LMFDB - Embedded newform 74.2.f.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			53.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	74.53
Dual form			74.2.f.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0209445 + 0.118782i) q^{5} -0.347296 q^{6} +(0.233956 - 1.32683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0209445 + 0.118782i) q^{5} -0.347296 q^{6} +(0.233956 - 1.32683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(-0.0603074 + 0.104455i) q^{10} +(-2.26604 - 3.92490i) q^{11} +(-0.326352 - 0.118782i) q^{12} +(-0.592396 - 0.497079i) q^{13} +(0.673648 - 1.16679i) q^{14} +(-0.00727396 - 0.0412527i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.29813 + 1.92836i) q^{17} +(-2.70574 + 0.984808i) q^{18} +(1.91875 - 0.698367i) q^{19} +(-0.0923963 + 0.0775297i) q^{20} +(0.0812519 + 0.460802i) q^{21} +(-0.786989 - 4.46324i) q^{22} +(-0.0282185 + 0.0488759i) q^{23} +(-0.266044 - 0.223238i) q^{24} +(4.68479 + 1.70513i) q^{25} +(-0.386659 - 0.669713i) q^{26} +(1.02094 - 1.76833i) q^{27} +(1.03209 - 0.866025i) q^{28} +(2.89053 + 5.00654i) q^{29} +(0.00727396 - 0.0412527i) q^{30} -3.34730 q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.20574 + 1.01173i) q^{33} +(-2.81908 + 1.02606i) q^{34} +(0.152704 + 0.0555796i) q^{35} -2.87939 q^{36} +(5.60607 + 2.36051i) q^{37} +2.04189 q^{38} +(0.252374 + 0.0918566i) q^{39} +(-0.113341 + 0.0412527i) q^{40} +(-5.47565 - 4.59462i) q^{41} +(-0.0812519 + 0.460802i) q^{42} +9.31315 q^{43} +(0.786989 - 4.46324i) q^{44} +(-0.173648 - 0.300767i) q^{45} +(-0.0432332 + 0.0362770i) q^{46} +(-4.25877 + 7.37641i) q^{47} +(-0.173648 - 0.300767i) q^{48} +(4.87211 + 1.77330i) q^{49} +(3.81908 + 3.20459i) q^{50} +(0.520945 - 0.902302i) q^{51} +(-0.134285 - 0.761570i) q^{52} +(0.482926 + 2.73881i) q^{53} +(1.56418 - 1.31250i) q^{54} +(0.513671 - 0.186961i) q^{55} +(1.26604 - 0.460802i) q^{56} +(-0.543233 + 0.455827i) q^{57} +(1.00387 + 5.69323i) q^{58} +(-2.25624 - 12.7958i) q^{59} +(0.0209445 - 0.0362770i) q^{60} +(-8.82295 - 7.40333i) q^{61} +(-3.14543 - 1.14484i) q^{62} +(1.93969 + 3.35965i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0714517 - 0.0599551i) q^{65} +(0.786989 + 1.36310i) q^{66} +(0.889185 - 5.04282i) q^{67} -3.00000 q^{68} +(0.00340357 - 0.0193026i) q^{69} +(0.124485 + 0.104455i) q^{70} +(-12.6236 + 4.59462i) q^{71} +(-2.70574 - 0.984808i) q^{72} -8.71688 q^{73} +(4.46064 + 4.13554i) q^{74} -1.73143 q^{75} +(1.91875 + 0.698367i) q^{76} +(-5.73783 + 2.08840i) q^{77} +(0.205737 + 0.172634i) q^{78} +(0.720285 - 4.08494i) q^{79} -0.120615 q^{80} +(1.37686 - 7.80856i) q^{81} +(-3.57398 - 6.19031i) q^{82} +(-4.53596 + 3.80612i) q^{83} +(-0.233956 + 0.405223i) q^{84} +(-0.180922 - 0.313366i) q^{85} +(8.75150 + 3.18528i) q^{86} +(-1.53802 - 1.29055i) q^{87} +(2.26604 - 3.92490i) q^{88} +(1.32295 + 7.50281i) q^{89} +(-0.0603074 - 0.342020i) q^{90} +(-0.798133 + 0.669713i) q^{91} +(-0.0530334 + 0.0193026i) q^{92} +(1.09240 - 0.397600i) q^{93} +(-6.52481 + 5.47497i) q^{94} +(0.0427664 + 0.242540i) q^{95} +(-0.0603074 - 0.342020i) q^{96} +(5.12061 - 8.86916i) q^{97} +(3.97178 + 3.33272i) q^{98} +(12.2626 + 4.46324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{10} - 9 q^{11} - 3 q^{12} + 3 q^{14} - 18 q^{15} - 6 q^{18} + 9 q^{19} + 3 q^{20} + 3 q^{21} + 3 q^{22} - 15 q^{23} + 3 q^{24} + 21 q^{25} - 9 q^{26} + 3 q^{27} - 3 q^{28} + 18 q^{30} - 18 q^{31} - 3 q^{33} + 3 q^{35} - 6 q^{36} + 9 q^{37} + 6 q^{38} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 3 q^{44} + 15 q^{46} - 3 q^{47} + 6 q^{50} + 9 q^{52} - 18 q^{53} - 9 q^{54} - 18 q^{55} + 3 q^{56} + 12 q^{57} - 18 q^{58} - 6 q^{59} - 3 q^{60} - 12 q^{61} - 3 q^{62} + 6 q^{63} - 3 q^{64} - 3 q^{66} - 3 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{70} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 18 q^{74} - 30 q^{75} + 9 q^{76} - 15 q^{77} - 9 q^{78} + 30 q^{79} - 12 q^{80} + 12 q^{81} - 6 q^{82} + 6 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{88} - 33 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 3 q^{93} - 12 q^{94} + 51 q^{95} - 6 q^{96} + 42 q^{97} + 9 q^{98} + 27 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^10 - 9 * q^11 - 3 * q^12 + 3 * q^14 - 18 * q^15 - 6 * q^18 + 9 * q^19 + 3 * q^20 + 3 * q^21 + 3 * q^22 - 15 * q^23 + 3 * q^24 + 21 * q^25 - 9 * q^26 + 3 * q^27 - 3 * q^28 + 18 * q^30 - 18 * q^31 - 3 * q^33 + 3 * q^35 - 6 * q^36 + 9 * q^37 + 6 * q^38 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 3 * q^44 + 15 * q^46 - 3 * q^47 + 6 * q^50 + 9 * q^52 - 18 * q^53 - 9 * q^54 - 18 * q^55 + 3 * q^56 + 12 * q^57 - 18 * q^58 - 6 * q^59 - 3 * q^60 - 12 * q^61 - 3 * q^62 + 6 * q^63 - 3 * q^64 - 3 * q^66 - 3 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^70 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 18 * q^74 - 30 * q^75 + 9 * q^76 - 15 * q^77 - 9 * q^78 + 30 * q^79 - 12 * q^80 + 12 * q^81 - 6 * q^82 + 6 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^88 - 33 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 3 * q^93 - 12 * q^94 + 51 * q^95 - 6 * q^96 + 42 * q^97 + 9 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	−0.434507	−	0.900669i	$-0.643077\pi$
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	0.246087	+	0.969248i	$0.420855\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.0209445	+	0.118782i	−0.00936668	+	0.0531211i	−0.989133	−	0.147024i	$-0.953030\pi$
$5$	−0.0209445	+	0.118782i	−0.00936668	+	0.0531211i	0.979766	+	0.200146i	$0.0641415\pi$
$6$	−0.347296			−0.141783
$7$	0.233956	−	1.32683i	0.0884269	−	0.501494i	−0.908137	−	0.418672i	$-0.862496\pi$
$7$	0.233956	−	1.32683i	0.0884269	−	0.501494i	0.996564	−	0.0828217i	$-0.0263932\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.20574	+	1.85083i	−0.735246	+	0.616944i
$10$	−0.0603074	+	0.104455i	−0.0190709	+	0.0330317i
$11$	−2.26604	−	3.92490i	−0.683238	−	1.18340i	−0.973987	−	0.226604i	$-0.927238\pi$
$11$	−2.26604	−	3.92490i	−0.683238	−	1.18340i	0.290749	−	0.956799i	$-0.406096\pi$
$12$	−0.326352	−	0.118782i	−0.0942097	−	0.0342895i
$13$	−0.592396	−	0.497079i	−0.164301	−	0.137865i	0.556930	−	0.830559i	$-0.311979\pi$
$13$	−0.592396	−	0.497079i	−0.164301	−	0.137865i	−0.721231	+	0.692694i	$0.756424\pi$
$14$	0.673648	−	1.16679i	0.180040	−	0.311839i
$15$	−0.00727396	−	0.0412527i	−0.00187813	−	0.0106514i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.29813	+	1.92836i	−0.557379	+	0.467697i	−0.877431	−	0.479703i	$-0.840744\pi$
$17$	−2.29813	+	1.92836i	−0.557379	+	0.467697i	0.320051	+	0.947400i	$0.396300\pi$
$18$	−2.70574	+	0.984808i	−0.637748	+	0.232121i
$19$	1.91875	−	0.698367i	0.440191	−	0.160216i	−0.112411	−	0.993662i	$-0.535857\pi$
$19$	1.91875	−	0.698367i	0.440191	−	0.160216i	0.552602	+	0.833445i	$0.313635\pi$
$20$	−0.0923963	+	0.0775297i	−0.0206604	+	0.0173362i
$21$	0.0812519	+	0.460802i	0.0177306	+	0.100555i
$22$	−0.786989	−	4.46324i	−0.167787	−	0.951565i
$23$	−0.0282185	+	0.0488759i	−0.00588396	+	0.0101913i	−0.868952	−	0.494896i	$-0.835206\pi$
$23$	−0.0282185	+	0.0488759i	−0.00588396	+	0.0101913i	0.863068	+	0.505087i	$0.168540\pi$
$24$	−0.266044	−	0.223238i	−0.0543061	−	0.0455682i
$25$	4.68479	+	1.70513i	0.936959	+	0.341025i
$26$	−0.386659	−	0.669713i	−0.0758301	−	0.131342i
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$	1.03209	−	0.866025i	0.195046	−	0.163663i
$29$	2.89053	+	5.00654i	0.536758	+	0.929692i	0.999076	+	0.0429778i	$0.0136845\pi$
$29$	2.89053	+	5.00654i	0.536758	+	0.929692i	−0.462318	+	0.886714i	$0.652982\pi$
$30$	0.00727396	−	0.0412527i	0.00132804	−	0.00753167i
$31$	−3.34730			−0.601192			−0.300596	−	0.953752i	$-0.597186\pi$
$31$	−3.34730			−0.601192			−0.300596	+	0.953752i	$0.597186\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	1.20574	+	1.01173i	0.209892	+	0.176120i
$34$	−2.81908	+	1.02606i	−0.483468	+	0.175968i
$35$	0.152704	+	0.0555796i	0.0258116	+	0.00939466i
$36$	−2.87939			−0.479898
$37$	5.60607	+	2.36051i	0.921632	+	0.388066i
$37$	5.60607	+	2.36051i	0.921632	+	0.388066i
$38$	2.04189			0.331238
$39$	0.252374	+	0.0918566i	0.0404122	+	0.0147088i
$40$	−0.113341	+	0.0412527i	−0.0179208	+	0.00652262i
$41$	−5.47565	−	4.59462i	−0.855153	−	0.717559i	0.105765	−	0.994391i	$-0.466271\pi$
$41$	−5.47565	−	4.59462i	−0.855153	−	0.717559i	−0.960918	+	0.276832i	$0.910715\pi$
$42$	−0.0812519	+	0.460802i	−0.0125374	+	0.0711034i
$43$	9.31315			1.42024			0.710121	−	0.704080i	$-0.248640\pi$
$43$	9.31315			1.42024			0.710121	+	0.704080i	$0.248640\pi$
$44$	0.786989	−	4.46324i	0.118643	−	0.672858i
$45$	−0.173648	−	0.300767i	−0.0258859	−	0.0448358i
$46$	−0.0432332	+	0.0362770i	−0.00637439	+	0.00534875i
$47$	−4.25877	+	7.37641i	−0.621206	+	1.07596i	0.368056	+	0.929804i	$0.380023\pi$
$47$	−4.25877	+	7.37641i	−0.621206	+	1.07596i	−0.989262	+	0.146156i	$0.953310\pi$
$48$	−0.173648	−	0.300767i	−0.0250640	−	0.0434120i
$49$	4.87211	+	1.77330i	0.696016	+	0.253329i
$50$	3.81908	+	3.20459i	0.540099	+	0.453197i
$51$	0.520945	−	0.902302i	0.0729468	−	0.126348i
$52$	−0.134285	−	0.761570i	−0.0186220	−	0.105611i
$53$	0.482926	+	2.73881i	0.0663350	+	0.376204i	0.999844	+	0.0176510i	$0.00561877\pi$
$53$	0.482926	+	2.73881i	0.0663350	+	0.376204i	−0.933509	+	0.358553i	$0.883270\pi$
$54$	1.56418	−	1.31250i	0.212858	−	0.178609i
$55$	0.513671	−	0.186961i	0.0692633	−	0.0252098i
$56$	1.26604	−	0.460802i	0.169182	−	0.0615773i
$57$	−0.543233	+	0.455827i	−0.0719530	+	0.0603757i
$58$	1.00387	+	5.69323i	0.131815	+	0.747558i
$59$	−2.25624	−	12.7958i	−0.293738	−	1.66587i	−0.672288	−	0.740290i	$-0.734688\pi$
$59$	−2.25624	−	12.7958i	−0.293738	−	1.66587i	0.378550	−	0.925581i	$-0.376423\pi$
$60$	0.0209445	−	0.0362770i	0.00270393	−	0.00468334i
$61$	−8.82295	−	7.40333i	−1.12966	−	0.947900i	−0.130611	−	0.991434i	$-0.541694\pi$
$61$	−8.82295	−	7.40333i	−1.12966	−	0.947900i	−0.999052	+	0.0435341i	$0.986138\pi$
$62$	−3.14543	−	1.14484i	−0.399470	−	0.145395i
$63$	1.93969	+	3.35965i	0.244378	+	0.423276i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0714517	−	0.0599551i	0.00886250	−	0.00743652i
$66$	0.786989	+	1.36310i	0.0968716	+	0.167787i
$67$	0.889185	−	5.04282i	0.108631	−	0.616079i	−0.881076	−	0.472974i	$-0.843180\pi$
$67$	0.889185	−	5.04282i	0.108631	−	0.616079i	0.989708	−	0.143104i	$-0.0457085\pi$
$68$	−3.00000			−0.363803
$69$	0.00340357	−	0.0193026i	0.000409741	−	0.00232376i
$70$	0.124485	+	0.104455i	0.0148788	+	0.0124848i
$71$	−12.6236	+	4.59462i	−1.49815	+	0.545281i	−0.955580	−	0.294732i	$-0.904770\pi$
$71$	−12.6236	+	4.59462i	−1.49815	+	0.545281i	−0.542567	+	0.840013i	$0.682547\pi$
$72$	−2.70574	−	0.984808i	−0.318874	−	0.116061i
$73$	−8.71688			−1.02023			−0.510117	−	0.860105i	$-0.670398\pi$
$73$	−8.71688			−1.02023			−0.510117	+	0.860105i	$0.670398\pi$
$74$	4.46064	+	4.13554i	0.518539	+	0.480747i
$75$	−1.73143			−0.199928
$76$	1.91875	+	0.698367i	0.220096	+	0.0801082i
$77$	−5.73783	+	2.08840i	−0.653886	+	0.237995i
$78$	0.205737	+	0.172634i	0.0232951	+	0.0195469i
$79$	0.720285	−	4.08494i	0.0810384	−	0.459592i	−0.917103	−	0.398650i	$-0.869479\pi$
$79$	0.720285	−	4.08494i	0.0810384	−	0.459592i	0.998141	−	0.0609412i	$-0.0194102\pi$
$80$	−0.120615			−0.0134851
$81$	1.37686	−	7.80856i	0.152984	−	0.867617i
$82$	−3.57398	−	6.19031i	−0.394680	−	0.683606i
$83$	−4.53596	+	3.80612i	−0.497886	+	0.417776i	−0.856843	−	0.515578i	$-0.827577\pi$
$83$	−4.53596	+	3.80612i	−0.497886	+	0.417776i	0.358956	+	0.933354i	$0.383133\pi$
$84$	−0.233956	+	0.405223i	−0.0255266	+	0.0442134i
$85$	−0.180922	−	0.313366i	−0.0196238	−	0.0339894i
$86$	8.75150	+	3.18528i	0.943698	+	0.343478i
$87$	−1.53802	−	1.29055i	−0.164893	−	0.138362i
$88$	2.26604	−	3.92490i	0.241561	−	0.418396i
$89$	1.32295	+	7.50281i	0.140232	+	0.795297i	0.971072	+	0.238785i	$0.0767492\pi$
$89$	1.32295	+	7.50281i	0.140232	+	0.795297i	−0.830840	+	0.556511i	$0.812140\pi$
$90$	−0.0603074	−	0.342020i	−0.00635696	−	0.0360521i
$91$	−0.798133	+	0.669713i	−0.0836671	+	0.0702050i
$92$	−0.0530334	+	0.0193026i	−0.00552912	+	0.00201243i
$93$	1.09240	−	0.397600i	0.113276	−	0.0412292i
$94$	−6.52481	+	5.47497i	−0.672983	+	0.564700i
$95$	0.0427664	+	0.242540i	0.00438774	+	0.0248841i
$96$	−0.0603074	−	0.342020i	−0.00615510	−	0.0349073i
$97$	5.12061	−	8.86916i	0.519920	−	0.900527i	−0.479812	−	0.877371i	$-0.659295\pi$
$97$	5.12061	−	8.86916i	0.519920	−	0.900527i	0.999732	−	0.0231560i	$-0.00737146\pi$
$98$	3.97178	+	3.33272i	0.401211	+	0.336656i
$99$	12.2626	+	4.46324i	1.23244	+	0.448572i
$100$	2.49273	+	4.31753i	0.249273	+	0.431753i
$101$	8.05690	−	13.9550i	0.801692	−	1.38857i	−0.116810	−	0.993154i	$-0.537267\pi$
$101$	8.05690	−	13.9550i	0.801692	−	1.38857i	0.918502	−	0.395417i	$-0.129400\pi$
$102$	0.798133	−	0.669713i	0.0790270	−	0.0663115i
$103$	9.81567	+	17.0012i	0.967167	+	1.67518i	0.703676	+	0.710521i	$0.251541\pi$
$103$	9.81567	+	17.0012i	0.967167	+	1.67518i	0.263491	+	0.964662i	$0.415126\pi$
$104$	0.134285	−	0.761570i	0.0131678	−	0.0746781i
$105$	−0.0564370			−0.00550769
$106$	−0.482926	+	2.73881i	−0.0469059	+	0.266017i
$107$	−0.488856	−	0.410199i	−0.0472595	−	0.0396554i	0.618852	−	0.785508i	$-0.287598\pi$
$107$	−0.488856	−	0.410199i	−0.0472595	−	0.0396554i	−0.666111	+	0.745852i	$0.732043\pi$
$108$	1.91875	−	0.698367i	0.184632	−	0.0672004i
$109$	−6.81908	−	2.48194i	−0.653149	−	0.237727i	−0.00587340	−	0.999983i	$-0.501870\pi$
$109$	−6.81908	−	2.48194i	−0.653149	−	0.237727i	−0.647276	+	0.762256i	$0.724092\pi$
$110$	0.546637			0.0521198
$111$	−2.10994	−	0.104455i	−0.200266	−	0.00991447i
$112$	1.34730			0.127308
$113$	12.9893	+	4.72773i	1.22193	+	0.444747i	0.870827	−	0.491589i	$-0.163584\pi$
$113$	12.9893	+	4.72773i	1.22193	+	0.444747i	0.351105	+	0.936336i	$0.385806\pi$
$114$	−0.666374	+	0.242540i	−0.0624117	+	0.0227160i
$115$	−0.00521457	−	0.00437554i	−0.000486261	−	0.000408021i
$116$	−1.00387	+	5.69323i	−0.0932070	+	0.528603i
$117$	2.22668			0.205857
$118$	2.25624	−	12.7958i	0.207704	−	1.17795i
$119$	2.02094	+	3.50038i	0.185260	+	0.320879i
$120$	0.0320889	−	0.0269258i	0.00292930	−	0.00245798i
$121$	−4.76991	+	8.26173i	−0.433629	+	0.751067i
$122$	−5.75877	−	9.97448i	−0.521375	−	0.903047i
$123$	2.33275	+	0.849051i	0.210337	+	0.0765564i
$124$	−2.56418	−	2.15160i	−0.230270	−	0.193219i
$125$	−0.602196	+	1.04303i	−0.0538621	+	0.0932919i
$126$	0.673648	+	3.82045i	0.0600133	+	0.340353i
$127$	2.10354	+	11.9298i	0.186659	+	1.05860i	0.923805	+	0.382863i	$0.125062\pi$
$127$	2.10354	+	11.9298i	0.186659	+	1.05860i	−0.737146	+	0.675733i	$0.763827\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−3.03936	+	1.10624i	−0.267601	+	0.0973988i
$130$	0.0876485	−	0.0319015i	0.00768728	−	0.00279794i
$131$	16.5817	−	13.9137i	1.44875	−	1.21565i	0.515267	−	0.857030i	$-0.327693\pi$
$131$	16.5817	−	13.9137i	1.44875	−	1.21565i	0.933485	−	0.358617i	$-0.116752\pi$
$132$	0.273318	+	1.55007i	0.0237893	+	0.134916i
$133$	−0.477711	−	2.70924i	−0.0414228	−	0.234921i
$134$	2.56031	−	4.43458i	0.221177	−	0.383090i
$135$	0.188663	+	0.158307i	0.0162375	+	0.0136249i
$136$	−2.81908	−	1.02606i	−0.241734	−	0.0879840i
$137$	−4.31908	−	7.48086i	−0.369004	−	0.639133i	0.620406	−	0.784281i	$-0.286968\pi$
$137$	−4.31908	−	7.48086i	−0.369004	−	0.639133i	−0.989410	+	0.145147i	$0.953634\pi$
$138$	0.00980018	−	0.0169744i	0.000834247	−	0.00144496i
$139$	−10.2686	+	8.61635i	−0.870969	+	0.730830i	−0.964302	−	0.264805i	$-0.914692\pi$
$139$	−10.2686	+	8.61635i	−0.870969	+	0.730830i	0.0933331	+	0.995635i	$0.470248\pi$
$140$	0.0812519	+	0.140732i	0.00686704	+	0.0118941i
$141$	0.513671	−	2.91317i	0.0432589	−	0.245333i
$142$	−13.4338			−1.12734
$143$	−0.608593	+	3.45150i	−0.0508931	+	0.288629i
$144$	−2.20574	−	1.85083i	−0.183811	−	0.154236i
$145$	−0.655230	+	0.238484i	−0.0544139	+	0.0198050i
$146$	−8.19119	−	2.98135i	−0.677908	−	0.246738i
$147$	−1.80066			−0.148516
$148$	2.77719	+	5.41177i	0.228284	+	0.444845i
$149$	4.39693			0.360210			0.180105	−	0.983647i	$-0.442356\pi$
$149$	4.39693			0.360210			0.180105	+	0.983647i	$0.442356\pi$
$150$	−1.62701	−	0.592184i	−0.132845	−	0.0483516i
$151$	−13.8550	+	5.04282i	−1.12751	+	0.410379i	−0.837387	−	0.546611i	$-0.815918\pi$
$151$	−13.8550	+	5.04282i	−1.12751	+	0.410379i	−0.290120	+	0.956990i	$0.593695\pi$
$152$	1.56418	+	1.31250i	0.126872	+	0.106458i
$153$	1.50000	−	8.50692i	0.121268	−	0.687744i
$154$	−6.10607			−0.492041
$155$	0.0701076	−	0.397600i	0.00563117	−	0.0319360i
$156$	0.134285	+	0.232589i	0.0107514	+	0.0186220i
$157$	−11.9907	+	10.0614i	−0.956959	+	0.802984i	−0.980456	−	0.196740i	$-0.936965\pi$
$157$	−11.9907	+	10.0614i	−0.956959	+	0.802984i	0.0234964	+	0.999724i	$0.492520\pi$
$158$	2.07398	−	3.59224i	0.164997	−	0.285783i
$159$	−0.482926	−	0.836452i	−0.0382985	−	0.0663350i
$160$	−0.113341	−	0.0412527i	−0.00896038	−	0.00326131i
$161$	0.0582480	+	0.0488759i	0.00459058	+	0.00385196i
$162$	3.96451	−	6.86673i	0.311481	−	0.539501i
$163$	−0.830222	−	4.70842i	−0.0650280	−	0.368792i	−0.999905	−	0.0138191i	$-0.995601\pi$
$163$	−0.830222	−	4.70842i	−0.0650280	−	0.368792i	0.934876	−	0.354973i	$-0.115510\pi$
$164$	−1.24123	−	7.03936i	−0.0969237	−	0.549682i
$165$	−0.145430	+	0.122030i	−0.0113217	+	0.00950002i
$166$	−5.56418	+	2.02520i	−0.431864	+	0.157186i
$167$	−1.88413	+	0.685768i	−0.145799	+	0.0530663i	−0.413889	−	0.910327i	$-0.635830\pi$
$167$	−1.88413	+	0.685768i	−0.145799	+	0.0530663i	0.268090	+	0.963394i	$0.413608\pi$
$168$	−0.358441	+	0.300767i	−0.0276543	+	0.0232047i
$169$	−2.15358	−	12.2136i	−0.165660	−	0.939505i
$170$	−0.0628336	−	0.356347i	−0.00481912	−	0.0273306i
$171$	−2.93969	+	5.09170i	−0.224804	+	0.389372i
$172$	7.13429	+	5.98638i	0.543984	+	0.456457i
$173$	12.9500	+	4.71340i	0.984567	+	0.358353i	0.783614	−	0.621248i	$-0.213374\pi$
$173$	12.9500	+	4.71340i	0.984567	+	0.358353i	0.200953	+	0.979601i	$0.435596\pi$
$174$	−1.00387	−	1.73875i	−0.0761032	−	0.131815i
$175$	3.35844	−	5.81699i	0.253874	−	0.439723i
$176$	3.47178	−	2.91317i	0.261695	−	0.219588i
$177$	2.25624	+	3.90793i	0.169590	+	0.293738i
$178$	−1.32295	+	7.50281i	−0.0991592	+	0.562360i
$179$	−14.7246			−1.10057			−0.550285	−	0.834977i	$-0.685481\pi$
$179$	−14.7246			−1.10057			−0.550285	+	0.834977i	$0.685481\pi$
$180$	0.0603074	−	0.342020i	0.00449505	−	0.0254927i
$181$	−8.34911	−	7.00573i	−0.620584	−	0.520732i	0.277403	−	0.960754i	$-0.410526\pi$
$181$	−8.34911	−	7.00573i	−0.620584	−	0.520732i	−0.897987	+	0.440022i	$0.854971\pi$
$182$	−0.979055	+	0.356347i	−0.0725724	+	0.0264142i
$183$	3.75877	+	1.36808i	0.277856	+	0.101131i
$184$	−0.0564370			−0.00416059
$185$	−0.397804	+	0.616462i	−0.0292471	+	0.0453232i
$186$	1.16250			0.0852389
$187$	12.7763	+	4.65020i	0.934296	+	0.340056i
$188$	−8.00387	+	2.91317i	−0.583742	+	0.212465i
$189$	−2.10741	−	1.76833i	−0.153292	−	0.128627i
$190$	−0.0427664	+	0.242540i	−0.00310260	+	0.0175957i
$191$	9.05737			0.655368			0.327684	−	0.944787i	$-0.393732\pi$
$191$	9.05737			0.655368			0.327684	+	0.944787i	$0.393732\pi$
$192$	0.0603074	−	0.342020i	0.00435231	−	0.0246832i
$193$	−6.29473	−	10.9028i	−0.453105	−	0.784800i	0.545472	−	0.838129i	$-0.316350\pi$
$193$	−6.29473	−	10.9028i	−0.453105	−	0.784800i	−0.998577	+	0.0533286i	$0.983017\pi$
$194$	7.84524	−	6.58294i	0.563255	−	0.472627i
$195$	−0.0161968	+	0.0280537i	−0.00115988	+	0.00200896i
$196$	2.59240	+	4.49016i	0.185171	+	0.320726i
$197$	11.2169	+	4.08261i	0.799170	+	0.290874i	0.709142	−	0.705065i	$-0.249082\pi$
$197$	11.2169	+	4.08261i	0.799170	+	0.290874i	0.0900273	+	0.995939i	$0.471305\pi$
$198$	9.99660	+	8.38814i	0.710427	+	0.596119i
$199$	−1.14543	+	1.98394i	−0.0811974	+	0.140638i	−0.903765	−	0.428030i	$-0.859208\pi$
$199$	−1.14543	+	1.98394i	−0.0811974	+	0.140638i	0.822567	+	0.568668i	$0.192541\pi$
$200$	0.865715	+	4.90971i	0.0612153	+	0.347169i
$201$	0.308811	+	1.75135i	0.0217818	+	0.123531i
$202$	12.3439	−	10.3578i	0.868513	−	0.728769i
$203$	7.31908	−	2.66393i	0.513699	−	0.186971i
$204$	0.979055	−	0.356347i	0.0685476	−	0.0249493i
$205$	0.660444	−	0.554179i	0.0461274	−	0.0387055i
$206$	3.40895	+	19.3331i	0.237513	+	1.34700i
$207$	−0.0282185	−	0.160035i	−0.00196132	−	0.0111232i
$208$	0.386659	−	0.669713i	0.0268100	−	0.0464363i
$209$	−7.08899	−	5.94837i	−0.490356	−	0.411457i
$210$	−0.0530334	−	0.0193026i	−0.00365965	−	0.00133200i
$211$	−0.477711	−	0.827420i	−0.0328870	−	0.0569620i	0.849113	−	0.528211i	$-0.177137\pi$
$211$	−0.477711	−	0.827420i	−0.0328870	−	0.0569620i	−0.882000	+	0.471249i	$0.843803\pi$
$212$	−1.39053	+	2.40847i	−0.0955020	+	0.165414i
$213$	3.57398	−	2.99892i	0.244885	−	0.205483i
$214$	−0.319078	−	0.552659i	−0.0218117	−	0.0377790i
$215$	−0.195060	+	1.10624i	−0.0133030	+	0.0754448i
$216$	2.04189			0.138933
$217$	−0.783119	+	4.44129i	−0.0531616	+	0.301494i
$218$	−5.55896	−	4.66452i	−0.376500	−	0.315921i
$219$	2.84477	−	1.03541i	0.192232	−	0.0699666i
$220$	0.513671	+	0.186961i	0.0346317	+	0.0126049i
$221$	2.31996			0.156057
$222$	−1.94697	−	0.819797i	−0.130672	−	0.0550212i
$223$	−17.8648			−1.19632			−0.598159	−	0.801377i	$-0.704101\pi$
$223$	−17.8648			−1.19632			−0.598159	+	0.801377i	$0.704101\pi$
$224$	1.26604	+	0.460802i	0.0845912	+	0.0307887i
$225$	−13.4893	+	4.90971i	−0.899288	+	0.327314i
$226$	10.5890	+	8.88522i	0.704369	+	0.591036i
$227$	1.53684	−	8.71583i	0.102003	−	0.578490i	−0.890372	−	0.455235i	$-0.849555\pi$
$227$	1.53684	−	8.71583i	0.102003	−	0.578490i	0.992375	−	0.123256i	$-0.0393335\pi$
$228$	−0.709141			−0.0469640
$229$	−3.02347	+	17.1470i	−0.199797	+	1.13310i	0.705624	+	0.708587i	$0.250667\pi$
$229$	−3.02347	+	17.1470i	−0.199797	+	1.13310i	−0.905420	+	0.424516i	$0.860444\pi$
$230$	−0.00340357	−	0.00589515i	−0.000224425	−	0.000388715i
$231$	1.62449	−	1.36310i	0.106883	−	0.0896857i
$232$	−2.89053	+	5.00654i	−0.189773	+	0.328696i
$233$	2.09627	+	3.63084i	0.137331	+	0.237864i	0.926485	−	0.376330i	$-0.122814\pi$
$233$	2.09627	+	3.63084i	0.137331	+	0.237864i	−0.789155	+	0.614195i	$0.789481\pi$
$234$	2.09240	+	0.761570i	0.136784	+	0.0497854i
$235$	−0.786989	−	0.660362i	−0.0513375	−	0.0430773i
$236$	6.49660	−	11.2524i	0.422892	−	0.732471i
$237$	0.250152	+	1.41868i	0.0162491	+	0.0921535i
$238$	0.701867	+	3.98048i	0.0454953	+	0.258016i
$239$	6.57011	−	5.51297i	0.424985	−	0.356605i	−0.405071	−	0.914285i	$-0.632753\pi$
$239$	6.57011	−	5.51297i	0.424985	−	0.356605i	0.830056	+	0.557681i	$0.188309\pi$
$240$	0.0393628	−	0.0143269i	0.00254086	−	0.000924798i
$241$	19.6532	−	7.15317i	1.26597	−	0.460776i	0.380203	−	0.924903i	$-0.375854\pi$
$241$	19.6532	−	7.15317i	1.26597	−	0.460776i	0.885769	+	0.464127i	$0.153632\pi$
$242$	−7.30793	+	6.13208i	−0.469772	+	0.394185i
$243$	1.54189	+	8.74449i	0.0989122	+	0.560959i
$244$	−2.00000	−	11.3426i	−0.128037	−	0.726133i
$245$	−0.312681	+	0.541580i	−0.0199765	+	0.0346003i
$246$	1.90167	+	1.59569i	0.121246	+	0.101738i
$247$	−1.48380	−	0.540060i	−0.0944121	−	0.0343632i
$248$	−1.67365	−	2.89884i	−0.106277	−	0.184077i
$249$	1.02822	−	1.78093i	0.0651607	−	0.112862i
$250$	−0.922618	+	0.774169i	−0.0583515	+	0.0489627i
$251$	−3.39780	−	5.88517i	−0.214467	−	0.371469i	0.738640	−	0.674100i	$-0.235468\pi$
$251$	−3.39780	−	5.88517i	−0.214467	−	0.371469i	−0.953108	+	0.302631i	$0.902135\pi$
$252$	−0.673648	+	3.82045i	−0.0424358	+	0.240666i
$253$	0.255777			0.0160806
$254$	−2.10354	+	11.9298i	−0.131988	+	0.748540i
$255$	0.0962667	+	0.0807773i	0.00602845	+	0.00505847i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	9.28611	+	3.37987i	0.579252	+	0.210830i	0.614996	−	0.788531i	$-0.289158\pi$
$257$	9.28611	+	3.37987i	0.579252	+	0.210830i	−0.0357438	+	0.999361i	$0.511380\pi$
$258$	−3.23442			−0.201366
$259$	4.44356	−	6.88603i	0.276110	−	0.427877i
$260$	0.0932736			0.00578458
$261$	−15.6420	−	5.69323i	−0.968217	−	0.352402i
$262$	20.3405	−	7.40333i	1.25664	−	0.457379i
$263$	−15.8195	−	13.2742i	−0.975475	−	0.818521i	0.00792564	−	0.999969i	$-0.497477\pi$
$263$	−15.8195	−	13.2742i	−0.975475	−	0.818521i	−0.983401	+	0.181448i	$0.941922\pi$
$264$	−0.273318	+	1.55007i	−0.0168216	+	0.0953999i
$265$	−0.335437			−0.0206057
$266$	0.477711	−	2.70924i	0.0292904	−	0.166114i
$267$	−1.32295	−	2.29141i	−0.0809631	−	0.140232i
$268$	3.92262	−	3.29147i	0.239612	−	0.201058i
$269$	−13.8131	+	23.9251i	−0.842203	+	1.45874i	0.0458262	+	0.998949i	$0.485408\pi$
$269$	−13.8131	+	23.9251i	−0.842203	+	1.45874i	−0.888029	+	0.459788i	$0.847925\pi$
$270$	0.123141	+	0.213286i	0.00749412	+	0.0129802i
$271$	−6.42989	−	2.34029i	−0.390588	−	0.142162i	0.139258	−	0.990256i	$-0.455528\pi$
$271$	−6.42989	−	2.34029i	−0.390588	−	0.142162i	−0.529846	+	0.848094i	$0.677750\pi$
$272$	−2.29813	−	1.92836i	−0.139345	−	0.116924i
$273$	0.180922	−	0.313366i	0.0109499	−	0.0189658i
$274$	−1.50000	−	8.50692i	−0.0906183	−	0.513922i
$275$	−3.92350	−	22.2513i	−0.236596	−	1.34180i
$276$	0.0150147	−	0.0125989i	0.000903782	−	0.000758363i
$277$	22.3957	−	8.15138i	1.34563	−	0.489769i	0.434049	−	0.900889i	$-0.357085\pi$
$277$	22.3957	−	8.15138i	1.34563	−	0.489769i	0.911581	+	0.411120i	$0.134862\pi$
$278$	−12.5963	+	4.58467i	−0.755474	+	0.274970i
$279$	7.38326	−	6.19529i	0.442024	−	0.370902i
$280$	0.0282185	+	0.160035i	0.00168638	+	0.00956392i
$281$	5.51367	+	31.2696i	0.328918	+	1.86539i	0.480575	+	0.876954i	$0.340428\pi$
$281$	5.51367	+	31.2696i	0.328918	+	1.86539i	−0.151657	+	0.988433i	$0.548461\pi$
$282$	1.47906	−	2.56180i	0.0880765	−	0.152553i
$283$	−4.52687	−	3.79850i	−0.269095	−	0.225797i	0.498248	−	0.867035i	$-0.333977\pi$
$283$	−4.52687	−	3.79850i	−0.269095	−	0.225797i	−0.767343	+	0.641237i	$0.778421\pi$
$284$	−12.6236	−	4.59462i	−0.749073	−	0.272640i
$285$	−0.0427664	−	0.0740736i	−0.00253326	−	0.00438774i
$286$	−1.75237	+	3.03520i	−0.103620	+	0.179475i
$287$	−7.37733	+	6.19031i	−0.435470	+	0.365403i
$288$	−1.43969	−	2.49362i	−0.0848347	−	0.146938i
$289$	−1.38919	+	7.87846i	−0.0817168	+	0.463439i
$290$	−0.697281			−0.0409458
$291$	−0.617622	+	3.50271i	−0.0362056	+	0.205332i
$292$	−6.67752	−	5.60310i	−0.390772	−	0.327897i
$293$	1.59240	−	0.579585i	0.0930288	−	0.0338597i	−0.295086	−	0.955471i	$-0.595348\pi$
$293$	1.59240	−	0.579585i	0.0930288	−	0.0338597i	0.388115	+	0.921611i	$0.373126\pi$
$294$	−1.69207	−	0.615862i	−0.0986833	−	0.0359178i
$295$	1.56717			0.0912442
$296$	0.758770	+	6.03525i	0.0441026	+	0.350792i
$297$	−9.25402			−0.536973
$298$	4.13176	+	1.50384i	0.239346	+	0.0871150i
$299$	0.0410117	−	0.0149270i	0.00237177	−	0.000863253i
$300$	−1.32635	−	1.11294i	−0.0765770	−	0.0642557i
$301$	2.17886	−	12.3569i	0.125588	−	0.712242i
$302$	−14.7442			−0.848435
$303$	−0.971782	+	5.51125i	−0.0558274	+	0.316613i
$304$	1.02094	+	1.76833i	0.0585552	+	0.101421i
$305$	1.06418	−	0.892951i	0.0609346	−	0.0511302i
$306$	4.31908	−	7.48086i	0.246905	−	0.427652i
$307$	6.11334	+	10.5886i	0.348907	+	0.604324i	0.986056	−	0.166417i	$-0.0532196\pi$
$307$	6.11334	+	10.5886i	0.348907	+	0.604324i	−0.637149	+	0.770741i	$0.719886\pi$
$308$	−5.73783	−	2.08840i	−0.326943	−	0.118998i
$309$	−5.22281	−	4.38246i	−0.297115	−	0.249309i
$310$	0.201867	−	0.349643i	0.0114653	−	0.0198584i
$311$	−0.212134	−	1.20307i	−0.0120290	−	0.0682198i	0.978202	−	0.207654i	$-0.0665828\pi$
$311$	−0.212134	−	1.20307i	−0.0120290	−	0.0682198i	−0.990231	+	0.139434i	$0.955472\pi$
$312$	0.0466368	+	0.264490i	0.00264029	+	0.0149738i
$313$	−13.3380	+	11.1919i	−0.753906	+	0.632602i	−0.936533	−	0.350580i	$-0.885985\pi$
$313$	−13.3380	+	11.1919i	−0.753906	+	0.632602i	0.182627	+	0.983182i	$0.441540\pi$
$314$	−14.7087	+	5.35354i	−0.830062	+	0.302118i
$315$	−0.439693	+	0.160035i	−0.0247739	+	0.00901695i
$316$	3.17752	−	2.66625i	0.178749	−	0.149989i
$317$	−1.51027	−	8.56515i	−0.0848250	−	0.481067i	−0.997394	−	0.0721443i	$-0.977016\pi$
$317$	−1.51027	−	8.56515i	−0.0848250	−	0.481067i	0.912569	−	0.408922i	$-0.134095\pi$
$318$	−0.167718	−	0.951178i	−0.00940518	−	0.0533394i
$319$	13.1001	−	22.6901i	0.733467	−	1.27040i
$320$	−0.0923963	−	0.0775297i	−0.00516511	−	0.00433404i
$321$	0.208263	+	0.0758016i	0.0116241	+	0.00423083i
$322$	0.0380187	+	0.0658503i	0.00211870	+	0.00366969i
$323$	−3.06283	+	5.30498i	−0.170421	+	0.295177i
$324$	6.07398	−	5.09667i	0.337443	−	0.283148i
$325$	−1.92767	−	3.33882i	−0.106928	−	0.185205i
$326$	0.830222	−	4.70842i	0.0459818	−	0.260775i
$327$	2.52023			0.139369
$328$	1.24123	−	7.03936i	0.0685354	−	0.388684i
$329$	8.79086	+	7.37641i	0.484656	+	0.406674i
$330$	−0.178396	+	0.0649308i	−0.00982037	+	0.00357432i
$331$	7.74510	+	2.81899i	0.425709	+	0.154945i	0.545985	−	0.837795i	$-0.316156\pi$
$331$	7.74510	+	2.81899i	0.425709	+	0.154945i	−0.120276	+	0.992741i	$0.538378\pi$
$332$	−5.92127			−0.324972
$333$	−16.7344	+	5.16923i	−0.917041	+	0.283272i
$334$	−2.00505			−0.109712
$335$	0.580375	+	0.211239i	0.0317092	+	0.0115412i
$336$	−0.439693	+	0.160035i	−0.0239872	+	0.00873063i
$337$	10.7456	+	9.01660i	0.585348	+	0.491166i	0.886699	−	0.462348i	$-0.152993\pi$
$337$	10.7456	+	9.01660i	0.585348	+	0.491166i	−0.301350	+	0.953514i	$0.597437\pi$
$338$	2.15358	−	12.2136i	0.117139	−	0.664330i
$339$	−4.80066			−0.260736
$340$	0.0628336	−	0.356347i	0.00340763	−	0.0193256i
$341$	7.58512	+	13.1378i	0.410757	+	0.711453i
$342$	−4.50387	+	3.77920i	−0.243541	+	0.204356i
$343$	8.20826	−	14.2171i	0.443205	−	0.767653i
$344$	4.65657	+	8.06542i	0.251066	+	0.434858i
$345$	0.00222152		0.000808567i	0.000119603		4.35318e-5i
$346$	10.5569	+	8.85829i	0.567543	+	0.476225i
$347$	−9.92262	+	17.1865i	−0.532674	+	0.922619i	0.466598	+	0.884470i	$0.345479\pi$
$347$	−9.92262	+	17.1865i	−0.532674	+	0.922619i	−0.999272	+	0.0381490i	$0.987854\pi$
$348$	−0.348641	−	1.97724i	−0.0186891	−	0.105991i
$349$	2.98633	+	16.9363i	0.159855	+	0.906580i	0.954212	+	0.299130i	$0.0966964\pi$
$349$	2.98633	+	16.9363i	0.159855	+	0.906580i	−0.794358	+	0.607450i	$0.792192\pi$
$350$	5.14543	−	4.31753i	0.275035	−	0.230782i
$351$	−1.48380	+	0.540060i	−0.0791996	+	0.0288263i
$352$	4.25877	−	1.55007i	0.226993	−	0.0826188i
$353$	12.9272	−	10.8472i	0.688046	−	0.577339i	−0.230299	−	0.973120i	$-0.573971\pi$
$353$	12.9272	−	10.8472i	0.688046	−	0.577339i	0.918345	+	0.395781i	$0.129526\pi$
$354$	0.783585	+	4.44393i	0.0416471	+	0.236192i
$355$	−0.281364	−	1.59569i	−0.0149332	−	0.0846906i
$356$	−3.80928	+	6.59786i	−0.201891	+	0.349686i
$357$	−1.07532	−	0.902302i	−0.0569121	−	0.0477549i
$358$	−13.8366	−	5.03612i	−0.731288	−	0.266167i
$359$	8.05690	+	13.9550i	0.425227	+	0.736515i	0.996442	−	0.0842859i	$-0.0268609\pi$
$359$	8.05690	+	13.9550i	0.425227	+	0.736515i	−0.571214	+	0.820801i	$0.693528\pi$
$360$	0.173648	−	0.300767i	0.00915206	−	0.0158518i
$361$	−11.3610	+	9.53298i	−0.597946	+	0.501736i
$362$	−5.44949	−	9.43880i	−0.286419	−	0.496092i
$363$	0.575322	−	3.26281i	0.0301966	−	0.171253i
$364$	−1.04189			−0.0546098
$365$	0.182571	−	1.03541i	0.00955620	−	0.0541959i
$366$	3.06418	+	2.57115i	0.160167	+	0.134396i
$367$	32.9666	−	11.9989i	1.72084	−	0.626336i	0.722931	−	0.690920i	$-0.242794\pi$
$367$	32.9666	−	11.9989i	1.72084	−	0.626336i	0.997912	+	0.0645839i	$0.0205720\pi$
$368$	−0.0530334	−	0.0193026i	−0.00276456	−	0.00100622i
$369$	20.5817			1.07144
$370$	−0.584655	+	0.443228i	−0.0303948	+	0.0230423i
$371$	3.74691			0.194530
$372$	1.09240	+	0.397600i	0.0566381	+	0.0206146i
$373$	27.9047	−	10.1565i	1.44485	−	0.525882i	0.503701	−	0.863878i	$-0.331971\pi$
$373$	27.9047	−	10.1565i	1.44485	−	0.525882i	0.941148	+	0.337996i	$0.109749\pi$
$374$	10.4153	+	8.73951i	0.538565	+	0.451909i
$375$	0.0726338	−	0.411927i	0.00375079	−	0.0212718i
$376$	−8.51754			−0.439259
$377$	0.776311	−	4.40268i	0.0399821	−	0.226750i
$378$	−1.37551	−	2.38246i	−0.0707488	−	0.122541i
$379$	0.321137	−	0.269466i	0.0164957	−	0.0138415i	−0.634502	−	0.772921i	$-0.718795\pi$
$379$	0.321137	−	0.269466i	0.0164957	−	0.0138415i	0.650998	+	0.759079i	$0.274351\pi$
$380$	−0.123141	+	0.213286i	−0.00631700	+	0.0109414i
$381$	−2.10354	−	3.64344i	−0.107768	−	0.186659i
$382$	8.51114	+	3.09780i	0.435468	+	0.158497i
$383$	−4.92443	−	4.13209i	−0.251627	−	0.211140i	0.508246	−	0.861212i	$-0.330294\pi$
$383$	−4.92443	−	4.13209i	−0.251627	−	0.211140i	−0.759872	+	0.650072i	$0.774739\pi$
$384$	0.173648	−	0.300767i	0.00886145	−	0.0153485i
$385$	−0.127889	−	0.725293i	−0.00651781	−	0.0369644i
$386$	−2.18614	−	12.3982i	−0.111271	−	0.631052i
$387$	−20.5424	+	17.2371i	−1.04423	+	0.876210i
$388$	9.62361	−	3.50271i	0.488565	−	0.177823i
$389$	2.92602	−	1.06498i	0.148355	−	0.0539969i	−0.266775	−	0.963759i	$-0.585958\pi$
$389$	2.92602	−	1.06498i	0.148355	−	0.0539969i	0.415130	+	0.909762i	$0.363736\pi$
$390$	−0.0248149	+	0.0208222i	−0.00125655	+	0.00105437i
$391$	−0.0294005	−	0.166739i	−0.00148685	−	0.00843234i
$392$	0.900330	+	5.10602i	0.0454735	+	0.257893i
$393$	−3.75877	+	6.51038i	−0.189605	+	0.328405i
$394$	9.14409	+	7.67280i	0.460672	+	0.386550i
$395$	0.470133	+	0.171114i	0.0236549	+	0.00860969i
$396$	6.52481	+	11.3013i	0.327884	+	0.567912i
$397$	−9.85369	+	17.0671i	−0.494543	+	0.856573i	−0.999980	−	0.00629016i	$-0.997998\pi$
$397$	−9.85369	+	17.0671i	−0.494543	+	0.856573i	0.505438	+	0.862863i	$0.331331\pi$
$398$	−1.75490	+	1.47254i	−0.0879652	+	0.0738116i
$399$	0.477711	+	0.827420i	0.0239155	+	0.0414228i
$400$	−0.865715	+	4.90971i	−0.0432857	+	0.245486i
$401$	18.9162			0.944631			0.472316	−	0.881430i	$-0.343418\pi$
$401$	18.9162			0.944631			0.472316	+	0.881430i	$0.343418\pi$
$402$	−0.308811	+	1.75135i	−0.0154021	+	0.0873496i
$403$	1.98293	+	1.66387i	0.0987766	+	0.0828834i
$404$	15.1420	−	5.51125i	0.753344	−	0.274195i
$405$	0.898681	+	0.327093i	0.0446558	+	0.0162534i
$406$	7.78880			0.386552
$407$	−3.43882	−	27.3523i	−0.170456	−	1.35580i
$408$	1.04189			0.0515812
$409$	−5.99020	−	2.18025i	−0.296196	−	0.107807i	0.189648	−	0.981852i	$-0.439265\pi$
$409$	−5.99020	−	2.18025i	−0.296196	−	0.107807i	−0.485844	+	0.874046i	$0.661488\pi$
$410$	0.810155	−	0.294872i	0.0400107	−	0.0145627i
$411$	2.29813	+	1.92836i	0.113359	+	0.0951191i
$412$	−3.40895	+	19.3331i	−0.167947	+	0.952474i
$413$	−17.5057			−0.861398
$414$	0.0282185	−	0.160035i	0.00138686	−	0.00786529i
$415$	−0.357097	−	0.618509i	−0.0175292	−	0.0303614i
$416$	0.592396	−	0.497079i	0.0290446	−	0.0243713i
$417$	2.32770	−	4.03169i	0.113988	−	0.197433i
$418$	−4.62701	−	8.01422i	−0.226315	−	0.391988i
$419$	−19.6258	−	7.14322i	−0.958785	−	0.348969i	−0.185227	−	0.982696i	$-0.559302\pi$
$419$	−19.6258	−	7.14322i	−0.958785	−	0.348969i	−0.773557	+	0.633727i	$0.781524\pi$
$420$	−0.0432332	−	0.0362770i	−0.00210957	−	0.00177014i
$421$	2.90420	−	5.03022i	0.141542	−	0.245158i	−0.786535	−	0.617545i	$-0.788127\pi$
$421$	2.90420	−	5.03022i	0.141542	−	0.245158i	0.928077	+	0.372387i	$0.121461\pi$
$422$	−0.165907	−	0.940908i	−0.00807625	−	0.0458027i
$423$	−4.25877	−	24.1527i	−0.207069	−	1.17434i
$424$	−2.13041	+	1.78763i	−0.103462	+	0.0868150i
$425$	−14.0544	+	5.11538i	−0.681737	+	0.248132i
$426$	4.38413	−	1.59569i	0.212412	−	0.0773116i
$427$	−11.8871	+	9.97448i	−0.575258	+	0.482699i
$428$	−0.110815	−	0.628461i	−0.00535642	−	0.0303778i
$429$	−0.211362	−	1.19869i	−0.0102047	−	0.0578735i
$430$	−0.561652	+	0.972809i	−0.0270852	+	0.0469130i
$431$	8.70233	+	7.30212i	0.419177	+	0.351731i	0.827850	−	0.560950i	$-0.189564\pi$
$431$	8.70233	+	7.30212i	0.419177	+	0.351731i	−0.408673	+	0.912681i	$0.634008\pi$
$432$	1.91875	+	0.698367i	0.0923158	+	0.0336002i
$433$	−17.8025	−	30.8348i	−0.855532	−	1.48183i	−0.876150	−	0.482038i	$-0.839897\pi$
$433$	−17.8025	−	30.8348i	−0.855532	−	1.48183i	0.0206183	−	0.999787i	$-0.493437\pi$
$434$	−2.25490	+	3.90560i	−0.108239	+	0.187475i
$435$	0.185508	−	0.155659i	0.00889442	−	0.00746330i
$436$	−3.62836	−	6.28450i	−0.173767	−	0.300973i
$437$	−0.0200109	+	0.113487i	−0.000957250	+	0.00542884i
$438$	3.02734			0.144652
$439$	3.90777	−	22.1620i	0.186507	−	1.05774i	−0.737496	−	0.675352i	$-0.763992\pi$
$439$	3.90777	−	22.1620i	0.186507	−	1.05774i	0.924003	−	0.382385i	$-0.124897\pi$
$440$	0.418748	+	0.351371i	0.0199630	+	0.0167510i
$441$	−14.0287	+	5.10602i	−0.668033	+	0.243144i
$442$	2.18004	+	0.793471i	0.103694	+	0.0377416i
$443$	−26.0942			−1.23977			−0.619887	−	0.784691i	$-0.712821\pi$
$443$	−26.0942			−1.23977			−0.619887	+	0.784691i	$0.712821\pi$
$444$	−1.54916	−	1.43626i	−0.0735200	−	0.0681618i
$445$	−0.918910			−0.0435605
$446$	−16.7875	−	6.11013i	−0.794909	−	0.289323i
$447$	−1.43494	+	0.522277i	−0.0678706	+	0.0247029i
$448$	1.03209	+	0.866025i	0.0487616	+	0.0409159i
$449$	−1.13310	+	6.42615i	−0.0534745	+	0.303269i	−0.999801	−	0.0199431i	$-0.993651\pi$
$449$	−1.13310	+	6.42615i	−0.0534745	+	0.303269i	0.946327	+	0.323212i	$0.104763\pi$
$450$	−14.3550			−0.676703
$451$	−5.62536	+	31.9030i	−0.264888	+	1.50225i
$452$	6.91147	+	11.9710i	0.325088	+	0.563070i
$453$	3.92262	−	3.29147i	0.184301	−	0.154647i
$454$	4.42514	−	7.66458i	0.207682	−	0.359716i
$455$	−0.0628336	−	0.108831i	−0.00294568	−	0.00510208i
$456$	−0.666374	−	0.242540i	−0.0312058	−	0.0113580i
$457$	−25.0835	−	21.0476i	−1.17336	−	0.984564i	−0.173358	−	0.984859i	$-0.555462\pi$
$457$	−25.0835	−	21.0476i	−1.17336	−	0.984564i	−1.00000		0.000294571i	$0.999906\pi$
$458$	−8.70574	+	15.0788i	−0.406792	+	0.704585i
$459$	1.06371	+	6.03260i	0.0496498	+	0.281578i
$460$	−0.00118205	−	0.00670372i	−5.51132e−5	−	0.000312562i
$461$	14.9722	−	12.5632i	0.697327	−	0.585127i	−0.223685	−	0.974662i	$-0.571809\pi$
$461$	14.9722	−	12.5632i	0.697327	−	0.585127i	0.921012	+	0.389535i	$0.127364\pi$
$462$	1.99273	−	0.725293i	0.0927100	−	0.0337437i
$463$	−40.2943	+	14.6659i	−1.87264	+	0.681584i	−0.907358	+	0.420359i	$0.861904\pi$
$463$	−40.2943	+	14.6659i	−1.87264	+	0.681584i	−0.965278	+	0.261224i	$0.915874\pi$
$464$	−4.42855	+	3.71599i	−0.205590	+	0.172511i
$465$	0.0243481	+	0.138085i	0.00112912	+	0.00640354i
$466$	0.728026	+	4.12884i	0.0337251	+	0.191265i
$467$	−10.5444	+	18.2635i	−0.487937	+	0.845132i	−0.999904	−	0.0138732i	$-0.995584\pi$
$467$	−10.5444	+	18.2635i	−0.487937	+	0.845132i	0.511966	+	0.859005i	$0.328917\pi$
$468$	1.70574	+	1.43128i	0.0788477	+	0.0661611i
$469$	−6.48293	−	2.35959i	−0.299354	−	0.108956i
$470$	−0.513671	−	0.889704i	−0.0236939	−	0.0410390i
$471$	2.71806	−	4.70782i	0.125242	−	0.216925i
$472$	9.95336	−	8.35186i	0.458141	−	0.384426i
$473$	−21.1040	−	36.5532i	−0.970363	−	1.68072i
$474$	−0.250152	+	1.41868i	−0.0114899	+	0.0651623i
$475$	10.1797			0.467079
$476$	−0.701867	+	3.98048i	−0.0321700	+	0.182445i
$477$	−6.13429	−	5.14728i	−0.280870	−	0.235678i
$478$	8.05943	−	2.93339i	0.368630	−	0.134170i
$479$	22.7430	+	8.27779i	1.03916	+	0.378222i	0.804560	−	0.593871i	$-0.202401\pi$
$479$	22.7430	+	8.27779i	1.03916	+	0.378222i	0.234596	+	0.972093i	$0.424623\pi$
$480$	0.0418891			0.00191197
$481$	−2.14765	−	4.18502i	−0.0979245	−	0.190820i
$482$	20.9145			0.952628
$483$	−0.0248149	−	0.00903189i	−0.00112912	−	0.000410965i
$484$	−8.96451	+	3.26281i	−0.407478	+	0.148310i
$485$	0.946251	+	0.793999i	0.0429671	+	0.0360536i
$486$	−1.54189	+	8.74449i	−0.0699415	+	0.396658i
$487$	28.9682			1.31268			0.656338	−	0.754467i	$-0.272105\pi$
$487$	28.9682			1.31268			0.656338	+	0.754467i	$0.272105\pi$
$488$	2.00000	−	11.3426i	0.0905357	−	0.513454i
$489$	0.830222	+	1.43799i	0.0375439	+	0.0650280i
$490$	−0.479055	+	0.401975i	−0.0216415	+	0.0181594i
$491$	14.0758	−	24.3800i	0.635231	−	1.10025i	−0.351235	−	0.936287i	$-0.614238\pi$
$491$	14.0758	−	24.3800i	0.635231	−	1.10025i	0.986466	−	0.163966i	$-0.0524286\pi$
$492$	1.24123	+	2.14987i	0.0559589	+	0.0969237i
$493$	−16.2973	−	5.93172i	−0.733991	−	0.267151i
$494$	−1.20961	−	1.01498i	−0.0544228	−	0.0456662i
$495$	−0.786989	+	1.36310i	−0.0353725	+	0.0612670i
$496$	−0.581252	−	3.29644i	−0.0260990	−	0.148015i
$497$	3.14290	+	17.8243i	0.140978	+	0.799529i
$498$	1.57532	−	1.32185i	0.0705919	−	0.0592336i
$499$	4.40255	−	1.60240i	0.197085	−	0.0717332i	−0.241592	−	0.970378i	$-0.577669\pi$
$499$	4.40255	−	1.60240i	0.197085	−	0.0717332i	0.438677	+	0.898645i	$0.355447\pi$
$500$	−1.13176	+	0.411927i	−0.0506138	+	0.0184219i
$501$	0.533433	−	0.447603i	0.0238320	−	0.0199974i
$502$	−1.18004	−	6.69237i	−0.0526680	−	0.298695i
$503$	4.39037	+	24.8990i	0.195757	+	1.11019i	0.911337	+	0.411661i	$0.135051\pi$
$503$	4.39037	+	24.8990i	0.195757	+	1.11019i	−0.715580	+	0.698531i	$0.753838\pi$
$504$	−1.93969	+	3.35965i	−0.0864008	+	0.149651i
$505$	1.48886	+	1.24930i	0.0662532	+	0.0555930i
$506$	0.240352	+	0.0874810i	0.0106850	+	0.00388901i
$507$	2.15358	+	3.73011i	0.0956439	+	0.165660i
$508$	−6.05690	+	10.4909i	−0.268732	+	0.465457i
$509$	16.3739	−	13.7394i	0.725761	−	0.608986i	−0.203211	−	0.979135i	$-0.565138\pi$
$509$	16.3739	−	13.7394i	0.725761	−	0.608986i	0.928972	+	0.370149i	$0.120693\pi$
$510$	0.0628336	+	0.108831i	0.00278232	+	0.00481912i
$511$	−2.03936	+	11.5658i	−0.0902161	+	0.511641i
$512$	−1.00000			−0.0441942
$513$	0.723993	−	4.10597i	0.0319651	−	0.181283i
$514$	7.57011	+	6.35207i	0.333903	+	0.280178i
$515$	−2.22503	+	0.809846i	−0.0980467	+	0.0356861i
$516$	−3.03936	−	1.10624i	−0.133800	−	0.0486994i
$517$	38.6023			1.69773
$518$	6.53074	−	4.95096i	0.286944	−	0.217533i
$519$	−4.78611			−0.210087
$520$	0.0876485	+	0.0319015i	0.00384364	+	0.00139897i
$521$	18.6853	−	6.80088i	0.818616	−	0.297952i	0.101438	−	0.994842i	$-0.467656\pi$
$521$	18.6853	−	6.80088i	0.818616	−	0.297952i	0.717178	+	0.696890i	$0.245433\pi$
$522$	−12.7515	−	10.6998i	−0.558118	−	0.468316i
$523$	−2.94919	+	16.7257i	−0.128959	+	0.731363i	0.849918	+	0.526914i	$0.176651\pi$
$523$	−2.94919	+	16.7257i	−0.128959	+	0.731363i	−0.978877	+	0.204448i	$0.934460\pi$
$524$	21.6459			0.945605
$525$	−0.405078	+	2.29731i	−0.0176790	+	0.100263i
$526$	−10.3255	−	17.8842i	−0.450212	−	0.779790i
$527$	7.69253	−	6.45480i	0.335092	−	0.281176i
$528$	−0.786989	+	1.36310i	−0.0342493	+	0.0593215i
$529$	11.4984	+	19.9158i	0.499931	+	0.865905i
$530$	−0.315207	−	0.114726i	−0.0136917	−	0.00498338i
$531$	28.6596	+	24.0482i	1.24372	+	1.04360i
$532$	1.37551	−	2.38246i	0.0596361	−	0.103293i
$533$	0.959866	+	5.44367i	0.0415764	+	0.235791i
$534$	−0.459455	−	2.60570i	−0.0198826	−	0.112760i
$535$	0.0589632	−	0.0494760i	0.00254920	−	0.00213903i
$536$	4.81180	−	1.75135i	0.207838	−	0.0756469i
$537$	4.80541	−	1.74903i	0.207369	−	0.0754760i
$538$	−21.1630	+	17.7578i	−0.912400	+	0.765595i
$539$	−4.08037	−	23.1410i	−0.175754	−	0.996751i
$540$	0.0427664	+	0.242540i	0.00184037	+	0.0104373i
$541$	−14.6348	+	25.3481i	−0.629197	+	1.08980i	0.358516	+	0.933524i	$0.383283\pi$
$541$	−14.6348	+	25.3481i	−0.629197	+	1.08980i	−0.987713	+	0.156278i	$0.950050\pi$
$542$	−5.24170	−	4.39831i	−0.225150	−	0.188923i
$543$	3.55690	+	1.29461i	0.152641	+	0.0555569i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	0.437633	−	0.758003i	0.0187461	−	0.0324693i
$546$	0.277189	−	0.232589i	0.0118626	−	0.00995389i
$547$	0.666841	+	1.15500i	0.0285121	+	0.0493843i	0.879929	−	0.475105i	$-0.157590\pi$
$547$	0.666841	+	1.15500i	0.0285121	+	0.0493843i	−0.851417	+	0.524489i	$0.824256\pi$
$548$	1.50000	−	8.50692i	0.0640768	−	0.363398i
$549$	33.1634			1.41538
$550$	3.92350	−	22.2513i	0.167298	−	0.948797i
$551$	9.04260	+	7.58765i	0.385228	+	0.323245i
$552$	0.0184183	−	0.00670372i	0.000783935	−	0.000285329i
$553$	−5.25150	−	1.91139i	−0.223316	−	0.0812805i
$554$	23.8331			1.01257
$555$	0.0565991	−	0.248436i	0.00240250	−	0.0105455i
$556$	−13.4047			−0.568485
$557$	−30.3790	−	11.0570i	−1.28720	−	0.468502i	−0.394392	−	0.918942i	$-0.629045\pi$
$557$	−30.3790	−	11.0570i	−1.28720	−	0.468502i	−0.892807	+	0.450440i	$0.851267\pi$
$558$	9.05690	−	3.29644i	0.383409	−	0.139550i
$559$	−5.51707	−	4.62937i	−0.233347	−	0.195802i
$560$	−0.0282185	+	0.160035i	−0.00119245	+	0.00676271i
$561$	−4.72193			−0.199360
$562$	−5.51367	+	31.2696i	−0.232580	+	1.31903i
$563$	8.34389	+	14.4520i	0.351653	+	0.609081i	0.986539	−	0.163525i	$-0.0522863\pi$
$563$	8.34389	+	14.4520i	0.351653	+	0.609081i	−0.634886	+	0.772606i	$0.718953\pi$
$564$	2.26604	−	1.90144i	0.0954177	−	0.0800649i
$565$	−0.833626	+	1.44388i	−0.0350709	+	0.0607446i
$566$	−2.95471	−	5.11770i	−0.124196	−	0.215113i
$567$	−10.0385	−	3.65371i	−0.421577	−	0.153441i
$568$	−10.2909	−	8.63506i	−0.431795	−	0.362319i
$569$	0.213011	−	0.368946i	0.00892989	−	0.0154670i	−0.861526	−	0.507714i	$-0.830491\pi$
$569$	0.213011	−	0.368946i	0.00892989	−	0.0154670i	0.870456	+	0.492247i	$0.163824\pi$
$570$	−0.0148526	−	0.0842334i	−0.000622108	−	0.00352815i
$571$	2.42262	+	13.7394i	0.101383	+	0.574974i	0.992603	+	0.121403i	$0.0387392\pi$
$571$	2.42262	+	13.7394i	0.101383	+	0.574974i	−0.891220	+	0.453571i	$0.850150\pi$
$572$	−2.68479	+	2.25281i	−0.112257	+	0.0941947i
$573$	−2.95589	+	1.07586i	−0.123484	+	0.0449445i
$574$	−9.04963	+	3.29380i	−0.377724	+	0.137480i
$575$	−0.215537	+	0.180857i	−0.00898852	+	0.00754227i
$576$	−0.500000	−	2.83564i	−0.0208333	−	0.118152i
$577$	−1.90373	−	10.7966i	−0.0792535	−	0.449469i	−0.998449	−	0.0556680i	$-0.982271\pi$
$577$	−1.90373	−	10.7966i	−0.0792535	−	0.449469i	0.919196	−	0.393801i	$-0.128840\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	3.34936	+	2.81044i	0.139194	+	0.116798i
$580$	−0.655230	−	0.238484i	−0.0272069	−	0.00990252i
$581$	3.98886	+	6.90890i	0.165486	+	0.286629i
$582$	−1.77837	+	3.08023i	−0.0737158	+	0.127680i
$583$	9.65523	−	8.10170i	0.399879	−	0.335538i
$584$	−4.35844	−	7.54904i	−0.180354	−	0.312382i
$585$	−0.0466368	+	0.264490i	−0.00192819	+	0.0109353i
$586$	1.69459			0.0700030
$587$	−2.21167	+	12.5430i	−0.0912853	+	0.517704i	0.904537	+	0.426395i	$0.140216\pi$
$587$	−2.21167	+	12.5430i	−0.0912853	+	0.517704i	−0.995823	+	0.0913099i	$0.970895\pi$
$588$	−1.37939	−	1.15744i	−0.0568849	−	0.0477321i
$589$	−6.42262	+	2.33764i	−0.264639	+	0.0963209i
$590$	1.47266	+	0.536004i	0.0606284	+	0.0220669i
$591$	−4.14559			−0.170527
$592$	−1.35117	+	5.93080i	−0.0555326	+	0.243754i
$593$	33.6786			1.38301			0.691507	−	0.722369i	$-0.256947\pi$
$593$	33.6786			1.38301			0.691507	+	0.722369i	$0.256947\pi$
$594$	−8.69594	−	3.16506i	−0.356799	−	0.129864i
$595$	−0.458111	+	0.166739i	−0.0187807	+	0.00683562i
$596$	3.36824	+	2.82629i	0.137969	+	0.115769i
$597$	0.138156	−	0.783520i	0.00565434	−	0.0320673i
$598$	0.0436438			0.00178473
$599$	−2.36484	+	13.4117i	−0.0966246	+	0.547986i	0.897613	+	0.440785i	$0.145300\pi$
$599$	−2.36484	+	13.4117i	−0.0966246	+	0.547986i	−0.994237	+	0.107201i	$0.965811\pi$
$600$	−0.865715	−	1.49946i	−0.0353427	−	0.0612153i
$601$	12.3962	−	10.4017i	0.505652	−	0.424292i	−0.353944	−	0.935267i	$-0.615160\pi$
$601$	12.3962	−	10.4017i	0.505652	−	0.424292i	0.859596	+	0.510974i	$0.170715\pi$
$602$	6.27379	−	10.8665i	0.255700	−	0.442886i
$603$	7.37211	+	12.7689i	0.300216	+	0.519989i
$604$	−13.8550	−	5.04282i	−0.563753	−	0.205189i
$605$	−0.881445	−	0.739620i	−0.0358358	−	0.0300698i
$606$	−2.79813	+	4.84651i	−0.113666	+	0.196876i
$607$	−7.17247	−	40.6771i	−0.291121	−	1.65103i	−0.682562	−	0.730828i	$-0.739134\pi$
$607$	−7.17247	−	40.6771i	−0.291121	−	1.65103i	0.391440	−	0.920204i	$-0.371977\pi$
$608$	0.354570	+	2.01087i	0.0143797	+	0.0815515i
$609$	−2.07217	+	1.73875i	−0.0839684	+	0.0704579i
$610$	1.30541	−	0.475129i	0.0528544	−	0.0192374i
$611$	6.18954	−	2.25281i	0.250402	−	0.0911389i
$612$	6.61721	−	5.55250i	0.267485	−	0.224446i
$613$	−5.40255	−	30.6394i	−0.218207	−	1.23751i	−0.875254	−	0.483664i	$-0.839306\pi$
$613$	−5.40255	−	30.6394i	−0.218207	−	1.23751i	0.657047	−	0.753850i	$-0.271805\pi$
$614$	2.12314	+	12.0409i	0.0856830	+	0.485932i
$615$	−0.149711	+	0.259306i	−0.00603691	+	0.0104562i
$616$	−4.67752	−	3.92490i	−0.188463	−	0.158139i
$617$	−17.9547	−	6.53498i	−0.722829	−	0.263088i	−0.0457029	−	0.998955i	$-0.514553\pi$
$617$	−17.9547	−	6.53498i	−0.722829	−	0.263088i	−0.677126	+	0.735867i	$0.736775\pi$
$618$	−3.40895	−	5.90447i	−0.137128	−	0.237513i
$619$	−19.4636	+	33.7120i	−0.782309	+	1.35500i	0.148284	+	0.988945i	$0.452625\pi$
$619$	−19.4636	+	33.7120i	−0.782309	+	1.35500i	−0.930593	+	0.366055i	$0.880708\pi$
$620$	0.309278	−	0.259515i	0.0124209	−	0.0104224i
$621$	0.0576190	+	0.0997991i	0.00231217	+	0.00400480i
$622$	0.212134	−	1.20307i	0.00850579	−	0.0482387i
$623$	10.2645			0.411237
$624$	−0.0466368	+	0.264490i	−0.00186697	+	0.0105881i
$625$	18.9841	+	15.9296i	0.759364	+	0.637182i
$626$	−16.3614	+	5.95507i	−0.653934	+	0.238013i
$627$	3.02007	+	1.09921i	0.120610	+	0.0438984i
$628$	−15.6527			−0.624611
$629$	−17.4354	+	5.38576i	−0.695195	+	0.214744i
$630$	−0.467911			−0.0186420
$631$	0.635163	+	0.231180i	0.0252854	+	0.00920314i	0.354632	−	0.935006i	$-0.384606\pi$
$631$	0.635163	+	0.231180i	0.0252854	+	0.00920314i	−0.329346	+	0.944209i	$0.606828\pi$
$632$	3.89780	−	1.41868i	0.155046	−	0.0564322i
$633$	0.254185	+	0.213286i	0.0101029	+	0.00847737i
$634$	1.51027	−	8.56515i	0.0599804	−	0.340166i
$635$	−1.46110			−0.0579821
$636$	0.167718	−	0.951178i	0.00665047	−	0.0377167i
$637$	−2.00475	−	3.47232i	−0.0794310	−	0.137579i
$638$	20.0706	−	16.8412i	0.794602	−	0.666750i
$639$	19.3405	−	33.4987i	0.765098	−	1.32519i
$640$	−0.0603074	−	0.104455i	−0.00238386	−	0.00412896i
$641$	−17.6853	−	6.43691i	−0.698526	−	0.254243i	−0.0317444	−	0.999496i	$-0.510106\pi$
$641$	−17.6853	−	6.43691i	−0.698526	−	0.254243i	−0.666781	+	0.745253i	$0.732328\pi$
$642$	0.169778	+	0.142460i	0.00670059	+	0.00562247i
$643$	−22.6582	+	39.2452i	−0.893553	+	1.54768i	−0.0579679	+	0.998318i	$0.518462\pi$
$643$	−22.6582	+	39.2452i	−0.893553	+	1.54768i	−0.835585	+	0.549361i	$0.814871\pi$
$644$	0.0132037	+	0.0748822i	0.000520300	+	0.00295077i
$645$	−0.0677435	−	0.384192i	−0.00266740	−	0.0151276i
$646$	−4.69253	+	3.93750i	−0.184625	+	0.154919i
$647$	−18.9859	+	6.91031i	−0.746413	+	0.271672i	−0.687096	−	0.726567i	$-0.741115\pi$
$647$	−18.9859	+	6.91031i	−0.746413	+	0.271672i	−0.0593177	+	0.998239i	$0.518893\pi$
$648$	7.45084	−	2.71188i	0.292697	−	0.106533i
$649$	−45.1095	+	37.8514i	−1.77070	+	1.48580i
$650$	−0.669473	−	3.79677i	−0.0262589	−	0.148922i
$651$	−0.271974	−	1.54244i	−0.0106595	−	0.0604531i
$652$	2.39053	−	4.14052i	0.0936204	−	0.162155i
$653$	−13.4586	−	11.2931i	−0.526675	−	0.441933i	0.340277	−	0.940325i	$-0.389479\pi$
$653$	−13.4586	−	11.2931i	−0.526675	−	0.441933i	−0.866951	+	0.498393i	$0.833924\pi$
$654$	2.36824	+	0.861969i	0.0926055	+	0.0337057i
$655$	1.30541	+	2.26103i	0.0510065	+	0.0883458i
$656$	3.57398	−	6.19031i	0.139540	−	0.241691i
$657$	19.2271	−	16.1335i	0.750123	−	0.629428i
$658$	5.73783	+	9.93821i	0.223684	+	0.387432i
$659$	5.65389	−	32.0648i	0.220244	−	1.24907i	−0.651327	−	0.758797i	$-0.725787\pi$
$659$	5.65389	−	32.0648i	0.220244	−	1.24907i	0.871571	−	0.490269i	$-0.163102\pi$
$660$	−0.189845			−0.00738971
$661$	4.07650	−	23.1190i	0.158558	−	0.899225i	−0.796903	−	0.604107i	$-0.793530\pi$
$661$	4.07650	−	23.1190i	0.158558	−	0.899225i	0.955461	−	0.295118i	$-0.0953590\pi$
$662$	6.31386	+	5.29796i	0.245395	+	0.205911i
$663$	−0.757122	+	0.275570i	−0.0294042	+	0.0107022i
$664$	−5.56418	−	2.02520i	−0.215932	−	0.0785928i
$665$	0.331815			0.0128672
$666$	−17.4932	−	0.866025i	−0.677847	−	0.0335578i
$667$	−0.326266			−0.0126331
$668$	−1.88413	−	0.685768i	−0.0728993	−	0.0265332i
$669$	5.83022	−	2.12203i	0.225409	−	0.0820423i
$670$	0.473126	+	0.397000i	0.0182784	+	0.0153374i
$671$	−9.06418	+	51.4055i	−0.349919	+	1.98449i
$672$	−0.467911			−0.0180501
$673$	2.29989	−	13.0433i	0.0886542	−	0.502783i	−0.907854	−	0.419287i	$-0.862280\pi$
$673$	2.29989	−	13.0433i	0.0886542	−	0.502783i	0.996508	−	0.0834962i	$-0.0266086\pi$
$674$	7.01367	+	12.1480i	0.270156	+	0.467925i
$675$	7.79813	−	6.54341i	0.300150	−	0.251856i
$676$	6.20099	−	10.7404i	0.238500	−	0.413093i
$677$	−2.69253	−	4.66360i	−0.103482	−	0.179237i	0.809635	−	0.586934i	$-0.199665\pi$
$677$	−2.69253	−	4.66360i	−0.103482	−	0.179237i	−0.913117	+	0.407697i	$0.866332\pi$
$678$	−4.51114	−	1.64192i	−0.173249	−	0.0630576i
$679$	−10.5699	−	8.86916i	−0.405634	−	0.340367i
$680$	0.180922	−	0.313366i	0.00693805	−	0.0120171i
$681$	0.533738	+	3.02698i	0.0204529	+	0.115994i
$682$	2.63429	+	14.9398i	0.100872	+	0.572074i
$683$	19.2547	−	16.1566i	0.736759	−	0.618214i	−0.195206	−	0.980762i	$-0.562538\pi$
$683$	19.2547	−	16.1566i	0.736759	−	0.618214i	0.931965	+	0.362548i	$0.118093\pi$
$684$	−5.52481	+	2.01087i	−0.211247	+	0.0768875i
$685$	0.979055	−	0.356347i	0.0374078	−	0.0136153i
$686$	12.5758	−	10.5523i	0.480146	−	0.402890i
$687$	−1.05004	−	5.95507i	−0.0400615	−	0.227200i
$688$	1.61721	+	9.17166i	0.0616556	+	0.349666i
$689$	1.07532	−	1.86251i	0.0409665	−	0.0709561i
$690$	0.00181100	+	0.00151961i	6.89436e−5	+	5.78505e-5i
$691$	−38.6467	−	14.0662i	−1.47019	−	0.535105i	−0.522037	−	0.852923i	$-0.674828\pi$
$691$	−38.6467	−	14.0662i	−1.47019	−	0.535105i	−0.948152	+	0.317818i	$0.897050\pi$
$692$	6.89053	+	11.9347i	0.261939	+	0.453691i
$693$	8.79086	−	15.2262i	0.333937	−	0.578396i
$694$	−15.2023	+	12.7563i	−0.577073	+	0.484221i
$695$	−0.808400	−	1.40019i	−0.0306644	−	0.0531123i
$696$	0.348641	−	1.97724i	0.0132152	−	0.0749470i
$697$	21.4439			0.812244
$698$	−2.98633	+	16.9363i	−0.113034	+	0.641049i
$699$	−1.11540	−	0.935932i	−0.0421883	−	0.0354002i
$700$	6.31180	−	2.29731i	0.238564	−	0.0868301i
$701$	−29.1523	−	10.6106i	−1.10107	−	0.400756i	−0.273357	−	0.961913i	$-0.588134\pi$
$701$	−29.1523	−	10.6106i	−1.10107	−	0.400756i	−0.827709	+	0.561157i	$0.810356\pi$
$702$	−1.57903			−0.0595967
$703$	12.4051	+	0.614134i	0.467868	+	0.0231625i
$704$	4.53209			0.170810
$705$	0.335275	+	0.122030i	0.0126272	+	0.00459592i
$706$	15.8576	−	5.77168i	0.596807	−	0.217220i
$707$	−16.6309	−	13.9550i	−0.625469	−	0.524831i
$708$	−0.783585	+	4.44393i	−0.0294489	+	0.167013i
$709$	−19.3773			−0.727731			−0.363865	−	0.931452i	$-0.618543\pi$
$709$	−19.3773			−0.727731			−0.363865	+	0.931452i	$0.618543\pi$
$710$	0.281364	−	1.59569i	0.0105594	−	0.0598853i
$711$	5.97178	+	10.3434i	0.223959	+	0.387909i
$712$	−5.83615	+	4.89711i	−0.218719	+	0.183527i
$713$	0.0944557	−	0.163602i	0.00353739	−	0.00612694i
$714$	−0.701867	−	1.21567i	−0.0262667	−	0.0454953i
$715$	−0.397231	−	0.144580i	−0.0148556	−	0.00540699i
$716$	−11.2797	−	9.46480i	−0.421543	−	0.353716i
$717$	−1.48932	+	2.57958i	−0.0556198	+	0.0963363i
$718$	2.79813	+	15.8690i	0.104425	+	0.592226i
$719$	−5.30675	−	30.0961i	−0.197908	−	1.12239i	−0.908216	−	0.418503i	$-0.862555\pi$
$719$	−5.30675	−	30.0961i	−0.197908	−	1.12239i	0.710307	−	0.703892i	$-0.248556\pi$
$720$	0.266044	−	0.223238i	0.00991489	−	0.00831958i
$721$	24.8542	−	9.04617i	0.925617	−	0.336897i
$722$	−13.9363	+	5.07239i	−0.518655	+	0.188775i
$723$	−5.56418	+	4.66890i	−0.206934	+	0.173638i
$724$	−1.89259	−	10.7334i	−0.0703375	−	0.398904i
$725$	5.00475	+	28.3833i	0.185872	+	1.05413i
$726$	1.65657	−	2.86927i	0.0614812	−	0.106489i
$727$	39.9843	+	33.5508i	1.48294	+	1.24433i	0.902979	+	0.429685i	$0.141375\pi$
$727$	39.9843	+	33.5508i	1.48294	+	1.24433i	0.579958	+	0.814647i	$0.303069\pi$
$728$	−0.979055	−	0.356347i	−0.0362862	−	0.0132071i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$	0.525692	−	0.910526i	0.0194567	−	0.0337001i
$731$	−21.4029	+	17.9591i	−0.791613	+	0.664242i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	0.211829	−	1.20134i	0.00782408	−	0.0443726i	−0.980646	−	0.195790i	$-0.937273\pi$
$733$	0.211829	−	1.20134i	0.00782408	−	0.0443726i	0.988470	+	0.151418i	$0.0483839\pi$
$734$	35.0823			1.29491
$735$	0.0377140	−	0.213887i	0.00139110	−	0.00788933i
$736$	−0.0432332	−	0.0362770i	−0.00159360	−	0.00133719i
$737$	−21.8075	+	7.93729i	−0.803290	+	0.292374i
$738$	19.3405	+	7.03936i	0.711933	+	0.259123i
$739$	−2.61318			−0.0961273			−0.0480637	−	0.998844i	$-0.515305\pi$
$739$	−2.61318			−0.0961273			−0.0480637	+	0.998844i	$0.515305\pi$
$740$	−0.700989	+	0.216534i	−0.0257689	+	0.00795995i
$741$	0.548392			0.0201457
$742$	3.52094	+	1.28152i	0.129258	+	0.0470460i
$743$	21.1989	−	7.71578i	0.777713	−	0.283064i	0.0774945	−	0.996993i	$-0.475308\pi$
$743$	21.1989	−	7.71578i	0.777713	−	0.283064i	0.700219	+	0.713928i	$0.253086\pi$
$744$	0.890530	+	0.747243i	0.0326484	+	0.0273953i
$745$	−0.0920916	+	0.522277i	−0.00337397	+	0.0191348i
$746$	29.6955			1.08723
$747$	2.96064	−	16.7906i	0.108324	−	0.614336i
$748$	6.79813	+	11.7747i	0.248564	+	0.430526i
$749$	−0.658633	+	0.552659i	−0.0240659	+	0.0201937i
$750$	0.209141	−	0.362242i	0.00763674	−	0.0132272i
$751$	−21.3346	−	36.9525i	−0.778509	−	1.34842i	−0.932801	−	0.360392i	$-0.882643\pi$
$751$	−21.3346	−	36.9525i	−0.778509	−	1.34842i	0.154292	−	0.988025i	$-0.450690\pi$
$752$	−8.00387	−	2.91317i	−0.291871	−	0.106232i
$753$	1.80793	+	1.51704i	0.0658848	+	0.0552839i
$754$	2.23530	−	3.87165i	0.0814048	−	0.140997i
$755$	−0.308811	−	1.75135i	−0.0112388	−	0.0637383i
$756$	−0.477711	−	2.70924i	−0.0173742	−	0.0985339i
$757$	−17.8610	+	14.9871i	−0.649168	+	0.544717i	−0.906818	−	0.421522i	$-0.861496\pi$
$757$	−17.8610	+	14.9871i	−0.649168	+	0.544717i	0.257650	+	0.966238i	$0.417052\pi$
$758$	0.393933	−	0.143380i	0.0143083	−	0.00520779i
$759$	−0.0834734	+	0.0303818i	−0.00302989	+	0.00110279i
$760$	−0.188663	+	0.158307i	−0.00684352	+	0.00574240i
$761$	−0.714822	−	4.05396i	−0.0259123	−	0.146956i	0.969107	−	0.246642i	$-0.0793272\pi$
$761$	−0.714822	−	4.05396i	−0.0259123	−	0.146956i	−0.995019	+	0.0996862i	$0.968216\pi$
$762$	−0.730552	−	4.14317i	−0.0264651	−	0.150091i
$763$	−4.88847	+	8.46708i	−0.176975	+	0.306529i
$764$	6.93835	+	5.82197i	0.251021	+	0.210631i
$765$	0.979055	+	0.356347i	0.0353978	+	0.0128838i
$766$	−3.21419	−	5.56715i	−0.116134	−	0.201149i
$767$	−5.02394	+	8.70172i	−0.181404	+	0.314201i
$768$	0.266044	−	0.223238i	0.00960005	−	0.00805540i
$769$	−3.09017	−	5.35234i	−0.111435	−	0.193010i	0.804914	−	0.593391i	$-0.202211\pi$
$769$	−3.09017	−	5.35234i	−0.111435	−	0.193010i	−0.916349	+	0.400381i	$0.868878\pi$
$770$	0.127889	−	0.725293i	0.00460879	−	0.0261377i
$771$	−3.43201			−0.123601
$772$	2.18614	−	12.3982i	0.0786808	−	0.446221i
$773$	13.8773	+	11.6445i	0.499133	+	0.418822i	0.857286	−	0.514841i	$-0.172149\pi$
$773$	13.8773	+	11.6445i	0.499133	+	0.418822i	−0.358153	+	0.933663i	$0.616593\pi$
$774$	−25.1989	+	9.17166i	−0.905757	+	0.329669i
$775$	−15.6814	−	5.70756i	−0.563292	−	0.205022i
$776$	10.2412			0.367639
$777$	−0.632226	+	2.77509i	−0.0226810	+	0.0995556i
$778$	3.11381			0.111635
$779$	−13.7151	−	4.99190i	−0.491395	−	0.178853i
$780$	−0.0304400	+	0.0110793i	−0.00108993	+	0.000396701i
$781$	46.6391	+	39.1348i	1.66888	+	1.40035i
$782$	0.0294005	−	0.166739i	0.00105136	−	0.00596257i
$783$	11.8043			0.421851
$784$	−0.900330	+	5.10602i	−0.0321546	+	0.182358i
$785$	−0.943974	−	1.63501i	−0.0336919	−	0.0583560i
$786$	−5.75877	+	4.83218i	−0.205409	+	0.172358i
$787$	13.9602	−	24.1798i	0.497628	−	0.861918i	−0.502368	−	0.864654i	$-0.667538\pi$
$787$	13.9602	−	24.1798i	0.497628	−	0.861918i	0.999996	+	0.00273640i	$0.000871024\pi$
$788$	5.96838	+	10.3375i	0.212615	+	0.368259i
$789$	6.73947	+	2.45297i	0.239932	+	0.0873280i
$790$	0.383256	+	0.321590i	0.0136356	+	0.0114416i
$791$	9.31180	−	16.1285i	0.331090	−	0.573464i
$792$	2.26604	+	12.8514i	0.0805204	+	0.456654i
$793$	1.54664	+	8.77141i	0.0549227	+	0.311482i
$794$	−15.0967	+	12.6677i	−0.535763	+	0.449559i
$795$	0.109470	−	0.0398440i	0.00388252	−	0.00141312i
$796$	−2.15270	+	0.783520i	−0.0763006	+	0.0277711i
$797$	−1.51114	+	1.26800i	−0.0535275	+	0.0449149i	−0.669159	−	0.743119i	$-0.733345\pi$
$797$	−1.51114	+	1.26800i	−0.0535275	+	0.0449149i	0.615631	+	0.788034i	$0.288901\pi$
$798$	0.165907	+	0.940908i	0.00587306	+	0.0333078i
$799$	−4.43717	−	25.1644i	−0.156976	−	0.890253i
$800$	−2.49273	+	4.31753i	−0.0881312	+	0.152648i
$801$	−16.8045	−	14.1007i	−0.593759	−	0.498223i
$802$	17.7754	+	6.46973i	0.627672	+	0.228454i
$803$	19.7528	+	34.2129i	0.697063	+	1.20735i
$804$	−0.889185	+	1.54011i	−0.0313592	+	0.0543156i
$805$	−0.00702557	+	0.00589515i	−0.000247619	+	0.000207777i
$806$	1.29426	+	2.24173i	0.0455885	+	0.0789615i
$807$	1.66607	−	9.44875i	0.0586484	−	0.332612i
$808$	16.1138			0.566882
$809$	2.72699	−	15.4655i	0.0958757	−	0.543738i	−0.898600	−	0.438769i	$-0.855415\pi$
$809$	2.72699	−	15.4655i	0.0958757	−	0.543738i	0.994475	−	0.104969i	$-0.0334743\pi$
$810$	0.732611	+	0.614734i	0.0257413	+	0.0215995i
$811$	38.0984	−	13.8667i	1.33782	−	0.486925i	0.428691	−	0.903451i	$-0.358975\pi$
$811$	38.0984	−	13.8667i	1.33782	−	0.486925i	0.909124	+	0.416526i	$0.136753\pi$
$812$	7.31908	+	2.66393i	0.256849	+	0.0934855i
$813$	2.37639			0.0833437
$814$	6.12361	−	26.8789i	0.214632	−	0.942105i
$815$	0.576666			0.0201997
$816$	0.979055	+	0.356347i	0.0342738	+	0.0124746i
$817$	17.8696	−	6.50400i	0.625178	−	0.227546i
$818$	−4.88326	−	4.09754i	−0.170739	−	0.143267i
$819$	0.520945	−	2.95442i	0.0182033	−	0.103236i
$820$	0.862149			0.0301075
$821$	−1.73190	+	9.82207i	−0.0604436	+	0.342793i	0.939556	+	0.342394i	$0.111238\pi$
$821$	−1.73190	+	9.82207i	−0.0604436	+	0.342793i	−1.00000		0.000398276i	$0.999873\pi$
$822$	1.50000	+	2.59808i	0.0523185	+	0.0906183i
$823$	−8.12180	+	6.81500i	−0.283108	+	0.237556i	−0.773272	−	0.634074i	$-0.781381\pi$
$823$	−8.12180	+	6.81500i	−0.283108	+	0.237556i	0.490164	+	0.871630i	$0.336937\pi$
$824$	−9.81567	+	17.0012i	−0.341945	+	0.592266i
$825$	3.92350	+	6.79569i	0.136599	+	0.236596i
$826$	−16.4500	−	5.98730i	−0.572367	−	0.208325i
$827$	19.3195	+	16.2110i	0.671806	+	0.563712i	0.913599	−	0.406615i	$-0.133291\pi$
$827$	19.3195	+	16.2110i	0.671806	+	0.563712i	−0.241793	+	0.970328i	$0.577736\pi$
$828$	0.0812519	−	0.140732i	0.00282370	−	0.00489079i
$829$	0.950532	+	5.39074i	0.0330134	+	0.187228i	0.996855	−	0.0792478i	$-0.0252519\pi$
$829$	0.950532	+	5.39074i	0.0330134	+	0.187228i	−0.963842	+	0.266476i	$0.914141\pi$
$830$	−0.124018	−	0.703343i	−0.00430474	−	0.0244134i
$831$	−6.34065	+	5.32044i	−0.219955	+	0.184564i
$832$	0.726682	−	0.264490i	0.0251932	−	0.00916956i
$833$	−14.6163	+	5.31991i	−0.506426	+	0.184324i
$834$	3.56624	−	2.99243i	0.123489	−	0.103619i
$835$	−0.0419949	−	0.238165i	−0.00145329	−	0.00824203i
$836$	−1.60694	−	9.11343i	−0.0555773	−	0.315195i
$837$	−3.41740	+	5.91912i	−0.118123	+	0.204595i
$838$	−15.9991	−	13.4249i	−0.552681	−	0.463754i
$839$	−12.7046	−	4.62408i	−0.438610	−	0.159641i	0.113271	−	0.993564i	$-0.463867\pi$
$839$	−12.7046	−	4.62408i	−0.438610	−	0.159641i	−0.551880	+	0.833923i	$0.686090\pi$
$840$	−0.0282185	−	0.0488759i	−0.000973631	−	0.00168638i
$841$	−2.21032	+	3.82839i	−0.0762180	+	0.132013i
$842$	4.44949	−	3.73357i	0.153340	−	0.128667i
$843$	−5.51367	−	9.54996i	−0.189901	−	0.328918i
$844$	0.165907	−	0.940908i	0.00571077	−	0.0323874i
$845$	1.49586			0.0514592
$846$	4.25877	−	24.1527i	0.146420	−	0.830387i
$847$	9.84595	+	8.26173i	0.338311	+	0.283877i
$848$	−2.61334	+	0.951178i	−0.0897425	+	0.0326636i
$849$	1.92855	+	0.701934i	0.0661876	+	0.0240903i
$850$	−14.9564			−0.512999
$851$	−0.273567	+	0.207391i	−0.00937775	+	0.00710928i
$852$	4.66550			0.159837
$853$	21.2570	+	7.73692i	0.727826	+	0.264907i	0.679244	−	0.733912i	$-0.262308\pi$
$853$	21.2570	+	7.73692i	0.727826	+	0.264907i	0.0485819	+	0.998819i	$0.484530\pi$
$854$	−14.5817	+	5.30731i	−0.498976	+	0.181612i
$855$	−0.543233	−	0.455827i	−0.0185782	−	0.0155889i
$856$	0.110815	−	0.628461i	0.00378756	−	0.0214803i
$857$	−28.4148			−0.970630			−0.485315	−	0.874339i	$-0.661295\pi$
$857$	−28.4148			−0.970630			−0.485315	+	0.874339i	$0.661295\pi$
$858$	0.211362	−	1.19869i	0.00721578	−	0.0409227i
$859$	−11.2618	−	19.5059i	−0.384246	−	0.665534i	0.607418	−	0.794382i	$-0.292205\pi$
$859$	−11.2618	−	19.5059i	−0.384246	−	0.665534i	−0.991664	+	0.128848i	$0.958872\pi$
$860$	−0.860500	+	0.722045i	−0.0293428	+	0.0246215i
$861$	1.67230	−	2.89652i	0.0569920	−	0.0987130i
$862$	5.68004	+	9.83813i	0.193463	+	0.335088i
$863$	9.35282	+	3.40415i	0.318374	+	0.115878i	0.496264	−	0.868172i	$-0.334705\pi$
$863$	9.35282	+	3.40415i	0.318374	+	0.115878i	−0.177890	+	0.984050i	$0.556927\pi$
$864$	1.56418	+	1.31250i	0.0532144	+	0.0446522i
$865$	−0.831100	+	1.43951i	−0.0282582	+	0.0489447i
$866$	−6.18273	−	35.0640i	−0.210098	−	1.19152i
$867$	−0.482459	−	2.73616i	−0.0163852	−	0.0929249i
$868$	−3.45471	+	2.89884i	−0.117260	+	0.0983932i
$869$	−17.6652	+	6.42960i	−0.599251	+	0.218109i
$870$	0.227559	−	0.0828247i	0.00771497	−	0.00280802i
$871$	−3.03343	+	2.54535i	−0.102784	+	0.0862460i
$872$	−1.26011	−	7.14647i	−0.0426729	−	0.242010i
$873$	5.12061	+	29.0404i	0.173307	+	0.982870i
$874$	−0.0576190	+	0.0997991i	−0.00194899	+	0.00337575i
$875$	1.24304	+	1.04303i	0.0420224	+	0.0352610i
$876$	2.84477	+	1.03541i	0.0961159	+	0.0349833i
$877$	−22.0021	−	38.1088i	−0.742959	−	1.28684i	−0.951142	−	0.308752i	$-0.900089\pi$
$877$	−22.0021	−	38.1088i	−0.742959	−	1.28684i	0.208184	−	0.978090i	$-0.433245\pi$
$878$	11.2520	−	19.4890i	0.379735	−	0.657721i
$879$	−0.450837	+	0.378297i	−0.0152064	+	0.0127596i
$880$	0.273318	+	0.473401i	0.00921356	+	0.0159584i
$881$	−2.13862	+	12.1287i	−0.0720520	+	0.408627i	0.927355	+	0.374184i	$0.122077\pi$
$881$	−2.13862	+	12.1287i	−0.0720520	+	0.408627i	−0.999407	+	0.0344437i	$0.989034\pi$
$882$	−14.9290			−0.502686
$883$	3.77244	−	21.3946i	0.126953	−	0.719985i	−0.853176	−	0.521623i	$-0.825327\pi$
$883$	3.77244	−	21.3946i	0.126953	−	0.719985i	0.980129	−	0.198362i	$-0.0635621\pi$
$884$	1.77719	+	1.49124i	0.0597733	+	0.0501558i
$885$	−0.511449	+	0.186152i	−0.0171922	+	0.00625744i
$886$	−24.5205	−	8.92474i	−0.823783	−	0.299833i
$887$	10.7145			0.359758			0.179879	−	0.983689i	$-0.442429\pi$
$887$	10.7145			0.359758			0.179879	+	0.983689i	$0.442429\pi$
$888$	−0.964508	−	1.87949i	−0.0323668	−	0.0630715i
$889$	16.3209			0.547385
$890$	−0.863493	−	0.314286i	−0.0289444	−	0.0105349i
$891$	−33.7679	+	12.2905i	−1.13127	+	0.411747i
$892$	−13.6853	−	11.4833i	−0.458216	−	0.384489i
$893$	−3.02007	+	17.1277i	−0.101063	+	0.573155i
$894$	−1.52704			−0.0510717
$895$	0.308400	−	1.74903i	0.0103087	−	0.0584635i
$896$	0.673648	+	1.16679i	0.0225050	+	0.0389798i
$897$	−0.0116112	+	0.00974294i	−0.000387686	+	0.000325307i
$898$	−3.26264	+	5.65106i	−0.108876	+	0.188578i
$899$	−9.67546	−	16.7584i	−0.322695	−	0.558923i
$900$	−13.4893	−	4.90971i	−0.449644	−	0.163657i
$901$	−6.39124	−	5.36289i	−0.212923	−	0.178664i
$902$	−16.1976	+	28.0550i	−0.539321	+	0.934131i
$903$	0.756711	+	4.29152i	0.0251818	+	0.142813i
$904$	2.40033	+	13.6129i	0.0798338	+	0.452760i
$905$	1.00703	−	0.844995i	0.0334747	−	0.0280886i
$906$	4.81180	−	1.75135i	0.159861	−	0.0581848i
$907$	−17.1122	+	6.22832i	−0.568200	+	0.206808i	−0.610114	−	0.792313i	$-0.708877\pi$
$907$	−17.1122	+	6.22832i	−0.568200	+	0.206808i	0.0419145	+	0.999121i	$0.486654\pi$
$908$	6.77972	−	5.68886i	0.224993	−	0.188791i
$909$	8.05690	+	45.6930i	0.267231	+	1.51554i
$910$	−0.0218219	−	0.123758i	−0.000723388	−	0.00410254i
$911$	−10.3072	+	17.8526i	−0.341493	+	0.591484i	−0.984710	−	0.174200i	$-0.944266\pi$
$911$	−10.3072	+	17.8526i	−0.341493	+	0.591484i	0.643217	+	0.765684i	$0.277599\pi$
$912$	−0.543233	−	0.455827i	−0.0179883	−	0.0150939i
$913$	25.2173	+	9.17836i	0.834572	+	0.303760i
$914$	−16.3721	−	28.3573i	−0.541541	−	0.937977i
$915$	−0.241230	+	0.417822i	−0.00797480	+	0.0138128i
$916$	−13.3380	+	11.1919i	−0.440699	+	0.369790i
$917$	−14.5817	−	25.2563i	−0.481531	−	0.834036i
$918$	−1.06371	+	6.03260i	−0.0351077	+	0.199106i
$919$	−25.1462			−0.829497			−0.414748	−	0.909936i	$-0.636130\pi$
$919$	−25.1462			−0.829497			−0.414748	+	0.909936i	$0.636130\pi$
$920$	0.00118205	−	0.00670372i	3.89709e−5	−	0.000221015i
$921$	−3.25284	−	2.72946i	−0.107185	−	0.0899387i
$922$	18.3662	−	6.68474i	0.604858	−	0.220150i
$923$	9.76207	+	3.55310i	0.321322	+	0.116952i
$924$	2.12061			0.0697631
$925$	22.2383	+	20.6176i	0.731191	+	0.677901i
$926$	−42.8803			−1.40913
$927$	−53.1173	−	19.3331i	−1.74460	−	0.634982i
$928$	−5.43242	+	1.97724i	−0.178328	+	0.0649060i
$929$	−23.1912	−	19.4597i	−0.760878	−	0.638453i	0.177477	−	0.984125i	$-0.443206\pi$
$929$	−23.1912	−	19.4597i	−0.760878	−	0.638453i	−0.938355	+	0.345672i	$0.887651\pi$
$930$	−0.0243481	+	0.138085i	−0.000798406	+	0.00452798i
$931$	10.5868			0.346967
$932$	−0.728026	+	4.12884i	−0.0238473	+	0.135245i
$933$	0.212134	+	0.367426i	0.00694494	+	0.0120290i
$934$	−16.1550	+	13.5556i	−0.528607	+	0.443554i
$935$	−0.819955	+	1.42020i	−0.0268154	+	0.0464456i
$936$	1.11334	+	1.92836i	0.0363907	+	0.0630305i
$937$	15.1686	+	5.52092i	0.495536	+	0.180361i	0.577685	−	0.816260i	$-0.303956\pi$
$937$	15.1686	+	5.52092i	0.495536	+	0.180361i	−0.0821489	+	0.996620i	$0.526178\pi$
$938$	−5.28493	−	4.43458i	−0.172559	−	0.144794i
$939$	3.02347	−	5.23680i	0.0986672	−	0.170897i
$940$	−0.178396	−	1.01173i	−0.00581863	−	0.0329991i
$941$	1.70733	+	9.68275i	0.0556574	+	0.315649i	0.999908	−	0.0135795i	$-0.00432262\pi$
$941$	1.70733	+	9.68275i	0.0556574	+	0.315649i	−0.944250	+	0.329228i	$0.893212\pi$
$942$	4.16431	−	3.49428i	0.135681	−	0.113850i
$943$	0.379081	−	0.137974i	0.0123446	−	0.00449305i
$944$	12.2096	−	4.44393i	0.397389	−	0.144638i
$945$	0.254185	−	0.213286i	0.00826863	−	0.00693821i
$946$	−7.32934	−	41.5668i	−0.238298	−	1.35145i
$947$	−9.23695	−	52.3853i	−0.300160	−	1.70229i	−0.645453	−	0.763800i	$-0.723331\pi$
$947$	−9.23695	−	52.3853i	−0.300160	−	1.70229i	0.345293	−	0.938495i	$-0.387780\pi$
$948$	−0.720285	+	1.24757i	−0.0233938	+	0.0405192i
$949$	5.16385	+	4.33298i	0.167626	+	0.140655i
$950$	9.56583	+	3.48168i	0.310356	+	0.112960i
$951$	1.51027	+	2.61586i	0.0489738	+	0.0848250i
$952$	−2.02094	+	3.50038i	−0.0654992	+	0.113448i
$953$	37.4181	−	31.3975i	1.21209	−	1.01706i	0.212891	−	0.977076i	$-0.431712\pi$
$953$	37.4181	−	31.3975i	1.21209	−	1.01706i	0.999200	−	0.0399889i	$-0.0127323\pi$
$954$	−4.00387	−	6.93491i	−0.129630	−	0.224526i
$955$	−0.189702	+	1.07586i	−0.00613863	+	0.0348139i
$956$	8.57667			0.277389
$957$	−1.58007	+	8.96102i	−0.0510764	+	0.289669i
$958$	18.5403	+	15.5572i	0.599010	+	0.502629i
$959$	−10.9363	+	3.98048i	−0.353151	+	0.128537i
$960$	0.0393628	+	0.0143269i	0.00127043	+	0.000462399i
$961$	−19.7956			−0.638568
$962$	−0.586771	−	4.66717i	−0.0189183	−	0.150476i
$963$	1.83750			0.0592125
$964$	19.6532	+	7.15317i	0.632986	+	0.230388i
$965$	1.42690	−	0.519349i	0.0459335	−	0.0167184i
$966$	−0.0202293	−	0.0169744i	−0.000650867	−	0.000546143i
$967$	1.45646	−	8.26001i	0.0468367	−	0.265624i	−0.952393	−	0.304874i	$-0.901386\pi$
$967$	1.45646	−	8.26001i	0.0468367	−	0.265624i	0.999229	+	0.0392499i	$0.0124968\pi$
$968$	−9.53983			−0.306622
$969$	0.369423	−	2.09510i	0.0118676	−	0.0673044i
$970$	0.617622	+	1.06975i	0.0198306	+	0.0343477i
$971$	31.6771	−	26.5802i	1.01657	−	0.853001i	0.0273745	−	0.999625i	$-0.491285\pi$
$971$	31.6771	−	26.5802i	1.01657	−	0.853001i	0.989192	+	0.146624i	$0.0468409\pi$
$972$	−4.43969	+	7.68977i	−0.142403	+	0.246650i
$973$	9.03003	+	15.6405i	0.289489	+	0.501410i
$974$	27.2212	+	9.90771i	0.872224	+	0.317464i
$975$	1.02569	+	0.860658i	0.0328484	+	0.0275631i
$976$	5.75877	−	9.97448i	0.184334	−	0.319275i
$977$	8.39662	+	47.6196i	0.268632	+	1.52349i	0.758490	+	0.651684i	$0.225937\pi$
$977$	8.39662	+	47.6196i	0.268632	+	1.52349i	−0.489859	+	0.871802i	$0.662952\pi$
$978$	0.288333	+	1.63522i	0.00921988	+	0.0522885i
$979$	26.4500	−	22.1942i	0.845344	−	0.709328i
$980$	−0.587649	+	0.213887i	−0.0187717	+	0.00683236i
$981$	19.6348	−	7.14647i	0.626889	−	0.228169i
$982$	21.5654	−	18.0955i	0.688178	−	0.577450i
$983$	9.44150	+	53.5454i	0.301137	+	1.70783i	0.641152	+	0.767414i	$0.278457\pi$
$983$	9.44150	+	53.5454i	0.301137	+	1.70783i	−0.340015	+	0.940420i	$0.610432\pi$
$984$	0.431074	+	2.44474i	0.0137422	+	0.0779356i
$985$	−0.719874	+	1.24686i	−0.0229371	+	0.0397282i
$986$	−13.2856	−	11.1480i	−0.423101	−	0.355024i
$987$	−3.74510	−	1.36310i	−0.119208	−	0.0433881i
$988$	−0.789515	−	1.36748i	−0.0251178	−	0.0435053i
$989$	−0.262803	+	0.455188i	−0.00835665	+	0.0144741i
$990$	−1.20574	+	1.01173i	−0.0383208	+	0.0321550i
$991$	15.9436	+	27.6151i	0.506464	+	0.877221i	0.999972	+	0.00748010i	$0.00238101\pi$
$991$	15.9436	+	27.6151i	0.506464	+	0.877221i	−0.493508	+	0.869741i	$0.664286\pi$
$992$	0.581252	−	3.29644i	0.0184548	−	0.104662i
$993$	−2.86247			−0.0908378
$994$	−3.14290	+	17.8243i	−0.0996868	+	0.565352i
$995$	−0.211667	−	0.177610i	−0.00671029	−	0.00563060i
$996$	1.93242	−	0.703343i	0.0612310	−	0.0222863i
$997$	0.490505	+	0.178529i	0.0155344	+	0.00565407i	0.349776	−	0.936833i	$-0.386258\pi$
$997$	0.490505	+	0.178529i	0.0155344	+	0.00565407i	−0.334241	+	0.942488i	$0.608480\pi$
$998$	4.68510			0.148304
$999$	9.89764	−	7.50341i	0.313148	−	0.237397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.a.53.1	yes	6
3.2	odd	2		666.2.x.c.127.1		6
4.3	odd	2		592.2.bc.b.497.1		6
37.7	even	9	inner	74.2.f.a.7.1	✓	6
37.9	even	9		2738.2.a.m.1.2		3
37.28	even	18		2738.2.a.p.1.2		3
111.44	odd	18		666.2.x.c.451.1		6
148.7	odd	18		592.2.bc.b.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.7.1	✓	6	37.7	even	9	inner
74.2.f.a.53.1	yes	6	1.1	even	1	trivial
592.2.bc.b.81.1		6	148.7	odd	18
592.2.bc.b.497.1		6	4.3	odd	2
666.2.x.c.127.1		6	3.2	odd	2
666.2.x.c.451.1		6	111.44	odd	18
2738.2.a.m.1.2		3	37.9	even	9
2738.2.a.p.1.2		3	37.28	even	18

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0209445 + 0.118782i) q^{5} -0.347296 q^{6} +(0.233956 - 1.32683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0209445 + 0.118782i) q^{5} -0.347296 q^{6} +(0.233956 - 1.32683i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(-0.0603074 + 0.104455i) q^{10} +(-2.26604 - 3.92490i) q^{11} +(-0.326352 - 0.118782i) q^{12} +(-0.592396 - 0.497079i) q^{13} +(0.673648 - 1.16679i) q^{14} +(-0.00727396 - 0.0412527i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.29813 + 1.92836i) q^{17} +(-2.70574 + 0.984808i) q^{18} +(1.91875 - 0.698367i) q^{19} +(-0.0923963 + 0.0775297i) q^{20} +(0.0812519 + 0.460802i) q^{21} +(-0.786989 - 4.46324i) q^{22} +(-0.0282185 + 0.0488759i) q^{23} +(-0.266044 - 0.223238i) q^{24} +(4.68479 + 1.70513i) q^{25} +(-0.386659 - 0.669713i) q^{26} +(1.02094 - 1.76833i) q^{27} +(1.03209 - 0.866025i) q^{28} +(2.89053 + 5.00654i) q^{29} +(0.00727396 - 0.0412527i) q^{30} -3.34730 q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.20574 + 1.01173i) q^{33} +(-2.81908 + 1.02606i) q^{34} +(0.152704 + 0.0555796i) q^{35} -2.87939 q^{36} +(5.60607 + 2.36051i) q^{37} +2.04189 q^{38} +(0.252374 + 0.0918566i) q^{39} +(-0.113341 + 0.0412527i) q^{40} +(-5.47565 - 4.59462i) q^{41} +(-0.0812519 + 0.460802i) q^{42} +9.31315 q^{43} +(0.786989 - 4.46324i) q^{44} +(-0.173648 - 0.300767i) q^{45} +(-0.0432332 + 0.0362770i) q^{46} +(-4.25877 + 7.37641i) q^{47} +(-0.173648 - 0.300767i) q^{48} +(4.87211 + 1.77330i) q^{49} +(3.81908 + 3.20459i) q^{50} +(0.520945 - 0.902302i) q^{51} +(-0.134285 - 0.761570i) q^{52} +(0.482926 + 2.73881i) q^{53} +(1.56418 - 1.31250i) q^{54} +(0.513671 - 0.186961i) q^{55} +(1.26604 - 0.460802i) q^{56} +(-0.543233 + 0.455827i) q^{57} +(1.00387 + 5.69323i) q^{58} +(-2.25624 - 12.7958i) q^{59} +(0.0209445 - 0.0362770i) q^{60} +(-8.82295 - 7.40333i) q^{61} +(-3.14543 - 1.14484i) q^{62} +(1.93969 + 3.35965i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0714517 - 0.0599551i) q^{65} +(0.786989 + 1.36310i) q^{66} +(0.889185 - 5.04282i) q^{67} -3.00000 q^{68} +(0.00340357 - 0.0193026i) q^{69} +(0.124485 + 0.104455i) q^{70} +(-12.6236 + 4.59462i) q^{71} +(-2.70574 - 0.984808i) q^{72} -8.71688 q^{73} +(4.46064 + 4.13554i) q^{74} -1.73143 q^{75} +(1.91875 + 0.698367i) q^{76} +(-5.73783 + 2.08840i) q^{77} +(0.205737 + 0.172634i) q^{78} +(0.720285 - 4.08494i) q^{79} -0.120615 q^{80} +(1.37686 - 7.80856i) q^{81} +(-3.57398 - 6.19031i) q^{82} +(-4.53596 + 3.80612i) q^{83} +(-0.233956 + 0.405223i) q^{84} +(-0.180922 - 0.313366i) q^{85} +(8.75150 + 3.18528i) q^{86} +(-1.53802 - 1.29055i) q^{87} +(2.26604 - 3.92490i) q^{88} +(1.32295 + 7.50281i) q^{89} +(-0.0603074 - 0.342020i) q^{90} +(-0.798133 + 0.669713i) q^{91} +(-0.0530334 + 0.0193026i) q^{92} +(1.09240 - 0.397600i) q^{93} +(-6.52481 + 5.47497i) q^{94} +(0.0427664 + 0.242540i) q^{95} +(-0.0603074 - 0.342020i) q^{96} +(5.12061 - 8.86916i) q^{97} +(3.97178 + 3.33272i) q^{98} +(12.2626 + 4.46324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{10} - 9 q^{11} - 3 q^{12} + 3 q^{14} - 18 q^{15} - 6 q^{18} + 9 q^{19} + 3 q^{20} + 3 q^{21} + 3 q^{22} - 15 q^{23} + 3 q^{24} + 21 q^{25} - 9 q^{26} + 3 q^{27} - 3 q^{28} + 18 q^{30} - 18 q^{31} - 3 q^{33} + 3 q^{35} - 6 q^{36} + 9 q^{37} + 6 q^{38} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 3 q^{44} + 15 q^{46} - 3 q^{47} + 6 q^{50} + 9 q^{52} - 18 q^{53} - 9 q^{54} - 18 q^{55} + 3 q^{56} + 12 q^{57} - 18 q^{58} - 6 q^{59} - 3 q^{60} - 12 q^{61} - 3 q^{62} + 6 q^{63} - 3 q^{64} - 3 q^{66} - 3 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{70} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 18 q^{74} - 30 q^{75} + 9 q^{76} - 15 q^{77} - 9 q^{78} + 30 q^{79} - 12 q^{80} + 12 q^{81} - 6 q^{82} + 6 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{88} - 33 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 3 q^{93} - 12 q^{94} + 51 q^{95} - 6 q^{96} + 42 q^{97} + 9 q^{98} + 27 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^10 - 9 * q^11 - 3 * q^12 + 3 * q^14 - 18 * q^15 - 6 * q^18 + 9 * q^19 + 3 * q^20 + 3 * q^21 + 3 * q^22 - 15 * q^23 + 3 * q^24 + 21 * q^25 - 9 * q^26 + 3 * q^27 - 3 * q^28 + 18 * q^30 - 18 * q^31 - 3 * q^33 + 3 * q^35 - 6 * q^36 + 9 * q^37 + 6 * q^38 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 3 * q^44 + 15 * q^46 - 3 * q^47 + 6 * q^50 + 9 * q^52 - 18 * q^53 - 9 * q^54 - 18 * q^55 + 3 * q^56 + 12 * q^57 - 18 * q^58 - 6 * q^59 - 3 * q^60 - 12 * q^61 - 3 * q^62 + 6 * q^63 - 3 * q^64 - 3 * q^66 - 3 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^70 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 18 * q^74 - 30 * q^75 + 9 * q^76 - 15 * q^77 - 9 * q^78 + 30 * q^79 - 12 * q^80 + 12 * q^81 - 6 * q^82 + 6 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^88 - 33 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 3 * q^93 - 12 * q^94 + 51 * q^95 - 6 * q^96 + 42 * q^97 + 9 * q^98 + 27 * q^99

Introduction

L-functions

Modular forms

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