LMFDB - Embedded newform 354.2.e.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	354.127
Dual form			354.2.e.b.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647386 + 0.762162i) q^{2} +(-0.796093 - 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.140789 + 0.265557i) q^{5} +(0.976621 - 0.214970i) q^{6} +(-0.694075 - 0.0754852i) q^{7} +(0.856857 + 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})$	\(q+(-0.647386 + 0.762162i) q^{2} +(-0.796093 - 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.140789 + 0.265557i) q^{5} +(0.976621 - 0.214970i) q^{6} +(-0.694075 - 0.0754852i) q^{7} +(0.856857 + 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(-0.293542 - 0.0646136i) q^{10} +(1.30975 + 0.441306i) q^{11} +(-0.468408 + 0.883512i) q^{12} +(1.02091 - 3.67700i) q^{13} +(0.506866 - 0.480129i) q^{14} +(0.0486267 - 0.296610i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(4.84839 - 0.527294i) q^{17} +(-0.907575 - 0.419889i) q^{18} +(0.200283 - 3.69400i) q^{19} +(0.239281 - 0.181897i) q^{20} +(0.506866 + 0.480129i) q^{21} +(-1.18426 + 0.712546i) q^{22} +(3.07555 - 1.42290i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(2.75524 - 4.06367i) q^{25} +(2.14154 + 3.15854i) q^{26} +(0.370138 - 0.928977i) q^{27} +(0.0377980 + 0.697143i) q^{28} +(2.55869 + 3.01233i) q^{29} +(0.194585 + 0.229083i) q^{30} +(0.0121354 + 0.223824i) q^{31} +(0.370138 - 0.928977i) q^{32} +(-0.775616 - 1.14395i) q^{33} +(-2.73690 + 4.03662i) q^{34} +(-0.0776727 - 0.194944i) q^{35} +(0.907575 - 0.419889i) q^{36} +(3.78404 - 2.27678i) q^{37} +(2.68577 + 2.54410i) q^{38} +(-3.03796 + 2.30940i) q^{39} +(-0.0162725 + 0.300129i) q^{40} +(5.51917 + 2.55344i) q^{41} +(-0.694075 + 0.0754852i) q^{42} +(-1.37218 + 0.462342i) q^{43} +(0.223599 - 1.36389i) q^{44} +(-0.218212 + 0.206702i) q^{45} +(-0.906589 + 3.26524i) q^{46} +(-1.73350 + 3.26973i) q^{47} +(0.947653 + 0.319302i) q^{48} +(-6.36030 - 1.40001i) q^{49} +(1.31347 + 4.73070i) q^{50} +(-4.17888 - 2.51435i) q^{51} +(-3.79372 - 0.412592i) q^{52} +(3.27478 - 0.720834i) q^{53} +(0.468408 + 0.883512i) q^{54} +(0.0672069 + 0.409944i) q^{55} +(-0.555806 - 0.422513i) q^{56} +(-2.39496 + 2.81956i) q^{57} -3.95234 q^{58} +(-6.83631 - 3.50212i) q^{59} -0.300570 q^{60} +(-1.04273 + 1.22760i) q^{61} +(-0.178446 - 0.135651i) q^{62} +(-0.112951 - 0.688970i) q^{63} +(0.468408 + 0.883512i) q^{64} +(1.12018 - 0.246571i) q^{65} +(1.37400 + 0.149431i) q^{66} +(-1.39950 - 0.842053i) q^{67} +(-1.30473 - 4.69921i) q^{68} +(-3.30953 - 0.728483i) q^{69} +(0.198863 + 0.0670047i) q^{70} +(-3.17992 + 5.99796i) q^{71} +(-0.267528 + 0.963550i) q^{72} +(3.29561 - 3.12177i) q^{73} +(-0.714458 + 4.35800i) q^{74} +(-4.65265 + 1.56766i) q^{75} +(-3.67774 + 0.399979i) q^{76} +(-0.875752 - 0.405166i) q^{77} +(0.206599 - 3.81050i) q^{78} +(-8.61555 + 6.54937i) q^{79} +(-0.218212 - 0.206702i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(-5.51917 + 2.55344i) q^{82} +(-2.75870 - 6.92381i) q^{83} +(0.391802 - 0.577865i) q^{84} +(0.822628 + 1.21329i) q^{85} +(0.535953 - 1.34514i) q^{86} +(-0.213976 - 3.94655i) q^{87} +(0.894752 + 1.05338i) q^{88} +(-2.12020 - 2.49609i) q^{89} +(-0.0162725 - 0.300129i) q^{90} +(-0.986148 + 2.47505i) q^{91} +(-1.90173 - 2.80484i) q^{92} +(0.125791 - 0.185528i) q^{93} +(-1.36982 - 3.43798i) q^{94} +(1.00917 - 0.466890i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(7.68744 + 7.28193i) q^{97} +(5.18461 - 3.94123i) q^{98} +(-0.0748253 + 1.38007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{21}{29}\right)$	$1$

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 $

$2$	−0.647386	+	0.762162i	−0.457771	+	0.538930i
$2$	−0.647386	+	0.762162i	−0.457771	+	0.538930i
$3$	−0.796093	−	0.605174i	−0.459625	−	0.349397i
$3$	−0.796093	−	0.605174i	−0.459625	−	0.349397i
$4$	−0.161782	−	0.986827i	−0.0808910	−	0.493413i
$5$	0.140789	+	0.265557i	0.0629629	+	0.118761i	0.912996	−	0.407969i	$-0.133763\pi$
$5$	0.140789	+	0.265557i	0.0629629	+	0.118761i	−0.850033	+	0.526730i	$0.823418\pi$
$6$	0.976621	−	0.214970i	0.398704	−	0.0877613i
$7$	−0.694075	−	0.0754852i	−0.262336	−	0.0285307i	−0.0239940	−	0.999712i	$-0.507638\pi$
$7$	−0.694075	−	0.0754852i	−0.262336	−	0.0285307i	−0.238342	+	0.971181i	$0.576604\pi$
$8$	0.856857	+	0.515554i	0.302945	+	0.182276i
$9$	0.267528	+	0.963550i	0.0891761	+	0.321183i
$10$	−0.293542	−	0.0646136i	−0.0928263	−	0.0204326i
$11$	1.30975	+	0.441306i	0.394904	+	0.133059i	0.509746	−	0.860325i	$-0.329739\pi$
$11$	1.30975	+	0.441306i	0.394904	+	0.133059i	−0.114841	+	0.993384i	$0.536636\pi$
$12$	−0.468408	+	0.883512i	−0.135218	+	0.255048i
$13$	1.02091	−	3.67700i	0.283150	−	1.01981i	−0.675996	−	0.736905i	$-0.736286\pi$
$13$	1.02091	−	3.67700i	0.283150	−	1.01981i	0.959146	−	0.282910i	$-0.0912997\pi$
$14$	0.506866	−	0.480129i	0.135466	−	0.128320i
$15$	0.0486267	−	0.296610i	0.0125554	−	0.0765844i
$16$	−0.947653	+	0.319302i	−0.236913	+	0.0798254i
$17$	4.84839	−	0.527294i	1.17591	−	0.127888i	0.500771	−	0.865580i	$-0.333050\pi$
$17$	4.84839	−	0.527294i	1.17591	−	0.127888i	0.675137	+	0.737692i	$0.264084\pi$
$18$	−0.907575	−	0.419889i	−0.213918	−	0.0989688i
$19$	0.200283	−	3.69400i	0.0459481	−	0.847463i	−0.881194	−	0.472754i	$-0.843260\pi$
$19$	0.200283	−	3.69400i	0.0459481	−	0.847463i	0.927143	−	0.374709i	$-0.122257\pi$
$20$	0.239281	−	0.181897i	0.0535049	−	0.0406734i
$21$	0.506866	+	0.480129i	0.110607	+	0.104773i
$22$	−1.18426	+	0.712546i	−0.252485	+	0.151915i
$23$	3.07555	−	1.42290i	0.641297	−	0.296696i	−0.0721614	−	0.997393i	$-0.522990\pi$
$23$	3.07555	−	1.42290i	0.641297	−	0.296696i	0.713459	+	0.700697i	$0.247128\pi$
$24$	−0.370138	−	0.928977i	−0.0755541	−	0.189627i
$25$	2.75524	−	4.06367i	0.551047	−	0.812734i
$26$	2.14154	+	3.15854i	0.419991	+	0.619440i
$27$	0.370138	−	0.928977i	0.0712331	−	0.178782i
$28$	0.0377980	+	0.697143i	0.00714315	+	0.131748i
$29$	2.55869	+	3.01233i	0.475137	+	0.559375i	0.946558	−	0.322534i	$-0.104535\pi$
$29$	2.55869	+	3.01233i	0.475137	+	0.559375i	−0.471421	+	0.881908i	$0.656259\pi$
$30$	0.194585	+	0.229083i	0.0355261	+	0.0418246i
$31$	0.0121354	+	0.223824i	0.00217958	+	0.0401999i	0.999421	−	0.0340280i	$-0.0108335\pi$
$31$	0.0121354	+	0.223824i	0.00217958	+	0.0401999i	−0.997241	+	0.0742279i	$0.976351\pi$
$32$	0.370138	−	0.928977i	0.0654318	−	0.164221i
$33$	−0.775616	−	1.14395i	−0.135017	−	0.199136i
$34$	−2.73690	+	4.03662i	−0.469374	+	0.692275i
$35$	−0.0776727	−	0.194944i	−0.0131291	−	0.0329515i
$36$	0.907575	−	0.419889i	0.151263	−	0.0699815i
$37$	3.78404	−	2.27678i	0.622092	−	0.374300i	−0.169340	−	0.985558i	$-0.554164\pi$
$37$	3.78404	−	2.27678i	0.622092	−	0.374300i	0.791432	+	0.611258i	$0.209336\pi$
$38$	2.68577	+	2.54410i	0.435689	+	0.412707i
$39$	−3.03796	+	2.30940i	−0.486464	+	0.369800i
$40$	−0.0162725	+	0.300129i	−0.00257291	+	0.0474545i
$41$	5.51917	+	2.55344i	0.861950	+	0.398780i	0.800502	−	0.599330i	$-0.204566\pi$
$41$	5.51917	+	2.55344i	0.861950	+	0.398780i	0.0614477	+	0.998110i	$0.480428\pi$
$42$	−0.694075	+	0.0754852i	−0.107098	+	0.0116476i
$43$	−1.37218	+	0.462342i	−0.209256	+	0.0705065i	−0.421977	−	0.906606i	$-0.638664\pi$
$43$	−1.37218	+	0.462342i	−0.209256	+	0.0705065i	0.212721	+	0.977113i	$0.431767\pi$
$44$	0.223599	−	1.36389i	0.0337088	−	0.205614i
$45$	−0.218212	+	0.206702i	−0.0325291	+	0.0308132i
$46$	−0.906589	+	3.26524i	−0.133669	+	0.481433i
$47$	−1.73350	+	3.26973i	−0.252857	+	0.476938i	−0.977149	−	0.212554i	$-0.931822\pi$
$47$	−1.73350	+	3.26973i	−0.252857	+	0.476938i	0.724292	+	0.689493i	$0.242167\pi$
$48$	0.947653	+	0.319302i	0.136782	+	0.0460872i
$49$	−6.36030	−	1.40001i	−0.908615	−	0.200001i
$50$	1.31347	+	4.73070i	0.185753	+	0.669022i
$51$	−4.17888	−	2.51435i	−0.585160	−	0.352079i
$52$	−3.79372	−	0.412592i	−0.526095	−	0.0572162i
$53$	3.27478	−	0.720834i	0.449826	−	0.0990142i	0.0157209	−	0.999876i	$-0.494996\pi$
$53$	3.27478	−	0.720834i	0.449826	−	0.0990142i	0.434105	+	0.900862i	$0.357065\pi$
$54$	0.468408	+	0.883512i	0.0637423	+	0.120231i
$55$	0.0672069	+	0.409944i	0.00906218	+	0.0552769i
$56$	−0.555806	−	0.422513i	−0.0742727	−	0.0564607i
$57$	−2.39496	+	2.81956i	−0.317220	+	0.373460i
$58$	−3.95234			−0.518968
$59$	−6.83631	−	3.50212i	−0.890012	−	0.455937i
$59$	−6.83631	−	3.50212i	−0.890012	−	0.455937i
$60$	−0.300570			−0.0388034
$61$	−1.04273	+	1.22760i	−0.133508	+	0.157178i	−0.824854	−	0.565346i	$-0.808743\pi$
$61$	−1.04273	+	1.22760i	−0.133508	+	0.157178i	0.691345	+	0.722525i	$0.257018\pi$
$62$	−0.178446	−	0.135651i	−0.0226627	−	0.0172277i
$63$	−0.112951	−	0.688970i	−0.0142305	−	0.0868021i
$64$	0.468408	+	0.883512i	0.0585511	+	0.110439i
$65$	1.12018	−	0.246571i	0.138942	−	0.0305834i
$66$	1.37400	+	0.149431i	0.169127	+	0.0183937i
$67$	−1.39950	−	0.842053i	−0.170977	−	0.102873i	0.427493	−	0.904019i	$-0.359397\pi$
$67$	−1.39950	−	0.842053i	−0.170977	−	0.102873i	−0.598470	+	0.801145i	$0.704224\pi$
$68$	−1.30473	−	4.69921i	−0.158222	−	0.569863i
$69$	−3.30953	−	0.728483i	−0.398421	−	0.0876991i
$70$	0.198863	+	0.0670047i	0.0237687	+	0.00800860i
$71$	−3.17992	+	5.99796i	−0.377387	+	0.711827i	−0.997346	−	0.0728068i	$-0.976804\pi$
$71$	−3.17992	+	5.99796i	−0.377387	+	0.711827i	0.619959	+	0.784634i	$0.287149\pi$
$72$	−0.267528	+	0.963550i	−0.0315285	+	0.113555i
$73$	3.29561	−	3.12177i	0.385722	−	0.365375i	−0.470129	−	0.882598i	$-0.655793\pi$
$73$	3.29561	−	3.12177i	0.385722	−	0.365375i	0.855851	+	0.517222i	$0.173034\pi$
$74$	−0.714458	+	4.35800i	−0.0830541	+	0.506608i
$75$	−4.65265	+	1.56766i	−0.537242	+	0.181018i
$76$	−3.67774	+	0.399979i	−0.421866	+	0.0458807i
$77$	−0.875752	−	0.405166i	−0.0998012	−	0.0461730i
$78$	0.206599	−	3.81050i	0.0233927	−	0.431454i
$79$	−8.61555	+	6.54937i	−0.969325	+	0.736862i	−0.964761	−	0.263128i	$-0.915246\pi$
$79$	−8.61555	+	6.54937i	−0.969325	+	0.736862i	−0.00456437	+	0.999990i	$0.501453\pi$
$80$	−0.218212	−	0.206702i	−0.0243969	−	0.0231099i
$81$	−0.856857	+	0.515554i	−0.0952064	+	0.0572838i
$82$	−5.51917	+	2.55344i	−0.609491	+	0.281980i
$83$	−2.75870	−	6.92381i	−0.302807	−	0.759987i	−0.999108	−	0.0422374i	$-0.986551\pi$
$83$	−2.75870	−	6.92381i	−0.302807	−	0.759987i	0.696301	−	0.717750i	$-0.254828\pi$
$84$	0.391802	−	0.577865i	0.0427492	−	0.0630503i
$85$	0.822628	+	1.21329i	0.0892266	+	0.131599i
$86$	0.535953	−	1.34514i	0.0577933	−	0.145050i
$87$	−0.213976	−	3.94655i	−0.0229406	−	0.423114i
$88$	0.894752	+	1.05338i	0.0953808	+	0.112291i
$89$	−2.12020	−	2.49609i	−0.224741	−	0.264585i	0.638223	−	0.769852i	$-0.279670\pi$
$89$	−2.12020	−	2.49609i	−0.224741	−	0.264585i	−0.862963	+	0.505267i	$0.831394\pi$
$90$	−0.0162725	−	0.300129i	−0.00171527	−	0.0316363i
$91$	−0.986148	+	2.47505i	−0.103376	+	0.259455i
$92$	−1.90173	−	2.80484i	−0.198269	−	0.292425i
$93$	0.125791	−	0.185528i	0.0130440	−	0.0192384i
$94$	−1.36982	−	3.43798i	−0.141286	−	0.354601i
$95$	1.00917	−	0.466890i	0.103538	−	0.0479019i
$96$	−0.856857	+	0.515554i	−0.0874526	+	0.0526185i
$97$	7.68744	+	7.28193i	0.780541	+	0.739368i	0.970154	−	0.242491i	$-0.0779645\pi$
$97$	7.68744	+	7.28193i	0.780541	+	0.739368i	−0.189612	+	0.981859i	$0.560723\pi$
$98$	5.18461	−	3.94123i	0.523724	−	0.398125i
$99$	−0.0748253	+	1.38007i	−0.00752023	+	0.138702i
$100$	−4.45588	−	2.06151i	−0.445588	−	0.206151i
$101$	−9.31499	+	1.01307i	−0.926876	+	0.100804i	−0.559090	−	0.829107i	$-0.688849\pi$
$101$	−9.31499	+	1.01307i	−0.926876	+	0.100804i	−0.367786	+	0.929911i	$0.619884\pi$
$102$	4.62169	−	1.55723i	0.457615	−	0.154188i
$103$	2.61161	−	15.9301i	0.257330	−	1.56964i	−0.469567	−	0.882897i	$-0.655590\pi$
$103$	2.61161	−	15.9301i	0.257330	−	1.56964i	0.726897	−	0.686747i	$-0.240962\pi$
$104$	2.77047	−	2.62432i	0.271666	−	0.257336i
$105$	−0.0561402	+	0.202199i	−0.00547873	+	0.0197326i
$106$	−1.57066	+	2.96257i	−0.152556	+	0.287751i
$107$	−9.94798	−	3.35186i	−0.961707	−	0.324037i	−0.205711	−	0.978613i	$-0.565951\pi$
$107$	−9.94798	−	3.35186i	−0.961707	−	0.324037i	−0.755996	+	0.654576i	$0.772847\pi$
$108$	−0.976621	−	0.214970i	−0.0939754	−	0.0206855i
$109$	1.13265	+	4.07943i	0.108488	+	0.390739i	0.997780	−	0.0666019i	$-0.0212158\pi$
$109$	1.13265	+	4.07943i	0.108488	+	0.390739i	−0.889292	+	0.457341i	$0.848802\pi$
$110$	−0.355953	−	0.214170i	−0.0339388	−	0.0204203i
$111$	−4.39029	−	0.477473i	−0.416708	−	0.0453197i
$112$	0.681845	−	0.150085i	0.0644283	−	0.0141817i
$113$	7.18468	+	13.5517i	0.675878	+	1.27484i	0.949730	+	0.313069i	$0.101357\pi$
$113$	7.18468	+	13.5517i	0.675878	+	1.27484i	−0.273852	+	0.961772i	$0.588298\pi$
$114$	−0.598501	−	3.65070i	−0.0560548	−	0.341919i
$115$	0.810867	+	0.616405i	0.0756137	+	0.0574801i
$116$	2.55869	−	3.01233i	0.237569	−	0.279687i
$117$	3.81609			0.352798
$118$	7.09492	−	2.94315i	0.653140	−	0.270939i
$119$	−3.40495			−0.312131
$120$	0.194585	−	0.229083i	0.0177631	−	0.0209123i
$121$	−7.23633	−	5.50091i	−0.657848	−	0.500083i
$122$	−0.260579	−	1.58946i	−0.0235918	−	0.143903i
$123$	−2.84850	−	5.37284i	−0.256840	−	0.484452i
$124$	0.218912	−	0.0481861i	0.0196589	−	0.00432724i
$125$	2.96108	+	0.322037i	0.264847	+	0.0288039i
$126$	0.598230	+	0.359943i	0.0532945	+	0.0320663i
$127$	2.02021	+	7.27615i	0.179265	+	0.645653i	0.997493	+	0.0707604i	$0.0225426\pi$
$127$	2.02021	+	7.27615i	0.179265	+	0.645653i	−0.818229	+	0.574893i	$0.805044\pi$
$128$	−0.976621	−	0.214970i	−0.0863219	−	0.0190009i
$129$	1.37218	+	0.462342i	0.120814	+	0.0407070i
$130$	−0.537265	+	1.01339i	−0.0471213	+	0.0888801i
$131$	−1.06715	+	3.84354i	−0.0932377	+	0.335812i	−0.995427	−	0.0955293i	$-0.969546\pi$
$131$	−1.06715	+	3.84354i	−0.0932377	+	0.335812i	0.902189	+	0.431341i	$0.141959\pi$
$132$	−1.00340	+	0.950468i	−0.0873345	+	0.0827277i
$133$	−0.417854	+	2.54880i	−0.0362325	+	0.221009i
$134$	1.54780	−	0.521515i	0.133710	−	0.0450520i
$135$	0.298808	−	0.0324973i	0.0257173	−	0.00279692i
$136$	4.42623	+	2.04779i	0.379546	+	0.175597i
$137$	−0.315326	+	5.81585i	−0.0269402	+	0.496882i	0.953663	+	0.300877i	$0.0972795\pi$
$137$	−0.315326	+	5.81585i	−0.0269402	+	0.496882i	−0.980603	+	0.196005i	$0.937203\pi$
$138$	2.69777	−	2.05079i	0.229649	−	0.174575i
$139$	9.24845	+	8.76060i	0.784444	+	0.743064i	0.970922	−	0.239395i	$-0.0769489\pi$
$139$	9.24845	+	8.76060i	0.784444	+	0.743064i	−0.186479	+	0.982459i	$0.559708\pi$
$140$	−0.179810	+	0.108188i	−0.0151967	+	0.00914354i
$141$	3.35878	−	1.55394i	0.282860	−	0.130865i
$142$	−2.51278	−	6.30661i	−0.210868	−	0.529239i
$143$	2.95982	−	4.36541i	0.247513	−	0.365054i
$144$	−0.561187	−	0.827689i	−0.0467656	−	0.0689741i
$145$	−0.439707	+	1.10358i	−0.0365157	+	0.0916475i
$146$	0.245760	+	4.53278i	0.0203393	+	0.375136i
$147$	4.21614	+	4.96363i	0.347742	+	0.409393i
$148$	−2.85897	−	3.36585i	−0.235006	−	0.276671i
$149$	0.635626	+	11.7234i	0.0520725	+	0.960422i	0.901517	+	0.432744i	$0.142454\pi$
$149$	0.635626	+	11.7234i	0.0520725	+	0.960422i	−0.849444	+	0.527678i	$0.823063\pi$
$150$	1.81725	−	4.56096i	0.148378	−	0.372401i
$151$	10.5275	+	15.5270i	0.856720	+	1.26357i	0.963074	+	0.269239i	$0.0867720\pi$
$151$	10.5275	+	15.5270i	0.856720	+	1.26357i	−0.106354	+	0.994328i	$0.533918\pi$
$152$	2.07607	−	3.06198i	0.168392	−	0.248359i
$153$	1.80516	+	4.53060i	0.145938	+	0.366277i
$154$	0.875752	−	0.405166i	0.0705701	−	0.0326492i
$155$	−0.0577294	+	0.0347346i	−0.00463693	+	0.00278995i
$156$	2.77047	+	2.62432i	0.221815	+	0.210114i
$157$	7.84280	−	5.96194i	0.625923	−	0.475815i	−0.243488	−	0.969904i	$-0.578292\pi$
$157$	7.84280	−	5.96194i	0.625923	−	0.475815i	0.869411	+	0.494089i	$0.164498\pi$
$158$	0.585907	−	10.8064i	0.0466123	−	0.859713i
$159$	−3.04326	−	1.40796i	−0.241346	−	0.111659i
$160$	0.298808	−	0.0324973i	0.0236228	−	0.00256914i
$161$	−2.24207	+	0.755442i	−0.176700	+	0.0595372i
$162$	0.161782	−	0.986827i	0.0127108	−	0.0775324i
$163$	2.53053	−	2.39704i	0.198206	−	0.187751i	−0.582159	−	0.813075i	$-0.697792\pi$
$163$	2.53053	−	2.39704i	0.198206	−	0.187751i	0.780365	+	0.625324i	$0.215033\pi$
$164$	1.62690	−	5.85957i	0.127040	−	0.457555i
$165$	0.194585	−	0.367026i	0.0151484	−	0.0285729i
$166$	7.06301	+	2.37981i	0.548196	+	0.184709i
$167$	−5.37592	−	1.18333i	−0.416002	−	0.0915689i	0.00203752	−	0.999998i	$-0.499351\pi$
$167$	−5.37592	−	1.18333i	−0.416002	−	0.0915689i	−0.418039	+	0.908429i	$0.637282\pi$
$168$	0.186780	+	0.672719i	0.0144104	+	0.0519014i
$169$	−1.33889	−	0.805581i	−0.102991	−	0.0619678i
$170$	−1.45728	−	0.158489i	−0.111768	−	0.0121555i
$171$	3.61294	−	0.795268i	0.276288	−	0.0608157i
$172$	0.678246	+	1.27931i	0.0517158	+	0.0975463i
$173$	−0.859232	−	5.24109i	−0.0653262	−	0.398472i	−0.999168	−	0.0407857i	$-0.987014\pi$
$173$	−0.859232	−	5.24109i	−0.0653262	−	0.398472i	0.933842	−	0.357687i	$-0.116434\pi$
$174$	3.14643	+	2.39186i	0.238530	+	0.181326i
$175$	−2.21909	+	2.61251i	−0.167747	+	0.197487i
$176$	−1.38210			−0.104180
$177$	3.32295	+	6.92517i	0.249768	+	0.520528i
$178$	3.27501			0.245473
$179$	9.28078	−	10.9262i	0.693678	−	0.816661i	−0.296712	−	0.954967i	$-0.595890\pi$
$179$	9.28078	−	10.9262i	0.693678	−	0.816661i	0.990389	+	0.138306i	$0.0441659\pi$
$180$	0.239281	+	0.181897i	0.0178350	+	0.0135578i
$181$	0.754642	+	4.60311i	0.0560921	+	0.342147i	0.999931	+	0.0117408i	$0.00373730\pi$
$181$	0.754642	+	4.60311i	0.0560921	+	0.342147i	−0.943839	+	0.330406i	$0.892814\pi$
$182$	−1.24797	−	2.35391i	−0.0925054	−	0.174484i
$183$	1.57303	−	0.346249i	0.116281	−	0.0255955i
$184$	3.36889	+	0.366389i	0.248358	+	0.0270106i
$185$	1.13737	+	0.684330i	0.0836208	+	0.0503130i
$186$	0.0599671	+	0.215982i	0.00439700	+	0.0158366i
$187$	6.58288	+	1.44900i	0.481388	+	0.105961i
$188$	3.50710	+	1.18168i	0.255782	+	0.0861829i
$189$	−0.327027	+	0.616839i	−0.0237877	+	0.0448685i
$190$	−0.297474	+	1.07141i	−0.0215811	+	0.0777279i
$191$	−10.3276	+	9.78281i	−0.747278	+	0.707859i	−0.963270	−	0.268536i	$-0.913460\pi$
$191$	−10.3276	+	9.78281i	−0.747278	+	0.707859i	0.215992	+	0.976395i	$0.430702\pi$
$192$	0.161782	−	0.986827i	0.0116756	−	0.0712181i
$193$	18.7261	−	6.30954i	1.34793	−	0.454171i	0.449498	−	0.893281i	$-0.351603\pi$
$193$	18.7261	−	6.30954i	1.34793	−	0.454171i	0.898433	+	0.439111i	$0.144706\pi$
$194$	−10.5268	+	1.14485i	−0.755777	+	0.0821957i
$195$	−1.04099	−	0.481613i	−0.0745468	−	0.0344890i
$196$	−0.352583	+	6.50301i	−0.0251845	+	0.464501i
$197$	1.45090	−	1.10294i	0.103372	−	0.0785816i	−0.552211	−	0.833704i	$-0.686216\pi$
$197$	1.45090	−	1.10294i	0.103372	−	0.0785816i	0.655584	+	0.755123i	$0.272423\pi$
$198$	−1.00340	−	0.950468i	−0.0713083	−	0.0675468i
$199$	−5.12568	+	3.08402i	−0.363349	+	0.218620i	−0.685507	−	0.728066i	$-0.740419\pi$
$199$	−5.12568	+	3.08402i	−0.363349	+	0.218620i	0.322158	+	0.946686i	$0.395592\pi$
$200$	4.45588	−	2.06151i	0.315079	−	0.145771i
$201$	0.604546	+	1.51730i	0.0426414	+	0.107022i
$202$	5.25827	−	7.75537i	0.369971	−	0.545666i
$203$	−1.54854	−	2.28392i	−0.108686	−	0.160300i
$204$	−1.80516	+	4.53060i	−0.126386	+	0.317206i
$205$	0.0989568	+	1.82515i	0.00691144	+	0.127474i
$206$	10.4506	+	12.3034i	0.728130	+	0.857221i
$207$	2.19384	+	2.58278i	0.152482	+	0.179516i
$208$	0.206599	+	3.81050i	0.0143251	+	0.264210i
$209$	1.89251	−	4.74984i	0.130907	−	0.328553i
$210$	−0.117764	−	0.173689i	−0.00812648	−	0.0119857i
$211$	11.8455	−	17.4707i	0.815475	−	1.20274i	−0.160968	−	0.986960i	$-0.551462\pi$
$211$	11.8455	−	17.4707i	0.815475	−	1.20274i	0.976443	−	0.215776i	$-0.0692281\pi$
$212$	−1.24114	−	3.11502i	−0.0852418	−	0.213941i
$213$	6.16132	−	2.85053i	0.422167	−	0.195315i
$214$	8.99485	−	5.41202i	0.614875	−	0.369958i
$215$	−0.315967	−	0.299300i	−0.0215488	−	0.0204121i
$216$	0.796093	−	0.605174i	0.0541673	−	0.0411769i
$217$	0.00847251	−	0.156266i	0.000575152	−	0.0106080i
$218$	−3.84245	−	1.77771i	−0.260244	−	0.120402i
$219$	−4.51283	+	0.490799i	−0.304949	+	0.0331652i
$220$	0.393671	−	0.132643i	0.0265413	−	0.00894280i
$221$	3.01093	−	18.3658i	0.202537	−	1.23542i
$222$	3.20613	−	3.03700i	0.215181	−	0.203830i
$223$	−0.834067	+	3.00404i	−0.0558533	+	0.201165i	−0.986212	−	0.165484i	$-0.947081\pi$
$223$	−0.834067	+	3.00404i	−0.0558533	+	0.201165i	0.930359	+	0.366649i	$0.119495\pi$
$224$	−0.327027	+	0.616839i	−0.0218504	+	0.0412143i
$225$	4.65265	+	1.56766i	0.310177	+	0.104511i
$226$	−14.9799	−	3.29732i	−0.996448	−	0.219335i
$227$	0.410343	+	1.47792i	0.0272354	+	0.0980930i	0.975919	−	0.218135i	$-0.0699973\pi$
$227$	0.410343	+	1.47792i	0.0272354	+	0.0980930i	−0.948683	+	0.316228i	$0.897584\pi$
$228$	3.16988	+	1.90726i	0.209931	+	0.126311i
$229$	−16.4332	−	1.78722i	−1.08594	−	0.118103i	−0.452400	−	0.891815i	$-0.649432\pi$
$229$	−16.4332	−	1.78722i	−1.08594	−	0.118103i	−0.633537	+	0.773712i	$0.718398\pi$
$230$	−0.994745	+	0.218960i	−0.0655915	+	0.0144378i
$231$	0.451984	+	0.852532i	0.0297384	+	0.0560925i
$232$	0.639418	+	3.90028i	0.0419798	+	0.256066i
$233$	−14.8072	−	11.2561i	−0.970050	−	0.737413i	−0.00513827	−	0.999987i	$-0.501636\pi$
$233$	−14.8072	−	11.2561i	−0.970050	−	0.737413i	−0.964912	+	0.262574i	$0.915429\pi$
$234$	−2.47049	+	2.90848i	−0.161501	+	0.190133i
$235$	−1.11236			−0.0725621
$236$	−2.34999	+	7.31283i	−0.152972	+	0.476025i
$237$	10.8223			0.702984
$238$	2.20432	−	2.59512i	0.142885	−	0.168217i
$239$	−21.2261	−	16.1356i	−1.37300	−	1.04373i	−0.992922	−	0.118772i	$-0.962104\pi$
$239$	−21.2261	−	16.1356i	−1.37300	−	1.04373i	−0.380078	−	0.924955i	$-0.624103\pi$
$240$	0.0486267	+	0.296610i	0.00313884	+	0.0191461i
$241$	−1.41029	−	2.66009i	−0.0908448	−	0.171351i	0.833926	−	0.551877i	$-0.186088\pi$
$241$	−1.41029	−	2.66009i	−0.0908448	−	0.171351i	−0.924771	+	0.380525i	$0.875743\pi$
$242$	8.87729	−	1.95404i	0.570654	−	0.125610i
$243$	0.994138	+	0.108119i	0.0637740	+	0.00693584i
$244$	1.38012	+	0.830394i	0.0883534	+	0.0531605i
$245$	−0.523681	−	1.88613i	−0.0334567	−	0.120500i
$246$	5.93905	+	1.30728i	0.378660	+	0.0833494i
$247$	−13.3784	−	4.50770i	−0.851245	−	0.286818i
$248$	−0.104995	+	0.198041i	−0.00666718	+	0.0125756i
$249$	−1.99393	+	7.18149i	−0.126360	+	0.455109i
$250$	−2.16241	+	2.04834i	−0.136763	+	0.129548i
$251$	0.0789541	−	0.481599i	0.00498354	−	0.0303982i	−0.984218	−	0.176962i	$-0.943373\pi$
$251$	0.0789541	−	0.481599i	0.00498354	−	0.0303982i	0.989201	+	0.146564i	$0.0468213\pi$
$252$	−0.661620	+	0.222926i	−0.0416782	+	0.0140430i
$253$	4.65614	−	0.506386i	0.292729	−	0.0318362i
$254$	−6.85346	−	3.17075i	−0.430024	−	0.198950i
$255$	0.0793607	−	1.46372i	0.00496976	−	0.0916618i
$256$	0.796093	−	0.605174i	0.0497558	−	0.0378234i
$257$	22.0575	+	20.8940i	1.37591	+	1.30333i	0.907641	+	0.419747i	$0.137881\pi$
$257$	22.0575	+	20.8940i	1.37591	+	1.30333i	0.468270	+	0.883585i	$0.344877\pi$
$258$	−1.24071	+	0.746512i	−0.0772434	+	0.0464758i
$259$	−2.79827	+	1.29462i	−0.173876	+	0.0804435i
$260$	−0.424549	−	1.06554i	−0.0263294	−	0.0660818i
$261$	−2.21800	+	3.27131i	−0.137291	+	0.202489i
$262$	−2.23854	−	3.30160i	−0.138297	−	0.203974i
$263$	−7.79692	+	19.5688i	−0.480779	+	1.20666i	0.466001	+	0.884784i	$0.345694\pi$
$263$	−7.79692	+	19.5688i	−0.480779	+	1.20666i	−0.946780	+	0.321880i	$0.895685\pi$
$264$	−0.0748253	−	1.38007i	−0.00460518	−	0.0849375i
$265$	0.652477	+	0.768155i	0.0400813	+	0.0471874i
$266$	−1.67208	−	1.96853i	−0.102522	−	0.120698i
$267$	0.177306	+	3.27021i	0.0108509	+	0.200134i
$268$	−0.604546	+	1.51730i	−0.0369285	+	0.0926836i
$269$	−8.48992	−	12.5217i	−0.517639	−	0.763461i	0.475586	−	0.879669i	$-0.342236\pi$
$269$	−8.48992	−	12.5217i	−0.517639	−	0.763461i	−0.993225	+	0.116209i	$0.962926\pi$
$270$	−0.168676	+	0.248778i	−0.0102653	+	0.0151402i
$271$	6.44960	+	16.1873i	0.391786	+	0.983308i	0.984102	+	0.177602i	$0.0568341\pi$
$271$	6.44960	+	16.1873i	0.391786	+	0.983308i	−0.592317	+	0.805705i	$0.701787\pi$
$272$	−4.42623	+	2.04779i	−0.268379	+	0.124166i
$273$	2.28290	−	1.37357i	0.138167	−	0.0831325i
$274$	−4.22849	−	4.00543i	−0.255452	−	0.241977i
$275$	5.40199	−	4.10649i	0.325752	−	0.247631i
$276$	−0.183464	+	3.38379i	−0.0110432	+	0.203680i
$277$	−9.03613	−	4.18056i	−0.542928	−	0.251185i	0.129202	−	0.991618i	$-0.458758\pi$
$277$	−9.03613	−	4.18056i	−0.542928	−	0.251185i	−0.672130	+	0.740433i	$0.734620\pi$
$278$	−12.6643	+	1.37733i	−0.759555	+	0.0826066i
$279$	−0.212419	+	0.0715722i	−0.0127172	+	0.00428491i
$280$	0.0339496	−	0.207083i	0.00202888	−	0.0123756i
$281$	−16.7807	+	15.8955i	−1.00105	+	0.948246i	−0.998660	−	0.0517516i	$-0.983520\pi$
$281$	−16.7807	+	15.8955i	−1.00105	+	0.948246i	−0.00239070	+	0.999997i	$0.500761\pi$
$282$	−0.990076	+	3.56593i	−0.0589582	+	0.212348i
$283$	12.9362	−	24.4003i	0.768979	−	1.45045i	−0.120133	−	0.992758i	$-0.538332\pi$
$283$	12.9362	−	24.4003i	0.768979	−	1.45045i	0.889112	−	0.457690i	$-0.151323\pi$
$284$	6.43340	+	2.16767i	0.381752	+	0.128627i
$285$	−1.08594	−	0.239033i	−0.0643255	−	0.0141591i
$286$	1.41100	+	5.08197i	0.0834343	+	0.300503i
$287$	−3.63797	−	2.18889i	−0.214743	−	0.129206i
$288$	0.994138	+	0.108119i	0.0585801	+	0.00637097i
$289$	6.62631	−	1.45856i	0.389783	−	0.0857977i
$290$	−0.556448	−	1.04957i	−0.0326757	−	0.0616330i
$291$	−1.71308	−	10.4493i	−0.100423	−	0.612551i
$292$	−3.61381	−	2.74715i	−0.211482	−	0.160765i
$293$	2.01659	−	2.37411i	0.117810	−	0.138697i	−0.700095	−	0.714049i	$-0.746859\pi$
$293$	2.01659	−	2.37411i	0.117810	−	0.138697i	0.817906	+	0.575352i	$0.195135\pi$
$294$	−6.51256			−0.379820
$295$	−0.0324676	−	2.30849i	−0.00189034	−	0.134406i
$296$	4.41618			0.256685
$297$	0.894752	−	1.05338i	0.0519188	−	0.0611235i
$298$	−9.34666	−	7.10514i	−0.541437	−	0.411590i
$299$	−2.09213	−	12.7615i	−0.120991	−	0.738014i
$300$	2.29973	+	4.33774i	0.132775	+	0.250440i
$301$	0.987297	−	0.217321i	0.0569069	−	0.0125261i
$302$	−18.6495	−	2.02825i	−1.07316	−	0.116713i
$303$	8.02868	+	4.83069i	0.461235	+	0.277516i
$304$	0.989702	+	3.56459i	0.0567633	+	0.204443i
$305$	−0.472804	−	0.104072i	−0.0270727	−	0.00595914i
$306$	−4.62169	−	1.55723i	−0.264204	−	0.0890208i
$307$	−2.45034	+	4.62183i	−0.139848	+	0.263782i	−0.943536	−	0.331269i	$-0.892523\pi$
$307$	−2.45034	+	4.62183i	−0.139848	+	0.263782i	0.803688	+	0.595051i	$0.202868\pi$
$308$	−0.258148	+	0.929764i	−0.0147093	+	0.0529782i
$309$	−11.7196	+	11.1014i	−0.666705	+	0.631536i
$310$	0.0108998	−	0.0664858i	0.000619067	−	0.00377614i
$311$	1.74740	−	0.588768i	0.0990860	−	0.0333860i	−0.269322	−	0.963050i	$-0.586800\pi$
$311$	1.74740	−	0.588768i	0.0990860	−	0.0333860i	0.368408	+	0.929664i	$0.379903\pi$
$312$	−3.79372	+	0.412592i	−0.214777	+	0.0233584i
$313$	−7.39199	−	3.41990i	−0.417820	−	0.193304i	0.199704	−	0.979856i	$-0.436002\pi$
$313$	−7.39199	−	3.41990i	−0.417820	−	0.193304i	−0.617524	+	0.786552i	$0.711864\pi$
$314$	−0.533355	+	9.83716i	−0.0300990	+	0.555143i
$315$	0.167058	−	0.126995i	0.00941268	−	0.00715533i
$316$	7.85694	+	7.44249i	0.441987	+	0.418673i
$317$	−0.244683	+	0.147221i	−0.0137428	+	0.00826875i	−0.522409	−	0.852695i	$-0.674966\pi$
$317$	−0.244683	+	0.147221i	−0.0137428	+	0.00826875i	0.508666	+	0.860964i	$0.330139\pi$
$318$	3.04326	−	1.40796i	0.170658	−	0.0789546i
$319$	2.02189	+	5.07456i	0.113204	+	0.284121i
$320$	−0.168676	+	0.248778i	−0.00942926	+	0.0139071i
$321$	5.89106	+	8.68866i	0.328807	+	0.484954i
$322$	0.875718	−	2.19789i	0.0488018	−	0.122483i
$323$	−0.976777	−	18.0156i	−0.0543493	−	1.00241i
$324$	0.647386	+	0.762162i	0.0359659	+	0.0423423i
$325$	−12.1292	−	14.2796i	−0.672809	−	0.792092i
$326$	0.188706	+	3.48048i	0.0104515	+	0.192766i
$327$	1.56707	−	3.93306i	0.0866594	−	0.217499i
$328$	3.41271	+	5.03336i	0.188435	+	0.277921i
$329$	1.44999	−	2.13858i	0.0799407	−	0.117904i
$330$	0.153762	+	0.385912i	0.00846430	+	0.0212438i
$331$	−25.8177	+	11.9445i	−1.41907	+	0.656531i	−0.971352	−	0.237644i	$-0.923625\pi$
$331$	−25.8177	+	11.9445i	−1.41907	+	0.656531i	−0.447717	+	0.894176i	$0.647763\pi$
$332$	−6.38630	+	3.84251i	−0.350493	+	0.210885i
$333$	3.20613	+	3.03700i	0.175695	+	0.166427i
$334$	4.38219	−	3.33125i	0.239783	−	0.182278i
$335$	0.0265779	−	0.490200i	0.00145210	−	0.0267825i
$336$	−0.633639	−	0.293153i	−0.0345679	−	0.0159928i
$337$	−27.0069	+	2.93718i	−1.47116	+	0.159998i	−0.808311	−	0.588755i	$-0.799618\pi$
$337$	−27.0069	+	2.93718i	−1.47116	+	0.159998i	−0.662848	+	0.748754i	$0.730653\pi$
$338$	1.48076	−	0.498926i	0.0805428	−	0.0271380i
$339$	2.48149	−	15.1364i	0.134776	−	0.822098i
$340$	1.06422	−	1.00808i	0.0577152	−	0.0546708i
$341$	−0.0828804	+	0.298508i	−0.00448823	+	0.0161651i
$342$	−1.73284	+	3.26849i	−0.0937015	+	0.176740i
$343$	8.94019	+	3.01230i	0.482725	+	0.162649i
$344$	−1.41413	−	0.311273i	−0.0762446	−	0.0167827i
$345$	−0.272493	−	0.981431i	−0.0146705	−	0.0528385i
$346$	4.55081	+	2.73813i	0.244653	+	0.147203i
$347$	3.17961	+	0.345804i	0.170691	+	0.0185637i	0.193065	−	0.981186i	$-0.438157\pi$
$347$	3.17961	+	0.345804i	0.170691	+	0.0185637i	−0.0223746	+	0.999750i	$0.507123\pi$
$348$	−3.85994	+	0.849637i	−0.206914	+	0.0455453i
$349$	4.42520	+	8.34681i	0.236875	+	0.446794i	0.973240	−	0.229790i	$-0.0738041\pi$
$349$	4.42520	+	8.34681i	0.236875	+	0.446794i	−0.736365	+	0.676585i	$0.763459\pi$
$350$	−0.554550	−	3.38261i	−0.0296420	−	0.180808i
$351$	−3.03796	−	2.30940i	−0.162155	−	0.123267i
$352$	0.894752	−	1.05338i	0.0476904	−	0.0561455i
$353$	−19.3797			−1.03148			−0.515740	−	0.856745i	$-0.672483\pi$
$353$	−19.3797			−1.03148			−0.515740	+	0.856745i	$0.672483\pi$
$354$	−7.42933	−	1.95064i	−0.394865	−	0.103675i
$355$	−2.04050			−0.108298
$356$	−2.12020	+	2.49609i	−0.112370	+	0.132293i
$357$	2.71066	+	2.06059i	0.143463	+	0.109058i
$358$	2.31927	+	14.1469i	0.122577	+	0.747688i
$359$	3.05653	+	5.76523i	0.161318	+	0.304277i	0.950973	−	0.309273i	$-0.100086\pi$
$359$	3.05653	+	5.76523i	0.161318	+	0.304277i	−0.789656	+	0.613550i	$0.789741\pi$
$360$	−0.293542	+	0.0646136i	−0.0154710	+	0.00340543i
$361$	5.28307	+	0.574568i	0.278056	+	0.0302404i
$362$	−3.99686	−	2.40483i	−0.210070	−	0.126395i
$363$	2.43178	+	8.75848i	0.127635	+	0.459701i
$364$	2.60198	+	0.572739i	0.136381	+	0.0300197i
$365$	1.29299	+	0.435660i	0.0676784	+	0.0228035i
$366$	−0.754457	+	1.42306i	−0.0394361	+	0.0743844i
$367$	−8.28291	+	29.8323i	−0.432364	+	1.55723i	0.351430	+	0.936214i	$0.385696\pi$
$367$	−8.28291	+	29.8323i	−0.432364	+	1.55723i	−0.783794	+	0.621021i	$0.786718\pi$
$368$	−2.46022	+	2.33045i	−0.128248	+	0.121483i
$369$	−0.983833	+	6.00112i	−0.0512163	+	0.312406i
$370$	−1.25789	+	0.423831i	−0.0653944	+	0.0220339i
$371$	−2.32736	+	0.253115i	−0.120830	+	0.0131411i
$372$	−0.203435	−	0.0941191i	−0.0105476	−	0.00487985i
$373$	1.35663	−	25.0216i	0.0702437	−	1.29557i	−0.724776	−	0.688985i	$-0.758057\pi$
$373$	1.35663	−	25.0216i	0.0702437	−	1.29557i	0.795019	−	0.606584i	$-0.207461\pi$
$374$	−5.36604	+	4.07916i	−0.277471	+	0.210928i
$375$	−2.16241	−	2.04834i	−0.111666	−	0.105776i
$376$	−3.17108	+	1.90798i	−0.163536	+	0.0983963i
$377$	13.6885	−	6.33298i	0.704994	−	0.326165i
$378$	−0.258418	−	0.648581i	−0.0132916	−	0.0333594i
$379$	5.21568	−	7.69255i	0.267911	−	0.395140i	−0.669808	−	0.742535i	$-0.733623\pi$
$379$	5.21568	−	7.69255i	0.267911	−	0.395140i	0.937719	+	0.347395i	$0.112934\pi$
$380$	−0.624004	−	0.920337i	−0.0320107	−	0.0472123i
$381$	2.79506	−	7.01507i	0.143195	−	0.359393i
$382$	−0.770148	−	14.2046i	−0.0394042	−	0.726768i
$383$	13.8164	+	16.2659i	0.705985	+	0.831149i	0.991889	−	0.127109i	$-0.0405698\pi$
$383$	13.8164	+	16.2659i	0.705985	+	0.831149i	−0.285904	+	0.958258i	$0.592294\pi$
$384$	0.647386	+	0.762162i	0.0330368	+	0.0388939i
$385$	−0.0157019	−	0.289605i	−0.000800244	−	0.0147596i
$386$	−7.31410	+	18.3570i	−0.372278	+	0.934347i
$387$	−0.812588	−	1.19848i	−0.0413062	−	0.0609220i
$388$	5.94231	−	8.76426i	0.301675	−	0.444938i
$389$	10.5518	+	26.4829i	0.534996	+	1.34274i	0.909574	+	0.415542i	$0.136408\pi$
$389$	10.5518	+	26.4829i	0.534996	+	1.34274i	−0.374578	+	0.927195i	$0.622213\pi$
$390$	1.04099	−	0.481613i	0.0527126	−	0.0243874i
$391$	14.1612	−	8.52051i	0.716163	−	0.430901i
$392$	−4.72809	−	4.47869i	−0.238805	−	0.226208i
$393$	3.17557	−	2.41400i	0.160186	−	0.121770i
$394$	−0.0986695	+	1.81985i	−0.00497090	+	0.0916828i
$395$	−2.95221	−	1.36584i	−0.148542	−	0.0687227i
$396$	1.37400	−	0.149431i	0.0690459	−	0.00750920i
$397$	−35.5315	+	11.9720i	−1.78327	+	0.600855i	−0.999789	−	0.0205549i	$-0.993457\pi$
$397$	−35.5315	+	11.9720i	−1.78327	+	0.600855i	−0.783486	+	0.621410i	$0.786560\pi$
$398$	0.967771	−	5.90314i	0.0485100	−	0.295898i
$399$	1.87512	−	1.77620i	0.0938732	−	0.0889214i
$400$	−1.31347	+	4.73070i	−0.0656736	+	0.236535i
$401$	−11.3475	+	21.4036i	−0.566666	+	1.06885i	0.420219	+	0.907423i	$0.361953\pi$
$401$	−11.3475	+	21.4036i	−0.566666	+	1.06885i	−0.986885	+	0.161423i	$0.948392\pi$
$402$	−1.54780	−	0.521515i	−0.0771973	−	0.0260108i
$403$	0.835387	+	0.183883i	0.0416136	+	0.00915985i
$404$	2.50672	+	9.02838i	0.124714	+	0.449179i
$405$	−0.257545	−	0.154960i	−0.0127975	−	0.00770001i
$406$	2.74322	+	0.298343i	0.136144	+	0.0148065i
$407$	5.96090	−	1.31209i	0.295471	−	0.0650380i
$408$	−2.28442	−	4.30887i	−0.113096	−	0.213321i
$409$	−2.09359	−	12.7703i	−0.103521	−	0.631453i	−0.986717	−	0.162448i	$-0.948061\pi$
$409$	−2.09359	−	12.7703i	−0.103521	−	0.631453i	0.883196	−	0.469005i	$-0.155387\pi$
$410$	−1.45512	−	1.10616i	−0.0718635	−	0.0546292i
$411$	3.77063	−	4.43913i	0.185992	−	0.218966i
$412$	−16.1428			−0.795299
$413$	4.48055	+	2.94677i	0.220474	+	0.145001i
$414$	−3.38876			−0.166548
$415$	1.45027	−	1.70739i	0.0711910	−	0.0838125i
$416$	−3.03796	−	2.30940i	−0.148948	−	0.113228i
$417$	−2.06094	−	12.5712i	−0.100925	−	0.615613i
$418$	2.39496	+	4.51738i	0.117141	+	0.220952i
$419$	16.5220	−	3.63677i	0.807154	−	0.177668i	0.207820	−	0.978167i	$-0.433363\pi$
$419$	16.5220	−	3.63677i	0.807154	−	0.177668i	0.599334	+	0.800499i	$0.295432\pi$
$420$	0.208618	+	0.0226885i	0.0101795	+	0.00110709i
$421$	−7.37008	−	4.43443i	−0.359196	−	0.216121i	0.324504	−	0.945884i	$-0.394803\pi$
$421$	−7.37008	−	4.43443i	−0.359196	−	0.216121i	−0.683700	+	0.729764i	$0.739630\pi$
$422$	5.64695	+	20.3385i	0.274889	+	0.990062i
$423$	−3.61430	−	0.795568i	−0.175733	−	0.0386819i
$424$	3.17765	+	1.07067i	0.154320	+	0.0519966i
$425$	11.2157	−	21.1551i	0.544042	−	1.02617i
$426$	−1.81619	+	6.54132i	−0.0879947	+	0.316928i
$427$	0.816401	−	0.773336i	0.0395084	−	0.0374243i
$428$	−1.69830	+	10.3592i	−0.0820907	+	0.500731i
$429$	−4.99813	+	1.68406i	−0.241312	+	0.0813074i
$430$	0.432667	−	0.0470554i	0.0208651	−	0.00226921i
$431$	13.3927	+	6.19614i	0.645105	+	0.298457i	0.715029	−	0.699095i	$-0.246414\pi$
$431$	13.3927	+	6.19614i	0.645105	+	0.298457i	−0.0699237	+	0.997552i	$0.522276\pi$
$432$	−0.0541389	+	0.998533i	−0.00260476	+	0.0480420i
$433$	18.9795	−	14.4278i	0.912096	−	0.693357i	−0.0399863	−	0.999200i	$-0.512731\pi$
$433$	18.9795	−	14.4278i	0.912096	−	0.693357i	0.952082	+	0.305843i	$0.0989383\pi$
$434$	0.113615	+	0.107622i	0.00545371	+	0.00516603i
$435$	1.01791	−	0.612454i	0.0488049	−	0.0293649i
$436$	3.84245	−	1.77771i	0.184020	−	0.0851367i
$437$	−4.64023	−	11.6461i	−0.221972	−	0.557108i
$438$	2.54747	−	3.75724i	0.121723	−	0.179528i
$439$	22.0091	+	32.4611i	1.05044	+	1.54928i	0.816768	+	0.576967i	$0.195764\pi$
$439$	22.0091	+	32.4611i	1.05044	+	1.54928i	0.233672	+	0.972316i	$0.424926\pi$
$440$	−0.153762	+	0.385912i	−0.00733030	+	0.0183977i
$441$	−0.352583	−	6.50301i	−0.0167897	−	0.309667i
$442$	12.0485	+	14.1846i	0.573089	+	0.674693i
$443$	−13.8131	−	16.2621i	−0.656282	−	0.772635i	0.328859	−	0.944379i	$-0.393336\pi$
$443$	−13.8131	−	16.2621i	−0.656282	−	0.772635i	−0.985142	+	0.171744i	$0.945060\pi$
$444$	0.239087	+	4.40970i	0.0113466	+	0.209275i
$445$	0.364353	−	0.914457i	0.0172720	−	0.0433494i
$446$	−1.74960	−	2.58047i	−0.0828460	−	0.122189i
$447$	6.58871	−	9.71761i	0.311635	−	0.459627i
$448$	−0.258418	−	0.648581i	−0.0122091	−	0.0306426i
$449$	11.5998	−	5.36663i	0.547428	−	0.253267i	−0.126625	−	0.991951i	$-0.540414\pi$
$449$	11.5998	−	5.36663i	0.547428	−	0.253267i	0.674052	+	0.738684i	$0.264552\pi$
$450$	−4.20688	+	2.53119i	−0.198314	+	0.119322i
$451$	6.10189	+	5.78001i	0.287327	+	0.272170i
$452$	12.2109	−	9.28246i	0.574351	−	0.436610i
$453$	1.01561	−	18.7319i	0.0477177	−	0.880102i
$454$	−1.39206	−	0.644038i	−0.0653328	−	0.0302262i
$455$	−0.796104	+	0.0865816i	−0.0373219	+	0.00405901i
$456$	−3.50578	+	1.18123i	−0.164173	+	0.0553163i
$457$	2.66782	−	16.2730i	0.124796	−	0.761219i	−0.848076	−	0.529874i	$-0.822239\pi$
$457$	2.66782	−	16.2730i	0.124796	−	0.761219i	0.972872	−	0.231345i	$-0.0743126\pi$
$458$	12.0008	−	11.3678i	0.560760	−	0.531180i
$459$	1.30473	−	4.69921i	0.0608996	−	0.219341i
$460$	0.477101	−	0.899908i	0.0222450	−	0.0419584i
$461$	15.8671	+	5.34626i	0.739006	+	0.249000i	0.663532	−	0.748148i	$-0.269056\pi$
$461$	15.8671	+	5.34626i	0.739006	+	0.249000i	0.0754740	+	0.997148i	$0.475953\pi$
$462$	−0.942376	−	0.207433i	−0.0438433	−	0.00965064i
$463$	4.17617	+	15.0412i	0.194083	+	0.699023i	0.994967	+	0.100204i	$0.0319495\pi$
$463$	4.17617	+	15.0412i	0.194083	+	0.699023i	−0.800884	+	0.598820i	$0.795637\pi$
$464$	−3.38659	−	2.03765i	−0.157219	−	0.0945953i
$465$	0.0669784	+	0.00728434i	0.00310605	+	0.000337803i
$466$	18.1649	−	3.99841i	0.841475	−	0.185223i
$467$	4.97240	+	9.37895i	0.230095	+	0.434006i	0.971496	−	0.237057i	$-0.0761828\pi$
$467$	4.97240	+	9.37895i	0.230095	+	0.434006i	−0.741400	+	0.671063i	$0.765838\pi$
$468$	−0.617375	−	3.76582i	−0.0285382	−	0.174075i
$469$	0.907797	+	0.690090i	0.0419182	+	0.0318654i
$470$	0.720124	−	0.847796i	0.0332168	−	0.0391059i
$471$	−9.85161			−0.453938
$472$	−4.05221	−	6.52530i	−0.186518	−	0.300351i
$473$	−2.00125			−0.0920176
$474$	−7.00620	+	8.24834i	−0.321806	+	0.378859i
$475$	−14.4594	−	10.9917i	−0.663442	−	0.504336i
$476$	0.550859	+	3.36009i	0.0252486	+	0.154010i
$477$	1.57066	+	2.96257i	0.0719154	+	0.135647i
$478$	26.0394	−	5.73171i	1.19102	−	0.262162i
$479$	4.30239	+	0.467913i	0.196581	+	0.0213795i	0.205880	−	0.978577i	$-0.433994\pi$
$479$	4.30239	+	0.467913i	0.196581	+	0.0213795i	−0.00929874	+	0.999957i	$0.502960\pi$
$480$	−0.257545	−	0.154960i	−0.0117553	−	0.00707291i
$481$	−4.50853	−	16.2383i	−0.205571	−	0.740402i
$482$	2.94042	+	0.647236i	0.133933	+	0.0294808i
$483$	2.24207	+	0.755442i	0.102018	+	0.0343738i
$484$	−4.25774	+	8.03095i	−0.193534	+	0.365043i
$485$	−0.851457	+	3.06667i	−0.0386627	+	0.139250i
$486$	−0.725995	+	0.687699i	−0.0329318	+	0.0311947i
$487$	−3.32077	+	20.2558i	−0.150479	+	0.917879i	0.798375	+	0.602161i	$0.205694\pi$
$487$	−3.32077	+	20.2558i	−0.150479	+	0.917879i	−0.948853	+	0.315718i	$0.897755\pi$
$488$	−1.52637	+	0.514293i	−0.0690954	+	0.0232810i
$489$	−3.46516	+	0.376859i	−0.156700	+	0.0170422i
$490$	1.77656	+	0.821924i	0.0802568	+	0.0371307i
$491$	0.780394	−	14.3935i	0.0352187	−	0.649571i	−0.926628	−	0.375980i	$-0.877306\pi$
$491$	0.780394	−	14.3935i	0.0352187	−	0.649571i	0.961846	−	0.273590i	$-0.0882112\pi$
$492$	−4.84122	+	3.68020i	−0.218259	+	0.165916i
$493$	13.9939	+	13.2558i	0.630255	+	0.597009i
$494$	12.0966	−	7.27826i	0.544250	−	0.327464i
$495$	−0.377022	+	0.174429i	−0.0169459	+	0.00784000i
$496$	−0.0829673	−	0.208232i	−0.00372534	−	0.00934991i
$497$	2.65986	−	3.92300i	0.119311	−	0.175970i
$498$	−4.18262	−	6.16890i	−0.187428	−	0.276435i
$499$	−10.4460	+	26.2174i	−0.467625	+	1.17365i	0.486350	+	0.873764i	$0.338328\pi$
$499$	−10.4460	+	26.2174i	−0.467625	+	1.17365i	−0.953975	+	0.299886i	$0.903051\pi$
$500$	−0.161255	−	2.97417i	−0.00721154	−	0.133009i
$501$	3.56361	+	4.19541i	0.159211	+	0.187437i
$502$	0.315942	+	0.371956i	0.0141012	+	0.0166012i
$503$	−0.977448	−	18.0280i	−0.0435823	−	0.803828i	−0.935867	−	0.352354i	$-0.885381\pi$
$503$	−0.977448	−	18.0280i	−0.0435823	−	0.803828i	0.892284	−	0.451474i	$-0.149101\pi$
$504$	0.258418	−	0.648581i	0.0115109	−	0.0288901i
$505$	−1.58048	−	2.33103i	−0.0703303	−	0.103729i
$506$	−2.62837	+	3.87656i	−0.116846	+	0.172334i
$507$	0.578361	+	1.45158i	0.0256859	+	0.0644668i
$508$	6.85346	−	3.17075i	0.304073	−	0.140679i
$509$	25.3547	−	15.2554i	1.12383	−	0.676185i	0.172698	−	0.984975i	$-0.444751\pi$
$509$	25.3547	−	15.2554i	1.12383	−	0.676185i	0.951130	+	0.308789i	$0.0999238\pi$
$510$	1.06422	+	1.00808i	0.0471243	+	0.0446385i
$511$	−2.52305	+	1.91797i	−0.111613	+	0.0848460i
$512$	−0.0541389	+	0.998533i	−0.00239262	+	0.0441294i
$513$	−3.35751	−	1.55335i	−0.148238	−	0.0685821i
$514$	−30.2044	+	3.28492i	−1.33226	+	0.144892i
$515$	4.59805	−	1.54926i	0.202614	−	0.0682686i
$516$	0.234257	−	1.42891i	0.0103126	−	0.0629040i
$517$	−3.71340	+	3.51752i	−0.163315	+	0.154700i
$518$	0.824852	−	2.97085i	0.0362419	−	0.130532i
$519$	−2.48774	+	4.69238i	−0.109200	+	0.205972i
$520$	1.08696	+	0.366239i	0.0476663	+	0.0160607i
$521$	−6.59247	−	1.45111i	−0.288821	−	0.0635744i	0.0681966	−	0.997672i	$-0.478276\pi$
$521$	−6.59247	−	1.45111i	−0.288821	−	0.0635744i	−0.357018	+	0.934097i	$0.616207\pi$
$522$	−1.05736	−	3.80828i	−0.0462796	−	0.166684i
$523$	−24.8169	−	14.9318i	−1.08517	−	0.652923i	−0.143561	−	0.989641i	$-0.545855\pi$
$523$	−24.8169	−	14.9318i	−1.08517	−	0.652923i	−0.941605	+	0.336718i	$0.890683\pi$
$524$	3.96555	+	0.431280i	0.173236	+	0.0188406i
$525$	3.34762	−	0.736868i	0.146102	−	0.0321595i
$526$	−9.86698	−	18.6111i	−0.430221	−	0.811482i
$527$	0.176858	+	1.07879i	0.00770405	+	0.0469926i
$528$	1.10028	+	0.836410i	0.0478835	+	0.0364001i
$529$	−7.45550	+	8.77730i	−0.324152	+	0.381622i
$530$	−1.00786			−0.0437788
$531$	1.54556	−	7.52404i	0.0670716	−	0.326516i
$532$	2.58282			0.111979
$533$	15.0236	−	17.6871i	0.650744	−	0.766115i
$534$	−2.60722	−	1.98195i	−0.112825	−	0.0857676i
$535$	−0.510459	−	3.11366i	−0.0220691	−	0.134615i
$536$	−0.765051	−	1.44304i	−0.0330452	−	0.0623298i
$537$	−14.0006	+	3.08177i	−0.604171	+	0.132988i
$538$	15.0398	+	1.63568i	0.648412	+	0.0705191i
$539$	−7.71257	−	4.64050i	−0.332204	−	0.199881i
$540$	−0.0804109	−	0.289614i	−0.00346033	−	0.0124630i
$541$	−37.3663	−	8.22495i	−1.60650	−	0.353618i	−0.680978	−	0.732304i	$-0.738445\pi$
$541$	−37.3663	−	8.22495i	−1.60650	−	0.353618i	−0.925525	+	0.378686i	$0.876376\pi$
$542$	−16.5127	−	5.56378i	−0.709282	−	0.238985i
$543$	2.18492	−	4.12119i	0.0937638	−	0.176857i
$544$	1.30473	−	4.69921i	0.0559399	−	0.201477i
$545$	−0.923857	+	0.875123i	−0.0395737	+	0.0374862i
$546$	−0.431031	+	2.62917i	−0.0184464	+	0.112518i
$547$	20.8992	−	7.04176i	0.893585	−	0.301084i	0.165207	−	0.986259i	$-0.447171\pi$
$547$	20.8992	−	7.04176i	0.893585	−	0.301084i	0.728378	+	0.685175i	$0.240274\pi$
$548$	5.79025	−	0.629728i	0.247347	−	0.0269006i
$549$	−1.46182	−	0.676308i	−0.0623888	−	0.0288641i
$550$	−0.367367	+	6.77568i	−0.0156646	+	0.288916i
$551$	11.6400	−	8.84850i	0.495881	−	0.376959i
$552$	−2.46022	−	2.33045i	−0.104714	−	0.0991904i
$553$	6.47422	−	3.89541i	0.275312	−	0.165650i
$554$	9.03613	−	4.18056i	0.383908	−	0.177615i
$555$	−0.491310	−	1.23310i	−0.0208550	−	0.0523420i
$556$	7.14896	−	10.5439i	0.303183	−	0.447162i
$557$	14.7240	+	21.7162i	0.623874	+	0.920145i	0.999979	−	0.00643177i	$-0.00204731\pi$
$557$	14.7240	+	21.7162i	0.623874	+	0.920145i	−0.376105	+	0.926577i	$0.622737\pi$
$558$	0.0829673	−	0.208232i	0.00351229	−	0.00881518i
$559$	0.299151	+	5.51752i	0.0126528	+	0.233366i
$560$	0.135853	+	0.159938i	0.00574082	+	0.00675862i
$561$	−4.36369	−	5.13733i	−0.184235	−	0.216898i
$562$	−1.25137	−	23.0801i	−0.0527857	−	0.973576i
$563$	6.34267	−	15.9189i	0.267312	−	0.670901i	−0.732641	−	0.680615i	$-0.761713\pi$
$563$	6.34267	−	15.9189i	0.267312	−	0.670901i	0.999953	+	0.00971362i	$0.00309199\pi$
$564$	−2.07686	−	3.06313i	−0.0874514	−	0.128981i
$565$	−2.58723	+	3.81588i	−0.108846	+	0.160535i
$566$	10.2223	+	25.6559i	0.429674	+	1.07840i
$567$	0.633639	−	0.293153i	0.0266104	−	0.0123113i
$568$	−5.81701	+	3.49998i	−0.244076	+	0.146856i
$569$	22.5765	+	21.3856i	0.946455	+	0.896530i	0.994753	−	0.102303i	$-0.0326212\pi$
$569$	22.5765	+	21.3856i	0.946455	+	0.896530i	−0.0482984	+	0.998833i	$0.515380\pi$
$570$	0.885204	−	0.672915i	0.0370771	−	0.0281853i
$571$	0.466502	−	8.60412i	0.0195225	−	0.360071i	−0.972408	−	0.233287i	$-0.925052\pi$
$571$	0.466502	−	8.60412i	0.0195225	−	0.360071i	0.991930	−	0.126784i	$-0.0404655\pi$
$572$	−4.78675	−	2.21459i	−0.200144	−	0.0925965i
$573$	14.1420	−	1.53804i	0.590792	−	0.0642525i
$574$	4.02346	−	1.35566i	0.167936	−	0.0565843i
$575$	2.69167	−	16.4185i	0.112250	−	0.684698i
$576$	−0.725995	+	0.687699i	−0.0302498	+	0.0286541i
$577$	−2.99344	+	10.7814i	−0.124619	+	0.448836i	−0.999361	−	0.0357533i	$-0.988617\pi$
$577$	−2.99344	+	10.7814i	−0.124619	+	0.448836i	0.874742	+	0.484589i	$0.161031\pi$
$578$	−3.17812	+	5.99458i	−0.132192	+	0.249341i
$579$	−18.7261	−	6.30954i	−0.778228	−	0.262216i
$580$	1.16018	+	0.255375i	0.0481739	+	0.0106039i
$581$	1.39210	+	5.01388i	0.0577540	+	0.208011i
$582$	9.07311	+	5.45911i	0.376093	+	0.226287i
$583$	4.60726	+	0.501069i	0.190813	+	0.0207522i
$584$	4.43331	−	0.975845i	0.183452	−	0.0403807i
$585$	0.537265	+	1.01339i	0.0222132	+	0.0418985i
$586$	0.503945	+	3.07393i	0.0208178	+	0.126983i
$587$	32.7931	+	24.9287i	1.35352	+	1.02892i	0.995456	+	0.0952191i	$0.0303552\pi$
$587$	32.7931	+	24.9287i	1.35352	+	1.02892i	0.358061	+	0.933698i	$0.383438\pi$
$588$	4.21614	−	4.96363i	0.173871	−	0.204697i
$589$	0.829236			0.0341681
$590$	1.78046	+	1.46974i	0.0733005	+	0.0605082i
$591$	−1.82252			−0.0749686
$592$	−2.85897	+	3.36585i	−0.117503	+	0.138335i
$593$	−27.0905	−	20.5937i	−1.11247	−	0.845681i	−0.123292	−	0.992370i	$-0.539345\pi$
$593$	−27.0905	−	20.5937i	−1.11247	−	0.845681i	−0.989183	+	0.146689i	$0.953138\pi$
$594$	0.223599	+	1.36389i	0.00917436	+	0.0559611i
$595$	−0.479380	−	0.904207i	−0.0196527	−	0.0370689i
$596$	11.4662	−	2.52389i	0.469673	−	0.103383i
$597$	5.94688	+	0.646762i	0.243390	+	0.0264702i
$598$	11.0807	+	6.66705i	0.453124	+	0.272636i
$599$	10.5541	+	38.0123i	0.431227	+	1.55314i	0.786024	+	0.618196i	$0.212136\pi$
$599$	10.5541	+	38.0123i	0.431227	+	1.55314i	−0.354797	+	0.934943i	$0.615450\pi$
$600$	−4.79487	−	1.05543i	−0.195750	−	0.0430878i
$601$	−17.6019	−	5.93076i	−0.717995	−	0.241921i	−0.0634947	−	0.997982i	$-0.520225\pi$
$601$	−17.6019	−	5.93076i	−0.717995	−	0.241921i	−0.654501	+	0.756061i	$0.727121\pi$
$602$	−0.473529	+	0.893171i	−0.0192996	+	0.0364029i
$603$	0.436954	−	1.57376i	0.0177941	−	0.0640887i
$604$	13.6193	−	12.9008i	0.554160	−	0.524928i
$605$	0.442008	−	2.69613i	0.0179702	−	0.109613i
$606$	−8.87943	+	2.99183i	−0.360702	+	0.121535i
$607$	8.95047	−	0.973422i	0.363288	−	0.0395100i	0.0753453	−	0.997158i	$-0.475994\pi$
$607$	8.95047	−	0.973422i	0.363288	−	0.0395100i	0.287943	+	0.957648i	$0.407029\pi$
$608$	−3.35751	−	1.55335i	−0.136165	−	0.0629967i
$609$	−0.149391	+	2.75535i	−0.00605362	+	0.111652i
$610$	0.385406	−	0.292978i	0.0156046	−	0.0118623i
$611$	10.2530	+	9.71217i	0.414793	+	0.392912i
$612$	4.17888	−	2.51435i	0.168921	−	0.101636i
$613$	−30.3874	+	14.0587i	−1.22734	+	0.567826i	−0.923023	−	0.384746i	$-0.874289\pi$
$613$	−30.3874	+	14.0587i	−1.22734	+	0.567826i	−0.304314	+	0.952572i	$0.598427\pi$
$614$	−1.93627	−	4.85967i	−0.0781414	−	0.196120i
$615$	1.02576	−	1.51288i	0.0413625	−	0.0610051i
$616$	−0.541510	−	0.798667i	−0.0218180	−	0.0321792i
$617$	−18.0012	+	45.1795i	−0.724699	+	1.81886i	−0.172780	+	0.984960i	$0.555275\pi$
$617$	−18.0012	+	45.1795i	−0.724699	+	1.81886i	−0.551919	+	0.833898i	$0.686104\pi$
$618$	−0.873954	−	16.1191i	−0.0351556	−	0.648406i
$619$	23.9305	+	28.1732i	0.961849	+	1.13238i	0.991142	+	0.132806i	$0.0423986\pi$
$619$	23.9305	+	28.1732i	0.961849	+	1.13238i	−0.0292928	+	0.999571i	$0.509326\pi$
$620$	0.0436166	+	0.0513494i	0.00175168	+	0.00206224i
$621$	−0.183464	−	3.38379i	−0.00736215	−	0.135787i
$622$	−0.682507	+	1.71296i	−0.0273660	+	0.0686836i
$623$	1.28316	+	1.89252i	0.0514087	+	0.0758221i
$624$	2.14154	−	3.15854i	0.0857303	−	0.126443i
$625$	−8.75489	−	21.9731i	−0.350196	−	0.878925i
$626$	7.39199	−	3.41990i	0.295443	−	0.136687i
$627$	−4.38109	+	2.63601i	−0.174964	+	0.105272i
$628$	−7.15222	−	6.77495i	−0.285405	−	0.270350i
$629$	17.1460	−	13.0340i	0.683654	−	0.519700i
$630$	−0.0113609	+	0.209540i	−0.000452630	+	0.00834828i
$631$	−1.25424	−	0.580271i	−0.0499303	−	0.0231002i	0.394765	−	0.918782i	$-0.370826\pi$
$631$	−1.25424	−	0.580271i	−0.0499303	−	0.0231002i	−0.444695	+	0.895682i	$0.646688\pi$
$632$	−10.7589	+	1.17010i	−0.427964	+	0.0465439i
$633$	−20.0029	+	6.73977i	−0.795045	+	0.267882i
$634$	0.0461983	−	0.281797i	0.00183477	−	0.0111916i
$635$	−1.64781	+	1.56088i	−0.0653912	+	0.0619418i
$636$	−0.897070	+	3.23096i	−0.0355711	+	0.128116i
$637$	−11.6411	+	21.9575i	−0.461239	+	0.869988i
$638$	−5.17658	−	1.74419i	−0.204943	−	0.0690533i
$639$	−6.63006	−	1.45939i	−0.262281	−	0.0577324i
$640$	−0.0804109	−	0.289614i	−0.00317852	−	0.0114480i
$641$	5.55968	+	3.34515i	0.219594	+	0.132125i	0.621101	−	0.783731i	$-0.286686\pi$
$641$	5.55968	+	3.34515i	0.219594	+	0.132125i	−0.401507	+	0.915856i	$0.631513\pi$
$642$	−10.4360	−	1.13498i	−0.411874	−	0.0447940i
$643$	36.3577	−	8.00294i	1.43381	−	0.315605i	0.570922	−	0.821004i	$-0.306586\pi$
$643$	36.3577	−	8.00294i	1.43381	−	0.315605i	0.862886	+	0.505399i	$0.168655\pi$
$644$	1.10822	+	2.09032i	0.0436699	+	0.0823701i
$645$	0.0704106	+	0.429485i	0.00277241	+	0.0169110i
$646$	14.3631	+	10.9186i	0.565110	+	0.429586i
$647$	0.700391	−	0.824564i	0.0275352	−	0.0324170i	−0.748222	−	0.663448i	$-0.769092\pi$
$647$	0.700391	−	0.824564i	0.0275352	−	0.0324170i	0.775757	+	0.631031i	$0.217368\pi$
$648$	−1.00000			−0.0392837
$649$	−7.40835	−	7.60381i	−0.290803	−	0.298476i
$650$	18.7357			0.734875
$651$	−0.101313	+	0.119275i	−0.00397078	+	0.00467476i
$652$	−2.77486	−	2.10939i	−0.108672	−	0.0826102i
$653$	3.12193	+	19.0429i	0.122170	+	0.745207i	0.974865	+	0.222797i	$0.0715187\pi$
$653$	3.12193	+	19.0429i	0.122170	+	0.745207i	−0.852694	+	0.522410i	$0.825033\pi$
$654$	1.98313	+	3.74057i	0.0775464	+	0.146268i
$655$	−1.17092	+	0.257740i	−0.0457517	+	0.0100707i
$656$	−6.04558	−	0.657496i	−0.236040	−	0.0256709i
$657$	3.88965	+	2.34032i	0.151750	+	0.0913047i
$658$	0.691239	+	2.48962i	0.0269473	+	0.0970554i
$659$	−11.8870	−	2.61653i	−0.463052	−	0.101925i	−0.0226836	−	0.999743i	$-0.507221\pi$
$659$	−11.8870	−	2.61653i	−0.463052	−	0.101925i	−0.440368	+	0.897817i	$0.645152\pi$
$660$	−0.393671	−	0.132643i	−0.0153236	−	0.00516313i
$661$	−15.7153	+	29.6422i	−0.611254	+	1.15295i	0.363903	+	0.931437i	$0.381444\pi$
$661$	−15.7153	+	29.6422i	−0.611254	+	1.15295i	−0.975158	+	0.221511i	$0.928901\pi$
$662$	7.61035	−	27.4100i	0.295785	−	1.06532i
$663$	−13.5115	+	12.7988i	−0.524743	+	0.497063i
$664$	1.20579	−	7.35498i	0.0467936	−	0.285428i
$665$	−0.735680	+	0.247879i	−0.0285284	+	0.00961235i
$666$	−4.39029	+	0.477473i	−0.170120	+	0.0185017i
$667$	12.1556	+	5.62380i	0.470669	+	0.217754i
$668$	−0.298014	+	5.49655i	−0.0115305	+	0.212668i
$669$	2.48196	−	1.88674i	0.0959582	−	0.0729455i
$670$	0.356406	+	0.337605i	0.0137691	+	0.0130428i
$671$	−1.90747	+	1.14769i	−0.0736370	+	0.0443059i
$672$	0.633639	−	0.293153i	0.0244432	−	0.0113086i
$673$	−3.76954	−	9.46084i	−0.145305	−	0.364689i	0.838253	−	0.545282i	$-0.183577\pi$
$673$	−3.76954	−	9.46084i	−0.145305	−	0.364689i	−0.983558	+	0.180594i	$0.942198\pi$
$674$	15.2453	−	22.4851i	0.587227	−	0.866095i
$675$	−2.75524	−	4.06367i	−0.106049	−	0.156411i
$676$	−0.578361	+	1.45158i	−0.0222447	+	0.0558299i
$677$	−1.03120	−	19.0194i	−0.0396322	−	0.730974i	−0.949057	−	0.315105i	$-0.897960\pi$
$677$	−1.03120	−	19.0194i	−0.0396322	−	0.730974i	0.909425	−	0.415869i	$-0.136522\pi$
$678$	9.92993	+	11.6904i	0.381357	+	0.448968i
$679$	−4.78598	−	5.63449i	−0.183669	−	0.216232i
$680$	0.0793607	+	1.46372i	0.00304334	+	0.0561312i
$681$	0.567728	−	1.42489i	0.0217554	−	0.0546019i
$682$	−0.173856	−	0.256419i	−0.00665729	−	0.00981877i
$683$	−11.9419	+	17.6129i	−0.456942	+	0.673939i	−0.984461	−	0.175604i	$-0.943812\pi$
$683$	−11.9419	+	17.6129i	−0.456942	+	0.673939i	0.527519	+	0.849543i	$0.323122\pi$
$684$	−1.36930	−	3.43668i	−0.0523565	−	0.131405i
$685$	−1.58883	+	0.735073i	−0.0607062	+	0.0280857i
$686$	−8.08362	+	4.86375i	−0.308634	+	0.185699i
$687$	12.0008	+	11.3678i	0.457859	+	0.433707i
$688$	1.15273	−	0.876280i	0.0439473	−	0.0334079i
$689$	0.692763	−	12.7773i	0.0263922	−	0.486775i
$690$	0.924418	+	0.427681i	0.0351920	+	0.0162816i
$691$	−6.84119	+	0.744024i	−0.260251	+	0.0283040i	−0.237314	−	0.971433i	$-0.576267\pi$
$691$	−6.84119	+	0.744024i	−0.260251	+	0.0283040i	−0.0229368	+	0.999737i	$0.507302\pi$
$692$	−5.03303	+	1.69583i	−0.191327	+	0.0644657i
$693$	0.156109	−	0.952224i	0.00593010	−	0.0361720i
$694$	−2.32200	+	2.19951i	−0.0881418	+	0.0834923i
$695$	−1.02435	+	3.68939i	−0.0388560	+	0.139946i
$696$	1.85131	−	3.49194i	0.0701738	−	0.132362i
$697$	28.1055	+	9.46985i	1.06457	+	0.358696i
$698$	−9.22643	−	2.03089i	−0.349226	−	0.0768704i
$699$	4.97597	+	17.9218i	0.188209	+	0.677866i
$700$	2.93710	+	1.76720i	0.111012	+	0.0667937i
$701$	−45.3329	−	4.93024i	−1.71220	−	0.186213i	−0.801136	−	0.598482i	$-0.795771\pi$
$701$	−45.3329	−	4.93024i	−1.71220	−	0.186213i	−0.911062	+	0.412269i	$0.864736\pi$
$702$	3.72687	−	0.820347i	0.140662	−	0.0309620i
$703$	−7.65255	−	14.4342i	−0.288621	−	0.544398i
$704$	0.223599	+	1.36389i	0.00842719	+	0.0514036i
$705$	0.885539	+	0.673169i	0.0333513	+	0.0253530i
$706$	12.5462	−	14.7705i	0.472181	−	0.555895i
$707$	6.54177			0.246028
$708$	6.29635	−	4.39954i	0.236631	−	0.165345i
$709$	−31.4576			−1.18141			−0.590707	−	0.806886i	$-0.701151\pi$
$709$	−31.4576			−1.18141			−0.590707	+	0.806886i	$0.701151\pi$
$710$	1.32099	−	1.55519i	0.0495759	−	0.0583653i
$711$	−8.61555	−	6.54937i	−0.323108	−	0.245621i
$712$	−0.529838	−	3.23187i	−0.0198565	−	0.121119i
$713$	0.355802	+	0.671114i	0.0133249	+	0.0251334i
$714$	−3.32534	+	0.731963i	−0.124448	+	0.0273930i
$715$	1.57598	+	0.171398i	0.0589381	+	0.00640991i
$716$	−12.2837	−	7.39086i	−0.459064	−	0.276209i
$717$	7.13305	+	25.6909i	0.266389	+	0.959445i
$718$	−6.37280	−	1.40276i	−0.237831	−	0.0523505i
$719$	19.4938	+	6.56824i	0.726997	+	0.244954i	0.658376	−	0.752689i	$-0.271244\pi$
$719$	19.4938	+	6.56824i	0.726997	+	0.244954i	0.0686210	+	0.997643i	$0.478140\pi$
$720$	0.140789	−	0.265557i	0.00524691	−	0.00989672i
$721$	−3.01514	+	10.8596i	−0.112290	+	0.404431i
$722$	−3.85810	+	3.65459i	−0.143584	+	0.136010i
$723$	−0.487095	+	2.97115i	−0.0181153	+	0.110498i
$724$	4.42038	−	1.48940i	0.164282	−	0.0553531i
$725$	19.2909	−	2.09801i	0.716446	−	0.0779182i
$726$	−8.24968	−	3.81671i	−0.306174	−	0.141651i
$727$	0.0563703	−	1.03969i	0.00209066	−	0.0385599i	−0.997302	−	0.0734088i	$-0.976612\pi$
$727$	0.0563703	−	1.03969i	0.00209066	−	0.0385599i	0.999393	+	0.0348489i	$0.0110950\pi$
$728$	−2.12101	+	1.61235i	−0.0786098	+	0.0597576i
$729$	−0.725995	−	0.687699i	−0.0268887	−	0.0254704i
$730$	−1.16911	+	0.703430i	−0.0432707	+	0.0260351i
$731$	−6.40909	+	2.96516i	−0.237049	+	0.109670i
$732$	−0.596175	−	1.49629i	−0.0220353	−	0.0553043i
$733$	14.7721	−	21.7871i	0.545618	−	0.804727i	−0.450498	−	0.892778i	$-0.648753\pi$
$733$	14.7721	−	21.7871i	0.545618	−	0.804727i	0.996116	+	0.0880509i	$0.0280638\pi$
$734$	−17.3748	−	25.6260i	−0.641317	−	0.945871i
$735$	−0.724537	+	1.81845i	−0.0267250	+	0.0670746i
$736$	−0.183464	−	3.38379i	−0.00676256	−	0.124728i
$737$	−1.46140	−	1.72049i	−0.0538312	−	0.0633750i
$738$	−3.93690	−	4.63488i	−0.144919	−	0.170612i
$739$	0.0238028	+	0.439016i	0.000875599	+	0.0161495i	0.998939	−	0.0460624i	$-0.0146673\pi$
$739$	0.0238028	+	0.439016i	0.000875599	+	0.0161495i	−0.998063	+	0.0622119i	$0.980185\pi$
$740$	0.491310	−	1.23310i	0.0180609	−	0.0453295i
$741$	7.92248	+	11.6848i	0.291040	+	0.429251i
$742$	1.31378	−	1.93769i	0.0482305	−	0.0711347i
$743$	16.3692	+	41.0835i	0.600527	+	1.50721i	0.843474	+	0.537170i	$0.180507\pi$
$743$	16.3692	+	41.0835i	0.600527	+	1.50721i	−0.242947	+	0.970040i	$0.578114\pi$
$744$	0.203435	−	0.0941191i	0.00745829	−	0.00345057i
$745$	−3.02375	+	1.81933i	−0.110782	+	0.0666551i
$746$	18.1922	+	17.2326i	0.666065	+	0.630931i
$747$	5.93341	−	4.51046i	0.217092	−	0.165029i
$748$	0.364922	−	6.73058i	0.0133429	−	0.246094i
$749$	6.65162	+	3.07737i	0.243045	+	0.112445i
$750$	2.96108	−	0.322037i	0.108123	−	0.0117591i
$751$	−30.8288	+	10.3874i	−1.12496	+	0.379043i	−0.819453	−	0.573146i	$-0.805723\pi$
$751$	−30.8288	+	10.3874i	−1.12496	+	0.379043i	−0.305508	+	0.952190i	$0.598826\pi$
$752$	0.598727	−	3.65207i	0.0218333	−	0.133177i
$753$	−0.354306	+	0.335616i	−0.0129116	+	0.0122305i
$754$	−4.03500	+	14.5327i	−0.146946	+	0.529251i
$755$	−2.64113	+	4.98169i	−0.0961204	+	0.181302i
$756$	0.661620	+	0.222926i	0.0240629	+	0.00810774i
$757$	−31.0442	−	6.83335i	−1.12832	−	0.248362i	−0.388686	−	0.921370i	$-0.627071\pi$
$757$	−31.0442	−	6.83335i	−1.12832	−	0.248362i	−0.739635	+	0.673008i	$0.765002\pi$
$758$	2.48641	+	8.95524i	0.0903105	+	0.325269i
$759$	−4.01318	−	2.41465i	−0.145669	−	0.0876461i
$760$	1.10542	+	0.120221i	0.0400977	+	0.00436089i
$761$	−49.7148	+	10.9431i	−1.80216	+	0.396685i	−0.983980	−	0.178277i	$-0.942948\pi$
$761$	−49.7148	+	10.9431i	−1.80216	+	0.396685i	−0.818180	+	0.574962i	$0.805017\pi$
$762$	3.53714	+	6.67175i	0.128137	+	0.241692i
$763$	−0.478206	−	2.91693i	−0.0173122	−	0.105600i
$764$	11.3248	+	8.60885i	0.409715	+	0.311457i
$765$	−0.948985	+	1.11723i	−0.0343106	+	0.0403936i
$766$	−21.3418			−0.771111
$767$	−19.8566	+	21.5617i	−0.716979	+	0.778549i
$768$	−1.00000			−0.0360844
$769$	29.1145	−	34.2762i	1.04989	−	1.23603i	0.0789111	−	0.996882i	$-0.474856\pi$
$769$	29.1145	−	34.2762i	1.04989	−	1.23603i	0.970983	−	0.239149i	$-0.0768685\pi$
$770$	0.230891	+	0.175519i	0.00832074	+	0.00632526i
$771$	−4.91534	−	29.9822i	−0.177022	−	1.07978i
$772$	−9.25596	−	17.4586i	−0.333129	−	0.628349i
$773$	−31.1682	+	6.86063i	−1.12104	+	0.246760i	−0.736559	−	0.676373i	$-0.763551\pi$
$773$	−31.1682	+	6.86063i	−1.12104	+	0.246760i	−0.384482	+	0.923133i	$0.625620\pi$
$774$	1.43949	+	0.156554i	0.0517415	+	0.00562722i
$775$	0.942981	+	0.567373i	0.0338729	+	0.0203806i
$776$	2.83281	+	10.2029i	0.101692	+	0.366261i
$777$	3.01115	+	0.662804i	0.108024	+	0.0237780i
$778$	−27.0153	−	9.10253i	−0.968547	−	0.326341i
$779$	10.5378	−	19.8764i	0.377556	−	0.712147i
$780$	−0.306855	+	1.10519i	−0.0109872	+	0.0395723i
$781$	−6.81184	+	6.45251i	−0.243747	+	0.230889i
$782$	−2.67376	+	16.3092i	−0.0956134	+	0.583216i
$783$	3.74545	−	1.26199i	0.133851	−	0.0450998i
$784$	6.47439	−	0.704132i	0.231228	−	0.0251476i
$785$	2.68742	+	1.24333i	0.0959180	+	0.0443764i
$786$	−0.215957	+	3.98309i	−0.00770292	+	0.142072i
$787$	8.82169	−	6.70607i	0.314459	−	0.239046i	−0.436024	−	0.899935i	$-0.643614\pi$
$787$	8.82169	−	6.70607i	0.314459	−	0.239046i	0.750483	+	0.660889i	$0.229821\pi$
$788$	−1.32314	−	1.25335i	−0.0471351	−	0.0446487i
$789$	18.0496	−	10.8601i	0.642583	−	0.386630i
$790$	2.95221	−	1.36584i	0.105035	−	0.0485943i
$791$	−3.96375	−	9.94826i	−0.140935	−	0.353719i
$792$	−0.775616	+	1.14395i	−0.0275603	+	0.0406484i
$793$	3.44934	+	5.08740i	0.122490	+	0.180659i
$794$	13.8780	−	34.8312i	0.492513	−	1.23611i
$795$	−0.0545646	−	1.00639i	−0.00193521	−	0.0356928i
$796$	3.87263	+	4.55921i	0.137262	+	0.161597i
$797$	−0.514612	−	0.605848i	−0.0182285	−	0.0214602i	0.752972	−	0.658052i	$-0.228619\pi$
$797$	−0.514612	−	0.605848i	−0.0182285	−	0.0214602i	−0.771201	+	0.636592i	$0.780344\pi$
$798$	0.139831	+	2.57903i	0.00494997	+	0.0912968i
$799$	−6.68057	+	16.7670i	−0.236342	+	0.593173i
$800$	−2.75524	−	4.06367i	−0.0974123	−	0.143672i
$801$	1.83790	−	2.71069i	0.0649389	−	0.0957776i
$802$	−8.96683	−	22.5050i	−0.316630	−	0.794680i
$803$	5.69408	−	2.63436i	0.200940	−	0.0929646i
$804$	1.39950	−	0.842053i	0.0493567	−	0.0296969i
$805$	−0.516273	−	0.489039i	−0.0181962	−	0.0172364i
$806$	−0.680967	+	0.517657i	−0.0239860	+	0.0182337i
$807$	−0.819040	+	15.1063i	−0.0288316	+	0.531767i
$808$	−8.50390	−	3.93432i	−0.299166	−	0.138409i
$809$	−31.1697	+	3.38991i	−1.09587	+	0.119183i	−0.638148	−	0.769914i	$-0.720299\pi$
$809$	−31.1697	+	3.38991i	−1.09587	+	0.119183i	−0.457720	+	0.889097i	$0.651334\pi$
$810$	0.284836	−	0.0959723i	0.0100081	−	0.00337212i
$811$	7.10682	−	43.3497i	0.249554	−	1.52221i	−0.503349	−	0.864083i	$-0.667899\pi$
$811$	7.10682	−	43.3497i	0.249554	−	1.52221i	0.752904	−	0.658131i	$-0.228653\pi$
$812$	−2.00331	+	1.89764i	−0.0703024	+	0.0665940i
$813$	4.66164	−	16.7897i	0.163491	−	0.588841i
$814$	−2.85898	+	5.39260i	−0.100207	+	0.189011i
$815$	0.992822	+	0.334521i	0.0347770	+	0.0117177i
$816$	4.76296	+	1.04841i	0.166737	+	0.0367016i
$817$	1.43307	+	5.16145i	0.0501367	+	0.180576i
$818$	11.0884	+	6.67169i	0.387698	+	0.233270i
$819$	−2.64865	−	0.288058i	−0.0925514	−	0.0100656i
$820$	1.78510	−	0.392930i	0.0623383	−	0.0137217i
$821$	−0.946157	−	1.78464i	−0.0330211	−	0.0622844i	0.866452	−	0.499260i	$-0.166395\pi$
$821$	−0.946157	−	1.78464i	−0.0330211	−	0.0622844i	−0.899474	+	0.436975i	$0.856050\pi$
$822$	0.942283	+	5.74767i	0.0328659	+	0.200473i
$823$	6.12444	+	4.65568i	0.213485	+	0.162287i	0.706452	−	0.707761i	$-0.250295\pi$
$823$	6.12444	+	4.65568i	0.213485	+	0.162287i	−0.492967	+	0.870048i	$0.664088\pi$
$824$	10.4506	−	12.3034i	0.364065	−	0.428610i
$825$	−6.78563			−0.236245
$826$	−5.14657	+	1.50721i	−0.179072	+	0.0524424i
$827$	−42.2345			−1.46864			−0.734319	−	0.678805i	$-0.762498\pi$
$827$	−42.2345			−1.46864			−0.734319	+	0.678805i	$0.762498\pi$
$828$	2.19384	−	2.58278i	0.0762411	−	0.0897579i
$829$	29.8093	+	22.6604i	1.03532	+	0.787029i	0.977423	−	0.211293i	$-0.0677675\pi$
$829$	29.8093	+	22.6604i	1.03532	+	0.787029i	0.0578966	+	0.998323i	$0.481561\pi$
$830$	0.362423	+	2.21068i	0.0125799	+	0.0767339i
$831$	4.66363	+	8.79654i	0.161780	+	0.305149i
$832$	3.72687	−	0.820347i	0.129206	−	0.0284404i
$833$	−31.5755	−	3.43404i	−1.09402	−	0.118982i
$834$	10.9155	+	6.56764i	0.377973	+	0.227419i
$835$	−0.442631	−	1.59421i	−0.0153179	−	0.0551700i
$836$	−4.99344	−	1.09914i	−0.172702	−	0.0380145i
$837$	0.212419	+	0.0715722i	0.00734226	+	0.00247390i
$838$	−7.92432	+	14.9469i	−0.273741	+	0.516331i
$839$	−1.84068	+	6.62953i	−0.0635474	+	0.228877i	−0.988504	−	0.151196i	$-0.951687\pi$
$839$	−1.84068	+	6.62953i	−0.0635474	+	0.228877i	0.924956	+	0.380073i	$0.124101\pi$
$840$	−0.152349	+	0.144312i	−0.00525653	+	0.00497925i
$841$	2.16448	−	13.2027i	0.0746372	−	0.455267i
$842$	8.15104	−	2.74640i	0.280903	−	0.0946474i
$843$	22.9785	−	2.49906i	0.791422	−	0.0860723i
$844$	−19.1570	−	8.86296i	−0.659410	−	0.305076i
$845$	0.0254267	−	0.468968i	0.000874705	−	0.0161330i
$846$	2.94620	−	2.23965i	0.101293	−	0.0770006i
$847$	4.60732	+	4.36428i	0.158309	+	0.149958i
$848$	−2.87319	+	1.72874i	−0.0986659	+	0.0593653i
$849$	−25.0649	+	11.5962i	−0.860225	+	0.397982i
$850$	8.86270	+	22.2437i	0.303988	+	0.762953i
$851$	8.39837	−	12.3867i	0.287893	−	0.424610i
$852$	−3.80977	−	5.61899i	−0.130521	−	0.192504i
$853$	−15.3061	+	38.4153i	−0.524070	+	1.31532i	0.394078	+	0.919077i	$0.371064\pi$
$853$	−15.3061	+	38.4153i	−0.524070	+	1.31532i	−0.918148	+	0.396239i	$0.870315\pi$
$854$	0.0608806	+	1.12288i	0.00208329	+	0.0384240i
$855$	0.719852	+	0.847475i	0.0246184	+	0.0289830i
$856$	−6.79593	−	8.00079i	−0.232280	−	0.273461i
$857$	−0.894373	−	16.4957i	−0.0305512	−	0.563484i	−0.973237	−	0.229803i	$-0.926192\pi$
$857$	−0.894373	−	16.4957i	−0.0305512	−	0.563484i	0.942686	−	0.333681i	$-0.108291\pi$
$858$	1.95219	−	4.89962i	0.0666466	−	0.167270i
$859$	−4.01215	−	5.91748i	−0.136893	−	0.201902i	0.753063	−	0.657948i	$-0.228575\pi$
$859$	−4.01215	−	5.91748i	−0.136893	−	0.201902i	−0.889956	+	0.456046i	$0.849265\pi$
$860$	−0.244239	+	0.360226i	−0.00832849	+	0.0122836i
$861$	1.57150	+	3.94417i	0.0535566	+	0.134417i
$862$	−13.3927	+	6.19614i	−0.456158	+	0.211041i
$863$	−44.7714	+	26.9381i	−1.52404	+	0.916983i	−0.526261	+	0.850323i	$0.676407\pi$
$863$	−44.7714	+	26.9381i	−1.52404	+	0.916983i	−0.997776	+	0.0666598i	$0.978766\pi$
$864$	−0.725995	−	0.687699i	−0.0246989	−	0.0233960i
$865$	1.27084	−	0.966064i	0.0432097	−	0.0328472i
$866$	−1.29071	+	23.8058i	−0.0438602	+	0.808955i
$867$	−6.15784	−	2.84892i	−0.209131	−	0.0967545i
$868$	−0.155578	+	0.0169202i	−0.00528068	+	0.000574308i
$869$	−14.1745	+	4.77594i	−0.480837	+	0.162013i
$870$	−0.192190	+	1.17230i	−0.00651584	+	0.0397449i
$871$	−4.52500	+	4.28630i	−0.153324	+	0.145236i
$872$	−1.13265	+	4.07943i	−0.0383563	+	0.138147i
$873$	−4.95990	+	9.35536i	−0.167867	+	0.316631i
$874$	11.8802	+	4.00292i	0.401855	+	0.135401i
$875$	−2.03090	−	0.447035i	−0.0686570	−	0.0151126i
$876$	1.21443	+	4.37397i	0.0410317	+	0.147783i
$877$	−40.9810	−	24.6575i	−1.38383	−	0.832624i	−0.387810	−	0.921739i	$-0.626768\pi$
$877$	−40.9810	−	24.6575i	−1.38383	−	0.832624i	−0.996021	+	0.0891158i	$0.971596\pi$
$878$	−38.9890	−	4.24031i	−1.31582	−	0.143104i
$879$	−3.04214	+	0.669625i	−0.102609	+	0.0225859i
$880$	−0.194585	−	0.367026i	−0.00655945	−	0.0123724i
$881$	−2.15002	−	13.1145i	−0.0724360	−	0.441840i	−0.997998	−	0.0632443i	$-0.979855\pi$
$881$	−2.15002	−	13.1145i	−0.0724360	−	0.441840i	0.925562	−	0.378596i	$-0.123593\pi$
$882$	5.18461	+	3.94123i	0.174575	+	0.132708i
$883$	8.45845	−	9.95806i	0.284650	−	0.335115i	−0.601191	−	0.799106i	$-0.705307\pi$
$883$	8.45845	−	9.95806i	0.284650	−	0.335115i	0.885840	+	0.463990i	$0.153583\pi$
$884$	−18.6110			−0.625956
$885$	−1.37119	+	1.85742i	−0.0460921	+	0.0624365i
$886$	21.3368			0.716823
$887$	34.2029	−	40.2667i	1.14842	−	1.35202i	0.222218	−	0.974997i	$-0.428670\pi$
$887$	34.2029	−	40.2667i	1.14842	−	1.35202i	0.926202	−	0.377028i	$-0.123054\pi$
$888$	−3.51569	−	2.67256i	−0.117979	−	0.0896852i
$889$	−0.852937	−	5.20268i	−0.0286066	−	0.174492i
$890$	0.461087	+	0.869703i	0.0154557	+	0.0291525i
$891$	−1.34979	+	0.297110i	−0.0452195	+	0.00995357i
$892$	3.09940	+	0.337080i	0.103776	+	0.0112863i
$893$	11.7312	+	7.05842i	0.392569	+	0.236201i
$894$	3.14096	+	11.3127i	0.105049	+	0.378354i
$895$	4.20816	+	0.926285i	0.140663	+	0.0309623i
$896$	0.661620	+	0.222926i	0.0221032	+	0.00744743i
$897$	−6.05737	+	11.4254i	−0.202250	+	0.381483i
$898$	−3.41930	+	12.3152i	−0.114103	+	0.410963i
$899$	−0.643179	+	0.609252i	−0.0214512	+	0.0203197i
$900$	0.794294	−	4.84498i	0.0264765	−	0.161499i
$901$	15.4973	−	5.22166i	0.516291	−	0.173959i
$902$	−8.35558	+	0.908725i	−0.278211	+	0.0302572i
$903$	−0.917497	−	0.424479i	−0.0305324	−	0.0141258i
$904$	−0.830409	+	15.3160i	−0.0276190	+	0.509403i
$905$	−1.11614	+	0.848469i	−0.0371018	+	0.0282041i
$906$	13.6193	+	12.9008i	0.452470	+	0.428602i
$907$	9.11419	−	5.48383i	0.302632	−	0.182087i	−0.356135	−	0.934434i	$-0.615906\pi$
$907$	9.11419	−	5.48383i	0.302632	−	0.182087i	0.658767	+	0.752347i	$0.271078\pi$
$908$	1.39206	−	0.644038i	0.0461973	−	0.0213731i
$909$	−3.46816	−	8.70443i	−0.115032	−	0.288708i
$910$	0.449398	−	0.662812i	0.0148974	−	0.0219720i
$911$	0.113977	+	0.168104i	0.00377624	+	0.00556954i	0.829572	−	0.558399i	$-0.188584\pi$
$911$	0.113977	+	0.168104i	0.00377624	+	0.00556954i	−0.825796	+	0.563969i	$0.809274\pi$
$912$	1.36930	−	3.43668i	0.0453421	−	0.113800i
$913$	−0.557685	−	10.2859i	−0.0184567	−	0.340413i
$914$	10.6756	+	12.5682i	0.353116	+	0.415720i
$915$	0.313414	+	0.368980i	0.0103611	+	0.0121981i
$916$	0.894922	+	16.5059i	0.0295691	+	0.545369i
$917$	1.03081	−	2.58715i	0.0340405	−	0.0854352i
$918$	2.73690	+	4.03662i	0.0903311	+	0.133228i
$919$	−3.98268	+	5.87401i	−0.131376	+	0.193766i	−0.887688	−	0.460446i	$-0.847689\pi$
$919$	−3.98268	+	5.87401i	−0.131376	+	0.193766i	0.756311	+	0.654212i	$0.227000\pi$
$920$	0.377007	+	0.946217i	0.0124296	+	0.0311958i
$921$	4.74771	−	2.19653i	0.156442	−	0.0723780i
$922$	−14.3469	+	8.63224i	−0.472490	+	0.284288i
$923$	18.8081	+	17.8159i	0.619075	+	0.586419i
$924$	0.768179	−	0.583954i	0.0252712	−	0.0192107i
$925$	1.17384	−	21.6501i	0.0385955	−	0.711852i
$926$	−14.1674	−	6.55455i	−0.465570	−	0.215396i
$927$	16.0482	−	1.74534i	0.527091	−	0.0573246i
$928$	3.74545	−	1.26199i	0.122950	−	0.0414268i
$929$	6.61135	−	40.3275i	0.216911	−	1.32310i	−0.623786	−	0.781595i	$-0.714406\pi$
$929$	6.61135	−	40.3275i	0.216911	−	1.32310i	0.840697	−	0.541506i	$-0.182146\pi$
$930$	−0.0489128	+	0.0463326i	−0.00160391	+	0.00151931i
$931$	−6.44550	+	23.2146i	−0.211243	+	0.760827i
$932$	−8.71230	+	16.4331i	−0.285381	+	0.538286i
$933$	−1.74740	−	0.588768i	−0.0572074	−	0.0192754i
$934$	−10.3673	−	2.28202i	−0.339230	−	0.0746701i
$935$	0.542007	+	1.95213i	0.0177255	+	0.0638416i
$936$	3.26985	+	1.96740i	0.106878	+	0.0643065i
$937$	14.8435	+	1.61433i	0.484915	+	0.0527377i	0.347312	−	0.937750i	$-0.387095\pi$
$937$	14.8435	+	1.61433i	0.484915	+	0.0527377i	0.137604	+	0.990487i	$0.456060\pi$
$938$	−1.11366	+	0.245134i	−0.0363621	+	0.00800391i
$939$	3.81508	+	7.19600i	0.124500	+	0.234832i
$940$	0.179959	+	1.09770i	0.00586962	+	0.0358031i
$941$	−1.88415	−	1.43229i	−0.0614214	−	0.0466913i	0.574013	−	0.818846i	$-0.305386\pi$
$941$	−1.88415	−	1.43229i	−0.0614214	−	0.0466913i	−0.635434	+	0.772155i	$0.719179\pi$
$942$	6.37780	−	7.50852i	0.207800	−	0.244641i
$943$	20.6078			0.671083
$944$	7.59668	+	1.13595i	0.247251	+	0.0369721i
$945$	−0.209848			−0.00682635
$946$	1.29558	−	1.52528i	0.0421230	−	0.0495911i
$947$	−21.4685	−	16.3199i	−0.697632	−	0.530326i	0.195173	−	0.980769i	$-0.437473\pi$
$947$	−21.4685	−	16.3199i	−0.697632	−	0.530326i	−0.892805	+	0.450443i	$0.851266\pi$
$948$	−1.75085	−	10.6797i	−0.0568650	−	0.346861i
$949$	−8.11420	−	15.3050i	−0.263398	−	0.496821i
$950$	17.7383	−	3.90449i	0.575506	−	0.126679i
$951$	0.283885	+	0.0308743i	0.00920560	+	0.00100117i
$952$	−2.91755	−	1.75543i	−0.0945585	−	0.0568939i
$953$	0.613085	+	2.20813i	0.0198598	+	0.0715285i	0.972816	−	0.231580i	$-0.0743894\pi$
$953$	0.613085	+	2.20813i	0.0198598	+	0.0715285i	−0.952956	+	0.303108i	$0.901976\pi$
$954$	−3.27478	−	0.720834i	−0.106025	−	0.0233379i
$955$	−4.05191	−	1.36525i	−0.131117	−	0.0441783i
$956$	−12.4891	+	23.5569i	−0.403925	+	0.761884i
$957$	1.46138	−	5.26342i	0.0472397	−	0.170142i
$958$	−3.14193	+	2.97620i	−0.101511	+	0.0961565i
$959$	0.657871	−	4.01283i	0.0212438	−	0.129581i
$960$	0.284836	−	0.0959723i	0.00919303	−	0.00309749i
$961$	30.7683	−	3.34626i	0.992527	−	0.107944i
$962$	15.2950	+	7.07620i	0.493129	+	0.228146i
$963$	0.568323	−	10.4821i	0.0183139	−	0.337781i
$964$	−2.39689	+	1.82207i	−0.0771986	+	0.0586848i
$965$	4.31197	+	4.08452i	0.138807	+	0.131485i
$966$	−2.02726	+	1.21976i	−0.0652259	+	0.0392451i
$967$	9.80152	−	4.53467i	0.315196	−	0.145825i	−0.255912	−	0.966700i	$-0.582376\pi$
$967$	9.80152	−	4.53467i	0.315196	−	0.145825i	0.571108	+	0.820875i	$0.306514\pi$
$968$	−3.36448	−	8.44422i	−0.108139	−	0.271407i
$969$	−10.1250	+	14.9332i	−0.325261	+	0.479724i
$970$	−1.78608	−	2.63427i	−0.0573475	−	0.0845813i
$971$	6.16932	−	15.4838i	0.197983	−	0.496900i	−0.796146	−	0.605105i	$-0.793131\pi$
$971$	6.16932	−	15.4838i	0.197983	−	0.496900i	0.994129	+	0.108205i	$0.0345104\pi$
$972$	−0.0541389	−	0.998533i	−0.00173651	−	0.0320280i
$973$	−5.75782	−	6.77863i	−0.184587	−	0.217313i
$974$	−13.2884	−	15.6443i	−0.425788	−	0.501276i
$975$	1.01433	+	18.7082i	0.0324846	+	0.599143i
$976$	0.596175	−	1.49629i	0.0190831	−	0.0478950i
$977$	12.2925	+	18.1300i	0.393271	+	0.580032i	0.971852	−	0.235594i	$-0.0757035\pi$
$977$	12.2925	+	18.1300i	0.393271	+	0.580032i	−0.578580	+	0.815625i	$0.696393\pi$
$978$	1.95607	−	2.88499i	0.0625482	−	0.0922518i
$979$	−1.67539	−	4.20491i	−0.0535457	−	0.134390i
$980$	−1.77656	+	0.821924i	−0.0567501	+	0.0262554i
$981$	−3.62772	+	2.18273i	−0.115824	+	0.0696891i
$982$	10.4650	+	9.91296i	0.333951	+	0.316335i
$983$	3.59282	−	2.73119i	0.114593	−	0.0871114i	−0.546308	−	0.837584i	$-0.683967\pi$
$983$	3.59282	−	2.73119i	0.114593	−	0.0871114i	0.660901	+	0.750473i	$0.270174\pi$
$984$	0.329231	−	6.07231i	0.0104955	−	0.193578i
$985$	0.497166	+	0.230013i	0.0158410	+	0.00732883i
$986$	−19.1625	+	2.08405i	−0.610259	+	0.0663696i
$987$	−2.44854	+	0.825010i	−0.0779380	+	0.0262604i
$988$	−2.28394	+	13.9314i	−0.0726617	+	0.443216i
$989$	−3.56236	+	3.37444i	−0.113276	+	0.107301i
$990$	0.111136	−	0.400275i	0.00353213	−	0.0127216i
$991$	13.7028	−	25.8462i	0.435283	−	0.821030i	−0.564708	−	0.825291i	$-0.691011\pi$
$991$	13.7028	−	25.8462i	0.435283	−	0.821030i	0.999991	+	0.00426024i	$0.00135608\pi$
$992$	0.212419	+	0.0715722i	0.00674430	+	0.00227242i
$993$	27.7818	+	6.11524i	0.881629	+	0.194061i
$994$	1.26800	+	4.56694i	0.0402186	+	0.144854i
$995$	−1.54062	−	0.926961i	−0.0488410	−	0.0293867i
$996$	7.40947	+	0.805829i	0.234778	+	0.0255337i
$997$	50.4003	−	11.0939i	1.59619	−	0.351349i	0.674198	−	0.738551i	$-0.264489\pi$
$997$	50.4003	−	11.0939i	1.59619	−	0.351349i	0.921995	+	0.387202i	$0.126558\pi$
$998$	−13.2193	−	24.9343i	−0.418450	−	0.789280i
$999$	−0.714458	−	4.35800i	−0.0226045	−	0.137881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.127.2	✓	56
59.46	even	29	inner	354.2.e.b.223.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.127.2	✓	56	1.1	even	1	trivial
354.2.e.b.223.2	yes	56	59.46	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647386 + 0.762162i) q^{2} +(-0.796093 - 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.140789 + 0.265557i) q^{5} +(0.976621 - 0.214970i) q^{6} +(-0.694075 - 0.0754852i) q^{7} +(0.856857 + 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})\)	\(q+(-0.647386 + 0.762162i) q^{2} +(-0.796093 - 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(0.140789 + 0.265557i) q^{5} +(0.976621 - 0.214970i) q^{6} +(-0.694075 - 0.0754852i) q^{7} +(0.856857 + 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(-0.293542 - 0.0646136i) q^{10} +(1.30975 + 0.441306i) q^{11} +(-0.468408 + 0.883512i) q^{12} +(1.02091 - 3.67700i) q^{13} +(0.506866 - 0.480129i) q^{14} +(0.0486267 - 0.296610i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(4.84839 - 0.527294i) q^{17} +(-0.907575 - 0.419889i) q^{18} +(0.200283 - 3.69400i) q^{19} +(0.239281 - 0.181897i) q^{20} +(0.506866 + 0.480129i) q^{21} +(-1.18426 + 0.712546i) q^{22} +(3.07555 - 1.42290i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(2.75524 - 4.06367i) q^{25} +(2.14154 + 3.15854i) q^{26} +(0.370138 - 0.928977i) q^{27} +(0.0377980 + 0.697143i) q^{28} +(2.55869 + 3.01233i) q^{29} +(0.194585 + 0.229083i) q^{30} +(0.0121354 + 0.223824i) q^{31} +(0.370138 - 0.928977i) q^{32} +(-0.775616 - 1.14395i) q^{33} +(-2.73690 + 4.03662i) q^{34} +(-0.0776727 - 0.194944i) q^{35} +(0.907575 - 0.419889i) q^{36} +(3.78404 - 2.27678i) q^{37} +(2.68577 + 2.54410i) q^{38} +(-3.03796 + 2.30940i) q^{39} +(-0.0162725 + 0.300129i) q^{40} +(5.51917 + 2.55344i) q^{41} +(-0.694075 + 0.0754852i) q^{42} +(-1.37218 + 0.462342i) q^{43} +(0.223599 - 1.36389i) q^{44} +(-0.218212 + 0.206702i) q^{45} +(-0.906589 + 3.26524i) q^{46} +(-1.73350 + 3.26973i) q^{47} +(0.947653 + 0.319302i) q^{48} +(-6.36030 - 1.40001i) q^{49} +(1.31347 + 4.73070i) q^{50} +(-4.17888 - 2.51435i) q^{51} +(-3.79372 - 0.412592i) q^{52} +(3.27478 - 0.720834i) q^{53} +(0.468408 + 0.883512i) q^{54} +(0.0672069 + 0.409944i) q^{55} +(-0.555806 - 0.422513i) q^{56} +(-2.39496 + 2.81956i) q^{57} -3.95234 q^{58} +(-6.83631 - 3.50212i) q^{59} -0.300570 q^{60} +(-1.04273 + 1.22760i) q^{61} +(-0.178446 - 0.135651i) q^{62} +(-0.112951 - 0.688970i) q^{63} +(0.468408 + 0.883512i) q^{64} +(1.12018 - 0.246571i) q^{65} +(1.37400 + 0.149431i) q^{66} +(-1.39950 - 0.842053i) q^{67} +(-1.30473 - 4.69921i) q^{68} +(-3.30953 - 0.728483i) q^{69} +(0.198863 + 0.0670047i) q^{70} +(-3.17992 + 5.99796i) q^{71} +(-0.267528 + 0.963550i) q^{72} +(3.29561 - 3.12177i) q^{73} +(-0.714458 + 4.35800i) q^{74} +(-4.65265 + 1.56766i) q^{75} +(-3.67774 + 0.399979i) q^{76} +(-0.875752 - 0.405166i) q^{77} +(0.206599 - 3.81050i) q^{78} +(-8.61555 + 6.54937i) q^{79} +(-0.218212 - 0.206702i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(-5.51917 + 2.55344i) q^{82} +(-2.75870 - 6.92381i) q^{83} +(0.391802 - 0.577865i) q^{84} +(0.822628 + 1.21329i) q^{85} +(0.535953 - 1.34514i) q^{86} +(-0.213976 - 3.94655i) q^{87} +(0.894752 + 1.05338i) q^{88} +(-2.12020 - 2.49609i) q^{89} +(-0.0162725 - 0.300129i) q^{90} +(-0.986148 + 2.47505i) q^{91} +(-1.90173 - 2.80484i) q^{92} +(0.125791 - 0.185528i) q^{93} +(-1.36982 - 3.43798i) q^{94} +(1.00917 - 0.466890i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(7.68744 + 7.28193i) q^{97} +(5.18461 - 3.94123i) q^{98} +(-0.0748253 + 1.38007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

L-functions

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