LMFDB - Embedded newform 430.2.k.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 6 x^{10} - 16 x^{9} + 44 x^{8} - 70 x^{7} + 141 x^{6} - 182 x^{5} + 270 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 6x^10 - 16x^9 + 44x^8 - 70x^7 + 141x^6 - 182x^5 + 270x^4 - 124x^3 + 115x^2 + 20*x + 1
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			121.2
Root			$2.10098 - 1.01178i$ of defining polynomial
Character	$\chi$	$=$	430.121
Dual form			430.2.k.a.231.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(0.241421 + 1.05773i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -1.08494 q^{6} +1.63589 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.64239 - 0.790933i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(0.241421 + 1.05773i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -1.08494 q^{6} +1.63589 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.64239 - 0.790933i) q^{9} +(0.623490 + 0.781831i) q^{10} +(2.69641 - 1.29852i) q^{11} +(0.241421 - 1.05773i) q^{12} +(-0.277479 + 0.347948i) q^{13} +(-0.364020 + 1.59487i) q^{14} +(0.977493 + 0.470736i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.29544 + 1.62443i) q^{17} +(0.405637 + 1.77721i) q^{18} +(1.27654 + 0.614748i) q^{19} +(-0.900969 + 0.433884i) q^{20} +(0.394938 + 1.73034i) q^{21} +(0.665958 + 2.91775i) q^{22} +(-5.17241 + 2.49090i) q^{23} +(0.977493 + 0.470736i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.277479 - 0.347948i) q^{26} +(3.26244 + 4.09097i) q^{27} +(-1.47389 - 0.709786i) q^{28} +(0.216187 - 0.947178i) q^{29} +(-0.676446 + 0.848237i) q^{30} +(-0.0222647 + 0.0975478i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.02446 + 2.53859i) q^{33} +(-1.87196 + 0.901490i) q^{34} +(1.01996 - 1.27899i) q^{35} -1.82292 q^{36} -1.24604 q^{37} +(-0.883392 + 1.10774i) q^{38} +(-0.435025 - 0.209497i) q^{39} +(-0.222521 - 0.974928i) q^{40} +(0.710366 - 3.11232i) q^{41} -1.77484 q^{42} +(-2.67430 + 5.98733i) q^{43} -2.99279 q^{44} +(0.405637 - 1.77721i) q^{45} +(-1.27748 - 5.59700i) q^{46} +(6.13522 + 2.95456i) q^{47} +(-0.676446 + 0.848237i) q^{48} -4.32386 q^{49} +1.00000 q^{50} +(-1.40547 + 1.76240i) q^{51} +(0.400969 - 0.193096i) q^{52} +(-5.80862 - 7.28378i) q^{53} +(-4.71437 + 2.27032i) q^{54} +(0.665958 - 2.91775i) q^{55} +(1.01996 - 1.27899i) q^{56} +(-0.342057 + 1.49865i) q^{57} +(0.875324 + 0.421534i) q^{58} +(-1.94958 - 2.44470i) q^{59} +(-0.676446 - 0.848237i) q^{60} +(-0.180263 - 0.789785i) q^{61} +(-0.0901477 - 0.0434129i) q^{62} +(2.68677 - 1.29388i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.0990311 + 0.433884i) q^{65} +(-2.92543 + 1.40881i) q^{66} +(12.7024 + 6.11715i) q^{67} +(-0.462337 - 2.02563i) q^{68} +(-3.88344 - 4.86967i) q^{69} +(1.01996 + 1.27899i) q^{70} +(-0.0610689 - 0.0294092i) q^{71} +(0.405637 - 1.77721i) q^{72} +(-3.48357 + 4.36826i) q^{73} +(0.277269 - 1.21479i) q^{74} +(0.977493 - 0.470736i) q^{75} +(-0.883392 - 1.10774i) q^{76} +(4.41103 - 2.12424i) q^{77} +(0.301047 - 0.377501i) q^{78} +1.36505 q^{79} +1.00000 q^{80} +(-0.129833 + 0.162805i) q^{81} +(2.87621 + 1.38511i) q^{82} +(-2.17407 - 9.52521i) q^{83} +(0.394938 - 1.73034i) q^{84} +2.07772 q^{85} +(-5.24213 - 3.93955i) q^{86} +1.05405 q^{87} +(0.665958 - 2.91775i) q^{88} +(-2.64830 - 11.6029i) q^{89} +(1.64239 + 0.790933i) q^{90} +(-0.453925 + 0.569204i) q^{91} +5.74094 q^{92} -0.108555 q^{93} +(-4.24570 + 5.32394i) q^{94} +(1.27654 - 0.614748i) q^{95} +(-0.676446 - 0.848237i) q^{96} +(8.71217 - 4.19556i) q^{97} +(0.962150 - 4.21546i) q^{98} +(3.40151 - 4.26536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	0.241421	+	1.05773i	0.139384	+	0.610683i	0.995571	+	0.0940157i	$0.0299704\pi$
$3$	0.241421	+	1.05773i	0.139384	+	0.610683i	−0.856186	+	0.516667i	$0.827172\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$6$	−1.08494			−0.442923
$7$	1.63589			0.618308			0.309154	−	0.951012i	$-0.399954\pi$
$7$	1.63589			0.618308			0.309154	+	0.951012i	$0.399954\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	1.64239	−	0.790933i	0.547463	−	0.263644i
$10$	0.623490	+	0.781831i	0.197165	+	0.247237i
$11$	2.69641	−	1.29852i	0.812997	−	0.391519i	0.0192864	−	0.999814i	$-0.493861\pi$
$11$	2.69641	−	1.29852i	0.812997	−	0.391519i	0.793711	+	0.608295i	$0.208146\pi$
$12$	0.241421	−	1.05773i	0.0696922	−	0.305341i
$13$	−0.277479	+	0.347948i	−0.0769588	+	0.0965033i	−0.818821	−	0.574050i	$-0.805372\pi$
$13$	−0.277479	+	0.347948i	−0.0769588	+	0.0965033i	0.741862	+	0.670553i	$0.233943\pi$
$14$	−0.364020	+	1.59487i	−0.0972884	+	0.426248i
$15$	0.977493	+	0.470736i	0.252388	+	0.121543i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	1.29544	+	1.62443i	0.314190	+	0.393982i	0.913703	−	0.406384i	$-0.133210\pi$
$17$	1.29544	+	1.62443i	0.314190	+	0.393982i	−0.599513	+	0.800365i	$0.704639\pi$
$18$	0.405637	+	1.77721i	0.0956095	+	0.418893i
$19$	1.27654	+	0.614748i	0.292858	+	0.141033i	0.574544	−	0.818474i	$-0.305179\pi$
$19$	1.27654	+	0.614748i	0.292858	+	0.141033i	−0.281686	+	0.959507i	$0.590894\pi$
$20$	−0.900969	+	0.433884i	−0.201463	+	0.0970194i
$21$	0.394938	+	1.73034i	0.0861825	+	0.377590i
$22$	0.665958	+	2.91775i	0.141983	+	0.622067i
$23$	−5.17241	+	2.49090i	−1.07852	+	0.519389i	−0.886844	−	0.462069i	$-0.847107\pi$
$23$	−5.17241	+	2.49090i	−1.07852	+	0.519389i	−0.191678	+	0.981458i	$0.561393\pi$
$24$	0.977493	+	0.470736i	0.199530	+	0.0960886i
$25$	−0.222521	−	0.974928i	−0.0445042	−	0.194986i
$26$	−0.277479	−	0.347948i	−0.0544181	−	0.0682382i
$27$	3.26244	+	4.09097i	0.627857	+	0.787308i
$28$	−1.47389	−	0.709786i	−0.278538	−	0.134137i
$29$	0.216187	−	0.947178i	0.0401449	−	0.175886i	−0.950881	−	0.309557i	$-0.899819\pi$
$29$	0.216187	−	0.947178i	0.0401449	−	0.175886i	0.991026	+	0.133671i	$0.0426764\pi$
$30$	−0.676446	+	0.848237i	−0.123502	+	0.154866i
$31$	−0.0222647	+	0.0975478i	−0.00399885	+	0.0175201i	−0.976888	−	0.213752i	$-0.931432\pi$
$31$	−0.0222647	+	0.0975478i	−0.00399885	+	0.0175201i	0.972889	+	0.231272i	$0.0742887\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	2.02446	+	2.53859i	0.352413	+	0.441912i
$34$	−1.87196	+	0.901490i	−0.321039	+	0.154604i
$35$	1.01996	−	1.27899i	0.172405	−	0.216189i
$36$	−1.82292			−0.303819
$37$	−1.24604			−0.204847			−0.102423	−	0.994741i	$-0.532660\pi$
$37$	−1.24604			−0.204847			−0.102423	+	0.994741i	$0.532660\pi$
$38$	−0.883392	+	1.10774i	−0.143305	+	0.179699i
$39$	−0.435025	−	0.209497i	−0.0696598	−	0.0335464i
$40$	−0.222521	−	0.974928i	−0.0351836	−	0.154150i
$41$	0.710366	−	3.11232i	0.110941	−	0.486062i	−0.888680	−	0.458527i	$-0.848377\pi$
$41$	0.710366	−	3.11232i	0.110941	−	0.486062i	0.999621	−	0.0275350i	$-0.00876578\pi$
$42$	−1.77484			−0.273863
$43$	−2.67430	+	5.98733i	−0.407826	+	0.913059i
$43$	−2.67430	+	5.98733i	−0.407826	+	0.913059i
$44$	−2.99279			−0.451179
$45$	0.405637	−	1.77721i	0.0604688	−	0.264931i
$46$	−1.27748	−	5.59700i	−0.188354	−	0.825233i
$47$	6.13522	+	2.95456i	0.894913	+	0.430967i	0.824049	−	0.566518i	$-0.191710\pi$
$47$	6.13522	+	2.95456i	0.894913	+	0.430967i	0.0708642	+	0.997486i	$0.477424\pi$
$48$	−0.676446	+	0.848237i	−0.0976366	+	0.122432i
$49$	−4.32386			−0.617695
$50$	1.00000			0.141421
$51$	−1.40547	+	1.76240i	−0.196805	+	0.246785i
$52$	0.400969	−	0.193096i	0.0556044	−	0.0267777i
$53$	−5.80862	−	7.28378i	−0.797876	−	1.00050i	−0.999777	−	0.0210989i	$-0.993284\pi$
$53$	−5.80862	−	7.28378i	−0.797876	−	1.00050i	0.201902	−	0.979406i	$-0.435288\pi$
$54$	−4.71437	+	2.27032i	−0.641544	+	0.308951i
$55$	0.665958	−	2.91775i	0.0897977	−	0.393429i
$56$	1.01996	−	1.27899i	0.136298	−	0.170912i
$57$	−0.342057	+	1.49865i	−0.0453066	+	0.198501i
$58$	0.875324	+	0.421534i	0.114936	+	0.0553501i
$59$	−1.94958	−	2.44470i	−0.253814	−	0.318273i	0.638557	−	0.769574i	$-0.279531\pi$
$59$	−1.94958	−	2.44470i	−0.253814	−	0.318273i	−0.892372	+	0.451301i	$0.850960\pi$
$60$	−0.676446	−	0.848237i	−0.0873288	−	0.109507i
$61$	−0.180263	−	0.789785i	−0.0230804	−	0.101122i	0.962076	−	0.272782i	$-0.0879439\pi$
$61$	−0.180263	−	0.789785i	−0.0230804	−	0.101122i	−0.985156	+	0.171661i	$0.945087\pi$
$62$	−0.0901477	−	0.0434129i	−0.0114488	−	0.00551344i
$63$	2.68677	−	1.29388i	0.338501	−	0.163014i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.0990311	+	0.433884i	0.0122833	+	0.0538167i
$66$	−2.92543	+	1.40881i	−0.360095	+	0.173413i
$67$	12.7024	+	6.11715i	1.55184	+	0.747329i	0.996444	−	0.0842538i	$-0.0268506\pi$
$67$	12.7024	+	6.11715i	1.55184	+	0.747329i	0.555401	+	0.831583i	$0.312565\pi$
$68$	−0.462337	−	2.02563i	−0.0560665	−	0.245644i
$69$	−3.88344	−	4.86967i	−0.467511	−	0.586240i
$70$	1.01996	+	1.27899i	0.121909	+	0.152869i
$71$	−0.0610689	−	0.0294092i	−0.00724755	−	0.00349024i	0.430256	−	0.902707i	$-0.358423\pi$
$71$	−0.0610689	−	0.0294092i	−0.00724755	−	0.00349024i	−0.437504	+	0.899216i	$0.644137\pi$
$72$	0.405637	−	1.77721i	0.0478048	−	0.209446i
$73$	−3.48357	+	4.36826i	−0.407721	+	0.511266i	−0.942719	−	0.333587i	$-0.891741\pi$
$73$	−3.48357	+	4.36826i	−0.407721	+	0.511266i	0.534998	+	0.844853i	$0.320312\pi$
$74$	0.277269	−	1.21479i	0.0322319	−	0.141217i
$75$	0.977493	−	0.470736i	0.112871	−	0.0543559i
$76$	−0.883392	−	1.10774i	−0.101332	−	0.127066i
$77$	4.41103	−	2.12424i	0.502683	−	0.242079i
$78$	0.301047	−	0.377501i	0.0340868	−	0.0427436i
$79$	1.36505			0.153581			0.0767903	−	0.997047i	$-0.475533\pi$
$79$	1.36505			0.153581			0.0767903	+	0.997047i	$0.475533\pi$
$80$	1.00000			0.111803
$81$	−0.129833	+	0.162805i	−0.0144259	+	0.0180895i
$82$	2.87621	+	1.38511i	0.317625	+	0.152960i
$83$	−2.17407	−	9.52521i	−0.238635	−	1.04553i	−0.942241	−	0.334937i	$-0.891285\pi$
$83$	−2.17407	−	9.52521i	−0.238635	−	1.04553i	0.703606	−	0.710591i	$-0.251572\pi$
$84$	0.394938	−	1.73034i	0.0430913	−	0.188795i
$85$	2.07772			0.225361
$86$	−5.24213	−	3.93955i	−0.565273	−	0.424813i
$87$	1.05405			0.113006
$88$	0.665958	−	2.91775i	0.0709913	−	0.311033i
$89$	−2.64830	−	11.6029i	−0.280719	−	1.22991i	−0.896874	−	0.442286i	$-0.854168\pi$
$89$	−2.64830	−	11.6029i	−0.280719	−	1.22991i	0.616155	−	0.787625i	$-0.288689\pi$
$90$	1.64239	+	0.790933i	0.173123	+	0.0833717i
$91$	−0.453925	+	0.569204i	−0.0475843	+	0.0596688i
$92$	5.74094			0.598534
$93$	−0.108555			−0.0112566
$94$	−4.24570	+	5.32394i	−0.437911	+	0.549123i
$95$	1.27654	−	0.614748i	0.130970	−	0.0630719i
$96$	−0.676446	−	0.848237i	−0.0690395	−	0.0865728i
$97$	8.71217	−	4.19556i	0.884586	−	0.425994i	0.0642889	−	0.997931i	$-0.479522\pi$
$97$	8.71217	−	4.19556i	0.884586	−	0.425994i	0.820298	+	0.571937i	$0.193808\pi$
$98$	0.962150	−	4.21546i	0.0971918	−	0.425825i
$99$	3.40151	−	4.26536i	0.341864	−	0.428684i
$100$	−0.222521	+	0.974928i	−0.0222521	+	0.0974928i
$101$	−10.6588	−	5.13301i	−1.06059	−	0.510754i	−0.179529	−	0.983753i	$-0.557457\pi$
$101$	−10.6588	−	5.13301i	−1.06059	−	0.510754i	−0.881063	+	0.472999i	$0.843171\pi$
$102$	−1.40547	−	1.76240i	−0.139162	−	0.174504i
$103$	0.0354737	+	0.0444826i	0.00349533	+	0.00438300i	0.783576	−	0.621296i	$-0.213393\pi$
$103$	0.0354737	+	0.0444826i	0.00349533	+	0.00438300i	−0.780081	+	0.625679i	$0.784822\pi$
$104$	0.0990311	+	0.433884i	0.00971080	+	0.0425458i
$105$	1.59907	+	0.770072i	0.156053	+	0.0751513i
$106$	8.39370	−	4.04220i	0.815269	−	0.392613i
$107$	−0.868132	−	3.80353i	−0.0839255	−	0.367702i	0.915473	−	0.402379i	$-0.131817\pi$
$107$	−0.868132	−	3.80353i	−0.0839255	−	0.367702i	−0.999399	+	0.0346777i	$0.988960\pi$
$108$	−1.16435	−	5.10136i	−0.112040	−	0.490879i
$109$	−14.3647	+	6.91767i	−1.37589	+	0.662592i	−0.968118	−	0.250493i	$-0.919407\pi$
$109$	−14.3647	+	6.91767i	−1.37589	+	0.662592i	−0.407769	+	0.913085i	$0.633693\pi$
$110$	2.69641	+	1.29852i	0.257092	+	0.123809i
$111$	−0.300819	−	1.31797i	−0.0285525	−	0.125097i
$112$	1.01996	+	1.27899i	0.0963772	+	0.120853i
$113$	−2.83420	−	3.55397i	−0.266619	−	0.334330i	0.630442	−	0.776236i	$-0.282874\pi$
$113$	−2.83420	−	3.55397i	−0.266619	−	0.334330i	−0.897061	+	0.441907i	$0.854302\pi$
$114$	−1.38496	−	0.666962i	−0.129714	−	0.0624667i
$115$	−1.27748	+	5.59700i	−0.119126	+	0.521923i
$116$	−0.605743	+	0.759577i	−0.0562418	+	0.0705250i
$117$	−0.180525	+	0.790933i	−0.0166896	+	0.0731218i
$118$	2.81723	−	1.35671i	0.259347	−	0.124895i
$119$	2.11919	+	2.65739i	0.194266	+	0.243602i
$120$	0.977493	−	0.470736i	0.0892325	−	0.0429721i
$121$	−1.27393	+	1.59746i	−0.115812	+	0.145224i
$122$	0.810096			0.0733426
$123$	3.46350			0.312293
$124$	0.0623842	−	0.0782273i	0.00560226	−	0.00702502i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	0.663577	+	2.90732i	0.0591162	+	0.259005i
$127$	−1.30271	+	5.70753i	−0.115596	+	0.506461i	0.883668	+	0.468114i	$0.155066\pi$
$127$	−1.30271	+	5.70753i	−0.115596	+	0.506461i	−0.999264	+	0.0383470i	$0.987791\pi$
$128$	1.00000			0.0883883
$129$	−6.97863	−	1.38323i	−0.614434	−	0.121786i
$130$	−0.445042			−0.0390328
$131$	3.22288	−	14.1204i	0.281585	−	1.23370i	−0.614177	−	0.789168i	$-0.710512\pi$
$131$	3.22288	−	14.1204i	0.281585	−	1.23370i	0.895762	−	0.444535i	$-0.146631\pi$
$132$	−0.722521	−	3.16557i	−0.0628874	−	0.275528i
$133$	2.08828	+	1.00566i	0.181077	+	0.0872019i
$134$	−8.79033	+	11.0227i	−0.759369	+	0.952219i
$135$	5.23255			0.450346
$136$	2.07772			0.178163
$137$	−0.714030	+	0.895365i	−0.0610037	+	0.0764962i	−0.811397	−	0.584495i	$-0.801293\pi$
$137$	−0.714030	+	0.895365i	−0.0610037	+	0.0764962i	0.750394	+	0.660991i	$0.229864\pi$
$138$	5.61173	−	2.70247i	0.477702	−	0.230049i
$139$	−11.7992	−	14.7957i	−1.00080	−	1.25496i	−0.966799	−	0.255537i	$-0.917748\pi$
$139$	−11.7992	−	14.7957i	−1.00080	−	1.25496i	−0.0339969	−	0.999422i	$-0.510824\pi$
$140$	−1.47389	+	0.709786i	−0.124566	+	0.0599879i
$141$	−1.64397	+	7.20272i	−0.138448	+	0.606578i
$142$	0.0422610	−	0.0529936i	0.00354647	−	0.00444713i
$143$	−0.296379	+	1.29852i	−0.0247845	+	0.108588i
$144$	1.64239	+	0.790933i	0.136866	+	0.0659111i
$145$	−0.605743	−	0.759577i	−0.0503042	−	0.0630795i
$146$	−3.48357	−	4.36826i	−0.288302	−	0.361520i
$147$	−1.04387	−	4.57350i	−0.0860970	−	0.377216i
$148$	1.12264	+	0.540634i	0.0922804	+	0.0444399i
$149$	1.81224	−	0.872730i	0.148465	−	0.0714968i	−0.358176	−	0.933654i	$-0.616601\pi$
$149$	1.81224	−	0.872730i	0.148465	−	0.0714968i	0.506641	+	0.862157i	$0.330887\pi$
$150$	0.241421	+	1.05773i	0.0197119	+	0.0863636i
$151$	1.88256	+	8.24804i	0.153201	+	0.671216i	0.991943	+	0.126687i	$0.0404344\pi$
$151$	1.88256	+	8.24804i	0.153201	+	0.671216i	−0.838742	+	0.544529i	$0.816708\pi$
$152$	1.27654	−	0.614748i	0.103541	−	0.0498627i
$153$	3.41243	+	1.64334i	0.275878	+	0.132856i
$154$	1.08943	+	4.77312i	0.0877890	+	0.384629i
$155$	0.0623842	+	0.0782273i	0.00501082	+	0.00628337i
$156$	0.301047	+	0.377501i	0.0241030	+	0.0302243i
$157$	−10.3963	−	5.00661i	−0.829717	−	0.399571i	−0.0297082	−	0.999559i	$-0.509458\pi$
$157$	−10.3963	−	5.00661i	−0.829717	−	0.399571i	−0.800009	+	0.599988i	$0.795172\pi$
$158$	−0.303753	+	1.33083i	−0.0241653	+	0.105875i
$159$	6.30198	−	7.90244i	0.499780	−	0.626704i
$160$	−0.222521	+	0.974928i	−0.0175918	+	0.0770748i
$161$	−8.46149	+	4.07484i	−0.666859	+	0.321142i
$162$	−0.129833	−	0.162805i	−0.0102006	−	0.0127912i
$163$	−12.5886	+	6.06234i	−0.986014	+	0.474839i	−0.856170	−	0.516695i	$-0.827162\pi$
$163$	−12.5886	+	6.06234i	−0.986014	+	0.474839i	−0.129845	+	0.991534i	$0.541448\pi$
$164$	−1.99040	+	2.49589i	−0.155424	+	0.194896i
$165$	3.24698			0.252777
$166$	9.77017			0.758312
$167$	−7.28711	+	9.13774i	−0.563893	+	0.707100i	−0.979272	−	0.202549i	$-0.935078\pi$
$167$	−7.28711	+	9.13774i	−0.563893	+	0.707100i	0.415379	+	0.909649i	$0.363649\pi$
$168$	1.59907	+	0.770072i	0.123371	+	0.0594124i
$169$	2.84870	+	12.4810i	0.219131	+	0.960074i
$170$	−0.462337	+	2.02563i	−0.0354596	+	0.155359i
$171$	2.58280			0.197512
$172$	5.00726	−	4.23407i	0.381800	−	0.322844i
$173$	−7.93558			−0.603331			−0.301666	−	0.953414i	$-0.597543\pi$
$173$	−7.93558			−0.603331			−0.301666	+	0.953414i	$0.597543\pi$
$174$	−0.234549	+	1.02763i	−0.0177811	+	0.0779042i
$175$	−0.364020	−	1.59487i	−0.0275173	−	0.120561i
$176$	2.69641	+	1.29852i	0.203249	+	0.0978797i
$177$	2.11517	−	2.65234i	0.158986	−	0.199362i
$178$	11.9013			0.892043
$179$	3.02942			0.226429			0.113215	−	0.993571i	$-0.463885\pi$
$179$	3.02942			0.226429			0.113215	+	0.993571i	$0.463885\pi$
$180$	−1.13657	+	1.42521i	−0.0847148	+	0.106229i
$181$	−12.9584	+	6.24044i	−0.963191	+	0.463848i	−0.848292	−	0.529529i	$-0.822369\pi$
$181$	−12.9584	+	6.24044i	−0.963191	+	0.463848i	−0.114899	+	0.993377i	$0.536654\pi$
$182$	−0.453925	−	0.569204i	−0.0336472	−	0.0421922i
$183$	0.791863	−	0.381341i	0.0585362	−	0.0281896i
$184$	−1.27748	+	5.59700i	−0.0941770	+	0.412616i
$185$	−0.776890	+	0.974190i	−0.0571181	+	0.0716238i
$186$	0.0241557	−	0.105833i	0.00177118	−	0.00776006i
$187$	5.60238	+	2.69797i	0.409687	+	0.197295i
$188$	−4.24570	−	5.32394i	−0.309650	−	0.388288i
$189$	5.33700	+	6.69238i	0.388209	+	0.486799i
$190$	0.315279	+	1.38133i	0.0228727	+	0.100212i
$191$	−0.0838345	−	0.0403726i	−0.00606605	−	0.00292126i	0.430848	−	0.902424i	$-0.358214\pi$
$191$	−0.0838345	−	0.0403726i	−0.00606605	−	0.00292126i	−0.436914	+	0.899503i	$0.643929\pi$
$192$	0.977493	−	0.470736i	0.0705445	−	0.0339724i
$193$	−0.469214	−	2.05576i	−0.0337748	−	0.147977i	0.955229	−	0.295868i	$-0.0956087\pi$
$193$	−0.469214	−	2.05576i	−0.0337748	−	0.147977i	−0.989004	+	0.147891i	$0.952752\pi$
$194$	2.15173	+	9.42733i	0.154485	+	0.676843i
$195$	−0.435025	+	0.209497i	−0.0311528	+	0.0150024i
$196$	3.89567	+	1.87605i	0.278262	+	0.134004i
$197$	−2.85041	−	12.4885i	−0.203084	−	0.889767i	−0.969046	−	0.246882i	$-0.920594\pi$
$197$	−2.85041	−	12.4885i	−0.203084	−	0.889767i	0.765962	−	0.642886i	$-0.222263\pi$
$198$	3.40151	+	4.26536i	0.241735	+	0.303126i
$199$	2.61778	+	3.28259i	0.185570	+	0.232697i	0.865911	−	0.500199i	$-0.166740\pi$
$199$	2.61778	+	3.28259i	0.185570	+	0.232697i	−0.680341	+	0.732896i	$0.738168\pi$
$200$	−0.900969	−	0.433884i	−0.0637081	−	0.0306802i
$201$	−3.40370	+	14.9126i	−0.240078	+	1.05185i
$202$	7.37613	−	9.24937i	0.518983	−	0.650784i
$203$	0.353658	−	1.54948i	0.0248219	−	0.108752i
$204$	2.03096	−	0.978058i	0.142196	−	0.0684778i
$205$	−1.99040	−	2.49589i	−0.139016	−	0.174320i
$206$	−0.0512610	+	0.0246860i	−0.00357152	+	0.00171996i
$207$	−6.52497	+	8.18206i	−0.453517	+	0.568692i
$208$	−0.445042			−0.0308581
$209$	4.24033			0.293310
$210$	−1.10659	+	1.38762i	−0.0763621	+	0.0957550i
$211$	24.9044	+	11.9933i	1.71449	+	0.825655i	0.990769	+	0.135563i	$0.0432842\pi$
$211$	24.9044	+	11.9933i	1.71449	+	0.825655i	0.723721	+	0.690092i	$0.242430\pi$
$212$	2.07307	+	9.08273i	0.142379	+	0.623804i
$213$	0.0163638	−	0.0716947i	0.00112123	−	0.00491244i
$214$	3.90135			0.266691
$215$	3.01369	+	5.82389i	0.205532	+	0.397186i
$216$	5.23255			0.356030
$217$	−0.0364225	+	0.159578i	−0.00247252	+	0.0108328i
$218$	−3.54778	−	15.5439i	−0.240286	−	1.05276i
$219$	−5.46146	−	2.63010i	−0.369051	−	0.177726i
$220$	−1.86597	+	2.33985i	−0.125804	+	0.157753i
$221$	−0.924673			−0.0622002
$222$	1.35187			0.0907314
$223$	−6.95885	+	8.72613i	−0.465999	+	0.584345i	−0.958186	−	0.286145i	$-0.907626\pi$
$223$	−6.95885	+	8.72613i	−0.465999	+	0.584345i	0.492187	+	0.870489i	$0.336198\pi$
$224$	−1.47389	+	0.709786i	−0.0984782	+	0.0474246i
$225$	−1.13657	−	1.42521i	−0.0757713	−	0.0950142i
$226$	4.09554	−	1.97231i	0.272431	−	0.131196i
$227$	−0.967601	+	4.23933i	−0.0642219	+	0.281375i	−0.996835	−	0.0795046i	$-0.974666\pi$
$227$	−0.967601	+	4.23933i	−0.0642219	+	0.281375i	0.932613	+	0.360879i	$0.117523\pi$
$228$	0.958423	−	1.20182i	0.0634731	−	0.0795928i
$229$	1.82022	−	7.97489i	0.120283	−	0.526996i	−0.878503	−	0.477737i	$-0.841457\pi$
$229$	1.82022	−	7.97489i	0.120283	−	0.526996i	0.998786	−	0.0492585i	$-0.0156858\pi$
$230$	−5.17241	−	2.49090i	−0.341058	−	0.164245i
$231$	3.31179	+	4.15286i	0.217900	+	0.273238i
$232$	−0.605743	−	0.759577i	−0.0397690	−	0.0498687i
$233$	2.62438	+	11.4982i	0.171929	+	0.753270i	0.985203	+	0.171389i	$0.0548256\pi$
$233$	2.62438	+	11.4982i	0.171929	+	0.753270i	−0.813274	+	0.581880i	$0.802317\pi$
$234$	−0.730932	−	0.351998i	−0.0477825	−	0.0230109i
$235$	6.13522	−	2.95456i	0.400217	−	0.192735i
$236$	0.695799	+	3.04849i	0.0452926	+	0.198440i
$237$	0.329553	+	1.44386i	0.0214067	+	0.0937890i
$238$	−3.06232	+	1.47474i	−0.198501	+	0.0955931i
$239$	0.339303	+	0.163399i	0.0219477	+	0.0105694i	0.444825	−	0.895617i	$-0.353266\pi$
$239$	0.339303	+	0.163399i	0.0219477	+	0.0105694i	−0.422878	+	0.906187i	$0.638980\pi$
$240$	0.241421	+	1.05773i	0.0155836	+	0.0682764i
$241$	6.49580	+	8.14548i	0.418431	+	0.524696i	0.945717	−	0.324992i	$-0.105362\pi$
$241$	6.49580	+	8.14548i	0.418431	+	0.524696i	−0.527285	+	0.849688i	$0.676790\pi$
$242$	−1.27393	−	1.59746i	−0.0818916	−	0.102689i
$243$	13.9395	+	6.71293i	0.894223	+	0.430635i
$244$	−0.180263	+	0.789785i	−0.0115402	+	0.0505608i
$245$	−2.69588	+	3.38053i	−0.172234	+	0.215974i
$246$	−0.770702	+	3.37666i	−0.0491381	+	0.215288i
$247$	−0.568113	+	0.273589i	−0.0361482	+	0.0174080i
$248$	0.0623842	+	0.0782273i	0.00396140	+	0.00496744i
$249$	9.55027	−	4.59917i	0.605224	−	0.291460i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−6.89996			−0.435522			−0.217761	−	0.976002i	$-0.569875\pi$
$251$	−6.89996			−0.435522			−0.217761	+	0.976002i	$0.569875\pi$
$252$	−2.98209			−0.187854
$253$	−10.7124	+	13.4330i	−0.673485	+	0.844523i
$254$	−5.27455	−	2.54009i	−0.330955	−	0.159379i
$255$	0.501605	+	2.19768i	0.0314117	+	0.137624i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−13.4947			−0.841777			−0.420889	−	0.907112i	$-0.638282\pi$
$257$	−13.4947			−0.841777			−0.420889	+	0.907112i	$0.638282\pi$
$258$	2.90144	−	6.49587i	0.180636	−	0.404415i
$259$	−2.03838			−0.126659
$260$	0.0990311	−	0.433884i	0.00614165	−	0.0269083i
$261$	−0.394091	−	1.72662i	−0.0243936	−	0.106875i
$262$	13.0492	+	6.28416i	0.806182	+	0.388237i
$263$	−1.20360	+	1.50927i	−0.0742174	+	0.0930656i	−0.817554	−	0.575852i	$-0.804671\pi$
$263$	−1.20360	+	1.50927i	−0.0742174	+	0.0930656i	0.743337	+	0.668917i	$0.233242\pi$
$264$	3.24698			0.199838
$265$	−9.31631			−0.572296
$266$	−1.44513	+	1.81214i	−0.0886067	+	0.111109i
$267$	11.6335	−	5.60239i	0.711957	−	0.342861i
$268$	−8.79033	−	11.0227i	−0.536955	−	0.673320i
$269$	−6.30192	+	3.03485i	−0.384235	+	0.185038i	−0.616022	−	0.787729i	$-0.711257\pi$
$269$	−6.30192	+	3.03485i	−0.384235	+	0.185038i	0.231787	+	0.972766i	$0.425543\pi$
$270$	−1.16435	+	5.10136i	−0.0708602	+	0.310459i
$271$	3.28905	−	4.12434i	0.199796	−	0.250536i	−0.671833	−	0.740703i	$-0.734493\pi$
$271$	3.28905	−	4.12434i	0.199796	−	0.250536i	0.871629	+	0.490167i	$0.163064\pi$
$272$	−0.462337	+	2.02563i	−0.0280333	+	0.122822i
$273$	−0.711654	−	0.342714i	−0.0430712	−	0.0207420i
$274$	−0.714030	−	0.895365i	−0.0431361	−	0.0540910i
$275$	−1.86597	−	2.33985i	−0.112522	−	0.141099i
$276$	1.38598	+	6.07239i	0.0834263	+	0.365515i
$277$	19.0506	+	9.17430i	1.14464	+	0.551230i	0.907420	−	0.420226i	$-0.138049\pi$
$277$	19.0506	+	9.17430i	1.14464	+	0.551230i	0.237221	+	0.971456i	$0.423763\pi$
$278$	17.0504	−	8.21102i	1.02261	−	0.492464i
$279$	0.0405866	+	0.177821i	0.00242985	+	0.0106459i
$280$	−0.364020	−	1.59487i	−0.0217543	−	0.0953120i
$281$	−20.1529	+	9.70515i	−1.20222	+	0.578960i	−0.924309	−	0.381645i	$-0.875358\pi$
$281$	−20.1529	+	9.70515i	−1.20222	+	0.578960i	−0.277915	+	0.960606i	$0.589643\pi$
$282$	−6.65631	−	3.20551i	−0.396378	−	0.190885i
$283$	4.35388	+	19.0756i	0.258811	+	1.13393i	0.922524	+	0.385939i	$0.126122\pi$
$283$	4.35388	+	19.0756i	0.258811	+	1.13393i	−0.663713	+	0.747987i	$0.731020\pi$
$284$	0.0422610	+	0.0529936i	0.00250773	+	0.00314459i
$285$	0.958423	+	1.20182i	0.0567721	+	0.0711899i
$286$	−1.20001	−	0.577896i	−0.0709583	−	0.0341717i
$287$	1.16208	−	5.09141i	0.0685955	−	0.300536i
$288$	−1.13657	+	1.42521i	−0.0669730	+	0.0839814i
$289$	2.82225	−	12.3651i	0.166015	−	0.727358i
$290$	0.875324	−	0.421534i	0.0514008	−	0.0247533i
$291$	6.54108	+	8.20226i	0.383445	+	0.480825i
$292$	5.03390	−	2.42420i	0.294587	−	0.141866i
$293$	−8.19557	+	10.2769i	−0.478790	+	0.600384i	−0.961299	−	0.275507i	$-0.911154\pi$
$293$	−8.19557	+	10.2769i	−0.478790	+	0.600384i	0.482509	+	0.875891i	$0.339726\pi$
$294$	4.69111			0.273591
$295$	−3.12689			−0.182055
$296$	−0.776890	+	0.974190i	−0.0451558	+	0.0566236i
$297$	14.1091	+	6.79458i	0.818692	+	0.394261i
$298$	0.447587	+	1.96101i	0.0259280	+	0.113598i
$299$	0.568532	−	2.49090i	0.0328790	−	0.144052i
$300$	−1.08494			−0.0626388
$301$	−4.37486	+	9.79462i	−0.252162	+	0.564552i
$302$	−8.46016			−0.486827
$303$	2.85610	−	12.5134i	0.164079	−	0.718876i
$304$	0.315279	+	1.38133i	0.0180825	+	0.0792245i
$305$	−0.729871	−	0.351487i	−0.0417923	−	0.0201261i
$306$	−2.36147	+	2.96119i	−0.134996	+	0.169280i
$307$	−1.60667			−0.0916975			−0.0458487	−	0.998948i	$-0.514599\pi$
$307$	−1.60667			−0.0916975			−0.0458487	+	0.998948i	$0.514599\pi$
$308$	−4.89587			−0.278968
$309$	−0.0384867	+	0.0482608i	−0.00218943	+	0.00274546i
$310$	−0.0901477	+	0.0434129i	−0.00512005	+	0.00246569i
$311$	−7.84155	−	9.83299i	−0.444654	−	0.557578i	0.508110	−	0.861292i	$-0.330345\pi$
$311$	−7.84155	−	9.83299i	−0.444654	−	0.557578i	−0.952763	+	0.303715i	$0.901773\pi$
$312$	−0.435025	+	0.209497i	−0.0246285	+	0.0118604i
$313$	1.45572	−	6.37792i	0.0822820	−	0.360501i	−0.916979	−	0.398935i	$-0.869380\pi$
$313$	1.45572	−	6.37792i	0.0822820	−	0.360501i	0.999261	+	0.0384341i	$0.0122370\pi$
$314$	7.19448	−	9.02160i	0.406008	−	0.509118i
$315$	0.663577	−	2.90732i	0.0373883	−	0.163809i
$316$	−1.22987	−	0.592275i	−0.0691857	−	0.0333181i
$317$	−22.0901	−	27.7001i	−1.24070	−	1.55579i	−0.698698	−	0.715417i	$-0.746237\pi$
$317$	−22.0901	−	27.7001i	−1.24070	−	1.55579i	−0.542005	−	0.840375i	$-0.682335\pi$
$318$	6.30198	+	7.90244i	0.353398	+	0.443147i
$319$	−0.647002	−	2.83470i	−0.0362251	−	0.158713i
$320$	−0.900969	−	0.433884i	−0.0503657	−	0.0242548i
$321$	3.81354	−	1.83650i	0.212851	−	0.102504i
$322$	−2.08982	−	9.15608i	−0.116461	−	0.510248i
$323$	0.655062	+	2.87001i	0.0364486	+	0.159692i
$324$	0.187614	−	0.0903500i	0.0104230	−	0.00501944i
$325$	0.400969	+	0.193096i	0.0222418	+	0.0107111i
$326$	−3.10912	−	13.6220i	−0.172198	−	0.754451i
$327$	−10.7850	−	13.5239i	−0.596411	−	0.747876i
$328$	−1.99040	−	2.49589i	−0.109902	−	0.137812i
$329$	10.0365	+	4.83334i	0.553332	+	0.266471i
$330$	−0.722521	+	3.16557i	−0.0397735	+	0.174259i
$331$	20.4398	−	25.6307i	1.12347	−	1.40879i	0.222493	−	0.974934i	$-0.428581\pi$
$331$	20.4398	−	25.6307i	1.12347	−	1.40879i	0.900981	−	0.433858i	$-0.142848\pi$
$332$	−2.17407	+	9.52521i	−0.119317	+	0.522764i
$333$	−2.04648	+	0.985531i	−0.112146	+	0.0540068i
$334$	−7.28711	−	9.13774i	−0.398733	−	0.499995i
$335$	12.7024	−	6.11715i	0.694006	−	0.334216i
$336$	−1.10659	+	1.38762i	−0.0603695	+	0.0757010i
$337$	15.1864			0.827254			0.413627	−	0.910446i	$-0.364262\pi$
$337$	15.1864			0.827254			0.413627	+	0.910446i	$0.364262\pi$
$338$	−12.8019			−0.696334
$339$	3.07492	−	3.85583i	0.167007	−	0.209420i
$340$	−1.87196	−	0.901490i	−0.101521	−	0.0488901i
$341$	0.0666333	+	0.291940i	0.00360840	+	0.0158094i
$342$	−0.574727	+	2.51804i	−0.0310777	+	0.136160i
$343$	−18.5246			−1.00023
$344$	3.01369	+	5.82389i	0.162487	+	0.314003i
$345$	−6.22855			−0.335334
$346$	1.76583	−	7.73662i	0.0949318	−	0.415923i
$347$	−1.80600	−	7.91260i	−0.0969511	−	0.424771i	0.903037	−	0.429562i	$-0.141332\pi$
$347$	−1.80600	−	7.91260i	−0.0969511	−	0.424771i	−0.999989	+	0.00479125i	$0.998475\pi$
$348$	−0.949670	−	0.457337i	−0.0509076	−	0.0245158i
$349$	20.3050	−	25.4616i	1.08690	−	1.36293i	0.160217	−	0.987082i	$-0.448781\pi$
$349$	20.3050	−	25.4616i	1.08690	−	1.36293i	0.926682	−	0.375847i	$-0.122648\pi$
$350$	1.63589			0.0874420
$351$	−2.32870			−0.124297
$352$	−1.86597	+	2.33985i	−0.0994566	+	0.124715i
$353$	21.3519	−	10.2826i	1.13645	−	0.547285i	0.231513	−	0.972832i	$-0.425633\pi$
$353$	21.3519	−	10.2826i	1.13645	−	0.547285i	0.904936	+	0.425547i	$0.139918\pi$
$354$	2.11517	+	2.65234i	0.112420	+	0.140970i
$355$	−0.0610689	+	0.0294092i	−0.00324120	+	0.00156088i
$356$	−2.64830	+	11.6029i	−0.140359	+	0.614955i
$357$	−2.29919	+	2.88309i	−0.121686	+	0.152589i
$358$	−0.674109	+	2.95347i	−0.0356278	+	0.156096i
$359$	5.77342	+	2.78033i	0.304709	+	0.146740i	0.579990	−	0.814624i	$-0.303056\pi$
$359$	5.77342	+	2.78033i	0.304709	+	0.146740i	−0.275281	+	0.961364i	$0.588771\pi$
$360$	−1.13657	−	1.42521i	−0.0599024	−	0.0751153i
$361$	−10.5947	−	13.2853i	−0.557614	−	0.699226i
$362$	−3.20046	−	14.0221i	−0.168213	−	0.736987i
$363$	−1.99725	−	0.961823i	−0.104828	−	0.0504826i
$364$	0.655941	−	0.315885i	0.0343807	−	0.0165568i
$365$	1.24327	+	5.44713i	0.0650758	+	0.285116i
$366$	0.195574	+	0.856866i	0.0102228	+	0.0447891i
$367$	−31.7787	+	15.3038i	−1.65883	+	0.798852i	−0.659965	+	0.751296i	$0.729429\pi$
$367$	−31.7787	+	15.3038i	−1.65883	+	0.798852i	−0.998869	+	0.0475556i	$0.984857\pi$
$368$	−5.17241	−	2.49090i	−0.269630	−	0.129847i
$369$	−1.29494	−	5.67349i	−0.0674118	−	0.295350i
$370$	−0.776890	−	0.974190i	−0.0403886	−	0.0506457i
$371$	−9.50227	−	11.9155i	−0.493333	−	0.618620i
$372$	0.0978045	+	0.0471002i	0.00507093	+	0.00244203i
$373$	0.950343	−	4.16372i	0.0492069	−	0.215589i	−0.944347	−	0.328951i	$-0.893305\pi$
$373$	0.950343	−	4.16372i	0.0492069	−	0.215589i	0.993554	+	0.113362i	$0.0361619\pi$
$374$	−3.87697	+	4.86157i	−0.200473	+	0.251386i
$375$	0.241421	−	1.05773i	0.0124669	−	0.0546211i
$376$	6.13522	−	2.95456i	0.316400	−	0.152370i
$377$	0.269581	+	0.338044i	0.0138841	+	0.0174101i
$378$	−7.71218	+	3.71399i	−0.396672	+	0.191027i
$379$	−3.62370	+	4.54398i	−0.186137	+	0.233408i	−0.866141	−	0.499800i	$-0.833407\pi$
$379$	−3.62370	+	4.54398i	−0.186137	+	0.233408i	0.680004	+	0.733209i	$0.261978\pi$
$380$	−1.41685			−0.0726829
$381$	−6.35154			−0.325399
$382$	0.0580153	−	0.0727488i	0.00296832	−	0.00372215i
$383$	22.9059	+	11.0309i	1.17044	+	0.563652i	0.915111	−	0.403203i	$-0.132103\pi$
$383$	22.9059	+	11.0309i	1.17044	+	0.563652i	0.255326	+	0.966855i	$0.417817\pi$
$384$	0.241421	+	1.05773i	0.0123200	+	0.0539773i
$385$	1.08943	−	4.77312i	0.0555227	−	0.243261i
$386$	2.10863			0.107326
$387$	0.343342	+	11.9487i	0.0174531	+	0.607388i
$388$	−9.66978			−0.490908
$389$	5.73149	−	25.1113i	0.290598	−	1.27319i	−0.593098	−	0.805131i	$-0.702095\pi$
$389$	5.73149	−	25.1113i	0.290598	−	1.27319i	0.883696	−	0.468062i	$-0.155048\pi$
$390$	−0.107442	−	0.470736i	−0.00544056	−	0.0238366i
$391$	−10.7468	−	5.17540i	−0.543490	−	0.261731i
$392$	−2.69588	+	3.38053i	−0.136163	+	0.170743i
$393$	15.7137			0.792650
$394$	12.8096			0.645341
$395$	0.851097	−	1.06724i	0.0428234	−	0.0536988i
$396$	−4.91532	+	2.36709i	−0.247004	+	0.118951i
$397$	−22.1107	−	27.7259i	−1.10970	−	1.39152i	−0.911469	−	0.411369i	$-0.865051\pi$
$397$	−22.1107	−	27.7259i	−1.10970	−	1.39152i	−0.198234	−	0.980155i	$-0.563521\pi$
$398$	−3.78280	+	1.82170i	−0.189615	+	0.0913136i
$399$	−0.559568	+	2.45163i	−0.0280134	+	0.122735i
$400$	0.623490	−	0.781831i	0.0311745	−	0.0390916i
$401$	−2.39517	+	10.4939i	−0.119609	+	0.524043i	0.879253	+	0.476355i	$0.158042\pi$
$401$	−2.39517	+	10.4939i	−0.119609	+	0.524043i	−0.998862	+	0.0476876i	$0.984815\pi$
$402$	−13.7813	−	6.63672i	−0.687348	−	0.331009i
$403$	−0.0277636	−	0.0348144i	−0.00138300	−	0.00173423i
$404$	7.37613	+	9.24937i	0.366976	+	0.460173i
$405$	0.0463368	+	0.203015i	0.00230249	+	0.0100879i
$406$	1.43193	+	0.689583i	0.0710657	+	0.0342234i
$407$	−3.35982	+	1.61800i	−0.166540	+	0.0802014i
$408$	0.501605	+	2.19768i	0.0248332	+	0.108801i
$409$	7.55181	+	33.0866i	0.373413	+	1.63603i	0.717118	+	0.696952i	$0.245461\pi$
$409$	7.55181	+	33.0866i	0.373413	+	1.63603i	−0.343705	+	0.939078i	$0.611682\pi$
$410$	2.87621	−	1.38511i	0.142046	−	0.0684058i
$411$	−1.11944	−	0.539094i	−0.0552179	−	0.0265915i
$412$	−0.0126604	−	0.0554689i	−0.000623734	−	0.00273276i
$413$	−3.18931	−	3.99926i	−0.156935	−	0.196791i
$414$	−6.52497	−	8.18206i	−0.320685	−	0.402126i
$415$	−8.80262	−	4.23912i	−0.432103	−	0.208090i
$416$	0.0990311	−	0.433884i	0.00485540	−	0.0212729i
$417$	12.8014	−	16.0524i	0.626887	−	0.786091i
$418$	−0.943562	+	4.13402i	−0.0461511	+	0.202201i
$419$	−5.76174	+	2.77471i	−0.281479	+	0.135553i	−0.569297	−	0.822132i	$-0.692785\pi$
$419$	−5.76174	+	2.77471i	−0.281479	+	0.135553i	0.287818	+	0.957685i	$0.407070\pi$
$420$	−1.10659	−	1.38762i	−0.0539961	−	0.0677090i
$421$	15.5515	−	7.48919i	0.757932	−	0.365001i	−0.0146695	−	0.999892i	$-0.504670\pi$
$421$	15.5515	−	7.48919i	0.757932	−	0.365001i	0.772601	+	0.634892i	$0.218955\pi$
$422$	−17.2344	+	21.6112i	−0.838957	+	1.05202i
$423$	12.4133			0.603554
$424$	−9.31631			−0.452440
$425$	1.29544	−	1.62443i	0.0628380	−	0.0787963i
$426$	0.0662559	+	0.0319071i	0.00321011	+	0.00154591i
$427$	−0.294891	−	1.29200i	−0.0142708	−	0.0625244i
$428$	−0.868132	+	3.80353i	−0.0419627	+	0.183851i
$429$	−1.44504			−0.0697673
$430$	−6.34848	+	1.64219i	−0.306151	+	0.0791935i
$431$	37.4573			1.80425			0.902127	−	0.431470i	$-0.142005\pi$
$431$	37.4573			1.80425			0.902127	+	0.431470i	$0.142005\pi$
$432$	−1.16435	+	5.10136i	−0.0560199	+	0.245439i
$433$	0.440045	+	1.92797i	0.0211472	+	0.0926521i	0.984400	−	0.175944i	$-0.0562976\pi$
$433$	0.440045	+	1.92797i	0.0211472	+	0.0926521i	−0.963253	+	0.268596i	$0.913440\pi$
$434$	−0.147472	−	0.0710187i	−0.00707887	−	0.00340901i
$435$	0.657192	−	0.824092i	0.0315099	−	0.0395122i
$436$	15.9436			0.763560
$437$	−8.13405			−0.389104
$438$	3.77945	−	4.73928i	0.180589	−	0.226452i
$439$	14.6745	−	7.06688i	0.700377	−	0.337284i	−0.0495803	−	0.998770i	$-0.515788\pi$
$439$	14.6745	−	7.06688i	0.700377	−	0.337284i	0.749957	+	0.661486i	$0.230074\pi$
$440$	−1.86597	−	2.33985i	−0.0889567	−	0.111548i
$441$	−7.10147	+	3.41989i	−0.338165	+	0.162852i
$442$	0.205759	−	0.901490i	0.00978696	−	0.0428795i
$443$	18.9360	−	23.7450i	0.899676	−	1.12816i	−0.0915262	−	0.995803i	$-0.529175\pi$
$443$	18.9360	−	23.7450i	0.899676	−	1.12816i	0.991202	−	0.132355i	$-0.0422540\pi$
$444$	−0.300819	+	1.31797i	−0.0142762	+	0.0625483i
$445$	−10.7227	−	5.16380i	−0.508307	−	0.244788i
$446$	−6.95885	−	8.72613i	−0.329511	−	0.413194i
$447$	1.36063	+	1.70617i	0.0643555	+	0.0806993i
$448$	−0.364020	−	1.59487i	−0.0171983	−	0.0753508i
$449$	28.5562	+	13.7519i	1.34765	+	0.648994i	0.961847	−	0.273587i	$-0.0882102\pi$
$449$	28.5562	+	13.7519i	1.34765	+	0.648994i	0.385803	+	0.922581i	$0.373924\pi$
$450$	1.64239	−	0.790933i	0.0774230	−	0.0372849i
$451$	−2.12597	−	9.31450i	−0.100108	−	0.438603i
$452$	1.01151	+	4.43173i	0.0475776	+	0.208451i
$453$	−8.26974	+	3.98250i	−0.388546	+	0.187114i
$454$	−3.91773	−	1.88668i	−0.183868	−	0.0885464i
$455$	0.162004	+	0.709786i	0.00759487	+	0.0332753i
$456$	0.958423	+	1.20182i	0.0448823	+	0.0562806i
$457$	−9.46691	−	11.8711i	−0.442843	−	0.555308i	0.509447	−	0.860502i	$-0.329850\pi$
$457$	−9.46691	−	11.8711i	−0.442843	−	0.555308i	−0.952290	+	0.305194i	$0.901279\pi$
$458$	7.36991	+	3.54916i	0.344373	+	0.165841i
$459$	−2.41920	+	10.5992i	−0.112919	+	0.494729i
$460$	3.57942	−	4.48845i	0.166891	−	0.209275i
$461$	−4.18664	+	18.3429i	−0.194991	+	0.854312i	0.778873	+	0.627182i	$0.215792\pi$
$461$	−4.18664	+	18.3429i	−0.194991	+	0.854312i	−0.973864	+	0.227131i	$0.927066\pi$
$462$	−4.78568	+	2.30466i	−0.222650	+	0.107223i
$463$	−2.68489	−	3.36675i	−0.124778	−	0.156466i	0.715519	−	0.698594i	$-0.246190\pi$
$463$	−2.68489	−	3.36675i	−0.124778	−	0.156466i	−0.840296	+	0.542127i	$0.817619\pi$
$464$	0.875324	−	0.421534i	0.0406359	−	0.0195692i
$465$	−0.0676828	+	0.0848715i	−0.00313871	+	0.00393582i
$466$	−11.7939			−0.546340
$467$	−30.4273			−1.40801			−0.704004	−	0.710196i	$-0.748606\pi$
$467$	−30.4273			−1.40801			−0.704004	+	0.710196i	$0.748606\pi$
$468$	0.505821	−	0.634279i	0.0233816	−	0.0293196i
$469$	20.7797	+	10.0070i	0.959519	+	0.462080i
$470$	1.51527	+	6.63885i	0.0698943	+	0.306227i
$471$	2.78577	−	12.2052i	0.128361	−	0.562388i
$472$	−3.12689			−0.143927
$473$	0.563685	+	19.6169i	0.0259183	+	0.901987i
$474$	−1.48100			−0.0680244
$475$	0.315279	−	1.38133i	0.0144660	−	0.0633796i
$476$	−0.756332	−	3.31371i	−0.0346664	−	0.151883i
$477$	−15.3010	−	7.36858i	−0.700585	−	0.337384i
$478$	−0.234805	+	0.294436i	−0.0107397	+	0.0134672i
$479$	−11.0274			−0.503855			−0.251927	−	0.967746i	$-0.581064\pi$
$479$	−11.0274			−0.503855			−0.251927	+	0.967746i	$0.581064\pi$
$480$	−1.08494			−0.0495203
$481$	0.345749	−	0.433555i	0.0157648	−	0.0197684i
$482$	−9.38671	+	4.52040i	−0.427553	+	0.205899i
$483$	−6.35287	−	7.96625i	−0.289066	−	0.362477i
$484$	1.84089	−	0.886525i	0.0836768	−	0.0402966i
$485$	2.15173	−	9.42733i	0.0977049	−	0.428073i
$486$	−9.64647	+	12.0963i	−0.437573	+	0.548699i
$487$	−3.53002	+	15.4660i	−0.159961	+	0.700833i	0.829796	+	0.558067i	$0.188457\pi$
$487$	−3.53002	+	15.4660i	−0.159961	+	0.700833i	−0.989756	+	0.142766i	$0.954400\pi$
$488$	−0.729871	−	0.351487i	−0.0330397	−	0.0159111i
$489$	−9.45149	−	11.8518i	−0.427411	−	0.535957i
$490$	−2.69588	−	3.38053i	−0.121788	−	0.152717i
$491$	5.35009	+	23.4403i	0.241446	+	1.05784i	0.939701	+	0.341996i	$0.111103\pi$
$491$	5.35009	+	23.4403i	0.241446	+	1.05784i	−0.698255	+	0.715849i	$0.746040\pi$
$492$	−3.12051	−	1.50276i	−0.140683	−	0.0677495i
$493$	1.81868	−	0.875830i	0.0819092	−	0.0394454i
$494$	−0.140312	−	0.614748i	−0.00631295	−	0.0276588i
$495$	−1.21398	−	5.31881i	−0.0545645	−	0.239063i
$496$	−0.0901477	+	0.0434129i	−0.00404775	+	0.00194930i
$497$	−0.0999021	−	0.0481103i	−0.00448122	−	0.00215804i
$498$	2.35872	+	10.3342i	0.105697	+	0.463088i
$499$	−3.84609	−	4.82284i	−0.172175	−	0.215900i	0.688256	−	0.725468i	$-0.258377\pi$
$499$	−3.84609	−	4.82284i	−0.172175	−	0.215900i	−0.860430	+	0.509568i	$0.829805\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	−11.4246	−	5.50178i	−0.510412	−	0.245801i
$502$	1.53539	−	6.72697i	0.0685277	−	0.300239i
$503$	5.05332	−	6.33667i	0.225317	−	0.282538i	−0.656304	−	0.754496i	$-0.727881\pi$
$503$	5.05332	−	6.33667i	0.225317	−	0.282538i	0.881621	+	0.471958i	$0.156453\pi$
$504$	0.663577	−	2.90732i	0.0295581	−	0.129502i
$505$	−10.6588	+	5.13301i	−0.474311	+	0.228416i
$506$	−10.7124	−	13.4330i	−0.476226	−	0.597168i
$507$	−12.5138	+	6.02633i	−0.555758	+	0.267639i
$508$	3.65010	−	4.57708i	0.161947	−	0.203075i
$509$	26.7819			1.18709			0.593543	−	0.804802i	$-0.297729\pi$
$509$	26.7819			1.18709			0.593543	+	0.804802i	$0.297729\pi$
$510$	−2.25419			−0.0998174
$511$	−5.69874	+	7.14599i	−0.252097	+	0.316120i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	1.64971	+	7.22787i	0.0728366	+	0.319118i
$514$	3.00286	−	13.1564i	0.132450	−	0.580303i
$515$	0.0568954			0.00250711
$516$	5.68737	+	4.27416i	0.250373	+	0.188159i
$517$	20.3796			0.896294
$518$	0.453582	−	1.98727i	0.0199292	−	0.0873157i
$519$	−1.91581	−	8.39373i	−0.0840949	−	0.368444i
$520$	0.400969	+	0.193096i	0.0175836	+	0.00846784i
$521$	5.96989	−	7.48600i	0.261546	−	0.327968i	−0.633668	−	0.773605i	$-0.718451\pi$
$521$	5.96989	−	7.48600i	0.261546	−	0.327968i	0.895214	+	0.445637i	$0.147023\pi$
$522$	1.77103			0.0775158
$523$	−12.7805			−0.558853			−0.279427	−	0.960167i	$-0.590144\pi$
$523$	−12.7805			−0.558853			−0.279427	+	0.960167i	$0.590144\pi$
$524$	−9.03032	+	11.3237i	−0.394491	+	0.494676i
$525$	1.59907	−	0.770072i	0.0697892	−	0.0336087i
$526$	−1.20360	−	1.50927i	−0.0524796	−	0.0658073i
$527$	−0.187302	+	0.0901998i	−0.00815900	+	0.00392917i
$528$	−0.722521	+	3.16557i	−0.0314437	+	0.137764i
$529$	6.20895	−	7.78577i	0.269954	−	0.338512i
$530$	2.07307	−	9.08273i	0.0900486	−	0.394529i
$531$	−5.13557	−	2.47316i	−0.222865	−	0.107326i
$532$	−1.44513	−	1.81214i	−0.0626544	−	0.0785662i
$533$	0.885812	+	1.11077i	0.0383688	+	0.0481129i
$534$	2.87323	+	12.5885i	0.124337	+	0.544756i
$535$	−3.51499	−	1.69273i	−0.151966	−	0.0731832i
$536$	12.7024	−	6.11715i	0.548660	−	0.264221i
$537$	0.731365	+	3.20432i	0.0315607	+	0.138277i
$538$	−1.55645	−	6.81924i	−0.0671032	−	0.293998i
$539$	−11.6589	+	5.61463i	−0.502184	+	0.241839i
$540$	−4.71437	−	2.27032i	−0.202874	−	0.0976990i
$541$	−3.02722	−	13.2631i	−0.130150	−	0.570227i	−0.997381	−	0.0723204i	$-0.976960\pi$
$541$	−3.02722	−	13.2631i	−0.130150	−	0.570227i	0.867231	−	0.497906i	$-0.165898\pi$
$542$	3.28905	+	4.12434i	0.141277	+	0.177156i
$543$	−9.72915	−	12.2000i	−0.417518	−	0.523551i
$544$	−1.87196	−	0.901490i	−0.0802597	−	0.0386510i
$545$	−3.54778	+	15.5439i	−0.151970	+	0.665826i
$546$	0.492480	−	0.617550i	0.0210762	−	0.0264287i
$547$	−5.53456	+	24.2485i	−0.236640	+	1.03679i	0.707362	+	0.706851i	$0.249885\pi$
$547$	−5.53456	+	24.2485i	−0.236640	+	1.03679i	−0.944003	+	0.329938i	$0.892972\pi$
$548$	1.03180	−	0.496890i	0.0440764	−	0.0212261i
$549$	−0.920730	−	1.15456i	−0.0392958	−	0.0492754i
$550$	2.69641	−	1.29852i	0.114975	−	0.0553691i
$551$	0.858247	−	1.07621i	0.0365625	−	0.0458480i
$552$	−6.22855			−0.265105
$553$	2.23308			0.0949602
$554$	−13.1834	+	16.5315i	−0.560111	+	0.702357i
$555$	−1.21799	−	0.586554i	−0.0517008	−	0.0248978i
$556$	4.21109	+	18.4500i	0.178590	+	0.782454i
$557$	−1.98674	+	8.70448i	−0.0841809	+	0.368821i	−0.999419	−	0.0340936i	$-0.989146\pi$
$557$	−1.98674	+	8.70448i	−0.0841809	+	0.368821i	0.915238	+	0.402914i	$0.132003\pi$
$558$	−0.182394			−0.00772137
$559$	−1.34122	−	2.59187i	−0.0567274	−	0.109625i
$560$	1.63589			0.0691290
$561$	−1.50120	+	6.57717i	−0.0633806	+	0.277689i
$562$	−4.97737	−	21.8073i	−0.209958	−	0.919884i
$563$	30.4234	+	14.6511i	1.28219	+	0.617472i	0.945953	−	0.324305i	$-0.105130\pi$
$563$	30.4234	+	14.6511i	1.28219	+	0.617472i	0.336240	+	0.941776i	$0.390845\pi$
$564$	4.60631	−	5.77613i	0.193961	−	0.243219i
$565$	−4.54570			−0.191239
$566$	−19.5662			−0.822427
$567$	−0.212392	+	0.266331i	−0.00891963	+	0.0111849i
$568$	−0.0610689	+	0.0294092i	−0.00256240	+	0.00123398i
$569$	14.8577	+	18.6310i	0.622867	+	0.781050i	0.988745	−	0.149613i	$-0.0478026\pi$
$569$	14.8577	+	18.6310i	0.622867	+	0.781050i	−0.365878	+	0.930663i	$0.619231\pi$
$570$	−1.38496	+	0.666962i	−0.0580097	+	0.0279360i
$571$	4.92954	−	21.5977i	0.206295	−	0.903836i	−0.760713	−	0.649089i	$-0.775150\pi$
$571$	4.92954	−	21.5977i	0.206295	−	0.903836i	0.967008	−	0.254748i	$-0.0819924\pi$
$572$	0.830435	−	1.04133i	0.0347223	−	0.0435403i
$573$	0.0224640	−	0.0984213i	0.000938448	−	0.00411161i
$574$	4.70517	+	2.26589i	0.196390	+	0.0945765i
$575$	3.57942	+	4.48845i	0.149272	+	0.187181i
$576$	−1.13657	−	1.42521i	−0.0473570	−	0.0593838i
$577$	0.844335	+	3.69927i	0.0351501	+	0.154003i	0.989457	−	0.144824i	$-0.0462617\pi$
$577$	0.844335	+	3.69927i	0.0351501	+	0.154003i	−0.954307	+	0.298827i	$0.903405\pi$
$578$	11.4271	+	5.50298i	0.475303	+	0.228894i
$579$	2.06117	−	0.992607i	0.0856593	−	0.0412513i
$580$	0.216187	+	0.947178i	0.00897668	+	0.0393294i
$581$	−3.55653	−	15.5822i	−0.147550	−	0.646458i
$582$	−9.45214	+	4.55191i	−0.391804	+	0.188683i
$583$	−25.1206	−	12.0974i	−1.04039	−	0.501024i
$584$	1.24327	+	5.44713i	0.0514470	+	0.225404i
$585$	0.505821	+	0.634279i	0.0209131	+	0.0262242i
$586$	−8.19557	−	10.2769i	−0.338556	−	0.424536i
$587$	−7.58756	−	3.65397i	−0.313172	−	0.150816i	0.270695	−	0.962665i	$-0.412747\pi$
$587$	−7.58756	−	3.65397i	−0.313172	−	0.150816i	−0.583867	+	0.811850i	$0.698461\pi$
$588$	−1.04387	+	4.57350i	−0.0430485	+	0.188608i
$589$	−0.0883890	+	0.110836i	−0.00364201	+	0.00456693i
$590$	0.695799	−	3.04849i	0.0286456	−	0.125504i
$591$	12.5213	−	6.02996i	0.515059	−	0.248039i
$592$	−0.776890	−	0.974190i	−0.0319300	−	0.0400389i
$593$	33.5071	−	16.1362i	1.37597	−	0.662634i	0.407836	−	0.913055i	$-0.366283\pi$
$593$	33.5071	−	16.1362i	1.37597	−	0.662634i	0.968137	+	0.250421i	$0.0805692\pi$
$594$	−9.76379	+	12.2434i	−0.400613	+	0.502353i
$595$	3.39892			0.139342
$596$	−2.01144			−0.0823917
$597$	−2.84012	+	3.56140i	−0.116238	+	0.145758i
$598$	2.30194	+	1.10855i	0.0941332	+	0.0453322i
$599$	7.75369	+	33.9711i	0.316807	+	1.38802i	0.843117	+	0.537730i	$0.180718\pi$
$599$	7.75369	+	33.9711i	0.316807	+	1.38802i	−0.526310	+	0.850293i	$0.676425\pi$
$600$	0.241421	−	1.05773i	0.00985596	−	0.0431818i
$601$	40.1096			1.63610			0.818052	−	0.575144i	$-0.195054\pi$
$601$	40.1096			1.63610			0.818052	+	0.575144i	$0.195054\pi$
$602$	−8.57555	−	6.44468i	−0.349513	−	0.262665i
$603$	25.7005			1.04661
$604$	1.88256	−	8.24804i	0.0766003	−	0.335608i
$605$	0.454662	+	1.99200i	0.0184846	+	0.0809865i
$606$	11.5641	+	5.56899i	0.469760	+	0.226225i
$607$	−16.3614	+	20.5165i	−0.664088	+	0.832740i	−0.993781	−	0.111348i	$-0.964483\pi$
$607$	−16.3614	+	20.5165i	−0.664088	+	0.832740i	0.329694	+	0.944088i	$0.393055\pi$
$608$	−1.41685			−0.0574609
$609$	1.72432			0.0698728
$610$	0.505087	−	0.633359i	0.0204504	−	0.0256439i
$611$	−2.73043	+	1.31490i	−0.110461	+	0.0531954i
$612$	−2.36147	−	2.96119i	−0.0954569	−	0.119699i
$613$	−17.7135	+	8.53039i	−0.715443	+	0.344539i	−0.755940	−	0.654640i	$-0.772820\pi$
$613$	−17.7135	+	8.53039i	−0.715443	+	0.344539i	0.0404974	+	0.999180i	$0.487106\pi$
$614$	0.357518	−	1.56639i	0.0144282	−	0.0632142i
$615$	2.15946	−	2.70787i	0.0870777	−	0.109192i
$616$	1.08943	−	4.77312i	0.0438945	−	0.192314i
$617$	34.5273	+	16.6275i	1.39002	+	0.669397i	0.971110	−	0.238633i	$-0.0766992\pi$
$617$	34.5273	+	16.6275i	1.39002	+	0.669397i	0.418906	+	0.908029i	$0.362414\pi$
$618$	−0.0384867	−	0.0482608i	−0.00154816	−	0.00194133i
$619$	8.22194	+	10.3100i	0.330468	+	0.414394i	0.919111	−	0.394000i	$-0.128909\pi$
$619$	8.22194	+	10.3100i	0.330468	+	0.414394i	−0.588643	+	0.808393i	$0.700337\pi$
$620$	−0.0222647	−	0.0975478i	−0.000894170	−	0.00391761i
$621$	−27.0649	−	13.0338i	−1.08608	−	0.523027i
$622$	11.3314	−	5.45690i	0.454347	−	0.218802i
$623$	−4.33232	−	18.9812i	−0.173571	−	0.760464i
$624$	−0.107442	−	0.470736i	−0.00430114	−	0.0188445i
$625$	−0.900969	+	0.433884i	−0.0360388	+	0.0173553i
$626$	5.89408	+	2.83844i	0.235575	+	0.113447i
$627$	1.02370	+	4.48514i	0.0408828	+	0.179119i
$628$	7.19448	+	9.02160i	0.287091	+	0.360001i
$629$	−1.61416	−	2.02409i	−0.0643608	−	0.0807059i
$630$	2.68677	+	1.29388i	0.107043	+	0.0515494i
$631$	−5.32917	+	23.3486i	−0.212151	+	0.929494i	0.750951	+	0.660358i	$0.229595\pi$
$631$	−5.32917	+	23.3486i	−0.212151	+	0.929494i	−0.963102	+	0.269137i	$0.913262\pi$
$632$	0.851097	−	1.06724i	0.0338548	−	0.0424526i
$633$	−6.67331	+	29.2377i	−0.265240	+	1.16209i
$634$	31.9211	−	15.3724i	1.26775	−	0.610516i
$635$	3.65010	+	4.57708i	0.144850	+	0.181636i
$636$	−9.10663	+	4.38552i	−0.361101	+	0.173897i
$637$	1.19978	−	1.50448i	0.0475371	−	0.0596096i
$638$	2.90760			0.115113
$639$	−0.123560			−0.00488795
$640$	0.623490	−	0.781831i	0.0246456	−	0.0309046i
$641$	26.2345	+	12.6339i	1.03620	+	0.499008i	0.873069	−	0.487596i	$-0.162126\pi$
$641$	26.2345	+	12.6339i	1.03620	+	0.499008i	0.163132	+	0.986604i	$0.447840\pi$
$642$	0.941867	+	4.12659i	0.0371725	+	0.162863i
$643$	−6.94810	+	30.4416i	−0.274006	+	1.20050i	0.631232	+	0.775594i	$0.282550\pi$
$643$	−6.94810	+	30.4416i	−0.274006	+	1.20050i	−0.905238	+	0.424905i	$0.860307\pi$
$644$	9.39154			0.370079
$645$	−5.43256	+	4.59369i	−0.213907	+	0.180876i
$646$	−2.94382			−0.115823
$647$	−4.95737	+	21.7196i	−0.194894	+	0.853887i	0.779025	+	0.626993i	$0.215714\pi$
$647$	−4.95737	+	21.7196i	−0.194894	+	0.853887i	−0.973919	+	0.226895i	$0.927143\pi$
$648$	0.0463368	+	0.203015i	0.00182028	+	0.00797517i
$649$	−8.43137	−	4.06033i	−0.330960	−	0.159382i
$650$	−0.277479	+	0.347948i	−0.0108836	+	0.0136476i
$651$	−0.177584			−0.00696005
$652$	13.9723			0.547197
$653$	16.1447	−	20.2448i	0.631790	−	0.792239i	−0.358160	−	0.933660i	$-0.616596\pi$
$653$	16.1447	−	20.2448i	0.631790	−	0.792239i	0.989950	+	0.141421i	$0.0451671\pi$
$654$	15.5848	−	7.50522i	0.609412	−	0.293477i
$655$	−9.03032	−	11.3237i	−0.352844	−	0.442452i
$656$	2.87621	−	1.38511i	0.112297	−	0.0540795i
$657$	−2.26638	+	9.92965i	−0.0884199	+	0.387393i
$658$	−6.94550	+	8.70938i	−0.270764	+	0.339527i
$659$	−7.27435	+	31.8710i	−0.283369	+	1.24152i	0.610075	+	0.792344i	$0.291139\pi$
$659$	−7.27435	+	31.8710i	−0.283369	+	1.24152i	−0.893444	+	0.449175i	$0.851718\pi$
$660$	−2.92543	−	1.40881i	−0.113872	−	0.0548379i
$661$	8.55393	+	10.7263i	0.332709	+	0.417204i	0.919844	−	0.392285i	$-0.128315\pi$
$661$	8.55393	+	10.7263i	0.332709	+	0.417204i	−0.587134	+	0.809490i	$0.699744\pi$
$662$	20.4398	+	25.6307i	0.794416	+	0.996166i
$663$	−0.223235	−	0.978058i	−0.00866974	−	0.0379846i
$664$	−8.80262	−	4.23912i	−0.341608	−	0.164510i
$665$	2.08828	−	1.00566i	0.0809799	−	0.0389979i
$666$	−0.505438	−	2.21447i	−0.0195853	−	0.0858089i
$667$	1.24112	+	5.43769i	0.0480562	+	0.210548i
$668$	10.5302	−	5.07107i	0.407425	−	0.196205i
$669$	−10.9099	−	5.25395i	−0.421802	−	0.203129i
$670$	3.13723	+	13.7451i	0.121202	+	0.531020i
$671$	−1.51162	−	1.89551i	−0.0583553	−	0.0731752i
$672$	−1.10659	−	1.38762i	−0.0426877	−	0.0535287i
$673$	18.4076	+	8.86465i	0.709562	+	0.341707i	0.753610	−	0.657322i	$-0.228311\pi$
$673$	18.4076	+	8.86465i	0.709562	+	0.341707i	−0.0440474	+	0.999029i	$0.514025\pi$
$674$	−3.37928	+	14.8056i	−0.130165	+	0.570291i
$675$	3.26244	−	4.09097i	0.125571	−	0.157462i
$676$	2.84870	−	12.4810i	0.109565	−	0.480037i
$677$	23.5660	−	11.3488i	0.905715	−	0.436169i	0.0777654	−	0.996972i	$-0.475221\pi$
$677$	23.5660	−	11.3488i	0.905715	−	0.436169i	0.827950	+	0.560802i	$0.189507\pi$
$678$	3.07492	+	3.85583i	0.118092	+	0.148082i
$679$	14.2521	−	6.86347i	0.546947	−	0.263396i
$680$	1.29544	−	1.62443i	0.0496778	−	0.0622940i
$681$	−4.71769			−0.180782
$682$	−0.299448			−0.0114664
$683$	0.117628	−	0.147501i	0.00450092	−	0.00564397i	−0.779576	−	0.626308i	$-0.784565\pi$
$683$	0.117628	−	0.147501i	0.00450092	−	0.00564397i	0.784077	+	0.620664i	$0.213137\pi$
$684$	−2.32702	−	1.12063i	−0.0889759	−	0.0428485i
$685$	0.254834	+	1.11650i	0.00973672	+	0.0426593i
$686$	4.12211	−	18.0601i	0.157383	−	0.689540i
$687$	8.87475			0.338593
$688$	−6.34848	+	1.64219i	−0.242034	+	0.0626079i
$689$	4.14615			0.157956
$690$	1.38598	−	6.07239i	0.0527634	−	0.231172i
$691$	−6.69969	−	29.3533i	−0.254868	−	1.11665i	−0.926657	−	0.375908i	$-0.877331\pi$
$691$	−6.69969	−	29.3533i	−0.254868	−	1.11665i	0.671789	−	0.740743i	$-0.265526\pi$
$692$	7.14971	+	3.44312i	0.271791	+	0.130888i
$693$	5.56449	−	6.97765i	0.211378	−	0.265059i
$694$	8.11609			0.308083
$695$	−18.9245			−0.717846
$696$	0.657192	−	0.824092i	0.0249108	−	0.0312371i
$697$	5.97597	−	2.87788i	0.226356	−	0.109007i
$698$	20.3050	+	25.4616i	0.768554	+	0.963736i
$699$	−11.5284	+	5.55179i	−0.436045	+	0.209988i
$700$	−0.364020	+	1.59487i	−0.0137587	+	0.0602806i
$701$	−3.29417	+	4.13075i	−0.124419	+	0.156016i	−0.840140	−	0.542370i	$-0.817527\pi$
$701$	−3.29417	+	4.13075i	−0.124419	+	0.156016i	0.715721	+	0.698387i	$0.246098\pi$
$702$	0.518186	−	2.27032i	0.0195577	−	0.0856877i
$703$	−1.59061	−	0.765998i	−0.0599911	−	0.0288902i
$704$	−1.86597	−	2.33985i	−0.0703264	−	0.0881866i
$705$	4.60631	+	5.77613i	0.173484	+	0.217542i
$706$	5.27349	+	23.1047i	0.198471	+	0.869556i
$707$	−17.4366	−	8.39705i	−0.655773	−	0.315803i
$708$	−3.05651	+	1.47194i	−0.114871	+	0.0553189i
$709$	5.88475	+	25.7828i	0.221006	+	0.968292i	0.956722	+	0.291002i	$0.0939886\pi$
$709$	5.88475	+	25.7828i	0.221006	+	0.968292i	−0.735716	+	0.677290i	$0.763154\pi$
$710$	−0.0150828	−	0.0660820i	−0.000566047	−	0.00248001i
$711$	2.24195	−	1.07967i	0.0840797	−	0.0404907i
$712$	−10.7227	−	5.16380i	−0.401852	−	0.193522i
$713$	−0.127820	−	0.560016i	−0.00478690	−	0.0209728i
$714$	−2.29919	−	2.88309i	−0.0860450	−	0.107897i
$715$	0.830435	+	1.04133i	0.0310565	+	0.0389437i
$716$	−2.72941	−	1.31442i	−0.102003	−	0.0491220i
$717$	−0.0909185	+	0.398340i	−0.00339541	+	0.0148763i
$718$	−3.99533	+	5.00998i	−0.149104	+	0.186971i
$719$	−4.15285	+	18.1948i	−0.154875	+	0.678553i	0.836551	+	0.547889i	$0.184568\pi$
$719$	−4.15285	+	18.1948i	−0.154875	+	0.678553i	−0.991427	+	0.130664i	$0.958289\pi$
$720$	1.64239	−	0.790933i	0.0612083	−	0.0294763i
$721$	0.0580311	+	0.0727687i	0.00216119	+	0.00271005i
$722$	15.3097	−	7.37278i	0.569770	−	0.274387i
$723$	−7.04753	+	8.83732i	−0.262100	+	0.328663i
$724$	14.3827			0.534531
$725$	−0.971536			−0.0360819
$726$	1.38214	−	1.73314i	0.0512959	−	0.0643230i
$727$	−27.1042	−	13.0527i	−1.00524	−	0.484098i	−0.142527	−	0.989791i	$-0.545523\pi$
$727$	−27.1042	−	13.0527i	−1.00524	−	0.484098i	−0.862714	+	0.505693i	$0.831237\pi$
$728$	0.162004	+	0.709786i	0.00600427	+	0.0263064i
$729$	−3.87421	+	16.9740i	−0.143489	+	0.628667i
$730$	−5.58721			−0.206792
$731$	−13.1904	+	3.41202i	−0.487864	+	0.126198i
$732$	−0.878902			−0.0324851
$733$	9.73079	−	42.6334i	0.359415	−	1.57470i	−0.395240	−	0.918578i	$-0.629339\pi$
$733$	9.73079	−	42.6334i	0.359415	−	1.57470i	0.754655	−	0.656122i	$-0.227804\pi$
$734$	−7.84869	−	34.3873i	−0.289700	−	1.26926i
$735$	−4.22655	−	2.03540i	−0.155899	−	0.0750768i
$736$	3.57942	−	4.48845i	0.131939	−	0.165446i
$737$	42.1941			1.55424
$738$	5.81940			0.214215
$739$	−14.9638	+	18.7640i	−0.550452	+	0.690245i	−0.976761	−	0.214333i	$-0.931242\pi$
$739$	−14.9638	+	18.7640i	−0.550452	+	0.690245i	0.426309	+	0.904578i	$0.359814\pi$
$740$	1.12264	−	0.540634i	0.0412690	−	0.0198741i
$741$	−0.426538	−	0.534862i	−0.0156693	−	0.0196487i
$742$	13.7312	−	6.61259i	0.504087	−	0.242756i
$743$	11.5462	−	50.5871i	0.423588	−	1.85586i	−0.0872545	−	0.996186i	$-0.527809\pi$
$743$	11.5462	−	50.5871i	0.423588	−	1.85586i	0.510842	−	0.859674i	$-0.329334\pi$
$744$	−0.0676828	+	0.0848715i	−0.00248137	+	0.00311154i
$745$	0.447587	−	1.96101i	0.0163983	−	0.0718457i
$746$	3.84786	+	1.85303i	0.140880	+	0.0678443i
$747$	−11.1045	−	13.9246i	−0.406291	−	0.509473i
$748$	−3.87697	−	4.86157i	−0.141756	−	0.177756i
$749$	−1.42017	−	6.22216i	−0.0518918	−	0.227353i
$750$	0.977493	+	0.470736i	0.0356930	+	0.0171888i
$751$	26.1150	−	12.5763i	0.952949	−	0.458916i	0.108230	−	0.994126i	$-0.465482\pi$
$751$	26.1150	−	12.5763i	0.952949	−	0.458916i	0.844719	+	0.535210i	$0.179767\pi$
$752$	1.51527	+	6.63885i	0.0552563	+	0.242094i
$753$	−1.66580	−	7.29833i	−0.0607050	−	0.265966i
$754$	−0.389556	+	0.187600i	−0.0141868	+	0.00683199i
$755$	7.62234	+	3.67072i	0.277405	+	0.133591i
$756$	−1.90475	−	8.34527i	−0.0692752	−	0.303514i
$757$	1.47406	+	1.84841i	0.0535755	+	0.0671816i	0.807897	−	0.589323i	$-0.200606\pi$
$757$	1.47406	+	1.84841i	0.0535755	+	0.0671816i	−0.754322	+	0.656505i	$0.772034\pi$
$758$	−3.62370	−	4.54398i	−0.131619	−	0.165045i
$759$	−16.7947	−	8.08790i	−0.609609	−	0.293572i
$760$	0.315279	−	1.38133i	0.0114364	−	0.0501060i
$761$	−5.13271	+	6.43621i	−0.186060	+	0.233312i	−0.866110	−	0.499854i	$-0.833387\pi$
$761$	−5.13271	+	6.43621i	−0.186060	+	0.233312i	0.680049	+	0.733167i	$0.261958\pi$
$762$	1.41335	−	6.19230i	0.0512003	−	0.224323i
$763$	−23.4990	+	11.3165i	−0.850723	+	0.409686i
$764$	0.0580153	+	0.0727488i	0.00209892	+	0.00263196i
$765$	3.41243	−	1.64334i	0.123377	−	0.0594150i
$766$	−15.8514	+	19.8770i	−0.572733	+	0.718185i
$767$	1.39160			0.0502477
$768$	−1.08494			−0.0391492
$769$	−19.3021	+	24.2041i	−0.696051	+	0.872820i	−0.996722	−	0.0809077i	$-0.974218\pi$
$769$	−19.3021	+	24.2041i	−0.696051	+	0.872820i	0.300671	+	0.953728i	$0.402790\pi$
$770$	4.41103	+	2.12424i	0.158962	+	0.0765522i
$771$	−3.25791	−	14.2738i	−0.117331	−	0.514059i
$772$	−0.469214	+	2.05576i	−0.0168874	+	0.0739884i
$773$	−37.4986			−1.34873			−0.674366	−	0.738397i	$-0.735583\pi$
$773$	−37.4986			−1.34873			−0.674366	+	0.738397i	$0.735583\pi$
$774$	−11.7255	−	2.32411i	−0.421466	−	0.0835383i
$775$	0.100056			0.00359413
$776$	2.15173	−	9.42733i	0.0772425	−	0.338422i
$777$	−0.492107	−	2.15606i	−0.0176542	−	0.0773482i
$778$	23.2063	+	11.1756i	0.831987	+	0.400664i
$779$	2.82010	−	3.53630i	0.101041	−	0.126701i
$780$	0.482842			0.0172885
$781$	−0.202855			−0.00725873
$782$	7.43703	−	9.32574i	0.265948	−	0.333488i
$783$	4.58018	−	2.20570i	0.163682	−	0.0788252i
$784$	−2.69588	−	3.38053i	−0.0962816	−	0.120733i
$785$	−10.3963	+	5.00661i	−0.371061	+	0.178693i
$786$	−3.49662	+	15.3197i	−0.124720	+	0.546435i
$787$	6.98310	−	8.75653i	0.248921	−	0.312137i	−0.641636	−	0.767010i	$-0.721744\pi$
$787$	6.98310	−	8.75653i	0.248921	−	0.312137i	0.890556	+	0.454873i	$0.150315\pi$
$788$	−2.85041	+	12.4885i	−0.101542	+	0.444884i
$789$	−1.88698	−	0.908723i	−0.0671783	−	0.0323514i
$790$	0.851097	+	1.06724i	0.0302807	+	0.0379708i
$791$	−4.63644	−	5.81391i	−0.164853	−	0.206719i
$792$	−1.21398	−	5.31881i	−0.0431370	−	0.188996i
$793$	0.324823	+	0.156427i	0.0115348	+	0.00555487i
$794$	31.9509	−	15.3867i	1.13389	−	0.546054i
$795$	−2.24915	−	9.85418i	−0.0797692	−	0.349492i
$796$	−0.934275	−	4.09333i	−0.0331145	−	0.145084i
$797$	−11.4056	+	5.49264i	−0.404006	+	0.194559i	−0.624841	−	0.780752i	$-0.714836\pi$
$797$	−11.4056	+	5.49264i	−0.404006	+	0.194559i	0.220835	+	0.975311i	$0.429122\pi$
$798$	−2.26564	−	1.09108i	−0.0802030	−	0.0386237i
$799$	3.14832	+	13.7937i	0.111379	+	0.487985i
$800$	0.623490	+	0.781831i	0.0220437	+	0.0276419i
$801$	−13.5267	−	16.9619i	−0.477942	−	0.599321i
$802$	−9.69787	−	4.67025i	−0.342444	−	0.164912i
$803$	−3.72085	+	16.3021i	−0.131306	+	0.575288i
$804$	9.53694	−	11.9589i	0.336342	−	0.421760i
$805$	−2.08982	+	9.15608i	−0.0736563	+	0.322709i
$806$	0.0401195	−	0.0193205i	0.00141315	−	0.000680537i
$807$	−4.73148	−	5.93308i	−0.166556	−	0.208854i
$808$	−10.6588	+	5.13301i	−0.374976	+	0.180579i
$809$	−15.8354	+	19.8570i	−0.556743	+	0.698134i	−0.977952	−	0.208830i	$-0.933035\pi$
$809$	−15.8354	+	19.8570i	−0.556743	+	0.698134i	0.421209	+	0.906964i	$0.361606\pi$
$810$	−0.208236			−0.00731665
$811$	−3.42225			−0.120172			−0.0600858	−	0.998193i	$-0.519137\pi$
$811$	−3.42225			−0.120172			−0.0600858	+	0.998193i	$0.519137\pi$
$812$	−0.990929	+	1.24259i	−0.0347748	+	0.0436062i
$813$	5.15650	+	2.48324i	0.180846	+	0.0870910i
$814$	−0.829807	−	3.63562i	−0.0290847	−	0.127428i
$815$	−3.10912	+	13.6220i	−0.108908	+	0.477157i
$816$	−2.25419			−0.0789126
$817$	−7.09454	+	5.99904i	−0.248207	+	0.209880i
$818$	−33.9375			−1.18660
$819$	−0.295320	+	1.29388i	−0.0103193	+	0.0452118i
$820$	0.710366	+	3.11232i	0.0248071	+	0.108687i
$821$	1.68657	+	0.812208i	0.0588616	+	0.0283462i	0.463083	−	0.886315i	$-0.346743\pi$
$821$	1.68657	+	0.812208i	0.0588616	+	0.0283462i	−0.404221	+	0.914661i	$0.632457\pi$
$822$	0.774676	−	0.971413i	0.0270199	−	0.0338819i
$823$	−15.2880			−0.532905			−0.266452	−	0.963848i	$-0.585852\pi$
$823$	−15.2880			−0.532905			−0.266452	+	0.963848i	$0.585852\pi$
$824$	0.0568954			0.00198205
$825$	2.02446	−	2.53859i	0.0704826	−	0.0883824i
$826$	4.60868	−	2.21942i	0.160356	−	0.0772236i
$827$	−17.3686	−	21.7795i	−0.603965	−	0.757348i	0.382025	−	0.924152i	$-0.375227\pi$
$827$	−17.3686	−	21.7795i	−0.603965	−	0.757348i	−0.985990	+	0.166804i	$0.946655\pi$
$828$	9.42886	−	4.54070i	0.327675	−	0.157800i
$829$	4.35936	−	19.0996i	0.151407	−	0.663357i	−0.841070	−	0.540926i	$-0.818074\pi$
$829$	4.35936	−	19.0996i	0.151407	−	0.663357i	0.992477	−	0.122431i	$-0.0390689\pi$
$830$	6.09160	−	7.63862i	0.211443	−	0.265141i
$831$	−5.10475	+	22.3654i	−0.177082	+	0.775846i
$832$	0.400969	+	0.193096i	0.0139011	+	0.00669441i
$833$	−5.60130	−	7.02381i	−0.194073	−	0.243360i
$834$	12.8014	+	16.0524i	0.443276	+	0.555850i
$835$	2.60074	+	11.3946i	0.0900023	+	0.394326i
$836$	−3.82041	−	1.83981i	−0.132131	−	0.0636312i
$837$	−0.471703	+	0.227160i	−0.0163044	+	0.00785180i
$838$	−1.42303	−	6.23471i	−0.0491578	−	0.215375i
$839$	−2.99971	−	13.1426i	−0.103562	−	0.453733i	−0.999945	−	0.0104539i	$-0.996672\pi$
$839$	−2.99971	−	13.1426i	−0.103562	−	0.453733i	0.896384	−	0.443279i	$-0.146185\pi$
$840$	1.59907	−	0.770072i	0.0551732	−	0.0265700i
$841$	25.2777	+	12.1731i	0.871644	+	0.419762i
$842$	3.84089	+	16.8280i	0.132366	+	0.579933i
$843$	−15.1308	−	18.9734i	−0.521133	−	0.653479i
$844$	−17.2344	−	21.6112i	−0.593232	−	0.743889i
$845$	11.5341	+	5.55455i	0.396787	+	0.191082i
$846$	−2.76221	+	12.1021i	−0.0949669	+	0.416077i
$847$	−2.08402	+	2.61327i	−0.0716077	+	0.0897932i
$848$	2.07307	−	9.08273i	0.0711896	−	0.311902i
$849$	−19.1258	+	9.21049i	−0.656395	+	0.316103i
$850$	1.29544	+	1.62443i	0.0444332	+	0.0557174i
$851$	6.44500	−	3.10375i	0.220932	−	0.106395i
$852$	−0.0458505	+	0.0574947i	−0.00157081	+	0.00196974i
$853$	−9.40293			−0.321950			−0.160975	−	0.986958i	$-0.551464\pi$
$853$	−9.40293			−0.321950			−0.160975	+	0.986958i	$0.551464\pi$
$854$	1.32523			0.0453484
$855$	1.61035	−	2.01931i	0.0550727	−	0.0690590i
$856$	−3.51499	−	1.69273i	−0.120140	−	0.0578564i
$857$	−5.65461	−	24.7745i	−0.193158	−	0.846280i	−0.974894	−	0.222670i	$-0.928523\pi$
$857$	−5.65461	−	24.7745i	−0.193158	−	0.846280i	0.781736	−	0.623610i	$-0.214334\pi$
$858$	0.321552	−	1.40881i	0.0109776	−	0.0480960i
$859$	−35.9089			−1.22520			−0.612598	−	0.790394i	$-0.709876\pi$
$859$	−35.9089			−1.22520			−0.612598	+	0.790394i	$0.709876\pi$
$860$	−0.188348	−	6.55473i	−0.00642261	−	0.223515i
$861$	5.66591			0.193094
$862$	−8.33503	+	36.5182i	−0.283892	+	1.24381i
$863$	−5.08031	−	22.2583i	−0.172936	−	0.757682i	−0.984780	−	0.173807i	$-0.944393\pi$
$863$	−5.08031	−	22.2583i	−0.172936	−	0.757682i	0.811844	−	0.583875i	$-0.198464\pi$
$864$	−4.71437	−	2.27032i	−0.160386	−	0.0772378i
$865$	−4.94775	+	6.20429i	−0.168229	+	0.210952i
$866$	−1.97755			−0.0671998
$867$	13.7603			0.467325
$868$	0.102054	−	0.127971i	0.00346393	−	0.00434363i
$869$	3.68074	−	1.77255i	0.124861	−	0.0601297i
$870$	0.657192	+	0.824092i	0.0222809	+	0.0279394i
$871$	−5.65310	+	2.72239i	−0.191548	+	0.0922446i
$872$	−3.54778	+	15.5439i	−0.120143	+	0.526381i
$873$	10.9904	−	13.7815i	0.371968	−	0.466433i
$874$	1.81000	−	7.93011i	0.0612241	−	0.268240i
$875$	−1.47389	−	0.709786i	−0.0498264	−	0.0239952i
$876$	3.77945	+	4.73928i	0.127696	+	0.160125i
$877$	24.0792	+	30.1943i	0.813095	+	1.01959i	0.999312	+	0.0370806i	$0.0118058\pi$
$877$	24.0792	+	30.1943i	0.813095	+	1.01959i	−0.186217	+	0.982509i	$0.559623\pi$
$878$	3.62431	+	15.8791i	0.122314	+	0.535895i
$879$	−12.8488	−	6.18767i	−0.433380	−	0.208705i
$880$	2.69641	−	1.29852i	0.0908959	−	0.0437731i
$881$	5.91113	+	25.8984i	0.199151	+	0.872538i	0.971444	+	0.237271i	$0.0762529\pi$
$881$	5.91113	+	25.8984i	0.199151	+	0.872538i	−0.772292	+	0.635267i	$0.780890\pi$
$882$	−1.75392	−	7.68442i	−0.0590575	−	0.258748i
$883$	−45.5716	+	21.9461i	−1.53361	+	0.738547i	−0.994603	−	0.103756i	$-0.966914\pi$
$883$	−45.5716	+	21.9461i	−1.53361	+	0.738547i	−0.539005	+	0.842303i	$0.681200\pi$
$884$	0.833102	+	0.401201i	0.0280202	+	0.0134938i
$885$	−0.754896	−	3.30742i	−0.0253756	−	0.111178i
$886$	18.9360	+	23.7450i	0.636167	+	0.797728i
$887$	−7.42639	−	9.31240i	−0.249354	−	0.312680i	0.641364	−	0.767237i	$-0.278369\pi$
$887$	−7.42639	−	9.31240i	−0.249354	−	0.312680i	−0.890718	+	0.454557i	$0.849798\pi$
$888$	−1.21799	−	0.586554i	−0.0408731	−	0.0196834i
$889$	−2.13108	+	9.33689i	−0.0714742	+	0.313149i
$890$	7.42036	−	9.30484i	0.248731	−	0.311899i
$891$	−0.138676	+	0.607579i	−0.00464582	+	0.0203547i
$892$	10.0558	−	4.84264i	0.336694	−	0.162143i
$893$	6.01552	+	7.54323i	0.201302	+	0.252425i
$894$	−1.96617	+	0.946856i	−0.0657584	+	0.0316676i
$895$	1.88881	−	2.36850i	0.0631360	−	0.0791701i
$896$	1.63589			0.0546513
$897$	2.77196			0.0925532
$898$	−19.7615	+	24.7801i	−0.659450	+	0.826924i
$899$	0.0875818	+	0.0421772i	0.00292102	+	0.00140669i
$900$	0.405637	+	1.77721i	0.0135212	+	0.0592404i
$901$	4.30727	−	18.8714i	0.143496	−	0.628697i
$902$	9.55404			0.318115
$903$	−11.4163	−	2.26281i	−0.379910	−	0.0753015i
$904$	−4.54570			−0.151188
$905$	−3.20046	+	14.0221i	−0.106387	+	0.466112i
$906$	−2.04246	−	8.94859i	−0.0678561	−	0.297297i
$907$	−23.8729	−	11.4966i	−0.792686	−	0.381737i	−0.00669649	−	0.999978i	$-0.502132\pi$
$907$	−23.8729	−	11.4966i	−0.792686	−	0.381737i	−0.785989	+	0.618240i	$0.787846\pi$
$908$	2.71116	−	3.39968i	0.0899729	−	0.112822i
$909$	−21.5658			−0.715292
$910$	−0.728040			−0.0241343
$911$	−27.5104	+	34.4969i	−0.911460	+	1.14293i	0.0778292	+	0.996967i	$0.475201\pi$
$911$	−27.5104	+	34.4969i	−0.911460	+	1.14293i	−0.989289	+	0.145968i	$0.953370\pi$
$912$	−1.38496	+	0.666962i	−0.0458607	+	0.0220853i
$913$	−18.2309	−	22.8608i	−0.603353	−	0.756581i
$914$	13.6801	−	6.58798i	0.452497	−	0.217911i
$915$	0.195574	−	0.856866i	0.00646548	−	0.0283271i
$916$	−5.10014	+	6.39537i	−0.168513	+	0.211309i
$917$	5.27228	−	23.0994i	0.174106	−	0.762809i
$918$	−9.79514	−	4.71709i	−0.323288	−	0.155687i
$919$	−16.1417	−	20.2411i	−0.532466	−	0.667691i	0.440738	−	0.897636i	$-0.354717\pi$
$919$	−16.1417	−	20.2411i	−0.532466	−	0.667691i	−0.973204	+	0.229945i	$0.926145\pi$
$920$	3.57942	+	4.48845i	0.118010	+	0.147980i
$921$	−0.387883	−	1.69943i	−0.0127812	−	0.0559981i
$922$	−16.9514	−	8.16334i	−0.558263	−	0.268845i
$923$	0.0271782	−	0.0130883i	0.000894582	−	0.000430808i
$924$	−1.18196	−	5.17853i	−0.0388838	−	0.170361i
$925$	0.277269	+	1.21479i	0.00911655	+	0.0399422i
$926$	3.87978	−	1.86840i	0.127498	−	0.0613996i
$927$	0.0934445	+	0.0450005i	0.00306912	+	0.00147801i
$928$	0.216187	+	0.947178i	0.00709669	+	0.0310926i
$929$	−24.6604	−	30.9232i	−0.809082	−	1.01456i	−0.999460	−	0.0328463i	$-0.989543\pi$
$929$	−24.6604	−	30.9232i	−0.809082	−	1.01456i	0.190378	−	0.981711i	$-0.439029\pi$
$930$	−0.0676828	−	0.0848715i	−0.00221941	−	0.00278305i
$931$	−5.51958	−	2.65809i	−0.180897	−	0.0871153i
$932$	2.62438	−	11.4982i	0.0859644	−	0.376635i
$933$	8.50758	−	10.6682i	0.278526	−	0.349260i
$934$	6.77072	−	29.6644i	0.221545	−	0.970650i
$935$	5.60238	−	2.69797i	0.183218	−	0.0882329i
$936$	0.505821	+	0.634279i	0.0165333	+	0.0207321i
$937$	53.2674	−	25.6523i	1.74017	−	0.838022i	0.757460	−	0.652882i	$-0.226440\pi$
$937$	53.2674	−	25.6523i	1.74017	−	0.838022i	0.982712	−	0.185140i	$-0.0592740\pi$
$938$	−14.3800	+	18.0320i	−0.469524	+	0.588765i
$939$	7.09758			0.231621
$940$	−6.80958			−0.222104
$941$	−34.9228	+	43.7918i	−1.13845	+	1.42757i	−0.250209	+	0.968192i	$0.580499\pi$
$941$	−34.9228	+	43.7918i	−1.13845	+	1.42757i	−0.888241	+	0.459379i	$0.848072\pi$
$942$	11.2793	+	5.43185i	0.367501	+	0.176979i
$943$	4.07817	+	17.8676i	0.132803	+	0.581850i
$944$	0.695799	−	3.04849i	0.0226463	−	0.0992200i
$945$	8.55988			0.278453
$946$	−19.2505	−	3.81562i	−0.625888	−	0.124057i
$947$	48.2996			1.56953			0.784763	−	0.619796i	$-0.212785\pi$
$947$	48.2996			1.56953			0.784763	+	0.619796i	$0.212785\pi$
$948$	0.329553	−	1.44386i	0.0107034	−	0.0468945i
$949$	−0.553308	−	2.42420i	−0.0179611	−	0.0786929i
$950$	1.27654	+	0.614748i	0.0414164	+	0.0199451i
$951$	23.9663	−	30.0528i	0.777161	−	0.974529i
$952$	3.39892			0.110160
$953$	23.5328			0.762304			0.381152	−	0.924512i	$-0.375528\pi$
$953$	23.5328			0.762304			0.381152	+	0.924512i	$0.375528\pi$
$954$	10.5886	−	13.2777i	0.342819	−	0.429882i
$955$	−0.0838345	+	0.0403726i	−0.00271282	+	0.00130643i
$956$	−0.234805	−	0.294436i	−0.00759412	−	0.00952273i
$957$	2.84216	−	1.36871i	0.0918739	−	0.0442441i
$958$	2.45383	−	10.7509i	0.0792795	−	0.347346i
$959$	−1.16807	+	1.46472i	−0.0377191	+	0.0472982i
$960$	0.241421	−	1.05773i	0.00779182	−	0.0341382i
$961$	27.9210	+	13.4461i	0.900678	+	0.433744i
$962$	0.345749	+	0.433555i	0.0111474	+	0.0139784i
$963$	−4.43415	−	5.56025i	−0.142889	−	0.179177i
$964$	−2.31833	−	10.1572i	−0.0746682	−	0.327143i
$965$	−1.89981	−	0.914899i	−0.0611570	−	0.0294517i
$966$	9.18017	−	4.42094i	0.295367	−	0.142241i
$967$	−0.548724	−	2.40412i	−0.0176458	−	0.0773112i	0.965338	−	0.261002i	$-0.0840528\pi$
$967$	−0.548724	−	2.40412i	−0.0176458	−	0.0773112i	−0.982984	+	0.183690i	$0.941196\pi$
$968$	0.454662	+	1.99200i	0.0146134	+	0.0640254i
$969$	−2.87756	+	1.38576i	−0.0924407	+	0.0445171i
$970$	8.71217	+	4.19556i	0.279731	+	0.134711i
$971$	−13.0717	−	57.2707i	−0.419490	−	1.83790i	−0.535340	−	0.844637i	$-0.679816\pi$
$971$	−13.0717	−	57.2707i	−0.419490	−	1.83790i	0.115850	−	0.993267i	$-0.463041\pi$
$972$	−9.64647	−	12.0963i	−0.309411	−	0.387989i
$973$	−19.3022	−	24.2042i	−0.618801	−	0.775951i
$974$	−14.2928	−	6.88303i	−0.457970	−	0.220547i
$975$	−0.107442	+	0.470736i	−0.00344091	+	0.0150756i
$976$	0.505087	−	0.633359i	0.0161674	−	0.0202733i
$977$	−9.60743	+	42.0929i	−0.307369	+	1.34667i	0.551371	+	0.834260i	$0.314105\pi$
$977$	−9.60743	+	42.0929i	−0.307369	+	1.34667i	−0.858740	+	0.512412i	$0.828752\pi$
$978$	13.6578	−	6.57725i	0.436728	−	0.210317i
$979$	−22.2076	−	27.8474i	−0.709757	−	0.890007i
$980$	3.89567	−	1.87605i	0.124443	−	0.0599283i
$981$	−18.1210	+	22.7230i	−0.578559	+	0.725490i
$982$	−24.0431			−0.767246
$983$	−14.7619			−0.470831			−0.235416	−	0.971895i	$-0.575645\pi$
$983$	−14.7619			−0.470831			−0.235416	+	0.971895i	$0.575645\pi$
$984$	2.15946	−	2.70787i	0.0688410	−	0.0863239i
$985$	−11.5411	−	5.55790i	−0.367730	−	0.177089i
$986$	0.449177	+	1.96797i	0.0143047	+	0.0626730i
$987$	−2.68936	+	11.7829i	−0.0856033	+	0.375052i
$988$	0.630558			0.0200607
$989$	−1.08129	−	37.6303i	−0.0343831	−	1.19657i
$990$	5.45559			0.173390
$991$	6.19956	−	27.1620i	0.196936	−	0.862831i	−0.775812	−	0.630964i	$-0.782660\pi$
$991$	6.19956	−	27.1620i	0.196936	−	0.862831i	0.972748	−	0.231867i	$-0.0744833\pi$
$992$	−0.0222647	−	0.0975478i	−0.000706903	−	0.00309715i
$993$	32.0451	+	15.4321i	1.01692	+	0.489723i
$994$	0.0691344	−	0.0866918i	0.00219281	−	0.00274970i
$995$	4.19859			0.133104
$996$	−10.6000			−0.335874
$997$	36.5862	−	45.8776i	1.15870	−	1.45296i	0.290405	−	0.956904i	$-0.406210\pi$
$997$	36.5862	−	45.8776i	1.15870	−	1.45296i	0.868291	−	0.496055i	$-0.165219\pi$
$998$	5.55776	−	2.67647i	0.175928	−	0.0847223i
$999$	−4.06512	−	5.09750i	−0.128615	−	0.161278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.a.121.2	✓	12
43.16	even	7	inner	430.2.k.a.231.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.a.121.2	✓	12	1.1	even	1	trivial
430.2.k.a.231.2	yes	12	43.16	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.241421 + 1.05773i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -1.08494 q^{6} +1.63589 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.64239 - 0.790933i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(0.241421 + 1.05773i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} -1.08494 q^{6} +1.63589 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.64239 - 0.790933i) q^{9} +(0.623490 + 0.781831i) q^{10} +(2.69641 - 1.29852i) q^{11} +(0.241421 - 1.05773i) q^{12} +(-0.277479 + 0.347948i) q^{13} +(-0.364020 + 1.59487i) q^{14} +(0.977493 + 0.470736i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.29544 + 1.62443i) q^{17} +(0.405637 + 1.77721i) q^{18} +(1.27654 + 0.614748i) q^{19} +(-0.900969 + 0.433884i) q^{20} +(0.394938 + 1.73034i) q^{21} +(0.665958 + 2.91775i) q^{22} +(-5.17241 + 2.49090i) q^{23} +(0.977493 + 0.470736i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.277479 - 0.347948i) q^{26} +(3.26244 + 4.09097i) q^{27} +(-1.47389 - 0.709786i) q^{28} +(0.216187 - 0.947178i) q^{29} +(-0.676446 + 0.848237i) q^{30} +(-0.0222647 + 0.0975478i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.02446 + 2.53859i) q^{33} +(-1.87196 + 0.901490i) q^{34} +(1.01996 - 1.27899i) q^{35} -1.82292 q^{36} -1.24604 q^{37} +(-0.883392 + 1.10774i) q^{38} +(-0.435025 - 0.209497i) q^{39} +(-0.222521 - 0.974928i) q^{40} +(0.710366 - 3.11232i) q^{41} -1.77484 q^{42} +(-2.67430 + 5.98733i) q^{43} -2.99279 q^{44} +(0.405637 - 1.77721i) q^{45} +(-1.27748 - 5.59700i) q^{46} +(6.13522 + 2.95456i) q^{47} +(-0.676446 + 0.848237i) q^{48} -4.32386 q^{49} +1.00000 q^{50} +(-1.40547 + 1.76240i) q^{51} +(0.400969 - 0.193096i) q^{52} +(-5.80862 - 7.28378i) q^{53} +(-4.71437 + 2.27032i) q^{54} +(0.665958 - 2.91775i) q^{55} +(1.01996 - 1.27899i) q^{56} +(-0.342057 + 1.49865i) q^{57} +(0.875324 + 0.421534i) q^{58} +(-1.94958 - 2.44470i) q^{59} +(-0.676446 - 0.848237i) q^{60} +(-0.180263 - 0.789785i) q^{61} +(-0.0901477 - 0.0434129i) q^{62} +(2.68677 - 1.29388i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.0990311 + 0.433884i) q^{65} +(-2.92543 + 1.40881i) q^{66} +(12.7024 + 6.11715i) q^{67} +(-0.462337 - 2.02563i) q^{68} +(-3.88344 - 4.86967i) q^{69} +(1.01996 + 1.27899i) q^{70} +(-0.0610689 - 0.0294092i) q^{71} +(0.405637 - 1.77721i) q^{72} +(-3.48357 + 4.36826i) q^{73} +(0.277269 - 1.21479i) q^{74} +(0.977493 - 0.470736i) q^{75} +(-0.883392 - 1.10774i) q^{76} +(4.41103 - 2.12424i) q^{77} +(0.301047 - 0.377501i) q^{78} +1.36505 q^{79} +1.00000 q^{80} +(-0.129833 + 0.162805i) q^{81} +(2.87621 + 1.38511i) q^{82} +(-2.17407 - 9.52521i) q^{83} +(0.394938 - 1.73034i) q^{84} +2.07772 q^{85} +(-5.24213 - 3.93955i) q^{86} +1.05405 q^{87} +(0.665958 - 2.91775i) q^{88} +(-2.64830 - 11.6029i) q^{89} +(1.64239 + 0.790933i) q^{90} +(-0.453925 + 0.569204i) q^{91} +5.74094 q^{92} -0.108555 q^{93} +(-4.24570 + 5.32394i) q^{94} +(1.27654 - 0.614748i) q^{95} +(-0.676446 - 0.848237i) q^{96} +(8.71217 - 4.19556i) q^{97} +(0.962150 - 4.21546i) q^{98} +(3.40151 - 4.26536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Introduction

L-functions

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