LMFDB - Embedded newform 798.2.bp.e.613.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			613.5
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.e.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.172004 - 0.975484i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-1.52438 - 2.16246i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.172004 - 0.975484i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-1.52438 - 2.16246i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.758792 + 0.636702i) q^{10} +(2.52196 + 4.36816i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.12356 + 6.37203i) q^{13} +(-0.222260 + 2.63640i) q^{14} +(-0.758792 + 0.636702i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.721582 + 4.09229i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.32305 - 3.68829i) q^{19} +0.990533 q^{20} +(-0.222260 + 2.63640i) q^{21} +(0.875867 - 4.96729i) q^{22} +(-5.01027 - 1.82359i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(3.77648 + 1.37453i) q^{25} +(3.23516 - 5.60346i) q^{26} +(0.500000 - 0.866025i) q^{27} +(1.86491 - 1.87673i) q^{28} +(-5.06217 - 1.84248i) q^{29} +0.990533 q^{30} +10.7274 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.875867 - 4.96729i) q^{33} +(3.18324 - 2.67106i) q^{34} +(-2.37165 + 1.11506i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.25963 + 7.37789i) q^{37} +(-0.591228 + 4.31862i) q^{38} +(3.23516 - 5.60346i) q^{39} +(-0.758792 - 0.636702i) q^{40} +(1.68326 - 9.54625i) q^{41} +(1.86491 - 1.87673i) q^{42} +(5.66452 + 4.75310i) q^{43} +(-3.86386 + 3.24217i) q^{44} +0.990533 q^{45} +(2.66591 + 4.61749i) q^{46} +(0.195247 + 1.10730i) q^{47} +(0.939693 + 0.342020i) q^{48} +(-2.35251 + 6.59285i) q^{49} +(-2.00942 - 3.48042i) q^{50} +(3.18324 - 2.67106i) q^{51} +(-6.08012 + 2.21298i) q^{52} +(1.39384 + 7.90487i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(4.69486 - 1.70879i) q^{55} +(-2.63494 + 0.238923i) q^{56} +(-0.591228 + 4.31862i) q^{57} +(2.69352 + 4.66532i) q^{58} +(-0.363360 + 2.06072i) q^{59} +(-0.758792 - 0.636702i) q^{60} +(4.64392 + 1.69025i) q^{61} +(-8.21768 - 6.89545i) q^{62} +(1.86491 - 1.87673i) q^{63} +(-0.500000 - 0.866025i) q^{64} +6.40907 q^{65} +(-3.86386 + 3.24217i) q^{66} +(-1.01708 + 0.853433i) q^{67} -4.15542 q^{68} +(2.66591 + 4.61749i) q^{69} +(2.53354 + 0.670283i) q^{70} +(5.55081 + 4.65768i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-5.98793 - 5.02447i) q^{73} +(1.47935 - 8.38983i) q^{74} +(-2.00942 - 3.48042i) q^{75} +(3.22886 - 2.92822i) q^{76} +(5.60156 - 12.1124i) q^{77} +(-6.08012 + 2.21298i) q^{78} +(11.2992 - 4.11256i) q^{79} +(0.172004 + 0.975484i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-7.42567 + 6.23087i) q^{82} +(3.13714 + 5.43368i) q^{83} +(-2.63494 + 0.238923i) q^{84} +(3.86785 + 1.40778i) q^{85} +(-1.28404 - 7.28217i) q^{86} +(2.69352 + 4.66532i) q^{87} +5.04392 q^{88} +(1.67953 - 1.40929i) q^{89} +(-0.758792 - 0.636702i) q^{90} +(12.0665 - 12.1431i) q^{91} +(0.925860 - 5.25081i) q^{92} +(-8.21768 - 6.89545i) q^{93} +(0.562191 - 0.973743i) q^{94} +(-3.99744 + 1.63170i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(0.0777896 - 0.0283131i) q^{97} +(6.03993 - 3.53826i) q^{98} +(-3.86386 + 3.24217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 6 q^{5} + 6 q^{7} + 21 q^{8}+O(q^{10}) $ 42 * q - 6 * q^5 + 6 * q^7 + 21 * q^8	$ 42 q - 6 q^{5} + 6 q^{7} + 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} + 3 q^{14} - 3 q^{15} - 6 q^{17} + 21 q^{18} + 18 q^{20} + 3 q^{21} + 3 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{26} + 21 q^{27} + 6 q^{28} + 15 q^{29} + 18 q^{30} - 6 q^{31} + 3 q^{33} - 3 q^{34} - 12 q^{35} + 21 q^{37} + 15 q^{38} - 3 q^{39} - 3 q^{40} + 9 q^{41} + 6 q^{42} - 12 q^{44} + 18 q^{45} + 12 q^{46} + 15 q^{47} + 30 q^{50} - 3 q^{51} + 9 q^{52} - 36 q^{53} - 27 q^{55} - 6 q^{56} + 15 q^{57} - 18 q^{58} - 3 q^{60} - 9 q^{61} - 6 q^{62} + 6 q^{63} - 21 q^{64} - 24 q^{65} - 12 q^{66} - 3 q^{67} + 12 q^{68} + 12 q^{69} - 24 q^{70} - 6 q^{71} - 15 q^{73} + 12 q^{74} + 30 q^{75} - 6 q^{76} + 21 q^{77} + 9 q^{78} + 21 q^{79} - 6 q^{80} - 18 q^{83} - 6 q^{84} - 30 q^{85} + 9 q^{86} - 18 q^{87} - 18 q^{88} + 12 q^{89} - 3 q^{90} - 18 q^{91} - 24 q^{92} - 6 q^{93} + 24 q^{94} - 27 q^{95} - 21 q^{96} - 3 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) $ 42 * q - 6 * q^5 + 6 * q^7 + 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 + 3 * q^14 - 3 * q^15 - 6 * q^17 + 21 * q^18 + 18 * q^20 + 3 * q^21 + 3 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^26 + 21 * q^27 + 6 * q^28 + 15 * q^29 + 18 * q^30 - 6 * q^31 + 3 * q^33 - 3 * q^34 - 12 * q^35 + 21 * q^37 + 15 * q^38 - 3 * q^39 - 3 * q^40 + 9 * q^41 + 6 * q^42 - 12 * q^44 + 18 * q^45 + 12 * q^46 + 15 * q^47 + 30 * q^50 - 3 * q^51 + 9 * q^52 - 36 * q^53 - 27 * q^55 - 6 * q^56 + 15 * q^57 - 18 * q^58 - 3 * q^60 - 9 * q^61 - 6 * q^62 + 6 * q^63 - 21 * q^64 - 24 * q^65 - 12 * q^66 - 3 * q^67 + 12 * q^68 + 12 * q^69 - 24 * q^70 - 6 * q^71 - 15 * q^73 + 12 * q^74 + 30 * q^75 - 6 * q^76 + 21 * q^77 + 9 * q^78 + 21 * q^79 - 6 * q^80 - 18 * q^83 - 6 * q^84 - 30 * q^85 + 9 * q^86 - 18 * q^87 - 18 * q^88 + 12 * q^89 - 3 * q^90 - 18 * q^91 - 24 * q^92 - 6 * q^93 + 24 * q^94 - 27 * q^95 - 21 * q^96 - 3 * q^97 + 24 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.172004	−	0.975484i	0.0769226	−	0.436250i	−0.921886	−	0.387460i	$-0.873352\pi$
$5$	0.172004	−	0.975484i	0.0769226	−	0.436250i	0.998809	−	0.0487897i	$-0.0155364\pi$
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	−1.52438	−	2.16246i	−0.576163	−	0.817335i
$7$	−1.52438	−	2.16246i	−0.576163	−	0.817335i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.758792	+	0.636702i	−0.239951	+	0.201343i
$11$	2.52196	+	4.36816i	0.760399	+	1.31705i	0.942645	+	0.333797i	$0.108330\pi$
$11$	2.52196	+	4.36816i	0.760399	+	1.31705i	−0.182246	+	0.983253i	$0.558337\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.12356	+	6.37203i	0.311619	+	1.76728i	0.590580	+	0.806979i	$0.298899\pi$
$13$	1.12356	+	6.37203i	0.311619	+	1.76728i	−0.278960	+	0.960303i	$0.589990\pi$
$14$	−0.222260	+	2.63640i	−0.0594014	+	0.704607i
$15$	−0.758792	+	0.636702i	−0.195919	+	0.164396i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.721582	+	4.09229i	−0.175009	+	0.992527i	0.763124	+	0.646252i	$0.223665\pi$
$17$	−0.721582	+	4.09229i	−0.175009	+	0.992527i	−0.938133	+	0.346275i	$0.887446\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.32305	−	3.68829i	−0.532943	−	0.846151i
$19$	−2.32305	−	3.68829i	−0.532943	−	0.846151i
$20$	0.990533			0.221490
$21$	−0.222260	+	2.63640i	−0.0485011	+	0.575309i
$22$	0.875867	−	4.96729i	0.186735	−	1.05903i
$23$	−5.01027	−	1.82359i	−1.04471	−	0.380244i	−0.238048	−	0.971253i	$-0.576507\pi$
$23$	−5.01027	−	1.82359i	−1.04471	−	0.380244i	−0.806665	+	0.591009i	$0.798730\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	3.77648	+	1.37453i	0.755296	+	0.274905i
$26$	3.23516	−	5.60346i	0.634467	−	1.09893i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	1.86491	−	1.87673i	0.352434	−	0.354669i
$29$	−5.06217	−	1.84248i	−0.940021	−	0.342140i	−0.173847	−	0.984773i	$-0.555620\pi$
$29$	−5.06217	−	1.84248i	−0.940021	−	0.342140i	−0.766174	+	0.642633i	$0.777842\pi$
$30$	0.990533			0.180846
$31$	10.7274			1.92670			0.963351	−	0.268245i	$-0.0864437\pi$
$31$	10.7274			1.92670			0.963351	+	0.268245i	$0.0864437\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.875867	−	4.96729i	0.152469	−	0.864694i
$34$	3.18324	−	2.67106i	0.545921	−	0.458082i
$35$	−2.37165	+	1.11506i	−0.400882	+	0.188479i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	4.25963	+	7.37789i	0.700279	+	1.21292i	0.968369	+	0.249524i	$0.0802742\pi$
$37$	4.25963	+	7.37789i	0.700279	+	1.21292i	−0.268090	+	0.963394i	$0.586392\pi$
$38$	−0.591228	+	4.31862i	−0.0959098	+	0.700572i
$39$	3.23516	−	5.60346i	0.518041	−	0.897272i
$40$	−0.758792	−	0.636702i	−0.119976	−	0.100671i
$41$	1.68326	−	9.54625i	0.262881	−	1.49087i	−0.512119	−	0.858914i	$-0.671140\pi$
$41$	1.68326	−	9.54625i	0.262881	−	1.49087i	0.775001	−	0.631960i	$-0.217749\pi$
$42$	1.86491	−	1.87673i	0.287761	−	0.289586i
$43$	5.66452	+	4.75310i	0.863832	+	0.724841i	0.962790	−	0.270251i	$-0.0871065\pi$
$43$	5.66452	+	4.75310i	0.863832	+	0.724841i	−0.0989581	+	0.995092i	$0.531551\pi$
$44$	−3.86386	+	3.24217i	−0.582499	+	0.488775i
$45$	0.990533			0.147660
$46$	2.66591	+	4.61749i	0.393067	+	0.680811i
$47$	0.195247	+	1.10730i	0.0284797	+	0.161516i	0.995731	−	0.0923052i	$-0.0294235\pi$
$47$	0.195247	+	1.10730i	0.0284797	+	0.161516i	−0.967251	+	0.253821i	$0.918312\pi$
$48$	0.939693	+	0.342020i	0.135633	+	0.0493664i
$49$	−2.35251	+	6.59285i	−0.336073	+	0.941836i
$50$	−2.00942	−	3.48042i	−0.284175	−	0.492206i
$51$	3.18324	−	2.67106i	0.445743	−	0.374023i
$52$	−6.08012	+	2.21298i	−0.843160	+	0.306885i
$53$	1.39384	+	7.90487i	0.191459	+	1.08582i	0.917372	+	0.398031i	$0.130306\pi$
$53$	1.39384	+	7.90487i	0.191459	+	1.08582i	−0.725913	+	0.687786i	$0.758583\pi$
$54$	−0.939693	+	0.342020i	−0.127876	+	0.0465430i
$55$	4.69486	−	1.70879i	0.633055	−	0.230413i
$56$	−2.63494	+	0.238923i	−0.352109	+	0.0319274i
$57$	−0.591228	+	4.31862i	−0.0783100	+	0.572015i
$58$	2.69352	+	4.66532i	0.353677	+	0.612587i
$59$	−0.363360	+	2.06072i	−0.0473054	+	0.268283i	−0.999282	−	0.0378885i	$-0.987937\pi$
$59$	−0.363360	+	2.06072i	−0.0473054	+	0.268283i	0.951977	+	0.306171i	$0.0990479\pi$
$60$	−0.758792	−	0.636702i	−0.0979596	−	0.0821979i
$61$	4.64392	+	1.69025i	0.594593	+	0.216414i	0.621748	−	0.783217i	$-0.286423\pi$
$61$	4.64392	+	1.69025i	0.594593	+	0.216414i	−0.0271553	+	0.999631i	$0.508645\pi$
$62$	−8.21768	−	6.89545i	−1.04365	−	0.875723i
$63$	1.86491	−	1.87673i	0.234956	−	0.236446i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.40907			0.794947
$66$	−3.86386	+	3.24217i	−0.475609	+	0.399083i
$67$	−1.01708	+	0.853433i	−0.124256	+	0.104263i	−0.702798	−	0.711389i	$-0.748066\pi$
$67$	−1.01708	+	0.853433i	−0.124256	+	0.104263i	0.578542	+	0.815653i	$0.303622\pi$
$68$	−4.15542			−0.503919
$69$	2.66591	+	4.61749i	0.320937	+	0.555880i
$70$	2.53354	+	0.670283i	0.302816	+	0.0801141i
$71$	5.55081	+	4.65768i	0.658760	+	0.552765i	0.909715	−	0.415234i	$-0.136300\pi$
$71$	5.55081	+	4.65768i	0.658760	+	0.552765i	−0.250955	+	0.967999i	$0.580745\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	−5.98793	−	5.02447i	−0.700834	−	0.588070i	0.221177	−	0.975234i	$-0.429010\pi$
$73$	−5.98793	−	5.02447i	−0.700834	−	0.588070i	−0.922011	+	0.387164i	$0.873455\pi$
$74$	1.47935	−	8.38983i	0.171971	−	0.975298i
$75$	−2.00942	−	3.48042i	−0.232028	−	0.401884i
$76$	3.22886	−	2.92822i	0.370376	−	0.335890i
$77$	5.60156	−	12.1124i	0.638357	−	1.38034i
$78$	−6.08012	+	2.21298i	−0.688438	+	0.250571i
$79$	11.2992	−	4.11256i	1.27125	−	0.462699i	0.383724	−	0.923448i	$-0.374641\pi$
$79$	11.2992	−	4.11256i	1.27125	−	0.462699i	0.887531	+	0.460749i	$0.152419\pi$
$80$	0.172004	+	0.975484i	0.0192307	+	0.109062i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−7.42567	+	6.23087i	−0.820028	+	0.688085i
$83$	3.13714	+	5.43368i	0.344346	+	0.596424i	0.985235	−	0.171209i	$-0.0547675\pi$
$83$	3.13714	+	5.43368i	0.344346	+	0.596424i	−0.640889	+	0.767633i	$0.721434\pi$
$84$	−2.63494	+	0.238923i	−0.287496	+	0.0260686i
$85$	3.86785	+	1.40778i	0.419528	+	0.152696i
$86$	−1.28404	−	7.28217i	−0.138462	−	0.785257i
$87$	2.69352	+	4.66532i	0.288776	+	0.500175i
$88$	5.04392			0.537683
$89$	1.67953	−	1.40929i	0.178029	−	0.149384i	−0.549419	−	0.835547i	$-0.685151\pi$
$89$	1.67953	−	1.40929i	0.178029	−	0.149384i	0.727448	+	0.686163i	$0.240706\pi$
$90$	−0.758792	−	0.636702i	−0.0799837	−	0.0671143i
$91$	12.0665	−	12.1431i	1.26492	−	1.27294i
$92$	0.925860	−	5.25081i	0.0965276	−	0.547435i
$93$	−8.21768	−	6.89545i	−0.852134	−	0.715025i
$94$	0.562191	−	0.973743i	0.0579856	−	0.100434i
$95$	−3.99744	+	1.63170i	−0.410129	+	0.167408i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	0.0777896	−	0.0283131i	0.00789834	−	0.00287476i	−0.338068	−	0.941122i	$-0.609773\pi$
$97$	0.0777896	−	0.0283131i	0.00789834	−	0.00287476i	0.345966	+	0.938247i	$0.387551\pi$
$98$	6.03993	−	3.53826i	0.610125	−	0.357418i
$99$	−3.86386	+	3.24217i	−0.388333	+	0.325850i
$100$	−0.697865	+	3.95779i	−0.0697865	+	0.395779i
$101$	−1.55534	−	0.566097i	−0.154762	−	0.0563287i	0.263478	−	0.964666i	$-0.415130\pi$
$101$	−1.55534	−	0.566097i	−0.154762	−	0.0563287i	−0.418239	+	0.908337i	$0.637353\pi$
$102$	−4.15542			−0.411448
$103$	1.16307			0.114600			0.0573002	−	0.998357i	$-0.481751\pi$
$103$	1.16307			0.114600			0.0573002	+	0.998357i	$0.481751\pi$
$104$	6.08012	+	2.21298i	0.596204	+	0.217001i
$105$	2.53354	+	0.670283i	0.247248	+	0.0654129i
$106$	4.01341	−	6.95142i	0.389816	−	0.675182i
$107$	−0.191144	+	0.331071i	−0.0184786	+	0.0320059i	−0.875117	−	0.483912i	$-0.839216\pi$
$107$	−0.191144	+	0.331071i	−0.0184786	+	0.0320059i	0.856638	+	0.515918i	$0.172549\pi$
$108$	0.939693	+	0.342020i	0.0904220	+	0.0329109i
$109$	0.893987	−	0.325385i	0.0856284	−	0.0311662i	−0.298851	−	0.954300i	$-0.596603\pi$
$109$	0.893987	−	0.325385i	0.0856284	−	0.0311662i	0.384479	+	0.923134i	$0.374381\pi$
$110$	−4.69486	−	1.70879i	−0.447637	−	0.162927i
$111$	1.47935	−	8.38983i	0.140414	−	0.796327i
$112$	2.17206	+	1.51068i	0.205240	+	0.142746i
$113$	−17.7699			−1.67165			−0.835827	−	0.548993i	$-0.815011\pi$
$113$	−17.7699			−1.67165			−0.835827	+	0.548993i	$0.815011\pi$
$114$	3.22886	−	2.92822i	0.302410	−	0.274253i
$115$	−2.64067	+	4.57377i	−0.246244	+	0.426506i
$116$	0.935451	−	5.30521i	0.0868545	−	0.492576i
$117$	−6.08012	+	2.21298i	−0.562107	+	0.204590i
$118$	1.60295	−	1.34504i	0.147564	−	0.123821i
$119$	9.94941	−	4.67783i	0.912061	−	0.428816i
$120$	0.172004	+	0.975484i	0.0157018	+	0.0890491i
$121$	−7.22055	+	12.5064i	−0.656414	+	1.13694i
$122$	−2.47098	−	4.27986i	−0.223712	−	0.387480i
$123$	−7.42567	+	6.23087i	−0.669550	+	0.561819i
$124$	1.86280	+	10.5644i	0.167284	+	0.948715i
$125$	4.46673	−	7.73660i	0.399517	−	0.691983i
$126$	−2.63494	+	0.238923i	−0.234739	+	0.0212849i
$127$	0.520545	+	2.95216i	0.0461909	+	0.261962i	0.999154	−	0.0411245i	$-0.0130940\pi$
$127$	0.520545	+	2.95216i	0.0461909	+	0.261962i	−0.952963	+	0.303086i	$0.901983\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−1.28404	−	7.28217i	−0.113054	−	0.641160i
$130$	−4.90963	−	4.11967i	−0.430603	−	0.361319i
$131$	−8.42486	−	7.06930i	−0.736084	−	0.617648i	0.195699	−	0.980664i	$-0.437302\pi$
$131$	−8.42486	−	7.06930i	−0.736084	−	0.617648i	−0.931783	+	0.363016i	$0.881747\pi$
$132$	5.04392			0.439017
$133$	−4.43457	+	10.6459i	−0.384526	+	0.923114i
$134$	1.32771			0.114696
$135$	−0.758792	−	0.636702i	−0.0653064	−	0.0547986i
$136$	3.18324	+	2.67106i	0.272961	+	0.229041i
$137$	3.87695	+	21.9873i	0.331231	+	1.87850i	0.461680	+	0.887047i	$0.347247\pi$
$137$	3.87695	+	21.9873i	0.331231	+	1.87850i	−0.130449	+	0.991455i	$0.541642\pi$
$138$	0.925860	−	5.25081i	0.0788144	−	0.446979i
$139$	−1.47667	−	8.37464i	−0.125250	−	0.710328i	−0.981159	−	0.193201i	$-0.938113\pi$
$139$	−1.47667	−	8.37464i	−0.125250	−	0.710328i	0.855909	−	0.517126i	$-0.172998\pi$
$140$	−1.50995	−	2.14199i	−0.127614	−	0.181031i
$141$	0.562191	−	0.973743i	0.0473450	−	0.0820040i
$142$	−1.25827	−	7.13598i	−0.105591	−	0.598838i
$143$	−25.0005	+	20.9779i	−2.09064	+	1.75426i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.66802	+	4.62115i	−0.221567	+	0.383766i
$146$	1.35735	+	7.69793i	0.112335	+	0.637085i
$147$	6.03993	−	3.53826i	0.498165	−	0.291830i
$148$	−6.52613	+	5.47607i	−0.536445	+	0.450130i
$149$	−6.46847	+	2.35433i	−0.529918	+	0.192874i	−0.593102	−	0.805128i	$-0.702097\pi$
$149$	−6.46847	+	2.35433i	−0.529918	+	0.192874i	0.0631837	+	0.998002i	$0.479875\pi$
$150$	−0.697865	+	3.95779i	−0.0569804	+	0.323152i
$151$	4.23448	−	7.33433i	0.344597	−	0.596859i	−0.640684	−	0.767805i	$-0.721349\pi$
$151$	4.23448	−	7.33433i	0.344597	−	0.596859i	0.985280	+	0.170946i	$0.0546823\pi$
$152$	−4.35567	+	0.167674i	−0.353292	+	0.0136002i
$153$	−4.15542			−0.335946
$154$	−12.0767	+	5.67802i	−0.973172	+	0.457548i
$155$	1.84516	−	10.4644i	0.148207	−	0.840523i
$156$	6.08012	+	2.21298i	0.486799	+	0.177180i
$157$	−9.33805	+	3.39877i	−0.745258	+	0.271252i	−0.686609	−	0.727027i	$-0.740901\pi$
$157$	−9.33805	+	3.39877i	−0.745258	+	0.271252i	−0.0586488	+	0.998279i	$0.518679\pi$
$158$	−11.2992	−	4.11256i	−0.898913	−	0.327178i
$159$	4.01341	−	6.95142i	0.318284	−	0.551284i
$160$	0.495266	−	0.857827i	0.0391542	−	0.0678171i
$161$	3.69412	+	13.6144i	0.291138	+	1.07296i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	−19.0152			−1.48939			−0.744694	−	0.667406i	$-0.767404\pi$
$163$	−19.0152			−1.48939			−0.744694	+	0.667406i	$0.767404\pi$
$164$	9.69352			0.756937
$165$	−4.69486	−	1.70879i	−0.365494	−	0.133029i
$166$	1.08952	−	6.17895i	0.0845629	−	0.479580i
$167$	7.68799	−	6.45099i	0.594915	−	0.499193i	−0.294892	−	0.955531i	$-0.595284\pi$
$167$	7.68799	−	6.45099i	0.594915	−	0.499193i	0.889807	+	0.456338i	$0.150839\pi$
$168$	2.17206	+	1.51068i	0.167578	+	0.116552i
$169$	−27.1243	+	9.87244i	−2.08649	+	0.759419i
$170$	−2.05804	−	3.56463i	−0.157845	−	0.273395i
$171$	3.22886	−	2.92822i	0.246917	−	0.223926i
$172$	−3.69726	+	6.40383i	−0.281913	+	0.488288i
$173$	−4.33867	−	3.64058i	−0.329863	−	0.276788i	0.462781	−	0.886473i	$-0.346852\pi$
$173$	−4.33867	−	3.64058i	−0.329863	−	0.276788i	−0.792644	+	0.609685i	$0.791296\pi$
$174$	0.935451	−	5.30521i	0.0709164	−	0.402187i
$175$	−2.78444	−	10.2618i	−0.210484	−	0.775720i
$176$	−3.86386	−	3.24217i	−0.291250	−	0.244388i
$177$	1.60295	−	1.34504i	0.120485	−	0.101099i
$178$	−2.19246			−0.164332
$179$	0.543291	+	0.941008i	0.0406075	+	0.0703343i	0.885615	−	0.464420i	$-0.153737\pi$
$179$	0.543291	+	0.941008i	0.0406075	+	0.0703343i	−0.845007	+	0.534755i	$0.820404\pi$
$180$	0.172004	+	0.975484i	0.0128204	+	0.0727083i
$181$	23.9527	+	8.71807i	1.78039	+	0.648009i	0.999734	+	0.0230469i	$0.00733672\pi$
$181$	23.9527	+	8.71807i	1.78039	+	0.648009i	0.780655	+	0.624962i	$0.214886\pi$
$182$	−17.0489	+	1.54591i	−1.26375	+	0.114590i
$183$	−2.47098	−	4.27986i	−0.182660	−	0.316376i
$184$	−4.08441	+	3.42722i	−0.301106	+	0.252658i
$185$	7.92969	−	2.88617i	0.583003	−	0.212196i
$186$	1.86280	+	10.5644i	0.136587	+	0.774623i
$187$	−19.6956	+	7.16861i	−1.44028	+	0.524221i
$188$	−1.05657	+	0.384561i	−0.0770585	+	0.0280470i
$189$	−2.63494	+	0.238923i	−0.191664	+	0.0173791i
$190$	4.11105	+	1.31955i	0.298247	+	0.0957305i
$191$	−4.71000	−	8.15797i	−0.340804	−	0.590290i	0.643778	−	0.765212i	$-0.277366\pi$
$191$	−4.71000	−	8.15797i	−0.340804	−	0.590290i	−0.984582	+	0.174922i	$0.944033\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	12.3512	+	10.3639i	0.889061	+	0.746011i	0.968022	−	0.250867i	$-0.0807156\pi$
$193$	12.3512	+	10.3639i	0.889061	+	0.746011i	−0.0789604	+	0.996878i	$0.525160\pi$
$194$	−0.0777896	−	0.0283131i	−0.00558497	−	0.00203276i
$195$	−4.90963	−	4.11967i	−0.351586	−	0.295016i
$196$	−6.90120	−	1.17193i	−0.492943	−	0.0837093i
$197$	11.9800	+	20.7500i	0.853542	+	1.47838i	0.877991	+	0.478677i	$0.158883\pi$
$197$	11.9800	+	20.7500i	0.853542	+	1.47838i	−0.0244492	+	0.999701i	$0.507783\pi$
$198$	5.04392			0.358456
$199$	−6.15908	+	5.16808i	−0.436605	+	0.366355i	−0.834437	−	0.551103i	$-0.814207\pi$
$199$	−6.15908	+	5.16808i	−0.436605	+	0.366355i	0.397832	+	0.917458i	$0.369763\pi$
$200$	3.07861	−	2.58326i	0.217691	−	0.182664i
$201$	1.32771			0.0936491
$202$	0.827578	+	1.43341i	0.0582282	+	0.100854i
$203$	3.73239	+	13.7554i	0.261963	+	0.965441i
$204$	3.18324	+	2.67106i	0.222871	+	0.187011i
$205$	−9.02269	−	3.28399i	−0.630172	−	0.229364i
$206$	−0.890961	−	0.747605i	−0.0620762	−	0.0520881i
$207$	0.925860	−	5.25081i	0.0643517	−	0.364957i
$208$	−3.23516	−	5.60346i	−0.224318	−	0.388530i
$209$	10.2524	−	19.4491i	0.709173	−	1.34533i
$210$	−1.50995	−	2.14199i	−0.104197	−	0.147812i
$211$	6.80273	−	2.47599i	0.468319	−	0.170454i	−0.0970715	−	0.995277i	$-0.530948\pi$
$211$	6.80273	−	2.47599i	0.468319	−	0.170454i	0.565391	+	0.824823i	$0.308725\pi$
$212$	−7.54274	+	2.74533i	−0.518037	+	0.188550i
$213$	−1.25827	−	7.13598i	−0.0862150	−	0.488949i
$214$	0.359233	−	0.130750i	0.0245567	−	0.00893790i
$215$	5.61090	−	4.70810i	0.382660	−	0.321090i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−16.3527	−	23.1977i	−1.11009	−	1.57476i
$218$	−0.893987	−	0.325385i	−0.0605484	−	0.0220378i
$219$	1.35735	+	7.69793i	0.0917214	+	0.520178i
$220$	2.49808	+	4.32681i	0.168421	+	0.291713i
$221$	−26.8869			−1.80861
$222$	−6.52613	+	5.47607i	−0.438005	+	0.367530i
$223$	6.32830	+	5.31007i	0.423774	+	0.355589i	0.829597	−	0.558363i	$-0.188570\pi$
$223$	6.32830	+	5.31007i	0.423774	+	0.355589i	−0.405822	+	0.913952i	$0.633015\pi$
$224$	−0.692846	−	2.55342i	−0.0462927	−	0.170608i
$225$	−0.697865	+	3.95779i	−0.0465243	+	0.263853i
$226$	13.6126	+	11.4223i	0.905494	+	0.759799i
$227$	13.8783	−	24.0380i	0.921137	−	1.59546i	0.123478	−	0.992347i	$-0.460595\pi$
$227$	13.8783	−	24.0380i	0.921137	−	1.59546i	0.797659	−	0.603108i	$-0.206071\pi$
$228$	−4.35567	+	0.167674i	−0.288461	+	0.0111045i
$229$	6.07874	+	10.5287i	0.401695	+	0.695756i	0.993931	−	0.110009i	$-0.0350880\pi$
$229$	6.07874	+	10.5287i	0.401695	+	0.695756i	−0.592236	+	0.805765i	$0.701755\pi$
$230$	4.96283	−	1.80632i	0.327240	−	0.119105i
$231$	−12.0767	+	5.67802i	−0.794591	+	0.373586i
$232$	−4.12672	+	3.46273i	−0.270932	+	0.227339i
$233$	−2.04059	+	11.5727i	−0.133683	+	0.758156i	0.842084	+	0.539346i	$0.181328\pi$
$233$	−2.04059	+	11.5727i	−0.133683	+	0.758156i	−0.975768	+	0.218810i	$0.929783\pi$
$234$	6.08012	+	2.21298i	0.397470	+	0.144667i
$235$	1.11374			0.0726522
$236$	−2.09251			−0.136211
$237$	−11.2992	−	4.11256i	−0.733959	−	0.267139i
$238$	−10.6285	−	2.81193i	−0.688946	−	0.182270i
$239$	−4.17783	+	7.23622i	−0.270242	+	0.468072i	−0.968924	−	0.247360i	$-0.920437\pi$
$239$	−4.17783	+	7.23622i	−0.270242	+	0.468072i	0.698682	+	0.715432i	$0.253770\pi$
$240$	0.495266	−	0.857827i	0.0319693	−	0.0553725i
$241$	0.658781	+	0.239777i	0.0424358	+	0.0154454i	0.363151	−	0.931730i	$-0.381701\pi$
$241$	0.658781	+	0.239777i	0.0424358	+	0.0154454i	−0.320715	+	0.947176i	$0.603923\pi$
$242$	13.5702	−	4.93915i	0.872325	−	0.317500i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	−0.858162	+	4.86688i	−0.0549382	+	0.311570i
$245$	6.02658	+	3.42883i	0.385024	+	0.219060i
$246$	9.69352			0.618036
$247$	20.8918	−	18.9465i	1.32931	−	1.20554i
$248$	5.36371	−	9.29022i	0.340596	−	0.589929i
$249$	1.08952	−	6.17895i	0.0690453	−	0.391575i
$250$	−8.39471	+	3.05542i	−0.530928	+	0.193242i
$251$	−18.7179	+	15.7062i	−1.18146	+	0.991365i	−0.181495	+	0.983392i	$0.558094\pi$
$251$	−18.7179	+	15.7062i	−1.18146	+	0.991365i	−0.999968	+	0.00797351i	$0.997462\pi$
$252$	2.17206	+	1.51068i	0.136827	+	0.0951640i
$253$	−4.66996	−	26.4847i	−0.293598	−	1.66508i
$254$	1.49885	−	2.59609i	0.0940463	−	0.162893i
$255$	−2.05804	−	3.56463i	−0.128880	−	0.223226i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.65402	+	9.38041i	0.103175	+	0.585134i	0.991934	+	0.126758i	$0.0404573\pi$
$257$	1.65402	+	9.38041i	0.103175	+	0.585134i	−0.888759	+	0.458375i	$0.848432\pi$
$258$	−3.69726	+	6.40383i	−0.230181	+	0.398685i
$259$	9.46112	−	20.4580i	0.587886	−	1.27120i
$260$	1.11292	+	6.31170i	0.0690206	+	0.391435i
$261$	0.935451	−	5.30521i	0.0579030	−	0.328384i
$262$	1.90976	+	10.8308i	0.117985	+	0.669129i
$263$	1.23371	+	1.03521i	0.0760741	+	0.0638337i	0.680032	−	0.733183i	$-0.261966\pi$
$263$	1.23371	+	1.03521i	0.0760741	+	0.0638337i	−0.603958	+	0.797016i	$0.706410\pi$
$264$	−3.86386	−	3.24217i	−0.237804	−	0.199542i
$265$	7.95082			0.488415
$266$	10.2401	−	5.30472i	0.627862	−	0.325253i
$267$	−2.19246			−0.134177
$268$	−1.01708	−	0.853433i	−0.0621281	−	0.0521317i
$269$	−7.96515	−	6.68356i	−0.485644	−	0.407504i	0.366818	−	0.930293i	$-0.380447\pi$
$269$	−7.96515	−	6.68356i	−0.485644	−	0.407504i	−0.852462	+	0.522789i	$0.824892\pi$
$270$	0.172004	+	0.975484i	0.0104678	+	0.0593661i
$271$	0.768520	−	4.35849i	0.0466842	−	0.264759i	−0.952528	−	0.304452i	$-0.901527\pi$
$271$	0.768520	−	4.35849i	0.0466842	−	0.264759i	0.999212	+	0.0396924i	$0.0126378\pi$
$272$	−0.721582	−	4.09229i	−0.0437523	−	0.248132i
$273$	−17.0489	+	1.54591i	−1.03185	+	0.0935626i
$274$	11.1632	−	19.3353i	0.674396	−	1.16809i
$275$	3.51997	+	19.9628i	0.212262	+	1.20380i
$276$	−4.08441	+	3.42722i	−0.245852	+	0.206295i
$277$	4.96505	+	8.59971i	0.298321	+	0.516707i	0.975752	−	0.218879i	$-0.0702402\pi$
$277$	4.96505	+	8.59971i	0.298321	+	0.516707i	−0.677431	+	0.735586i	$0.736907\pi$
$278$	−4.25192	+	7.36453i	−0.255013	+	0.441695i
$279$	1.86280	+	10.5644i	0.111523	+	0.632477i
$280$	−0.220156	+	2.61144i	−0.0131568	+	0.156063i
$281$	−23.2006	+	19.4676i	−1.38403	+	1.16134i	−0.416342	+	0.909208i	$0.636688\pi$
$281$	−23.2006	+	19.4676i	−1.38403	+	1.16134i	−0.967692	+	0.252135i	$0.918867\pi$
$282$	−1.05657	+	0.384561i	−0.0629180	+	0.0229003i
$283$	−3.09343	+	17.5437i	−0.183886	+	1.04287i	0.743493	+	0.668743i	$0.233167\pi$
$283$	−3.09343	+	17.5437i	−0.183886	+	1.04287i	−0.927379	+	0.374123i	$0.877944\pi$
$284$	−3.62303	+	6.27528i	−0.214987	+	0.372369i
$285$	4.11105	+	1.31955i	0.243518	+	0.0781636i
$286$	32.6358			1.92979
$287$	−23.2094	+	10.9122i	−1.37001	+	0.644124i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	−0.251418	−	0.0915087i	−0.0147893	−	0.00538286i
$290$	5.01425	−	1.82504i	0.294447	−	0.107170i
$291$	−0.0777896	−	0.0283131i	−0.00456011	−	0.00165974i
$292$	3.90834	−	6.76945i	0.228718	−	0.396152i
$293$	14.1976	−	24.5910i	0.829433	−	1.43662i	−0.0690507	−	0.997613i	$-0.521997\pi$
$293$	14.1976	−	24.5910i	0.829433	−	1.43662i	0.898484	−	0.439007i	$-0.144670\pi$
$294$	−6.90120	−	1.17193i	−0.402486	−	0.0683484i
$295$	1.94770	+	0.708904i	0.113399	+	0.0412740i
$296$	8.51926			0.495172
$297$	5.04392			0.292678
$298$	6.46847	+	2.35433i	0.374709	+	0.136383i
$299$	5.99061	−	33.9745i	0.346446	−	1.96479i
$300$	3.07861	−	2.58326i	0.177744	−	0.149145i
$301$	1.64350	−	19.4949i	0.0947299	−	1.12367i
$302$	−7.95821	+	2.89655i	−0.457944	+	0.166678i
$303$	0.827578	+	1.43341i	0.0475431	+	0.0823471i
$304$	3.44442	+	2.67133i	0.197551	+	0.153211i
$305$	2.44759	−	4.23934i	0.140148	−	0.242744i
$306$	3.18324	+	2.67106i	0.181974	+	0.152694i
$307$	−3.55013	+	20.1338i	−0.202617	+	1.14910i	0.698530	+	0.715581i	$0.253838\pi$
$307$	−3.55013	+	20.1338i	−0.202617	+	1.14910i	−0.901146	+	0.433515i	$0.857273\pi$
$308$	12.9011	+	3.41316i	0.735108	+	0.194483i
$309$	−0.890961	−	0.747605i	−0.0506850	−	0.0425298i
$310$	−8.13988	+	6.83017i	−0.462314	+	0.387928i
$311$	2.77528			0.157372			0.0786859	−	0.996899i	$-0.474928\pi$
$311$	2.77528			0.157372			0.0786859	+	0.996899i	$0.474928\pi$
$312$	−3.23516	−	5.60346i	−0.183155	−	0.317234i
$313$	−6.10741	−	34.6369i	−0.345211	−	1.95779i	−0.280353	−	0.959897i	$-0.590451\pi$
$313$	−6.10741	−	34.6369i	−0.345211	−	1.95779i	−0.0648587	−	0.997894i	$-0.520660\pi$
$314$	9.33805	+	3.39877i	0.526977	+	0.191804i
$315$	−1.50995	−	2.14199i	−0.0850762	−	0.120688i
$316$	6.01216	+	10.4134i	0.338210	+	0.585797i
$317$	5.17997	−	4.34651i	0.290936	−	0.244124i	−0.485624	−	0.874168i	$-0.661407\pi$
$317$	5.17997	−	4.34651i	0.290936	−	0.244124i	0.776560	+	0.630044i	$0.216963\pi$
$318$	−7.54274	+	2.74533i	−0.422976	+	0.153951i
$319$	−4.71834	−	26.7590i	−0.264176	−	1.49822i
$320$	−0.930796	+	0.338782i	−0.0520331	+	0.0189385i
$321$	0.359233	−	0.130750i	0.0200504	−	0.00729777i
$322$	5.92129	−	12.8038i	0.329980	−	0.713525i
$323$	16.7698	−	6.84519i	0.933098	−	0.380877i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−4.51541	+	25.6082i	−0.250470	+	1.42049i
$326$	14.5665	+	12.2228i	0.806764	+	0.676956i
$327$	−0.893987	−	0.325385i	−0.0494376	−	0.0179938i
$328$	−7.42567	−	6.23087i	−0.410014	−	0.344042i
$329$	2.09687	−	2.11016i	0.115604	−	0.116337i
$330$	2.49808	+	4.32681i	0.137515	+	0.238183i
$331$	−2.32951			−0.128042			−0.0640208	−	0.997949i	$-0.520392\pi$
$331$	−2.32951			−0.128042			−0.0640208	+	0.997949i	$0.520392\pi$
$332$	−4.80637	+	4.03303i	−0.263784	+	0.221341i
$333$	−6.52613	+	5.47607i	−0.357630	+	0.300087i
$334$	−10.0360			−0.549143
$335$	0.657568	+	1.13894i	0.0359268	+	0.0622270i
$336$	−0.692846	−	2.55342i	−0.0377978	−	0.139301i
$337$	−7.63367	−	6.40541i	−0.415832	−	0.348925i	0.410743	−	0.911751i	$-0.365269\pi$
$337$	−7.63367	−	6.40541i	−0.415832	−	0.348925i	−0.826575	+	0.562827i	$0.809714\pi$
$338$	27.1243	+	9.87244i	1.47537	+	0.536990i
$339$	13.6126	+	11.4223i	0.739333	+	0.620374i
$340$	−0.714751	+	4.05355i	−0.0387628	+	0.219835i
$341$	27.0541	+	46.8591i	1.46506	+	2.53756i
$342$	−4.35567	+	0.167674i	−0.235528	+	0.00906680i
$343$	17.8429	−	4.96282i	0.963428	−	0.267967i
$344$	6.94857	−	2.52907i	0.374642	−	0.136358i
$345$	4.96283	−	1.80632i	0.267190	−	0.0972492i
$346$	0.983497	+	5.57769i	0.0528731	+	0.299858i
$347$	−6.10025	+	2.22031i	−0.327479	+	0.119193i	−0.500527	−	0.865721i	$-0.666860\pi$
$347$	−6.10025	+	2.22031i	−0.327479	+	0.119193i	0.173049	+	0.984913i	$0.444638\pi$
$348$	−4.12672	+	3.46273i	−0.221215	+	0.185622i
$349$	5.30197	+	9.18328i	0.283808	+	0.491570i	0.972319	−	0.233656i	$-0.0750689\pi$
$349$	5.30197	+	9.18328i	0.283808	+	0.491570i	−0.688512	+	0.725225i	$0.741736\pi$
$350$	−4.46316	+	9.65080i	−0.238566	+	0.515857i
$351$	6.08012	+	2.21298i	0.324533	+	0.118120i
$352$	0.875867	+	4.96729i	0.0466839	+	0.264757i
$353$	−13.8686	−	24.0211i	−0.738152	−	1.27852i	−0.953327	−	0.301941i	$-0.902365\pi$
$353$	−13.8686	−	24.0211i	−0.738152	−	1.27852i	0.215175	−	0.976576i	$-0.430968\pi$
$354$	−2.09251			−0.111215
$355$	5.49826	−	4.61359i	0.291817	−	0.244864i
$356$	1.67953	+	1.40929i	0.0890147	+	0.0746922i
$357$	−10.6285	−	2.81193i	−0.562522	−	0.148823i
$358$	0.188683	−	1.07008i	0.00997221	−	0.0565552i
$359$	−4.48238	−	3.76116i	−0.236571	−	0.198507i	0.516793	−	0.856110i	$-0.327126\pi$
$359$	−4.48238	−	3.76116i	−0.236571	−	0.198507i	−0.753364	+	0.657604i	$0.771570\pi$
$360$	0.495266	−	0.857827i	0.0261028	−	0.0452114i
$361$	−8.20691	+	17.1361i	−0.431943	+	0.901901i
$362$	−12.7450	−	22.0749i	−0.669860	−	1.16023i
$363$	13.5702	−	4.93915i	0.712250	−	0.259238i
$364$	14.0539	+	9.77460i	0.736626	+	0.512328i
$365$	−5.93124	+	4.97690i	−0.310455	+	0.260503i
$366$	−0.858162	+	4.86688i	−0.0448568	+	0.254396i
$367$	−30.2749	−	11.0191i	−1.58033	−	0.575195i	−0.605058	−	0.796181i	$-0.706850\pi$
$367$	−30.2749	−	11.0191i	−1.58033	−	0.575195i	−0.975277	+	0.220987i	$0.929072\pi$
$368$	5.33181			0.277940
$369$	9.69352			0.504625
$370$	−7.92969	−	2.88617i	−0.412245	−	0.150045i
$371$	14.9692	−	15.0642i	0.777165	−	0.782093i
$372$	5.36371	−	9.29022i	0.278095	−	0.481675i
$373$	10.6258	−	18.4044i	0.550183	−	0.952946i	−0.448077	−	0.893995i	$-0.647891\pi$
$373$	10.6258	−	18.4044i	0.550183	−	0.952946i	0.998261	−	0.0589510i	$-0.0187756\pi$
$374$	19.6956	+	7.16861i	1.01844	+	0.370680i
$375$	−8.39471	+	3.05542i	−0.433501	+	0.157781i
$376$	1.05657	+	0.384561i	0.0544886	+	0.0198322i
$377$	6.05267	−	34.3264i	0.311729	−	1.76790i
$378$	2.17206	+	1.51068i	0.111719	+	0.0777011i
$379$	−32.9847			−1.69431			−0.847156	−	0.531344i	$-0.821687\pi$
$379$	−32.9847			−1.69431			−0.847156	+	0.531344i	$0.821687\pi$
$380$	−2.30105	−	3.65337i	−0.118042	−	0.187414i
$381$	1.49885	−	2.59609i	0.0767885	−	0.133002i
$382$	−1.63577	+	9.27690i	−0.0836931	+	0.474647i
$383$	20.4418	−	7.44021i	1.04453	−	0.380177i	0.237933	−	0.971282i	$-0.423530\pi$
$383$	20.4418	−	7.44021i	1.04453	−	0.380177i	0.806595	+	0.591105i	$0.201308\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	−10.8520	−	7.54762i	−0.553067	−	0.384662i
$386$	−2.79980	−	15.8784i	−0.142506	−	0.808191i
$387$	−3.69726	+	6.40383i	−0.187942	+	0.325525i
$388$	0.0413910	+	0.0716913i	0.00210131	+	0.00363957i
$389$	−10.9828	+	9.21569i	−0.556852	+	0.467254i	−0.877253	−	0.480028i	$-0.840627\pi$
$389$	−10.9828	+	9.21569i	−0.556852	+	0.467254i	0.320402	+	0.947282i	$0.396182\pi$
$390$	1.11292	+	6.31170i	0.0563550	+	0.319605i
$391$	11.0780	−	19.1876i	0.560237	−	0.970359i
$392$	4.53332	+	5.33376i	0.228967	+	0.269395i
$393$	1.90976	+	10.8308i	0.0963347	+	0.546341i
$394$	4.16062	−	23.5961i	0.209609	−	1.18875i
$395$	−2.06823	−	11.7295i	−0.104064	−	0.590177i
$396$	−3.86386	−	3.24217i	−0.194166	−	0.162925i
$397$	0.0973557	+	0.0816912i	0.00488614	+	0.00409996i	0.645227	−	0.763991i	$-0.276763\pi$
$397$	0.0973557	+	0.0816912i	0.00488614	+	0.00409996i	−0.640341	+	0.768091i	$0.721207\pi$
$398$	8.04011			0.403014
$399$	10.2401	−	5.30472i	0.512647	−	0.265568i
$400$	−4.01884			−0.200942
$401$	9.16364	+	7.68920i	0.457610	+	0.383981i	0.842251	−	0.539086i	$-0.181230\pi$
$401$	9.16364	+	7.68920i	0.457610	+	0.383981i	−0.384641	+	0.923066i	$0.625675\pi$
$402$	−1.01708	−	0.853433i	−0.0507274	−	0.0425654i
$403$	12.0529	+	68.3554i	0.600398	+	3.40502i
$404$	0.287415	−	1.63001i	0.0142994	−	0.0810960i
$405$	0.172004	+	0.975484i	0.00854696	+	0.0484722i
$406$	5.98263	−	12.9364i	0.296913	−	0.642022i
$407$	−21.4852	+	37.2135i	−1.06498	+	1.84460i
$408$	−0.721582	−	4.09229i	−0.0357236	−	0.202599i
$409$	20.6197	−	17.3020i	1.01958	−	0.855528i	0.0300037	−	0.999550i	$-0.490448\pi$
$409$	20.6197	−	17.3020i	1.01958	−	0.855528i	0.989574	+	0.144022i	$0.0460037\pi$
$410$	4.80087	+	8.31536i	0.237098	+	0.410666i
$411$	11.1632	−	19.3353i	0.550642	−	0.953740i
$412$	0.201965	+	1.14540i	0.00995008	+	0.0564297i
$413$	5.01013	−	2.35557i	0.246532	−	0.115910i
$414$	−4.08441	+	3.42722i	−0.200738	+	0.168439i
$415$	5.84007	−	2.12561i	0.286678	−	0.104342i
$416$	−1.12356	+	6.37203i	−0.0550871	+	0.312414i
$417$	−4.25192	+	7.36453i	−0.208217	+	0.360643i
$418$	−20.3555	+	8.30880i	−0.995618	+	0.406396i
$419$	4.81154			0.235059			0.117530	−	0.993069i	$-0.462502\pi$
$419$	4.81154			0.235059			0.117530	+	0.993069i	$0.462502\pi$
$420$	−0.220156	+	2.61144i	−0.0107425	+	0.127425i
$421$	5.32406	−	30.1942i	0.259479	−	1.47158i	−0.524831	−	0.851207i	$-0.675871\pi$
$421$	5.32406	−	30.1942i	0.259479	−	1.47158i	0.784309	−	0.620370i	$-0.213017\pi$
$422$	−6.80273	−	2.47599i	−0.331152	−	0.120529i
$423$	−1.05657	+	0.384561i	−0.0513723	+	0.0186980i
$424$	7.54274	+	2.74533i	0.366308	+	0.133325i
$425$	−8.35000	+	14.4626i	−0.405035	+	0.701541i
$426$	−3.62303	+	6.27528i	−0.175537	+	0.304038i
$427$	−3.42401	−	12.6189i	−0.165700	−	0.610672i
$428$	−0.359233	−	0.130750i	−0.0173642	−	0.00632005i
$429$	32.6358			1.57567
$430$	−7.32451			−0.353219
$431$	−4.96619	−	1.80754i	−0.239213	−	0.0870664i	0.219632	−	0.975583i	$-0.429514\pi$
$431$	−4.96619	−	1.80754i	−0.239213	−	0.0870664i	−0.458845	+	0.888516i	$0.651737\pi$
$432$	−0.173648	+	0.984808i	−0.00835465	+	0.0473816i
$433$	−22.1928	+	18.6220i	−1.06652	+	0.894916i	−0.994733	−	0.102504i	$-0.967315\pi$
$433$	−22.1928	+	18.6220i	−1.06652	+	0.894916i	−0.0717870	+	0.997420i	$0.522870\pi$
$434$	−2.38427	+	28.2818i	−0.114449	+	1.35757i
$435$	5.01425	−	1.82504i	0.240415	−	0.0875038i
$436$	0.475680	+	0.823903i	0.0227810	+	0.0394578i
$437$	4.91317	+	22.7156i	0.235029	+	1.08663i
$438$	3.90834	−	6.76945i	0.186748	−	0.323457i
$439$	10.3347	+	8.67185i	0.493249	+	0.413885i	0.855189	−	0.518317i	$-0.173441\pi$
$439$	10.3347	+	8.67185i	0.493249	+	0.413885i	−0.361940	+	0.932201i	$0.617886\pi$
$440$	0.867575	−	4.92026i	0.0413600	−	0.234564i
$441$	−6.90120	−	1.17193i	−0.328629	−	0.0558062i
$442$	20.5966	+	17.2826i	0.979680	+	0.822049i
$443$	28.5805	−	23.9819i	1.35790	−	1.13942i	0.381278	−	0.924460i	$-0.375484\pi$
$443$	28.5805	−	23.9819i	1.35790	−	1.13942i	0.976624	−	0.214955i	$-0.0689605\pi$
$444$	8.51926			0.404306
$445$	−1.08585	−	1.88075i	−0.0514744	−	0.0891563i
$446$	−1.43451	−	8.13550i	−0.0679260	−	0.385227i
$447$	6.46847	+	2.35433i	0.305948	+	0.111356i
$448$	−1.11056	+	2.40139i	−0.0524689	+	0.113455i
$449$	6.64980	+	11.5178i	0.313823	+	0.543558i	0.979187	−	0.202962i	$-0.0650567\pi$
$449$	6.64980	+	11.5178i	0.313823	+	0.543558i	−0.665363	+	0.746520i	$0.731723\pi$
$450$	3.07861	−	2.58326i	0.145127	−	0.121776i
$451$	45.9447	−	16.7225i	2.16345	−	0.787432i
$452$	−3.08572	−	17.5000i	−0.145140	−	0.823129i
$453$	−7.95821	+	2.89655i	−0.373909	+	0.136092i
$454$	−26.0827	+	9.49333i	−1.22412	+	0.445544i
$455$	−9.76988	−	13.8594i	−0.458019	−	0.649738i
$456$	3.44442	+	2.67133i	0.161300	+	0.125096i
$457$	−14.5416	−	25.1868i	−0.680228	−	1.17819i	−0.974911	−	0.222594i	$-0.928548\pi$
$457$	−14.5416	−	25.1868i	−0.680228	−	1.17819i	0.294683	−	0.955595i	$-0.404786\pi$
$458$	2.11113	−	11.9728i	0.0986464	−	0.559452i
$459$	3.18324	+	2.67106i	0.148581	+	0.124674i
$460$	−4.96283	−	1.80632i	−0.231393	−	0.0842203i
$461$	26.3111	+	22.0776i	1.22543	+	1.02826i	0.998522	+	0.0543416i	$0.0173060\pi$
$461$	26.3111	+	22.0776i	1.22543	+	1.02826i	0.226908	+	0.973916i	$0.427138\pi$
$462$	12.9011	+	3.41316i	0.600213	+	0.158795i
$463$	−6.64026	−	11.5013i	−0.308599	−	0.534509i	0.669457	−	0.742851i	$-0.266527\pi$
$463$	−6.64026	−	11.5013i	−0.308599	−	0.534509i	−0.978056	+	0.208342i	$0.933193\pi$
$464$	5.38705			0.250087
$465$	−8.13988	+	6.83017i	−0.377478	+	0.316742i
$466$	9.00200	−	7.55357i	0.417009	−	0.349912i
$467$	8.45759			0.391371			0.195685	−	0.980667i	$-0.437307\pi$
$467$	8.45759			0.391371			0.195685	+	0.980667i	$0.437307\pi$
$468$	−3.23516	−	5.60346i	−0.149545	−	0.259020i
$469$	3.39594	+	0.898444i	0.156810	+	0.0414863i
$470$	−0.853172	−	0.715896i	−0.0393539	−	0.0330218i
$471$	9.33805	+	3.39877i	0.430275	+	0.156607i
$472$	1.60295	+	1.34504i	0.0737819	+	0.0619104i
$473$	−6.47661	+	36.7307i	−0.297795	+	1.68888i
$474$	6.01216	+	10.4134i	0.276148	+	0.478302i
$475$	−3.70329	−	17.1218i	−0.169919	−	0.785603i
$476$	6.33446	+	8.98596i	0.290340	+	0.411871i
$477$	−7.54274	+	2.74533i	−0.345358	+	0.125700i
$478$	7.85176	−	2.85781i	0.359131	−	0.130713i
$479$	−3.83562	−	21.7529i	−0.175254	−	0.993914i	−0.937851	−	0.347039i	$-0.887187\pi$
$479$	−3.83562	−	21.7529i	−0.175254	−	0.993914i	0.762597	−	0.646874i	$-0.223924\pi$
$480$	−0.930796	+	0.338782i	−0.0424848	+	0.0154632i
$481$	−42.2262	+	35.4320i	−1.92535	+	1.61556i
$482$	−0.350530	−	0.607136i	−0.0159662	−	0.0276543i
$483$	5.92129	−	12.8038i	0.269428	−	0.582591i
$484$	−13.5702	−	4.93915i	−0.616827	−	0.224507i
$485$	−0.0142388	−	0.0807525i	−0.000646553	−	0.00366678i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−1.58675			−0.0719025			−0.0359512	−	0.999354i	$-0.511446\pi$
$487$	−1.58675			−0.0719025			−0.0359512	+	0.999354i	$0.511446\pi$
$488$	3.78576	−	3.17663i	0.171373	−	0.143799i
$489$	14.5665	+	12.2228i	0.658720	+	0.552732i
$490$	−2.41262	−	6.50045i	−0.108991	−	0.293660i
$491$	2.77772	−	15.7532i	0.125357	−	0.710933i	−0.855739	−	0.517408i	$-0.826897\pi$
$491$	2.77772	−	15.7532i	0.125357	−	0.710933i	0.981095	−	0.193525i	$-0.0619920\pi$
$492$	−7.42567	−	6.23087i	−0.334775	−	0.280910i
$493$	11.1927	−	19.3864i	0.504096	−	0.873119i
$494$	−28.1826	+	1.08491i	−1.26800	+	0.0488123i
$495$	2.49808	+	4.32681i	0.112280	+	0.194475i
$496$	−10.0805	+	3.66899i	−0.452627	+	0.164743i
$497$	1.61051	−	19.1035i	0.0722412	−	0.856910i
$498$	−4.80637	+	4.03303i	−0.215379	+	0.180724i
$499$	1.78705	−	10.1349i	0.0799995	−	0.453700i	−0.918325	−	0.395828i	$-0.870458\pi$
$499$	1.78705	−	10.1349i	0.0799995	−	0.453700i	0.998324	−	0.0578714i	$-0.0184313\pi$
$500$	8.39471	+	3.05542i	0.375423	+	0.136643i
$501$	−10.0360			−0.448374
$502$	24.4345			1.09056
$503$	−30.0852	−	10.9501i	−1.34143	−	0.488241i	−0.431168	−	0.902272i	$-0.641898\pi$
$503$	−30.0852	−	10.9501i	−1.34143	−	0.488241i	−0.910263	+	0.414031i	$0.864121\pi$
$504$	−0.692846	−	2.55342i	−0.0308618	−	0.113738i
$505$	−0.819743	+	1.41984i	−0.0364781	+	0.0631819i
$506$	−13.4466	+	23.2902i	−0.597775	+	1.03538i
$507$	27.1243	+	9.87244i	1.20463	+	0.438451i
$508$	−2.81692	+	1.02527i	−0.124981	+	0.0454892i
$509$	11.3483	+	4.13046i	0.503006	+	0.183079i	0.581046	−	0.813871i	$-0.302644\pi$
$509$	11.3483	+	4.13046i	0.503006	+	0.183079i	−0.0780394	+	0.996950i	$0.524866\pi$
$510$	−0.714751	+	4.05355i	−0.0316497	+	0.179494i
$511$	−1.73733	+	20.6079i	−0.0768552	+	0.911640i
$512$	−1.00000			−0.0441942
$513$	−4.35567	+	0.167674i	−0.192308	+	0.00740301i
$514$	4.76256	−	8.24899i	0.210067	−	0.363847i
$515$	0.200053	−	1.13455i	0.00881537	−	0.0499944i
$516$	6.94857	−	2.52907i	0.305894	−	0.111336i
$517$	−4.34446	+	3.64543i	−0.191069	+	0.160326i
$518$	−20.3978	+	9.59027i	−0.896229	+	0.421372i
$519$	0.983497	+	5.57769i	0.0431707	+	0.244833i
$520$	3.20453	−	5.55042i	0.140528	−	0.243402i
$521$	4.79077	+	8.29786i	0.209887	+	0.363536i	0.951679	−	0.307095i	$-0.0993569\pi$
$521$	4.79077	+	8.29786i	0.209887	+	0.363536i	−0.741791	+	0.670631i	$0.766024\pi$
$522$	−4.12672	+	3.46273i	−0.180622	+	0.151560i
$523$	2.58288	+	14.6483i	0.112942	+	0.640524i	0.987749	+	0.156053i	$0.0498769\pi$
$523$	2.58288	+	14.6483i	0.112942	+	0.640524i	−0.874807	+	0.484471i	$0.839012\pi$
$524$	5.49894	−	9.52444i	0.240222	−	0.416077i
$525$	−4.46316	+	9.65080i	−0.194788	+	0.421196i
$526$	−0.279660	−	1.58603i	−0.0121938	−	0.0691543i
$527$	−7.74071	+	43.8998i	−0.337191	+	1.91230i
$528$	0.875867	+	4.96729i	0.0381172	+	0.216173i
$529$	4.15827	+	3.48920i	0.180794	+	0.151705i
$530$	−6.09068	−	5.11069i	−0.264562	−	0.221994i
$531$	−2.09251			−0.0908071
$532$	−11.2542	−	2.51857i	−0.487931	−	0.109194i
$533$	62.7202			2.71671
$534$	1.67953	+	1.40929i	0.0726802	+	0.0609859i
$535$	0.290077	+	0.243404i	0.0125411	+	0.0105233i
$536$	0.230554	+	1.30753i	0.00995840	+	0.0564769i
$537$	0.188683	−	1.07008i	0.00814228	−	0.0461772i
$538$	1.80555	+	10.2398i	0.0778429	+	0.441469i
$539$	−34.7316	+	6.35077i	−1.49599	+	0.273547i
$540$	0.495266	−	0.857827i	0.0213129	−	0.0369150i
$541$	3.96526	+	22.4881i	0.170480	+	0.966838i	0.943233	+	0.332132i	$0.107768\pi$
$541$	3.96526	+	22.4881i	0.170480	+	0.966838i	−0.772753	+	0.634707i	$0.781121\pi$
$542$	−3.39030	+	2.84480i	−0.145626	+	0.122195i
$543$	−12.7450	−	22.0749i	−0.546939	−	0.947326i
$544$	−2.07771	+	3.59870i	−0.0890812	+	0.154293i
$545$	−0.163638	−	0.928038i	−0.00700949	−	0.0397528i
$546$	14.0539	+	9.77460i	0.601452	+	0.418314i
$547$	13.9502	−	11.7056i	0.596468	−	0.500496i	−0.293840	−	0.955855i	$-0.594933\pi$
$547$	13.9502	−	11.7056i	0.596468	−	0.500496i	0.890308	+	0.455359i	$0.150489\pi$
$548$	−20.9800	+	7.63611i	−0.896223	+	0.326198i
$549$	−0.858162	+	4.86688i	−0.0366255	+	0.207713i
$550$	10.1354	−	17.5550i	0.432173	−	0.748546i
$551$	4.96407	+	22.9509i	0.211476	+	0.977741i
$552$	5.33181			0.226937
$553$	−26.1175	−	18.1649i	−1.11063	−	0.772451i
$554$	1.72434	−	9.77923i	0.0732603	−	0.415480i
$555$	−7.92969	−	2.88617i	−0.336597	−	0.122511i
$556$	7.99099	−	2.90848i	0.338893	−	0.123347i
$557$	6.17319	+	2.24686i	0.261566	+	0.0952024i	0.469475	−	0.882946i	$-0.344443\pi$
$557$	6.17319	+	2.24686i	0.261566	+	0.0952024i	−0.207908	+	0.978148i	$0.566666\pi$
$558$	5.36371	−	9.29022i	0.227064	−	0.393286i
$559$	−23.9224	+	41.4349i	−1.01181	+	1.75251i
$560$	1.84725	−	1.85897i	0.0780606	−	0.0785556i
$561$	19.6956	+	7.16861i	0.831549	+	0.302659i
$562$	30.2863			1.27755
$563$	24.2244			1.02093			0.510467	−	0.859897i	$-0.329472\pi$
$563$	24.2244			1.02093			0.510467	+	0.859897i	$0.329472\pi$
$564$	1.05657	+	0.384561i	0.0444898	+	0.0161929i
$565$	−3.05650	+	17.3343i	−0.128588	+	0.729259i
$566$	13.6466	−	11.4509i	0.573609	−	0.481315i
$567$	2.17206	+	1.51068i	0.0912179	+	0.0634427i
$568$	6.80908	−	2.47830i	0.285702	−	0.103987i
$569$	−15.8434	−	27.4415i	−0.664188	−	1.15041i	−0.979505	−	0.201421i	$-0.935444\pi$
$569$	−15.8434	−	27.4415i	−0.664188	−	1.15041i	0.315316	−	0.948987i	$-0.397889\pi$
$570$	−2.30105	−	3.65337i	−0.0963805	−	0.153023i
$571$	8.78211	−	15.2111i	0.367520	−	0.636563i	−0.621657	−	0.783289i	$-0.713540\pi$
$571$	8.78211	−	15.2111i	0.367520	−	0.636563i	0.989177	+	0.146726i	$0.0468737\pi$
$572$	−25.0005	−	20.9779i	−1.04532	−	0.877129i
$573$	−1.63577	+	9.27690i	−0.0683352	+	0.387548i
$574$	24.7936	+	6.55950i	1.03487	+	0.273788i
$575$	−16.4146	−	13.7735i	−0.684536	−	0.574394i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	1.38908			0.0578282			0.0289141	−	0.999582i	$-0.490795\pi$
$577$	1.38908			0.0578282			0.0289141	+	0.999582i	$0.490795\pi$
$578$	0.133777	+	0.231708i	0.00556438	+	0.00963778i
$579$	−2.79980	−	15.8784i	−0.116356	−	0.659885i
$580$	−5.01425	−	1.82504i	−0.208205	−	0.0757805i
$581$	6.96794	−	15.0670i	0.289079	−	0.625083i
$582$	0.0413910	+	0.0716913i	0.00171571	+	0.00297170i
$583$	−31.0145	+	26.0243i	−1.28449	+	1.07782i
$584$	−7.34528	+	2.67346i	−0.303950	+	0.110629i
$585$	1.11292	+	6.31170i	0.0460137	+	0.260957i
$586$	−26.6828	+	9.71173i	−1.10226	+	0.401188i
$587$	1.06194	−	0.386514i	0.0438309	−	0.0159532i	−0.320012	−	0.947414i	$-0.603687\pi$
$587$	1.06194	−	0.386514i	0.0438309	−	0.0159532i	0.363843	+	0.931460i	$0.381465\pi$
$588$	4.53332	+	5.33376i	0.186951	+	0.219960i
$589$	−24.9203	−	39.5658i	−1.02682	−	1.63028i
$590$	−1.03635	−	1.79501i	−0.0426658	−	0.0738993i
$591$	4.16062	−	23.5961i	0.171145	−	0.970612i
$592$	−6.52613	−	5.47607i	−0.268222	−	0.225065i
$593$	−14.6840	−	5.34452i	−0.602998	−	0.219473i	0.0224390	−	0.999748i	$-0.492857\pi$
$593$	−14.6840	−	5.34452i	−0.602998	−	0.219473i	−0.625437	+	0.780275i	$0.715079\pi$
$594$	−3.86386	−	3.24217i	−0.158536	−	0.133028i
$595$	−2.85181	−	10.5101i	−0.116913	−	0.430872i
$596$	−3.44180	−	5.96138i	−0.140982	−	0.244188i
$597$	8.04011			0.329060
$598$	−26.4274	+	22.1752i	−1.08070	+	0.906813i
$599$	19.5541	−	16.4078i	0.798958	−	0.670405i	−0.148987	−	0.988839i	$-0.547601\pi$
$599$	19.5541	−	16.4078i	0.798958	−	0.670405i	0.947945	+	0.318434i	$0.103157\pi$
$600$	−4.01884			−0.164069
$601$	−6.04790	−	10.4753i	−0.246699	−	0.427295i	0.715909	−	0.698194i	$-0.246013\pi$
$601$	−6.04790	−	10.4753i	−0.246699	−	0.427295i	−0.962608	+	0.270899i	$0.912679\pi$
$602$	−13.7901	+	13.8775i	−0.562041	+	0.565606i
$603$	−1.01708	−	0.853433i	−0.0414188	−	0.0347545i
$604$	7.95821	+	2.89655i	0.323815	+	0.117859i
$605$	10.9578	+	9.19468i	0.445498	+	0.373817i
$606$	0.287415	−	1.63001i	0.0116754	−	0.0662146i
$607$	−13.4825	−	23.3523i	−0.547237	−	0.947842i	−0.998462	−	0.0554321i	$-0.982346\pi$
$607$	−13.4825	−	23.3523i	−0.547237	−	0.947842i	0.451226	−	0.892410i	$-0.350987\pi$
$608$	−0.921482	−	4.26038i	−0.0373710	−	0.172781i
$609$	5.98263	−	12.9364i	0.242428	−	0.524209i
$610$	−4.59996	+	1.67425i	−0.186247	+	0.0677883i
$611$	−6.83637	+	2.48824i	−0.276570	+	0.100663i
$612$	−0.721582	−	4.09229i	−0.0291682	−	0.165421i
$613$	39.0403	−	14.2095i	1.57682	−	0.573917i	0.602314	−	0.798259i	$-0.294246\pi$
$613$	39.0403	−	14.2095i	1.57682	−	0.573917i	0.974510	+	0.224342i	$0.0720234\pi$
$614$	15.6613	−	13.1414i	0.632039	−	0.530344i
$615$	4.80087	+	8.31536i	0.193590	+	0.335308i
$616$	−7.68887	−	10.9073i	−0.309793	−	0.439467i
$617$	−8.20916	−	2.98789i	−0.330488	−	0.120288i	0.171446	−	0.985193i	$-0.445156\pi$
$617$	−8.20916	−	2.98789i	−0.330488	−	0.120288i	−0.501935	+	0.864906i	$0.667378\pi$
$618$	0.201965	+	1.14540i	0.00812421	+	0.0460747i
$619$	−17.8671	−	30.9467i	−0.718138	−	1.24385i	−0.961737	−	0.273975i	$-0.911661\pi$
$619$	−17.8671	−	30.9467i	−0.718138	−	1.24385i	0.243599	−	0.969876i	$-0.421672\pi$
$620$	10.6259			0.426745
$621$	−4.08441	+	3.42722i	−0.163902	+	0.137530i
$622$	−2.12599	−	1.78392i	−0.0852444	−	0.0715285i
$623$	−5.60778	−	1.48362i	−0.224671	−	0.0594398i
$624$	−1.12356	+	6.37203i	−0.0449784	+	0.255085i
$625$	8.61443	+	7.22836i	0.344577	+	0.289135i
$626$	−17.5856	+	30.4591i	−0.702862	+	1.21739i
$627$	−20.3555	+	8.30880i	−0.812919	+	0.331821i
$628$	−4.96867	−	8.60599i	−0.198272	−	0.343417i
$629$	−33.2662	+	12.1079i	−1.32641	+	0.482774i
$630$	−0.220156	+	2.61144i	−0.00877121	+	0.104042i
$631$	−21.0713	+	17.6809i	−0.838834	+	0.703865i	−0.957301	−	0.289093i	$-0.906646\pi$
$631$	−21.0713	+	17.6809i	−0.838834	+	0.703865i	0.118467	+	0.992958i	$0.462202\pi$
$632$	2.08800	−	11.8416i	0.0830562	−	0.471035i
$633$	−6.80273	−	2.47599i	−0.270384	−	0.0984118i
$634$	−6.76197			−0.268552
$635$	2.96932			0.117834
$636$	7.54274	+	2.74533i	0.299089	+	0.108859i
$637$	−44.6530	−	7.58277i	−1.76922	−	0.300440i
$638$	−13.5859	+	23.5315i	−0.537872	+	0.931621i
$639$	−3.62303	+	6.27528i	−0.143325	+	0.248246i
$640$	0.930796	+	0.338782i	0.0367930	+	0.0133915i
$641$	29.4209	−	10.7083i	1.16205	−	0.422953i	0.312223	−	0.950009i	$-0.398926\pi$
$641$	29.4209	−	10.7083i	1.16205	−	0.422953i	0.849831	+	0.527056i	$0.176704\pi$
$642$	−0.359233	−	0.130750i	−0.0141778	−	0.00516030i
$643$	−0.0462868	+	0.262506i	−0.00182537	+	0.0103522i	−0.985707	−	0.168470i	$-0.946117\pi$
$643$	−0.0462868	+	0.262506i	−0.00182537	+	0.0103522i	0.983881	+	0.178822i	$0.0572286\pi$
$644$	−12.7661	+	6.00211i	−0.503053	+	0.236516i
$645$	−7.32451			−0.288402
$646$	−17.2464	−	5.53571i	−0.678552	−	0.217800i
$647$	3.79354	−	6.57060i	0.149139	−	0.258317i	−0.781770	−	0.623567i	$-0.785683\pi$
$647$	3.79354	−	6.57060i	0.149139	−	0.258317i	0.930910	+	0.365250i	$0.119016\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−9.91792	+	3.60983i	−0.389312	+	0.141698i
$650$	19.9196	−	16.7146i	0.781312	−	0.655599i
$651$	−2.38427	+	28.2818i	−0.0934471	+	1.10845i
$652$	−3.30196	−	18.7263i	−0.129315	−	0.733380i
$653$	4.82988	−	8.36560i	0.189008	−	0.327371i	−0.755912	−	0.654673i	$-0.772806\pi$
$653$	4.82988	−	8.36560i	0.189008	−	0.327371i	0.944920	+	0.327302i	$0.106139\pi$
$654$	0.475680	+	0.823903i	0.0186006	+	0.0322171i
$655$	−8.34510	+	7.00237i	−0.326070	+	0.273605i
$656$	1.68326	+	9.54625i	0.0657203	+	0.372719i
$657$	3.90834	−	6.76945i	0.152479	−	0.264101i
$658$	−2.96268	+	0.268640i	−0.115497	+	0.0104727i
$659$	4.61611	+	26.1793i	0.179818	+	1.01980i	0.932434	+	0.361340i	$0.117681\pi$
$659$	4.61611	+	26.1793i	0.179818	+	1.01980i	−0.752616	+	0.658460i	$0.771208\pi$
$660$	0.867575	−	4.92026i	0.0337703	−	0.191521i
$661$	−2.25218	−	12.7727i	−0.0875997	−	0.496802i	−0.996765	−	0.0803677i	$-0.974391\pi$
$661$	−2.25218	−	12.7727i	−0.0875997	−	0.496802i	0.909166	−	0.416435i	$-0.136721\pi$
$662$	1.78451	+	1.49738i	0.0693569	+	0.0581974i
$663$	20.5966	+	17.2826i	0.799905	+	0.671200i
$664$	6.27427			0.243489
$665$	9.62212	+	6.15699i	0.373130	+	0.238758i
$666$	8.51926			0.330115
$667$	22.0029	+	18.4626i	0.851956	+	0.714876i
$668$	7.68799	+	6.45099i	0.297457	+	0.249596i
$669$	−1.43451	−	8.13550i	−0.0554613	−	0.314537i
$670$	0.228371	−	1.29516i	0.00882274	−	0.0500362i
$671$	4.32850	+	24.5481i	0.167100	+	0.947670i
$672$	−1.11056	+	2.40139i	−0.0428407	+	0.0926355i
$673$	2.13134	−	3.69160i	0.0821573	−	0.142301i	−0.822019	−	0.569460i	$-0.807152\pi$
$673$	2.13134	−	3.69160i	0.0821573	−	0.142301i	0.904176	+	0.427159i	$0.140486\pi$
$674$	1.73041	+	9.81365i	0.0666530	+	0.378008i
$675$	3.07861	−	2.58326i	0.118496	−	0.0994299i
$676$	−14.4325	−	24.9979i	−0.555098	−	0.961458i
$677$	19.6025	−	33.9526i	0.753386	−	1.30490i	−0.192787	−	0.981241i	$-0.561753\pi$
$677$	19.6025	−	33.9526i	0.753386	−	1.30490i	0.946173	−	0.323662i	$-0.104914\pi$
$678$	−3.08572	−	17.5000i	−0.118506	−	0.672082i
$679$	−0.179807	−	0.125057i	−0.00690037	−	0.00479926i
$680$	3.15310	−	2.64577i	0.120916	−	0.101461i
$681$	−26.0827	+	9.49333i	−0.999492	+	0.363785i
$682$	9.39579	−	53.2862i	0.359784	−	2.04043i
$683$	1.72495	−	2.98771i	0.0660035	−	0.114321i	−0.831135	−	0.556070i	$-0.812308\pi$
$683$	1.72495	−	2.98771i	0.0660035	−	0.114321i	0.897139	+	0.441749i	$0.145642\pi$
$684$	3.44442	+	2.67133i	0.131701	+	0.102141i
$685$	22.1151			0.844975
$686$	−16.8585	−	7.66748i	−0.643661	−	0.292746i
$687$	2.11113	−	11.9728i	0.0805445	−	0.456790i
$688$	−6.94857	−	2.52907i	−0.264912	−	0.0964200i
$689$	−48.8039	+	17.7632i	−1.85928	+	0.676723i
$690$	−4.96283	−	1.80632i	−0.188932	−	0.0687656i
$691$	4.95647	−	8.58486i	0.188553	−	0.326583i	−0.756215	−	0.654323i	$-0.772954\pi$
$691$	4.95647	−	8.58486i	0.188553	−	0.326583i	0.944768	+	0.327740i	$0.106287\pi$
$692$	2.83187	−	4.90494i	0.107651	−	0.186458i
$693$	12.9011	+	3.41316i	0.490072	+	0.129655i
$694$	6.10025	+	2.22031i	0.231562	+	0.0842818i
$695$	−8.42332			−0.319515
$696$	5.38705			0.204196
$697$	37.8515	+	13.7768i	1.43373	+	0.521834i
$698$	1.84135	−	10.4428i	0.0696963	−	0.395267i
$699$	9.00200	−	7.55357i	0.340487	−	0.285702i
$700$	9.62239	−	4.52408i	0.363692	−	0.170994i
$701$	40.9377	−	14.9001i	1.54620	−	0.562769i	0.578674	−	0.815559i	$-0.303570\pi$
$701$	40.9377	−	14.9001i	1.54620	−	0.562769i	0.967521	+	0.252790i	$0.0813482\pi$
$702$	−3.23516	−	5.60346i	−0.122103	−	0.211489i
$703$	17.3165	−	32.8499i	0.653103	−	1.23896i
$704$	2.52196	−	4.36816i	0.0950499	−	0.164631i
$705$	−0.853172	−	0.715896i	−0.0321323	−	0.0269622i
$706$	−4.81652	+	27.3158i	−0.181272	+	1.02805i
$707$	1.14677	+	4.22631i	0.0431286	+	0.158947i
$708$	1.60295	+	1.34504i	0.0602427	+	0.0505496i
$709$	−37.4657	+	31.4375i	−1.40706	+	1.18066i	−0.449192	+	0.893435i	$0.648288\pi$
$709$	−37.4657	+	31.4375i	−1.40706	+	1.18066i	−0.957863	+	0.287225i	$0.907267\pi$
$710$	−7.17747			−0.269366
$711$	6.01216	+	10.4134i	0.225474	+	0.390532i
$712$	−0.380717	−	2.15916i	−0.0142680	−	0.0809178i
$713$	−53.7472	−	19.5624i	−2.01285	−	0.732617i
$714$	6.33446	+	8.98596i	0.237061	+	0.336291i
$715$	16.1634	+	27.9958i	0.604477	+	1.04698i
$716$	−0.832371	+	0.698442i	−0.0311072	+	0.0261020i
$717$	7.85176	−	2.85781i	0.293229	−	0.106727i
$718$	1.01607	+	5.76244i	0.0379195	+	0.215052i
$719$	−5.87287	+	2.13755i	−0.219021	+	0.0797172i	−0.449200	−	0.893431i	$-0.648291\pi$
$719$	−5.87287	+	2.13755i	−0.219021	+	0.0797172i	0.230179	+	0.973148i	$0.426069\pi$
$720$	−0.930796	+	0.338782i	−0.0346887	+	0.0126257i
$721$	−1.77296	−	2.51509i	−0.0660285	−	0.0936669i
$722$	17.3017	−	7.85173i	0.643904	−	0.292211i
$723$	−0.350530	−	0.607136i	−0.0130363	−	0.0225796i
$724$	−4.42628	+	25.1027i	−0.164501	+	0.932934i
$725$	−16.5846	−	13.9162i	−0.615938	−	0.516834i
$726$	−13.5702	−	4.93915i	−0.503637	−	0.183309i
$727$	−0.699346	−	0.586821i	−0.0259373	−	0.0217640i	0.629727	−	0.776817i	$-0.283167\pi$
$727$	−0.699346	−	0.586821i	−0.0259373	−	0.0217640i	−0.655664	+	0.755053i	$0.727611\pi$
$728$	−4.48294	−	16.5215i	−0.166149	−	0.612326i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	7.74268			0.286570
$731$	−23.5385	+	19.7512i	−0.870603	+	0.730523i
$732$	3.78576	−	3.17663i	0.139926	−	0.117412i
$733$	7.37537			0.272415			0.136208	−	0.990680i	$-0.456509\pi$
$733$	7.37537			0.272415			0.136208	+	0.990680i	$0.456509\pi$
$734$	16.1089	+	27.9015i	0.594591	+	1.02986i
$735$	−2.41262	−	6.50045i	−0.0889908	−	0.239773i
$736$	−4.08441	−	3.42722i	−0.150553	−	0.126329i
$737$	−6.29297	−	2.29045i	−0.231804	−	0.0843699i
$738$	−7.42567	−	6.23087i	−0.273343	−	0.229362i
$739$	1.78190	−	10.1057i	0.0655482	−	0.371743i	−0.934334	−	0.356399i	$-0.884005\pi$
$739$	1.78190	−	10.1057i	0.0655482	−	0.371743i	0.999882	−	0.0153440i	$-0.00488435\pi$
$740$	4.21930	+	7.30805i	0.155105	+	0.268649i
$741$	−28.1826	+	1.08491i	−1.03531	+	0.0398551i
$742$	−21.1502	+	1.91779i	−0.776447	+	0.0704042i
$743$	−20.2823	+	7.38217i	−0.744087	+	0.270826i	−0.686115	−	0.727493i	$-0.740686\pi$
$743$	−20.2823	+	7.38217i	−0.744087	+	0.270826i	−0.0579717	+	0.998318i	$0.518463\pi$
$744$	−10.0805	+	3.66899i	−0.369568	+	0.134512i
$745$	1.18401	+	6.71485i	0.0433787	+	0.246013i
$746$	−19.9700	+	7.26848i	−0.731153	+	0.266118i
$747$	−4.80637	+	4.03303i	−0.175856	+	0.147561i
$748$	−10.4798	−	18.1516i	−0.383180	−	0.663687i
$749$	1.00731	−	0.0913373i	0.0368062	−	0.00333739i
$750$	8.39471	+	3.05542i	0.306531	+	0.111568i
$751$	0.311928	+	1.76903i	0.0113824	+	0.0645528i	0.989970	−	0.141278i	$-0.0451213\pi$
$751$	0.311928	+	1.76903i	0.0113824	+	0.0645528i	−0.978587	+	0.205831i	$0.934010\pi$
$752$	−0.562191	−	0.973743i	−0.0205010	−	0.0355088i
$753$	24.4345			0.890442
$754$	−26.7012	+	22.4050i	−0.972401	+	0.815941i
$755$	−6.42617	−	5.39220i	−0.233872	−	0.196242i
$756$	−0.692846	−	2.55342i	−0.0251986	−	0.0928671i
$757$	−4.92890	+	27.9532i	−0.179144	+	1.01598i	0.754107	+	0.656751i	$0.228070\pi$
$757$	−4.92890	+	27.9532i	−0.179144	+	1.01598i	−0.933251	+	0.359225i	$0.883041\pi$
$758$	25.2678	+	21.2022i	0.917767	+	0.770098i
$759$	−13.4466	+	23.2902i	−0.488081	+	0.845381i
$760$	−0.585630	+	4.27773i	−0.0212430	+	0.155170i
$761$	−3.95420	−	6.84887i	−0.143340	−	0.248271i	0.785413	−	0.618972i	$-0.212451\pi$
$761$	−3.95420	−	6.84887i	−0.143340	−	0.248271i	−0.928752	+	0.370701i	$0.879117\pi$
$762$	−2.81692	+	1.02527i	−0.102046	+	0.0371418i
$763$	−2.06641	−	1.43720i	−0.0748091	−	0.0520303i
$764$	7.21615	−	6.05507i	0.261071	−	0.219065i
$765$	−0.714751	+	4.05355i	−0.0258419	+	0.146556i
$766$	−20.4418	−	7.44021i	−0.738593	−	0.268826i
$767$	−13.5392			−0.488872
$768$	−1.00000			−0.0360844
$769$	0.365428	+	0.133005i	0.0131777	+	0.00479629i	0.348601	−	0.937271i	$-0.386657\pi$
$769$	0.365428	+	0.133005i	0.0131777	+	0.00479629i	−0.335423	+	0.942068i	$0.608879\pi$
$770$	3.46157	+	12.7573i	0.124746	+	0.459742i
$771$	4.76256	−	8.24899i	0.171519	−	0.297080i
$772$	−8.06170	+	13.9633i	−0.290147	+	0.502549i
$773$	−9.76217	−	3.55314i	−0.351121	−	0.127797i	0.160438	−	0.987046i	$-0.448709\pi$
$773$	−9.76217	−	3.55314i	−0.351121	−	0.127797i	−0.511558	+	0.859248i	$0.670932\pi$
$774$	6.94857	−	2.52907i	0.249761	−	0.0909056i
$775$	40.5119	+	14.7451i	1.45523	+	0.529660i
$776$	0.0143749	−	0.0815243i	0.000516030	−	0.00292655i
$777$	−20.3978	+	9.59027i	−0.731768	+	0.344049i
$778$	14.3371			0.514009
$779$	−39.1196	+	15.9680i	−1.40161	+	0.572114i
$780$	3.20453	−	5.55042i	0.114741	−	0.198737i
$781$	−6.34659	+	35.9933i	−0.227099	+	1.28794i
$782$	−20.8198	+	7.57778i	−0.744514	+	0.270981i
$783$	−4.12672	+	3.46273i	−0.147477	+	0.123748i
$784$	−0.0442544	−	6.99986i	−0.00158051	−	0.249995i
$785$	1.70927	+	9.69373i	0.0610063	+	0.345984i
$786$	5.49894	−	9.52444i	0.196141	−	0.339726i
$787$	−11.7909	−	20.4224i	−0.420299	−	0.727979i	0.575669	−	0.817683i	$-0.304742\pi$
$787$	−11.7909	−	20.4224i	−0.420299	−	0.727979i	−0.995969	+	0.0897031i	$0.971408\pi$
$788$	−18.3545	+	15.4012i	−0.653851	+	0.548646i
$789$	−0.279660	−	1.58603i	−0.00995617	−	0.0564643i
$790$	−5.95524	+	10.3148i	−0.211878	+	0.366983i
$791$	27.0882	+	38.4268i	0.963145	+	1.36630i
$792$	0.875867	+	4.96729i	0.0311226	+	0.176505i
$793$	−5.55259	+	31.4903i	−0.197178	+	1.11825i
$794$	−0.0220688	−	0.125158i	−0.000783191	−	0.00444170i
$795$	−6.09068	−	5.11069i	−0.216014	−	0.181257i
$796$	−6.15908	−	5.16808i	−0.218303	−	0.183178i
$797$	−20.6407			−0.731132			−0.365566	−	0.930785i	$-0.619125\pi$
$797$	−20.6407			−0.731132			−0.365566	+	0.930785i	$0.619125\pi$
$798$	−11.2542	−	2.51857i	−0.398394	−	0.0891563i
$799$	−4.67228			−0.165293
$800$	3.07861	+	2.58326i	0.108845	+	0.0913322i
$801$	1.67953	+	1.40929i	0.0593431	+	0.0497948i
$802$	−2.07723	−	11.7805i	−0.0733495	−	0.415985i
$803$	6.84638	−	38.8277i	0.241603	−	1.37020i
$804$	0.230554	+	1.30753i	0.00813100	+	0.0461132i
$805$	13.9160	−	1.26183i	0.490475	−	0.0444737i
$806$	34.7049	−	60.1107i	1.22243	−	2.11731i
$807$	1.80555	+	10.2398i	0.0635585	+	0.360458i
$808$	−1.26792	+	1.06391i	−0.0446054	+	0.0374283i
$809$	−13.7454	−	23.8077i	−0.483263	−	0.837035i	0.516553	−	0.856255i	$-0.327215\pi$
$809$	−13.7454	−	23.8077i	−0.483263	−	0.837035i	−0.999815	+	0.0192200i	$0.993882\pi$
$810$	0.495266	−	0.857827i	0.0174019	−	0.0301410i
$811$	−0.350391	−	1.98716i	−0.0123039	−	0.0697788i	0.978038	−	0.208429i	$-0.0668349\pi$
$811$	−0.350391	−	1.98716i	−0.0123039	−	0.0697788i	−0.990341	+	0.138650i	$0.955724\pi$
$812$	−12.8983	+	6.06429i	−0.452642	+	0.212815i
$813$	−3.39030	+	2.84480i	−0.118903	+	0.0997716i
$814$	40.3790	−	14.6968i	1.41528	−	0.515121i
$815$	−3.27070	+	18.5491i	−0.114568	+	0.649745i
$816$	−2.07771	+	3.59870i	−0.0727345	+	0.125980i
$817$	4.37184	−	31.9341i	0.152951	−	1.11723i
$818$	−26.9171			−0.941134
$819$	14.0539	+	9.77460i	0.491084	+	0.341552i
$820$	1.66733	−	9.45588i	0.0582256	−	0.330214i
$821$	3.45943	+	1.25913i	0.120735	+	0.0439439i	0.401681	−	0.915780i	$-0.368426\pi$
$821$	3.45943	+	1.25913i	0.120735	+	0.0439439i	−0.280946	+	0.959724i	$0.590648\pi$
$822$	−20.9800	+	7.63611i	−0.731763	+	0.266340i
$823$	17.3493	+	6.31465i	0.604760	+	0.220115i	0.626209	−	0.779655i	$-0.284606\pi$
$823$	17.3493	+	6.31465i	0.604760	+	0.220115i	−0.0214487	+	0.999770i	$0.506828\pi$
$824$	0.581534	−	1.00725i	0.0202587	−	0.0350891i
$825$	10.1354	−	17.5550i	0.352868	−	0.611185i
$826$	−5.35211	−	1.41598i	−0.186224	−	0.0492681i
$827$	−15.3178	−	5.57524i	−0.532654	−	0.193870i	0.0616692	−	0.998097i	$-0.480358\pi$
$827$	−15.3178	−	5.57524i	−0.532654	−	0.193870i	−0.594323	+	0.804227i	$0.702580\pi$
$828$	5.33181			0.185293
$829$	−39.0069			−1.35477			−0.677383	−	0.735630i	$-0.736886\pi$
$829$	−39.0069			−1.35477			−0.677383	+	0.735630i	$0.736886\pi$
$830$	−5.84007	−	2.12561i	−0.202712	−	0.0737811i
$831$	1.72434	−	9.77923i	0.0598168	−	0.339238i
$832$	4.95656	−	4.15904i	0.171838	−	0.144189i
$833$	−25.2824	−	14.3844i	−0.875982	−	0.498391i
$834$	7.99099	−	2.90848i	0.276705	−	0.100712i
$835$	−4.97047	−	8.60911i	−0.172010	−	0.297931i
$836$	20.9340	+	6.71933i	0.724017	+	0.232393i
$837$	5.36371	−	9.29022i	0.185397	−	0.321117i
$838$	−3.68586	−	3.09280i	−0.127326	−	0.106839i
$839$	−3.44515	+	19.5384i	−0.118940	+	0.674540i	0.865784	+	0.500417i	$0.166820\pi$
$839$	−3.44515	+	19.5384i	−0.118940	+	0.674540i	−0.984724	+	0.174123i	$0.944291\pi$
$840$	1.84725	−	1.85897i	0.0637362	−	0.0641404i
$841$	0.0155511	+	0.0130489i	0.000536245	+	0.000449963i
$842$	−23.4869	+	19.7079i	−0.809413	+	0.679178i
$843$	30.2863			1.04312
$844$	3.61966	+	6.26943i	0.124594	+	0.215803i
$845$	4.96492	+	28.1574i	0.170798	+	0.968646i
$846$	1.05657	+	0.384561i	0.0363257	+	0.0132215i
$847$	38.0514	−	3.45031i	1.30746	−	0.118554i
$848$	−4.01341	−	6.95142i	−0.137821	−	0.238713i
$849$	13.6466	−	11.4509i	0.468350	−	0.392992i
$850$	15.6929	−	5.71174i	0.538261	−	0.195911i
$851$	−7.88764	−	44.7330i	−0.270385	−	1.53343i
$852$	6.80908	−	2.47830i	0.233275	−	0.0849052i
$853$	14.0839	−	5.12611i	0.482222	−	0.175515i	−0.0894588	−	0.995991i	$-0.528514\pi$
$853$	14.0839	−	5.12611i	0.482222	−	0.175515i	0.571681	+	0.820476i	$0.306292\pi$
$854$	−5.48833	+	11.8676i	−0.187807	+	0.406099i
$855$	−2.30105	−	3.65337i	−0.0786944	−	0.124943i
$856$	0.191144	+	0.331071i	0.00653317	+	0.0113158i
$857$	0.844723	−	4.79066i	0.0288552	−	0.163646i	−0.966975	−	0.254871i	$-0.917967\pi$
$857$	0.844723	−	4.79066i	0.0288552	−	0.163646i	0.995830	+	0.0912248i	$0.0290782\pi$
$858$	−25.0005	−	20.9779i	−0.853501	−	0.716173i
$859$	14.3142	+	5.20995i	0.488395	+	0.177761i	0.574467	−	0.818528i	$-0.305209\pi$
$859$	14.3142	+	5.20995i	0.488395	+	0.177761i	−0.0860721	+	0.996289i	$0.527432\pi$
$860$	5.61090	+	4.70810i	0.191330	+	0.160545i
$861$	24.7936	+	6.55950i	0.844964	+	0.223547i
$862$	2.64245	+	4.57686i	0.0900023	+	0.155889i
$863$	−14.7856			−0.503308			−0.251654	−	0.967817i	$-0.580974\pi$
$863$	−14.7856			−0.503308			−0.251654	+	0.967817i	$0.580974\pi$
$864$	0.766044	−	0.642788i	0.0260614	−	0.0218681i
$865$	−4.29760	+	3.60611i	−0.146123	+	0.122611i
$866$	28.9707			0.984464
$867$	0.133777	+	0.231708i	0.00454330	+	0.00786922i
$868$	20.0056	−	20.1325i	0.679035	−	0.683342i
$869$	46.4603	+	38.9848i	1.57606	+	1.32247i
$870$	−5.01425	−	1.82504i	−0.169999	−	0.0618745i
$871$	−6.58085	−	5.52199i	−0.222984	−	0.187105i
$872$	0.165202	−	0.936908i	0.00559445	−	0.0317277i
$873$	0.0413910	+	0.0716913i	0.00140087	+	0.00242638i
$874$	10.8376	−	20.5593i	0.366587	−	0.695427i
$875$	−23.5391	+	2.13441i	−0.795768	+	0.0721561i
$876$	−7.34528	+	2.67346i	−0.248174	+	0.0903280i
$877$	−9.91817	+	3.60992i	−0.334913	+	0.121898i	−0.504002	−	0.863702i	$-0.668140\pi$
$877$	−9.91817	+	3.60992i	−0.334913	+	0.121898i	0.169089	+	0.985601i	$0.445917\pi$
$878$	−2.34269	−	13.2860i	−0.0790619	−	0.448382i
$879$	−26.6828	+	9.71173i	−0.899988	+	0.327569i
$880$	−3.82728	+	3.21147i	−0.129018	+	0.108259i
$881$	10.0448	+	17.3981i	0.338418	+	0.586157i	0.984135	−	0.177420i	$-0.0567750\pi$
$881$	10.0448	+	17.3981i	0.338418	+	0.586157i	−0.645718	+	0.763576i	$0.723442\pi$
$882$	4.53332	+	5.33376i	0.152645	+	0.179597i
$883$	7.22844	+	2.63094i	0.243256	+	0.0885381i	0.460771	−	0.887519i	$-0.347573\pi$
$883$	7.22844	+	2.63094i	0.243256	+	0.0885381i	−0.217515	+	0.976057i	$0.569795\pi$
$884$	−4.66887	−	26.4785i	−0.157031	−	0.890567i
$885$	−1.03635	−	1.79501i	−0.0348365	−	0.0603385i
$886$	−37.3092			−1.25343
$887$	−6.43578	+	5.40026i	−0.216092	+	0.181323i	−0.744408	−	0.667725i	$-0.767268\pi$
$887$	−6.43578	+	5.40026i	−0.216092	+	0.181323i	0.528316	+	0.849048i	$0.322824\pi$
$888$	−6.52613	−	5.47607i	−0.219003	−	0.183765i
$889$	5.59043	−	5.62589i	0.187497	−	0.188686i
$890$	−0.377113	+	2.13871i	−0.0126409	+	0.0716899i
$891$	−3.86386	−	3.24217i	−0.129444	−	0.108617i
$892$	−4.13050	+	7.15424i	−0.138300	+	0.239542i
$893$	3.63047	−	3.29244i	0.121489	−	0.110177i
$894$	−3.44180	−	5.96138i	−0.115111	−	0.199378i
$895$	1.01139	−	0.368115i	0.0338070	−	0.0123047i
$896$	2.39432	−	1.12572i	0.0799886	−	0.0376076i
$897$	−26.4274	+	22.1752i	−0.882386	+	0.740410i
$898$	2.30945	−	13.0975i	0.0770673	−	0.437071i
$899$	−54.3040	−	19.7650i	−1.81114	−	0.659201i
$900$	−4.01884			−0.133961
$901$	−33.3548			−1.11121
$902$	−45.9447	−	16.7225i	−1.52979	−	0.556798i
$903$	−13.7901	+	13.8775i	−0.458905	+	0.461815i
$904$	−8.88496	+	15.3892i	−0.295510	+	0.511838i
$905$	12.6243	−	21.8659i	0.419646	−	0.726848i
$906$	7.95821	+	2.89655i	0.264394	+	0.0962315i
$907$	36.4499	−	13.2667i	1.21030	−	0.440513i	0.343491	−	0.939156i	$-0.388390\pi$
$907$	36.4499	−	13.2667i	1.21030	−	0.440513i	0.866807	+	0.498643i	$0.166168\pi$
$908$	26.0827	+	9.49333i	0.865585	+	0.315047i
$909$	0.287415	−	1.63001i	0.00953295	−	0.0540640i
$910$	−1.42448	+	16.8969i	−0.0472210	+	0.560126i
$911$	29.2972			0.970660			0.485330	−	0.874331i	$-0.338699\pi$
$911$	29.2972			0.970660			0.485330	+	0.874331i	$0.338699\pi$
$912$	−0.921482	−	4.26038i	−0.0305133	−	0.141075i
$913$	−15.8235	+	27.4070i	−0.523680	+	0.907041i
$914$	−5.05025	+	28.6414i	−0.167047	+	0.947373i
$915$	−4.59996	+	1.67425i	−0.152070	+	0.0553489i
$916$	−9.31318	+	7.81468i	−0.307716	+	0.258204i
$917$	−2.44439	+	28.9948i	−0.0807207	+	0.957493i
$918$	−0.721582	−	4.09229i	−0.0238158	−	0.135066i
$919$	9.45044	−	16.3686i	0.311741	−	0.539952i	−0.666998	−	0.745059i	$-0.732421\pi$
$919$	9.45044	−	16.3686i	0.311741	−	0.539952i	0.978739	+	0.205108i	$0.0657545\pi$
$920$	2.64067	+	4.57377i	0.0870603	+	0.150793i
$921$	15.6613	−	13.1414i	0.516058	−	0.433024i
$922$	−5.96424	−	33.8249i	−0.196422	−	1.11396i
$923$	−23.4422	+	40.6031i	−0.771609	+	1.33647i
$924$	−7.68887	−	10.9073i	−0.252945	−	0.358824i
$925$	5.94529	+	33.7174i	0.195480	+	1.10862i
$926$	−2.30614	+	13.0788i	−0.0757844	+	0.429795i
$927$	0.201965	+	1.14540i	0.00663339	+	0.0376198i
$928$	−4.12672	−	3.46273i	−0.135466	−	0.113670i
$929$	−11.3075	−	9.48816i	−0.370988	−	0.311296i	0.438164	−	0.898895i	$-0.355629\pi$
$929$	−11.3075	−	9.48816i	−0.370988	−	0.311296i	−0.809152	+	0.587599i	$0.800073\pi$
$930$	10.6259			0.348436
$931$	29.7813	−	6.63878i	0.976043	−	0.217577i
$932$	−11.7513			−0.384926
$933$	−2.12599	−	1.78392i	−0.0696017	−	0.0584028i
$934$	−6.47889	−	5.43643i	−0.211996	−	0.177886i
$935$	3.60514	+	20.4458i	0.117901	+	0.668648i
$936$	−1.12356	+	6.37203i	−0.0367247	+	0.208276i
$937$	−7.78241	−	44.1362i	−0.254240	−	1.44187i	−0.798016	−	0.602637i	$-0.794117\pi$
$937$	−7.78241	−	44.1362i	−0.254240	−	1.44187i	0.543776	−	0.839231i	$-0.316994\pi$
$938$	−2.02393	−	2.87112i	−0.0660838	−	0.0937453i
$939$	−17.5856	+	30.4591i	−0.573884	+	0.993997i
$940$	0.193398	+	1.09682i	0.00630796	+	0.0357742i
$941$	37.2863	−	31.2869i	1.21550	−	1.01992i	0.216451	−	0.976294i	$-0.430552\pi$
$941$	37.2863	−	31.2869i	1.21550	−	1.01992i	0.999048	−	0.0436307i	$-0.0138925\pi$
$942$	−4.96867	−	8.60599i	−0.161888	−	0.280398i
$943$	−25.8420	+	44.7597i	−0.841532	+	1.45758i
$944$	−0.363360	−	2.06072i	−0.0118264	−	0.0670706i
$945$	−0.220156	+	2.61144i	−0.00716166	+	0.0849501i
$946$	28.5714	−	23.9742i	0.928936	−	0.779470i
$947$	12.8222	−	4.66690i	0.416665	−	0.151654i	−0.125176	−	0.992135i	$-0.539950\pi$
$947$	12.8222	−	4.66690i	0.416665	−	0.151654i	0.541841	+	0.840481i	$0.317727\pi$
$948$	2.08800	−	11.8416i	0.0678151	−	0.384599i
$949$	25.2882	−	43.8005i	0.820891	−	1.42183i
$950$	−8.16881	+	15.4965i	−0.265031	+	0.502773i
$951$	−6.76197			−0.219272
$952$	0.923584	−	10.9554i	0.0299335	−	0.355065i
$953$	6.36555	−	36.1009i	0.206201	−	1.16942i	−0.689339	−	0.724439i	$-0.742099\pi$
$953$	6.36555	−	36.1009i	0.206201	−	1.16942i	0.895539	−	0.444982i	$-0.146790\pi$
$954$	7.54274	+	2.74533i	0.244205	+	0.0888834i
$955$	−8.76811	+	3.19133i	−0.283729	+	0.103269i
$956$	−7.85176	−	2.85781i	−0.253944	−	0.0924280i
$957$	−13.5859	+	23.5315i	−0.439170	+	0.760665i
$958$	−11.0442	+	19.1291i	−0.356822	+	0.618035i
$959$	41.6368	−	41.9009i	1.34452	−	1.35305i
$960$	0.930796	+	0.338782i	0.0300413	+	0.0109341i
$961$	84.0775			2.71218
$962$	55.1224			1.77722
$963$	−0.359233	−	0.130750i	−0.0115761	−	0.00421337i
$964$	−0.121738	+	0.690409i	−0.00392091	+	0.0222366i
$965$	12.2343	−	10.2658i	0.393836	−	0.330468i
$966$	−12.7661	+	6.00211i	−0.410741	+	0.193115i
$967$	−38.7224	+	14.0938i	−1.24523	+	0.453227i	−0.878787	−	0.477214i	$-0.841647\pi$
$967$	−38.7224	+	14.0938i	−1.24523	+	0.453227i	−0.366443	+	0.930441i	$0.619424\pi$
$968$	7.22055	+	12.5064i	0.232077	+	0.401970i
$969$	−17.2464	−	5.53571i	−0.554035	−	0.177833i
$970$	−0.0409991	+	0.0710126i	−0.00131640	+	0.00228008i
$971$	36.0767	+	30.2719i	1.15776	+	0.971472i	0.999872	−	0.0159860i	$-0.00508872\pi$
$971$	36.0767	+	30.2719i	1.15776	+	0.971472i	0.157883	+	0.987458i	$0.449533\pi$
$972$	−0.173648	+	0.984808i	−0.00556977	+	0.0315877i
$973$	−15.8588	+	15.9594i	−0.508411	+	0.511636i
$974$	1.21552	+	1.01994i	0.0389478	+	0.0326811i
$975$	19.9196	−	16.7146i	0.637939	−	0.535294i
$976$	−4.94196			−0.158188
$977$	−23.6733	−	41.0034i	−0.757377	−	1.31182i	−0.944184	−	0.329419i	$-0.893147\pi$
$977$	−23.6733	−	41.0034i	−0.757377	−	1.31182i	0.186807	−	0.982397i	$-0.440186\pi$
$978$	−3.30196	−	18.7263i	−0.105585	−	0.598802i
$979$	10.3917	+	3.78227i	0.332120	+	0.120882i
$980$	−2.33024	+	6.53044i	−0.0744367	+	0.208607i
$981$	0.475680	+	0.823903i	0.0151873	+	0.0263052i
$982$	−12.2538	+	10.2822i	−0.391035	+	0.328118i
$983$	11.0523	−	4.02272i	0.352515	−	0.128305i	−0.159692	−	0.987167i	$-0.551050\pi$
$983$	11.0523	−	4.02272i	0.352515	−	0.128305i	0.512207	+	0.858862i	$0.328828\pi$
$984$	1.68326	+	9.54625i	0.0536604	+	0.304323i
$985$	22.3019	−	8.11724i	0.710599	−	0.258637i
$986$	−21.0355	+	7.65628i	−0.669906	+	0.243826i
$987$	−2.96268	+	0.268640i	−0.0943031	+	0.00855092i
$988$	22.2865	+	17.2843i	0.709028	+	0.549888i
$989$	−19.7131	−	34.1441i	−0.626839	−	1.08572i
$990$	0.867575	−	4.92026i	0.0275733	−	0.156376i
$991$	−6.93364	−	5.81801i	−0.220254	−	0.184815i	0.525984	−	0.850495i	$-0.323697\pi$
$991$	−6.93364	−	5.81801i	−0.220254	−	0.184815i	−0.746238	+	0.665680i	$0.768142\pi$
$992$	10.0805	+	3.66899i	0.320055	+	0.116491i
$993$	1.78451	+	1.49738i	0.0566297	+	0.0475179i
$994$	−13.5132	+	13.5989i	−0.428614	+	0.431332i
$995$	3.98199	+	6.89702i	0.126238	+	0.218650i
$996$	6.27427			0.198808
$997$	7.47386	−	6.27132i	0.236700	−	0.198615i	−0.516720	−	0.856154i	$-0.672847\pi$
$997$	7.47386	−	6.27132i	0.236700	−	0.198615i	0.753420	+	0.657540i	$0.228403\pi$
$998$	−7.88354	+	6.61508i	−0.249549	+	0.209397i
$999$	8.51926			0.269537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.e.613.5	yes	42
7.2	even	3		798.2.bq.f.499.3	yes	42
19.4	even	9		798.2.bq.f.403.3	yes	42
133.23	even	9	inner	798.2.bp.e.289.5	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.e.289.5	✓	42	133.23	even	9	inner
798.2.bp.e.613.5	yes	42	1.1	even	1	trivial
798.2.bq.f.403.3	yes	42	19.4	even	9
798.2.bq.f.499.3	yes	42	7.2	even	3

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.172004 - 0.975484i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-1.52438 - 2.16246i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.172004 - 0.975484i) q^{5} +(0.173648 + 0.984808i) q^{6} +(-1.52438 - 2.16246i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.758792 + 0.636702i) q^{10} +(2.52196 + 4.36816i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.12356 + 6.37203i) q^{13} +(-0.222260 + 2.63640i) q^{14} +(-0.758792 + 0.636702i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.721582 + 4.09229i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.32305 - 3.68829i) q^{19} +0.990533 q^{20} +(-0.222260 + 2.63640i) q^{21} +(0.875867 - 4.96729i) q^{22} +(-5.01027 - 1.82359i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(3.77648 + 1.37453i) q^{25} +(3.23516 - 5.60346i) q^{26} +(0.500000 - 0.866025i) q^{27} +(1.86491 - 1.87673i) q^{28} +(-5.06217 - 1.84248i) q^{29} +0.990533 q^{30} +10.7274 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.875867 - 4.96729i) q^{33} +(3.18324 - 2.67106i) q^{34} +(-2.37165 + 1.11506i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.25963 + 7.37789i) q^{37} +(-0.591228 + 4.31862i) q^{38} +(3.23516 - 5.60346i) q^{39} +(-0.758792 - 0.636702i) q^{40} +(1.68326 - 9.54625i) q^{41} +(1.86491 - 1.87673i) q^{42} +(5.66452 + 4.75310i) q^{43} +(-3.86386 + 3.24217i) q^{44} +0.990533 q^{45} +(2.66591 + 4.61749i) q^{46} +(0.195247 + 1.10730i) q^{47} +(0.939693 + 0.342020i) q^{48} +(-2.35251 + 6.59285i) q^{49} +(-2.00942 - 3.48042i) q^{50} +(3.18324 - 2.67106i) q^{51} +(-6.08012 + 2.21298i) q^{52} +(1.39384 + 7.90487i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(4.69486 - 1.70879i) q^{55} +(-2.63494 + 0.238923i) q^{56} +(-0.591228 + 4.31862i) q^{57} +(2.69352 + 4.66532i) q^{58} +(-0.363360 + 2.06072i) q^{59} +(-0.758792 - 0.636702i) q^{60} +(4.64392 + 1.69025i) q^{61} +(-8.21768 - 6.89545i) q^{62} +(1.86491 - 1.87673i) q^{63} +(-0.500000 - 0.866025i) q^{64} +6.40907 q^{65} +(-3.86386 + 3.24217i) q^{66} +(-1.01708 + 0.853433i) q^{67} -4.15542 q^{68} +(2.66591 + 4.61749i) q^{69} +(2.53354 + 0.670283i) q^{70} +(5.55081 + 4.65768i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-5.98793 - 5.02447i) q^{73} +(1.47935 - 8.38983i) q^{74} +(-2.00942 - 3.48042i) q^{75} +(3.22886 - 2.92822i) q^{76} +(5.60156 - 12.1124i) q^{77} +(-6.08012 + 2.21298i) q^{78} +(11.2992 - 4.11256i) q^{79} +(0.172004 + 0.975484i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-7.42567 + 6.23087i) q^{82} +(3.13714 + 5.43368i) q^{83} +(-2.63494 + 0.238923i) q^{84} +(3.86785 + 1.40778i) q^{85} +(-1.28404 - 7.28217i) q^{86} +(2.69352 + 4.66532i) q^{87} +5.04392 q^{88} +(1.67953 - 1.40929i) q^{89} +(-0.758792 - 0.636702i) q^{90} +(12.0665 - 12.1431i) q^{91} +(0.925860 - 5.25081i) q^{92} +(-8.21768 - 6.89545i) q^{93} +(0.562191 - 0.973743i) q^{94} +(-3.99744 + 1.63170i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(0.0777896 - 0.0283131i) q^{97} +(6.03993 - 3.53826i) q^{98} +(-3.86386 + 3.24217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 6 q^{5} + 6 q^{7} + 21 q^{8}+O(q^{10}) \) 42 * q - 6 * q^5 + 6 * q^7 + 21 * q^8	\( 42 q - 6 q^{5} + 6 q^{7} + 21 q^{8} - 3 q^{10} - 9 q^{11} + 21 q^{12} + 3 q^{14} - 3 q^{15} - 6 q^{17} + 21 q^{18} + 18 q^{20} + 3 q^{21} + 3 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{26} + 21 q^{27} + 6 q^{28} + 15 q^{29} + 18 q^{30} - 6 q^{31} + 3 q^{33} - 3 q^{34} - 12 q^{35} + 21 q^{37} + 15 q^{38} - 3 q^{39} - 3 q^{40} + 9 q^{41} + 6 q^{42} - 12 q^{44} + 18 q^{45} + 12 q^{46} + 15 q^{47} + 30 q^{50} - 3 q^{51} + 9 q^{52} - 36 q^{53} - 27 q^{55} - 6 q^{56} + 15 q^{57} - 18 q^{58} - 3 q^{60} - 9 q^{61} - 6 q^{62} + 6 q^{63} - 21 q^{64} - 24 q^{65} - 12 q^{66} - 3 q^{67} + 12 q^{68} + 12 q^{69} - 24 q^{70} - 6 q^{71} - 15 q^{73} + 12 q^{74} + 30 q^{75} - 6 q^{76} + 21 q^{77} + 9 q^{78} + 21 q^{79} - 6 q^{80} - 18 q^{83} - 6 q^{84} - 30 q^{85} + 9 q^{86} - 18 q^{87} - 18 q^{88} + 12 q^{89} - 3 q^{90} - 18 q^{91} - 24 q^{92} - 6 q^{93} + 24 q^{94} - 27 q^{95} - 21 q^{96} - 3 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) \) 42 * q - 6 * q^5 + 6 * q^7 + 21 * q^8 - 3 * q^10 - 9 * q^11 + 21 * q^12 + 3 * q^14 - 3 * q^15 - 6 * q^17 + 21 * q^18 + 18 * q^20 + 3 * q^21 + 3 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^26 + 21 * q^27 + 6 * q^28 + 15 * q^29 + 18 * q^30 - 6 * q^31 + 3 * q^33 - 3 * q^34 - 12 * q^35 + 21 * q^37 + 15 * q^38 - 3 * q^39 - 3 * q^40 + 9 * q^41 + 6 * q^42 - 12 * q^44 + 18 * q^45 + 12 * q^46 + 15 * q^47 + 30 * q^50 - 3 * q^51 + 9 * q^52 - 36 * q^53 - 27 * q^55 - 6 * q^56 + 15 * q^57 - 18 * q^58 - 3 * q^60 - 9 * q^61 - 6 * q^62 + 6 * q^63 - 21 * q^64 - 24 * q^65 - 12 * q^66 - 3 * q^67 + 12 * q^68 + 12 * q^69 - 24 * q^70 - 6 * q^71 - 15 * q^73 + 12 * q^74 + 30 * q^75 - 6 * q^76 + 21 * q^77 + 9 * q^78 + 21 * q^79 - 6 * q^80 - 18 * q^83 - 6 * q^84 - 30 * q^85 + 9 * q^86 - 18 * q^87 - 18 * q^88 + 12 * q^89 - 3 * q^90 - 18 * q^91 - 24 * q^92 - 6 * q^93 + 24 * q^94 - 27 * q^95 - 21 * q^96 - 3 * q^97 + 24 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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