LMFDB - Embedded newform 605.2.e.b.362.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.1
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79273 + 1.79273i) q^{2} +(-1.41767 + 1.41767i) q^{3} -4.42777i q^{4} +(1.69208 - 1.46180i) q^{5} -5.08300i q^{6} +(-1.27846 + 1.27846i) q^{7} +(4.35233 + 4.35233i) q^{8} -1.01958i q^{9} +O(q^{10})$	\(q+(-1.79273 + 1.79273i) q^{2} +(-1.41767 + 1.41767i) q^{3} -4.42777i q^{4} +(1.69208 - 1.46180i) q^{5} -5.08300i q^{6} +(-1.27846 + 1.27846i) q^{7} +(4.35233 + 4.35233i) q^{8} -1.01958i q^{9} +(-0.412838 + 5.65406i) q^{10} +(6.27711 + 6.27711i) q^{12} +(1.59509 + 1.59509i) q^{13} -4.58388i q^{14} +(-0.326467 + 4.47116i) q^{15} -6.74958 q^{16} +(-2.37874 + 2.37874i) q^{17} +(1.82783 + 1.82783i) q^{18} -1.30587 q^{19} +(-6.47250 - 7.49215i) q^{20} -3.62488i q^{21} +(-3.16488 + 3.16488i) q^{23} -12.3403 q^{24} +(0.726289 - 4.94697i) q^{25} -5.71913 q^{26} +(-2.80758 - 2.80758i) q^{27} +(5.66074 + 5.66074i) q^{28} -2.93651 q^{29} +(-7.43033 - 8.60086i) q^{30} -4.01029 q^{31} +(3.39552 - 3.39552i) q^{32} -8.52886i q^{34} +(-0.294410 + 4.03213i) q^{35} -4.51446 q^{36} +(-2.26906 - 2.26906i) q^{37} +(2.34107 - 2.34107i) q^{38} -4.52262 q^{39} +(13.7267 + 1.00227i) q^{40} +1.30369i q^{41} +(6.49844 + 6.49844i) q^{42} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} -11.3475i q^{46} +(5.46143 + 5.46143i) q^{47} +(9.56868 - 9.56868i) q^{48} +3.73106i q^{49} +(7.56654 + 10.1706i) q^{50} -6.74453i q^{51} +(7.06268 - 7.06268i) q^{52} +(4.50356 - 4.50356i) q^{53} +10.0665 q^{54} -11.1286 q^{56} +(1.85129 - 1.85129i) q^{57} +(5.26438 - 5.26438i) q^{58} +12.3878i q^{59} +(19.7973 + 1.44552i) q^{60} -9.31002i q^{61} +(7.18936 - 7.18936i) q^{62} +(1.30349 + 1.30349i) q^{63} -1.32466i q^{64} +(5.03072 + 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(10.5325 + 10.5325i) q^{68} -8.97350i q^{69} +(-6.70072 - 7.75631i) q^{70} -6.77125 q^{71} +(4.43754 - 4.43754i) q^{72} +(-6.67785 - 6.67785i) q^{73} +8.13562 q^{74} +(5.98353 + 8.04281i) q^{75} +5.78207i q^{76} +(8.10784 - 8.10784i) q^{78} -1.14511 q^{79} +(-11.4208 + 9.86653i) q^{80} +11.0192 q^{81} +(-2.33716 - 2.33716i) q^{82} +(-7.39974 - 7.39974i) q^{83} -16.0501 q^{84} +(-0.547785 + 7.50225i) q^{85} +16.3293 q^{86} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(5.76476 + 0.420921i) q^{90} -4.07853 q^{91} +(14.0133 + 14.0133i) q^{92} +(5.68526 - 5.68526i) q^{93} -19.5817 q^{94} +(-2.20963 + 1.90891i) q^{95} +9.62745i q^{96} +(-0.550166 - 0.550166i) q^{97} +(-6.68878 - 6.68878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.79273	+	1.79273i	−1.26765	+	1.26765i	−0.320354	+	0.947298i	$0.603802\pi$
$2$	−1.79273	+	1.79273i	−1.26765	+	1.26765i	−0.947298	+	0.320354i	$0.896198\pi$
$3$	−1.41767	+	1.41767i	−0.818492	+	0.818492i	−0.985890	−	0.167397i	$-0.946464\pi$
$3$	−1.41767	+	1.41767i	−0.818492	+	0.818492i	0.167397	+	0.985890i	$0.446464\pi$
$4$		−	4.42777i		−	2.21388i
$5$	1.69208	−	1.46180i	0.756723	−	0.653736i
$5$	1.69208	−	1.46180i	0.756723	−	0.653736i
$6$		−	5.08300i		−	2.07513i
$7$	−1.27846	+	1.27846i	−0.483214	+	0.483214i	−0.906157	−	0.422942i	$-0.860997\pi$
$7$	−1.27846	+	1.27846i	−0.483214	+	0.483214i	0.422942	+	0.906157i	$0.360997\pi$
$8$	4.35233	+	4.35233i	1.53878	+	1.53878i
$9$		−	1.01958i		−	0.339860i
$10$	−0.412838	+	5.65406i	−0.130551	+	1.78797i
$11$		0			0
$11$		0			0
$12$	6.27711	+	6.27711i	1.81205	+	1.81205i
$13$	1.59509	+	1.59509i	0.442398	+	0.442398i	0.892817	−	0.450419i	$-0.148725\pi$
$13$	1.59509	+	1.59509i	0.442398	+	0.442398i	−0.450419	+	0.892817i	$0.648725\pi$
$14$		−	4.58388i		−	1.22509i
$15$	−0.326467	+	4.47116i	−0.0842935	+	1.15445i
$16$	−6.74958			−1.68739
$17$	−2.37874	+	2.37874i	−0.576928	+	0.576928i	−0.934056	−	0.357128i	$-0.883756\pi$
$17$	−2.37874	+	2.37874i	−0.576928	+	0.576928i	0.357128	+	0.934056i	$0.383756\pi$
$18$	1.82783	+	1.82783i	0.430824	+	0.430824i
$19$	−1.30587			−0.299586			−0.149793	−	0.988717i	$-0.547861\pi$
$19$	−1.30587			−0.299586			−0.149793	+	0.988717i	$0.547861\pi$
$20$	−6.47250	−	7.49215i	−1.44730	−	1.67530i
$21$		−	3.62488i		−	0.791014i
$22$		0			0
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	−0.955362	−	0.295439i	$-0.904534\pi$
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	0.295439	+	0.955362i	$0.404534\pi$
$24$	−12.3403			−2.51896
$25$	0.726289	−	4.94697i	0.145258	−	0.989394i
$26$	−5.71913			−1.12161
$27$	−2.80758	−	2.80758i	−0.540320	−	0.540320i
$28$	5.66074	+	5.66074i	1.06978	+	1.06978i
$29$	−2.93651			−0.545297			−0.272648	−	0.962114i	$-0.587900\pi$
$29$	−2.93651			−0.545297			−0.272648	+	0.962114i	$0.587900\pi$
$30$	−7.43033	−	8.60086i	−1.35659	−	1.57030i
$31$	−4.01029			−0.720269			−0.360134	−	0.932900i	$-0.617269\pi$
$31$	−4.01029			−0.720269			−0.360134	+	0.932900i	$0.617269\pi$
$32$	3.39552	−	3.39552i	0.600248	−	0.600248i
$33$		0			0
$34$		−	8.52886i		−	1.46269i
$35$	−0.294410	+	4.03213i	−0.0497644	+	0.681554i
$36$	−4.51446			−0.752409
$37$	−2.26906	−	2.26906i	−0.373031	−	0.373031i	0.495549	−	0.868580i	$-0.334967\pi$
$37$	−2.26906	−	2.26906i	−0.373031	−	0.373031i	−0.868580	+	0.495549i	$0.834967\pi$
$38$	2.34107	−	2.34107i	0.379771	−	0.379771i
$39$	−4.52262			−0.724199
$40$	13.7267	+	1.00227i	2.17039	+	0.158473i
$41$			1.30369i			0.203602i	0.994805	+	0.101801i	$0.0324604\pi$
$41$			1.30369i			0.203602i	−0.994805	+	0.101801i	$0.967540\pi$
$42$	6.49844	+	6.49844i	1.00273	+	1.00273i
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	0.268698	−	0.963224i	$-0.413407\pi$
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	−0.963224	+	0.268698i	$0.913407\pi$
$44$		0			0
$45$	−1.49042	−	1.72521i	−0.222178	−	0.257179i
$46$		−	11.3475i		−	1.67310i
$47$	5.46143	+	5.46143i	0.796632	+	0.796632i	0.982563	−	0.185931i	$-0.0595302\pi$
$47$	5.46143	+	5.46143i	0.796632	+	0.796632i	−0.185931	+	0.982563i	$0.559530\pi$
$48$	9.56868	−	9.56868i	1.38112	−	1.38112i
$49$			3.73106i			0.533008i
$50$	7.56654	+	10.1706i	1.07007	+	1.43834i
$51$		−	6.74453i		−	0.944422i
$52$	7.06268	−	7.06268i	0.979418	−	0.979418i
$53$	4.50356	−	4.50356i	0.618612	−	0.618612i	−0.326564	−	0.945175i	$-0.605891\pi$
$53$	4.50356	−	4.50356i	0.618612	−	0.618612i	0.945175	+	0.326564i	$0.105891\pi$
$54$	10.0665			1.36988
$55$		0			0
$56$	−11.1286			−1.48712
$57$	1.85129	−	1.85129i	0.245209	−	0.245209i
$58$	5.26438	−	5.26438i	0.691247	−	0.691247i
$59$			12.3878i			1.61275i	0.591404	+	0.806376i	$0.298574\pi$
$59$			12.3878i			1.61275i	−0.591404	+	0.806376i	$0.701426\pi$
$60$	19.7973	+	1.44552i	2.55582	+	0.186616i
$61$		−	9.31002i		−	1.19203i	−0.802975	−	0.596013i	$-0.796751\pi$
$61$		−	9.31002i		−	1.19203i	0.802975	−	0.596013i	$-0.203249\pi$
$62$	7.18936	−	7.18936i	0.913050	−	0.913050i
$63$	1.30349	+	1.30349i	0.164225	+	0.164225i
$64$		−	1.32466i		−	0.165583i
$65$	5.03072	+	0.367324i	0.623984	+	0.0455609i
$66$		0			0
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	0.540512	−	0.841336i	$-0.318231\pi$
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	−0.841336	+	0.540512i	$0.818231\pi$
$68$	10.5325	+	10.5325i	1.27725	+	1.27725i
$69$		−	8.97350i		−	1.08028i
$70$	−6.70072	−	7.75631i	−0.800889	−	0.927057i
$71$	−6.77125			−0.803599			−0.401800	−	0.915728i	$-0.631615\pi$
$71$	−6.77125			−0.803599			−0.401800	+	0.915728i	$0.631615\pi$
$72$	4.43754	−	4.43754i	0.522969	−	0.522969i
$73$	−6.67785	−	6.67785i	−0.781583	−	0.781583i	0.198515	−	0.980098i	$-0.436388\pi$
$73$	−6.67785	−	6.67785i	−0.781583	−	0.781583i	−0.980098	+	0.198515i	$0.936388\pi$
$74$	8.13562			0.945746
$75$	5.98353	+	8.04281i	0.690919	+	0.928704i
$76$			5.78207i			0.663249i
$77$		0			0
$78$	8.10784	−	8.10784i	0.918032	−	0.918032i
$79$	−1.14511			−0.128835			−0.0644177	−	0.997923i	$-0.520519\pi$
$79$	−1.14511			−0.128835			−0.0644177	+	0.997923i	$0.520519\pi$
$80$	−11.4208	+	9.86653i	−1.27689	+	1.10311i
$81$	11.0192			1.22436
$82$	−2.33716	−	2.33716i	−0.258096	−	0.258096i
$83$	−7.39974	−	7.39974i	−0.812227	−	0.812227i	0.172740	−	0.984967i	$-0.444738\pi$
$83$	−7.39974	−	7.39974i	−0.812227	−	0.812227i	−0.984967	+	0.172740i	$0.944738\pi$
$84$	−16.0501			−1.75121
$85$	−0.547785	+	7.50225i	−0.0594157	+	0.813733i
$86$	16.3293			1.76083
$87$	4.16301	−	4.16301i	0.446321	−	0.446321i
$88$		0			0
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$	5.76476	+	0.420921i	0.607659	+	0.0443689i
$91$	−4.07853			−0.427546
$92$	14.0133	+	14.0133i	1.46099	+	1.46099i
$93$	5.68526	−	5.68526i	0.589535	−	0.589535i
$94$	−19.5817			−2.01970
$95$	−2.20963	+	1.90891i	−0.226704	+	0.195850i
$96$			9.62745i			0.982597i
$97$	−0.550166	−	0.550166i	−0.0558608	−	0.0558608i	0.678625	−	0.734485i	$-0.262576\pi$
$97$	−0.550166	−	0.550166i	−0.0558608	−	0.0558608i	−0.734485	+	0.678625i	$0.762576\pi$
$98$	−6.68878	−	6.68878i	−0.675669	−	0.675669i
$99$		0			0
$100$	−21.9040	−	3.21584i	−2.19040	−	0.321584i
$101$		−	9.76766i		−	0.971919i	−0.873981	−	0.485959i	$-0.838470\pi$
$101$		−	9.76766i		−	0.971919i	0.873981	−	0.485959i	$-0.161530\pi$
$102$	12.0911	+	12.0911i	1.19720	+	1.19720i
$103$	−3.30351	+	3.30351i	−0.325504	+	0.325504i	−0.850874	−	0.525370i	$-0.823927\pi$
$103$	−3.30351	+	3.30351i	−0.325504	+	0.325504i	0.525370	+	0.850874i	$0.323927\pi$
$104$			13.8847i			1.36151i
$105$	−5.29885	−	6.13360i	−0.517115	−	0.598578i
$106$			16.1473i			1.56837i
$107$	−10.8200	+	10.8200i	−1.04601	+	1.04601i	−0.0471159	+	0.998889i	$0.515003\pi$
$107$	−10.8200	+	10.8200i	−1.04601	+	1.04601i	−0.998889	+	0.0471159i	$0.984997\pi$
$108$	−12.4313	+	12.4313i	−1.19621	+	1.19621i
$109$	−17.8837			−1.71295			−0.856476	−	0.516187i	$-0.827351\pi$
$109$	−17.8837			−1.71295			−0.856476	+	0.516187i	$0.827351\pi$
$110$		0			0
$111$	6.43355			0.610646
$112$	8.62910	−	8.62910i	0.815373	−	0.815373i
$113$	−5.28177	+	5.28177i	−0.496867	+	0.496867i	−0.910461	−	0.413594i	$-0.864273\pi$
$113$	−5.28177	+	5.28177i	−0.496867	+	0.496867i	0.413594	+	0.910461i	$0.364273\pi$
$114$			6.63772i			0.621679i
$115$	−0.728821	+	9.98165i	−0.0679629	+	0.930793i
$116$			13.0022i			1.20722i
$117$	1.62632	−	1.62632i	0.150353	−	0.150353i
$118$	−22.2080	−	22.2080i	−2.04441	−	2.04441i
$119$		−	6.08226i		−	0.557560i
$120$	−20.8809	+	18.0391i	−1.90615	+	1.64674i
$121$		0			0
$122$	16.6904	+	16.6904i	1.51107	+	1.51107i
$123$	−1.84820	−	1.84820i	−0.166646	−	0.166646i
$124$			17.7566i			1.59459i
$125$	−6.00253	−	9.43237i	−0.536883	−	0.843657i
$126$	−4.67363			−0.416360
$127$	0.145798	−	0.145798i	0.0129375	−	0.0129375i	−0.700608	−	0.713546i	$-0.747088\pi$
$127$	0.145798	−	0.145798i	0.0129375	−	0.0129375i	0.713546	+	0.700608i	$0.247088\pi$
$128$	9.16580	+	9.16580i	0.810150	+	0.810150i
$129$	12.9130			1.13693
$130$	−9.67724	+	8.36022i	−0.848750	+	0.733240i
$131$		−	0.551708i		−	0.0482029i	−0.999710	−	0.0241015i	$-0.992328\pi$
$131$		−	0.551708i		−	0.0482029i	0.999710	−	0.0241015i	$-0.00767248\pi$
$132$		0			0
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$	8.82869			0.762682
$135$	−8.85479	−	0.646543i	−0.762099	−	0.0556455i
$136$	−20.7061			−1.77553
$137$	−10.9435	−	10.9435i	−0.934965	−	0.934965i	0.0630456	−	0.998011i	$-0.479919\pi$
$137$	−10.9435	−	10.9435i	−0.934965	−	0.934965i	−0.998011	+	0.0630456i	$0.979919\pi$
$138$	16.0871	+	16.0871i	1.36942	+	1.36942i
$139$	1.42272			0.120674			0.0603369	−	0.998178i	$-0.480782\pi$
$139$	1.42272			0.120674			0.0603369	+	0.998178i	$0.480782\pi$
$140$	17.8533	+	1.30358i	1.50888	+	0.110173i
$141$	−15.4850			−1.30407
$142$	12.1390	−	12.1390i	1.01868	−	1.01868i
$143$		0			0
$144$			6.88173i			0.573477i
$145$	−4.96882	+	4.29259i	−0.412638	+	0.356480i
$146$	23.9432			1.98155
$147$	−5.28941	−	5.28941i	−0.436263	−	0.436263i
$148$	−10.0469	+	10.0469i	−0.825846	+	0.825846i
$149$	23.8050			1.95018			0.975091	−	0.221805i	$-0.0711950\pi$
$149$	23.8050			1.95018			0.975091	+	0.221805i	$0.0711950\pi$
$150$	−25.1455	−	3.69173i	−2.05312	−	0.301429i
$151$		−	14.3861i		−	1.17072i	−0.810773	−	0.585361i	$-0.800953\pi$
$151$		−	14.3861i		−	1.17072i	0.810773	−	0.585361i	$-0.199047\pi$
$152$	−5.68356	−	5.68356i	−0.460998	−	0.460998i
$153$	2.42531	+	2.42531i	0.196075	+	0.196075i
$154$		0			0
$155$	−6.78574	+	5.86223i	−0.545044	+	0.470866i
$156$			20.0251i			1.60329i
$157$	−9.54161	−	9.54161i	−0.761503	−	0.761503i	0.215091	−	0.976594i	$-0.430995\pi$
$157$	−9.54161	−	9.54161i	−0.761503	−	0.761503i	−0.976594	+	0.215091i	$0.930995\pi$
$158$	2.05288	−	2.05288i	0.163318	−	0.163318i
$159$			12.7691i			1.01266i
$160$	0.781934	−	10.7091i	0.0618173	−	0.846626i
$161$		−	8.09236i		−	0.637768i
$162$	−19.7544	+	19.7544i	−1.55206	+	1.55206i
$163$	0.758875	−	0.758875i	0.0594397	−	0.0594397i	−0.676762	−	0.736202i	$-0.736617\pi$
$163$	0.758875	−	0.758875i	0.0594397	−	0.0594397i	0.736202	+	0.676762i	$0.236617\pi$
$164$	5.77242			0.450750
$165$		0			0
$166$	26.5315			2.05924
$167$	−1.33773	+	1.33773i	−0.103516	+	0.103516i	−0.756968	−	0.653452i	$-0.773320\pi$
$167$	−1.33773	+	1.33773i	−0.103516	+	0.103516i	0.653452	+	0.756968i	$0.273320\pi$
$168$	15.7767	−	15.7767i	1.21720	−	1.21720i
$169$		−	7.91138i		−	0.608568i
$170$	−12.4675	−	14.4315i	−0.956212	−	1.10685i
$171$			1.33143i			0.101817i
$172$	−20.1654	+	20.1654i	−1.53760	+	1.53760i
$173$	13.3978	+	13.3978i	1.01861	+	1.01861i	0.999823	+	0.0187899i	$0.00598137\pi$
$173$	13.3978	+	13.3978i	1.01861	+	1.01861i	0.0187899	+	0.999823i	$0.494019\pi$
$174$			14.9263i			1.13156i
$175$	5.39599	+	7.25306i	0.407898	+	0.548280i
$176$		0			0
$177$	−17.5618	−	17.5618i	−1.32002	−	1.32002i
$178$	−6.91533	−	6.91533i	−0.518326	−	0.518326i
$179$			16.3829i			1.22451i	0.790659	+	0.612256i	$0.209738\pi$
$179$			16.3829i			1.22451i	−0.790659	+	0.612256i	$0.790262\pi$
$180$	−7.63883	+	6.59923i	−0.569365	+	0.491877i
$181$	14.8635			1.10479			0.552396	−	0.833582i	$-0.313714\pi$
$181$	14.8635			1.10479			0.552396	+	0.833582i	$0.313714\pi$
$182$	7.31171	−	7.31171i	0.541980	−	0.541980i
$183$	13.1985	+	13.1985i	0.975664	+	0.975664i
$184$	−27.5492			−2.03095
$185$	−7.15634	−	0.522528i	−0.526144	−	0.0384170i
$186$			20.3843i			1.49465i
$187$		0			0
$188$	24.1819	−	24.1819i	1.76365	−	1.76365i
$189$	7.17879			0.522180
$190$	0.539111	−	7.38345i	0.0391112	−	0.535651i
$191$	−1.90958			−0.138172			−0.0690861	−	0.997611i	$-0.522008\pi$
$191$	−1.90958			−0.138172			−0.0690861	+	0.997611i	$0.522008\pi$
$192$	1.87794	+	1.87794i	0.135528	+	0.135528i
$193$	8.04894	+	8.04894i	0.579376	+	0.579376i	0.934731	−	0.355355i	$-0.115640\pi$
$193$	8.04894	+	8.04894i	0.579376	+	0.579376i	−0.355355	+	0.934731i	$0.615640\pi$
$194$	1.97260			0.141624
$195$	−7.65265	+	6.61116i	−0.548018	+	0.473435i
$196$	16.5202			1.18002
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	−0.999872	−	0.0160086i	$-0.994904\pi$
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	0.0160086	+	0.999872i	$0.494904\pi$
$198$		0			0
$199$			22.3508i			1.58441i	0.610258	+	0.792203i	$0.291066\pi$
$199$			22.3508i			1.58441i	−0.610258	+	0.792203i	$0.708934\pi$
$200$	24.6919	−	18.3698i	1.74598	−	1.29894i
$201$	6.98162			0.492446
$202$	17.5108	+	17.5108i	1.23205	+	1.23205i
$203$	3.75423	−	3.75423i	0.263495	−	0.263495i
$204$	−29.8632			−2.09084
$205$	1.90573	+	2.20594i	0.133102	+	0.154070i
$206$		−	11.8446i		−	0.825252i
$207$	3.22684	+	3.22684i	0.224281	+	0.224281i
$208$	−10.7662	−	10.7662i	−0.746501	−	0.746501i
$209$		0			0
$210$	20.4953	+	1.49649i	1.41431	+	0.103267i
$211$			0.376542i			0.0259222i	0.999916	+	0.0129611i	$0.00412577\pi$
$211$			0.376542i			0.0259222i	−0.999916	+	0.0129611i	$0.995874\pi$
$212$	−19.9407	−	19.9407i	−1.36953	−	1.36953i
$213$	9.59940	−	9.59940i	0.657740	−	0.657740i
$214$		−	38.7946i		−	2.65194i
$215$	−14.3638	−	1.04879i	−0.979600	−	0.0715266i
$216$		−	24.4391i		−	1.66287i
$217$	5.12701	−	5.12701i	0.348044	−	0.348044i
$218$	32.0607	−	32.0607i	2.17143	−	2.17143i
$219$	18.9340			1.27944
$220$		0			0
$221$	−7.58859			−0.510464
$222$	−11.5336	+	11.5336i	−0.774086	+	0.774086i
$223$	−5.38065	+	5.38065i	−0.360315	+	0.360315i	−0.863929	−	0.503614i	$-0.832003\pi$
$223$	−5.38065	+	5.38065i	−0.360315	+	0.360315i	0.503614	+	0.863929i	$0.332003\pi$
$224$			8.68210i			0.580097i
$225$	−5.04382	−	0.740509i	−0.336255	−	0.0493673i
$226$		−	18.9376i		−	1.25971i
$227$	−5.80016	+	5.80016i	−0.384970	+	0.384970i	−0.872889	−	0.487919i	$-0.837756\pi$
$227$	−5.80016	+	5.80016i	−0.384970	+	0.384970i	0.487919	+	0.872889i	$0.337756\pi$
$228$	−8.19707	−	8.19707i	−0.542864	−	0.542864i
$229$			7.58916i			0.501506i	0.968051	+	0.250753i	$0.0806781\pi$
$229$			7.58916i			0.501506i	−0.968051	+	0.250753i	$0.919322\pi$
$230$	−16.5878	−	19.2010i	−1.09377	−	1.26608i
$231$		0			0
$232$	−12.7807	−	12.7807i	−0.839092	−	0.839092i
$233$	18.5383	+	18.5383i	1.21449	+	1.21449i	0.969535	+	0.244952i	$0.0787722\pi$
$233$	18.5383	+	18.5383i	1.21449	+	1.21449i	0.244952	+	0.969535i	$0.421228\pi$
$234$			5.83110i			0.381191i
$235$	17.2247	+	1.25768i	1.12362	+	0.0820421i
$236$	54.8502			3.57044
$237$	1.62339	−	1.62339i	0.105451	−	0.105451i
$238$	10.9038	+	10.9038i	0.706791	+	0.706791i
$239$	−2.27601			−0.147223			−0.0736115	−	0.997287i	$-0.523452\pi$
$239$	−2.27601			−0.147223			−0.0736115	+	0.997287i	$0.523452\pi$
$240$	2.20352	−	30.1785i	0.142236	−	1.94801i
$241$			6.29531i			0.405517i	0.979229	+	0.202758i	$0.0649906\pi$
$241$			6.29531i			0.405517i	−0.979229	+	0.202758i	$0.935009\pi$
$242$		0			0
$243$	−7.19883	+	7.19883i	−0.461805	+	0.461805i
$244$	−41.2226			−2.63901
$245$	5.45405	+	6.31326i	0.348447	+	0.403339i
$246$	6.62664			0.422499
$247$	−2.08297	−	2.08297i	−0.132536	−	0.132536i
$248$	−17.4541	−	17.4541i	−1.10834	−	1.10834i
$249$	20.9808			1.32960
$250$	27.6706	+	6.14878i	1.75004	+	0.388883i
$251$	−26.5949			−1.67865			−0.839326	−	0.543628i	$-0.817050\pi$
$251$	−26.5949			−1.67865			−0.839326	+	0.543628i	$0.817050\pi$
$252$	5.77157	−	5.77157i	0.363575	−	0.363575i
$253$		0			0
$254$			0.522752i			0.0328004i
$255$	−9.85914	−	11.4123i	−0.617403	−	0.714666i
$256$	−30.2143			−1.88839
$257$	−13.9825	−	13.9825i	−0.872202	−	0.872202i	0.120510	−	0.992712i	$-0.461547\pi$
$257$	−13.9825	−	13.9825i	−0.872202	−	0.872202i	−0.992712	+	0.120510i	$0.961547\pi$
$258$	−23.1496	+	23.1496i	−1.44123	+	1.44123i
$259$	5.80182			0.360507
$260$	1.62642	−	22.2749i	0.100867	−	1.38143i
$261$			2.99401i			0.185324i
$262$	0.989064	+	0.989064i	0.0611046	+	0.0611046i
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	0.865609	−	0.500721i	$-0.166932\pi$
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	−0.500721	+	0.865609i	$0.666932\pi$
$264$		0			0
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$			5.98594i			0.367021i
$267$	−5.46857	−	5.46857i	−0.334671	−	0.334671i
$268$	−10.9027	+	10.9027i	−0.665991	+	0.665991i
$269$			9.71067i			0.592070i	0.955177	+	0.296035i	$0.0956645\pi$
$269$			9.71067i			0.592070i	−0.955177	+	0.296035i	$0.904336\pi$
$270$	17.0333	−	14.7152i	1.03662	−	0.895537i
$271$		−	3.05146i		−	0.185363i	−0.995696	−	0.0926816i	$-0.970456\pi$
$271$		−	3.05146i		−	0.185363i	0.995696	−	0.0926816i	$-0.0295439\pi$
$272$	16.0555	−	16.0555i	0.973506	−	0.973506i
$273$	5.78201	−	5.78201i	0.349943	−	0.349943i
$274$	39.2374			2.37042
$275$		0			0
$276$	−39.7326			−2.39162
$277$	−1.68302	+	1.68302i	−0.101123	+	0.101123i	−0.755858	−	0.654735i	$-0.772780\pi$
$277$	−1.68302	+	1.68302i	−0.101123	+	0.101123i	0.654735	+	0.755858i	$0.272780\pi$
$278$	−2.55056	+	2.55056i	−0.152972	+	0.152972i
$279$			4.08880i			0.244790i
$280$	−18.8305	+	16.2678i	−1.12534	+	0.972185i
$281$			28.2321i			1.68418i	0.539333	+	0.842092i	$0.318676\pi$
$281$			28.2321i			1.68418i	−0.539333	+	0.842092i	$0.681324\pi$
$282$	27.7605	−	27.7605i	1.65311	−	1.65311i
$283$	12.0303	+	12.0303i	0.715128	+	0.715128i	0.967603	−	0.252475i	$-0.0812446\pi$
$283$	12.0303	+	12.0303i	0.715128	+	0.715128i	−0.252475	+	0.967603i	$0.581245\pi$
$284$			29.9815i			1.77907i
$285$	0.426322	−	5.83874i	0.0252532	−	0.345857i
$286$		0			0
$287$	−1.66672	−	1.66672i	−0.0983831	−	0.0983831i
$288$	−3.46200	−	3.46200i	−0.204000	−	0.204000i
$289$			5.68324i			0.334308i
$290$	1.21230	−	16.6032i	0.0711889	−	0.974975i
$291$	1.55991			0.0914434
$292$	−29.5679	+	29.5679i	−1.73033	+	1.73033i
$293$	−7.55536	−	7.55536i	−0.441389	−	0.441389i	0.451090	−	0.892479i	$-0.351035\pi$
$293$	−7.55536	−	7.55536i	−0.441389	−	0.441389i	−0.892479	+	0.451090i	$0.851035\pi$
$294$	18.9650			1.10606
$295$	18.1084	+	20.9611i	1.05431	+	1.22041i
$296$		−	19.7514i		−	1.14803i
$297$		0			0
$298$	−42.6760	+	42.6760i	−2.47215	+	2.47215i
$299$	−10.0965			−0.583897
$300$	35.6117	−	26.4937i	2.05604	−	1.52961i
$301$	11.6450			0.671210
$302$	25.7904	+	25.7904i	1.48407	+	1.48407i
$303$	13.8473	+	13.8473i	0.795508	+	0.795508i
$304$	8.81405			0.505520
$305$	−13.6094	−	15.7533i	−0.779270	−	0.902033i
$306$	−8.69585			−0.497108
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.392474	−	0.919763i	$-0.371619\pi$
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.919763	−	0.392474i	$-0.128381\pi$
$308$		0			0
$309$		−	9.36657i		−	0.532846i
$310$	1.65560	−	22.6744i	0.0940316	−	1.28782i
$311$	13.8886			0.787553			0.393776	−	0.919206i	$-0.371168\pi$
$311$	13.8886			0.787553			0.393776	+	0.919206i	$0.371168\pi$
$312$	−19.6839	−	19.6839i	−1.11438	−	1.11438i
$313$	−12.2952	+	12.2952i	−0.694965	+	0.694965i	−0.963320	−	0.268355i	$-0.913520\pi$
$313$	−12.2952	+	12.2952i	−0.694965	+	0.694965i	0.268355	+	0.963320i	$0.413520\pi$
$314$	34.2111			1.93064
$315$	4.11107	+	0.300174i	0.231632	+	0.0169129i
$316$			5.07030i			0.285227i
$317$	11.4247	+	11.4247i	0.641677	+	0.641677i	0.950968	−	0.309291i	$-0.100092\pi$
$317$	11.4247	+	11.4247i	0.641677	+	0.641677i	−0.309291	+	0.950968i	$0.600092\pi$
$318$	−22.8916	−	22.8916i	−1.28370	−	1.28370i
$319$		0			0
$320$	−1.93639	−	2.24144i	−0.108248	−	0.125300i
$321$		−	30.6783i		−	1.71229i
$322$	14.5074	+	14.5074i	0.808467	+	0.808467i
$323$	3.10631	−	3.10631i	0.172840	−	0.172840i
$324$		−	48.7904i		−	2.71058i
$325$	9.04935	−	6.73236i	0.501968	−	0.373444i
$326$			2.72092i			0.150698i
$327$	25.3532	−	25.3532i	1.40204	−	1.40204i
$328$	−5.67407	+	5.67407i	−0.313298	+	0.313298i
$329$	−13.9645			−0.769887
$330$		0			0
$331$	14.6837			0.807090			0.403545	−	0.914960i	$-0.367778\pi$
$331$	14.6837			0.807090			0.403545	+	0.914960i	$0.367778\pi$
$332$	−32.7643	+	32.7643i	−1.79818	+	1.79818i
$333$	−2.31348	+	2.31348i	−0.126778	+	0.126778i
$334$		−	4.79637i		−	0.262446i
$335$	−7.76598	−	0.567042i	−0.424301	−	0.0309808i
$336$			24.4664i			1.33475i
$337$	−9.53964	+	9.53964i	−0.519658	+	0.519658i	−0.917468	−	0.397810i	$-0.869770\pi$
$337$	−9.53964	+	9.53964i	−0.519658	+	0.519658i	0.397810	+	0.917468i	$0.369770\pi$
$338$	14.1830	+	14.1830i	0.771452	+	0.771452i
$339$		−	14.9756i		−	0.813364i
$340$	33.2182	+	2.42547i	1.80151	+	0.131539i
$341$		0			0
$342$	−2.38690	−	2.38690i	−0.129069	−	0.129069i
$343$	−13.7193	−	13.7193i	−0.740771	−	0.740771i
$344$		−	39.6437i		−	2.13745i
$345$	−13.1175	−	15.1839i	−0.706220	−	0.817474i
$346$	−48.0372			−2.58249
$347$	−8.65203	+	8.65203i	−0.464465	+	0.464465i	−0.900116	−	0.435650i	$-0.856518\pi$
$347$	−8.65203	+	8.65203i	−0.464465	+	0.464465i	0.435650	+	0.900116i	$0.356518\pi$
$348$	−18.4328	−	18.4328i	−0.988103	−	0.988103i
$349$	−20.3713			−1.09045			−0.545225	−	0.838290i	$-0.683556\pi$
$349$	−20.3713			−1.09045			−0.545225	+	0.838290i	$0.683556\pi$
$350$	−22.6763	−	3.32923i	−1.21210	−	0.177955i
$351$		−	8.95670i		−	0.478073i
$352$		0			0
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	−0.237495	−	0.971389i	$-0.576326\pi$
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	0.971389	+	0.237495i	$0.0763264\pi$
$354$	62.9671			3.34666
$355$	−11.4575	+	9.89820i	−0.608102	+	0.525342i
$356$	17.0798			0.905228
$357$	8.62264	+	8.62264i	0.456358	+	0.456358i
$358$	−29.3701	−	29.3701i	−1.55226	−	1.55226i
$359$	16.5198			0.871883			0.435941	−	0.899975i	$-0.356415\pi$
$359$	16.5198			0.871883			0.435941	+	0.899975i	$0.356415\pi$
$360$	1.02190	−	13.9955i	0.0538587	−	0.737627i
$361$	−17.2947			−0.910248
$362$	−26.6462	+	26.6462i	−1.40049	+	1.40049i
$363$		0			0
$364$			18.0588i			0.946537i
$365$	−21.0611	−	1.53780i	−1.10239	−	0.0804923i
$366$	−47.3228			−2.47360
$367$	4.55474	+	4.55474i	0.237755	+	0.237755i	0.815920	−	0.578165i	$-0.196231\pi$
$367$	4.55474	+	4.55474i	0.237755	+	0.237755i	−0.578165	+	0.815920i	$0.696231\pi$
$368$	21.3616	−	21.3616i	1.11355	−	1.11355i
$369$	1.32921			0.0691959
$370$	13.7661	−	11.8926i	0.715667	−	0.618268i
$371$			11.5153i			0.597844i
$372$	−25.1730	−	25.1730i	−1.30516	−	1.30516i
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	0.410021	−	0.912076i	$-0.365522\pi$
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	−0.912076	+	0.410021i	$0.865522\pi$
$374$		0			0
$375$	21.8816	+	4.86238i	1.12996	+	0.251092i
$376$			47.5399i			2.45168i
$377$	−4.68400	−	4.68400i	−0.241238	−	0.241238i
$378$	−12.8696	+	12.8696i	−0.661943	+	0.661943i
$379$		−	21.5011i		−	1.10444i	−0.833700	−	0.552218i	$-0.813782\pi$
$379$		−	21.5011i		−	1.10444i	0.833700	−	0.552218i	$-0.186218\pi$
$380$	8.45222	+	9.78374i	0.433590	+	0.501895i
$381$			0.413386i			0.0211784i
$382$	3.42336	−	3.42336i	0.175154	−	0.175154i
$383$	0.214560	−	0.214560i	0.0109635	−	0.0109635i	−0.701604	−	0.712567i	$-0.747532\pi$
$383$	0.214560	−	0.214560i	0.0109635	−	0.0109635i	0.712567	+	0.701604i	$0.247532\pi$
$384$	−25.9882			−1.32620
$385$		0			0
$386$	−28.8592			−1.46889
$387$	−4.64348	+	4.64348i	−0.236041	+	0.236041i
$388$	−2.43600	+	2.43600i	−0.123669	+	0.123669i
$389$			3.60132i			0.182594i	0.995824	+	0.0912971i	$0.0291013\pi$
$389$			3.60132i			0.182594i	−0.995824	+	0.0912971i	$0.970899\pi$
$390$	1.86711	−	25.5712i	0.0945447	−	1.29485i
$391$		−	15.0568i		−	0.761455i
$392$	−16.2388	+	16.2388i	−0.820183	+	0.820183i
$393$	0.782140	+	0.782140i	0.0394537	+	0.0394537i
$394$		−	49.5123i		−	2.49439i
$395$	−1.93763	+	1.67393i	−0.0974927	+	0.0842244i
$396$		0			0
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$	−40.0690	−	40.0690i	−2.00848	−	2.00848i
$399$			4.73361i			0.236977i
$400$	−4.90215	+	33.3900i	−0.245107	+	1.66950i
$401$	−9.99733			−0.499243			−0.249621	−	0.968344i	$-0.580306\pi$
$401$	−9.99733			−0.499243			−0.249621	+	0.968344i	$0.580306\pi$
$402$	−12.5162	+	12.5162i	−0.624250	+	0.624250i
$403$	−6.39677	−	6.39677i	−0.318646	−	0.318646i
$404$	−43.2489			−2.15171
$405$	18.6454	−	16.1078i	0.926497	−	0.800405i
$406$			13.4606i			0.668040i
$407$		0			0
$408$	29.3544	−	29.3544i	1.45326	−	1.45326i
$409$	30.3912			1.50275			0.751374	−	0.659877i	$-0.229391\pi$
$409$	30.3912			1.50275			0.751374	+	0.659877i	$0.229391\pi$
$410$	−7.37112	−	0.538211i	−0.364034	−	0.0265803i
$411$	31.0285			1.53052
$412$	14.6272	+	14.6272i	0.720629	+	0.720629i
$413$	−15.8373	−	15.8373i	−0.779304	−	0.779304i
$414$	−11.5697			−0.568620
$415$	−23.3379	−	1.70404i	−1.14561	−	0.0836482i
$416$	10.8323			0.531098
$417$	−2.01695	+	2.01695i	−0.0987706	+	0.0987706i
$418$		0			0
$419$		−	7.48185i		−	0.365512i	−0.983158	−	0.182756i	$-0.941498\pi$
$419$		−	7.48185i		−	0.365512i	0.983158	−	0.182756i	$-0.0585019\pi$
$420$	−27.1582	+	23.4621i	−1.32518	+	1.14483i
$421$	20.4230			0.995356			0.497678	−	0.867362i	$-0.334186\pi$
$421$	20.4230			0.995356			0.497678	+	0.867362i	$0.334186\pi$
$422$	−0.675039	−	0.675039i	−0.0328604	−	0.0328604i
$423$	5.56836	−	5.56836i	0.270743	−	0.270743i
$424$	39.2020			1.90382
$425$	10.0399	+	13.4952i	0.487006	+	0.654612i
$426$			34.4183i			1.66757i
$427$	11.9025	+	11.9025i	0.576004	+	0.576004i
$428$	47.9083	+	47.9083i	2.31573	+	2.31573i
$429$		0			0
$430$	27.6305	−	23.8702i	1.33246	−	1.15112i
$431$			33.6660i			1.62163i	0.585301	+	0.810816i	$0.300976\pi$
$431$			33.6660i			1.62163i	−0.585301	+	0.810816i	$0.699024\pi$
$432$	18.9500	+	18.9500i	0.911733	+	0.911733i
$433$	−8.20184	+	8.20184i	−0.394155	+	0.394155i	−0.876166	−	0.482010i	$-0.839907\pi$
$433$	−8.20184	+	8.20184i	−0.394155	+	0.394155i	0.482010	+	0.876166i	$0.339907\pi$
$434$			18.3827i			0.882397i
$435$	0.958675	−	13.1296i	0.0459650	−	0.629518i
$436$			79.1850i			3.79227i
$437$	4.13290	−	4.13290i	0.197704	−	0.197704i
$438$	−33.9435	+	33.9435i	−1.62188	+	1.62188i
$439$	10.7242			0.511837			0.255918	−	0.966698i	$-0.417622\pi$
$439$	10.7242			0.511837			0.255918	+	0.966698i	$0.417622\pi$
$440$		0			0
$441$	3.80411			0.181148
$442$	13.6043	−	13.6043i	0.647091	−	0.647091i
$443$	28.5202	−	28.5202i	1.35504	−	1.35504i	0.475111	−	0.879926i	$-0.342408\pi$
$443$	28.5202	−	28.5202i	1.35504	−	1.35504i	0.879926	−	0.475111i	$-0.157592\pi$
$444$		−	28.4863i		−	1.35190i
$445$	5.63879	+	6.52709i	0.267304	+	0.309414i
$446$		−	19.2921i		−	0.913508i
$447$	−33.7476	+	33.7476i	−1.59621	+	1.59621i
$448$	1.69353	+	1.69353i	0.0800120	+	0.0800120i
$449$			3.64160i			0.171858i	0.996301	+	0.0859290i	$0.0273858\pi$
$449$			3.64160i			0.171858i	−0.996301	+	0.0859290i	$0.972614\pi$
$450$	10.3698	−	7.71468i	0.488835	−	0.363674i
$451$		0			0
$452$	23.3865	+	23.3865i	1.10001	+	1.10001i
$453$	20.3947	+	20.3947i	0.958227	+	0.958227i
$454$		−	20.7962i		−	0.976016i
$455$	−6.90121	+	5.96199i	−0.323534	+	0.279502i
$456$	16.1148			0.754646
$457$	12.7935	−	12.7935i	0.598453	−	0.598453i	−0.341448	−	0.939901i	$-0.610917\pi$
$457$	12.7935	−	12.7935i	0.598453	−	0.598453i	0.939901	+	0.341448i	$0.110917\pi$
$458$	−13.6053	−	13.6053i	−0.635735	−	0.635735i
$459$	13.3570			0.623451
$460$	44.1964	+	3.22705i	2.06067	+	0.150462i
$461$			35.5884i			1.65751i	0.559608	+	0.828757i	$0.310952\pi$
$461$			35.5884i			1.65751i	−0.559608	+	0.828757i	$0.689048\pi$
$462$		0			0
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	−0.803266	−	0.595620i	$-0.796907\pi$
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	0.595620	+	0.803266i	$0.296907\pi$
$464$	19.8202			0.920131
$465$	1.30923	−	17.9307i	0.0607140	−	0.831514i
$466$	−66.4685			−3.07909
$467$	−6.11843	−	6.11843i	−0.283127	−	0.283127i	0.551228	−	0.834355i	$-0.314160\pi$
$467$	−6.11843	−	6.11843i	−0.283127	−	0.283127i	−0.834355	+	0.551228i	$0.814160\pi$
$468$	−7.20096	−	7.20096i	−0.332865	−	0.332865i
$469$	6.29607			0.290726
$470$	−33.1339	+	28.6246i	−1.52835	+	1.32035i
$471$	27.0537			1.24657
$472$	−53.9157	+	53.9157i	−2.48167	+	2.48167i
$473$		0			0
$474$			5.82062i			0.267350i
$475$	−0.948437	+	6.46008i	−0.0435173	+	0.296409i
$476$	−26.9308			−1.23437
$477$	−4.59173	−	4.59173i	−0.210241	−	0.210241i
$478$	4.08028	−	4.08028i	0.186628	−	0.186628i
$479$	−15.3836			−0.702892			−0.351446	−	0.936208i	$-0.614310\pi$
$479$	−15.3836			−0.702892			−0.351446	+	0.936208i	$0.614310\pi$
$480$	14.0734	+	16.2904i	0.642360	+	0.743554i
$481$		−	7.23870i		−	0.330056i
$482$	−11.2858	−	11.2858i	−0.514054	−	0.514054i
$483$	11.4723	+	11.4723i	0.522008	+	0.522008i
$484$		0			0
$485$	−1.73516	−	0.126694i	−0.0787894	−	0.00575290i
$486$		−	25.8111i		−	1.17082i
$487$	4.20472	+	4.20472i	0.190534	+	0.190534i	0.795927	−	0.605393i	$-0.206984\pi$
$487$	4.20472	+	4.20472i	0.190534	+	0.190534i	−0.605393	+	0.795927i	$0.706984\pi$
$488$	40.5203	−	40.5203i	1.83427	−	1.83427i
$489$			2.15167i			0.0973019i
$490$	−21.0956	−	1.54032i	−0.953003	−	0.0695846i
$491$		−	40.9507i		−	1.84808i	−0.382298	−	0.924039i	$-0.624867\pi$
$491$		−	40.9507i		−	1.84808i	0.382298	−	0.924039i	$-0.375133\pi$
$492$	−8.18338	+	8.18338i	−0.368935	+	0.368935i
$493$	6.98519	−	6.98519i	0.314597	−	0.314597i
$494$	7.46842			0.336020
$495$		0			0
$496$	27.0678			1.21538
$497$	8.65680	−	8.65680i	0.388311	−	0.388311i
$498$	−37.6129	+	37.6129i	−1.68547	+	1.68547i
$499$			23.1868i			1.03798i	0.854779	+	0.518992i	$0.173692\pi$
$499$			23.1868i			1.03798i	−0.854779	+	0.518992i	$0.826308\pi$
$500$	−41.7643	+	26.5778i	−1.86776	+	1.18860i
$501$		−	3.79291i		−	0.169455i
$502$	47.6774	−	47.6774i	2.12795	−	2.12795i
$503$	−2.36415	−	2.36415i	−0.105412	−	0.105412i	0.652434	−	0.757846i	$-0.273748\pi$
$503$	−2.36415	−	2.36415i	−0.105412	−	0.105412i	−0.757846	+	0.652434i	$0.773748\pi$
$504$			11.3465i			0.505412i
$505$	−14.2784	−	16.5277i	−0.635379	−	0.735473i
$506$		0			0
$507$	11.2157	+	11.2157i	0.498108	+	0.498108i
$508$	−0.645558	−	0.645558i	−0.0286420	−	0.0286420i
$509$			22.1462i			0.981612i	0.871269	+	0.490806i	$0.163298\pi$
$509$			22.1462i			0.981612i	−0.871269	+	0.490806i	$0.836702\pi$
$510$	38.1340	+	2.78439i	1.68860	+	0.123295i
$511$	17.0748			0.755344
$512$	35.8345	−	35.8345i	1.58368	−	1.58368i
$513$	3.66633	+	3.66633i	0.161872	+	0.161872i
$514$	50.1336			2.21130
$515$	−0.760746	+	10.4189i	−0.0335225	+	0.459110i
$516$		−	57.1759i		−	2.51703i
$517$		0			0
$518$	−10.4011	+	10.4011i	−0.456998	+	0.456998i
$519$	−37.9872			−1.66745
$520$	20.2967	+	23.4941i	0.890067	+	1.03028i
$521$	−10.6262			−0.465543			−0.232772	−	0.972531i	$-0.574779\pi$
$521$	−10.6262			−0.465543			−0.232772	+	0.972531i	$0.574779\pi$
$522$	−5.36745	−	5.36745i	−0.234927	−	0.234927i
$523$	30.5658	+	30.5658i	1.33655	+	1.33655i	0.899380	+	0.437167i	$0.144018\pi$
$523$	30.5658	+	30.5658i	1.33655	+	1.33655i	0.437167	+	0.899380i	$0.355982\pi$
$524$	−2.44283			−0.106716
$525$	−17.9322	−	2.63271i	−0.782625	−	0.114901i
$526$	−21.2169			−0.925101
$527$	9.53941	−	9.53941i	0.415543	−	0.415543i
$528$		0			0
$529$			2.96712i			0.129005i
$530$	23.6042	+	27.3226i	1.02530	+	1.18682i
$531$	12.6303			0.548109
$532$	−7.39217	−	7.39217i	−0.320491	−	0.320491i
$533$	−2.07950	+	2.07950i	−0.0900729	+	0.0900729i
$534$	19.6073			0.848492
$535$	−2.49167	+	34.1249i	−0.107724	+	1.47535i
$536$		−	21.4340i		−	0.925807i
$537$	−23.2255	−	23.2255i	−1.00225	−	1.00225i
$538$	−17.4086	−	17.4086i	−0.750538	−	0.750538i
$539$		0			0
$540$	−2.86274	+	39.2069i	−0.123193	+	1.68720i
$541$			21.1112i			0.907643i	0.891093	+	0.453821i	$0.149940\pi$
$541$			21.1112i			0.907643i	−0.891093	+	0.453821i	$0.850060\pi$
$542$	5.47045	+	5.47045i	0.234976	+	0.234976i
$543$	−21.0715	+	21.0715i	−0.904264	+	0.904264i
$544$			16.1541i			0.692600i
$545$	−30.2608	+	26.1424i	−1.29623	+	1.11982i
$546$			20.7312i			0.887212i
$547$	0.985647	−	0.985647i	0.0421432	−	0.0421432i	−0.685721	−	0.727864i	$-0.740513\pi$
$547$	0.985647	−	0.985647i	0.0421432	−	0.0421432i	0.727864	+	0.685721i	$0.240513\pi$
$548$	−48.4552	+	48.4552i	−2.06990	+	2.06990i
$549$	−9.49230			−0.405121
$550$		0			0
$551$	3.83469			0.163363
$552$	39.0556	−	39.0556i	1.66232	−	1.66232i
$553$	1.46399	−	1.46399i	0.0622551	−	0.0622551i
$554$		−	6.03440i		−	0.256377i
$555$	10.8861	−	9.40455i	0.462089	−	0.399201i
$556$		−	6.29949i		−	0.267158i
$557$	−2.70987	+	2.70987i	−0.114821	+	0.114821i	−0.762183	−	0.647362i	$-0.775872\pi$
$557$	−2.70987	+	2.70987i	−0.114821	+	0.114821i	0.647362	+	0.762183i	$0.275872\pi$
$558$	−7.33012	−	7.33012i	−0.310309	−	0.310309i
$559$		−	14.5291i		−	0.614514i
$560$	1.98715	−	27.2152i	0.0839722	−	1.15005i
$561$		0			0
$562$	−50.6125	−	50.6125i	−2.13496	−	2.13496i
$563$	1.72685	+	1.72685i	0.0727781	+	0.0727781i	0.742559	−	0.669781i	$-0.233612\pi$
$563$	1.72685	+	1.72685i	0.0727781	+	0.0727781i	−0.669781	+	0.742559i	$0.733612\pi$
$564$			68.5640i			2.88707i
$565$	−1.21631	+	16.6581i	−0.0511705	+	0.700811i
$566$	−43.1342			−1.81307
$567$	−14.0876	+	14.0876i	−0.591626	+	0.591626i
$568$	−29.4707	−	29.4707i	−1.23656	−	1.23656i
$569$	−6.44490			−0.270184			−0.135092	−	0.990833i	$-0.543133\pi$
$569$	−6.44490			−0.270184			−0.135092	+	0.990833i	$0.543133\pi$
$570$	9.70301	+	11.2316i	0.406414	+	0.470439i
$571$			13.2864i			0.556019i	0.960578	+	0.278009i	$0.0896747\pi$
$571$			13.2864i			0.556019i	−0.960578	+	0.278009i	$0.910325\pi$
$572$		0			0
$573$	2.70715	−	2.70715i	0.113093	−	0.113093i
$574$	5.97595			0.249431
$575$	13.3579	+	17.9552i	0.557064	+	0.748782i
$576$	−1.35060			−0.0562749
$577$	13.2432	+	13.2432i	0.551320	+	0.551320i	0.926822	−	0.375502i	$-0.122530\pi$
$577$	13.2432	+	13.2432i	0.551320	+	0.551320i	−0.375502	+	0.926822i	$0.622530\pi$
$578$	−10.1885	−	10.1885i	−0.423786	−	0.423786i
$579$	−22.8215			−0.948429
$580$	19.0066	+	22.0008i	0.789206	+	0.913533i
$581$	18.9206			0.784959
$582$	−2.79649	+	2.79649i	−0.115918	+	0.115918i
$583$		0			0
$584$		−	58.1284i		−	2.40537i
$585$	0.374516	−	5.12922i	0.0154843	−	0.212067i
$586$	27.0894			1.11905
$587$	5.96027	+	5.96027i	0.246006	+	0.246006i	0.819329	−	0.573323i	$-0.194346\pi$
$587$	5.96027	+	5.96027i	0.246006	+	0.246006i	−0.573323	+	0.819329i	$0.694346\pi$
$588$	−23.4203	+	23.4203i	−0.965836	+	0.965836i
$589$	5.23690			0.215783
$590$	−70.0412	−	5.11414i	−2.88355	−	0.210546i
$591$		−	39.1537i		−	1.61057i
$592$	15.3152	+	15.3152i	0.629450	+	0.629450i
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	0.611610	−	0.791160i	$-0.290522\pi$
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	−0.791160	+	0.611610i	$0.790522\pi$
$594$		0			0
$595$	−8.89103	−	10.2917i	−0.364497	−	0.421918i
$596$		−	105.403i		−	4.31747i
$597$	−31.6861	−	31.6861i	−1.29682	−	1.29682i
$598$	18.1003	−	18.1003i	0.740178	−	0.740178i
$599$		−	36.5897i		−	1.49502i	−0.664253	−	0.747508i	$-0.731250\pi$
$599$		−	36.5897i		−	1.49502i	0.664253	−	0.747508i	$-0.268750\pi$
$600$	−8.96266	+	61.0473i	−0.365899	+	2.49224i
$601$		−	10.7707i		−	0.439347i	−0.975573	−	0.219674i	$-0.929501\pi$
$601$		−	10.7707i		−	0.439347i	0.975573	−	0.219674i	$-0.0704993\pi$
$602$	−20.8764	+	20.8764i	−0.850860	+	0.850860i
$603$	−2.51057	+	2.51057i	−0.102238	+	0.102238i
$604$	−63.6982			−2.59184
$605$		0			0
$606$	−49.6491			−2.01686
$607$	23.4018	−	23.4018i	0.949851	−	0.949851i	−0.0489504	−	0.998801i	$-0.515588\pi$
$607$	23.4018	−	23.4018i	0.949851	−	0.949851i	0.998801	+	0.0489504i	$0.0155876\pi$
$608$	−4.43409	+	4.43409i	−0.179826	+	0.179826i
$609$			10.6445i			0.431337i
$610$	52.6394	+	3.84353i	2.13131	+	0.155620i
$611$			17.4229i			0.704857i
$612$	10.7387	−	10.7387i	0.434086	−	0.434086i
$613$	−15.3008	−	15.3008i	−0.617992	−	0.617992i	0.327024	−	0.945016i	$-0.393954\pi$
$613$	−15.3008	−	15.3008i	−0.617992	−	0.617992i	−0.945016	+	0.327024i	$0.893954\pi$
$614$			82.4378i			3.32692i
$615$	−5.82899	−	0.425611i	−0.235048	−	0.0171623i
$616$		0			0
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	0.0616431	−	0.998098i	$-0.480366\pi$
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	−0.998098	+	0.0616431i	$0.980366\pi$
$618$	16.7917	+	16.7917i	0.675463	+	0.675463i
$619$		−	41.4239i		−	1.66497i	−0.554050	−	0.832483i	$-0.686918\pi$
$619$		−	41.4239i		−	1.66497i	0.554050	−	0.832483i	$-0.313082\pi$
$620$	25.9566	+	30.0457i	1.04244	+	1.20666i
$621$	17.7713			0.713138
$622$	−24.8986	+	24.8986i	−0.998342	+	0.998342i
$623$	−4.93159	−	4.93159i	−0.197580	−	0.197580i
$624$	30.5258			1.22201
$625$	−23.9450	−	7.18586i	−0.957800	−	0.287435i
$626$		−	44.0839i		−	1.76195i
$627$		0			0
$628$	−42.2480	+	42.2480i	−1.68588	+	1.68588i
$629$	10.7950			0.430424
$630$	−7.90817	+	6.83191i	−0.315069	+	0.272190i
$631$	−31.4596			−1.25239			−0.626193	−	0.779668i	$-0.715388\pi$
$631$	−31.4596			−1.25239			−0.626193	+	0.779668i	$0.715388\pi$
$632$	−4.98392	−	4.98392i	−0.198250	−	0.198250i
$633$	−0.533813	−	0.533813i	−0.0212172	−	0.0212172i
$634$	−40.9629			−1.62685
$635$	0.0335749	−	0.459829i	0.00133238	−	0.0182477i
$636$	56.5387			2.24191
$637$	−5.95137	+	5.95137i	−0.235802	+	0.235802i
$638$		0			0
$639$			6.90382i			0.273111i
$640$	28.9078	+	2.11074i	1.14268	+	0.0834343i
$641$	20.5215			0.810551			0.405275	−	0.914195i	$-0.367176\pi$
$641$	20.5215			0.810551			0.405275	+	0.914195i	$0.367176\pi$
$642$	54.9979	+	54.9979i	2.17059	+	2.17059i
$643$	12.4612	−	12.4612i	0.491422	−	0.491422i	−0.417332	−	0.908754i	$-0.637035\pi$
$643$	12.4612	−	12.4612i	0.491422	−	0.491422i	0.908754	+	0.417332i	$0.137035\pi$
$644$	−35.8311			−1.41194
$645$	21.8499	−	18.8762i	0.860339	−	0.743251i
$646$			11.1376i			0.438201i
$647$	4.07400	+	4.07400i	0.160166	+	0.160166i	0.782640	−	0.622474i	$-0.213873\pi$
$647$	4.07400	+	4.07400i	0.160166	+	0.160166i	−0.622474	+	0.782640i	$0.713873\pi$
$648$	47.9592	+	47.9592i	1.88401	+	1.88401i
$649$		0			0
$650$	−4.15374	+	28.2924i	−0.162923	+	1.10972i
$651$			14.5368i			0.569743i
$652$	−3.36012	−	3.36012i	−0.131593	−	0.131593i
$653$	−4.12540	+	4.12540i	−0.161439	+	0.161439i	−0.783204	−	0.621765i	$-0.786416\pi$
$653$	−4.12540	+	4.12540i	−0.161439	+	0.161439i	0.621765	+	0.783204i	$0.286416\pi$
$654$			90.9031i			3.55459i
$655$	−0.806486	−	0.933536i	−0.0315120	−	0.0364763i
$656$		−	8.79933i		−	0.343556i
$657$	−6.80859	+	6.80859i	−0.265628	+	0.265628i
$658$	25.0346	−	25.0346i	0.975949	−	0.975949i
$659$	5.21347			0.203088			0.101544	−	0.994831i	$-0.467622\pi$
$659$	5.21347			0.203088			0.101544	+	0.994831i	$0.467622\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$	−26.3240	+	26.3240i	−1.02311	+	1.02311i
$663$	10.7581	−	10.7581i	0.417811	−	0.417811i
$664$		−	64.4122i		−	2.49968i
$665$	0.384460	−	5.26542i	0.0149087	−	0.204184i
$666$		−	8.29490i		−	0.321421i
$667$	9.29370	−	9.29370i	0.359854	−	0.359854i
$668$	5.92314	+	5.92314i	0.229173	+	0.229173i
$669$		−	15.2560i		−	0.589830i
$670$	14.9389	−	12.9058i	0.577139	−	0.498593i
$671$		0			0
$672$	−12.3084	−	12.3084i	−0.474805	−	0.474805i
$673$	0.395546	+	0.395546i	0.0152472	+	0.0152472i	0.714689	−	0.699442i	$-0.246568\pi$
$673$	0.395546	+	0.395546i	0.0152472	+	0.0152472i	−0.699442	+	0.714689i	$0.746568\pi$
$674$		−	34.2040i		−	1.31749i
$675$	−15.9282	+	11.8499i	−0.613075	+	0.456103i
$676$	−35.0297			−1.34730
$677$	20.5853	−	20.5853i	0.791158	−	0.791158i	−0.190524	−	0.981683i	$-0.561019\pi$
$677$	20.5853	−	20.5853i	0.791158	−	0.791158i	0.981683	+	0.190524i	$0.0610187\pi$
$678$	26.8473	+	26.8473i	1.03106	+	1.03106i
$679$	1.40673			0.0539855
$680$	−35.0364	+	30.2681i	−1.34359	+	1.16073i
$681$		−	16.4454i		−	0.630190i
$682$		0			0
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	−0.595425	−	0.803411i	$-0.703016\pi$
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	0.803411	+	0.595425i	$0.203016\pi$
$684$	5.89527			0.225411
$685$	−34.5145	−	2.52011i	−1.31873	−	0.0962886i
$686$	49.1899			1.87808
$687$	−10.7589	−	10.7589i	−0.410479	−	0.410479i
$688$	30.7397	+	30.7397i	1.17194	+	1.17194i
$689$	14.3672			0.547345
$690$	50.7367	+	3.70460i	1.93151	+	0.141032i
$691$	−9.44012			−0.359119			−0.179560	−	0.983747i	$-0.557467\pi$
$691$	−9.44012			−0.359119			−0.179560	+	0.983747i	$0.557467\pi$
$692$	59.3222	−	59.3222i	2.25509	−	2.25509i
$693$		0			0
$694$		−	31.0215i		−	1.17756i
$695$	2.40737	−	2.07974i	0.0913166	−	0.0788889i
$696$	36.2376			1.37358
$697$	−3.10112	−	3.10112i	−0.117463	−	0.117463i
$698$	36.5202	−	36.5202i	1.38231	−	1.38231i
$699$	−52.5625			−1.98810
$700$	32.1148	−	23.8922i	1.21383	−	0.903039i
$701$		−	19.7085i		−	0.744379i	−0.928157	−	0.372189i	$-0.878607\pi$
$701$		−	19.7085i		−	0.744379i	0.928157	−	0.372189i	$-0.121393\pi$
$702$	16.0569	+	16.0569i	0.606030	+	0.606030i
$703$	2.96308	+	2.96308i	0.111755	+	0.111755i
$704$		0			0
$705$	−26.2019	+	22.6360i	−0.986822	+	0.852520i
$706$			49.4385i			1.86064i
$707$	12.4876	+	12.4876i	0.469645	+	0.469645i
$708$	−77.7595	+	77.7595i	−2.92238	+	2.92238i
$709$			44.4596i			1.66971i	0.550467	+	0.834857i	$0.314450\pi$
$709$			44.4596i			1.66971i	−0.550467	+	0.834857i	$0.685550\pi$
$710$	2.79543	−	38.2850i	0.104910	−	1.43681i
$711$			1.16753i			0.0437859i
$712$	−16.7888	+	16.7888i	−0.629187	+	0.629187i
$713$	12.6921	−	12.6921i	0.475321	−	0.475321i
$714$	−30.9161			−1.15701
$715$		0			0
$716$	72.5395			2.71093
$717$	3.22664	−	3.22664i	0.120501	−	0.120501i
$718$	−29.6156	+	29.6156i	−1.10524	+	1.10524i
$719$		−	23.9887i		−	0.894629i	−0.894377	−	0.447315i	$-0.852380\pi$
$719$		−	23.9887i		−	0.894629i	0.894377	−	0.447315i	$-0.147620\pi$
$720$	10.0597	+	11.6445i	0.374903	+	0.433963i
$721$		−	8.44684i		−	0.314577i
$722$	31.0048	−	31.0048i	1.15388	−	1.15388i
$723$	−8.92468	−	8.92468i	−0.331912	−	0.331912i
$724$		−	65.8119i		−	2.44588i
$725$	−2.13276	+	14.5268i	−0.0792087	+	0.539513i
$726$		0			0
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	0.300379	−	0.953820i	$-0.402887\pi$
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	−0.953820	+	0.300379i	$0.902887\pi$
$728$	−17.7511	−	17.7511i	−0.657900	−	0.657900i
$729$			12.6464i			0.468387i
$730$	40.5138	−	35.0001i	1.49948	−	1.29541i
$731$	21.6670			0.801383
$732$	58.4400	−	58.4400i	2.16001	−	2.16001i
$733$	−0.0382554	−	0.0382554i	−0.00141300	−	0.00141300i	0.706400	−	0.707813i	$-0.250318\pi$
$733$	−0.0382554	−	0.0382554i	−0.00141300	−	0.00141300i	−0.707813	+	0.706400i	$0.750318\pi$
$734$	−16.3308			−0.602782
$735$	−16.6822	−	1.21807i	−0.615331	−	0.0449291i
$736$			21.4928i			0.792235i
$737$		0			0
$738$	−2.38292	+	2.38292i	−0.0877163	+	0.0877163i
$739$	19.2550			0.708305			0.354153	−	0.935188i	$-0.384769\pi$
$739$	19.2550			0.708305			0.354153	+	0.935188i	$0.384769\pi$
$740$	−2.31363	+	31.6866i	−0.0850508	+	1.16482i
$741$	5.90594			0.216960
$742$	−20.6438	−	20.6438i	−0.757858	−	0.757858i
$743$	−5.26688	−	5.26688i	−0.193223	−	0.193223i	0.603864	−	0.797087i	$-0.293627\pi$
$743$	−5.26688	−	5.26688i	−0.193223	−	0.193223i	−0.797087	+	0.603864i	$0.793627\pi$
$744$	49.4883			1.81433
$745$	40.2800	−	34.7981i	1.47575	−	1.27490i
$746$	34.7657			1.27286
$747$	−7.54462	+	7.54462i	−0.276043	+	0.276043i
$748$		0			0
$749$		−	27.6659i		−	1.01089i
$750$	−47.9448	+	30.5109i	−1.75070	+	1.11410i
$751$	−30.1486			−1.10014			−0.550069	−	0.835119i	$-0.685399\pi$
$751$	−30.1486			−1.10014			−0.550069	+	0.835119i	$0.685399\pi$
$752$	−36.8624	−	36.8624i	−1.34423	−	1.34423i
$753$	37.7027	−	37.7027i	1.37396	−	1.37396i
$754$	16.7943			0.611612
$755$	−21.0295	−	24.3424i	−0.765344	−	0.885912i
$756$		−	31.7860i		−	1.15605i
$757$	31.4681	+	31.4681i	1.14373	+	1.14373i	0.987763	+	0.155964i	$0.0498484\pi$
$757$	31.4681	+	31.4681i	1.14373	+	1.14373i	0.155964	+	0.987763i	$0.450152\pi$
$758$	38.5456	+	38.5456i	1.40004	+	1.40004i
$759$		0			0
$760$	−17.9253	−	1.30883i	−0.650218	−	0.0474764i
$761$		−	47.1118i		−	1.70780i	−0.520435	−	0.853902i	$-0.674230\pi$
$761$		−	47.1118i		−	1.70780i	0.520435	−	0.853902i	$-0.325770\pi$
$762$	−0.741090	−	0.741090i	−0.0268469	−	0.0268469i
$763$	22.8637	−	22.8637i	0.827722	−	0.827722i
$764$			8.45517i			0.305897i
$765$	7.64913	+	0.558510i	0.276555	+	0.0201930i
$766$			0.769298i			0.0277959i
$767$	−19.7596	+	19.7596i	−0.713478	+	0.713478i
$768$	42.8339	−	42.8339i	1.54564	−	1.54564i
$769$	−29.7849			−1.07407			−0.537036	−	0.843559i	$-0.680456\pi$
$769$	−29.7849			−1.07407			−0.537036	+	0.843559i	$0.680456\pi$
$770$		0			0
$771$	39.6451			1.42778
$772$	35.6388	−	35.6388i	1.28267	−	1.28267i
$773$	5.03698	−	5.03698i	0.181167	−	0.181167i	−0.610697	−	0.791864i	$-0.709111\pi$
$773$	5.03698	−	5.03698i	0.181167	−	0.181167i	0.791864	+	0.610697i	$0.209111\pi$
$774$		−	16.6490i		−	0.598436i
$775$	−2.91263	+	19.8388i	−0.104625	+	0.712629i
$776$		−	4.78900i		−	0.171915i
$777$	−8.22506	+	8.22506i	−0.295073	+	0.295073i
$778$	−6.45620	−	6.45620i	−0.231466	−	0.231466i
$779$		−	1.70244i		−	0.0609962i
$780$	29.2727	+	33.8842i	1.04813	+	1.21325i
$781$		0			0
$782$	26.9928	+	26.9928i	0.965260	+	0.965260i
$783$	8.24451	+	8.24451i	0.294635	+	0.294635i
$784$		−	25.1831i		−	0.899395i
$785$	−30.0931	−	2.19728i	−1.07407	−	0.0784244i
$786$	−2.80433			−0.100027
$787$	20.4049	−	20.4049i	0.727357	−	0.727357i	−0.242735	−	0.970093i	$-0.578045\pi$
$787$	20.4049	−	20.4049i	0.727357	−	0.727357i	0.970093	+	0.242735i	$0.0780446\pi$
$788$	61.1438	+	61.1438i	2.17816	+	2.17816i
$789$	−16.7781			−0.597315
$790$	0.472746	−	6.47455i	0.0168196	−	0.230354i
$791$		−	13.5051i		−	0.480187i
$792$		0			0
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$	−79.5188			−2.82202
$795$	18.6659	+	21.6064i	0.662011	+	0.766301i
$796$	98.9641			3.50769
$797$	−21.8770	−	21.8770i	−0.774923	−	0.774923i	0.204039	−	0.978963i	$-0.434593\pi$
$797$	−21.8770	−	21.8770i	−0.774923	−	0.774923i	−0.978963	+	0.204039i	$0.934593\pi$
$798$	−8.48609	−	8.48609i	−0.300404	−	0.300404i
$799$	−25.9826			−0.919198
$800$	−14.3314	−	19.2636i	−0.506691	−	0.681073i
$801$	3.93295			0.138964
$802$	17.9225	−	17.9225i	0.632866	−	0.632866i
$803$		0			0
$804$		−	30.9130i		−	1.09022i
$805$	−11.8294	−	13.6930i	−0.416932	−	0.482613i
$806$	22.9354			0.807863
$807$	−13.7665	−	13.7665i	−0.484605	−	0.484605i
$808$	42.5121	−	42.5121i	1.49557	−	1.49557i
$809$	−19.6707			−0.691584			−0.345792	−	0.938311i	$-0.612390\pi$
$809$	−19.6707			−0.691584			−0.345792	+	0.938311i	$0.612390\pi$
$810$	−4.54914	+	62.3032i	−0.159840	+	2.18911i
$811$			42.2600i			1.48395i	0.670428	+	0.741975i	$0.266110\pi$
$811$			42.2600i			1.48395i	−0.670428	+	0.741975i	$0.733890\pi$
$812$	−16.6228	−	16.6228i	−0.583347	−	0.583347i
$813$	4.32597	+	4.32597i	0.151718	+	0.151718i
$814$		0			0
$815$	0.174757	−	2.39340i	0.00612147	−	0.0838373i
$816$			45.5227i			1.59361i
$817$	5.94732	+	5.94732i	0.208070	+	0.208070i
$818$	−54.4832	+	54.4832i	−1.90496	+	1.90496i
$819$			4.15838i			0.145306i
$820$	9.76741	−	8.43811i	0.341093	−	0.294672i
$821$			53.1732i			1.85576i	0.372881	+	0.927879i	$0.378370\pi$
$821$			53.1732i			1.85576i	−0.372881	+	0.927879i	$0.621630\pi$
$822$	−55.6258	+	55.6258i	−1.94017	+	1.94017i
$823$	−0.990270	+	0.990270i	−0.0345186	+	0.0345186i	−0.724155	−	0.689637i	$-0.757770\pi$
$823$	−0.990270	+	0.990270i	−0.0345186	+	0.0345186i	0.689637	+	0.724155i	$0.257770\pi$
$824$	−28.7559			−1.00176
$825$		0			0
$826$	56.7841			1.97577
$827$	−12.2233	+	12.2233i	−0.425045	+	0.425045i	−0.886936	−	0.461891i	$-0.847171\pi$
$827$	−12.2233	+	12.2233i	−0.425045	+	0.425045i	0.461891	+	0.886936i	$0.347171\pi$
$828$	14.2877	−	14.2877i	0.496532	−	0.496532i
$829$			35.8923i			1.24659i	0.781987	+	0.623295i	$0.214206\pi$
$829$			35.8923i			1.24659i	−0.781987	+	0.623295i	$0.785794\pi$
$830$	44.8935	−	38.7837i	1.55827	−	1.34620i
$831$		−	4.77194i		−	0.165537i
$832$	2.11296	−	2.11296i	0.0732536	−	0.0732536i
$833$	−8.87520	−	8.87520i	−0.307507	−	0.307507i
$834$		−	7.23171i		−	0.250414i
$835$	−0.308058	+	4.21903i	−0.0106608	+	0.146006i
$836$		0			0
$837$	11.2592	+	11.2592i	0.389176	+	0.389176i
$838$	13.4129	+	13.4129i	0.463342	+	0.463342i
$839$		−	4.96077i		−	0.171265i	−0.996327	−	0.0856324i	$-0.972709\pi$
$839$		−	4.96077i		−	0.171265i	0.996327	−	0.0856324i	$-0.0272911\pi$
$840$	3.63312	−	49.7578i	0.125355	−	1.71681i
$841$	−20.3769			−0.702651
$842$	−36.6130	+	36.6130i	−1.26177	+	1.26177i
$843$	−40.0238	−	40.0238i	−1.37849	−	1.37849i
$844$	1.66724			0.0573888
$845$	−11.5648	−	13.3867i	−0.397843	−	0.460517i
$846$			19.9651i			0.686415i
$847$		0			0
$848$	−30.3971	+	30.3971i	−1.04384	+	1.04384i
$849$	−34.1101			−1.17065
$850$	−42.1920	−	6.19442i	−1.44717	−	0.212467i
$851$	14.3626			0.492343
$852$	−42.5039	−	42.5039i	−1.45616	−	1.45616i
$853$	−18.7929	−	18.7929i	−0.643457	−	0.643457i	0.307947	−	0.951404i	$-0.400358\pi$
$853$	−18.7929	−	18.7929i	−0.643457	−	0.643457i	−0.951404	+	0.307947i	$0.900358\pi$
$854$	−42.6761			−1.46034
$855$	1.94629	+	2.25290i	0.0665616	+	0.0770474i
$856$	−94.1841			−3.21915
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	−0.689051	−	0.724712i	$-0.741973\pi$
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	0.724712	+	0.689051i	$0.241973\pi$
$858$		0			0
$859$			13.9402i			0.475633i	0.971310	+	0.237816i	$0.0764316\pi$
$859$			13.9402i			0.475633i	−0.971310	+	0.237816i	$0.923568\pi$
$860$	−4.64378	+	63.5994i	−0.158352	+	2.16872i
$861$	4.72571			0.161052
$862$	−60.3540	−	60.3540i	−2.05567	−	2.05567i
$863$	−36.2809	+	36.2809i	−1.23502	+	1.23502i	−0.273002	+	0.962013i	$0.588017\pi$
$863$	−36.2809	+	36.2809i	−1.23502	+	1.23502i	−0.962013	+	0.273002i	$0.911983\pi$
$864$	−19.0664			−0.648652
$865$	42.2550	+	3.08530i	1.43671	+	0.104903i
$866$		−	29.4074i		−	0.999304i
$867$	−8.05696	−	8.05696i	−0.273629	−	0.273629i
$868$	−22.7012	−	22.7012i	−0.770529	−	0.770529i
$869$		0			0
$870$	21.8192	+	25.2565i	0.739742	+	0.856277i
$871$		−	7.85536i		−	0.266169i
$872$	−77.8359	−	77.8359i	−2.63586	−	2.63586i
$873$	−0.560937	+	0.560937i	−0.0189848	+	0.0189848i
$874$			14.8184i			0.501239i
$875$	19.7330	+	4.38493i	0.667096	+	0.148238i
$876$		−	83.8352i		−	2.83253i
$877$	4.71867	−	4.71867i	0.159338	−	0.159338i	−0.622935	−	0.782273i	$-0.714060\pi$
$877$	4.71867	−	4.71867i	0.159338	−	0.159338i	0.782273	+	0.622935i	$0.214060\pi$
$878$	−19.2255	+	19.2255i	−0.648831	+	0.648831i
$879$	21.4220			0.722546
$880$		0			0
$881$	−14.4573			−0.487080			−0.243540	−	0.969891i	$-0.578309\pi$
$881$	−14.4573			−0.487080			−0.243540	+	0.969891i	$0.578309\pi$
$882$	−6.81974	+	6.81974i	−0.229633	+	0.229633i
$883$	7.39720	−	7.39720i	0.248936	−	0.248936i	−0.571598	−	0.820534i	$-0.693676\pi$
$883$	7.39720	−	7.39720i	0.248936	−	0.248936i	0.820534	+	0.571598i	$0.193676\pi$
$884$			33.6005i			1.13011i
$885$	−55.3878	−	4.04420i	−1.86184	−	0.135944i
$886$			102.258i			3.43543i
$887$	6.98839	−	6.98839i	0.234647	−	0.234647i	−0.579982	−	0.814629i	$-0.696940\pi$
$887$	6.98839	−	6.98839i	0.234647	−	0.234647i	0.814629	+	0.579982i	$0.196940\pi$
$888$	28.0009	+	28.0009i	0.939650	+	0.939650i
$889$			0.372794i			0.0125031i
$890$	−21.8101	−	1.59249i	−0.731078	−	0.0533805i
$891$		0			0
$892$	23.8243	+	23.8243i	0.797695	+	0.797695i
$893$	−7.13190	−	7.13190i	−0.238660	−	0.238660i
$894$		−	121.001i		−	4.04688i
$895$	23.9485	+	27.7212i	0.800508	+	0.926616i
$896$	−23.4363			−0.782952
$897$	14.3135	−	14.3135i	0.477915	−	0.477915i
$898$	−6.52842	−	6.52842i	−0.217856	−	0.217856i
$899$	11.7763			0.392760
$900$	−3.27880	+	22.3329i	−0.109293	+	0.744429i
$901$			21.4256i			0.713789i
$902$		0			0
$903$	−16.5088	+	16.5088i	−0.549380	+	0.549380i
$904$	−45.9760			−1.52914
$905$	25.1502	−	21.7274i	0.836021	−	0.722243i
$906$	−73.1245			−2.42940
$907$	−8.18203	−	8.18203i	−0.271680	−	0.271680i	0.558096	−	0.829776i	$-0.311532\pi$
$907$	−8.18203	−	8.18203i	−0.271680	−	0.271680i	−0.829776	+	0.558096i	$0.811532\pi$
$908$	25.6817	+	25.6817i	0.852278	+	0.852278i
$909$	−9.95890			−0.330316
$910$	1.68377	−	23.0603i	0.0558165	−	0.764440i
$911$	−8.72151			−0.288957			−0.144478	−	0.989508i	$-0.546150\pi$
$911$	−8.72151			−0.288957			−0.144478	+	0.989508i	$0.546150\pi$
$912$	−12.4954	+	12.4954i	−0.413765	+	0.413765i
$913$		0			0
$914$			45.8704i			1.51726i
$915$	41.6266	+	3.03942i	1.37613	+	0.100480i
$916$	33.6030			1.11027
$917$	0.705339	+	0.705339i	0.0232923	+	0.0232923i
$918$	−23.9455	+	23.9455i	−0.790319	+	0.790319i
$919$	−5.77661			−0.190553			−0.0952764	−	0.995451i	$-0.530373\pi$
$919$	−5.77661			−0.190553			−0.0952764	+	0.995451i	$0.530373\pi$
$920$	−46.6155	+	40.2713i	−1.53687	+	1.32771i
$921$			65.1909i			2.14811i
$922$	−63.8003	−	63.8003i	−2.10115	−	2.10115i
$923$	−10.8007	−	10.8007i	−0.355511	−	0.355511i
$924$		0			0
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$		−	16.0199i		−	0.526448i
$927$	3.36819	+	3.36819i	0.110626	+	0.110626i
$928$	−9.97098	+	9.97098i	−0.327314	+	0.327314i
$929$			18.1392i			0.595128i	0.954702	+	0.297564i	$0.0961741\pi$
$929$			18.1392i			0.595128i	−0.954702	+	0.297564i	$0.903826\pi$
$930$	29.7977	+	34.4919i	0.977106	+	1.13103i
$931$		−	4.87226i		−	0.159682i
$932$	82.0834	−	82.0834i	2.68873	−	2.68873i
$933$	−19.6895	+	19.6895i	−0.644606	+	0.644606i
$934$	21.9374			0.717813
$935$		0			0
$936$	14.1566			0.462722
$937$	−22.7256	+	22.7256i	−0.742414	+	0.742414i	−0.973042	−	0.230628i	$-0.925922\pi$
$937$	−22.7256	+	22.7256i	−0.742414	+	0.742414i	0.230628	+	0.973042i	$0.425922\pi$
$938$	−11.2872	+	11.2872i	−0.368539	+	0.368539i
$939$		−	34.8610i		−	1.13765i
$940$	5.56872	−	76.2670i	0.181632	−	2.48755i
$941$		−	5.21117i		−	0.169879i	−0.996386	−	0.0849397i	$-0.972930\pi$
$941$		−	5.21117i		−	0.169879i	0.996386	−	0.0849397i	$-0.0270698\pi$
$942$	−48.5000	+	48.5000i	−1.58022	+	1.58022i
$943$	−4.12600	−	4.12600i	−0.134361	−	0.134361i
$944$		−	83.6123i		−	2.72135i
$945$	12.1471	−	10.4940i	0.395146	−	0.341368i
$946$		0			0
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	0.698195	−	0.715908i	$-0.253987\pi$
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	−0.715908	+	0.698195i	$0.753987\pi$
$948$	−7.18801	−	7.18801i	−0.233456	−	0.233456i
$949$		−	21.3035i		−	0.691542i
$950$	−9.88089	−	13.2815i	−0.320578	−	0.430908i
$951$	−32.3930			−1.05042
$952$	26.4720	−	26.4720i	0.857962	−	0.857962i
$953$	9.60331	+	9.60331i	0.311082	+	0.311082i	0.845328	−	0.534247i	$-0.179405\pi$
$953$	9.60331	+	9.60331i	0.311082	+	0.311082i	−0.534247	+	0.845328i	$0.679405\pi$
$954$	16.4635			0.533025
$955$	−3.23117	+	2.79142i	−0.104558	+	0.0903282i
$956$			10.0777i			0.325935i
$957$		0			0
$958$	27.5786	−	27.5786i	0.891023	−	0.891023i
$959$	27.9817			0.903577
$960$	5.92279	+	0.432459i	0.191157	+	0.0139576i
$961$	−14.9176			−0.481213
$962$	12.9770	+	12.9770i	0.418396	+	0.418396i
$963$	11.0318	+	11.0318i	0.355495	+	0.355495i
$964$	27.8742			0.897767
$965$	25.3854	+	1.85355i	0.817186	+	0.0596677i
$966$	−41.1335			−1.32345
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	−0.997429	−	0.0716619i	$-0.977170\pi$
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	0.0716619	+	0.997429i	$0.477170\pi$
$968$		0			0
$969$			8.80745i			0.282936i
$970$	3.33780	−	2.88354i	0.107170	−	0.0925849i
$971$	−29.3752			−0.942696			−0.471348	−	0.881947i	$-0.656232\pi$
$971$	−29.3752			−0.942696			−0.471348	+	0.881947i	$0.656232\pi$
$972$	31.8747	+	31.8747i	1.02238	+	1.02238i
$973$	−1.81890	+	1.81890i	−0.0583113	+	0.0583113i
$974$	−15.0759			−0.483062
$975$	−3.28473	+	22.3733i	−0.105196	+	0.716518i
$976$			62.8387i			2.01142i
$977$	−16.5429	−	16.5429i	−0.529255	−	0.529255i	0.391095	−	0.920350i	$-0.372096\pi$
$977$	−16.5429	−	16.5429i	−0.529255	−	0.529255i	−0.920350	+	0.391095i	$0.872096\pi$
$978$	−3.85737	−	3.85737i	−0.123345	−	0.123345i
$979$		0			0
$980$	27.9536	−	24.1493i	0.892946	−	0.771420i
$981$			18.2339i			0.582163i
$982$	73.4135	+	73.4135i	2.34272	+	2.34272i
$983$	14.7486	−	14.7486i	0.470406	−	0.470406i	−0.431640	−	0.902046i	$-0.642065\pi$
$983$	14.7486	−	14.7486i	0.470406	−	0.470406i	0.902046	+	0.431640i	$0.142065\pi$
$984$		−	16.0879i		−	0.512864i
$985$	−3.18004	+	43.5525i	−0.101324	+	1.38770i
$986$			25.0451i			0.797599i
$987$	19.7970	−	19.7970i	0.630147	−	0.630147i
$988$	−9.22292	+	9.22292i	−0.293420	+	0.293420i
$989$	28.8277			0.916666
$990$		0			0
$991$	−6.50787			−0.206729			−0.103365	−	0.994644i	$-0.532961\pi$
$991$	−6.50787			−0.206729			−0.103365	+	0.994644i	$0.532961\pi$
$992$	−13.6170	+	13.6170i	−0.432340	+	0.432340i
$993$	−20.8167	+	20.8167i	−0.660597	+	0.660597i
$994$			31.0386i			0.984485i
$995$	32.6724	+	37.8194i	1.03578	+	1.19896i
$996$		−	92.8980i		−	2.94359i
$997$	18.6716	−	18.6716i	0.591335	−	0.591335i	−0.346657	−	0.937992i	$-0.612683\pi$
$997$	18.6716	−	18.6716i	0.591335	−	0.591335i	0.937992	+	0.346657i	$0.112683\pi$
$998$	−41.5677	−	41.5677i	−1.31580	−	1.31580i
$999$			12.7411i			0.403112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.362.1		32
5.3	odd	4	inner	605.2.e.b.483.16		32
11.2	odd	10		605.2.m.d.282.1		32
11.3	even	5		605.2.m.e.112.4		32
11.4	even	5		55.2.l.a.17.1	yes	32
11.5	even	5		605.2.m.d.602.4		32
11.6	odd	10		605.2.m.c.602.1		32
11.7	odd	10		605.2.m.e.457.4		32
11.8	odd	10		55.2.l.a.2.1	✓	32
11.9	even	5		605.2.m.c.282.4		32
11.10	odd	2	inner	605.2.e.b.362.16		32
33.8	even	10		495.2.bj.a.442.4		32
33.26	odd	10		495.2.bj.a.127.4		32
44.15	odd	10		880.2.cm.a.17.1		32
44.19	even	10		880.2.cm.a.497.1		32
55.3	odd	20		605.2.m.e.233.4		32
55.4	even	10		275.2.bm.b.182.4		32
55.8	even	20		55.2.l.a.13.1	yes	32
55.13	even	20		605.2.m.d.403.4		32
55.18	even	20		605.2.m.e.578.4		32
55.19	odd	10		275.2.bm.b.57.4		32
55.28	even	20		605.2.m.c.118.4		32
55.37	odd	20		275.2.bm.b.193.4		32
55.38	odd	20		605.2.m.d.118.1		32
55.43	even	4	inner	605.2.e.b.483.1		32
55.48	odd	20		55.2.l.a.28.1	yes	32
55.52	even	20		275.2.bm.b.68.4		32
55.53	odd	20		605.2.m.c.403.1		32
165.8	odd	20		495.2.bj.a.343.4		32
165.158	even	20		495.2.bj.a.28.4		32
220.63	odd	20		880.2.cm.a.673.1		32
220.103	even	20		880.2.cm.a.193.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	11.8	odd	10
55.2.l.a.13.1	yes	32	55.8	even	20
55.2.l.a.17.1	yes	32	11.4	even	5
55.2.l.a.28.1	yes	32	55.48	odd	20
275.2.bm.b.57.4		32	55.19	odd	10
275.2.bm.b.68.4		32	55.52	even	20
275.2.bm.b.182.4		32	55.4	even	10
275.2.bm.b.193.4		32	55.37	odd	20
495.2.bj.a.28.4		32	165.158	even	20
495.2.bj.a.127.4		32	33.26	odd	10
495.2.bj.a.343.4		32	165.8	odd	20
495.2.bj.a.442.4		32	33.8	even	10
605.2.e.b.362.1		32	1.1	even	1	trivial
605.2.e.b.362.16		32	11.10	odd	2	inner
605.2.e.b.483.1		32	55.43	even	4	inner
605.2.e.b.483.16		32	5.3	odd	4	inner
605.2.m.c.118.4		32	55.28	even	20
605.2.m.c.282.4		32	11.9	even	5
605.2.m.c.403.1		32	55.53	odd	20
605.2.m.c.602.1		32	11.6	odd	10
605.2.m.d.118.1		32	55.38	odd	20
605.2.m.d.282.1		32	11.2	odd	10
605.2.m.d.403.4		32	55.13	even	20
605.2.m.d.602.4		32	11.5	even	5
605.2.m.e.112.4		32	11.3	even	5
605.2.m.e.233.4		32	55.3	odd	20
605.2.m.e.457.4		32	11.7	odd	10
605.2.m.e.578.4		32	55.18	even	20
880.2.cm.a.17.1		32	44.15	odd	10
880.2.cm.a.193.1		32	220.103	even	20
880.2.cm.a.497.1		32	44.19	even	10
880.2.cm.a.673.1		32	220.63	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79273 + 1.79273i) q^{2} +(-1.41767 + 1.41767i) q^{3} -4.42777i q^{4} +(1.69208 - 1.46180i) q^{5} -5.08300i q^{6} +(-1.27846 + 1.27846i) q^{7} +(4.35233 + 4.35233i) q^{8} -1.01958i q^{9} +O(q^{10})\)	\(q+(-1.79273 + 1.79273i) q^{2} +(-1.41767 + 1.41767i) q^{3} -4.42777i q^{4} +(1.69208 - 1.46180i) q^{5} -5.08300i q^{6} +(-1.27846 + 1.27846i) q^{7} +(4.35233 + 4.35233i) q^{8} -1.01958i q^{9} +(-0.412838 + 5.65406i) q^{10} +(6.27711 + 6.27711i) q^{12} +(1.59509 + 1.59509i) q^{13} -4.58388i q^{14} +(-0.326467 + 4.47116i) q^{15} -6.74958 q^{16} +(-2.37874 + 2.37874i) q^{17} +(1.82783 + 1.82783i) q^{18} -1.30587 q^{19} +(-6.47250 - 7.49215i) q^{20} -3.62488i q^{21} +(-3.16488 + 3.16488i) q^{23} -12.3403 q^{24} +(0.726289 - 4.94697i) q^{25} -5.71913 q^{26} +(-2.80758 - 2.80758i) q^{27} +(5.66074 + 5.66074i) q^{28} -2.93651 q^{29} +(-7.43033 - 8.60086i) q^{30} -4.01029 q^{31} +(3.39552 - 3.39552i) q^{32} -8.52886i q^{34} +(-0.294410 + 4.03213i) q^{35} -4.51446 q^{36} +(-2.26906 - 2.26906i) q^{37} +(2.34107 - 2.34107i) q^{38} -4.52262 q^{39} +(13.7267 + 1.00227i) q^{40} +1.30369i q^{41} +(6.49844 + 6.49844i) q^{42} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} -11.3475i q^{46} +(5.46143 + 5.46143i) q^{47} +(9.56868 - 9.56868i) q^{48} +3.73106i q^{49} +(7.56654 + 10.1706i) q^{50} -6.74453i q^{51} +(7.06268 - 7.06268i) q^{52} +(4.50356 - 4.50356i) q^{53} +10.0665 q^{54} -11.1286 q^{56} +(1.85129 - 1.85129i) q^{57} +(5.26438 - 5.26438i) q^{58} +12.3878i q^{59} +(19.7973 + 1.44552i) q^{60} -9.31002i q^{61} +(7.18936 - 7.18936i) q^{62} +(1.30349 + 1.30349i) q^{63} -1.32466i q^{64} +(5.03072 + 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(10.5325 + 10.5325i) q^{68} -8.97350i q^{69} +(-6.70072 - 7.75631i) q^{70} -6.77125 q^{71} +(4.43754 - 4.43754i) q^{72} +(-6.67785 - 6.67785i) q^{73} +8.13562 q^{74} +(5.98353 + 8.04281i) q^{75} +5.78207i q^{76} +(8.10784 - 8.10784i) q^{78} -1.14511 q^{79} +(-11.4208 + 9.86653i) q^{80} +11.0192 q^{81} +(-2.33716 - 2.33716i) q^{82} +(-7.39974 - 7.39974i) q^{83} -16.0501 q^{84} +(-0.547785 + 7.50225i) q^{85} +16.3293 q^{86} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(5.76476 + 0.420921i) q^{90} -4.07853 q^{91} +(14.0133 + 14.0133i) q^{92} +(5.68526 - 5.68526i) q^{93} -19.5817 q^{94} +(-2.20963 + 1.90891i) q^{95} +9.62745i q^{96} +(-0.550166 - 0.550166i) q^{97} +(-6.68878 - 6.68878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

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