LMFDB - Embedded newform 1148.2.ba.a.701.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.3
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48140i q^{3} +(-0.290583 + 0.894324i) q^{5} +(0.587785 - 0.809017i) q^{7} -3.15734 q^{9} +O(q^{10})$	\(q-2.48140i q^{3} +(-0.290583 + 0.894324i) q^{5} +(0.587785 - 0.809017i) q^{7} -3.15734 q^{9} +(-4.02708 + 1.30848i) q^{11} +(-0.240563 - 0.331107i) q^{13} +(2.21917 + 0.721053i) q^{15} +(-5.71360 + 1.85646i) q^{17} +(1.00657 - 1.38542i) q^{19} +(-2.00749 - 1.45853i) q^{21} +(-5.11944 + 3.71949i) q^{23} +(3.32971 + 2.41918i) q^{25} +0.390417i q^{27} +(-9.37915 - 3.04747i) q^{29} +(-1.49869 - 4.61250i) q^{31} +(3.24686 + 9.99280i) q^{33} +(0.552722 + 0.760757i) q^{35} +(0.163973 - 0.504656i) q^{37} +(-0.821608 + 0.596933i) q^{39} +(-4.52690 + 4.52848i) q^{41} +(1.57161 - 1.14184i) q^{43} +(0.917470 - 2.82368i) q^{45} +(2.18249 + 3.00394i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(4.60662 + 14.1777i) q^{51} +(-7.53525 - 2.44835i) q^{53} -3.98174i q^{55} +(-3.43778 - 2.49769i) q^{57} +(6.26650 - 4.55288i) q^{59} +(1.42520 + 1.03547i) q^{61} +(-1.85584 + 2.55434i) q^{63} +(0.366020 - 0.118927i) q^{65} +(-0.101027 - 0.0328257i) q^{67} +(9.22953 + 12.7034i) q^{69} +(10.7155 - 3.48166i) q^{71} -13.0783 q^{73} +(6.00294 - 8.26233i) q^{75} +(-1.30848 + 4.02708i) q^{77} +12.2934i q^{79} -8.50323 q^{81} +5.83718 q^{83} -5.64926i q^{85} +(-7.56199 + 23.2734i) q^{87} +(7.82125 - 10.7650i) q^{89} -0.409270 q^{91} +(-11.4454 + 3.71885i) q^{93} +(0.946522 + 1.30278i) q^{95} +(4.00664 + 1.30184i) q^{97} +(12.7149 - 4.13131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$		−	2.48140i		−	1.43264i	−0.697774	−	0.716318i	$-0.745826\pi$
$3$		−	2.48140i		−	1.43264i	0.697774	−	0.716318i	$-0.254174\pi$
$4$		0			0
$5$	−0.290583	+	0.894324i	−0.129953	+	0.399954i	−0.994771	−	0.102132i	$-0.967434\pi$
$5$	−0.290583	+	0.894324i	−0.129953	+	0.399954i	0.864818	+	0.502085i	$0.167434\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$		0			0
$9$	−3.15734			−1.05245
$10$		0			0
$11$	−4.02708	+	1.30848i	−1.21421	+	0.394521i	−0.844971	−	0.534813i	$-0.820382\pi$
$11$	−4.02708	+	1.30848i	−1.21421	+	0.394521i	−0.369240	+	0.929334i	$0.620382\pi$
$12$		0			0
$13$	−0.240563	−	0.331107i	−0.0667202	−	0.0918325i	0.774353	−	0.632754i	$-0.218076\pi$
$13$	−0.240563	−	0.331107i	−0.0667202	−	0.0918325i	−0.841073	+	0.540922i	$0.818076\pi$
$14$		0			0
$15$	2.21917	+	0.721053i	0.572988	+	0.186175i
$16$		0			0
$17$	−5.71360	+	1.85646i	−1.38575	+	0.450258i	−0.904556	−	0.426356i	$-0.859797\pi$
$17$	−5.71360	+	1.85646i	−1.38575	+	0.450258i	−0.481195	+	0.876613i	$0.659797\pi$
$18$		0			0
$19$	1.00657	−	1.38542i	0.230922	−	0.317837i	−0.677794	−	0.735252i	$-0.737064\pi$
$19$	1.00657	−	1.38542i	0.230922	−	0.317837i	0.908716	+	0.417415i	$0.137064\pi$
$20$		0			0
$21$	−2.00749	−	1.45853i	−0.438071	−	0.318277i
$22$		0			0
$23$	−5.11944	+	3.71949i	−1.06748	+	0.775567i	−0.975457	−	0.220190i	$-0.929332\pi$
$23$	−5.11944	+	3.71949i	−1.06748	+	0.775567i	−0.0920194	+	0.995757i	$0.529332\pi$
$24$		0			0
$25$	3.32971	+	2.41918i	0.665942	+	0.483835i
$26$		0			0
$27$			0.390417i			0.0751358i
$28$		0			0
$29$	−9.37915	−	3.04747i	−1.74166	−	0.565901i	−0.746613	−	0.665259i	$-0.768321\pi$
$29$	−9.37915	−	3.04747i	−1.74166	−	0.565901i	−0.995052	+	0.0993581i	$0.968321\pi$
$30$		0			0
$31$	−1.49869	−	4.61250i	−0.269173	−	0.828429i	−0.990703	−	0.136045i	$-0.956561\pi$
$31$	−1.49869	−	4.61250i	−0.269173	−	0.828429i	0.721530	−	0.692383i	$-0.243439\pi$
$32$		0			0
$33$	3.24686	+	9.99280i	0.565205	+	1.73952i
$34$		0			0
$35$	0.552722	+	0.760757i	0.0934271	+	0.128591i
$36$		0			0
$37$	0.163973	−	0.504656i	0.0269569	−	0.0829649i	−0.936673	−	0.350205i	$-0.886112\pi$
$37$	0.163973	−	0.504656i	0.0269569	−	0.0829649i	0.963630	+	0.267240i	$0.0861118\pi$
$38$		0			0
$39$	−0.821608	+	0.596933i	−0.131563	+	0.0955858i
$40$		0			0
$41$	−4.52690	+	4.52848i	−0.706984	+	0.707230i
$41$	−4.52690	+	4.52848i	−0.706984	+	0.707230i
$42$		0			0
$43$	1.57161	−	1.14184i	0.239669	−	0.174129i	−0.461467	−	0.887157i	$-0.652677\pi$
$43$	1.57161	−	1.14184i	0.239669	−	0.174129i	0.701136	+	0.713028i	$0.252677\pi$
$44$		0			0
$45$	0.917470	−	2.82368i	0.136768	−	0.420930i
$46$		0			0
$47$	2.18249	+	3.00394i	0.318349	+	0.438170i	0.937962	−	0.346738i	$-0.112711\pi$
$47$	2.18249	+	3.00394i	0.318349	+	0.438170i	−0.619613	+	0.784907i	$0.712711\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	4.60662	+	14.1777i	0.645055	+	1.98528i
$52$		0			0
$53$	−7.53525	−	2.44835i	−1.03505	−	0.336307i	−0.258263	−	0.966075i	$-0.583150\pi$
$53$	−7.53525	−	2.44835i	−1.03505	−	0.336307i	−0.776784	+	0.629768i	$0.783150\pi$
$54$		0			0
$55$		−	3.98174i		−	0.536897i
$56$		0			0
$57$	−3.43778	−	2.49769i	−0.455345	−	0.330827i
$58$		0			0
$59$	6.26650	−	4.55288i	0.815829	−	0.592734i	−0.0996857	−	0.995019i	$-0.531784\pi$
$59$	6.26650	−	4.55288i	0.815829	−	0.592734i	0.915515	+	0.402285i	$0.131784\pi$
$60$		0			0
$61$	1.42520	+	1.03547i	0.182478	+	0.132578i	0.675274	−	0.737567i	$-0.264025\pi$
$61$	1.42520	+	1.03547i	0.182478	+	0.132578i	−0.492796	+	0.870145i	$0.664025\pi$
$62$		0			0
$63$	−1.85584	+	2.55434i	−0.233813	+	0.321817i
$64$		0			0
$65$	0.366020	−	0.118927i	0.0453992	−	0.0147511i
$66$		0			0
$67$	−0.101027	−	0.0328257i	−0.0123424	−	0.00401029i	0.302839	−	0.953042i	$-0.402065\pi$
$67$	−0.101027	−	0.0328257i	−0.0123424	−	0.00401029i	−0.315182	+	0.949031i	$0.602065\pi$
$68$		0			0
$69$	9.22953	+	12.7034i	1.11111	+	1.52931i
$70$		0			0
$71$	10.7155	−	3.48166i	1.27169	−	0.413197i	0.406044	−	0.913853i	$-0.366908\pi$
$71$	10.7155	−	3.48166i	1.27169	−	0.413197i	0.865646	+	0.500656i	$0.166908\pi$
$72$		0			0
$73$	−13.0783			−1.53070			−0.765349	−	0.643616i	$-0.777433\pi$
$73$	−13.0783			−1.53070			−0.765349	+	0.643616i	$0.777433\pi$
$74$		0			0
$75$	6.00294	−	8.26233i	0.693159	−	0.954052i
$76$		0			0
$77$	−1.30848	+	4.02708i	−0.149115	+	0.458929i
$78$		0			0
$79$			12.2934i			1.38311i	0.722324	+	0.691555i	$0.243074\pi$
$79$			12.2934i			1.38311i	−0.722324	+	0.691555i	$0.756926\pi$
$80$		0			0
$81$	−8.50323			−0.944804
$82$		0			0
$83$	5.83718			0.640713			0.320357	−	0.947297i	$-0.396197\pi$
$83$	5.83718			0.640713			0.320357	+	0.947297i	$0.396197\pi$
$84$		0			0
$85$		−	5.64926i		−	0.612749i
$86$		0			0
$87$	−7.56199	+	23.2734i	−0.810730	+	2.49517i
$88$		0			0
$89$	7.82125	−	10.7650i	0.829051	−	1.14109i	−0.159048	−	0.987271i	$-0.550842\pi$
$89$	7.82125	−	10.7650i	0.829051	−	1.14109i	0.988099	−	0.153820i	$-0.0491576\pi$
$90$		0			0
$91$	−0.409270			−0.0429032
$92$		0			0
$93$	−11.4454	+	3.71885i	−1.18684	+	0.385627i
$94$		0			0
$95$	0.946522	+	1.30278i	0.0971111	+	0.133662i
$96$		0			0
$97$	4.00664	+	1.30184i	0.406813	+	0.132182i	0.505273	−	0.862959i	$-0.331392\pi$
$97$	4.00664	+	1.30184i	0.406813	+	0.132182i	−0.0984602	+	0.995141i	$0.531392\pi$
$98$		0			0
$99$	12.7149	−	4.13131i	1.27789	−	0.415212i
$100$		0			0
$101$	−6.01998	+	8.28579i	−0.599010	+	0.824467i	−0.995617	−	0.0935217i	$-0.970188\pi$
$101$	−6.01998	+	8.28579i	−0.599010	+	0.824467i	0.396607	+	0.917988i	$0.370188\pi$
$102$		0			0
$103$	8.31417	+	6.04060i	0.819219	+	0.595198i	0.916489	−	0.400060i	$-0.131011\pi$
$103$	8.31417	+	6.04060i	0.819219	+	0.595198i	−0.0972695	+	0.995258i	$0.531011\pi$
$104$		0			0
$105$	1.88774	−	1.37152i	0.184225	−	0.133847i
$106$		0			0
$107$	−14.6398	−	10.6364i	−1.41528	−	1.02826i	−0.992528	−	0.122015i	$-0.961064\pi$
$107$	−14.6398	−	10.6364i	−1.41528	−	1.02826i	−0.422751	−	0.906246i	$-0.638936\pi$
$108$		0			0
$109$			11.6015i			1.11122i	0.831444	+	0.555609i	$0.187515\pi$
$109$			11.6015i			1.11122i	−0.831444	+	0.555609i	$0.812485\pi$
$110$		0			0
$111$	−1.25225	−	0.406881i	−0.118858	−	0.0386195i
$112$		0			0
$113$	−0.394673	−	1.21468i	−0.0371277	−	0.114267i	0.930775	−	0.365593i	$-0.119134\pi$
$113$	−0.394673	−	1.21468i	−0.0371277	−	0.114267i	−0.967903	+	0.251325i	$0.919134\pi$
$114$		0			0
$115$	−1.83880	−	5.65926i	−0.171469	−	0.527728i
$116$		0			0
$117$	0.759539	+	1.04542i	0.0702194	+	0.0966487i
$118$		0			0
$119$	−1.85646	+	5.71360i	−0.170181	+	0.523765i
$120$		0			0
$121$	5.60609	−	4.07306i	0.509645	−	0.370278i
$122$		0			0
$123$	11.2370	+	11.2331i	1.01320	+	1.01285i
$124$		0			0
$125$	−6.93487	+	5.03848i	−0.620274	+	0.450655i
$126$		0			0
$127$	−1.03890	+	3.19741i	−0.0921875	+	0.283724i	−0.986511	−	0.163698i	$-0.947658\pi$
$127$	−1.03890	+	3.19741i	−0.0921875	+	0.283724i	0.894323	+	0.447422i	$0.147658\pi$
$128$		0			0
$129$	−2.83337	−	3.89979i	−0.249464	−	0.343358i
$130$		0			0
$131$	2.53651	+	7.80658i	0.221616	+	0.682064i	0.998617	+	0.0525651i	$0.0167397\pi$
$131$	2.53651	+	7.80658i	0.221616	+	0.682064i	−0.777002	+	0.629499i	$0.783260\pi$
$132$		0			0
$133$	−0.529183	−	1.62866i	−0.0458860	−	0.141223i
$134$		0			0
$135$	−0.349159	−	0.113449i	−0.0300509	−	0.00976411i
$136$		0			0
$137$		−	10.5364i		−	0.900185i	−0.892982	−	0.450093i	$-0.851391\pi$
$137$		−	10.5364i		−	0.900185i	0.892982	−	0.450093i	$-0.148609\pi$
$138$		0			0
$139$	−7.04435	−	5.11802i	−0.597494	−	0.434105i	0.247494	−	0.968889i	$-0.420393\pi$
$139$	−7.04435	−	5.11802i	−0.597494	−	0.434105i	−0.844988	+	0.534785i	$0.820393\pi$
$140$		0			0
$141$	7.45397	−	5.41563i	0.627738	−	0.456078i
$142$		0			0
$143$	1.40201	+	1.01862i	0.117242	+	0.0851815i
$144$		0			0
$145$	5.45085	−	7.50245i	0.452668	−	0.623045i
$146$		0			0
$147$	−2.35995	+	0.766794i	−0.194645	+	0.0632441i
$148$		0			0
$149$	0.506028	+	0.164418i	0.0414554	+	0.0134697i	0.329671	−	0.944096i	$-0.393062\pi$
$149$	0.506028	+	0.164418i	0.0414554	+	0.0134697i	−0.288216	+	0.957565i	$0.593062\pi$
$150$		0			0
$151$	−9.31474	−	12.8206i	−0.758023	−	1.04333i	−0.997376	−	0.0723966i	$-0.976935\pi$
$151$	−9.31474	−	12.8206i	−0.758023	−	1.04333i	0.239353	−	0.970933i	$-0.423065\pi$
$152$		0			0
$153$	18.0398	−	5.86147i	1.45843	−	0.473872i
$154$		0			0
$155$	4.56056			0.366313
$156$		0			0
$157$	6.94650	−	9.56103i	0.554391	−	0.763053i	−0.436209	−	0.899845i	$-0.643679\pi$
$157$	6.94650	−	9.56103i	0.554391	−	0.763053i	0.990600	+	0.136792i	$0.0436792\pi$
$158$		0			0
$159$	−6.07534	+	18.6980i	−0.481806	+	1.48285i
$160$		0			0
$161$			6.32797i			0.498714i
$162$		0			0
$163$	5.06376			0.396625			0.198312	−	0.980139i	$-0.436454\pi$
$163$	5.06376			0.396625			0.198312	+	0.980139i	$0.436454\pi$
$164$		0			0
$165$	−9.88028			−0.769178
$166$		0			0
$167$		−	13.6896i		−	1.05933i	−0.848207	−	0.529665i	$-0.822318\pi$
$167$		−	13.6896i		−	1.05933i	0.848207	−	0.529665i	$-0.177682\pi$
$168$		0			0
$169$	3.96546	−	12.2044i	0.305035	−	0.938802i
$170$		0			0
$171$	−3.17807	+	4.37424i	−0.243033	+	0.334506i
$172$		0			0
$173$	11.0500			0.840115			0.420057	−	0.907498i	$-0.362010\pi$
$173$	11.0500			0.840115			0.420057	+	0.907498i	$0.362010\pi$
$174$		0			0
$175$	3.91431	−	1.27184i	0.295894	−	0.0961417i
$176$		0			0
$177$	−11.2975	−	15.5497i	−0.849173	−	1.16879i
$178$		0			0
$179$	−5.62729	−	1.82842i	−0.420604	−	0.136662i	0.0910657	−	0.995845i	$-0.470973\pi$
$179$	−5.62729	−	1.82842i	−0.420604	−	0.136662i	−0.511669	+	0.859183i	$0.670973\pi$
$180$		0			0
$181$	−2.37971	+	0.773214i	−0.176882	+	0.0574725i	−0.396119	−	0.918199i	$-0.629643\pi$
$181$	−2.37971	+	0.773214i	−0.176882	+	0.0574725i	0.219237	+	0.975672i	$0.429643\pi$
$182$		0			0
$183$	2.56941	−	3.53649i	0.189936	−	0.261425i
$184$		0			0
$185$	0.403678	+	0.293289i	0.0296790	+	0.0215630i
$186$		0			0
$187$	20.5800	−	14.9522i	1.50496	−	1.09342i
$188$		0			0
$189$	0.315854	+	0.229481i	0.0229750	+	0.0166923i
$190$		0			0
$191$		−	25.2417i		−	1.82643i	−0.407483	−	0.913213i	$-0.633593\pi$
$191$		−	25.2417i		−	1.82643i	0.407483	−	0.913213i	$-0.366407\pi$
$192$		0			0
$193$	−21.7490	−	7.06669i	−1.56553	−	0.508671i	−0.607252	−	0.794509i	$-0.707728\pi$
$193$	−21.7490	−	7.06669i	−1.56553	−	0.508671i	−0.958278	+	0.285838i	$0.907728\pi$
$194$		0			0
$195$	−0.295106	−	0.908242i	−0.0211330	−	0.0650406i
$196$		0			0
$197$	−4.60184	−	14.1630i	−0.327867	−	1.00907i	−0.970130	−	0.242587i	$-0.922004\pi$
$197$	−4.60184	−	14.1630i	−0.327867	−	1.00907i	0.642262	−	0.766485i	$-0.277996\pi$
$198$		0			0
$199$	7.28475	+	10.0266i	0.516402	+	0.710766i	0.984982	−	0.172655i	$-0.0552344\pi$
$199$	7.28475	+	10.0266i	0.516402	+	0.710766i	−0.468581	+	0.883421i	$0.655234\pi$
$200$		0			0
$201$	−0.0814535	+	0.250688i	−0.00574529	+	0.0176822i
$202$		0			0
$203$	−7.97838	+	5.79663i	−0.559973	+	0.406844i
$204$		0			0
$205$	−2.73448	−	5.36442i	−0.190985	−	0.374667i
$206$		0			0
$207$	16.1638	−	11.7437i	1.12346	−	0.816242i
$208$		0			0
$209$	−2.24073	+	6.89627i	−0.154995	+	0.477025i
$210$		0			0
$211$	−11.5195	−	15.8552i	−0.793033	−	1.09152i	−0.993724	−	0.111862i	$-0.964319\pi$
$211$	−11.5195	−	15.8552i	−0.793033	−	1.09152i	0.200691	−	0.979655i	$-0.435681\pi$
$212$		0			0
$213$	−8.63939	−	26.5893i	−0.591961	−	1.82187i
$214$		0			0
$215$	0.564493	+	1.73733i	0.0384981	+	0.118485i
$216$		0			0
$217$	−4.61250	−	1.49869i	−0.313117	−	0.101738i
$218$		0			0
$219$			32.4524i			2.19293i
$220$		0			0
$221$	1.98917	+	1.44521i	0.133806	+	0.0972156i
$222$		0			0
$223$	−7.38787	+	5.36760i	−0.494728	+	0.359441i	−0.807000	−	0.590552i	$-0.798910\pi$
$223$	−7.38787	+	5.36760i	−0.494728	+	0.359441i	0.312271	+	0.949993i	$0.398910\pi$
$224$		0			0
$225$	−10.5130	−	7.63815i	−0.700868	−	0.509210i
$226$		0			0
$227$	15.6800	−	21.5817i	1.04072	−	1.43243i	0.144133	−	0.989558i	$-0.453961\pi$
$227$	15.6800	−	21.5817i	1.04072	−	1.43243i	0.896586	−	0.442869i	$-0.146039\pi$
$228$		0			0
$229$	−8.54659	+	2.77696i	−0.564775	+	0.183506i	−0.577468	−	0.816413i	$-0.695959\pi$
$229$	−8.54659	+	2.77696i	−0.564775	+	0.183506i	0.0126938	+	0.999919i	$0.495959\pi$
$230$		0			0
$231$	9.99280	+	3.24686i	0.657478	+	0.213627i
$232$		0			0
$233$	−0.883465	−	1.21598i	−0.0578777	−	0.0796618i	0.779097	−	0.626903i	$-0.215678\pi$
$233$	−0.883465	−	1.21598i	−0.0578777	−	0.0796618i	−0.836975	+	0.547242i	$0.815678\pi$
$234$		0			0
$235$	−3.32069	+	1.07896i	−0.216618	+	0.0703834i
$236$		0			0
$237$	30.5047			1.98149
$238$		0			0
$239$	−12.2982	+	16.9270i	−0.795502	+	1.09491i	0.197899	+	0.980222i	$0.436588\pi$
$239$	−12.2982	+	16.9270i	−0.795502	+	1.09491i	−0.993401	+	0.114692i	$0.963412\pi$
$240$		0			0
$241$	−4.84027	+	14.8968i	−0.311789	+	0.959589i	0.665266	+	0.746606i	$0.268318\pi$
$241$	−4.84027	+	14.8968i	−0.311789	+	0.959589i	−0.977056	+	0.212983i	$0.931682\pi$
$242$		0			0
$243$			22.2712i			1.42870i
$244$		0			0
$245$	0.940348			0.0600766
$246$		0			0
$247$	−0.700864			−0.0445949
$248$		0			0
$249$		−	14.4844i		−	0.917909i
$250$		0			0
$251$	−8.25059	+	25.3927i	−0.520773	+	1.60277i	0.251754	+	0.967791i	$0.418993\pi$
$251$	−8.25059	+	25.3927i	−0.520773	+	1.60277i	−0.772527	+	0.634982i	$0.781007\pi$
$252$		0			0
$253$	15.7495	−	21.6774i	0.990164	−	1.36284i
$254$		0			0
$255$	−14.0181			−0.877846
$256$		0			0
$257$	−21.6492	+	7.03426i	−1.35044	+	0.438785i	−0.892841	−	0.450373i	$-0.851291\pi$
$257$	−21.6492	+	7.03426i	−1.35044	+	0.438785i	−0.457601	+	0.889158i	$0.651291\pi$
$258$		0			0
$259$	−0.311894	−	0.429286i	−0.0193802	−	0.0266745i
$260$		0			0
$261$	29.6131	+	9.62189i	1.83301	+	0.595580i
$262$		0			0
$263$	−17.1456	+	5.57094i	−1.05724	+	0.343519i	−0.785506	−	0.618853i	$-0.787597\pi$
$263$	−17.1456	+	5.57094i	−1.05724	+	0.343519i	−0.271735	+	0.962372i	$0.587597\pi$
$264$		0			0
$265$	4.37924	−	6.02751i	0.269015	−	0.370267i
$266$		0			0
$267$	−26.7123	−	19.4076i	−1.63477	−	1.18773i
$268$		0			0
$269$	23.8795	−	17.3495i	1.45596	−	1.05782i	0.471568	−	0.881830i	$-0.343688\pi$
$269$	23.8795	−	17.3495i	1.45596	−	1.05782i	0.984392	−	0.175987i	$-0.0563118\pi$
$270$		0			0
$271$	4.05745	+	2.94791i	0.246473	+	0.179073i	0.704162	−	0.710039i	$-0.251323\pi$
$271$	4.05745	+	2.94791i	0.246473	+	0.179073i	−0.457689	+	0.889112i	$0.651323\pi$
$272$		0			0
$273$			1.01556i			0.0614647i
$274$		0			0
$275$	−16.5745	−	5.38537i	−0.999477	−	0.324750i
$276$		0			0
$277$	−8.73161	−	26.8731i	−0.524632	−	1.61465i	−0.765043	−	0.643979i	$-0.777282\pi$
$277$	−8.73161	−	26.8731i	−0.524632	−	1.61465i	0.240412	−	0.970671i	$-0.422718\pi$
$278$		0			0
$279$	4.73187	+	14.5632i	0.283290	+	0.871876i
$280$		0			0
$281$	−2.66581	−	3.66918i	−0.159029	−	0.218885i	0.722066	−	0.691825i	$-0.243193\pi$
$281$	−2.66581	−	3.66918i	−0.159029	−	0.218885i	−0.881095	+	0.472940i	$0.843193\pi$
$282$		0			0
$283$	9.58369	−	29.4956i	0.569691	−	1.75333i	−0.0838912	−	0.996475i	$-0.526735\pi$
$283$	9.58369	−	29.4956i	0.569691	−	1.75333i	0.653583	−	0.756855i	$-0.273265\pi$
$284$		0			0
$285$	3.23270	−	2.34870i	0.191489	−	0.139125i
$286$		0			0
$287$	1.00277	+	6.32412i	0.0591916	+	0.373301i
$288$		0			0
$289$	15.4455	−	11.2218i	0.908557	−	0.660105i
$290$		0			0
$291$	3.23038	−	9.94208i	0.189368	−	0.582815i
$292$		0			0
$293$	7.07029	+	9.73142i	0.413051	+	0.568516i	0.963959	−	0.266050i	$-0.0857186\pi$
$293$	7.07029	+	9.73142i	0.413051	+	0.568516i	−0.550908	+	0.834566i	$0.685719\pi$
$294$		0			0
$295$	2.25081	+	6.92727i	0.131047	+	0.403321i
$296$		0			0
$297$	−0.510853	−	1.57224i	−0.0296427	−	0.0912308i
$298$		0			0
$299$	2.46310	+	0.800308i	0.142444	+	0.0462830i
$300$		0			0
$301$		−	1.94262i		−	0.111971i
$302$		0			0
$303$	20.5603	+	14.9380i	1.18116	+	0.858163i
$304$		0			0
$305$	−1.34018	+	0.973701i	−0.0767388	+	0.0557540i
$306$		0			0
$307$	2.88020	+	2.09259i	0.164382	+	0.119430i	0.666935	−	0.745116i	$-0.267606\pi$
$307$	2.88020	+	2.09259i	0.164382	+	0.119430i	−0.502553	+	0.864546i	$0.667606\pi$
$308$		0			0
$309$	14.9891	−	20.6308i	0.852702	−	1.17364i
$310$		0			0
$311$	−5.34369	+	1.73627i	−0.303013	+	0.0984548i	−0.456577	−	0.889684i	$-0.650925\pi$
$311$	−5.34369	+	1.73627i	−0.303013	+	0.0984548i	0.153564	+	0.988139i	$0.450925\pi$
$312$		0			0
$313$	4.47629	+	1.45443i	0.253015	+	0.0822095i	0.432778	−	0.901500i	$-0.357533\pi$
$313$	4.47629	+	1.45443i	0.253015	+	0.0822095i	−0.179764	+	0.983710i	$0.557533\pi$
$314$		0			0
$315$	−1.74513	−	2.40197i	−0.0983270	−	0.135336i
$316$		0			0
$317$	14.4296	−	4.68847i	0.810449	−	0.263331i	0.125661	−	0.992073i	$-0.459895\pi$
$317$	14.4296	−	4.68847i	0.810449	−	0.263331i	0.684788	+	0.728742i	$0.259895\pi$
$318$		0			0
$319$	41.7582			2.33801
$320$		0			0
$321$	−26.3932	+	36.3271i	−1.47312	+	2.02758i
$322$		0			0
$323$	−3.17914	+	9.78438i	−0.176892	+	0.544417i
$324$		0			0
$325$		−	1.68445i		−	0.0934366i
$326$		0			0
$327$	28.7878			1.59197
$328$		0			0
$329$	3.71307			0.204708
$330$		0			0
$331$		−	0.954772i		−	0.0524790i	−0.999656	−	0.0262395i	$-0.991647\pi$
$331$		−	0.954772i		−	0.0524790i	0.999656	−	0.0262395i	$-0.00835325\pi$
$332$		0			0
$333$	−0.517717	+	1.59337i	−0.0283707	+	0.0873160i
$334$		0			0
$335$	0.0587135	−	0.0808122i	0.00320786	−	0.00441524i
$336$		0			0
$337$	2.64017			0.143819			0.0719095	−	0.997411i	$-0.477091\pi$
$337$	2.64017			0.143819			0.0719095	+	0.997411i	$0.477091\pi$
$338$		0			0
$339$	−3.01410	+	0.979342i	−0.163704	+	0.0531905i
$340$		0			0
$341$	12.0707	+	16.6139i	0.653665	+	0.899693i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	−14.0429	+	4.56280i	−0.756043	+	0.245653i
$346$		0			0
$347$	20.7114	−	28.5068i	1.11185	−	1.53033i	0.293183	−	0.956056i	$-0.405285\pi$
$347$	20.7114	−	28.5068i	1.11185	−	1.53033i	0.818665	−	0.574271i	$-0.194715\pi$
$348$		0			0
$349$	14.3278	+	10.4097i	0.766947	+	0.557220i	0.901033	−	0.433750i	$-0.142810\pi$
$349$	14.3278	+	10.4097i	0.766947	+	0.557220i	−0.134086	+	0.990970i	$0.542810\pi$
$350$		0			0
$351$	0.129270	−	0.0939200i	0.00689991	−	0.00501308i
$352$		0			0
$353$	−7.73727	−	5.62145i	−0.411813	−	0.299200i	0.362522	−	0.931975i	$-0.381916\pi$
$353$	−7.73727	−	5.62145i	−0.411813	−	0.299200i	−0.774335	+	0.632775i	$0.781916\pi$
$354$		0			0
$355$			10.5948i			0.562314i
$356$		0			0
$357$	14.1777	+	4.60662i	0.750364	+	0.243808i
$358$		0			0
$359$	8.30048	+	25.5463i	0.438083	+	1.34828i	0.889894	+	0.456167i	$0.150778\pi$
$359$	8.30048	+	25.5463i	0.438083	+	1.34828i	−0.451812	+	0.892113i	$0.649222\pi$
$360$		0			0
$361$	4.96511	+	15.2810i	0.261322	+	0.804265i
$362$		0			0
$363$	−10.1069	−	13.9109i	−0.530474	−	0.730135i
$364$		0			0
$365$	3.80033	−	11.6962i	0.198918	−	0.612208i
$366$		0			0
$367$	−8.12390	+	5.90236i	−0.424064	+	0.308100i	−0.779271	−	0.626687i	$-0.784410\pi$
$367$	−8.12390	+	5.90236i	−0.424064	+	0.308100i	0.355207	+	0.934788i	$0.384410\pi$
$368$		0			0
$369$	14.2930	−	14.2979i	0.744062	−	0.744321i
$370$		0			0
$371$	−6.40987	+	4.65704i	−0.332784	+	0.241782i
$372$		0			0
$373$	−7.95739	+	24.4903i	−0.412018	+	1.26806i	0.502873	+	0.864360i	$0.332276\pi$
$373$	−7.95739	+	24.4903i	−0.412018	+	1.26806i	−0.914891	+	0.403701i	$0.867724\pi$
$374$		0			0
$375$	12.5025	+	17.2082i	0.645625	+	0.888626i
$376$		0			0
$377$	1.24724	+	3.83861i	0.0642361	+	0.197698i
$378$		0			0
$379$	0.632902	+	1.94787i	0.0325100	+	0.100055i	0.965995	−	0.258561i	$-0.0832484\pi$
$379$	0.632902	+	1.94787i	0.0325100	+	0.100055i	−0.933485	+	0.358617i	$0.883248\pi$
$380$		0			0
$381$	7.93404	+	2.57793i	0.406473	+	0.132071i
$382$		0			0
$383$		−	2.31824i		−	0.118457i	−0.998244	−	0.0592284i	$-0.981136\pi$
$383$		−	2.31824i		−	0.118457i	0.998244	−	0.0592284i	$-0.0188640\pi$
$384$		0			0
$385$	−3.22129	−	2.34041i	−0.164172	−	0.119278i
$386$		0			0
$387$	−4.96211	+	3.60518i	−0.252238	+	0.183262i
$388$		0			0
$389$	6.24083	+	4.53423i	0.316423	+	0.229895i	0.734648	−	0.678449i	$-0.237348\pi$
$389$	6.24083	+	4.53423i	0.316423	+	0.229895i	−0.418225	+	0.908344i	$0.637348\pi$
$390$		0			0
$391$	22.3453	−	30.7557i	1.13005	−	1.55538i
$392$		0			0
$393$	19.3712	−	6.29409i	0.977149	−	0.317495i
$394$		0			0
$395$	−10.9942	−	3.57224i	−0.553180	−	0.179739i
$396$		0			0
$397$	−7.58289	−	10.4370i	−0.380574	−	0.523816i	0.575162	−	0.818039i	$-0.304939\pi$
$397$	−7.58289	−	10.4370i	−0.380574	−	0.523816i	−0.955737	+	0.294224i	$0.904939\pi$
$398$		0			0
$399$	−4.04135	+	1.31311i	−0.202320	+	0.0657379i
$400$		0			0
$401$	9.57018			0.477912			0.238956	−	0.971030i	$-0.423195\pi$
$401$	9.57018			0.477912			0.238956	+	0.971030i	$0.423195\pi$
$402$		0			0
$403$	−1.16670	+	1.60582i	−0.0581174	+	0.0799917i
$404$		0			0
$405$	2.47090	−	7.60464i	0.122780	−	0.377878i
$406$		0			0
$407$			2.24684i			0.111372i
$408$		0			0
$409$	16.5471			0.818200			0.409100	−	0.912489i	$-0.365843\pi$
$409$	16.5471			0.818200			0.409100	+	0.912489i	$0.365843\pi$
$410$		0			0
$411$	−26.1450			−1.28964
$412$		0			0
$413$		−	7.74582i		−	0.381147i
$414$		0			0
$415$	−1.69619	+	5.22032i	−0.0832625	+	0.256256i
$416$		0			0
$417$	−12.6998	+	17.4798i	−0.621914	+	0.855991i
$418$		0			0
$419$	−5.65535			−0.276282			−0.138141	−	0.990413i	$-0.544113\pi$
$419$	−5.65535			−0.276282			−0.138141	+	0.990413i	$0.544113\pi$
$420$		0			0
$421$	−3.65657	+	1.18809i	−0.178210	+	0.0579040i	−0.396763	−	0.917921i	$-0.629866\pi$
$421$	−3.65657	+	1.18809i	−0.178210	+	0.0579040i	0.218553	+	0.975825i	$0.429866\pi$
$422$		0			0
$423$	−6.89086	−	9.48445i	−0.335045	−	0.461150i
$424$		0			0
$425$	−23.5157	−	7.64072i	−1.14068	−	0.370629i
$426$		0			0
$427$	1.67542	−	0.544378i	0.0810795	−	0.0263443i
$428$		0			0
$429$	2.52761	−	3.47895i	0.122034	−	0.167965i
$430$		0			0
$431$	7.90770	+	5.74528i	0.380900	+	0.276740i	0.761716	−	0.647910i	$-0.224357\pi$
$431$	7.90770	+	5.74528i	0.380900	+	0.276740i	−0.380816	+	0.924651i	$0.624357\pi$
$432$		0			0
$433$	−29.0399	+	21.0988i	−1.39557	+	1.01394i	−0.400343	+	0.916365i	$0.631109\pi$
$433$	−29.0399	+	21.0988i	−1.39557	+	1.01394i	−0.995228	+	0.0975762i	$0.968891\pi$
$434$		0			0
$435$	−18.6166	−	13.5257i	−0.892596	−	0.648509i
$436$		0			0
$437$			10.8365i			0.518379i
$438$		0			0
$439$	−27.1421	−	8.81902i	−1.29542	−	0.420909i	−0.421437	−	0.906858i	$-0.638474\pi$
$439$	−27.1421	−	8.81902i	−1.29542	−	0.420909i	−0.873987	+	0.485949i	$0.838474\pi$
$440$		0			0
$441$	0.975671	+	3.00281i	0.0464605	+	0.142991i
$442$		0			0
$443$	7.11863	+	21.9089i	0.338216	+	1.04092i	0.965116	+	0.261823i	$0.0843235\pi$
$443$	7.11863	+	21.9089i	0.338216	+	1.04092i	−0.626900	+	0.779100i	$0.715676\pi$
$444$		0			0
$445$	7.35470	+	10.1229i	0.348646	+	0.479870i
$446$		0			0
$447$	0.407988	−	1.25566i	0.0192972	−	0.0593905i
$448$		0			0
$449$	−33.8394	+	24.5857i	−1.59698	+	1.16027i	−0.703972	+	0.710228i	$0.748592\pi$
$449$	−33.8394	+	24.5857i	−1.59698	+	1.16027i	−0.893006	+	0.450044i	$0.851408\pi$
$450$		0			0
$451$	12.3048	−	24.1599i	0.579410	−	1.13765i
$452$		0			0
$453$	−31.8131	+	23.1136i	−1.49471	+	1.08597i
$454$		0			0
$455$	0.118927	−	0.366020i	0.00557539	−	0.0171593i
$456$		0			0
$457$	6.09734	+	8.39226i	0.285221	+	0.392573i	0.927455	−	0.373936i	$-0.121992\pi$
$457$	6.09734	+	8.39226i	0.285221	+	0.392573i	−0.642233	+	0.766509i	$0.721992\pi$
$458$		0			0
$459$	−0.724794	−	2.23069i	−0.0338305	−	0.104120i
$460$		0			0
$461$	1.59397	+	4.90574i	0.0742386	+	0.228483i	0.981290	−	0.192538i	$-0.0616719\pi$
$461$	1.59397	+	4.90574i	0.0742386	+	0.228483i	−0.907051	+	0.421021i	$0.861672\pi$
$462$		0			0
$463$	−26.6336	−	8.65378i	−1.23777	−	0.402175i	−0.384246	−	0.923231i	$-0.625539\pi$
$463$	−26.6336	−	8.65378i	−1.23777	−	0.402175i	−0.853523	+	0.521055i	$0.825539\pi$
$464$		0			0
$465$		−	11.3166i		−	0.524793i
$466$		0			0
$467$	−0.0164463	−	0.0119489i	−0.000761043	−	0.000552930i	0.587405	−	0.809293i	$-0.300150\pi$
$467$	−0.0164463	−	0.0119489i	−0.000761043	−	0.000552930i	−0.588166	+	0.808740i	$0.700150\pi$
$468$		0			0
$469$	−0.0859387	+	0.0624381i	−0.00396828	+	0.00288312i
$470$		0			0
$471$	−23.7247	−	17.2370i	−1.09318	−	0.794240i
$472$		0			0
$473$	−4.83493	+	6.65471i	−0.222310	+	0.305984i
$474$		0			0
$475$	6.70314	−	2.17798i	0.307561	−	0.0999327i
$476$		0			0
$477$	23.7913	+	7.73028i	1.08933	+	0.353945i
$478$		0			0
$479$	21.0985	+	29.0396i	0.964017	+	1.32686i	0.945012	+	0.327036i	$0.106050\pi$
$479$	21.0985	+	29.0396i	0.964017	+	1.32686i	0.0190048	+	0.999819i	$0.493950\pi$
$480$		0			0
$481$	−0.206541	+	0.0671091i	−0.00941744	+	0.00305991i
$482$		0			0
$483$	15.7022			0.714476
$484$		0			0
$485$	−2.32853	+	3.20494i	−0.105733	+	0.145529i
$486$		0			0
$487$	−7.11168	+	21.8875i	−0.322261	+	0.991818i	0.650401	+	0.759591i	$0.274601\pi$
$487$	−7.11168	+	21.8875i	−0.322261	+	0.991818i	−0.972662	+	0.232226i	$0.925399\pi$
$488$		0			0
$489$		−	12.5652i		−	0.568219i
$490$		0			0
$491$	−2.82550			−0.127513			−0.0637566	−	0.997965i	$-0.520308\pi$
$491$	−2.82550			−0.127513			−0.0637566	+	0.997965i	$0.520308\pi$
$492$		0			0
$493$	59.2462			2.66831
$494$		0			0
$495$			12.5717i			0.565055i
$496$		0			0
$497$	3.48166	−	10.7155i	0.156174	−	0.480654i
$498$		0			0
$499$	−2.98341	+	4.10631i	−0.133556	+	0.183824i	−0.870557	−	0.492068i	$-0.836241\pi$
$499$	−2.98341	+	4.10631i	−0.133556	+	0.183824i	0.737001	+	0.675892i	$0.236241\pi$
$500$		0			0
$501$	−33.9692			−1.51763
$502$		0			0
$503$	16.4679	−	5.35076i	0.734269	−	0.238578i	0.0820703	−	0.996627i	$-0.473847\pi$
$503$	16.4679	−	5.35076i	0.734269	−	0.238578i	0.652199	+	0.758048i	$0.273847\pi$
$504$		0			0
$505$	−5.66087	−	7.79152i	−0.251905	−	0.346718i
$506$		0			0
$507$	−30.2841	−	9.83989i	−1.34496	−	0.437005i
$508$		0			0
$509$	−1.14072	+	0.370642i	−0.0505614	+	0.0164284i	−0.334189	−	0.942506i	$-0.608462\pi$
$509$	−1.14072	+	0.370642i	−0.0505614	+	0.0164284i	0.283627	+	0.958935i	$0.408462\pi$
$510$		0			0
$511$	−7.68722	+	10.5806i	−0.340063	+	0.468056i
$512$		0			0
$513$	0.540891	+	0.392981i	0.0238809	+	0.0173505i
$514$		0			0
$515$	−7.81821	+	5.68026i	−0.344511	+	0.250302i
$516$		0			0
$517$	−12.7197	−	9.24137i	−0.559410	−	0.406435i
$518$		0			0
$519$		−	27.4194i		−	1.20358i
$520$		0			0
$521$	−21.4049	−	6.95489i	−0.937768	−	0.304699i	−0.200032	−	0.979789i	$-0.564105\pi$
$521$	−21.4049	−	6.95489i	−0.937768	−	0.304699i	−0.737735	+	0.675090i	$0.764105\pi$
$522$		0			0
$523$	−0.00157227	−	0.00483894i	−6.87504e−5	−	0.000211592i	0.951022	−	0.309123i	$-0.100035\pi$
$523$	−0.00157227	−	0.00483894i	−6.87504e−5	−	0.000211592i	−0.951091	+	0.308911i	$0.900035\pi$
$524$		0			0
$525$	−3.15593	−	9.71296i	−0.137736	−	0.423908i
$526$		0			0
$527$	17.1258	+	23.5717i	0.746013	+	1.02680i
$528$		0			0
$529$	5.26665	−	16.2091i	0.228985	−	0.704742i
$530$		0			0
$531$	−19.7855	+	14.3750i	−0.858616	+	0.623821i
$532$		0			0
$533$	2.58842	+	0.409503i	0.112117	+	0.0177376i
$534$		0			0
$535$	13.7665	−	10.0019i	0.595176	−	0.432421i
$536$		0			0
$537$	−4.53703	+	13.9636i	−0.195787	+	0.602572i
$538$		0			0
$539$	2.48887	+	3.42564i	0.107203	+	0.147553i
$540$		0			0
$541$	−8.90489	−	27.4064i	−0.382851	−	1.17829i	−0.938027	−	0.346562i	$-0.887349\pi$
$541$	−8.90489	−	27.4064i	−0.382851	−	1.17829i	0.555176	−	0.831733i	$-0.312651\pi$
$542$		0			0
$543$	1.91865	+	5.90500i	0.0823372	+	0.253408i
$544$		0			0
$545$	−10.3755	−	3.37119i	−0.444436	−	0.144406i
$546$		0			0
$547$		−	7.70290i		−	0.329352i	−0.986348	−	0.164676i	$-0.947342\pi$
$547$		−	7.70290i		−	0.329352i	0.986348	−	0.164676i	$-0.0526579\pi$
$548$		0			0
$549$	−4.49984	−	3.26933i	−0.192049	−	0.139531i
$550$		0			0
$551$	−13.6628	+	9.92657i	−0.582053	+	0.422886i
$552$		0			0
$553$	9.94553	+	7.22585i	0.422927	+	0.307274i
$554$		0			0
$555$	0.727767	−	1.00169i	0.0308920	−	0.0425192i
$556$		0			0
$557$	13.4758	−	4.37855i	0.570988	−	0.185525i	−0.00927143	−	0.999957i	$-0.502951\pi$
$557$	13.4758	−	4.37855i	0.570988	−	0.185525i	0.580259	+	0.814432i	$0.302951\pi$
$558$		0			0
$559$	−0.756143	−	0.245686i	−0.0319815	−	0.0103914i
$560$		0			0
$561$	−37.1025	−	51.0672i	−1.56647	−	2.15606i
$562$		0			0
$563$	−2.48728	+	0.808168i	−0.104827	+	0.0340602i	−0.360961	−	0.932581i	$-0.617551\pi$
$563$	−2.48728	+	0.808168i	−0.104827	+	0.0340602i	0.256134	+	0.966641i	$0.417551\pi$
$564$		0			0
$565$	1.20100			0.0505265
$566$		0			0
$567$	−4.99807	+	6.87926i	−0.209899	+	0.288902i
$568$		0			0
$569$	1.01321	−	3.11835i	0.0424761	−	0.130728i	−0.927570	−	0.373650i	$-0.878106\pi$
$569$	1.01321	−	3.11835i	0.0424761	−	0.130728i	0.970046	+	0.242922i	$0.0781060\pi$
$570$		0			0
$571$		−	11.1718i		−	0.467523i	−0.972294	−	0.233762i	$-0.924896\pi$
$571$		−	11.1718i		−	0.467523i	0.972294	−	0.233762i	$-0.0751036\pi$
$572$		0			0
$573$	−62.6347			−2.61660
$574$		0			0
$575$	−26.0443			−1.08612
$576$		0			0
$577$		−	41.6262i		−	1.73292i	−0.499245	−	0.866461i	$-0.666389\pi$
$577$		−	41.6262i		−	1.73292i	0.499245	−	0.866461i	$-0.333611\pi$
$578$		0			0
$579$	−17.5353	+	53.9680i	−0.728741	+	2.24283i
$580$		0			0
$581$	3.43101	−	4.72237i	0.142342	−	0.195917i
$582$		0			0
$583$	33.5487			1.38945
$584$		0			0
$585$	−1.15565	+	0.375493i	−0.0477802	+	0.0155247i
$586$		0			0
$587$	1.36992	+	1.88553i	0.0565425	+	0.0778241i	0.836352	−	0.548193i	$-0.184684\pi$
$587$	1.36992	+	1.88553i	0.0565425	+	0.0778241i	−0.779809	+	0.626017i	$0.784684\pi$
$588$		0			0
$589$	−7.89877	−	2.56647i	−0.325463	−	0.105749i
$590$		0			0
$591$	−35.1440	+	11.4190i	−1.44563	+	0.469714i
$592$		0			0
$593$	−13.8511	+	19.0643i	−0.568795	+	0.782879i	−0.992411	−	0.122963i	$-0.960760\pi$
$593$	−13.8511	+	19.0643i	−0.568795	+	0.782879i	0.423617	+	0.905842i	$0.360760\pi$
$594$		0			0
$595$	−4.57035	−	3.32055i	−0.187366	−	0.136129i
$596$		0			0
$597$	24.8800	−	18.0764i	1.01827	−	0.739816i
$598$		0			0
$599$	16.3747	+	11.8969i	0.669052	+	0.486094i	0.869708	−	0.493567i	$-0.164307\pi$
$599$	16.3747	+	11.8969i	0.669052	+	0.486094i	−0.200656	+	0.979662i	$0.564307\pi$
$600$		0			0
$601$			42.3220i			1.72635i	0.504906	+	0.863175i	$0.331527\pi$
$601$			42.3220i			1.72635i	−0.504906	+	0.863175i	$0.668473\pi$
$602$		0			0
$603$	0.318976	+	0.103642i	0.0129897	+	0.00422061i
$604$		0			0
$605$	2.01360	+	6.19722i	0.0818645	+	0.251953i
$606$		0			0
$607$	5.12132	+	15.7618i	0.207868	+	0.639752i	0.999583	+	0.0288617i	$0.00918823\pi$
$607$	5.12132	+	15.7618i	0.207868	+	0.639752i	−0.791716	+	0.610890i	$0.790812\pi$
$608$		0			0
$609$	14.3838	+	19.7975i	0.582859	+	0.802237i
$610$		0			0
$611$	0.469598	−	1.44527i	0.0189979	−	0.0584695i
$612$		0			0
$613$	−11.5239	+	8.37258i	−0.465445	+	0.338165i	−0.795663	−	0.605739i	$-0.792878\pi$
$613$	−11.5239	+	8.37258i	−0.465445	+	0.338165i	0.330219	+	0.943905i	$0.392878\pi$
$614$		0			0
$615$	−13.3113	+	6.78534i	−0.536762	+	0.273611i
$616$		0			0
$617$	−28.2521	+	20.5263i	−1.13739	+	0.826359i	−0.986753	−	0.162231i	$-0.948131\pi$
$617$	−28.2521	+	20.5263i	−1.13739	+	0.826359i	−0.150632	+	0.988590i	$0.548131\pi$
$618$		0			0
$619$	4.34953	−	13.3865i	0.174822	−	0.538048i	−0.824803	−	0.565420i	$-0.808714\pi$
$619$	4.34953	−	13.3865i	0.174822	−	0.538048i	0.999625	+	0.0273725i	$0.00871404\pi$
$620$		0			0
$621$	−1.45215	−	1.99872i	−0.0582729	−	0.0802057i
$622$		0			0
$623$	−4.11188	−	12.6551i	−0.164739	−	0.507014i
$624$		0			0
$625$	3.86831	+	11.9054i	0.154732	+	0.476217i
$626$		0			0
$627$	17.1124	+	5.56015i	0.683403	+	0.222051i
$628$		0			0
$629$			3.18781i			0.127106i
$630$		0			0
$631$	−15.1389	−	10.9991i	−0.602671	−	0.437866i	0.244155	−	0.969736i	$-0.421489\pi$
$631$	−15.1389	−	10.9991i	−0.602671	−	0.437866i	−0.846826	+	0.531870i	$0.821489\pi$
$632$		0			0
$633$	−39.3430	+	28.5844i	−1.56375	+	1.13613i
$634$		0			0
$635$	−2.55763	−	1.85823i	−0.101496	−	0.0737415i
$636$		0			0
$637$	−0.240563	+	0.331107i	−0.00953146	+	0.0131189i
$638$		0			0
$639$	−33.8323	+	10.9928i	−1.33839	+	0.434868i
$640$		0			0
$641$	19.9801	+	6.49193i	0.789167	+	0.256416i	0.675749	−	0.737131i	$-0.263820\pi$
$641$	19.9801	+	6.49193i	0.789167	+	0.256416i	0.113418	+	0.993547i	$0.463820\pi$
$642$		0			0
$643$	−12.7634	−	17.5673i	−0.503339	−	0.692787i	0.479439	−	0.877575i	$-0.340840\pi$
$643$	−12.7634	−	17.5673i	−0.503339	−	0.692787i	−0.982778	+	0.184788i	$0.940840\pi$
$644$		0			0
$645$	4.31101	−	1.40073i	0.169746	−	0.0551537i
$646$		0			0
$647$	24.6602			0.969491			0.484745	−	0.874655i	$-0.338912\pi$
$647$	24.6602			0.969491			0.484745	+	0.874655i	$0.338912\pi$
$648$		0			0
$649$	−19.2784	+	26.5344i	−0.756742	+	1.04157i
$650$		0			0
$651$	−3.71885	+	11.4454i	−0.145753	+	0.448582i
$652$		0			0
$653$		−	7.31669i		−	0.286324i	−0.989699	−	0.143162i	$-0.954273\pi$
$653$		−	7.31669i		−	0.286324i	0.989699	−	0.143162i	$-0.0457270\pi$
$654$		0			0
$655$	−7.71868			−0.301594
$656$		0			0
$657$	41.2926			1.61098
$658$		0			0
$659$		−	9.44322i		−	0.367856i	−0.982940	−	0.183928i	$-0.941119\pi$
$659$		−	9.44322i		−	0.367856i	0.982940	−	0.183928i	$-0.0588813\pi$
$660$		0			0
$661$	−5.28532	+	16.2666i	−0.205575	+	0.632696i	0.794114	+	0.607769i	$0.207935\pi$
$661$	−5.28532	+	16.2666i	−0.205575	+	0.632696i	−0.999689	+	0.0249269i	$0.992065\pi$
$662$		0			0
$663$	3.58615	−	4.93592i	0.139275	−	0.191695i
$664$		0			0
$665$	1.61032			0.0624455
$666$		0			0
$667$	59.3510	−	19.2843i	2.29808	−	0.746691i
$668$		0			0
$669$	13.3192	+	18.3323i	0.514948	+	0.708766i
$670$		0			0
$671$	−7.09429	−	2.30508i	−0.273872	−	0.0889865i
$672$		0			0
$673$	25.4296	−	8.26257i	0.980239	−	0.318499i	0.225296	−	0.974290i	$-0.427665\pi$
$673$	25.4296	−	8.26257i	0.980239	−	0.318499i	0.754942	+	0.655791i	$0.227665\pi$
$674$		0			0
$675$	−0.944488	+	1.29998i	−0.0363533	+	0.0500361i
$676$		0			0
$677$	−30.5006	−	22.1600i	−1.17223	−	0.851678i	−0.180959	−	0.983491i	$-0.557920\pi$
$677$	−30.5006	−	22.1600i	−1.17223	−	0.851678i	−0.991275	+	0.131813i	$0.957920\pi$
$678$		0			0
$679$	3.40826	−	2.47624i	0.130797	−	0.0950295i
$680$		0			0
$681$	−53.5528	−	38.9084i	−2.05215	−	1.49097i
$682$		0			0
$683$		−	35.3934i		−	1.35429i	−0.735850	−	0.677145i	$-0.763217\pi$
$683$		−	35.3934i		−	1.35429i	0.735850	−	0.677145i	$-0.236783\pi$
$684$		0			0
$685$	9.42295	+	3.06170i	0.360032	+	0.116982i
$686$		0			0
$687$	6.89073	+	21.2075i	0.262898	+	0.809116i
$688$		0			0
$689$	1.00204	+	3.08396i	0.0381746	+	0.117489i
$690$		0			0
$691$	−11.4795	−	15.8002i	−0.436702	−	0.601069i	0.532773	−	0.846258i	$-0.321150\pi$
$691$	−11.4795	−	15.8002i	−0.436702	−	0.601069i	−0.969475	+	0.245189i	$0.921150\pi$
$692$		0			0
$693$	4.13131	−	12.7149i	0.156935	−	0.482998i
$694$		0			0
$695$	6.62414	−	4.81272i	0.251268	−	0.182557i
$696$		0			0
$697$	17.4580	−	34.2779i	0.661268	−	1.29837i
$698$		0			0
$699$	−3.01734	+	2.19223i	−0.114126	+	0.0829177i
$700$		0			0
$701$	−6.13506	+	18.8818i	−0.231718	+	0.713154i	0.765822	+	0.643053i	$0.222332\pi$
$701$	−6.13506	+	18.8818i	−0.231718	+	0.713154i	−0.997540	+	0.0701017i	$0.977668\pi$
$702$		0			0
$703$	−0.534110	−	0.735140i	−0.0201444	−	0.0277263i
$704$		0			0
$705$	2.67732	+	8.23995i	0.100834	+	0.310335i
$706$		0			0
$707$	3.16489	+	9.74053i	0.119028	+	0.366330i
$708$		0			0
$709$	−29.6939	−	9.64814i	−1.11518	−	0.362344i	−0.307253	−	0.951628i	$-0.599410\pi$
$709$	−29.6939	−	9.64814i	−1.11518	−	0.362344i	−0.807926	+	0.589284i	$0.799410\pi$
$710$		0			0
$711$		−	38.8143i		−	1.45565i
$712$		0			0
$713$	24.8286	+	18.0390i	0.929838	+	0.675567i
$714$		0			0
$715$	−1.31838	+	0.957859i	−0.0493046	+	0.0358219i
$716$		0			0
$717$	42.0025	+	30.5166i	1.56861	+	1.13966i
$718$		0			0
$719$	−7.94159	+	10.9307i	−0.296171	+	0.407645i	−0.931006	−	0.365003i	$-0.881068\pi$
$719$	−7.94159	+	10.9307i	−0.296171	+	0.407645i	0.634835	+	0.772648i	$0.281068\pi$
$720$		0			0
$721$	9.77389	−	3.17573i	0.363999	−	0.118270i
$722$		0			0
$723$	36.9650	+	12.0106i	1.37474	+	0.446681i
$724$		0			0
$725$	−23.8575	−	32.8370i	−0.886044	−	1.21954i
$726$		0			0
$727$	24.5634	−	7.98114i	0.911007	−	0.296004i	0.184234	−	0.982882i	$-0.441019\pi$
$727$	24.5634	−	7.98114i	0.911007	−	0.296004i	0.726773	+	0.686878i	$0.241019\pi$
$728$		0			0
$729$	29.7539			1.10200
$730$		0			0
$731$	−6.85977	+	9.44166i	−0.253718	+	0.349213i
$732$		0			0
$733$	−0.517998	+	1.59423i	−0.0191327	+	0.0588844i	−0.960167	−	0.279427i	$-0.909856\pi$
$733$	−0.517998	+	1.59423i	−0.0191327	+	0.0588844i	0.941034	+	0.338311i	$0.109856\pi$
$734$		0			0
$735$		−	2.33338i		−	0.0860679i
$736$		0			0
$737$	0.449796			0.0165684
$738$		0			0
$739$	12.1788			0.448006			0.224003	−	0.974588i	$-0.428087\pi$
$739$	12.1788			0.448006			0.224003	+	0.974588i	$0.428087\pi$
$740$		0			0
$741$			1.73912i			0.0638883i
$742$		0			0
$743$	−2.01097	+	6.18913i	−0.0737754	+	0.227057i	−0.981144	−	0.193279i	$-0.938088\pi$
$743$	−2.01097	+	6.18913i	−0.0737754	+	0.227057i	0.907369	+	0.420336i	$0.138088\pi$
$744$		0			0
$745$	−0.294087	+	0.404776i	−0.0107745	+	0.0148298i
$746$		0			0
$747$	−18.4299			−0.674316
$748$		0			0
$749$	−17.2101	+	5.59189i	−0.628842	+	0.204323i
$750$		0			0
$751$	27.3589	+	37.6562i	0.998339	+	1.37410i	0.926339	+	0.376691i	$0.122938\pi$
$751$	27.3589	+	37.6562i	0.998339	+	1.37410i	0.0720000	+	0.997405i	$0.477062\pi$
$752$		0			0
$753$	63.0094	+	20.4730i	2.29619	+	0.746078i
$754$		0			0
$755$	14.1725	−	4.60493i	0.515791	−	0.167591i
$756$		0			0
$757$	−27.3986	+	37.7109i	−0.995818	+	1.37063i	−0.0679613	+	0.997688i	$0.521649\pi$
$757$	−27.3986	+	37.7109i	−0.995818	+	1.37063i	−0.927856	+	0.372938i	$0.878351\pi$
$758$		0			0
$759$	−53.7902	−	39.0808i	−1.95246	−	1.41854i
$760$		0			0
$761$	−19.1094	+	13.8838i	−0.692714	+	0.503286i	−0.877551	−	0.479483i	$-0.840824\pi$
$761$	−19.1094	+	13.8838i	−0.692714	+	0.503286i	0.184837	+	0.982769i	$0.440824\pi$
$762$		0			0
$763$	9.38578	+	6.81917i	0.339788	+	0.246870i
$764$		0			0
$765$			17.8366i			0.644885i
$766$		0			0
$767$	−3.01498	−	0.979626i	−0.108865	−	0.0353722i
$768$		0			0
$769$	11.2756	+	34.7028i	0.406610	+	1.25142i	0.919544	+	0.392988i	$0.128559\pi$
$769$	11.2756	+	34.7028i	0.406610	+	1.25142i	−0.512934	+	0.858428i	$0.671441\pi$
$770$		0			0
$771$	17.4548	+	53.7203i	0.628619	+	1.93469i
$772$		0			0
$773$	19.6440	+	27.0377i	0.706547	+	0.972479i	0.999864	+	0.0164635i	$0.00524073\pi$
$773$	19.6440	+	27.0377i	0.706547	+	0.972479i	−0.293317	+	0.956015i	$0.594759\pi$
$774$		0			0
$775$	6.16823	−	18.9839i	0.221569	−	0.681921i
$776$		0			0
$777$	−1.06523	+	0.773934i	−0.0382149	+	0.0277647i
$778$		0			0
$779$	1.71722	+	10.8299i	0.0615256	+	0.388020i
$780$		0			0
$781$	−38.5963	+	28.0419i	−1.38109	+	1.00342i
$782$		0			0
$783$	1.18978	−	3.66178i	0.0425194	−	0.130861i
$784$		0			0
$785$	6.53212	+	8.99069i	0.233141	+	0.320892i
$786$		0			0
$787$	−8.72276	−	26.8459i	−0.310933	−	0.956953i	−0.977396	−	0.211415i	$-0.932193\pi$
$787$	−8.72276	−	26.8459i	−0.310933	−	0.956953i	0.666464	−	0.745538i	$-0.267807\pi$
$788$		0			0
$789$	13.8237	+	42.5450i	0.492137	+	1.51464i
$790$		0			0
$791$	−1.21468	−	0.394673i	−0.0431890	−	0.0140330i
$792$		0			0
$793$		−	0.720989i		−	0.0256031i
$794$		0			0
$795$	−14.9566	−	10.8666i	−0.530457	−	0.385400i
$796$		0			0
$797$	13.1740	−	9.57149i	0.466648	−	0.339040i	−0.329486	−	0.944161i	$-0.606875\pi$
$797$	13.1740	−	9.57149i	0.466648	−	0.339040i	0.796133	+	0.605121i	$0.206875\pi$
$798$		0			0
$799$	−18.0466	−	13.1116i	−0.638442	−	0.463855i
$800$		0			0
$801$	−24.6943	+	33.9888i	−0.872531	+	1.20094i
$802$		0			0
$803$	52.6673	−	17.1127i	1.85859	−	0.603892i
$804$		0			0
$805$	−5.65926	−	1.83880i	−0.199463	−	0.0648093i
$806$		0			0
$807$	−43.0510	−	59.2546i	−1.51547	−	2.08586i
$808$		0			0
$809$	−27.2113	+	8.84149i	−0.956699	+	0.310850i	−0.745435	−	0.666579i	$-0.767758\pi$
$809$	−27.2113	+	8.84149i	−0.956699	+	0.310850i	−0.211264	+	0.977429i	$0.567758\pi$
$810$		0			0
$811$	−16.8745			−0.592542			−0.296271	−	0.955104i	$-0.595743\pi$
$811$	−16.8745			−0.592542			−0.296271	+	0.955104i	$0.595743\pi$
$812$		0			0
$813$	7.31494	−	10.0682i	0.256546	−	0.353106i
$814$		0			0
$815$	−1.47145	+	4.52864i	−0.0515425	+	0.158631i
$816$		0			0
$817$		−	3.32668i		−	0.116386i
$818$		0			0
$819$	1.29220			0.0451533
$820$		0			0
$821$	−5.07406			−0.177086			−0.0885430	−	0.996072i	$-0.528221\pi$
$821$	−5.07406			−0.177086			−0.0885430	+	0.996072i	$0.528221\pi$
$822$		0			0
$823$		−	41.4819i		−	1.44597i	−0.690865	−	0.722983i	$-0.742770\pi$
$823$		−	41.4819i		−	1.44597i	0.690865	−	0.722983i	$-0.257230\pi$
$824$		0			0
$825$	−13.3632	+	41.1278i	−0.465248	+	1.43189i
$826$		0			0
$827$	26.6546	−	36.6869i	0.926872	−	1.27573i	−0.0341950	−	0.999415i	$-0.510887\pi$
$827$	26.6546	−	36.6869i	0.926872	−	1.27573i	0.961067	−	0.276315i	$-0.0891133\pi$
$828$		0			0
$829$	47.8287			1.66116			0.830579	−	0.556901i	$-0.188010\pi$
$829$	47.8287			1.66116			0.830579	+	0.556901i	$0.188010\pi$
$830$		0			0
$831$	−66.6829	+	21.6666i	−2.31321	+	0.751606i
$832$		0			0
$833$	3.53120	+	4.86028i	0.122349	+	0.168399i
$834$		0			0
$835$	12.2429	+	3.97796i	0.423683	+	0.137663i
$836$		0			0
$837$	1.80080	−	0.585115i	0.0622447	−	0.0202245i
$838$		0			0
$839$	7.00855	−	9.64645i	0.241962	−	0.333032i	−0.670714	−	0.741716i	$-0.734012\pi$
$839$	7.00855	−	9.64645i	0.241962	−	0.333032i	0.912676	+	0.408684i	$0.134012\pi$
$840$		0			0
$841$	55.2199	+	40.1196i	1.90413	+	1.38343i
$842$		0			0
$843$	−9.10469	+	6.61495i	−0.313582	+	0.227831i
$844$		0			0
$845$	9.76241	+	7.09281i	0.335837	+	0.244000i
$846$		0			0
$847$		−	6.92951i		−	0.238101i
$848$		0			0
$849$	−73.1903	−	23.7810i	−2.51188	−	0.816160i
$850$		0			0
$851$	1.03761	+	3.19345i	0.0355689	+	0.109470i
$852$		0			0
$853$	17.2568	+	53.1109i	0.590861	+	1.81848i	0.574338	+	0.818618i	$0.305260\pi$
$853$	17.2568	+	53.1109i	0.590861	+	1.81848i	0.0165225	+	0.999863i	$0.494740\pi$
$854$		0			0
$855$	−2.98849	−	4.11330i	−0.102204	−	0.140672i
$856$		0			0
$857$	−6.98628	+	21.5016i	−0.238647	+	0.734480i	0.757970	+	0.652290i	$0.226191\pi$
$857$	−6.98628	+	21.5016i	−0.238647	+	0.734480i	−0.996617	+	0.0821899i	$0.973809\pi$
$858$		0			0
$859$	2.41179	−	1.75227i	0.0822893	−	0.0597867i	−0.545880	−	0.837863i	$-0.683805\pi$
$859$	2.41179	−	1.75227i	0.0822893	−	0.0597867i	0.628169	+	0.778077i	$0.283805\pi$
$860$		0			0
$861$	15.6927	−	2.48827i	0.534804	−	0.0848001i
$862$		0			0
$863$	16.7792	−	12.1908i	0.571172	−	0.414981i	−0.264359	−	0.964424i	$-0.585160\pi$
$863$	16.7792	−	12.1908i	0.571172	−	0.414981i	0.835531	+	0.549444i	$0.185160\pi$
$864$		0			0
$865$	−3.21094	+	9.88227i	−0.109175	+	0.336007i
$866$		0			0
$867$	−27.8457	−	38.3263i	−0.945690	−	1.30163i
$868$		0			0
$869$	−16.0856	−	49.5063i	−0.545666	−	1.67939i
$870$		0			0
$871$	0.0134346	+	0.0413473i	0.000455213	+	0.00140100i
$872$		0			0
$873$	−12.6503	−	4.11034i	−0.428149	−	0.139114i
$874$		0			0
$875$			8.57197i			0.289785i
$876$		0			0
$877$	37.6900	+	27.3834i	1.27270	+	0.924672i	0.999307	−	0.0372301i	$-0.0118535\pi$
$877$	37.6900	+	27.3834i	1.27270	+	0.924672i	0.273395	+	0.961902i	$0.411853\pi$
$878$		0			0
$879$	24.1475	−	17.5442i	0.814476	−	0.591751i
$880$		0			0
$881$	−21.0611	−	15.3018i	−0.709568	−	0.515531i	0.173466	−	0.984840i	$-0.444503\pi$
$881$	−21.0611	−	15.3018i	−0.709568	−	0.515531i	−0.883034	+	0.469309i	$0.844503\pi$
$882$		0			0
$883$	−8.46173	+	11.6466i	−0.284760	+	0.391939i	−0.927303	−	0.374311i	$-0.877879\pi$
$883$	−8.46173	+	11.6466i	−0.284760	+	0.391939i	0.642543	+	0.766249i	$0.277879\pi$
$884$		0			0
$885$	17.1893	−	5.58515i	0.577813	−	0.187743i
$886$		0			0
$887$	38.8900	+	12.6361i	1.30580	+	0.424279i	0.877595	−	0.479404i	$-0.159147\pi$
$887$	38.8900	+	12.6361i	1.30580	+	0.424279i	0.428203	+	0.903683i	$0.359147\pi$
$888$		0			0
$889$	1.97611	+	2.71988i	0.0662765	+	0.0912217i
$890$		0			0
$891$	34.2432	−	11.1263i	1.14719	−	0.372745i
$892$		0			0
$893$	6.35854			0.212780
$894$		0			0
$895$	3.27040	−	4.50131i	0.109317	−	0.150462i
$896$		0			0
$897$	1.98588	−	6.11192i	0.0663067	−	0.204071i
$898$		0			0
$899$			47.8285i			1.59517i
$900$		0			0
$901$	47.5987			1.58574
$902$		0			0
$903$	−4.82041			−0.160413
$904$		0			0
$905$		−	2.35291i		−	0.0782134i
$906$		0			0
$907$	16.0393	−	49.3638i	0.532575	−	1.63910i	−0.216255	−	0.976337i	$-0.569384\pi$
$907$	16.0393	−	49.3638i	0.532575	−	1.63910i	0.748831	−	0.662761i	$-0.230616\pi$
$908$		0			0
$909$	19.0071	−	26.1610i	0.630426	−	0.867707i
$910$		0			0
$911$	3.82840			0.126841			0.0634203	−	0.997987i	$-0.479799\pi$
$911$	3.82840			0.126841			0.0634203	+	0.997987i	$0.479799\pi$
$912$		0			0
$913$	−23.5068	+	7.63782i	−0.777961	+	0.252775i
$914$		0			0
$915$	2.41614	+	3.32553i	0.0798751	+	0.109939i
$916$		0			0
$917$	7.80658	+	2.53651i	0.257796	+	0.0837630i
$918$		0			0
$919$	17.4109	−	5.65716i	0.574334	−	0.186612i	−0.00742681	−	0.999972i	$-0.502364\pi$
$919$	17.4109	−	5.65716i	0.574334	−	0.186612i	0.581761	+	0.813360i	$0.302364\pi$
$920$		0			0
$921$	5.19255	−	7.14693i	0.171100	−	0.235499i
$922$		0			0
$923$	−3.73055	−	2.71040i	−0.122792	−	0.0892139i
$924$		0			0
$925$	1.76683	−	1.28368i	0.0580930	−	0.0422071i
$926$		0			0
$927$	−26.2506	−	19.0722i	−0.862184	−	0.626413i
$928$		0			0
$929$		−	36.0351i		−	1.18227i	−0.806571	−	0.591137i	$-0.798679\pi$
$929$		−	36.0351i		−	1.18227i	0.806571	−	0.591137i	$-0.201321\pi$
$930$		0			0
$931$	−1.62866	−	0.529183i	−0.0533771	−	0.0173433i
$932$		0			0
$933$	4.30837	+	13.2598i	0.141050	+	0.434107i
$934$		0			0
$935$	7.39194	+	22.7500i	0.241742	+	0.744006i
$936$		0			0
$937$	−15.0628	−	20.7322i	−0.492081	−	0.677291i	0.488689	−	0.872458i	$-0.337475\pi$
$937$	−15.0628	−	20.7322i	−0.492081	−	0.677291i	−0.980770	+	0.195167i	$0.937475\pi$
$938$		0			0
$939$	3.60903	−	11.1075i	0.117776	−	0.362478i
$940$		0			0
$941$	34.2291	−	24.8689i	1.11584	−	0.810702i	0.132263	−	0.991215i	$-0.457776\pi$
$941$	34.2291	−	24.8689i	1.11584	−	0.810702i	0.983573	+	0.180512i	$0.0577755\pi$
$942$		0			0
$943$	6.33157	−	40.0210i	0.206184	−	1.30326i
$944$		0			0
$945$	−0.297013	+	0.215792i	−0.00966182	+	0.00701973i
$946$		0			0
$947$	−2.12039	+	6.52589i	−0.0689034	+	0.212063i	−0.979579	−	0.201059i	$-0.935562\pi$
$947$	−2.12039	+	6.52589i	−0.0689034	+	0.212063i	0.910676	+	0.413122i	$0.135562\pi$
$948$		0			0
$949$	3.14615	+	4.33031i	0.102128	+	0.140568i
$950$		0			0
$951$	−11.6340	−	35.8057i	−0.377257	−	1.16108i
$952$		0			0
$953$	8.58361	+	26.4176i	0.278050	+	0.855751i	0.988396	+	0.151898i	$0.0485386\pi$
$953$	8.58361	+	26.4176i	0.278050	+	0.855751i	−0.710346	+	0.703853i	$0.751461\pi$
$954$		0			0
$955$	22.5743	+	7.33482i	0.730486	+	0.237349i
$956$		0			0
$957$		−	103.619i		−	3.34951i
$958$		0			0
$959$	−8.52412	−	6.19314i	−0.275258	−	0.199987i
$960$		0			0
$961$	6.05048	−	4.39593i	0.195177	−	0.141804i
$962$		0			0
$963$	46.2227	+	33.5827i	1.48950	+	1.08219i
$964$		0			0
$965$	12.6398	−	17.3972i	0.406890	−	0.560036i
$966$		0			0
$967$	−39.1634	+	12.7249i	−1.25941	+	0.409207i	−0.861284	−	0.508124i	$-0.830339\pi$
$967$	−39.1634	+	12.7249i	−1.25941	+	0.409207i	−0.398125	+	0.917331i	$0.630339\pi$
$968$		0			0
$969$	24.2789	+	7.88870i	0.779952	+	0.253422i
$970$		0			0
$971$	9.94094	+	13.6825i	0.319020	+	0.439093i	0.938168	−	0.346181i	$-0.112522\pi$
$971$	9.94094	+	13.6825i	0.319020	+	0.439093i	−0.619148	+	0.785275i	$0.712522\pi$
$972$		0			0
$973$	−8.28113	+	2.69070i	−0.265481	+	0.0862600i
$974$		0			0
$975$	−4.17980			−0.133861
$976$		0			0
$977$	−34.3726	+	47.3099i	−1.09968	+	1.51358i	−0.263868	+	0.964559i	$0.584998\pi$
$977$	−34.3726	+	47.3099i	−1.09968	+	1.51358i	−0.835810	+	0.549019i	$0.815002\pi$
$978$		0			0
$979$	−17.4110	+	53.5856i	−0.556458	+	1.71260i
$980$		0			0
$981$		−	36.6297i		−	1.16950i
$982$		0			0
$983$	44.6761			1.42495			0.712473	−	0.701699i	$-0.247575\pi$
$983$	44.6761			1.42495			0.712473	+	0.701699i	$0.247575\pi$
$984$		0			0
$985$	14.0035			0.446189
$986$		0			0
$987$		−	9.21362i		−	0.293273i
$988$		0			0
$989$	−3.79870	+	11.6912i	−0.120791	+	0.371758i
$990$		0			0
$991$	−20.5980	+	28.3508i	−0.654318	+	0.900592i	−0.999277	−	0.0380261i	$-0.987893\pi$
$991$	−20.5980	+	28.3508i	−0.654318	+	0.900592i	0.344958	+	0.938618i	$0.387893\pi$
$992$		0			0
$993$	−2.36917			−0.0751833
$994$		0			0
$995$	−11.0838	+	3.60136i	−0.351382	+	0.114171i
$996$		0			0
$997$	11.0183	+	15.1653i	0.348952	+	0.480291i	0.947029	−	0.321148i	$-0.104069\pi$
$997$	11.0183	+	15.1653i	0.348952	+	0.480291i	−0.598078	+	0.801438i	$0.704069\pi$
$998$		0			0
$999$	0.197026	+	0.0640177i	0.00623363	+	0.00202543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.3	yes	80
41.31	even	10	inner	1148.2.ba.a.113.18	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.18	✓	80	41.31	even	10	inner
1148.2.ba.a.701.3	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.48140i q^{3} +(-0.290583 + 0.894324i) q^{5} +(0.587785 - 0.809017i) q^{7} -3.15734 q^{9} +O(q^{10})\)	\(q-2.48140i q^{3} +(-0.290583 + 0.894324i) q^{5} +(0.587785 - 0.809017i) q^{7} -3.15734 q^{9} +(-4.02708 + 1.30848i) q^{11} +(-0.240563 - 0.331107i) q^{13} +(2.21917 + 0.721053i) q^{15} +(-5.71360 + 1.85646i) q^{17} +(1.00657 - 1.38542i) q^{19} +(-2.00749 - 1.45853i) q^{21} +(-5.11944 + 3.71949i) q^{23} +(3.32971 + 2.41918i) q^{25} +0.390417i q^{27} +(-9.37915 - 3.04747i) q^{29} +(-1.49869 - 4.61250i) q^{31} +(3.24686 + 9.99280i) q^{33} +(0.552722 + 0.760757i) q^{35} +(0.163973 - 0.504656i) q^{37} +(-0.821608 + 0.596933i) q^{39} +(-4.52690 + 4.52848i) q^{41} +(1.57161 - 1.14184i) q^{43} +(0.917470 - 2.82368i) q^{45} +(2.18249 + 3.00394i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(4.60662 + 14.1777i) q^{51} +(-7.53525 - 2.44835i) q^{53} -3.98174i q^{55} +(-3.43778 - 2.49769i) q^{57} +(6.26650 - 4.55288i) q^{59} +(1.42520 + 1.03547i) q^{61} +(-1.85584 + 2.55434i) q^{63} +(0.366020 - 0.118927i) q^{65} +(-0.101027 - 0.0328257i) q^{67} +(9.22953 + 12.7034i) q^{69} +(10.7155 - 3.48166i) q^{71} -13.0783 q^{73} +(6.00294 - 8.26233i) q^{75} +(-1.30848 + 4.02708i) q^{77} +12.2934i q^{79} -8.50323 q^{81} +5.83718 q^{83} -5.64926i q^{85} +(-7.56199 + 23.2734i) q^{87} +(7.82125 - 10.7650i) q^{89} -0.409270 q^{91} +(-11.4454 + 3.71885i) q^{93} +(0.946522 + 1.30278i) q^{95} +(4.00664 + 1.30184i) q^{97} +(12.7149 - 4.13131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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