LMFDB - Embedded newform 234.2.y.a.119.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(11,234)] 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("234.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			119.12
Character	$\chi$	$=$	234.119
Dual form			234.2.y.a.59.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(1.12657 - 1.31562i) q^{3} +1.00000i q^{4} +(0.398313 - 1.48652i) q^{5} +(1.72688 - 0.133677i) q^{6} +(0.370254 - 1.38181i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.461689 - 2.96426i) q^{9} +(1.33278 - 0.769482i) q^{10} +(-0.350901 + 0.350901i) q^{11} +(1.31562 + 1.12657i) q^{12} +(0.183180 + 3.60090i) q^{13} +(1.23890 - 0.715277i) q^{14} +(-1.50697 - 2.19870i) q^{15} -1.00000 q^{16} +(-1.10510 + 1.91408i) q^{17} +(1.76959 - 2.42251i) q^{18} +(0.805124 + 3.00476i) q^{19} +(1.48652 + 0.398313i) q^{20} +(-1.40081 - 2.04381i) q^{21} -0.496250 q^{22} +(-0.887787 + 1.53769i) q^{23} +(0.133677 + 1.72688i) q^{24} +(2.27902 + 1.31580i) q^{25} +(-2.41669 + 2.67575i) q^{26} +(-4.41995 - 2.73204i) q^{27} +(1.38181 + 0.370254i) q^{28} -4.71069i q^{29} +(0.489127 - 2.62030i) q^{30} +(0.303918 + 0.0814346i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.0663371 + 0.856966i) q^{33} +(-2.13488 + 0.572040i) q^{34} +(-1.90661 - 1.10078i) q^{35} +(2.96426 - 0.461689i) q^{36} +(-2.95350 + 11.0226i) q^{37} +(-1.55538 + 2.69400i) q^{38} +(4.94376 + 3.81566i) q^{39} +(0.769482 + 1.33278i) q^{40} +(-7.77966 + 2.08455i) q^{41} +(0.454671 - 2.43572i) q^{42} +(1.40486 - 0.811094i) q^{43} +(-0.350901 - 0.350901i) q^{44} +(-4.59034 - 0.494392i) q^{45} +(-1.71507 + 0.459552i) q^{46} +(-3.17219 - 11.8388i) q^{47} +(-1.12657 + 1.31562i) q^{48} +(4.28987 + 2.47676i) q^{49} +(0.681106 + 2.54192i) q^{50} +(1.27323 + 3.61023i) q^{51} +(-3.60090 + 0.183180i) q^{52} -2.02719i q^{53} +(-1.19354 - 5.05722i) q^{54} +(0.381855 + 0.661392i) q^{55} +(0.715277 + 1.23890i) q^{56} +(4.86014 + 2.32584i) q^{57} +(3.33096 - 3.33096i) q^{58} +(-1.98083 + 1.98083i) q^{59} +(2.19870 - 1.50697i) q^{60} +(-3.39659 - 5.88306i) q^{61} +(0.157320 + 0.272485i) q^{62} +(-4.26698 - 0.459565i) q^{63} -1.00000i q^{64} +(5.42578 + 1.16198i) q^{65} +(-0.559059 + 0.652874i) q^{66} +(-2.05043 - 7.65232i) q^{67} +(-1.91408 - 1.10510i) q^{68} +(1.02286 + 2.90030i) q^{69} +(-0.569808 - 2.12655i) q^{70} +(-10.8566 + 2.90902i) q^{71} +(2.42251 + 1.76959i) q^{72} +(4.45270 + 4.45270i) q^{73} +(-9.88261 + 5.70573i) q^{74} +(4.29856 - 1.51599i) q^{75} +(-3.00476 + 0.805124i) q^{76} +(0.354956 + 0.614801i) q^{77} +(0.797688 + 6.19384i) q^{78} +(4.77307 - 8.26720i) q^{79} +(-0.398313 + 1.48652i) q^{80} +(-8.57369 + 2.73713i) q^{81} +(-6.97505 - 4.02705i) q^{82} +(8.13149 - 2.17883i) q^{83} +(2.04381 - 1.40081i) q^{84} +(2.40516 + 2.40516i) q^{85} +(1.56691 + 0.419853i) q^{86} +(-6.19746 - 5.30692i) q^{87} -0.496250i q^{88} +(-3.41203 - 0.914251i) q^{89} +(-2.89628 - 3.59545i) q^{90} +(5.04357 + 1.08013i) q^{91} +(-1.53769 - 0.887787i) q^{92} +(0.449521 - 0.308098i) q^{93} +(6.12820 - 10.6144i) q^{94} +4.78735 q^{95} +(-1.72688 + 0.133677i) q^{96} +(-7.11700 - 1.90700i) q^{97} +(1.28206 + 4.78473i) q^{98} +(1.20217 + 0.878156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.12657	−	1.31562i	0.650424	−	0.759571i
$3$	1.12657	−	1.31562i	0.650424	−	0.759571i
$4$			1.00000i			0.500000i
$5$	0.398313	−	1.48652i	0.178131	−	0.664794i	−0.817866	−	0.575409i	$-0.804843\pi$
$5$	0.398313	−	1.48652i	0.178131	−	0.664794i	0.995997	−	0.0893855i	$-0.0284903\pi$
$6$	1.72688	−	0.133677i	0.704998	−	0.0545734i
$7$	0.370254	−	1.38181i	0.139943	−	0.522274i	−0.859986	−	0.510318i	$-0.829528\pi$
$7$	0.370254	−	1.38181i	0.139943	−	0.522274i	0.999929	−	0.0119560i	$-0.00380579\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.461689	−	2.96426i	−0.153896	−	0.988087i
$10$	1.33278	−	0.769482i	0.421463	−	0.243332i
$11$	−0.350901	+	0.350901i	−0.105801	+	0.105801i	−0.758026	−	0.652225i	$-0.773836\pi$
$11$	−0.350901	+	0.350901i	−0.105801	+	0.105801i	0.652225	+	0.758026i	$0.273836\pi$
$12$	1.31562	+	1.12657i	0.379786	+	0.325212i
$13$	0.183180	+	3.60090i	0.0508050	+	0.998709i
$13$	0.183180	+	3.60090i	0.0508050	+	0.998709i
$14$	1.23890	−	0.715277i	0.331109	−	0.191166i
$15$	−1.50697	−	2.19870i	−0.389098	−	0.567701i
$16$	−1.00000			−0.250000
$17$	−1.10510	+	1.91408i	−0.268025	+	0.464233i	−0.968352	−	0.249589i	$-0.919704\pi$
$17$	−1.10510	+	1.91408i	−0.268025	+	0.464233i	0.700327	+	0.713823i	$0.253038\pi$
$18$	1.76959	−	2.42251i	0.417095	−	0.570992i
$19$	0.805124	+	3.00476i	0.184708	+	0.689340i	0.994693	+	0.102889i	$0.0328086\pi$
$19$	0.805124	+	3.00476i	0.184708	+	0.689340i	−0.809985	+	0.586451i	$0.800525\pi$
$20$	1.48652	+	0.398313i	0.332397	+	0.0890655i
$21$	−1.40081	−	2.04381i	−0.305682	−	0.445997i
$22$	−0.496250			−0.105801
$23$	−0.887787	+	1.53769i	−0.185116	+	0.320631i	−0.943616	−	0.331043i	$-0.892600\pi$
$23$	−0.887787	+	1.53769i	−0.185116	+	0.320631i	0.758499	+	0.651674i	$0.225933\pi$
$24$	0.133677	+	1.72688i	0.0272867	+	0.352499i
$25$	2.27902	+	1.31580i	0.455805	+	0.263159i
$26$	−2.41669	+	2.67575i	−0.473952	+	0.524757i
$27$	−4.41995	−	2.73204i	−0.850620	−	0.525781i
$28$	1.38181	+	0.370254i	0.261137	+	0.0699715i
$29$		−	4.71069i		−	0.874754i	−0.899278	−	0.437377i	$-0.855908\pi$
$29$		−	4.71069i		−	0.874754i	0.899278	−	0.437377i	$-0.144092\pi$
$30$	0.489127	−	2.62030i	0.0893019	−	0.478400i
$31$	0.303918	+	0.0814346i	0.0545853	+	0.0146261i	0.286008	−	0.958227i	$-0.407671\pi$
$31$	0.303918	+	0.0814346i	0.0545853	+	0.0146261i	−0.231423	+	0.972853i	$0.574338\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.0663371	+	0.856966i	0.0115478	+	0.149179i
$34$	−2.13488	+	0.572040i	−0.366129	+	0.0981040i
$35$	−1.90661	−	1.10078i	−0.322277	−	0.186067i
$36$	2.96426	−	0.461689i	0.494043	−	0.0769482i
$37$	−2.95350	+	11.0226i	−0.485553	+	1.81211i	0.0920063	+	0.995758i	$0.470672\pi$
$37$	−2.95350	+	11.0226i	−0.485553	+	1.81211i	−0.577559	+	0.816349i	$0.695995\pi$
$38$	−1.55538	+	2.69400i	−0.252316	+	0.437024i
$39$	4.94376	+	3.81566i	0.791635	+	0.610994i
$40$	0.769482	+	1.33278i	0.121666	+	0.210731i
$41$	−7.77966	+	2.08455i	−1.21498	+	0.325553i	−0.808714	−	0.588202i	$-0.799836\pi$
$41$	−7.77966	+	2.08455i	−1.21498	+	0.325553i	−0.406265	+	0.913755i	$0.633169\pi$
$42$	0.454671	−	2.43572i	0.0701572	−	0.375839i
$43$	1.40486	−	0.811094i	0.214239	−	0.123691i	−0.389041	−	0.921220i	$-0.627194\pi$
$43$	1.40486	−	0.811094i	0.214239	−	0.123691i	0.603280	+	0.797530i	$0.293860\pi$
$44$	−0.350901	−	0.350901i	−0.0529004	−	0.0529004i
$45$	−4.59034	−	0.494392i	−0.684288	−	0.0736996i
$46$	−1.71507	+	0.459552i	−0.252874	+	0.0677573i
$47$	−3.17219	−	11.8388i	−0.462711	−	1.72686i	−0.664368	−	0.747406i	$-0.731299\pi$
$47$	−3.17219	−	11.8388i	−0.462711	−	1.72686i	0.201656	−	0.979456i	$-0.435368\pi$
$48$	−1.12657	+	1.31562i	−0.162606	+	0.189893i
$49$	4.28987	+	2.47676i	0.612839	+	0.353823i
$50$	0.681106	+	2.54192i	0.0963229	+	0.359482i
$51$	1.27323	+	3.61023i	0.178288	+	0.505533i
$52$	−3.60090	+	0.183180i	−0.499354	+	0.0254025i
$53$		−	2.02719i		−	0.278456i	−0.990260	−	0.139228i	$-0.955538\pi$
$53$		−	2.02719i		−	0.278456i	0.990260	−	0.139228i	$-0.0444621\pi$
$54$	−1.19354	−	5.05722i	−0.162420	−	0.688200i
$55$	0.381855	+	0.661392i	0.0514893	+	0.0891821i
$56$	0.715277	+	1.23890i	0.0955828	+	0.165554i
$57$	4.86014	+	2.32584i	0.643741	+	0.308065i
$58$	3.33096	−	3.33096i	0.437377	−	0.437377i
$59$	−1.98083	+	1.98083i	−0.257882	+	0.257882i	−0.824192	−	0.566310i	$-0.808370\pi$
$59$	−1.98083	+	1.98083i	−0.257882	+	0.257882i	0.566310	+	0.824192i	$0.308370\pi$
$60$	2.19870	−	1.50697i	0.283851	−	0.194549i
$61$	−3.39659	−	5.88306i	−0.434888	−	0.753249i	0.562398	−	0.826867i	$-0.309879\pi$
$61$	−3.39659	−	5.88306i	−0.434888	−	0.753249i	−0.997287	+	0.0736177i	$0.976546\pi$
$62$	0.157320	+	0.272485i	0.0199796	+	0.0346057i
$63$	−4.26698	−	0.459565i	−0.537589	−	0.0578997i
$64$		−	1.00000i		−	0.125000i
$65$	5.42578	+	1.16198i	0.672986	+	0.144126i
$66$	−0.559059	+	0.652874i	−0.0688154	+	0.0803632i
$67$	−2.05043	−	7.65232i	−0.250500	−	0.934880i	−0.970539	−	0.240945i	$-0.922542\pi$
$67$	−2.05043	−	7.65232i	−0.250500	−	0.934880i	0.720038	−	0.693934i	$-0.244124\pi$
$68$	−1.91408	−	1.10510i	−0.232117	−	0.134013i
$69$	1.02286	+	2.90030i	0.123138	+	0.349155i
$70$	−0.569808	−	2.12655i	−0.0681051	−	0.254172i
$71$	−10.8566	+	2.90902i	−1.28844	+	0.345237i	−0.837069	−	0.547097i	$-0.815733\pi$
$71$	−10.8566	+	2.90902i	−1.28844	+	0.345237i	−0.451374	+	0.892335i	$0.649066\pi$
$72$	2.42251	+	1.76959i	0.285496	+	0.208548i
$73$	4.45270	+	4.45270i	0.521149	+	0.521149i	0.917918	−	0.396769i	$-0.129869\pi$
$73$	4.45270	+	4.45270i	0.521149	+	0.521149i	−0.396769	+	0.917918i	$0.629869\pi$
$74$	−9.88261	+	5.70573i	−1.14883	+	0.663277i
$75$	4.29856	−	1.51599i	0.496355	−	0.175051i
$76$	−3.00476	+	0.805124i	−0.344670	+	0.0923540i
$77$	0.354956	+	0.614801i	0.0404510	+	0.0700631i
$78$	0.797688	+	6.19384i	0.0903203	+	0.701315i
$79$	4.77307	−	8.26720i	0.537012	−	0.930133i	−0.462051	−	0.886853i	$-0.652886\pi$
$79$	4.77307	−	8.26720i	0.537012	−	0.930133i	0.999063	−	0.0432790i	$-0.0137805\pi$
$80$	−0.398313	+	1.48652i	−0.0445328	+	0.166199i
$81$	−8.57369	+	2.73713i	−0.952632	+	0.304126i
$82$	−6.97505	−	4.02705i	−0.770266	−	0.444713i
$83$	8.13149	−	2.17883i	0.892547	−	0.239157i	0.216734	−	0.976231i	$-0.430460\pi$
$83$	8.13149	−	2.17883i	0.892547	−	0.239157i	0.675813	+	0.737073i	$0.263793\pi$
$84$	2.04381	−	1.40081i	0.222998	−	0.152841i
$85$	2.40516	+	2.40516i	0.260876	+	0.260876i
$86$	1.56691	+	0.419853i	0.168965	+	0.0452739i
$87$	−6.19746	−	5.30692i	−0.664438	−	0.568961i
$88$		−	0.496250i		−	0.0529004i
$89$	−3.41203	−	0.914251i	−0.361674	−	0.0969104i	0.0734055	−	0.997302i	$-0.476613\pi$
$89$	−3.41203	−	0.914251i	−0.361674	−	0.0969104i	−0.435080	+	0.900392i	$0.643280\pi$
$90$	−2.89628	−	3.59545i	−0.305294	−	0.378994i
$91$	5.04357	+	1.08013i	0.528710	+	0.113228i
$92$	−1.53769	−	0.887787i	−0.160315	−	0.0925582i
$93$	0.449521	−	0.308098i	0.0466132	−	0.0319482i
$94$	6.12820	−	10.6144i	0.632075	−	1.09479i
$95$	4.78735			0.491171
$96$	−1.72688	+	0.133677i	−0.176249	+	0.0136433i
$97$	−7.11700	−	1.90700i	−0.722622	−	0.193626i	−0.121281	−	0.992618i	$-0.538700\pi$
$97$	−7.11700	−	1.90700i	−0.722622	−	0.193626i	−0.601341	+	0.798992i	$0.705367\pi$
$98$	1.28206	+	4.78473i	0.129508	+	0.483331i
$99$	1.20217	+	0.878156i	0.120823	+	0.0882580i
$100$	−1.31580	+	2.27902i	−0.131580	+	0.227902i
$101$	5.51878			0.549139			0.274569	−	0.961567i	$-0.411465\pi$
$101$	5.51878			0.549139			0.274569	+	0.961567i	$0.411465\pi$
$102$	−1.65250	+	3.45313i	−0.163622	+	0.341910i
$103$	13.0560	−	7.53787i	1.28644	−	0.742729i	0.308426	−	0.951248i	$-0.400198\pi$
$103$	13.0560	−	7.53787i	1.28644	−	0.742729i	0.978018	+	0.208520i	$0.0668646\pi$
$104$	−2.67575	−	2.41669i	−0.262378	−	0.236976i
$105$	−3.59614	+	1.26826i	−0.350947	+	0.123770i
$106$	1.43344	−	1.43344i	0.139228	−	0.139228i
$107$	10.8647	−	6.27276i	1.05033	−	0.606411i	0.127591	−	0.991827i	$-0.459276\pi$
$107$	10.8647	−	6.27276i	1.05033	−	0.606411i	0.922743	+	0.385416i	$0.125942\pi$
$108$	2.73204	−	4.41995i	0.262890	−	0.425310i
$109$	−6.92733	+	6.92733i	−0.663518	+	0.663518i	−0.956208	−	0.292690i	$-0.905450\pi$
$109$	−6.92733	+	6.92733i	−0.663518	+	0.663518i	0.292690	+	0.956208i	$0.405450\pi$
$110$	−0.197663	+	0.737687i	−0.0188464	+	0.0703357i
$111$	11.1742	+	16.3034i	1.06061	+	1.54745i
$112$	−0.370254	+	1.38181i	−0.0349858	+	0.130569i
$113$			14.3065i			1.34585i	0.739713	+	0.672923i	$0.234961\pi$
$113$			14.3065i			1.34585i	−0.739713	+	0.672923i	$0.765039\pi$
$114$	1.79202	+	5.08125i	0.167838	+	0.475903i
$115$	1.93220	+	1.93220i	0.180179	+	0.180179i
$116$	4.71069			0.437377
$117$	10.5894	−	2.20549i	0.978992	−	0.203897i
$118$	−2.80131			−0.257882
$119$	2.23573	+	2.23573i	0.204949	+	0.204949i
$120$	2.62030	+	0.489127i	0.239200	+	0.0446510i
$121$			10.7537i			0.977612i
$122$	1.75820	−	6.56170i	0.159180	−	0.594069i
$123$	−6.02185	+	12.5834i	−0.542972	+	1.13461i
$124$	−0.0814346	+	0.303918i	−0.00731304	+	0.0272926i
$125$	8.30479	−	8.30479i	0.742803	−	0.742803i
$126$	−2.69225	−	3.34217i	−0.239845	−	0.297744i
$127$	2.50743	−	1.44766i	0.222498	−	0.128459i	−0.384608	−	0.923080i	$-0.625663\pi$
$127$	2.50743	−	1.44766i	0.222498	−	0.128459i	0.607106	+	0.794621i	$0.292330\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	0.515578	−	2.76200i	0.0453941	−	0.243181i
$130$	3.01496	+	4.65825i	0.264430	+	0.408556i
$131$	11.3218	−	6.53662i	0.989186	−	0.571107i	0.0841553	−	0.996453i	$-0.473181\pi$
$131$	11.3218	−	6.53662i	0.989186	−	0.571107i	0.905031	+	0.425346i	$0.139847\pi$
$132$	−0.856966	+	0.0663371i	−0.0745893	+	0.00577390i
$133$	4.45011			0.385873
$134$	3.96113	−	6.86088i	0.342190	−	0.592690i
$135$	−5.82176	+	5.48216i	−0.501058	+	0.471829i
$136$	−0.572040	−	2.13488i	−0.0490520	−	0.183065i
$137$	6.29012	+	1.68543i	0.537401	+	0.143996i	0.517304	−	0.855802i	$-0.326936\pi$
$137$	6.29012	+	1.68543i	0.537401	+	0.143996i	0.0200975	+	0.999798i	$0.493602\pi$
$138$	−1.32755	+	2.77409i	−0.113009	+	0.236146i
$139$	16.6819			1.41494			0.707470	−	0.706743i	$-0.249836\pi$
$139$	16.6819			1.41494			0.707470	+	0.706743i	$0.249836\pi$
$140$	1.10078	−	1.90661i	0.0930333	−	0.161138i
$141$	−19.1490	−	9.16380i	−1.61263	−	0.771731i
$142$	−9.73378	−	5.61980i	−0.816840	−	0.471603i
$143$	−1.32784	−	1.19928i	−0.111039	−	0.100289i
$144$	0.461689	+	2.96426i	0.0384741	+	0.247022i
$145$	−7.00256	−	1.87633i	−0.581531	−	0.155821i
$146$			6.29707i			0.521149i
$147$	8.09130	−	2.85359i	0.667359	−	0.235360i
$148$	−11.0226	−	2.95350i	−0.906054	−	0.242776i
$149$	7.43995	+	7.43995i	0.609505	+	0.609505i	0.942817	−	0.333312i	$-0.108166\pi$
$149$	7.43995	+	7.43995i	0.609505	+	0.609505i	−0.333312	+	0.942817i	$0.608166\pi$
$150$	4.11150	+	1.96757i	0.335703	+	0.160652i
$151$	−16.6015	+	4.44836i	−1.35101	+	0.362002i	−0.860508	−	0.509437i	$-0.829854\pi$
$151$	−16.6015	+	4.44836i	−1.35101	+	0.362002i	−0.490503	+	0.871440i	$0.663187\pi$
$152$	−2.69400	−	1.55538i	−0.218512	−	0.126158i
$153$	6.18405	+	2.39208i	0.499951	+	0.193388i
$154$	−0.183739	+	0.685722i	−0.0148061	+	0.0552570i
$155$	0.242109	−	0.419345i	0.0194467	−	0.0336826i
$156$	−3.81566	+	4.94376i	−0.305497	+	0.395817i
$157$	−10.9518	−	18.9690i	−0.874046	−	1.51389i	−0.857775	−	0.514025i	$-0.828154\pi$
$157$	−10.9518	−	18.9690i	−0.874046	−	1.51389i	−0.0162709	−	0.999868i	$-0.505179\pi$
$158$	9.22086	−	2.47072i	0.733572	−	0.196560i
$159$	−2.66700	−	2.28377i	−0.211507	−	0.181115i
$160$	−1.33278	+	0.769482i	−0.105366	+	0.0608329i
$161$	1.79609	+	1.79609i	0.141552	+	0.141552i
$162$	−7.99796	−	4.12707i	−0.628379	−	0.324253i
$163$	5.13664	−	1.37636i	0.402333	−	0.107805i	−0.0519776	−	0.998648i	$-0.516552\pi$
$163$	5.13664	−	1.37636i	0.402333	−	0.107805i	0.454310	+	0.890844i	$0.349886\pi$
$164$	−2.08455	−	7.77966i	−0.162776	−	0.607490i
$165$	1.30032	+	0.242729i	0.101230	+	0.0188964i
$166$	7.29049	+	4.20917i	0.565852	+	0.326695i
$167$	−2.80800	−	10.4796i	−0.217290	−	0.810937i	−0.985348	−	0.170557i	$-0.945443\pi$
$167$	−2.80800	−	10.4796i	−0.217290	−	0.810937i	0.768058	−	0.640380i	$-0.221223\pi$
$168$	2.43572	+	0.454671i	0.187920	+	0.0350786i
$169$	−12.9329	+	1.31923i	−0.994838	+	0.101479i
$170$			3.40141i			0.260876i
$171$	8.53518	−	3.77386i	0.652702	−	0.288595i
$172$	0.811094	+	1.40486i	0.0618453	+	0.107119i
$173$	0.802919	+	1.39070i	0.0610448	+	0.105733i	0.894933	−	0.446201i	$-0.147223\pi$
$173$	0.802919	+	1.39070i	0.0610448	+	0.105733i	−0.833888	+	0.551934i	$0.813890\pi$
$174$	−0.629711	−	8.13483i	−0.0477383	−	0.616700i
$175$	2.66200	−	2.66200i	0.201228	−	0.201228i
$176$	0.350901	−	0.350901i	0.0264502	−	0.0264502i
$177$	0.374471	+	4.83754i	0.0281470	+	0.363612i
$178$	−1.76620	−	3.05914i	−0.132382	−	0.229292i
$179$	−5.02903	−	8.71053i	−0.375887	−	0.651056i	0.614572	−	0.788861i	$-0.289329\pi$
$179$	−5.02903	−	8.71053i	−0.375887	−	0.651056i	−0.990459	+	0.137805i	$0.955995\pi$
$180$	0.494392	−	4.59034i	0.0368498	−	0.342144i
$181$		−	11.9484i		−	0.888116i	−0.895998	−	0.444058i	$-0.853538\pi$
$181$		−	11.9484i		−	0.888116i	0.895998	−	0.444058i	$-0.146462\pi$
$182$	2.80258	+	4.33011i	0.207741	+	0.320969i
$183$	−11.5663	−	2.15907i	−0.855008	−	0.159603i
$184$	−0.459552	−	1.71507i	−0.0338786	−	0.126437i
$185$	15.2090	+	8.78091i	1.11819	+	0.645585i
$186$	0.535717	+	0.100001i	0.0392807	+	0.00733245i
$187$	−0.283875	−	1.05943i	−0.0207590	−	0.0774735i
$188$	11.8388	−	3.17219i	0.863431	−	0.231356i
$189$	−5.41166	+	5.09598i	−0.393640	+	0.370678i
$190$	3.38516	+	3.38516i	0.245586	+	0.245586i
$191$	−18.9189	+	10.9228i	−1.36892	+	0.790347i	−0.990790	−	0.135405i	$-0.956767\pi$
$191$	−18.9189	+	10.9228i	−1.36892	+	0.790347i	−0.378131	+	0.925752i	$0.623433\pi$
$192$	−1.31562	−	1.12657i	−0.0949464	−	0.0813030i
$193$	−12.6457	+	3.38840i	−0.910257	+	0.243903i	−0.683416	−	0.730029i	$-0.739506\pi$
$193$	−12.6457	+	3.38840i	−0.910257	+	0.243903i	−0.226841	+	0.973932i	$0.572840\pi$
$194$	−3.68403	−	6.38093i	−0.264498	−	0.458124i
$195$	7.64123	−	5.82919i	0.547200	−	0.417437i
$196$	−2.47676	+	4.28987i	−0.176911	+	0.306419i
$197$	0.638138	−	2.38157i	0.0454655	−	0.169680i	−0.939460	−	0.342659i	$-0.888673\pi$
$197$	0.638138	−	2.38157i	0.0454655	−	0.169680i	0.984926	+	0.172979i	$0.0553393\pi$
$198$	0.229113	+	1.47101i	0.0162824	+	0.104540i
$199$	−18.1467	−	10.4770i	−1.28639	−	0.742697i	−0.308380	−	0.951263i	$-0.599787\pi$
$199$	−18.1467	−	10.4770i	−1.28639	−	0.742697i	−0.978008	+	0.208567i	$0.933120\pi$
$200$	−2.54192	+	0.681106i	−0.179741	+	0.0481615i
$201$	−12.3775	−	5.92328i	−0.873039	−	0.417796i
$202$	3.90236	+	3.90236i	0.274569	+	0.274569i
$203$	−6.50928	−	1.74416i	−0.456862	−	0.122416i
$204$	−3.61023	+	1.27323i	−0.252766	+	0.0891440i
$205$			12.3950i			0.865702i
$206$	14.5621	+	3.90189i	1.01459	+	0.271858i
$207$	4.96800	+	1.92170i	0.345300	+	0.133567i
$208$	−0.183180	−	3.60090i	−0.0127013	−	0.249677i
$209$	−1.33689	−	0.771857i	−0.0924750	−	0.0533904i
$210$	−3.43965	−	1.64606i	−0.237359	−	0.113589i
$211$	7.06391	−	12.2350i	0.486299	−	0.842295i	−0.513577	−	0.858044i	$-0.671680\pi$
$211$	7.06391	−	12.2350i	0.486299	−	0.842295i	0.999876	+	0.0157485i	$0.00501311\pi$
$212$	2.02719			0.139228
$213$	−8.40356	+	17.5603i	−0.575803	+	1.20322i
$214$	12.1180	+	3.24702i	0.828372	+	0.221962i
$215$	−0.646139	−	2.41142i	−0.0440663	−	0.164458i
$216$	5.05722	−	1.19354i	0.344100	−	0.0812099i
$217$	0.225054	−	0.389805i	0.0152777	−	0.0264617i
$218$	−9.79673			−0.663518
$219$	10.8743	−	0.841773i	0.734818	−	0.0568817i
$220$	−0.661392	+	0.381855i	−0.0445911	+	0.0257447i
$221$	−7.09484	−	3.62871i	−0.477251	−	0.244094i
$222$	−3.62689	+	19.4296i	−0.243421	+	1.30403i
$223$	−6.48118	+	6.48118i	−0.434012	+	0.434012i	−0.889991	−	0.455979i	$-0.849289\pi$
$223$	−6.48118	+	6.48118i	−0.434012	+	0.434012i	0.455979	+	0.889991i	$0.349289\pi$
$224$	−1.23890	+	0.715277i	−0.0827772	+	0.0477914i
$225$	2.84816	−	7.36311i	0.189877	−	0.490874i
$226$	−10.1162	+	10.1162i	−0.672923	+	0.672923i
$227$	−6.83510	+	25.5089i	−0.453661	+	1.69309i	0.238333	+	0.971184i	$0.423399\pi$
$227$	−6.83510	+	25.5089i	−0.453661	+	1.69309i	−0.691994	+	0.721903i	$0.743267\pi$
$228$	−2.32584	+	4.86014i	−0.154032	+	0.321871i
$229$	−3.68017	+	13.7346i	−0.243193	+	0.907607i	0.731091	+	0.682280i	$0.239012\pi$
$229$	−3.68017	+	13.7346i	−0.243193	+	0.907607i	−0.974283	+	0.225327i	$0.927655\pi$
$230$			2.73254i			0.180179i
$231$	1.20872	+	0.225630i	0.0795282	+	0.0148454i
$232$	3.33096	+	3.33096i	0.218688	+	0.218688i
$233$	21.4490			1.40517			0.702586	−	0.711599i	$-0.252029\pi$
$233$	21.4490			1.40517			0.702586	+	0.711599i	$0.252029\pi$
$234$	9.04737	+	5.92834i	0.591445	+	0.387547i
$235$	−18.8622			−1.23043
$236$	−1.98083	−	1.98083i	−0.128941	−	0.128941i
$237$	−5.49927	−	15.5931i	−0.357216	−	1.01288i
$238$			3.16180i			0.204949i
$239$	2.03511	−	7.59513i	0.131640	−	0.491288i	−0.868349	−	0.495954i	$-0.834819\pi$
$239$	2.03511	−	7.59513i	0.131640	−	0.491288i	0.999989	+	0.00466587i	$0.00148520\pi$
$240$	1.50697	+	2.19870i	0.0972744	+	0.141925i
$241$	4.79042	−	17.8781i	0.308578	−	1.15163i	−0.621243	−	0.783618i	$-0.713372\pi$
$241$	4.79042	−	17.8781i	0.308578	−	1.15163i	0.929821	−	0.368011i	$-0.119961\pi$
$242$	−7.60404	+	7.60404i	−0.488806	+	0.488806i
$243$	−6.05782	+	14.3632i	−0.388610	+	0.921403i
$244$	5.88306	−	3.39659i	0.376624	−	0.217444i
$245$	5.39048	−	5.39048i	0.344385	−	0.344385i
$246$	−13.1559	+	4.63975i	−0.838791	+	0.295819i
$247$	−10.6724	+	3.44958i	−0.679066	+	0.219491i
$248$	−0.272485	+	0.157320i	−0.0173028	+	0.00998980i
$249$	6.29418	−	13.1525i	0.398877	−	0.833506i
$250$	11.7447			0.742803
$251$	−11.0446	+	19.1298i	−0.697127	+	1.20746i	0.272331	+	0.962204i	$0.412205\pi$
$251$	−11.0446	+	19.1298i	−0.697127	+	1.20746i	−0.969458	+	0.245256i	$0.921128\pi$
$252$	0.459565	−	4.26698i	0.0289499	−	0.268795i
$253$	−0.228053	−	0.851104i	−0.0143375	−	0.0535084i
$254$	2.79667	+	0.749366i	0.175479	+	0.0470194i
$255$	5.87384	−	0.454689i	0.367834	−	0.0284738i
$256$	1.00000			0.0625000
$257$	−15.1040	+	26.1609i	−0.942162	+	1.63187i	−0.180825	+	0.983515i	$0.557877\pi$
$257$	−15.1040	+	26.1609i	−0.942162	+	1.63187i	−0.761336	+	0.648357i	$0.775456\pi$
$258$	2.31760	−	1.58846i	0.144287	−	0.0988934i
$259$	14.1376	+	8.16235i	0.878468	+	0.507183i
$260$	−1.16198	+	5.42578i	−0.0720631	+	0.336493i
$261$	−13.9637	+	2.17488i	−0.864333	+	0.134621i
$262$	12.6278	+	3.38360i	0.780147	+	0.209040i
$263$		−	5.51204i		−	0.339887i	−0.985454	−	0.169943i	$-0.945641\pi$
$263$		−	5.51204i		−	0.339887i	0.985454	−	0.169943i	$-0.0543585\pi$
$264$	−0.652874	−	0.559059i	−0.0401816	−	0.0344077i
$265$	−3.01347	−	0.807457i	−0.185116	−	0.0496017i
$266$	3.14670	+	3.14670i	0.192937	+	0.192937i
$267$	−5.04669	+	3.45895i	−0.308852	+	0.211685i
$268$	7.65232	−	2.05043i	0.467440	−	0.125250i
$269$	−16.8180	−	9.70985i	−1.02541	−	0.592020i	−0.109743	−	0.993960i	$-0.535003\pi$
$269$	−16.8180	−	9.70985i	−1.02541	−	0.592020i	−0.915666	+	0.401940i	$0.868336\pi$
$270$	−7.99308	−	0.240134i	−0.486444	−	0.0146141i
$271$	5.79813	−	21.6389i	0.352212	−	1.31447i	−0.531746	−	0.846904i	$-0.678464\pi$
$271$	5.79813	−	21.6389i	0.352212	−	1.31447i	0.883957	−	0.467567i	$-0.154869\pi$
$272$	1.10510	−	1.91408i	0.0670063	−	0.116058i
$273$	7.10296	−	5.41856i	0.429890	−	0.327946i
$274$	3.25601	+	5.63957i	0.196703	+	0.340699i
$275$	−1.26143	+	0.337999i	−0.0760669	+	0.0203821i
$276$	−2.90030	+	1.02286i	−0.174578	+	0.0615689i
$277$	−7.64138	+	4.41176i	−0.459126	+	0.265077i	−0.711677	−	0.702507i	$-0.752064\pi$
$277$	−7.64138	+	4.41176i	−0.459126	+	0.265077i	0.252551	+	0.967584i	$0.418731\pi$
$278$	11.7959	+	11.7959i	0.707470	+	0.707470i
$279$	0.101078	−	0.938490i	0.00605137	−	0.0561859i
$280$	2.12655	−	0.569808i	0.127086	−	0.0340525i
$281$	−4.63444	−	17.2960i	−0.276467	−	1.03179i	−0.954852	−	0.297083i	$-0.903986\pi$
$281$	−4.63444	−	17.2960i	−0.276467	−	1.03179i	0.678384	−	0.734707i	$-0.262680\pi$
$282$	−7.06057	−	20.0201i	−0.420451	−	1.19218i
$283$	−6.33288	−	3.65629i	−0.376451	−	0.217344i	0.299822	−	0.953995i	$-0.403073\pi$
$283$	−6.33288	−	3.65629i	−0.376451	−	0.217344i	−0.676273	+	0.736651i	$0.736406\pi$
$284$	−2.90902	−	10.8566i	−0.172619	−	0.644222i
$285$	5.39327	−	6.29831i	0.319470	−	0.373080i
$286$	−0.0909031	−	1.78694i	−0.00537521	−	0.105664i
$287$			11.5218i			0.680111i
$288$	−1.76959	+	2.42251i	−0.104274	+	0.142748i
$289$	6.05752	+	10.4919i	0.356325	+	0.617173i
$290$	−3.62479	−	6.27833i	−0.212855	−	0.368676i
$291$	−10.5267	+	7.21488i	−0.617084	+	0.422944i
$292$	−4.45270	+	4.45270i	−0.260575	+	0.260575i
$293$	10.0863	−	10.0863i	0.589246	−	0.589246i	−0.348181	−	0.937427i	$-0.613201\pi$
$293$	10.0863	−	10.0863i	0.589246	−	0.589246i	0.937427	+	0.348181i	$0.113201\pi$
$294$	7.73920	+	3.70362i	0.451359	+	0.216000i
$295$	2.15556	+	3.73354i	0.125502	+	0.217375i
$296$	−5.70573	−	9.88261i	−0.331639	−	0.574415i
$297$	2.50964	−	0.592292i	0.145624	−	0.0343683i
$298$			10.5217i			0.609505i
$299$	−5.69969	−	2.91515i	−0.329622	−	0.168588i
$300$	1.51599	+	4.29856i	0.0875256	+	0.248177i
$301$	−0.600622	−	2.24155i	−0.0346193	−	0.129201i
$302$	−14.8845	−	8.59357i	−0.856506	−	0.494504i
$303$	6.21728	−	7.26059i	0.357173	−	0.417110i
$304$	−0.805124	−	3.00476i	−0.0461770	−	0.172335i
$305$	−10.0982	+	2.70581i	−0.578223	+	0.154934i
$306$	2.68133	+	6.06424i	0.153281	+	0.346670i
$307$	15.5883	+	15.5883i	0.889669	+	0.889669i	0.994491	−	0.104822i	$-0.0334273\pi$
$307$	15.5883	+	15.5883i	0.889669	+	0.889669i	−0.104822	+	0.994491i	$0.533427\pi$
$308$	−0.614801	+	0.354956i	−0.0350316	+	0.0202255i
$309$	4.79150	−	25.6686i	0.272579	−	1.46023i
$310$	0.467719	−	0.125325i	0.0265646	−	0.00711798i
$311$	−12.3786	−	21.4403i	−0.701923	−	1.21577i	−0.967790	−	0.251757i	$-0.918992\pi$
$311$	−12.3786	−	21.4403i	−0.701923	−	1.21577i	0.265867	−	0.964010i	$-0.414342\pi$
$312$	−6.19384	+	0.797688i	−0.350657	+	0.0451602i
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.0920148	−	0.995758i	$-0.470669\pi$
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.816344	−	0.577566i	$-0.195997\pi$
$314$	5.66905	−	21.1572i	0.319923	−	1.19397i
$315$	−2.38275	+	6.15992i	−0.134253	+	0.347072i
$316$	8.26720	+	4.77307i	0.465066	+	0.268506i
$317$	28.9067	−	7.74554i	1.62356	−	0.435033i	0.671518	−	0.740988i	$-0.265643\pi$
$317$	28.9067	−	7.74554i	1.62356	−	0.435033i	0.952046	+	0.305956i	$0.0989759\pi$
$318$	−0.270989	−	3.50073i	−0.0151963	−	0.196311i
$319$	1.65299	+	1.65299i	0.0925496	+	0.0925496i
$320$	−1.48652	−	0.398313i	−0.0830993	−	0.0222664i
$321$	3.98733	−	21.3605i	0.222551	−	1.19223i
$322$			2.54005i			0.141552i
$323$	−6.64110	−	1.77948i	−0.369521	−	0.0990128i
$324$	−2.73713	−	8.57369i	−0.152063	−	0.476316i
$325$	−4.32057	+	8.44756i	−0.239662	+	0.468586i
$326$	4.60538	+	2.65892i	0.255069	+	0.147264i
$327$	1.30960	+	16.9178i	0.0724208	+	0.935557i
$328$	4.02705	−	6.97505i	0.222357	−	0.385133i
$329$	−17.5334			−0.966649
$330$	0.747833	+	1.09110i	0.0411668	+	0.0600633i
$331$	−6.40799	−	1.71702i	−0.352215	−	0.0943758i	0.0783735	−	0.996924i	$-0.475027\pi$
$331$	−6.40799	−	1.71702i	−0.352215	−	0.0943758i	−0.430589	+	0.902548i	$0.641694\pi$
$332$	2.17883	+	8.13149i	0.119579	+	0.446273i
$333$	34.0375	+	3.66593i	1.86524	+	0.200892i
$334$	5.42465	−	9.39577i	0.296824	−	0.514113i
$335$	−12.1921			−0.666124
$336$	1.40081	+	2.04381i	0.0764205	+	0.111499i
$337$	−20.1675	+	11.6437i	−1.09859	+	0.634274i	−0.935851	−	0.352395i	$-0.885367\pi$
$337$	−20.1675	+	11.6437i	−1.09859	+	0.634274i	−0.162743	+	0.986669i	$0.552034\pi$
$338$	−10.0778	−	8.21210i	−0.548158	−	0.446679i
$339$	18.8219	+	16.1173i	1.02227	+	0.875371i
$340$	−2.40516	+	2.40516i	−0.130438	+	0.130438i
$341$	−0.135221	+	0.0780698i	−0.00732262	+	0.00422772i
$342$	8.70381	+	3.36676i	0.470648	+	0.182054i
$343$	12.0916	−	12.0916i	0.652886	−	0.652886i
$344$	−0.419853	+	1.56691i	−0.0226370	+	0.0844823i
$345$	4.71879	−	0.365278i	0.254051	−	0.0196659i
$346$	−0.415621	+	1.55112i	−0.0223439	+	0.0833887i
$347$			20.1798i			1.08331i	0.840601	+	0.541655i	$0.182202\pi$
$347$			20.1798i			1.08331i	−0.840601	+	0.541655i	$0.817798\pi$
$348$	5.30692	−	6.19746i	0.284481	−	0.332219i
$349$	17.7481	+	17.7481i	0.950033	+	0.950033i	0.998810	−	0.0487771i	$-0.0155324\pi$
$349$	17.7481	+	17.7481i	0.950033	+	0.950033i	−0.0487771	+	0.998810i	$0.515532\pi$
$350$	3.76463			0.201228
$351$	9.02813	−	16.4162i	0.481886	−	0.876234i
$352$	0.496250			0.0264502
$353$	18.4478	+	18.4478i	0.981880	+	0.981880i	0.999839	−	0.0179591i	$-0.00571687\pi$
$353$	18.4478	+	18.4478i	0.981880	+	0.981880i	−0.0179591	+	0.999839i	$0.505717\pi$
$354$	−3.15587	+	3.68545i	−0.167733	+	0.195880i
$355$			17.2973i			0.918047i
$356$	0.914251	−	3.41203i	0.0484552	−	0.180837i
$357$	5.46006	−	0.422659i	0.288977	−	0.0223695i
$358$	2.60322	−	9.71534i	0.137584	−	0.513471i
$359$	−23.1726	+	23.1726i	−1.22300	+	1.22300i	−0.256444	+	0.966559i	$0.582551\pi$
$359$	−23.1726	+	23.1726i	−1.22300	+	1.22300i	−0.966559	+	0.256444i	$0.917449\pi$
$360$	3.59545	−	2.89628i	0.189497	−	0.152647i
$361$	8.07411	−	4.66159i	0.424953	−	0.245347i
$362$	8.44878	−	8.44878i	0.444058	−	0.444058i
$363$	14.1478	+	12.1148i	0.742566	+	0.635863i
$364$	−1.08013	+	5.04357i	−0.0566141	+	0.264355i
$365$	8.39262	−	4.84548i	0.439290	−	0.253624i
$366$	−6.65194	−	9.70532i	−0.347703	−	0.507305i
$367$	0.585320			0.0305535			0.0152767	−	0.999883i	$-0.495137\pi$
$367$	0.585320			0.0305535			0.0152767	+	0.999883i	$0.495137\pi$
$368$	0.887787	−	1.53769i	0.0462791	−	0.0801577i
$369$	9.77095	+	22.0985i	0.508655	+	1.15040i
$370$	4.54533	+	16.9634i	0.236301	+	0.881886i
$371$	−2.80119	−	0.750577i	−0.145431	−	0.0389680i
$372$	0.308098	+	0.449521i	0.0159741	+	0.0233066i
$373$	27.3780			1.41758			0.708790	−	0.705420i	$-0.249242\pi$
$373$	27.3780			1.41758			0.708790	+	0.705420i	$0.249242\pi$
$374$	0.548404	−	0.949863i	0.0283573	−	0.0491162i
$375$	−1.57000	−	20.2818i	−0.0810745	−	1.04735i
$376$	10.6144	+	6.12820i	0.547393	+	0.316038i
$377$	16.9627	−	0.862906i	0.873624	−	0.0444419i
$378$	−7.43002	−	0.223218i	−0.382159	−	0.0114811i
$379$	3.11912	+	0.835766i	0.160219	+	0.0429304i	0.338037	−	0.941133i	$-0.390237\pi$
$379$	3.11912	+	0.835766i	0.160219	+	0.0429304i	−0.177818	+	0.984063i	$0.556904\pi$
$380$			4.78735i			0.245586i
$381$	0.920218	−	4.92970i	0.0471442	−	0.252556i
$382$	−21.1013	−	5.65407i	−1.07963	−	0.289287i
$383$	−9.97127	−	9.97127i	−0.509508	−	0.509508i	0.404867	−	0.914375i	$-0.367318\pi$
$383$	−9.97127	−	9.97127i	−0.509508	−	0.509508i	−0.914375	+	0.404867i	$0.867318\pi$
$384$	−0.133677	−	1.72688i	−0.00682167	−	0.0881247i
$385$	1.05530	−	0.282767i	0.0537831	−	0.0144111i
$386$	−11.3378	−	6.54589i	−0.577080	−	0.333177i
$387$	−3.05290	−	3.78989i	−0.155188	−	0.192651i
$388$	1.90700	−	7.11700i	0.0968130	−	0.361311i
$389$	−9.97462	+	17.2765i	−0.505733	+	0.875956i	0.494245	+	0.869323i	$0.335445\pi$
$389$	−9.97462	+	17.2765i	−0.505733	+	0.875956i	−0.999978	+	0.00663286i	$0.997889\pi$
$390$	9.52503	+	1.28131i	0.482319	+	0.0648815i
$391$	−1.96218	−	3.39859i	−0.0992317	−	0.171874i
$392$	−4.78473	+	1.28206i	−0.241665	+	0.0647540i
$393$	4.15505	−	22.2590i	0.209595	−	1.12282i
$394$	2.13525	−	1.23279i	0.107572	−	0.0621070i
$395$	−10.3882	−	10.3882i	−0.522688	−	0.522688i
$396$	−0.878156	+	1.20217i	−0.0441290	+	0.0604114i
$397$	17.9027	−	4.79700i	0.898509	−	0.240755i	0.220133	−	0.975470i	$-0.429351\pi$
$397$	17.9027	−	4.79700i	0.898509	−	0.240755i	0.678376	+	0.734715i	$0.262684\pi$
$398$	−5.42331	−	20.2401i	−0.271846	−	1.01454i
$399$	5.01335	−	5.85463i	0.250981	−	0.293098i
$400$	−2.27902	−	1.31580i	−0.113951	−	0.0657898i
$401$	4.08357	+	15.2401i	0.203924	+	0.761055i	0.989775	+	0.142639i	$0.0455586\pi$
$401$	4.08357	+	15.2401i	0.203924	+	0.761055i	−0.785851	+	0.618416i	$0.787775\pi$
$402$	−4.56380	−	12.9406i	−0.227622	−	0.645417i
$403$	−0.237566	+	1.10929i	−0.0118340	+	0.0552579i
$404$			5.51878i			0.274569i
$405$	0.653806	+	13.8352i	0.0324879	+	0.687478i
$406$	−3.36945	−	5.83606i	−0.167223	−	0.289639i
$407$	−2.83147	−	4.90424i	−0.140351	−	0.243094i
$408$	−3.45313	−	1.65250i	−0.170955	−	0.0818112i
$409$	7.86755	−	7.86755i	0.389025	−	0.389025i	−0.485314	−	0.874340i	$-0.661295\pi$
$409$	7.86755	−	7.86755i	0.389025	−	0.389025i	0.874340	+	0.485314i	$0.161295\pi$
$410$	−8.76456	+	8.76456i	−0.432851	+	0.432851i
$411$	9.30363	−	6.37663i	0.458914	−	0.314536i
$412$	7.53787	+	13.0560i	0.371364	+	0.643222i
$413$	2.00371	+	3.47053i	0.0985963	+	0.170774i
$414$	2.15406	+	4.87175i	0.105866	+	0.239434i
$415$		−	12.9555i		−	0.635961i
$416$	2.41669	−	2.67575i	0.118488	−	0.131189i
$417$	18.7933	−	21.9470i	0.920312	−	1.07475i
$418$	−0.399542	−	1.49111i	−0.0195423	−	0.0729327i
$419$	0.396684	+	0.229025i	0.0193793	+	0.0111886i	0.509658	−	0.860377i	$-0.329772\pi$
$419$	0.396684	+	0.229025i	0.0193793	+	0.0111886i	−0.490279	+	0.871566i	$0.663105\pi$
$420$	−1.26826	−	3.59614i	−0.0618849	−	0.175474i
$421$	−1.17205	−	4.37413i	−0.0571220	−	0.213182i	0.931466	−	0.363829i	$-0.118531\pi$
$421$	−1.17205	−	4.37413i	−0.0571220	−	0.213182i	−0.988588	+	0.150647i	$0.951864\pi$
$422$	13.6464	−	3.65655i	0.664297	−	0.177998i
$423$	−33.6286	+	14.8690i	−1.63508	+	0.722957i
$424$	1.43344	+	1.43344i	0.0696140	+	0.0696140i
$425$	−5.03708	+	2.90816i	−0.244334	+	0.141067i
$426$	−18.3593	+	6.47482i	−0.889509	+	0.313706i
$427$	−9.38686	+	2.51520i	−0.454262	+	0.121719i
$428$	6.27276	+	10.8647i	0.303205	+	0.525167i
$429$	−3.07369	+	0.395852i	−0.148399	+	0.0191119i
$430$	1.24824	−	2.16202i	0.0601957	−	0.104262i
$431$	−3.86478	+	14.4235i	−0.186160	+	0.694758i	0.808220	+	0.588881i	$0.200431\pi$
$431$	−3.86478	+	14.4235i	−0.186160	+	0.694758i	−0.994379	+	0.105876i	$0.966235\pi$
$432$	4.41995	+	2.73204i	0.212655	+	0.131445i
$433$	−3.91621	−	2.26103i	−0.188201	−	0.108658i	0.402939	−	0.915227i	$-0.367989\pi$
$433$	−3.91621	−	2.26103i	−0.188201	−	0.108658i	−0.591140	+	0.806569i	$0.701322\pi$
$434$	0.434771	−	0.116497i	0.0208697	−	0.00559201i
$435$	−10.3574	+	7.09887i	−0.496599	+	0.340365i
$436$	−6.92733	−	6.92733i	−0.331759	−	0.331759i
$437$	−5.33518	−	1.42956i	−0.255216	−	0.0683850i
$438$	8.28452	+	7.09408i	0.395850	+	0.338968i
$439$			13.3562i			0.637455i	0.947846	+	0.318728i	$0.103256\pi$
$439$			13.3562i			0.637455i	−0.947846	+	0.318728i	$0.896744\pi$
$440$	−0.737687	−	0.197663i	−0.0351679	−	0.00942320i
$441$	5.36117	−	13.8598i	0.255294	−	0.659990i
$442$	−2.45092	−	7.58270i	−0.116579	−	0.360672i
$443$	26.7016	+	15.4162i	1.26863	+	0.732445i	0.974729	−	0.223390i	$-0.0717124\pi$
$443$	26.7016	+	15.4162i	1.26863	+	0.732445i	0.293903	+	0.955835i	$0.405046\pi$
$444$	−16.3034	+	11.1742i	−0.773725	+	0.530305i
$445$	−2.71811	+	4.70791i	−0.128851	+	0.223176i
$446$	−9.16578			−0.434012
$447$	18.1697	−	1.40651i	0.859399	−	0.0665254i
$448$	−1.38181	−	0.370254i	−0.0652843	−	0.0174929i
$449$	−10.3894	−	38.7738i	−0.490306	−	1.82985i	−0.554874	−	0.831934i	$-0.687234\pi$
$449$	−10.3894	−	38.7738i	−0.490306	−	1.82985i	0.0645682	−	0.997913i	$-0.479433\pi$
$450$	7.22046	−	3.19255i	0.340376	−	0.150498i
$451$	1.99842	−	3.46137i	0.0941020	−	0.162989i
$452$	−14.3065			−0.672923
$453$	−12.8504	+	26.8526i	−0.603764	+	1.26164i
$454$	−22.8707	+	13.2044i	−1.07337	+	0.619713i
$455$	3.61456	−	7.06716i	0.169453	−	0.331314i
$456$	−5.08125	+	1.79202i	−0.237951	+	0.0839192i
$457$	−11.6746	+	11.6746i	−0.546115	+	0.546115i	−0.925315	−	0.379199i	$-0.876199\pi$
$457$	−11.6746	+	11.6746i	−0.546115	+	0.546115i	0.379199	+	0.925315i	$0.376199\pi$
$458$	−12.3141	+	7.10955i	−0.575400	+	0.332207i
$459$	10.1138	−	5.44099i	0.472072	−	0.253964i
$460$	−1.93220	+	1.93220i	−0.0900893	+	0.0900893i
$461$	3.57300	−	13.3346i	0.166411	−	0.621055i	−0.831445	−	0.555607i	$-0.812486\pi$
$461$	3.57300	−	13.3346i	0.166411	−	0.621055i	0.997856	−	0.0654474i	$-0.0208475\pi$
$462$	0.695152	+	1.01424i	0.0323414	+	0.0471868i
$463$	−9.96318	+	37.1831i	−0.463028	+	1.72805i	0.200316	+	0.979731i	$0.435803\pi$
$463$	−9.96318	+	37.1831i	−0.463028	+	1.72805i	−0.663345	+	0.748314i	$0.730864\pi$
$464$			4.71069i			0.218688i
$465$	−0.278945	−	0.790943i	−0.0129358	−	0.0366791i
$466$	15.1667	+	15.1667i	0.702586	+	0.702586i
$467$	−8.54433			−0.395385			−0.197692	−	0.980264i	$-0.563345\pi$
$467$	−8.54433			−0.395385			−0.197692	+	0.980264i	$0.563345\pi$
$468$	2.20549	+	10.5894i	0.101949	+	0.489496i
$469$	−11.3332			−0.523319
$470$	−13.3376	−	13.3376i	−0.615216	−	0.615216i
$471$	−37.2938	−	6.96157i	−1.71841	−	0.320772i
$472$		−	2.80131i		−	0.128941i
$473$	−0.208352	+	0.777580i	−0.00958003	+	0.0357532i
$474$	7.13741	−	14.9145i	0.327832	−	0.685048i
$475$	−2.11876	+	7.90731i	−0.0972152	+	0.362812i
$476$	−2.23573	+	2.23573i	−0.102474	+	0.102474i
$477$	−6.00912	+	0.935932i	−0.275139	+	0.0428534i
$478$	6.80960	−	3.93153i	0.311464	−	0.179824i
$479$	−6.26732	+	6.26732i	−0.286361	+	0.286361i	−0.835640	−	0.549278i	$-0.814903\pi$
$479$	−6.26732	+	6.26732i	−0.286361	+	0.286361i	0.549278	+	0.835640i	$0.314903\pi$
$480$	−0.489127	+	2.62030i	−0.0223255	+	0.119600i
$481$	−40.2323	−	8.61612i	−1.83444	−	0.392861i
$482$	16.0291	−	9.25438i	0.730104	−	0.421526i
$483$	4.38638	−	0.339546i	0.199587	−	0.0154499i
$484$	−10.7537			−0.488806
$485$	−5.66959	+	9.82002i	−0.257443	+	0.445904i
$486$	−14.4399	+	5.87282i	−0.655006	+	0.266396i
$487$	−2.81256	−	10.4966i	−0.127449	−	0.475648i	0.872466	−	0.488675i	$-0.162520\pi$
$487$	−2.81256	−	10.4966i	−0.127449	−	0.475648i	−0.999915	+	0.0130276i	$0.995853\pi$
$488$	6.56170	+	1.75820i	0.297034	+	0.0795901i
$489$	3.97601	−	8.30840i	0.179802	−	0.375719i
$490$	7.62328			0.344385
$491$	−8.67309	+	15.0222i	−0.391411	+	0.677944i	−0.992636	−	0.121136i	$-0.961346\pi$
$491$	−8.67309	+	15.0222i	−0.391411	+	0.677944i	0.601225	+	0.799080i	$0.294680\pi$
$492$	−12.5834	−	6.02185i	−0.567305	−	0.271486i
$493$	9.01666	+	5.20577i	0.406090	+	0.234456i
$494$	−9.98571	−	5.10727i	−0.449279	−	0.229787i
$495$	1.78424	−	1.43728i	0.0801957	−	0.0646007i
$496$	−0.303918	−	0.0814346i	−0.0136463	−	0.00365652i
$497$			16.0788i			0.721235i
$498$	13.7509	−	4.84957i	0.616192	−	0.217315i
$499$	11.4069	+	3.05648i	0.510644	+	0.136827i	0.504936	−	0.863157i	$-0.331516\pi$
$499$	11.4069	+	3.05648i	0.510644	+	0.136827i	0.00570844	+	0.999984i	$0.498183\pi$
$500$	8.30479	+	8.30479i	0.371401	+	0.371401i
$501$	−16.9506	−	8.11174i	−0.757295	−	0.362406i
$502$	−21.3365	+	5.71709i	−0.952294	+	0.255166i
$503$	20.1247	+	11.6190i	0.897316	+	0.518066i	0.876329	−	0.481714i	$-0.159986\pi$
$503$	20.1247	+	11.6190i	0.897316	+	0.518066i	0.0209877	+	0.999780i	$0.493319\pi$
$504$	3.34217	−	2.69225i	0.148872	−	0.119922i
$505$	2.19820	−	8.20380i	0.0978186	−	0.365064i
$506$	0.440564	−	0.763079i	0.0195855	−	0.0339230i
$507$	−12.8342	+	18.5009i	−0.569986	+	0.821654i
$508$	1.44766	+	2.50743i	0.0642297	+	0.111249i
$509$	−3.45775	+	0.926500i	−0.153262	+	0.0410664i	−0.334634	−	0.942348i	$-0.608613\pi$
$509$	−3.45775	+	0.926500i	−0.153262	+	0.0410664i	0.181372	+	0.983415i	$0.441946\pi$
$510$	4.47494	+	3.83191i	0.198154	+	0.169680i
$511$	7.80141	−	4.50415i	0.345114	−	0.199252i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.65051	−	15.4805i	0.205325	−	0.683482i
$514$	−29.1787	+	7.81841i	−1.28702	+	0.344855i
$515$	−6.00487	−	22.4105i	−0.264606	−	0.987523i
$516$	2.76200	+	0.515578i	0.121590	+	0.0226971i
$517$	5.26737	+	3.04112i	0.231659	+	0.133748i
$518$	4.22514	+	15.7684i	0.185642	+	0.692826i
$519$	2.73416	+	0.510381i	0.120017	+	0.0224033i
$520$	−4.65825	+	3.01496i	−0.204278	+	0.132215i
$521$			4.89726i			0.214553i	0.994229	+	0.107277i	$0.0342130\pi$
$521$			4.89726i			0.214553i	−0.994229	+	0.107277i	$0.965787\pi$
$522$	−11.4117	−	8.33598i	−0.499477	−	0.364856i
$523$	0.745466	+	1.29119i	0.0325970	+	0.0564596i	0.881864	−	0.471504i	$-0.156289\pi$
$523$	0.745466	+	1.29119i	0.0325970	+	0.0564596i	−0.849267	+	0.527964i	$0.822956\pi$
$524$	6.53662	+	11.3218i	0.285553	+	0.494593i
$525$	−0.503244	−	6.50108i	−0.0219634	−	0.283730i
$526$	3.89760	−	3.89760i	0.169943	−	0.169943i
$527$	−0.491731	+	0.491731i	−0.0214202	+	0.0214202i
$528$	−0.0663371	−	0.856966i	−0.00288695	−	0.0372947i
$529$	9.92367	+	17.1883i	0.431464	+	0.747317i
$530$	−1.55989	−	2.70180i	−0.0677572	−	0.117359i
$531$	6.78622	+	4.95716i	0.294497	+	0.215123i
$532$			4.45011i			0.192937i
$533$	−8.93134	−	27.6319i	−0.386859	−	1.19687i
$534$	−6.01440	−	1.12270i	−0.260268	−	0.0485838i
$535$	−4.99704	−	18.6492i	−0.216041	−	0.806276i
$536$	6.86088	+	3.96113i	0.296345	+	0.171095i
$537$	−17.1253	−	3.19674i	−0.739009	−	0.137949i
$538$	−5.02619	−	18.7580i	−0.216694	−	0.808714i
$539$	−2.37442	+	0.636224i	−0.102274	+	0.0274041i
$540$	−5.48216	−	5.82176i	−0.235915	−	0.250529i
$541$	−1.70268	−	1.70268i	−0.0732039	−	0.0732039i	0.669557	−	0.742761i	$-0.266484\pi$
$541$	−1.70268	−	1.70268i	−0.0732039	−	0.0732039i	−0.742761	+	0.669557i	$0.766484\pi$
$542$	19.4009	−	11.2011i	0.833341	−	0.481130i
$543$	−15.7195	−	13.4607i	−0.674587	−	0.577652i
$544$	2.13488	−	0.572040i	0.0915323	−	0.0245260i
$545$	7.53840	+	13.0569i	0.322910	+	0.559296i
$546$	8.85405	+	1.19105i	0.378918	+	0.0509721i
$547$	6.38104	−	11.0523i	0.272833	−	0.472561i	−0.696753	−	0.717311i	$-0.745373\pi$
$547$	6.38104	−	11.0523i	0.272833	−	0.472561i	0.969586	+	0.244750i	$0.0787059\pi$
$548$	−1.68543	+	6.29012i	−0.0719981	+	0.268701i
$549$	−15.8708	+	12.7845i	−0.677348	+	0.545630i
$550$	−1.13097	−	0.652963i	−0.0482245	−	0.0278424i
$551$	14.1545	−	3.79269i	0.603003	−	0.161574i
$552$	−2.77409	−	1.32755i	−0.118073	−	0.0565043i
$553$	−9.65643	−	9.65643i	−0.410633	−	0.410633i
$554$	−8.52286	−	2.28369i	−0.362102	−	0.0970248i
$555$	28.6862	−	10.1169i	1.21766	−	0.429438i
$556$			16.6819i			0.707470i
$557$	11.2158	+	3.00527i	0.475229	+	0.127337i	0.488480	−	0.872575i	$-0.337551\pi$
$557$	11.2158	+	3.00527i	0.475229	+	0.127337i	−0.0132513	+	0.999912i	$0.504218\pi$
$558$	0.735085	−	0.592140i	0.0311186	−	0.0250673i
$559$	3.17801	+	4.91016i	0.134415	+	0.207678i
$560$	1.90661	+	1.10078i	0.0805692	+	0.0465166i
$561$	−1.71361	−	0.820055i	−0.0723488	−	0.0346227i
$562$	8.95305	−	15.5071i	0.377661	−	0.654129i
$563$	40.8646			1.72224			0.861119	−	0.508403i	$-0.169764\pi$
$563$	40.8646			1.72224			0.861119	+	0.508403i	$0.169764\pi$
$564$	9.16380	−	19.1490i	0.385866	−	0.806317i
$565$	21.2670	+	5.69848i	0.894710	+	0.239737i
$566$	−1.89264	−	7.06341i	−0.0795534	−	0.296897i
$567$	0.607750	+	12.8606i	0.0255231	+	0.540096i
$568$	5.61980	−	9.73378i	0.235802	−	0.408420i
$569$	−6.41366			−0.268875			−0.134437	−	0.990922i	$-0.542923\pi$
$569$	−6.41366			−0.268875			−0.134437	+	0.990922i	$0.542923\pi$
$570$	8.26719	−	0.639958i	0.346275	−	0.0268049i
$571$	−11.8701	+	6.85319i	−0.496747	+	0.286797i	−0.727369	−	0.686246i	$-0.759257\pi$
$571$	−11.8701	+	6.85319i	−0.496747	+	0.286797i	0.230622	+	0.973043i	$0.425924\pi$
$572$	1.19928	−	1.32784i	0.0501445	−	0.0555197i
$573$	−6.94317	+	37.1953i	−0.290055	+	1.55385i
$574$	−8.14715	+	8.14715i	−0.340056	+	0.340056i
$575$	−4.04658	+	2.33629i	−0.168754	+	0.0974301i
$576$	−2.96426	+	0.461689i	−0.123511	+	0.0192370i
$577$	−10.8626	+	10.8626i	−0.452214	+	0.452214i	−0.896089	−	0.443875i	$-0.853604\pi$
$577$	−10.8626	+	10.8626i	−0.452214	+	0.452214i	0.443875	+	0.896089i	$0.353604\pi$
$578$	−3.13561	+	11.7022i	−0.130424	+	0.486749i
$579$	−9.78840	+	20.4541i	−0.406792	+	0.850045i
$580$	1.87633	−	7.00256i	0.0779104	−	0.290766i
$581$		−	12.0429i		−	0.499623i
$582$	−12.5452	−	2.34178i	−0.520014	−	0.0970700i
$583$	0.711344	+	0.711344i	0.0294609	+	0.0294609i
$584$	−6.29707			−0.260575
$585$	0.939392	−	16.6199i	0.0388391	−	0.687149i
$586$	14.2641			0.589246
$587$	1.80828	+	1.80828i	0.0746357	+	0.0746357i	0.743439	−	0.668804i	$-0.233193\pi$
$587$	1.80828	+	1.80828i	0.0746357	+	0.0746357i	−0.668804	+	0.743439i	$0.733193\pi$
$588$	2.85359	+	8.09130i	0.117680	+	0.333679i
$589$			0.978767i			0.0403294i
$590$	−1.11580	+	4.16422i	−0.0459368	+	0.171438i
$591$	−2.41432	−	3.52254i	−0.0993118	−	0.144898i
$592$	2.95350	−	11.0226i	0.121388	−	0.453027i
$593$	15.9796	−	15.9796i	0.656204	−	0.656204i	−0.298276	−	0.954480i	$-0.596412\pi$
$593$	15.9796	−	15.9796i	0.656204	−	0.656204i	0.954480	+	0.298276i	$0.0964115\pi$
$594$	2.19340	+	1.35577i	0.0899963	+	0.0556280i
$595$	4.21399	−	2.43295i	0.172757	−	0.0997411i
$596$	−7.43995	+	7.43995i	−0.304752	+	0.304752i
$597$	−34.2273	+	12.0711i	−1.40083	+	0.494035i
$598$	−1.96897	−	6.09161i	−0.0805170	−	0.249105i
$599$	20.6867	−	11.9435i	0.845237	−	0.487998i	−0.0138036	−	0.999905i	$-0.504394\pi$
$599$	20.6867	−	11.9435i	0.845237	−	0.487998i	0.859041	+	0.511907i	$0.171061\pi$
$600$	−1.96757	+	4.11150i	−0.0803259	+	0.167851i
$601$	−25.4119			−1.03657			−0.518287	−	0.855207i	$-0.673430\pi$
$601$	−25.4119			−1.03657			−0.518287	+	0.855207i	$0.673430\pi$
$602$	1.16031	−	2.00972i	0.0472908	−	0.0819101i
$603$	−21.7368	+	9.61101i	−0.885191	+	0.391391i
$604$	−4.44836	−	16.6015i	−0.181001	−	0.675505i
$605$	15.9857	+	4.28335i	0.649911	+	0.174143i
$606$	9.53029	−	0.737733i	0.387142	−	0.0299683i
$607$	20.6007			0.836156			0.418078	−	0.908411i	$-0.362704\pi$
$607$	20.6007			0.836156			0.418078	+	0.908411i	$0.362704\pi$
$608$	1.55538	−	2.69400i	0.0630790	−	0.109256i
$609$	−9.62778	+	6.59880i	−0.390137	+	0.267397i
$610$	−9.05382	−	5.22722i	−0.366578	−	0.211644i
$611$	42.0491	−	13.5913i	1.70112	−	0.549847i
$612$	−2.39208	+	6.18405i	−0.0966942	+	0.249975i
$613$	−6.32348	−	1.69437i	−0.255403	−	0.0684350i	0.128846	−	0.991665i	$-0.458873\pi$
$613$	−6.32348	−	1.69437i	−0.255403	−	0.0684350i	−0.384249	+	0.923230i	$0.625539\pi$
$614$			22.0451i			0.889669i
$615$	16.3070	+	13.9638i	0.657562	+	0.563074i
$616$	−0.685722	−	0.183739i	−0.0276285	−	0.00740304i
$617$	11.2968	+	11.2968i	0.454794	+	0.454794i	0.896942	−	0.442148i	$-0.145784\pi$
$617$	11.2968	+	11.2968i	0.454794	+	0.454794i	−0.442148	+	0.896942i	$0.645784\pi$
$618$	21.5385	−	14.7623i	0.866407	−	0.593828i
$619$	−21.8012	+	5.84160i	−0.876263	+	0.234794i	−0.668794	−	0.743448i	$-0.733189\pi$
$619$	−21.8012	+	5.84160i	−0.876263	+	0.234794i	−0.207469	+	0.978242i	$0.566523\pi$
$620$	0.419345	+	0.242109i	0.0168413	+	0.00972334i
$621$	8.12500	−	4.37106i	0.326045	−	0.175405i
$622$	6.40761	−	23.9135i	0.256922	−	0.958845i
$623$	−2.52664	+	4.37627i	−0.101228	+	0.175331i
$624$	−4.94376	−	3.81566i	−0.197909	−	0.152749i
$625$	−2.45839	−	4.25805i	−0.0983355	−	0.170322i
$626$	31.0458	−	8.31871i	1.24084	−	0.332482i
$627$	−2.52157	+	0.889291i	−0.100702	+	0.0355149i
$628$	18.9690	−	10.9518i	0.756946	−	0.437023i
$629$	−17.8343	−	17.8343i	−0.711100	−	0.711100i
$630$	−6.04058	+	2.67087i	−0.240663	+	0.106410i
$631$	−16.8737	+	4.52128i	−0.671730	+	0.179989i	−0.578534	−	0.815658i	$-0.696375\pi$
$631$	−16.8737	+	4.52128i	−0.671730	+	0.179989i	−0.0931960	+	0.995648i	$0.529708\pi$
$632$	2.47072	+	9.22086i	0.0982801	+	0.366786i
$633$	−8.13865	−	23.0770i	−0.323482	−	0.917228i
$634$	25.9171	+	14.9632i	1.02930	+	0.594266i
$635$	−1.15325	−	4.30397i	−0.0457652	−	0.170798i
$636$	2.28377	−	2.66700i	0.0905573	−	0.105754i
$637$	−8.13273	+	15.9011i	−0.322230	+	0.630023i
$638$			2.33768i			0.0925496i
$639$	13.6355	+	30.8388i	0.539411	+	1.21996i
$640$	−0.769482	−	1.33278i	−0.0304164	−	0.0526828i
$641$	−18.2842	−	31.6691i	−0.722182	−	1.25086i	−0.960123	−	0.279577i	$-0.909806\pi$
$641$	−18.2842	−	31.6691i	−0.722182	−	1.25086i	0.237941	−	0.971280i	$-0.423527\pi$
$642$	17.9236	−	12.2847i	0.707389	−	0.484838i
$643$	24.7378	−	24.7378i	0.975563	−	0.975563i	−0.0241455	−	0.999708i	$-0.507687\pi$
$643$	24.7378	−	24.7378i	0.975563	−	0.975563i	0.999708	+	0.0241455i	$0.00768651\pi$
$644$	−1.79609	+	1.79609i	−0.0707758	+	0.0707758i
$645$	−3.90042	−	1.86656i	−0.153579	−	0.0734958i
$646$	−3.43769	−	5.95425i	−0.135254	−	0.234267i
$647$	9.58684	+	16.6049i	0.376897	+	0.652806i	0.990609	−	0.136725i	$-0.0436576\pi$
$647$	9.58684	+	16.6049i	0.376897	+	0.652806i	−0.613712	+	0.789530i	$0.710324\pi$
$648$	4.12707	−	7.99796i	0.162126	−	0.314189i
$649$		−	1.39015i		−	0.0545682i
$650$	−9.02843	+	2.91822i	−0.354124	+	0.114462i
$651$	−0.259295	−	0.735226i	−0.0101626	−	0.0288158i
$652$	1.37636	+	5.13664i	0.0539023	+	0.201166i
$653$	5.74222	+	3.31527i	0.224710	+	0.129737i	0.608129	−	0.793838i	$-0.291920\pi$
$653$	5.74222	+	3.31527i	0.224710	+	0.129737i	−0.383419	+	0.923574i	$0.625253\pi$
$654$	−11.0367	+	12.8887i	−0.431568	+	0.503989i
$655$	−5.20724	−	19.4337i	−0.203464	−	0.759337i
$656$	7.77966	−	2.08455i	0.303745	−	0.0813882i
$657$	11.1432	−	15.2547i	0.434738	−	0.595144i
$658$	−12.3980	−	12.3980i	−0.483325	−	0.483325i
$659$	−18.7561	+	10.8289i	−0.730636	+	0.421833i	−0.818655	−	0.574286i	$-0.805280\pi$
$659$	−18.7561	+	10.8289i	−0.730636	+	0.421833i	0.0880190	+	0.996119i	$0.471946\pi$
$660$	−0.242729	+	1.30032i	−0.00944821	+	0.0506150i
$661$	−9.98561	+	2.67564i	−0.388395	+	0.104070i	−0.447732	−	0.894168i	$-0.647768\pi$
$661$	−9.98561	+	2.67564i	−0.388395	+	0.104070i	0.0593368	+	0.998238i	$0.481101\pi$
$662$	−3.31702	−	5.74525i	−0.128920	−	0.223295i
$663$	−12.7668	+	5.24609i	−0.495822	+	0.203741i
$664$	−4.20917	+	7.29049i	−0.163347	+	0.282926i
$665$	1.77254	−	6.61519i	0.0687360	−	0.256526i
$666$	21.4760	+	26.6604i	0.832176	+	1.03307i
$667$	7.24360	+	4.18209i	0.280473	+	0.161931i
$668$	10.4796	−	2.80800i	0.405469	−	0.108645i
$669$	1.22525	+	15.8282i	0.0473710	+	0.611955i
$670$	−8.62110	−	8.62110i	−0.333062	−	0.333062i
$671$	3.25624	+	0.872508i	0.125706	+	0.0336828i
$672$	−0.454671	+	2.43572i	−0.0175393	+	0.0939599i
$673$		−	26.3007i		−	1.01382i	−0.862000	−	0.506908i	$-0.830788\pi$
$673$		−	26.3007i		−	1.01382i	0.862000	−	0.506908i	$-0.169212\pi$
$674$	−22.4939	−	6.02723i	−0.866434	−	0.232160i
$675$	−6.47838	−	12.0421i	−0.249353	−	0.463502i
$676$	−1.31923	−	12.9329i	−0.0507394	−	0.497419i
$677$	−0.260338	−	0.150306i	−0.0100056	−	0.00577673i	0.494989	−	0.868899i	$-0.335172\pi$
$677$	−0.260338	−	0.150306i	−0.0100056	−	0.00577673i	−0.504994	+	0.863123i	$0.668505\pi$
$678$	1.91245	+	24.7057i	0.0734473	+	0.948818i
$679$	−5.27020	+	9.12826i	−0.202252	+	0.350310i
$680$	−3.40141			−0.130438
$681$	25.8597	+	37.7299i	0.990948	+	1.44581i
$682$	−0.150819	−	0.0404119i	−0.00577517	−	0.00154745i
$683$	−0.894421	−	3.33802i	−0.0342241	−	0.127726i	0.946700	−	0.322116i	$-0.104394\pi$
$683$	−0.894421	−	3.33802i	−0.0342241	−	0.127726i	−0.980924	+	0.194390i	$0.937727\pi$
$684$	3.77386	+	8.53518i	0.144297	+	0.326351i
$685$	5.01088	−	8.67909i	0.191456	−	0.331611i
$686$	17.1001			0.652886
$687$	13.9235	+	20.3146i	0.531214	+	0.775052i
$688$	−1.40486	+	0.811094i	−0.0535596	+	0.0309227i
$689$	7.29970	−	0.371341i	0.278097	−	0.0141470i
$690$	3.59498	+	3.07840i	0.136858	+	0.117193i
$691$	23.6513	−	23.6513i	0.899738	−	0.899738i	−0.0956749	−	0.995413i	$-0.530501\pi$
$691$	23.6513	−	23.6513i	0.899738	−	0.899738i	0.995413	+	0.0956749i	$0.0305009\pi$
$692$	−1.39070	+	0.802919i	−0.0528663	+	0.0305224i
$693$	1.65855	−	1.33603i	0.0630032	−	0.0507515i
$694$	−14.2693	+	14.2693i	−0.541655	+	0.541655i
$695$	6.64462	−	24.7981i	0.252045	−	0.940644i
$696$	8.13483	−	0.629711i	0.308350	−	0.0238691i
$697$	4.60727	−	17.1946i	0.174513	−	0.651290i
$698$			25.0996i			0.950033i
$699$	24.1638	−	28.2187i	0.913958	−	1.06733i
$700$	2.66200	+	2.66200i	0.100614	+	0.100614i
$701$	−14.8908			−0.562418			−0.281209	−	0.959647i	$-0.590735\pi$
$701$	−14.8908			−0.562418			−0.281209	+	0.959647i	$0.590735\pi$
$702$	17.9919	−	5.22418i	0.679060	−	0.197174i
$703$	−35.4983			−1.33884
$704$	0.350901	+	0.350901i	0.0132251	+	0.0132251i
$705$	−21.2495	+	24.8153i	−0.800302	+	0.934600i
$706$			26.0892i			0.981880i
$707$	2.04335	−	7.62589i	0.0768481	−	0.286801i
$708$	−4.83754	+	0.374471i	−0.181806	+	0.0140735i
$709$	−6.37553	+	23.7938i	−0.239438	+	0.893595i	0.736660	+	0.676264i	$0.236402\pi$
$709$	−6.37553	+	23.7938i	−0.239438	+	0.893595i	−0.976098	+	0.217332i	$0.930265\pi$
$710$	−12.2311	+	12.2311i	−0.459024	+	0.459024i
$711$	−26.7098	−	10.3317i	−1.00170	−	0.387471i
$712$	3.05914	−	1.76620i	0.114646	−	0.0661910i
$713$	−0.395036	+	0.395036i	−0.0147942	+	0.0147942i
$714$	4.15971	+	3.56198i	0.155673	+	0.133304i
$715$	−2.31166	+	1.49617i	−0.0864510	+	0.0559537i
$716$	8.71053	−	5.02903i	0.325528	−	0.187944i
$717$	−7.69958	−	11.2338i	−0.287546	−	0.419536i
$718$	−32.7710			−1.22300
$719$	17.8371	−	30.8948i	0.665213	−	1.15218i	−0.314014	−	0.949418i	$-0.601674\pi$
$719$	17.8371	−	30.8948i	0.665213	−	1.15218i	0.979227	−	0.202765i	$-0.0649928\pi$
$720$	4.59034	+	0.494392i	0.171072	+	0.0184249i
$721$	−5.58186	−	20.8318i	−0.207879	−	0.775816i
$722$	9.00550	+	2.41302i	0.335150	+	0.0898031i
$723$	−18.1240	−	26.4432i	−0.674037	−	0.983435i
$724$	11.9484			0.444058
$725$	6.19831	−	10.7358i	0.230199	−	0.398717i
$726$	1.43753	+	18.5705i	0.0533516	+	0.689214i
$727$	8.14708	+	4.70372i	0.302159	+	0.174451i	0.643412	−	0.765520i	$-0.277518\pi$
$727$	8.14708	+	4.70372i	0.302159	+	0.174451i	−0.341254	+	0.939971i	$0.610851\pi$
$728$	−4.33011	+	2.80258i	−0.160484	+	0.103870i
$729$	12.0720	+	24.1509i	0.447110	+	0.894479i
$730$	9.36075	+	2.50821i	0.346457	+	0.0928328i
$731$			3.58535i			0.132609i
$732$	2.15907	−	11.5663i	0.0798014	−	0.427504i
$733$	31.2706	+	8.37893i	1.15501	+	0.309483i	0.784970	−	0.619534i	$-0.212678\pi$
$733$	31.2706	+	8.37893i	1.15501	+	0.309483i	0.370037	+	0.929017i	$0.379345\pi$
$734$	0.413884	+	0.413884i	0.0152767	+	0.0152767i
$735$	−1.01906	−	13.1645i	−0.0375885	−	0.485581i
$736$	1.71507	−	0.459552i	0.0632184	−	0.0169393i
$737$	3.40471	+	1.96571i	0.125414	+	0.0724079i
$738$	−8.71692	+	22.5351i	−0.320874	+	0.829529i
$739$	7.68766	−	28.6907i	0.282795	−	1.05541i	−0.667640	−	0.744484i	$-0.732696\pi$
$739$	7.68766	−	28.6907i	0.282795	−	1.05541i	0.950436	−	0.310922i	$-0.100638\pi$
$740$	−8.78091	+	15.2090i	−0.322793	+	0.559093i
$741$	−7.48481	+	17.9269i	−0.274961	+	0.658561i
$742$	−1.45000	−	2.51148i	−0.0532313	−	0.0921993i
$743$	−23.8066	+	6.37897i	−0.873381	+	0.234022i	−0.667549	−	0.744566i	$-0.732657\pi$
$743$	−23.8066	+	6.37897i	−0.873381	+	0.234022i	−0.205832	+	0.978587i	$0.565990\pi$
$744$	−0.100001	+	0.535717i	−0.00366623	+	0.0196404i
$745$	14.0231	−	8.09624i	0.513767	−	0.296623i
$746$	19.3592	+	19.3592i	0.708790	+	0.708790i
$747$	−10.2128	−	23.0979i	−0.373668	−	0.845109i
$748$	1.05943	−	0.283875i	0.0387368	−	0.0103795i
$749$	−4.64503	−	17.3355i	−0.169726	−	0.633425i
$750$	13.2312	−	15.4516i	0.483137	−	0.564211i
$751$	−19.1669	−	11.0660i	−0.699411	−	0.403805i	0.107717	−	0.994182i	$-0.465646\pi$
$751$	−19.1669	−	11.0660i	−0.699411	−	0.403805i	−0.807128	+	0.590376i	$0.798979\pi$
$752$	3.17219	+	11.8388i	0.115678	+	0.431716i
$753$	12.7250	+	36.0814i	0.463723	+	1.31488i
$754$	12.6046	+	11.3843i	0.459033	+	0.414591i
$755$			26.4504i			0.962628i
$756$	−5.09598	−	5.41166i	−0.185339	−	0.196820i
$757$	25.1440	+	43.5507i	0.913875	+	1.58288i	0.808540	+	0.588442i	$0.200258\pi$
$757$	25.1440	+	43.5507i	0.913875	+	1.58288i	0.105336	+	0.994437i	$0.466408\pi$
$758$	1.61458	+	2.79653i	0.0586440	+	0.101574i
$759$	−1.37664	−	0.658797i	−0.0499690	−	0.0239128i
$760$	−3.38516	+	3.38516i	−0.122793	+	0.122793i
$761$	5.92790	−	5.92790i	0.214886	−	0.214886i	−0.591453	−	0.806339i	$-0.701446\pi$
$761$	5.92790	−	5.92790i	0.214886	−	0.214886i	0.806339	+	0.591453i	$0.201446\pi$
$762$	4.13652	−	2.83513i	0.149850	−	0.102706i
$763$	7.00737	+	12.1371i	0.253684	+	0.439393i
$764$	−10.9228	−	18.9189i	−0.395174	−	0.684461i
$765$	6.01908	−	8.23995i	0.217620	−	0.297916i
$766$		−	14.1015i		−	0.509508i
$767$	−7.49560	−	6.76990i	−0.270650	−	0.244447i
$768$	1.12657	−	1.31562i	0.0406515	−	0.0474732i
$769$	−4.01166	−	14.9717i	−0.144664	−	0.539894i	−0.999770	−	0.0214405i	$-0.993175\pi$
$769$	−4.01166	−	14.9717i	−0.144664	−	0.539894i	0.855106	−	0.518453i	$-0.173492\pi$
$770$	0.946157	+	0.546264i	0.0340971	+	0.0196860i
$771$	17.4020	+	49.3431i	0.626718	+	1.77705i
$772$	−3.38840	−	12.6457i	−0.121951	−	0.455128i
$773$	6.28210	−	1.68328i	0.225951	−	0.0605435i	−0.144067	−	0.989568i	$-0.546018\pi$
$773$	6.28210	−	1.68328i	0.225951	−	0.0605435i	0.370018	+	0.929024i	$0.379351\pi$
$774$	0.521127	−	4.83858i	0.0187315	−	0.173919i
$775$	0.585485	+	0.585485i	0.0210313	+	0.0210313i
$776$	6.38093	−	3.68403i	0.229062	−	0.132249i
$777$	26.6655	−	9.40421i	0.956619	−	0.337374i
$778$	−19.2695	+	5.16324i	−0.690844	+	0.185111i
$779$	−12.5272	−	21.6977i	−0.448833	−	0.777401i
$780$	5.82919	+	7.64123i	0.208719	+	0.273600i
$781$	2.78882	−	4.83038i	0.0997919	−	0.172845i
$782$	1.01570	−	3.79064i	0.0363213	−	0.135553i
$783$	−12.8698	+	20.8210i	−0.459929	+	0.744083i
$784$	−4.28987	−	2.47676i	−0.153210	−	0.0884557i
$785$	−32.5601	+	8.72447i	−1.16212	+	0.311390i
$786$	18.6776	−	12.8014i	0.666207	−	0.456612i
$787$	−37.8815	−	37.8815i	−1.35033	−	1.35033i	−0.885290	−	0.465040i	$-0.846040\pi$
$787$	−37.8815	−	37.8815i	−1.35033	−	1.35033i	−0.465040	−	0.885290i	$-0.653960\pi$
$788$	2.38157	+	0.638138i	0.0848398	+	0.0227327i
$789$	−7.25173	−	6.20969i	−0.258168	−	0.221071i
$790$		−	14.6912i		−	0.522688i
$791$	19.7689	+	5.29706i	0.702901	+	0.188342i
$792$	−1.47101	+	0.229113i	−0.0522702	+	0.00814118i
$793$	20.5621	−	13.3084i	0.730182	−	0.472596i
$794$	16.0511	+	9.26710i	0.569632	+	0.328877i
$795$	−4.45718	+	3.05491i	−0.158080	+	0.108347i
$796$	10.4770	−	18.1467i	0.371348	−	0.643194i
$797$	−46.6716			−1.65319			−0.826597	−	0.562794i	$-0.809726\pi$
$797$	−46.6716			−1.65319			−0.826597	+	0.562794i	$0.809726\pi$
$798$	7.68482	−	0.594876i	0.272040	−	0.0210584i
$799$	26.1660	+	7.01115i	0.925685	+	0.248037i
$800$	−0.681106	−	2.54192i	−0.0240807	−	0.0898705i
$801$	−1.13478	+	10.5362i	−0.0400955	+	0.372280i
$802$	−7.88886	+	13.6639i	−0.278565	+	0.482489i
$803$	−3.12492			−0.110276
$804$	5.92328	−	12.3775i	0.208898	−	0.436520i
$805$	3.38533	−	1.95452i	0.119317	−	0.0688879i
$806$	−0.952374	+	0.616405i	−0.0335459	+	0.0217119i
$807$	−31.7210	+	11.1872i	−1.11663	+	0.393807i
$808$	−3.90236	+	3.90236i	−0.137285	+	0.137285i
$809$	−3.13155	+	1.80800i	−0.110099	+	0.0635659i	−0.554039	−	0.832491i	$-0.686914\pi$
$809$	−3.13155	+	1.80800i	−0.110099	+	0.0635659i	0.443939	+	0.896057i	$0.353581\pi$
$810$	−9.32068	+	10.2453i	−0.327495	+	0.359983i
$811$	0.430194	−	0.430194i	0.0151062	−	0.0151062i	−0.699513	−	0.714620i	$-0.746600\pi$
$811$	0.430194	−	0.430194i	0.0151062	−	0.0151062i	0.714620	+	0.699513i	$0.246600\pi$
$812$	1.74416	−	6.50928i	0.0612078	−	0.228431i
$813$	−21.9365	−	32.0058i	−0.769347	−	1.12249i
$814$	1.46567	−	5.46997i	0.0513719	−	0.191722i
$815$		−	8.18396i		−	0.286672i
$816$	−1.27323	−	3.61023i	−0.0445720	−	0.126383i
$817$	3.56823	+	3.56823i	0.124837	+	0.124837i
$818$	11.1264			0.389025
$819$	0.873218	−	15.4491i	0.0305127	−	0.539837i
$820$	−12.3950			−0.432851
$821$	36.5520	+	36.5520i	1.27567	+	1.27567i	0.943065	+	0.332608i	$0.107929\pi$
$821$	36.5520	+	36.5520i	1.27567	+	1.27567i	0.332608	+	0.943065i	$0.392071\pi$
$822$	11.0876	+	2.06970i	0.386725	+	0.0721892i
$823$			18.6304i			0.649413i	0.945815	+	0.324707i	$0.105266\pi$
$823$			18.6304i			0.649413i	−0.945815	+	0.324707i	$0.894734\pi$
$824$	−3.90189	+	14.5621i	−0.135929	+	0.507293i
$825$	−0.976408	+	2.04033i	−0.0339942	+	0.0710353i
$826$	−1.03720	+	3.87088i	−0.0360888	+	0.134685i
$827$	23.9908	−	23.9908i	0.834244	−	0.834244i	−0.153851	−	0.988094i	$-0.549167\pi$
$827$	23.9908	−	23.9908i	0.834244	−	0.834244i	0.988094	+	0.153851i	$0.0491675\pi$
$828$	−1.92170	+	4.96800i	−0.0667835	+	0.172650i
$829$	−11.0843	+	6.39953i	−0.384974	+	0.222265i	−0.679980	−	0.733230i	$-0.738012\pi$
$829$	−11.0843	+	6.39953i	−0.384974	+	0.222265i	0.295006	+	0.955495i	$0.404678\pi$
$830$	9.16093	−	9.16093i	0.317981	−	0.317981i
$831$	−2.80436	+	15.0233i	−0.0972823	+	0.521151i
$832$	3.60090	−	0.183180i	0.124839	−	0.00635063i
$833$	−9.48144	+	5.47411i	−0.328513	+	0.189667i
$834$	28.8077	−	2.22998i	0.997530	−	0.0772181i
$835$	−16.6967			−0.577812
$836$	0.771857	−	1.33689i	0.0266952	−	0.0462375i
$837$	−1.12082	−	1.19025i	−0.0387412	−	0.0411411i
$838$	0.118552	+	0.442443i	0.00409532	+	0.0152839i
$839$	−20.3835	−	5.46173i	−0.703715	−	0.188560i	−0.110821	−	0.993840i	$-0.535348\pi$
$839$	−20.3835	−	5.46173i	−0.703715	−	0.188560i	−0.592894	+	0.805280i	$0.702015\pi$
$840$	1.64606	−	3.43965i	0.0567944	−	0.118679i
$841$	6.80936			0.234806
$842$	2.26422	−	3.92174i	0.0780301	−	0.135152i
$843$	−27.9758	−	13.3879i	−0.963539	−	0.461105i
$844$	12.2350	+	7.06391i	0.421148	+	0.243150i
$845$	−3.19028	+	19.7505i	−0.109749	+	0.679439i
$846$	−34.2930	−	13.2650i	−1.17902	−	0.456062i
$847$	14.8596	+	3.98162i	0.510582	+	0.136810i
$848$			2.02719i			0.0696140i
$849$	−11.9447	+	4.21258i	−0.409941	+	0.144575i
$850$	−5.61814	−	1.50537i	−0.192700	−	0.0516339i
$851$	−14.3273	−	14.3273i	−0.491134	−	0.491134i
$852$	−17.5603	−	8.40356i	−0.601608	−	0.287901i
$853$	9.10083	−	2.43856i	0.311606	−	0.0834947i	−0.0996268	−	0.995025i	$-0.531765\pi$
$853$	9.10083	−	2.43856i	0.311606	−	0.0834947i	0.411233	+	0.911530i	$0.365098\pi$
$854$	−8.41603	−	4.85900i	−0.287991	−	0.166272i
$855$	−2.21027	−	14.1909i	−0.0755895	−	0.485320i
$856$	−3.24702	+	12.1180i	−0.110981	+	0.414186i
$857$	−7.45337	+	12.9096i	−0.254602	+	0.440984i	−0.964787	−	0.263031i	$-0.915278\pi$
$857$	−7.45337	+	12.9096i	−0.254602	+	0.440984i	0.710185	+	0.704015i	$0.248611\pi$
$858$	−2.45334	−	1.89352i	−0.0837556	−	0.0646437i
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	0.991838	+	0.127504i	$0.0406967\pi$
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	−0.385497	+	0.922709i	$0.625970\pi$
$860$	2.41142	−	0.646139i	0.0822288	−	0.0220331i
$861$	15.1583	+	12.9801i	0.516593	+	0.442361i
$862$	−12.9318	+	7.46617i	−0.440459	+	0.254299i
$863$	0.118264	+	0.118264i	0.00402577	+	0.00402577i	0.709117	−	0.705091i	$-0.249094\pi$
$863$	0.118264	+	0.118264i	0.00402577	+	0.00402577i	−0.705091	+	0.709117i	$0.749094\pi$
$864$	1.19354	+	5.05722i	0.0406050	+	0.172050i
$865$	2.38712	−	0.639626i	0.0811644	−	0.0217479i
$866$	−1.17039	−	4.36797i	−0.0397716	−	0.148430i
$867$	20.6276	+	3.85051i	0.700549	+	0.130770i
$868$	0.389805	+	0.225054i	0.0132308	+	0.00763883i
$869$	1.22610	+	4.57585i	0.0415924	+	0.155225i
$870$	−12.3434	−	2.30413i	−0.418482	−	0.0781172i
$871$	27.1796	−	8.78515i	0.920946	−	0.297673i
$872$		−	9.79673i		−	0.331759i
$873$	−2.36699	+	21.9771i	−0.0801104	+	0.743812i
$874$	−2.76169	−	4.78339i	−0.0934156	−	0.161801i
$875$	−8.40074	−	14.5505i	−0.283997	−	0.491897i
$876$	0.841773	+	10.8743i	0.0284409	+	0.367409i
$877$	30.2480	−	30.2480i	1.02140	−	1.02140i	0.0216349	−	0.999766i	$-0.493113\pi$
$877$	30.2480	−	30.2480i	1.02140	−	1.02140i	0.999766	−	0.0216349i	$-0.00688713\pi$
$878$	−9.44424	+	9.44424i	−0.318728	+	0.318728i
$879$	−1.90679	−	24.6325i	−0.0643143	−	0.830834i
$880$	−0.381855	−	0.661392i	−0.0128723	−	0.0222955i
$881$	13.3432	+	23.1111i	0.449544	+	0.778633i	0.998356	−	0.0573124i	$-0.0182531\pi$
$881$	13.3432	+	23.1111i	0.449544	+	0.778633i	−0.548812	+	0.835946i	$0.684920\pi$
$882$	13.5913	−	6.00943i	0.457642	−	0.202348i
$883$			11.8585i			0.399071i	0.979891	+	0.199536i	$0.0639433\pi$
$883$			11.8585i			0.399071i	−0.979891	+	0.199536i	$0.936057\pi$
$884$	3.62871	−	7.09484i	0.122047	−	0.238625i
$885$	7.34029	+	1.37020i	0.246741	+	0.0460587i
$886$	7.98000	+	29.7818i	0.268093	+	1.00054i
$887$	45.7185	+	26.3956i	1.53508	+	0.886277i	0.999116	+	0.0420331i	$0.0133835\pi$
$887$	45.7185	+	26.3956i	1.53508	+	0.886277i	0.535960	+	0.844243i	$0.319950\pi$
$888$	−19.4296	−	3.62689i	−0.652015	−	0.121710i
$889$	−1.07201	−	4.00079i	−0.0359540	−	0.134182i
$890$	−5.25099	+	1.40700i	−0.176014	+	0.0471627i
$891$	2.04805	−	3.96898i	0.0686124	−	0.132966i
$892$	−6.48118	−	6.48118i	−0.217006	−	0.217006i
$893$	33.0187	−	19.0634i	1.10493	−	0.637931i
$894$	13.8425	+	11.8534i	0.462962	+	0.396437i
$895$	−14.9515	+	4.00626i	−0.499775	+	0.133914i
$896$	−0.715277	−	1.23890i	−0.0238957	−	0.0413886i
$897$	−10.2563	+	4.21449i	−0.342448	+	0.140718i
$898$	20.0708	−	34.7636i	0.669771	−	1.16008i
$899$	0.383613	−	1.43167i	0.0127942	−	0.0477487i
$900$	7.36311	+	2.84816i	0.245437	+	0.0949387i
$901$	3.88021	+	2.24024i	0.129269	+	0.0746333i
$902$	3.86065	−	1.03446i	0.128546	−	0.0344437i
$903$	−3.62566	−	1.73507i	−0.120655	−	0.0577396i
$904$	−10.1162	−	10.1162i	−0.336461	−	0.336461i
$905$	−17.7616	−	4.75920i	−0.590414	−	0.158201i
$906$	−28.0742	+	9.90104i	−0.932704	+	0.328940i
$907$			18.4318i			0.612019i	0.952028	+	0.306009i	$0.0989939\pi$
$907$			18.4318i			0.612019i	−0.952028	+	0.306009i	$0.901006\pi$
$908$	−25.5089	−	6.83510i	−0.846544	−	0.226831i
$909$	−2.54796	−	16.3591i	−0.0845105	−	0.542597i
$910$	7.55312	−	2.44136i	0.250383	−	0.0809303i
$911$	−37.3282	−	21.5514i	−1.23674	−	0.714030i	−0.268311	−	0.963332i	$-0.586466\pi$
$911$	−37.3282	−	21.5514i	−1.23674	−	0.714030i	−0.968426	+	0.249302i	$0.919799\pi$
$912$	−4.86014	−	2.32584i	−0.160935	−	0.0770161i
$913$	−2.08880	+	3.61790i	−0.0691291	+	0.119735i
$914$	−16.5104			−0.546115
$915$	−7.81653	+	16.3337i	−0.258406	+	0.539974i
$916$	−13.7346	−	3.68017i	−0.453804	−	0.121596i
$917$	−4.84042	−	18.0647i	−0.159845	−	0.596549i
$918$	10.9989	+	3.30419i	0.363018	+	0.109054i
$919$	−25.3781	+	43.9562i	−0.837147	+	1.44998i	0.0551224	+	0.998480i	$0.482445\pi$
$919$	−25.3781	+	43.9562i	−0.837147	+	1.44998i	−0.892270	+	0.451502i	$0.850888\pi$
$920$	−2.73254			−0.0900893
$921$	38.0694	−	2.94692i	1.25443	−	0.0971045i
$922$	11.9555	−	6.90250i	0.393733	−	0.227322i
$923$	−12.4638	−	38.5607i	−0.410251	−	1.26924i
$924$	−0.225630	+	1.20872i	−0.00742269	+	0.0397641i
$925$	−21.2346	+	21.2346i	−0.698190	+	0.698190i
$926$	−33.3375	+	19.2474i	−1.09554	+	0.632508i
$927$	−28.3720	−	35.2212i	−0.931860	−	1.15682i
$928$	−3.33096	+	3.33096i	−0.109344	+	0.109344i
$929$	−12.0290	+	44.8930i	−0.394660	+	1.47289i	0.427698	+	0.903922i	$0.359325\pi$
$929$	−12.0290	+	44.8930i	−0.394660	+	1.47289i	−0.822358	+	0.568970i	$0.807342\pi$
$930$	0.362038	−	0.756525i	0.0118717	−	0.0248074i
$931$	−3.98820	+	14.8841i	−0.130708	+	0.487808i
$932$			21.4490i			0.702586i
$933$	−42.1524	−	7.86852i	−1.38001	−	0.257604i
$934$	−6.04176	−	6.04176i	−0.197692	−	0.197692i
$935$	−1.68795			−0.0552018
$936$	−5.92834	+	9.04737i	−0.193774	+	0.295722i
$937$	−13.9838			−0.456832			−0.228416	−	0.973564i	$-0.573355\pi$
$937$	−13.9838			−0.456832			−0.228416	+	0.973564i	$0.573355\pi$
$938$	−8.01380	−	8.01380i	−0.261660	−	0.261660i
$939$	−18.5156	−	52.5006i	−0.604232	−	1.71329i
$940$		−	18.8622i		−	0.615216i
$941$	6.63944	−	24.7787i	0.216440	−	0.807764i	−0.769215	−	0.638990i	$-0.779353\pi$
$941$	6.63944	−	24.7787i	0.216440	−	0.807764i	0.985655	−	0.168774i	$-0.0539808\pi$
$942$	−21.4482	−	31.2933i	−0.698819	−	1.01959i
$943$	3.70128	−	13.8134i	0.120530	−	0.449825i
$944$	1.98083	−	1.98083i	0.0644704	−	0.0644704i
$945$	5.41976	+	10.0744i	0.176305	+	0.327719i
$946$	−0.697159	+	0.402505i	−0.0226666	+	0.0130866i
$947$	−1.95156	+	1.95156i	−0.0634171	+	0.0634171i	−0.738104	−	0.674687i	$-0.764279\pi$
$947$	−1.95156	+	1.95156i	−0.0634171	+	0.0634171i	0.674687	+	0.738104i	$0.264279\pi$
$948$	15.5931	−	5.49927i	0.506440	−	0.178608i
$949$	−15.2181	+	16.8494i	−0.493999	+	0.546953i
$950$	−7.08950	+	4.09312i	−0.230014	+	0.132798i
$951$	22.3753	−	46.7560i	0.725567	−	1.51617i
$952$	−3.16180			−0.102474
$953$	−14.2452	+	24.6735i	−0.461448	+	0.799252i	−0.999033	−	0.0439575i	$-0.986003\pi$
$953$	−14.2452	+	24.6735i	−0.461448	+	0.799252i	0.537585	+	0.843210i	$0.319337\pi$
$954$	−4.91090	−	3.58729i	−0.158996	−	0.116143i
$955$	8.70140	+	32.4741i	0.281571	+	1.05084i
$956$	7.59513	+	2.03511i	0.245644	+	0.0658201i
$957$	4.03690	−	0.312494i	0.130495	−	0.0101015i
$958$	−8.86333			−0.286361
$959$	4.65789	−	8.06770i	0.150411	−	0.260520i
$960$	−2.19870	+	1.50697i	−0.0709627	+	0.0486372i
$961$	−26.7611	−	15.4505i	−0.863260	−	0.498403i
$962$	−22.3560	−	34.5411i	−0.720787	−	1.11365i
$963$	−23.6102	−	29.3099i	−0.760829	−	0.944497i
$964$	17.8781	+	4.79042i	0.575815	+	0.154289i
$965$			20.1478i			0.648580i
$966$	3.34173	+	2.86154i	0.107518	+	0.0920686i
$967$	10.1930	+	2.73120i	0.327783	+	0.0878293i	0.418958	−	0.908006i	$-0.362395\pi$
$967$	10.1930	+	2.73120i	0.327783	+	0.0878293i	−0.0911745	+	0.995835i	$0.529062\pi$
$968$	−7.60404	−	7.60404i	−0.244403	−	0.244403i
$969$	−9.82277	+	6.73244i	−0.315553	+	0.216277i
$970$	−10.9528	+	2.93480i	−0.351674	+	0.0942306i
$971$	36.5800	+	21.1195i	1.17391	+	0.677756i	0.954597	−	0.297899i	$-0.0962859\pi$
$971$	36.5800	+	21.1195i	1.17391	+	0.677756i	0.219310	+	0.975655i	$0.429619\pi$
$972$	−14.3632	−	6.05782i	−0.460701	−	0.194305i
$973$	6.17655	−	23.0512i	0.198011	−	0.738987i
$974$	5.43346	−	9.41102i	0.174099	−	0.301549i
$975$	6.24632	+	15.2010i	0.200042	+	0.486820i
$976$	3.39659	+	5.88306i	0.108722	+	0.188312i
$977$	−50.9962	+	13.6644i	−1.63151	+	0.437162i	−0.954355	−	0.298676i	$-0.903455\pi$
$977$	−50.9962	+	13.6644i	−1.63151	+	0.437162i	−0.677157	+	0.735838i	$0.736788\pi$
$978$	8.68640	−	3.06346i	0.277760	−	0.0979587i
$979$	1.51810	−	0.876475i	0.0485186	−	0.0280122i
$980$	5.39048	+	5.39048i	0.172192	+	0.172192i
$981$	23.7327	+	17.3361i	0.757727	+	0.553501i
$982$	−16.7551	+	4.48952i	−0.534678	+	0.143266i
$983$	8.76515	+	32.7120i	0.279565	+	1.04335i	0.952720	+	0.303849i	$0.0982719\pi$
$983$	8.76515	+	32.7120i	0.279565	+	1.04335i	−0.673155	+	0.739501i	$0.735061\pi$
$984$	−4.63975	−	13.1559i	−0.147910	−	0.419395i
$985$	−3.28608	−	1.89722i	−0.104703	−	0.0604504i
$986$	2.69470	+	10.0568i	0.0858169	+	0.320273i
$987$	−19.7526	+	23.0673i	−0.628732	+	0.734239i
$988$	−3.44958	−	10.6724i	−0.109746	−	0.339533i
$989$			2.88031i			0.0915887i
$990$	2.27796	+	0.245342i	0.0723982	+	0.00779747i
$991$	20.3156	+	35.1877i	0.645347	+	1.11777i	0.984221	+	0.176942i	$0.0566205\pi$
$991$	20.3156	+	35.1877i	0.645347	+	1.11777i	−0.338874	+	0.940832i	$0.610046\pi$
$992$	−0.157320	−	0.272485i	−0.00499490	−	0.00865142i
$993$	−9.47797	+	6.49612i	−0.300774	+	0.206148i
$994$	−11.3695	+	11.3695i	−0.360617	+	0.360617i
$995$	−22.8024	+	22.8024i	−0.722886	+	0.722886i
$996$	13.1525	+	6.29418i	0.416753	+	0.199439i
$997$	−7.67103	−	13.2866i	−0.242944	−	0.420791i	0.718608	−	0.695416i	$-0.244780\pi$
$997$	−7.67103	−	13.2866i	−0.242944	−	0.420791i	−0.961552	+	0.274624i	$0.911446\pi$
$998$	5.90466	+	10.2272i	0.186909	+	0.323735i
$999$	43.1685	−	40.6504i	1.36579	−	1.28612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.119.12	yes	56
3.2	odd	2		702.2.bb.a.197.2		56
9.4	even	3		702.2.bc.a.665.2		56
9.5	odd	6		234.2.z.a.41.8	yes	56
13.7	odd	12		234.2.z.a.137.8	yes	56
39.20	even	12		702.2.bc.a.683.2		56
117.59	even	12	inner	234.2.y.a.59.12	✓	56
117.85	odd	12		702.2.bb.a.449.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.12	✓	56	117.59	even	12	inner
234.2.y.a.119.12	yes	56	1.1	even	1	trivial
234.2.z.a.41.8	yes	56	9.5	odd	6
234.2.z.a.137.8	yes	56	13.7	odd	12
702.2.bb.a.197.2		56	3.2	odd	2
702.2.bb.a.449.2		56	117.85	odd	12
702.2.bc.a.665.2		56	9.4	even	3
702.2.bc.a.683.2		56	39.20	even	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.12657 - 1.31562i) q^{3} +1.00000i q^{4} +(0.398313 - 1.48652i) q^{5} +(1.72688 - 0.133677i) q^{6} +(0.370254 - 1.38181i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.461689 - 2.96426i) q^{9} +(1.33278 - 0.769482i) q^{10} +(-0.350901 + 0.350901i) q^{11} +(1.31562 + 1.12657i) q^{12} +(0.183180 + 3.60090i) q^{13} +(1.23890 - 0.715277i) q^{14} +(-1.50697 - 2.19870i) q^{15} -1.00000 q^{16} +(-1.10510 + 1.91408i) q^{17} +(1.76959 - 2.42251i) q^{18} +(0.805124 + 3.00476i) q^{19} +(1.48652 + 0.398313i) q^{20} +(-1.40081 - 2.04381i) q^{21} -0.496250 q^{22} +(-0.887787 + 1.53769i) q^{23} +(0.133677 + 1.72688i) q^{24} +(2.27902 + 1.31580i) q^{25} +(-2.41669 + 2.67575i) q^{26} +(-4.41995 - 2.73204i) q^{27} +(1.38181 + 0.370254i) q^{28} -4.71069i q^{29} +(0.489127 - 2.62030i) q^{30} +(0.303918 + 0.0814346i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.0663371 + 0.856966i) q^{33} +(-2.13488 + 0.572040i) q^{34} +(-1.90661 - 1.10078i) q^{35} +(2.96426 - 0.461689i) q^{36} +(-2.95350 + 11.0226i) q^{37} +(-1.55538 + 2.69400i) q^{38} +(4.94376 + 3.81566i) q^{39} +(0.769482 + 1.33278i) q^{40} +(-7.77966 + 2.08455i) q^{41} +(0.454671 - 2.43572i) q^{42} +(1.40486 - 0.811094i) q^{43} +(-0.350901 - 0.350901i) q^{44} +(-4.59034 - 0.494392i) q^{45} +(-1.71507 + 0.459552i) q^{46} +(-3.17219 - 11.8388i) q^{47} +(-1.12657 + 1.31562i) q^{48} +(4.28987 + 2.47676i) q^{49} +(0.681106 + 2.54192i) q^{50} +(1.27323 + 3.61023i) q^{51} +(-3.60090 + 0.183180i) q^{52} -2.02719i q^{53} +(-1.19354 - 5.05722i) q^{54} +(0.381855 + 0.661392i) q^{55} +(0.715277 + 1.23890i) q^{56} +(4.86014 + 2.32584i) q^{57} +(3.33096 - 3.33096i) q^{58} +(-1.98083 + 1.98083i) q^{59} +(2.19870 - 1.50697i) q^{60} +(-3.39659 - 5.88306i) q^{61} +(0.157320 + 0.272485i) q^{62} +(-4.26698 - 0.459565i) q^{63} -1.00000i q^{64} +(5.42578 + 1.16198i) q^{65} +(-0.559059 + 0.652874i) q^{66} +(-2.05043 - 7.65232i) q^{67} +(-1.91408 - 1.10510i) q^{68} +(1.02286 + 2.90030i) q^{69} +(-0.569808 - 2.12655i) q^{70} +(-10.8566 + 2.90902i) q^{71} +(2.42251 + 1.76959i) q^{72} +(4.45270 + 4.45270i) q^{73} +(-9.88261 + 5.70573i) q^{74} +(4.29856 - 1.51599i) q^{75} +(-3.00476 + 0.805124i) q^{76} +(0.354956 + 0.614801i) q^{77} +(0.797688 + 6.19384i) q^{78} +(4.77307 - 8.26720i) q^{79} +(-0.398313 + 1.48652i) q^{80} +(-8.57369 + 2.73713i) q^{81} +(-6.97505 - 4.02705i) q^{82} +(8.13149 - 2.17883i) q^{83} +(2.04381 - 1.40081i) q^{84} +(2.40516 + 2.40516i) q^{85} +(1.56691 + 0.419853i) q^{86} +(-6.19746 - 5.30692i) q^{87} -0.496250i q^{88} +(-3.41203 - 0.914251i) q^{89} +(-2.89628 - 3.59545i) q^{90} +(5.04357 + 1.08013i) q^{91} +(-1.53769 - 0.887787i) q^{92} +(0.449521 - 0.308098i) q^{93} +(6.12820 - 10.6144i) q^{94} +4.78735 q^{95} +(-1.72688 + 0.133677i) q^{96} +(-7.11700 - 1.90700i) q^{97} +(1.28206 + 4.78473i) q^{98} +(1.20217 + 0.878156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more