LMFDB - Embedded newform 471.2.q.b.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.67476 + 0.659270i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.94881 + 2.59734i) q^{4} +(0.358425 - 0.269339i) q^{5} +(-1.90833 - 1.98678i) q^{6} +(-1.72808 + 0.906968i) q^{7} +(7.40054 + 6.55631i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(2.67476 + 0.659270i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.94881 + 2.59734i) q^{4} +(0.358425 - 0.269339i) q^{5} +(-1.90833 - 1.98678i) q^{6} +(-1.72808 + 0.906968i) q^{7} +(7.40054 + 6.55631i) q^{8} +(0.428693 + 0.903450i) q^{9} +(1.13627 - 0.484119i) q^{10} +(0.336441 + 0.350272i) q^{11} +(-2.79450 - 4.84021i) q^{12} +(-0.131750 + 0.228197i) q^{13} +(-5.22015 + 1.28665i) q^{14} +(-0.446890 + 0.0360767i) q^{15} +(9.12250 + 13.2162i) q^{16} +(1.10355 - 0.829263i) q^{17} +(0.551034 + 2.69914i) q^{18} +(1.49593 - 7.32757i) q^{19} +(2.47334 - 0.401957i) q^{20} +(1.94530 + 0.157041i) q^{21} +(0.668977 + 1.15870i) q^{22} +(-4.69084 - 6.79585i) q^{23} +(-2.75074 - 9.49666i) q^{24} +(-1.33516 + 4.60951i) q^{25} +(-0.502843 + 0.523515i) q^{26} +(0.120537 - 0.992709i) q^{27} -10.9077 q^{28} +(-0.319803 + 2.63381i) q^{29} +(-1.21911 - 0.198124i) q^{30} +(-2.27624 - 2.78789i) q^{31} +(8.67549 + 22.8754i) q^{32} +(-0.0971482 - 0.475863i) q^{33} +(3.49844 - 1.49055i) q^{34} +(-0.375107 + 0.790520i) q^{35} +(-0.225046 + 5.58447i) q^{36} +(-5.17571 - 3.88930i) q^{37} +(8.83212 - 18.6133i) q^{38} +(0.233317 - 0.122454i) q^{39} +(4.41841 + 0.356691i) q^{40} +(0.755226 - 1.09413i) q^{41} +(5.09969 + 1.70253i) q^{42} +(-5.47935 + 3.46493i) q^{43} +(0.755209 + 2.60728i) q^{44} +(0.396989 + 0.208356i) q^{45} +(-8.06658 - 21.2698i) q^{46} +(4.91754 + 2.09517i) q^{47} +(-0.646627 - 16.0459i) q^{48} +(-1.81277 + 2.62625i) q^{49} +(-6.61016 + 11.4491i) q^{50} +(-1.37592 + 0.111076i) q^{51} +(-1.24471 + 0.787107i) q^{52} +(-9.29946 + 3.10462i) q^{53} +(0.976870 - 2.57580i) q^{54} +(0.214931 + 0.0349297i) q^{55} +(-18.7351 - 4.61779i) q^{56} +(-5.18069 + 5.39367i) q^{57} +(-2.59179 + 6.83399i) q^{58} +(-3.72369 + 3.29890i) q^{59} +(-2.30528 - 0.982187i) q^{60} +(2.05079 - 10.0454i) q^{61} +(-4.25043 - 8.95760i) q^{62} +(-1.56022 - 1.17243i) q^{63} +(4.25246 + 35.0222i) q^{64} +(0.0142400 + 0.117277i) q^{65} +(0.0538740 - 1.33687i) q^{66} +(-1.89861 - 1.68202i) q^{67} +(7.61513 - 1.23758i) q^{68} +(0.332499 + 8.25088i) q^{69} +(-1.52449 + 1.86716i) q^{70} +(10.1552 - 3.39030i) q^{71} +(-2.75074 + 9.49666i) q^{72} +(8.10850 + 5.12751i) q^{73} +(-11.2797 - 13.8151i) q^{74} +(3.59209 - 3.18232i) q^{75} +(26.4353 - 32.3773i) q^{76} +(-0.899084 - 0.300159i) q^{77} +(0.704799 - 0.173717i) q^{78} +(14.9767 - 3.69142i) q^{79} +(6.82937 + 2.27998i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(2.74138 - 2.42865i) q^{82} +(5.32075 + 6.51673i) q^{83} +(9.21905 + 5.82977i) q^{84} +(0.172187 - 0.594457i) q^{85} +(-16.9403 + 5.65550i) q^{86} +(1.67798 - 2.05515i) q^{87} +(0.193354 + 4.79802i) q^{88} +(-15.1352 + 2.45970i) q^{89} +(0.924488 + 0.819025i) q^{90} +(0.0207069 - 0.513837i) q^{91} +(-5.56296 - 45.8151i) q^{92} +(0.433825 + 3.57287i) q^{93} +(11.7720 + 8.84607i) q^{94} +(-1.43742 - 3.02930i) q^{95} +(4.89368 - 23.9708i) q^{96} +(-2.22025 - 0.945962i) q^{97} +(-6.58015 + 5.82950i) q^{98} +(-0.172224 + 0.454117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	2.67476	+	0.659270i	1.89134	+	0.466174i	0.999915	+	0.0130124i	$0.00414211\pi$
$2$	2.67476	+	0.659270i	1.89134	+	0.466174i	0.891428	+	0.453162i	$0.149704\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	4.94881	+	2.59734i	2.47441	+	1.29867i
$5$	0.358425	−	0.269339i	0.160293	−	0.120452i	−0.517569	−	0.855641i	$-0.673163\pi$
$5$	0.358425	−	0.269339i	0.160293	−	0.120452i	0.677862	+	0.735189i	$0.262907\pi$
$6$	−1.90833	−	1.98678i	−0.779071	−	0.811099i
$7$	−1.72808	+	0.906968i	−0.653154	+	0.342802i	−0.758537	−	0.651630i	$-0.774086\pi$
$7$	−1.72808	+	0.906968i	−0.653154	+	0.342802i	0.105383	+	0.994432i	$0.466393\pi$
$8$	7.40054	+	6.55631i	2.61649	+	2.31800i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	1.13627	−	0.484119i	0.359320	−	0.153092i
$11$	0.336441	+	0.350272i	0.101441	+	0.105611i	0.769987	−	0.638059i	$-0.220263\pi$
$11$	0.336441	+	0.350272i	0.101441	+	0.105611i	−0.668546	+	0.743671i	$0.733083\pi$
$12$	−2.79450	−	4.84021i	−0.806702	−	1.39725i
$13$	−0.131750	+	0.228197i	−0.0365408	+	0.0632906i	−0.883717	−	0.468021i	$-0.844967\pi$
$13$	−0.131750	+	0.228197i	−0.0365408	+	0.0632906i	0.847177	+	0.531311i	$0.178301\pi$
$14$	−5.22015	+	1.28665i	−1.39514	+	0.343872i
$15$	−0.446890	+	0.0360767i	−0.115386	+	0.00931496i
$16$	9.12250	+	13.2162i	2.28062	+	3.30405i
$17$	1.10355	−	0.829263i	0.267650	−	0.201126i	−0.458441	−	0.888725i	$-0.651592\pi$
$17$	1.10355	−	0.829263i	0.267650	−	0.201126i	0.726090	+	0.687599i	$0.241335\pi$
$18$	0.551034	+	2.69914i	0.129880	+	0.636194i
$19$	1.49593	−	7.32757i	0.343191	−	1.68106i	−0.331891	−	0.943318i	$-0.607687\pi$
$19$	1.49593	−	7.32757i	0.343191	−	1.68106i	0.675082	−	0.737743i	$-0.264108\pi$
$20$	2.47334	−	0.401957i	0.553056	−	0.0898804i
$21$	1.94530	+	0.157041i	0.424500	+	0.0342692i
$22$	0.668977	+	1.15870i	0.142626	+	0.247036i
$23$	−4.69084	−	6.79585i	−0.978107	−	1.41703i	−0.907750	−	0.419511i	$-0.862202\pi$
$23$	−4.69084	−	6.79585i	−0.978107	−	1.41703i	−0.0703568	−	0.997522i	$-0.522414\pi$
$24$	−2.75074	−	9.49666i	−0.561493	−	1.93850i
$25$	−1.33516	+	4.60951i	−0.267032	+	0.921903i
$26$	−0.502843	+	0.523515i	−0.0986157	+	0.102670i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−10.9077			−2.06135
$29$	−0.319803	+	2.63381i	−0.0593858	+	0.489086i	0.932424	+	0.361365i	$0.117689\pi$
$29$	−0.319803	+	2.63381i	−0.0593858	+	0.489086i	−0.991810	+	0.127721i	$0.959234\pi$
$30$	−1.21911	−	0.198124i	−0.222578	−	0.0361724i
$31$	−2.27624	−	2.78789i	−0.408825	−	0.500720i	0.528617	−	0.848860i	$-0.322711\pi$
$31$	−2.27624	−	2.78789i	−0.408825	−	0.500720i	−0.937442	+	0.348141i	$0.886813\pi$
$32$	8.67549	+	22.8754i	1.53363	+	4.04384i
$33$	−0.0971482	−	0.475863i	−0.0169113	−	0.0828371i
$34$	3.49844	−	1.49055i	0.599977	−	0.255626i
$35$	−0.375107	+	0.790520i	−0.0634046	+	0.133622i
$36$	−0.225046	+	5.58447i	−0.0375077	+	0.930744i
$37$	−5.17571	−	3.88930i	−0.850882	−	0.639397i	0.0831690	−	0.996535i	$-0.473496\pi$
$37$	−5.17571	−	3.88930i	−0.850882	−	0.639397i	−0.934051	+	0.357139i	$0.883752\pi$
$38$	8.83212	−	18.6133i	1.43276	−	3.01948i
$39$	0.233317	−	0.122454i	0.0373607	−	0.0196084i
$40$	4.41841	+	0.356691i	0.698612	+	0.0563978i
$41$	0.755226	−	1.09413i	0.117946	−	0.170875i	−0.759564	−	0.650433i	$-0.774588\pi$
$41$	0.755226	−	1.09413i	0.117946	−	0.170875i	0.877510	+	0.479558i	$0.159203\pi$
$42$	5.09969	+	1.70253i	0.786900	+	0.262706i
$43$	−5.47935	+	3.46493i	−0.835593	+	0.528397i	−0.882396	−	0.470507i	$-0.844071\pi$
$43$	−5.47935	+	3.46493i	−0.835593	+	0.528397i	0.0468030	+	0.998904i	$0.485097\pi$
$44$	0.755209	+	2.60728i	0.113852	+	0.393063i
$45$	0.396989	+	0.208356i	0.0591796	+	0.0310598i
$46$	−8.06658	−	21.2698i	−1.18935	−	3.13606i
$47$	4.91754	+	2.09517i	0.717297	+	0.305612i	0.719603	−	0.694386i	$-0.244324\pi$
$47$	4.91754	+	2.09517i	0.717297	+	0.305612i	−0.00230602	+	0.999997i	$0.500734\pi$
$48$	−0.646627	−	16.0459i	−0.0933325	−	2.31602i
$49$	−1.81277	+	2.62625i	−0.258967	+	0.375179i
$50$	−6.61016	+	11.4491i	−0.934818	+	1.61915i
$51$	−1.37592	+	0.111076i	−0.192667	+	0.0155537i
$52$	−1.24471	+	0.787107i	−0.172610	+	0.109152i
$53$	−9.29946	+	3.10462i	−1.27738	+	0.426452i	−0.872812	−	0.488056i	$-0.837706\pi$
$53$	−9.29946	+	3.10462i	−1.27738	+	0.426452i	−0.404567	+	0.914508i	$0.632578\pi$
$54$	0.976870	−	2.57580i	0.132935	−	0.350521i
$55$	0.214931	+	0.0349297i	0.0289813	+	0.00470992i
$56$	−18.7351	−	4.61779i	−2.50359	−	0.617078i
$57$	−5.18069	+	5.39367i	−0.686199	+	0.714409i
$58$	−2.59179	+	6.83399i	−0.340319	+	0.897346i
$59$	−3.72369	+	3.29890i	−0.484783	+	0.429481i	−0.869782	−	0.493437i	$-0.835740\pi$
$59$	−3.72369	+	3.29890i	−0.484783	+	0.429481i	0.384998	+	0.922917i	$0.374202\pi$
$60$	−2.30528	−	0.982187i	−0.297610	−	0.126800i
$61$	2.05079	−	10.0454i	0.262577	−	1.28618i	−0.607915	−	0.794002i	$-0.707994\pi$
$61$	2.05079	−	10.0454i	0.262577	−	1.28618i	0.870492	−	0.492183i	$-0.163801\pi$
$62$	−4.25043	−	8.95760i	−0.539806	−	1.13762i
$63$	−1.56022	−	1.17243i	−0.196569	−	0.147712i
$64$	4.25246	+	35.0222i	0.531557	+	4.37777i
$65$	0.0142400	+	0.117277i	0.00176626	+	0.0145464i
$66$	0.0538740	−	1.33687i	0.00663142	−	0.164557i
$67$	−1.89861	−	1.68202i	−0.231953	−	0.205492i	0.539138	−	0.842217i	$-0.318750\pi$
$67$	−1.89861	−	1.68202i	−0.231953	−	0.205492i	−0.771091	+	0.636725i	$0.780289\pi$
$68$	7.61513	−	1.23758i	0.923470	−	0.150078i
$69$	0.332499	+	8.25088i	0.0400282	+	0.993289i
$70$	−1.52449	+	1.86716i	−0.182211	+	0.223168i
$71$	10.1552	−	3.39030i	1.20520	−	0.402354i	0.358046	−	0.933704i	$-0.383443\pi$
$71$	10.1552	−	3.39030i	1.20520	−	0.402354i	0.847153	+	0.531350i	$0.178315\pi$
$72$	−2.75074	+	9.49666i	−0.324178	+	1.11919i
$73$	8.10850	+	5.12751i	0.949028	+	0.600129i	0.916798	−	0.399351i	$-0.130765\pi$
$73$	8.10850	+	5.12751i	0.949028	+	0.600129i	0.0322304	+	0.999480i	$0.489739\pi$
$74$	−11.2797	−	13.8151i	−1.31124	−	1.60598i
$75$	3.59209	−	3.18232i	0.414779	−	0.367462i
$76$	26.4353	−	32.3773i	3.03233	−	3.71393i
$77$	−0.899084	−	0.300159i	−0.102460	−	0.0342062i
$78$	0.704799	−	0.173717i	0.0798028	−	0.0196696i
$79$	14.9767	−	3.69142i	1.68501	−	0.415317i	0.723552	−	0.690270i	$-0.242508\pi$
$79$	14.9767	−	3.69142i	1.68501	−	0.415317i	0.961458	+	0.274953i	$0.0886622\pi$
$80$	6.82937	+	2.27998i	0.763547	+	0.254910i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	2.74138	−	2.42865i	0.302735	−	0.268200i
$83$	5.32075	+	6.51673i	0.584028	+	0.715304i	0.979108	−	0.203343i	$-0.0651805\pi$
$83$	5.32075	+	6.51673i	0.584028	+	0.715304i	−0.395080	+	0.918647i	$0.629283\pi$
$84$	9.21905	+	5.82977i	1.00588	+	0.636080i
$85$	0.172187	−	0.594457i	0.0186763	−	0.0644779i
$86$	−16.9403	+	5.65550i	−1.82672	+	0.609848i
$87$	1.67798	−	2.05515i	0.179898	−	0.220335i
$88$	0.193354	+	4.79802i	0.0206116	+	0.511470i
$89$	−15.1352	+	2.45970i	−1.60432	+	0.260728i	−0.895634	−	0.444791i	$-0.853278\pi$
$89$	−15.1352	+	2.45970i	−1.60432	+	0.260728i	−0.708691	+	0.705519i	$0.750714\pi$
$90$	0.924488	+	0.819025i	0.0974496	+	0.0863328i
$91$	0.0207069	−	0.513837i	0.00217068	−	0.0538648i
$92$	−5.56296	−	45.8151i	−0.579978	−	4.77655i
$93$	0.433825	+	3.57287i	0.0449855	+	0.370489i
$94$	11.7720	+	8.84607i	1.21419	+	0.912402i
$95$	−1.43742	−	3.02930i	−0.147476	−	0.310800i
$96$	4.89368	−	23.9708i	0.499459	−	2.44651i
$97$	−2.22025	−	0.945962i	−0.225433	−	0.0960479i	0.276297	−	0.961072i	$-0.410893\pi$
$97$	−2.22025	−	0.945962i	−0.225433	−	0.0960479i	−0.501730	+	0.865024i	$0.667303\pi$
$98$	−6.58015	+	5.82950i	−0.664695	+	0.588869i
$99$	−0.172224	+	0.454117i	−0.0173092	+	0.0456405i
$100$	−18.5799	+	19.3438i	−1.85799	+	1.93438i
$101$	8.50988	+	2.09750i	0.846765	+	0.208709i	0.638748	−	0.769416i	$-0.279453\pi$
$101$	8.50988	+	2.09750i	0.846765	+	0.208709i	0.208017	+	0.978125i	$0.433299\pi$
$102$	−3.75349	−	0.610002i	−0.371651	−	0.0603992i
$103$	2.15223	−	5.67498i	0.212066	−	0.559172i	−0.786204	−	0.617967i	$-0.787957\pi$
$103$	2.15223	−	5.67498i	0.212066	−	0.559172i	0.998270	+	0.0587949i	$0.0187258\pi$
$104$	−2.47115	+	0.824992i	−0.242316	+	0.0808971i
$105$	0.739542	−	0.467658i	0.0721720	−	0.0456388i
$106$	−26.9206	+	2.17326i	−2.61476	+	0.211086i
$107$	0.885459	−	1.53366i	0.0856006	−	0.148265i	−0.820046	−	0.572297i	$-0.806052\pi$
$107$	0.885459	−	1.53366i	0.0856006	−	0.148265i	0.905647	+	0.424032i	$0.139386\pi$
$108$	3.17491	−	4.59966i	0.305506	−	0.442602i
$109$	0.0936308	+	2.32342i	0.00896820	+	0.222544i	0.997458	+	0.0712563i	$0.0227008\pi$
$109$	0.0936308	+	2.32342i	0.00896820	+	0.222544i	−0.988490	+	0.151287i	$0.951658\pi$
$110$	0.551862	+	0.235126i	0.0526179	+	0.0224184i
$111$	2.29577	+	6.05344i	0.217905	+	0.574567i
$112$	−27.7511	−	14.5649i	−2.62223	−	1.37625i
$113$	3.31893	+	11.4583i	0.312219	+	1.07790i	0.951173	+	0.308659i	$0.0998803\pi$
$113$	3.31893	+	11.4583i	0.312219	+	1.07790i	−0.638954	+	0.769245i	$0.720633\pi$
$114$	−17.4130	+	11.0113i	−1.63088	+	1.03130i
$115$	−3.51170	−	1.17238i	−0.327468	−	0.109325i
$116$	−8.42354	+	12.2036i	−0.782106	+	1.13308i
$117$	−0.262645	−	0.0212029i	−0.0242816	−	0.00196021i
$118$	−12.1349	+	6.36887i	−1.11711	+	0.586302i
$119$	−1.15491	+	2.43392i	−0.105870	+	0.223117i
$120$	−3.54376	−	2.66296i	−0.323499	−	0.243094i
$121$	0.433427	−	10.7554i	0.0394025	−	0.977762i
$122$	12.1080	−	25.5171i	1.09621	−	2.31021i
$123$	−1.22309	+	0.521108i	−0.110282	+	0.0469868i
$124$	−4.02360	−	19.7089i	−0.361330	−	1.76991i
$125$	1.55789	+	4.10782i	0.139342	+	0.367415i
$126$	−3.40027	−	4.16457i	−0.302920	−	0.371009i
$127$	8.05418	+	1.30893i	0.714693	+	0.116149i	0.506876	−	0.862019i	$-0.330800\pi$
$127$	8.05418	+	1.30893i	0.714693	+	0.116149i	0.207817	+	0.978168i	$0.433364\pi$
$128$	−5.81681	+	47.9058i	−0.514139	+	4.23431i
$129$	6.48298			0.570795
$130$	−0.0392286	+	0.323076i	−0.00344057	+	0.0283357i
$131$	−13.1067	+	13.6456i	−1.14514	+	1.19222i	−0.166632	+	0.986019i	$0.553289\pi$
$131$	−13.1067	+	13.6456i	−1.14514	+	1.19222i	−0.978510	+	0.206200i	$0.933890\pi$
$132$	0.755209	−	2.60728i	0.0657325	−	0.226935i
$133$	4.06078	+	14.0194i	0.352114	+	1.21564i
$134$	−3.96943	−	5.75072i	−0.342907	−	0.496786i
$135$	−0.224172	−	0.388277i	−0.0192936	−	0.0334176i
$136$	13.6038	+	1.09821i	1.16651	+	0.0941706i
$137$	1.62868	−	0.264686i	0.139148	−	0.0226137i	−0.0904385	−	0.995902i	$-0.528827\pi$
$137$	1.62868	−	0.264686i	0.139148	−	0.0226137i	0.229586	+	0.973288i	$0.426263\pi$
$138$	−4.55020	+	22.2884i	−0.387339	+	1.89731i
$139$	−3.74813	−	18.3595i	−0.317912	−	1.55724i	−0.753720	−	0.657196i	$-0.771742\pi$
$139$	−3.74813	−	18.3595i	−0.317912	−	1.55724i	0.435808	−	0.900040i	$-0.356463\pi$
$140$	−3.90958	+	2.93786i	−0.330420	+	0.248294i
$141$	−3.03646	−	4.39907i	−0.255716	−	0.370469i
$142$	29.3978	−	2.37324i	2.46701	−	0.199158i
$143$	−0.124257	+	0.0306267i	−0.0103909	+	0.00256113i
$144$	−8.02945	+	13.9074i	−0.669121	+	1.15895i
$145$	0.594763	+	1.03016i	0.0493924	+	0.0855501i
$146$	18.3079	+	19.0606i	1.51517	+	1.57746i
$147$	2.93578	−	1.25082i	0.242139	−	0.103166i
$148$	−15.5118	−	32.6905i	−1.27506	−	2.68714i
$149$	17.7515	+	15.7264i	1.45426	+	1.28836i	0.884494	+	0.466551i	$0.154504\pi$
$149$	17.7515	+	15.7264i	1.45426	+	1.28836i	0.569764	+	0.821809i	$0.307035\pi$
$150$	11.7060	−	6.14379i	0.955792	−	0.501638i
$151$	−3.66882	−	3.81964i	−0.298564	−	0.310838i	0.554975	−	0.831867i	$-0.312728\pi$
$151$	−3.66882	−	3.81964i	−0.298564	−	0.310838i	−0.853539	+	0.521029i	$0.825548\pi$
$152$	59.1125	−	44.4202i	4.79466	−	3.60295i
$153$	1.22228	+	0.641503i	0.0988156	+	0.0518624i
$154$	−2.20695	−	1.39559i	−0.177841	−	0.112460i
$155$	−1.56675	−	0.386169i	−0.125844	−	0.0310178i
$156$	1.47270			0.117910
$157$	−6.93761	−	10.4341i	−0.553681	−	0.832729i
$157$	−6.93761	−	10.4341i	−0.553681	−	0.832729i
$158$	42.4928			3.38054
$159$	9.51912	+	2.34625i	0.754916	+	0.186070i
$160$	9.27075	+	5.86247i	0.732917	+	0.463469i
$161$	14.2698	+	7.48936i	1.12462	+	0.590244i
$162$	−2.20232	+	1.65493i	−0.173030	+	0.130024i
$163$	−9.96703	−	10.3768i	−0.780678	−	0.812772i	0.205466	−	0.978664i	$-0.434129\pi$
$163$	−9.96703	−	10.3768i	−0.780678	−	0.812772i	−0.986144	+	0.165892i	$0.946950\pi$
$164$	6.57930	−	3.45308i	0.513757	−	0.269641i
$165$	−0.162989	−	0.144395i	−0.0126887	−	0.0112412i
$166$	9.93545	+	20.9385i	0.771141	+	1.62514i
$167$	−16.8256	+	7.16871i	−1.30200	+	0.554731i	−0.927960	−	0.372680i	$-0.878439\pi$
$167$	−16.8256	+	7.16871i	−1.30200	+	0.554731i	−0.374042	+	0.927412i	$0.622029\pi$
$168$	13.3667	+	13.9162i	1.03126	+	1.07366i
$169$	6.46528	+	11.1982i	0.497330	+	0.861400i
$170$	0.852466	−	1.47652i	0.0653812	−	0.113244i
$171$	7.26140	−	1.78977i	0.555293	−	0.136867i
$172$	−36.1159	+	2.91557i	−2.75381	+	0.222310i
$173$	3.16774	+	4.58926i	0.240839	+	0.348915i	0.924700	−	0.380697i	$-0.124316\pi$
$173$	3.16774	+	4.58926i	0.240839	+	0.348915i	−0.683861	+	0.729612i	$0.739701\pi$
$174$	5.84309	−	4.39079i	0.442963	−	0.332865i
$175$	−1.87341	−	9.17658i	−0.141617	−	0.693684i
$176$	−1.56009	+	7.64184i	−0.117596	+	0.576025i
$177$	4.91038	−	0.798014i	0.369087	−	0.0599824i
$178$	−42.1046	−	3.39904i	−3.15587	−	0.254769i
$179$	12.1245	+	21.0002i	0.906226	+	1.56963i	0.819263	+	0.573418i	$0.194383\pi$
$179$	12.1245	+	21.0002i	0.906226	+	1.56963i	0.0869628	+	0.996212i	$0.472284\pi$
$180$	1.42345	+	2.06223i	0.106098	+	0.153709i
$181$	4.38667	+	15.1445i	0.326058	+	1.12568i	0.941363	+	0.337395i	$0.109546\pi$
$181$	4.38667	+	15.1445i	0.326058	+	1.12568i	−0.615305	+	0.788289i	$0.710967\pi$
$182$	0.394144	−	1.36074i	0.0292159	−	0.100865i
$183$	−7.10224	+	7.39422i	−0.525013	+	0.546596i
$184$	9.84095	−	81.0475i	0.725485	−	5.97490i
$185$	−2.90265			−0.213407
$186$	−1.19511	+	9.84259i	−0.0876295	+	0.721694i
$187$	0.661747	+	0.107544i	0.0483917	+	0.00786442i
$188$	18.8941	+	23.1411i	1.37800	+	1.68774i
$189$	0.692058	+	1.82481i	0.0503398	+	0.132735i
$190$	−1.84763	−	9.05031i	−0.134041	−	0.656578i
$191$	1.60030	−	0.681826i	0.115794	−	0.0493352i	−0.333293	−	0.942823i	$-0.608160\pi$
$191$	1.60030	−	0.681826i	0.115794	−	0.0493352i	0.449087	+	0.893488i	$0.351749\pi$
$192$	15.1240	−	31.8732i	1.09148	−	2.30025i
$193$	−0.733186	+	18.1938i	−0.0527759	+	1.30962i	0.728332	+	0.685224i	$0.240296\pi$
$193$	−0.733186	+	18.1938i	−0.0527759	+	1.30962i	−0.781108	+	0.624396i	$0.785345\pi$
$194$	−5.31501	−	3.99397i	−0.381595	−	0.286750i
$195$	0.0506451	−	0.106732i	0.00362677	−	0.00764325i
$196$	−15.7923	+	8.28846i	−1.12802	+	0.592033i
$197$	19.3646	+	1.56327i	1.37967	+	0.111379i	0.747918	−	0.663791i	$-0.231054\pi$
$197$	19.3646	+	1.56327i	1.37967	+	0.111379i	0.631753	+	0.775170i	$0.282336\pi$
$198$	−0.760044	+	1.10111i	−0.0540140	+	0.0782528i
$199$	11.2069	+	3.74140i	0.794434	+	0.265221i	0.684781	−	0.728749i	$-0.259898\pi$
$199$	11.2069	+	3.74140i	0.794434	+	0.265221i	0.109653	+	0.993970i	$0.465026\pi$
$200$	−40.1023	+	25.3592i	−2.83566	+	1.79316i
$201$	0.705705	+	2.43637i	0.0497766	+	0.171849i
$202$	21.3791	+	11.2206i	1.50423	+	0.789480i
$203$	−1.83614	−	4.84150i	−0.128872	−	0.339806i
$204$	−7.09767	−	3.02404i	−0.496937	−	0.211725i
$205$	−0.0240009	−	0.595577i	−0.00167630	−	0.0415969i
$206$	9.49806	−	13.7603i	0.661761	−	0.958727i
$207$	4.12879	−	7.15127i	0.286971	−	0.497048i
$208$	−4.21779	+	0.340496i	−0.292451	+	0.0236091i
$209$	3.06994	−	1.94131i	0.212352	−	0.134283i
$210$	2.28641	−	0.763317i	0.157778	−	0.0526739i
$211$	3.46344	−	9.13234i	0.238433	−	0.628696i	−0.761375	−	0.648312i	$-0.775475\pi$
$211$	3.46344	−	9.13234i	0.238433	−	0.628696i	0.999808	+	0.0196162i	$0.00624443\pi$
$212$	−54.0850	−	8.78967i	−3.71457	−	0.603677i
$213$	−10.3951	−	2.56215i	−0.712258	−	0.175556i
$214$	3.37949	−	3.51842i	0.231017	−	0.240514i
$215$	−1.03070	+	2.71772i	−0.0702929	+	0.185347i
$216$	7.40054	−	6.55631i	0.503543	−	0.446100i
$217$	6.46206	+	2.75323i	0.438673	+	0.186901i
$218$	−1.28132	+	6.27634i	−0.0867822	+	0.425087i
$219$	−4.11275	−	8.66743i	−0.277914	−	0.585691i
$220$	0.972929	+	0.731109i	0.0655949	+	0.0492913i
$221$	0.0438433	+	0.361082i	0.00294922	+	0.0242890i
$222$	2.14978	+	17.7050i	0.144284	+	1.18828i
$223$	−0.0500806	+	1.24274i	−0.00335364	+	0.0832198i	0.996645	+	0.0818409i	$0.0260799\pi$
$223$	−0.0500806	+	1.24274i	−0.00335364	+	0.0832198i	−0.999999	+	0.00137889i	$0.999561\pi$
$224$	−35.7392	−	31.6622i	−2.38793	−	2.11552i
$225$	−4.73684	+	0.769812i	−0.315789	+	0.0513208i
$226$	1.32326	+	32.8363i	0.0880217	+	2.18424i
$227$	−2.76103	+	3.38165i	−0.183256	+	0.224448i	−0.858060	−	0.513549i	$-0.828331\pi$
$227$	−2.76103	+	3.38165i	−0.183256	+	0.224448i	0.674804	+	0.737997i	$0.264228\pi$
$228$	−39.6474	+	13.2363i	−2.62571	+	0.876592i
$229$	3.66710	−	12.6603i	0.242329	−	0.836617i	−0.743482	−	0.668756i	$-0.766827\pi$
$229$	3.66710	−	12.6603i	0.242329	−	0.836617i	0.985811	−	0.167861i	$-0.0536858\pi$
$230$	−8.62006	−	5.45099i	−0.568390	−	0.359428i
$231$	0.599473	+	0.734221i	0.0394424	+	0.0483082i
$232$	−19.6348	+	17.3949i	−1.28909	+	1.14203i
$233$	−7.83108	+	9.59133i	−0.513031	+	0.628349i	−0.964546	−	0.263914i	$-0.914986\pi$
$233$	−7.83108	+	9.59133i	−0.513031	+	0.628349i	0.451515	+	0.892264i	$0.350884\pi$
$234$	−0.688535	−	0.229867i	−0.0450110	−	0.0150269i
$235$	2.32688	−	0.573525i	0.151789	−	0.0374126i
$236$	−26.9962	+	6.65397i	−1.75730	+	0.433137i
$237$	−14.6311	−	4.88458i	−0.950391	−	0.317287i
$238$	−4.69372	+	5.74876i	−0.304249	+	0.372637i
$239$	−9.03604	+	8.00523i	−0.584493	+	0.517815i	−0.902737	−	0.430193i	$-0.858445\pi$
$239$	−9.03604	+	8.00523i	−0.584493	+	0.517815i	0.318244	+	0.948009i	$0.396907\pi$
$240$	−4.55355	−	5.57708i	−0.293930	−	0.359999i
$241$	−3.15503	−	1.99512i	−0.203233	−	0.128517i	0.428972	−	0.903318i	$-0.358876\pi$
$241$	−3.15503	−	1.99512i	−0.203233	−	0.128517i	−0.632206	+	0.774801i	$0.717850\pi$
$242$	8.25002	−	28.4824i	0.530331	−	1.83092i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	36.2403	−	44.3863i	2.32005	−	2.84154i
$245$	0.0576095	+	1.42957i	0.00368054	+	0.0913316i
$246$	−3.61502	+	0.587498i	−0.230485	+	0.0374575i
$247$	1.47504	+	1.30677i	0.0938548	+	0.0831481i
$248$	1.43284	−	35.5556i	0.0909856	−	2.25778i
$249$	−1.01407	−	8.35163i	−0.0642642	−	0.529263i
$250$	1.45883	+	12.0145i	0.0922643	+	0.759865i
$251$	−24.7601	−	18.6060i	−1.56284	−	1.17440i	−0.908256	−	0.418416i	$-0.862585\pi$
$251$	−24.7601	−	18.6060i	−1.56284	−	1.17440i	−0.654589	−	0.755985i	$-0.727158\pi$
$252$	−4.67603	−	9.85453i	−0.294562	−	0.620777i
$253$	0.802208	−	3.92948i	0.0504344	−	0.247044i
$254$	20.6801	+	8.81096i	1.29758	+	0.552849i
$255$	−0.463248	+	0.410401i	−0.0290097	+	0.0257003i
$256$	−22.1210	+	58.3282i	−1.38256	+	3.64551i
$257$	2.60901	−	2.71627i	0.162746	−	0.169436i	−0.634837	−	0.772646i	$-0.718933\pi$
$257$	2.60901	−	2.71627i	0.162746	−	0.169436i	0.797582	+	0.603210i	$0.206112\pi$
$258$	17.3404	+	4.27404i	1.07957	+	0.266090i
$259$	12.4715	+	2.02682i	0.774944	+	0.125941i
$260$	−0.234137	+	0.617368i	−0.0145206	+	0.0382875i
$261$	−2.51661	+	0.840169i	−0.155775	+	0.0520052i
$262$	−44.0536	+	27.8578i	−2.72164	+	1.72106i
$263$	−2.96476	+	0.239341i	−0.182815	+	0.0147584i	−0.171535	−	0.985178i	$-0.554873\pi$
$263$	−2.96476	+	0.239341i	−0.182815	+	0.0147584i	−0.0112801	+	0.999936i	$0.503591\pi$
$264$	2.40096	−	4.15858i	0.147769	−	0.255943i
$265$	−2.49697	+	3.61748i	−0.153387	+	0.222220i
$266$	1.61903	+	40.1758i	0.0992690	+	2.46334i
$267$	14.1067	+	6.01031i	0.863318	+	0.367825i
$268$	−5.02710	−	13.2554i	−0.307079	−	0.809700i
$269$	−8.77868	−	4.60741i	−0.535245	−	0.280918i	0.175366	−	0.984503i	$-0.443889\pi$
$269$	−8.77868	−	4.60741i	−0.535245	−	0.280918i	−0.710611	+	0.703585i	$0.751581\pi$
$270$	−0.343627	−	1.18634i	−0.0209125	−	0.0721983i
$271$	−6.22590	+	3.93702i	−0.378197	+	0.239157i	−0.710015	−	0.704186i	$-0.751312\pi$
$271$	−6.22590	+	3.93702i	−0.378197	+	0.239157i	0.331819	+	0.943343i	$0.392338\pi$
$272$	21.0268	+	7.01979i	1.27494	+	0.425637i
$273$	−0.292130	+	0.423223i	−0.0176805	+	0.0256146i
$274$	4.53083	+	0.365767i	0.273718	+	0.0220968i
$275$	−2.06379	+	1.08316i	−0.124451	+	0.0653170i
$276$	−19.7848	+	41.6957i	−1.19091	+	2.50978i
$277$	−20.0673	−	15.0796i	−1.20572	−	0.906043i	−0.208321	−	0.978060i	$-0.566800\pi$
$277$	−20.0673	−	15.0796i	−1.20572	−	0.906043i	−0.997403	+	0.0720171i	$0.977056\pi$
$278$	2.07854	−	51.5785i	0.124663	−	3.09347i
$279$	1.54291	−	3.25162i	0.0923717	−	0.194669i
$280$	−7.95889	+	3.39096i	−0.475634	+	0.202649i
$281$	−0.962841	−	4.71631i	−0.0574383	−	0.281351i	0.940920	−	0.338629i	$-0.109963\pi$
$281$	−0.962841	−	4.71631i	−0.0574383	−	0.281351i	−0.998358	+	0.0572776i	$0.981758\pi$
$282$	−5.22164	−	13.7683i	−0.310944	−	0.819892i
$283$	−3.85058	−	4.71610i	−0.228893	−	0.280343i	0.647370	−	0.762176i	$-0.275869\pi$
$283$	−3.85058	−	4.71610i	−0.228893	−	0.280343i	−0.876263	+	0.481833i	$0.839971\pi$
$284$	59.0618	+	9.59848i	3.50468	+	0.569565i
$285$	−0.404164	+	3.32859i	−0.0239406	+	0.197168i
$286$	−0.352550			−0.0208467
$287$	−0.312749	+	2.57572i	−0.0184610	+	0.152040i
$288$	−16.9477	+	17.6444i	−0.998651	+	1.03971i
$289$	−4.19955	+	14.4985i	−0.247033	+	0.852856i
$290$	0.911697	+	3.14754i	0.0535367	+	0.184830i
$291$	1.37095	+	1.98617i	0.0803666	+	0.116431i
$292$	26.8096	+	46.4356i	1.56891	+	2.71744i
$293$	0.305571	+	0.0246682i	0.0178516	+	0.00144113i	0.0893892	−	0.995997i	$-0.471509\pi$
$293$	0.305571	+	0.0246682i	0.0178516	+	0.00144113i	−0.0715375	+	0.997438i	$0.522791\pi$
$294$	8.67714	−	1.41017i	0.506061	−	0.0822430i
$295$	−0.446141	+	2.18535i	−0.0259754	+	0.127236i
$296$	−12.8037	−	62.7165i	−0.744198	−	3.64532i
$297$	0.388272	−	0.291768i	0.0225298	−	0.0169301i
$298$	37.1130	+	53.7675i	2.14990	+	3.11467i
$299$	2.16881	−	0.175085i	0.125426	−	0.0101254i
$300$	26.0421	−	6.41881i	1.50354	−	0.370590i
$301$	6.32619	−	10.9573i	0.364636	−	0.631568i
$302$	−7.29504	−	12.6354i	−0.419783	−	0.727085i
$303$	−6.07143	−	6.32102i	−0.348794	−	0.363133i
$304$	110.489	−	47.0752i	6.33701	−	2.69995i
$305$	−1.97057	−	4.15289i	−0.112835	−	0.237794i
$306$	2.84639	+	2.52168i	0.162717	+	0.144155i
$307$	20.5449	−	10.7828i	1.17256	−	0.615407i	0.238018	−	0.971261i	$-0.423502\pi$
$307$	20.5449	−	10.7828i	1.17256	−	0.615407i	0.934541	+	0.355854i	$0.115810\pi$
$308$	−3.66979	−	3.82065i	−0.209106	−	0.217702i
$309$	−4.85213	+	3.64614i	−0.276028	+	0.207422i
$310$	−3.93609	−	2.06582i	−0.223555	−	0.117331i
$311$	18.8956	+	11.9489i	1.07147	+	0.677558i	0.949116	−	0.314928i	$-0.101980\pi$
$311$	18.8956	+	11.9489i	1.07147	+	0.677558i	0.122357	+	0.992486i	$0.460955\pi$
$312$	2.52952	+	0.623472i	0.143206	+	0.0352971i
$313$	−28.7310			−1.62397			−0.811985	−	0.583678i	$-0.801613\pi$
$313$	−28.7310			−1.62397			−0.811985	+	0.583678i	$0.801613\pi$
$314$	−11.6776	−	32.4824i	−0.659005	−	1.83309i
$315$	−0.875001			−0.0493007
$316$	83.7047	+	20.6314i	4.70876	+	1.16060i
$317$	16.5697	+	10.4781i	0.930649	+	0.588507i	0.911496	−	0.411310i	$-0.134928\pi$
$317$	16.5697	+	10.4781i	0.930649	+	0.588507i	0.0191536	+	0.999817i	$0.493903\pi$
$318$	23.9146	+	12.5513i	1.34106	+	0.703845i
$319$	−1.03015	+	0.774105i	−0.0576771	+	0.0433415i
$320$	10.9570	+	11.4075i	0.612516	+	0.637697i
$321$	−1.56807	+	0.822987i	−0.0875212	+	0.0459346i
$322$	33.2308	+	29.4399i	1.85188	+	1.64062i
$323$	−4.42565	−	9.32685i	−0.246250	−	0.518960i
$324$	−5.14176	+	2.19070i	−0.285654	+	0.121706i
$325$	−0.875972	−	0.911983i	−0.0485902	−	0.0505877i
$326$	−19.8183	−	34.3264i	−1.09764	−	1.90116i
$327$	1.16265	−	2.01378i	0.0642950	−	0.111362i
$328$	12.7626	−	3.14569i	0.704694	−	0.173692i
$329$	−10.3982	+	0.839427i	−0.573270	+	0.0462791i
$330$	−0.340761	−	0.493677i	−0.0187583	−	0.0271761i
$331$	−2.81407	+	2.11464i	−0.154675	+	0.116231i	−0.675262	−	0.737578i	$-0.735970\pi$
$331$	−2.81407	+	2.11464i	−0.154675	+	0.116231i	0.520587	+	0.853809i	$0.325713\pi$
$332$	9.40523	+	46.0699i	0.516179	+	2.52841i
$333$	1.29500	−	6.34331i	0.0709654	−	0.347612i
$334$	−49.7306	+	8.08200i	−2.72114	+	0.442228i
$335$	−1.13355	−	0.0915093i	−0.0619322	−	0.00499968i
$336$	15.6705	+	27.1421i	0.854897	+	1.48073i
$337$	15.9692	+	23.1354i	0.869899	+	1.26027i	0.964321	+	0.264734i	$0.0852843\pi$
$337$	15.9692	+	23.1354i	0.869899	+	1.26027i	−0.0944222	+	0.995532i	$0.530100\pi$
$338$	9.91047	+	34.2149i	0.539058	+	1.86105i
$339$	3.31893	−	11.4583i	0.180260	−	0.622328i
$340$	2.39612	−	2.49463i	0.129948	−	0.135290i
$341$	0.210699	−	1.73527i	0.0114100	−	0.0939699i
$342$	20.6025			1.11405
$343$	2.39739	−	19.7443i	0.129447	−	1.06609i
$344$	−63.2673	−	10.2819i	−3.41115	−	0.554365i
$345$	2.34146	+	2.86777i	0.126060	+	0.154395i
$346$	5.44739	+	14.3636i	0.292853	+	0.772191i
$347$	−3.34887	−	16.4039i	−0.179777	−	0.880606i	−0.965173	−	0.261612i	$-0.915746\pi$
$347$	−3.34887	−	16.4039i	−0.179777	−	0.880606i	0.785396	−	0.618994i	$-0.212459\pi$
$348$	13.6419	−	5.81227i	0.731283	−	0.311570i
$349$	13.3672	−	28.1707i	0.715528	−	1.50794i	−0.139980	−	0.990154i	$-0.544704\pi$
$349$	13.3672	−	28.1707i	0.715528	−	1.50794i	0.855508	−	0.517789i	$-0.173245\pi$
$350$	1.03891	−	25.7803i	0.0555320	−	1.37801i
$351$	0.210653	+	0.158295i	0.0112438	+	0.00844918i
$352$	−5.09383	+	10.7350i	−0.271502	+	0.572178i
$353$	−17.0976	+	8.97352i	−0.910014	+	0.477612i	−0.853679	−	0.520800i	$-0.825634\pi$
$353$	−17.0976	+	8.97352i	−0.910014	+	0.477612i	−0.0563350	+	0.998412i	$0.517941\pi$
$354$	13.6602	+	1.10277i	0.726032	+	0.0586114i
$355$	2.72673	−	3.95036i	0.144720	−	0.209663i
$356$	−81.2898	−	27.1385i	−4.30835	−	1.43834i
$357$	2.27696	−	1.43986i	0.120510	−	0.0762057i
$358$	18.5853	+	64.1639i	0.982264	+	3.39117i
$359$	−1.95432	−	1.02570i	−0.103145	−	0.0541346i	0.412362	−	0.911020i	$-0.364704\pi$
$359$	−1.95432	−	1.02570i	−0.103145	−	0.0541346i	−0.515507	+	0.856886i	$0.672396\pi$
$360$	1.57189	+	4.14472i	0.0828457	+	0.218446i
$361$	−33.9759	−	14.4758i	−1.78821	−	0.761883i
$362$	1.74896	+	43.4000i	0.0919234	+	2.28105i
$363$	−6.11472	+	8.85869i	−0.320939	+	0.464961i
$364$	1.43708	−	2.48910i	0.0753236	−	0.130464i
$365$	4.28733	−	0.346109i	0.224409	−	0.0181162i
$366$	−23.8716	+	15.0955i	−1.24779	+	0.789054i
$367$	−21.7846	+	7.27277i	−1.13715	+	0.379635i	−0.822045	−	0.569423i	$-0.807167\pi$
$367$	−21.7846	+	7.27277i	−1.13715	+	0.379635i	−0.315102	+	0.949058i	$0.602039\pi$
$368$	47.0233	−	123.990i	2.45126	−	6.46344i
$369$	1.31225	+	0.213262i	0.0683133	+	0.0111020i
$370$	−7.76389	−	1.91363i	−0.403625	−	0.0994847i
$371$	13.2545	−	13.7994i	0.688137	−	0.716427i
$372$	−7.13303	+	18.8082i	−0.369830	+	0.975162i
$373$	−14.5504	+	12.8905i	−0.753390	+	0.667445i	−0.949723	−	0.313092i	$-0.898635\pi$
$373$	−14.5504	+	12.8905i	−0.753390	+	0.667445i	0.196333	+	0.980537i	$0.437097\pi$
$374$	1.69912	+	0.723926i	0.0878592	+	0.0374333i
$375$	0.878776	−	4.30453i	0.0453798	−	0.222285i
$376$	22.6559	+	47.7463i	1.16839	+	2.46233i
$377$	−0.558895	−	0.419982i	−0.0287846	−	0.0216302i
$378$	0.648051	+	5.33718i	0.0333321	+	0.274515i
$379$	−2.98899	−	24.6165i	−0.153534	−	1.26447i	−0.842112	−	0.539303i	$-0.818688\pi$
$379$	−2.98899	−	24.6165i	−0.153534	−	1.26447i	0.688578	−	0.725163i	$-0.258235\pi$
$380$	0.754588	−	18.7249i	0.0387095	−	0.960567i
$381$	−6.10774	−	5.41098i	−0.312909	−	0.277213i
$382$	4.72994	−	0.768691i	0.242005	−	0.0393296i
$383$	1.09560	+	27.1870i	0.0559825	+	1.38919i	0.746264	+	0.665651i	$0.231846\pi$
$383$	1.09560	+	27.1870i	0.0559825	+	1.38919i	−0.690281	+	0.723541i	$0.742513\pi$
$384$	30.5203	−	37.3806i	1.55748	−	1.90757i
$385$	−0.403099	+	0.134574i	−0.0205438	+	0.00685853i
$386$	−13.9557	+	48.1808i	−0.710328	+	2.45234i
$387$	−5.47935	−	3.46493i	−0.278531	−	0.176132i
$388$	−8.53064	−	10.4481i	−0.433077	−	0.530424i
$389$	21.7924	−	19.3064i	1.10492	−	0.978873i	0.105040	−	0.994468i	$-0.466503\pi$
$389$	21.7924	−	19.3064i	1.10492	−	0.978873i	0.999878	+	0.0155954i	$0.00496437\pi$
$390$	0.205829	−	0.252095i	0.0104226	−	0.0127653i
$391$	−10.8121	−	3.60961i	−0.546792	−	0.182546i
$392$	−30.6340	+	7.55061i	−1.54725	+	0.381363i
$393$	18.3708	−	4.52799i	0.926683	−	0.228407i
$394$	50.7651	+	16.9479i	2.55751	+	0.853822i
$395$	4.37378	−	5.35690i	0.220069	−	0.269535i
$396$	−2.03180	+	1.80002i	−0.102102	+	0.0904543i
$397$	5.06984	+	6.20943i	0.254448	+	0.311642i	0.885994	−	0.463696i	$-0.153477\pi$
$397$	5.06984	+	6.20943i	0.254448	+	0.311642i	−0.631547	+	0.775338i	$0.717580\pi$
$398$	27.5091	+	17.3957i	1.37891	+	0.871969i
$399$	4.06078	−	14.0194i	0.203293	−	0.701849i
$400$	−73.1004	+	24.4045i	−3.65502	+	1.22022i
$401$	10.8177	−	13.2493i	0.540210	−	0.661637i	−0.430304	−	0.902684i	$-0.641593\pi$
$401$	10.8177	−	13.2493i	0.540210	−	0.661637i	0.970513	+	0.241047i	$0.0774909\pi$
$402$	0.281364	+	6.98198i	0.0140332	+	0.348229i
$403$	0.936083	−	0.152128i	0.0466296	−	0.00757805i
$404$	36.6659	+	32.4831i	1.82420	+	1.61610i
$405$	−0.0180530	+	0.447980i	−0.000897060	+	0.0222603i
$406$	−1.71938	−	14.1604i	−0.0853314	−	0.702767i
$407$	−0.379010	−	3.12143i	−0.0187868	−	0.154724i
$408$	−10.9108	−	8.19894i	−0.540165	−	0.405908i
$409$	9.37929	+	19.7664i	0.463776	+	0.977388i	0.991757	+	0.128131i	$0.0408979\pi$
$409$	9.37929	+	19.7664i	0.463776	+	0.977388i	−0.527981	+	0.849256i	$0.677051\pi$
$410$	0.328449	−	1.60885i	0.0162209	−	0.0794554i
$411$	−1.51801	−	0.646764i	−0.0748779	−	0.0319025i
$412$	25.3908	−	22.4943i	1.25092	−	1.10822i
$413$	3.44285	−	9.07805i	0.169412	−	0.446702i
$414$	15.7581	−	16.4060i	0.774471	−	0.806309i
$415$	3.66230	+	0.902676i	0.179775	+	0.0443106i
$416$	−6.36310	−	1.03410i	−0.311977	−	0.0507012i
$417$	−6.64467	+	17.5205i	−0.325391	+	0.857985i
$418$	9.49122	−	3.16863i	0.464231	−	0.154983i
$419$	2.32579	−	1.47074i	0.113622	−	0.0718504i	−0.476446	−	0.879204i	$-0.658075\pi$
$419$	2.32579	−	1.47074i	0.113622	−	0.0718504i	0.590068	+	0.807353i	$0.299101\pi$
$420$	4.87452	−	0.393512i	0.237852	−	0.0192014i
$421$	0.462384	−	0.800873i	0.0225352	−	0.0390322i	−0.854538	−	0.519389i	$-0.826160\pi$
$421$	0.462384	−	0.800873i	0.0225352	−	0.0390322i	0.877073	+	0.480357i	$0.159493\pi$
$422$	15.2846	−	22.1435i	0.744040	−	1.07793i
$423$	0.215232	+	5.34094i	0.0104650	+	0.259685i
$424$	−89.1759	−	37.9943i	−4.33076	−	1.84517i
$425$	2.34908	+	6.19402i	0.113947	+	0.300454i
$426$	−26.1152	−	13.7063i	−1.26528	−	0.664073i
$427$	5.56695	+	19.2193i	0.269403	+	0.930089i
$428$	8.36540	−	5.28996i	0.404357	−	0.255700i
$429$	0.121390	+	0.0405259i	0.00586076	+	0.00195661i
$430$	−4.54858	+	6.58976i	−0.219352	+	0.317786i
$431$	9.30764	+	0.751390i	0.448333	+	0.0361932i	0.302572	−	0.953127i	$-0.402155\pi$
$431$	9.30764	+	0.751390i	0.448333	+	0.0361932i	0.145761	+	0.989320i	$0.453437\pi$
$432$	14.2195	−	7.46294i	0.684134	−	0.359061i
$433$	17.0999	−	36.0373i	0.821769	−	1.73184i	0.153194	−	0.988196i	$-0.451044\pi$
$433$	17.0999	−	36.0373i	0.821769	−	1.73184i	0.668575	−	0.743645i	$-0.266905\pi$
$434$	15.4694	+	11.6245i	0.742553	+	0.557993i
$435$	0.0478974	−	1.18856i	0.00229650	−	0.0569871i
$436$	−5.57135	+	11.7414i	−0.266819	+	0.562310i
$437$	−56.8143	+	24.2063i	−2.71780	+	1.15794i
$438$	−5.28645	−	25.8948i	−0.252596	−	1.23730i
$439$	−3.46501	−	9.13647i	−0.165376	−	0.436060i	0.826553	−	0.562859i	$-0.190299\pi$
$439$	−3.46501	−	9.13647i	−0.165376	−	0.436060i	−0.991928	+	0.126799i	$0.959530\pi$
$440$	1.36160	+	1.66765i	0.0649115	+	0.0795022i
$441$	−3.14981	−	0.511894i	−0.149991	−	0.0243759i
$442$	−0.120780	+	0.994714i	−0.00574493	+	0.0473137i
$443$	−33.2522			−1.57986			−0.789929	−	0.613198i	$-0.789883\pi$
$443$	−33.2522			−1.57986			−0.789929	+	0.613198i	$0.789883\pi$
$444$	−4.36150	+	35.9202i	−0.206988	+	1.70470i
$445$	−4.76233	+	4.95811i	−0.225756	+	0.235037i
$446$	−0.953253	+	3.29101i	−0.0451378	+	0.155834i
$447$	−6.59813	−	22.7794i	−0.312081	−	1.07743i
$448$	−39.1126	−	56.6644i	−1.84790	−	2.67714i
$449$	−16.8911	−	29.2563i	−0.797142	−	1.38069i	−0.921470	−	0.388449i	$-0.873011\pi$
$449$	−16.8911	−	29.2563i	−0.797142	−	1.38069i	0.124329	−	0.992241i	$-0.460322\pi$
$450$	−13.1774	−	1.06379i	−0.621191	−	0.0501477i
$451$	0.637334	−	0.103577i	0.0300109	−	0.00487724i
$452$	−13.3362	+	65.3253i	−0.627284	+	3.07264i
$453$	1.05938	+	5.18918i	0.0497740	+	0.243809i
$454$	−9.61452	+	7.22484i	−0.451232	+	0.339079i
$455$	−0.130974	−	0.189749i	−0.00614018	−	0.00889558i
$456$	−73.7024	+	5.94987i	−3.45143	+	0.278628i
$457$	16.1886	−	3.99013i	0.757271	−	0.186651i	0.158267	−	0.987396i	$-0.449409\pi$
$457$	16.1886	−	3.99013i	0.757271	−	0.186651i	0.599004	+	0.800746i	$0.295563\pi$
$458$	18.1552	−	31.4457i	0.848337	−	1.46936i
$459$	−0.690199	−	1.19546i	−0.0322157	−	0.0557992i
$460$	−14.3337	−	14.9229i	−0.668312	−	0.695786i
$461$	23.8156	−	10.1469i	1.10920	−	0.472587i	0.241866	−	0.970310i	$-0.422241\pi$
$461$	23.8156	−	10.1469i	1.10920	−	0.472587i	0.867336	+	0.497723i	$0.165830\pi$
$462$	1.11940	+	2.35908i	0.0520791	+	0.109754i
$463$	3.52096	+	3.11930i	0.163633	+	0.144966i	0.740966	−	0.671543i	$-0.234368\pi$
$463$	3.52096	+	3.11930i	0.163633	+	0.144966i	−0.577333	+	0.816509i	$0.695907\pi$
$464$	−37.7264	+	19.8004i	−1.75141	+	0.919208i
$465$	1.11781	+	1.16376i	0.0518370	+	0.0539681i
$466$	−27.2696	+	20.4918i	−1.26324	+	0.949262i
$467$	9.16190	+	4.80853i	0.423962	+	0.222512i	0.663190	−	0.748451i	$-0.269202\pi$
$467$	9.16190	+	4.80853i	0.423962	+	0.222512i	−0.239228	+	0.970963i	$0.576894\pi$
$468$	−1.24471	−	0.787107i	−0.0575368	−	0.0363840i
$469$	4.80651	+	1.18470i	0.221944	+	0.0547042i
$470$	6.60196			0.304526
$471$	0.286949	+	12.5267i	0.0132219	+	0.577199i
$472$	−49.1860			−2.26397
$473$	−3.05715	−	0.753520i	−0.140568	−	0.0346469i
$474$	−35.9145	−	22.7109i	−1.64961	−	1.04315i
$475$	31.7792	+	16.6790i	1.45813	+	0.765286i
$476$	−12.0371	+	9.04532i	−0.551721	+	0.414592i
$477$	−6.79148	−	7.07068i	−0.310960	−	0.323744i
$478$	−29.4469	+	15.4549i	−1.34687	+	0.706891i
$479$	−21.5490	−	19.0908i	−0.984600	−	0.872279i	0.00721393	−	0.999974i	$-0.497704\pi$
$479$	−21.5490	−	19.0908i	−0.984600	−	0.872279i	−0.991813	+	0.127695i	$0.959242\pi$
$480$	−4.70226	−	9.90980i	−0.214628	−	0.452318i
$481$	1.56943	−	0.668670i	0.0715597	−	0.0304887i
$482$	−7.12364	−	7.41649i	−0.324473	−	0.337812i
$483$	−8.05787	−	13.9566i	−0.366646	−	0.635049i
$484$	30.0803	−	52.1006i	1.36729	−	2.36821i
$485$	−1.05058	+	0.258944i	−0.0477043	+	0.0117581i
$486$	2.74588	−	0.221670i	0.124556	−	0.0100552i
$487$	−8.97280	−	12.9993i	−0.406596	−	0.589056i	0.565178	−	0.824969i	$-0.308807\pi$
$487$	−8.97280	−	12.9993i	−0.406596	−	0.589056i	−0.971774	+	0.235913i	$0.924192\pi$
$488$	81.0378	−	60.8960i	3.66841	−	2.75663i
$489$	2.87800	+	14.0974i	0.130148	+	0.637506i
$490$	−0.788378	+	3.86173i	−0.0356153	+	0.174455i
$491$	−13.4928	+	2.19279i	−0.608920	+	0.0989592i	−0.457050	−	0.889441i	$-0.651094\pi$
$491$	−13.4928	+	2.19279i	−0.608920	+	0.0989592i	−0.151871	+	0.988400i	$0.548530\pi$
$492$	−7.40632	−	0.597900i	−0.333903	−	0.0269554i
$493$	1.83120	+	3.17174i	0.0824733	+	0.142848i
$494$	3.08388	+	4.46777i	0.138750	+	0.201014i
$495$	0.0605821	+	0.209154i	0.00272296	+	0.00940076i
$496$	16.0803	−	55.5158i	0.722029	−	2.49273i
$497$	−14.4741	+	15.0691i	−0.649253	+	0.675944i
$498$	2.79358	−	23.0072i	0.125183	−	1.03098i
$499$	8.00015			0.358136			0.179068	−	0.983837i	$-0.442692\pi$
$499$	8.00015			0.358136			0.179068	+	0.983837i	$0.442692\pi$
$500$	−2.95968	+	24.3752i	−0.132361	+	1.09009i
$501$	18.0522	+	2.93377i	0.806515	+	0.131071i
$502$	−53.9611	−	66.0903i	−2.40840	−	2.94975i
$503$	−10.3218	−	27.2163i	−0.460225	−	1.21351i	−0.941520	−	0.336956i	$-0.890603\pi$
$503$	−10.3218	−	27.2163i	−0.460225	−	1.21351i	0.481295	−	0.876559i	$-0.340166\pi$
$504$	−3.85966	−	18.9059i	−0.171923	−	0.842134i
$505$	3.61509	−	1.54025i	0.160869	−	0.0685401i
$506$	4.73630	−	9.98155i	0.210554	−	0.443734i
$507$	0.520661	−	12.9201i	0.0231234	−	0.573801i
$508$	36.4589	+	27.3971i	1.61760	+	1.21555i
$509$	9.72755	−	20.5004i	0.431166	−	0.908663i	−0.565317	−	0.824873i	$-0.691246\pi$
$509$	9.72755	−	20.5004i	0.431166	−	0.908663i	0.996483	−	0.0837896i	$-0.0267024\pi$
$510$	−1.50964	+	0.792322i	−0.0668481	+	0.0350846i
$511$	−18.6627	−	1.50661i	−0.825587	−	0.0666483i
$512$	−42.7955	+	61.9999i	−1.89131	+	2.74004i
$513$	−7.09383	−	2.36827i	−0.313200	−	0.104562i
$514$	8.76924	−	5.54533i	0.386795	−	0.244594i
$515$	−0.757077	−	2.61373i	−0.0333608	−	0.115175i
$516$	32.0831	+	16.8385i	1.41238	+	0.741273i
$517$	0.920584	+	2.42738i	0.0404872	+	0.106756i
$518$	32.0222	+	13.6434i	1.40697	+	0.599456i
$519$	−0.224538	−	5.57184i	−0.00985611	−	0.244577i
$520$	−0.663521	+	0.961275i	−0.0290973	+	0.0421547i
$521$	−4.06940	+	7.04840i	−0.178283	+	0.308796i	−0.941293	−	0.337592i	$-0.890388\pi$
$521$	−4.06940	+	7.04840i	−0.178283	+	0.308796i	0.763009	+	0.646388i	$0.223721\pi$
$522$	−7.28525	+	0.588126i	−0.318867	+	0.0257416i
$523$	−25.7098	+	16.2579i	−1.12421	+	0.710908i	−0.961237	−	0.275723i	$-0.911083\pi$
$523$	−25.7098	+	16.2579i	−1.12421	+	0.710908i	−0.162973	+	0.986630i	$0.552108\pi$
$524$	−100.305	+	33.4867i	−4.38184	+	1.46287i
$525$	−3.32118	+	8.75723i	−0.144948	+	0.382197i
$526$	−8.08783	−	1.31440i	−0.352646	−	0.0573106i
$527$	−4.82383	−	1.18897i	−0.210130	−	0.0517923i
$528$	5.40288	−	5.62499i	0.235130	−	0.244796i
$529$	−16.0237	+	42.2511i	−0.696684	+	1.83700i
$530$	−9.06369	+	8.02973i	−0.393702	+	0.348789i
$531$	−4.57672	−	1.94996i	−0.198613	−	0.0846209i
$532$	−16.3172	+	79.9267i	−0.707438	+	3.46526i
$533$	0.150178	+	0.316492i	0.00650491	+	0.0137088i
$534$	33.7697	+	25.3763i	1.46136	+	1.09814i
$535$	−0.0957037	−	0.788191i	−0.00413763	−	0.0340765i
$536$	−3.02290	−	24.8958i	−0.130569	−	1.07533i
$537$	0.976407	−	24.2293i	0.0421351	−	1.04557i
$538$	−20.4434	−	18.1112i	−0.881376	−	0.780831i
$539$	−1.52980	+	0.248616i	−0.0658930	+	0.0107086i
$540$	−0.100898	−	2.50376i	−0.00434196	−	0.107745i
$541$	1.77926	−	2.17920i	0.0764963	−	0.0936910i	−0.734939	−	0.678133i	$-0.762789\pi$
$541$	1.77926	−	2.17920i	0.0764963	−	0.0936910i	0.811435	+	0.584442i	$0.198687\pi$
$542$	−19.2484	+	6.42605i	−0.826788	+	0.276023i
$543$	4.38667	−	15.1445i	0.188250	−	0.649914i
$544$	28.5435	+	18.0498i	1.22379	+	0.773881i
$545$	0.659348	+	0.807555i	0.0282434	+	0.0345919i
$546$	−1.06040	+	0.939429i	−0.0453808	+	0.0402038i
$547$	28.6358	−	35.0725i	1.22438	−	1.49959i	0.417717	−	0.908577i	$-0.362830\pi$
$547$	28.6358	−	35.0725i	1.22438	−	1.49959i	0.806661	−	0.591014i	$-0.201272\pi$
$548$	8.74751	+	2.92035i	0.373675	+	0.124751i
$549$	9.95470	−	2.45361i	0.424856	−	0.104718i
$550$	−6.23424	+	1.53660i	−0.265829	+	0.0655210i
$551$	18.8210	+	6.28339i	0.801803	+	0.267681i
$552$	−51.6346	+	63.2409i	−2.19772	+	2.69171i
$553$	−22.5330	+	19.9625i	−0.958199	+	0.848890i
$554$	−43.7337	−	53.5640i	−1.85807	−	2.27572i
$555$	2.45329	+	1.55136i	0.104136	+	0.0658518i
$556$	29.1371	−	100.593i	1.23569	−	4.26610i
$557$	17.5475	−	5.85823i	0.743513	−	0.248221i	0.0804232	−	0.996761i	$-0.474373\pi$
$557$	17.5475	−	5.85823i	0.743513	−	0.248221i	0.663090	+	0.748540i	$0.269245\pi$
$558$	6.27062	−	7.68011i	0.265456	−	0.325125i
$559$	−0.0687848	−	1.70688i	−0.00290929	−	0.0721932i
$560$	−13.8696	+	2.25403i	−0.586097	+	0.0952501i
$561$	−0.501823	−	0.444577i	−0.0211870	−	0.0187700i
$562$	0.533948	−	13.2498i	0.0225232	−	0.558908i
$563$	1.16824	+	9.62133i	0.0492355	+	0.405491i	0.996402	+	0.0847494i	$0.0270090\pi$
$563$	1.16824	+	9.62133i	0.0492355	+	0.405491i	−0.947167	+	0.320741i	$0.896068\pi$
$564$	−3.60100	−	29.6569i	−0.151629	−	1.24878i
$565$	4.27575	+	3.21302i	0.179882	+	0.135173i
$566$	−7.19020	−	15.1530i	−0.302227	−	0.636929i
$567$	0.390376	−	1.91219i	0.0163943	−	0.0803044i
$568$	97.3817	+	41.4905i	4.08605	+	1.74090i
$569$	17.8180	−	15.7853i	0.746968	−	0.661756i	−0.201191	−	0.979552i	$-0.564481\pi$
$569$	17.8180	−	15.7853i	0.746968	−	0.661756i	0.948159	+	0.317796i	$0.102943\pi$
$570$	−3.27548	+	8.63673i	−0.137195	+	0.361753i
$571$	−25.1868	+	26.2223i	−1.05404	+	1.09737i	−0.0589598	+	0.998260i	$0.518778\pi$
$571$	−25.1868	+	26.2223i	−1.05404	+	1.09737i	−0.995077	+	0.0991079i	$0.968401\pi$
$572$	−0.694474	−	0.171172i	−0.0290374	−	0.00715708i
$573$	−1.71697	−	0.279035i	−0.0717276	−	0.0116569i
$574$	−2.53462	+	6.68326i	−0.105793	+	0.278954i
$575$	37.5886	−	12.5489i	1.56755	−	0.523326i
$576$	−29.8178	+	18.8556i	−1.24241	+	0.785651i
$577$	28.0641	−	2.26557i	1.16832	−	0.0943169i	0.518963	−	0.854797i	$-0.326318\pi$
$577$	28.0641	−	2.26557i	1.16832	−	0.0943169i	0.649362	+	0.760480i	$0.275036\pi$
$578$	−20.7913	+	36.0115i	−0.864803	+	1.49788i
$579$	10.3437	−	14.9854i	0.429868	−	0.622771i
$580$	0.267698	+	6.64286i	0.0111156	+	0.275830i
$581$	−15.1052	−	6.43571i	−0.626668	−	0.266998i
$582$	2.35755	+	6.21636i	0.0977237	+	0.257676i
$583$	−4.21618	−	2.21282i	−0.174616	−	0.0916458i
$584$	26.3898	+	91.1082i	1.09202	+	3.77008i
$585$	−0.0998494	+	0.0631409i	−0.00412826	+	0.00261056i
$586$	0.801066	+	0.267435i	0.0330917	+	0.0110476i
$587$	15.1921	−	22.0095i	0.627044	−	0.908430i	−0.372766	−	0.927925i	$-0.621591\pi$
$587$	15.1921	−	22.0095i	0.627044	−	0.908430i	0.999810	+	0.0194955i	$0.00620601\pi$
$588$	17.7774	+	1.43514i	0.733128	+	0.0591842i
$589$	−23.8336	+	12.5088i	−0.982045	+	0.515417i
$590$	−2.63406	+	5.55116i	−0.108442	+	0.228537i
$591$	−15.5313	−	11.6710i	−0.638870	−	0.480080i
$592$	4.18636	−	103.883i	0.172058	−	4.26958i
$593$	−13.4760	+	28.4001i	−0.553393	+	1.16625i	0.413367	+	0.910564i	$0.364353\pi$
$593$	−13.4760	+	28.4001i	−0.553393	+	1.16625i	−0.966760	+	0.255686i	$0.917699\pi$
$594$	1.23089	−	0.524433i	0.0505040	−	0.0215177i
$595$	0.241601	+	1.18344i	0.00990467	+	0.0485163i
$596$	47.0019	+	123.934i	1.92527	+	5.07652i
$597$	−7.47228	−	9.15188i	−0.305820	−	0.374562i
$598$	5.91649	+	0.961523i	0.241943	+	0.0393196i
$599$	−2.14545	+	17.6693i	−0.0876606	+	0.721950i	0.880923	+	0.473260i	$0.156923\pi$
$599$	−2.14545	+	17.6693i	−0.0876606	+	0.721950i	−0.968583	+	0.248690i	$0.920000\pi$
$600$	47.4477			1.93704
$601$	−1.45330	+	11.9690i	−0.0592814	+	0.488227i	0.932586	+	0.360949i	$0.117547\pi$
$601$	−1.45330	+	11.9690i	−0.0592814	+	0.488227i	−0.991867	+	0.127278i	$0.959376\pi$
$602$	24.1449	−	25.1375i	0.984072	−	1.02453i
$603$	0.705705	−	2.43637i	0.0287385	−	0.0992168i
$604$	−8.23539	−	28.4319i	−0.335093	−	1.15688i
$605$	−2.74149	−	3.97174i	−0.111458	−	0.161474i
$606$	−12.0724	−	20.9100i	−0.490406	−	0.849409i
$607$	−6.96810	−	0.562523i	−0.282826	−	0.0228321i	−0.0617605	−	0.998091i	$-0.519672\pi$
$607$	−6.96810	−	0.562523i	−0.282826	−	0.0228321i	−0.221066	+	0.975259i	$0.570954\pi$
$608$	180.599	−	29.3502i	7.32426	−	1.19031i
$609$	−1.03573	+	5.07334i	−0.0419699	+	0.205582i
$610$	−2.53294	−	12.4071i	−0.102556	−	0.502350i
$611$	−1.12600	+	0.846132i	−0.0455530	+	0.0342308i
$612$	4.38264	+	6.34935i	0.177158	+	0.256657i
$613$	−8.04932	+	0.649808i	−0.325109	+	0.0262455i	−0.241944	−	0.970290i	$-0.577785\pi$
$613$	−8.04932	+	0.649808i	−0.325109	+	0.0262455i	−0.0831652	+	0.996536i	$0.526503\pi$
$614$	62.0615	−	15.2968i	2.50460	−	0.617328i
$615$	−0.298030	+	0.516203i	−0.0120177	+	0.0208153i
$616$	−4.68578	−	8.11601i	−0.188795	−	0.327003i
$617$	−10.5688	−	11.0033i	−0.425483	−	0.442975i	0.473608	−	0.880736i	$-0.342951\pi$
$617$	−10.5688	−	11.0033i	−0.425483	−	0.442975i	−0.899092	+	0.437761i	$0.855772\pi$
$618$	−15.3821	+	6.55369i	−0.618758	+	0.263628i
$619$	0.667098	+	1.40588i	0.0268129	+	0.0565071i	0.916415	−	0.400229i	$-0.131070\pi$
$619$	0.667098	+	1.40588i	0.0268129	+	0.0565071i	−0.889602	+	0.456736i	$0.849018\pi$
$620$	−6.75053	−	5.98045i	−0.271108	−	0.240181i
$621$	−7.31172	+	3.83749i	−0.293409	+	0.153993i
$622$	42.6638	+	44.4177i	1.71066	+	1.78099i
$623$	23.9240	−	17.9777i	0.958493	−	0.720261i
$624$	3.74682	+	1.96648i	0.149993	+	0.0787223i
$625$	−18.6155	−	11.7717i	−0.744620	−	0.470869i
$626$	−76.8486	−	18.9415i	−3.07149	−	0.757054i
$627$	−3.63225			−0.145058
$628$	−7.23215	−	69.6555i	−0.288594	−	2.77956i
$629$	−8.93690			−0.356338
$630$	−2.34042	−	0.576862i	−0.0932446	−	0.0229827i
$631$	19.8022	+	12.5221i	0.788312	+	0.498498i	0.866944	−	0.498406i	$-0.166081\pi$
$631$	19.8022	+	12.5221i	0.788312	+	0.498498i	−0.0786323	+	0.996904i	$0.525055\pi$
$632$	135.038	+	70.8733i	5.37151	+	2.81919i
$633$	−7.80819	+	5.86747i	−0.310348	+	0.233211i
$634$	37.4123	+	38.9503i	1.48583	+	1.54691i
$635$	3.23937	−	1.70015i	0.128550	−	0.0674684i
$636$	41.0143	+	36.3355i	1.62632	+	1.44080i
$637$	−0.360472	−	0.759678i	−0.0142824	−	0.0300996i
$638$	−3.26574	+	1.39140i	−0.129292	+	0.0550862i
$639$	7.41642	+	7.72131i	0.293389	+	0.305450i
$640$	10.8180	+	18.7373i	0.427619	+	0.740658i
$641$	9.99822	−	17.3174i	0.394906	−	0.683997i	−0.598183	−	0.801359i	$-0.704110\pi$
$641$	9.99822	−	17.3174i	0.394906	−	0.683997i	0.993089	+	0.117362i	$0.0374438\pi$
$642$	−4.73679	+	1.16751i	−0.186946	+	0.0460781i
$643$	−11.7145	+	0.945688i	−0.461973	+	0.0372943i	−0.309263	−	0.950977i	$-0.600082\pi$
$643$	−11.7145	+	0.945688i	−0.461973	+	0.0372943i	−0.152710	+	0.988271i	$0.548800\pi$
$644$	51.1661	+	74.1268i	2.01623	+	2.92101i
$645$	2.32366	−	1.74612i	0.0914941	−	0.0687534i
$646$	−5.68865	−	27.8648i	−0.223817	−	1.09633i
$647$	−5.77097	+	28.2681i	−0.226880	+	1.11133i	0.693544	+	0.720414i	$0.256048\pi$
$647$	−5.77097	+	28.2681i	−0.226880	+	1.11133i	−0.920425	+	0.390920i	$0.872157\pi$
$648$	−9.75899	+	1.58599i	−0.383369	+	0.0623036i
$649$	−2.40832	−	0.194420i	−0.0945348	−	0.00763164i
$650$	−1.74177	−	3.01684i	−0.0683180	−	0.118330i
$651$	−3.99016	−	5.78075i	−0.156387	−	0.226565i
$652$	−22.3730	−	77.2404i	−0.876193	−	3.02497i
$653$	3.25246	−	11.2288i	0.127278	−	0.439416i	−0.871413	−	0.490549i	$-0.836796\pi$
$653$	3.25246	−	11.2288i	0.127278	−	0.439416i	0.998692	+	0.0511332i	$0.0162833\pi$
$654$	4.43745	−	4.61987i	0.173518	−	0.180651i
$655$	−1.02250	+	8.42107i	−0.0399525	+	0.329038i
$656$	21.3499			0.833572
$657$	−1.15639	+	9.52375i	−0.0451152	+	0.371557i
$658$	−28.3661	−	4.60993i	−1.10582	−	0.179714i
$659$	7.08725	+	8.68030i	0.276080	+	0.338137i	0.893969	−	0.448129i	$-0.147909\pi$
$659$	7.08725	+	8.68030i	0.276080	+	0.338137i	−0.617889	+	0.786265i	$0.712012\pi$
$660$	−0.431557	−	1.13792i	−0.0167983	−	0.0442936i
$661$	3.37398	+	16.5268i	0.131233	+	0.642819i	0.991189	+	0.132453i	$0.0422852\pi$
$661$	3.37398	+	16.5268i	0.131233	+	0.642819i	−0.859957	+	0.510367i	$0.829510\pi$
$662$	−8.92110	+	3.80092i	−0.346728	+	0.147727i
$663$	0.155930	−	0.328616i	0.00605582	−	0.0127624i
$664$	−3.34929	+	83.1118i	−0.129978	+	3.22536i
$665$	5.23146	+	3.93119i	0.202867	+	0.152445i
$666$	7.64577	−	16.1131i	0.296268	−	0.624371i
$667$	19.3991	−	10.1814i	0.751137	−	0.394227i
$668$	−101.886	−	8.22510i	−3.94209	−	0.318239i
$669$	0.706528	−	1.02358i	0.0273159	−	0.0395740i
$670$	−2.97164	−	0.992078i	−0.114804	−	0.0383273i
$671$	4.20861	−	2.66136i	0.162471	−	0.102741i
$672$	13.2841	+	45.8620i	0.512445	+	1.76916i
$673$	−33.5748	−	17.6214i	−1.29421	−	0.679255i	−0.329898	−	0.944016i	$-0.607014\pi$
$673$	−33.5748	−	17.6214i	−1.29421	−	0.679255i	−0.964314	+	0.264761i	$0.914707\pi$
$674$	27.4614	+	72.4098i	1.05777	+	2.78912i
$675$	4.41497	+	1.88104i	0.169932	+	0.0724014i
$676$	2.90998	+	72.2103i	0.111922	+	2.77732i
$677$	18.5506	−	26.8752i	0.712958	−	1.03290i	−0.284289	−	0.958739i	$-0.591757\pi$
$677$	18.5506	−	26.8752i	0.712958	−	1.03290i	0.997246	−	0.0741588i	$-0.0236272\pi$
$678$	16.4315	−	28.4601i	0.631046	−	1.09300i
$679$	4.69474	−	0.378999i	0.180168	−	0.0145446i
$680$	5.17172	−	3.27040i	0.198326	−	0.125414i
$681$	4.14097	−	1.38246i	0.158682	−	0.0529759i
$682$	1.70758	−	4.50252i	0.0653866	−	0.172410i
$683$	−14.7556	−	2.39802i	−0.564608	−	0.0917577i	−0.128593	−	0.991697i	$-0.541046\pi$
$683$	−14.7556	−	2.39802i	−0.564608	−	0.0917577i	−0.436014	+	0.899940i	$0.643610\pi$
$684$	40.5839	+	10.0030i	1.55177	+	0.382476i
$685$	0.512469	−	0.533537i	0.0195805	−	0.0203854i
$686$	19.4293	−	51.2309i	0.741814	−	1.95600i
$687$	−9.86590	+	8.74043i	−0.376408	+	0.333468i
$688$	−95.7787	−	40.8075i	−3.65153	−	1.55577i
$689$	0.516737	−	2.53115i	0.0196861	−	0.0964290i
$690$	4.37222	+	9.21425i	0.166447	+	0.350781i
$691$	28.5529	+	21.4561i	1.08621	+	0.816230i	0.983935	−	0.178526i	$-0.0571330\pi$
$691$	28.5529	+	21.4561i	1.08621	+	0.816230i	0.102270	+	0.994757i	$0.467389\pi$
$692$	3.75668	+	30.9391i	0.142808	+	1.17613i
$693$	−0.114252	−	0.940954i	−0.00434009	−	0.0357439i
$694$	1.85713	−	46.0843i	0.0704958	−	1.74934i
$695$	−6.28836	−	5.57100i	−0.238531	−	0.211320i
$696$	25.8921	−	4.20788i	0.981438	−	0.159499i
$697$	−0.0738960	−	1.83371i	−0.00279901	−	0.0694567i
$698$	54.3261	−	66.5374i	2.05627	−	2.51848i
$699$	11.7450	−	3.92105i	0.444236	−	0.148308i
$700$	14.5635	−	50.2790i	0.550449	−	1.90037i
$701$	0.0185349	+	0.0117208i	0.000700054	+	0.000442687i	0.534816	−	0.844969i	$-0.320381\pi$
$701$	0.0185349	+	0.0117208i	0.000700054	+	0.000442687i	−0.534116	+	0.845411i	$0.679355\pi$
$702$	0.459087	+	0.562280i	0.0173271	+	0.0212219i
$703$	−36.2416	+	32.1073i	−1.36688	+	1.21095i
$704$	−10.8366	+	13.2724i	−0.408419	+	0.500223i
$705$	−2.27319	−	0.758901i	−0.0856131	−	0.0285819i
$706$	−51.6480	+	12.7301i	−1.94380	+	0.479103i
$707$	−16.6081	+	4.09354i	−0.624614	+	0.153953i
$708$	26.3733	+	8.80469i	0.991168	+	0.330900i
$709$	−5.36888	+	6.57568i	−0.201632	+	0.246955i	−0.865516	−	0.500881i	$-0.833010\pi$
$709$	−5.36888	+	6.57568i	−0.201632	+	0.246955i	0.663884	+	0.747836i	$0.268907\pi$
$710$	9.89772	−	8.76861i	0.371455	−	0.329080i
$711$	9.75541	+	11.9482i	0.365857	+	0.448093i
$712$	−128.135	−	81.0277i	−4.80206	−	3.03664i
$713$	−8.26860	+	28.5465i	−0.309662	+	1.06908i
$714$	7.03960	−	2.35016i	0.263450	−	0.0879527i
$715$	−0.0362880	+	0.0444447i	−0.00135709	+	0.00166214i
$716$	5.45714	+	135.417i	0.203943	+	5.06079i
$717$	11.9157	−	1.93649i	0.445000	−	0.0723195i
$718$	−4.55112	−	4.03194i	−0.169846	−	0.150471i
$719$	−1.04883	+	26.0265i	−0.0391149	+	0.970625i	0.853856	+	0.520510i	$0.174258\pi$
$719$	−1.04883	+	26.0265i	−0.0391149	+	0.970625i	−0.892970	+	0.450115i	$0.851383\pi$
$720$	0.867853	+	7.14741i	0.0323430	+	0.266368i
$721$	1.42778	+	11.7588i	0.0531734	+	0.437922i
$722$	−81.3340	−	61.1186i	−3.02694	−	2.27460i
$723$	1.60028	+	3.37251i	0.0595149	+	0.125425i
$724$	−17.6267	+	86.3411i	−0.655089	+	3.20884i
$725$	−11.7136	−	4.99070i	−0.435032	−	0.185350i
$726$	−22.1957	+	19.6637i	−0.823759	+	0.729787i
$727$	−4.10754	+	10.8307i	−0.152340	+	0.401688i	−0.989361	−	0.145483i	$-0.953526\pi$
$727$	−4.10754	+	10.8307i	−0.152340	+	0.401688i	0.837020	+	0.547172i	$0.184295\pi$
$728$	3.52212	−	3.66691i	0.130538	−	0.135905i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	11.6958	+	1.90075i	0.432880	+	0.0703498i
$731$	−3.17339	+	8.36754i	−0.117372	+	0.309485i
$732$	−54.3529	+	18.1457i	−2.00894	+	0.670683i
$733$	−7.28224	+	4.60501i	−0.268976	+	0.170090i	−0.662144	−	0.749377i	$-0.730353\pi$
$733$	−7.28224	+	4.60501i	−0.268976	+	0.170090i	0.393168	+	0.919466i	$0.371379\pi$
$734$	−63.0634	+	5.09100i	−2.32771	+	0.187912i
$735$	0.715363	−	1.23904i	0.0263866	−	0.0457029i
$736$	114.762	−	166.262i	4.23020	−	6.12850i
$737$	−0.0496050	−	1.23093i	−0.00182722	−	0.0453421i
$738$	3.36937	+	1.43556i	0.124028	+	0.0528436i
$739$	−9.19458	−	24.2441i	−0.338228	−	0.891835i	−0.990949	−	0.134236i	$-0.957142\pi$
$739$	−9.19458	−	24.2441i	−0.338228	−	0.891835i	0.652721	−	0.757598i	$-0.273627\pi$
$740$	−14.3646	−	7.53915i	−0.528055	−	0.277145i
$741$	−0.548266	−	1.89283i	−0.0201411	−	0.0695350i
$742$	44.5500	−	28.1717i	1.63548	−	1.03422i
$743$	−8.78796	−	2.93385i	−0.322399	−	0.107633i	0.150862	−	0.988555i	$-0.451795\pi$
$743$	−8.78796	−	2.93385i	−0.322399	−	0.107633i	−0.473261	+	0.880922i	$0.656923\pi$
$744$	−20.2143	+	29.2855i	−0.741092	+	1.07366i
$745$	10.5983	+	0.855585i	0.388292	+	0.0313462i
$746$	−47.4171	+	24.8864i	−1.73607	+	0.911157i
$747$	−3.60658	+	7.60071i	−0.131958	+	0.278095i
$748$	2.99553	+	2.25100i	0.109528	+	0.0823046i
$749$	−0.139166	+	3.45338i	−0.00508503	+	0.126184i
$750$	5.18836	−	10.9342i	0.189452	−	0.399262i
$751$	23.7044	−	10.0995i	0.864985	−	0.368536i	0.0865402	−	0.996248i	$-0.472419\pi$
$751$	23.7044	−	10.0995i	0.864985	−	0.368536i	0.778445	+	0.627712i	$0.216009\pi$
$752$	17.1700	+	84.1045i	0.626127	+	3.06697i
$753$	10.9827	+	28.9591i	0.400233	+	1.05533i
$754$	−1.21803	−	1.49182i	−0.0443580	−	0.0543287i
$755$	−2.34378	−	0.380901i	−0.0852987	−	0.0138624i
$756$	−1.31477	+	10.8281i	−0.0478178	+	0.393815i
$757$	49.0248			1.78184			0.890919	−	0.454162i	$-0.150061\pi$
$757$	49.0248			1.78184			0.890919	+	0.454162i	$0.150061\pi$
$758$	8.23410	−	67.8139i	0.299076	−	2.46311i
$759$	−2.77819	+	2.89240i	−0.100842	+	0.104987i
$760$	9.22333	−	31.8426i	0.334565	−	1.15505i
$761$	−9.57490	−	33.0564i	−0.347090	−	1.19829i	−0.924290	−	0.381690i	$-0.875342\pi$
$761$	−9.57490	−	33.0564i	−0.347090	−	1.19829i	0.577201	−	0.816602i	$-0.304145\pi$
$762$	−12.7695	−	18.4997i	−0.462588	−	0.670175i
$763$	−2.26907	−	3.93015i	−0.0821460	−	0.142281i
$764$	9.69054	+	0.782301i	0.350591	+	0.0283027i
$765$	0.610878	−	0.0992773i	0.0220863	−	0.00358938i
$766$	−14.9931	+	73.4412i	−0.541723	+	2.65354i
$767$	−0.262205	−	1.28437i	−0.00946769	−	0.0463758i
$768$	49.8708	−	37.4755i	1.79956	−	1.35228i
$769$	3.10882	+	4.50390i	0.112107	+	0.162415i	0.875021	−	0.484085i	$-0.160847\pi$
$769$	3.10882	+	4.50390i	0.112107	+	0.162415i	−0.762914	+	0.646500i	$0.776232\pi$
$770$	−1.16691	+	0.0942031i	−0.0420527	+	0.00339484i
$771$	−3.65686	+	0.901335i	−0.131699	+	0.0324608i
$772$	−50.8839	+	88.1334i	−1.83135	+	3.17199i
$773$	−11.7167	−	20.2940i	−0.421422	−	0.729924i	0.574657	−	0.818394i	$-0.305135\pi$
$773$	−11.7167	−	20.2940i	−0.421422	−	0.729924i	−0.996079	+	0.0884705i	$0.971802\pi$
$774$	−12.3716	−	12.8802i	−0.444690	−	0.462971i
$775$	15.8900	−	6.77008i	0.570784	−	0.243189i
$776$	−10.2291	−	21.5573i	−0.367202	−	0.773862i
$777$	−9.45755	−	8.37866i	−0.339288	−	0.300583i
$778$	71.0177	−	37.2729i	2.54611	−	1.33630i
$779$	−6.88757	−	7.17072i	−0.246773	−	0.256918i
$780$	0.527852	−	0.396655i	0.0189001	−	0.0142025i
$781$	4.60415	+	2.41644i	0.164749	+	0.0864672i
$782$	−26.5401	−	16.7830i	−0.949073	−	0.600158i
$783$	2.57606	+	0.634942i	0.0920609	+	0.0226910i
$784$	−51.2461			−1.83022
$785$	−5.29691	−	1.87126i	−0.189055	−	0.0667882i
$786$	52.1227			1.85915
$787$	−5.89454	−	1.45287i	−0.210118	−	0.0517894i	0.132852	−	0.991136i	$-0.457587\pi$
$787$	−5.89454	−	1.45287i	−0.210118	−	0.0517894i	−0.342969	+	0.939347i	$0.611433\pi$
$788$	91.7714	+	58.0327i	3.26922	+	2.06733i
$789$	2.63371	+	1.38228i	0.0937625	+	0.0492104i
$790$	15.2305	−	11.4450i	0.541876	−	0.407193i
$791$	−16.1277	−	16.7907i	−0.573434	−	0.597009i
$792$	−4.25188	+	2.23156i	−0.151084	+	0.0792950i
$793$	2.02215	+	1.79147i	0.0718086	+	0.0636169i
$794$	9.46693	+	19.9511i	0.335969	+	0.708040i
$795$	4.04383	−	1.72292i	0.143420	−	0.0611055i
$796$	45.7430	+	47.6235i	1.62132	+	1.68797i
$797$	−8.53965	−	14.7911i	−0.302490	−	0.523928i	0.674209	−	0.738540i	$-0.264485\pi$
$797$	−8.53965	−	14.7911i	−0.302490	−	0.523928i	−0.976699	+	0.214612i	$0.931151\pi$
$798$	20.1042	−	34.8215i	0.711681	−	1.23267i
$799$	7.16419	−	1.76581i	0.253451	−	0.0624700i
$800$	−117.028	+	9.44745i	−4.13755	+	0.334018i
$801$	−8.71056	−	12.6194i	−0.307772	−	0.445885i
$802$	37.6696	−	28.3069i	1.33016	−	0.999551i
$803$	0.932011	+	4.56529i	0.0328899	+	0.161106i
$804$	−2.83569	+	13.8901i	−0.100007	+	0.489866i
$805$	7.13182	−	1.15903i	0.251364	−	0.0408506i
$806$	2.60410	+	0.210224i	0.0917253	+	0.00740484i
$807$	4.95715	+	8.58604i	0.174500	+	0.302243i
$808$	49.2259	+	71.3160i	1.73176	+	2.50889i
$809$	2.48307	+	8.57255i	0.0873001	+	0.301395i	0.992273	−	0.124074i	$-0.0395962\pi$
$809$	2.48307	+	8.57255i	0.0873001	+	0.301395i	−0.904973	+	0.425469i	$0.860109\pi$
$810$	−0.343627	+	1.18634i	−0.0120738	+	0.0416837i
$811$	−7.05082	+	7.34069i	−0.247588	+	0.257766i	−0.833387	−	0.552690i	$-0.813601\pi$
$811$	−7.05082	+	7.34069i	−0.247588	+	0.257766i	0.585799	+	0.810456i	$0.300781\pi$
$812$	3.48830	−	28.7287i	0.122415	−	1.00818i
$813$	7.36627			0.258346
$814$	1.04410	−	8.59896i	0.0365958	−	0.301393i
$815$	−6.36730	−	1.03479i	−0.223037	−	0.0362470i
$816$	−14.0198	−	17.1712i	−0.490792	−	0.601112i
$817$	17.1928	+	45.3337i	0.601500	+	1.58602i
$818$	12.0560	+	59.0541i	0.421527	+	2.06478i
$819$	0.473103	−	0.201570i	0.0165316	−	0.00704344i
$820$	1.42814	−	3.00974i	0.0498727	−	0.105105i
$821$	−0.441217	+	10.9487i	−0.0153986	+	0.382111i	0.973054	+	0.230579i	$0.0740619\pi$
$821$	−0.441217	+	10.9487i	−0.0153986	+	0.382111i	−0.988452	+	0.151533i	$0.951579\pi$
$822$	−3.63393	−	2.73072i	−0.126748	−	0.0952447i
$823$	8.44069	−	17.7884i	0.294224	−	0.620064i	−0.701477	−	0.712692i	$-0.747476\pi$
$823$	8.44069	−	17.7884i	0.294224	−	0.620064i	0.995701	+	0.0926285i	$0.0295269\pi$
$824$	53.1346	−	27.8872i	1.85103	−	0.971496i
$825$	2.32321	+	0.187549i	0.0808837	+	0.00652961i
$826$	15.1937	−	22.0119i	0.528656	−	0.765891i
$827$	20.6279	+	6.88660i	0.717302	+	0.239471i	0.651810	−	0.758383i	$-0.274010\pi$
$827$	20.6279	+	6.88660i	0.717302	+	0.239471i	0.0654921	+	0.997853i	$0.479138\pi$
$828$	39.0068	−	24.6664i	1.35558	−	0.857218i
$829$	4.24059	+	14.6402i	0.147282	+	0.508476i	0.999901	−	0.0140565i	$-0.00447448\pi$
$829$	4.24059	+	14.6402i	0.147282	+	0.508476i	−0.852619	+	0.522533i	$0.824987\pi$
$830$	9.20068	+	4.82889i	0.319360	+	0.167613i
$831$	8.90113	+	23.4704i	0.308777	+	0.814178i
$832$	−8.55223	−	3.64376i	−0.296495	−	0.126325i
$833$	0.177373	+	4.40146i	0.00614561	+	0.152502i
$834$	−29.3237	+	42.4827i	−1.01540	+	1.47106i
$835$	−4.09990	+	7.10123i	−0.141883	+	0.245748i
$836$	20.2348	−	1.63352i	0.699835	−	0.0564965i
$837$	−3.04193	+	1.92360i	−0.105145	+	0.0664894i
$838$	7.19056	−	2.40056i	0.248394	−	0.0829260i
$839$	14.9636	−	39.4557i	0.516600	−	1.36216i	−0.382312	−	0.924033i	$-0.624872\pi$
$839$	14.9636	−	39.4557i	0.516600	−	1.36216i	0.898912	−	0.438129i	$-0.144359\pi$
$840$	8.53913	+	1.38774i	0.294628	+	0.0478817i
$841$	21.3226	+	5.25556i	0.735263	+	0.181226i
$842$	1.76476	−	1.83731i	0.0608177	−	0.0633179i
$843$	−1.70692	+	4.50078i	−0.0587895	+	0.155015i
$844$	40.8597	−	36.1985i	1.40645	−	1.24600i
$845$	5.33343	+	2.27236i	0.183476	+	0.0781717i
$846$	−2.94542	+	14.4276i	−0.101266	+	0.496033i
$847$	9.00579	+	18.9793i	0.309443	+	0.652137i
$848$	−125.866	−	94.5819i	−4.32224	−	3.24795i
$849$	0.733875	+	6.04400i	0.0251865	+	0.207430i
$850$	2.19971	+	18.1162i	0.0754494	+	0.621382i
$851$	−2.15265	+	53.4174i	−0.0737919	+	1.83113i
$852$	−44.7884	−	39.6791i	−1.53443	−	1.35938i
$853$	−41.2923	+	6.71065i	−1.41382	+	0.229768i	−0.818863	−	0.573989i	$-0.805395\pi$
$853$	−41.2923	+	6.71065i	−1.41382	+	0.229768i	−0.594958	+	0.803757i	$0.702831\pi$
$854$	2.21954	+	55.0773i	0.0759511	+	1.88471i
$855$	2.12061	−	2.59728i	0.0725233	−	0.0888250i
$856$	16.6080	−	5.54457i	0.567651	−	0.189510i
$857$	−0.00444074	+	0.0153312i	−0.000151693	+	0.000523705i	−0.960594	−	0.277956i	$-0.910343\pi$
$857$	−0.00444074	+	0.0153312i	−0.000151693	+	0.000523705i	0.960442	+	0.278479i	$0.0898304\pi$
$858$	0.297972	+	0.188426i	0.0101726	+	0.00643276i
$859$	−13.3845	−	16.3930i	−0.456673	−	0.559323i	0.494022	−	0.869449i	$-0.335526\pi$
$859$	−13.3845	−	16.3930i	−0.456673	−	0.559323i	−0.950695	+	0.310126i	$0.899629\pi$
$860$	−12.1596	+	10.7724i	−0.414637	+	0.367337i
$861$	1.64097	−	2.00982i	0.0559240	−	0.0684944i
$862$	24.4004	+	8.14604i	0.831080	+	0.277455i
$863$	23.1011	−	5.69391i	0.786371	−	0.193823i	0.174370	−	0.984680i	$-0.444211\pi$
$863$	23.1011	−	5.69391i	0.786371	−	0.193823i	0.612001	+	0.790857i	$0.290365\pi$
$864$	23.7543	−	5.85492i	0.808139	−	0.199188i
$865$	2.37146	+	0.791711i	0.0806322	+	0.0269190i
$866$	69.4965	−	85.1178i	2.36159	−	2.89242i
$867$	11.2984	−	10.0095i	0.383714	−	0.339941i
$868$	24.8285	+	30.4093i	0.842733	+	1.03216i
$869$	6.33178	+	4.00397i	0.214791	+	0.135826i
$870$	0.911697	−	3.14754i	0.0309094	−	0.106712i
$871$	0.633976	−	0.211652i	0.0214814	−	0.00717156i
$872$	−14.5402	+	17.8085i	−0.492392	+	0.603071i
$873$	−0.0971767	−	2.41142i	−0.00328893	−	0.0816141i
$874$	−167.923	+	27.2902i	−5.68009	+	0.923104i
$875$	−6.41783	−	5.68570i	−0.216962	−	0.192212i
$876$	2.15903	−	53.5757i	0.0729468	−	1.81016i
$877$	3.90076	+	32.1256i	0.131719	+	1.08480i	0.897286	+	0.441449i	$0.145535\pi$
$877$	3.90076	+	32.1256i	0.131719	+	1.08480i	−0.765567	+	0.643356i	$0.777542\pi$
$878$	−3.24467	−	26.7223i	−0.109502	−	0.901833i
$879$	−0.245081	−	0.184166i	−0.00826637	−	0.00621178i
$880$	1.49907	+	3.15922i	0.0505336	+	0.106497i
$881$	−1.90823	+	9.34714i	−0.0642900	+	0.314913i	−0.999201	−	0.0399694i	$-0.987274\pi$
$881$	−1.90823	+	9.34714i	−0.0642900	+	0.314913i	0.934911	+	0.354882i	$0.115479\pi$
$882$	−8.08753	−	3.44577i	−0.272321	−	0.116025i
$883$	24.7214	−	21.9012i	0.831941	−	0.737035i	−0.135325	−	0.990801i	$-0.543208\pi$
$883$	24.7214	−	21.9012i	0.831941	−	0.737035i	0.967266	+	0.253766i	$0.0816694\pi$
$884$	−0.720880	+	1.90080i	−0.0242458	+	0.0639309i
$885$	1.54507	−	1.60858i	0.0519369	−	0.0540720i
$886$	−88.9417	−	21.9222i	−2.98806	−	0.736489i
$887$	−6.14182	−	0.998142i	−0.206222	−	0.0335143i	0.0564226	−	0.998407i	$-0.482031\pi$
$887$	−6.14182	−	0.998142i	−0.206222	−	0.0335143i	−0.262645	+	0.964893i	$0.584595\pi$
$888$	−22.6983	+	59.8505i	−0.761705	+	2.00845i
$889$	−15.1055	+	5.04294i	−0.506621	+	0.169135i
$890$	−16.0068	+	10.1221i	−0.536551	+	0.339294i
$891$	−0.484103	+	0.0390809i	−0.0162181	+	0.00130926i
$892$	−3.47564	+	6.01999i	−0.116373	+	0.201564i
$893$	22.7088	−	32.8994i	0.759922	−	1.10094i
$894$	−2.63067	−	65.2794i	−0.0879828	−	2.18327i
$895$	10.0019	+	4.26141i	0.334326	+	0.142443i
$896$	−33.3971	−	88.0608i	−1.11572	−	2.94191i
$897$	−1.92664	−	1.01118i	−0.0643285	−	0.0337622i
$898$	−25.8920	−	89.3895i	−0.864027	−	2.98297i
$899$	8.07072	−	5.10361i	0.269174	−	0.170215i
$900$	−25.4412	−	8.49352i	−0.848040	−	0.283117i
$901$	−7.68786	+	11.1378i	−0.256120	+	0.371054i
$902$	1.77300	+	0.143132i	0.0590345	+	0.00476576i
$903$	−11.2031	+	5.87986i	−0.372817	+	0.195669i
$904$	−50.5621	+	106.557i	−1.68167	+	3.54405i
$905$	5.65130	+	4.24668i	0.187856	+	0.141164i
$906$	−0.587484	+	14.5783i	−0.0195178	+	0.484330i
$907$	−5.42655	+	11.4362i	−0.180186	+	0.379733i	−0.973367	−	0.229252i	$-0.926372\pi$
$907$	−5.42655	+	11.4362i	−0.180186	+	0.379733i	0.793181	+	0.608986i	$0.208423\pi$
$908$	−22.4471	+	9.56381i	−0.744933	+	0.317386i
$909$	1.75314	+	8.58744i	0.0581479	+	0.284827i
$910$	−0.225230	−	0.593882i	−0.00746629	−	0.0196870i
$911$	28.3093	+	34.6726i	0.937929	+	1.14875i	0.988679	+	0.150043i	$0.0479412\pi$
$911$	28.3093	+	34.6726i	0.937929	+	1.14875i	−0.0507505	+	0.998711i	$0.516161\pi$
$912$	−118.545	−	19.2654i	−3.92541	−	0.637941i
$913$	−0.492513	+	4.05621i	−0.0162998	+	0.134241i
$914$	45.9313			1.51927
$915$	−0.554071	+	4.56318i	−0.0183170	+	0.150854i
$916$	51.0309	−	53.1288i	1.68611	−	1.75542i
$917$	10.2735	−	35.4681i	0.339259	−	1.17126i
$918$	−1.05799	−	3.65260i	−0.0349188	−	0.120554i
$919$	30.5466	+	44.2544i	1.00764	+	1.45982i	0.883998	+	0.467490i	$0.154842\pi$
$919$	30.5466	+	44.2544i	1.00764	+	1.45982i	0.123641	+	0.992327i	$0.460543\pi$
$920$	−18.3020	−	31.7000i	−0.603400	−	1.04512i
$921$	−23.1274	−	1.86703i	−0.762073	−	0.0615209i
$922$	70.3906	−	11.4396i	2.31819	−	0.376743i
$923$	−0.564286	+	2.76406i	−0.0185737	+	0.0909801i
$924$	1.05966	+	5.19055i	0.0348602	+	0.170757i
$925$	24.8382	−	18.6647i	0.816675	−	0.613691i
$926$	7.36127	+	10.6646i	0.241906	+	0.350462i
$927$	6.04971	−	0.488383i	0.198698	−	0.0160406i
$928$	−63.0239	+	15.5340i	−2.06886	+	0.509929i
$929$	7.12800	−	12.3461i	0.233862	−	0.405061i	−0.725079	−	0.688665i	$-0.758197\pi$
$929$	7.12800	−	12.3461i	0.233862	−	0.405061i	0.958941	+	0.283605i	$0.0915303\pi$
$930$	2.22264	+	3.84972i	0.0728831	+	0.126237i
$931$	16.5323	+	17.2119i	0.541823	+	0.564098i
$932$	−63.6665	+	27.1258i	−2.08546	+	0.888534i
$933$	−9.58413	−	20.1981i	−0.313770	−	0.661257i
$934$	21.3358	+	18.9019i	0.698128	+	0.618488i
$935$	0.266153	−	0.139688i	0.00870412	−	0.00456828i
$936$	−1.80470	−	1.87890i	−0.0589886	−	0.0614136i
$937$	0.144214	−	0.108370i	0.00471125	−	0.00354028i	−0.598384	−	0.801209i	$-0.704190\pi$
$937$	0.144214	−	0.108370i	0.00471125	−	0.00354028i	0.603095	+	0.797669i	$0.293934\pi$
$938$	12.0752	+	6.33757i	0.394270	+	0.206929i
$939$	24.2831	+	15.3557i	0.792450	+	0.501115i
$940$	13.0049	+	3.20543i	0.424174	+	0.104550i
$941$	−1.07096			−0.0349123			−0.0174562	−	0.999848i	$-0.505557\pi$
$941$	−1.07096			−0.0349123			−0.0174562	+	0.999848i	$0.505557\pi$
$942$	−7.49094	+	33.6951i	−0.244068	+	1.09785i
$943$	−10.9782			−0.357500
$944$	−77.5684	−	19.1189i	−2.52464	−	0.622267i
$945$	0.739542	+	0.467658i	0.0240573	+	0.0152129i
$946$	−7.68038	−	4.03097i	−0.249711	−	0.131058i
$947$	−23.4393	+	17.6135i	−0.761675	+	0.572362i	−0.909034	−	0.416721i	$-0.863179\pi$
$947$	−23.4393	+	17.6135i	−0.761675	+	0.572362i	0.147359	+	0.989083i	$0.452923\pi$
$948$	−59.7196	−	62.1747i	−1.93960	−	2.01934i
$949$	−2.23838	+	1.17479i	−0.0726608	+	0.0381353i
$950$	74.0060	+	65.5636i	2.40107	+	2.12716i
$951$	−8.40441	−	17.7119i	−0.272532	−	0.574348i
$952$	−24.5045	+	10.4404i	−0.794194	+	0.338375i
$953$	17.9274	+	18.6644i	0.580724	+	0.604598i	0.945151	−	0.326634i	$-0.105915\pi$
$953$	17.9274	+	18.6644i	0.580724	+	0.604598i	−0.364427	+	0.931232i	$0.618735\pi$
$954$	−13.5041	−	23.3898i	−0.437212	−	0.757273i
$955$	0.389947	−	0.675408i	0.0126184	−	0.0218557i
$956$	−65.5099	+	16.1468i	−2.11874	+	0.522223i
$957$	1.28440	−	0.103688i	0.0415188	−	0.00335175i
$958$	−45.0526	−	65.2699i	−1.45558	−	2.10877i
$959$	−2.57443	+	1.93456i	−0.0831328	+	0.0624702i
$960$	−3.16386	−	15.4976i	−0.102113	−	0.500184i
$961$	3.60974	−	17.6817i	0.116443	−	0.570377i
$962$	4.63868	−	0.753859i	0.149557	−	0.0243054i
$963$	1.76518	+	0.142500i	0.0568820	+	0.00459199i
$964$	−10.4317	−	18.0682i	−0.335981	−	0.581936i
$965$	4.63751	+	6.71860i	0.149287	+	0.216279i
$966$	−12.3517	−	42.6430i	−0.397410	−	1.37202i
$967$	−0.316722	+	1.09345i	−0.0101851	+	0.0351630i	−0.965450	−	0.260589i	$-0.916083\pi$
$967$	−0.316722	+	1.09345i	−0.0101851	+	0.0351630i	0.955265	+	0.295752i	$0.0955703\pi$
$968$	73.7232	−	76.7540i	2.36955	−	2.46697i
$969$	−1.24437	+	10.2483i	−0.0399750	+	0.329224i
$970$	−2.98076			−0.0957066
$971$	2.91965	−	24.0454i	0.0936959	−	0.771655i	−0.867815	−	0.496888i	$-0.834476\pi$
$971$	2.91965	−	24.0454i	0.0936959	−	0.771655i	0.961511	−	0.274767i	$-0.0886008\pi$
$972$	5.51662	+	0.896538i	0.176946	+	0.0287565i
$973$	23.1286	+	28.3274i	0.741469	+	0.908134i
$974$	−15.4300	−	40.6857i	−0.494410	−	1.30365i
$975$	0.252939	+	1.23898i	0.00810053	+	0.0396790i
$976$	151.471	−	64.5357i	4.84846	−	2.06574i
$977$	−17.8395	+	37.5959i	−0.570735	+	1.20280i	0.388829	+	0.921310i	$0.372880\pi$
$977$	−17.8395	+	37.5959i	−0.570735	+	1.20280i	−0.959564	+	0.281489i	$0.909172\pi$
$978$	−1.59601	+	39.6046i	−0.0510347	+	1.26641i
$979$	−5.95366	−	4.47389i	−0.190280	−	0.142986i
$980$	−3.42796	+	7.22428i	−0.109502	+	0.230771i
$981$	−2.05896	+	1.08063i	−0.0657375	+	0.0345017i
$982$	−37.5356	−	3.03019i	−1.19781	−	0.0966972i
$983$	−25.6315	+	37.1336i	−0.817517	+	1.18438i	0.162744	+	0.986668i	$0.447966\pi$
$983$	−25.6315	+	37.1336i	−0.817517	+	1.18438i	−0.980261	+	0.197709i	$0.936650\pi$
$984$	−12.4680	−	4.16245i	−0.397467	−	0.132694i
$985$	7.36181	−	4.65533i	0.234567	−	0.148331i
$986$	2.80701	+	9.69091i	0.0893933	+	0.308621i
$987$	9.23708	+	4.84799i	0.294019	+	0.154313i
$988$	3.90558	+	10.2982i	0.124253	+	0.327628i
$989$	49.2499	+	20.9834i	1.56606	+	0.667234i
$990$	0.0241540	+	0.599376i	0.000767666	+	0.0190494i
$991$	11.5260	−	16.6982i	0.366134	−	0.530436i	−0.596011	−	0.802977i	$-0.703248\pi$
$991$	11.5260	−	16.6982i	0.366134	−	0.530436i	0.962144	+	0.272540i	$0.0878637\pi$
$992$	44.0266	−	76.2562i	1.39784	−	2.42114i
$993$	3.50863	−	0.283246i	0.111343	−	0.00898853i
$994$	−48.6495	+	30.7641i	−1.54307	+	0.975777i
$995$	5.02453	−	1.67743i	0.159288	−	0.0531782i
$996$	16.6736	−	43.9646i	0.528322	−	1.39307i
$997$	5.86642	+	0.953386i	0.185791	+	0.0301940i	0.252595	−	0.967572i	$-0.418716\pi$
$997$	5.86642	+	0.953386i	0.185791	+	0.0301940i	−0.0668036	+	0.997766i	$0.521280\pi$
$998$	21.3985	+	5.27426i	0.677358	+	0.166954i
$999$	−4.48480	+	4.66918i	−0.141893	+	0.147726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.14	✓	336
157.124	even	39	inner	471.2.q.b.124.14	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.14	✓	336	1.1	even	1	trivial
471.2.q.b.124.14	yes	336	157.124	even	39	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.67476 + 0.659270i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.94881 + 2.59734i) q^{4} +(0.358425 - 0.269339i) q^{5} +(-1.90833 - 1.98678i) q^{6} +(-1.72808 + 0.906968i) q^{7} +(7.40054 + 6.55631i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(2.67476 + 0.659270i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(4.94881 + 2.59734i) q^{4} +(0.358425 - 0.269339i) q^{5} +(-1.90833 - 1.98678i) q^{6} +(-1.72808 + 0.906968i) q^{7} +(7.40054 + 6.55631i) q^{8} +(0.428693 + 0.903450i) q^{9} +(1.13627 - 0.484119i) q^{10} +(0.336441 + 0.350272i) q^{11} +(-2.79450 - 4.84021i) q^{12} +(-0.131750 + 0.228197i) q^{13} +(-5.22015 + 1.28665i) q^{14} +(-0.446890 + 0.0360767i) q^{15} +(9.12250 + 13.2162i) q^{16} +(1.10355 - 0.829263i) q^{17} +(0.551034 + 2.69914i) q^{18} +(1.49593 - 7.32757i) q^{19} +(2.47334 - 0.401957i) q^{20} +(1.94530 + 0.157041i) q^{21} +(0.668977 + 1.15870i) q^{22} +(-4.69084 - 6.79585i) q^{23} +(-2.75074 - 9.49666i) q^{24} +(-1.33516 + 4.60951i) q^{25} +(-0.502843 + 0.523515i) q^{26} +(0.120537 - 0.992709i) q^{27} -10.9077 q^{28} +(-0.319803 + 2.63381i) q^{29} +(-1.21911 - 0.198124i) q^{30} +(-2.27624 - 2.78789i) q^{31} +(8.67549 + 22.8754i) q^{32} +(-0.0971482 - 0.475863i) q^{33} +(3.49844 - 1.49055i) q^{34} +(-0.375107 + 0.790520i) q^{35} +(-0.225046 + 5.58447i) q^{36} +(-5.17571 - 3.88930i) q^{37} +(8.83212 - 18.6133i) q^{38} +(0.233317 - 0.122454i) q^{39} +(4.41841 + 0.356691i) q^{40} +(0.755226 - 1.09413i) q^{41} +(5.09969 + 1.70253i) q^{42} +(-5.47935 + 3.46493i) q^{43} +(0.755209 + 2.60728i) q^{44} +(0.396989 + 0.208356i) q^{45} +(-8.06658 - 21.2698i) q^{46} +(4.91754 + 2.09517i) q^{47} +(-0.646627 - 16.0459i) q^{48} +(-1.81277 + 2.62625i) q^{49} +(-6.61016 + 11.4491i) q^{50} +(-1.37592 + 0.111076i) q^{51} +(-1.24471 + 0.787107i) q^{52} +(-9.29946 + 3.10462i) q^{53} +(0.976870 - 2.57580i) q^{54} +(0.214931 + 0.0349297i) q^{55} +(-18.7351 - 4.61779i) q^{56} +(-5.18069 + 5.39367i) q^{57} +(-2.59179 + 6.83399i) q^{58} +(-3.72369 + 3.29890i) q^{59} +(-2.30528 - 0.982187i) q^{60} +(2.05079 - 10.0454i) q^{61} +(-4.25043 - 8.95760i) q^{62} +(-1.56022 - 1.17243i) q^{63} +(4.25246 + 35.0222i) q^{64} +(0.0142400 + 0.117277i) q^{65} +(0.0538740 - 1.33687i) q^{66} +(-1.89861 - 1.68202i) q^{67} +(7.61513 - 1.23758i) q^{68} +(0.332499 + 8.25088i) q^{69} +(-1.52449 + 1.86716i) q^{70} +(10.1552 - 3.39030i) q^{71} +(-2.75074 + 9.49666i) q^{72} +(8.10850 + 5.12751i) q^{73} +(-11.2797 - 13.8151i) q^{74} +(3.59209 - 3.18232i) q^{75} +(26.4353 - 32.3773i) q^{76} +(-0.899084 - 0.300159i) q^{77} +(0.704799 - 0.173717i) q^{78} +(14.9767 - 3.69142i) q^{79} +(6.82937 + 2.27998i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(2.74138 - 2.42865i) q^{82} +(5.32075 + 6.51673i) q^{83} +(9.21905 + 5.82977i) q^{84} +(0.172187 - 0.594457i) q^{85} +(-16.9403 + 5.65550i) q^{86} +(1.67798 - 2.05515i) q^{87} +(0.193354 + 4.79802i) q^{88} +(-15.1352 + 2.45970i) q^{89} +(0.924488 + 0.819025i) q^{90} +(0.0207069 - 0.513837i) q^{91} +(-5.56296 - 45.8151i) q^{92} +(0.433825 + 3.57287i) q^{93} +(11.7720 + 8.84607i) q^{94} +(-1.43742 - 3.02930i) q^{95} +(4.89368 - 23.9708i) q^{96} +(-2.22025 - 0.945962i) q^{97} +(-6.58015 + 5.82950i) q^{98} +(-0.172224 + 0.454117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more