LMFDB - Embedded newform 98.2.g.b.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	98.39
Dual form			98.2.g.b.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988831 - 0.149042i) q^{2} +(1.88469 - 1.28496i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.269665 + 3.59844i) q^{5} +(-2.05516 + 0.989712i) q^{6} +(0.415648 - 2.61290i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.804920 - 2.05090i) q^{9} +O(q^{10})$	\(q+(-0.988831 - 0.149042i) q^{2} +(1.88469 - 1.28496i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.269665 + 3.59844i) q^{5} +(-2.05516 + 0.989712i) q^{6} +(0.415648 - 2.61290i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.804920 - 2.05090i) q^{9} +(0.269665 - 3.59844i) q^{10} +(-1.05244 - 2.68158i) q^{11} +(2.17971 - 0.672352i) q^{12} +(-1.54725 + 1.94018i) q^{13} +(-0.800437 + 2.52177i) q^{14} +(5.13209 + 6.43544i) q^{15} +(0.826239 + 0.563320i) q^{16} +(1.45541 + 1.35043i) q^{17} +(-1.10160 + 1.90803i) q^{18} +(-3.17965 - 5.50732i) q^{19} +(-0.802972 + 3.51805i) q^{20} +(-2.57411 - 5.45861i) q^{21} +(0.641019 + 2.80849i) q^{22} +(-5.98455 + 5.55285i) q^{23} +(-2.25558 + 0.339973i) q^{24} +(-7.93186 + 1.19554i) q^{25} +(1.81913 - 1.68791i) q^{26} +(0.404441 + 1.77197i) q^{27} +(1.16735 - 2.37430i) q^{28} +(0.0991081 - 0.434221i) q^{29} +(-4.11562 - 7.12846i) q^{30} +(-0.567124 + 0.982288i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-5.42927 - 3.70161i) q^{33} +(-1.23789 - 1.55226i) q^{34} +(9.51443 + 0.791072i) q^{35} +(1.37367 - 1.72253i) q^{36} +(4.67351 - 1.44159i) q^{37} +(2.32332 + 5.91971i) q^{38} +(-0.423020 + 5.64481i) q^{39} +(1.31834 - 3.35908i) q^{40} +(1.93251 + 0.930648i) q^{41} +(1.73179 + 5.78129i) q^{42} +(-2.92907 + 1.41056i) q^{43} +(-0.215276 - 2.87266i) q^{44} +(7.59710 + 2.34339i) q^{45} +(6.74531 - 4.59888i) q^{46} +(10.0180 + 1.50998i) q^{47} +2.28105 q^{48} +(-6.65447 - 2.17209i) q^{49} +8.02146 q^{50} +(4.47826 + 0.674989i) q^{51} +(-2.05039 + 1.39793i) q^{52} +(-11.2965 - 3.48451i) q^{53} +(-0.135825 - 1.81246i) q^{54} +(9.36569 - 4.51028i) q^{55} +(-1.50818 + 2.17380i) q^{56} +(-13.0694 - 6.29388i) q^{57} +(-0.162718 + 0.414600i) q^{58} +(0.383862 - 5.12228i) q^{59} +(3.00721 + 7.66224i) q^{60} +(14.0726 - 4.34083i) q^{61} +(0.707192 - 0.886791i) q^{62} +(-5.02424 - 2.95563i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-7.39887 - 5.04446i) q^{65} +(4.81693 + 4.46946i) q^{66} +(0.137960 - 0.238953i) q^{67} +(0.992709 + 1.71942i) q^{68} +(-4.14384 + 18.1553i) q^{69} +(-9.29026 - 2.20029i) q^{70} +(-1.34821 - 5.90690i) q^{71} +(-1.61506 + 1.49856i) q^{72} +(7.92634 - 1.19470i) q^{73} +(-4.83617 + 0.728935i) q^{74} +(-13.4129 + 12.4454i) q^{75} +(-1.41508 - 6.19987i) q^{76} +(-7.44414 + 1.63533i) q^{77} +(1.25961 - 5.51871i) q^{78} +(2.51399 + 4.35435i) q^{79} +(-1.80426 + 3.12507i) q^{80} +(7.88435 + 7.31560i) q^{81} +(-1.77222 - 1.20828i) q^{82} +(-6.53590 - 8.19576i) q^{83} +(-0.850796 - 5.97483i) q^{84} +(-4.46695 + 5.60138i) q^{85} +(3.10659 - 0.958255i) q^{86} +(-0.371169 - 0.945724i) q^{87} +(-0.215276 + 2.87266i) q^{88} +(0.966314 - 2.46213i) q^{89} +(-7.16298 - 3.44951i) q^{90} +(4.42640 + 4.84923i) q^{91} +(-7.35540 + 3.54217i) q^{92} +(0.193348 + 2.58005i) q^{93} +(-9.68110 - 2.98622i) q^{94} +(18.9603 - 12.9269i) q^{95} +(-2.25558 - 0.339973i) q^{96} +6.92509 q^{97} +(6.25642 + 3.13963i) q^{98} -6.34679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$3$	1.88469	−	1.28496i	1.08813	−	0.741874i	0.120112	−	0.992760i	$-0.461675\pi$
$3$	1.88469	−	1.28496i	1.08813	−	0.741874i	0.968016	+	0.250887i	$0.0807222\pi$
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	0.269665	+	3.59844i	0.120598	+	1.60927i	0.649348	+	0.760491i	$0.275042\pi$
$5$	0.269665	+	3.59844i	0.120598	+	1.60927i	−0.528750	+	0.848778i	$0.677339\pi$
$6$	−2.05516	+	0.989712i	−0.839014	+	0.404048i
$7$	0.415648	−	2.61290i	0.157100	−	0.987583i
$7$	0.415648	−	2.61290i	0.157100	−	0.987583i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	0.804920	−	2.05090i	0.268307	−	0.683634i
$10$	0.269665	−	3.59844i	0.0852757	−	1.13793i
$11$	−1.05244	−	2.68158i	−0.317324	−	0.808527i	−0.997170	−	0.0751732i	$-0.976049\pi$
$11$	−1.05244	−	2.68158i	−0.317324	−	0.808527i	0.679847	−	0.733354i	$-0.262046\pi$
$12$	2.17971	−	0.672352i	0.629229	−	0.194091i
$13$	−1.54725	+	1.94018i	−0.429129	+	0.538110i	−0.948642	−	0.316352i	$-0.897542\pi$
$13$	−1.54725	+	1.94018i	−0.429129	+	0.538110i	0.519513	+	0.854462i	$0.326113\pi$
$14$	−0.800437	+	2.52177i	−0.213926	+	0.673970i
$15$	5.13209	+	6.43544i	1.32510	+	1.66162i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	1.45541	+	1.35043i	0.352990	+	0.327527i	0.836659	−	0.547724i	$-0.184506\pi$
$17$	1.45541	+	1.35043i	0.352990	+	0.327527i	−0.483669	+	0.875251i	$0.660696\pi$
$18$	−1.10160	+	1.90803i	−0.259650	+	0.449727i
$19$	−3.17965	−	5.50732i	−0.729463	−	1.26347i	−0.957111	−	0.289723i	$-0.906437\pi$
$19$	−3.17965	−	5.50732i	−0.729463	−	1.26347i	0.227648	−	0.973744i	$-0.426897\pi$
$20$	−0.802972	+	3.51805i	−0.179550	+	0.786660i
$21$	−2.57411	−	5.45861i	−0.561716	−	1.19117i
$22$	0.641019	+	2.80849i	0.136666	+	0.598772i
$23$	−5.98455	+	5.55285i	−1.24786	+	1.15785i	−0.266886	+	0.963728i	$0.585995\pi$
$23$	−5.98455	+	5.55285i	−1.24786	+	1.15785i	−0.980978	+	0.194121i	$0.937815\pi$
$24$	−2.25558	+	0.339973i	−0.460417	+	0.0693967i
$25$	−7.93186	+	1.19554i	−1.58637	+	0.239107i
$26$	1.81913	−	1.68791i	0.356761	−	0.331026i
$27$	0.404441	+	1.77197i	0.0778347	+	0.341016i
$28$	1.16735	−	2.37430i	0.220608	−	0.448701i
$29$	0.0991081	−	0.434221i	0.0184039	−	0.0806328i	−0.964892	−	0.262647i	$-0.915405\pi$
$29$	0.0991081	−	0.434221i	0.0184039	−	0.0806328i	0.983296	+	0.182014i	$0.0582617\pi$
$30$	−4.11562	−	7.12846i	−0.751406	−	1.30147i
$31$	−0.567124	+	0.982288i	−0.101859	+	0.176424i	−0.912450	−	0.409187i	$-0.865812\pi$
$31$	−0.567124	+	0.982288i	−0.101859	+	0.176424i	0.810592	+	0.585612i	$0.199146\pi$
$32$	−0.733052	−	0.680173i	−0.129586	−	0.120239i
$33$	−5.42927	−	3.70161i	−0.945114	−	0.644368i
$34$	−1.23789	−	1.55226i	−0.212296	−	0.266211i
$35$	9.51443	+	0.791072i	1.60823	+	0.133716i
$36$	1.37367	−	1.72253i	0.228946	−	0.287089i
$37$	4.67351	−	1.44159i	0.768320	−	0.236995i	0.114273	−	0.993449i	$-0.463546\pi$
$37$	4.67351	−	1.44159i	0.768320	−	0.236995i	0.654047	+	0.756454i	$0.273070\pi$
$38$	2.32332	+	5.91971i	0.376892	+	0.960304i
$39$	−0.423020	+	5.64481i	−0.0677374	+	0.903892i
$40$	1.31834	−	3.35908i	0.208448	−	0.531117i
$41$	1.93251	+	0.930648i	0.301807	+	0.145343i	0.578658	−	0.815570i	$-0.303577\pi$
$41$	1.93251	+	0.930648i	0.301807	+	0.145343i	−0.276851	+	0.960913i	$0.589291\pi$
$42$	1.73179	+	5.78129i	0.267222	+	0.892072i
$43$	−2.92907	+	1.41056i	−0.446679	+	0.215109i	−0.643681	−	0.765294i	$-0.722594\pi$
$43$	−2.92907	+	1.41056i	−0.446679	+	0.215109i	0.197002	+	0.980403i	$0.436879\pi$
$44$	−0.215276	−	2.87266i	−0.0324541	−	0.433070i
$45$	7.59710	+	2.34339i	1.13251	+	0.349333i
$46$	6.74531	−	4.59888i	0.994542	−	0.678067i
$47$	10.0180	+	1.50998i	1.46128	+	0.220253i	0.831069	−	0.556170i	$-0.187730\pi$
$47$	10.0180	+	1.50998i	1.46128	+	0.220253i	0.630213	+	0.776423i	$0.282968\pi$
$48$	2.28105			0.329242
$49$	−6.65447	−	2.17209i	−0.950639	−	0.310298i
$50$	8.02146			1.13441
$51$	4.47826	+	0.674989i	0.627082	+	0.0945174i
$52$	−2.05039	+	1.39793i	−0.284337	+	0.193858i
$53$	−11.2965	−	3.48451i	−1.55170	−	0.478635i	−0.603779	−	0.797152i	$-0.706339\pi$
$53$	−11.2965	−	3.48451i	−1.55170	−	0.478635i	−0.947917	+	0.318517i	$0.896815\pi$
$54$	−0.135825	−	1.81246i	−0.0184834	−	0.246644i
$55$	9.36569	−	4.51028i	1.26287	−	0.608166i
$56$	−1.50818	+	2.17380i	−0.201539	+	0.290486i
$57$	−13.0694	−	6.29388i	−1.73108	−	0.833645i
$58$	−0.162718	+	0.414600i	−0.0213660	+	0.0544396i
$59$	0.383862	−	5.12228i	0.0499746	−	0.666864i	−0.914820	−	0.403861i	$-0.867668\pi$
$59$	0.383862	−	5.12228i	0.0499746	−	0.666864i	0.964795	−	0.263003i	$-0.0847130\pi$
$60$	3.00721	+	7.66224i	0.388229	+	0.989191i
$61$	14.0726	−	4.34083i	1.80181	−	0.555786i	0.802642	−	0.596461i	$-0.203427\pi$
$61$	14.0726	−	4.34083i	1.80181	−	0.555786i	0.999172	+	0.0406748i	$0.0129508\pi$
$62$	0.707192	−	0.886791i	0.0898135	−	0.112623i
$63$	−5.02424	−	2.95563i	−0.632994	−	0.372374i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−7.39887	−	5.04446i	−0.917716	−	0.625688i
$66$	4.81693	+	4.46946i	0.592923	+	0.550152i
$67$	0.137960	−	0.238953i	0.0168545	−	0.0291928i	−0.857475	−	0.514525i	$-0.827968\pi$
$67$	0.137960	−	0.238953i	0.0168545	−	0.0291928i	0.874330	+	0.485333i	$0.161301\pi$
$68$	0.992709	+	1.71942i	0.120384	+	0.208511i
$69$	−4.14384	+	18.1553i	−0.498859	+	2.18565i
$70$	−9.29026	−	2.20029i	−1.11040	−	0.262985i
$71$	−1.34821	−	5.90690i	−0.160003	−	0.701020i	−0.989742	−	0.142868i	$-0.954368\pi$
$71$	−1.34821	−	5.90690i	−0.160003	−	0.701020i	0.829738	−	0.558152i	$-0.188490\pi$
$72$	−1.61506	+	1.49856i	−0.190337	+	0.176607i
$73$	7.92634	−	1.19470i	0.927708	−	0.139830i	0.332228	−	0.943199i	$-0.392200\pi$
$73$	7.92634	−	1.19470i	0.927708	−	0.139830i	0.595481	+	0.803370i	$0.296962\pi$
$74$	−4.83617	+	0.728935i	−0.562193	+	0.0847369i
$75$	−13.4129	+	12.4454i	−1.54879	+	1.43707i
$76$	−1.41508	−	6.19987i	−0.162321	−	0.711174i
$77$	−7.44414	+	1.63533i	−0.848339	+	0.186364i
$78$	1.25961	−	5.51871i	0.142623	−	0.624871i
$79$	2.51399	+	4.35435i	0.282846	+	0.489903i	0.972084	−	0.234631i	$-0.0753883\pi$
$79$	2.51399	+	4.35435i	0.282846	+	0.489903i	−0.689239	+	0.724534i	$0.742055\pi$
$80$	−1.80426	+	3.12507i	−0.201723	+	0.349394i
$81$	7.88435	+	7.31560i	0.876038	+	0.812845i
$82$	−1.77222	−	1.20828i	−0.195709	−	0.133432i
$83$	−6.53590	−	8.19576i	−0.717408	−	0.899601i	0.280780	−	0.959772i	$-0.409407\pi$
$83$	−6.53590	−	8.19576i	−0.717408	−	0.899601i	−0.998188	+	0.0601708i	$0.980835\pi$
$84$	−0.850796	−	5.97483i	−0.0928294	−	0.651907i
$85$	−4.46695	+	5.60138i	−0.484509	+	0.607555i
$86$	3.10659	−	0.958255i	0.334992	−	0.103331i
$87$	−0.371169	−	0.945724i	−0.0397935	−	0.101392i
$88$	−0.215276	+	2.87266i	−0.0229485	+	0.306226i
$89$	0.966314	−	2.46213i	0.102429	−	0.260985i	−0.870467	−	0.492226i	$-0.836183\pi$
$89$	0.966314	−	2.46213i	0.102429	−	0.260985i	0.972896	+	0.231241i	$0.0742786\pi$
$90$	−7.16298	−	3.44951i	−0.755044	−	0.363610i
$91$	4.42640	+	4.84923i	0.464012	+	0.508337i
$92$	−7.35540	+	3.54217i	−0.766853	+	0.369297i
$93$	0.193348	+	2.58005i	0.0200492	+	0.267538i
$94$	−9.68110	−	2.98622i	−0.998529	−	0.308005i
$95$	18.9603	−	12.9269i	1.94529	−	1.32627i
$96$	−2.25558	−	0.339973i	−0.230209	−	0.0346984i
$97$	6.92509			0.703137			0.351568	−	0.936162i	$-0.385648\pi$
$97$	6.92509			0.703137			0.351568	+	0.936162i	$0.385648\pi$
$98$	6.25642	+	3.13963i	0.631993	+	0.317150i
$99$	−6.34679			−0.637877
$100$	−7.93186	−	1.19554i	−0.793186	−	0.119554i
$101$	−2.60626	+	1.77692i	−0.259333	+	0.176810i	−0.686006	−	0.727596i	$-0.740638\pi$
$101$	−2.60626	+	1.77692i	−0.259333	+	0.176810i	0.426674	+	0.904406i	$0.359685\pi$
$102$	−4.32764	−	1.33490i	−0.428500	−	0.132175i
$103$	1.05279	+	14.0485i	0.103734	+	1.38424i	0.769772	+	0.638319i	$0.220370\pi$
$103$	1.05279	+	14.0485i	0.103734	+	1.38424i	−0.666038	+	0.745918i	$0.732011\pi$
$104$	2.23583	−	1.07672i	0.219242	−	0.105581i
$105$	18.9483	−	10.7348i	1.84916	−	1.04761i
$106$	10.6510	+	5.12925i	1.03452	+	0.498197i
$107$	−3.51284	+	8.95058i	−0.339600	+	0.865285i	0.654425	+	0.756127i	$0.272911\pi$
$107$	−3.51284	+	8.95058i	−0.339600	+	0.865285i	−0.994024	+	0.109158i	$0.965184\pi$
$108$	−0.135825	+	1.81246i	−0.0130698	+	0.174404i
$109$	0.247494	+	0.630605i	0.0237056	+	0.0604010i	0.942237	−	0.334948i	$-0.108719\pi$
$109$	0.247494	+	0.630605i	0.0237056	+	0.0604010i	−0.918531	+	0.395349i	$0.870624\pi$
$110$	−9.93330	+	3.06402i	−0.947103	+	0.292143i
$111$	6.95575	−	8.72223i	0.660210	−	0.827878i
$112$	1.81532	−	1.92474i	0.171532	−	0.181870i
$113$	2.52298	+	3.16371i	0.237342	+	0.297617i	0.886210	−	0.463284i	$-0.153329\pi$
$113$	2.52298	+	3.16371i	0.237342	+	0.297617i	−0.648868	+	0.760901i	$0.724757\pi$
$114$	11.9854	+	8.17147i	1.12253	+	0.765329i
$115$	−21.5954	−	20.0376i	−2.01378	−	1.86851i
$116$	0.222694	−	0.385717i	0.0206766	−	0.0358129i
$117$	2.73372	+	4.73494i	0.252732	+	0.437745i
$118$	−1.14301	+	5.00786i	−0.105223	+	0.461011i
$119$	4.13347	−	3.24155i	0.378914	−	0.297152i
$120$	−1.83162	−	8.02486i	−0.167203	−	0.732566i
$121$	1.98033	−	1.83748i	0.180030	−	0.167043i
$122$	−14.5624	+	2.19493i	−1.31842	+	0.198720i
$123$	4.83804	−	0.729217i	0.436231	−	0.0657513i
$124$	−0.831463	+	0.771485i	−0.0746676	+	0.0692814i
$125$	−2.42615	−	10.6296i	−0.217001	−	0.950744i
$126$	4.52761	+	3.67144i	0.403351	+	0.327078i
$127$	−2.10034	+	9.20218i	−0.186375	+	0.816561i	0.792133	+	0.610349i	$0.208971\pi$
$127$	−2.10034	+	9.20218i	−0.186375	+	0.816561i	−0.978507	+	0.206212i	$0.933886\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.70787	+	6.42223i	−0.326460	+	0.565446i
$130$	6.56439	+	6.09086i	0.575735	+	0.534204i
$131$	−5.86659	−	3.99978i	−0.512567	−	0.349462i	0.279252	−	0.960218i	$-0.409913\pi$
$131$	−5.86659	−	3.99978i	−0.512567	−	0.349462i	−0.791819	+	0.610756i	$0.790866\pi$
$132$	−4.09699	−	5.13746i	−0.356597	−	0.447159i
$133$	−15.7117	+	6.01901i	−1.36238	+	0.521914i
$134$	−0.172033	+	0.215722i	−0.0148614	+	0.0186356i
$135$	−6.26726	+	1.93319i	−0.539400	+	0.166383i
$136$	−0.725355	−	1.84817i	−0.0621987	−	0.158480i
$137$	0.511001	−	6.81884i	0.0436578	−	0.582573i	−0.931884	−	0.362757i	$-0.881835\pi$
$137$	0.511001	−	6.81884i	0.0436578	−	0.582573i	0.975541	−	0.219815i	$-0.0705455\pi$
$138$	6.80347	−	17.3349i	0.579149	−	1.47565i
$139$	5.83562	+	2.81028i	0.494971	+	0.238365i	0.664679	−	0.747129i	$-0.268568\pi$
$139$	5.83562	+	2.81028i	0.494971	+	0.238365i	−0.169708	+	0.985494i	$0.554283\pi$
$140$	8.85856	+	3.56036i	0.748685	+	0.300905i
$141$	20.8212	−	10.0270i	1.75346	−	0.844423i
$142$	0.452775	+	6.04187i	0.0379961	+	0.507022i
$143$	6.83115	+	2.10713i	0.571249	+	0.176207i
$144$	1.82037	−	1.24111i	0.151698	−	0.103426i
$145$	1.58924	+	0.239540i	0.131979	+	0.0198927i
$146$	−8.01587			−0.663399
$147$	−15.3327	+	4.45703i	−1.26462	+	0.367609i
$148$	4.89079			0.402021
$149$	20.8581	+	3.14385i	1.70876	+	0.257554i	0.929413	−	0.369040i	$-0.120314\pi$
$149$	20.8581	+	3.14385i	1.70876	+	0.257554i	0.779346	+	0.626594i	$0.215552\pi$
$150$	15.1180	−	10.3073i	1.23438	−	0.841585i
$151$	−8.30710	−	2.56240i	−0.676023	−	0.208525i	−0.0623123	−	0.998057i	$-0.519847\pi$
$151$	−8.30710	−	2.56240i	−0.676023	−	0.208525i	−0.613710	+	0.789531i	$0.710324\pi$
$152$	0.475232	+	6.34153i	0.0385464	+	0.514366i
$153$	3.94109	−	1.89793i	0.318618	−	0.153438i
$154$	7.60473	−	0.507577i	0.612807	−	0.0409017i
$155$	−3.68763	−	1.77587i	−0.296198	−	0.142641i
$156$	−2.06806	+	5.26934i	−0.165577	+	0.421885i
$157$	−0.103957	+	1.38720i	−0.00829664	+	0.110711i	−0.999815	−	0.0192594i	$-0.993869\pi$
$157$	−0.103957	+	1.38720i	−0.00829664	+	0.110711i	0.991518	+	0.129970i	$0.0414882\pi$
$158$	−1.83692	−	4.68041i	−0.146138	−	0.372353i
$159$	−25.7680	+	7.94836i	−2.04353	+	0.630346i
$160$	2.24988	−	2.82126i	0.177869	−	0.223040i
$161$	12.0216	+	17.9450i	0.947432	+	1.41427i
$162$	−6.70595	−	8.40900i	−0.526869	−	0.660673i
$163$	4.68991	+	3.19752i	0.367342	+	0.250449i	0.732896	−	0.680341i	$-0.238168\pi$
$163$	4.68991	+	3.19752i	0.367342	+	0.250449i	−0.365554	+	0.930790i	$0.619121\pi$
$164$	1.57234	+	1.45892i	0.122779	+	0.113922i
$165$	11.8559	−	20.5351i	0.922982	−	1.59865i
$166$	5.24138	+	9.07834i	0.406810	+	0.704616i
$167$	1.22922	−	5.38557i	0.0951200	−	0.416748i	−0.904839	−	0.425753i	$-0.860009\pi$
$167$	1.22922	−	5.38557i	0.0951200	−	0.416748i	0.999959	+	0.00900508i	$0.00286644\pi$
$168$	−0.0492088	+	6.03490i	−0.00379654	+	0.465602i
$169$	1.52243	+	6.67018i	0.117110	+	0.513091i
$170$	5.25190	−	4.87305i	0.402802	−	0.373746i
$171$	−13.8543	+	2.08821i	−1.05947	+	0.159689i
$172$	−3.21471	+	0.484539i	−0.245119	+	0.0369458i
$173$	−1.35156	+	1.25407i	−0.102757	+	0.0953450i	−0.729879	−	0.683577i	$-0.760424\pi$
$173$	−1.35156	+	1.25407i	−0.102757	+	0.0953450i	0.627121	+	0.778922i	$0.284233\pi$
$174$	0.226071	+	0.990481i	0.0171384	+	0.0750881i
$175$	−0.173046	+	21.2221i	−0.0130810	+	1.60424i
$176$	0.641019	−	2.80849i	0.0483186	−	0.211698i
$177$	−5.85848	−	10.1472i	−0.440350	−	0.762709i
$178$	−1.32248	+	2.29061i	−0.0991242	+	0.171688i
$179$	2.83332	+	2.62894i	0.211773	+	0.196496i	0.778926	−	0.627116i	$-0.215765\pi$
$179$	2.83332	+	2.62894i	0.211773	+	0.196496i	−0.567153	+	0.823612i	$0.691955\pi$
$180$	6.56885	+	4.47857i	0.489613	+	0.333813i
$181$	−2.98137	−	3.73852i	−0.221603	−	0.277882i	0.658585	−	0.752506i	$-0.271155\pi$
$181$	−2.98137	−	3.73852i	−0.221603	−	0.277882i	−0.880188	+	0.474624i	$0.842584\pi$
$182$	−3.65422	−	5.45479i	−0.270869	−	0.404336i
$183$	20.9448	−	26.2639i	1.54828	−	1.94149i
$184$	7.80118	−	2.40635i	0.575111	−	0.177398i
$185$	6.44774	+	16.4286i	0.474047	+	1.20785i
$186$	0.193348	−	2.58005i	0.0141769	−	0.189178i
$187$	2.08954	−	5.32406i	0.152802	−	0.389334i
$188$	9.12789	+	4.39576i	0.665720	+	0.320594i
$189$	4.79808	−	0.320247i	0.349009	−	0.0232946i
$190$	−20.6752	+	9.95665i	−1.49994	+	0.722331i
$191$	−1.18265	−	15.7813i	−0.0855733	−	1.14190i	−0.860365	−	0.509679i	$-0.829764\pi$
$191$	−1.18265	−	15.7813i	−0.0855733	−	1.14190i	0.774791	−	0.632217i	$-0.217855\pi$
$192$	2.17971	+	0.672352i	0.157307	+	0.0485228i
$193$	−11.9290	+	8.13307i	−0.858670	+	0.585431i	−0.910632	−	0.413218i	$-0.864405\pi$
$193$	−11.9290	+	8.13307i	−0.858670	+	0.585431i	0.0519623	+	0.998649i	$0.483452\pi$
$194$	−6.84775	−	1.03213i	−0.491640	−	0.0741027i
$195$	−20.4265			−1.46278
$196$	−5.71860	−	4.03703i	−0.408471	−	0.288359i
$197$	−19.4655			−1.38686			−0.693431	−	0.720523i	$-0.743902\pi$
$197$	−19.4655			−1.38686			−0.693431	+	0.720523i	$0.743902\pi$
$198$	6.27590	+	0.945940i	0.446009	+	0.0672251i
$199$	6.35112	−	4.33012i	0.450219	−	0.306954i	−0.316900	−	0.948459i	$-0.602642\pi$
$199$	6.35112	−	4.33012i	0.450219	−	0.306954i	0.767119	+	0.641505i	$0.221690\pi$
$200$	7.66509	+	2.36437i	0.542003	+	0.167186i
$201$	−0.0470341	−	0.627627i	−0.00331753	−	0.0442694i
$202$	2.84199	−	1.36863i	0.199962	−	0.0962964i
$203$	−1.09338	−	0.439442i	−0.0767403	−	0.0308428i
$204$	4.08035	+	1.96499i	0.285681	+	0.137577i
$205$	−2.82774	+	7.20497i	−0.197498	+	0.503217i
$206$	1.05279	−	14.0485i	0.0733512	−	0.978804i
$207$	6.57127	+	16.7433i	0.456735	+	1.16374i
$208$	−2.37134	+	0.731461i	−0.164423	+	0.0507177i
$209$	−11.4219	+	14.3226i	−0.790071	+	0.990718i
$210$	−20.3366	+	7.79076i	−1.40336	+	0.537614i
$211$	−16.2713	−	20.4036i	−1.12016	−	1.40464i	−0.903603	−	0.428370i	$-0.859088\pi$
$211$	−16.2713	−	20.4036i	−1.12016	−	1.40464i	−0.216560	−	0.976269i	$-0.569484\pi$
$212$	−9.76757	−	6.65941i	−0.670839	−	0.457370i
$213$	−10.1311	−	9.40030i	−0.694172	−	0.644098i
$214$	4.80762	−	8.32705i	0.328642	−	0.569225i
$215$	−5.86569	−	10.1597i	−0.400037	−	0.692885i
$216$	0.404441	−	1.77197i	0.0275187	−	0.120567i
$217$	2.33089	+	1.89012i	0.158231	+	0.128310i
$218$	−0.150743	−	0.660448i	−0.0102096	−	0.0447312i
$219$	13.4036	−	12.4367i	0.905730	−	0.840395i
$220$	10.2790	−	1.54931i	0.693012	−	0.104455i
$221$	−4.87196	+	0.734330i	−0.327724	+	0.0493964i
$222$	−8.17804	+	7.58811i	−0.548874	+	0.509281i
$223$	1.80443	+	7.90572i	0.120834	+	0.529406i	0.998722	+	0.0505412i	$0.0160946\pi$
$223$	1.80443	+	7.90572i	0.120834	+	0.529406i	−0.877888	+	0.478865i	$0.841048\pi$
$224$	−2.08191	+	1.63268i	−0.139104	+	0.109088i
$225$	−3.93259	+	17.2298i	−0.262172	+	1.14865i
$226$	−2.02327	−	3.50441i	−0.134586	−	0.233110i
$227$	−1.07533	+	1.86253i	−0.0713723	+	0.123620i	−0.899503	−	0.436915i	$-0.856071\pi$
$227$	−1.07533	+	1.86253i	−0.0713723	+	0.123620i	0.828131	+	0.560535i	$0.189405\pi$
$228$	−10.6336	−	9.86653i	−0.704227	−	0.653427i
$229$	−8.76572	−	5.97636i	−0.579255	−	0.394929i	0.237949	−	0.971278i	$-0.423525\pi$
$229$	−8.76572	−	5.97636i	−0.579255	−	0.394929i	−0.817204	+	0.576348i	$0.804477\pi$
$230$	18.3677	+	23.0324i	1.21113	+	1.51871i
$231$	−11.9286	+	12.6476i	−0.784844	+	0.832148i
$232$	−0.277695	+	0.348218i	−0.0182315	+	0.0228616i
$233$	−5.55204	+	1.71258i	−0.363726	+	0.112195i	−0.471231	−	0.882010i	$-0.656190\pi$
$233$	−5.55204	+	1.71258i	−0.363726	+	0.112195i	0.107505	+	0.994205i	$0.465714\pi$
$234$	−1.99748	−	5.08950i	−0.130579	−	0.332711i
$235$	−2.73203	+	36.4565i	−0.178218	+	2.37816i
$236$	1.87663	−	4.78157i	0.122158	−	0.311253i
$237$	10.3333	+	4.97624i	0.671218	+	0.323242i
$238$	−4.57043	+	2.58928i	−0.296257	+	0.167838i
$239$	−3.30242	+	1.59036i	−0.213616	+	0.102872i	−0.537632	−	0.843180i	$-0.680681\pi$
$239$	−3.30242	+	1.59036i	−0.213616	+	0.102872i	0.324016	+	0.946051i	$0.394967\pi$
$240$	0.615121	+	8.20822i	0.0397059	+	0.529838i
$241$	10.6067	+	3.27173i	0.683237	+	0.210751i	0.616894	−	0.787046i	$-0.288391\pi$
$241$	10.6067	+	3.27173i	0.683237	+	0.210751i	0.0663431	+	0.997797i	$0.478867\pi$
$242$	−2.23207	+	1.52180i	−0.143483	+	0.0978251i
$243$	18.8681	+	2.84391i	1.21039	+	0.182437i
$244$	14.7269			0.942793
$245$	6.02164	−	24.5314i	0.384709	−	1.56726i
$246$	−4.89268			−0.311946
$247$	15.6049	+	2.35206i	0.992918	+	0.149658i
$248$	0.937160	−	0.638945i	0.0595097	−	0.0405730i
$249$	−22.8494	−	7.04811i	−1.44802	−	0.446656i
$250$	0.814782	+	10.8725i	0.0515314	+	0.687638i
$251$	−7.69131	+	3.70394i	−0.485471	+	0.233791i	−0.660576	−	0.750759i	$-0.729688\pi$
$251$	−7.69131	+	3.70394i	−0.485471	+	0.233791i	0.175105	+	0.984550i	$0.443974\pi$
$252$	−3.92984	−	4.30523i	−0.247556	−	0.271204i
$253$	21.1888	+	10.2040i	1.33213	+	0.641519i
$254$	3.44839	−	8.78636i	0.216371	−	0.551305i
$255$	−1.22127	+	16.2967i	−0.0764791	+	1.02054i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	11.6498	−	3.59347i	0.726692	−	0.224155i	0.0907302	−	0.995876i	$-0.471080\pi$
$257$	11.6498	−	3.59347i	0.726692	−	0.224155i	0.635961	+	0.771721i	$0.280604\pi$
$258$	4.62364	−	5.79787i	0.287855	−	0.360959i
$259$	−1.82419	−	12.8106i	−0.113349	−	0.796011i
$260$	−5.58327	−	7.00120i	−0.346260	−	0.434196i
$261$	−0.810770	−	0.552774i	−0.0501854	−	0.0342158i
$262$	5.20493	+	4.82947i	0.321562	+	0.298366i
$263$	8.81574	−	15.2693i	0.543602	−	0.941546i	−0.455092	−	0.890445i	$-0.650394\pi$
$263$	8.81574	−	15.2693i	0.543602	−	0.941546i	0.998693	−	0.0511014i	$-0.0162732\pi$
$264$	3.28553	+	5.69071i	0.202210	+	0.350239i
$265$	9.49252	−	41.5894i	0.583121	−	2.55482i
$266$	16.4333	−	3.61007i	1.00759	−	0.221348i
$267$	−1.34254	−	5.88203i	−0.0821619	−	0.359975i
$268$	0.202263	−	0.187673i	0.0123552	−	0.0114639i
$269$	−22.1327	+	3.33597i	−1.34946	+	0.203398i	−0.783682	−	0.621162i	$-0.786661\pi$
$269$	−22.1327	+	3.33597i	−1.34946	+	0.203398i	−0.565775	+	0.824560i	$0.691423\pi$
$270$	6.48539	−	0.977515i	0.394688	−	0.0594896i
$271$	−7.66841	+	7.11524i	−0.465823	+	0.432220i	−0.877839	−	0.478956i	$-0.841015\pi$
$271$	−7.66841	+	7.11524i	−0.465823	+	0.432220i	0.412016	+	0.911177i	$0.364825\pi$
$272$	0.441797	+	1.93564i	0.0267879	+	0.117365i
$273$	14.5735	+	3.45156i	0.882027	+	0.208898i
$274$	−1.52159	+	6.66652i	−0.0919225	+	0.402739i
$275$	11.5538	+	20.0117i	0.696718	+	1.20675i
$276$	−9.31112	+	16.1273i	−0.560463	+	0.970751i
$277$	−16.1701	−	15.0037i	−0.971567	−	0.901483i	0.0235955	−	0.999722i	$-0.492489\pi$
$277$	−16.1701	−	15.0037i	−0.971567	−	0.901483i	−0.995163	+	0.0982388i	$0.968679\pi$
$278$	−5.35159	−	3.64865i	−0.320967	−	0.218831i
$279$	1.55809	+	1.95378i	0.0932802	+	0.116970i
$280$	−8.22897	−	4.84089i	−0.491775	−	0.289298i
$281$	−7.20823	+	9.03883i	−0.430007	+	0.539211i	−0.948879	−	0.315640i	$-0.897781\pi$
$281$	−7.20823	+	9.03883i	−0.430007	+	0.539211i	0.518872	+	0.854852i	$0.326352\pi$
$282$	−22.0831	+	6.81173i	−1.31503	+	0.405633i
$283$	−0.419071	−	1.06778i	−0.0249112	−	0.0634727i	0.917877	−	0.396865i	$-0.129902\pi$
$283$	−0.419071	−	1.06778i	−0.0249112	−	0.0634727i	−0.942788	+	0.333392i	$0.891807\pi$
$284$	0.452775	−	6.04187i	0.0268673	−	0.358519i
$285$	19.1238	−	48.7266i	1.13279	−	2.88631i
$286$	−6.44080	−	3.10173i	−0.380852	−	0.183409i
$287$	3.23493	−	4.66263i	0.190952	−	0.275226i
$288$	−1.98502	+	0.955933i	−0.116968	+	0.0563289i
$289$	−0.975834	−	13.0216i	−0.0574020	−	0.765977i
$290$	−1.53579	−	0.473728i	−0.0901847	−	0.0278183i
$291$	13.0517	−	8.89849i	0.765103	−	0.521639i
$292$	7.92634	+	1.19470i	0.463854	+	0.0699148i
$293$	−17.0085			−0.993646			−0.496823	−	0.867852i	$-0.665500\pi$
$293$	−17.0085			−0.993646			−0.496823	+	0.867852i	$0.665500\pi$
$294$	15.8257	−	2.12202i	0.922976	−	0.123759i
$295$	18.5357			1.07919
$296$	−4.83617	−	0.728935i	−0.281096	−	0.0423685i
$297$	4.32603	−	2.94944i	0.251022	−	0.171144i
$298$	−20.1565	−	6.21747i	−1.16764	−	0.360168i
$299$	−1.51399	−	20.2027i	−0.0875561	−	1.16835i
$300$	−16.4854	+	7.93893i	−0.951782	+	0.458354i
$301$	2.46820	+	8.23965i	0.142265	+	0.474926i
$302$	7.83241	+	3.77189i	0.450705	+	0.217048i
$303$	−2.62873	+	6.69790i	−0.151017	+	0.384784i
$304$	0.475232	−	6.34153i	0.0272564	−	0.363711i
$305$	19.4151	+	49.4688i	1.11170	+	2.83258i
$306$	−4.17994	+	1.28934i	−0.238951	+	0.0737067i
$307$	8.12144	−	10.1840i	0.463515	−	0.581229i	−0.494055	−	0.869431i	$-0.664486\pi$
$307$	8.12144	−	10.1840i	0.463515	−	0.581229i	0.957570	+	0.288201i	$0.0930573\pi$
$308$	−7.59544	−	0.631519i	−0.432791	−	0.0359842i
$309$	20.0359	+	25.1243i	1.13981	+	1.42927i
$310$	3.38177	+	2.30565i	0.192071	+	0.130952i
$311$	15.9626	+	14.8111i	0.905154	+	0.839860i	0.987641	−	0.156732i	$-0.0500960\pi$
$311$	15.9626	+	14.8111i	0.905154	+	0.839860i	−0.0824876	+	0.996592i	$0.526286\pi$
$312$	2.83032	−	4.90225i	0.160235	−	0.277535i
$313$	13.5355	+	23.4441i	0.765070	+	1.32514i	0.940210	+	0.340596i	$0.110629\pi$
$313$	13.5355	+	23.4441i	0.765070	+	1.32514i	−0.175140	+	0.984544i	$0.556038\pi$
$314$	0.309548	−	1.35622i	0.0174688	−	0.0765357i
$315$	9.28077	−	18.8764i	0.522912	−	1.06357i
$316$	1.11883	+	4.90191i	0.0629391	+	0.275754i
$317$	−19.8753	+	18.4416i	−1.11631	+	1.03578i	−0.117219	+	0.993106i	$0.537398\pi$
$317$	−19.8753	+	18.4416i	−1.11631	+	1.03578i	−0.999089	+	0.0426767i	$0.986411\pi$
$318$	26.6648	−	4.01907i	1.49529	−	0.225378i
$319$	−1.26870	+	0.191226i	−0.0710338	+	0.0107066i
$320$	−2.64524	+	2.45442i	−0.147873	+	0.137206i
$321$	4.88053	+	21.3830i	0.272404	+	1.19348i
$322$	−9.21272	−	19.5363i	−0.513405	−	1.08872i
$323$	2.80952	−	12.3093i	0.156326	−	0.684909i
$324$	5.37775	+	9.31454i	0.298764	+	0.517475i
$325$	9.95298	−	17.2391i	0.552092	−	0.956251i
$326$	−4.16096	−	3.86080i	−0.230454	−	0.213830i
$327$	1.27675	+	0.870476i	0.0706047	+	0.0481374i
$328$	−1.33734	−	1.67697i	−0.0738421	−	0.0925951i
$329$	8.10939	−	25.5485i	0.447085	−	1.40853i
$330$	−14.7841	+	18.5387i	−0.813837	+	1.02052i
$331$	−8.44645	+	2.60539i	−0.464259	+	0.143205i	−0.518056	−	0.855347i	$-0.673344\pi$
$331$	−8.44645	+	2.60539i	−0.464259	+	0.143205i	0.0537965	+	0.998552i	$0.482868\pi$
$332$	−3.82979	−	9.75813i	−0.210187	−	0.535547i
$333$	0.805246	−	10.7453i	0.0441272	−	0.588837i
$334$	−2.01817	+	5.14221i	−0.110429	+	0.281369i
$335$	0.897060	+	0.432001i	0.0490116	+	0.0236028i
$336$	0.948114	−	5.96016i	0.0517239	−	0.325153i
$337$	28.6107	−	13.7782i	1.55852	−	0.750545i	0.561487	−	0.827486i	$-0.310230\pi$
$337$	28.6107	−	13.7782i	1.55852	−	0.750545i	0.997036	+	0.0769411i	$0.0245153\pi$
$338$	−0.511282	−	6.82259i	−0.0278101	−	0.371100i
$339$	8.82029	+	2.72070i	0.479052	+	0.147768i
$340$	−5.91953	+	4.03587i	−0.321032	+	0.218876i
$341$	3.23095	+	0.486988i	0.174966	+	0.0263719i
$342$	14.0108			0.757619
$343$	−8.44136	+	16.4846i	−0.455791	+	0.890087i
$344$	3.25102			0.175283
$345$	−66.4483	−	10.0155i	−3.57745	−	0.539214i
$346$	1.52338	−	1.03862i	0.0818972	−	0.0558366i
$347$	24.0647	+	7.42299i	1.29186	+	0.398487i	0.863147	−	0.504952i	$-0.168490\pi$
$347$	24.0647	+	7.42299i	1.29186	+	0.398487i	0.428716	+	0.903439i	$0.358966\pi$
$348$	−0.0759222	−	1.01311i	−0.00406986	−	0.0543085i
$349$	−31.3996	+	15.1212i	−1.68078	+	0.809422i	−0.683981	+	0.729500i	$0.739753\pi$
$349$	−31.3996	+	15.1212i	−1.68078	+	0.809422i	−0.996801	+	0.0799220i	$0.974533\pi$
$350$	3.33410	−	20.9592i	0.178215	−	1.12032i
$351$	−4.06372	−	1.95698i	−0.216905	−	0.104456i
$352$	−1.05244	+	2.68158i	−0.0560954	+	0.142929i
$353$	0.639811	−	8.53768i	0.0340537	−	0.454415i	−0.953948	−	0.299972i	$-0.903023\pi$
$353$	0.639811	−	8.53768i	0.0340537	−	0.454415i	0.988002	−	0.154443i	$-0.0493583\pi$
$354$	4.28068	+	10.9070i	0.227516	+	0.579701i
$355$	20.8920	−	6.44434i	1.10883	−	0.342030i
$356$	1.64911	−	2.06792i	0.0874025	−	0.109599i
$357$	3.62506	−	11.4207i	0.191858	−	0.604446i
$358$	−2.40985	−	3.02186i	−0.127365	−	0.159710i
$359$	−17.8444	−	12.1661i	−0.941792	−	0.642103i	−0.00801895	−	0.999968i	$-0.502553\pi$
$359$	−17.8444	−	12.1661i	−0.941792	−	0.642103i	−0.933773	+	0.357865i	$0.883505\pi$
$360$	−5.82799	−	5.40758i	−0.307162	−	0.285005i
$361$	−10.7204	+	18.5683i	−0.564232	+	0.977278i
$362$	2.39087	+	4.14111i	0.125661	+	0.217652i
$363$	1.37123	−	6.00773i	0.0719707	−	0.315324i
$364$	2.80041	+	5.93849i	0.146781	+	0.311262i
$365$	6.43653	+	28.2003i	0.336903	+	1.47607i
$366$	−24.6253	+	22.8489i	−1.28718	+	1.19433i
$367$	−17.2405	+	2.59858i	−0.899946	+	0.135645i	−0.582689	−	0.812695i	$-0.698000\pi$
$367$	−17.2405	+	2.59858i	−0.899946	+	0.135645i	−0.317256	+	0.948340i	$0.602762\pi$
$368$	−8.07269	+	1.21676i	−0.420818	+	0.0634281i
$369$	3.46418	−	3.21429i	0.180338	−	0.167329i
$370$	−3.92717	−	17.2061i	−0.204164	−	0.894500i
$371$	−13.8001	+	28.0683i	−0.716463	+	1.45723i
$372$	−0.575724	+	2.52241i	−0.0298499	+	0.130781i
$373$	−17.6024	−	30.4883i	−0.911419	−	1.57862i	−0.812062	−	0.583572i	$-0.801655\pi$
$373$	−17.6024	−	30.4883i	−0.911419	−	1.57862i	−0.0993569	−	0.995052i	$-0.531679\pi$
$374$	−2.85971	+	4.95317i	−0.147872	+	0.256122i
$375$	−18.2312	−	16.9161i	−0.941457	−	0.873544i
$376$	−8.37079	−	5.70711i	−0.431690	−	0.294322i
$377$	0.689124	+	0.864134i	0.0354917	+	0.0445052i
$378$	−4.79222	−	0.398447i	−0.246485	−	0.0204939i
$379$	−9.19446	+	11.5295i	−0.472288	+	0.592230i	−0.959730	−	0.280925i	$-0.909359\pi$
$379$	−9.19446	+	11.5295i	−0.472288	+	0.592230i	0.487442	+	0.873155i	$0.337930\pi$
$380$	21.9282	−	6.76396i	1.12489	−	0.346984i
$381$	7.86596	+	20.0421i	0.402985	+	1.02679i
$382$	−1.18265	+	15.7813i	−0.0605094	+	0.807442i
$383$	−8.42624	+	21.4697i	−0.430561	+	1.09705i	0.536814	+	0.843701i	$0.319628\pi$
$383$	−8.42624	+	21.4697i	−0.430561	+	1.09705i	−0.967375	+	0.253350i	$0.918467\pi$
$384$	−2.05516	−	0.989712i	−0.104877	−	0.0505060i
$385$	−7.89207	−	26.3463i	−0.402217	−	1.34273i
$386$	13.0080	−	6.26430i	0.662088	−	0.318845i
$387$	0.535266	+	7.14262i	0.0272091	+	0.363080i
$388$	6.61743	+	2.04121i	0.335949	+	0.103627i
$389$	0.505955	−	0.344955i	0.0256530	−	0.0174899i	−0.550426	−	0.834884i	$-0.685535\pi$
$389$	0.505955	−	0.344955i	0.0256530	−	0.0174899i	0.576079	+	0.817394i	$0.304582\pi$
$390$	20.1984	+	3.04442i	1.02279	+	0.154160i
$391$	−16.2087			−0.819710
$392$	5.05304	+	4.84425i	0.255217	+	0.244672i
$393$	−16.1963			−0.816995
$394$	19.2481	+	2.90119i	0.969707	+	0.146160i
$395$	−14.9909	+	10.2206i	−0.754275	+	0.514256i
$396$	−6.06482	−	1.87075i	−0.304769	−	0.0940087i
$397$	2.32471	+	31.0211i	0.116674	+	1.55690i	0.681576	+	0.731747i	$0.261295\pi$
$397$	2.32471	+	31.0211i	0.116674	+	1.55690i	−0.564902	+	0.825158i	$0.691086\pi$
$398$	−6.92555	+	3.33517i	−0.347147	+	0.167177i
$399$	−21.8775	+	31.5329i	−1.09525	+	1.57862i
$400$	−7.22708	−	3.48038i	−0.361354	−	0.174019i
$401$	9.62510	−	24.5244i	0.480655	−	1.22469i	−0.460787	−	0.887511i	$-0.652433\pi$
$401$	9.62510	−	24.5244i	0.480655	−	1.22469i	0.941441	−	0.337177i	$-0.109472\pi$
$402$	−0.0470341	+	0.627627i	−0.00234585	+	0.0313032i
$403$	−1.02834	−	2.62017i	−0.0512252	−	0.130520i
$404$	−3.01423	+	0.929766i	−0.149963	+	0.0462576i
$405$	−24.1986	+	30.3441i	−1.20244	+	1.50781i
$406$	1.01567	+	0.597494i	0.0504070	+	0.0296531i
$407$	−8.78433	−	11.0152i	−0.435423	−	0.546003i
$408$	−3.74191	−	2.55119i	−0.185252	−	0.126303i
$409$	−18.8146	−	17.4574i	−0.930324	−	0.863215i	0.0605281	−	0.998166i	$-0.480722\pi$
$409$	−18.8146	−	17.4574i	−0.930324	−	0.863215i	−0.990852	+	0.134952i	$0.956912\pi$
$410$	3.87001	−	6.70305i	0.191126	−	0.331040i
$411$	−7.79887	−	13.5080i	−0.384690	−	0.666303i
$412$	−3.13485	+	13.7347i	−0.154443	+	0.676658i
$413$	−13.2244	−	3.13205i	−0.650732	−	0.154118i
$414$	−4.00241	−	17.5357i	−0.196708	−	0.861833i
$415$	27.7294	−	25.7291i	1.36118	−	1.26299i
$416$	2.45387	−	0.369862i	0.120311	−	0.0181340i
$417$	14.6095	−	2.20202i	0.715428	−	0.107833i
$418$	13.4290	−	12.4603i	0.656836	−	0.609454i
$419$	4.19499	+	18.3794i	0.204938	+	0.897894i	0.967877	+	0.251423i	$0.0808987\pi$
$419$	4.19499	+	18.3794i	0.204938	+	0.897894i	−0.762939	+	0.646471i	$0.776244\pi$
$420$	21.2706	−	4.67274i	1.03790	−	0.228006i
$421$	4.48914	−	19.6682i	0.218787	−	0.958571i	−0.739588	−	0.673060i	$-0.764980\pi$
$421$	4.48914	−	19.6682i	0.218787	−	0.958571i	0.958376	−	0.285511i	$-0.0921632\pi$
$422$	13.0486	+	22.6008i	0.635195	+	1.10019i
$423$	11.1605	−	19.3306i	0.542644	−	0.939886i
$424$	8.66594	+	8.04082i	0.420855	+	0.390497i
$425$	−13.1586	−	8.97140i	−0.638287	−	0.435177i
$426$	8.61692	+	10.8053i	0.417491	+	0.523517i
$427$	−5.49289	−	38.5746i	−0.265820	−	1.86675i
$428$	−5.99501	+	7.51750i	−0.289780	+	0.363372i
$429$	15.5822	−	4.80648i	0.752316	−	0.232059i
$430$	4.28596	+	10.9204i	0.206687	+	0.526631i
$431$	1.69157	−	22.5725i	0.0814802	−	1.08728i	−0.795246	−	0.606287i	$-0.792658\pi$
$431$	1.69157	−	22.5725i	0.0814802	−	1.08728i	0.876726	−	0.480990i	$-0.159723\pi$
$432$	−0.664022	+	1.69190i	−0.0319478	+	0.0814016i
$433$	−6.96455	−	3.35395i	−0.334695	−	0.161181i	0.258986	−	0.965881i	$-0.416612\pi$
$433$	−6.96455	−	3.35395i	−0.334695	−	0.161181i	−0.593681	+	0.804700i	$0.702326\pi$
$434$	−2.02315	−	2.21641i	−0.0971144	−	0.106391i
$435$	3.30303	−	1.59066i	0.158368	−	0.0762662i
$436$	0.0506246	+	0.675539i	0.00242448	+	0.0323524i
$437$	49.6101	+	15.3027i	2.37317	+	0.732027i
$438$	−15.1075	+	10.3001i	−0.721863	+	0.492158i
$439$	16.0062	+	2.41255i	0.763937	+	0.115145i	0.519442	−	0.854506i	$-0.326140\pi$
$439$	16.0062	+	2.41255i	0.763937	+	0.115145i	0.244495	+	0.969651i	$0.421378\pi$
$440$	−10.3951			−0.495568
$441$	−9.81106	+	11.8993i	−0.467193	+	0.566634i
$442$	4.92699			0.234353
$443$	−10.2126	−	1.53930i	−0.485214	−	0.0731343i	−0.0981203	−	0.995175i	$-0.531283\pi$
$443$	−10.2126	−	1.53930i	−0.485214	−	0.0731343i	−0.387094	+	0.922040i	$0.626521\pi$
$444$	9.21765	−	6.28448i	0.437450	−	0.298248i
$445$	9.12039	+	2.81327i	0.432348	+	0.133362i
$446$	−0.605989	−	8.08636i	−0.0286944	−	0.382900i
$447$	43.3508	−	20.8766i	2.05042	−	0.987431i
$448$	2.30200	−	1.30415i	0.108759	−	0.0616153i
$449$	−18.5514	−	8.93389i	−0.875495	−	0.421616i	−0.0585179	−	0.998286i	$-0.518637\pi$
$449$	−18.5514	−	8.93389i	−0.875495	−	0.421616i	−0.816977	+	0.576670i	$0.804352\pi$
$450$	6.45663	−	16.4512i	0.304368	−	0.775518i
$451$	0.461751	−	6.16163i	0.0217430	−	0.290140i
$452$	1.47837	+	3.76682i	0.0695365	+	0.177176i
$453$	−18.9489	+	5.84497i	−0.890299	+	0.274621i
$454$	1.34092	−	1.68146i	0.0629324	−	0.0789147i
$455$	−16.2560	+	17.2358i	−0.762092	+	0.808025i
$456$	9.04429	+	11.3412i	0.423538	+	0.531100i
$457$	11.9746	+	8.16412i	0.560147	+	0.381902i	0.810042	−	0.586371i	$-0.199444\pi$
$457$	11.9746	+	8.16412i	0.560147	+	0.381902i	−0.249896	+	0.968273i	$0.580396\pi$
$458$	7.77708	+	7.21608i	0.363399	+	0.337185i
$459$	−1.80429	+	3.12512i	−0.0842170	+	0.145868i
$460$	−14.7298	−	25.5127i	−0.686780	−	1.18954i
$461$	−1.66900	+	7.31238i	−0.0777332	+	0.340572i	−0.998808	−	0.0488146i	$-0.984456\pi$
$461$	−1.66900	+	7.31238i	−0.0777332	+	0.340572i	0.921075	+	0.389386i	$0.127313\pi$
$462$	13.6804	−	10.7284i	0.636469	−	0.499132i
$463$	8.39447	+	36.7786i	0.390124	+	1.70924i	0.664215	+	0.747541i	$0.268766\pi$
$463$	8.39447	+	36.7786i	0.390124	+	1.70924i	−0.274091	+	0.961704i	$0.588377\pi$
$464$	0.326492	−	0.302941i	0.0151570	−	0.0140637i
$465$	−9.23199	+	1.39150i	−0.428123	+	0.0645292i
$466$	5.74527	−	0.865960i	0.266144	−	0.0401148i
$467$	24.5560	−	22.7846i	1.13632	−	1.05435i	0.138364	−	0.990381i	$-0.455816\pi$
$467$	24.5560	−	22.7846i	1.13632	−	1.05435i	0.997952	−	0.0639660i	$-0.0203749\pi$
$468$	1.21662	+	5.33036i	0.0562383	+	0.246396i
$469$	−0.567018	−	0.459795i	−0.0261824	−	0.0212314i
$470$	8.13507	−	35.6421i	0.375243	−	1.64405i
$471$	1.58658	+	2.74804i	0.0731057	+	0.126623i
$472$	−2.56832	+	4.44846i	−0.118217	+	0.204757i
$473$	6.86522	+	6.36999i	0.315663	+	0.292893i
$474$	−9.47619	−	6.46076i	−0.435256	−	0.296752i
$475$	31.8048	+	39.8819i	1.45930	+	1.82991i
$476$	4.90529	−	1.87917i	0.224834	−	0.0861318i
$477$	−16.2392	+	20.3633i	−0.743541	+	0.932371i
$478$	3.50256	−	1.08040i	0.160204	−	0.0494162i
$479$	0.459602	+	1.17105i	0.0209998	+	0.0535065i	0.940989	−	0.338437i	$-0.109898\pi$
$479$	0.459602	+	1.17105i	0.0209998	+	0.0535065i	−0.919989	+	0.391943i	$0.871803\pi$
$480$	0.615121	−	8.20822i	0.0280763	−	0.374652i
$481$	−4.43412	+	11.2980i	−0.202178	+	0.515142i
$482$	−10.0006	−	4.81604i	−0.455515	−	0.219364i
$483$	45.7157	+	18.3736i	2.08013	+	0.836030i
$484$	2.43395	−	1.17213i	0.110634	−	0.0532787i
$485$	1.86746	+	24.9195i	0.0847969	+	1.13154i
$486$	−18.2335	−	5.62430i	−0.827090	−	0.255123i
$487$	−11.6768	+	7.96109i	−0.529125	+	0.360751i	−0.798224	−	0.602361i	$-0.794227\pi$
$487$	−11.6768	+	7.96109i	−0.529125	+	0.360751i	0.269099	+	0.963113i	$0.413274\pi$
$488$	−14.5624	−	2.19493i	−0.659209	−	0.0993598i
$489$	12.9477			0.585517
$490$	−9.61061	+	23.3600i	−0.434163	+	1.05530i
$491$	12.0263			0.542738			0.271369	−	0.962475i	$-0.412524\pi$
$491$	12.0263			0.542738			0.271369	+	0.962475i	$0.412524\pi$
$492$	4.83804	+	0.729217i	0.218116	+	0.0328756i
$493$	0.730627	−	0.498133i	0.0329058	−	0.0224348i
$494$	−15.0801	−	4.65159i	−0.678485	−	0.209285i
$495$	−1.71151	−	22.8385i	−0.0769267	−	1.02652i
$496$	−1.02192	+	0.492132i	−0.0458857	+	0.0220974i
$497$	−15.9945	+	1.06755i	−0.717452	+	0.0478862i
$498$	21.5437	+	10.3749i	0.965398	+	0.464911i
$499$	5.14021	−	13.0970i	0.230107	−	0.586304i	−0.768455	−	0.639904i	$-0.778974\pi$
$499$	5.14021	−	13.0970i	0.230107	−	0.586304i	0.998562	+	0.0535998i	$0.0170695\pi$
$500$	0.814782	−	10.8725i	0.0364382	−	0.486234i
$501$	−4.60355	−	11.7297i	−0.205671	−	0.524042i
$502$	8.15745	−	2.51624i	0.364085	−	0.112305i
$503$	9.69313	−	12.1548i	0.432195	−	0.541956i	−0.517272	−	0.855821i	$-0.673053\pi$
$503$	9.69313	−	12.1548i	0.432195	−	0.541956i	0.949468	+	0.313865i	$0.101624\pi$
$504$	3.24428	+	4.84286i	0.144512	+	0.215718i
$505$	−7.09695	−	8.89929i	−0.315810	−	0.396013i
$506$	−19.4313	−	13.2480i	−0.863827	−	0.588948i
$507$	11.4402	+	10.6150i	0.508079	+	0.471428i
$508$	−4.71941	+	8.17426i	−0.209390	+	0.362674i
$509$	−5.79283	−	10.0335i	−0.256763	−	0.444726i	0.708610	−	0.705600i	$-0.249323\pi$
$509$	−5.79283	−	10.0335i	−0.256763	−	0.444726i	−0.965373	+	0.260874i	$0.915989\pi$
$510$	3.63654	−	15.9327i	0.161029	−	0.705512i
$511$	0.172925	−	21.2073i	0.00764976	−	0.938156i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	8.47283	−	7.86164i	0.374085	−	0.347100i
$514$	−12.0552	+	1.81703i	−0.531733	+	0.0801458i
$515$	−50.2686	+	7.57678i	−2.21510	+	0.333873i
$516$	−5.43613	+	5.04399i	−0.239312	+	0.222049i
$517$	−6.49429	−	28.4534i	−0.285619	−	1.25138i
$518$	−0.105508	+	12.9394i	−0.00463577	+	0.568524i
$519$	−0.935854	+	4.10024i	−0.0410794	+	0.179981i
$520$	4.47744	+	7.75515i	0.196349	+	0.340086i
$521$	0.639985	−	1.10849i	0.0280383	−	0.0485637i	−0.851666	−	0.524085i	$-0.824407\pi$
$521$	0.639985	−	1.10849i	0.0280383	−	0.0485637i	0.879704	+	0.475522i	$0.157741\pi$
$522$	0.719328	+	0.667439i	0.0314841	+	0.0292130i
$523$	−10.7045	−	7.29818i	−0.468073	−	0.319127i	0.306212	−	0.951963i	$-0.400938\pi$
$523$	−10.7045	−	7.29818i	−0.468073	−	0.319127i	−0.774286	+	0.632836i	$0.781891\pi$
$524$	−4.42700	−	5.55129i	−0.193395	−	0.242509i
$525$	26.9434	+	40.2195i	1.17591	+	1.75532i
$526$	−10.9930	+	13.7848i	−0.479320	+	0.601048i
$527$	−2.15191	+	0.663776i	−0.0937386	+	0.0289145i
$528$	−2.40068	−	6.11683i	−0.104476	−	0.266201i
$529$	3.26189	−	43.5268i	0.141821	−	1.89247i
$530$	−15.5851	+	39.7101i	−0.676973	+	1.72490i
$531$	−10.1963	−	4.91029i	−0.442482	−	0.213088i
$532$	−16.7878	+	1.12050i	−0.727843	+	0.0485798i
$533$	−4.79569	+	2.30948i	−0.207725	+	0.100035i
$534$	0.450869	+	6.01643i	0.0195110	+	0.260356i
$535$	−33.1554	−	10.2271i	−1.43343	−	0.442155i
$536$	−0.227975	+	0.155431i	−0.00984703	+	0.00671359i
$537$	8.71804	+	1.31403i	0.376211	+	0.0567047i
$538$	22.3827			0.964988
$539$	1.17882	+	20.1305i	0.0507754	+	0.867083i
$540$	−6.55864			−0.282239
$541$	7.64210	+	1.15186i	0.328560	+	0.0495224i	0.311251	−	0.950328i	$-0.399252\pi$
$541$	7.64210	+	1.15186i	0.328560	+	0.0495224i	0.0173088	+	0.999850i	$0.494490\pi$
$542$	8.64323	−	5.89286i	0.371259	−	0.253120i
$543$	−10.4228	−	3.21502i	−0.447286	−	0.137970i
$544$	−0.148370	−	1.97987i	−0.00636133	−	0.0848861i
$545$	−2.20245	+	1.06064i	−0.0943426	+	0.0454330i
$546$	−13.8963	−	5.58507i	−0.594706	−	0.239019i
$547$	−25.5255	−	12.2924i	−1.09139	−	0.525587i	−0.200450	−	0.979704i	$-0.564240\pi$
$547$	−25.5255	−	12.2924i	−1.09139	−	0.525587i	−0.890942	+	0.454117i	$0.849955\pi$
$548$	2.49819	−	6.36528i	0.106717	−	0.271911i
$549$	2.42472	−	32.3556i	0.103484	−	1.38090i
$550$	−8.44213	−	21.5102i	−0.359973	−	0.917197i
$551$	−2.70652	+	0.834852i	−0.115302	+	0.0355659i
$552$	11.6108	−	14.5594i	0.494187	−	0.619691i
$553$	12.4224	−	4.75891i	0.528255	−	0.202370i
$554$	13.7533	+	17.2461i	0.584322	+	0.732717i
$555$	33.2621	+	22.6777i	1.41190	+	0.962616i
$556$	4.74801	+	4.40551i	0.201360	+	0.186835i
$557$	−1.72112	+	2.98107i	−0.0729262	+	0.126312i	−0.900183	−	0.435513i	$-0.856567\pi$
$557$	−1.72112	+	2.98107i	−0.0729262	+	0.126312i	0.827256	+	0.561825i	$0.189900\pi$
$558$	−1.24949	−	2.16418i	−0.0528951	−	0.0916170i
$559$	1.79523	−	7.86542i	0.0759302	−	0.332672i
$560$	7.41556	+	6.01328i	0.313365	+	0.254108i
$561$	−2.90308	−	12.7192i	−0.122568	−	0.537005i
$562$	8.47489	−	7.86354i	0.357491	−	0.331704i
$563$	16.9507	−	2.55490i	0.714386	−	0.107676i	0.218214	−	0.975901i	$-0.429977\pi$
$563$	16.9507	−	2.55490i	0.714386	−	0.107676i	0.496171	+	0.868225i	$0.334739\pi$
$564$	22.8517	−	3.44434i	0.962229	−	0.145033i
$565$	−10.7041	+	9.93191i	−0.450323	+	0.417839i
$566$	0.255247	+	1.11831i	0.0107288	+	0.0470060i
$567$	22.3920	−	17.5603i	0.940377	−	0.737462i
$568$	−1.34821	+	5.90690i	−0.0565697	+	0.247848i
$569$	13.1728	+	22.8159i	0.552231	+	0.956493i	0.998113	+	0.0614008i	$0.0195568\pi$
$569$	13.1728	+	22.8159i	0.552231	+	0.956493i	−0.445882	+	0.895092i	$0.647110\pi$
$570$	−26.1725	+	45.3321i	−1.09624	+	1.89875i
$571$	4.71750	+	4.37720i	0.197421	+	0.183180i	0.772689	−	0.634785i	$-0.218911\pi$
$571$	4.71750	+	4.37720i	0.197421	+	0.183180i	−0.575267	+	0.817965i	$0.695102\pi$
$572$	5.90657	+	4.02703i	0.246966	+	0.168379i
$573$	−22.5073	−	28.2233i	−0.940257	−	1.17905i
$574$	−3.89373	+	4.12841i	−0.162521	+	0.172317i
$575$	40.8300	−	51.1992i	1.70273	−	2.13515i
$576$	2.10532	−	0.649405i	0.0877216	−	0.0270585i
$577$	2.64563	+	6.74095i	0.110139	+	0.280629i	0.975307	−	0.220852i	$-0.0708838\pi$
$577$	2.64563	+	6.74095i	0.110139	+	0.280629i	−0.865168	+	0.501481i	$0.832789\pi$
$578$	−0.975834	+	13.0216i	−0.0405893	+	0.541627i
$579$	−12.0319	+	30.6567i	−0.500027	+	1.27405i
$580$	1.44803	+	0.697335i	0.0601262	+	0.0289553i
$581$	−24.1313	+	13.6711i	−1.00114	+	0.567173i
$582$	−14.2322	+	6.85385i	−0.589942	+	0.284101i
$583$	2.54493	+	33.9598i	0.105400	+	1.40647i
$584$	−7.65975	−	2.36272i	−0.316963	−	0.0977701i
$585$	−16.3012	+	11.1140i	−0.673971	+	0.459506i
$586$	16.8185	+	2.53498i	0.694766	+	0.104719i
$587$	26.7230			1.10297			0.551487	−	0.834183i	$-0.314060\pi$
$587$	26.7230			1.10297			0.551487	+	0.834183i	$0.314060\pi$
$588$	−15.9652	−	0.260380i	−0.658396	−	0.0107379i
$589$	7.21304			0.297208
$590$	−18.3287	−	2.76260i	−0.754580	−	0.113735i
$591$	−36.6866	+	25.0125i	−1.50908	+	1.02888i
$592$	4.67351	+	1.44159i	0.192080	+	0.0592488i
$593$	1.46843	+	19.5949i	0.0603013	+	0.804665i	0.942589	+	0.333955i	$0.108383\pi$
$593$	1.46843	+	19.5949i	0.0603013	+	0.804665i	−0.882288	+	0.470710i	$0.843998\pi$
$594$	−4.71731	+	2.27173i	−0.193553	+	0.0932104i
$595$	12.7792	+	13.9999i	0.523894	+	0.573939i
$596$	19.0047	+	9.15220i	0.778464	+	0.374889i
$597$	6.40587	−	16.3219i	0.262175	−	0.668011i
$598$	−1.51399	+	20.2027i	−0.0619115	+	0.826151i
$599$	−3.83880	−	9.78110i	−0.156849	−	0.399645i	0.830749	−	0.556647i	$-0.187912\pi$
$599$	−3.83880	−	9.78110i	−0.156849	−	0.399645i	−0.987598	+	0.157002i	$0.949817\pi$
$600$	17.4845	−	5.39324i	0.713800	−	0.220178i
$601$	−2.17535	+	2.72780i	−0.0887344	+	0.111269i	−0.824217	−	0.566274i	$-0.808384\pi$
$601$	−2.17535	+	2.72780i	−0.0887344	+	0.111269i	0.735482	+	0.677544i	$0.236956\pi$
$602$	−1.21258	−	8.51549i	−0.0494210	−	0.347066i
$603$	−0.379023	−	0.475280i	−0.0154350	−	0.0193549i
$604$	−7.18276	−	4.89712i	−0.292262	−	0.199261i
$605$	7.14607	+	6.63058i	0.290529	+	0.269571i
$606$	3.59764	−	6.23130i	0.146144	−	0.253129i
$607$	2.29867	+	3.98141i	0.0933002	+	0.161601i	0.908898	−	0.417019i	$-0.136925\pi$
$607$	2.29867	+	3.98141i	0.0933002	+	0.161601i	−0.815598	+	0.578619i	$0.803592\pi$
$608$	−1.41508	+	6.19987i	−0.0573890	+	0.251438i
$609$	−2.62536	+	0.576740i	−0.106385	+	0.0233707i
$610$	−11.8253	−	51.8100i	−0.478792	−	2.09773i
$611$	−18.4300	+	17.1005i	−0.745598	+	0.691814i
$612$	4.32542	−	0.651952i	0.174845	−	0.0263536i
$613$	41.1905	−	6.20846i	1.66367	−	0.250757i	0.751250	−	0.660018i	$-0.229451\pi$
$613$	41.1905	−	6.20846i	1.66367	−	0.250757i	0.912418	+	0.409261i	$0.134213\pi$
$614$	−9.54857	+	8.85978i	−0.385349	+	0.357551i
$615$	3.92869	+	17.2127i	0.158420	+	0.694084i
$616$	7.41649	+	1.75651i	0.298819	+	0.0707717i
$617$	5.00177	−	21.9142i	0.201364	−	0.882231i	−0.768744	−	0.639556i	$-0.779118\pi$
$617$	5.00177	−	21.9142i	0.201364	−	0.882231i	0.970108	−	0.242675i	$-0.0780248\pi$
$618$	−16.0676	−	27.8299i	−0.646333	−	1.11948i
$619$	18.3393	−	31.7646i	0.737120	−	1.27673i	−0.216668	−	0.976245i	$-0.569519\pi$
$619$	18.3393	−	31.7646i	0.737120	−	1.27673i	0.953787	−	0.300483i	$-0.0971479\pi$
$620$	−3.00036	−	2.78392i	−0.120497	−	0.111805i
$621$	−12.2599	−	8.35864i	−0.491972	−	0.335421i
$622$	−13.5768	−	17.0248i	−0.544380	−	0.682631i
$623$	−6.03164	−	3.54826i	−0.241653	−	0.142158i
$624$	−3.52935	+	4.42566i	−0.141287	+	0.177168i
$625$	−0.729599	+	0.225052i	−0.0291840	+	0.00900206i
$626$	−9.89012	−	25.1996i	−0.395289	−	1.00718i
$627$	−3.12278	+	41.6706i	−0.124712	+	1.66416i
$628$	−0.508224	+	1.29493i	−0.0202803	+	0.0516735i
$629$	8.74865	+	4.21313i	0.348831	+	0.167988i
$630$	−11.9905	+	17.2824i	−0.477713	+	0.688546i
$631$	−32.1213	+	15.4688i	−1.27873	+	0.615804i	−0.945064	−	0.326887i	$-0.894000\pi$
$631$	−32.1213	+	15.4688i	−1.27873	+	0.615804i	−0.333667	+	0.942691i	$0.608286\pi$
$632$	−0.375741	−	5.01391i	−0.0149462	−	0.199443i
$633$	−56.8843	−	17.5465i	−2.26095	−	0.697410i
$634$	22.4019	−	15.2734i	0.889693	−	0.606582i
$635$	−33.6798	−	5.07642i	−1.33654	−	0.201451i
$636$	−26.9660			−1.06927
$637$	14.5104	−	9.55015i	0.574921	−	0.378391i
$638$	1.28303			0.0507958
$639$	−13.1997	−	1.98953i	−0.522171	−	0.0787046i
$640$	2.98150	−	2.03275i	0.117854	−	0.0803517i
$641$	18.4091	+	5.67845i	0.727116	+	0.224285i	0.636147	−	0.771568i	$-0.280527\pi$
$641$	18.4091	+	5.67845i	0.727116	+	0.224285i	0.0909691	+	0.995854i	$0.471004\pi$
$642$	−1.63905	−	21.8716i	−0.0646880	−	0.863202i
$643$	−19.6359	+	9.45613i	−0.774362	+	0.372913i	−0.778958	−	0.627076i	$-0.784251\pi$
$643$	−19.6359	+	9.45613i	−0.774362	+	0.372913i	0.00459553	+	0.999989i	$0.498537\pi$
$644$	6.19809	+	20.6912i	0.244239	+	0.815348i
$645$	−24.1099	−	11.6107i	−0.949325	−	0.457171i
$646$	−4.61275	+	11.7531i	−0.181486	+	0.462420i
$647$	−1.16311	+	15.5207i	−0.0457267	+	0.610181i	0.926523	+	0.376237i	$0.122782\pi$
$647$	−1.16311	+	15.5207i	−0.0457267	+	0.610181i	−0.972250	+	0.233944i	$0.924837\pi$
$648$	−3.92943	−	10.0120i	−0.154363	−	0.393309i
$649$	−14.1398	+	4.36155i	−0.555036	+	0.171206i
$650$	−12.4112	+	15.5631i	−0.486806	+	0.610435i
$651$	6.82176	+	0.567192i	0.267366	+	0.0222300i
$652$	3.53906	+	4.43784i	0.138600	+	0.173799i
$653$	34.7351	+	23.6820i	1.35929	+	0.926748i	0.999979	−	0.00646938i	$-0.00205928\pi$
$653$	34.7351	+	23.6820i	1.35929	+	0.926748i	0.359311	+	0.933218i	$0.383012\pi$
$654$	−1.13276	−	1.05104i	−0.0442943	−	0.0410991i
$655$	12.8109	−	22.1892i	0.500564	−	0.867002i
$656$	1.07246	+	1.85756i	0.0418726	+	0.0725255i
$657$	3.92985	−	17.2178i	0.153318	−	0.671730i
$658$	−11.8266	+	24.0545i	−0.461050	+	0.937742i
$659$	8.54571	+	37.4412i	0.332894	+	1.45850i	0.813499	+	0.581566i	$0.197560\pi$
$659$	8.54571	+	37.4412i	0.332894	+	1.45850i	−0.480606	+	0.876937i	$0.659583\pi$
$660$	17.3820	−	16.1281i	0.676594	−	0.627787i
$661$	21.7250	−	3.27451i	0.845003	−	0.127364i	0.287749	−	0.957706i	$-0.407093\pi$
$661$	21.7250	−	3.27451i	0.845003	−	0.127364i	0.557254	+	0.830342i	$0.311855\pi$
$662$	8.74043	−	1.31741i	0.339706	−	0.0512025i
$663$	−8.23857	+	7.64428i	−0.319960	+	0.296879i
$664$	2.33264	+	10.2199i	0.0905238	+	0.396611i
$665$	−25.8959	−	54.9144i	−1.00420	−	2.12949i
$666$	−2.39775	+	10.5052i	−0.0929110	+	0.407070i
$667$	1.81805	+	3.14895i	0.0703950	+	0.121928i
$668$	2.76203	−	4.78398i	0.106866	−	0.185098i
$669$	13.5594	+	12.5812i	0.524235	+	0.486419i
$670$	−0.822654	−	0.560876i	−0.0317819	−	0.0216685i
$671$	−26.4509	−	33.1684i	−1.02113	−	1.28045i
$672$	−1.82584	+	5.75228i	−0.0704333	+	0.221899i
$673$	8.21377	−	10.2997i	0.316617	−	0.397026i	−0.597901	−	0.801570i	$-0.703998\pi$
$673$	8.21377	−	10.2997i	0.316617	−	0.397026i	0.914518	+	0.404544i	$0.132570\pi$
$674$	−30.3446	+	9.36008i	−1.16883	+	0.360537i
$675$	−5.32642	−	13.5715i	−0.205014	−	0.522368i
$676$	−0.511282	+	6.82259i	−0.0196647	+	0.262407i
$677$	−1.58394	+	4.03581i	−0.0608757	+	0.155109i	−0.958075	−	0.286517i	$-0.907503\pi$
$677$	−1.58394	+	4.03581i	−0.0608757	+	0.155109i	0.897200	+	0.441625i	$0.145598\pi$
$678$	−8.31627	−	4.00491i	−0.319385	−	0.153808i
$679$	2.87840	−	18.0946i	0.110463	−	0.694406i
$680$	6.45493	−	3.10853i	0.247535	−	0.119207i
$681$	0.366609	+	4.89206i	0.0140485	+	0.187464i
$682$	−3.12228	−	0.963097i	−0.119558	−	0.0368789i
$683$	42.6521	−	29.0797i	1.63204	−	1.11270i	0.727688	−	0.685908i	$-0.240595\pi$
$683$	42.6521	−	29.0797i	1.63204	−	1.11270i	0.904348	−	0.426795i	$-0.140357\pi$
$684$	−13.8543	−	2.08821i	−0.529734	−	0.0798446i
$685$	24.6749			0.942781
$686$	10.8040	−	15.0424i	0.412498	−	0.574322i
$687$	−24.2001			−0.923291
$688$	−3.21471	−	0.484539i	−0.122560	−	0.0184729i
$689$	24.2391	−	16.5259i	0.923436	−	0.629588i
$690$	64.2134	+	19.8072i	2.44456	+	0.754047i
$691$	0.731068	+	9.75542i	0.0278111	+	0.371114i	0.993693	+	0.112132i	$0.0357679\pi$
$691$	0.731068	+	9.75542i	0.0278111	+	0.371114i	−0.965882	+	0.258982i	$0.916613\pi$
$692$	−1.66116	+	0.799973i	−0.0631478	+	0.0304104i
$693$	−2.63803	+	16.5835i	−0.100210	+	0.629956i
$694$	−22.6896	−	10.9267i	−0.861286	−	0.414774i
$695$	−8.53896	+	21.7569i	−0.323901	+	0.825287i
$696$	−0.0759222	+	1.01311i	−0.00287783	+	0.0384019i
$697$	1.55583	+	3.96419i	0.0589313	+	0.150154i
$698$	33.3026	−	10.2725i	1.26052	−	0.388819i
$699$	−8.26329	+	10.3618i	−0.312546	+	0.391921i
$700$	−6.42067	+	20.2282i	−0.242679	+	0.764555i
$701$	−3.67671	−	4.61045i	−0.138867	−	0.174134i	0.707535	−	0.706679i	$-0.249807\pi$
$701$	−3.67671	−	4.61045i	−0.138867	−	0.174134i	−0.846402	+	0.532544i	$0.821236\pi$
$702$	3.72666	+	2.54079i	0.140654	+	0.0958960i
$703$	−22.7994	−	21.1548i	−0.859896	−	0.797867i
$704$	1.44036	−	2.49477i	0.0542855	−	0.0940252i
$705$	41.6961	+	72.2198i	1.57037	+	2.71996i
$706$	−1.90514	+	8.34696i	−0.0717009	+	0.314142i
$707$	3.55962	+	7.54847i	0.133873	+	0.283889i
$708$	−2.60727	−	11.4232i	−0.0979871	−	0.429310i
$709$	12.5585	−	11.6526i	0.471646	−	0.437623i	−0.408193	−	0.912896i	$-0.633841\pi$
$709$	12.5585	−	11.6526i	0.471646	−	0.437623i	0.879839	+	0.475272i	$0.157650\pi$
$710$	−21.6192	+	3.25857i	−0.811353	+	0.122292i
$711$	10.9539	−	1.65104i	0.410804	−	0.0619187i
$712$	−1.93890	+	1.79903i	−0.0726632	+	0.0674216i
$713$	−2.06051	−	9.02770i	−0.0771669	−	0.338090i
$714$	−5.28673	+	10.7528i	−0.197851	+	0.402415i
$715$	−5.74025	+	25.1497i	−0.214673	+	0.940544i
$716$	1.93255	+	3.34728i	0.0722229	+	0.125094i
$717$	−4.18049	+	7.24083i	−0.156123	+	0.270414i
$718$	15.8318	+	14.6898i	0.590839	+	0.548219i
$719$	35.0022	+	23.8641i	1.30536	+	0.889981i	0.998098	−	0.0616428i	$-0.0196340\pi$
$719$	35.0022	+	23.8641i	1.30536	+	0.889981i	0.307265	+	0.951624i	$0.400586\pi$
$720$	4.95694	+	6.21580i	0.184734	+	0.231649i
$721$	37.1448	+	3.08839i	1.38335	+	0.115018i
$722$	13.3681	−	16.7631i	0.497510	−	0.623858i
$723$	24.1944	−	7.46299i	0.899801	−	0.277552i
$724$	−1.74697	−	4.45120i	−0.0649255	−	0.165428i
$725$	−0.266985	+	3.56267i	−0.00991558	+	0.132314i
$726$	−2.25132	+	5.73626i	−0.0835542	+	0.212893i
$727$	−37.6005	−	18.1074i	−1.39452	−	0.671568i	−0.422482	−	0.906371i	$-0.638841\pi$
$727$	−37.6005	−	18.1074i	−1.39452	−	0.671568i	−0.972043	+	0.234804i	$0.924555\pi$
$728$	−1.88404	−	6.28954i	−0.0698273	−	0.233106i
$729$	10.1439	−	4.88502i	0.375698	−	0.180927i
$730$	−2.16160	−	28.8446i	−0.0800046	−	1.06759i
$731$	−6.16787	−	1.90254i	−0.228127	−	0.0703679i
$732$	27.7557	−	18.9235i	1.02588	−	0.699433i
$733$	−37.1833	−	5.60447i	−1.37340	−	0.207006i	−0.579456	−	0.815003i	$-0.696735\pi$
$733$	−37.1833	−	5.60447i	−1.37340	−	0.207006i	−0.793939	+	0.607997i	$0.791973\pi$
$734$	17.4352			0.643546
$735$	−20.1730	−	53.9718i	−0.744093	−	1.99078i
$736$	8.16388			0.300925
$737$	−0.785967	−	0.118465i	−0.0289515	−	0.00436373i
$738$	−3.90455	+	2.66208i	−0.143729	+	0.0979925i
$739$	−6.55661	−	2.02244i	−0.241189	−	0.0743968i	0.171804	−	0.985131i	$-0.445040\pi$
$739$	−6.55661	−	2.02244i	−0.241189	−	0.0743968i	−0.412993	+	0.910734i	$0.635517\pi$
$740$	1.31888	+	17.5992i	0.0484829	+	0.646959i
$741$	32.4328	−	15.6188i	1.19145	−	0.573772i
$742$	17.8293	−	25.6980i	0.654534	−	0.943404i
$743$	−26.0524	−	12.5462i	−0.955768	−	0.460274i	−0.110063	−	0.993925i	$-0.535105\pi$
$743$	−26.0524	−	12.5462i	−0.955768	−	0.460274i	−0.845705	+	0.533651i	$0.820820\pi$
$744$	0.945240	−	2.40843i	0.0346542	−	0.0882974i
$745$	−5.68823	+	75.9042i	−0.208401	+	2.78091i
$746$	12.8618	+	32.7713i	0.470903	+	1.19984i
$747$	−22.0696	+	6.80756i	−0.807483	+	0.249076i
$748$	3.56600	−	4.47162i	0.130386	−	0.163499i
$749$	21.9269	+	12.8990i	0.801190	+	0.471319i
$750$	15.5064	+	19.4444i	0.566213	+	0.710009i
$751$	−21.8923	−	14.9259i	−0.798861	−	0.544654i	0.0936896	−	0.995601i	$-0.470134\pi$
$751$	−21.8923	−	14.9259i	−0.798861	−	0.544654i	−0.892551	+	0.450947i	$0.851086\pi$
$752$	7.42669	+	6.89096i	0.270824	+	0.251288i
$753$	−9.73635	+	16.8638i	−0.354812	+	0.614553i
$754$	−0.552635	−	0.957191i	−0.0201258	−	0.0348588i
$755$	6.98050	−	30.5836i	0.254046	−	1.11305i
$756$	4.67931	+	1.10824i	0.170185	+	0.0403063i
$757$	−0.841851	−	3.68839i	−0.0305976	−	0.134057i	0.957322	−	0.289023i	$-0.0933303\pi$
$757$	−0.841851	−	3.68839i	−0.0305976	−	0.134057i	−0.987920	+	0.154966i	$0.950473\pi$
$758$	10.8101	−	10.0303i	0.392642	−	0.364319i
$759$	53.0462	−	7.99542i	1.92545	−	0.290215i
$760$	−22.6914	+	3.42018i	−0.823104	+	0.124063i
$761$	17.3867	−	16.1325i	0.630267	−	0.584803i	−0.298981	−	0.954259i	$-0.596647\pi$
$761$	17.3867	−	16.1325i	0.630267	−	0.584803i	0.929248	+	0.369456i	$0.120456\pi$
$762$	−4.79098	−	20.9906i	−0.173559	−	0.760411i
$763$	1.75058	−	0.384568i	0.0633751	−	0.0139223i
$764$	3.52152	−	15.4288i	0.127404	−	0.558194i
$765$	7.89234	+	13.6699i	0.285348	+	0.494238i
$766$	11.5320	−	19.9741i	0.416669	−	0.721692i
$767$	9.34424	+	8.67019i	0.337401	+	0.313062i
$768$	1.88469	+	1.28496i	0.0680080	+	0.0463671i
$769$	18.8313	+	23.6137i	0.679075	+	0.851533i	0.995269	−	0.0971616i	$-0.0309764\pi$
$769$	18.8313	+	23.6137i	0.679075	+	0.851533i	−0.316194	+	0.948695i	$0.602405\pi$
$770$	3.87722	+	27.2283i	0.139725	+	0.981239i
$771$	17.3387	−	21.7421i	0.624440	−	0.783022i
$772$	−13.7963	+	4.25560i	−0.496540	+	0.153162i
$773$	−8.00637	−	20.3999i	−0.287969	−	0.733734i	−0.999516	−	0.0310953i	$-0.990100\pi$
$773$	−8.00637	−	20.3999i	−0.287969	−	0.733734i	0.711547	−	0.702638i	$-0.247995\pi$
$774$	0.535266	−	7.14262i	0.0192397	−	0.256736i
$775$	3.32399	−	8.46939i	0.119401	−	0.304230i
$776$	−6.23929	−	3.00469i	−0.223978	−	0.107862i
$777$	−19.8992	−	21.8000i	−0.713878	−	0.782072i
$778$	−0.551717	+	0.265693i	−0.0197800	+	0.00952555i
$779$	−1.01934	−	13.6021i	−0.0365215	−	0.487345i
$780$	−19.5191	−	6.02083i	−0.698894	−	0.215580i
$781$	−14.4209	+	9.83202i	−0.516021	+	0.351817i
$782$	16.0277	+	2.41578i	0.573148	+	0.0863882i
$783$	0.809510			0.0289295
$784$	−4.27460	−	5.54326i	−0.152664	−	0.197974i
$785$	−5.01980			−0.179164
$786$	16.0154	+	2.41393i	0.571250	+	0.0861022i
$787$	−34.8825	+	23.7825i	−1.24343	+	0.847755i	−0.992736	−	0.120312i	$-0.961611\pi$
$787$	−34.8825	+	23.7825i	−1.24343	+	0.847755i	−0.250692	+	0.968067i	$0.580658\pi$
$788$	−18.6007	−	5.73757i	−0.662624	−	0.204392i
$789$	−3.00552	−	40.1059i	−0.106999	−	1.42781i
$790$	16.3468	−	7.87220i	0.581593	−	0.280080i
$791$	9.31513	−	5.27729i	0.331208	−	0.187639i
$792$	5.71826	+	2.75377i	0.203190	+	0.0978510i
$793$	−13.3518	+	34.0198i	−0.474136	+	1.20808i
$794$	2.32471	−	31.0211i	0.0825009	−	1.10090i
$795$	−35.5504	−	90.5809i	−1.26084	−	3.21257i
$796$	7.34528	−	2.26572i	0.260347	−	0.0803063i
$797$	14.7157	−	18.4529i	0.521256	−	0.653635i	−0.449619	−	0.893221i	$-0.648440\pi$
$797$	14.7157	−	18.4529i	0.521256	−	0.653635i	0.970875	+	0.239586i	$0.0770116\pi$
$798$	26.3329	−	27.9200i	0.932175	−	0.988359i
$799$	12.5413	+	15.7263i	0.443679	+	0.556356i
$800$	6.62764	+	4.51865i	0.234322	+	0.159758i
$801$	−4.27178	−	3.96363i	−0.150936	−	0.140048i
$802$	−13.1728	+	22.8159i	−0.465146	+	0.805657i
$803$	−11.5457	−	19.9978i	−0.407440	−	0.705706i
$804$	0.140052	−	0.613606i	0.00493924	−	0.0216402i
$805$	−61.3323	+	48.0980i	−2.16168	+	1.69523i
$806$	0.626338	+	2.74417i	0.0220618	+	0.0966592i
$807$	−37.4269	+	34.7270i	−1.31749	+	1.22245i
$808$	3.11914	−	0.470134i	0.109731	−	0.0165393i
$809$	−33.1304	+	4.99360i	−1.16480	+	0.175566i	−0.702849	−	0.711339i	$-0.748089\pi$
$809$	−33.1304	+	4.99360i	−1.16480	+	0.175566i	−0.461953	+	0.886905i	$0.652851\pi$
$810$	28.4509	−	26.3985i	0.999661	−	0.927550i
$811$	−1.09486	−	4.79691i	−0.0384459	−	0.168442i	0.952060	−	0.305910i	$-0.0989608\pi$
$811$	−1.09486	−	4.79691i	−0.0384459	−	0.168442i	−0.990506	+	0.137468i	$0.956104\pi$
$812$	−0.915277	−	0.742199i	−0.0321199	−	0.0260461i
$813$	−5.30978	+	23.2637i	−0.186222	+	0.815893i
$814$	7.04449	+	12.2014i	0.246909	+	0.427659i
$815$	−10.2414	+	17.7386i	−0.358740	+	0.621356i
$816$	3.31988	+	3.08040i	0.116219	+	0.107835i
$817$	17.0819	+	11.6462i	0.597619	+	0.407449i
$818$	16.0026	+	20.0666i	0.559518	+	0.701613i
$819$	13.5082	−	5.17486i	0.472014	−	0.180824i
$820$	−4.82582	+	6.05138i	−0.168525	+	0.211324i
$821$	−6.79848	+	2.09705i	−0.237269	+	0.0731877i	−0.411109	−	0.911586i	$-0.634858\pi$
$821$	−6.79848	+	2.09705i	−0.237269	+	0.0731877i	0.173840	+	0.984774i	$0.444382\pi$
$822$	5.69850	+	14.5195i	0.198758	+	0.506427i
$823$	−1.33887	+	17.8659i	−0.0466699	+	0.622767i	0.924006	+	0.382377i	$0.124894\pi$
$823$	−1.33887	+	17.8659i	−0.0466699	+	0.622767i	−0.970676	+	0.240390i	$0.922725\pi$
$824$	5.14688	−	13.1140i	0.179300	−	0.456849i
$825$	47.4896	+	22.8698i	1.65338	+	0.796224i
$826$	12.6099	+	5.06807i	0.438756	+	0.176341i
$827$	−25.7438	+	12.3975i	−0.895198	+	0.431105i	−0.824152	−	0.566368i	$-0.808348\pi$
$827$	−25.7438	+	12.3975i	−0.895198	+	0.431105i	−0.0710461	+	0.997473i	$0.522634\pi$
$828$	1.34415	+	17.9364i	0.0467123	+	0.623332i
$829$	48.4359	+	14.9405i	1.68225	+	0.518905i	0.981000	−	0.194010i	$-0.0621494\pi$
$829$	48.4359	+	14.9405i	1.68225	+	0.518905i	0.701250	+	0.712915i	$0.252626\pi$
$830$	−31.2544	+	21.3089i	−1.08486	+	0.739643i
$831$	−49.7548	−	7.49934i	−1.72598	−	0.260149i
$832$	−2.48159			−0.0860336
$833$	−6.75177	−	12.1477i	−0.233935	−	0.420892i
$834$	−14.7745			−0.511598
$835$	19.7111	+	2.97097i	0.682131	+	0.102815i
$836$	−15.1362	+	10.3197i	−0.523495	+	0.356913i
$837$	−1.96995	−	0.607650i	−0.0680916	−	0.0210035i
$838$	−1.40882	−	18.7994i	−0.0486668	−	0.649414i
$839$	21.3007	−	10.2579i	0.735382	−	0.354142i	−0.0284161	−	0.999596i	$-0.509046\pi$
$839$	21.3007	−	10.2579i	0.735382	−	0.354142i	0.763799	+	0.645455i	$0.223332\pi$
$840$	−21.7295	+	1.45033i	−0.749738	+	0.0500411i
$841$	25.9494	+	12.4966i	0.894806	+	0.430916i
$842$	−7.37040	+	18.7795i	−0.254001	+	0.647183i
$843$	−1.97074	+	26.2977i	−0.0678760	+	0.905742i
$844$	−9.53436	−	24.2931i	−0.328186	−	0.836205i
$845$	−23.5917	+	7.27707i	−0.811578	+	0.250339i
$846$	−13.9170	+	17.4513i	−0.478475	+	0.599988i
$847$	−3.97802	−	5.93814i	−0.136686	−	0.204037i
$848$	−7.37073	−	9.24260i	−0.253112	−	0.317392i
$849$	−2.16187	−	1.47394i	−0.0741953	−	0.0505855i
$850$	11.6745	+	10.8324i	0.400434	+	0.371548i
$851$	−19.9639	+	34.5785i	−0.684354	+	1.18534i
$852$	−6.91023	−	11.9689i	−0.236741	−	0.410047i
$853$	−11.4541	+	50.1837i	−0.392181	+	1.71826i	0.264760	+	0.964314i	$0.414707\pi$
$853$	−11.4541	+	50.1837i	−0.392181	+	1.71826i	−0.656940	+	0.753942i	$0.728150\pi$
$854$	−0.317701	+	38.9624i	−0.0108715	+	1.33327i
$855$	−11.2503	−	49.2908i	−0.384753	−	1.68571i
$856$	7.04848	−	6.54003i	0.240912	−	0.223534i
$857$	−38.3282	+	5.77704i	−1.30927	+	0.197340i	−0.766337	−	0.642439i	$-0.777923\pi$
$857$	−38.3282	+	5.77704i	−1.30927	+	0.197340i	−0.542928	+	0.839779i	$0.682684\pi$
$858$	−16.1245	+	2.43038i	−0.550483	+	0.0829719i
$859$	6.68191	−	6.19991i	0.227984	−	0.211538i	−0.557907	−	0.829904i	$-0.688395\pi$
$859$	6.68191	−	6.19991i	0.227984	−	0.211538i	0.785891	+	0.618366i	$0.212205\pi$
$860$	−2.61048	−	11.4373i	−0.0890166	−	0.390007i
$861$	0.105549	−	12.9444i	0.00359710	−	0.441144i
$862$	−5.03693	+	22.0682i	−0.171559	+	0.751647i
$863$	−20.9972	−	36.3683i	−0.714754	−	1.23799i	−0.963054	−	0.269307i	$-0.913205\pi$
$863$	−20.9972	−	36.3683i	−0.714754	−	1.23799i	0.248301	−	0.968683i	$-0.420128\pi$
$864$	0.908770	−	1.57404i	0.0309170	−	0.0535498i
$865$	−4.87715	−	4.52534i	−0.165828	−	0.153866i
$866$	6.38688	+	4.35450i	0.217035	+	0.147972i
$867$	−18.5714	−	23.2878i	−0.630719	−	0.790896i
$868$	1.67022	+	2.49319i	0.0566908	+	0.0846245i
$869$	9.03072	−	11.3242i	0.306346	−	0.384146i
$870$	−3.50322	+	1.08060i	−0.118770	+	0.0366358i
$871$	0.250156	+	0.637386i	0.00847620	+	0.0215970i
$872$	0.0506246	−	0.675539i	0.00171437	−	0.0228766i
$873$	5.57414	−	14.2027i	0.188656	−	0.480688i
$874$	−46.7753	−	22.5258i	−1.58220	−	0.761946i
$875$	−28.7826	+	1.92109i	−0.973029	+	0.0649447i
$876$	16.4739	−	7.93340i	0.556601	−	0.268045i
$877$	−0.309770	−	4.13359i	−0.0104602	−	0.139581i	0.989529	−	0.144338i	$-0.0461051\pi$
$877$	−0.309770	−	4.13359i	−0.0104602	−	0.139581i	−0.999989	+	0.00475617i	$0.998486\pi$
$878$	−15.4679	−	4.77122i	−0.522016	−	0.161021i
$879$	−32.0558	+	21.8553i	−1.08121	+	0.737159i
$880$	10.2790	+	1.54931i	0.346506	+	0.0522274i
$881$	36.0415			1.21427			0.607135	−	0.794599i	$-0.292319\pi$
$881$	36.0415			1.21427			0.607135	+	0.794599i	$0.292319\pi$
$882$	11.4750	−	10.3041i	0.386383	−	0.346959i
$883$	22.4586			0.755791			0.377896	−	0.925848i	$-0.376648\pi$
$883$	22.4586			0.755791			0.377896	+	0.925848i	$0.376648\pi$
$884$	−4.87196	−	0.734330i	−0.163862	−	0.0246982i
$885$	34.9341	−	23.8177i	1.17430	−	0.800623i
$886$	9.86909	+	3.04421i	0.331559	+	0.102272i
$887$	−0.671570	−	8.96148i	−0.0225491	−	0.300897i	−0.997064	−	0.0765738i	$-0.975602\pi$
$887$	−0.671570	−	8.96148i	−0.0225491	−	0.300897i	0.974515	−	0.224323i	$-0.0720171\pi$
$888$	−10.0513	+	4.84047i	−0.337301	+	0.162436i
$889$	23.1713	+	9.31283i	0.777142	+	0.312342i
$890$	−8.59922	−	4.14117i	−0.288247	−	0.138812i
$891$	11.3196	−	28.8418i	0.379220	−	0.966236i
$892$	−0.605989	+	8.08636i	−0.0202900	+	0.270751i
$893$	−23.5380	−	59.9738i	−0.787668	−	2.00695i
$894$	−45.9781	+	14.1824i	−1.53774	+	0.474329i
$895$	−8.69602	+	10.9045i	−0.290676	+	0.364496i
$896$	−2.47066	+	0.946488i	−0.0825390	+	0.0316199i
$897$	−28.8132	−	36.1306i	−0.962044	−	1.20636i
$898$	17.0127	+	11.5990i	0.567720	+	0.387065i
$899$	0.370323	+	0.343610i	0.0123510	+	0.0114600i
$900$	−8.83644	+	15.3052i	−0.294548	+	0.510172i
$901$	−11.7355	−	20.3265i	−0.390967	−	0.677175i
$902$	−1.37494	+	6.02399i	−0.0457804	+	0.200577i
$903$	15.2395	+	12.3577i	0.507137	+	0.411238i
$904$	−0.900440	−	3.94508i	−0.0299482	−	0.131212i
$905$	12.6488	−	11.7364i	0.420462	−	0.390132i
$906$	19.6084	−	2.95550i	0.651447	−	0.0981898i
$907$	23.1097	−	3.48322i	0.767344	−	0.115658i	0.246306	−	0.969192i	$-0.420783\pi$
$907$	23.1097	−	3.48322i	0.767344	−	0.115658i	0.521038	+	0.853534i	$0.325545\pi$
$908$	−1.57655	+	1.46282i	−0.0523196	+	0.0485455i
$909$	1.54646	+	6.77546i	0.0512927	+	0.224728i
$910$	18.6433	−	14.6204i	0.618019	−	0.484663i
$911$	−13.0163	+	57.0282i	−0.431250	+	1.88943i	0.0252059	+	0.999682i	$0.491976\pi$
$911$	−13.0163	+	57.0282i	−0.431250	+	1.88943i	−0.456456	+	0.889746i	$0.650881\pi$
$912$	−7.25296	−	12.5625i	−0.240169	−	0.415986i
$913$	−15.0989	+	26.1521i	−0.499702	+	0.865509i
$914$	−10.6240	−	9.85765i	−0.351411	−	0.326062i
$915$	100.157	+	68.2860i	3.31109	+	2.25746i
$916$	−6.61472	−	8.29459i	−0.218556	−	0.274061i
$917$	−12.8894	+	13.6663i	−0.425647	+	0.451302i
$918$	2.24991	−	2.82130i	0.0742581	−	0.0931168i
$919$	−24.6253	+	7.59590i	−0.812313	+	0.250565i	−0.672962	−	0.739677i	$-0.734978\pi$
$919$	−24.6253	+	7.59590i	−0.812313	+	0.250565i	−0.139352	+	0.990243i	$0.544502\pi$
$920$	10.7628	+	27.4231i	0.354839	+	0.904114i
$921$	2.22042	−	29.6294i	0.0731652	−	0.976322i
$922$	2.74022	−	6.98196i	0.0902442	−	0.229938i
$923$	13.5465	+	6.52365i	0.445888	+	0.214728i
$924$	−15.1266	+	8.56964i	−0.497628	+	0.281921i
$925$	−35.3462	+	17.0218i	−1.16217	+	0.559674i
$926$	−2.81915	−	37.6189i	−0.0926429	−	1.23623i
$927$	29.6595	+	9.14873i	0.974144	+	0.300484i
$928$	−0.367997	+	0.250896i	−0.0120801	+	0.00823606i
$929$	11.3508	+	1.71085i	0.372406	+	0.0561312i	0.332579	−	0.943075i	$-0.392081\pi$
$929$	11.3508	+	1.71085i	0.372406	+	0.0561312i	0.0398273	+	0.999207i	$0.487319\pi$
$930$	9.33627			0.306148
$931$	9.19653	+	43.5548i	0.301404	+	1.42745i
$932$	−5.81016			−0.190318
$933$	49.1162	+	7.40308i	1.60799	+	0.242366i
$934$	−27.6776	+	18.8703i	−0.905639	+	0.617454i
$935$	19.7218	+	6.08336i	0.644971	+	0.198947i
$936$	−0.408582	−	5.45215i	−0.0133549	−	0.178209i
$937$	14.4170	−	6.94287i	0.470983	−	0.226814i	−0.183309	−	0.983055i	$-0.558681\pi$
$937$	14.4170	−	6.94287i	0.470983	−	0.226814i	0.654292	+	0.756242i	$0.272967\pi$
$938$	0.492156	+	0.539169i	0.0160694	+	0.0176045i
$939$	55.6350	+	26.7924i	1.81558	+	0.874337i
$940$	−13.3564	+	34.0315i	−0.435637	+	1.10999i
$941$	3.47254	−	46.3379i	0.113202	−	1.51057i	−0.594520	−	0.804081i	$-0.702658\pi$
$941$	3.47254	−	46.3379i	0.113202	−	1.51057i	0.707722	−	0.706491i	$-0.249723\pi$
$942$	−1.15929	−	2.95381i	−0.0377716	−	0.0962404i
$943$	−16.7329	+	5.16143i	−0.544899	+	0.168079i
$944$	3.20264	−	4.01599i	0.104237	−	0.130709i
$945$	2.44627	+	17.1792i	0.0795771	+	0.558841i
$946$	−5.83914	−	7.32206i	−0.189847	−	0.238061i
$947$	−34.1615	−	23.2909i	−1.11010	−	0.756853i	−0.137769	−	0.990464i	$-0.543993\pi$
$947$	−34.1615	−	23.2909i	−1.11010	−	0.756853i	−0.972330	+	0.233612i	$0.924945\pi$
$948$	8.40742	+	7.80095i	0.273060	+	0.253363i
$949$	−9.94605	+	17.2271i	−0.322863	+	0.559214i
$950$	−25.5055	−	44.1767i	−0.827506	−	1.43328i
$951$	−13.7621	+	60.2958i	−0.446267	+	1.95522i
$952$	−5.13058	+	1.12709i	−0.166283	+	0.0365292i
$953$	1.03534	+	4.53613i	0.0335380	+	0.146940i	0.988925	−	0.148418i	$-0.0474182\pi$
$953$	1.03534	+	4.53613i	0.0335380	+	0.146940i	−0.955387	+	0.295358i	$0.904561\pi$
$954$	19.0928	−	17.7155i	0.618152	−	0.573562i
$955$	56.4691	−	8.51135i	1.82730	−	0.275421i
$956$	−3.62447	+	0.546301i	−0.117224	+	0.0176686i
$957$	−2.14540	+	1.99064i	−0.0693510	+	0.0643483i
$958$	−0.279933	−	1.22647i	−0.00904423	−	0.0396254i
$959$	−17.6045	−	4.16943i	−0.568480	−	0.134638i
$960$	−1.83162	+	8.02486i	−0.0591154	+	0.259001i
$961$	14.8567	+	25.7326i	0.479250	+	0.830085i
$962$	6.06847	−	10.5109i	0.195655	−	0.338885i
$963$	15.5292	+	14.4090i	0.500422	+	0.464324i
$964$	9.17111	+	6.25276i	0.295382	+	0.201388i
$965$	−32.4832	−	40.7326i	−1.04567	−	1.31123i
$966$	−42.4666	−	24.9820i	−1.36634	−	0.803782i
$967$	−29.6245	+	37.1479i	−0.952659	+	1.19460i	0.0281461	+	0.999604i	$0.491040\pi$
$967$	−29.6245	+	37.1479i	−0.952659	+	1.19460i	−0.980805	+	0.194992i	$0.937532\pi$
$968$	−2.58147	+	0.796277i	−0.0829715	+	0.0255933i
$969$	−10.5219	−	26.8095i	−0.338013	−	0.861244i
$970$	1.86746	−	24.9195i	0.0599605	−	0.800117i
$971$	0.495489	−	1.26248i	0.0159010	−	0.0405150i	−0.922703	−	0.385512i	$-0.874025\pi$
$971$	0.495489	−	1.26248i	0.0159010	−	0.0405150i	0.938604	+	0.344997i	$0.112120\pi$
$972$	17.1916	+	8.27905i	0.551421	+	0.265551i
$973$	9.76855	−	14.0798i	0.313165	−	0.451377i
$974$	12.7329	−	6.13184i	0.407988	−	0.196477i
$975$	−3.39323	−	45.2796i	−0.108670	−	1.45011i
$976$	14.0726	+	4.34083i	0.450454	+	0.138947i
$977$	−17.3368	+	11.8200i	−0.554653	+	0.378156i	−0.807967	−	0.589228i	$-0.799432\pi$
$977$	−17.3368	+	11.8200i	−0.554653	+	0.378156i	0.253314	+	0.967384i	$0.418479\pi$
$978$	−12.8031	−	1.92976i	−0.409399	−	0.0617069i
$979$	−7.61938			−0.243517
$980$	12.9849	−	21.6667i	0.414787	−	0.692116i
$981$	1.49252			0.0476525
$982$	−11.8919	−	1.79242i	−0.379487	−	0.0571985i
$983$	49.8728	−	34.0027i	1.59070	−	1.08452i	0.642755	−	0.766072i	$-0.277791\pi$
$983$	49.8728	−	34.0027i	1.59070	−	1.08452i	0.947941	−	0.318446i	$-0.103161\pi$
$984$	−4.67532	−	1.44214i	−0.149044	−	0.0459739i
$985$	−5.24918	−	70.0455i	−0.167253	−	2.23183i
$986$	−0.796709	+	0.383675i	−0.0253724	+	0.0122187i
$987$	−17.5452	−	58.5714i	−0.558468	−	1.86435i
$988$	14.2184	+	6.84720i	0.452346	+	0.217839i
$989$	9.69649	−	24.7063i	0.308330	−	0.785613i
$990$	−1.71151	+	22.8385i	−0.0543954	+	0.725856i
$991$	−0.805768	−	2.05306i	−0.0255961	−	0.0652177i	0.917504	−	0.397726i	$-0.130200\pi$
$991$	−0.805768	−	2.05306i	−0.0255961	−	0.0652177i	−0.943100	+	0.332508i	$0.892105\pi$
$992$	1.08386	−	0.334326i	0.0344125	−	0.0106148i
$993$	−12.5712	+	15.7637i	−0.398934	+	0.500247i
$994$	15.9750	+	1.32823i	0.506695	+	0.0421289i
$995$	17.2943	+	21.6864i	0.548267	+	0.687505i
$996$	−19.7568	−	13.4700i	−0.626019	−	0.426812i
$997$	−5.33534	−	4.95048i	−0.168972	−	0.156783i	0.591154	−	0.806559i	$-0.298672\pi$
$997$	−5.33534	−	4.95048i	−0.168972	−	0.156783i	−0.760126	+	0.649775i	$0.774863\pi$
$998$	−7.03481	+	12.1846i	−0.222683	+	0.385698i
$999$	4.44461	+	7.69828i	0.140621	+	0.243563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.39.2	✓	24
3.2	odd	2		882.2.z.b.235.1		24
4.3	odd	2		784.2.bg.b.529.1		24
7.2	even	3		686.2.g.f.569.2		24
7.3	odd	6		686.2.e.d.295.4		24
7.4	even	3		686.2.e.c.295.1		24
7.5	odd	6		686.2.g.d.569.1		24
7.6	odd	2		686.2.g.e.165.1		24
49.3	odd	42		686.2.e.d.393.4		24
49.5	odd	42		686.2.g.e.79.1		24
49.8	even	7		686.2.g.f.557.2		24
49.17	odd	42		4802.2.a.l.1.3		12
49.32	even	21		4802.2.a.o.1.10		12
49.41	odd	14		686.2.g.d.557.1		24
49.44	even	21	inner	98.2.g.b.93.2	yes	24
49.46	even	21		686.2.e.c.393.1		24
147.44	odd	42		882.2.z.b.289.1		24
196.191	odd	42		784.2.bg.b.289.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.39.2	✓	24	1.1	even	1	trivial
98.2.g.b.93.2	yes	24	49.44	even	21	inner
686.2.e.c.295.1		24	7.4	even	3
686.2.e.c.393.1		24	49.46	even	21
686.2.e.d.295.4		24	7.3	odd	6
686.2.e.d.393.4		24	49.3	odd	42
686.2.g.d.557.1		24	49.41	odd	14
686.2.g.d.569.1		24	7.5	odd	6
686.2.g.e.79.1		24	49.5	odd	42
686.2.g.e.165.1		24	7.6	odd	2
686.2.g.f.557.2		24	49.8	even	7
686.2.g.f.569.2		24	7.2	even	3
784.2.bg.b.289.1		24	196.191	odd	42
784.2.bg.b.529.1		24	4.3	odd	2
882.2.z.b.235.1		24	3.2	odd	2
882.2.z.b.289.1		24	147.44	odd	42
4802.2.a.l.1.3		12	49.17	odd	42
4802.2.a.o.1.10		12	49.32	even	21

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988831 - 0.149042i) q^{2} +(1.88469 - 1.28496i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.269665 + 3.59844i) q^{5} +(-2.05516 + 0.989712i) q^{6} +(0.415648 - 2.61290i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.804920 - 2.05090i) q^{9} +O(q^{10})\)	\(q+(-0.988831 - 0.149042i) q^{2} +(1.88469 - 1.28496i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.269665 + 3.59844i) q^{5} +(-2.05516 + 0.989712i) q^{6} +(0.415648 - 2.61290i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.804920 - 2.05090i) q^{9} +(0.269665 - 3.59844i) q^{10} +(-1.05244 - 2.68158i) q^{11} +(2.17971 - 0.672352i) q^{12} +(-1.54725 + 1.94018i) q^{13} +(-0.800437 + 2.52177i) q^{14} +(5.13209 + 6.43544i) q^{15} +(0.826239 + 0.563320i) q^{16} +(1.45541 + 1.35043i) q^{17} +(-1.10160 + 1.90803i) q^{18} +(-3.17965 - 5.50732i) q^{19} +(-0.802972 + 3.51805i) q^{20} +(-2.57411 - 5.45861i) q^{21} +(0.641019 + 2.80849i) q^{22} +(-5.98455 + 5.55285i) q^{23} +(-2.25558 + 0.339973i) q^{24} +(-7.93186 + 1.19554i) q^{25} +(1.81913 - 1.68791i) q^{26} +(0.404441 + 1.77197i) q^{27} +(1.16735 - 2.37430i) q^{28} +(0.0991081 - 0.434221i) q^{29} +(-4.11562 - 7.12846i) q^{30} +(-0.567124 + 0.982288i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-5.42927 - 3.70161i) q^{33} +(-1.23789 - 1.55226i) q^{34} +(9.51443 + 0.791072i) q^{35} +(1.37367 - 1.72253i) q^{36} +(4.67351 - 1.44159i) q^{37} +(2.32332 + 5.91971i) q^{38} +(-0.423020 + 5.64481i) q^{39} +(1.31834 - 3.35908i) q^{40} +(1.93251 + 0.930648i) q^{41} +(1.73179 + 5.78129i) q^{42} +(-2.92907 + 1.41056i) q^{43} +(-0.215276 - 2.87266i) q^{44} +(7.59710 + 2.34339i) q^{45} +(6.74531 - 4.59888i) q^{46} +(10.0180 + 1.50998i) q^{47} +2.28105 q^{48} +(-6.65447 - 2.17209i) q^{49} +8.02146 q^{50} +(4.47826 + 0.674989i) q^{51} +(-2.05039 + 1.39793i) q^{52} +(-11.2965 - 3.48451i) q^{53} +(-0.135825 - 1.81246i) q^{54} +(9.36569 - 4.51028i) q^{55} +(-1.50818 + 2.17380i) q^{56} +(-13.0694 - 6.29388i) q^{57} +(-0.162718 + 0.414600i) q^{58} +(0.383862 - 5.12228i) q^{59} +(3.00721 + 7.66224i) q^{60} +(14.0726 - 4.34083i) q^{61} +(0.707192 - 0.886791i) q^{62} +(-5.02424 - 2.95563i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-7.39887 - 5.04446i) q^{65} +(4.81693 + 4.46946i) q^{66} +(0.137960 - 0.238953i) q^{67} +(0.992709 + 1.71942i) q^{68} +(-4.14384 + 18.1553i) q^{69} +(-9.29026 - 2.20029i) q^{70} +(-1.34821 - 5.90690i) q^{71} +(-1.61506 + 1.49856i) q^{72} +(7.92634 - 1.19470i) q^{73} +(-4.83617 + 0.728935i) q^{74} +(-13.4129 + 12.4454i) q^{75} +(-1.41508 - 6.19987i) q^{76} +(-7.44414 + 1.63533i) q^{77} +(1.25961 - 5.51871i) q^{78} +(2.51399 + 4.35435i) q^{79} +(-1.80426 + 3.12507i) q^{80} +(7.88435 + 7.31560i) q^{81} +(-1.77222 - 1.20828i) q^{82} +(-6.53590 - 8.19576i) q^{83} +(-0.850796 - 5.97483i) q^{84} +(-4.46695 + 5.60138i) q^{85} +(3.10659 - 0.958255i) q^{86} +(-0.371169 - 0.945724i) q^{87} +(-0.215276 + 2.87266i) q^{88} +(0.966314 - 2.46213i) q^{89} +(-7.16298 - 3.44951i) q^{90} +(4.42640 + 4.84923i) q^{91} +(-7.35540 + 3.54217i) q^{92} +(0.193348 + 2.58005i) q^{93} +(-9.68110 - 2.98622i) q^{94} +(18.9603 - 12.9269i) q^{95} +(-2.25558 - 0.339973i) q^{96} +6.92509 q^{97} +(6.25642 + 3.13963i) q^{98} -6.34679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

Modular forms

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