LMFDB - Embedded newform 104.2.e.c.77.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(77,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.77"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4521217600.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 $ x^8 + x^6 - 2x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.8
Root			$-1.29437 + 0.569745i$ of defining polynomial
Character	$\chi$	$=$	104.77
Dual form			104.2.e.c.77.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29437 + 0.569745i) q^{2} -2.94984i q^{3} +(1.35078 + 1.47492i) q^{4} -1.81616 q^{5} +(1.68066 - 3.81818i) q^{6} +1.13949i q^{7} +(0.908080 + 2.67869i) q^{8} -5.70156 q^{9} +(-2.35078 - 1.03475i) q^{10} +4.40490 q^{11} +(4.35078 - 3.98459i) q^{12} +(-2.58874 + 2.50967i) q^{13} +(-0.649219 + 1.47492i) q^{14} +5.35738i q^{15} +(-0.350781 + 3.98459i) q^{16} +0.701562 q^{17} +(-7.37992 - 3.24844i) q^{18} -5.95005 q^{19} +(-2.45323 - 2.67869i) q^{20} +3.36131 q^{21} +(5.70156 + 2.50967i) q^{22} +4.00000 q^{23} +(7.90172 - 2.67869i) q^{24} -1.70156 q^{25} +(-4.78065 + 1.77352i) q^{26} +7.96918i q^{27} +(-1.68066 + 1.53920i) q^{28} -5.01934i q^{29} +(-3.05234 + 6.93443i) q^{30} -8.77585i q^{31} +(-2.72424 + 4.95767i) q^{32} -12.9937i q^{33} +(0.908080 + 0.399712i) q^{34} -2.06950i q^{35} +(-7.70156 - 8.40935i) q^{36} -3.36131 q^{37} +(-7.70156 - 3.39001i) q^{38} +(7.40312 + 7.63636i) q^{39} +(-1.64922 - 4.86493i) q^{40} +(4.35078 + 1.91509i) q^{42} -2.94984i q^{43} +(5.95005 + 6.49687i) q^{44} +10.3550 q^{45} +(5.17748 + 2.27898i) q^{46} +1.13949i q^{47} +(11.7539 + 1.03475i) q^{48} +5.70156 q^{49} +(-2.20245 - 0.969457i) q^{50} -2.06950i q^{51} +(-7.19838 - 0.428169i) q^{52} +11.7994i q^{53} +(-4.54040 + 10.3151i) q^{54} -8.00000 q^{55} +(-3.05234 + 1.03475i) q^{56} +17.5517i q^{57} +(2.85974 - 6.49687i) q^{58} +5.95005 q^{59} +(-7.90172 + 7.23665i) q^{60} +(5.00000 - 11.3592i) q^{62} -6.49687i q^{63} +(-6.35078 + 4.86493i) q^{64} +(4.70156 - 4.55796i) q^{65} +(7.40312 - 16.8187i) q^{66} +7.49521 q^{67} +(0.947657 + 1.03475i) q^{68} -11.7994i q^{69} +(1.17909 - 2.67869i) q^{70} -11.8543i q^{71} +(-5.17748 - 15.2727i) q^{72} +8.43579i q^{73} +(-4.35078 - 1.91509i) q^{74} +5.01934i q^{75} +(-8.03722 - 8.77585i) q^{76} +5.01934i q^{77} +(5.23159 + 14.1022i) q^{78} -10.8062 q^{79} +(0.637075 - 7.23665i) q^{80} +6.40312 q^{81} +2.85974 q^{83} +(4.54040 + 4.95767i) q^{84} -1.27415 q^{85} +(1.68066 - 3.81818i) q^{86} -14.8062 q^{87} +(4.00000 + 11.7994i) q^{88} -8.43579i q^{89} +(13.4031 + 5.89968i) q^{90} +(-2.85974 - 2.94984i) q^{91} +(5.40312 + 5.89968i) q^{92} -25.8874 q^{93} +(-0.649219 + 1.47492i) q^{94} +10.8062 q^{95} +(14.6243 + 8.03608i) q^{96} +12.9937i q^{97} +(7.37992 + 3.24844i) q^{98} -25.1148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 20 q^{9} - 6 q^{10} + 22 q^{12} - 18 q^{14} + 10 q^{16} - 20 q^{17} + 20 q^{22} + 32 q^{23} + 12 q^{25} - 14 q^{26} + 14 q^{30} - 36 q^{36} - 36 q^{38} + 8 q^{39} - 26 q^{40} + 22 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 20 * q^9 - 6 * q^10 + 22 * q^12 - 18 * q^14 + 10 * q^16 - 20 * q^17 + 20 * q^22 + 32 * q^23 + 12 * q^25 - 14 * q^26 + 14 * q^30 - 36 * q^36 - 36 * q^38 + 8 * q^39 - 26 * q^40 + 22 * q^42 + 30 * q^48 + 20 * q^49 - 4 * q^52 - 64 * q^55 + 14 * q^56 + 40 * q^62 - 38 * q^64 + 12 * q^65 + 8 * q^66 + 46 * q^68 - 22 * q^74 - 22 * q^78 + 16 * q^79 - 16 * q^87 + 32 * q^88 + 56 * q^90 - 8 * q^92 - 18 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.29437	+	0.569745i	0.915257	+	0.402871i
$2$	1.29437	+	0.569745i	0.915257	+	0.402871i
$3$		−	2.94984i		−	1.70309i	−0.524280	−	0.851546i	$-0.675666\pi$
$3$		−	2.94984i		−	1.70309i	0.524280	−	0.851546i	$-0.324334\pi$
$4$	1.35078	+	1.47492i	0.675391	+	0.737460i
$5$	−1.81616			−0.812212			−0.406106	−	0.913826i	$-0.633114\pi$
$5$	−1.81616			−0.812212			−0.406106	+	0.913826i	$0.633114\pi$
$6$	1.68066	−	3.81818i	0.686126	−	1.55877i
$7$			1.13949i			0.430687i	0.976538	+	0.215343i	$0.0690871\pi$
$7$			1.13949i			0.430687i	−0.976538	+	0.215343i	$0.930913\pi$
$8$	0.908080	+	2.67869i	0.321055	+	0.947061i
$9$	−5.70156			−1.90052
$10$	−2.35078	−	1.03475i	−0.743382	−	0.327216i
$11$	4.40490			1.32813			0.664063	−	0.747676i	$-0.268831\pi$
$11$	4.40490			1.32813			0.664063	+	0.747676i	$0.268831\pi$
$12$	4.35078	−	3.98459i	1.25596	−	1.15025i
$13$	−2.58874	+	2.50967i	−0.717987	+	0.696057i
$13$	−2.58874	+	2.50967i	−0.717987	+	0.696057i
$14$	−0.649219	+	1.47492i	−0.173511	+	0.394189i
$15$			5.35738i			1.38327i
$16$	−0.350781	+	3.98459i	−0.0876953	+	0.996147i
$17$	0.701562			0.170154			0.0850769	−	0.996374i	$-0.472886\pi$
$17$	0.701562			0.170154			0.0850769	+	0.996374i	$0.472886\pi$
$18$	−7.37992	−	3.24844i	−1.73946	−	0.765664i
$19$	−5.95005			−1.36504			−0.682518	−	0.730869i	$-0.739115\pi$
$19$	−5.95005			−1.36504			−0.682518	+	0.730869i	$0.739115\pi$
$20$	−2.45323	−	2.67869i	−0.548560	−	0.598974i
$21$	3.36131			0.733499
$22$	5.70156	+	2.50967i	1.21558	+	0.535063i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	7.90172	−	2.67869i	1.61293	−	0.546786i
$25$	−1.70156			−0.340312
$26$	−4.78065	+	1.77352i	−0.937563	+	0.347815i
$27$			7.96918i			1.53367i
$28$	−1.68066	+	1.53920i	−0.317614	+	0.290882i
$29$		−	5.01934i		−	0.932068i	−0.884767	−	0.466034i	$-0.845683\pi$
$29$		−	5.01934i		−	0.932068i	0.884767	−	0.466034i	$-0.154317\pi$
$30$	−3.05234	+	6.93443i	−0.557279	+	1.26605i
$31$		−	8.77585i		−	1.57619i	−0.615554	−	0.788095i	$-0.711068\pi$
$31$		−	8.77585i		−	1.57619i	0.615554	−	0.788095i	$-0.288932\pi$
$32$	−2.72424	+	4.95767i	−0.481582	+	0.876401i
$33$		−	12.9937i		−	2.26192i
$34$	0.908080	+	0.399712i	0.155734	+	0.0685500i
$35$		−	2.06950i		−	0.349809i
$36$	−7.70156	−	8.40935i	−1.28359	−	1.40156i
$37$	−3.36131			−0.552597			−0.276298	−	0.961072i	$-0.589108\pi$
$37$	−3.36131			−0.552597			−0.276298	+	0.961072i	$0.589108\pi$
$38$	−7.70156	−	3.39001i	−1.24936	−	0.549933i
$39$	7.40312	+	7.63636i	1.18545	+	1.22280i
$40$	−1.64922	−	4.86493i	−0.260764	−	0.769214i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	4.35078	+	1.91509i	0.671340	+	0.295505i
$43$		−	2.94984i		−	0.449847i	−0.974376	−	0.224923i	$-0.927787\pi$
$43$		−	2.94984i		−	0.449847i	0.974376	−	0.224923i	$-0.0722131\pi$
$44$	5.95005	+	6.49687i	0.897004	+	0.979441i
$45$	10.3550			1.54362
$46$	5.17748	+	2.27898i	0.763377	+	0.336017i
$47$			1.13949i			0.166212i	0.996541	+	0.0831059i	$0.0264840\pi$
$47$			1.13949i			0.166212i	−0.996541	+	0.0831059i	$0.973516\pi$
$48$	11.7539	+	1.03475i	1.69653	+	0.149353i
$49$	5.70156			0.814509
$50$	−2.20245	−	0.969457i	−0.311473	−	0.137102i
$51$		−	2.06950i		−	0.289788i
$52$	−7.19838	−	0.428169i	−0.998236	−	0.0593763i
$53$			11.7994i			1.62077i	0.585900	+	0.810384i	$0.300741\pi$
$53$			11.7994i			1.62077i	−0.585900	+	0.810384i	$0.699259\pi$
$54$	−4.54040	+	10.3151i	−0.617870	+	1.40370i
$55$	−8.00000			−1.07872
$56$	−3.05234	+	1.03475i	−0.407887	+	0.138274i
$57$			17.5517i			2.32478i
$58$	2.85974	−	6.49687i	0.375503	−	0.853081i
$59$	5.95005			0.774631			0.387315	−	0.921947i	$-0.373402\pi$
$59$	5.95005			0.774631			0.387315	+	0.921947i	$0.373402\pi$
$60$	−7.90172	+	7.23665i	−1.02011	+	0.934248i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	5.00000	−	11.3592i	0.635001	−	1.44262i
$63$		−	6.49687i		−	0.818529i
$64$	−6.35078	+	4.86493i	−0.793848	+	0.608117i
$65$	4.70156	−	4.55796i	0.583157	−	0.565345i
$66$	7.40312	−	16.8187i	0.911262	−	2.07024i
$67$	7.49521			0.915685			0.457843	−	0.889033i	$-0.348622\pi$
$67$	7.49521			0.915685			0.457843	+	0.889033i	$0.348622\pi$
$68$	0.947657	+	1.03475i	0.114920	+	0.125482i
$69$		−	11.7994i		−	1.42048i
$70$	1.17909	−	2.67869i	0.140928	−	0.320165i
$71$		−	11.8543i		−	1.40684i	−0.710774	−	0.703421i	$-0.751655\pi$
$71$		−	11.8543i		−	1.40684i	0.710774	−	0.703421i	$-0.248345\pi$
$72$	−5.17748	−	15.2727i	−0.610171	−	1.79991i
$73$			8.43579i			0.987334i	0.869651	+	0.493667i	$0.164344\pi$
$73$			8.43579i			0.987334i	−0.869651	+	0.493667i	$0.835656\pi$
$74$	−4.35078	−	1.91509i	−0.505768	−	0.222625i
$75$			5.01934i			0.579583i
$76$	−8.03722	−	8.77585i	−0.921932	−	1.00666i
$77$			5.01934i			0.572007i
$78$	5.23159	+	14.1022i	0.592361	+	1.59676i
$79$	−10.8062			−1.21580			−0.607899	−	0.794014i	$-0.707987\pi$
$79$	−10.8062			−1.21580			−0.607899	+	0.794014i	$0.707987\pi$
$80$	0.637075	−	7.23665i	0.0712271	−	0.809082i
$81$	6.40312			0.711458
$82$		0			0
$83$	2.85974			0.313898			0.156949	−	0.987607i	$-0.449834\pi$
$83$	2.85974			0.313898			0.156949	+	0.987607i	$0.449834\pi$
$84$	4.54040	+	4.95767i	0.495398	+	0.540926i
$85$	−1.27415			−0.138201
$86$	1.68066	−	3.81818i	0.181230	−	0.411725i
$87$	−14.8062			−1.58740
$88$	4.00000	+	11.7994i	0.426401	+	1.25782i
$89$		−	8.43579i		−	0.894192i	−0.894486	−	0.447096i	$-0.852458\pi$
$89$		−	8.43579i		−	0.894192i	0.894486	−	0.447096i	$-0.147542\pi$
$90$	13.4031	+	5.89968i	1.41281	+	0.621881i
$91$	−2.85974	−	2.94984i	−0.299783	−	0.309227i
$92$	5.40312	+	5.89968i	0.563315	+	0.615084i
$93$	−25.8874			−2.68440
$94$	−0.649219	+	1.47492i	−0.0669618	+	0.152126i
$95$	10.8062			1.10870
$96$	14.6243	+	8.03608i	1.49259	+	0.820179i
$97$			12.9937i			1.31932i	0.751566	+	0.659658i	$0.229299\pi$
$97$			12.9937i			1.31932i	−0.751566	+	0.659658i	$0.770701\pi$
$98$	7.37992	+	3.24844i	0.745485	+	0.328142i
$99$	−25.1148			−2.52413
$100$	−2.29844	−	2.50967i	−0.229844	−	0.250967i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	1.17909	−	2.67869i	0.116747	−	0.265230i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	−9.07341	−	4.65545i	−0.889721	−	0.456504i
$105$	−6.10469			−0.595756
$106$	−6.72263	+	15.2727i	−0.652960	+	1.48342i
$107$		−	0.880344i		−	0.0851061i	−0.999094	−	0.0425530i	$-0.986451\pi$
$107$		−	0.880344i		−	0.0851061i	0.999094	−	0.0425530i	$-0.0135491\pi$
$108$	−11.7539	+	10.7646i	−1.13102	+	1.03583i
$109$	6.99364			0.669869			0.334934	−	0.942241i	$-0.391286\pi$
$109$	6.99364			0.669869			0.334934	+	0.942241i	$0.391286\pi$
$110$	−10.3550	−	4.55796i	−0.987306	−	0.434585i
$111$			9.91534i			0.941123i
$112$	−4.54040	−	0.399712i	−0.429028	−	0.0377692i
$113$	−1.40312			−0.131995			−0.0659974	−	0.997820i	$-0.521023\pi$
$113$	−1.40312			−0.131995			−0.0659974	+	0.997820i	$0.521023\pi$
$114$	−10.0000	+	22.7184i	−0.936586	+	2.12777i
$115$	−7.26464			−0.677431
$116$	7.40312	−	6.78003i	0.687363	−	0.629510i
$117$	14.7598	−	14.3090i	1.36455	−	1.32287i
$118$	7.70156	+	3.39001i	0.708986	+	0.312076i
$119$			0.799423i			0.0732830i
$120$	−14.3508	+	4.86493i	−1.31004	+	0.444106i
$121$	8.40312			0.763920
$122$		0			0
$123$		0			0
$124$	12.9437	−	11.8543i	1.16238	−	1.06454i
$125$	12.1711			1.08862
$126$	3.70156	−	8.40935i	0.329761	−	0.749165i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−10.9920	+	2.67869i	−0.971567	+	0.236765i
$129$	−8.70156			−0.766130
$130$	8.68243	−	3.22099i	0.761500	−	0.282500i
$131$		−	1.18915i		−	0.103897i	−0.998650	−	0.0519484i	$-0.983457\pi$
$131$		−	1.18915i		−	0.103897i	0.998650	−	0.0519484i	$-0.0165431\pi$
$132$	19.1647	−	17.5517i	1.66808	−	1.52768i
$133$		−	6.78003i		−	0.587903i
$134$	9.70156	+	4.27036i	0.838087	+	0.368903i
$135$		−	14.4733i		−	1.24566i
$136$	0.637075	+	1.87927i	0.0546287	+	0.161146i
$137$		−	4.55796i		−	0.389413i	−0.980862	−	0.194706i	$-0.937625\pi$
$137$		−	4.55796i		−	0.389413i	0.980862	−	0.194706i	$-0.0623754\pi$
$138$	6.72263	−	15.2727i	0.572268	−	1.30010i
$139$			18.8882i			1.60208i	0.598613	+	0.801038i	$0.295719\pi$
$139$			18.8882i			1.60208i	−0.598613	+	0.801038i	$0.704281\pi$
$140$	3.05234	−	2.79544i	0.257970	−	0.236258i
$141$	3.36131			0.283074
$142$	6.75391	−	15.3438i	0.566775	−	1.28762i
$143$	−11.4031	+	11.0548i	−0.953577	+	0.924452i
$144$	2.00000	−	22.7184i	0.166667	−	1.89320i
$145$			9.11592i			0.757036i
$146$	−4.80625	+	10.9190i	−0.397768	+	0.903665i
$147$		−	16.8187i		−	1.38718i
$148$	−4.54040	−	4.95767i	−0.373219	−	0.407518i
$149$	−2.08717			−0.170987			−0.0854936	−	0.996339i	$-0.527247\pi$
$149$	−2.08717			−0.170987			−0.0854936	+	0.996339i	$0.527247\pi$
$150$	−2.85974	+	6.49687i	−0.233497	+	0.530468i
$151$			5.69745i			0.463652i	0.972757	+	0.231826i	$0.0744700\pi$
$151$			5.69745i			0.463652i	−0.972757	+	0.231826i	$0.925530\pi$
$152$	−5.40312	−	15.9384i	−0.438251	−	1.29277i
$153$	−4.00000			−0.323381
$154$	−2.85974	+	6.49687i	−0.230445	+	0.523533i
$155$			15.9384i			1.28020i
$156$	−1.26303	+	21.2341i	−0.101123	+	1.70009i
$157$		−	16.8187i		−	1.34228i	−0.741331	−	0.671139i	$-0.765805\pi$
$157$		−	16.8187i		−	1.34228i	0.741331	−	0.671139i	$-0.234195\pi$
$158$	−13.9873	−	6.15681i	−1.11277	−	0.489809i
$159$	34.8062			2.76032
$160$	4.94766	−	9.00393i	0.391147	−	0.711823i
$161$			4.55796i			0.359218i
$162$	8.28800	+	3.64815i	0.651167	+	0.286626i
$163$	2.85974			0.223992			0.111996	−	0.993709i	$-0.464276\pi$
$163$	2.85974			0.223992			0.111996	+	0.993709i	$0.464276\pi$
$164$		0			0
$165$			23.5987i			1.83716i
$166$	3.70156	+	1.62932i	0.287297	+	0.126460i
$167$			4.21789i			0.326390i	0.986594	+	0.163195i	$0.0521800\pi$
$167$			4.21789i			0.326390i	−0.986594	+	0.163195i	$0.947820\pi$
$168$	3.05234	+	9.00393i	0.235493	+	0.694668i
$169$	0.403124	−	12.9937i	0.0310096	−	0.999519i
$170$	−1.64922	−	0.725940i	−0.126489	−	0.0556771i
$171$	33.9246			2.59428
$172$	4.35078	−	3.98459i	0.331744	−	0.303822i
$173$			11.7994i			0.897089i	0.893760	+	0.448545i	$0.148057\pi$
$173$			11.7994i			0.897089i	−0.893760	+	0.448545i	$0.851943\pi$
$174$	−19.1647	−	8.43579i	−1.45288	−	0.639515i
$175$		−	1.93891i		−	0.146568i
$176$	−1.54515	+	17.5517i	−0.116470	+	1.32301i
$177$		−	17.5517i		−	1.31927i
$178$	4.80625	−	10.9190i	0.360244	−	0.818415i
$179$		−	12.9885i		−	0.970807i	−0.874290	−	0.485404i	$-0.838673\pi$
$179$		−	12.9885i		−	0.970807i	0.874290	−	0.485404i	$-0.161327\pi$
$180$	13.9873	+	15.2727i	1.04255	+	1.13836i
$181$			6.78003i			0.503955i	0.967733	+	0.251978i	$0.0810810\pi$
$181$			6.78003i			0.503955i	−0.967733	+	0.251978i	$0.918919\pi$
$182$	−2.02090	−	5.44751i	−0.149799	−	0.403796i
$183$		0			0
$184$	3.63232	+	10.7148i	0.267778	+	0.789903i
$185$	6.10469			0.448825
$186$	−33.5078	−	14.7492i	−2.45691	−	1.08146i
$187$	3.09031			0.225986
$188$	−1.68066	+	1.53920i	−0.122575	+	0.112258i
$189$	−9.08080			−0.660531
$190$	13.9873	+	6.15681i	1.01474	+	0.446662i
$191$	22.8062			1.65020			0.825101	−	0.564985i	$-0.191118\pi$
$191$	22.8062			1.65020			0.825101	+	0.564985i	$0.191118\pi$
$192$	14.3508	+	18.7338i	1.03568	+	1.35200i
$193$			8.43579i			0.607221i	0.952796	+	0.303611i	$0.0981922\pi$
$193$			8.43579i			0.607221i	−0.952796	+	0.303611i	$0.901808\pi$
$194$	−7.40312	+	16.8187i	−0.531513	+	1.20751i
$195$	−13.4453	−	13.8689i	−0.962835	−	0.993170i
$196$	7.70156	+	8.40935i	0.550112	+	0.600668i
$197$	−3.36131			−0.239484			−0.119742	−	0.992805i	$-0.538207\pi$
$197$	−3.36131			−0.239484			−0.119742	+	0.992805i	$0.538207\pi$
$198$	−32.5078	−	14.3090i	−2.31023	−	1.01690i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−1.54515	−	4.55796i	−0.109259	−	0.322296i
$201$		−	22.1097i		−	1.55950i
$202$		0			0
$203$	5.71949			0.401429
$204$	3.05234	−	2.79544i	0.213707	−	0.195720i
$205$		0			0
$206$	5.17748	+	2.27898i	0.360732	+	0.158784i
$207$	−22.8062			−1.58514
$208$	−9.09192	−	11.1954i	−0.630411	−	0.776261i
$209$	−26.2094			−1.81294
$210$	−7.90172	−	3.47812i	−0.545270	−	0.240013i
$211$		−	1.18915i		−	0.0818646i	−0.999162	−	0.0409323i	$-0.986967\pi$
$211$		−	1.18915i		−	0.0818646i	0.999162	−	0.0409323i	$-0.0130328\pi$
$212$	−17.4031	+	15.9384i	−1.19525	+	1.09465i
$213$	−34.9682			−2.39598
$214$	0.501572	−	1.13949i	0.0342867	−	0.0778939i
$215$			5.35738i			0.365371i
$216$	−21.3470	+	7.23665i	−1.45248	+	0.492392i
$217$	10.0000			0.678844
$218$	9.05234	+	3.98459i	0.613102	+	0.269870i
$219$	24.8842			1.68152
$220$	−10.8062	−	11.7994i	−0.728557	−	0.795513i
$221$	−1.81616	+	1.76069i	−0.122168	+	0.118437i
$222$	−5.64922	+	12.8341i	−0.379151	+	0.861369i
$223$		−	20.9702i		−	1.40427i	−0.712045	−	0.702134i	$-0.752231\pi$
$223$		−	20.9702i		−	1.40427i	0.712045	−	0.702134i	$-0.247769\pi$
$224$	−5.64922	−	3.10425i	−0.377454	−	0.207411i
$225$	9.70156			0.646771
$226$	−1.81616	−	0.799423i	−0.120809	−	0.0531768i
$227$	−16.3050			−1.08220			−0.541101	−	0.840958i	$-0.681992\pi$
$227$	−16.3050			−1.08220			−0.541101	+	0.840958i	$0.681992\pi$
$228$	−25.8874	+	23.7085i	−1.71443	+	1.57013i
$229$	18.8937			1.24853			0.624267	−	0.781211i	$-0.285398\pi$
$229$	18.8937			1.24853			0.624267	+	0.781211i	$0.285398\pi$
$230$	−9.40312	−	4.13899i	−0.620024	−	0.272917i
$231$	14.8062			0.974180
$232$	13.4453	−	4.55796i	0.882725	−	0.299245i
$233$	12.1047			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$233$	12.1047			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$234$	27.2572	−	10.1118i	1.78186	−	0.661030i
$235$		−	2.06950i		−	0.134999i
$236$	8.03722	+	8.77585i	0.523178	+	0.571259i
$237$			31.8767i			2.07062i
$238$	−0.455467	+	1.03475i	−0.0295236	+	0.0670728i
$239$			9.57528i			0.619373i	0.950839	+	0.309687i	$0.100224\pi$
$239$			9.57528i			0.619373i	−0.950839	+	0.309687i	$0.899776\pi$
$240$	−21.3470	−	1.87927i	−1.37794	−	0.121306i
$241$			17.5517i			1.13060i	0.824884	+	0.565302i	$0.191241\pi$
$241$			17.5517i			1.13060i	−0.824884	+	0.565302i	$0.808759\pi$
$242$	10.8767	+	4.78764i	0.699183	+	0.307761i
$243$			5.01934i			0.321991i
$244$		0			0
$245$	−10.3550			−0.661554
$246$		0			0
$247$	15.4031	−	14.9327i	0.980077	−	0.950142i
$248$	23.5078	−	7.96918i	1.49275	−	0.506043i
$249$		−	8.43579i		−	0.534596i
$250$	15.7539	+	6.93443i	0.996364	+	0.438572i
$251$			9.15833i			0.578069i	0.957319	+	0.289034i	$0.0933342\pi$
$251$			9.15833i			0.578069i	−0.957319	+	0.289034i	$0.906666\pi$
$252$	9.58237	−	8.77585i	0.603633	−	0.552827i
$253$	17.6196			1.10773
$254$	−15.5324	−	6.83694i	−0.974591	−	0.428988i
$255$			3.75854i			0.235369i
$256$	−15.7539	−	2.79544i	−0.984619	−	0.174715i
$257$	−25.5078			−1.59113			−0.795567	−	0.605866i	$-0.792827\pi$
$257$	−25.5078			−1.59113			−0.795567	+	0.605866i	$0.792827\pi$
$258$	−11.2630	−	4.95767i	−0.701206	−	0.308651i
$259$		−	3.83019i		−	0.237996i
$260$	13.0734	+	0.777623i	0.810779	+	0.0482262i
$261$			28.6181i			1.77141i
$262$	0.677514	−	1.53920i	0.0418569	−	0.0950922i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$	34.8062	−	11.7994i	2.14218	−	0.726201i
$265$		−	21.4295i		−	1.31641i
$266$	3.86289	−	8.77585i	0.236849	−	0.538082i
$267$	−24.8842			−1.52289
$268$	10.1244	+	11.0548i	0.618445	+	0.675282i
$269$		−	18.5794i		−	1.13281i	−0.824129	−	0.566403i	$-0.808335\pi$
$269$		−	18.5794i		−	1.13281i	0.824129	−	0.566403i	$-0.191665\pi$
$270$	8.24609	−	18.7338i	0.501841	−	1.14010i
$271$			18.0111i			1.09409i	0.837102	+	0.547047i	$0.184248\pi$
$271$			18.0111i			1.09409i	−0.837102	+	0.547047i	$0.815752\pi$
$272$	−0.246095	+	2.79544i	−0.0149217	+	0.169498i
$273$	−8.70156	+	8.43579i	−0.526642	+	0.510557i
$274$	2.59688	−	5.89968i	0.156883	−	0.356413i
$275$	−7.49521			−0.451978
$276$	17.4031	−	15.9384i	1.04754	−	0.959376i
$277$		−	23.5987i		−	1.41791i	−0.705254	−	0.708955i	$-0.749167\pi$
$277$		−	23.5987i		−	1.41791i	0.705254	−	0.708955i	$-0.250833\pi$
$278$	−10.7615	+	24.4483i	−0.645429	+	1.46631i
$279$			50.0361i			2.99558i
$280$	5.54354	−	1.87927i	0.331290	−	0.112308i
$281$		−	17.5517i		−	1.04705i	−0.852011	−	0.523524i	$-0.824617\pi$
$281$		−	17.5517i		−	1.04705i	0.852011	−	0.523524i	$-0.175383\pi$
$282$	4.35078	+	1.91509i	0.259085	+	0.114042i
$283$		−	10.9190i		−	0.649068i	−0.945874	−	0.324534i	$-0.894792\pi$
$283$		−	10.9190i		−	0.649068i	0.945874	−	0.324534i	$-0.105208\pi$
$284$	17.4841	−	16.0125i	1.03749	−	0.950167i
$285$		−	31.8767i		−	1.88821i
$286$	−21.0583	+	7.81216i	−1.24520	+	0.461943i
$287$		0			0
$288$	15.5324	−	28.2665i	0.915257	−	1.66562i
$289$	−16.5078			−0.971048
$290$	−5.19375	+	11.7994i	−0.304988	+	0.692883i
$291$	38.3295			2.24691
$292$	−12.4421	+	11.3949i	−0.728120	+	0.666836i
$293$	23.5292			1.37459			0.687295	−	0.726378i	$-0.258798\pi$
$293$	23.5292			1.37459			0.687295	+	0.726378i	$0.258798\pi$
$294$	9.58237	−	21.7696i	0.558855	−	1.26963i
$295$	−10.8062			−0.629164
$296$	−3.05234	−	9.00393i	−0.177414	−	0.523343i
$297$			35.1034i			2.03691i
$298$	−2.70156	−	1.18915i	−0.156497	−	0.0688857i
$299$	−10.3550	+	10.0387i	−0.598842	+	0.580552i
$300$	−7.40312	+	6.78003i	−0.427420	+	0.391445i
$301$	3.36131			0.193743
$302$	−3.24609	+	7.37460i	−0.186792	+	0.424361i
$303$		0			0
$304$	2.08717	−	23.7085i	0.119707	−	1.35978i
$305$		0			0
$306$	−5.17748	−	2.27898i	−0.295977	−	0.130281i
$307$	−8.57923			−0.489642			−0.244821	−	0.969568i	$-0.578729\pi$
$307$	−8.57923			−0.489642			−0.244821	+	0.969568i	$0.578729\pi$
$308$	−7.40312	+	6.78003i	−0.421832	+	0.386328i
$309$		−	11.7994i		−	0.671242i
$310$	−9.08080	+	20.6301i	−0.515755	+	1.17171i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	−13.7328	+	26.7651i	−0.777469	+	1.51528i
$313$	7.50781			0.424367			0.212183	−	0.977230i	$-0.431943\pi$
$313$	7.50781			0.424367			0.212183	+	0.977230i	$0.431943\pi$
$314$	9.58237	−	21.7696i	0.540765	−	1.22853i
$315$			11.7994i			0.664819i
$316$	−14.5969	−	15.9384i	−0.821138	−	0.896603i
$317$	−20.1679			−1.13274			−0.566371	−	0.824151i	$-0.691653\pi$
$317$	−20.1679			−1.13274			−0.566371	+	0.824151i	$0.691653\pi$
$318$	45.0521	+	19.8307i	2.52640	+	1.11205i
$319$		−	22.1097i		−	1.23790i
$320$	11.5340	−	8.83550i	0.644772	−	0.493919i
$321$	−2.59688			−0.144943
$322$	−2.59688	+	5.89968i	−0.144718	+	0.328776i
$323$	−4.17433			−0.232266
$324$	8.64922	+	9.44410i	0.480512	+	0.524672i
$325$	4.40490	−	4.27036i	0.244340	−	0.236877i
$326$	3.70156	+	1.62932i	0.205011	+	0.0902399i
$327$		−	20.6301i		−	1.14085i
$328$		0			0
$329$	−1.29844			−0.0715852
$330$	−13.4453	+	30.5455i	−0.740137	+	1.68147i
$331$	−23.5696			−1.29550			−0.647752	−	0.761851i	$-0.724291\pi$
$331$	−23.5696			−1.29550			−0.647752	+	0.761851i	$0.724291\pi$
$332$	3.86289	+	4.21789i	0.212003	+	0.231487i
$333$	19.1647			1.05022
$334$	−2.40312	+	5.45951i	−0.131493	+	0.298731i
$335$	−13.6125			−0.743730
$336$	−1.17909	+	13.3935i	−0.0643244	+	0.730673i
$337$	20.7016			1.12769			0.563843	−	0.825882i	$-0.309322\pi$
$337$	20.7016			1.12769			0.563843	+	0.825882i	$0.309322\pi$
$338$	7.92492	−	16.5890i	0.431059	−	0.902324i
$339$			4.13899i			0.224799i
$340$	−1.72110	−	1.87927i	−0.0933396	−	0.101918i
$341$		−	38.6567i		−	2.09338i
$342$	43.9109	+	19.3284i	2.37443	+	1.04516i
$343$			14.4733i			0.781485i
$344$	7.90172	−	2.67869i	0.426032	−	0.144425i
$345$			21.4295i			1.15373i
$346$	−6.72263	+	15.2727i	−0.361411	+	0.821067i
$347$		−	24.7879i		−	1.33068i	−0.746539	−	0.665342i	$-0.768286\pi$
$347$		−	24.7879i		−	1.33068i	0.746539	−	0.665342i	$-0.231714\pi$
$348$	−20.0000	−	21.8380i	−1.07211	−	1.17064i
$349$	−32.8810			−1.76008			−0.880040	−	0.474899i	$-0.842484\pi$
$349$	−32.8810			−1.76008			−0.880040	+	0.474899i	$0.842484\pi$
$350$	1.10469	−	2.50967i	0.0590480	−	0.134147i
$351$	−20.0000	−	20.6301i	−1.06752	−	1.10115i
$352$	−12.0000	+	21.8380i	−0.639602	+	1.16397i
$353$			13.6739i			0.727787i	0.931441	+	0.363894i	$0.118553\pi$
$353$			13.6739i			0.727787i	−0.931441	+	0.363894i	$0.881447\pi$
$354$	10.0000	−	22.7184i	0.531494	−	1.20747i
$355$			21.5292i			1.14265i
$356$	12.4421	−	11.3949i	0.659431	−	0.603929i
$357$	2.35817			0.124808
$358$	7.40014	−	16.8119i	0.391110	−	0.888538i
$359$			0.340067i			0.0179481i	0.999960	+	0.00897403i	$0.00285656\pi$
$359$			0.340067i			0.0179481i	−0.999960	+	0.00897403i	$0.997143\pi$
$360$	9.40312	+	27.7377i	0.495588	+	1.46191i
$361$	16.4031			0.863322
$362$	−3.86289	+	8.77585i	−0.203029	+	0.461249i
$363$		−	24.7879i		−	1.30103i
$364$	0.487894	−	8.20248i	0.0255726	−	0.429927i
$365$		−	15.3207i		−	0.801924i
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	−1.40312	+	15.9384i	−0.0731429	+	0.830844i
$369$		0			0
$370$	7.90172	+	3.47812i	0.410791	+	0.180819i
$371$	−13.4453			−0.698043
$372$	−34.9682	−	38.1818i	−1.81302	−	1.97964i
$373$			18.5794i			0.962004i	0.876719	+	0.481002i	$0.159727\pi$
$373$			18.5794i			0.962004i	−0.876719	+	0.481002i	$0.840273\pi$
$374$	4.00000	+	1.76069i	0.206835	+	0.0910430i
$375$		−	35.9028i		−	1.85401i
$376$	−3.05234	+	1.03475i	−0.157413	+	0.0533631i
$377$	12.5969	+	12.9937i	0.648772	+	0.669212i
$378$	−11.7539	−	5.17374i	−0.604556	−	0.266109i
$379$	−5.95005			−0.305634			−0.152817	−	0.988255i	$-0.548834\pi$
$379$	−5.95005			−0.305634			−0.152817	+	0.988255i	$0.548834\pi$
$380$	14.5969	+	15.9384i	0.748804	+	0.817620i
$381$			35.3981i			1.81350i
$382$	29.5197	+	12.9937i	1.51036	+	0.664818i
$383$			14.1332i			0.722175i	0.932532	+	0.361087i	$0.117594\pi$
$383$			14.1332i			0.722175i	−0.932532	+	0.361087i	$0.882406\pi$
$384$	7.90172	+	32.4247i	0.403233	+	1.65467i
$385$		−	9.11592i		−	0.464590i
$386$	−4.80625	+	10.9190i	−0.244632	+	0.555763i
$387$			16.8187i			0.854943i
$388$	−19.1647	+	17.5517i	−0.972943	+	0.891053i
$389$			26.8574i			1.36172i	0.732412	+	0.680862i	$0.238394\pi$
$389$			26.8574i			1.36172i	−0.732412	+	0.680862i	$0.761606\pi$
$390$	−9.50141	−	25.6118i	−0.481123	−	1.29690i
$391$	2.80625			0.141918
$392$	5.17748	+	15.2727i	0.261502	+	0.771389i
$393$	−3.50781			−0.176946
$394$	−4.35078	−	1.91509i	−0.219189	−	0.0964810i
$395$	19.6259			0.987485
$396$	−33.9246	−	37.0423i	−1.70477	−	1.86145i
$397$	3.63232			0.182301			0.0911505	−	0.995837i	$-0.470946\pi$
$397$	3.63232			0.182301			0.0911505	+	0.995837i	$0.470946\pi$
$398$		0			0
$399$	−20.0000			−1.00125
$400$	0.596876	−	6.78003i	0.0298438	−	0.339001i
$401$		−	17.5517i		−	0.876491i	−0.898855	−	0.438245i	$-0.855600\pi$
$401$		−	17.5517i		−	0.876491i	0.898855	−	0.438245i	$-0.144400\pi$
$402$	12.5969	−	28.6181i	0.628275	−	1.42734i
$403$	22.0245	+	22.7184i	1.09712	+	1.13168i
$404$		0			0
$405$	−11.6291			−0.577855
$406$	7.40312	+	3.25865i	0.367411	+	0.161724i
$407$	−14.8062			−0.733918
$408$	5.54354	−	1.87927i	0.274446	−	0.0930377i
$409$		−	13.6739i		−	0.676130i	−0.941123	−	0.338065i	$-0.890228\pi$
$409$		−	13.6739i		−	0.676130i	0.941123	−	0.338065i	$-0.109772\pi$
$410$		0			0
$411$	−13.4453			−0.663206
$412$	5.40312	+	5.89968i	0.266193	+	0.290656i
$413$			6.78003i			0.333623i
$414$	−29.5197	−	12.9937i	−1.45081	−	0.638608i
$415$	−5.19375			−0.254951
$416$	−5.38977	−	19.6711i	−0.264255	−	0.964453i
$417$	55.7172			2.72848
$418$	−33.9246	−	14.9327i	−1.65931	−	0.730380i
$419$		−	26.5486i		−	1.29698i	−0.761222	−	0.648491i	$-0.775400\pi$
$419$		−	26.5486i		−	1.29698i	0.761222	−	0.648491i	$-0.224600\pi$
$420$	−8.24609	−	9.00393i	−0.402368	−	0.439347i
$421$	9.62281			0.468987			0.234494	−	0.972118i	$-0.424657\pi$
$421$	9.62281			0.468987			0.234494	+	0.972118i	$0.424657\pi$
$422$	0.677514	−	1.53920i	0.0329809	−	0.0749272i
$423$		−	6.49687i		−	0.315889i
$424$	−31.6069	+	10.7148i	−1.53496	+	0.520355i
$425$	−1.19375			−0.0579055
$426$	−45.2617	−	19.9229i	−2.19294	−	0.965270i
$427$		0			0
$428$	1.29844	−	1.18915i	0.0627624	−	0.0574799i
$429$	32.6100	+	33.6374i	1.57443	+	1.62403i
$430$	−3.05234	+	6.93443i	−0.147197	+	0.334408i
$431$		−	29.4060i		−	1.41644i	−0.705994	−	0.708218i	$-0.749499\pi$
$431$		−	29.4060i		−	1.41644i	0.705994	−	0.708218i	$-0.250501\pi$
$432$	−31.7539	−	2.79544i	−1.52776	−	0.134496i
$433$	−29.5078			−1.41805			−0.709027	−	0.705181i	$-0.750866\pi$
$433$	−29.5078			−1.41805			−0.709027	+	0.705181i	$0.750866\pi$
$434$	12.9437	+	5.69745i	0.621317	+	0.273486i
$435$	26.8905			1.28930
$436$	9.44687	+	10.3151i	0.452423	+	0.494002i
$437$	−23.8002			−1.13852
$438$	32.2094	+	14.1777i	1.53902	+	0.677435i
$439$	10.8062			0.515754			0.257877	−	0.966178i	$-0.416977\pi$
$439$	10.8062			0.515754			0.257877	+	0.966178i	$0.416977\pi$
$440$	−7.26464	−	21.4295i	−0.346328	−	1.02161i
$441$	−32.5078			−1.54799
$442$	−3.35392	+	1.24423i	−0.159530	+	0.0591821i
$443$		−	2.94984i		−	0.140151i	−0.997542	−	0.0700756i	$-0.977676\pi$
$443$		−	2.94984i		−	0.140151i	0.997542	−	0.0700756i	$-0.0223240\pi$
$444$	−14.6243	+	13.3935i	−0.694041	+	0.635625i
$445$			15.3207i			0.726273i
$446$	11.9477	−	27.1431i	0.565738	−	1.28527i
$447$			6.15681i			0.291207i
$448$	−5.54354	−	7.23665i	−0.261908	−	0.341900i
$449$			38.9812i			1.83964i	0.392342	+	0.919819i	$0.371665\pi$
$449$			38.9812i			1.83964i	−0.392342	+	0.919819i	$0.628335\pi$
$450$	12.5574	+	5.52742i	0.591961	+	0.260565i
$451$		0			0
$452$	−1.89531	−	2.06950i	−0.0891481	−	0.0973409i
$453$	16.8066			0.789642
$454$	−21.1047	−	9.28970i	−0.990492	−	0.435987i
$455$	5.19375	+	5.35738i	0.243487	+	0.251158i
$456$	−47.0156	+	15.9384i	−2.20171	+	0.746382i
$457$			30.5455i			1.42886i	0.699709	+	0.714428i	$0.253313\pi$
$457$			30.5455i			1.42886i	−0.699709	+	0.714428i	$0.746687\pi$
$458$	24.4555	+	10.7646i	1.14273	+	0.502997i
$459$			5.59087i			0.260960i
$460$	−9.81294	−	10.7148i	−0.457531	−	0.499579i
$461$	−10.6260			−0.494900			−0.247450	−	0.968901i	$-0.579593\pi$
$461$	−10.6260			−0.494900			−0.247450	+	0.968901i	$0.579593\pi$
$462$	19.1647	+	8.43579i	0.891625	+	0.392468i
$463$			17.2116i			0.799893i	0.916539	+	0.399946i	$0.130971\pi$
$463$			17.2116i			0.799893i	−0.916539	+	0.399946i	$0.869029\pi$
$464$	20.0000	+	1.76069i	0.928477	+	0.0817379i
$465$	47.0156			2.18030
$466$	15.6679	+	6.89659i	0.725803	+	0.319478i
$467$			12.6797i			0.586747i	0.955998	+	0.293373i	$0.0947779\pi$
$467$			12.6797i			0.586747i	−0.955998	+	0.293373i	$0.905222\pi$
$468$	41.0420	+	2.44123i	1.89717	+	0.112846i
$469$			8.54071i			0.394374i
$470$	1.17909	−	2.67869i	0.0543872	−	0.123559i
$471$	−49.6125			−2.28602
$472$	5.40312	+	15.9384i	0.248699	+	0.733622i
$473$		−	12.9937i		−	0.597453i
$474$	−18.1616	+	41.2602i	−0.834190	+	1.89514i
$475$	10.1244			0.464539
$476$	−1.17909	+	1.07985i	−0.0540433	+	0.0494946i
$477$		−	67.2748i		−	3.08030i
$478$	−5.45547	+	12.3939i	−0.249527	+	0.566886i
$479$		−	2.73834i		−	0.125118i	−0.998041	−	0.0625589i	$-0.980074\pi$
$479$		−	2.73834i		−	0.125118i	0.998041	−	0.0625589i	$-0.0199261\pi$
$480$	−26.5602	−	14.5948i	−1.21230	−	0.666158i
$481$	8.70156	−	8.43579i	0.396757	−	0.384639i
$482$	−10.0000	+	22.7184i	−0.455488	+	1.03479i
$483$	13.4453			0.611780
$484$	11.3508	+	12.3939i	0.515945	+	0.563361i
$485$		−	23.5987i		−	1.07156i
$486$	−2.85974	+	6.49687i	−0.129721	+	0.294704i
$487$		−	25.6474i		−	1.16220i	−0.813834	−	0.581098i	$-0.802623\pi$
$487$		−	25.6474i		−	1.16220i	0.813834	−	0.581098i	$-0.197377\pi$
$488$		0			0
$489$		−	8.43579i		−	0.381479i
$490$	−13.4031	−	5.89968i	−0.605491	−	0.266520i
$491$			30.6876i			1.38491i	0.721461	+	0.692455i	$0.243471\pi$
$491$			30.6876i			1.38491i	−0.721461	+	0.692455i	$0.756529\pi$
$492$		0			0
$493$		−	3.52138i		−	0.158595i
$494$	28.4451	−	10.5525i	1.27981	−	0.474780i
$495$	45.6125			2.05013
$496$	34.9682	+	3.07840i	1.57012	+	0.138224i
$497$	13.5078			0.605908
$498$	4.80625	−	10.9190i	0.215373	−	0.489293i
$499$	−1.77572			−0.0794922			−0.0397461	−	0.999210i	$-0.512655\pi$
$499$	−1.77572			−0.0794922			−0.0397461	+	0.999210i	$0.512655\pi$
$500$	16.4405	+	17.9514i	0.735242	+	0.802812i
$501$	12.4421			0.555873
$502$	−5.21791	+	11.8543i	−0.232887	+	0.529081i
$503$	25.6125			1.14200			0.571002	−	0.820948i	$-0.306555\pi$
$503$	25.6125			1.14200			0.571002	+	0.820948i	$0.306555\pi$
$504$	17.4031	−	5.89968i	0.775197	−	0.262793i
$505$		0			0
$506$	22.8062	+	10.0387i	1.01386	+	0.446274i
$507$	−38.3295	−	1.18915i	−1.70227	−	0.0528121i
$508$	−16.2094	−	17.6990i	−0.719175	−	0.785268i
$509$	9.81294			0.434951			0.217475	−	0.976066i	$-0.430218\pi$
$509$	9.81294			0.434951			0.217475	+	0.976066i	$0.430218\pi$
$510$	−2.14141	+	4.86493i	−0.0948232	+	0.215423i
$511$	−9.61250			−0.425232
$512$	−18.7987	−	12.5940i	−0.830792	−	0.556583i
$513$		−	47.4170i		−	2.09351i
$514$	−33.0165	−	14.5329i	−1.45630	−	0.641021i
$515$	−7.26464			−0.320118
$516$	−11.7539	−	12.8341i	−0.517437	−	0.564990i
$517$			5.01934i			0.220750i
$518$	2.18223	−	4.95767i	0.0958817	−	0.217828i
$519$	34.8062			1.52782
$520$	16.4788	+	8.45504i	0.722642	+	0.370778i
$521$	−6.10469			−0.267451			−0.133726	−	0.991018i	$-0.542694\pi$
$521$	−6.10469			−0.267451			−0.133726	+	0.991018i	$0.542694\pi$
$522$	−16.3050	+	37.0423i	−0.713651	+	1.62130i
$523$		−	10.9190i		−	0.477455i	−0.971087	−	0.238728i	$-0.923270\pi$
$523$		−	10.9190i		−	0.477455i	0.971087	−	0.238728i	$-0.0767303\pi$
$524$	1.75391	−	1.60628i	0.0766197	−	0.0701709i
$525$	−5.71949			−0.249619
$526$	−20.7099	−	9.11592i	−0.902995	−	0.397473i
$527$		−	6.15681i		−	0.268195i
$528$	51.7748	+	4.55796i	2.25321	+	0.198360i
$529$	−7.00000			−0.304348
$530$	12.2094	−	27.7377i	0.530341	−	1.20485i
$531$	−33.9246			−1.47220
$532$	10.0000	−	9.15833i	0.433555	−	0.397064i
$533$		0			0
$534$	−32.2094	−	14.1777i	−1.39384	−	0.613528i
$535$			1.59885i			0.0691242i
$536$	6.80625	+	20.0774i	0.293985	+	0.867209i
$537$	−38.3141			−1.65337
$538$	10.5855	−	24.0486i	0.456374	−	1.03681i
$539$	25.1148			1.08177
$540$	21.3470	−	19.5503i	0.918628	−	0.841310i
$541$	−10.6260			−0.456846			−0.228423	−	0.973562i	$-0.573357\pi$
$541$	−10.6260			−0.456846			−0.228423	+	0.973562i	$0.573357\pi$
$542$	−10.2617	+	23.3130i	−0.440778	+	1.00138i
$543$	20.0000			0.858282
$544$	−1.91122	+	3.47812i	−0.0819430	+	0.149123i
$545$	−12.7016			−0.544075
$546$	−16.0693	+	5.96135i	−0.687702	+	0.255122i
$547$		−	6.47122i		−	0.276689i	−0.990384	−	0.138345i	$-0.955822\pi$
$547$		−	6.47122i		−	0.276689i	0.990384	−	0.138345i	$-0.0441782\pi$
$548$	6.72263	−	6.15681i	0.287177	−	0.263006i
$549$		0			0
$550$	−9.70156	−	4.27036i	−0.413676	−	0.182089i
$551$			29.8653i			1.27231i
$552$	31.6069	−	10.7148i	1.34528	−	0.456051i
$553$		−	12.3136i		−	0.523628i
$554$	13.4453	−	30.5455i	0.571234	−	1.29775i
$555$		−	18.0079i		−	0.764391i
$556$	−27.8586	+	25.5138i	−1.18147	+	1.08203i
$557$	24.6132			1.04290			0.521448	−	0.853283i	$-0.325392\pi$
$557$	24.6132			1.04290			0.521448	+	0.853283i	$0.325392\pi$
$558$	−28.5078	+	64.7651i	−1.20683	+	2.74173i
$559$	7.40312	+	7.63636i	0.313119	+	0.322984i
$560$	8.24609	+	0.725940i	0.348461	+	0.0306766i
$561$		−	9.11592i		−	0.384875i
$562$	10.0000	−	22.7184i	0.421825	−	0.958317i
$563$		−	16.5099i		−	0.695809i	−0.937530	−	0.347905i	$-0.886893\pi$
$563$		−	16.5099i		−	0.695809i	0.937530	−	0.347905i	$-0.113107\pi$
$564$	4.54040	+	4.95767i	0.191185	+	0.208756i
$565$	2.54830			0.107208
$566$	6.22106	−	14.1332i	0.261491	−	0.594064i
$567$			7.29630i			0.306416i
$568$	31.7539	−	10.7646i	1.33236	−	0.451673i
$569$	−13.5078			−0.566277			−0.283138	−	0.959079i	$-0.591376\pi$
$569$	−13.5078			−0.566277			−0.283138	+	0.959079i	$0.591376\pi$
$570$	18.1616	−	41.2602i	0.760706	−	1.72820i
$571$		−	1.18915i		−	0.0497645i	−0.999690	−	0.0248822i	$-0.992079\pi$
$571$		−	1.18915i		−	0.0497645i	0.999690	−	0.0248822i	$-0.00792108\pi$
$572$	−31.7081	−	1.88604i	−1.32578	−	0.0788593i
$573$		−	67.2748i		−	2.81045i
$574$		0			0
$575$	−6.80625			−0.283840
$576$	36.2094	−	27.7377i	1.50872	−	1.15574i
$577$		−	39.6614i		−	1.65112i	−0.564311	−	0.825562i	$-0.690858\pi$
$577$		−	39.6614i		−	1.65112i	0.564311	−	0.825562i	$-0.309142\pi$
$578$	−21.3672	−	9.40524i	−0.888758	−	0.391207i
$579$	24.8842			1.03415
$580$	−13.4453	+	12.3136i	−0.558284	+	0.511295i
$581$			3.25865i			0.135192i
$582$	49.6125	+	21.8380i	2.05650	+	0.905216i
$583$			51.9750i			2.15258i
$584$	−22.5969	+	7.66037i	−0.935065	+	0.316988i
$585$	−26.8062	+	25.9875i	−1.10830	+	1.07445i
$586$	30.4555	+	13.4056i	1.25810	+	0.553782i
$587$	11.6695			0.481653			0.240827	−	0.970568i	$-0.422581\pi$
$587$	11.6695			0.481653			0.240827	+	0.970568i	$0.422581\pi$
$588$	24.8062	−	22.7184i	1.02299	−	0.936890i
$589$			52.2168i			2.15156i
$590$	−13.9873	−	6.15681i	−0.575847	−	0.253472i
$591$			9.91534i			0.407863i
$592$	1.17909	−	13.3935i	0.0484601	−	0.550468i
$593$			25.9875i			1.06718i	0.845744	+	0.533589i	$0.179157\pi$
$593$			25.9875i			1.06718i	−0.845744	+	0.533589i	$0.820843\pi$
$594$	−20.0000	+	45.4368i	−0.820610	+	1.86429i
$595$		−	1.45188i		−	0.0595213i
$596$	−2.81930	−	3.07840i	−0.115483	−	0.126096i
$597$		0			0
$598$	−19.1226	+	7.09407i	−0.781982	+	0.290098i
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$	−13.4453	+	4.55796i	−0.548900	+	0.186078i
$601$	−26.1047			−1.06483			−0.532416	−	0.846483i	$-0.678716\pi$
$601$	−26.1047			−1.06483			−0.532416	+	0.846483i	$0.678716\pi$
$602$	4.35078	+	1.91509i	0.177325	+	0.0780534i
$603$	−42.7344			−1.74028
$604$	−8.40329	+	7.69601i	−0.341925	+	0.313146i
$605$	−15.2614			−0.620465
$606$		0			0
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$	16.2094	−	29.4984i	0.657377	−	1.19632i
$609$		−	16.8716i		−	0.683671i
$610$		0			0
$611$	−2.85974	−	2.94984i	−0.115693	−	0.119338i
$612$	−5.40312	−	5.89968i	−0.218408	−	0.238481i
$613$	−37.3263			−1.50760			−0.753798	−	0.657106i	$-0.771781\pi$
$613$	−37.3263			−1.50760			−0.753798	+	0.657106i	$0.771781\pi$
$614$	−11.1047	−	4.88797i	−0.448149	−	0.197263i
$615$		0			0
$616$	−13.4453	+	4.55796i	−0.541725	+	0.183645i
$617$			48.0972i			1.93632i	0.250334	+	0.968159i	$0.419460\pi$
$617$			48.0972i			1.93632i	−0.250334	+	0.968159i	$0.580540\pi$
$618$	6.72263	−	15.2727i	0.270424	−	0.614359i
$619$	−1.77572			−0.0713723			−0.0356861	−	0.999363i	$-0.511362\pi$
$619$	−1.77572			−0.0713723			−0.0356861	+	0.999363i	$0.511362\pi$
$620$	−23.5078	+	21.5292i	−0.944096	+	0.864635i
$621$			31.8767i			1.27917i
$622$	15.5324	+	6.83694i	0.622794	+	0.274136i
$623$	9.61250			0.385117
$624$	−33.0247	+	26.8197i	−1.32204	+	1.07365i
$625$	−13.5969			−0.543875
$626$	9.71788	+	4.27754i	0.388404	+	0.170965i
$627$			77.3135i			3.08760i
$628$	24.8062	−	22.7184i	0.989877	−	0.906562i
$629$	−2.35817			−0.0940264
$630$	−6.72263	+	15.2727i	−0.267836	+	0.608480i
$631$		−	29.4060i		−	1.17063i	−0.810805	−	0.585317i	$-0.800970\pi$
$631$		−	29.4060i		−	1.17063i	0.810805	−	0.585317i	$-0.199030\pi$
$632$	−9.81294	−	28.9466i	−0.390338	−	1.15143i
$633$	−3.50781			−0.139423
$634$	−26.1047	−	11.4906i	−1.03675	−	0.456348i
$635$	21.7939			0.864865
$636$	47.0156	+	51.3364i	1.86429	+	2.03562i
$637$	−14.7598	+	14.3090i	−0.584806	+	0.566945i
$638$	12.5969	−	28.6181i	0.498715	−	1.13300i
$639$			67.5878i			2.67373i
$640$	19.9633	−	4.86493i	0.789118	−	0.192303i
$641$	37.4031			1.47733			0.738667	−	0.674070i	$-0.235455\pi$
$641$	37.4031			1.47733			0.738667	+	0.674070i	$0.235455\pi$
$642$	−3.36131	−	1.47956i	−0.132661	−	0.0583935i
$643$	7.03407			0.277397			0.138698	−	0.990335i	$-0.455708\pi$
$643$	7.03407			0.277397			0.138698	+	0.990335i	$0.455708\pi$
$644$	−6.72263	+	6.15681i	−0.264909	+	0.242612i
$645$	15.8034			0.622259
$646$	−5.40312	−	2.37830i	−0.212583	−	0.0935732i
$647$	−42.8062			−1.68289			−0.841444	−	0.540345i	$-0.818294\pi$
$647$	−42.8062			−1.68289			−0.841444	+	0.540345i	$0.818294\pi$
$648$	5.81455	+	17.1520i	0.228417	+	0.673794i
$649$	26.2094			1.02881
$650$	8.13458	−	3.01775i	0.319064	−	0.118366i
$651$		−	29.4984i		−	1.15613i
$652$	3.86289	+	4.21789i	0.151282	+	0.165185i
$653$			18.5794i			0.727068i	0.931581	+	0.363534i	$0.118430\pi$
$653$			18.5794i			0.727068i	−0.931581	+	0.363534i	$0.881570\pi$
$654$	11.7539	−	26.7030i	0.459614	−	1.04417i
$655$			2.15969i			0.0843861i
$656$		0			0
$657$		−	48.0972i		−	1.87645i
$658$	−1.68066	−	0.739779i	−0.0655188	−	0.0288396i
$659$		−	34.5177i		−	1.34462i	−0.740269	−	0.672310i	$-0.765302\pi$
$659$		−	34.5177i		−	1.34462i	0.740269	−	0.672310i	$-0.234698\pi$
$660$	−34.8062	+	31.8767i	−1.35483	+	1.24080i
$661$	24.3422			0.946803			0.473401	−	0.880847i	$-0.343026\pi$
$661$	24.3422			0.946803			0.473401	+	0.880847i	$0.343026\pi$
$662$	−30.5078	−	13.4287i	−1.18572	−	0.521921i
$663$	5.19375	+	5.35738i	0.201709	+	0.208064i
$664$	2.59688	+	7.66037i	0.100778	+	0.297280i
$665$			12.3136i			0.477501i
$666$	24.8062	+	10.9190i	0.961223	+	0.423103i
$667$		−	20.0774i		−	0.777398i
$668$	−6.22106	+	5.69745i	−0.240700	+	0.220441i
$669$	−61.8587			−2.39160
$670$	−17.6196	−	7.75565i	−0.680704	−	0.299627i
$671$		0			0
$672$	−9.15703	+	16.6643i	−0.353240	+	0.642839i
$673$	−44.9109			−1.73119			−0.865595	−	0.500745i	$-0.833059\pi$
$673$	−44.9109			−1.73119			−0.865595	+	0.500745i	$0.833059\pi$
$674$	26.7955	+	11.7946i	1.03212	+	0.454312i
$675$		−	13.5601i		−	0.521927i
$676$	19.7093	−	16.9571i	0.758049	−	0.652197i
$677$			35.3981i			1.36046i	0.732999	+	0.680230i	$0.238120\pi$
$677$			35.3981i			1.36046i	−0.732999	+	0.680230i	$0.761880\pi$
$678$	−2.35817	+	5.35738i	−0.0905650	+	0.205749i
$679$	−14.8062			−0.568212
$680$	−1.15703	−	3.41305i	−0.0443701	−	0.130885i
$681$			48.0972i			1.84309i
$682$	22.0245	−	50.0361i	0.843361	−	1.91598i
$683$	−41.1892			−1.57606			−0.788031	−	0.615635i	$-0.788899\pi$
$683$	−41.1892			−1.57606			−0.788031	+	0.615635i	$0.788899\pi$
$684$	45.8247	+	50.0361i	1.75215	+	1.91318i
$685$			8.27799i			0.316286i
$686$	−8.24609	+	18.7338i	−0.314837	+	0.715260i
$687$		−	55.7335i		−	2.12637i
$688$	11.7539	+	1.03475i	0.448113	+	0.0394494i
$689$	−29.6125	−	30.5455i	−1.12815	−	1.16369i
$690$	−12.2094	+	27.7377i	−0.464803	+	1.05596i
$691$	4.40490			0.167570			0.0837851	−	0.996484i	$-0.473299\pi$
$691$	4.40490			0.167570			0.0837851	+	0.996484i	$0.473299\pi$
$692$	−17.4031	+	15.9384i	−0.661568	+	0.605885i
$693$		−	28.6181i		−	1.08711i
$694$	14.1228	−	32.0847i	0.536093	−	1.21792i
$695$		−	34.3040i		−	1.30122i
$696$	−13.4453	−	39.6614i	−0.509641	−	1.50336i
$697$		0			0
$698$	−42.5602	−	18.7338i	−1.61093	−	0.709085i
$699$		−	35.7069i		−	1.35056i
$700$	2.85974	−	2.61905i	0.108088	−	0.0989907i
$701$		−	6.78003i		−	0.256078i	−0.991769	−	0.128039i	$-0.959132\pi$
$701$		−	6.78003i		−	0.256078i	0.991769	−	0.128039i	$-0.0408683\pi$
$702$	−14.1335	−	38.0979i	−0.533433	−	1.43791i
$703$	20.0000			0.754314
$704$	−27.9745	+	21.4295i	−1.05433	+	0.807656i
$705$	−6.10469			−0.229916
$706$	−7.79063	+	17.6990i	−0.293204	+	0.666112i
$707$		0			0
$708$	25.8874	−	23.7085i	0.972907	−	0.891021i
$709$	−46.1361			−1.73268			−0.866340	−	0.499455i	$-0.833533\pi$
$709$	−46.1361			−1.73268			−0.866340	+	0.499455i	$0.833533\pi$
$710$	−12.2662	+	27.8668i	−0.460341	+	1.04582i
$711$	61.6125			2.31065
$712$	22.5969	−	7.66037i	0.846854	−	0.287085i
$713$		−	35.1034i		−	1.31463i
$714$	3.05234	+	1.34356i	0.114231	+	0.0502813i
$715$	20.7099	−	20.0774i	0.774506	−	0.750850i
$716$	19.1570	−	17.5446i	0.715932	−	0.655674i
$717$	28.2455			1.05485
$718$	−0.193752	+	0.440172i	−0.00723074	+	0.0164271i
$719$	−30.8062			−1.14888			−0.574440	−	0.818547i	$-0.694780\pi$
$719$	−30.8062			−1.14888			−0.574440	+	0.818547i	$0.694780\pi$
$720$	−3.63232	+	41.2602i	−0.135369	+	1.53768i
$721$			4.55796i			0.169747i
$722$	21.2317	+	9.34560i	0.790162	+	0.347807i
$723$	51.7748			1.92552
$724$	−10.0000	+	9.15833i	−0.371647	+	0.340367i
$725$			8.54071i			0.317194i
$726$	14.1228	−	32.0847i	0.524145	−	1.19077i
$727$	17.1938			0.637681			0.318840	−	0.947808i	$-0.396707\pi$
$727$	17.1938			0.637681			0.318840	+	0.947808i	$0.396707\pi$
$728$	5.30484	−	10.3391i	0.196610	−	0.383191i
$729$	34.0156			1.25984
$730$	8.72892	−	19.8307i	0.323072	−	0.733967i
$731$		−	2.06950i		−	0.0765431i
$732$		0			0
$733$	11.6291			0.429531			0.214765	−	0.976666i	$-0.431101\pi$
$733$	11.6291			0.429531			0.214765	+	0.976666i	$0.431101\pi$
$734$	10.3550	+	4.55796i	0.382208	+	0.168237i
$735$			30.5455i			1.12669i
$736$	−10.8970	+	19.8307i	−0.401667	+	0.730969i
$737$	33.0156			1.21615
$738$		0			0
$739$	45.8247			1.68569			0.842844	−	0.538157i	$-0.180879\pi$
$739$	45.8247			1.68569			0.842844	+	0.538157i	$0.180879\pi$
$740$	8.24609	+	9.00393i	0.303132	+	0.330991i
$741$	−44.0490	−	45.4368i	−1.61818	−	1.66916i
$742$	−17.4031	−	7.66037i	−0.638889	−	0.281221i
$743$			1.81962i			0.0667555i	0.999443	+	0.0333778i	$0.0106264\pi$
$743$			1.81962i			0.0667555i	−0.999443	+	0.0333778i	$0.989374\pi$
$744$	−23.5078	−	69.3443i	−0.861838	−	2.54229i
$745$	3.79063			0.138878
$746$	−10.5855	+	24.0486i	−0.387563	+	0.880481i
$747$	−16.3050			−0.596569
$748$	4.17433	+	4.55796i	0.152629	+	0.166656i
$749$	1.00314			0.0366541
$750$	20.4555	−	46.4715i	0.746928	−	1.69690i
$751$	44.4187			1.62086			0.810432	−	0.585833i	$-0.199233\pi$
$751$	44.4187			1.62086			0.810432	+	0.585833i	$0.199233\pi$
$752$	−4.54040	−	0.399712i	−0.165571	−	0.0145760i
$753$	27.0156			0.984504
$754$	8.90188	+	23.9957i	0.324187	+	0.873872i
$755$		−	10.3475i		−	0.376583i
$756$	−12.2662	−	13.3935i	−0.446116	−	0.487115i
$757$			8.27799i			0.300869i	0.988620	+	0.150434i	$0.0480672\pi$
$757$			8.27799i			0.300869i	−0.988620	+	0.150434i	$0.951933\pi$
$758$	−7.70156	−	3.39001i	−0.279733	−	0.123131i
$759$		−	51.9750i		−	1.88657i
$760$	9.81294	+	28.9466i	0.355953	+	1.05000i
$761$		−	47.4170i		−	1.71887i	−0.511248	−	0.859433i	$-0.670817\pi$
$761$		−	47.4170i		−	1.71887i	0.511248	−	0.859433i	$-0.329183\pi$
$762$	−20.1679	+	45.8182i	−0.730606	+	1.65982i
$763$			7.96918i			0.288504i
$764$	30.8062	+	33.6374i	1.11453	+	1.21696i
$765$	7.26464			0.262654
$766$	−8.05234	+	18.2936i	−0.290943	+	0.660975i
$767$	−15.4031	+	14.9327i	−0.556175	+	0.539187i
$768$	−8.24609	+	46.4715i	−0.297555	+	1.67690i
$769$			3.87783i			0.139838i	0.997553	+	0.0699190i	$0.0222741\pi$
$769$			3.87783i			0.139838i	−0.997553	+	0.0699190i	$0.977726\pi$
$770$	5.19375	−	11.7994i	0.187170	−	0.425220i
$771$			75.2440i			2.70985i
$772$	−12.4421	+	11.3949i	−0.447802	+	0.410111i
$773$	47.9523			1.72472			0.862362	−	0.506292i	$-0.168984\pi$
$773$	47.9523			1.72472			0.862362	+	0.506292i	$0.168984\pi$
$774$	−9.58237	+	21.7696i	−0.344431	+	0.782492i
$775$			14.9327i			0.536397i
$776$	−34.8062	+	11.7994i	−1.24947	+	0.423572i
$777$	−11.2984			−0.405329
$778$	−15.3019	+	34.7634i	−0.548598	+	1.24633i
$779$		0			0
$780$	2.29387	−	38.5645i	0.0821336	−	1.38083i
$781$		−	52.2168i		−	1.86846i
$782$	3.63232	+	1.59885i	0.129892	+	0.0571746i
$783$	40.0000			1.42948
$784$	−2.00000	+	22.7184i	−0.0714286	+	0.811371i
$785$			30.5455i			1.09021i
$786$	−4.54040	−	1.99856i	−0.161951	−	0.0712862i
$787$	43.1955			1.53975			0.769877	−	0.638192i	$-0.220318\pi$
$787$	43.1955			1.53975			0.769877	+	0.638192i	$0.220318\pi$
$788$	−4.54040	−	4.95767i	−0.161745	−	0.176610i
$789$			47.1975i			1.68027i
$790$	25.4031	+	11.1817i	0.903803	+	0.397829i
$791$		−	1.59885i		−	0.0568484i
$792$	−22.8062	−	67.2748i	−0.810385	−	2.39051i
$793$		0			0
$794$	4.70156	+	2.06950i	0.166852	+	0.0734437i
$795$	−63.2137			−2.24196
$796$		0			0
$797$			10.3014i			0.364894i	0.983216	+	0.182447i	$0.0584019\pi$
$797$			10.3014i			0.364894i	−0.983216	+	0.182447i	$0.941598\pi$
$798$	−25.8874	−	11.3949i	−0.916403	−	0.403375i
$799$			0.799423i			0.0282816i
$800$	4.63546	−	8.43579i	0.163888	−	0.298250i
$801$			48.0972i			1.69943i
$802$	10.0000	−	22.7184i	0.353112	−	0.802214i
$803$			37.1588i			1.31130i
$804$	32.6100	−	29.8653i	1.15007	−	1.05327i
$805$		−	8.27799i		−	0.291761i
$806$	15.5641	+	41.9543i	0.548223	+	1.47778i
$807$	−54.8062			−1.92927
$808$		0			0
$809$	23.5078			0.826491			0.413245	−	0.910620i	$-0.364395\pi$
$809$	23.5078			0.826491			0.413245	+	0.910620i	$0.364395\pi$
$810$	−15.0523	−	6.62562i	−0.528885	−	0.232801i
$811$	−31.2954			−1.09893			−0.549465	−	0.835516i	$-0.685169\pi$
$811$	−31.2954			−1.09893			−0.549465	+	0.835516i	$0.685169\pi$
$812$	7.72577	+	8.43579i	0.271121	+	0.296038i
$813$	53.1298			1.86334
$814$	−19.1647	−	8.43579i	−0.671724	−	0.295674i
$815$	−5.19375			−0.181929
$816$	8.24609	+	0.725940i	0.288671	+	0.0254130i
$817$			17.5517i			0.614057i
$818$	7.79063	−	17.6990i	0.272393	−	0.618833i
$819$	16.3050	+	16.8187i	0.569743	+	0.587693i
$820$		0			0
$821$	33.4230			1.16647			0.583236	−	0.812303i	$-0.301786\pi$
$821$	33.4230			1.16647			0.583236	+	0.812303i	$0.301786\pi$
$822$	−17.4031	−	7.66037i	−0.607004	−	0.267186i
$823$	25.6125			0.892796			0.446398	−	0.894835i	$-0.352707\pi$
$823$	25.6125			0.892796			0.446398	+	0.894835i	$0.352707\pi$
$824$	3.63232	+	10.7148i	0.126538	+	0.373267i
$825$			22.1097i			0.769760i
$826$	−3.86289	+	8.77585i	−0.134407	+	0.305351i
$827$	15.2210			0.529285			0.264643	−	0.964347i	$-0.414746\pi$
$827$	15.2210			0.529285			0.264643	+	0.964347i	$0.414746\pi$
$828$	−30.8062	−	33.6374i	−1.07059	−	1.16898i
$829$		−	43.6761i		−	1.51693i	−0.651712	−	0.758466i	$-0.725949\pi$
$829$		−	43.6761i		−	1.51693i	0.651712	−	0.758466i	$-0.274051\pi$
$830$	−6.72263	−	2.95911i	−0.233346	−	0.102712i
$831$	−69.6125			−2.41483
$832$	4.23113	−	28.5324i	0.146688	−	0.989183i
$833$	4.00000			0.138592
$834$	72.1186	+	31.7446i	2.49726	+	1.09923i
$835$		−	7.66037i		−	0.265098i
$836$	−35.4031	−	38.6567i	−1.22444	−	1.33697i
$837$	69.9364			2.41735
$838$	15.1259	−	34.3636i	0.522516	−	1.18707i
$839$			0.340067i			0.0117404i	0.999983	+	0.00587021i	$0.00186856\pi$
$839$			0.340067i			0.0117404i	−0.999983	+	0.00587021i	$0.998131\pi$
$840$	−5.54354	−	16.3526i	−0.191270	−	0.564217i
$841$	3.80625			0.131250
$842$	12.4555	+	5.48255i	0.429244	+	0.188941i
$843$	−51.7748			−1.78322
$844$	1.75391	−	1.60628i	0.0603719	−	0.0552906i
$845$	−0.732138	+	23.5987i	−0.0251863	+	0.811821i
$846$	3.70156	−	8.40935i	0.127262	−	0.289119i
$847$			9.57528i			0.329010i
$848$	−47.0156	−	4.13899i	−1.61452	−	0.142134i
$849$	−32.2094			−1.10542
$850$	−1.54515	−	0.680134i	−0.0529984	−	0.0233284i
$851$	−13.4453			−0.460898
$852$	−47.2344	−	51.5753i	−1.61822	−	1.76694i
$853$	−16.3454			−0.559657			−0.279829	−	0.960050i	$-0.590278\pi$
$853$	−16.3454			−0.559657			−0.279829	+	0.960050i	$0.590278\pi$
$854$		0			0
$855$	−61.6125			−2.10710
$856$	2.35817	−	0.799423i	0.0806006	−	0.0273237i
$857$	−12.8062			−0.437453			−0.218727	−	0.975786i	$-0.570190\pi$
$857$	−12.8062			−0.437453			−0.218727	+	0.975786i	$0.570190\pi$
$858$	23.0446	+	62.1186i	0.786731	+	2.12069i
$859$		−	20.9577i		−	0.715067i	−0.933900	−	0.357534i	$-0.883618\pi$
$859$		−	20.9577i		−	0.715067i	0.933900	−	0.357534i	$-0.116382\pi$
$860$	−7.90172	+	7.23665i	−0.269446	+	0.246768i
$861$		0			0
$862$	16.7539	−	38.0622i	0.570640	−	1.29640i
$863$		−	38.5219i		−	1.31130i	−0.755065	−	0.655650i	$-0.772395\pi$
$863$		−	38.5219i		−	1.31130i	0.755065	−	0.655650i	$-0.227605\pi$
$864$	−39.5086	−	21.7100i	−1.34411	−	0.738588i
$865$		−	21.4295i		−	0.728626i
$866$	−38.1940	−	16.8119i	−1.29788	−	0.571293i
$867$			48.6954i			1.65378i
$868$	13.5078	+	14.7492i	0.458485	+	0.500621i
$869$	−47.6004			−1.61473
$870$	34.8062	+	15.3207i	1.18004	+	0.519422i
$871$	−19.4031	+	18.8105i	−0.657450	+	0.637369i
$872$	6.35078	+	18.7338i	0.215065	+	0.634406i
$873$		−	74.0847i		−	2.50739i
$874$	−30.8062	−	13.5601i	−1.04204	−	0.458676i
$875$			13.8689i			0.468853i
$876$	33.6131	+	36.7023i	1.13568	+	1.24005i
$877$	56.1392			1.89569			0.947843	−	0.318737i	$-0.103259\pi$
$877$	56.1392			1.89569			0.947843	+	0.318737i	$0.103259\pi$
$878$	13.9873	+	6.15681i	0.472048	+	0.207782i
$879$		−	69.4074i		−	2.34105i
$880$	2.80625	−	31.8767i	0.0945986	−	1.07456i
$881$	29.2984			0.987089			0.493545	−	0.869720i	$-0.335701\pi$
$881$	29.2984			0.987089			0.493545	+	0.869720i	$0.335701\pi$
$882$	−42.0771	−	18.5212i	−1.41681	−	0.623640i
$883$			28.9269i			0.973467i	0.873551	+	0.486733i	$0.161812\pi$
$883$			28.9269i			0.973467i	−0.873551	+	0.486733i	$0.838188\pi$
$884$	−5.05011	−	0.300387i	−0.169854	−	0.0101031i
$885$			31.8767i			1.07152i
$886$	1.68066	−	3.81818i	0.0564628	−	0.128274i
$887$	51.2250			1.71997			0.859983	−	0.510322i	$-0.170474\pi$
$887$	51.2250			1.71997			0.859983	+	0.510322i	$0.170474\pi$
$888$	−26.5602	+	9.00393i	−0.891300	+	0.302152i
$889$		−	13.6739i		−	0.458607i
$890$	−8.72892	+	19.8307i	−0.292594	+	0.664726i
$891$	28.2051			0.944907
$892$	30.9293	−	28.3261i	1.03559	−	0.948429i
$893$		−	6.78003i		−	0.226885i
$894$	−3.50781	+	7.96918i	−0.117319	+	0.266529i
$895$			23.5892i			0.788501i
$896$	−3.05234	−	12.5253i	−0.101972	−	0.418441i
$897$	29.6125	+	30.5455i	0.988732	+	1.01988i
$898$	−22.2094	+	50.4561i	−0.741136	+	1.68374i
$899$	−44.0490			−1.46912
$900$	13.1047	+	14.3090i	0.436823	+	0.476968i
$901$			8.27799i			0.275780i
$902$		0			0
$903$		−	9.91534i		−	0.329962i
$904$	−1.27415	−	3.75854i	−0.0423776	−	0.125007i
$905$		−	12.3136i		−	0.409318i
$906$	21.7539	+	9.57546i	0.722725	+	0.318123i
$907$		−	43.1045i		−	1.43126i	−0.698478	−	0.715631i	$-0.746139\pi$
$907$		−	43.1045i		−	1.43126i	0.698478	−	0.715631i	$-0.253861\pi$
$908$	−22.0245	−	24.0486i	−0.730908	−	0.798080i
$909$		0			0
$910$	3.67029	+	9.89354i	0.121669	+	0.327968i
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$	−69.9364	−	6.15681i	−2.31582	−	0.203872i
$913$	12.5969			0.416896
$914$	−17.4031	+	39.5371i	−0.575644	+	1.30777i
$915$		0			0
$916$	25.5213	+	27.8668i	0.843248	+	0.920744i
$917$	1.35503			0.0447470
$918$	−3.18537	+	7.23665i	−0.105133	+	0.238845i
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$	−6.59688	−	19.4597i	−0.217493	−	0.641568i
$921$			25.3074i			0.833906i
$922$	−13.7539	−	6.05409i	−0.452961	−	0.199381i
$923$	29.7503	+	30.6876i	0.979242	+	1.01009i
$924$	20.0000	+	21.8380i	0.657952	+	0.718419i
$925$	5.71949			0.188056
$926$	−9.80625	+	22.2782i	−0.322253	+	0.732107i
$927$	−22.8062			−0.749055
$928$	24.8842	+	13.6739i	0.816865	+	0.448867i
$929$			38.9812i			1.27893i	0.768819	+	0.639467i	$0.220845\pi$
$929$			38.9812i			1.27893i	−0.768819	+	0.639467i	$0.779155\pi$
$930$	60.8556	+	26.7869i	1.99553	+	0.878378i
$931$	−33.9246			−1.11183
$932$	16.3508	+	17.8535i	0.535588	+	0.584809i
$933$		−	35.3981i		−	1.15888i
$934$	−7.22420	+	16.4122i	−0.236383	+	0.537024i
$935$	−5.61250			−0.183548
$936$	51.7326	+	26.5433i	1.69093	+	0.867596i
$937$	−12.8062			−0.418362			−0.209181	−	0.977877i	$-0.567080\pi$
$937$	−12.8062			−0.418362			−0.209181	+	0.977877i	$0.567080\pi$
$938$	−4.86603	+	11.0548i	−0.158882	+	0.360953i
$939$		−	22.1468i		−	0.722735i
$940$	3.05234	−	2.79544i	0.0995565	−	0.0911771i
$941$	−26.7004			−0.870408			−0.435204	−	0.900332i	$-0.643324\pi$
$941$	−26.7004			−0.870408			−0.435204	+	0.900332i	$0.643324\pi$
$942$	−64.2169	−	28.2665i	−2.09230	−	0.920972i
$943$		0			0
$944$	−2.08717	+	23.7085i	−0.0679315	+	0.771646i
$945$	16.4922			0.536491
$946$	7.40312	−	16.8187i	0.240696	−	0.546823i
$947$	7.49521			0.243562			0.121781	−	0.992557i	$-0.461140\pi$
$947$	7.49521			0.243562			0.121781	+	0.992557i	$0.461140\pi$
$948$	−47.0156	+	43.0585i	−1.52700	+	1.39847i
$949$	−21.1710	−	21.8380i	−0.687241	−	0.708893i
$950$	13.1047	+	5.76832i	0.425172	+	0.187149i
$951$			59.4921i			1.92916i
$952$	−2.14141	+	0.725940i	−0.0694034	+	0.0235279i
$953$	44.5234			1.44226			0.721128	−	0.692802i	$-0.243624\pi$
$953$	44.5234			1.44226			0.721128	+	0.692802i	$0.243624\pi$
$954$	38.3295	−	87.0784i	1.24096	−	2.81927i
$955$	−41.4198			−1.34031
$956$	−14.1228	+	12.9341i	−0.456763	+	0.418319i
$957$	−65.2200			−2.10826
$958$	1.56015	−	3.54442i	0.0504063	−	0.114515i
$959$	5.19375			0.167715
$960$	−26.0633	−	34.0236i	−0.841190	−	1.09811i
$961$	−46.0156			−1.48437
$962$	16.0693	−	5.96135i	0.518094	−	0.192202i
$963$			5.01934i			0.161746i
$964$	−25.8874	+	23.7085i	−0.833776	+	0.763600i
$965$		−	15.3207i		−	0.493192i
$966$	17.4031	+	7.66037i	0.559936	+	0.246468i
$967$			6.37758i			0.205089i	0.994728	+	0.102545i	$0.0326985\pi$
$967$			6.37758i			0.205089i	−0.994728	+	0.102545i	$0.967302\pi$
$968$	7.63071	+	22.5094i	0.245260	+	0.723479i
$969$			12.3136i			0.395570i
$970$	13.4453	−	30.5455i	0.431701	−	0.980756i
$971$			17.1275i			0.549648i	0.961495	+	0.274824i	$0.0886196\pi$
$971$			17.1275i			0.549648i	−0.961495	+	0.274824i	$0.911380\pi$
$972$	−7.40312	+	6.78003i	−0.237455	+	0.217469i
$973$	−21.5229			−0.689993
$974$	14.6125	−	33.1972i	0.468215	−	1.06371i
$975$	−12.5969	−	12.9937i	−0.403423	−	0.416133i
$976$		0			0
$977$		−	22.1097i		−	0.707351i	−0.935368	−	0.353675i	$-0.884932\pi$
$977$		−	22.1097i		−	0.707351i	0.935368	−	0.353675i	$-0.115068\pi$
$978$	4.80625	−	10.9190i	0.153687	−	0.349152i
$979$		−	37.1588i		−	1.18760i
$980$	−13.9873	−	15.2727i	−0.446807	−	0.487869i
$981$	−39.8746			−1.27310
$982$	−17.4841	+	39.7210i	−0.557940	+	1.26755i
$983$		−	56.0736i		−	1.78847i	−0.447598	−	0.894235i	$-0.647720\pi$
$983$		−	56.0736i		−	1.78847i	0.447598	−	0.894235i	$-0.352280\pi$
$984$		0			0
$985$	6.10469			0.194511
$986$	2.00629	−	4.55796i	0.0638932	−	0.145155i
$987$			3.83019i			0.121916i
$988$	42.8307	+	2.54763i	1.36263	+	0.0810508i
$989$		−	11.7994i		−	0.375198i
$990$	59.0394	+	25.9875i	1.87640	+	0.825937i
$991$	−9.61250			−0.305351			−0.152676	−	0.988276i	$-0.548789\pi$
$991$	−9.61250			−0.305351			−0.152676	+	0.988276i	$0.548789\pi$
$992$	43.5078	+	23.9075i	1.38137	+	0.759065i
$993$			69.5267i			2.20636i
$994$	17.4841	+	7.69601i	0.554562	+	0.244103i
$995$		0			0
$996$	12.4421	−	11.3949i	0.394244	−	0.361061i
$997$			3.52138i			0.111523i	0.998444	+	0.0557616i	$0.0177587\pi$
$997$			3.52138i			0.111523i	−0.998444	+	0.0557616i	$0.982241\pi$
$998$	−2.29844	−	1.01171i	−0.0727558	−	0.0320251i
$999$		−	26.7869i		−	0.847501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.e.c.77.8	yes	8
3.2	odd	2		936.2.m.f.181.1		8
4.3	odd	2		416.2.e.c.337.7		8
8.3	odd	2		416.2.e.c.337.2		8
8.5	even	2	inner	104.2.e.c.77.2	yes	8
12.11	even	2		3744.2.m.g.1585.5		8
13.12	even	2	inner	104.2.e.c.77.1	✓	8
24.5	odd	2		936.2.m.f.181.7		8
24.11	even	2		3744.2.m.g.1585.3		8
39.38	odd	2		936.2.m.f.181.8		8
52.51	odd	2		416.2.e.c.337.8		8
104.51	odd	2		416.2.e.c.337.1		8
104.77	even	2	inner	104.2.e.c.77.7	yes	8
156.155	even	2		3744.2.m.g.1585.4		8
312.77	odd	2		936.2.m.f.181.2		8
312.155	even	2		3744.2.m.g.1585.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.e.c.77.1	✓	8	13.12	even	2	inner
104.2.e.c.77.2	yes	8	8.5	even	2	inner
104.2.e.c.77.7	yes	8	104.77	even	2	inner
104.2.e.c.77.8	yes	8	1.1	even	1	trivial
416.2.e.c.337.1		8	104.51	odd	2
416.2.e.c.337.2		8	8.3	odd	2
416.2.e.c.337.7		8	4.3	odd	2
416.2.e.c.337.8		8	52.51	odd	2
936.2.m.f.181.1		8	3.2	odd	2
936.2.m.f.181.2		8	312.77	odd	2
936.2.m.f.181.7		8	24.5	odd	2
936.2.m.f.181.8		8	39.38	odd	2
3744.2.m.g.1585.3		8	24.11	even	2
3744.2.m.g.1585.4		8	156.155	even	2
3744.2.m.g.1585.5		8	12.11	even	2
3744.2.m.g.1585.6		8	312.155	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29437 + 0.569745i) q^{2} -2.94984i q^{3} +(1.35078 + 1.47492i) q^{4} -1.81616 q^{5} +(1.68066 - 3.81818i) q^{6} +1.13949i q^{7} +(0.908080 + 2.67869i) q^{8} -5.70156 q^{9} +(-2.35078 - 1.03475i) q^{10} +4.40490 q^{11} +(4.35078 - 3.98459i) q^{12} +(-2.58874 + 2.50967i) q^{13} +(-0.649219 + 1.47492i) q^{14} +5.35738i q^{15} +(-0.350781 + 3.98459i) q^{16} +0.701562 q^{17} +(-7.37992 - 3.24844i) q^{18} -5.95005 q^{19} +(-2.45323 - 2.67869i) q^{20} +3.36131 q^{21} +(5.70156 + 2.50967i) q^{22} +4.00000 q^{23} +(7.90172 - 2.67869i) q^{24} -1.70156 q^{25} +(-4.78065 + 1.77352i) q^{26} +7.96918i q^{27} +(-1.68066 + 1.53920i) q^{28} -5.01934i q^{29} +(-3.05234 + 6.93443i) q^{30} -8.77585i q^{31} +(-2.72424 + 4.95767i) q^{32} -12.9937i q^{33} +(0.908080 + 0.399712i) q^{34} -2.06950i q^{35} +(-7.70156 - 8.40935i) q^{36} -3.36131 q^{37} +(-7.70156 - 3.39001i) q^{38} +(7.40312 + 7.63636i) q^{39} +(-1.64922 - 4.86493i) q^{40} +(4.35078 + 1.91509i) q^{42} -2.94984i q^{43} +(5.95005 + 6.49687i) q^{44} +10.3550 q^{45} +(5.17748 + 2.27898i) q^{46} +1.13949i q^{47} +(11.7539 + 1.03475i) q^{48} +5.70156 q^{49} +(-2.20245 - 0.969457i) q^{50} -2.06950i q^{51} +(-7.19838 - 0.428169i) q^{52} +11.7994i q^{53} +(-4.54040 + 10.3151i) q^{54} -8.00000 q^{55} +(-3.05234 + 1.03475i) q^{56} +17.5517i q^{57} +(2.85974 - 6.49687i) q^{58} +5.95005 q^{59} +(-7.90172 + 7.23665i) q^{60} +(5.00000 - 11.3592i) q^{62} -6.49687i q^{63} +(-6.35078 + 4.86493i) q^{64} +(4.70156 - 4.55796i) q^{65} +(7.40312 - 16.8187i) q^{66} +7.49521 q^{67} +(0.947657 + 1.03475i) q^{68} -11.7994i q^{69} +(1.17909 - 2.67869i) q^{70} -11.8543i q^{71} +(-5.17748 - 15.2727i) q^{72} +8.43579i q^{73} +(-4.35078 - 1.91509i) q^{74} +5.01934i q^{75} +(-8.03722 - 8.77585i) q^{76} +5.01934i q^{77} +(5.23159 + 14.1022i) q^{78} -10.8062 q^{79} +(0.637075 - 7.23665i) q^{80} +6.40312 q^{81} +2.85974 q^{83} +(4.54040 + 4.95767i) q^{84} -1.27415 q^{85} +(1.68066 - 3.81818i) q^{86} -14.8062 q^{87} +(4.00000 + 11.7994i) q^{88} -8.43579i q^{89} +(13.4031 + 5.89968i) q^{90} +(-2.85974 - 2.94984i) q^{91} +(5.40312 + 5.89968i) q^{92} -25.8874 q^{93} +(-0.649219 + 1.47492i) q^{94} +10.8062 q^{95} +(14.6243 + 8.03608i) q^{96} +12.9937i q^{97} +(7.37992 + 3.24844i) q^{98} -25.1148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 20 q^{9} - 6 q^{10} + 22 q^{12} - 18 q^{14} + 10 q^{16} - 20 q^{17} + 20 q^{22} + 32 q^{23} + 12 q^{25} - 14 q^{26} + 14 q^{30} - 36 q^{36} - 36 q^{38} + 8 q^{39} - 26 q^{40} + 22 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 20 * q^9 - 6 * q^10 + 22 * q^12 - 18 * q^14 + 10 * q^16 - 20 * q^17 + 20 * q^22 + 32 * q^23 + 12 * q^25 - 14 * q^26 + 14 * q^30 - 36 * q^36 - 36 * q^38 + 8 * q^39 - 26 * q^40 + 22 * q^42 + 30 * q^48 + 20 * q^49 - 4 * q^52 - 64 * q^55 + 14 * q^56 + 40 * q^62 - 38 * q^64 + 12 * q^65 + 8 * q^66 + 46 * q^68 - 22 * q^74 - 22 * q^78 + 16 * q^79 - 16 * q^87 + 32 * q^88 + 56 * q^90 - 8 * q^92 - 18 * q^94 - 16 * q^95

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