LMFDB - Embedded newform 138.2.e.d.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.d.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.47672 - 1.59169i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.151894 + 1.05645i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.47672 - 1.59169i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.151894 + 1.05645i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.418986 + 2.91411i) q^{10} +(-1.74302 - 3.81667i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.834716 + 5.80558i) q^{13} +(-0.897877 - 0.577031i) q^{14} +(2.82482 - 0.829443i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.51479 + 4.05628i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.59283 - 1.83823i) q^{19} +(-2.82482 - 0.829443i) q^{20} +(-0.443376 + 0.970858i) q^{21} +4.19584 q^{22} +(-2.13467 - 4.29455i) q^{23} +1.00000 q^{24} +(1.52357 - 3.33616i) q^{25} +(-5.62769 - 1.65244i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.897877 - 0.577031i) q^{28} +(5.90509 - 6.81484i) q^{29} +(-0.418986 + 2.91411i) q^{30} +(-4.40357 + 1.29301i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.597131 - 4.15314i) q^{33} +(-2.22963 - 4.88220i) q^{34} +(1.30533 + 2.85828i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-7.22349 - 4.64226i) q^{37} +(2.33380 - 0.685265i) q^{38} +(-0.834716 + 5.80558i) q^{39} +(1.92796 - 2.22499i) q^{40} +(-3.67379 + 2.36100i) q^{41} +(-0.698939 - 0.806618i) q^{42} +(0.521162 + 0.153027i) q^{43} +(-1.74302 + 3.81667i) q^{44} +2.94408 q^{45} +(4.79324 - 0.157744i) q^{46} -1.61130 q^{47} +(-0.415415 + 0.909632i) q^{48} +(5.62345 + 1.65119i) q^{49} +(2.40176 + 2.77178i) q^{50} +(-4.51520 + 2.90174i) q^{51} +(3.84094 - 4.43268i) q^{52} +(-0.409819 + 2.85036i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-10.3919 - 6.67848i) q^{55} +(0.151894 + 1.05645i) q^{56} +(-1.01042 - 2.21252i) q^{57} +(3.74593 + 8.20244i) q^{58} +(-0.0614238 - 0.427212i) q^{59} +(-2.47672 - 1.59169i) q^{60} +(1.04061 - 0.305550i) q^{61} +(0.653151 - 4.54276i) q^{62} +(-0.698939 + 0.806618i) q^{63} +(0.841254 - 0.540641i) q^{64} +(11.3080 + 13.0502i) q^{65} +(4.02588 + 1.18211i) q^{66} +(-1.19561 + 2.61803i) q^{67} +5.36723 q^{68} +(-0.838287 - 4.72200i) q^{69} -3.14224 q^{70} +(-2.66906 + 5.84442i) q^{71} +(0.959493 + 0.281733i) q^{72} +(8.77594 + 10.1280i) q^{73} +(7.22349 - 4.64226i) q^{74} +(2.40176 - 2.77178i) q^{75} +(-0.346156 + 2.40757i) q^{76} +(4.29686 - 1.26167i) q^{77} +(-4.93418 - 3.17101i) q^{78} +(0.186826 + 1.29941i) q^{79} +(1.22301 + 2.67803i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.621496 - 4.32260i) q^{82} +(10.9598 + 7.04340i) q^{83} +(1.02408 - 0.300696i) q^{84} +(-2.24879 + 15.6407i) q^{85} +(-0.355697 + 0.410496i) q^{86} +(7.58585 - 4.87513i) q^{87} +(-2.74769 - 3.17101i) q^{88} +(-6.91251 - 2.02970i) q^{89} +(-1.22301 + 2.67803i) q^{90} -6.26006 q^{91} +(-1.84769 + 4.42561i) q^{92} -4.58948 q^{93} +(0.669357 - 1.46569i) q^{94} +(-6.87088 - 2.01747i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(9.65194 - 6.20292i) q^{97} +(-3.83804 + 4.42934i) q^{98} +(0.597131 - 4.15314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

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
$5$	2.47672	−	1.59169i	1.10762	−	0.711825i	0.146848	−	0.989159i	$-0.453087\pi$
$5$	2.47672	−	1.59169i	1.10762	−	0.711825i	0.960773	+	0.277334i	$0.0894510\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	−0.151894	+	1.05645i	−0.0574105	+	0.399299i	0.940772	+	0.339039i	$0.110102\pi$
$7$	−0.151894	+	1.05645i	−0.0574105	+	0.399299i	−0.998183	+	0.0602596i	$0.980807\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.418986	+	2.91411i	0.132495	+	0.921523i
$11$	−1.74302	−	3.81667i	−0.525539	−	1.15077i	−0.967299	−	0.253637i	$-0.918373\pi$
$11$	−1.74302	−	3.81667i	−0.525539	−	1.15077i	0.441760	−	0.897133i	$-0.354354\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	0.834716	+	5.80558i	0.231508	+	1.61018i	0.691583	+	0.722297i	$0.256914\pi$
$13$	0.834716	+	5.80558i	0.231508	+	1.61018i	−0.460075	+	0.887880i	$0.652177\pi$
$14$	−0.897877	−	0.577031i	−0.239968	−	0.154218i
$15$	2.82482	−	0.829443i	0.729366	−	0.214161i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−3.51479	+	4.05628i	−0.852461	+	0.983792i	−0.999986	−	0.00526614i	$-0.998324\pi$
$17$	−3.51479	+	4.05628i	−0.852461	+	0.983792i	0.147525	+	0.989058i	$0.452869\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−1.59283	−	1.83823i	−0.365421	−	0.421718i	0.543028	−	0.839715i	$-0.317278\pi$
$19$	−1.59283	−	1.83823i	−0.365421	−	0.421718i	−0.908449	+	0.417997i	$0.862732\pi$
$20$	−2.82482	−	0.829443i	−0.631649	−	0.185469i
$21$	−0.443376	+	0.970858i	−0.0967526	+	0.211859i
$22$	4.19584			0.894557
$23$	−2.13467	−	4.29455i	−0.445110	−	0.895476i
$23$	−2.13467	−	4.29455i	−0.445110	−	0.895476i
$24$	1.00000			0.204124
$25$	1.52357	−	3.33616i	0.304715	−	0.667232i
$26$	−5.62769	−	1.65244i	−1.10368	−	0.324070i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	0.897877	−	0.577031i	0.169683	−	0.109049i
$29$	5.90509	−	6.81484i	1.09655	−	1.26548i	0.135000	−	0.990846i	$-0.456897\pi$
$29$	5.90509	−	6.81484i	1.09655	−	1.26548i	0.961548	−	0.274638i	$-0.0885579\pi$
$30$	−0.418986	+	2.91411i	−0.0764960	+	0.532041i
$31$	−4.40357	+	1.29301i	−0.790905	+	0.232231i	−0.652144	−	0.758095i	$-0.726130\pi$
$31$	−4.40357	+	1.29301i	−0.790905	+	0.232231i	−0.138761	+	0.990326i	$0.544312\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.597131	−	4.15314i	−0.103947	−	0.722968i
$34$	−2.22963	−	4.88220i	−0.382378	−	0.837290i
$35$	1.30533	+	2.85828i	0.220642	+	0.483138i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−7.22349	−	4.64226i	−1.18753	−	0.763182i	−0.210778	−	0.977534i	$-0.567600\pi$
$37$	−7.22349	−	4.64226i	−1.18753	−	0.763182i	−0.976757	+	0.214352i	$0.931236\pi$
$38$	2.33380	−	0.685265i	0.378592	−	0.111165i
$39$	−0.834716	+	5.80558i	−0.133661	+	0.929636i
$40$	1.92796	−	2.22499i	0.304837	−	0.351801i
$41$	−3.67379	+	2.36100i	−0.573750	+	0.368727i	−0.795110	−	0.606465i	$-0.792587\pi$
$41$	−3.67379	+	2.36100i	−0.573750	+	0.368727i	0.221360	+	0.975192i	$0.428951\pi$
$42$	−0.698939	−	0.806618i	−0.107849	−	0.124464i
$43$	0.521162	+	0.153027i	0.0794764	+	0.0233364i	0.321229	−	0.947002i	$-0.395904\pi$
$43$	0.521162	+	0.153027i	0.0794764	+	0.0233364i	−0.241753	+	0.970338i	$0.577722\pi$
$44$	−1.74302	+	3.81667i	−0.262770	+	0.575385i
$45$	2.94408			0.438877
$46$	4.79324	−	0.157744i	0.706724	−	0.0232580i
$47$	−1.61130			−0.235032			−0.117516	−	0.993071i	$-0.537493\pi$
$47$	−1.61130			−0.235032			−0.117516	+	0.993071i	$0.537493\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	5.62345	+	1.65119i	0.803349	+	0.235885i
$50$	2.40176	+	2.77178i	0.339661	+	0.391989i
$51$	−4.51520	+	2.90174i	−0.632254	+	0.406325i
$52$	3.84094	−	4.43268i	0.532642	−	0.614702i
$53$	−0.409819	+	2.85036i	−0.0562930	+	0.391526i	0.942123	+	0.335267i	$0.108826\pi$
$53$	−0.409819	+	2.85036i	−0.0562930	+	0.391526i	−0.998416	+	0.0562595i	$0.982083\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−10.3919	−	6.67848i	−1.40125	−	0.900526i
$56$	0.151894	+	1.05645i	0.0202977	+	0.141173i
$57$	−1.01042	−	2.21252i	−0.133834	−	0.293055i
$58$	3.74593	+	8.20244i	0.491865	+	1.07703i
$59$	−0.0614238	−	0.427212i	−0.00799670	−	0.0556182i	0.985432	−	0.170068i	$-0.0543987\pi$
$59$	−0.0614238	−	0.427212i	−0.00799670	−	0.0556182i	−0.993429	+	0.114450i	$0.963490\pi$
$60$	−2.47672	−	1.59169i	−0.319743	−	0.205486i
$61$	1.04061	−	0.305550i	0.133236	−	0.0391217i	−0.214434	−	0.976738i	$-0.568791\pi$
$61$	1.04061	−	0.305550i	0.133236	−	0.0391217i	0.347671	+	0.937617i	$0.386973\pi$
$62$	0.653151	−	4.54276i	0.0829502	−	0.576931i
$63$	−0.698939	+	0.806618i	−0.0880580	+	0.101624i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	11.3080	+	13.0502i	1.40259	+	1.61867i
$66$	4.02588	+	1.18211i	0.495552	+	0.145507i
$67$	−1.19561	+	2.61803i	−0.146067	+	0.319843i	−0.968498	−	0.249023i	$-0.919890\pi$
$67$	−1.19561	+	2.61803i	−0.146067	+	0.319843i	0.822430	+	0.568866i	$0.192618\pi$
$68$	5.36723			0.650872
$69$	−0.838287	−	4.72200i	−0.100918	−	0.568462i
$70$	−3.14224			−0.375570
$71$	−2.66906	+	5.84442i	−0.316759	+	0.693605i	−0.999307	−	0.0372358i	$-0.988145\pi$
$71$	−2.66906	+	5.84442i	−0.316759	+	0.693605i	0.682548	+	0.730841i	$0.260872\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	8.77594	+	10.1280i	1.02715	+	1.18539i	0.982476	+	0.186389i	$0.0596783\pi$
$73$	8.77594	+	10.1280i	1.02715	+	1.18539i	0.0446704	+	0.999002i	$0.485776\pi$
$74$	7.22349	−	4.64226i	0.839714	−	0.539651i
$75$	2.40176	−	2.77178i	0.277332	−	0.320058i
$76$	−0.346156	+	2.40757i	−0.0397068	+	0.276167i
$77$	4.29686	−	1.26167i	0.489673	−	0.143781i
$78$	−4.93418	−	3.17101i	−0.558686	−	0.359046i
$79$	0.186826	+	1.29941i	0.0210196	+	0.146195i	0.997628	−	0.0688290i	$-0.0219263\pi$
$79$	0.186826	+	1.29941i	0.0210196	+	0.146195i	−0.976609	+	0.215024i	$0.931017\pi$
$80$	1.22301	+	2.67803i	0.136737	+	0.299413i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.621496	−	4.32260i	−0.0686327	−	0.477351i
$83$	10.9598	+	7.04340i	1.20299	+	0.773114i	0.979471	−	0.201586i	$-0.0646094\pi$
$83$	10.9598	+	7.04340i	1.20299	+	0.773114i	0.223518	+	0.974700i	$0.428246\pi$
$84$	1.02408	−	0.300696i	0.111736	−	0.0328086i
$85$	−2.24879	+	15.6407i	−0.243916	+	1.69647i
$86$	−0.355697	+	0.410496i	−0.0383558	+	0.0442649i
$87$	7.58585	−	4.87513i	0.813289	−	0.522669i
$88$	−2.74769	−	3.17101i	−0.292905	−	0.338031i
$89$	−6.91251	−	2.02970i	−0.732724	−	0.215147i	−0.105976	−	0.994369i	$-0.533797\pi$
$89$	−6.91251	−	2.02970i	−0.732724	−	0.215147i	−0.626749	+	0.779221i	$0.715615\pi$
$90$	−1.22301	+	2.67803i	−0.128917	+	0.282289i
$91$	−6.26006			−0.656233
$92$	−1.84769	+	4.42561i	−0.192635	+	0.461402i
$93$	−4.58948			−0.475907
$94$	0.669357	−	1.46569i	0.0690389	−	0.151174i
$95$	−6.87088	−	2.01747i	−0.704937	−	0.206988i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	9.65194	−	6.20292i	0.980006	−	0.629812i	0.0505409	−	0.998722i	$-0.483905\pi$
$97$	9.65194	−	6.20292i	0.980006	−	0.629812i	0.929465	+	0.368910i	$0.120269\pi$
$98$	−3.83804	+	4.42934i	−0.387701	+	0.447431i
$99$	0.597131	−	4.15314i	0.0600139	−	0.417406i
$100$	−3.51903	+	1.03328i	−0.351903	+	0.103328i
$101$	−13.0578	−	8.39172i	−1.29930	−	0.835008i	−0.306162	−	0.951979i	$-0.599045\pi$
$101$	−13.0578	−	8.39172i	−1.29930	−	0.835008i	−0.993135	+	0.116972i	$0.962681\pi$
$102$	−0.763836	−	5.31260i	−0.0756310	−	0.526025i
$103$	−7.30113	−	15.9873i	−0.719402	−	1.57527i	−0.814740	−	0.579826i	$-0.803121\pi$
$103$	−7.30113	−	15.9873i	−0.719402	−	1.57527i	0.0953384	−	0.995445i	$-0.469607\pi$
$104$	2.43652	+	5.33524i	0.238921	+	0.523164i
$105$	0.447187	+	3.11026i	0.0436410	+	0.303530i
$106$	−2.42253	−	1.55686i	−0.235297	−	0.151216i
$107$	9.30959	−	2.73354i	0.899992	−	0.264262i	0.201170	−	0.979556i	$-0.435526\pi$
$107$	9.30959	−	2.73354i	0.899992	−	0.264262i	0.698823	+	0.715295i	$0.253708\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	6.46567	−	7.46178i	0.619299	−	0.714709i	−0.356275	−	0.934381i	$-0.615953\pi$
$109$	6.46567	−	7.46178i	0.619299	−	0.714709i	0.975574	+	0.219672i	$0.0704988\pi$
$110$	10.3919	−	6.67848i	0.990830	−	0.636768i
$111$	−5.62301	−	6.48930i	−0.533713	−	0.615937i
$112$	−1.02408	−	0.300696i	−0.0967660	−	0.0284131i
$113$	3.76094	−	8.23531i	0.353800	−	0.774713i	−0.646134	−	0.763224i	$-0.723615\pi$
$113$	3.76094	−	8.23531i	0.353800	−	0.774713i	0.999934	−	0.0114894i	$-0.00365726\pi$
$114$	2.43232			0.227808
$115$	−12.1226	−	7.23865i	−1.13043	−	0.675008i
$116$	−9.01732			−0.837237
$117$	−2.43652	+	5.33524i	−0.225257	+	0.493243i
$118$	0.414122	+	0.121597i	0.0381230	+	0.0111939i
$119$	−3.75136	−	4.32930i	−0.343887	−	0.396867i
$120$	2.47672	−	1.59169i	0.226092	−	0.145301i
$121$	−4.32543	+	4.99181i	−0.393221	+	0.453801i
$122$	−0.154346	+	1.07350i	−0.0139739	+	0.0971903i
$123$	−4.19015	+	1.23034i	−0.377813	+	0.110936i
$124$	3.86091	+	2.48126i	0.346720	+	0.222824i
$125$	0.558260	+	3.88278i	0.0499322	+	0.347286i
$126$	−0.443376	−	0.970858i	−0.0394991	−	0.0864909i
$127$	5.10228	+	11.1724i	0.452754	+	0.991393i	0.989080	+	0.147382i	$0.0470847\pi$
$127$	5.10228	+	11.1724i	0.452754	+	0.991393i	−0.536326	+	0.844011i	$0.680188\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	0.456938	+	0.293657i	0.0402312	+	0.0258550i
$130$	−16.5684	+	4.86491i	−1.45314	+	0.426681i
$131$	−3.19189	+	22.2001i	−0.278877	+	1.93963i	0.0585665	+	0.998284i	$0.481347\pi$
$131$	−3.19189	+	22.2001i	−0.278877	+	1.93963i	−0.337443	+	0.941346i	$0.609562\pi$
$132$	−2.74769	+	3.17101i	−0.239156	+	0.276001i
$133$	2.18393	−	1.40353i	0.189371	−	0.121701i
$134$	−1.88477	−	2.17514i	−0.162819	−	0.187903i
$135$	2.82482	+	0.829443i	0.243122	+	0.0713870i
$136$	−2.22963	+	4.88220i	−0.191189	+	0.418645i
$137$	4.22885			0.361295			0.180647	−	0.983548i	$-0.442181\pi$
$137$	4.22885			0.361295			0.180647	+	0.983548i	$0.442181\pi$
$138$	4.64352	+	1.19906i	0.395283	+	0.102071i
$139$	6.61895			0.561412			0.280706	−	0.959794i	$-0.409431\pi$
$139$	6.61895			0.561412			0.280706	+	0.959794i	$0.409431\pi$
$140$	1.30533	−	2.85828i	0.110321	−	0.241569i
$141$	−1.54603	−	0.453955i	−0.130199	−	0.0382299i
$142$	−4.20751	−	4.85572i	−0.353086	−	0.407483i
$143$	20.7031	−	13.3051i	1.73128	−	1.11262i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	3.77813	−	26.2775i	0.313757	−	2.18223i
$146$	−12.8584	+	3.77556i	−1.06417	+	0.312468i
$147$	4.93046	+	3.16862i	0.406658	+	0.261343i
$148$	1.22200	+	8.49918i	0.100448	+	0.698628i
$149$	−1.46152	−	3.20028i	−0.119732	−	0.262177i	0.840271	−	0.542167i	$-0.182396\pi$
$149$	−1.46152	−	3.20028i	−0.119732	−	0.262177i	−0.960003	+	0.279990i	$0.909669\pi$
$150$	1.52357	+	3.33616i	0.124399	+	0.272396i
$151$	−2.72272	−	18.9370i	−0.221572	−	1.54107i	−0.732094	−	0.681204i	$-0.761457\pi$
$151$	−2.72272	−	18.9370i	−0.221572	−	1.54107i	0.510522	−	0.859865i	$-0.329452\pi$
$152$	−2.04620	−	1.31501i	−0.165969	−	0.106662i
$153$	−5.14982	+	1.51212i	−0.416338	+	0.122248i
$154$	−0.637323	+	4.43268i	−0.0513570	+	0.357196i
$155$	−8.84833	+	10.2115i	−0.710715	+	0.820209i
$156$	4.93418	−	3.17101i	0.395051	−	0.253884i
$157$	15.0902	+	17.4150i	1.20433	+	1.38987i	0.899186	+	0.437566i	$0.144159\pi$
$157$	15.0902	+	17.4150i	1.20433	+	1.38987i	0.305144	+	0.952306i	$0.401295\pi$
$158$	−1.25959	−	0.369849i	−0.100208	−	0.0294236i
$159$	−1.19626	+	2.61944i	−0.0948693	+	0.207735i
$160$	−2.94408			−0.232750
$161$	4.86120	−	1.60285i	0.383116	−	0.126322i
$162$	−1.00000			−0.0785674
$163$	−3.72694	+	8.16087i	−0.291917	+	0.639209i	−0.997594	−	0.0693247i	$-0.977916\pi$
$163$	−3.72694	+	8.16087i	−0.291917	+	0.639209i	0.705677	+	0.708533i	$0.250643\pi$
$164$	4.19015	+	1.23034i	0.327196	+	0.0960734i
$165$	−8.08942	−	9.33569i	−0.629761	−	0.726783i
$166$	−10.9598	+	7.04340i	−0.850642	+	0.546674i
$167$	−3.26093	+	3.76332i	−0.252339	+	0.291214i	−0.867759	−	0.496984i	$-0.834441\pi$
$167$	−3.26093	+	3.76332i	−0.252339	+	0.291214i	0.615421	+	0.788199i	$0.288986\pi$
$168$	−0.151894	+	1.05645i	−0.0117189	+	0.0815065i
$169$	−20.5345	+	6.02949i	−1.57958	+	0.463807i
$170$	−13.2931	−	8.54295i	−1.01953	−	0.655215i
$171$	−0.346156	−	2.40757i	−0.0264712	−	0.184111i
$172$	−0.225638	−	0.494079i	−0.0172048	−	0.0376732i
$173$	−5.06771	−	11.0967i	−0.385291	−	0.843670i	−0.998552	−	0.0537896i	$-0.982870\pi$
$173$	−5.06771	−	11.0967i	−0.385291	−	0.843670i	0.613261	−	0.789880i	$-0.289857\pi$
$174$	1.28330	+	8.92554i	0.0972866	+	0.676643i
$175$	3.29305	+	2.11631i	0.248931	+	0.159978i
$176$	4.02588	−	1.18211i	0.303462	−	0.0891046i
$177$	0.0614238	−	0.427212i	0.00461689	−	0.0321112i
$178$	4.71784	−	5.44467i	0.353617	−	0.408095i
$179$	8.90515	−	5.72299i	0.665602	−	0.427757i	−0.163735	−	0.986504i	$-0.552354\pi$
$179$	8.90515	−	5.72299i	0.665602	−	0.427757i	0.829338	+	0.558748i	$0.188718\pi$
$180$	−1.92796	−	2.22499i	−0.143702	−	0.165841i
$181$	21.5175	+	6.31810i	1.59938	+	0.469620i	0.955374	−	0.295400i	$-0.0954528\pi$
$181$	21.5175	+	6.31810i	1.59938	+	0.469620i	0.644006	+	0.765020i	$0.277271\pi$
$182$	2.60052	−	5.69435i	0.192764	−	0.422093i
$183$	1.08454			0.0801716
$184$	−3.25812	−	3.51919i	−0.240192	−	0.259438i
$185$	−25.2796			−1.85859
$186$	1.90654	−	4.17473i	0.139794	−	0.306106i
$187$	21.6078	+	6.34463i	1.58012	+	0.463965i
$188$	1.05518	+	1.21774i	0.0769566	+	0.0888126i
$189$	−0.897877	+	0.577031i	−0.0653110	+	0.0419728i
$190$	4.68942	−	5.41188i	0.340207	−	0.392619i
$191$	0.807404	−	5.61562i	0.0584217	−	0.406332i	−0.939536	−	0.342451i	$-0.888743\pi$
$191$	0.807404	−	5.61562i	0.0584217	−	0.406332i	0.997958	−	0.0638812i	$-0.0203479\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	1.61317	+	1.03672i	0.116119	+	0.0746250i	0.597411	−	0.801935i	$-0.296196\pi$
$193$	1.61317	+	1.03672i	0.116119	+	0.0746250i	−0.481292	+	0.876560i	$0.659832\pi$
$194$	1.63282	+	11.3565i	0.117230	+	0.815349i
$195$	7.17331	+	15.7074i	0.513692	+	1.12483i
$196$	−2.43469	−	5.33122i	−0.173906	−	0.380801i
$197$	−1.14154	−	7.93960i	−0.0813315	−	0.565673i	−0.989217	−	0.146455i	$-0.953213\pi$
$197$	−1.14154	−	7.93960i	−0.0813315	−	0.565673i	0.907886	−	0.419218i	$-0.137696\pi$
$198$	3.52977	+	2.26844i	0.250850	+	0.161211i
$199$	14.4780	−	4.25114i	1.02632	−	0.301355i	0.275107	−	0.961414i	$-0.411287\pi$
$199$	14.4780	−	4.25114i	1.02632	−	0.301355i	0.751214	+	0.660059i	$0.229469\pi$
$200$	0.521953	−	3.63026i	0.0369077	−	0.256698i
$201$	−1.88477	+	2.17514i	−0.132941	+	0.153422i
$202$	13.0578	−	8.39172i	0.918742	−	0.590439i
$203$	6.30255	+	7.27354i	0.442353	+	0.510502i
$204$	5.14982	+	1.51212i	0.360559	+	0.105870i
$205$	−5.34096	+	11.6951i	−0.373029	+	0.816819i
$206$	17.5755			1.22454
$207$	0.526011	−	4.76690i	0.0365603	−	0.331322i
$208$	−5.86528			−0.406684
$209$	−4.23958	+	9.28338i	−0.293258	+	0.642145i
$210$	−3.01496	−	0.885271i	−0.208052	−	0.0610895i
$211$	14.4100	+	16.6300i	0.992024	+	1.14486i	0.989452	+	0.144860i	$0.0462730\pi$
$211$	14.4100	+	16.6300i	0.992024	+	1.14486i	0.00257137	+	0.999997i	$0.499182\pi$
$212$	2.42253	−	1.55686i	0.166380	−	0.106926i
$213$	−4.20751	+	4.85572i	−0.288294	+	0.332709i
$214$	−1.38083	+	9.60386i	−0.0943914	+	0.656506i
$215$	1.53434	−	0.450523i	0.104641	−	0.0307254i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−0.697114	−	4.84853i	−0.0473231	−	0.329140i
$218$	4.10154	+	8.98111i	0.277791	+	0.608278i
$219$	5.56708	+	12.1902i	0.376188	+	0.823737i
$220$	1.75800	+	12.2272i	0.118524	+	0.824355i
$221$	−26.4829	−	17.0195i	−1.78143	−	1.14486i
$222$	8.23876	−	2.41912i	0.552950	−	0.162361i
$223$	3.16488	−	22.0122i	0.211936	−	1.47405i	−0.554746	−	0.832020i	$-0.687184\pi$
$223$	3.16488	−	22.0122i	0.211936	−	1.47405i	0.766682	−	0.642027i	$-0.221906\pi$
$224$	0.698939	−	0.806618i	0.0466998	−	0.0538944i
$225$	3.08538	−	1.98285i	0.205692	−	0.132190i
$226$	5.92875	+	6.84214i	0.394375	+	0.455133i
$227$	−13.5344	−	3.97405i	−0.898307	−	0.263767i	−0.200196	−	0.979756i	$-0.564158\pi$
$227$	−13.5344	−	3.97405i	−0.898307	−	0.263767i	−0.698111	+	0.715989i	$0.745976\pi$
$228$	−1.01042	+	2.21252i	−0.0669169	+	0.146528i
$229$	−8.87229			−0.586297			−0.293149	−	0.956067i	$-0.594703\pi$
$229$	−8.87229			−0.586297			−0.293149	+	0.956067i	$0.594703\pi$
$230$	11.6204	−	8.02003i	0.766227	−	0.528825i
$231$	4.47826			0.294648
$232$	3.74593	−	8.20244i	0.245932	−	0.538517i
$233$	−6.87234	−	2.01790i	−0.450222	−	0.132197i	0.0487581	−	0.998811i	$-0.484474\pi$
$233$	−6.87234	−	2.01790i	−0.450222	−	0.132197i	−0.498980	+	0.866614i	$0.666292\pi$
$234$	−3.84094	−	4.43268i	−0.251090	−	0.289773i
$235$	−3.99073	+	2.56468i	−0.260326	+	0.167302i
$236$	−0.282641	+	0.326185i	−0.0183984	+	0.0212329i
$237$	−0.186826	+	1.29941i	−0.0121357	+	0.0844054i
$238$	5.49644	−	1.61390i	0.356282	−	0.104614i
$239$	17.9431	+	11.5313i	1.16064	+	0.745900i	0.971730	−	0.236093i	$-0.0758671\pi$
$239$	17.9431	+	11.5313i	1.16064	+	0.745900i	0.188913	+	0.981994i	$0.439503\pi$
$240$	0.418986	+	2.91411i	0.0270454	+	0.188105i
$241$	−7.03867	−	15.4125i	−0.453401	−	0.992809i	−0.988942	−	0.148300i	$-0.952620\pi$
$241$	−7.03867	−	15.4125i	−0.453401	−	0.992809i	0.535542	−	0.844509i	$-0.320107\pi$
$242$	−2.74386	−	6.00822i	−0.176382	−	0.386223i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	−0.912374	−	0.586347i	−0.0584087	−	0.0375370i
$245$	16.5559	−	4.86124i	1.05772	−	0.310573i
$246$	0.621496	−	4.32260i	0.0396251	−	0.275599i
$247$	9.34240	−	10.7817i	0.594443	−	0.686024i
$248$	−3.86091	+	2.48126i	−0.245168	+	0.157560i
$249$	8.53145	+	9.84582i	0.540659	+	0.623953i
$250$	−3.76381	−	1.10515i	−0.238044	−	0.0698961i
$251$	−12.3350	+	27.0099i	−0.778579	+	1.70485i	−0.0717955	+	0.997419i	$0.522873\pi$
$251$	−12.3350	+	27.0099i	−0.778579	+	1.70485i	−0.706783	+	0.707430i	$0.749854\pi$
$252$	1.06731			0.0672341
$253$	−12.6701	+	15.6328i	−0.796565	+	0.982827i
$254$	−12.2824			−0.770664
$255$	−6.56419	+	14.3736i	−0.411066	+	0.900108i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−3.09138	−	3.56764i	−0.192835	−	0.222543i	0.651096	−	0.758996i	$-0.274310\pi$
$257$	−3.09138	−	3.56764i	−0.192835	−	0.222543i	−0.843931	+	0.536452i	$0.819764\pi$
$258$	−0.456938	+	0.293657i	−0.0284477	+	0.0182823i
$259$	6.00149	−	6.92609i	0.372915	−	0.430366i
$260$	2.45747	−	17.0921i	0.152406	−	1.06000i
$261$	8.65206	−	2.54047i	0.535549	−	0.157251i
$262$	−18.8679	−	12.1257i	−1.16567	−	0.749127i
$263$	−2.76109	−	19.2038i	−0.170256	−	1.18416i	−0.878342	−	0.478033i	$-0.841350\pi$
$263$	−2.76109	−	19.2038i	−0.170256	−	1.18416i	0.708086	−	0.706126i	$-0.249559\pi$
$264$	−1.74302	−	3.81667i	−0.107275	−	0.234900i
$265$	3.52187	+	7.71182i	0.216347	+	0.473734i
$266$	0.369455	+	2.56962i	0.0226527	+	0.157553i
$267$	−6.06067	−	3.89496i	−0.370907	−	0.238367i
$268$	2.76153	−	0.810859i	0.168687	−	0.0495311i
$269$	−0.313108	+	2.17772i	−0.0190905	+	0.132778i	−0.997138	−	0.0756055i	$-0.975911\pi$
$269$	−0.313108	+	2.17772i	−0.0190905	+	0.132778i	0.978047	+	0.208383i	$0.0668201\pi$
$270$	−1.92796	+	2.22499i	−0.117332	+	0.135408i
$271$	−24.4453	+	15.7101i	−1.48495	+	0.954319i	−0.488287	+	0.872683i	$0.662378\pi$
$271$	−24.4453	+	15.7101i	−1.48495	+	0.954319i	−0.996662	+	0.0816353i	$0.973986\pi$
$272$	−3.51479	−	4.05628i	−0.213115	−	0.245948i
$273$	−6.00648	−	1.76366i	−0.363529	−	0.106742i
$274$	−1.75673	+	3.84669i	−0.106128	+	0.232387i
$275$	−15.3887			−0.927971
$276$	−3.01969	+	3.72579i	−0.181764	+	0.224266i
$277$	5.48016			0.329271			0.164636	−	0.986354i	$-0.447355\pi$
$277$	5.48016			0.329271			0.164636	+	0.986354i	$0.447355\pi$
$278$	−2.74961	+	6.02081i	−0.164911	+	0.361104i
$279$	−4.40357	−	1.29301i	−0.263635	−	0.0774102i
$280$	2.05773	+	2.37475i	0.122973	+	0.141918i
$281$	−16.1491	+	10.3784i	−0.963377	+	0.619125i	−0.924931	−	0.380136i	$-0.875877\pi$
$281$	−16.1491	+	10.3784i	−0.963377	+	0.619125i	−0.0384466	+	0.999261i	$0.512241\pi$
$282$	1.05518	−	1.21774i	0.0628348	−	0.0725152i
$283$	−1.95699	+	13.6111i	−0.116331	+	0.809098i	0.845210	+	0.534435i	$0.179475\pi$
$283$	−1.95699	+	13.6111i	−0.116331	+	0.809098i	−0.961540	+	0.274663i	$0.911434\pi$
$284$	6.16478	−	1.81014i	0.365813	−	0.107412i
$285$	−6.02417	−	3.87150i	−0.356841	−	0.229328i
$286$	3.50234	+	24.3593i	0.207098	+	1.44040i
$287$	−1.93624	−	4.23978i	−0.114293	−	0.250267i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−1.68033	−	11.6869i	−0.0988428	−	0.687467i
$290$	22.3333	+	14.3528i	1.31146	+	0.842823i
$291$	11.0085	−	3.23240i	0.645332	−	0.189486i
$292$	1.90719	−	13.2648i	0.111610	−	0.776266i
$293$	0.556992	−	0.642804i	0.0325398	−	0.0375530i	−0.739246	−	0.673435i	$-0.764818\pi$
$293$	0.556992	−	0.642804i	0.0325398	−	0.0375530i	0.771786	+	0.635882i	$0.219364\pi$
$294$	−4.93046	+	3.16862i	−0.287550	+	0.184797i
$295$	−0.832117	−	0.960315i	−0.0484478	−	0.0559117i
$296$	−8.23876	−	2.41912i	−0.478868	−	0.140608i
$297$	1.74302	−	3.81667i	0.101140	−	0.221466i
$298$	3.51821			0.203805
$299$	23.1505	−	15.9777i	1.33883	−	0.924016i
$300$	−3.66759			−0.211749
$301$	−0.240826	+	0.527335i	−0.0138810	+	0.0303951i
$302$	18.3567	+	5.39002i	1.05631	+	0.310161i
$303$	−10.1646	−	11.7306i	−0.583942	−	0.673905i
$304$	2.04620	−	1.31501i	0.117358	−	0.0754212i
$305$	2.09095	−	2.41309i	0.119728	−	0.138173i
$306$	0.763836	−	5.31260i	0.0436656	−	0.303701i
$307$	−6.52363	+	1.91551i	−0.372323	+	0.109324i	−0.462540	−	0.886598i	$-0.653062\pi$
$307$	−6.52363	+	1.91551i	−0.372323	+	0.109324i	0.0902174	+	0.995922i	$0.471244\pi$
$308$	−3.76735	−	2.42113i	−0.214665	−	0.137957i
$309$	−2.50126	−	17.3966i	−0.142292	−	0.989659i
$310$	−5.61299	−	12.2907i	−0.318797	−	0.698067i
$311$	−5.96225	−	13.0555i	−0.338088	−	0.740310i	0.661868	−	0.749620i	$-0.269764\pi$
$311$	−5.96225	−	13.0555i	−0.338088	−	0.740310i	−0.999957	+	0.00931005i	$0.997036\pi$
$312$	0.834716	+	5.80558i	0.0472565	+	0.328676i
$313$	2.78966	+	1.79280i	0.157681	+	0.101335i	0.617102	−	0.786883i	$-0.288307\pi$
$313$	2.78966	+	1.79280i	0.157681	+	0.101335i	−0.459421	+	0.888219i	$0.651943\pi$
$314$	−22.1100	+	6.49208i	−1.24774	+	0.366369i
$315$	−0.447187	+	3.11026i	−0.0251962	+	0.175243i
$316$	0.859680	−	0.992123i	0.0483608	−	0.0558113i
$317$	−16.4694	+	10.5842i	−0.925012	+	0.594469i	−0.914108	−	0.405472i	$-0.867107\pi$
$317$	−16.4694	+	10.5842i	−0.925012	+	0.594469i	−0.0109042	+	0.999941i	$0.503471\pi$
$318$	−1.88578	−	2.17631i	−0.105749	−	0.122041i
$319$	−36.3027	−	10.6594i	−2.03256	−	0.596813i
$320$	1.22301	−	2.67803i	0.0683686	−	0.149706i
$321$	9.70262			0.541547
$322$	−0.561416	+	5.08775i	−0.0312865	+	0.283529i
$323$	13.0548			0.726390
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	20.6401	+	6.06048i	1.14491	+	0.336175i
$326$	−5.87516	−	6.78030i	−0.325395	−	0.375526i
$327$	8.30599	−	5.33794i	0.459322	−	0.295188i
$328$	−2.85981	+	3.30039i	−0.157906	+	0.182234i
$329$	0.244746	−	1.70225i	0.0134933	−	0.0938479i
$330$	11.8525	−	3.48021i	0.652459	−	0.191579i
$331$	3.01005	+	1.93444i	0.165447	+	0.106327i	0.620744	−	0.784013i	$-0.286831\pi$
$331$	3.01005	+	1.93444i	0.165447	+	0.106327i	−0.455297	+	0.890340i	$0.650467\pi$
$332$	−1.85406	−	12.8953i	−0.101755	−	0.707720i
$333$	−3.56699	−	7.81063i	−0.195470	−	0.428020i
$334$	−2.06859	−	4.52959i	−0.113188	−	0.247848i
$335$	1.20589	+	8.38715i	0.0658848	+	0.458239i
$336$	−0.897877	−	0.577031i	−0.0489832	−	0.0314796i
$337$	−26.1806	+	7.68732i	−1.42615	+	0.418755i	−0.901580	−	0.432613i	$-0.857591\pi$
$337$	−26.1806	+	7.68732i	−1.42615	+	0.418755i	−0.524568	+	0.851368i	$0.675773\pi$
$338$	3.04575	−	21.1836i	0.165667	−	1.15224i
$339$	5.92875	−	6.84214i	0.322006	−	0.371614i
$340$	13.2931	−	8.54295i	0.720919	−	0.463307i
$341$	12.6105	+	14.5533i	0.682896	+	0.788103i
$342$	2.33380	+	0.685265i	0.126197	+	0.0370549i
$343$	−5.70219	+	12.4861i	−0.307890	+	0.674184i
$344$	0.543164			0.0292854
$345$	−9.59215	−	10.3608i	−0.516424	−	0.557804i
$346$	12.1992			0.655831
$347$	10.8471	−	23.7519i	0.582304	−	1.27507i	−0.357679	−	0.933845i	$-0.616432\pi$
$347$	10.8471	−	23.7519i	0.582304	−	1.27507i	0.939982	−	0.341223i	$-0.110841\pi$
$348$	−8.65206	−	2.54047i	−0.463799	−	0.136184i
$349$	−10.8357	−	12.5051i	−0.580022	−	0.669381i	0.387588	−	0.921833i	$-0.373308\pi$
$349$	−10.8357	−	12.5051i	−0.580022	−	0.669381i	−0.967609	+	0.252452i	$0.918763\pi$
$350$	−3.29305	+	2.11631i	−0.176021	+	0.113122i
$351$	−3.84094	+	4.43268i	−0.205014	+	0.236599i
$352$	−0.597131	+	4.15314i	−0.0318272	+	0.221363i
$353$	7.19931	−	2.11391i	0.383181	−	0.112512i	−0.0844685	−	0.996426i	$-0.526919\pi$
$353$	7.19931	−	2.11391i	0.383181	−	0.112512i	0.467649	+	0.883914i	$0.345101\pi$
$354$	0.363089	+	0.233343i	0.0192980	+	0.0124021i
$355$	2.69200	+	18.7233i	0.142877	+	0.993729i
$356$	2.99279	+	6.55329i	0.158617	+	0.347324i
$357$	−2.37970	−	5.21082i	−0.125947	−	0.275786i
$358$	1.50648	+	10.4778i	0.0796202	+	0.553771i
$359$	−2.88413	−	1.85351i	−0.152218	−	0.0978248i	0.462315	−	0.886716i	$-0.347019\pi$
$359$	−2.88413	−	1.85351i	−0.152218	−	0.0978248i	−0.614533	+	0.788891i	$0.710655\pi$
$360$	2.82482	−	0.829443i	0.148881	−	0.0437155i
$361$	1.86202	−	12.9506i	0.0980010	−	0.681612i
$362$	−14.6858	+	16.9483i	−0.771870	+	0.890785i
$363$	−5.55657	+	3.57099i	−0.291644	+	0.187428i
$364$	4.09947	+	4.73104i	0.214871	+	0.247974i
$365$	37.8561	+	11.1156i	1.98148	+	0.581815i
$366$	−0.450535	+	0.986533i	−0.0235498	+	0.0515669i
$367$	−6.27368			−0.327483			−0.163742	−	0.986503i	$-0.552356\pi$
$367$	−6.27368			−0.327483			−0.163742	+	0.986503i	$0.552356\pi$
$368$	4.55464	−	1.50176i	0.237427	−	0.0782849i
$369$	−4.36705			−0.227339
$370$	10.5015	−	22.9951i	0.545947	−	1.19546i
$371$	−2.94900	−	0.865903i	−0.153104	−	0.0449554i
$372$	3.00547	+	3.46850i	0.155826	+	0.179833i
$373$	−8.62549	+	5.54327i	−0.446611	+	0.287019i	−0.744552	−	0.667565i	$-0.767337\pi$
$373$	−8.62549	+	5.54327i	−0.446611	+	0.287019i	0.297941	+	0.954584i	$0.403700\pi$
$374$	−14.7475	+	17.0195i	−0.762575	+	0.880058i
$375$	−0.558260	+	3.88278i	−0.0288284	+	0.200506i
$376$	−1.54603	+	0.453955i	−0.0797303	+	0.0234109i
$377$	44.4931	+	28.5940i	2.29151	+	1.47267i
$378$	−0.151894	−	1.05645i	−0.00781258	−	0.0543377i
$379$	−8.22602	−	18.0125i	−0.422542	−	0.925238i	−0.994479	−	0.104940i	$-0.966535\pi$
$379$	−8.22602	−	18.0125i	−0.422542	−	0.925238i	0.571936	−	0.820298i	$-0.306192\pi$
$380$	2.97477	+	6.51383i	0.152602	+	0.334152i
$381$	1.74796	+	12.1573i	0.0895509	+	0.622840i
$382$	4.77274	+	3.06725i	0.244195	+	0.156934i
$383$	6.43842	−	1.89049i	0.328988	−	0.0965996i	−0.113068	−	0.993587i	$-0.536068\pi$
$383$	6.43842	−	1.89049i	0.328988	−	0.0965996i	0.442055	+	0.896988i	$0.354249\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	8.63391	−	9.96407i	0.440025	−	0.507816i
$386$	−1.61317	+	1.03672i	−0.0821084	+	0.0527678i
$387$	0.355697	+	0.410496i	0.0180811	+	0.0208667i
$388$	−11.0085	−	3.23240i	−0.558874	−	0.164100i
$389$	−4.92999	+	10.7952i	−0.249960	+	0.547337i	−0.992468	−	0.122500i	$-0.960909\pi$
$389$	−4.92999	+	10.7952i	−0.249960	+	0.547337i	0.742508	+	0.669837i	$0.233636\pi$
$390$	−17.2678			−0.874390
$391$	24.9228	+	6.43561i	1.26040	+	0.325463i
$392$	5.86085			0.296018
$393$	−9.31708	+	20.4016i	−0.469984	+	1.02912i
$394$	7.69633	+	2.25985i	0.387735	+	0.113849i
$395$	2.53096	+	2.92089i	0.127347	+	0.146966i
$396$	−3.52977	+	2.26844i	−0.177378	+	0.113994i
$397$	−3.14471	+	3.62919i	−0.157828	+	0.182144i	−0.829156	−	0.559017i	$-0.811179\pi$
$397$	−3.14471	+	3.62919i	−0.157828	+	0.182144i	0.671328	+	0.741160i	$0.265724\pi$
$398$	−2.14743	+	14.9357i	−0.107641	+	0.748658i
$399$	2.49088	−	0.731389i	0.124700	−	0.0366152i
$400$	3.08538	+	1.98285i	0.154269	+	0.0991425i
$401$	−2.30938	−	16.0621i	−0.115325	−	0.802102i	−0.962596	−	0.270941i	$-0.912665\pi$
$401$	−2.30938	−	16.0621i	−0.115325	−	0.802102i	0.847271	−	0.531161i	$-0.178244\pi$
$402$	−1.19561	−	2.61803i	−0.0596317	−	0.130575i
$403$	−11.1824	−	24.4860i	−0.557033	−	1.21973i
$404$	2.20898	+	15.3638i	0.109901	+	0.764378i
$405$	2.47672	+	1.59169i	0.123069	+	0.0790916i
$406$	−9.23442	+	2.71147i	−0.458296	+	0.134568i
$407$	−5.12731	+	35.6612i	−0.254151	+	1.76766i
$408$	−3.51479	+	4.05628i	−0.174008	+	0.200816i
$409$	21.6257	−	13.8980i	1.06932	−	0.687212i	0.117255	−	0.993102i	$-0.462590\pi$
$409$	21.6257	−	13.8980i	1.06932	−	0.687212i	0.952067	+	0.305890i	$0.0989540\pi$
$410$	−8.41950	−	9.71662i	−0.415809	−	0.479869i
$411$	4.05755	+	1.19140i	0.200144	+	0.0587676i
$412$	−7.30113	+	15.9873i	−0.359701	+	0.787635i
$413$	0.460656			0.0226674
$414$	4.11761	+	2.45872i	0.202369	+	0.120839i
$415$	38.3551			1.88278
$416$	2.43652	−	5.33524i	0.119460	−	0.261582i
$417$	6.35084	+	1.86477i	0.311002	+	0.0913184i
$418$	−6.68328	−	7.71291i	−0.326890	−	0.377251i
$419$	−1.28477	+	0.825669i	−0.0627649	+	0.0403366i	−0.571647	−	0.820500i	$-0.693695\pi$
$419$	−1.28477	+	0.825669i	−0.0627649	+	0.0403366i	0.508882	+	0.860836i	$0.330059\pi$
$420$	2.05773	−	2.37475i	0.100407	−	0.115876i
$421$	2.17221	−	15.1080i	0.105867	−	0.736320i	−0.865873	−	0.500264i	$-0.833236\pi$
$421$	2.17221	−	15.1080i	0.105867	−	0.736320i	0.971740	−	0.236056i	$-0.0758547\pi$
$422$	−21.1133	+	6.19942i	−1.02778	+	0.301783i
$423$	−1.35551	−	0.871133i	−0.0659071	−	0.0423559i
$424$	0.409819	+	2.85036i	0.0199026	+	0.138425i
$425$	8.17736	+	17.9059i	0.396660	+	0.868565i
$426$	−2.66906	−	5.84442i	−0.129316	−	0.283163i
$427$	0.164735	+	1.14576i	0.00797209	+	0.0554471i
$428$	−8.16236	−	5.24563i	−0.394543	−	0.253557i
$429$	23.6129	−	6.93338i	1.14004	−	0.334747i
$430$	−0.227578	+	1.58284i	−0.0109748	+	0.0763313i
$431$	−1.10430	+	1.27443i	−0.0531924	+	0.0613873i	−0.781722	−	0.623627i	$-0.785659\pi$
$431$	−1.10430	+	1.27443i	−0.0531924	+	0.0613873i	0.728530	+	0.685014i	$0.240204\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	−9.91925	−	11.4474i	−0.476689	−	0.550128i	0.465571	−	0.885010i	$-0.345849\pi$
$433$	−9.91925	−	11.4474i	−0.476689	−	0.550128i	−0.942260	+	0.334882i	$0.891303\pi$
$434$	4.69997	+	1.38004i	0.225606	+	0.0662438i
$435$	11.0283	−	24.1486i	0.528767	−	1.15784i
$436$	−9.87335			−0.472848
$437$	−4.49419	+	10.7645i	−0.214986	+	0.514937i
$438$	−13.4012			−0.640336
$439$	−7.06459	+	15.4693i	−0.337175	+	0.738309i	−0.999945	−	0.0105135i	$-0.996653\pi$
$439$	−7.06459	+	15.4693i	−0.337175	+	0.738309i	0.662770	+	0.748823i	$0.269381\pi$
$440$	−11.8525	−	3.48021i	−0.565046	−	0.165913i
$441$	3.83804	+	4.42934i	0.182764	+	0.210921i
$442$	26.4829	−	17.0195i	1.25966	−	0.809536i
$443$	9.98045	−	11.5180i	0.474185	−	0.547239i	−0.467386	−	0.884054i	$-0.654804\pi$
$443$	9.98045	−	11.5180i	0.474185	−	0.547239i	0.941571	+	0.336814i	$0.109350\pi$
$444$	−1.22200	+	8.49918i	−0.0579934	+	0.403353i
$445$	−20.3510	+	5.97558i	−0.964728	+	0.283270i
$446$	18.7083	+	12.0231i	0.885863	+	0.569310i
$447$	−0.500694	−	3.48240i	−0.0236820	−	0.164712i
$448$	0.443376	+	0.970858i	0.0209476	+	0.0458687i
$449$	−0.207060	−	0.453399i	−0.00977177	−	0.0213972i	0.904683	−	0.426085i	$-0.140108\pi$
$449$	−0.207060	−	0.453399i	−0.00977177	−	0.0213972i	−0.914455	+	0.404688i	$0.867380\pi$
$450$	0.521953	+	3.63026i	0.0246051	+	0.171132i
$451$	15.4147	+	9.90640i	0.725848	+	0.466474i
$452$	−8.68673	+	2.55065i	−0.408589	+	0.119973i
$453$	2.72272	−	18.9370i	0.127925	−	0.889736i
$454$	9.23730	−	10.6604i	0.433528	−	0.500318i
$455$	−15.5044	+	9.96407i	−0.726857	+	0.467123i
$456$	−1.59283	−	1.83823i	−0.0745912	−	0.0860829i
$457$	7.30868	+	2.14602i	0.341886	+	0.100387i	0.448168	−	0.893949i	$-0.352077\pi$
$457$	7.30868	+	2.14602i	0.341886	+	0.100387i	−0.106282	+	0.994336i	$0.533895\pi$
$458$	3.68568	−	8.07052i	0.172221	−	0.377111i
$459$	−5.36723			−0.250521
$460$	2.46798	+	13.9019i	0.115070	+	0.648181i
$461$	14.5940			0.679709			0.339855	−	0.940478i	$-0.389622\pi$
$461$	14.5940			0.679709			0.339855	+	0.940478i	$0.389622\pi$
$462$	−1.86034	+	4.07357i	−0.0865507	+	0.189520i
$463$	−33.4669	−	9.82675i	−1.55534	−	0.456688i	−0.612646	−	0.790357i	$-0.709895\pi$
$463$	−33.4669	−	9.82675i	−1.55534	−	0.456688i	−0.942690	+	0.333669i	$0.891713\pi$
$464$	5.90509	+	6.81484i	0.274137	+	0.316371i
$465$	−11.3668	+	7.30502i	−0.527124	+	0.338762i
$466$	4.69042	−	5.41303i	0.217279	−	0.250754i
$467$	−1.81080	+	12.5944i	−0.0837939	+	0.582799i	0.904059	+	0.427407i	$0.140573\pi$
$467$	−1.81080	+	12.5944i	−0.0837939	+	0.582799i	−0.987853	+	0.155392i	$0.950336\pi$
$468$	5.62769	−	1.65244i	0.260140	−	0.0763840i
$469$	−2.58420	−	1.66076i	−0.119327	−	0.0766869i
$470$	−0.675111	−	4.69550i	−0.0311405	−	0.216587i
$471$	9.57258	+	20.9610i	0.441081	+	0.965833i
$472$	−0.179295	−	0.392602i	−0.00825273	−	0.0180710i
$473$	−0.324340	−	2.25583i	−0.0149132	−	0.103723i
$474$	−1.10437	−	0.709736i	−0.0507254	−	0.0325992i
$475$	−8.55942	+	2.51327i	−0.392733	+	0.115317i
$476$	−0.815249	+	5.67018i	−0.0373669	+	0.259892i
$477$	−1.88578	+	2.17631i	−0.0863439	+	0.0996462i
$478$	−17.9431	+	11.5313i	−0.820699	+	0.527431i
$479$	−4.39108	−	5.06758i	−0.200634	−	0.231544i	0.646513	−	0.762903i	$-0.276227\pi$
$479$	−4.39108	−	5.06758i	−0.200634	−	0.231544i	−0.847146	+	0.531360i	$0.821681\pi$
$480$	−2.82482	−	0.829443i	−0.128935	−	0.0378587i
$481$	20.9214	−	45.8115i	0.953934	−	2.08882i
$482$	16.9437			0.771765
$483$	5.11586	−	0.168361i	0.232780	−	0.00766070i
$484$	6.60511			0.300232
$485$	14.0320	−	30.7258i	0.637160	−	1.39518i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	19.5530	+	22.5653i	0.886030	+	1.02253i	0.999579	+	0.0290004i	$0.00923241\pi$
$487$	19.5530	+	22.5653i	0.886030	+	1.02253i	−0.113550	+	0.993532i	$0.536222\pi$
$488$	0.912374	−	0.586347i	0.0413012	−	0.0265427i
$489$	−5.87516	+	6.78030i	−0.265684	+	0.306616i
$490$	−2.45561	+	17.0792i	−0.110933	+	0.771558i
$491$	−4.98861	+	1.46479i	−0.225133	+	0.0661049i	−0.392353	−	0.919815i	$-0.628339\pi$
$491$	−4.98861	+	1.46479i	−0.225133	+	0.0661049i	0.167221	+	0.985919i	$0.446521\pi$
$492$	3.67379	+	2.36100i	0.165627	+	0.106442i
$493$	6.88775	+	47.9054i	0.310209	+	2.15755i
$494$	5.92641	+	12.9770i	0.266642	+	0.583864i
$495$	−5.13158	−	11.2366i	−0.230647	−	0.505047i
$496$	−0.653151	−	4.54276i	−0.0293273	−	0.203976i
$497$	−5.76890	−	3.70745i	−0.258771	−	0.166302i
$498$	−12.5002	+	3.67038i	−0.560146	+	0.164474i
$499$	2.00133	−	13.9195i	0.0895916	−	0.623124i	−0.894712	−	0.446643i	$-0.852620\pi$
$499$	2.00133	−	13.9195i	0.0895916	−	0.623124i	0.984304	−	0.176481i	$-0.0564714\pi$
$500$	2.56883	−	2.96458i	0.114881	−	0.132580i
$501$	−4.18909	+	2.69217i	−0.187155	+	0.120277i
$502$	−19.4449	−	22.4406i	−0.867869	−	1.00157i
$503$	23.7212	+	6.96518i	1.05768	+	0.310562i	0.763915	−	0.645317i	$-0.223275\pi$
$503$	23.7212	+	6.96518i	1.05768	+	0.310562i	0.293762	+	0.955879i	$0.405093\pi$
$504$	−0.443376	+	0.970858i	−0.0197495	+	0.0432455i
$505$	−45.6974			−2.03351
$506$	−8.95675	−	18.0193i	−0.398176	−	0.801054i
$507$	−21.4015			−0.950472
$508$	5.10228	−	11.1724i	0.226377	−	0.495697i
$509$	−17.5533	−	5.15410i	−0.778035	−	0.228452i	−0.131480	−	0.991319i	$-0.541973\pi$
$509$	−17.5533	−	5.15410i	−0.778035	−	0.228452i	−0.646555	+	0.762867i	$0.723791\pi$
$510$	−10.3478	−	11.9420i	−0.458208	−	0.528801i
$511$	−12.0327	+	7.73293i	−0.532294	+	0.342085i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.346156	−	2.40757i	0.0152831	−	0.106297i
$514$	4.52944	−	1.32997i	0.199785	−	0.0586622i
$515$	−43.5296	−	27.9747i	−1.91814	−	1.23271i
$516$	−0.0773003	−	0.537635i	−0.00340295	−	0.0236681i
$517$	2.80852	+	6.14980i	0.123518	+	0.270468i
$518$	3.80708	+	8.33635i	0.167274	+	0.366278i
$519$	−1.73612	−	12.0750i	−0.0762073	−	0.530033i
$520$	14.5266	+	9.33569i	0.637034	+	0.409397i
$521$	15.8178	−	4.64451i	0.692988	−	0.203480i	0.0837733	−	0.996485i	$-0.473303\pi$
$521$	15.8178	−	4.64451i	0.692988	−	0.203480i	0.609215	+	0.793005i	$0.291485\pi$
$522$	−1.28330	+	8.92554i	−0.0561684	+	0.390660i
$523$	10.6183	−	12.2542i	0.464306	−	0.535837i	−0.474513	−	0.880248i	$-0.657376\pi$
$523$	10.6183	−	12.2542i	0.464306	−	0.535837i	0.938819	+	0.344411i	$0.111921\pi$
$524$	18.8679	−	12.1257i	0.824250	−	0.529713i
$525$	2.56342	+	2.95835i	0.111877	+	0.129113i
$526$	18.6154	+	5.46598i	0.811671	+	0.238328i
$527$	10.2328	−	22.4067i	0.445749	−	0.976053i
$528$	4.19584			0.182601
$529$	−13.8864	+	18.3349i	−0.603755	+	0.797170i
$530$	−8.47796			−0.368259
$531$	0.179295	−	0.392602i	0.00778075	−	0.0170375i
$532$	−2.49088	−	0.731389i	−0.107993	−	0.0317097i
$533$	−16.7736	−	19.3577i	−0.726544	−	0.838476i
$534$	6.06067	−	3.89496i	0.262271	−	0.168551i
$535$	18.7063	−	21.5882i	0.808742	−	0.933339i
$536$	−0.409599	+	2.84882i	−0.0176920	+	0.123050i
$537$	10.1568	−	2.98230i	0.438298	−	0.128696i
$538$	−1.85085	−	1.18947i	−0.0797958	−	0.0512817i
$539$	−3.49970	−	24.3409i	−0.150743	−	1.04844i
$540$	−1.22301	−	2.67803i	−0.0526301	−	0.115244i
$541$	−2.89899	−	6.34790i	−0.124637	−	0.272917i	0.837020	−	0.547173i	$-0.184296\pi$
$541$	−2.89899	−	6.34790i	−0.124637	−	0.272917i	−0.961657	+	0.274255i	$0.911569\pi$
$542$	−4.13542	−	28.7625i	−0.177631	−	1.23545i
$543$	18.8658	+	12.1243i	0.809611	+	0.520305i
$544$	5.14982	−	1.51212i	0.220797	−	0.0648317i
$545$	4.13679	−	28.7720i	0.177201	−	1.23246i
$546$	4.09947	−	4.73104i	0.175441	−	0.202470i
$547$	−36.0522	+	23.1693i	−1.54148	+	0.990649i	−0.554070	+	0.832470i	$0.686926\pi$
$547$	−36.0522	+	23.1693i	−1.54148	+	0.990649i	−0.987410	+	0.158179i	$0.949438\pi$
$548$	−2.76931	−	3.19595i	−0.118299	−	0.136524i
$549$	1.04061	+	0.305550i	0.0444121	+	0.0130406i
$550$	6.39268	−	13.9980i	0.272585	−	0.596877i
$551$	−21.9330			−0.934379
$552$	−2.13467	−	4.29455i	−0.0908576	−	0.182788i
$553$	−1.40113			−0.0595820
$554$	−2.27654	+	4.98493i	−0.0967210	+	0.211789i
$555$	−24.2556	−	7.12207i	−1.02959	−	0.302315i
$556$	−4.33449	−	5.00227i	−0.183823	−	0.212144i
$557$	−19.4597	+	12.5060i	−0.824536	+	0.529897i	−0.883537	−	0.468361i	$-0.844845\pi$
$557$	−19.4597	+	12.5060i	−0.824536	+	0.529897i	0.0590015	+	0.998258i	$0.481208\pi$
$558$	3.00547	−	3.46850i	0.127232	−	0.146833i
$559$	−0.453387	+	3.15338i	−0.0191762	+	0.133374i
$560$	−3.01496	+	0.885271i	−0.127405	+	0.0374095i
$561$	18.9451	+	12.1753i	0.799861	+	0.514040i
$562$	−2.73195	−	19.0011i	−0.115240	−	0.801515i
$563$	12.9279	+	28.3081i	0.544845	+	1.19304i	0.959148	+	0.282905i	$0.0912980\pi$
$563$	12.9279	+	28.3081i	0.544845	+	1.19304i	−0.414303	+	0.910139i	$0.635975\pi$
$564$	0.669357	+	1.46569i	0.0281850	+	0.0617166i
$565$	−3.79327	−	26.3828i	−0.159584	−	1.10993i
$566$	−11.5682	−	7.43441i	−0.486246	−	0.312491i
$567$	−1.02408	+	0.300696i	−0.0430071	+	0.0126280i
$568$	−0.914379	+	6.35964i	−0.0383665	+	0.266845i
$569$	−17.0555	+	19.6831i	−0.715003	+	0.825157i	−0.990697	−	0.136088i	$-0.956547\pi$
$569$	−17.0555	+	19.6831i	−0.715003	+	0.825157i	0.275694	+	0.961245i	$0.411092\pi$
$570$	6.02417	−	3.87150i	0.252325	−	0.162159i
$571$	−3.29341	−	3.80080i	−0.137825	−	0.159059i	0.682641	−	0.730754i	$-0.260831\pi$
$571$	−3.29341	−	3.80080i	−0.137825	−	0.159059i	−0.820466	+	0.571695i	$0.806286\pi$
$572$	−23.6129	−	6.93338i	−0.987306	−	0.289899i
$573$	2.35680	−	5.16067i	0.0984568	−	0.215590i
$574$	4.66099			0.194546
$575$	−17.5796	+	0.578539i	−0.733122	+	0.0241268i
$576$	1.00000			0.0416667
$577$	−11.7759	+	25.7855i	−0.490236	+	1.07347i	0.489285	+	0.872124i	$0.337258\pi$
$577$	−11.7759	+	25.7855i	−0.490236	+	1.07347i	−0.979521	+	0.201343i	$0.935470\pi$
$578$	11.3288	+	3.32645i	0.471218	+	0.138362i
$579$	1.25575	+	1.44921i	0.0521872	+	0.0602272i
$580$	−22.3333	+	14.3528i	−0.927341	+	0.595966i
$581$	−9.10569	+	10.5085i	−0.377768	+	0.435967i
$582$	−1.63282	+	11.3565i	−0.0676825	+	0.470742i
$583$	11.5932	−	3.40407i	0.480141	−	0.140982i
$584$	11.2738	+	7.24526i	0.466515	+	0.299811i
$585$	2.45747	+	17.0921i	0.101604	+	0.706670i
$586$	0.353332	+	0.773688i	0.0145960	+	0.0319608i
$587$	4.70486	+	10.3022i	0.194191	+	0.425218i	0.981532	−	0.191300i	$-0.0612702\pi$
$587$	4.70486	+	10.3022i	0.194191	+	0.425218i	−0.787341	+	0.616518i	$0.788543\pi$
$588$	−0.834086	−	5.80120i	−0.0343971	−	0.239237i
$589$	9.39099	+	6.03522i	0.386949	+	0.248677i
$590$	1.21921	−	0.357992i	0.0501940	−	0.0147383i
$591$	1.14154	−	7.93960i	0.0469568	−	0.326592i
$592$	5.62301	−	6.48930i	0.231104	−	0.266709i
$593$	2.99628	−	1.92559i	0.123042	−	0.0790746i	−0.477672	−	0.878538i	$-0.658519\pi$
$593$	2.99628	−	1.92559i	0.123042	−	0.0790746i	0.600714	+	0.799464i	$0.294883\pi$
$594$	2.74769	+	3.17101i	0.112739	+	0.130108i
$595$	−16.1820	−	4.75145i	−0.663396	−	0.194791i
$596$	−1.46152	+	3.20028i	−0.0598661	+	0.131088i
$597$	15.0893			0.617562
$598$	4.91678	+	27.6958i	0.201062	+	1.13257i
$599$	−28.0028			−1.14417			−0.572083	−	0.820196i	$-0.693864\pi$
$599$	−28.0028			−1.14417			−0.572083	+	0.820196i	$0.693864\pi$
$600$	1.52357	−	3.33616i	0.0621996	−	0.136198i
$601$	21.3296	+	6.26294i	0.870054	+	0.255471i	0.686138	−	0.727471i	$-0.259305\pi$
$601$	21.3296	+	6.26294i	0.870054	+	0.255471i	0.183916	+	0.982942i	$0.441123\pi$
$602$	−0.379638	−	0.438126i	−0.0154729	−	0.0178567i
$603$	−2.42123	+	1.55603i	−0.0985999	+	0.0633663i
$604$	−12.5286	+	14.4588i	−0.509781	+	0.588319i
$605$	−2.76745	+	19.2480i	−0.112513	+	0.782543i
$606$	14.8931	−	4.37300i	0.604989	−	0.177641i
$607$	12.7781	+	8.21198i	0.518647	+	0.333314i	0.773636	−	0.633630i	$-0.218436\pi$
$607$	12.7781	+	8.21198i	0.518647	+	0.333314i	−0.254990	+	0.966944i	$0.582072\pi$
$608$	0.346156	+	2.40757i	0.0140385	+	0.0976397i
$609$	3.99806	+	8.75454i	0.162010	+	0.354752i
$610$	1.32641	+	2.90443i	0.0537047	+	0.117597i
$611$	−1.34498	−	9.35451i	−0.0544119	−	0.378443i
$612$	4.51520	+	2.90174i	0.182516	+	0.117296i
$613$	−16.4705	+	4.83616i	−0.665235	+	0.195331i	−0.596880	−	0.802330i	$-0.703593\pi$
$613$	−16.4705	+	4.83616i	−0.665235	+	0.195331i	−0.0683551	+	0.997661i	$0.521775\pi$
$614$	0.967604	−	6.72983i	0.0390493	−	0.271594i
$615$	−8.41950	+	9.71662i	−0.339507	+	0.391812i
$616$	3.76735	−	2.42113i	0.151791	−	0.0975502i
$617$	−25.5443	−	29.4797i	−1.02837	−	1.18681i	−0.982193	−	0.187873i	$-0.939841\pi$
$617$	−25.5443	−	29.4797i	−1.02837	−	1.18681i	−0.0461802	−	0.998933i	$-0.514705\pi$
$618$	16.8636	+	4.95160i	0.678353	+	0.199182i
$619$	−4.54357	+	9.94902i	−0.182621	+	0.399885i	−0.978696	−	0.205313i	$-0.934179\pi$
$619$	−4.54357	+	9.94902i	−0.182621	+	0.399885i	0.796075	+	0.605198i	$0.206906\pi$
$620$	13.5118			0.542646
$621$	1.84769	−	4.42561i	0.0741454	−	0.177594i
$622$	14.3525			0.575484
$623$	3.19423	−	6.99439i	0.127974	−	0.280224i
$624$	−5.62769	−	1.65244i	−0.225288	−	0.0661505i
$625$	19.5716	+	22.5869i	0.782866	+	0.903475i
$626$	−2.78966	+	1.79280i	−0.111497	+	0.0716548i
$627$	−6.68328	+	7.71291i	−0.266904	+	0.308024i
$628$	3.27942	−	22.8089i	0.130863	−	0.910172i
$629$	44.2193	−	12.9840i	1.76314	−	0.517704i
$630$	−2.64342	−	1.69882i	−0.105316	−	0.0676827i
$631$	−4.60826	−	32.0511i	−0.183452	−	1.27594i	−0.848524	−	0.529156i	$-0.822508\pi$
$631$	−4.60826	−	32.0511i	−0.183452	−	1.27594i	0.665072	−	0.746779i	$-0.268401\pi$
$632$	0.545343	+	1.19414i	0.0216926	+	0.0475002i
$633$	9.14106	+	20.0161i	0.363324	+	0.795570i
$634$	−2.78612	−	19.3779i	−0.110651	−	0.769595i
$635$	30.4199	+	19.5497i	1.20718	+	0.775806i
$636$	2.76302	−	0.811296i	0.109561	−	0.0321700i
$637$	−4.89215	+	34.0256i	−0.193834	+	1.34814i
$638$	24.7768	−	28.5940i	0.980924	−	1.13205i
$639$	−5.40509	+	3.47364i	−0.213822	+	0.137415i
$640$	1.92796	+	2.22499i	0.0762093	+	0.0879503i
$641$	25.5918	+	7.51443i	1.01081	+	0.296802i	0.744887	−	0.667191i	$-0.232503\pi$
$641$	25.5918	+	7.51443i	1.01081	+	0.296802i	0.265928	+	0.963993i	$0.414322\pi$
$642$	−4.03061	+	8.82581i	−0.159076	+	0.348327i
$643$	4.32227			0.170454			0.0852268	−	0.996362i	$-0.472839\pi$
$643$	4.32227			0.170454			0.0852268	+	0.996362i	$0.472839\pi$
$644$	−4.39476	−	2.62421i	−0.173178	−	0.103408i
$645$	1.59912			0.0629651
$646$	−5.42317	+	11.8751i	−0.213372	+	0.467219i
$647$	−36.5856	−	10.7425i	−1.43833	−	0.422331i	−0.532664	−	0.846327i	$-0.678809\pi$
$647$	−36.5856	−	10.7425i	−1.43833	−	0.422331i	−0.905664	+	0.423996i	$0.860627\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−1.52347	+	0.979072i	−0.0598013	+	0.0384319i
$650$	−14.0870	+	16.2573i	−0.552538	+	0.637663i
$651$	0.697114	−	4.84853i	0.0273220	−	0.190029i
$652$	8.60820	−	2.52760i	0.337123	−	0.0989883i
$653$	8.85523	+	5.69091i	0.346532	+	0.222703i	0.702315	−	0.711866i	$-0.252150\pi$
$653$	8.85523	+	5.69091i	0.346532	+	0.222703i	−0.355784	+	0.934568i	$0.615786\pi$
$654$	1.40512	+	9.77285i	0.0549447	+	0.382149i
$655$	27.4302	+	60.0638i	1.07179	+	2.34689i
$656$	−1.81414	−	3.97241i	−0.0708301	−	0.155096i
$657$	1.90719	+	13.2648i	0.0744068	+	0.517510i
$658$	1.44675	+	0.929768i	0.0564001	+	0.0362461i
$659$	−19.9109	+	5.84637i	−0.775619	+	0.227742i	−0.645504	−	0.763757i	$-0.723353\pi$
$659$	−19.9109	+	5.84637i	−0.775619	+	0.227742i	−0.130115	+	0.991499i	$0.541535\pi$
$660$	−1.75800	+	12.2272i	−0.0684300	+	0.475941i
$661$	7.65931	−	8.83932i	0.297913	−	0.343810i	−0.586983	−	0.809600i	$-0.699684\pi$
$661$	7.65931	−	8.83932i	0.297913	−	0.343810i	0.884895	+	0.465790i	$0.154230\pi$
$662$	−3.01005	+	1.93444i	−0.116989	+	0.0751843i
$663$	−20.6152	−	23.7912i	−0.800628	−	0.923973i
$664$	12.5002	+	3.67038i	0.485100	+	0.142438i
$665$	3.17499	−	6.95227i	0.123121	−	0.269597i
$666$	8.58658			0.332723
$667$	−41.8721	−	10.8123i	−1.62129	−	0.418653i
$668$	4.97958			0.192666
$669$	9.23824	−	20.2289i	0.357171	−	0.782095i
$670$	−8.13017	−	2.38723i	−0.314096	−	0.0922268i
$671$	−2.97999	−	3.43909i	−0.115041	−	0.132764i
$672$	0.897877	−	0.577031i	0.0346364	−	0.0222594i
$673$	9.25493	−	10.6808i	0.356751	−	0.411713i	−0.548797	−	0.835955i	$-0.684914\pi$
$673$	9.25493	−	10.6808i	0.356751	−	0.411713i	0.905549	+	0.424243i	$0.139460\pi$
$674$	3.88318	−	27.0081i	0.149575	−	1.04031i
$675$	3.51903	−	1.03328i	0.135448	−	0.0397710i
$676$	18.0041	+	11.5705i	0.692464	+	0.445019i
$677$	−0.486078	−	3.38075i	−0.0186815	−	0.129933i	0.978346	−	0.206974i	$-0.0663617\pi$
$677$	−0.486078	−	3.38075i	−0.0186815	−	0.129933i	−0.997028	+	0.0770416i	$0.975453\pi$
$678$	3.76094	+	8.23531i	0.144438	+	0.316275i
$679$	5.08698	+	11.1389i	0.195220	+	0.427473i
$680$	2.24879	+	15.6407i	0.0862372	+	0.599793i
$681$	−11.8665	−	7.62614i	−0.454726	−	0.292234i
$682$	−18.4767	+	5.42525i	−0.707509	+	0.207743i
$683$	−0.593229	+	4.12600i	−0.0226993	+	0.157877i	−0.998018	−	0.0629231i	$-0.979958\pi$
$683$	−0.593229	+	4.12600i	−0.0226993	+	0.157877i	0.975319	+	0.220800i	$0.0708668\pi$
$684$	−1.59283	+	1.83823i	−0.0609035	+	0.0702864i
$685$	10.4737	−	6.73101i	0.400178	−	0.257179i
$686$	−8.98895	−	10.3738i	−0.343200	−	0.396073i
$687$	−8.51290	−	2.49961i	−0.324787	−	0.0953662i
$688$	−0.225638	+	0.494079i	−0.00860238	+	0.0188366i
$689$	−16.8900			−0.643459
$690$	13.4092	−	4.42131i	0.510480	−	0.168316i
$691$	36.7618			1.39849			0.699243	−	0.714884i	$-0.253520\pi$
$691$	36.7618			1.39849			0.699243	+	0.714884i	$0.253520\pi$
$692$	−5.06771	+	11.0967i	−0.192646	+	0.421835i
$693$	4.29686	+	1.26167i	0.163224	+	0.0479270i
$694$	17.0994	+	19.7338i	0.649085	+	0.749084i
$695$	16.3933	−	10.5353i	0.621832	−	0.399627i
$696$	5.90509	−	6.81484i	0.223832	−	0.258316i
$697$	3.33571	−	23.2004i	0.126349	−	0.878776i
$698$	15.8763	−	4.66171i	0.600928	−	0.176448i
$699$	−6.02545	−	3.87232i	−0.227903	−	0.146465i
$700$	−0.557085	−	3.87461i	−0.0210558	−	0.146447i
$701$	4.71530	+	10.3251i	0.178095	+	0.389973i	0.977535	−	0.210772i	$-0.0675979\pi$
$701$	4.71530	+	10.3251i	0.178095	+	0.389973i	−0.799441	+	0.600745i	$0.794871\pi$
$702$	−2.43652	−	5.33524i	−0.0919607	−	0.201366i
$703$	2.97229	+	20.6728i	0.112102	+	0.779688i
$704$	−3.52977	−	2.26844i	−0.133033	−	0.0854952i
$705$	−4.55163	+	1.33648i	−0.171424	+	0.0503347i
$706$	−1.06782	+	7.42687i	−0.0401881	+	0.279514i
$707$	10.8488	−	12.5202i	0.408011	−	0.470870i
$708$	−0.363089	+	0.233343i	−0.0136457	+	0.00876958i
$709$	18.2818	+	21.0983i	0.686586	+	0.792363i	0.986875	−	0.161486i	$-0.0516285\pi$
$709$	18.2818	+	21.0983i	0.686586	+	0.792363i	−0.300289	+	0.953848i	$0.597083\pi$
$710$	−18.1496	−	5.32920i	−0.681142	−	0.200001i
$711$	−0.545343	+	1.19414i	−0.0204520	+	0.0447836i
$712$	−7.20433			−0.269994
$713$	14.9531	+	16.1512i	0.559996	+	0.604868i
$714$	5.72849			0.214383
$715$	30.0981	−	65.9057i	1.12561	−	2.46473i
$716$	−10.1568	−	2.98230i	−0.379577	−	0.111454i
$717$	13.9675	+	16.1194i	0.521627	+	0.601990i
$718$	2.88413	−	1.85351i	0.107635	−	0.0691726i
$719$	3.60399	−	4.15923i	0.134406	−	0.155113i	−0.684556	−	0.728960i	$-0.740004\pi$
$719$	3.60399	−	4.15923i	0.134406	−	0.155113i	0.818963	+	0.573847i	$0.194550\pi$
$720$	−0.418986	+	2.91411i	−0.0156147	+	0.108603i
$721$	17.9987	−	5.28488i	0.670305	−	0.196819i
$722$	11.0068	+	7.07364i	0.409631	+	0.263254i
$723$	−2.41134	−	16.7712i	−0.0896787	−	0.623729i
$724$	−9.31604	−	20.3993i	−0.346228	−	0.758133i
$725$	−13.7386	−	30.0832i	−0.510237	−	1.11726i
$726$	−0.940005	−	6.53788i	−0.0348869	−	0.242643i
$727$	−6.36734	−	4.09204i	−0.236151	−	0.151765i	0.417213	−	0.908809i	$-0.363007\pi$
$727$	−6.36734	−	4.09204i	−0.236151	−	0.151765i	−0.653365	+	0.757043i	$0.726643\pi$
$728$	−6.00648	+	1.76366i	−0.222615	+	0.0653657i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−25.8371	+	29.8176i	−0.956273	+	1.10360i
$731$	−2.45249	+	1.57612i	−0.0907087	+	0.0582949i
$732$	−0.710223	−	0.819641i	−0.0262506	−	0.0302948i
$733$	−46.3321	−	13.6043i	−1.71132	−	0.502488i	−0.728184	−	0.685382i	$-0.759635\pi$
$733$	−46.3321	−	13.6043i	−1.71132	−	0.502488i	−0.983133	+	0.182894i	$0.941454\pi$
$734$	2.60618	−	5.70674i	0.0961958	−	0.210639i
$735$	17.2548			0.636453
$736$	−0.526011	+	4.76690i	−0.0193890	+	0.175710i
$737$	12.0761			0.444830
$738$	1.81414	−	3.97241i	0.0667793	−	0.146226i
$739$	36.9215	+	10.8411i	1.35818	+	0.398798i	0.878121	−	0.478439i	$-0.158797\pi$
$739$	36.9215	+	10.8411i	1.35818	+	0.398798i	0.480059	+	0.877236i	$0.340615\pi$
$740$	16.5546	+	19.1050i	0.608559	+	0.702314i
$741$	12.0015	−	7.71291i	0.440887	−	0.283341i
$742$	2.01271	−	2.32279i	0.0738889	−	0.0852723i
$743$	−4.87878	+	33.9327i	−0.178985	+	1.24487i	0.680132	+	0.733090i	$0.261922\pi$
$743$	−4.87878	+	33.9327i	−0.178985	+	1.24487i	−0.859117	+	0.511779i	$0.828987\pi$
$744$	−4.40357	+	1.29301i	−0.161443	+	0.0474039i
$745$	−8.71361	−	5.59990i	−0.319242	−	0.205164i
$746$	−1.45917	−	10.1488i	−0.0534242	−	0.371573i
$747$	5.41198	+	11.8506i	0.198014	+	0.433590i
$748$	−9.35516	−	20.4850i	−0.342059	−	0.749004i
$749$	1.47377	+	10.2503i	0.0538503	+	0.374537i
$750$	−3.29999	−	2.12078i	−0.120499	−	0.0774398i
$751$	−24.8177	+	7.28714i	−0.905611	+	0.265911i	−0.701192	−	0.712972i	$-0.747349\pi$
$751$	−24.8177	+	7.28714i	−0.905611	+	0.265911i	−0.204419	+	0.978884i	$0.565530\pi$
$752$	0.229312	−	1.59490i	0.00836213	−	0.0581599i
$753$	−19.4449	+	22.4406i	−0.708612	+	0.817782i
$754$	−44.4931	+	28.5940i	−1.62034	+	1.04133i
$755$	−36.8852	−	42.5678i	−1.34239	−	1.54920i
$756$	1.02408	+	0.300696i	0.0372453	+	0.0109362i
$757$	6.84038	−	14.9783i	0.248618	−	0.544397i	−0.743642	−	0.668578i	$-0.766903\pi$
$757$	6.84038	−	14.9783i	0.248618	−	0.544397i	0.992260	+	0.124181i	$0.0396304\pi$
$758$	19.8019			0.719238
$759$	−16.5612	+	11.4300i	−0.601133	+	0.414882i
$760$	−7.16095			−0.259755
$761$	−12.8854	+	28.2150i	−0.467094	+	1.02279i	0.518719	+	0.854945i	$0.326409\pi$
$761$	−12.8854	+	28.2150i	−0.467094	+	1.02279i	−0.985813	+	0.167848i	$0.946318\pi$
$762$	−11.7848	−	3.46034i	−0.426920	−	0.125355i
$763$	6.90087	+	7.96402i	0.249828	+	0.288317i
$764$	−4.77274	+	3.06725i	−0.172672	+	0.110969i
$765$	−10.3478	+	11.9420i	−0.374126	+	0.431764i
$766$	−0.954965	+	6.64193i	−0.0345043	+	0.239983i
$767$	2.42894	−	0.713201i	0.0877039	−	0.0257522i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	−1.06161	−	7.38365i	−0.0382826	−	0.266261i	0.961686	−	0.274152i	$-0.0883973\pi$
$769$	−1.06161	−	7.38365i	−0.0382826	−	0.266261i	−0.999969	+	0.00789110i	$0.997488\pi$
$770$	5.47698	+	11.9929i	0.197377	+	0.432194i
$771$	−1.96104	−	4.29407i	−0.0706250	−	0.154647i
$772$	−0.272900	−	1.89806i	−0.00982190	−	0.0683128i
$773$	−7.36262	−	4.73167i	−0.264815	−	0.170186i	0.401495	−	0.915861i	$-0.368491\pi$
$773$	−7.36262	−	4.73167i	−0.264815	−	0.170186i	−0.666310	+	0.745675i	$0.732127\pi$
$774$	−0.521162	+	0.153027i	−0.0187328	+	0.00550044i
$775$	−2.39549	+	16.6610i	−0.0860486	+	0.598481i
$776$	7.51340	−	8.67093i	0.269715	−	0.311268i
$777$	7.70970	−	4.95472i	0.276584	−	0.177750i
$778$	−7.77164	−	8.96895i	−0.278627	−	0.321552i
$779$	10.1918	+	2.99258i	0.365159	+	0.107220i
$780$	7.17331	−	15.7074i	0.256846	−	0.562414i
$781$	26.9585			0.964650
$782$	−16.2073	+	19.9971i	−0.579574	+	0.715096i
$783$	9.01732			0.322253
$784$	−2.43469	+	5.33122i	−0.0869531	+	0.190401i
$785$	65.0935	+	19.1132i	2.32329	+	0.682179i
$786$	−14.6875	−	16.9502i	−0.523884	−	0.604594i
$787$	−17.7866	+	11.4307i	−0.634023	+	0.407462i	−0.817797	−	0.575507i	$-0.804805\pi$
$787$	−17.7866	+	11.4307i	−0.634023	+	0.407462i	0.183774	+	0.982968i	$0.441168\pi$
$788$	−5.25280	+	6.06205i	−0.187123	+	0.215952i
$789$	2.76109	−	19.2038i	0.0982976	−	0.683675i
$790$	−3.70833	+	1.08887i	−0.131937	+	0.0387401i
$791$	8.12889	+	5.22412i	0.289030	+	0.185748i
$792$	−0.597131	−	4.15314i	−0.0212181	−	0.147575i
$793$	2.64251	+	5.78629i	0.0938382	+	0.205477i
$794$	−1.99487	−	4.36815i	−0.0707952	−	0.155020i
$795$	1.20654	+	8.39167i	0.0427915	+	0.297622i
$796$	−12.6939	−	8.15787i	−0.449923	−	0.289148i
$797$	−22.1110	+	6.49239i	−0.783214	+	0.229972i	−0.648806	−	0.760954i	$-0.724731\pi$
$797$	−22.1110	+	6.49239i	−0.783214	+	0.229972i	−0.134408	+	0.990926i	$0.542913\pi$
$798$	−0.369455	+	2.56962i	−0.0130786	+	0.0909634i
$799$	5.66336	−	6.53587i	0.200355	−	0.231222i
$800$	−3.08538	+	1.98285i	−0.109085	+	0.0701044i
$801$	−4.71784	−	5.44467i	−0.166697	−	0.192378i
$802$	15.5699	+	4.57175i	0.549794	+	0.161434i
$803$	23.3586	−	51.1482i	0.824306	−	1.80498i
$804$	2.87812			0.101503
$805$	9.48858	−	11.7073i	0.334429	−	0.412629i
$806$	26.9185			0.948165
$807$	−0.913959	+	2.00129i	−0.0321729	+	0.0704487i
$808$	−14.8931	−	4.37300i	−0.523936	−	0.153842i
$809$	−8.35194	−	9.63865i	−0.293639	−	0.338877i	0.589691	−	0.807629i	$-0.299249\pi$
$809$	−8.35194	−	9.63865i	−0.293639	−	0.338877i	−0.883330	+	0.468752i	$0.844704\pi$
$810$	−2.47672	+	1.59169i	−0.0870229	+	0.0559262i
$811$	16.3239	−	18.8388i	0.573210	−	0.661520i	−0.392921	−	0.919572i	$-0.628535\pi$
$811$	16.3239	−	18.8388i	0.573210	−	0.661520i	0.966131	+	0.258053i	$0.0830808\pi$
$812$	1.36968	−	9.52631i	0.0480662	−	0.334308i
$813$	−27.8812	+	8.18665i	−0.977835	+	0.287118i
$814$	−30.3086	−	19.4782i	−1.06232	−	0.682710i
$815$	3.75898	+	26.1443i	0.131671	+	0.915794i
$816$	−2.22963	−	4.88220i	−0.0780525	−	0.170911i
$817$	−0.548825	−	1.20176i	−0.0192010	−	0.0420443i
$818$	3.65842	+	25.4449i	0.127914	+	0.889659i
$819$	−5.26630	−	3.38444i	−0.184019	−	0.118262i
$820$	12.3361	−	3.62221i	0.430796	−	0.126493i
$821$	2.74707	−	19.1063i	0.0958733	−	0.666813i	−0.884043	−	0.467405i	$-0.845189\pi$
$821$	2.74707	−	19.1063i	0.0958733	−	0.666813i	0.979917	−	0.199408i	$-0.0639020\pi$
$822$	−2.76931	+	3.19595i	−0.0965906	+	0.111472i
$823$	19.8677	−	12.7682i	0.692546	−	0.445072i	−0.146444	−	0.989219i	$-0.546783\pi$
$823$	19.8677	−	12.7682i	0.692546	−	0.445072i	0.838990	+	0.544147i	$0.183146\pi$
$824$	−11.5095	−	13.2827i	−0.400953	−	0.462724i
$825$	−14.7653	−	4.33548i	−0.514062	−	0.150942i
$826$	−0.191363	+	0.419027i	−0.00665838	+	0.0145798i
$827$	−8.84206			−0.307469			−0.153734	−	0.988112i	$-0.549130\pi$
$827$	−8.84206			−0.307469			−0.153734	+	0.988112i	$0.549130\pi$
$828$	−3.94704	+	2.72412i	−0.137169	+	0.0946698i
$829$	19.0563			0.661853			0.330926	−	0.943657i	$-0.392639\pi$
$829$	19.0563			0.661853			0.330926	+	0.943657i	$0.392639\pi$
$830$	−15.9333	+	34.8890i	−0.553052	+	1.21102i
$831$	5.25818	+	1.54394i	0.182404	+	0.0535587i
$832$	3.84094	+	4.43268i	0.133161	+	0.153676i
$833$	−26.4629	+	17.0067i	−0.916885	+	0.589246i
$834$	−4.33449	+	5.00227i	−0.150091	+	0.173214i
$835$	−2.08638	+	14.5111i	−0.0722020	+	0.502176i
$836$	9.79225	−	2.87526i	0.338672	−	0.0994431i
$837$	−3.86091	−	2.48126i	−0.133453	−	0.0857648i
$838$	−0.217344	−	1.51166i	−0.00750802	−	0.0522194i
$839$	−18.8332	−	41.2389i	−0.650194	−	1.42373i	−0.891384	−	0.453249i	$-0.850265\pi$
$839$	−18.8332	−	41.2389i	−0.650194	−	1.42373i	0.241190	−	0.970478i	$-0.422462\pi$
$840$	1.30533	+	2.85828i	0.0450383	+	0.0986201i
$841$	−7.44478	−	51.7796i	−0.256717	−	1.78550i
$842$	12.8404	+	8.25201i	0.442508	+	0.284383i
$843$	−18.4189	+	5.40829i	−0.634382	+	0.186271i
$844$	3.13159	−	21.7807i	0.107794	−	0.749721i
$845$	−41.2612	+	47.6179i	−1.41943	+	1.63811i
$846$	1.35551	−	0.871133i	0.0466034	−	0.0299502i
$847$	−4.61657	−	5.32780i	−0.158627	−	0.183065i
$848$	−2.76302	−	0.811296i	−0.0948825	−	0.0278600i
$849$	−5.71241	+	12.5084i	−0.196050	+	0.429289i
$850$	−19.6848			−0.675183
$851$	−4.51663	+	40.9313i	−0.154828	+	1.40311i
$852$	6.42504			0.220118
$853$	18.5846	−	40.6945i	0.636324	−	1.39335i	−0.266707	−	0.963778i	$-0.585936\pi$
$853$	18.5846	−	40.6945i	0.636324	−	1.39335i	0.903030	−	0.429577i	$-0.141337\pi$
$854$	−1.11065	−	0.326117i	−0.0380057	−	0.0111595i
$855$	−4.68942	−	5.41188i	−0.160375	−	0.185083i
$856$	8.16236	−	5.24563i	0.278984	−	0.179292i
$857$	0.538599	−	0.621576i	0.0183982	−	0.0212326i	−0.746476	−	0.665412i	$-0.768256\pi$
$857$	0.538599	−	0.621576i	0.0183982	−	0.0212326i	0.764874	+	0.644180i	$0.222801\pi$
$858$	−3.50234	+	24.3593i	−0.119568	+	0.831612i
$859$	−23.1852	+	6.80778i	−0.791067	+	0.232278i	−0.652214	−	0.758035i	$-0.726160\pi$
$859$	−23.1852	+	6.80778i	−0.791067	+	0.232278i	−0.138853	+	0.990313i	$0.544342\pi$
$860$	−1.34526	−	0.864548i	−0.0458731	−	0.0294808i
$861$	−0.663328	−	4.61355i	−0.0226061	−	0.157229i
$862$	−0.700522	−	1.53393i	−0.0238599	−	0.0522458i
$863$	9.08323	+	19.8895i	0.309197	+	0.677046i	0.998892	−	0.0470531i	$-0.0149830\pi$
$863$	9.08323	+	19.8895i	0.309197	+	0.677046i	−0.689696	+	0.724099i	$0.742256\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	−30.2138	−	19.4173i	−1.02730	−	0.660207i
$866$	14.5336	−	4.26744i	0.493870	−	0.145013i
$867$	1.68033	−	11.6869i	0.0570669	−	0.396909i
$868$	−3.20776	+	3.70196i	−0.108879	+	0.125653i
$869$	4.63377	−	2.97794i	0.157190	−	0.101020i
$870$	17.3850	+	20.0634i	0.589408	+	0.680213i
$871$	−16.1971	−	4.75591i	−0.548819	−	0.161148i
$872$	4.10154	−	8.98111i	0.138896	−	0.304139i
$873$	11.4733			0.388312
$874$	−7.92479	−	8.55980i	−0.268060	−	0.289539i
$875$	−4.18674			−0.141538
$876$	5.56708	−	12.1902i	0.188094	−	0.411868i
$877$	−33.5280	−	9.84472i	−1.13216	−	0.332432i	−0.338604	−	0.940929i	$-0.609955\pi$
$877$	−33.5280	−	9.84472i	−1.13216	−	0.332432i	−0.793557	+	0.608496i	$0.791773\pi$
$878$	−11.1366	−	12.8524i	−0.375843	−	0.433746i
$879$	0.715529	−	0.459843i	0.0241342	−	0.0155101i
$880$	8.08942	−	9.33569i	0.272694	−	0.314706i
$881$	1.64055	−	11.4103i	0.0552716	−	0.384423i	−0.943344	−	0.331817i	$-0.892338\pi$
$881$	1.64055	−	11.4103i	0.0552716	−	0.384423i	0.998615	−	0.0526055i	$-0.0167526\pi$
$882$	−5.62345	+	1.65119i	−0.189351	+	0.0555986i
$883$	47.0000	+	30.2050i	1.58167	+	1.01648i	0.975186	+	0.221388i	$0.0710588\pi$
$883$	47.0000	+	30.2050i	1.58167	+	1.01648i	0.606489	+	0.795092i	$0.292578\pi$
$884$	4.48011	+	31.1598i	0.150682	+	1.04802i
$885$	−0.527859	−	1.15585i	−0.0177438	−	0.0388535i
$886$	6.33116	+	13.8633i	0.212699	+	0.465747i
$887$	6.59756	+	45.8871i	0.221525	+	1.54074i	0.732276	+	0.681008i	$0.238458\pi$
$887$	6.59756	+	45.8871i	0.221525	+	1.54074i	−0.510751	+	0.859729i	$0.670633\pi$
$888$	−7.22349	−	4.64226i	−0.242404	−	0.155784i
$889$	−12.5781	+	3.69325i	−0.421855	+	0.123868i
$890$	3.01851	−	20.9942i	0.101181	−	0.703728i
$891$	2.74769	−	3.17101i	0.0920512	−	0.106233i
$892$	−18.7083	+	12.0231i	−0.626400	+	0.402563i
$893$	2.56653	+	2.96193i	0.0858856	+	0.0991172i
$894$	3.37570	+	0.991195i	0.112900	+	0.0331505i
$895$	12.9463	−	28.3485i	0.432747	−	0.947585i
$896$	−1.06731			−0.0356563
$897$	26.7142	−	8.80826i	0.891961	−	0.294099i
$898$	0.498442			0.0166332
$899$	−17.1919	+	37.6449i	−0.573381	+	1.25553i
$900$	−3.51903	−	1.03328i	−0.117301	−	0.0344427i
$901$	−10.1214	−	11.6807i	−0.337193	−	0.389141i
$902$	−15.4147	+	9.90640i	−0.513252	+	0.329847i
$903$	−0.379638	+	0.438126i	−0.0126336	+	0.0145799i
$904$	1.28844	−	8.96130i	0.0428529	−	0.298049i
$905$	63.3491	−	18.6010i	2.10579	−	0.618317i
$906$	16.0946	+	10.3434i	0.534708	+	0.343636i
$907$	2.84332	+	19.7758i	0.0944110	+	0.656643i	0.980989	+	0.194064i	$0.0621669\pi$
$907$	2.84332	+	19.7758i	0.0944110	+	0.656643i	−0.886578	+	0.462579i	$0.846924\pi$
$908$	5.85974	+	12.8310i	0.194462	+	0.425813i
$909$	−6.44799	−	14.1191i	−0.213866	−	0.468302i
$910$	−2.62288	−	18.2425i	−0.0869475	−	0.604733i
$911$	−11.7821	−	7.57188i	−0.390357	−	0.250867i	0.330710	−	0.943732i	$-0.392712\pi$
$911$	−11.7821	−	7.57188i	−0.390357	−	0.250867i	−0.721067	+	0.692865i	$0.756348\pi$
$912$	2.33380	−	0.685265i	0.0772797	−	0.0226914i
$913$	7.77935	−	54.1066i	0.257459	−	1.79067i
$914$	−4.98823	+	5.75672i	−0.164996	+	0.190415i
$915$	2.68610	−	1.72625i	0.0887997	−	0.0570681i
$916$	5.81011	+	6.70523i	0.191972	+	0.221547i
$917$	−22.9683	−	6.74411i	−0.758481	−	0.222710i
$918$	2.22963	−	4.88220i	0.0735886	−	0.161137i
$919$	44.6314			1.47226			0.736128	−	0.676843i	$-0.236652\pi$
$919$	44.6314			1.47226			0.736128	+	0.676843i	$0.236652\pi$
$920$	−13.6709	−	3.53012i	−0.450716	−	0.116385i
$921$	−6.79904			−0.224036
$922$	−6.06256	+	13.2751i	−0.199660	+	0.437194i
$923$	−36.1581	−	10.6170i	−1.19016	−	0.349462i
$924$	−2.93264	−	3.38444i	−0.0964767	−	0.111340i
$925$	−26.4928	+	17.0259i	−0.871079	+	0.559808i
$926$	22.8414	−	26.3603i	0.750614	−	0.866254i
$927$	2.50126	−	17.3966i	0.0821521	−	0.571380i
$928$	−8.65206	+	2.54047i	−0.284018	+	0.0833951i
$929$	0.500592	+	0.321711i	0.0164239	+	0.0105550i	0.548827	−	0.835936i	$-0.315075\pi$
$929$	0.500592	+	0.321711i	0.0164239	+	0.0105550i	−0.532403	+	0.846491i	$0.678711\pi$
$930$	−1.92293	−	13.3742i	−0.0630552	−	0.438559i
$931$	−5.92194	−	12.9672i	−0.194084	−	0.424984i
$932$	2.97540	+	6.51521i	0.0974623	+	0.213413i
$933$	−2.04258	−	14.2064i	−0.0668709	−	0.465098i
$934$	−10.7040	−	6.87906i	−0.350247	−	0.225090i
$935$	63.6151	−	18.6791i	2.08044	−	0.610871i
$936$	−0.834716	+	5.80558i	−0.0272835	+	0.189761i
$937$	−25.7146	+	29.6762i	−0.840059	+	0.969480i	−0.999844	−	0.0176717i	$-0.994375\pi$
$937$	−25.7146	+	29.6762i	−0.840059	+	0.969480i	0.159784	+	0.987152i	$0.448920\pi$
$938$	2.58420	−	1.66076i	0.0843770	−	0.0542258i
$939$	2.17157	+	2.50612i	0.0708664	+	0.0817841i
$940$	4.55163	+	1.33648i	0.148458	+	0.0435911i
$941$	9.65946	−	21.1513i	0.314889	−	0.689511i	−0.684324	−	0.729178i	$-0.739902\pi$
$941$	9.65946	−	21.1513i	0.314889	−	0.689511i	0.999213	+	0.0396670i	$0.0126297\pi$
$942$	−23.0434			−0.750795
$943$	17.9818	+	10.7373i	0.585568	+	0.349656i
$944$	0.431605			0.0140475
$945$	−1.30533	+	2.85828i	−0.0424625	+	0.0929799i
$946$	2.18671	+	0.642077i	0.0710962	+	0.0208757i
$947$	0.176041	+	0.203162i	0.00572056	+	0.00660188i	0.758603	−	0.651554i	$-0.225882\pi$
$947$	0.176041	+	0.203162i	0.00572056	+	0.00660188i	−0.752882	+	0.658155i	$0.771337\pi$
$948$	1.10437	−	0.709736i	0.0358683	−	0.0230511i
$949$	−51.4733	+	59.4034i	−1.67090	+	1.92832i
$950$	1.26956	−	8.82997i	0.0411899	−	0.286482i
$951$	−18.7842	+	5.51553i	−0.609118	+	0.178853i
$952$	−4.81911	−	3.09705i	−0.156188	−	0.100376i
$953$	6.53924	+	45.4814i	0.211827	+	1.47329i	0.767050	+	0.641587i	$0.221724\pi$
$953$	6.53924	+	45.4814i	0.211827	+	1.47329i	−0.555223	+	0.831701i	$0.687367\pi$
$954$	−1.19626	−	2.61944i	−0.0387302	−	0.0848074i
$955$	−6.93861	−	15.1934i	−0.224528	−	0.491648i
$956$	−3.03544	−	21.1119i	−0.0981730	−	0.682808i
$957$	−31.8291	−	20.4553i	−1.02889	−	0.661226i
$958$	6.43376	−	1.88912i	0.207865	−	0.0610347i
$959$	−0.642336	+	4.46755i	−0.0207421	+	0.144265i
$960$	1.92796	−	2.22499i	0.0622247	−	0.0718111i
$961$	−8.35929	+	5.37219i	−0.269654	+	0.173296i
$962$	32.9805	+	38.0616i	1.06333	+	1.22715i
$963$	9.30959	+	2.73354i	0.299997	+	0.0880872i
$964$	−7.03867	+	15.4125i	−0.226700	+	0.496404i
$965$	5.64551			0.181735
$966$	−1.97206	+	4.72349i	−0.0634500	+	0.151976i
$967$	19.3102			0.620974			0.310487	−	0.950578i	$-0.399508\pi$
$967$	19.3102			0.620974			0.310487	+	0.950578i	$0.399508\pi$
$968$	−2.74386	+	6.00822i	−0.0881910	+	0.193111i
$969$	12.5260	+	3.67797i	0.402394	+	0.118153i
$970$	22.1200	+	25.5279i	0.710232	+	0.819651i
$971$	−10.9655	+	7.04713i	−0.351901	+	0.226153i	−0.704634	−	0.709571i	$-0.748889\pi$
$971$	−10.9655	+	7.04713i	−0.351901	+	0.226153i	0.352733	+	0.935724i	$0.385252\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−1.00538	+	6.99256i	−0.0322310	+	0.224171i
$974$	−28.6487	+	8.41203i	−0.917965	+	0.269539i
$975$	18.0966	+	11.6300i	0.579554	+	0.372457i
$976$	0.154346	+	1.07350i	0.00494050	+	0.0343620i
$977$	−19.1077	−	41.8400i	−0.611310	−	1.33858i	−0.921674	−	0.387964i	$-0.873178\pi$
$977$	−19.1077	−	41.8400i	−0.611310	−	1.33858i	0.310365	−	0.950618i	$-0.399549\pi$
$978$	−3.72694	−	8.16087i	−0.119175	−	0.260956i
$979$	4.30193	+	29.9206i	0.137490	+	0.956266i
$980$	−14.5157	−	9.32865i	−0.463686	−	0.297993i
$981$	9.47341	−	2.78164i	0.302463	−	0.0888111i
$982$	0.739925	−	5.14629i	0.0236119	−	0.164225i
$983$	25.8151	−	29.7922i	0.823374	−	0.950224i	−0.176043	−	0.984383i	$-0.556330\pi$
$983$	25.8151	−	29.7922i	0.823374	−	0.950224i	0.999416	+	0.0341584i	$0.0108751\pi$
$984$	−3.67379	+	2.36100i	−0.117116	+	0.0752661i
$985$	−15.4646	−	17.8472i	−0.492745	−	0.568658i
$986$	−46.4375	−	13.6353i	−1.47887	−	0.434236i
$987$	0.714411	−	1.56434i	0.0227399	−	0.0497935i
$988$	−14.2662			−0.453870
$989$	−0.455327	−	2.56482i	−0.0144786	−	0.0815565i
$990$	12.3529			0.392601
$991$	1.26185	−	2.76308i	0.0400841	−	0.0877720i	−0.888531	−	0.458817i	$-0.848273\pi$
$991$	1.26185	−	2.76308i	0.0400841	−	0.0877720i	0.928615	+	0.371045i	$0.121001\pi$
$992$	4.40357	+	1.29301i	0.139814	+	0.0410530i
$993$	2.34313	+	2.70411i	0.0743569	+	0.0858125i
$994$	5.76890	−	3.70745i	0.182978	−	0.117593i
$995$	29.0915	−	33.5734i	0.922263	−	1.06435i
$996$	1.85406	−	12.8953i	0.0587482	−	0.408602i
$997$	54.9991	−	16.1492i	1.74184	−	0.511450i	0.752691	−	0.658374i	$-0.228756\pi$
$997$	54.9991	−	16.1492i	1.74184	−	0.511450i	0.989148	+	0.146925i	$0.0469375\pi$
$998$	11.8303	+	7.60285i	0.374480	+	0.240664i
$999$	−1.22200	−	8.49918i	−0.0386623	−	0.268902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.d.121.1	yes	10
3.2	odd	2		414.2.i.a.397.1		10
23.2	even	11		3174.2.a.x.1.5		5
23.4	even	11	inner	138.2.e.d.73.1	✓	10
23.21	odd	22		3174.2.a.w.1.1		5
69.2	odd	22		9522.2.a.bx.1.1		5
69.44	even	22		9522.2.a.by.1.5		5
69.50	odd	22		414.2.i.a.73.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.73.1	✓	10	23.4	even	11	inner
138.2.e.d.121.1	yes	10	1.1	even	1	trivial
414.2.i.a.73.1		10	69.50	odd	22
414.2.i.a.397.1		10	3.2	odd	2
3174.2.a.w.1.1		5	23.21	odd	22
3174.2.a.x.1.5		5	23.2	even	11
9522.2.a.bx.1.1		5	69.2	odd	22
9522.2.a.by.1.5		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)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.47672 - 1.59169i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.151894 + 1.05645i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.47672 - 1.59169i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.151894 + 1.05645i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.418986 + 2.91411i) q^{10} +(-1.74302 - 3.81667i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.834716 + 5.80558i) q^{13} +(-0.897877 - 0.577031i) q^{14} +(2.82482 - 0.829443i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.51479 + 4.05628i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.59283 - 1.83823i) q^{19} +(-2.82482 - 0.829443i) q^{20} +(-0.443376 + 0.970858i) q^{21} +4.19584 q^{22} +(-2.13467 - 4.29455i) q^{23} +1.00000 q^{24} +(1.52357 - 3.33616i) q^{25} +(-5.62769 - 1.65244i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.897877 - 0.577031i) q^{28} +(5.90509 - 6.81484i) q^{29} +(-0.418986 + 2.91411i) q^{30} +(-4.40357 + 1.29301i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.597131 - 4.15314i) q^{33} +(-2.22963 - 4.88220i) q^{34} +(1.30533 + 2.85828i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-7.22349 - 4.64226i) q^{37} +(2.33380 - 0.685265i) q^{38} +(-0.834716 + 5.80558i) q^{39} +(1.92796 - 2.22499i) q^{40} +(-3.67379 + 2.36100i) q^{41} +(-0.698939 - 0.806618i) q^{42} +(0.521162 + 0.153027i) q^{43} +(-1.74302 + 3.81667i) q^{44} +2.94408 q^{45} +(4.79324 - 0.157744i) q^{46} -1.61130 q^{47} +(-0.415415 + 0.909632i) q^{48} +(5.62345 + 1.65119i) q^{49} +(2.40176 + 2.77178i) q^{50} +(-4.51520 + 2.90174i) q^{51} +(3.84094 - 4.43268i) q^{52} +(-0.409819 + 2.85036i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-10.3919 - 6.67848i) q^{55} +(0.151894 + 1.05645i) q^{56} +(-1.01042 - 2.21252i) q^{57} +(3.74593 + 8.20244i) q^{58} +(-0.0614238 - 0.427212i) q^{59} +(-2.47672 - 1.59169i) q^{60} +(1.04061 - 0.305550i) q^{61} +(0.653151 - 4.54276i) q^{62} +(-0.698939 + 0.806618i) q^{63} +(0.841254 - 0.540641i) q^{64} +(11.3080 + 13.0502i) q^{65} +(4.02588 + 1.18211i) q^{66} +(-1.19561 + 2.61803i) q^{67} +5.36723 q^{68} +(-0.838287 - 4.72200i) q^{69} -3.14224 q^{70} +(-2.66906 + 5.84442i) q^{71} +(0.959493 + 0.281733i) q^{72} +(8.77594 + 10.1280i) q^{73} +(7.22349 - 4.64226i) q^{74} +(2.40176 - 2.77178i) q^{75} +(-0.346156 + 2.40757i) q^{76} +(4.29686 - 1.26167i) q^{77} +(-4.93418 - 3.17101i) q^{78} +(0.186826 + 1.29941i) q^{79} +(1.22301 + 2.67803i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.621496 - 4.32260i) q^{82} +(10.9598 + 7.04340i) q^{83} +(1.02408 - 0.300696i) q^{84} +(-2.24879 + 15.6407i) q^{85} +(-0.355697 + 0.410496i) q^{86} +(7.58585 - 4.87513i) q^{87} +(-2.74769 - 3.17101i) q^{88} +(-6.91251 - 2.02970i) q^{89} +(-1.22301 + 2.67803i) q^{90} -6.26006 q^{91} +(-1.84769 + 4.42561i) q^{92} -4.58948 q^{93} +(0.669357 - 1.46569i) q^{94} +(-6.87088 - 2.01747i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(9.65194 - 6.20292i) q^{97} +(-3.83804 + 4.42934i) q^{98} +(0.597131 - 4.15314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

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