LMFDB - Embedded newform 138.2.e.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	138.121
Dual form			138.2.e.c.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.43450 - 1.56456i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.394306 - 2.74246i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.43450 - 1.56456i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.394306 - 2.74246i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.411844 + 2.86444i) q^{10} +(2.26413 + 4.95774i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.0520365 - 0.361922i) q^{13} +(2.33083 + 1.49793i) q^{14} +(-2.77667 + 0.815304i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.12405 - 4.75941i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-4.01801 - 4.63704i) q^{19} +(-2.77667 - 0.815304i) q^{20} +(-1.15098 + 2.52028i) q^{21} -5.45027 q^{22} +(-0.965501 + 4.69764i) q^{23} -1.00000 q^{24} +(1.40187 - 3.06967i) q^{25} +(0.350833 + 0.103014i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.33083 + 1.49793i) q^{28} +(-2.23325 + 2.57731i) q^{29} +(0.411844 - 2.86444i) q^{30} +(-7.37071 + 2.16423i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.775655 - 5.39480i) q^{33} +(2.61612 + 5.72850i) q^{34} +(-3.33080 - 7.29343i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(4.06209 + 2.61055i) q^{37} +(5.88714 - 1.72862i) q^{38} +(-0.0520365 + 0.361922i) q^{39} +(1.89510 - 2.18706i) q^{40} +(-3.56427 + 2.29062i) q^{41} +(-1.81440 - 2.09393i) q^{42} +(6.75145 + 1.98241i) q^{43} +(2.26413 - 4.95774i) q^{44} +2.89389 q^{45} +(-3.87204 - 2.82972i) q^{46} -6.68409 q^{47} +(0.415415 - 0.909632i) q^{48} +(-0.649167 - 0.190613i) q^{49} +(2.20991 + 2.55037i) q^{50} +(-5.29788 + 3.40474i) q^{51} +(-0.239446 + 0.276335i) q^{52} +(-1.01536 + 7.06200i) q^{53} +(0.959493 - 0.281733i) q^{54} +(13.2687 + 8.52726i) q^{55} +(-0.394306 - 2.74246i) q^{56} +(2.54885 + 5.58121i) q^{57} +(-1.41668 - 3.10209i) q^{58} +(-0.0626320 - 0.435615i) q^{59} +(2.43450 + 1.56456i) q^{60} +(-7.80450 + 2.29161i) q^{61} +(1.09325 - 7.60369i) q^{62} +(1.81440 - 2.09393i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.692931 - 0.799685i) q^{65} +(5.22950 + 1.53552i) q^{66} +(1.84829 - 4.04720i) q^{67} -6.29760 q^{68} +(2.24987 - 4.23534i) q^{69} +8.01801 q^{70} +(-0.586952 + 1.28525i) q^{71} +(0.959493 + 0.281733i) q^{72} +(2.58092 + 2.97855i) q^{73} +(-4.06209 + 2.61055i) q^{74} +(-2.20991 + 2.55037i) q^{75} +(-0.873198 + 6.07322i) q^{76} +(14.4892 - 4.25441i) q^{77} +(-0.307599 - 0.197682i) q^{78} +(0.565652 + 3.93420i) q^{79} +(1.20217 + 2.63238i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.602967 - 4.19373i) q^{82} +(13.5461 + 8.70557i) q^{83} +(2.65843 - 0.780586i) q^{84} +(2.59363 - 18.0391i) q^{85} +(-4.60791 + 5.31782i) q^{86} +(2.86890 - 1.84373i) q^{87} +(3.56917 + 4.11904i) q^{88} +(-13.2033 - 3.87683i) q^{89} +(-1.20217 + 2.63238i) q^{90} -1.01308 q^{91} +(4.18251 - 2.34662i) q^{92} +7.68188 q^{93} +(2.77667 - 6.08006i) q^{94} +(-17.0368 - 5.00244i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-3.64397 + 2.34184i) q^{97} +(0.443061 - 0.511320i) q^{98} +(-0.775655 + 5.39480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	2.43450	−	1.56456i	1.08874	−	0.699691i	0.132181	−	0.991226i	$-0.457802\pi$
$5$	2.43450	−	1.56456i	1.08874	−	0.699691i	0.956560	+	0.291534i	$0.0941658\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	0.394306	−	2.74246i	0.149034	−	1.03655i	−0.768772	−	0.639523i	$-0.779132\pi$
$7$	0.394306	−	2.74246i	0.149034	−	1.03655i	0.917806	−	0.397030i	$-0.129959\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.411844	+	2.86444i	0.130237	+	0.905815i
$11$	2.26413	+	4.95774i	0.682659	+	1.49482i	0.859800	+	0.510630i	$0.170588\pi$
$11$	2.26413	+	4.95774i	0.682659	+	1.49482i	−0.177141	+	0.984185i	$0.556685\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.0520365	−	0.361922i	−0.0144323	−	0.100379i	0.981332	−	0.192321i	$-0.0616016\pi$
$13$	−0.0520365	−	0.361922i	−0.0144323	−	0.100379i	−0.995764	+	0.0919422i	$0.970692\pi$
$14$	2.33083	+	1.49793i	0.622941	+	0.400340i
$15$	−2.77667	+	0.815304i	−0.716933	+	0.210511i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	4.12405	−	4.75941i	1.00023	−	1.15433i	0.0122207	−	0.999925i	$-0.496110\pi$
$17$	4.12405	−	4.75941i	1.00023	−	1.15433i	0.988008	−	0.154401i	$-0.0493446\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−4.01801	−	4.63704i	−0.921796	−	1.06381i	−0.997773	−	0.0666993i	$-0.978753\pi$
$19$	−4.01801	−	4.63704i	−0.921796	−	1.06381i	0.0759775	−	0.997110i	$-0.475792\pi$
$20$	−2.77667	−	0.815304i	−0.620883	−	0.182308i
$21$	−1.15098	+	2.52028i	−0.251163	+	0.549971i
$22$	−5.45027			−1.16200
$23$	−0.965501	+	4.69764i	−0.201321	+	0.979525i
$23$	−0.965501	+	4.69764i	−0.201321	+	0.979525i
$24$	−1.00000			−0.204124
$25$	1.40187	−	3.06967i	0.280374	−	0.613933i
$26$	0.350833	+	0.103014i	0.0688039	+	0.0202027i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−2.33083	+	1.49793i	−0.440485	+	0.283083i
$29$	−2.23325	+	2.57731i	−0.414704	+	0.478594i	−0.924216	−	0.381869i	$-0.875280\pi$
$29$	−2.23325	+	2.57731i	−0.414704	+	0.478594i	0.509512	+	0.860463i	$0.329826\pi$
$30$	0.411844	−	2.86444i	0.0751921	−	0.522973i
$31$	−7.37071	+	2.16423i	−1.32382	+	0.388708i	−0.865869	−	0.500270i	$-0.833234\pi$
$31$	−7.37071	+	2.16423i	−1.32382	+	0.388708i	−0.457949	+	0.888979i	$0.651416\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.775655	−	5.39480i	−0.135024	−	0.939114i
$34$	2.61612	+	5.72850i	0.448660	+	0.982429i
$35$	−3.33080	−	7.29343i	−0.563008	−	1.23282i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	4.06209	+	2.61055i	0.667804	+	0.429171i	0.830133	−	0.557565i	$-0.188264\pi$
$37$	4.06209	+	2.61055i	0.667804	+	0.429171i	−0.162329	+	0.986737i	$0.551901\pi$
$38$	5.88714	−	1.72862i	0.955020	−	0.280419i
$39$	−0.0520365	+	0.361922i	−0.00833251	+	0.0579539i
$40$	1.89510	−	2.18706i	0.299641	−	0.345804i
$41$	−3.56427	+	2.29062i	−0.556645	+	0.357734i	−0.788518	−	0.615012i	$-0.789151\pi$
$41$	−3.56427	+	2.29062i	−0.556645	+	0.357734i	0.231873	+	0.972746i	$0.425515\pi$
$42$	−1.81440	−	2.09393i	−0.279968	−	0.323100i
$43$	6.75145	+	1.98241i	1.02959	+	0.302314i	0.752543	−	0.658543i	$-0.228827\pi$
$43$	6.75145	+	1.98241i	1.02959	+	0.302314i	0.277044	+	0.960857i	$0.410645\pi$
$44$	2.26413	−	4.95774i	0.341330	−	0.747408i
$45$	2.89389			0.431396
$46$	−3.87204	−	2.82972i	−0.570901	−	0.417219i
$47$	−6.68409			−0.974975			−0.487487	−	0.873130i	$-0.662086\pi$
$47$	−6.68409			−0.974975			−0.487487	+	0.873130i	$0.662086\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−0.649167	−	0.190613i	−0.0927382	−	0.0272304i
$50$	2.20991	+	2.55037i	0.312528	+	0.360677i
$51$	−5.29788	+	3.40474i	−0.741851	+	0.476759i
$52$	−0.239446	+	0.276335i	−0.0332051	+	0.0383208i
$53$	−1.01536	+	7.06200i	−0.139471	+	0.970040i	0.793110	+	0.609078i	$0.208461\pi$
$53$	−1.01536	+	7.06200i	−0.139471	+	0.970040i	−0.932581	+	0.360962i	$0.882449\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	13.2687	+	8.52726i	1.78915	+	1.14982i
$56$	−0.394306	−	2.74246i	−0.0526914	−	0.366477i
$57$	2.54885	+	5.58121i	0.337604	+	0.739249i
$58$	−1.41668	−	3.10209i	−0.186019	−	0.407324i
$59$	−0.0626320	−	0.435615i	−0.00815399	−	0.0567122i	0.985338	−	0.170613i	$-0.0545746\pi$
$59$	−0.0626320	−	0.435615i	−0.00815399	−	0.0567122i	−0.993492	+	0.113900i	$0.963666\pi$
$60$	2.43450	+	1.56456i	0.314292	+	0.201983i
$61$	−7.80450	+	2.29161i	−0.999264	+	0.293411i	−0.740154	−	0.672437i	$-0.765247\pi$
$61$	−7.80450	+	2.29161i	−0.999264	+	0.293411i	−0.259110	+	0.965848i	$0.583429\pi$
$62$	1.09325	−	7.60369i	0.138842	−	0.965669i
$63$	1.81440	−	2.09393i	0.228593	−	0.263810i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.692931	−	0.799685i	−0.0859475	−	0.0991887i
$66$	5.22950	+	1.53552i	0.643707	+	0.189009i
$67$	1.84829	−	4.04720i	0.225805	−	0.494444i	−0.762490	−	0.647000i	$-0.776023\pi$
$67$	1.84829	−	4.04720i	0.225805	−	0.494444i	0.988295	+	0.152556i	$0.0487505\pi$
$68$	−6.29760			−0.763696
$69$	2.24987	−	4.23534i	0.270852	−	0.509875i
$70$	8.01801			0.958335
$71$	−0.586952	+	1.28525i	−0.0696584	+	0.152531i	−0.941258	−	0.337687i	$-0.890355\pi$
$71$	−0.586952	+	1.28525i	−0.0696584	+	0.152531i	0.871600	+	0.490218i	$0.163083\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	2.58092	+	2.97855i	0.302074	+	0.348612i	0.886411	−	0.462899i	$-0.153191\pi$
$73$	2.58092	+	2.97855i	0.302074	+	0.348612i	−0.584337	+	0.811511i	$0.698645\pi$
$74$	−4.06209	+	2.61055i	−0.472209	+	0.303470i
$75$	−2.20991	+	2.55037i	−0.255178	+	0.294491i
$76$	−0.873198	+	6.07322i	−0.100163	+	0.696647i
$77$	14.4892	−	4.25441i	1.65120	−	0.484835i
$78$	−0.307599	−	0.197682i	−0.0348287	−	0.0223831i
$79$	0.565652	+	3.93420i	0.0636408	+	0.442632i	0.996582	+	0.0826040i	$0.0263237\pi$
$79$	0.565652	+	3.93420i	0.0636408	+	0.442632i	−0.932942	+	0.360028i	$0.882767\pi$
$80$	1.20217	+	2.63238i	0.134406	+	0.294309i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.602967	−	4.19373i	−0.0665866	−	0.463120i
$83$	13.5461	+	8.70557i	1.48688	+	0.955561i	0.996459	+	0.0840759i	$0.0267938\pi$
$83$	13.5461	+	8.70557i	1.48688	+	0.955561i	0.490422	+	0.871485i	$0.336843\pi$
$84$	2.65843	−	0.780586i	0.290059	−	0.0851689i
$85$	2.59363	−	18.0391i	0.281319	−	1.95661i
$86$	−4.60791	+	5.31782i	−0.496884	+	0.573435i
$87$	2.86890	−	1.84373i	0.307578	−	0.197669i
$88$	3.56917	+	4.11904i	0.380475	+	0.439091i
$89$	−13.2033	−	3.87683i	−1.39954	−	0.410943i	−0.507017	−	0.861936i	$-0.669252\pi$
$89$	−13.2033	−	3.87683i	−1.39954	−	0.410943i	−0.892528	+	0.450993i	$0.851070\pi$
$90$	−1.20217	+	2.63238i	−0.126720	+	0.277477i
$91$	−1.01308			−0.106199
$92$	4.18251	−	2.34662i	0.436057	−	0.244652i
$93$	7.68188			0.796574
$94$	2.77667	−	6.08006i	0.286392	−	0.627110i
$95$	−17.0368	−	5.00244i	−1.74793	−	0.513240i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−3.64397	+	2.34184i	−0.369989	+	0.237778i	−0.712401	−	0.701772i	$-0.752392\pi$
$97$	−3.64397	+	2.34184i	−0.369989	+	0.237778i	0.342412	+	0.939550i	$0.388756\pi$
$98$	0.443061	−	0.511320i	0.0447560	−	0.0516511i
$99$	−0.775655	+	5.39480i	−0.0779562	+	0.542198i
$100$	−3.23793	+	0.950741i	−0.323793	+	0.0950741i
$101$	5.40610	+	3.47429i	0.537927	+	0.345705i	0.781228	−	0.624246i	$-0.214594\pi$
$101$	5.40610	+	3.47429i	0.537927	+	0.345705i	−0.243301	+	0.969951i	$0.578230\pi$
$102$	−0.896242	−	6.23350i	−0.0887412	−	0.617208i
$103$	−5.10326	−	11.1746i	−0.502839	−	1.10106i	−0.975536	−	0.219839i	$-0.929447\pi$
$103$	−5.10326	−	11.1746i	−0.502839	−	1.10106i	0.472697	−	0.881225i	$-0.343280\pi$
$104$	−0.151894	−	0.332601i	−0.0148944	−	0.0326142i
$105$	1.14108	+	7.93639i	0.111358	+	0.774513i
$106$	−6.00202	−	3.85727i	−0.582968	−	0.374651i
$107$	−9.53368	+	2.79934i	−0.921656	+	0.270623i	−0.707939	−	0.706273i	$-0.750375\pi$
$107$	−9.53368	+	2.79934i	−0.921656	+	0.270623i	−0.213716	+	0.976896i	$0.568557\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	6.81481	−	7.86470i	0.652740	−	0.753302i	−0.328833	−	0.944388i	$-0.606655\pi$
$109$	6.81481	−	7.86470i	0.652740	−	0.753302i	0.981573	+	0.191086i	$0.0612009\pi$
$110$	−13.2687	+	8.52726i	−1.26512	+	0.813043i
$111$	−3.16207	−	3.64923i	−0.300131	−	0.346369i
$112$	2.65843	+	0.780586i	0.251198	+	0.0737584i
$113$	4.46613	−	9.77947i	0.420138	−	0.919975i	−0.574687	−	0.818373i	$-0.694876\pi$
$113$	4.46613	−	9.77947i	0.420138	−	0.919975i	0.994825	−	0.101601i	$-0.0323966\pi$
$114$	−6.13568			−0.574659
$115$	4.99921	+	12.9470i	0.466179	+	1.20731i
$116$	3.41027			0.316635
$117$	0.151894	−	0.332601i	0.0140426	−	0.0307490i
$118$	0.422268	+	0.123989i	0.0388729	+	0.0114141i
$119$	−11.4264	−	13.1867i	−1.04745	−	1.20882i
$120$	−2.43450	+	1.56456i	−0.222238	+	0.142824i
$121$	−12.2495	+	14.1367i	−1.11359	+	1.28515i
$122$	1.15759	−	8.05120i	0.104803	−	0.728921i
$123$	4.06523	−	1.19366i	0.366550	−	0.107629i
$124$	6.46241	+	4.15314i	0.580341	+	0.372963i
$125$	0.669402	+	4.65579i	0.0598731	+	0.416427i
$126$	1.15098	+	2.52028i	0.102537	+	0.224525i
$127$	−4.03228	−	8.82946i	−0.357807	−	0.783488i	−0.999858	−	0.0168262i	$-0.994644\pi$
$127$	−4.03228	−	8.82946i	−0.357807	−	0.783488i	0.642052	−	0.766661i	$-0.278083\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−5.91946	−	3.80421i	−0.521180	−	0.334942i
$130$	1.01527	−	0.298111i	0.0890453	−	0.0261461i
$131$	1.86823	−	12.9938i	0.163228	−	1.13527i	−0.729271	−	0.684225i	$-0.760141\pi$
$131$	1.86823	−	12.9938i	0.163228	−	1.13527i	0.892499	−	0.451049i	$-0.148950\pi$
$132$	−3.56917	+	4.11904i	−0.310656	+	0.358517i
$133$	−14.3012	+	9.19084i	−1.24007	+	0.796947i
$134$	2.91365	+	3.36253i	0.251701	+	0.290479i
$135$	−2.77667	−	0.815304i	−0.238978	−	0.0701702i
$136$	2.61612	−	5.72850i	0.224330	−	0.491215i
$137$	−3.83057			−0.327268			−0.163634	−	0.986521i	$-0.552322\pi$
$137$	−3.83057			−0.327268			−0.163634	+	0.986521i	$0.552322\pi$
$138$	2.91797	+	3.80598i	0.248394	+	0.323986i
$139$	17.3000			1.46736			0.733682	−	0.679494i	$-0.237800\pi$
$139$	17.3000			1.46736			0.733682	+	0.679494i	$0.237800\pi$
$140$	−3.33080	+	7.29343i	−0.281504	+	0.616408i
$141$	6.41334	+	1.88313i	0.540100	+	0.158588i
$142$	−0.925273	−	1.06782i	−0.0776471	−	0.0896096i
$143$	1.67650	−	1.07742i	0.140196	−	0.0900984i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−1.40450	+	9.76850i	−0.116637	+	0.811230i
$146$	−3.78154	+	1.11036i	−0.312962	+	0.0918940i
$147$	0.569170	+	0.365783i	0.0469443	+	0.0301693i
$148$	−0.687184	−	4.77947i	−0.0564862	−	0.392870i
$149$	6.04641	+	13.2398i	0.495341	+	1.08465i	0.977956	+	0.208813i	$0.0669599\pi$
$149$	6.04641	+	13.2398i	0.495341	+	1.08465i	−0.482615	+	0.875833i	$0.660313\pi$
$150$	−1.40187	−	3.06967i	−0.114462	−	0.250637i
$151$	1.35418	+	9.41856i	0.110202	+	0.766471i	0.967722	+	0.252021i	$0.0810951\pi$
$151$	1.35418	+	9.41856i	0.110202	+	0.766471i	−0.857520	+	0.514451i	$0.827996\pi$
$152$	−5.16166	−	3.31720i	−0.418666	−	0.269060i
$153$	6.04250	−	1.77424i	0.488507	−	0.143439i
$154$	−2.14908	+	14.9472i	−0.173178	+	1.20448i
$155$	−14.5579	+	16.8007i	−1.16932	+	1.34947i
$156$	0.307599	−	0.197682i	0.0246276	−	0.0158272i
$157$	−15.6273	−	18.0349i	−1.24720	−	1.43934i	−0.854318	−	0.519750i	$-0.826025\pi$
$157$	−15.6273	−	18.0349i	−1.24720	−	1.43934i	−0.392878	−	0.919591i	$-0.628521\pi$
$158$	−3.81365	−	1.11979i	−0.303398	−	0.0890856i
$159$	2.96383	−	6.48988i	0.235047	−	0.514681i
$160$	−2.89389			−0.228782
$161$	12.5024	+	4.50016i	0.985326	+	0.354662i
$162$	−1.00000			−0.0785674
$163$	3.39382	−	7.43143i	0.265824	−	0.582074i	−0.728904	−	0.684616i	$-0.759970\pi$
$163$	3.39382	−	7.43143i	0.265824	−	0.582074i	0.994729	+	0.102541i	$0.0326974\pi$
$164$	4.06523	+	1.19366i	0.317441	+	0.0932091i
$165$	−10.3288	−	11.9201i	−0.804096	−	0.927976i
$166$	−13.5461	+	8.70557i	−1.05138	+	0.675684i
$167$	6.70343	−	7.73618i	0.518727	−	0.598643i	−0.434584	−	0.900631i	$-0.643105\pi$
$167$	6.70343	−	7.73618i	0.518727	−	0.598643i	0.953312	+	0.301988i	$0.0976502\pi$
$168$	−0.394306	+	2.74246i	−0.0304214	+	0.211586i
$169$	12.3451	−	3.62486i	0.949625	−	0.278835i
$170$	15.3315	+	9.85295i	1.17587	+	0.755687i
$171$	−0.873198	−	6.07322i	−0.0667751	−	0.464431i
$172$	−2.92306	−	6.40061i	−0.222881	−	0.488042i
$173$	−1.40929	−	3.08592i	−0.107147	−	0.234618i	0.848463	−	0.529255i	$-0.177529\pi$
$173$	−1.40929	−	3.08592i	−0.107147	−	0.234618i	−0.955609	+	0.294637i	$0.904801\pi$
$174$	0.485332	+	3.37556i	0.0367929	+	0.255900i
$175$	−7.86567	−	5.05496i	−0.594589	−	0.382119i
$176$	−5.22950	+	1.53552i	−0.394188	+	0.115744i
$177$	−0.0626320	+	0.435615i	−0.00470771	+	0.0327428i
$178$	9.01133	−	10.3996i	0.675428	−	0.779485i
$179$	5.74526	−	3.69226i	0.429421	−	0.275972i	−0.308025	−	0.951378i	$-0.599668\pi$
$179$	5.74526	−	3.69226i	0.429421	−	0.275972i	0.737446	+	0.675406i	$0.236032\pi$
$180$	−1.89510	−	2.18706i	−0.141252	−	0.163014i
$181$	−0.902420	−	0.264975i	−0.0670764	−	0.0196954i	0.248022	−	0.968754i	$-0.420219\pi$
$181$	−0.902420	−	0.264975i	−0.0670764	−	0.0196954i	−0.315099	+	0.949059i	$0.602038\pi$
$182$	0.420847	−	0.921526i	0.0311952	−	0.0683080i
$183$	8.13399			0.601282
$184$	0.397086	+	4.77936i	0.0292736	+	0.352339i
$185$	13.9735			1.02735
$186$	−3.19117	+	6.98768i	−0.233988	+	0.512362i
$187$	32.9333	+	9.67008i	2.40832	+	0.707147i
$188$	4.37715	+	5.05150i	0.319236	+	0.368418i
$189$	−2.33083	+	1.49793i	−0.169543	+	0.108959i
$190$	11.6277	−	13.4191i	0.843563	−	0.973523i
$191$	0.290991	−	2.02388i	0.0210553	−	0.146443i	−0.976582	−	0.215146i	$-0.930977\pi$
$191$	0.290991	−	2.02388i	0.0210553	−	0.146443i	0.997637	+	0.0687033i	$0.0218862\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	−19.8456	−	12.7540i	−1.42852	−	0.918054i	−0.999894	−	0.0145713i	$-0.995362\pi$
$193$	−19.8456	−	12.7540i	−1.42852	−	0.918054i	−0.428625	−	0.903482i	$-0.641002\pi$
$194$	−0.616451	−	4.28751i	−0.0442586	−	0.307825i
$195$	0.439565	+	0.962513i	0.0314779	+	0.0689270i
$196$	0.281059	+	0.615433i	0.0200756	+	0.0439595i
$197$	0.479933	+	3.33801i	0.0341938	+	0.237823i	0.999750	−	0.0223725i	$-0.00712197\pi$
$197$	0.479933	+	3.33801i	0.0341938	+	0.237823i	−0.965556	+	0.260196i	$0.916213\pi$
$198$	−4.58506	−	2.94664i	−0.325846	−	0.209409i
$199$	−20.7972	+	6.10661i	−1.47427	+	0.432886i	−0.917486	−	0.397768i	$-0.869785\pi$
$199$	−20.7972	+	6.10661i	−1.47427	+	0.432886i	−0.556789	+	0.830654i	$0.687967\pi$
$200$	0.480259	−	3.34027i	0.0339594	−	0.236193i
$201$	−2.91365	+	3.36253i	−0.205513	+	0.237175i
$202$	−5.40610	+	3.47429i	−0.380372	+	0.244450i
$203$	6.18758	+	7.14085i	0.434283	+	0.501190i
$204$	6.04250	+	1.77424i	0.423060	+	0.124222i
$205$	−5.09341	+	11.1530i	−0.355739	+	0.778959i
$206$	12.2847			0.855917
$207$	−3.35197	+	3.42992i	−0.232978	+	0.238396i
$208$	0.365644			0.0253528
$209$	13.8919	−	30.4191i	0.960926	−	2.10413i
$210$	−7.69322	−	2.25893i	−0.530883	−	0.155881i
$211$	15.0163	+	17.3298i	1.03377	+	1.19303i	0.980917	+	0.194429i	$0.0622854\pi$
$211$	15.0163	+	17.3298i	1.03377	+	1.19303i	0.0528511	+	0.998602i	$0.483169\pi$
$212$	6.00202	−	3.85727i	0.412221	−	0.264918i
$213$	0.925273	−	1.06782i	0.0633986	−	0.0731659i
$214$	1.41406	−	9.83503i	0.0966634	−	0.672309i
$215$	19.5380	−	5.73687i	1.33248	−	0.391251i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	3.02901	+	21.0673i	0.205623	+	1.43014i
$218$	4.32301	+	9.46608i	0.292791	+	0.641124i
$219$	−1.63723	−	3.58502i	−0.110633	−	0.242253i
$220$	−2.24466	−	15.6120i	−0.151335	−	1.05256i
$221$	−1.93714	−	1.24492i	−0.130306	−	0.0837425i
$222$	4.63303	−	1.36038i	0.310948	−	0.0913027i
$223$	2.82161	−	19.6247i	0.188949	−	1.31417i	−0.645787	−	0.763518i	$-0.723470\pi$
$223$	2.82161	−	19.6247i	0.188949	−	1.31417i	0.834736	−	0.550651i	$-0.185620\pi$
$224$	−1.81440	+	2.09393i	−0.121230	+	0.139906i
$225$	2.83891	−	1.82446i	0.189261	−	0.121631i
$226$	7.04042	+	8.12507i	0.468322	+	0.540472i
$227$	19.1242	+	5.61537i	1.26932	+	0.372705i	0.845954	−	0.533255i	$-0.179032\pi$
$227$	19.1242	+	5.61537i	1.26932	+	0.372705i	0.423362	+	0.905960i	$0.360850\pi$
$228$	2.54885	−	5.58121i	0.168802	−	0.369625i
$229$	−16.2991			−1.07708			−0.538539	−	0.842601i	$-0.681023\pi$
$229$	−16.2991			−1.07708			−0.538539	+	0.842601i	$0.681023\pi$
$230$	−13.8537	−	0.830924i	−0.913488	−	0.0547895i
$231$	−15.1009			−0.993564
$232$	−1.41668	+	3.10209i	−0.0930094	+	0.203662i
$233$	−17.8818	−	5.25056i	−1.17147	−	0.343976i	−0.362593	−	0.931948i	$-0.618108\pi$
$233$	−17.8818	−	5.25056i	−1.17147	−	0.343976i	−0.808881	+	0.587972i	$0.799927\pi$
$234$	0.239446	+	0.276335i	0.0156531	+	0.0180646i
$235$	−16.2724	+	10.4576i	−1.06149	+	0.682181i
$236$	−0.288201	+	0.332601i	−0.0187603	+	0.0216505i
$237$	0.565652	−	3.93420i	0.0367431	−	0.255554i
$238$	16.7417	−	4.91582i	1.08521	−	0.318645i
$239$	3.70719	+	2.38247i	0.239798	+	0.154109i	0.655021	−	0.755611i	$-0.272660\pi$
$239$	3.70719	+	2.38247i	0.239798	+	0.154109i	−0.415222	+	0.909720i	$0.636296\pi$
$240$	−0.411844	−	2.86444i	−0.0265844	−	0.184899i
$241$	5.44932	+	11.9323i	0.351022	+	0.768630i	0.999970	+	0.00779736i	$0.00248200\pi$
$241$	5.44932	+	11.9323i	0.351022	+	0.768630i	−0.648948	+	0.760833i	$0.724791\pi$
$242$	−7.77054	−	17.0151i	−0.499509	−	1.09377i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	6.84275	+	4.39757i	0.438062	+	0.281525i
$245$	−1.87862	+	0.551613i	−0.120021	+	0.0352413i
$246$	−0.602967	+	4.19373i	−0.0384438	+	0.267382i
$247$	−1.46916	+	1.69550i	−0.0934805	+	0.107882i
$248$	−6.46241	+	4.15314i	−0.410363	+	0.263724i
$249$	−10.5448	−	12.1693i	−0.668248	−	0.771200i
$250$	−4.51314	−	1.32518i	−0.285436	−	0.0838115i
$251$	−3.82791	+	8.38196i	−0.241616	+	0.529065i	−0.991126	−	0.132928i	$-0.957562\pi$
$251$	−3.82791	+	8.38196i	−0.241616	+	0.529065i	0.749510	+	0.661993i	$0.230289\pi$
$252$	−2.77066			−0.174535
$253$	−25.4757	+	5.84934i	−1.60164	+	0.367745i
$254$	9.70663			0.609048
$255$	−7.57077	+	16.5777i	−0.474100	+	1.03813i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−1.59428	−	1.83990i	−0.0994485	−	0.114770i	0.703844	−	0.710355i	$-0.251466\pi$
$257$	−1.59428	−	1.83990i	−0.0994485	−	0.114770i	−0.803292	+	0.595585i	$0.796920\pi$
$258$	5.91946	−	3.80421i	0.368530	−	0.236840i
$259$	8.76104	−	10.1108i	0.544384	−	0.628253i
$260$	−0.150588	+	1.04736i	−0.00933908	+	0.0649548i
$261$	−3.27213	+	0.960783i	−0.202540	+	0.0594710i
$262$	11.0435	+	7.09722i	0.682269	+	0.438468i
$263$	0.513250	+	3.56974i	0.0316484	+	0.220119i	0.999508	−	0.0313727i	$-0.00998788\pi$
$263$	0.513250	+	3.56974i	0.0316484	+	0.220119i	−0.967859	+	0.251492i	$0.919079\pi$
$264$	−2.26413	−	4.95774i	−0.139347	−	0.305128i
$265$	8.57700	+	18.7810i	0.526881	+	1.15371i
$266$	−2.41934	−	16.8269i	−0.148339	−	1.03172i
$267$	11.5762	+	7.43959i	0.708453	+	0.455295i
$268$	−4.26904	+	1.25350i	−0.260773	+	0.0765699i
$269$	−3.21946	+	22.3918i	−0.196294	+	1.36525i	0.618628	+	0.785684i	$0.287689\pi$
$269$	−3.21946	+	22.3918i	−0.196294	+	1.36525i	−0.814922	+	0.579570i	$0.803220\pi$
$270$	1.89510	−	2.18706i	0.115332	−	0.133100i
$271$	11.5214	−	7.40434i	0.699874	−	0.449782i	−0.141710	−	0.989908i	$-0.545260\pi$
$271$	11.5214	−	7.40434i	0.699874	−	0.449782i	0.841584	+	0.540127i	$0.181624\pi$
$272$	4.12405	+	4.75941i	0.250057	+	0.288581i
$273$	0.972039	+	0.285416i	0.0588305	+	0.0172742i
$274$	1.59128	−	3.48441i	0.0961326	−	0.210501i
$275$	18.3926			1.10912
$276$	−4.67421	+	1.07322i	−0.281354	+	0.0646002i
$277$	−10.2577			−0.616324			−0.308162	−	0.951334i	$-0.599714\pi$
$277$	−10.2577			−0.616324			−0.308162	+	0.951334i	$0.599714\pi$
$278$	−7.18666	+	15.7366i	−0.431027	+	0.943818i
$279$	−7.37071	−	2.16423i	−0.441273	−	0.129569i
$280$	−5.25068	−	6.05960i	−0.313788	−	0.362131i
$281$	−2.62009	+	1.68383i	−0.156302	+	0.100449i	−0.616454	−	0.787391i	$-0.711431\pi$
$281$	−2.62009	+	1.68383i	−0.156302	+	0.100449i	0.460152	+	0.887840i	$0.347795\pi$
$282$	−4.37715	+	5.05150i	−0.260655	+	0.300812i
$283$	1.35249	−	9.40677i	0.0803972	−	0.559174i	−0.909316	−	0.416107i	$-0.863394\pi$
$283$	1.35249	−	9.40677i	0.0803972	−	0.559174i	0.989713	−	0.143068i	$-0.0456967\pi$
$284$	1.35570	−	0.398068i	0.0804458	−	0.0236210i
$285$	14.9373	+	9.59962i	0.884809	+	0.568632i
$286$	0.283613	+	1.97257i	0.0167704	+	0.116641i
$287$	4.87651	+	10.6781i	0.287851	+	0.630307i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−3.22482	−	22.4291i	−0.189695	−	1.31936i
$290$	−8.30229	−	5.33556i	−0.487527	−	0.313315i
$291$	4.15614	−	1.22035i	0.243637	−	0.0715383i
$292$	0.560888	−	3.90107i	0.0328235	−	0.228293i
$293$	−16.4960	+	19.0374i	−0.963704	+	1.11217i	0.0299335	+	0.999552i	$0.490470\pi$
$293$	−16.4960	+	19.0374i	−0.963704	+	1.11217i	−0.993638	+	0.112622i	$0.964075\pi$
$294$	−0.569170	+	0.365783i	−0.0331947	+	0.0213329i
$295$	−0.834022	−	0.962513i	−0.0485586	−	0.0560397i
$296$	4.63303	+	1.36038i	0.269289	+	0.0790704i
$297$	2.26413	−	4.95774i	0.131378	−	0.287677i
$298$	−14.5551			−0.843155
$299$	1.75042	+	0.104987i	0.101229	+	0.00607157i
$300$	3.37462			0.194834
$301$	8.09881	−	17.7339i	0.466808	−	1.02217i
$302$	−9.12997	−	2.68080i	−0.525371	−	0.154263i
$303$	−4.20829	−	4.85663i	−0.241760	−	0.279006i
$304$	5.16166	−	3.31720i	0.296042	−	0.190254i
$305$	−15.4147	+	17.7895i	−0.882643	+	1.01862i
$306$	−0.896242	+	6.23350i	−0.0512347	+	0.356345i
$307$	−1.27637	+	0.374777i	−0.0728464	+	0.0213896i	−0.317953	−	0.948107i	$-0.602995\pi$
$307$	−1.27637	+	0.374777i	−0.0728464	+	0.0213896i	0.245106	+	0.969496i	$0.421177\pi$
$308$	−12.7037	−	8.16415i	−0.723858	−	0.465195i
$309$	1.74830	+	12.1597i	0.0994572	+	0.691740i
$310$	−9.23490	−	20.2216i	−0.524507	−	1.14851i
$311$	−3.61737	−	7.92093i	−0.205122	−	0.449155i	0.778912	−	0.627133i	$-0.215772\pi$
$311$	−3.61737	−	7.92093i	−0.205122	−	0.449155i	−0.984034	+	0.177978i	$0.943044\pi$
$312$	0.0520365	+	0.361922i	0.00294599	+	0.0204898i
$313$	10.7667	+	6.91932i	0.608568	+	0.391103i	0.808320	−	0.588744i	$-0.200377\pi$
$313$	10.7667	+	6.91932i	0.608568	+	0.391103i	−0.199752	+	0.979847i	$0.564014\pi$
$314$	22.8969	−	6.72315i	1.29215	−	0.379409i
$315$	1.14108	−	7.93639i	0.0642926	−	0.447165i
$316$	2.60284	−	3.00384i	0.146421	−	0.168979i
$317$	11.0873	−	7.12540i	0.622727	−	0.400202i	−0.190884	−	0.981613i	$-0.561135\pi$
$317$	11.0873	−	7.12540i	0.622727	−	0.400202i	0.813610	+	0.581410i	$0.197499\pi$
$318$	4.67218	+	5.39198i	0.262003	+	0.302367i
$319$	−17.8340	−	5.23653i	−0.998512	−	0.293190i
$320$	1.20217	−	2.63238i	0.0672032	−	0.147154i
$321$	9.93617			0.554583
$322$	−9.28717	+	9.50314i	−0.517554	+	0.529589i
$323$	−38.6400			−2.14999
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−1.18393	−	0.347633i	−0.0656725	−	0.0192832i
$326$	5.35002	+	6.17425i	0.296310	+	0.341960i
$327$	−8.75450	+	5.62618i	−0.484125	+	0.311128i
$328$	−2.77455	+	3.20200i	−0.153199	+	0.176801i
$329$	−2.63558	+	18.3309i	−0.145304	+	1.01061i
$330$	15.1336	−	4.44363i	0.833078	−	0.244614i
$331$	−26.6439	−	17.1230i	−1.46448	−	0.941166i	−0.998407	−	0.0564208i	$-0.982031\pi$
$331$	−26.6439	−	17.1230i	−1.46448	−	0.941166i	−0.466075	−	0.884745i	$-0.654332\pi$
$332$	−2.29160	−	15.9384i	−0.125768	−	0.874735i
$333$	2.00588	+	4.39227i	0.109922	+	0.240695i
$334$	4.25237	+	9.31138i	0.232679	+	0.509496i
$335$	−1.83241	−	12.7447i	−0.100115	−	0.696315i
$336$	−2.33083	−	1.49793i	−0.127157	−	0.0817190i
$337$	−8.77072	+	2.57532i	−0.477772	+	0.140286i	−0.511747	−	0.859136i	$-0.671001\pi$
$337$	−8.77072	+	2.57532i	−0.477772	+	0.140286i	0.0339752	+	0.999423i	$0.489183\pi$
$338$	−1.83107	+	12.7353i	−0.0995969	+	0.692711i
$339$	−7.04042	+	8.12507i	−0.382383	+	0.441293i
$340$	−15.3315	+	9.85295i	−0.831467	+	0.534351i
$341$	−27.4179	−	31.6420i	−1.48476	−	1.71351i
$342$	5.88714	+	1.72862i	0.318340	+	0.0934731i
$343$	7.27811	−	15.9368i	0.392981	−	0.860508i
$344$	7.03648			0.379381
$345$	−1.14913	−	13.8310i	−0.0618668	−	0.744635i
$346$	3.39250			0.182382
$347$	7.40034	−	16.2045i	0.397271	−	0.869903i	−0.600268	−	0.799799i	$-0.704940\pi$
$347$	7.40034	−	16.2045i	0.397271	−	0.869903i	0.997540	−	0.0701041i	$-0.0223332\pi$
$348$	−3.27213	−	0.960783i	−0.175404	−	0.0515034i
$349$	13.6513	+	15.7545i	0.730739	+	0.843318i	0.992555	−	0.121800i	$-0.0388666\pi$
$349$	13.6513	+	15.7545i	0.730739	+	0.843318i	−0.261815	+	0.965118i	$0.584321\pi$
$350$	7.86567	−	5.05496i	0.420438	−	0.270199i
$351$	−0.239446	+	0.276335i	−0.0127807	+	0.0147497i
$352$	0.775655	−	5.39480i	0.0413425	−	0.287544i
$353$	−21.2394	+	6.23645i	−1.13046	+	0.331933i	−0.792888	−	0.609367i	$-0.791424\pi$
$353$	−21.2394	+	6.23645i	−1.13046	+	0.331933i	−0.337571	+	0.941300i	$0.609605\pi$
$354$	−0.370231	−	0.237933i	−0.0196776	−	0.0126460i
$355$	0.581907	+	4.04725i	0.0308844	+	0.214806i
$356$	5.71639	+	12.5172i	0.302968	+	0.663408i
$357$	7.24838	+	15.8717i	0.383625	+	0.840021i
$358$	0.971926	+	6.75990i	0.0513679	+	0.357272i
$359$	−23.4475	−	15.0688i	−1.23751	−	0.795302i	−0.252470	−	0.967605i	$-0.581243\pi$
$359$	−23.4475	−	15.0688i	−1.23751	−	0.795302i	−0.985044	+	0.172303i	$0.944879\pi$
$360$	2.77667	−	0.815304i	0.146343	−	0.0429703i
$361$	−2.65368	+	18.4567i	−0.139667	+	0.971407i
$362$	0.615908	−	0.710796i	0.0323714	−	0.0373586i
$363$	15.7360	−	10.1129i	0.825928	−	0.530792i
$364$	0.663423	+	0.765631i	0.0347728	+	0.0401300i
$365$	10.9434	+	3.21326i	0.572802	+	0.168190i
$366$	−3.37898	+	7.39894i	−0.176622	+	0.386749i
$367$	17.5832			0.917835			0.458917	−	0.888479i	$-0.348237\pi$
$367$	17.5832			0.917835			0.458917	+	0.888479i	$0.348237\pi$
$368$	−4.51242	−	1.62422i	−0.235226	−	0.0846682i
$369$	−4.23685			−0.220562
$370$	−5.80481	+	12.7108i	−0.301777	+	0.660800i
$371$	18.9669	+	5.56918i	0.984712	+	0.289138i
$372$	−5.03056	−	5.80558i	−0.260822	−	0.301005i
$373$	22.2145	−	14.2764i	1.15022	−	0.739205i	0.180541	−	0.983567i	$-0.442215\pi$
$373$	22.2145	−	14.2764i	1.15022	−	0.739205i	0.969684	+	0.244363i	$0.0785788\pi$
$374$	−22.4772	+	25.9401i	−1.16227	+	1.34133i
$375$	0.669402	−	4.65579i	0.0345678	−	0.240424i
$376$	−6.41334	+	1.88313i	−0.330743	+	0.0971148i
$377$	1.04900	+	0.674148i	0.0540260	+	0.0347204i
$378$	−0.394306	−	2.74246i	−0.0202809	−	0.141057i
$379$	1.05257	+	2.30481i	0.0540671	+	0.118390i	0.934737	−	0.355339i	$-0.115635\pi$
$379$	1.05257	+	2.30481i	0.0540671	+	0.118390i	−0.880670	+	0.473730i	$0.842907\pi$
$380$	7.37611	+	16.1514i	0.378386	+	0.828551i
$381$	1.38140	+	9.60783i	0.0707711	+	0.492224i
$382$	1.72011	+	1.10545i	0.0880084	+	0.0565596i
$383$	−3.40668	+	1.00029i	−0.174073	+	0.0511124i	−0.367608	−	0.929981i	$-0.619823\pi$
$383$	−3.40668	+	1.00029i	−0.174073	+	0.0511124i	0.193535	+	0.981093i	$0.438005\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	28.6176	−	33.0265i	1.45849	−	1.68319i
$386$	19.8456	−	12.7540i	1.01012	−	0.649162i
$387$	4.60791	+	5.31782i	0.234233	+	0.270320i
$388$	4.15614	+	1.22035i	0.210996	+	0.0619540i
$389$	11.5072	−	25.1973i	0.583439	−	1.27755i	−0.355887	−	0.934529i	$-0.615821\pi$
$389$	11.5072	−	25.1973i	0.583439	−	1.27755i	0.939326	−	0.343025i	$-0.111452\pi$
$390$	−1.05813			−0.0535807
$391$	18.3762	+	23.9685i	0.929324	+	1.21214i
$392$	−0.676573			−0.0341721
$393$	−5.45333	+	11.9411i	−0.275084	+	0.602350i
$394$	−3.23573	−	0.950097i	−0.163014	−	0.0478652i
$395$	7.53236	+	8.69280i	0.378994	+	0.437382i
$396$	4.58506	−	2.94664i	0.230408	−	0.148074i
$397$	13.9539	−	16.1037i	0.700329	−	0.808222i	−0.288468	−	0.957489i	$-0.593146\pi$
$397$	13.9539	−	16.1037i	0.700329	−	0.808222i	0.988797	+	0.149267i	$0.0476915\pi$
$398$	3.08470	−	21.4546i	0.154622	−	1.07542i
$399$	16.3113	−	4.78942i	0.816585	−	0.239771i
$400$	2.83891	+	1.82446i	0.141946	+	0.0912230i
$401$	−1.55920	−	10.8445i	−0.0778629	−	0.541549i	−0.990996	−	0.133888i	$-0.957254\pi$
$401$	−1.55920	−	10.8445i	−0.0778629	−	0.541549i	0.913134	−	0.407661i	$-0.133655\pi$
$402$	−1.84829	−	4.04720i	−0.0921845	−	0.201856i
$403$	1.16683	+	2.55500i	0.0581240	+	0.127274i
$404$	−0.914549	−	6.36083i	−0.0455005	−	0.316463i
$405$	2.43450	+	1.56456i	0.120971	+	0.0777435i
$406$	−9.06596	+	2.66201i	−0.449936	+	0.132113i
$407$	−3.74534	+	26.0494i	−0.185650	+	1.29122i
$408$	−4.12405	+	4.75941i	−0.204171	+	0.235626i
$409$	24.3974	−	15.6793i	1.20638	−	0.775290i	0.226327	−	0.974051i	$-0.427328\pi$
$409$	24.3974	−	15.6793i	1.20638	−	0.775290i	0.980048	+	0.198761i	$0.0636918\pi$
$410$	−8.02925	−	9.26625i	−0.396536	−	0.457627i
$411$	3.67541	+	1.07920i	0.181295	+	0.0532329i
$412$	−5.10326	+	11.1746i	−0.251419	+	0.550532i
$413$	−1.21935			−0.0600005
$414$	−1.72750	−	4.47389i	−0.0849022	−	0.219880i
$415$	46.5984			2.28743
$416$	−0.151894	+	0.332601i	−0.00744721	+	0.0163071i
$417$	−16.5992	−	4.87396i	−0.812866	−	0.238679i
$418$	21.8993	+	25.2731i	1.07113	+	1.23615i
$419$	−7.03546	+	4.52142i	−0.343705	+	0.220886i	−0.701092	−	0.713071i	$-0.747304\pi$
$419$	−7.03546	+	4.52142i	−0.343705	+	0.220886i	0.357387	+	0.933956i	$0.383668\pi$
$420$	5.25068	−	6.05960i	0.256207	−	0.295678i
$421$	1.50874	−	10.4935i	0.0735315	−	0.511423i	−0.919455	−	0.393195i	$-0.871370\pi$
$421$	1.50874	−	10.4935i	0.0735315	−	0.511423i	0.992987	−	0.118228i	$-0.0377213\pi$
$422$	−22.0017	+	6.46029i	−1.07103	+	0.314482i
$423$	−5.62301	−	3.61369i	−0.273400	−	0.175704i
$424$	1.01536	+	7.06200i	0.0493103	+	0.342961i
$425$	−8.82841	−	19.3315i	−0.428241	−	0.937717i
$426$	0.586952	+	1.28525i	0.0284379	+	0.0622704i
$427$	3.20728	+	22.3072i	0.155211	+	1.07952i
$428$	8.35884	+	5.37190i	0.404040	+	0.259660i
$429$	−1.91213	+	0.561453i	−0.0923187	+	0.0271072i
$430$	−2.89793	+	20.1556i	−0.139751	+	0.971987i
$431$	−0.308153	+	0.355628i	−0.0148432	+	0.0171300i	−0.763123	−	0.646254i	$-0.776335\pi$
$431$	−0.308153	+	0.355628i	−0.0148432	+	0.0171300i	0.748279	+	0.663384i	$0.230880\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	18.9929	+	21.9190i	0.912743	+	1.05336i	0.998372	+	0.0570343i	$0.0181644\pi$
$433$	18.9929	+	21.9190i	0.912743	+	1.05336i	−0.0856295	+	0.996327i	$0.527290\pi$
$434$	−20.4217	−	5.99637i	−0.980275	−	0.287835i
$435$	4.09971	−	8.97712i	0.196566	−	0.430420i
$436$	−10.4065			−0.498381
$437$	25.6625	−	14.3981i	1.22760	−	0.688755i
$438$	3.94118			0.188317
$439$	−6.26627	+	13.7212i	−0.299073	+	0.654878i	−0.998191	−	0.0601285i	$-0.980849\pi$
$439$	−6.26627	+	13.7212i	−0.299073	+	0.654878i	0.699118	+	0.715006i	$0.253576\pi$
$440$	15.1336	+	4.44363i	0.721467	+	0.211842i
$441$	−0.443061	−	0.511320i	−0.0210982	−	0.0243486i
$442$	1.93714	−	1.24492i	0.0921401	−	0.0592149i
$443$	17.4014	−	20.0823i	0.826765	−	0.954137i	−0.172760	−	0.984964i	$-0.555268\pi$
$443$	17.4014	−	20.0823i	0.826765	−	0.954137i	0.999525	+	0.0308265i	$0.00981393\pi$
$444$	−0.687184	+	4.77947i	−0.0326123	+	0.226824i
$445$	−38.2089	+	11.2191i	−1.81127	+	0.531838i
$446$	16.6791	+	10.7190i	0.789780	+	0.507561i
$447$	−2.07141	−	14.4070i	−0.0979742	−	0.681426i
$448$	−1.15098	−	2.52028i	−0.0543785	−	0.119072i
$449$	1.61015	+	3.52574i	0.0759878	+	0.166390i	0.943813	−	0.330479i	$-0.107210\pi$
$449$	1.61015	+	3.52574i	0.0759878	+	0.166390i	−0.867826	+	0.496869i	$0.834483\pi$
$450$	0.480259	+	3.34027i	0.0226396	+	0.157462i
$451$	−19.4262	−	12.4845i	−0.914746	−	0.587871i
$452$	−10.3155	+	3.02891i	−0.485201	+	0.142468i
$453$	1.35418	−	9.41856i	0.0636251	−	0.442522i
$454$	−13.0524	+	15.0633i	−0.612579	+	0.706954i
$455$	−2.46633	+	1.58501i	−0.115623	+	0.0743066i
$456$	4.01801	+	4.63704i	0.188161	+	0.217149i
$457$	−3.09150	−	0.907746i	−0.144614	−	0.0424626i	0.208624	−	0.977996i	$-0.433101\pi$
$457$	−3.09150	−	0.907746i	−0.144614	−	0.0424626i	−0.353239	+	0.935533i	$0.614920\pi$
$458$	6.77091	−	14.8262i	0.316384	−	0.692784i
$459$	−6.29760			−0.293947
$460$	6.51088	−	12.2566i	0.303572	−	0.571468i
$461$	−25.7463			−1.19912			−0.599562	−	0.800329i	$-0.704658\pi$
$461$	−25.7463			−1.19912			−0.599562	+	0.800329i	$0.704658\pi$
$462$	6.27313	−	13.7362i	0.291852	−	0.639067i
$463$	−17.8150	−	5.23097i	−0.827936	−	0.243104i	−0.159806	−	0.987148i	$-0.551087\pi$
$463$	−17.8150	−	5.23097i	−0.827936	−	0.243104i	−0.668130	+	0.744045i	$0.732905\pi$
$464$	−2.23325	−	2.57731i	−0.103676	−	0.119649i
$465$	18.7015	−	12.0187i	0.867262	−	0.557356i
$466$	12.2044	−	14.0847i	0.565360	−	0.652460i
$467$	−0.885467	+	6.15856i	−0.0409745	+	0.284984i	0.959024	+	0.283325i	$0.0914374\pi$
$467$	−0.885467	+	6.15856i	−0.0409745	+	0.284984i	−0.999999	+	0.00165959i	$0.999472\pi$
$468$	−0.350833	+	0.103014i	−0.0162172	+	0.00476181i
$469$	−10.3705	−	6.66471i	−0.478865	−	0.307748i
$470$	−2.75280	−	19.1462i	−0.126977	−	0.883147i
$471$	9.91329	+	21.7071i	0.456780	+	1.00021i
$472$	−0.182822	−	0.400324i	−0.00841506	−	0.0184264i
$473$	5.45788	+	37.9604i	0.250953	+	1.74542i
$474$	3.34369	+	2.14886i	0.153581	+	0.0987004i
$475$	−19.8669	+	5.83344i	−0.911555	+	0.267657i
$476$	−2.48318	+	17.2709i	−0.113817	+	0.791611i
$477$	−4.67218	+	5.39198i	−0.213924	+	0.246882i
$478$	−3.70719	+	2.38247i	−0.169563	+	0.108972i
$479$	6.76132	+	7.80298i	0.308933	+	0.356527i	0.888891	−	0.458119i	$-0.151477\pi$
$479$	6.76132	+	7.80298i	0.308933	+	0.356527i	−0.579958	+	0.814646i	$0.696931\pi$
$480$	2.77667	+	0.815304i	0.126737	+	0.0372134i
$481$	0.733438	−	1.60600i	0.0334419	−	0.0732275i
$482$	−13.1178			−0.597498
$483$	−10.7281	−	7.84020i	−0.488146	−	0.356742i
$484$	18.7055			0.850249
$485$	−5.20730	+	11.4024i	−0.236451	+	0.517757i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−16.4493	−	18.9835i	−0.745387	−	0.860223i	0.248726	−	0.968574i	$-0.419988\pi$
$487$	−16.4493	−	18.9835i	−0.745387	−	0.860223i	−0.994113	+	0.108351i	$0.965443\pi$
$488$	−6.84275	+	4.39757i	−0.309757	+	0.199068i
$489$	−5.35002	+	6.17425i	−0.241936	+	0.279209i
$490$	0.278643	−	1.93800i	0.0125878	−	0.0875500i
$491$	−1.47060	+	0.431806i	−0.0663671	+	0.0194871i	−0.314748	−	0.949175i	$-0.601920\pi$
$491$	−1.47060	+	0.431806i	−0.0663671	+	0.0194871i	0.248380	+	0.968663i	$0.420102\pi$
$492$	−3.56427	−	2.29062i	−0.160690	−	0.103269i
$493$	3.05642	+	21.2579i	0.137654	+	0.957408i
$494$	−0.931972	−	2.04073i	−0.0419314	−	0.0918170i
$495$	6.55214	+	14.3472i	0.294497	+	0.644858i
$496$	−1.09325	−	7.60369i	−0.0490882	−	0.341416i
$497$	3.29330	+	2.11648i	0.147725	+	0.0949369i
$498$	15.4501	−	4.53655i	0.692334	−	0.203288i
$499$	3.33474	−	23.1936i	0.149283	−	1.03829i	−0.768113	−	0.640314i	$-0.778804\pi$
$499$	3.33474	−	23.1936i	0.149283	−	1.03829i	0.917397	−	0.397974i	$-0.130287\pi$
$500$	3.08025	−	3.55480i	0.137753	−	0.158975i
$501$	−8.61143	+	5.53423i	−0.384730	+	0.247251i
$502$	−6.03433	−	6.96399i	−0.269325	−	0.310818i
$503$	−9.03611	−	2.65324i	−0.402900	−	0.118302i	0.0740030	−	0.997258i	$-0.476423\pi$
$503$	−9.03611	−	2.65324i	−0.402900	−	0.118302i	−0.476903	+	0.878956i	$0.658241\pi$
$504$	1.15098	−	2.52028i	0.0512685	−	0.112262i
$505$	18.5969			0.827549
$506$	5.26224	−	25.6034i	0.233935	−	1.13821i
$507$	−12.8663			−0.571413
$508$	−4.03228	+	8.82946i	−0.178903	+	0.391744i
$509$	−9.58906	−	2.81560i	−0.425027	−	0.124799i	0.0622217	−	0.998062i	$-0.480181\pi$
$509$	−9.58906	−	2.81560i	−0.425027	−	0.124799i	−0.487249	+	0.873263i	$0.662000\pi$
$510$	−11.9346	−	13.7732i	−0.528471	−	0.609889i
$511$	9.18622	−	5.90363i	0.406375	−	0.261161i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.873198	+	6.07322i	−0.0385526	+	0.268139i
$514$	2.33592	−	0.685888i	0.103033	−	0.0302532i
$515$	−29.9071	−	19.2201i	−1.31787	−	0.846941i
$516$	1.00140	+	6.96486i	0.0440840	+	0.306611i
$517$	−15.1336	−	33.1380i	−0.665576	−	1.45741i
$518$	5.55762	+	12.1695i	0.244188	+	0.534697i
$519$	0.482803	+	3.35797i	0.0211927	+	0.147398i
$520$	−0.890159	−	0.572071i	−0.0390361	−	0.0250870i
$521$	37.0292	−	10.8728i	1.62228	−	0.476345i	0.660650	−	0.750694i	$-0.270281\pi$
$521$	37.0292	−	10.8728i	1.62228	−	0.476345i	0.961630	+	0.274349i	$0.0884624\pi$
$522$	0.485332	−	3.37556i	0.0212424	−	0.147744i
$523$	6.29792	−	7.26819i	0.275389	−	0.317816i	−0.601160	−	0.799129i	$-0.705295\pi$
$523$	6.29792	−	7.26819i	0.275389	−	0.317816i	0.876549	+	0.481313i	$0.159840\pi$
$524$	−11.0435	+	7.09722i	−0.482437	+	0.310044i
$525$	6.12291	+	7.06622i	0.267226	+	0.308395i
$526$	−3.46036	−	1.01605i	−0.150879	−	0.0443020i
$527$	−20.0967	+	44.0056i	−0.875426	+	1.91691i
$528$	5.45027			0.237193
$529$	−21.1356	−	9.07115i	−0.918940	−	0.394398i
$530$	−20.6468			−0.896841
$531$	0.182822	−	0.400324i	0.00793379	−	0.0173726i
$532$	16.3113	+	4.78942i	0.707184	+	0.207648i
$533$	1.01450	+	1.17079i	0.0439427	+	0.0507126i
$534$	−11.5762	+	7.43959i	−0.500952	+	0.321942i
$535$	−18.8300	+	21.7310i	−0.814092	+	0.939512i
$536$	0.633197	−	4.40398i	0.0273499	−	0.190223i
$537$	−6.55277	+	1.92407i	−0.282773	+	0.0830296i
$538$	−19.0309	−	12.2304i	−0.820481	−	0.527291i
$539$	−0.524787	−	3.64998i	−0.0226042	−	0.157216i
$540$	1.20217	+	2.63238i	0.0517330	+	0.113280i
$541$	5.98880	+	13.1137i	0.257479	+	0.563800i	0.993588	−	0.113063i	$-0.0360662\pi$
$541$	5.98880	+	13.1137i	0.257479	+	0.563800i	−0.736109	+	0.676863i	$0.763339\pi$
$542$	1.94907	+	13.5561i	0.0837198	+	0.582284i
$543$	0.791214	+	0.508482i	0.0339542	+	0.0218211i
$544$	−6.04250	+	1.77424i	−0.259070	+	0.0760699i
$545$	4.28585	−	29.8088i	0.183586	−	1.27687i
$546$	−0.663423	+	0.765631i	−0.0283919	+	0.0327660i
$547$	−11.8995	+	7.64737i	−0.508788	+	0.326978i	−0.769723	−	0.638378i	$-0.779605\pi$
$547$	−11.8995	+	7.64737i	−0.508788	+	0.326978i	0.260935	+	0.965356i	$0.415969\pi$
$548$	2.50849	+	2.89496i	0.107158	+	0.123666i
$549$	−7.80450	−	2.29161i	−0.333088	−	0.0978035i
$550$	−7.64057	+	16.7305i	−0.325795	+	0.713392i
$551$	20.9243			0.891405
$552$	0.965501	−	4.69764i	0.0410945	−	0.199945i
$553$	11.0124			0.468296
$554$	4.26119	−	9.33071i	0.181041	−	0.396424i
$555$	−13.4075	−	3.93679i	−0.569116	−	0.167108i
$556$	−11.3291	−	13.0744i	−0.480459	−	0.554479i
$557$	8.83021	−	5.67483i	0.374148	−	0.240450i	−0.340030	−	0.940415i	$-0.610437\pi$
$557$	8.83021	−	5.67483i	0.374148	−	0.240450i	0.714178	+	0.699964i	$0.246801\pi$
$558$	5.03056	−	5.80558i	0.212961	−	0.245770i
$559$	0.366154	−	2.54666i	0.0154867	−	0.107712i
$560$	7.69322	−	2.25893i	0.325098	−	0.0954573i
$561$	−28.8749	−	18.5568i	−1.21910	−	0.783467i
$562$	−0.443241	−	3.08281i	−0.0186970	−	0.130040i
$563$	−9.84751	−	21.5630i	−0.415023	−	0.908774i	−0.995524	−	0.0945139i	$-0.969870\pi$
$563$	−9.84751	−	21.5630i	−0.415023	−	0.908774i	0.580500	−	0.814260i	$-0.302857\pi$
$564$	−2.77667	−	6.08006i	−0.116919	−	0.256017i
$565$	−4.42774	−	30.7956i	−0.186276	−	1.29558i
$566$	7.99486	+	5.13798i	0.336049	+	0.215965i
$567$	2.65843	−	0.780586i	0.111644	−	0.0327815i
$568$	−0.201081	+	1.39855i	−0.00843717	+	0.0586818i
$569$	−6.40005	+	7.38606i	−0.268304	+	0.309640i	−0.873874	−	0.486153i	$-0.838400\pi$
$569$	−6.40005	+	7.38606i	−0.268304	+	0.309640i	0.605570	+	0.795792i	$0.292945\pi$
$570$	−14.9373	+	9.59962i	−0.625655	+	0.402084i
$571$	16.1753	+	18.6673i	0.676916	+	0.781203i	0.985442	−	0.170013i	$-0.0543810\pi$
$571$	16.1753	+	18.6673i	0.676916	+	0.781203i	−0.308526	+	0.951216i	$0.599836\pi$
$572$	−1.91213	−	0.561453i	−0.0799503	−	0.0234755i
$573$	−0.849398	+	1.85992i	−0.0354841	+	0.0776993i
$574$	−11.7389			−0.489972
$575$	13.0667	+	9.54924i	0.544918	+	0.398231i
$576$	1.00000			0.0416667
$577$	−0.394559	+	0.863965i	−0.0164257	+	0.0359673i	−0.917667	−	0.397350i	$-0.869930\pi$
$577$	−0.394559	+	0.863965i	−0.0164257	+	0.0359673i	0.901241	+	0.433317i	$0.142657\pi$
$578$	21.7419	+	6.38399i	0.904343	+	0.265539i
$579$	15.4485	+	17.8285i	0.642018	+	0.740929i
$580$	8.30229	−	5.33556i	0.344734	−	0.221547i
$581$	29.2160	−	33.7171i	1.21209	−	1.39882i
$582$	−0.616451	+	4.28751i	−0.0255527	+	0.177723i
$583$	−37.3105	+	10.9553i	−1.54524	+	0.453724i
$584$	3.31553	+	2.13076i	0.137198	+	0.0881716i
$585$	−0.150588	−	1.04736i	−0.00622606	−	0.0433032i
$586$	−10.4643	−	22.9137i	−0.432277	−	0.946554i
$587$	1.71897	+	3.76402i	0.0709494	+	0.155358i	0.941784	−	0.336219i	$-0.109148\pi$
$587$	1.71897	+	3.76402i	0.0709494	+	0.155358i	−0.870834	+	0.491576i	$0.836421\pi$
$588$	−0.0962864	−	0.669687i	−0.00397079	−	0.0276174i
$589$	39.6512	+	25.4823i	1.63380	+	1.04998i
$590$	1.22200	−	0.358811i	0.0503088	−	0.0147720i
$591$	0.479933	−	3.33801i	0.0197418	−	0.137307i
$592$	−3.16207	+	3.64923i	−0.129960	+	0.149982i
$593$	−31.0039	+	19.9250i	−1.27318	+	0.818221i	−0.990030	−	0.140855i	$-0.955015\pi$
$593$	−31.0039	+	19.9250i	−1.27318	+	0.818221i	−0.283147	+	0.959077i	$0.591378\pi$
$594$	3.56917	+	4.11904i	0.146445	+	0.169006i
$595$	−48.4488	−	14.2259i	−1.98621	−	0.583203i
$596$	6.04641	−	13.2398i	0.247671	−	0.542323i
$597$	21.6752			0.887107
$598$	−0.822651	+	1.54862i	−0.0336407	+	0.0633280i
$599$	1.06163			0.0433771			0.0216885	−	0.999765i	$-0.493096\pi$
$599$	1.06163			0.0433771			0.0216885	+	0.999765i	$0.493096\pi$
$600$	−1.40187	+	3.06967i	−0.0572311	+	0.125319i
$601$	7.52005	+	2.20809i	0.306749	+	0.0900697i	0.431484	−	0.902120i	$-0.357990\pi$
$601$	7.52005	+	2.20809i	0.306749	+	0.0900697i	−0.124735	+	0.992190i	$0.539808\pi$
$602$	12.7670	+	14.7339i	0.520343	+	0.600508i
$603$	3.74296	−	2.40546i	0.152425	−	0.0979578i
$604$	6.23127	−	7.19127i	0.253547	−	0.292608i
$605$	−7.70374	+	53.5807i	−0.313202	+	2.17836i
$606$	6.16593	−	1.81048i	0.250474	−	0.0735458i
$607$	−1.37597	−	0.884282i	−0.0558489	−	0.0358919i	0.512418	−	0.858736i	$-0.328750\pi$
$607$	−1.37597	−	0.884282i	−0.0558489	−	0.0358919i	−0.568267	+	0.822844i	$0.692386\pi$
$608$	0.873198	+	6.07322i	0.0354129	+	0.246302i
$609$	−3.92513	−	8.59484i	−0.159054	−	0.348281i
$610$	−9.77841	−	21.4117i	−0.395916	−	0.866936i
$611$	0.347817	+	2.41912i	0.0140712	+	0.0978671i
$612$	−5.29788	−	3.40474i	−0.214154	−	0.137628i
$613$	26.5787	−	7.80421i	1.07350	−	0.315209i	0.303226	−	0.952919i	$-0.401936\pi$
$613$	26.5787	−	7.80421i	1.07350	−	0.315209i	0.770277	+	0.637710i	$0.220118\pi$
$614$	0.189315	−	1.31672i	0.00764015	−	0.0531384i
$615$	8.02925	−	9.26625i	0.323771	−	0.373651i
$616$	12.7037	−	8.16415i	0.511845	−	0.328943i
$617$	7.51758	+	8.67575i	0.302646	+	0.349273i	0.886619	−	0.462501i	$-0.153048\pi$
$617$	7.51758	+	8.67575i	0.302646	+	0.349273i	−0.583972	+	0.811774i	$0.698502\pi$
$618$	−11.7871	−	3.46101i	−0.474147	−	0.139222i
$619$	−17.4123	+	38.1276i	−0.699858	+	1.53248i	0.140285	+	0.990111i	$0.455198\pi$
$619$	−17.4123	+	38.1276i	−0.699858	+	1.53248i	−0.840143	+	0.542365i	$0.817529\pi$
$620$	22.2305			0.892800
$621$	4.18251	−	2.34662i	0.167838	−	0.0941667i
$622$	8.70784			0.349152
$623$	−15.8382	+	34.6808i	−0.634544	+	1.38946i
$624$	−0.350833	−	0.103014i	−0.0140445	−	0.00412385i
$625$	19.9635	+	23.0391i	0.798538	+	0.921562i
$626$	−10.7667	+	6.91932i	−0.430323	+	0.276552i
$627$	−21.8993	+	25.2731i	−0.874573	+	1.00931i
$628$	−3.39614	+	23.6207i	−0.135521	+	0.942568i
$629$	29.1769	−	8.56712i	1.16336	−	0.341593i
$630$	6.74518	+	4.33486i	0.268734	+	0.172705i
$631$	3.46844	+	24.1235i	0.138076	+	0.960343i	0.934591	+	0.355724i	$0.115766\pi$
$631$	3.46844	+	24.1235i	0.138076	+	0.960343i	−0.796515	+	0.604619i	$0.793325\pi$
$632$	1.65113	+	3.61547i	0.0656784	+	0.143816i
$633$	−9.52571	−	20.8584i	−0.378613	−	0.829047i
$634$	1.87564	+	13.0454i	0.0744913	+	0.518099i
$635$	−23.6308	−	15.1866i	−0.937758	−	0.602661i
$636$	−6.84562	+	2.01005i	−0.271446	+	0.0797038i
$637$	−0.0352065	+	0.244867i	−0.00139493	+	0.00970198i
$638$	12.1718	−	14.0470i	0.481887	−	0.556127i
$639$	−1.18863	+	0.763888i	−0.0470216	+	0.0302189i
$640$	1.89510	+	2.18706i	0.0749103	+	0.0864511i
$641$	36.3068	+	10.6606i	1.43403	+	0.421070i	0.904228	−	0.427049i	$-0.140447\pi$
$641$	36.3068	+	10.6606i	1.43403	+	0.421070i	0.529805	+	0.848119i	$0.322265\pi$
$642$	−4.12763	+	9.03826i	−0.162905	+	0.356711i
$643$	−5.62757			−0.221930			−0.110965	−	0.993824i	$-0.535394\pi$
$643$	−5.62757			−0.221930			−0.110965	+	0.993824i	$0.535394\pi$
$644$	−4.78633	−	12.3957i	−0.188608	−	0.488457i
$645$	−20.3628			−0.801785
$646$	16.0516	−	35.1482i	0.631544	−	1.38289i
$647$	23.6526	+	6.94504i	0.929881	+	0.273038i	0.711387	−	0.702801i	$-0.248067\pi$
$647$	23.6526	+	6.94504i	0.929881	+	0.273038i	0.218494	+	0.975838i	$0.429886\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	2.01786	−	1.29680i	0.0792079	−	0.0509039i
$650$	0.808039	−	0.932527i	0.0316939	−	0.0365767i
$651$	3.02901	−	21.0673i	0.118716	−	0.825691i
$652$	−7.83878	+	2.30167i	−0.306990	+	0.0901405i
$653$	34.8323	+	22.3853i	1.36309	+	0.876006i	0.998478	−	0.0551529i	$-0.0175646\pi$
$653$	34.8323	+	22.3853i	1.36309	+	0.876006i	0.364614	+	0.931159i	$0.381201\pi$
$654$	−1.48100	−	10.3006i	−0.0579116	−	0.402784i
$655$	−15.7814	−	34.5564i	−0.616629	−	1.35023i
$656$	−1.76005	−	3.85398i	−0.0687185	−	0.150473i
$657$	0.560888	+	3.90107i	0.0218823	+	0.152195i
$658$	−15.5795	−	10.0123i	−0.607351	−	0.390321i
$659$	14.6710	−	4.30780i	0.571502	−	0.167808i	0.0168022	−	0.999859i	$-0.494651\pi$
$659$	14.6710	−	4.30780i	0.571502	−	0.167808i	0.554699	+	0.832051i	$0.312833\pi$
$660$	−2.24466	+	15.6120i	−0.0873734	+	0.607695i
$661$	10.7039	−	12.3530i	0.416333	−	0.480474i	−0.508383	−	0.861131i	$-0.669757\pi$
$661$	10.7039	−	12.3530i	0.416333	−	0.480474i	0.924716	+	0.380657i	$0.124302\pi$
$662$	26.6439	−	17.1230i	1.03555	−	0.665505i
$663$	1.50793	+	1.74025i	0.0585633	+	0.0675856i
$664$	15.4501	+	4.53655i	0.599579	+	0.176052i
$665$	−20.4367	+	44.7502i	−0.792502	+	1.73534i
$666$	−4.82862			−0.187105
$667$	−9.95106	−	12.9794i	−0.385306	−	0.502564i
$668$	−10.2364			−0.396059
$669$	−8.23624	+	18.0348i	−0.318431	+	0.697268i
$670$	12.3542	+	3.62751i	0.477283	+	0.140143i
$671$	−29.0316	−	33.5042i	−1.12075	−	1.29342i
$672$	2.33083	−	1.49793i	0.0899137	−	0.0577840i
$673$	26.4324	−	30.5046i	1.01890	−	1.17587i	0.0345886	−	0.999402i	$-0.488988\pi$
$673$	26.4324	−	30.5046i	1.01890	−	1.17587i	0.984307	−	0.176466i	$-0.0564666\pi$
$674$	1.30090	−	9.04796i	0.0501088	−	0.348514i
$675$	−3.23793	+	0.950741i	−0.124628	+	0.0365940i
$676$	−10.8238	−	6.95605i	−0.416301	−	0.267540i
$677$	−0.668686	−	4.65081i	−0.0256997	−	0.178745i	0.972929	−	0.231106i	$-0.0742345\pi$
$677$	−0.668686	−	4.65081i	−0.0256997	−	0.178745i	−0.998628	+	0.0523609i	$0.983325\pi$
$678$	−4.46613	−	9.77947i	−0.171521	−	0.375578i
$679$	4.98556	+	10.9169i	0.191328	+	0.418950i
$680$	−2.59363	−	18.0391i	−0.0994611	−	0.691767i
$681$	−16.7675	−	10.7758i	−0.642532	−	0.412930i
$682$	40.1724	−	11.7957i	1.53828	−	0.451680i
$683$	−4.09817	+	28.5034i	−0.156812	+	1.09065i	0.747648	+	0.664095i	$0.231183\pi$
$683$	−4.09817	+	28.5034i	−0.156812	+	1.09065i	−0.904460	+	0.426558i	$0.859726\pi$
$684$	−4.01801	+	4.63704i	−0.153633	+	0.177301i
$685$	−9.32553	+	5.99315i	−0.356310	+	0.228987i
$686$	11.4732	+	13.2408i	0.438049	+	0.505536i
$687$	15.6389	+	4.59200i	0.596662	+	0.175196i
$688$	−2.92306	+	6.40061i	−0.111441	+	0.244021i
$689$	2.60873			0.0993846
$690$	13.0585	+	4.70031i	0.497127	+	0.178938i
$691$	−27.0579			−1.02933			−0.514666	−	0.857391i	$-0.672084\pi$
$691$	−27.0579			−1.02933			−0.514666	+	0.857391i	$0.672084\pi$
$692$	−1.40929	+	3.08592i	−0.0535733	+	0.117309i
$693$	14.4892	+	4.25441i	0.550398	+	0.161612i
$694$	11.6659	+	13.4632i	0.442832	+	0.511055i
$695$	42.1167	−	27.0668i	1.59758	−	1.02670i
$696$	2.23325	−	2.57731i	0.0846511	−	0.0976926i
$697$	−3.79724	+	26.4104i	−0.143831	+	1.00037i
$698$	−20.0018	+	5.87305i	−0.757078	+	0.222298i
$699$	15.6782	+	10.0758i	0.593003	+	0.381100i
$700$	1.33064	+	9.25478i	0.0502933	+	0.349798i
$701$	−13.5565	−	29.6846i	−0.512023	−	1.12117i	−0.972372	−	0.233436i	$-0.925003\pi$
$701$	−13.5565	−	29.6846i	−0.512023	−	1.12117i	0.460350	−	0.887738i	$-0.347724\pi$
$702$	−0.151894	−	0.332601i	−0.00573287	−	0.0125532i
$703$	−4.21634	−	29.3253i	−0.159022	−	1.10602i
$704$	4.58506	+	2.94664i	0.172806	+	0.111056i
$705$	18.5595	−	5.44957i	0.698992	−	0.205243i
$706$	3.15029	−	21.9108i	0.118563	−	0.824622i
$707$	11.6598	−	13.4561i	0.438510	−	0.506068i
$708$	0.370231	−	0.237933i	0.0139141	−	0.00894207i
$709$	−27.8915	−	32.1885i	−1.04749	−	1.20886i	−0.977417	−	0.211322i	$-0.932223\pi$
$709$	−27.8915	−	32.1885i	−1.04749	−	1.20886i	−0.0700701	−	0.997542i	$-0.522322\pi$
$710$	−3.92324	−	1.15197i	−0.147237	−	0.0432326i
$711$	−1.65113	+	3.61547i	−0.0619222	+	0.135591i
$712$	−13.7607			−0.515703
$713$	−3.05037	−	36.7145i	−0.114237	−	1.37497i
$714$	−17.4485			−0.652995
$715$	2.39575	−	5.24596i	0.0895959	−	0.196188i
$716$	−6.55277	−	1.92407i	−0.244889	−	0.0719058i
$717$	−2.88581	−	3.33040i	−0.107772	−	0.124376i
$718$	23.4475	−	15.0688i	0.875054	−	0.562363i
$719$	−11.9137	+	13.7491i	−0.444305	+	0.512756i	−0.933087	−	0.359650i	$-0.882896\pi$
$719$	−11.9137	+	13.7491i	−0.444305	+	0.512756i	0.488782	+	0.872406i	$0.337441\pi$
$720$	−0.411844	+	2.86444i	−0.0153485	+	0.106751i
$721$	−32.6581	+	9.58928i	−1.21625	+	0.357123i
$722$	−15.6865	−	10.0811i	−0.583790	−	0.375179i
$723$	−1.86685	−	12.9843i	−0.0694291	−	0.482890i
$724$	0.390705	+	0.855525i	0.0145204	+	0.0317953i
$725$	4.78075	+	10.4684i	0.177553	+	0.388786i
$726$	2.66207	+	18.5151i	0.0987986	+	0.687159i
$727$	1.52173	+	0.977954i	0.0564377	+	0.0362703i	0.568555	−	0.822645i	$-0.307502\pi$
$727$	1.52173	+	0.977954i	0.0564377	+	0.0362703i	−0.512118	+	0.858915i	$0.671139\pi$
$728$	−0.972039	+	0.285416i	−0.0360262	+	0.0105782i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−7.46892	+	8.61960i	−0.276437	+	0.319026i
$731$	37.2784	−	23.9574i	1.37879	−	0.886095i
$732$	−5.32663	−	6.14726i	−0.196878	−	0.227209i
$733$	16.3902	+	4.81260i	0.605386	+	0.177757i	0.570039	−	0.821618i	$-0.306928\pi$
$733$	16.3902	+	4.81260i	0.605386	+	0.177757i	0.0353471	+	0.999375i	$0.488746\pi$
$734$	−7.30432	+	15.9942i	−0.269607	+	0.590358i
$735$	1.95793			0.0722194
$736$	3.35197	−	3.42992i	0.123555	−	0.126428i
$737$	24.2497			0.893250
$738$	1.76005	−	3.85398i	0.0647884	−	0.141867i
$739$	39.2196	+	11.5159i	1.44272	+	0.423620i	0.907127	−	0.420857i	$-0.138271\pi$
$739$	39.2196	+	11.5159i	1.44272	+	0.423620i	0.535591	+	0.844477i	$0.320089\pi$
$740$	−9.15070	−	10.5605i	−0.336387	−	0.388211i
$741$	1.88733	−	1.21291i	0.0693327	−	0.0445575i
$742$	−12.9450	+	14.9394i	−0.475227	+	0.548442i
$743$	5.24294	−	36.4654i	0.192345	−	1.33779i	−0.633436	−	0.773795i	$-0.718356\pi$
$743$	5.24294	−	36.4654i	0.192345	−	1.33779i	0.825780	−	0.563992i	$-0.190735\pi$
$744$	7.37071	−	2.16423i	0.270223	−	0.0793447i
$745$	35.4344	+	22.7723i	1.29822	+	0.834312i
$746$	3.75803	+	26.1377i	0.137591	+	0.956969i
$747$	6.68915	+	14.6472i	0.244743	+	0.535913i
$748$	−14.2586	−	31.2219i	−0.521344	−	1.14158i
$749$	3.91789	+	27.2496i	0.143157	+	0.995677i
$750$	3.95698	+	2.54299i	0.144488	+	0.0928570i
$751$	−1.84969	+	0.543119i	−0.0674963	+	0.0198187i	−0.315306	−	0.948990i	$-0.602107\pi$
$751$	−1.84969	+	0.543119i	−0.0674963	+	0.0198187i	0.247810	+	0.968809i	$0.420289\pi$
$752$	0.951245	−	6.61606i	0.0346883	−	0.241263i
$753$	6.03433	−	6.96399i	0.219903	−	0.253782i
$754$	−1.04900	+	0.674148i	−0.0382022	+	0.0245510i
$755$	18.0326	+	20.8108i	0.656275	+	0.757381i
$756$	2.65843	+	0.780586i	0.0966862	+	0.0283896i
$757$	−9.77413	+	21.4024i	−0.355247	+	0.777882i	0.644663	+	0.764467i	$0.276998\pi$
$757$	−9.77413	+	21.4024i	−0.355247	+	0.777882i	−0.999910	+	0.0134152i	$0.995730\pi$
$758$	−2.53379			−0.0920313
$759$	26.0917	+	1.56494i	0.947069	+	0.0568036i
$760$	−17.7560			−0.644078
$761$	7.99143	−	17.4988i	0.289689	−	0.634331i	−0.707703	−	0.706511i	$-0.750268\pi$
$761$	7.99143	−	17.4988i	0.289689	−	0.634331i	0.997392	+	0.0721799i	$0.0229956\pi$
$762$	−9.31344	−	2.73467i	−0.337390	−	0.0990667i
$763$	−18.8815	−	21.7904i	−0.683557	−	0.788867i
$764$	−1.72011	+	1.10545i	−0.0622313	+	0.0399937i
$765$	11.9346	−	13.7732i	0.431495	−	0.497972i
$766$	0.505288	−	3.51436i	0.0182568	−	0.126979i
$767$	−0.154399	+	0.0453358i	−0.00557504	+	0.00163698i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	2.94235	+	20.4645i	0.106104	+	0.737967i	0.971527	+	0.236927i	$0.0761402\pi$
$769$	2.94235	+	20.4645i	0.106104	+	0.737967i	−0.865424	+	0.501041i	$0.832951\pi$
$770$	18.1538	+	39.7512i	0.654216	+	1.43253i
$771$	1.01134	+	2.21453i	0.0364226	+	0.0797544i
$772$	3.35728	+	23.3504i	0.120831	+	0.840400i
$773$	−9.50279	−	6.10708i	−0.341792	−	0.219656i	0.358472	−	0.933541i	$-0.383298\pi$
$773$	−9.50279	−	6.10708i	−0.341792	−	0.219656i	−0.700264	+	0.713884i	$0.746934\pi$
$774$	−6.75145	+	1.98241i	−0.242676	+	0.0712561i
$775$	−3.68929	+	25.6596i	−0.132523	+	0.921719i
$776$	−2.83659	+	3.27360i	−0.101828	+	0.117515i
$777$	−11.2547	+	7.23295i	−0.403760	+	0.259481i
$778$	18.1400	+	20.9347i	0.650350	+	0.750544i
$779$	24.9429	+	7.32391i	0.893674	+	0.262406i
$780$	0.439565	−	0.962513i	0.0157389	−	0.0344635i
$781$	−7.70086			−0.275558
$782$	−29.4363	+	6.75870i	−1.05264	+	0.241691i
$783$	3.41027			0.121873
$784$	0.281059	−	0.615433i	0.0100378	−	0.0219797i
$785$	−66.2613	−	19.4561i	−2.36497	−	0.694417i
$786$	−8.59664	−	9.92105i	−0.306632	−	0.353872i
$787$	−24.6527	+	15.8433i	−0.878774	+	0.564754i	−0.900425	−	0.435012i	$-0.856744\pi$
$787$	−24.6527	+	15.8433i	−0.878774	+	0.564754i	0.0216507	+	0.999766i	$0.493108\pi$
$788$	2.20841	−	2.54864i	0.0786713	−	0.0907916i
$789$	0.513250	−	3.56974i	0.0182722	−	0.127086i
$790$	−11.0363	+	3.24055i	−0.392654	+	0.115294i
$791$	−25.0588	−	16.1043i	−0.890988	−	0.572603i
$792$	0.775655	+	5.39480i	0.0275617	+	0.191696i
$793$	1.23550	+	2.70537i	0.0438740	+	0.0960707i
$794$	8.85177	+	19.3827i	0.314138	+	0.687866i
$795$	−2.93835	−	20.4367i	−0.104213	−	0.724814i
$796$	18.2343	+	11.7185i	0.646299	+	0.415351i
$797$	−31.8929	+	9.36459i	−1.12970	+	0.331711i	−0.792591	−	0.609754i	$-0.791268\pi$
$797$	−31.8929	+	9.36459i	−1.12970	+	0.331711i	−0.337112	+	0.941464i	$0.609450\pi$
$798$	−2.41934	+	16.8269i	−0.0856436	+	0.595664i
$799$	−27.5655	+	31.8123i	−0.975198	+	1.12544i
$800$	−2.83891	+	1.82446i	−0.100371	+	0.0645044i
$801$	−9.01133	−	10.3996i	−0.318400	−	0.367453i
$802$	10.5122	+	3.08667i	0.371199	+	0.108994i
$803$	−8.92333	+	19.5394i	−0.314897	+	0.689529i
$804$	4.44927			0.156914
$805$	37.4778	−	8.60507i	1.32092	−	0.303289i
$806$	−2.80883			−0.0989368
$807$	9.39756	−	20.5778i	0.330810	−	0.724372i
$808$	6.16593	+	1.81048i	0.216917	+	0.0636925i
$809$	−24.3450	−	28.0956i	−0.855924	−	0.987789i	0.144074	−	0.989567i	$-0.453980\pi$
$809$	−24.3450	−	28.0956i	−0.855924	−	0.987789i	−0.999998	+	0.00177791i	$0.999434\pi$
$810$	−2.43450	+	1.56456i	−0.0855396	+	0.0549729i
$811$	1.19838	−	1.38300i	0.0420808	−	0.0485638i	−0.734319	−	0.678805i	$-0.762498\pi$
$811$	1.19838	−	1.38300i	0.0420808	−	0.0485638i	0.776400	+	0.630241i	$0.217044\pi$
$812$	1.34469	−	9.35253i	0.0471894	−	0.328209i
$813$	−13.1407	+	3.85847i	−0.460865	+	0.135322i
$814$	−22.1395	−	14.2282i	−0.775989	−	0.498698i
$815$	−3.36465	−	23.4016i	−0.117858	−	0.819723i
$816$	−2.61612	−	5.72850i	−0.0915824	−	0.200538i
$817$	−17.9349	−	39.2721i	−0.627464	−	1.37396i
$818$	4.12731	+	28.7061i	0.144308	+	1.00368i
$819$	−0.852253	−	0.547710i	−0.0297801	−	0.0191385i
$820$	11.7643	−	3.45432i	0.410829	−	0.120630i
$821$	4.33882	−	30.1772i	0.151426	−	1.05319i	−0.762407	−	0.647098i	$-0.775982\pi$
$821$	4.33882	−	30.1772i	0.151426	−	1.05319i	0.913832	−	0.406092i	$-0.133109\pi$
$822$	−2.50849	+	2.89496i	−0.0874937	+	0.100973i
$823$	42.2413	−	27.1468i	1.47244	−	0.946280i	0.474626	−	0.880187i	$-0.342583\pi$
$823$	42.2413	−	27.1468i	1.47244	−	0.946280i	0.997814	−	0.0660922i	$-0.0210531\pi$
$824$	−8.04478	−	9.28417i	−0.280253	−	0.323429i
$825$	−17.6476	−	5.18180i	−0.614410	−	0.180407i
$826$	0.506538	−	1.10916i	0.0176247	−	0.0385927i
$827$	−47.7273			−1.65964			−0.829821	−	0.558030i	$-0.811557\pi$
$827$	−47.7273			−1.65964			−0.829821	+	0.558030i	$0.811557\pi$
$828$	4.78723	+	0.287130i	0.166368	+	0.00997846i
$829$	−53.8283			−1.86953			−0.934767	−	0.355262i	$-0.884392\pi$
$829$	−53.8283			−1.86953			−0.934767	+	0.355262i	$0.884392\pi$
$830$	−19.3577	+	42.3874i	−0.671915	+	1.47129i
$831$	9.84217	+	2.88992i	0.341421	+	0.100250i
$832$	−0.239446	−	0.276335i	−0.00830129	−	0.00958020i
$833$	−3.58440	+	2.30356i	−0.124192	+	0.0798135i
$834$	11.3291	−	13.0744i	0.392293	−	0.452731i
$835$	4.21581	−	29.3216i	0.145894	−	1.01472i
$836$	−32.0865	+	9.42145i	−1.10974	+	0.325848i
$837$	6.46241	+	4.15314i	0.223373	+	0.143553i
$838$	−1.19019	−	8.27795i	−0.0411144	−	0.285957i
$839$	−2.95446	−	6.46937i	−0.101999	−	0.223347i	0.851751	−	0.523946i	$-0.175541\pi$
$839$	−2.95446	−	6.46937i	−0.101999	−	0.223347i	−0.953751	+	0.300599i	$0.902813\pi$
$840$	3.33080	+	7.29343i	0.114924	+	0.251647i
$841$	2.47202	+	17.1933i	0.0852420	+	0.592871i
$842$	8.91849	+	5.73157i	0.307352	+	0.197523i
$843$	2.98835	−	0.877459i	0.102924	−	0.0302213i
$844$	3.26336	−	22.6972i	0.112330	−	0.781269i
$845$	24.3829	−	28.1394i	0.838797	−	0.968024i
$846$	5.62301	−	3.61369i	0.193323	−	0.124241i
$847$	33.9392	+	39.1679i	1.16616	+	1.34583i
$848$	−6.84562	−	2.01005i	−0.235079	−	0.0690255i
$849$	−3.94790	+	8.64469i	−0.135491	+	0.296685i
$850$	21.2520			0.728938
$851$	−16.1854	+	16.5618i	−0.554827	+	0.567730i
$852$	−1.41293			−0.0484062
$853$	−5.38730	+	11.7965i	−0.184458	+	0.403906i	−0.979159	−	0.203094i	$-0.934900\pi$
$853$	−5.38730	+	11.7965i	−0.184458	+	0.403906i	0.794701	+	0.607001i	$0.207627\pi$
$854$	−21.6237	−	6.34928i	−0.739946	−	0.217268i
$855$	−11.6277	−	13.4191i	−0.397659	−	0.458923i
$856$	−8.35884	+	5.37190i	−0.285699	+	0.183608i
$857$	−16.3004	+	18.8117i	−0.556812	+	0.642595i	−0.962457	−	0.271436i	$-0.912501\pi$
$857$	−16.3004	+	18.8117i	−0.556812	+	0.642595i	0.405645	+	0.914031i	$0.367047\pi$
$858$	0.283613	−	1.97257i	0.00968240	−	0.0673426i
$859$	19.5842	−	5.75043i	0.668204	−	0.196202i	0.0700007	−	0.997547i	$-0.477700\pi$
$859$	19.5842	−	5.75043i	0.668204	−	0.196202i	0.598203	+	0.801345i	$0.295882\pi$
$860$	−17.1303	−	11.0090i	−0.584138	−	0.375403i
$861$	−1.67062	−	11.6194i	−0.0569345	−	0.395988i
$862$	−0.195479	−	0.428039i	−0.00665804	−	0.0145791i
$863$	14.8781	+	32.5785i	0.506457	+	1.10899i	0.974316	+	0.225183i	$0.0722980\pi$
$863$	14.8781	+	32.5785i	0.506457	+	1.10899i	−0.467860	+	0.883803i	$0.654975\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	−8.25903	−	5.30776i	−0.280815	−	0.180469i
$866$	−27.8282	+	8.17110i	−0.945641	+	0.277665i
$867$	−3.22482	+	22.4291i	−0.109521	+	0.761732i
$868$	13.9380	−	16.0853i	0.473086	−	0.545970i
$869$	−18.2240	+	11.7119i	−0.618208	+	0.397298i
$870$	6.46279	+	7.45846i	0.219109	+	0.252865i
$871$	−1.56095	−	0.458336i	−0.0528907	−	0.0155301i
$872$	4.32301	−	9.46608i	0.146396	−	0.320562i
$873$	−4.33160			−0.146602
$874$	2.43639	+	29.3246i	0.0824122	+	0.991921i
$875$	13.0323			0.440571
$876$	−1.63723	+	3.58502i	−0.0553167	+	0.121127i
$877$	−4.24819	−	1.24738i	−0.143451	−	0.0421211i	0.209219	−	0.977869i	$-0.432908\pi$
$877$	−4.24819	−	1.24738i	−0.143451	−	0.0421211i	−0.352670	+	0.935748i	$0.614726\pi$
$878$	−9.87815	−	11.4000i	−0.333372	−	0.384731i
$879$	21.1912	−	13.6188i	0.714761	−	0.459349i
$880$	−10.3288	+	11.9201i	−0.348184	+	0.401825i
$881$	4.17060	−	29.0071i	0.140511	−	0.977276i	−0.790546	−	0.612402i	$-0.790203\pi$
$881$	4.17060	−	29.0071i	0.140511	−	0.977276i	0.931057	−	0.364873i	$-0.118888\pi$
$882$	0.649167	−	0.190613i	0.0218586	−	0.00641827i
$883$	9.76420	+	6.27507i	0.328591	+	0.211173i	0.694526	−	0.719468i	$-0.255614\pi$
$883$	9.76420	+	6.27507i	0.328591	+	0.211173i	−0.365934	+	0.930641i	$0.619251\pi$
$884$	0.327705	+	2.27924i	0.0110219	+	0.0766591i
$885$	0.529067	+	1.15850i	0.0177844	+	0.0389424i
$886$	11.0387	+	24.1713i	0.370852	+	0.812052i
$887$	1.44706	+	10.0646i	0.0485877	+	0.337935i	0.999587	+	0.0287413i	$0.00914990\pi$
$887$	1.44706	+	10.0646i	0.0485877	+	0.337935i	−0.950999	+	0.309193i	$0.899941\pi$
$888$	−4.06209	−	2.61055i	−0.136315	−	0.0876043i
$889$	−25.8044	+	7.57686i	−0.865452	+	0.254120i
$890$	5.66725	−	39.4166i	0.189967	−	1.32125i
$891$	−3.56917	+	4.11904i	−0.119572	+	0.137993i
$892$	−16.6791	+	10.7190i	−0.558459	+	0.358900i
$893$	26.8568	+	30.9944i	0.898727	+	1.03719i
$894$	13.9655	+	4.10065i	0.467077	+	0.137146i
$895$	8.21009	−	17.9776i	0.274433	−	0.600925i
$896$	2.77066			0.0925614
$897$	−1.64994	−	0.593885i	−0.0550898	−	0.0198292i
$898$	−3.87601			−0.129344
$899$	10.8827	−	23.8299i	0.362960	−	0.794771i
$900$	−3.23793	−	0.950741i	−0.107931	−	0.0316914i
$901$	29.4235	+	33.9566i	0.980240	+	1.13126i
$902$	19.4262	−	12.4845i	0.646823	−	0.415688i
$903$	−12.7670	+	14.7339i	−0.424858	+	0.490313i
$904$	1.53003	−	10.6416i	0.0508880	−	0.353934i
$905$	−2.61151	+	0.766808i	−0.0868095	+	0.0254896i
$906$	8.00487	+	5.14442i	0.265944	+	0.170912i
$907$	4.32726	+	30.0968i	0.143684	+	0.999347i	0.926285	+	0.376823i	$0.122984\pi$
$907$	4.32726	+	30.0968i	0.143684	+	0.999347i	−0.782601	+	0.622524i	$0.786107\pi$
$908$	−8.27987	−	18.1304i	−0.274777	−	0.601678i
$909$	2.66956	+	5.84551i	0.0885436	+	0.193883i
$910$	−0.417229	−	2.90189i	−0.0138310	−	0.0961968i
$911$	11.2501	+	7.23002i	0.372734	+	0.239541i	0.713574	−	0.700580i	$-0.247075\pi$
$911$	11.2501	+	7.23002i	0.372734	+	0.239541i	−0.340841	+	0.940121i	$0.610712\pi$
$912$	−5.88714	+	1.72862i	−0.194943	+	0.0572403i
$913$	−12.4898	+	86.8688i	−0.413353	+	2.87494i
$914$	2.10997	−	2.43503i	0.0697916	−	0.0805438i
$915$	19.8022	−	12.7261i	0.654640	−	0.420712i
$916$	10.6737	+	12.3181i	0.352668	+	0.407000i
$917$	−34.8984	−	10.2471i	−1.15245	−	0.338389i
$918$	2.61612	−	5.72850i	0.0863447	−	0.189069i
$919$	−28.5942			−0.943237			−0.471618	−	0.881803i	$-0.656330\pi$
$919$	−28.5942			−0.943237			−0.471618	+	0.881803i	$0.656330\pi$
$920$	8.44430	+	11.0141i	0.278400	+	0.363124i
$921$	1.33026			0.0438335
$922$	10.6954	−	23.4196i	0.352234	−	0.771284i
$923$	0.495702	+	0.145551i	0.0163162	+	0.00479088i
$924$	9.88897	+	11.4125i	0.325323	+	0.375443i
$925$	13.7080	−	8.80962i	0.450717	−	0.289658i
$926$	12.1589	−	14.0321i	0.399566	−	0.461124i
$927$	1.74830	−	12.1597i	0.0574216	−	0.399376i
$928$	3.27213	−	0.960783i	0.107413	−	0.0315393i
$929$	−44.8992	−	28.8549i	−1.47309	−	0.946700i	−0.997760	−	0.0668947i	$-0.978691\pi$
$929$	−44.8992	−	28.8549i	−1.47309	−	0.946700i	−0.475334	−	0.879805i	$-0.657673\pi$
$930$	3.16374	+	22.0043i	0.103743	+	0.721548i
$931$	1.72449	+	3.77610i	0.0565177	+	0.123757i
$932$	7.74196	+	16.9525i	0.253596	+	0.555299i
$933$	1.23925	+	8.61920i	0.0405714	+	0.282180i
$934$	−5.23419	−	3.36381i	−0.171268	−	0.110067i
$935$	95.3054	−	27.9842i	3.11682	−	0.915181i
$936$	0.0520365	−	0.361922i	0.00170087	−	0.0118298i
$937$	27.4714	−	31.7036i	0.897450	−	1.03571i	−0.101713	−	0.994814i	$-0.532432\pi$
$937$	27.4714	−	31.7036i	0.897450	−	1.03571i	0.999163	−	0.0408993i	$-0.0130223\pi$
$938$	10.3705	−	6.66471i	0.338609	−	0.217610i
$939$	−8.38115	−	9.67236i	−0.273508	−	0.315646i
$940$	18.5595	+	5.44957i	0.605345	+	0.177745i
$941$	8.63855	−	18.9158i	0.281609	−	0.616637i	−0.714982	−	0.699143i	$-0.753565\pi$
$941$	8.63855	−	18.9158i	0.281609	−	0.616637i	0.996591	+	0.0825060i	$0.0262924\pi$
$942$	−23.8636			−0.777518
$943$	−7.31918	−	18.9552i	−0.238345	−	0.617267i
$944$	0.440095			0.0143239
$945$	−3.33080	+	7.29343i	−0.108351	+	0.237255i
$946$	−36.7973	−	10.8046i	−1.19638	−	0.351289i
$947$	−25.7079	−	29.6685i	−0.835395	−	0.964097i	0.164357	−	0.986401i	$-0.447445\pi$
$947$	−25.7079	−	29.6685i	−0.835395	−	0.964097i	−0.999751	+	0.0223042i	$0.992900\pi$
$948$	−3.34369	+	2.14886i	−0.108598	+	0.0697917i
$949$	0.943699	−	1.08909i	0.0306338	−	0.0353532i
$950$	2.94671	−	20.4948i	0.0956040	−	0.664941i
$951$	−12.6457	+	3.71311i	−0.410064	+	0.120406i
$952$	−14.6786	−	9.43338i	−0.475737	−	0.305738i
$953$	−2.93480	−	20.4120i	−0.0950675	−	0.661209i	−0.980511	−	0.196462i	$-0.937055\pi$
$953$	−2.93480	−	20.4120i	−0.0950675	−	0.661209i	0.885444	−	0.464746i	$-0.153854\pi$
$954$	−2.96383	−	6.48988i	−0.0959575	−	0.210118i
$955$	−2.45807	−	5.38242i	−0.0795412	−	0.174171i
$956$	−0.627146	−	4.36190i	−0.0202834	−	0.141074i
$957$	15.6363	+	10.0488i	0.505449	+	0.324833i
$958$	−9.90660	+	2.90884i	−0.320068	+	0.0939803i
$959$	−1.51042	+	10.5052i	−0.0487740	+	0.339231i
$960$	−1.89510	+	2.18706i	−0.0611640	+	0.0705870i
$961$	23.5646	−	15.1440i	0.760147	−	0.488517i
$962$	1.15619	+	1.33432i	0.0372771	+	0.0430201i
$963$	−9.53368	−	2.79934i	−0.307219	−	0.0902075i
$964$	5.44932	−	11.9323i	0.175511	−	0.384315i
$965$	−68.2685			−2.19764
$966$	11.5883	−	6.50170i	0.372848	−	0.209189i
$967$	−12.2331			−0.393391			−0.196696	−	0.980465i	$-0.563021\pi$
$967$	−12.2331			−0.393391			−0.196696	+	0.980465i	$0.563021\pi$
$968$	−7.77054	+	17.0151i	−0.249754	+	0.546886i
$969$	37.0748	+	10.8862i	1.19102	+	0.349714i
$970$	−8.20880	−	9.47346i	−0.263569	−	0.304174i
$971$	−12.2126	+	7.84857i	−0.391922	+	0.251873i	−0.721729	−	0.692175i	$-0.756652\pi$
$971$	−12.2126	+	7.84857i	−0.391922	+	0.251873i	0.329808	+	0.944048i	$0.393016\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	6.82148	−	47.4445i	0.218687	−	1.52100i
$974$	24.1012	−	7.07676i	0.772253	−	0.226754i
$975$	1.03803	+	0.667102i	0.0332436	+	0.0213644i
$976$	−1.15759	−	8.05120i	−0.0370535	−	0.257713i
$977$	1.95709	+	4.28543i	0.0626129	+	0.137103i	0.938352	−	0.345682i	$-0.112352\pi$
$977$	1.95709	+	4.28543i	0.0626129	+	0.137103i	−0.875739	+	0.482785i	$0.839625\pi$
$978$	−3.39382	−	7.43143i	−0.108522	−	0.237631i
$979$	−10.6735	−	74.2361i	−0.341128	−	2.37260i
$980$	1.64712	+	1.05854i	0.0526152	+	0.0338138i
$981$	9.98496	−	2.93185i	0.318795	−	0.0936067i
$982$	0.218123	−	1.51708i	0.00696059	−	0.0484120i
$983$	−19.0233	+	21.9541i	−0.606750	+	0.700227i	−0.973135	−	0.230236i	$-0.926050\pi$
$983$	−19.0233	+	21.9541i	−0.606750	+	0.700227i	0.366384	+	0.930464i	$0.380595\pi$
$984$	3.56427	−	2.29062i	0.113625	−	0.0730222i
$985$	6.39090	+	7.37550i	0.203631	+	0.235003i
$986$	−20.6065	−	6.05063i	−0.656246	−	0.192691i
$987$	7.69322	−	16.8458i	0.244878	−	0.536208i
$988$	2.24347			0.0713743
$989$	−15.8312	+	29.8019i	−0.503401	+	0.947644i
$990$	−15.7725			−0.501283
$991$	−7.58329	+	16.6051i	−0.240891	+	0.527478i	−0.991004	−	0.133832i	$-0.957272\pi$
$991$	−7.58329	+	16.6051i	−0.240891	+	0.527478i	0.750113	+	0.661310i	$0.229999\pi$
$992$	7.37071	+	2.16423i	0.234020	+	0.0687145i
$993$	20.7405	+	23.9359i	0.658181	+	0.759582i
$994$	−3.29330	+	2.11648i	−0.104457	+	0.0671305i
$995$	−41.0766	+	47.4049i	−1.30222	+	1.50284i
$996$	−2.29160	+	15.9384i	−0.0726121	+	0.505028i
$997$	−18.5836	+	5.45665i	−0.588549	+	0.172814i	−0.562430	−	0.826845i	$-0.690133\pi$
$997$	−18.5836	+	5.45665i	−0.588549	+	0.172814i	−0.0261198	+	0.999659i	$0.508315\pi$
$998$	19.7123	+	12.6684i	0.623983	+	0.401010i
$999$	−0.687184	−	4.77947i	−0.0217415	−	0.151216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.c.121.1	yes	10
3.2	odd	2		414.2.i.b.397.1		10
23.2	even	11		3174.2.a.z.1.3		5
23.4	even	11	inner	138.2.e.c.73.1	✓	10
23.21	odd	22		3174.2.a.y.1.3		5
69.2	odd	22		9522.2.a.bv.1.3		5
69.44	even	22		9522.2.a.ca.1.3		5
69.50	odd	22		414.2.i.b.73.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.73.1	✓	10	23.4	even	11	inner
138.2.e.c.121.1	yes	10	1.1	even	1	trivial
414.2.i.b.73.1		10	69.50	odd	22
414.2.i.b.397.1		10	3.2	odd	2
3174.2.a.y.1.3		5	23.21	odd	22
3174.2.a.z.1.3		5	23.2	even	11
9522.2.a.bv.1.3		5	69.2	odd	22
9522.2.a.ca.1.3		5	69.44	even	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.43450 - 1.56456i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.394306 - 2.74246i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.43450 - 1.56456i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.394306 - 2.74246i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.411844 + 2.86444i) q^{10} +(2.26413 + 4.95774i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.0520365 - 0.361922i) q^{13} +(2.33083 + 1.49793i) q^{14} +(-2.77667 + 0.815304i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.12405 - 4.75941i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-4.01801 - 4.63704i) q^{19} +(-2.77667 - 0.815304i) q^{20} +(-1.15098 + 2.52028i) q^{21} -5.45027 q^{22} +(-0.965501 + 4.69764i) q^{23} -1.00000 q^{24} +(1.40187 - 3.06967i) q^{25} +(0.350833 + 0.103014i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.33083 + 1.49793i) q^{28} +(-2.23325 + 2.57731i) q^{29} +(0.411844 - 2.86444i) q^{30} +(-7.37071 + 2.16423i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.775655 - 5.39480i) q^{33} +(2.61612 + 5.72850i) q^{34} +(-3.33080 - 7.29343i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(4.06209 + 2.61055i) q^{37} +(5.88714 - 1.72862i) q^{38} +(-0.0520365 + 0.361922i) q^{39} +(1.89510 - 2.18706i) q^{40} +(-3.56427 + 2.29062i) q^{41} +(-1.81440 - 2.09393i) q^{42} +(6.75145 + 1.98241i) q^{43} +(2.26413 - 4.95774i) q^{44} +2.89389 q^{45} +(-3.87204 - 2.82972i) q^{46} -6.68409 q^{47} +(0.415415 - 0.909632i) q^{48} +(-0.649167 - 0.190613i) q^{49} +(2.20991 + 2.55037i) q^{50} +(-5.29788 + 3.40474i) q^{51} +(-0.239446 + 0.276335i) q^{52} +(-1.01536 + 7.06200i) q^{53} +(0.959493 - 0.281733i) q^{54} +(13.2687 + 8.52726i) q^{55} +(-0.394306 - 2.74246i) q^{56} +(2.54885 + 5.58121i) q^{57} +(-1.41668 - 3.10209i) q^{58} +(-0.0626320 - 0.435615i) q^{59} +(2.43450 + 1.56456i) q^{60} +(-7.80450 + 2.29161i) q^{61} +(1.09325 - 7.60369i) q^{62} +(1.81440 - 2.09393i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.692931 - 0.799685i) q^{65} +(5.22950 + 1.53552i) q^{66} +(1.84829 - 4.04720i) q^{67} -6.29760 q^{68} +(2.24987 - 4.23534i) q^{69} +8.01801 q^{70} +(-0.586952 + 1.28525i) q^{71} +(0.959493 + 0.281733i) q^{72} +(2.58092 + 2.97855i) q^{73} +(-4.06209 + 2.61055i) q^{74} +(-2.20991 + 2.55037i) q^{75} +(-0.873198 + 6.07322i) q^{76} +(14.4892 - 4.25441i) q^{77} +(-0.307599 - 0.197682i) q^{78} +(0.565652 + 3.93420i) q^{79} +(1.20217 + 2.63238i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.602967 - 4.19373i) q^{82} +(13.5461 + 8.70557i) q^{83} +(2.65843 - 0.780586i) q^{84} +(2.59363 - 18.0391i) q^{85} +(-4.60791 + 5.31782i) q^{86} +(2.86890 - 1.84373i) q^{87} +(3.56917 + 4.11904i) q^{88} +(-13.2033 - 3.87683i) q^{89} +(-1.20217 + 2.63238i) q^{90} -1.01308 q^{91} +(4.18251 - 2.34662i) q^{92} +7.68188 q^{93} +(2.77667 - 6.08006i) q^{94} +(-17.0368 - 5.00244i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-3.64397 + 2.34184i) q^{97} +(0.443061 - 0.511320i) q^{98} +(-0.775655 + 5.39480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Introduction

L-functions

Modular forms

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