LMFDB - Embedded newform 342.2.v.b.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(25,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 14]))

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

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

chi := DirichletCharacter("342.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	342.157
Dual form			342.2.v.b.61.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.349550 + 1.69641i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.92444 - 0.700437i) q^{5} +(-0.822662 + 1.52421i) q^{6} +(0.703408 - 1.21834i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.75563 + 1.18596i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.349550 + 1.69641i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.92444 - 0.700437i) q^{5} +(-0.822662 + 1.52421i) q^{6} +(0.703408 - 1.21834i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.75563 + 1.18596i) q^{9} +(1.92444 + 0.700437i) q^{10} +4.18241 q^{11} +(-1.60994 + 0.638818i) q^{12} +(2.00491 + 0.729728i) q^{13} +(1.32197 - 0.481159i) q^{14} +(1.86092 + 3.01980i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-6.80180 + 2.47565i) q^{17} +(-2.87326 - 0.862786i) q^{18} +(-4.20921 - 1.13250i) q^{19} +(1.02397 + 1.77357i) q^{20} +(2.31268 + 0.767400i) q^{21} +(3.20391 + 2.68840i) q^{22} +(-0.705455 - 4.00083i) q^{23} +(-1.64391 - 0.545487i) q^{24} +(-0.617381 + 0.518044i) q^{25} +(1.06679 + 1.84773i) q^{26} +(-2.97511 - 4.26013i) q^{27} +(1.32197 + 0.481159i) q^{28} +(-1.58877 - 9.01038i) q^{29} +(-0.515545 + 3.50947i) q^{30} -3.69336 q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.46196 + 7.09509i) q^{33} +(-6.80180 - 2.47565i) q^{34} +(0.500294 - 2.83731i) q^{35} +(-1.64645 - 2.50783i) q^{36} +8.68625 q^{37} +(-2.49649 - 3.57317i) q^{38} +(-0.537103 + 3.65623i) q^{39} +(-0.355621 + 2.01683i) q^{40} +(8.26453 + 6.93476i) q^{41} +(1.27834 + 2.07442i) q^{42} +(-1.10760 + 6.28152i) q^{43} +(0.726267 + 4.11887i) q^{44} +(-4.47234 + 4.21245i) q^{45} +(2.03128 - 3.51827i) q^{46} +(-1.57032 - 8.90575i) q^{47} +(-0.908677 - 1.47455i) q^{48} +(2.51043 + 4.34820i) q^{49} -0.805933 q^{50} +(-6.57729 - 10.6733i) q^{51} +(-0.370492 + 2.10117i) q^{52} +(4.42019 - 3.70898i) q^{53} +(0.459295 - 5.17581i) q^{54} +(8.04877 - 2.92951i) q^{55} +(0.703408 + 1.21834i) q^{56} +(0.449851 - 7.53642i) q^{57} +(4.57469 - 7.92359i) q^{58} +(1.87481 - 10.6326i) q^{59} +(-2.65078 + 2.35703i) q^{60} +(-1.06442 - 0.387417i) q^{61} +(-2.82928 - 2.37404i) q^{62} +(-0.493430 + 4.19150i) q^{63} +(-0.500000 - 0.866025i) q^{64} +4.36945 q^{65} +(-3.44071 + 6.37488i) q^{66} +(-2.94231 + 2.46889i) q^{67} +(-3.61916 - 6.26857i) q^{68} +(6.54047 - 2.59523i) q^{69} +(2.20703 - 1.85192i) q^{70} +(-3.85529 - 3.23497i) q^{71} +(0.350743 - 2.97943i) q^{72} +(-1.09776 + 6.22570i) q^{73} +(6.65405 + 5.58341i) q^{74} +(-1.09462 - 0.866250i) q^{75} +(0.384368 - 4.34192i) q^{76} +(2.94194 - 5.09559i) q^{77} +(-2.76162 + 2.45559i) q^{78} +(-1.24518 + 0.453209i) q^{79} +(-1.56881 + 1.31639i) q^{80} +(6.18699 - 6.53614i) q^{81} +(1.87342 + 10.6247i) q^{82} +(-1.25669 + 2.17665i) q^{83} +(-0.354149 + 2.41080i) q^{84} +(-11.3556 + 9.52846i) q^{85} +(-4.88615 + 4.09997i) q^{86} +(14.7300 - 5.84479i) q^{87} +(-2.09120 + 3.62207i) q^{88} +(-0.623365 - 3.53528i) q^{89} +(-6.13373 + 0.352160i) q^{90} +(2.29932 - 1.92936i) q^{91} +(3.81755 - 1.38947i) q^{92} +(-1.29101 - 6.26546i) q^{93} +(4.52157 - 7.83158i) q^{94} +(-8.89360 + 0.768874i) q^{95} +(0.251738 - 1.71366i) q^{96} +(-4.46477 - 3.74639i) q^{97} +(-0.871865 + 4.94459i) q^{98} +(-11.5252 + 4.96017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{3} + 6 q^{6} - 12 q^{7} - 33 q^{8} + 6 q^{9}+O(q^{10}) $ 66 * q + 6 * q^3 + 6 * q^6 - 12 * q^7 - 33 * q^8 + 6 * q^9	$ 66 q + 6 q^{3} + 6 q^{6} - 12 q^{7} - 33 q^{8} + 6 q^{9} - 3 q^{13} - 3 q^{14} - 3 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} + 6 q^{23} - 3 q^{24} - 12 q^{25} + 3 q^{27} - 3 q^{28} - 18 q^{29} + 45 q^{33} + 9 q^{34} - 18 q^{35} + 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{41} - 3 q^{43} - 12 q^{44} + 9 q^{45} - 18 q^{47} - 3 q^{48} - 57 q^{49} + 126 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} - 9 q^{54} + 36 q^{55} - 12 q^{56} + 48 q^{57} - 18 q^{58} - 39 q^{59} - 30 q^{60} - 54 q^{61} - 21 q^{62} - 54 q^{63} - 33 q^{64} + 24 q^{65} - 27 q^{66} + 6 q^{67} - 6 q^{68} - 15 q^{69} + 36 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} + 6 q^{74} + 15 q^{78} + 21 q^{79} + 138 q^{81} + 6 q^{82} + 12 q^{83} - 24 q^{84} - 36 q^{85} - 3 q^{86} + 30 q^{87} + 9 q^{89} - 42 q^{90} + 27 q^{91} - 12 q^{92} - 9 q^{93} - 6 q^{94} - 3 q^{95} - 30 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 66 * q + 6 * q^3 + 6 * q^6 - 12 * q^7 - 33 * q^8 + 6 * q^9 - 3 * q^13 - 3 * q^14 - 3 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 + 6 * q^23 - 3 * q^24 - 12 * q^25 + 3 * q^27 - 3 * q^28 - 18 * q^29 + 45 * q^33 + 9 * q^34 - 18 * q^35 + 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^41 - 3 * q^43 - 12 * q^44 + 9 * q^45 - 18 * q^47 - 3 * q^48 - 57 * q^49 + 126 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 - 9 * q^54 + 36 * q^55 - 12 * q^56 + 48 * q^57 - 18 * q^58 - 39 * q^59 - 30 * q^60 - 54 * q^61 - 21 * q^62 - 54 * q^63 - 33 * q^64 + 24 * q^65 - 27 * q^66 + 6 * q^67 - 6 * q^68 - 15 * q^69 + 36 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 + 6 * q^74 + 15 * q^78 + 21 * q^79 + 138 * q^81 + 6 * q^82 + 12 * q^83 - 24 * q^84 - 36 * q^85 - 3 * q^86 + 30 * q^87 + 9 * q^89 - 42 * q^90 + 27 * q^91 - 12 * q^92 - 9 * q^93 - 6 * q^94 - 3 * q^95 - 30 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.349550	+	1.69641i	0.201813	+	0.979424i
$3$	0.349550	+	1.69641i	0.201813	+	0.979424i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	1.92444	−	0.700437i	0.860634	−	0.313245i	0.126266	−	0.991996i	$-0.459701\pi$
$5$	1.92444	−	0.700437i	0.860634	−	0.313245i	0.734368	+	0.678751i	$0.237479\pi$
$6$	−0.822662	+	1.52421i	−0.335850	+	0.622258i
$7$	0.703408	−	1.21834i	0.265863	−	0.460489i	−0.701926	−	0.712250i	$-0.747676\pi$
$7$	0.703408	−	1.21834i	0.265863	−	0.460489i	0.967789	+	0.251761i	$0.0810097\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.75563	+	1.18596i	−0.918543	+	0.395320i
$10$	1.92444	+	0.700437i	0.608560	+	0.221498i
$11$	4.18241			1.26104			0.630522	−	0.776172i	$-0.282841\pi$
$11$	4.18241			1.26104			0.630522	+	0.776172i	$0.282841\pi$
$12$	−1.60994	+	0.638818i	−0.464750	+	0.184411i
$13$	2.00491	+	0.729728i	0.556062	+	0.202390i	0.604738	−	0.796425i	$-0.293278\pi$
$13$	2.00491	+	0.729728i	0.556062	+	0.202390i	−0.0486759	+	0.998815i	$0.515500\pi$
$14$	1.32197	−	0.481159i	0.353313	−	0.128595i
$15$	1.86092	+	3.01980i	0.480487	+	0.779709i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−6.80180	+	2.47565i	−1.64968	+	0.600434i	−0.988691	−	0.149964i	$-0.952084\pi$
$17$	−6.80180	+	2.47565i	−1.64968	+	0.600434i	−0.660986	+	0.750398i	$0.729862\pi$
$18$	−2.87326	−	0.862786i	−0.677233	−	0.203361i
$19$	−4.20921	−	1.13250i	−0.965659	−	0.259812i
$19$	−4.20921	−	1.13250i	−0.965659	−	0.259812i
$20$	1.02397	+	1.77357i	0.228967	+	0.396582i
$21$	2.31268	+	0.767400i	0.504668	+	0.167460i
$22$	3.20391	+	2.68840i	0.683076	+	0.573169i
$23$	−0.705455	−	4.00083i	−0.147098	−	0.834231i	−0.965659	−	0.259813i	$-0.916339\pi$
$23$	−0.705455	−	4.00083i	−0.147098	−	0.834231i	0.818562	−	0.574419i	$-0.194772\pi$
$24$	−1.64391	−	0.545487i	−0.335562	−	0.111347i
$25$	−0.617381	+	0.518044i	−0.123476	+	0.103609i
$26$	1.06679	+	1.84773i	0.209215	+	0.362371i
$27$	−2.97511	−	4.26013i	−0.572560	−	0.819863i
$28$	1.32197	+	0.481159i	0.249830	+	0.0909306i
$29$	−1.58877	−	9.01038i	−0.295028	−	1.67319i	−0.667090	−	0.744977i	$-0.732460\pi$
$29$	−1.58877	−	9.01038i	−0.295028	−	1.67319i	0.372062	−	0.928208i	$-0.378651\pi$
$30$	−0.515545	+	3.50947i	−0.0941251	+	0.640740i
$31$	−3.69336			−0.663346			−0.331673	−	0.943394i	$-0.607613\pi$
$31$	−3.69336			−0.663346			−0.331673	+	0.943394i	$0.607613\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	1.46196	+	7.09509i	0.254494	+	1.23510i
$34$	−6.80180	−	2.47565i	−1.16650	−	0.424571i
$35$	0.500294	−	2.83731i	0.0845651	−	0.479593i
$36$	−1.64645	−	2.50783i	−0.274409	−	0.417971i
$37$	8.68625			1.42801			0.714005	−	0.700140i	$-0.246879\pi$
$37$	8.68625			1.42801			0.714005	+	0.700140i	$0.246879\pi$
$38$	−2.49649	−	3.57317i	−0.404984	−	0.579645i
$39$	−0.537103	+	3.65623i	−0.0860053	+	0.585465i
$40$	−0.355621	+	2.01683i	−0.0562287	+	0.318889i
$41$	8.26453	+	6.93476i	1.29070	+	1.08303i	0.991673	+	0.128785i	$0.0411076\pi$
$41$	8.26453	+	6.93476i	1.29070	+	1.08303i	0.299030	+	0.954244i	$0.403337\pi$
$42$	1.27834	+	2.07442i	0.197252	+	0.320091i
$43$	−1.10760	+	6.28152i	−0.168908	+	0.957923i	0.776036	+	0.630689i	$0.217228\pi$
$43$	−1.10760	+	6.28152i	−0.168908	+	0.957923i	−0.944943	+	0.327234i	$0.893884\pi$
$44$	0.726267	+	4.11887i	0.109489	+	0.620942i
$45$	−4.47234	+	4.21245i	−0.666697	+	0.627955i
$46$	2.03128	−	3.51827i	0.299495	−	0.518741i
$47$	−1.57032	−	8.90575i	−0.229055	−	1.29904i	−0.854779	−	0.518992i	$-0.826307\pi$
$47$	−1.57032	−	8.90575i	−0.229055	−	1.29904i	0.625724	−	0.780045i	$-0.284804\pi$
$48$	−0.908677	−	1.47455i	−0.131156	−	0.212833i
$49$	2.51043	+	4.34820i	0.358633	+	0.621171i
$50$	−0.805933			−0.113976
$51$	−6.57729	−	10.6733i	−0.921005	−	1.49456i
$52$	−0.370492	+	2.10117i	−0.0513780	+	0.291379i
$53$	4.42019	−	3.70898i	0.607160	−	0.509468i	−0.286578	−	0.958057i	$-0.592518\pi$
$53$	4.42019	−	3.70898i	0.607160	−	0.509468i	0.893738	+	0.448589i	$0.148073\pi$
$54$	0.459295	−	5.17581i	0.0625021	−	0.704339i
$55$	8.04877	−	2.92951i	1.08530	−	0.395016i
$56$	0.703408	+	1.21834i	0.0939968	+	0.162807i
$57$	0.449851	−	7.53642i	0.0595842	−	0.998223i
$58$	4.57469	−	7.92359i	0.600686	−	1.04042i
$59$	1.87481	−	10.6326i	0.244079	−	1.38424i	−0.578543	−	0.815652i	$-0.696378\pi$
$59$	1.87481	−	10.6326i	0.244079	−	1.38424i	0.822622	−	0.568589i	$-0.192511\pi$
$60$	−2.65078	+	2.35703i	−0.342214	+	0.304291i
$61$	−1.06442	−	0.387417i	−0.136285	−	0.0496036i	0.272977	−	0.962020i	$-0.411992\pi$
$61$	−1.06442	−	0.387417i	−0.136285	−	0.0496036i	−0.409262	+	0.912417i	$0.634214\pi$
$62$	−2.82928	−	2.37404i	−0.359318	−	0.301504i
$63$	−0.493430	+	4.19150i	−0.0621664	+	0.528080i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	4.36945			0.541963
$66$	−3.44071	+	6.37488i	−0.423522	+	0.784694i
$67$	−2.94231	+	2.46889i	−0.359460	+	0.301623i	−0.804575	−	0.593850i	$-0.797607\pi$
$67$	−2.94231	+	2.46889i	−0.359460	+	0.301623i	0.445116	+	0.895473i	$0.353163\pi$
$68$	−3.61916	−	6.26857i	−0.438888	−	0.760176i
$69$	6.54047	−	2.59523i	0.787380	−	0.312429i
$70$	2.20703	−	1.85192i	0.263791	−	0.221347i
$71$	−3.85529	−	3.23497i	−0.457539	−	0.383920i	0.384686	−	0.923048i	$-0.374310\pi$
$71$	−3.85529	−	3.23497i	−0.457539	−	0.383920i	−0.842224	+	0.539127i	$0.818754\pi$
$72$	0.350743	−	2.97943i	0.0413354	−	0.351129i
$73$	−1.09776	+	6.22570i	−0.128483	+	0.728663i	0.850695	+	0.525659i	$0.176181\pi$
$73$	−1.09776	+	6.22570i	−0.128483	+	0.728663i	−0.979178	+	0.203003i	$0.934930\pi$
$74$	6.65405	+	5.58341i	0.773518	+	0.649059i
$75$	−1.09462	−	0.866250i	−0.126396	−	0.100026i
$76$	0.384368	−	4.34192i	0.0440901	−	0.498052i
$77$	2.94194	−	5.09559i	0.335265	−	0.580696i
$78$	−2.76162	+	2.45559i	−0.312692	+	0.278041i
$79$	−1.24518	+	0.453209i	−0.140094	+	0.0509900i	−0.411115	−	0.911583i	$-0.634861\pi$
$79$	−1.24518	+	0.453209i	−0.140094	+	0.0509900i	0.271022	+	0.962573i	$0.412638\pi$
$80$	−1.56881	+	1.31639i	−0.175399	+	0.147177i
$81$	6.18699	−	6.53614i	0.687444	−	0.726238i
$82$	1.87342	+	10.6247i	0.206884	+	1.17330i
$83$	−1.25669	+	2.17665i	−0.137940	+	0.238919i	−0.926717	−	0.375761i	$-0.877381\pi$
$83$	−1.25669	+	2.17665i	−0.137940	+	0.238919i	0.788777	+	0.614680i	$0.210715\pi$
$84$	−0.354149	+	2.41080i	−0.0386408	+	0.263040i
$85$	−11.3556	+	9.52846i	−1.23169	+	1.03351i
$86$	−4.88615	+	4.09997i	−0.526888	+	0.442111i
$87$	14.7300	−	5.84479i	1.57922	−	0.626627i
$88$	−2.09120	+	3.62207i	−0.222923	+	0.386114i
$89$	−0.623365	−	3.53528i	−0.0660765	−	0.374739i	−0.999857	−	0.0168930i	$-0.994623\pi$
$89$	−0.623365	−	3.53528i	−0.0660765	−	0.374739i	0.933781	−	0.357846i	$-0.116489\pi$
$90$	−6.13373	+	0.352160i	−0.646551	+	0.0371209i
$91$	2.29932	−	1.92936i	0.241035	−	0.202252i
$92$	3.81755	−	1.38947i	0.398007	−	0.144863i
$93$	−1.29101	−	6.26546i	−0.133872	−	0.649698i
$94$	4.52157	−	7.83158i	0.466364	−	0.807766i
$95$	−8.89360	+	0.768874i	−0.912464	+	0.0788848i
$96$	0.251738	−	1.71366i	0.0256929	−	0.174900i
$97$	−4.46477	−	3.74639i	−0.453329	−	0.380388i	0.387341	−	0.921937i	$-0.373394\pi$
$97$	−4.46477	−	3.74639i	−0.453329	−	0.380388i	−0.840669	+	0.541549i	$0.817838\pi$
$98$	−0.871865	+	4.94459i	−0.0880716	+	0.499479i
$99$	−11.5252	+	4.96017i	−1.15832	+	0.498516i
$100$	−0.617381	−	0.518044i	−0.0617381	−	0.0518044i
$101$	−6.24149	+	5.23724i	−0.621052	+	0.521124i	−0.898134	−	0.439722i	$-0.855077\pi$
$101$	−6.24149	+	5.23724i	−0.621052	+	0.521124i	0.277082	+	0.960846i	$0.410633\pi$
$102$	1.82216	−	12.4040i	0.180421	−	1.22818i
$103$	1.68055	+	2.91080i	0.165590	+	0.286810i	0.936865	−	0.349693i	$-0.113714\pi$
$103$	1.68055	+	2.91080i	0.165590	+	0.286810i	−0.771275	+	0.636502i	$0.780381\pi$
$104$	−1.63442	+	1.37144i	−0.160268	+	0.134481i
$105$	4.98812	−	0.143075i	0.486791	−	0.0139627i
$106$	5.77015			0.560447
$107$	−5.80019	−	10.0462i	−0.560726	−	0.971205i	−0.997433	−	0.0716018i	$-0.977189\pi$
$107$	−5.80019	−	10.0462i	−0.560726	−	0.971205i	0.436708	−	0.899603i	$-0.356144\pi$
$108$	3.67879	−	3.66967i	0.353992	−	0.353115i
$109$	7.31555	+	6.13848i	0.700703	+	0.587960i	0.921974	−	0.387253i	$-0.126576\pi$
$109$	7.31555	+	6.13848i	0.700703	+	0.587960i	−0.221271	+	0.975212i	$0.571020\pi$
$110$	8.04877	+	2.92951i	0.767421	+	0.279318i
$111$	3.03628	+	14.7355i	0.288191	+	1.39863i
$112$	−0.244291	+	1.38544i	−0.0230833	+	0.130912i
$113$	−5.25828	+	9.10760i	−0.494657	+	0.856771i	−0.999981	−	0.00615871i	$-0.998040\pi$
$113$	−5.25828	+	9.10760i	−0.494657	+	0.856771i	0.505324	+	0.862930i	$0.331373\pi$
$114$	5.18892	−	5.48407i	0.485987	−	0.513631i
$115$	−4.15994	−	7.20522i	−0.387916	−	0.671890i
$116$	8.59760	−	3.12927i	0.798267	−	0.290546i
$117$	−6.39022	+	0.366886i	−0.590776	+	0.0339186i
$118$	8.27066	−	6.93991i	0.761376	−	0.638870i
$119$	−1.76826	+	10.0283i	−0.162096	+	0.919291i
$120$	−3.54568	+	0.101702i	−0.323675	+	0.00928404i
$121$	6.49253			0.590230
$122$	−0.566365	−	0.980973i	−0.0512763	−	0.0888132i
$123$	−8.87536	+	16.4441i	−0.800264	+	1.48271i
$124$	−0.641345	−	3.63725i	−0.0575945	−	0.326634i
$125$	−5.94511	+	10.2972i	−0.531747	+	0.921012i
$126$	−3.07224	+	2.89371i	−0.273697	+	0.257792i
$127$	−1.66002	−	9.41447i	−0.147303	−	0.835399i	−0.965489	−	0.260445i	$-0.916131\pi$
$127$	−1.66002	−	9.41447i	−0.147303	−	0.835399i	0.818185	−	0.574954i	$-0.194980\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−11.0432	+	0.316755i	−0.972300	+	0.0278887i
$130$	3.34719	+	2.80863i	0.293568	+	0.246333i
$131$	1.96297	−	11.1325i	0.171505	−	0.972654i	−0.770596	−	0.637324i	$-0.780041\pi$
$131$	1.96297	−	11.1325i	0.171505	−	0.972654i	0.942101	−	0.335330i	$-0.108848\pi$
$132$	−6.73343	+	2.67180i	−0.586070	+	0.232550i
$133$	−4.34055	+	4.33164i	−0.376374	+	0.375601i
$134$	−3.84091			−0.331804
$135$	−8.70936	−	6.11447i	−0.749583	−	0.526250i
$136$	1.25692	−	7.12835i	0.107780	−	0.611251i
$137$	−8.41920	−	3.06434i	−0.719301	−	0.261804i	−0.0436717	−	0.999046i	$-0.513906\pi$
$137$	−8.41920	−	3.06434i	−0.719301	−	0.261804i	−0.675629	+	0.737242i	$0.736128\pi$
$138$	6.67848	+	2.21607i	0.568510	+	0.188644i
$139$	11.9596	+	4.35293i	1.01440	+	0.369211i	0.795120	−	0.606452i	$-0.207408\pi$
$139$	11.9596	+	4.35293i	1.01440	+	0.369211i	0.219278	+	0.975663i	$0.429630\pi$
$140$	2.88108			0.243496
$141$	14.5589	−	5.77692i	1.22608	−	0.486504i
$142$	−0.873923	−	4.95626i	−0.0733380	−	0.415920i
$143$	8.38535	+	3.05202i	0.701218	+	0.255223i
$144$	2.18382	−	2.05692i	0.181985	−	0.171410i
$145$	−9.36870	−	16.2271i	−0.778028	−	1.34758i
$146$	−4.84273	+	4.06354i	−0.400787	+	0.336301i
$147$	−6.49882	+	5.77864i	−0.536014	+	0.476615i
$148$	1.50835	+	8.55429i	0.123986	+	0.703158i
$149$	8.86134	+	7.43554i	0.725949	+	0.609143i	0.929024	−	0.370020i	$-0.120649\pi$
$149$	8.86134	+	7.43554i	0.725949	+	0.609143i	−0.203075	+	0.979163i	$0.565094\pi$
$150$	−0.281714	−	1.36719i	−0.0230018	−	0.111631i
$151$	1.47754	+	2.55918i	0.120241	+	0.208263i	0.919863	−	0.392241i	$-0.128300\pi$
$151$	1.47754	+	2.55918i	0.120241	+	0.208263i	−0.799622	+	0.600504i	$0.794967\pi$
$152$	3.08538	−	3.07904i	0.250257	−	0.249743i
$153$	15.8072	−	14.8886i	1.27794	−	1.20368i
$154$	5.52904	−	2.01240i	0.445542	−	0.162164i
$155$	−7.10763	+	2.58697i	−0.570898	+	0.207790i
$156$	−3.69395	+	0.105954i	−0.295753	+	0.00848314i
$157$	−9.78351	+	3.56091i	−0.780809	+	0.284191i	−0.701510	−	0.712660i	$-0.747490\pi$
$157$	−9.78351	+	3.56091i	−0.780809	+	0.284191i	−0.0792992	+	0.996851i	$0.525268\pi$
$158$	−1.24518	−	0.453209i	−0.0990613	−	0.0360554i
$159$	7.83704	+	6.20200i	0.621518	+	0.491850i
$160$	−2.04794			−0.161904
$161$	−5.37059	−	1.95474i	−0.423262	−	0.154055i
$162$	8.94086	−	1.03005i	0.702460	−	0.0809285i
$163$	−9.24296	+	16.0093i	−0.723964	+	1.25394i	0.235435	+	0.971890i	$0.424349\pi$
$163$	−9.24296	+	16.0093i	−0.723964	+	1.25394i	−0.959399	+	0.282053i	$0.908985\pi$
$164$	−5.39429	+	9.34318i	−0.421223	+	0.729580i
$165$	7.78311	+	12.6300i	0.605914	+	0.983246i
$166$	−2.36181	+	0.859627i	−0.183312	+	0.0667200i
$167$	4.06707	+	23.0655i	0.314719	+	1.78486i	0.573790	+	0.819003i	$0.305473\pi$
$167$	4.06707	+	23.0655i	0.314719	+	1.78486i	−0.259071	+	0.965858i	$0.583416\pi$
$168$	−1.82093	+	1.61914i	−0.140488	+	0.124919i
$169$	−6.47142	−	5.43016i	−0.497801	−	0.417705i
$170$	−14.8237			−1.13692
$171$	12.9421	−	1.87122i	0.989709	−	0.143096i
$172$	−6.37842			−0.486350
$173$	0.225896	+	0.189549i	0.0171745	+	0.0144112i	0.651334	−	0.758791i	$-0.274209\pi$
$173$	0.225896	+	0.189549i	0.0171745	+	0.0144112i	−0.634160	+	0.773202i	$0.718654\pi$
$174$	15.0408	+	4.99087i	1.14024	+	0.378357i
$175$	0.196882	+	1.11657i	0.0148829	+	0.0844051i
$176$	−3.93018	+	1.43047i	−0.296248	+	0.107826i
$177$	18.6925	−	0.536162i	1.40502	−	0.0403004i
$178$	1.79491	−	3.10887i	0.134534	−	0.233020i
$179$	6.57989	−	11.3967i	0.491804	−	0.851830i	−0.508151	−	0.861268i	$-0.669671\pi$
$179$	6.57989	−	11.3967i	0.491804	−	0.851830i	0.999955	+	0.00943785i	$0.00300420\pi$
$180$	−4.92507	−	3.67291i	−0.367093	−	0.273763i
$181$	14.7097	+	5.35391i	1.09337	+	0.397953i	0.824867	−	0.565327i	$-0.191250\pi$
$181$	14.7097	+	5.35391i	1.09337	+	0.397953i	0.268500	+	0.963280i	$0.413472\pi$
$182$	3.00156			0.222490
$183$	0.285151	−	1.94111i	0.0210790	−	0.143491i
$184$	3.81755	+	1.38947i	0.281434	+	0.102433i
$185$	16.7161	−	6.08418i	1.22899	−	0.447318i
$186$	3.03839	−	5.62946i	0.222785	−	0.412772i
$187$	−28.4479	+	10.3542i	−2.08031	+	0.757173i
$188$	8.49777	−	3.09293i	0.619763	−	0.225575i
$189$	−7.28300	+	0.628078i	−0.529760	+	0.0456860i
$190$	−7.30711	−	5.12770i	−0.530114	−	0.372003i
$191$	−2.83824	−	4.91597i	−0.205368	−	0.355707i	0.744882	−	0.667196i	$-0.232506\pi$
$191$	−2.83824	−	4.91597i	−0.205368	−	0.355707i	−0.950250	+	0.311489i	$0.899172\pi$
$192$	1.29436	−	1.15093i	0.0934125	−	0.0830609i
$193$	6.35705	+	5.33420i	0.457591	+	0.383964i	0.842244	−	0.539097i	$-0.181234\pi$
$193$	6.35705	+	5.33420i	0.457591	+	0.383964i	−0.384653	+	0.923061i	$0.625679\pi$
$194$	−1.01208	−	5.73980i	−0.0726632	−	0.412093i
$195$	1.52734	+	7.41239i	0.109375	+	0.530812i
$196$	−3.84621	+	3.22735i	−0.274729	+	0.230525i
$197$	2.79959	+	4.84903i	0.199463	+	0.345479i	0.948354	−	0.317213i	$-0.102747\pi$
$197$	2.79959	+	4.84903i	0.199463	+	0.345479i	−0.748892	+	0.662692i	$0.769414\pi$
$198$	−12.0171	−	3.60852i	−0.854020	−	0.256446i
$199$	−18.5256	−	6.74276i	−1.31324	−	0.477982i	−0.411957	−	0.911203i	$-0.635155\pi$
$199$	−18.5256	−	6.74276i	−1.31324	−	0.477982i	−0.901287	+	0.433222i	$0.857377\pi$
$200$	−0.139949	−	0.793689i	−0.00989588	−	0.0561223i
$201$	−5.21673	−	4.12837i	−0.367960	−	0.291192i
$202$	−8.14769			−0.573270
$203$	−12.0952	−	4.40231i	−0.848920	−	0.308981i
$204$	9.36900	−	8.33076i	0.655961	−	0.583270i
$205$	20.7619	+	7.55672i	1.45008	+	0.527784i
$206$	−0.583649	+	3.31004i	−0.0406648	+	0.230621i
$207$	6.68881	+	10.1882i	0.464904	+	0.708127i
$208$	−2.13358			−0.147937
$209$	−17.6046	−	4.73656i	−1.21774	−	0.327634i
$210$	3.91309	+	3.09670i	0.270029	+	0.213693i
$211$	0.0820139	−	0.465124i	0.00564607	−	0.0320204i	−0.981855	−	0.189635i	$-0.939269\pi$
$211$	0.0820139	−	0.465124i	0.00564607	−	0.0320204i	0.987501	+	0.157615i	$0.0503805\pi$
$212$	4.42019	+	3.70898i	0.303580	+	0.254734i
$213$	4.14023	−	7.67094i	0.283684	−	0.525604i
$214$	2.01439	−	11.4241i	0.137701	−	0.780939i
$215$	2.26830	+	12.8642i	0.154697	+	0.877330i
$216$	5.17694	−	0.446454i	0.352246	−	0.0303773i
$217$	−2.59794	+	4.49976i	−0.176359	+	0.305463i
$218$	1.65830	+	9.40470i	0.112314	+	0.636966i
$219$	−10.9451	+	0.313940i	−0.739599	+	0.0212141i
$220$	4.28266	+	7.41779i	0.288737	+	0.500107i
$221$	−15.4435			−1.03884
$222$	−7.14585	+	13.2397i	−0.479598	+	0.888591i
$223$	1.35473	−	7.68306i	0.0907194	−	0.514496i	−0.905256	−	0.424867i	$-0.860321\pi$
$223$	1.35473	−	7.68306i	0.0907194	−	0.514496i	0.995975	−	0.0896286i	$-0.0285680\pi$
$224$	−1.07768	+	0.904284i	−0.0720058	+	0.0604200i
$225$	1.08689	−	2.15973i	0.0724595	−	0.143982i
$226$	−9.88232	+	3.59687i	−0.657362	+	0.239260i
$227$	10.1380	+	17.5596i	0.672885	+	1.16547i	0.977082	+	0.212862i	$0.0682785\pi$
$227$	10.1380	+	17.5596i	0.672885	+	1.16547i	−0.304197	+	0.952609i	$0.598388\pi$
$228$	7.50004	−	0.865669i	0.496702	−	0.0573304i
$229$	−12.3117	+	21.3245i	−0.813581	+	1.40916i	0.0967619	+	0.995308i	$0.469151\pi$
$229$	−12.3117	+	21.3245i	−0.813581	+	1.40916i	−0.910343	+	0.413856i	$0.864182\pi$
$230$	1.44473	−	8.19348i	0.0952627	−	0.540262i
$231$	9.67257	+	3.20958i	0.636408	+	0.211175i
$232$	8.59760	+	3.12927i	0.564460	+	0.205447i
$233$	18.3529	+	15.3999i	1.20234	+	1.00888i	0.999560	+	0.0296598i	$0.00944241\pi$
$233$	18.3529	+	15.3999i	1.20234	+	1.00888i	0.202781	+	0.979224i	$0.435002\pi$
$234$	−5.13102	−	3.82650i	−0.335425	−	0.250146i
$235$	−9.25991	−	16.0386i	−0.604050	−	1.04624i
$236$	10.7966			0.702798
$237$	−1.20408	−	1.95392i	−0.0782135	−	0.126921i
$238$	−7.80062	+	6.54550i	−0.505639	+	0.424281i
$239$	8.74364	+	15.1444i	0.565579	+	0.979611i	0.996996	+	0.0774585i	$0.0246805\pi$
$239$	8.74364	+	15.1444i	0.565579	+	0.979611i	−0.431417	+	0.902153i	$0.641986\pi$
$240$	−2.78152	−	2.20121i	−0.179546	−	0.142088i
$241$	10.5964	−	8.89145i	0.682575	−	0.572749i	−0.234182	−	0.972193i	$-0.575241\pi$
$241$	10.5964	−	8.89145i	0.682575	−	0.572749i	0.916758	+	0.399444i	$0.130797\pi$
$242$	4.97356	+	4.17332i	0.319713	+	0.268271i
$243$	13.2506	+	8.21099i	0.850030	+	0.526735i
$244$	0.196697	−	1.11552i	0.0125922	−	0.0714140i
$245$	7.87681	+	6.60943i	0.503231	+	0.422261i
$246$	−17.3690	+	6.89194i	−1.10741	+	0.439414i
$247$	−7.61267	−	5.34213i	−0.484383	−	0.339911i
$248$	1.84668	−	3.19854i	0.117264	−	0.203108i
$249$	−4.13177	−	1.37102i	−0.261841	−	0.0868847i
$250$	−11.1731	+	4.06669i	−0.706652	+	0.257200i
$251$	−11.3840	+	9.55233i	−0.718554	+	0.602938i	−0.926985	−	0.375099i	$-0.877609\pi$
$251$	−11.3840	+	9.55233i	−0.718554	+	0.602938i	0.208431	+	0.978037i	$0.433164\pi$
$252$	−4.21351	+	0.241913i	−0.265426	+	0.0152391i
$253$	−2.95050	−	16.7331i	−0.185496	−	1.05200i
$254$	4.77985	−	8.27894i	0.299915	−	0.519467i
$255$	−20.1335	−	15.9331i	−1.26081	−	0.997768i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−9.84458	+	8.26059i	−0.614088	+	0.515281i	−0.895939	−	0.444177i	$-0.853496\pi$
$257$	−9.84458	+	8.26059i	−0.614088	+	0.515281i	0.281851	+	0.959458i	$0.409052\pi$
$258$	−8.66320	−	6.85579i	−0.539347	−	0.426823i
$259$	6.10998	−	10.5828i	0.379656	−	0.657583i
$260$	0.758747	+	4.30307i	0.0470555	+	0.266865i
$261$	15.0640	+	22.9450i	0.932440	+	1.42026i
$262$	8.65957	−	7.26624i	0.534990	−	0.448910i
$263$	8.17833	−	2.97667i	0.504298	−	0.183549i	−0.0773284	−	0.997006i	$-0.524639\pi$
$263$	8.17833	−	2.97667i	0.504298	−	0.183549i	0.581626	+	0.813456i	$0.302417\pi$
$264$	−6.87550	−	2.28145i	−0.423158	−	0.140414i
$265$	5.90847	−	10.2338i	0.362954	−	0.628655i
$266$	−6.10938	+	0.528171i	−0.374590	+	0.0323843i
$267$	5.77939	−	2.29324i	0.353693	−	0.140344i
$268$	−2.94231	−	2.46889i	−0.179730	−	0.150811i
$269$	4.29203	−	24.3413i	0.261690	−	1.48412i	−0.516609	−	0.856221i	$-0.672806\pi$
$269$	4.29203	−	24.3413i	0.261690	−	1.48412i	0.778299	−	0.627894i	$-0.216083\pi$
$270$	−2.74145	−	10.2822i	−0.166839	−	0.625757i
$271$	−19.5526	−	16.4066i	−1.18773	−	0.996628i	−0.999896	−	0.0144276i	$-0.995407\pi$
$271$	−19.5526	−	16.4066i	−1.18773	−	0.996628i	−0.187839	−	0.982200i	$-0.560148\pi$
$272$	5.54487	−	4.65270i	0.336207	−	0.282111i
$273$	4.07672	+	3.22619i	0.246734	+	0.195258i
$274$	−4.47976	−	7.75917i	−0.270632	−	0.468749i
$275$	−2.58214	+	2.16667i	−0.155709	+	0.130655i
$276$	3.69155	+	5.99045i	0.222205	+	0.360583i
$277$	−9.62944			−0.578577			−0.289288	−	0.957242i	$-0.593419\pi$
$277$	−9.62944			−0.578577			−0.289288	+	0.957242i	$0.593419\pi$
$278$	6.36356	+	11.0220i	0.381661	+	0.661056i
$279$	10.1775	−	4.38018i	0.609312	−	0.262234i
$280$	2.20703	+	1.85192i	0.131895	+	0.110673i
$281$	−4.64237	−	1.68968i	−0.276940	−	0.100798i	0.199816	−	0.979833i	$-0.435965\pi$
$281$	−4.64237	−	1.68968i	−0.276940	−	0.100798i	−0.476757	+	0.879035i	$0.658188\pi$
$282$	14.8661	+	4.93291i	0.885264	+	0.293751i
$283$	0.674628	−	3.82601i	0.0401025	−	0.227433i	−0.958169	−	0.286203i	$-0.907607\pi$
$283$	0.674628	−	3.82601i	0.0401025	−	0.227433i	0.998272	+	0.0587704i	$0.0187180\pi$
$284$	2.51636	−	4.35846i	0.149319	−	0.258627i
$285$	−4.41308	−	14.8185i	−0.261408	−	0.877769i
$286$	4.46175	+	7.72798i	0.263829	+	0.456965i
$287$	14.2622	−	5.19103i	0.841873	−	0.306417i
$288$	2.99507	−	0.171958i	0.176486	−	0.0101327i
$289$	27.1128	−	22.7504i	1.59487	−	1.33826i
$290$	3.25371	−	18.4527i	0.191065	−	1.08358i
$291$	4.79476	−	8.88364i	0.281074	−	0.520768i
$292$	−6.32174			−0.369952
$293$	5.76450	+	9.98440i	0.336766	+	0.583295i	0.983822	−	0.179147i	$-0.0573337\pi$
$293$	5.76450	+	9.98440i	0.336766	+	0.583295i	−0.647057	+	0.762442i	$0.724000\pi$
$294$	−8.69282	+	0.249338i	−0.506976	+	0.0145417i
$295$	−3.83950	−	21.7749i	−0.223544	−	1.26778i
$296$	−4.34313	+	7.52251i	−0.252439	+	0.437237i
$297$	−12.4431	−	17.8176i	−0.722023	−	1.03388i
$298$	2.00870	+	11.3919i	0.116361	+	0.659916i
$299$	1.50514	−	8.53610i	0.0870448	−	0.493655i
$300$	0.663011	−	1.22841i	0.0382789	−	0.0709225i
$301$	6.87392	+	5.76790i	0.396206	+	0.332456i
$302$	−0.513146	+	2.91019i	−0.0295282	+	0.167463i
$303$	−11.0662	−	8.75747i	−0.635738	−	0.503104i
$304$	4.34270	−	0.375437i	0.249071	−	0.0215328i
$305$	−2.31977			−0.132829
$306$	21.6793	−	1.24469i	1.23932	−	0.0711540i
$307$	−0.650952	+	3.69173i	−0.0371518	+	0.210698i	−0.997733	−	0.0673026i	$-0.978561\pi$
$307$	−0.650952	+	3.69173i	−0.0371518	+	0.210698i	0.960581	+	0.278001i	$0.0896718\pi$
$308$	5.52904	+	2.01240i	0.315046	+	0.114667i
$309$	−4.35048	+	3.86838i	−0.247490	+	0.220064i
$310$	−7.10763	−	2.58697i	−0.403686	−	0.146930i
$311$	5.05137			0.286437			0.143219	−	0.989691i	$-0.454255\pi$
$311$	5.05137			0.286437			0.143219	+	0.989691i	$0.454255\pi$
$312$	−2.89784	−	2.29326i	−0.164058	−	0.129830i
$313$	4.87436	+	27.6439i	0.275515	+	1.56252i	0.737321	+	0.675543i	$0.236091\pi$
$313$	4.87436	+	27.6439i	0.275515	+	1.56252i	−0.461805	+	0.886981i	$0.652798\pi$
$314$	−9.78351	−	3.56091i	−0.552116	−	0.200954i
$315$	1.98631	+	8.41190i	0.111916	+	0.473957i
$316$	−0.662547	−	1.14757i	−0.0372712	−	0.0645556i
$317$	−14.6111	+	12.2602i	−0.820640	+	0.688599i	−0.953122	−	0.302587i	$-0.902150\pi$
$317$	−14.6111	+	12.2602i	−0.820640	+	0.688599i	0.132482	+	0.991185i	$0.457705\pi$
$318$	2.01696	+	9.78856i	0.113105	+	0.548915i
$319$	−6.64489	−	37.6851i	−0.372043	−	2.10996i
$320$	−1.56881	−	1.31639i	−0.0876994	−	0.0735885i
$321$	15.0151	−	13.3512i	0.838060	−	0.745190i
$322$	−2.85763	−	4.94956i	−0.159250	−	0.275828i
$323$	31.4339	−	2.71754i	1.74903	−	0.151208i
$324$	7.51120	+	4.95801i	0.417289	+	0.275445i
$325$	−1.61582	+	0.588112i	−0.0896297	+	0.0326226i
$326$	−17.3711	+	6.32255i	−0.962095	+	0.350174i
$327$	−7.85624	+	14.5559i	−0.434451	+	0.804943i
$328$	−10.1379	+	3.68991i	−0.559774	+	0.203741i
$329$	−11.9548	−	4.35119i	−0.659089	−	0.239889i
$330$	−2.15622	+	14.6781i	−0.118696	+	0.808000i
$331$	−10.9185			−0.600135			−0.300067	−	0.953918i	$-0.597009\pi$
$331$	−10.9185			−0.600135			−0.300067	+	0.953918i	$0.597009\pi$
$332$	−2.36181	−	0.859627i	−0.129621	−	0.0471782i
$333$	−23.9361	+	10.3016i	−1.31169	+	0.564522i
$334$	−11.7107	+	20.2835i	−0.640779	+	1.10986i
$335$	−3.93298	+	6.81212i	−0.214882	+	0.372186i
$336$	−2.43567	+	0.0698630i	−0.132877	+	0.00381134i
$337$	24.3513	−	8.86314i	1.32650	−	0.482806i	0.420964	−	0.907077i	$-0.361692\pi$
$337$	24.3513	−	8.86314i	1.32650	−	0.482806i	0.905535	+	0.424271i	$0.139470\pi$
$338$	−1.46695	−	8.31949i	−0.0797916	−	0.452521i
$339$	−17.2883	−	5.73664i	−0.938970	−	0.311572i
$340$	−11.3556	−	9.52846i	−0.615843	−	0.516754i
$341$	−15.4471			−0.836508
$342$	11.1170	+	6.88560i	0.601141	+	0.372330i
$343$	16.9112			0.913116
$344$	−4.88615	−	4.09997i	−0.263444	−	0.221056i
$345$	10.7689	−	9.57555i	0.579779	−	0.515530i
$346$	0.0512064	+	0.290406i	0.00275288	+	0.0156123i
$347$	−0.839789	+	0.305658i	−0.0450822	+	0.0164086i	−0.364463	−	0.931218i	$-0.618747\pi$
$347$	−0.839789	+	0.305658i	−0.0450822	+	0.0164086i	0.319381	+	0.947627i	$0.396525\pi$
$348$	8.31382	+	13.4912i	0.445668	+	0.723207i
$349$	7.16946	−	12.4179i	0.383773	−	0.664714i	−0.607826	−	0.794071i	$-0.707958\pi$
$349$	7.16946	−	12.4179i	0.383773	−	0.664714i	0.991598	+	0.129357i	$0.0412913\pi$
$350$	−0.566900	+	0.981899i	−0.0303021	+	0.0524847i
$351$	−2.85609	−	10.7122i	−0.152447	−	0.571775i
$352$	−3.93018	−	1.43047i	−0.209479	−	0.0762442i
$353$	−15.3576			−0.817402			−0.408701	−	0.912668i	$-0.634018\pi$
$353$	−15.3576			−0.817402			−0.408701	+	0.912668i	$0.634018\pi$
$354$	14.6640	+	11.6046i	0.779380	+	0.616778i
$355$	−9.68515	−	3.52511i	−0.514034	−	0.187093i
$356$	3.37332	−	1.22779i	0.178786	−	0.0650727i
$357$	−17.6302	+	0.505691i	−0.933089	+	0.0267640i
$358$	12.3662	−	4.50091i	0.653572	−	0.237881i
$359$	25.1271	−	9.14550i	1.32616	−	0.482681i	0.420730	−	0.907186i	$-0.361774\pi$
$359$	25.1271	−	9.14550i	1.32616	−	0.482681i	0.905426	+	0.424505i	$0.139552\pi$
$360$	−1.41192	−	5.97939i	−0.0744147	−	0.315141i
$361$	16.4349	+	9.53382i	0.864995	+	0.501780i
$362$	7.82689	+	13.5566i	0.411372	+	0.712518i
$363$	2.26946	+	11.0140i	0.119116	+	0.578085i
$364$	2.29932	+	1.92936i	0.120517	+	0.101126i
$365$	2.24815	+	12.7499i	0.117673	+	0.667359i
$366$	1.46616	−	1.30369i	0.0766375	−	0.0681449i
$367$	−8.02343	+	6.73246i	−0.418820	+	0.351432i	−0.827714	−	0.561150i	$-0.810359\pi$
$367$	−8.02343	+	6.73246i	−0.418820	+	0.351432i	0.408894	+	0.912582i	$0.365915\pi$
$368$	2.03128	+	3.51827i	0.105888	+	0.183403i
$369$	−30.9983	−	9.30823i	−1.61371	−	0.484567i
$370$	16.7161	+	6.08418i	0.869031	+	0.316301i
$371$	−1.40960	−	7.99422i	−0.0731826	−	0.415039i
$372$	5.94609	−	2.35938i	0.308290	−	0.122328i
$373$	−3.09962			−0.160492			−0.0802462	−	0.996775i	$-0.525571\pi$
$373$	−3.09962			−0.160492			−0.0802462	+	0.996775i	$0.525571\pi$
$374$	−28.4479	−	10.3542i	−1.47100	−	0.535402i
$375$	−19.5465	−	6.48596i	−1.00937	−	0.334934i
$376$	8.49777	+	3.09293i	0.438239	+	0.159506i
$377$	3.38977	−	19.2244i	0.174582	−	0.990105i
$378$	−5.98282	−	4.20029i	−0.307723	−	0.216039i
$379$	−3.65811			−0.187905			−0.0939523	−	0.995577i	$-0.529950\pi$
$379$	−3.65811			−0.187905			−0.0939523	+	0.995577i	$0.529950\pi$
$380$	−2.30155	−	8.62497i	−0.118067	−	0.442452i
$381$	15.3906	−	6.10691i	0.788482	−	0.312867i
$382$	0.985710	−	5.59024i	0.0504333	−	0.286022i
$383$	−16.1117	−	13.5193i	−0.823270	−	0.690806i	0.130465	−	0.991453i	$-0.458353\pi$
$383$	−16.1117	−	13.5193i	−0.823270	−	0.690806i	−0.953735	+	0.300647i	$0.902797\pi$
$384$	1.73134	−	0.0496604i	0.0883520	−	0.00253422i
$385$	2.09243	−	11.8668i	0.106640	−	0.604787i
$386$	1.44103	+	8.17247i	0.0733463	+	0.415968i
$387$	−4.39750	−	18.6231i	−0.223537	−	0.946666i
$388$	2.91417	−	5.04749i	0.147945	−	0.256248i
$389$	−1.28668	−	7.29715i	−0.0652374	−	0.369980i	−0.999896	−	0.0144329i	$-0.995406\pi$
$389$	−1.28668	−	7.29715i	−0.0652374	−	0.369980i	0.934658	−	0.355547i	$-0.115705\pi$
$390$	−3.59458	+	6.65997i	−0.182019	+	0.337241i
$391$	14.7030	+	25.4664i	0.743564	+	1.28789i
$392$	−5.02087			−0.253592
$393$	19.5715	−	0.561374i	0.987252	−	0.0283176i
$394$	−0.972287	+	5.51412i	−0.0489831	+	0.277797i
$395$	−2.07883	+	1.74434i	−0.104597	+	0.0877674i
$396$	−6.88614	−	10.4887i	−0.346042	−	0.527079i
$397$	−17.6292	+	6.41651i	−0.884785	+	0.322036i	−0.744139	−	0.668024i	$-0.767140\pi$
$397$	−17.6292	+	6.41651i	−0.884785	+	0.322036i	−0.140646	+	0.990060i	$0.544918\pi$
$398$	−9.85726	−	17.0733i	−0.494100	−	0.855806i
$399$	−8.86548	−	5.84925i	−0.443829	−	0.292829i
$400$	0.402967	−	0.697959i	0.0201483	−	0.0348979i
$401$	3.92082	−	22.2361i	0.195796	−	1.11042i	−0.715484	−	0.698629i	$-0.753794\pi$
$401$	3.92082	−	22.2361i	0.195796	−	1.11042i	0.911280	−	0.411787i	$-0.135095\pi$
$402$	−1.34259	−	6.51576i	−0.0669622	−	0.324977i
$403$	−7.40485	−	2.69514i	−0.368862	−	0.134255i
$404$	−6.24149	−	5.23724i	−0.310526	−	0.260562i
$405$	7.32832	−	16.9120i	0.364147	−	0.840363i
$406$	−6.43574	−	11.1470i	−0.319401	−	0.553218i
$407$	36.3294			1.80078
$408$	12.5320	−	0.359458i	0.620426	−	0.0177958i
$409$	−15.7639	+	13.2275i	−0.779475	+	0.654058i	−0.943117	−	0.332462i	$-0.892121\pi$
$409$	−15.7639	+	13.2275i	−0.779475	+	0.654058i	0.163641	+	0.986520i	$0.447676\pi$
$410$	11.0472	+	19.1343i	0.545582	+	0.944976i
$411$	2.25545	−	15.3536i	0.111253	−	0.757336i
$412$	−2.57475	+	2.16048i	−0.126849	+	0.106439i
$413$	−11.6353	−	9.76317i	−0.572536	−	0.480414i
$414$	−1.42491	+	12.1041i	−0.0700305	+	0.594883i
$415$	−0.893812	+	5.06906i	−0.0438755	+	0.248830i
$416$	−1.63442	−	1.37144i	−0.0801339	−	0.0672403i
$417$	−3.20390	+	21.8099i	−0.156895	+	1.06804i
$418$	−10.4413	−	14.9445i	−0.510702	−	0.730957i
$419$	4.10584	−	7.11153i	0.200584	−	0.347421i	−0.748133	−	0.663549i	$-0.769049\pi$
$419$	4.10584	−	7.11153i	0.200584	−	0.347421i	0.948717	+	0.316128i	$0.102383\pi$
$420$	1.00708	+	4.88750i	0.0491405	+	0.238485i
$421$	18.1615	−	6.61026i	0.885139	−	0.322164i	0.140857	−	0.990030i	$-0.455014\pi$
$421$	18.1615	−	6.61026i	0.885139	−	0.322164i	0.744282	+	0.667866i	$0.232792\pi$
$422$	0.361802	−	0.303588i	0.0176123	−	0.0147784i
$423$	14.8891	+	22.6786i	0.723933	+	1.10267i
$424$	1.00198	+	5.68249i	0.0486603	+	0.275966i
$425$	2.91680	−	5.05205i	0.141486	−	0.245060i
$426$	8.10239	−	3.21499i	0.392562	−	0.155767i
$427$	−1.22072	+	1.02431i	−0.0590750	+	0.0495698i
$428$	8.88641	−	7.45658i	0.429541	−	0.360427i
$429$	−2.24638	+	15.2918i	−0.108456	+	0.738297i
$430$	−6.53132	+	11.3126i	−0.314968	+	0.545541i
$431$	2.30835	+	13.0913i	0.111189	+	0.630586i	0.988567	+	0.150785i	$0.0481801\pi$
$431$	2.30835	+	13.0913i	0.111189	+	0.630586i	−0.877377	+	0.479801i	$0.840709\pi$
$432$	4.25274	+	2.98567i	0.204610	+	0.143648i
$433$	−7.71664	+	6.47503i	−0.370838	+	0.311170i	−0.809093	−	0.587681i	$-0.800041\pi$
$433$	−7.71664	+	6.47503i	−0.370838	+	0.311170i	0.438255	+	0.898851i	$0.355597\pi$
$434$	−4.88252	+	1.77709i	−0.234369	+	0.0853032i
$435$	24.2530	−	21.5653i	1.16284	−	1.03398i
$436$	−4.77489	+	8.27035i	−0.228676	+	0.396078i
$437$	−1.56152	+	17.6393i	−0.0746975	+	0.843801i
$438$	−8.58621	−	6.79486i	−0.410265	−	0.324671i
$439$	16.3574	+	13.7255i	0.780696	+	0.655082i	0.943424	−	0.331589i	$-0.107585\pi$
$439$	16.3574	+	13.7255i	0.780696	+	0.655082i	−0.162728	+	0.986671i	$0.552029\pi$
$440$	−1.48735	+	8.43520i	−0.0709068	+	0.402132i
$441$	−12.0746	−	9.00475i	−0.574982	−	0.428798i
$442$	−11.8304	−	9.92691i	−0.562716	−	0.472175i
$443$	13.7666	−	11.5515i	0.654069	−	0.548829i	−0.254234	−	0.967143i	$-0.581823\pi$
$443$	13.7666	−	11.5515i	0.654069	−	0.548829i	0.908303	+	0.418314i	$0.137379\pi$
$444$	−13.9844	+	5.54894i	−0.663668	+	0.263341i
$445$	−3.67587	−	6.36679i	−0.174253	−	0.301815i
$446$	5.97636	−	5.01476i	0.282989	−	0.237456i
$447$	−9.51627	+	17.6316i	−0.450104	+	0.833945i
$448$	−1.40682			−0.0664658
$449$	−18.7575	−	32.4890i	−0.885221	−	1.53325i	−0.845460	−	0.534039i	$-0.820673\pi$
$449$	−18.7575	−	32.4890i	−0.885221	−	1.53325i	−0.0397619	−	0.999209i	$-0.512660\pi$
$450$	2.22085	−	0.955805i	0.104692	−	0.0450571i
$451$	34.5656	+	29.0040i	1.62763	+	1.36575i
$452$	−9.88232	−	3.59687i	−0.464825	−	0.169183i
$453$	−3.82495	+	3.40108i	−0.179712	+	0.159797i
$454$	−3.52090	+	19.9680i	−0.165244	+	0.937146i
$455$	3.07351	−	5.32347i	0.144088	−	0.249568i
$456$	6.30181	+	4.15779i	0.295109	+	0.194706i
$457$	−15.3316	−	26.5551i	−0.717182	−	1.24220i	−0.962112	−	0.272655i	$-0.912098\pi$
$457$	−15.3316	−	26.5551i	−0.717182	−	1.24220i	0.244930	−	0.969541i	$-0.421235\pi$
$458$	−23.1384	+	8.42171i	−1.08119	+	0.393520i
$459$	30.7827	+	21.6112i	1.43681	+	1.00873i
$460$	6.37339	−	5.34791i	0.297161	−	0.249348i
$461$	−4.29115	+	24.3363i	−0.199859	+	1.13346i	0.705468	+	0.708741i	$0.250737\pi$
$461$	−4.29115	+	24.3363i	−0.199859	+	1.13346i	−0.905327	+	0.424715i	$0.860374\pi$
$462$	5.34654	+	8.67609i	0.248744	+	0.403648i
$463$	10.5618			0.490849			0.245424	−	0.969416i	$-0.421073\pi$
$463$	10.5618			0.490849			0.245424	+	0.969416i	$0.421073\pi$
$464$	4.57469	+	7.92359i	0.212375	+	0.367844i
$465$	−6.87303	−	11.1532i	−0.318729	−	0.517217i
$466$	4.16027	+	23.5941i	0.192721	+	1.09297i
$467$	3.05559	−	5.29244i	0.141396	−	0.244905i	−0.786627	−	0.617429i	$-0.788174\pi$
$467$	3.05559	−	5.29244i	0.141396	−	0.244905i	0.928023	+	0.372524i	$0.121508\pi$
$468$	−1.47096	−	6.22943i	−0.0679952	−	0.287955i
$469$	0.938299	+	5.32136i	0.0433266	+	0.245718i
$470$	3.21593	−	18.2385i	0.148340	−	0.841277i
$471$	−9.46059	−	15.3522i	−0.435921	−	0.707390i
$472$	8.27066	+	6.93991i	0.380688	+	0.319435i
$473$	−4.63244	+	26.2719i	−0.213000	+	1.20798i
$474$	0.333576	−	2.27076i	0.0153217	−	0.104299i
$475$	3.18537	−	1.48137i	0.146155	−	0.0679701i
$476$	−10.1830			−0.466736
$477$	−7.78171	+	15.4628i	−0.356300	+	0.707991i
$478$	−3.03663	+	17.2216i	−0.138892	+	0.787698i
$479$	−35.0589	−	12.7604i	−1.60188	−	0.583037i	−0.622069	−	0.782962i	$-0.713708\pi$
$479$	−35.0589	−	12.7604i	−1.60188	−	0.583037i	−0.979811	+	0.199926i	$0.935930\pi$
$480$	−0.715858	−	3.47415i	−0.0326743	−	0.158573i
$481$	17.4152	+	6.33860i	0.794063	+	0.289015i
$482$	13.8326			0.630059
$483$	1.43875	−	9.79402i	0.0654653	−	0.445643i
$484$	1.12742	+	6.39389i	0.0512461	+	0.290631i
$485$	−11.2163	−	4.08239i	−0.509305	−	0.185372i
$486$	4.87267	+	14.8073i	0.221029	+	0.671674i
$487$	20.3942	+	35.3238i	0.924151	+	1.60068i	0.792921	+	0.609324i	$0.208559\pi$
$487$	20.3942	+	35.3238i	0.924151	+	1.60068i	0.131230	+	0.991352i	$0.458107\pi$
$488$	0.867722	−	0.728105i	0.0392799	−	0.0329598i
$489$	−30.3892	−	10.0838i	−1.37425	−	0.456006i
$490$	1.78553	+	10.1262i	0.0806620	+	0.457457i
$491$	20.3964	+	17.1147i	0.920479	+	0.772373i	0.974083	−	0.226189i	$-0.0726266\pi$
$491$	20.3964	+	17.1147i	0.920479	+	0.772373i	−0.0536046	+	0.998562i	$0.517071\pi$
$492$	−17.7355	−	5.88503i	−0.799576	−	0.265318i
$493$	33.1131	+	57.3535i	1.49134	+	2.58307i
$494$	−2.39779	−	8.98564i	−0.107882	−	0.404283i
$495$	−18.7052	+	17.6182i	−0.840734	+	0.791879i
$496$	3.47062	−	1.26320i	0.155835	−	0.0567195i
$497$	−6.65313	+	2.42154i	−0.298434	+	0.108621i
$498$	−2.28385	−	3.70611i	−0.102342	−	0.166075i
$499$	25.7408	−	9.36890i	1.15232	−	0.419409i	0.305971	−	0.952041i	$-0.401019\pi$
$499$	25.7408	−	9.36890i	1.15232	−	0.419409i	0.846347	+	0.532632i	$0.178797\pi$
$500$	−11.1731	−	4.06669i	−0.499678	−	0.181868i
$501$	−37.7069	+	14.9620i	−1.68462	+	0.668451i
$502$	−14.8608			−0.663270
$503$	−5.41852	−	1.97218i	−0.241600	−	0.0879352i	0.218382	−	0.975863i	$-0.429922\pi$
$503$	−5.41852	−	1.97218i	−0.241600	−	0.0879352i	−0.459982	+	0.887928i	$0.652144\pi$
$504$	−3.38323	−	2.52308i	−0.150701	−	0.112387i
$505$	−8.34300	+	14.4505i	−0.371259	+	0.643039i
$506$	8.49562	−	14.7149i	0.377677	−	0.654155i
$507$	6.94971	−	12.8763i	0.308648	−	0.571857i
$508$	8.98318	−	3.26961i	0.398564	−	0.145066i
$509$	1.02479	+	5.81188i	0.0454231	+	0.257607i	0.999060	−	0.0433531i	$-0.0138040\pi$
$509$	1.02479	+	5.81188i	0.0454231	+	0.257607i	−0.953637	+	0.300960i	$0.902693\pi$
$510$	−5.18161	−	25.1470i	−0.229445	−	1.11353i
$511$	6.81283	+	5.71665i	0.301382	+	0.252890i
$512$	1.00000			0.0441942
$513$	7.69828	+	21.3011i	0.339887	+	0.940466i
$514$	−12.8512			−0.566842
$515$	5.27295	+	4.42453i	0.232354	+	0.194968i
$516$	−2.22958	−	10.8204i	−0.0981516	−	0.476343i
$517$	−6.56773	−	37.2475i	−0.288849	−	1.63814i
$518$	11.4830	−	4.17947i	0.504534	−	0.183635i
$519$	−0.242592	+	0.449469i	−0.0106486	+	0.0197295i
$520$	−2.18472	+	3.78405i	−0.0958065	+	0.165942i
$521$	−14.5847	+	25.2615i	−0.638969	+	1.10673i	0.346690	+	0.937980i	$0.387306\pi$
$521$	−14.5847	+	25.2615i	−0.638969	+	1.10673i	−0.985659	+	0.168748i	$0.946028\pi$
$522$	−3.20908	+	27.2599i	−0.140457	+	1.19313i
$523$	20.8643	+	7.59399i	0.912333	+	0.332062i	0.755184	−	0.655513i	$-0.227547\pi$
$523$	20.8643	+	7.59399i	0.912333	+	0.332062i	0.157149	+	0.987575i	$0.449770\pi$
$524$	11.3043			0.493829
$525$	−1.82535	+	0.724292i	−0.0796648	+	0.0316107i
$526$	8.17833	+	2.97667i	0.356592	+	0.129789i
$527$	25.1215	−	9.14346i	1.09431	−	0.398295i
$528$	−3.80045	−	6.16718i	−0.165394	−	0.268392i
$529$	6.10393	−	2.22165i	0.265388	−	0.0965934i
$530$	11.1043	−	4.04163i	0.482339	−	0.175557i
$531$	7.44353	+	31.5228i	0.323021	+	1.36797i
$532$	−5.01956	−	3.52243i	−0.217625	−	0.152717i
$533$	11.5091	+	19.9344i	0.498517	+	0.863456i
$534$	5.90133	+	1.95820i	0.255376	+	0.0847395i
$535$	−18.1989	−	15.2706i	−0.786805	−	0.660208i
$536$	−0.666967	−	3.78256i	−0.0288086	−	0.163382i
$537$	21.6335	+	7.17850i	0.933555	+	0.309775i
$538$	18.9342	−	15.8877i	0.816310	−	0.684966i
$539$	10.4997	+	18.1859i	0.452252	+	0.783324i
$540$	4.50922	−	9.63882i	0.194046	−	0.414789i
$541$	−31.7280	−	11.5481i	−1.36410	−	0.496490i	−0.446777	−	0.894645i	$-0.647428\pi$
$541$	−31.7280	−	11.5481i	−1.36410	−	0.496490i	−0.917318	+	0.398155i	$0.869650\pi$
$542$	−4.43221	−	25.1363i	−0.190380	−	1.07970i
$543$	−3.94065	+	26.8253i	−0.169109	+	1.15118i
$544$	7.23832			0.310340
$545$	18.3779	+	6.68902i	0.787224	+	0.286526i
$546$	1.04919	+	5.09188i	0.0449013	+	0.217912i
$547$	−25.7400	−	9.36858i	−1.10056	−	0.400571i	−0.273038	−	0.962003i	$-0.588028\pi$
$547$	−25.7400	−	9.36858i	−1.10056	−	0.400571i	−0.827523	+	0.561432i	$0.810251\pi$
$548$	1.55580	−	8.82341i	0.0664607	−	0.376917i
$549$	3.39260	−	0.194782i	0.144793	−	0.00831309i
$550$	−3.37074			−0.143729
$551$	−3.51673	+	39.7259i	−0.149818	+	1.69238i
$552$	−1.02270	+	6.96183i	−0.0435289	+	0.296315i
$553$	−0.323709	+	1.83584i	−0.0137655	+	0.0780680i
$554$	−7.37658	−	6.18968i	−0.313401	−	0.262974i
$555$	16.1644	+	26.2307i	0.686140	+	1.11343i
$556$	−2.21004	+	12.5338i	−0.0937266	+	0.531550i
$557$	1.23359	+	6.99603i	0.0522689	+	0.296431i	0.999725	−	0.0234546i	$-0.00746650\pi$
$557$	1.23359	+	6.99603i	0.0522689	+	0.296431i	−0.947456	+	0.319886i	$0.896355\pi$
$558$	10.6120	+	3.18658i	0.449240	+	0.134899i
$559$	−6.80444	+	11.7856i	−0.287797	+	0.498479i
$560$	0.500294	+	2.83731i	0.0211413	+	0.119898i
$561$	−27.5089	−	44.6400i	−1.16143	−	1.88470i
$562$	−2.47015	−	4.27843i	−0.104197	−	0.180475i
$563$	−16.0285			−0.675522			−0.337761	−	0.941232i	$-0.609670\pi$
$563$	−16.0285			−0.675522			−0.337761	+	0.941232i	$0.609670\pi$
$564$	8.21728	+	13.3346i	0.346010	+	0.561487i
$565$	−3.73991	+	21.2101i	−0.157339	+	0.892315i
$566$	2.97611	−	2.49725i	0.125095	−	0.104967i
$567$	−3.61125	−	12.1354i	−0.151658	−	0.509640i
$568$	4.72921	−	1.72129i	0.198433	−	0.0722238i
$569$	−18.9076	−	32.7490i	−0.792649	−	1.37291i	−0.924321	−	0.381616i	$-0.875368\pi$
$569$	−18.9076	−	32.7490i	−0.792649	−	1.37291i	0.131672	−	0.991293i	$-0.457966\pi$
$570$	6.14450	−	14.1883i	0.257365	−	0.594281i
$571$	9.25405	−	16.0285i	0.387270	−	0.670771i	−0.604811	−	0.796369i	$-0.706752\pi$
$571$	9.25405	−	16.0285i	0.387270	−	0.670771i	0.992081	+	0.125598i	$0.0400849\pi$
$572$	−1.54955	+	8.78793i	−0.0647899	+	0.367442i
$573$	7.34741	−	6.53320i	0.306943	−	0.272928i
$574$	14.2622	+	5.19103i	0.595294	+	0.216669i
$575$	2.50814	+	2.10458i	0.104597	+	0.0877671i
$576$	2.40489	+	1.79347i	0.100204	+	0.0747277i
$577$	14.6098	+	25.3049i	0.608213	+	1.05346i	0.991535	+	0.129842i	$0.0414469\pi$
$577$	14.6098	+	25.3049i	0.608213	+	1.05346i	−0.383321	+	0.923615i	$0.625220\pi$
$578$	35.3933			1.47217
$579$	−6.82690	+	12.6488i	−0.283716	+	0.525664i
$580$	14.3537	−	12.0442i	0.596004	−	0.500107i
$581$	1.76793	+	3.06215i	0.0733462	+	0.127039i
$582$	9.38329	−	3.72325i	0.388950	−	0.154334i
$583$	18.4870	−	15.5125i	0.765655	−	0.642461i
$584$	−4.84273	−	4.06354i	−0.200394	−	0.168150i
$585$	−12.0406	+	5.18200i	−0.497817	+	0.214249i
$586$	−2.00199	+	11.3538i	−0.0827014	+	0.469023i
$587$	−11.1332	−	9.34190i	−0.459518	−	0.385581i	0.383436	−	0.923568i	$-0.374741\pi$
$587$	−11.1332	−	9.34190i	−0.459518	−	0.385581i	−0.842954	+	0.537986i	$0.819185\pi$
$588$	−6.81936	−	5.39664i	−0.281226	−	0.222554i
$589$	15.5461	+	4.18271i	0.640567	+	0.172346i
$590$	11.0554	−	19.1485i	0.455143	−	0.788331i
$591$	−7.24736	+	6.44424i	−0.298117	+	0.265080i
$592$	−8.16241	+	2.97087i	−0.335473	+	0.122102i
$593$	26.4073	−	22.1584i	1.08442	−	0.909936i	0.0881394	−	0.996108i	$-0.471908\pi$
$593$	26.4073	−	22.1584i	1.08442	−	0.909936i	0.996280	+	0.0861720i	$0.0274634\pi$
$594$	1.92096	−	21.6474i	0.0788178	−	0.888202i
$595$	3.62129	+	20.5373i	0.148458	+	0.841949i
$596$	−5.78383	+	10.0179i	−0.236915	+	0.410348i
$597$	4.96289	−	33.7840i	0.203118	−	1.38269i
$598$	6.63991	−	5.57154i	0.271526	−	0.227837i
$599$	−23.7430	+	19.9227i	−0.970113	+	0.814021i	−0.982568	−	0.185901i	$-0.940480\pi$
$599$	−23.7430	+	19.9227i	−0.970113	+	0.814021i	0.0124557	+	0.999922i	$0.496035\pi$
$600$	1.29751	−	0.514845i	0.0529704	−	0.0210184i
$601$	−9.55876	+	16.5563i	−0.389910	+	0.675344i	−0.992437	−	0.122755i	$-0.960827\pi$
$601$	−9.55876	+	16.5563i	−0.389910	+	0.675344i	0.602527	+	0.798098i	$0.294161\pi$
$602$	1.55819	+	8.83694i	0.0635071	+	0.360167i
$603$	5.17990	−	10.2928i	0.210942	−	0.419155i
$604$	−2.26373	+	1.89949i	−0.0921098	+	0.0772893i
$605$	12.4945	−	4.54761i	0.507972	−	0.184887i
$606$	−2.84802	−	13.8218i	−0.115693	−	0.561474i
$607$	15.0369	−	26.0446i	0.610327	−	1.05712i	−0.380858	−	0.924634i	$-0.624371\pi$
$607$	15.0369	−	26.0446i	0.610327	−	1.05712i	0.991185	−	0.132484i	$-0.0422953\pi$
$608$	3.56803	+	2.50383i	0.144703	+	0.101544i
$609$	3.24024	−	22.0573i	0.131301	−	0.893809i
$610$	−1.77704	−	1.49112i	−0.0719504	−	0.0603736i
$611$	3.35041	−	19.0011i	0.135543	−	0.768703i
$612$	17.4073	+	12.9817i	0.703650	+	0.524753i
$613$	23.0106	+	19.3082i	0.929389	+	0.779850i	0.975708	−	0.219077i	$-0.0703045\pi$
$613$	23.0106	+	19.3082i	0.929389	+	0.779850i	−0.0463186	+	0.998927i	$0.514749\pi$
$614$	−2.87166	+	2.40961i	−0.115891	+	0.0972438i
$615$	−5.56199	+	37.8622i	−0.224281	+	1.52675i
$616$	2.94194	+	5.09559i	0.118534	+	0.205307i
$617$	22.0778	−	18.5255i	0.888818	−	0.745807i	−0.0791543	−	0.996862i	$-0.525222\pi$
$617$	22.0778	−	18.5255i	0.888818	−	0.745807i	0.967973	+	0.251055i	$0.0807775\pi$
$618$	−5.81921	+	0.166914i	−0.234083	+	0.00671425i
$619$	−23.4330			−0.941852			−0.470926	−	0.882173i	$-0.656080\pi$
$619$	−23.4330			−0.941852			−0.470926	+	0.882173i	$0.656080\pi$
$620$	−3.78189	−	6.55043i	−0.151884	−	0.263071i
$621$	−14.9453	+	14.9082i	−0.599733	+	0.598247i
$622$	3.86958	+	3.24696i	0.155156	+	0.130191i
$623$	−4.74564	−	1.72727i	−0.190130	−	0.0692017i
$624$	−0.745793	−	3.61943i	−0.0298556	−	0.144893i
$625$	−3.52867	+	20.0121i	−0.141147	+	0.800483i
$626$	−14.0352	+	24.3096i	−0.560958	+	0.971608i
$627$	1.88146	−	31.5204i	0.0751382	−	1.25880i
$628$	−5.20570	−	9.01653i	−0.207730	−	0.359799i
$629$	−59.0821	+	21.5041i	−2.35576	+	0.857426i
$630$	−3.88546	+	7.72066i	−0.154800	+	0.307599i
$631$	28.7487	−	24.1230i	1.14447	−	0.960321i	0.144891	−	0.989448i	$-0.453717\pi$
$631$	28.7487	−	24.1230i	1.14447	−	0.960321i	0.999576	+	0.0291263i	$0.00927249\pi$
$632$	0.230100	−	1.30496i	0.00915289	−	0.0519086i
$633$	0.817710	−	0.0234546i	0.0325010	−	0.000932235i
$634$	−19.0734			−0.757502
$635$	−9.78886	−	16.9548i	−0.388459	−	0.672831i
$636$	−4.74689	+	8.79494i	−0.188226	+	0.348742i
$637$	1.86019	+	10.5497i	0.0737036	+	0.417994i
$638$	19.1332	−	33.1397i	0.757491	−	1.31201i
$639$	14.4603	+	4.34216i	0.572041	+	0.171773i
$640$	−0.355621	−	2.01683i	−0.0140572	−	0.0797222i
$641$	7.18231	−	40.7329i	0.283684	−	1.60885i	−0.426264	−	0.904599i	$-0.640170\pi$
$641$	7.18231	−	40.7329i	0.283684	−	1.60885i	0.709948	−	0.704254i	$-0.248718\pi$
$642$	20.0842	−	0.576079i	0.792660	−	0.0227360i
$643$	5.75505	+	4.82906i	0.226957	+	0.190439i	0.749174	−	0.662373i	$-0.230451\pi$
$643$	5.75505	+	4.82906i	0.226957	+	0.190439i	−0.522217	+	0.852812i	$0.674895\pi$
$644$	0.992445	−	5.62844i	0.0391078	−	0.221791i
$645$	−21.0301	+	8.34465i	−0.828059	+	0.328570i
$646$	25.8265	+	18.1235i	1.01613	+	0.713061i
$647$	15.4302			0.606625			0.303312	−	0.952891i	$-0.401907\pi$
$647$	15.4302			0.606625			0.303312	+	0.952891i	$0.401907\pi$
$648$	2.56697	+	8.62616i	0.100840	+	0.338868i
$649$	7.84120	−	44.4697i	0.307794	−	1.74559i
$650$	−1.61582	−	0.588112i	−0.0633778	−	0.0230676i
$651$	−8.54155	−	2.83428i	−0.334770	−	0.111084i
$652$	−17.3711	−	6.32255i	−0.680304	−	0.247610i
$653$	1.62375			0.0635422			0.0317711	−	0.999495i	$-0.489885\pi$
$653$	1.62375			0.0635422			0.0317711	+	0.999495i	$0.489885\pi$
$654$	−15.3746	+	6.10057i	−0.601194	+	0.238551i
$655$	−4.02004	−	22.7988i	−0.157076	−	0.890822i
$656$	−10.1379	−	3.68991i	−0.395820	−	0.144067i
$657$	−4.35842	−	18.4576i	−0.170038	−	0.720100i
$658$	−6.36101	−	11.0176i	−0.247978	−	0.429511i
$659$	12.6602	−	10.6231i	0.493170	−	0.413819i	−0.361990	−	0.932182i	$-0.617903\pi$
$659$	12.6602	−	10.6231i	0.493170	−	0.413819i	0.855161	+	0.518363i	$0.173458\pi$
$660$	−11.0866	+	9.85805i	−0.431546	+	0.383724i
$661$	−5.98819	−	33.9607i	−0.232913	−	1.32092i	−0.846964	−	0.531651i	$-0.821572\pi$
$661$	−5.98819	−	33.9607i	−0.232913	−	1.32092i	0.614050	−	0.789267i	$-0.289539\pi$
$662$	−8.36405	−	7.01827i	−0.325078	−	0.272773i
$663$	−5.39828	−	26.1986i	−0.209652	−	1.01747i
$664$	−1.25669	−	2.17665i	−0.0487691	−	0.0844705i
$665$	−5.31908	+	11.3762i	−0.206265	+	0.441152i
$666$	−24.9578	−	7.49438i	−0.967096	−	0.290401i
$667$	−34.9282	+	12.7128i	−1.35243	+	0.492243i
$668$	−22.0088	+	8.01056i	−0.851547	+	0.309938i
$669$	13.5072	−	0.387429i	0.522218	−	0.0149789i
$670$	−7.39158	+	2.69032i	−0.285562	+	0.103936i
$671$	−4.45183	−	1.62033i	−0.171861	−	0.0625523i
$672$	−1.91074	−	1.51210i	−0.0737085	−	0.0583307i
$673$	19.8152			0.763818			0.381909	−	0.924200i	$-0.375267\pi$
$673$	19.8152			0.763818			0.381909	+	0.924200i	$0.375267\pi$
$674$	24.3513	+	8.86314i	0.937977	+	0.341396i
$675$	4.04371	+	1.08889i	0.155642	+	0.0419113i
$676$	4.22392	−	7.31604i	0.162458	−	0.281386i
$677$	−21.4427	+	37.1399i	−0.824111	+	1.42740i	0.0784854	+	0.996915i	$0.474992\pi$
$677$	−21.4427	+	37.1399i	−0.824111	+	1.42740i	−0.902597	+	0.430487i	$0.858342\pi$
$678$	−9.55614	−	15.5072i	−0.367001	−	0.595551i
$679$	−7.70492	+	2.80436i	−0.295688	+	0.107622i
$680$	−2.57410	−	14.5985i	−0.0987123	−	0.559825i
$681$	−26.2446	+	23.3362i	−1.00569	+	0.894247i
$682$	−11.8332	−	9.92922i	−0.453116	−	0.380209i
$683$	−17.3519			−0.663953			−0.331976	−	0.943288i	$-0.607715\pi$
$683$	−17.3519			−0.663953			−0.331976	+	0.943288i	$0.607715\pi$
$684$	4.09017	+	12.4206i	0.156392	+	0.474912i
$685$	−18.3486			−0.701063
$686$	12.9547	+	10.8703i	0.494612	+	0.415029i
$687$	−40.4787	−	13.4318i	−1.54436	−	0.512454i
$688$	−1.10760	−	6.28152i	−0.0422269	−	0.239481i
$689$	11.5686	−	4.21064i	0.440730	−	0.160413i
$690$	14.4045	−	0.413168i	0.548371	−	0.0157290i
$691$	−5.53505	+	9.58699i	−0.210563	+	0.364706i	−0.951891	−	0.306437i	$-0.900863\pi$
$691$	−5.53505	+	9.58699i	−0.210563	+	0.364706i	0.741328	+	0.671143i	$0.234196\pi$
$692$	−0.147443	+	0.255379i	−0.00560494	+	0.00970805i
$693$	−2.06373	+	17.5306i	−0.0783945	+	0.665931i
$694$	−0.839789	−	0.305658i	−0.0318779	−	0.0116026i
$695$	26.0644			0.988679
$696$	−2.30324	+	15.6789i	−0.0873043	+	0.594308i
$697$	−73.3817	−	26.7088i	−2.77953	−	1.01167i
$698$	13.4742	−	4.90420i	0.510005	−	0.185627i
$699$	−19.7094	+	36.5172i	−0.745478	+	1.38121i
$700$	−1.06542	+	0.387782i	−0.0402692	+	0.0146568i
$701$	24.2791	−	8.83689i	0.917011	−	0.333765i	0.159962	−	0.987123i	$-0.448863\pi$
$701$	24.2791	−	8.83689i	0.917011	−	0.333765i	0.757049	+	0.653359i	$0.226641\pi$
$702$	4.69778	−	10.0419i	0.177306	−	0.379006i
$703$	−36.5623	−	9.83714i	−1.37897	−	0.371015i
$704$	−2.09120	−	3.62207i	−0.0788152	−	0.136512i
$705$	23.9713	−	21.3149i	0.902813	−	0.802766i
$706$	−11.7646	−	9.87166i	−0.442766	−	0.371525i
$707$	1.99041	+	11.2882i	0.0748570	+	0.424535i
$708$	3.77394	+	18.3155i	0.141833	+	0.688337i
$709$	16.9378	−	14.2125i	0.636112	−	0.533761i	−0.266710	−	0.963777i	$-0.585936\pi$
$709$	16.9378	−	14.2125i	0.636112	−	0.533761i	0.902821	+	0.430016i	$0.141492\pi$
$710$	−5.15336	−	8.92588i	−0.193402	−	0.334982i
$711$	2.89377	−	2.72561i	0.108525	−	0.102218i
$712$	3.37332	+	1.22779i	0.126421	+	0.0460133i
$713$	2.60550	+	14.7765i	0.0975766	+	0.553384i
$714$	−13.8306	−	10.9451i	−0.517596	−	0.409610i
$715$	18.2748			0.683439
$716$	12.3662	+	4.50091i	0.462145	+	0.168207i
$717$	−22.6349	+	20.1265i	−0.845314	+	0.751640i
$718$	25.1271	+	9.14550i	0.937734	+	0.341307i
$719$	−4.88647	+	27.7125i	−0.182234	+	1.03350i	0.747223	+	0.664574i	$0.231387\pi$
$719$	−4.88647	+	27.7125i	−0.182234	+	1.03350i	−0.929457	+	0.368930i	$0.879724\pi$
$720$	2.76188	−	5.48804i	0.102929	−	0.204527i
$721$	4.72845			0.176097
$722$	6.46165	+	17.8675i	0.240478	+	0.664959i
$723$	18.7875	+	14.8679i	0.698716	+	0.552943i
$724$	−2.71825	+	15.4160i	−0.101023	+	0.572930i
$725$	5.64865	+	4.73978i	0.209786	+	0.176031i
$726$	−5.34116	+	9.89600i	−0.198229	+	0.367275i
$727$	4.89996	−	27.7890i	0.181729	−	1.03064i	−0.748357	−	0.663297i	$-0.769157\pi$
$727$	4.89996	−	27.7890i	0.181729	−	1.03064i	0.930086	−	0.367342i	$-0.119732\pi$
$728$	0.521215	+	2.95595i	0.0193175	+	0.109555i
$729$	−9.29746	+	25.3487i	−0.344350	+	0.938841i
$730$	−6.47328	+	11.2120i	−0.239587	+	0.414976i
$731$	−8.01717	−	45.4676i	−0.296526	−	1.68168i
$732$	1.96114	−	0.0562518i	0.0724858	−	0.00207913i
$733$	−3.89835	−	6.75214i	−0.143989	−	0.249396i	0.785006	−	0.619488i	$-0.212660\pi$
$733$	−3.89835	−	6.75214i	−0.143989	−	0.249396i	−0.928995	+	0.370092i	$0.879326\pi$
$734$	−10.4738			−0.386597
$735$	−8.45898	+	15.6726i	−0.312014	+	0.578094i
$736$	−0.705455	+	4.00083i	−0.0260034	+	0.147473i
$737$	−12.3059	+	10.3259i	−0.453294	+	0.380359i
$738$	−17.7629	−	27.0559i	−0.653861	−	0.995940i
$739$	−40.5662	+	14.7649i	−1.49225	+	0.543136i	−0.954042	−	0.299674i	$-0.903122\pi$
$739$	−40.5662	+	14.7649i	−1.49225	+	0.543136i	−0.538211	+	0.842810i	$0.680900\pi$
$740$	8.89447	+	15.4057i	0.326967	+	0.566324i
$741$	6.40144	−	14.7816i	0.235163	−	0.543015i
$742$	4.05877	−	7.03000i	0.149002	−	0.258079i
$743$	6.62348	−	37.5636i	0.242992	−	1.37808i	−0.582119	−	0.813104i	$-0.697776\pi$
$743$	6.62348	−	37.5636i	0.242992	−	1.37808i	0.825110	−	0.564971i	$-0.191113\pi$
$744$	6.07155	+	2.01468i	0.222594	+	0.0738617i
$745$	22.2612	+	8.10242i	0.815588	+	0.296850i
$746$	−2.37445	−	1.99240i	−0.0869348	−	0.0729469i
$747$	0.881550	−	7.48843i	0.0322542	−	0.273987i
$748$	−15.1368	−	26.2177i	−0.553456	−	0.958614i
$749$	−16.3196			−0.596305
$750$	−10.8044	−	17.5328i	−0.394519	−	0.640206i
$751$	8.68807	−	7.29016i	0.317032	−	0.266022i	−0.470359	−	0.882475i	$-0.655876\pi$
$751$	8.68807	−	7.29016i	0.317032	−	0.266022i	0.787391	+	0.616453i	$0.211431\pi$
$752$	4.52157	+	7.83158i	0.164885	+	0.285588i
$753$	−20.1840	−	15.9730i	−0.735545	−	0.582088i
$754$	14.9539	−	12.5478i	0.544589	−	0.456964i
$755$	4.63598	+	3.89005i	0.168721	+	0.141574i
$756$	−1.88322	−	7.06329i	−0.0684919	−	0.256889i
$757$	−6.12290	+	34.7247i	−0.222541	+	1.26209i	0.644791	+	0.764359i	$0.276945\pi$
$757$	−6.12290	+	34.7247i	−0.222541	+	1.26209i	−0.867331	+	0.497731i	$0.834167\pi$
$758$	−2.80228	−	2.35139i	−0.101783	−	0.0854063i
$759$	27.3549	−	10.8543i	0.992920	−	0.393987i
$760$	3.78094	−	8.08652i	0.137149	−	0.293329i
$761$	−7.92202	+	13.7213i	−0.287173	+	0.497398i	−0.973134	−	0.230240i	$-0.926049\pi$
$761$	−7.92202	+	13.7213i	−0.287173	+	0.497398i	0.685961	+	0.727638i	$0.259382\pi$
$762$	15.7153	+	5.21470i	0.569305	+	0.188908i
$763$	12.6246	−	4.59497i	0.457040	−	0.166349i
$764$	4.34843	−	3.64877i	0.157321	−	0.132008i
$765$	19.9914	−	39.7242i	0.722790	−	1.43623i
$766$	−3.65223	−	20.7128i	−0.131960	−	0.748385i
$767$	11.5177	−	19.9492i	0.415880	−	0.720325i
$768$	1.35820	+	1.07484i	0.0490099	+	0.0387850i
$769$	27.3968	−	22.9887i	0.987955	−	0.828993i	0.00268454	−	0.999996i	$-0.499145\pi$
$769$	27.3968	−	22.9887i	0.987955	−	0.828993i	0.985270	+	0.171004i	$0.0547010\pi$
$770$	9.23071	−	7.74549i	0.332652	−	0.279128i
$771$	−17.4545	−	13.8130i	−0.628610	−	0.497463i
$772$	−4.14927	+	7.18675i	−0.149336	+	0.258657i
$773$	−3.58808	−	20.3490i	−0.129054	−	0.731903i	−0.978817	−	0.204738i	$-0.934366\pi$
$773$	−3.58808	−	20.3490i	−0.129054	−	0.731903i	0.849763	−	0.527166i	$-0.176745\pi$
$774$	8.60203	−	17.0928i	0.309194	−	0.614388i
$775$	2.28021	−	1.91332i	0.0819074	−	0.0687285i
$776$	5.47685	−	1.99341i	0.196607	−	0.0715593i
$777$	20.0885	+	6.66583i	0.720672	+	0.239135i
$778$	3.70486	−	6.41700i	0.132826	−	0.230061i
$779$	−26.9336	−	38.5494i	−0.964995	−	1.38118i
$780$	−7.03456	+	2.79128i	−0.251878	+	0.0999440i
$781$	−16.1244	−	13.5300i	−0.576976	−	0.484140i
$782$	−5.10631	+	28.9593i	−0.182601	+	1.03558i
$783$	−33.6586	+	33.5752i	−1.20286	+	1.19988i
$784$	−3.84621	−	3.22735i	−0.137365	−	0.115263i
$785$	−16.3336	+	13.7055i	−0.582969	+	0.489169i
$786$	15.3535	+	12.1503i	0.547641	+	0.433387i
$787$	19.1435	+	33.1576i	0.682394	+	1.18194i	0.974248	+	0.225478i	$0.0723943\pi$
$787$	19.1435	+	33.1576i	0.682394	+	1.18194i	−0.291855	+	0.956463i	$0.594272\pi$
$788$	−4.28922	+	3.59908i	−0.152797	+	0.128212i
$789$	7.90839	+	12.8333i	0.281546	+	0.456879i
$790$	−2.71372			−0.0965497
$791$	7.39743	+	12.8127i	0.263022	+	0.455568i
$792$	1.46695	−	12.4612i	0.0521257	−	0.442788i
$793$	−1.85135	−	1.55347i	−0.0657435	−	0.0551654i
$794$	−17.6292	−	6.41651i	−0.625638	−	0.227714i
$795$	19.4260	+	6.44599i	0.688969	+	0.228616i
$796$	3.42339	−	19.4150i	0.121339	−	0.688147i
$797$	12.8470	−	22.2516i	0.455063	−	0.788192i	−0.543629	−	0.839326i	$-0.682950\pi$
$797$	12.8470	−	22.2516i	0.455063	−	0.788192i	0.998692	+	0.0511334i	$0.0162834\pi$
$798$	−3.03153	−	10.1794i	−0.107315	−	0.360347i
$799$	32.7285	+	56.6875i	1.15785	+	2.00546i
$800$	0.757329	−	0.275645i	0.0267756	−	0.00974554i
$801$	5.91046	+	9.00263i	0.208836	+	0.318092i
$802$	17.2966	−	14.5136i	0.610763	−	0.512491i
$803$	−4.59127	+	26.0384i	−0.162022	+	0.918875i
$804$	3.15977	−	5.85436i	0.111436	−	0.206467i
$805$	−11.7045			−0.412530
$806$	−3.94004	−	6.82434i	−0.138782	−	0.240377i
$807$	42.7932	−	1.22745i	1.50639	−	0.0432082i
$808$	−1.41483	−	8.02391i	−0.0497736	−	0.282280i
$809$	21.3817	−	37.0341i	0.751739	−	1.30205i	−0.195240	−	0.980755i	$-0.562549\pi$
$809$	21.3817	−	37.0341i	0.751739	−	1.30205i	0.946979	−	0.321294i	$-0.104118\pi$
$810$	16.4846	−	8.24478i	0.579211	−	0.289692i
$811$	−2.67702	−	15.1821i	−0.0940027	−	0.533116i	−0.995048	−	0.0993917i	$-0.968310\pi$
$811$	−2.67702	−	15.1821i	−0.0940027	−	0.533116i	0.901046	−	0.433724i	$-0.142801\pi$
$812$	2.23511	−	12.6759i	0.0784370	−	0.444838i
$813$	20.9977	−	38.9041i	0.736421	−	1.36443i
$814$	27.8300	+	23.3521i	0.975440	+	0.818491i
$815$	−6.57399	+	37.2829i	−0.230277	+	1.30596i
$816$	9.83111	+	7.78004i	0.344158	+	0.272356i
$817$	11.7759	−	25.1859i	0.411987	−	0.881143i
$818$	−20.5783			−0.719504
$819$	−4.04794	+	8.04352i	−0.141446	+	0.281063i
$820$	−3.83665	+	21.7587i	−0.133982	+	0.759847i
$821$	2.85709	+	1.03990i	0.0997131	+	0.0362926i	0.391395	−	0.920223i	$-0.371993\pi$
$821$	2.85709	+	1.03990i	0.0997131	+	0.0362926i	−0.291682	+	0.956515i	$0.594215\pi$
$822$	11.5969	−	10.3117i	0.404487	−	0.359663i
$823$	−46.3510	−	16.8704i	−1.61570	−	0.588065i	−0.633140	−	0.774037i	$-0.718234\pi$
$823$	−46.3510	−	16.8704i	−1.61570	−	0.588065i	−0.982555	+	0.185972i	$0.940457\pi$
$824$	−3.36110			−0.117090
$825$	−4.57815	−	3.62301i	−0.159391	−	0.126137i
$826$	−2.63751	−	14.9581i	−0.0917706	−	0.520457i
$827$	18.9351	+	6.89180i	0.658437	+	0.239651i	0.649561	−	0.760309i	$-0.274953\pi$
$827$	18.9351	+	6.89180i	0.658437	+	0.239651i	0.00887563	+	0.999961i	$0.497175\pi$
$828$	−8.87189	+	8.35635i	−0.308320	+	0.290403i
$829$	−24.6333	−	42.6661i	−0.855550	−	1.48186i	−0.876134	−	0.482067i	$-0.839886\pi$
$829$	−24.6333	−	42.6661i	−0.855550	−	1.48186i	0.0205846	−	0.999788i	$-0.493447\pi$
$830$	−3.94303	+	3.30859i	−0.136865	+	0.114843i
$831$	−3.36597	−	16.3355i	−0.116764	−	0.566672i
$832$	−0.370492	−	2.10117i	−0.0128445	−	0.0728448i
$833$	−27.8401	−	23.3606i	−0.964602	−	0.809397i
$834$	−16.4735	+	14.6480i	−0.570430	+	0.507217i
$835$	23.9827	+	41.5393i	0.829957	+	1.43753i
$836$	1.60759	−	18.1597i	0.0555995	−	0.628065i
$837$	10.9881	+	15.7342i	0.379806	+	0.543853i
$838$	7.71646	−	2.80856i	0.266561	−	0.0970202i
$839$	33.0082	−	12.0140i	1.13957	−	0.414769i	0.297811	−	0.954625i	$-0.403743\pi$
$839$	33.0082	−	12.0140i	1.13957	−	0.414769i	0.841758	+	0.539856i	$0.181521\pi$
$840$	−2.37015	+	4.39138i	−0.0817781	+	0.151517i
$841$	−51.4116	+	18.7123i	−1.77281	+	0.645252i
$842$	18.1615	+	6.61026i	0.625888	+	0.227805i
$843$	1.24366	−	8.46600i	0.0428340	−	0.291585i
$844$	0.472299			0.0162572
$845$	−16.2573	−	5.91718i	−0.559269	−	0.203557i
$846$	−3.17181	+	26.9433i	−0.109049	+	0.926331i
$847$	4.56689	−	7.91009i	0.156920	−	0.271794i
$848$	−2.88508	+	4.99710i	−0.0990739	+	0.171601i
$849$	6.72630	−	0.192932i	0.230846	−	0.00662141i
$850$	5.48179	−	1.99521i	0.188024	−	0.0684351i
$851$	−6.12776	−	34.7522i	−0.210057	−	1.19129i
$852$	8.27335	+	2.74529i	0.283440	+	0.0940519i
$853$	0.370401	+	0.310803i	0.0126823	+	0.0106417i	0.649107	−	0.760697i	$-0.275143\pi$
$853$	0.370401	+	0.310803i	0.0126823	+	0.0106417i	−0.636424	+	0.771339i	$0.719587\pi$
$854$	−1.59354			−0.0545299
$855$	23.5956	−	12.6662i	0.806953	−	0.433175i
$856$	11.6004			0.396493
$857$	20.4425	+	17.1533i	0.698301	+	0.585944i	0.921290	−	0.388877i	$-0.127137\pi$
$857$	20.4425	+	17.1533i	0.698301	+	0.585944i	−0.222989	+	0.974821i	$0.571581\pi$
$858$	−11.5502	+	10.2703i	−0.394319	+	0.350622i
$859$	7.73570	+	43.8714i	0.263939	+	1.49687i	0.772040	+	0.635574i	$0.219237\pi$
$859$	7.73570	+	43.8714i	0.263939	+	1.49687i	−0.508101	+	0.861297i	$0.669652\pi$
$860$	−12.2749	+	4.46769i	−0.418569	+	0.152347i
$861$	13.7915	+	22.3801i	0.470012	+	0.762712i
$862$	−6.64663	+	11.5123i	−0.226385	+	0.392111i
$863$	1.78209	−	3.08667i	0.0606630	−	0.105071i	−0.834099	−	0.551615i	$-0.814012\pi$
$863$	1.78209	−	3.08667i	0.0606630	−	0.105071i	0.894762	+	0.446543i	$0.147345\pi$
$864$	1.33864	+	5.02076i	0.0455413	+	0.170810i
$865$	0.567490	+	0.206549i	0.0192952	+	0.00702289i
$866$	−10.0734			−0.342307
$867$	48.0713	+	38.0421i	1.63259	+	1.29198i
$868$	−4.88252	−	1.77709i	−0.165724	−	0.0603185i
$869$	−5.20785	+	1.89550i	−0.176664	+	0.0643006i
$870$	32.4408	−	0.930506i	1.09985	−	0.0315471i
$871$	−7.70067	+	2.80282i	−0.260927	+	0.0949698i
$872$	−8.97386	+	3.26622i	−0.303893	+	0.110608i
$873$	16.7463	+	5.02861i	0.566777	+	0.170193i
$874$	−12.5345	+	12.5087i	−0.423986	+	0.423115i
$875$	8.36367	+	14.4863i	0.282744	+	0.489726i
$876$	−2.20976	−	10.7243i	−0.0746610	−	0.362340i
$877$	5.22432	+	4.38373i	0.176413	+	0.148028i	0.726719	−	0.686935i	$-0.241044\pi$
$877$	5.22432	+	4.38373i	0.176413	+	0.148028i	−0.550306	+	0.834963i	$0.685489\pi$
$878$	3.70792	+	21.0287i	0.125136	+	0.709683i
$879$	−14.9227	+	13.2690i	−0.503330	+	0.447553i
$880$	−6.56142	+	5.50569i	−0.221185	+	0.185597i
$881$	7.74997	+	13.4233i	0.261103	+	0.452244i	0.966535	−	0.256534i	$-0.0825804\pi$
$881$	7.74997	+	13.4233i	0.261103	+	0.452244i	−0.705432	+	0.708777i	$0.749247\pi$
$882$	−3.46156	−	14.6595i	−0.116557	−	0.493610i
$883$	−14.3585	−	5.22606i	−0.483201	−	0.175871i	0.0889220	−	0.996039i	$-0.471658\pi$
$883$	−14.3585	−	5.22606i	−0.483201	−	0.175871i	−0.572123	+	0.820168i	$0.693880\pi$
$884$	−2.68174	−	15.2089i	−0.0901967	−	0.511531i
$885$	35.5971	−	14.1248i	1.19658	−	0.474799i
$886$	17.9710			0.603746
$887$	9.60278	+	3.49513i	0.322430	+	0.117355i	0.498164	−	0.867083i	$-0.334008\pi$
$887$	9.60278	+	3.49513i	0.322430	+	0.117355i	−0.175734	+	0.984438i	$0.556230\pi$
$888$	−14.2794	−	4.73824i	−0.479186	−	0.159005i
$889$	−12.6377	−	4.59974i	−0.423854	−	0.154270i
$890$	1.27661	−	7.24004i	0.0427922	−	0.242687i
$891$	25.8765	−	27.3368i	0.866896	−	0.915817i
$892$	7.80158			0.261216
$893$	−3.47589	+	39.2646i	−0.116316	+	1.31394i
$894$	−18.6232	+	7.38963i	−0.622854	+	0.247146i
$895$	4.67990	−	26.5410i	0.156432	−	0.887169i
$896$	−1.07768	−	0.904284i	−0.0360029	−	0.0302100i
$897$	15.0069	−	0.430445i	0.501065	−	0.0143722i
$898$	6.51441	−	36.9451i	0.217389	−	1.23287i
$899$	5.86790	+	33.2785i	0.195706	+	1.10990i
$900$	2.31565	+	0.695348i	0.0771884	+	0.0231783i
$901$	−20.8831	+	36.1706i	−0.695717	+	1.20502i
$902$	7.83539	+	44.4367i	0.260890	+	1.47958i
$903$	−7.38197	+	13.6772i	−0.245656	+	0.455148i
$904$	−5.25828	−	9.10760i	−0.174888	−	0.302914i
$905$	32.0580			1.06565
$906$	−5.11626	+	0.146751i	−0.169976	+	0.00487547i
$907$	0.204431	−	1.15939i	0.00678803	−	0.0384969i	−0.981226	−	0.192863i	$-0.938223\pi$
$907$	0.204431	−	1.15939i	0.00678803	−	0.0384969i	0.988014	+	0.154367i	$0.0493337\pi$
$908$	−15.5324	+	13.0332i	−0.515460	+	0.432522i
$909$	10.9881	−	21.8341i	0.364452	−	0.724190i
$910$	5.77630	−	2.10240i	0.191483	−	0.0696939i
$911$	−4.02033	−	6.96341i	−0.133199	−	0.230708i	0.791709	−	0.610899i	$-0.209192\pi$
$911$	−4.02033	−	6.96341i	−0.133199	−	0.230708i	−0.924908	+	0.380191i	$0.875858\pi$
$912$	2.15489	+	7.23578i	0.0713554	+	0.239601i
$913$	−5.25599	+	9.10364i	−0.173948	+	0.301287i
$914$	5.32461	−	30.1974i	0.176122	−	0.998840i
$915$	−0.810874	−	3.93528i	−0.0268067	−	0.130096i
$916$	−23.1384	−	8.42171i	−0.764516	−	0.278261i
$917$	−12.1824	−	10.2223i	−0.402299	−	0.337569i
$918$	9.68948	+	36.3419i	0.319800	+	1.19946i
$919$	−18.9164	−	32.7642i	−0.623996	−	1.08079i	−0.988734	−	0.149683i	$-0.952175\pi$
$919$	−18.9164	−	32.7642i	−0.623996	−	1.08079i	0.364738	−	0.931110i	$-0.381158\pi$
$920$	8.31987			0.274298
$921$	−6.49024	+	0.186161i	−0.213861	+	0.00613421i
$922$	−18.9303	+	15.8844i	−0.623436	+	0.523125i
$923$	−5.36886	−	9.29914i	−0.176718	−	0.306085i
$924$	−1.48119	+	10.0830i	−0.0487277	+	0.331705i
$925$	−5.36272	+	4.49986i	−0.176325	+	0.147954i
$926$	8.09081	+	6.78900i	0.265881	+	0.223100i
$927$	−8.08307	−	6.02802i	−0.265483	−	0.197986i
$928$	−1.58877	+	9.01038i	−0.0521540	+	0.295780i
$929$	39.6494	+	33.2698i	1.30085	+	1.09155i	0.989997	+	0.141089i	$0.0450604\pi$
$929$	39.6494	+	33.2698i	1.30085	+	1.09155i	0.310857	+	0.950457i	$0.399384\pi$
$930$	1.90409	−	12.9617i	0.0624376	−	0.425032i
$931$	−5.64263	−	21.1455i	−0.184930	−	0.693017i
$932$	−11.9790	+	20.7483i	−0.392386	+	0.679633i
$933$	1.76571	+	8.56921i	0.0578066	+	0.280543i
$934$	5.74263	−	2.09015i	0.187905	−	0.0683917i
$935$	−47.4937	+	39.8519i	−1.55321	+	1.30330i
$936$	2.87738	−	5.71753i	0.0940500	−	0.186883i
$937$	−3.02674	−	17.1655i	−0.0988794	−	0.560773i	−0.993489	−	0.113925i	$-0.963658\pi$
$937$	−3.02674	−	17.1655i	−0.0988794	−	0.560773i	0.894610	−	0.446848i	$-0.147453\pi$
$938$	−2.70173	+	4.67953i	−0.0882145	+	0.152792i
$939$	−45.1916	+	17.9318i	−1.47477	+	0.585183i
$940$	14.1870	−	11.9043i	0.462729	−	0.388276i
$941$	19.3602	−	16.2452i	0.631126	−	0.529577i	−0.270153	−	0.962817i	$-0.587074\pi$
$941$	19.3602	−	16.2452i	0.631126	−	0.529577i	0.901279	+	0.433240i	$0.142630\pi$
$942$	2.62094	−	17.8416i	0.0853949	−	0.581310i
$943$	21.9146	−	37.9572i	0.713637	−	1.23606i
$944$	1.87481	+	10.6326i	0.0610198	+	0.346060i
$945$	−13.5757	+	6.30998i	−0.441619	+	0.205264i
$946$	−20.4359	+	17.1477i	−0.664428	+	0.557521i
$947$	30.6808	−	11.1669i	0.996991	−	0.362875i	0.208568	−	0.978008i	$-0.433120\pi$
$947$	30.6808	−	11.1669i	0.996991	−	0.362875i	0.788423	+	0.615133i	$0.210898\pi$
$948$	1.71515	−	1.52508i	0.0557055	−	0.0495324i
$949$	−6.74397	+	11.6809i	−0.218919	+	0.379178i
$950$	3.39234	+	0.912715i	0.110062	+	0.0296124i
$951$	−25.9056	−	20.5009i	−0.840046	−	0.664787i
$952$	−7.80062	−	6.54550i	−0.252819	−	0.212141i
$953$	−8.23069	+	46.6786i	−0.266618	+	1.51207i	0.497769	+	0.867310i	$0.334153\pi$
$953$	−8.23069	+	46.6786i	−0.266618	+	1.51207i	−0.764387	+	0.644758i	$0.776958\pi$
$954$	−15.9004	+	6.84318i	−0.514795	+	0.221556i
$955$	−8.90534	−	7.47247i	−0.288170	−	0.241803i
$956$	−13.3960	+	11.2406i	−0.433259	+	0.363547i
$957$	61.6067	−	24.4453i	1.99146	−	0.790204i
$958$	−18.6544	−	32.3104i	−0.602697	−	1.04390i
$959$	−9.65553	+	8.10195i	−0.311793	+	0.261626i
$960$	1.68476	−	3.12150i	0.0543755	−	0.100746i
$961$	−17.3591			−0.559971
$962$	9.26641	+	16.0499i	0.298761	+	0.517469i
$963$	27.8976	+	20.8049i	0.898988	+	0.670428i
$964$	10.5964	+	8.89145i	0.341288	+	0.286374i
$965$	15.9700	+	5.81261i	0.514093	+	0.187115i
$966$	7.39762	−	6.57784i	0.238014	−	0.211639i
$967$	−1.82044	+	10.3242i	−0.0585414	+	0.332005i	−0.999987	−	0.00516103i	$-0.998357\pi$
$967$	−1.82044	+	10.3242i	−0.0585414	+	0.332005i	0.941445	+	0.337166i	$0.109468\pi$
$968$	−3.24626	+	5.62269i	−0.104339	+	0.180720i
$969$	15.5978	+	52.3749i	0.501072	+	1.68252i
$970$	−5.96805	−	10.3370i	−0.191623	−	0.331900i
$971$	−4.83606	+	1.76018i	−0.155196	+	0.0564869i	−0.418450	−	0.908240i	$-0.637427\pi$
$971$	−4.83606	+	1.76018i	−0.155196	+	0.0564869i	0.263254	+	0.964727i	$0.415204\pi$
$972$	−5.78529	+	14.4752i	−0.185563	+	0.464291i
$973$	13.7158	−	11.5089i	0.439708	−	0.368959i
$974$	−7.08284	+	40.1688i	−0.226949	+	1.28709i
$975$	−1.56249	−	2.53553i	−0.0500397	−	0.0812019i
$976$	1.13273			0.0362578
$977$	16.7497	+	29.0114i	0.535872	+	0.928157i	0.999121	+	0.0419286i	$0.0133502\pi$
$977$	16.7497	+	29.0114i	0.535872	+	0.928157i	−0.463249	+	0.886228i	$0.653316\pi$
$978$	−16.7977	−	27.2585i	−0.537132	−	0.871629i
$979$	−2.60716	−	14.7860i	−0.0833253	−	0.472561i
$980$	−5.14122	+	8.90486i	−0.164230	+	0.284455i
$981$	−27.4390	−	8.23941i	−0.876059	−	0.263064i
$982$	4.62350	+	26.2212i	0.147542	+	0.836751i
$983$	4.97606	−	28.2207i	0.158712	−	0.900099i	−0.796602	−	0.604505i	$-0.793371\pi$
$983$	4.97606	−	28.2207i	0.158712	−	0.900099i	0.955313	−	0.295595i	$-0.0955178\pi$
$984$	−9.80333	−	15.9083i	−0.312519	−	0.507139i
$985$	8.78408	+	7.37071i	0.279884	+	0.234850i
$986$	−11.5000	+	65.2200i	−0.366236	+	2.07703i
$987$	3.20262	−	21.8012i	0.101940	−	0.693940i
$988$	3.93904	−	8.42467i	0.125318	−	0.268025i
$989$	25.9127			0.823975
$990$	−25.6537	+	1.47288i	−0.815329	+	0.0468111i
$991$	3.00174	−	17.0237i	0.0953535	−	0.540777i	−0.899285	−	0.437363i	$-0.855912\pi$
$991$	3.00174	−	17.0237i	0.0953535	−	0.540777i	0.994638	−	0.103413i	$-0.0329765\pi$
$992$	3.47062	+	1.26320i	0.110192	+	0.0401067i
$993$	−3.81656	−	18.5223i	−0.121115	−	0.587786i
$994$	−6.65313	−	2.42154i	−0.211024	−	0.0768066i
$995$	−40.3742			−1.27995
$996$	0.632713	−	4.30708i	0.0200483	−	0.136475i
$997$	4.69926	+	26.6509i	0.148827	+	0.844041i	0.964214	+	0.265125i	$0.0854131\pi$
$997$	4.69926	+	26.6509i	0.148827	+	0.844041i	−0.815387	+	0.578916i	$0.803476\pi$
$998$	25.7408	+	9.36890i	0.814812	+	0.296567i
$999$	−25.8425	−	37.0046i	−0.817622	−	1.17077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.v.b.157.6	yes	66
9.7	even	3		342.2.w.b.43.5	yes	66
19.4	even	9		342.2.w.b.175.5	yes	66
171.61	even	9	inner	342.2.v.b.61.6	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.v.b.61.6	✓	66	171.61	even	9	inner
342.2.v.b.157.6	yes	66	1.1	even	1	trivial
342.2.w.b.43.5	yes	66	9.7	even	3
342.2.w.b.175.5	yes	66	19.4	even	9

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.349550 + 1.69641i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.92444 - 0.700437i) q^{5} +(-0.822662 + 1.52421i) q^{6} +(0.703408 - 1.21834i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.75563 + 1.18596i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.349550 + 1.69641i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.92444 - 0.700437i) q^{5} +(-0.822662 + 1.52421i) q^{6} +(0.703408 - 1.21834i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.75563 + 1.18596i) q^{9} +(1.92444 + 0.700437i) q^{10} +4.18241 q^{11} +(-1.60994 + 0.638818i) q^{12} +(2.00491 + 0.729728i) q^{13} +(1.32197 - 0.481159i) q^{14} +(1.86092 + 3.01980i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-6.80180 + 2.47565i) q^{17} +(-2.87326 - 0.862786i) q^{18} +(-4.20921 - 1.13250i) q^{19} +(1.02397 + 1.77357i) q^{20} +(2.31268 + 0.767400i) q^{21} +(3.20391 + 2.68840i) q^{22} +(-0.705455 - 4.00083i) q^{23} +(-1.64391 - 0.545487i) q^{24} +(-0.617381 + 0.518044i) q^{25} +(1.06679 + 1.84773i) q^{26} +(-2.97511 - 4.26013i) q^{27} +(1.32197 + 0.481159i) q^{28} +(-1.58877 - 9.01038i) q^{29} +(-0.515545 + 3.50947i) q^{30} -3.69336 q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.46196 + 7.09509i) q^{33} +(-6.80180 - 2.47565i) q^{34} +(0.500294 - 2.83731i) q^{35} +(-1.64645 - 2.50783i) q^{36} +8.68625 q^{37} +(-2.49649 - 3.57317i) q^{38} +(-0.537103 + 3.65623i) q^{39} +(-0.355621 + 2.01683i) q^{40} +(8.26453 + 6.93476i) q^{41} +(1.27834 + 2.07442i) q^{42} +(-1.10760 + 6.28152i) q^{43} +(0.726267 + 4.11887i) q^{44} +(-4.47234 + 4.21245i) q^{45} +(2.03128 - 3.51827i) q^{46} +(-1.57032 - 8.90575i) q^{47} +(-0.908677 - 1.47455i) q^{48} +(2.51043 + 4.34820i) q^{49} -0.805933 q^{50} +(-6.57729 - 10.6733i) q^{51} +(-0.370492 + 2.10117i) q^{52} +(4.42019 - 3.70898i) q^{53} +(0.459295 - 5.17581i) q^{54} +(8.04877 - 2.92951i) q^{55} +(0.703408 + 1.21834i) q^{56} +(0.449851 - 7.53642i) q^{57} +(4.57469 - 7.92359i) q^{58} +(1.87481 - 10.6326i) q^{59} +(-2.65078 + 2.35703i) q^{60} +(-1.06442 - 0.387417i) q^{61} +(-2.82928 - 2.37404i) q^{62} +(-0.493430 + 4.19150i) q^{63} +(-0.500000 - 0.866025i) q^{64} +4.36945 q^{65} +(-3.44071 + 6.37488i) q^{66} +(-2.94231 + 2.46889i) q^{67} +(-3.61916 - 6.26857i) q^{68} +(6.54047 - 2.59523i) q^{69} +(2.20703 - 1.85192i) q^{70} +(-3.85529 - 3.23497i) q^{71} +(0.350743 - 2.97943i) q^{72} +(-1.09776 + 6.22570i) q^{73} +(6.65405 + 5.58341i) q^{74} +(-1.09462 - 0.866250i) q^{75} +(0.384368 - 4.34192i) q^{76} +(2.94194 - 5.09559i) q^{77} +(-2.76162 + 2.45559i) q^{78} +(-1.24518 + 0.453209i) q^{79} +(-1.56881 + 1.31639i) q^{80} +(6.18699 - 6.53614i) q^{81} +(1.87342 + 10.6247i) q^{82} +(-1.25669 + 2.17665i) q^{83} +(-0.354149 + 2.41080i) q^{84} +(-11.3556 + 9.52846i) q^{85} +(-4.88615 + 4.09997i) q^{86} +(14.7300 - 5.84479i) q^{87} +(-2.09120 + 3.62207i) q^{88} +(-0.623365 - 3.53528i) q^{89} +(-6.13373 + 0.352160i) q^{90} +(2.29932 - 1.92936i) q^{91} +(3.81755 - 1.38947i) q^{92} +(-1.29101 - 6.26546i) q^{93} +(4.52157 - 7.83158i) q^{94} +(-8.89360 + 0.768874i) q^{95} +(0.251738 - 1.71366i) q^{96} +(-4.46477 - 3.74639i) q^{97} +(-0.871865 + 4.94459i) q^{98} +(-11.5252 + 4.96017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{3} + 6 q^{6} - 12 q^{7} - 33 q^{8} + 6 q^{9}+O(q^{10}) \) 66 * q + 6 * q^3 + 6 * q^6 - 12 * q^7 - 33 * q^8 + 6 * q^9	\( 66 q + 6 q^{3} + 6 q^{6} - 12 q^{7} - 33 q^{8} + 6 q^{9} - 3 q^{13} - 3 q^{14} - 3 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} + 6 q^{23} - 3 q^{24} - 12 q^{25} + 3 q^{27} - 3 q^{28} - 18 q^{29} + 45 q^{33} + 9 q^{34} - 18 q^{35} + 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{41} - 3 q^{43} - 12 q^{44} + 9 q^{45} - 18 q^{47} - 3 q^{48} - 57 q^{49} + 126 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} - 9 q^{54} + 36 q^{55} - 12 q^{56} + 48 q^{57} - 18 q^{58} - 39 q^{59} - 30 q^{60} - 54 q^{61} - 21 q^{62} - 54 q^{63} - 33 q^{64} + 24 q^{65} - 27 q^{66} + 6 q^{67} - 6 q^{68} - 15 q^{69} + 36 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} + 6 q^{74} + 15 q^{78} + 21 q^{79} + 138 q^{81} + 6 q^{82} + 12 q^{83} - 24 q^{84} - 36 q^{85} - 3 q^{86} + 30 q^{87} + 9 q^{89} - 42 q^{90} + 27 q^{91} - 12 q^{92} - 9 q^{93} - 6 q^{94} - 3 q^{95} - 30 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 66 * q + 6 * q^3 + 6 * q^6 - 12 * q^7 - 33 * q^8 + 6 * q^9 - 3 * q^13 - 3 * q^14 - 3 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 + 6 * q^23 - 3 * q^24 - 12 * q^25 + 3 * q^27 - 3 * q^28 - 18 * q^29 + 45 * q^33 + 9 * q^34 - 18 * q^35 + 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^41 - 3 * q^43 - 12 * q^44 + 9 * q^45 - 18 * q^47 - 3 * q^48 - 57 * q^49 + 126 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 - 9 * q^54 + 36 * q^55 - 12 * q^56 + 48 * q^57 - 18 * q^58 - 39 * q^59 - 30 * q^60 - 54 * q^61 - 21 * q^62 - 54 * q^63 - 33 * q^64 + 24 * q^65 - 27 * q^66 + 6 * q^67 - 6 * q^68 - 15 * q^69 + 36 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 + 6 * q^74 + 15 * q^78 + 21 * q^79 + 138 * q^81 + 6 * q^82 + 12 * q^83 - 24 * q^84 - 36 * q^85 - 3 * q^86 + 30 * q^87 + 9 * q^89 - 42 * q^90 + 27 * q^91 - 12 * q^92 - 9 * q^93 - 6 * q^94 - 3 * q^95 - 30 * q^97 + 24 * q^98 - 24 * q^99

Introduction

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