LMFDB - Embedded newform 702.2.bc.a.665.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] 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("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			665.8
Character	$\chi$	$=$	702.665
Dual form			702.2.bc.a.683.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-3.32591 + 0.891175i) q^{5} +(-0.0201488 - 0.0201488i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98193 + 1.72162i) q^{10} +(1.12616 + 4.20290i) q^{11} +(1.39839 + 3.32333i) q^{13} +(-0.0246771 - 0.0142473i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.35521 + 5.81139i) q^{17} +(-0.521462 - 1.94612i) q^{19} +(-2.43473 + 2.43473i) q^{20} +(2.17558 + 3.76822i) q^{22} -0.528142 q^{23} +(5.93735 - 3.42793i) q^{25} +(2.21088 + 2.84816i) q^{26} +(-0.0275237 - 0.00737496i) q^{28} +(7.19404 + 4.15348i) q^{29} +(-0.373424 - 1.39364i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.73678 + 6.48176i) q^{34} +(0.0849690 + 0.0490569i) q^{35} +(-2.09857 + 7.83198i) q^{37} +(-1.00739 - 1.74484i) q^{38} +(-1.72162 + 2.98193i) q^{40} +(-3.55302 - 3.55302i) q^{41} +8.76179i q^{43} +(3.07674 + 3.07674i) q^{44} +(-0.510146 + 0.136693i) q^{46} +(0.775777 + 0.207869i) q^{47} -6.99919i q^{49} +(4.84783 - 4.84783i) q^{50} +(2.87270 + 2.17889i) q^{52} -5.06566i q^{53} +(-7.49104 - 12.9749i) q^{55} -0.0284946 q^{56} +(8.02391 + 2.15000i) q^{58} +(-13.8214 - 3.70343i) q^{59} -0.0214935 q^{61} +(-0.721399 - 1.24950i) q^{62} -1.00000i q^{64} +(-7.61257 - 9.80688i) q^{65} +(-0.668189 + 0.668189i) q^{67} +6.71041i q^{68} +(0.0947706 + 0.0253937i) q^{70} +(9.32969 - 2.49988i) q^{71} +(6.53713 + 6.53713i) q^{73} +8.10826i q^{74} +(-1.42466 - 1.42466i) q^{76} +(0.0619924 - 0.107374i) q^{77} +(1.40950 + 2.44132i) q^{79} +(-0.891175 + 3.32591i) q^{80} +(-4.35155 - 2.51237i) q^{82} +(3.80210 - 14.1896i) q^{83} +(5.98015 - 22.3182i) q^{85} +(2.26772 + 8.46324i) q^{86} +(3.76822 + 2.17558i) q^{88} +(-10.8696 - 2.91249i) q^{89} +(0.0387852 - 0.0951367i) q^{91} +(-0.457384 + 0.264071i) q^{92} +0.803143 q^{94} +(3.46867 + 6.00791i) q^{95} +(0.333814 - 0.333814i) q^{97} +(-1.81152 - 6.76070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−3.32591	+	0.891175i	−1.48739	+	0.398545i	−0.908855	−	0.417111i	$-0.863043\pi$
$5$	−3.32591	+	0.891175i	−1.48739	+	0.398545i	−0.578536	+	0.815657i	$0.696376\pi$
$6$		0			0
$7$	−0.0201488	−	0.0201488i	−0.00761551	−	0.00761551i	0.703289	−	0.710904i	$-0.251714\pi$
$7$	−0.0201488	−	0.0201488i	−0.00761551	−	0.00761551i	−0.710904	+	0.703289i	$0.751714\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.98193	+	1.72162i	−0.942969	+	0.544423i
$11$	1.12616	+	4.20290i	0.339551	+	1.26722i	0.898850	+	0.438256i	$0.144404\pi$
$11$	1.12616	+	4.20290i	0.339551	+	1.26722i	−0.559299	+	0.828966i	$0.688930\pi$
$12$		0			0
$13$	1.39839	+	3.32333i	0.387843	+	0.921726i
$13$	1.39839	+	3.32333i	0.387843	+	0.921726i
$14$	−0.0246771	−	0.0142473i	−0.00659523	−	0.00380776i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.35521	+	5.81139i	−0.813757	+	1.40947i	0.0964602	+	0.995337i	$0.469248\pi$
$17$	−3.35521	+	5.81139i	−0.813757	+	1.40947i	−0.910217	+	0.414131i	$0.864085\pi$
$18$		0			0
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	0.879960	−	0.475048i	$-0.157569\pi$
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	−0.999592	+	0.0285767i	$0.990903\pi$
$20$	−2.43473	+	2.43473i	−0.544423	+	0.544423i
$21$		0			0
$22$	2.17558	+	3.76822i	0.463835	+	0.803387i
$23$	−0.528142			−0.110125			−0.0550626	−	0.998483i	$-0.517536\pi$
$23$	−0.528142			−0.110125			−0.0550626	+	0.998483i	$0.517536\pi$
$24$		0			0
$25$	5.93735	−	3.42793i	1.18747	−	0.685587i
$26$	2.21088	+	2.84816i	0.433589	+	0.558570i
$27$		0			0
$28$	−0.0275237	−	0.00737496i	−0.00520149	−	0.00139374i
$29$	7.19404	+	4.15348i	1.33590	+	0.771282i	0.986197	−	0.165578i	$-0.0529491\pi$
$29$	7.19404	+	4.15348i	1.33590	+	0.771282i	0.349703	+	0.936861i	$0.386282\pi$
$30$		0			0
$31$	−0.373424	−	1.39364i	−0.0670689	−	0.250305i	0.924249	−	0.381790i	$-0.124692\pi$
$31$	−0.373424	−	1.39364i	−0.0670689	−	0.250305i	−0.991318	+	0.131485i	$0.958025\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$	−1.73678	+	6.48176i	−0.297856	+	1.11161i
$35$	0.0849690	+	0.0490569i	0.0143624	+	0.00829212i
$36$		0			0
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	0.547605	+	0.836737i	$0.315540\pi$
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	−0.892608	+	0.450833i	$0.851127\pi$
$38$	−1.00739	−	1.74484i	−0.163420	−	0.283051i
$39$		0			0
$40$	−1.72162	+	2.98193i	−0.272212	+	0.471484i
$41$	−3.55302	−	3.55302i	−0.554889	−	0.554889i	0.372959	−	0.927848i	$-0.378343\pi$
$41$	−3.55302	−	3.55302i	−0.554889	−	0.554889i	−0.927848	+	0.372959i	$0.878343\pi$
$42$		0			0
$43$			8.76179i			1.33616i	0.744089	+	0.668080i	$0.232884\pi$
$43$			8.76179i			1.33616i	−0.744089	+	0.668080i	$0.767116\pi$
$44$	3.07674	+	3.07674i	0.463835	+	0.463835i
$45$		0			0
$46$	−0.510146	+	0.136693i	−0.0752169	+	0.0201543i
$47$	0.775777	+	0.207869i	0.113159	+	0.0303208i	0.314954	−	0.949107i	$-0.398011\pi$
$47$	0.775777	+	0.207869i	0.113159	+	0.0303208i	−0.201795	+	0.979428i	$0.564678\pi$
$48$		0			0
$49$		−	6.99919i		−	0.999884i
$50$	4.84783	−	4.84783i	0.685587	−	0.685587i
$51$		0			0
$52$	2.87270	+	2.17889i	0.398372	+	0.302158i
$53$		−	5.06566i		−	0.695822i	−0.937527	−	0.347911i	$-0.886891\pi$
$53$		−	5.06566i		−	0.695822i	0.937527	−	0.347911i	$-0.113109\pi$
$54$		0			0
$55$	−7.49104	−	12.9749i	−1.01009	−	1.74953i
$56$	−0.0284946			−0.00380776
$57$		0			0
$58$	8.02391	+	2.15000i	1.05359	+	0.282309i
$59$	−13.8214	−	3.70343i	−1.79939	−	0.482145i	−0.805508	−	0.592585i	$-0.798107\pi$
$59$	−13.8214	−	3.70343i	−1.79939	−	0.482145i	−0.993883	+	0.110440i	$0.964774\pi$
$60$		0			0
$61$	−0.0214935			−0.00275196			−0.00137598	−	0.999999i	$-0.500438\pi$
$61$	−0.0214935			−0.00275196			−0.00137598	+	0.999999i	$0.500438\pi$
$62$	−0.721399	−	1.24950i	−0.0916178	−	0.158687i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−7.61257	−	9.80688i	−0.944223	−	1.21639i
$66$		0			0
$67$	−0.668189	+	0.668189i	−0.0816322	+	0.0816322i	−0.746744	−	0.665112i	$-0.768384\pi$
$67$	−0.668189	+	0.668189i	−0.0816322	+	0.0816322i	0.665112	+	0.746744i	$0.268384\pi$
$68$			6.71041i			0.813757i
$69$		0			0
$70$	0.0947706	+	0.0253937i	0.0113273	+	0.00303513i
$71$	9.32969	−	2.49988i	1.10723	−	0.296682i	0.341525	−	0.939873i	$-0.389057\pi$
$71$	9.32969	−	2.49988i	1.10723	−	0.296682i	0.765706	+	0.643191i	$0.222390\pi$
$72$		0			0
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	0.977242	−	0.212129i	$-0.0680396\pi$
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	−0.212129	+	0.977242i	$0.568040\pi$
$74$			8.10826i			0.942566i
$75$		0			0
$76$	−1.42466	−	1.42466i	−0.163420	−	0.163420i
$77$	0.0619924	−	0.107374i	0.00706469	−	0.0122364i
$78$		0			0
$79$	1.40950	+	2.44132i	0.158581	+	0.274670i	0.934357	−	0.356338i	$-0.115975\pi$
$79$	1.40950	+	2.44132i	0.158581	+	0.274670i	−0.775776	+	0.631008i	$0.782641\pi$
$80$	−0.891175	+	3.32591i	−0.0996364	+	0.371848i
$81$		0			0
$82$	−4.35155	−	2.51237i	−0.480548	−	0.277444i
$83$	3.80210	−	14.1896i	0.417335	−	1.55752i	−0.362777	−	0.931876i	$-0.618171\pi$
$83$	3.80210	−	14.1896i	0.417335	−	1.55752i	0.780112	−	0.625640i	$-0.215162\pi$
$84$		0			0
$85$	5.98015	−	22.3182i	0.648638	−	2.42075i
$86$	2.26772	+	8.46324i	0.244534	+	0.912615i
$87$		0			0
$88$	3.76822	+	2.17558i	0.401693	+	0.231918i
$89$	−10.8696	−	2.91249i	−1.15217	−	0.308724i	−0.368337	−	0.929692i	$-0.620073\pi$
$89$	−10.8696	−	2.91249i	−1.15217	−	0.308724i	−0.783835	+	0.620969i	$0.786739\pi$
$90$		0			0
$91$	0.0387852	−	0.0951367i	0.00406579	−	0.00997303i
$92$	−0.457384	+	0.264071i	−0.0476856	+	0.0275313i
$93$		0			0
$94$	0.803143			0.0828379
$95$	3.46867	+	6.00791i	0.355878	+	0.616399i
$96$		0			0
$97$	0.333814	−	0.333814i	0.0338937	−	0.0338937i	−0.689957	−	0.723851i	$-0.742371\pi$
$97$	0.333814	−	0.333814i	0.0338937	−	0.0338937i	0.723851	+	0.689957i	$0.242371\pi$
$98$	−1.81152	−	6.76070i	−0.182991	−	0.682933i
$99$		0			0
$100$	3.42793	−	5.93735i	0.342793	−	0.593735i
$101$	2.74544	−	4.75523i	0.273181	−	0.473163i	−0.696494	−	0.717563i	$-0.745258\pi$
$101$	2.74544	−	4.75523i	0.273181	−	0.473163i	0.969675	+	0.244400i	$0.0785909\pi$
$102$		0			0
$103$	3.62390	+	2.09226i	0.357073	+	0.206156i	0.667796	−	0.744344i	$-0.267238\pi$
$103$	3.62390	+	2.09226i	0.357073	+	0.206156i	−0.310723	+	0.950501i	$0.600571\pi$
$104$	3.33876	+	1.36114i	0.327392	+	0.133471i
$105$		0			0
$106$	−1.31109	−	4.89306i	−0.127344	−	0.475256i
$107$	2.85234	−	1.64680i	0.275746	−	0.159202i	−0.355750	−	0.934581i	$-0.615774\pi$
$107$	2.85234	−	1.64680i	0.275746	−	0.159202i	0.631496	+	0.775379i	$0.282441\pi$
$108$		0			0
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	−0.916823	−	0.399294i	$-0.869255\pi$
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	0.399294	+	0.916823i	$0.369255\pi$
$110$	−10.5939	−	10.5939i	−1.01009	−	1.01009i
$111$		0			0
$112$	−0.0275237	+	0.00737496i	−0.00260075	+	0.000696868i
$113$	−0.503942	+	0.290951i	−0.0474068	+	0.0273704i	−0.523516	−	0.852016i	$-0.675380\pi$
$113$	−0.503942	+	0.290951i	−0.0474068	+	0.0273704i	0.476109	+	0.879386i	$0.342047\pi$
$114$		0			0
$115$	1.75655	−	0.470666i	0.163799	−	0.0438899i
$116$	8.30696			0.771282
$117$		0			0
$118$	−14.3089			−1.31725
$119$	0.184695	−	0.0494890i	0.0169310	−	0.00453665i
$120$		0			0
$121$	−6.86984	+	3.96631i	−0.624531	+	0.360573i
$122$	−0.0207611	+	0.00556292i	−0.00187962	+	0.000503644i
$123$		0			0
$124$	−1.02021	−	1.02021i	−0.0916178	−	0.0916178i
$125$	−4.51854	+	4.51854i	−0.404150	+	0.404150i
$126$		0			0
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	−0.0694101	−	0.997588i	$-0.522112\pi$
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	0.829232	+	0.558905i	$0.188778\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	−9.89139	−	7.50244i	−0.867532	−	0.658008i
$131$	15.6965	+	9.06236i	1.37141	+	0.791782i	0.991105	−	0.133081i	$-0.0424871\pi$
$131$	15.6965	+	9.06236i	1.37141	+	0.791782i	0.380301	+	0.924863i	$0.375820\pi$
$132$		0			0
$133$	−0.0287051	+	0.0497187i	−0.00248905	+	0.00431116i
$134$	−0.472481	+	0.818361i	−0.0408161	+	0.0706956i
$135$		0			0
$136$	1.73678	+	6.48176i	0.148928	+	0.555806i
$137$	−11.8200	+	11.8200i	−1.00985	+	1.00985i	−0.00990200	+	0.999951i	$0.503152\pi$
$137$	−11.8200	+	11.8200i	−1.00985	+	1.00985i	−0.999951	+	0.00990200i	$0.996848\pi$
$138$		0			0
$139$	−2.54241	−	4.40359i	−0.215645	−	0.373508i	0.737827	−	0.674990i	$-0.235852\pi$
$139$	−2.54241	−	4.40359i	−0.215645	−	0.373508i	−0.953472	+	0.301482i	$0.902519\pi$
$140$	0.0981137			0.00829212
$141$		0			0
$142$	8.36477	−	4.82940i	0.701956	−	0.405275i
$143$	−12.3928	+	9.61989i	−1.03634	+	0.804456i
$144$		0			0
$145$	−27.6282	−	7.40295i	−2.29440	−	0.614782i
$146$	8.00631	+	4.62245i	0.662607	+	0.382557i
$147$		0			0
$148$	2.09857	+	7.83198i	0.172502	+	0.643785i
$149$	1.36845	−	5.10712i	0.112108	−	0.418392i	−0.886947	−	0.461872i	$-0.847178\pi$
$149$	1.36845	−	5.10712i	0.112108	−	0.418392i	0.999054	+	0.0434804i	$0.0138446\pi$
$150$		0			0
$151$	−2.52008	+	9.40508i	−0.205082	+	0.765375i	0.784343	+	0.620327i	$0.213000\pi$
$151$	−2.52008	+	9.40508i	−0.205082	+	0.765375i	−0.989425	+	0.145047i	$0.953667\pi$
$152$	−1.74484	−	1.00739i	−0.141526	−	0.0817098i
$153$		0			0
$154$	0.0320896	−	0.119760i	0.00258586	−	0.00965055i
$155$	2.48395	+	4.30232i	0.199515	+	0.345571i
$156$		0			0
$157$	4.81339	−	8.33703i	0.384150	−	0.665368i	−0.607501	−	0.794319i	$-0.707828\pi$
$157$	4.81339	−	8.33703i	0.384150	−	0.665368i	0.991651	+	0.128952i	$0.0411612\pi$
$158$	1.99333	+	1.99333i	0.158581	+	0.158581i
$159$		0			0
$160$			3.44323i			0.272212i
$161$	0.0106414	+	0.0106414i	0.000838659	+	0.000838659i
$162$		0			0
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.186142	−	0.982523i	$-0.440402\pi$
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.652465	+	0.757819i	$0.273735\pi$
$164$	−4.85352	−	1.30050i	−0.378996	−	0.101552i
$165$		0			0
$166$		−	14.6902i		−	1.14018i
$167$	10.5531	−	10.5531i	0.816620	−	0.816620i	−0.168997	−	0.985617i	$-0.554053\pi$
$167$	10.5531	−	10.5531i	0.816620	−	0.816620i	0.985617	+	0.168997i	$0.0540528\pi$
$168$		0			0
$169$	−9.08903	+	9.29459i	−0.699156	+	0.714969i
$170$		−	23.1055i		−	1.77211i
$171$		0			0
$172$	4.38090	+	7.58793i	0.334040	+	0.578574i
$173$	19.0603			1.44912			0.724562	−	0.689210i	$-0.242042\pi$
$173$	19.0603			1.44912			0.724562	+	0.689210i	$0.242042\pi$
$174$		0			0
$175$	−0.188699	−	0.0505617i	−0.0142643	−	0.00382211i
$176$	4.20290	+	1.12616i	0.316805	+	0.0848878i
$177$		0			0
$178$	−11.2530			−0.843449
$179$	12.0533	+	20.8769i	0.900906	+	1.56041i	0.826320	+	0.563200i	$0.190430\pi$
$179$	12.0533	+	20.8769i	0.900906	+	1.56041i	0.0745856	+	0.997215i	$0.476237\pi$
$180$		0			0
$181$		−	1.16505i		−	0.0865977i	−0.999062	−	0.0432988i	$-0.986213\pi$
$181$		−	1.16505i		−	0.0865977i	0.999062	−	0.0432988i	$-0.0137868\pi$
$182$	0.0128404	−	0.101933i	0.000951797	−	0.00755580i
$183$		0			0
$184$	−0.373453	+	0.373453i	−0.0275313	+	0.0275313i
$185$		−	27.9187i		−	2.05262i
$186$		0			0
$187$	−28.2032	−	7.55702i	−2.06242	−	0.552624i
$188$	0.775777	−	0.207869i	0.0565793	−	0.0151604i
$189$		0			0
$190$	4.90544	+	4.90544i	0.355878	+	0.355878i
$191$		−	11.5646i		−	0.836783i	−0.908267	−	0.418392i	$-0.862594\pi$
$191$		−	11.5646i		−	0.836783i	0.908267	−	0.418392i	$-0.137406\pi$
$192$		0			0
$193$	−1.01826	−	1.01826i	−0.0732962	−	0.0732962i	0.669508	−	0.742805i	$-0.266505\pi$
$193$	−1.01826	−	1.01826i	−0.0732962	−	0.0732962i	−0.742805	+	0.669508i	$0.766505\pi$
$194$	0.236042	−	0.408837i	0.0169468	−	0.0293528i
$195$		0			0
$196$	−3.49959	−	6.06147i	−0.249971	−	0.432962i
$197$	1.07594	−	4.01546i	0.0766575	−	0.286090i	−0.916947	−	0.399010i	$-0.869354\pi$
$197$	1.07594	−	4.01546i	0.0766575	−	0.286090i	0.993604	+	0.112920i	$0.0360205\pi$
$198$		0			0
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	0.561910	−	0.827198i	$-0.310067\pi$
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	−0.435419	+	0.900228i	$0.643400\pi$
$200$	1.77443	−	6.62226i	0.125471	−	0.468264i
$201$		0			0
$202$	1.42114	−	5.30377i	0.0999912	−	0.373172i
$203$	−0.0612635	−	0.228638i	−0.00429985	−	0.0160473i
$204$		0			0
$205$	14.9834	+	8.65067i	1.04649	+	0.604189i
$206$	4.04193	+	1.08303i	0.281615	+	0.0754585i
$207$		0			0
$208$	3.57728	+	0.450627i	0.248040	+	0.0312453i
$209$	7.59210	−	4.38330i	0.525157	−	0.303199i
$210$		0			0
$211$	19.1496			1.31831			0.659157	−	0.752005i	$-0.270913\pi$
$211$	19.1496			1.31831			0.659157	+	0.752005i	$0.270913\pi$
$212$	−2.53283	−	4.38699i	−0.173956	−	0.301300i
$213$		0			0
$214$	2.32893	−	2.32893i	0.159202	−	0.159202i
$215$	−7.80829	−	29.1409i	−0.532521	−	1.98739i
$216$		0			0
$217$	−0.0205560	+	0.0356041i	−0.00139543	+	0.00241696i
$218$	−3.82061	+	6.61749i	−0.258764	+	0.448193i
$219$		0			0
$220$	−12.9749	−	7.49104i	−0.874765	−	0.505046i
$221$	−24.0050	−	3.02389i	−1.61475	−	0.203409i
$222$		0			0
$223$	6.83797	+	25.5197i	0.457905	+	1.70892i	0.679406	+	0.733763i	$0.262238\pi$
$223$	6.83797	+	25.5197i	0.457905	+	1.70892i	−0.221501	+	0.975160i	$0.571096\pi$
$224$	−0.0246771	+	0.0142473i	−0.00164881	+	0.000951939i
$225$		0			0
$226$	−0.411467	+	0.411467i	−0.0273704	+	0.0273704i
$227$	3.63037	+	3.63037i	0.240956	+	0.240956i	0.817246	−	0.576289i	$-0.195500\pi$
$227$	3.63037	+	3.63037i	0.240956	+	0.240956i	−0.576289	+	0.817246i	$0.695500\pi$
$228$		0			0
$229$	−7.67020	+	2.05522i	−0.506861	+	0.135813i	−0.503182	−	0.864180i	$-0.667838\pi$
$229$	−7.67020	+	2.05522i	−0.506861	+	0.135813i	−0.00367870	+	0.999993i	$0.501171\pi$
$230$	1.57488	−	0.909258i	0.103845	−	0.0599547i
$231$		0			0
$232$	8.02391	−	2.15000i	0.526795	−	0.141154i
$233$	0.240333			0.0157448			0.00787238	−	0.999969i	$-0.497494\pi$
$233$	0.240333			0.0157448			0.00787238	+	0.999969i	$0.497494\pi$
$234$		0			0
$235$	−2.76541			−0.180395
$236$	−13.8214	+	3.70343i	−0.899695	+	0.241073i
$237$		0			0
$238$	0.165593	−	0.0956054i	0.0107338	−	0.00619718i
$239$	6.49603	−	1.74060i	0.420193	−	0.112590i	−0.0425261	−	0.999095i	$-0.513541\pi$
$239$	6.49603	−	1.74060i	0.420193	−	0.112590i	0.462719	+	0.886505i	$0.346874\pi$
$240$		0			0
$241$	−18.3499	−	18.3499i	−1.18202	−	1.18202i	−0.979220	−	0.202800i	$-0.934996\pi$
$241$	−18.3499	−	18.3499i	−1.18202	−	1.18202i	−0.202800	−	0.979220i	$-0.565004\pi$
$242$	−5.60920	+	5.60920i	−0.360573	+	0.360573i
$243$		0			0
$244$	−0.0186139	+	0.0107467i	−0.00119163	+	0.000687990i
$245$	6.23750	+	23.2787i	0.398499	+	1.48722i
$246$		0			0
$247$	5.73840	−	4.45442i	0.365125	−	0.283428i
$248$	−1.24950	−	0.721399i	−0.0793434	−	0.0458089i
$249$		0			0
$250$	−3.19509	+	5.53406i	−0.202075	+	0.350005i
$251$	−10.2804	+	17.8061i	−0.648892	+	1.12391i	0.334496	+	0.942397i	$0.391434\pi$
$251$	−10.2804	+	17.8061i	−0.648892	+	1.12391i	−0.983388	+	0.181517i	$0.941899\pi$
$252$		0			0
$253$	−0.594774	−	2.21973i	−0.0373931	−	0.139553i
$254$	6.99146	−	6.99146i	0.438683	−	0.438683i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.4381			−0.963002			−0.481501	−	0.876446i	$-0.659908\pi$
$257$	−15.4381			−0.963002			−0.481501	+	0.876446i	$0.659908\pi$
$258$		0			0
$259$	0.200088	−	0.115521i	0.0124329	−	0.00717813i
$260$	−11.4961	−	4.68673i	−0.712959	−	0.290658i
$261$		0			0
$262$	17.5071	+	4.69102i	1.08159	+	0.289812i
$263$	10.9321	+	6.31167i	0.674104	+	0.389194i	0.797630	−	0.603147i	$-0.206087\pi$
$263$	10.9321	+	6.31167i	0.674104	+	0.389194i	−0.123526	+	0.992341i	$0.539420\pi$
$264$		0			0
$265$	4.51439	+	16.8479i	0.277317	+	1.03496i
$266$	−0.0148589	+	0.0554540i	−0.000911055	+	0.00340010i
$267$		0			0
$268$	−0.244574	+	0.912763i	−0.0149397	+	0.0557559i
$269$	13.5676	+	7.83325i	0.827230	+	0.477602i	0.852903	−	0.522069i	$-0.174840\pi$
$269$	13.5676	+	7.83325i	0.827230	+	0.477602i	−0.0256732	+	0.999670i	$0.508173\pi$
$270$		0			0
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	0.690537	+	0.723297i	$0.257374\pi$
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	−0.959671	+	0.281126i	$0.909292\pi$
$272$	3.35521	+	5.81139i	0.203439	+	0.352367i
$273$		0			0
$274$	−8.35802	+	14.4765i	−0.504926	+	0.874558i
$275$	21.0937	+	21.0937i	1.27200	+	1.27200i
$276$		0			0
$277$		−	19.5532i		−	1.17484i	−0.809284	−	0.587418i	$-0.800144\pi$
$277$		−	19.5532i		−	1.17484i	0.809284	−	0.587418i	$-0.199856\pi$
$278$	−3.59552	−	3.59552i	−0.215645	−	0.215645i
$279$		0			0
$280$	0.0947706	−	0.0253937i	0.00566363	−	0.00151756i
$281$	−29.5609	−	7.92083i	−1.76346	−	0.472517i	−0.776044	−	0.630679i	$-0.782777\pi$
$281$	−29.5609	−	7.92083i	−1.76346	−	0.472517i	−0.987413	+	0.158162i	$0.949443\pi$
$282$		0			0
$283$			23.6188i			1.40399i	0.712182	+	0.701995i	$0.247707\pi$
$283$			23.6188i			1.40399i	−0.712182	+	0.701995i	$0.752293\pi$
$284$	6.82981	−	6.82981i	0.405275	−	0.405275i
$285$		0			0
$286$	−9.48072	+	12.4996i	−0.560607	+	0.739116i
$287$			0.143178i			0.00845153i
$288$		0			0
$289$	−14.0148	−	24.2744i	−0.824401	−	1.42790i
$290$	−28.6028			−1.67962
$291$		0			0
$292$	8.92988	+	2.39276i	0.522582	+	0.140025i
$293$	21.3337	+	5.71634i	1.24633	+	0.333952i	0.820917	−	0.571048i	$-0.193463\pi$
$293$	21.3337	+	5.71634i	1.24633	+	0.333952i	0.425411	+	0.905000i	$0.360130\pi$
$294$		0			0
$295$	49.2691			2.86856
$296$	4.05413	+	7.02196i	0.235642	+	0.408143i
$297$		0			0
$298$		−	5.28728i		−	0.306284i
$299$	−0.738546	−	1.75519i	−0.0427112	−	0.101505i
$300$		0			0
$301$	0.176539	−	0.176539i	0.0101755	−	0.0101755i
$302$			9.73686i			0.560293i
$303$		0			0
$304$	−1.94612	−	0.521462i	−0.111618	−	0.0299079i
$305$	0.0714854	−	0.0191545i	0.00409324	−	0.00109678i
$306$		0			0
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	0.787461	−	0.616364i	$-0.211395\pi$
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	−0.616364	+	0.787461i	$0.711395\pi$
$308$		−	0.123985i		−	0.00706469i
$309$		0			0
$310$	3.51283	+	3.51283i	0.199515	+	0.199515i
$311$	−15.1300	+	26.2059i	−0.857943	+	1.48600i	0.0159450	+	0.999873i	$0.494924\pi$
$311$	−15.1300	+	26.2059i	−0.857943	+	1.48600i	−0.873888	+	0.486128i	$0.838409\pi$
$312$		0			0
$313$	−16.7332	−	28.9828i	−0.945817	−	1.63820i	−0.754107	−	0.656751i	$-0.771930\pi$
$313$	−16.7332	−	28.9828i	−0.945817	−	1.63820i	−0.191710	−	0.981452i	$-0.561403\pi$
$314$	2.49159	−	9.29875i	0.140609	−	0.524759i
$315$		0			0
$316$	2.44132	+	1.40950i	0.137335	+	0.0792905i
$317$	−2.88814	+	10.7787i	−0.162214	+	0.605392i	0.836165	+	0.548478i	$0.184793\pi$
$317$	−2.88814	+	10.7787i	−0.162214	+	0.605392i	−0.998379	+	0.0569135i	$0.981874\pi$
$318$		0			0
$319$	−9.35500	+	34.9133i	−0.523779	+	1.95477i
$320$	0.891175	+	3.32591i	0.0498182	+	0.185924i
$321$		0			0
$322$	0.0130330	+	0.00752460i	0.000726300	+	0.000419330i
$323$	13.0593	+	3.49922i	0.726638	+	0.194702i
$324$		0			0
$325$	19.6949	+	14.9382i	1.09247	+	0.828623i
$326$	9.59929	−	5.54215i	0.531655	−	0.306951i
$327$		0			0
$328$	−5.02473			−0.277444
$329$	−0.0114426	−	0.0198192i	−0.000630853	−	0.00109267i
$330$		0			0
$331$	2.92713	−	2.92713i	0.160890	−	0.160890i	−0.622071	−	0.782961i	$-0.713709\pi$
$331$	2.92713	−	2.92713i	0.160890	−	0.160890i	0.782961	+	0.622071i	$0.213709\pi$
$332$	−3.80210	−	14.1896i	−0.208668	−	0.778758i
$333$		0			0
$334$	7.46214	−	12.9248i	0.408310	−	0.707213i
$335$	1.62686	−	2.81781i	0.0888850	−	0.153953i
$336$		0			0
$337$	−14.3966	−	8.31187i	−0.784232	−	0.452777i	0.0536959	−	0.998557i	$-0.482900\pi$
$337$	−14.3966	−	8.31187i	−0.784232	−	0.452777i	−0.837928	+	0.545781i	$0.816233\pi$
$338$	−6.37371	+	11.3303i	−0.346684	+	0.616287i
$339$		0			0
$340$	−5.98015	−	22.3182i	−0.324319	−	1.21038i
$341$	5.43678	−	3.13893i	0.294418	−	0.169982i
$342$		0			0
$343$	−0.282066	+	0.282066i	−0.0152301	+	0.0152301i
$344$	6.19552	+	6.19552i	0.334040	+	0.334040i
$345$		0			0
$346$	18.4108	−	4.93316i	0.989770	−	0.265208i
$347$	17.6269	−	10.1769i	0.946261	−	0.546324i	0.0543438	−	0.998522i	$-0.482693\pi$
$347$	17.6269	−	10.1769i	0.946261	−	0.546324i	0.891918	+	0.452198i	$0.149360\pi$
$348$		0			0
$349$	18.8920	−	5.06210i	1.01127	−	0.270968i	0.285108	−	0.958495i	$-0.407971\pi$
$349$	18.8920	−	5.06210i	1.01127	−	0.270968i	0.726158	+	0.687527i	$0.241304\pi$
$350$	−0.195355			−0.0104422
$351$		0			0
$352$	4.35116			0.231918
$353$	9.77585	−	2.61943i	0.520316	−	0.139418i	0.0109033	−	0.999941i	$-0.496529\pi$
$353$	9.77585	−	2.61943i	0.520316	−	0.139418i	0.509413	+	0.860522i	$0.329863\pi$
$354$		0			0
$355$	−28.8019	+	16.6288i	−1.52864	+	0.882564i
$356$	−10.8696	+	2.91249i	−0.576086	+	0.154362i
$357$		0			0
$358$	17.0459	+	17.0459i	0.900906	+	0.900906i
$359$	1.10596	−	1.10596i	0.0583705	−	0.0583705i	−0.677319	−	0.735689i	$-0.736858\pi$
$359$	1.10596	−	1.10596i	0.0583705	−	0.0583705i	0.735689	+	0.677319i	$0.236858\pi$
$360$		0			0
$361$	12.9390	−	7.47034i	0.681001	−	0.393176i
$362$	−0.301538	−	1.12535i	−0.0158485	−	0.0591473i
$363$		0			0
$364$	−0.0139794	−	0.101783i	−0.000732718	−	0.00533490i
$365$	−27.5676	−	15.9162i	−1.44296	−	0.833091i
$366$		0			0
$367$	3.11681	−	5.39847i	0.162696	−	0.281798i	−0.773139	−	0.634237i	$-0.781314\pi$
$367$	3.11681	−	5.39847i	0.162696	−	0.281798i	0.935835	+	0.352439i	$0.114648\pi$
$368$	−0.264071	+	0.457384i	−0.0137656	+	0.0238428i
$369$		0			0
$370$	−7.22588	−	26.9673i	−0.375656	−	1.40197i
$371$	−0.102067	+	0.102067i	−0.00529904	+	0.00529904i
$372$		0			0
$373$	10.5545	+	18.2810i	0.546493	+	0.946554i	0.998511	+	0.0545455i	$0.0173710\pi$
$373$	10.5545	+	18.2810i	0.546493	+	0.946554i	−0.452018	+	0.892009i	$0.649296\pi$
$374$	−29.1981			−1.50980
$375$		0			0
$376$	0.695542	−	0.401572i	0.0358699	−	0.0207095i
$377$	−3.74334	+	29.7163i	−0.192792	+	1.53047i
$378$		0			0
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	0.291769	−	0.956489i	$-0.405756\pi$
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	−0.225565	+	0.974228i	$0.572423\pi$
$380$	6.00791	+	3.46867i	0.308199	+	0.177939i
$381$		0			0
$382$	−2.99313	−	11.1705i	−0.153142	−	0.571534i
$383$	−6.69236	+	24.9762i	−0.341963	+	1.27622i	0.554156	+	0.832413i	$0.313041\pi$
$383$	−6.69236	+	24.9762i	−0.341963	+	1.27622i	−0.896120	+	0.443812i	$0.853626\pi$
$384$		0			0
$385$	−0.110492	+	0.412362i	−0.00563120	+	0.0210159i
$386$	−1.24711	−	0.720021i	−0.0634764	−	0.0366481i
$387$		0			0
$388$	0.122184	−	0.455998i	0.00620297	−	0.0231498i
$389$	−7.30331	−	12.6497i	−0.370292	−	0.641365i	0.619318	−	0.785140i	$-0.287409\pi$
$389$	−7.30331	−	12.6497i	−0.370292	−	0.641365i	−0.989610	+	0.143775i	$0.954076\pi$
$390$		0			0
$391$	1.77202	−	3.06924i	0.0896151	−	0.155218i
$392$	−4.94917	−	4.94917i	−0.249971	−	0.249971i
$393$		0			0
$394$		−	4.15711i		−	0.209432i
$395$	−6.86351	−	6.86351i	−0.345341	−	0.345341i
$396$		0			0
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	−0.185772	−	0.982593i	$-0.559479\pi$
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	0.330413	+	0.943837i	$0.392812\pi$
$398$	1.99021	+	0.533275i	0.0997601	+	0.0267307i
$399$		0			0
$400$		−	6.85587i		−	0.342793i
$401$	7.83107	−	7.83107i	0.391065	−	0.391065i	−0.484002	−	0.875067i	$-0.660817\pi$
$401$	7.83107	−	7.83107i	0.391065	−	0.391065i	0.875067	+	0.484002i	$0.160817\pi$
$402$		0			0
$403$	4.10932	−	3.18985i	0.204700	−	0.158898i
$404$		−	5.49087i		−	0.273181i
$405$		0			0
$406$	−0.118352	−	0.204992i	−0.00587371	−	0.0101736i
$407$	−35.2804			−1.74878
$408$		0			0
$409$	−14.1786	−	3.79916i	−0.701089	−	0.187856i	−0.109371	−	0.994001i	$-0.534884\pi$
$409$	−14.1786	−	3.79916i	−0.701089	−	0.187856i	−0.591718	+	0.806145i	$0.701550\pi$
$410$	16.7118	+	4.47792i	0.825337	+	0.221148i
$411$		0			0
$412$	4.18452			0.206156
$413$	0.203864	+	0.353103i	0.0100315	+	0.0173751i
$414$		0			0
$415$			50.5818i			2.48296i
$416$	3.57202	−	0.490596i	0.175133	−	0.0240535i
$417$		0			0
$418$	6.19893	−	6.19893i	0.303199	−	0.303199i
$419$		−	28.1641i		−	1.37591i	−0.725755	−	0.687953i	$-0.758509\pi$
$419$		−	28.1641i		−	1.37591i	0.725755	−	0.687953i	$-0.241491\pi$
$420$		0			0
$421$	7.03106	+	1.88397i	0.342673	+	0.0918189i	0.426051	−	0.904699i	$-0.359904\pi$
$421$	7.03106	+	1.88397i	0.342673	+	0.0918189i	−0.0833784	+	0.996518i	$0.526571\pi$
$422$	18.4971	−	4.95629i	0.900425	−	0.241268i
$423$		0			0
$424$	−3.58197	−	3.58197i	−0.173956	−	0.173956i
$425$			46.0057i			2.23160i
$426$		0			0
$427$	0.000433067	0	0.000433067i	2.09576e−5	0	2.09576e-5i
$428$	1.64680	−	2.85234i	0.0796011	−	0.137873i
$429$		0			0
$430$	−15.0845	−	26.1270i	−0.727437	−	1.25996i
$431$	4.90556	−	18.3078i	0.236292	−	0.881855i	−0.741270	−	0.671207i	$-0.765776\pi$
$431$	4.90556	−	18.3078i	0.236292	−	0.881855i	0.977562	−	0.210648i	$-0.0675573\pi$
$432$		0			0
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.982381	−	0.186890i	$-0.0598407\pi$
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.329339	+	0.944212i	$0.393174\pi$
$434$	−0.0106406	+	0.0397112i	−0.000510764	+	0.00190620i
$435$		0			0
$436$	−1.97769	+	7.38085i	−0.0947143	+	0.353479i
$437$	0.275406	+	1.02783i	0.0131744	+	0.0491677i
$438$		0			0
$439$	11.1606	+	6.44360i	0.532668	+	0.307536i	0.742102	−	0.670287i	$-0.233829\pi$
$439$	11.1606	+	6.44360i	0.532668	+	0.307536i	−0.209434	+	0.977823i	$0.567162\pi$
$440$	−14.4716	−	3.87765i	−0.689905	−	0.184860i
$441$		0			0
$442$	−23.9697	+	3.29210i	−1.14012	+	0.156589i
$443$	10.9018	−	6.29415i	0.517959	−	0.299044i	−0.218140	−	0.975917i	$-0.569999\pi$
$443$	10.9018	−	6.29415i	0.517959	−	0.299044i	0.736099	+	0.676874i	$0.236666\pi$
$444$		0			0
$445$	38.7467			1.83677
$446$	13.2099	+	22.8803i	0.625509	+	1.08341i
$447$		0			0
$448$	−0.0201488	+	0.0201488i	−0.000951939	+	0.000951939i
$449$	1.16977	+	4.36565i	0.0552050	+	0.206028i	0.988020	−	0.154329i	$-0.0493216\pi$
$449$	1.16977	+	4.36565i	0.0552050	+	0.206028i	−0.932814	+	0.360357i	$0.882655\pi$
$450$		0			0
$451$	10.9317	−	18.9343i	0.514754	−	0.891581i
$452$	−0.290951	+	0.503942i	−0.0136852	+	0.0237034i
$453$		0			0
$454$	4.44628	+	2.56706i	0.208674	+	0.120478i
$455$	−0.0442127	+	0.350980i	−0.00207272	+	0.0164542i
$456$		0			0
$457$	2.63241	+	9.82430i	0.123139	+	0.459562i	0.999767	−	0.0216084i	$-0.00687869\pi$
$457$	2.63241	+	9.82430i	0.123139	+	0.459562i	−0.876627	+	0.481170i	$0.840212\pi$
$458$	−6.87691	+	3.97039i	−0.321337	+	0.185524i
$459$		0			0
$460$	1.28588	−	1.28588i	0.0599547	−	0.0599547i
$461$	19.2384	+	19.2384i	0.896021	+	0.896021i	0.995081	−	0.0990604i	$-0.0315837\pi$
$461$	19.2384	+	19.2384i	0.896021	+	0.896021i	−0.0990604	+	0.995081i	$0.531584\pi$
$462$		0			0
$463$	11.4472	−	3.06727i	0.531996	−	0.142548i	0.0171864	−	0.999852i	$-0.494529\pi$
$463$	11.4472	−	3.06727i	0.531996	−	0.142548i	0.514810	+	0.857304i	$0.327862\pi$
$464$	7.19404	−	4.15348i	0.333975	−	0.192821i
$465$		0			0
$466$	0.232144	−	0.0622029i	0.0107539	−	0.00288149i
$467$	0.615879			0.0284995			0.0142497	−	0.999898i	$-0.495464\pi$
$467$	0.615879			0.0284995			0.0142497	+	0.999898i	$0.495464\pi$
$468$		0			0
$469$	0.0269263			0.00124334
$470$	−2.67118	+	0.715741i	−0.123212	+	0.0330147i
$471$		0			0
$472$	−12.3919	+	7.15447i	−0.570384	+	0.329311i
$473$	−36.8249	+	9.86721i	−1.69321	+	0.453695i
$474$		0			0
$475$	−9.76728	−	9.76728i	−0.448153	−	0.448153i
$476$	0.135206	−	0.135206i	0.00619718	−	0.00619718i
$477$		0			0
$478$	5.82418	−	3.36259i	0.266392	−	0.153801i
$479$	−5.18682	−	19.3575i	−0.236992	−	0.884466i	−0.977241	−	0.212133i	$-0.931959\pi$
$479$	−5.18682	−	19.3575i	−0.236992	−	0.884466i	0.740249	−	0.672333i	$-0.234708\pi$
$480$		0			0
$481$	−28.9629	+	3.97788i	−1.32059	+	0.181376i
$482$	−22.4739	−	12.9753i	−1.02366	−	0.591010i
$483$		0			0
$484$	−3.96631	+	6.86984i	−0.180287	+	0.312266i
$485$	−0.812748	+	1.40772i	−0.0369050	+	0.0639213i
$486$		0			0
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	−0.971845	−	0.235620i	$-0.924288\pi$
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	0.723833	−	0.689975i	$-0.242379\pi$
$488$	−0.0151982	+	0.0151982i	−0.000687990	+	0.000687990i
$489$		0			0
$490$	12.0499	+	20.8711i	0.544360	+	0.942859i
$491$	19.7513			0.891362			0.445681	−	0.895192i	$-0.352961\pi$
$491$	19.7513			0.891362			0.445681	+	0.895192i	$0.352961\pi$
$492$		0			0
$493$	−48.2750	+	27.8716i	−2.17420	+	1.25527i
$494$	4.38998	−	5.78784i	0.197514	−	0.260407i
$495$		0			0
$496$	−1.39364	−	0.373424i	−0.0625761	−	0.0167672i
$497$	−0.238351	−	0.137612i	−0.0106915	−	0.00617275i
$498$		0			0
$499$	−1.37420	−	5.12859i	−0.0615177	−	0.229587i	0.928321	−	0.371778i	$-0.121252\pi$
$499$	−1.37420	−	5.12859i	−0.0615177	−	0.229587i	−0.989839	+	0.142191i	$0.954585\pi$
$500$	−1.65390	+	6.17244i	−0.0739647	+	0.276040i
$501$		0			0
$502$	−5.32152	+	19.8602i	−0.237511	+	0.886403i
$503$	16.2322	+	9.37164i	0.723756	+	0.417861i	0.816134	−	0.577863i	$-0.196113\pi$
$503$	16.2322	+	9.37164i	0.723756	+	0.417861i	−0.0923776	+	0.995724i	$0.529447\pi$
$504$		0			0
$505$	−4.89333	+	18.2621i	−0.217750	+	0.812654i
$506$	−1.14901	−	1.99015i	−0.0510799	−	0.0884731i
$507$		0			0
$508$	4.94371	−	8.56275i	0.219342	−	0.379911i
$509$	12.0815	+	12.0815i	0.535502	+	0.535502i	0.922204	−	0.386703i	$-0.126386\pi$
$509$	12.0815	+	12.0815i	0.535502	+	0.535502i	−0.386703	+	0.922204i	$0.626386\pi$
$510$		0			0
$511$		−	0.263430i		−	0.0116535i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−14.9121	+	3.99567i	−0.657743	+	0.176242i
$515$	−13.9173	−	3.72914i	−0.613271	−	0.164325i
$516$		0			0
$517$			3.49461i			0.153693i
$518$	0.163371	−	0.163371i	0.00717813	−	0.00717813i
$519$		0			0
$520$	−12.3174	−	1.55161i	−0.540154	−	0.0680427i
$521$			6.18564i			0.270998i	0.990777	+	0.135499i	$0.0432637\pi$
$521$			6.18564i			0.270998i	−0.990777	+	0.135499i	$0.956736\pi$
$522$		0			0
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	0.929453	−	0.368941i	$-0.120280\pi$
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	−0.784239	+	0.620459i	$0.786946\pi$
$524$	18.1247			0.791782
$525$		0			0
$526$	12.1932	+	3.26716i	0.531649	+	0.142455i
$527$	9.35188	+	2.50583i	0.407374	+	0.109156i
$528$		0			0
$529$	−22.7211			−0.987872
$530$	8.72113	+	15.1054i	0.378822	+	0.656139i
$531$		0			0
$532$			0.0574102i			0.00248905i
$533$	6.83937	−	16.7764i	0.296246	−	0.726665i
$534$		0			0
$535$	−8.01904	+	8.01904i	−0.346693	+	0.346693i
$536$			0.944962i			0.0408161i
$537$		0			0
$538$	15.1327	+	4.05479i	0.652416	+	0.174814i
$539$	29.4169	−	7.88223i	1.26708	−	0.339512i
$540$		0			0
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	0.794273	−	0.607561i	$-0.207852\pi$
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	−0.607561	+	0.794273i	$0.707852\pi$
$542$			17.1182i			0.735289i
$543$		0			0
$544$	4.74498	+	4.74498i	0.203439	+	0.203439i
$545$	13.1553	−	22.7856i	0.563509	−	0.976027i
$546$		0			0
$547$	−16.4189	−	28.4384i	−0.702022	−	1.21594i	−0.967755	−	0.251892i	$-0.918947\pi$
$547$	−16.4189	−	28.4384i	−0.702022	−	1.21594i	0.265733	−	0.964047i	$-0.414386\pi$
$548$	−4.32643	+	16.1465i	−0.184816	+	0.689742i
$549$		0			0
$550$	25.8344	+	14.9155i	1.10158	+	0.635999i
$551$	4.33176	−	16.1664i	0.184539	−	0.688710i
$552$		0			0
$553$	0.0207900	−	0.0775892i	0.000884079	−	0.00329943i
$554$	−5.06073	−	18.8869i	−0.215010	−	0.802428i
$555$		0			0
$556$	−4.40359	−	2.54241i	−0.186754	−	0.107822i
$557$	7.73861	+	2.07355i	0.327895	+	0.0878593i	0.419011	−	0.907981i	$-0.362377\pi$
$557$	7.73861	+	2.07355i	0.327895	+	0.0878593i	−0.0911160	+	0.995840i	$0.529043\pi$
$558$		0			0
$559$	−29.1183	+	12.2524i	−1.23157	+	0.518220i
$560$	0.0849690	−	0.0490569i	0.00359059	−	0.00207303i
$561$		0			0
$562$	−30.6037			−1.29094
$563$	−7.44232	−	12.8905i	−0.313656	−	0.543269i	0.665495	−	0.746403i	$-0.268221\pi$
$563$	−7.44232	−	12.8905i	−0.313656	−	0.543269i	−0.979151	+	0.203134i	$0.934887\pi$
$564$		0			0
$565$	1.41678	−	1.41678i	0.0596042	−	0.0596042i
$566$	6.11299	+	22.8140i	0.256948	+	0.958943i
$567$		0			0
$568$	4.82940	−	8.36477i	0.202637	−	0.350978i
$569$	4.45227	−	7.71156i	0.186649	−	0.323285i	−0.757482	−	0.652856i	$-0.773571\pi$
$569$	4.45227	−	7.71156i	0.186649	−	0.323285i	0.944131	+	0.329571i	$0.106904\pi$
$570$		0			0
$571$	0.862884	+	0.498186i	0.0361106	+	0.0208484i	0.517947	−	0.855413i	$-0.326697\pi$
$571$	0.862884	+	0.498186i	0.0361106	+	0.0208484i	−0.481836	+	0.876261i	$0.660030\pi$
$572$	−5.92254	+	14.5275i	−0.247634	+	0.607424i
$573$		0			0
$574$	0.0370572	+	0.138299i	0.00154674	+	0.00577250i
$575$	−3.13576	+	1.81043i	−0.130770	+	0.0755003i
$576$		0			0
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	−0.948247	−	0.317534i	$-0.897145\pi$
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	0.317534	+	0.948247i	$0.397145\pi$
$578$	−19.8199	−	19.8199i	−0.824401	−	0.824401i
$579$		0			0
$580$	−27.6282	+	7.40295i	−1.14720	+	0.307391i
$581$	−0.362511	+	0.209296i	−0.0150395	+	0.00868306i
$582$		0			0
$583$	21.2905	−	5.70477i	0.881762	−	0.236267i
$584$	9.24490			0.382557
$585$		0			0
$586$	22.0863			0.912375
$587$	6.18262	−	1.65663i	0.255184	−	0.0683763i	−0.128959	−	0.991650i	$-0.541164\pi$
$587$	6.18262	−	1.65663i	0.255184	−	0.0683763i	0.384143	+	0.923274i	$0.374497\pi$
$588$		0			0
$589$	−2.51746	+	1.45346i	−0.103730	+	0.0598886i
$590$	47.5903	−	12.7518i	1.95926	−	0.524982i
$591$		0			0
$592$	5.73341	+	5.73341i	0.235642	+	0.235642i
$593$	−24.4287	+	24.4287i	−1.00317	+	1.00317i	−0.00317304	+	0.999995i	$0.501010\pi$
$593$	−24.4287	+	24.4287i	−1.00317	+	1.00317i	−0.999995	+	0.00317304i	$0.998990\pi$
$594$		0			0
$595$	−0.570177	+	0.329192i	−0.0233750	+	0.0134955i
$596$	−1.36845	−	5.10712i	−0.0560538	−	0.209196i
$597$		0			0
$598$	−1.16766	−	1.50423i	−0.0477490	−	0.0615126i
$599$	−36.9806	−	21.3507i	−1.51099	−	0.872368i	−0.999918	−	0.0128274i	$-0.995917\pi$
$599$	−36.9806	−	21.3507i	−1.51099	−	0.872368i	−0.511068	−	0.859540i	$-0.670750\pi$
$600$		0			0
$601$	13.5165	−	23.4112i	0.551349	−	0.954965i	−0.446829	−	0.894620i	$-0.647447\pi$
$601$	13.5165	−	23.4112i	0.551349	−	0.954965i	0.998178	−	0.0603449i	$-0.0192201\pi$
$602$	0.124832	−	0.216215i	0.00508777	−	0.00881228i
$603$		0			0
$604$	2.52008	+	9.40508i	0.102541	+	0.382687i
$605$	19.3138	−	19.3138i	0.785218	−	0.785218i
$606$		0			0
$607$	−23.5378	−	40.7687i	−0.955370	−	1.65475i	−0.733519	−	0.679669i	$-0.762124\pi$
$607$	−23.5378	−	40.7687i	−0.955370	−	1.65475i	−0.221851	−	0.975081i	$-0.571210\pi$
$608$	−2.01477			−0.0817098
$609$		0			0
$610$	0.0640921	−	0.0370036i	0.00259501	−	0.00149823i
$611$	0.394019	+	2.86884i	0.0159403	+	0.116061i
$612$		0			0
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.687217	−	0.726452i	$-0.258832\pi$
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.231922	+	0.972734i	$0.425499\pi$
$614$	3.67161	+	2.11981i	0.148174	+	0.0855484i
$615$		0			0
$616$	−0.0320896	−	0.119760i	−0.00129293	−	0.00482527i
$617$	−1.25606	+	4.68769i	−0.0505672	+	0.188719i	−0.986589	−	0.163222i	$-0.947811\pi$
$617$	−1.25606	+	4.68769i	−0.0505672	+	0.188719i	0.936022	+	0.351941i	$0.114478\pi$
$618$		0			0
$619$	−6.61442	+	24.6854i	−0.265856	+	0.992188i	0.695868	+	0.718170i	$0.255020\pi$
$619$	−6.61442	+	24.6854i	−0.265856	+	0.992188i	−0.961724	+	0.274019i	$0.911647\pi$
$620$	4.30232	+	2.48395i	0.172785	+	0.0997577i
$621$		0			0
$622$	−7.83186	+	29.2289i	−0.314029	+	1.17197i
$623$	0.160325	+	0.277691i	0.00642329	+	0.0111255i
$624$		0			0
$625$	−6.13822	+	10.6317i	−0.245529	+	0.425268i
$626$	−23.6643	−	23.6643i	−0.945817	−	0.945817i
$627$		0			0
$628$		−	9.62677i		−	0.384150i
$629$	−38.4735	−	38.4735i	−1.53404	−	1.53404i
$630$		0			0
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.136440	−	0.990648i	$-0.456434\pi$
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.613484	+	0.789707i	$0.289767\pi$
$632$	2.72294	+	0.729610i	0.108313	+	0.0290223i
$633$		0			0
$634$			11.1589i			0.443177i
$635$	−24.0732	+	24.0732i	−0.955317	+	0.955317i
$636$		0			0
$637$	23.2606	−	9.78757i	0.921619	−	0.387798i
$638$			36.1449i			1.43099i
$639$		0			0
$640$	1.72162	+	2.98193i	0.0680529	+	0.117871i
$641$	22.8781			0.903629			0.451814	−	0.892112i	$-0.350777\pi$
$641$	22.8781			0.903629			0.451814	+	0.892112i	$0.350777\pi$
$642$		0			0
$643$	−12.7791	−	3.42415i	−0.503959	−	0.135035i	−0.00212223	−	0.999998i	$-0.500676\pi$
$643$	−12.7791	−	3.42415i	−0.503959	−	0.135035i	−0.501837	+	0.864962i	$0.667342\pi$
$644$	0.0145364	+	0.00389502i	0.000572815	+	0.000153485i
$645$		0			0
$646$	13.5200			0.531936
$647$	−5.87399	−	10.1741i	−0.230930	−	0.399983i	0.727152	−	0.686477i	$-0.240844\pi$
$647$	−5.87399	−	10.1741i	−0.230930	−	0.399983i	−0.958082	+	0.286493i	$0.907510\pi$
$648$		0			0
$649$		−	62.2606i		−	2.44394i
$650$	22.8901	+	9.33179i	0.897822	+	0.366023i
$651$		0			0
$652$	7.83779	−	7.83779i	0.306951	−	0.306951i
$653$			9.22206i			0.360887i	0.983585	+	0.180444i	$0.0577533\pi$
$653$			9.22206i			0.360887i	−0.983585	+	0.180444i	$0.942247\pi$
$654$		0			0
$655$	−60.2811	−	16.1523i	−2.35538	−	0.631122i
$656$	−4.85352	+	1.30050i	−0.189498	+	0.0507759i
$657$		0			0
$658$	−0.0161823	−	0.0161823i	−0.000630853	−	0.000630853i
$659$			4.26895i			0.166295i	0.996537	+	0.0831474i	$0.0264972\pi$
$659$			4.26895i			0.166295i	−0.996537	+	0.0831474i	$0.973503\pi$
$660$		0			0
$661$	−31.5763	−	31.5763i	−1.22818	−	1.22818i	−0.964654	−	0.263522i	$-0.915116\pi$
$661$	−31.5763	−	31.5763i	−1.22818	−	1.22818i	−0.263522	−	0.964654i	$-0.584884\pi$
$662$	2.06979	−	3.58499i	0.0804448	−	0.139335i
$663$		0			0
$664$	−7.34510	−	12.7221i	−0.285045	−	0.493713i
$665$	0.0511626	−	0.190941i	0.00198400	−	0.00740438i
$666$		0			0
$667$	−3.79947	−	2.19363i	−0.147116	−	0.0849375i
$668$	3.86269	−	14.4157i	0.149452	−	0.557762i
$669$		0			0
$670$	0.842126	−	3.14286i	0.0325342	−	0.121419i
$671$	−0.0242052	−	0.0903350i	−0.000934431	−	0.00348734i
$672$		0			0
$673$	−4.88433	−	2.81997i	−0.188277	−	0.108702i	0.402899	−	0.915245i	$-0.368003\pi$
$673$	−4.88433	−	2.81997i	−0.188277	−	0.108702i	−0.591176	+	0.806543i	$0.701336\pi$
$674$	−16.0573	−	4.30254i	−0.618504	−	0.165728i
$675$		0			0
$676$	−3.22404	+	12.5939i	−0.124001	+	0.484380i
$677$	21.2676	−	12.2789i	0.817381	−	0.471915i	−0.0321318	−	0.999484i	$-0.510230\pi$
$677$	21.2676	−	12.2789i	0.817381	−	0.471915i	0.849512	+	0.527569i	$0.176896\pi$
$678$		0			0
$679$	−0.0134519			−0.000516235
$680$	−11.5528	−	20.0100i	−0.443028	−	0.767347i
$681$		0			0
$682$	4.43911	−	4.43911i	0.169982	−	0.169982i
$683$	−7.16139	−	26.7267i	−0.274023	−	1.02267i	−0.956493	−	0.291755i	$-0.905761\pi$
$683$	−7.16139	−	26.7267i	−0.274023	−	1.02267i	0.682470	−	0.730913i	$-0.260906\pi$
$684$		0			0
$685$	28.7786	−	49.8460i	1.09957	−	1.90452i
$686$	−0.199451	+	0.345459i	−0.00761507	+	0.0131897i
$687$		0			0
$688$	7.58793	+	4.38090i	0.289287	+	0.167020i
$689$	16.8349	−	7.08375i	0.641357	−	0.269870i
$690$		0			0
$691$	−2.04478	−	7.63123i	−0.0777871	−	0.290306i	0.916064	−	0.401033i	$-0.131349\pi$
$691$	−2.04478	−	7.63123i	−0.0777871	−	0.290306i	−0.993851	+	0.110727i	$0.964682\pi$
$692$	16.5067	−	9.53013i	0.627489	−	0.362281i
$693$		0			0
$694$	14.3923	−	14.3923i	0.546324	−	0.546324i
$695$	12.3802	+	12.3802i	0.469608	+	0.469608i
$696$		0			0
$697$	32.5691	−	8.72687i	1.23364	−	0.330554i
$698$	16.9381	−	9.77922i	0.641117	−	0.370149i
$699$		0			0
$700$	−0.188699	+	0.0505617i	−0.00713215	+	0.00191105i
$701$	−39.9569			−1.50915			−0.754575	−	0.656214i	$-0.772157\pi$
$701$	−39.9569			−1.50915			−0.754575	+	0.656214i	$0.772157\pi$
$702$		0			0
$703$	16.3363			0.616136
$704$	4.20290	−	1.12616i	0.158403	−	0.0424439i
$705$		0			0
$706$	8.76479	−	5.06035i	0.329867	−	0.190449i
$707$	−0.151129	+	0.0404949i	−0.00568380	+	0.00152297i
$708$		0			0
$709$	−35.9885	−	35.9885i	−1.35158	−	1.35158i	−0.883898	−	0.467680i	$-0.845090\pi$
$709$	−35.9885	−	35.9885i	−1.35158	−	1.35158i	−0.467680	−	0.883898i	$-0.654910\pi$
$710$	−23.5166	+	23.5166i	−0.882564	+	0.882564i
$711$		0			0
$712$	−9.74539	+	5.62650i	−0.365224	+	0.210862i
$713$	0.197221	+	0.736038i	0.00738597	+	0.0275648i
$714$		0			0
$715$	32.6444	−	43.0390i	1.22083	−	1.60957i
$716$	20.8769	+	12.0533i	0.780207	+	0.450453i
$717$		0			0
$718$	0.782034	−	1.35452i	0.0291853	−	0.0505504i
$719$	0.750575	−	1.30003i	0.0279917	−	0.0484831i	−0.851690	−	0.524046i	$-0.824422\pi$
$719$	0.750575	−	1.30003i	0.0279917	−	0.0484831i	0.879682	+	0.475563i	$0.157755\pi$
$720$		0			0
$721$	−0.0308606	−	0.115173i	−0.00114931	−	0.00428928i
$722$	10.5647	−	10.5647i	0.393176	−	0.393176i
$723$		0			0
$724$	−0.582526	−	1.00897i	−0.0216494	−	0.0374979i
$725$	56.9514			2.11512
$726$		0			0
$727$	41.9032	−	24.1928i	1.55410	−	0.897261i	0.556301	−	0.830981i	$-0.312220\pi$
$727$	41.9032	−	24.1928i	1.55410	−	0.897261i	0.997801	−	0.0662809i	$-0.0211133\pi$
$728$	−0.0398465	−	0.0946971i	−0.00147681	−	0.00350971i
$729$		0			0
$730$	−30.7477	−	8.23882i	−1.13802	−	0.304932i
$731$	−50.9182	−	29.3976i	−1.88328	−	1.08731i
$732$		0			0
$733$	−6.15729	−	22.9793i	−0.227425	−	0.848761i	−0.981419	−	0.191879i	$-0.938542\pi$
$733$	−6.15729	−	22.9793i	−0.227425	−	0.848761i	0.753994	−	0.656882i	$-0.228125\pi$
$734$	1.61338	−	6.02121i	0.0595509	−	0.222247i
$735$		0			0
$736$	−0.136693	+	0.510146i	−0.00503857	+	0.0188042i
$737$	−3.56082	−	2.05584i	−0.131164	−	0.0757279i
$738$		0			0
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	−0.282786	−	0.959183i	$-0.591259\pi$
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	0.724491	−	0.689284i	$-0.242075\pi$
$740$	−13.9593	−	24.1783i	−0.513155	−	0.888811i
$741$		0			0
$742$	−0.0721721	+	0.125006i	−0.00264952	+	0.00458911i
$743$	25.5083	+	25.5083i	0.935809	+	0.935809i	0.998061	−	0.0622513i	$-0.0198280\pi$
$743$	25.5083	+	25.5083i	0.935809	+	0.935809i	−0.0622513	+	0.998061i	$0.519828\pi$
$744$		0			0
$745$			18.2053i			0.666992i
$746$	14.9264	+	14.9264i	0.546493	+	0.546493i
$747$		0			0
$748$	−28.2032	+	7.55702i	−1.03121	+	0.276312i
$749$	−0.0906521	−	0.0242902i	−0.00331236	−	0.000887543i
$750$		0			0
$751$			17.5054i			0.638780i	0.947623	+	0.319390i	$0.103478\pi$
$751$			17.5054i			0.638780i	−0.947623	+	0.319390i	$0.896522\pi$
$752$	0.567908	−	0.567908i	0.0207095	−	0.0207095i
$753$		0			0
$754$	4.07537	+	29.6726i	0.148416	+	1.08061i
$755$		−	33.5263i		−	1.22015i
$756$		0			0
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	0.880484	−	0.474076i	$-0.157218\pi$
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	−0.850804	+	0.525483i	$0.823885\pi$
$758$	1.33432			0.0484645
$759$		0			0
$760$	6.70095	+	1.79552i	0.243069	+	0.0651302i
$761$	−17.1049	−	4.58324i	−0.620051	−	0.166142i	−0.0649002	−	0.997892i	$-0.520673\pi$
$761$	−17.1049	−	4.58324i	−0.620051	−	0.166142i	−0.555151	+	0.831750i	$0.687340\pi$
$762$		0			0
$763$	0.217734			0.00788249
$764$	−5.78229	−	10.0152i	−0.209196	−	0.362338i
$765$		0			0
$766$			25.8573i			0.934261i
$767$	−7.01992	−	51.1118i	−0.253475	−	1.84554i
$768$		0			0
$769$	14.4842	−	14.4842i	0.522312	−	0.522312i	−0.395957	−	0.918269i	$-0.629587\pi$
$769$	14.4842	−	14.4842i	0.522312	−	0.522312i	0.918269	+	0.395957i	$0.129587\pi$
$770$			0.426909i			0.0153847i
$771$		0			0
$772$	−1.39097	−	0.372710i	−0.0500622	−	0.0134141i
$773$	−8.74973	+	2.34448i	−0.314706	+	0.0843252i	−0.412715	−	0.910860i	$-0.635419\pi$
$773$	−8.74973	+	2.34448i	−0.314706	+	0.0843252i	0.0980088	+	0.995186i	$0.468753\pi$
$774$		0			0
$775$	−6.99444	−	6.99444i	−0.251248	−	0.251248i
$776$		−	0.472084i		−	0.0169468i
$777$		0			0
$778$	−10.3284	−	10.3284i	−0.370292	−	0.370292i
$779$	−5.06185	+	8.76738i	−0.181360	+	0.314124i
$780$		0			0
$781$	21.0135	+	36.3965i	0.751923	+	1.30237i
$782$	0.917267	−	3.42329i	0.0328014	−	0.122416i
$783$		0			0
$784$	−6.06147	−	3.49959i	−0.216481	−	0.124986i
$785$	−8.57914	+	32.0178i	−0.306203	+	1.14276i
$786$		0			0
$787$	−4.89695	+	18.2757i	−0.174558	+	0.651458i	0.822069	+	0.569388i	$0.192820\pi$
$787$	−4.89695	+	18.2757i	−0.174558	+	0.651458i	−0.996627	+	0.0820699i	$0.973847\pi$
$788$	−1.07594	−	4.01546i	−0.0383288	−	0.143045i
$789$		0			0
$790$	−8.40604	−	4.85323i	−0.299074	−	0.172670i
$791$	0.0160161	+	0.00429150i	0.000569467	+	0.000152588i
$792$		0			0
$793$	−0.0300562	−	0.0714299i	−0.00106733	−	0.00253655i
$794$	2.58388	−	1.49180i	0.0916983	−	0.0529421i
$795$		0			0
$796$	2.06042			0.0730295
$797$	−16.8536	−	29.1913i	−0.596986	−	1.03401i	−0.993263	−	0.115879i	$-0.963031\pi$
$797$	−16.8536	−	29.1913i	−0.596986	−	1.03401i	0.396277	−	0.918131i	$-0.370302\pi$
$798$		0			0
$799$	−3.81090	+	3.81090i	−0.134820	+	0.134820i
$800$	−1.77443	−	6.62226i	−0.0627355	−	0.234132i
$801$		0			0
$802$	5.53740	−	9.59106i	0.195533	−	0.338672i
$803$	−20.1130	+	34.8368i	−0.709773	+	1.22936i
$804$		0			0
$805$	−0.0448757	−	0.0259090i	−0.00158166	−	0.000913171i
$806$	3.14371	−	4.14473i	0.110732	−	0.145992i
$807$		0			0
$808$	−1.42114	−	5.30377i	−0.0499956	−	0.186586i
$809$	9.20764	−	5.31603i	0.323723	−	0.186902i	−0.329328	−	0.944216i	$-0.606822\pi$
$809$	9.20764	−	5.31603i	0.323723	−	0.186902i	0.653051	+	0.757314i	$0.273489\pi$
$810$		0			0
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	−0.559874	−	0.828578i	$-0.689151\pi$
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	0.828578	+	0.559874i	$0.189151\pi$
$812$	−0.167375	−	0.167375i	−0.00587371	−	0.00587371i
$813$		0			0
$814$	−34.0782	+	9.13123i	−1.19444	+	0.320049i
$815$	−33.0526	+	19.0829i	−1.15778	+	0.668446i
$816$		0			0
$817$	17.0515	−	4.56894i	0.596557	−	0.159847i
$818$	−14.6788			−0.513233
$819$		0			0
$820$	17.3013			0.604189
$821$	−14.8427	+	3.97709i	−0.518013	+	0.138801i	−0.508347	−	0.861152i	$-0.669743\pi$
$821$	−14.8427	+	3.97709i	−0.518013	+	0.138801i	−0.00966583	+	0.999953i	$0.503077\pi$
$822$		0			0
$823$	13.1817	−	7.61045i	0.459485	−	0.265284i	−0.252343	−	0.967638i	$-0.581201\pi$
$823$	13.1817	−	7.61045i	0.459485	−	0.265284i	0.711828	+	0.702354i	$0.247868\pi$
$824$	4.04193	−	1.08303i	0.140807	−	0.0377292i
$825$		0			0
$826$	0.288307	+	0.288307i	0.0100315	+	0.0100315i
$827$	−16.9790	+	16.9790i	−0.590418	+	0.590418i	−0.937744	−	0.347326i	$-0.887090\pi$
$827$	−16.9790	+	16.9790i	−0.590418	+	0.590418i	0.347326	+	0.937744i	$0.387090\pi$
$828$		0			0
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	−0.732335	−	0.680944i	$-0.761570\pi$
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	0.223547	+	0.974693i	$0.428236\pi$
$830$	13.0915	+	48.8583i	0.454414	+	1.69590i
$831$		0			0
$832$	3.32333	−	1.39839i	0.115216	−	0.0484803i
$833$	40.6750	+	23.4837i	1.40930	+	0.813662i
$834$		0			0
$835$	−25.6939	+	44.5031i	−0.889174	+	1.54009i
$836$	4.38330	−	7.59210i	0.151600	−	0.262578i
$837$		0			0
$838$	−7.28940	−	27.2044i	−0.251808	−	0.939761i
$839$	−16.7213	+	16.7213i	−0.577282	+	0.577282i	−0.934154	−	0.356871i	$-0.883844\pi$
$839$	−16.7213	+	16.7213i	−0.577282	+	0.577282i	0.356871	+	0.934154i	$0.383844\pi$
$840$		0			0
$841$	20.0028	+	34.6459i	0.689752	+	1.19469i
$842$	7.27909			0.250854
$843$		0			0
$844$	16.5841	−	9.57481i	0.570847	−	0.329579i
$845$	21.9462	−	39.0129i	0.754972	−	1.34208i
$846$		0			0
$847$	0.218335	+	0.0585027i	0.00750208	+	0.00201018i
$848$	−4.38699	−	2.53283i	−0.150650	−	0.0869778i
$849$		0			0
$850$	11.9071	+	44.4381i	0.408412	+	1.52421i
$851$	1.10834	−	4.13640i	0.0379935	−	0.141794i
$852$		0			0
$853$	−14.8432	+	55.3955i	−0.508221	+	1.89671i	−0.0706986	+	0.997498i	$0.522523\pi$
$853$	−14.8432	+	55.3955i	−0.508221	+	1.89671i	−0.437522	+	0.899208i	$0.644144\pi$
$854$	0.000530397	0	0.000306225i	1.81498e−5	0	1.04788e-5i
$855$		0			0
$856$	0.852446	−	3.18137i	0.0291360	−	0.108737i
$857$	−9.63613	−	16.6903i	−0.329164	−	0.570129i	0.653182	−	0.757201i	$-0.273434\pi$
$857$	−9.63613	−	16.6903i	−0.329164	−	0.570129i	−0.982346	+	0.187072i	$0.940100\pi$
$858$		0			0
$859$	−21.1198	+	36.5805i	−0.720597	+	1.24811i	0.240164	+	0.970732i	$0.422799\pi$
$859$	−21.1198	+	36.5805i	−0.720597	+	1.24811i	−0.960761	+	0.277378i	$0.910534\pi$
$860$	−21.3326	−	21.3326i	−0.727437	−	0.727437i
$861$		0			0
$862$		−	18.9536i		−	0.645563i
$863$	−4.51248	−	4.51248i	−0.153607	−	0.153607i	0.626120	−	0.779727i	$-0.284642\pi$
$863$	−4.51248	−	4.51248i	−0.153607	−	0.153607i	−0.779727	+	0.626120i	$0.784642\pi$
$864$		0			0
$865$	−63.3927	+	16.9860i	−2.15542	+	0.577542i
$866$	30.4438	+	8.15738i	1.03452	+	0.277199i
$867$		0			0
$868$			0.0411120i			0.00139543i
$869$	−8.67331	+	8.67331i	−0.294222	+	0.294222i
$870$		0			0
$871$	−3.15500	−	1.28623i	−0.106903	−	0.0435821i
$872$			7.64122i			0.258764i
$873$		0			0
$874$	0.532043	+	0.921525i	0.0179966	+	0.0311711i
$875$	0.182086			0.00615563
$876$		0			0
$877$	11.6623	+	3.12491i	0.393808	+	0.105521i	0.450288	−	0.892883i	$-0.351321\pi$
$877$	11.6623	+	3.12491i	0.393808	+	0.105521i	−0.0564803	+	0.998404i	$0.517988\pi$
$878$	12.4481	+	3.33545i	0.420102	+	0.112566i
$879$		0			0
$880$	−14.9821			−0.505046
$881$	23.1313	+	40.0646i	0.779314	+	1.34981i	0.932337	+	0.361589i	$0.117766\pi$
$881$	23.1313	+	40.0646i	0.779314	+	1.34981i	−0.153023	+	0.988223i	$0.548901\pi$
$882$		0			0
$883$			5.00836i			0.168545i	0.996443	+	0.0842723i	$0.0268566\pi$
$883$			5.00836i			0.168545i	−0.996443	+	0.0842723i	$0.973143\pi$
$884$	−22.3009	+	9.38375i	−0.750061	+	0.315610i
$885$		0			0
$886$	8.90127	−	8.90127i	0.299044	−	0.299044i
$887$			21.6986i			0.728567i	0.931288	+	0.364284i	$0.118686\pi$
$887$			21.6986i			0.728567i	−0.931288	+	0.364284i	$0.881314\pi$
$888$		0			0
$889$	−0.272138	−	0.0729193i	−0.00912723	−	0.00244563i
$890$	37.4265	−	10.0284i	1.25454	−	0.336153i
$891$		0			0
$892$	18.6817	+	18.6817i	0.625509	+	0.625509i
$893$		−	1.61815i		−	0.0541494i
$894$		0			0
$895$	−58.6932	−	58.6932i	−1.96190	−	1.96190i
$896$	−0.0142473	+	0.0246771i	−0.000475970	+	0.000824403i
$897$		0			0
$898$	2.25983	+	3.91414i	0.0754115	+	0.130616i
$899$	3.10202	−	11.5769i	0.103458	−	0.386111i
$900$		0			0
$901$	29.4385	+	16.9963i	0.980740	+	0.566230i
$902$	5.65867	−	21.1185i	0.188413	−	0.703167i
$903$		0			0
$904$	−0.150607	+	0.562074i	−0.00500912	+	0.0186943i
$905$	1.03827	+	3.87486i	0.0345131	+	0.128805i
$906$		0			0
$907$	26.6615	+	15.3930i	0.885282	+	0.511118i	0.872396	−	0.488799i	$-0.162565\pi$
$907$	26.6615	+	15.3930i	0.885282	+	0.511118i	0.0128856	+	0.999917i	$0.495898\pi$
$908$	4.95918	+	1.32881i	0.164576	+	0.0440981i
$909$		0			0
$910$	0.0481342	+	0.350464i	0.00159563	+	0.0116178i
$911$	−13.1044	+	7.56582i	−0.434168	+	0.250667i	−0.701120	−	0.713043i	$-0.747316\pi$
$911$	−13.1044	+	7.56582i	−0.434168	+	0.250667i	0.266953	+	0.963710i	$0.413983\pi$
$912$		0			0
$913$	63.9194			2.11542
$914$	5.08543	+	8.80823i	0.168211	+	0.291350i
$915$		0			0
$916$	−5.61498	+	5.61498i	−0.185524	+	0.185524i
$917$	−0.133669	−	0.498859i	−0.00441414	−	0.0164738i
$918$		0			0
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.0323673	+	0.999476i	$0.510305\pi$
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.849388	+	0.527769i	$0.823029\pi$
$920$	0.909258	−	1.57488i	0.0299773	−	0.0519223i
$921$		0			0
$922$	23.5621	+	13.6036i	0.775977	+	0.448011i
$923$	21.3544	+	27.5098i	0.702890	+	0.905497i
$924$		0			0
$925$	14.3875	+	53.6950i	0.473059	+	1.76548i
$926$	10.2633	−	5.92551i	0.337272	−	0.194724i
$927$		0			0
$928$	5.87391	−	5.87391i	0.192821	−	0.192821i
$929$	−37.9968	−	37.9968i	−1.24663	−	1.24663i	−0.957197	−	0.289436i	$-0.906532\pi$
$929$	−37.9968	−	37.9968i	−1.24663	−	1.24663i	−0.289436	−	0.957197i	$-0.593468\pi$
$930$		0			0
$931$	−13.6213	+	3.64981i	−0.446419	+	0.119618i
$932$	0.208135	−	0.120167i	0.00681769	−	0.00393619i
$933$		0			0
$934$	0.594893	−	0.159401i	0.0194655	−	0.00521576i
$935$	100.536			3.28787
$936$		0			0
$937$	−2.41921			−0.0790323			−0.0395162	−	0.999219i	$-0.512582\pi$
$937$	−2.41921			−0.0790323			−0.0395162	+	0.999219i	$0.512582\pi$
$938$	0.0260088	−	0.00696905i	0.000849219	−	0.000227548i
$939$		0			0
$940$	−2.39492	+	1.38271i	−0.0781135	+	0.0450989i
$941$	0.0432503	−	0.0115889i	0.00140992	−	0.000377786i	−0.258114	−	0.966114i	$-0.583101\pi$
$941$	0.0432503	−	0.0115889i	0.00140992	−	0.000377786i	0.259524	+	0.965737i	$0.416434\pi$
$942$		0			0
$943$	1.87650	+	1.87650i	0.0611072	+	0.0611072i
$944$	−10.1180	+	10.1180i	−0.329311	+	0.329311i
$945$		0			0
$946$	−33.0163	+	19.0620i	−1.07345	+	0.619759i
$947$	6.08611	+	22.7137i	0.197772	+	0.738095i	0.991532	+	0.129864i	$0.0414540\pi$
$947$	6.08611	+	22.7137i	0.197772	+	0.738095i	−0.793760	+	0.608231i	$0.791879\pi$
$948$		0			0
$949$	−12.5836	+	30.8665i	−0.408481	+	1.00197i
$950$	−11.9624	−	6.90651i	−0.388112	−	0.224077i
$951$		0			0
$952$	0.0956054	−	0.165593i	0.00309859	−	0.00536691i
$953$	13.8021	−	23.9060i	0.447095	−	0.774392i	−0.551100	−	0.834439i	$-0.685792\pi$
$953$	13.8021	−	23.9060i	0.447095	−	0.774392i	0.998196	+	0.0600474i	$0.0191252\pi$
$954$		0			0
$955$	10.3061	+	38.4627i	0.333496	+	1.24462i
$956$	4.75542	−	4.75542i	0.153801	−	0.153801i
$957$		0			0
$958$	−10.0202	−	17.3554i	−0.323737	−	0.560729i
$959$	0.476318			0.0153811
$960$		0			0
$961$	25.0440	−	14.4592i	0.807871	−	0.466425i
$962$	−26.9464	+	11.3385i	−0.868788	+	0.365567i
$963$		0			0
$964$	−25.0664	−	6.71652i	−0.807335	−	0.216325i
$965$	4.29410	+	2.47920i	0.138232	+	0.0798083i
$966$		0			0
$967$	−8.31034	−	31.0146i	−0.267243	−	0.997363i	−0.960863	−	0.277023i	$-0.910652\pi$
$967$	−8.31034	−	31.0146i	−0.267243	−	0.997363i	0.693621	−	0.720340i	$-0.256014\pi$
$968$	−2.05311	+	7.66231i	−0.0659895	+	0.246276i
$969$		0			0
$970$	−0.420710	+	1.57011i	−0.0135082	+	0.0504132i
$971$	−16.6187	−	9.59478i	−0.533318	−	0.307911i	0.209049	−	0.977905i	$-0.432963\pi$
$971$	−16.6187	−	9.59478i	−0.533318	−	0.307911i	−0.742366	+	0.669994i	$0.766297\pi$
$972$		0			0
$973$	−0.0375004	+	0.139953i	−0.00120221	+	0.00448670i
$974$	−10.5733	−	18.3135i	−0.338791	−	0.586804i
$975$		0			0
$976$	−0.0107467	+	0.0186139i	−0.000343995	+	0.000595817i
$977$	−21.6436	−	21.6436i	−0.692440	−	0.692440i	0.270328	−	0.962768i	$-0.412868\pi$
$977$	−21.6436	−	21.6436i	−0.692440	−	0.692440i	−0.962768	+	0.270328i	$0.912868\pi$
$978$		0			0
$979$		−	48.9637i		−	1.56489i
$980$	17.0412	+	17.0412i	0.544360	+	0.544360i
$981$		0			0
$982$	19.0783	−	5.11201i	0.608812	−	0.163131i
$983$	21.8828	+	5.86347i	0.697952	+	0.187016i	0.590313	−	0.807175i	$-0.299004\pi$
$983$	21.8828	+	5.86347i	0.697952	+	0.187016i	0.107639	+	0.994190i	$0.465671\pi$
$984$		0			0
$985$			14.3139i			0.456079i
$986$	−39.4163	+	39.4163i	−1.25527	+	1.25527i
$987$		0			0
$988$	2.74239	−	6.72684i	0.0872470	−	0.214009i
$989$		−	4.62747i		−	0.147145i
$990$		0			0
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	−0.995997	−	0.0893845i	$-0.971510\pi$
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	0.420589	−	0.907251i	$-0.361823\pi$
$992$	−1.44280			−0.0458089
$993$		0			0
$994$	−0.265846	−	0.0712333i	−0.00843213	−	0.00225938i
$995$	−6.85276	−	1.83619i	−0.217247	−	0.0582111i
$996$		0			0
$997$	−17.7685			−0.562733			−0.281366	−	0.959600i	$-0.590788\pi$
$997$	−17.7685			−0.562733			−0.281366	+	0.959600i	$0.590788\pi$
$998$	−2.65476	−	4.59817i	−0.0840348	−	0.145553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.665.8		56
3.2	odd	2		234.2.z.a.41.2	yes	56
9.2	odd	6		702.2.bb.a.197.8		56
9.7	even	3		234.2.y.a.119.3	yes	56
13.7	odd	12		702.2.bb.a.449.8		56
39.20	even	12		234.2.y.a.59.3	✓	56
117.7	odd	12		234.2.z.a.137.2	yes	56
117.20	even	12	inner	702.2.bc.a.683.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.3	✓	56	39.20	even	12
234.2.y.a.119.3	yes	56	9.7	even	3
234.2.z.a.41.2	yes	56	3.2	odd	2
234.2.z.a.137.2	yes	56	117.7	odd	12
702.2.bb.a.197.8		56	9.2	odd	6
702.2.bb.a.449.8		56	13.7	odd	12
702.2.bc.a.665.8		56	1.1	even	1	trivial
702.2.bc.a.683.8		56	117.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-3.32591 + 0.891175i) q^{5} +(-0.0201488 - 0.0201488i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98193 + 1.72162i) q^{10} +(1.12616 + 4.20290i) q^{11} +(1.39839 + 3.32333i) q^{13} +(-0.0246771 - 0.0142473i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.35521 + 5.81139i) q^{17} +(-0.521462 - 1.94612i) q^{19} +(-2.43473 + 2.43473i) q^{20} +(2.17558 + 3.76822i) q^{22} -0.528142 q^{23} +(5.93735 - 3.42793i) q^{25} +(2.21088 + 2.84816i) q^{26} +(-0.0275237 - 0.00737496i) q^{28} +(7.19404 + 4.15348i) q^{29} +(-0.373424 - 1.39364i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.73678 + 6.48176i) q^{34} +(0.0849690 + 0.0490569i) q^{35} +(-2.09857 + 7.83198i) q^{37} +(-1.00739 - 1.74484i) q^{38} +(-1.72162 + 2.98193i) q^{40} +(-3.55302 - 3.55302i) q^{41} +8.76179i q^{43} +(3.07674 + 3.07674i) q^{44} +(-0.510146 + 0.136693i) q^{46} +(0.775777 + 0.207869i) q^{47} -6.99919i q^{49} +(4.84783 - 4.84783i) q^{50} +(2.87270 + 2.17889i) q^{52} -5.06566i q^{53} +(-7.49104 - 12.9749i) q^{55} -0.0284946 q^{56} +(8.02391 + 2.15000i) q^{58} +(-13.8214 - 3.70343i) q^{59} -0.0214935 q^{61} +(-0.721399 - 1.24950i) q^{62} -1.00000i q^{64} +(-7.61257 - 9.80688i) q^{65} +(-0.668189 + 0.668189i) q^{67} +6.71041i q^{68} +(0.0947706 + 0.0253937i) q^{70} +(9.32969 - 2.49988i) q^{71} +(6.53713 + 6.53713i) q^{73} +8.10826i q^{74} +(-1.42466 - 1.42466i) q^{76} +(0.0619924 - 0.107374i) q^{77} +(1.40950 + 2.44132i) q^{79} +(-0.891175 + 3.32591i) q^{80} +(-4.35155 - 2.51237i) q^{82} +(3.80210 - 14.1896i) q^{83} +(5.98015 - 22.3182i) q^{85} +(2.26772 + 8.46324i) q^{86} +(3.76822 + 2.17558i) q^{88} +(-10.8696 - 2.91249i) q^{89} +(0.0387852 - 0.0951367i) q^{91} +(-0.457384 + 0.264071i) q^{92} +0.803143 q^{94} +(3.46867 + 6.00791i) q^{95} +(0.333814 - 0.333814i) q^{97} +(-1.81152 - 6.76070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

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