LMFDB - Embedded newform 841.2.d.o.778.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,2,2,-8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			778.4
Character	$\chi$	$=$	841.778
Dual form			841.2.d.o.574.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.318763 - 0.399716i) q^{2} +(0.599151 + 2.62505i) q^{3} +(0.386879 - 1.69503i) q^{4} +(1.37406 + 1.72301i) q^{5} +(0.858287 - 1.07626i) q^{6} +(0.289736 + 1.26942i) q^{7} +(-1.72210 + 0.829321i) q^{8} +(-3.82900 + 1.84395i) q^{9} +(0.250717 - 1.09846i) q^{10} +(4.51253 + 2.17312i) q^{11} +4.68133 q^{12} +(-2.82708 - 1.36145i) q^{13} +(0.415048 - 0.520454i) q^{14} +(-3.69973 + 4.63931i) q^{15} +(-2.25245 - 1.08472i) q^{16} +1.37659 q^{17} +(1.95760 + 0.942730i) q^{18} +(-1.32448 + 5.80294i) q^{19} +(3.45214 - 1.66246i) q^{20} +(-3.15868 + 1.52114i) q^{21} +(-0.569796 - 2.49644i) q^{22} +(0.539524 - 0.676542i) q^{23} +(-3.20881 - 4.02372i) q^{24} +(0.0318655 - 0.139612i) q^{25} +(0.356974 + 1.56401i) q^{26} +(-2.09827 - 2.63114i) q^{27} +2.26379 q^{28} +3.03374 q^{30} +(-1.71085 - 2.14534i) q^{31} +(1.13506 + 4.97304i) q^{32} +(-3.00087 + 13.1477i) q^{33} +(-0.438804 - 0.550243i) q^{34} +(-1.78910 + 2.24347i) q^{35} +(1.64419 + 7.20365i) q^{36} +(5.31570 - 2.55991i) q^{37} +(2.74172 - 1.32034i) q^{38} +(1.88003 - 8.23694i) q^{39} +(-3.79519 - 1.82767i) q^{40} +1.90869 q^{41} +(1.61489 + 0.777692i) q^{42} +(-6.86728 + 8.61130i) q^{43} +(5.42930 - 6.80813i) q^{44} +(-8.43841 - 4.06373i) q^{45} -0.442405 q^{46} +(-2.59174 - 1.24812i) q^{47} +(1.49789 - 6.56270i) q^{48} +(4.77931 - 2.30160i) q^{49} +(-0.0659625 + 0.0317659i) q^{50} +(0.824782 + 3.61361i) q^{51} +(-3.40143 + 4.26526i) q^{52} +(-3.61812 - 4.53698i) q^{53} +(-0.382860 + 1.67742i) q^{54} +(2.45616 + 10.7611i) q^{55} +(-1.55171 - 1.94578i) q^{56} -16.0266 q^{57} -4.35304 q^{59} +(6.43241 + 8.06599i) q^{60} +(-1.20950 - 5.29918i) q^{61} +(-0.312171 + 1.36771i) q^{62} +(-3.45014 - 4.32634i) q^{63} +(-1.49150 + 1.87028i) q^{64} +(-1.53877 - 6.74180i) q^{65} +(6.21189 - 2.99149i) q^{66} +(2.12879 - 1.02517i) q^{67} +(0.532572 - 2.33335i) q^{68} +(2.09921 + 1.01093i) q^{69} +1.46705 q^{70} +(14.0459 + 6.76414i) q^{71} +(5.06471 - 6.35094i) q^{72} +(-2.11765 + 2.65545i) q^{73} +(-2.71768 - 1.30877i) q^{74} +0.385580 q^{75} +(9.32373 + 4.49007i) q^{76} +(-1.45115 + 6.35791i) q^{77} +(-3.89172 + 1.87415i) q^{78} +(1.90656 - 0.918152i) q^{79} +(-1.22600 - 5.37146i) q^{80} +(-2.29955 + 2.88355i) q^{81} +(-0.608420 - 0.762935i) q^{82} +(-1.41502 + 6.19962i) q^{83} +(1.35635 + 5.94255i) q^{84} +(1.89151 + 2.37187i) q^{85} +5.63110 q^{86} -9.57325 q^{88} +(-7.43999 - 9.32945i) q^{89} +(1.06552 + 4.66833i) q^{90} +(0.909139 - 3.98320i) q^{91} +(-0.938027 - 1.17625i) q^{92} +(4.60658 - 5.77647i) q^{93} +(0.327258 + 1.43381i) q^{94} +(-11.8184 + 5.69146i) q^{95} +(-12.3744 + 5.95920i) q^{96} +(-2.54198 + 11.1372i) q^{97} +(-2.44345 - 1.17670i) q^{98} -21.2856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) $ 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−0.318763	−	0.399716i	−0.225399	−	0.282642i	0.656254	−	0.754540i	$-0.272140\pi$
$2$	−0.318763	−	0.399716i	−0.225399	−	0.282642i	−0.881653	+	0.471899i	$0.843569\pi$
$3$	0.599151	+	2.62505i	0.345920	+	1.51557i	0.786347	+	0.617785i	$0.211970\pi$
$3$	0.599151	+	2.62505i	0.345920	+	1.51557i	−0.440427	+	0.897788i	$0.645173\pi$
$4$	0.386879	−	1.69503i	0.193439	−	0.847514i
$5$	1.37406	+	1.72301i	0.614496	+	0.770554i	0.987558	−	0.157252i	$-0.0502636\pi$
$5$	1.37406	+	1.72301i	0.614496	+	0.770554i	−0.373062	+	0.927806i	$0.621692\pi$
$6$	0.858287	−	1.07626i	0.350394	−	0.439380i
$7$	0.289736	+	1.26942i	0.109510	+	0.479794i	0.999707	+	0.0242179i	$0.00770954\pi$
$7$	0.289736	+	1.26942i	0.109510	+	0.479794i	−0.890197	+	0.455576i	$0.849433\pi$
$8$	−1.72210	+	0.829321i	−0.608855	+	0.293209i
$9$	−3.82900	+	1.84395i	−1.27633	+	0.614650i
$10$	0.250717	−	1.09846i	0.0792837	−	0.347365i
$11$	4.51253	+	2.17312i	1.36058	+	0.655221i	0.964766	−	0.263110i	$-0.0847483\pi$
$11$	4.51253	+	2.17312i	1.36058	+	0.655221i	0.395814	+	0.918331i	$0.370463\pi$
$12$	4.68133			1.35138
$13$	−2.82708	−	1.36145i	−0.784091	−	0.377598i	−0.00139212	−	0.999999i	$-0.500443\pi$
$13$	−2.82708	−	1.36145i	−0.784091	−	0.377598i	−0.782699	+	0.622401i	$0.786157\pi$
$14$	0.415048	−	0.520454i	0.110926	−	0.139097i
$15$	−3.69973	+	4.63931i	−0.955265	+	1.19786i
$16$	−2.25245	−	1.08472i	−0.563112	−	0.271180i
$17$	1.37659			0.333871			0.166936	−	0.985968i	$-0.446613\pi$
$17$	1.37659			0.333871			0.166936	+	0.985968i	$0.446613\pi$
$18$	1.95760	+	0.942730i	0.461411	+	0.222204i
$19$	−1.32448	+	5.80294i	−0.303857	+	1.33129i	0.560394	+	0.828226i	$0.310650\pi$
$19$	−1.32448	+	5.80294i	−0.303857	+	1.33129i	−0.864252	+	0.503060i	$0.832207\pi$
$20$	3.45214	−	1.66246i	0.771923	−	0.371738i
$21$	−3.15868	+	1.52114i	−0.689281	+	0.331940i
$22$	−0.569796	−	2.49644i	−0.121481	−	0.532243i
$23$	0.539524	−	0.676542i	0.112499	−	0.141069i	−0.722394	−	0.691482i	$-0.756958\pi$
$23$	0.539524	−	0.676542i	0.112499	−	0.141069i	0.834893	+	0.550413i	$0.185530\pi$
$24$	−3.20881	−	4.02372i	−0.654995	−	0.821338i
$25$	0.0318655	−	0.139612i	0.00637309	−	0.0279223i
$26$	0.356974	+	1.56401i	0.0700085	+	0.306727i
$27$	−2.09827	−	2.63114i	−0.403811	−	0.506364i
$28$	2.26379			0.427815
$29$		0			0
$29$		0			0
$30$	3.03374			0.553882
$31$	−1.71085	−	2.14534i	−0.307279	−	0.385315i	0.604083	−	0.796921i	$-0.293539\pi$
$31$	−1.71085	−	2.14534i	−0.307279	−	0.385315i	−0.911362	+	0.411606i	$0.864968\pi$
$32$	1.13506	+	4.97304i	0.200653	+	0.879118i
$33$	−3.00087	+	13.1477i	−0.522384	+	2.28871i
$34$	−0.438804	−	0.550243i	−0.0752543	−	0.0943659i
$35$	−1.78910	+	2.24347i	−0.302414	+	0.379215i
$36$	1.64419	+	7.20365i	0.274031	+	1.20061i
$37$	5.31570	−	2.55991i	0.873897	−	0.420846i	0.0575050	−	0.998345i	$-0.481685\pi$
$37$	5.31570	−	2.55991i	0.873897	−	0.420846i	0.816392	+	0.577499i	$0.195971\pi$
$38$	2.74172	−	1.32034i	0.444766	−	0.214188i
$39$	1.88003	−	8.23694i	0.301045	−	1.31897i
$40$	−3.79519	−	1.82767i	−0.600073	−	0.288980i
$41$	1.90869			0.298088			0.149044	−	0.988831i	$-0.452380\pi$
$41$	1.90869			0.298088			0.149044	+	0.988831i	$0.452380\pi$
$42$	1.61489	+	0.777692i	0.249184	+	0.120001i
$43$	−6.86728	+	8.61130i	−1.04725	+	1.31321i	−0.0992078	+	0.995067i	$0.531631\pi$
$43$	−6.86728	+	8.61130i	−1.04725	+	1.31321i	−0.948043	+	0.318144i	$0.896941\pi$
$44$	5.42930	−	6.80813i	0.818498	−	1.02636i
$45$	−8.43841	−	4.06373i	−1.25792	−	0.605784i
$46$	−0.442405			−0.0652290
$47$	−2.59174	−	1.24812i	−0.378044	−	0.182056i	0.235206	−	0.971946i	$-0.424424\pi$
$47$	−2.59174	−	1.24812i	−0.378044	−	0.182056i	−0.613249	+	0.789889i	$0.710138\pi$
$48$	1.49789	−	6.56270i	0.216202	−	0.947244i
$49$	4.77931	−	2.30160i	0.682759	−	0.328799i
$50$	−0.0659625	+	0.0317659i	−0.00932851	+	0.00449237i
$51$	0.824782	+	3.61361i	0.115493	+	0.506006i
$52$	−3.40143	+	4.26526i	−0.471694	+	0.591485i
$53$	−3.61812	−	4.53698i	−0.496987	−	0.623202i	0.468559	−	0.883432i	$-0.344773\pi$
$53$	−3.61812	−	4.53698i	−0.496987	−	0.623202i	−0.965547	+	0.260230i	$0.916202\pi$
$54$	−0.382860	+	1.67742i	−0.0521007	+	0.228268i
$55$	2.45616	+	10.7611i	0.331188	+	1.45103i
$56$	−1.55171	−	1.94578i	−0.207356	−	0.260016i
$57$	−16.0266			−2.12277
$58$		0			0
$59$	−4.35304			−0.566717			−0.283359	−	0.959014i	$-0.591449\pi$
$59$	−4.35304			−0.566717			−0.283359	+	0.959014i	$0.591449\pi$
$60$	6.43241	+	8.06599i	0.830421	+	1.04131i
$61$	−1.20950	−	5.29918i	−0.154861	−	0.678490i	−0.991431	−	0.130630i	$-0.958300\pi$
$61$	−1.20950	−	5.29918i	−0.154861	−	0.678490i	0.836570	−	0.547860i	$-0.184557\pi$
$62$	−0.312171	+	1.36771i	−0.0396458	+	0.173699i
$63$	−3.45014	−	4.32634i	−0.434677	−	0.545067i
$64$	−1.49150	+	1.87028i	−0.186437	+	0.233785i
$65$	−1.53877	−	6.74180i	−0.190861	−	0.836217i
$66$	6.21189	−	2.99149i	0.764630	−	0.368227i
$67$	2.12879	−	1.02517i	0.260073	−	0.125245i	−0.299304	−	0.954158i	$-0.596755\pi$
$67$	2.12879	−	1.02517i	0.260073	−	0.125245i	0.559377	+	0.828913i	$0.311040\pi$
$68$	0.532572	−	2.33335i	0.0645838	−	0.282960i
$69$	2.09921	+	1.01093i	0.252716	+	0.121701i
$70$	1.46705			0.175346
$71$	14.0459	+	6.76414i	1.66694	+	0.802755i	0.998245	+	0.0592169i	$0.0188604\pi$
$71$	14.0459	+	6.76414i	1.66694	+	0.802755i	0.668693	+	0.743538i	$0.266854\pi$
$72$	5.06471	−	6.35094i	0.596882	−	0.748466i
$73$	−2.11765	+	2.65545i	−0.247853	+	0.310797i	−0.890158	−	0.455651i	$-0.849406\pi$
$73$	−2.11765	+	2.65545i	−0.247853	+	0.310797i	0.642306	+	0.766448i	$0.277978\pi$
$74$	−2.71768	−	1.30877i	−0.315924	−	0.152141i
$75$	0.385580			0.0445230
$76$	9.32373	+	4.49007i	1.06950	+	0.515046i
$77$	−1.45115	+	6.35791i	−0.165374	+	0.724551i
$78$	−3.89172	+	1.87415i	−0.440650	+	0.212206i
$79$	1.90656	−	0.918152i	0.214505	−	0.103300i	−0.323546	−	0.946212i	$-0.604875\pi$
$79$	1.90656	−	0.918152i	0.214505	−	0.103300i	0.538051	+	0.842912i	$0.319161\pi$
$80$	−1.22600	−	5.37146i	−0.137071	−	0.600547i
$81$	−2.29955	+	2.88355i	−0.255506	+	0.320394i
$82$	−0.608420	−	0.762935i	−0.0671887	−	0.0842520i
$83$	−1.41502	+	6.19962i	−0.155319	+	0.680497i	0.835968	+	0.548778i	$0.184907\pi$
$83$	−1.41502	+	6.19962i	−0.155319	+	0.680497i	−0.991287	+	0.131719i	$0.957950\pi$
$84$	1.35635	+	5.94255i	0.147990	+	0.648386i
$85$	1.89151	+	2.37187i	0.205163	+	0.257266i
$86$	5.63110			0.607217
$87$		0			0
$88$	−9.57325			−1.02051
$89$	−7.43999	−	9.32945i	−0.788637	−	0.988920i	−0.999934	−	0.0114978i	$-0.996340\pi$
$89$	−7.43999	−	9.32945i	−0.788637	−	0.988920i	0.211297	−	0.977422i	$-0.432231\pi$
$90$	1.06552	+	4.66833i	0.112315	+	0.492085i
$91$	0.909139	−	3.98320i	0.0953037	−	0.417553i
$92$	−0.938027	−	1.17625i	−0.0977961	−	0.122632i
$93$	4.60658	−	5.77647i	0.477680	−	0.598992i
$94$	0.327258	+	1.43381i	0.0337541	+	0.147886i
$95$	−11.8184	+	5.69146i	−1.21255	+	0.583932i
$96$	−12.3744	+	5.95920i	−1.26296	+	0.608208i
$97$	−2.54198	+	11.1372i	−0.258099	+	1.13081i	0.665182	+	0.746681i	$0.268354\pi$
$97$	−2.54198	+	11.1372i	−0.258099	+	1.13081i	−0.923281	+	0.384125i	$0.874503\pi$
$98$	−2.44345	−	1.17670i	−0.246826	−	0.118865i
$99$	−21.2856			−2.13929
$100$	−0.224318	−	0.108026i	−0.0224318	−	0.0108026i
$101$	0.607598	−	0.761904i	0.0604583	−	0.0758123i	−0.750683	−	0.660663i	$-0.770275\pi$
$101$	0.607598	−	0.761904i	0.0604583	−	0.0758123i	0.811141	+	0.584850i	$0.198847\pi$
$102$	1.18151	−	1.48156i	0.116986	−	0.146696i
$103$	7.00699	+	3.37439i	0.690419	+	0.332488i	0.745981	−	0.665967i	$-0.231981\pi$
$103$	7.00699	+	3.37439i	0.690419	+	0.332488i	−0.0555620	+	0.998455i	$0.517695\pi$
$104$	5.99760			0.588113
$105$	−6.96115	−	3.35232i	−0.679339	−	0.327152i
$106$	−0.660181	+	2.89244i	−0.0641224	+	0.280939i
$107$	4.90967	−	2.36437i	0.474636	−	0.228573i	−0.181244	−	0.983438i	$-0.558012\pi$
$107$	4.90967	−	2.36437i	0.474636	−	0.228573i	0.655879	+	0.754866i	$0.272298\pi$
$108$	−5.27163	+	2.53868i	−0.507263	+	0.244285i
$109$	1.75603	+	7.69365i	0.168197	+	0.736918i	0.986718	+	0.162442i	$0.0519371\pi$
$109$	1.75603	+	7.69365i	0.168197	+	0.736918i	−0.818521	+	0.574476i	$0.805206\pi$
$110$	3.51846	−	4.41201i	0.335472	−	0.420669i
$111$	9.90480	+	12.4202i	0.940122	+	1.17888i
$112$	0.724347	−	3.17357i	0.0684444	−	0.299874i
$113$	−3.84982	−	16.8672i	−0.362160	−	1.58673i	−0.747700	−	0.664037i	$-0.768842\pi$
$113$	−3.84982	−	16.8672i	−0.362160	−	1.58673i	0.385539	−	0.922691i	$-0.374015\pi$
$114$	5.10867	+	6.40608i	0.478471	+	0.599984i
$115$	1.90703			0.177831
$116$		0			0
$117$	13.3353			1.23285
$118$	1.38759	+	1.73998i	0.127738	+	0.160178i
$119$	0.398846	+	1.74746i	0.0365622	+	0.160189i
$120$	2.52383	−	11.0576i	0.230393	−	1.00942i
$121$	8.78210	+	11.0124i	0.798373	+	1.00113i
$122$	−1.73262	+	2.17264i	−0.156864	+	0.196701i
$123$	1.14359	+	5.01042i	0.103114	+	0.451774i
$124$	−4.29831	+	2.06996i	−0.386000	+	0.185888i
$125$	10.2122	−	4.91793i	0.913405	−	0.439873i
$126$	−0.629530	+	2.75815i	−0.0560829	+	0.245715i
$127$	4.96990	+	2.39338i	0.441007	+	0.212378i	0.641192	−	0.767380i	$-0.278440\pi$
$127$	4.96990	+	2.39338i	0.441007	+	0.212378i	−0.200185	+	0.979758i	$0.564154\pi$
$128$	11.4249			1.00983
$129$	−26.7196	−	12.8675i	−2.35253	−	1.13292i
$130$	−2.20430	+	2.76410i	−0.193330	+	0.242428i
$131$	0.0176400	−	0.0221199i	0.00154122	−	0.00193263i	−0.781060	−	0.624456i	$-0.785321\pi$
$131$	0.0176400	−	0.0221199i	0.00154122	−	0.00193263i	0.782601	+	0.622523i	$0.213892\pi$
$132$	21.1247	+	10.1731i	1.83867	+	0.885454i
$133$	−7.75009			−0.672018
$134$	−1.08836	−	0.524125i	−0.0940197	−	0.0452775i
$135$	1.65035	−	7.23067i	0.142040	−	0.622317i
$136$	−2.37062	+	1.14163i	−0.203279	+	0.0978940i
$137$	5.54516	−	2.67041i	0.473755	−	0.228149i	−0.181742	−	0.983346i	$-0.558173\pi$
$137$	5.54516	−	2.67041i	0.473755	−	0.228149i	0.655497	+	0.755198i	$0.272459\pi$
$138$	−0.265067	−	1.16134i	−0.0225640	−	0.0988594i
$139$	7.73636	−	9.70108i	0.656189	−	0.822835i	−0.336733	−	0.941600i	$-0.609322\pi$
$139$	7.73636	−	9.70108i	0.656189	−	0.822835i	0.992922	+	0.118765i	$0.0378935\pi$
$140$	3.11057	+	3.90053i	0.262891	+	0.329655i
$141$	1.72352	−	7.55126i	0.145147	−	0.635930i
$142$	−1.77357	−	7.77051i	−0.148835	−	0.652087i
$143$	−9.79869	−	12.2872i	−0.819408	−	1.02750i
$144$	10.6248			0.885400
$145$		0			0
$146$	1.73646			0.143710
$147$	8.90534	+	11.1669i	0.734500	+	0.921034i
$148$	−2.28258	−	10.0006i	−0.187627	−	0.822047i
$149$	4.63016	−	20.2860i	0.379317	−	1.66190i	−0.320252	−	0.947332i	$-0.603768\pi$
$149$	4.63016	−	20.2860i	0.379317	−	1.66190i	0.699570	−	0.714565i	$-0.253375\pi$
$150$	−0.122909	−	0.154122i	−0.0100354	−	0.0125840i
$151$	12.4875	−	15.6588i	1.01621	−	1.27429i	0.0550017	−	0.998486i	$-0.482484\pi$
$151$	12.4875	−	15.6588i	1.01621	−	1.27429i	0.961213	−	0.275807i	$-0.0889450\pi$
$152$	−2.53160	−	11.0917i	−0.205340	−	0.899654i
$153$	−5.27095	+	2.53836i	−0.426131	+	0.205214i
$154$	3.00393	−	1.44662i	0.242063	−	0.116572i
$155$	1.34564	−	5.89565i	0.108085	−	0.473550i
$156$	−13.2345	−	6.37340i	−1.05961	−	0.510280i
$157$	11.7893			0.940890			0.470445	−	0.882429i	$-0.344093\pi$
$157$	11.7893			0.940890			0.470445	+	0.882429i	$0.344093\pi$
$158$	−0.974741	−	0.469410i	−0.0775462	−	0.0373443i
$159$	9.74201	−	12.2161i	0.772591	−	0.968799i
$160$	−7.00896	+	8.78896i	−0.554107	+	0.694828i
$161$	1.01513	+	0.488862i	0.0800037	+	0.0385277i
$162$	1.88561			0.148148
$163$	−2.25838	−	1.08758i	−0.176890	−	0.0851859i	0.343343	−	0.939210i	$-0.388441\pi$
$163$	−2.25838	−	1.08758i	−0.176890	−	0.0851859i	−0.520233	+	0.854024i	$0.674155\pi$
$164$	0.738433	−	3.23529i	0.0576619	−	0.252633i
$165$	−26.7769	+	12.8951i	−2.08458	+	1.00388i
$166$	2.92914	−	1.41060i	0.227346	−	0.109484i
$167$	0.594332	+	2.60394i	0.0459908	+	0.201499i	0.992704	−	0.120580i	$-0.0384755\pi$
$167$	0.594332	+	2.60394i	0.0459908	+	0.201499i	−0.946713	+	0.322079i	$0.895618\pi$
$168$	4.17806	−	5.23912i	0.322344	−	0.404207i
$169$	−1.96653	−	2.46596i	−0.151272	−	0.189689i
$170$	0.345134	−	1.51213i	0.0264705	−	0.115975i
$171$	−5.62889	−	24.6618i	−0.430452	−	1.88593i
$172$	11.9396	+	14.9718i	0.910384	+	1.14159i
$173$	23.5982			1.79414			0.897071	−	0.441887i	$-0.145691\pi$
$173$	23.5982			1.79414			0.897071	+	0.441887i	$0.145691\pi$
$174$		0			0
$175$	0.186458			0.0140949
$176$	−7.80701	−	9.78968i	−0.588475	−	0.737925i
$177$	−2.60813	−	11.4269i	−0.196039	−	0.858902i
$178$	−1.35754	+	5.94776i	−0.101752	+	0.445803i
$179$	−13.0674	−	16.3859i	−0.976700	−	1.22474i	−0.974417	−	0.224746i	$-0.927845\pi$
$179$	−13.0674	−	16.3859i	−0.976700	−	1.22474i	−0.00228261	−	0.999997i	$-0.500727\pi$
$180$	−10.1528	+	12.7312i	−0.756743	+	0.948925i
$181$	−2.02358	−	8.86589i	−0.150412	−	0.658996i	−0.992765	−	0.120071i	$-0.961688\pi$
$181$	−2.02358	−	8.86589i	−0.150412	−	0.658996i	0.842354	−	0.538925i	$-0.181169\pi$
$182$	−1.88195	+	0.906298i	−0.139499	+	0.0671793i
$183$	13.1859	−	6.35001i	0.974732	−	0.469406i
$184$	−0.368046	+	1.61251i	−0.0271327	+	0.118876i
$185$	11.7148	+	5.64156i	0.861291	+	0.414776i
$186$	−3.77735			−0.276969
$187$	6.21189	+	2.99149i	0.454258	+	0.218759i
$188$	−3.11828	+	3.91020i	−0.227424	+	0.285180i
$189$	2.73207	−	3.42591i	0.198729	−	0.249198i
$190$	6.04225	+	2.90979i	0.438351	+	0.211099i
$191$	−19.2700			−1.39433			−0.697163	−	0.716912i	$-0.745555\pi$
$191$	−19.2700			−1.39433			−0.697163	+	0.716912i	$0.745555\pi$
$192$	−5.80321	−	2.79468i	−0.418810	−	0.201688i
$193$	1.18338	−	5.18472i	0.0851815	−	0.373204i	−0.914313	−	0.405009i	$-0.867268\pi$
$193$	1.18338	−	5.18472i	0.0851815	−	0.373204i	0.999494	+	0.0318048i	$0.0101255\pi$
$194$	5.26198	−	2.53404i	0.377788	−	0.181933i
$195$	16.7756	−	8.07871i	1.20133	−	0.578528i
$196$	−2.05225	−	8.99150i	−0.146589	−	0.642250i
$197$	−6.21783	+	7.79692i	−0.443002	+	0.555507i	−0.952332	−	0.305064i	$-0.901322\pi$
$197$	−6.21783	+	7.79692i	−0.443002	+	0.555507i	0.509329	+	0.860572i	$0.329893\pi$
$198$	6.78506	+	8.50820i	0.482193	+	0.604651i
$199$	4.93778	−	21.6338i	0.350030	−	1.53358i	−0.427079	−	0.904214i	$-0.640457\pi$
$199$	4.93778	−	21.6338i	0.350030	−	1.53358i	0.777109	−	0.629366i	$-0.216686\pi$
$200$	0.0609073	+	0.266852i	0.00430680	+	0.0188693i
$201$	3.96660	+	4.97395i	0.279782	+	0.350836i
$202$	−0.498225			−0.0350550
$203$		0			0
$204$	6.44425			0.451188
$205$	2.62265	+	3.28870i	0.183174	+	0.229693i
$206$	−0.884771	−	3.87643i	−0.0616449	−	0.270084i
$207$	−0.818330	+	3.58534i	−0.0568779	+	0.249198i
$208$	4.89105	+	6.13319i	0.339134	+	0.425260i
$209$	−18.5873	+	23.3077i	−1.28571	+	1.61223i
$210$	0.878983	+	3.85107i	0.0606556	+	0.265749i
$211$	6.58638	−	3.17184i	0.453425	−	0.218358i	−0.193210	−	0.981157i	$-0.561890\pi$
$211$	6.58638	−	3.17184i	0.453425	−	0.218358i	0.646635	+	0.762799i	$0.276176\pi$
$212$	−9.09008	+	4.37755i	−0.624309	+	0.300652i
$213$	−9.34061	+	40.9239i	−0.640008	+	2.80406i
$214$	−2.51010	−	1.20880i	−0.171587	−	0.0826318i
$215$	−24.2734			−1.65543
$216$	5.79549	+	2.79096i	0.394333	+	0.189901i
$217$	2.22764	−	2.79337i	0.151222	−	0.189626i
$218$	2.51552	−	3.15436i	0.170372	−	0.213640i
$219$	−8.23950	−	3.96793i	−0.556774	−	0.268128i
$220$	19.1906			1.29383
$221$	−3.89172	−	1.87415i	−0.261785	−	0.126069i
$222$	1.80728	−	7.91821i	0.121297	−	0.531435i
$223$	−4.95547	+	2.38643i	−0.331843	+	0.159807i	−0.592384	−	0.805656i	$-0.701813\pi$
$223$	−4.95547	+	2.38643i	−0.331843	+	0.159807i	0.260541	+	0.965463i	$0.416099\pi$
$224$	−5.98398	+	2.88173i	−0.399822	+	0.192544i
$225$	0.135424	+	0.593332i	0.00902828	+	0.0395555i
$226$	−5.51489	+	6.91545i	−0.366845	+	0.460009i
$227$	9.82060	+	12.3146i	0.651816	+	0.817351i	0.992425	−	0.122854i	$-0.0392046\pi$
$227$	9.82060	+	12.3146i	0.651816	+	0.817351i	−0.340609	+	0.940205i	$0.610633\pi$
$228$	−6.20035	+	27.1655i	−0.410628	+	1.79908i
$229$	3.30048	+	14.4603i	0.218102	+	0.955566i	0.958879	+	0.283815i	$0.0916002\pi$
$229$	3.30048	+	14.4603i	0.218102	+	0.955566i	−0.740777	+	0.671751i	$0.765543\pi$
$230$	−0.607889	−	0.762269i	−0.0400830	−	0.0502625i
$231$	−17.5593			−1.15532
$232$		0			0
$233$	−15.8867			−1.04078			−0.520388	−	0.853930i	$-0.674213\pi$
$233$	−15.8867			−1.04078			−0.520388	+	0.853930i	$0.674213\pi$
$234$	−4.25081	−	5.33035i	−0.277884	−	0.348456i
$235$	−1.41068	−	6.18058i	−0.0920224	−	0.403176i
$236$	−1.68410	+	7.37852i	−0.109625	+	0.480301i
$237$	3.55251	+	4.45471i	0.230761	+	0.289365i
$238$	0.571349	−	0.716450i	0.0370351	−	0.0464405i
$239$	−2.09168	−	9.16427i	−0.135300	−	0.592787i	−0.996432	−	0.0844052i	$-0.973101\pi$
$239$	−2.09168	−	9.16427i	−0.135300	−	0.592787i	0.861132	−	0.508382i	$-0.169756\pi$
$240$	13.3658	−	6.43663i	0.862758	−	0.415483i
$241$	9.40638	−	4.52987i	0.605918	−	0.291795i	−0.105659	−	0.994402i	$-0.533695\pi$
$241$	9.40638	−	4.52987i	0.605918	−	0.291795i	0.711578	+	0.702608i	$0.247981\pi$
$242$	1.60243	−	7.02069i	0.103008	−	0.451307i
$243$	−18.0435	−	8.68929i	−1.15749	−	0.557418i
$244$	−9.45018			−0.604986
$245$	10.5327	+	5.07229i	0.672911	+	0.324057i
$246$	1.63821	−	2.05425i	0.104448	−	0.130974i
$247$	11.6448	−	14.6022i	0.740943	−	0.929113i
$248$	4.72544	+	2.27565i	0.300066	+	0.144504i
$249$	−17.1221			−1.08507
$250$	−5.22103	−	2.51432i	−0.330207	−	0.159019i
$251$	3.28934	−	14.4115i	0.207621	−	0.909649i	−0.758523	−	0.651646i	$-0.774079\pi$
$251$	3.28934	−	14.4115i	0.207621	−	0.909649i	0.966144	−	0.258002i	$-0.0830642\pi$
$252$	−8.66804	+	4.17431i	−0.546035	+	0.262957i
$253$	3.90483	−	1.88047i	0.245495	−	0.118224i
$254$	−0.627548	−	2.74947i	−0.0393759	−	0.172517i
$255$	−5.09299	+	6.38641i	−0.318935	+	0.399932i
$256$	−0.658828	−	0.826145i	−0.0411768	−	0.0516340i
$257$	−0.385080	+	1.68715i	−0.0240206	+	0.105241i	−0.985517	−	0.169576i	$-0.945760\pi$
$257$	−0.385080	+	1.68715i	−0.0240206	+	0.105241i	0.961496	+	0.274817i	$0.0886173\pi$
$258$	3.37388	+	14.7819i	0.210049	+	0.920283i
$259$	4.78974	+	6.00614i	0.297620	+	0.373203i
$260$	−12.0228			−0.745625
$261$		0			0
$262$	−0.0144647			−0.000893630
$263$	−8.43648	−	10.5790i	−0.520216	−	0.652330i	0.450439	−	0.892807i	$-0.351268\pi$
$263$	−8.43648	−	10.5790i	−0.520216	−	0.652330i	−0.970655	+	0.240477i	$0.922696\pi$
$264$	−5.73582	−	25.1303i	−0.353015	−	1.54666i
$265$	2.84577	−	12.4681i	0.174814	−	0.765911i
$266$	2.47044	+	3.09783i	0.151472	+	0.189940i
$267$	20.0326	−	25.1201i	1.22598	−	1.53732i
$268$	−0.914110	−	4.00498i	−0.0558381	−	0.244643i
$269$	26.9294	−	12.9685i	1.64191	−	0.790704i	0.642205	−	0.766533i	$-0.278020\pi$
$269$	26.9294	−	12.9685i	1.64191	−	0.790704i	0.999708	−	0.0241706i	$-0.00769450\pi$
$270$	−3.41628	+	1.64520i	−0.207908	+	0.100123i
$271$	2.08368	−	9.12919i	0.126574	−	0.554559i	−0.871379	−	0.490611i	$-0.836774\pi$
$271$	2.08368	−	9.12919i	0.126574	−	0.554559i	0.997953	−	0.0639481i	$-0.0203692\pi$
$272$	−3.10069	−	1.49321i	−0.188007	−	0.0905393i
$273$	11.0008			0.665799
$274$	−2.83500	−	1.36526i	−0.171268	−	0.0824785i
$275$	0.447187	−	0.560755i	0.0269664	−	0.0338148i
$276$	2.52569	−	3.16712i	0.152029	−	0.190638i
$277$	−20.2017	−	9.72863i	−1.21380	−	0.584537i	−0.286224	−	0.958163i	$-0.592400\pi$
$277$	−20.2017	−	9.72863i	−1.21380	−	0.584537i	−0.927579	+	0.373626i	$0.878114\pi$
$278$	−6.34374			−0.380472
$279$	10.5068	+	5.05980i	0.629024	+	0.302922i
$280$	1.22047	−	5.34722i	0.0729369	−	0.319557i
$281$	7.84928	−	3.78002i	0.468249	−	0.225497i	−0.184854	−	0.982766i	$-0.559181\pi$
$281$	7.84928	−	3.78002i	0.468249	−	0.225497i	0.653103	+	0.757269i	$0.273467\pi$
$282$	−3.56775	+	1.71814i	−0.212456	+	0.102314i
$283$	3.21723	+	14.0956i	0.191244	+	0.837896i	0.975944	+	0.218020i	$0.0699599\pi$
$283$	3.21723	+	14.0956i	0.191244	+	0.837896i	−0.784700	+	0.619876i	$0.787183\pi$
$284$	16.8994	−	21.1912i	1.00280	−	1.25747i
$285$	−22.0214	−	27.6140i	−1.30444	−	1.63571i
$286$	−1.78792	+	7.83338i	−0.105722	+	0.463198i
$287$	0.553017	+	2.42292i	0.0326435	+	0.143021i
$288$	−13.5162	−	16.9488i	−0.796450	−	0.998717i
$289$	−15.1050			−0.888530
$290$		0			0
$291$	−30.7586			−1.80310
$292$	3.68179	+	4.61682i	0.215461	+	0.270179i
$293$	7.28889	+	31.9347i	0.425822	+	1.86565i	0.496328	+	0.868135i	$0.334681\pi$
$293$	7.28889	+	31.9347i	0.425822	+	1.86565i	−0.0705061	+	0.997511i	$0.522461\pi$
$294$	1.62491	−	7.11920i	0.0947668	−	0.415200i
$295$	−5.98132	−	7.50033i	−0.348246	−	0.436686i
$296$	−7.03120	+	8.81685i	−0.408680	+	0.512469i
$297$	−3.75070	−	16.4329i	−0.217638	−	0.953533i
$298$	−9.58457	+	4.61568i	−0.555219	+	0.267379i
$299$	−2.44636	+	1.17810i	−0.141476	+	0.0681315i
$300$	0.149173	−	0.653569i	0.00861249	−	0.0377338i
$301$	−12.9210	−	6.22243i	−0.744755	−	0.358655i
$302$	−10.2396			−0.589222
$303$	2.36408	+	1.13848i	0.135813	+	0.0654040i
$304$	9.27790	−	11.6341i	0.532124	−	0.667263i
$305$	7.46862	−	9.36535i	0.427652	−	0.536258i
$306$	2.69480	+	1.29775i	0.154052	+	0.0741874i
$307$	28.4921			1.62613			0.813065	−	0.582173i	$-0.197798\pi$
$307$	28.4921			1.62613			0.813065	+	0.582173i	$0.197798\pi$
$308$	10.2154	+	4.91948i	0.582077	+	0.280313i
$309$	−4.65970	+	20.4155i	−0.265081	+	1.16140i
$310$	−2.78552	+	1.34144i	−0.158207	+	0.0761885i
$311$	−19.6480	+	9.46196i	−1.11413	+	0.536539i	−0.898075	−	0.439842i	$-0.855035\pi$
$311$	−19.6480	+	9.46196i	−1.11413	+	0.536539i	−0.216059	+	0.976380i	$0.569320\pi$
$312$	3.59347	+	15.7440i	0.203440	+	0.891328i
$313$	−14.9186	+	18.7074i	−0.843251	+	1.05740i	0.154339	+	0.988018i	$0.450675\pi$
$313$	−14.9186	+	18.7074i	−0.843251	+	1.05740i	−0.997590	+	0.0693848i	$0.977896\pi$
$314$	−3.75799	−	4.71237i	−0.212076	−	0.265935i
$315$	2.71365	−	11.8893i	0.152897	−	0.669884i
$316$	−0.818684	−	3.58689i	−0.0460546	−	0.201778i
$317$	−5.83121	−	7.31211i	−0.327514	−	0.410689i	0.590626	−	0.806945i	$-0.298881\pi$
$317$	−5.83121	−	7.31211i	−0.327514	−	0.410689i	−0.918140	+	0.396256i	$0.870309\pi$
$318$	−7.98835			−0.447964
$319$		0			0
$320$	−5.27191			−0.294709
$321$	9.14824	+	11.4715i	0.510605	+	0.640278i
$322$	−0.128180	−	0.561595i	−0.00714322	−	0.0312965i
$323$	−1.82326	+	7.98825i	−0.101449	+	0.444478i
$324$	3.99804	+	5.01339i	0.222114	+	0.278522i
$325$	−0.280161	+	0.351310i	−0.0155405	+	0.0194872i
$326$	0.285166	+	1.24939i	0.0157939	+	0.0691974i
$327$	−19.1441	+	9.21932i	−1.05867	+	0.509829i
$328$	−3.28696	+	1.58292i	−0.181492	+	0.0874021i
$329$	0.833458	−	3.65162i	0.0459500	−	0.201320i
$330$	13.6898	+	6.59268i	0.753601	+	0.362915i
$331$	10.2474			0.563247			0.281623	−	0.959525i	$-0.409127\pi$
$331$	10.2474			0.563247			0.281623	+	0.959525i	$0.409127\pi$
$332$	9.96108	+	4.79700i	0.546685	+	0.263270i
$333$	−15.6335	+	19.6038i	−0.856711	+	1.07428i
$334$	0.851384	−	1.06760i	0.0465857	−	0.0584166i
$335$	4.69146	+	2.25929i	0.256322	+	0.123438i
$336$	8.76478			0.478158
$337$	−14.3647	−	6.91766i	−0.782493	−	0.376829i	−0.000407467	−	1.00000i	$-0.500130\pi$
$337$	−14.3647	−	6.91766i	−0.782493	−	0.376829i	−0.782085	+	0.623171i	$0.785844\pi$
$338$	−0.358824	+	1.57211i	−0.0195174	+	0.0855114i
$339$	41.9705	−	20.2119i	2.27953	−	1.09776i
$340$	4.75217	−	2.28853i	0.257723	−	0.124113i
$341$	−3.05819	−	13.3988i	−0.165611	−	0.725587i
$342$	−8.06342	+	10.1112i	−0.436020	+	0.546751i
$343$	9.98917	+	12.5260i	0.539365	+	0.676342i
$344$	4.68463	−	20.5247i	0.252578	−	1.10662i
$345$	1.14260	+	5.00604i	0.0615153	+	0.269516i
$346$	−7.52224	−	9.43259i	−0.404398	−	0.507099i
$347$	36.7925			1.97513			0.987563	−	0.157224i	$-0.0502544\pi$
$347$	36.7925			1.97513			0.987563	+	0.157224i	$0.0502544\pi$
$348$		0			0
$349$	32.4894			1.73912			0.869558	−	0.493831i	$-0.164404\pi$
$349$	32.4894			1.73912			0.869558	+	0.493831i	$0.164404\pi$
$350$	−0.0594358	−	0.0745301i	−0.00317698	−	0.00398380i
$351$	2.34980	+	10.2951i	0.125423	+	0.549514i
$352$	−5.68500	+	24.9076i	−0.303012	+	1.32758i
$353$	−7.49252	−	9.39533i	−0.398787	−	0.500063i	0.541380	−	0.840778i	$-0.317902\pi$
$353$	−7.49252	−	9.39533i	−0.398787	−	0.500063i	−0.940166	+	0.340715i	$0.889331\pi$
$354$	−3.73616	+	4.68499i	−0.198574	+	0.249004i
$355$	7.64513	+	33.4955i	0.405761	+	1.77776i
$356$	−18.6920	+	9.00161i	−0.990676	+	0.477085i
$357$	−4.34820	+	2.09398i	−0.230131	+	0.110825i
$358$	−2.38433	+	10.4465i	−0.126016	+	0.552112i
$359$	3.52153	+	1.69588i	0.185859	+	0.0895052i	0.524499	−	0.851411i	$-0.324253\pi$
$359$	3.52153	+	1.69588i	0.185859	+	0.0895052i	−0.338640	+	0.940916i	$0.609967\pi$
$360$	17.9019			0.943515
$361$	−14.8015	−	7.12801i	−0.779024	−	0.375158i
$362$	−2.89879	+	3.63497i	−0.152357	+	0.191050i
$363$	−23.6463	+	29.6515i	−1.24111	+	1.55630i
$364$	−6.39990	−	3.08203i	−0.335446	−	0.161542i
$365$	−7.48515			−0.391791
$366$	−6.74138	−	3.24648i	−0.352378	−	0.169696i
$367$	−2.84545	+	12.4667i	−0.148532	+	0.650759i	0.844762	+	0.535142i	$0.179742\pi$
$367$	−2.84545	+	12.4667i	−0.148532	+	0.650759i	−0.993294	+	0.115617i	$0.963115\pi$
$368$	−1.94911	+	0.938642i	−0.101604	+	0.0489301i
$369$	−7.30839	+	3.51954i	−0.380460	+	0.183220i
$370$	−1.47923	−	6.48092i	−0.0769014	−	0.336927i
$371$	4.71101	−	5.90743i	0.244584	−	0.306698i
$372$	−8.00908	−	10.0431i	−0.415251	−	0.520709i
$373$	−5.56002	+	24.3600i	−0.287887	+	1.26131i	0.599532	+	0.800351i	$0.295353\pi$
$373$	−5.56002	+	24.3600i	−0.287887	+	1.26131i	−0.887419	+	0.460964i	$0.847504\pi$
$374$	−0.784373	−	3.43656i	−0.0405590	−	0.177700i
$375$	19.0284	+	23.8609i	0.982624	+	1.23217i
$376$	5.49833			0.283555
$377$		0			0
$378$	−2.24027			−0.115227
$379$	8.12732	+	10.1913i	0.417472	+	0.523494i	0.945451	−	0.325764i	$-0.105621\pi$
$379$	8.12732	+	10.1913i	0.417472	+	0.523494i	−0.527979	+	0.849258i	$0.677050\pi$
$380$	5.07488	+	22.2345i	0.260336	+	1.14061i
$381$	−3.30502	+	14.4802i	−0.169321	+	0.741845i
$382$	6.14255	+	7.70251i	0.314280	+	0.394095i
$383$	14.9856	−	18.7913i	0.765728	−	0.960193i	−0.234200	−	0.972188i	$-0.575247\pi$
$383$	14.9856	−	18.7913i	0.765728	−	0.960193i	0.999928	+	0.0119957i	$0.00381846\pi$
$384$	6.84522	+	29.9909i	0.349319	+	1.53047i
$385$	−12.9487	+	6.23577i	−0.659927	+	0.317804i
$386$	−2.44963	+	1.17968i	−0.124683	+	0.0600441i
$387$	10.4160	−	45.6356i	0.529477	−	2.31979i
$388$	17.8943	+	8.61746i	0.908447	+	0.437485i
$389$	−17.6717			−0.895991			−0.447995	−	0.894036i	$-0.647862\pi$
$389$	−17.6717			−0.895991			−0.447995	+	0.894036i	$0.647862\pi$
$390$	−8.57662	−	4.13028i	−0.434294	−	0.209145i
$391$	0.742702	−	0.931318i	0.0375600	−	0.0470988i
$392$	−6.32170	+	7.92717i	−0.319294	+	0.400382i
$393$	0.0686350	+	0.0330529i	0.00346218	+	0.00166730i
$394$	5.09856			0.256862
$395$	4.20171	+	2.02344i	0.211411	+	0.101810i
$396$	−8.23496	+	36.0797i	−0.413822	+	1.81307i
$397$	−27.2566	+	13.1261i	−1.36797	+	0.658780i	−0.966399	−	0.257047i	$-0.917250\pi$
$397$	−27.2566	+	13.1261i	−1.36797	+	0.658780i	−0.401572	+	0.915827i	$0.631536\pi$
$398$	−10.2214	+	4.92235i	−0.512350	+	0.246735i
$399$	−4.64347	−	20.3444i	−0.232464	−	1.01849i
$400$	−0.223215	+	0.279903i	−0.0111608	+	0.0139951i
$401$	−7.70463	−	9.66129i	−0.384751	−	0.482462i	0.551310	−	0.834300i	$-0.314128\pi$
$401$	−7.70463	−	9.66129i	−0.384751	−	0.482462i	−0.936061	+	0.351838i	$0.885557\pi$
$402$	0.723765	−	3.17102i	0.0360981	−	0.158156i
$403$	1.91594	+	8.39430i	0.0954400	+	0.418150i
$404$	−1.05638	−	1.32466i	−0.0525569	−	0.0659043i
$405$	−8.12810			−0.403889
$406$		0			0
$407$	29.5503			1.46475
$408$	−4.41720	−	5.53899i	−0.218684	−	0.274221i
$409$	1.35893	+	5.95386i	0.0671948	+	0.294400i	0.997349	−	0.0727701i	$-0.0231839\pi$
$409$	1.35893	+	5.95386i	0.0671948	+	0.294400i	−0.930154	+	0.367170i	$0.880327\pi$
$410$	0.478542	−	2.09663i	0.0236335	−	0.103545i
$411$	10.3323	+	12.9564i	0.509657	+	0.639090i
$412$	8.43054	−	10.5716i	0.415343	−	0.520823i
$413$	−1.26123	−	5.52581i	−0.0620611	−	0.271907i
$414$	1.69397	−	0.815773i	0.0832541	−	0.0400930i
$415$	−12.6263	+	6.08052i	−0.619803	+	0.298481i
$416$	3.56163	−	15.6045i	0.174623	−	0.765074i
$417$	30.1011	+	14.4959i	1.47406	+	0.709868i
$418$	15.2414			0.745480
$419$	−10.4580	−	5.03629i	−0.510905	−	0.246039i	0.160626	−	0.987015i	$-0.448649\pi$
$419$	−10.4580	−	5.03629i	−0.510905	−	0.246039i	−0.671531	+	0.740976i	$0.734363\pi$
$420$	−8.37539	+	10.5024i	−0.408677	+	0.512465i
$421$	−12.6486	+	15.8608i	−0.616453	+	0.773008i	−0.987841	−	0.155470i	$-0.950311\pi$
$421$	−12.6486	+	15.8608i	−0.616453	+	0.773008i	0.371387	+	0.928478i	$0.378882\pi$
$422$	−3.36733	−	1.62162i	−0.163919	−	0.0789391i
$423$	12.2252			0.594412
$424$	9.99339	+	4.81256i	0.485322	+	0.233719i
$425$	0.0438655	−	0.192187i	0.00212779	−	0.00932246i
$426$	19.3353	−	9.31141i	0.936801	−	0.451139i
$427$	6.37642	−	3.07072i	0.308577	−	0.148603i
$428$	−2.10823	−	9.23675i	−0.101905	−	0.446475i
$429$	26.3836	−	33.0839i	1.27381	−	1.59731i
$430$	7.73745	+	9.70245i	0.373133	+	0.467894i
$431$	−3.77923	+	16.5579i	−0.182039	+	0.797566i	0.798619	+	0.601837i	$0.205564\pi$
$431$	−3.77923	+	16.5579i	−0.182039	+	0.797566i	−0.980658	+	0.195729i	$0.937293\pi$
$432$	1.87218	+	8.20254i	0.0900751	+	0.394645i
$433$	−9.93547	−	12.4587i	−0.477468	−	0.598726i	0.483514	−	0.875337i	$-0.339360\pi$
$433$	−9.93547	−	12.4587i	−0.477468	−	0.598726i	−0.960982	+	0.276610i	$0.910789\pi$
$434$	−1.82664			−0.0876815
$435$		0			0
$436$	13.7203			0.657084
$437$	3.21134	+	4.02690i	0.153619	+	0.192633i
$438$	1.04040	+	4.55828i	0.0497122	+	0.217803i
$439$	1.20240	−	5.26804i	0.0573872	−	0.251430i	−0.938095	−	0.346378i	$-0.887411\pi$
$439$	1.20240	−	5.26804i	0.0573872	−	0.251430i	0.995482	+	0.0949482i	$0.0302685\pi$
$440$	−13.1542	−	16.4948i	−0.627101	−	0.786360i
$441$	−14.0560	+	17.6256i	−0.669332	+	0.839316i
$442$	0.491406	+	2.15299i	0.0233738	+	0.102407i
$443$	17.1647	−	8.26609i	0.815520	−	0.392734i	0.0208553	−	0.999783i	$-0.493361\pi$
$443$	17.1647	−	8.26609i	0.815520	−	0.392734i	0.794665	+	0.607049i	$0.207647\pi$
$444$	24.8846	−	11.9838i	1.18097	−	0.568725i
$445$	5.85179	−	25.6384i	0.277402	−	1.21538i
$446$	2.53351	+	1.22007i	0.119965	+	0.0577722i
$447$	56.0260			2.64994
$448$	−2.80630	−	1.35144i	−0.132585	−	0.0638497i
$449$	−11.0279	+	13.8286i	−0.520440	+	0.652611i	−0.970702	−	0.240285i	$-0.922759\pi$
$449$	−11.0279	+	13.8286i	−0.520440	+	0.652611i	0.450262	+	0.892896i	$0.351330\pi$
$450$	0.193996	−	0.243263i	0.00914506	−	0.0114675i
$451$	8.61304	+	4.14782i	0.405572	+	0.195313i
$452$	−30.0797			−1.41483
$453$	48.5869	+	23.3982i	2.28281	+	1.09935i
$454$	1.79192	−	7.85089i	0.0840987	−	0.368461i
$455$	8.11231	−	3.90668i	0.380311	−	0.183148i
$456$	27.5994	−	13.2912i	1.29246	−	0.622416i
$457$	3.35962	+	14.7195i	0.157157	+	0.688548i	0.990697	+	0.136089i	$0.0434532\pi$
$457$	3.35962	+	14.7195i	0.157157	+	0.688548i	−0.833540	+	0.552459i	$0.813690\pi$
$458$	4.72795	−	5.92867i	0.220923	−	0.277028i
$459$	−2.88844	−	3.62199i	−0.134821	−	0.169060i
$460$	0.737788	−	3.23246i	0.0343996	−	0.150714i
$461$	−4.96261	−	21.7426i	−0.231132	−	1.01266i	−0.948703	−	0.316170i	$-0.897603\pi$
$461$	−4.96261	−	21.7426i	−0.231132	−	1.01266i	0.717571	−	0.696486i	$-0.245254\pi$
$462$	5.59724	+	7.01872i	0.260407	+	0.326541i
$463$	−26.7391			−1.24267			−0.621335	−	0.783545i	$-0.713409\pi$
$463$	−26.7391			−1.24267			−0.621335	+	0.783545i	$0.713409\pi$
$464$		0			0
$465$	16.2826			0.755088
$466$	5.06410	+	6.35018i	0.234590	+	0.294166i
$467$	2.57262	+	11.2714i	0.119047	+	0.521578i	0.998924	+	0.0463768i	$0.0147675\pi$
$467$	2.57262	+	11.2714i	0.119047	+	0.521578i	−0.879877	+	0.475201i	$0.842375\pi$
$468$	5.15916	−	22.6038i	0.238482	−	1.04486i
$469$	1.91816	+	2.40529i	0.0885722	+	0.111066i
$470$	−2.02080	+	2.53401i	−0.0932127	+	0.116885i
$471$	7.06358	+	30.9475i	0.325472	+	1.42599i
$472$	7.49637	−	3.61006i	0.345049	−	0.166167i
$473$	−49.7022	+	23.9353i	−2.28531	+	1.10055i
$474$	0.648210	−	2.83999i	0.0297732	−	0.130445i
$475$	0.767953	+	0.369827i	0.0352361	+	0.0169688i
$476$	3.11630			0.142835
$477$	22.2198	+	10.7005i	1.01737	+	0.489941i
$478$	−2.99635	+	3.75730i	−0.137050	+	0.171855i
$479$	−15.1683	+	19.0204i	−0.693056	+	0.869065i	−0.996483	−	0.0837900i	$-0.973298\pi$
$479$	−15.1683	+	19.0204i	−0.693056	+	0.869065i	0.303428	+	0.952854i	$0.401869\pi$
$480$	−27.2709	−	13.1330i	−1.24474	−	0.599435i
$481$	−18.5131			−0.844125
$482$	−4.80906	−	2.31592i	−0.219047	−	0.105487i
$483$	−0.675070	+	2.95768i	−0.0307168	+	0.134579i
$484$	22.0639	−	10.6254i	1.00291	−	0.482974i
$485$	−22.6823	+	10.9232i	−1.02995	+	0.495997i
$486$	2.27835	+	9.98208i	0.103348	+	0.452796i
$487$	0.802361	−	1.00613i	0.0363584	−	0.0455920i	−0.763320	−	0.646021i	$-0.776432\pi$
$487$	0.802361	−	1.00613i	0.0363584	−	0.0455920i	0.799678	+	0.600429i	$0.205003\pi$
$488$	6.47760	+	8.12266i	0.293227	+	0.367695i
$489$	1.50184	−	6.58000i	0.0679156	−	0.297558i
$490$	−1.32996	−	5.82695i	−0.0600816	−	0.263235i
$491$	−20.3622	−	25.5334i	−0.918933	−	1.15231i	−0.987963	−	0.154691i	$-0.950562\pi$
$491$	−20.3622	−	25.5334i	−0.918933	−	1.15231i	0.0690296	−	0.997615i	$-0.478010\pi$
$492$	8.93522			0.402831
$493$		0			0
$494$	−9.54865			−0.429614
$495$	−29.2476	−	36.6754i	−1.31458	−	1.64844i
$496$	1.52651	+	6.68807i	0.0685423	+	0.300303i
$497$	−4.51691	+	19.7899i	−0.202611	+	0.887696i
$498$	5.45790	+	6.84398i	0.244574	+	0.306686i
$499$	−6.53615	+	8.19607i	−0.292598	+	0.366907i	−0.906303	−	0.422629i	$-0.861107\pi$
$499$	−6.53615	+	8.19607i	−0.292598	+	0.366907i	0.613704	+	0.789536i	$0.289679\pi$
$500$	−4.38514	−	19.2126i	−0.196109	−	0.859212i
$501$	−6.47938	+	3.12030i	−0.289477	+	0.139405i
$502$	−6.80904	+	3.27906i	−0.303902	+	0.146352i
$503$	−0.843435	+	3.69533i	−0.0376069	+	0.164767i	−0.990244	−	0.139342i	$-0.955501\pi$
$503$	−0.843435	+	3.69533i	−0.0376069	+	0.164767i	0.952637	+	0.304108i	$0.0983585\pi$
$504$	9.52941	+	4.58912i	0.424474	+	0.204416i
$505$	2.14764			0.0955689
$506$	−1.99637	−	0.961399i	−0.0887493	−	0.0427394i
$507$	5.29501	−	6.63973i	0.235160	−	0.294881i
$508$	5.97959	−	7.49817i	0.265301	−	0.332677i
$509$	7.22423	+	3.47900i	0.320208	+	0.154204i	0.587082	−	0.809527i	$-0.300276\pi$
$509$	7.22423	+	3.47900i	0.320208	+	0.154204i	−0.266874	+	0.963731i	$0.585991\pi$
$510$	4.17620			0.184925
$511$	−3.98443	−	1.91880i	−0.176261	−	0.0848828i
$512$	4.96433	−	21.7502i	0.219395	−	0.961231i
$513$	18.0475	−	8.69121i	0.796816	−	0.383726i
$514$	0.797127	−	0.383876i	0.0351598	−	0.0169321i
$515$	3.81389	+	16.7097i	0.168060	+	0.736319i
$516$	−32.1480	+	40.3123i	−1.41524	+	1.77465i
$517$	−8.98300	−	11.2643i	−0.395072	−	0.495404i
$518$	0.873959	−	3.82907i	0.0383996	−	0.168239i
$519$	14.1389	+	61.9466i	0.620629	+	2.71915i
$520$	8.24103	+	10.3339i	0.361393	+	0.453173i
$521$	−6.39024			−0.279962			−0.139981	−	0.990154i	$-0.544704\pi$
$521$	−6.39024			−0.279962			−0.139981	+	0.990154i	$0.544704\pi$
$522$		0			0
$523$	−16.3261			−0.713891			−0.356946	−	0.934125i	$-0.616182\pi$
$523$	−16.3261			−0.713891			−0.356946	+	0.934125i	$0.616182\pi$
$524$	−0.0306693	−	0.0384581i	−0.00133979	−	0.00168005i
$525$	0.111716	+	0.489461i	0.00487570	+	0.0213618i
$526$	−1.53936	+	6.74439i	−0.0671194	+	0.294069i
$527$	−2.35514	−	2.95325i	−0.102591	−	0.128646i
$528$	21.0208	−	26.3593i	0.914814	−	1.14714i
$529$	4.95136	+	21.6933i	0.215276	+	0.943188i
$530$	−5.89083	+	2.83688i	−0.255881	+	0.123226i
$531$	16.6678	−	8.02679i	0.723321	−	0.348333i
$532$	−2.99835	+	13.1366i	−0.129995	+	0.569545i
$533$	−5.39603	−	2.59859i	−0.233728	−	0.112557i
$534$	−16.4265			−0.710846
$535$	10.8200	+	5.21064i	0.467790	+	0.225276i
$536$	−2.81580	+	3.53090i	−0.121624	+	0.152512i
$537$	35.1846	−	44.1201i	1.51833	−	1.90392i
$538$	−13.7678	−	6.63022i	−0.593572	−	0.285849i
$539$	26.5684			1.14438
$540$	−11.6177	−	5.59479i	−0.499946	−	0.240761i
$541$	−4.88681	+	21.4105i	−0.210100	+	0.920509i	0.754397	+	0.656418i	$0.227929\pi$
$541$	−4.88681	+	21.4105i	−0.210100	+	0.920509i	−0.964498	+	0.264091i	$0.914928\pi$
$542$	−4.31328	+	2.07717i	−0.185271	+	0.0892219i
$543$	22.0610	−	10.6240i	0.946727	−	0.455920i
$544$	1.56251	+	6.84581i	0.0669922	+	0.293512i
$545$	−10.8434	+	13.5972i	−0.464479	+	0.582438i
$546$	−3.50665	−	4.39720i	−0.150071	−	0.188183i
$547$	−0.913490	+	4.00226i	−0.0390580	+	0.171124i	−0.990695	−	0.136100i	$-0.956543\pi$
$547$	−0.913490	+	4.00226i	−0.0390580	+	0.171124i	0.951637	+	0.307224i	$0.0994002\pi$
$548$	−2.38111	−	10.4323i	−0.101716	−	0.445647i
$549$	14.4026	+	18.0603i	0.614688	+	0.770795i
$550$	−0.366689			−0.0156357
$551$		0			0
$552$	−4.45344			−0.189551
$553$	1.71792	+	2.15420i	0.0730532	+	0.0916058i
$554$	2.55086	+	11.1761i	0.108376	+	0.474826i
$555$	−7.79044	+	34.1322i	−0.330686	+	1.44883i
$556$	−13.4506	−	16.8665i	−0.570431	−	0.715298i
$557$	−15.5194	+	19.4607i	−0.657579	+	0.824578i	−0.993077	−	0.117463i	$-0.962524\pi$
$557$	−15.5194	+	19.4607i	−0.657579	+	0.824578i	0.335498	+	0.942041i	$0.391095\pi$
$558$	−1.32669	−	5.81260i	−0.0561632	−	0.246067i
$559$	31.1382	−	14.9954i	1.31701	−	0.634236i
$560$	6.46340	−	3.11261i	0.273128	−	0.131532i
$561$	−4.13095	+	18.0989i	−0.174409	+	0.764135i
$562$	−4.01299	−	1.93255i	−0.169278	−	0.0815199i
$563$	−22.6338			−0.953902			−0.476951	−	0.878930i	$-0.658258\pi$
$563$	−22.6338			−0.953902			−0.476951	+	0.878930i	$0.658258\pi$
$564$	−12.1328	−	5.84284i	−0.510882	−	0.246028i
$565$	23.7724	−	29.8097i	1.00011	−	1.25410i
$566$	4.60870	−	5.77912i	0.193718	−	0.242915i
$567$	−4.32668	−	2.08362i	−0.181704	−	0.0875038i
$568$	−29.7981			−1.25030
$569$	9.36806	+	4.51142i	0.392729	+	0.189128i	0.619818	−	0.784746i	$-0.287206\pi$
$569$	9.36806	+	4.51142i	0.392729	+	0.189128i	−0.227089	+	0.973874i	$0.572921\pi$
$570$	−4.01814	+	17.6046i	−0.168301	+	0.737376i
$571$	−32.1437	+	15.4796i	−1.34517	+	0.647800i	−0.961279	−	0.275578i	$-0.911131\pi$
$571$	−32.1437	+	15.4796i	−1.34517	+	0.647800i	−0.383892	+	0.923378i	$0.625417\pi$
$572$	−24.6180	+	11.8554i	−1.02933	+	0.495699i
$573$	−11.5456	−	50.5847i	−0.482325	−	2.11321i
$574$	0.792200	−	0.993387i	0.0330658	−	0.0414632i
$575$	−0.0772610	−	0.0968823i	−0.00322201	−	0.00404027i
$576$	2.26225	−	9.91155i	0.0942603	−	0.412981i
$577$	0.357991	+	1.56846i	0.0149033	+	0.0652958i	0.981833	−	0.189748i	$-0.0607672\pi$
$577$	0.357991	+	1.56846i	0.0149033	+	0.0652958i	−0.966929	+	0.255044i	$0.917910\pi$
$578$	4.81491	+	6.03771i	0.200274	+	0.251136i
$579$	14.3192			0.595085
$580$		0			0
$581$	−8.27988			−0.343507
$582$	9.80470	+	12.2947i	0.406418	+	0.509632i
$583$	−6.46748	−	28.3359i	−0.267856	−	1.17355i
$584$	1.44459	−	6.32918i	0.0597777	−	0.261903i
$585$	18.3235	+	22.9770i	0.757584	+	0.949980i
$586$	10.4414	−	13.0931i	0.431330	−	0.540870i
$587$	−5.50834	−	24.1336i	−0.227354	−	0.996102i	−0.951788	−	0.306758i	$-0.900756\pi$
$587$	−5.50834	−	24.1336i	−0.227354	−	0.996102i	0.724434	−	0.689344i	$-0.242101\pi$
$588$	22.3735	−	10.7745i	0.922670	−	0.444334i
$589$	14.7153	−	7.08652i	0.606334	−	0.291995i
$590$	−1.09138	+	4.78165i	−0.0449314	+	0.196857i
$591$	−24.1927	−	11.6506i	−0.995156	−	0.479242i
$592$	−14.7501			−0.606227
$593$	9.19662	+	4.42886i	0.377660	+	0.181871i	0.613077	−	0.790023i	$-0.289931\pi$
$593$	9.19662	+	4.42886i	0.377660	+	0.181871i	−0.235417	+	0.971894i	$0.575646\pi$
$594$	−5.37290	+	6.73741i	−0.220453	+	0.276439i
$595$	−2.46285	+	3.08832i	−0.100967	+	0.126609i
$596$	−32.5941	−	15.6965i	−1.33511	−	0.642953i
$597$	59.7483			2.44534
$598$	1.25071	+	0.602312i	0.0511455	+	0.0246304i
$599$	4.17765	−	18.3035i	0.170694	−	0.747860i	−0.815020	−	0.579433i	$-0.803274\pi$
$599$	4.17765	−	18.3035i	0.170694	−	0.747860i	0.985714	−	0.168427i	$-0.0538688\pi$
$600$	−0.664008	+	0.319770i	−0.0271080	+	0.0130545i
$601$	−36.7693	+	17.7072i	−1.49985	+	0.722290i	−0.990403	−	0.138211i	$-0.955865\pi$
$601$	−36.7693	+	17.7072i	−1.49985	+	0.722290i	−0.509448	+	0.860501i	$0.670151\pi$
$602$	1.63153	+	7.14821i	0.0664963	+	0.291339i
$603$	−6.26078	+	7.85077i	−0.254959	+	0.319708i
$604$	−21.7109	−	27.2246i	−0.883405	−	1.10775i
$605$	−6.90740	+	30.2633i	−0.280826	+	1.23038i
$606$	−0.298512	−	1.30787i	−0.0121262	−	0.0531284i
$607$	−7.29721	−	9.15041i	−0.296185	−	0.371404i	0.611365	−	0.791349i	$-0.290621\pi$
$607$	−7.29721	−	9.15041i	−0.296185	−	0.371404i	−0.907550	+	0.419945i	$0.862049\pi$
$608$	−30.3616			−1.23133
$609$		0			0
$610$	−6.12419			−0.247961
$611$	5.62781	+	7.05704i	0.227677	+	0.285497i
$612$	2.26336	+	9.91644i	0.0914910	+	0.400848i
$613$	−3.08627	+	13.5218i	−0.124653	+	0.546142i	0.873577	+	0.486685i	$0.161794\pi$
$613$	−3.08627	+	13.5218i	−0.124653	+	0.546142i	−0.998231	+	0.0594571i	$0.981063\pi$
$614$	−9.08221	−	11.3887i	−0.366528	−	0.459612i
$615$	−7.06164	+	8.85502i	−0.284753	+	0.357069i
$616$	−2.77371	−	12.1524i	−0.111756	−	0.489636i
$617$	−22.7317	+	10.9470i	−0.915142	+	0.440709i	−0.831334	−	0.555773i	$-0.812422\pi$
$617$	−22.7317	+	10.9470i	−0.915142	+	0.440709i	−0.0838079	+	0.996482i	$0.526708\pi$
$618$	9.64572	−	4.64514i	0.388008	−	0.186855i
$619$	−6.43162	+	28.1788i	−0.258509	+	1.13260i	0.664338	+	0.747432i	$0.268714\pi$
$619$	−6.43162	+	28.1788i	−0.258509	+	1.13260i	−0.922847	+	0.385168i	$0.874144\pi$
$620$	−9.47268	−	4.56180i	−0.380432	−	0.183206i
$621$	−2.91215			−0.116860
$622$	10.0451	+	4.83748i	0.402773	+	0.193965i
$623$	9.68732	−	12.1475i	0.388114	−	0.486680i
$624$	−13.1694	+	16.5140i	−0.527200	+	0.661088i
$625$	21.8606	+	10.5275i	0.874426	+	0.421101i
$626$	12.2331			0.488934
$627$	−72.3205	−	34.8277i	−2.88820	−	1.39088i
$628$	4.56104	−	19.9832i	0.182005	−	0.797417i
$629$	7.31752	−	3.52393i	0.291769	−	0.140508i
$630$	−5.61733	+	2.70516i	−0.223800	+	0.107776i
$631$	−3.49292	−	15.3035i	−0.139051	−	0.609222i	−0.995645	−	0.0932302i	$-0.970281\pi$
$631$	−3.49292	−	15.3035i	−0.139051	−	0.609222i	0.856594	−	0.515992i	$-0.172576\pi$
$632$	−2.52185	+	3.16230i	−0.100314	+	0.125790i
$633$	12.2725	+	15.3892i	0.487787	+	0.611665i
$634$	−1.06399	+	4.66166i	−0.0422565	+	0.185138i
$635$	2.70510	+	11.8518i	0.107349	+	0.470326i
$636$	−16.9376	−	21.2391i	−0.671621	−	0.842186i
$637$	−16.6450			−0.659499
$638$		0			0
$639$	−66.2544			−2.62098
$640$	15.6984	+	19.6852i	0.620534	+	0.778125i
$641$	−7.24207	−	31.7296i	−0.286045	−	1.25324i	−0.889902	−	0.456152i	$-0.849228\pi$
$641$	−7.24207	−	31.7296i	−0.286045	−	1.25324i	0.603857	−	0.797092i	$-0.293630\pi$
$642$	1.66923	−	7.31339i	0.0658794	−	0.288636i
$643$	15.3163	+	19.2061i	0.604017	+	0.757413i	0.985998	−	0.166757i	$-0.0533295\pi$
$643$	15.3163	+	19.2061i	0.604017	+	0.757413i	−0.381981	+	0.924170i	$0.624758\pi$
$644$	1.22137	−	1.53155i	0.0481286	−	0.0603514i
$645$	−14.5434	−	63.7189i	−0.572647	−	2.50893i
$646$	3.77422	−	1.81757i	0.148495	−	0.0715112i
$647$	−11.7322	+	5.64994i	−0.461242	+	0.222122i	−0.650050	−	0.759892i	$-0.725252\pi$
$647$	−11.7322	+	5.64994i	−0.461242	+	0.222122i	0.188808	+	0.982014i	$0.439538\pi$
$648$	1.56868	−	6.87283i	0.0616235	−	0.269990i
$649$	−19.6432	−	9.45968i	−0.771064	−	0.371325i
$650$	0.229729			0.00901071
$651$	8.66742	+	4.17401i	0.339703	+	0.163592i
$652$	−2.71720	+	3.40726i	−0.106414	+	0.133439i
$653$	18.6792	−	23.4230i	0.730974	−	0.916612i	−0.267929	−	0.963439i	$-0.586339\pi$
$653$	18.6792	−	23.4230i	0.730974	−	0.916612i	0.998903	+	0.0468264i	$0.0149108\pi$
$654$	9.78753	+	4.71343i	0.382723	+	0.184310i
$655$	0.0623513			0.00243627
$656$	−4.29923	−	2.07040i	−0.167857	−	0.0808355i
$657$	3.21198	−	14.0726i	0.125311	−	0.549024i
$658$	−1.72528	+	0.830853i	−0.0672586	+	0.0323900i
$659$	12.7950	−	6.16174i	0.498422	−	0.240027i	−0.167745	−	0.985830i	$-0.553648\pi$
$659$	12.7950	−	6.16174i	0.498422	−	0.240027i	0.666166	+	0.745803i	$0.267934\pi$
$660$	11.4981	+	50.3764i	0.447563	+	1.96090i
$661$	25.1774	−	31.5715i	0.979288	−	1.22799i	0.00562783	−	0.999984i	$-0.498209\pi$
$661$	25.1774	−	31.5715i	0.979288	−	1.22799i	0.973660	−	0.228004i	$-0.0732200\pi$
$662$	−3.26648	−	4.09604i	−0.126955	−	0.159197i
$663$	2.58802	−	11.3389i	0.100510	−	0.440365i
$664$	−2.70466	−	11.8499i	−0.104961	−	0.459865i
$665$	−10.6491	−	13.3535i	−0.412953	−	0.517826i
$666$	12.8193			0.496739
$667$		0			0
$668$	4.64368			0.179669
$669$	−9.23357	−	11.5785i	−0.356990	−	0.447652i
$670$	−0.592389	−	2.59543i	−0.0228860	−	0.100270i
$671$	6.05783	−	26.5411i	0.233860	−	1.02461i
$672$	−11.1500	−	13.9817i	−0.430121	−	0.539355i
$673$	−25.4347	+	31.8941i	−0.980436	+	1.22943i	−0.00711674	+	0.999975i	$0.502265\pi$
$673$	−25.4347	+	31.8941i	−0.980436	+	1.22943i	−0.973320	+	0.229454i	$0.926306\pi$
$674$	1.81382	+	7.94687i	0.0698658	+	0.306102i
$675$	−0.434201	+	0.209100i	−0.0167124	+	0.00804826i
$676$	−4.94067	+	2.37930i	−0.190026	+	0.0915116i
$677$	4.58142	−	20.0725i	0.176078	−	0.771449i	−0.807339	−	0.590088i	$-0.799093\pi$
$677$	4.58142	−	20.0725i	0.176078	−	0.771449i	0.983417	−	0.181360i	$-0.0580500\pi$
$678$	−21.4577	−	10.3335i	−0.824076	−	0.396854i
$679$	−14.8742			−0.570818
$680$	−5.22441	−	2.51594i	−0.200347	−	0.0964820i
$681$	−26.4425	+	33.1579i	−1.01328	+	1.27061i
$682$	−4.38088	+	5.49345i	−0.167753	+	0.210355i
$683$	−11.3859	−	5.48315i	−0.435668	−	0.209807i	0.203177	−	0.979142i	$-0.434873\pi$
$683$	−11.3859	−	5.48315i	−0.435668	−	0.209807i	−0.638845	+	0.769335i	$0.720588\pi$
$684$	−43.9801			−1.68162
$685$	12.2205	+	5.88509i	0.466922	+	0.224858i
$686$	1.82267	−	7.98566i	0.0695900	−	0.304894i
$687$	−35.9816	+	17.3278i	−1.37278	+	0.661098i
$688$	24.8090	−	11.9474i	0.945836	−	0.455490i
$689$	4.05185	+	17.7523i	0.154363	+	0.676309i
$690$	1.63678	−	2.05245i	0.0623110	−	0.0781355i
$691$	−13.7900	−	17.2921i	−0.524595	−	0.657821i	0.446983	−	0.894543i	$-0.352499\pi$
$691$	−13.7900	−	17.2921i	−0.524595	−	0.657821i	−0.971578	+	0.236722i	$0.923927\pi$
$692$	9.12966	−	39.9997i	0.347058	−	1.52056i
$693$	−6.16721	−	27.0203i	−0.234273	−	1.02642i
$694$	−11.7281	−	14.7065i	−0.445192	−	0.558253i
$695$	27.3453			1.03726
$696$		0			0
$697$	2.62748			0.0995229
$698$	−10.3564	−	12.9865i	−0.391995	−	0.491546i
$699$	−9.51856	−	41.7035i	−0.360025	−	1.57737i
$700$	0.0721366	−	0.316051i	0.00272651	−	0.0119456i
$701$	1.36403	+	1.71044i	0.0515187	+	0.0646024i	0.806923	−	0.590656i	$-0.201131\pi$
$701$	1.36403	+	1.71044i	0.0515187	+	0.0646024i	−0.755405	+	0.655259i	$0.772560\pi$
$702$	3.36610	−	4.22095i	0.127045	−	0.159310i
$703$	7.81444	+	34.2373i	0.294727	+	1.29128i
$704$	−10.7948	+	5.19849i	−0.406843	+	0.195925i
$705$	15.3791	−	7.40619i	0.579211	−	0.278933i
$706$	−1.36712	+	5.98976i	−0.0514524	+	0.225428i
$707$	1.14322	+	0.550544i	0.0429951	+	0.0207053i
$708$	−20.3780			−0.765852
$709$	−26.8470	−	12.9288i	−1.00826	−	0.485552i	−0.144525	−	0.989501i	$-0.546166\pi$
$709$	−26.8470	−	12.9288i	−1.00826	−	0.485552i	−0.863733	+	0.503949i	$0.831880\pi$
$710$	10.9517	−	13.7330i	0.411010	−	0.515390i
$711$	−5.60721	+	7.03122i	−0.210287	+	0.263691i
$712$	20.5495	+	9.89613i	0.770126	+	0.370873i
$713$	−2.37446			−0.0889244
$714$	2.22304	+	1.07056i	0.0831952	+	0.0400647i
$715$	7.70699	−	33.7665i	0.288225	−	1.26280i
$716$	−32.8301	+	15.8101i	−1.22692	+	0.590853i
$717$	22.8034	−	10.9816i	0.851610	−	0.410114i
$718$	−0.444663	−	1.94820i	−0.0165947	−	0.0727060i
$719$	5.06984	−	6.35738i	0.189073	−	0.237090i	−0.678255	−	0.734826i	$-0.737264\pi$
$719$	5.06984	−	6.35738i	0.189073	−	0.237090i	0.867329	+	0.497736i	$0.165835\pi$
$720$	14.5991	+	18.3067i	0.544075	+	0.682249i
$721$	−2.25333	+	9.87246i	−0.0839182	+	0.367670i
$722$	1.86898	+	8.18852i	0.0695561	+	0.304745i
$723$	17.5270	+	21.9781i	0.651836	+	0.817376i
$724$	−15.8108			−0.587604
$725$		0			0
$726$	19.3898			0.719621
$727$	−6.36211	−	7.97784i	−0.235958	−	0.295882i	0.649728	−	0.760167i	$-0.274883\pi$
$727$	−6.36211	−	7.97784i	−0.235958	−	0.295882i	−0.885686	+	0.464285i	$0.846311\pi$
$728$	1.73772	+	7.61344i	0.0644041	+	0.282173i
$729$	9.53694	−	41.7841i	0.353220	−	1.54756i
$730$	2.38599	+	2.99193i	0.0883093	+	0.110736i
$731$	−9.45340	+	11.8542i	−0.349647	+	0.438443i
$732$	−5.66208	−	24.8072i	−0.209277	−	0.916900i
$733$	−22.2177	+	10.6995i	−0.820629	+	0.395194i	−0.796592	−	0.604517i	$-0.793366\pi$
$733$	−22.2177	+	10.6995i	−0.820629	+	0.395194i	−0.0240365	+	0.999711i	$0.507652\pi$
$734$	5.89018	−	2.83656i	0.217410	−	0.104699i
$735$	−7.00433	+	30.6880i	−0.258359	+	1.13194i
$736$	3.97687	+	1.91516i	0.146589	+	0.0705937i
$737$	11.8341			0.435913
$738$	3.73646	+	1.79938i	0.137541	+	0.0662362i
$739$	2.60098	−	3.26153i	0.0956786	−	0.119977i	−0.731687	−	0.681640i	$-0.761267\pi$
$739$	2.60098	−	3.26153i	0.0956786	−	0.119977i	0.827366	+	0.561663i	$0.189838\pi$
$740$	14.0948	−	17.6743i	0.518136	−	0.649722i
$741$	45.3084	+	21.8194i	1.66445	+	0.801555i
$742$	−3.86299			−0.141815
$743$	−2.52140	−	1.21424i	−0.0925010	−	0.0445462i	0.387061	−	0.922054i	$-0.373490\pi$
$743$	−2.52140	−	1.21424i	−0.0925010	−	0.0445462i	−0.479562	+	0.877508i	$0.659205\pi$
$744$	−3.14245	+	13.7680i	−0.115208	+	0.504759i
$745$	41.3152	−	19.8963i	1.51367	−	0.728945i
$746$	11.5094	−	5.54264i	0.421389	−	0.202930i
$747$	−6.01367	−	26.3476i	−0.220029	−	0.964008i
$748$	7.47390	−	9.37197i	0.273273	−	0.342673i
$749$	4.42388	+	5.54737i	0.161645	+	0.202696i
$750$	3.47202	−	15.2119i	0.126780	−	0.555461i
$751$	−3.27124	−	14.3322i	−0.119369	−	0.522991i	−0.998889	−	0.0471282i	$-0.984993\pi$
$751$	−3.27124	−	14.3322i	−0.119369	−	0.522991i	0.879520	−	0.475863i	$-0.157864\pi$
$752$	4.48390	+	5.62263i	0.163511	+	0.205036i
$753$	39.8019			1.45046
$754$		0			0
$755$	44.1387			1.60637
$756$	−4.75003	−	5.95634i	−0.172757	−	0.216630i
$757$	5.10374	+	22.3609i	0.185499	+	0.812722i	0.978952	+	0.204091i	$0.0654239\pi$
$757$	5.10374	+	22.3609i	0.185499	+	0.812722i	−0.793453	+	0.608631i	$0.791719\pi$
$758$	1.48295	−	6.49723i	0.0538632	−	0.235990i
$759$	7.27590	+	9.12369i	0.264099	+	0.331169i
$760$	15.6325	−	19.6026i	0.567051	−	0.711060i
$761$	2.80870	+	12.3057i	0.101815	+	0.446081i	0.999979	+	0.00642120i	$0.00204395\pi$
$761$	2.80870	+	12.3057i	0.101815	+	0.446081i	−0.898164	+	0.439660i	$0.855099\pi$
$762$	6.84149	−	3.29469i	0.247841	−	0.119354i
$763$	−9.25766	+	4.45825i	−0.335150	+	0.161400i
$764$	−7.45515	+	32.6631i	−0.269718	+	1.18171i
$765$	−11.6162	−	5.59407i	−0.419985	−	0.202254i
$766$	−12.2880			−0.443985
$767$	12.3064	+	5.92644i	0.444358	+	0.213991i
$768$	1.77393	−	2.22444i	0.0640113	−	0.0802677i
$769$	−2.19931	+	2.75784i	−0.0793090	+	0.0994503i	−0.819903	−	0.572502i	$-0.805973\pi$
$769$	−2.19931	+	2.75784i	−0.0793090	+	0.0994503i	0.740594	+	0.671953i	$0.234544\pi$
$770$	6.62010	+	3.18807i	0.238572	+	0.114890i
$771$	−4.65956			−0.167810
$772$	−8.33042	−	4.01172i	−0.299818	−	0.144385i
$773$	−5.83174	+	25.5505i	−0.209753	+	0.918989i	0.754978	+	0.655751i	$0.227648\pi$
$773$	−5.83174	+	25.5505i	−0.209753	+	0.918989i	−0.964731	+	0.263238i	$0.915209\pi$
$774$	−21.5615	+	10.3835i	−0.775012	+	0.373226i
$775$	−0.354032	+	0.170493i	−0.0127172	+	0.00612429i
$776$	−4.85872	−	21.2874i	−0.174418	−	0.764174i
$777$	−12.8966	+	16.1719i	−0.462665	+	0.580163i
$778$	5.63308	+	7.06366i	0.201956	+	0.253244i
$779$	−2.52803	+	11.0760i	−0.0905762	+	0.396840i
$780$	−7.20350	−	31.5606i	−0.257927	−	1.13005i
$781$	48.6832	+	61.0468i	1.74202	+	2.18442i
$782$	−0.609008			−0.0217781
$783$		0			0
$784$	−13.2617			−0.473634
$785$	16.1992	+	20.3131i	0.578173	+	0.725006i
$786$	−0.00866651	−	0.0379705i	−0.000309124	−	0.00135436i
$787$	4.00807	−	17.5605i	0.142872	−	0.625964i	−0.851888	−	0.523724i	$-0.824542\pi$
$787$	4.00807	−	17.5605i	0.142872	−	0.625964i	0.994760	−	0.102239i	$-0.0326007\pi$
$788$	10.8104	+	13.5559i	0.385106	+	0.482907i
$789$	22.7157	−	28.4846i	0.808701	−	1.01408i
$790$	−0.530549	−	2.32449i	−0.0188761	−	0.0827015i
$791$	20.2960	−	9.77404i	0.721642	−	0.347525i
$792$	36.6560	−	17.6526i	1.30251	−	0.627258i
$793$	−3.79520	+	16.6279i	−0.134772	+	0.590473i
$794$	13.9351	+	6.71079i	0.494538	+	0.238157i
$795$	34.4345			1.22127
$796$	−34.7596	−	16.7393i	−1.23202	−	0.593310i
$797$	21.8058	−	27.3437i	0.772402	−	0.968562i	−0.227584	−	0.973758i	$-0.573083\pi$
$797$	21.8058	−	27.3437i	0.772402	−	0.968562i	0.999986	+	0.00519652i	$0.00165411\pi$
$798$	−6.65180	+	8.34110i	−0.235471	+	0.295272i
$799$	−3.56775	−	1.71814i	−0.126218	−	0.0607834i
$800$	0.730464			0.0258258
$801$	45.6908	+	22.0035i	1.61440	+	0.777456i
$802$	−1.40582	+	6.15932i	−0.0496414	+	0.217493i
$803$	−15.3266	+	7.38090i	−0.540864	+	0.260466i
$804$	9.96558	−	4.79917i	0.351459	−	0.169254i
$805$	0.552534	+	2.42081i	0.0194743	+	0.0853223i
$806$	2.74460	−	3.44162i	0.0966745	−	0.121226i
$807$	50.1777	+	62.9209i	1.76634	+	2.21492i
$808$	−0.414484	+	1.81597i	−0.0145815	+	0.0638856i
$809$	−8.51401	−	37.3023i	−0.299337	−	1.31148i	−0.871118	−	0.491074i	$-0.836605\pi$
$809$	−8.51401	−	37.3023i	−0.299337	−	1.31148i	0.571781	−	0.820406i	$-0.306253\pi$
$810$	2.59093	+	3.24893i	0.0910362	+	0.114156i
$811$	31.7116			1.11354			0.556772	−	0.830665i	$-0.312040\pi$
$811$	31.7116			1.11354			0.556772	+	0.830665i	$0.312040\pi$
$812$		0			0
$813$	25.2130			0.884260
$814$	−9.41952	−	11.8117i	−0.330154	−	0.414000i
$815$	−1.22923	−	5.38562i	−0.0430581	−	0.188650i
$816$	2.06198	−	9.03412i	0.0721837	−	0.316257i
$817$	−40.8752	−	51.2559i	−1.43004	−	1.79322i
$818$	1.94668	−	2.44106i	0.0680640	−	0.0853495i
$819$	3.86373	+	16.9281i	0.135010	+	0.591515i
$820$	6.58908	−	3.17314i	0.230101	−	0.110811i
$821$	19.3601	−	9.32331i	0.675671	−	0.325386i	−0.0643911	−	0.997925i	$-0.520511\pi$
$821$	19.3601	−	9.32331i	0.675671	−	0.325386i	0.740062	+	0.672539i	$0.234796\pi$
$822$	1.88529	−	8.26000i	0.0657571	−	0.288101i
$823$	8.02119	+	3.86280i	0.279601	+	0.134649i	0.568429	−	0.822732i	$-0.307551\pi$
$823$	8.02119	+	3.86280i	0.279601	+	0.134649i	−0.288828	+	0.957381i	$0.593266\pi$
$824$	−14.8652			−0.517854
$825$	1.73994	+	0.837912i	0.0605770	+	0.0291724i
$826$	−1.80672	+	2.26556i	−0.0628639	+	0.0788288i
$827$	−17.1049	+	21.4488i	−0.594794	+	0.745848i	−0.984557	−	0.175067i	$-0.943986\pi$
$827$	−17.1049	+	21.4488i	−0.594794	+	0.745848i	0.389762	+	0.920916i	$0.372557\pi$
$828$	5.76065	+	2.77418i	0.200197	+	0.0964096i
$829$	−40.4211			−1.40388			−0.701942	−	0.712234i	$-0.747683\pi$
$829$	−40.4211			−1.40388			−0.701942	+	0.712234i	$0.747683\pi$
$830$	6.45529	+	3.10870i	0.224066	+	0.107905i
$831$	13.4343	−	58.8594i	0.466030	−	2.04181i
$832$	6.76287	−	3.25683i	0.234460	−	0.112910i
$833$	6.57913	−	3.16834i	0.227953	−	0.109777i
$834$	−3.80085	−	16.6526i	−0.131613	−	0.576633i
$835$	−3.66997	+	4.60200i	−0.127005	+	0.159259i
$836$	32.3161	+	40.5232i	1.11768	+	1.40152i
$837$	−2.05488	+	9.00301i	−0.0710270	+	0.311189i
$838$	1.32052	+	5.78560i	0.0456168	+	0.199860i
$839$	5.05362	+	6.33704i	0.174470	+	0.218779i	0.861376	−	0.507968i	$-0.169603\pi$
$839$	5.05362	+	6.33704i	0.174470	+	0.218779i	−0.686906	+	0.726746i	$0.741032\pi$
$840$	14.7680			0.509543
$841$		0			0
$842$	10.3717			0.357432
$843$	14.6256	+	18.3400i	0.503734	+	0.631662i
$844$	−2.82821	−	12.3912i	−0.0973511	−	0.426523i
$845$	1.54674	−	6.77672i	0.0532095	−	0.233126i
$846$	−3.89695	−	4.88662i	−0.133980	−	0.168005i
$847$	−11.4348	+	14.3388i	−0.392905	+	0.492688i
$848$	3.22827	+	14.1440i	0.110859	+	0.485706i
$849$	−35.0740	+	16.8908i	−1.20374	+	0.579690i
$850$	−0.0908030	+	0.0437284i	−0.00311452	+	0.00149987i
$851$	1.13607	−	4.97743i	0.0389439	−	0.170624i
$852$	65.7534	+	31.6652i	2.25267	+	1.08483i
$853$	−12.7043			−0.434988			−0.217494	−	0.976062i	$-0.569788\pi$
$853$	−12.7043			−0.434988			−0.217494	+	0.976062i	$0.569788\pi$
$854$	−3.25998	−	1.56992i	−0.111554	−	0.0537217i
$855$	34.7581	−	43.5853i	1.18870	−	1.49059i
$856$	−6.49413	+	8.14339i	−0.221965	+	0.278335i
$857$	41.6417	+	20.0536i	1.42245	+	0.685018i	0.977578	−	0.210574i	$-0.0675332\pi$
$857$	41.6417	+	20.0536i	1.42245	+	0.685018i	0.444877	+	0.895592i	$0.353248\pi$
$858$	−21.6343			−0.738581
$859$	5.45292	+	2.62599i	0.186051	+	0.0895975i	0.524590	−	0.851355i	$-0.324218\pi$
$859$	5.45292	+	2.62599i	0.186051	+	0.0895975i	−0.338539	+	0.940952i	$0.609933\pi$
$860$	−9.39086	+	41.1440i	−0.320226	+	1.40300i
$861$	−6.02896	+	2.90339i	−0.205466	+	0.0989474i
$862$	7.82313	−	3.76742i	0.266457	−	0.128319i
$863$	2.92205	+	12.8023i	0.0994677	+	0.435796i	0.999999	+	0.00100628i	$0.000320308\pi$
$863$	2.92205	+	12.8023i	0.0994677	+	0.435796i	−0.900532	+	0.434790i	$0.856823\pi$
$864$	10.7031	−	13.4213i	0.364127	−	0.456601i
$865$	32.4253	+	40.6600i	1.10249	+	1.38248i
$866$	−1.81288	+	7.94273i	−0.0616040	+	0.269905i
$867$	−9.05018	−	39.6514i	−0.307360	−	1.34663i
$868$	−3.87301	−	4.85660i	−0.131458	−	0.164844i
$869$	10.5987			0.359536
$870$		0			0
$871$	−7.41398			−0.251213
$872$	−9.40456	−	11.7929i	−0.318479	−	0.399360i
$873$	−10.8031	−	47.3315i	−0.365630	−	1.60193i
$874$	0.585958	−	2.56725i	0.0198203	−	0.0868385i
$875$	9.20172	+	11.5386i	0.311075	+	0.390076i
$876$	−9.91344	+	12.4311i	−0.334944	+	0.420007i
$877$	−6.84826	−	30.0042i	−0.231249	−	1.01317i	−0.948605	−	0.316462i	$-0.897505\pi$
$877$	−6.84826	−	30.0042i	−0.231249	−	1.01317i	0.717356	−	0.696707i	$-0.245352\pi$
$878$	−2.48900	+	1.19864i	−0.0839996	+	0.0404521i
$879$	−79.4631	+	38.2674i	−2.68022	+	1.29073i
$880$	6.14046	−	26.9031i	0.206995	−	0.906904i
$881$	26.5971	+	12.8085i	0.896080	+	0.431530i	0.824472	−	0.565903i	$-0.191472\pi$
$881$	26.5971	+	12.8085i	0.896080	+	0.431530i	0.0716088	+	0.997433i	$0.477187\pi$
$882$	11.5258			0.388093
$883$	−32.4541	−	15.6291i	−1.09217	−	0.525960i	−0.200980	−	0.979595i	$-0.564413\pi$
$883$	−32.4541	−	15.6291i	−1.09217	−	0.525960i	−0.891187	+	0.453635i	$0.850127\pi$
$884$	−4.68236	+	5.87150i	−0.157485	+	0.197480i
$885$	16.1050	−	20.1951i	0.541365	−	0.678851i
$886$	−8.77555	−	4.22608i	−0.294820	−	0.141978i
$887$	14.2942			0.479952			0.239976	−	0.970779i	$-0.422860\pi$
$887$	14.2942			0.479952			0.239976	+	0.970779i	$0.422860\pi$
$888$	−27.3574	−	13.1746i	−0.918055	−	0.442112i
$889$	−1.59823	+	7.00232i	−0.0536030	+	0.234850i
$890$	−12.1134	+	5.83350i	−0.406042	+	0.195539i
$891$	−16.6431	+	8.01490i	−0.557565	+	0.268509i
$892$	2.12789	+	9.32291i	0.0712472	+	0.312154i
$893$	10.6755	−	13.3866i	0.357241	−	0.447965i
$894$	−17.8590	−	22.3945i	−0.597294	−	0.748984i
$895$	10.2779	−	45.0304i	0.343552	−	1.50520i
$896$	3.31019	+	14.5029i	0.110586	+	0.484508i
$897$	−4.55832	−	5.71595i	−0.152198	−	0.190850i
$898$	9.04279			0.301762
$899$		0			0
$900$	1.05811			0.0352702
$901$	−4.98066	−	6.24554i	−0.165930	−	0.208069i
$902$	−1.08757	−	4.76494i	−0.0362120	−	0.158655i
$903$	8.59256	−	37.6465i	0.285943	−	1.25280i
$904$	20.6181	+	25.8542i	0.685746	+	0.859899i
$905$	12.4955	−	15.6689i	0.415365	−	0.520851i
$906$	−6.13506	−	26.8794i	−0.203824	−	0.893010i
$907$	−18.1541	+	8.74258i	−0.602798	+	0.290292i	−0.710285	−	0.703914i	$-0.751434\pi$
$907$	−18.1541	+	8.74258i	−0.602798	+	0.290292i	0.107487	+	0.994207i	$0.465720\pi$
$908$	24.6730	−	11.8819i	0.818803	−	0.394315i
$909$	−0.921582	+	4.03772i	−0.0305670	+	0.133923i
$910$	−4.14746	−	1.99731i	−0.137487	−	0.0662102i
$911$	18.4045			0.609769			0.304885	−	0.952389i	$-0.401382\pi$
$911$	18.4045			0.609769			0.304885	+	0.952389i	$0.401382\pi$
$912$	36.0990	+	17.3844i	1.19536	+	0.575654i
$913$	−19.8579	+	24.9010i	−0.657199	+	0.824102i
$914$	4.81268	−	6.03491i	0.159189	−	0.199617i
$915$	29.0593	+	13.9942i	0.960672	+	0.462635i
$916$	25.7875			0.852044
$917$	0.0331903	+	0.0159836i	0.00109604	+	0.000527825i
$918$	−0.527040	+	2.30911i	−0.0173949	+	0.0762120i
$919$	−4.79102	+	2.30724i	−0.158041	+	0.0761087i	−0.511232	−	0.859443i	$-0.670811\pi$
$919$	−4.79102	+	2.30724i	−0.158041	+	0.0761087i	0.353191	+	0.935551i	$0.385097\pi$
$920$	−3.28409	+	1.58154i	−0.108273	+	0.0521417i
$921$	17.0711	+	74.7932i	0.562510	+	2.46452i
$922$	−7.10897	+	8.91437i	−0.234122	+	0.293579i
$923$	−30.4998	−	38.2455i	−1.00391	−	1.25887i
$924$	−6.79332	+	29.7635i	−0.223484	+	0.979146i
$925$	−0.188006	−	0.823707i	−0.00618159	−	0.0270833i
$926$	8.52341	+	10.6880i	0.280097	+	0.351230i
$927$	−33.0520			−1.08557
$928$		0			0
$929$	−1.90689			−0.0625630			−0.0312815	−	0.999511i	$-0.509959\pi$
$929$	−1.90689			−0.0625630			−0.0312815	+	0.999511i	$0.509959\pi$
$930$	−5.19029	−	6.50841i	−0.170196	−	0.213419i
$931$	7.02591	+	30.7825i	0.230265	+	1.00886i
$932$	−6.14625	+	26.9285i	−0.201327	+	0.882071i
$933$	−36.6102	−	45.9078i	−1.19857	−	1.50295i
$934$	3.68530	−	4.62121i	0.120587	−	0.151211i
$935$	3.38111	+	14.8136i	0.110574	+	0.484457i
$936$	−22.9648	+	11.0593i	−0.750629	+	0.361484i
$937$	3.03904	−	1.46353i	0.0992812	−	0.0478113i	−0.383584	−	0.923506i	$-0.625310\pi$
$937$	3.03904	−	1.46353i	0.0992812	−	0.0478113i	0.482865	+	0.875695i	$0.339596\pi$
$938$	0.349996	−	1.53343i	0.0114278	−	0.0500684i
$939$	−58.0463	−	27.9536i	−1.89427	−	0.912232i
$940$	−11.0220			−0.359498
$941$	17.8667	+	8.60413i	0.582437	+	0.280487i	0.701812	−	0.712363i	$-0.252375\pi$
$941$	17.8667	+	8.60413i	0.582437	+	0.280487i	−0.119375	+	0.992849i	$0.538089\pi$
$942$	10.1186	−	12.6883i	0.329682	−	0.413409i
$943$	1.02979	−	1.29131i	0.0335345	−	0.0420509i
$944$	9.80499	+	4.72183i	0.319125	+	0.153683i
$945$	9.65689			0.314139
$946$	25.4105	+	12.2371i	0.826167	+	0.397861i
$947$	9.01536	−	39.4989i	0.292960	−	1.28354i	−0.587424	−	0.809279i	$-0.699858\pi$
$947$	9.01536	−	39.4989i	0.292960	−	1.28354i	0.880384	−	0.474262i	$-0.157285\pi$
$948$	8.92525	−	4.29817i	0.289879	−	0.139598i
$949$	9.60204	−	4.62410i	0.311696	−	0.150105i
$950$	−0.0969692	−	0.424850i	−0.00314610	−	0.0137840i
$951$	15.7009	−	19.6883i	0.509136	−	0.638437i
$952$	−2.13606	−	2.67853i	−0.0692300	−	0.0868117i
$953$	0.521127	−	2.28321i	0.0168810	−	0.0739604i	−0.965786	−	0.259341i	$-0.916495\pi$
$953$	0.521127	−	2.28321i	0.0168810	−	0.0739604i	0.982667	+	0.185381i	$0.0593518\pi$
$954$	−2.80568	−	12.2925i	−0.0908374	−	0.397985i
$955$	−26.4780	−	33.2024i	−0.856809	−	1.07440i
$956$	−16.3429			−0.528567
$957$		0			0
$958$	12.4378			0.401848
$959$	4.99649	+	6.26540i	0.161345	+	0.202320i
$960$	−3.15867	−	13.8390i	−0.101946	−	0.446653i
$961$	5.22267	−	22.8820i	0.168473	−	0.738130i
$962$	5.90129	+	7.39998i	0.190265	+	0.238585i
$963$	−14.4394	+	18.1064i	−0.465302	+	0.583470i
$964$	−4.03913	−	17.6966i	−0.130092	−	0.569968i
$965$	10.5594	−	5.08512i	0.339918	−	0.163696i
$966$	1.39742	−	0.672961i	0.0449612	−	0.0216522i
$967$	2.94367	−	12.8970i	0.0946619	−	0.414741i	−0.905287	−	0.424799i	$-0.860345\pi$
$967$	2.94367	−	12.8970i	0.0946619	−	0.414741i	0.999949	+	0.0100585i	$0.00320177\pi$
$968$	−24.2565	−	11.6813i	−0.779633	−	0.375451i
$969$	−22.0620			−0.708732
$970$	11.5964	+	5.58455i	0.372339	+	0.179309i
$971$	−12.8689	+	16.1371i	−0.412983	+	0.517865i	−0.944201	−	0.329371i	$-0.893163\pi$
$971$	−12.8689	+	16.1371i	−0.412983	+	0.517865i	0.531217	+	0.847236i	$0.321735\pi$
$972$	−21.7092	+	27.2225i	−0.696323	+	0.873162i
$973$	14.5562	+	7.00990i	0.466650	+	0.224727i
$974$	−0.657928			−0.0210814
$975$	−1.09007	−	0.524948i	−0.0349100	−	0.0168118i
$976$	−3.02379	+	13.2481i	−0.0967891	+	0.424061i
$977$	2.43493	−	1.17260i	0.0779004	−	0.0375149i	−0.394528	−	0.918884i	$-0.629092\pi$
$977$	2.43493	−	1.17260i	0.0779004	−	0.0375149i	0.472428	+	0.881369i	$0.343378\pi$
$978$	−3.10886	+	1.49715i	−0.0994104	+	0.0478735i
$979$	−13.2992	−	58.2674i	−0.425043	−	1.86224i
$980$	12.6726	−	15.8909i	0.404810	−	0.507616i
$981$	−20.9105	−	26.2210i	−0.667622	−	0.837172i
$982$	−3.71539	+	16.2782i	−0.118563	+	0.519458i
$983$	3.24559	+	14.2199i	0.103518	+	0.453543i	0.999946	+	0.0103539i	$0.00329582\pi$
$983$	3.24559	+	14.2199i	0.103518	+	0.453543i	−0.896428	+	0.443189i	$0.853847\pi$
$984$	−6.12463	−	7.68004i	−0.195246	−	0.244831i
$985$	−21.9778			−0.700272
$986$		0			0
$987$	10.0850			0.321011
$988$	−20.2459	−	25.3876i	−0.644108	−	0.807686i
$989$	2.12084	+	9.29201i	0.0674388	+	0.295469i
$990$	−5.33667	+	23.3815i	−0.169611	+	0.743112i
$991$	13.9345	+	17.4733i	0.442644	+	0.555058i	0.952238	−	0.305357i	$-0.0987759\pi$
$991$	13.9345	+	17.4733i	0.442644	+	0.555058i	−0.509594	+	0.860415i	$0.670204\pi$
$992$	8.72695	−	10.9433i	0.277081	−	0.347449i
$993$	6.13973	+	26.8999i	0.194838	+	0.853642i
$994$	9.35014	−	4.50279i	0.296568	−	0.142820i
$995$	44.0601	−	21.2182i	1.39680	−	0.672663i
$996$	−6.62419	+	29.0225i	−0.209896	+	0.919612i
$997$	−49.0288	−	23.6110i	−1.55276	−	0.747768i	−0.556229	−	0.831029i	$-0.687752\pi$
$997$	−49.0288	−	23.6110i	−1.55276	−	0.747768i	−0.996528	+	0.0832607i	$0.973467\pi$
$998$	5.35958			0.169655
$999$	−17.8892	−	8.61501i	−0.565991	−	0.272567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.o.778.4		36
29.2	odd	28		841.2.e.l.270.6		72
29.3	odd	28		841.2.e.l.651.7		72
29.4	even	14		841.2.d.n.645.4		36
29.5	even	14		841.2.d.n.571.4		36
29.6	even	14		841.2.d.n.574.3		36
29.7	even	7	inner	841.2.d.o.190.3		36
29.8	odd	28		841.2.b.d.840.6		12
29.9	even	14		841.2.a.h.1.3	yes	6
29.10	odd	28		841.2.e.l.196.6		72
29.11	odd	28		841.2.e.l.236.6		72
29.12	odd	4		841.2.e.l.63.7		72
29.13	even	14		841.2.d.n.605.4		36
29.14	odd	28		841.2.e.l.267.7		72
29.15	odd	28		841.2.e.l.267.6		72
29.16	even	7	inner	841.2.d.o.605.3		36
29.17	odd	4		841.2.e.l.63.6		72
29.18	odd	28		841.2.e.l.236.7		72
29.19	odd	28		841.2.e.l.196.7		72
29.20	even	7		841.2.a.g.1.4	✓	6
29.21	odd	28		841.2.b.d.840.7		12
29.22	even	14		841.2.d.n.190.4		36
29.23	even	7	inner	841.2.d.o.574.4		36
29.24	even	7	inner	841.2.d.o.571.3		36
29.25	even	7	inner	841.2.d.o.645.3		36
29.26	odd	28		841.2.e.l.651.6		72
29.27	odd	28		841.2.e.l.270.7		72
29.28	even	2		841.2.d.n.778.3		36
87.20	odd	14		7569.2.a.bc.1.3		6
87.38	odd	14		7569.2.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.4	✓	6	29.20	even	7
841.2.a.h.1.3	yes	6	29.9	even	14
841.2.b.d.840.6		12	29.8	odd	28
841.2.b.d.840.7		12	29.21	odd	28
841.2.d.n.190.4		36	29.22	even	14
841.2.d.n.571.4		36	29.5	even	14
841.2.d.n.574.3		36	29.6	even	14
841.2.d.n.605.4		36	29.13	even	14
841.2.d.n.645.4		36	29.4	even	14
841.2.d.n.778.3		36	29.28	even	2
841.2.d.o.190.3		36	29.7	even	7	inner
841.2.d.o.571.3		36	29.24	even	7	inner
841.2.d.o.574.4		36	29.23	even	7	inner
841.2.d.o.605.3		36	29.16	even	7	inner
841.2.d.o.645.3		36	29.25	even	7	inner
841.2.d.o.778.4		36	1.1	even	1	trivial
841.2.e.l.63.6		72	29.17	odd	4
841.2.e.l.63.7		72	29.12	odd	4
841.2.e.l.196.6		72	29.10	odd	28
841.2.e.l.196.7		72	29.19	odd	28
841.2.e.l.236.6		72	29.11	odd	28
841.2.e.l.236.7		72	29.18	odd	28
841.2.e.l.267.6		72	29.15	odd	28
841.2.e.l.267.7		72	29.14	odd	28
841.2.e.l.270.6		72	29.2	odd	28
841.2.e.l.270.7		72	29.27	odd	28
841.2.e.l.651.6		72	29.26	odd	28
841.2.e.l.651.7		72	29.3	odd	28
7569.2.a.y.1.4		6	87.38	odd	14
7569.2.a.bc.1.3		6	87.20	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.318763 - 0.399716i) q^{2} +(0.599151 + 2.62505i) q^{3} +(0.386879 - 1.69503i) q^{4} +(1.37406 + 1.72301i) q^{5} +(0.858287 - 1.07626i) q^{6} +(0.289736 + 1.26942i) q^{7} +(-1.72210 + 0.829321i) q^{8} +(-3.82900 + 1.84395i) q^{9} +(0.250717 - 1.09846i) q^{10} +(4.51253 + 2.17312i) q^{11} +4.68133 q^{12} +(-2.82708 - 1.36145i) q^{13} +(0.415048 - 0.520454i) q^{14} +(-3.69973 + 4.63931i) q^{15} +(-2.25245 - 1.08472i) q^{16} +1.37659 q^{17} +(1.95760 + 0.942730i) q^{18} +(-1.32448 + 5.80294i) q^{19} +(3.45214 - 1.66246i) q^{20} +(-3.15868 + 1.52114i) q^{21} +(-0.569796 - 2.49644i) q^{22} +(0.539524 - 0.676542i) q^{23} +(-3.20881 - 4.02372i) q^{24} +(0.0318655 - 0.139612i) q^{25} +(0.356974 + 1.56401i) q^{26} +(-2.09827 - 2.63114i) q^{27} +2.26379 q^{28} +3.03374 q^{30} +(-1.71085 - 2.14534i) q^{31} +(1.13506 + 4.97304i) q^{32} +(-3.00087 + 13.1477i) q^{33} +(-0.438804 - 0.550243i) q^{34} +(-1.78910 + 2.24347i) q^{35} +(1.64419 + 7.20365i) q^{36} +(5.31570 - 2.55991i) q^{37} +(2.74172 - 1.32034i) q^{38} +(1.88003 - 8.23694i) q^{39} +(-3.79519 - 1.82767i) q^{40} +1.90869 q^{41} +(1.61489 + 0.777692i) q^{42} +(-6.86728 + 8.61130i) q^{43} +(5.42930 - 6.80813i) q^{44} +(-8.43841 - 4.06373i) q^{45} -0.442405 q^{46} +(-2.59174 - 1.24812i) q^{47} +(1.49789 - 6.56270i) q^{48} +(4.77931 - 2.30160i) q^{49} +(-0.0659625 + 0.0317659i) q^{50} +(0.824782 + 3.61361i) q^{51} +(-3.40143 + 4.26526i) q^{52} +(-3.61812 - 4.53698i) q^{53} +(-0.382860 + 1.67742i) q^{54} +(2.45616 + 10.7611i) q^{55} +(-1.55171 - 1.94578i) q^{56} -16.0266 q^{57} -4.35304 q^{59} +(6.43241 + 8.06599i) q^{60} +(-1.20950 - 5.29918i) q^{61} +(-0.312171 + 1.36771i) q^{62} +(-3.45014 - 4.32634i) q^{63} +(-1.49150 + 1.87028i) q^{64} +(-1.53877 - 6.74180i) q^{65} +(6.21189 - 2.99149i) q^{66} +(2.12879 - 1.02517i) q^{67} +(0.532572 - 2.33335i) q^{68} +(2.09921 + 1.01093i) q^{69} +1.46705 q^{70} +(14.0459 + 6.76414i) q^{71} +(5.06471 - 6.35094i) q^{72} +(-2.11765 + 2.65545i) q^{73} +(-2.71768 - 1.30877i) q^{74} +0.385580 q^{75} +(9.32373 + 4.49007i) q^{76} +(-1.45115 + 6.35791i) q^{77} +(-3.89172 + 1.87415i) q^{78} +(1.90656 - 0.918152i) q^{79} +(-1.22600 - 5.37146i) q^{80} +(-2.29955 + 2.88355i) q^{81} +(-0.608420 - 0.762935i) q^{82} +(-1.41502 + 6.19962i) q^{83} +(1.35635 + 5.94255i) q^{84} +(1.89151 + 2.37187i) q^{85} +5.63110 q^{86} -9.57325 q^{88} +(-7.43999 - 9.32945i) q^{89} +(1.06552 + 4.66833i) q^{90} +(0.909139 - 3.98320i) q^{91} +(-0.938027 - 1.17625i) q^{92} +(4.60658 - 5.77647i) q^{93} +(0.327258 + 1.43381i) q^{94} +(-11.8184 + 5.69146i) q^{95} +(-12.3744 + 5.95920i) q^{96} +(-2.54198 + 11.1372i) q^{97} +(-2.44345 - 1.17670i) q^{98} -21.2856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

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