LMFDB - Embedded newform 374.2.r.b.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [374,2,Mod(9,374)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(374, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([24, 5]))

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

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

chi := DirichletCharacter("374.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 374 = 2 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	374.r (of order $40$, degree $16$, 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:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			9.10
Character	$\chi$	$=$	374.9
Dual form			374.2.r.b.291.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 + 0.891007i) q^{2} +(3.07895 - 0.739191i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.951174 - 0.0748590i) q^{5} +(2.05644 + 2.40778i) q^{6} +(-0.0553730 + 0.230645i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(6.26053 - 3.18990i) q^{9} +O(q^{10})$	\(q+(0.453990 + 0.891007i) q^{2} +(3.07895 - 0.739191i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.951174 - 0.0748590i) q^{5} +(2.05644 + 2.40778i) q^{6} +(-0.0553730 + 0.230645i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(6.26053 - 3.18990i) q^{9} +(-0.365124 - 0.881488i) q^{10} +(2.33817 - 2.35222i) q^{11} +(-1.21174 + 2.92541i) q^{12} +(-1.35403 - 0.439951i) q^{13} +(-0.230645 + 0.0553730i) q^{14} +(-2.98396 + 0.472612i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(0.277629 + 4.11375i) q^{17} +(5.68444 + 4.12999i) q^{18} +(-0.637682 + 4.02616i) q^{19} +(0.619648 - 0.725515i) q^{20} +0.751076i q^{21} +(3.15735 + 1.01544i) q^{22} +(-4.69476 + 1.94463i) q^{23} +(-3.15668 + 0.248436i) q^{24} +(-4.03931 - 0.639764i) q^{25} +(-0.222718 - 1.40618i) q^{26} +(9.69459 - 8.27996i) q^{27} +(-0.154048 - 0.180367i) q^{28} +(-2.08071 + 1.27506i) q^{29} +(-1.77579 - 2.44416i) q^{30} +(1.51364 - 1.77224i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.46038 - 8.97074i) q^{33} +(-3.53934 + 2.11497i) q^{34} +(0.0699352 - 0.215238i) q^{35} +(-1.09916 + 6.93985i) q^{36} +(-3.02068 - 4.92931i) q^{37} +(-3.87684 + 1.25966i) q^{38} +(-4.49421 - 0.353702i) q^{39} +(0.927753 + 0.222734i) q^{40} +(-5.89859 - 3.61466i) q^{41} +(-0.669214 + 0.340982i) q^{42} +(1.15134 + 1.15134i) q^{43} +(0.528646 + 3.27422i) q^{44} +(-6.19365 + 2.56549i) q^{45} +(-3.86406 - 3.30022i) q^{46} +(-4.26995 - 5.87709i) q^{47} +(-1.65446 - 2.69984i) q^{48} +(6.18691 + 3.15239i) q^{49} +(-1.26378 - 3.88950i) q^{50} +(3.89565 + 12.4608i) q^{51} +(1.15181 - 0.836837i) q^{52} +(-4.58662 - 9.00175i) q^{53} +(11.7787 + 4.87892i) q^{54} +(-2.40009 + 2.06234i) q^{55} +(0.0907721 - 0.219143i) q^{56} +(1.01271 + 12.8677i) q^{57} +(-2.08071 - 1.27506i) q^{58} +(2.29929 + 14.5171i) q^{59} +(1.37157 - 2.69187i) q^{60} +(2.45331 - 2.09532i) q^{61} +(2.26626 + 0.544080i) q^{62} +(0.389070 + 1.62059i) q^{63} +(0.951057 + 0.309017i) q^{64} +(1.25499 + 0.519832i) q^{65} +(10.4719 + 0.792599i) q^{66} +6.41814 q^{67} +(-3.49128 - 2.19339i) q^{68} +(-13.0175 + 9.45776i) q^{69} +(0.223529 - 0.0354035i) q^{70} +(0.801073 - 10.1786i) q^{71} +(-6.68246 + 2.17126i) q^{72} +(0.437925 - 0.268361i) q^{73} +(3.02068 - 4.92931i) q^{74} +(-12.9098 + 1.01602i) q^{75} +(-2.88242 - 2.88242i) q^{76} +(0.413057 + 0.669537i) q^{77} +(-1.72518 - 4.16495i) q^{78} +(1.00744 + 12.8008i) q^{79} +(0.222734 + 0.927753i) q^{80} +(11.3387 - 15.6064i) q^{81} +(0.542782 - 6.89670i) q^{82} +(-5.16438 - 2.63139i) q^{83} +(-0.607634 - 0.441472i) q^{84} +(0.0438777 - 3.93367i) q^{85} +(-0.503154 + 1.54855i) q^{86} +(-5.46390 + 5.46390i) q^{87} +(-2.67735 + 1.95749i) q^{88} -5.06302i q^{89} +(-5.09773 - 4.35387i) q^{90} +(0.176449 - 0.287939i) q^{91} +(1.18627 - 4.94117i) q^{92} +(3.35039 - 6.57552i) q^{93} +(3.29800 - 6.47270i) q^{94} +(0.907941 - 3.78185i) q^{95} +(1.65446 - 2.69984i) q^{96} +(7.72288 + 6.59596i) q^{97} +6.94374i q^{98} +(7.13483 - 22.1847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{5} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^5 + 8 * q^9	$ 160 q + 8 q^{5} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{14} - 8 q^{15} + 40 q^{16} - 12 q^{17} + 32 q^{18} + 12 q^{19} - 8 q^{22} + 32 q^{23} + 12 q^{24} - 8 q^{25} + 36 q^{27} - 4 q^{28} + 8 q^{29} - 40 q^{31} + 48 q^{33} + 8 q^{34} + 16 q^{35} - 12 q^{36} + 8 q^{37} - 16 q^{39} + 28 q^{41} + 60 q^{42} - 56 q^{43} - 8 q^{44} + 28 q^{46} - 116 q^{49} - 80 q^{50} + 8 q^{52} + 8 q^{53} - 8 q^{54} - 148 q^{57} + 8 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} - 40 q^{62} - 72 q^{63} + 144 q^{65} - 28 q^{66} - 256 q^{67} - 8 q^{69} + 8 q^{70} - 60 q^{71} - 8 q^{73} - 8 q^{74} - 116 q^{75} + 8 q^{76} - 60 q^{77} - 16 q^{78} + 40 q^{79} + 12 q^{80} - 16 q^{82} + 76 q^{83} - 56 q^{84} + 36 q^{85} - 8 q^{86} - 144 q^{87} - 4 q^{88} - 40 q^{90} + 44 q^{91} - 32 q^{92} - 40 q^{93} - 4 q^{94} + 36 q^{95} - 124 q^{97} - 176 q^{99}+O(q^{100}) $ 160 * q + 8 * q^5 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^14 - 8 * q^15 + 40 * q^16 - 12 * q^17 + 32 * q^18 + 12 * q^19 - 8 * q^22 + 32 * q^23 + 12 * q^24 - 8 * q^25 + 36 * q^27 - 4 * q^28 + 8 * q^29 - 40 * q^31 + 48 * q^33 + 8 * q^34 + 16 * q^35 - 12 * q^36 + 8 * q^37 - 16 * q^39 + 28 * q^41 + 60 * q^42 - 56 * q^43 - 8 * q^44 + 28 * q^46 - 116 * q^49 - 80 * q^50 + 8 * q^52 + 8 * q^53 - 8 * q^54 - 148 * q^57 + 8 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 - 40 * q^62 - 72 * q^63 + 144 * q^65 - 28 * q^66 - 256 * q^67 - 8 * q^69 + 8 * q^70 - 60 * q^71 - 8 * q^73 - 8 * q^74 - 116 * q^75 + 8 * q^76 - 60 * q^77 - 16 * q^78 + 40 * q^79 + 12 * q^80 - 16 * q^82 + 76 * q^83 - 56 * q^84 + 36 * q^85 - 8 * q^86 - 144 * q^87 - 4 * q^88 - 40 * q^90 + 44 * q^91 - 32 * q^92 - 40 * q^93 - 4 * q^94 + 36 * q^95 - 124 * q^97 - 176 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$.

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$3$	3.07895	−	0.739191i	1.77763	−	0.426772i	0.794144	−	0.607730i	$-0.207920\pi$
$3$	3.07895	−	0.739191i	1.77763	−	0.426772i	0.983491	+	0.180958i	$0.0579198\pi$
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	−0.951174	−	0.0748590i	−0.425378	−	0.0334780i	−0.136036	−	0.990704i	$-0.543436\pi$
$5$	−0.951174	−	0.0748590i	−0.425378	−	0.0334780i	−0.289342	+	0.957226i	$0.593436\pi$
$6$	2.05644	+	2.40778i	0.839538	+	0.982973i
$7$	−0.0553730	+	0.230645i	−0.0209290	+	0.0871756i	−0.981857	−	0.189623i	$-0.939273\pi$
$7$	−0.0553730	+	0.230645i	−0.0209290	+	0.0871756i	0.960928	+	0.276799i	$0.0892735\pi$
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$	6.26053	−	3.18990i	2.08684	−	1.06330i
$10$	−0.365124	−	0.881488i	−0.115462	−	0.278751i
$11$	2.33817	−	2.35222i	0.704985	−	0.709222i
$11$	2.33817	−	2.35222i	0.704985	−	0.709222i
$12$	−1.21174	+	2.92541i	−0.349801	+	0.844493i
$13$	−1.35403	−	0.439951i	−0.375541	−	0.122021i	0.115164	−	0.993346i	$-0.463261\pi$
$13$	−1.35403	−	0.439951i	−0.375541	−	0.122021i	−0.490705	+	0.871326i	$0.663261\pi$
$14$	−0.230645	+	0.0553730i	−0.0616425	+	0.0147990i
$15$	−2.98396	+	0.472612i	−0.770454	+	0.122028i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	0.277629	+	4.11375i	0.0673349	+	0.997730i
$17$	0.277629	+	4.11375i	0.0673349	+	0.997730i
$18$	5.68444	+	4.12999i	1.33984	+	0.973448i
$19$	−0.637682	+	4.02616i	−0.146294	+	0.923666i	0.799916	+	0.600112i	$0.204877\pi$
$19$	−0.637682	+	4.02616i	−0.146294	+	0.923666i	−0.946210	+	0.323553i	$0.895123\pi$
$20$	0.619648	−	0.725515i	0.138558	−	0.162230i
$21$			0.751076i			0.163898i
$22$	3.15735	+	1.01544i	0.673150	+	0.216492i
$23$	−4.69476	+	1.94463i	−0.978925	+	0.405484i	−0.814027	−	0.580827i	$-0.802729\pi$
$23$	−4.69476	+	1.94463i	−0.978925	+	0.405484i	−0.164898	+	0.986311i	$0.552729\pi$
$24$	−3.15668	+	0.248436i	−0.644355	+	0.0507118i
$25$	−4.03931	−	0.639764i	−0.807863	−	0.127953i
$26$	−0.222718	−	1.40618i	−0.0436785	−	0.275776i
$27$	9.69459	−	8.27996i	1.86572	−	1.59348i
$28$	−0.154048	−	0.180367i	−0.0291124	−	0.0340862i
$29$	−2.08071	+	1.27506i	−0.386379	+	0.236773i	−0.702099	−	0.712079i	$-0.747754\pi$
$29$	−2.08071	+	1.27506i	−0.386379	+	0.236773i	0.315721	+	0.948852i	$0.397754\pi$
$30$	−1.77579	−	2.44416i	−0.324213	−	0.446241i
$31$	1.51364	−	1.77224i	0.271857	−	0.318304i	−0.607636	−	0.794216i	$-0.707882\pi$
$31$	1.51364	−	1.77224i	0.271857	−	0.318304i	0.879493	+	0.475912i	$0.157882\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.46038	−	8.97074i	0.950529	−	1.56161i
$34$	−3.53934	+	2.11497i	−0.606991	+	0.362715i
$35$	0.0699352	−	0.215238i	0.0118212	−	0.0363819i
$36$	−1.09916	+	6.93985i	−0.183194	+	1.15664i
$37$	−3.02068	−	4.92931i	−0.496597	−	0.810373i	0.501914	−	0.864917i	$-0.332629\pi$
$37$	−3.02068	−	4.92931i	−0.496597	−	0.810373i	−0.998511	+	0.0545446i	$0.982629\pi$
$38$	−3.87684	+	1.25966i	−0.628907	+	0.204344i
$39$	−4.49421	−	0.353702i	−0.719649	−	0.0566376i
$40$	0.927753	+	0.222734i	0.146691	+	0.0352173i
$41$	−5.89859	−	3.61466i	−0.921205	−	0.564515i	−0.0209030	−	0.999782i	$-0.506654\pi$
$41$	−5.89859	−	3.61466i	−0.921205	−	0.564515i	−0.900302	+	0.435267i	$0.856654\pi$
$42$	−0.669214	+	0.340982i	−0.103262	+	0.0526146i
$43$	1.15134	+	1.15134i	0.175578	+	0.175578i	0.789425	−	0.613847i	$-0.210379\pi$
$43$	1.15134	+	1.15134i	0.175578	+	0.175578i	−0.613847	+	0.789425i	$0.710379\pi$
$44$	0.528646	+	3.27422i	0.0796965	+	0.493608i
$45$	−6.19365	+	2.56549i	−0.923294	+	0.382441i
$46$	−3.86406	−	3.30022i	−0.569724	−	0.486590i
$47$	−4.26995	−	5.87709i	−0.622837	−	0.857261i	0.374719	−	0.927139i	$-0.377739\pi$
$47$	−4.26995	−	5.87709i	−0.622837	−	0.857261i	−0.997556	+	0.0698772i	$0.977739\pi$
$48$	−1.65446	−	2.69984i	−0.238801	−	0.389688i
$49$	6.18691	+	3.15239i	0.883845	+	0.450342i
$50$	−1.26378	−	3.88950i	−0.178725	−	0.550059i
$51$	3.89565	+	12.4608i	0.545501	+	1.74486i
$52$	1.15181	−	0.836837i	0.159727	−	0.116048i
$53$	−4.58662	−	9.00175i	−0.630021	−	1.23649i	−0.956624	−	0.291324i	$-0.905904\pi$
$53$	−4.58662	−	9.00175i	−0.630021	−	1.23649i	0.326604	−	0.945161i	$-0.394096\pi$
$54$	11.7787	+	4.87892i	1.60288	+	0.663937i
$55$	−2.40009	+	2.06234i	−0.323629	+	0.278086i
$56$	0.0907721	−	0.219143i	0.0121299	−	0.0292842i
$57$	1.01271	+	12.8677i	0.134137	+	1.70437i
$58$	−2.08071	−	1.27506i	−0.273211	−	0.167424i
$59$	2.29929	+	14.5171i	0.299342	+	1.88997i	0.436953	+	0.899484i	$0.356058\pi$
$59$	2.29929	+	14.5171i	0.299342	+	1.88997i	−0.137611	+	0.990486i	$0.543942\pi$
$60$	1.37157	−	2.69187i	0.177069	−	0.347518i
$61$	2.45331	−	2.09532i	0.314114	−	0.268278i	−0.478387	−	0.878149i	$-0.658779\pi$
$61$	2.45331	−	2.09532i	0.314114	−	0.268278i	0.792501	+	0.609870i	$0.208779\pi$
$62$	2.26626	+	0.544080i	0.287815	+	0.0690982i
$63$	0.389070	+	1.62059i	0.0490182	+	0.204176i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	1.25499	+	0.519832i	0.155662	+	0.0644772i
$66$	10.4719	+	0.792599i	1.28901	+	0.0975622i
$67$	6.41814			0.784101			0.392050	−	0.919944i	$-0.371766\pi$
$67$	6.41814			0.784101			0.392050	+	0.919944i	$0.371766\pi$
$68$	−3.49128	−	2.19339i	−0.423380	−	0.265988i
$69$	−13.0175	+	9.45776i	−1.56712	+	1.13858i
$70$	0.223529	−	0.0354035i	0.0267168	−	0.00423152i
$71$	0.801073	−	10.1786i	0.0950699	−	1.20798i	−0.745587	−	0.666409i	$-0.767831\pi$
$71$	0.801073	−	10.1786i	0.0950699	−	1.20798i	0.840656	−	0.541569i	$-0.182169\pi$
$72$	−6.68246	+	2.17126i	−0.787536	+	0.255886i
$73$	0.437925	−	0.268361i	0.0512553	−	0.0314093i	−0.496635	−	0.867960i	$-0.665431\pi$
$73$	0.437925	−	0.268361i	0.0512553	−	0.0314093i	0.547890	+	0.836550i	$0.315431\pi$
$74$	3.02068	−	4.92931i	0.351147	−	0.573020i
$75$	−12.9098	+	1.01602i	−1.49069	+	0.117320i
$76$	−2.88242	−	2.88242i	−0.330636	−	0.330636i
$77$	0.413057	+	0.669537i	0.0470722	+	0.0763008i
$78$	−1.72518	−	4.16495i	−0.195338	−	0.471587i
$79$	1.00744	+	12.8008i	0.113346	+	1.44020i	0.746095	+	0.665840i	$0.231927\pi$
$79$	1.00744	+	12.8008i	0.113346	+	1.44020i	−0.632749	+	0.774357i	$0.718073\pi$
$80$	0.222734	+	0.927753i	0.0249024	+	0.103726i
$81$	11.3387	−	15.6064i	1.25986	−	1.73405i
$82$	0.542782	−	6.89670i	0.0599403	−	0.761613i
$83$	−5.16438	−	2.63139i	−0.566865	−	0.288832i	0.146976	−	0.989140i	$-0.453046\pi$
$83$	−5.16438	−	2.63139i	−0.566865	−	0.288832i	−0.713841	+	0.700308i	$0.753046\pi$
$84$	−0.607634	−	0.441472i	−0.0662983	−	0.0481685i
$85$	0.0438777	−	3.93367i	0.00475920	−	0.426667i
$86$	−0.503154	+	1.54855i	−0.0542565	+	0.166984i
$87$	−5.46390	+	5.46390i	−0.585792	+	0.585792i
$88$	−2.67735	+	1.95749i	−0.285407	+	0.208669i
$89$		−	5.06302i		−	0.536679i	−0.963324	−	0.268340i	$-0.913525\pi$
$89$		−	5.06302i		−	0.536679i	0.963324	−	0.268340i	$-0.0864749\pi$
$90$	−5.09773	−	4.35387i	−0.537348	−	0.458938i
$91$	0.176449	−	0.287939i	0.0184969	−	0.0301842i
$92$	1.18627	−	4.94117i	0.123677	−	0.515152i
$93$	3.35039	−	6.57552i	0.347420	−	0.681849i
$94$	3.29800	−	6.47270i	0.340163	−	0.667608i
$95$	0.907941	−	3.78185i	0.0931528	−	0.388009i
$96$	1.65446	−	2.69984i	0.168858	−	0.275551i
$97$	7.72288	+	6.59596i	0.784139	+	0.669718i	0.948534	−	0.316676i	$-0.102567\pi$
$97$	7.72288	+	6.59596i	0.784139	+	0.669718i	−0.164394	+	0.986395i	$0.552567\pi$
$98$			6.94374i			0.701423i
$99$	7.13483	−	22.1847i	0.717078	−	2.22965i
$100$	2.89183	−	2.89183i	0.289183	−	0.289183i
$101$	−5.49531	+	16.9128i	−0.546804	+	1.68289i	0.169859	+	0.985468i	$0.445669\pi$
$101$	−5.49531	+	16.9128i	−0.546804	+	1.68289i	−0.716663	+	0.697420i	$0.754331\pi$
$102$	−9.33408	+	9.12814i	−0.924212	+	0.903821i
$103$	3.42706	+	2.48991i	0.337678	+	0.245338i	0.743682	−	0.668534i	$-0.233078\pi$
$103$	3.42706	+	2.48991i	0.337678	+	0.245338i	−0.406003	+	0.913872i	$0.633078\pi$
$104$	1.26854	+	0.646352i	0.124390	+	0.0633800i
$105$	0.0562249	−	0.714404i	0.00548698	−	0.0697187i
$106$	5.93834	−	8.17342i	0.576782	−	0.793873i
$107$	−3.65926	−	15.2419i	−0.353754	−	1.47349i	−0.811471	−	0.584393i	$-0.801333\pi$
$107$	−3.65926	−	15.2419i	−0.353754	−	1.47349i	0.457717	−	0.889098i	$-0.348667\pi$
$108$	1.00029	+	12.7099i	0.0962532	+	1.22301i
$109$	2.87001	+	6.92883i	0.274898	+	0.663661i	0.999679	−	0.0253169i	$-0.00805949\pi$
$109$	2.87001	+	6.92883i	0.274898	+	0.663661i	−0.724782	+	0.688978i	$0.758059\pi$
$110$	−2.92718	−	1.20222i	−0.279096	−	0.114627i
$111$	−12.9442	−	12.9442i	−1.22861	−	1.22861i
$112$	0.236468	−	0.0186104i	0.0223441	−	0.00175852i
$113$	4.90888	−	8.01057i	0.461789	−	0.753571i	−0.533977	−	0.845499i	$-0.679303\pi$
$113$	4.90888	−	8.01057i	0.461789	−	0.753571i	0.995766	+	0.0919282i	$0.0293030\pi$
$114$	−11.0055	+	6.74417i	−1.03076	+	0.631649i
$115$	4.61111	−	1.49824i	0.429988	−	0.139712i
$116$	0.191465	−	2.43280i	0.0177771	−	0.225879i
$117$	−9.88036	+	1.56489i	−0.913439	+	0.144675i
$118$	−11.8910	+	8.63932i	−1.09466	+	0.795314i
$119$	−0.964188	−	0.163757i	−0.0883870	−	0.0150115i
$120$	3.02115			0.275792
$121$	−0.0659123	−	10.9998i	−0.00599203	−	0.999982i
$122$	2.98072	+	1.23466i	0.269862	+	0.111780i
$123$	−20.8334	−	6.76918i	−1.87848	−	0.610357i
$124$	0.544080	+	2.26626i	0.0488598	+	0.203516i
$125$	8.43296	+	2.02458i	0.754267	+	0.181084i
$126$	−1.26733	+	1.08240i	−0.112902	+	0.0964277i
$127$	−4.38228	+	8.60071i	−0.388864	+	0.763189i	−0.999589	−	0.0286535i	$-0.990878\pi$
$127$	−4.38228	+	8.60071i	−0.388864	+	0.763189i	0.610725	+	0.791843i	$0.290878\pi$
$128$	0.156434	+	0.987688i	0.0138270	+	0.0873001i
$129$	4.39598	+	2.69386i	0.387045	+	0.237181i
$130$	0.106578	+	1.35420i	0.00934749	+	0.118771i
$131$	2.08789	−	5.04061i	0.182420	−	0.440401i	−0.806044	−	0.591855i	$-0.798396\pi$
$131$	2.08789	−	5.04061i	0.182420	−	0.440401i	0.988464	+	0.151455i	$0.0483957\pi$
$132$	4.04795	+	9.69041i	0.352329	+	0.843442i
$133$	−0.893304	−	0.370019i	−0.0774593	−	0.0320847i
$134$	2.91378	+	5.71861i	0.251712	+	0.494012i
$135$	−9.84107	+	7.14996i	−0.846985	+	0.615370i
$136$	0.369321	−	4.10653i	0.0316690	−	0.352132i
$137$	0.610990	+	1.88043i	0.0522004	+	0.160656i	0.973758	−	0.227585i	$-0.0730828\pi$
$137$	0.610990	+	1.88043i	0.0522004	+	0.160656i	−0.921558	+	0.388241i	$0.873083\pi$
$138$	−14.3367	−	7.30494i	−1.22042	−	0.621837i
$139$	−1.87595	−	3.06128i	−0.159116	−	0.259654i	0.763140	−	0.646233i	$-0.223657\pi$
$139$	−1.87595	−	3.06128i	−0.159116	−	0.259654i	−0.922256	+	0.386579i	$0.873657\pi$
$140$	0.133025	+	0.183093i	0.0112426	+	0.0154742i
$141$	−17.4913	−	14.9390i	−1.47303	−	1.25809i
$142$	9.43288	−	3.90723i	0.791590	−	0.327887i
$143$	−4.20082	+	2.15630i	−0.351290	+	0.180319i
$144$	−4.96838	−	4.96838i	−0.414032	−	0.414032i
$145$	2.07457	−	1.05705i	0.172284	−	0.0877830i
$146$	0.437925	+	0.268361i	0.0362429	+	0.0222097i
$147$	21.3794	+	5.13275i	1.76335	+	0.423342i
$148$	5.76340	+	0.453590i	0.473749	+	0.0372848i
$149$	16.3467	−	5.31136i	1.33917	−	0.435123i	0.450135	−	0.892960i	$-0.351376\pi$
$149$	16.3467	−	5.31136i	1.33917	−	0.435123i	0.889036	+	0.457837i	$0.151376\pi$
$150$	−6.76619	−	11.0414i	−0.552457	−	0.901528i
$151$	−1.01623	+	6.41625i	−0.0826999	+	0.522147i	0.911209	+	0.411944i	$0.135150\pi$
$151$	−1.01623	+	6.41625i	−0.0826999	+	0.522147i	−0.993909	+	0.110203i	$0.964850\pi$
$152$	1.25966	−	3.87684i	0.102172	−	0.314453i
$153$	14.8605	+	24.8686i	1.20140	+	2.01051i
$154$	−0.409038	+	0.672000i	−0.0329612	+	0.0541513i
$155$	−1.57240	+	1.57240i	−0.126298	+	0.126298i
$156$	2.92778	−	3.42799i	0.234410	−	0.274459i
$157$	12.9014	+	17.7573i	1.02964	+	1.41718i	0.905214	+	0.424956i	$0.139710\pi$
$157$	12.9014	+	17.7573i	1.02964	+	1.41718i	0.124430	+	0.992228i	$0.460290\pi$
$158$	−10.9482	+	6.70906i	−0.870991	+	0.533744i
$159$	−20.7760	−	24.3256i	−1.64764	−	1.92914i
$160$	−0.725515	+	0.619648i	−0.0573570	+	0.0489875i
$161$	−0.188557	−	1.19050i	−0.0148604	−	0.0938248i
$162$	19.0531	+	3.01772i	1.49695	+	0.237094i
$163$	2.15645	−	0.169716i	0.168906	−	0.0132932i	0.00627588	−	0.999980i	$-0.498002\pi$
$163$	2.15645	−	0.169716i	0.168906	−	0.0132932i	0.162630	+	0.986687i	$0.448002\pi$
$164$	6.39142	−	2.64741i	0.499086	−	0.206728i
$165$	−5.86531	+	8.12398i	−0.456614	+	0.632451i
$166$		−	5.79612i		−	0.449867i
$167$	14.1255	−	16.5388i	1.09306	−	1.27981i	0.135753	−	0.990743i	$-0.456655\pi$
$167$	14.1255	−	16.5388i	1.09306	−	1.27981i	0.957309	−	0.289068i	$-0.0933453\pi$
$168$	0.117494	−	0.741829i	0.00906488	−	0.0572334i
$169$	−8.87738	−	6.44979i	−0.682875	−	0.496138i
$170$	3.52485	−	1.74676i	0.270344	−	0.133970i
$171$	8.85083	+	27.2401i	0.676840	+	2.08310i
$172$	−1.60819	+	0.254713i	−0.122624	+	0.0194217i
$173$	−2.60010	+	0.624228i	−0.197682	+	0.0474592i	−0.331077	−	0.943604i	$-0.607412\pi$
$173$	−2.60010	+	0.624228i	−0.197682	+	0.0474592i	0.133395	+	0.991063i	$0.457412\pi$
$174$	−7.34894	−	2.38781i	−0.557121	−	0.181020i
$175$	0.371227	−	0.896222i	0.0280621	−	0.0677480i
$176$	−2.95963	−	1.49686i	−0.223091	−	0.112830i
$177$	17.8103	+	42.9980i	1.33871	+	3.23193i
$178$	4.51119	−	2.29856i	0.338128	−	0.172285i
$179$	−16.3336	−	2.58698i	−1.22083	−	0.193360i	−0.487432	−	0.873161i	$-0.662066\pi$
$179$	−16.3336	−	2.58698i	−1.22083	−	0.193360i	−0.733397	+	0.679801i	$0.762066\pi$
$180$	1.56501	−	6.51872i	0.116649	−	0.485877i
$181$	8.49371	+	9.94486i	0.631333	+	0.739195i	0.980207	−	0.197974i	$-0.0634361\pi$
$181$	8.49371	+	9.94486i	0.631333	+	0.739195i	−0.348875	+	0.937169i	$0.613436\pi$
$182$	0.336662	+	0.0264959i	0.0249550	+	0.00196400i
$183$	6.00477	−	8.26486i	0.443885	−	0.610956i
$184$	4.94117	−	1.18627i	0.364268	−	0.0874529i
$185$	2.50419	+	4.91475i	0.184112	+	0.361340i
$186$	7.37987			0.541119
$187$	10.3256	+	8.96560i	0.755083	+	0.655630i
$188$	7.26448			0.529817
$189$	1.37291	+	2.69449i	0.0998647	+	0.195996i
$190$	3.78185	−	0.907941i	0.274364	−	0.0658690i
$191$	−11.5569	+	15.9067i	−0.836226	+	1.15097i	0.150506	+	0.988609i	$0.451910\pi$
$191$	−11.5569	+	15.9067i	−0.836226	+	1.15097i	−0.986732	+	0.162358i	$0.948090\pi$
$192$	3.15668	+	0.248436i	0.227814	+	0.0179293i
$193$	13.1472	+	15.3933i	0.946353	+	1.10804i	0.994023	+	0.109174i	$0.0348205\pi$
$193$	13.1472	+	15.3933i	0.946353	+	1.10804i	−0.0476698	+	0.998863i	$0.515180\pi$
$194$	−2.37093	+	9.87564i	−0.170223	+	0.709029i
$195$	4.24830	+	0.672864i	0.304227	+	0.0481848i
$196$	−6.18691	+	3.15239i	−0.441922	+	0.225171i
$197$	9.86829	+	23.8242i	0.703087	+	1.69740i	0.716592	+	0.697493i	$0.245701\pi$
$197$	9.86829	+	23.8242i	0.703087	+	1.69740i	−0.0135054	+	0.999909i	$0.504299\pi$
$198$	23.0059	−	3.71446i	1.63495	−	0.263975i
$199$	1.91988	−	4.63501i	0.136097	−	0.328567i	−0.841107	−	0.540868i	$-0.818096\pi$
$199$	1.91988	−	4.63501i	0.136097	−	0.328567i	0.977204	+	0.212301i	$0.0680958\pi$
$200$	3.88950	+	1.26378i	0.275029	+	0.0893624i
$201$	19.7612	−	4.74423i	1.39384	−	0.334632i
$202$	−17.5642	+	2.78190i	−1.23582	+	0.195734i
$203$	−0.178872	−	0.550510i	−0.0125543	−	0.0386382i
$204$	−12.3708	−	4.17263i	−0.866131	−	0.292143i
$205$	5.33999	+	3.87973i	0.372961	+	0.270972i
$206$	−0.662669	+	4.18393i	−0.0461703	+	0.291508i
$207$	−23.1885	+	27.1502i	−1.61171	+	1.88707i
$208$			1.42371i			0.0987167i
$209$	7.97943	+	10.9138i	0.551949	+	0.754926i
$210$	0.662065	−	0.274236i	0.0456868	−	0.0189241i
$211$	17.5715	−	1.38291i	1.20967	−	0.0952035i	0.542468	−	0.840076i	$-0.317490\pi$
$211$	17.5715	−	1.38291i	1.20967	−	0.0952035i	0.667207	+	0.744873i	$0.267490\pi$
$212$	9.97852	+	1.58044i	0.685327	+	0.108545i
$213$	−5.05747	−	31.9316i	−0.346532	−	2.18792i
$214$	11.9194	−	10.1801i	0.814791	−	0.695898i
$215$	−1.00894	−	1.18131i	−0.0688089	−	0.0805649i
$216$	−10.8705	+	6.66145i	−0.739644	+	0.453254i
$217$	0.324944	+	0.447247i	0.0220586	+	0.0303611i
$218$	−4.87067	+	5.70282i	−0.329884	+	0.386244i
$219$	1.14998	−	1.14998i	0.0777085	−	0.0777085i
$220$	−0.257730	−	3.15393i	−0.0173761	−	0.212638i
$221$	1.43393	−	5.69229i	0.0964566	−	0.382905i
$222$	5.65684	−	17.4100i	0.379662	−	1.16848i
$223$	3.76182	−	23.7512i	0.251910	−	1.59050i	−0.459797	−	0.888024i	$-0.652078\pi$
$223$	3.76182	−	23.7512i	0.251910	−	1.59050i	0.711708	−	0.702476i	$-0.247922\pi$
$224$	0.123936	+	0.202245i	0.00828082	+	0.0135131i
$225$	−27.3290	+	8.87974i	−1.82193	+	0.591983i
$226$	9.36606	+	0.737125i	0.623021	+	0.0490328i
$227$	−26.3744	−	6.33194i	−1.75053	−	0.420266i	−0.773577	−	0.633703i	$-0.781534\pi$
$227$	−26.3744	−	6.33194i	−1.75053	−	0.420266i	−0.976957	+	0.213437i	$0.931534\pi$
$228$	−11.0055	−	6.74417i	−0.728856	−	0.446643i
$229$	15.1467	−	7.71761i	1.00092	−	0.509994i	0.124848	−	0.992176i	$-0.460156\pi$
$229$	15.1467	−	7.71761i	1.00092	−	0.509994i	0.876071	+	0.482182i	$0.160156\pi$
$230$	3.42834	+	3.42834i	0.226058	+	0.226058i
$231$	1.76670	+	1.75614i	0.116240	+	0.115546i
$232$	2.25456	−	0.933870i	0.148019	−	0.0613115i
$233$	5.47385	+	4.67511i	0.358604	+	0.306277i	0.810437	−	0.585826i	$-0.199230\pi$
$233$	5.47385	+	4.67511i	0.358604	+	0.306277i	−0.451833	+	0.892103i	$0.649230\pi$
$234$	−5.87992	−	8.09301i	−0.384382	−	0.529057i
$235$	3.62152	+	5.90978i	0.236242	+	0.385511i
$236$	−13.0961	−	6.67280i	−0.852484	−	0.434362i
$237$	12.5641	+	38.6682i	0.816124	+	2.51177i
$238$	−0.291824	−	0.933442i	−0.0189161	−	0.0605061i
$239$	−3.92447	+	2.85129i	−0.253853	+	0.184435i	−0.707433	−	0.706781i	$-0.750147\pi$
$239$	−3.92447	+	2.85129i	−0.253853	+	0.184435i	0.453580	+	0.891216i	$0.350147\pi$
$240$	1.37157	+	2.69187i	0.0885347	+	0.173759i
$241$	−3.78065	−	1.56600i	−0.243533	−	0.100875i	0.257579	−	0.966257i	$-0.417075\pi$
$241$	−3.78065	−	1.56600i	−0.243533	−	0.100875i	−0.501112	+	0.865383i	$0.667075\pi$
$242$	9.77097	−	5.05253i	0.628102	−	0.324789i
$243$	8.73856	−	21.0967i	0.560579	−	1.35336i
$244$	0.253133	+	3.21636i	0.0162052	+	0.205907i
$245$	−5.64885	−	3.46162i	−0.360892	−	0.221155i
$246$	−3.42678	−	21.6358i	−0.218484	−	1.37945i
$247$	2.63476	−	5.17100i	0.167646	−	0.329023i
$248$	−1.77224	+	1.51364i	−0.112537	+	0.0961161i
$249$	−17.8460	−	4.28444i	−1.13094	−	0.271516i
$250$	2.02458	+	8.43296i	0.128045	+	0.533348i
$251$	−13.0767	−	4.24887i	−0.825393	−	0.268187i	−0.134290	−	0.990942i	$-0.542875\pi$
$251$	−13.0767	−	4.24887i	−0.825393	−	0.268187i	−0.691104	+	0.722756i	$0.742875\pi$
$252$	−1.53978	−	0.637797i	−0.0969969	−	0.0401774i
$253$	−6.40294	+	15.5900i	−0.402549	+	0.980136i
$254$	−9.65280			−0.605670
$255$	−2.77264	−	12.1440i	−0.173629	−	0.760489i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.578281	+	0.0915908i	−0.0360722	+	0.00571327i	−0.174444	−	0.984667i	$-0.555813\pi$
$257$	−0.578281	+	0.0915908i	−0.0360722	+	0.00571327i	0.138372	+	0.990380i	$0.455813\pi$
$258$	−0.404514	+	5.13984i	−0.0251839	+	0.319992i
$259$	1.30418	−	0.423755i	0.0810380	−	0.0263309i
$260$	−1.15821	+	0.709755i	−0.0718294	+	0.0440171i
$261$	−8.95905	+	14.6198i	−0.554551	+	0.904945i
$262$	5.43910	−	0.428067i	0.336029	−	0.0264460i
$263$	−16.0648	−	16.0648i	−0.990601	−	0.990601i	0.00935519	−	0.999956i	$-0.497022\pi$
$263$	−16.0648	−	16.0648i	−0.990601	−	0.990601i	−0.999956	+	0.00935519i	$0.997022\pi$
$264$	−6.79648	+	8.00611i	−0.418295	+	0.492742i
$265$	3.68881	+	8.90558i	0.226602	+	0.547066i
$266$	−0.0758625	−	0.963925i	−0.00465143	−	0.0591020i
$267$	−3.74254	−	15.5888i	−0.229040	−	0.954019i
$268$	−3.77249	+	5.19239i	−0.230441	+	0.317175i
$269$	0.186057	−	2.36408i	0.0113441	−	0.144140i	−0.988637	−	0.150324i	$-0.951968\pi$
$269$	0.186057	−	2.36408i	0.0113441	−	0.144140i	0.999981	+	0.00618365i	$0.00196833\pi$
$270$	−10.8384	−	5.52245i	−0.659605	−	0.336085i
$271$	−16.8312	−	12.2285i	−1.02242	−	0.742831i	−0.0556421	−	0.998451i	$-0.517721\pi$
$271$	−16.8312	−	12.2285i	−1.02242	−	0.742831i	−0.966777	+	0.255619i	$0.917721\pi$
$272$	3.82661	−	1.53526i	0.232023	−	0.0930887i
$273$	0.330437	−	1.01698i	0.0199990	−	0.0615505i
$274$	−1.39810	+	1.39810i	−0.0844621	+	0.0844621i
$275$	−10.9495	+	8.00549i	−0.660278	+	0.482749i
$276$		−	16.0905i		−	0.968535i
$277$	−0.668219	−	0.570713i	−0.0401494	−	0.0342908i	0.629147	−	0.777286i	$-0.283404\pi$
$277$	−0.668219	−	0.570713i	−0.0401494	−	0.0342908i	−0.669296	+	0.742996i	$0.733404\pi$
$278$	1.87595	−	3.06128i	0.112512	−	0.183603i
$279$	3.82290	−	15.9235i	0.228871	−	0.953316i
$280$	−0.102745	+	0.201648i	−0.00614018	+	0.0120508i
$281$	8.32272	−	16.3343i	0.496492	−	0.974420i	−0.497756	−	0.867317i	$-0.665843\pi$
$281$	8.32272	−	16.3343i	0.496492	−	0.974420i	0.994248	−	0.107103i	$-0.0341575\pi$
$282$	5.36984	−	22.3670i	0.319769	−	1.33194i
$283$	8.94328	−	14.5941i	0.531623	−	0.867530i	−0.468248	−	0.883597i	$-0.655115\pi$
$283$	8.94328	−	14.5941i	0.531623	−	0.867530i	0.999871	+	0.0160672i	$0.00511457\pi$
$284$	7.76380	+	6.63091i	0.460697	+	0.393472i
$285$		−	12.3153i		−	0.729494i
$286$	−3.82841	−	2.76402i	−0.226379	−	0.163440i
$287$	1.16033	−	1.16033i	0.0684918	−	0.0684918i
$288$	2.17126	−	6.68246i	0.127943	−	0.393768i
$289$	−16.8458	+	2.28419i	−0.990932	+	0.134364i
$290$	1.88367	+	1.36857i	0.110613	+	0.0803650i
$291$	28.6541	+	14.6000i	1.67973	+	0.855865i
$292$	−0.0402974	+	0.512027i	−0.00235823	+	0.0299641i
$293$	19.2710	−	26.5243i	1.12583	−	1.54957i	0.330063	−	0.943959i	$-0.392930\pi$
$293$	19.2710	−	26.5243i	1.12583	−	1.54957i	0.795763	−	0.605608i	$-0.207070\pi$
$294$	5.13275	+	21.3794i	0.299348	+	1.24687i
$295$	−1.10029	−	13.9805i	−0.0640611	−	0.813973i
$296$	2.21238	+	5.34116i	0.128592	+	0.310448i
$297$	3.19129	−	42.1638i	0.185177	−	2.44659i
$298$	12.1537	+	12.1537i	0.704044	+	0.704044i
$299$	7.21240	−	0.567628i	0.417104	−	0.0328268i
$300$	6.76619	−	11.0414i	0.390646	−	0.637477i
$301$	−0.329304	+	0.201798i	−0.0189808	+	0.0116314i
$302$	−6.17828	+	2.00744i	−0.355520	+	0.115515i
$303$	−4.41799	+	56.1359i	−0.253807	+	3.22492i
$304$	4.02616	−	0.637682i	0.230916	−	0.0365736i
$305$	−2.49037	+	1.80936i	−0.142598	+	0.103604i
$306$	−15.4116	+	24.5310i	−0.881021	+	1.40234i
$307$	3.64845			0.208228			0.104114	−	0.994565i	$-0.466799\pi$
$307$	3.64845			0.208228			0.104114	+	0.994565i	$0.466799\pi$
$308$	−0.784456	−	0.0593737i	−0.0446985	−	0.00338313i
$309$	12.3923	+	5.13305i	0.704972	+	0.292009i
$310$	−2.11487	−	0.687164i	−0.120117	−	0.0390283i
$311$	7.18753	+	29.9382i	0.407567	+	1.69764i	0.678133	+	0.734939i	$0.262789\pi$
$311$	7.18753	+	29.9382i	0.407567	+	1.69764i	−0.270566	+	0.962701i	$0.587211\pi$
$312$	4.38355	+	1.05240i	0.248169	+	0.0595802i
$313$	7.61578	−	6.50449i	0.430469	−	0.367656i	−0.407654	−	0.913137i	$-0.633653\pi$
$313$	7.61578	−	6.50449i	0.430469	−	0.367656i	0.838123	+	0.545481i	$0.183653\pi$
$314$	−9.96472	+	19.5569i	−0.562342	+	1.10366i
$315$	−0.248757	−	1.57059i	−0.0140159	−	0.0884929i
$316$	−10.9482	−	6.70906i	−0.615883	−	0.377414i
$317$	0.787038	+	10.0003i	0.0442045	+	0.561671i	0.978646	+	0.205554i	$0.0658996\pi$
$317$	0.787038	+	10.0003i	0.0442045	+	0.561671i	−0.934441	+	0.356117i	$0.884100\pi$
$318$	12.2421	−	29.5551i	0.686505	−	1.65737i
$319$	−1.86583	+	7.87562i	−0.104466	+	0.440950i
$320$	−0.881488	−	0.365124i	−0.0492767	−	0.0204111i
$321$	−22.5334	−	44.2242i	−1.25769	−	2.46836i
$322$	0.975143	−	0.708483i	0.0543426	−	0.0394822i
$323$	−16.7397	−	1.50548i	−0.931420	−	0.0837673i
$324$	5.96113	+	18.3465i	0.331174	+	1.01925i
$325$	5.18789	+	2.64336i	0.287772	+	0.146627i
$326$	1.13022	+	1.84436i	0.0625973	+	0.102150i
$327$	13.9584	+	19.2120i	0.771900	+	1.06243i
$328$	5.26051	+	4.49290i	0.290463	+	0.248079i
$329$	1.59196	−	0.659412i	0.0877676	−	0.0363545i
$330$	−9.90131	−	1.53782i	−0.545049	−	0.0846542i
$331$	8.05922	+	8.05922i	0.442975	+	0.442975i	0.893011	−	0.450036i	$-0.148589\pi$
$331$	8.05922	+	8.05922i	0.442975	+	0.442975i	−0.450036	+	0.893011i	$0.648589\pi$
$332$	5.16438	−	2.63139i	0.283432	−	0.144416i
$333$	−34.6351	−	21.2244i	−1.89799	−	1.16309i
$334$	21.1490	+	5.07743i	1.15722	+	0.277824i
$335$	−6.10477	−	0.480456i	−0.333539	−	0.0262501i
$336$	0.714316	−	0.232095i	0.0389691	−	0.0126618i
$337$	−14.0368	−	22.9059i	−0.764631	−	1.24776i	−0.963492	−	0.267736i	$-0.913724\pi$
$337$	−14.0368	−	22.9059i	−0.764631	−	1.24776i	0.198862	−	0.980028i	$-0.436276\pi$
$338$	1.71656	−	10.8379i	0.0933687	−	0.589507i
$339$	9.19288	−	28.2928i	0.499289	−	1.53665i
$340$	3.15662	+	2.34765i	0.171192	+	0.127319i
$341$	−0.629566	−	7.70422i	−0.0340929	−	0.417207i
$342$	−20.2529	+	20.2529i	−1.09515	+	1.09515i
$343$	−2.14801	+	2.51500i	−0.115982	+	0.135797i
$344$	−0.957056	−	1.31727i	−0.0516010	−	0.0710227i
$345$	13.0899	−	8.02150i	0.704737	−	0.431863i
$346$	−1.73661	−	2.03331i	−0.0933608	−	0.109311i
$347$	−18.7055	+	15.9760i	−1.00416	+	0.857635i	−0.989829	−	0.142262i	$-0.954563\pi$
$347$	−18.7055	+	15.9760i	−1.00416	+	0.857635i	−0.0143331	+	0.999897i	$0.504563\pi$
$348$	−1.20879	−	7.63199i	−0.0647979	−	0.409118i
$349$	−3.17988	−	0.503644i	−0.170215	−	0.0269594i	0.0707450	−	0.997494i	$-0.477462\pi$
$349$	−3.17988	−	0.503644i	−0.170215	−	0.0269594i	−0.240960	+	0.970535i	$0.577462\pi$
$350$	0.967073	−	0.0761103i	0.0516922	−	0.00406827i
$351$	−16.7696	+	6.94618i	−0.895093	+	0.370760i
$352$	−0.00993670	−	3.31661i	−0.000529628	−	0.176776i
$353$			6.56177i			0.349248i	0.984635	+	0.174624i	$0.0558710\pi$
$353$			6.56177i			0.349248i	−0.984635	+	0.174624i	$0.944129\pi$
$354$	−30.2258	+	35.3898i	−1.60648	+	1.88095i
$355$	−1.52392	+	9.62165i	−0.0808813	+	0.510664i
$356$	4.09607	+	2.97597i	0.217091	+	0.157726i
$357$	−3.08974	+	0.208521i	−0.163526	+	0.0110361i
$358$	−5.11027	−	15.7278i	−0.270086	−	0.831239i
$359$	19.0534	−	3.01777i	1.00560	−	0.159272i	0.368154	−	0.929765i	$-0.379990\pi$
$359$	19.0534	−	3.01777i	1.00560	−	0.159272i	0.637448	+	0.770493i	$0.279990\pi$
$360$	6.51872	−	1.56501i	0.343567	−	0.0824831i
$361$	2.26671	+	0.736498i	0.119300	+	0.0387631i
$362$	−5.00487	+	12.0828i	−0.263050	+	0.635059i
$363$	−8.33390	−	33.8192i	−0.437416	−	1.77505i
$364$	0.129233	+	0.311997i	0.00677367	+	0.0163531i
$365$	−0.436632	+	0.222475i	−0.0228544	+	0.0116449i
$366$	10.0902	+	1.59812i	0.527421	+	0.0835352i
$367$	−3.83646	+	15.9800i	−0.200262	+	0.834149i	0.778250	+	0.627955i	$0.216108\pi$
$367$	−3.83646	+	15.9800i	−0.200262	+	0.834149i	−0.978511	+	0.206194i	$0.933892\pi$
$368$	3.30022	+	3.86406i	0.172036	+	0.201428i
$369$	−48.4587	−	3.81378i	−2.52266	−	0.198537i
$370$	−3.24220	+	4.46250i	−0.168554	+	0.231994i
$371$	2.33018	−	0.559427i	0.120977	−	0.0290440i
$372$	3.35039	+	6.57552i	0.173710	+	0.340925i
$373$	−9.72344			−0.503461			−0.251730	−	0.967797i	$-0.581000\pi$
$373$	−9.72344			−0.503461			−0.251730	+	0.967797i	$0.581000\pi$
$374$	−3.30068	+	13.2705i	−0.170674	+	0.686200i
$375$	27.4613			1.41809
$376$	3.29800	+	6.47270i	0.170082	+	0.333804i
$377$	3.37832	−	0.811062i	0.173992	−	0.0417718i
$378$	−1.77752	+	2.44655i	−0.0914259	+	0.125837i
$379$	25.2774	+	1.98937i	1.29841	+	0.102187i	0.708748	−	0.705462i	$-0.249260\pi$
$379$	25.2774	+	1.98937i	1.29841	+	0.102187i	0.589663	+	0.807649i	$0.299260\pi$
$380$	2.52590	+	2.95745i	0.129576	+	0.151714i
$381$	−7.13526	+	29.7205i	−0.365551	+	1.52263i
$382$	−19.4197	−	3.07577i	−0.993597	−	0.157370i
$383$	21.1786	−	10.7911i	1.08218	−	0.551397i	0.180398	−	0.983594i	$-0.442261\pi$
$383$	21.1786	−	10.7911i	1.08218	−	0.551397i	0.901779	+	0.432197i	$0.142261\pi$
$384$	1.21174	+	2.92541i	0.0618366	+	0.149287i
$385$	−0.342768	−	0.667767i	−0.0174691	−	0.0340326i
$386$	−7.74688	+	18.7026i	−0.394306	+	0.951939i
$387$	10.8807	+	3.53534i	0.553095	+	0.179711i
$388$	−9.87564	+	2.37093i	−0.501359	+	0.120366i
$389$	4.24406	−	0.672193i	0.215182	−	0.0340815i	−0.0479124	−	0.998852i	$-0.515257\pi$
$389$	4.24406	−	0.672193i	0.215182	−	0.0340815i	0.263095	+	0.964770i	$0.415257\pi$
$390$	1.32916	+	4.09073i	0.0673046	+	0.207142i
$391$	−9.30313	−	18.7732i	−0.470480	−	0.949400i
$392$	−5.61760	−	4.08143i	−0.283732	−	0.206143i
$393$	2.70254	−	17.0632i	0.136325	−	0.860723i
$394$	−16.7474	+	19.6087i	−0.843721	+	0.987870i
$395$		−	12.2512i		−	0.616423i
$396$	13.7540	+	18.8120i	0.691167	+	0.945340i
$397$	21.9528	−	9.09317i	1.10178	−	0.456373i	0.243682	−	0.969855i	$-0.421645\pi$
$397$	21.9528	−	9.09317i	1.10178	−	0.456373i	0.858100	+	0.513482i	$0.171645\pi$
$398$	5.00143	−	0.393621i	0.250699	−	0.0197304i
$399$	−3.02396	−	0.478948i	−0.151387	−	0.0239774i
$400$	0.639764	+	4.03931i	0.0319882	+	0.201966i
$401$	−14.0226	+	11.9764i	−0.700255	+	0.598075i	−0.926634	−	0.375965i	$-0.877311\pi$
$401$	−14.0226	+	11.9764i	−0.700255	+	0.598075i	0.226379	+	0.974039i	$0.427311\pi$
$402$	13.1985	+	15.4535i	0.658282	+	0.770750i
$403$	−2.82921	+	1.73374i	−0.140933	+	0.0863639i
$404$	−10.4527	−	14.3869i	−0.520041	−	0.715775i
$405$	−11.9534	+	13.9956i	−0.593969	+	0.695449i
$406$	0.409302	−	0.409302i	0.0203133	−	0.0203133i
$407$	−18.6577	−	4.42024i	−0.924828	−	0.219103i
$408$	−1.89839	−	12.9168i	−0.0939843	−	0.639478i
$409$	5.53895	−	17.0471i	0.273883	−	0.842926i	−0.715629	−	0.698480i	$-0.753860\pi$
$409$	5.53895	−	17.0471i	0.273883	−	0.842926i	0.989513	−	0.144446i	$-0.0461400\pi$
$410$	−1.03256	+	6.51933i	−0.0509945	+	0.321967i
$411$	3.27121	+	5.33813i	0.161357	+	0.263311i
$412$	−4.02875	+	1.30902i	−0.198482	+	0.0644908i
$413$	−3.47562	−	0.273538i	−0.171024	−	0.0134599i
$414$	−34.7184	−	8.33515i	−1.70632	−	0.409650i
$415$	4.71525	+	2.88951i	0.231462	+	0.141840i
$416$	−1.26854	+	0.646352i	−0.0621952	+	0.0316900i
$417$	−8.03885	−	8.03885i	−0.393664	−	0.393664i
$418$	−6.10171	+	12.0645i	−0.298444	+	0.590094i
$419$	3.68723	−	1.52730i	0.180133	−	0.0746135i	−0.290794	−	0.956786i	$-0.593919\pi$
$419$	3.68723	−	1.52730i	0.180133	−	0.0746135i	0.470927	+	0.882172i	$0.343919\pi$
$420$	0.544917	+	0.465403i	0.0265892	+	0.0227094i
$421$	−10.6625	−	14.6757i	−0.519660	−	0.715250i	0.465851	−	0.884863i	$-0.345748\pi$
$421$	−10.6625	−	14.6757i	−0.519660	−	0.715250i	−0.985511	+	0.169613i	$0.945748\pi$
$422$	9.20950	+	15.0285i	0.448311	+	0.731577i
$423$	−45.4795	−	23.1730i	−2.21129	−	1.12671i
$424$	3.12197	+	9.60843i	0.151616	+	0.466627i
$425$	1.51040	−	16.7943i	0.0732651	−	0.814645i
$426$	26.1552	−	19.0029i	1.26722	−	0.920692i
$427$	0.347428	+	0.681867i	0.0168132	+	0.0329978i
$428$	14.4818	+	5.99857i	0.700005	+	0.289952i
$429$	−11.3402	+	9.74437i	−0.547511	+	0.470462i
$430$	0.594510	−	1.43527i	0.0286698	−	0.0692150i
$431$	1.81451	+	23.0555i	0.0874017	+	1.11054i	0.871660	+	0.490110i	$0.163044\pi$
$431$	1.81451	+	23.0555i	0.0874017	+	1.11054i	−0.784259	+	0.620434i	$0.786956\pi$
$432$	−10.8705	−	6.66145i	−0.523007	−	0.320499i
$433$	4.33017	+	27.3396i	0.208095	+	1.31386i	0.841593	+	0.540113i	$0.181619\pi$
$433$	4.33017	+	27.3396i	0.208095	+	1.31386i	−0.633498	+	0.773744i	$0.718381\pi$
$434$	−0.250979	+	0.492573i	−0.0120474	+	0.0236443i
$435$	5.60615	−	4.78810i	0.268794	−	0.229572i
$436$	−7.29249	−	1.75077i	−0.349247	−	0.0838468i
$437$	−4.83565	−	20.1419i	−0.231321	−	0.963520i
$438$	1.54672	+	0.502560i	0.0739052	+	0.0240132i
$439$	2.32291	+	0.962180i	0.110866	+	0.0459223i	0.437427	−	0.899254i	$-0.355890\pi$
$439$	2.32291	+	0.962180i	0.110866	+	0.0459223i	−0.326561	+	0.945176i	$0.605890\pi$
$440$	2.69317	−	1.66149i	0.128392	−	0.0792086i
$441$	48.7892			2.32329
$442$	5.72286	−	1.30660i	0.272209	−	0.0621487i
$443$	−22.9503	+	16.6744i	−1.09040	+	0.792223i	−0.979467	−	0.201604i	$-0.935384\pi$
$443$	−22.9503	+	16.6744i	−1.09040	+	0.792223i	−0.110935	+	0.993828i	$0.535384\pi$
$444$	18.0805	−	2.86368i	0.858065	−	0.135904i
$445$	−0.379013	+	4.81582i	−0.0179669	+	0.228292i
$446$	22.8703	−	7.43102i	1.08294	−	0.351869i
$447$	46.4045	−	28.4367i	2.19486	−	1.34501i
$448$	−0.123936	+	0.202245i	−0.00585543	+	0.00955519i
$449$	18.8360	−	1.48242i	0.888925	−	0.0699600i	0.374233	−	0.927335i	$-0.377906\pi$
$449$	18.8360	−	1.48242i	0.888925	−	0.0699600i	0.514693	+	0.857375i	$0.327906\pi$
$450$	−20.3190	−	20.3190i	−0.957848	−	0.957848i
$451$	−22.2944	+	5.42311i	−1.04980	+	0.255364i
$452$	3.59532	+	8.67986i	0.169110	+	0.408266i
$453$	1.61390	+	20.5065i	0.0758276	+	0.963480i
$454$	−6.33194	−	26.3744i	−0.297173	−	1.23781i
$455$	−0.189389	+	0.260671i	−0.00887869	+	0.0122205i
$456$	1.01271	−	12.8677i	0.0474246	−	0.602587i
$457$	−18.8142	−	9.58631i	−0.880090	−	0.448428i	−0.0452853	−	0.998974i	$-0.514420\pi$
$457$	−18.8142	−	9.58631i	−0.880090	−	0.448428i	−0.834805	+	0.550546i	$0.814420\pi$
$458$	13.7529	+	9.99205i	0.642630	+	0.466898i
$459$	36.7532	+	37.5823i	1.71549	+	1.75419i
$460$	−1.49824	+	4.61111i	−0.0698558	+	0.214994i
$461$	−12.8806	+	12.8806i	−0.599911	+	0.599911i	−0.940289	−	0.340378i	$-0.889445\pi$
$461$	−12.8806	+	12.8806i	−0.599911	+	0.599911i	0.340378	+	0.940289i	$0.389445\pi$
$462$	−0.762672	+	2.37141i	−0.0354827	+	0.110328i
$463$		−	31.9350i		−	1.48414i	−0.670320	−	0.742072i	$-0.733843\pi$
$463$		−	31.9350i		−	1.48414i	0.670320	−	0.742072i	$-0.266157\pi$
$464$	1.85563	+	1.58486i	0.0861456	+	0.0735753i
$465$	−3.67904	+	6.00365i	−0.170612	+	0.278413i
$466$	−1.68048	+	6.99969i	−0.0778466	+	0.324255i
$467$	3.06329	−	6.01205i	0.141752	−	0.278204i	−0.809205	−	0.587526i	$-0.800102\pi$
$467$	3.06329	−	6.01205i	0.141752	−	0.278204i	0.950957	+	0.309322i	$0.100102\pi$
$468$	4.54150	−	8.91320i	0.209931	−	0.412013i
$469$	−0.355392	+	1.48031i	−0.0164105	+	0.0683545i
$470$	−3.62152	+	5.90978i	−0.167048	+	0.272598i
$471$	52.8488	+	45.1372i	2.43515	+	2.07981i
$472$		−	14.6981i		−	0.676535i
$473$	5.40024	−	0.0161793i	0.248303	−	0.000743927i
$474$	−28.7497	+	28.7497i	−1.32052	+	1.32052i
$475$	5.15159	−	15.8550i	0.236371	−	0.727476i
$476$	0.699218	−	0.683791i	0.0320486	−	0.0313415i
$477$	−57.4293	−	41.7249i	−2.62951	−	1.91045i
$478$	−4.32219	−	2.20227i	−0.197692	−	0.100729i
$479$	1.62768	−	20.6816i	0.0743706	−	0.944968i	−0.840655	−	0.541571i	$-0.817830\pi$
$479$	1.62768	−	20.6816i	0.0743706	−	0.944968i	0.915025	−	0.403396i	$-0.132170\pi$
$480$	−1.77579	+	2.44416i	−0.0810533	+	0.111560i
$481$	1.92144	+	8.00339i	0.0876103	+	0.364923i
$482$	−0.321066	−	4.07953i	−0.0146242	−	0.185817i
$483$	−1.46057	−	3.52612i	−0.0664582	−	0.160444i
$484$	8.93777	+	6.41220i	0.406262	+	0.291464i
$485$	−6.85203	−	6.85203i	−0.311135	−	0.311135i
$486$	22.7646	−	1.79161i	1.03262	−	0.0812691i
$487$	3.43804	−	5.61037i	0.155792	−	0.254230i	−0.765215	−	0.643774i	$-0.777368\pi$
$487$	3.43804	−	5.61037i	0.155792	−	0.254230i	0.921008	+	0.389544i	$0.127368\pi$
$488$	−2.75088	+	1.68574i	−0.124527	+	0.0763100i
$489$	6.51414	−	2.11657i	0.294580	−	0.0957148i
$490$	0.519801	−	6.60470i	0.0234822	−	0.298370i
$491$	−17.1071	+	2.70950i	−0.772033	+	0.122278i	−0.530009	−	0.847992i	$-0.677811\pi$
$491$	−17.1071	+	2.70950i	−0.772033	+	0.122278i	−0.242024	+	0.970270i	$0.577811\pi$
$492$	17.7219	−	12.8757i	0.798967	−	0.580484i
$493$	−5.82295	−	8.20554i	−0.262253	−	0.369559i
$494$	5.80355			0.261114
$495$	−8.44719	+	20.5674i	−0.379673	+	0.924436i
$496$	−2.15324	−	0.891902i	−0.0966834	−	0.0400476i
$497$	2.30329	+	0.748383i	0.103316	+	0.0335696i
$498$	−4.28444	−	17.8460i	−0.191991	−	0.799698i
$499$	−38.1192	−	9.15161i	−1.70645	−	0.409682i	−0.741257	−	0.671221i	$-0.765770\pi$
$499$	−38.1192	−	9.15161i	−1.70645	−	0.409682i	−0.965193	+	0.261539i	$0.915770\pi$
$500$	−6.59469	+	5.63240i	−0.294923	+	0.251888i
$501$	31.2663	−	61.3636i	1.39688	−	2.74152i
$502$	−2.15092	−	13.5804i	−0.0960002	−	0.606121i
$503$	−8.39593	−	5.14503i	−0.374356	−	0.229406i	0.322575	−	0.946544i	$-0.395452\pi$
$503$	−8.39593	−	5.14503i	−0.374356	−	0.229406i	−0.696931	+	0.717138i	$0.745452\pi$
$504$	−0.130763	−	1.66151i	−0.00582466	−	0.0740093i
$505$	6.49307	−	15.6757i	0.288938	−	0.697558i
$506$	−16.7977	+	1.37266i	−0.746748	+	0.0610220i
$507$	−32.1007	−	13.2965i	−1.42564	−	0.590520i
$508$	−4.38228	−	8.60071i	−0.194432	−	0.381595i
$509$	−31.1239	+	22.6128i	−1.37954	+	1.00230i	−0.382618	+	0.923907i	$0.624978\pi$
$509$	−31.1239	+	22.6128i	−1.37954	+	1.00230i	−0.996923	+	0.0783888i	$0.975022\pi$
$510$	9.56166	−	7.98372i	0.423397	−	0.353525i
$511$	0.0376469	+	0.115865i	0.00166540	+	0.00512557i
$512$	−0.891007	−	0.453990i	−0.0393773	−	0.0200637i
$513$	27.1544	+	44.3120i	1.19890	+	1.95642i
$514$	−0.344142	−	0.473671i	−0.0151795	−	0.0208927i
$515$	−3.07334	−	2.62488i	−0.135428	−	0.115666i
$516$	−4.76327	+	1.97301i	−0.209691	+	0.0868570i
$517$	−23.8081	−	3.69775i	−1.04708	−	0.162627i
$518$	0.969655	+	0.969655i	0.0426042	+	0.0426042i
$519$	−7.54415	+	3.84394i	−0.331152	+	0.168730i
$520$	−1.15821	−	0.709755i	−0.0507911	−	0.0311248i
$521$	36.2889	+	8.71219i	1.58984	+	0.381688i	0.929367	−	0.369158i	$-0.120354\pi$
$521$	36.2889	+	8.71219i	1.58984	+	0.381688i	0.660478	+	0.750846i	$0.270354\pi$
$522$	−17.0937	−	1.34530i	−0.748171	−	0.0588823i
$523$	−14.6577	+	4.76259i	−0.640939	+	0.208254i	−0.611414	−	0.791311i	$-0.709399\pi$
$523$	−14.6577	+	4.76259i	−0.640939	+	0.208254i	−0.0295241	+	0.999564i	$0.509399\pi$
$524$	2.85071	+	4.65194i	0.124534	+	0.203221i
$525$	0.480512	−	3.03383i	0.0209713	−	0.132407i
$526$	7.02060	−	21.6072i	0.306113	−	0.942118i
$527$	7.71078	+	5.73470i	0.335887	+	0.249807i
$528$	−10.2190	−	2.42101i	−0.444726	−	0.105361i
$529$	1.99572	−	1.99572i	0.0867705	−	0.0867705i
$530$	−6.26025	+	7.32981i	−0.271928	+	0.318386i
$531$	60.7030	+	83.5505i	2.63428	+	3.62578i
$532$	0.824423	−	0.505207i	0.0357433	−	0.0219035i
$533$	6.39660	+	7.48945i	0.277067	+	0.324404i
$534$	12.1907	−	10.4118i	0.527541	−	0.450563i
$535$	2.33960	+	14.7716i	0.101150	+	0.638634i
$536$	−6.33912	−	1.00402i	−0.273808	−	0.0433670i
$537$	−52.2026	+	4.10843i	−2.25271	+	0.177292i
$538$	2.19088	−	0.907490i	0.0944554	−	0.0391247i
$539$	21.8812	−	7.18218i	0.942490	−	0.309358i
$540$		−	12.1642i		−	0.523465i
$541$	−6.92966	+	8.11359i	−0.297929	+	0.348830i	−0.889097	−	0.457718i	$-0.848667\pi$
$541$	−6.92966	+	8.11359i	−0.297929	+	0.348830i	0.591168	+	0.806548i	$0.298667\pi$
$542$	3.25453	−	20.5483i	0.139794	−	0.882625i
$543$	33.5029	+	24.3413i	1.43775	+	1.04458i
$544$	3.10517	+	2.71255i	0.133133	+	0.116299i
$545$	−2.21120	−	6.80537i	−0.0947173	−	0.291510i
$546$	1.05615	−	0.167278i	0.0451991	−	0.00715884i
$547$	−25.0652	+	6.01762i	−1.07171	+	0.257295i	−0.730654	−	0.682748i	$-0.760785\pi$
$547$	−25.0652	+	6.01762i	−1.07171	+	0.257295i	−0.341057	+	0.940043i	$0.610785\pi$
$548$	−1.88043	−	0.610990i	−0.0803282	−	0.0261002i
$549$	8.67513	−	20.9436i	0.370246	−	0.893852i
$550$	−12.1039	−	6.12164i	−0.516112	−	0.261027i
$551$	−3.80678	−	9.19038i	−0.162174	−	0.391523i
$552$	14.3367	−	7.30494i	0.610212	−	0.310919i
$553$	−3.00821	−	0.476454i	−0.127922	−	0.0202609i
$554$	0.205144	−	0.854486i	0.00871573	−	0.0363036i
$555$	11.3432	+	13.2812i	0.481493	+	0.563756i
$556$	3.57929	+	0.281696i	0.151796	+	0.0119466i
$557$	15.6849	−	21.5884i	0.664592	−	0.914732i	−0.335031	−	0.942207i	$-0.608747\pi$
$557$	15.6849	−	21.5884i	0.664592	−	0.914732i	0.999622	+	0.0274754i	$0.00874679\pi$
$558$	15.9235	−	3.82290i	0.674096	−	0.161836i
$559$	−1.05242	−	2.06548i	−0.0445125	−	0.0873607i
$560$	−0.226315			−0.00956356
$561$	38.4193	+	19.9721i	1.62207	+	0.843222i
$562$	18.3324			0.773304
$563$	−15.2342	−	29.8988i	−0.642044	−	1.26008i	−0.951054	−	0.309024i	$-0.899998\pi$
$563$	−15.2342	−	29.8988i	−0.642044	−	1.26008i	0.309010	−	0.951059i	$-0.400002\pi$
$564$	22.3670	−	5.36984i	0.941820	−	0.226111i
$565$	−5.26887	+	7.25197i	−0.221663	+	0.305093i
$566$	17.0636	+	1.34294i	0.717237	+	0.0564478i
$567$	2.97169	+	3.47940i	0.124799	+	0.146121i
$568$	−2.38349	+	9.92797i	−0.100009	+	0.416568i
$569$	−23.9931	−	3.80013i	−1.00584	−	0.159310i	−0.368285	−	0.929713i	$-0.620055\pi$
$569$	−23.9931	−	3.80013i	−1.00584	−	0.159310i	−0.637557	+	0.770403i	$0.720055\pi$
$570$	10.9730	−	5.59102i	0.459608	−	0.234182i
$571$	4.49055	+	10.8411i	0.187924	+	0.453688i	0.989560	−	0.144125i	$-0.0460367\pi$
$571$	4.49055	+	10.8411i	0.187924	+	0.453688i	−0.801636	+	0.597813i	$0.796037\pi$
$572$	0.724695	−	4.66598i	0.0303010	−	0.195094i
$573$	−23.8250	+	57.5187i	−0.995304	+	2.40288i
$574$	1.56063	+	0.507081i	0.0651396	+	0.0211651i
$575$	20.2077	−	4.85144i	0.842720	−	0.202319i
$576$	6.93985	−	1.09916i	0.289160	−	0.0457985i
$577$	−0.993741	−	3.05842i	−0.0413700	−	0.127324i	0.928238	−	0.371986i	$-0.121323\pi$
$577$	−0.993741	−	3.05842i	−0.0413700	−	0.127324i	−0.969608	+	0.244662i	$0.921323\pi$
$578$	−9.68308	−	13.9728i	−0.402763	−	0.581190i
$579$	51.8581	+	37.6771i	2.15515	+	1.56581i
$580$	−0.364234	+	2.29968i	−0.0151240	+	0.0954890i
$581$	0.892883	−	1.04543i	0.0370430	−	0.0433718i
$582$			32.1592i			1.33304i
$583$	−31.8984	−	10.2589i	−1.32110	−	0.424879i
$584$	−0.474514	+	0.196550i	−0.0196355	+	0.00813331i
$585$	9.51509	−	0.748853i	0.393400	−	0.0309613i
$586$	32.3822	+	5.12884i	1.33770	+	0.211870i
$587$	−0.338642	−	2.13810i	−0.0139773	−	0.0882489i	0.979714	−	0.200403i	$-0.0642251\pi$
$587$	−0.338642	−	2.13810i	−0.0139773	−	0.0882489i	−0.993691	+	0.112154i	$0.964225\pi$
$588$	−16.7190	+	14.2794i	−0.689480	+	0.588872i
$589$	6.17012	+	7.22428i	0.254235	+	0.297671i
$590$	11.9572	−	7.32735i	0.492268	−	0.301662i
$591$	47.9946	+	66.0589i	1.97423	+	2.71730i
$592$	−3.75461	+	4.39608i	−0.154313	+	0.180678i
$593$	12.0452	−	12.0452i	0.494638	−	0.494638i	−0.415126	−	0.909764i	$-0.636263\pi$
$593$	12.0452	−	12.0452i	0.494638	−	0.494638i	0.909764	+	0.415126i	$0.136263\pi$
$594$	39.0170	−	16.2985i	1.60089	−	0.668736i
$595$	0.904853	+	0.227939i	0.0370953	+	0.00934460i
$596$	−5.31136	+	16.3467i	−0.217562	+	0.669586i
$597$	2.48507	−	15.6901i	0.101707	−	0.642154i
$598$	3.78012	+	6.16860i	0.154581	+	0.252253i
$599$	−11.3810	+	3.69790i	−0.465014	+	0.151092i	−0.532147	−	0.846652i	$-0.678615\pi$
$599$	−11.3810	+	3.69790i	−0.465014	+	0.151092i	0.0671335	+	0.997744i	$0.478615\pi$
$600$	12.9098	+	1.01602i	0.527039	+	0.0414789i
$601$	10.0351	+	2.40922i	0.409340	+	0.0982739i	0.432886	−	0.901449i	$-0.357495\pi$
$601$	10.0351	+	2.40922i	0.409340	+	0.0982739i	−0.0235452	+	0.999723i	$0.507495\pi$
$602$	−0.329304	−	0.201798i	−0.0134214	−	0.00822466i
$603$	40.1810	−	20.4732i	1.63630	−	0.833734i
$604$	−4.59353	−	4.59353i	−0.186908	−	0.186908i
$605$	−0.760741	+	10.4677i	−0.0309285	+	0.425571i
$606$	−52.0231	+	21.5487i	−2.11330	+	0.875356i
$607$	0.924604	+	0.789686i	0.0375285	+	0.0320524i	0.668015	−	0.744148i	$-0.267144\pi$
$607$	0.924604	+	0.789686i	0.0375285	+	0.0320524i	−0.630486	+	0.776201i	$0.717144\pi$
$608$	2.39602	+	3.29784i	0.0971714	+	0.133745i
$609$	−0.957670	−	1.56277i	−0.0388067	−	0.0633268i
$610$	−2.74276	−	1.39751i	−0.111051	−	0.0565834i
$611$	3.19602	+	9.83633i	0.129297	+	0.397936i
$612$	−28.8540	−	2.59498i	−1.16635	−	0.104896i
$613$	−10.0618	+	7.31029i	−0.406390	+	0.295260i	−0.772139	−	0.635454i	$-0.780813\pi$
$613$	−10.0618	+	7.31029i	−0.406390	+	0.295260i	0.365748	+	0.930714i	$0.380813\pi$
$614$	1.65636	+	3.25079i	0.0668452	+	0.131191i
$615$	19.3095	+	7.99824i	0.778633	+	0.322520i
$616$	−0.303233	−	0.725910i	−0.0122176	−	0.0292478i
$617$	14.0281	−	33.8668i	0.564750	−	1.36343i	−0.341180	−	0.939998i	$-0.610827\pi$
$617$	14.0281	−	33.8668i	0.564750	−	1.36343i	0.905930	−	0.423428i	$-0.139173\pi$
$618$	1.05240	+	13.3720i	0.0423336	+	0.537899i
$619$	3.80397	+	2.33108i	0.152895	+	0.0936939i	0.596841	−	0.802359i	$-0.296422\pi$
$619$	3.80397	+	2.33108i	0.152895	+	0.0936939i	−0.443947	+	0.896053i	$0.646422\pi$
$620$	−0.347865	−	2.19633i	−0.0139706	−	0.0882069i
$621$	−29.4123	+	57.7248i	−1.18027	+	2.31642i
$622$	−23.4121	+	19.9958i	−0.938739	+	0.801758i
$623$	1.16776	+	0.280355i	0.0467853	+	0.0112322i
$624$	1.05240	+	4.38355i	0.0421296	+	0.175482i
$625$	11.5778	+	3.76187i	0.463114	+	0.150475i
$626$	9.25304	+	3.83273i	0.369826	+	0.153187i
$627$	32.6357	+	27.7049i	1.30334	+	1.10643i
$628$	−21.9492			−0.875868
$629$	19.4393	−	13.7948i	0.775095	−	0.550036i
$630$	1.28647	−	0.934679i	0.0512544	−	0.0372385i
$631$	−21.7795	+	3.44954i	−0.867029	+	0.137324i	−0.574075	−	0.818803i	$-0.694638\pi$
$631$	−21.7795	+	3.44954i	−0.867029	+	0.137324i	−0.292954	+	0.956127i	$0.594638\pi$
$632$	1.00744	−	12.8008i	0.0400738	−	0.509187i
$633$	53.0797	−	17.2466i	2.10973	−	0.685493i
$634$	−8.55300	+	5.24128i	−0.339683	+	0.208158i
$635$	4.81215	−	7.85272i	0.190964	−	0.311626i
$636$	31.8916	−	2.50993i	1.26459	−	0.0995250i
$637$	−6.99038	−	6.99038i	−0.276969	−	0.276969i
$638$	−7.86430	+	1.91299i	−0.311351	+	0.0757359i
$639$	−27.4536	−	66.2788i	−1.08605	−	2.62195i
$640$	−0.0748590	−	0.951174i	−0.00295906	−	0.0375985i
$641$	−0.912504	−	3.80085i	−0.0360418	−	0.150125i	0.951447	−	0.307811i	$-0.0995965\pi$
$641$	−0.912504	−	3.80085i	−0.0360418	−	0.150125i	−0.987489	+	0.157686i	$0.949596\pi$
$642$	29.1741	−	40.1548i	1.15141	−	1.58478i
$643$	0.633770	−	8.05281i	0.0249935	−	0.317572i	−0.971694	−	0.236243i	$-0.924084\pi$
$643$	0.633770	−	8.05281i	0.0249935	−	0.317572i	0.996687	−	0.0813285i	$-0.0259163\pi$
$644$	1.07397	+	0.547214i	0.0423203	+	0.0215633i
$645$	−3.97968	−	2.89141i	−0.156700	−	0.113849i
$646$	−6.25825	−	15.5986i	−0.246228	−	0.613720i
$647$	7.46761	−	22.9829i	0.293582	−	0.903553i	−0.690112	−	0.723703i	$-0.742439\pi$
$647$	7.46761	−	22.9829i	0.293582	−	0.903553i	0.983694	−	0.179850i	$-0.0575613\pi$
$648$	−13.6405	+	13.6405i	−0.535851	+	0.535851i
$649$	39.5237	+	28.5351i	1.55144	+	1.12010i
$650$			5.82251i			0.228378i
$651$	1.33109	+	1.13686i	0.0521695	+	0.0445569i
$652$	−1.13022	+	1.84436i	−0.0442630	+	0.0722306i
$653$	−7.63363	+	31.7964i	−0.298727	+	1.24429i	0.597925	+	0.801552i	$0.295992\pi$
$653$	−7.63363	+	31.7964i	−0.298727	+	1.24429i	−0.896652	+	0.442736i	$0.854008\pi$
$654$	−10.7811	+	21.1591i	−0.421574	+	0.827386i
$655$	−2.36328	+	4.63820i	−0.0923411	+	0.181230i
$656$	−1.61498	+	6.72688i	−0.0630544	+	0.262641i
$657$	1.88560	−	3.07702i	0.0735642	−	0.120046i
$658$	1.31028	+	1.11908i	0.0510798	+	0.0436263i
$659$			31.8846i			1.24205i	0.783792	+	0.621024i	$0.213283\pi$
$659$			31.8846i			1.24205i	−0.783792	+	0.621024i	$0.786717\pi$
$660$	−3.12490	−	9.52029i	−0.121636	−	0.370577i
$661$	−22.5916	+	22.5916i	−0.878712	+	0.878712i	−0.993401	−	0.114690i	$-0.963413\pi$
$661$	−22.5916	+	22.5916i	−0.878712	+	0.878712i	0.114690	+	0.993401i	$0.463413\pi$
$662$	−3.52201	+	10.8396i	−0.136887	+	0.421294i
$663$	0.207318	−	18.5862i	0.00805156	−	0.721830i
$664$	4.68916	+	3.40688i	0.181975	+	0.132212i
$665$	0.821989	+	0.418824i	0.0318754	+	0.0162413i
$666$	3.18708	−	40.4957i	0.123497	−	1.56918i
$667$	7.28892	−	10.0323i	0.282228	−	0.388454i
$668$	5.07743	+	21.1490i	0.196452	+	0.818279i
$669$	−5.97422	−	75.9096i	−0.230977	−	2.93484i
$670$	−2.34342	−	5.65751i	−0.0905342	−	0.218569i
$671$	0.807585	−	10.6699i	0.0311765	−	0.411909i
$672$	0.531091	+	0.531091i	0.0204873	+	0.0204873i
$673$	−28.3878	+	2.23417i	−1.09427	+	0.0861210i	−0.612722	−	0.790298i	$-0.709926\pi$
$673$	−28.3878	+	2.23417i	−1.09427	+	0.0861210i	−0.481549	+	0.876419i	$0.659926\pi$
$674$	14.0368	−	22.9059i	0.540675	−	0.882302i
$675$	−44.4567	+	27.2431i	−1.71114	+	1.04859i
$676$	10.4360	−	3.39086i	0.401384	−	0.130418i
$677$	−0.685913	+	8.71535i	−0.0263618	+	0.334958i	0.969568	+	0.244823i	$0.0787299\pi$
$677$	−0.685913	+	8.71535i	−0.0263618	+	0.334958i	−0.995930	+	0.0901351i	$0.971270\pi$
$678$	29.3825	−	4.65373i	1.12843	−	0.178726i
$679$	−1.94896	+	1.41600i	−0.0747944	+	0.0543413i
$680$	−0.658700	+	3.87838i	−0.0252600	+	0.148729i
$681$	−85.8862			−3.29117
$682$	6.57869	−	4.05859i	0.251911	−	0.155411i
$683$	−36.1795	−	14.9860i	−1.38437	−	0.573424i	−0.438723	−	0.898622i	$-0.644569\pi$
$683$	−36.1795	−	14.9860i	−1.38437	−	0.573424i	−0.945646	+	0.325198i	$0.894569\pi$
$684$	−27.2401	−	8.85083i	−1.04155	−	0.338420i
$685$	−0.440391	−	1.83436i	−0.0168265	−	0.0700873i
$686$	−3.21605	−	0.772106i	−0.122789	−	0.0294791i
$687$	40.9311	−	34.9584i	1.56162	−	1.33375i
$688$	0.739206	−	1.45077i	0.0281819	−	0.0553102i
$689$	2.25010	+	14.2065i	0.0857218	+	0.541226i
$690$	13.0899	+	8.02150i	0.498324	+	0.305373i
$691$	−0.867598	−	11.0239i	−0.0330050	−	0.419368i	−0.991119	−	0.132980i	$-0.957545\pi$
$691$	−0.867598	−	11.0239i	−0.0330050	−	0.419368i	0.958114	−	0.286388i	$-0.0924546\pi$
$692$	1.02329	−	2.47044i	0.0388996	−	0.0939119i
$693$	4.72171	+	2.87405i	0.179363	+	0.109176i
$694$	−22.7268	−	9.41375i	−0.862698	−	0.357341i
$695$	1.55520	+	3.05224i	0.0589919	+	0.115778i
$696$	6.25138	−	4.54189i	0.236958	−	0.172160i
$697$	13.2322	−	25.2688i	0.501204	−	0.957125i
$698$	−0.994886	−	3.06194i	−0.0376570	−	0.115896i
$699$	20.3095	+	10.3482i	0.768177	+	0.391406i
$700$	0.506857	+	0.827115i	0.0191574	+	0.0312620i
$701$	−27.2871	−	37.5575i	−1.03062	−	1.41853i	−0.904481	−	0.426515i	$-0.859741\pi$
$701$	−27.2871	−	37.5575i	−1.03062	−	1.41853i	−0.126140	−	0.992012i	$-0.540259\pi$
$702$	−13.8023	−	11.7883i	−0.520935	−	0.444920i
$703$	21.7724	−	9.01844i	0.821163	−	0.340137i
$704$	2.95061	−	1.51456i	0.111205	−	0.0570822i
$705$	15.5189	+	15.5189i	0.584477	+	0.584477i
$706$	−5.84658	+	2.97898i	−0.220039	+	0.112116i
$707$	−3.59657	−	2.20398i	−0.135263	−	0.0828891i
$708$	−45.2548	−	10.8647i	−1.70078	−	0.408321i
$709$	−0.593688	−	0.0467242i	−0.0222964	−	0.00175477i	0.0673060	−	0.997732i	$-0.478560\pi$
$709$	−0.593688	−	0.0467242i	−0.0222964	−	0.00175477i	−0.0896024	+	0.995978i	$0.528560\pi$
$710$	−9.26480	+	3.01032i	−0.347702	+	0.112975i
$711$	47.1402	+	76.9258i	1.76790	+	2.88494i
$712$	−0.792031	+	5.00069i	−0.0296826	+	0.187409i
$713$	−3.65980	+	11.2637i	−0.137061	+	0.421830i
$714$	−1.58851	−	2.65831i	−0.0594483	−	0.0994848i
$715$	4.15713	−	1.73655i	0.155468	−	0.0649433i
$716$	11.6935	−	11.6935i	0.437008	−	0.437008i
$717$	−9.97560	+	11.6799i	−0.372546	+	0.436195i
$718$	11.3389	+	15.6067i	0.423165	+	0.582437i
$719$	−11.2108	+	6.87001i	−0.418094	+	0.256208i	−0.715598	−	0.698512i	$-0.753846\pi$
$719$	−11.2108	+	6.87001i	−0.418094	+	0.256208i	0.297504	+	0.954720i	$0.403846\pi$
$720$	4.35387	+	5.09773i	0.162259	+	0.189981i
$721$	−0.764051	+	0.652561i	−0.0284547	+	0.0243026i
$722$	0.372839	+	2.35402i	0.0138756	+	0.0876074i
$723$	−12.7980	−	2.02701i	−0.475963	−	0.0753851i
$724$	−13.0380	+	1.02612i	−0.484555	+	0.0381353i
$725$	9.22039	−	3.81921i	0.342437	−	0.141842i
$726$	26.3496	−	22.7791i	0.977925	−	0.845413i
$727$			18.4442i			0.684059i	0.939689	+	0.342029i	$0.111114\pi$
$727$			18.4442i			0.684059i	−0.939689	+	0.342029i	$0.888886\pi$
$728$	−0.219321	+	0.256791i	−0.00812856	+	0.00951732i
$729$	2.25793	−	14.2560i	0.0836270	−	0.528000i
$730$	−0.396454	−	0.288041i	−0.0146734	−	0.0106609i
$731$	−4.41668	+	5.05597i	−0.163357	+	0.187002i
$732$	3.15689	+	9.71592i	0.116682	+	0.359111i
$733$	−34.0766	+	5.39720i	−1.25865	+	0.199350i	−0.749892	−	0.661560i	$-0.769894\pi$
$733$	−34.0766	+	5.39720i	−1.25865	+	0.199350i	−0.508756	+	0.860911i	$0.669894\pi$
$734$	−15.9800	+	3.83646i	−0.589833	+	0.141606i
$735$	−19.9513	−	6.48258i	−0.735916	−	0.239114i
$736$	−1.94463	+	4.69476i	−0.0716801	+	0.173051i
$737$	15.0067	−	15.0969i	0.552779	−	0.556102i
$738$	−18.6017	−	44.9084i	−0.684737	−	1.65310i
$739$	−46.2854	+	23.5836i	−1.70263	+	0.867536i	−0.717329	+	0.696734i	$0.754636\pi$
$739$	−46.2854	+	23.5836i	−1.70263	+	0.867536i	−0.985305	+	0.170801i	$0.945364\pi$
$740$	−5.44805	−	0.862886i	−0.200274	−	0.0317203i
$741$	4.28994	−	17.8689i	0.157595	−	0.656429i
$742$	1.55633	+	1.82223i	0.0571348	+	0.0668963i
$743$	−11.4950	−	0.904680i	−0.421712	−	0.0331895i	−0.134172	−	0.990958i	$-0.542838\pi$
$743$	−11.4950	−	0.904680i	−0.421712	−	0.0331895i	−0.287540	+	0.957769i	$0.592838\pi$
$744$	−4.33778	+	5.97044i	−0.159031	+	0.218887i
$745$	−15.9461	+	3.82833i	−0.584221	+	0.140259i
$746$	−4.41435	−	8.66365i	−0.161621	−	0.317199i
$747$	−40.7256			−1.49007
$748$	−13.3226	+	3.08374i	−0.487121	+	0.112753i
$749$	3.71809			0.135856
$750$	12.4671	+	24.4682i	0.455236	+	0.893451i
$751$	19.7453	−	4.74042i	0.720515	−	0.172980i	0.143425	−	0.989661i	$-0.454188\pi$
$751$	19.7453	−	4.74042i	0.720515	−	0.172980i	0.577089	+	0.816681i	$0.304188\pi$
$752$	−4.26995	+	5.87709i	−0.155709	+	0.214315i
$753$	−43.4032	−	3.41591i	−1.58170	−	0.124483i
$754$	2.25639	+	2.64189i	0.0821727	+	0.0962119i
$755$	1.44693	−	6.02690i	0.0526592	−	0.219341i
$756$	−2.98687	−	0.473074i	−0.108631	−	0.0172055i
$757$	−17.7535	+	9.04588i	−0.645263	+	0.328778i	−0.745814	−	0.666154i	$-0.767939\pi$
$757$	−17.7535	+	9.04588i	−0.645263	+	0.328778i	0.100551	+	0.994932i	$0.467939\pi$
$758$	9.70314	+	23.4255i	0.352434	+	0.850851i
$759$	−8.19035	+	52.7339i	−0.297291	+	1.91412i
$760$	−1.48837	+	3.59325i	−0.0539890	+	0.130341i
$761$	24.1010	+	7.83090i	0.873662	+	0.283870i	0.711323	−	0.702865i	$-0.248096\pi$
$761$	24.1010	+	7.83090i	0.873662	+	0.283870i	0.162339	+	0.986735i	$0.448096\pi$
$762$	−29.7205	+	7.13526i	−1.07666	+	0.258483i
$763$	−1.75702	+	0.278285i	−0.0636084	+	0.0100746i
$764$	−6.07581	−	18.6994i	−0.219815	−	0.676521i
$765$	−12.2733	−	24.7668i	−0.443743	−	0.895447i
$766$	19.2298	+	13.9713i	0.694801	+	0.504802i
$767$	3.27353	−	20.6682i	0.118200	−	0.746287i
$768$	−2.05644	+	2.40778i	−0.0742054	+	0.0868833i
$769$			4.56246i			0.164526i	0.996611	+	0.0822632i	$0.0262148\pi$
$769$			4.56246i			0.164526i	−0.996611	+	0.0822632i	$0.973785\pi$
$770$	0.439372	−	0.608569i	0.0158339	−	0.0219313i
$771$	−1.71280	+	0.709464i	−0.0616849	+	0.0255507i
$772$	−20.1812	+	1.58829i	−0.726336	+	0.0571639i
$773$	−18.8154	−	2.98006i	−0.676742	−	0.107185i	−0.191403	−	0.981511i	$-0.561304\pi$
$773$	−18.8154	−	2.98006i	−0.676742	−	0.107185i	−0.485339	+	0.874326i	$0.661304\pi$
$774$	1.78970	+	11.2997i	0.0643296	+	0.406161i
$775$	−7.24787	+	6.19027i	−0.260351	+	0.222361i
$776$	−6.59596	−	7.72288i	−0.236781	−	0.277235i
$777$	3.70228	−	2.26876i	0.132819	−	0.0813914i
$778$	2.52569	+	3.47631i	0.0905504	+	0.124632i
$779$	18.3146	−	21.4437i	0.656190	−	0.768300i
$780$	−3.04144	+	3.04144i	−0.108901	+	0.108901i
$781$	−22.0693	−	25.6836i	−0.789702	−	0.919032i
$782$	12.5035	−	16.8120i	0.447124	−	0.601196i
$783$	−9.61419	+	29.5894i	−0.343583	+	1.05744i
$784$	1.08624	−	6.85825i	0.0387943	−	0.244937i
$785$	−10.9422	−	17.8560i	−0.390544	−	0.637309i
$786$	16.4303	−	5.33853i	0.586050	−	0.190419i
$787$	−23.0080	−	1.81077i	−0.820147	−	0.0645470i	−0.338560	−	0.940945i	$-0.609940\pi$
$787$	−23.0080	−	1.81077i	−0.820147	−	0.0645470i	−0.481588	+	0.876398i	$0.659940\pi$
$788$	−25.0746	−	6.01988i	−0.893245	−	0.214449i
$789$	−61.3379	−	37.5879i	−2.18369	−	1.33817i
$790$	10.9159	−	5.56191i	0.388369	−	0.197884i
$791$	1.57578	+	1.57578i	0.0560282	+	0.0560282i
$792$	−10.5174	+	20.7954i	−0.373721	+	0.738933i
$793$	−4.24369	+	1.75780i	−0.150698	+	0.0624211i
$794$	18.0685	+	15.4319i	0.641226	+	0.547658i
$795$	17.9406	+	24.6931i	0.636288	+	0.875775i
$796$	2.62132	+	4.27761i	0.0929102	+	0.151616i
$797$	29.2481	+	14.9026i	1.03602	+	0.527878i	0.887392	−	0.461015i	$-0.152515\pi$
$797$	29.2481	+	14.9026i	1.03602	+	0.527878i	0.148627	+	0.988893i	$0.452515\pi$
$798$	−0.946102	−	2.91180i	−0.0334917	−	0.103077i
$799$	22.9914	−	19.1972i	0.813377	−	0.679147i
$800$	−3.30861	+	2.40384i	−0.116977	+	0.0849887i
$801$	−16.1505	−	31.6972i	−0.570651	−	1.11997i
$802$	−17.0372	−	7.05704i	−0.601605	−	0.249193i
$803$	0.392699	−	1.65757i	0.0138580	−	0.0584944i
$804$	−7.77715	+	18.7757i	−0.274279	+	0.662168i
$805$	0.0902308	+	1.14649i	0.00318022	+	0.0404085i
$806$	−2.82921	−	1.73374i	−0.0996548	−	0.0610685i
$807$	−1.17464	−	7.41641i	−0.0413494	−	0.261070i
$808$	8.07340	−	15.8449i	0.284021	−	0.557423i
$809$	33.1030	−	28.2726i	1.16384	−	0.994013i	0.163868	−	0.986482i	$-0.447603\pi$
$809$	33.1030	−	28.2726i	1.16384	−	0.994013i	0.999972	−	0.00753054i	$-0.00239707\pi$
$810$	−17.8969	−	4.29667i	−0.628834	−	0.150970i
$811$	−1.98947	−	8.28674i	−0.0698598	−	0.290987i	0.926494	−	0.376311i	$-0.122807\pi$
$811$	−1.98947	−	8.28674i	−0.0698598	−	0.290987i	−0.996353	+	0.0853239i	$0.972807\pi$
$812$	0.550510	+	0.178872i	0.0193191	+	0.00627716i
$813$	−60.8616	−	25.2097i	−2.13451	−	0.884142i
$814$	−4.53196	−	18.6309i	−0.158845	−	0.653012i
$815$	−2.06386			−0.0722939
$816$	10.6471	−	7.55559i	0.372724	−	0.264499i
$817$	−5.36967	+	3.90129i	−0.187861	+	0.136489i
$818$	17.7037	−	2.80400i	0.618997	−	0.0980394i
$819$	0.186169	−	2.36551i	0.00650529	−	0.0826575i
$820$	−6.27754	+	2.03970i	−0.219221	+	0.0712293i
$821$	−6.88643	+	4.22001i	−0.240338	+	0.147279i	−0.637452	−	0.770490i	$-0.720012\pi$
$821$	−6.88643	+	4.22001i	−0.240338	+	0.147279i	0.397114	+	0.917769i	$0.370012\pi$
$822$	−3.27121	+	5.33813i	−0.114097	+	0.186189i
$823$	33.6826	−	2.65087i	1.17410	−	0.0924037i	0.523637	−	0.851942i	$-0.324575\pi$
$823$	33.6826	−	2.65087i	1.17410	−	0.0924037i	0.650463	+	0.759538i	$0.274575\pi$
$824$	−2.99536	−	2.99536i	−0.104348	−	0.104348i
$825$	−27.7953	+	32.7423i	−0.967709	+	1.13994i
$826$	−1.33418	−	3.22099i	−0.0464219	−	0.112072i
$827$	0.303677	+	3.85858i	0.0105599	+	0.134176i	0.999937	−	0.0111932i	$-0.00356299\pi$
$827$	0.303677	+	3.85858i	0.0105599	+	0.134176i	−0.989377	+	0.145369i	$0.953563\pi$
$828$	−8.33515	−	34.7184i	−0.289667	−	1.20655i
$829$	−3.81043	+	5.24460i	−0.132342	+	0.182153i	−0.870045	−	0.492972i	$-0.835910\pi$
$829$	−3.81043	+	5.24460i	−0.132342	+	0.182153i	0.737703	+	0.675125i	$0.235910\pi$
$830$	−0.433892	+	5.51312i	−0.0150606	+	0.191363i
$831$	−2.47928	−	1.26326i	−0.0860053	−	0.0438219i
$832$	−1.15181	−	0.836837i	−0.0399318	−	0.0290121i
$833$	−11.2505	+	26.3266i	−0.389806	+	0.912163i
$834$	3.51311	−	10.8122i	0.121649	−	0.374397i
$835$	−14.6739	+	14.6739i	−0.507810	+	0.507810i
$836$	−13.5197	+	0.0405055i	−0.467587	+	0.00140091i
$837$		−	29.7140i		−	1.02707i
$838$	3.03480	+	2.59197i	0.104836	+	0.0895380i
$839$	−9.18547	+	14.9893i	−0.317118	+	0.517489i	−0.970991	−	0.239115i	$-0.923143\pi$
$839$	−9.18547	+	14.9893i	−0.317118	+	0.517489i	0.653874	+	0.756604i	$0.273143\pi$
$840$	−0.167290	+	0.696813i	−0.00577206	+	0.0240423i
$841$	−10.4621	+	20.5331i	−0.360763	+	0.708038i
$842$	8.23546	−	16.1630i	0.283813	−	0.557014i
$843$	13.5511	−	56.4445i	0.466725	−	1.94405i
$844$	−9.20950	+	15.0285i	−0.317004	+	0.517303i
$845$	7.96111	+	6.79943i	0.273870	+	0.233907i
$846$		−	51.0428i		−	1.75489i
$847$	2.54070	+	0.593889i	0.0872995	+	0.0204063i
$848$	−7.14383	+	7.14383i	−0.245320	+	0.245320i
$849$	16.7481	−	51.5454i	0.574794	−	1.76903i
$850$	15.6496	−	6.27869i	0.536776	−	0.215357i
$851$	23.7671	+	17.2678i	0.814725	+	0.591932i
$852$	28.8059	+	14.6773i	0.986874	+	0.502837i
$853$	3.16996	−	40.2781i	0.108537	−	1.37910i	−0.665709	−	0.746212i	$-0.731871\pi$
$853$	3.16996	−	40.2781i	0.108537	−	1.37910i	0.774246	−	0.632885i	$-0.218129\pi$
$854$	−0.449819	+	0.619122i	−0.0153925	+	0.0211859i
$855$	−6.37952	−	26.5726i	−0.218175	−	0.908764i
$856$	1.22985	+	15.6267i	0.0420353	+	0.534109i
$857$	19.2488	+	46.4707i	0.657527	+	1.58741i	0.801612	+	0.597845i	$0.203976\pi$
$857$	19.2488	+	46.4707i	0.657527	+	1.58741i	−0.144085	+	0.989565i	$0.546024\pi$
$858$	−13.8306	−	5.68035i	−0.472170	−	0.193924i
$859$	−16.6206	−	16.6206i	−0.567089	−	0.567089i	0.364223	−	0.931312i	$-0.381335\pi$
$859$	−16.6206	−	16.6206i	−0.567089	−	0.567089i	−0.931312	+	0.364223i	$0.881335\pi$
$860$	1.54874	−	0.121888i	0.0528116	−	0.00415636i
$861$	2.71488	−	4.43029i	0.0925230	−	0.150984i
$862$	−19.7188	+	12.0837i	−0.671626	+	0.411573i
$863$	−51.5689	+	16.7557i	−1.75542	+	0.570372i	−0.996710	−	0.0810516i	$-0.974172\pi$
$863$	−51.5689	+	16.7557i	−1.75542	+	0.570372i	−0.758714	+	0.651424i	$0.774172\pi$
$864$	1.00029	−	12.7099i	0.0340307	−	0.432400i
$865$	2.51987	−	0.399109i	0.0856783	−	0.0135701i
$866$	−22.3939	+	16.2701i	−0.760976	+	0.552881i
$867$	−50.1791	+	19.4852i	−1.70417	+	0.661753i
$868$	−0.552828			−0.0187642
$869$	32.4658	+	27.5606i	1.10133	+	0.934930i
$870$	6.81137	+	2.82136i	0.230927	+	0.0956531i
$871$	−8.69037	−	2.82367i	−0.294462	−	0.0956764i
$872$	−1.75077	−	7.29249i	−0.0592886	−	0.246955i
$873$	69.3897	+	16.6590i	2.34849	+	0.563822i
$874$	15.7513	−	13.4528i	0.532794	−	0.455049i
$875$	−0.933916	+	1.83291i	−0.0315721	+	0.0619638i
$876$	0.254412	+	1.60630i	0.00859579	+	0.0542717i
$877$	35.4939	+	21.7507i	1.19854	+	0.734468i	0.970949	−	0.239288i	$-0.0769141\pi$
$877$	35.4939	+	21.7507i	1.19854	+	0.734468i	0.227594	+	0.973756i	$0.426914\pi$
$878$	0.197270	+	2.50655i	0.00665752	+	0.0845919i
$879$	39.7281	−	95.9121i	1.34000	−	3.23504i
$880$	2.70307	+	1.64533i	0.0911206	+	0.0554639i
$881$	30.1220	+	12.4769i	1.01484	+	0.420359i	0.827217	−	0.561883i	$-0.189923\pi$
$881$	30.1220	+	12.4769i	1.01484	+	0.420359i	0.187619	+	0.982242i	$0.439923\pi$
$882$	22.1498	+	43.4715i	0.745823	+	1.46376i
$883$	−31.7481	+	23.0664i	−1.06841	+	0.776245i	−0.975626	−	0.219441i	$-0.929577\pi$
$883$	−31.7481	+	23.0664i	−1.06841	+	0.776245i	−0.0927842	+	0.995686i	$0.529577\pi$
$884$	3.76231	+	4.50592i	0.126540	+	0.151550i
$885$	−13.7220	−	42.2318i	−0.461258	−	1.41961i
$886$	−25.2762	−	12.8789i	−0.849170	−	0.432674i
$887$	−0.411085	−	0.670830i	−0.0138029	−	0.0225243i	0.845664	−	0.533715i	$-0.179205\pi$
$887$	−0.411085	−	0.670830i	−0.0138029	−	0.0225243i	−0.859467	+	0.511191i	$0.829205\pi$
$888$	10.7599	+	14.8098i	0.361080	+	0.496984i
$889$	−1.74105	−	1.48700i	−0.0583929	−	0.0498723i
$890$	−4.46299	+	1.84863i	−0.149600	+	0.0619663i
$891$	−10.1979	−	63.1618i	−0.341643	−	2.11600i
$892$	17.0040	+	17.0040i	0.569336	+	0.569336i
$893$	26.3850	−	13.4438i	0.882940	−	0.449881i
$894$	46.4045	+	28.4367i	1.55200	+	0.951067i
$895$	15.3424	+	3.68339i	0.512840	+	0.123122i
$896$	−0.236468	−	0.0186104i	−0.00789983	−	0.000621730i
$897$	21.7870	−	7.07904i	0.727448	−	0.236362i
$898$	9.87221	+	16.1100i	0.329440	+	0.537597i
$899$	−0.889726	+	5.61751i	−0.0296740	+	0.187354i
$900$	8.87974	−	27.3290i	0.295991	−	0.910967i
$901$	35.7576	−	21.3673i	1.19126	−	0.711850i
$902$	−14.9535	−	17.4024i	−0.497896	−	0.579437i
$903$	−0.864744	+	0.864744i	−0.0287769	+	0.0287769i
$904$	−6.10158	+	7.14403i	−0.202935	+	0.237607i
$905$	−7.33454	−	10.0951i	−0.243808	−	0.335573i
$906$	−17.5387	+	10.7478i	−0.582686	+	0.357070i
$907$	17.1907	+	20.1278i	0.570809	+	0.668332i	0.968450	−	0.249210i	$-0.0801709\pi$
$907$	17.1907	+	20.1278i	0.570809	+	0.668332i	−0.397640	+	0.917541i	$0.630171\pi$
$908$	20.6252	−	17.6156i	0.684470	−	0.584593i
$909$	19.5466	+	123.413i	0.648321	+	4.09334i
$910$	−0.318241	−	0.0504044i	−0.0105496	−	0.00167089i
$911$	45.0830	−	3.54811i	1.49367	−	0.117554i	0.694861	−	0.719144i	$-0.255466\pi$
$911$	45.0830	−	3.54811i	1.49367	−	0.117554i	0.798805	+	0.601590i	$0.205466\pi$
$912$	11.9250	−	4.93950i	0.394876	−	0.163563i
$913$	−18.2648	+	5.99516i	−0.604477	+	0.198411i
$914$		−	21.1157i		−	0.698444i
$915$	−6.33028	+	7.41181i	−0.209273	+	0.245027i
$916$	−2.65931	+	16.7902i	−0.0878660	+	0.554764i
$917$	1.04698	+	0.760675i	0.0345743	+	0.0251197i
$918$	−16.8005	+	49.8093i	−0.554500	+	1.64395i
$919$	12.4752	+	38.3947i	0.411519	+	1.26653i	0.915328	+	0.402710i	$0.131932\pi$
$919$	12.4752	+	38.3947i	0.411519	+	1.26653i	−0.503808	+	0.863815i	$0.668068\pi$
$920$	−4.78871	+	0.758458i	−0.157879	+	0.0250056i
$921$	11.2334	−	2.69690i	0.370153	−	0.0888659i
$922$	−17.3244	−	5.62904i	−0.570549	−	0.185383i
$923$	−5.56277	+	13.4297i	−0.183101	+	0.442044i
$924$	−2.45919	+	0.397054i	−0.0809014	+	0.0130621i
$925$	9.04789	+	21.8435i	0.297493	+	0.718211i
$926$	28.4543	−	14.4982i	0.935066	−	0.476440i
$927$	29.3978	+	4.65615i	0.965549	+	0.152928i
$928$	−0.569681	+	2.37289i	−0.0187007	+	0.0778940i
$929$	0.488076	+	0.571464i	0.0160133	+	0.0187491i	0.768355	−	0.640024i	$-0.221076\pi$
$929$	0.488076	+	0.571464i	0.0160133	+	0.0187491i	−0.752342	+	0.658773i	$0.771076\pi$
$930$	−7.01955	−	0.552450i	−0.230180	−	0.0181156i
$931$	−16.6373	+	22.8993i	−0.545266	+	0.750495i
$932$	−6.99969	+	1.68048i	−0.229283	+	0.0550459i
$933$	44.2601	+	86.8654i	1.44901	+	2.84385i
$934$	6.74748			0.220784
$935$	−9.15029	−	9.30081i	−0.299246	−	0.304169i
$936$	10.0035			0.326975
$937$	−19.1441	−	37.5724i	−0.625411	−	1.22744i	−0.958648	−	0.284595i	$-0.908141\pi$
$937$	−19.1441	−	37.5724i	−0.625411	−	1.22744i	0.333237	−	0.942843i	$-0.391859\pi$
$938$	−1.48031	+	0.355392i	−0.0483339	+	0.0116039i
$939$	18.6406	−	25.6565i	0.608312	−	0.837270i
$940$	−6.90979	−	0.543812i	−0.225372	−	0.0177372i
$941$	5.67621	+	6.64598i	0.185039	+	0.216653i	0.845170	−	0.534498i	$-0.179499\pi$
$941$	5.67621	+	6.64598i	0.185039	+	0.216653i	−0.660131	+	0.751151i	$0.729499\pi$
$942$	−16.2246	+	67.5805i	−0.528628	+	2.20189i
$943$	34.7216	+	5.49937i	1.13069	+	0.179084i
$944$	13.0961	−	6.67280i	0.426242	−	0.217181i
$945$	−1.10417	−	2.66571i	−0.0359187	−	0.0867155i
$946$	2.46607	+	4.80430i	0.0801789	+	0.156201i
$947$	−8.96965	+	21.6546i	−0.291474	+	0.703682i	−0.999998	−	0.00200561i	$-0.999362\pi$
$947$	−8.96965	+	21.6546i	−0.291474	+	0.703682i	0.708524	+	0.705687i	$0.249362\pi$
$948$	−38.6682	−	12.5641i	−1.25589	−	0.408062i
$949$	−0.711030	+	0.170703i	−0.0230810	+	0.00554126i
$950$	16.4657	−	2.60790i	0.534217	−	0.0846116i
$951$	9.81536	+	30.2086i	0.318285	+	0.979581i
$952$	0.926701	+	0.312573i	0.0300345	+	0.0101305i
$953$	31.1485	+	22.6307i	1.00900	+	0.733081i	0.963999	−	0.265906i	$-0.0856711\pi$
$953$	31.1485	+	22.6307i	1.00900	+	0.733081i	0.0450003	+	0.998987i	$0.485671\pi$
$954$	11.1047	−	70.1126i	0.359529	−	2.26998i
$955$	12.1834	−	14.2649i	0.394244	−	0.461601i
$956$		−	4.85091i		−	0.156890i
$957$	0.0767822	+	25.6279i	0.00248201	+	0.828431i
$958$	19.1664	−	7.93899i	0.619239	−	0.256497i
$959$	−0.467545	+	0.0367966i	−0.0150978	+	0.00118822i
$960$	−2.98396	−	0.472612i	−0.0963068	−	0.0152535i
$961$	3.99973	+	25.2533i	0.129023	+	0.814622i
$962$	−6.25875	+	5.34548i	−0.201790	+	0.172345i
$963$	−71.5290	−	83.7497i	−2.30499	−	2.69880i
$964$	3.48913	−	2.13814i	0.112377	−	0.0688648i
$965$	−11.3529	−	15.6259i	−0.365463	−	0.503017i
$966$	2.47871	−	2.90220i	0.0797513	−	0.0933768i
$967$	−3.28281	+	3.28281i	−0.105568	+	0.105568i	−0.757918	−	0.652350i	$-0.773783\pi$
$967$	−3.28281	+	3.28281i	−0.105568	+	0.105568i	0.652350	+	0.757918i	$0.273783\pi$
$968$	−1.65565	+	10.8747i	−0.0532145	+	0.349526i
$969$	−52.6535	+	7.73851i	−1.69147	+	0.248597i
$970$	2.99445	−	9.21597i	0.0961460	−	0.295907i
$971$	−1.18660	+	7.49187i	−0.0380797	+	0.240426i	−0.999385	−	0.0350586i	$-0.988838\pi$
$971$	−1.18660	+	7.49187i	−0.0380797	+	0.240426i	0.961306	+	0.275484i	$0.0888382\pi$
$972$	11.9312	+	19.4700i	0.382694	+	0.624500i
$973$	0.809946	−	0.263167i	0.0259657	−	0.00843676i
$974$	6.55971	+	0.516261i	0.210187	+	0.0165421i
$975$	17.9272	+	4.30395i	0.574131	+	0.137837i
$976$	−2.75088	−	1.68574i	−0.0880536	−	0.0539593i
$977$	5.01182	−	2.55365i	0.160342	−	0.0816985i	−0.371978	−	0.928242i	$-0.621320\pi$
$977$	5.01182	−	2.55365i	0.160342	−	0.0816985i	0.532320	+	0.846543i	$0.321320\pi$
$978$	4.84324	+	4.84324i	0.154870	+	0.154870i
$979$	−11.9094	−	11.8382i	−0.380625	−	0.378351i
$980$	6.12082	−	2.53533i	0.195522	−	0.0809880i
$981$	40.0701	+	34.2231i	1.27934	+	1.09266i
$982$	−10.1806	−	14.0125i	−0.324877	−	0.447155i
$983$	−2.51381	−	4.10217i	−0.0801781	−	0.130839i	0.810038	−	0.586378i	$-0.199447\pi$
$983$	−2.51381	−	4.10217i	−0.0801781	−	0.130839i	−0.890216	+	0.455539i	$0.849447\pi$
$984$	19.5180	+	9.94490i	0.622210	+	0.317032i
$985$	−7.60301	−	23.3997i	−0.242252	−	0.745575i
$986$	4.66762	−	8.91353i	0.148647	−	0.283865i
$987$	4.41414	−	3.20706i	0.140504	−	0.102082i
$988$	2.63476	+	5.17100i	0.0838228	+	0.164512i
$989$	−7.64420	−	3.16633i	−0.243071	−	0.100683i
$990$	−22.1606	+	1.81090i	−0.704311	+	0.0575542i
$991$	−8.92669	+	21.5509i	−0.283566	+	0.684588i	−0.999913	−	0.0131552i	$-0.995812\pi$
$991$	−8.92669	+	21.5509i	−0.283566	+	0.684588i	0.716348	+	0.697743i	$0.245812\pi$
$992$	−0.182861	−	2.32347i	−0.00580584	−	0.0737702i
$993$	30.7713	+	18.8567i	0.976497	+	0.598398i
$994$	0.378856	+	2.39200i	0.0120166	+	0.0758697i
$995$	−2.17311	+	4.26498i	−0.0688924	+	0.135209i
$996$	13.9558	−	11.9194i	0.442207	−	0.377680i
$997$	−12.6069	−	3.02665i	−0.399264	−	0.0958548i	0.0288405	−	0.999584i	$-0.490819\pi$
$997$	−12.6069	−	3.02665i	−0.399264	−	0.0958548i	−0.428105	+	0.903729i	$0.640819\pi$
$998$	−9.15161	−	38.1192i	−0.289689	−	1.20664i
$999$	−70.0987	−	22.7765i	−2.21783	−	0.720615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.r.b.9.10	✓	160
11.5	even	5	inner	374.2.r.b.247.10	yes	160
17.2	even	8	inner	374.2.r.b.53.10	yes	160
187.104	even	40	inner	374.2.r.b.291.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.r.b.9.10	✓	160	1.1	even	1	trivial
374.2.r.b.53.10	yes	160	17.2	even	8	inner
374.2.r.b.247.10	yes	160	11.5	even	5	inner
374.2.r.b.291.10	yes	160	187.104	even	40	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.r (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 + 0.891007i) q^{2} +(3.07895 - 0.739191i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.951174 - 0.0748590i) q^{5} +(2.05644 + 2.40778i) q^{6} +(-0.0553730 + 0.230645i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(6.26053 - 3.18990i) q^{9} +O(q^{10})\)	\(q+(0.453990 + 0.891007i) q^{2} +(3.07895 - 0.739191i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.951174 - 0.0748590i) q^{5} +(2.05644 + 2.40778i) q^{6} +(-0.0553730 + 0.230645i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(6.26053 - 3.18990i) q^{9} +(-0.365124 - 0.881488i) q^{10} +(2.33817 - 2.35222i) q^{11} +(-1.21174 + 2.92541i) q^{12} +(-1.35403 - 0.439951i) q^{13} +(-0.230645 + 0.0553730i) q^{14} +(-2.98396 + 0.472612i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(0.277629 + 4.11375i) q^{17} +(5.68444 + 4.12999i) q^{18} +(-0.637682 + 4.02616i) q^{19} +(0.619648 - 0.725515i) q^{20} +0.751076i q^{21} +(3.15735 + 1.01544i) q^{22} +(-4.69476 + 1.94463i) q^{23} +(-3.15668 + 0.248436i) q^{24} +(-4.03931 - 0.639764i) q^{25} +(-0.222718 - 1.40618i) q^{26} +(9.69459 - 8.27996i) q^{27} +(-0.154048 - 0.180367i) q^{28} +(-2.08071 + 1.27506i) q^{29} +(-1.77579 - 2.44416i) q^{30} +(1.51364 - 1.77224i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.46038 - 8.97074i) q^{33} +(-3.53934 + 2.11497i) q^{34} +(0.0699352 - 0.215238i) q^{35} +(-1.09916 + 6.93985i) q^{36} +(-3.02068 - 4.92931i) q^{37} +(-3.87684 + 1.25966i) q^{38} +(-4.49421 - 0.353702i) q^{39} +(0.927753 + 0.222734i) q^{40} +(-5.89859 - 3.61466i) q^{41} +(-0.669214 + 0.340982i) q^{42} +(1.15134 + 1.15134i) q^{43} +(0.528646 + 3.27422i) q^{44} +(-6.19365 + 2.56549i) q^{45} +(-3.86406 - 3.30022i) q^{46} +(-4.26995 - 5.87709i) q^{47} +(-1.65446 - 2.69984i) q^{48} +(6.18691 + 3.15239i) q^{49} +(-1.26378 - 3.88950i) q^{50} +(3.89565 + 12.4608i) q^{51} +(1.15181 - 0.836837i) q^{52} +(-4.58662 - 9.00175i) q^{53} +(11.7787 + 4.87892i) q^{54} +(-2.40009 + 2.06234i) q^{55} +(0.0907721 - 0.219143i) q^{56} +(1.01271 + 12.8677i) q^{57} +(-2.08071 - 1.27506i) q^{58} +(2.29929 + 14.5171i) q^{59} +(1.37157 - 2.69187i) q^{60} +(2.45331 - 2.09532i) q^{61} +(2.26626 + 0.544080i) q^{62} +(0.389070 + 1.62059i) q^{63} +(0.951057 + 0.309017i) q^{64} +(1.25499 + 0.519832i) q^{65} +(10.4719 + 0.792599i) q^{66} +6.41814 q^{67} +(-3.49128 - 2.19339i) q^{68} +(-13.0175 + 9.45776i) q^{69} +(0.223529 - 0.0354035i) q^{70} +(0.801073 - 10.1786i) q^{71} +(-6.68246 + 2.17126i) q^{72} +(0.437925 - 0.268361i) q^{73} +(3.02068 - 4.92931i) q^{74} +(-12.9098 + 1.01602i) q^{75} +(-2.88242 - 2.88242i) q^{76} +(0.413057 + 0.669537i) q^{77} +(-1.72518 - 4.16495i) q^{78} +(1.00744 + 12.8008i) q^{79} +(0.222734 + 0.927753i) q^{80} +(11.3387 - 15.6064i) q^{81} +(0.542782 - 6.89670i) q^{82} +(-5.16438 - 2.63139i) q^{83} +(-0.607634 - 0.441472i) q^{84} +(0.0438777 - 3.93367i) q^{85} +(-0.503154 + 1.54855i) q^{86} +(-5.46390 + 5.46390i) q^{87} +(-2.67735 + 1.95749i) q^{88} -5.06302i q^{89} +(-5.09773 - 4.35387i) q^{90} +(0.176449 - 0.287939i) q^{91} +(1.18627 - 4.94117i) q^{92} +(3.35039 - 6.57552i) q^{93} +(3.29800 - 6.47270i) q^{94} +(0.907941 - 3.78185i) q^{95} +(1.65446 - 2.69984i) q^{96} +(7.72288 + 6.59596i) q^{97} +6.94374i q^{98} +(7.13483 - 22.1847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{5} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^5 + 8 * q^9	\( 160 q + 8 q^{5} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{14} - 8 q^{15} + 40 q^{16} - 12 q^{17} + 32 q^{18} + 12 q^{19} - 8 q^{22} + 32 q^{23} + 12 q^{24} - 8 q^{25} + 36 q^{27} - 4 q^{28} + 8 q^{29} - 40 q^{31} + 48 q^{33} + 8 q^{34} + 16 q^{35} - 12 q^{36} + 8 q^{37} - 16 q^{39} + 28 q^{41} + 60 q^{42} - 56 q^{43} - 8 q^{44} + 28 q^{46} - 116 q^{49} - 80 q^{50} + 8 q^{52} + 8 q^{53} - 8 q^{54} - 148 q^{57} + 8 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} - 40 q^{62} - 72 q^{63} + 144 q^{65} - 28 q^{66} - 256 q^{67} - 8 q^{69} + 8 q^{70} - 60 q^{71} - 8 q^{73} - 8 q^{74} - 116 q^{75} + 8 q^{76} - 60 q^{77} - 16 q^{78} + 40 q^{79} + 12 q^{80} - 16 q^{82} + 76 q^{83} - 56 q^{84} + 36 q^{85} - 8 q^{86} - 144 q^{87} - 4 q^{88} - 40 q^{90} + 44 q^{91} - 32 q^{92} - 40 q^{93} - 4 q^{94} + 36 q^{95} - 124 q^{97} - 176 q^{99}+O(q^{100}) \) 160 * q + 8 * q^5 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^14 - 8 * q^15 + 40 * q^16 - 12 * q^17 + 32 * q^18 + 12 * q^19 - 8 * q^22 + 32 * q^23 + 12 * q^24 - 8 * q^25 + 36 * q^27 - 4 * q^28 + 8 * q^29 - 40 * q^31 + 48 * q^33 + 8 * q^34 + 16 * q^35 - 12 * q^36 + 8 * q^37 - 16 * q^39 + 28 * q^41 + 60 * q^42 - 56 * q^43 - 8 * q^44 + 28 * q^46 - 116 * q^49 - 80 * q^50 + 8 * q^52 + 8 * q^53 - 8 * q^54 - 148 * q^57 + 8 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 - 40 * q^62 - 72 * q^63 + 144 * q^65 - 28 * q^66 - 256 * q^67 - 8 * q^69 + 8 * q^70 - 60 * q^71 - 8 * q^73 - 8 * q^74 - 116 * q^75 + 8 * q^76 - 60 * q^77 - 16 * q^78 + 40 * q^79 + 12 * q^80 - 16 * q^82 + 76 * q^83 - 56 * q^84 + 36 * q^85 - 8 * q^86 - 144 * q^87 - 4 * q^88 - 40 * q^90 + 44 * q^91 - 32 * q^92 - 40 * q^93 - 4 * q^94 + 36 * q^95 - 124 * q^97 - 176 * q^99

Introduction

L-functions

Modular forms

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