LMFDB - Embedded newform 784.2.bp.b.703.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(47,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 5]))

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

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

chi := DirichletCharacter("784.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bp (of order $42$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			703.3
Character	$\chi$	$=$	784.703
Dual form			784.2.bp.b.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00318 - 0.309439i) q^{3} +(-2.49710 - 2.69123i) q^{5} +(-1.72063 - 2.00983i) q^{7} +(-1.56810 - 1.06912i) q^{9} +O(q^{10})$	\(q+(-1.00318 - 0.309439i) q^{3} +(-2.49710 - 2.69123i) q^{5} +(-1.72063 - 2.00983i) q^{7} +(-1.56810 - 1.06912i) q^{9} +(1.80116 + 2.64181i) q^{11} +(0.664877 - 1.38063i) q^{13} +(1.67226 + 3.47248i) q^{15} +(-4.82102 + 1.89211i) q^{17} +(0.131720 + 0.228145i) q^{19} +(1.10418 + 2.54865i) q^{21} +(4.84233 + 1.90047i) q^{23} +(-0.633579 + 8.45452i) q^{25} +(3.20591 + 4.02009i) q^{27} +(3.81637 - 4.78557i) q^{29} +(-2.31746 + 4.01395i) q^{31} +(-0.989399 - 3.20755i) q^{33} +(-1.11235 + 9.64937i) q^{35} +(1.04839 + 0.158019i) q^{37} +(-1.09421 + 1.17928i) q^{39} +(-10.7323 + 2.44957i) q^{41} +(3.75304 + 0.856607i) q^{43} +(1.03847 + 6.88982i) q^{45} +(0.532135 + 7.10085i) q^{47} +(-1.07886 + 6.91636i) q^{49} +(5.42183 - 0.406310i) q^{51} +(-0.650029 + 0.0979760i) q^{53} +(2.61206 - 11.4442i) q^{55} +(-0.0615411 - 0.269629i) q^{57} +(-7.61615 - 7.06676i) q^{59} +(1.80831 - 11.9973i) q^{61} +(0.549384 + 4.99118i) q^{63} +(-5.37586 + 1.65823i) q^{65} +(-3.37430 - 1.94815i) q^{67} +(-4.26963 - 3.40492i) q^{69} +(-7.90969 + 6.30776i) q^{71} +(1.99052 + 0.149169i) q^{73} +(3.25175 - 8.28533i) q^{75} +(2.21048 - 8.16561i) q^{77} +(-10.5737 + 6.10473i) q^{79} +(0.107999 + 0.275176i) q^{81} +(8.11176 - 3.90642i) q^{83} +(17.1307 + 8.24970i) q^{85} +(-5.30934 + 3.61984i) q^{87} +(-2.98889 + 4.38389i) q^{89} +(-3.91885 + 1.03926i) q^{91} +(3.56689 - 3.30959i) q^{93} +(0.285075 - 0.924190i) q^{95} -7.53069i q^{97} -6.06828i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9	$ 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9} + 18 q^{11} + 16 q^{17} + 7 q^{19} + 5 q^{21} + 54 q^{23} - 4 q^{25} - 53 q^{27} - 16 q^{29} + 5 q^{31} - 3 q^{33} - 9 q^{35} + 2 q^{37} - 43 q^{39} - 28 q^{41} - 111 q^{45} - 60 q^{47} - 58 q^{49} - 3 q^{51} - 70 q^{53} + 69 q^{55} + 31 q^{57} + 9 q^{59} - 8 q^{61} + 93 q^{63} - 8 q^{65} - 21 q^{67} - 56 q^{69} - 63 q^{71} - 24 q^{73} + 2 q^{75} - 18 q^{77} + 21 q^{79} + 45 q^{81} + 60 q^{83} + 6 q^{85} - 6 q^{87} + 7 q^{89} + 66 q^{93} + 15 q^{95}+O(q^{100}) $ 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9 + 18 * q^11 + 16 * q^17 + 7 * q^19 + 5 * q^21 + 54 * q^23 - 4 * q^25 - 53 * q^27 - 16 * q^29 + 5 * q^31 - 3 * q^33 - 9 * q^35 + 2 * q^37 - 43 * q^39 - 28 * q^41 - 111 * q^45 - 60 * q^47 - 58 * q^49 - 3 * q^51 - 70 * q^53 + 69 * q^55 + 31 * q^57 + 9 * q^59 - 8 * q^61 + 93 * q^63 - 8 * q^65 - 21 * q^67 - 56 * q^69 - 63 * q^71 - 24 * q^73 + 2 * q^75 - 18 * q^77 + 21 * q^79 + 45 * q^81 + 60 * q^83 + 6 * q^85 - 6 * q^87 + 7 * q^89 + 66 * q^93 + 15 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{25}{42}\right)$

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			0
$2$		0			0
$3$	−1.00318	−	0.309439i	−0.579185	−	0.178655i	−0.00869864	−	0.999962i	$-0.502769\pi$
$3$	−1.00318	−	0.309439i	−0.579185	−	0.178655i	−0.570486	+	0.821307i	$0.693245\pi$
$4$		0			0
$5$	−2.49710	−	2.69123i	−1.11674	−	1.20356i	−0.976971	−	0.213371i	$-0.931556\pi$
$5$	−2.49710	−	2.69123i	−1.11674	−	1.20356i	−0.139765	−	0.990185i	$-0.544635\pi$
$6$		0			0
$7$	−1.72063	−	2.00983i	−0.650337	−	0.759646i
$7$	−1.72063	−	2.00983i	−0.650337	−	0.759646i
$8$		0			0
$9$	−1.56810	−	1.06912i	−0.522702	−	0.356372i
$10$		0			0
$11$	1.80116	+	2.64181i	0.543069	+	0.796536i	0.995450	−	0.0952889i	$-0.0303775\pi$
$11$	1.80116	+	2.64181i	0.543069	+	0.796536i	−0.452381	+	0.891825i	$0.649425\pi$
$12$		0			0
$13$	0.664877	−	1.38063i	0.184404	−	0.382918i	−0.788189	−	0.615433i	$-0.788981\pi$
$13$	0.664877	−	1.38063i	0.184404	−	0.382918i	0.972593	+	0.232515i	$0.0746955\pi$
$14$		0			0
$15$	1.67226	+	3.47248i	0.431775	+	0.896591i
$16$		0			0
$17$	−4.82102	+	1.89211i	−1.16927	+	0.458905i	−0.868934	−	0.494929i	$-0.835194\pi$
$17$	−4.82102	+	1.89211i	−1.16927	+	0.458905i	−0.300336	+	0.953833i	$0.597099\pi$
$18$		0			0
$19$	0.131720	+	0.228145i	0.0302186	+	0.0523401i	0.880739	−	0.473602i	$-0.157046\pi$
$19$	0.131720	+	0.228145i	0.0302186	+	0.0523401i	−0.850521	+	0.525942i	$0.823713\pi$
$20$		0			0
$21$	1.10418	+	2.54865i	0.240951	+	0.556161i
$22$		0			0
$23$	4.84233	+	1.90047i	1.00970	+	0.396276i	0.811793	−	0.583946i	$-0.198492\pi$
$23$	4.84233	+	1.90047i	1.00970	+	0.396276i	0.197902	+	0.980222i	$0.436587\pi$
$24$		0			0
$25$	−0.633579	+	8.45452i	−0.126716	+	1.69090i
$26$		0			0
$27$	3.20591	+	4.02009i	0.616978	+	0.773666i
$28$		0			0
$29$	3.81637	−	4.78557i	0.708682	−	0.888659i	−0.288957	−	0.957342i	$-0.593308\pi$
$29$	3.81637	−	4.78557i	0.708682	−	0.888659i	0.997639	+	0.0686834i	$0.0218798\pi$
$30$		0			0
$31$	−2.31746	+	4.01395i	−0.416227	+	0.720927i	−0.995556	−	0.0941668i	$-0.969981\pi$
$31$	−2.31746	+	4.01395i	−0.416227	+	0.720927i	0.579329	+	0.815094i	$0.303315\pi$
$32$		0			0
$33$	−0.989399	−	3.20755i	−0.172232	−	0.558363i
$34$		0			0
$35$	−1.11235	+	9.64937i	−0.188021	+	1.63104i
$36$		0			0
$37$	1.04839	+	0.158019i	0.172354	+	0.0259782i	0.234652	−	0.972079i	$-0.424605\pi$
$37$	1.04839	+	0.158019i	0.172354	+	0.0259782i	−0.0622980	+	0.998058i	$0.519843\pi$
$38$		0			0
$39$	−1.09421	+	1.17928i	−0.175214	+	0.188836i
$40$		0			0
$41$	−10.7323	+	2.44957i	−1.67610	+	0.382559i	−0.951750	−	0.306873i	$-0.900717\pi$
$41$	−10.7323	+	2.44957i	−1.67610	+	0.382559i	−0.724350	+	0.689432i	$0.757860\pi$
$42$		0			0
$43$	3.75304	+	0.856607i	0.572333	+	0.130631i	0.498886	−	0.866668i	$-0.333743\pi$
$43$	3.75304	+	0.856607i	0.572333	+	0.130631i	0.0734475	+	0.997299i	$0.476600\pi$
$44$		0			0
$45$	1.03847	+	6.88982i	0.154806	+	1.02707i
$46$		0			0
$47$	0.532135	+	7.10085i	0.0776199	+	1.03577i	0.890991	+	0.454021i	$0.150011\pi$
$47$	0.532135	+	7.10085i	0.0776199	+	1.03577i	−0.813371	+	0.581745i	$0.802370\pi$
$48$		0			0
$49$	−1.07886	+	6.91636i	−0.154123	+	0.988052i
$50$		0			0
$51$	5.42183	−	0.406310i	0.759209	−	0.0568948i
$52$		0			0
$53$	−0.650029	+	0.0979760i	−0.0892883	+	0.0134580i	−0.193534	−	0.981093i	$-0.561995\pi$
$53$	−0.650029	+	0.0979760i	−0.0892883	+	0.0134580i	0.104246	+	0.994552i	$0.466757\pi$
$54$		0			0
$55$	2.61206	−	11.4442i	0.352210	−	1.54313i
$56$		0			0
$57$	−0.0615411	−	0.269629i	−0.00815132	−	0.0357133i
$58$		0			0
$59$	−7.61615	−	7.06676i	−0.991539	−	0.920014i	0.00525816	−	0.999986i	$-0.498326\pi$
$59$	−7.61615	−	7.06676i	−0.991539	−	0.920014i	−0.996797	+	0.0799725i	$0.974517\pi$
$60$		0			0
$61$	1.80831	−	11.9973i	0.231530	−	1.53610i	−0.507038	−	0.861923i	$-0.669260\pi$
$61$	1.80831	−	11.9973i	0.231530	−	1.53610i	0.738569	−	0.674178i	$-0.235502\pi$
$62$		0			0
$63$	0.549384	+	4.99118i	0.0692158	+	0.628830i
$64$		0			0
$65$	−5.37586	+	1.65823i	−0.666793	+	0.205678i
$66$		0			0
$67$	−3.37430	−	1.94815i	−0.412236	−	0.238005i	0.279514	−	0.960142i	$-0.409827\pi$
$67$	−3.37430	−	1.94815i	−0.412236	−	0.238005i	−0.691750	+	0.722137i	$0.743160\pi$
$68$		0			0
$69$	−4.26963	−	3.40492i	−0.514003	−	0.409904i
$70$		0			0
$71$	−7.90969	+	6.30776i	−0.938707	+	0.748594i	−0.967993	−	0.250977i	$-0.919248\pi$
$71$	−7.90969	+	6.30776i	−0.938707	+	0.748594i	0.0292859	+	0.999571i	$0.490677\pi$
$72$		0			0
$73$	1.99052	+	0.149169i	0.232973	+	0.0174589i	0.190705	−	0.981647i	$-0.438923\pi$
$73$	1.99052	+	0.149169i	0.232973	+	0.0174589i	0.0422679	+	0.999106i	$0.486542\pi$
$74$		0			0
$75$	3.25175	−	8.28533i	0.375480	−	0.956707i
$76$		0			0
$77$	2.21048	−	8.16561i	0.251907	−	0.930557i
$78$		0			0
$79$	−10.5737	+	6.10473i	−1.18963	+	0.686835i	−0.958223	−	0.286021i	$-0.907667\pi$
$79$	−10.5737	+	6.10473i	−1.18963	+	0.686835i	−0.231410	+	0.972856i	$0.574334\pi$
$80$		0			0
$81$	0.107999	+	0.275176i	0.0119998	+	0.0305751i
$82$		0			0
$83$	8.11176	−	3.90642i	0.890381	−	0.428785i	0.0679759	−	0.997687i	$-0.478346\pi$
$83$	8.11176	−	3.90642i	0.890381	−	0.428785i	0.822405	+	0.568902i	$0.192632\pi$
$84$		0			0
$85$	17.1307	+	8.24970i	1.85808	+	0.894806i
$86$		0			0
$87$	−5.30934	+	3.61984i	−0.569221	+	0.388088i
$88$		0			0
$89$	−2.98889	+	4.38389i	−0.316821	+	0.464691i	−0.951308	−	0.308242i	$-0.900259\pi$
$89$	−2.98889	+	4.38389i	−0.316821	+	0.464691i	0.634487	+	0.772934i	$0.281212\pi$
$90$		0			0
$91$	−3.91885	+	1.03926i	−0.410807	+	0.108944i
$92$		0			0
$93$	3.56689	−	3.30959i	0.369870	−	0.343189i
$94$		0			0
$95$	0.285075	−	0.924190i	0.0292480	−	0.0948198i
$96$		0			0
$97$		−	7.53069i		−	0.764626i	−0.924033	−	0.382313i	$-0.875128\pi$
$97$		−	7.53069i		−	0.764626i	0.924033	−	0.382313i	$-0.124872\pi$
$98$		0			0
$99$		−	6.06828i		−	0.609885i
$100$		0			0
$101$	−5.56751	+	18.0494i	−0.553988	+	1.79598i	0.0497006	+	0.998764i	$0.484173\pi$
$101$	−5.56751	+	18.0494i	−0.553988	+	1.79598i	−0.603688	+	0.797220i	$0.706303\pi$
$102$		0			0
$103$	5.44924	−	5.05616i	0.536930	−	0.498198i	−0.364453	−	0.931222i	$-0.618744\pi$
$103$	5.44924	−	5.05616i	0.536930	−	0.498198i	0.901382	+	0.433024i	$0.142553\pi$
$104$		0			0
$105$	4.10177	−	9.33582i	0.400292	−	0.911083i
$106$		0			0
$107$	−8.66939	+	12.7157i	−0.838101	+	1.22927i	0.133123	+	0.991100i	$0.457500\pi$
$107$	−8.66939	+	12.7157i	−0.838101	+	1.22927i	−0.971224	+	0.238169i	$0.923453\pi$
$108$		0			0
$109$	−0.806043	+	0.549551i	−0.0772049	+	0.0526374i	−0.601307	−	0.799018i	$-0.705353\pi$
$109$	−0.806043	+	0.549551i	−0.0772049	+	0.0526374i	0.524102	+	0.851655i	$0.324401\pi$
$110$		0			0
$111$	−1.00282	−	0.482934i	−0.0951838	−	0.0458381i
$112$		0			0
$113$	8.75049	−	4.21401i	0.823177	−	0.396421i	0.0256251	−	0.999672i	$-0.491842\pi$
$113$	8.75049	−	4.21401i	0.823177	−	0.396421i	0.797552	+	0.603251i	$0.206128\pi$
$114$		0			0
$115$	−6.97715	−	17.7775i	−0.650623	−	1.65776i
$116$		0			0
$117$	−2.51865	+	1.45414i	−0.232849	+	0.134436i
$118$		0			0
$119$	12.0980	+	6.43383i	1.10902	+	0.589788i
$120$		0			0
$121$	0.283749	−	0.722981i	0.0257954	−	0.0657256i
$122$		0			0
$123$	11.5244	+	0.863632i	1.03912	+	0.0778711i
$124$		0			0
$125$	9.98361	−	7.96166i	0.892961	−	0.712113i
$126$		0			0
$127$	−2.74513	−	2.18917i	−0.243591	−	0.194257i	0.494083	−	0.869415i	$-0.335504\pi$
$127$	−2.74513	−	2.18917i	−0.243591	−	0.194257i	−0.737673	+	0.675158i	$0.764075\pi$
$128$		0			0
$129$	−3.49990	−	2.02067i	−0.308149	−	0.177910i
$130$		0			0
$131$	−4.42482	+	1.36488i	−0.386598	+	0.119250i	−0.481961	−	0.876193i	$-0.660075\pi$
$131$	−4.42482	+	1.36488i	−0.386598	+	0.119250i	0.0953623	+	0.995443i	$0.469599\pi$
$132$		0			0
$133$	0.231893	−	0.657288i	0.0201077	−	0.0569941i
$134$		0			0
$135$	2.81351	−	18.6664i	0.242148	−	1.60655i
$136$		0			0
$137$	−1.37204	−	1.27307i	−0.117221	−	0.108766i	0.619384	−	0.785088i	$-0.287382\pi$
$137$	−1.37204	−	1.27307i	−0.117221	−	0.108766i	−0.736606	+	0.676322i	$0.763573\pi$
$138$		0			0
$139$	−1.14867	−	5.03266i	−0.0974291	−	0.426865i	0.902564	−	0.430555i	$-0.141682\pi$
$139$	−1.14867	−	5.03266i	−0.0974291	−	0.426865i	−0.999993	+	0.00369079i	$0.998825\pi$
$140$		0			0
$141$	1.66346	−	7.28807i	0.140088	−	0.613767i
$142$		0			0
$143$	4.84491	−	0.730253i	0.405152	−	0.0610668i
$144$		0			0
$145$	−22.4089	+	1.67932i	−1.86096	+	0.139460i
$146$		0			0
$147$	3.22248	−	6.60449i	0.265786	−	0.544729i
$148$		0			0
$149$	1.61314	+	21.5259i	0.132154	+	1.76347i	0.531866	+	0.846828i	$0.321491\pi$
$149$	1.61314	+	21.5259i	0.132154	+	1.76347i	−0.399712	+	0.916641i	$0.630890\pi$
$150$		0			0
$151$	−2.87079	−	19.0465i	−0.233622	−	1.54998i	−0.730959	−	0.682422i	$-0.760927\pi$
$151$	−2.87079	−	19.0465i	−0.233622	−	1.54998i	0.497337	−	0.867558i	$-0.334311\pi$
$152$		0			0
$153$	9.58276	+	2.18720i	0.774720	+	0.176825i
$154$		0			0
$155$	16.5894	−	3.78642i	1.33249	−	0.304133i
$156$		0			0
$157$	11.5284	−	12.4246i	0.920064	−	0.991593i	−0.0799226	−	0.996801i	$-0.525467\pi$
$157$	11.5284	−	12.4246i	0.920064	−	0.991593i	0.999986	+	0.00520806i	$0.00165779\pi$
$158$		0			0
$159$	0.682411	+	0.102857i	0.0541187	+	0.00815709i
$160$		0			0
$161$	−4.51222	−	13.0023i	−0.355613	−	1.02472i
$162$		0			0
$163$	6.89567	+	22.3552i	0.540111	+	1.75100i	0.652969	+	0.757384i	$0.273523\pi$
$163$	6.89567	+	22.3552i	0.540111	+	1.75100i	−0.112859	+	0.993611i	$0.536001\pi$
$164$		0			0
$165$	−6.16164	+	10.6723i	−0.479683	+	0.830836i
$166$		0			0
$167$	0.362227	−	0.454218i	0.0280300	−	0.0351485i	−0.767619	−	0.640907i	$-0.778559\pi$
$167$	0.362227	−	0.454218i	0.0280300	−	0.0351485i	0.795649	+	0.605758i	$0.207130\pi$
$168$		0			0
$169$	6.64129	+	8.32791i	0.510868	+	0.640609i
$170$		0			0
$171$	0.0373634	−	0.498579i	0.00285725	−	0.0381273i
$172$		0			0
$173$	−1.87488	−	0.735835i	−0.142544	−	0.0559445i	0.292996	−	0.956114i	$-0.405348\pi$
$173$	−1.87488	−	0.735835i	−0.142544	−	0.0559445i	−0.435541	+	0.900169i	$0.643443\pi$
$174$		0			0
$175$	18.0823	−	13.2737i	1.36690	−	1.00340i
$176$		0			0
$177$	5.45362	+	9.44595i	0.409919	+	0.710001i
$178$		0			0
$179$	−17.1978	+	6.74965i	−1.28543	+	0.504493i	−0.906997	−	0.421137i	$-0.861631\pi$
$179$	−17.1978	+	6.74965i	−1.28543	+	0.504493i	−0.378430	+	0.925630i	$0.623536\pi$
$180$		0			0
$181$	−7.84862	−	16.2978i	−0.583384	−	1.21141i	−0.958675	−	0.284502i	$-0.908172\pi$
$181$	−7.84862	−	16.2978i	−0.583384	−	1.21141i	0.375292	−	0.926907i	$-0.377542\pi$
$182$		0			0
$183$	−5.52650	+	11.4759i	−0.408531	+	0.848322i
$184$		0			0
$185$	−2.19267	−	3.21605i	−0.161208	−	0.236449i
$186$		0			0
$187$	−13.6820	−	9.32824i	−1.00053	−	0.682149i
$188$		0			0
$189$	2.56352	−	13.3604i	0.186468	−	0.971828i
$190$		0			0
$191$	−15.6031	−	16.8161i	−1.12900	−	1.21677i	−0.973440	−	0.228943i	$-0.926473\pi$
$191$	−15.6031	−	16.8161i	−1.12900	−	1.21677i	−0.155557	−	0.987827i	$-0.549717\pi$
$192$		0			0
$193$	−23.3806	−	7.21196i	−1.68297	−	0.519128i	−0.701819	−	0.712355i	$-0.747628\pi$
$193$	−23.3806	−	7.21196i	−1.68297	−	0.519128i	−0.981154	+	0.193227i	$0.938105\pi$
$194$		0			0
$195$	5.90606			0.422942
$196$		0			0
$197$	−7.60236			−0.541646			−0.270823	−	0.962629i	$-0.587296\pi$
$197$	−7.60236			−0.541646			−0.270823	+	0.962629i	$0.587296\pi$
$198$		0			0
$199$	21.2909	+	6.56737i	1.50927	+	0.465549i	0.935458	−	0.353437i	$-0.114987\pi$
$199$	21.2909	+	6.56737i	1.50927	+	0.465549i	0.573814	+	0.818986i	$0.305463\pi$
$200$		0			0
$201$	2.78219	+	2.99848i	0.196240	+	0.211497i
$202$		0			0
$203$	−16.1848	+	0.563938i	−1.13595	+	0.0395807i
$204$		0			0
$205$	33.3919	+	22.7662i	2.33219	+	1.59006i
$206$		0			0
$207$	−5.56145	−	8.15715i	−0.386548	−	0.566961i
$208$		0			0
$209$	−0.365469	+	0.758904i	−0.0252800	+	0.0524945i
$210$		0			0
$211$	−6.19544	−	12.8650i	−0.426511	−	0.885660i	−0.997887	−	0.0649714i	$-0.979304\pi$
$211$	−6.19544	−	12.8650i	−0.426511	−	0.885660i	0.571376	−	0.820689i	$-0.306410\pi$
$212$		0			0
$213$	9.88669	−	3.88024i	0.677425	−	0.265870i
$214$		0			0
$215$	−7.06638	−	12.2393i	−0.481923	−	0.834716i
$216$		0			0
$217$	12.0549	−	2.24883i	0.818337	−	0.152660i
$218$		0			0
$219$	−1.95069	−	0.765588i	−0.131815	−	0.0517336i
$220$		0			0
$221$	−0.593078	+	7.91408i	−0.0398947	+	0.532358i
$222$		0			0
$223$	−1.39957	−	1.75500i	−0.0937219	−	0.117523i	0.732759	−	0.680488i	$-0.238232\pi$
$223$	−1.39957	−	1.75500i	−0.0937219	−	0.117523i	−0.826481	+	0.562965i	$0.809661\pi$
$224$		0			0
$225$	10.0324	−	12.5802i	0.668825	−	0.838680i
$226$		0			0
$227$	−11.7293	+	20.3158i	−0.778502	+	1.34841i	0.154302	+	0.988024i	$0.450687\pi$
$227$	−11.7293	+	20.3158i	−0.778502	+	1.34841i	−0.932805	+	0.360382i	$0.882646\pi$
$228$		0			0
$229$	−0.271250	−	0.879372i	−0.0179247	−	0.0581105i	0.946169	−	0.323674i	$-0.104918\pi$
$229$	−0.271250	−	0.879372i	−0.0179247	−	0.0581105i	−0.964093	+	0.265564i	$0.914442\pi$
$230$		0			0
$231$	−4.74426	+	7.50754i	−0.312149	+	0.493960i
$232$		0			0
$233$	14.3665	+	2.16541i	0.941182	+	0.141860i	0.601673	−	0.798742i	$-0.294501\pi$
$233$	14.3665	+	2.16541i	0.941182	+	0.141860i	0.339509	+	0.940603i	$0.389739\pi$
$234$		0			0
$235$	17.7812	−	19.1636i	1.15992	−	1.25010i
$236$		0			0
$237$	12.4963	−	2.85221i	0.811724	−	0.185271i
$238$		0			0
$239$	−10.9930	−	2.50909i	−0.711081	−	0.162300i	−0.148344	−	0.988936i	$-0.547394\pi$
$239$	−10.9930	−	2.50909i	−0.711081	−	0.162300i	−0.562737	+	0.826636i	$0.690252\pi$
$240$		0			0
$241$	2.89796	+	19.2267i	0.186674	+	1.23850i	0.864255	+	0.503054i	$0.167790\pi$
$241$	2.89796	+	19.2267i	0.186674	+	1.23850i	−0.677581	+	0.735449i	$0.736971\pi$
$242$		0			0
$243$	−1.17595	−	15.6920i	−0.0754373	−	1.00664i
$244$		0			0
$245$	21.3076	−	14.3674i	1.36129	−	0.917897i
$246$		0			0
$247$	0.402562	−	0.0301678i	0.0256144	−	0.00191953i
$248$		0			0
$249$	−9.34633	+	1.40873i	−0.592300	+	0.0892748i
$250$		0			0
$251$	−4.54979	+	19.9339i	−0.287180	+	1.25822i	0.601196	+	0.799102i	$0.294691\pi$
$251$	−4.54979	+	19.9339i	−0.287180	+	1.25822i	−0.888376	+	0.459116i	$0.848166\pi$
$252$		0			0
$253$	3.70110	+	16.2156i	0.232686	+	1.01946i
$254$		0			0
$255$	−14.6323	−	13.5768i	−0.916312	−	0.850213i
$256$		0			0
$257$	0.170169	−	1.12900i	0.0106148	−	0.0704248i	−0.982896	−	0.184160i	$-0.941043\pi$
$257$	0.170169	−	1.12900i	0.0106148	−	0.0704248i	0.993511	+	0.113735i	$0.0362816\pi$
$258$		0			0
$259$	−1.48630	−	2.37898i	−0.0923541	−	0.147823i
$260$		0			0
$261$	−11.1008	+	3.42414i	−0.687122	+	0.211949i
$262$		0			0
$263$	−11.0249	−	6.36524i	−0.679825	−	0.392497i	0.119964	−	0.992778i	$-0.461722\pi$
$263$	−11.0249	−	6.36524i	−0.679825	−	0.392497i	−0.799789	+	0.600281i	$0.795055\pi$
$264$		0			0
$265$	1.88686	+	1.50472i	0.115909	+	0.0924343i
$266$		0			0
$267$	4.35493	−	3.47294i	0.266517	−	0.212540i
$268$		0			0
$269$	−8.74339	−	0.655227i	−0.533094	−	0.0399499i	−0.194536	−	0.980895i	$-0.562320\pi$
$269$	−8.74339	−	0.655227i	−0.533094	−	0.0399499i	−0.338558	+	0.940946i	$0.609939\pi$
$270$		0			0
$271$	−2.96433	+	7.55298i	−0.180070	+	0.458811i	−0.992199	−	0.124668i	$-0.960214\pi$
$271$	−2.96433	+	7.55298i	−0.180070	+	0.458811i	0.812129	+	0.583479i	$0.198309\pi$
$272$		0			0
$273$	4.25288	+	0.170079i	0.257396	+	0.0102936i
$274$		0			0
$275$	−23.4764	+	13.5541i	−1.41568	+	0.817344i
$276$		0			0
$277$	−7.53446	−	19.1975i	−0.452702	−	1.15347i	−0.957039	−	0.289959i	$-0.906358\pi$
$277$	−7.53446	−	19.1975i	−0.452702	−	1.15347i	0.504337	−	0.863507i	$-0.331737\pi$
$278$		0			0
$279$	7.92539	−	3.81667i	0.474481	−	0.228498i
$280$		0			0
$281$	−14.3628	−	6.91674i	−0.856810	−	0.412618i	−0.0467093	−	0.998909i	$-0.514873\pi$
$281$	−14.3628	−	6.91674i	−0.856810	−	0.412618i	−0.810101	+	0.586290i	$0.800588\pi$
$282$		0			0
$283$	−8.57824	+	5.84855i	−0.509924	+	0.347660i	−0.790791	−	0.612087i	$-0.790330\pi$
$283$	−8.57824	+	5.84855i	−0.509924	+	0.347660i	0.280867	+	0.959747i	$0.409378\pi$
$284$		0			0
$285$	−0.571961	+	0.838912i	−0.0338800	+	0.0496929i
$286$		0			0
$287$	23.3895	+	17.3553i	1.38064	+	1.02445i
$288$		0			0
$289$	7.20030	−	6.68090i	0.423547	−	0.392994i
$290$		0			0
$291$	−2.33029	+	7.55462i	−0.136604	+	0.442860i
$292$		0			0
$293$		−	6.61901i		−	0.386686i	−0.981131	−	0.193343i	$-0.938067\pi$
$293$		−	6.61901i		−	0.386686i	0.981131	−	0.193343i	$-0.0619331\pi$
$294$		0			0
$295$			38.1432i			2.22078i
$296$		0			0
$297$	−4.84596	+	15.7102i	−0.281191	+	0.911599i
$298$		0			0
$299$	5.84340	−	5.42189i	0.337933	−	0.313556i
$300$		0			0
$301$	−4.73596	−	9.01689i	−0.272976	−	0.519725i
$302$		0			0
$303$	11.1704	−	16.3840i	0.641722	−	0.941234i
$304$		0			0
$305$	−36.8031	+	25.0920i	−2.10734	+	1.43676i
$306$		0			0
$307$	26.4649	+	12.7448i	1.51043	+	0.727384i	0.991822	−	0.127628i	$-0.0407364\pi$
$307$	26.4649	+	12.7448i	1.51043	+	0.727384i	0.518607	+	0.855013i	$0.326451\pi$
$308$		0			0
$309$	−7.03113	+	3.38601i	−0.399987	+	0.192624i
$310$		0			0
$311$	−2.49904	−	6.36746i	−0.141708	−	0.361066i	0.842346	−	0.538937i	$-0.181174\pi$
$311$	−2.49904	−	6.36746i	−0.141708	−	0.361066i	−0.984054	+	0.177872i	$0.943079\pi$
$312$		0			0
$313$	−28.6332	+	16.5314i	−1.61844	+	0.934409i	−0.631121	+	0.775684i	$0.717405\pi$
$313$	−28.6332	+	16.5314i	−1.61844	+	0.934409i	−0.987323	+	0.158725i	$0.949262\pi$
$314$		0			0
$315$	12.0606	−	13.9420i	0.679536	−	0.785542i
$316$		0			0
$317$	7.15824	−	18.2389i	0.402047	−	1.02440i	−0.576265	−	0.817263i	$-0.695490\pi$
$317$	7.15824	−	18.2389i	0.402047	−	1.02440i	0.978312	−	0.207136i	$-0.0664143\pi$
$318$		0			0
$319$	19.5165	+	1.46256i	1.09271	+	0.0818874i
$320$		0			0
$321$	12.6317	−	10.0734i	0.705030	−	0.562243i
$322$		0			0
$323$	−1.06670	−	0.850665i	−0.0593528	−	0.0473323i
$324$		0			0
$325$	11.2513	+	6.49595i	0.624111	+	0.360331i
$326$		0			0
$327$	0.978657	−	0.301876i	0.0541198	−	0.0166938i
$328$		0			0
$329$	13.3559	−	13.2874i	0.736336	−	0.732560i
$330$		0			0
$331$	−1.93431	+	12.8333i	−0.106320	+	0.705384i	0.870634	+	0.491931i	$0.163709\pi$
$331$	−1.93431	+	12.8333i	−0.106320	+	0.705384i	−0.976953	+	0.213452i	$0.931529\pi$
$332$		0			0
$333$	−1.47504	−	1.36864i	−0.0808319	−	0.0750011i
$334$		0			0
$335$	3.18303	+	13.9457i	0.173907	+	0.761938i
$336$		0			0
$337$	−6.78563	+	29.7298i	−0.369637	+	1.61948i	0.358139	+	0.933668i	$0.383411\pi$
$337$	−6.78563	+	29.7298i	−0.369637	+	1.61948i	−0.727775	+	0.685816i	$0.759446\pi$
$338$		0			0
$339$	−10.0823	+	1.51966i	−0.547594	+	0.0825365i
$340$		0			0
$341$	−14.7782	+	1.10747i	−0.800285	+	0.0599730i
$342$		0			0
$343$	15.7571	−	9.73217i	0.850801	−	0.525488i
$344$		0			0
$345$	1.49827	+	19.9930i	0.0806640	+	1.07639i
$346$		0			0
$347$	−3.41652	−	22.6671i	−0.183408	−	1.21683i	−0.871201	−	0.490927i	$-0.836658\pi$
$347$	−3.41652	−	22.6671i	−0.183408	−	1.21683i	0.687792	−	0.725907i	$-0.258580\pi$
$348$		0			0
$349$	−20.1243	−	4.59324i	−1.07723	−	0.245870i	−0.353135	−	0.935572i	$-0.614884\pi$
$349$	−20.1243	−	4.59324i	−1.07723	−	0.245870i	−0.724093	+	0.689702i	$0.757741\pi$
$350$		0			0
$351$	7.68179	−	1.75332i	0.410024	−	0.0935852i
$352$		0			0
$353$	−10.0083	+	10.7864i	−0.532691	+	0.574104i	−0.940857	−	0.338804i	$-0.889978\pi$
$353$	−10.0083	+	10.7864i	−0.532691	+	0.574104i	0.408167	+	0.912907i	$0.366168\pi$
$354$		0			0
$355$	36.7269	+	5.53569i	1.94926	+	0.293804i
$356$		0			0
$357$	−10.1456	−	10.1979i	−0.536961	−	0.539729i
$358$		0			0
$359$	9.83596	+	31.8874i	0.519122	+	1.68295i	0.712371	+	0.701803i	$0.247621\pi$
$359$	9.83596	+	31.8874i	0.519122	+	1.68295i	−0.193249	+	0.981150i	$0.561903\pi$
$360$		0			0
$361$	9.46530	−	16.3944i	0.498174	−	0.862862i
$362$		0			0
$363$	−0.508369	+	0.637475i	−0.0266825	+	0.0334588i
$364$		0			0
$365$	−4.56908	−	5.72944i	−0.239156	−	0.299893i
$366$		0			0
$367$	−2.13872	+	28.5392i	−0.111640	+	1.48973i	0.607196	+	0.794552i	$0.292294\pi$
$367$	−2.13872	+	28.5392i	−0.111640	+	1.48973i	−0.718836	+	0.695180i	$0.755325\pi$
$368$		0			0
$369$	19.4482	+	7.63286i	1.01243	+	0.397351i
$370$		0			0
$371$	1.31537	+	1.13787i	0.0682908	+	0.0590752i
$372$		0			0
$373$	−6.23279	−	10.7955i	−0.322722	−	0.558970i	0.658327	−	0.752732i	$-0.271264\pi$
$373$	−6.23279	−	10.7955i	−0.322722	−	0.558970i	−0.981049	+	0.193762i	$0.937931\pi$
$374$		0			0
$375$	−12.4790	+	4.89764i	−0.644412	+	0.252913i
$376$		0			0
$377$	−4.06970	−	8.45081i	−0.209600	−	0.435239i
$378$		0			0
$379$	−14.5234	+	30.1582i	−0.746019	+	1.54912i	0.0872059	+	0.996190i	$0.472206\pi$
$379$	−14.5234	+	30.1582i	−0.746019	+	1.54912i	−0.833225	+	0.552934i	$0.813508\pi$
$380$		0			0
$381$	2.07643	+	3.04557i	0.106379	+	0.156029i
$382$		0			0
$383$	13.7722	+	9.38976i	0.703729	+	0.479794i	0.861549	−	0.507674i	$-0.169494\pi$
$383$	13.7722	+	9.38976i	0.703729	+	0.479794i	−0.157821	+	0.987468i	$0.550447\pi$
$384$		0			0
$385$	−27.4953	+	14.4414i	−1.40129	+	0.736002i
$386$		0			0
$387$	−4.96935	−	5.35568i	−0.252606	−	0.272245i
$388$		0			0
$389$	6.29611	+	1.94209i	0.319225	+	0.0984680i	0.450227	−	0.892914i	$-0.351343\pi$
$389$	6.29611	+	1.94209i	0.319225	+	0.0984680i	−0.131002	+	0.991382i	$0.541819\pi$
$390$		0			0
$391$	−26.9409			−1.36246
$392$		0			0
$393$	4.86122			0.245216
$394$		0			0
$395$	42.8328	+	13.2122i	2.15515	+	0.664776i
$396$		0			0
$397$	−8.56772	−	9.23381i	−0.430002	−	0.463431i	0.480465	−	0.877014i	$-0.340468\pi$
$397$	−8.56772	−	9.23381i	−0.430002	−	0.463431i	−0.910467	+	0.413582i	$0.864277\pi$
$398$		0			0
$399$	−0.436021	+	0.587620i	−0.0218283	+	0.0294178i
$400$		0			0
$401$	4.15626	+	2.83369i	0.207554	+	0.141508i	0.662636	−	0.748942i	$-0.269438\pi$
$401$	4.15626	+	2.83369i	0.207554	+	0.141508i	−0.455082	+	0.890449i	$0.650390\pi$
$402$		0			0
$403$	4.00096	+	5.86833i	0.199302	+	0.292323i
$404$		0			0
$405$	0.470879	−	0.977791i	0.0233982	−	0.0485868i
$406$		0			0
$407$	1.47086	+	3.05427i	0.0729077	+	0.151394i
$408$		0			0
$409$	9.91117	−	3.88985i	0.490076	−	0.192341i	−0.107418	−	0.994214i	$-0.534258\pi$
$409$	9.91117	−	3.88985i	0.490076	−	0.192341i	0.597494	+	0.801873i	$0.296163\pi$
$410$		0			0
$411$	0.982463	+	1.70168i	0.0484613	+	0.0839375i
$412$		0			0
$413$	−1.09842	+	27.4665i	−0.0540499	+	1.35154i
$414$		0			0
$415$	−30.7689	−	12.0759i	−1.51039	−	0.592783i
$416$		0			0
$417$	−0.404981	+	5.40409i	−0.0198320	+	0.264640i
$418$		0			0
$419$	−2.50452	−	3.14057i	−0.122354	−	0.153427i	0.716882	−	0.697195i	$-0.245569\pi$
$419$	−2.50452	−	3.14057i	−0.122354	−	0.153427i	−0.839236	+	0.543768i	$0.816997\pi$
$420$		0			0
$421$	9.88691	−	12.3978i	0.481859	−	0.604232i	−0.480171	−	0.877175i	$-0.659426\pi$
$421$	9.88691	−	12.3978i	0.481859	−	0.604232i	0.962030	+	0.272943i	$0.0879970\pi$
$422$		0			0
$423$	6.75719	−	11.7038i	0.328546	−	0.569058i
$424$		0			0
$425$	−12.9424	−	41.9582i	−0.627799	−	2.03527i
$426$		0			0
$427$	−27.2241	+	17.0086i	−1.31747	+	0.823103i
$428$		0			0
$429$	−5.08627	−	0.766632i	−0.245568	−	0.0370134i
$430$		0			0
$431$	−15.6328	+	16.8481i	−0.753003	+	0.811545i	−0.987005	−	0.160692i	$-0.948627\pi$
$431$	−15.6328	+	16.8481i	−0.753003	+	0.811545i	0.234001	+	0.972236i	$0.424818\pi$
$432$		0			0
$433$	−18.9246	+	4.31941i	−0.909458	+	0.207578i	−0.651562	−	0.758595i	$-0.725886\pi$
$433$	−18.9246	+	4.31941i	−0.909458	+	0.207578i	−0.257895	+	0.966173i	$0.583029\pi$
$434$		0			0
$435$	22.9998	+	5.24955i	1.10275	+	0.251697i
$436$		0			0
$437$	0.204246	+	1.35508i	0.00977041	+	0.0648225i
$438$		0			0
$439$	−1.63694	−	21.8434i	−0.0781269	−	1.04253i	−0.889180	−	0.457558i	$-0.848724\pi$
$439$	−1.63694	−	21.8434i	−0.0781269	−	1.04253i	0.811053	−	0.584973i	$-0.198895\pi$
$440$		0			0
$441$	9.08616	−	9.69215i	0.432674	−	0.461531i
$442$		0			0
$443$	22.0186	−	1.65006i	1.04613	−	0.0783968i	0.459442	−	0.888208i	$-0.348049\pi$
$443$	22.0186	−	1.65006i	1.04613	−	0.0783968i	0.586691	+	0.809811i	$0.300430\pi$
$444$		0			0
$445$	19.2616	−	2.90322i	0.913088	−	0.137626i
$446$		0			0
$447$	5.04268	−	22.0934i	0.238511	−	1.04498i
$448$		0			0
$449$	−5.33581	−	23.3777i	−0.251813	−	1.10326i	−0.929764	−	0.368156i	$-0.879989\pi$
$449$	−5.33581	−	23.3777i	−0.251813	−	1.10326i	0.677951	−	0.735107i	$-0.262868\pi$
$450$		0			0
$451$	−25.8018	−	23.9406i	−1.21496	−	1.12732i
$452$		0			0
$453$	−3.01381	+	19.9953i	−0.141601	+	0.939462i
$454$		0			0
$455$	12.5826	+	7.95138i	0.589883	+	0.372766i
$456$		0			0
$457$	8.77541	−	2.70686i	0.410496	−	0.126621i	−0.0826275	−	0.996581i	$-0.526331\pi$
$457$	8.77541	−	2.70686i	0.410496	−	0.126621i	0.493124	+	0.869959i	$0.335855\pi$
$458$		0			0
$459$	−23.0622	−	13.3150i	−1.07645	−	0.621490i
$460$		0			0
$461$	−19.4702	−	15.5270i	−0.906817	−	0.723163i	0.0545267	−	0.998512i	$-0.482635\pi$
$461$	−19.4702	−	15.5270i	−0.906817	−	0.723163i	−0.961344	+	0.275349i	$0.911206\pi$
$462$		0			0
$463$	8.67733	−	6.91994i	0.403270	−	0.321597i	−0.400763	−	0.916182i	$-0.631255\pi$
$463$	8.67733	−	6.91994i	0.403270	−	0.321597i	0.804033	+	0.594585i	$0.202684\pi$
$464$		0			0
$465$	−17.8138	−	1.33496i	−0.826093	−	0.0619071i
$466$		0			0
$467$	−5.15642	+	13.1383i	−0.238611	+	0.607970i	−0.999146	−	0.0413268i	$-0.986842\pi$
$467$	−5.15642	+	13.1383i	−0.238611	+	0.607970i	0.760535	+	0.649297i	$0.224937\pi$
$468$		0			0
$469$	1.89046	+	10.1338i	0.0872933	+	0.467937i
$470$		0			0
$471$	−15.4097	+	8.89677i	−0.710040	+	0.409942i
$472$		0			0
$473$	4.49682	+	11.4577i	0.206764	+	0.526826i
$474$		0			0
$475$	−2.01231	+	0.969079i	−0.0923313	+	0.0444644i
$476$		0			0
$477$	1.12406	+	0.541319i	0.0514672	+	0.0247853i
$478$		0			0
$479$	−16.5947	+	11.3140i	−0.758229	+	0.516952i	−0.879634	−	0.475651i	$-0.842212\pi$
$479$	−16.5947	+	11.3140i	−0.758229	+	0.516952i	0.121405	+	0.992603i	$0.461260\pi$
$480$		0			0
$481$	0.915217	−	1.34238i	0.0417303	−	0.0612071i
$482$		0			0
$483$	0.503139	+	14.4399i	0.0228936	+	0.657036i
$484$		0			0
$485$	−20.2668	+	18.8049i	−0.920270	+	0.853886i
$486$		0			0
$487$	−9.71986	+	31.5110i	−0.440449	+	1.42790i	0.414909	+	0.909863i	$0.363813\pi$
$487$	−9.71986	+	31.5110i	−0.440449	+	1.42790i	−0.855358	+	0.518037i	$0.826663\pi$
$488$		0			0
$489$		−	24.5600i		−	1.11064i
$490$		0			0
$491$		−	11.7405i		−	0.529840i	−0.964270	−	0.264920i	$-0.914654\pi$
$491$		−	11.7405i		−	0.529840i	0.964270	−	0.264920i	$-0.0853455\pi$
$492$		0			0
$493$	−9.34396	+	30.2924i	−0.420831	+	1.36430i
$494$		0			0
$495$	−16.3312	+	15.1531i	−0.734031	+	0.681081i
$496$		0			0
$497$	26.2872	+	5.04382i	1.17914	+	0.226246i
$498$		0			0
$499$	6.19878	−	9.09194i	0.277495	−	0.407011i	−0.662037	−	0.749471i	$-0.730308\pi$
$499$	6.19878	−	9.09194i	0.277495	−	0.407011i	0.939532	+	0.342460i	$0.111260\pi$
$500$		0			0
$501$	−0.503931	+	0.343574i	−0.0225140	+	0.0153498i
$502$		0			0
$503$	−0.275391	−	0.132621i	−0.0122791	−	0.00591328i	0.427734	−	0.903905i	$-0.359312\pi$
$503$	−0.275391	−	0.132621i	−0.0122791	−	0.00591328i	−0.440013	+	0.897991i	$0.645026\pi$
$504$		0			0
$505$	62.4778	−	30.0877i	2.78023	−	1.33889i
$506$		0			0
$507$	−4.08541	−	10.4094i	−0.181439	−	0.462300i
$508$		0			0
$509$	22.6100	−	13.0539i	1.00217	−	0.578603i	0.0932807	−	0.995640i	$-0.470265\pi$
$509$	22.6100	−	13.0539i	1.00217	−	0.578603i	0.908890	+	0.417036i	$0.136931\pi$
$510$		0			0
$511$	−3.12515	−	4.25728i	−0.138248	−	0.188331i
$512$		0			0
$513$	−0.494882	+	1.26094i	−0.0218496	+	0.0556718i
$514$		0			0
$515$	−27.2146	−	2.03945i	−1.19922	−	0.0898690i
$516$		0			0
$517$	−17.8006	+	14.1955i	−0.782872	+	0.624319i
$518$		0			0
$519$	1.65314	+	1.31833i	0.0725647	+	0.0578684i
$520$		0			0
$521$	−23.4070	−	13.5141i	−1.02548	−	0.592062i	−0.109794	−	0.993954i	$-0.535019\pi$
$521$	−23.4070	−	13.5141i	−1.02548	−	0.592062i	−0.915687	+	0.401893i	$0.868352\pi$
$522$		0			0
$523$	31.1175	−	9.59848i	1.36067	−	0.419712i	0.473356	−	0.880871i	$-0.343042\pi$
$523$	31.1175	−	9.59848i	1.36067	−	0.419712i	0.887317	+	0.461159i	$0.152566\pi$
$524$		0			0
$525$	−22.2472	+	7.72050i	−0.970947	+	0.336950i
$526$		0			0
$527$	3.57766	−	23.7362i	0.155845	−	1.03397i
$528$		0			0
$529$	2.97614	+	2.76146i	0.129397	+	0.120063i
$530$		0			0
$531$	4.38775	+	19.2240i	0.190412	+	0.834249i
$532$		0			0
$533$	−3.75369	+	16.4460i	−0.162590	+	0.712355i
$534$		0			0
$535$	55.8691	−	8.42091i	2.41543	−	0.364068i
$536$		0			0
$537$	19.3411	−	1.44941i	0.834629	−	0.0625468i
$538$		0			0
$539$	−20.2149	+	9.60730i	−0.870718	+	0.413816i
$540$		0			0
$541$	0.942710	+	12.5796i	0.0405303	+	0.540839i	0.980103	+	0.198489i	$0.0636035\pi$
$541$	0.942710	+	12.5796i	0.0405303	+	0.540839i	−0.939573	+	0.342349i	$0.888777\pi$
$542$		0			0
$543$	2.83037	+	18.7783i	0.121463	+	0.805853i
$544$		0			0
$545$	3.49174	+	0.796967i	0.149570	+	0.0341383i
$546$		0			0
$547$	14.6089	−	3.33438i	0.624630	−	0.142568i	0.101521	−	0.994833i	$-0.467629\pi$
$547$	14.6089	−	3.33438i	0.624630	−	0.142568i	0.523109	+	0.852266i	$0.324772\pi$
$548$		0			0
$549$	−15.6622	+	16.8798i	−0.668445	+	0.720412i
$550$		0			0
$551$	1.59450	+	0.240332i	0.0679279	+	0.0102385i
$552$		0			0
$553$	30.4629	+	10.7474i	1.29541	+	0.457026i
$554$		0			0
$555$	1.20446	+	3.90477i	0.0511265	+	0.165748i
$556$		0			0
$557$	−7.65436	+	13.2577i	−0.324326	+	0.561749i	−0.981376	−	0.192098i	$-0.938471\pi$
$557$	−7.65436	+	13.2577i	−0.324326	+	0.561749i	0.657050	+	0.753847i	$0.271804\pi$
$558$		0			0
$559$	3.67797	−	4.61202i	0.155561	−	0.195068i
$560$		0			0
$561$	10.8390	+	13.5916i	0.457622	+	0.573839i
$562$		0			0
$563$	−0.202847	+	2.70680i	−0.00854897	+	0.114078i	−0.999846	−	0.0175687i	$-0.994407\pi$
$563$	−0.202847	+	2.70680i	−0.00854897	+	0.114078i	0.991297	+	0.131647i	$0.0420265\pi$
$564$		0			0
$565$	−33.1917	−	13.0268i	−1.39639	−	0.548041i
$566$		0			0
$567$	0.367232	−	0.690536i	0.0154223	−	0.0289998i
$568$		0			0
$569$	−18.6800	−	32.3547i	−0.783106	−	1.35638i	−0.930124	−	0.367245i	$-0.880301\pi$
$569$	−18.6800	−	32.3547i	−0.783106	−	1.35638i	0.147018	−	0.989134i	$-0.453032\pi$
$570$		0			0
$571$	18.0837	−	7.09734i	0.756781	−	0.297015i	0.0445945	−	0.999005i	$-0.485800\pi$
$571$	18.0837	−	7.09734i	0.756781	−	0.297015i	0.712186	+	0.701991i	$0.247705\pi$
$572$		0			0
$573$	10.4491	+	21.6977i	0.436516	+	0.906435i
$574$		0			0
$575$	−19.1356	+	39.7355i	−0.798009	+	1.65708i
$576$		0			0
$577$	2.08338	+	3.05576i	0.0867323	+	0.127213i	0.867153	−	0.498042i	$-0.165947\pi$
$577$	2.08338	+	3.05576i	0.0867323	+	0.127213i	−0.780421	+	0.625255i	$0.784995\pi$
$578$		0			0
$579$	21.2232	+	14.4698i	0.882007	+	0.601342i
$580$		0			0
$581$	−21.8086	−	9.58179i	−0.904773	−	0.397520i
$582$		0			0
$583$	−1.42964	−	1.54078i	−0.0592095	−	0.0638127i
$584$		0			0
$585$	10.2028	+	3.14713i	0.421832	+	0.130118i
$586$		0			0
$587$	−9.18411			−0.379069			−0.189534	−	0.981874i	$-0.560698\pi$
$587$	−9.18411			−0.379069			−0.189534	+	0.981874i	$0.560698\pi$
$588$		0			0
$589$	−1.22102			−0.0503112
$590$		0			0
$591$	7.62651	+	2.35247i	0.313713	+	0.0967676i
$592$		0			0
$593$	9.70139	+	10.4556i	0.398388	+	0.429360i	0.900106	−	0.435671i	$-0.143489\pi$
$593$	9.70139	+	10.4556i	0.398388	+	0.429360i	−0.501718	+	0.865031i	$0.667298\pi$
$594$		0			0
$595$	−12.8950	−	48.6245i	−0.528645	−	1.99341i
$596$		0			0
$597$	−19.3263	−	13.1765i	−0.790975	−	0.539277i
$598$		0			0
$599$	14.1272	+	20.7208i	0.577222	+	0.846629i	0.998171	−	0.0604555i	$-0.0192553\pi$
$599$	14.1272	+	20.7208i	0.577222	+	0.846629i	−0.420949	+	0.907084i	$0.638303\pi$
$600$		0			0
$601$	−1.66073	+	3.44855i	−0.0677427	+	0.140669i	−0.932091	−	0.362225i	$-0.882017\pi$
$601$	−1.66073	+	3.44855i	−0.0677427	+	0.140669i	0.864348	+	0.502894i	$0.167731\pi$
$602$		0			0
$603$	3.20845	+	6.66242i	0.130658	+	0.271315i
$604$		0			0
$605$	−2.65426	+	1.04172i	−0.107911	+	0.0423519i
$606$		0			0
$607$	−14.7890	−	25.6153i	−0.600266	−	1.03969i	−0.992780	−	0.119946i	$-0.961728\pi$
$607$	−14.7890	−	25.6153i	−0.600266	−	1.03969i	0.392514	−	0.919746i	$-0.371605\pi$
$608$		0			0
$609$	16.4107	+	4.44247i	0.664995	+	0.180018i
$610$		0			0
$611$	10.1575	+	3.98651i	0.410927	+	0.161277i
$612$		0			0
$613$	1.05740	−	14.1100i	0.0427080	−	0.569898i	−0.934271	−	0.356563i	$-0.883948\pi$
$613$	1.05740	−	14.1100i	0.0427080	−	0.569898i	0.976979	−	0.213335i	$-0.0684326\pi$
$614$		0			0
$615$	−26.4533	−	33.1713i	−1.06670	−	1.33760i
$616$		0			0
$617$	4.44886	−	5.57870i	0.179104	−	0.224590i	−0.684173	−	0.729320i	$-0.739837\pi$
$617$	4.44886	−	5.57870i	0.179104	−	0.224590i	0.863277	+	0.504730i	$0.168408\pi$
$618$		0			0
$619$	−3.76021	+	6.51287i	−0.151136	+	0.261775i	−0.931645	−	0.363369i	$-0.881626\pi$
$619$	−3.76021	+	6.51287i	−0.151136	+	0.261775i	0.780510	+	0.625144i	$0.214960\pi$
$620$		0			0
$621$	7.88401	+	25.5593i	0.316374	+	1.02566i
$622$		0			0
$623$	13.9537	−	1.53589i	0.559042	−	0.0615342i
$624$		0			0
$625$	−4.43906	−	0.669081i	−0.177562	−	0.0267632i
$626$		0			0
$627$	0.601465	−	0.648225i	0.0240202	−	0.0258876i
$628$		0			0
$629$	−5.35330	+	1.22186i	−0.213450	+	0.0487186i
$630$		0			0
$631$	−34.5167	−	7.87821i	−1.37409	−	0.313626i	−0.529166	−	0.848518i	$-0.677495\pi$
$631$	−34.5167	−	7.87821i	−1.37409	−	0.313626i	−0.844921	+	0.534892i	$0.820352\pi$
$632$		0			0
$633$	2.23420	+	14.8229i	0.0888014	+	0.589159i
$634$		0			0
$635$	0.963299	+	12.8543i	0.0382274	+	0.510109i
$636$		0			0
$637$	8.83163	+	6.08804i	0.349922	+	0.241217i
$638$		0			0
$639$	19.1469	−	1.43487i	0.757442	−	0.0567624i
$640$		0			0
$641$	6.44673	−	0.971687i	0.254630	−	0.0383793i	−0.0204866	−	0.999790i	$-0.506522\pi$
$641$	6.44673	−	0.971687i	0.254630	−	0.0383793i	0.275117	+	0.961411i	$0.411283\pi$
$642$		0			0
$643$	4.47764	−	19.6178i	0.176581	−	0.773652i	−0.806612	−	0.591082i	$-0.798701\pi$
$643$	4.47764	−	19.6178i	0.176581	−	0.773652i	0.983193	−	0.182570i	$-0.0584417\pi$
$644$		0			0
$645$	3.30150	+	14.4648i	0.129997	+	0.569552i
$646$		0			0
$647$	−33.0138	−	30.6323i	−1.29791	−	1.20428i	−0.965279	−	0.261222i	$-0.915875\pi$
$647$	−33.0138	−	30.6323i	−1.29791	−	1.20428i	−0.332627	−	0.943058i	$-0.607935\pi$
$648$		0			0
$649$	4.95116	−	32.8488i	0.194350	−	1.28943i
$650$		0			0
$651$	−12.7890	−	1.47428i	−0.501242	−	0.0577814i
$652$		0			0
$653$	14.6117	−	4.50711i	0.571799	−	0.176377i	0.00464622	−	0.999989i	$-0.498521\pi$
$653$	14.6117	−	4.50711i	0.571799	−	0.176377i	0.567153	+	0.823613i	$0.308045\pi$
$654$		0			0
$655$	14.7224	+	8.49999i	0.575252	+	0.332122i
$656$		0			0
$657$	−2.96187	−	2.36201i	−0.115553	−	0.0921508i
$658$		0			0
$659$	24.5951	−	19.6139i	0.958088	−	0.764049i	−0.0137002	−	0.999906i	$-0.504361\pi$
$659$	24.5951	−	19.6139i	0.958088	−	0.764049i	0.971788	+	0.235857i	$0.0757896\pi$
$660$		0			0
$661$	−9.58705	−	0.718450i	−0.372893	−	0.0279445i	−0.113034	−	0.993591i	$-0.536057\pi$
$661$	−9.58705	−	0.718450i	−0.372893	−	0.0279445i	−0.259859	+	0.965647i	$0.583676\pi$
$662$		0			0
$663$	3.04389	−	7.75570i	0.118215	−	0.301206i
$664$		0			0
$665$	−2.34798	+	1.01724i	−0.0910506	+	0.0394467i
$666$		0			0
$667$	27.5750	−	15.9204i	1.06771	−	0.616441i
$668$		0			0
$669$	0.860947	+	2.19366i	0.0332861	+	0.0848116i
$670$		0			0
$671$	34.9518	−	16.8319i	1.34930	−	0.649787i
$672$		0			0
$673$	16.1053	+	7.75590i	0.620814	+	0.298968i	0.717727	−	0.696325i	$-0.245183\pi$
$673$	16.1053	+	7.75590i	0.620814	+	0.298968i	−0.0969133	+	0.995293i	$0.530897\pi$
$674$		0			0
$675$	−36.0191	+	24.5574i	−1.38638	+	0.945215i
$676$		0			0
$677$	8.97489	−	13.1637i	0.344933	−	0.505924i	−0.614096	−	0.789231i	$-0.710479\pi$
$677$	8.97489	−	13.1637i	0.344933	−	0.505924i	0.959029	+	0.283307i	$0.0914317\pi$
$678$		0			0
$679$	−15.1354	+	12.9575i	−0.580845	+	0.497265i
$680$		0			0
$681$	18.0531	−	16.7508i	0.691796	−	0.641893i
$682$		0			0
$683$	9.24299	−	29.9651i	0.353673	−	1.14658i	−0.587662	−	0.809107i	$-0.699951\pi$
$683$	9.24299	−	29.9651i	0.353673	−	1.14658i	0.941335	−	0.337474i	$-0.109572\pi$
$684$		0			0
$685$			6.87146i			0.262545i
$686$		0			0
$687$			0.966101i			0.0368591i
$688$		0			0
$689$	−0.296920	+	0.962591i	−0.0113118	+	0.0366718i
$690$		0			0
$691$	−14.6046	+	13.5510i	−0.555583	+	0.515506i	−0.907235	−	0.420625i	$-0.861811\pi$
$691$	−14.6046	+	13.5510i	−0.555583	+	0.515506i	0.351651	+	0.936131i	$0.385620\pi$
$692$		0			0
$693$	−12.1962	+	10.4413i	−0.463297	+	0.396631i
$694$		0			0
$695$	−10.6757	+	15.6584i	−0.404953	+	0.593957i
$696$		0			0
$697$	47.1057	−	32.1161i	1.78426	−	1.21649i
$698$		0			0
$699$	−13.7421	−	6.61785i	−0.519774	−	0.250310i
$700$		0			0
$701$	0.460605	−	0.221816i	0.0173968	−	0.00837787i	−0.425165	−	0.905116i	$-0.639784\pi$
$701$	0.460605	−	0.221816i	0.0173968	−	0.00837787i	0.442562	+	0.896738i	$0.354070\pi$
$702$		0			0
$703$	0.102042	+	0.260000i	0.00384860	+	0.00980607i
$704$		0			0
$705$	−23.7677	+	13.7223i	−0.895144	+	0.516811i
$706$		0			0
$707$	45.8560	−	19.8666i	1.72459	−	0.747161i
$708$		0			0
$709$	2.12572	−	5.41626i	0.0798333	−	0.203412i	−0.885384	−	0.464860i	$-0.846105\pi$
$709$	2.12572	−	5.41626i	0.0798333	−	0.203412i	0.965218	+	0.261448i	$0.0842000\pi$
$710$		0			0
$711$	23.1073	+	1.73165i	0.866592	+	0.0649421i
$712$		0			0
$713$	−18.8503	+	15.0326i	−0.705949	+	0.562975i
$714$		0			0
$715$	−14.0635	−	11.2153i	−0.525945	−	0.419427i
$716$		0			0
$717$	10.2516	+	5.91874i	0.382852	+	0.221039i
$718$		0			0
$719$	−15.5960	+	4.81072i	−0.581632	+	0.179410i	−0.571589	−	0.820540i	$-0.693673\pi$
$719$	−15.5960	+	4.81072i	−0.581632	+	0.179410i	−0.0100426	+	0.999950i	$0.503197\pi$
$720$		0			0
$721$	−19.5382	−	2.25229i	−0.727640	−	0.0838798i
$722$		0			0
$723$	3.04233	−	20.1846i	0.113146	−	0.750672i
$724$		0			0
$725$	38.0418	+	35.2976i	1.41284	+	1.31092i
$726$		0			0
$727$	1.57169	+	6.88602i	0.0582907	+	0.255388i	0.995675	−	0.0929098i	$-0.0296168\pi$
$727$	1.57169	+	6.88602i	0.0582907	+	0.255388i	−0.937384	+	0.348298i	$0.886760\pi$
$728$		0			0
$729$	−3.47869	+	15.2411i	−0.128840	+	0.564486i
$730$		0			0
$731$	−19.7143	+	2.97145i	−0.729160	+	0.109903i
$732$		0			0
$733$	31.1702	−	2.33588i	1.15130	−	0.0862777i	0.514627	−	0.857414i	$-0.327931\pi$
$733$	31.1702	−	2.33588i	1.15130	−	0.0862777i	0.636670	+	0.771137i	$0.280311\pi$
$734$		0			0
$735$	−25.8211	+	7.81962i	−0.952425	+	0.288431i
$736$		0			0
$737$	−0.930989	−	12.4232i	−0.0342934	−	0.457614i
$738$		0			0
$739$	−4.45343	−	29.5466i	−0.163822	−	1.08689i	−0.908019	−	0.418929i	$-0.862406\pi$
$739$	−4.45343	−	29.5466i	−0.163822	−	1.08689i	0.744197	−	0.667960i	$-0.232832\pi$
$740$		0			0
$741$	−0.413176	−	0.0943047i	−0.0151784	−	0.00346437i
$742$		0			0
$743$	14.6923	−	3.35341i	0.539007	−	0.123025i	0.0556533	−	0.998450i	$-0.482276\pi$
$743$	14.6923	−	3.35341i	0.539007	−	0.123025i	0.483353	+	0.875425i	$0.339419\pi$
$744$		0			0
$745$	53.9030	−	58.0936i	1.97485	−	2.12838i
$746$		0			0
$747$	−16.8965	−	2.54674i	−0.618211	−	0.0931803i
$748$		0			0
$749$	40.4732	−	4.45491i	1.47886	−	0.162779i
$750$		0			0
$751$	−10.2428	−	33.2062i	−0.373763	−	1.21171i	−0.925839	−	0.377917i	$-0.876640\pi$
$751$	−10.2428	−	33.2062i	−0.373763	−	1.21171i	0.552076	−	0.833794i	$-0.313836\pi$
$752$		0			0
$753$	10.7326	−	18.5894i	0.391117	−	0.677434i
$754$		0			0
$755$	−44.0898	+	55.2869i	−1.60459	+	2.01209i
$756$		0			0
$757$	−26.3084	−	32.9897i	−0.956196	−	1.19903i	−0.979936	−	0.199313i	$-0.936129\pi$
$757$	−26.3084	−	32.9897i	−0.956196	−	1.19903i	0.0237404	−	0.999718i	$-0.492442\pi$
$758$		0			0
$759$	1.30487	−	17.4123i	0.0473640	−	0.632028i
$760$		0			0
$761$	39.7243	+	15.5907i	1.44001	+	0.565161i	0.951568	−	0.307438i	$-0.0994716\pi$
$761$	39.7243	+	15.5907i	1.44001	+	0.565161i	0.488438	+	0.872599i	$0.337567\pi$
$762$		0			0
$763$	2.49141	+	0.674439i	0.0901951	+	0.0244163i
$764$		0			0
$765$	−18.0428	−	31.2511i	−0.652339	−	1.12989i
$766$		0			0
$767$	−14.8204	+	5.81657i	−0.535133	+	0.210024i
$768$		0			0
$769$	8.18815	+	17.0029i	0.295272	+	0.613139i	0.994843	−	0.101424i	$-0.0323399\pi$
$769$	8.18815	+	17.0029i	0.295272	+	0.613139i	−0.699571	+	0.714563i	$0.746626\pi$
$770$		0			0
$771$	−0.520065	+	1.07993i	−0.0187297	+	0.0388926i
$772$		0			0
$773$	−18.1093	−	26.5614i	−0.651345	−	0.955348i	−0.999837	−	0.0180362i	$-0.994259\pi$
$773$	−18.1093	−	26.5614i	−0.651345	−	0.955348i	0.348492	−	0.937312i	$-0.386694\pi$
$774$		0			0
$775$	−32.4677	−	22.1361i	−1.16628	−	0.795153i
$776$		0			0
$777$	0.754871	+	2.84646i	0.0270808	+	0.102116i
$778$		0			0
$779$	−1.97251	−	2.12586i	−0.0706726	−	0.0761669i
$780$		0			0
$781$	−30.9105	−	9.53463i	−1.10606	−	0.341176i
$782$		0			0
$783$	31.4734			1.12477
$784$		0			0
$785$	−62.2250			−2.22091
$786$		0			0
$787$	−14.5188	−	4.47845i	−0.517538	−	0.159639i	0.0249727	−	0.999688i	$-0.492050\pi$
$787$	−14.5188	−	4.47845i	−0.517538	−	0.159639i	−0.542511	+	0.840049i	$0.682526\pi$
$788$		0			0
$789$	9.09029	+	9.79700i	0.323623	+	0.348782i
$790$		0			0
$791$	−23.5258	−	10.3363i	−0.836482	−	0.367515i
$792$		0			0
$793$	−15.3616	−	10.4734i	−0.545506	−	0.371920i
$794$		0			0
$795$	−1.42724	−	2.09337i	−0.0506189	−	0.0742442i
$796$		0			0
$797$	0.473355	−	0.982931i	0.0167671	−	0.0348172i	−0.892417	−	0.451211i	$-0.850992\pi$
$797$	0.473355	−	0.982931i	0.0167671	−	0.0348172i	0.909184	+	0.416394i	$0.136706\pi$
$798$		0			0
$799$	−16.0010	−	33.2265i	−0.566076	−	1.17547i
$800$		0			0
$801$	9.37377	−	3.67893i	0.331206	−	0.129989i
$802$		0			0
$803$	3.19116	+	5.52726i	0.112614	+	0.195053i
$804$		0			0
$805$	−23.7247	+	44.6114i	−0.836186	+	1.57235i
$806$		0			0
$807$	8.56842	+	3.36286i	0.301623	+	0.118378i
$808$		0			0
$809$	−1.22977	+	16.4101i	−0.0432364	+	0.576950i	0.932949	+	0.360010i	$0.117227\pi$
$809$	−1.22977	+	16.4101i	−0.0432364	+	0.576950i	−0.976185	+	0.216940i	$0.930392\pi$
$810$		0			0
$811$	−15.1380	−	18.9824i	−0.531566	−	0.666563i	0.441454	−	0.897284i	$-0.354463\pi$
$811$	−15.1380	−	18.9824i	−0.531566	−	0.666563i	−0.973020	+	0.230721i	$0.925892\pi$
$812$		0			0
$813$	5.31093	−	6.65970i	0.186263	−	0.233566i
$814$		0			0
$815$	42.9439	−	74.3810i	1.50426	−	2.60545i
$816$		0			0
$817$	0.298919	+	0.969071i	0.0104578	+	0.0339035i
$818$		0			0
$819$	7.25625	+	2.56003i	0.253554	+	0.0894545i
$820$		0			0
$821$	20.0745	+	3.02575i	0.700606	+	0.105599i	0.489680	−	0.871902i	$-0.337114\pi$
$821$	20.0745	+	3.02575i	0.700606	+	0.105599i	0.210927	+	0.977502i	$0.432352\pi$
$822$		0			0
$823$	32.5867	−	35.1201i	1.13590	−	1.22421i	0.164599	−	0.986361i	$-0.447367\pi$
$823$	32.5867	−	35.1201i	1.13590	−	1.22421i	0.971302	−	0.237850i	$-0.0764427\pi$
$824$		0			0
$825$	27.7452	−	6.33266i	0.965963	−	0.220475i
$826$		0			0
$827$	17.5228	+	3.99947i	0.609328	+	0.139075i	0.516041	−	0.856564i	$-0.327405\pi$
$827$	17.5228	+	3.99947i	0.609328	+	0.139075i	0.0932874	+	0.995639i	$0.470262\pi$
$828$		0			0
$829$	−2.39683	−	15.9019i	−0.0832454	−	0.552297i	−0.991111	−	0.133036i	$-0.957527\pi$
$829$	−2.39683	−	15.9019i	−0.0832454	−	0.552297i	0.907866	−	0.419261i	$-0.137711\pi$
$830$		0			0
$831$	1.61794	+	21.5899i	0.0561258	+	0.748947i
$832$		0			0
$833$	−7.88531	−	35.3853i	−0.273210	−	1.22603i
$834$		0			0
$835$	−2.12692	+	0.159391i	−0.0736052	+	0.00551595i
$836$		0			0
$837$	−23.5660	+	3.55200i	−0.814560	+	0.122775i
$838$		0			0
$839$	11.4353	−	50.1014i	0.394791	−	1.72969i	−0.252632	−	0.967562i	$-0.581296\pi$
$839$	11.4353	−	50.1014i	0.394791	−	1.72969i	0.647423	−	0.762131i	$-0.275847\pi$
$840$		0			0
$841$	−1.88395	−	8.25410i	−0.0649636	−	0.284624i
$842$		0			0
$843$	12.2681	+	11.3831i	0.422535	+	0.392055i
$844$		0			0
$845$	5.82839	−	38.6689i	0.200503	−	1.33025i
$846$		0			0
$847$	−1.94130	+	0.673695i	−0.0667038	+	0.0231484i
$848$		0			0
$849$	10.4153	−	3.21268i	0.357451	−	0.110259i
$850$		0			0
$851$	4.77634	+	2.75762i	0.163731	+	0.0945300i
$852$		0			0
$853$	−7.19065	−	5.73435i	−0.246203	−	0.196340i	0.492611	−	0.870250i	$-0.336042\pi$
$853$	−7.19065	−	5.73435i	−0.246203	−	0.196340i	−0.738814	+	0.673909i	$0.764614\pi$
$854$		0			0
$855$	−1.43509	+	1.14445i	−0.0490791	+	0.0391393i
$856$		0			0
$857$	6.40978	+	0.480346i	0.218954	+	0.0164083i	0.183755	−	0.982972i	$-0.441175\pi$
$857$	6.40978	+	0.480346i	0.218954	+	0.0164083i	0.0351985	+	0.999380i	$0.488794\pi$
$858$		0			0
$859$	4.26989	−	10.8795i	0.145687	−	0.371204i	−0.839340	−	0.543607i	$-0.817058\pi$
$859$	4.26989	−	10.8795i	0.145687	−	0.371204i	0.985026	+	0.172404i	$0.0551533\pi$
$860$		0			0
$861$	−18.0934	−	24.6481i	−0.616622	−	0.840004i
$862$		0			0
$863$	−2.68327	+	1.54919i	−0.0913397	+	0.0527350i	−0.544974	−	0.838453i	$-0.683461\pi$
$863$	−2.68327	+	1.54919i	−0.0913397	+	0.0527350i	0.453634	+	0.891188i	$0.350127\pi$
$864$		0			0
$865$	2.70145	+	6.88318i	0.0918521	+	0.234035i
$866$		0			0
$867$	−9.29051	+	4.47407i	−0.315522	+	0.151947i
$868$		0			0
$869$	−35.1724	−	16.9381i	−1.19314	−	0.574587i
$870$		0			0
$871$	−4.93317	+	3.36338i	−0.167154	+	0.113964i
$872$		0			0
$873$	−8.05118	+	11.8089i	−0.272491	+	0.399671i
$874$		0			0
$875$	−33.1797	−	6.36632i	−1.12168	−	0.215221i
$876$		0			0
$877$	−18.9164	+	17.5519i	−0.638762	+	0.592685i	−0.931603	−	0.363476i	$-0.881590\pi$
$877$	−18.9164	+	17.5519i	−0.638762	+	0.592685i	0.292841	+	0.956161i	$0.405399\pi$
$878$		0			0
$879$	−2.04818	+	6.64004i	−0.0690834	+	0.223963i
$880$		0			0
$881$			44.0012i			1.48244i	0.671263	+	0.741219i	$0.265752\pi$
$881$			44.0012i			1.48244i	−0.671263	+	0.741219i	$0.734248\pi$
$882$		0			0
$883$		−	14.9883i		−	0.504395i	−0.967676	−	0.252198i	$-0.918847\pi$
$883$		−	14.9883i		−	0.504395i	0.967676	−	0.252198i	$-0.0811533\pi$
$884$		0			0
$885$	11.8030	−	38.2644i	0.396754	−	1.28624i
$886$		0			0
$887$	−1.46612	+	1.36036i	−0.0492274	+	0.0456763i	−0.704403	−	0.709800i	$-0.748785\pi$
$887$	−1.46612	+	1.36036i	−0.0492274	+	0.0456763i	0.655176	+	0.755477i	$0.272595\pi$
$888$		0			0
$889$	0.323490	+	9.28399i	0.0108495	+	0.311375i
$890$		0			0
$891$	−0.532441	+	0.780947i	−0.0178374	+	0.0261627i
$892$		0			0
$893$	−1.54993	+	1.05673i	−0.0518665	+	0.0353620i
$894$		0			0
$895$	61.1096	+	29.4288i	2.04267	+	0.983697i
$896$		0			0
$897$	−7.53971	+	3.63093i	−0.251744	+	0.121233i
$898$		0			0
$899$	10.3648	+	26.4091i	0.345685	+	0.880792i
$900$		0			0
$901$	2.94842	−	1.70227i	0.0982262	−	0.0567109i
$902$		0			0
$903$	1.96082	+	10.5110i	0.0652522	+	0.349785i
$904$		0			0
$905$	−24.2625	+	61.8198i	−0.806512	+	2.05496i
$906$		0			0
$907$	−50.5002	−	3.78446i	−1.67683	−	0.125661i	−0.797956	−	0.602715i	$-0.794085\pi$
$907$	−50.5002	−	3.78446i	−1.67683	−	0.125661i	−0.878874	+	0.477054i	$0.841705\pi$
$908$		0			0
$909$	28.0274	−	22.3511i	0.929609	−	0.741338i
$910$		0			0
$911$	−32.7548	−	26.1211i	−1.08521	−	0.865430i	−0.0937231	−	0.995598i	$-0.529877\pi$
$911$	−32.7548	−	26.1211i	−1.08521	−	0.865430i	−0.991492	+	0.130168i	$0.958448\pi$
$912$		0			0
$913$	24.9306	+	14.3937i	0.825081	+	0.476361i
$914$		0			0
$915$	44.6845	−	13.7833i	1.47722	−	0.455663i
$916$		0			0
$917$	10.3567	+	6.54471i	0.342007	+	0.216125i
$918$		0			0
$919$	−5.10289	+	33.8555i	−0.168329	+	1.11679i	0.731913	+	0.681398i	$0.238628\pi$
$919$	−5.10289	+	33.8555i	−0.168329	+	1.11679i	−0.900242	+	0.435390i	$0.856610\pi$
$920$		0			0
$921$	−22.6052	−	20.9746i	−0.744867	−	0.691135i
$922$		0			0
$923$	3.44973	+	15.1142i	0.113549	+	0.497491i
$924$		0			0
$925$	−2.00022	+	8.76352i	−0.0657667	+	0.288143i
$926$		0			0
$927$	−13.9506	+	2.10272i	−0.458198	+	0.0690622i
$928$		0			0
$929$	10.7637	−	0.806629i	0.353146	−	0.0264646i	0.103024	−	0.994679i	$-0.467148\pi$
$929$	10.7637	−	0.806629i	0.353146	−	0.0264646i	0.250122	+	0.968214i	$0.419529\pi$
$930$		0			0
$931$	−1.72004	+	0.664884i	−0.0563721	+	0.0217907i
$932$		0			0
$933$	0.536642	+	7.16099i	0.0175689	+	0.234440i
$934$		0			0
$935$	9.06088	+	60.1150i	0.296323	+	1.96597i
$936$		0			0
$937$	47.3563	+	10.8088i	1.54706	+	0.353107i	0.908973	−	0.416855i	$-0.136868\pi$
$937$	47.3563	+	10.8088i	1.54706	+	0.353107i	0.638090	+	0.769962i	$0.279725\pi$
$938$		0			0
$939$	33.8396	−	7.72367i	1.10431	−	0.252053i
$940$		0			0
$941$	11.8218	−	12.7408i	0.385379	−	0.415340i	−0.510331	−	0.859978i	$-0.670477\pi$
$941$	11.8218	−	12.7408i	0.385379	−	0.415340i	0.895710	+	0.444638i	$0.146668\pi$
$942$		0			0
$943$	−56.6246	−	8.53478i	−1.84395	−	0.277931i
$944$		0			0
$945$	−42.3574	+	26.4633i	−1.37789	+	0.860851i
$946$		0			0
$947$	5.80091	+	18.8061i	0.188504	+	0.611116i	0.999655	+	0.0262781i	$0.00836555\pi$
$947$	5.80091	+	18.8061i	0.188504	+	0.611116i	−0.811150	+	0.584838i	$0.801158\pi$
$948$		0			0
$949$	1.52940	−	2.64899i	0.0496464	−	0.0859900i
$950$		0			0
$951$	−12.8248	+	16.0818i	−0.415873	+	0.521488i
$952$		0			0
$953$	4.90752	+	6.15384i	0.158970	+	0.199342i	0.854937	−	0.518731i	$-0.173595\pi$
$953$	4.90752	+	6.15384i	0.158970	+	0.199342i	−0.695967	+	0.718074i	$0.745024\pi$
$954$		0			0
$955$	−6.29365	+	83.9829i	−0.203658	+	2.71762i
$956$		0			0
$957$	−19.1259	−	7.50636i	−0.618252	−	0.242646i
$958$		0			0
$959$	−0.197880	+	4.94805i	−0.00638987	+	0.159781i
$960$		0			0
$961$	4.75879	+	8.24247i	0.153509	+	0.265886i
$962$		0			0
$963$	27.1890	−	10.6709i	0.876154	−	0.343865i
$964$		0			0
$965$	38.9746	+	80.9316i	1.25464	+	2.60528i
$966$		0			0
$967$	3.62090	−	7.51887i	0.116440	−	0.241791i	−0.834601	−	0.550855i	$-0.814302\pi$
$967$	3.62090	−	7.51887i	0.116440	−	0.241791i	0.951041	+	0.309065i	$0.100016\pi$
$968$		0			0
$969$	0.806860	+	1.18345i	0.0259201	+	0.0380178i
$970$		0			0
$971$	10.4436	+	7.12035i	0.335152	+	0.228503i	0.719188	−	0.694815i	$-0.244514\pi$
$971$	10.4436	+	7.12035i	0.335152	+	0.228503i	−0.384036	+	0.923318i	$0.625466\pi$
$972$		0			0
$973$	−8.13837	+	10.9680i	−0.260904	+	0.351618i
$974$		0			0
$975$	−9.27696	−	9.99819i	−0.297101	−	0.320198i
$976$		0			0
$977$	28.9224	+	8.92139i	0.925311	+	0.285421i	0.720559	−	0.693393i	$-0.243885\pi$
$977$	28.9224	+	8.92139i	0.925311	+	0.285421i	0.204752	+	0.978814i	$0.434361\pi$
$978$		0			0
$979$	−16.9649			−0.542199
$980$		0			0
$981$	1.85149			0.0591137
$982$		0			0
$983$	54.7659	+	16.8930i	1.74676	+	0.538805i	0.992976	−	0.118316i	$-0.0377495\pi$
$983$	54.7659	+	16.8930i	1.74676	+	0.538805i	0.753786	+	0.657120i	$0.228226\pi$
$984$		0			0
$985$	18.9838	+	20.4597i	0.604875	+	0.651901i
$986$		0			0
$987$	−17.5100	+	9.19681i	−0.557350	+	0.292738i
$988$		0			0
$989$	16.5455	+	11.2805i	0.526116	+	0.358700i
$990$		0			0
$991$	18.7310	+	27.4734i	0.595011	+	0.872720i	0.999118	−	0.0419913i	$-0.0133702\pi$
$991$	18.7310	+	27.4734i	0.595011	+	0.872720i	−0.404107	+	0.914712i	$0.632418\pi$
$992$		0			0
$993$	5.91160	−	12.2756i	0.187599	−	0.389553i
$994$		0			0
$995$	−35.4911	−	73.6981i	−1.12514	−	2.33639i
$996$		0			0
$997$	2.79991	−	1.09889i	0.0886741	−	0.0348020i	−0.320589	−	0.947218i	$-0.603881\pi$
$997$	2.79991	−	1.09889i	0.0886741	−	0.0348020i	0.409263	+	0.912416i	$0.365786\pi$
$998$		0			0
$999$	2.72580	+	4.72122i	0.0862403	+	0.149373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bp.b.703.3	yes	108
4.3	odd	2		784.2.bp.a.703.7	yes	108
49.26	odd	42		784.2.bp.a.271.7	✓	108
196.75	even	42	inner	784.2.bp.b.271.3	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bp.a.271.7	✓	108	49.26	odd	42
784.2.bp.a.703.7	yes	108	4.3	odd	2
784.2.bp.b.271.3	yes	108	196.75	even	42	inner
784.2.bp.b.703.3	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bp (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00318 - 0.309439i) q^{3} +(-2.49710 - 2.69123i) q^{5} +(-1.72063 - 2.00983i) q^{7} +(-1.56810 - 1.06912i) q^{9} +O(q^{10})\)	\(q+(-1.00318 - 0.309439i) q^{3} +(-2.49710 - 2.69123i) q^{5} +(-1.72063 - 2.00983i) q^{7} +(-1.56810 - 1.06912i) q^{9} +(1.80116 + 2.64181i) q^{11} +(0.664877 - 1.38063i) q^{13} +(1.67226 + 3.47248i) q^{15} +(-4.82102 + 1.89211i) q^{17} +(0.131720 + 0.228145i) q^{19} +(1.10418 + 2.54865i) q^{21} +(4.84233 + 1.90047i) q^{23} +(-0.633579 + 8.45452i) q^{25} +(3.20591 + 4.02009i) q^{27} +(3.81637 - 4.78557i) q^{29} +(-2.31746 + 4.01395i) q^{31} +(-0.989399 - 3.20755i) q^{33} +(-1.11235 + 9.64937i) q^{35} +(1.04839 + 0.158019i) q^{37} +(-1.09421 + 1.17928i) q^{39} +(-10.7323 + 2.44957i) q^{41} +(3.75304 + 0.856607i) q^{43} +(1.03847 + 6.88982i) q^{45} +(0.532135 + 7.10085i) q^{47} +(-1.07886 + 6.91636i) q^{49} +(5.42183 - 0.406310i) q^{51} +(-0.650029 + 0.0979760i) q^{53} +(2.61206 - 11.4442i) q^{55} +(-0.0615411 - 0.269629i) q^{57} +(-7.61615 - 7.06676i) q^{59} +(1.80831 - 11.9973i) q^{61} +(0.549384 + 4.99118i) q^{63} +(-5.37586 + 1.65823i) q^{65} +(-3.37430 - 1.94815i) q^{67} +(-4.26963 - 3.40492i) q^{69} +(-7.90969 + 6.30776i) q^{71} +(1.99052 + 0.149169i) q^{73} +(3.25175 - 8.28533i) q^{75} +(2.21048 - 8.16561i) q^{77} +(-10.5737 + 6.10473i) q^{79} +(0.107999 + 0.275176i) q^{81} +(8.11176 - 3.90642i) q^{83} +(17.1307 + 8.24970i) q^{85} +(-5.30934 + 3.61984i) q^{87} +(-2.98889 + 4.38389i) q^{89} +(-3.91885 + 1.03926i) q^{91} +(3.56689 - 3.30959i) q^{93} +(0.285075 - 0.924190i) q^{95} -7.53069i q^{97} -6.06828i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9	\( 108 q + q^{3} - 3 q^{5} - 4 q^{7} + 8 q^{9} + 18 q^{11} + 16 q^{17} + 7 q^{19} + 5 q^{21} + 54 q^{23} - 4 q^{25} - 53 q^{27} - 16 q^{29} + 5 q^{31} - 3 q^{33} - 9 q^{35} + 2 q^{37} - 43 q^{39} - 28 q^{41} - 111 q^{45} - 60 q^{47} - 58 q^{49} - 3 q^{51} - 70 q^{53} + 69 q^{55} + 31 q^{57} + 9 q^{59} - 8 q^{61} + 93 q^{63} - 8 q^{65} - 21 q^{67} - 56 q^{69} - 63 q^{71} - 24 q^{73} + 2 q^{75} - 18 q^{77} + 21 q^{79} + 45 q^{81} + 60 q^{83} + 6 q^{85} - 6 q^{87} + 7 q^{89} + 66 q^{93} + 15 q^{95}+O(q^{100}) \) 108 * q + q^3 - 3 * q^5 - 4 * q^7 + 8 * q^9 + 18 * q^11 + 16 * q^17 + 7 * q^19 + 5 * q^21 + 54 * q^23 - 4 * q^25 - 53 * q^27 - 16 * q^29 + 5 * q^31 - 3 * q^33 - 9 * q^35 + 2 * q^37 - 43 * q^39 - 28 * q^41 - 111 * q^45 - 60 * q^47 - 58 * q^49 - 3 * q^51 - 70 * q^53 + 69 * q^55 + 31 * q^57 + 9 * q^59 - 8 * q^61 + 93 * q^63 - 8 * q^65 - 21 * q^67 - 56 * q^69 - 63 * q^71 - 24 * q^73 + 2 * q^75 - 18 * q^77 + 21 * q^79 + 45 * q^81 + 60 * q^83 + 6 * q^85 - 6 * q^87 + 7 * q^89 + 66 * q^93 + 15 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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