LMFDB - Embedded newform 380.2.be.b.51.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.19
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37453 + 0.332649i) q^{2} +(1.86185 + 0.677657i) q^{3} +(1.77869 + 0.914475i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.33375 + 1.55080i) q^{6} +(-1.89621 - 1.09478i) q^{7} +(2.14067 + 1.84866i) q^{8} +(0.709122 + 0.595024i) q^{9} +O(q^{10})$	\(q+(1.37453 + 0.332649i) q^{2} +(1.86185 + 0.677657i) q^{3} +(1.77869 + 0.914475i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.33375 + 1.55080i) q^{6} +(-1.89621 - 1.09478i) q^{7} +(2.14067 + 1.84866i) q^{8} +(0.709122 + 0.595024i) q^{9} +(0.0889099 - 1.41142i) q^{10} +(-1.11884 + 0.645961i) q^{11} +(2.69195 + 2.90795i) q^{12} +(1.54509 + 4.24510i) q^{13} +(-2.24223 - 2.13558i) q^{14} +(0.344055 - 1.95124i) q^{15} +(2.32747 + 3.25313i) q^{16} +(3.21680 - 2.69921i) q^{17} +(0.776779 + 1.05377i) q^{18} +(-0.583643 - 4.31965i) q^{19} +(0.591716 - 1.91046i) q^{20} +(-2.78857 - 3.32329i) q^{21} +(-1.75276 + 0.515715i) q^{22} +(-7.68844 - 1.35568i) q^{23} +(2.73285 + 4.89256i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.711650 + 6.34900i) q^{26} +(-2.05495 - 3.55928i) q^{27} +(-2.37163 - 3.68131i) q^{28} +(-5.00853 + 5.96893i) q^{29} +(1.12199 - 2.56759i) q^{30} +(-0.801118 + 1.38758i) q^{31} +(2.11704 + 5.24577i) q^{32} +(-2.52084 + 0.444493i) q^{33} +(5.31949 - 2.64010i) q^{34} +(-0.748873 + 2.05751i) q^{35} +(0.717174 + 1.70684i) q^{36} -0.916035i q^{37} +(0.634690 - 6.13165i) q^{38} +8.95076i q^{39} +(1.44885 - 2.42916i) q^{40} +(3.58454 - 9.84843i) q^{41} +(-2.72750 - 5.49560i) q^{42} +(-3.96610 + 0.699331i) q^{43} +(-2.58078 + 0.125815i) q^{44} +(0.462847 - 0.801674i) q^{45} +(-10.1171 - 4.42098i) q^{46} +(0.117552 - 0.140092i) q^{47} +(2.12889 + 7.63406i) q^{48} +(-1.10292 - 1.91031i) q^{49} +(-1.40541 + 0.157531i) q^{50} +(7.81833 - 2.84564i) q^{51} +(-1.13380 + 8.96365i) q^{52} +(11.2420 + 1.98226i) q^{53} +(-1.64061 - 5.57592i) q^{54} +(0.830431 + 0.989670i) q^{55} +(-2.03530 - 5.84901i) q^{56} +(1.84059 - 8.43803i) q^{57} +(-8.86996 + 6.53842i) q^{58} +(-5.65551 + 4.74554i) q^{59} +(2.39632 - 3.15601i) q^{60} +(-0.489472 + 2.77593i) q^{61} +(-1.56274 + 1.64078i) q^{62} +(-0.693227 - 1.90462i) q^{63} +(1.16494 + 7.91473i) q^{64} +(3.91230 - 2.25877i) q^{65} +(-3.61285 - 0.227586i) q^{66} +(7.03072 + 5.89947i) q^{67} +(8.19005 - 1.85938i) q^{68} +(-13.3960 - 7.73419i) q^{69} +(-1.71378 + 2.57901i) q^{70} +(-0.824318 - 4.67494i) q^{71} +(0.418002 + 2.58467i) q^{72} +(2.41720 + 0.879790i) q^{73} +(0.304718 - 1.25912i) q^{74} -1.98134 q^{75} +(2.91209 - 8.21704i) q^{76} +2.82874 q^{77} +(-2.97746 + 12.3031i) q^{78} +(10.9331 + 3.97931i) q^{79} +(2.79955 - 2.85701i) q^{80} +(-1.89627 - 10.7543i) q^{81} +(8.20314 - 12.3446i) q^{82} +(-4.79084 - 2.76600i) q^{83} +(-1.92094 - 8.46118i) q^{84} +(-3.21680 - 2.69921i) q^{85} +(-5.68418 - 0.358066i) q^{86} +(-13.3700 + 7.71918i) q^{87} +(-3.58922 - 0.685556i) q^{88} +(5.59996 + 15.3858i) q^{89} +(0.902875 - 0.947963i) q^{90} +(1.71762 - 9.74113i) q^{91} +(-12.4356 - 9.44222i) q^{92} +(-2.43186 + 2.04057i) q^{93} +(0.208180 - 0.153458i) q^{94} +(-4.15267 + 1.32487i) q^{95} +(0.386765 + 11.2015i) q^{96} +(3.27224 + 3.89970i) q^{97} +(-0.880537 - 2.99267i) q^{98} +(-1.17776 - 0.207670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	1.37453	+	0.332649i	0.971943	+	0.235218i
$2$	1.37453	+	0.332649i	0.971943	+	0.235218i
$3$	1.86185	+	0.677657i	1.07494	+	0.391245i	0.818021	−	0.575188i	$-0.195071\pi$
$3$	1.86185	+	0.677657i	1.07494	+	0.391245i	0.256917	+	0.966434i	$0.417293\pi$
$4$	1.77869	+	0.914475i	0.889345	+	0.457237i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	2.33375	+	1.55080i	0.952750	+	0.633113i
$7$	−1.89621	−	1.09478i	−0.716701	−	0.413787i	0.0968363	−	0.995300i	$-0.469128\pi$
$7$	−1.89621	−	1.09478i	−0.716701	−	0.413787i	−0.813537	+	0.581513i	$0.802461\pi$
$8$	2.14067	+	1.84866i	0.756841	+	0.653599i
$9$	0.709122	+	0.595024i	0.236374	+	0.198341i
$10$	0.0889099	−	1.41142i	0.0281158	−	0.446329i
$11$	−1.11884	+	0.645961i	−0.337342	+	0.194765i	−0.659096	−	0.752059i	$-0.729061\pi$
$11$	−1.11884	+	0.645961i	−0.337342	+	0.194765i	0.321754	+	0.946823i	$0.395728\pi$
$12$	2.69195	+	2.90795i	0.777098	+	0.839454i
$13$	1.54509	+	4.24510i	0.428530	+	1.17738i	0.946705	+	0.322103i	$0.104390\pi$
$13$	1.54509	+	4.24510i	0.428530	+	1.17738i	−0.518174	+	0.855275i	$0.673388\pi$
$14$	−2.24223	−	2.13558i	−0.599262	−	0.570759i
$15$	0.344055	−	1.95124i	0.0888347	−	0.503807i
$16$	2.32747	+	3.25313i	0.581868	+	0.813283i
$17$	3.21680	−	2.69921i	0.780188	−	0.654656i	−0.163108	−	0.986608i	$-0.552152\pi$
$17$	3.21680	−	2.69921i	0.780188	−	0.654656i	0.943296	+	0.331953i	$0.107707\pi$
$18$	0.776779	+	1.05377i	0.183089	+	0.248376i
$19$	−0.583643	−	4.31965i	−0.133897	−	0.990995i
$19$	−0.583643	−	4.31965i	−0.133897	−	0.990995i
$20$	0.591716	−	1.91046i	0.132312	−	0.427193i
$21$	−2.78857	−	3.32329i	−0.608517	−	0.725202i
$22$	−1.75276	+	0.515715i	−0.373689	+	0.109951i
$23$	−7.68844	−	1.35568i	−1.60315	−	0.282679i	−0.700694	−	0.713461i	$-0.747126\pi$
$23$	−7.68844	−	1.35568i	−1.60315	−	0.282679i	−0.902456	+	0.430783i	$0.858237\pi$
$24$	2.73285	+	4.89256i	0.557840	+	0.998689i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	0.711650	+	6.34900i	0.139566	+	1.24514i
$27$	−2.05495	−	3.55928i	−0.395475	−	0.684983i
$28$	−2.37163	−	3.68131i	−0.448195	−	0.695702i
$29$	−5.00853	+	5.96893i	−0.930061	+	1.10840i	0.0638218	+	0.997961i	$0.479671\pi$
$29$	−5.00853	+	5.96893i	−0.930061	+	1.10840i	−0.993883	+	0.110442i	$0.964773\pi$
$30$	1.12199	−	2.56759i	0.204847	−	0.468776i
$31$	−0.801118	+	1.38758i	−0.143885	+	0.249216i	−0.928956	−	0.370189i	$-0.879293\pi$
$31$	−0.801118	+	1.38758i	−0.143885	+	0.249216i	0.785071	+	0.619405i	$0.212626\pi$
$32$	2.11704	+	5.24577i	0.374243	+	0.927331i
$33$	−2.52084	+	0.444493i	−0.438823	+	0.0773763i
$34$	5.31949	−	2.64010i	0.912285	−	0.452773i
$35$	−0.748873	+	2.05751i	−0.126583	+	0.347783i
$36$	0.717174	+	1.70684i	0.119529	+	0.284473i
$37$		−	0.916035i		−	0.150595i	−0.997161	−	0.0752976i	$-0.976009\pi$
$37$		−	0.916035i		−	0.150595i	0.997161	−	0.0752976i	$-0.0239907\pi$
$38$	0.634690	−	6.13165i	0.102960	−	0.994685i
$39$			8.95076i			1.43327i
$40$	1.44885	−	2.42916i	0.229083	−	0.384085i
$41$	3.58454	−	9.84843i	0.559811	−	1.53807i	−0.260104	−	0.965581i	$-0.583757\pi$
$41$	3.58454	−	9.84843i	0.559811	−	1.53807i	0.819914	−	0.572486i	$-0.194021\pi$
$42$	−2.72750	−	5.49560i	−0.420862	−	0.847989i
$43$	−3.96610	+	0.699331i	−0.604825	+	0.106647i	−0.467671	−	0.883903i	$-0.654907\pi$
$43$	−3.96610	+	0.699331i	−0.604825	+	0.106647i	−0.137154	+	0.990550i	$0.543796\pi$
$44$	−2.58078	+	0.125815i	−0.389067	+	0.0189674i
$45$	0.462847	−	0.801674i	0.0689971	−	0.119507i
$46$	−10.1171	−	4.42098i	−1.49168	−	0.651838i
$47$	0.117552	−	0.140092i	0.0171467	−	0.0204346i	−0.757403	−	0.652948i	$-0.773532\pi$
$47$	0.117552	−	0.140092i	0.0171467	−	0.0204346i	0.774550	+	0.632513i	$0.217977\pi$
$48$	2.12889	+	7.63406i	0.307278	+	1.10188i
$49$	−1.10292	−	1.91031i	−0.157560	−	0.272902i
$50$	−1.40541	+	0.157531i	−0.198755	+	0.0222782i
$51$	7.81833	−	2.84564i	1.09478	−	0.398469i
$52$	−1.13380	+	8.96365i	−0.157230	+	1.24303i
$53$	11.2420	+	1.98226i	1.54420	+	0.272284i	0.879892	−	0.475173i	$-0.157615\pi$
$53$	11.2420	+	1.98226i	1.54420	+	0.272284i	0.664310	+	0.747458i	$0.268726\pi$
$54$	−1.64061	−	5.57592i	−0.223259	−	0.758787i
$55$	0.830431	+	0.989670i	0.111975	+	0.133447i
$56$	−2.03530	−	5.84901i	−0.271978	−	0.781606i
$57$	1.84059	−	8.43803i	0.243792	−	1.11764i
$58$	−8.86996	+	6.53842i	−1.16468	+	0.858537i
$59$	−5.65551	+	4.74554i	−0.736285	+	0.617817i	−0.931837	−	0.362877i	$-0.881795\pi$
$59$	−5.65551	+	4.74554i	−0.736285	+	0.617817i	0.195552	+	0.980693i	$0.437350\pi$
$60$	2.39632	−	3.15601i	0.309364	−	0.407439i
$61$	−0.489472	+	2.77593i	−0.0626705	+	0.355422i	0.937306	+	0.348508i	$0.113312\pi$
$61$	−0.489472	+	2.77593i	−0.0626705	+	0.355422i	−0.999976	+	0.00691341i	$0.997799\pi$
$62$	−1.56274	+	1.64078i	−0.198468	+	0.208379i
$63$	−0.693227	−	1.90462i	−0.0873384	−	0.239960i
$64$	1.16494	+	7.91473i	0.145617	+	0.989341i
$65$	3.91230	−	2.25877i	0.485261	−	0.280166i
$66$	−3.61285	−	0.227586i	−0.444711	−	0.0280138i
$67$	7.03072	+	5.89947i	0.858939	+	0.720735i	0.961739	−	0.273967i	$-0.0883359\pi$
$67$	7.03072	+	5.89947i	0.858939	+	0.720735i	−0.102800	+	0.994702i	$0.532780\pi$
$68$	8.19005	−	1.85938i	0.993189	−	0.225483i
$69$	−13.3960	−	7.73419i	−1.61269	−	0.931087i
$70$	−1.71378	+	2.57901i	−0.204836	+	0.308250i
$71$	−0.824318	−	4.67494i	−0.0978286	−	0.554813i	−0.993844	−	0.110790i	$-0.964662\pi$
$71$	−0.824318	−	4.67494i	−0.0978286	−	0.554813i	0.896015	−	0.444023i	$-0.146449\pi$
$72$	0.418002	+	2.58467i	0.0492620	+	0.304607i
$73$	2.41720	+	0.879790i	0.282912	+	0.102972i	0.479579	−	0.877499i	$-0.340789\pi$
$73$	2.41720	+	0.879790i	0.282912	+	0.102972i	−0.196667	+	0.980470i	$0.563012\pi$
$74$	0.304718	−	1.25912i	0.0354228	−	0.146370i
$75$	−1.98134			−0.228785
$76$	2.91209	−	8.21704i	0.334040	−	0.942559i
$77$	2.82874			0.322365
$78$	−2.97746	+	12.3031i	−0.337131	+	1.39305i
$79$	10.9331	+	3.97931i	1.23006	+	0.447707i	0.873620	−	0.486610i	$-0.161767\pi$
$79$	10.9331	+	3.97931i	1.23006	+	0.447707i	0.356445	+	0.934316i	$0.383989\pi$
$80$	2.79955	−	2.85701i	0.312999	−	0.319424i
$81$	−1.89627	−	10.7543i	−0.210696	−	1.19492i
$82$	8.20314	−	12.3446i	0.905885	−	1.36323i
$83$	−4.79084	−	2.76600i	−0.525864	−	0.303607i	0.213467	−	0.976950i	$-0.431524\pi$
$83$	−4.79084	−	2.76600i	−0.525864	−	0.303607i	−0.739330	+	0.673343i	$0.764858\pi$
$84$	−1.92094	−	8.46118i	−0.209592	−	0.923191i
$85$	−3.21680	−	2.69921i	−0.348911	−	0.292771i
$86$	−5.68418	−	0.358066i	−0.612940	−	0.0386112i
$87$	−13.3700	+	7.71918i	−1.43342	+	0.827583i
$88$	−3.58922	−	0.685556i	−0.382612	−	0.0730805i
$89$	5.59996	+	15.3858i	0.593594	+	1.63089i	0.763781	+	0.645475i	$0.223341\pi$
$89$	5.59996	+	15.3858i	0.593594	+	1.63089i	−0.170187	+	0.985412i	$0.554437\pi$
$90$	0.902875	−	0.947963i	0.0951714	−	0.0999241i
$91$	1.71762	−	9.74113i	0.180056	−	1.02115i
$92$	−12.4356	−	9.44222i	−1.29650	−	0.984419i
$93$	−2.43186	+	2.04057i	−0.252172	+	0.211598i
$94$	0.208180	−	0.153458i	0.0214721	−	0.0158280i
$95$	−4.15267	+	1.32487i	−0.426055	+	0.135929i
$96$	0.386765	+	11.2015i	0.0394740	+	1.14324i
$97$	3.27224	+	3.89970i	0.332245	+	0.395955i	0.906142	−	0.422973i	$-0.139013\pi$
$97$	3.27224	+	3.89970i	0.332245	+	0.395955i	−0.573897	+	0.818928i	$0.694569\pi$
$98$	−0.880537	−	2.99267i	−0.0889476	−	0.302306i
$99$	−1.17776	−	0.207670i	−0.118369	−	0.0208716i
$100$	−1.98419	−	0.250978i	−0.198419	−	0.0250978i
$101$	−5.56628	+	2.02596i	−0.553866	+	0.201591i	−0.603763	−	0.797164i	$-0.706333\pi$
$101$	−5.56628	+	2.02596i	−0.553866	+	0.201591i	0.0498975	+	0.998754i	$0.484111\pi$
$102$	11.6932	−	1.31067i	1.15780	−	0.129776i
$103$	2.90093	+	5.02455i	0.285837	+	0.495084i	0.972812	−	0.231597i	$-0.0743951\pi$
$103$	2.90093	+	5.02455i	0.285837	+	0.495084i	−0.686975	+	0.726681i	$0.741062\pi$
$104$	−4.54020	+	11.9437i	−0.445203	+	1.17118i
$105$	−2.78857	+	3.32329i	−0.272137	+	0.324320i
$106$	14.7931	+	6.46431i	1.43683	+	0.627869i
$107$	8.14346	−	14.1049i	0.787258	−	1.36357i	−0.140383	−	0.990097i	$-0.544833\pi$
$107$	8.14346	−	14.1049i	0.787258	−	1.36357i	0.927641	−	0.373474i	$-0.121833\pi$
$108$	−0.400247	−	8.21005i	−0.0385138	−	0.790012i
$109$	−4.65630	+	0.821031i	−0.445992	+	0.0786405i	−0.392134	−	0.919908i	$-0.628263\pi$
$109$	−4.65630	+	0.821031i	−0.445992	+	0.0786405i	−0.0538583	+	0.998549i	$0.517152\pi$
$110$	0.812244	+	1.63658i	0.0774444	+	0.156041i
$111$	0.620758	−	1.70552i	0.0589197	−	0.161881i
$112$	−0.851918	−	8.71670i	−0.0804987	−	0.823651i
$113$		−	2.91511i		−	0.274231i	−0.990555	−	0.137115i	$-0.956217\pi$
$113$		−	2.91511i		−	0.274231i	0.990555	−	0.137115i	$-0.0437831\pi$
$114$	5.33685	−	10.9861i	0.499842	−	1.02894i
$115$			7.80704i			0.728011i
$116$	−14.3671	+	6.03670i	−1.33395	+	0.560494i
$117$	−1.43028	+	3.92966i	−0.132229	+	0.363297i
$118$	−9.35230	+	4.64161i	−0.860949	+	0.427295i
$119$	−9.05477	+	1.59660i	−0.830050	+	0.146360i
$120$	4.34367	−	3.54091i	0.396521	−	0.323240i
$121$	−4.66547	+	8.08083i	−0.424134	+	0.734621i
$122$	−1.59621	+	3.65279i	−0.144514	+	0.330708i
$123$	13.3477	−	15.9072i	1.20352	−	1.43430i
$124$	−2.69384	+	1.73547i	−0.241914	+	0.155849i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−0.319292	−	2.84857i	−0.0284448	−	0.253771i
$127$	−1.25704	+	0.457526i	−0.111545	+	0.0405989i	−0.397189	−	0.917737i	$-0.630014\pi$
$127$	−1.25704	+	0.457526i	−0.111545	+	0.0405989i	0.285645	+	0.958336i	$0.407792\pi$
$128$	−1.03158	+	11.2666i	−0.0911794	+	0.995834i
$129$	−7.85818	−	1.38561i	−0.691874	−	0.121996i
$130$	6.12897	−	1.80333i	0.537546	−	0.158163i
$131$	3.15773	+	3.76323i	0.275892	+	0.328795i	0.886142	−	0.463414i	$-0.153376\pi$
$131$	3.15773	+	3.76323i	0.275892	+	0.328795i	−0.610250	+	0.792209i	$0.708931\pi$
$132$	−4.89028	−	1.51463i	−0.425644	−	0.131832i
$133$	−3.62235	+	8.82993i	−0.314097	+	0.765652i
$134$	7.70151	+	10.4478i	0.665309	+	0.902551i
$135$	−3.14837	+	2.64179i	−0.270968	+	0.227369i
$136$	11.8760	+	0.168627i	1.01836	+	0.0144596i
$137$	3.80659	−	21.5882i	0.325219	−	1.84441i	−0.182916	−	0.983129i	$-0.558553\pi$
$137$	3.80659	−	21.5882i	0.325219	−	1.84441i	0.508134	−	0.861278i	$-0.330335\pi$
$138$	−15.8405	−	15.0871i	−1.34843	−	1.28430i
$139$	3.72398	+	10.2316i	0.315864	+	0.867830i	0.991443	+	0.130542i	$0.0416717\pi$
$139$	3.72398	+	10.2316i	0.315864	+	0.867830i	−0.675579	+	0.737288i	$0.736106\pi$
$140$	−3.21355	+	2.97485i	−0.271595	+	0.251421i
$141$	0.313798	−	0.181171i	0.0264265	−	0.0152574i
$142$	0.422061	−	6.70008i	0.0354185	−	0.562258i
$143$	−4.47087	−	3.75150i	−0.373873	−	0.313717i
$144$	−0.285232	+	3.69177i	−0.0237693	+	0.307648i
$145$	6.74798	+	3.89595i	0.560389	+	0.323541i
$146$	3.02987	+	2.01338i	0.250753	+	0.166629i
$147$	−0.758930	−	4.30411i	−0.0625955	−	0.354997i
$148$	0.837691	−	1.62934i	0.0688578	−	0.133931i
$149$	−12.8628	−	4.68167i	−1.05376	−	0.383538i	−0.243680	−	0.969856i	$-0.578355\pi$
$149$	−12.8628	−	4.68167i	−1.05376	−	0.383538i	−0.810081	+	0.586318i	$0.800577\pi$
$150$	−2.72341	−	0.659090i	−0.222366	−	0.0538144i
$151$	−3.10658			−0.252810			−0.126405	−	0.991979i	$-0.540344\pi$
$151$	−3.10658			−0.252810			−0.126405	+	0.991979i	$0.540344\pi$
$152$	6.73616	−	10.3259i	0.546375	−	0.837541i
$153$	3.88720			0.314262
$154$	3.88820	+	0.940977i	0.313320	+	0.0758261i
$155$	1.50561	+	0.547997i	0.120933	+	0.0440162i
$156$	−8.18525	+	15.9206i	−0.655344	+	1.27467i
$157$	1.97079	+	11.1769i	0.157286	+	0.892016i	0.956666	+	0.291189i	$0.0940508\pi$
$157$	1.97079	+	11.1769i	0.157286	+	0.892016i	−0.799379	+	0.600827i	$0.794838\pi$
$158$	13.7041	+	9.10656i	1.09024	+	0.724479i
$159$	19.5875	+	11.3089i	1.55339	+	0.896851i
$160$	4.79846	−	2.99579i	0.379352	−	0.236838i
$161$	13.0947	+	10.9878i	1.03201	+	0.865959i
$162$	0.970912	−	15.4129i	0.0762820	−	1.21095i
$163$	12.7994	−	7.38973i	1.00253	−	0.578808i	0.0935307	−	0.995616i	$-0.470185\pi$
$163$	12.7994	−	7.38973i	1.00253	−	0.578808i	0.908994	+	0.416808i	$0.136851\pi$
$164$	15.3819	−	14.2393i	1.20113	−	1.11191i
$165$	0.875480	+	2.40536i	0.0681560	+	0.187257i
$166$	−5.66507	−	5.39563i	−0.439695	−	0.418782i
$167$	2.06323	−	11.7012i	0.159658	−	0.905463i	−0.794746	−	0.606943i	$-0.792396\pi$
$167$	2.06323	−	11.7012i	0.159658	−	0.905463i	0.954403	−	0.298520i	$-0.0964931\pi$
$168$	0.174209	−	12.2692i	0.0134405	−	0.946588i
$169$	−5.67496	+	4.76186i	−0.436536	+	0.366297i
$170$	−3.52371	−	4.78023i	−0.270256	−	0.366627i
$171$	2.15642	−	3.41044i	0.164906	−	0.260803i
$172$	−7.69399	−	2.38301i	−0.586661	−	0.181703i
$173$	4.31273	+	5.13971i	0.327891	+	0.390765i	0.904654	−	0.426146i	$-0.140129\pi$
$173$	4.31273	+	5.13971i	0.327891	+	0.390765i	−0.576764	+	0.816911i	$0.695685\pi$
$174$	−20.9453	+	6.16276i	−1.58786	+	0.467197i
$175$	2.15629	+	0.380213i	0.163000	+	0.0287414i
$176$	−4.70546	−	2.13627i	−0.354687	−	0.161027i
$177$	−13.7456	+	5.00297i	−1.03318	+	0.376046i
$178$	2.57928	+	23.0111i	0.193325	+	1.72475i
$179$	9.28011	+	16.0736i	0.693628	+	1.20140i	0.970641	+	0.240532i	$0.0773221\pi$
$179$	9.28011	+	16.0736i	0.693628	+	1.20140i	−0.277013	+	0.960866i	$0.589345\pi$
$180$	1.55637	−	1.00267i	0.116005	−	0.0747344i
$181$	−0.226799	+	0.270289i	−0.0168579	+	0.0200904i	−0.774408	−	0.632687i	$-0.781952\pi$
$181$	−0.226799	+	0.270289i	−0.0168579	+	0.0200904i	0.757550	+	0.652778i	$0.226396\pi$
$182$	5.60131	−	12.8182i	0.415197	−	0.950145i
$183$	−2.79245	+	4.83667i	−0.206424	+	0.357537i
$184$	−13.9522	−	17.1153i	−1.02857	−	1.26176i
$185$	−0.902119	+	0.159068i	−0.0663251	+	0.0116949i
$186$	−4.02147	+	1.99588i	−0.294868	+	0.146345i
$187$	−1.85549	+	5.09791i	−0.135687	+	0.372796i
$188$	0.337199	−	0.141683i	0.0245927	−	0.0103333i
$189$			8.99886i			0.654571i
$190$	−6.14871	+	0.439703i	−0.446074	+	0.0318994i
$191$		−	3.47946i		−	0.251765i	−0.992045	−	0.125882i	$-0.959824\pi$
$191$		−	3.47946i		−	0.251765i	0.992045	−	0.125882i	$-0.0401762\pi$
$192$	−3.19453	+	15.5254i	−0.230545	+	1.12045i
$193$	−4.59149	+	12.6150i	−0.330503	+	0.908050i	0.657478	+	0.753474i	$0.271623\pi$
$193$	−4.59149	+	12.6150i	−0.330503	+	0.908050i	−0.987981	+	0.154576i	$0.950599\pi$
$194$	3.20057	+	6.44878i	0.229788	+	0.462996i
$195$	8.81478	−	1.55428i	0.631239	−	0.111305i
$196$	−0.214818	−	4.40644i	−0.0153441	−	0.314746i
$197$	10.1224	−	17.5325i	0.721192	−	1.24914i	−0.239330	−	0.970938i	$-0.576928\pi$
$197$	10.1224	−	17.5325i	0.721192	−	1.24914i	0.960522	−	0.278203i	$-0.0897387\pi$
$198$	−1.54978	−	0.677229i	−0.110138	−	0.0481285i
$199$	−1.34495	+	1.60284i	−0.0953406	+	0.113623i	−0.811605	−	0.584206i	$-0.801406\pi$
$199$	−1.34495	+	1.60284i	−0.0953406	+	0.113623i	0.716265	+	0.697829i	$0.245850\pi$
$200$	−2.64385	−	1.00502i	−0.186948	−	0.0710654i
$201$	9.09230	+	15.7483i	0.641321	+	1.11080i
$202$	−8.32498	+	0.933135i	−0.585743	+	0.0656551i
$203$	16.0319	−	5.83513i	1.12522	−	0.409546i
$204$	16.5086	+	2.08816i	1.15584	+	0.146200i
$205$	−10.3213	−	1.81992i	−0.720868	−	0.127109i
$206$	2.31601	+	7.87141i	0.161364	+	0.548427i
$207$	−4.64538	−	5.53615i	−0.322876	−	0.384789i
$208$	−10.2137	+	14.9067i	−0.708194	+	1.03359i
$209$	3.44333	+	4.45597i	0.238180	+	0.308226i
$210$	−4.93848	+	3.64036i	−0.340787	+	0.251209i
$211$	−4.51259	+	3.78651i	−0.310659	+	0.260674i	−0.784764	−	0.619794i	$-0.787216\pi$
$211$	−4.51259	+	3.78651i	−0.310659	+	0.260674i	0.474105	+	0.880468i	$0.342772\pi$
$212$	18.1832	+	13.8063i	1.24883	+	0.948222i
$213$	1.63325	−	9.26263i	0.111909	−	0.634665i
$214$	15.8854	−	16.6787i	1.08591	−	1.14013i
$215$	1.37741	+	3.78441i	0.0939388	+	0.258095i
$216$	2.18091	−	11.4181i	0.148392	−	0.776906i
$217$	3.03818	−	1.75409i	0.206245	−	0.119076i
$218$	−6.67336	−	0.420377i	−0.451977	−	0.0284716i
$219$	3.90427	+	3.27607i	0.263826	+	0.221376i
$220$	0.572051	+	2.51972i	0.0385677	+	0.169880i
$221$	16.4287	+	9.48509i	1.10511	+	0.638036i
$222$	1.42059	−	2.13780i	0.0953439	−	0.143480i
$223$	−3.74352	−	21.2306i	−0.250685	−	1.42170i	−0.806911	−	0.590673i	$-0.798862\pi$
$223$	−3.74352	−	21.2306i	−0.250685	−	1.42170i	0.556226	−	0.831031i	$-0.312249\pi$
$224$	1.72861	−	12.2648i	0.115498	−	0.819476i
$225$	−0.869867	−	0.316606i	−0.0579912	−	0.0211071i
$226$	0.969709	−	4.00692i	0.0645041	−	0.266536i
$227$	13.0082			0.863387			0.431693	−	0.902020i	$-0.357916\pi$
$227$	13.0082			0.863387			0.431693	+	0.902020i	$0.357916\pi$
$228$	10.9902	−	13.3255i	0.727844	−	0.882501i
$229$	12.4762			0.824449			0.412225	−	0.911082i	$-0.364752\pi$
$229$	12.4762			0.824449			0.412225	+	0.911082i	$0.364752\pi$
$230$	−2.59701	+	10.7311i	−0.171241	+	0.707585i
$231$	5.26668	+	1.91691i	0.346522	+	0.126124i
$232$	−21.7561	+	3.51847i	−1.42836	+	0.230999i
$233$	−3.93848	−	22.3362i	−0.258018	−	1.46329i	−0.788205	−	0.615413i	$-0.788989\pi$
$233$	−3.93848	−	22.3362i	−0.258018	−	1.46329i	0.530186	−	0.847881i	$-0.322122\pi$
$234$	−3.27316	+	4.92567i	−0.213973	+	0.322001i
$235$	−0.158377	−	0.0914389i	−0.0103314	−	0.00596481i
$236$	−14.3991	+	3.26902i	−0.937300	+	0.212795i
$237$	17.6591	+	14.8177i	1.14708	+	0.962514i
$238$	−12.9772	−	0.817479i	−0.841187	−	0.0529893i
$239$	−24.7712	+	14.3017i	−1.60232	+	0.925097i	−0.611292	+	0.791405i	$0.709350\pi$
$239$	−24.7712	+	14.3017i	−1.60232	+	0.925097i	−0.991023	+	0.133692i	$0.957317\pi$
$240$	7.14841	−	3.42219i	0.461428	−	0.220901i
$241$	8.91259	+	24.4871i	0.574110	+	1.57736i	0.797946	+	0.602728i	$0.205920\pi$
$241$	8.91259	+	24.4871i	0.574110	+	1.57736i	−0.223836	+	0.974627i	$0.571858\pi$
$242$	−9.10093	+	9.55541i	−0.585030	+	0.614245i
$243$	1.61612	−	9.16545i	0.103674	−	0.587964i
$244$	−3.40914	+	4.48991i	−0.218248	+	0.287437i
$245$	−1.68977	+	1.41789i	−0.107955	+	0.0905854i
$246$	23.6384	−	17.4249i	1.50713	−	1.11097i
$247$	17.4355	−	9.15186i	1.10940	−	0.582319i
$248$	−4.28008	+	1.48935i	−0.271785	+	0.0945740i
$249$	−7.04542	−	8.39641i	−0.446486	−	0.532101i
$250$	0.399185	+	1.35671i	0.0252467	+	0.0858056i
$251$	−10.7702	−	1.89908i	−0.679809	−	0.119869i	−0.176927	−	0.984224i	$-0.556616\pi$
$251$	−10.7702	−	1.89908i	−0.679809	−	0.119869i	−0.502882	+	0.864355i	$0.667727\pi$
$252$	0.508697	−	4.02167i	0.0320449	−	0.253342i
$253$	9.47783	−	3.44965i	0.595866	−	0.216877i
$254$	−1.88004	+	0.210731i	−0.117964	+	0.0132225i
$255$	−4.16004	−	7.20541i	−0.260512	−	0.451220i
$256$	−5.16576	+	15.1431i	−0.322860	+	0.946447i
$257$	−17.5407	+	20.9042i	−1.09416	+	1.30397i	−0.144907	+	0.989445i	$0.546288\pi$
$257$	−17.5407	+	20.9042i	−1.09416	+	1.30397i	−0.949251	+	0.314521i	$0.898156\pi$
$258$	−10.3404	−	4.51859i	−0.643767	−	0.281315i
$259$	−1.00286	+	1.73700i	−0.0623144	+	0.107932i
$260$	9.02436	−	0.439945i	0.559667	−	0.0272843i
$261$	−7.10332	+	1.25251i	−0.439685	+	0.0775283i
$262$	3.08857	+	6.22311i	0.190812	+	0.384465i
$263$	0.0231579	−	0.0636259i	0.00142798	−	0.00392334i	−0.938977	−	0.343981i	$-0.888224\pi$
$263$	0.0231579	−	0.0636259i	0.00142798	−	0.00392334i	0.940405	+	0.340058i	$0.110447\pi$
$264$	−6.21801	−	3.70866i	−0.382692	−	0.228252i
$265$		−	11.4154i		−	0.701242i
$266$	−7.91631	+	10.9321i	−0.485380	+	0.670288i
$267$			32.4408i			1.98534i
$268$	7.11054	+	16.9227i	0.434345	+	1.03372i
$269$	8.21093	−	22.5593i	0.500629	−	1.37547i	−0.390032	−	0.920801i	$-0.627536\pi$
$269$	8.21093	−	22.5593i	0.500629	−	1.37547i	0.890662	−	0.454667i	$-0.150242\pi$
$270$	−5.20633	+	2.58393i	−0.316847	+	0.157253i
$271$	−28.6082	+	5.04439i	−1.73782	+	0.306425i	−0.950640	−	0.310296i	$-0.899572\pi$
$271$	−28.6082	+	5.04439i	−1.73782	+	0.306425i	−0.787182	+	0.616721i	$0.788461\pi$
$272$	16.2679	+	4.18233i	0.986387	+	0.253591i
$273$	9.79910	−	16.9725i	0.593069	−	1.02722i
$274$	12.4136	−	28.4075i	0.749932	−	1.71616i
$275$	0.830431	−	0.989670i	0.0500769	−	0.0596793i
$276$	−16.7546	−	26.0070i	−1.00851	−	1.56544i
$277$	2.89701	+	5.01778i	0.174065	+	0.301489i	0.939837	−	0.341623i	$-0.110976\pi$
$277$	2.89701	+	5.01778i	0.174065	+	0.301489i	−0.765772	+	0.643112i	$0.777643\pi$
$278$	1.71523	+	15.3024i	0.102872	+	0.917778i
$279$	−1.39373	+	0.507277i	−0.0834406	+	0.0303699i
$280$	−5.40672	+	3.02004i	−0.323113	+	0.180482i
$281$	−18.1992	−	3.20900i	−1.08567	−	0.191433i	−0.397949	−	0.917408i	$-0.630278\pi$
$281$	−18.1992	−	3.20900i	−1.08567	−	0.191433i	−0.687722	+	0.725974i	$0.741389\pi$
$282$	0.491592	−	0.144641i	0.0292739	−	0.00861327i
$283$	8.16320	+	9.72852i	0.485252	+	0.578301i	0.952003	−	0.306088i	$-0.0990202\pi$
$283$	8.16320	+	9.72852i	0.485252	+	0.578301i	−0.466751	+	0.884389i	$0.654576\pi$
$284$	2.80891	−	9.06909i	0.166678	−	0.538151i
$285$	−8.62946	−	0.347374i	−0.511165	−	0.0205767i
$286$	−4.89743	−	6.64380i	−0.289591	−	0.392856i
$287$	−17.5789	+	14.7504i	−1.03765	+	0.870691i
$288$	−1.62012	+	4.97959i	−0.0954668	+	0.293425i
$289$	0.110014	−	0.623920i	0.00647141	−	0.0367012i
$290$	7.97934	+	7.59982i	0.468563	+	0.446277i
$291$	3.44975	+	9.47810i	0.202228	+	0.555616i
$292$	3.49491	+	3.77534i	0.204524	+	0.220935i
$293$	16.7147	−	9.65026i	0.976486	−	0.563774i	0.0752785	−	0.997163i	$-0.476015\pi$
$293$	16.7147	−	9.65026i	0.976486	−	0.563774i	0.901207	+	0.433388i	$0.142682\pi$
$294$	0.388581	−	6.16860i	0.0226625	−	0.359760i
$295$	5.65551	+	4.74554i	0.329277	+	0.276296i
$296$	1.69343	−	1.96093i	0.0984289	−	0.113977i
$297$	4.59831	+	2.65483i	0.266821	+	0.154049i
$298$	−16.1230	−	10.7139i	−0.933980	−	0.620641i
$299$	−6.12433	−	34.7328i	−0.354179	−	2.00865i
$300$	−3.52418	−	1.81188i	−0.203469	−	0.104609i
$301$	8.28619	+	3.01593i	0.477608	+	0.173835i
$302$	−4.27010	−	1.03340i	−0.245717	−	0.0594655i
$303$	−11.7365			−0.674243
$304$	12.6940	−	11.9525i	0.728050	−	0.685524i
$305$	2.81876			0.161402
$306$	5.34309	+	1.29307i	0.305444	+	0.0739201i
$307$	11.2786	+	4.10507i	0.643702	+	0.234289i	0.643184	−	0.765711i	$-0.277613\pi$
$307$	11.2786	+	4.10507i	0.643702	+	0.234289i	0.000518029		1.00000i	$0.499835\pi$
$308$	5.03144	+	2.58681i	0.286693	+	0.147397i
$309$	1.99616	+	11.3208i	0.113558	+	0.644017i
$310$	1.88722	+	1.25408i	0.107187	+	0.0712270i
$311$	8.04275	+	4.64348i	0.456062	+	0.263308i	0.710387	−	0.703811i	$-0.248520\pi$
$311$	8.04275	+	4.64348i	0.456062	+	0.263308i	−0.254325	+	0.967119i	$0.581853\pi$
$312$	−16.5469	+	19.1606i	−0.936783	+	1.08476i
$313$	−14.5905	−	12.2429i	−0.824705	−	0.692010i	0.129364	−	0.991597i	$-0.458707\pi$
$313$	−14.5905	−	12.2429i	−0.824705	−	0.692010i	−0.954069	+	0.299587i	$0.903151\pi$
$314$	−1.00907	+	16.0187i	−0.0569451	+	0.903985i
$315$	−1.75531	+	1.01343i	−0.0989006	+	0.0571003i
$316$	15.8075	+	17.0760i	0.889243	+	0.960597i
$317$	−8.89622	−	24.4422i	−0.499662	−	1.37281i	−0.891603	−	0.452819i	$-0.850419\pi$
$317$	−8.89622	−	24.4422i	−0.499662	−	1.37281i	0.391941	−	0.919990i	$-0.371804\pi$
$318$	23.1618	+	22.0602i	1.29885	+	1.23707i
$319$	1.74803	−	9.91358i	0.0978710	−	0.555054i
$320$	7.59220	−	2.52162i	0.424417	−	0.140963i
$321$	24.7202	−	20.7427i	1.37974	−	1.15774i
$322$	14.3441	+	19.4591i	0.799365	+	1.08441i
$323$	−13.5371	−	12.3201i	−0.753225	−	0.685506i
$324$	6.46164	−	20.8626i	0.358980	−	1.15903i
$325$	−2.90382	−	3.46063i	−0.161075	−	0.191961i
$326$	20.0514	−	5.89973i	1.11054	−	0.326756i
$327$	−9.22569	−	1.62674i	−0.510182	−	0.0899588i
$328$	25.8797	−	14.4557i	1.42897	−	0.798181i
$329$	−0.376273	+	0.136952i	−0.0207446	+	0.00755042i
$330$	0.403236	+	3.59748i	0.0221974	+	0.198035i
$331$	8.29050	+	14.3596i	0.455687	+	0.789273i	0.998727	−	0.0504337i	$-0.0160604\pi$
$331$	8.29050	+	14.3596i	0.455687	+	0.789273i	−0.543041	+	0.839706i	$0.682727\pi$
$332$	−5.99199	−	9.30095i	−0.328853	−	0.510456i
$333$	0.545063	−	0.649581i	0.0298693	−	0.0355968i
$334$	6.72836	−	15.3973i	0.368159	−	0.842504i
$335$	4.58897	−	7.94834i	0.250722	−	0.434264i
$336$	4.32079	−	16.8065i	0.235718	−	0.916868i
$337$	−1.74633	+	0.307926i	−0.0951289	+	0.0167738i	−0.221010	−	0.975272i	$-0.570935\pi$
$337$	−1.74633	+	0.307926i	−0.0951289	+	0.0167738i	0.125881	+	0.992045i	$0.459824\pi$
$338$	−9.38446	+	4.65757i	−0.510447	+	0.253338i
$339$	1.97545	−	5.42749i	0.107291	−	0.294781i
$340$	−3.25332	−	7.74274i	−0.176436	−	0.419909i
$341$		−	2.06996i		−	0.112095i
$342$	4.09856	−	3.97044i	0.221624	−	0.214697i
$343$			20.1567i			1.08836i
$344$	−9.78294	−	5.83492i	−0.527461	−	0.314598i
$345$	−5.29050	+	14.5355i	−0.284831	+	0.782566i
$346$	4.21827	+	8.49933i	0.226776	+	0.456927i
$347$	−7.38708	+	1.30254i	−0.396559	+	0.0699241i	−0.368372	−	0.929679i	$-0.620085\pi$
$347$	−7.38708	+	1.30254i	−0.396559	+	0.0699241i	−0.0281873	+	0.999603i	$0.508973\pi$
$348$	−30.8401	+	1.50348i	−1.65320	+	0.0805951i
$349$	−1.46884	+	2.54411i	−0.0786253	+	0.136183i	−0.902657	−	0.430361i	$-0.858386\pi$
$349$	−1.46884	+	2.54411i	−0.0786253	+	0.136183i	0.824032	+	0.566544i	$0.191720\pi$
$350$	2.83742	+	1.23990i	0.151667	+	0.0662757i
$351$	11.9344	−	14.2229i	0.637011	−	0.759160i
$352$	−5.75719	−	4.50164i	−0.306859	−	0.239938i
$353$	4.66770	+	8.08470i	0.248437	+	0.430305i	0.963092	−	0.269171i	$-0.0867498\pi$
$353$	4.66770	+	8.08470i	0.248437	+	0.430305i	−0.714655	+	0.699477i	$0.753417\pi$
$354$	−20.5580	+	2.30431i	−1.09264	+	0.122473i
$355$	−4.46078	+	1.62359i	−0.236753	+	0.0861712i
$356$	−4.10930	+	32.4875i	−0.217793	+	1.72183i
$357$	−17.9406	−	3.16340i	−0.949515	−	0.167425i
$358$	7.40895	+	25.1808i	0.391575	+	1.33084i
$359$	−5.98924	−	7.13770i	−0.316100	−	0.376713i	0.584477	−	0.811411i	$-0.301300\pi$
$359$	−5.98924	−	7.13770i	−0.316100	−	0.376713i	−0.900577	+	0.434697i	$0.856855\pi$
$360$	2.47282	−	0.860475i	0.130329	−	0.0453510i
$361$	−18.3187	+	5.04226i	−0.964143	+	0.265382i
$362$	−0.401655	+	0.296077i	−0.0211105	+	0.0155615i
$363$	−14.1624	+	11.8837i	−0.743334	+	0.623732i
$364$	11.9631	−	15.7557i	0.627039	−	0.825824i
$365$	0.446681	−	2.53325i	0.0233803	−	0.132597i
$366$	−5.44724	+	5.71926i	−0.284732	+	0.298951i
$367$	−3.80625	−	10.4576i	−0.198685	−	0.545881i	0.799838	−	0.600216i	$-0.204919\pi$
$367$	−3.80625	−	10.4576i	−0.198685	−	0.545881i	−0.998523	+	0.0543343i	$0.982696\pi$
$368$	−13.4844	−	28.1668i	−0.702924	−	1.46830i
$369$	8.40193	−	4.85086i	0.437387	−	0.252526i
$370$	−1.29291	−	0.0814446i	−0.0672150	−	0.00423410i
$371$	−19.1470	−	16.0662i	−0.994063	−	0.834118i
$372$	−6.19158	+	1.40567i	−0.321018	+	0.0728806i
$373$	−25.9924	−	15.0067i	−1.34583	−	0.777017i	−0.358177	−	0.933654i	$-0.616602\pi$
$373$	−25.9924	−	15.0067i	−1.34583	−	0.777017i	−0.987656	+	0.156636i	$0.949935\pi$
$374$	−4.24624	+	6.39002i	−0.219568	+	0.330420i
$375$	0.344055	+	1.95124i	0.0177669	+	0.100761i
$376$	0.510622	−	0.0825794i	0.0263333	−	0.00425871i
$377$	−33.0773	−	12.0392i	−1.70357	−	0.620048i
$378$	−2.99346	+	12.3692i	−0.153967	+	0.636205i
$379$	5.04463			0.259125			0.129563	−	0.991571i	$-0.458643\pi$
$379$	5.04463			0.259125			0.129563	+	0.991571i	$0.458643\pi$
$380$	−8.59788	−	1.44098i	−0.441062	−	0.0739205i
$381$	−2.65047			−0.135788
$382$	1.15744	−	4.78263i	0.0592197	−	0.244701i
$383$	6.88904	+	2.50740i	0.352013	+	0.128122i	0.511974	−	0.859001i	$-0.328914\pi$
$383$	6.88904	+	2.50740i	0.352013	+	0.128122i	−0.159960	+	0.987123i	$0.551137\pi$
$384$	−9.55552	+	20.2776i	−0.487628	+	1.03479i
$385$	−0.491205	−	2.78576i	−0.0250341	−	0.141976i
$386$	−10.5075	+	15.8124i	−0.534820	+	0.804832i
$387$	−3.22857	−	1.86402i	−0.164118	−	0.0947533i
$388$	2.25412	+	9.92874i	0.114435	+	0.504055i
$389$	−20.2543	−	16.9954i	−1.02694	−	0.861701i	−0.0364526	−	0.999335i	$-0.511606\pi$
$389$	−20.2543	−	16.9954i	−1.02694	−	0.861701i	−0.990483	+	0.137634i	$0.956050\pi$
$390$	12.6332	+	0.795811i	0.639709	+	0.0402975i
$391$	−28.3914	+	16.3918i	−1.43582	+	0.828969i
$392$	1.17052	−	6.12827i	0.0591204	−	0.309524i
$393$	3.32903	+	9.14642i	0.167927	+	0.461376i
$394$	19.7458	−	20.7319i	0.994778	−	1.04446i
$395$	2.02035	−	11.4580i	0.101655	−	0.576512i
$396$	−1.90495	−	1.44641i	−0.0957274	−	0.0726847i
$397$	−7.44283	+	6.24527i	−0.373545	+	0.313441i	−0.810162	−	0.586206i	$-0.800621\pi$
$397$	−7.44283	+	6.24527i	−0.373545	+	0.313441i	0.436617	+	0.899647i	$0.356176\pi$
$398$	−2.38186	+	1.75577i	−0.119392	+	0.0880087i
$399$	−12.7279	+	13.9853i	−0.637193	+	0.700139i
$400$	−3.29974	−	2.26090i	−0.164987	−	0.113045i
$401$	−23.8773	−	28.4559i	−1.19238	−	1.42102i	−0.882546	−	0.470226i	$-0.844172\pi$
$401$	−23.8773	−	28.4559i	−1.19238	−	1.42102i	−0.309830	−	0.950792i	$-0.600272\pi$
$402$	7.25901	+	24.6712i	0.362047	+	1.23049i
$403$	−7.12820	−	1.25689i	−0.355081	−	0.0626103i
$404$	−11.7534	−	1.48667i	−0.584752	−	0.0739646i
$405$	−10.2616	+	3.73492i	−0.509903	+	0.185590i
$406$	23.9775	−	2.68760i	1.18998	−	0.133383i
$407$	0.591723	+	1.02489i	0.0293306	+	0.0508021i
$408$	21.9971	+	8.36183i	1.08902	+	0.413972i
$409$	4.06396	−	4.84324i	0.200950	−	0.239483i	−0.656153	−	0.754628i	$-0.727818\pi$
$409$	4.06396	−	4.84324i	0.200950	−	0.239483i	0.857103	+	0.515145i	$0.172262\pi$
$410$	−13.5815	−	5.93490i	−0.670744	−	0.293104i
$411$	21.7167	−	37.6144i	1.07121	−	1.85538i
$412$	0.565020	+	11.5899i	0.0278366	+	0.570996i
$413$	15.9194	−	2.80702i	0.783341	−	0.138124i
$414$	−4.54364	−	9.15491i	−0.223308	−	0.449939i
$415$	−1.89205	+	5.19837i	−0.0928772	+	0.255178i
$416$	−18.9978	+	17.0922i	−0.931444	+	0.838015i
$417$			21.5732i			1.05644i
$418$	3.25069	+	7.27031i	0.158997	+	0.355602i
$419$		−	25.9110i		−	1.26583i	−0.774220	−	0.632917i	$-0.781857\pi$
$419$		−	25.9110i		−	1.26583i	0.774220	−	0.632917i	$-0.218143\pi$
$420$	−7.99907	+	3.36102i	−0.390315	+	0.164001i
$421$	8.49411	−	23.3374i	0.413978	−	1.13739i	−0.541079	−	0.840972i	$-0.681984\pi$
$421$	8.49411	−	23.3374i	0.413978	−	1.13739i	0.955057	−	0.296423i	$-0.0957937\pi$
$422$	−7.46228	+	3.70358i	−0.363258	+	0.180287i
$423$	0.166717	−	0.0293967i	0.00810605	−	0.00142932i
$424$	20.4008	+	25.0259i	0.990751	+	1.21536i
$425$	−2.09962	+	3.63664i	−0.101846	+	0.176403i
$426$	5.32616	−	12.1885i	0.258054	−	0.590535i
$427$	3.96718	−	4.72790i	0.191985	−	0.228799i
$428$	27.3832	−	17.6412i	1.32362	−	0.852721i
$429$	−5.78184	−	10.0144i	−0.279150	−	0.483502i
$430$	0.634421	+	5.66000i	0.0305945	+	0.272949i
$431$	−17.7777	+	6.47056i	−0.856322	+	0.311676i	−0.732615	−	0.680643i	$-0.761701\pi$
$431$	−17.7777	+	6.47056i	−0.856322	+	0.311676i	−0.123707	+	0.992319i	$0.539478\pi$
$432$	6.79597	−	14.9691i	0.326971	−	0.720203i
$433$	−3.37452	−	0.595018i	−0.162169	−	0.0285948i	0.0919741	−	0.995761i	$-0.470682\pi$
$433$	−3.37452	−	0.595018i	−0.162169	−	0.0285948i	−0.254143	+	0.967167i	$0.581793\pi$
$434$	4.75958	−	1.40041i	0.228467	−	0.0672221i
$435$	9.92358	+	11.8265i	0.475799	+	0.567036i
$436$	−9.03292	−	2.79771i	−0.432598	−	0.133986i
$437$	−1.36876	+	34.0026i	−0.0654764	+	1.62656i
$438$	4.27677	+	5.80182i	0.204352	+	0.277222i
$439$	−23.6939	+	19.8816i	−1.13085	+	0.948895i	−0.999101	−	0.0423886i	$-0.986503\pi$
$439$	−23.6939	+	19.8816i	−1.13085	+	0.948895i	−0.131747	+	0.991283i	$0.542059\pi$
$440$	−0.0518791	+	3.65374i	−0.00247324	+	0.174185i
$441$	0.354577	−	2.01091i	0.0168846	−	0.0957575i
$442$	19.4266	+	18.5026i	0.924027	+	0.880077i
$443$	−7.87237	−	21.6292i	−0.374028	−	1.02763i	−0.973789	−	0.227454i	$-0.926960\pi$
$443$	−7.87237	−	21.6292i	−0.374028	−	1.02763i	0.599761	−	0.800179i	$-0.295262\pi$
$444$	2.66379	−	2.46592i	0.126418	−	0.117027i
$445$	14.1796	−	8.18659i	0.672177	−	0.388082i
$446$	1.91673	−	30.4274i	0.0907597	−	1.44078i
$447$	−20.7760	−	17.4331i	−0.982670	−	0.824558i
$448$	6.45590	−	16.2834i	0.305013	−	0.769316i
$449$	−13.6870	−	7.90217i	−0.645928	−	0.372926i	0.140967	−	0.990014i	$-0.454979\pi$
$449$	−13.6870	−	7.90217i	−0.645928	−	0.372926i	−0.786894	+	0.617088i	$0.788312\pi$
$450$	−1.09034	−	0.724546i	−0.0513993	−	0.0341554i
$451$	2.35119	+	13.3343i	0.110713	+	0.627886i
$452$	2.66580	−	5.18508i	0.125389	−	0.243886i
$453$	−5.78398	−	2.10520i	−0.271755	−	0.0989107i
$454$	17.8803	+	4.32718i	0.839162	+	0.203084i
$455$	−9.89141			−0.463716
$456$	19.5391	−	14.6604i	0.915003	−	0.686538i
$457$	22.5800			1.05625			0.528125	−	0.849167i	$-0.322895\pi$
$457$	22.5800			1.05625			0.528125	+	0.849167i	$0.322895\pi$
$458$	17.1489	+	4.15019i	0.801317	+	0.193926i
$459$	−16.2176	−	5.90273i	−0.756973	−	0.275516i
$460$	−7.13935	+	13.8863i	−0.332874	+	0.647452i
$461$	0.325413	+	1.84551i	0.0151560	+	0.0859538i	0.991448	−	0.130506i	$-0.0416601\pi$
$461$	0.325413	+	1.84551i	0.0151560	+	0.0859538i	−0.976292	+	0.216460i	$0.930549\pi$
$462$	6.60157	+	4.38682i	0.307133	+	0.204093i
$463$	19.0509	+	10.9990i	0.885369	+	0.511168i	0.872425	−	0.488748i	$-0.162546\pi$
$463$	19.0509	+	10.9990i	0.885369	+	0.511168i	0.0129441	+	0.999916i	$0.495880\pi$
$464$	−31.0750	−	2.40090i	−1.44262	−	0.111459i
$465$	2.43186	+	2.04057i	0.112775	+	0.0946293i
$466$	2.01655	−	32.0120i	0.0934147	−	1.48293i
$467$	−1.02822	+	0.593642i	−0.0475802	+	0.0274705i	−0.523601	−	0.851963i	$-0.675412\pi$
$467$	−1.02822	+	0.593642i	−0.0475802	+	0.0274705i	0.476021	+	0.879434i	$0.342079\pi$
$468$	−6.13759	+	5.68169i	−0.283710	+	0.262636i
$469$	−6.87312	−	18.8837i	−0.317371	−	0.871970i
$470$	−0.187277	−	0.178370i	−0.00863845	−	0.00822758i
$471$	−3.90480	+	22.1452i	−0.179924	+	1.02040i
$472$	−20.8795	−	0.296466i	−0.961055	−	0.0136459i
$473$	3.98568	−	3.34439i	0.183262	−	0.153775i
$474$	19.3439	+	26.2417i	0.888495	+	1.20532i
$475$	2.02585	+	3.85952i	0.0929524	+	0.177087i
$476$	−17.5657	−	5.44051i	−0.805122	−	0.249365i
$477$	6.79243	+	8.09491i	0.311004	+	0.370640i
$478$	−38.8063	+	11.4180i	−1.77496	+	0.522247i
$479$	13.8408	+	2.44051i	0.632404	+	0.111510i	0.480656	−	0.876909i	$-0.340399\pi$
$479$	13.8408	+	2.44051i	0.632404	+	0.111510i	0.151748	+	0.988419i	$0.451510\pi$
$480$	10.9641	−	2.32600i	0.500441	−	0.106167i
$481$	3.88866	−	1.41536i	0.177308	−	0.0645347i
$482$	4.10504	+	36.6232i	0.186979	+	1.66814i
$483$	16.9345	+	29.3313i	0.770544	+	1.33462i
$484$	−15.6881	+	10.1068i	−0.713097	+	0.459401i
$485$	3.27224	−	3.89970i	0.148585	−	0.177076i
$486$	5.27028	−	12.0606i	0.239065	−	0.547081i
$487$	21.3490	−	36.9775i	0.967414	−	1.67561i	0.264431	−	0.964405i	$-0.414816\pi$
$487$	21.3490	−	36.9775i	0.967414	−	1.67561i	0.702983	−	0.711207i	$-0.251851\pi$
$488$	−6.17955	+	5.03749i	−0.279735	+	0.228037i
$489$	28.8382	−	5.08495i	1.30411	−	0.229950i
$490$	−2.79430	+	1.38683i	−0.126234	+	0.0626507i
$491$	10.4057	−	28.5895i	0.469603	−	1.29022i	−0.448464	−	0.893801i	$-0.648029\pi$
$491$	10.4057	−	28.5895i	0.469603	−	1.29022i	0.918068	−	0.396424i	$-0.129749\pi$
$492$	38.2882	−	16.0878i	1.72616	−	0.725294i
$493$			32.7200i			1.47363i
$494$	27.0101	−	6.77963i	1.21524	−	0.305030i
$495$			1.19592i			0.0537528i
$496$	−6.37855	+	0.623402i	−0.286405	+	0.0279916i
$497$	−3.55494	+	9.76713i	−0.159461	+	0.438116i
$498$	−6.89112	−	13.8848i	−0.308798	−	0.622193i
$499$	37.0657	−	6.53568i	1.65929	−	0.292577i	0.736085	−	0.676889i	$-0.236672\pi$
$499$	37.0657	−	6.53568i	1.65929	−	0.292577i	0.923203	+	0.384312i	$0.125561\pi$
$500$	0.0973861	+	1.99763i	0.00435524	+	0.0893366i
$501$	11.7708	−	20.3876i	0.525880	−	0.910851i
$502$	−14.1723	−	6.19304i	−0.632540	−	0.276409i
$503$	−2.75267	+	3.28050i	−0.122735	+	0.146270i	−0.823913	−	0.566716i	$-0.808214\pi$
$503$	−2.75267	+	3.28050i	−0.122735	+	0.146270i	0.701178	+	0.712987i	$0.252658\pi$
$504$	2.03703	−	5.35871i	0.0907364	−	0.238696i
$505$	2.96176	+	5.12991i	0.131796	+	0.228278i
$506$	14.1751	−	1.58887i	0.630161	−	0.0706338i
$507$	−13.7928	+	5.02018i	−0.612561	+	0.222954i
$508$	−2.65429	−	0.335737i	−0.117765	−	0.0148959i
$509$	23.2550	+	4.10048i	1.03076	+	0.181751i	0.663350	−	0.748309i	$-0.269134\pi$
$509$	23.2550	+	4.10048i	1.03076	+	0.181751i	0.367409	+	0.930060i	$0.380245\pi$
$510$	−3.32125	−	11.2879i	−0.147068	−	0.499837i
$511$	−3.62035	−	4.31457i	−0.160155	−	0.190865i
$512$	−12.1379	+	19.0964i	−0.536423	+	0.843949i
$513$	−14.1755	+	10.9540i	−0.625862	+	0.483631i
$514$	−31.0640	+	22.8986i	−1.37017	+	1.01001i
$515$	4.44448	−	3.72936i	0.195847	−	0.164335i
$516$	−12.7102	−	9.65068i	−0.559534	−	0.424848i
$517$	−0.0410268	+	0.232674i	−0.00180435	+	0.0102330i
$518$	−1.95627	+	2.05396i	−0.0859536	+	0.0902460i
$519$	4.54668	+	12.4919i	0.199577	+	0.548334i
$520$	12.5506	+	2.39722i	0.550382	+	0.105125i
$521$	11.2260	−	6.48134i	0.491821	−	0.283953i	−0.233509	−	0.972355i	$-0.575021\pi$
$521$	11.2260	−	6.48134i	0.491821	−	0.283953i	0.725329	+	0.688402i	$0.241687\pi$
$522$	−10.1804	−	0.641299i	−0.445584	−	0.0280689i
$523$	−21.5486	−	18.0814i	−0.942255	−	0.790646i	0.0357214	−	0.999362i	$-0.488627\pi$
$523$	−21.5486	−	18.0814i	−0.942255	−	0.790646i	−0.977976	+	0.208716i	$0.933072\pi$
$524$	2.17523	+	9.58129i	0.0950255	+	0.418560i
$525$	3.75703	+	2.16912i	0.163970	+	0.0946684i
$526$	0.0529964	−	0.0797525i	0.00231075	−	0.00347737i
$527$	1.16833	+	6.62594i	0.0508934	+	0.288631i
$528$	−7.31319	−	7.16610i	−0.318266	−	0.311864i
$529$	35.6613	+	12.9796i	1.55049	+	0.564332i
$530$	3.79732	−	15.6908i	0.164945	−	0.681566i
$531$	−6.83416			−0.296577
$532$	−14.5178	+	12.3932i	−0.629426	+	0.537311i
$533$	47.3460			2.05078
$534$	−10.7914	+	44.5910i	−0.466989	+	1.92964i
$535$	−15.3047	−	5.57045i	−0.661680	−	0.240832i
$536$	4.14435	+	25.6262i	0.179009	+	1.10688i
$537$	6.38574	+	36.2153i	0.275565	+	1.56281i
$538$	18.7906	−	28.2772i	0.810118	−	1.21912i
$539$	2.46797	+	1.42488i	0.106303	+	0.0613741i
$540$	−8.01582	+	1.81983i	−0.344946	+	0.0783129i
$541$	−15.4251	−	12.9432i	−0.663176	−	0.556471i	0.247861	−	0.968796i	$-0.420272\pi$
$541$	−15.4251	−	12.9432i	−0.663176	−	0.556471i	−0.911037	+	0.412325i	$0.864717\pi$
$542$	−41.0009	−	2.58279i	−1.76114	−	0.110940i
$543$	−0.605429	+	0.349545i	−0.0259815	+	0.0150004i
$544$	20.9696	+	11.1603i	0.899062	+	0.478492i
$545$	1.61711	+	4.44299i	0.0692696	+	0.190317i
$546$	19.1151	−	20.0697i	0.818051	−	0.858903i
$547$	−3.81947	+	21.6613i	−0.163309	+	0.926171i	0.787482	+	0.616338i	$0.211384\pi$
$547$	−3.81947	+	21.6613i	−0.163309	+	0.926171i	−0.950791	+	0.309833i	$0.899727\pi$
$548$	26.5126	−	34.9177i	1.13256	−	1.49161i
$549$	−1.99884	+	1.67723i	−0.0853086	+	0.0715824i
$550$	1.47067	−	1.08409i	0.0627095	−	0.0462259i
$551$	28.7069	+	18.1514i	1.22295	+	0.773274i
$552$	−14.3786	−	41.3210i	−0.611993	−	1.75874i
$553$	−16.3749	−	19.5149i	−0.696333	−	0.829857i
$554$	2.31289	+	7.86079i	0.0982652	+	0.333973i
$555$	−1.78740	−	0.315167i	−0.0758709	−	0.0133781i
$556$	−2.73270	+	21.6043i	−0.115892	+	0.916225i
$557$	22.9155	−	8.34058i	0.970963	−	0.353402i	0.192643	−	0.981269i	$-0.438294\pi$
$557$	22.9155	−	8.34058i	0.970963	−	0.353402i	0.778320	+	0.627867i	$0.216072\pi$
$558$	−2.08448	+	0.233646i	−0.0882430	+	0.00989103i
$559$	−9.09671	−	15.7560i	−0.384750	−	0.666406i
$560$	−8.43634	+	2.35261i	−0.356500	+	0.0994161i
$561$	−6.90926	+	8.23414i	−0.291709	+	0.347646i
$562$	−23.9479	−	10.4648i	−1.01018	−	0.441432i
$563$	−13.8351	+	23.9630i	−0.583078	+	1.00992i	0.412034	+	0.911169i	$0.364819\pi$
$563$	−13.8351	+	23.9630i	−0.583078	+	1.00992i	−0.995112	+	0.0987526i	$0.968515\pi$
$564$	0.723825	−	0.0352871i	0.0304785	−	0.00148586i
$565$	−2.87082	+	0.506204i	−0.120777	+	0.0212962i
$566$	7.98441	+	16.0877i	0.335610	+	0.676215i
$567$	−8.17782	+	22.4684i	−0.343436	+	0.943583i
$568$	6.87777	−	11.5314i	0.288585	−	0.483846i
$569$			25.6287i			1.07441i	0.843452	+	0.537204i	$0.180520\pi$
$569$			25.6287i			1.07441i	−0.843452	+	0.537204i	$0.819480\pi$
$570$	−11.7459	−	3.34806i	−0.491983	−	0.140235i
$571$		−	2.53311i		−	0.106007i	−0.998594	−	0.0530037i	$-0.983120\pi$
$571$		−	2.53311i		−	0.106007i	0.998594	−	0.0530037i	$-0.0168795\pi$
$572$	−4.52163	−	10.7613i	−0.189059	−	0.449951i
$573$	2.35788	−	6.47821i	0.0985017	−	0.270631i
$574$	−29.0695	+	14.4274i	−1.21334	+	0.602188i
$575$	7.68844	−	1.35568i	0.320630	−	0.0565357i
$576$	−3.88337	+	6.30568i	−0.161807	+	0.262737i
$577$	5.13545	−	8.89487i	0.213792	−	0.370298i	−0.739106	−	0.673589i	$-0.764752\pi$
$577$	5.13545	−	8.89487i	0.213792	−	0.370298i	0.952898	+	0.303291i	$0.0980853\pi$
$578$	0.358764	−	0.821004i	0.0149226	−	0.0341492i
$579$	−17.0973	+	20.3758i	−0.710540	+	0.846789i
$580$	8.43981	+	13.1005i	0.350444	+	0.543970i
$581$	6.05631	+	10.4898i	0.251258	+	0.435191i
$582$	1.58892	+	14.1755i	0.0658626	+	0.587595i
$583$	−13.8584	+	5.04404i	−0.573956	+	0.208903i
$584$	3.54800	+	6.35192i	0.146817	+	0.262844i
$585$	4.11832	+	0.726171i	0.170272	+	0.0300235i
$586$	26.1851	−	7.70447i	1.08170	−	0.318269i
$587$	30.0628	+	35.8275i	1.24083	+	1.47876i	0.820769	+	0.571260i	$0.193545\pi$
$587$	30.0628	+	35.8275i	1.24083	+	1.47876i	0.420056	+	0.907498i	$0.362010\pi$
$588$	2.58610	−	8.34969i	0.106649	−	0.344336i
$589$	6.46141	+	2.65070i	0.266238	+	0.109220i
$590$	6.19510	+	8.40421i	0.255048	+	0.345996i
$591$	30.7274	−	25.7834i	1.26396	−	1.06059i
$592$	2.97998	−	2.13205i	0.122477	−	0.0876265i
$593$	0.217227	−	1.23195i	0.00892044	−	0.0505903i	−0.980023	−	0.198886i	$-0.936268\pi$
$593$	0.217227	−	1.23195i	0.00892044	−	0.0505903i	0.988943	+	0.148296i	$0.0473787\pi$
$594$	5.43740	+	5.17878i	0.223099	+	0.212488i
$595$	3.14469	+	8.63997i	0.128920	+	0.354204i
$596$	−18.5976	−	20.0899i	−0.761789	−	0.822916i
$597$	−3.59026	+	2.07284i	−0.146940	+	0.0848356i
$598$	3.13573	−	49.7787i	0.128230	−	2.03560i
$599$	11.6153	+	9.74643i	0.474590	+	0.398228i	0.848466	−	0.529251i	$-0.177527\pi$
$599$	11.6153	+	9.74643i	0.474590	+	0.398228i	−0.373876	+	0.927479i	$0.621971\pi$
$600$	−4.24139	−	3.66281i	−0.173154	−	0.149534i
$601$	−38.0644	−	21.9765i	−1.55268	−	0.896440i	−0.997922	−	0.0644268i	$-0.979478\pi$
$601$	−38.0644	−	21.9765i	−1.55268	−	0.896440i	−0.554756	−	0.832013i	$-0.687189\pi$
$602$	10.3864	+	6.90188i	0.423318	+	0.281300i
$603$	1.47531	+	8.36689i	0.0600792	+	0.340726i
$604$	−5.52564	−	2.84089i	−0.224835	−	0.115594i
$605$	8.76821	+	3.19137i	0.356479	+	0.129748i
$606$	−16.1322	−	3.90413i	−0.655325	−	0.158594i
$607$	−25.7674			−1.04587			−0.522934	−	0.852373i	$-0.675162\pi$
$607$	−25.7674			−1.04587			−0.522934	+	0.852373i	$0.675162\pi$
$608$	21.4243	−	12.2065i	0.868870	−	0.495040i
$609$	33.8032			1.36977
$610$	3.87448	+	0.937657i	0.156873	+	0.0379646i
$611$	0.776333	+	0.282562i	0.0314071	+	0.0114312i
$612$	6.91412	+	3.55475i	0.279487	+	0.143692i
$613$	3.48096	+	19.7415i	0.140595	+	0.797352i	0.970799	+	0.239893i	$0.0771125\pi$
$613$	3.48096	+	19.7415i	0.140595	+	0.797352i	−0.830205	+	0.557459i	$0.811776\pi$
$614$	14.1372	+	9.39436i	0.570533	+	0.379126i
$615$	−17.9833	−	10.3827i	−0.725158	−	0.418670i
$616$	6.05539	+	5.22936i	0.243979	+	0.210697i
$617$	0.897505	+	0.753096i	0.0361322	+	0.0303185i	0.660675	−	0.750672i	$-0.270270\pi$
$617$	0.897505	+	0.753096i	0.0361322	+	0.0303185i	−0.624543	+	0.780991i	$0.714715\pi$
$618$	−1.02206	+	16.2248i	−0.0411132	+	0.652658i
$619$	3.68904	−	2.12987i	0.148275	−	0.0856067i	−0.424027	−	0.905650i	$-0.639384\pi$
$619$	3.68904	−	2.12987i	0.148275	−	0.0856067i	0.572302	+	0.820043i	$0.306050\pi$
$620$	2.17688	+	2.35156i	0.0874257	+	0.0944408i
$621$	10.9741	+	30.1511i	0.440376	+	1.20992i
$622$	9.51038	+	9.05804i	0.381332	+	0.363194i
$623$	6.22529	−	35.3054i	0.249411	−	1.41448i
$624$	−29.1180	+	20.8326i	−1.16565	+	0.833973i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−15.9826	−	21.6818i	−0.638793	−	0.866580i
$627$	3.39132	+	10.6297i	0.135436	+	0.424511i
$628$	−6.71559	+	21.6825i	−0.267981	+	0.865227i
$629$	−2.47258	−	2.94670i	−0.0985880	−	0.117493i
$630$	−2.74985	+	0.809091i	−0.109557	+	0.0322350i
$631$	40.0594	+	7.06355i	1.59474	+	0.281196i	0.899281	−	0.437371i	$-0.144090\pi$
$631$	40.0594	+	7.06355i	1.59474	+	0.281196i	0.695458	+	0.718566i	$0.255201\pi$
$632$	16.0477	+	28.7298i	0.638343	+	1.14281i
$633$	−10.9677	+	3.99192i	−0.435927	+	0.158664i
$634$	−4.09750	−	36.5559i	−0.162732	−	1.45182i
$635$	0.668859	+	1.15850i	0.0265428	+	0.0459736i
$636$	24.4984	+	38.0272i	0.971426	+	1.50788i
$637$	6.40535	−	7.63360i	0.253789	−	0.302454i
$638$	5.70047	−	13.0451i	0.225684	−	0.516460i
$639$	2.19716	−	3.80559i	0.0869183	−	0.150547i
$640$	11.2745	−	0.940516i	0.445666	−	0.0371772i
$641$	−29.4624	+	5.19502i	−1.16370	+	0.205191i	−0.721948	−	0.691948i	$-0.756753\pi$
$641$	−29.4624	+	5.19502i	−1.16370	+	0.205191i	−0.441749	+	0.897139i	$0.645642\pi$
$642$	40.8787	−	20.2884i	1.61335	−	0.800718i
$643$	12.0728	−	33.1698i	0.476106	−	1.30809i	−0.436667	−	0.899623i	$-0.643841\pi$
$643$	12.0728	−	33.1698i	0.476106	−	1.30809i	0.912773	−	0.408467i	$-0.133937\pi$
$644$	13.2434	+	31.5187i	0.521864	+	1.24201i
$645$			7.97941i			0.314189i
$646$	−14.5090	−	21.4375i	−0.570848	−	0.843445i
$647$			3.28925i			0.129314i	0.997908	+	0.0646568i	$0.0205953\pi$
$647$			3.28925i			0.129314i	−0.997908	+	0.0646568i	$0.979405\pi$
$648$	15.8217	−	26.5269i	0.621534	−	1.04207i
$649$	3.26217	−	8.96273i	0.128051	−	0.351818i
$650$	−2.84022	−	5.72271i	−0.111403	−	0.224463i
$651$	6.84530	−	1.20701i	0.268288	−	0.0473065i
$652$	29.5239	−	1.43931i	1.15624	−	0.0563679i
$653$	−15.9137	+	27.5634i	−0.622753	+	1.07864i	0.366218	+	0.930529i	$0.380652\pi$
$653$	−15.9137	+	27.5634i	−0.622753	+	1.07864i	−0.988971	+	0.148110i	$0.952681\pi$
$654$	−12.1399	−	5.30492i	−0.474707	−	0.207439i
$655$	3.15773	−	3.76323i	0.123383	−	0.147042i
$656$	40.3812	−	11.2610i	1.57662	−	0.439667i
$657$	1.19060	+	2.06217i	0.0464496	+	0.0804530i
$658$	−0.562757	+	0.0630786i	−0.0219386	+	0.00245906i
$659$	−0.310492	+	0.113010i	−0.0120950	+	0.00440224i	−0.348061	−	0.937472i	$-0.613160\pi$
$659$	−0.310492	+	0.113010i	−0.0120950	+	0.00440224i	0.335966	+	0.941874i	$0.390937\pi$
$660$	−0.642436	+	5.07899i	−0.0250068	+	0.197700i
$661$	−9.26849	−	1.63428i	−0.360502	−	0.0635663i	−0.00953646	−	0.999955i	$-0.503036\pi$
$661$	−9.26849	−	1.63428i	−0.360502	−	0.0635663i	−0.350966	+	0.936388i	$0.614147\pi$
$662$	6.61888	+	22.4955i	0.257250	+	0.874314i
$663$	24.1600	+	28.7928i	0.938297	+	1.11822i
$664$	−5.14224	−	14.7777i	−0.199558	−	0.573486i
$665$	9.32480	+	2.03402i	0.361600	+	0.0788757i
$666$	0.965291	−	0.711557i	0.0374043	−	0.0275723i
$667$	46.5997	−	39.1018i	1.80435	−	1.51403i
$668$	14.3703	−	18.9260i	0.556002	−	0.732267i
$669$	7.41718	−	42.0649i	0.286765	−	1.62632i
$670$	8.95171	−	9.39874i	0.345835	−	0.363105i
$671$	−1.24551	−	3.42200i	−0.0480822	−	0.132105i
$672$	11.5297	−	21.6638i	0.444769	−	0.835698i
$673$	−25.3526	+	14.6374i	−0.977273	+	0.564229i	−0.901446	−	0.432892i	$-0.857493\pi$
$673$	−25.3526	+	14.6374i	−0.977273	+	0.564229i	−0.0758271	+	0.997121i	$0.524160\pi$
$674$	−2.50283	−	0.157662i	−0.0964053	−	0.00607290i
$675$	3.14837	+	2.64179i	0.121181	+	0.101683i
$676$	−14.4486	+	3.28026i	−0.555715	+	0.126164i
$677$	−1.08122	−	0.624242i	−0.0415546	−	0.0239916i	0.479079	−	0.877772i	$-0.340971\pi$
$677$	−1.08122	−	0.624242i	−0.0415546	−	0.0239916i	−0.520633	+	0.853780i	$0.674304\pi$
$678$	4.52077	−	6.80314i	0.173619	−	0.261273i
$679$	−1.93555	−	10.9770i	−0.0742795	−	0.421260i
$680$	−1.89618	−	11.7249i	−0.0727154	−	0.449629i
$681$	24.2193	+	8.81512i	0.928087	+	0.337796i
$682$	0.688571	−	2.84524i	0.0263668	−	0.108950i
$683$	−35.6390			−1.36369			−0.681844	−	0.731498i	$-0.738822\pi$
$683$	−35.6390			−1.36369			−0.681844	+	0.731498i	$0.738822\pi$
$684$	6.95437	−	4.09412i	0.265907	−	0.156543i
$685$	−21.9213			−0.837568
$686$	−6.70511	+	27.7061i	−0.256002	+	1.05782i
$687$	23.2287	+	8.45457i	0.886232	+	0.322562i
$688$	−11.5060	−	11.2746i	−0.438662	−	0.429840i
$689$	8.95494	+	50.7860i	0.341156	+	1.93479i
$690$	−12.1072	+	18.2197i	−0.460913	+	0.693612i
$691$	40.9046	+	23.6163i	1.55608	+	0.898405i	0.997626	+	0.0688718i	$0.0219399\pi$
$691$	40.9046	+	23.6163i	1.55608	+	0.898405i	0.558457	+	0.829533i	$0.311393\pi$
$692$	2.97087	+	13.0858i	0.112935	+	0.497449i
$693$	2.00592	+	1.68317i	0.0761986	+	0.0639383i
$694$	−10.5871	−	0.666916i	−0.401880	−	0.0253158i
$695$	9.42946	−	5.44410i	0.357680	−	0.206506i
$696$	−42.8909	−	8.19234i	−1.62577	−	0.310530i
$697$	−15.0523	−	41.3558i	−0.570146	−	1.56646i
$698$	−2.86527	+	3.00836i	−0.108452	+	0.113868i
$699$	7.80345	−	44.2556i	0.295154	−	1.67390i
$700$	3.48768	+	2.64816i	0.131822	+	0.100091i
$701$	−5.47588	+	4.59481i	−0.206821	+	0.173544i	−0.740315	−	0.672261i	$-0.765323\pi$
$701$	−5.47588	+	4.59481i	−0.206821	+	0.173544i	0.533493	+	0.845804i	$0.320879\pi$
$702$	21.1355	−	15.5798i	0.797706	−	0.588023i
$703$	−3.95695	+	0.534637i	−0.149239	+	0.0201642i
$704$	−6.41598	−	8.10279i	−0.241811	−	0.305385i
$705$	−0.232909	−	0.277570i	−0.00877186	−	0.0104539i
$706$	3.72655	+	12.6654i	0.140251	+	0.476669i
$707$	12.7728	+	2.25219i	0.480372	+	0.0847025i
$708$	−29.0242	−	3.67123i	−1.09079	−	0.137973i
$709$	−11.5660	+	4.20970i	−0.434372	+	0.158099i	−0.549946	−	0.835200i	$-0.685352\pi$
$709$	−11.5660	+	4.20970i	−0.434372	+	0.158099i	0.115574	+	0.993299i	$0.463129\pi$
$710$	−6.67158	+	0.747807i	−0.250380	+	0.0280647i
$711$	5.38509	+	9.32725i	0.201957	+	0.349799i
$712$	−16.4553	+	43.2882i	−0.616689	+	1.62230i
$713$	8.04045	−	9.58224i	0.301117	−	0.358858i
$714$	−23.6076	−	10.3161i	−0.883492	−	0.386071i
$715$	−2.91815	+	5.05439i	−0.109133	+	0.189023i
$716$	1.80751	+	37.0764i	0.0675497	+	1.38561i
$717$	−55.8118	+	9.84112i	−2.08433	+	0.367523i
$718$	−5.85807	−	11.8033i	−0.218621	−	0.440496i
$719$	9.31093	−	25.5816i	0.347239	−	0.954031i	−0.635997	−	0.771692i	$-0.719411\pi$
$719$	9.31093	−	25.5816i	0.347239	−	0.954031i	0.983236	−	0.182339i	$-0.0583669\pi$
$720$	3.68522	−	0.360171i	0.137340	−	0.0134228i
$721$		−	12.7035i		−	0.473103i
$722$	−26.8570	+	0.837059i	−0.999515	+	0.0311521i
$723$			51.6310i			1.92018i
$724$	−0.650578	+	0.273358i	−0.0241786	+	0.0101593i
$725$	2.66498	−	7.32198i	0.0989750	−	0.271932i
$726$	−23.4198	+	11.6234i	−0.869191	+	0.431385i
$727$	−15.2599	+	2.69073i	−0.565959	+	0.0997938i	−0.449304	−	0.893379i	$-0.648328\pi$
$727$	−15.2599	+	2.69073i	−0.565959	+	0.0997938i	−0.116654	+	0.993173i	$0.537217\pi$
$728$	21.6849	−	17.6773i	0.803695	−	0.655163i
$729$	−7.16027	+	12.4020i	−0.265195	+	0.459332i
$730$	1.45666	−	3.33346i	0.0539135	−	0.123377i
$731$	−10.8705	+	12.9550i	−0.402060	+	0.479157i
$732$	−9.38992	+	6.04930i	−0.347061	+	0.223589i
$733$	19.2675	+	33.3722i	0.711660	+	1.23263i	0.964234	+	0.265053i	$0.0853895\pi$
$733$	19.2675	+	33.3722i	0.711660	+	1.23263i	−0.252574	+	0.967578i	$0.581277\pi$
$734$	−1.75311	−	15.6404i	−0.0647087	−	0.577299i
$735$	−4.10693	+	1.49480i	−0.151486	+	0.0551366i
$736$	−9.16513	−	43.2018i	−0.337831	−	1.59244i
$737$	−11.6771	−	2.05898i	−0.430130	−	0.0758435i
$738$	13.1624	−	3.87278i	0.484514	−	0.142559i
$739$	−24.2525	−	28.9029i	−0.892141	−	1.06321i	−0.997631	−	0.0687918i	$-0.978086\pi$
$739$	−24.2525	−	28.9029i	−0.892141	−	1.06321i	0.105490	−	0.994420i	$-0.466359\pi$
$740$	−1.75005	−	0.542033i	−0.0643332	−	0.0199255i
$741$	38.6641	−	5.22405i	1.42036	−	0.191910i
$742$	−20.9738	−	28.4528i	−0.769972	−	1.04454i
$743$	6.59531	−	5.53412i	0.241958	−	0.203027i	−0.513742	−	0.857945i	$-0.671741\pi$
$743$	6.59531	−	5.53412i	0.241958	−	0.203027i	0.755700	+	0.654918i	$0.227297\pi$
$744$	−8.97813	−	0.127480i	−0.329154	−	0.00467363i
$745$	−2.37695	+	13.4803i	−0.0870846	+	0.493882i
$746$	−30.7354	−	29.2736i	−1.12530	−	1.07178i
$747$	−1.75146	−	4.81210i	−0.0640826	−	0.176065i
$748$	−7.96224	+	7.37080i	−0.291128	+	0.269503i
$749$	−30.8835	+	17.8306i	−1.12846	+	0.651515i
$750$	−0.176160	+	2.79649i	−0.00643247	+	0.102113i
$751$	−34.7067	−	29.1224i	−1.26646	−	1.06269i	−0.994962	−	0.100252i	$-0.968035\pi$
$751$	−34.7067	−	29.1224i	−1.26646	−	1.06269i	−0.271503	−	0.962438i	$-0.587521\pi$
$752$	0.729337	+	0.0563496i	0.0265962	+	0.00205486i
$753$	−18.7655	−	10.8343i	−0.683854	−	0.394824i
$754$	−41.4611	−	27.5514i	−1.50992	−	1.00336i
$755$	0.539452	+	3.05938i	0.0196327	+	0.111342i
$756$	−8.22923	+	16.0062i	−0.299294	+	0.582139i
$757$	−2.24560	−	0.817332i	−0.0816178	−	0.0297064i	0.300889	−	0.953659i	$-0.402717\pi$
$757$	−2.24560	−	0.817332i	−0.0816178	−	0.0297064i	−0.382506	+	0.923953i	$0.624939\pi$
$758$	6.93401	+	1.67809i	0.251855	+	0.0609510i
$759$	19.9839			0.725371
$760$	−11.3387	−	4.84075i	−0.411300	−	0.175592i
$761$	−34.1499			−1.23793			−0.618967	−	0.785417i	$-0.712449\pi$
$761$	−34.1499			−1.23793			−0.618967	+	0.785417i	$0.712449\pi$
$762$	−3.64316	−	0.881675i	−0.131978	−	0.0319397i
$763$	9.72818	+	3.54077i	0.352184	+	0.128184i
$764$	3.18188	−	6.18887i	0.115116	−	0.223905i
$765$	−0.675005	−	3.82815i	−0.0244049	−	0.138407i
$766$	8.63513	+	5.73815i	0.312000	+	0.207328i
$767$	−28.8835	−	16.6759i	−1.04292	−	0.602133i
$768$	−19.8797	+	24.6936i	−0.717347	+	0.891054i
$769$	−11.4917	−	9.64269i	−0.414401	−	0.347724i	0.411627	−	0.911352i	$-0.364961\pi$
$769$	−11.4917	−	9.64269i	−0.414401	−	0.347724i	−0.826029	+	0.563628i	$0.809405\pi$
$770$	0.251503	−	3.99253i	0.00906353	−	0.143881i
$771$	−46.8239	+	27.0338i	−1.68632	+	0.973598i
$772$	−19.7030	+	18.2394i	−0.709125	+	0.656451i
$773$	−1.44066	−	3.95817i	−0.0518168	−	0.142365i	0.911084	−	0.412220i	$-0.135247\pi$
$773$	−1.44066	−	3.95817i	−0.0518168	−	0.142365i	−0.962901	+	0.269855i	$0.913024\pi$
$774$	−3.81772	−	3.63614i	−0.137225	−	0.130698i
$775$	0.278225	−	1.57789i	0.00999415	−	0.0566796i
$776$	−0.204425	+	14.3972i	−0.00733843	+	0.516830i
$777$	−3.04425	+	2.55443i	−0.109212	+	0.0916397i
$778$	−22.1868	−	30.0984i	−0.795435	−	1.07908i
$779$	−44.6339	−	9.73597i	−1.59917	−	0.348827i
$780$	17.1001	+	5.29631i	0.612282	+	0.189638i
$781$	3.94211	+	4.69802i	0.141060	+	0.168108i
$782$	−44.4777	+	13.0867i	−1.59052	+	0.467980i
$783$	31.5374	+	5.56089i	1.12705	+	0.198730i
$784$	3.64749	−	8.03414i	0.130267	−	0.286933i
$785$	10.6649	−	3.88171i	0.380647	−	0.138544i
$786$	1.53331	+	13.6795i	0.0546914	+	0.487930i
$787$	0.0582833	+	0.100950i	0.00207758	+	0.00359847i	0.867062	−	0.498200i	$-0.166005\pi$
$787$	0.0582833	+	0.100950i	0.00207758	+	0.00359847i	−0.864985	+	0.501798i	$0.832672\pi$
$788$	34.0377	−	21.9282i	1.21254	−	0.781161i
$789$	0.0862330	−	0.102769i	0.00306998	−	0.00365866i
$790$	6.58851	−	15.0773i	0.234409	−	0.536426i
$791$	−3.19140	+	5.52767i	−0.113473	+	0.196541i
$792$	−2.13727	−	2.62182i	−0.0759448	−	0.0931622i
$793$	−12.5404	+	2.21121i	−0.445322	+	0.0785223i
$794$	−12.3079	+	6.10849i	−0.436791	+	0.216782i
$795$	7.73571	−	21.2537i	0.274358	−	0.753791i
$796$	−3.85800	+	1.62104i	−0.136743	+	0.0574563i
$797$		−	51.6825i		−	1.83069i	−0.402673	−	0.915344i	$-0.631919\pi$
$797$		−	51.6825i		−	1.83069i	0.402673	−	0.915344i	$-0.368081\pi$
$798$	−22.1472	+	14.9893i	−0.784001	+	0.530616i
$799$		−	0.767946i		−	0.0271680i
$800$	−3.78353	−	4.20535i	−0.133768	−	0.148681i
$801$	−5.18385	+	14.2425i	−0.183162	+	0.503234i
$802$	−23.3544	−	47.0563i	−0.824671	−	1.66162i
$803$	−3.27277	+	0.577077i	−0.115493	+	0.0203646i
$804$	1.77093	+	36.3261i	0.0624558	+	1.28112i
$805$	8.54699	−	14.8038i	0.301242	−	0.521766i
$806$	−9.37984	−	4.09883i	−0.330391	−	0.144375i
$807$	30.5750	−	36.4379i	1.07629	−	1.28267i
$808$	−15.6609	−	5.95323i	−0.550948	−	0.209434i
$809$	1.18083	+	2.04525i	0.0415156	+	0.0719071i	0.886037	−	0.463615i	$-0.153448\pi$
$809$	1.18083	+	2.04525i	0.0415156	+	0.0719071i	−0.844521	+	0.535522i	$0.820115\pi$
$810$	−15.3473	+	1.72026i	−0.539251	+	0.0604438i
$811$	−14.7579	+	5.37144i	−0.518220	+	0.188617i	−0.587871	−	0.808955i	$-0.700034\pi$
$811$	−14.7579	+	5.37144i	−0.518220	+	0.188617i	0.0696508	+	0.997571i	$0.477811\pi$
$812$	33.8519	+	4.28188i	1.18797	+	0.150265i
$813$	−56.6824	−	9.99463i	−1.98794	−	0.350527i
$814$	0.472414	+	1.60559i	0.0165581	+	0.0562758i
$815$	−9.50005	−	11.3217i	−0.332772	−	0.396583i
$816$	27.4542	+	18.8109i	0.961088	+	0.658514i
$817$	5.33565	+	16.7240i	0.186671	+	0.585099i
$818$	7.19715	−	5.30532i	0.251642	−	0.185496i
$819$	7.01422	−	5.88563i	0.245097	−	0.205660i
$820$	−16.6940	−	12.6756i	−0.582981	−	0.442651i
$821$	−5.05077	+	28.6443i	−0.176273	+	0.999694i	0.760391	+	0.649465i	$0.225007\pi$
$821$	−5.05077	+	28.6443i	−0.176273	+	0.999694i	−0.936664	+	0.350228i	$0.886104\pi$
$822$	42.3627	−	44.4783i	1.47757	−	1.55136i
$823$	0.122761	+	0.337284i	0.00427920	+	0.0117570i	0.941814	−	0.336135i	$-0.109120\pi$
$823$	0.122761	+	0.337284i	0.00427920	+	0.0117570i	−0.937535	+	0.347892i	$0.886898\pi$
$824$	−3.07874	+	16.1187i	−0.107253	+	0.561523i
$825$	2.21679	−	1.27987i	0.0771788	−	0.0445592i
$826$	22.8155	+	1.43722i	0.793852	+	0.0500074i
$827$	21.1504	+	17.7473i	0.735472	+	0.617134i	0.931617	−	0.363441i	$-0.118398\pi$
$827$	21.1504	+	17.7473i	0.735472	+	0.617134i	−0.196146	+	0.980575i	$0.562843\pi$
$828$	−3.20002	−	14.0952i	−0.111208	−	0.489841i
$829$	3.78214	+	2.18362i	0.131359	+	0.0758403i	0.564240	−	0.825611i	$-0.309169\pi$
$829$	3.78214	+	2.18362i	0.131359	+	0.0758403i	−0.432880	+	0.901451i	$0.642503\pi$
$830$	−4.32992	+	6.51595i	−0.150294	+	0.226172i
$831$	1.99347	+	11.3055i	0.0691526	+	0.392184i
$832$	−31.7988	+	17.1742i	−1.10243	+	0.595409i
$833$	−8.70421	−	3.16807i	−0.301583	−	0.109767i
$834$	−7.17630	+	29.6531i	−0.248495	+	1.02680i
$835$	−11.8817			−0.411182
$836$	2.04973	+	11.0746i	0.0708914	+	0.383024i
$837$	6.58503			0.227612
$838$	8.61926	−	35.6155i	0.297747	−	1.23032i
$839$	32.7249	+	11.9109i	1.12979	+	0.411210i	0.838216	−	0.545338i	$-0.183599\pi$
$839$	32.7249	+	11.9109i	1.12979	+	0.411210i	0.291574	+	0.956548i	$0.405821\pi$
$840$	−12.1130	+	1.95896i	−0.417940	+	0.0675905i
$841$	−5.50700	−	31.2318i	−0.189897	−	1.07696i
$842$	19.4386	−	29.2525i	0.669899	−	1.00811i
$843$	−31.7094	−	18.3075i	−1.09213	−	0.630542i
$844$	−11.4892	+	2.60838i	−0.395473	+	0.0897841i
$845$	5.67496	+	4.76186i	0.195225	+	0.163813i
$846$	0.238937	+	0.0150514i	0.00821482	+	0.000517479i
$847$	17.6934	−	10.2153i	0.607954	−	0.351002i
$848$	19.7168	+	41.1852i	0.677077	+	1.41431i
$849$	8.60603	+	23.6449i	0.295358	+	0.811490i
$850$	−4.09572	+	4.30025i	−0.140482	+	0.147497i
$851$	−1.24185	+	7.04288i	−0.0425701	+	0.241427i
$852$	11.3755	−	14.9818i	0.389718	−	0.513267i
$853$	−12.3783	+	10.3866i	−0.423823	+	0.355630i	−0.829615	−	0.558336i	$-0.811440\pi$
$853$	−12.3783	+	10.3866i	−0.423823	+	0.355630i	0.405792	+	0.913965i	$0.366996\pi$
$854$	7.02575	−	5.17898i	0.240416	−	0.177221i
$855$	−3.73309	−	1.53144i	−0.127669	−	0.0523743i
$856$	43.5076	−	15.1395i	1.48706	−	0.517456i
$857$	15.5585	+	18.5419i	0.531467	+	0.633378i	0.963252	−	0.268599i	$-0.0865606\pi$
$857$	15.5585	+	18.5419i	0.531467	+	0.633378i	−0.431785	+	0.901976i	$0.642116\pi$
$858$	−4.61605	−	15.6885i	−0.157589	−	0.535597i
$859$	−0.572651	−	0.100974i	−0.0195386	−	0.00344518i	0.163870	−	0.986482i	$-0.447602\pi$
$859$	−0.572651	−	0.100974i	−0.0195386	−	0.00344518i	−0.183409	+	0.983037i	$0.558713\pi$
$860$	−1.01076	+	7.99090i	−0.0344666	+	0.272487i
$861$	−42.7250	+	15.5506i	−1.45606	+	0.529964i
$862$	−26.5885	+	2.98027i	−0.905608	+	0.101508i
$863$	25.1829	+	43.6180i	0.857235	+	1.48477i	0.874556	+	0.484924i	$0.161153\pi$
$863$	25.1829	+	43.6180i	0.857235	+	1.48477i	−0.0173211	+	0.999850i	$0.505514\pi$
$864$	14.3208	−	18.3149i	0.487202	−	0.623086i
$865$	4.31273	−	5.13971i	0.146637	−	0.174755i
$866$	−4.44046	−	1.94040i	−0.150893	−	0.0659376i
$867$	0.627633	−	1.08709i	0.0213155	−	0.0369196i
$868$	7.00805	−	0.341649i	0.237869	−	0.0115963i
$869$	−14.8028	+	2.61013i	−0.502150	+	0.0885426i
$870$	9.70624	+	19.5570i	0.329073	+	0.663043i
$871$	−14.1807	+	38.9613i	−0.480496	+	1.32015i
$872$	−11.4854	−	6.85034i	−0.388945	−	0.231982i
$873$			4.71243i			0.159492i
$874$	−13.1923	+	46.2824i	−0.446237	+	1.56553i
$875$		−	2.18956i		−	0.0740206i
$876$	3.94859	+	9.39746i	0.133411	+	0.317511i
$877$	10.3316	−	28.3858i	0.348873	−	0.958522i	−0.633852	−	0.773454i	$-0.718527\pi$
$877$	10.3316	−	28.3858i	0.348873	−	0.958522i	0.982726	−	0.185068i	$-0.0592505\pi$
$878$	−39.1817	+	19.4461i	−1.32232	+	0.656275i
$879$	37.6599	−	6.64045i	1.27024	−	0.223977i
$880$	−1.28672	+	5.00493i	−0.0433754	+	0.168716i
$881$	6.99092	−	12.1086i	0.235530	−	0.407950i	−0.723897	−	0.689909i	$-0.757651\pi$
$881$	6.99092	−	12.1086i	0.235530	−	0.407950i	0.959427	+	0.281958i	$0.0909840\pi$
$882$	1.15631	−	2.64611i	0.0389348	−	0.0890992i
$883$	−3.37021	+	4.01646i	−0.113417	+	0.135165i	−0.819766	−	0.572699i	$-0.805896\pi$
$883$	−3.37021	+	4.01646i	−0.113417	+	0.135165i	0.706349	+	0.707864i	$0.250341\pi$
$884$	20.5476	+	31.8946i	0.691091	+	1.07273i
$885$	7.31386	+	12.6680i	0.245853	+	0.425829i
$886$	−3.62593	−	32.3488i	−0.121815	−	1.08678i
$887$	−55.9468	+	20.3630i	−1.87851	+	0.683722i	−0.928819	+	0.370534i	$0.879175\pi$
$887$	−55.9468	+	20.3630i	−1.87851	+	0.683722i	−0.949691	+	0.313188i	$0.898603\pi$
$888$	4.48175	−	2.50338i	0.150398	−	0.0840080i
$889$	2.88451	+	0.508617i	0.0967434	+	0.0170585i
$890$	22.2136	−	6.53592i	0.744601	−	0.219085i
$891$	9.06845	+	10.8074i	0.303805	+	0.362060i
$892$	12.7563	−	41.1859i	0.427111	−	1.37901i
$893$	−0.673758	−	0.426017i	−0.0225465	−	0.0142561i
$894$	−22.7582	−	30.8735i	−0.761148	−	1.03257i
$895$	14.2179	−	11.9303i	0.475254	−	0.398785i
$896$	14.2905	−	20.2345i	0.477412	−	0.675987i
$897$	12.1344	−	68.8174i	0.405154	−	2.29774i
$898$	−16.1845	−	15.4148i	−0.540085	−	0.514397i
$899$	−4.26993	−	11.7315i	−0.142410	−	0.391269i
$900$	−1.25770	−	1.35862i	−0.0419232	−	0.0452872i
$901$	41.5137	−	23.9679i	1.38302	−	0.798487i
$902$	−1.20384	+	19.1105i	−0.0400834	+	0.636311i
$903$	13.3838	+	11.2304i	0.445387	+	0.373724i
$904$	5.38904	−	6.24029i	0.179237	−	0.207549i
$905$	0.305566	+	0.176419i	0.0101574	+	0.00586436i
$906$	−7.24998	−	4.81770i	−0.240865	−	0.160057i
$907$	−2.96464	−	16.8133i	−0.0984391	−	0.558276i	−0.993639	−	0.112611i	$-0.964079\pi$
$907$	−2.96464	−	16.8133i	−0.0984391	−	0.558276i	0.895200	−	0.445665i	$-0.147033\pi$
$908$	23.1376	+	11.8957i	0.767849	+	0.394773i
$909$	−5.15267	−	1.87542i	−0.170903	−	0.0622037i
$910$	−13.5961	−	3.29037i	−0.450706	−	0.109075i
$911$	38.8521			1.28723			0.643613	−	0.765351i	$-0.277435\pi$
$911$	38.8521			1.28723			0.643613	+	0.765351i	$0.277435\pi$
$912$	31.7340	−	13.6516i	1.05082	−	0.452050i
$913$	7.14690			0.236528
$914$	31.0370	+	7.51122i	1.02661	+	0.248449i
$915$	5.24809	+	1.91015i	0.173497	+	0.0631476i
$916$	22.1912	+	11.4092i	0.733219	+	0.376969i
$917$	−1.86781	−	10.5929i	−0.0616807	−	0.349809i
$918$	−20.3281	−	13.5083i	−0.670928	−	0.445839i
$919$	40.0921	+	23.1472i	1.32252	+	0.763556i	0.984130	−	0.177451i	$-0.0567853\pi$
$919$	40.0921	+	23.1472i	1.32252	+	0.763556i	0.338387	+	0.941007i	$0.390119\pi$
$920$	−14.4325	+	16.7123i	−0.475827	+	0.550988i
$921$	18.2172	+	15.2860i	0.600276	+	0.503691i
$922$	−0.166615	+	2.64496i	−0.00548718	+	0.0871072i
$923$	18.5719	−	10.7225i	0.611302	−	0.352936i
$924$	7.61481	+	8.22584i	0.250509	+	0.270610i
$925$	0.313303	+	0.860792i	0.0103013	+	0.0283027i
$926$	22.5273	+	21.4558i	0.740292	+	0.705081i
$927$	−0.932619	+	5.28915i	−0.0306312	+	0.173718i
$928$	−41.9149	−	13.6372i	−1.37593	−	0.447662i
$929$	40.2400	−	33.7654i	1.32023	−	1.10781i	0.333976	−	0.942582i	$-0.391610\pi$
$929$	40.2400	−	33.7654i	1.32023	−	1.10781i	0.986256	−	0.165224i	$-0.0528348\pi$
$930$	2.66388	+	3.61379i	0.0873521	+	0.118501i
$931$	−7.60816	+	5.87916i	−0.249347	+	0.192682i
$932$	13.4206	−	43.3308i	0.439606	−	1.41935i
$933$	11.8277	+	14.0957i	0.387221	+	0.461472i
$934$	−1.61079	+	0.473945i	−0.0527068	+	0.0155080i
$935$	5.34266	+	0.942055i	0.174724	+	0.0308085i
$936$	−10.3263	+	5.76801i	−0.337527	+	0.188533i
$937$	34.5874	−	12.5888i	1.12992	−	0.411258i	0.291657	−	0.956523i	$-0.405793\pi$
$937$	34.5874	−	12.5888i	1.12992	−	0.411258i	0.838264	+	0.545265i	$0.183571\pi$
$938$	−3.16568	−	28.2427i	−0.103363	−	0.922156i
$939$	−18.8688	−	32.6818i	−0.615761	−	1.06653i
$940$	−0.198084	−	0.307473i	−0.00646080	−	0.0100287i
$941$	−23.4769	+	27.9787i	−0.765327	+	0.912081i	−0.998172	−	0.0604331i	$-0.980752\pi$
$941$	−23.4769	+	27.9787i	−0.765327	+	0.912081i	0.232846	+	0.972514i	$0.425196\pi$
$942$	−12.7339	+	29.1405i	−0.414892	+	0.949448i
$943$	−40.9108	+	70.8596i	−1.33224	+	2.30751i
$944$	−28.6009	−	7.35304i	−0.930881	−	0.239321i
$945$	8.86215	−	1.56264i	0.288286	−	0.0508325i
$946$	6.59096	−	3.27114i	0.214291	−	0.106354i
$947$	−9.51078	+	26.1307i	−0.309059	+	0.849132i	0.683782	+	0.729686i	$0.260334\pi$
$947$	−9.51078	+	26.1307i	−0.309059	+	0.849132i	−0.992841	+	0.119446i	$0.961888\pi$
$948$	17.8596	+	42.5049i	0.580052	+	1.38049i
$949$			11.6206i			0.377221i
$950$	1.50074	+	5.97895i	0.0486903	+	0.193983i
$951$		−	51.5362i		−	1.67117i
$952$	−22.3349	−	13.3214i	−0.723877	−	0.431748i
$953$	3.45241	−	9.48542i	0.111835	−	0.307263i	−0.871132	−	0.491050i	$-0.836613\pi$
$953$	3.45241	−	9.48542i	0.111835	−	0.307263i	0.982966	+	0.183787i	$0.0588356\pi$
$954$	6.64367	+	13.3862i	0.215097	+	0.433395i
$955$	−3.42660	+	0.604201i	−0.110882	+	0.0195515i
$956$	−57.1388	+	2.78557i	−1.84800	+	0.0900916i
$957$	9.97257	−	17.2730i	0.322368	−	0.558357i
$958$	18.2129	+	7.95871i	0.588431	+	0.257134i
$959$	−30.8524	+	36.7685i	−0.996277	+	1.18732i
$960$	15.8443	+	0.450035i	0.511373	+	0.0145248i
$961$	14.2164	+	24.6236i	0.458594	+	0.794308i
$962$	5.81591	−	0.651897i	0.187512	−	0.0210180i
$963$	14.1675	−	5.15653i	0.456540	−	0.166167i
$964$	−6.54015	+	51.7054i	−0.210644	+	1.66532i
$965$	13.2207	+	2.33116i	0.425589	+	0.0750428i
$966$	13.5200	+	45.9502i	0.434997	+	1.47842i
$967$	−19.1468	−	22.8183i	−0.615720	−	0.733787i	0.364608	−	0.931161i	$-0.381203\pi$
$967$	−19.1468	−	22.8183i	−0.615720	−	0.733787i	−0.980328	+	0.197374i	$0.936759\pi$
$968$	−24.9259	+	8.67354i	−0.801149	+	0.278778i
$969$	−16.8553	−	32.1116i	−0.541469	−	1.03157i
$970$	5.79504	−	4.27177i	0.186067	−	0.137158i
$971$	5.20283	−	4.36569i	0.166967	−	0.140102i	−0.555476	−	0.831533i	$-0.687464\pi$
$971$	5.20283	−	4.36569i	0.166967	−	0.140102i	0.722443	+	0.691431i	$0.243019\pi$
$972$	11.2561	−	14.8246i	0.361041	−	0.475499i
$973$	4.13983	−	23.4782i	0.132717	−	0.752675i
$974$	41.6454	−	43.7251i	1.33441	−	1.40104i
$975$	−3.06134	−	8.41096i	−0.0980413	−	0.269366i
$976$	−10.1697	+	4.86859i	−0.325525	+	0.155840i
$977$	10.2026	−	5.89048i	0.326410	−	0.188453i	−0.327836	−	0.944735i	$-0.606319\pi$
$977$	10.2026	−	5.89048i	0.326410	−	0.188453i	0.654246	+	0.756282i	$0.272986\pi$
$978$	41.3306	+	2.60356i	1.32161	+	0.0832525i
$979$	−16.2040	−	13.5968i	−0.517883	−	0.434556i
$980$	−4.30220	+	0.976725i	−0.137429	+	0.0312003i
$981$	−3.79042	−	2.18840i	−0.121019	−	0.0698702i
$982$	23.8133	−	35.8358i	0.759912	−	1.14357i
$983$	7.75067	+	43.9562i	0.247208	+	1.40199i	0.815309	+	0.579027i	$0.196567\pi$
$983$	7.75067	+	43.9562i	0.247208	+	1.40199i	−0.568101	+	0.822959i	$0.692322\pi$
$984$	57.9800	−	9.37671i	1.84833	−	0.298919i
$985$	−19.0239	−	6.92414i	−0.606152	−	0.220621i
$986$	−10.8843	+	44.9747i	−0.346625	+	1.43229i
$987$	−0.793369			−0.0252532
$988$	39.3816	−	0.333948i	1.25289	−	0.0106243i
$989$	31.4412			0.999772
$990$	−0.397823	+	1.64384i	−0.0126436	+	0.0522446i
$991$	−51.3219	−	18.6796i	−1.63029	−	0.593378i	−0.644989	−	0.764192i	$-0.723138\pi$
$991$	−51.3219	−	18.6796i	−1.63029	−	0.593378i	−0.985303	+	0.170814i	$0.945360\pi$
$992$	−8.97491	−	1.26493i	−0.284954	−	0.0401616i
$993$	5.70478	+	32.3534i	0.181036	+	1.02670i
$994$	−8.13542	+	12.2427i	−0.258040	+	0.388315i
$995$	1.81204	+	1.04618i	0.0574455	+	0.0331662i
$996$	−4.85331	−	21.3775i	−0.153783	−	0.677371i
$997$	−7.88491	−	6.61622i	−0.249718	−	0.209538i	0.509333	−	0.860569i	$-0.329892\pi$
$997$	−7.88491	−	6.61622i	−0.249718	−	0.209538i	−0.759051	+	0.651032i	$0.774337\pi$
$998$	53.1222	+	3.34635i	1.68155	+	0.105927i
$999$	−3.26042	+	1.88241i	−0.103155	+	0.0595567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.19	yes	120
4.3	odd	2	inner	380.2.be.b.51.10	✓	120
19.3	odd	18	inner	380.2.be.b.231.10	yes	120
76.3	even	18	inner	380.2.be.b.231.19	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.10	✓	120	4.3	odd	2	inner
380.2.be.b.51.19	yes	120	1.1	even	1	trivial
380.2.be.b.231.10	yes	120	19.3	odd	18	inner
380.2.be.b.231.19	yes	120	76.3	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37453 + 0.332649i) q^{2} +(1.86185 + 0.677657i) q^{3} +(1.77869 + 0.914475i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.33375 + 1.55080i) q^{6} +(-1.89621 - 1.09478i) q^{7} +(2.14067 + 1.84866i) q^{8} +(0.709122 + 0.595024i) q^{9} +O(q^{10})\)	\(q+(1.37453 + 0.332649i) q^{2} +(1.86185 + 0.677657i) q^{3} +(1.77869 + 0.914475i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.33375 + 1.55080i) q^{6} +(-1.89621 - 1.09478i) q^{7} +(2.14067 + 1.84866i) q^{8} +(0.709122 + 0.595024i) q^{9} +(0.0889099 - 1.41142i) q^{10} +(-1.11884 + 0.645961i) q^{11} +(2.69195 + 2.90795i) q^{12} +(1.54509 + 4.24510i) q^{13} +(-2.24223 - 2.13558i) q^{14} +(0.344055 - 1.95124i) q^{15} +(2.32747 + 3.25313i) q^{16} +(3.21680 - 2.69921i) q^{17} +(0.776779 + 1.05377i) q^{18} +(-0.583643 - 4.31965i) q^{19} +(0.591716 - 1.91046i) q^{20} +(-2.78857 - 3.32329i) q^{21} +(-1.75276 + 0.515715i) q^{22} +(-7.68844 - 1.35568i) q^{23} +(2.73285 + 4.89256i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.711650 + 6.34900i) q^{26} +(-2.05495 - 3.55928i) q^{27} +(-2.37163 - 3.68131i) q^{28} +(-5.00853 + 5.96893i) q^{29} +(1.12199 - 2.56759i) q^{30} +(-0.801118 + 1.38758i) q^{31} +(2.11704 + 5.24577i) q^{32} +(-2.52084 + 0.444493i) q^{33} +(5.31949 - 2.64010i) q^{34} +(-0.748873 + 2.05751i) q^{35} +(0.717174 + 1.70684i) q^{36} -0.916035i q^{37} +(0.634690 - 6.13165i) q^{38} +8.95076i q^{39} +(1.44885 - 2.42916i) q^{40} +(3.58454 - 9.84843i) q^{41} +(-2.72750 - 5.49560i) q^{42} +(-3.96610 + 0.699331i) q^{43} +(-2.58078 + 0.125815i) q^{44} +(0.462847 - 0.801674i) q^{45} +(-10.1171 - 4.42098i) q^{46} +(0.117552 - 0.140092i) q^{47} +(2.12889 + 7.63406i) q^{48} +(-1.10292 - 1.91031i) q^{49} +(-1.40541 + 0.157531i) q^{50} +(7.81833 - 2.84564i) q^{51} +(-1.13380 + 8.96365i) q^{52} +(11.2420 + 1.98226i) q^{53} +(-1.64061 - 5.57592i) q^{54} +(0.830431 + 0.989670i) q^{55} +(-2.03530 - 5.84901i) q^{56} +(1.84059 - 8.43803i) q^{57} +(-8.86996 + 6.53842i) q^{58} +(-5.65551 + 4.74554i) q^{59} +(2.39632 - 3.15601i) q^{60} +(-0.489472 + 2.77593i) q^{61} +(-1.56274 + 1.64078i) q^{62} +(-0.693227 - 1.90462i) q^{63} +(1.16494 + 7.91473i) q^{64} +(3.91230 - 2.25877i) q^{65} +(-3.61285 - 0.227586i) q^{66} +(7.03072 + 5.89947i) q^{67} +(8.19005 - 1.85938i) q^{68} +(-13.3960 - 7.73419i) q^{69} +(-1.71378 + 2.57901i) q^{70} +(-0.824318 - 4.67494i) q^{71} +(0.418002 + 2.58467i) q^{72} +(2.41720 + 0.879790i) q^{73} +(0.304718 - 1.25912i) q^{74} -1.98134 q^{75} +(2.91209 - 8.21704i) q^{76} +2.82874 q^{77} +(-2.97746 + 12.3031i) q^{78} +(10.9331 + 3.97931i) q^{79} +(2.79955 - 2.85701i) q^{80} +(-1.89627 - 10.7543i) q^{81} +(8.20314 - 12.3446i) q^{82} +(-4.79084 - 2.76600i) q^{83} +(-1.92094 - 8.46118i) q^{84} +(-3.21680 - 2.69921i) q^{85} +(-5.68418 - 0.358066i) q^{86} +(-13.3700 + 7.71918i) q^{87} +(-3.58922 - 0.685556i) q^{88} +(5.59996 + 15.3858i) q^{89} +(0.902875 - 0.947963i) q^{90} +(1.71762 - 9.74113i) q^{91} +(-12.4356 - 9.44222i) q^{92} +(-2.43186 + 2.04057i) q^{93} +(0.208180 - 0.153458i) q^{94} +(-4.15267 + 1.32487i) q^{95} +(0.386765 + 11.2015i) q^{96} +(3.27224 + 3.89970i) q^{97} +(-0.880537 - 2.99267i) q^{98} +(-1.17776 - 0.207670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

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