LMFDB - Embedded newform 845.2.f.f.408.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			408.20
Character	$\chi$	$=$	845.408
Dual form			845.2.f.f.437.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.689692i q^{2} +(-0.0621871 - 0.0621871i) q^{3} +1.52433 q^{4} +(-0.454257 + 2.18944i) q^{5} +(0.0428900 - 0.0428900i) q^{6} -0.806945 q^{7} +2.43070i q^{8} -2.99227i q^{9} +(-1.51004 - 0.313297i) q^{10} +(0.314448 + 0.314448i) q^{11} +(-0.0947934 - 0.0947934i) q^{12} -0.556544i q^{14} +(0.164404 - 0.107906i) q^{15} +1.37222 q^{16} +(3.71523 + 3.71523i) q^{17} +2.06374 q^{18} +(4.78901 + 4.78901i) q^{19} +(-0.692436 + 3.33742i) q^{20} +(0.0501816 + 0.0501816i) q^{21} +(-0.216872 + 0.216872i) q^{22} +(-3.80361 + 3.80361i) q^{23} +(0.151158 - 0.151158i) q^{24} +(-4.58730 - 1.98914i) q^{25} +(-0.372642 + 0.372642i) q^{27} -1.23005 q^{28} +4.79138i q^{29} +(0.0744220 + 0.113388i) q^{30} +(-0.106205 + 0.106205i) q^{31} +5.80780i q^{32} -0.0391092i q^{33} +(-2.56236 + 2.56236i) q^{34} +(0.366561 - 1.76676i) q^{35} -4.56119i q^{36} -5.97196 q^{37} +(-3.30294 + 3.30294i) q^{38} +(-5.32187 - 1.10416i) q^{40} +(6.13599 - 6.13599i) q^{41} +(-0.0346098 + 0.0346098i) q^{42} +(6.82846 - 6.82846i) q^{43} +(0.479320 + 0.479320i) q^{44} +(6.55139 + 1.35926i) q^{45} +(-2.62332 - 2.62332i) q^{46} -9.32662 q^{47} +(-0.0853343 - 0.0853343i) q^{48} -6.34884 q^{49} +(1.37189 - 3.16382i) q^{50} -0.462079i q^{51} +(5.61903 + 5.61903i) q^{53} +(-0.257008 - 0.257008i) q^{54} +(-0.831304 + 0.545624i) q^{55} -1.96144i q^{56} -0.595630i q^{57} -3.30457 q^{58} +(-1.55637 + 1.55637i) q^{59} +(0.250605 - 0.164484i) q^{60} +3.03084 q^{61} +(-0.0732484 - 0.0732484i) q^{62} +2.41459i q^{63} -1.26116 q^{64} +0.0269733 q^{66} +11.6119i q^{67} +(5.66322 + 5.66322i) q^{68} +0.473071 q^{69} +(1.21852 + 0.252814i) q^{70} +(1.00931 - 1.00931i) q^{71} +7.27329 q^{72} +0.265877i q^{73} -4.11881i q^{74} +(0.161572 + 0.408970i) q^{75} +(7.30001 + 7.30001i) q^{76} +(-0.253742 - 0.253742i) q^{77} -8.98397i q^{79} +(-0.623340 + 3.00439i) q^{80} -8.93045 q^{81} +(4.23194 + 4.23194i) q^{82} +2.59025 q^{83} +(0.0764931 + 0.0764931i) q^{84} +(-9.82194 + 6.44660i) q^{85} +(4.70953 + 4.70953i) q^{86} +(0.297962 - 0.297962i) q^{87} +(-0.764327 + 0.764327i) q^{88} +(6.10204 - 6.10204i) q^{89} +(-0.937469 + 4.51844i) q^{90} +(-5.79794 + 5.79794i) q^{92} +0.0132091 q^{93} -6.43250i q^{94} +(-12.6607 + 8.30982i) q^{95} +(0.361171 - 0.361171i) q^{96} -14.4934i q^{97} -4.37874i q^{98} +(0.940911 - 0.940911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) $ 72 * q - 4 * q^3 - 80 * q^4 - 12 * q^10 + 64 * q^12 + 80 * q^16 + 8 * q^17 + 24 * q^22 + 36 * q^23 - 48 * q^25 - 64 * q^27 - 4 * q^30 + 80 * q^35 + 28 * q^38 - 24 * q^40 - 56 * q^42 + 76 * q^43 - 76 * q^48 + 8 * q^49 - 16 * q^53 + 12 * q^55 + 8 * q^61 + 148 * q^62 - 120 * q^64 + 40 * q^66 - 48 * q^68 - 40 * q^69 - 164 * q^75 + 172 * q^77 + 16 * q^81 + 44 * q^82 + 20 * q^87 + 124 * q^88 - 300 * q^90 - 4 * q^92 - 92 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			0.689692i			0.487686i	0.969815	+	0.243843i	$0.0784081\pi$
$2$			0.689692i			0.487686i	−0.969815	+	0.243843i	$0.921592\pi$
$3$	−0.0621871	−	0.0621871i	−0.0359038	−	0.0359038i	0.688927	−	0.724831i	$-0.258082\pi$
$3$	−0.0621871	−	0.0621871i	−0.0359038	−	0.0359038i	−0.724831	+	0.688927i	$0.758082\pi$
$4$	1.52433			0.762163
$5$	−0.454257	+	2.18944i	−0.203150	+	0.979148i
$5$	−0.454257	+	2.18944i	−0.203150	+	0.979148i
$6$	0.0428900	−	0.0428900i	0.0175098	−	0.0175098i
$7$	−0.806945			−0.304997			−0.152498	−	0.988304i	$-0.548732\pi$
$7$	−0.806945			−0.304997			−0.152498	+	0.988304i	$0.548732\pi$
$8$			2.43070i			0.859382i
$9$		−	2.99227i		−	0.997422i
$10$	−1.51004	−	0.313297i	−0.477516	−	0.0990733i
$11$	0.314448	+	0.314448i	0.0948095	+	0.0948095i	0.752921	−	0.658111i	$-0.228644\pi$
$11$	0.314448	+	0.314448i	0.0948095	+	0.0948095i	−0.658111	+	0.752921i	$0.728644\pi$
$12$	−0.0947934	−	0.0947934i	−0.0273645	−	0.0273645i
$13$		0			0
$13$		0			0
$14$		−	0.556544i		−	0.148743i
$15$	0.164404	−	0.107906i	0.0424489	−	0.0278612i
$16$	1.37222			0.343054
$17$	3.71523	+	3.71523i	0.901075	+	0.901075i	0.995529	−	0.0944538i	$-0.0301105\pi$
$17$	3.71523	+	3.71523i	0.901075	+	0.901075i	−0.0944538	+	0.995529i	$0.530110\pi$
$18$	2.06374			0.486428
$19$	4.78901	+	4.78901i	1.09867	+	1.09867i	0.994566	+	0.104109i	$0.0331991\pi$
$19$	4.78901	+	4.78901i	1.09867	+	1.09867i	0.104109	+	0.994566i	$0.466801\pi$
$20$	−0.692436	+	3.33742i	−0.154833	+	0.746270i
$21$	0.0501816	+	0.0501816i	0.0109505	+	0.0109505i
$22$	−0.216872	+	0.216872i	−0.0462372	+	0.0462372i
$23$	−3.80361	+	3.80361i	−0.793108	+	0.793108i	−0.981998	−	0.188891i	$-0.939511\pi$
$23$	−3.80361	+	3.80361i	−0.793108	+	0.793108i	0.188891	+	0.981998i	$0.439511\pi$
$24$	0.151158	−	0.151158i	0.0308550	−	0.0308550i
$25$	−4.58730	−	1.98914i	−0.917460	−	0.397828i
$26$		0			0
$27$	−0.372642	+	0.372642i	−0.0717149	+	0.0717149i
$28$	−1.23005			−0.232457
$29$			4.79138i			0.889736i	0.895596	+	0.444868i	$0.146749\pi$
$29$			4.79138i			0.889736i	−0.895596	+	0.444868i	$0.853251\pi$
$30$	0.0744220	+	0.113388i	0.0135875	+	0.0207017i
$31$	−0.106205	+	0.106205i	−0.0190749	+	0.0190749i	−0.716580	−	0.697505i	$-0.754293\pi$
$31$	−0.106205	+	0.106205i	−0.0190749	+	0.0190749i	0.697505	+	0.716580i	$0.254293\pi$
$32$			5.80780i			1.02668i
$33$		−	0.0391092i		−	0.00680804i
$34$	−2.56236	+	2.56236i	−0.439442	+	0.439442i
$35$	0.366561	−	1.76676i	0.0619600	−	0.298637i
$36$		−	4.56119i		−	0.760198i
$37$	−5.97196			−0.981784			−0.490892	−	0.871220i	$-0.663329\pi$
$37$	−5.97196			−0.981784			−0.490892	+	0.871220i	$0.663329\pi$
$38$	−3.30294	+	3.30294i	−0.535808	+	0.535808i
$39$		0			0
$40$	−5.32187	−	1.10416i	−0.841461	−	0.174583i
$41$	6.13599	−	6.13599i	0.958281	−	0.958281i	−0.0408834	−	0.999164i	$-0.513017\pi$
$41$	6.13599	−	6.13599i	0.958281	−	0.958281i	0.999164	+	0.0408834i	$0.0130172\pi$
$42$	−0.0346098	+	0.0346098i	−0.00534041	+	0.00534041i
$43$	6.82846	−	6.82846i	1.04133	−	1.04133i	0.0422217	−	0.999108i	$-0.486556\pi$
$43$	6.82846	−	6.82846i	1.04133	−	1.04133i	0.999108	−	0.0422217i	$-0.0134436\pi$
$44$	0.479320	+	0.479320i	0.0722603	+	0.0722603i
$45$	6.55139	+	1.35926i	0.976623	+	0.202626i
$46$	−2.62332	−	2.62332i	−0.386787	−	0.386787i
$47$	−9.32662			−1.36043			−0.680214	−	0.733014i	$-0.738113\pi$
$47$	−9.32662			−1.36043			−0.680214	+	0.733014i	$0.738113\pi$
$48$	−0.0853343	−	0.0853343i	−0.0123169	−	0.0123169i
$49$	−6.34884			−0.906977
$50$	1.37189	−	3.16382i	0.194015	−	0.447432i
$51$		−	0.462079i		−	0.0647040i
$52$		0			0
$53$	5.61903	+	5.61903i	0.771833	+	0.771833i	0.978427	−	0.206594i	$-0.0662378\pi$
$53$	5.61903	+	5.61903i	0.771833	+	0.771833i	−0.206594	+	0.978427i	$0.566238\pi$
$54$	−0.257008	−	0.257008i	−0.0349744	−	0.0349744i
$55$	−0.831304	+	0.545624i	−0.112093	+	0.0735720i
$56$		−	1.96144i		−	0.262108i
$57$		−	0.595630i		−	0.0788931i
$58$	−3.30457			−0.433912
$59$	−1.55637	+	1.55637i	−0.202622	+	0.202622i	−0.801122	−	0.598500i	$-0.795763\pi$
$59$	−1.55637	+	1.55637i	−0.202622	+	0.202622i	0.598500	+	0.801122i	$0.295763\pi$
$60$	0.250605	−	0.164484i	0.0323530	−	0.0212348i
$61$	3.03084			0.388059			0.194029	−	0.980996i	$-0.437844\pi$
$61$	3.03084			0.388059			0.194029	+	0.980996i	$0.437844\pi$
$62$	−0.0732484	−	0.0732484i	−0.00930256	−	0.00930256i
$63$			2.41459i			0.304210i
$64$	−1.26116			−0.157645
$65$		0			0
$66$	0.0269733			0.00332018
$67$			11.6119i			1.41862i	0.704899	+	0.709308i	$0.250992\pi$
$67$			11.6119i			1.41862i	−0.704899	+	0.709308i	$0.749008\pi$
$68$	5.66322	+	5.66322i	0.686766	+	0.686766i
$69$	0.473071			0.0569511
$70$	1.21852	+	0.252814i	0.145641	+	0.0302170i
$71$	1.00931	−	1.00931i	0.119783	−	0.119783i	−0.644674	−	0.764457i	$-0.723007\pi$
$71$	1.00931	−	1.00931i	0.119783	−	0.119783i	0.764457	+	0.644674i	$0.223007\pi$
$72$	7.27329			0.857166
$73$			0.265877i			0.0311186i	0.999879	+	0.0155593i	$0.00495288\pi$
$73$			0.265877i			0.0311186i	−0.999879	+	0.0155593i	$0.995047\pi$
$74$		−	4.11881i		−	0.478802i
$75$	0.161572	+	0.408970i	0.0186568	+	0.0472238i
$76$	7.30001	+	7.30001i	0.837369	+	0.837369i
$77$	−0.253742	−	0.253742i	−0.0289166	−	0.0289166i
$78$		0			0
$79$		−	8.98397i		−	1.01078i	−0.862892	−	0.505388i	$-0.831350\pi$
$79$		−	8.98397i		−	1.01078i	0.862892	−	0.505388i	$-0.168650\pi$
$80$	−0.623340	+	3.00439i	−0.0696915	+	0.335901i
$81$	−8.93045			−0.992272
$82$	4.23194	+	4.23194i	0.467340	+	0.467340i
$83$	2.59025			0.284317			0.142159	−	0.989844i	$-0.454596\pi$
$83$	2.59025			0.284317			0.142159	+	0.989844i	$0.454596\pi$
$84$	0.0764931	+	0.0764931i	0.00834608	+	0.00834608i
$85$	−9.82194	+	6.44660i	−1.06534	+	0.699232i
$86$	4.70953	+	4.70953i	0.507842	+	0.507842i
$87$	0.297962	−	0.297962i	0.0319449	−	0.0319449i
$88$	−0.764327	+	0.764327i	−0.0814776	+	0.0814776i
$89$	6.10204	−	6.10204i	0.646815	−	0.646815i	−0.305407	−	0.952222i	$-0.598792\pi$
$89$	6.10204	−	6.10204i	0.646815	−	0.646815i	0.952222	+	0.305407i	$0.0987925\pi$
$90$	−0.937469	+	4.51844i	−0.0988179	+	0.476285i
$91$		0			0
$92$	−5.79794	+	5.79794i	−0.604477	+	0.604477i
$93$	0.0132091			0.00136972
$94$		−	6.43250i		−	0.663461i
$95$	−12.6607	+	8.30982i	−1.29896	+	0.852569i
$96$	0.361171	−	0.361171i	0.0368618	−	0.0368618i
$97$		−	14.4934i		−	1.47158i	−0.677210	−	0.735789i	$-0.736811\pi$
$97$		−	14.4934i		−	1.47158i	0.677210	−	0.735789i	$-0.263189\pi$
$98$		−	4.37874i		−	0.442320i
$99$	0.940911	−	0.940911i	0.0945651	−	0.0945651i
$100$	−6.99254	−	3.03209i	−0.699254	−	0.303209i
$101$		−	3.93288i		−	0.391336i	−0.980670	−	0.195668i	$-0.937312\pi$
$101$		−	3.93288i		−	0.391336i	0.980670	−	0.195668i	$-0.0626875\pi$
$102$	0.318692			0.0315552
$103$	12.2725	−	12.2725i	1.20924	−	1.20924i	0.237970	−	0.971272i	$-0.423518\pi$
$103$	12.2725	−	12.2725i	1.20924	−	1.20924i	0.971272	−	0.237970i	$-0.0764820\pi$
$104$		0			0
$105$	−0.132665	+	0.0870743i	−0.0129468	+	0.00849758i
$106$	−3.87540	+	3.87540i	−0.376412	+	0.376412i
$107$	−3.47737	+	3.47737i	−0.336170	+	0.336170i	−0.854924	−	0.518754i	$-0.826396\pi$
$107$	−3.47737	+	3.47737i	−0.336170	+	0.336170i	0.518754	+	0.854924i	$0.326396\pi$
$108$	−0.568027	+	0.568027i	−0.0546585	+	0.0546585i
$109$	−5.74206	−	5.74206i	−0.549990	−	0.549990i	0.376448	−	0.926438i	$-0.377145\pi$
$109$	−5.74206	−	5.74206i	−0.549990	−	0.549990i	−0.926438	+	0.376448i	$0.877145\pi$
$110$	−0.376313	−	0.573344i	−0.0358800	−	0.0546662i
$111$	0.371379	+	0.371379i	0.0352497	+	0.0352497i
$112$	−1.10730			−0.104630
$113$	3.36820	+	3.36820i	0.316853	+	0.316853i	0.847557	−	0.530704i	$-0.178072\pi$
$113$	3.36820	+	3.36820i	0.316853	+	0.316853i	−0.530704	+	0.847557i	$0.678072\pi$
$114$	0.410801			0.0384751
$115$	−6.59996	−	10.0556i	−0.615450	−	0.937689i
$116$			7.30362i			0.678124i
$117$		0			0
$118$	−1.07342	−	1.07342i	−0.0988159	−	0.0988159i
$119$	−2.99799	−	2.99799i	−0.274825	−	0.274825i
$120$	0.262287	+	0.399616i	0.0239434	+	0.0364798i
$121$		−	10.8022i		−	0.982022i
$122$			2.09034i			0.189251i
$123$	−0.763159			−0.0688117
$124$	−0.161890	+	0.161890i	−0.0145382	+	0.0145382i
$125$	6.43891	−	9.14004i	0.575914	−	0.817510i
$126$	−1.66533			−0.148359
$127$	10.3616	+	10.3616i	0.919445	+	0.919445i	0.996989	−	0.0775440i	$-0.0247078\pi$
$127$	10.3616	+	10.3616i	0.919445	+	0.919445i	−0.0775440	+	0.996989i	$0.524708\pi$
$128$			10.7458i			0.949803i
$129$	−0.849284			−0.0747753
$130$		0			0
$131$	21.1674			1.84941			0.924704	−	0.380686i	$-0.124312\pi$
$131$	21.1674			1.84941			0.924704	+	0.380686i	$0.124312\pi$
$132$		−	0.0596151i		−	0.00518883i
$133$	−3.86447	−	3.86447i	−0.335092	−	0.335092i
$134$	−8.00861			−0.691838
$135$	−0.646602	−	0.985152i	−0.0556506	−	0.0847884i
$136$	−9.03060	+	9.03060i	−0.774368	+	0.774368i
$137$	15.2364			1.30173			0.650867	−	0.759192i	$-0.274406\pi$
$137$	15.2364			1.30173			0.650867	+	0.759192i	$0.274406\pi$
$138$			0.326273i			0.0277742i
$139$			11.8714i			1.00692i	0.864019	+	0.503459i	$0.167939\pi$
$139$			11.8714i			1.00692i	−0.864019	+	0.503459i	$0.832061\pi$
$140$	0.558758	−	2.69311i	0.0472236	−	0.227610i
$141$	0.579996	+	0.579996i	0.0488445	+	0.0488445i
$142$	0.696114	+	0.696114i	0.0584166	+	0.0584166i
$143$		0			0
$144$		−	4.10604i		−	0.342170i
$145$	−10.4904	−	2.17652i	−0.871183	−	0.180750i
$146$	−0.183373			−0.0151761
$147$	0.394816	+	0.394816i	0.0325639	+	0.0325639i
$148$	−9.10321			−0.748279
$149$	−9.54060	−	9.54060i	−0.781597	−	0.781597i	0.198504	−	0.980100i	$-0.436392\pi$
$149$	−9.54060	−	9.54060i	−0.781597	−	0.781597i	−0.980100	+	0.198504i	$0.936392\pi$
$150$	−0.282063	+	0.111435i	−0.0230304	+	0.00909864i
$151$	3.86706	+	3.86706i	0.314697	+	0.314697i	0.846726	−	0.532029i	$-0.178570\pi$
$151$	3.86706	+	3.86706i	0.314697	+	0.314697i	−0.532029	+	0.846726i	$0.678570\pi$
$152$	−11.6406	+	11.6406i	−0.944181	+	0.944181i
$153$	11.1170	−	11.1170i	0.898752	−	0.898752i
$154$	0.175004	−	0.175004i	0.0141022	−	0.0141022i
$155$	−0.184284	−	0.280773i	−0.0148021	−	0.0225522i
$156$		0			0
$157$	−12.0199	+	12.0199i	−0.959293	+	0.959293i	−0.999203	−	0.0399100i	$-0.987293\pi$
$157$	−12.0199	+	12.0199i	−0.959293	+	0.959293i	0.0399100	+	0.999203i	$0.487293\pi$
$158$	6.19617			0.492941
$159$		−	0.698863i		−	0.0554234i
$160$	−12.7158	−	2.63824i	−1.00528	−	0.208571i
$161$	3.06931	−	3.06931i	0.241895	−	0.241895i
$162$		−	6.15926i		−	0.483917i
$163$		−	20.9573i		−	1.64150i	−0.571288	−	0.820750i	$-0.693556\pi$
$163$		−	20.9573i		−	1.64150i	0.571288	−	0.820750i	$-0.306444\pi$
$164$	9.35324	−	9.35324i	0.730366	−	0.730366i
$165$	0.0856272	+	0.0177656i	0.00666607	+	0.00138305i
$166$			1.78648i			0.138657i
$167$	−17.8277			−1.37955			−0.689773	−	0.724026i	$-0.742289\pi$
$167$	−17.8277			−1.37955			−0.689773	+	0.724026i	$0.742289\pi$
$168$	−0.121976	+	0.121976i	−0.00941068	+	0.00941068i
$169$		0			0
$170$	−4.44617	−	6.77411i	−0.341006	−	0.519551i
$171$	14.3300	−	14.3300i	1.09584	−	1.09584i
$172$	10.4088	−	10.4088i	0.793663	−	0.793663i
$173$	4.52475	−	4.52475i	0.344010	−	0.344010i	−0.513862	−	0.857873i	$-0.671786\pi$
$173$	4.52475	−	4.52475i	0.344010	−	0.344010i	0.857873	+	0.513862i	$0.171786\pi$
$174$	0.205502	+	0.205502i	0.0155791	+	0.0155791i
$175$	3.70170	+	1.60513i	0.279822	+	0.121336i
$176$	0.431490	+	0.431490i	0.0325248	+	0.0325248i
$177$	0.193572			0.0145498
$178$	4.20853	+	4.20853i	0.315442	+	0.315442i
$179$	5.20422			0.388982			0.194491	−	0.980904i	$-0.437695\pi$
$179$	5.20422			0.388982			0.194491	+	0.980904i	$0.437695\pi$
$180$	9.98645	+	2.07195i	0.744346	+	0.154434i
$181$		−	10.7283i		−	0.797430i	−0.917075	−	0.398715i	$-0.869456\pi$
$181$		−	10.7283i		−	0.797430i	0.917075	−	0.398715i	$-0.130544\pi$
$182$		0			0
$183$	−0.188479	−	0.188479i	−0.0139328	−	0.0139328i
$184$	−9.24543	−	9.24543i	−0.681582	−	0.681582i
$185$	2.71281	−	13.0753i	0.199449	−	0.961312i
$186$			0.00911022i			0.000667993i
$187$			2.33649i			0.170861i
$188$	−14.2168			−1.03687
$189$	0.300702	−	0.300702i	0.0218728	−	0.0218728i
$190$	−5.73121	−	8.73198i	−0.415786	−	0.633485i
$191$	16.1353			1.16751			0.583753	−	0.811931i	$-0.301584\pi$
$191$	16.1353			1.16751			0.583753	+	0.811931i	$0.301584\pi$
$192$	0.0784279	+	0.0784279i	0.00566005	+	0.00566005i
$193$		−	7.60539i		−	0.547448i	−0.961808	−	0.273724i	$-0.911744\pi$
$193$		−	7.60539i		−	0.547448i	0.961808	−	0.273724i	$-0.0882555\pi$
$194$	9.99596			0.717668
$195$		0			0
$196$	−9.67770			−0.691264
$197$		−	4.90103i		−	0.349184i	−0.984641	−	0.174592i	$-0.944139\pi$
$197$		−	4.90103i		−	0.349184i	0.984641	−	0.174592i	$-0.0558606\pi$
$198$	0.648938	+	0.648938i	0.0461180	+	0.0461180i
$199$	−19.9759			−1.41605			−0.708027	−	0.706186i	$-0.750414\pi$
$199$	−19.9759			−1.41605			−0.708027	+	0.706186i	$0.750414\pi$
$200$	4.83499	−	11.1503i	0.341886	−	0.788448i
$201$	0.722109	−	0.722109i	0.0509336	−	0.0509336i
$202$	2.71248			0.190849
$203$		−	3.86638i		−	0.271367i
$204$		−	0.704358i		−	0.0493150i
$205$	10.6471	+	16.2217i	0.743623	+	1.13297i
$206$	8.46422	+	8.46422i	0.589730	+	0.589730i
$207$	11.3814	+	11.3814i	0.791063	+	0.791063i
$208$		0			0
$209$			3.01179i			0.208330i
$210$	−0.0600544	−	0.0914980i	−0.00414415	−	0.00631396i
$211$	11.6968			0.805238			0.402619	−	0.915368i	$-0.368100\pi$
$211$	11.6968			0.805238			0.402619	+	0.915368i	$0.368100\pi$
$212$	8.56523	+	8.56523i	0.588262	+	0.588262i
$213$	−0.125532			−0.00860134
$214$	−2.39831	−	2.39831i	−0.163945	−	0.163945i
$215$	11.8486	+	18.0524i	0.808070	+	1.23116i
$216$	−0.905780	−	0.905780i	−0.0616305	−	0.0616305i
$217$	0.0857012	−	0.0857012i	0.00581778	−	0.00581778i
$218$	3.96025	−	3.96025i	0.268222	−	0.268222i
$219$	0.0165342	−	0.0165342i	0.00111727	−	0.00111727i
$220$	−1.26718	+	0.831709i	−0.0854331	+	0.0560738i
$221$		0			0
$222$	−0.256137	+	0.256137i	−0.0171908	+	0.0171908i
$223$	−2.83093			−0.189573			−0.0947864	−	0.995498i	$-0.530217\pi$
$223$	−2.83093			−0.189573			−0.0947864	+	0.995498i	$0.530217\pi$
$224$		−	4.68658i		−	0.313135i
$225$	−5.95203	+	13.7264i	−0.396802	+	0.915095i
$226$	−2.32302	+	2.32302i	−0.154525	+	0.154525i
$227$		−	15.4930i		−	1.02830i	−0.857699	−	0.514152i	$-0.828107\pi$
$227$		−	15.4930i		−	1.02830i	0.857699	−	0.514152i	$-0.171893\pi$
$228$		−	0.907934i		−	0.0601294i
$229$	14.5346	−	14.5346i	0.960475	−	0.960475i	−0.0387727	−	0.999248i	$-0.512345\pi$
$229$	14.5346	−	14.5346i	0.960475	−	0.960475i	0.999248	+	0.0387727i	$0.0123448\pi$
$230$	6.93526	−	4.55194i	0.457298	−	0.300146i
$231$			0.0315590i			0.00207643i
$232$	−11.6464			−0.764623
$233$	−4.84530	+	4.84530i	−0.317426	+	0.317426i	−0.847778	−	0.530352i	$-0.822060\pi$
$233$	−4.84530	+	4.84530i	−0.317426	+	0.317426i	0.530352	+	0.847778i	$0.322060\pi$
$234$		0			0
$235$	4.23668	−	20.4201i	0.276371	−	1.33206i
$236$	−2.37241	+	2.37241i	−0.154431	+	0.154431i
$237$	−0.558687	+	0.558687i	−0.0362906	+	0.0362906i
$238$	2.06769	−	2.06769i	0.134028	−	0.134028i
$239$	10.0017	+	10.0017i	0.646957	+	0.646957i	0.952257	−	0.305299i	$-0.0987564\pi$
$239$	10.0017	+	10.0017i	0.646957	+	0.646957i	−0.305299	+	0.952257i	$0.598756\pi$
$240$	0.225598	−	0.148071i	0.0145623	−	0.00955792i
$241$	−17.2524	−	17.2524i	−1.11132	−	1.11132i	−0.992972	−	0.118350i	$-0.962239\pi$
$241$	−17.2524	−	17.2524i	−1.11132	−	1.11132i	−0.118350	−	0.992972i	$-0.537761\pi$
$242$	7.45022			0.478918
$243$	1.67328	+	1.67328i	0.107341	+	0.107341i
$244$	4.61998			0.295764
$245$	2.88401	−	13.9004i	0.184252	−	0.888064i
$246$		−	0.526345i		−	0.0335585i
$247$		0			0
$248$	−0.258151	−	0.258151i	−0.0163926	−	0.0163926i
$249$	−0.161080	−	0.161080i	−0.0102081	−	0.0102081i
$250$	6.30381	+	4.44087i	0.398688	+	0.280865i
$251$		−	5.39488i		−	0.340522i	−0.985399	−	0.170261i	$-0.945539\pi$
$251$		−	5.39488i		−	0.340522i	0.985399	−	0.170261i	$-0.0544611\pi$
$252$			3.68063i			0.231858i
$253$	−2.39207			−0.150388
$254$	−7.14632	+	7.14632i	−0.448400	+	0.448400i
$255$	1.01169	+	0.209903i	0.0633548	+	0.0131446i
$256$	−9.93361			−0.620850
$257$	−0.280852	−	0.280852i	−0.0175191	−	0.0175191i	0.698293	−	0.715812i	$-0.253943\pi$
$257$	−0.280852	−	0.280852i	−0.0175191	−	0.0175191i	−0.715812	+	0.698293i	$0.753943\pi$
$258$		−	0.585744i		−	0.0364669i
$259$	4.81905			0.299441
$260$		0			0
$261$	14.3371			0.887442
$262$			14.5990i			0.901930i
$263$	−19.1244	−	19.1244i	−1.17926	−	1.17926i	−0.979933	−	0.199327i	$-0.936124\pi$
$263$	−19.1244	−	19.1244i	−1.17926	−	1.17926i	−0.199327	−	0.979933i	$-0.563876\pi$
$264$	0.0950626			0.00585070
$265$	−14.8550	+	9.75005i	−0.912536	+	0.598941i
$266$	2.66529	−	2.66529i	0.163420	−	0.163420i
$267$	−0.758937			−0.0464462
$268$			17.7003i			1.08122i
$269$		−	6.80280i		−	0.414774i	−0.978259	−	0.207387i	$-0.933504\pi$
$269$		−	6.80280i		−	0.414774i	0.978259	−	0.207387i	$-0.0664960\pi$
$270$	0.679452	−	0.445956i	0.0413501	−	0.0271400i
$271$	−1.19369	−	1.19369i	−0.0725115	−	0.0725115i	0.669921	−	0.742432i	$-0.266328\pi$
$271$	−1.19369	−	1.19369i	−0.0725115	−	0.0725115i	−0.742432	+	0.669921i	$0.766328\pi$
$272$	5.09810	+	5.09810i	0.309118	+	0.309118i
$273$		0			0
$274$			10.5084i			0.634837i
$275$	−0.816986	−	2.06795i	−0.0492661	−	0.124702i
$276$	0.721114			0.0434060
$277$	7.48071	+	7.48071i	0.449472	+	0.449472i	0.895179	−	0.445707i	$-0.147048\pi$
$277$	7.48071	+	7.48071i	0.449472	+	0.449472i	−0.445707	+	0.895179i	$0.647048\pi$
$278$	−8.18759			−0.491059
$279$	0.317792	+	0.317792i	0.0190257	+	0.0190257i
$280$	4.29446	+	0.890998i	0.256643	+	0.0532473i
$281$	−0.943634	−	0.943634i	−0.0562925	−	0.0562925i	0.678400	−	0.734693i	$-0.262674\pi$
$281$	−0.943634	−	0.943634i	−0.0562925	−	0.0562925i	−0.734693	+	0.678400i	$0.762674\pi$
$282$	−0.400018	+	0.400018i	−0.0238208	+	0.0238208i
$283$	−3.00754	+	3.00754i	−0.178779	+	0.178779i	−0.790824	−	0.612044i	$-0.790347\pi$
$283$	−3.00754	+	3.00754i	−0.178779	+	0.178779i	0.612044	+	0.790824i	$0.290347\pi$
$284$	1.53852	−	1.53852i	0.0912944	−	0.0912944i
$285$	1.30410	+	0.270569i	0.0772480	+	0.0160271i
$286$		0			0
$287$	−4.95141	+	4.95141i	−0.292272	+	0.292272i
$288$	17.3785			1.02404
$289$			10.6059i			0.623874i
$290$	1.50113	−	7.23517i	0.0881491	−	0.424864i
$291$	−0.901301	+	0.901301i	−0.0528352	+	0.0528352i
$292$			0.405284i			0.0237174i
$293$		−	6.74295i		−	0.393927i	−0.980411	−	0.196964i	$-0.936892\pi$
$293$		−	6.74295i		−	0.393927i	0.980411	−	0.196964i	$-0.0631081\pi$
$294$	−0.272301	+	0.272301i	−0.0158809	+	0.0158809i
$295$	−2.70059	−	4.11457i	−0.157234	−	0.239560i
$296$		−	14.5160i		−	0.843727i
$297$	−0.234353			−0.0135985
$298$	6.58008	−	6.58008i	0.381174	−	0.381174i
$299$		0			0
$300$	0.246289	+	0.623403i	0.0142195	+	0.0359922i
$301$	−5.51019	+	5.51019i	−0.317602	+	0.317602i
$302$	−2.66708	+	2.66708i	−0.153473	+	0.153473i
$303$	−0.244575	+	0.244575i	−0.0140504	+	0.0140504i
$304$	6.57157	+	6.57157i	0.376905	+	0.376905i
$305$	−1.37678	+	6.63583i	−0.0788341	+	0.379967i
$306$	7.66727	+	7.66727i	0.438309	+	0.438309i
$307$	−9.60697			−0.548298			−0.274149	−	0.961687i	$-0.588396\pi$
$307$	−9.60697			−0.548298			−0.274149	+	0.961687i	$0.588396\pi$
$308$	−0.386785	−	0.386785i	−0.0220391	−	0.0220391i
$309$	−1.52638			−0.0868327
$310$	0.193647	−	0.127099i	0.0109984	−	0.00721876i
$311$			5.22449i			0.296254i	0.988968	+	0.148127i	$0.0473244\pi$
$311$			5.22449i			0.296254i	−0.988968	+	0.148127i	$0.952676\pi$
$312$		0			0
$313$	2.37979	+	2.37979i	0.134514	+	0.134514i	0.771158	−	0.636644i	$-0.219678\pi$
$313$	2.37979	+	2.37979i	0.134514	+	0.134514i	−0.636644	+	0.771158i	$0.719678\pi$
$314$	−8.29003	−	8.29003i	−0.467834	−	0.467834i
$315$	−5.28661	−	1.09685i	−0.297867	−	0.0618003i
$316$		−	13.6945i		−	0.770375i
$317$		−	14.8061i		−	0.831593i	−0.909458	−	0.415796i	$-0.863503\pi$
$317$		−	14.8061i		−	0.831593i	0.909458	−	0.415796i	$-0.136497\pi$
$318$	0.482000			0.0270292
$319$	−1.50664	+	1.50664i	−0.0843555	+	0.0843555i
$320$	0.572891	−	2.76123i	0.0320256	−	0.154358i
$321$	0.432495			0.0241395
$322$	2.11687	+	2.11687i	0.117969	+	0.117969i
$323$			35.5846i			1.97998i
$324$	−13.6129			−0.756273
$325$		0			0
$326$	14.4541			0.800536
$327$			0.714165i			0.0394934i
$328$	14.9147	+	14.9147i	0.823529	+	0.823529i
$329$	7.52607			0.414926
$330$	−0.0122528	+	0.0590564i	−0.000674495	+	0.00325095i
$331$	−11.0229	+	11.0229i	−0.605871	+	0.605871i	−0.941864	−	0.335993i	$-0.890928\pi$
$331$	−11.0229	+	11.0229i	−0.605871	+	0.605871i	0.335993	+	0.941864i	$0.390928\pi$
$332$	3.94839			0.216696
$333$			17.8697i			0.979253i
$334$		−	12.2956i		−	0.672784i
$335$	−25.4235	−	5.27477i	−1.38903	−	0.288192i
$336$	0.0688601	+	0.0688601i	0.00375663	+	0.00375663i
$337$	−18.1944	−	18.1944i	−0.991112	−	0.991112i	0.00884867	−	0.999961i	$-0.497183\pi$
$337$	−18.1944	−	18.1944i	−0.991112	−	0.991112i	−0.999961	+	0.00884867i	$0.997183\pi$
$338$		0			0
$339$		−	0.418917i		−	0.0227525i
$340$	−14.9718	+	9.82672i	−0.811962	+	0.532929i
$341$	−0.0667915			−0.00361696
$342$	9.88328	+	9.88328i	0.534427	+	0.534427i
$343$	10.7718			0.581622
$344$	16.5979	+	16.5979i	0.894900	+	0.894900i
$345$	−0.214896	+	1.03576i	−0.0115696	+	0.0557635i
$346$	3.12068	+	3.12068i	0.167769	+	0.167769i
$347$	−16.9091	+	16.9091i	−0.907730	+	0.907730i	−0.996089	−	0.0883583i	$-0.971838\pi$
$347$	−16.9091	+	16.9091i	−0.907730	+	0.907730i	0.0883583	+	0.996089i	$0.471838\pi$
$348$	0.454191	−	0.454191i	0.0243472	−	0.0243472i
$349$	7.73307	−	7.73307i	0.413942	−	0.413942i	−0.469167	−	0.883109i	$-0.655446\pi$
$349$	7.73307	−	7.73307i	0.413942	−	0.413942i	0.883109	+	0.469167i	$0.155446\pi$
$350$	−1.10704	+	2.55303i	−0.0591739	+	0.136465i
$351$		0			0
$352$	−1.82625	+	1.82625i	−0.0973394	+	0.0973394i
$353$	0.867256			0.0461594			0.0230797	−	0.999734i	$-0.492653\pi$
$353$	0.867256			0.0461594			0.0230797	+	0.999734i	$0.492653\pi$
$354$			0.133505i			0.00709572i
$355$	1.75134	+	2.66832i	0.0929516	+	0.141620i
$356$	9.30149	−	9.30149i	0.492978	−	0.492978i
$357$			0.372872i			0.0197345i
$358$			3.58931i			0.189701i
$359$	−19.2831	+	19.2831i	−1.01773	+	1.01773i	−0.0178852	+	0.999840i	$0.505693\pi$
$359$	−19.2831	+	19.2831i	−1.01773	+	1.01773i	−0.999840	+	0.0178852i	$0.994307\pi$
$360$	−3.30395	+	15.9244i	−0.174133	+	0.839292i
$361$			26.8693i			1.41417i
$362$	7.39924			0.388895
$363$	−0.671761	+	0.671761i	−0.0352583	+	0.0352583i
$364$		0			0
$365$	−0.582123	−	0.120777i	−0.0304697	−	0.00632174i
$366$	0.129992	−	0.129992i	0.00679481	−	0.00679481i
$367$	−11.7243	+	11.7243i	−0.612003	+	0.612003i	−0.943468	−	0.331465i	$-0.892457\pi$
$367$	−11.7243	+	11.7243i	−0.612003	+	0.612003i	0.331465	+	0.943468i	$0.392457\pi$
$368$	−5.21938	+	5.21938i	−0.272079	+	0.272079i
$369$	−18.3605	−	18.3605i	−0.955810	−	0.955810i
$370$	9.01790	+	1.87100i	0.468818	+	0.0972687i
$371$	−4.53425	−	4.53425i	−0.235407	−	0.235407i
$372$	0.0201350			0.00104395
$373$	−5.18869	−	5.18869i	−0.268660	−	0.268660i	0.559900	−	0.828560i	$-0.310840\pi$
$373$	−5.18869	−	5.18869i	−0.268660	−	0.268660i	−0.828560	+	0.559900i	$0.810840\pi$
$374$	−1.61146			−0.0833265
$375$	−0.968811	+	0.167976i	−0.0500292	+	0.00867422i
$376$		−	22.6702i		−	1.16913i
$377$		0			0
$378$	0.207391	+	0.207391i	0.0106671	+	0.0106671i
$379$	23.7312	+	23.7312i	1.21899	+	1.21899i	0.967986	+	0.251004i	$0.0807608\pi$
$379$	23.7312	+	23.7312i	1.21899	+	1.21899i	0.251004	+	0.967986i	$0.419239\pi$
$380$	−19.2990	+	12.6669i	−0.990019	+	0.649796i
$381$		−	1.28872i		−	0.0660231i
$382$			11.1284i			0.569376i
$383$	29.3750			1.50099			0.750497	−	0.660874i	$-0.229814\pi$
$383$	29.3750			1.50099			0.750497	+	0.660874i	$0.229814\pi$
$384$	0.668250	−	0.668250i	0.0341015	−	0.0341015i
$385$	0.670817	−	0.440289i	0.0341880	−	0.0224392i
$386$	5.24538			0.266983
$387$	−20.4326	−	20.4326i	−1.03865	−	1.03865i
$388$		−	22.0926i		−	1.12158i
$389$	−28.8837			−1.46446			−0.732231	−	0.681056i	$-0.761521\pi$
$389$	−28.8837			−1.46446			−0.732231	+	0.681056i	$0.761521\pi$
$390$		0			0
$391$	−28.2626			−1.42930
$392$		−	15.4321i		−	0.779439i
$393$	−1.31634	−	1.31634i	−0.0664007	−	0.0664007i
$394$	3.38020			0.170292
$395$	19.6699	+	4.08103i	0.989698	+	0.205339i
$396$	1.43425	−	1.43425i	0.0720740	−	0.0720740i
$397$	5.89089			0.295655			0.147828	−	0.989013i	$-0.452772\pi$
$397$	5.89089			0.295655			0.147828	+	0.989013i	$0.452772\pi$
$398$		−	13.7772i		−	0.690589i
$399$			0.480641i			0.0240621i
$400$	−6.29477	−	2.72953i	−0.314739	−	0.136476i
$401$	−2.56134	−	2.56134i	−0.127907	−	0.127907i	0.640255	−	0.768162i	$-0.278829\pi$
$401$	−2.56134	−	2.56134i	−0.127907	−	0.127907i	−0.768162	+	0.640255i	$0.778829\pi$
$402$	0.498032	+	0.498032i	0.0248396	+	0.0248396i
$403$		0			0
$404$		−	5.99499i		−	0.298262i
$405$	4.05672	−	19.5527i	0.201580	−	0.971581i
$406$	2.66661			0.132342
$407$	−1.87787	−	1.87787i	−0.0930825	−	0.0930825i
$408$	1.12317			0.0556054
$409$	8.48983	+	8.48983i	0.419795	+	0.419795i	0.885133	−	0.465338i	$-0.154067\pi$
$409$	8.48983	+	8.48983i	0.419795	+	0.419795i	−0.465338	+	0.885133i	$0.654067\pi$
$410$	−11.1880	+	7.34320i	−0.552535	+	0.362655i
$411$	−0.947508	−	0.947508i	−0.0467371	−	0.0467371i
$412$	18.7072	−	18.7072i	0.921639	−	0.921639i
$413$	1.25590	−	1.25590i	0.0617990	−	0.0617990i
$414$	−7.84967	+	7.84967i	−0.385790	+	0.385790i
$415$	−1.17664	+	5.67120i	−0.0577590	+	0.278388i
$416$		0			0
$417$	0.738247	−	0.738247i	0.0361521	−	0.0361521i
$418$	−2.07720			−0.101599
$419$			12.6173i			0.616393i	0.951323	+	0.308197i	$0.0997255\pi$
$419$			12.6173i			0.616393i	−0.951323	+	0.308197i	$0.900275\pi$
$420$	−0.202225	+	0.132730i	−0.00986755	+	0.00647654i
$421$	−2.72216	+	2.72216i	−0.132670	+	0.132670i	−0.770323	−	0.637653i	$-0.779905\pi$
$421$	−2.72216	+	2.72216i	−0.132670	+	0.132670i	0.637653	+	0.770323i	$0.279905\pi$
$422$			8.06716i			0.392703i
$423$			27.9077i			1.35692i
$424$	−13.6582	+	13.6582i	−0.663299	+	0.663299i
$425$	−9.65277	−	24.4330i	−0.468228	−	1.18517i
$426$		−	0.0865787i		−	0.00419475i
$427$	−2.44572			−0.118357
$428$	−5.30063	+	5.30063i	−0.256216	+	0.256216i
$429$		0			0
$430$	−12.4506	+	8.17190i	−0.600420	+	0.394084i
$431$	−9.87188	+	9.87188i	−0.475512	+	0.475512i	−0.903693	−	0.428181i	$-0.859155\pi$
$431$	−9.87188	+	9.87188i	−0.475512	+	0.475512i	0.428181	+	0.903693i	$0.359155\pi$
$432$	−0.511346	+	0.511346i	−0.0246021	+	0.0246021i
$433$	24.1128	−	24.1128i	1.15879	−	1.15879i	0.174050	−	0.984737i	$-0.444315\pi$
$433$	24.1128	−	24.1128i	1.15879	−	1.15879i	0.984737	−	0.174050i	$-0.0556853\pi$
$434$	0.0591074	+	0.0591074i	0.00283725	+	0.00283725i
$435$	0.517019	+	0.787721i	0.0247891	+	0.0377683i
$436$	−8.75277	−	8.75277i	−0.419182	−	0.419182i
$437$	−36.4311			−1.74273
$438$	0.0114035	+	0.0114035i	0.000544879	+	0.000544879i
$439$	−29.0839			−1.38810			−0.694049	−	0.719927i	$-0.744175\pi$
$439$	−29.0839			−1.38810			−0.694049	+	0.719927i	$0.744175\pi$
$440$	−1.32625	−	2.02065i	−0.0632264	−	0.0963307i
$441$			18.9974i			0.904639i
$442$		0			0
$443$	7.18973	+	7.18973i	0.341594	+	0.341594i	0.856966	−	0.515372i	$-0.172346\pi$
$443$	7.18973	+	7.18973i	0.341594	+	0.341594i	−0.515372	+	0.856966i	$0.672346\pi$
$444$	0.566103	+	0.566103i	0.0268660	+	0.0268660i
$445$	10.5882	+	16.1320i	0.501927	+	0.764728i
$446$		−	1.95247i		−	0.0924520i
$447$			1.18661i			0.0561245i
$448$	1.01769			0.0480812
$449$	−11.2814	+	11.2814i	−0.532401	+	0.532401i	−0.921286	−	0.388885i	$-0.872860\pi$
$449$	−11.2814	+	11.2814i	−0.532401	+	0.532401i	0.388885	+	0.921286i	$0.372860\pi$
$450$	−9.46700	−	4.10507i	−0.446279	−	0.193515i
$451$	3.85889			0.181708
$452$	5.13423	+	5.13423i	0.241494	+	0.241494i
$453$		−	0.480963i		−	0.0225976i
$454$	10.6854			0.501490
$455$		0			0
$456$	1.44780			0.0677993
$457$			19.2290i			0.899495i	0.893156	+	0.449748i	$0.148486\pi$
$457$			19.2290i			0.899495i	−0.893156	+	0.449748i	$0.851514\pi$
$458$	10.0244	+	10.0244i	0.468410	+	0.468410i
$459$	−2.76890			−0.129241
$460$	−10.0605	−	15.3280i	−0.469073	−	0.714672i
$461$	−3.13390	+	3.13390i	−0.145960	+	0.145960i	−0.776311	−	0.630350i	$-0.782911\pi$
$461$	−3.13390	+	3.13390i	−0.145960	+	0.145960i	0.630350	+	0.776311i	$0.282911\pi$
$462$	−0.0217660			−0.00101264
$463$		−	12.2584i		−	0.569696i	−0.958573	−	0.284848i	$-0.908057\pi$
$463$		−	12.2584i		−	0.569696i	0.958573	−	0.284848i	$-0.0919431\pi$
$464$			6.57481i			0.305228i
$465$	−0.00600033	+	0.0289206i	−0.000278259	+	0.00134116i
$466$	−3.34177	−	3.34177i	−0.154804	−	0.154804i
$467$	10.5138	+	10.5138i	0.486522	+	0.486522i	0.907207	−	0.420685i	$-0.138210\pi$
$467$	10.5138	+	10.5138i	0.486522	+	0.486522i	−0.420685	+	0.907207i	$0.638210\pi$
$468$		0			0
$469$		−	9.37014i		−	0.432673i
$470$	14.0836	+	2.92201i	0.649627	+	0.134782i
$471$	1.49497			0.0688845
$472$	−3.78306	−	3.78306i	−0.174130	−	0.174130i
$473$	4.29438			0.197456
$474$	−0.385322	−	0.385322i	−0.0176984	−	0.0176984i
$475$	−12.4426	−	31.4947i	−0.570907	−	1.44507i
$476$	−4.56991	−	4.56991i	−0.209461	−	0.209461i
$477$	16.8136	−	16.8136i	0.769843	−	0.769843i
$478$	−6.89810	+	6.89810i	−0.315512	+	0.315512i
$479$	8.32128	−	8.32128i	0.380209	−	0.380209i	−0.490968	−	0.871177i	$-0.663357\pi$
$479$	8.32128	−	8.32128i	0.380209	−	0.380209i	0.871177	+	0.490968i	$0.163357\pi$
$480$	0.626697	+	0.954826i	0.0286047	+	0.0435816i
$481$		0			0
$482$	11.8988	−	11.8988i	0.541976	−	0.541976i
$483$	−0.381743			−0.0173699
$484$		−	16.4661i		−	0.748461i
$485$	31.7324	+	6.58372i	1.44089	+	0.298951i
$486$	−1.15405	+	1.15405i	−0.0523488	+	0.0523488i
$487$			26.4997i			1.20082i	0.799694	+	0.600408i	$0.204995\pi$
$487$			26.4997i			1.20082i	−0.799694	+	0.600408i	$0.795005\pi$
$488$			7.36705i			0.333491i
$489$	−1.30327	+	1.30327i	−0.0589360	+	0.0589360i
$490$	9.58700	+	1.98907i	0.433096	+	0.0898572i
$491$		−	14.2507i		−	0.643123i	−0.946889	−	0.321562i	$-0.895792\pi$
$491$		−	14.2507i		−	0.643123i	0.946889	−	0.321562i	$-0.104208\pi$
$492$	−1.16330			−0.0524457
$493$	−17.8011	+	17.8011i	−0.801719	+	0.801719i
$494$		0			0
$495$	1.63265	+	2.48748i	0.0733823	+	0.111804i
$496$	−0.145736	+	0.145736i	−0.00654373	+	0.00654373i
$497$	−0.814460	+	0.814460i	−0.0365335	+	0.0365335i
$498$	0.111096	−	0.111096i	0.00497832	−	0.00497832i
$499$	20.1666	+	20.1666i	0.902783	+	0.902783i	0.995676	−	0.0928929i	$-0.0296114\pi$
$499$	20.1666	+	20.1666i	0.902783	+	0.902783i	−0.0928929	+	0.995676i	$0.529611\pi$
$500$	9.81500	−	13.9324i	0.438940	−	0.623076i
$501$	1.10865	+	1.10865i	0.0495308	+	0.0495308i
$502$	3.72081			0.166068
$503$	−6.41738	−	6.41738i	−0.286137	−	0.286137i	0.549414	−	0.835551i	$-0.314851\pi$
$503$	−6.41738	−	6.41738i	−0.286137	−	0.286137i	−0.835551	+	0.549414i	$0.814851\pi$
$504$	−5.86915			−0.261433
$505$	8.61081	+	1.78654i	0.383176	+	0.0794999i
$506$		−	1.64979i		−	0.0733422i
$507$		0			0
$508$	15.7945	+	15.7945i	0.700767	+	0.700767i
$509$	9.67201	+	9.67201i	0.428704	+	0.428704i	0.888187	−	0.459483i	$-0.151965\pi$
$509$	9.67201	+	9.67201i	0.428704	+	0.428704i	−0.459483	+	0.888187i	$0.651965\pi$
$510$	−0.144768	+	0.697757i	−0.00641044	+	0.0308972i
$511$		−	0.214548i		−	0.00949107i
$512$			14.6405i			0.647023i
$513$	−3.56917			−0.157583
$514$	0.193701	−	0.193701i	0.00854380	−	0.00854380i
$515$	21.2950	+	32.4447i	0.938369	+	1.42968i
$516$	−1.29459			−0.0569909
$517$	−2.93273	−	2.93273i	−0.128981	−	0.128981i
$518$			3.32366i			0.146033i
$519$	−0.562762			−0.0247025
$520$		0			0
$521$	−29.1893			−1.27881			−0.639403	−	0.768872i	$-0.720819\pi$
$521$	−29.1893			−1.27881			−0.639403	+	0.768872i	$0.720819\pi$
$522$			9.88816i			0.432793i
$523$	10.0289	+	10.0289i	0.438533	+	0.438533i	0.891518	−	0.452985i	$-0.149641\pi$
$523$	10.0289	+	10.0289i	0.438533	+	0.438533i	−0.452985	+	0.891518i	$0.649641\pi$
$524$	32.2661			1.40955
$525$	−0.130380	−	0.330016i	−0.00569025	−	0.0144031i
$526$	13.1899	−	13.1899i	0.575108	−	0.575108i
$527$	−0.789148			−0.0343758
$528$		−	0.0536663i		−	0.00233553i
$529$		−	5.93490i		−	0.258039i
$530$	−6.72453	−	10.2454i	−0.292095	−	0.445031i
$531$	4.65707	+	4.65707i	0.202100	+	0.202100i
$532$	−5.89071	−	5.89071i	−0.255395	−	0.255395i
$533$		0			0
$534$		−	0.523432i		−	0.0226511i
$535$	−6.03387	−	9.19310i	−0.260867	−	0.397452i
$536$	−28.2249			−1.21913
$537$	−0.323635	−	0.323635i	−0.0139659	−	0.0139659i
$538$	4.69184			0.202279
$539$	−1.99638	−	1.99638i	−0.0859901	−	0.0859901i
$540$	−0.985632	−	1.50169i	−0.0424148	−	0.0646226i
$541$	10.8210	+	10.8210i	0.465233	+	0.465233i	0.900366	−	0.435133i	$-0.143299\pi$
$541$	10.8210	+	10.8210i	0.465233	+	0.465233i	−0.435133	+	0.900366i	$0.643299\pi$
$542$	0.823278	−	0.823278i	0.0353628	−	0.0353628i
$543$	−0.667164	+	0.667164i	−0.0286307	+	0.0286307i
$544$	−21.5773	+	21.5773i	−0.925120	+	0.925120i
$545$	15.1803	−	9.96353i	0.650251	−	0.426791i
$546$		0			0
$547$	0.334432	−	0.334432i	0.0142993	−	0.0142993i	−0.699921	−	0.714220i	$-0.746781\pi$
$547$	0.334432	−	0.334432i	0.0142993	−	0.0142993i	0.714220	+	0.699921i	$0.246781\pi$
$548$	23.2252			0.992133
$549$		−	9.06906i		−	0.387058i
$550$	1.42624	−	0.563469i	0.0608153	−	0.0240264i
$551$	−22.9460	+	22.9460i	−0.977531	+	0.977531i
$552$			1.14989i			0.0489427i
$553$			7.24957i			0.308283i
$554$	−5.15938	+	5.15938i	−0.219201	+	0.219201i
$555$	−0.981814	+	0.644411i	−0.0416757	+	0.0273537i
$556$			18.0958i			0.767435i
$557$	34.3584			1.45581			0.727906	−	0.685677i	$-0.240494\pi$
$557$	34.3584			1.45581			0.727906	+	0.685677i	$0.240494\pi$
$558$	−0.219179	+	0.219179i	−0.00927857	+	0.00927857i
$559$		0			0
$560$	0.503001	−	2.42438i	0.0212557	−	0.102449i
$561$	0.145300	−	0.145300i	0.00613455	−	0.00613455i
$562$	0.650816	−	0.650816i	0.0274530	−	0.0274530i
$563$	−19.0692	+	19.0692i	−0.803671	+	0.803671i	−0.983667	−	0.179996i	$-0.942391\pi$
$563$	−19.0692	+	19.0692i	−0.803671	+	0.803671i	0.179996	+	0.983667i	$0.442391\pi$
$564$	0.884102	+	0.884102i	0.0372274	+	0.0372274i
$565$	−8.90450	+	5.84444i	−0.374615	+	0.245878i
$566$	−2.07427	−	2.07427i	−0.0871882	−	0.0871882i
$567$	7.20638			0.302640
$568$	2.45333	+	2.45333i	0.102940	+	0.102940i
$569$	36.5069			1.53045			0.765224	−	0.643765i	$-0.222628\pi$
$569$	36.5069			1.53045			0.765224	+	0.643765i	$0.222628\pi$
$570$	−0.186609	+	0.899425i	−0.00781620	+	0.0376728i
$571$		−	31.2687i		−	1.30855i	−0.756255	−	0.654277i	$-0.772973\pi$
$571$		−	31.2687i		−	1.30855i	0.756255	−	0.654277i	$-0.227027\pi$
$572$		0			0
$573$	−1.00341	−	1.00341i	−0.0419178	−	0.0419178i
$574$	−3.41495	−	3.41495i	−0.142537	−	0.142537i
$575$	25.0142	−	9.88240i	1.04316	−	0.412125i
$576$			3.77373i			0.157239i
$577$		−	28.3409i		−	1.17985i	−0.807460	−	0.589923i	$-0.799158\pi$
$577$		−	28.3409i		−	1.17985i	0.807460	−	0.589923i	$-0.200842\pi$
$578$	−7.31477			−0.304254
$579$	−0.472958	+	0.472958i	−0.0196554	+	0.0196554i
$580$	−15.9908	−	3.31772i	−0.663983	−	0.137761i
$581$	−2.09019			−0.0867158
$582$	−0.621620	−	0.621620i	−0.0257670	−	0.0257670i
$583$			3.53378i			0.146354i
$584$	−0.646268			−0.0267427
$585$		0			0
$586$	4.65056			0.192113
$587$		−	21.1182i		−	0.871643i	−0.900033	−	0.435822i	$-0.856458\pi$
$587$		−	21.1182i		−	0.871643i	0.900033	−	0.435822i	$-0.143542\pi$
$588$	0.601828	+	0.601828i	0.0248190	+	0.0248190i
$589$	−1.01723			−0.0419142
$590$	2.83779	−	1.86257i	0.116830	−	0.0766809i
$591$	−0.304781	+	0.304781i	−0.0125370	+	0.0125370i
$592$	−8.19483			−0.336805
$593$		−	12.8500i		−	0.527685i	−0.964566	−	0.263843i	$-0.915010\pi$
$593$		−	12.8500i		−	0.527685i	0.964566	−	0.263843i	$-0.0849899\pi$
$594$		−	0.161631i		−	0.00663180i
$595$	7.92577	−	5.20206i	0.324925	−	0.213264i
$596$	−14.5430	−	14.5430i	−0.595704	−	0.595704i
$597$	1.24224	+	1.24224i	0.0508416	+	0.0508416i
$598$		0			0
$599$		−	3.15330i		−	0.128840i	−0.997923	−	0.0644201i	$-0.979480\pi$
$599$		−	3.15330i		−	0.128840i	0.997923	−	0.0644201i	$-0.0205198\pi$
$600$	−0.994082	+	0.392734i	−0.0405832	+	0.0160333i
$601$	23.7424			0.968472			0.484236	−	0.874938i	$-0.339098\pi$
$601$	23.7424			0.968472			0.484236	+	0.874938i	$0.339098\pi$
$602$	−3.80033	−	3.80033i	−0.154890	−	0.154890i
$603$	34.7458			1.41496
$604$	5.89466	+	5.89466i	0.239850	+	0.239850i
$605$	23.6509	+	4.90700i	0.961545	+	0.199498i
$606$	−0.168681	−	0.168681i	−0.00685220	−	0.00685220i
$607$	−3.00186	+	3.00186i	−0.121842	+	0.121842i	−0.765399	−	0.643557i	$-0.777458\pi$
$607$	−3.00186	+	3.00186i	−0.121842	+	0.121842i	0.643557	+	0.765399i	$0.277458\pi$
$608$	−27.8136	+	27.8136i	−1.12799	+	1.12799i
$609$	−0.240439	+	0.240439i	−0.00974308	+	0.00974308i
$610$	−4.57668	−	0.949553i	−0.185304	−	0.0384463i
$611$		0			0
$612$	16.9458	−	16.9458i	0.684995	−	0.684995i
$613$	−43.6898			−1.76461			−0.882306	−	0.470676i	$-0.844010\pi$
$613$	−43.6898			−1.76461			−0.882306	+	0.470676i	$0.844010\pi$
$614$		−	6.62585i		−	0.267397i
$615$	0.346670	−	1.67089i	0.0139791	−	0.0673769i
$616$	0.616770	−	0.616770i	0.0248504	−	0.0248504i
$617$			14.4409i			0.581367i	0.956819	+	0.290684i	$0.0938827\pi$
$617$			14.4409i			0.581367i	−0.956819	+	0.290684i	$0.906117\pi$
$618$		−	1.05273i		−	0.0423471i
$619$	3.86804	−	3.86804i	0.155470	−	0.155470i	−0.625086	−	0.780556i	$-0.714936\pi$
$619$	3.86804	−	3.86804i	0.155470	−	0.155470i	0.780556	+	0.625086i	$0.214936\pi$
$620$	−0.280909	−	0.427989i	−0.0112816	−	0.0171884i
$621$		−	2.83477i		−	0.113755i
$622$	−3.60329			−0.144479
$623$	−4.92401	+	4.92401i	−0.197276	+	0.197276i
$624$		0			0
$625$	17.0867	+	18.2495i	0.683466	+	0.729982i
$626$	−1.64132	+	1.64132i	−0.0656004	+	0.0656004i
$627$	0.187294	−	0.187294i	0.00747982	−	0.00747982i
$628$	−18.3223	+	18.3223i	−0.731137	+	0.731137i
$629$	−22.1872	−	22.1872i	−0.884662	−	0.884662i
$630$	0.756486	−	3.64613i	0.0301391	−	0.145265i
$631$	19.3475	+	19.3475i	0.770211	+	0.770211i	0.978143	−	0.207932i	$-0.0666734\pi$
$631$	19.3475	+	19.3475i	0.770211	+	0.770211i	−0.207932	+	0.978143i	$0.566673\pi$
$632$	21.8373			0.868642
$633$	−0.727388	−	0.727388i	−0.0289111	−	0.0289111i
$634$	10.2116			0.405556
$635$	−27.3930	+	17.9793i	−1.08706	+	0.713487i
$636$		−	1.06529i		−	0.0422417i
$637$		0			0
$638$	−1.03911	−	1.03911i	−0.0411390	−	0.0411390i
$639$	−3.02013	−	3.02013i	−0.119475	−	0.119475i
$640$	−23.5273	−	4.88135i	−0.929998	−	0.192952i
$641$			35.8310i			1.41524i	0.706593	+	0.707620i	$0.250231\pi$
$641$			35.8310i			1.41524i	−0.706593	+	0.707620i	$0.749769\pi$
$642$			0.298288i			0.0117725i
$643$	−5.93411			−0.234019			−0.117009	−	0.993131i	$-0.537331\pi$
$643$	−5.93411			−0.234019			−0.117009	+	0.993131i	$0.537331\pi$
$644$	4.67862	−	4.67862i	0.184363	−	0.184363i
$645$	0.385793	−	1.85946i	0.0151906	−	0.0732161i
$646$	−24.5424			−0.965607
$647$	4.39835	+	4.39835i	0.172917	+	0.172917i	0.788260	−	0.615343i	$-0.210982\pi$
$647$	4.39835	+	4.39835i	0.172917	+	0.172917i	−0.615343	+	0.788260i	$0.710982\pi$
$648$		−	21.7072i		−	0.852740i
$649$	−0.978793			−0.0384210
$650$		0			0
$651$	−0.0106590			−0.000417760
$652$		−	31.9457i		−	1.25109i
$653$	−21.8121	−	21.8121i	−0.853575	−	0.853575i	0.136997	−	0.990571i	$-0.456255\pi$
$653$	−21.8121	−	21.8121i	−0.853575	−	0.853575i	−0.990571	+	0.136997i	$0.956255\pi$
$654$	−0.492553			−0.0192604
$655$	−9.61546	+	46.3449i	−0.375707	+	1.81084i
$656$	8.41991	−	8.41991i	0.328742	−	0.328742i
$657$	0.795576			0.0310384
$658$			5.19067i			0.202353i
$659$			26.7893i			1.04356i	0.853079	+	0.521782i	$0.174733\pi$
$659$			26.7893i			1.04356i	−0.853079	+	0.521782i	$0.825267\pi$
$660$	0.130524	+	0.0270806i	0.00508063	+	0.00105411i
$661$	−9.23307	−	9.23307i	−0.359125	−	0.359125i	0.504365	−	0.863490i	$-0.331726\pi$
$661$	−9.23307	−	9.23307i	−0.359125	−	0.359125i	−0.863490	+	0.504365i	$0.831726\pi$
$662$	−7.60238	−	7.60238i	−0.295475	−	0.295475i
$663$		0			0
$664$			6.29612i			0.244337i
$665$	10.2165	−	6.70557i	0.396179	−	0.260031i
$666$	−12.3246			−0.477568
$667$	−18.2245	−	18.2245i	−0.705657	−	0.705657i
$668$	−27.1751			−1.05144
$669$	0.176047	+	0.176047i	0.00680638	+	0.00680638i
$670$	3.63797	−	17.5344i	0.140547	−	0.677412i
$671$	0.953039	+	0.953039i	0.0367917	+	0.0367917i
$672$	−0.291445	+	0.291445i	−0.0112427	+	0.0112427i
$673$	23.0361	−	23.0361i	0.887977	−	0.887977i	−0.106351	−	0.994329i	$-0.533917\pi$
$673$	23.0361	−	23.0361i	0.887977	−	0.887977i	0.994329	+	0.106351i	$0.0339168\pi$
$674$	12.5485	−	12.5485i	0.483351	−	0.483351i
$675$	2.45066	−	0.968184i	0.0943258	−	0.0372654i
$676$		0			0
$677$	7.47403	−	7.47403i	0.287250	−	0.287250i	−0.548742	−	0.835992i	$-0.684893\pi$
$677$	7.47403	−	7.47403i	0.287250	−	0.287250i	0.835992	+	0.548742i	$0.184893\pi$
$678$	0.288924			0.0110960
$679$			11.6954i			0.448827i
$680$	−15.6698	−	23.8742i	−0.600908	−	0.915533i
$681$	−0.963464	+	0.963464i	−0.0369200	+	0.0369200i
$682$		−	0.0460656i		−	0.00176394i
$683$		−	1.28980i		−	0.0493526i	−0.999695	−	0.0246763i	$-0.992144\pi$
$683$		−	1.28980i		−	0.0493526i	0.999695	−	0.0246763i	$-0.00785551\pi$
$684$	21.8436	−	21.8436i	0.835210	−	0.835210i
$685$	−6.92124	+	33.3592i	−0.264447	+	1.27459i
$686$			7.42921i			0.283649i
$687$	−1.80773			−0.0689693
$688$	9.37013	−	9.37013i	0.357233	−	0.357233i
$689$		0			0
$690$	−0.714356	−	0.148212i	−0.0271951	−	0.00564233i
$691$	−13.2988	+	13.2988i	−0.505911	+	0.505911i	−0.913269	−	0.407358i	$-0.866450\pi$
$691$	−13.2988	+	13.2988i	−0.505911	+	0.505911i	0.407358	+	0.913269i	$0.366450\pi$
$692$	6.89719	−	6.89719i	0.262192	−	0.262192i
$693$	−0.759263	+	0.759263i	−0.0288420	+	0.0288420i
$694$	−11.6621	−	11.6621i	−0.442687	−	0.442687i
$695$	−25.9917	−	5.39266i	−0.985921	−	0.204555i
$696$	0.724256	+	0.724256i	0.0274528	+	0.0274528i
$697$	45.5932			1.72697
$698$	5.33344	+	5.33344i	0.201874	+	0.201874i
$699$	0.602631			0.0227936
$700$	5.64260	+	2.44673i	0.213270	+	0.0924778i
$701$			21.8278i			0.824425i	0.911088	+	0.412212i	$0.135244\pi$
$701$			21.8278i			0.824425i	−0.911088	+	0.412212i	$0.864756\pi$
$702$		0			0
$703$	−28.5998	−	28.5998i	−1.07866	−	1.07866i
$704$	−0.396569	−	0.396569i	−0.0149462	−	0.0149462i
$705$	−1.53333	+	1.00640i	−0.0577487	+	0.0379032i
$706$			0.598139i			0.0225113i
$707$			3.17362i			0.119356i
$708$	0.295067			0.0110893
$709$	18.2874	−	18.2874i	0.686798	−	0.686798i	−0.274725	−	0.961523i	$-0.588587\pi$
$709$	18.2874	−	18.2874i	0.686798	−	0.686798i	0.961523	+	0.274725i	$0.0885867\pi$
$710$	−1.84032	+	1.20789i	−0.0690658	+	0.0453312i
$711$	−26.8824			−1.00817
$712$	14.8322	+	14.8322i	0.555861	+	0.555861i
$713$		−	0.807921i		−	0.0302569i
$714$	−0.257167			−0.00962423
$715$		0			0
$716$	7.93292			0.296467
$717$		−	1.24396i		−	0.0464564i
$718$	−13.2994	−	13.2994i	−0.496330	−	0.496330i
$719$	−17.7717			−0.662771			−0.331385	−	0.943495i	$-0.607516\pi$
$719$	−17.7717			−0.662771			−0.331385	+	0.943495i	$0.607516\pi$
$720$	8.98993	+	1.86520i	0.335035	+	0.0695118i
$721$	−9.90321	+	9.90321i	−0.368815	+	0.368815i
$722$	−18.5315			−0.689672
$723$			2.14575i			0.0798013i
$724$		−	16.3535i		−	0.607772i
$725$	9.53071	−	21.9795i	0.353962	−	0.816298i
$726$	−0.463308	−	0.463308i	−0.0171950	−	0.0171950i
$727$	14.6033	+	14.6033i	0.541607	+	0.541607i	0.924000	−	0.382393i	$-0.124900\pi$
$727$	14.6033	+	14.6033i	0.541607	+	0.541607i	−0.382393	+	0.924000i	$0.624900\pi$
$728$		0			0
$729$			26.5832i			0.984564i
$730$	0.0832987	−	0.401485i	0.00308302	−	0.0148596i
$731$	50.7386			1.87663
$732$	−0.287303	−	0.287303i	−0.0106190	−	0.0106190i
$733$	5.44505			0.201118			0.100559	−	0.994931i	$-0.467937\pi$
$733$	5.44505			0.201118			0.100559	+	0.994931i	$0.467937\pi$
$734$	−8.08614	−	8.08614i	−0.298465	−	0.298465i
$735$	−1.04377	+	0.685078i	−0.0385002	+	0.0252695i
$736$	−22.0906	−	22.0906i	−0.814271	−	0.814271i
$737$	−3.65132	+	3.65132i	−0.134498	+	0.134498i
$738$	12.6631	−	12.6631i	0.466135	−	0.466135i
$739$	−21.6891	+	21.6891i	−0.797846	+	0.797846i	−0.982756	−	0.184910i	$-0.940801\pi$
$739$	−21.6891	+	21.6891i	−0.797846	+	0.797846i	0.184910	+	0.982756i	$0.440801\pi$
$740$	4.13520	−	19.9309i	0.152013	−	0.732676i
$741$		0			0
$742$	3.12723	−	3.12723i	0.114804	−	0.114804i
$743$	0.675576			0.0247845			0.0123922	−	0.999923i	$-0.496055\pi$
$743$	0.675576			0.0247845			0.0123922	+	0.999923i	$0.496055\pi$
$744$			0.0321074i			0.00117711i
$745$	25.2225	−	16.5547i	0.924080	−	0.606517i
$746$	3.57860	−	3.57860i	0.131022	−	0.131022i
$747$		−	7.75072i		−	0.283584i
$748$			3.56157i			0.130224i
$749$	2.80604	−	2.80604i	0.102531	−	0.102531i
$750$	−0.115851	−	0.668181i	−0.00423029	−	0.0243985i
$751$			5.64380i			0.205945i	0.994684	+	0.102973i	$0.0328354\pi$
$751$			5.64380i			0.205945i	−0.994684	+	0.102973i	$0.967165\pi$
$752$	−12.7982			−0.466701
$753$	−0.335492	+	0.335492i	−0.0122260	+	0.0122260i
$754$		0			0
$755$	−10.2233	+	6.71006i	−0.372065	+	0.244204i
$756$	0.458367	−	0.458367i	0.0166706	−	0.0166706i
$757$	21.3676	−	21.3676i	0.776619	−	0.776619i	−0.202635	−	0.979254i	$-0.564951\pi$
$757$	21.3676	−	21.3676i	0.776619	−	0.776619i	0.979254	+	0.202635i	$0.0649506\pi$
$758$	−16.3672	+	16.3672i	−0.594484	+	0.594484i
$759$	0.148756	+	0.148756i	0.00539950	+	0.00539950i
$760$	−20.1987	−	30.7743i	−0.732682	−	1.11630i
$761$	13.3384	+	13.3384i	0.483516	+	0.483516i	0.906253	−	0.422736i	$-0.138930\pi$
$761$	13.3384	+	13.3384i	0.483516	+	0.483516i	−0.422736	+	0.906253i	$0.638930\pi$
$762$	0.888819			0.0321985
$763$	4.63353	+	4.63353i	0.167745	+	0.167745i
$764$	24.5954			0.889829
$765$	19.2900	+	29.3899i	0.697430	+	1.06259i
$766$			20.2597i			0.732013i
$767$		0			0
$768$	0.617743	+	0.617743i	0.0222909	+	0.0222909i
$769$	8.21751	+	8.21751i	0.296331	+	0.296331i	0.839575	−	0.543244i	$-0.182804\pi$
$769$	8.21751	+	8.21751i	0.296331	+	0.296331i	−0.543244	+	0.839575i	$0.682804\pi$
$770$	0.303664	+	0.462657i	0.0109433	+	0.0166730i
$771$			0.0349307i			0.00125800i
$772$		−	11.5931i		−	0.417244i
$773$	−8.29320			−0.298286			−0.149143	−	0.988816i	$-0.547651\pi$
$773$	−8.29320			−0.298286			−0.149143	+	0.988816i	$0.547651\pi$
$774$	14.0922	−	14.0922i	0.506533	−	0.506533i
$775$	0.698448	−	0.275937i	0.0250890	−	0.00991194i
$776$	35.2290			1.26465
$777$	−0.299683	−	0.299683i	−0.0107511	−	0.0107511i
$778$		−	19.9209i		−	0.714198i
$779$	58.7707			2.10568
$780$		0			0
$781$	0.634752			0.0227132
$782$		−	19.4925i		−	0.697049i
$783$	−1.78547	−	1.78547i	−0.0638074	−	0.0638074i
$784$	−8.71199			−0.311142
$785$	−20.8568	−	31.7770i	−0.744409	−	1.13417i
$786$	0.907871	−	0.907871i	0.0323827	−	0.0323827i
$787$	−48.6606			−1.73456			−0.867282	−	0.497817i	$-0.834135\pi$
$787$	−48.6606			−1.73456			−0.867282	+	0.497817i	$0.834135\pi$
$788$		−	7.47076i		−	0.266135i
$789$			2.37858i			0.0846797i
$790$	−2.81465	+	13.5661i	−0.100141	+	0.482662i
$791$	−2.71795	−	2.71795i	−0.0966392	−	0.0966392i
$792$	2.28707	+	2.28707i	0.0812675	+	0.0812675i
$793$		0			0
$794$			4.06290i			0.144187i
$795$	1.53012	+	0.317463i	0.0542677	+	0.0112593i
$796$	−30.4498			−1.07926
$797$	−36.6678	−	36.6678i	−1.29884	−	1.29884i	−0.929159	−	0.369679i	$-0.879468\pi$
$797$	−36.6678	−	36.6678i	−1.29884	−	1.29884i	−0.369679	−	0.929159i	$-0.620532\pi$
$798$	−0.331494			−0.0117348
$799$	−34.6505	−	34.6505i	−1.22585	−	1.22585i
$800$	11.5525	−	26.6421i	0.408443	−	0.941942i
$801$	−18.2589	−	18.2589i	−0.645147	−	0.645147i
$802$	1.76653	−	1.76653i	0.0623785	−	0.0623785i
$803$	−0.0836045	+	0.0836045i	−0.00295034	+	0.00295034i
$804$	1.10073	−	1.10073i	0.0388197	−	0.0388197i
$805$	5.32581	+	8.11432i	0.187710	+	0.285992i
$806$		0			0
$807$	−0.423047	+	0.423047i	−0.0148920	+	0.0148920i
$808$	9.55965			0.336307
$809$			11.3889i			0.400413i	0.979754	+	0.200206i	$0.0641613\pi$
$809$			11.3889i			0.400413i	−0.979754	+	0.200206i	$0.935839\pi$
$810$	13.4853	+	2.79789i	0.473826	+	0.0983077i
$811$	23.0388	−	23.0388i	0.809003	−	0.809003i	−0.175480	−	0.984483i	$-0.556148\pi$
$811$	23.0388	−	23.0388i	0.809003	−	0.809003i	0.984483	+	0.175480i	$0.0561477\pi$
$812$		−	5.89362i		−	0.206825i
$813$			0.148464i			0.00520687i
$814$	1.29515	−	1.29515i	0.0453950	−	0.0453950i
$815$	45.8847	+	9.51999i	1.60727	+	0.333471i
$816$		−	0.634073i		−	0.0221970i
$817$	65.4031			2.28817
$818$	−5.85536	+	5.85536i	−0.204728	+	0.204728i
$819$		0			0
$820$	16.2296	+	24.7271i	0.566762	+	0.863509i
$821$	7.31750	−	7.31750i	0.255383	−	0.255383i	−0.567790	−	0.823173i	$-0.692202\pi$
$821$	7.31750	−	7.31750i	0.255383	−	0.255383i	0.823173	+	0.567790i	$0.192202\pi$
$822$	0.653489	−	0.653489i	0.0227930	−	0.0227930i
$823$	−7.13667	+	7.13667i	−0.248769	+	0.248769i	−0.820465	−	0.571697i	$-0.806285\pi$
$823$	−7.13667	+	7.13667i	−0.248769	+	0.248769i	0.571697	+	0.820465i	$0.306285\pi$
$824$	29.8307	+	29.8307i	1.03920	+	1.03920i
$825$	−0.0777936	+	0.179406i	−0.00270842	+	0.00624610i
$826$	0.866187	+	0.866187i	0.0301385	+	0.0301385i
$827$	8.88196			0.308856			0.154428	−	0.988004i	$-0.450647\pi$
$827$	8.88196			0.308856			0.154428	+	0.988004i	$0.450647\pi$
$828$	17.3490	+	17.3490i	0.602918	+	0.602918i
$829$	10.4462			0.362812			0.181406	−	0.983408i	$-0.441935\pi$
$829$	10.4462			0.362812			0.181406	+	0.983408i	$0.441935\pi$
$830$	−3.91138	−	0.811519i	−0.135766	−	0.0281682i
$831$		−	0.930407i		−	0.0322755i
$832$		0			0
$833$	−23.5874	−	23.5874i	−0.817255	−	0.817255i
$834$	0.509163	+	0.509163i	0.0176309	+	0.0176309i
$835$	8.09834	−	39.0326i	0.280255	−	1.35078i
$836$			4.59094i			0.158781i
$837$		−	0.0791525i		−	0.00273591i
$838$	−8.70202			−0.300606
$839$	18.5309	−	18.5309i	0.639759	−	0.639759i	−0.310737	−	0.950496i	$-0.600576\pi$
$839$	18.5309	−	18.5309i	0.639759	−	0.639759i	0.950496	+	0.310737i	$0.100576\pi$
$840$	−0.211651	−	0.322469i	−0.00730267	−	0.0111262i
$841$	6.04271			0.208369
$842$	−1.87745	−	1.87745i	−0.0647012	−	0.0647012i
$843$			0.117364i			0.00404222i
$844$	17.8297			0.613723
$845$		0			0
$846$	−19.2477			−0.661751
$847$			8.71682i			0.299513i
$848$	7.71053	+	7.71053i	0.264781	+	0.264781i
$849$	0.374060			0.0128377
$850$	16.8512	−	6.65744i	0.577992	−	0.228348i
$851$	22.7150	−	22.7150i	0.778661	−	0.778661i
$852$	−0.191352			−0.00655562
$853$		−	30.8130i		−	1.05502i	−0.849550	−	0.527509i	$-0.823126\pi$
$853$		−	30.8130i		−	1.05502i	0.849550	−	0.527509i	$-0.176874\pi$
$854$		−	1.68679i		−	0.0577208i
$855$	24.8652	+	37.8842i	0.850371	+	1.29561i
$856$	−8.45243	−	8.45243i	−0.288898	−	0.288898i
$857$	−7.54399	−	7.54399i	−0.257698	−	0.257698i	0.566419	−	0.824117i	$-0.308328\pi$
$857$	−7.54399	−	7.54399i	−0.257698	−	0.257698i	−0.824117	+	0.566419i	$0.808328\pi$
$858$		0			0
$859$		−	9.75562i		−	0.332857i	−0.986053	−	0.166429i	$-0.946776\pi$
$859$		−	9.75562i		−	0.332857i	0.986053	−	0.166429i	$-0.0532235\pi$
$860$	18.0612	+	27.5177i	0.615880	+	0.938346i
$861$	0.615828			0.0209873
$862$	−6.80856	−	6.80856i	−0.231900	−	0.231900i
$863$	−35.0410			−1.19281			−0.596405	−	0.802683i	$-0.703405\pi$
$863$	−35.0410			−1.19281			−0.596405	+	0.802683i	$0.703405\pi$
$864$	−2.16423	−	2.16423i	−0.0736286	−	0.0736286i
$865$	7.85127	+	11.9621i	0.266951	+	0.406723i
$866$	16.6304	+	16.6304i	0.565124	+	0.565124i
$867$	0.659548	−	0.659548i	0.0223994	−	0.0223994i
$868$	0.130637	−	0.130637i	0.00443409	−	0.00443409i
$869$	2.82499	−	2.82499i	0.0958311	−	0.0958311i
$870$	−0.543285	+	0.356584i	−0.0184191	+	0.0120893i
$871$		0			0
$872$	13.9572	−	13.9572i	0.472651	−	0.472651i
$873$	−43.3680			−1.46778
$874$		−	25.1262i		−	0.849907i
$875$	−5.19585	+	7.37551i	−0.175652	+	0.249338i
$876$	0.0252034	−	0.0252034i	0.000851545	−	0.000851545i
$877$		−	37.9152i		−	1.28030i	−0.768248	−	0.640152i	$-0.778871\pi$
$877$		−	37.9152i		−	1.28030i	0.768248	−	0.640152i	$-0.221129\pi$
$878$		−	20.0589i		−	0.676956i
$879$	−0.419325	+	0.419325i	−0.0141435	+	0.0141435i
$880$	−1.14073	+	0.748715i	−0.0384540	+	0.0252392i
$881$		−	18.6214i		−	0.627370i	−0.949527	−	0.313685i	$-0.898436\pi$
$881$		−	18.6214i		−	0.627370i	0.949527	−	0.313685i	$-0.101564\pi$
$882$	−13.1024			−0.441179
$883$	13.2901	−	13.2901i	0.447248	−	0.447248i	−0.447191	−	0.894439i	$-0.647575\pi$
$883$	13.2901	−	13.2901i	0.447248	−	0.447248i	0.894439	+	0.447191i	$0.147575\pi$
$884$		0			0
$885$	−0.0879316	+	0.423815i	−0.00295579	+	0.0142464i
$886$	−4.95870	+	4.95870i	−0.166591	+	0.166591i
$887$	−27.6979	+	27.6979i	−0.930004	+	0.930004i	−0.997706	−	0.0677017i	$-0.978433\pi$
$887$	−27.6979	+	27.6979i	−0.930004	+	0.930004i	0.0677017	+	0.997706i	$0.478433\pi$
$888$	−0.902711	+	0.902711i	−0.0302930	+	0.0302930i
$889$	−8.36126	−	8.36126i	−0.280428	−	0.280428i
$890$	−11.1261	+	7.30257i	−0.372947	+	0.244783i
$891$	−2.80816	−	2.80816i	−0.0940768	−	0.0940768i
$892$	−4.31525			−0.144485
$893$	−44.6653	−	44.6653i	−1.49467	−	1.49467i
$894$	−0.818392			−0.0273711
$895$	−2.36405	+	11.3943i	−0.0790216	+	0.380870i
$896$		−	8.67127i		−	0.289687i
$897$		0			0
$898$	−7.78067	−	7.78067i	−0.259644	−	0.259644i
$899$	−0.508866	−	0.508866i	−0.0169716	−	0.0169716i
$900$	−9.07283	+	20.9235i	−0.302428	+	0.697451i
$901$			41.7520i			1.39096i
$902$			2.66145i			0.0886165i
$903$	0.685326			0.0228062
$904$	−8.18707	+	8.18707i	−0.272298	+	0.272298i
$905$	23.4890	+	4.87342i	0.780802	+	0.161998i
$906$	0.331716			0.0110205
$907$	−26.8910	−	26.8910i	−0.892900	−	0.892900i	0.101895	−	0.994795i	$-0.467510\pi$
$907$	−26.8910	−	26.8910i	−0.892900	−	0.892900i	−0.994795	+	0.101895i	$0.967510\pi$
$908$		−	23.6163i		−	0.783735i
$909$	−11.7682			−0.390327
$910$		0			0
$911$	−30.2074			−1.00081			−0.500407	−	0.865790i	$-0.666816\pi$
$911$	−30.2074			−1.00081			−0.500407	+	0.865790i	$0.666816\pi$
$912$		−	0.817334i		−	0.0270646i
$913$	0.814499	+	0.814499i	0.0269560	+	0.0269560i
$914$	−13.2621			−0.438671
$915$	0.498281	−	0.327046i	0.0164727	−	0.0108118i
$916$	22.1555	−	22.1555i	0.732038	−	0.732038i
$917$	−17.0810			−0.564063
$918$		−	1.90969i		−	0.0630291i
$919$			39.1747i			1.29225i	0.763230	+	0.646127i	$0.223612\pi$
$919$			39.1747i			1.29225i	−0.763230	+	0.646127i	$0.776388\pi$
$920$	24.4421	−	16.0425i	0.805833	−	0.528906i
$921$	0.597430	+	0.597430i	0.0196860	+	0.0196860i
$922$	−2.16143	−	2.16143i	−0.0711828	−	0.0711828i
$923$		0			0
$924$			0.0481061i			0.00158258i
$925$	27.3952	+	11.8791i	0.900748	+	0.390581i
$926$	8.45451			0.277833
$927$	−36.7225	−	36.7225i	−1.20612	−	1.20612i
$928$	−27.8274			−0.913478
$929$	−24.2932	−	24.2932i	−0.797034	−	0.797034i	0.185593	−	0.982627i	$-0.440579\pi$
$929$	−24.2932	−	24.2932i	−0.797034	−	0.797034i	−0.982627	+	0.185593i	$0.940579\pi$
$930$	−0.0199463	−	0.00413838i	−0.000654064	−	0.000135703i
$931$	−30.4047	−	30.4047i	−0.996473	−	0.996473i
$932$	−7.38582	+	7.38582i	−0.241930	+	0.241930i
$933$	0.324896	−	0.324896i	0.0106366	−	0.0106366i
$934$	−7.25130	+	7.25130i	−0.237270	+	0.237270i
$935$	−5.11561	−	1.06137i	−0.167298	−	0.0347104i
$936$		0			0
$937$	12.4007	−	12.4007i	0.405113	−	0.405113i	−0.474917	−	0.880030i	$-0.657522\pi$
$937$	12.4007	−	12.4007i	0.405113	−	0.405113i	0.880030	+	0.474917i	$0.157522\pi$
$938$	6.46251			0.211008
$939$		−	0.295985i		−	0.00965910i
$940$	6.45809	−	31.1269i	0.210640	−	1.01525i
$941$	0.542863	−	0.542863i	0.0176968	−	0.0176968i	−0.698203	−	0.715900i	$-0.746017\pi$
$941$	0.542863	−	0.542863i	0.0176968	−	0.0176968i	0.715900	+	0.698203i	$0.246017\pi$
$942$			1.03107i			0.0335940i
$943$			46.6778i			1.52004i
$944$	−2.13568	+	2.13568i	−0.0695104	+	0.0695104i
$945$	0.521772	+	0.794964i	0.0169733	+	0.0258602i
$946$			2.96180i			0.0962965i
$947$	27.7644			0.902222			0.451111	−	0.892468i	$-0.351028\pi$
$947$	27.7644			0.902222			0.451111	+	0.892468i	$0.351028\pi$
$948$	−0.851621	+	0.851621i	−0.0276594	+	0.0276594i
$949$		0			0
$950$	21.7216	−	8.58158i	0.704742	−	0.278423i
$951$	−0.920748	+	0.920748i	−0.0298573	+	0.0298573i
$952$	7.28720	−	7.28720i	0.236180	−	0.236180i
$953$	−6.15610	+	6.15610i	−0.199416	+	0.199416i	−0.799750	−	0.600334i	$-0.795034\pi$
$953$	−6.15610	+	6.15610i	−0.199416	+	0.199416i	0.600334	+	0.799750i	$0.295034\pi$
$954$	11.5962	+	11.5962i	0.375442	+	0.375442i
$955$	−7.32955	+	35.3272i	−0.237179	+	1.14316i
$956$	15.2459	+	15.2459i	0.493087	+	0.493087i
$957$	0.187387			0.00605736
$958$	5.73912	+	5.73912i	0.185423	+	0.185423i
$959$	−12.2949			−0.397024
$960$	−0.207340	+	0.136087i	−0.00669186	+	0.00439218i
$961$			30.9774i			0.999272i
$962$		0			0
$963$	10.4052	+	10.4052i	0.335303	+	0.335303i
$964$	−26.2982	−	26.2982i	−0.847008	−	0.847008i
$965$	16.6516	+	3.45480i	0.536033	+	0.111214i
$966$		−	0.263285i		−	0.00847105i
$967$			0.785304i			0.0252537i	0.999920	+	0.0126268i	$0.00401935\pi$
$967$			0.785304i			0.0252537i	−0.999920	+	0.0126268i	$0.995981\pi$
$968$	26.2570			0.843932
$969$	2.21290	−	2.21290i	0.0710886	−	0.0710886i
$970$	−4.54074	+	21.8856i	−0.145794	+	0.702703i
$971$	−47.2589			−1.51661			−0.758305	−	0.651900i	$-0.773972\pi$
$971$	−47.2589			−1.51661			−0.758305	+	0.651900i	$0.773972\pi$
$972$	2.55063	+	2.55063i	0.0818115	+	0.0818115i
$973$		−	9.57955i		−	0.307106i
$974$	−18.2766			−0.585621
$975$		0			0
$976$	4.15897			0.133125
$977$			4.40336i			0.140876i	0.997516	+	0.0704380i	$0.0224397\pi$
$977$			4.40336i			0.140876i	−0.997516	+	0.0704380i	$0.977560\pi$
$978$	−0.898856	−	0.898856i	−0.0287423	−	0.0287423i
$979$	3.83754			0.122648
$980$	4.39616	−	21.1887i	0.140430	−	0.676849i
$981$	−17.1818	+	17.1818i	−0.548572	+	0.548572i
$982$	9.82856			0.313642
$983$		−	33.3973i		−	1.06521i	−0.846364	−	0.532604i	$-0.821213\pi$
$983$		−	33.3973i		−	1.06521i	0.846364	−	0.532604i	$-0.178787\pi$
$984$		−	1.85501i		−	0.0591355i
$985$	10.7305	+	2.22633i	0.341902	+	0.0709366i
$986$	−12.2772	−	12.2772i	−0.390987	−	0.390987i
$987$	−0.468025	−	0.468025i	−0.0148974	−	0.0148974i
$988$		0			0
$989$			51.9456i			1.65177i
$990$	−1.71560	+	1.12603i	−0.0545252	+	0.0357875i
$991$	−46.0539			−1.46295			−0.731475	−	0.681868i	$-0.761168\pi$
$991$	−46.0539			−1.46295			−0.731475	+	0.681868i	$0.761168\pi$
$992$	−0.616815	−	0.616815i	−0.0195839	−	0.0195839i
$993$	1.37096			0.0435061
$994$	−0.561726	−	0.561726i	−0.0178169	−	0.0178169i
$995$	9.07419	−	43.7360i	0.287671	−	1.38653i
$996$	−0.245539	−	0.245539i	−0.00778020	−	0.00778020i
$997$	9.23126	−	9.23126i	0.292357	−	0.292357i	−0.545654	−	0.838011i	$-0.683719\pi$
$997$	9.23126	−	9.23126i	0.292357	−	0.292357i	0.838011	+	0.545654i	$0.183719\pi$
$998$	−13.9088	+	13.9088i	−0.440275	+	0.440275i
$999$	2.22540	−	2.22540i	0.0704086	−	0.0704086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.f.408.20	yes	72
5.2	odd	4		845.2.k.f.577.17	yes	72
13.2	odd	12		845.2.o.i.488.17		144
13.3	even	3		845.2.t.i.188.17		144
13.4	even	6		845.2.t.i.418.17		144
13.5	odd	4		845.2.k.f.268.20	yes	72
13.6	odd	12		845.2.o.i.258.17		144
13.7	odd	12		845.2.o.i.258.20		144
13.8	odd	4		845.2.k.f.268.17	yes	72
13.9	even	3		845.2.t.i.418.20		144
13.10	even	6		845.2.t.i.188.20		144
13.11	odd	12		845.2.o.i.488.20		144
13.12	even	2	inner	845.2.f.f.408.17	✓	72
65.2	even	12		845.2.t.i.657.17		144
65.7	even	12		845.2.t.i.427.17		144
65.12	odd	4		845.2.k.f.577.20	yes	72
65.17	odd	12		845.2.o.i.587.17		144
65.22	odd	12		845.2.o.i.587.20		144
65.32	even	12		845.2.t.i.427.20		144
65.37	even	12		845.2.t.i.657.20		144
65.42	odd	12		845.2.o.i.357.20		144
65.47	even	4	inner	845.2.f.f.437.17	yes	72
65.57	even	4	inner	845.2.f.f.437.20	yes	72
65.62	odd	12		845.2.o.i.357.17		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.17	✓	72	13.12	even	2	inner
845.2.f.f.408.20	yes	72	1.1	even	1	trivial
845.2.f.f.437.17	yes	72	65.47	even	4	inner
845.2.f.f.437.20	yes	72	65.57	even	4	inner
845.2.k.f.268.17	yes	72	13.8	odd	4
845.2.k.f.268.20	yes	72	13.5	odd	4
845.2.k.f.577.17	yes	72	5.2	odd	4
845.2.k.f.577.20	yes	72	65.12	odd	4
845.2.o.i.258.17		144	13.6	odd	12
845.2.o.i.258.20		144	13.7	odd	12
845.2.o.i.357.17		144	65.62	odd	12
845.2.o.i.357.20		144	65.42	odd	12
845.2.o.i.488.17		144	13.2	odd	12
845.2.o.i.488.20		144	13.11	odd	12
845.2.o.i.587.17		144	65.17	odd	12
845.2.o.i.587.20		144	65.22	odd	12
845.2.t.i.188.17		144	13.3	even	3
845.2.t.i.188.20		144	13.10	even	6
845.2.t.i.418.17		144	13.4	even	6
845.2.t.i.418.20		144	13.9	even	3
845.2.t.i.427.17		144	65.7	even	12
845.2.t.i.427.20		144	65.32	even	12
845.2.t.i.657.17		144	65.2	even	12
845.2.t.i.657.20		144	65.37	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.689692i q^{2} +(-0.0621871 - 0.0621871i) q^{3} +1.52433 q^{4} +(-0.454257 + 2.18944i) q^{5} +(0.0428900 - 0.0428900i) q^{6} -0.806945 q^{7} +2.43070i q^{8} -2.99227i q^{9} +(-1.51004 - 0.313297i) q^{10} +(0.314448 + 0.314448i) q^{11} +(-0.0947934 - 0.0947934i) q^{12} -0.556544i q^{14} +(0.164404 - 0.107906i) q^{15} +1.37222 q^{16} +(3.71523 + 3.71523i) q^{17} +2.06374 q^{18} +(4.78901 + 4.78901i) q^{19} +(-0.692436 + 3.33742i) q^{20} +(0.0501816 + 0.0501816i) q^{21} +(-0.216872 + 0.216872i) q^{22} +(-3.80361 + 3.80361i) q^{23} +(0.151158 - 0.151158i) q^{24} +(-4.58730 - 1.98914i) q^{25} +(-0.372642 + 0.372642i) q^{27} -1.23005 q^{28} +4.79138i q^{29} +(0.0744220 + 0.113388i) q^{30} +(-0.106205 + 0.106205i) q^{31} +5.80780i q^{32} -0.0391092i q^{33} +(-2.56236 + 2.56236i) q^{34} +(0.366561 - 1.76676i) q^{35} -4.56119i q^{36} -5.97196 q^{37} +(-3.30294 + 3.30294i) q^{38} +(-5.32187 - 1.10416i) q^{40} +(6.13599 - 6.13599i) q^{41} +(-0.0346098 + 0.0346098i) q^{42} +(6.82846 - 6.82846i) q^{43} +(0.479320 + 0.479320i) q^{44} +(6.55139 + 1.35926i) q^{45} +(-2.62332 - 2.62332i) q^{46} -9.32662 q^{47} +(-0.0853343 - 0.0853343i) q^{48} -6.34884 q^{49} +(1.37189 - 3.16382i) q^{50} -0.462079i q^{51} +(5.61903 + 5.61903i) q^{53} +(-0.257008 - 0.257008i) q^{54} +(-0.831304 + 0.545624i) q^{55} -1.96144i q^{56} -0.595630i q^{57} -3.30457 q^{58} +(-1.55637 + 1.55637i) q^{59} +(0.250605 - 0.164484i) q^{60} +3.03084 q^{61} +(-0.0732484 - 0.0732484i) q^{62} +2.41459i q^{63} -1.26116 q^{64} +0.0269733 q^{66} +11.6119i q^{67} +(5.66322 + 5.66322i) q^{68} +0.473071 q^{69} +(1.21852 + 0.252814i) q^{70} +(1.00931 - 1.00931i) q^{71} +7.27329 q^{72} +0.265877i q^{73} -4.11881i q^{74} +(0.161572 + 0.408970i) q^{75} +(7.30001 + 7.30001i) q^{76} +(-0.253742 - 0.253742i) q^{77} -8.98397i q^{79} +(-0.623340 + 3.00439i) q^{80} -8.93045 q^{81} +(4.23194 + 4.23194i) q^{82} +2.59025 q^{83} +(0.0764931 + 0.0764931i) q^{84} +(-9.82194 + 6.44660i) q^{85} +(4.70953 + 4.70953i) q^{86} +(0.297962 - 0.297962i) q^{87} +(-0.764327 + 0.764327i) q^{88} +(6.10204 - 6.10204i) q^{89} +(-0.937469 + 4.51844i) q^{90} +(-5.79794 + 5.79794i) q^{92} +0.0132091 q^{93} -6.43250i q^{94} +(-12.6607 + 8.30982i) q^{95} +(0.361171 - 0.361171i) q^{96} -14.4934i q^{97} -4.37874i q^{98} +(0.940911 - 0.940911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) \) 72 * q - 4 * q^3 - 80 * q^4 - 12 * q^10 + 64 * q^12 + 80 * q^16 + 8 * q^17 + 24 * q^22 + 36 * q^23 - 48 * q^25 - 64 * q^27 - 4 * q^30 + 80 * q^35 + 28 * q^38 - 24 * q^40 - 56 * q^42 + 76 * q^43 - 76 * q^48 + 8 * q^49 - 16 * q^53 + 12 * q^55 + 8 * q^61 + 148 * q^62 - 120 * q^64 + 40 * q^66 - 48 * q^68 - 40 * q^69 - 164 * q^75 + 172 * q^77 + 16 * q^81 + 44 * q^82 + 20 * q^87 + 124 * q^88 - 300 * q^90 - 4 * q^92 - 92 * q^95

Introduction

L-functions

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