LMFDB - Embedded newform 845.2.k.e.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(268,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.268"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.1
Root			$2.25081i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.e.268.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.25081 q^{2} +(1.40490 - 1.40490i) q^{3} +3.06613 q^{4} +(-2.22228 - 0.247944i) q^{5} +(-3.16216 + 3.16216i) q^{6} -1.27718i q^{7} -2.39966 q^{8} -0.947480i q^{9} +(5.00192 + 0.558075i) q^{10} +(3.86239 + 3.86239i) q^{11} +(4.30760 - 4.30760i) q^{12} +2.87469i q^{14} +(-3.47041 + 2.77374i) q^{15} -0.731101 q^{16} +(-2.27799 + 2.27799i) q^{17} +2.13259i q^{18} +(0.861676 + 0.861676i) q^{19} +(-6.81380 - 0.760230i) q^{20} +(-1.79431 - 1.79431i) q^{21} +(-8.69350 - 8.69350i) q^{22} +(-0.117133 - 0.117133i) q^{23} +(-3.37127 + 3.37127i) q^{24} +(4.87705 + 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} -3.91601i q^{28} +9.71181i q^{29} +(7.81123 - 6.24315i) q^{30} +(0.233305 - 0.233305i) q^{31} +6.44488 q^{32} +10.8525 q^{33} +(5.12732 - 5.12732i) q^{34} +(-0.316670 + 2.83826i) q^{35} -2.90510i q^{36} +1.32163i q^{37} +(-1.93947 - 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(0.354016 - 0.354016i) q^{41} +(4.03865 + 4.03865i) q^{42} +(-4.71126 - 4.71126i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-0.234922 + 2.10556i) q^{45} +(0.263643 + 0.263643i) q^{46} +3.20027i q^{47} +(-1.02712 + 1.02712i) q^{48} +5.36880 q^{49} +(-10.9773 - 2.48039i) q^{50} +6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-6.49039 - 6.49039i) q^{54} +(-7.62565 - 9.54097i) q^{55} +3.06480i q^{56} +2.42113 q^{57} -21.8594i q^{58} +(0.00162606 - 0.00162606i) q^{59} +(-10.6407 + 8.50465i) q^{60} +1.39199 q^{61} +(-0.525123 + 0.525123i) q^{62} -1.21011 q^{63} -13.0440 q^{64} -24.4270 q^{66} +6.07436 q^{67} +(-6.98462 + 6.98462i) q^{68} -0.329120 q^{69} +(0.712764 - 6.38837i) q^{70} +(-8.59633 + 8.59633i) q^{71} +2.27363i q^{72} +7.34614 q^{73} -2.97474i q^{74} +(8.39996 - 5.30355i) q^{75} +(2.64201 + 2.64201i) q^{76} +(4.93298 - 4.93298i) q^{77} -11.1774i q^{79} +(1.62471 + 0.181272i) q^{80} +10.9447 q^{81} +(-0.796822 + 0.796822i) q^{82} -2.65539i q^{83} +(-5.50160 - 5.50160i) q^{84} +(5.62715 - 4.49752i) q^{85} +(10.6041 + 10.6041i) q^{86} +(13.6441 + 13.6441i) q^{87} +(-9.26841 - 9.26841i) q^{88} +(5.09904 - 5.09904i) q^{89} +(0.528764 - 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} -0.655538i q^{93} -7.20320i q^{94} +(-1.70124 - 2.12853i) q^{95} +(9.05440 - 9.05440i) q^{96} +4.18070 q^{97} -12.0841 q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.25081			−1.59156			−0.795780	−	0.605585i	$-0.792939\pi$
$2$	−2.25081			−1.59156			−0.795780	+	0.605585i	$0.792939\pi$
$3$	1.40490	−	1.40490i	0.811119	−	0.811119i	−0.173683	−	0.984802i	$-0.555567\pi$
$3$	1.40490	−	1.40490i	0.811119	−	0.811119i	0.984802	+	0.173683i	$0.0555668\pi$
$4$	3.06613			1.53307
$5$	−2.22228	−	0.247944i	−0.993833	−	0.110884i
$5$	−2.22228	−	0.247944i	−0.993833	−	0.110884i
$6$	−3.16216	+	3.16216i	−1.29094	+	1.29094i
$7$		−	1.27718i		−	0.482730i	−0.970434	−	0.241365i	$-0.922405\pi$
$7$		−	1.27718i		−	0.482730i	0.970434	−	0.241365i	$-0.0775951\pi$
$8$	−2.39966			−0.848406
$9$		−	0.947480i		−	0.315827i
$10$	5.00192	+	0.558075i	1.58175	+	0.176479i
$11$	3.86239	+	3.86239i	1.16455	+	1.16455i	0.983467	+	0.181088i	$0.0579619\pi$
$11$	3.86239	+	3.86239i	1.16455	+	1.16455i	0.181088	+	0.983467i	$0.442038\pi$
$12$	4.30760	−	4.30760i	1.24350	−	1.24350i
$13$		0			0
$13$		0			0
$14$			2.87469i			0.768294i
$15$	−3.47041	+	2.77374i	−0.896057	+	0.716177i
$16$	−0.731101			−0.182775
$17$	−2.27799	+	2.27799i	−0.552494	+	0.552494i	−0.927160	−	0.374666i	$-0.877757\pi$
$17$	−2.27799	+	2.27799i	−0.552494	+	0.552494i	0.374666	+	0.927160i	$0.377757\pi$
$18$			2.13259i			0.502657i
$19$	0.861676	+	0.861676i	0.197682	+	0.197682i	0.799006	−	0.601324i	$-0.205360\pi$
$19$	0.861676	+	0.861676i	0.197682	+	0.197682i	−0.601324	+	0.799006i	$0.705360\pi$
$20$	−6.81380	−	0.760230i	−1.52361	−	0.169993i
$21$	−1.79431	−	1.79431i	−0.391551	−	0.391551i
$22$	−8.69350	−	8.69350i	−1.85346	−	1.85346i
$23$	−0.117133	−	0.117133i	−0.0244239	−	0.0244239i	0.694789	−	0.719213i	$-0.255498\pi$
$23$	−0.117133	−	0.117133i	−0.0244239	−	0.0244239i	−0.719213	+	0.694789i	$0.755498\pi$
$24$	−3.37127	+	3.37127i	−0.688158	+	0.688158i
$25$	4.87705	+	1.10200i	0.975409	+	0.220401i
$26$		0			0
$27$	2.88358	+	2.88358i	0.554946	+	0.554946i
$28$		−	3.91601i		−	0.740057i
$29$			9.71181i			1.80344i	0.432322	+	0.901719i	$0.357694\pi$
$29$			9.71181i			1.80344i	−0.432322	+	0.901719i	$0.642306\pi$
$30$	7.81123	−	6.24315i	1.42613	−	1.13984i
$31$	0.233305	−	0.233305i	0.0419027	−	0.0419027i	−0.685845	−	0.727748i	$-0.740567\pi$
$31$	0.233305	−	0.233305i	0.0419027	−	0.0419027i	0.727748	+	0.685845i	$0.240567\pi$
$32$	6.44488			1.13930
$33$	10.8525			1.88918
$34$	5.12732	−	5.12732i	0.879328	−	0.879328i
$35$	−0.316670	+	2.83826i	−0.0535271	+	0.479753i
$36$		−	2.90510i		−	0.484183i
$37$			1.32163i			0.217275i	0.994081	+	0.108638i	$0.0346488\pi$
$37$			1.32163i			0.217275i	−0.994081	+	0.108638i	$0.965351\pi$
$38$	−1.93947	−	1.93947i	−0.314623	−	0.314623i
$39$		0			0
$40$	5.33270	+	0.594981i	0.843175	+	0.0940747i
$41$	0.354016	−	0.354016i	0.0552880	−	0.0552880i	−0.678922	−	0.734210i	$-0.737553\pi$
$41$	0.354016	−	0.354016i	0.0552880	−	0.0552880i	0.734210	+	0.678922i	$0.237553\pi$
$42$	4.03865	+	4.03865i	0.623178	+	0.623178i
$43$	−4.71126	−	4.71126i	−0.718460	−	0.718460i	0.249830	−	0.968290i	$-0.419625\pi$
$43$	−4.71126	−	4.71126i	−0.718460	−	0.718460i	−0.968290	+	0.249830i	$0.919625\pi$
$44$	11.8426	+	11.8426i	1.78534	+	1.78534i
$45$	−0.234922	+	2.10556i	−0.0350201	+	0.313879i
$46$	0.263643	+	0.263643i	0.0388721	+	0.0388721i
$47$			3.20027i			0.466808i	0.972380	+	0.233404i	$0.0749864\pi$
$47$			3.20027i			0.466808i	−0.972380	+	0.233404i	$0.925014\pi$
$48$	−1.02712	+	1.02712i	−0.148252	+	0.148252i
$49$	5.36880			0.766972
$50$	−10.9773	−	2.48039i	−1.55242	−	0.350781i
$51$			6.40069i			0.896276i
$52$		0			0
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	−0.327086	−	0.944995i	$-0.606067\pi$
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	0.944995	+	0.327086i	$0.106067\pi$
$54$	−6.49039	−	6.49039i	−0.883230	−	0.883230i
$55$	−7.62565	−	9.54097i	−1.02824	−	1.28650i
$56$			3.06480i			0.409551i
$57$	2.42113			0.320687
$58$		−	21.8594i		−	2.87028i
$59$	0.00162606	−	0.00162606i	0.000211694	−	0.000211694i	−0.707001	−	0.707213i	$-0.749952\pi$
$59$	0.00162606	−	0.00162606i	0.000211694	−	0.000211694i	0.707213	+	0.707001i	$0.249952\pi$
$60$	−10.6407	+	8.50465i	−1.37371	+	1.09795i
$61$	1.39199			0.178226			0.0891128	−	0.996022i	$-0.471597\pi$
$61$	1.39199			0.178226			0.0891128	+	0.996022i	$0.471597\pi$
$62$	−0.525123	+	0.525123i	−0.0666907	+	0.0666907i
$63$	−1.21011			−0.152459
$64$	−13.0440			−1.63050
$65$		0			0
$66$	−24.4270			−3.00675
$67$	6.07436			0.742101			0.371050	−	0.928613i	$-0.378998\pi$
$67$	6.07436			0.742101			0.371050	+	0.928613i	$0.378998\pi$
$68$	−6.98462	+	6.98462i	−0.847009	+	0.847009i
$69$	−0.329120			−0.0396213
$70$	0.712764	−	6.38837i	0.0851916	−	0.763557i
$71$	−8.59633	+	8.59633i	−1.02020	+	1.02020i	−0.0204050	+	0.999792i	$0.506496\pi$
$71$	−8.59633	+	8.59633i	−1.02020	+	1.02020i	−0.999792	+	0.0204050i	$0.993504\pi$
$72$			2.27363i			0.267949i
$73$	7.34614			0.859801			0.429901	−	0.902876i	$-0.358549\pi$
$73$	7.34614			0.859801			0.429901	+	0.902876i	$0.358549\pi$
$74$		−	2.97474i		−	0.345806i
$75$	8.39996	−	5.30355i	0.969944	−	0.612402i
$76$	2.64201	+	2.64201i	0.303060	+	0.303060i
$77$	4.93298	−	4.93298i	0.562166	−	0.562166i
$78$		0			0
$79$		−	11.1774i		−	1.25756i	−0.777584	−	0.628779i	$-0.783555\pi$
$79$		−	11.1774i		−	1.25756i	0.777584	−	0.628779i	$-0.216445\pi$
$80$	1.62471	+	0.181272i	0.181648	+	0.0202669i
$81$	10.9447			1.21608
$82$	−0.796822	+	0.796822i	−0.0879943	+	0.0879943i
$83$		−	2.65539i		−	0.291467i	−0.989324	−	0.145733i	$-0.953446\pi$
$83$		−	2.65539i		−	0.291467i	0.989324	−	0.145733i	$-0.0465542\pi$
$84$	−5.50160	−	5.50160i	−0.600274	−	0.600274i
$85$	5.62715	−	4.49752i	0.610350	−	0.487824i
$86$	10.6041	+	10.6041i	1.14347	+	1.14347i
$87$	13.6441	+	13.6441i	1.46280	+	1.46280i
$88$	−9.26841	−	9.26841i	−0.988016	−	0.988016i
$89$	5.09904	−	5.09904i	0.540497	−	0.540497i	−0.383178	−	0.923675i	$-0.625170\pi$
$89$	5.09904	−	5.09904i	0.540497	−	0.540497i	0.923675	+	0.383178i	$0.125170\pi$
$90$	0.528764	−	4.73922i	0.0557367	−	0.499558i
$91$		0			0
$92$	−0.359145	−	0.359145i	−0.0374434	−	0.0374434i
$93$		−	0.655538i		−	0.0679762i
$94$		−	7.20320i		−	0.742953i
$95$	−1.70124	−	2.12853i	−0.174543	−	0.218383i
$96$	9.05440	−	9.05440i	0.924111	−	0.924111i
$97$	4.18070			0.424486			0.212243	−	0.977217i	$-0.431923\pi$
$97$	4.18070			0.424486			0.212243	+	0.977217i	$0.431923\pi$
$98$	−12.0841			−1.22068
$99$	3.65954	−	3.65954i	0.367797	−	0.367797i
$100$	14.9537	+	3.37888i	1.49537	+	0.337888i
$101$			8.62930i			0.858647i	0.903151	+	0.429323i	$0.141248\pi$
$101$			8.62930i			0.858647i	−0.903151	+	0.429323i	$0.858752\pi$
$102$		−	14.4067i		−	1.42648i
$103$	−1.07603	−	1.07603i	−0.106025	−	0.106025i	0.652104	−	0.758129i	$-0.273886\pi$
$103$	−1.07603	−	1.07603i	−0.106025	−	0.106025i	−0.758129	+	0.652104i	$0.773886\pi$
$104$		0			0
$105$	3.54258	+	4.43236i	0.345720	+	0.432554i
$106$	−10.1251	+	10.1251i	−0.983440	+	0.983440i
$107$	10.2713	+	10.2713i	0.992966	+	0.992966i	0.999975	−	0.00700981i	$-0.00223131\pi$
$107$	10.2713	+	10.2713i	0.992966	+	0.992966i	−0.00700981	+	0.999975i	$0.502231\pi$
$108$	8.84144	+	8.84144i	0.850768	+	0.850768i
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	0.896177	−	0.443696i	$-0.146333\pi$
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	−0.443696	+	0.896177i	$0.646333\pi$
$110$	17.1639	+	21.4749i	1.63651	+	2.04755i
$111$	1.85676	+	1.85676i	0.176236	+	0.176236i
$112$			0.933751i			0.0882311i
$113$	8.05734	−	8.05734i	0.757971	−	0.757971i	−0.217982	−	0.975953i	$-0.569947\pi$
$113$	8.05734	−	8.05734i	0.757971	−	0.757971i	0.975953	+	0.217982i	$0.0699474\pi$
$114$	−5.44951			−0.510393
$115$	0.231259	+	0.289344i	0.0215651	+	0.0269815i
$116$			29.7777i			2.76479i
$117$		0			0
$118$	−0.00365994	+	0.00365994i	−0.000336925	+	0.000336925i
$119$	2.90941	+	2.90941i	0.266705	+	0.266705i
$120$	8.32780	−	6.65602i	0.760220	−	0.607609i
$121$			18.8361i			1.71238i
$122$	−3.13309			−0.283657
$123$		−	0.994714i		−	0.0896903i
$124$	0.715342	−	0.715342i	0.0642396	−	0.0642396i
$125$	−10.5649	−	3.65819i	−0.944956	−	0.327199i
$126$	2.72372			0.242648
$127$	−0.370894	+	0.370894i	−0.0329115	+	0.0329115i	−0.723371	−	0.690460i	$-0.757408\pi$
$127$	−0.370894	+	0.370894i	−0.0329115	+	0.0329115i	0.690460	+	0.723371i	$0.257408\pi$
$128$	16.4697			1.45573
$129$	−13.2377			−1.16551
$130$		0			0
$131$	5.09883			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$131$	5.09883			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$132$	33.2753			2.89624
$133$	1.10052	−	1.10052i	0.0954271	−	0.0954271i
$134$	−13.6722			−1.18110
$135$	−5.69316	−	7.12309i	−0.489989	−	0.613058i
$136$	5.46639	−	5.46639i	0.468739	−	0.468739i
$137$			3.80346i			0.324952i	0.986713	+	0.162476i	$0.0519480\pi$
$137$			3.80346i			0.324952i	−0.986713	+	0.162476i	$0.948052\pi$
$138$	0.740785			0.0630598
$139$			1.47821i			0.125380i	0.998033	+	0.0626902i	$0.0199680\pi$
$139$			1.47821i			0.125380i	−0.998033	+	0.0626902i	$0.980032\pi$
$140$	−0.970953	+	8.70248i	−0.0820605	+	0.735493i
$141$	4.49606	+	4.49606i	0.378637	+	0.378637i
$142$	19.3487	−	19.3487i	1.62371	−	1.62371i
$143$		0			0
$144$			0.692704i			0.0577253i
$145$	2.40799	−	21.5824i	0.199973	−	1.79232i
$146$	−16.5347			−1.36843
$147$	7.54262	−	7.54262i	0.622105	−	0.622105i
$148$			4.05230i			0.333097i
$149$	12.1736	+	12.1736i	0.997302	+	0.997302i	0.999996	−	0.00269418i	$-0.000857587\pi$
$149$	12.1736	+	12.1736i	0.997302	+	0.997302i	−0.00269418	+	0.999996i	$0.500858\pi$
$150$	−18.9067	+	11.9373i	−1.54372	+	0.974675i
$151$	−10.0539	−	10.0539i	−0.818178	−	0.818178i	0.167666	−	0.985844i	$-0.446377\pi$
$151$	−10.0539	−	10.0539i	−0.818178	−	0.818178i	−0.985844	+	0.167666i	$0.946377\pi$
$152$	−2.06773	−	2.06773i	−0.167715	−	0.167715i
$153$	2.15835	+	2.15835i	0.174492	+	0.174492i
$154$	−11.1032	+	11.1032i	−0.894721	+	0.894721i
$155$	−0.576314	+	0.460621i	−0.0462907	+	0.0369980i
$156$		0			0
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	0.818996	−	0.573799i	$-0.194531\pi$
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	−0.573799	+	0.818996i	$0.694531\pi$
$158$			25.1582i			2.00148i
$159$		−	12.6397i		−	1.00240i
$160$	−14.3223	−	1.59797i	−1.13228	−	0.126331i
$161$	−0.149600	+	0.149600i	−0.0117902	+	0.0117902i
$162$	−24.6345			−1.93547
$163$	9.20501			0.720992			0.360496	−	0.932761i	$-0.382607\pi$
$163$	9.20501			0.720992			0.360496	+	0.932761i	$0.382607\pi$
$164$	1.08546	−	1.08546i	0.0847602	−	0.0847602i
$165$	−24.1174	−	2.69082i	−1.87753	−	0.209480i
$166$			5.97677i			0.463887i
$167$		−	12.6387i		−	0.978014i	−0.872280	−	0.489007i	$-0.837359\pi$
$167$		−	12.6387i		−	0.978014i	0.872280	−	0.489007i	$-0.162641\pi$
$168$	4.30574	+	4.30574i	0.332195	+	0.332195i
$169$		0			0
$170$	−12.6656	+	10.1230i	−0.971409	+	0.776402i
$171$	0.816421	−	0.816421i	0.0624333	−	0.0624333i
$172$	−14.4453	−	14.4453i	−1.10145	−	1.10145i
$173$	−9.69831	−	9.69831i	−0.737349	−	0.737349i	0.234716	−	0.972064i	$-0.424584\pi$
$173$	−9.69831	−	9.69831i	−0.737349	−	0.737349i	−0.972064	+	0.234716i	$0.924584\pi$
$174$	−30.7103	−	30.7103i	−2.32814	−	2.32814i
$175$	1.40746	−	6.22889i	0.106394	−	0.470860i
$176$	−2.82380	−	2.82380i	−0.212852	−	0.212852i
$177$		−	0.00456889i		−	0.000343419i
$178$	−11.4770	+	11.4770i	−0.860234	+	0.860234i
$179$	−12.6425			−0.944946			−0.472473	−	0.881345i	$-0.656639\pi$
$179$	−12.6425			−0.944946			−0.472473	+	0.881345i	$0.656639\pi$
$180$	−0.720302	+	6.45594i	−0.0536882	+	0.481197i
$181$			8.16619i			0.606988i	0.952833	+	0.303494i	$0.0981533\pi$
$181$			8.16619i			0.606988i	−0.952833	+	0.303494i	$0.901847\pi$
$182$		0			0
$183$	1.95560	−	1.95560i	0.144562	−	0.144562i
$184$	0.281079	+	0.281079i	0.0207214	+	0.0207214i
$185$	0.327691	−	2.93704i	0.0240923	−	0.215935i
$186$			1.47549i			0.108188i
$187$	−17.5970			−1.28682
$188$			9.81246i			0.715647i
$189$	3.68287	−	3.68287i	0.267889	−	0.267889i
$190$	3.82916	+	4.79091i	0.277796	+	0.347569i
$191$	−14.7538			−1.06755			−0.533775	−	0.845626i	$-0.679227\pi$
$191$	−14.7538			−1.06755			−0.533775	+	0.845626i	$0.679227\pi$
$192$	−18.3255	+	18.3255i	−1.32253	+	1.32253i
$193$	−15.0969			−1.08670			−0.543349	−	0.839507i	$-0.682844\pi$
$193$	−15.0969			−1.08670			−0.543349	+	0.839507i	$0.682844\pi$
$194$	−9.40995			−0.675595
$195$		0			0
$196$	16.4614			1.17582
$197$	−15.3715			−1.09518			−0.547588	−	0.836748i	$-0.684454\pi$
$197$	−15.3715			−1.09518			−0.547588	+	0.836748i	$0.684454\pi$
$198$	−8.23691	+	8.23691i	−0.585372	+	0.585372i
$199$	11.4562			0.812109			0.406054	−	0.913849i	$-0.366904\pi$
$199$	11.4562			0.812109			0.406054	+	0.913849i	$0.366904\pi$
$200$	−11.7032	−	2.64443i	−0.827544	−	0.186989i
$201$	8.53385	−	8.53385i	0.601932	−	0.601932i
$202$		−	19.4229i		−	1.36659i
$203$	12.4038			0.870574
$204$			19.6254i			1.37405i
$205$	−0.874499	+	0.698946i	−0.0610777	+	0.0488165i
$206$	2.42194	+	2.42194i	0.168745	+	0.168745i
$207$	−0.110981	+	0.110981i	−0.00771372	+	0.00771372i
$208$		0			0
$209$			6.65626i			0.460423i
$210$	−7.97366	−	9.97638i	−0.550234	−	0.688435i
$211$	3.18391			0.219189			0.109595	−	0.993976i	$-0.465045\pi$
$211$	3.18391			0.219189			0.109595	+	0.993976i	$0.465045\pi$
$212$	13.7928	−	13.7928i	0.947295	−	0.947295i
$213$			24.1539i			1.65500i
$214$	−23.1187	−	23.1187i	−1.58037	−	1.58037i
$215$	9.30159	+	11.6379i	0.634363	+	0.793695i
$216$	−6.91961	−	6.91961i	−0.470820	−	0.470820i
$217$	−0.297973	−	0.297973i	−0.0202277	−	0.0202277i
$218$	−10.6329	−	10.6329i	−0.720152	−	0.720152i
$219$	10.3206	−	10.3206i	0.697401	−	0.697401i
$220$	−23.3813	−	29.2539i	−1.57636	−	1.97230i
$221$		0			0
$222$	−4.17921	−	4.17921i	−0.280490	−	0.280490i
$223$			11.8775i			0.795375i	0.917521	+	0.397688i	$0.130187\pi$
$223$			11.8775i			0.795375i	−0.917521	+	0.397688i	$0.869813\pi$
$224$		−	8.23130i		−	0.549977i
$225$	1.04413	−	4.62090i	0.0696084	−	0.308060i
$226$	−18.1355	+	18.1355i	−1.20636	+	1.20636i
$227$	−27.6666			−1.83630			−0.918149	−	0.396236i	$-0.870316\pi$
$227$	−27.6666			−1.83630			−0.918149	+	0.396236i	$0.870316\pi$
$228$	7.42352			0.491634
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	−0.990435	−	0.137980i	$-0.955939\pi$
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	0.137980	+	0.990435i	$0.455939\pi$
$230$	−0.520520	−	0.651258i	−0.0343221	−	0.0429427i
$231$		−	13.8607i		−	0.911966i
$232$		−	23.3050i		−	1.53005i
$233$	16.3545	+	16.3545i	1.07142	+	1.07142i	0.997246	+	0.0741712i	$0.0236311\pi$
$233$	16.3545	+	16.3545i	1.07142	+	1.07142i	0.0741712	+	0.997246i	$0.476369\pi$
$234$		0			0
$235$	0.793489	−	7.11190i	0.0517615	−	0.463929i
$236$	0.00498570	−	0.00498570i	0.000324541	−	0.000324541i
$237$	−15.7031	−	15.7031i	−1.02003	−	1.02003i
$238$	−6.54853	−	6.54853i	−0.424478	−	0.424478i
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	0.786690	−	0.617349i	$-0.211793\pi$
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	−0.617349	+	0.786690i	$0.711793\pi$
$240$	2.53722	−	2.02788i	0.163777	−	0.130899i
$241$	14.7152	+	14.7152i	0.947888	+	0.947888i	0.998708	−	0.0508198i	$-0.0161834\pi$
$241$	14.7152	+	14.7152i	0.947888	+	0.947888i	−0.0508198	+	0.998708i	$0.516183\pi$
$242$		−	42.3965i		−	2.72535i
$243$	6.72548	−	6.72548i	0.431439	−	0.431439i
$244$	4.26801			0.273232
$245$	−11.9310	−	1.33116i	−0.762242	−	0.0850449i
$246$			2.23891i			0.142748i
$247$		0			0
$248$	−0.559851	+	0.559851i	−0.0355505	+	0.0355505i
$249$	−3.73055	−	3.73055i	−0.236414	−	0.236414i
$250$	23.7796	+	8.23389i	1.50395	+	0.520757i
$251$		−	2.36772i		−	0.149449i	−0.997204	−	0.0747245i	$-0.976192\pi$
$251$		−	2.36772i		−	0.149449i	0.997204	−	0.0747245i	$-0.0238078\pi$
$252$	−3.71034			−0.233730
$253$		−	0.904826i		−	0.0568859i
$254$	0.834811	−	0.834811i	0.0523807	−	0.0523807i
$255$	1.58701	−	14.2241i	0.0993827	−	0.890749i
$256$	−10.9822			−0.686387
$257$	0.615209	−	0.615209i	0.0383757	−	0.0383757i	−0.687659	−	0.726034i	$-0.741361\pi$
$257$	0.615209	−	0.615209i	0.0383757	−	0.0383757i	0.726034	+	0.687659i	$0.241361\pi$
$258$	29.7954			1.85498
$259$	1.68797			0.104885
$260$		0			0
$261$	9.20175			0.569574
$262$	−11.4765			−0.709019
$263$	−10.7397	+	10.7397i	−0.662236	+	0.662236i	−0.955907	−	0.293670i	$-0.905123\pi$
$263$	−10.7397	+	10.7397i	−0.662236	+	0.662236i	0.293670	+	0.955907i	$0.405123\pi$
$264$	−26.0424			−1.60280
$265$	−11.1122	+	8.88144i	−0.682615	+	0.545582i
$266$	−2.47706	+	2.47706i	−0.151878	+	0.151878i
$267$		−	14.3273i		−	0.876814i
$268$	18.6248			1.13769
$269$		−	24.3816i		−	1.48657i	−0.668975	−	0.743285i	$-0.733267\pi$
$269$		−	24.3816i		−	1.48657i	0.668975	−	0.743285i	$-0.266733\pi$
$270$	12.8142	+	16.0327i	0.779847	+	0.975719i
$271$	9.27487	+	9.27487i	0.563408	+	0.563408i	0.930274	−	0.366866i	$-0.119569\pi$
$271$	9.27487	+	9.27487i	0.563408	+	0.563408i	−0.366866	+	0.930274i	$0.619569\pi$
$272$	1.66544	−	1.66544i	0.100982	−	0.100982i
$273$		0			0
$274$		−	8.56086i		−	0.517181i
$275$	14.5807	+	23.0934i	0.879249	+	1.39259i
$276$	−1.00912			−0.0607421
$277$	−8.64616	+	8.64616i	−0.519498	+	0.519498i	−0.917419	−	0.397922i	$-0.869732\pi$
$277$	−8.64616	+	8.64616i	−0.519498	+	0.519498i	0.397922	+	0.917419i	$0.369732\pi$
$278$		−	3.32717i		−	0.199550i
$279$	−0.221051	−	0.221051i	−0.0132340	−	0.0132340i
$280$	0.759900	−	6.81085i	0.0454127	−	0.407026i
$281$	−6.43529	−	6.43529i	−0.383897	−	0.383897i	0.488607	−	0.872504i	$-0.337505\pi$
$281$	−6.43529	−	6.43529i	−0.383897	−	0.383897i	−0.872504	+	0.488607i	$0.837505\pi$
$282$	−10.1198	−	10.1198i	−0.602623	−	0.602623i
$283$	−19.3416	−	19.3416i	−1.14974	−	1.14974i	−0.986603	−	0.163137i	$-0.947839\pi$
$283$	−19.3416	−	19.3416i	−1.14974	−	1.14974i	−0.163137	−	0.986603i	$-0.552161\pi$
$284$	−26.3575	+	26.3575i	−1.56403	+	1.56403i
$285$	−5.38044	−	0.600307i	−0.318710	−	0.0355591i
$286$		0			0
$287$	−0.452144	−	0.452144i	−0.0266892	−	0.0266892i
$288$		−	6.10639i		−	0.359823i
$289$			6.62152i			0.389501i
$290$	−5.41992	+	48.5777i	−0.318268	+	2.85258i
$291$	5.87346	−	5.87346i	0.344308	−	0.344308i
$292$	22.5242			1.31813
$293$	−26.1241			−1.52618			−0.763092	−	0.646289i	$-0.776320\pi$
$293$	−26.1241			−1.52618			−0.763092	+	0.646289i	$0.776320\pi$
$294$	−16.9770	+	16.9770i	−0.990118	+	0.990118i
$295$	−0.00401672	+	0.00321038i	−0.000233863	+	0.000186915i
$296$		−	3.17146i		−	0.184338i
$297$			22.2750i			1.29253i
$298$	−27.4005	−	27.4005i	−1.58727	−	1.58727i
$299$		0			0
$300$	25.7554	−	16.2614i	1.48699	−	0.938852i
$301$	−6.01714	+	6.01714i	−0.346822	+	0.346822i
$302$	22.6295	+	22.6295i	1.30218	+	1.30218i
$303$	12.1233	+	12.1233i	0.696464	+	0.696464i
$304$	−0.629972	−	0.629972i	−0.0361314	−	0.0361314i
$305$	−3.09338	−	0.345135i	−0.177127	−	0.0197624i
$306$	−4.85803	−	4.85803i	−0.277715	−	0.277715i
$307$			14.7038i			0.839189i	0.907712	+	0.419595i	$0.137828\pi$
$307$			14.7038i			0.839189i	−0.907712	+	0.419595i	$0.862172\pi$
$308$	15.1252	−	15.1252i	0.861837	−	0.861837i
$309$	−3.02343			−0.171997
$310$	1.29717	−	1.03677i	0.0736744	−	0.0588845i
$311$		−	31.8525i		−	1.80619i	−0.429440	−	0.903095i	$-0.641289\pi$
$311$		−	31.8525i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$312$		0			0
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	−0.959438	−	0.281919i	$-0.909029\pi$
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	0.281919	+	0.959438i	$0.409029\pi$
$314$	−6.91516	−	6.91516i	−0.390245	−	0.390245i
$315$	2.68919	+	0.300039i	0.151519	+	0.0169053i
$316$		−	34.2714i		−	1.92792i
$317$	15.5627			0.874088			0.437044	−	0.899440i	$-0.356025\pi$
$317$	15.5627			0.874088			0.437044	+	0.899440i	$0.356025\pi$
$318$			28.4496i			1.59537i
$319$	−37.5108	+	37.5108i	−2.10020	+	2.10020i
$320$	28.9874	+	3.23418i	1.62044	+	0.180796i
$321$	28.8603			1.61083
$322$	0.336721	−	0.336721i	0.0187647	−	0.0187647i
$323$	−3.92578			−0.218436
$324$	33.5580			1.86433
$325$		0			0
$326$	−20.7187			−1.14750
$327$	13.2736			0.734032
$328$	−0.849517	+	0.849517i	−0.0469067	+	0.0469067i
$329$	4.08734			0.225342
$330$	54.2835	+	6.05653i	2.98821	+	0.333401i
$331$	12.0656	−	12.0656i	0.663187	−	0.663187i	−0.292943	−	0.956130i	$-0.594635\pi$
$331$	12.0656	−	12.0656i	0.663187	−	0.663187i	0.956130	+	0.292943i	$0.0946346\pi$
$332$		−	8.14177i		−	0.446838i
$333$	1.25222			0.0686212
$334$			28.4473i			1.55657i
$335$	−13.4989	−	1.50610i	−0.737524	−	0.0822871i
$336$	1.31182	+	1.31182i	0.0715659	+	0.0715659i
$337$	−25.0560	+	25.0560i	−1.36489	+	1.36489i	−0.497319	+	0.867568i	$0.665682\pi$
$337$	−25.0560	+	25.0560i	−1.36489	+	1.36489i	−0.867568	+	0.497319i	$0.834318\pi$
$338$		0			0
$339$		−	22.6395i		−	1.22961i
$340$	17.2536	−	13.7900i	0.935706	−	0.747866i
$341$	1.80223			0.0975961
$342$	−1.83761	+	1.83761i	−0.0993663	+	0.0993663i
$343$		−	15.7972i		−	0.852971i
$344$	11.3054	+	11.3054i	0.609546	+	0.609546i
$345$	0.731396	+	0.0816033i	0.0393770	+	0.00439337i
$346$	21.8290	+	21.8290i	1.17354	+	1.17354i
$347$	9.12161	+	9.12161i	0.489674	+	0.489674i	0.908203	−	0.418529i	$-0.137454\pi$
$347$	9.12161	+	9.12161i	0.489674	+	0.489674i	−0.418529	+	0.908203i	$0.637454\pi$
$348$	41.8346	+	41.8346i	2.24257	+	2.24257i
$349$	18.9866	−	18.9866i	1.01633	−	1.01633i	0.0164642	−	0.999864i	$-0.494759\pi$
$349$	18.9866	−	18.9866i	1.01633	−	1.01633i	0.999864	−	0.0164642i	$-0.00524094\pi$
$350$	−3.16792	+	14.0200i	−0.169332	+	0.749402i
$351$		0			0
$352$	24.8926	+	24.8926i	1.32678	+	1.32678i
$353$		−	23.3117i		−	1.24076i	−0.784303	−	0.620378i	$-0.786979\pi$
$353$		−	23.3117i		−	1.24076i	0.784303	−	0.620378i	$-0.213021\pi$
$354$			0.0102837i			0.000546571i
$355$	21.2349	−	16.9720i	1.12703	−	0.900782i
$356$	15.6343	−	15.6343i	0.828617	−	0.828617i
$357$	8.17486			0.432660
$358$	28.4559			1.50394
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	−0.906435	−	0.422344i	$-0.861207\pi$
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	0.422344	+	0.906435i	$0.361207\pi$
$360$	0.563732	−	5.05263i	0.0297113	−	0.266297i
$361$		−	17.5150i		−	0.921844i
$362$		−	18.3805i		−	0.966059i
$363$	26.4629	+	26.4629i	1.38894	+	1.38894i
$364$		0			0
$365$	−16.3252	−	1.82143i	−0.854499	−	0.0953382i
$366$	−4.40168	+	4.40168i	−0.230079	+	0.230079i
$367$	10.5124	+	10.5124i	0.548741	+	0.548741i	0.926077	−	0.377335i	$-0.123160\pi$
$367$	10.5124	+	10.5124i	0.548741	+	0.548741i	−0.377335	+	0.926077i	$0.623160\pi$
$368$	0.0856360	+	0.0856360i	0.00446408	+	0.00446408i
$369$	−0.335423	−	0.335423i	−0.0174614	−	0.0174614i
$370$	−0.737570	+	6.61070i	−0.0383444	+	0.343674i
$371$	−5.74534	−	5.74534i	−0.298283	−	0.298283i
$372$		−	2.00997i		−	0.104212i
$373$	4.37075	−	4.37075i	0.226309	−	0.226309i	−0.584840	−	0.811149i	$-0.698843\pi$
$373$	4.37075	−	4.37075i	0.226309	−	0.226309i	0.811149	+	0.584840i	$0.198843\pi$
$374$	39.6074			2.04805
$375$	−19.9820	+	9.70326i	−1.03187	+	0.501074i
$376$		−	7.67955i		−	0.396043i
$377$		0			0
$378$	−8.28942	+	8.28942i	−0.426362	+	0.426362i
$379$	12.9181	+	12.9181i	0.663556	+	0.663556i	0.956216	−	0.292660i	$-0.0945405\pi$
$379$	12.9181	+	12.9181i	0.663556	+	0.663556i	−0.292660	+	0.956216i	$0.594540\pi$
$380$	−5.21622	−	6.52636i	−0.267586	−	0.334795i
$381$			1.04214i			0.0533903i
$382$	33.2081			1.69907
$383$		−	10.2434i		−	0.523414i	−0.965147	−	0.261707i	$-0.915715\pi$
$383$		−	10.2434i		−	0.523414i	0.965147	−	0.261707i	$-0.0842854\pi$
$384$	23.1383	−	23.1383i	1.18077	−	1.18077i
$385$	−12.1856	+	9.73936i	−0.621034	+	0.496364i
$386$	33.9802			1.72955
$387$	−4.46382	+	4.46382i	−0.226909	+	0.226909i
$388$	12.8186			0.650765
$389$	3.41200			0.172995			0.0864977	−	0.996252i	$-0.472432\pi$
$389$	3.41200			0.172995			0.0864977	+	0.996252i	$0.472432\pi$
$390$		0			0
$391$	0.533655			0.0269881
$392$	−12.8833			−0.650704
$393$	7.16333	−	7.16333i	0.361342	−	0.361342i
$394$	34.5983			1.74304
$395$	−2.77138	+	24.8393i	−0.139443	+	1.24980i
$396$	11.2206	−	11.2206i	0.563858	−	0.563858i
$397$		−	11.9321i		−	0.598853i	−0.954119	−	0.299426i	$-0.903205\pi$
$397$		−	11.9321i		−	0.598853i	0.954119	−	0.299426i	$-0.0967953\pi$
$398$	−25.7857			−1.29252
$399$		−	3.09223i		−	0.154805i
$400$	−3.56561	−	0.805675i	−0.178281	−	0.0402838i
$401$	−2.88224	−	2.88224i	−0.143932	−	0.143932i	0.631469	−	0.775401i	$-0.282452\pi$
$401$	−2.88224	−	2.88224i	−0.143932	−	0.143932i	−0.775401	+	0.631469i	$0.782452\pi$
$402$	−19.2081	+	19.2081i	−0.958011	+	0.958011i
$403$		0			0
$404$			26.4586i			1.31636i
$405$	−24.3222	−	2.71368i	−1.20858	−	0.134844i
$406$	−27.9185			−1.38557
$407$	−5.10466	+	5.10466i	−0.253029	+	0.253029i
$408$		−	15.3595i		−	0.760406i
$409$	4.90669	+	4.90669i	0.242620	+	0.242620i	0.817933	−	0.575313i	$-0.195120\pi$
$409$	4.90669	+	4.90669i	0.242620	+	0.242620i	−0.575313	+	0.817933i	$0.695120\pi$
$410$	1.96833	−	1.57319i	0.0972088	−	0.0776945i
$411$	5.34348	+	5.34348i	0.263574	+	0.263574i
$412$	−3.29926	−	3.29926i	−0.162543	−	0.162543i
$413$	−0.00207677	−	0.00207677i	−0.000102191	−	0.000102191i
$414$	0.249797	−	0.249797i	0.0122768	−	0.0122768i
$415$	−0.658389	+	5.90102i	−0.0323190	+	0.289670i
$416$		0			0
$417$	2.07674	+	2.07674i	0.101698	+	0.101698i
$418$		−	14.9820i		−	0.732791i
$419$		−	21.2287i		−	1.03709i	−0.855050	−	0.518546i	$-0.826474\pi$
$419$		−	21.2287i		−	1.03709i	0.855050	−	0.518546i	$-0.173526\pi$
$420$	10.8620	+	13.5902i	0.530012	+	0.663133i
$421$	−3.15727	+	3.15727i	−0.153876	+	0.153876i	−0.779847	−	0.625971i	$-0.784703\pi$
$421$	−3.15727	+	3.15727i	−0.153876	+	0.153876i	0.625971	+	0.779847i	$0.284703\pi$
$422$	−7.16636			−0.348853
$423$	3.03219			0.147430
$424$	−10.7947	+	10.7947i	−0.524238	+	0.524238i
$425$	−13.6202	+	8.59952i	−0.660678	+	0.417138i
$426$		−	54.3659i		−	2.63403i
$427$		−	1.77782i		−	0.0860349i
$428$	31.4932	+	31.4932i	1.52228	+	1.52228i
$429$		0			0
$430$	−20.9361	−	26.1946i	−1.00963	−	1.26321i
$431$	25.3455	−	25.3455i	1.22085	−	1.22085i	0.253522	−	0.967330i	$-0.418411\pi$
$431$	25.3455	−	25.3455i	1.22085	−	1.22085i	0.967330	−	0.253522i	$-0.0815889\pi$
$432$	−2.10819	−	2.10819i	−0.101430	−	0.101430i
$433$	5.72268	+	5.72268i	0.275014	+	0.275014i	0.831115	−	0.556101i	$-0.187703\pi$
$433$	5.72268	+	5.72268i	0.275014	+	0.275014i	−0.556101	+	0.831115i	$0.687703\pi$
$434$	0.670679	+	0.670679i	0.0321936	+	0.0321936i
$435$	−26.9380	−	33.7040i	−1.29158	−	1.61598i
$436$	14.4845	+	14.4845i	0.693684	+	0.693684i
$437$		−	0.201861i		−	0.00965633i
$438$	−23.2296	+	23.2296i	−1.10996	+	1.10996i
$439$	28.6671			1.36821			0.684104	−	0.729384i	$-0.260193\pi$
$439$	28.6671			1.36821			0.684104	+	0.729384i	$0.260193\pi$
$440$	18.2989	+	22.8950i	0.872368	+	1.09148i
$441$		−	5.08683i		−	0.242230i
$442$		0			0
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	−0.985412	−	0.170184i	$-0.945564\pi$
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	0.170184	+	0.985412i	$0.445564\pi$
$444$	5.69307	+	5.69307i	0.270181	+	0.270181i
$445$	−12.5958	+	10.0672i	−0.597096	+	0.477231i
$446$		−	26.7339i		−	1.26589i
$447$	34.2054			1.61786
$448$			16.6596i			0.787090i
$449$	6.48150	−	6.48150i	0.305881	−	0.305881i	−0.537428	−	0.843309i	$-0.680604\pi$
$449$	6.48150	−	6.48150i	0.305881	−	0.305881i	0.843309	+	0.537428i	$0.180604\pi$
$450$	−2.35012	+	10.4008i	−0.110786	+	0.490297i
$451$	2.73470			0.128772
$452$	24.7049	−	24.7049i	1.16202	−	1.16202i
$453$	−28.2495			−1.32728
$454$	62.2722			2.92258
$455$		0			0
$456$	−5.80989			−0.272073
$457$	−21.4798			−1.00478			−0.502391	−	0.864640i	$-0.667546\pi$
$457$	−21.4798			−1.00478			−0.502391	+	0.864640i	$0.667546\pi$
$458$	29.0354	−	29.0354i	1.35673	−	1.35673i
$459$	−13.1375			−0.613208
$460$	0.709072	+	0.887168i	0.0330607	+	0.0413644i
$461$	3.59137	−	3.59137i	0.167267	−	0.167267i	−0.618510	−	0.785777i	$-0.712263\pi$
$461$	3.59137	−	3.59137i	0.167267	−	0.167267i	0.785777	+	0.618510i	$0.212263\pi$
$462$			31.1977i			1.45145i
$463$	−20.0793			−0.933163			−0.466581	−	0.884478i	$-0.654515\pi$
$463$	−20.0793			−0.933163			−0.466581	+	0.884478i	$0.654515\pi$
$464$		−	7.10032i		−	0.329624i
$465$	−0.162537	+	1.45679i	−0.00753747	+	0.0675570i
$466$	−36.8107	−	36.8107i	−1.70522	−	1.70522i
$467$	21.4507	−	21.4507i	0.992618	−	0.992618i	−0.00735447	−	0.999973i	$-0.502341\pi$
$467$	21.4507	−	21.4507i	0.992618	−	0.992618i	0.999973	+	0.00735447i	$0.00234102\pi$
$468$		0			0
$469$		−	7.75807i		−	0.358234i
$470$	−1.78599	+	16.0075i	−0.0823816	+	0.738372i
$471$	8.63254			0.397767
$472$	−0.00390197	+	0.00390197i	−0.000179603	+	0.000179603i
$473$		−	36.3934i		−	1.67337i
$474$	35.3447	+	35.3447i	1.62344	+	1.62344i
$475$	3.25287	+	5.15200i	0.149252	+	0.236390i
$476$	8.92064	+	8.92064i	0.408877	+	0.408877i
$477$	−4.26219	−	4.26219i	−0.195152	−	0.195152i
$478$	−5.89248	−	5.89248i	−0.269516	−	0.269516i
$479$	−21.9979	+	21.9979i	−1.00511	+	1.00511i	−0.00512249	+	0.999987i	$0.501631\pi$
$479$	−21.9979	+	21.9979i	−1.00511	+	1.00511i	−0.999987	+	0.00512249i	$0.998369\pi$
$480$	−22.3664	+	17.8764i	−1.02088	+	0.815943i
$481$		0			0
$482$	−33.1210	−	33.1210i	−1.50862	−	1.50862i
$483$			0.420346i			0.0191264i
$484$			57.7541i			2.62518i
$485$	−9.29068	−	1.03658i	−0.421868	−	0.0470687i
$486$	−15.1377	+	15.1377i	−0.686662	+	0.686662i
$487$	19.4316			0.880529			0.440264	−	0.897868i	$-0.354885\pi$
$487$	19.4316			0.880529			0.440264	+	0.897868i	$0.354885\pi$
$488$	−3.34029			−0.151208
$489$	12.9321	−	12.9321i	0.584810	−	0.584810i
$490$	26.8543	+	2.99619i	1.21315	+	0.135354i
$491$			35.3136i			1.59368i	0.604191	+	0.796839i	$0.293496\pi$
$491$			35.3136i			1.59368i	−0.604191	+	0.796839i	$0.706504\pi$
$492$		−	3.04992i		−	0.137501i
$493$	−22.1234	−	22.1234i	−0.996389	−	0.996389i
$494$		0			0
$495$	−9.03988	+	7.22515i	−0.406312	+	0.324746i
$496$	−0.170569	+	0.170569i	−0.00765878	+	0.00765878i
$497$	10.9791	+	10.9791i	0.492480	+	0.492480i
$498$	8.39676	+	8.39676i	0.376268	+	0.376268i
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	0.886161	−	0.463377i	$-0.153362\pi$
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	−0.463377	+	0.886161i	$0.653362\pi$
$500$	−32.3934	−	11.2165i	−1.44868	−	0.501617i
$501$	−17.7561	−	17.7561i	−0.793285	−	0.793285i
$502$			5.32928i			0.237857i
$503$	−17.0606	+	17.0606i	−0.760693	+	0.760693i	−0.976448	−	0.215754i	$-0.930779\pi$
$503$	−17.0606	+	17.0606i	−0.760693	+	0.760693i	0.215754	+	0.976448i	$0.430779\pi$
$504$	2.90384			0.129347
$505$	2.13958	−	19.1767i	0.0952102	−	0.853352i
$506$			2.03659i			0.0905374i
$507$		0			0
$508$	−1.13721	+	1.13721i	−0.0504555	+	0.0504555i
$509$	2.63199	+	2.63199i	0.116661	+	0.116661i	0.763027	−	0.646366i	$-0.223712\pi$
$509$	2.63199	+	2.63199i	0.116661	+	0.116661i	−0.646366	+	0.763027i	$0.723712\pi$
$510$	−3.57206	+	32.0158i	−0.158174	+	1.41768i
$511$		−	9.38238i		−	0.415052i
$512$	−8.22064			−0.363304
$513$			4.96943i			0.219406i
$514$	−1.38472	+	1.38472i	−0.0610772	+	0.0610772i
$515$	2.12445	+	2.65804i	0.0936144	+	0.117127i
$516$	−40.5884			−1.78681
$517$	−12.3607	+	12.3607i	−0.543623	+	0.543623i
$518$	−3.79929			−0.166931
$519$	−27.2503			−1.19615
$520$		0			0
$521$	45.2323			1.98166			0.990832	−	0.135103i	$-0.0431364\pi$
$521$	45.2323			1.98166			0.990832	+	0.135103i	$0.0431364\pi$
$522$	−20.7114			−0.906511
$523$	0.807155	−	0.807155i	0.0352944	−	0.0352944i	−0.689239	−	0.724534i	$-0.742055\pi$
$523$	0.807155	−	0.807155i	0.0352944	−	0.0352944i	0.724534	+	0.689239i	$0.242055\pi$
$524$	15.6337			0.682960
$525$	−6.77362	−	10.7283i	−0.295625	−	0.468221i
$526$	24.1729	−	24.1729i	1.05399	−	1.05399i
$527$			1.06293i			0.0463020i
$528$	−7.93430			−0.345296
$529$		−	22.9726i		−	0.998807i
$530$	25.0113	−	19.9904i	1.08642	−	0.868328i
$531$	−0.00154066	−	0.00154066i	−6.68587e−5	−	6.68587e-5i
$532$	3.37434	−	3.37434i	0.146296	−	0.146296i
$533$		0			0
$534$			32.2479i			1.39550i
$535$	−20.2790	−	25.3724i	−0.876738	−	1.09695i
$536$	−14.5764			−0.629603
$537$	−17.7615	+	17.7615i	−0.766463	+	0.766463i
$538$			54.8782i			2.36597i
$539$	20.7364	+	20.7364i	0.893180	+	0.893180i
$540$	−17.4560	−	21.8403i	−0.751185	−	0.939858i
$541$	22.3573	+	22.3573i	0.961218	+	0.961218i	0.999276	−	0.0380580i	$-0.0121172\pi$
$541$	22.3573	+	22.3573i	0.961218	+	0.961218i	−0.0380580	+	0.999276i	$0.512117\pi$
$542$	−20.8759	−	20.8759i	−0.896698	−	0.896698i
$543$	11.4727	+	11.4727i	0.492339	+	0.492339i
$544$	−14.6814	+	14.6814i	−0.629459	+	0.629459i
$545$	−9.32685	−	11.6694i	−0.399518	−	0.499864i
$546$		0			0
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	0.587050	−	0.809550i	$-0.300289\pi$
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	−0.809550	+	0.587050i	$0.800289\pi$
$548$			11.6619i			0.498173i
$549$		−	1.31888i		−	0.0562884i
$550$	−32.8183	−	51.9789i	−1.39938	−	2.21639i
$551$	−8.36844	+	8.36844i	−0.356507	+	0.356507i
$552$	0.789774			0.0336150
$553$	−14.2756			−0.607061
$554$	19.4608	−	19.4608i	0.826812	−	0.826812i
$555$	−3.66586	−	4.58661i	−0.155607	−	0.194691i
$556$			4.53239i			0.192216i
$557$			6.58643i			0.279076i	0.990217	+	0.139538i	$0.0445617\pi$
$557$			6.58643i			0.279076i	−0.990217	+	0.139538i	$0.955438\pi$
$558$	0.497544	+	0.497544i	0.0210627	+	0.0210627i
$559$		0			0
$560$	0.231518	−	2.07505i	0.00978343	−	0.0876871i
$561$	−24.7220	+	24.7220i	−1.04376	+	1.04376i
$562$	14.4846	+	14.4846i	0.610996	+	0.610996i
$563$	20.7568	+	20.7568i	0.874794	+	0.874794i	0.992990	−	0.118197i	$-0.0377113\pi$
$563$	20.7568	+	20.7568i	0.874794	+	0.874794i	−0.118197	+	0.992990i	$0.537711\pi$
$564$	13.7855	+	13.7855i	0.580475	+	0.580475i
$565$	−19.9034	+	15.9079i	−0.837344	+	0.669250i
$566$	43.5343	+	43.5343i	1.82988	+	1.82988i
$567$		−	13.9784i		−	0.587039i
$568$	20.6282	−	20.6282i	0.865542	−	0.865542i
$569$	−33.9087			−1.42153			−0.710763	−	0.703432i	$-0.751650\pi$
$569$	−33.9087			−1.42153			−0.710763	+	0.703432i	$0.751650\pi$
$570$	12.1103	+	1.35117i	0.507246	+	0.0565945i
$571$		−	33.5525i		−	1.40413i	−0.712113	−	0.702065i	$-0.752262\pi$
$571$		−	33.5525i		−	1.40413i	0.712113	−	0.702065i	$-0.247738\pi$
$572$		0			0
$573$	−20.7277	+	20.7277i	−0.865910	+	0.865910i
$574$	1.01769	+	1.01769i	0.0424775	+	0.0424775i
$575$	−0.442182	−	0.700343i	−0.0184403	−	0.0292063i
$576$			12.3589i			0.514954i
$577$	11.0413			0.459654			0.229827	−	0.973232i	$-0.426184\pi$
$577$	11.0413			0.459654			0.229827	+	0.973232i	$0.426184\pi$
$578$		−	14.9038i		−	0.619914i
$579$	−21.2096	+	21.2096i	−0.881442	+	0.881442i
$580$	7.38321	−	66.1743i	0.306571	−	2.74774i
$581$	−3.39142			−0.140700
$582$	−13.2200	+	13.2200i	−0.547988	+	0.547988i
$583$	34.7495			1.43918
$584$	−17.6282			−0.729461
$585$		0			0
$586$	58.8002			2.42902
$587$	23.5058			0.970190			0.485095	−	0.874461i	$-0.338785\pi$
$587$	23.5058			0.970190			0.485095	+	0.874461i	$0.338785\pi$
$588$	23.1267	−	23.1267i	0.953728	−	0.953728i
$589$	0.402066			0.0165668
$590$	0.00904086	−	0.00722594i	0.000372206	−	0.000297487i
$591$	−21.5954	+	21.5954i	−0.888317	+	0.888317i
$592$		−	0.966247i		−	0.0397125i
$593$	−30.6582			−1.25898			−0.629491	−	0.777007i	$-0.716737\pi$
$593$	−30.6582			−1.25898			−0.629491	+	0.777007i	$0.716737\pi$
$594$		−	50.1368i		−	2.05714i
$595$	−5.74416	−	7.18690i	−0.235487	−	0.294634i
$596$	37.3259	+	37.3259i	1.52893	+	1.52893i
$597$	16.0948	−	16.0948i	0.658717	−	0.658717i
$598$		0			0
$599$			7.49378i			0.306188i	0.988212	+	0.153094i	$0.0489237\pi$
$599$			7.49378i			0.306188i	−0.988212	+	0.153094i	$0.951076\pi$
$600$	−20.1570	+	12.7267i	−0.822906	+	0.519566i
$601$	−14.0931			−0.574868			−0.287434	−	0.957801i	$-0.592802\pi$
$601$	−14.0931			−0.574868			−0.287434	+	0.957801i	$0.592802\pi$
$602$	13.5434	−	13.5434i	0.551989	−	0.551989i
$603$		−	5.75533i		−	0.234375i
$604$	−30.8267	−	30.8267i	−1.25432	−	1.25432i
$605$	4.67031	−	41.8591i	0.189875	−	1.70182i
$606$	−27.2872	−	27.2872i	−1.10847	−	1.10847i
$607$	10.6631	+	10.6631i	0.432801	+	0.432801i	0.889580	−	0.456779i	$-0.150997\pi$
$607$	10.6631	+	10.6631i	0.432801	+	0.432801i	−0.456779	+	0.889580i	$0.650997\pi$
$608$	5.55340	+	5.55340i	0.225220	+	0.225220i
$609$	17.4260	−	17.4260i	0.706139	−	0.706139i
$610$	6.96260	+	0.776832i	0.281908	+	0.0314530i
$611$		0			0
$612$	6.61779	+	6.61779i	0.267508	+	0.267508i
$613$		−	11.9161i		−	0.481288i	−0.970613	−	0.240644i	$-0.922641\pi$
$613$		−	11.9161i		−	0.481288i	0.970613	−	0.240644i	$-0.0773587\pi$
$614$		−	33.0954i		−	1.33562i
$615$	−0.246634	+	2.21053i	−0.00994522	+	0.0891372i
$616$	−11.8375	+	11.8375i	−0.476945	+	0.476945i
$617$	−38.8317			−1.56330			−0.781652	−	0.623714i	$-0.785623\pi$
$617$	−38.8317			−1.56330			−0.781652	+	0.623714i	$0.785623\pi$
$618$	6.80516			0.273744
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	−0.339461	−	0.940620i	$-0.610245\pi$
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	0.940620	+	0.339461i	$0.110245\pi$
$620$	−1.76706	+	1.41233i	−0.0709667	+	0.0567203i
$621$		−	0.675525i		−	0.0271079i
$622$			71.6939i			2.87466i
$623$	−6.51241	−	6.51241i	−0.260914	−	0.260914i
$624$		0			0
$625$	22.5712	+	10.7490i	0.902847	+	0.429961i
$626$	26.9794	−	26.9794i	1.07831	−	1.07831i
$627$	9.35137	+	9.35137i	0.373458	+	0.373458i
$628$	9.42008	+	9.42008i	0.375902	+	0.375902i
$629$	−3.01067	−	3.01067i	−0.120043	−	0.120043i
$630$	−6.05286	−	0.675330i	−0.241152	−	0.0269058i
$631$	−27.6170	−	27.6170i	−1.09942	−	1.09942i	−0.994479	−	0.104938i	$-0.966535\pi$
$631$	−27.6170	−	27.6170i	−1.09942	−	1.09942i	−0.104938	−	0.994479i	$-0.533465\pi$
$632$			26.8219i			1.06692i
$633$	4.47307	−	4.47307i	0.177788	−	0.177788i
$634$	−35.0286			−1.39116
$635$	0.916191	−	0.732269i	0.0363579	−	0.0290592i
$636$		−	38.7550i		−	1.53674i
$637$		0			0
$638$	84.4296	−	84.4296i	3.34260	−	3.34260i
$639$	8.14485	+	8.14485i	0.322205	+	0.322205i
$640$	−36.6003	−	4.08357i	−1.44675	−	0.161417i
$641$		−	8.72499i		−	0.344617i	−0.985043	−	0.172308i	$-0.944877\pi$
$641$		−	8.72499i		−	0.344617i	0.985043	−	0.172308i	$-0.0551225\pi$
$642$	−64.9590			−2.56373
$643$		−	14.7970i		−	0.583538i	−0.956489	−	0.291769i	$-0.905756\pi$
$643$		−	14.7970i		−	0.583538i	0.956489	−	0.291769i	$-0.0942439\pi$
$644$	−0.458694	+	0.458694i	−0.0180751	+	0.0180751i
$645$	29.4178	+	3.28220i	1.15832	+	0.129237i
$646$	8.83617			0.347655
$647$	23.9537	−	23.9537i	0.941716	−	0.941716i	−0.0566765	−	0.998393i	$-0.518050\pi$
$647$	23.9537	−	23.9537i	0.941716	−	0.941716i	0.998393	+	0.0566765i	$0.0180504\pi$
$648$	−26.2636			−1.03173
$649$	0.0125609			0.000493060
$650$		0			0
$651$	−0.837243			−0.0328141
$652$	28.2238			1.10533
$653$	−14.3176	+	14.3176i	−0.560289	+	0.560289i	−0.929390	−	0.369100i	$-0.879666\pi$
$653$	−14.3176	+	14.3176i	−0.560289	+	0.560289i	0.369100	+	0.929390i	$0.379666\pi$
$654$	−29.8763			−1.16826
$655$	−11.3310	−	1.26422i	−0.442739	−	0.0493973i
$656$	−0.258822	+	0.258822i	−0.0101053	+	0.0101053i
$657$		−	6.96032i		−	0.271548i
$658$	−9.19981			−0.358646
$659$			30.2898i			1.17992i	0.807432	+	0.589961i	$0.200857\pi$
$659$			30.2898i			1.17992i	−0.807432	+	0.589961i	$0.799143\pi$
$660$	−73.9470	−	8.25042i	−2.87838	−	0.321147i
$661$	15.4711	+	15.4711i	0.601754	+	0.601754i	0.940778	−	0.339024i	$-0.110097\pi$
$661$	15.4711	+	15.4711i	0.601754	+	0.601754i	−0.339024	+	0.940778i	$0.610097\pi$
$662$	−27.1574	+	27.1574i	−1.05550	+	1.05550i
$663$		0			0
$664$			6.37202i			0.247282i
$665$	−2.71853	+	2.17279i	−0.105420	+	0.0842573i
$666$	−2.81851			−0.109215
$667$	1.13757	−	1.13757i	0.0440470	−	0.0440470i
$668$		−	38.7520i		−	1.49936i
$669$	16.6867	+	16.6867i	0.645143	+	0.645143i
$670$	30.3834	+	3.38994i	1.17381	+	0.130965i
$671$	5.37640	+	5.37640i	0.207553	+	0.207553i
$672$	−11.5641	−	11.5641i	−0.446096	−	0.446096i
$673$	−0.406042	−	0.406042i	−0.0156518	−	0.0156518i	0.699238	−	0.714889i	$-0.253523\pi$
$673$	−0.406042	−	0.406042i	−0.0156518	−	0.0156518i	−0.714889	+	0.699238i	$0.753523\pi$
$674$	56.3962	−	56.3962i	2.17230	−	2.17230i
$675$	10.8857	+	17.2411i	0.418989	+	0.663610i
$676$		0			0
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	0.450111	−	0.892973i	$-0.351385\pi$
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	−0.892973	+	0.450111i	$0.851385\pi$
$678$			50.9571i			1.95700i
$679$		−	5.33952i		−	0.204912i
$680$	−13.5032	+	10.7925i	−0.517825	+	0.413873i
$681$	−38.8688	+	38.8688i	−1.48946	+	1.48946i
$682$	−4.05646			−0.155330
$683$	20.1058			0.769326			0.384663	−	0.923057i	$-0.374318\pi$
$683$	20.1058			0.769326			0.384663	+	0.923057i	$0.374318\pi$
$684$	2.50325	−	2.50325i	0.0957143	−	0.0957143i
$685$	0.943047	−	8.45236i	0.0360320	−	0.322948i
$686$			35.5565i			1.35755i
$687$			36.2463i			1.38288i
$688$	3.44440	+	3.44440i	0.131317	+	0.131317i
$689$		0			0
$690$	−1.64623	−	0.183673i	−0.0626709	−	0.00699232i
$691$	−30.6415	+	30.6415i	−1.16566	+	1.16566i	−0.182443	+	0.983216i	$0.558400\pi$
$691$	−30.6415	+	30.6415i	−1.16566	+	1.16566i	−0.983216	+	0.182443i	$0.941600\pi$
$692$	−29.7363	−	29.7363i	−1.13040	−	1.13040i
$693$	−4.67390	−	4.67390i	−0.177547	−	0.177547i
$694$	−20.5310	−	20.5310i	−0.779346	−	0.779346i
$695$	0.366514	−	3.28500i	0.0139027	−	0.124607i
$696$	−32.7412	−	32.7412i	−1.24105	−	1.24105i
$697$			1.61289i			0.0610926i
$698$	−42.7351	+	42.7351i	−1.61755	+	1.61755i
$699$	45.9527			1.73809
$700$	4.31546	−	19.0986i	0.163109	−	0.721859i
$701$		−	8.03468i		−	0.303466i	−0.988422	−	0.151733i	$-0.951515\pi$
$701$		−	8.03468i		−	0.303466i	0.988422	−	0.151733i	$-0.0484853\pi$
$702$		0			0
$703$	−1.13882	+	1.13882i	−0.0429514	+	0.0429514i
$704$	−50.3809	−	50.3809i	−1.89880	−	1.89880i
$705$	−8.87673	−	11.1063i	−0.334317	−	0.418286i
$706$			52.4701i			1.97474i
$707$	11.0212			0.414495
$708$		−	0.0140088i		−	0.000526483i
$709$	16.0704	−	16.0704i	0.603536	−	0.603536i	−0.337713	−	0.941249i	$-0.609653\pi$
$709$	16.0704	−	16.0704i	0.603536	−	0.603536i	0.941249	+	0.337713i	$0.109653\pi$
$710$	−47.7956	+	38.2008i	−1.79374	+	1.43365i
$711$	−10.5904			−0.397170
$712$	−12.2359	+	12.2359i	−0.458561	+	0.458561i
$713$	−0.0546553			−0.00204686
$714$	−18.4000			−0.688604
$715$		0			0
$716$	−38.7636			−1.44866
$717$	7.35589			0.274711
$718$	20.6449	−	20.6449i	0.770460	−	0.770460i
$719$	42.9573			1.60204			0.801018	−	0.598640i	$-0.204292\pi$
$719$	42.9573			1.60204			0.801018	+	0.598640i	$0.204292\pi$
$720$	0.171752	−	1.53938i	0.00640081	−	0.0573693i
$721$	−1.37429	+	1.37429i	−0.0511813	+	0.0511813i
$722$			39.4229i			1.46717i
$723$	41.3467			1.53770
$724$			25.0386i			0.930553i
$725$	−10.7024	+	47.3650i	−0.397479	+	1.75909i
$726$	−59.5628	−	59.5628i	−2.21058	−	2.21058i
$727$	1.42786	−	1.42786i	0.0529563	−	0.0529563i	−0.680133	−	0.733089i	$-0.738078\pi$
$727$	1.42786	−	1.42786i	0.0529563	−	0.0529563i	0.733089	+	0.680133i	$0.238078\pi$
$728$		0			0
$729$			13.9369i			0.516183i
$730$	36.7448	+	4.09970i	1.35999	+	0.151737i
$731$	21.4644			0.793889
$732$	5.99613	−	5.99613i	0.221623	−	0.221623i
$733$		−	32.1064i		−	1.18588i	−0.805247	−	0.592939i	$-0.797967\pi$
$733$		−	32.1064i		−	1.18588i	0.805247	−	0.592939i	$-0.202033\pi$
$734$	−23.6613	−	23.6613i	−0.873355	−	0.873355i
$735$	−18.6320	+	14.8917i	−0.687250	+	0.549287i
$736$	−0.754907	−	0.754907i	−0.0278262	−	0.0278262i
$737$	23.4615	+	23.4615i	0.864217	+	0.864217i
$738$	0.754973	+	0.754973i	0.0277909	+	0.0277909i
$739$	−14.5283	+	14.5283i	−0.534431	+	0.534431i	−0.921888	−	0.387457i	$-0.873354\pi$
$739$	−14.5283	+	14.5283i	−0.534431	+	0.534431i	0.387457	+	0.921888i	$0.373354\pi$
$740$	1.00474	−	9.00534i	0.0369351	−	0.331043i
$741$		0			0
$742$	12.9317	+	12.9317i	0.474736	+	0.474736i
$743$		−	22.5040i		−	0.825593i	−0.910823	−	0.412797i	$-0.864552\pi$
$743$		−	22.5040i		−	0.825593i	0.910823	−	0.412797i	$-0.135448\pi$
$744$			1.57307i			0.0576714i
$745$	−24.0348	−	30.0716i	−0.880567	−	1.10174i
$746$	−9.83771	+	9.83771i	−0.360184	+	0.360184i
$747$	−2.51593			−0.0920530
$748$	−53.9547			−1.97278
$749$	13.1184	−	13.1184i	0.479334	−	0.479334i
$750$	44.9757	−	21.8402i	1.64228	−	0.797490i
$751$		−	1.66512i		−	0.0607611i	−0.999538	−	0.0303806i	$-0.990328\pi$
$751$		−	1.66512i		−	0.0607611i	0.999538	−	0.0303806i	$-0.00967192\pi$
$752$		−	2.33972i		−	0.0853209i
$753$	−3.32640	−	3.32640i	−0.121221	−	0.121221i
$754$		0			0
$755$	19.8498	+	24.8355i	0.722410	+	0.903855i
$756$	11.2921	−	11.2921i	0.410692	−	0.410692i
$757$	−27.5976	−	27.5976i	−1.00305	−	1.00305i	−0.999995	−	0.00305681i	$-0.999027\pi$
$757$	−27.5976	−	27.5976i	−1.00305	−	1.00305i	−0.00305681	−	0.999995i	$-0.500973\pi$
$758$	−29.0761	−	29.0761i	−1.05609	−	1.05609i
$759$	−1.27119	−	1.27119i	−0.0461412	−	0.0461412i
$760$	4.08238	+	5.10774i	0.148084	+	0.185277i
$761$	−11.5012	−	11.5012i	−0.416918	−	0.416918i	0.467222	−	0.884140i	$-0.345255\pi$
$761$	−11.5012	−	11.5012i	−0.416918	−	0.416918i	−0.884140	+	0.467222i	$0.845255\pi$
$762$		−	2.34565i		−	0.0849739i
$763$	6.03348	−	6.03348i	0.218426	−	0.218426i
$764$	−45.2372			−1.63663
$765$	−4.26131	−	5.33161i	−0.154068	−	0.192765i
$766$			23.0560i			0.833045i
$767$		0			0
$768$	−15.4289	+	15.4289i	−0.556741	+	0.556741i
$769$	28.2209	+	28.2209i	1.01767	+	1.01767i	0.999841	+	0.0178298i	$0.00567570\pi$
$769$	28.2209	+	28.2209i	1.01767	+	1.01767i	0.0178298	+	0.999841i	$0.494324\pi$
$770$	27.4274	−	21.9214i	0.988414	−	0.789993i
$771$		−	1.72861i		−	0.0622544i
$772$	−46.2891			−1.66598
$773$		−	20.5887i		−	0.740525i	−0.928927	−	0.370262i	$-0.879268\pi$
$773$		−	20.5887i		−	0.740525i	0.928927	−	0.370262i	$-0.120732\pi$
$774$	10.0472	−	10.0472i	0.361139	−	0.361139i
$775$	1.39494	−	0.880735i	0.0501077	−	0.0316369i
$776$	−10.0322			−0.360137
$777$	2.37142	−	2.37142i	0.0850744	−	0.0850744i
$778$	−7.67976			−0.275333
$779$	0.610095			0.0218589
$780$		0			0
$781$	−66.4048			−2.37615
$782$	−1.20115			−0.0429532
$783$	−28.0048	+	28.0048i	−1.00081	+	1.00081i
$784$	−3.92514			−0.140183
$785$	−6.06575	−	7.58927i	−0.216496	−	0.270873i
$786$	−16.1233	+	16.1233i	−0.575098	+	0.575098i
$787$			28.6489i			1.02122i	0.859812	+	0.510611i	$0.170581\pi$
$787$			28.6489i			1.02122i	−0.859812	+	0.510611i	$0.829419\pi$
$788$	−47.1311			−1.67898
$789$			30.1763i			1.07430i
$790$	6.23783	−	55.9085i	0.221932	−	1.98914i
$791$	−10.2907	−	10.2907i	−0.365895	−	0.365895i
$792$	−8.78163	+	8.78163i	−0.312042	+	0.312042i
$793$		0			0
$794$			26.8568i			0.953111i
$795$	−3.13395	+	28.0890i	−0.111150	+	0.996214i
$796$	35.1262			1.24502
$797$	6.21167	−	6.21167i	0.220029	−	0.220029i	−0.588482	−	0.808510i	$-0.700274\pi$
$797$	6.21167	−	6.21167i	0.220029	−	0.220029i	0.808510	+	0.588482i	$0.200274\pi$
$798$			6.96002i			0.246382i
$799$	−7.29019	−	7.29019i	−0.257909	−	0.257909i
$800$	31.4320	+	7.10227i	1.11129	+	0.251103i
$801$	−4.83124	−	4.83124i	−0.170703	−	0.170703i
$802$	6.48736	+	6.48736i	0.229077	+	0.229077i
$803$	28.3737	+	28.3737i	1.00129	+	1.00129i
$804$	26.1659	−	26.1659i	0.922801	−	0.922801i
$805$	0.369546	−	0.295361i	0.0130248	−	0.0104101i
$806$		0			0
$807$	−34.2536	−	34.2536i	−1.20578	−	1.20578i
$808$		−	20.7073i		−	0.728482i
$809$		−	0.947514i		−	0.0333128i	−0.999861	−	0.0166564i	$-0.994698\pi$
$809$		−	0.947514i		−	0.0333128i	0.999861	−	0.0166564i	$-0.00530214\pi$
$810$	54.7446	+	6.10797i	1.92353	+	0.214612i
$811$	28.8041	−	28.8041i	1.01145	−	1.01145i	0.0115151	−	0.999934i	$-0.496335\pi$
$811$	28.8041	−	28.8041i	1.01145	−	1.01145i	0.999934	−	0.0115151i	$-0.00366545\pi$
$812$	38.0316			1.33465
$813$	26.0605			0.913981
$814$	11.4896	−	11.4896i	0.402711	−	0.402711i
$815$	−20.4561	−	2.28233i	−0.716546	−	0.0799465i
$816$		−	4.67955i		−	0.163817i
$817$		−	8.11915i		−	0.284053i
$818$	−11.0440	−	11.0440i	−0.386145	−	0.386145i
$819$		0			0
$820$	−2.68133	+	2.14306i	−0.0936361	+	0.0748390i
$821$	0.951434	−	0.951434i	0.0332053	−	0.0332053i	−0.690309	−	0.723514i	$-0.742526\pi$
$821$	0.951434	−	0.951434i	0.0332053	−	0.0332053i	0.723514	+	0.690309i	$0.242526\pi$
$822$	−12.0271	−	12.0271i	−0.419495	−	0.419495i
$823$	−23.3838	−	23.3838i	−0.815109	−	0.815109i	0.170286	−	0.985395i	$-0.445531\pi$
$823$	−23.3838	−	23.3838i	−0.815109	−	0.815109i	−0.985395	+	0.170286i	$0.945531\pi$
$824$	2.58211	+	2.58211i	0.0899520	+	0.0899520i
$825$	52.9283	+	11.9595i	1.84273	+	0.416377i
$826$	0.00467441	+	0.00467441i	0.000162644	+	0.000162644i
$827$		−	26.4195i		−	0.918697i	−0.888256	−	0.459349i	$-0.848083\pi$
$827$		−	26.4195i		−	0.918697i	0.888256	−	0.459349i	$-0.151917\pi$
$828$	−0.340282	+	0.340282i	−0.0118256	+	0.0118256i
$829$	2.46068			0.0854629			0.0427314	−	0.999087i	$-0.486394\pi$
$829$	2.46068			0.0854629			0.0427314	+	0.999087i	$0.486394\pi$
$830$	1.48191	−	13.2820i	0.0514377	−	0.461027i
$831$			24.2940i			0.842748i
$832$		0			0
$833$	−12.2301	+	12.2301i	−0.423747	+	0.423747i
$834$	−4.67434	−	4.67434i	−0.161859	−	0.161859i
$835$	−3.13370	+	28.0868i	−0.108446	+	0.971983i
$836$			20.4090i			0.705859i
$837$	1.34551			0.0465075
$838$			47.7818i			1.65059i
$839$	35.6002	−	35.6002i	1.22906	−	1.22906i	0.264736	−	0.964321i	$-0.414715\pi$
$839$	35.6002	−	35.6002i	1.22906	−	1.22906i	0.964321	−	0.264736i	$-0.0852847\pi$
$840$	−8.50096	−	10.6361i	−0.293311	−	0.366981i
$841$	−65.3193			−2.25239
$842$	7.10641	−	7.10641i	0.244903	−	0.244903i
$843$	−18.0819			−0.622773
$844$	9.76228			0.336032
$845$		0			0
$846$	−6.82488			−0.234644
$847$	24.0572			0.826616
$848$	−3.28882	+	3.28882i	−0.112939	+	0.112939i
$849$	−54.3461			−1.86515
$850$	30.6565	−	19.3559i	1.05151	−	0.663900i
$851$	0.154807	−	0.154807i	0.00530670	−	0.00530670i
$852$			74.0592i			2.53723i
$853$	42.9612			1.47096			0.735481	−	0.677545i	$-0.236956\pi$
$853$	42.9612			1.47096			0.735481	+	0.677545i	$0.236956\pi$
$854$			4.00154i			0.136930i
$855$	−2.01674	+	1.61189i	−0.0689711	+	0.0551254i
$856$	−24.6476	−	24.6476i	−0.842438	−	0.842438i
$857$	−29.0789	+	29.0789i	−0.993316	+	0.993316i	−0.999978	−	0.00666151i	$-0.997880\pi$
$857$	−29.0789	+	29.0789i	−0.993316	+	0.993316i	0.00666151	+	0.999978i	$0.497880\pi$
$858$		0			0
$859$		−	42.1283i		−	1.43740i	−0.695321	−	0.718700i	$-0.744738\pi$
$859$		−	42.1283i		−	1.43740i	0.695321	−	0.718700i	$-0.255262\pi$
$860$	28.5199	+	35.6832i	0.972521	+	1.21679i
$861$	−1.27043			−0.0432962
$862$	−57.0479	+	57.0479i	−1.94306	+	1.94306i
$863$		−	6.80768i		−	0.231736i	−0.993265	−	0.115868i	$-0.963035\pi$
$863$		−	6.80768i		−	0.231736i	0.993265	−	0.115868i	$-0.0369650\pi$
$864$	18.5843	+	18.5843i	0.632252	+	0.632252i
$865$	19.1477	+	23.9570i	0.651041	+	0.814562i
$866$	−12.8806	−	12.8806i	−0.437702	−	0.437702i
$867$	9.30256	+	9.30256i	0.315931	+	0.315931i
$868$	−0.913624	−	0.913624i	−0.0310104	−	0.0310104i
$869$	43.1715	−	43.1715i	1.46449	−	1.46449i
$870$	60.6323	+	75.8612i	2.05563	+	2.57194i
$871$		0			0
$872$	−11.3361	−	11.3361i	−0.383888	−	0.383888i
$873$		−	3.96113i		−	0.134064i
$874$			0.454351i			0.0153686i
$875$	−4.67219	+	13.4934i	−0.157949	+	0.456159i
$876$	31.6443	−	31.6443i	1.06916	−	1.06916i
$877$	47.6814			1.61009			0.805043	−	0.593217i	$-0.202142\pi$
$877$	47.6814			1.61009			0.805043	+	0.593217i	$0.202142\pi$
$878$	−64.5242			−2.17759
$879$	−36.7017	+	36.7017i	−1.23792	+	1.23792i
$880$	5.57512	+	6.97541i	0.187937	+	0.235141i
$881$		−	5.12384i		−	0.172627i	−0.996268	−	0.0863133i	$-0.972491\pi$
$881$		−	5.12384i		−	0.172627i	0.996268	−	0.0863133i	$-0.0275086\pi$
$882$			11.4495i			0.385524i
$883$	14.8283	+	14.8283i	0.499014	+	0.499014i	0.911131	−	0.412117i	$-0.135211\pi$
$883$	14.8283	+	14.8283i	0.499014	+	0.499014i	−0.412117	+	0.911131i	$0.635211\pi$
$884$		0			0
$885$	−0.00113283	+	0.0101533i	−3.80796e−5	+	0.000341301i
$886$	38.6206	−	38.6206i	1.29749	−	1.29749i
$887$	−7.44750	−	7.44750i	−0.250063	−	0.250063i	0.570934	−	0.820996i	$-0.306581\pi$
$887$	−7.44750	−	7.44750i	−0.250063	−	0.250063i	−0.820996	+	0.570934i	$0.806581\pi$
$888$	−4.45558	−	4.45558i	−0.149520	−	0.149520i
$889$	0.473700	+	0.473700i	0.0158874	+	0.0158874i
$890$	28.3506	−	22.6593i	0.950315	−	0.759543i
$891$	42.2728	+	42.2728i	1.41619	+	1.41619i
$892$			36.4179i			1.21936i
$893$	−2.75760	+	2.75760i	−0.0922795	+	0.0922795i
$894$	−76.9898			−2.57492
$895$	28.0952	+	3.13464i	0.939119	+	0.104779i
$896$		−	21.0349i		−	0.702725i
$897$		0			0
$898$	−14.5886	+	14.5886i	−0.486828	+	0.486828i
$899$	2.26581	+	2.26581i	0.0755690	+	0.0755690i
$900$	3.20143	−	14.1683i	0.106714	−	0.472277i
$901$			20.4948i			0.682782i
$902$	−6.15528			−0.204948
$903$			16.9069i			0.562628i
$904$	−19.3348	+	19.3348i	−0.643067	+	0.643067i
$905$	2.02476	−	18.1476i	0.0673053	−	0.603245i
$906$	63.5842			2.11244
$907$	15.2289	−	15.2289i	0.505668	−	0.505668i	−0.407526	−	0.913194i	$-0.633608\pi$
$907$	15.2289	−	15.2289i	0.505668	−	0.505668i	0.913194	+	0.407526i	$0.133608\pi$
$908$	−84.8295			−2.81517
$909$	8.17608			0.271184
$910$		0			0
$911$	−16.6400			−0.551309			−0.275654	−	0.961257i	$-0.588895\pi$
$911$	−16.6400			−0.551309			−0.275654	+	0.961257i	$0.588895\pi$
$912$	−1.77009			−0.0586137
$913$	10.2562	−	10.2562i	0.339429	−	0.339429i
$914$	48.3469			1.59917
$915$	−4.83077	+	3.86101i	−0.159700	+	0.127641i
$916$	−39.5530	+	39.5530i	−1.30687	+	1.30687i
$917$		−	6.51214i		−	0.215050i
$918$	29.5701			0.975958
$919$		−	6.87460i		−	0.226772i	−0.993551	−	0.113386i	$-0.963830\pi$
$919$		−	6.87460i		−	0.226772i	0.993551	−	0.113386i	$-0.0361697\pi$
$920$	−0.554943	−	0.694327i	−0.0182959	−	0.0228913i
$921$	20.6573	+	20.6573i	0.680682	+	0.680682i
$922$	−8.08349	+	8.08349i	−0.266216	+	0.266216i
$923$		0			0
$924$		−	42.4987i		−	1.39810i
$925$	−1.45644	+	6.44566i	−0.0478875	+	0.211932i
$926$	45.1946			1.48519
$927$	−1.01952	+	1.01952i	−0.0334854	+	0.0334854i
$928$			62.5915i			2.05467i
$929$	−31.4342	−	31.4342i	−1.03132	−	1.03132i	−0.999493	−	0.0318293i	$-0.989867\pi$
$929$	−31.4342	−	31.4342i	−1.03132	−	1.03132i	−0.0318293	−	0.999493i	$-0.510133\pi$
$930$	0.365839	−	3.27895i	0.0119963	−	0.107521i
$931$	4.62617	+	4.62617i	0.151617	+	0.151617i
$932$	50.1449	+	50.1449i	1.64255	+	1.64255i
$933$	−44.7495	−	44.7495i	−1.46503	−	1.46503i
$934$	−48.2813	+	48.2813i	−1.57981	+	1.57981i
$935$	39.1054	+	4.36307i	1.27888	+	0.142688i
$936$		0			0
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	0.888738	−	0.458415i	$-0.151583\pi$
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	−0.458415	+	0.888738i	$0.651583\pi$
$938$			17.4619i			0.570152i
$939$			33.6797i			1.09910i
$940$	2.43294	−	21.8060i	0.0793538	−	0.711234i
$941$	40.0251	−	40.0251i	1.30478	−	1.30478i	0.379650	−	0.925130i	$-0.376045\pi$
$941$	40.0251	−	40.0251i	1.30478	−	1.30478i	0.925130	−	0.379650i	$-0.123955\pi$
$942$	−19.4302			−0.633070
$943$	−0.0829339			−0.00270070
$944$	−0.00118881	+	0.00118881i	−3.86925e−5	+	3.86925e-5i
$945$	−9.09750	+	7.27121i	−0.295942	+	0.236532i
$946$			81.9146i			2.66327i
$947$		−	58.8943i		−	1.91381i	−0.290404	−	0.956904i	$-0.593790\pi$
$947$		−	58.8943i		−	1.91381i	0.290404	−	0.956904i	$-0.406210\pi$
$948$	−48.1479	−	48.1479i	−1.56377	−	1.56377i
$949$		0			0
$950$	−7.32157	−	11.5962i	−0.237543	−	0.376229i
$951$	21.8640	−	21.8640i	0.708989	−	0.708989i
$952$	−6.98159	−	6.98159i	−0.226275	−	0.226275i
$953$	−12.6246	−	12.6246i	−0.408953	−	0.408953i	0.472421	−	0.881373i	$-0.343380\pi$
$953$	−12.6246	−	12.6246i	−0.408953	−	0.408953i	−0.881373	+	0.472421i	$0.843380\pi$
$954$	9.59336	+	9.59336i	0.310596	+	0.310596i
$955$	32.7872	+	3.65813i	1.06097	+	0.118374i
$956$	8.02696	+	8.02696i	0.259610	+	0.259610i
$957$			105.398i			3.40703i
$958$	49.5130	−	49.5130i	1.59969	−	1.59969i
$959$	4.85772			0.156864
$960$	45.2680	−	36.1806i	1.46102	−	1.16772i
$961$			30.8911i			0.996488i
$962$		0			0
$963$	9.73187	−	9.73187i	0.313605	−	0.313605i
$964$	45.1187	+	45.1187i	1.45317	+	1.45317i
$965$	33.5495	+	3.74319i	1.08000	+	0.120498i
$966$		−	0.946118i		−	0.0304409i
$967$	−23.2093			−0.746360			−0.373180	−	0.927759i	$-0.621733\pi$
$967$	−23.2093			−0.746360			−0.373180	+	0.927759i	$0.621733\pi$
$968$		−	45.2002i		−	1.45279i
$969$	−5.51532	+	5.51532i	−0.177178	+	0.177178i
$970$	20.9115	+	2.33314i	0.671429	+	0.0749127i
$971$	42.3865			1.36025			0.680123	−	0.733098i	$-0.261926\pi$
$971$	42.3865			1.36025			0.680123	+	0.733098i	$0.261926\pi$
$972$	20.6212	−	20.6212i	0.661425	−	0.661425i
$973$	1.88795			0.0605249
$974$	−43.7367			−1.40141
$975$		0			0
$976$	−1.01768			−0.0325752
$977$	−24.4098			−0.780938			−0.390469	−	0.920616i	$-0.627687\pi$
$977$	−24.4098			−0.780938			−0.390469	+	0.920616i	$0.627687\pi$
$978$	−29.1077	+	29.1077i	−0.930761	+	0.930761i
$979$	39.3890			1.25888
$980$	−36.5819	−	4.08152i	−1.16857	−	0.130379i
$981$	4.47594	−	4.47594i	0.142906	−	0.142906i
$982$		−	79.4840i		−	2.53644i
$983$	−4.47004			−0.142572			−0.0712860	−	0.997456i	$-0.522710\pi$
$983$	−4.47004			−0.142572			−0.0712860	+	0.997456i	$0.522710\pi$
$984$			2.38697i			0.0760938i
$985$	34.1598	+	3.81128i	1.08842	+	0.121438i
$986$	49.7955	+	49.7955i	1.58581	+	1.58581i
$987$	5.74230	−	5.74230i	0.182779	−	0.182779i
$988$		0			0
$989$			1.10369i			0.0350952i
$990$	20.3470	−	16.2624i	0.646671	−	0.516854i
$991$	−49.5350			−1.57353			−0.786766	−	0.617251i	$-0.788246\pi$
$991$	−49.5350			−1.57353			−0.786766	+	0.617251i	$0.788246\pi$
$992$	1.50362	−	1.50362i	0.0477400	−	0.0477400i
$993$		−	33.9020i		−	1.07585i
$994$	−24.7118	−	24.7118i	−0.783812	−	0.783812i
$995$	−25.4589	−	2.84050i	−0.807101	−	0.0900499i
$996$	−11.4384	−	11.4384i	−0.362439	−	0.362439i
$997$	−24.7788	−	24.7788i	−0.784753	−	0.784753i	0.195876	−	0.980629i	$-0.437245\pi$
$997$	−24.7788	−	24.7788i	−0.784753	−	0.784753i	−0.980629	+	0.195876i	$0.937245\pi$
$998$	−21.2573	−	21.2573i	−0.672888	−	0.672888i
$999$	−3.81104	+	3.81104i	−0.120576	+	0.120576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.e.577.1		20
5.3	odd	4		845.2.f.e.408.10		20
13.2	odd	12		845.2.t.e.657.1		20
13.3	even	3		65.2.o.a.32.5	✓	20
13.4	even	6		845.2.o.f.587.1		20
13.5	odd	4		845.2.f.d.437.10		20
13.6	odd	12		845.2.t.g.427.5		20
13.7	odd	12		65.2.t.a.37.1	yes	20
13.8	odd	4		845.2.f.e.437.1		20
13.9	even	3		845.2.o.e.587.5		20
13.10	even	6		845.2.o.g.357.1		20
13.11	odd	12		845.2.t.f.657.5		20
13.12	even	2		845.2.k.d.577.10		20
39.20	even	12		585.2.dp.a.37.5		20
39.29	odd	6		585.2.cf.a.487.1		20
65.3	odd	12		65.2.t.a.58.1	yes	20
65.7	even	12		325.2.s.b.193.1		20
65.8	even	4	inner	845.2.k.e.268.1		20
65.18	even	4		845.2.k.d.268.10		20
65.23	odd	12		845.2.t.g.188.5		20
65.28	even	12		845.2.o.f.488.1		20
65.29	even	6		325.2.s.b.32.1		20
65.33	even	12		65.2.o.a.63.5	yes	20
65.38	odd	4		845.2.f.d.408.1		20
65.42	odd	12		325.2.x.b.318.5		20
65.43	odd	12		845.2.t.e.418.1		20
65.48	odd	12		845.2.t.f.418.5		20
65.58	even	12		845.2.o.g.258.1		20
65.59	odd	12		325.2.x.b.232.5		20
65.63	even	12		845.2.o.e.488.5		20
195.68	even	12		585.2.dp.a.253.5		20
195.98	odd	12		585.2.cf.a.388.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	13.3	even	3
65.2.o.a.63.5	yes	20	65.33	even	12
65.2.t.a.37.1	yes	20	13.7	odd	12
65.2.t.a.58.1	yes	20	65.3	odd	12
325.2.s.b.32.1		20	65.29	even	6
325.2.s.b.193.1		20	65.7	even	12
325.2.x.b.232.5		20	65.59	odd	12
325.2.x.b.318.5		20	65.42	odd	12
585.2.cf.a.388.1		20	195.98	odd	12
585.2.cf.a.487.1		20	39.29	odd	6
585.2.dp.a.37.5		20	39.20	even	12
585.2.dp.a.253.5		20	195.68	even	12
845.2.f.d.408.1		20	65.38	odd	4
845.2.f.d.437.10		20	13.5	odd	4
845.2.f.e.408.10		20	5.3	odd	4
845.2.f.e.437.1		20	13.8	odd	4
845.2.k.d.268.10		20	65.18	even	4
845.2.k.d.577.10		20	13.12	even	2
845.2.k.e.268.1		20	65.8	even	4	inner
845.2.k.e.577.1		20	1.1	even	1	trivial
845.2.o.e.488.5		20	65.63	even	12
845.2.o.e.587.5		20	13.9	even	3
845.2.o.f.488.1		20	65.28	even	12
845.2.o.f.587.1		20	13.4	even	6
845.2.o.g.258.1		20	65.58	even	12
845.2.o.g.357.1		20	13.10	even	6
845.2.t.e.418.1		20	65.43	odd	12
845.2.t.e.657.1		20	13.2	odd	12
845.2.t.f.418.5		20	65.48	odd	12
845.2.t.f.657.5		20	13.11	odd	12
845.2.t.g.188.5		20	65.23	odd	12
845.2.t.g.427.5		20	13.6	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.25081 q^{2} +(1.40490 - 1.40490i) q^{3} +3.06613 q^{4} +(-2.22228 - 0.247944i) q^{5} +(-3.16216 + 3.16216i) q^{6} -1.27718i q^{7} -2.39966 q^{8} -0.947480i q^{9} +(5.00192 + 0.558075i) q^{10} +(3.86239 + 3.86239i) q^{11} +(4.30760 - 4.30760i) q^{12} +2.87469i q^{14} +(-3.47041 + 2.77374i) q^{15} -0.731101 q^{16} +(-2.27799 + 2.27799i) q^{17} +2.13259i q^{18} +(0.861676 + 0.861676i) q^{19} +(-6.81380 - 0.760230i) q^{20} +(-1.79431 - 1.79431i) q^{21} +(-8.69350 - 8.69350i) q^{22} +(-0.117133 - 0.117133i) q^{23} +(-3.37127 + 3.37127i) q^{24} +(4.87705 + 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} -3.91601i q^{28} +9.71181i q^{29} +(7.81123 - 6.24315i) q^{30} +(0.233305 - 0.233305i) q^{31} +6.44488 q^{32} +10.8525 q^{33} +(5.12732 - 5.12732i) q^{34} +(-0.316670 + 2.83826i) q^{35} -2.90510i q^{36} +1.32163i q^{37} +(-1.93947 - 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(0.354016 - 0.354016i) q^{41} +(4.03865 + 4.03865i) q^{42} +(-4.71126 - 4.71126i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-0.234922 + 2.10556i) q^{45} +(0.263643 + 0.263643i) q^{46} +3.20027i q^{47} +(-1.02712 + 1.02712i) q^{48} +5.36880 q^{49} +(-10.9773 - 2.48039i) q^{50} +6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-6.49039 - 6.49039i) q^{54} +(-7.62565 - 9.54097i) q^{55} +3.06480i q^{56} +2.42113 q^{57} -21.8594i q^{58} +(0.00162606 - 0.00162606i) q^{59} +(-10.6407 + 8.50465i) q^{60} +1.39199 q^{61} +(-0.525123 + 0.525123i) q^{62} -1.21011 q^{63} -13.0440 q^{64} -24.4270 q^{66} +6.07436 q^{67} +(-6.98462 + 6.98462i) q^{68} -0.329120 q^{69} +(0.712764 - 6.38837i) q^{70} +(-8.59633 + 8.59633i) q^{71} +2.27363i q^{72} +7.34614 q^{73} -2.97474i q^{74} +(8.39996 - 5.30355i) q^{75} +(2.64201 + 2.64201i) q^{76} +(4.93298 - 4.93298i) q^{77} -11.1774i q^{79} +(1.62471 + 0.181272i) q^{80} +10.9447 q^{81} +(-0.796822 + 0.796822i) q^{82} -2.65539i q^{83} +(-5.50160 - 5.50160i) q^{84} +(5.62715 - 4.49752i) q^{85} +(10.6041 + 10.6041i) q^{86} +(13.6441 + 13.6441i) q^{87} +(-9.26841 - 9.26841i) q^{88} +(5.09904 - 5.09904i) q^{89} +(0.528764 - 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} -0.655538i q^{93} -7.20320i q^{94} +(-1.70124 - 2.12853i) q^{95} +(9.05440 - 9.05440i) q^{96} +4.18070 q^{97} -12.0841 q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Introduction

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