LMFDB - Embedded newform 189.2.g.b.172.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(100,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.5
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	189.172
Dual form			189.2.g.b.100.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(0.0802402 - 2.64453i) q^{7} -0.446582 q^{8} +O(q^{10})$	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(0.0802402 - 2.64453i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} -1.66404 q^{11} +(0.0999454 - 0.173111i) q^{13} +(-4.62094 - 2.85818i) q^{14} +(1.75890 - 3.04650i) q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +(-0.162147 - 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +6.18184 q^{23} -4.97861 q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} +(2.46757 + 4.27396i) q^{29} +(1.25890 + 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(6.43931 + 11.1532i) q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +14.2062 q^{38} -0.0653107 q^{40} +(-1.15895 + 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(-0.905887 + 1.56904i) q^{47} +(-6.98712 - 0.424396i) q^{49} +(-5.11215 + 8.85451i) q^{50} -0.443250 q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(-0.0358339 + 1.18100i) q^{56} +10.1350 q^{58} +(-2.28549 - 3.95859i) q^{59} +(0.339138 - 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} +13.9059 q^{68} +(-0.675792 - 0.417996i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} -14.3765 q^{74} +(7.66972 - 13.2843i) q^{76} +(-0.133523 + 4.40061i) q^{77} +(-6.39787 + 11.0814i) q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} -3.86493 q^{86} +0.743131 q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +(-6.85398 - 11.8714i) q^{92} +(1.86037 + 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(-3.98514 - 6.90246i) q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.02682	−	1.77851i	0.726073	−	1.25760i	−0.232458	−	0.972607i	$-0.574677\pi$
$2$	1.02682	−	1.77851i	0.726073	−	1.25760i	0.958531	−	0.284989i	$-0.0919900\pi$
$3$		0			0
$3$		0			0
$4$	−1.10873	−	1.92038i	−0.554365	−	0.960188i
$5$	0.146246			0.0654030			0.0327015	−	0.999465i	$-0.489589\pi$
$5$	0.146246			0.0654030			0.0327015	+	0.999465i	$0.489589\pi$
$6$		0			0
$7$	0.0802402	−	2.64453i	0.0303280	−	0.999540i
$7$	0.0802402	−	2.64453i	0.0303280	−	0.999540i
$8$	−0.446582			−0.157891
$9$		0			0
$10$	0.150168	−	0.260099i	0.0474874	−	0.0822506i
$11$	−1.66404			−0.501727			−0.250864	−	0.968022i	$-0.580715\pi$
$11$	−1.66404			−0.501727			−0.250864	+	0.968022i	$0.580715\pi$
$12$		0			0
$13$	0.0999454	−	0.173111i	0.0277199	−	0.0480122i	−0.851833	−	0.523814i	$-0.824509\pi$
$13$	0.0999454	−	0.173111i	0.0277199	−	0.0480122i	0.879553	+	0.475802i	$0.157842\pi$
$14$	−4.62094	−	2.85818i	−1.23500	−	0.763880i
$15$		0			0
$16$	1.75890	−	3.04650i	0.439724	−	0.761625i
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$18$		0			0
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	0.923787	+	0.382907i	$0.125077\pi$
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	−0.130287	+	0.991476i	$0.541590\pi$
$20$	−0.162147	−	0.280847i	−0.0362571	−	0.0627992i
$21$		0			0
$22$	−1.70867	+	2.95951i	−0.364291	+	0.630970i
$23$	6.18184			1.28900			0.644501	−	0.764604i	$-0.277065\pi$
$23$	6.18184			1.28900			0.644501	+	0.764604i	$0.277065\pi$
$24$		0			0
$25$	−4.97861			−0.995722
$26$	−0.205252	−	0.355508i	−0.0402533	−	0.0697208i
$27$		0			0
$28$	−5.16746	+	2.77798i	−0.976559	+	0.524989i
$29$	2.46757	+	4.27396i	0.458217	+	0.793655i	0.998867	−	0.0475930i	$-0.0151551\pi$
$29$	2.46757	+	4.27396i	0.458217	+	0.793655i	−0.540650	+	0.841248i	$0.681822\pi$
$30$		0			0
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	0.956650	−	0.291239i	$-0.0940675\pi$
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	−0.730546	+	0.682864i	$0.760734\pi$
$32$	−4.05873	−	7.02993i	−0.717490	−	1.24273i
$33$		0			0
$34$	6.43931	+	11.1532i	1.10433	+	1.91276i
$35$	0.0117348	−	0.386752i	0.00198354	−	0.0653730i
$36$		0			0
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	14.2062			2.30456
$39$		0			0
$40$	−0.0653107			−0.0103265
$41$	−1.15895	+	2.00736i	−0.180998	+	0.313498i	−0.942221	−	0.334993i	$-0.891266\pi$
$41$	−1.15895	+	2.00736i	−0.180998	+	0.313498i	0.761223	+	0.648491i	$0.224599\pi$
$42$		0			0
$43$	−0.940993	−	1.62985i	−0.143500	−	0.248550i	0.785312	−	0.619100i	$-0.212502\pi$
$43$	−0.940993	−	1.62985i	−0.143500	−	0.248550i	−0.928812	+	0.370550i	$0.879169\pi$
$44$	1.84497	+	3.19558i	0.278140	+	0.481752i
$45$		0			0
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	−0.905887	+	1.56904i	−0.132137	+	0.228868i	−0.924500	−	0.381181i	$-0.875517\pi$
$47$	−0.905887	+	1.56904i	−0.132137	+	0.228868i	0.792363	+	0.610050i	$0.208851\pi$
$48$		0			0
$49$	−6.98712	−	0.424396i	−0.998160	−	0.0606280i
$50$	−5.11215	+	8.85451i	−0.722967	+	1.25222i
$51$		0			0
$52$	−0.443250			−0.0614677
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	−0.621948	−	0.783058i	$-0.713659\pi$
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	0.989123	+	0.147094i	$0.0469920\pi$
$54$		0			0
$55$	−0.243359			−0.0328145
$56$	−0.0358339	+	1.18100i	−0.00478850	+	0.157818i
$57$		0			0
$58$	10.1350			1.33080
$59$	−2.28549	−	3.95859i	−0.297546	−	0.515364i	0.678028	−	0.735036i	$-0.262835\pi$
$59$	−2.28549	−	3.95859i	−0.297546	−	0.515364i	−0.975574	+	0.219672i	$0.929501\pi$
$60$		0			0
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	−0.843498	−	0.537133i	$-0.819507\pi$
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	0.886920	+	0.461924i	$0.152841\pi$
$62$	5.17066			0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	0.0146166	−	0.0253167i	0.00181296	−	0.00314015i
$66$		0			0
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	0.990760	−	0.135630i	$-0.0433057\pi$
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	−0.612838	+	0.790208i	$0.709972\pi$
$68$	13.9059			1.68634
$69$		0			0
$70$	−0.675792	−	0.417996i	−0.0807726	−	0.0499600i
$71$	−1.27749			−0.151611			−0.0758053	−	0.997123i	$-0.524153\pi$
$71$	−1.27749			−0.151611			−0.0758053	+	0.997123i	$0.524153\pi$
$72$		0			0
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	−0.907986	−	0.419000i	$-0.862381\pi$
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	0.816858	+	0.576839i	$0.195714\pi$
$74$	−14.3765			−1.67123
$75$		0			0
$76$	7.66972	−	13.2843i	0.879777	−	1.52382i
$77$	−0.133523	+	4.40061i	−0.0152164	+	0.501496i
$78$		0			0
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	0.241255	+	0.970462i	$0.422441\pi$
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	−0.961072	+	0.276298i	$0.910892\pi$
$80$	0.257231	−	0.445537i	0.0287593	−	0.0498126i
$81$		0			0
$82$	2.38008	+	4.12241i	0.262835	+	0.455244i
$83$	−3.75687	−	6.50709i	−0.412370	−	0.714246i	0.582778	−	0.812631i	$-0.301966\pi$
$83$	−3.75687	−	6.50709i	−0.412370	−	0.714246i	−0.995148	+	0.0983854i	$0.968632\pi$
$84$		0			0
$85$	−0.458561	+	0.794251i	−0.0497379	+	0.0861486i
$86$	−3.86493			−0.416766
$87$		0			0
$88$	0.743131			0.0792181
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	0.519155	−	0.854680i	$-0.326247\pi$
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	−0.999752	+	0.0222619i	$0.992913\pi$
$90$		0			0
$91$	−0.449777	−	0.278199i	−0.0471494	−	0.0291632i
$92$	−6.85398	−	11.8714i	−0.714577	−	1.23768i
$93$		0			0
$94$	1.86037	+	3.22226i	0.191883	+	0.332350i
$95$	0.505833	+	0.876128i	0.0518973	+	0.0898888i
$96$		0			0
$97$	−3.98514	−	6.90246i	−0.404630	−	0.700839i	0.589649	−	0.807660i	$-0.299266\pi$
$97$	−3.98514	−	6.90246i	−0.404630	−	0.700839i	−0.994278	+	0.106821i	$0.965933\pi$
$98$	−7.92933	+	11.9909i	−0.800983	+	1.21126i
$99$		0			0
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	−14.8430			−1.47693			−0.738467	−	0.674290i	$-0.764450\pi$
$101$	−14.8430			−1.47693			−0.738467	+	0.674290i	$0.764450\pi$
$102$		0			0
$103$	−0.203948			−0.0200956			−0.0100478	−	0.999950i	$-0.503198\pi$
$103$	−0.203948			−0.0200956			−0.0100478	+	0.999950i	$0.503198\pi$
$104$	−0.0446339	+	0.0773081i	−0.00437671	+	0.00758068i
$105$		0			0
$106$	−5.48953	−	9.50815i	−0.533191	−	0.923513i
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	0.646985	−	0.762503i	$-0.276030\pi$
$107$	−3.48444	−	6.03524i	−0.336854	−	0.583448i	−0.983839	+	0.179054i	$0.942696\pi$
$108$		0			0
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	−0.249886	+	0.432816i	−0.0238257	+	0.0412674i
$111$		0			0
$112$	−7.91544	−	4.89592i	−0.747939	−	0.462621i
$113$	0.0193234	−	0.0334691i	0.00181779	−	0.00314851i	−0.865115	−	0.501573i	$-0.832755\pi$
$113$	0.0193234	−	0.0334691i	0.00181779	−	0.00314851i	0.866933	+	0.498425i	$0.166088\pi$
$114$		0			0
$115$	0.904067			0.0843047
$116$	5.47174	−	9.47733i	0.508038	−	0.879948i
$117$		0			0
$118$	−9.38718			−0.864160
$119$	14.1107	+	8.72785i	1.29353	+	0.800081i
$120$		0			0
$121$	−8.23097			−0.748270
$122$	−0.696469	−	1.20632i	−0.0630553	−	0.109215i
$123$		0			0
$124$	2.79155	−	4.83511i	0.250689	−	0.434206i
$125$	−1.45933			−0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	−1.77577	+	3.07572i	−0.156957	+	0.271858i
$129$		0			0
$130$	−0.0300173	−	0.0519914i	−0.00263269	−	0.00455995i
$131$	19.8333			1.73284			0.866422	−	0.499312i	$-0.166414\pi$
$131$	19.8333			1.73284			0.866422	+	0.499312i	$0.166414\pi$
$132$		0			0
$133$	16.1204	−	8.66618i	1.39782	−	0.751453i
$134$	12.7056			1.09759
$135$		0			0
$136$	1.40028	−	2.42536i	0.120073	−	0.207973i
$137$	6.44509			0.550642			0.275321	−	0.961352i	$-0.411216\pi$
$137$	6.44509			0.550642			0.275321	+	0.961352i	$0.411216\pi$
$138$		0			0
$139$	6.26527	−	10.8518i	0.531413	−	0.920435i	−0.467914	−	0.883774i	$-0.654994\pi$
$139$	6.26527	−	10.8518i	0.531413	−	0.920435i	0.999328	−	0.0366611i	$-0.0116722\pi$
$140$	−0.755719	+	0.406268i	−0.0638699	+	0.0343359i
$141$		0			0
$142$	−1.31176	+	2.27203i	−0.110080	+	0.190665i
$143$	−0.166313	+	0.288063i	−0.0139078	+	0.0240890i
$144$		0			0
$145$	0.360872	+	0.625048i	0.0299688	+	0.0519074i
$146$	1.59897	+	2.76950i	0.132332	+	0.229206i
$147$		0			0
$148$	−7.76161	+	13.4435i	−0.638000	+	1.10505i
$149$	−17.7673			−1.45555			−0.727776	−	0.685815i	$-0.759446\pi$
$149$	−17.7673			−1.45555			−0.727776	+	0.685815i	$0.759446\pi$
$150$		0			0
$151$	8.46599			0.688953			0.344476	−	0.938795i	$-0.388056\pi$
$151$	8.46599			0.688953			0.344476	+	0.938795i	$0.388056\pi$
$152$	−1.54463	−	2.67538i	−0.125286	−	0.217002i
$153$		0			0
$154$	7.68942	+	4.75612i	0.619631	+	0.383259i
$155$	0.184108	+	0.318885i	0.0147879	+	0.0256135i
$156$		0			0
$157$	−2.84968	−	4.93579i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$157$	−2.84968	−	4.93579i	−0.227429	−	0.393919i	−0.957045	+	0.289938i	$0.906365\pi$
$158$	13.1390	+	22.7573i	1.04528	+	1.81048i
$159$		0			0
$160$	−0.593572	−	1.02810i	−0.0469260	−	0.0812782i
$161$	0.496032	−	16.3481i	0.0390928	−	1.28841i
$162$		0			0
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	5.13986			0.401355
$165$		0			0
$166$	−15.4306			−1.19764
$167$	5.78723	−	10.0238i	0.447829	−	0.775663i	−0.550415	−	0.834891i	$-0.685530\pi$
$167$	5.78723	−	10.0238i	0.447829	−	0.775663i	0.998244	+	0.0592278i	$0.0188638\pi$
$168$		0			0
$169$	6.48002	+	11.2237i	0.498463	+	0.863364i
$170$	0.941721	+	1.63111i	0.0722267	+	0.125100i
$171$		0			0
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	−7.95546	+	13.7793i	−0.604842	+	1.04762i	0.387234	+	0.921981i	$0.373430\pi$
$173$	−7.95546	+	13.7793i	−0.604842	+	1.04762i	−0.992076	+	0.125636i	$0.959903\pi$
$174$		0			0
$175$	−0.399485	+	13.1661i	−0.0301982	+	0.995264i
$176$	−2.92688	+	5.06950i	−0.220622	+	0.382128i
$177$		0			0
$178$	−18.6222			−1.39579
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	−0.973751	−	0.227615i	$-0.926907\pi$
$179$	−3.87665	+	6.71456i	−0.289755	+	0.501870i	0.683996	+	0.729485i	$0.260240\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$	−0.956621	+	0.514271i	−0.0709095	+	0.0381203i
$183$		0			0
$184$	−2.76070			−0.203521
$185$	−0.511893	−	0.886625i	−0.0376351	−	0.0651860i
$186$		0			0
$187$	5.21769	−	9.03730i	0.381555	−	0.660873i
$188$	4.01754			0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	−2.48383	+	4.30211i	−0.179723	+	0.311290i	−0.941786	−	0.336214i	$-0.890854\pi$
$191$	−2.48383	+	4.30211i	−0.179723	+	0.311290i	0.762062	+	0.647504i	$0.224187\pi$
$192$		0			0
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	0.999093	+	0.0425800i	$0.0135577\pi$
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	−0.462671	+	0.886530i	$0.653109\pi$
$194$	−16.3681			−1.17516
$195$		0			0
$196$	6.93183	+	13.8884i	0.495131	+	0.992031i
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	0.259098	+	0.965851i	$0.416575\pi$
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	−0.966001	+	0.258540i	$0.916759\pi$
$200$	2.22336			0.157215
$201$		0			0
$202$	−15.2411	+	26.3984i	−1.07236	+	1.85739i
$203$	11.5006	−	6.18264i	0.807186	−	0.433936i
$204$		0			0
$205$	−0.169492	+	0.293568i	−0.0118378	+	0.0205037i
$206$	−0.209419	+	0.362724i	−0.0145909	+	0.0252722i
$207$		0			0
$208$	−0.351587	−	0.608967i	−0.0243782	−	0.0422243i
$209$	−5.75556	−	9.96893i	−0.398121	−	0.689565i
$210$		0			0
$211$	11.7569	−	20.3636i	0.809381	−	1.40189i	−0.103912	−	0.994587i	$-0.533136\pi$
$211$	11.7569	−	20.3636i	0.809381	−	1.40189i	0.913293	−	0.407303i	$-0.133531\pi$
$212$	−11.8548			−0.814193
$213$		0			0
$214$	−14.3116			−0.978323
$215$	−0.137616	−	0.238358i	−0.00938535	−	0.0162559i
$216$		0			0
$217$	5.86735	−	3.15424i	0.398302	−	0.214123i
$218$	−6.83983	−	11.8469i	−0.463252	−	0.802376i
$219$		0			0
$220$	0.269819	+	0.467340i	0.0181912	+	0.0315081i
$221$	0.626768	+	1.08559i	0.0421610	+	0.0730250i
$222$		0			0
$223$	2.03052	+	3.51696i	0.135974	+	0.235513i	0.925969	−	0.377600i	$-0.123250\pi$
$223$	2.03052	+	3.51696i	0.135974	+	0.235513i	−0.789995	+	0.613113i	$0.789917\pi$
$224$	−18.9166	+	10.1694i	−1.26392	+	0.679470i
$225$		0			0
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	3.85285			0.255723			0.127861	−	0.991792i	$-0.459189\pi$
$227$	3.85285			0.255723			0.127861	+	0.991792i	$0.459189\pi$
$228$		0			0
$229$	13.1162			0.866746			0.433373	−	0.901215i	$-0.357323\pi$
$229$	13.1162			0.866746			0.433373	+	0.901215i	$0.357323\pi$
$230$	0.928316	−	1.60789i	0.0612113	−	0.106021i
$231$		0			0
$232$	−1.10197	−	1.90868i	−0.0723481	−	0.125311i
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	0.996223	+	0.0868284i	$0.0276732\pi$
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	−0.422916	+	0.906169i	$0.638993\pi$
$234$		0			0
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	−5.06798	+	8.77801i	−0.329898	+	0.571400i
$237$		0			0
$238$	30.0117	−	16.1340i	1.94537	−	1.04581i
$239$	−3.65857	+	6.33683i	−0.236653	+	0.409895i	−0.959752	−	0.280849i	$-0.909384\pi$
$239$	−3.65857	+	6.33683i	−0.236653	+	0.409895i	0.723099	+	0.690745i	$0.242717\pi$
$240$		0			0
$241$	6.23107			0.401378			0.200689	−	0.979655i	$-0.435682\pi$
$241$	6.23107			0.401378			0.200689	+	0.979655i	$0.435682\pi$
$242$	−8.45174	+	14.6389i	−0.543299	+	0.941021i
$243$		0			0
$244$	−1.50405			−0.0962868
$245$	−1.02184	−	0.0620661i	−0.0652827	−	0.00396526i
$246$		0			0
$247$	1.38276			0.0879829
$248$	−0.562201	−	0.973761i	−0.0356998	−	0.0618339i
$249$		0			0
$250$	−1.49847	+	2.59543i	−0.0947717	+	0.164149i
$251$	−5.65283			−0.356803			−0.178402	−	0.983958i	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	13.8404	−	23.9722i	0.868422	−	1.50415i
$255$		0			0
$256$	−5.98801	−	10.3715i	−0.374250	−	0.648221i
$257$	−11.8016			−0.736166			−0.368083	−	0.929793i	$-0.619986\pi$
$257$	−11.8016			−0.736166			−0.368083	+	0.929793i	$0.619986\pi$
$258$		0			0
$259$	−16.3135	+	8.77001i	−1.01367	+	0.544942i
$260$	−0.0648233			−0.00402017
$261$		0			0
$262$	20.3653	−	35.2737i	1.25817	−	2.17922i
$263$	22.2401			1.37138			0.685691	−	0.727893i	$-0.259500\pi$
$263$	22.2401			1.37138			0.685691	+	0.727893i	$0.259500\pi$
$264$		0			0
$265$	0.390925	−	0.677101i	0.0240143	−	0.0415940i
$266$	1.13991	−	37.5689i	0.0698925	−	2.30350i
$267$		0			0
$268$	6.85953	−	11.8810i	0.419012	−	0.725750i
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	−0.827313	−	0.561741i	$-0.810132\pi$
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	0.900138	+	0.435604i	$0.143465\pi$
$270$		0			0
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	−0.966534	−	0.256537i	$-0.917419\pi$
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	0.261100	−	0.965312i	$-0.415915\pi$
$272$	11.0302	+	19.1049i	0.668806	+	1.15841i
$273$		0			0
$274$	6.61797	−	11.4627i	0.399806	−	0.692484i
$275$	8.28461			0.499581
$276$		0			0
$277$	−4.61800			−0.277469			−0.138734	−	0.990330i	$-0.544303\pi$
$277$	−4.61800			−0.277469			−0.138734	+	0.990330i	$0.544303\pi$
$278$	−12.8666	−	22.2857i	−0.771690	−	1.33661i
$279$		0			0
$280$	−0.00524055	+	0.172716i	−0.000313183	+	0.0103218i
$281$	−5.90841	−	10.2337i	−0.352466	−	0.610489i	0.634215	−	0.773157i	$-0.281324\pi$
$281$	−5.90841	−	10.2337i	−0.352466	−	0.610489i	−0.986681	+	0.162668i	$0.947990\pi$
$282$		0			0
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	0.528370	−	0.849014i	$-0.322803\pi$
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	−0.999453	+	0.0330753i	$0.989470\pi$
$284$	1.41639	+	2.45327i	0.0840475	+	0.145575i
$285$		0			0
$286$	0.341548	+	0.591579i	0.0201962	+	0.0349808i
$287$	5.21555	+	3.22596i	0.307864	+	0.190422i
$288$		0			0
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	1.48220			0.0870381
$291$		0			0
$292$	3.45304			0.202074
$293$	−7.04804	+	12.2076i	−0.411751	+	0.713173i	−0.995081	−	0.0990615i	$-0.968416\pi$
$293$	−7.04804	+	12.2076i	−0.411751	+	0.713173i	0.583330	+	0.812235i	$0.301749\pi$
$294$		0			0
$295$	−0.334243	−	0.578927i	−0.0194604	−	0.0337064i
$296$	1.56314	+	2.70744i	0.0908557	+	0.157367i
$297$		0			0
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	0.617846	−	1.07014i	0.0357310	−	0.0618878i
$300$		0			0
$301$	−4.38569	+	2.35771i	−0.252787	+	0.135896i
$302$	8.69307	−	15.0568i	0.500230	−	0.866424i
$303$		0			0
$304$	24.3346			1.39569
$305$	0.0495974	−	0.0859053i	0.00283994	−	0.00491892i
$306$		0			0
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$	8.59887	−	4.62267i	0.489966	−	0.263401i
$309$		0			0
$310$	0.756186			0.0429485
$311$	−7.02785	−	12.1726i	−0.398513	−	0.690244i	0.595030	−	0.803704i	$-0.297140\pi$
$311$	−7.02785	−	12.1726i	−0.398513	−	0.690244i	−0.993543	+	0.113459i	$0.963807\pi$
$312$		0			0
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	0.375925	+	0.926650i	$0.377325\pi$
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	−0.990465	+	0.137764i	$0.956008\pi$
$314$	−11.7045			−0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	4.28148	−	7.41575i	0.240472	−	0.416510i	−0.720377	−	0.693583i	$-0.756031\pi$
$317$	4.28148	−	7.41575i	0.240472	−	0.416510i	0.960849	+	0.277073i	$0.0893644\pi$
$318$		0			0
$319$	−4.10614	−	7.11204i	−0.229900	−	0.398198i
$320$	−1.40905			−0.0787682
$321$		0			0
$322$	−28.5659	−	17.6688i	−1.59191	−	0.984642i
$323$	−43.3808			−2.41377
$324$		0			0
$325$	−0.497589	+	0.861850i	−0.0276013	+	0.0478068i
$326$	−4.36471			−0.241739
$327$		0			0
$328$	0.517568	−	0.896453i	0.0285779	−	0.0494984i
$329$	4.07670	+	2.52155i	0.224756	+	0.139018i
$330$		0			0
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	−0.975703	−	0.219097i	$-0.929689\pi$
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	0.677595	+	0.735435i	$0.263022\pi$
$332$	−8.33070	+	14.4292i	−0.457207	+	0.791905i
$333$		0			0
$334$	−11.8849	−	20.5853i	−0.650314	−	1.12638i
$335$	0.452399	+	0.783578i	0.0247172	+	0.0428114i
$336$		0			0
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	−0.816819	−	0.576893i	$-0.804265\pi$
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	0.908014	+	0.418940i	$0.137598\pi$
$338$	26.6153			1.44768
$339$		0			0
$340$	2.03368			0.110292
$341$	−2.09486	−	3.62840i	−0.113443	−	0.196489i
$342$		0			0
$343$	−1.68298	+	18.4436i	−0.0908723	+	0.995863i
$344$	0.420231	+	0.727861i	0.0226573	+	0.0392437i
$345$		0			0
$346$	16.3377	+	28.2977i	0.878319	+	1.52129i
$347$	−5.76652	−	9.98790i	−0.309563	−	0.536178i	0.668704	−	0.743529i	$-0.266849\pi$
$347$	−5.76652	−	9.98790i	−0.309563	−	0.536178i	−0.978267	+	0.207350i	$0.933516\pi$
$348$		0			0
$349$	−4.44917	−	7.70619i	−0.238159	−	0.412503i	0.722027	−	0.691865i	$-0.243211\pi$
$349$	−4.44917	−	7.70619i	−0.238159	−	0.412503i	−0.960186	+	0.279362i	$0.909877\pi$
$350$	23.0058	+	14.2297i	1.22971	+	0.760612i
$351$		0			0
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	2.64699			0.140885			0.0704424	−	0.997516i	$-0.477559\pi$
$353$	2.64699			0.140885			0.0704424	+	0.997516i	$0.477559\pi$
$354$		0			0
$355$	−0.186828			−0.00991579
$356$	−10.0538	+	17.4137i	−0.532852	+	0.922926i
$357$		0			0
$358$	7.96127	+	13.7893i	0.420766	+	0.728789i
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	0.973360	+	0.229284i	$0.0736384\pi$
$359$	12.9835	+	22.4882i	0.685245	+	1.18688i	−0.288114	+	0.957596i	$0.593028\pi$
$360$		0			0
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	−12.4880	+	21.6299i	−0.656357	+	1.13684i
$363$		0			0
$364$	−0.0355664	+	1.17219i	−0.00186419	+	0.0614394i
$365$	−0.113867	+	0.197224i	−0.00596009	+	0.0103232i
$366$		0			0
$367$	17.5874			0.918056			0.459028	−	0.888422i	$-0.348198\pi$
$367$	17.5874			0.918056			0.459028	+	0.888422i	$0.348198\pi$
$368$	10.8732	−	18.8330i	0.566806	−	0.981736i
$369$		0			0
$370$	−2.10249			−0.109303
$371$	−12.0294	−	7.44052i	−0.624536	−	0.386293i
$372$		0			0
$373$	0.815075			0.0422030			0.0211015	−	0.999777i	$-0.493283\pi$
$373$	0.815075			0.0422030			0.0211015	+	0.999777i	$0.493283\pi$
$374$	−10.7153	−	18.5594i	−0.554074	−	0.959684i
$375$		0			0
$376$	0.404553	−	0.700707i	0.0208632	−	0.0361362i
$377$	0.986490			0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	1.12166	−	1.94278i	0.0575401	−	0.0996624i
$381$		0			0
$382$	5.10090	+	8.83501i	0.260985	+	0.452039i
$383$	−17.8928			−0.914278			−0.457139	−	0.889395i	$-0.651126\pi$
$383$	−17.8928			−0.914278			−0.457139	+	0.889395i	$0.651126\pi$
$384$		0			0
$385$	−0.0195272	+	0.643571i	−0.000995196	+	0.0327994i
$386$	30.6084			1.55793
$387$		0			0
$388$	−8.83688	+	15.3059i	−0.448625	+	0.777041i
$389$	−15.6278			−0.792363			−0.396181	−	0.918172i	$-0.629665\pi$
$389$	−15.6278			−0.792363			−0.396181	+	0.918172i	$0.629665\pi$
$390$		0			0
$391$	−19.3835	+	33.5731i	−0.980264	+	1.69787i
$392$	3.12033	+	0.189528i	0.157600	+	0.00957260i
$393$		0			0
$394$	21.8311	−	37.8126i	1.09984	−	1.90497i
$395$	−0.935661	+	1.62061i	−0.0470782	+	0.0815419i
$396$		0			0
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	0.999817	−	0.0191225i	$-0.00608724\pi$
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	−0.516469	+	0.856306i	$0.672754\pi$
$398$	20.4791	+	35.4709i	1.02653	+	1.77799i
$399$		0			0
$400$	−8.75687	+	15.1673i	−0.437843	+	0.758367i
$401$	−14.3013			−0.714172			−0.357086	−	0.934072i	$-0.616230\pi$
$401$	−14.3013			−0.714172			−0.357086	+	0.934072i	$0.616230\pi$
$402$		0			0
$403$	0.503284			0.0250704
$404$	16.4569	+	28.5041i	0.818760	+	1.41813i
$405$		0			0
$406$	0.813237	−	26.8024i	0.0403603	−	1.33018i
$407$	5.82452	+	10.0884i	0.288711	+	0.500062i
$408$		0			0
$409$	−15.9305	−	27.5924i	−0.787712	−	1.36436i	−0.927366	−	0.374156i	$-0.877932\pi$
$409$	−15.9305	−	27.5924i	−0.787712	−	1.36436i	0.139654	−	0.990200i	$-0.455401\pi$
$410$	0.348076	+	0.602885i	0.0171902	+	0.0297744i
$411$		0			0
$412$	0.226124	+	0.391657i	0.0111403	+	0.0192956i
$413$	−10.6520	+	5.72643i	−0.524151	+	0.281779i
$414$		0			0
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	−1.62261			−0.0795549
$417$		0			0
$418$	−23.6398			−1.15626
$419$	−11.9480	+	20.6945i	−0.583697	+	1.01099i	0.411339	+	0.911482i	$0.365061\pi$
$419$	−11.9480	+	20.6945i	−0.583697	+	1.01099i	−0.995036	+	0.0995110i	$0.968272\pi$
$420$		0			0
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	0.834696	−	0.550711i	$-0.185643\pi$
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	−0.894278	+	0.447513i	$0.852310\pi$
$422$	−24.1446	−	41.8197i	−1.17534	−	2.03575i
$423$		0			0
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	15.6107	−	27.0385i	0.757230	−	1.31156i
$426$		0			0
$427$	−1.52620	−	0.943995i	−0.0738579	−	0.0456831i
$428$	−7.72661	+	13.3829i	−0.373480	+	0.646886i
$429$		0			0
$430$	−0.565230			−0.0272578
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	−0.919244	−	0.393688i	$-0.871199\pi$
$431$	−2.46382	+	4.26746i	−0.118678	+	0.205556i	0.800566	+	0.599244i	$0.204532\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$	0.414895	−	13.6740i	0.0199156	−	0.656372i
$435$		0			0
$436$	−14.7709			−0.707395
$437$	21.3817	+	37.0341i	1.02282	+	1.77158i
$438$		0			0
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	−0.893758	−	0.448550i	$-0.851941\pi$
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	0.835334	+	0.549742i	$0.185274\pi$
$440$	0.108680			0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	−13.1475	+	22.7722i	−0.624657	+	1.08194i	0.363950	+	0.931419i	$0.381428\pi$
$443$	−13.1475	+	22.7722i	−0.624657	+	1.08194i	−0.988607	+	0.150520i	$0.951905\pi$
$444$		0			0
$445$	−0.663069	−	1.14847i	−0.0314325	−	0.0544427i
$446$	8.33993			0.394907
$447$		0			0
$448$	−0.773099	+	25.4796i	−0.0365255	+	1.20380i
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	1.92854	−	3.34034i	0.0908116	−	0.157290i
$452$	−0.0856976			−0.00403087
$453$		0			0
$454$	3.95620	−	6.85233i	0.185673	−	0.321596i
$455$	−0.0657779	−	0.0406855i	−0.00308372	−	0.00190736i
$456$		0			0
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	−0.738874	−	0.673844i	$-0.764642\pi$
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	0.953003	+	0.302961i	$0.0979754\pi$
$458$	13.4681	−	23.3274i	0.629321	−	1.09002i
$459$		0			0
$460$	−1.00237	−	1.73615i	−0.0467355	−	0.0809483i
$461$	−14.6152	−	25.3143i	−0.680698	−	1.17900i	−0.974768	−	0.223220i	$-0.928343\pi$
$461$	−14.6152	−	25.3143i	−0.680698	−	1.17900i	0.294070	−	0.955784i	$-0.404990\pi$
$462$		0			0
$463$	−8.21031	+	14.2207i	−0.381565	+	0.660891i	−0.991286	−	0.131726i	$-0.957948\pi$
$463$	−8.21031	+	14.2207i	−0.381565	+	0.660891i	0.609721	+	0.792616i	$0.291282\pi$
$464$	17.3608			0.805956
$465$		0			0
$466$	35.9435			1.66505
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	0.631554	−	0.775332i	$-0.282418\pi$
$467$	−7.68632	−	13.3131i	−0.355680	−	0.616057i	−0.987234	+	0.159276i	$0.949084\pi$
$468$		0			0
$469$	14.4175	−	7.75073i	0.665739	−	0.357895i
$470$	0.272071	+	0.471241i	0.0125497	+	0.0217367i
$471$		0			0
$472$	1.02066	+	1.76784i	0.0469797	+	0.0813713i
$473$	1.56585	+	2.71213i	0.0719979	+	0.124704i
$474$		0			0
$475$	−17.2200	−	29.8259i	−0.790106	−	1.36850i
$476$	1.11581	−	36.7747i	0.0511432	−	1.68556i
$477$		0			0
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	37.9291			1.73303			0.866513	−	0.499155i	$-0.166356\pi$
$479$	37.9291			1.73303			0.866513	+	0.499155i	$0.166356\pi$
$480$		0			0
$481$	−1.39933			−0.0638038
$482$	6.39820	−	11.0820i	0.291430	−	0.504772i
$483$		0			0
$484$	9.12591	+	15.8065i	0.414814	+	0.718479i
$485$	−0.582809	−	1.00946i	−0.0264640	−	0.0458370i
$486$		0			0
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	−0.151453	+	0.262324i	−0.00685595	+	0.0118749i
$489$		0			0
$490$	−1.15963	+	1.75361i	−0.0523867	+	0.0792202i
$491$	15.1876	−	26.3056i	0.685405	−	1.18716i	−0.287904	−	0.957659i	$-0.592958\pi$
$491$	15.1876	−	26.3056i	0.685405	−	1.18716i	0.973309	−	0.229497i	$-0.0737082\pi$
$492$		0			0
$493$	−30.9488			−1.39386
$494$	1.41985	−	2.45925i	0.0638820	−	0.110647i
$495$		0			0
$496$	8.85709			0.397695
$497$	−0.102506	+	3.37837i	−0.00459804	+	0.151541i
$498$		0			0
$499$	9.26871			0.414925			0.207462	−	0.978243i	$-0.433480\pi$
$499$	9.26871			0.414925			0.207462	+	0.978243i	$0.433480\pi$
$500$	1.61800	+	2.80246i	0.0723592	+	0.125330i
$501$		0			0
$502$	−5.80445	+	10.0536i	−0.259065	+	0.448715i
$503$	22.4230			0.999791			0.499896	−	0.866086i	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	−10.5627	+	18.2952i	−0.469571	+	0.813321i
$507$		0			0
$508$	−14.9444	−	25.8844i	−0.663050	−	1.14844i
$509$	37.6414			1.66843			0.834213	−	0.551443i	$-0.185923\pi$
$509$	37.6414			1.66843			0.834213	+	0.551443i	$0.185923\pi$
$510$		0			0
$511$	3.50389	+	2.16725i	0.155003	+	0.0958736i
$512$	−31.6976			−1.40085
$513$		0			0
$514$	−12.1182	+	20.9893i	−0.534511	+	0.925800i
$515$	−0.0298266			−0.00131432
$516$		0			0
$517$	1.50743	−	2.61095i	0.0662969	−	0.114830i
$518$	−1.15357	+	38.0190i	−0.0506849	+	1.67046i
$519$		0			0
$520$	−0.00652751	+	0.0113060i	−0.000286250	+	0.000495800i
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	0.175067	+	0.984556i	$0.443986\pi$
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	−0.940185	+	0.340666i	$0.889348\pi$
$522$		0			0
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	−0.999751	−	0.0223069i	$-0.992899\pi$
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	0.480557	−	0.876963i	$-0.340434\pi$
$524$	−21.9898	−	38.0874i	−0.960628	−	1.66386i
$525$		0			0
$526$	22.8366	−	39.5542i	0.995723	−	1.72464i
$527$	−15.7894			−0.687795
$528$		0			0
$529$	15.2151			0.661526
$530$	−0.802820	−	1.39053i	−0.0348723	−	0.0604006i
$531$		0			0
$532$	−34.5155	−	21.3488i	−1.49644	−	0.925587i
$533$	0.231664	+	0.401254i	0.0100345	+	0.0173802i
$534$		0			0
$535$	−0.509585	−	0.882627i	−0.0220313	−	0.0381593i
$536$	−1.38147	−	2.39277i	−0.0596702	−	0.103352i
$537$		0			0
$538$	−2.45292	−	4.24857i	−0.105753	−	0.183169i
$539$	11.6269	+	0.706212i	0.500804	+	0.0304187i
$540$		0			0
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	−47.6976			−2.04879
$543$		0			0
$544$	50.9055			2.18255
$545$	0.487083	−	0.843653i	0.0208643	−	0.0361381i
$546$		0			0
$547$	−10.0046	−	17.3284i	−0.427765	−	0.740910i	0.568910	−	0.822400i	$-0.307365\pi$
$547$	−10.0046	−	17.3284i	−0.427765	−	0.740910i	−0.996674	+	0.0814901i	$0.974032\pi$
$548$	−7.14586	−	12.3770i	−0.305256	−	0.528719i
$549$		0			0
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	−17.0696	+	29.5654i	−0.727190	+	1.25953i
$552$		0			0
$553$	28.7919	+	17.8086i	1.22436	+	0.757297i
$554$	−4.74187	+	8.21316i	−0.201463	+	0.348944i
$555$		0			0
$556$	−27.7860			−1.17839
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	−0.863413	−	0.504497i	$-0.831678\pi$
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	0.868614	+	0.495489i	$0.165011\pi$
$558$		0			0
$559$	−0.376192			−0.0159112
$560$	−1.15760	−	0.716007i	−0.0489175	−	0.0302568i
$561$		0			0
$562$	−24.2676			−1.02367
$563$	−22.1255	−	38.3224i	−0.932477	−	1.61510i	−0.779073	−	0.626934i	$-0.784310\pi$
$563$	−22.1255	−	38.3224i	−0.932477	−	1.61510i	−0.153404	−	0.988164i	$-0.549024\pi$
$564$		0			0
$565$	0.00282596	−	0.00489471i	0.000118889	−	0.000205922i
$566$	−32.5496			−1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	−2.76767	+	4.79374i	−0.116027	+	0.200964i	−0.918190	−	0.396141i	$-0.870349\pi$
$569$	−2.76767	+	4.79374i	−0.116027	+	0.200964i	0.802163	+	0.597105i	$0.203682\pi$
$570$		0			0
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	0.905761	−	0.423788i	$-0.139300\pi$
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	−0.819892	+	0.572518i	$0.805966\pi$
$572$	0.737585			0.0308400
$573$		0			0
$574$	11.0928	−	5.96341i	0.463006	−	0.248908i
$575$	−30.7770			−1.28349
$576$		0			0
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	−0.918781	−	0.394767i	$-0.870825\pi$
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	0.801269	+	0.598305i	$0.204159\pi$
$578$	−45.8512			−1.90716
$579$		0			0
$580$	0.800218	−	1.38602i	0.0332272	−	0.0575513i
$581$	−17.5097	+	9.41304i	−0.726423	+	0.390519i
$582$		0			0
$583$	−4.44809	+	7.70433i	−0.184221	+	0.319081i
$584$	0.347710	−	0.602252i	0.0143884	−	0.0249214i
$585$		0			0
$586$	14.4742	+	25.0700i	0.597923	+	1.03563i
$587$	−9.36644	−	16.2232i	−0.386595	−	0.669601i	0.605394	−	0.795926i	$-0.293015\pi$
$587$	−9.36644	−	16.2232i	−0.386595	−	0.669601i	−0.991989	+	0.126324i	$0.959682\pi$
$588$		0			0
$589$	−8.70852	+	15.0836i	−0.358828	+	0.621509i
$590$	−1.37283			−0.0565187
$591$		0			0
$592$	−24.6262			−1.01213
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	0.992107	−	0.125398i	$-0.0400207\pi$
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	−0.604651	+	0.796491i	$0.706687\pi$
$594$		0			0
$595$	2.06363	+	1.27641i	0.0846005	+	0.0523277i
$596$	19.6991	+	34.1198i	0.806906	+	1.39760i
$597$		0			0
$598$	−1.26884	−	2.19769i	−0.0518866	−	0.0898702i
$599$	1.33726	+	2.31620i	0.0546388	+	0.0946372i	0.892051	−	0.451934i	$-0.149266\pi$
$599$	1.33726	+	2.31620i	0.0546388	+	0.0946372i	−0.837412	+	0.546572i	$0.815933\pi$
$600$		0			0
$601$	−6.60716	−	11.4439i	−0.269511	−	0.466808i	0.699224	−	0.714902i	$-0.253529\pi$
$601$	−6.60716	−	11.4439i	−0.269511	−	0.466808i	−0.968736	+	0.248095i	$0.920196\pi$
$602$	−0.310123	+	10.2209i	−0.0126397	+	0.416575i
$603$		0			0
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	−1.20374			−0.0489391
$606$		0			0
$607$	25.8052			1.04740			0.523701	−	0.851902i	$-0.324551\pi$
$607$	25.8052			1.04740			0.523701	+	0.851902i	$0.324551\pi$
$608$	28.0766	−	48.6301i	1.13866	−	1.97221i
$609$		0			0
$610$	−0.101856	−	0.176419i	−0.00412401	−	0.00714299i
$611$	0.181079	+	0.313637i	0.00732565	+	0.0126884i
$612$		0			0
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	28.1263	−	48.7162i	1.13509	−	1.96603i
$615$		0			0
$616$	0.0596290	−	1.96524i	0.00240252	−	0.0791816i
$617$	4.76588	−	8.25474i	0.191867	−	0.332323i	−0.754002	−	0.656872i	$-0.771879\pi$
$617$	4.76588	−	8.25474i	0.191867	−	0.332323i	0.945869	+	0.324549i	$0.105212\pi$
$618$		0			0
$619$	34.7071			1.39500			0.697499	−	0.716586i	$-0.254296\pi$
$619$	34.7071			1.39500			0.697499	+	0.716586i	$0.254296\pi$
$620$	0.408253	−	0.707114i	0.0163958	−	0.0283984i
$621$		0			0
$622$	−28.8654			−1.15740
$623$	−21.1314	+	11.3600i	−0.846610	+	0.455130i
$624$		0			0
$625$	24.6796			0.987186
$626$	22.3279	+	38.6730i	0.892402	+	1.54568i
$627$		0			0
$628$	−6.31904	+	10.9449i	−0.252157	+	0.436749i
$629$	43.9006			1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	2.85718	−	4.94877i	0.113652	−	0.196852i
$633$		0			0
$634$	−8.79265	−	15.2293i	−0.349201	−	0.604833i
$635$	1.97122			0.0782256
$636$		0			0
$637$	−0.771798	+	1.16713i	−0.0305798	+	0.0462433i
$638$	−16.8651			−0.667696
$639$		0			0
$640$	−0.259699	+	0.449811i	−0.0102655	+	0.0177804i
$641$	44.1844			1.74518			0.872590	−	0.488454i	$-0.162439\pi$
$641$	44.1844			1.74518			0.872590	+	0.488454i	$0.162439\pi$
$642$		0			0
$643$	7.24065	−	12.5412i	0.285543	−	0.494575i	−0.687197	−	0.726471i	$-0.741159\pi$
$643$	7.24065	−	12.5412i	0.285543	−	0.494575i	0.972741	+	0.231895i	$0.0744926\pi$
$644$	−31.9444	+	17.1730i	−1.25879	+	0.676712i
$645$		0			0
$646$	−44.5444	+	77.1532i	−1.75258	+	3.03555i
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	−0.327245	−	0.944940i	$-0.606120\pi$
$647$	16.6536	−	28.8448i	0.654719	−	1.13401i	0.981964	−	0.189068i	$-0.0605465\pi$
$648$		0			0
$649$	3.80315	+	6.58725i	0.149287	+	0.258572i
$650$	1.02187	+	1.76993i	0.0400811	+	0.0694225i
$651$		0			0
$652$	−2.35643	+	4.08146i	−0.0922850	+	0.159842i
$653$	9.06643			0.354797			0.177398	−	0.984139i	$-0.443232\pi$
$653$	9.06643			0.354797			0.177398	+	0.984139i	$0.443232\pi$
$654$		0			0
$655$	2.90054			0.113333
$656$	4.07696	+	7.06150i	0.159178	+	0.275705i
$657$		0			0
$658$	8.67065	−	4.66126i	0.338017	−	0.181715i
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	−0.987489	−	0.157686i	$-0.949596\pi$
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	0.357184	−	0.934034i	$-0.383737\pi$
$660$		0			0
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	0.937858	−	0.347020i	$-0.112806\pi$
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	−0.769457	+	0.638699i	$0.779473\pi$
$662$	11.1382	+	19.2919i	0.432897	+	0.749799i
$663$		0			0
$664$	1.67775	+	2.90595i	0.0651094	+	0.112773i
$665$	2.35754	−	1.26739i	0.0914214	−	0.0491473i
$666$		0			0
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	−25.6659			−0.993043
$669$		0			0
$670$	1.85813			0.0717860
$671$	−0.564339	+	0.977464i	−0.0217861	+	0.0377346i
$672$		0			0
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	0.971237	−	0.238114i	$-0.0765291\pi$
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	−0.691831	+	0.722059i	$0.743196\pi$
$674$	−3.43803	−	5.95484i	−0.132428	−	0.229372i
$675$		0			0
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	19.1657	−	33.1960i	0.736600	−	1.27583i	−0.217418	−	0.976078i	$-0.569764\pi$
$677$	19.1657	−	33.1960i	0.736600	−	1.27583i	0.954018	−	0.299749i	$-0.0969030\pi$
$678$		0			0
$679$	−18.5736	+	9.98498i	−0.712788	+	0.383188i
$680$	0.204785	−	0.354698i	0.00785315	−	0.0136021i
$681$		0			0
$682$	−8.60418			−0.329471
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	−0.795570	−	0.605861i	$-0.792829\pi$
$683$	3.31659	−	5.74450i	0.126906	−	0.219807i	0.922476	+	0.386054i	$0.126162\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$	31.0740	+	21.9315i	1.18641	+	0.837350i
$687$		0			0
$688$	−6.62044			−0.252402
$689$	−0.534322	−	0.925472i	−0.0203560	−	0.0352577i
$690$		0			0
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	−0.553190	−	0.833055i	$-0.686590\pi$
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	0.998042	+	0.0625490i	$0.0199230\pi$
$692$	35.2818			1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	0.916269	−	1.58702i	0.0347561	−	0.0601992i
$696$		0			0
$697$	−7.26791	−	12.5884i	−0.275292	−	0.476819i
$698$	−18.2740			−0.691683
$699$		0			0
$700$	25.7268	−	13.8305i	0.972381	−	0.522743i
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	24.2131	−	41.9383i	0.913214	−	1.58173i
$704$	16.0327			0.604256
$705$		0			0
$706$	2.71799	−	4.70769i	0.102293	−	0.177176i
$707$	−1.19101	+	39.2528i	−0.0447924	+	1.47625i
$708$		0			0
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	−0.968167	−	0.250305i	$-0.919469\pi$
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	0.700854	+	0.713305i	$0.252802\pi$
$710$	−0.191839	+	0.332275i	−0.00719959	+	0.0124701i
$711$		0			0
$712$	2.02478	+	3.50702i	0.0758817	+	0.131431i
$713$	7.78230	+	13.4793i	0.291449	+	0.504805i
$714$		0			0
$715$	−0.0243226	+	0.0421280i	−0.000909613	+	0.00157550i
$716$	17.1926			0.642519
$717$		0			0
$718$	53.3272			1.99015
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	0.707422	−	0.706792i	$-0.249858\pi$
$719$	−6.92848	−	12.0005i	−0.258389	−	0.447542i	−0.965810	+	0.259249i	$0.916525\pi$
$720$		0			0
$721$	−0.0163649	+	0.539348i	−0.000609459	+	0.0200864i
$722$	29.6268	+	51.3151i	1.10259	+	1.90975i
$723$		0			0
$724$	13.4842	+	23.3553i	0.501136	+	0.867993i
$725$	−12.2851	−	21.2784i	−0.456257	−	0.790260i
$726$		0			0
$727$	15.7000	+	27.1932i	0.582280	+	1.00854i	0.995208	+	0.0977755i	$0.0311727\pi$
$727$	15.7000	+	27.1932i	0.582280	+	1.00854i	−0.412928	+	0.910764i	$0.635494\pi$
$728$	0.200862	+	0.124239i	0.00744446	+	0.00460460i
$729$		0			0
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	11.8021			0.436518
$732$		0			0
$733$	−26.6006			−0.982515			−0.491257	−	0.871014i	$-0.663463\pi$
$733$	−26.6006			−0.982515			−0.491257	+	0.871014i	$0.663463\pi$
$734$	18.0592	−	31.2794i	0.666576	−	1.15454i
$735$		0			0
$736$	−25.0904	−	43.4579i	−0.924845	−	1.60188i
$737$	−5.14757	−	8.91586i	−0.189613	−	0.328420i
$738$		0			0
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	−1.13510	+	1.96605i	−0.0417272	+	0.0722736i
$741$		0			0
$742$	−25.5851	+	13.7543i	−0.939259	+	0.504937i
$743$	−19.3008	+	33.4299i	−0.708076	+	1.22642i	0.257493	+	0.966280i	$0.417103\pi$
$743$	−19.3008	+	33.4299i	−0.708076	+	1.22642i	−0.965570	+	0.260144i	$0.916230\pi$
$744$		0			0
$745$	−2.59839			−0.0951975
$746$	0.836938	−	1.44962i	0.0306425	−	0.0530743i
$747$		0			0
$748$	−23.1400			−0.846082
$749$	−16.2400	+	8.73047i	−0.593396	+	0.319004i
$750$		0			0
$751$	−37.8996			−1.38297			−0.691487	−	0.722389i	$-0.743044\pi$
$751$	−37.8996			−1.38297			−0.691487	+	0.722389i	$0.743044\pi$
$752$	3.18673	+	5.51957i	0.116208	+	0.201278i
$753$		0			0
$754$	1.01295	−	1.75448i	0.0368895	−	0.0638944i
$755$	1.23811			0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	−20.9793	+	36.3371i	−0.762001	+	1.31982i
$759$		0			0
$760$	−0.225896	−	0.391263i	−0.00819411	−	0.0141926i
$761$	−27.7470			−1.00583			−0.502913	−	0.864337i	$-0.667739\pi$
$761$	−27.7470			−1.00583			−0.502913	+	0.864337i	$0.667739\pi$
$762$		0			0
$763$	−14.9884	−	9.27072i	−0.542616	−	0.335623i
$764$	11.0156			0.398529
$765$		0			0
$766$	−18.3727	+	31.8224i	−0.663832	+	1.14979i
$767$	−0.913698			−0.0329917
$768$		0			0
$769$	−6.07668	+	10.5251i	−0.219131	+	0.379546i	−0.954542	−	0.298075i	$-0.903655\pi$
$769$	−6.07668	+	10.5251i	−0.219131	+	0.379546i	0.735412	+	0.677621i	$0.236989\pi$
$770$	1.12454	+	0.695562i	0.0405258	+	0.0250663i
$771$		0			0
$772$	16.5250	−	28.6221i	0.594747	−	1.03013i
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	−0.201682	−	0.979451i	$-0.564641\pi$
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	0.949071	−	0.315063i	$-0.102026\pi$
$774$		0			0
$775$	−6.26756	−	10.8557i	−0.225137	−	0.389950i
$776$	1.77969	+	3.08252i	0.0638873	+	0.110656i
$777$		0			0
$778$	−16.0470	+	27.7942i	−0.575313	+	0.996472i
$779$	−16.0343			−0.574488
$780$		0			0
$781$	2.12580			0.0760671
$782$	39.8068	+	68.9473i	1.42349	+	2.46555i
$783$		0			0
$784$	−13.5826	+	20.5398i	−0.485091	+	0.733564i
$785$	−0.416753	−	0.721837i	−0.0148746	−	0.0257635i
$786$		0			0
$787$	10.4484	+	18.0972i	0.372446	+	0.645096i	0.989941	−	0.141479i	$-0.0451857\pi$
$787$	10.4484	+	18.0972i	0.372446	+	0.645096i	−0.617495	+	0.786575i	$0.711852\pi$
$788$	−23.5725	−	40.8288i	−0.839736	−	1.45447i
$789$		0			0
$790$	1.92152	+	3.32816i	0.0683645	+	0.118411i
$791$	−0.0869596	−	0.0537869i	−0.00309193	−	0.00191244i
$792$		0			0
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	39.5558			1.40378
$795$		0			0
$796$	44.2254			1.56753
$797$	0.319383	−	0.553188i	0.0113131	−	0.0195949i	−0.860313	−	0.509765i	$-0.829732\pi$
$797$	0.319383	−	0.553188i	0.0113131	−	0.0195949i	0.871627	+	0.490171i	$0.163066\pi$
$798$		0			0
$799$	−5.68091	−	9.83963i	−0.200976	−	0.348101i
$800$	20.2069	+	34.9993i	0.714420	+	1.23741i
$801$		0			0
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	1.29563	−	2.24409i	0.0457217	−	0.0791923i
$804$		0			0
$805$	0.0725425	−	2.39084i	0.00255679	−	0.0842659i
$806$	0.516783	−	0.895095i	0.0182029	−	0.0315284i
$807$		0			0
$808$	6.62862			0.233194
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.0474686	+	0.998873i	$0.515115\pi$
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.841315	+	0.540545i	$0.818218\pi$
$810$		0			0
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$	−24.6241	−	15.2307i	−0.864135	−	0.534491i
$813$		0			0
$814$	23.9230			0.838501
$815$	−0.155411	−	0.269180i	−0.00544382	−	0.00942897i
$816$		0			0
$817$	6.50939	−	11.2746i	0.227735	−	0.394448i
$818$	−65.4311			−2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	21.7207	−	37.6213i	0.758056	−	1.31299i	−0.185784	−	0.982591i	$-0.559483\pi$
$821$	21.7207	−	37.6213i	0.758056	−	1.31299i	0.943841	−	0.330401i	$-0.107184\pi$
$822$		0			0
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	0.829398	−	0.558659i	$-0.188684\pi$
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	−0.898511	+	0.438950i	$0.855350\pi$
$824$	0.0910797			0.00317291
$825$		0			0
$826$	−0.753229	+	24.8247i	−0.0262082	+	0.863763i
$827$	−29.3159			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$827$	−29.3159			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$828$		0			0
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	0.382940	+	0.923773i	$0.374912\pi$
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	−0.991481	+	0.130251i	$0.958422\pi$
$830$	−2.25665			−0.0783295
$831$		0			0
$832$	−0.962955	+	1.66789i	−0.0333844	+	0.0578236i
$833$	24.2134	−	36.6159i	0.838943	−	1.26867i
$834$		0			0
$835$	0.846358	−	1.46593i	0.0292894	−	0.0507308i
$836$	−12.7627	+	22.1057i	−0.441408	+	0.764541i
$837$		0			0
$838$	24.5369	+	42.4992i	0.847614	+	1.46811i
$839$	18.7921	+	32.5489i	0.648777	+	1.12371i	0.983415	+	0.181368i	$0.0580524\pi$
$839$	18.7921	+	32.5489i	0.648777	+	1.12371i	−0.334639	+	0.942347i	$0.608614\pi$
$840$		0			0
$841$	2.32218	−	4.02213i	0.0800750	−	0.138694i
$842$	−5.02119			−0.173042
$843$		0			0
$844$	−52.1411			−1.79477
$845$	0.947675	+	1.64142i	0.0326010	+	0.0564666i
$846$		0			0
$847$	−0.660455	+	21.7671i	−0.0226935	+	0.747926i
$848$	−9.40331	−	16.2870i	−0.322911	−	0.559298i
$849$		0			0
$850$	−32.0588	−	55.5275i	−1.09961	−	1.90458i
$851$	−21.6378	−	37.4778i	−0.741735	−	1.28472i
$852$		0			0
$853$	16.3849	+	28.3795i	0.561009	+	0.971696i	0.997409	+	0.0719434i	$0.0229201\pi$
$853$	16.3849	+	28.3795i	0.561009	+	0.971696i	−0.436400	+	0.899753i	$0.643747\pi$
$854$	−3.24604	+	1.74504i	−0.111077	+	0.0597140i
$855$		0			0
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	−27.5347			−0.940566			−0.470283	−	0.882516i	$-0.655848\pi$
$857$	−27.5347			−0.940566			−0.470283	+	0.882516i	$0.655848\pi$
$858$		0			0
$859$	−46.5101			−1.58690			−0.793451	−	0.608634i	$-0.791718\pi$
$859$	−46.5101			−1.58690			−0.793451	+	0.608634i	$0.791718\pi$
$860$	−0.305158	+	0.528549i	−0.0104058	+	0.0180234i
$861$		0			0
$862$	5.05981	+	8.76384i	0.172338	+	0.298498i
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	0.821502	−	0.570205i	$-0.193136\pi$
$863$	−2.44007	−	4.22633i	−0.0830610	−	0.143866i	−0.904563	+	0.426339i	$0.859803\pi$
$864$		0			0
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	31.6814	−	54.8739i	1.07658	−	1.86469i
$867$		0			0
$868$	−12.5626	−	7.77033i	−0.426403	−	0.263742i
$869$	10.6463	−	18.4400i	0.361152	−	0.625533i
$870$		0			0
$871$	1.23669			0.0419037
$872$	−1.48738	+	2.57622i	−0.0503690	+	0.0872417i
$873$		0			0
$874$	87.8207			2.97058
$875$	−0.117097	+	3.85924i	−0.00395860	+	0.130466i
$876$		0			0
$877$	39.2892			1.32670			0.663352	−	0.748308i	$-0.269133\pi$
$877$	39.2892			1.32670			0.663352	+	0.748308i	$0.269133\pi$
$878$	2.51388	+	4.35418i	0.0848395	+	0.146946i
$879$		0			0
$880$	−0.428043	+	0.741392i	−0.0144293	+	0.0249923i
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	1.38983	−	2.40726i	0.0467451	−	0.0809649i
$885$		0			0
$886$	27.0003	+	46.7659i	0.907094	+	1.57113i
$887$	22.9600			0.770922			0.385461	−	0.922724i	$-0.374042\pi$
$887$	22.9600			0.770922			0.385461	+	0.922724i	$0.374042\pi$
$888$		0			0
$889$	1.08155	−	35.6453i	0.0362739	−	1.19550i
$890$	−2.72342			−0.0912891
$891$		0			0
$892$	4.50259	−	7.79871i	0.150758	−	0.261120i
$893$	−12.5331			−0.419404
$894$		0			0
$895$	−0.566944	+	0.981976i	−0.0189508	+	0.0328238i
$896$	7.99137	+	4.94288i	0.266973	+	0.165130i
$897$		0			0
$898$	39.7460	−	68.8420i	1.32634	−	2.29729i
$899$	−6.21284	+	10.7610i	−0.207210	+	0.358898i
$900$		0			0
$901$	16.7631	+	29.0345i	0.558459	+	0.967280i
$902$	−3.96054	−	6.85986i	−0.131872	−	0.228408i
$903$		0			0
$904$	−0.00862948	+	0.0149467i	−0.000287012	+	0.000497120i
$905$	−1.77862			−0.0591232
$906$		0			0
$907$	−27.8982			−0.926345			−0.463173	−	0.886268i	$-0.653289\pi$
$907$	−27.8982			−0.926345			−0.463173	+	0.886268i	$0.653289\pi$
$908$	−4.27177	−	7.39892i	−0.141764	−	0.245542i
$909$		0			0
$910$	−0.139902	+	0.0752099i	−0.00463770	+	0.00249318i
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	0.989333	+	0.145670i	$0.0465337\pi$
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	−0.368513	+	0.929623i	$0.620133\pi$
$912$		0			0
$913$	6.25158	+	10.8281i	0.206897	+	0.358356i
$914$	−9.40068	−	16.2825i	−0.310947	−	0.538576i
$915$		0			0
$916$	−14.5424	−	25.1881i	−0.480493	−	0.832239i
$917$	1.59143	−	52.4499i	0.0525536	−	1.73205i
$918$		0			0
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	−0.403740			−0.0133109
$921$		0			0
$922$	−60.0289			−1.97695
$923$	−0.127680	+	0.221147i	−0.00420262	+	0.00727916i
$924$		0			0
$925$	17.4263	+	30.1832i	0.572972	+	0.992417i
$926$	16.8611	+	29.2042i	0.554089	+	0.959710i
$927$		0			0
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	−22.9675	+	39.7809i	−0.753540	+	1.30517i	0.192556	+	0.981286i	$0.438322\pi$
$929$	−22.9675	+	39.7809i	−0.753540	+	1.30517i	−0.946097	+	0.323884i	$0.895011\pi$
$930$		0			0
$931$	−21.6245	−	43.3263i	−0.708715	−	1.41996i
$932$	19.4053	−	33.6110i	0.635642	−	1.10096i
$933$		0			0
$934$	−31.5699			−1.03300
$935$	0.763064	−	1.32167i	0.0249549	−	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$	1.01950	−	33.6003i	0.0332878	−	1.09709i
$939$		0			0
$940$	0.587547			0.0191637
$941$	24.7002	+	42.7819i	0.805202	+	1.39465i	0.916154	+	0.400825i	$0.131277\pi$
$941$	24.7002	+	42.7819i	0.805202	+	1.39465i	−0.110952	+	0.993826i	$0.535390\pi$
$942$		0			0
$943$	−7.16445	+	12.4092i	−0.233307	+	0.404099i
$944$	−16.0798			−0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	15.8253	−	27.4102i	0.514252	−	0.890711i	−0.485611	−	0.874175i	$-0.661403\pi$
$947$	15.8253	−	27.4102i	0.514252	−	0.890711i	0.999863	−	0.0165357i	$-0.00526371\pi$
$948$		0			0
$949$	0.155636	+	0.269569i	0.00505214	+	0.00875057i
$950$	−70.7274			−2.29470
$951$		0			0
$952$	−6.30159	−	3.89771i	−0.204236	−	0.126325i
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	−0.363249	+	0.629165i	−0.0117545	+	0.0203593i
$956$	16.2255			0.524769
$957$		0			0
$958$	38.9465	−	67.4573i	1.25830	−	2.17945i
$959$	0.517156	−	17.0443i	0.0166998	−	0.550388i
$960$		0			0
$961$	12.3304	−	21.3568i	0.397753	−	0.688929i
$962$	−1.43686	+	2.48871i	−0.0463262	+	0.0802394i
$963$		0			0
$964$	−6.90857	−	11.9660i	−0.222510	−	0.385399i
$965$	1.08985	+	1.88768i	0.0350836	+	0.0607666i
$966$		0			0
$967$	4.98525	−	8.63470i	0.160315	−	0.277673i	−0.774667	−	0.632370i	$-0.782082\pi$
$967$	4.98525	−	8.63470i	0.160315	−	0.277673i	0.934982	+	0.354696i	$0.115416\pi$
$968$	3.67581			0.118145
$969$		0			0
$970$	−2.39377			−0.0768592
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	0.857519	−	0.514453i	$-0.172005\pi$
$971$	−0.522554	−	0.905090i	−0.0167695	−	0.0290457i	−0.874288	+	0.485407i	$0.838671\pi$
$972$		0			0
$973$	−28.1951	−	17.4395i	−0.903895	−	0.559084i
$974$	−4.72847	−	8.18994i	−0.151510	−	0.262423i
$975$		0			0
$976$	−1.19302	−	2.06637i	−0.0381875	−	0.0661428i
$977$	−9.44308	−	16.3559i	−0.302111	−	0.523272i	0.674503	−	0.738272i	$-0.264358\pi$
$977$	−9.44308	−	16.3559i	−0.302111	−	0.523272i	−0.976614	+	0.215001i	$0.931025\pi$
$978$		0			0
$979$	7.54466	+	13.0677i	0.241128	+	0.417647i
$980$	1.01375	+	2.03112i	0.0323830	+	0.0648819i
$981$		0			0
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	−2.28891			−0.0730050			−0.0365025	−	0.999334i	$-0.511622\pi$
$983$	−2.28891			−0.0730050			−0.0365025	+	0.999334i	$0.511622\pi$
$984$		0			0
$985$	3.10930			0.0990707
$986$	−31.7789	+	55.0427i	−1.01205	+	1.75292i
$987$		0			0
$988$	−1.53311	−	2.65542i	−0.0487746	−	0.0844801i
$989$	−5.81707	−	10.0755i	−0.184972	−	0.320381i
$990$		0			0
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	10.2191	−	17.6999i	0.324455	−	0.561973i
$993$		0			0
$994$	5.90321	+	3.65130i	0.187239	+	0.115812i
$995$	−1.45837	+	2.52598i	−0.0462336	+	0.0800789i
$996$		0			0
$997$	37.0151			1.17228			0.586139	−	0.810210i	$-0.300647\pi$
$997$	37.0151			1.17228			0.586139	+	0.810210i	$0.300647\pi$
$998$	9.51732	−	16.4845i	0.301266	−	0.521807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.g.b.172.5		10
3.2	odd	2		63.2.g.b.4.1	✓	10
4.3	odd	2		3024.2.t.i.1873.3		10
7.2	even	3		189.2.h.b.37.1		10
7.3	odd	6		1323.2.f.f.442.5		10
7.4	even	3		1323.2.f.e.442.5		10
7.5	odd	6		1323.2.h.f.226.1		10
7.6	odd	2		1323.2.g.f.361.5		10
9.2	odd	6		63.2.h.b.25.5	yes	10
9.4	even	3		567.2.e.e.487.5		10
9.5	odd	6		567.2.e.f.487.1		10
9.7	even	3		189.2.h.b.46.1		10
12.11	even	2		1008.2.t.i.193.2		10
21.2	odd	6		63.2.h.b.58.5	yes	10
21.5	even	6		441.2.h.f.373.5		10
21.11	odd	6		441.2.f.e.148.1		10
21.17	even	6		441.2.f.f.148.1		10
21.20	even	2		441.2.g.f.67.1		10
28.23	odd	6		3024.2.q.i.2305.3		10
36.7	odd	6		3024.2.q.i.2881.3		10
36.11	even	6		1008.2.q.i.529.5		10
63.2	odd	6		63.2.g.b.16.1	yes	10
63.4	even	3		3969.2.a.bc.1.1		5
63.11	odd	6		441.2.f.e.295.1		10
63.16	even	3	inner	189.2.g.b.100.5		10
63.20	even	6		441.2.h.f.214.5		10
63.23	odd	6		567.2.e.f.163.1		10
63.25	even	3		1323.2.f.e.883.5		10
63.31	odd	6		3969.2.a.bb.1.1		5
63.32	odd	6		3969.2.a.z.1.5		5
63.34	odd	6		1323.2.h.f.802.1		10
63.38	even	6		441.2.f.f.295.1		10
63.47	even	6		441.2.g.f.79.1		10
63.52	odd	6		1323.2.f.f.883.5		10
63.58	even	3		567.2.e.e.163.5		10
63.59	even	6		3969.2.a.ba.1.5		5
63.61	odd	6		1323.2.g.f.667.5		10
84.23	even	6		1008.2.q.i.625.5		10
252.79	odd	6		3024.2.t.i.289.3		10
252.191	even	6		1008.2.t.i.961.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	3.2	odd	2
63.2.g.b.16.1	yes	10	63.2	odd	6
63.2.h.b.25.5	yes	10	9.2	odd	6
63.2.h.b.58.5	yes	10	21.2	odd	6
189.2.g.b.100.5		10	63.16	even	3	inner
189.2.g.b.172.5		10	1.1	even	1	trivial
189.2.h.b.37.1		10	7.2	even	3
189.2.h.b.46.1		10	9.7	even	3
441.2.f.e.148.1		10	21.11	odd	6
441.2.f.e.295.1		10	63.11	odd	6
441.2.f.f.148.1		10	21.17	even	6
441.2.f.f.295.1		10	63.38	even	6
441.2.g.f.67.1		10	21.20	even	2
441.2.g.f.79.1		10	63.47	even	6
441.2.h.f.214.5		10	63.20	even	6
441.2.h.f.373.5		10	21.5	even	6
567.2.e.e.163.5		10	63.58	even	3
567.2.e.e.487.5		10	9.4	even	3
567.2.e.f.163.1		10	63.23	odd	6
567.2.e.f.487.1		10	9.5	odd	6
1008.2.q.i.529.5		10	36.11	even	6
1008.2.q.i.625.5		10	84.23	even	6
1008.2.t.i.193.2		10	12.11	even	2
1008.2.t.i.961.2		10	252.191	even	6
1323.2.f.e.442.5		10	7.4	even	3
1323.2.f.e.883.5		10	63.25	even	3
1323.2.f.f.442.5		10	7.3	odd	6
1323.2.f.f.883.5		10	63.52	odd	6
1323.2.g.f.361.5		10	7.6	odd	2
1323.2.g.f.667.5		10	63.61	odd	6
1323.2.h.f.226.1		10	7.5	odd	6
1323.2.h.f.802.1		10	63.34	odd	6
3024.2.q.i.2305.3		10	28.23	odd	6
3024.2.q.i.2881.3		10	36.7	odd	6
3024.2.t.i.289.3		10	252.79	odd	6
3024.2.t.i.1873.3		10	4.3	odd	2
3969.2.a.z.1.5		5	63.32	odd	6
3969.2.a.ba.1.5		5	63.59	even	6
3969.2.a.bb.1.1		5	63.31	odd	6
3969.2.a.bc.1.1		5	63.4	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(0.0802402 - 2.64453i) q^{7} -0.446582 q^{8} +O(q^{10})\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +0.146246 q^{5} +(0.0802402 - 2.64453i) q^{7} -0.446582 q^{8} +(0.150168 - 0.260099i) q^{10} -1.66404 q^{11} +(0.0999454 - 0.173111i) q^{13} +(-4.62094 - 2.85818i) q^{14} +(1.75890 - 3.04650i) q^{16} +(-3.13555 + 5.43093i) q^{17} +(3.45879 + 5.99080i) q^{19} +(-0.162147 - 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +6.18184 q^{23} -4.97861 q^{25} +(-0.205252 - 0.355508i) q^{26} +(-5.16746 + 2.77798i) q^{28} +(2.46757 + 4.27396i) q^{29} +(1.25890 + 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(6.43931 + 11.1532i) q^{34} +(0.0117348 - 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +14.2062 q^{38} -0.0653107 q^{40} +(-1.15895 + 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(-0.905887 + 1.56904i) q^{47} +(-6.98712 - 0.424396i) q^{49} +(-5.11215 + 8.85451i) q^{50} -0.443250 q^{52} +(2.67307 - 4.62989i) q^{53} -0.243359 q^{55} +(-0.0358339 + 1.18100i) q^{56} +10.1350 q^{58} +(-2.28549 - 3.95859i) q^{59} +(0.339138 - 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} +13.9059 q^{68} +(-0.675792 - 0.417996i) q^{70} -1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} -14.3765 q^{74} +(7.66972 - 13.2843i) q^{76} +(-0.133523 + 4.40061i) q^{77} +(-6.39787 + 11.0814i) q^{79} +(0.257231 - 0.445537i) q^{80} +(2.38008 + 4.12241i) q^{82} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} -3.86493 q^{86} +0.743131 q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.449777 - 0.278199i) q^{91} +(-6.85398 - 11.8714i) q^{92} +(1.86037 + 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(-3.98514 - 6.90246i) q^{97} +(-7.92933 + 11.9909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more