LMFDB - Embedded newform 390.2.s.c.77.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(77,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("390.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.s (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.11
Character	$\chi$	$=$	390.77
Dual form			390.2.s.c.233.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.14719 + 1.29768i) q^{3} +1.00000i q^{4} +(-2.23605 + 0.00995019i) q^{5} +(-0.106413 + 1.72878i) q^{6} +(-1.03162 + 1.03162i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.367928 + 2.97735i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.14719 + 1.29768i) q^{3} +1.00000i q^{4} +(-2.23605 + 0.00995019i) q^{5} +(-0.106413 + 1.72878i) q^{6} +(-1.03162 + 1.03162i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.367928 + 2.97735i) q^{9} +(-1.58816 - 1.57409i) q^{10} -3.70213 q^{11} +(-1.29768 + 1.14719i) q^{12} +(1.20959 + 3.39660i) q^{13} -1.45893 q^{14} +(-2.57807 - 2.89025i) q^{15} -1.00000 q^{16} +(1.82396 - 1.82396i) q^{17} +(-2.36547 + 1.84514i) q^{18} +6.37656 q^{19} +(-0.00995019 - 2.23605i) q^{20} +(-2.52217 - 0.155249i) q^{21} +(-2.61780 - 2.61780i) q^{22} +(3.59028 + 3.59028i) q^{23} +(-1.72878 - 0.106413i) q^{24} +(4.99980 - 0.0444982i) q^{25} +(-1.54645 + 3.25707i) q^{26} +(-4.28572 + 2.93813i) q^{27} +(-1.03162 - 1.03162i) q^{28} -0.495771 q^{29} +(0.220742 - 3.86669i) q^{30} -2.88858i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.24703 - 4.80417i) q^{33} +2.57947 q^{34} +(2.29649 - 2.31702i) q^{35} +(-2.97735 - 0.367928i) q^{36} +(2.07537 - 2.07537i) q^{37} +(4.50891 + 4.50891i) q^{38} +(-3.02006 + 5.46619i) q^{39} +(1.57409 - 1.58816i) q^{40} -1.65794 q^{41} +(-1.67367 - 1.89322i) q^{42} +(8.68616 - 8.68616i) q^{43} -3.70213i q^{44} +(0.793079 - 6.66116i) q^{45} +5.07742i q^{46} +(2.79640 + 2.79640i) q^{47} +(-1.14719 - 1.29768i) q^{48} +4.87151i q^{49} +(3.56686 + 3.50393i) q^{50} +(4.45933 + 0.274489i) q^{51} +(-3.39660 + 1.20959i) q^{52} +(-5.90440 - 5.90440i) q^{53} +(-5.10803 - 0.952895i) q^{54} +(8.27814 - 0.0368369i) q^{55} -1.45893i q^{56} +(7.31510 + 8.27471i) q^{57} +(-0.350563 - 0.350563i) q^{58} -0.692553i q^{59} +(2.89025 - 2.57807i) q^{60} -12.0684 q^{61} +(2.04253 - 2.04253i) q^{62} +(-2.69194 - 3.45107i) q^{63} -1.00000i q^{64} +(-2.73849 - 7.58292i) q^{65} +(0.393954 - 6.40017i) q^{66} +(-6.79503 + 6.79503i) q^{67} +(1.82396 + 1.82396i) q^{68} +(-0.540302 + 8.77773i) q^{69} +(3.26224 - 0.0145167i) q^{70} +4.41216 q^{71} +(-1.84514 - 2.36547i) q^{72} +(8.02368 + 8.02368i) q^{73} +2.93502 q^{74} +(5.79345 + 6.43708i) q^{75} +6.37656i q^{76} +(3.81920 - 3.81920i) q^{77} +(-6.00069 + 1.72967i) q^{78} +6.09995i q^{79} +(2.23605 - 0.00995019i) q^{80} +(-8.72926 - 2.19090i) q^{81} +(-1.17234 - 1.17234i) q^{82} +(4.84469 - 4.84469i) q^{83} +(0.155249 - 2.52217i) q^{84} +(-4.06031 + 4.09661i) q^{85} +12.2841 q^{86} +(-0.568742 - 0.643350i) q^{87} +(2.61780 - 2.61780i) q^{88} -2.66725i q^{89} +(5.27094 - 4.14936i) q^{90} +(-4.75185 - 2.25617i) q^{91} +(-3.59028 + 3.59028i) q^{92} +(3.74844 - 3.31373i) q^{93} +3.95471i q^{94} +(-14.2583 + 0.0634480i) q^{95} +(0.106413 - 1.72878i) q^{96} +(6.98302 - 6.98302i) q^{97} +(-3.44468 + 3.44468i) q^{98} +(1.36212 - 11.0226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 + 12 * q^9	$ 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) $ 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.14719	+	1.29768i	0.662328	+	0.749214i
$3$	1.14719	+	1.29768i	0.662328	+	0.749214i
$4$			1.00000i			0.500000i
$5$	−2.23605	+	0.00995019i	−0.999990	+	0.00444986i
$5$	−2.23605	+	0.00995019i	−0.999990	+	0.00444986i
$6$	−0.106413	+	1.72878i	−0.0434428	+	0.705771i
$7$	−1.03162	+	1.03162i	−0.389917	+	0.389917i	−0.874658	−	0.484741i	$-0.838914\pi$
$7$	−1.03162	+	1.03162i	−0.389917	+	0.389917i	0.484741	+	0.874658i	$0.338914\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.367928	+	2.97735i	−0.122643	+	0.992451i
$10$	−1.58816	−	1.57409i	−0.502220	−	0.497770i
$11$	−3.70213			−1.11623			−0.558117	−	0.829762i	$-0.688476\pi$
$11$	−3.70213			−1.11623			−0.558117	+	0.829762i	$0.688476\pi$
$12$	−1.29768	+	1.14719i	−0.374607	+	0.331164i
$13$	1.20959	+	3.39660i	0.335480	+	0.942047i
$13$	1.20959	+	3.39660i	0.335480	+	0.942047i
$14$	−1.45893			−0.389917
$15$	−2.57807	−	2.89025i	−0.665656	−	0.746259i
$16$	−1.00000			−0.250000
$17$	1.82396	−	1.82396i	0.442376	−	0.442376i	−0.450434	−	0.892810i	$-0.648731\pi$
$17$	1.82396	−	1.82396i	0.442376	−	0.442376i	0.892810	+	0.450434i	$0.148731\pi$
$18$	−2.36547	+	1.84514i	−0.557547	+	0.434904i
$19$	6.37656			1.46288			0.731442	−	0.681904i	$-0.238848\pi$
$19$	6.37656			1.46288			0.731442	+	0.681904i	$0.238848\pi$
$20$	−0.00995019	−	2.23605i	−0.00222493	−	0.499995i
$21$	−2.52217	−	0.155249i	−0.550384	−	0.0338781i
$22$	−2.61780	−	2.61780i	−0.558117	−	0.558117i
$23$	3.59028	+	3.59028i	0.748624	+	0.748624i	0.974221	−	0.225596i	$-0.0724331\pi$
$23$	3.59028	+	3.59028i	0.748624	+	0.748624i	−0.225596	+	0.974221i	$0.572433\pi$
$24$	−1.72878	−	0.106413i	−0.352886	−	0.0217214i
$25$	4.99980	−	0.0444982i	0.999960	−	0.00889964i
$26$	−1.54645	+	3.25707i	−0.303284	+	0.638764i
$27$	−4.28572	+	2.93813i	−0.824788	+	0.565443i
$28$	−1.03162	−	1.03162i	−0.194958	−	0.194958i
$29$	−0.495771			−0.0920624			−0.0460312	−	0.998940i	$-0.514657\pi$
$29$	−0.495771			−0.0920624			−0.0460312	+	0.998940i	$0.514657\pi$
$30$	0.220742	−	3.86669i	0.0403018	−	0.705957i
$31$		−	2.88858i		−	0.518803i	−0.965770	−	0.259402i	$-0.916475\pi$
$31$		−	2.88858i		−	0.518803i	0.965770	−	0.259402i	$-0.0835254\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.24703	−	4.80417i	−0.739314	−	0.836298i
$34$	2.57947			0.442376
$35$	2.29649	−	2.31702i	0.388178	−	0.391648i
$36$	−2.97735	−	0.367928i	−0.496225	−	0.0613214i
$37$	2.07537	−	2.07537i	0.341189	−	0.341189i	−0.515625	−	0.856814i	$-0.672440\pi$
$37$	2.07537	−	2.07537i	0.341189	−	0.341189i	0.856814	+	0.515625i	$0.172440\pi$
$38$	4.50891	+	4.50891i	0.731442	+	0.731442i
$39$	−3.02006	+	5.46619i	−0.483597	+	0.875291i
$40$	1.57409	−	1.58816i	0.248885	−	0.251110i
$41$	−1.65794			−0.258927			−0.129463	−	0.991584i	$-0.541325\pi$
$41$	−1.65794			−0.258927			−0.129463	+	0.991584i	$0.541325\pi$
$42$	−1.67367	−	1.89322i	−0.258253	−	0.292131i
$43$	8.68616	−	8.68616i	1.32463	−	1.32463i	0.414643	−	0.909984i	$-0.363906\pi$
$43$	8.68616	−	8.68616i	1.32463	−	1.32463i	0.909984	−	0.414643i	$-0.136094\pi$
$44$		−	3.70213i		−	0.558117i
$45$	0.793079	−	6.66116i	0.118225	−	0.992987i
$46$			5.07742i			0.748624i
$47$	2.79640	+	2.79640i	0.407897	+	0.407897i	0.881005	−	0.473108i	$-0.156868\pi$
$47$	2.79640	+	2.79640i	0.407897	+	0.407897i	−0.473108	+	0.881005i	$0.656868\pi$
$48$	−1.14719	−	1.29768i	−0.165582	−	0.187303i
$49$			4.87151i			0.695930i
$50$	3.56686	+	3.50393i	0.504430	+	0.495530i
$51$	4.45933	+	0.274489i	0.624432	+	0.0384361i
$52$	−3.39660	+	1.20959i	−0.471024	+	0.167740i
$53$	−5.90440	−	5.90440i	−0.811031	−	0.811031i	0.173757	−	0.984788i	$-0.444409\pi$
$53$	−5.90440	−	5.90440i	−0.811031	−	0.811031i	−0.984788	+	0.173757i	$0.944409\pi$
$54$	−5.10803	−	0.952895i	−0.695115	−	0.129673i
$55$	8.27814	−	0.0368369i	1.11622	−	0.00496709i
$56$		−	1.45893i		−	0.194958i
$57$	7.31510	+	8.27471i	0.968909	+	1.09601i
$58$	−0.350563	−	0.350563i	−0.0460312	−	0.0460312i
$59$		−	0.692553i		−	0.0901628i	−0.998983	−	0.0450814i	$-0.985645\pi$
$59$		−	0.692553i		−	0.0901628i	0.998983	−	0.0450814i	$-0.0143547\pi$
$60$	2.89025	−	2.57807i	0.373130	−	0.332828i
$61$	−12.0684			−1.54520			−0.772601	−	0.634892i	$-0.781045\pi$
$61$	−12.0684			−1.54520			−0.772601	+	0.634892i	$0.781045\pi$
$62$	2.04253	−	2.04253i	0.259402	−	0.259402i
$63$	−2.69194	−	3.45107i	−0.339153	−	0.434793i
$64$		−	1.00000i		−	0.125000i
$65$	−2.73849	−	7.58292i	−0.339668	−	0.940545i
$66$	0.393954	−	6.40017i	0.0484924	−	0.787806i
$67$	−6.79503	+	6.79503i	−0.830145	+	0.830145i	−0.987536	−	0.157391i	$-0.949692\pi$
$67$	−6.79503	+	6.79503i	−0.830145	+	0.830145i	0.157391	+	0.987536i	$0.449692\pi$
$68$	1.82396	+	1.82396i	0.221188	+	0.221188i
$69$	−0.540302	+	8.77773i	−0.0650447	+	1.05671i
$70$	3.26224	−	0.0145167i	0.389913	−	0.00173507i
$71$	4.41216			0.523627			0.261813	−	0.965119i	$-0.415680\pi$
$71$	4.41216			0.523627			0.261813	+	0.965119i	$0.415680\pi$
$72$	−1.84514	−	2.36547i	−0.217452	−	0.278773i
$73$	8.02368	+	8.02368i	0.939101	+	0.939101i	0.998249	−	0.0591482i	$-0.0188385\pi$
$73$	8.02368	+	8.02368i	0.939101	+	0.939101i	−0.0591482	+	0.998249i	$0.518838\pi$
$74$	2.93502			0.341189
$75$	5.79345	+	6.43708i	0.668970	+	0.743290i
$76$			6.37656i			0.731442i
$77$	3.81920	−	3.81920i	0.435238	−	0.435238i
$78$	−6.00069	+	1.72967i	−0.679444	+	0.195847i
$79$			6.09995i			0.686298i	0.939281	+	0.343149i	$0.111494\pi$
$79$			6.09995i			0.686298i	−0.939281	+	0.343149i	$0.888506\pi$
$80$	2.23605	−	0.00995019i	0.249998	−	0.00111247i
$81$	−8.72926	−	2.19090i	−0.969918	−	0.243434i
$82$	−1.17234	−	1.17234i	−0.129463	−	0.129463i
$83$	4.84469	−	4.84469i	0.531774	−	0.531774i	−0.389326	−	0.921100i	$-0.627292\pi$
$83$	4.84469	−	4.84469i	0.531774	−	0.531774i	0.921100	+	0.389326i	$0.127292\pi$
$84$	0.155249	−	2.52217i	0.0169391	−	0.275192i
$85$	−4.06031	+	4.09661i	−0.440403	+	0.444340i
$86$	12.2841			1.32463
$87$	−0.568742	−	0.643350i	−0.0609755	−	0.0689744i
$88$	2.61780	−	2.61780i	0.279059	−	0.279059i
$89$		−	2.66725i		−	0.282728i	−0.989958	−	0.141364i	$-0.954851\pi$
$89$		−	2.66725i		−	0.282728i	0.989958	−	0.141364i	$-0.0451488\pi$
$90$	5.27094	−	4.14936i	0.555606	−	0.437381i
$91$	−4.75185	−	2.25617i	−0.498129	−	0.236511i
$92$	−3.59028	+	3.59028i	−0.374312	+	0.374312i
$93$	3.74844	−	3.31373i	0.388695	−	0.343618i
$94$			3.95471i			0.407897i
$95$	−14.2583	+	0.0634480i	−1.46287	+	0.00650963i
$96$	0.106413	−	1.72878i	0.0108607	−	0.176443i
$97$	6.98302	−	6.98302i	0.709019	−	0.709019i	−0.257310	−	0.966329i	$-0.582836\pi$
$97$	6.98302	−	6.98302i	0.709019	−	0.709019i	0.966329	+	0.257310i	$0.0828362\pi$
$98$	−3.44468	+	3.44468i	−0.347965	+	0.347965i
$99$	1.36212	−	11.0226i	0.136898	−	1.10781i
$100$	0.0444982	+	4.99980i	0.00444982	+	0.499980i
$101$			15.5880i			1.55106i	0.631309	+	0.775531i	$0.282518\pi$
$101$			15.5880i			1.55106i	−0.631309	+	0.775531i	$0.717482\pi$
$102$	2.95913	+	3.34732i	0.292998	+	0.331434i
$103$	4.08174	−	4.08174i	0.402185	−	0.402185i	−0.476817	−	0.879003i	$-0.658210\pi$
$103$	4.08174	−	4.08174i	0.402185	−	0.402185i	0.879003	+	0.476817i	$0.158210\pi$
$104$	−3.25707	−	1.54645i	−0.319382	−	0.151642i
$105$	5.64124	+	0.322048i	0.550529	+	0.0314287i
$106$		−	8.35008i		−	0.811031i
$107$	10.6375	−	10.6375i	1.02836	−	1.02836i	0.0287790	−	0.999586i	$-0.490838\pi$
$107$	10.6375	−	10.6375i	1.02836	−	1.02836i	0.999586	−	0.0287790i	$-0.00916189\pi$
$108$	−2.93813	−	4.28572i	−0.282721	−	0.412394i
$109$	12.9928			1.24448			0.622242	−	0.782825i	$-0.286222\pi$
$109$	12.9928			1.24448			0.622242	+	0.782825i	$0.286222\pi$
$110$	5.87957	+	5.82748i	0.560595	+	0.555628i
$111$	5.07400	+	0.312323i	0.481603	+	0.0296444i
$112$	1.03162	−	1.03162i	0.0974791	−	0.0974791i
$113$	−5.71439	−	5.71439i	−0.537565	−	0.537565i	0.385248	−	0.922813i	$-0.374116\pi$
$113$	−5.71439	−	5.71439i	−0.537565	−	0.537565i	−0.922813	+	0.385248i	$0.874116\pi$
$114$	−0.678547	+	11.0237i	−0.0635518	+	1.03246i
$115$	−8.06375	−	7.99230i	−0.751948	−	0.745286i
$116$		−	0.495771i		−	0.0460312i
$117$	−10.5579	+	2.35167i	−0.976080	+	0.217412i
$118$	0.489709	−	0.489709i	0.0450814	−	0.0450814i
$119$			3.76328i			0.344979i
$120$	3.86669	+	0.220742i	0.352979	+	0.0201509i
$121$	2.70578			0.245980
$122$	−8.53366	−	8.53366i	−0.772601	−	0.772601i
$123$	−1.90197	−	2.15147i	−0.171495	−	0.193992i
$124$	2.88858			0.259402
$125$	−11.1793	+	0.149249i	−0.999911	+	0.0133492i
$126$	0.536783	−	4.34376i	0.0478204	−	0.386973i
$127$	−13.1211	−	13.1211i	−1.16431	−	1.16431i	−0.983522	−	0.180786i	$-0.942136\pi$
$127$	−13.1211	−	13.1211i	−1.16431	−	1.16431i	−0.180786	−	0.983522i	$-0.557864\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	21.2365	+	1.30718i	1.86977	+	0.115091i
$130$	3.42553	−	7.29834i	0.300438	−	0.640107i
$131$		−	11.4677i		−	1.00193i	−0.865466	−	0.500967i	$-0.832978\pi$
$131$		−	11.4677i		−	1.00193i	0.865466	−	0.500967i	$-0.167022\pi$
$132$	4.80417	−	4.24703i	0.418149	−	0.369657i
$133$	−6.57820	+	6.57820i	−0.570402	+	0.570402i
$134$	−9.60963			−0.830145
$135$	9.55384	−	6.61243i	0.822263	−	0.569107i
$136$			2.57947i			0.221188i
$137$	9.53679	+	9.53679i	0.814783	+	0.814783i	0.985347	−	0.170564i	$-0.0545589\pi$
$137$	9.53679	+	9.53679i	0.814783	+	0.814783i	−0.170564	+	0.985347i	$0.554559\pi$
$138$	−6.58885	+	5.82474i	−0.560880	+	0.495835i
$139$		−	2.09695i		−	0.177861i	−0.996038	−	0.0889305i	$-0.971655\pi$
$139$		−	2.09695i		−	0.177861i	0.996038	−	0.0889305i	$-0.0283449\pi$
$140$	2.31702	+	2.29649i	0.195824	+	0.194089i
$141$	−0.420831	+	6.83681i	−0.0354404	+	0.575763i
$142$	3.11987	+	3.11987i	0.261813	+	0.261813i
$143$	−4.47806	−	12.5747i	−0.374474	−	1.05155i
$144$	0.367928	−	2.97735i	0.0306607	−	0.248113i
$145$	1.10857	−	0.00493302i	0.0920615	−	0.000409665i
$146$			11.3472i			0.939101i
$147$	−6.32164	+	5.58853i	−0.521400	+	0.460934i
$148$	2.07537	+	2.07537i	0.170595	+	0.170595i
$149$			21.4810i			1.75980i	0.475163	+	0.879898i	$0.342389\pi$
$149$			21.4810i			1.75980i	−0.475163	+	0.879898i	$0.657611\pi$
$150$	−0.455115	+	8.64829i	−0.0371600	+	0.706130i
$151$			4.31897i			0.351473i	0.984437	+	0.175736i	$0.0562306\pi$
$151$			4.31897i			0.351473i	−0.984437	+	0.175736i	$0.943769\pi$
$152$	−4.50891	+	4.50891i	−0.365721	+	0.365721i
$153$	4.75949	+	6.10166i	0.384782	+	0.493290i
$154$	5.40117			0.435238
$155$	0.0287419	+	6.45899i	0.00230860	+	0.518798i
$156$	−5.46619	−	3.02006i	−0.437645	−	0.241799i
$157$	−2.78660	−	2.78660i	−0.222395	−	0.222395i	0.587111	−	0.809506i	$-0.300265\pi$
$157$	−2.78660	−	2.78660i	−0.222395	−	0.222395i	−0.809506	+	0.587111i	$0.800265\pi$
$158$	−4.31332	+	4.31332i	−0.343149	+	0.343149i
$159$	0.888554	−	14.4354i	0.0704669	−	1.14480i
$160$	1.58816	+	1.57409i	0.125555	+	0.124443i
$161$	−7.40762			−0.583802
$162$	−4.62331	−	7.72172i	−0.363242	−	0.606676i
$163$	−13.8871	−	13.8871i	−1.08772	−	1.08772i	−0.995763	−	0.0919595i	$-0.970687\pi$
$163$	−13.8871	−	13.8871i	−1.08772	−	1.08772i	−0.0919595	−	0.995763i	$-0.529313\pi$
$164$		−	1.65794i		−	0.129463i
$165$	9.54436	+	10.7001i	0.743028	+	0.833000i
$166$	6.85143			0.531774
$167$	−13.3857	−	13.3857i	−1.03582	−	1.03582i	−0.999334	−	0.0364854i	$-0.988384\pi$
$167$	−13.3857	−	13.3857i	−1.03582	−	1.03582i	−0.0364854	−	0.999334i	$-0.511616\pi$
$168$	1.89322	−	1.67367i	0.146065	−	0.129126i
$169$	−10.0738	+	8.21698i	−0.774907	+	0.632075i
$170$	−5.76782	+	0.0256662i	−0.442371	+	0.00196851i
$171$	−2.34612	+	18.9853i	−0.179412	+	1.45184i
$172$	8.68616	+	8.68616i	0.662314	+	0.662314i
$173$	0.386807	+	0.386807i	0.0294084	+	0.0294084i	0.721658	−	0.692250i	$-0.243380\pi$
$173$	0.386807	+	0.386807i	0.0294084	+	0.0294084i	−0.692250	+	0.721658i	$0.743380\pi$
$174$	0.0527564	−	0.857079i	0.00399945	−	0.0649750i
$175$	−5.11200	+	5.20381i	−0.386431	+	0.393371i
$176$	3.70213			0.279059
$177$	0.898710	−	0.794488i	0.0675512	−	0.0597173i
$178$	1.88603	−	1.88603i	0.141364	−	0.141364i
$179$	23.6190			1.76537			0.882684	−	0.469967i	$-0.155734\pi$
$179$	23.6190			1.76537			0.882684	+	0.469967i	$0.155734\pi$
$180$	6.66116	+	0.793079i	0.496493	+	0.0591126i
$181$	−10.1453			−0.754094			−0.377047	−	0.926194i	$-0.623061\pi$
$181$	−10.1453			−0.754094			−0.377047	+	0.926194i	$0.623061\pi$
$182$	−1.76471	−	4.95542i	−0.130809	−	0.367320i
$183$	−13.8447	−	15.6609i	−1.02343	−	1.15769i
$184$	−5.07742			−0.374312
$185$	−4.61998	+	4.66128i	−0.339667	+	0.342704i
$186$	4.99371	+	0.307381i	0.366156	+	0.0225383i
$187$	−6.75254	+	6.75254i	−0.493795	+	0.493795i
$188$	−2.79640	+	2.79640i	−0.203948	+	0.203948i
$189$	1.39021	−	7.45228i	0.101123	−	0.542074i
$190$	−10.1270	−	10.0373i	−0.734689	−	0.728180i
$191$			15.5138i			1.12254i	0.827632	+	0.561271i	$0.189688\pi$
$191$			15.5138i			1.12254i	−0.827632	+	0.561271i	$0.810312\pi$
$192$	1.29768	−	1.14719i	0.0936517	−	0.0827910i
$193$	5.80655	+	5.80655i	0.417965	+	0.417965i	0.884502	−	0.466537i	$-0.154499\pi$
$193$	5.80655	+	5.80655i	0.417965	+	0.417965i	−0.466537	+	0.884502i	$0.654499\pi$
$194$	9.87549			0.709019
$195$	6.69861	−	12.2527i	0.479698	−	0.877434i
$196$	−4.87151			−0.347965
$197$	−8.00755	−	8.00755i	−0.570514	−	0.570514i	0.361758	−	0.932272i	$-0.382177\pi$
$197$	−8.00755	−	8.00755i	−0.570514	−	0.570514i	−0.932272	+	0.361758i	$0.882177\pi$
$198$	8.75728	−	6.83096i	0.622353	−	0.485455i
$199$		−	11.1959i		−	0.793656i	−0.917893	−	0.396828i	$-0.870111\pi$
$199$		−	11.1959i		−	0.793656i	0.917893	−	0.396828i	$-0.129889\pi$
$200$	−3.50393	+	3.56686i	−0.247765	+	0.252215i
$201$	−16.6129	−	1.02259i	−1.17179	−	0.0721277i
$202$	−11.0224	+	11.0224i	−0.775531	+	0.775531i
$203$	0.511449	−	0.511449i	0.0358966	−	0.0358966i
$204$	−0.274489	+	4.45933i	−0.0192180	+	0.312216i
$205$	3.70723	−	0.0164968i	0.258924	−	0.00115219i
$206$	5.77245			0.402185
$207$	−12.0105	+	9.36856i	−0.834786	+	0.651160i
$208$	−1.20959	−	3.39660i	−0.0838699	−	0.235512i
$209$	−23.6069			−1.63292
$210$	3.76124	+	4.21668i	0.259550	+	0.290979i
$211$	3.34994			0.230619			0.115310	−	0.993330i	$-0.463214\pi$
$211$	3.34994			0.230619			0.115310	+	0.993330i	$0.463214\pi$
$212$	5.90440	−	5.90440i	0.405516	−	0.405516i
$213$	5.06156	+	5.72555i	0.346813	+	0.392308i
$214$	15.0437			1.02836
$215$	−19.3362	+	19.5091i	−1.31872	+	1.33051i
$216$	0.952895	−	5.10803i	0.0648363	−	0.347558i
$217$	2.97992	+	2.97992i	0.202290	+	0.202290i
$218$	9.18729	+	9.18729i	0.622242	+	0.622242i
$219$	−1.20749	+	19.6168i	−0.0815944	+	1.32558i
$220$	0.0368369	+	8.27814i	0.00248354	+	0.558112i
$221$	8.40151	+	3.98902i	0.565147	+	0.268331i
$222$	3.36701	+	3.80871i	0.225979	+	0.255624i
$223$	8.84969	+	8.84969i	0.592619	+	0.592619i	0.938338	−	0.345719i	$-0.112365\pi$
$223$	8.84969	+	8.84969i	0.592619	+	0.592619i	−0.345719	+	0.938338i	$0.612365\pi$
$224$	1.45893			0.0974791
$225$	−1.70708	+	14.9025i	−0.113805	+	0.993503i
$226$		−	8.08137i		−	0.537565i
$227$	−7.63136	−	7.63136i	−0.506511	−	0.506511i	0.406942	−	0.913454i	$-0.366595\pi$
$227$	−7.63136	−	7.63136i	−0.506511	−	0.506511i	−0.913454	+	0.406942i	$0.866595\pi$
$228$	−8.27471	+	7.31510i	−0.548006	+	0.484454i
$229$	−23.0299			−1.52186			−0.760929	−	0.648836i	$-0.775256\pi$
$229$	−23.0299			−1.52186			−0.760929	+	0.648836i	$0.775256\pi$
$230$	−0.0505213	−	11.3533i	−0.00333128	−	0.748617i
$231$	9.33742	+	0.574753i	0.614357	+	0.0378160i
$232$	0.350563	−	0.350563i	0.0230156	−	0.0230156i
$233$	19.7471	+	19.7471i	1.29368	+	1.29368i	0.932495	+	0.361182i	$0.117627\pi$
$233$	19.7471	+	19.7471i	1.29368	+	1.29368i	0.361182	+	0.932495i	$0.382373\pi$
$234$	−9.12846	−	5.80270i	−0.596746	−	0.379334i
$235$	−6.28070	−	6.22505i	−0.409708	−	0.406078i
$236$	0.692553			0.0450814
$237$	−7.91576	+	6.99778i	−0.514184	+	0.454554i
$238$	−2.66104	+	2.66104i	−0.172490	+	0.172490i
$239$		−	2.46770i		−	0.159622i	−0.996810	−	0.0798112i	$-0.974568\pi$
$239$		−	2.46770i		−	0.159622i	0.996810	−	0.0798112i	$-0.0254317\pi$
$240$	2.57807	+	2.89025i	0.166414	+	0.186565i
$241$		−	21.2063i		−	1.36602i	−0.730410	−	0.683009i	$-0.760671\pi$
$241$		−	21.2063i		−	1.36602i	0.730410	−	0.683009i	$-0.239329\pi$
$242$	1.91327	+	1.91327i	0.122990	+	0.122990i
$243$	−7.17100	−	13.8411i	−0.460020	−	0.887909i
$244$		−	12.0684i		−	0.772601i
$245$	−0.0484725	−	10.8929i	−0.00309679	−	0.695923i
$246$	0.176426	−	2.86621i	0.0112485	−	0.182743i
$247$	7.71302	+	21.6586i	0.490768	+	1.37811i
$248$	2.04253	+	2.04253i	0.129701	+	0.129701i
$249$	11.8446	+	0.729079i	0.750621	+	0.0462035i
$250$	−8.01052	−	7.79945i	−0.506630	−	0.493281i
$251$		−	21.0780i		−	1.33043i	−0.746651	−	0.665216i	$-0.768339\pi$
$251$		−	21.0780i		−	1.33043i	0.746651	−	0.665216i	$-0.231661\pi$
$252$	3.45107	−	2.69194i	0.217397	−	0.169576i
$253$	−13.2917	−	13.2917i	−0.835640	−	0.835640i
$254$		−	18.5560i		−	1.16431i
$255$	−9.97401	−	0.569398i	−0.624597	−	0.0356571i
$256$	1.00000			0.0625000
$257$	8.49660	−	8.49660i	0.530003	−	0.530003i	−0.390570	−	0.920573i	$-0.627722\pi$
$257$	8.49660	−	8.49660i	0.530003	−	0.530003i	0.920573	+	0.390570i	$0.127722\pi$
$258$	14.0921	+	15.9408i	0.877338	+	0.992429i
$259$			4.28200i			0.266071i
$260$	7.58292	−	2.73849i	0.470273	−	0.169834i
$261$	0.182408	−	1.47609i	0.0112908	−	0.0913674i
$262$	8.10886	−	8.10886i	0.500967	−	0.500967i
$263$	12.5564	+	12.5564i	0.774263	+	0.774263i	0.978849	−	0.204585i	$-0.0655846\pi$
$263$	12.5564	+	12.5564i	0.774263	+	0.774263i	−0.204585	+	0.978849i	$0.565585\pi$
$264$	6.40017	+	0.393954i	0.393903	+	0.0242462i
$265$	13.2612	+	13.1437i	0.814632	+	0.807414i
$266$	−9.30298			−0.570402
$267$	3.46123	−	3.05983i	0.211824	−	0.187259i
$268$	−6.79503	−	6.79503i	−0.415073	−	0.415073i
$269$	−17.2259			−1.05028			−0.525140	−	0.851016i	$-0.675987\pi$
$269$	−17.2259			−1.05028			−0.525140	+	0.851016i	$0.675987\pi$
$270$	11.4313	+	2.07989i	0.695685	+	0.126578i
$271$		−	9.68987i		−	0.588617i	−0.955710	−	0.294309i	$-0.904911\pi$
$271$		−	9.68987i		−	0.588617i	0.955710	−	0.294309i	$-0.0950894\pi$
$272$	−1.82396	+	1.82396i	−0.110594	+	0.110594i
$273$	−2.52348	−	8.75461i	−0.152728	−	0.529853i
$274$			13.4871i			0.814783i
$275$	−18.5099	+	0.164738i	−1.11619	+	0.00993408i
$276$	−8.77773	−	0.540302i	−0.528357	−	0.0325224i
$277$	−15.4074	−	15.4074i	−0.925743	−	0.925743i	0.0716840	−	0.997427i	$-0.477163\pi$
$277$	−15.4074	−	15.4074i	−0.925743	−	0.925743i	−0.997427	+	0.0716840i	$0.977163\pi$
$278$	1.48277	−	1.48277i	0.0889305	−	0.0889305i
$279$	8.60031	+	1.06279i	0.514887	+	0.0636275i
$280$	0.0145167	+	3.26224i	0.000867537	+	0.194956i
$281$	10.7797			0.643064			0.321532	−	0.946899i	$-0.395802\pi$
$281$	10.7797			0.643064			0.321532	+	0.946899i	$0.395802\pi$
$282$	−5.13193	+	4.53678i	−0.305602	+	0.270161i
$283$	−4.45748	+	4.45748i	−0.264970	+	0.264970i	−0.827069	−	0.562100i	$-0.809994\pi$
$283$	−4.45748	+	4.45748i	−0.264970	+	0.264970i	0.562100	+	0.827069i	$0.309994\pi$
$284$			4.41216i			0.261813i
$285$	−16.4392	−	18.4298i	−0.973776	−	1.09169i
$286$	5.72516	−	12.0581i	0.338536	−	0.713010i
$287$	1.71037	−	1.71037i	0.100960	−	0.100960i
$288$	2.36547	−	1.84514i	0.139387	−	0.108726i
$289$			10.3463i			0.608608i
$290$	0.787363	+	0.780387i	0.0462356	+	0.0458259i
$291$	17.0725	+	1.05088i	1.00081	+	0.0616035i
$292$	−8.02368	+	8.02368i	−0.469550	+	0.469550i
$293$	6.26863	−	6.26863i	0.366217	−	0.366217i	−0.499878	−	0.866096i	$-0.666622\pi$
$293$	6.26863	−	6.26863i	0.366217	−	0.366217i	0.866096	+	0.499878i	$0.166622\pi$
$294$	−8.42177	−	0.518391i	−0.491167	−	0.0302332i
$295$	0.00689104	+	1.54858i	0.000401212	+	0.0901619i
$296$			2.93502i			0.170595i
$297$	15.8663	−	10.8773i	0.920657	−	0.631167i
$298$	−15.1894	+	15.1894i	−0.879898	+	0.879898i
$299$	−7.85198	+	16.5375i	−0.454091	+	0.956388i
$300$	−6.43708	+	5.79345i	−0.371645	+	0.334485i
$301$			17.9217i			1.03299i
$302$	−3.05397	+	3.05397i	−0.175736	+	0.175736i
$303$	−20.2282	+	17.8823i	−1.16208	+	1.02731i
$304$	−6.37656			−0.365721
$305$	26.9855	−	0.120083i	1.54519	−	0.00687593i
$306$	−0.949060	+	7.67999i	−0.0542541	+	0.439036i
$307$	18.3933	−	18.3933i	1.04976	−	1.04976i	0.0510636	−	0.998695i	$-0.483739\pi$
$307$	18.3933	−	18.3933i	1.04976	−	1.04976i	0.998695	−	0.0510636i	$-0.0162611\pi$
$308$	3.81920	+	3.81920i	0.217619	+	0.217619i
$309$	9.97928	+	0.614262i	0.567702	+	0.0349441i
$310$	−4.54687	+	4.58752i	−0.258245	+	0.260553i
$311$			1.77908i			0.100882i	0.998727	+	0.0504412i	$0.0160627\pi$
$311$			1.77908i			0.100882i	−0.998727	+	0.0504412i	$0.983937\pi$
$312$	−1.72967	−	6.00069i	−0.0979233	−	0.339722i
$313$	−14.6637	+	14.6637i	−0.828840	+	0.828840i	−0.987356	−	0.158516i	$-0.949329\pi$
$313$	−14.6637	+	14.6637i	−0.828840	+	0.828840i	0.158516	+	0.987356i	$0.449329\pi$
$314$		−	3.94085i		−	0.222395i
$315$	6.05364	+	7.68996i	0.341084	+	0.433280i
$316$	−6.09995			−0.343149
$317$	7.54686	+	7.54686i	0.423874	+	0.423874i	0.886535	−	0.462661i	$-0.153105\pi$
$317$	7.54686	+	7.54686i	0.423874	+	0.423874i	−0.462661	+	0.886535i	$0.653105\pi$
$318$	10.8357	−	9.57909i	0.607636	−	0.537169i
$319$	1.83541			0.102763
$320$	0.00995019	+	2.23605i	0.000556233	+	0.124999i
$321$	26.0072	+	1.60084i	1.45158	+	0.0893501i
$322$	−5.23798	−	5.23798i	−0.291901	−	0.291901i
$323$	11.6306	−	11.6306i	0.647144	−	0.647144i
$324$	2.19090	−	8.72926i	0.121717	−	0.484959i
$325$	6.19885	+	16.9285i	0.343850	+	0.939025i
$326$		−	19.6393i		−	1.08772i
$327$	14.9051	+	16.8604i	0.824257	+	0.932384i
$328$	1.17234	−	1.17234i	0.0647317	−	0.0647317i
$329$	−5.76965			−0.318091
$330$	−0.817216	+	14.3150i	−0.0449863	+	0.788014i
$331$		−	4.18973i		−	0.230288i	−0.993349	−	0.115144i	$-0.963267\pi$
$331$		−	4.18973i		−	0.230288i	0.993349	−	0.115144i	$-0.0367330\pi$
$332$	4.84469	+	4.84469i	0.265887	+	0.265887i
$333$	5.41553	+	6.94270i	0.296769	+	0.380458i
$334$		−	18.9303i		−	1.03582i
$335$	15.1264	−	15.2616i	0.826443	−	0.833831i
$336$	2.52217	+	0.155249i	0.137596	+	0.00846954i
$337$	15.4822	+	15.4822i	0.843371	+	0.843371i	0.989296	−	0.145925i	$-0.0466157\pi$
$337$	15.4822	+	15.4822i	0.843371	+	0.843371i	−0.145925	+	0.989296i	$0.546616\pi$
$338$	−12.9335	−	1.31296i	−0.703491	−	0.0714157i
$339$	0.859961	−	13.9709i	0.0467067	−	0.758795i
$340$	−4.09661	−	4.06031i	−0.222170	−	0.220201i
$341$			10.6939i			0.579106i
$342$	−15.0836	+	11.7657i	−0.815626	+	0.636214i
$343$	−12.2469	−	12.2469i	−0.661271	−	0.661271i
$344$			12.2841i			0.662314i
$345$	1.12080	−	19.6328i	0.0603418	−	1.05699i
$346$			0.547027i			0.0294084i
$347$	9.96769	−	9.96769i	0.535094	−	0.535094i	−0.386990	−	0.922084i	$-0.626485\pi$
$347$	9.96769	−	9.96769i	0.535094	−	0.535094i	0.922084	+	0.386990i	$0.126485\pi$
$348$	0.643350	−	0.568742i	0.0344872	−	0.0304878i
$349$	−24.7426			−1.32444			−0.662220	−	0.749309i	$-0.730386\pi$
$349$	−24.7426			−1.32444			−0.662220	+	0.749309i	$0.730386\pi$
$350$	−7.29438	+	0.0649199i	−0.389901	+	0.00347012i
$351$	−15.1636	−	11.0030i	−0.809373	−	0.587295i
$352$	2.61780	+	2.61780i	0.139529	+	0.139529i
$353$	4.17093	−	4.17093i	0.221996	−	0.221996i	−0.587342	−	0.809339i	$-0.699826\pi$
$353$	4.17093	−	4.17093i	0.221996	−	0.221996i	0.809339	+	0.587342i	$0.199826\pi$
$354$	1.19727	+	0.0736965i	0.0636343	+	0.00391692i
$355$	−9.86578	+	0.0439018i	−0.523621	+	0.00233007i
$356$	2.66725			0.141364
$357$	−4.88352	+	4.31718i	−0.258463	+	0.228489i
$358$	16.7012	+	16.7012i	0.882684	+	0.882684i
$359$		−	2.55214i		−	0.134697i	−0.997730	−	0.0673485i	$-0.978546\pi$
$359$		−	2.55214i		−	0.134697i	0.997730	−	0.0673485i	$-0.0214539\pi$
$360$	4.14936	+	5.27094i	0.218690	+	0.277803i
$361$	21.6605			1.14003
$362$	−7.17381	−	7.17381i	−0.377047	−	0.377047i
$363$	3.10403	+	3.51122i	0.162919	+	0.184291i
$364$	2.25617	−	4.75185i	0.118255	−	0.249064i
$365$	−18.0212	−	17.8615i	−0.943271	−	0.934913i
$366$	1.28423	−	20.8636i	0.0671279	−	1.09056i
$367$	13.0614	+	13.0614i	0.681800	+	0.681800i	0.960406	−	0.278605i	$-0.0898722\pi$
$367$	13.0614	+	13.0614i	0.681800	+	0.681800i	−0.278605	+	0.960406i	$0.589872\pi$
$368$	−3.59028	−	3.59028i	−0.187156	−	0.187156i
$369$	0.610003	−	4.93627i	0.0317555	−	0.256972i
$370$	−6.56284	+	0.0292040i	−0.341186	+	0.00151824i
$371$	12.1822			0.632469
$372$	3.31373	+	3.74844i	0.171809	+	0.194347i
$373$	12.4877	−	12.4877i	0.646591	−	0.646591i	−0.305577	−	0.952167i	$-0.598849\pi$
$373$	12.4877	−	12.4877i	0.646591	−	0.646591i	0.952167	+	0.305577i	$0.0988492\pi$
$374$	−9.54954			−0.493795
$375$	−13.0185	−	14.3360i	−0.672271	−	0.740305i
$376$	−3.95471			−0.203948
$377$	−0.599679	−	1.68394i	−0.0308851	−	0.0867271i
$378$	6.25259	−	4.28653i	0.321598	−	0.220475i
$379$	−1.70213			−0.0874324			−0.0437162	−	0.999044i	$-0.513920\pi$
$379$	−1.70213			−0.0874324			−0.0437162	+	0.999044i	$0.513920\pi$
$380$	−0.0634480	−	14.2583i	−0.00325481	−	0.731434i
$381$	1.97460	−	32.0793i	0.101162	−	1.64347i
$382$	−10.9699	+	10.9699i	−0.561271	+	0.561271i
$383$	24.8875	−	24.8875i	1.27169	−	1.27169i	0.326494	−	0.945199i	$-0.394133\pi$
$383$	24.8875	−	24.8875i	1.27169	−	1.27169i	0.945199	−	0.326494i	$-0.105867\pi$
$384$	1.72878	+	0.106413i	0.0882214	+	0.00543035i
$385$	−8.50191	+	8.57791i	−0.433297	+	0.437171i
$386$			8.21170i			0.417965i
$387$	22.6659	+	29.0576i	1.15217	+	1.47708i
$388$	6.98302	+	6.98302i	0.354509	+	0.354509i
$389$	18.6976			0.948005			0.474002	−	0.880524i	$-0.342809\pi$
$389$	18.6976			0.948005			0.474002	+	0.880524i	$0.342809\pi$
$390$	13.4006	−	3.92733i	0.678566	−	0.198868i
$391$	13.0971			0.662346
$392$	−3.44468	−	3.44468i	−0.173983	−	0.173983i
$393$	14.8813	−	13.1555i	0.750663	−	0.663609i
$394$		−	11.3244i		−	0.570514i
$395$	−0.0606957	−	13.6398i	−0.00305393	−	0.686291i
$396$	11.0226	+	1.36212i	0.553904	+	0.0684490i
$397$	6.85449	−	6.85449i	0.344017	−	0.344017i	−0.513858	−	0.857875i	$-0.671784\pi$
$397$	6.85449	−	6.85449i	0.344017	−	0.344017i	0.857875	+	0.513858i	$0.171784\pi$
$398$	7.91669	−	7.91669i	0.396828	−	0.396828i
$399$	−16.0828	−	0.989956i	−0.805147	−	0.0495598i
$400$	−4.99980	+	0.0444982i	−0.249990	+	0.00222491i
$401$	−19.0194			−0.949781			−0.474891	−	0.880045i	$-0.657512\pi$
$401$	−19.0194			−0.949781			−0.474891	+	0.880045i	$0.657512\pi$
$402$	−11.0240	−	12.4702i	−0.549829	−	0.621956i
$403$	9.81134	−	3.49399i	0.488737	−	0.174048i
$404$	−15.5880			−0.775531
$405$	19.5408	+	4.81210i	0.970991	+	0.239115i
$406$	0.723297			0.0358966
$407$	−7.68330	+	7.68330i	−0.380847	+	0.380847i
$408$	−3.34732	+	2.95913i	−0.165717	+	0.146499i
$409$	−22.4228			−1.10874			−0.554368	−	0.832272i	$-0.687040\pi$
$409$	−22.4228			−1.10874			−0.554368	+	0.832272i	$0.687040\pi$
$410$	2.63307	+	2.60974i	0.130038	+	0.128886i
$411$	−1.43519	+	23.3161i	−0.0707929	+	1.15010i
$412$	4.08174	+	4.08174i	0.201093	+	0.201093i
$413$	0.714453	+	0.714453i	0.0351560	+	0.0351560i
$414$	−15.1173	−	1.86812i	−0.742973	−	0.0918133i
$415$	−10.7847	+	10.8812i	−0.529402	+	0.534135i
$416$	1.54645	−	3.25707i	0.0758210	−	0.159691i
$417$	2.72116	−	2.40559i	0.133256	−	0.117802i
$418$	−16.6926	−	16.6926i	−0.816460	−	0.816460i
$419$	−0.535876			−0.0261792			−0.0130896	−	0.999914i	$-0.504167\pi$
$419$	−0.535876			−0.0261792			−0.0130896	+	0.999914i	$0.504167\pi$
$420$	−0.322048	+	5.64124i	−0.0157143	+	0.275264i
$421$		−	23.5915i		−	1.14978i	−0.818231	−	0.574890i	$-0.805045\pi$
$421$		−	23.5915i		−	1.14978i	0.818231	−	0.574890i	$-0.194955\pi$
$422$	2.36877	+	2.36877i	0.115310	+	0.115310i
$423$	−9.35474	+	7.29699i	−0.454843	+	0.354792i
$424$	8.35008			0.405516
$425$	9.03828	−	9.20061i	0.438421	−	0.446295i
$426$	−0.469510	+	7.62764i	−0.0227478	+	0.369561i
$427$	12.4500	−	12.4500i	0.602500	−	0.602500i
$428$	10.6375	+	10.6375i	0.514182	+	0.514182i
$429$	11.1807	−	20.2365i	0.539808	−	0.977030i
$430$	−27.4678	+	0.122229i	−1.32461	+	0.00589441i
$431$	15.0604			0.725432			0.362716	−	0.931900i	$-0.381849\pi$
$431$	15.0604			0.725432			0.362716	+	0.931900i	$0.381849\pi$
$432$	4.28572	−	2.93813i	0.206197	−	0.141361i
$433$	8.41585	−	8.41585i	0.404440	−	0.404440i	−0.475355	−	0.879794i	$-0.657680\pi$
$433$	8.41585	−	8.41585i	0.404440	−	0.404440i	0.879794	+	0.475355i	$0.157680\pi$
$434$			4.21424i			0.202290i
$435$	1.27813	+	1.43290i	0.0612818	+	0.0687024i
$436$			12.9928i			0.622242i
$437$	22.8936	+	22.8936i	1.09515	+	1.09515i
$438$	−14.7250	+	13.0174i	−0.703587	+	0.621993i
$439$		−	35.6347i		−	1.70075i	−0.526176	−	0.850376i	$-0.676375\pi$
$439$		−	35.6347i		−	1.70075i	0.526176	−	0.850376i	$-0.323625\pi$
$440$	−5.82748	+	5.87957i	−0.277814	+	0.280298i
$441$	−14.5042	−	1.79237i	−0.690676	−	0.0853508i
$442$	3.12010	+	8.76143i	0.148408	+	0.416739i
$443$	13.8316	+	13.8316i	0.657158	+	0.657158i	0.954707	−	0.297549i	$-0.0961691\pi$
$443$	13.8316	+	13.8316i	0.657158	+	0.657158i	−0.297549	+	0.954707i	$0.596169\pi$
$444$	−0.312323	+	5.07400i	−0.0148222	+	0.240801i
$445$	0.0265397	+	5.96409i	0.00125810	+	0.282725i
$446$			12.5153i			0.592619i
$447$	−27.8755	+	24.6428i	−1.31846	+	1.16556i
$448$	1.03162	+	1.03162i	0.0487396	+	0.0487396i
$449$		−	17.9365i		−	0.846477i	−0.906018	−	0.423239i	$-0.860893\pi$
$449$		−	17.9365i		−	0.846477i	0.906018	−	0.423239i	$-0.139107\pi$
$450$	−11.7448	+	9.33060i	−0.553654	+	0.439849i
$451$	6.13791			0.289023
$452$	5.71439	−	5.71439i	0.268782	−	0.268782i
$453$	−5.60462	+	4.95466i	−0.263328	+	0.232790i
$454$		−	10.7924i		−	0.506511i
$455$	10.6478	+	4.99762i	0.499176	+	0.234292i
$456$	−11.0237	−	0.678547i	−0.516230	−	0.0317759i
$457$	23.6112	−	23.6112i	1.10449	−	1.10449i	0.110624	−	0.993862i	$-0.464715\pi$
$457$	23.6112	−	23.6112i	1.10449	−	1.10449i	0.993862	−	0.110624i	$-0.0352850\pi$
$458$	−16.2846	−	16.2846i	−0.760929	−	0.760929i
$459$	−2.45796	+	13.1760i	−0.114728	+	0.615004i
$460$	7.99230	−	8.06375i	0.372643	−	0.375974i
$461$	−25.8095			−1.20207			−0.601035	−	0.799223i	$-0.705245\pi$
$461$	−25.8095			−1.20207			−0.601035	+	0.799223i	$0.705245\pi$
$462$	6.19614	+	7.00897i	0.288271	+	0.326087i
$463$	20.9097	+	20.9097i	0.971756	+	0.971756i	0.999612	−	0.0278563i	$-0.00886808\pi$
$463$	20.9097	+	20.9097i	0.971756	+	0.971756i	−0.0278563	+	0.999612i	$0.508868\pi$
$464$	0.495771			0.0230156
$465$	−8.34870	+	7.44696i	−0.387162	+	0.345344i
$466$			27.9267i			1.29368i
$467$	3.81021	−	3.81021i	0.176315	−	0.176315i	−0.613432	−	0.789747i	$-0.710212\pi$
$467$	3.81021	−	3.81021i	0.176315	−	0.176315i	0.789747	+	0.613432i	$0.210212\pi$
$468$	−2.35167	−	10.5579i	−0.108706	−	0.488040i
$469$		−	14.0198i		−	0.647375i
$470$	−0.0393501	−	8.84290i	−0.00181508	−	0.407893i
$471$	0.419356	−	6.81285i	0.0193229	−	0.313920i
$472$	0.489709	+	0.489709i	0.0225407	+	0.0225407i
$473$	−32.1573	+	32.1573i	−1.47859	+	1.47859i
$474$	−10.5455	−	0.649112i	−0.484369	−	0.0298147i
$475$	31.8815	−	0.283745i	1.46283	−	0.0130191i
$476$	−3.76328			−0.172490
$477$	19.7519	−	15.4071i	0.904376	−	0.705441i
$478$	1.74493	−	1.74493i	0.0798112	−	0.0798112i
$479$			11.7705i			0.537807i	0.963167	+	0.268903i	$0.0866612\pi$
$479$			11.7705i			0.537807i	−0.963167	+	0.268903i	$0.913339\pi$
$480$	−0.220742	+	3.86669i	−0.0100754	+	0.176489i
$481$	9.55956	+	4.53886i	0.435878	+	0.206954i
$482$	14.9951	−	14.9951i	0.683009	−	0.683009i
$483$	−8.49792	−	9.61269i	−0.386669	−	0.437393i
$484$			2.70578i			0.122990i
$485$	−15.5449	+	15.6838i	−0.705857	+	0.712167i
$486$	4.71649	−	14.8578i	0.213944	−	0.673964i
$487$	3.51182	−	3.51182i	0.159136	−	0.159136i	−0.623048	−	0.782184i	$-0.714106\pi$
$487$	3.51182	−	3.51182i	0.159136	−	0.159136i	0.782184	+	0.623048i	$0.214106\pi$
$488$	8.53366	−	8.53366i	0.386300	−	0.386300i
$489$	2.08988	−	33.9521i	0.0945074	−	1.53537i
$490$	7.66818	−	7.73673i	0.346413	−	0.349510i
$491$			32.8608i			1.48299i	0.670960	+	0.741494i	$0.265882\pi$
$491$			32.8608i			1.48299i	−0.670960	+	0.741494i	$0.734118\pi$
$492$	2.15147	−	1.90197i	0.0969958	−	0.0857473i
$493$	−0.904267	+	0.904267i	−0.0407262	+	0.0407262i
$494$	−9.86104	+	20.7689i	−0.443669	+	0.934436i
$495$	−2.93608	+	24.6605i	−0.131967	+	1.10841i
$496$			2.88858i			0.129701i
$497$	−4.55168	+	4.55168i	−0.204171	+	0.204171i
$498$	7.85986	+	8.89094i	0.352209	+	0.398412i
$499$	−18.0149			−0.806460			−0.403230	−	0.915099i	$-0.632112\pi$
$499$	−18.0149			−0.806460			−0.403230	+	0.915099i	$0.632112\pi$
$500$	−0.149249	−	11.1793i	−0.00667462	−	0.499955i
$501$	2.01442	−	32.7263i	0.0899978	−	1.46210i
$502$	14.9044	−	14.9044i	0.665216	−	0.665216i
$503$	2.42308	+	2.42308i	0.108040	+	0.108040i	0.759060	−	0.651020i	$-0.225659\pi$
$503$	2.42308	+	2.42308i	0.108040	+	0.108040i	−0.651020	+	0.759060i	$0.725659\pi$
$504$	4.34376	+	0.536783i	0.193487	+	0.0239102i
$505$	−0.155103	−	34.8554i	−0.00690201	−	1.55105i
$506$		−	18.7973i		−	0.835640i
$507$	−22.2195	−	3.64611i	−0.986802	−	0.161929i
$508$	13.1211	−	13.1211i	0.582154	−	0.582154i
$509$		−	3.24224i		−	0.143710i	−0.997415	−	0.0718550i	$-0.977108\pi$
$509$		−	3.24224i		−	0.143710i	0.997415	−	0.0718550i	$-0.0228919\pi$
$510$	−6.65006	−	7.45531i	−0.294470	−	0.330127i
$511$	−16.5548			−0.732342
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−27.3282	+	18.7351i	−1.20657	+	0.827176i
$514$	12.0160			0.530003
$515$	−9.08633	+	9.16756i	−0.400392	+	0.403971i
$516$	−1.30718	+	21.2365i	−0.0575455	+	0.934883i
$517$	−10.3526	−	10.3526i	−0.455308	−	0.455308i
$518$	−3.02783	+	3.02783i	−0.133035	+	0.133035i
$519$	−0.0582106	+	0.945689i	−0.00255516	+	0.0415111i
$520$	7.29834	+	3.42553i	0.320053	+	0.150219i
$521$			22.6886i			0.994006i	0.867749	+	0.497003i	$0.165566\pi$
$521$			22.6886i			0.994006i	−0.867749	+	0.497003i	$0.834434\pi$
$522$	1.17273	−	0.914768i	0.0513291	−	0.0400383i
$523$	−31.3120	+	31.3120i	−1.36918	+	1.36918i	−0.507563	+	0.861615i	$0.669453\pi$
$523$	−31.3120	+	31.3120i	−1.36918	+	1.36918i	−0.861615	+	0.507563i	$0.830547\pi$
$524$	11.4677			0.500967
$525$	−12.6173	−	0.663983i	−0.550663	−	0.0289786i
$526$			17.7575i			0.774263i
$527$	−5.26865	−	5.26865i	−0.229506	−	0.229506i
$528$	4.24703	+	4.80417i	0.184828	+	0.209075i
$529$			2.78017i			0.120877i
$530$	0.0830849	+	18.6712i	0.00360898	+	0.811023i
$531$	2.06198	+	0.254810i	0.0894821	+	0.0110578i
$532$	−6.57820	−	6.57820i	−0.285201	−	0.285201i
$533$	−2.00543	−	5.63136i	−0.0868647	−	0.243921i
$534$	4.61109	+	0.283829i	0.199541	+	0.0122825i
$535$	−23.6801	+	23.8918i	−1.02378	+	1.03293i
$536$		−	9.60963i		−	0.415073i
$537$	27.0954	+	30.6498i	1.16925	+	1.32264i
$538$	−12.1805	−	12.1805i	−0.525140	−	0.525140i
$539$		−	18.0350i		−	0.776821i
$540$	6.61243	+	9.55384i	0.284554	+	0.411132i
$541$			23.3486i			1.00383i	0.864916	+	0.501916i	$0.167371\pi$
$541$			23.3486i			1.00383i	−0.864916	+	0.501916i	$0.832629\pi$
$542$	6.85177	−	6.85177i	0.294309	−	0.294309i
$543$	−11.6386	−	13.1653i	−0.499458	−	0.564978i
$544$	−2.57947			−0.110594
$545$	−29.0525	+	0.129281i	−1.24447	+	0.00553778i
$546$	4.40608	−	7.97481i	0.188563	−	0.341290i
$547$	0.00983851	+	0.00983851i	0.000420664	+	0.000420664i	0.707317	−	0.706896i	$-0.249905\pi$
$547$	0.00983851	+	0.00983851i	0.000420664	+	0.000420664i	−0.706896	+	0.707317i	$0.749905\pi$
$548$	−9.53679	+	9.53679i	−0.407391	+	0.407391i
$549$	4.44031	−	35.9319i	0.189508	−	1.53354i
$550$	−13.2050	−	12.9720i	−0.563062	−	0.553128i
$551$	−3.16131			−0.134677
$552$	−5.82474	−	6.58885i	−0.247918	−	0.280440i
$553$	−6.29284	−	6.29284i	−0.267599	−	0.267599i
$554$		−	21.7894i		−	0.925743i
$555$	−11.3488	−	0.647882i	−0.481730	−	0.0275011i
$556$	2.09695			0.0889305
$557$	20.4431	+	20.4431i	0.866200	+	0.866200i	0.992049	−	0.125849i	$-0.0401655\pi$
$557$	20.4431	+	20.4431i	0.866200	+	0.866200i	−0.125849	+	0.992049i	$0.540165\pi$
$558$	5.32983	+	6.83284i	0.225630	+	0.289257i
$559$	40.0101	+	18.9967i	1.69225	+	0.803476i
$560$	−2.29649	+	2.31702i	−0.0970444	+	0.0979119i
$561$	−16.5090	−	1.01619i	−0.697012	−	0.0429037i
$562$	7.62241	+	7.62241i	0.321532	+	0.321532i
$563$	−4.05212	−	4.05212i	−0.170777	−	0.170777i	0.616544	−	0.787321i	$-0.288532\pi$
$563$	−4.05212	−	4.05212i	−0.170777	−	0.170777i	−0.787321	+	0.616544i	$0.788532\pi$
$564$	−6.83681	−	0.420831i	−0.287882	−	0.0177202i
$565$	12.8345	+	12.7208i	0.539952	+	0.535167i
$566$	−6.30383			−0.264970
$567$	11.2655	−	6.74511i	0.473106	−	0.283268i
$568$	−3.11987	+	3.11987i	−0.130907	+	0.130907i
$569$	−21.1653			−0.887297			−0.443648	−	0.896201i	$-0.646316\pi$
$569$	−21.1653			−0.887297			−0.443648	+	0.896201i	$0.646316\pi$
$570$	1.40757	−	24.6562i	0.0589568	−	1.03273i
$571$	2.14561			0.0897912			0.0448956	−	0.998992i	$-0.485704\pi$
$571$	2.14561			0.0897912			0.0448956	+	0.998992i	$0.485704\pi$
$572$	12.5747	−	4.47806i	0.525773	−	0.187237i
$573$	−20.1320	+	17.7973i	−0.841024	+	0.743492i
$574$	2.41883			0.100960
$575$	18.1104	+	17.7909i	0.755257	+	0.741932i
$576$	2.97735	+	0.367928i	0.124056	+	0.0153303i
$577$	−20.9845	+	20.9845i	−0.873597	+	0.873597i	−0.992862	−	0.119266i	$-0.961946\pi$
$577$	−20.9845	+	20.9845i	−0.873597	+	0.873597i	0.119266	+	0.992862i	$0.461946\pi$
$578$	−7.31596	+	7.31596i	−0.304304	+	0.304304i
$579$	−0.873829	+	14.1962i	−0.0363151	+	0.589974i
$580$	0.00493302	+	1.10857i	0.000204832	+	0.0460307i
$581$			9.99578i			0.414695i
$582$	11.3290	+	12.8152i	0.469603	+	0.531207i
$583$	21.8588	+	21.8588i	0.905301	+	0.905301i
$584$	−11.3472			−0.469550
$585$	23.5846	−	5.36349i	0.975103	−	0.221753i
$586$	8.86519			0.366217
$587$	−25.6210	−	25.6210i	−1.05749	−	1.05749i	−0.998243	−	0.0592474i	$-0.981130\pi$
$587$	−25.6210	−	25.6210i	−1.05749	−	1.05749i	−0.0592474	−	0.998243i	$-0.518870\pi$
$588$	−5.58853	−	6.32164i	−0.230467	−	0.260700i
$589$		−	18.4192i		−	0.758949i
$590$	−1.09014	+	1.09988i	−0.0448803	+	0.0452815i
$591$	1.20506	−	19.5774i	0.0495695	−	0.805305i
$592$	−2.07537	+	2.07537i	−0.0852973	+	0.0852973i
$593$	−33.6720	+	33.6720i	−1.38274	+	1.38274i	−0.543033	+	0.839712i	$0.682724\pi$
$593$	−33.6720	+	33.6720i	−1.38274	+	1.38274i	−0.839712	+	0.543033i	$0.817276\pi$
$594$	18.9106	+	3.52774i	0.775912	+	0.144745i
$595$	−0.0374453	−	8.41486i	−0.00153511	−	0.344976i
$596$	−21.4810			−0.879898
$597$	14.5286	−	12.8438i	0.594618	−	0.525661i
$598$	−17.2460	+	6.14159i	−0.705240	+	0.251148i
$599$	28.6778			1.17174			0.585871	−	0.810404i	$-0.300753\pi$
$599$	28.6778			1.17174			0.585871	+	0.810404i	$0.300753\pi$
$600$	−8.64829	−	0.455115i	−0.353065	−	0.0185800i
$601$	35.1548			1.43399			0.716997	−	0.697077i	$-0.245516\pi$
$601$	35.1548			1.43399			0.716997	+	0.697077i	$0.245516\pi$
$602$	−12.6725	+	12.6725i	−0.516494	+	0.516494i
$603$	−17.7311	−	22.7313i	−0.722067	−	0.925690i
$604$	−4.31897			−0.175736
$605$	−6.05024	+	0.0269230i	−0.245977	+	0.00109458i
$606$	−26.9482	−	1.65876i	−1.09469	−	0.0673825i
$607$	3.38326	+	3.38326i	0.137322	+	0.137322i	0.772426	−	0.635104i	$-0.219043\pi$
$607$	3.38326	+	3.38326i	0.137322	+	0.137322i	−0.635104	+	0.772426i	$0.719043\pi$
$608$	−4.50891	−	4.50891i	−0.182860	−	0.182860i
$609$	1.25042	+	0.0769681i	0.0506696	+	0.00311890i
$610$	19.1666	+	18.9967i	0.776031	+	0.769155i
$611$	−6.11576	+	12.8807i	−0.247417	+	0.521099i
$612$	−6.10166	+	4.75949i	−0.246645	+	0.192391i
$613$	20.5151	+	20.5151i	0.828596	+	0.828596i	0.987323	−	0.158727i	$-0.0507388\pi$
$613$	20.5151	+	20.5151i	0.828596	+	0.828596i	−0.158727	+	0.987323i	$0.550739\pi$
$614$	26.0120			1.04976
$615$	4.27429	+	4.79186i	0.172356	+	0.193227i
$616$			5.40117i			0.217619i
$617$	−4.49927	−	4.49927i	−0.181134	−	0.181134i	0.610716	−	0.791850i	$-0.290882\pi$
$617$	−4.49927	−	4.49927i	−0.181134	−	0.181134i	−0.791850	+	0.610716i	$0.790882\pi$
$618$	6.62207	+	7.49077i	0.266379	+	0.301323i
$619$	−5.23035			−0.210226			−0.105113	−	0.994460i	$-0.533520\pi$
$619$	−5.23035			−0.210226			−0.105113	+	0.994460i	$0.533520\pi$
$620$	−6.45899	+	0.0287419i	−0.259399	+	0.00115430i
$621$	−25.9356	−	4.83824i	−1.04076	−	0.194152i
$622$	−1.25800	+	1.25800i	−0.0504412	+	0.0504412i
$623$	2.75159	+	2.75159i	0.110240	+	0.110240i
$624$	3.02006	−	5.46619i	0.120899	−	0.218823i
$625$	24.9960	−	0.444964i	0.999842	−	0.0177986i
$626$	−20.7376			−0.828840
$627$	−27.0815	−	30.6341i	−1.08153	−	1.22341i
$628$	2.78660	−	2.78660i	0.111197	−	0.111197i
$629$		−	7.57080i		−	0.301867i
$630$	−1.15705	+	9.71819i	−0.0460980	+	0.387182i
$631$		−	31.1770i		−	1.24114i	−0.784152	−	0.620568i	$-0.786902\pi$
$631$		−	31.1770i		−	1.24114i	0.784152	−	0.620568i	$-0.213098\pi$
$632$	−4.31332	−	4.31332i	−0.171574	−	0.171574i
$633$	3.84301	+	4.34714i	0.152746	+	0.172783i
$634$			10.6729i			0.423874i
$635$	29.4699	+	29.2088i	1.16948	+	1.15912i
$636$	14.4354	+	0.888554i	0.572402	+	0.0352335i
$637$	−16.5466	+	5.89253i	−0.655599	+	0.233470i
$638$	1.29783	+	1.29783i	0.0513816	+	0.0513816i
$639$	−1.62336	+	13.1365i	−0.0642190	+	0.519674i
$640$	−1.57409	+	1.58816i	−0.0622213	+	0.0627775i
$641$		−	4.46954i		−	0.176536i	−0.996097	−	0.0882681i	$-0.971867\pi$
$641$		−	4.46954i		−	0.176536i	0.996097	−	0.0882681i	$-0.0281332\pi$
$642$	17.2579	+	19.5218i	0.681115	+	0.770465i
$643$	9.58366	+	9.58366i	0.377943	+	0.377943i	0.870359	−	0.492417i	$-0.163886\pi$
$643$	9.58366	+	9.58366i	0.377943	+	0.377943i	−0.492417	+	0.870359i	$0.663886\pi$
$644$		−	7.40762i		−	0.291901i
$645$	−47.4987	−	2.71161i	−1.87026	−	0.106770i
$646$	16.4482			0.647144
$647$	−12.0307	+	12.0307i	−0.472977	+	0.472977i	−0.902877	−	0.429900i	$-0.858549\pi$
$647$	−12.0307	+	12.0307i	−0.472977	+	0.472977i	0.429900	+	0.902877i	$0.358549\pi$
$648$	7.72172	−	4.62331i	0.303338	−	0.181621i
$649$			2.56392i			0.100643i
$650$	−7.58701	+	16.3535i	−0.297587	+	0.641437i
$651$	−0.448449	+	7.28549i	−0.0175761	+	0.285541i
$652$	13.8871	−	13.8871i	0.543861	−	0.543861i
$653$	−7.52183	−	7.52183i	−0.294352	−	0.294352i	0.544445	−	0.838797i	$-0.316740\pi$
$653$	−7.52183	−	7.52183i	−0.294352	−	0.294352i	−0.838797	+	0.544445i	$0.816740\pi$
$654$	−1.38260	+	22.4617i	−0.0540639	+	0.878321i
$655$	0.114105	+	25.6422i	0.00445847	+	1.00192i
$656$	1.65794			0.0647317
$657$	−26.8415	+	20.9372i	−1.04719	+	0.816838i
$658$	−4.07976	−	4.07976i	−0.159046	−	0.159046i
$659$	−35.5017			−1.38295			−0.691475	−	0.722400i	$-0.743039\pi$
$659$	−35.5017			−1.38295			−0.691475	+	0.722400i	$0.743039\pi$
$660$	−10.7001	+	9.54436i	−0.416500	+	0.371514i
$661$			22.1943i			0.863260i	0.902051	+	0.431630i	$0.142061\pi$
$661$			22.1943i			0.863260i	−0.902051	+	0.431630i	$0.857939\pi$
$662$	2.96259	−	2.96259i	0.115144	−	0.115144i
$663$	4.46163	+	15.4786i	0.173276	+	0.601139i
$664$			6.85143i			0.265887i
$665$	14.6437	−	14.7746i	0.567859	−	0.572935i
$666$	−1.07988	+	8.73859i	−0.0418444	+	0.338613i
$667$	−1.77996	−	1.77996i	−0.0689202	−	0.0689202i
$668$	13.3857	−	13.3857i	0.517910	−	0.517910i
$669$	−1.33179	+	21.6363i	−0.0514901	+	0.836507i
$670$	21.4876	−	0.0956176i	0.830137	−	0.00369403i
$671$	44.6788			1.72481
$672$	1.67367	+	1.89322i	0.0645632	+	0.0730327i
$673$	9.51386	−	9.51386i	0.366732	−	0.366732i	−0.499552	−	0.866284i	$-0.666502\pi$
$673$	9.51386	−	9.51386i	0.366732	−	0.366732i	0.866284	+	0.499552i	$0.166502\pi$
$674$			21.8952i			0.843371i
$675$	−21.2970	+	14.8808i	−0.819723	+	0.572761i
$676$	−8.21698	−	10.0738i	−0.316038	−	0.387453i
$677$	−17.0253	+	17.0253i	−0.654337	+	0.654337i	−0.954034	−	0.299697i	$-0.903114\pi$
$677$	−17.0253	+	17.0253i	−0.654337	+	0.654337i	0.299697	+	0.954034i	$0.403114\pi$
$678$	10.4870	−	9.27084i	0.402751	−	0.356044i
$679$			14.4077i			0.552916i
$680$	−0.0256662	−	5.76782i	−0.000984255	−	0.221186i
$681$	1.14845	−	18.6576i	0.0440086	−	0.714962i
$682$	−7.56172	+	7.56172i	−0.289553	+	0.289553i
$683$	−28.1737	+	28.1737i	−1.07804	+	1.07804i	−0.0813495	+	0.996686i	$0.525923\pi$
$683$	−28.1737	+	28.1737i	−1.07804	+	1.07804i	−0.996686	+	0.0813495i	$0.974077\pi$
$684$	−18.9853	−	2.34612i	−0.725920	−	0.0897060i
$685$	−21.4196	−	21.2298i	−0.818400	−	0.811149i
$686$		−	17.3198i		−	0.661271i
$687$	−26.4196	−	29.8853i	−1.00797	−	1.14020i
$688$	−8.68616	+	8.68616i	−0.331157	+	0.331157i
$689$	12.9130	−	27.1968i	0.491945	−	1.03611i
$690$	14.6750	−	13.0900i	0.558668	−	0.498326i
$691$			7.58330i			0.288482i	0.989543	+	0.144241i	$0.0460741\pi$
$691$			7.58330i			0.288482i	−0.989543	+	0.144241i	$0.953926\pi$
$692$	−0.386807	+	0.386807i	−0.0147042	+	0.0147042i
$693$	9.96592	+	12.7763i	0.378574	+	0.485332i
$694$	14.0964			0.535094
$695$	0.0208651	+	4.68888i	0.000791457	+	0.177859i
$696$	0.857079	+	0.0527564i	0.0324875	+	0.00199972i
$697$	−3.02402	+	3.02402i	−0.114543	+	0.114543i
$698$	−17.4957	−	17.4957i	−0.662220	−	0.662220i
$699$	−2.97175	+	48.2790i	−0.112402	+	1.82608i
$700$	−5.20381	−	5.11200i	−0.196686	−	0.193216i
$701$		−	19.1834i		−	0.724547i	−0.932072	−	0.362273i	$-0.882001\pi$
$701$		−	19.1834i		−	0.724547i	0.932072	−	0.362273i	$-0.117999\pi$
$702$	−2.94202	−	18.5026i	−0.111039	−	0.698334i
$703$	13.2337	−	13.2337i	0.499120	−	0.499120i
$704$			3.70213i			0.139529i
$705$	0.872970	−	15.2916i	0.0328779	−	0.575915i
$706$	5.89859			0.221996
$707$	−16.0809	−	16.0809i	−0.604785	−	0.604785i
$708$	0.794488	+	0.898710i	0.0298587	+	0.0337756i
$709$	−2.73514			−0.102720			−0.0513602	−	0.998680i	$-0.516356\pi$
$709$	−2.73514			−0.102720			−0.0513602	+	0.998680i	$0.516356\pi$
$710$	−7.00721	−	6.94512i	−0.262976	−	0.260646i
$711$	−18.1617	−	2.24434i	−0.681117	−	0.0841694i
$712$	1.88603	+	1.88603i	0.0706820	+	0.0706820i
$713$	10.3708	−	10.3708i	0.388389	−	0.388389i
$714$	−6.50588	−	0.400461i	−0.243476	−	0.0149869i
$715$	10.1383	+	28.0730i	0.379150	+	1.04987i
$716$			23.6190i			0.882684i
$717$	3.20228	−	2.83091i	0.119591	−	0.105722i
$718$	1.80464	−	1.80464i	0.0673485	−	0.0673485i
$719$	52.8821			1.97217			0.986084	−	0.166248i	$-0.0531652\pi$
$719$	52.8821			1.97217			0.986084	+	0.166248i	$0.0531652\pi$
$720$	−0.793079	+	6.66116i	−0.0295563	+	0.248247i
$721$			8.42162i			0.313637i
$722$	15.3163	+	15.3163i	0.570014	+	0.570014i
$723$	27.5189	−	24.3276i	1.02344	−	0.904752i
$724$		−	10.1453i		−	0.377047i
$725$	−2.47876	+	0.0220609i	−0.0920587	+	0.000819322i
$726$	−0.287929	+	4.67769i	−0.0106860	+	0.173605i
$727$	−2.36804	−	2.36804i	−0.0878259	−	0.0878259i	0.661829	−	0.749655i	$-0.269781\pi$
$727$	−2.36804	−	2.36804i	−0.0878259	−	0.0878259i	−0.749655	+	0.661829i	$0.769781\pi$
$728$	4.95542	−	1.76471i	0.183660	−	0.0654045i
$729$	9.73483	−	25.1840i	0.360549	−	0.932740i
$730$	−0.112907	−	25.3729i	−0.00417887	−	0.939092i
$731$		−	31.6864i		−	1.17197i
$732$	15.6609	−	13.8447i	0.578843	−	0.511715i
$733$	−3.85830	−	3.85830i	−0.142510	−	0.142510i	0.632253	−	0.774762i	$-0.282130\pi$
$733$	−3.85830	−	3.85830i	−0.142510	−	0.142510i	−0.774762	+	0.632253i	$0.782130\pi$
$734$			18.4716i			0.681800i
$735$	14.0799	−	12.5591i	0.519344	−	0.463250i
$736$		−	5.07742i		−	0.187156i
$737$	25.1561	−	25.1561i	0.926637	−	0.926637i
$738$	3.92181	−	3.05914i	0.144364	−	0.112608i
$739$	−31.7224			−1.16693			−0.583464	−	0.812139i	$-0.698303\pi$
$739$	−31.7224			−1.16693			−0.583464	+	0.812139i	$0.698303\pi$
$740$	−4.66128	−	4.61998i	−0.171352	−	0.169834i
$741$	−19.2576	+	34.8555i	−0.707446	+	1.28045i
$742$	8.61412	+	8.61412i	0.316234	+	0.316234i
$743$	−13.7641	+	13.7641i	−0.504957	+	0.504957i	−0.912974	−	0.408017i	$-0.866220\pi$
$743$	−13.7641	+	13.7641i	−0.504957	+	0.504957i	0.408017	+	0.912974i	$0.366220\pi$
$744$	−0.307381	+	4.99371i	−0.0112691	+	0.183078i
$745$	−0.213741	−	48.0326i	−0.00783085	−	1.75978i
$746$	17.6603			0.646591
$747$	12.6419	+	16.2069i	0.462541	+	0.592978i
$748$	−6.75254	−	6.75254i	−0.246897	−	0.246897i
$749$			21.9477i			0.801953i
$750$	0.931606	−	19.3425i	0.0340174	−	0.706288i
$751$	−36.2372			−1.32231			−0.661157	−	0.750247i	$-0.729934\pi$
$751$	−36.2372			−1.32231			−0.661157	+	0.750247i	$0.729934\pi$
$752$	−2.79640	−	2.79640i	−0.101974	−	0.101974i
$753$	27.3524	−	24.1804i	0.996779	−	0.881183i
$754$	0.766686	−	1.61476i	0.0279210	−	0.0588061i
$755$	−0.0429746	−	9.65741i	−0.00156400	−	0.351469i
$756$	7.45228	+	1.39021i	0.271037	+	0.0505615i
$757$	−21.7590	−	21.7590i	−0.790845	−	0.790845i	0.190787	−	0.981632i	$-0.438896\pi$
$757$	−21.7590	−	21.7590i	−0.790845	−	0.790845i	−0.981632	+	0.190787i	$0.938896\pi$
$758$	−1.20359	−	1.20359i	−0.0437162	−	0.0437162i
$759$	2.00027	−	32.4963i	0.0726051	−	1.17954i
$760$	10.0373	−	10.1270i	0.364090	−	0.367345i
$761$	−14.1444			−0.512735			−0.256367	−	0.966579i	$-0.582526\pi$
$761$	−14.1444			−0.512735			−0.256367	+	0.966579i	$0.582526\pi$
$762$	24.0797	−	21.2872i	0.872316	−	0.771155i
$763$	−13.4037	+	13.4037i	−0.485245	+	0.485245i
$764$	−15.5138			−0.561271
$765$	−10.7031	−	13.5962i	−0.386973	−	0.491573i
$766$	35.1963			1.27169
$767$	2.35233	−	0.837705i	0.0849376	−	0.0302478i
$768$	1.14719	+	1.29768i	0.0413955	+	0.0468259i
$769$	17.8477			0.643604			0.321802	−	0.946807i	$-0.395712\pi$
$769$	17.8477			0.643604			0.321802	+	0.946807i	$0.395712\pi$
$770$	−12.0773	+	0.0537426i	−0.435234	+	0.00193675i
$771$	20.7730	+	1.27866i	0.748122	+	0.0460497i
$772$	−5.80655	+	5.80655i	−0.208982	+	0.208982i
$773$	17.8480	−	17.8480i	0.641948	−	0.641948i	−0.309086	−	0.951034i	$-0.600023\pi$
$773$	17.8480	−	17.8480i	0.641948	−	0.641948i	0.951034	+	0.309086i	$0.100023\pi$
$774$	−4.51966	+	36.5741i	−0.162456	+	1.31463i
$775$	−0.128536	−	14.4423i	−0.00461716	−	0.518783i
$776$			9.87549i			0.354509i
$777$	−5.55665	+	4.91225i	−0.199344	+	0.176226i
$778$	13.2212	+	13.2212i	0.474002	+	0.474002i
$779$	−10.5720			−0.378780
$780$	12.2527	+	6.69861i	0.438717	+	0.239849i
$781$	−16.3344			−0.584490
$782$	9.26101	+	9.26101i	0.331173	+	0.331173i
$783$	2.12474	−	1.45664i	0.0759319	−	0.0520560i
$784$		−	4.87151i		−	0.173983i
$785$	6.25869	+	6.20324i	0.223382	+	0.221403i
$786$	19.8251	+	1.22031i	0.707136	+	0.0435268i
$787$	−7.56156	+	7.56156i	−0.269540	+	0.269540i	−0.828915	−	0.559375i	$-0.811041\pi$
$787$	−7.56156	+	7.56156i	−0.269540	+	0.269540i	0.559375	+	0.828915i	$0.311041\pi$
$788$	8.00755	−	8.00755i	0.285257	−	0.285257i
$789$	−1.88962	+	30.6988i	−0.0672723	+	1.09291i
$790$	9.60185	−	9.68769i	0.341619	−	0.344673i
$791$	11.7902			0.419211
$792$	6.83096	+	8.75728i	0.242727	+	0.311177i
$793$	−14.5978	−	40.9916i	−0.518384	−	1.45565i
$794$	9.69372			0.344017
$795$	−1.84321	+	32.2871i	−0.0653720	+	1.14511i
$796$	11.1959			0.396828
$797$	12.1869	−	12.1869i	0.431680	−	0.431680i	−0.457519	−	0.889200i	$-0.651262\pi$
$797$	12.1869	−	12.1869i	0.431680	−	0.431680i	0.889200	+	0.457519i	$0.151262\pi$
$798$	−10.6723	−	12.0723i	−0.377794	−	0.427353i
$799$	10.2010			0.360887
$800$	−3.56686	−	3.50393i	−0.126108	−	0.123883i
$801$	7.94134	+	0.981356i	0.280594	+	0.0346745i
$802$	−13.4487	−	13.4487i	−0.474891	−	0.474891i
$803$	−29.7047	−	29.7047i	−1.04826	−	1.04826i
$804$	1.02259	−	16.6129i	0.0360638	−	0.585893i
$805$	16.5638	−	0.0737072i	0.583796	−	0.00259784i
$806$	9.40828	+	4.46704i	0.331393	+	0.157345i
$807$	−19.7613	−	22.3536i	−0.695630	−	0.786884i
$808$	−11.0224	−	11.0224i	−0.387766	−	0.387766i
$809$	−27.7750			−0.976516			−0.488258	−	0.872699i	$-0.662368\pi$
$809$	−27.7750			−0.976516			−0.488258	+	0.872699i	$0.662368\pi$
$810$	10.4148	+	17.2201i	0.365938	+	0.605053i
$811$		−	5.31945i		−	0.186791i	−0.995629	−	0.0933957i	$-0.970228\pi$
$811$		−	5.31945i		−	0.186791i	0.995629	−	0.0933957i	$-0.0297722\pi$
$812$	0.511449	+	0.511449i	0.0179483	+	0.0179483i
$813$	12.5743	−	11.1161i	0.441000	−	0.389858i
$814$	−10.8658			−0.380847
$815$	31.1904	+	30.9140i	1.09255	+	1.08287i
$816$	−4.45933	−	0.274489i	−0.156108	−	0.00960902i
$817$	55.3878	−	55.3878i	1.93777	−	1.93777i
$818$	−15.8553	−	15.8553i	−0.554368	−	0.554368i
$819$	8.46575	−	13.3178i	0.295817	−	0.465362i
$820$	0.0164968	+	3.70723i	0.000576094	+	0.129462i
$821$	35.6438			1.24398			0.621989	−	0.783026i	$-0.286325\pi$
$821$	35.6438			1.24398			0.621989	+	0.783026i	$0.286325\pi$
$822$	−17.5018	+	15.4722i	−0.610447	+	0.539654i
$823$	19.4031	−	19.4031i	0.676350	−	0.676350i	−0.282822	−	0.959172i	$-0.591271\pi$
$823$	19.4031	−	19.4031i	0.676350	−	0.676350i	0.959172	+	0.282822i	$0.0912706\pi$
$824$			5.77245i			0.201093i
$825$	−21.4481	−	23.8309i	−0.746727	−	0.829686i
$826$			1.01039i			0.0351560i
$827$	−18.4487	−	18.4487i	−0.641525	−	0.641525i	0.309406	−	0.950930i	$-0.399870\pi$
$827$	−18.4487	−	18.4487i	−0.641525	−	0.641525i	−0.950930	+	0.309406i	$0.899870\pi$
$828$	−9.36856	−	12.0105i	−0.325580	−	0.417393i
$829$		−	21.9653i		−	0.762885i	−0.924393	−	0.381443i	$-0.875427\pi$
$829$		−	21.9653i		−	0.762885i	0.924393	−	0.381443i	$-0.124573\pi$
$830$	−15.3201	+	0.0681730i	−0.531769	+	0.00236632i
$831$	2.31867	−	37.6691i	0.0804338	−	1.30673i
$832$	3.39660	−	1.20959i	0.117756	−	0.0419350i
$833$	8.88545	+	8.88545i	0.307863	+	0.307863i
$834$	3.62516	+	0.223142i	0.125529	+	0.00772678i
$835$	30.0643	+	29.7979i	1.04042	+	1.03120i
$836$		−	23.6069i		−	0.816460i
$837$	8.48700	+	12.3796i	0.293354	+	0.427903i
$838$	−0.378921	−	0.378921i	−0.0130896	−	0.0130896i
$839$		−	28.4339i		−	0.981647i	−0.871259	−	0.490823i	$-0.836696\pi$
$839$		−	28.4339i		−	0.981647i	0.871259	−	0.490823i	$-0.163304\pi$
$840$	−4.21668	+	3.76124i	−0.145489	+	0.129775i
$841$	−28.7542			−0.991525
$842$	16.6817	−	16.6817i	0.574890	−	0.574890i
$843$	12.3663	+	13.9886i	0.425919	+	0.481792i
$844$			3.34994i			0.115310i
$845$	22.4437	−	18.4738i	0.772086	−	0.635517i
$846$	−11.7746	−	1.45505i	−0.404817	−	0.0500256i
$847$	−2.79134	+	2.79134i	−0.0959115	+	0.0959115i
$848$	5.90440	+	5.90440i	0.202758	+	0.202758i
$849$	−10.8979	−	0.670808i	−0.374016	−	0.0230221i
$850$	12.8968	−	0.114782i	0.442358	−	0.00393698i
$851$	14.9023			0.510845
$852$	−5.72555	+	5.06156i	−0.196154	+	0.173406i
$853$	−13.9812	−	13.9812i	−0.478707	−	0.478707i	0.426011	−	0.904718i	$-0.359918\pi$
$853$	−13.9812	−	13.9812i	−0.478707	−	0.478707i	−0.904718	+	0.426011i	$0.859918\pi$
$854$	17.6070			0.602500
$855$	5.05712	−	42.4753i	0.172950	−	1.45262i
$856$			15.0437i			0.514182i
$857$	−37.1382	+	37.1382i	−1.26862	+	1.26862i	−0.321815	+	0.946803i	$0.604293\pi$
$857$	−37.1382	+	37.1382i	−1.26862	+	1.26862i	−0.946803	+	0.321815i	$0.895707\pi$
$858$	22.2153	−	6.40347i	0.758419	−	0.218611i
$859$			28.5944i			0.975628i	0.872948	+	0.487814i	$0.162205\pi$
$859$			28.5944i			0.975628i	−0.872948	+	0.487814i	$0.837795\pi$
$860$	−19.5091	−	19.3362i	−0.665254	−	0.659360i
$861$	4.18162	+	0.257394i	0.142509	+	0.00877196i
$862$	10.6493	+	10.6493i	0.362716	+	0.362716i
$863$	28.9597	−	28.9597i	0.985800	−	0.985800i	−0.0141001	−	0.999901i	$-0.504488\pi$
$863$	28.9597	−	28.9597i	0.985800	−	0.985800i	0.999901	+	0.0141001i	$0.00448836\pi$
$864$	5.10803	+	0.952895i	0.173779	+	0.0324181i
$865$	−0.868766	−	0.861068i	−0.0295389	−	0.0292772i
$866$	11.9018			0.404440
$867$	−13.4262	+	11.8692i	−0.455977	+	0.403098i
$868$	−2.97992	+	2.97992i	−0.101145	+	0.101145i
$869$		−	22.5828i		−	0.766070i
$870$	−0.109438	+	1.91699i	−0.00371028	+	0.0649921i
$871$	−31.2992	−	14.8608i	−1.06053	−	0.503539i
$872$	−9.18729	+	9.18729i	−0.311121	+	0.311121i
$873$	18.2217	+	23.3602i	0.616710	+	0.790622i
$874$			32.3765i			1.09515i
$875$	11.3789	−	11.6868i	0.384677	−	0.395087i
$876$	−19.6168	−	1.20749i	−0.662790	−	0.0407972i
$877$	−28.6850	+	28.6850i	−0.968623	+	0.968623i	−0.999522	−	0.0308995i	$-0.990163\pi$
$877$	−28.6850	+	28.6850i	−0.968623	+	0.968623i	0.0308995	+	0.999522i	$0.490163\pi$
$878$	25.1975	−	25.1975i	0.850376	−	0.850376i
$879$	15.3259	+	0.943369i	0.516931	+	0.0318190i
$880$	−8.27814	+	0.0368369i	−0.279056	+	0.00124177i
$881$		−	32.8722i		−	1.10749i	−0.832686	−	0.553746i	$-0.813198\pi$
$881$		−	32.8722i		−	1.10749i	0.832686	−	0.553746i	$-0.186802\pi$
$882$	−8.98863	−	11.5234i	−0.302663	−	0.388014i
$883$	10.1933	−	10.1933i	0.343032	−	0.343032i	−0.514474	−	0.857506i	$-0.672013\pi$
$883$	10.1933	−	10.1933i	0.343032	−	0.343032i	0.857506	+	0.514474i	$0.172013\pi$
$884$	−3.98902	+	8.40151i	−0.134165	+	0.282573i
$885$	−2.00165	+	1.78545i	−0.0672848	+	0.0600173i
$886$			19.5608i			0.657158i
$887$	0.276224	−	0.276224i	0.00927471	−	0.00927471i	−0.702454	−	0.711729i	$-0.747912\pi$
$887$	0.276224	−	0.276224i	0.00927471	−	0.00927471i	0.711729	+	0.702454i	$0.247912\pi$
$888$	−3.80871	+	3.36701i	−0.127812	+	0.112990i
$889$	27.0720			0.907967
$890$	−4.19848	+	4.23602i	−0.140734	+	0.141992i
$891$	32.3169	+	8.11101i	1.08266	+	0.271729i
$892$	−8.84969	+	8.84969i	−0.296309	+	0.296309i
$893$	17.8314	+	17.8314i	0.596705	+	0.596705i
$894$	−37.1360	−	2.28586i	−1.24201	−	0.0764505i
$895$	−52.8132	+	0.235014i	−1.76535	+	0.00785564i
$896$			1.45893i			0.0487396i
$897$	−30.4680	+	8.78226i	−1.01730	+	0.293231i
$898$	12.6830	−	12.6830i	0.423239	−	0.423239i
$899$			1.43207i			0.0477623i
$900$	−14.9025	−	1.70708i	−0.496752	−	0.0569027i
$901$	−21.5388			−0.717561
$902$	4.34016	+	4.34016i	0.144512	+	0.144512i
$903$	−23.2565	+	20.5595i	−0.773929	+	0.684177i
$904$	8.08137			0.268782
$905$	22.6854	−	0.100948i	0.754087	−	0.00335562i
$906$	−7.46654	−	0.459593i	−0.248059	−	0.0152690i
$907$	−11.6761	−	11.6761i	−0.387698	−	0.387698i	0.486168	−	0.873866i	$-0.338394\pi$
$907$	−11.6761	−	11.6761i	−0.387698	−	0.387698i	−0.873866	+	0.486168i	$0.838394\pi$
$908$	7.63136	−	7.63136i	0.253256	−	0.253256i
$909$	−46.4109	−	5.73526i	−1.53935	−	0.190226i
$910$	3.99528	+	11.0630i	0.132442	+	0.366734i
$911$		−	22.6478i		−	0.750355i	−0.926953	−	0.375177i	$-0.877582\pi$
$911$		−	22.6478i		−	0.750355i	0.926953	−	0.375177i	$-0.122418\pi$
$912$	−7.31510	−	8.27471i	−0.242227	−	0.274003i
$913$	−17.9357	+	17.9357i	−0.593585	+	0.593585i
$914$	33.3913			1.10449
$915$	31.1132	+	34.8807i	1.02857	+	1.15312i
$916$		−	23.0299i		−	0.760929i
$917$	11.8303	+	11.8303i	0.390671	+	0.390671i
$918$	−11.0549	+	7.57881i	−0.364866	+	0.250138i
$919$			13.8196i			0.455867i	0.973677	+	0.227933i	$0.0731969\pi$
$919$			13.8196i			0.455867i	−0.973677	+	0.227933i	$0.926803\pi$
$920$	11.3533	−	0.0505213i	0.374309	−	0.00166564i
$921$	44.9690	+	2.76801i	1.48178	+	0.0912090i
$922$	−18.2501	−	18.2501i	−0.601035	−	0.601035i
$923$	5.33690	+	14.9863i	0.175666	+	0.493281i
$924$	−0.574753	+	9.33742i	−0.0189080	+	0.307179i
$925$	10.2841	−	10.4688i	0.338139	−	0.344212i
$926$			29.5708i			0.971756i
$927$	10.6510	+	13.6546i	0.349824	+	0.448474i
$928$	0.350563	+	0.350563i	0.0115078	+	0.0115078i
$929$			5.46712i			0.179371i	0.995970	+	0.0896853i	$0.0285861\pi$
$929$			5.46712i			0.179371i	−0.995970	+	0.0896853i	$0.971414\pi$
$930$	−11.1692	−	0.637630i	−0.366253	−	0.0209087i
$931$			31.0635i			1.01806i
$932$	−19.7471	+	19.7471i	−0.646839	+	0.646839i
$933$	−2.30867	+	2.04094i	−0.0755825	+	0.0668172i
$934$	5.38845			0.176315
$935$	15.0318	−	15.1662i	0.491593	−	0.495987i
$936$	5.80270	−	9.12846i	0.189667	−	0.298373i
$937$	23.3846	+	23.3846i	0.763942	+	0.763942i	0.977033	−	0.213090i	$-0.0683529\pi$
$937$	23.3846	+	23.3846i	0.763942	+	0.763942i	−0.213090	+	0.977033i	$0.568353\pi$
$938$	9.91351	−	9.91351i	0.323687	−	0.323687i
$939$	−35.8507	−	2.20674i	−1.16994	−	0.0720143i
$940$	6.22505	−	6.28070i	0.203039	−	0.204854i
$941$	−32.6174			−1.06330			−0.531648	−	0.846965i	$-0.678427\pi$
$941$	−32.6174			−1.06330			−0.531648	+	0.846965i	$0.678427\pi$
$942$	5.11394	−	4.52088i	0.166621	−	0.147298i
$943$	−5.95247	−	5.95247i	−0.193839	−	0.193839i
$944$			0.692553i			0.0225407i
$945$	−3.03442	+	16.6775i	−0.0987098	+	0.542518i
$946$	−45.4773			−1.47859
$947$	17.6795	+	17.6795i	0.574506	+	0.574506i	0.933384	−	0.358879i	$-0.116841\pi$
$947$	17.6795	+	17.6795i	0.574506	+	0.574506i	−0.358879	+	0.933384i	$0.616841\pi$
$948$	−6.99778	−	7.91576i	−0.227277	−	0.257092i
$949$	−17.5479	+	36.9586i	−0.569628	+	1.19973i
$950$	22.7443	+	22.3430i	0.737922	+	0.724903i
$951$	−1.13573	+	18.4510i	−0.0368285	+	0.598316i
$952$	−2.66104	−	2.66104i	−0.0862448	−	0.0862448i
$953$	33.1565	+	33.1565i	1.07404	+	1.07404i	0.997030	+	0.0770143i	$0.0245387\pi$
$953$	33.1565	+	33.1565i	1.07404	+	1.07404i	0.0770143	+	0.997030i	$0.475461\pi$
$954$	24.8611	+	3.07223i	0.804908	+	0.0994670i
$955$	−0.154366	−	34.6897i	−0.00499516	−	1.12253i
$956$	2.46770			0.0798112
$957$	2.10556	+	2.38177i	0.0680630	+	0.0769916i
$958$	−8.32298	+	8.32298i	−0.268903	+	0.268903i
$959$	−19.6767			−0.635395
$960$	−2.89025	+	2.57807i	−0.0932824	+	0.0832069i
$961$	22.6561			0.730843
$962$	3.55017	+	9.96909i	0.114462	+	0.321416i
$963$	27.7577	+	35.5854i	0.894480	+	1.14672i
$964$	21.2063			0.683009
$965$	−13.0415	−	12.9259i	−0.419820	−	0.416100i
$966$	0.788265	−	12.8061i	0.0253620	−	0.412031i
$967$	−20.1304	+	20.1304i	−0.647349	+	0.647349i	−0.952351	−	0.305003i	$-0.901343\pi$
$967$	−20.1304	+	20.1304i	−0.647349	+	0.647349i	0.305003	+	0.952351i	$0.401343\pi$
$968$	−1.91327	+	1.91327i	−0.0614949	+	0.0614949i
$969$	28.4352	+	1.75029i	0.913471	+	0.0562275i
$970$	−22.0820	+	0.0982630i	−0.709012	+	0.00315504i
$971$		−	32.3175i		−	1.03712i	−0.855042	−	0.518559i	$-0.826469\pi$
$971$		−	32.3175i		−	1.03712i	0.855042	−	0.518559i	$-0.173531\pi$
$972$	13.8411	−	7.17100i	0.443954	−	0.230010i
$973$	2.16326	+	2.16326i	0.0693509	+	0.0693509i
$974$	4.96646			0.159136
$975$	−14.8565	+	27.4642i	−0.475788	+	0.879560i
$976$	12.0684			0.386300
$977$	14.1829	+	14.1829i	0.453752	+	0.453752i	0.896598	−	0.442846i	$-0.146031\pi$
$977$	14.1829	+	14.1829i	0.453752	+	0.453752i	−0.442846	+	0.896598i	$0.646031\pi$
$978$	25.4855	−	22.5300i	0.814937	−	0.720429i
$979$			9.87451i			0.315591i
$980$	10.8929	−	0.0484725i	0.347962	−	0.00154840i
$981$	−4.78041	+	38.6841i	−0.152627	+	1.23509i
$982$	−23.2361	+	23.2361i	−0.741494	+	0.741494i
$983$	−12.7080	+	12.7080i	−0.405323	+	0.405323i	−0.880104	−	0.474781i	$-0.842527\pi$
$983$	−12.7080	+	12.7080i	−0.405323	+	0.405323i	0.474781	+	0.880104i	$0.342527\pi$
$984$	2.86621	+	0.176426i	0.0913715	+	0.00562426i
$985$	17.9849	+	17.8256i	0.573047	+	0.567970i
$986$	−1.27883			−0.0407262
$987$	−6.61887	−	7.48715i	−0.210681	−	0.238318i
$988$	−21.6586	+	7.71302i	−0.689053	+	0.245384i
$989$	62.3714			1.98330
$990$	−19.5137	+	15.3615i	−0.620187	+	0.488220i
$991$	−5.24927			−0.166748			−0.0833742	−	0.996518i	$-0.526570\pi$
$991$	−5.24927			−0.166748			−0.0833742	+	0.996518i	$0.526570\pi$
$992$	−2.04253	+	2.04253i	−0.0648504	+	0.0648504i
$993$	5.43692	−	4.80640i	0.172535	−	0.152527i
$994$	−6.43705			−0.204171
$995$	0.111401	+	25.0345i	0.00353166	+	0.793648i
$996$	−0.729079	+	11.8446i	−0.0231018	+	0.375311i
$997$	−20.0308	−	20.0308i	−0.634381	−	0.634381i	0.314782	−	0.949164i	$-0.398068\pi$
$997$	−20.0308	−	20.0308i	−0.634381	−	0.634381i	−0.949164	+	0.314782i	$0.898068\pi$
$998$	−12.7385	−	12.7385i	−0.403230	−	0.403230i
$999$	−2.79676	+	14.9922i	−0.0884857	+	0.474331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.s.c.77.11	yes	24
3.2	odd	2		390.2.s.b.77.2	✓	24
5.3	odd	4		390.2.s.b.233.8	yes	24
13.12	even	2	inner	390.2.s.c.77.5	yes	24
15.8	even	4	inner	390.2.s.c.233.5	yes	24
39.38	odd	2		390.2.s.b.77.8	yes	24
65.38	odd	4		390.2.s.b.233.2	yes	24
195.38	even	4	inner	390.2.s.c.233.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.b.77.2	✓	24	3.2	odd	2
390.2.s.b.77.8	yes	24	39.38	odd	2
390.2.s.b.233.2	yes	24	65.38	odd	4
390.2.s.b.233.8	yes	24	5.3	odd	4
390.2.s.c.77.5	yes	24	13.12	even	2	inner
390.2.s.c.77.11	yes	24	1.1	even	1	trivial
390.2.s.c.233.5	yes	24	15.8	even	4	inner
390.2.s.c.233.11	yes	24	195.38	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.14719 + 1.29768i) q^{3} +1.00000i q^{4} +(-2.23605 + 0.00995019i) q^{5} +(-0.106413 + 1.72878i) q^{6} +(-1.03162 + 1.03162i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.367928 + 2.97735i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.14719 + 1.29768i) q^{3} +1.00000i q^{4} +(-2.23605 + 0.00995019i) q^{5} +(-0.106413 + 1.72878i) q^{6} +(-1.03162 + 1.03162i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.367928 + 2.97735i) q^{9} +(-1.58816 - 1.57409i) q^{10} -3.70213 q^{11} +(-1.29768 + 1.14719i) q^{12} +(1.20959 + 3.39660i) q^{13} -1.45893 q^{14} +(-2.57807 - 2.89025i) q^{15} -1.00000 q^{16} +(1.82396 - 1.82396i) q^{17} +(-2.36547 + 1.84514i) q^{18} +6.37656 q^{19} +(-0.00995019 - 2.23605i) q^{20} +(-2.52217 - 0.155249i) q^{21} +(-2.61780 - 2.61780i) q^{22} +(3.59028 + 3.59028i) q^{23} +(-1.72878 - 0.106413i) q^{24} +(4.99980 - 0.0444982i) q^{25} +(-1.54645 + 3.25707i) q^{26} +(-4.28572 + 2.93813i) q^{27} +(-1.03162 - 1.03162i) q^{28} -0.495771 q^{29} +(0.220742 - 3.86669i) q^{30} -2.88858i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.24703 - 4.80417i) q^{33} +2.57947 q^{34} +(2.29649 - 2.31702i) q^{35} +(-2.97735 - 0.367928i) q^{36} +(2.07537 - 2.07537i) q^{37} +(4.50891 + 4.50891i) q^{38} +(-3.02006 + 5.46619i) q^{39} +(1.57409 - 1.58816i) q^{40} -1.65794 q^{41} +(-1.67367 - 1.89322i) q^{42} +(8.68616 - 8.68616i) q^{43} -3.70213i q^{44} +(0.793079 - 6.66116i) q^{45} +5.07742i q^{46} +(2.79640 + 2.79640i) q^{47} +(-1.14719 - 1.29768i) q^{48} +4.87151i q^{49} +(3.56686 + 3.50393i) q^{50} +(4.45933 + 0.274489i) q^{51} +(-3.39660 + 1.20959i) q^{52} +(-5.90440 - 5.90440i) q^{53} +(-5.10803 - 0.952895i) q^{54} +(8.27814 - 0.0368369i) q^{55} -1.45893i q^{56} +(7.31510 + 8.27471i) q^{57} +(-0.350563 - 0.350563i) q^{58} -0.692553i q^{59} +(2.89025 - 2.57807i) q^{60} -12.0684 q^{61} +(2.04253 - 2.04253i) q^{62} +(-2.69194 - 3.45107i) q^{63} -1.00000i q^{64} +(-2.73849 - 7.58292i) q^{65} +(0.393954 - 6.40017i) q^{66} +(-6.79503 + 6.79503i) q^{67} +(1.82396 + 1.82396i) q^{68} +(-0.540302 + 8.77773i) q^{69} +(3.26224 - 0.0145167i) q^{70} +4.41216 q^{71} +(-1.84514 - 2.36547i) q^{72} +(8.02368 + 8.02368i) q^{73} +2.93502 q^{74} +(5.79345 + 6.43708i) q^{75} +6.37656i q^{76} +(3.81920 - 3.81920i) q^{77} +(-6.00069 + 1.72967i) q^{78} +6.09995i q^{79} +(2.23605 - 0.00995019i) q^{80} +(-8.72926 - 2.19090i) q^{81} +(-1.17234 - 1.17234i) q^{82} +(4.84469 - 4.84469i) q^{83} +(0.155249 - 2.52217i) q^{84} +(-4.06031 + 4.09661i) q^{85} +12.2841 q^{86} +(-0.568742 - 0.643350i) q^{87} +(2.61780 - 2.61780i) q^{88} -2.66725i q^{89} +(5.27094 - 4.14936i) q^{90} +(-4.75185 - 2.25617i) q^{91} +(-3.59028 + 3.59028i) q^{92} +(3.74844 - 3.31373i) q^{93} +3.95471i q^{94} +(-14.2583 + 0.0634480i) q^{95} +(0.106413 - 1.72878i) q^{96} +(6.98302 - 6.98302i) q^{97} +(-3.44468 + 3.44468i) q^{98} +(1.36212 - 11.0226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 + 12 * q^9	\( 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) \) 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

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