$0.780346\pi$
$32$	−7.59216	−	2.76332i	−1.34212	−	0.488490i
$33$	−0.305395	+	0.399870i	−0.0531624	+	0.0696085i
$34$	−1.63488	+	9.27184i	−0.280379	+	1.59011i
$35$		0			0
$36$	6.09401	+	1.60333i	1.01567	+	0.267222i
$37$	5.47398	+	9.48122i	0.899917	+	1.55870i	0.827598	+	0.561321i	$0.189707\pi$
$37$	5.47398	+	9.48122i	0.899917	+	1.55870i	0.0723191	+	0.997382i	$0.476960\pi$
$38$	6.66375	−	2.42541i	1.08100	−	0.393453i
$39$	0.457496	−	1.46253i	0.0732579	−	0.234193i
$40$		0			0
$41$	−7.28901	+	6.11620i	−1.13835	+	0.955190i	−0.999384	−	0.0351066i	$-0.988823\pi$
$41$	−7.28901	+	6.11620i	−1.13835	+	0.955190i	−0.138968	+	0.990297i	$0.544378\pi$
$42$	0.393647	−	1.25842i	0.0607411	−	0.194179i
$43$	9.54330	−	3.47348i	1.45534	−	0.529701i	0.511263	−	0.859424i	$-0.329178\pi$
$43$	9.54330	−	3.47348i	1.45534	−	0.529701i	0.944077	+	0.329724i	$0.106956\pi$
$44$	0.305088	+	0.528427i	0.0459937	+	0.0796634i
$45$		0			0
$46$	−0.553021	+	0.957860i	−0.0815385	+	0.141229i
$47$	−1.09967	+	6.23654i	−0.160403	+	0.909693i	0.793275	+	0.608864i	$0.208374\pi$
$47$	−1.09967	+	6.23654i	−0.160403	+	0.909693i	−0.953678	+	0.300829i	$0.902737\pi$
$48$	−3.98331	+	5.21557i	−0.574941	+	0.752803i
$49$	6.44504	+	2.34580i	0.920720	+	0.335115i
$50$		0			0
$51$	7.15152	+	3.70228i	1.00141	+	0.518423i
$52$	−1.42360	−	1.19454i	−0.197417	−	0.165653i
$53$	12.2148			1.67783			0.838913	−	0.544265i	$-0.183191\pi$
$53$	12.2148			1.67783			0.838913	+	0.544265i	$0.183191\pi$
$54$	5.59303	−	8.91238i	0.761115	−	1.21282i
$55$		0			0
$56$	−0.0585889	−	0.0491619i	−0.00782927	−	0.00656954i
$57$	−0.278306	−	6.05925i	−0.0368625	−	0.802567i
$58$	2.13583	+	12.1129i	0.280448	+	1.59050i
$59$	−1.18778	−	0.432318i	−0.154636	−	0.0562830i	0.263542	−	0.964648i	$-0.415109\pi$
$59$	−1.18778	−	0.432318i	−0.154636	−	0.0562830i	−0.418179	+	0.908365i	$0.637331\pi$
$60$		0			0
$61$	0.499613	−	2.83345i	0.0639690	−	0.362786i	−0.935974	−	0.352070i	$-0.885478\pi$
$61$	0.499613	−	2.83345i	0.0639690	−	0.362786i	0.999943	−	0.0107158i	$-0.00341102\pi$
$62$	5.55830	−	9.62726i	0.705905	−	1.22266i
$63$	−0.926782	−	0.642702i	−0.116764	−	0.0809728i
$64$	4.39127	+	7.60590i	0.548909	+	0.950737i
$65$		0			0
$66$	0.994211	−	0.222775i	0.122379	−	0.0274217i
$67$	−6.78495	+	5.69325i	−0.828913	+	0.695541i	−0.955041	−	0.296473i	$-0.904189\pi$
$67$	−6.78495	+	5.69325i	−0.828913	+	0.695541i	0.126128	+	0.992014i	$0.459745\pi$
$68$	7.48114	−	6.27742i	0.907222	−	0.761249i
$69$	0.640723	+	0.696054i	0.0771339	+	0.0837951i
$70$		0			0
$71$	5.36876	+	9.29896i	0.637154	+	1.10358i	0.986054	+	0.166424i	$0.0532219\pi$
$71$	5.36876	+	9.29896i	0.637154	+	1.10358i	−0.348900	+	0.937160i	$0.613445\pi$
$72$	−0.352330	−	0.498359i	−0.0415225	−	0.0587322i
$73$	0.389512	−	0.674654i	0.0455889	−	0.0789623i	−0.842331	−	0.538961i	$-0.818817\pi$
$73$	0.389512	−	0.674654i	0.0455889	−	0.0789623i	0.887919	+	0.459999i	$0.152150\pi$
$74$	3.84964	−	21.8324i	0.447512	−	2.53797i
$75$		0			0
$76$	−6.91222	−	2.51584i	−0.792886	−	0.288587i
$77$	−0.0189640	−	0.107550i	−0.00216115	−	0.0122565i
$78$	−2.61334	+	1.67321i	−0.295902	+	0.189454i
$79$	5.29571	+	4.44363i	0.595813	+	0.499947i	0.890097	−	0.455771i	$-0.150637\pi$
$79$	5.29571	+	4.44363i	0.595813	+	0.499947i	−0.294283	+	0.955718i	$0.595081\pi$
$80$		0			0
$81$	−5.84732	−	6.84170i	−0.649702	−	0.760189i
$82$	19.2678			2.12777
$83$	6.88221	+	5.77486i	0.755421	+	0.633874i	0.936931	−	0.349516i	$-0.113654\pi$
$83$	6.88221	+	5.77486i	0.755421	+	0.633874i	−0.181509	+	0.983389i	$0.558098\pi$
$84$	−1.15186	+	0.737486i	−0.125678	+	0.0804664i
$85$		0			0
$86$	−19.3248	−	7.03366i	−2.08385	−	0.758459i
$87$	10.4337	+	1.34958i	1.11861	+	0.144690i
$88$	0.0102624	−	0.0582011i	0.00109398	−	0.00620426i
$89$	−3.11061	+	5.38773i	−0.329724	+	0.571099i	−0.982457	−	0.186489i	$-0.940289\pi$
$89$	−3.11061	+	5.38773i	−0.329724	+	0.571099i	0.652733	+	0.757588i	$0.273622\pi$
$90$		0			0
$91$	0.166306	+	0.288050i	0.0174336	+	0.0301959i
$92$	1.07809	−	0.392394i	0.112399	−	0.0409099i
$93$	−6.43977	−	6.99589i	−0.667773	−	0.725440i
$94$	9.82342	−	8.24283i	1.01321	−	0.850183i
$95$		0			0
$96$	13.6553	−	3.05978i	1.39369	−	0.312288i
$97$	−13.1743	+	4.79504i	−1.33765	+	0.486863i	−0.909070	−	0.416643i	$-0.863206\pi$
$97$	−13.1743	+	4.79504i	−1.33765	+	0.486863i	−0.428575	+	0.903506i	$0.640984\pi$
$98$	−6.94427	−	12.0278i	−0.701477	−	1.21499i
$99$	0.0720209	−	0.868504i	0.00723838	−	0.0872880i
$100$		0			0
$101$	−0.698390	+	3.96077i	−0.0694924	+	0.394111i	0.930145	+	0.367192i	$0.119681\pi$
$101$	−0.698390	+	3.96077i	−0.0694924	+	0.394111i	−0.999638	+	0.0269191i	$0.991430\pi$
$102$	−6.27455	−	15.0516i	−0.621273	−	1.49033i
$103$	0.484326	+	0.176280i	0.0477221	+	0.0173694i	0.365771	−	0.930705i	$-0.380805\pi$
$103$	0.484326	+	0.176280i	0.0477221	+	0.0173694i	−0.318049	+	0.948074i	$0.603028\pi$
$104$	0.0312556	+	0.177260i	0.00306487	+	0.0173817i
$105$		0			0
$106$	−18.9477	−	15.8990i	−1.84036	−	1.54425i
$107$	17.9687			1.73710			0.868552	−	0.495598i	$-0.165051\pi$
$107$	17.9687			1.73710			0.868552	+	0.495598i	$0.165051\pi$
$108$	−10.3867	+	3.35267i	−0.999456	+	0.322611i
$109$	−1.10502			−0.105842			−0.0529209	−	0.998599i	$-0.516853\pi$
$109$	−1.10502			−0.105842			−0.0529209	+	0.998599i	$0.516853\pi$
$110$		0			0
$111$	−16.8397	−	8.71775i	−1.59835	−	0.827453i
$112$	−0.247350	−	1.40279i	−0.0233724	−	0.132551i
$113$	−8.53194	−	3.10537i	−0.802618	−	0.292129i	−0.0920470	−	0.995755i	$-0.529341\pi$
$113$	−8.53194	−	3.10537i	−0.802618	−	0.292129i	−0.710571	+	0.703626i	$0.751563\pi$
$114$	−7.45513	+	9.76142i	−0.698237	+	0.914241i
$115$		0			0
$116$	6.37918	−	11.0491i	0.592292	−	1.02588i
$117$	0.698573	+	2.56065i	0.0645831	+	0.236732i
$118$	1.27979	+	2.21666i	0.117814	+	0.204060i
$119$	−1.64250	+	0.597820i	−0.150567	+	0.0548020i
$120$		0			0
$121$	−8.36184	+	7.01642i	−0.760168	+	0.637856i
$122$	−4.46308	+	3.74497i	−0.404068	+	0.339053i
$123$	4.92022	−	15.7291i	0.443641	−	1.41824i
$124$	−10.8357	+	3.94387i	−0.973074	+	0.354170i
$125$		0			0
$126$	0.601080	+	2.20328i	0.0535484	+	0.196284i
$127$	−5.39923	+	9.35175i	−0.479105	+	0.829833i	−0.999713	−	0.0239622i	$-0.992372\pi$
$127$	−5.39923	+	9.35175i	−0.479105	+	0.829833i	0.520608	+	0.853796i	$0.325705\pi$
$128$	0.282262	−	1.60079i	0.0249487	−	0.141491i
$129$	−10.6767	+	13.9796i	−0.940028	+	1.23083i
$130$		0			0
$131$	2.14908	+	12.1880i	0.187766	+	1.06487i	0.922350	+	0.386356i	$0.126266\pi$
$131$	2.14908	+	12.1880i	0.187766	+	1.06487i	−0.734584	+	0.678518i	$0.762623\pi$
$132$	−0.938545	−	0.485876i	−0.0816898	−	0.0422901i
$133$	1.00853	+	0.846260i	0.0874510	+	0.0733801i
$134$	17.9353			1.54938
$135$		0			0
$136$	−0.945886			−0.0811091
$137$	12.6386	+	10.6051i	1.07979	+	0.906052i	0.995903	−	0.0904234i	$-0.0288220\pi$
$137$	12.6386	+	10.6051i	1.07979	+	0.906052i	0.0838872	+	0.996475i	$0.473266\pi$
$138$	−0.0878978	−	1.91370i	−0.00748236	−	0.162905i
$139$	−2.14103	−	12.1424i	−0.181600	−	1.02990i	−0.930247	−	0.366935i	$-0.880407\pi$
$139$	−2.14103	−	12.1424i	−0.181600	−	1.02990i	0.748647	−	0.662969i	$-0.230704\pi$
$140$		0			0
$141$	−4.22046	−	10.1242i	−0.355427	−	0.852609i
$142$	3.77564	−	21.4127i	0.316845	−	1.79692i
$143$	−0.128507	+	0.222580i	−0.0107463	+	0.0186131i
$144$	0.939380	−	11.3280i	0.0782817	−	0.944003i
$145$		0			0
$146$	−1.48236	+	0.539534i	−0.122681	+	0.0446522i
$147$	−11.5921	+	2.59747i	−0.956101	+	0.214236i
$148$	−17.6158	+	14.7814i	−1.44801	+	1.21503i
$149$	−7.81833	+	6.56036i	−0.640503	+	0.537446i	−0.904173	−	0.427167i	$-0.859512\pi$
$149$	−7.81833	+	6.56036i	−0.640503	+	0.537446i	0.263670	+	0.964613i	$0.415067\pi$
$150$		0			0
$151$	16.7786	−	6.10690i	1.36542	−	0.496972i	0.447695	−	0.894187i	$-0.352245\pi$
$151$	16.7786	−	6.10690i	1.36542	−	0.496972i	0.917726	+	0.397214i	$0.130023\pi$
$152$	0.356227	+	0.617003i	0.0288938	+	0.0500456i
$153$	−13.8895	+	1.27861i	−1.12290	+	0.103369i
$154$	−0.110572	+	0.191517i	−0.00891016	+	0.0154329i
$155$		0			0
$156$	3.19220	+	0.412907i	0.255581	+	0.0330590i
$157$	−10.8531	−	3.95020i	−0.866170	−	0.315260i	−0.129555	−	0.991572i	$-0.541355\pi$
$157$	−10.8531	−	3.95020i	−0.866170	−	0.315260i	−0.736615	+	0.676312i	$0.763577\pi$
$158$	−2.43084	−	13.7860i	−0.193387	−	1.09675i
$159$	−17.8175	+	11.4078i	−1.41302	+	0.904699i
$160$		0			0
$161$	−0.205341			−0.0161831
$162$	0.165131	+	18.2239i	0.0129739	+	1.43180i
$163$	−6.26212			−0.490487			−0.245244	−	0.969461i	$-0.578868\pi$
$163$	−6.26212			−0.490487			−0.245244	+	0.969461i	$0.578868\pi$
$164$	−15.3103	−	12.8469i	−1.19553	−	1.00317i
$165$		0			0
$166$	−3.15908	−	17.9161i	−0.245192	−	1.39056i
$167$	−14.7179	−	5.35688i	−1.13891	−	0.414528i	−0.297388	−	0.954757i	$-0.596116\pi$
$167$	−14.7179	−	5.35688i	−1.13891	−	0.414528i	−0.841518	+	0.540229i	$0.818338\pi$
$168$	0.131377	+	0.0169934i	0.0101360	+	0.00131107i
$169$	−2.12150	+	12.0316i	−0.163192	+	0.925509i
$170$		0			0
$171$	6.06492	+	8.57862i	0.463796	+	0.656023i
$172$	10.6659	+	18.4739i	0.813270	+	1.40862i
$173$	−8.57107	+	3.11962i	−0.651647	+	0.237180i	−0.646626	−	0.762807i	$-0.723820\pi$
$173$	−8.57107	+	3.11962i	−0.651647	+	0.237180i	−0.00502090	+	0.999987i	$0.501598\pi$
$174$	−14.4282	−	15.6741i	−1.09380	−	1.18825i
$175$		0			0
$176$	0.843168	−	0.707502i	0.0635562	−	0.0533300i
$177$	2.13636	−	0.478700i	0.160579	−	0.0359813i
$178$	11.8380	−	4.30868i	0.887295	−	0.322949i
$179$	1.32110	+	2.28821i	0.0987437	+	0.171029i	0.911165	−	0.412042i	$-0.135184\pi$
$179$	1.32110	+	2.28821i	0.0987437	+	0.171029i	−0.812421	+	0.583071i	$0.801851\pi$
$180$		0			0
$181$	3.54912	−	6.14725i	0.263804	−	0.456922i	−0.703446	−	0.710749i	$-0.748356\pi$
$181$	3.54912	−	6.14725i	0.263804	−	0.456922i	0.967250	+	0.253827i	$0.0816895\pi$
$182$	0.116957	−	0.663294i	0.00866940	−	0.0491666i
$183$	1.91748	+	4.59972i	0.141744	+	0.340021i
$184$	−0.104420	−	0.0380056i	−0.00769791	−	0.00280181i
$185$		0			0
$186$	0.883443	+	19.2342i	0.0647772	+	1.41032i
$187$	−1.03464	−	0.868169i	−0.0756606	−	0.0634868i
$188$	−13.3017			−0.970128
$189$	1.95213	+	0.0719439i	0.141996	+	0.00523315i
$190$		0			0
$191$	3.97951	+	3.33921i	0.287948	+	0.241617i	0.775307	−	0.631585i	$-0.217595\pi$
$191$	3.97951	+	3.33921i	0.287948	+	0.241617i	−0.487359	+	0.873202i	$0.662040\pi$
$192$	−13.5089	−	6.99344i	−0.974921	−	0.504708i
$193$	0.681015	+	3.86223i	0.0490205	+	0.278009i	0.999458	−	0.0329051i	$-0.0104759\pi$
$193$	0.681015	+	3.86223i	0.0490205	+	0.278009i	−0.950438	+	0.310914i	$0.899365\pi$
$194$	26.6774	+	9.70978i	1.91533	+	0.697121i
$195$		0			0
$196$	−2.50165	+	14.1875i	−0.178689	+	1.01340i
$197$	5.18583	−	8.98212i	0.369475	−	0.639950i	−0.620008	−	0.784595i	$-0.712871\pi$
$197$	5.18583	−	8.98212i	0.369475	−	0.639950i	0.989484	+	0.144646i	$0.0462042\pi$
$198$	−1.24218	+	1.25349i	−0.0882780	+	0.0890816i
$199$	−5.95479	−	10.3140i	−0.422124	−	0.731140i	0.574023	−	0.818839i	$-0.305382\pi$
$199$	−5.95479	−	10.3140i	−0.422124	−	0.731140i	−0.996147	+	0.0876991i	$0.972049\pi$
$200$		0			0
$201$	4.57997	−	14.6414i	0.323046	−	1.03272i
$202$	6.23876	−	5.23494i	0.438958	−	0.368329i
$203$	−1.74926	+	1.46780i	−0.122774	+	0.103019i
$204$	−5.04991	+	16.1437i	−0.353565	+	1.13028i
$205$		0			0
$206$	−0.521842	−	0.903856i	−0.0363584	−	0.0629747i
$207$	−1.58468	−	0.416929i	−0.110143	−	0.0289786i
$208$	−1.67613	+	2.90315i	−0.116219	+	0.201297i
$209$	−0.176655	+	1.00186i	−0.0122195	+	0.0693000i
$210$		0			0
$211$	−2.30091	−	0.837462i	−0.158401	−	0.0576532i	0.261603	−	0.965176i	$-0.415749\pi$
$211$	−2.30091	−	0.837462i	−0.158401	−	0.0576532i	−0.420004	+	0.907522i	$0.637971\pi$
$212$	4.45524	+	25.2669i	0.305987	+	1.73534i
$213$	−16.5160	−	8.55017i	−1.13166	−	0.585848i
$214$	−27.8733	−	23.3885i	−1.90538	−	1.59880i
$215$		0			0
$216$	0.979375	+	0.397895i	0.0666380	+	0.0270733i
$217$	2.06384			0.140103
$218$	1.71412	+	1.43832i	0.116095	+	0.0974152i
$219$	0.0619094	+	1.34789i	0.00418345	+	0.0910818i
$220$		0			0
$221$	3.86546	+	1.40691i	0.260019	+	0.0946391i
$222$	14.7747	+	35.4419i	0.991611	+	2.37871i
$223$	−3.12885	+	17.7446i	−0.209523	+	1.18826i	0.680639	+	0.732619i	$0.261702\pi$
$223$	−3.12885	+	17.7446i	−0.209523	+	1.18826i	−0.890162	+	0.455645i	$0.849409\pi$
$224$	−1.51869	+	2.63045i	−0.101472	+	0.175755i
$225$		0			0
$226$	9.19282	+	15.9224i	0.611497	+	1.05914i
$227$	5.02409	−	1.82862i	0.333460	−	0.121370i	−0.169863	−	0.985468i	$-0.554333\pi$
$227$	5.02409	−	1.82862i	0.333460	−	0.121370i	0.503324	+	0.864098i	$0.332110\pi$
$228$	12.4324	−	2.78576i	0.823355	−	0.184491i
$229$	16.5031	−	13.8477i	1.09055	−	0.915083i	0.0937994	−	0.995591i	$-0.470099\pi$
$229$	16.5031	−	13.8477i	1.09055	−	0.915083i	0.996754	+	0.0805082i	$0.0256543\pi$
$230$		0			0
$231$	0.128107	+	0.139171i	0.00842885	+	0.00915675i
$232$	−1.16120	+	0.422641i	−0.0762363	+	0.0277477i
$233$	−12.7820	−	22.1390i	−0.837375	−	1.45038i	−0.892082	−	0.451874i	$-0.850756\pi$
$233$	−12.7820	−	22.1390i	−0.837375	−	1.45038i	0.0547064	−	0.998502i	$-0.482578\pi$
$234$	2.24936	−	4.88138i	0.147045	−	0.319106i
$235$		0			0
$236$	0.461039	−	2.61468i	0.0300111	−	0.170201i
$237$	−11.8748	−	1.53599i	−0.771353	−	0.0997735i
$238$	3.32599	+	1.21056i	0.215592	+	0.0784691i
$239$	1.60685	+	9.11290i	0.103939	+	0.589465i	0.991639	+	0.129043i	$0.0411906\pi$
$239$	1.60685	+	9.11290i	0.103939	+	0.589465i	−0.887700	+	0.460421i	$0.847698\pi$
$240$		0			0
$241$	−22.0268	−	18.4827i	−1.41887	−	1.19058i	−0.951940	−	0.306283i	$-0.900914\pi$
$241$	−22.0268	−	18.4827i	−1.41887	−	1.19058i	−0.466933	−	0.884293i	$-0.654641\pi$
$242$	22.1037			1.42088
$243$	14.9191	+	4.51886i	0.957062	+	0.289885i
$244$	6.04338			0.386888
$245$		0			0
$246$	−28.1056	+	17.9949i	−1.79195	+	1.14731i
$247$	−0.538026	−	3.05130i	−0.0342338	−	0.194149i
$248$	1.04950	+	0.381986i	0.0666432	+	0.0242562i
$249$	−15.4323	−	1.99615i	−0.977985	−	0.126501i
$250$		0			0
$251$	5.86206	−	10.1534i	0.370010	−	0.640876i	−0.619557	−	0.784952i	$-0.712688\pi$
$251$	5.86206	−	10.1534i	0.370010	−	0.640876i	0.989567	+	0.144076i	$0.0460210\pi$
$252$	0.991429	−	2.15152i	0.0624541	−	0.135533i
$253$	−0.0793348	−	0.137412i	−0.00498774	−	0.00863901i
$254$	20.5478	−	7.47878i	1.28928	−	0.469260i
$255$		0			0
$256$	10.9342	−	9.17485i	0.683385	−	0.573428i
$257$	2.82575	−	2.37109i	0.176265	−	0.147904i	−0.550387	−	0.834910i	$-0.685520\pi$
$257$	2.82575	−	2.37109i	0.176265	−	0.147904i	0.726652	+	0.687006i	$0.241075\pi$
$258$	34.7578	−	7.78827i	2.16393	−	0.484876i
$259$	3.86758	−	1.40769i	0.240320	−	0.0874693i
$260$		0			0
$261$	−16.4798	+	7.77576i	−1.02008	+	0.481308i
$262$	12.5305	−	21.7035i	0.774138	−	1.34085i
$263$	−3.83968	+	21.7759i	−0.236765	+	1.34276i	0.602099	+	0.798421i	$0.294331\pi$
$263$	−3.83968	+	21.7759i	−0.236765	+	1.34276i	−0.838864	+	0.544340i	$0.816780\pi$
$264$	0.0393865	+	0.0944815i	0.00242407	+	0.00581494i
$265$		0			0
$266$	−0.462939	−	2.62546i	−0.0283846	−	0.160977i
$267$	−0.494404	−	10.7641i	−0.0302570	−	0.658754i
$268$	−14.2516	−	11.9585i	−0.870553	−	0.730480i
$269$	25.3331			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$269$	25.3331			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$270$		0			0
$271$	28.7783			1.74816			0.874079	−	0.485783i	$-0.161466\pi$
$271$	28.7783			1.74816			0.874079	+	0.485783i	$0.161466\pi$
$272$	−13.4950	−	11.3237i	−0.818255	−	0.686598i
$273$	−0.511609	−	0.264855i	−0.0309640	−	0.0160298i
$274$	−5.80140	−	32.9014i	−0.350475	−	1.98764i
$275$		0			0
$276$	−1.20613	+	1.57925i	−0.0726004	+	0.0950598i
$277$	3.42530	−	19.4258i	0.205806	−	1.16718i	−0.690360	−	0.723466i	$-0.742548\pi$
$277$	3.42530	−	19.4258i	0.205806	−	1.16718i	0.896166	−	0.443719i	$-0.146341\pi$
$278$	−12.4836	+	21.6222i	−0.748715	+	1.29681i
$279$	15.9273	+	4.19047i	0.953544	+	0.250877i
$280$		0			0
$281$	−8.19525	+	2.98283i	−0.488887	+	0.177940i	−0.574689	−	0.818372i	$-0.694877\pi$
$281$	−8.19525	+	2.98283i	−0.488887	+	0.177940i	0.0858017	+	0.996312i	$0.472655\pi$
$282$	−6.63100	+	21.1982i	−0.394870	+	1.26233i
$283$	5.69001	−	4.77449i	0.338236	−	0.283814i	−0.457810	−	0.889050i	$-0.651366\pi$
$283$	5.69001	−	4.77449i	0.338236	−	0.283814i	0.796046	+	0.605236i	$0.206921\pi$
$284$	−17.2772	+	14.4973i	−1.02521	+	0.860257i
$285$		0			0
$286$	0.489056	−	0.178002i	0.0289185	−	0.0105255i
$287$	1.78857	+	3.09789i	0.105576	+	0.182862i
$288$	−17.0612	+	17.2165i	−1.00534	+	1.01449i
$289$	−2.30851	+	3.99846i	−0.135795	+	0.235204i
$290$		0			0
$291$	14.7389	−	19.2984i	0.864007	−	1.13129i
$292$	1.53763	+	0.559652i	0.0899831	+	0.0327512i
$293$	0.328799	+	1.86471i	0.0192086	+	0.108937i	0.992905	−	0.118914i	$-0.0379412\pi$
$293$	0.328799	+	1.86471i	0.0192086	+	0.108937i	−0.973696	+	0.227851i	$0.926830\pi$
$294$	21.3627	+	11.0593i	1.24590	+	0.644991i
$295$		0			0
$296$	2.22728			0.129458
$297$	0.706072	+	1.33414i	0.0409705	+	0.0774145i
$298$	20.6670			1.19721
$299$	0.370191	+	0.310627i	0.0214087	+	0.0179640i
$300$		0			0
$301$	−0.662985	−	3.75998i	−0.0382138	−	0.216721i
$302$	−33.9759	−	12.3662i	−1.95510	−	0.711597i
$303$	−2.68037	−	6.42976i	−0.153983	−	0.369380i
$304$	−2.30413	+	13.0674i	−0.132151	+	0.749466i
$305$		0			0
$306$	23.2098	+	16.0955i	1.32682	+	0.920117i
$307$	−7.11195	−	12.3183i	−0.405900	−	0.703040i	0.588525	−	0.808479i	$-0.299709\pi$
$307$	−7.11195	−	12.3183i	−0.405900	−	0.703040i	−0.994426	+	0.105439i	$0.966375\pi$
$308$	0.215556	−	0.0784561i	0.0122825	−	0.00447045i
$309$	−0.871114	+	0.195193i	−0.0495559	+	0.0111041i
$310$		0			0
$311$	11.2222	−	9.41658i	0.636355	−	0.533965i	−0.266541	−	0.963824i	$-0.585881\pi$
$311$	11.2222	−	9.41658i	0.636355	−	0.533965i	0.902896	+	0.429858i	$0.141436\pi$
$312$	−0.211141	−	0.229375i	−0.0119535	−	0.0129858i
$313$	24.3151	−	8.84996i	1.37437	−	0.500229i	0.453902	−	0.891051i	$-0.350032\pi$
$313$	24.3151	−	8.84996i	1.37437	−	0.500229i	0.920466	+	0.390822i	$0.127809\pi$
$314$	11.6938	+	20.2542i	0.659917	+	1.14301i
$315$		0			0
$316$	−7.26032	+	12.5752i	−0.408425	+	0.707413i
$317$	3.17156	−	17.9868i	0.178133	−	1.01024i	−0.756333	−	0.654187i	$-0.773011\pi$
$317$	3.17156	−	17.9868i	0.178133	−	1.01024i	0.934466	−	0.356053i	$-0.115878\pi$
$318$	42.4873	+	5.49568i	2.38257	+	0.308182i
$319$	−1.65807	−	0.603489i	−0.0928342	−	0.0337889i
$320$		0			0
$321$	−26.2107	+	16.7817i	−1.46294	+	0.936661i
$322$	0.318527	+	0.267276i	0.0177508	+	0.0148947i
$323$	16.2822			0.905968
$324$	12.0197	−	14.5910i	0.667760	−	0.810609i
$325$		0			0
$326$	9.71387	+	8.15090i	0.538001	+	0.451437i
$327$	1.61188	−	1.03202i	0.0891371	−	0.0570709i
$328$	0.336144	+	1.90637i	0.0185605	+	0.105262i
$329$	2.23717	+	0.814263i	0.123339	+	0.0448918i
$330$		0			0
$331$	−5.49188	+	31.1460i	−0.301861	+	1.71194i	0.336062	+	0.941840i	$0.390905\pi$
$331$	−5.49188	+	31.1460i	−0.301861	+	1.71194i	−0.637923	+	0.770100i	$0.720206\pi$
$332$	−9.43539	+	16.3426i	−0.517835	+	0.896916i
$333$	32.7056	−	3.01074i	1.79226	−	0.164987i
$334$	15.8580	+	27.4668i	0.867709	+	1.50292i
$335$		0			0
$336$	1.67093	+	1.81522i	0.0911565	+	0.0990285i
$337$	5.87047	−	4.92591i	0.319785	−	0.268332i	−0.468737	−	0.883338i	$-0.655291\pi$
$337$	5.87047	−	4.92591i	0.319785	−	0.268332i	0.788522	+	0.615006i	$0.210846\pi$
$338$	18.9515	−	15.9022i	1.03083	−	0.864965i
$339$	15.3456	−	3.43854i	0.833461	−	0.186756i
$340$		0			0
$341$	0.797378	+	1.38110i	0.0431804	+	0.0747907i
$342$	1.75814	−	21.2015i	0.0950691	−	1.14644i
$343$	2.60503	−	4.51204i	0.140658	−	0.243627i
$344$	0.358777	−	2.03472i	0.0193439	−	0.109705i
$345$		0			0
$346$	17.3561	+	6.31710i	0.933069	+	0.339609i
$347$	0.616506	+	3.49638i	0.0330958	+	0.187695i	0.996874	−	0.0790102i	$-0.0251760\pi$
$347$	0.616506	+	3.49638i	0.0330958	+	0.187695i	−0.963778	+	0.266706i	$0.914065\pi$
$348$	1.01391	+	22.0749i	0.0543515	+	1.18334i
$349$	−3.58455	−	3.00779i	−0.191876	−	0.161003i	0.541788	−	0.840515i	$-0.317747\pi$
$349$	−3.58455	−	3.00779i	−0.191876	−	0.161003i	−0.733665	+	0.679511i	$0.762192\pi$
$350$		0			0
$351$	−3.41048	−	3.08276i	−0.182038	−	0.164545i
$352$	−2.34703			−0.125097
$353$	12.0080	+	10.0759i	0.639120	+	0.536286i	0.903748	−	0.428065i	$-0.140805\pi$
$353$	12.0080	+	10.0759i	0.639120	+	0.536286i	−0.264628	+	0.964351i	$0.585249\pi$
$354$	−3.93703	−	2.03817i	−0.209251	−	0.108327i
$355$		0			0
$356$	−12.2794	−	4.46934i	−0.650807	−	0.236874i
$357$	1.83756	−	2.40602i	0.0972539	−	0.127340i
$358$	0.929080	−	5.26907i	0.0491034	−	0.278479i
$359$	−1.36397	+	2.36247i	−0.0719876	+	0.124686i	−0.899772	−	0.436360i	$-0.856268\pi$
$359$	−1.36397	+	2.36247i	−0.0719876	+	0.124686i	0.827785	+	0.561046i	$0.189601\pi$
$360$		0			0
$361$	3.36800	+	5.83355i	0.177263	+	0.307029i
$362$	−13.5068	+	4.91608i	−0.709902	+	0.258383i
$363$	5.64440	−	18.0442i	0.296254	−	0.947074i
$364$	−0.535189	+	0.449077i	−0.0280516	+	0.0235380i
$365$		0			0
$366$	3.01266	−	9.63096i	0.157474	−	0.503418i
$367$	−29.9725	+	10.9091i	−1.56455	+	0.569450i	−0.971773	−	0.235916i	$-0.924191\pi$
$367$	−29.9725	+	10.9091i	−1.56455	+	0.569450i	−0.592778	+	0.805366i	$0.701969\pi$
$368$	−1.03478	−	1.79228i	−0.0539414	−	0.0934293i
$369$	7.51293	+	27.5390i	0.391107	+	1.43362i
$370$		0			0
$371$	0.797399	−	4.52228i	0.0413989	−	0.234785i
$372$	12.1225	−	15.8727i	0.628525	−	0.822962i
$373$	−5.82118	−	2.11873i	−0.301409	−	0.109704i	0.186888	−	0.982381i	$-0.440160\pi$
$373$	−5.82118	−	2.11873i	−0.301409	−	0.109704i	−0.488298	+	0.872677i	$0.662382\pi$
$374$	0.474924	+	2.69343i	0.0245577	+	0.139274i
$375$		0			0
$376$	0.986932	+	0.828134i	0.0508971	+	0.0427078i
$377$	5.37398			0.276774
$378$	−2.93451	−	2.65253i	−0.150935	−	0.136431i
$379$	24.4506			1.25595			0.627973	−	0.778235i	$-0.283885\pi$
$379$	24.4506			1.25595			0.627973	+	0.778235i	$0.283885\pi$
$380$		0			0
$381$	−0.858161	−	18.6838i	−0.0439649	−	0.957200i
$382$	−1.82668	−	10.3596i	−0.0934612	−	0.530045i
$383$	7.01885	+	2.55465i	0.358647	+	0.130537i	0.515058	−	0.857155i	$-0.327770\pi$
$383$	7.01885	+	2.55465i	0.358647	+	0.130537i	−0.156411	+	0.987692i	$0.549993\pi$
$384$	1.08330	+	2.59866i	0.0552821	+	0.132612i
$385$		0			0
$386$	3.97075	−	6.87755i	0.202106	−	0.350058i
$387$	2.51787	−	30.3631i	0.127990	−	1.54344i
$388$	−14.7240	−	25.5028i	−0.747500	−	1.29471i
$389$	−26.7061	+	9.72022i	−1.35405	+	0.492835i	−0.914210	−	0.405240i	$-0.867188\pi$
$389$	−26.7061	+	9.72022i	−1.35405	+	0.492835i	−0.439842	+	0.898075i	$0.644966\pi$
$390$		0			0
$391$	−1.94539	+	1.63238i	−0.0983826	+	0.0825528i
$392$	1.06889	−	0.896909i	0.0539873	−	0.0453007i
$393$	−14.5177	−	15.7714i	−0.732320	−	0.795562i
$394$	−19.7356	+	7.18318i	−0.994266	+	0.361883i
$395$		0			0
$396$	1.82282	−	0.167801i	0.0916001	−	0.00843231i
$397$	−14.4933	+	25.1031i	−0.727396	+	1.25989i	0.230585	+	0.973052i	$0.425936\pi$
$397$	−14.4933	+	25.1031i	−0.727396	+	1.25989i	−0.957980	+	0.286834i	$0.907397\pi$
$398$	−4.18777	+	23.7501i	−0.209914	+	1.19048i
$399$	−2.26149	−	0.292520i	−0.113216	−	0.0146443i
$400$		0			0
$401$	5.27642	+	29.9241i	0.263492	+	1.49434i	0.773296	+	0.634046i	$0.218607\pi$
$401$	5.27642	+	29.9241i	0.263492	+	1.49434i	−0.509804	+	0.860291i	$0.670282\pi$
$402$	−26.1620	+	16.7505i	−1.30484	+	0.835437i
$403$	−3.72071	−	3.12205i	−0.185342	−	0.155520i
$404$	−8.44780			−0.420294
$405$		0			0
$406$	4.62398			0.229484
$407$	2.43627	+	2.04428i	0.120762	+	0.101331i
$408$	1.37975	−	0.883398i	0.0683078	−	0.0437347i
$409$	−0.726985	−	4.12294i	−0.0359471	−	0.203866i	0.961545	−	0.274649i	$-0.0885615\pi$
$409$	−0.726985	−	4.12294i	−0.0359471	−	0.203866i	−0.997492	+	0.0707824i	$0.977450\pi$
$410$		0			0
$411$	−28.3402	−	3.66577i	−1.39792	−	0.180819i
$412$	−0.187992	+	1.06615i	−0.00926168	+	0.0525256i
$413$	−0.237598	+	0.411531i	−0.0116914	+	0.0202501i
$414$	1.91549	+	2.70940i	0.0941414	+	0.133160i
$415$		0			0
$416$	6.71711	−	2.44483i	0.329333	−	0.119868i
$417$	14.4633	+	15.7123i	0.708271	+	0.769436i
$418$	1.57807	−	1.32416i	0.0771858	−	0.0647666i
$419$	−17.7641	+	14.9058i	−0.867832	+	0.728197i	−0.963640	−	0.267203i	$-0.913901\pi$
$419$	−17.7641	+	14.9058i	−0.867832	+	0.728197i	0.0958087	+	0.995400i	$0.469456\pi$
$420$		0			0
$421$	6.96568	−	2.53530i	0.339487	−	0.123563i	−0.166651	−	0.986016i	$-0.553295\pi$
$421$	6.96568	−	2.53530i	0.339487	−	0.123563i	0.506137	+	0.862453i	$0.331073\pi$
$422$	2.47913	+	4.29399i	0.120682	+	0.209028i
$423$	15.6117	+	10.8263i	0.759065	+	0.526394i
$424$	1.24250	−	2.15207i	0.0603411	−	0.104514i
$425$		0			0
$426$	14.4907	+	34.7606i	0.702075	+	1.68416i
$427$	−1.01641	−	0.369944i	−0.0491877	−	0.0179029i
$428$	6.55396	+	37.1694i	0.316798	+	1.79665i
$429$	−0.0204250	−	0.444692i	−0.000986129	−	0.0214699i
$430$		0			0
$431$	3.55875			0.171419			0.0857095	−	0.996320i	$-0.472684\pi$
$431$	3.55875			0.171419			0.0857095	+	0.996320i	$0.472684\pi$
$432$	9.20941	+	17.4014i	0.443088	+	0.837223i
$433$	−39.5383			−1.90009			−0.950046	−	0.312111i	$-0.898964\pi$
$433$	−39.5383			−1.90009			−0.950046	+	0.312111i	$0.898964\pi$
$434$	−3.20145	−	2.68633i	−0.153674	−	0.128948i
$435$		0			0
$436$	−0.403048	−	2.28580i	−0.0193025	−	0.109470i
$437$	1.79745	+	0.654218i	0.0859837	+	0.0312955i
$438$	1.65840	−	2.17144i	0.0792415	−	0.103755i
$439$	−0.368776	+	2.09143i	−0.0176007	+	0.0998186i	−0.992343	−	0.123516i	$-0.960583\pi$
$439$	−0.368776	+	2.09143i	−0.0176007	+	0.0998186i	0.974742	+	0.223334i	$0.0716942\pi$
$440$		0			0
$441$	14.4834	−	14.6152i	0.689684	−	0.695962i
$442$	−4.16487	−	7.21377i	−0.198103	−	0.343124i
$443$	−15.2652	+	5.55606i	−0.725270	+	0.263977i	−0.678161	−	0.734913i	$-0.737223\pi$
$443$	−15.2652	+	5.55606i	−0.725270	+	0.263977i	−0.0471084	+	0.998890i	$0.515001\pi$
$444$	11.8910	−	38.0136i	0.564323	−	1.80404i
$445$		0			0
$446$	27.9502	−	23.4530i	1.32348	−	1.11053i
$447$	5.27752	−	16.8713i	0.249618	−	0.797987i
$448$	3.10260	−	1.12926i	0.146584	−	0.0533523i
$449$	−17.8132	−	30.8534i	−0.840658	−	1.45606i	−0.889339	−	0.457249i	$-0.848835\pi$
$449$	−17.8132	−	30.8534i	−0.840658	−	1.45606i	0.0486805	−	0.998814i	$-0.484498\pi$
$450$		0			0
$451$	−1.38205	+	2.39378i	−0.0650781	+	0.112719i
$452$	3.31168	−	18.7815i	0.155768	−	0.883406i
$453$	−18.7712	+	24.5782i	−0.881947	+	1.15478i
$454$	−10.1736	−	3.70288i	−0.477470	−	0.173785i
$455$		0			0
$456$	−1.09587	−	0.567320i	−0.0513186	−	0.0265672i
$457$	19.7485	+	16.5710i	0.923796	+	0.775157i	0.974693	−	0.223547i	$-0.0717636\pi$
$457$	19.7485	+	16.5710i	0.923796	+	0.775157i	−0.0508970	+	0.998704i	$0.516208\pi$
$458$	−43.6242			−2.03842
$459$	19.0663	−	14.8370i	0.889938	−	0.692532i
$460$		0			0
$461$	−26.3039	−	22.0716i	−1.22509	−	1.02798i	−0.998542	−	0.0539762i	$-0.982810\pi$
$461$	−26.3039	−	22.0716i	−1.22509	−	1.02798i	−0.226551	−	0.973999i	$-0.572745\pi$
$462$	−0.0175745	−	0.382630i	−0.000817639	−	0.0178016i
$463$	−5.12509	−	29.0659i	−0.238183	−	1.35080i	−0.835805	−	0.549026i	$-0.814999\pi$
$463$	−5.12509	−	29.0659i	−0.238183	−	1.35080i	0.597622	−	0.801778i	$-0.296112\pi$
$464$	−21.6265	−	7.87140i	−1.00398	−	0.365421i
$465$		0			0
$466$	−8.98908	+	50.9796i	−0.416411	+	2.36158i
$467$	−8.31964	+	14.4100i	−0.384987	+	0.666817i	−0.991767	−	0.128053i	$-0.959127\pi$
$467$	−8.31964	+	14.4100i	−0.384987	+	0.666817i	0.606780	+	0.794869i	$0.292461\pi$
$468$	−5.04205	+	2.37902i	−0.233069	+	0.109970i
$469$	1.66488	+	2.88366i	0.0768770	+	0.133155i
$470$		0			0
$471$	19.5205	−	4.37400i	0.899455	−	0.201543i
$472$	−0.196991	+	0.165295i	−0.00906725	+	0.00760833i
$473$	2.25999	−	1.89635i	0.103914	−	0.0871944i
$474$	16.4211	+	17.8392i	0.754245	+	0.819380i
$475$		0			0
$476$	−1.83571	−	3.17955i	−0.0841397	−	0.145734i
$477$	15.3359	−	33.2808i	0.702184	−	1.52382i
$478$	9.36897	−	16.2275i	0.428527	−	0.742230i
$479$	0.965663	−	5.47655i	0.0441223	−	0.250230i	−0.954767	−	0.297356i	$-0.903895\pi$
$479$	0.965663	−	5.47655i	0.0441223	−	0.250230i	0.998889	+	0.0471262i	$0.0150063\pi$
$480$		0			0
$481$	−9.10199	−	3.31285i	−0.415015	−	0.151053i
$482$	10.1108	+	57.3411i	0.460534	+	2.61182i
$483$	0.299528	−	0.191775i	0.0136290	−	0.00872609i
$484$	−17.5638	−	14.7378i	−0.798354	−	0.669898i
$485$		0			0
$486$	−17.2608	−	26.4287i	−0.782968	−	1.19883i
$487$	−17.5069			−0.793314			−0.396657	−	0.917967i	$-0.629830\pi$
$487$	−17.5069			−0.793314			−0.396657	+	0.917967i	$0.629830\pi$
$488$	−0.448393	−	0.376246i	−0.0202978	−	0.0170319i
$489$	9.13446	−	5.84843i	0.413075	−	0.264475i
$490$		0			0
$491$	25.2199	+	9.17930i	1.13816	+	0.414256i	0.841248	−	0.540649i	$-0.181821\pi$
$491$	25.2199	+	9.17930i	1.13816	+	0.414256i	0.296911	+	0.954905i	$0.404044\pi$
$492$	34.3311	+	4.44068i	1.54777	+	0.200201i
$493$	−4.90396	+	27.8118i	−0.220863	+	1.25258i
$494$	−3.13704	+	5.43351i	−0.141142	+	0.244465i
$495$		0			0
$496$	10.4003	+	18.0139i	0.466988	+	0.808847i
$497$	3.79324	−	1.38063i	0.170150	−	0.0619295i
$498$	21.3406	+	23.1835i	0.956294	+	1.03888i
$499$	4.46524	−	3.74678i	0.199892	−	0.167729i	−0.537347	−	0.843361i	$-0.680574\pi$
$499$	4.46524	−	3.74678i	0.199892	−	0.167729i	0.737239	+	0.675632i	$0.236129\pi$
$500$		0			0
$501$	26.4718	−	5.93160i	1.18267	−	0.265004i
$502$	−22.3091	+	8.11986i	−0.995705	+	0.362407i
$503$	15.2521	+	26.4175i	0.680059	+	1.17790i	0.974963	+	0.222369i	$0.0713790\pi$
$503$	15.2521	+	26.4175i	0.680059	+	1.17790i	−0.294904	+	0.955527i	$0.595288\pi$
$504$	−0.207508	+	0.0979097i	−0.00924316	+	0.00436124i
$505$		0			0
$506$	−0.0557931	+	0.316419i	−0.00248031	+	0.0140665i
$507$	−8.14218	−	19.5317i	−0.361607	−	0.867433i
$508$	−21.3139	−	7.75764i	−0.945654	−	0.344190i
$509$	−5.46355	−	30.9853i	−0.242167	−	1.37340i	−0.826980	−	0.562231i	$-0.809943\pi$
$509$	−5.46355	−	30.9853i	−0.242167	−	1.37340i	0.584813	−	0.811168i	$-0.301168\pi$
$510$		0			0
$511$	−0.224349	−	0.188252i	−0.00992464	−	0.00832776i
$512$	−32.1543			−1.42103
$513$	−16.8587	−	6.84925i	−0.744330	−	0.302402i
$514$	−7.46958			−0.329469
$515$		0			0
$516$	−32.8117	−	16.9863i	−1.44446	−	0.747782i
$517$	0.319449	+	1.81168i	0.0140493	+	0.0796778i
$518$	−7.83171	−	2.85051i	−0.344106	−	0.125244i
$519$	9.58897	−	12.5554i	0.420909	−	0.551120i
$520$		0			0
$521$	−4.14101	+	7.17245i	−0.181421	+	0.314231i	−0.942365	−	0.334587i	$-0.891403\pi$
$521$	−4.14101	+	7.17245i	−0.181421	+	0.314231i	0.760944	+	0.648818i	$0.224736\pi$
$522$	35.6848	+	9.38864i	1.56188	+	0.410930i
$523$	−8.91120	−	15.4347i	−0.389660	−	0.674910i	0.602744	−	0.797935i	$-0.294074\pi$
$523$	−8.91120	−	15.4347i	−0.389660	−	0.674910i	−0.992404	+	0.123024i	$0.960741\pi$
$524$	−24.4278	+	8.89098i	−1.06713	+	0.388404i
$525$		0			0
$526$	34.3001	−	28.7812i	1.49556	−	1.25492i
$527$	19.5527	−	16.4067i	0.851730	−	0.714686i
$528$	−0.569154	+	1.81949i	−0.0247693	+	0.0791831i
$529$	21.3326	−	7.76443i	0.927504	−	0.337584i
$530$		0			0
$531$	−2.66920	+	2.69350i	−0.115834	+	0.116888i
$532$	−1.38268	+	2.39488i	−0.0599469	+	0.103831i
$533$	1.46185	−	8.29054i	0.0633196	−	0.359103i
$534$	−13.2439	+	17.3409i	−0.573118	+	0.750416i
$535$		0			0
$536$	0.312899	+	1.77454i	0.0135152	+	0.0766483i
$537$	−4.06412	−	2.10396i	−0.175380	−	0.0907925i
$538$	−39.2970	−	32.9741i	−1.69421	−	1.42161i
$539$	1.99241			0.0858191
$540$		0			0
$541$	−34.8916			−1.50011			−0.750054	−	0.661376i	$-0.769973\pi$
$541$	−34.8916			−1.50011			−0.750054	+	0.661376i	$0.769973\pi$
$542$	−44.6412	−	37.4584i	−1.91750	−	1.60898i
$543$	0.564101	+	12.2816i	0.0242079	+	0.527052i
$544$	6.52300	+	36.9938i	0.279671	+	1.58610i
$545$		0			0
$546$	0.448872	+	1.07677i	0.0192099	+	0.0460814i
$547$	−4.30509	+	24.4154i	−0.184072	+	1.04393i	0.743069	+	0.669214i	$0.233369\pi$
$547$	−4.30509	+	24.4154i	−0.184072	+	1.04393i	−0.927142	+	0.374711i	$0.877742\pi$
$548$	−17.3273	+	30.0118i	−0.740187	+	1.28204i
$549$	−7.09285	−	4.91873i	−0.302715	−	0.209926i
$550$		0			0
$551$	19.9885	−	7.27523i	0.851540	−	0.309935i
$552$	0.187810	−	0.0420831i	0.00799373	−	0.00179117i
$553$	1.99088	−	1.67054i	0.0846607	−	0.0710388i
$554$	−30.5984	+	25.6751i	−1.30000	+	1.09083i
$555$		0			0
$556$	24.3363	−	8.85768i	1.03209	−	0.375649i
$557$	15.5900	+	27.0026i	0.660568	+	1.14414i	0.980467	+	0.196686i	$0.0630180\pi$
$557$	15.5900	+	27.0026i	0.660568	+	1.14414i	−0.319898	+	0.947452i	$0.603649\pi$
$558$	−19.2522	−	27.2316i	−0.815012	−	1.15281i
$559$	−4.49262	+	7.78145i	−0.190018	+	0.329120i
$560$		0			0
$561$	2.32003	+	0.300093i	0.0979519	+	0.0126699i
$562$	16.5951	+	6.04011i	0.700020	+	0.254787i
$563$	1.99921	+	11.3381i	0.0842567	+	0.477844i	0.997514	+	0.0704615i	$0.0224472\pi$
$563$	1.99921	+	11.3381i	0.0842567	+	0.477844i	−0.913258	+	0.407382i	$0.866442\pi$
$564$	19.4030	−	12.4230i	0.817015	−	0.523102i
$565$		0			0
$566$	−15.0410			−0.632219
$567$	−2.91473	+	1.71822i	−0.122407	+	0.0721584i
$568$	2.18446			0.0916580
$569$	0.688909	+	0.578063i	0.0288805	+	0.0242337i	0.657114	−	0.753791i	$-0.271777\pi$
$569$	0.688909	+	0.578063i	0.0288805	+	0.0242337i	−0.628233	+	0.778025i	$0.716222\pi$
$570$		0			0
$571$	7.41437	+	42.0490i	0.310282	+	1.75969i	0.597538	+	0.801841i	$0.296146\pi$
$571$	7.41437	+	42.0490i	0.310282	+	1.75969i	−0.287256	+	0.957854i	$0.592743\pi$
$572$	−0.507292	−	0.184639i	−0.0212109	−	0.00772015i
$573$	−8.92347	−	1.15424i	−0.372783	−	0.0482190i
$574$	1.25783	−	7.13351i	0.0525008	−	0.297747i
$575$		0			0
$576$	26.2367	−	2.41524i	1.09319	−	0.100635i
$577$	−6.22274	−	10.7781i	−0.259056	−	0.448698i	0.706933	−	0.707280i	$-0.250078\pi$
$577$	−6.22274	−	10.7781i	−0.259056	−	0.448698i	−0.965989	+	0.258582i	$0.916745\pi$
$578$	8.78546	−	3.19765i	0.365427	−	0.133005i
$579$	−4.60046	−	4.99775i	−0.191189	−	0.207699i
$580$		0			0
$581$	2.58731	−	2.17101i	0.107340	−	0.0900688i
$582$	−47.9822	+	10.7515i	−1.98893	+	0.445664i
$583$	3.33434	−	1.21360i	0.138094	−	0.0502622i
$584$	−0.0792431	−	0.137253i	−0.00327910	−	0.00567957i
$585$		0			0
$586$	1.91711	−	3.32053i	0.0791950	−	0.137170i
$587$	−1.91101	+	10.8379i	−0.0788758	+	0.447327i	0.919635	+	0.392774i	$0.128484\pi$
$587$	−1.91101	+	10.8379i	−0.0788758	+	0.447327i	−0.998511	+	0.0545530i	$0.982627\pi$
$588$	−9.60115	−	23.0315i	−0.395945	−	0.949804i
$589$	−18.0658	−	6.57541i	−0.744388	−	0.270935i
$590$		0			0
$591$	0.824242	+	17.9453i	0.0339048	+	0.738172i
$592$	31.7767	+	26.6638i	1.30601	+	1.09588i
$593$	9.57442			0.393174			0.196587	−	0.980486i	$-0.437014\pi$
$593$	9.57442			0.393174			0.196587	+	0.980486i	$0.437014\pi$
$594$	0.641273	−	2.98856i	0.0263117	−	0.122622i
$595$		0			0
$596$	−16.4222	−	13.7798i	−0.672678	−	0.564444i
$597$	18.3188	+	9.48348i	0.749738	+	0.388133i
$598$	−0.169926	−	0.963696i	−0.00694878	−	0.0394085i
$599$	−30.9256	−	11.2560i	−1.26359	−	0.459908i	−0.378616	−	0.925554i	$-0.623600\pi$
$599$	−30.9256	−	11.2560i	−1.26359	−	0.459908i	−0.884971	+	0.465646i	$0.845822\pi$
$600$		0			0
$601$	−2.22127	+	12.5974i	−0.0906074	+	0.513860i	0.905398	+	0.424564i	$0.139573\pi$
$601$	−2.22127	+	12.5974i	−0.0906074	+	0.513860i	−0.996005	+	0.0892957i	$0.971538\pi$
$602$	−3.86563	+	6.69547i	−0.157551	+	0.272887i
$603$	6.99338	+	25.6345i	0.284793	+	1.04392i
$604$	18.7523	+	32.4800i	0.763021	+	1.32159i
$605$		0			0
$606$	−4.21128	+	13.4627i	−0.171072	+	0.546886i
$607$	28.7032	−	24.0848i	1.16503	−	0.977573i	0.165064	−	0.986283i	$-0.447217\pi$
$607$	28.7032	−	24.0848i	1.16503	−	0.977573i	0.999962	+	0.00870958i	$0.00277238\pi$
$608$	21.6745	−	18.1871i	0.879018	−	0.737583i
$609$	1.18078	−	3.77475i	0.0478477	−	0.152961i
$610$		0			0
$611$	−2.80143	−	4.85221i	−0.113334	−	0.196300i
$612$	−7.71096	−	28.2649i	−0.311697	−	1.14254i
$613$	1.30760	−	2.26483i	0.0528136	−	0.0914758i	−0.838410	−	0.545040i	$-0.816514\pi$
$613$	1.30760	−	2.26483i	0.0528136	−	0.0914758i	0.891224	+	0.453564i	$0.149848\pi$
$614$	−5.00156	+	28.3653i	−0.201847	+	1.14473i
$615$		0			0
$616$	−0.0208779	−	0.00759892i	−0.000841193	−	0.000306169i
$617$	1.11998	+	6.35172i	0.0450887	+	0.255711i	0.999017	−	0.0443232i	$-0.0141131\pi$
$617$	1.11998	+	6.35172i	0.0450887	+	0.255711i	−0.953929	+	0.300034i	$0.903002\pi$
$618$	1.60535	+	0.831075i	0.0645766	+	0.0334307i
$619$	−0.0522006	−	0.0438015i	−0.00209812	−	0.00176053i	0.641738	−	0.766924i	$-0.278214\pi$
$619$	−0.0522006	−	0.0438015i	−0.00209812	−	0.00176053i	−0.643836	+	0.765163i	$0.722658\pi$
$620$		0			0
$621$	2.70094	−	0.871826i	0.108385	−	0.0349852i
$622$	−29.6649			−1.18945
$623$	1.79164	+	1.50336i	0.0717804	+	0.0602309i
$624$	−0.266407	−	5.80018i	−0.0106648	−	0.232193i
$625$		0			0
$626$	−49.2370	−	17.9208i	−1.96791	−	0.716260i
$627$	−0.677989	−	1.62638i	−0.0270763	−	0.0649514i
$628$	4.21263	−	23.8910i	0.168102	−	0.953355i
$629$	25.4508	−	44.0821i	1.01479	−	1.75767i
$630$		0			0
$631$	−22.5451	−	39.0492i	−0.897506	−	1.55453i	−0.830673	−	0.556761i	$-0.812044\pi$
$631$	−22.5451	−	39.0492i	−0.897506	−	1.55453i	−0.0668329	−	0.997764i	$-0.521289\pi$
$632$	1.32159	−	0.481019i	0.0525700	−	0.0191339i
$633$	4.13843	−	0.927309i	0.164488	−	0.0368572i
$634$	−28.3317	+	23.7732i	−1.12520	+	0.944153i
$635$		0			0
$636$	−30.0965	−	32.6956i	−1.19340	−	1.29646i
$637$	−5.70220	+	2.07543i	−0.225930	+	0.0822316i
$638$	1.78651	+	3.09432i	0.0707284	+	0.122505i
$639$	32.0769	−	2.95286i	1.26894	−	0.116813i
$640$		0			0
$641$	6.39211	−	36.2514i	0.252473	−	1.43185i	−0.550004	−	0.835162i	$-0.685374\pi$
$641$	6.39211	−	36.2514i	0.252473	−	1.43185i	0.802477	−	0.596683i	$-0.203515\pi$
$642$	62.5017	+	8.08451i	2.46675	+	0.319070i
$643$	−4.60918	−	1.67760i	−0.181768	−	0.0661582i	0.249533	−	0.968366i	$-0.419723\pi$
$643$	−4.60918	−	1.67760i	−0.181768	−	0.0661582i	−0.431301	+	0.902208i	$0.641945\pi$
$644$	−0.0748965	−	0.424759i	−0.00295134	−	0.0167379i
$645$		0			0
$646$	−25.2572	−	21.1933i	−0.993730	−	0.833838i
$647$	−37.6519			−1.48025			−0.740125	−	0.672469i	$-0.765234\pi$
$647$	−37.6519			−1.48025			−0.740125	+	0.672469i	$0.765234\pi$
$648$	−1.80021	+	0.334271i	−0.0707188	+	0.0131314i
$649$	−0.367190			−0.0144135
$650$		0			0
$651$	−3.01049	+	1.92750i	−0.117990	+	0.0755445i
$652$	−2.28406	−	12.9536i	−0.0894507	−	0.507300i
$653$	−21.5387	−	7.83944i	−0.842874	−	0.306781i	−0.115743	−	0.993279i	$-0.536925\pi$
$653$	−21.5387	−	7.83944i	−0.842874	−	0.306781i	−0.727132	+	0.686498i	$0.759147\pi$
$654$	−3.84366	−	0.497172i	−0.150299	−	0.0194410i
$655$		0			0
$656$	−18.0263	+	31.2224i	−0.703807	+	1.21903i
$657$	−1.34915	−	1.90832i	−0.0526353	−	0.0744508i
$658$	−2.41046	−	4.17504i	−0.0939694	−	0.162760i
$659$	4.41936	−	1.60852i	0.172154	−	0.0626589i	−0.254505	−	0.967071i	$-0.581913\pi$
$659$	4.41936	−	1.60852i	0.172154	−	0.0626589i	0.426659	+	0.904412i	$0.359690\pi$
$660$		0			0
$661$	−25.3416	+	21.2641i	−0.985675	+	0.827079i	−0.984936	−	0.172920i	$-0.944680\pi$
$661$	−25.3416	+	21.2641i	−0.985675	+	0.827079i	−0.000739053		1.00000i	$0.500235\pi$
$662$	49.0593	−	41.1657i	1.90675	−	1.59995i
$663$	−6.95245	+	1.55785i	−0.270011	+	0.0605020i
$664$	1.71752	−	0.625125i	0.0666526	−	0.0242596i
$665$		0			0
$666$	−54.6521	−	37.9000i	−2.11773	−	1.46859i
$667$	−1.65884	+	2.87319i	−0.0642304	+	0.111250i
$668$	5.71277	−	32.3987i	0.221034	−	1.25354i
$669$	−12.0083	−	28.8059i	−0.464268	−	1.11370i
$670$		0			0
$671$	−0.145135	−	0.823103i	−0.00560288	−	0.0317755i
$672$	−0.241383	−	5.25537i	−0.00931155	−	0.202730i
$673$	34.0702	+	28.5883i	1.31331	+	1.10200i	0.987678	+	0.156500i	$0.0500212\pi$
$673$	34.0702	+	28.5883i	1.31331	+	1.10200i	0.325631	+	0.945497i	$0.394423\pi$
$674$	−15.5180			−0.597731
$675$		0			0
$676$	−25.6619			−0.986996
$677$	6.56883	+	5.51191i	0.252461	+	0.211840i	0.760231	−	0.649653i	$-0.225086\pi$
$677$	6.56883	+	5.51191i	0.252461	+	0.211840i	−0.507770	+	0.861492i	$0.669530\pi$
$678$	−28.2800	−	14.6403i	−1.08609	−	0.562257i
$679$	0.915233	+	5.19055i	0.0351234	+	0.199195i
$680$		0			0
$681$	−5.62075	+	7.35956i	−0.215388	+	0.282019i
$682$	0.560765	−	3.18026i	0.0214728	−	0.121778i
$683$	21.9820	−	38.0739i	0.841117	−	1.45686i	−0.0478347	−	0.998855i	$-0.515232\pi$
$683$	21.9820	−	38.0739i	0.841117	−	1.45686i	0.888951	−	0.458002i	$-0.151435\pi$
$684$	−15.5332	+	15.6746i	−0.593928	+	0.599334i
$685$		0			0
$686$	−9.91390	+	3.60836i	−0.378514	+	0.137768i
$687$	−11.1399	+	35.6123i	−0.425013	+	1.35869i
$688$	29.4773	−	24.7344i	1.12381	−	0.942991i
$689$	−8.27859	+	6.94656i	−0.315389	+	0.264643i
$690$		0			0
$691$	20.7711	−	7.56005i	0.790169	−	0.287598i	0.0847628	−	0.996401i	$-0.472987\pi$
$691$	20.7711	−	7.56005i	0.790169	−	0.287598i	0.705406	+	0.708803i	$0.250765\pi$
$692$	−9.57933	−	16.5919i	−0.364152	−	0.630729i
$693$	−0.316845	−	0.0833617i	−0.0120359	−	0.00316665i
$694$	3.59462	−	6.22607i	0.136450	−	0.236338i
$695$		0			0
$696$	1.29910	−	1.70098i	0.0492423	−	0.0644756i
$697$	41.5717	+	15.1309i	1.57464	+	0.573123i
$698$	1.64538	+	9.33144i	0.0622787	+	0.353200i
$699$	39.3213	+	20.3563i	1.48727	+	0.769947i
$700$		0			0
$701$	−0.728282			−0.0275068			−0.0137534	−	0.999905i	$-0.504378\pi$
$701$	−0.728282			−0.0275068			−0.0137534	+	0.999905i	$0.504378\pi$
$702$	1.27780	+	9.22116i	0.0482274	+	0.348030i
$703$	−38.3398			−1.44601
$704$	1.95440	+	1.63993i	0.0736591	+	0.0618073i
$705$		0			0
$706$	−5.51192	−	31.2596i	−0.207444	−	1.17647i
$707$	1.42080	+	0.517130i	0.0534348	+	0.0194487i
$708$	1.76944	+	4.24458i	0.0664996	+	0.159521i
$709$	2.85514	−	16.1923i	0.107227	−	0.608115i	−0.883080	−	0.469222i	$-0.844535\pi$
$709$	2.85514	−	16.1923i	0.107227	−	0.608115i	0.990307	−	0.138893i	$-0.0443544\pi$
$710$		0			0
$711$	18.7562	−	8.84981i	0.703411	−	0.331894i
$712$	0.632829	+	1.09609i	0.0237163	+	0.0410778i
$713$	2.81771	−	1.02556i	0.105524	−	0.0384076i
$714$	−5.98216	+	1.34044i	−0.223877	+	0.0501646i
$715$		0			0
$716$	−4.25144	+	3.56738i	−0.158884	+	0.133319i
$717$	−10.8548	−	11.7922i	−0.405379	−	0.440386i
$718$	5.19084	−	1.88931i	0.193720	−	0.0705085i
$719$	18.6844	+	32.3624i	0.696811	+	1.20691i	0.969566	+	0.244829i	$0.0787318\pi$
$719$	18.6844	+	32.3624i	0.696811	+	1.20691i	−0.272755	+	0.962083i	$0.587935\pi$
$720$		0			0
$721$	0.0968819	−	0.167804i	0.00360807	−	0.00624936i
$722$	2.36859	−	13.4329i	0.0881497	−	0.499922i
$723$	49.3919	+	6.38878i	1.83690	+	0.237601i
$724$	14.0105	+	5.09939i	0.520694	+	0.189517i
$725$		0			0
$726$	−32.2423	+	20.6435i	−1.19662	+	0.766150i
$727$	3.88514	+	3.26002i	0.144092	+	0.120907i	0.711984	−	0.702195i	$-0.247797\pi$
$727$	3.88514	+	3.26002i	0.144092	+	0.120907i	−0.567893	+	0.823103i	$0.692241\pi$
$728$	0.0676673			0.00250792
$729$	−25.9826	+	7.34192i	−0.962319	+	0.271923i
$730$		0			0
$731$	−36.1714	−	30.3514i	−1.33785	−	1.12259i
$732$	−8.81539	+	5.64413i	−0.325826	+	0.208613i
$733$	4.35439	+	24.6950i	0.160833	+	0.912129i	0.953257	+	0.302159i	$0.0977075\pi$
$733$	4.35439	+	24.6950i	0.160833	+	0.912129i	−0.792424	+	0.609970i	$0.791181\pi$
$734$	60.6931	+	22.0905i	2.24022	+	0.815375i
$735$		0			0
$736$	−0.766310	+	4.34596i	−0.0282466	+	0.160194i
$737$	−1.28647	+	2.22824i	−0.0473879	+	0.0820783i
$738$	24.1911	−	52.4977i	0.890487	−	1.93247i
$739$	−23.1354	−	40.0717i	−0.851050	−	1.47406i	−0.880262	−	0.474489i	$-0.842633\pi$
$739$	−23.1354	−	40.0717i	−0.851050	−	1.47406i	0.0292117	−	0.999573i	$-0.490700\pi$
$740$		0			0
$741$	3.63453	+	3.94840i	0.133518	+	0.145048i
$742$	−7.12322	+	5.97709i	−0.261502	+	0.219426i
$743$	−25.1018	+	21.0629i	−0.920896	+	0.772723i	−0.974160	−	0.225857i	$-0.927482\pi$
$743$	−25.1018	+	21.0629i	−0.920896	+	0.772723i	0.0532649	+	0.998580i	$0.483037\pi$
$744$	−1.88764	+	0.422968i	−0.0692042	+	0.0155068i
$745$		0			0
$746$	6.27208	+	10.8636i	0.229637	+	0.397743i
$747$	24.3752	−	11.5011i	0.891842	−	0.420802i
$748$	1.41848	−	2.45688i	0.0518647	−	0.0898323i
$749$	1.17303	−	6.65257i	0.0428615	−	0.243080i
$750$		0			0
$751$	11.8075	+	4.29756i	0.430860	+	0.156820i	0.548341	−	0.836255i	$-0.315260\pi$
$751$	11.8075	+	4.29756i	0.430860	+	0.156820i	−0.117481	+	0.993075i	$0.537482\pi$
$752$	4.16662	+	23.6301i	0.151941	+	0.861700i
$753$	0.931722	+	20.2854i	0.0339538	+	0.739240i
$754$	−8.33617	−	6.99488i	−0.303585	−	0.254738i
$755$		0			0
$756$	0.563203	+	4.06432i	0.0204835	+	0.147818i
$757$	35.3551			1.28500			0.642501	−	0.766285i	$-0.277897\pi$
$757$	35.3551			1.28500			0.642501	+	0.766285i	$0.277897\pi$
$758$	−37.9281	−	31.8254i	−1.37761	−	1.15595i
$759$	0.244059	+	0.126347i	0.00885876	+	0.00458611i
$760$		0			0
$761$	4.34791	+	1.58251i	0.157612	+	0.0573660i	0.419621	−	0.907699i	$-0.362163\pi$
$761$	4.34791	+	1.58251i	0.157612	+	0.0573660i	−0.262009	+	0.965065i	$0.584385\pi$
$762$	−22.9880	+	30.0995i	−0.832768	+	1.09039i
$763$	−0.0721376	+	0.409113i	−0.00261156	+	0.0148109i
$764$	−5.45584	+	9.44980i	−0.197386	+	0.341882i
$765$		0			0
$766$	−7.56253	−	13.0987i	−0.273245	−	0.473275i
$767$	1.05088	−	0.382490i	0.0379452	−	0.0138109i
$768$	−7.38076	+	23.5950i	−0.266330	+	0.851412i
$769$	−10.2592	+	8.60849i	−0.369956	+	0.310430i	−0.808744	−	0.588161i	$-0.799852\pi$
$769$	−10.2592	+	8.60849i	−0.369956	+	0.310430i	0.438788	+	0.898591i	$0.355408\pi$
$770$		0			0
$771$	−1.90743	+	6.09774i	−0.0686946	+	0.219605i
$772$	−7.74084	+	2.81744i	−0.278599	+	0.101402i
$773$	11.6796	+	20.2297i	0.420087	+	0.727612i	0.995948	−	0.0899361i	$-0.0286663\pi$
$773$	11.6796	+	20.2297i	0.420087	+	0.727612i	−0.575861	+	0.817548i	$0.695333\pi$
$774$	−43.4270	+	43.8222i	−1.56095	+	1.57516i
$775$		0			0

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55121 - 1.30162i) q^{2} +(-1.45868 + 0.933937i) q^{3} +(0.364742 + 2.06856i) q^{4} +(3.47836 + 0.449921i) q^{6} +(0.0652816 - 0.370230i) q^{7} +(0.101721 - 0.176186i) q^{8} +(1.25552 - 2.72464i) q^{9} +O(q^{10})\)	\(q+(-1.55121 - 1.30162i) q^{2} +(-1.45868 + 0.933937i) q^{3} +(0.364742 + 2.06856i) q^{4} +(3.47836 + 0.449921i) q^{6} +(0.0652816 - 0.370230i) q^{7} +(0.101721 - 0.176186i) q^{8} +(1.25552 - 2.72464i) q^{9} +(0.272976 - 0.0993552i) q^{11} +(-2.46395 - 2.67673i) q^{12} +(-0.677752 + 0.568702i) q^{13} +(-0.583165 + 0.489333i) q^{14} +(3.56047 - 1.29590i) q^{16} +(-2.32471 - 4.02651i) q^{17} +(-5.49403 + 2.59227i) q^{18} +(-1.75100 + 3.03282i) q^{19} +(0.250547 + 0.601018i) q^{21} +(-0.552766 - 0.201190i) q^{22} +(-0.0948473 - 0.537906i) q^{23} +(0.0161677 + 0.352001i) q^{24} +1.79157 q^{26} +(0.713228 + 5.14697i) q^{27} +0.789653 q^{28} +(-4.65300 - 3.90433i) q^{29} +(0.953291 + 5.40638i) q^{31} +(-7.59216 - 2.76332i) q^{32} +(-0.305395 + 0.399870i) q^{33} +(-1.63488 + 9.27184i) q^{34} +(6.09401 + 1.60333i) q^{36} +(5.47398 + 9.48122i) q^{37} +(6.66375 - 2.42541i) q^{38} +(0.457496 - 1.46253i) q^{39} +(-7.28901 + 6.11620i) q^{41} +(0.393647 - 1.25842i) q^{42} +(9.54330 - 3.47348i) q^{43} +(0.305088 + 0.528427i) q^{44} +(-0.553021 + 0.957860i) q^{46} +(-1.09967 + 6.23654i) q^{47} +(-3.98331 + 5.21557i) q^{48} +(6.44504 + 2.34580i) q^{49} +(7.15152 + 3.70228i) q^{51} +(-1.42360 - 1.19454i) q^{52} +12.2148 q^{53} +(5.59303 - 8.91238i) q^{54} +(-0.0585889 - 0.0491619i) q^{56} +(-0.278306 - 6.05925i) q^{57} +(2.13583 + 12.1129i) q^{58} +(-1.18778 - 0.432318i) q^{59} +(0.499613 - 2.83345i) q^{61} +(5.55830 - 9.62726i) q^{62} +(-0.926782 - 0.642702i) q^{63} +(4.39127 + 7.60590i) q^{64} +(0.994211 - 0.222775i) q^{66} +(-6.78495 + 5.69325i) q^{67} +(7.48114 - 6.27742i) q^{68} +(0.640723 + 0.696054i) q^{69} +(5.36876 + 9.29896i) q^{71} +(-0.352330 - 0.498359i) q^{72} +(0.389512 - 0.674654i) q^{73} +(3.84964 - 21.8324i) q^{74} +(-6.91222 - 2.51584i) q^{76} +(-0.0189640 - 0.107550i) q^{77} +(-2.61334 + 1.67321i) q^{78} +(5.29571 + 4.44363i) q^{79} +(-5.84732 - 6.84170i) q^{81} +19.2678 q^{82} +(6.88221 + 5.77486i) q^{83} +(-1.15186 + 0.737486i) q^{84} +(-19.3248 - 7.03366i) q^{86} +(10.4337 + 1.34958i) q^{87} +(0.0102624 - 0.0582011i) q^{88} +(-3.11061 + 5.38773i) q^{89} +(0.166306 + 0.288050i) q^{91} +(1.07809 - 0.392394i) q^{92} +(-6.43977 - 6.99589i) q^{93} +(9.82342 - 8.24283i) q^{94} +(13.6553 - 3.05978i) q^{96} +(-13.1743 + 4.79504i) q^{97} +(-6.94427 - 12.0278i) q^{98} +(0.0720209 - 0.868504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

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