LMFDB - Embedded newform 100.2.g.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,2,Mod(21,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("100.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	100.g (of order $5$, degree $4$, 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:	$0.798504020213$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			21.1
Root			$-0.861543 - 2.65156i$ of defining polynomial
Character	$\chi$	$=$	100.21
Dual form			100.2.g.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25555 - 1.63875i) q^{3} +(-2.20302 - 0.383000i) q^{5} -2.70809 q^{7} +(1.47494 + 4.53940i) q^{9} +O(q^{10})$	\(q+(-2.25555 - 1.63875i) q^{3} +(-2.20302 - 0.383000i) q^{5} -2.70809 q^{7} +(1.47494 + 4.53940i) q^{9} +(1.91120 - 5.88208i) q^{11} +(-0.0683725 - 0.210429i) q^{13} +(4.34139 + 4.47409i) q^{15} +(2.51204 - 1.82510i) q^{17} +(-2.68270 + 1.94909i) q^{19} +(6.10822 + 4.43788i) q^{21} +(0.557161 - 1.71477i) q^{23} +(4.70662 + 1.68752i) q^{25} +(1.52753 - 4.70124i) q^{27} +(-3.77603 - 2.74345i) q^{29} +(-4.04356 + 2.93782i) q^{31} +(-13.9501 + 10.1353i) q^{33} +(5.96598 + 1.03720i) q^{35} +(-2.00918 - 6.18361i) q^{37} +(-0.190623 + 0.586678i) q^{39} +(-1.15044 - 3.54068i) q^{41} +11.1384 q^{43} +(-1.51074 - 10.5653i) q^{45} +(-3.60959 - 2.62252i) q^{47} +0.333733 q^{49} -8.65692 q^{51} +(2.32993 + 1.69279i) q^{53} +(-6.46327 + 12.2264i) q^{55} +9.24503 q^{57} +(-1.06770 - 3.28603i) q^{59} +(1.57525 - 4.84813i) q^{61} +(-3.99427 - 12.2931i) q^{63} +(0.0700319 + 0.489766i) q^{65} +(-7.18245 + 5.21835i) q^{67} +(-4.06678 + 2.95469i) q^{69} +(7.37333 + 5.35704i) q^{71} +(1.08812 - 3.34888i) q^{73} +(-7.85060 - 11.5193i) q^{75} +(-5.17571 + 15.9292i) q^{77} +(4.24945 + 3.08741i) q^{79} +(0.434757 - 0.315869i) q^{81} +(-0.598743 + 0.435012i) q^{83} +(-6.23310 + 3.05863i) q^{85} +(4.02119 + 12.3760i) q^{87} +(4.99625 - 15.3769i) q^{89} +(0.185159 + 0.569860i) q^{91} +13.9348 q^{93} +(6.65654 - 3.26642i) q^{95} +(8.09228 + 5.87939i) q^{97} +29.5201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 3 * q^9	$ 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9} - 5 q^{11} - 2 q^{13} + 18 q^{15} + q^{17} - 8 q^{19} + 2 q^{21} - 6 q^{23} - 26 q^{25} - 34 q^{27} - 18 q^{29} + 12 q^{31} - 35 q^{33} - 3 q^{35} + 13 q^{37} + 22 q^{39} - 23 q^{41} + 50 q^{43} + 71 q^{45} + q^{47} + 34 q^{49} + 14 q^{51} + 21 q^{53} + 5 q^{55} + 72 q^{57} + 9 q^{59} - 26 q^{61} - 32 q^{63} - 18 q^{65} - 37 q^{67} - 44 q^{69} + 21 q^{71} + 18 q^{73} - 73 q^{75} - 60 q^{77} - 24 q^{79} + 18 q^{81} - 46 q^{83} - 16 q^{85} + 57 q^{87} - 2 q^{89} - 32 q^{91} + 22 q^{93} + 6 q^{95} - 7 q^{97} + 40 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 3 * q^9 - 5 * q^11 - 2 * q^13 + 18 * q^15 + q^17 - 8 * q^19 + 2 * q^21 - 6 * q^23 - 26 * q^25 - 34 * q^27 - 18 * q^29 + 12 * q^31 - 35 * q^33 - 3 * q^35 + 13 * q^37 + 22 * q^39 - 23 * q^41 + 50 * q^43 + 71 * q^45 + q^47 + 34 * q^49 + 14 * q^51 + 21 * q^53 + 5 * q^55 + 72 * q^57 + 9 * q^59 - 26 * q^61 - 32 * q^63 - 18 * q^65 - 37 * q^67 - 44 * q^69 + 21 * q^71 + 18 * q^73 - 73 * q^75 - 60 * q^77 - 24 * q^79 + 18 * q^81 - 46 * q^83 - 16 * q^85 + 57 * q^87 - 2 * q^89 - 32 * q^91 + 22 * q^93 + 6 * q^95 - 7 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.25555	−	1.63875i	−1.30224	−	0.946134i	−0.302267	−	0.953223i	$-0.597743\pi$
$3$	−2.25555	−	1.63875i	−1.30224	−	0.946134i	−0.999975	+	0.00708906i	$0.997743\pi$
$4$		0			0
$5$	−2.20302	−	0.383000i	−0.985222	−	0.171283i
$5$	−2.20302	−	0.383000i	−0.985222	−	0.171283i
$6$		0			0
$7$	−2.70809			−1.02356			−0.511780	−	0.859116i	$-0.671014\pi$
$7$	−2.70809			−1.02356			−0.511780	+	0.859116i	$0.671014\pi$
$8$		0			0
$9$	1.47494	+	4.53940i	0.491647	+	1.51313i
$10$		0			0
$11$	1.91120	−	5.88208i	0.576250	−	1.77351i	−0.0556334	−	0.998451i	$-0.517718\pi$
$11$	1.91120	−	5.88208i	0.576250	−	1.77351i	0.631883	−	0.775064i	$-0.282282\pi$
$12$		0			0
$13$	−0.0683725	−	0.210429i	−0.0189631	−	0.0583625i	0.941127	−	0.338053i	$-0.109768\pi$
$13$	−0.0683725	−	0.210429i	−0.0189631	−	0.0583625i	−0.960090	+	0.279690i	$0.909768\pi$
$14$		0			0
$15$	4.34139	+	4.47409i	1.12094	+	1.15520i
$16$		0			0
$17$	2.51204	−	1.82510i	0.609259	−	0.442653i	−0.239894	−	0.970799i	$-0.577113\pi$
$17$	2.51204	−	1.82510i	0.609259	−	0.442653i	0.849153	+	0.528146i	$0.177113\pi$
$18$		0			0
$19$	−2.68270	+	1.94909i	−0.615452	+	0.447152i	−0.851330	−	0.524630i	$-0.824204\pi$
$19$	−2.68270	+	1.94909i	−0.615452	+	0.447152i	0.235878	+	0.971783i	$0.424204\pi$
$20$		0			0
$21$	6.10822	+	4.43788i	1.33292	+	0.968426i
$22$		0			0
$23$	0.557161	−	1.71477i	0.116176	−	0.357554i	−0.876014	−	0.482285i	$-0.839807\pi$
$23$	0.557161	−	1.71477i	0.116176	−	0.357554i	0.992191	+	0.124732i	$0.0398070\pi$
$24$		0			0
$25$	4.70662	+	1.68752i	0.941324	+	0.337503i
$26$		0			0
$27$	1.52753	−	4.70124i	0.293973	−	0.904755i
$28$		0			0
$29$	−3.77603	−	2.74345i	−0.701191	−	0.509445i	0.179129	−	0.983826i	$-0.442672\pi$
$29$	−3.77603	−	2.74345i	−0.701191	−	0.509445i	−0.880320	+	0.474380i	$0.842672\pi$
$30$		0			0
$31$	−4.04356	+	2.93782i	−0.726245	+	0.527648i	−0.888373	−	0.459122i	$-0.848164\pi$
$31$	−4.04356	+	2.93782i	−0.726245	+	0.527648i	0.162128	+	0.986770i	$0.448164\pi$
$32$		0			0
$33$	−13.9501	+	10.1353i	−2.42840	+	1.76434i
$34$		0			0
$35$	5.96598	+	1.03720i	1.00843	+	0.175318i
$36$		0			0
$37$	−2.00918	−	6.18361i	−0.330306	−	1.01658i	−0.968988	−	0.247108i	$-0.920520\pi$
$37$	−2.00918	−	6.18361i	−0.330306	−	1.01658i	0.638682	−	0.769471i	$-0.279480\pi$
$38$		0			0
$39$	−0.190623	+	0.586678i	−0.0305242	+	0.0939437i
$40$		0			0
$41$	−1.15044	−	3.54068i	−0.179668	−	0.552962i	0.820148	−	0.572152i	$-0.193891\pi$
$41$	−1.15044	−	3.54068i	−0.179668	−	0.552962i	−0.999816	+	0.0191899i	$0.993891\pi$
$42$		0			0
$43$	11.1384			1.69859			0.849295	−	0.527918i	$-0.177027\pi$
$43$	11.1384			1.69859			0.849295	+	0.527918i	$0.177027\pi$
$44$		0			0
$45$	−1.51074	−	10.5653i	−0.225208	−	1.57498i
$46$		0			0
$47$	−3.60959	−	2.62252i	−0.526513	−	0.382534i	0.292539	−	0.956254i	$-0.405500\pi$
$47$	−3.60959	−	2.62252i	−0.526513	−	0.382534i	−0.819052	+	0.573719i	$0.805500\pi$
$48$		0			0
$49$	0.333733			0.0476761
$50$		0			0
$51$	−8.65692			−1.21221
$52$		0			0
$53$	2.32993	+	1.69279i	0.320040	+	0.232523i	0.736193	−	0.676772i	$-0.236622\pi$
$53$	2.32993	+	1.69279i	0.320040	+	0.232523i	−0.416153	+	0.909295i	$0.636622\pi$
$54$		0			0
$55$	−6.46327	+	12.2264i	−0.871507	+	1.64860i
$56$		0			0
$57$	9.24503			1.22453
$58$		0			0
$59$	−1.06770	−	3.28603i	−0.139002	−	0.427805i	0.857189	−	0.515002i	$-0.172209\pi$
$59$	−1.06770	−	3.28603i	−0.139002	−	0.427805i	−0.996191	+	0.0871975i	$0.972209\pi$
$60$		0			0
$61$	1.57525	−	4.84813i	0.201691	−	0.620740i	−0.798142	−	0.602469i	$-0.794184\pi$
$61$	1.57525	−	4.84813i	0.201691	−	0.620740i	0.999833	−	0.0182712i	$-0.00581621\pi$
$62$		0			0
$63$	−3.99427	−	12.2931i	−0.503231	−	1.54879i
$64$		0			0
$65$	0.0700319	+	0.489766i	0.00868639	+	0.0607481i
$66$		0			0
$67$	−7.18245	+	5.21835i	−0.877476	+	0.637523i	−0.932582	−	0.360957i	$-0.882450\pi$
$67$	−7.18245	+	5.21835i	−0.877476	+	0.637523i	0.0551069	+	0.998480i	$0.482450\pi$
$68$		0			0
$69$	−4.06678	+	2.95469i	−0.489583	+	0.355703i
$70$		0			0
$71$	7.37333	+	5.35704i	0.875054	+	0.635764i	0.931938	−	0.362617i	$-0.118117\pi$
$71$	7.37333	+	5.35704i	0.875054	+	0.635764i	−0.0568844	+	0.998381i	$0.518117\pi$
$72$		0			0
$73$	1.08812	−	3.34888i	0.127355	−	0.391957i	−0.866968	−	0.498364i	$-0.833934\pi$
$73$	1.08812	−	3.34888i	0.127355	−	0.391957i	0.994323	+	0.106406i	$0.0339344\pi$
$74$		0			0
$75$	−7.85060	−	11.5193i	−0.906509	−	1.33013i
$76$		0			0
$77$	−5.17571	+	15.9292i	−0.589827	+	1.81530i
$78$		0			0
$79$	4.24945	+	3.08741i	0.478100	+	0.347360i	0.800590	−	0.599213i	$-0.204520\pi$
$79$	4.24945	+	3.08741i	0.478100	+	0.347360i	−0.322489	+	0.946573i	$0.604520\pi$
$80$		0			0
$81$	0.434757	−	0.315869i	0.0483063	−	0.0350966i
$82$		0			0
$83$	−0.598743	+	0.435012i	−0.0657205	+	0.0477488i	−0.620160	−	0.784475i	$-0.712933\pi$
$83$	−0.598743	+	0.435012i	−0.0657205	+	0.0477488i	0.554440	+	0.832224i	$0.312933\pi$
$84$		0			0
$85$	−6.23310	+	3.05863i	−0.676074	+	0.331756i
$86$		0			0
$87$	4.02119	+	12.3760i	0.431117	+	1.32684i
$88$		0			0
$89$	4.99625	−	15.3769i	0.529602	−	1.62995i	−0.225431	−	0.974259i	$-0.572379\pi$
$89$	4.99625	−	15.3769i	0.529602	−	1.62995i	0.755033	−	0.655687i	$-0.227621\pi$
$90$		0			0
$91$	0.185159	+	0.569860i	0.0194099	+	0.0597375i
$92$		0			0
$93$	13.9348			1.44497
$94$		0			0
$95$	6.65654	−	3.26642i	0.682947	−	0.335128i
$96$		0			0
$97$	8.09228	+	5.87939i	0.821647	+	0.596961i	0.917184	−	0.398465i	$-0.130457\pi$
$97$	8.09228	+	5.87939i	0.821647	+	0.596961i	−0.0955370	+	0.995426i	$0.530457\pi$
$98$		0			0
$99$	29.5201			2.96688
$100$		0			0
$101$	6.90049			0.686624			0.343312	−	0.939221i	$-0.388451\pi$
$101$	6.90049			0.686624			0.343312	+	0.939221i	$0.388451\pi$
$102$		0			0
$103$	7.94303	+	5.77095i	0.782650	+	0.568629i	0.905773	−	0.423763i	$-0.139291\pi$
$103$	7.94303	+	5.77095i	0.782650	+	0.568629i	−0.123123	+	0.992391i	$0.539291\pi$
$104$		0			0
$105$	−11.7568	−	12.1162i	−1.14735	−	1.18242i
$106$		0			0
$107$	−4.56250			−0.441073			−0.220537	−	0.975379i	$-0.570781\pi$
$107$	−4.56250			−0.441073			−0.220537	+	0.975379i	$0.570781\pi$
$108$		0			0
$109$	3.70250	+	11.3951i	0.354635	+	1.09145i	0.956221	+	0.292646i	$0.0945359\pi$
$109$	3.70250	+	11.3951i	0.354635	+	1.09145i	−0.601586	+	0.798808i	$0.705464\pi$
$110$		0			0
$111$	−5.60161	+	17.2400i	−0.531681	+	1.63635i
$112$		0			0
$113$	−1.80641	−	5.55956i	−0.169933	−	0.522999i	0.829433	−	0.558606i	$-0.188664\pi$
$113$	−1.80641	−	5.55956i	−0.169933	−	0.522999i	−0.999366	+	0.0356067i	$0.988664\pi$
$114$		0			0
$115$	−1.88420	+	3.56428i	−0.175702	+	0.332371i
$116$		0			0
$117$	0.854377	−	0.620741i	0.0789871	−	0.0573875i
$118$		0			0
$119$	−6.80282	+	4.94254i	−0.623614	+	0.453082i
$120$		0			0
$121$	−22.0470	−	16.0181i	−2.00427	−	1.45619i
$122$		0			0
$123$	−3.20744	+	9.87147i	−0.289205	+	0.890081i
$124$		0			0
$125$	−9.72248	−	5.52027i	−0.869605	−	0.493748i
$126$		0			0
$127$	6.06630	−	18.6702i	0.538297	−	1.65671i	−0.198118	−	0.980178i	$-0.563483\pi$
$127$	6.06630	−	18.6702i	0.538297	−	1.65671i	0.736415	−	0.676530i	$-0.236517\pi$
$128$		0			0
$129$	−25.1232	−	18.2531i	−2.21198	−	1.60709i
$130$		0			0
$131$	−3.99325	+	2.90127i	−0.348892	+	0.253485i	−0.748404	−	0.663243i	$-0.769180\pi$
$131$	−3.99325	+	2.90127i	−0.348892	+	0.253485i	0.399512	+	0.916728i	$0.369180\pi$
$132$		0			0
$133$	7.26497	−	5.27831i	0.629953	−	0.457688i
$134$		0			0
$135$	−5.16575	+	9.77191i	−0.444597	+	0.841032i
$136$		0			0
$137$	3.21276	+	9.88785i	0.274484	+	0.844776i	0.989355	+	0.145520i	$0.0464854\pi$
$137$	3.21276	+	9.88785i	0.274484	+	0.844776i	−0.714871	+	0.699256i	$0.753515\pi$
$138$		0			0
$139$	4.49777	−	13.8427i	0.381496	−	1.17412i	−0.557494	−	0.830181i	$-0.688237\pi$
$139$	4.49777	−	13.8427i	0.381496	−	1.17412i	0.938990	−	0.343944i	$-0.111763\pi$
$140$		0			0
$141$	3.84395	+	11.8305i	0.323719	+	0.996304i
$142$		0			0
$143$	−1.36843			−0.114434
$144$		0			0
$145$	7.26794	+	7.49010i	0.603570	+	0.622019i
$146$		0			0
$147$	−0.752751	−	0.546906i	−0.0620859	−	0.0451080i
$148$		0			0
$149$	−19.2003			−1.57295			−0.786477	−	0.617620i	$-0.788097\pi$
$149$	−19.2003			−1.57295			−0.786477	+	0.617620i	$0.788097\pi$
$150$		0			0
$151$	−7.90466			−0.643272			−0.321636	−	0.946863i	$-0.604233\pi$
$151$	−7.90466			−0.643272			−0.321636	+	0.946863i	$0.604233\pi$
$152$		0			0
$153$	11.9900	+	8.71124i	0.969334	+	0.704262i
$154$		0			0
$155$	10.0332	−	4.92340i	0.805890	−	0.395457i
$156$		0			0
$157$	−12.3625			−0.986634			−0.493317	−	0.869849i	$-0.664216\pi$
$157$	−12.3625			−0.986634			−0.493317	+	0.869849i	$0.664216\pi$
$158$		0			0
$159$	−2.48120	−	7.63635i	−0.196772	−	0.605602i
$160$		0			0
$161$	−1.50884	+	4.64374i	−0.118913	+	0.365978i
$162$		0			0
$163$	−4.38241	−	13.4877i	−0.343257	−	1.05643i	−0.962511	−	0.271244i	$-0.912565\pi$
$163$	−4.38241	−	13.4877i	−0.343257	−	1.05643i	0.619254	−	0.785191i	$-0.287435\pi$
$164$		0			0
$165$	34.6142	−	16.9855i	2.69471	−	1.32232i
$166$		0			0
$167$	8.49753	−	6.17381i	0.657558	−	0.477744i	−0.208279	−	0.978069i	$-0.566786\pi$
$167$	8.49753	−	6.17381i	0.657558	−	0.477744i	0.865838	+	0.500325i	$0.166786\pi$
$168$		0			0
$169$	10.4776	−	7.61243i	0.805970	−	0.585572i
$170$		0			0
$171$	−12.8045	−	9.30304i	−0.979187	−	0.711421i
$172$		0			0
$173$	−7.12904	+	21.9409i	−0.542011	+	1.66814i	0.185983	+	0.982553i	$0.440453\pi$
$173$	−7.12904	+	21.9409i	−0.542011	+	1.66814i	−0.727993	+	0.685584i	$0.759547\pi$
$174$		0			0
$175$	−12.7459	−	4.56994i	−0.963502	−	0.345455i
$176$		0			0
$177$	−2.97675	+	9.16149i	−0.223746	+	0.688620i
$178$		0			0
$179$	4.70983	+	3.42189i	0.352029	+	0.255764i	0.749720	−	0.661755i	$-0.230188\pi$
$179$	4.70983	+	3.42189i	0.352029	+	0.255764i	−0.397691	+	0.917520i	$0.630188\pi$
$180$		0			0
$181$	5.90139	−	4.28761i	0.438647	−	0.318696i	−0.346450	−	0.938068i	$-0.612613\pi$
$181$	5.90139	−	4.28761i	0.438647	−	0.318696i	0.785097	+	0.619373i	$0.212613\pi$
$182$		0			0
$183$	−11.4980	+	8.35375i	−0.849953	+	0.617527i
$184$		0			0
$185$	2.05794	+	14.3921i	0.151303	+	1.05813i
$186$		0			0
$187$	−5.93439	−	18.2642i	−0.433966	−	1.33561i
$188$		0			0
$189$	−4.13667	+	12.7314i	−0.300899	+	0.926071i
$190$		0			0
$191$	−0.213245	−	0.656301i	−0.0154299	−	0.0474882i	0.943045	−	0.332665i	$-0.107948\pi$
$191$	−0.213245	−	0.656301i	−0.0154299	−	0.0474882i	−0.958475	+	0.285177i	$0.907948\pi$
$192$		0			0
$193$	−1.54724			−0.111373			−0.0556864	−	0.998448i	$-0.517735\pi$
$193$	−1.54724			−0.111373			−0.0556864	+	0.998448i	$0.517735\pi$
$194$		0			0
$195$	0.644646	−	1.21946i	0.0461640	−	0.0873272i
$196$		0			0
$197$	−0.349257	−	0.253750i	−0.0248835	−	0.0180789i	0.575274	−	0.817961i	$-0.304895\pi$
$197$	−0.349257	−	0.253750i	−0.0248835	−	0.0180789i	−0.600157	+	0.799882i	$0.704895\pi$
$198$		0			0
$199$	−1.78236			−0.126348			−0.0631739	−	0.998003i	$-0.520122\pi$
$199$	−1.78236			−0.126348			−0.0631739	+	0.998003i	$0.520122\pi$
$200$		0			0
$201$	24.7520			1.74587
$202$		0			0
$203$	10.2258	+	7.42949i	0.717712	+	0.521448i
$204$		0			0
$205$	1.17836	+	8.24083i	0.0823002	+	0.575564i
$206$		0			0
$207$	8.60580			0.598144
$208$		0			0
$209$	6.33754	+	19.5050i	0.438377	+	1.34919i
$210$		0			0
$211$	−5.96947	+	18.3721i	−0.410955	+	1.26479i	0.504864	+	0.863199i	$0.331543\pi$
$211$	−5.96947	+	18.3721i	−0.410955	+	1.26479i	−0.915819	+	0.401591i	$0.868457\pi$
$212$		0			0
$213$	−7.85206	−	24.1661i	−0.538014	−	1.65584i
$214$		0			0
$215$	−24.5382	−	4.26601i	−1.67349	−	0.290939i
$216$		0			0
$217$	10.9503	−	7.95587i	0.743356	−	0.540080i
$218$		0			0
$219$	−7.94230	+	5.77042i	−0.536691	+	0.389929i
$220$		0			0
$221$	−0.555809	−	0.403819i	−0.0373878	−	0.0271638i
$222$		0			0
$223$	5.58844	−	17.1994i	0.374229	−	1.15176i	−0.569768	−	0.821806i	$-0.692967\pi$
$223$	5.58844	−	17.1994i	0.374229	−	1.15176i	0.943997	−	0.329954i	$-0.107033\pi$
$224$		0			0
$225$	−0.718324	+	23.8542i	−0.0478883	+	1.59028i
$226$		0			0
$227$	−1.31830	+	4.05730i	−0.0874985	+	0.269293i	−0.985226	−	0.171258i	$-0.945217\pi$
$227$	−1.31830	+	4.05730i	−0.0874985	+	0.269293i	0.897728	+	0.440551i	$0.145217\pi$
$228$		0			0
$229$	22.4488	+	16.3100i	1.48346	+	1.07780i	0.976422	+	0.215872i	$0.0692594\pi$
$229$	22.4488	+	16.3100i	1.48346	+	1.07780i	0.507037	+	0.861924i	$0.330741\pi$
$230$		0			0
$231$	37.7781	−	27.4474i	2.48561	−	1.80590i
$232$		0			0
$233$	−8.04210	+	5.84293i	−0.526855	+	0.382783i	−0.819180	−	0.573536i	$-0.805571\pi$
$233$	−8.04210	+	5.84293i	−0.526855	+	0.382783i	0.292325	+	0.956319i	$0.405571\pi$
$234$		0			0
$235$	6.94759	+	7.15995i	0.453211	+	0.467064i
$236$		0			0
$237$	−4.52535	−	13.9276i	−0.293953	−	0.904694i
$238$		0			0
$239$	−2.35260	+	7.24055i	−0.152177	+	0.468352i	−0.997864	−	0.0653270i	$-0.979191\pi$
$239$	−2.35260	+	7.24055i	−0.152177	+	0.468352i	0.845687	+	0.533679i	$0.179191\pi$
$240$		0			0
$241$	−1.25097	−	3.85010i	−0.0805822	−	0.248007i	0.902647	−	0.430382i	$-0.141621\pi$
$241$	−1.25097	−	3.85010i	−0.0805822	−	0.248007i	−0.983229	+	0.182376i	$0.941621\pi$
$242$		0			0
$243$	−16.3278			−1.04743
$244$		0			0
$245$	−0.735221	−	0.127820i	−0.0469716	−	0.00816610i
$246$		0			0
$247$	0.593568	+	0.431252i	0.0377678	+	0.0274399i
$248$		0			0
$249$	2.06337			0.130761
$250$		0			0
$251$	15.3929			0.971591			0.485795	−	0.874073i	$-0.338530\pi$
$251$	15.3929			0.971591			0.485795	+	0.874073i	$0.338530\pi$
$252$		0			0
$253$	−9.02155	−	6.55454i	−0.567180	−	0.412080i
$254$		0			0
$255$	19.0714	+	3.31560i	1.19430	+	0.207631i
$256$		0			0
$257$	3.06508			0.191194			0.0955972	−	0.995420i	$-0.469524\pi$
$257$	3.06508			0.191194			0.0955972	+	0.995420i	$0.469524\pi$
$258$		0			0
$259$	5.44102	+	16.7457i	0.338089	+	1.04053i
$260$		0			0
$261$	6.88419	−	21.1874i	0.426121	−	1.31146i
$262$		0			0
$263$	−3.26006	−	10.0334i	−0.201024	−	0.618687i	−0.999853	−	0.0171300i	$-0.994547\pi$
$263$	−3.26006	−	10.0334i	−0.201024	−	0.618687i	0.798830	−	0.601557i	$-0.205453\pi$
$264$		0			0
$265$	−4.48454	−	4.62162i	−0.275483	−	0.283904i
$266$		0			0
$267$	−36.4682	+	26.4957i	−2.23182	+	1.62151i
$268$		0			0
$269$	−0.543008	+	0.394519i	−0.0331078	+	0.0240542i	−0.604216	−	0.796821i	$-0.706514\pi$
$269$	−0.543008	+	0.394519i	−0.0331078	+	0.0240542i	0.571108	+	0.820875i	$0.306514\pi$
$270$		0			0
$271$	14.9299	+	10.8472i	0.906928	+	0.658922i	0.940236	−	0.340523i	$-0.110604\pi$
$271$	14.9299	+	10.8472i	0.906928	+	0.658922i	−0.0333080	+	0.999445i	$0.510604\pi$
$272$		0			0
$273$	0.516225	−	1.58878i	0.0312433	−	0.0961571i
$274$		0			0
$275$	18.9214	−	24.4596i	1.14100	−	1.47497i
$276$		0			0
$277$	−1.27109	+	3.91201i	−0.0763724	+	0.235050i	−0.981953	−	0.189124i	$-0.939435\pi$
$277$	−1.27109	+	3.91201i	−0.0763724	+	0.235050i	0.905581	+	0.424173i	$0.139435\pi$
$278$		0			0
$279$	−19.3000	−	14.0222i	−1.15546	−	0.839490i
$280$		0			0
$281$	−6.75134	+	4.90514i	−0.402751	+	0.292616i	−0.770661	−	0.637246i	$-0.780074\pi$
$281$	−6.75134	+	4.90514i	−0.402751	+	0.292616i	0.367909	+	0.929862i	$0.380074\pi$
$282$		0			0
$283$	−0.272848	+	0.198236i	−0.0162191	+	0.0117839i	−0.595865	−	0.803084i	$-0.703191\pi$
$283$	−0.272848	+	0.198236i	−0.0162191	+	0.0117839i	0.579646	+	0.814868i	$0.303191\pi$
$284$		0			0
$285$	−20.3670	−	3.54085i	−1.20644	−	0.209742i
$286$		0			0
$287$	3.11549	+	9.58848i	0.183901	+	0.565990i
$288$		0			0
$289$	−2.27395	+	6.99849i	−0.133762	+	0.411676i
$290$		0			0
$291$	−8.61768	−	26.5225i	−0.505177	−	1.55478i
$292$		0			0
$293$	−22.5665			−1.31835			−0.659174	−	0.751990i	$-0.729094\pi$
$293$	−22.5665			−1.31835			−0.659174	+	0.751990i	$0.729094\pi$
$294$		0			0
$295$	1.09361	+	7.64813i	0.0636724	+	0.445291i
$296$		0			0
$297$	−24.7337	−	17.9701i	−1.43519	−	1.04273i
$298$		0			0
$299$	−0.398931			−0.0230708
$300$		0			0
$301$	−30.1638			−1.73861
$302$		0			0
$303$	−15.5644	−	11.3082i	−0.894151	−	0.649639i
$304$		0			0
$305$	−5.32716	+	10.0772i	−0.305032	+	0.577020i
$306$		0			0
$307$	0.775011			0.0442322			0.0221161	−	0.999755i	$-0.492960\pi$
$307$	0.775011			0.0442322			0.0221161	+	0.999755i	$0.492960\pi$
$308$		0			0
$309$	−8.45874	−	26.0333i	−0.481201	−	1.48098i
$310$		0			0
$311$	2.23153	−	6.86793i	0.126538	−	0.389445i	−0.867640	−	0.497193i	$-0.834364\pi$
$311$	2.23153	−	6.86793i	0.126538	−	0.389445i	0.994178	+	0.107748i	$0.0343641\pi$
$312$		0			0
$313$	7.54307	+	23.2152i	0.426360	+	1.31220i	0.901686	+	0.432391i	$0.142330\pi$
$313$	7.54307	+	23.2152i	0.426360	+	1.31220i	−0.475326	+	0.879810i	$0.657670\pi$
$314$		0			0
$315$	4.09121	+	28.6118i	0.230514	+	1.61209i
$316$		0			0
$317$	20.1580	−	14.6456i	1.13219	−	0.822581i	0.146175	−	0.989259i	$-0.453304\pi$
$317$	20.1580	−	14.6456i	1.13219	−	0.822581i	0.986011	+	0.166677i	$0.0533038\pi$
$318$		0			0
$319$	−23.3540	+	16.9676i	−1.30757	+	0.950005i
$320$		0			0
$321$	10.2909	+	7.47680i	0.574384	+	0.417314i
$322$		0			0
$323$	−3.18174	+	9.79240i	−0.177037	+	0.544863i
$324$		0			0
$325$	0.0332987	−	1.10579i	0.00184708	−	0.0613381i
$326$		0			0
$327$	10.3226	−	31.7697i	0.570842	−	1.75687i
$328$		0			0
$329$	9.77509	+	7.10202i	0.538918	+	0.391547i
$330$		0			0
$331$	−4.24549	+	3.08453i	−0.233353	+	0.169541i	−0.698317	−	0.715789i	$-0.746067\pi$
$331$	−4.24549	+	3.08453i	−0.233353	+	0.169541i	0.464964	+	0.885330i	$0.346067\pi$
$332$		0			0
$333$	25.1065	−	18.2409i	1.37583	−	0.999596i
$334$		0			0
$335$	17.8217	−	8.74527i	0.973705	−	0.477805i
$336$		0			0
$337$	−9.28987	−	28.5913i	−0.506051	−	1.55747i	−0.798996	−	0.601336i	$-0.794635\pi$
$337$	−9.28987	−	28.5913i	−0.506051	−	1.55747i	0.292945	−	0.956129i	$-0.405365\pi$
$338$		0			0
$339$	−5.03630	+	15.5001i	−0.273534	+	0.841851i
$340$		0			0
$341$	9.55242	+	29.3993i	0.517293	+	1.59206i
$342$		0			0
$343$	18.0528			0.974761
$344$		0			0
$345$	10.0909	−	4.95167i	0.543274	−	0.266589i
$346$		0			0
$347$	12.7137	+	9.23702i	0.682505	+	0.495869i	0.874188	−	0.485588i	$-0.161394\pi$
$347$	12.7137	+	9.23702i	0.682505	+	0.495869i	−0.191683	+	0.981457i	$0.561394\pi$
$348$		0			0
$349$	13.5808			0.726961			0.363481	−	0.931602i	$-0.381588\pi$
$349$	13.5808			0.726961			0.363481	+	0.931602i	$0.381588\pi$
$350$		0			0
$351$	−1.09372			−0.0583784
$352$		0			0
$353$	−25.1732	−	18.2894i	−1.33984	−	0.973448i	−0.999450	−	0.0331617i	$-0.989442\pi$
$353$	−25.1732	−	18.2894i	−1.33984	−	0.973448i	−0.340386	−	0.940286i	$-0.610558\pi$
$354$		0			0
$355$	−14.1919	−	14.6257i	−0.753227	−	0.776250i
$356$		0			0
$357$	23.4437			1.24077
$358$		0			0
$359$	−8.22663	−	25.3190i	−0.434185	−	1.33628i	−0.893919	−	0.448228i	$-0.852055\pi$
$359$	−8.22663	−	25.3190i	−0.434185	−	1.33628i	0.459734	−	0.888057i	$-0.347945\pi$
$360$		0			0
$361$	−2.47343	+	7.61243i	−0.130180	+	0.400654i
$362$		0			0
$363$	23.4784	+	72.2592i	1.23230	+	3.79262i
$364$		0			0
$365$	−3.67977	+	6.96092i	−0.192608	+	0.364351i
$366$		0			0
$367$	20.3126	−	14.7579i	1.06031	−	0.770358i	0.0861618	−	0.996281i	$-0.472540\pi$
$367$	20.3126	−	14.7579i	1.06031	−	0.770358i	0.974145	+	0.225923i	$0.0725398\pi$
$368$		0			0
$369$	14.3758	−	10.4446i	0.748373	−	0.543725i
$370$		0			0
$371$	−6.30964	−	4.58422i	−0.327580	−	0.238001i
$372$		0			0
$373$	−0.896671	+	2.75967i	−0.0464279	+	0.142890i	−0.971583	−	0.236699i	$-0.923935\pi$
$373$	−0.896671	+	2.75967i	−0.0464279	+	0.142890i	0.925155	+	0.379589i	$0.123935\pi$
$374$		0			0
$375$	12.8832	+	28.3840i	0.665284	+	1.46574i
$376$		0			0
$377$	−0.319124	+	0.982163i	−0.0164357	+	0.0505839i
$378$		0			0
$379$	3.22416	+	2.34249i	0.165614	+	0.120326i	0.667505	−	0.744605i	$-0.267362\pi$
$379$	3.22416	+	2.34249i	0.165614	+	0.120326i	−0.501891	+	0.864931i	$0.667362\pi$
$380$		0			0
$381$	−44.2786	+	32.1703i	−2.26846	+	1.64813i
$382$		0			0
$383$	0.00459892	−	0.00334131i	0.000234994	−	0.000170733i	−0.587668	−	0.809102i	$-0.699954\pi$
$383$	0.00459892	−	0.00334131i	0.000234994	−	0.000170733i	0.587903	+	0.808932i	$0.299954\pi$
$384$		0			0
$385$	17.5031	−	33.1101i	0.892040	−	1.68745i
$386$		0			0
$387$	16.4285	+	50.5617i	0.835107	+	2.57020i
$388$		0			0
$389$	8.00519	−	24.6374i	0.405879	−	1.24917i	−0.514280	−	0.857623i	$-0.671941\pi$
$389$	8.00519	−	24.6374i	0.405879	−	1.24917i	0.920159	−	0.391545i	$-0.128059\pi$
$390$		0			0
$391$	−1.73002	−	5.32444i	−0.0874906	−	0.269268i
$392$		0			0
$393$	13.7614			0.694173
$394$		0			0
$395$	−8.17916	−	8.42917i	−0.411538	−	0.424117i
$396$		0			0
$397$	−9.16678	−	6.66006i	−0.460068	−	0.334259i	0.333490	−	0.942754i	$-0.391774\pi$
$397$	−9.16678	−	6.66006i	−0.460068	−	0.334259i	−0.793558	+	0.608495i	$0.791774\pi$
$398$		0			0
$399$	−25.0363			−1.25338
$400$		0			0
$401$	6.06828			0.303035			0.151518	−	0.988455i	$-0.451584\pi$
$401$	6.06828			0.303035			0.151518	+	0.988455i	$0.451584\pi$
$402$		0			0
$403$	0.894671	+	0.650016i	0.0445667	+	0.0323796i
$404$		0			0
$405$	−1.07876	+	0.529356i	−0.0536039	+	0.0263039i
$406$		0			0
$407$	−40.2124			−1.99326
$408$		0			0
$409$	0.847821	+	2.60932i	0.0419220	+	0.129023i	0.969827	−	0.243794i	$-0.0783920\pi$
$409$	0.847821	+	2.60932i	0.0419220	+	0.129023i	−0.927905	+	0.372817i	$0.878392\pi$
$410$		0			0
$411$	8.95721	−	27.5675i	0.441827	−	1.35980i
$412$		0			0
$413$	2.89141	+	8.89885i	0.142277	+	0.437884i
$414$		0			0
$415$	1.48565	−	0.729023i	0.0729278	−	0.0357863i
$416$		0			0
$417$	−32.8298	+	23.8522i	−1.60768	+	1.16805i
$418$		0			0
$419$	16.1307	−	11.7196i	0.788036	−	0.572541i	−0.119344	−	0.992853i	$-0.538079\pi$
$419$	16.1307	−	11.7196i	0.788036	−	0.572541i	0.907380	+	0.420312i	$0.138079\pi$
$420$		0			0
$421$	16.8329	+	12.2298i	0.820383	+	0.596043i	0.916822	−	0.399296i	$-0.130745\pi$
$421$	16.8329	+	12.2298i	0.820383	+	0.596043i	−0.0964392	+	0.995339i	$0.530745\pi$
$422$		0			0
$423$	6.58075	−	20.2535i	0.319967	−	0.984757i
$424$		0			0
$425$	14.9031	−	4.35097i	0.722907	−	0.211053i
$426$		0			0
$427$	−4.26592	+	13.1292i	−0.206443	+	0.635365i
$428$		0			0
$429$	3.08657	+	2.24253i	0.149021	+	0.108270i
$430$		0			0
$431$	−22.9738	+	16.6915i	−1.10661	+	0.803999i	−0.982126	−	0.188222i	$-0.939727\pi$
$431$	−22.9738	+	16.6915i	−1.10661	+	0.803999i	−0.124484	+	0.992222i	$0.539727\pi$
$432$		0			0
$433$	0.856621	−	0.622371i	0.0411666	−	0.0299093i	−0.567012	−	0.823710i	$-0.691901\pi$
$433$	0.856621	−	0.622371i	0.0411666	−	0.0299093i	0.608178	+	0.793800i	$0.291901\pi$
$434$		0			0
$435$	−4.11879	−	28.8046i	−0.197481	−	1.38108i
$436$		0			0
$437$	1.84754	+	5.68615i	0.0883800	+	0.272006i
$438$		0			0
$439$	1.86423	−	5.73752i	0.0889750	−	0.273837i	−0.896662	−	0.442716i	$-0.854015\pi$
$439$	1.86423	−	5.73752i	0.0889750	−	0.273837i	0.985637	+	0.168879i	$0.0540149\pi$
$440$		0			0
$441$	0.492237	+	1.51495i	0.0234398	+	0.0721404i
$442$		0			0
$443$	4.65442			0.221138			0.110569	−	0.993868i	$-0.464733\pi$
$443$	4.65442			0.221138			0.110569	+	0.993868i	$0.464733\pi$
$444$		0			0
$445$	−16.8962	+	31.9621i	−0.800957	+	1.51515i
$446$		0			0
$447$	43.3073	+	31.4646i	2.04837	+	1.48823i
$448$		0			0
$449$	2.06662			0.0975300			0.0487650	−	0.998810i	$-0.484471\pi$
$449$	2.06662			0.0975300			0.0487650	+	0.998810i	$0.484471\pi$
$450$		0			0
$451$	−23.0253			−1.08422
$452$		0			0
$453$	17.8294	+	12.9538i	0.837696	+	0.608622i
$454$		0			0
$455$	−0.189652	−	1.32633i	−0.00889105	−	0.0621793i
$456$		0			0
$457$	13.1891			0.616962			0.308481	−	0.951231i	$-0.400179\pi$
$457$	13.1891			0.616962			0.308481	+	0.951231i	$0.400179\pi$
$458$		0			0
$459$	−4.74305	−	14.5976i	−0.221387	−	0.681358i
$460$		0			0
$461$	12.8573	−	39.5708i	0.598825	−	1.84299i	0.0641445	−	0.997941i	$-0.479568\pi$
$461$	12.8573	−	39.5708i	0.598825	−	1.84299i	0.534681	−	0.845054i	$-0.320432\pi$
$462$		0			0
$463$	−4.50402	−	13.8619i	−0.209320	−	0.644219i	−0.999508	−	0.0313558i	$-0.990018\pi$
$463$	−4.50402	−	13.8619i	−0.209320	−	0.644219i	0.790189	−	0.612864i	$-0.209982\pi$
$464$		0			0
$465$	−30.6987	−	5.33703i	−1.42362	−	0.247499i
$466$		0			0
$467$	23.8991	−	17.3637i	1.10592	−	0.803495i	0.123901	−	0.992295i	$-0.460460\pi$
$467$	23.8991	−	17.3637i	1.10592	−	0.803495i	0.982016	+	0.188799i	$0.0604596\pi$
$468$		0			0
$469$	19.4507	−	14.1318i	0.898149	−	0.652544i
$470$		0			0
$471$	27.8842	+	20.2591i	1.28484	+	0.933489i
$472$		0			0
$473$	21.2878	−	65.5170i	0.978813	−	3.01248i
$474$		0			0
$475$	−15.9156	+	4.64655i	−0.730256	+	0.213198i
$476$		0			0
$477$	−4.24776	+	13.0732i	−0.194491	+	0.598583i
$478$		0			0
$479$	16.1865	+	11.7602i	0.739581	+	0.537337i	0.892580	−	0.450889i	$-0.148893\pi$
$479$	16.1865	+	11.7602i	0.739581	+	0.537337i	−0.152999	+	0.988226i	$0.548893\pi$
$480$		0			0
$481$	−1.16384	+	0.845577i	−0.0530664	+	0.0385550i
$482$		0			0
$483$	11.0132	−	8.00156i	0.501118	−	0.364083i
$484$		0			0
$485$	−15.5757	−	16.0518i	−0.707255	−	0.728873i
$486$		0			0
$487$	4.89158	+	15.0547i	0.221659	+	0.682195i	0.998614	+	0.0526389i	$0.0167632\pi$
$487$	4.89158	+	15.0547i	0.221659	+	0.682195i	−0.776955	+	0.629556i	$0.783237\pi$
$488$		0			0
$489$	−12.2182	+	37.6038i	−0.552526	+	1.70050i
$490$		0			0
$491$	1.59500	+	4.90889i	0.0719811	+	0.221535i	0.980575	−	0.196146i	$-0.0628428\pi$
$491$	1.59500	+	4.90889i	0.0719811	+	0.221535i	−0.908593	+	0.417682i	$0.862843\pi$
$492$		0			0
$493$	−14.4926			−0.652715
$494$		0			0
$495$	−65.0334	−	11.3062i	−2.92303	−	0.508175i
$496$		0			0
$497$	−19.9676	−	14.5073i	−0.895671	−	0.650743i
$498$		0			0
$499$	−35.9077			−1.60745			−0.803724	−	0.595002i	$-0.797151\pi$
$499$	−35.9077			−1.60745			−0.803724	+	0.595002i	$0.797151\pi$
$500$		0			0
$501$	−29.2839			−1.30831
$502$		0			0
$503$	−6.48332	−	4.71041i	−0.289077	−	0.210027i	0.433790	−	0.901014i	$-0.357176\pi$
$503$	−6.48332	−	4.71041i	−0.289077	−	0.210027i	−0.722867	+	0.690987i	$0.757176\pi$
$504$		0			0
$505$	−15.2019	−	2.64289i	−0.676477	−	0.117607i
$506$		0			0
$507$	−36.1077			−1.60360
$508$		0			0
$509$	−0.562705	−	1.73183i	−0.0249415	−	0.0767619i	0.937811	−	0.347146i	$-0.112849\pi$
$509$	−0.562705	−	1.73183i	−0.0249415	−	0.0767619i	−0.962752	+	0.270384i	$0.912849\pi$
$510$		0			0
$511$	−2.94672	+	9.06907i	−0.130355	+	0.401192i
$512$		0			0
$513$	5.06527	+	15.5893i	0.223637	+	0.688284i
$514$		0			0
$515$	−15.2884	−	15.7557i	−0.673688	−	0.694280i
$516$		0			0
$517$	−22.3246	+	16.2197i	−0.981833	+	0.713344i
$518$		0			0
$519$	52.0356	−	37.8061i	2.28411	−	1.65950i
$520$		0			0
$521$	−24.8215	−	18.0339i	−1.08745	−	0.790079i	−0.108484	−	0.994098i	$-0.534600\pi$
$521$	−24.8215	−	18.0339i	−1.08745	−	0.790079i	−0.978967	+	0.204019i	$0.934600\pi$
$522$		0			0
$523$	−3.64258	+	11.2107i	−0.159279	+	0.490210i	−0.998569	−	0.0534734i	$-0.982971\pi$
$523$	−3.64258	+	11.2107i	−0.159279	+	0.490210i	0.839290	+	0.543683i	$0.182971\pi$
$524$		0			0
$525$	21.2601	+	31.1952i	0.927867	+	1.36147i
$526$		0			0
$527$	−4.79576	+	14.7598i	−0.208907	+	0.642949i
$528$		0			0
$529$	15.9774	+	11.6083i	0.694669	+	0.504707i
$530$		0			0
$531$	13.3418	−	9.69341i	0.578986	−	0.420658i
$532$		0			0
$533$	−0.666404	+	0.484171i	−0.0288652	+	0.0209718i
$534$		0			0
$535$	10.0513	+	1.74744i	0.434555	+	0.0755483i
$536$		0			0
$537$	−5.01562	−	15.4365i	−0.216440	−	0.666134i
$538$		0			0
$539$	0.637832	−	1.96304i	0.0274734	−	0.0845543i
$540$		0			0
$541$	−8.62453	−	26.5436i	−0.370798	−	1.14120i	−0.946270	−	0.323377i	$-0.895182\pi$
$541$	−8.62453	−	26.5436i	−0.370798	−	1.14120i	0.575473	−	0.817821i	$-0.304818\pi$
$542$		0			0
$543$	−20.3372			−0.872754
$544$		0			0
$545$	−3.79236	−	26.5218i	−0.162447	−	1.13607i
$546$		0			0
$547$	14.3474	+	10.4240i	0.613451	+	0.445698i	0.850628	−	0.525768i	$-0.176222\pi$
$547$	14.3474	+	10.4240i	0.613451	+	0.445698i	−0.237177	+	0.971466i	$0.576222\pi$
$548$		0			0
$549$	24.3311			1.03842
$550$		0			0
$551$	15.4772			0.659350
$552$		0			0
$553$	−11.5079	−	8.36096i	−0.489365	−	0.355544i
$554$		0			0
$555$	18.9434	−	35.8346i	0.804102	−	1.52110i
$556$		0			0
$557$	32.3697			1.37155			0.685775	−	0.727814i	$-0.259464\pi$
$557$	32.3697			1.37155			0.685775	+	0.727814i	$0.259464\pi$
$558$		0			0
$559$	−0.761561	−	2.34384i	−0.0322106	−	0.0991340i
$560$		0			0
$561$	−16.5452	+	50.9207i	−0.698537	+	2.14988i
$562$		0			0
$563$	12.4896	+	38.4390i	0.526374	+	1.62001i	0.761583	+	0.648068i	$0.224423\pi$
$563$	12.4896	+	38.4390i	0.526374	+	1.62001i	−0.235209	+	0.971945i	$0.575577\pi$
$564$		0			0
$565$	1.85025	+	12.9397i	0.0778407	+	0.544377i
$566$		0			0
$567$	−1.17736	+	0.855402i	−0.0494444	+	0.0359235i
$568$		0			0
$569$	−18.4838	+	13.4293i	−0.774882	+	0.562985i	−0.903439	−	0.428717i	$-0.858966\pi$
$569$	−18.4838	+	13.4293i	−0.774882	+	0.562985i	0.128556	+	0.991702i	$0.458966\pi$
$570$		0			0
$571$	25.0776	+	18.2199i	1.04946	+	0.762480i	0.972110	−	0.234523i	$-0.0753530\pi$
$571$	25.0776	+	18.2199i	1.04946	+	0.762480i	0.0773536	+	0.997004i	$0.475353\pi$
$572$		0			0
$573$	−0.594530	+	1.82977i	−0.0248368	+	0.0764399i
$574$		0			0
$575$	5.51604	−	7.13054i	0.230035	−	0.297364i
$576$		0			0
$577$	−13.2010	+	40.6284i	−0.549564	+	1.69138i	0.160321	+	0.987065i	$0.448747\pi$
$577$	−13.2010	+	40.6284i	−0.549564	+	1.69138i	−0.709884	+	0.704318i	$0.751253\pi$
$578$		0			0
$579$	3.48988	+	2.53554i	0.145034	+	0.105374i
$580$		0			0
$581$	1.62145	−	1.17805i	0.0672689	−	0.0488737i
$582$		0			0
$583$	14.4101	−	10.4696i	0.596806	−	0.433605i
$584$		0			0
$585$	−2.11996	+	1.04028i	−0.0876494	+	0.0430103i
$586$		0			0
$587$	−6.70607	−	20.6392i	−0.276789	−	0.851869i	−0.988740	−	0.149640i	$-0.952188\pi$
$587$	−6.70607	−	20.6392i	−0.276789	−	0.851869i	0.711951	−	0.702229i	$-0.247812\pi$
$588$		0			0
$589$	5.12156	−	15.7625i	0.211030	−	0.649485i
$590$		0			0
$591$	0.371933	+	1.14469i	0.0152993	+	0.0470863i
$592$		0			0
$593$	36.6696			1.50584			0.752920	−	0.658113i	$-0.228645\pi$
$593$	36.6696			1.50584			0.752920	+	0.658113i	$0.228645\pi$
$594$		0			0
$595$	16.8798	−	8.28305i	0.692003	−	0.339572i
$596$		0			0
$597$	4.02019	+	2.92084i	0.164535	+	0.119542i
$598$		0			0
$599$	−37.2180			−1.52069			−0.760343	−	0.649521i	$-0.774969\pi$
$599$	−37.2180			−1.52069			−0.760343	+	0.649521i	$0.774969\pi$
$600$		0			0
$601$	24.3070			0.991505			0.495752	−	0.868464i	$-0.334892\pi$
$601$	24.3070			0.991505			0.495752	+	0.868464i	$0.334892\pi$
$602$		0			0
$603$	−34.2819	−	24.9073i	−1.39607	−	1.01430i
$604$		0			0
$605$	42.4351	+	43.7322i	1.72523	+	1.77797i
$606$		0			0
$607$	30.4134			1.23444			0.617222	−	0.786789i	$-0.288258\pi$
$607$	30.4134			1.23444			0.617222	+	0.786789i	$0.288258\pi$
$608$		0			0
$609$	−10.8897	−	33.5152i	−0.441275	−	1.35810i
$610$		0			0
$611$	−0.305058	+	0.938871i	−0.0123413	+	0.0379827i
$612$		0			0
$613$	7.48825	+	23.0465i	0.302447	+	0.930837i	0.980617	+	0.195932i	$0.0627733\pi$
$613$	7.48825	+	23.0465i	0.302447	+	0.930837i	−0.678170	+	0.734905i	$0.737227\pi$
$614$		0			0
$615$	10.8468	−	20.5186i	0.437386	−	0.827391i
$616$		0			0
$617$	16.7300	−	12.1551i	0.673525	−	0.489345i	−0.197678	−	0.980267i	$-0.563340\pi$
$617$	16.7300	−	12.1551i	0.673525	−	0.489345i	0.871203	+	0.490922i	$0.163340\pi$
$618$		0			0
$619$	15.5455	−	11.2945i	0.624827	−	0.453963i	−0.229777	−	0.973243i	$-0.573800\pi$
$619$	15.5455	−	11.2945i	0.624827	−	0.453963i	0.854604	+	0.519280i	$0.173800\pi$
$620$		0			0
$621$	−7.21046	−	5.23870i	−0.289346	−	0.210222i
$622$		0			0
$623$	−13.5303	+	41.6419i	−0.542079	+	1.66835i
$624$		0			0
$625$	19.3046	+	15.8850i	0.772183	+	0.635400i
$626$		0			0
$627$	17.6691	−	54.3800i	0.705638	−	2.17173i
$628$		0			0
$629$	−16.3329	−	11.8665i	−0.651234	−	0.473149i
$630$		0			0
$631$	5.43088	−	3.94576i	0.216200	−	0.157078i	−0.474415	−	0.880302i	$-0.657340\pi$
$631$	5.43088	−	3.94576i	0.216200	−	0.157078i	0.690614	+	0.723223i	$0.257340\pi$
$632$		0			0
$633$	43.5718	−	31.6568i	1.73182	−	1.25824i
$634$		0			0
$635$	−20.5149	+	38.8074i	−0.814108	+	1.54002i
$636$		0			0
$637$	−0.0228182	−	0.0702271i	−0.000904088	−	0.00278250i
$638$		0			0
$639$	−13.4425	+	41.3719i	−0.531779	+	1.63665i
$640$		0			0
$641$	5.89451	+	18.1414i	0.232819	+	0.716544i	0.997403	+	0.0720196i	$0.0229444\pi$
$641$	5.89451	+	18.1414i	0.232819	+	0.716544i	−0.764584	+	0.644524i	$0.777056\pi$
$642$		0			0
$643$	−41.2632			−1.62726			−0.813631	−	0.581381i	$-0.802512\pi$
$643$	−41.2632			−1.62726			−0.813631	+	0.581381i	$0.802512\pi$
$644$		0			0
$645$	48.3561	+	49.8342i	1.90402	+	1.96222i
$646$		0			0
$647$	−26.0095	−	18.8970i	−1.02254	−	0.742917i	−0.0557361	−	0.998446i	$-0.517751\pi$
$647$	−26.0095	−	18.8970i	−1.02254	−	0.742917i	−0.966802	+	0.255528i	$0.917751\pi$
$648$		0			0
$649$	−21.3693			−0.838818
$650$		0			0
$651$	−37.7367			−1.47902
$652$		0			0
$653$	24.0456	+	17.4701i	0.940976	+	0.683659i	0.948655	−	0.316311i	$-0.102444\pi$
$653$	24.0456	+	17.4701i	0.940976	+	0.683659i	−0.00767929	+	0.999971i	$0.502444\pi$
$654$		0			0
$655$	9.90841	−	4.86214i	0.387154	−	0.189980i
$656$		0			0
$657$	16.8069			0.655698
$658$		0			0
$659$	15.1405	+	46.5976i	0.589789	+	1.81518i	0.579121	+	0.815241i	$0.303396\pi$
$659$	15.1405	+	46.5976i	0.589789	+	1.81518i	0.0106678	+	0.999943i	$0.496604\pi$
$660$		0			0
$661$	6.05603	−	18.6386i	0.235552	−	0.724956i	−0.761495	−	0.648171i	$-0.775534\pi$
$661$	6.05603	−	18.6386i	0.235552	−	0.724956i	0.997048	−	0.0767853i	$-0.0244656\pi$
$662$		0			0
$663$	0.591896	+	1.82167i	0.0229873	+	0.0707477i
$664$		0			0
$665$	−18.0265	+	8.84576i	−0.699037	+	0.343024i
$666$		0			0
$667$	−6.80823	+	4.94647i	−0.263616	+	0.191528i
$668$		0			0
$669$	−40.7906	+	29.6361i	−1.57706	+	1.14580i
$670$		0			0
$671$	−25.5065	−	18.5316i	−0.984667	−	0.715403i
$672$		0			0
$673$	−6.95009	+	21.3902i	−0.267906	+	0.824531i	0.723103	+	0.690740i	$0.242715\pi$
$673$	−6.95009	+	21.3902i	−0.267906	+	0.824531i	−0.991010	+	0.133791i	$0.957285\pi$
$674$		0			0
$675$	15.1229	−	19.5493i	0.582081	−	0.752451i
$676$		0			0
$677$	0.0323639	−	0.0996058i	0.00124385	−	0.00382816i	−0.950433	−	0.310930i	$-0.899359\pi$
$677$	0.0323639	−	0.0996058i	0.00124385	−	0.00382816i	0.951677	+	0.307102i	$0.0993594\pi$
$678$		0			0
$679$	−21.9146	−	15.9219i	−0.841005	−	0.611026i
$680$		0			0
$681$	9.62240	−	6.99108i	0.368731	−	0.267899i
$682$		0			0
$683$	29.4255	−	21.3789i	1.12594	−	0.818041i	0.140838	−	0.990033i	$-0.455020\pi$
$683$	29.4255	−	21.3789i	1.12594	−	0.818041i	0.985098	+	0.171992i	$0.0550202\pi$
$684$		0			0
$685$	−3.29073	−	23.0137i	−0.125732	−	0.879307i
$686$		0			0
$687$	−23.9063	−	73.5761i	−0.912083	−	2.80710i
$688$		0			0
$689$	0.196909	−	0.606024i	0.00750165	−	0.0230877i
$690$		0			0
$691$	−1.53638	−	4.72848i	−0.0584465	−	0.179880i	0.917571	−	0.397572i	$-0.130147\pi$
$691$	−1.53638	−	4.72848i	−0.0584465	−	0.179880i	−0.976017	+	0.217692i	$0.930147\pi$
$692$		0			0
$693$	−79.9429			−3.03678
$694$		0			0
$695$	−15.2105	+	28.7732i	−0.576966	+	1.09143i
$696$		0			0
$697$	−9.35207	−	6.79467i	−0.354235	−	0.257367i
$698$		0			0
$699$	27.7145			1.04826
$700$		0			0
$701$	8.80733			0.332648			0.166324	−	0.986071i	$-0.446810\pi$
$701$	8.80733			0.332648			0.166324	+	0.986071i	$0.446810\pi$
$702$		0			0
$703$	17.4424	+	12.6727i	0.657853	+	0.477959i
$704$		0			0
$705$	−3.93724	−	27.5350i	−0.148285	−	1.03703i
$706$		0			0
$707$	−18.6871			−0.702801
$708$		0			0
$709$	−10.9565	−	33.7206i	−0.411480	−	1.26641i	−0.915362	−	0.402633i	$-0.868095\pi$
$709$	−10.9565	−	33.7206i	−0.411480	−	1.26641i	0.503882	−	0.863773i	$-0.331905\pi$
$710$		0			0
$711$	−7.74729	+	23.8437i	−0.290546	+	0.894209i
$712$		0			0
$713$	2.78476	+	8.57060i	0.104290	+	0.320972i
$714$		0			0
$715$	3.01469	+	0.524110i	0.112743	+	0.0196006i
$716$		0			0
$717$	17.1719	−	12.4761i	0.641295	−	0.465928i
$718$		0			0
$719$	−0.880663	+	0.639839i	−0.0328432	+	0.0238620i	−0.604086	−	0.796919i	$-0.706462\pi$
$719$	−0.880663	+	0.639839i	−0.0328432	+	0.0238620i	0.571243	+	0.820781i	$0.306462\pi$
$720$		0			0
$721$	−21.5104	−	15.6282i	−0.801090	−	0.582026i
$722$		0			0
$723$	−3.48773	+	10.7341i	−0.129710	+	0.399206i
$724$		0			0
$725$	−13.1427	−	19.2845i	−0.488109	−	0.716208i
$726$		0			0
$727$	2.92535	−	9.00331i	0.108495	−	0.333914i	−0.882040	−	0.471175i	$-0.843830\pi$
$727$	2.92535	−	9.00331i	0.108495	−	0.333914i	0.990535	+	0.137261i	$0.0438299\pi$
$728$		0			0
$729$	35.5239	+	25.8096i	1.31570	+	0.955911i
$730$		0			0
$731$	27.9801	−	20.3287i	1.03488	−	0.751886i
$732$		0			0
$733$	−25.2568	+	18.3501i	−0.932880	+	0.677777i	−0.946696	−	0.322128i	$-0.895602\pi$
$733$	−25.2568	+	18.3501i	−0.932880	+	0.677777i	0.0138164	+	0.999905i	$0.495602\pi$
$734$		0			0
$735$	1.44886	+	1.49315i	0.0534421	+	0.0550757i
$736$		0			0
$737$	16.9677	+	52.2211i	0.625012	+	1.92359i
$738$		0			0
$739$	7.98543	−	24.5766i	0.293749	−	0.904066i	−0.689890	−	0.723914i	$-0.742341\pi$
$739$	7.98543	−	24.5766i	0.293749	−	0.904066i	0.983639	−	0.180152i	$-0.0576589\pi$
$740$		0			0
$741$	−0.632106	−	1.94542i	−0.0232210	−	0.0714669i
$742$		0			0
$743$	−28.7892			−1.05617			−0.528086	−	0.849191i	$-0.677090\pi$
$743$	−28.7892			−1.05617			−0.528086	+	0.849191i	$0.677090\pi$
$744$		0			0
$745$	42.2988	+	7.35373i	1.54971	+	0.269420i
$746$		0			0
$747$	−2.85781	−	2.07632i	−0.104562	−	0.0759685i
$748$		0			0
$749$	12.3556			0.451465
$750$		0			0
$751$	51.1434			1.86625			0.933125	−	0.359551i	$-0.117070\pi$
$751$	51.1434			1.86625			0.933125	+	0.359551i	$0.117070\pi$
$752$		0			0
$753$	−34.7194	−	25.2251i	−1.26525	−	0.919255i
$754$		0			0
$755$	17.4142	+	3.02749i	0.633766	+	0.110182i
$756$		0			0
$757$	−39.1759			−1.42387			−0.711937	−	0.702243i	$-0.752182\pi$
$757$	−39.1759			−1.42387			−0.711937	+	0.702243i	$0.752182\pi$
$758$		0			0
$759$	9.60728	+	29.5682i	0.348722	+	1.07326i
$760$		0			0
$761$	−5.88506	+	18.1123i	−0.213333	+	0.656572i	0.785935	+	0.618310i	$0.212182\pi$
$761$	−5.88506	+	18.1123i	−0.213333	+	0.656572i	−0.999268	+	0.0382622i	$0.987818\pi$
$762$		0			0
$763$	−10.0267	−	30.8590i	−0.362991	−	1.11717i
$764$		0			0
$765$	−23.0778	−	23.7832i	−0.834381	−	0.859885i
$766$		0			0
$767$	−0.618475	+	0.449348i	−0.0223318	+	0.0162250i
$768$		0			0
$769$	−32.8071	+	23.8358i	−1.18305	+	0.859539i	−0.992513	−	0.122140i	$-0.961024\pi$
$769$	−32.8071	+	23.8358i	−1.18305	+	0.859539i	−0.190542	+	0.981679i	$0.561024\pi$
$770$		0			0
$771$	−6.91344	−	5.02290i	−0.248981	−	0.180896i
$772$		0			0
$773$	9.30015	−	28.6229i	0.334503	−	1.02950i	−0.632463	−	0.774591i	$-0.717956\pi$
$773$	9.30015	−	28.6229i	0.334503	−	1.02950i	0.966966	−	0.254905i	$-0.0820441\pi$
$774$		0			0
$775$	−23.9891	+	7.00363i	−0.861715	+	0.251578i
$776$		0			0
$777$	15.1696	−	46.6873i	0.544208	−	1.67490i
$778$		0			0
$779$	9.98740	+	7.25627i	0.357836	+	0.259983i
$780$		0			0
$781$	45.6025	−	33.1322i	1.63179	−	1.18556i
$782$		0			0
$783$	−18.6656	+	13.5614i	−0.667054	+	0.484643i
$784$		0			0
$785$	27.2349	+	4.73484i	0.972054	+	0.168994i
$786$		0			0
$787$	4.41827	+	13.5980i	0.157494	+	0.484717i	0.998405	−	0.0564563i	$-0.0179802\pi$
$787$	4.41827	+	13.5980i	0.157494	+	0.484717i	−0.840911	+	0.541174i	$0.817980\pi$
$788$		0			0
$789$	−9.08908	+	27.9733i	−0.323580	+	0.995876i
$790$		0			0
$791$	4.89192	+	15.0558i	0.173937	+	0.535322i
$792$		0			0
$793$	−1.12789			−0.0400526
$794$		0			0
$795$	2.54142	+	17.7733i	0.0901348	+	0.630356i
$796$		0			0
$797$	−39.2055	−	28.4844i	−1.38873	−	1.00897i	−0.996003	−	0.0893148i	$-0.971532\pi$
$797$	−39.2055	−	28.4844i	−1.38873	−	1.00897i	−0.392725	−	0.919656i	$-0.628468\pi$
$798$		0			0
$799$	−13.8538			−0.490113
$800$		0			0
$801$	77.1711			2.72671
$802$		0			0
$803$	−17.6188	−	12.8008i	−0.621754	−	0.451731i
$804$		0			0
$805$	5.10256	−	9.65237i	0.179842	−	0.340201i
$806$		0			0
$807$	1.87130			0.0658729
$808$		0			0
$809$	−5.23619	−	16.1153i	−0.184095	−	0.566585i	0.815837	−	0.578282i	$-0.196277\pi$
$809$	−5.23619	−	16.1153i	−0.184095	−	0.566585i	−0.999932	+	0.0116969i	$0.996277\pi$
$810$		0			0
$811$	−4.40687	+	13.5629i	−0.154746	+	0.476259i	−0.998135	−	0.0610441i	$-0.980557\pi$
$811$	−4.40687	+	13.5629i	−0.154746	+	0.476259i	0.843389	+	0.537303i	$0.180557\pi$
$812$		0			0
$813$	−15.8993	−	48.9329i	−0.557611	−	1.71615i
$814$		0			0
$815$	4.48877	+	31.3921i	0.157235	+	1.09962i
$816$		0			0
$817$	−29.8809	+	21.7098i	−1.04540	+	0.759529i
$818$		0			0
$819$	−2.31373	+	1.68102i	−0.0808481	+	0.0587396i
$820$		0			0
$821$	−37.0734	−	26.9354i	−1.29387	−	0.940051i	−0.293993	−	0.955808i	$-0.594984\pi$
$821$	−37.0734	−	26.9354i	−1.29387	−	0.940051i	−0.999876	+	0.0157566i	$0.994984\pi$
$822$		0			0
$823$	4.23127	−	13.0225i	0.147493	−	0.453936i	−0.849830	−	0.527056i	$-0.823296\pi$
$823$	4.23127	−	13.0225i	0.147493	−	0.453936i	0.997323	+	0.0731202i	$0.0232957\pi$
$824$		0			0
$825$	−82.7614	+	24.1622i	−2.88138	+	0.841220i
$826$		0			0
$827$	−11.6526	+	35.8630i	−0.405201	+	1.24708i	0.515527	+	0.856873i	$0.327596\pi$
$827$	−11.6526	+	35.8630i	−0.405201	+	1.24708i	−0.920728	+	0.390206i	$0.872404\pi$
$828$		0			0
$829$	0.233422	+	0.169591i	0.00810707	+	0.00589013i	0.591831	−	0.806062i	$-0.298405\pi$
$829$	0.233422	+	0.169591i	0.00810707	+	0.00589013i	−0.583724	+	0.811952i	$0.698405\pi$
$830$		0			0
$831$	9.27782	−	6.74073i	0.321844	−	0.233833i
$832$		0			0
$833$	0.838351	−	0.609097i	0.0290471	−	0.0211040i
$834$		0			0
$835$	−21.0848	+	10.3465i	−0.729670	+	0.358056i
$836$		0			0
$837$	7.63476	+	23.4974i	0.263896	+	0.812188i
$838$		0			0
$839$	−9.73467	+	29.9602i	−0.336078	+	1.03434i	0.630110	+	0.776505i	$0.283010\pi$
$839$	−9.73467	+	29.9602i	−0.336078	+	1.03434i	−0.966189	+	0.257836i	$0.916990\pi$
$840$		0			0
$841$	−2.22959	−	6.86196i	−0.0768823	−	0.236619i
$842$		0			0
$843$	23.2663			0.801334
$844$		0			0
$845$	−25.9980	+	12.7574i	−0.894358	+	0.438869i
$846$		0			0
$847$	59.7052	+	43.3784i	2.05150	+	1.49050i
$848$		0			0
$849$	0.940282			0.0322704
$850$		0			0
$851$	−11.7229			−0.401855
$852$		0			0
$853$	19.3025	+	14.0241i	0.660905	+	0.480175i	0.866968	−	0.498363i	$-0.166065\pi$
$853$	19.3025	+	14.0241i	0.660905	+	0.480175i	−0.206064	+	0.978539i	$0.566065\pi$
$854$		0			0
$855$	24.6456	+	25.3990i	0.842863	+	0.868626i
$856$		0			0
$857$	−20.4806			−0.699606			−0.349803	−	0.936823i	$-0.613751\pi$
$857$	−20.4806			−0.699606			−0.349803	+	0.936823i	$0.613751\pi$
$858$		0			0
$859$	−4.48753	−	13.8112i	−0.153113	−	0.471232i	0.844852	−	0.535000i	$-0.179688\pi$
$859$	−4.48753	−	13.8112i	−0.153113	−	0.471232i	−0.997965	+	0.0637677i	$0.979688\pi$
$860$		0			0
$861$	8.68601	−	26.7328i	0.296019	−	0.911052i
$862$		0			0
$863$	−10.7636	−	33.1270i	−0.366397	−	1.12766i	−0.949101	−	0.314971i	$-0.898005\pi$
$863$	−10.7636	−	33.1270i	−0.366397	−	1.12766i	0.582704	−	0.812684i	$-0.301995\pi$
$864$		0			0
$865$	24.1088	−	45.6059i	0.819724	−	1.55065i
$866$		0			0
$867$	16.5978	−	12.0590i	0.563691	−	0.409545i
$868$		0			0
$869$	26.2819	−	19.0950i	0.891554	−	0.647752i
$870$		0			0
$871$	1.58917	+	1.15460i	0.0538471	+	0.0391222i
$872$		0			0
$873$	−14.7533	+	45.4059i	−0.499323	+	1.53676i
$874$		0			0
$875$	26.3293	+	14.9494i	0.890093	+	0.505381i
$876$		0			0
$877$	16.8588	−	51.8861i	0.569282	−	1.75207i	−0.0855896	−	0.996330i	$-0.527277\pi$
$877$	16.8588	−	51.8861i	0.569282	−	1.75207i	0.654872	−	0.755740i	$-0.272723\pi$
$878$		0			0
$879$	50.8998	+	36.9809i	1.71681	+	1.24733i
$880$		0			0
$881$	−0.341311	+	0.247977i	−0.0114991	+	0.00835457i	−0.593520	−	0.804819i	$-0.702262\pi$
$881$	−0.341311	+	0.247977i	−0.0114991	+	0.00835457i	0.582021	+	0.813174i	$0.302262\pi$
$882$		0			0
$883$	38.9094	−	28.2693i	1.30940	−	0.951338i	0.309405	−	0.950930i	$-0.399870\pi$
$883$	38.9094	−	28.2693i	1.30940	−	0.951338i	1.00000		0.000407592i	$-0.000129741\pi$
$884$		0			0
$885$	10.0667	−	19.0429i	0.338388	−	0.640119i
$886$		0			0
$887$	8.03221	+	24.7206i	0.269695	+	0.830036i	0.990574	+	0.136976i	$0.0437382\pi$
$887$	8.03221	+	24.7206i	0.269695	+	0.830036i	−0.720879	+	0.693061i	$0.756262\pi$
$888$		0			0
$889$	−16.4281	+	50.5604i	−0.550980	+	1.69574i
$890$		0			0
$891$	−1.02706	−	3.16097i	−0.0344078	−	0.105896i
$892$		0			0
$893$	14.7950			0.495095
$894$		0			0
$895$	−9.06528	−	9.34237i	−0.303019	−	0.312281i
$896$		0			0
$897$	0.899809	+	0.653749i	0.0300437	+	0.0218280i
$898$		0			0
$899$	23.3284			0.778045
$900$		0			0
$901$	8.94239			0.297914
$902$		0			0
$903$	68.0358	+	49.4309i	2.26409	+	1.64496i
$904$		0			0
$905$	−14.6431	+	7.18548i	−0.486752	+	0.238853i
$906$		0			0
$907$	−26.3462			−0.874810			−0.437405	−	0.899265i	$-0.644102\pi$
$907$	−26.3462			−0.874810			−0.437405	+	0.899265i	$0.644102\pi$
$908$		0			0
$909$	10.1778	+	31.3241i	0.337577	+	1.03895i
$910$		0			0
$911$	5.15123	−	15.8539i	0.170668	−	0.525262i	−0.828741	−	0.559632i	$-0.810942\pi$
$911$	5.15123	−	15.8539i	0.170668	−	0.525262i	0.999409	+	0.0343701i	$0.0109425\pi$
$912$		0			0
$913$	1.41446	+	4.35325i	0.0468117	+	0.144072i
$914$		0			0
$915$	28.5298	−	13.9998i	0.943164	−	0.462819i
$916$		0			0
$917$	10.8141	−	7.85688i	0.357112	−	0.259457i
$918$		0			0
$919$	9.43609	−	6.85572i	0.311268	−	0.226149i	−0.421173	−	0.906981i	$-0.638381\pi$
$919$	9.43609	−	6.85572i	0.311268	−	0.226149i	0.732440	+	0.680831i	$0.238381\pi$
$920$		0			0
$921$	−1.74808	−	1.27005i	−0.0576011	−	0.0418496i
$922$		0			0
$923$	0.623143	−	1.91784i	0.0205110	−	0.0631264i
$924$		0			0
$925$	0.978505	−	32.4944i	0.0321731	−	1.06841i
$926$		0			0
$927$	−14.4812	+	44.5685i	−0.475624	+	1.46382i
$928$		0			0
$929$	−5.57900	−	4.05338i	−0.183041	−	0.132987i	0.492492	−	0.870317i	$-0.336086\pi$
$929$	−5.57900	−	4.05338i	−0.183041	−	0.132987i	−0.675533	+	0.737330i	$0.736086\pi$
$930$		0			0
$931$	−0.895304	+	0.650476i	−0.0293424	+	0.0213185i
$932$		0			0
$933$	−16.2882	+	11.8340i	−0.533250	+	0.387429i
$934$		0			0
$935$	6.07842	+	42.5093i	0.198786	+	1.39020i
$936$		0			0
$937$	−4.38520	−	13.4963i	−0.143258	−	0.440903i	0.853525	−	0.521052i	$-0.174460\pi$
$937$	−4.38520	−	13.4963i	−0.143258	−	0.440903i	−0.996783	+	0.0801490i	$0.974460\pi$
$938$		0			0
$939$	21.0302	−	64.7243i	0.686294	−	2.11220i
$940$		0			0
$941$	16.1342	+	49.6559i	0.525959	+	1.61874i	0.762411	+	0.647093i	$0.224015\pi$
$941$	16.1342	+	49.6559i	0.525959	+	1.61874i	−0.236452	+	0.971643i	$0.575985\pi$
$942$		0			0
$943$	−6.71243			−0.218587
$944$		0			0
$945$	13.9893	−	26.4632i	0.455072	−	0.860847i
$946$		0			0
$947$	−37.3041	−	27.1030i	−1.21222	−	0.880729i	−0.216789	−	0.976218i	$-0.569558\pi$
$947$	−37.3041	−	27.1030i	−1.21222	−	0.880729i	−0.995430	+	0.0954891i	$0.969558\pi$
$948$		0			0
$949$	−0.779100			−0.0252906
$950$		0			0
$951$	−69.4680			−2.25265
$952$		0			0
$953$	8.85255	+	6.43175i	0.286762	+	0.208345i	0.721862	−	0.692038i	$-0.243287\pi$
$953$	8.85255	+	6.43175i	0.286762	+	0.208345i	−0.435099	+	0.900382i	$0.643287\pi$
$954$		0			0
$955$	0.218420	+	1.52752i	0.00706792	+	0.0494293i
$956$		0			0
$957$	80.4817			2.60161
$958$		0			0
$959$	−8.70043	−	26.7772i	−0.280951	−	0.864680i
$960$		0			0
$961$	−1.85992	+	5.72424i	−0.0599974	+	0.184653i
$962$		0			0
$963$	−6.72942	−	20.7110i	−0.216852	−	0.667403i
$964$		0			0
$965$	3.40860	+	0.592593i	0.109727	+	0.0190762i
$966$		0			0
$967$	−30.5553	+	22.1997i	−0.982592	+	0.713895i	−0.958286	−	0.285809i	$-0.907738\pi$
$967$	−30.5553	+	22.1997i	−0.982592	+	0.713895i	−0.0243059	+	0.999705i	$0.507738\pi$
$968$		0			0
$969$	23.2239	−	16.8731i	0.746059	−	0.542043i
$970$		0			0
$971$	−4.91458	−	3.57065i	−0.157716	−	0.114588i	0.506128	−	0.862458i	$-0.331076\pi$
$971$	−4.91458	−	3.57065i	−0.157716	−	0.114588i	−0.663844	+	0.747871i	$0.731076\pi$
$972$		0			0
$973$	−12.1804	+	37.4873i	−0.390485	+	1.20179i
$974$		0			0
$975$	−1.88722	+	2.43959i	−0.0604395	+	0.0781295i
$976$		0			0
$977$	−1.17670	+	3.62152i	−0.0376461	+	0.115863i	−0.968114	−	0.250512i	$-0.919401\pi$
$977$	−1.17670	+	3.62152i	−0.0376461	+	0.115863i	0.930467	+	0.366375i	$0.119401\pi$
$978$		0			0
$979$	−80.8992	−	58.7767i	−2.58555	−	1.87851i
$980$		0			0
$981$	−46.2661	+	33.6143i	−1.47716	+	1.07322i
$982$		0			0
$983$	−43.8645	+	31.8694i	−1.39906	+	1.01648i	−0.404259	+	0.914645i	$0.632470\pi$
$983$	−43.8645	+	31.8694i	−1.39906	+	1.01648i	−0.994802	+	0.101832i	$0.967530\pi$
$984$		0			0
$985$	0.672235	+	0.692782i	0.0214192	+	0.0220739i
$986$		0			0
$987$	−10.4097	−	32.0379i	−0.331346	−	1.01978i
$988$		0			0
$989$	6.20589	−	19.0998i	0.197336	−	0.607337i
$990$		0			0
$991$	−0.742481	−	2.28512i	−0.0235857	−	0.0725892i	0.938571	−	0.345087i	$-0.112150\pi$
$991$	−0.742481	−	2.28512i	−0.0235857	−	0.0725892i	−0.962157	+	0.272497i	$0.912150\pi$
$992$		0			0
$993$	14.6307			0.464291
$994$		0			0
$995$	3.92657	+	0.682642i	0.124481	+	0.0216412i
$996$		0			0
$997$	38.4271	+	27.9189i	1.21700	+	0.884201i	0.995847	−	0.0910386i	$-0.0290187\pi$
$997$	38.4271	+	27.9189i	1.21700	+	0.884201i	0.221151	+	0.975240i	$0.429019\pi$
$998$		0			0
$999$	−32.1397			−1.01686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.2.g.a.21.1	✓	12
3.2	odd	2		900.2.n.c.721.3		12
4.3	odd	2		400.2.u.f.321.3		12
5.2	odd	4		500.2.i.b.149.1		24
5.3	odd	4		500.2.i.b.149.6		24
5.4	even	2		500.2.g.a.101.3		12
25.6	even	5	inner	100.2.g.a.81.1	yes	12
25.8	odd	20		500.2.i.b.349.1		24
25.9	even	10		2500.2.a.c.1.2		6
25.12	odd	20		2500.2.c.c.1249.2		12
25.13	odd	20		2500.2.c.c.1249.11		12
25.16	even	5		2500.2.a.d.1.5		6
25.17	odd	20		500.2.i.b.349.6		24
25.19	even	10		500.2.g.a.401.3		12
75.56	odd	10		900.2.n.c.181.3		12
100.31	odd	10		400.2.u.f.81.3		12
100.59	odd	10		10000.2.a.bd.1.5		6
100.91	odd	10		10000.2.a.bc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.21.1	✓	12	1.1	even	1	trivial
100.2.g.a.81.1	yes	12	25.6	even	5	inner
400.2.u.f.81.3		12	100.31	odd	10
400.2.u.f.321.3		12	4.3	odd	2
500.2.g.a.101.3		12	5.4	even	2
500.2.g.a.401.3		12	25.19	even	10
500.2.i.b.149.1		24	5.2	odd	4
500.2.i.b.149.6		24	5.3	odd	4
500.2.i.b.349.1		24	25.8	odd	20
500.2.i.b.349.6		24	25.17	odd	20
900.2.n.c.181.3		12	75.56	odd	10
900.2.n.c.721.3		12	3.2	odd	2
2500.2.a.c.1.2		6	25.9	even	10
2500.2.a.d.1.5		6	25.16	even	5
2500.2.c.c.1249.2		12	25.12	odd	20
2500.2.c.c.1249.11		12	25.13	odd	20
10000.2.a.bc.1.2		6	100.91	odd	10
10000.2.a.bd.1.5		6	100.59	odd	10

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25555 - 1.63875i) q^{3} +(-2.20302 - 0.383000i) q^{5} -2.70809 q^{7} +(1.47494 + 4.53940i) q^{9} +O(q^{10})\)	\(q+(-2.25555 - 1.63875i) q^{3} +(-2.20302 - 0.383000i) q^{5} -2.70809 q^{7} +(1.47494 + 4.53940i) q^{9} +(1.91120 - 5.88208i) q^{11} +(-0.0683725 - 0.210429i) q^{13} +(4.34139 + 4.47409i) q^{15} +(2.51204 - 1.82510i) q^{17} +(-2.68270 + 1.94909i) q^{19} +(6.10822 + 4.43788i) q^{21} +(0.557161 - 1.71477i) q^{23} +(4.70662 + 1.68752i) q^{25} +(1.52753 - 4.70124i) q^{27} +(-3.77603 - 2.74345i) q^{29} +(-4.04356 + 2.93782i) q^{31} +(-13.9501 + 10.1353i) q^{33} +(5.96598 + 1.03720i) q^{35} +(-2.00918 - 6.18361i) q^{37} +(-0.190623 + 0.586678i) q^{39} +(-1.15044 - 3.54068i) q^{41} +11.1384 q^{43} +(-1.51074 - 10.5653i) q^{45} +(-3.60959 - 2.62252i) q^{47} +0.333733 q^{49} -8.65692 q^{51} +(2.32993 + 1.69279i) q^{53} +(-6.46327 + 12.2264i) q^{55} +9.24503 q^{57} +(-1.06770 - 3.28603i) q^{59} +(1.57525 - 4.84813i) q^{61} +(-3.99427 - 12.2931i) q^{63} +(0.0700319 + 0.489766i) q^{65} +(-7.18245 + 5.21835i) q^{67} +(-4.06678 + 2.95469i) q^{69} +(7.37333 + 5.35704i) q^{71} +(1.08812 - 3.34888i) q^{73} +(-7.85060 - 11.5193i) q^{75} +(-5.17571 + 15.9292i) q^{77} +(4.24945 + 3.08741i) q^{79} +(0.434757 - 0.315869i) q^{81} +(-0.598743 + 0.435012i) q^{83} +(-6.23310 + 3.05863i) q^{85} +(4.02119 + 12.3760i) q^{87} +(4.99625 - 15.3769i) q^{89} +(0.185159 + 0.569860i) q^{91} +13.9348 q^{93} +(6.65654 - 3.26642i) q^{95} +(8.09228 + 5.87939i) q^{97} +29.5201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 3 * q^9	\( 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9} - 5 q^{11} - 2 q^{13} + 18 q^{15} + q^{17} - 8 q^{19} + 2 q^{21} - 6 q^{23} - 26 q^{25} - 34 q^{27} - 18 q^{29} + 12 q^{31} - 35 q^{33} - 3 q^{35} + 13 q^{37} + 22 q^{39} - 23 q^{41} + 50 q^{43} + 71 q^{45} + q^{47} + 34 q^{49} + 14 q^{51} + 21 q^{53} + 5 q^{55} + 72 q^{57} + 9 q^{59} - 26 q^{61} - 32 q^{63} - 18 q^{65} - 37 q^{67} - 44 q^{69} + 21 q^{71} + 18 q^{73} - 73 q^{75} - 60 q^{77} - 24 q^{79} + 18 q^{81} - 46 q^{83} - 16 q^{85} + 57 q^{87} - 2 q^{89} - 32 q^{91} + 22 q^{93} + 6 q^{95} - 7 q^{97} + 40 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 3 * q^9 - 5 * q^11 - 2 * q^13 + 18 * q^15 + q^17 - 8 * q^19 + 2 * q^21 - 6 * q^23 - 26 * q^25 - 34 * q^27 - 18 * q^29 + 12 * q^31 - 35 * q^33 - 3 * q^35 + 13 * q^37 + 22 * q^39 - 23 * q^41 + 50 * q^43 + 71 * q^45 + q^47 + 34 * q^49 + 14 * q^51 + 21 * q^53 + 5 * q^55 + 72 * q^57 + 9 * q^59 - 26 * q^61 - 32 * q^63 - 18 * q^65 - 37 * q^67 - 44 * q^69 + 21 * q^71 + 18 * q^73 - 73 * q^75 - 60 * q^77 - 24 * q^79 + 18 * q^81 - 46 * q^83 - 16 * q^85 + 57 * q^87 - 2 * q^89 - 32 * q^91 + 22 * q^93 + 6 * q^95 - 7 * q^97 + 40 * q^99

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