LMFDB - Embedded newform 525.2.n.b.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 31 x^{18} - 74 x^{17} + 109 x^{16} - 72 x^{15} - 51 x^{14} + 9 x^{13} + 866 x^{12} + \cdots + 3125 $ x^20 - 8x^19 + 31x^18 - 74x^17 + 109x^16 - 72x^15 - 51x^14 + 9x^13 + 866x^12 - 3240x^11 + 6385x^10 - 6775x^9 + 330x^8 + 11325x^7 - 18525x^6 + 12000x^5 + 5875x^4 - 21250x^3 + 22500x^2 - 12500*x + 3125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.4
Root			$-0.238506 + 1.88710i$ of defining polynomial
Character	$\chi$	$=$	525.316
Dual form			525.2.n.b.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.269002 + 0.195442i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.583869 - 1.79696i) q^{4} +(-0.418871 - 2.19649i) q^{5} +(0.102750 - 0.316231i) q^{6} -1.00000 q^{7} +(0.399639 - 1.22996i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.269002 + 0.195442i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.583869 - 1.79696i) q^{4} +(-0.418871 - 2.19649i) q^{5} +(0.102750 - 0.316231i) q^{6} -1.00000 q^{7} +(0.399639 - 1.22996i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.316607 - 0.672725i) q^{10} +(-0.240778 - 0.174935i) q^{11} +(-1.52859 + 1.11059i) q^{12} +(0.725677 - 0.527236i) q^{13} +(-0.269002 - 0.195442i) q^{14} +(-1.95954 + 1.07712i) q^{15} +(-2.70929 + 1.96841i) q^{16} +(-0.496003 + 1.52654i) q^{17} -0.332505 q^{18} +(-0.214905 + 0.661409i) q^{19} +(-3.70244 + 2.03516i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-0.0305801 - 0.0941159i) q^{22} +(-0.313727 - 0.227936i) q^{23} -1.29326 q^{24} +(-4.64909 + 1.84009i) q^{25} +0.298253 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.583869 + 1.79696i) q^{28} +(-1.71326 - 5.27289i) q^{29} +(-0.737636 - 0.0932282i) q^{30} +(0.911863 - 2.80643i) q^{31} -3.70003 q^{32} +(-0.0919688 + 0.283051i) q^{33} +(-0.431776 + 0.313703i) q^{34} +(0.418871 + 2.19649i) q^{35} +(1.52859 + 1.11059i) q^{36} +(-9.77301 + 7.10051i) q^{37} +(-0.187077 + 0.135919i) q^{38} +(-0.725677 - 0.527236i) q^{39} +(-2.86899 - 0.362605i) q^{40} +(6.11269 - 4.44113i) q^{41} +(-0.102750 + 0.316231i) q^{42} +7.36272 q^{43} +(-0.173770 + 0.534808i) q^{44} +(1.62994 + 1.53079i) q^{45} +(-0.0398451 - 0.122631i) q^{46} +(-1.04098 - 3.20382i) q^{47} +(2.70929 + 1.96841i) q^{48} +1.00000 q^{49} +(-1.61025 - 0.413639i) q^{50} +1.60510 q^{51} +(-1.37112 - 0.996180i) q^{52} +(-2.52816 - 7.78088i) q^{53} +(0.102750 + 0.316231i) q^{54} +(-0.283388 + 0.602139i) q^{55} +(-0.399639 + 1.22996i) q^{56} +0.695446 q^{57} +(0.569670 - 1.75326i) q^{58} +(8.59335 - 6.24344i) q^{59} +(3.07967 + 2.89233i) q^{60} +(-7.67713 - 5.57776i) q^{61} +(0.793786 - 0.576720i) q^{62} +(0.809017 - 0.587785i) q^{63} +(4.42326 + 3.21369i) q^{64} +(-1.46203 - 1.37310i) q^{65} +(-0.0800598 + 0.0581668i) q^{66} +(0.840130 - 2.58565i) q^{67} +3.03274 q^{68} +(-0.119833 + 0.368808i) q^{69} +(-0.316607 + 0.672725i) q^{70} +(-2.01106 - 6.18940i) q^{71} +(0.399639 + 1.22996i) q^{72} +(10.1076 + 7.34362i) q^{73} -4.01670 q^{74} +(3.18668 + 3.85293i) q^{75} +1.31400 q^{76} +(0.240778 + 0.174935i) q^{77} +(-0.0921652 - 0.283655i) q^{78} +(-1.55222 - 4.77724i) q^{79} +(5.45843 + 5.12640i) q^{80} +(0.309017 - 0.951057i) q^{81} +2.51231 q^{82} +(2.96394 - 9.12206i) q^{83} +(1.52859 - 1.11059i) q^{84} +(3.56079 + 0.450040i) q^{85} +(1.98059 + 1.43898i) q^{86} +(-4.48539 + 3.25882i) q^{87} +(-0.311388 + 0.226236i) q^{88} +(-7.95249 - 5.77782i) q^{89} +(0.139277 + 0.730343i) q^{90} +(-0.725677 + 0.527236i) q^{91} +(-0.226417 + 0.696841i) q^{92} -2.95085 q^{93} +(0.346133 - 1.06529i) q^{94} +(1.54279 + 0.194990i) q^{95} +(1.14337 + 3.51894i) q^{96} +(0.127712 + 0.393057i) q^{97} +(0.269002 + 0.195442i) q^{98} +0.297617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	0.269002	+	0.195442i	0.190213	+	0.138198i	0.678816	−	0.734308i	$-0.262493\pi$
$2$	0.269002	+	0.195442i	0.190213	+	0.138198i	−0.488603	+	0.872506i	$0.662493\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.583869	−	1.79696i	−0.291935	−	0.898482i
$5$	−0.418871	−	2.19649i	−0.187325	−	0.982298i
$5$	−0.418871	−	2.19649i	−0.187325	−	0.982298i
$6$	0.102750	−	0.316231i	0.0419474	−	0.129101i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.399639	−	1.22996i	0.141294	−	0.434857i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.316607	−	0.672725i	0.100120	−	0.212734i
$11$	−0.240778	−	0.174935i	−0.0725972	−	0.0527449i	0.550895	−	0.834575i	$-0.314287\pi$
$11$	−0.240778	−	0.174935i	−0.0725972	−	0.0527449i	−0.623492	+	0.781830i	$0.714287\pi$
$12$	−1.52859	+	1.11059i	−0.441266	+	0.320598i
$13$	0.725677	−	0.527236i	0.201267	−	0.146229i	−0.482587	−	0.875848i	$-0.660303\pi$
$13$	0.725677	−	0.527236i	0.201267	−	0.146229i	0.683854	+	0.729619i	$0.260303\pi$
$14$	−0.269002	−	0.195442i	−0.0718939	−	0.0522340i
$15$	−1.95954	+	1.07712i	−0.505952	+	0.278112i
$16$	−2.70929	+	1.96841i	−0.677322	+	0.492103i
$17$	−0.496003	+	1.52654i	−0.120298	+	0.370241i	−0.993015	−	0.117986i	$-0.962356\pi$
$17$	−0.496003	+	1.52654i	−0.120298	+	0.370241i	0.872717	+	0.488227i	$0.162356\pi$
$18$	−0.332505			−0.0783722
$19$	−0.214905	+	0.661409i	−0.0493025	+	0.151738i	−0.972677	−	0.232163i	$-0.925420\pi$
$19$	−0.214905	+	0.661409i	−0.0493025	+	0.151738i	0.923374	+	0.383901i	$0.125420\pi$
$20$	−3.70244	+	2.03516i	−0.827891	+	0.455075i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	−0.0305801	−	0.0941159i	−0.00651970	−	0.0200656i
$23$	−0.313727	−	0.227936i	−0.0654166	−	0.0475280i	0.554596	−	0.832120i	$-0.312873\pi$
$23$	−0.313727	−	0.227936i	−0.0654166	−	0.0475280i	−0.620013	+	0.784592i	$0.712873\pi$
$24$	−1.29326			−0.263985
$25$	−4.64909	+	1.84009i	−0.929819	+	0.368018i
$26$	0.298253			0.0584922
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.583869	+	1.79696i	0.110341	+	0.339594i
$29$	−1.71326	−	5.27289i	−0.318145	−	0.979151i	−0.974440	−	0.224646i	$-0.927877\pi$
$29$	−1.71326	−	5.27289i	−0.318145	−	0.979151i	0.656295	−	0.754504i	$-0.272123\pi$
$30$	−0.737636	−	0.0932282i	−0.134673	−	0.0170211i
$31$	0.911863	−	2.80643i	0.163776	−	0.504049i	−0.835168	−	0.549994i	$-0.814630\pi$
$31$	0.911863	−	2.80643i	0.163776	−	0.504049i	0.998944	+	0.0459450i	$0.0146299\pi$
$32$	−3.70003			−0.654080
$33$	−0.0919688	+	0.283051i	−0.0160097	+	0.0492728i
$34$	−0.431776	+	0.313703i	−0.0740489	+	0.0537997i
$35$	0.418871	+	2.19649i	0.0708021	+	0.371274i
$36$	1.52859	+	1.11059i	0.254765	+	0.185098i
$37$	−9.77301	+	7.10051i	−1.60667	+	1.16732i	−0.733803	+	0.679362i	$0.762257\pi$
$37$	−9.77301	+	7.10051i	−1.60667	+	1.16732i	−0.872869	+	0.487954i	$0.837743\pi$
$38$	−0.187077	+	0.135919i	−0.0303478	+	0.0220490i
$39$	−0.725677	−	0.527236i	−0.116201	−	0.0844253i
$40$	−2.86899	−	0.362605i	−0.453627	−	0.0573330i
$41$	6.11269	−	4.44113i	0.954641	−	0.693587i	0.00274105	−	0.999996i	$-0.499127\pi$
$41$	6.11269	−	4.44113i	0.954641	−	0.693587i	0.951900	+	0.306409i	$0.0991275\pi$
$42$	−0.102750	+	0.316231i	−0.0158546	+	0.0487955i
$43$	7.36272			1.12280			0.561402	−	0.827543i	$-0.310262\pi$
$43$	7.36272			1.12280			0.561402	+	0.827543i	$0.310262\pi$
$44$	−0.173770	+	0.534808i	−0.0261968	+	0.0806253i
$45$	1.62994	+	1.53079i	0.242976	+	0.228196i
$46$	−0.0398451	−	0.122631i	−0.00587484	−	0.0180809i
$47$	−1.04098	−	3.20382i	−0.151843	−	0.467325i	0.845984	−	0.533208i	$-0.179014\pi$
$47$	−1.04098	−	3.20382i	−0.151843	−	0.467325i	−0.997827	+	0.0658827i	$0.979014\pi$
$48$	2.70929	+	1.96841i	0.391052	+	0.284116i
$49$	1.00000			0.142857
$50$	−1.61025	−	0.413639i	−0.227723	−	0.0584973i
$51$	1.60510			0.224759
$52$	−1.37112	−	0.996180i	−0.190141	−	0.138145i
$53$	−2.52816	−	7.78088i	−0.347270	−	1.06879i	−0.960358	−	0.278771i	$-0.910073\pi$
$53$	−2.52816	−	7.78088i	−0.347270	−	1.06879i	0.613088	−	0.790015i	$-0.289927\pi$
$54$	0.102750	+	0.316231i	0.0139825	+	0.0430336i
$55$	−0.283388	+	0.602139i	−0.0382120	+	0.0811925i
$56$	−0.399639	+	1.22996i	−0.0534040	+	0.164361i
$57$	0.695446			0.0921141
$58$	0.569670	−	1.75326i	0.0748013	−	0.230215i
$59$	8.59335	−	6.24344i	1.11876	−	0.812826i	0.134739	−	0.990881i	$-0.456981\pi$
$59$	8.59335	−	6.24344i	1.11876	−	0.812826i	0.984021	+	0.178055i	$0.0569805\pi$
$60$	3.07967	+	2.89233i	0.397583	+	0.373398i
$61$	−7.67713	−	5.57776i	−0.982955	−	0.714159i	−0.0245882	−	0.999698i	$-0.507827\pi$
$61$	−7.67713	−	5.57776i	−0.982955	−	0.714159i	−0.958367	+	0.285539i	$0.907827\pi$
$62$	0.793786	−	0.576720i	0.100811	−	0.0732434i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	4.42326	+	3.21369i	0.552907	+	0.401711i
$65$	−1.46203	−	1.37310i	−0.181343	−	0.170312i
$66$	−0.0800598	+	0.0581668i	−0.00985468	+	0.00715984i
$67$	0.840130	−	2.58565i	0.102638	−	0.315888i	−0.886531	−	0.462670i	$-0.846892\pi$
$67$	0.840130	−	2.58565i	0.102638	−	0.315888i	0.989169	+	0.146782i	$0.0468916\pi$
$68$	3.03274			0.367774
$69$	−0.119833	+	0.368808i	−0.0144262	+	0.0443993i
$70$	−0.316607	+	0.672725i	−0.0378418	+	0.0804060i
$71$	−2.01106	−	6.18940i	−0.238669	−	0.734547i	−0.996614	−	0.0822283i	$-0.973796\pi$
$71$	−2.01106	−	6.18940i	−0.238669	−	0.734547i	0.757945	−	0.652319i	$-0.226204\pi$
$72$	0.399639	+	1.22996i	0.0470979	+	0.144952i
$73$	10.1076	+	7.34362i	1.18301	+	0.859505i	0.992508	−	0.122182i	$-0.0389892\pi$
$73$	10.1076	+	7.34362i	1.18301	+	0.859505i	0.190500	+	0.981687i	$0.438989\pi$
$74$	−4.01670			−0.466932
$75$	3.18668	+	3.85293i	0.367966	+	0.444898i
$76$	1.31400			0.150727
$77$	0.240778	+	0.174935i	0.0274391	+	0.0199357i
$78$	−0.0921652	−	0.283655i	−0.0104357	−	0.0321176i
$79$	−1.55222	−	4.77724i	−0.174638	−	0.537481i	0.824978	−	0.565164i	$-0.191187\pi$
$79$	−1.55222	−	4.77724i	−0.174638	−	0.537481i	−0.999617	+	0.0276827i	$0.991187\pi$
$80$	5.45843	+	5.12640i	0.610271	+	0.573149i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.51231			0.277438
$83$	2.96394	−	9.12206i	0.325334	−	1.00128i	−0.645955	−	0.763376i	$-0.723541\pi$
$83$	2.96394	−	9.12206i	0.325334	−	1.00128i	0.971289	−	0.237901i	$-0.0764594\pi$
$84$	1.52859	−	1.11059i	0.166783	−	0.121175i
$85$	3.56079	+	0.450040i	0.386221	+	0.0488137i
$86$	1.98059	+	1.43898i	0.213572	+	0.155169i
$87$	−4.48539	+	3.25882i	−0.480884	+	0.349383i
$88$	−0.311388	+	0.226236i	−0.0331940	+	0.0241169i
$89$	−7.95249	−	5.77782i	−0.842962	−	0.612448i	0.0802346	−	0.996776i	$-0.474433\pi$
$89$	−7.95249	−	5.77782i	−0.842962	−	0.612448i	−0.923196	+	0.384328i	$0.874433\pi$
$90$	0.139277	+	0.730343i	0.0146811	+	0.0769849i
$91$	−0.725677	+	0.527236i	−0.0760717	+	0.0552693i
$92$	−0.226417	+	0.696841i	−0.0236057	+	0.0726507i
$93$	−2.95085			−0.305989
$94$	0.346133	−	1.06529i	0.0357009	−	0.109876i
$95$	1.54279	+	0.194990i	0.158287	+	0.0200055i
$96$	1.14337	+	3.51894i	0.116695	+	0.359150i
$97$	0.127712	+	0.393057i	0.0129672	+	0.0399088i	0.957331	−	0.288995i	$-0.0933209\pi$
$97$	0.127712	+	0.393057i	0.0129672	+	0.0399088i	−0.944364	+	0.328903i	$0.893321\pi$
$98$	0.269002	+	0.195442i	0.0271733	+	0.0197426i
$99$	0.297617			0.0299117
$100$	6.02104	+	7.27989i	0.602104	+	0.727989i
$101$	13.4179			1.33513			0.667563	−	0.744553i	$-0.267337\pi$
$101$	13.4179			1.33513			0.667563	+	0.744553i	$0.267337\pi$
$102$	0.431776	+	0.313703i	0.0427522	+	0.0310613i
$103$	6.11484	+	18.8195i	0.602513	+	1.85434i	0.513059	+	0.858353i	$0.328512\pi$
$103$	6.11484	+	18.8195i	0.602513	+	1.85434i	0.0894541	+	0.995991i	$0.471488\pi$
$104$	−0.358471	−	1.10326i	−0.0351510	−	0.108184i
$105$	1.95954	−	1.07712i	0.191232	−	0.105116i
$106$	0.840627	−	2.58718i	0.0816489	−	0.251289i
$107$	−5.66506			−0.547662			−0.273831	−	0.961778i	$-0.588291\pi$
$107$	−5.66506			−0.547662			−0.273831	+	0.961778i	$0.588291\pi$
$108$	0.583869	−	1.79696i	0.0561828	−	0.172913i
$109$	−0.554604	+	0.402943i	−0.0531214	+	0.0385950i	−0.614029	−	0.789283i	$-0.710452\pi$
$109$	−0.554604	+	0.402943i	−0.0531214	+	0.0385950i	0.560908	+	0.827878i	$0.310452\pi$
$110$	−0.193915	+	0.106591i	−0.0184891	+	0.0101631i
$111$	9.77301	+	7.10051i	0.927613	+	0.673950i
$112$	2.70929	−	1.96841i	0.256004	−	0.185998i
$113$	−5.30248	+	3.85248i	−0.498815	+	0.362410i	−0.808564	−	0.588408i	$-0.799755\pi$
$113$	−5.30248	+	3.85248i	−0.498815	+	0.362410i	0.309749	+	0.950818i	$0.399755\pi$
$114$	0.187077	+	0.135919i	0.0175213	+	0.0127300i
$115$	−0.369247	+	0.784573i	−0.0344325	+	0.0731618i
$116$	−8.47487	+	6.15735i	−0.786872	+	0.571696i
$117$	−0.277184	+	0.853085i	−0.0256257	+	0.0788677i
$118$	3.53186			0.325134
$119$	0.496003	−	1.52654i	0.0454685	−	0.139938i
$120$	0.541709	+	2.84062i	0.0494510	+	0.259312i
$121$	−3.37182	−	10.3774i	−0.306529	−	0.943398i
$122$	−0.975039	−	3.00086i	−0.0882759	−	0.271685i
$123$	−6.11269	−	4.44113i	−0.551162	−	0.400443i
$124$	−5.57546			−0.500691
$125$	5.98910	+	9.44091i	0.535681	+	0.844420i
$126$	0.332505			0.0296219
$127$	3.14259	+	2.28323i	0.278860	+	0.202604i	0.718420	−	0.695610i	$-0.244866\pi$
$127$	3.14259	+	2.28323i	0.278860	+	0.202604i	−0.439560	+	0.898213i	$0.644866\pi$
$128$	2.84853	+	8.76686i	0.251776	+	0.774888i
$129$	−2.27521	−	7.00236i	−0.200321	−	0.616524i
$130$	−0.124929	−	0.655108i	−0.0109570	−	0.0574568i
$131$	4.02249	−	12.3800i	0.351447	−	1.08164i	−0.606594	−	0.795012i	$-0.707465\pi$
$131$	4.02249	−	12.3800i	0.351447	−	1.08164i	0.958041	−	0.286631i	$-0.0925353\pi$
$132$	0.562330			0.0489446
$133$	0.214905	−	0.661409i	0.0186346	−	0.0573514i
$134$	0.731342	−	0.531351i	0.0631783	−	0.0459017i
$135$	0.952188	−	2.02320i	0.0819513	−	0.174129i
$136$	1.67937	+	1.22013i	0.144004	+	0.104625i
$137$	−8.94111	+	6.49610i	−0.763891	+	0.554999i	−0.900101	−	0.435681i	$-0.856508\pi$
$137$	−8.94111	+	6.49610i	−0.763891	+	0.554999i	0.136210	+	0.990680i	$0.456508\pi$
$138$	−0.104316	+	0.0757900i	−0.00887996	+	0.00645167i
$139$	3.00629	+	2.18420i	0.254990	+	0.185261i	0.707936	−	0.706277i	$-0.249627\pi$
$139$	3.00629	+	2.18420i	0.254990	+	0.185261i	−0.452945	+	0.891538i	$0.649627\pi$
$140$	3.70244	−	2.03516i	0.312913	−	0.172002i
$141$	−2.72533	+	1.98007i	−0.229514	+	0.166752i
$142$	0.668688	−	2.05801i	0.0561150	−	0.172704i
$143$	−0.266959			−0.0223242
$144$	1.03486	−	3.18496i	0.0862380	−	0.265413i
$145$	−10.8642	+	5.97182i	−0.902221	+	0.495933i
$146$	1.28373	+	3.95090i	0.106242	+	0.326979i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	18.4655	+	13.4160i	1.51786	+	1.10279i
$149$	6.93831			0.568409			0.284204	−	0.958764i	$-0.408271\pi$
$149$	6.93831			0.568409			0.284204	+	0.958764i	$0.408271\pi$
$150$	0.104200	+	1.65926i	0.00850791	+	0.135478i
$151$	−1.57556			−0.128217			−0.0641086	−	0.997943i	$-0.520420\pi$
$151$	−1.57556			−0.128217			−0.0641086	+	0.997943i	$0.520420\pi$
$152$	0.727624	+	0.528650i	0.0590181	+	0.0428791i
$153$	−0.496003	−	1.52654i	−0.0400995	−	0.123414i
$154$	0.0305801	+	0.0941159i	0.00246422	+	0.00758408i
$155$	−6.54623	−	0.827363i	−0.525806	−	0.0664554i
$156$	−0.523723	+	1.61185i	−0.0419314	+	0.129052i
$157$	1.63024			0.130107			0.0650536	−	0.997882i	$-0.479278\pi$
$157$	1.63024			0.130107			0.0650536	+	0.997882i	$0.479278\pi$
$158$	0.516121	−	1.58846i	0.0410604	−	0.126371i
$159$	−6.61881	+	4.80885i	−0.524906	+	0.381366i
$160$	1.54984	+	8.12707i	0.122525	+	0.642501i
$161$	0.313727	+	0.227936i	0.0247252	+	0.0179639i
$162$	0.269002	−	0.195442i	0.0211348	−	0.0153553i
$163$	7.12442	−	5.17619i	0.558027	−	0.405431i	−0.272709	−	0.962097i	$-0.587920\pi$
$163$	7.12442	−	5.17619i	0.558027	−	0.405431i	0.830736	+	0.556666i	$0.187920\pi$
$164$	−11.5496	−	8.39124i	−0.901869	−	0.655246i
$165$	0.660240	+	0.0834463i	0.0513996	+	0.00649628i
$166$	2.58014	−	1.87458i	0.200258	−	0.145496i
$167$	2.61474	−	8.04734i	0.202335	−	0.622722i	−0.797478	−	0.603348i	$-0.793833\pi$
$167$	2.61474	−	8.04734i	0.202335	−	0.622722i	0.999812	−	0.0193735i	$-0.00616716\pi$
$168$	1.29326			0.0997771
$169$	−3.76859	+	11.5985i	−0.289892	+	0.892195i
$170$	0.869904	+	0.816988i	0.0667186	+	0.0626601i
$171$	−0.214905	−	0.661409i	−0.0164342	−	0.0505792i
$172$	−4.29886	−	13.2305i	−0.327785	−	1.00882i
$173$	4.38570	+	3.18639i	0.333438	+	0.242257i	0.741888	−	0.670524i	$-0.233931\pi$
$173$	4.38570	+	3.18639i	0.333438	+	0.242257i	−0.408450	+	0.912781i	$0.633931\pi$
$174$	−1.84349			−0.139755
$175$	4.64909	−	1.84009i	0.351438	−	0.139098i
$176$	0.996680			0.0751276
$177$	−8.59335	−	6.24344i	−0.645916	−	0.469285i
$178$	−1.01001	−	3.10849i	−0.0757035	−	0.232992i
$179$	−5.26264	−	16.1967i	−0.393348	−	1.21060i	−0.930241	−	0.366950i	$-0.880402\pi$
$179$	−5.26264	−	16.1967i	−0.393348	−	1.21060i	0.536893	−	0.843650i	$-0.319598\pi$
$180$	1.79910	−	3.82272i	0.134097	−	0.284928i
$181$	5.55106	−	17.0844i	0.412607	−	1.26987i	−0.501767	−	0.865003i	$-0.667316\pi$
$181$	5.55106	−	17.0844i	0.412607	−	1.26987i	0.914374	−	0.404871i	$-0.132684\pi$
$182$	−0.298253			−0.0221080
$183$	−2.93240	+	9.02500i	−0.216769	+	0.667147i
$184$	−0.405731	+	0.294780i	−0.0299109	+	0.0217315i
$185$	19.6898	+	18.4921i	1.44762	+	1.35956i
$186$	−0.793786	−	0.576720i	−0.0582032	−	0.0422871i
$187$	0.386472	−	0.280788i	0.0282616	−	0.0205333i
$188$	−5.14935	+	3.74122i	−0.375555	+	0.272857i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	0.376905	+	0.353979i	0.0273436	+	0.0256803i
$191$	4.76382	−	3.46112i	0.344698	−	0.250438i	−0.401943	−	0.915665i	$-0.631665\pi$
$191$	4.76382	−	3.46112i	0.344698	−	0.250438i	0.746641	+	0.665227i	$0.231665\pi$
$192$	1.68953	−	5.19985i	0.121932	−	0.375267i
$193$	−7.77537			−0.559683			−0.279842	−	0.960046i	$-0.590282\pi$
$193$	−7.77537			−0.559683			−0.279842	+	0.960046i	$0.590282\pi$
$194$	−0.0424648	+	0.130693i	−0.00304880	+	0.00938324i
$195$	−0.854100	+	1.81478i	−0.0611634	+	0.129959i
$196$	−0.583869	−	1.79696i	−0.0417049	−	0.128355i
$197$	−0.00362465	−	0.0111555i	−0.000258246	−	0.000794799i	0.950927	−	0.309414i	$-0.100133\pi$
$197$	−0.00362465	−	0.0111555i	−0.000258246	−	0.000794799i	−0.951186	+	0.308620i	$0.900133\pi$
$198$	0.0800598	+	0.0581668i	0.00568960	+	0.00413374i
$199$	−4.31497			−0.305880			−0.152940	−	0.988235i	$-0.548874\pi$
$199$	−4.31497			−0.305880			−0.152940	+	0.988235i	$0.548874\pi$
$200$	0.405280	+	6.45358i	0.0286577	+	0.456337i
$201$	−2.71872			−0.191764
$202$	3.60943	+	2.62241i	0.253959	+	0.184512i
$203$	1.71326	+	5.27289i	0.120248	+	0.370084i
$204$	−0.937168	−	2.88431i	−0.0656149	−	0.201942i
$205$	−12.3153	−	11.5662i	−0.860137	−	0.807816i
$206$	−2.03322	+	6.25760i	−0.141661	+	0.435987i
$207$	0.387788			0.0269531
$208$	−0.928252	+	2.85687i	−0.0643627	+	0.198088i
$209$	0.167448	−	0.121658i	0.0115826	−	0.00841526i
$210$	0.737636	+	0.0932282i	0.0509017	+	0.00643336i
$211$	3.31349	+	2.40739i	0.228110	+	0.165732i	0.695970	−	0.718071i	$-0.254975\pi$
$211$	3.31349	+	2.40739i	0.228110	+	0.165732i	−0.467860	+	0.883803i	$0.654975\pi$
$212$	−12.5058	+	9.08603i	−0.858905	+	0.624031i
$213$	−5.26502	+	3.82526i	−0.360753	+	0.262103i
$214$	−1.52391	−	1.10719i	−0.104173	−	0.0756859i
$215$	−3.08403	−	16.1721i	−0.210329	−	1.10293i
$216$	1.04627	−	0.760159i	0.0711896	−	0.0517223i
$217$	−0.911863	+	2.80643i	−0.0619013	+	0.190513i
$218$	−0.227942			−0.0154382
$219$	3.86077	−	11.8822i	0.260886	−	0.802926i
$220$	1.24748	+	0.157667i	0.0841054	+	0.0106299i
$221$	0.444908	+	1.36929i	0.0299278	+	0.0921082i
$222$	1.24123	+	3.82011i	0.0833058	+	0.256389i
$223$	−3.69642	−	2.68561i	−0.247531	−	0.179842i	0.457101	−	0.889415i	$-0.348888\pi$
$223$	−3.69642	−	2.68561i	−0.247531	−	0.179842i	−0.704632	+	0.709573i	$0.748888\pi$
$224$	3.70003			0.247219
$225$	2.67962	−	4.22133i	0.178641	−	0.281422i
$226$	−2.17931			−0.144966
$227$	19.0901	+	13.8698i	1.26705	+	0.920568i	0.999081	−	0.0428582i	$-0.0136464\pi$
$227$	19.0901	+	13.8698i	1.26705	+	0.920568i	0.267973	+	0.963427i	$0.413646\pi$
$228$	−0.406050	−	1.24969i	−0.0268913	−	0.0827629i
$229$	0.374390	+	1.15225i	0.0247404	+	0.0761431i	0.962664	−	0.270698i	$-0.0872544\pi$
$229$	0.374390	+	1.15225i	0.0247404	+	0.0761431i	−0.937924	+	0.346841i	$0.887254\pi$
$230$	−0.252667	+	0.138886i	−0.0166603	+	0.00915785i
$231$	0.0919688	−	0.283051i	0.00605110	−	0.0186234i
$232$	−7.17014			−0.470743
$233$	4.43509	−	13.6498i	0.290552	−	0.894229i	−0.694127	−	0.719853i	$-0.744209\pi$
$233$	4.43509	−	13.6498i	0.290552	−	0.894229i	0.984679	−	0.174376i	$-0.0557907\pi$
$234$	−0.241292	+	0.175309i	−0.0157737	+	0.0114603i
$235$	−6.60111	+	3.62850i	−0.430609	+	0.236697i
$236$	−16.2366	−	11.7966i	−1.05691	−	0.767893i
$237$	−4.06376	+	2.95250i	−0.263970	+	0.191785i
$238$	0.431776	−	0.313703i	0.0279879	−	0.0203344i
$239$	4.27554	+	3.10636i	0.276562	+	0.200934i	0.717416	−	0.696645i	$-0.245325\pi$
$239$	4.27554	+	3.10636i	0.276562	+	0.200934i	−0.440855	+	0.897579i	$0.645325\pi$
$240$	3.18875	−	6.77542i	0.205833	−	0.437352i
$241$	−8.55292	+	6.21406i	−0.550942	+	0.400283i	−0.828133	−	0.560532i	$-0.810597\pi$
$241$	−8.55292	+	6.21406i	−0.550942	+	0.400283i	0.277191	+	0.960815i	$0.410597\pi$
$242$	1.12115	−	3.45053i	0.0720700	−	0.221809i
$243$	−1.00000			−0.0641500
$244$	−5.54060	+	17.0522i	−0.354700	+	1.09166i
$245$	−0.418871	−	2.19649i	−0.0267607	−	0.140328i
$246$	−0.776346	−	2.38935i	−0.0494980	−	0.152339i
$247$	0.192767	+	0.593275i	0.0122654	+	0.0377492i
$248$	−3.08738	−	2.24312i	−0.196049	−	0.142438i
$249$	−9.59151			−0.607837
$250$	−0.234065	+	3.71015i	−0.0148036	+	0.234650i
$251$	23.4125			1.47779			0.738894	−	0.673822i	$-0.235349\pi$
$251$	23.4125			1.47779			0.738894	+	0.673822i	$0.235349\pi$
$252$	−1.52859	−	1.11059i	−0.0962921	−	0.0699603i
$253$	0.0356644	+	0.109764i	0.00224220	+	0.00690079i
$254$	0.399127	+	1.22839i	0.0250435	+	0.0770759i
$255$	−0.672330	−	3.52558i	−0.0421029	−	0.220780i
$256$	2.43192	−	7.48468i	0.151995	−	0.467792i
$257$	−3.45400			−0.215455			−0.107727	−	0.994180i	$-0.534357\pi$
$257$	−3.45400			−0.215455			−0.107727	+	0.994180i	$0.534357\pi$
$258$	0.756518	−	2.32832i	0.0470987	−	0.144955i
$259$	9.77301	−	7.10051i	0.607265	−	0.441204i
$260$	−1.61377	+	3.42893i	−0.100082	+	0.212653i
$261$	4.48539	+	3.25882i	0.277638	+	0.201716i
$262$	3.50162	−	2.54408i	0.216331	−	0.157174i
$263$	−19.0390	+	13.8326i	−1.17399	+	0.852957i	−0.991482	−	0.130247i	$-0.958423\pi$
$263$	−19.0390	+	13.8326i	−1.17399	+	0.852957i	−0.182513	+	0.983203i	$0.558423\pi$
$264$	0.311388	+	0.226236i	0.0191646	+	0.0139239i
$265$	−16.0316	+	8.81225i	−0.984814	+	0.541332i
$266$	0.187077	−	0.135919i	0.0114704	−	0.00833374i
$267$	−3.03758	+	9.34871i	−0.185897	+	0.572132i
$268$	−5.13685			−0.313783
$269$	−6.32337	+	19.4613i	−0.385543	+	1.18658i	0.550543	+	0.834807i	$0.314421\pi$
$269$	−6.32337	+	19.4613i	−0.385543	+	1.18658i	−0.936086	+	0.351772i	$0.885579\pi$
$270$	0.651558	−	0.358149i	0.0396526	−	0.0217962i
$271$	−4.01967	−	12.3713i	−0.244177	−	0.751501i	−0.995771	−	0.0918740i	$-0.970714\pi$
$271$	−4.01967	−	12.3713i	−0.244177	−	0.751501i	0.751593	−	0.659627i	$-0.229286\pi$
$272$	−1.66105	−	5.11218i	−0.100716	−	0.309971i
$273$	0.725677	+	0.527236i	0.0439200	+	0.0319097i
$274$	−3.67479			−0.222002
$275$	1.44129	+	0.370238i	0.0869133	+	0.0223262i
$276$	0.732702			0.0441035
$277$	−23.7245	−	17.2368i	−1.42547	−	1.03566i	−0.990839	−	0.135050i	$-0.956880\pi$
$277$	−23.7245	−	17.2368i	−1.42547	−	1.03566i	−0.434626	−	0.900611i	$-0.643120\pi$
$278$	0.381816	+	1.17511i	0.0228998	+	0.0704783i
$279$	0.911863	+	2.80643i	0.0545918	+	0.168016i
$280$	2.86899	+	0.362605i	0.171455	+	0.0216698i
$281$	2.72771	−	8.39502i	0.162721	−	0.500805i	−0.836140	−	0.548516i	$-0.815193\pi$
$281$	2.72771	−	8.39502i	0.162721	−	0.500805i	0.998861	+	0.0477116i	$0.0151928\pi$
$282$	−1.12011			−0.0667015
$283$	7.17177	−	22.0724i	0.426317	−	1.31207i	−0.475410	−	0.879764i	$-0.657700\pi$
$283$	7.17177	−	22.0724i	0.426317	−	1.31207i	0.901727	−	0.432305i	$-0.142300\pi$
$284$	−9.94794	+	7.22760i	−0.590302	+	0.428879i
$285$	−0.291302	−	1.52754i	−0.0172553	−	0.0904835i
$286$	−0.0718126	−	0.0521749i	−0.00424637	−	0.00308517i
$287$	−6.11269	+	4.44113i	−0.360820	+	0.262151i
$288$	2.99339	−	2.17483i	0.176387	−	0.128153i
$289$	11.6690	+	8.47801i	0.686411	+	0.498707i
$290$	−4.08963	−	0.516880i	−0.240152	−	0.0303522i
$291$	0.334354	−	0.242922i	0.0196002	−	0.0142404i
$292$	7.29469	−	22.4507i	0.426889	−	1.31383i
$293$	−6.48549			−0.378886			−0.189443	−	0.981892i	$-0.560668\pi$
$293$	−6.48549			−0.378886			−0.189443	+	0.981892i	$0.560668\pi$
$294$	0.102750	−	0.316231i	0.00599249	−	0.0184430i
$295$	−17.3131	−	16.2600i	−1.00801	−	0.946692i
$296$	4.82768	+	14.8581i	0.280603	+	0.863608i
$297$	−0.0919688	−	0.283051i	−0.00533657	−	0.0164243i
$298$	1.86642	+	1.35604i	0.108119	+	0.0785530i
$299$	−0.347841			−0.0201161
$300$	5.06298	−	7.97595i	0.292311	−	0.460492i
$301$	−7.36272			−0.424380
$302$	−0.423829	−	0.307930i	−0.0243886	−	0.0177194i
$303$	−4.14634	−	12.7611i	−0.238201	−	0.733108i
$304$	−0.719687	−	2.21497i	−0.0412769	−	0.127037i
$305$	−9.03574	+	19.1991i	−0.517385	+	1.09933i
$306$	0.164924	−	0.507583i	0.00942806	−	0.0290166i
$307$	26.7751			1.52814			0.764069	−	0.645135i	$-0.223199\pi$
$307$	26.7751			1.52814			0.764069	+	0.645135i	$0.223199\pi$
$308$	0.173770	−	0.534808i	0.00990144	−	0.0304735i
$309$	16.0089	−	11.6311i	0.910712	−	0.661671i
$310$	−1.59925	−	1.50197i	−0.0908313	−	0.0853061i
$311$	−2.82300	−	2.05103i	−0.160077	−	0.116303i	0.504863	−	0.863200i	$-0.331543\pi$
$311$	−2.82300	−	2.05103i	−0.160077	−	0.116303i	−0.664940	+	0.746897i	$0.731543\pi$
$312$	−0.938489	+	0.681852i	−0.0531315	+	0.0386023i
$313$	−11.1213	+	8.08013i	−0.628616	+	0.456716i	−0.855920	−	0.517108i	$-0.827009\pi$
$313$	−11.1213	+	8.08013i	−0.628616	+	0.456716i	0.227305	+	0.973824i	$0.427009\pi$
$314$	0.438538	+	0.318617i	0.0247481	+	0.0179806i
$315$	−1.62994	−	1.53079i	−0.0918365	−	0.0862501i
$316$	−7.67824	+	5.57857i	−0.431935	+	0.313819i
$317$	−8.94470	+	27.5290i	−0.502385	+	1.54618i	0.302739	+	0.953073i	$0.402099\pi$
$317$	−8.94470	+	27.5290i	−0.502385	+	1.54618i	−0.805124	+	0.593107i	$0.797901\pi$
$318$	−2.72033			−0.152548
$319$	−0.509897	+	1.56930i	−0.0285488	+	0.0878641i
$320$	5.20604	−	11.0617i	0.291026	−	0.618370i
$321$	1.75060	+	5.38779i	0.0977090	+	0.300717i
$322$	0.0398451	+	0.122631i	0.00222048	+	0.00683394i
$323$	−0.903074	−	0.656122i	−0.0502484	−	0.0365076i
$324$	−1.88944			−0.104969
$325$	−2.40358	+	3.78648i	−0.133327	+	0.210036i
$326$	2.92813			0.162174
$327$	0.554604	+	0.402943i	0.0306697	+	0.0222828i
$328$	−3.01955	−	9.29322i	−0.166727	−	0.513132i
$329$	1.04098	+	3.20382i	0.0573913	+	0.176632i
$330$	0.161297	+	0.151486i	0.00887913	+	0.00833901i
$331$	7.42008	−	22.8367i	0.407844	−	1.25522i	−0.510652	−	0.859787i	$-0.670596\pi$
$331$	7.42008	−	22.8367i	0.407844	−	1.25522i	0.918497	−	0.395429i	$-0.129404\pi$
$332$	−18.1226			−0.994606
$333$	3.73296	−	11.4889i	0.204565	−	0.629586i
$334$	2.27616	−	1.65372i	0.124546	−	0.0904878i
$335$	−6.03126	−	0.762277i	−0.329523	−	0.0416476i
$336$	−2.70929	−	1.96841i	−0.147804	−	0.107386i
$337$	−0.696584	+	0.506098i	−0.0379453	+	0.0275689i	−0.606596	−	0.795010i	$-0.707466\pi$
$337$	−0.696584	+	0.506098i	−0.0379453	+	0.0275689i	0.568651	+	0.822579i	$0.307466\pi$
$338$	−3.28060	+	2.38349i	−0.178441	+	0.129645i
$339$	5.30248	+	3.85248i	0.287991	+	0.209238i
$340$	−1.27033	−	6.66137i	−0.0688932	−	0.361264i
$341$	−0.710499	+	0.516208i	−0.0384757	+	0.0279542i
$342$	0.0714569	−	0.219922i	0.00386395	−	0.0118920i
$343$	−1.00000			−0.0539949
$344$	2.94243	−	9.05587i	0.158645	−	0.488260i
$345$	0.860277	+	0.108728i	0.0463157	+	0.00585374i
$346$	0.557008	+	1.71430i	0.0299450	+	0.0921611i
$347$	7.13573	+	21.9615i	0.383066	+	1.17896i	0.937873	+	0.346978i	$0.112792\pi$
$347$	7.13573	+	21.9615i	0.383066	+	1.17896i	−0.554807	+	0.831979i	$0.687208\pi$
$348$	8.47487	+	6.15735i	0.454301	+	0.330069i
$349$	−31.0155			−1.66022			−0.830112	−	0.557596i	$-0.811724\pi$
$349$	−31.0155			−1.66022			−0.830112	+	0.557596i	$0.811724\pi$
$350$	1.61025	+	0.413639i	0.0860713	+	0.0221099i
$351$	0.896987			0.0478776
$352$	0.890885	+	0.647266i	0.0474843	+	0.0344994i
$353$	2.91933	+	8.98478i	0.155380	+	0.478212i	0.998199	−	0.0599857i	$-0.0191055\pi$
$353$	2.91933	+	8.98478i	0.155380	+	0.478212i	−0.842819	+	0.538197i	$0.819106\pi$
$354$	−1.09140	−	3.35900i	−0.0580075	−	0.178529i
$355$	−12.7526	+	7.00982i	−0.676836	+	0.372043i
$356$	−5.73932	+	17.6638i	−0.304184	+	0.936181i
$357$	−1.60510			−0.0849509
$358$	1.74985	−	5.38550i	0.0924827	−	0.284632i
$359$	13.0691	−	9.49525i	0.689760	−	0.501140i	−0.186821	−	0.982394i	$-0.559819\pi$
$359$	13.0691	−	9.49525i	0.689760	−	0.501140i	0.876581	+	0.481254i	$0.159819\pi$
$360$	2.53420	−	1.39300i	0.133564	−	0.0734174i
$361$	14.9800	+	10.8836i	0.788423	+	0.572823i
$362$	4.83225	−	3.51084i	0.253978	−	0.184526i
$363$	−8.82753	+	6.41357i	−0.463325	+	0.336625i
$364$	1.37112	+	0.996180i	0.0718664	+	0.0522140i
$365$	11.8964	−	25.2773i	0.622683	−	1.32307i
$366$	−2.55269	+	1.85463i	−0.133431	+	0.0969433i
$367$	3.36722	−	10.3632i	0.175767	−	0.540957i	−0.823900	−	0.566735i	$-0.808206\pi$
$367$	3.36722	−	10.3632i	0.175767	−	0.540957i	0.999668	+	0.0257782i	$0.00820637\pi$
$368$	1.29865			0.0676968
$369$	−2.33484	+	7.18589i	−0.121547	+	0.374083i
$370$	1.68248	+	8.82262i	0.0874679	+	0.458666i
$371$	2.52816	+	7.78088i	0.131256	+	0.403963i
$372$	1.72291	+	5.30258i	0.0893288	+	0.274926i
$373$	16.0834	+	11.6853i	0.832768	+	0.605041i	0.920341	−	0.391117i	$-0.127911\pi$
$373$	16.0834	+	11.6853i	0.832768	+	0.605041i	−0.0875733	+	0.996158i	$0.527911\pi$
$374$	0.158840			0.00821340
$375$	7.12810	−	8.61337i	0.368094	−	0.444793i
$376$	−4.35660			−0.224674
$377$	−4.02333	−	2.92312i	−0.207212	−	0.150548i
$378$	−0.102750	−	0.316231i	−0.00528488	−	0.0162652i
$379$	6.83969	+	21.0504i	0.351331	+	1.08129i	0.958106	+	0.286413i	$0.0924629\pi$
$379$	6.83969	+	21.0504i	0.351331	+	1.08129i	−0.606775	+	0.794874i	$0.707537\pi$
$380$	−0.550398	−	2.88619i	−0.0282348	−	0.148058i
$381$	1.20036	−	3.69434i	0.0614965	−	0.189267i
$382$	1.95793			0.100176
$383$	5.61520	−	17.2818i	0.286923	−	0.883059i	−0.698892	−	0.715227i	$-0.746323\pi$
$383$	5.61520	−	17.2818i	0.286923	−	0.883059i	0.985816	−	0.167832i	$-0.0536766\pi$
$384$	7.45754	−	5.41822i	0.380566	−	0.276497i
$385$	0.283388	−	0.602139i	0.0144428	−	0.0306879i
$386$	−2.09159	−	1.51963i	−0.106459	−	0.0773472i
$387$	−5.95657	+	4.32770i	−0.302789	+	0.219989i
$388$	0.631742	−	0.458987i	0.0320718	−	0.0233015i
$389$	19.6166	+	14.2523i	0.994603	+	0.722621i	0.960924	−	0.276811i	$-0.0892777\pi$
$389$	19.6166	+	14.2523i	0.994603	+	0.722621i	0.0336787	+	0.999433i	$0.489278\pi$
$390$	−0.584439	+	0.321254i	−0.0295942	+	0.0162674i
$391$	0.503563	−	0.365860i	0.0254663	−	0.0185024i
$392$	0.399639	−	1.22996i	0.0201848	−	0.0621225i
$393$	−13.0171			−0.656624
$394$	0.00120522	−	0.00370927i	6.07179e−5	−	0.000186871i
$395$	−9.84296	+	5.41047i	−0.495253	+	0.272230i
$396$	−0.173770	−	0.534808i	−0.00873225	−	0.0268751i
$397$	6.60905	+	20.3405i	0.331698	+	1.02086i	0.968326	+	0.249691i	$0.0803291\pi$
$397$	6.60905	+	20.3405i	0.331698	+	1.02086i	−0.636627	+	0.771172i	$0.719671\pi$
$398$	−1.16074	−	0.843325i	−0.0581825	−	0.0422721i
$399$	−0.695446			−0.0348159
$400$	8.97368	−	14.1367i	0.448684	−	0.706833i
$401$	−26.6770			−1.33219			−0.666093	−	0.745869i	$-0.732035\pi$
$401$	−26.6770			−1.33219			−0.666093	+	0.745869i	$0.732035\pi$
$402$	−0.731342	−	0.531351i	−0.0364760	−	0.0265014i
$403$	−0.817929	−	2.51733i	−0.0407440	−	0.125397i
$404$	−7.83427	−	24.1114i	−0.389770	−	1.19959i
$405$	−2.21842	−	0.280381i	−0.110234	−	0.0139322i
$406$	−0.569670	+	1.75326i	−0.0282722	+	0.0870130i
$407$	3.59525			0.178210
$408$	0.641461	−	1.97421i	0.0317570	−	0.0977381i
$409$	−15.6119	+	11.3427i	−0.771957	+	0.560860i	−0.902555	−	0.430576i	$-0.858311\pi$
$409$	−15.6119	+	11.3427i	−0.771957	+	0.560860i	0.130597	+	0.991436i	$0.458311\pi$
$410$	−1.05233	−	5.51825i	−0.0519710	−	0.272527i
$411$	8.94111	+	6.49610i	0.441033	+	0.320429i
$412$	30.2478	−	21.9763i	1.49020	−	1.08269i
$413$	−8.59335	+	6.24344i	−0.422851	+	0.307219i
$414$	0.104316	+	0.0757900i	0.00512685	+	0.00372487i
$415$	−21.2780	−	2.68928i	−1.04450	−	0.132011i
$416$	−2.68503	+	1.95079i	−0.131644	+	0.0956453i
$417$	1.14830	−	3.53411i	0.0562325	−	0.173066i
$418$	0.0688209			0.00336614
$419$	−8.37803	+	25.7849i	−0.409294	+	1.25968i	0.507963	+	0.861379i	$0.330399\pi$
$419$	−8.37803	+	25.7849i	−0.409294	+	1.25968i	−0.917256	+	0.398297i	$0.869601\pi$
$420$	−3.07967	−	2.89233i	−0.150272	−	0.141131i
$421$	−4.55275	−	14.0119i	−0.221888	−	0.682900i	−0.998593	−	0.0530352i	$-0.983110\pi$
$421$	−4.55275	−	14.0119i	−0.221888	−	0.682900i	0.776705	−	0.629864i	$-0.216890\pi$
$422$	0.420832	+	1.29519i	0.0204858	+	0.0630487i
$423$	2.72533	+	1.98007i	0.132510	+	0.0962743i
$424$	−10.5805			−0.513837
$425$	−0.503005	−	8.00972i	−0.0243993	−	0.388529i
$426$	−2.16392			−0.104842
$427$	7.67713	+	5.57776i	0.371522	+	0.269927i
$428$	3.30765	+	10.1799i	0.159881	+	0.492065i
$429$	0.0824948	+	0.253893i	0.00398289	+	0.0122581i
$430$	2.33109	−	4.95308i	0.112415	−	0.238859i
$431$	−12.7322	+	39.1857i	−0.613289	+	1.88751i	−0.189025	+	0.981972i	$0.560533\pi$
$431$	−12.7322	+	39.1857i	−0.613289	+	1.88751i	−0.424265	+	0.905538i	$0.639467\pi$
$432$	−3.34886			−0.161122
$433$	7.33108	−	22.5627i	0.352309	−	1.08430i	−0.605244	−	0.796040i	$-0.706925\pi$
$433$	7.33108	−	22.5627i	0.352309	−	1.08430i	0.957553	−	0.288256i	$-0.0930755\pi$
$434$	−0.793786	+	0.576720i	−0.0381030	+	0.0276834i
$435$	9.03676	+	8.48706i	0.433279	+	0.406923i
$436$	1.04789	+	0.761338i	0.0501849	+	0.0364615i
$437$	0.218180	−	0.158517i	0.0104370	−	0.00758291i
$438$	3.36084	−	2.44179i	0.160587	−	0.116673i
$439$	29.3678	+	21.3370i	1.40165	+	1.01836i	0.994471	+	0.105010i	$0.0334876\pi$
$439$	29.3678	+	21.3370i	1.40165	+	1.01836i	0.407179	+	0.913348i	$0.366512\pi$
$440$	0.627356	+	0.589195i	0.0299080	+	0.0280888i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	−0.147934	+	0.455295i	−0.00703652	+	0.0216562i
$443$	−6.16378			−0.292850			−0.146425	−	0.989222i	$-0.546777\pi$
$443$	−6.16378			−0.292850			−0.146425	+	0.989222i	$0.546777\pi$
$444$	7.05320	−	21.7075i	0.334730	−	1.03019i
$445$	−9.35983	+	19.8877i	−0.443698	+	0.942766i
$446$	−0.469467	−	1.44487i	−0.0222299	−	0.0684166i
$447$	−2.14406	−	6.59873i	−0.101410	−	0.312109i
$448$	−4.42326	−	3.21369i	−0.208979	−	0.151832i
$449$	36.6453			1.72940			0.864698	−	0.502292i	$-0.167510\pi$
$449$	36.6453			1.72940			0.864698	+	0.502292i	$0.167510\pi$
$450$	1.54585	−	0.611839i	0.0728720	−	0.0288424i
$451$	−2.24871			−0.105887
$452$	10.0187	+	7.27902i	0.471241	+	0.342376i
$453$	0.486874	+	1.49844i	0.0228753	+	0.0704031i
$454$	2.42455	+	7.46200i	0.113790	+	0.350209i
$455$	1.46203	+	1.37310i	0.0685410	+	0.0643717i
$456$	0.277927	−	0.855373i	0.0130151	−	0.0400565i
$457$	12.5928			0.589065			0.294533	−	0.955641i	$-0.404836\pi$
$457$	12.5928			0.589065			0.294533	+	0.955641i	$0.404836\pi$
$458$	−0.124487	+	0.383131i	−0.00581688	+	0.0179025i
$459$	−1.29855	+	0.943454i	−0.0606113	+	0.0440367i
$460$	1.62544	+	0.205436i	0.0757866	+	0.00957850i
$461$	22.7786	+	16.5496i	1.06090	+	0.770791i	0.974255	−	0.225448i	$-0.0723845\pi$
$461$	22.7786	+	16.5496i	1.06090	+	0.770791i	0.0866478	+	0.996239i	$0.472385\pi$
$462$	0.0800598	−	0.0581668i	0.00372472	−	0.00270617i
$463$	8.70366	−	6.32358i	0.404494	−	0.293882i	−0.366875	−	0.930270i	$-0.619572\pi$
$463$	8.70366	−	6.32358i	0.404494	−	0.293882i	0.771369	+	0.636388i	$0.219572\pi$
$464$	15.0210	+	10.9134i	0.697330	+	0.506640i
$465$	1.23603	+	6.48150i	0.0573194	+	0.300572i
$466$	3.86079	−	2.80503i	0.178848	−	0.129940i
$467$	−2.56607	+	7.89756i	−0.118744	+	0.365456i	−0.992709	−	0.120532i	$-0.961540\pi$
$467$	−2.56607	+	7.89756i	−0.118744	+	0.365456i	0.873966	+	0.485988i	$0.161540\pi$
$468$	1.69480			0.0783423
$469$	−0.840130	+	2.58565i	−0.0387936	+	0.119394i
$470$	−2.48487	−	0.314058i	−0.114619	−	0.0144864i
$471$	−0.503772	−	1.55045i	−0.0232126	−	0.0714409i
$472$	−4.24495	−	13.0646i	−0.195390	−	0.601348i
$473$	−1.77278	−	1.28800i	−0.0815124	−	0.0592222i
$474$	−1.67020			−0.0767150
$475$	−0.217938	−	3.47039i	−0.00999969	−	0.159233i
$476$	−3.03274			−0.139005
$477$	6.61881	+	4.80885i	0.303055	+	0.220182i
$478$	0.543018	+	1.67124i	0.0248371	+	0.0764407i
$479$	−1.84591	−	5.68114i	−0.0843419	−	0.259578i	0.899988	−	0.435915i	$-0.143575\pi$
$479$	−1.84591	−	5.68114i	−0.0843419	−	0.259578i	−0.984330	+	0.176337i	$0.943575\pi$
$480$	7.25038	−	3.98539i	0.330933	−	0.181907i
$481$	−3.34841	+	10.3054i	−0.152674	+	0.469884i
$482$	−3.51524			−0.160115
$483$	0.119833	−	0.368808i	0.00545259	−	0.0167814i
$484$	−16.6791	+	12.1181i	−0.758140	+	0.550821i
$485$	0.809848	−	0.445157i	0.0367733	−	0.0202135i
$486$	−0.269002	−	0.195442i	−0.0122022	−	0.00886542i
$487$	26.7916	−	19.4652i	1.21404	−	0.882053i	0.218450	−	0.975848i	$-0.429900\pi$
$487$	26.7916	−	19.4652i	1.21404	−	0.882053i	0.995591	+	0.0937954i	$0.0299000\pi$
$488$	−9.92852	+	7.21349i	−0.449443	+	0.326539i
$489$	−7.12442	−	5.17619i	−0.322177	−	0.234076i
$490$	0.316607	−	0.672725i	0.0143029	−	0.0303906i
$491$	−7.10913	+	5.16509i	−0.320831	+	0.233097i	−0.736530	−	0.676405i	$-0.763537\pi$
$491$	−7.10913	+	5.16509i	−0.320831	+	0.233097i	0.415699	+	0.909502i	$0.363537\pi$
$492$	−4.41154	+	13.5773i	−0.198887	+	0.612113i
$493$	8.89906			0.400794
$494$	−0.0640959	+	0.197267i	−0.00288381	+	0.00887546i
$495$	−0.124663	−	0.653712i	−0.00560320	−	0.0293822i
$496$	3.05371	+	9.39835i	0.137116	+	0.421998i
$497$	2.01106	+	6.18940i	0.0902083	+	0.277633i
$498$	−2.58014	−	1.87458i	−0.115619	−	0.0840019i
$499$	24.4923			1.09643			0.548214	−	0.836338i	$-0.315308\pi$
$499$	24.4923			1.09643			0.548214	+	0.836338i	$0.315308\pi$
$500$	13.4681	−	16.2745i	0.602313	−	0.727816i
$501$	−8.46147			−0.378031
$502$	6.29803	+	4.57579i	0.281095	+	0.204227i
$503$	−13.3291	−	41.0227i	−0.594315	−	1.82911i	−0.558107	−	0.829769i	$-0.688472\pi$
$503$	−13.3291	−	41.0227i	−0.594315	−	1.82911i	−0.0362083	−	0.999344i	$-0.511528\pi$
$504$	−0.399639	−	1.22996i	−0.0178013	−	0.0547869i
$505$	−5.62035	−	29.4721i	−0.250102	−	1.31149i
$506$	−0.0118586	+	0.0364970i	−0.000527179	+	0.00162249i
$507$	12.1954			0.541617
$508$	2.26802	−	6.98024i	0.100627	−	0.309698i
$509$	9.11298	−	6.62097i	0.403926	−	0.293469i	−0.367212	−	0.930137i	$-0.619688\pi$
$509$	9.11298	−	6.62097i	0.403926	−	0.293469i	0.771138	+	0.636668i	$0.219688\pi$
$510$	0.508187	−	1.07979i	0.0225029	−	0.0478139i
$511$	−10.1076	−	7.34362i	−0.447135	−	0.324862i
$512$	17.0321	−	12.3745i	0.752719	−	0.546882i
$513$	−0.562628	+	0.408773i	−0.0248406	+	0.0180478i
$514$	−0.929135	−	0.675056i	−0.0409824	−	0.0297754i
$515$	38.7755	−	21.3141i	1.70865	−	0.939212i
$516$	−11.2546	+	8.17693i	−0.495455	+	0.359969i
$517$	−0.309815	+	0.953513i	−0.0136257	+	0.0419354i
$518$	4.01670			0.176484
$519$	1.67519	−	5.15569i	0.0735325	−	0.226310i
$520$	−2.27314	+	1.24950i	−0.0996839	+	0.0547942i
$521$	3.36735	+	10.3636i	0.147526	+	0.454039i	0.997327	−	0.0730648i	$-0.0232780\pi$
$521$	3.36735	+	10.3636i	0.147526	+	0.454039i	−0.849801	+	0.527104i	$0.823278\pi$
$522$	0.569670	+	1.75326i	0.0249338	+	0.0767382i
$523$	25.6010	+	18.6002i	1.11945	+	0.813331i	0.984126	−	0.177469i	$-0.0567911\pi$
$523$	25.6010	+	18.6002i	1.11945	+	0.813331i	0.135328	+	0.990801i	$0.456791\pi$
$524$	−24.5950			−1.07444
$525$	−3.18668	−	3.85293i	−0.139078	−	0.168156i
$526$	−7.82501			−0.341187
$527$	3.83184	+	2.78399i	0.166918	+	0.121273i
$528$	−0.307991	−	0.947899i	−0.0134036	−	0.0412520i
$529$	−7.06092	−	21.7313i	−0.306997	−	0.944838i
$530$	−6.03482	−	0.762728i	−0.262136	−	0.0331308i
$531$	−3.28237	+	10.1021i	−0.142443	+	0.438393i
$532$	−1.31400			−0.0569693
$533$	2.09432	−	6.44565i	0.0907150	−	0.279192i
$534$	−2.64424	+	1.92116i	−0.114428	+	0.0831365i
$535$	2.37293	+	12.4432i	0.102591	+	0.537967i
$536$	−2.84451	−	2.06666i	−0.122864	−	0.0892660i
$537$	−13.7778	+	10.0101i	−0.594554	+	0.431969i
$538$	−5.50456	+	3.99930i	−0.237318	+	0.172422i
$539$	−0.240778	−	0.174935i	−0.0103710	−	0.00753499i
$540$	−4.19157	−	0.529763i	−0.180377	−	0.0227974i
$541$	−4.85115	+	3.52457i	−0.208567	+	0.151533i	−0.687165	−	0.726501i	$-0.741145\pi$
$541$	−4.85115	+	3.52457i	−0.208567	+	0.151533i	0.478598	+	0.878034i	$0.341145\pi$
$542$	1.33656	−	4.11351i	0.0574102	−	0.176690i
$543$	−17.9636			−0.770892
$544$	1.83523	−	5.64825i	0.0786848	−	0.242167i
$545$	1.11737	+	1.04940i	0.0478627	+	0.0449513i
$546$	0.0921652	+	0.283655i	0.00394431	+	0.0121393i
$547$	1.02995	+	3.16986i	0.0440374	+	0.135533i	0.970658	−	0.240465i	$-0.0772999\pi$
$547$	1.02995	+	3.16986i	0.0440374	+	0.135533i	−0.926620	+	0.375998i	$0.877300\pi$
$548$	16.8937	+	12.2740i	0.721663	+	0.524319i
$549$	9.48945			0.405000
$550$	0.315351	+	0.381284i	0.0134466	+	0.0162580i
$551$	3.85572			0.164259
$552$	0.405731	+	0.294780i	0.0172690	+	0.0125467i
$553$	1.55222	+	4.77724i	0.0660071	+	0.203149i
$554$	−3.01314	−	9.27350i	−0.128016	−	0.393993i
$555$	11.5025	−	24.4405i	0.488255	−	1.03744i
$556$	2.16965	−	6.67748i	0.0920135	−	0.283188i
$557$	34.7824			1.47378			0.736889	−	0.676014i	$-0.236294\pi$
$557$	34.7824			1.47378			0.736889	+	0.676014i	$0.236294\pi$
$558$	−0.303199	+	0.933152i	−0.0128355	+	0.0395035i
$559$	5.34296	−	3.88189i	0.225983	−	0.164186i
$560$	−5.45843	−	5.12640i	−0.230661	−	0.216630i
$561$	−0.386472	−	0.280788i	−0.0163169	−	0.0118549i
$562$	2.37450	−	1.72517i	0.100162	−	0.0727720i
$563$	−16.8742	+	12.2598i	−0.711162	+	0.516689i	−0.883548	−	0.468340i	$-0.844852\pi$
$563$	−16.8742	+	12.2598i	−0.711162	+	0.516689i	0.172386	+	0.985029i	$0.444852\pi$
$564$	5.14935	+	3.74122i	0.216827	+	0.157534i
$565$	10.6830	+	10.0331i	0.449435	+	0.422097i
$566$	6.24310	−	4.53587i	0.262417	−	0.190657i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	−8.41643			−0.353146
$569$	−9.47397	+	29.1579i	−0.397169	+	1.22236i	0.530090	+	0.847942i	$0.322158\pi$
$569$	−9.47397	+	29.1579i	−0.397169	+	1.22236i	−0.927259	+	0.374420i	$0.877842\pi$
$570$	0.220183	−	0.467844i	0.00922247	−	0.0195958i
$571$	7.67700	+	23.6274i	0.321273	+	0.988775i	0.973095	+	0.230404i	$0.0740047\pi$
$571$	7.67700	+	23.6274i	0.321273	+	0.988775i	−0.651823	+	0.758371i	$0.725995\pi$
$572$	0.155869	+	0.479716i	0.00651721	+	0.0200579i
$573$	−4.76382	−	3.46112i	−0.199012	−	0.144590i
$574$	−2.51231			−0.104862
$575$	1.87797	+	0.482411i	0.0783167	+	0.0201179i
$576$	−5.46745			−0.227810
$577$	11.9152	+	8.65687i	0.496035	+	0.360390i	0.807500	−	0.589867i	$-0.200820\pi$
$577$	11.9152	+	8.65687i	0.496035	+	0.360390i	−0.311466	+	0.950257i	$0.600820\pi$
$578$	1.48203	+	4.56121i	0.0616442	+	0.189721i
$579$	2.40272	+	7.39481i	0.0998536	+	0.307318i
$580$	17.0744	+	16.0358i	0.708976	+	0.665850i
$581$	−2.96394	+	9.12206i	−0.122965	+	0.378447i
$582$	0.137419			0.00569621
$583$	−0.752425	+	2.31572i	−0.0311622	+	0.0959075i
$584$	13.0718	−	9.49720i	0.540914	−	0.392997i
$585$	1.98989	+	0.251498i	0.0822720	+	0.0103982i
$586$	−1.74461	−	1.26753i	−0.0720692	−	0.0523614i
$587$	33.5597	−	24.3825i	1.38516	−	1.00637i	0.388778	−	0.921331i	$-0.372897\pi$
$587$	33.5597	−	24.3825i	1.38516	−	1.00637i	0.996377	−	0.0850427i	$-0.0271027\pi$
$588$	−1.52859	+	1.11059i	−0.0630380	+	0.0457998i
$589$	1.66023	+	1.20623i	0.0684086	+	0.0497018i
$590$	−1.47939	−	7.75768i	−0.0609057	−	0.319379i
$591$	−0.00948946	+	0.00689450i	−0.000390344	+	0.000283602i
$592$	12.5012	−	38.4746i	0.513795	−	1.58130i
$593$	−8.17093			−0.335540			−0.167770	−	0.985826i	$-0.553657\pi$
$593$	−8.17093			−0.335540			−0.167770	+	0.985826i	$0.553657\pi$
$594$	0.0305801	−	0.0941159i	0.00125472	−	0.00386162i
$595$	−3.56079	−	0.450040i	−0.145978	−	0.0184498i
$596$	−4.05107	−	12.4679i	−0.165938	−	0.510705i
$597$	1.33340	+	4.10378i	0.0545724	+	0.167957i
$598$	−0.0935700	−	0.0679826i	−0.00382636	−	0.00278001i
$599$	12.8995			0.527059			0.263529	−	0.964651i	$-0.415113\pi$
$599$	12.8995			0.527059			0.263529	+	0.964651i	$0.415113\pi$
$600$	6.01248	−	2.37971i	0.245459	−	0.0971513i
$601$	−19.7750			−0.806639			−0.403320	−	0.915059i	$-0.632144\pi$
$601$	−19.7750			−0.806639			−0.403320	+	0.915059i	$0.632144\pi$
$602$	−1.98059	−	1.43898i	−0.0807228	−	0.0586485i
$603$	0.840130	+	2.58565i	0.0342127	+	0.105296i
$604$	0.919920	+	2.83122i	0.0374310	+	0.115201i
$605$	−21.3814	+	11.7529i	−0.869278	+	0.477824i
$606$	1.37868	−	4.24315i	0.0560051	−	0.172366i
$607$	13.3412			0.541501			0.270750	−	0.962650i	$-0.412728\pi$
$607$	13.3412			0.541501			0.270750	+	0.962650i	$0.412728\pi$
$608$	0.795155	−	2.44723i	0.0322478	−	0.0992485i
$609$	4.48539	−	3.25882i	0.181757	−	0.132054i
$610$	−6.18293	+	3.39863i	−0.250340	+	0.137607i
$611$	−2.44459	−	1.77610i	−0.0988974	−	0.0718532i
$612$	−2.45354	+	1.78260i	−0.0991784	+	0.0720574i
$613$	−7.55891	+	5.49187i	−0.305302	+	0.221815i	−0.729878	−	0.683578i	$-0.760423\pi$
$613$	−7.55891	+	5.49187i	−0.305302	+	0.221815i	0.424576	+	0.905392i	$0.360423\pi$
$614$	7.20258	+	5.23298i	0.290672	+	0.211186i
$615$	−7.19444	+	15.2867i	−0.290108	+	0.616418i
$616$	0.311388	−	0.226236i	0.0125462	−	0.00911533i
$617$	−10.0262	+	30.8575i	−0.403640	+	1.24228i	0.518385	+	0.855147i	$0.326533\pi$
$617$	−10.0262	+	30.8575i	−0.403640	+	1.24228i	−0.922025	+	0.387130i	$0.873467\pi$
$618$	6.57963			0.264671
$619$	−7.46869	+	22.9863i	−0.300192	+	0.923895i	0.681236	+	0.732064i	$0.261443\pi$
$619$	−7.46869	+	22.9863i	−0.300192	+	0.923895i	−0.981428	+	0.191832i	$0.938557\pi$
$620$	2.33540	+	12.2464i	0.0937919	+	0.491828i
$621$	−0.119833	−	0.368808i	−0.00480874	−	0.0147998i
$622$	−0.358537	−	1.10346i	−0.0143760	−	0.0442448i
$623$	7.95249	+	5.77782i	0.318610	+	0.231483i
$624$	3.00389			0.120252
$625$	18.2281	−	17.1095i	0.729126	−	0.684380i
$626$	−4.57086			−0.182688
$627$	−0.167448	−	0.121658i	−0.00668722	−	0.00485855i
$628$	−0.951846	−	2.92948i	−0.0379828	−	0.116899i
$629$	−5.99177	−	18.4408i	−0.238908	−	0.735282i
$630$	−0.139277	−	0.730343i	−0.00554892	−	0.0290976i
$631$	−13.2902	+	40.9030i	−0.529074	+	1.62832i	0.227044	+	0.973885i	$0.427094\pi$
$631$	−13.2902	+	40.9030i	−0.529074	+	1.62832i	−0.756117	+	0.654436i	$0.772906\pi$
$632$	−6.49615			−0.258403
$633$	1.26564	−	3.89524i	0.0503047	−	0.154822i
$634$	−7.78645	+	5.65719i	−0.309240	+	0.224676i
$635$	3.69873	−	7.85904i	0.146780	−	0.311876i
$636$	12.5058	+	9.08603i	0.495889	+	0.360285i
$637$	0.725677	−	0.527236i	0.0287524	−	0.0208898i
$638$	−0.443871	+	0.322491i	−0.0175730	+	0.0127675i
$639$	5.26502	+	3.82526i	0.208281	+	0.151325i
$640$	18.0631	−	9.92893i	0.714007	−	0.392475i
$641$	32.1665	−	23.3703i	1.27050	−	0.923073i	0.271278	−	0.962501i	$-0.412554\pi$
$641$	32.1665	−	23.3703i	1.27050	−	0.923073i	0.999222	+	0.0394284i	$0.0125537\pi$
$642$	−0.582084	+	1.79147i	−0.0229730	+	0.0707037i
$643$	−49.7339			−1.96131			−0.980657	−	0.195736i	$-0.937290\pi$
$643$	−49.7339			−1.96131			−0.980657	+	0.195736i	$0.937290\pi$
$644$	0.226417	−	0.696841i	0.00892210	−	0.0274594i
$645$	−14.4276	+	7.93054i	−0.568085	+	0.312265i
$646$	−0.114696	−	0.352997i	−0.00451264	−	0.0138885i
$647$	−8.62890	−	26.5570i	−0.339237	−	1.04406i	−0.964597	−	0.263728i	$-0.915048\pi$
$647$	−8.62890	−	26.5570i	−0.339237	−	1.04406i	0.625360	−	0.780337i	$-0.284952\pi$
$648$	−1.04627	−	0.760159i	−0.0411013	−	0.0298619i
$649$	−3.16128			−0.124091
$650$	−1.38661	+	0.548812i	−0.0543871	+	0.0215262i
$651$	2.95085			0.115653
$652$	−13.4612	−	9.78011i	−0.527180	−	0.383019i
$653$	3.51349	+	10.8134i	0.137494	+	0.423162i	0.995970	−	0.0896920i	$-0.0285883\pi$
$653$	3.51349	+	10.8134i	0.137494	+	0.423162i	−0.858476	+	0.512854i	$0.828588\pi$
$654$	0.0704379	+	0.216786i	0.00275434	+	0.00847698i
$655$	−28.8773	−	3.64974i	−1.12833	−	0.142607i
$656$	−7.81906	+	24.0646i	−0.305283	+	0.939564i
$657$	−12.4937			−0.487426
$658$	−0.346133	+	1.06529i	−0.0134937	+	0.0415292i
$659$	14.5436	−	10.5666i	0.566540	−	0.411615i	−0.267307	−	0.963611i	$-0.586134\pi$
$659$	14.5436	−	10.5666i	0.566540	−	0.411615i	0.833847	+	0.551996i	$0.186134\pi$
$660$	−0.235544	−	1.23515i	−0.00916853	−	0.0480781i
$661$	−36.4101	−	26.4535i	−1.41619	−	1.02892i	−0.992386	−	0.123166i	$-0.960695\pi$
$661$	−36.4101	−	26.4535i	−1.41619	−	1.02892i	−0.423802	−	0.905755i	$-0.639305\pi$
$662$	6.45925	−	4.69292i	0.251046	−	0.182396i
$663$	1.16479	−	0.846266i	0.0452365	−	0.0328662i
$664$	−10.0353	−	7.29107i	−0.389445	−	0.282948i
$665$	−1.54279	−	0.194990i	−0.0598269	−	0.00756139i
$666$	3.24958	−	2.36096i	0.125919	−	0.0914852i
$667$	−0.664384	+	2.04476i	−0.0257250	+	0.0791735i
$668$	−15.9875			−0.618573
$669$	−1.41191	+	4.34540i	−0.0545875	+	0.168003i
$670$	−1.47344	−	1.38381i	−0.0569240	−	0.0534614i
$671$	0.872734	+	2.68600i	0.0336915	+	0.103692i
$672$	−1.14337	−	3.51894i	−0.0441066	−	0.135746i
$673$	0.298345	+	0.216761i	0.0115004	+	0.00835551i	0.593521	−	0.804819i	$-0.297738\pi$
$673$	0.298345	+	0.216761i	0.0115004	+	0.00835551i	−0.582020	+	0.813174i	$0.697738\pi$
$674$	−0.286295			−0.0110277
$675$	−4.84277	−	1.24401i	−0.186398	−	0.0478818i
$676$	23.0425			0.886250
$677$	−22.4379	−	16.3021i	−0.862358	−	0.626540i	0.0661674	−	0.997809i	$-0.478923\pi$
$677$	−22.4379	−	16.3021i	−0.862358	−	0.626540i	−0.928525	+	0.371269i	$0.878923\pi$
$678$	0.673445	+	2.07265i	0.0258635	+	0.0795997i
$679$	−0.127712	−	0.393057i	−0.00490113	−	0.0150841i
$680$	1.97656	−	4.19978i	0.0757977	−	0.161054i
$681$	7.29176	−	22.4417i	0.279421	−	0.859970i
$682$	−0.292014			−0.0111818
$683$	9.43557	−	29.0397i	0.361042	−	1.11117i	−0.591381	−	0.806393i	$-0.701417\pi$
$683$	9.43557	−	29.0397i	0.361042	−	1.11117i	0.952423	−	0.304780i	$-0.0985831\pi$
$684$	−1.06305	+	0.772352i	−0.0406468	+	0.0295316i
$685$	18.0138	+	16.9180i	0.688270	+	0.646403i
$686$	−0.269002	−	0.195442i	−0.0102706	−	0.00746200i
$687$	0.980167	−	0.712133i	0.0373957	−	0.0271696i
$688$	−19.9477	+	14.4929i	−0.760500	+	0.552536i
$689$	−5.93699	−	4.31347i	−0.226181	−	0.164330i
$690$	0.210166	+	0.197382i	0.00800090	+	0.00751421i
$691$	−4.56670	+	3.31790i	−0.173725	+	0.126219i	−0.671250	−	0.741231i	$-0.734242\pi$
$691$	−4.56670	+	3.31790i	−0.173725	+	0.126219i	0.497525	+	0.867450i	$0.334242\pi$
$692$	3.16516	−	9.74138i	0.120322	−	0.370312i
$693$	−0.297617			−0.0113055
$694$	−2.37267	+	7.30233i	−0.0900653	+	0.277192i
$695$	3.53831	−	7.51817i	0.134216	−	0.285180i
$696$	2.21570	+	6.81921i	0.0839857	+	0.258482i
$697$	3.74765	+	11.5341i	0.141952	+	0.436884i
$698$	−8.34326	−	6.06173i	−0.315797	−	0.229440i
$699$	−14.3523			−0.542852
$700$	−6.02104	−	7.27989i	−0.227574	−	0.275154i
$701$	−19.7121			−0.744515			−0.372258	−	0.928129i	$-0.621416\pi$
$701$	−19.7121			−0.744515			−0.372258	+	0.928129i	$0.621416\pi$
$702$	0.241292	+	0.175309i	0.00910696	+	0.00661660i
$703$	−2.59607	−	7.98988i	−0.0979127	−	0.301344i
$704$	−0.502835	−	1.54757i	−0.0189513	−	0.0583261i
$705$	5.49076	+	5.15676i	0.206794	+	0.194215i
$706$	−0.970693	+	2.98749i	−0.0365325	+	0.112436i
$707$	−13.4179			−0.504630
$708$	−6.20184	+	19.0873i	−0.233079	+	0.717345i
$709$	26.7134	−	19.4084i	1.00324	−	0.728899i	0.0404623	−	0.999181i	$-0.487117\pi$
$709$	26.7134	−	19.4084i	1.00324	−	0.728899i	0.962781	+	0.270282i	$0.0871169\pi$
$710$	−4.80048	−	0.606722i	−0.180159	−	0.0227699i
$711$	4.06376	+	2.95250i	0.152403	+	0.110727i
$712$	−10.2846	+	7.47222i	−0.385433	+	0.280033i
$713$	−0.925762	+	0.672606i	−0.0346701	+	0.0251893i
$714$	−0.431776	−	0.313703i	−0.0161588	−	0.0117401i
$715$	0.111821	+	0.586371i	0.00418188	+	0.0219290i
$716$	−26.0323	+	18.9135i	−0.972871	+	0.706832i
$717$	1.63311	−	5.02620i	0.0609897	−	0.187707i
$718$	5.37138			0.200458
$719$	−1.02799	+	3.16383i	−0.0383376	+	0.117991i	−0.968394	−	0.249426i	$-0.919758\pi$
$719$	−1.02799	+	3.16383i	−0.0383376	+	0.117991i	0.930056	+	0.367417i	$0.119758\pi$
$720$	−7.42919	−	0.938958i	−0.276870	−	0.0349929i
$721$	−6.11484	−	18.8195i	−0.227729	−	0.700876i
$722$	1.90255	+	5.85545i	0.0708056	+	0.217917i
$723$	8.55292	+	6.21406i	0.318087	+	0.231103i
$724$	−33.9412			−1.26141
$725$	17.6677	+	21.3616i	0.656162	+	0.793350i
$726$	−3.62811			−0.134652
$727$	−8.88237	−	6.45342i	−0.329429	−	0.239344i	0.410759	−	0.911744i	$-0.365264\pi$
$727$	−8.88237	−	6.45342i	−0.329429	−	0.239344i	−0.740188	+	0.672400i	$0.765264\pi$
$728$	0.358471	+	1.10326i	0.0132858	+	0.0408895i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	8.14038	−	4.47460i	0.301289	−	0.165612i
$731$	−3.65193	+	11.2395i	−0.135072	+	0.415708i
$732$	17.9298			0.662703
$733$	−2.79306	+	8.59615i	−0.103164	+	0.317506i	−0.989295	−	0.145929i	$-0.953383\pi$
$733$	−2.79306	+	8.59615i	−0.103164	+	0.317506i	0.886131	+	0.463434i	$0.153383\pi$
$734$	2.93120	−	2.12964i	0.108193	−	0.0786065i
$735$	−1.95954	+	1.07712i	−0.0722788	+	0.0397302i
$736$	1.16080	+	0.843371i	0.0427877	+	0.0310871i
$737$	−0.654606	+	0.475599i	−0.0241127	+	0.0175189i
$738$	−2.03250	+	1.47670i	−0.0748174	+	0.0543580i
$739$	36.4386	+	26.4742i	1.34041	+	0.973868i	0.999429	+	0.0337992i	$0.0107607\pi$
$739$	36.4386	+	26.4742i	1.34041	+	0.973868i	0.340985	+	0.940069i	$0.389239\pi$
$740$	21.7333	−	46.1788i	0.798933	−	1.69757i
$741$	0.504670	−	0.366664i	0.0185395	−	0.0134697i
$742$	−0.840627	+	2.58718i	−0.0308604	+	0.0949785i
$743$	−38.3473			−1.40682			−0.703412	−	0.710782i	$-0.748341\pi$
$743$	−38.3473			−1.40682			−0.703412	+	0.710782i	$0.748341\pi$
$744$	−1.17928	+	3.62944i	−0.0432344	+	0.133062i
$745$	−2.90626	−	15.2399i	−0.106477	−	0.558347i
$746$	2.04269	+	6.28674i	0.0747880	+	0.230174i
$747$	2.96394	+	9.12206i	0.108445	+	0.333759i
$748$	−0.730216	−	0.530533i	−0.0266993	−	0.0193982i
$749$	5.66506			0.206997
$750$	3.60089	−	0.923889i	0.131486	−	0.0337357i
$751$	−29.0152			−1.05878			−0.529389	−	0.848379i	$-0.677579\pi$
$751$	−29.0152			−1.05878			−0.529389	+	0.848379i	$0.677579\pi$
$752$	9.12677	+	6.63099i	0.332819	+	0.241807i
$753$	−7.23488	−	22.2667i	−0.263654	−	0.811442i
$754$	−0.510986	−	1.57265i	−0.0186090	−	0.0572727i
$755$	0.659956	+	3.46069i	0.0240183	+	0.125947i
$756$	−0.583869	+	1.79696i	−0.0212351	+	0.0653550i
$757$	−27.6716			−1.00574			−0.502871	−	0.864361i	$-0.667723\pi$
$757$	−27.6716			−1.00574			−0.502871	+	0.864361i	$0.667723\pi$
$758$	−2.27423	+	6.99937i	−0.0826039	+	0.254229i
$759$	0.0933706	−	0.0678377i	0.00338914	−	0.00246235i
$760$	0.856390	−	1.81965i	0.0310645	−	0.0660057i
$761$	−27.2220	−	19.7780i	−0.986798	−	0.716951i	−0.0275805	−	0.999620i	$-0.508780\pi$
$761$	−27.2220	−	19.7780i	−0.986798	−	0.716951i	−0.959218	+	0.282669i	$0.908780\pi$
$762$	1.04493	−	0.759185i	0.0378538	−	0.0275024i
$763$	0.554604	−	0.402943i	0.0200780	−	0.0145875i
$764$	−9.00096	−	6.53958i	−0.325643	−	0.236594i
$765$	−3.14526	+	1.72889i	−0.113717	+	0.0625081i
$766$	4.88809	−	3.55140i	0.176614	−	0.128317i
$767$	2.94424	−	9.06144i	0.106310	−	0.327190i
$768$	−7.86986			−0.283979
$769$	−5.39569	+	16.6062i	−0.194574	+	0.598836i	0.805408	+	0.592721i	$0.201946\pi$
$769$	−5.39569	+	16.6062i	−0.194574	+	0.598836i	−0.999981	+	0.00611464i	$0.998054\pi$
$770$	0.193915	−	0.106591i	0.00698822	−	0.00384128i
$771$	1.06735	+	3.28495i	0.0384395	+	0.118305i
$772$	4.53980	+	13.9721i	0.163391	+	0.502865i
$773$	−27.8016	−	20.1990i	−0.999953	−	0.726508i	−0.0378747	−	0.999282i	$-0.512059\pi$
$773$	−27.8016	−	20.1990i	−0.999953	−	0.726508i	−0.962078	+	0.272774i	$0.912059\pi$
$774$	−2.44814			−0.0879967
$775$	0.924735	+	14.7253i	0.0332175	+	0.528947i
$776$	0.534484			0.0191868
$777$	−9.77301	−	7.10051i	−0.350605	−	0.254729i
$778$	2.49142	+	7.66782i	0.0893219	+	0.274905i
$779$	1.62375	+	4.99740i	0.0581770	+	0.179050i
$780$	3.75978	+	0.475191i	0.134622	+	0.0170146i
$781$	−0.598526	+	1.84207i	−0.0214170	+	0.0659146i
$782$	0.206964			0.00740102
$783$	1.71326	−	5.27289i	0.0612271	−	0.188438i
$784$	−2.70929	+	1.96841i	−0.0967603	+	0.0703005i
$785$	−0.682860	−	3.58080i	−0.0243723	−	0.127804i
$786$	−3.50162	−	2.54408i	−0.124899	−	0.0907442i
$787$	−3.92827	+	2.85405i	−0.140028	+	0.101736i	−0.655594	−	0.755114i	$-0.727582\pi$
$787$	−3.92827	+	2.85405i	−0.140028	+	0.101736i	0.515566	+	0.856850i	$0.327582\pi$
$788$	−0.0179298	+	0.0130267i	−0.000638722	+	0.000464059i
$789$	19.0390	+	13.8326i	0.677806	+	0.492455i
$790$	−3.70521	−	0.468293i	−0.131825	−	0.0166611i
$791$	5.30248	−	3.85248i	0.188534	−	0.136978i
$792$	0.118940	−	0.366058i	0.00422633	−	0.0130073i
$793$	−8.51191			−0.302267
$794$	−2.19754	+	6.76334i	−0.0779879	+	0.240022i
$795$	13.3350	+	12.5238i	0.472943	+	0.444175i
$796$	2.51938	+	7.75385i	0.0892970	+	0.274828i
$797$	−15.0371	−	46.2794i	−0.532641	−	1.63930i	−0.748691	−	0.662919i	$-0.769317\pi$
$797$	−15.0371	−	46.2794i	−0.532641	−	1.63930i	0.216050	−	0.976382i	$-0.430683\pi$
$798$	−0.187077	−	0.135919i	−0.00662244	−	0.00481149i
$799$	5.40710			0.191289
$800$	17.2018	−	6.80839i	0.608176	−	0.240713i
$801$	9.82981			0.347319
$802$	−7.17618	−	5.21380i	−0.253400	−	0.184106i
$803$	−1.14903	−	3.53635i	−0.0405484	−	0.124795i
$804$	1.58738	+	4.88544i	0.0559824	+	0.172296i
$805$	0.369247	−	0.784573i	0.0130142	−	0.0276526i
$806$	0.271966	−	0.837025i	0.00957959	−	0.0294829i
$807$	20.4629			0.720327
$808$	5.36230	−	16.5035i	0.188645	−	0.580590i
$809$	−41.9081	+	30.4480i	−1.47341	+	1.07050i	−0.493803	+	0.869574i	$0.664394\pi$
$809$	−41.9081	+	30.4480i	−1.47341	+	1.07050i	−0.979607	+	0.200922i	$0.935606\pi$
$810$	−0.541962	−	0.508995i	−0.0190426	−	0.0178843i
$811$	21.1248	+	15.3480i	0.741791	+	0.538943i	0.893271	−	0.449518i	$-0.148404\pi$
$811$	21.1248	+	15.3480i	0.741791	+	0.538943i	−0.151481	+	0.988460i	$0.548404\pi$
$812$	8.47487	−	6.15735i	0.297410	−	0.216081i
$813$	−10.5236	+	7.64586i	−0.369080	+	0.268152i
$814$	0.967130	+	0.702661i	0.0338979	+	0.0246283i
$815$	−14.3536	−	13.4805i	−0.502786	−	0.472202i
$816$	−4.34868	+	3.15950i	−0.152234	+	0.110605i
$817$	−1.58228	+	4.86977i	−0.0553571	+	0.170372i
$818$	−6.41647			−0.224346
$819$	0.277184	−	0.853085i	0.00968560	−	0.0298092i
$820$	−13.5935	+	28.8833i	−0.474704	+	1.00865i
$821$	−13.9219	−	42.8471i	−0.485876	−	1.49537i	−0.830708	−	0.556709i	$-0.812064\pi$
$821$	−13.9219	−	42.8471i	−0.485876	−	1.49537i	0.344832	−	0.938665i	$-0.387936\pi$
$822$	1.13557	+	3.49493i	0.0396076	+	0.121900i
$823$	24.0345	+	17.4621i	0.837790	+	0.608690i	0.921752	−	0.387779i	$-0.126758\pi$
$823$	24.0345	+	17.4621i	0.837790	+	0.608690i	−0.0839625	+	0.996469i	$0.526758\pi$
$824$	25.5911			0.891507
$825$	−0.0932671	−	1.48516i	−0.00324714	−	0.0517067i
$826$	−3.53186			−0.122889
$827$	−23.6449	−	17.1790i	−0.822212	−	0.597372i	0.0951332	−	0.995465i	$-0.469672\pi$
$827$	−23.6449	−	17.1790i	−0.822212	−	0.597372i	−0.917345	+	0.398092i	$0.869672\pi$
$828$	−0.226417	−	0.696841i	−0.00786855	−	0.0242169i
$829$	15.5003	+	47.7051i	0.538349	+	1.65687i	0.736300	+	0.676655i	$0.236571\pi$
$829$	15.5003	+	47.7051i	0.538349	+	1.65687i	−0.197951	+	0.980212i	$0.563429\pi$
$830$	−5.19823	−	4.88203i	−0.180433	−	0.169458i
$831$	−9.06194	+	27.8898i	−0.314355	+	0.967486i
$832$	4.90423			0.170024
$833$	−0.496003	+	1.52654i	−0.0171855	+	0.0528915i
$834$	0.999607	−	0.726257i	0.0346136	−	0.0251482i
$835$	−18.7711	−	2.37244i	−0.649601	−	0.0821016i
$836$	−0.316383	−	0.229865i	−0.0109423	−	0.00795006i
$837$	2.38729	−	1.73447i	0.0825168	−	0.0599520i
$838$	−7.29316	+	5.29879i	−0.251938	+	0.183044i
$839$	−39.4613	−	28.6703i	−1.36235	−	0.989808i	−0.998291	−	0.0584334i	$-0.981389\pi$
$839$	−39.4613	−	28.6703i	−1.36235	−	0.989808i	−0.364062	−	0.931375i	$-0.618611\pi$
$840$	−0.541709	−	2.84062i	−0.0186907	−	0.0980109i
$841$	−1.40657	+	1.02193i	−0.0485024	+	0.0352391i
$842$	1.51381	−	4.65904i	0.0521695	−	0.160561i
$843$	−8.82704			−0.304020
$844$	2.39135	−	7.35982i	0.0823137	−	0.253335i
$845$	27.0545	+	3.41936i	0.930705	+	0.117630i
$846$	0.346133	+	1.06529i	0.0119003	+	0.0366253i
$847$	3.37182	+	10.3774i	0.115857	+	0.356571i
$848$	22.1655	+	16.1042i	0.761167	+	0.553020i
$849$	−23.2083			−0.796508
$850$	1.43012	−	2.25294i	0.0490529	−	0.0772753i
$851$	4.68452			0.160583
$852$	9.94794	+	7.22760i	0.340811	+	0.247614i
$853$	−16.4757	−	50.7070i	−0.564118	−	1.73618i	−0.670559	−	0.741856i	$-0.733946\pi$
$853$	−16.4757	−	50.7070i	−0.564118	−	1.73618i	0.106441	−	0.994319i	$-0.466054\pi$
$854$	0.975039	+	3.00086i	0.0333651	+	0.102687i
$855$	−1.36276	+	0.749080i	−0.0466053	+	0.0256180i
$856$	−2.26398	+	6.96781i	−0.0773812	+	0.238155i
$857$	−10.0286			−0.342570			−0.171285	−	0.985222i	$-0.554792\pi$
$857$	−10.0286			−0.342570			−0.171285	+	0.985222i	$0.554792\pi$
$858$	−0.0274300	+	0.0844207i	−0.000936443	+	0.00288208i
$859$	31.1092	−	22.6022i	1.06143	−	0.771176i	0.0870796	−	0.996201i	$-0.472247\pi$
$859$	31.1092	−	22.6022i	1.06143	−	0.771176i	0.974353	+	0.225026i	$0.0722465\pi$
$860$	−27.2600	+	14.9843i	−0.929559	+	0.510960i
$861$	6.11269	+	4.44113i	0.208320	+	0.151353i
$862$	−11.0835	+	8.05265i	−0.377506	+	0.274274i
$863$	30.7722	−	22.3573i	1.04750	−	0.761051i	0.0757617	−	0.997126i	$-0.475861\pi$
$863$	30.7722	−	22.3573i	1.04750	−	0.761051i	0.971735	+	0.236075i	$0.0758612\pi$
$864$	−2.99339	−	2.17483i	−0.101837	−	0.0739891i
$865$	5.16183	−	10.9678i	0.175507	−	0.372916i
$866$	6.38178	−	4.63663i	0.216862	−	0.157559i
$867$	4.45715	−	13.7177i	0.151373	−	0.465878i
$868$	5.57546			0.189243
$869$	−0.461967	+	1.42179i	−0.0156712	+	0.0482309i
$870$	0.772185	+	4.04920i	0.0261795	+	0.137281i
$871$	−0.753585	−	2.31930i	−0.0255343	−	0.0785864i
$872$	0.273964	+	0.843174i	0.00927759	+	0.0285535i
$873$	−0.334354	−	0.242922i	−0.0113162	−	0.00822167i
$874$	0.0896719			0.00303320
$875$	−5.98910	−	9.44091i	−0.202468	−	0.319161i
$876$	−23.6061			−0.797576
$877$	−20.9383	−	15.2126i	−0.707038	−	0.513693i	0.175179	−	0.984537i	$-0.443950\pi$
$877$	−20.9383	−	15.2126i	−0.707038	−	0.513693i	−0.882217	+	0.470844i	$0.843950\pi$
$878$	3.72988	+	11.4794i	0.125877	+	0.387411i
$879$	2.00413	+	6.16806i	0.0675975	+	0.208044i
$880$	−0.417481	−	2.18919i	−0.0140733	−	0.0737977i
$881$	3.30565	−	10.1737i	0.111370	−	0.342762i	−0.879803	−	0.475339i	$-0.842325\pi$
$881$	3.30565	−	10.1737i	0.111370	−	0.342762i	0.991173	+	0.132577i	$0.0423253\pi$
$882$	−0.332505			−0.0111960
$883$	−1.84328	+	5.67304i	−0.0620313	+	0.190913i	−0.977270	−	0.212000i	$-0.932002\pi$
$883$	−1.84328	+	5.67304i	−0.0620313	+	0.190913i	0.915238	+	0.402913i	$0.132002\pi$
$884$	2.20079	−	1.59897i	0.0740206	−	0.0537791i
$885$	−10.1141	+	21.4904i	−0.339982	+	0.722391i
$886$	−1.65807	−	1.20466i	−0.0557040	−	0.0404713i
$887$	−10.4092	+	7.56270i	−0.349506	+	0.253931i	−0.748662	−	0.662952i	$-0.769303\pi$
$887$	−10.4092	+	7.56270i	−0.349506	+	0.253931i	0.399156	+	0.916883i	$0.369303\pi$
$888$	12.6390	−	9.18280i	0.424138	−	0.308154i
$889$	−3.14259	−	2.28323i	−0.105399	−	0.0765770i
$890$	−6.40470	+	3.52053i	−0.214686	+	0.118009i
$891$	−0.240778	+	0.174935i	−0.00806635	+	0.00586055i
$892$	−2.66772	+	8.21038i	−0.0893217	+	0.274904i
$893$	2.34275			0.0783970
$894$	0.712910	−	2.19411i	0.0238433	−	0.0733821i
$895$	−33.3715	+	18.3436i	−1.11549	+	0.613160i
$896$	−2.84853	−	8.76686i	−0.0951626	−	0.292880i
$897$	0.107489	+	0.330816i	0.00358894	+	0.0110456i
$898$	9.85766	+	7.16201i	0.328954	+	0.238999i
$899$	−16.3602			−0.545644
$900$	−9.15013	−	2.35048i	−0.305004	−	0.0783492i
$901$	13.1318			0.437484
$902$	−0.604907	−	0.439491i	−0.0201412	−	0.0146334i
$903$	2.27521	+	7.00236i	0.0757141	+	0.233024i
$904$	2.61932	+	8.06145i	0.0871174	+	0.268120i
$905$	−39.8508	−	5.03666i	−1.32469	−	0.167424i
$906$	−0.161888	+	0.498241i	−0.00537838	+	0.0165529i
$907$	16.9061			0.561358			0.280679	−	0.959802i	$-0.409440\pi$
$907$	16.9061			0.561358			0.280679	+	0.959802i	$0.409440\pi$
$908$	13.7774	−	42.4023i	0.457218	−	1.40717i
$909$	−10.8553	+	7.88682i	−0.360047	+	0.261589i
$910$	0.124929	+	0.655108i	0.00414137	+	0.0217166i
$911$	−11.1329	−	8.08854i	−0.368850	−	0.267985i	0.387884	−	0.921708i	$-0.373206\pi$
$911$	−11.1329	−	8.08854i	−0.368850	−	0.267985i	−0.756734	+	0.653723i	$0.773206\pi$
$912$	−1.88416	+	1.36893i	−0.0623909	+	0.0453297i
$913$	−2.30942	+	1.67789i	−0.0764306	+	0.0555301i
$914$	3.38749	+	2.46115i	0.112048	+	0.0814077i
$915$	21.0516	+	2.66066i	0.695944	+	0.0879588i
$916$	1.85197	−	1.34553i	0.0611907	−	0.0444576i
$917$	−4.02249	+	12.3800i	−0.132834	+	0.408822i
$918$	−0.533704			−0.0176149
$919$	8.47403	−	26.0804i	0.279533	−	0.860313i	−0.708452	−	0.705759i	$-0.750606\pi$
$919$	8.47403	−	26.0804i	0.279533	−	0.860313i	0.987984	−	0.154554i	$-0.0493939\pi$
$920$	0.817430	+	0.767706i	0.0269499	+	0.0253105i
$921$	−8.27397	−	25.4647i	−0.272637	−	0.839089i
$922$	2.89301	+	8.90376i	0.0952761	+	0.293230i
$923$	−4.72265	−	3.43121i	−0.155448	−	0.112940i
$924$	−0.562330			−0.0184993
$925$	32.3701	−	50.9941i	1.06432	−	1.67668i
$926$	3.57720			0.117554
$927$	−16.0089	−	11.6311i	−0.525800	−	0.382016i
$928$	6.33914	+	19.5099i	0.208092	+	0.640443i
$929$	−4.72956	−	14.5561i	−0.155172	−	0.477570i	0.843006	−	0.537904i	$-0.180784\pi$
$929$	−4.72956	−	14.5561i	−0.155172	−	0.477570i	−0.998178	+	0.0603336i	$0.980784\pi$
$930$	−0.934262	+	1.98511i	−0.0306356	+	0.0650944i
$931$	−0.214905	+	0.661409i	−0.00704322	+	0.0216768i
$932$	−27.1177			−0.888271
$933$	−1.07829	+	3.31863i	−0.0353016	+	0.108647i
$934$	−2.23379	+	1.62295i	−0.0730919	+	0.0531044i
$935$	−0.778629	−	0.731266i	−0.0254639	−	0.0239150i
$936$	0.938489	+	0.681852i	0.0306755	+	0.0222870i
$937$	10.4250	−	7.57424i	0.340571	−	0.247440i	−0.404331	−	0.914613i	$-0.632496\pi$
$937$	10.4250	−	7.57424i	0.340571	−	0.247440i	0.744903	+	0.667173i	$0.232496\pi$
$938$	−0.731342	+	0.531351i	−0.0238791	+	0.0173492i
$939$	11.1213	+	8.08013i	0.362931	+	0.263685i
$940$	10.3745	+	9.74339i	0.338378	+	0.317794i
$941$	34.5371	−	25.0927i	1.12588	−	0.817997i	0.140787	−	0.990040i	$-0.455037\pi$
$941$	34.5371	−	25.0927i	1.12588	−	0.817997i	0.985089	+	0.172043i	$0.0550367\pi$
$942$	0.167507	−	0.515533i	0.00545766	−	0.0167970i
$943$	−2.93001			−0.0954142
$944$	−10.9922	+	33.8305i	−0.357766	+	1.10109i
$945$	−0.952188	+	2.02320i	−0.0309747	+	0.0658147i
$946$	−0.225153	−	0.692949i	−0.00732035	−	0.0225297i
$947$	−5.62336	−	17.3069i	−0.182735	−	0.562399i	0.817167	−	0.576400i	$-0.195543\pi$
$947$	−5.62336	−	17.3069i	−0.182735	−	0.562399i	−0.999902	+	0.0140013i	$0.995543\pi$
$948$	7.67824	+	5.57857i	0.249378	+	0.181183i
$949$	11.2067			0.363784
$950$	0.619634	−	0.976139i	0.0201036	−	0.0316701i
$951$	28.9457			0.938627
$952$	−1.67937	−	1.22013i	−0.0544286	−	0.0395447i
$953$	−7.83452	−	24.1122i	−0.253785	−	0.781070i	−0.994067	−	0.108773i	$-0.965308\pi$
$953$	−7.83452	−	24.1122i	−0.253785	−	0.781070i	0.740282	−	0.672297i	$-0.234692\pi$
$954$	0.840627	+	2.58718i	0.0272163	+	0.0837632i
$955$	−9.59773	−	9.01390i	−0.310575	−	0.291683i
$956$	3.08567	−	9.49671i	0.0997976	−	0.307146i
$957$	1.65006			0.0533389
$958$	0.613776	−	1.88901i	0.0198302	−	0.0610311i
$959$	8.94111	−	6.49610i	0.288724	−	0.209770i
$960$	−12.1291	−	1.53297i	−0.391465	−	0.0494764i
$961$	18.0350	+	13.1032i	0.581774	+	0.422683i
$962$	−2.91483	+	2.11775i	−0.0939778	+	0.0682789i
$963$	4.58313	−	3.32984i	0.147689	−	0.107303i
$964$	16.1602	+	11.7411i	0.520486	+	0.378155i
$965$	3.25688	+	17.0785i	0.104843	+	0.549776i
$966$	0.104316	−	0.0757900i	0.00335631	−	0.00243850i
$967$	−14.1045	+	43.4091i	−0.453570	+	1.39594i	0.419237	+	0.907877i	$0.362298\pi$
$967$	−14.1045	+	43.4091i	−0.453570	+	1.39594i	−0.872806	+	0.488067i	$0.837702\pi$
$968$	−14.1113			−0.453554
$969$	−0.344944	+	1.06163i	−0.0110812	+	0.0341044i
$970$	0.304853	+	0.0385297i	0.00978825	+	0.00123712i
$971$	8.86521	+	27.2843i	0.284498	+	0.875595i	0.986549	+	0.163468i	$0.0522681\pi$
$971$	8.86521	+	27.2843i	0.284498	+	0.875595i	−0.702050	+	0.712127i	$0.747732\pi$
$972$	0.583869	+	1.79696i	0.0187276	+	0.0576377i
$973$	−3.00629	−	2.18420i	−0.0963772	−	0.0700222i
$974$	11.0113			0.352825
$975$	4.34390	+	1.11586i	0.139116	+	0.0357360i
$976$	31.7789			1.01722
$977$	17.5596	+	12.7578i	0.561781	+	0.408158i	0.832110	−	0.554610i	$-0.187133\pi$
$977$	17.5596	+	12.7578i	0.561781	+	0.408158i	−0.270329	+	0.962768i	$0.587133\pi$
$978$	−0.904842	−	2.78482i	−0.0289336	−	0.0890486i
$979$	0.904036	+	2.78234i	0.0288931	+	0.0889239i
$980$	−3.70244	+	2.03516i	−0.118270	+	0.0650107i
$981$	0.211840	−	0.651976i	0.00676353	−	0.0208160i
$982$	−2.92185			−0.0932399
$983$	−0.275471	+	0.847812i	−0.00878615	+	0.0270410i	−0.955353	−	0.295465i	$-0.904525\pi$
$983$	−0.275471	+	0.847812i	−0.00878615	+	0.0270410i	0.946567	+	0.322506i	$0.104525\pi$
$984$	−7.90529	+	5.74353i	−0.252011	+	0.183097i
$985$	−0.0229847	+	0.0126342i	−0.000732354	+	0.000402560i
$986$	2.39387	+	1.73925i	0.0762363	+	0.0553889i
$987$	2.72533	−	1.98007i	0.0867483	−	0.0630263i
$988$	0.953543	−	0.692790i	0.0303362	−	0.0220406i
$989$	−2.30988	−	1.67823i	−0.0734501	−	0.0533646i
$990$	0.0942279	−	0.200215i	0.00299476	−	0.00636324i
$991$	28.2377	−	20.5159i	0.896999	−	0.651708i	−0.0406945	−	0.999172i	$-0.512957\pi$
$991$	28.2377	−	20.5159i	0.896999	−	0.651708i	0.937693	+	0.347464i	$0.112957\pi$
$992$	−3.37393	+	10.3839i	−0.107122	+	0.329688i
$993$	−24.0119			−0.761994
$994$	−0.668688	+	2.05801i	−0.0212095	+	0.0652761i
$995$	1.80742	+	9.47777i	0.0572990	+	0.300465i
$996$	5.60018	+	17.2356i	0.177449	+	0.546131i
$997$	5.26664	+	16.2091i	0.166796	+	0.513346i	0.999164	−	0.0408773i	$-0.0130153\pi$
$997$	5.26664	+	16.2091i	0.166796	+	0.513346i	−0.832368	+	0.554224i	$0.813015\pi$
$998$	6.58850	+	4.78683i	0.208555	+	0.151524i
$999$	−12.0801			−0.382198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.b.316.4	yes	20
25.11	even	5	inner	525.2.n.b.211.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.b.211.4	✓	20	25.11	even	5	inner
525.2.n.b.316.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.269002 + 0.195442i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.583869 - 1.79696i) q^{4} +(-0.418871 - 2.19649i) q^{5} +(0.102750 - 0.316231i) q^{6} -1.00000 q^{7} +(0.399639 - 1.22996i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.269002 + 0.195442i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.583869 - 1.79696i) q^{4} +(-0.418871 - 2.19649i) q^{5} +(0.102750 - 0.316231i) q^{6} -1.00000 q^{7} +(0.399639 - 1.22996i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.316607 - 0.672725i) q^{10} +(-0.240778 - 0.174935i) q^{11} +(-1.52859 + 1.11059i) q^{12} +(0.725677 - 0.527236i) q^{13} +(-0.269002 - 0.195442i) q^{14} +(-1.95954 + 1.07712i) q^{15} +(-2.70929 + 1.96841i) q^{16} +(-0.496003 + 1.52654i) q^{17} -0.332505 q^{18} +(-0.214905 + 0.661409i) q^{19} +(-3.70244 + 2.03516i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-0.0305801 - 0.0941159i) q^{22} +(-0.313727 - 0.227936i) q^{23} -1.29326 q^{24} +(-4.64909 + 1.84009i) q^{25} +0.298253 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.583869 + 1.79696i) q^{28} +(-1.71326 - 5.27289i) q^{29} +(-0.737636 - 0.0932282i) q^{30} +(0.911863 - 2.80643i) q^{31} -3.70003 q^{32} +(-0.0919688 + 0.283051i) q^{33} +(-0.431776 + 0.313703i) q^{34} +(0.418871 + 2.19649i) q^{35} +(1.52859 + 1.11059i) q^{36} +(-9.77301 + 7.10051i) q^{37} +(-0.187077 + 0.135919i) q^{38} +(-0.725677 - 0.527236i) q^{39} +(-2.86899 - 0.362605i) q^{40} +(6.11269 - 4.44113i) q^{41} +(-0.102750 + 0.316231i) q^{42} +7.36272 q^{43} +(-0.173770 + 0.534808i) q^{44} +(1.62994 + 1.53079i) q^{45} +(-0.0398451 - 0.122631i) q^{46} +(-1.04098 - 3.20382i) q^{47} +(2.70929 + 1.96841i) q^{48} +1.00000 q^{49} +(-1.61025 - 0.413639i) q^{50} +1.60510 q^{51} +(-1.37112 - 0.996180i) q^{52} +(-2.52816 - 7.78088i) q^{53} +(0.102750 + 0.316231i) q^{54} +(-0.283388 + 0.602139i) q^{55} +(-0.399639 + 1.22996i) q^{56} +0.695446 q^{57} +(0.569670 - 1.75326i) q^{58} +(8.59335 - 6.24344i) q^{59} +(3.07967 + 2.89233i) q^{60} +(-7.67713 - 5.57776i) q^{61} +(0.793786 - 0.576720i) q^{62} +(0.809017 - 0.587785i) q^{63} +(4.42326 + 3.21369i) q^{64} +(-1.46203 - 1.37310i) q^{65} +(-0.0800598 + 0.0581668i) q^{66} +(0.840130 - 2.58565i) q^{67} +3.03274 q^{68} +(-0.119833 + 0.368808i) q^{69} +(-0.316607 + 0.672725i) q^{70} +(-2.01106 - 6.18940i) q^{71} +(0.399639 + 1.22996i) q^{72} +(10.1076 + 7.34362i) q^{73} -4.01670 q^{74} +(3.18668 + 3.85293i) q^{75} +1.31400 q^{76} +(0.240778 + 0.174935i) q^{77} +(-0.0921652 - 0.283655i) q^{78} +(-1.55222 - 4.77724i) q^{79} +(5.45843 + 5.12640i) q^{80} +(0.309017 - 0.951057i) q^{81} +2.51231 q^{82} +(2.96394 - 9.12206i) q^{83} +(1.52859 - 1.11059i) q^{84} +(3.56079 + 0.450040i) q^{85} +(1.98059 + 1.43898i) q^{86} +(-4.48539 + 3.25882i) q^{87} +(-0.311388 + 0.226236i) q^{88} +(-7.95249 - 5.77782i) q^{89} +(0.139277 + 0.730343i) q^{90} +(-0.725677 + 0.527236i) q^{91} +(-0.226417 + 0.696841i) q^{92} -2.95085 q^{93} +(0.346133 - 1.06529i) q^{94} +(1.54279 + 0.194990i) q^{95} +(1.14337 + 3.51894i) q^{96} +(0.127712 + 0.393057i) q^{97} +(0.269002 + 0.195442i) q^{98} +0.297617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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