LMFDB - Embedded newform 87.2.g.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.2
Root			$1.03105 - 0.496527i$ of defining polynomial
Character	$\chi$	$=$	87.7
Dual form			87.2.g.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0321271 + 0.140758i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.78316 - 0.858723i) q^{4} +(-0.345850 - 1.51527i) q^{5} +(0.0321271 - 0.140758i) q^{6} +(1.37625 + 0.662766i) q^{7} +(0.358196 + 0.449164i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(0.0321271 + 0.140758i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.78316 - 0.858723i) q^{4} +(-0.345850 - 1.51527i) q^{5} +(0.0321271 - 0.140758i) q^{6} +(1.37625 + 0.662766i) q^{7} +(0.358196 + 0.449164i) q^{8} +(0.623490 + 0.781831i) q^{9} +(0.202175 - 0.0973624i) q^{10} +(-0.478737 + 0.600317i) q^{11} -1.97916 q^{12} +(-1.63237 + 2.04693i) q^{13} +(-0.0490748 + 0.215011i) q^{14} +(-0.345850 + 1.51527i) q^{15} +(2.41625 - 3.02988i) q^{16} -3.51434 q^{17} +(-0.0900182 + 0.112879i) q^{18} +(-4.72829 + 2.27702i) q^{19} +(-1.91790 - 2.40497i) q^{20} +(-0.952393 - 1.19426i) q^{21} +(-0.0998798 - 0.0480996i) q^{22} +(-1.89083 + 8.28425i) q^{23} +(-0.127839 - 0.560098i) q^{24} +(2.32842 - 1.12131i) q^{25} +(-0.340565 - 0.164008i) q^{26} +(-0.222521 - 0.974928i) q^{27} +3.02320 q^{28} +(3.40207 - 4.17443i) q^{29} -0.224397 q^{30} +(0.315006 + 1.38013i) q^{31} +(1.53932 + 0.741300i) q^{32} +(0.691794 - 0.333151i) q^{33} +(-0.112906 - 0.494672i) q^{34} +(0.528293 - 2.31460i) q^{35} +(1.78316 + 0.858723i) q^{36} +(-1.87409 - 2.35004i) q^{37} +(-0.472416 - 0.592391i) q^{38} +(2.35885 - 1.13596i) q^{39} +(0.556722 - 0.698107i) q^{40} +5.79055 q^{41} +(0.137505 - 0.172425i) q^{42} +(-0.955986 + 4.18845i) q^{43} +(-0.338157 + 1.48156i) q^{44} +(0.969050 - 1.21515i) q^{45} -1.22682 q^{46} +(1.10631 - 1.38727i) q^{47} +(-3.49158 + 1.68146i) q^{48} +(-2.90963 - 3.64856i) q^{49} +(0.232638 + 0.291719i) q^{50} +(3.16631 + 1.52482i) q^{51} +(-1.15303 + 5.05176i) q^{52} +(-1.50686 - 6.60199i) q^{53} +(0.130080 - 0.0626432i) q^{54} +(1.07521 + 0.517795i) q^{55} +(0.195276 + 0.855561i) q^{56} +5.24800 q^{57} +(0.696884 + 0.344757i) q^{58} +14.9605 q^{59} +(0.684491 + 2.99895i) q^{60} +(-12.3585 - 5.95153i) q^{61} +(-0.184144 + 0.0886793i) q^{62} +(0.339905 + 1.48922i) q^{63} +(1.66981 - 7.31591i) q^{64} +(3.66621 + 1.76555i) q^{65} +(0.0691190 + 0.0866725i) q^{66} +(-4.54833 - 5.70342i) q^{67} +(-6.26662 + 3.01785i) q^{68} +(5.29798 - 6.64345i) q^{69} +0.342772 q^{70} +(-2.99945 + 3.76119i) q^{71} +(-0.127839 + 0.560098i) q^{72} +(-2.04705 + 8.96872i) q^{73} +(0.270578 - 0.339294i) q^{74} -2.58435 q^{75} +(-6.47595 + 8.12058i) q^{76} +(-1.05673 + 0.508894i) q^{77} +(0.235679 + 0.295532i) q^{78} +(0.340352 + 0.426788i) q^{79} +(-5.42674 - 2.61338i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.186034 + 0.815067i) q^{82} +(-10.4943 + 5.05376i) q^{83} +(-2.72381 - 1.31172i) q^{84} +(1.21543 + 5.32517i) q^{85} -0.620271 q^{86} +(-4.87638 + 2.28493i) q^{87} -0.441122 q^{88} +(-3.06588 - 13.4325i) q^{89} +(0.202175 + 0.0973624i) q^{90} +(-3.60319 + 1.73520i) q^{91} +(3.74224 + 16.3958i) q^{92} +(0.315006 - 1.38013i) q^{93} +(0.230813 + 0.111154i) q^{94} +(5.08558 + 6.37712i) q^{95} +(-1.06525 - 1.33578i) q^{96} +(1.60034 - 0.770683i) q^{97} +(0.420086 - 0.526771i) q^{98} -0.767834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	0.0321271	+	0.140758i	0.0227173	+	0.0995310i	0.985016	−	0.172465i	$-0.0551733\pi$
$2$	0.0321271	+	0.140758i	0.0227173	+	0.0995310i	−0.962298	+	0.271996i	$0.912316\pi$
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	1.78316	−	0.858723i	0.891579	−	0.429362i
$5$	−0.345850	−	1.51527i	−0.154669	−	0.677649i	−0.991491	−	0.130174i	$-0.958446\pi$
$5$	−0.345850	−	1.51527i	−0.154669	−	0.677649i	0.836822	−	0.547475i	$-0.184411\pi$
$6$	0.0321271	−	0.140758i	0.0131158	−	0.0574642i
$7$	1.37625	+	0.662766i	0.520173	+	0.250502i	0.675499	−	0.737361i	$-0.263928\pi$
$7$	1.37625	+	0.662766i	0.520173	+	0.250502i	−0.155326	+	0.987863i	$0.549643\pi$
$8$	0.358196	+	0.449164i	0.126641	+	0.158803i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	0.202175	−	0.0973624i	0.0639334	−	0.0307887i
$11$	−0.478737	+	0.600317i	−0.144345	+	0.181002i	−0.848748	−	0.528797i	$-0.822643\pi$
$11$	−0.478737	+	0.600317i	−0.144345	+	0.181002i	0.704404	+	0.709800i	$0.251215\pi$
$12$	−1.97916			−0.571333
$13$	−1.63237	+	2.04693i	−0.452739	+	0.567716i	−0.954851	−	0.297086i	$-0.903985\pi$
$13$	−1.63237	+	2.04693i	−0.452739	+	0.567716i	0.502112	+	0.864803i	$0.332557\pi$
$14$	−0.0490748	+	0.215011i	−0.0131158	+	0.0574641i
$15$	−0.345850	+	1.51527i	−0.0892981	+	0.391241i
$16$	2.41625	−	3.02988i	0.604063	−	0.757471i
$17$	−3.51434			−0.852353			−0.426176	−	0.904640i	$-0.640140\pi$
$17$	−3.51434			−0.852353			−0.426176	+	0.904640i	$0.640140\pi$
$18$	−0.0900182	+	0.112879i	−0.0212175	+	0.0266059i
$19$	−4.72829	+	2.27702i	−1.08474	+	0.522385i	−0.888831	−	0.458236i	$-0.848481\pi$
$19$	−4.72829	+	2.27702i	−1.08474	+	0.522385i	−0.195913	+	0.980621i	$0.562767\pi$
$20$	−1.91790	−	2.40497i	−0.428856	−	0.537768i
$21$	−0.952393	−	1.19426i	−0.207829	−	0.260610i
$22$	−0.0998798	−	0.0480996i	−0.0212945	−	0.0102549i
$23$	−1.89083	+	8.28425i	−0.394264	+	1.72739i	0.255106	+	0.966913i	$0.417890\pi$
$23$	−1.89083	+	8.28425i	−0.394264	+	1.72739i	−0.649371	+	0.760472i	$0.724968\pi$
$24$	−0.127839	−	0.560098i	−0.0260950	−	0.114330i
$25$	2.32842	−	1.12131i	0.465684	−	0.224261i
$26$	−0.340565	−	0.164008i	−0.0667904	−	0.0321645i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	3.02320			0.571331
$29$	3.40207	−	4.17443i	0.631749	−	0.775173i
$29$	3.40207	−	4.17443i	0.631749	−	0.775173i
$30$	−0.224397			−0.0409692
$31$	0.315006	+	1.38013i	0.0565768	+	0.247879i	0.995306	−	0.0967760i	$-0.0308531\pi$
$31$	0.315006	+	1.38013i	0.0565768	+	0.247879i	−0.938729	+	0.344655i	$0.887996\pi$
$32$	1.53932	+	0.741300i	0.272117	+	0.131044i
$33$	0.691794	−	0.333151i	0.120426	−	0.0579941i
$34$	−0.112906	−	0.494672i	−0.0193631	−	0.0848355i
$35$	0.528293	−	2.31460i	0.0892978	−	0.391239i
$36$	1.78316	+	0.858723i	0.297193	+	0.143121i
$37$	−1.87409	−	2.35004i	−0.308099	−	0.386344i	0.603542	−	0.797331i	$-0.293756\pi$
$37$	−1.87409	−	2.35004i	−0.308099	−	0.386344i	−0.911641	+	0.410987i	$0.865184\pi$
$38$	−0.472416	−	0.592391i	−0.0766360	−	0.0960984i
$39$	2.35885	−	1.13596i	0.377718	−	0.181899i
$40$	0.556722	−	0.698107i	0.0880254	−	0.110380i
$41$	5.79055			0.904332			0.452166	−	0.891934i	$-0.350651\pi$
$41$	5.79055			0.904332			0.452166	+	0.891934i	$0.350651\pi$
$42$	0.137505	−	0.172425i	0.0212174	−	0.0266058i
$43$	−0.955986	+	4.18845i	−0.145787	+	0.638733i	0.848242	+	0.529609i	$0.177661\pi$
$43$	−0.955986	+	4.18845i	−0.145787	+	0.638733i	−0.994028	+	0.109123i	$0.965196\pi$
$44$	−0.338157	+	1.48156i	−0.0509790	+	0.223354i
$45$	0.969050	−	1.21515i	0.144458	−	0.181144i
$46$	−1.22682			−0.180885
$47$	1.10631	−	1.38727i	0.161372	−	0.202355i	−0.694571	−	0.719424i	$-0.744406\pi$
$47$	1.10631	−	1.38727i	0.161372	−	0.202355i	0.855943	+	0.517070i	$0.172977\pi$
$48$	−3.49158	+	1.68146i	−0.503967	+	0.242698i
$49$	−2.90963	−	3.64856i	−0.415661	−	0.521223i
$50$	0.232638	+	0.291719i	0.0329000	+	0.0412553i
$51$	3.16631	+	1.52482i	0.443372	+	0.213517i
$52$	−1.15303	+	5.05176i	−0.159897	+	0.700552i
$53$	−1.50686	−	6.60199i	−0.206983	−	0.906853i	−0.966561	−	0.256437i	$-0.917451\pi$
$53$	−1.50686	−	6.60199i	−0.206983	−	0.906853i	0.759578	−	0.650417i	$-0.225406\pi$
$54$	0.130080	−	0.0626432i	0.0177016	−	0.00852466i
$55$	1.07521	+	0.517795i	0.144982	+	0.0698194i
$56$	0.195276	+	0.855561i	0.0260949	+	0.114329i
$57$	5.24800			0.695115
$58$	0.696884	+	0.344757i	0.0915054	+	0.0452688i
$59$	14.9605			1.94769			0.973845	−	0.227213i	$-0.0729614\pi$
$59$	14.9605			1.94769			0.973845	+	0.227213i	$0.0729614\pi$
$60$	0.684491	+	2.99895i	0.0883674	+	0.387163i
$61$	−12.3585	−	5.95153i	−1.58234	−	0.762016i	−0.583594	−	0.812046i	$-0.698354\pi$
$61$	−12.3585	−	5.95153i	−1.58234	−	0.762016i	−0.998748	+	0.0500301i	$0.984068\pi$
$62$	−0.184144	+	0.0886793i	−0.0233864	+	0.0112623i
$63$	0.339905	+	1.48922i	0.0428240	+	0.187624i
$64$	1.66981	−	7.31591i	0.208726	−	0.914489i
$65$	3.66621	+	1.76555i	0.454737	+	0.218990i
$66$	0.0691190	+	0.0866725i	0.00850796	+	0.0106686i
$67$	−4.54833	−	5.70342i	−0.555666	−	0.696784i	0.422084	−	0.906557i	$-0.361299\pi$
$67$	−4.54833	−	5.70342i	−0.555666	−	0.696784i	−0.977750	+	0.209773i	$0.932727\pi$
$68$	−6.26662	+	3.01785i	−0.759939	+	0.365968i
$69$	5.29798	−	6.64345i	0.637801	−	0.799778i
$70$	0.342772			0.0409690
$71$	−2.99945	+	3.76119i	−0.355969	+	0.446371i	−0.927283	−	0.374360i	$-0.877862\pi$
$71$	−2.99945	+	3.76119i	−0.355969	+	0.446371i	0.571314	+	0.820731i	$0.306434\pi$
$72$	−0.127839	+	0.560098i	−0.0150659	+	0.0660082i
$73$	−2.04705	+	8.96872i	−0.239589	+	1.04971i	0.701796	+	0.712378i	$0.252382\pi$
$73$	−2.04705	+	8.96872i	−0.239589	+	1.04971i	−0.941386	+	0.337332i	$0.890476\pi$
$74$	0.270578	−	0.339294i	0.0314540	−	0.0394421i
$75$	−2.58435			−0.298415
$76$	−6.47595	+	8.12058i	−0.742842	+	0.931495i
$77$	−1.05673	+	0.508894i	−0.120426	+	0.0579939i
$78$	0.235679	+	0.295532i	0.0266853	+	0.0334624i
$79$	0.340352	+	0.426788i	0.0382926	+	0.0480174i	0.800609	−	0.599187i	$-0.204509\pi$
$79$	0.340352	+	0.426788i	0.0382926	+	0.0480174i	−0.762316	+	0.647204i	$0.775938\pi$
$80$	−5.42674	−	2.61338i	−0.606728	−	0.292185i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	0.186034	+	0.815067i	0.0205440	+	0.0900090i
$83$	−10.4943	+	5.05376i	−1.15189	+	0.554723i	−0.909602	−	0.415481i	$-0.863613\pi$
$83$	−10.4943	+	5.05376i	−1.15189	+	0.554723i	−0.242292	+	0.970203i	$0.577899\pi$
$84$	−2.72381	−	1.31172i	−0.297192	−	0.143120i
$85$	1.21543	+	5.32517i	0.131832	+	0.577596i
$86$	−0.620271			−0.0668856
$87$	−4.87638	+	2.28493i	−0.522803	+	0.244970i
$88$	−0.441122			−0.0470238
$89$	−3.06588	−	13.4325i	−0.324982	−	1.42384i	−0.828565	−	0.559893i	$-0.810842\pi$
$89$	−3.06588	−	13.4325i	−0.324982	−	1.42384i	0.503583	−	0.863947i	$-0.332015\pi$
$90$	0.202175	+	0.0973624i	0.0213111	+	0.0102629i
$91$	−3.60319	+	1.73520i	−0.377717	+	0.181899i
$92$	3.74224	+	16.3958i	0.390155	+	1.70938i
$93$	0.315006	−	1.38013i	0.0326646	−	0.143113i
$94$	0.230813	+	0.111154i	0.0238065	+	0.0114646i
$95$	5.08558	+	6.37712i	0.521770	+	0.654278i
$96$	−1.06525	−	1.33578i	−0.108721	−	0.136332i
$97$	1.60034	−	0.770683i	0.162490	−	0.0782510i	−0.350871	−	0.936424i	$-0.614114\pi$
$97$	1.60034	−	0.770683i	0.162490	−	0.0782510i	0.513361	+	0.858173i	$0.328400\pi$
$98$	0.420086	−	0.526771i	0.0424351	−	0.0532119i
$99$	−0.767834			−0.0771702
$100$	3.18904	−	3.99893i	0.318904	−	0.399893i
$101$	0.993780	−	4.35404i	0.0988848	−	0.433243i	−0.901115	−	0.433580i	$-0.857250\pi$
$101$	0.993780	−	4.35404i	0.0988848	−	0.433243i	1.00000		0.000337172i	$0.000107325\pi$
$102$	−0.112906	+	0.494672i	−0.0111793	+	0.0489798i
$103$	6.43434	−	8.06841i	0.633995	−	0.795004i	−0.356243	−	0.934393i	$-0.615942\pi$
$103$	6.43434	−	8.06841i	0.633995	−	0.795004i	0.990238	+	0.139389i	$0.0445139\pi$
$104$	−1.50412			−0.147491
$105$	−1.48024	+	1.85617i	−0.144457	+	0.181143i
$106$	0.880873	−	0.424206i	0.0855579	−	0.0412025i
$107$	−9.78294	−	12.2674i	−0.945753	−	1.18594i	−0.982434	−	0.186610i	$-0.940250\pi$
$107$	−9.78294	−	12.2674i	−0.945753	−	1.18594i	0.0366812	−	0.999327i	$-0.488321\pi$
$108$	−1.23398	−	1.54737i	−0.118740	−	0.148895i
$109$	8.86268	+	4.26804i	0.848891	+	0.408804i	0.807166	−	0.590325i	$-0.201000\pi$
$109$	8.86268	+	4.26804i	0.848891	+	0.408804i	0.0417249	+	0.999129i	$0.486715\pi$
$110$	−0.0383403	+	0.167980i	−0.00365561	+	0.0160163i
$111$	0.668856	+	2.93045i	0.0634850	+	0.278146i
$112$	5.33346	−	2.56846i	0.503965	−	0.242697i
$113$	11.4046	+	5.49216i	1.07285	+	0.516659i	0.885026	−	0.465542i	$-0.154141\pi$
$113$	11.4046	+	5.49216i	1.07285	+	0.516659i	0.187829	+	0.982202i	$0.439855\pi$
$114$	0.168603	+	0.738699i	0.0157911	+	0.0691855i
$115$	13.2068			1.23154
$116$	2.48175	−	10.3651i	0.230424	−	0.962376i
$117$	−2.61812			−0.242046
$118$	0.480637	+	2.10581i	0.0442463	+	0.193856i
$119$	−4.83661	−	2.32919i	−0.443371	−	0.213516i
$120$	−0.804486	+	0.387420i	−0.0734392	+	0.0353664i
$121$	2.31654	+	10.1494i	0.210594	+	0.922675i
$122$	0.440684	−	1.93076i	0.0398976	−	0.174803i
$123$	−5.21710	−	2.51243i	−0.470411	−	0.226538i
$124$	1.74686	+	2.19049i	0.156872	+	0.196712i
$125$	−7.34962	−	9.21613i	−0.657370	−	0.824316i
$126$	−0.198700	+	0.0956888i	−0.0177016	+	0.00852464i
$127$	12.0574	−	15.1195i	1.06992	−	1.34164i	0.133390	−	0.991064i	$-0.457414\pi$
$127$	12.0574	−	15.1195i	1.06992	−	1.34164i	0.936534	−	0.350578i	$-0.114015\pi$
$128$	4.50046			0.397788
$129$	2.67861	−	3.35888i	0.235839	−	0.295733i
$130$	−0.130731	+	0.572770i	−0.0114659	+	0.0502353i
$131$	−3.74018	+	16.3868i	−0.326781	+	1.43172i	0.498446	+	0.866921i	$0.333904\pi$
$131$	−3.74018	+	16.3868i	−0.326781	+	1.43172i	−0.825227	+	0.564801i	$0.808953\pi$
$132$	0.947494	−	1.18812i	0.0824688	−	0.103413i
$133$	−8.01644			−0.695113
$134$	0.656678	−	0.823448i	0.0567283	−	0.0711351i
$135$	−1.40032	+	0.674358i	−0.120520	+	0.0580395i
$136$	−1.25882	−	1.57851i	−0.107943	−	0.135357i
$137$	11.3794	+	14.2693i	0.972210	+	1.21911i	0.975698	+	0.219119i	$0.0703183\pi$
$137$	11.3794	+	14.2693i	0.972210	+	1.21911i	−0.00348811	+	0.999994i	$0.501110\pi$
$138$	1.10533	+	0.532298i	0.0940918	+	0.0453122i
$139$	1.52781	−	6.69377i	0.129587	−	0.567758i	−0.867889	−	0.496758i	$-0.834524\pi$
$139$	1.52781	−	6.69377i	0.129587	−	0.567758i	0.997476	−	0.0710004i	$-0.0226192\pi$
$140$	−1.04557	−	4.58096i	−0.0883671	−	0.387162i
$141$	−1.59867	+	0.769879i	−0.134632	+	0.0648355i
$142$	−0.625781	−	0.301360i	−0.0525144	−	0.0252896i
$143$	−0.447330	−	1.95988i	−0.0374076	−	0.163893i
$144$	3.87536			0.322947
$145$	−7.50199	−	3.71132i	−0.623007	−	0.308209i
$146$	−1.32819			−0.109921
$147$	1.03843	+	4.54968i	0.0856486	+	0.375251i
$148$	−5.35983	−	2.58116i	−0.440576	−	0.212170i
$149$	1.64542	−	0.792394i	0.134798	−	0.0649154i	−0.365269	−	0.930902i	$-0.619023\pi$
$149$	1.64542	−	0.792394i	0.134798	−	0.0649154i	0.500067	+	0.865987i	$0.333309\pi$
$150$	−0.0830277	−	0.363768i	−0.00677918	−	0.0297015i
$151$	−1.46012	+	6.39722i	−0.118823	+	0.520599i	0.880125	+	0.474742i	$0.157459\pi$
$151$	−1.46012	+	6.39722i	−0.118823	+	0.520599i	−0.998948	+	0.0458562i	$0.985398\pi$
$152$	−2.71641	−	1.30816i	−0.220330	−	0.106105i
$153$	−2.19116	−	2.74762i	−0.177144	−	0.222132i
$154$	−0.105581	−	0.132394i	−0.00850793	−	0.0106686i
$155$	1.98232	−	0.954637i	0.159224	−	0.0766783i
$156$	3.23072	−	4.05119i	0.258665	−	0.324355i
$157$	20.8825			1.66661			0.833304	−	0.552815i	$-0.186447\pi$
$157$	20.8825			1.66661			0.833304	+	0.552815i	$0.186447\pi$
$158$	−0.0491393	+	0.0616187i	−0.00390931	+	0.00490212i
$159$	−1.50686	+	6.60199i	−0.119502	+	0.523572i
$160$	0.590892	−	2.58887i	0.0467141	−	0.204668i
$161$	−8.09277	+	10.1480i	−0.637799	+	0.799775i
$162$	−0.144378			−0.0113434
$163$	−0.155754	+	0.195310i	−0.0121996	+	0.0152979i	−0.787894	−	0.615811i	$-0.788828\pi$
$163$	−0.155754	+	0.195310i	−0.0121996	+	0.0152979i	0.775694	+	0.631109i	$0.217400\pi$
$164$	10.3255	−	4.97248i	0.806283	−	0.388285i
$165$	−0.744070	−	0.933034i	−0.0579257	−	0.0726366i
$166$	−1.04851	−	1.31479i	−0.0813800	−	0.102047i
$167$	−12.0865	−	5.82055i	−0.935281	−	0.450408i	−0.0967789	−	0.995306i	$-0.530854\pi$
$167$	−12.0865	−	5.82055i	−0.935281	−	0.450408i	−0.838502	+	0.544898i	$0.816568\pi$
$168$	0.195276	−	0.855561i	0.0150659	−	0.0660080i
$169$	1.36749	+	5.99135i	0.105191	+	0.460873i
$170$	−0.710512	+	0.342165i	−0.0544938	+	0.0262428i
$171$	−4.72829	−	2.27702i	−0.361581	−	0.174128i
$172$	1.89204	+	8.28959i	0.144267	+	0.632075i
$173$	−3.51856			−0.267511			−0.133755	−	0.991014i	$-0.542704\pi$
$173$	−3.51856			−0.267511			−0.133755	+	0.991014i	$0.542704\pi$
$174$	−0.478287	−	0.612982i	−0.0362588	−	0.0464700i
$175$	3.94765			0.298414
$176$	0.662141	+	2.90103i	0.0499108	+	0.218673i
$177$	−13.4789	−	6.49111i	−1.01314	−	0.487902i
$178$	1.79223	−	0.863094i	0.134333	−	0.0646916i
$179$	0.543093	+	2.37945i	0.0405927	+	0.177848i	0.991160	−	0.132669i	$-0.0423548\pi$
$179$	0.543093	+	2.37945i	0.0405927	+	0.177848i	−0.950568	+	0.310517i	$0.899498\pi$
$180$	0.684491	−	2.99895i	0.0510189	−	0.223529i
$181$	0.583248	+	0.280877i	0.0433525	+	0.0208775i	0.455434	−	0.890269i	$-0.349484\pi$
$181$	0.583248	+	0.280877i	0.0433525	+	0.0208775i	−0.412082	+	0.911147i	$0.635198\pi$
$182$	−0.360004	−	0.451431i	−0.0266853	−	0.0334623i
$183$	8.55234	+	10.7243i	0.632207	+	0.792762i
$184$	−4.39827	+	2.11810i	−0.324245	+	0.156148i
$185$	−2.91278	+	3.65251i	−0.214152	+	0.268538i
$186$	0.204385			0.0149862
$187$	1.68244	−	2.10972i	0.123032	−	0.154278i
$188$	0.781447	−	3.42374i	0.0569929	−	0.249702i
$189$	0.339905	−	1.48922i	0.0247245	−	0.108325i
$190$	−0.734246	+	0.920715i	−0.0532678	+	0.0667957i
$191$	−20.7888			−1.50422			−0.752112	−	0.659035i	$-0.770965\pi$
$191$	−20.7888			−1.50422			−0.752112	+	0.659035i	$0.770965\pi$
$192$	−4.67870	+	5.86691i	−0.337656	+	0.423408i
$193$	−18.2385	+	8.78319i	−1.31284	+	0.632228i	−0.953616	−	0.301025i	$-0.902671\pi$
$193$	−18.2385	+	8.78319i	−1.31284	+	0.632228i	−0.359219	+	0.933253i	$0.616957\pi$
$194$	0.159894	+	0.200501i	0.0114797	+	0.0143951i
$195$	−2.53709	−	3.18141i	−0.181685	−	0.227826i
$196$	−8.32143	−	4.00739i	−0.594388	−	0.286242i
$197$	−0.766446	+	3.35802i	−0.0546070	+	0.239249i	−0.994865	−	0.101215i	$-0.967727\pi$
$197$	−0.766446	+	3.35802i	−0.0546070	+	0.239249i	0.940258	+	0.340464i	$0.110584\pi$
$198$	−0.0246683	−	0.108079i	−0.00175310	−	0.00768083i
$199$	−10.8360	+	5.21833i	−0.768142	+	0.369918i	−0.776557	−	0.630047i	$-0.783036\pi$
$199$	−10.8360	+	5.21833i	−0.768142	+	0.369918i	0.00841481	+	0.999965i	$0.497321\pi$
$200$	1.33768	+	0.644194i	0.0945884	+	0.0455514i
$201$	1.62328	+	7.11205i	0.114497	+	0.501645i
$202$	0.644793			0.0453675
$203$	7.44877	−	3.49028i	0.522801	−	0.244970i
$204$	6.95542			0.486977
$205$	−2.00266	−	8.77424i	−0.139872	−	0.612819i
$206$	1.34241	+	0.646471i	0.0935302	+	0.0450418i
$207$	−7.65580	+	3.68684i	−0.532115	+	0.256253i
$208$	2.25774	+	9.89179i	0.156546	+	0.685873i
$209$	0.896669	−	3.92857i	0.0620239	−	0.271745i
$210$	−0.308827	−	0.148723i	−0.0213111	−	0.0102629i
$211$	2.59412	+	3.25292i	0.178586	+	0.223940i	0.863065	−	0.505092i	$-0.168542\pi$
$211$	2.59412	+	3.25292i	0.178586	+	0.223940i	−0.684479	+	0.729033i	$0.739970\pi$
$212$	−8.35626	−	10.4784i	−0.573910	−	0.719660i
$213$	4.33433	−	2.08730i	0.296983	−	0.143020i
$214$	1.41244	−	1.77115i	0.0965525	−	0.121073i
$215$	6.67725			0.455385
$216$	0.358196	−	0.449164i	0.0243722	−	0.0305617i
$217$	−0.481178	+	2.10818i	−0.0326645	+	0.143113i
$218$	−0.316029	+	1.38461i	−0.0214042	+	0.0937778i
$219$	5.73571	−	7.19236i	0.387584	−	0.486014i
$220$	2.36191			0.159240
$221$	5.73671	−	7.19361i	0.385893	−	0.483895i
$222$	−0.390996	+	0.188294i	−0.0262419	+	0.0126374i
$223$	−2.93272	−	3.67751i	−0.196389	−	0.246264i	0.673880	−	0.738841i	$-0.264627\pi$
$223$	−2.93272	−	3.67751i	−0.196389	−	0.246264i	−0.870269	+	0.492577i	$0.836055\pi$
$224$	1.62718	+	2.04042i	0.108721	+	0.136332i
$225$	2.32842	+	1.12131i	0.155228	+	0.0747538i
$226$	−0.406670	+	1.78174i	−0.0270513	+	0.118519i
$227$	3.04552	+	13.3433i	0.202138	+	0.885625i	0.969632	+	0.244568i	$0.0786463\pi$
$227$	3.04552	+	13.3433i	0.202138	+	0.885625i	−0.767494	+	0.641056i	$0.778497\pi$
$228$	9.35802	−	4.50658i	0.619750	−	0.298456i
$229$	−18.1945	−	8.76201i	−1.20233	−	0.579010i	−0.277988	−	0.960584i	$-0.589668\pi$
$229$	−18.1945	−	8.76201i	−1.20233	−	0.579010i	−0.924338	+	0.381575i	$0.875382\pi$
$230$	0.424296	+	1.85896i	0.0279773	+	0.122576i
$231$	1.17288			0.0771700
$232$	3.09361	+	0.0328216i	0.203106	+	0.00215484i
$233$	−7.28500			−0.477257			−0.238628	−	0.971111i	$-0.576698\pi$
$233$	−7.28500			−0.477257			−0.238628	+	0.971111i	$0.576698\pi$
$234$	−0.0841127	−	0.368522i	−0.00549862	−	0.0240910i
$235$	−2.48471	−	1.19657i	−0.162085	−	0.0780559i
$236$	26.6769	−	12.8469i	1.73652	−	0.836263i
$237$	−0.121470	−	0.532196i	−0.00789034	−	0.0345698i
$238$	0.172466	−	0.755621i	0.0111793	−	0.0489796i
$239$	21.0551	+	10.1396i	1.36194	+	0.655878i	0.965069	−	0.261995i	$-0.0843805\pi$
$239$	21.0551	+	10.1396i	1.36194	+	0.655878i	0.396875	+	0.917873i	$0.370095\pi$
$240$	3.75542	+	4.70915i	0.242412	+	0.303974i
$241$	15.8736	+	19.9049i	1.02251	+	1.28219i	0.958759	+	0.284220i	$0.0917347\pi$
$241$	15.8736	+	19.9049i	1.02251	+	1.28219i	0.0637504	+	0.997966i	$0.479694\pi$
$242$	−1.35419	+	0.652143i	−0.0870506	+	0.0419213i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	−27.1478			−1.73796
$245$	−4.52225	+	5.67072i	−0.288916	+	0.362289i
$246$	0.186034	−	0.815067i	0.0118611	−	0.0519667i
$247$	3.05742	−	13.3954i	0.194539	−	0.852331i
$248$	−0.507071	+	0.635847i	−0.0321991	+	0.0403763i
$249$	11.6477			0.738145
$250$	1.06112	−	1.33061i	0.0671113	−	0.0841549i
$251$	11.7619	−	5.66425i	0.742406	−	0.357524i	−0.0241437	−	0.999708i	$-0.507686\pi$
$251$	11.7619	−	5.66425i	0.742406	−	0.357524i	0.766550	+	0.642184i	$0.221972\pi$
$252$	1.88493	+	2.36363i	0.118740	+	0.148895i
$253$	−4.06796	−	5.10107i	−0.255751	−	0.320701i
$254$	2.51557	+	1.21143i	0.157841	+	0.0760121i
$255$	1.21543	−	5.32517i	0.0761135	−	0.333475i
$256$	−3.19503	−	13.9984i	−0.199690	−	0.874897i
$257$	−1.23614	+	0.595293i	−0.0771082	+	0.0371333i	−0.472040	−	0.881577i	$-0.656482\pi$
$257$	−1.23614	+	0.595293i	−0.0771082	+	0.0371333i	0.394932	+	0.918710i	$0.370768\pi$
$258$	0.558845	+	0.269126i	0.0347922	+	0.0167550i
$259$	−1.02169	−	4.47632i	−0.0634848	−	0.278145i
$260$	8.05354			0.499459
$261$	5.38486	+	0.0571304i	0.333315	+	0.00353629i
$262$	−2.42674			−0.149924
$263$	−4.61815	−	20.2334i	−0.284767	−	1.24765i	−0.891603	−	0.452819i	$-0.850418\pi$
$263$	−4.61815	−	20.2334i	−0.284767	−	1.24765i	0.606836	−	0.794827i	$-0.292439\pi$
$264$	0.397437	+	0.191396i	0.0244606	+	0.0117796i
$265$	−9.48264	+	4.56660i	−0.582514	+	0.280524i
$266$	−0.257545	−	1.12838i	−0.0157911	−	0.0691853i
$267$	−3.06588	+	13.4325i	−0.187629	+	0.822054i
$268$	−13.0080	−	6.26434i	−0.794592	−	0.382656i
$269$	0.597581	+	0.749343i	0.0364352	+	0.0456883i	0.799715	−	0.600379i	$-0.204984\pi$
$269$	0.597581	+	0.749343i	0.0364352	+	0.0456883i	−0.763280	+	0.646068i	$0.776412\pi$
$270$	−0.139909	−	0.175441i	−0.00851462	−	0.0106770i
$271$	19.0251	−	9.16200i	1.15569	−	0.556552i	0.244953	−	0.969535i	$-0.421227\pi$
$271$	19.0251	−	9.16200i	1.15569	−	0.556552i	0.910739	+	0.412983i	$0.135513\pi$
$272$	−8.49153	+	10.6480i	−0.514874	+	0.645632i
$273$	3.99924			0.242045
$274$	−1.64294	+	2.06018i	−0.0992535	+	0.124460i
$275$	−0.441560	+	1.93460i	−0.0266271	+	0.116661i
$276$	3.74224	−	16.3958i	0.225256	−	0.986912i
$277$	6.49558	−	8.14520i	0.390282	−	0.489398i	−0.547411	−	0.836864i	$-0.684386\pi$
$277$	6.49558	−	8.14520i	0.390282	−	0.489398i	0.937693	+	0.347466i	$0.112958\pi$
$278$	0.991286			0.0594534
$279$	−0.882627	+	1.10678i	−0.0528415	+	0.0662612i
$280$	1.22887	−	0.591792i	0.0734390	−	0.0353663i
$281$	2.08541	+	2.61502i	0.124405	+	0.155999i	0.840133	−	0.542380i	$-0.182477\pi$
$281$	2.08541	+	2.61502i	0.124405	+	0.155999i	−0.715728	+	0.698379i	$0.753905\pi$
$282$	−0.159727	−	0.200292i	−0.00951162	−	0.0119272i
$283$	14.2126	+	6.84442i	0.844850	+	0.406858i	0.805663	−	0.592374i	$-0.201809\pi$
$283$	14.2126	+	6.84442i	0.844850	+	0.406858i	0.0391866	+	0.999232i	$0.487523\pi$
$284$	−2.11867	+	9.28249i	−0.125720	+	0.550814i
$285$	−1.81502	−	7.95213i	−0.107513	−	0.471044i
$286$	0.261498	−	0.125931i	0.0154627	−	0.00744643i
$287$	7.96923	+	3.83778i	0.470409	+	0.226537i
$288$	0.380182	+	1.66569i	0.0224024	+	0.0981514i
$289$	−4.64941			−0.273495
$290$	0.281381	−	1.17520i	0.0165233	−	0.0690101i
$291$	−1.77624			−0.104125
$292$	4.05143	+	17.7505i	0.237092	+	1.03877i
$293$	14.2429	+	6.85902i	0.832079	+	0.400708i	0.800894	−	0.598806i	$-0.204358\pi$
$293$	14.2429	+	6.85902i	0.832079	+	0.400708i	0.0311843	+	0.999514i	$0.490072\pi$
$294$	−0.607042	+	0.292336i	−0.0354034	+	0.0170494i
$295$	−5.17409	−	22.6692i	−0.301247	−	1.31985i
$296$	0.384259	−	1.68355i	0.0223346	−	0.0978543i
$297$	0.691794	+	0.333151i	0.0401420	+	0.0193314i
$298$	0.164398	+	0.206149i	0.00952335	+	0.0119419i
$299$	−13.8707	−	17.3934i	−0.802166	−	1.00588i
$300$	−4.60830	+	2.21924i	−0.266060	+	0.128128i
$301$	−4.09164	+	5.13075i	−0.235838	+	0.295732i
$302$	−0.947370			−0.0545150
$303$	−2.78451	+	3.49167i	−0.159966	+	0.200591i
$304$	−4.52562	+	19.8280i	−0.259562	+	1.13721i
$305$	−4.74398	+	20.7848i	−0.271640	+	1.19013i
$306$	0.316354	−	0.396696i	0.0180848	−	0.0226776i
$307$	8.83474			0.504225			0.252113	−	0.967698i	$-0.418875\pi$
$307$	8.83474			0.504225			0.252113	+	0.967698i	$0.418875\pi$
$308$	−1.44732	+	1.81488i	−0.0824685	+	0.103412i
$309$	−9.29790	+	4.47763i	−0.528939	+	0.254723i
$310$	0.198059	+	0.248358i	0.0112490	+	0.0141058i
$311$	−8.09774	−	10.1542i	−0.459181	−	0.575795i	0.497304	−	0.867576i	$-0.334323\pi$
$311$	−8.09774	−	10.1542i	−0.459181	−	0.575795i	−0.956485	+	0.291782i	$0.905752\pi$
$312$	1.35516	+	0.652612i	0.0767210	+	0.0369469i
$313$	−4.25967	+	18.6628i	−0.240771	+	1.05489i	0.699546	+	0.714587i	$0.253385\pi$
$313$	−4.25967	+	18.6628i	−0.240771	+	1.05489i	−0.940317	+	0.340299i	$0.889472\pi$
$314$	0.670895	+	2.93938i	0.0378608	+	0.165879i
$315$	2.13902	−	1.03010i	0.120520	−	0.0580393i
$316$	0.973393	+	0.468762i	0.0547577	+	0.0263699i
$317$	−5.92875	−	25.9755i	−0.332992	−	1.45893i	−0.813307	−	0.581835i	$-0.802335\pi$
$317$	−5.92875	−	25.9755i	−0.332992	−	1.45893i	0.480315	−	0.877096i	$-0.340522\pi$
$318$	−0.977695			−0.0548264
$319$	0.877286	+	4.04078i	0.0491186	+	0.226240i
$320$	−11.6631			−0.651986
$321$	3.49149	+	15.2972i	0.194876	+	0.853808i
$322$	−1.68841	−	0.813096i	−0.0940915	−	0.0453121i
$323$	16.6168	−	8.00224i	0.924584	−	0.445256i
$324$	0.440403	+	1.92953i	0.0244669	+	0.107196i
$325$	−1.50561	+	6.59650i	−0.0835162	+	0.365908i
$326$	−0.0324954	−	0.0156490i	−0.00179975	−	0.000866715i
$327$	−6.13316	−	7.69074i	−0.339165	−	0.425299i
$328$	2.07415	+	2.60091i	0.114526	+	0.143611i
$329$	2.44200	−	1.17601i	0.134632	−	0.0648353i
$330$	0.107427	−	0.134709i	0.00591367	−	0.00741551i
$331$	−2.21519			−0.121758			−0.0608789	−	0.998145i	$-0.519390\pi$
$331$	−2.21519			−0.121758			−0.0608789	+	0.998145i	$0.519390\pi$
$332$	−14.3731	+	18.0233i	−0.788827	+	0.989158i
$333$	0.668856	−	2.93045i	0.0366531	−	0.160588i
$334$	0.430985	−	1.88827i	0.0235825	−	0.103321i
$335$	−7.06917	+	8.86446i	−0.386230	+	0.484317i
$336$	−5.91970			−0.322946
$337$	4.99853	−	6.26796i	0.272288	−	0.341438i	−0.626821	−	0.779163i	$-0.715644\pi$
$337$	4.99853	−	6.26796i	0.272288	−	0.341438i	0.899109	+	0.437725i	$0.144216\pi$
$338$	−0.799398	+	0.384970i	−0.0434815	+	0.0209396i
$339$	−7.89223	−	9.89654i	−0.428647	−	0.537506i
$340$	6.74016	+	8.45189i	0.365536	+	0.458368i
$341$	−0.979321	−	0.471616i	−0.0530332	−	0.0255394i
$342$	0.168603	−	0.738699i	0.00911702	−	0.0399443i
$343$	−3.96557	−	17.3743i	−0.214120	−	0.938123i
$344$	−2.22373	+	1.07089i	−0.119896	+	0.0577386i
$345$	−11.8989	−	5.73022i	−0.640616	−	0.308504i
$346$	−0.113041	−	0.495265i	−0.00607713	−	0.0266256i
$347$	−26.2715			−1.41033			−0.705165	−	0.709044i	$-0.749127\pi$
$347$	−26.2715			−1.41033			−0.705165	+	0.709044i	$0.749127\pi$
$348$	−6.73323	+	8.26185i	−0.360939	+	0.442882i
$349$	−3.86308			−0.206786			−0.103393	−	0.994641i	$-0.532970\pi$
$349$	−3.86308			−0.206786			−0.103393	+	0.994641i	$0.532970\pi$
$350$	0.126827	+	0.555663i	0.00677916	+	0.0297015i
$351$	2.35885	+	1.13596i	0.125906	+	0.0606331i
$352$	−1.18195	+	0.569195i	−0.0629979	+	0.0303382i
$353$	−4.46526	−	19.5636i	−0.237662	−	1.04126i	−0.943104	−	0.332497i	$-0.892109\pi$
$353$	−4.46526	−	19.5636i	−0.237662	−	1.04126i	0.705442	−	0.708767i	$-0.250748\pi$
$354$	0.480637	−	2.10581i	0.0255456	−	0.111923i
$355$	6.73657	+	3.24416i	0.357540	+	0.172182i
$356$	−17.0017	−	21.3195i	−0.901089	−	1.12993i
$357$	3.34703	+	4.19705i	0.177144	+	0.222131i
$358$	−0.317478	+	0.152889i	−0.0167792	+	0.00808046i
$359$	−13.2185	+	16.5755i	−0.697645	+	0.874819i	−0.996845	−	0.0793713i	$-0.974709\pi$
$359$	−13.2185	+	16.5755i	−0.697645	+	0.874819i	0.299200	+	0.954190i	$0.403280\pi$
$360$	0.892912			0.0470606
$361$	5.32557	−	6.67806i	0.280293	−	0.351477i
$362$	−0.0207977	+	0.0911206i	−0.00109310	+	0.00478919i
$363$	2.31654	−	10.1494i	0.121587	−	0.532706i
$364$	−4.93499	+	6.18828i	−0.258664	+	0.324354i
$365$	14.2980			0.748391
$366$	−1.23477	+	1.54835i	−0.0645424	+	0.0809336i
$367$	17.6518	−	8.50065i	0.921416	−	0.443730i	0.0878394	−	0.996135i	$-0.472004\pi$
$367$	17.6518	−	8.50065i	0.921416	−	0.443730i	0.833576	+	0.552404i	$0.186289\pi$
$368$	20.5316	+	25.7458i	1.07028	+	1.34209i
$369$	3.61035	+	4.52723i	0.187947	+	0.235678i
$370$	−0.607700	−	0.292653i	−0.0315928	−	0.0152143i
$371$	2.30176	−	10.0847i	0.119502	−	0.523570i
$372$	−0.623446	−	2.73149i	−0.0323242	−	0.141621i
$373$	−0.177910	+	0.0856769i	−0.00921182	+	0.00443618i	−0.438484	−	0.898739i	$-0.644484\pi$
$373$	−0.177910	+	0.0856769i	−0.00921182	+	0.00443618i	0.429272	+	0.903175i	$0.358770\pi$
$374$	0.351012	+	0.169038i	0.0181504	+	0.00874076i
$375$	2.62305	+	11.4923i	0.135454	+	0.593461i
$376$	1.01939			0.0525711
$377$	2.99133	+	13.7780i	0.154061	+	0.709605i
$378$	0.220540			0.0113434
$379$	5.00474	+	21.9272i	0.257076	+	1.12632i	0.924360	+	0.381521i	$0.124600\pi$
$379$	5.00474	+	21.9272i	0.257076	+	1.12632i	−0.667284	+	0.744804i	$0.732543\pi$
$380$	14.5446	+	7.00429i	0.746121	+	0.359313i
$381$	−17.4235	+	8.39071i	−0.892632	+	0.429869i
$382$	−0.667884	−	2.92619i	−0.0341719	−	0.149717i
$383$	0.134254	−	0.588207i	0.00686008	−	0.0300560i	−0.971382	−	0.237522i	$-0.923665\pi$
$383$	0.134254	−	0.588207i	0.00686008	−	0.0300560i	0.978242	+	0.207467i	$0.0665218\pi$
$384$	−4.05478	−	1.95268i	−0.206919	−	0.0996472i
$385$	1.13658	+	1.42523i	0.0579256	+	0.0726364i
$386$	−1.82226	−	2.28504i	−0.0927503	−	0.116305i
$387$	−3.87071	+	1.86404i	−0.196759	+	0.0947542i
$388$	2.19185	−	2.74850i	0.111275	−	0.139534i
$389$	−21.8263			−1.10664			−0.553318	−	0.832970i	$-0.686638\pi$
$389$	−21.8263			−1.10664			−0.553318	+	0.832970i	$0.686638\pi$
$390$	0.366300	−	0.459326i	0.0185483	−	0.0232589i
$391$	6.64500	−	29.1137i	0.336052	−	1.47234i
$392$	0.596583	−	2.61380i	0.0301320	−	0.132017i
$393$	10.4798	−	13.1412i	0.528634	−	0.662886i
$394$	−0.497292			−0.0250532
$395$	0.528987	−	0.663329i	0.0266162	−	0.0333757i
$396$	−1.36917	+	0.659357i	−0.0688033	+	0.0331339i
$397$	9.00827	+	11.2960i	0.452112	+	0.566931i	0.954690	−	0.297601i	$-0.0961865\pi$
$397$	9.00827	+	11.2960i	0.452112	+	0.566931i	−0.502578	+	0.864532i	$0.667615\pi$
$398$	−1.08265	−	1.35760i	−0.0542684	−	0.0680504i
$399$	7.22256	+	3.47820i	0.361580	+	0.174128i
$400$	2.22861	−	9.76419i	0.111431	−	0.488210i
$401$	5.86987	+	25.7176i	0.293128	+	1.28428i	0.880146	+	0.474702i	$0.157444\pi$
$401$	5.86987	+	25.7176i	0.293128	+	1.28428i	−0.587019	+	0.809573i	$0.699699\pi$
$402$	−0.948927	+	0.456979i	−0.0473282	+	0.0227920i
$403$	−3.33924	−	1.60809i	−0.166339	−	0.0801049i
$404$	−1.96685	−	8.61731i	−0.0978542	−	0.428727i
$405$	1.55424			0.0772306
$406$	0.730592	+	0.936342i	0.0362587	+	0.0464699i
$407$	2.30796			0.114402
$408$	0.449269	+	1.96838i	0.0222421	+	0.0974491i
$409$	28.0056	+	13.4868i	1.38479	+	0.666878i	0.970014	−	0.243048i	$-0.0781471\pi$
$409$	28.0056	+	13.4868i	1.38479	+	0.666878i	0.414772	+	0.909925i	$0.363861\pi$
$410$	1.17070	−	0.563782i	0.0578170	−	0.0278432i
$411$	−4.06127	−	17.7936i	−0.200328	−	0.877693i
$412$	4.54491	−	19.9126i	0.223912	−	0.981022i
$413$	20.5894	+	9.91531i	1.01314	+	0.487901i
$414$	−0.764911	−	0.959168i	−0.0375933	−	0.0471405i
$415$	11.2872	+	14.1538i	0.554069	+	0.694781i
$416$	−4.03014	+	1.94081i	−0.197594	+	0.0951562i
$417$	−4.28083	+	5.36799i	−0.209633	+	0.262871i
$418$	0.581785			0.0284560
$419$	12.6866	−	15.9085i	0.619782	−	0.777182i	−0.368532	−	0.929615i	$-0.620139\pi$
$419$	12.6866	−	15.9085i	0.619782	−	0.777182i	0.988314	+	0.152433i	$0.0487109\pi$
$420$	−1.04557	+	4.58096i	−0.0510188	+	0.223528i
$421$	1.89714	−	8.31193i	0.0924611	−	0.405099i	−0.907425	−	0.420215i	$-0.861955\pi$
$421$	1.89714	−	8.31193i	0.0924611	−	0.405099i	0.999886	+	0.0151163i	$0.00481185\pi$
$422$	−0.374533	+	0.469650i	−0.0182320	+	0.0228622i
$423$	1.77439			0.0862738
$424$	2.42562	−	3.04164i	0.117799	−	0.147715i
$425$	−8.18286	+	3.94066i	−0.396927	+	0.191150i
$426$	0.433054	+	0.543033i	0.0209815	+	0.0263100i
$427$	−13.0639	−	16.3816i	−0.632205	−	0.792760i
$428$	−27.9788	−	13.4739i	−1.35241	−	0.651286i
$429$	−0.447330	+	1.95988i	−0.0215973	+	0.0946240i
$430$	0.214521	+	0.939877i	0.0103451	+	0.0453249i
$431$	4.29075	−	2.06632i	0.206678	−	0.0995309i	−0.327681	−	0.944788i	$-0.606267\pi$
$431$	4.29075	−	2.06632i	0.206678	−	0.0995309i	0.534359	+	0.845257i	$0.320553\pi$
$432$	−3.49158	−	1.68146i	−0.167989	−	0.0808992i
$433$	−0.940217	−	4.11936i	−0.0451839	−	0.197964i	0.947298	−	0.320353i	$-0.103802\pi$
$433$	−0.940217	−	4.11936i	−0.0451839	−	0.197964i	−0.992482	+	0.122389i	$0.960944\pi$
$434$	−0.312202			−0.0149862
$435$	5.14878	+	6.59878i	0.246865	+	0.316387i
$436$	19.4686			0.932377
$437$	−9.92306	−	43.4758i	−0.474684	−	2.07973i
$438$	1.19665	+	0.576278i	0.0571783	+	0.0275356i
$439$	−24.6771	+	11.8839i	−1.17777	+	0.567186i	−0.917262	−	0.398285i	$-0.869606\pi$
$439$	−24.6771	+	11.8839i	−1.17777	+	0.567186i	−0.260512	+	0.965471i	$0.583891\pi$
$440$	0.152562	+	0.668418i	0.00727311	+	0.0318656i
$441$	1.03843	−	4.54968i	0.0494492	−	0.216651i
$442$	1.19686	+	0.576379i	0.0569290	+	0.0274155i
$443$	0.484554	+	0.607611i	0.0230219	+	0.0288685i	0.793209	−	0.608949i	$-0.208409\pi$
$443$	0.484554	+	0.607611i	0.0230219	+	0.0288685i	−0.770187	+	0.637818i	$0.779837\pi$
$444$	3.70912	+	4.65109i	0.176027	+	0.220731i
$445$	−19.2935	+	9.29125i	−0.914598	+	0.440447i
$446$	0.423420	−	0.530952i	0.0200495	−	0.0251413i
$447$	−1.82628			−0.0863801
$448$	7.14681	−	8.96182i	0.337655	−	0.423406i
$449$	0.695827	−	3.04862i	0.0328381	−	0.143873i	−0.955851	−	0.293851i	$-0.905063\pi$
$449$	0.695827	−	3.04862i	0.0328381	−	0.143873i	0.988689	+	0.149978i	$0.0479202\pi$
$450$	−0.0830277	+	0.363768i	−0.00391396	+	0.0171482i
$451$	−2.77215	+	3.47616i	−0.130535	+	0.163686i
$452$	25.0524			1.17837
$453$	4.09118	−	5.13017i	0.192220	−	0.241037i
$454$	−1.78033	+	0.857362i	−0.0835551	+	0.0402380i
$455$	3.87546	+	4.85967i	0.181684	+	0.227825i
$456$	1.87982	+	2.35721i	0.0880304	+	0.110387i
$457$	25.7939	+	12.4217i	1.20659	+	0.581061i	0.925546	−	0.378635i	$-0.123607\pi$
$457$	25.7939	+	12.4217i	1.20659	+	0.581061i	0.281039	+	0.959696i	$0.409321\pi$
$458$	0.648787	−	2.84252i	0.0303158	−	0.132822i
$459$	0.782014	+	3.42623i	0.0365013	+	0.159923i
$460$	23.5498	−	11.3410i	1.09801	−	0.528776i
$461$	25.1273	+	12.1007i	1.17029	+	0.563584i	0.915069	−	0.403297i	$-0.132136\pi$
$461$	25.1273	+	12.1007i	1.17029	+	0.563584i	0.255226	+	0.966882i	$0.417850\pi$
$462$	0.0376813	+	0.165093i	0.00175309	+	0.00768080i
$463$	−18.3196			−0.851382			−0.425691	−	0.904869i	$-0.639969\pi$
$463$	−18.3196			−0.851382			−0.425691	+	0.904869i	$0.639969\pi$
$464$	−4.42778	−	20.3944i	−0.205555	−	0.946784i
$465$	−2.20021			−0.102032
$466$	−0.234046	−	1.02542i	−0.0108420	−	0.0475018i
$467$	19.7132	+	9.49337i	0.912218	+	0.439301i	0.830286	−	0.557337i	$-0.188177\pi$
$467$	19.7132	+	9.49337i	0.912218	+	0.439301i	0.0819314	+	0.996638i	$0.473891\pi$
$468$	−4.66852	+	2.24824i	−0.215803	+	0.103925i
$469$	−2.47959	−	10.8638i	−0.114497	−	0.501644i
$470$	0.0886008	−	0.388186i	0.00408685	−	0.0179057i
$471$	−18.8145	−	9.06059i	−0.866927	−	0.417490i
$472$	5.35879	+	6.71971i	0.246658	+	0.309300i
$473$	−2.05673	−	2.57906i	−0.0945686	−	0.118585i
$474$	0.0710083	−	0.0341958i	0.00326152	−	0.00157067i
$475$	−8.45619	+	10.6037i	−0.387997	+	0.486533i
$476$	−10.6246			−0.486976
$477$	4.22213	−	5.29439i	0.193318	−	0.242413i
$478$	−0.750793	+	3.28944i	−0.0343405	+	0.150455i
$479$	−5.21867	+	22.8645i	−0.238447	+	1.04471i	0.703960	+	0.710239i	$0.251413\pi$
$479$	−5.21867	+	22.8645i	−0.238447	+	1.04471i	−0.942408	+	0.334467i	$0.891444\pi$
$480$	−1.65564	+	2.07611i	−0.0755694	+	0.0947611i
$481$	7.86958			0.358822
$482$	−2.29180	+	2.87383i	−0.104389	+	0.130899i
$483$	11.6944	−	5.63172i	0.532113	−	0.256252i
$484$	12.8463	+	16.1087i	0.583922	+	0.732216i
$485$	−1.72127	−	2.15840i	−0.0781588	−	0.0980081i
$486$	0.130080	+	0.0626432i	0.00590055	+	0.00284155i
$487$	7.92727	−	34.7316i	0.359219	−	1.57384i	−0.395926	−	0.918282i	$-0.629576\pi$
$487$	7.92727	−	34.7316i	0.359219	−	1.57384i	0.755145	−	0.655558i	$-0.227567\pi$
$488$	−1.75355	−	7.68280i	−0.0793794	−	0.347784i
$489$	0.225072	−	0.108389i	0.0101781	−	0.00490151i
$490$	−0.943486	−	0.454359i	−0.0426224	−	0.0205259i
$491$	−0.624505	−	2.73613i	−0.0281835	−	0.123480i	0.958879	−	0.283814i	$-0.0915999\pi$
$491$	−0.624505	−	2.73613i	−0.0281835	−	0.123480i	−0.987063	+	0.160334i	$0.948743\pi$
$492$	−11.4604			−0.516675
$493$	−11.9560	+	14.6704i	−0.538473	+	0.660721i
$494$	1.98374			0.0892527
$495$	0.265555	+	1.16347i	0.0119358	+	0.0522943i
$496$	4.94277	+	2.38031i	0.221937	+	0.106879i
$497$	−6.62078	+	3.18840i	−0.296982	+	0.143019i
$498$	0.374208	+	1.63951i	0.0167687	+	0.0734683i
$499$	−9.04769	+	39.6405i	−0.405030	+	1.77455i	0.201497	+	0.979489i	$0.435420\pi$
$499$	−9.04769	+	39.6405i	−0.405030	+	1.77455i	−0.606527	+	0.795063i	$0.707438\pi$
$500$	−21.0196	−	10.1225i	−0.940026	−	0.452693i
$501$	8.36411	+	10.4883i	0.373681	+	0.468581i
$502$	1.17517	+	1.47361i	0.0524502	+	0.0657705i
$503$	16.7015	−	8.04304i	0.744685	−	0.358621i	−0.0227560	−	0.999741i	$-0.507244\pi$
$503$	16.7015	−	8.04304i	0.744685	−	0.358621i	0.767441	+	0.641120i	$0.221530\pi$
$504$	−0.547152	+	0.686107i	−0.0243721	+	0.0305616i
$505$	−6.94123			−0.308881
$506$	0.587324	−	0.736481i	0.0261097	−	0.0327406i
$507$	1.36749	−	5.99135i	0.0607323	−	0.266085i
$508$	8.51679	−	37.3145i	0.377871	−	1.65556i
$509$	−26.5311	+	33.2689i	−1.17597	+	1.47462i	−0.327916	+	0.944707i	$0.606346\pi$
$509$	−26.5311	+	33.2689i	−1.17597	+	1.47462i	−0.848053	+	0.529911i	$0.822225\pi$
$510$	0.788609			0.0349202
$511$	−8.76142	+	10.9865i	−0.387582	+	0.486013i
$512$	9.97729	−	4.80481i	0.440938	−	0.212345i
$513$	3.27208	+	4.10306i	0.144466	+	0.181154i
$514$	−0.123506	−	0.154871i	−0.00544761	−	0.00683108i
$515$	−14.4511	−	6.95929i	−0.636793	−	0.306663i
$516$	1.89204	−	8.28959i	0.0832926	−	0.364929i
$517$	0.303171	+	1.32828i	0.0133334	+	0.0584176i
$518$	0.597254	−	0.287623i	0.0262419	−	0.0126374i
$519$	3.17011	+	1.52664i	0.139152	+	0.0670123i
$520$	0.520199	+	2.27914i	0.0228122	+	0.0999469i
$521$	−27.6372			−1.21081			−0.605404	−	0.795919i	$-0.706988\pi$
$521$	−27.6372			−1.21081			−0.605404	+	0.795919i	$0.706988\pi$
$522$	0.164958	+	0.759798i	0.00722004	+	0.0332555i
$523$	−21.3122			−0.931919			−0.465959	−	0.884806i	$-0.654291\pi$
$523$	−21.3122			−0.931919			−0.465959	+	0.884806i	$0.654291\pi$
$524$	7.40240	+	32.4320i	0.323375	+	1.41680i
$525$	−3.55671	−	1.71282i	−0.155227	−	0.0747536i
$526$	2.69965	−	1.30008i	0.117710	−	0.0566863i
$527$	−1.10704	−	4.85025i	−0.0482233	−	0.211280i
$528$	0.662141	−	2.90103i	0.0288160	−	0.126251i
$529$	−44.3313	−	21.3488i	−1.92745	−	0.928209i
$530$	−0.947436	−	1.18805i	−0.0411540	−	0.0516054i
$531$	9.32771	+	11.6966i	0.404788	+	0.507588i
$532$	−14.2946	+	6.88390i	−0.619748	+	0.298455i
$533$	−9.45234	+	11.8529i	−0.409426	+	0.513404i
$534$	−1.98923			−0.0860823
$535$	−15.2050	+	19.0665i	−0.657370	+	0.824316i
$536$	0.932577	−	4.08589i	0.0402812	−	0.176483i
$537$	0.543093	−	2.37945i	0.0234362	−	0.102681i
$538$	−0.0862775	+	0.108189i	−0.00371969	+	0.00466434i
$539$	3.58324			0.154341
$540$	−1.91790	+	2.40497i	−0.0825333	+	0.103494i
$541$	−19.9182	+	9.59210i	−0.856350	+	0.412397i	−0.809931	−	0.586525i	$-0.800495\pi$
$541$	−19.9182	+	9.59210i	−0.856350	+	0.412397i	−0.0464196	+	0.998922i	$0.514781\pi$
$542$	1.90085	+	2.38359i	0.0816484	+	0.102384i
$543$	−0.403620	−	0.506124i	−0.0173210	−	0.0217198i
$544$	−5.40971	−	2.60518i	−0.231939	−	0.111696i
$545$	3.40207	−	14.9054i	0.145729	−	0.638479i
$546$	0.128484	+	0.562925i	0.00549860	+	0.0240910i
$547$	−14.8690	+	7.16051i	−0.635751	+	0.306161i	−0.723857	−	0.689950i	$-0.757633\pi$
$547$	−14.8690	+	7.16051i	−0.635751	+	0.306161i	0.0881066	+	0.996111i	$0.471918\pi$
$548$	32.5447	+	15.6727i	1.39024	+	0.669505i
$549$	−3.05229	−	13.3730i	−0.130269	−	0.570744i
$550$	−0.286497			−0.0122163
$551$	−6.58070	+	27.4845i	−0.280347	+	1.17088i
$552$	4.88171			0.207779
$553$	0.185548	+	0.812940i	0.00789031	+	0.0345697i
$554$	1.35519	+	0.652624i	0.0575764	+	0.0277273i
$555$	4.20909	−	2.02699i	0.178666	−	0.0860410i
$556$	−3.02377	−	13.2480i	−0.128236	−	0.561841i
$557$	−1.21930	+	5.34211i	−0.0516635	+	0.226353i	−0.994168	−	0.107840i	$-0.965607\pi$
$557$	−1.21930	+	5.34211i	−0.0516635	+	0.226353i	0.942505	+	0.334193i	$0.108464\pi$
$558$	−0.184144	−	0.0886793i	−0.00779545	−	0.00375409i
$559$	−7.01294	−	8.79395i	−0.296616	−	0.371944i
$560$	−5.73649	−	7.19333i	−0.242411	−	0.303974i
$561$	−2.43120	+	1.17080i	−0.102645	+	0.0494314i
$562$	−0.301087	+	0.377551i	−0.0127006	+	0.0159260i
$563$	13.7797			0.580744			0.290372	−	0.956914i	$-0.406221\pi$
$563$	13.7797			0.580744			0.290372	+	0.956914i	$0.406221\pi$
$564$	−2.18957	+	2.74563i	−0.0921974	+	0.115612i
$565$	4.37782	−	19.1805i	0.184176	−	0.806929i
$566$	−0.506798	+	2.22043i	−0.0213023	+	0.0933315i
$567$	−0.952393	+	1.19426i	−0.0399968	+	0.0501544i
$568$	−2.76378			−0.115966
$569$	22.4007	−	28.0895i	0.939085	−	1.17758i	−0.0448404	−	0.998994i	$-0.514278\pi$
$569$	22.4007	−	28.0895i	0.939085	−	1.17758i	0.983925	−	0.178581i	$-0.0571506\pi$
$570$	1.06102	−	0.510958i	0.0444411	−	0.0214017i
$571$	−4.09271	−	5.13210i	−0.171275	−	0.214772i	0.688784	−	0.724966i	$-0.258145\pi$
$571$	−4.09271	−	5.13210i	−0.171275	−	0.214772i	−0.860059	+	0.510195i	$0.829573\pi$
$572$	−2.48066	−	3.11064i	−0.103721	−	0.130063i
$573$	18.7301	+	9.01992i	0.782459	+	0.376813i
$574$	−0.284170	+	1.24503i	−0.0118610	+	0.0519666i
$575$	4.88656	+	21.4094i	0.203783	+	0.892834i
$576$	6.76092	−	3.25589i	0.281705	−	0.135662i
$577$	7.26885	+	3.50050i	0.302606	+	0.145728i	0.579025	−	0.815310i	$-0.303433\pi$
$577$	7.26885	+	3.50050i	0.302606	+	0.145728i	−0.276419	+	0.961037i	$0.589148\pi$
$578$	−0.149372	−	0.654442i	−0.00621307	−	0.0272212i
$579$	20.2432			0.841278
$580$	−16.5642	−	0.175738i	−0.687792	−	0.00729710i
$581$	−17.7922			−0.738143
$582$	−0.0570656	−	0.250021i	−0.00236544	−	0.0103637i
$583$	4.68468	+	2.25602i	0.194019	+	0.0934348i
$584$	−4.76167	+	2.29310i	−0.197039	+	0.0948892i
$585$	0.905478	+	3.96716i	0.0374369	+	0.164022i
$586$	−0.507879	+	2.22516i	−0.0209803	+	0.0919206i
$587$	7.25462	+	3.49364i	0.299430	+	0.144198i	0.577567	−	0.816344i	$-0.304002\pi$
$587$	7.25462	+	3.49364i	0.299430	+	0.144198i	−0.278136	+	0.960542i	$0.589717\pi$
$588$	5.75860	+	7.22106i	0.237481	+	0.297792i
$589$	−4.63203	−	5.80838i	−0.190860	−	0.239330i
$590$	3.02464	−	1.45659i	0.124522	−	0.0599668i
$591$	2.14753	−	2.69292i	0.0883377	−	0.110772i
$592$	−11.6486			−0.478755
$593$	21.4831	−	26.9390i	0.882206	−	1.10625i	−0.111448	−	0.993770i	$-0.535549\pi$
$593$	21.4831	−	26.9390i	0.882206	−	1.10625i	0.993654	−	0.112481i	$-0.0358798\pi$
$594$	−0.0246683	+	0.108079i	−0.00101215	+	0.00443453i
$595$	−1.85660	+	8.13430i	−0.0761132	+	0.333474i
$596$	2.25360	−	2.82592i	0.0923110	−	0.115754i
$597$	12.0270			0.492234
$598$	2.00263	−	2.51122i	0.0818936	−	0.102691i
$599$	28.5373	−	13.7428i	1.16600	−	0.561517i	0.252199	−	0.967675i	$-0.418846\pi$
$599$	28.5373	−	13.7428i	1.16600	−	0.561517i	0.913802	+	0.406159i	$0.133132\pi$
$600$	−0.925704	−	1.16080i	−0.0377917	−	0.0473893i
$601$	2.41007	+	3.02214i	0.0983089	+	0.123275i	0.828552	−	0.559911i	$-0.189165\pi$
$601$	2.41007	+	3.02214i	0.0983089	+	0.123275i	−0.730244	+	0.683187i	$0.760593\pi$
$602$	−0.853647	−	0.411095i	−0.0347921	−	0.0167550i
$603$	1.62328	−	7.11205i	0.0661050	−	0.289625i
$604$	2.88981	+	12.6611i	0.117585	+	0.515173i
$605$	14.5779	−	7.02036i	0.592677	−	0.285418i
$606$	−0.580938	−	0.279765i	−0.0235990	−	0.0113647i
$607$	−0.295851	−	1.29621i	−0.0120082	−	0.0526115i	0.968569	−	0.248746i	$-0.0800183\pi$
$607$	−0.295851	−	1.29621i	−0.0120082	−	0.0526115i	−0.980577	+	0.196134i	$0.937161\pi$
$608$	−8.96633			−0.363633
$609$	−8.22549	−	0.0872679i	−0.333314	−	0.00353628i
$610$	−3.07803			−0.124626
$611$	1.03374	+	4.52910i	0.0418205	+	0.183228i
$612$	−6.26662	−	3.01785i	−0.253313	−	0.121989i
$613$	−2.72323	+	1.31144i	−0.109990	+	0.0529684i	−0.488070	−	0.872805i	$-0.662299\pi$
$613$	−2.72323	+	1.31144i	−0.109990	+	0.0529684i	0.378080	+	0.925773i	$0.376585\pi$
$614$	0.283835	+	1.24356i	0.0114546	+	0.0501860i
$615$	−2.00266	+	8.77424i	−0.0807551	+	0.353811i
$616$	−0.607094	−	0.292361i	−0.0244605	−	0.0117796i
$617$	1.20090	+	1.50588i	0.0483464	+	0.0606244i	0.805417	−	0.592709i	$-0.201942\pi$
$617$	1.20090	+	1.50588i	0.0483464	+	0.0606244i	−0.757070	+	0.653333i	$0.773370\pi$
$618$	−0.928977	−	1.16490i	−0.0373689	−	0.0468592i
$619$	−0.266348	+	0.128266i	−0.0107054	+	0.00515546i	−0.439229	−	0.898375i	$-0.644748\pi$
$619$	−0.266348	+	0.128266i	−0.0107054	+	0.00515546i	0.428523	+	0.903531i	$0.359034\pi$
$620$	2.71503	−	3.40454i	0.109038	−	0.136729i
$621$	8.49729			0.340985
$622$	1.16914	−	1.46605i	0.0468781	−	0.0587832i
$623$	4.68319	−	20.5184i	0.187628	−	0.822052i
$624$	2.25774	−	9.89179i	0.0903818	−	0.395989i
$625$	−3.36646	+	4.22141i	−0.134658	+	0.168856i
$626$	−2.76380			−0.110464
$627$	−2.51241	+	3.15046i	−0.100336	+	0.125817i
$628$	37.2368	−	17.9323i	1.48591	−	0.715577i
$629$	6.58620	+	8.25883i	0.262609	+	0.329301i
$630$	0.213715	+	0.267990i	0.00851459	+	0.0106770i
$631$	−29.7396	−	14.3219i	−1.18392	−	0.570144i	−0.264867	−	0.964285i	$-0.585328\pi$
$631$	−29.7396	−	14.3219i	−1.18392	−	0.570144i	−0.919050	+	0.394141i	$0.871042\pi$
$632$	−0.0697849	+	0.305748i	−0.00277589	+	0.0121620i
$633$	−0.925830	−	4.05633i	−0.0367984	−	0.161225i
$634$	3.46579	−	1.66904i	0.137644	−	0.0662860i
$635$	−27.0802	−	13.0411i	−1.07465	−	0.517522i
$636$	2.98231	+	13.0664i	0.118256	+	0.518115i
$637$	12.2179			0.484093
$638$	−0.540587	+	0.253303i	−0.0214020	+	0.0100284i
$639$	−4.81074			−0.190310
$640$	−1.55649	−	6.81941i	−0.0615255	−	0.269561i
$641$	19.3740	+	9.33001i	0.765226	+	0.368513i	0.775429	−	0.631435i	$-0.217534\pi$
$641$	19.3740	+	9.33001i	0.765226	+	0.368513i	−0.0102034	+	0.999948i	$0.503248\pi$
$642$	−2.04104	+	0.982911i	−0.0805533	+	0.0387924i
$643$	3.70655	+	16.2394i	0.146172	+	0.640421i	0.993928	+	0.110034i	$0.0350961\pi$
$643$	3.70655	+	16.2394i	0.146172	+	0.640421i	−0.847756	+	0.530387i	$0.822047\pi$
$644$	−5.71634	+	25.0449i	−0.225255	+	0.986909i
$645$	−6.01600	−	2.89715i	−0.236880	−	0.114075i
$646$	1.66023	+	2.08186i	0.0653209	+	0.0819098i
$647$	−0.400169	−	0.501796i	−0.0157323	−	0.0197276i	0.773903	−	0.633304i	$-0.218302\pi$
$647$	−0.400169	−	0.501796i	−0.0157323	−	0.0197276i	−0.789635	+	0.613576i	$0.789730\pi$
$648$	−0.517609	+	0.249267i	−0.0203336	+	0.00979214i
$649$	−7.16213	+	8.98103i	−0.281138	+	0.352536i
$650$	−0.976882			−0.0383165
$651$	1.34823	−	1.69063i	0.0528414	−	0.0662610i
$652$	−0.110018	+	0.482018i	−0.00430862	+	0.0188773i
$653$	9.30253	−	40.7570i	0.364036	−	1.59495i	−0.378804	−	0.925477i	$-0.623664\pi$
$653$	9.30253	−	40.7570i	0.364036	−	1.59495i	0.742840	−	0.669469i	$-0.233478\pi$
$654$	0.885493	−	1.11037i	0.0346255	−	0.0434190i
$655$	26.1239			1.02075
$656$	13.9914	−	17.5447i	0.546273	−	0.685005i
$657$	−8.28835	+	3.99146i	−0.323359	+	0.155722i
$658$	0.243987	+	0.305950i	0.00951159	+	0.0119272i
$659$	−3.91860	−	4.91377i	−0.152647	−	0.191413i	0.699628	−	0.714507i	$-0.253349\pi$
$659$	−3.91860	−	4.91377i	−0.152647	−	0.191413i	−0.852275	+	0.523094i	$0.824778\pi$
$660$	−2.12801	−	1.02480i	−0.0828327	−	0.0398901i
$661$	4.51078	−	19.7630i	0.175449	−	0.768693i	−0.808245	−	0.588846i	$-0.799583\pi$
$661$	4.51078	−	19.7630i	0.175449	−	0.768693i	0.983695	−	0.179847i	$-0.0575603\pi$
$662$	−0.0711676	−	0.311805i	−0.00276601	−	0.0121187i
$663$	−8.28979	+	3.99215i	−0.321949	+	0.155042i
$664$	−6.02897	−	2.90340i	−0.233969	−	0.112674i
$665$	2.77248	+	12.1470i	0.107512	+	0.471042i
$666$	0.433973			0.0168161
$667$	28.1493	+	36.0767i	1.08995	+	1.39690i
$668$	−26.5504			−1.02726
$669$	1.04668	+	4.58578i	0.0404668	+	0.177297i
$670$	−1.47486	−	0.710253i	−0.0569787	−	0.0274395i
$671$	9.48926	−	4.56979i	0.366329	−	0.176415i
$672$	−0.580735	−	2.54437i	−0.0224024	−	0.0981511i
$673$	4.83575	−	21.1868i	0.186405	−	0.816692i	−0.792088	−	0.610407i	$-0.791006\pi$
$673$	4.83575	−	21.1868i	0.186405	−	0.816692i	0.978492	−	0.206284i	$-0.0661371\pi$
$674$	1.04286	+	0.502213i	0.0401693	+	0.0193445i
$675$	−1.61132	−	2.02053i	−0.0620196	−	0.0777701i
$676$	7.58336	+	9.50923i	0.291668	+	0.365740i
$677$	−14.2342	+	6.85484i	−0.547066	+	0.263453i	−0.686937	−	0.726717i	$-0.741045\pi$
$677$	−14.2342	+	6.85484i	−0.547066	+	0.263453i	0.139872	+	0.990170i	$0.455331\pi$
$678$	1.13946	−	1.42884i	0.0437608	−	0.0548743i
$679$	2.71325			0.104125
$680$	−1.95651	+	2.45338i	−0.0750287	+	0.0940830i
$681$	3.04552	−	13.3433i	0.116704	−	0.511316i
$682$	0.0349210	−	0.152999i	0.00133719	−	0.00585863i
$683$	−21.3231	+	26.7383i	−0.815907	+	1.02311i	0.183291	+	0.983059i	$0.441325\pi$
$683$	−21.3231	+	26.7383i	−0.815907	+	1.02311i	−0.999197	+	0.0400557i	$0.987246\pi$
$684$	−10.3866			−0.397142
$685$	17.6863	−	22.1779i	0.675759	−	0.847376i
$686$	2.31817	−	1.11637i	0.0885081	−	0.0426232i
$687$	12.5910	+	15.7886i	0.480376	+	0.602372i
$688$	10.3806	+	13.0169i	0.395757	+	0.496263i
$689$	15.9736	+	7.69247i	0.608545	+	0.293060i
$690$	0.424296	−	1.85896i	0.0161527	−	0.0707695i
$691$	7.64507	+	33.4953i	0.290832	+	1.27422i	0.883370	+	0.468677i	$0.155269\pi$
$691$	7.64507	+	33.4953i	0.290832	+	1.27422i	−0.592537	+	0.805543i	$0.701874\pi$
$692$	−6.27414	+	3.02147i	−0.238507	+	0.114859i
$693$	−1.05673	−	0.508894i	−0.0401419	−	0.0193313i
$694$	−0.844028	−	3.69793i	−0.0320389	−	0.140371i
$695$	−10.6713			−0.404784
$696$	−2.77301	−	1.37184i	−0.105111	−	0.0519995i
$697$	−20.3500			−0.770810
$698$	−0.124109	−	0.543759i	−0.00469761	−	0.0205816i
$699$	6.56356	+	3.16085i	0.248257	+	0.119554i
$700$	7.03928	−	3.38994i	0.266060	−	0.128128i
$701$	−0.382708	−	1.67675i	−0.0144547	−	0.0633301i	0.967186	−	0.254069i	$-0.0817689\pi$
$701$	−0.382708	−	1.67675i	−0.0144547	−	0.0633301i	−0.981641	+	0.190738i	$0.938912\pi$
$702$	−0.0841127	+	0.368522i	−0.00317463	+	0.0139090i
$703$	14.2123	+	6.84430i	0.536029	+	0.258138i
$704$	3.59247	+	4.50481i	0.135396	+	0.169781i
$705$	1.71947	+	2.15615i	0.0647591	+	0.0812054i
$706$	2.61028	−	1.25704i	0.0982391	−	0.0473094i
$707$	4.25340	−	5.33359i	0.159965	−	0.200590i
$708$	−29.6091			−1.11278
$709$	26.2297	−	32.8910i	0.985077	−	1.23525i	0.0131625	−	0.999913i	$-0.495810\pi$
$709$	26.2297	−	32.8910i	0.985077	−	1.23525i	0.971915	−	0.235334i	$-0.0756184\pi$
$710$	−0.240215	+	1.05245i	−0.00901512	+	0.0394978i
$711$	−0.121470	+	0.532196i	−0.00455549	+	0.0199589i
$712$	4.93520	−	6.18854i	0.184954	−	0.231925i
$713$	−12.0290			−0.450489
$714$	−0.483238	+	0.605961i	−0.0180847	+	0.0226775i
$715$	−2.81504	+	1.35565i	−0.105276	+	0.0506984i
$716$	3.01171	+	3.77656i	0.112553	+	0.141137i
$717$	−14.5706	−	18.2710i	−0.544149	−	0.682342i
$718$	−2.75780	−	1.32809i	−0.102920	−	0.0495638i
$719$	−0.447704	+	1.96152i	−0.0166965	+	0.0731523i	−0.982590	−	0.185788i	$-0.940516\pi$
$719$	−0.447704	+	1.96152i	−0.0166965	+	0.0731523i	0.965893	+	0.258940i	$0.0833733\pi$
$720$	−1.34030	−	5.87222i	−0.0499499	−	0.218845i
$721$	14.2027	−	6.83967i	0.528937	−	0.254723i
$722$	1.11109	+	0.535071i	0.0413503	+	0.0199133i
$723$	−5.66523	−	24.8210i	−0.210692	−	0.923102i
$724$	1.28122			0.0476161
$725$	3.24063	−	13.5346i	0.120354	−	0.502662i
$726$	1.50304			0.0557829
$727$	−1.63010	−	7.14193i	−0.0604570	−	0.264880i	0.935662	−	0.352898i	$-0.114804\pi$
$727$	−1.63010	−	7.14193i	−0.0604570	−	0.264880i	−0.996119	+	0.0880183i	$0.971947\pi$
$728$	−2.07004	−	0.996878i	−0.0767207	−	0.0369468i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	0.459353	+	2.01256i	0.0170014	+	0.0744881i
$731$	3.35966	−	14.7196i	0.124262	−	0.544425i
$732$	24.4594	+	11.7790i	0.904044	+	0.435365i
$733$	3.27009	+	4.10056i	0.120783	+	0.151458i	0.838547	−	0.544829i	$-0.183406\pi$
$733$	3.27009	+	4.10056i	0.120783	+	0.151458i	−0.717764	+	0.696287i	$0.754834\pi$
$734$	1.76364	+	2.21153i	0.0650970	+	0.0816291i
$735$	6.53484	−	3.14701i	0.241041	−	0.116079i
$736$	−9.05170	+	11.3505i	−0.333650	+	0.418384i
$737$	5.60131			0.206327
$738$	−0.521255	+	0.653633i	−0.0191876	+	0.0240605i
$739$	−5.24580	+	22.9833i	−0.192970	+	0.845456i	0.782028	+	0.623243i	$0.214185\pi$
$739$	−5.24580	+	22.9833i	−0.192970	+	0.845456i	−0.974998	+	0.222213i	$0.928672\pi$
$740$	−2.05745	+	9.01428i	−0.0756334	+	0.331372i
$741$	−8.56670	+	10.7423i	−0.314706	+	0.394628i
$742$	1.49345			0.0548262
$743$	−12.1730	+	15.2644i	−0.446582	+	0.559997i	−0.953265	−	0.302136i	$-0.902300\pi$
$743$	−12.1730	+	15.2644i	−0.446582	+	0.559997i	0.506682	+	0.862133i	$0.330872\pi$
$744$	0.732739	−	0.352869i	0.0268635	−	0.0129368i
$745$	−1.76976	−	2.21921i	−0.0648389	−	0.0813054i
$746$	−0.0177754	−	0.0222897i	−0.000650805	−	0.000816084i
$747$	−10.4943	−	5.05376i	−0.383965	−	0.184908i
$748$	1.18840	−	5.20671i	0.0434521	−	0.190376i
$749$	−5.33333	−	23.3668i	−0.194876	−	0.853805i
$750$	−1.53337	+	0.738430i	−0.0559906	+	0.0269637i
$751$	−1.27601	−	0.614494i	−0.0465622	−	0.0224232i	0.410458	−	0.911880i	$-0.365369\pi$
$751$	−1.27601	−	0.614494i	−0.0465622	−	0.0224232i	−0.457020	+	0.889456i	$0.651083\pi$
$752$	−1.53014	−	6.70400i	−0.0557986	−	0.244470i
$753$	−13.0548			−0.475742
$754$	−1.84327	+	0.863702i	−0.0671278	+	0.0314542i
$755$	10.1985			0.371161
$756$	−0.672725	−	2.94740i	−0.0244668	−	0.107196i
$757$	−39.0305	−	18.7961i	−1.41859	−	0.683156i	−0.441751	−	0.897138i	$-0.645642\pi$
$757$	−39.0305	−	18.7961i	−1.41859	−	0.683156i	−0.976838	+	0.213982i	$0.931357\pi$
$758$	−2.92564	+	1.40892i	−0.106264	+	0.0511741i
$759$	1.45184	+	6.36093i	0.0526984	+	0.230887i
$760$	−1.04273	+	4.56852i	−0.0378240	+	0.165718i
$761$	−0.433634	−	0.208827i	−0.0157192	−	0.00756998i	0.426008	−	0.904720i	$-0.359920\pi$
$761$	−0.433634	−	0.208827i	−0.0157192	−	0.00756998i	−0.441727	+	0.897150i	$0.645634\pi$
$762$	−1.74083	−	2.18293i	−0.0630635	−	0.0790791i
$763$	9.36853	+	11.7478i	0.339164	+	0.425298i
$764$	−37.0697	+	17.8518i	−1.34113	+	0.645856i

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0321271 + 0.140758i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.78316 - 0.858723i) q^{4} +(-0.345850 - 1.51527i) q^{5} +(0.0321271 - 0.140758i) q^{6} +(1.37625 + 0.662766i) q^{7} +(0.358196 + 0.449164i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(0.0321271 + 0.140758i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.78316 - 0.858723i) q^{4} +(-0.345850 - 1.51527i) q^{5} +(0.0321271 - 0.140758i) q^{6} +(1.37625 + 0.662766i) q^{7} +(0.358196 + 0.449164i) q^{8} +(0.623490 + 0.781831i) q^{9} +(0.202175 - 0.0973624i) q^{10} +(-0.478737 + 0.600317i) q^{11} -1.97916 q^{12} +(-1.63237 + 2.04693i) q^{13} +(-0.0490748 + 0.215011i) q^{14} +(-0.345850 + 1.51527i) q^{15} +(2.41625 - 3.02988i) q^{16} -3.51434 q^{17} +(-0.0900182 + 0.112879i) q^{18} +(-4.72829 + 2.27702i) q^{19} +(-1.91790 - 2.40497i) q^{20} +(-0.952393 - 1.19426i) q^{21} +(-0.0998798 - 0.0480996i) q^{22} +(-1.89083 + 8.28425i) q^{23} +(-0.127839 - 0.560098i) q^{24} +(2.32842 - 1.12131i) q^{25} +(-0.340565 - 0.164008i) q^{26} +(-0.222521 - 0.974928i) q^{27} +3.02320 q^{28} +(3.40207 - 4.17443i) q^{29} -0.224397 q^{30} +(0.315006 + 1.38013i) q^{31} +(1.53932 + 0.741300i) q^{32} +(0.691794 - 0.333151i) q^{33} +(-0.112906 - 0.494672i) q^{34} +(0.528293 - 2.31460i) q^{35} +(1.78316 + 0.858723i) q^{36} +(-1.87409 - 2.35004i) q^{37} +(-0.472416 - 0.592391i) q^{38} +(2.35885 - 1.13596i) q^{39} +(0.556722 - 0.698107i) q^{40} +5.79055 q^{41} +(0.137505 - 0.172425i) q^{42} +(-0.955986 + 4.18845i) q^{43} +(-0.338157 + 1.48156i) q^{44} +(0.969050 - 1.21515i) q^{45} -1.22682 q^{46} +(1.10631 - 1.38727i) q^{47} +(-3.49158 + 1.68146i) q^{48} +(-2.90963 - 3.64856i) q^{49} +(0.232638 + 0.291719i) q^{50} +(3.16631 + 1.52482i) q^{51} +(-1.15303 + 5.05176i) q^{52} +(-1.50686 - 6.60199i) q^{53} +(0.130080 - 0.0626432i) q^{54} +(1.07521 + 0.517795i) q^{55} +(0.195276 + 0.855561i) q^{56} +5.24800 q^{57} +(0.696884 + 0.344757i) q^{58} +14.9605 q^{59} +(0.684491 + 2.99895i) q^{60} +(-12.3585 - 5.95153i) q^{61} +(-0.184144 + 0.0886793i) q^{62} +(0.339905 + 1.48922i) q^{63} +(1.66981 - 7.31591i) q^{64} +(3.66621 + 1.76555i) q^{65} +(0.0691190 + 0.0866725i) q^{66} +(-4.54833 - 5.70342i) q^{67} +(-6.26662 + 3.01785i) q^{68} +(5.29798 - 6.64345i) q^{69} +0.342772 q^{70} +(-2.99945 + 3.76119i) q^{71} +(-0.127839 + 0.560098i) q^{72} +(-2.04705 + 8.96872i) q^{73} +(0.270578 - 0.339294i) q^{74} -2.58435 q^{75} +(-6.47595 + 8.12058i) q^{76} +(-1.05673 + 0.508894i) q^{77} +(0.235679 + 0.295532i) q^{78} +(0.340352 + 0.426788i) q^{79} +(-5.42674 - 2.61338i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.186034 + 0.815067i) q^{82} +(-10.4943 + 5.05376i) q^{83} +(-2.72381 - 1.31172i) q^{84} +(1.21543 + 5.32517i) q^{85} -0.620271 q^{86} +(-4.87638 + 2.28493i) q^{87} -0.441122 q^{88} +(-3.06588 - 13.4325i) q^{89} +(0.202175 + 0.0973624i) q^{90} +(-3.60319 + 1.73520i) q^{91} +(3.74224 + 16.3958i) q^{92} +(0.315006 - 1.38013i) q^{93} +(0.230813 + 0.111154i) q^{94} +(5.08558 + 6.37712i) q^{95} +(-1.06525 - 1.33578i) q^{96} +(1.60034 - 0.770683i) q^{97} +(0.420086 - 0.526771i) q^{98} -0.767834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more