LMFDB - Embedded newform 841.2.e.l.267.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] 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("841.63"); 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([11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,0,16,-4,-6,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.6
Character	$\chi$	$=$	841.267
Dual form			841.2.e.l.63.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.399716 - 0.318763i) q^{2} +(2.62505 + 0.599151i) 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} +(-0.829321 + 1.72210i) q^{8} +(3.82900 + 1.84395i) q^{9} +(1.09846 - 0.250717i) q^{10} +(2.17312 + 4.51253i) q^{11} -4.68133i q^{12} +(2.82708 - 1.36145i) q^{13} +(-0.520454 + 0.415048i) q^{14} +(-4.63931 + 3.69973i) q^{15} +(-2.25245 + 1.08472i) q^{16} +1.37659i q^{17} +(-0.942730 - 1.95760i) q^{18} +(5.80294 - 1.32448i) q^{19} +(3.45214 + 1.66246i) q^{20} +(1.52114 - 3.15868i) 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} +(-1.56401 - 0.356974i) q^{26} +(2.63114 + 2.09827i) q^{27} -2.26379 q^{28} +3.03374 q^{30} +(-2.14534 - 1.71085i) q^{31} +(4.97304 + 1.13506i) 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} +(2.55991 - 5.31570i) q^{37} +(-2.74172 - 1.32034i) q^{38} +(8.23694 - 1.88003i) q^{39} +(-1.82767 - 3.79519i) q^{40} -1.90869i q^{41} +(-1.61489 + 0.777692i) q^{42} +(8.61130 - 6.86728i) q^{43} +(6.80813 - 5.42930i) q^{44} +(-8.43841 + 4.06373i) q^{45} -0.442405i q^{46} +(1.24812 + 2.59174i) q^{47} +(-6.56270 + 1.49789i) q^{48} +(4.77931 + 2.30160i) q^{49} +(0.0317659 - 0.0659625i) 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} +(-10.7611 - 2.45616i) q^{55} +(1.94578 + 1.55171i) q^{56} +16.0266 q^{57} -4.35304 q^{59} +(8.06599 + 6.43241i) q^{60} +(-5.29918 - 1.20950i) 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} +(2.99149 - 6.21189i) q^{66} +(-2.12879 - 1.02517i) q^{67} +(2.33335 - 0.532572i) q^{68} +(1.01093 + 2.09921i) q^{69} -1.46705i q^{70} +(-14.0459 + 6.76414i) q^{71} +(-6.35094 + 5.06471i) q^{72} +(-2.65545 + 2.11765i) q^{73} +(-2.71768 + 1.30877i) q^{74} +0.385580i q^{75} +(-4.49007 - 9.32373i) q^{76} +(6.35791 - 1.45115i) q^{77} +(-3.89172 - 1.87415i) q^{78} +(-0.918152 + 1.90656i) 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} +(-5.94255 - 1.35635i) q^{84} +(-2.37187 - 1.89151i) q^{85} -5.63110 q^{86} -9.57325 q^{88} +(-9.32945 - 7.43999i) q^{89} +(4.66833 + 1.06552i) 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} +(-5.69146 + 11.8184i) q^{95} +(12.3744 + 5.95920i) q^{96} +(-11.1372 + 2.54198i) q^{97} +(-1.17670 - 2.44345i) q^{98} +21.2856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{4} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 12 q^{9} - 12 q^{13} - 8 q^{16} + 10 q^{20} - 8 q^{22} + 10 q^{23} + 20 q^{24} - 12 q^{25} + 60 q^{28} + 312 q^{30} + 54 q^{33} - 8 q^{35} + 42 q^{36} + 82 q^{38}+ \cdots - 74 q^{96}+O(q^{100}) $ 72 * q + 16 * q^4 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 12 * q^9 - 12 * q^13 - 8 * q^16 + 10 * q^20 - 8 * q^22 + 10 * q^23 + 20 * q^24 - 12 * q^25 + 60 * q^28 + 312 * q^30 + 54 * q^33 - 8 * q^35 + 42 * q^36 + 82 * q^38 - 42 * q^42 - 32 * q^45 + 24 * q^49 - 46 * q^51 + 26 * q^53 - 38 * q^54 + 192 * q^57 - 204 * q^59 - 18 * q^63 + 2 * q^64 - 64 * q^65 - 18 * q^67 + 72 * q^74 + 10 * q^80 + 44 * q^81 - 38 * q^82 + 48 * q^83 - 204 * q^86 + 252 * q^88 + 32 * q^91 - 46 * q^92 - 24 * q^93 + 74 * q^94 - 74 * q^96

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	−0.399716	−	0.318763i	−0.282642	−	0.225399i	0.471899	−	0.881653i	$-0.343569\pi$
$2$	−0.399716	−	0.318763i	−0.282642	−	0.225399i	−0.754540	+	0.656254i	$0.772140\pi$
$3$	2.62505	+	0.599151i	1.51557	+	0.345920i	0.897788	−	0.440427i	$-0.145173\pi$
$3$	2.62505	+	0.599151i	1.51557	+	0.345920i	0.617785	+	0.786347i	$0.288030\pi$
$4$	−0.386879	−	1.69503i	−0.193439	−	0.847514i
$5$	−1.37406	+	1.72301i	−0.614496	+	0.770554i	−0.987558	−	0.157252i	$-0.949736\pi$
$5$	−1.37406	+	1.72301i	−0.614496	+	0.770554i	0.373062	+	0.927806i	$0.378308\pi$
$6$	−0.858287	−	1.07626i	−0.350394	−	0.439380i
$7$	0.289736	−	1.26942i	0.109510	−	0.479794i	−0.890197	−	0.455576i	$-0.849433\pi$
$7$	0.289736	−	1.26942i	0.109510	−	0.479794i	0.999707	−	0.0242179i	$-0.00770954\pi$
$8$	−0.829321	+	1.72210i	−0.293209	+	0.608855i
$9$	3.82900	+	1.84395i	1.27633	+	0.614650i
$10$	1.09846	−	0.250717i	0.347365	−	0.0792837i
$11$	2.17312	+	4.51253i	0.655221	+	1.36058i	0.918331	+	0.395814i	$0.129537\pi$
$11$	2.17312	+	4.51253i	0.655221	+	1.36058i	−0.263110	+	0.964766i	$0.584748\pi$
$12$		−	4.68133i		−	1.35138i
$13$	2.82708	−	1.36145i	0.784091	−	0.377598i	0.00139212	−	0.999999i	$-0.499557\pi$
$13$	2.82708	−	1.36145i	0.784091	−	0.377598i	0.782699	+	0.622401i	$0.213843\pi$
$14$	−0.520454	+	0.415048i	−0.139097	+	0.110926i
$15$	−4.63931	+	3.69973i	−1.19786	+	0.955265i
$16$	−2.25245	+	1.08472i	−0.563112	+	0.271180i
$17$			1.37659i			0.333871i	0.985968	+	0.166936i	$0.0533872\pi$
$17$			1.37659i			0.333871i	−0.985968	+	0.166936i	$0.946613\pi$
$18$	−0.942730	−	1.95760i	−0.222204	−	0.461411i
$19$	5.80294	−	1.32448i	1.33129	−	0.303857i	0.503060	−	0.864252i	$-0.332207\pi$
$19$	5.80294	−	1.32448i	1.33129	−	0.303857i	0.828226	+	0.560394i	$0.189350\pi$
$20$	3.45214	+	1.66246i	0.771923	+	0.371738i
$21$	1.52114	−	3.15868i	0.331940	−	0.689281i
$22$	0.569796	−	2.49644i	0.121481	−	0.532243i
$23$	0.539524	+	0.676542i	0.112499	+	0.141069i	0.834893	−	0.550413i	$-0.185530\pi$
$23$	0.539524	+	0.676542i	0.112499	+	0.141069i	−0.722394	+	0.691482i	$0.756958\pi$
$24$	−3.20881	+	4.02372i	−0.654995	+	0.821338i
$25$	0.0318655	+	0.139612i	0.00637309	+	0.0279223i
$26$	−1.56401	−	0.356974i	−0.306727	−	0.0700085i
$27$	2.63114	+	2.09827i	0.506364	+	0.403811i
$28$	−2.26379			−0.427815
$29$		0			0
$29$		0			0
$30$	3.03374			0.553882
$31$	−2.14534	−	1.71085i	−0.385315	−	0.307279i	0.411606	−	0.911362i	$-0.364968\pi$
$31$	−2.14534	−	1.71085i	−0.385315	−	0.307279i	−0.796921	+	0.604083i	$0.793539\pi$
$32$	4.97304	+	1.13506i	0.879118	+	0.200653i
$33$	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
$37$	2.55991	−	5.31570i	0.420846	−	0.873897i	−0.577499	−	0.816392i	$-0.695971\pi$
$37$	2.55991	−	5.31570i	0.420846	−	0.873897i	0.998345	−	0.0575050i	$-0.0183145\pi$
$38$	−2.74172	−	1.32034i	−0.444766	−	0.214188i
$39$	8.23694	−	1.88003i	1.31897	−	0.301045i
$40$	−1.82767	−	3.79519i	−0.288980	−	0.600073i
$41$		−	1.90869i		−	0.298088i	−0.988831	−	0.149044i	$-0.952380\pi$
$41$		−	1.90869i		−	0.298088i	0.988831	−	0.149044i	$-0.0476196\pi$
$42$	−1.61489	+	0.777692i	−0.249184	+	0.120001i
$43$	8.61130	−	6.86728i	1.31321	−	1.04725i	0.318144	−	0.948043i	$-0.396941\pi$
$43$	8.61130	−	6.86728i	1.31321	−	1.04725i	0.995067	−	0.0992078i	$-0.0316308\pi$
$44$	6.80813	−	5.42930i	1.02636	−	0.818498i
$45$	−8.43841	+	4.06373i	−1.25792	+	0.605784i
$46$		−	0.442405i		−	0.0652290i
$47$	1.24812	+	2.59174i	0.182056	+	0.378044i	0.971946	−	0.235206i	$-0.0755763\pi$
$47$	1.24812	+	2.59174i	0.182056	+	0.378044i	−0.789889	+	0.613249i	$0.789862\pi$
$48$	−6.56270	+	1.49789i	−0.947244	+	0.216202i
$49$	4.77931	+	2.30160i	0.682759	+	0.328799i
$50$	0.0317659	−	0.0659625i	0.00449237	−	0.00932851i
$51$	−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	−0.965547	−	0.260230i	$-0.916202\pi$
$53$	−3.61812	+	4.53698i	−0.496987	+	0.623202i	0.468559	+	0.883432i	$0.344773\pi$
$54$	−0.382860	−	1.67742i	−0.0521007	−	0.228268i
$55$	−10.7611	−	2.45616i	−1.45103	−	0.331188i
$56$	1.94578	+	1.55171i	0.260016	+	0.207356i
$57$	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	$0.591449\pi$
$60$	8.06599	+	6.43241i	1.04131	+	0.830421i
$61$	−5.29918	−	1.20950i	−0.678490	−	0.154861i	−0.130630	−	0.991431i	$-0.541700\pi$
$61$	−5.29918	−	1.20950i	−0.678490	−	0.154861i	−0.547860	+	0.836570i	$0.684557\pi$
$62$	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
$66$	2.99149	−	6.21189i	0.368227	−	0.764630i
$67$	−2.12879	−	1.02517i	−0.260073	−	0.125245i	0.299304	−	0.954158i	$-0.403245\pi$
$67$	−2.12879	−	1.02517i	−0.260073	−	0.125245i	−0.559377	+	0.828913i	$0.688960\pi$
$68$	2.33335	−	0.532572i	0.282960	−	0.0645838i
$69$	1.01093	+	2.09921i	0.121701	+	0.252716i
$70$		−	1.46705i		−	0.175346i
$71$	−14.0459	+	6.76414i	−1.66694	+	0.802755i	−0.668693	+	0.743538i	$0.733146\pi$
$71$	−14.0459	+	6.76414i	−1.66694	+	0.802755i	−0.998245	+	0.0592169i	$0.981140\pi$
$72$	−6.35094	+	5.06471i	−0.748466	+	0.596882i
$73$	−2.65545	+	2.11765i	−0.310797	+	0.247853i	−0.766448	−	0.642306i	$-0.777978\pi$
$73$	−2.65545	+	2.11765i	−0.310797	+	0.247853i	0.455651	+	0.890158i	$0.349406\pi$
$74$	−2.71768	+	1.30877i	−0.315924	+	0.152141i
$75$			0.385580i			0.0445230i
$76$	−4.49007	−	9.32373i	−0.515046	−	1.06950i
$77$	6.35791	−	1.45115i	0.724551	−	0.165374i
$78$	−3.89172	−	1.87415i	−0.440650	−	0.212206i
$79$	−0.918152	+	1.90656i	−0.103300	+	0.214505i	−0.946212	−	0.323546i	$-0.895125\pi$
$79$	−0.918152	+	1.90656i	−0.103300	+	0.214505i	0.842912	+	0.538051i	$0.180839\pi$
$80$	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	−0.991287	−	0.131719i	$-0.957950\pi$
$83$	−1.41502	−	6.19962i	−0.155319	−	0.680497i	0.835968	−	0.548778i	$-0.184907\pi$
$84$	−5.94255	−	1.35635i	−0.648386	−	0.147990i
$85$	−2.37187	−	1.89151i	−0.257266	−	0.205163i
$86$	−5.63110			−0.607217
$87$		0			0
$88$	−9.57325			−1.02051
$89$	−9.32945	−	7.43999i	−0.988920	−	0.788637i	−0.0114978	−	0.999934i	$-0.503660\pi$
$89$	−9.32945	−	7.43999i	−0.988920	−	0.788637i	−0.977422	+	0.211297i	$0.932231\pi$
$90$	4.66833	+	1.06552i	0.492085	+	0.112315i
$91$	−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
$95$	−5.69146	+	11.8184i	−0.583932	+	1.21255i
$96$	12.3744	+	5.95920i	1.26296	+	0.608208i
$97$	−11.1372	+	2.54198i	−1.13081	+	0.258099i	−0.746681	−	0.665182i	$-0.768354\pi$
$97$	−11.1372	+	2.54198i	−1.13081	+	0.258099i	−0.384125	+	0.923281i	$0.625497\pi$
$98$	−1.17670	−	2.44345i	−0.118865	−	0.246826i
$99$			21.2856i			2.13929i
$100$	0.224318	−	0.108026i	0.0224318	−	0.0108026i
$101$	−0.761904	+	0.607598i	−0.0758123	+	0.0604583i	−0.660663	−	0.750683i	$-0.729725\pi$
$101$	−0.761904	+	0.607598i	−0.0758123	+	0.0604583i	0.584850	+	0.811141i	$0.301153\pi$
$102$	1.48156	−	1.18151i	0.146696	−	0.116986i
$103$	7.00699	−	3.37439i	0.690419	−	0.332488i	−0.0555620	−	0.998455i	$-0.517695\pi$
$103$	7.00699	−	3.37439i	0.690419	−	0.332488i	0.745981	+	0.665967i	$0.231981\pi$
$104$			5.99760i			0.588113i
$105$	3.35232	+	6.96115i	0.327152	+	0.679339i
$106$	2.89244	−	0.660181i	0.280939	−	0.0641224i
$107$	4.90967	+	2.36437i	0.474636	+	0.228573i	0.655879	−	0.754866i	$-0.272298\pi$
$107$	4.90967	+	2.36437i	0.474636	+	0.228573i	−0.181244	+	0.983438i	$0.558012\pi$
$108$	2.53868	−	5.27163i	0.244285	−	0.507263i
$109$	−1.75603	+	7.69365i	−0.168197	+	0.736918i	0.818521	+	0.574476i	$0.194794\pi$
$109$	−1.75603	+	7.69365i	−0.168197	+	0.736918i	−0.986718	+	0.162442i	$0.948063\pi$
$110$	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
$113$	16.8672	+	3.84982i	1.58673	+	0.362160i	0.922691	−	0.385539i	$-0.125985\pi$
$113$	16.8672	+	3.84982i	1.58673	+	0.362160i	0.664037	+	0.747700i	$0.268842\pi$
$114$	−6.40608	−	5.10867i	−0.599984	−	0.478471i
$115$	−1.90703			−0.177831
$116$		0			0
$117$	13.3353			1.23285
$118$	1.73998	+	1.38759i	0.160178	+	0.127738i
$119$	1.74746	+	0.398846i	0.160189	+	0.0365622i
$120$	−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
$124$	−2.06996	+	4.29831i	−0.185888	+	0.386000i
$125$	−10.2122	−	4.91793i	−0.913405	−	0.439873i
$126$	−2.75815	+	0.629530i	−0.245715	+	0.0560829i
$127$	2.39338	+	4.96990i	0.212378	+	0.441007i	0.979758	−	0.200185i	$-0.0641543\pi$
$127$	2.39338	+	4.96990i	0.212378	+	0.441007i	−0.767380	+	0.641192i	$0.778440\pi$
$128$		−	11.4249i		−	1.00983i
$129$	26.7196	−	12.8675i	2.35253	−	1.13292i
$130$	2.76410	−	2.20430i	0.242428	−	0.193330i
$131$	0.0221199	−	0.0176400i	0.00193263	−	0.00154122i	−0.622523	−	0.782601i	$-0.713892\pi$
$131$	0.0221199	−	0.0176400i	0.00193263	−	0.00154122i	0.624456	+	0.781060i	$0.285321\pi$
$132$	21.1247	−	10.1731i	1.83867	−	0.885454i
$133$		−	7.75009i		−	0.672018i
$134$	0.524125	+	1.08836i	0.0452775	+	0.0940197i
$135$	−7.23067	+	1.65035i	−0.622317	+	0.142040i
$136$	−2.37062	−	1.14163i	−0.203279	−	0.0978940i
$137$	−2.67041	+	5.54516i	−0.228149	+	0.473755i	−0.983346	−	0.181742i	$-0.941827\pi$
$137$	−2.67041	+	5.54516i	−0.228149	+	0.473755i	0.755198	+	0.655497i	$0.227541\pi$
$138$	0.265067	−	1.16134i	0.0225640	−	0.0988594i
$139$	7.73636	+	9.70108i	0.656189	+	0.822835i	0.992922	−	0.118765i	$-0.0378935\pi$
$139$	7.73636	+	9.70108i	0.656189	+	0.822835i	−0.336733	+	0.941600i	$0.609322\pi$
$140$	3.11057	−	3.90053i	0.262891	−	0.329655i
$141$	1.72352	+	7.55126i	0.145147	+	0.635930i
$142$	7.77051	+	1.77357i	0.652087	+	0.148835i
$143$	12.2872	+	9.79869i	1.02750	+	0.819408i
$144$	−10.6248			−0.885400
$145$		0			0
$146$	1.73646			0.143710
$147$	11.1669	+	8.90534i	0.921034	+	0.734500i
$148$	−10.0006	−	2.28258i	−0.822047	−	0.187627i
$149$	−4.63016	−	20.2860i	−0.379317	−	1.66190i	−0.699570	−	0.714565i	$-0.746625\pi$
$149$	−4.63016	−	20.2860i	−0.379317	−	1.66190i	0.320252	−	0.947332i	$-0.396232\pi$
$150$	0.122909	−	0.154122i	0.0100354	−	0.0125840i
$151$	−12.4875	−	15.6588i	−1.01621	−	1.27429i	−0.961213	−	0.275807i	$-0.911055\pi$
$151$	−12.4875	−	15.6588i	−1.01621	−	1.27429i	−0.0550017	−	0.998486i	$-0.517516\pi$
$152$	−2.53160	+	11.0917i	−0.205340	+	0.899654i
$153$	−2.53836	+	5.27095i	−0.205214	+	0.426131i
$154$	−3.00393	−	1.44662i	−0.242063	−	0.116572i
$155$	5.89565	−	1.34564i	0.473550	−	0.108085i
$156$	−6.37340	−	13.2345i	−0.510280	−	1.05961i
$157$		−	11.7893i		−	0.940890i	−0.882429	−	0.470445i	$-0.844093\pi$
$157$		−	11.7893i		−	0.940890i	0.882429	−	0.470445i	$-0.155907\pi$
$158$	0.974741	−	0.469410i	0.0775462	−	0.0373443i
$159$	−12.2161	+	9.74201i	−0.968799	+	0.772591i
$160$	−8.78896	+	7.00896i	−0.694828	+	0.554107i
$161$	1.01513	−	0.488862i	0.0800037	−	0.0385277i
$162$			1.88561i			0.148148i
$163$	1.08758	+	2.25838i	0.0851859	+	0.176890i	0.939210	−	0.343343i	$-0.111559\pi$
$163$	1.08758	+	2.25838i	0.0851859	+	0.176890i	−0.854024	+	0.520233i	$0.825845\pi$
$164$	−3.23529	+	0.738433i	−0.252633	+	0.0576619i
$165$	−26.7769	−	12.8951i	−2.08458	−	1.00388i
$166$	−1.41060	+	2.92914i	−0.109484	+	0.227346i
$167$	−0.594332	+	2.60394i	−0.0459908	+	0.201499i	−0.992704	−	0.120580i	$-0.961525\pi$
$167$	−0.594332	+	2.60394i	−0.0459908	+	0.201499i	0.946713	+	0.322079i	$0.104382\pi$
$168$	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
$171$	24.6618	+	5.62889i	1.88593	+	0.430452i
$172$	−14.9718	−	11.9396i	−1.14159	−	0.910384i
$173$	−23.5982			−1.79414			−0.897071	−	0.441887i	$-0.854309\pi$
$173$	−23.5982			−1.79414			−0.897071	+	0.441887i	$0.854309\pi$
$174$		0			0
$175$	0.186458			0.0140949
$176$	−9.78968	−	7.80701i	−0.737925	−	0.588475i
$177$	−11.4269	−	2.60813i	−0.858902	−	0.196039i
$178$	1.35754	+	5.94776i	0.101752	+	0.445803i
$179$	13.0674	−	16.3859i	0.976700	−	1.22474i	0.00228261	−	0.999997i	$-0.499273\pi$
$179$	13.0674	−	16.3859i	0.976700	−	1.22474i	0.974417	−	0.224746i	$-0.0721551\pi$
$180$	10.1528	+	12.7312i	0.756743	+	0.948925i
$181$	−2.02358	+	8.86589i	−0.150412	+	0.658996i	0.842354	+	0.538925i	$0.181169\pi$
$181$	−2.02358	+	8.86589i	−0.150412	+	0.658996i	−0.992765	+	0.120071i	$0.961688\pi$
$182$	−0.906298	+	1.88195i	−0.0671793	+	0.139499i
$183$	−13.1859	−	6.35001i	−0.974732	−	0.469406i
$184$	−1.61251	+	0.368046i	−0.118876	+	0.0271327i
$185$	5.64156	+	11.7148i	0.414776	+	0.861291i
$186$			3.77735i			0.276969i
$187$	−6.21189	+	2.99149i	−0.454258	+	0.218759i
$188$	3.91020	−	3.11828i	0.285180	−	0.227424i
$189$	3.42591	−	2.73207i	0.249198	−	0.198729i
$190$	6.04225	−	2.90979i	0.438351	−	0.211099i
$191$		−	19.2700i		−	1.39433i	−0.716912	−	0.697163i	$-0.754445\pi$
$191$		−	19.2700i		−	1.39433i	0.716912	−	0.697163i	$-0.245555\pi$
$192$	2.79468	+	5.80321i	0.201688	+	0.418810i
$193$	−5.18472	+	1.18338i	−0.373204	+	0.0851815i	−0.405009	−	0.914313i	$-0.632732\pi$
$193$	−5.18472	+	1.18338i	−0.373204	+	0.0851815i	0.0318048	+	0.999494i	$0.489875\pi$
$194$	5.26198	+	2.53404i	0.377788	+	0.181933i
$195$	−8.07871	+	16.7756i	−0.578528	+	1.20133i
$196$	2.05225	−	8.99150i	0.146589	−	0.642250i
$197$	−6.21783	−	7.79692i	−0.443002	−	0.555507i	0.509329	−	0.860572i	$-0.329893\pi$
$197$	−6.21783	−	7.79692i	−0.443002	−	0.555507i	−0.952332	+	0.305064i	$0.901322\pi$
$198$	6.78506	−	8.50820i	0.482193	−	0.604651i
$199$	4.93778	+	21.6338i	0.350030	+	1.53358i	0.777109	+	0.629366i	$0.216686\pi$
$199$	4.93778	+	21.6338i	0.350030	+	1.53358i	−0.427079	+	0.904214i	$0.640457\pi$
$200$	−0.266852	−	0.0609073i	−0.0188693	−	0.00430680i
$201$	−4.97395	−	3.96660i	−0.350836	−	0.279782i
$202$	0.498225			0.0350550
$203$		0			0
$204$	6.44425			0.451188
$205$	3.28870	+	2.62265i	0.229693	+	0.183174i
$206$	−3.87643	−	0.884771i	−0.270084	−	0.0616449i
$207$	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
$211$	3.17184	−	6.58638i	0.218358	−	0.453425i	−0.762799	−	0.646635i	$-0.776176\pi$
$211$	3.17184	−	6.58638i	0.218358	−	0.453425i	0.981157	+	0.193210i	$0.0618899\pi$
$212$	9.09008	+	4.37755i	0.624309	+	0.300652i
$213$	−40.9239	+	9.34061i	−2.80406	+	0.640008i
$214$	−1.20880	−	2.51010i	−0.0826318	−	0.171587i
$215$			24.2734i			1.65543i
$216$	−5.79549	+	2.79096i	−0.394333	+	0.189901i
$217$	−2.79337	+	2.22764i	−0.189626	+	0.151222i
$218$	3.15436	−	2.51552i	0.213640	−	0.170372i
$219$	−8.23950	+	3.96793i	−0.556774	+	0.268128i
$220$			19.1906i			1.29383i
$221$	1.87415	+	3.89172i	0.126069	+	0.261785i
$222$	−7.91821	+	1.80728i	−0.531435	+	0.121297i
$223$	−4.95547	−	2.38643i	−0.331843	−	0.159807i	0.260541	−	0.965463i	$-0.416099\pi$
$223$	−4.95547	−	2.38643i	−0.331843	−	0.159807i	−0.592384	+	0.805656i	$0.701813\pi$
$224$	2.88173	−	5.98398i	0.192544	−	0.399822i
$225$	−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	−0.340609	−	0.940205i	$-0.610633\pi$
$227$	9.82060	−	12.3146i	0.651816	−	0.817351i	0.992425	+	0.122854i	$0.0392046\pi$
$228$	−6.20035	−	27.1655i	−0.410628	−	1.79908i
$229$	−14.4603	−	3.30048i	−0.955566	−	0.218102i	−0.283815	−	0.958879i	$-0.591600\pi$
$229$	−14.4603	−	3.30048i	−0.955566	−	0.218102i	−0.671751	+	0.740777i	$0.734457\pi$
$230$	0.762269	+	0.607889i	0.0502625	+	0.0400830i
$231$	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	$0.674213\pi$
$234$	−5.33035	−	4.25081i	−0.348456	−	0.277884i
$235$	−6.18058	−	1.41068i	−0.403176	−	0.0920224i
$236$	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	0.861132	+	0.508382i	$0.169756\pi$
$239$	−2.09168	+	9.16427i	−0.135300	+	0.592787i	−0.996432	+	0.0844052i	$0.973101\pi$
$240$	6.43663	−	13.3658i	0.415483	−	0.862758i
$241$	−9.40638	−	4.52987i	−0.605918	−	0.291795i	0.105659	−	0.994402i	$-0.466305\pi$
$241$	−9.40638	−	4.52987i	−0.605918	−	0.291795i	−0.711578	+	0.702608i	$0.752019\pi$
$242$	7.02069	−	1.60243i	0.451307	−	0.103008i
$243$	−8.68929	−	18.0435i	−0.557418	−	1.15749i
$244$			9.45018i			0.604986i
$245$	−10.5327	+	5.07229i	−0.672911	+	0.324057i
$246$	−2.05425	+	1.63821i	−0.130974	+	0.104448i
$247$	14.6022	−	11.6448i	0.929113	−	0.740943i
$248$	4.72544	−	2.27565i	0.300066	−	0.144504i
$249$		−	17.1221i		−	1.08507i
$250$	2.51432	+	5.22103i	0.159019	+	0.330207i
$251$	−14.4115	+	3.28934i	−0.909649	+	0.207621i	−0.651646	−	0.758523i	$-0.725921\pi$
$251$	−14.4115	+	3.28934i	−0.909649	+	0.207621i	−0.258002	+	0.966144i	$0.583064\pi$
$252$	−8.66804	−	4.17431i	−0.546035	−	0.262957i
$253$	−1.88047	+	3.90483i	−0.118224	+	0.245495i
$254$	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	0.961496	−	0.274817i	$-0.0886173\pi$
$257$	−0.385080	−	1.68715i	−0.0240206	−	0.105241i	−0.985517	+	0.169576i	$0.945760\pi$
$258$	−14.7819	−	3.37388i	−0.920283	−	0.210049i
$259$	−6.00614	−	4.78974i	−0.373203	−	0.297620i
$260$	12.0228			0.745625
$261$		0			0
$262$	−0.0144647			−0.000893630
$263$	−10.5790	−	8.43648i	−0.652330	−	0.520216i	0.240477	−	0.970655i	$-0.422696\pi$
$263$	−10.5790	−	8.43648i	−0.652330	−	0.520216i	−0.892807	+	0.450439i	$0.851268\pi$
$264$	−25.1303	−	5.73582i	−1.54666	−	0.353015i
$265$	−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
$269$	12.9685	−	26.9294i	0.790704	−	1.64191i	0.0241706	−	0.999708i	$-0.492306\pi$
$269$	12.9685	−	26.9294i	0.790704	−	1.64191i	0.766533	−	0.642205i	$-0.221980\pi$
$270$	3.41628	+	1.64520i	0.207908	+	0.100123i
$271$	9.12919	−	2.08368i	0.554559	−	0.126574i	0.0639481	−	0.997953i	$-0.479631\pi$
$271$	9.12919	−	2.08368i	0.554559	−	0.126574i	0.490611	+	0.871379i	$0.336774\pi$
$272$	−1.49321	−	3.10069i	−0.0905393	−	0.188007i
$273$		−	11.0008i		−	0.665799i
$274$	2.83500	−	1.36526i	0.171268	−	0.0824785i
$275$	−0.560755	+	0.447187i	−0.0338148	+	0.0269664i
$276$	3.16712	−	2.52569i	0.190638	−	0.152029i
$277$	−20.2017	+	9.72863i	−1.21380	+	0.584537i	−0.927579	−	0.373626i	$-0.878114\pi$
$277$	−20.2017	+	9.72863i	−1.21380	+	0.584537i	−0.286224	+	0.958163i	$0.592400\pi$
$278$		−	6.34374i		−	0.380472i
$279$	−5.05980	−	10.5068i	−0.302922	−	0.629024i
$280$	−5.34722	+	1.22047i	−0.319557	+	0.0729369i
$281$	7.84928	+	3.78002i	0.468249	+	0.225497i	0.653103	−	0.757269i	$-0.273467\pi$
$281$	7.84928	+	3.78002i	0.468249	+	0.225497i	−0.184854	+	0.982766i	$0.559181\pi$
$282$	1.71814	−	3.56775i	0.102314	−	0.212456i
$283$	−3.21723	+	14.0956i	−0.191244	+	0.837896i	0.784700	+	0.619876i	$0.212817\pi$
$283$	−3.21723	+	14.0956i	−0.191244	+	0.837896i	−0.975944	+	0.218020i	$0.930040\pi$
$284$	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
$287$	−2.42292	−	0.553017i	−0.143021	−	0.0326435i
$288$	16.9488	+	13.5162i	0.998717	+	0.796450i
$289$	15.1050			0.888530
$290$		0			0
$291$	−30.7586			−1.80310
$292$	4.61682	+	3.68179i	0.270179	+	0.215461i
$293$	31.9347	+	7.28889i	1.86565	+	0.425822i	0.997511	−	0.0705061i	$-0.0224614\pi$
$293$	31.9347	+	7.28889i	1.86565	+	0.425822i	0.868135	+	0.496328i	$0.165319\pi$
$294$	−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
$298$	−4.61568	+	9.58457i	−0.267379	+	0.555219i
$299$	2.44636	+	1.17810i	0.141476	+	0.0681315i
$300$	0.653569	−	0.149173i	0.0377338	−	0.00861249i
$301$	−6.22243	−	12.9210i	−0.358655	−	0.744755i
$302$			10.2396i			0.589222i
$303$	−2.36408	+	1.13848i	−0.135813	+	0.0654040i
$304$	−11.6341	+	9.27790i	−0.667263	+	0.532124i
$305$	9.36535	−	7.46862i	0.536258	−	0.427652i
$306$	2.69480	−	1.29775i	0.154052	−	0.0741874i
$307$			28.4921i			1.62613i	0.582173	+	0.813065i	$0.302202\pi$
$307$			28.4921i			1.62613i	−0.582173	+	0.813065i	$0.697798\pi$
$308$	−4.91948	−	10.2154i	−0.280313	−	0.582077i
$309$	20.4155	−	4.65970i	1.16140	−	0.265081i
$310$	−2.78552	−	1.34144i	−0.158207	−	0.0761885i
$311$	9.46196	−	19.6480i	0.536539	−	1.11413i	−0.439842	−	0.898075i	$-0.644965\pi$
$311$	9.46196	−	19.6480i	0.536539	−	1.11413i	0.976380	−	0.216059i	$-0.0693203\pi$
$312$	−3.59347	+	15.7440i	−0.203440	+	0.891328i
$313$	−14.9186	−	18.7074i	−0.843251	−	1.05740i	−0.997590	−	0.0693848i	$-0.977896\pi$
$313$	−14.9186	−	18.7074i	−0.843251	−	1.05740i	0.154339	−	0.988018i	$-0.450675\pi$
$314$	−3.75799	+	4.71237i	−0.212076	+	0.265935i
$315$	2.71365	+	11.8893i	0.152897	+	0.669884i
$316$	3.58689	+	0.818684i	0.201778	+	0.0460546i
$317$	7.31211	+	5.83121i	0.410689	+	0.327514i	0.806945	−	0.590626i	$-0.201119\pi$
$317$	7.31211	+	5.83121i	0.410689	+	0.327514i	−0.396256	+	0.918140i	$0.629691\pi$
$318$	7.98835			0.447964
$319$		0			0
$320$	−5.27191			−0.294709
$321$	11.4715	+	9.14824i	0.640278	+	0.510605i
$322$	−0.561595	−	0.128180i	−0.0312965	−	0.00714322i
$323$	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
$327$	−9.21932	+	19.1441i	−0.509829	+	1.05867i
$328$	3.28696	+	1.58292i	0.181492	+	0.0874021i
$329$	3.65162	−	0.833458i	0.201320	−	0.0459500i
$330$	6.59268	+	13.6898i	0.362915	+	0.753601i
$331$		−	10.2474i		−	0.563247i	−0.959525	−	0.281623i	$-0.909127\pi$
$331$		−	10.2474i		−	0.563247i	0.959525	−	0.281623i	$-0.0908729\pi$
$332$	−9.96108	+	4.79700i	−0.546685	+	0.263270i
$333$	19.6038	−	15.6335i	1.07428	−	0.856711i
$334$	1.06760	−	0.851384i	0.0584166	−	0.0465857i
$335$	4.69146	−	2.25929i	0.256322	−	0.123438i
$336$			8.76478i			0.478158i
$337$	6.91766	+	14.3647i	0.376829	+	0.782493i	1.00000		0.000407467i	$0.000129701\pi$
$337$	6.91766	+	14.3647i	0.376829	+	0.782493i	−0.623171	+	0.782085i	$0.714156\pi$
$338$	1.57211	−	0.358824i	0.0855114	−	0.0195174i
$339$	41.9705	+	20.2119i	2.27953	+	1.09776i
$340$	−2.28853	+	4.75217i	−0.124113	+	0.257723i
$341$	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
$345$	−5.00604	−	1.14260i	−0.269516	−	0.0615153i
$346$	9.43259	+	7.52224i	0.507099	+	0.404398i
$347$	−36.7925			−1.97513			−0.987563	−	0.157224i	$-0.949746\pi$
$347$	−36.7925			−1.97513			−0.987563	+	0.157224i	$0.949746\pi$
$348$		0			0
$349$	32.4894			1.73912			0.869558	−	0.493831i	$-0.164404\pi$
$349$	32.4894			1.73912			0.869558	+	0.493831i	$0.164404\pi$
$350$	−0.0745301	−	0.0594358i	−0.00398380	−	0.00317698i
$351$	10.2951	+	2.34980i	0.549514	+	0.125423i
$352$	5.68500	+	24.9076i	0.303012	+	1.32758i
$353$	7.49252	−	9.39533i	0.398787	−	0.500063i	−0.541380	−	0.840778i	$-0.682098\pi$
$353$	7.49252	−	9.39533i	0.398787	−	0.500063i	0.940166	+	0.340715i	$0.110669\pi$
$354$	3.73616	+	4.68499i	0.198574	+	0.249004i
$355$	7.64513	−	33.4955i	0.405761	−	1.77776i
$356$	−9.00161	+	18.6920i	−0.477085	+	0.990676i
$357$	4.34820	+	2.09398i	0.230131	+	0.110825i
$358$	−10.4465	+	2.38433i	−0.552112	+	0.126016i
$359$	1.69588	+	3.52153i	0.0895052	+	0.185859i	0.940916	−	0.338640i	$-0.109967\pi$
$359$	1.69588	+	3.52153i	0.0895052	+	0.185859i	−0.851411	+	0.524499i	$0.824253\pi$
$360$		−	17.9019i		−	0.943515i
$361$	14.8015	−	7.12801i	0.779024	−	0.375158i
$362$	3.63497	−	2.89879i	0.191050	−	0.152357i
$363$	−29.6515	+	23.6463i	−1.55630	+	1.24111i
$364$	−6.39990	+	3.08203i	−0.335446	+	0.161542i
$365$		−	7.48515i		−	0.391791i
$366$	3.24648	+	6.74138i	0.169696	+	0.352378i
$367$	12.4667	−	2.84545i	0.650759	−	0.148532i	0.115617	−	0.993294i	$-0.463115\pi$
$367$	12.4667	−	2.84545i	0.650759	−	0.148532i	0.535142	+	0.844762i	$0.320258\pi$
$368$	−1.94911	−	0.938642i	−0.101604	−	0.0489301i
$369$	3.51954	−	7.30839i	0.183220	−	0.380460i
$370$	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	−0.887419	−	0.460964i	$-0.847504\pi$
$373$	−5.56002	−	24.3600i	−0.287887	−	1.26131i	0.599532	−	0.800351i	$-0.295353\pi$
$374$	3.43656	+	0.784373i	0.177700	+	0.0405590i
$375$	−23.8609	−	19.0284i	−1.23217	−	0.982624i
$376$	−5.49833			−0.283555
$377$		0			0
$378$	−2.24027			−0.115227
$379$	10.1913	+	8.12732i	0.523494	+	0.417472i	0.849258	−	0.527979i	$-0.177050\pi$
$379$	10.1913	+	8.12732i	0.523494	+	0.417472i	−0.325764	+	0.945451i	$0.605621\pi$
$380$	22.2345	+	5.07488i	1.14061	+	0.260336i
$381$	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	$-0.424753\pi$
$383$	−14.9856	−	18.7913i	−0.765728	−	0.960193i	−0.999928	+	0.0119957i	$0.996182\pi$
$384$	6.84522	−	29.9909i	0.349319	−	1.53047i
$385$	−6.23577	+	12.9487i	−0.317804	+	0.659927i
$386$	2.44963	+	1.17968i	0.124683	+	0.0600441i
$387$	45.6356	−	10.4160i	2.31979	−	0.529477i
$388$	8.61746	+	17.8943i	0.437485	+	0.908447i
$389$			17.6717i			0.895991i	0.894036	+	0.447995i	$0.147862\pi$
$389$			17.6717i			0.895991i	−0.894036	+	0.447995i	$0.852138\pi$
$390$	8.57662	−	4.13028i	0.434294	−	0.209145i
$391$	−0.931318	+	0.742702i	−0.0470988	+	0.0375600i
$392$	−7.92717	+	6.32170i	−0.400382	+	0.319294i
$393$	0.0686350	−	0.0330529i	0.00346218	−	0.00166730i
$394$			5.09856i			0.256862i
$395$	−2.02344	−	4.20171i	−0.101810	−	0.211411i
$396$	36.0797	−	8.23496i	1.81307	−	0.413822i
$397$	−27.2566	−	13.1261i	−1.36797	−	0.658780i	−0.401572	−	0.915827i	$-0.631536\pi$
$397$	−27.2566	−	13.1261i	−1.36797	−	0.658780i	−0.966399	+	0.257047i	$0.917250\pi$
$398$	4.92235	−	10.2214i	0.246735	−	0.512350i
$399$	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	−0.936061	−	0.351838i	$-0.885557\pi$
$401$	−7.70463	+	9.66129i	−0.384751	+	0.482462i	0.551310	+	0.834300i	$0.314128\pi$
$402$	0.723765	+	3.17102i	0.0360981	+	0.158156i
$403$	−8.39430	−	1.91594i	−0.418150	−	0.0954400i
$404$	1.32466	+	1.05638i	0.0659043	+	0.0525569i
$405$	8.12810			0.403889
$406$		0			0
$407$	29.5503			1.46475
$408$	−5.53899	−	4.41720i	−0.274221	−	0.218684i
$409$	5.95386	+	1.35893i	0.294400	+	0.0671948i	0.367170	−	0.930154i	$-0.380327\pi$
$409$	5.95386	+	1.35893i	0.294400	+	0.0671948i	−0.0727701	+	0.997349i	$0.523184\pi$
$410$	−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
$414$	0.815773	−	1.69397i	0.0400930	−	0.0832541i
$415$	12.6263	+	6.08052i	0.619803	+	0.298481i
$416$	15.6045	−	3.56163i	0.765074	−	0.174623i
$417$	14.4959	+	30.1011i	0.709868	+	1.47406i
$418$		−	15.2414i		−	0.745480i
$419$	10.4580	−	5.03629i	0.510905	−	0.246039i	−0.160626	−	0.987015i	$-0.551351\pi$
$419$	10.4580	−	5.03629i	0.510905	−	0.246039i	0.671531	+	0.740976i	$0.265637\pi$
$420$	10.5024	−	8.37539i	0.512465	−	0.408677i
$421$	−15.8608	+	12.6486i	−0.773008	+	0.616453i	−0.928478	−	0.371387i	$-0.878882\pi$
$421$	−15.8608	+	12.6486i	−0.773008	+	0.616453i	0.155470	+	0.987841i	$0.450311\pi$
$422$	−3.36733	+	1.62162i	−0.163919	+	0.0789391i
$423$			12.2252i			0.594412i
$424$	−4.81256	−	9.99339i	−0.233719	−	0.485322i
$425$	−0.192187	+	0.0438655i	−0.00932246	+	0.00212779i
$426$	19.3353	+	9.31141i	0.936801	+	0.451139i
$427$	−3.07072	+	6.37642i	−0.148603	+	0.308577i
$428$	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	−0.980658	−	0.195729i	$-0.937293\pi$
$431$	−3.77923	−	16.5579i	−0.182039	−	0.797566i	0.798619	−	0.601837i	$-0.205564\pi$
$432$	−8.20254	−	1.87218i	−0.394645	−	0.0900751i
$433$	12.4587	+	9.93547i	0.598726	+	0.477468i	0.875337	−	0.483514i	$-0.160640\pi$
$433$	12.4587	+	9.93547i	0.598726	+	0.477468i	−0.276610	+	0.960982i	$0.589211\pi$
$434$	1.82664			0.0876815
$435$		0			0
$436$	13.7203			0.657084
$437$	4.02690	+	3.21134i	0.192633	+	0.153619i
$438$	4.55828	+	1.04040i	0.217803	+	0.0497122i
$439$	−1.20240	−	5.26804i	−0.0573872	−	0.251430i	0.938095	−	0.346378i	$-0.112589\pi$
$439$	−1.20240	−	5.26804i	−0.0573872	−	0.251430i	−0.995482	+	0.0949482i	$0.969731\pi$
$440$	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
$443$	8.26609	−	17.1647i	0.392734	−	0.815520i	−0.607049	−	0.794665i	$-0.707647\pi$
$443$	8.26609	−	17.1647i	0.392734	−	0.815520i	0.999783	−	0.0208553i	$-0.00663894\pi$
$444$	−24.8846	−	11.9838i	−1.18097	−	0.568725i
$445$	25.6384	−	5.85179i	1.21538	−	0.277402i
$446$	1.22007	+	2.53351i	0.0577722	+	0.119965i
$447$		−	56.0260i		−	2.64994i
$448$	2.80630	−	1.35144i	0.132585	−	0.0638497i
$449$	13.8286	−	11.0279i	0.652611	−	0.520440i	−0.240285	−	0.970702i	$-0.577241\pi$
$449$	13.8286	−	11.0279i	0.652611	−	0.520440i	0.892896	+	0.450262i	$0.148670\pi$
$450$	0.243263	−	0.193996i	0.0114675	−	0.00914506i
$451$	8.61304	−	4.14782i	0.405572	−	0.195313i
$452$		−	30.0797i		−	1.41483i
$453$	−23.3982	−	48.5869i	−1.09935	−	2.28281i
$454$	−7.85089	+	1.79192i	−0.368461	+	0.0840987i
$455$	8.11231	+	3.90668i	0.380311	+	0.183148i
$456$	−13.2912	+	27.5994i	−0.622416	+	1.29246i
$457$	−3.35962	+	14.7195i	−0.157157	+	0.688548i	0.833540	+	0.552459i	$0.186310\pi$
$457$	−3.35962	+	14.7195i	−0.157157	+	0.688548i	−0.990697	+	0.136089i	$0.956547\pi$
$458$	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
$461$	21.7426	+	4.96261i	1.01266	+	0.231132i	0.696486	−	0.717571i	$-0.254746\pi$
$461$	21.7426	+	4.96261i	1.01266	+	0.231132i	0.316170	+	0.948703i	$0.397603\pi$
$462$	−7.01872	−	5.59724i	−0.326541	−	0.260407i
$463$	26.7391			1.24267			0.621335	−	0.783545i	$-0.286591\pi$
$463$	26.7391			1.24267			0.621335	+	0.783545i	$0.286591\pi$
$464$		0			0
$465$	16.2826			0.755088
$466$	6.35018	+	5.06410i	0.294166	+	0.234590i
$467$	11.2714	+	2.57262i	0.521578	+	0.119047i	0.475201	−	0.879877i	$-0.342375\pi$
$467$	11.2714	+	2.57262i	0.521578	+	0.119047i	0.0463768	+	0.998924i	$0.485233\pi$
$468$	−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
$472$	3.61006	−	7.49637i	0.166167	−	0.345049i
$473$	49.7022	+	23.9353i	2.28531	+	1.10055i
$474$	2.83999	−	0.648210i	0.130445	−	0.0297732i
$475$	0.369827	+	0.767953i	0.0169688	+	0.0352361i
$476$		−	3.11630i		−	0.142835i
$477$	−22.2198	+	10.7005i	−1.01737	+	0.489941i
$478$	3.75730	−	2.99635i	0.171855	−	0.137050i
$479$	−19.0204	+	15.1683i	−0.869065	+	0.693056i	−0.952854	−	0.303428i	$-0.901869\pi$
$479$	−19.0204	+	15.1683i	−0.869065	+	0.693056i	0.0837900	+	0.996483i	$0.473298\pi$
$480$	−27.2709	+	13.1330i	−1.24474	+	0.599435i
$481$		−	18.5131i		−	0.844125i
$482$	2.31592	+	4.80906i	0.105487	+	0.219047i
$483$	2.95768	−	0.675070i	0.134579	−	0.0307168i
$484$	22.0639	+	10.6254i	1.00291	+	0.482974i
$485$	10.9232	−	22.6823i	0.495997	−	1.02995i
$486$	−2.27835	+	9.98208i	−0.103348	+	0.452796i
$487$	0.802361	+	1.00613i	0.0363584	+	0.0455920i	0.799678	−	0.600429i	$-0.205003\pi$
$487$	0.802361	+	1.00613i	0.0363584	+	0.0455920i	−0.763320	+	0.646021i	$0.776432\pi$
$488$	6.47760	−	8.12266i	0.293227	−	0.367695i
$489$	1.50184	+	6.58000i	0.0679156	+	0.297558i
$490$	5.82695	+	1.32996i	0.263235	+	0.0600816i
$491$	25.5334	+	20.3622i	1.15231	+	0.918933i	0.997615	−	0.0690296i	$-0.0219903\pi$
$491$	25.5334	+	20.3622i	1.15231	+	0.918933i	0.154691	+	0.987963i	$0.450562\pi$
$492$	−8.93522			−0.402831
$493$		0			0
$494$	−9.54865			−0.429614
$495$	−36.6754	−	29.2476i	−1.64844	−	1.31458i
$496$	6.68807	+	1.52651i	0.300303	+	0.0685423i
$497$	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	$-0.138893\pi$
$499$	6.53615	+	8.19607i	0.292598	+	0.366907i	−0.613704	+	0.789536i	$0.710321\pi$
$500$	−4.38514	+	19.2126i	−0.196109	+	0.859212i
$501$	−3.12030	+	6.47938i	−0.139405	+	0.289477i
$502$	6.80904	+	3.27906i	0.303902	+	0.146352i
$503$	−3.69533	+	0.843435i	−0.164767	+	0.0376069i	−0.304108	−	0.952637i	$-0.598358\pi$
$503$	−3.69533	+	0.843435i	−0.164767	+	0.0376069i	0.139342	+	0.990244i	$0.455501\pi$
$504$	4.58912	+	9.52941i	0.204416	+	0.424474i
$505$		−	2.14764i		−	0.0955689i
$506$	1.99637	−	0.961399i	0.0887493	−	0.0427394i
$507$	−6.63973	+	5.29501i	−0.294881	+	0.235160i
$508$	7.49817	−	5.97959i	0.332677	−	0.265301i
$509$	7.22423	−	3.47900i	0.320208	−	0.154204i	−0.266874	−	0.963731i	$-0.585991\pi$
$509$	7.22423	−	3.47900i	0.320208	−	0.154204i	0.587082	+	0.809527i	$0.300276\pi$
$510$			4.17620i			0.184925i
$511$	1.91880	+	3.98443i	0.0848828	+	0.176261i
$512$	−21.7502	+	4.96433i	−0.961231	+	0.219395i
$513$	18.0475	+	8.69121i	0.796816	+	0.383726i
$514$	−0.383876	+	0.797127i	−0.0169321	+	0.0351598i
$515$	−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
$519$	−61.9466	−	14.1389i	−2.71915	−	0.620629i
$520$	−10.3339	−	8.24103i	−0.453173	−	0.361393i
$521$	6.39024			0.279962			0.139981	−	0.990154i	$-0.455296\pi$
$521$	6.39024			0.279962			0.139981	+	0.990154i	$0.455296\pi$
$522$		0			0
$523$	−16.3261			−0.713891			−0.356946	−	0.934125i	$-0.616182\pi$
$523$	−16.3261			−0.713891			−0.356946	+	0.934125i	$0.616182\pi$
$524$	−0.0384581	−	0.0306693i	−0.00168005	−	0.00133979i
$525$	0.489461	+	0.111716i	0.0213618	+	0.00487570i
$526$	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
$530$	−2.83688	+	5.89083i	−0.123226	+	0.255881i
$531$	−16.6678	−	8.02679i	−0.723321	−	0.348333i
$532$	−13.1366	+	2.99835i	−0.569545	+	0.129995i
$533$	−2.59859	−	5.39603i	−0.112557	−	0.233728i
$534$			16.4265i			0.710846i
$535$	−10.8200	+	5.21064i	−0.467790	+	0.225276i
$536$	3.53090	−	2.81580i	0.152512	−	0.121624i
$537$	44.1201	−	35.1846i	1.90392	−	1.51833i
$538$	−13.7678	+	6.63022i	−0.593572	+	0.285849i
$539$			26.5684i			1.14438i
$540$	5.59479	+	11.6177i	0.240761	+	0.499946i
$541$	21.4105	−	4.88681i	0.920509	−	0.210100i	0.264091	−	0.964498i	$-0.414928\pi$
$541$	21.4105	−	4.88681i	0.920509	−	0.210100i	0.656418	+	0.754397i	$0.272071\pi$
$542$	−4.31328	−	2.07717i	−0.185271	−	0.0892219i
$543$	−10.6240	+	22.0610i	−0.455920	+	0.946727i
$544$	−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	0.951637	−	0.307224i	$-0.0994002\pi$
$547$	−0.913490	−	4.00226i	−0.0390580	−	0.171124i	−0.990695	+	0.136100i	$0.956543\pi$
$548$	10.4323	+	2.38111i	0.445647	+	0.101716i
$549$	−18.0603	−	14.4026i	−0.770795	−	0.614688i
$550$	0.366689			0.0156357
$551$		0			0
$552$	−4.45344			−0.189551
$553$	2.15420	+	1.71792i	0.0916058	+	0.0730532i
$554$	11.1761	+	2.55086i	0.474826	+	0.108376i
$555$	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	$-0.0374761\pi$
$557$	15.5194	+	19.4607i	0.657579	+	0.824578i	−0.335498	+	0.942041i	$0.608905\pi$
$558$	−1.32669	+	5.81260i	−0.0561632	+	0.246067i
$559$	14.9954	−	31.1382i	0.634236	−	1.31701i
$560$	−6.46340	−	3.11261i	−0.273128	−	0.131532i
$561$	−18.0989	+	4.13095i	−0.764135	+	0.174409i
$562$	−1.93255	−	4.01299i	−0.0815199	−	0.169278i
$563$			22.6338i			0.953902i	0.878930	+	0.476951i	$0.158258\pi$
$563$			22.6338i			0.953902i	−0.878930	+	0.476951i	$0.841742\pi$
$564$	12.1328	−	5.84284i	0.510882	−	0.246028i
$565$	−29.8097	+	23.7724i	−1.25410	+	1.00011i
$566$	5.77912	−	4.60870i	0.242915	−	0.193718i
$567$	−4.32668	+	2.08362i	−0.181704	+	0.0875038i
$568$		−	29.7981i		−	1.25030i
$569$	−4.51142	−	9.36806i	−0.189128	−	0.392729i	0.784746	−	0.619818i	$-0.212794\pi$
$569$	−4.51142	−	9.36806i	−0.189128	−	0.392729i	−0.973874	+	0.227089i	$0.927079\pi$
$570$	17.6046	−	4.01814i	0.737376	−	0.168301i
$571$	−32.1437	−	15.4796i	−1.34517	−	0.647800i	−0.383892	−	0.923378i	$-0.625417\pi$
$571$	−32.1437	−	15.4796i	−1.34517	−	0.647800i	−0.961279	+	0.275578i	$0.911131\pi$
$572$	11.8554	−	24.6180i	0.495699	−	1.02933i
$573$	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
$577$	−1.56846	−	0.357991i	−0.0652958	−	0.0149033i	0.189748	−	0.981833i	$-0.439233\pi$
$577$	−1.56846	−	0.357991i	−0.0652958	−	0.0149033i	−0.255044	+	0.966929i	$0.582090\pi$
$578$	−6.03771	−	4.81491i	−0.251136	−	0.200274i
$579$	−14.3192			−0.595085
$580$		0			0
$581$	−8.27988			−0.343507
$582$	12.2947	+	9.80470i	0.509632	+	0.406418i
$583$	−28.3359	−	6.46748i	−1.17355	−	0.267856i
$584$	−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	0.724434	+	0.689344i	$0.242101\pi$
$587$	−5.50834	+	24.1336i	−0.227354	+	0.996102i	−0.951788	+	0.306758i	$0.900756\pi$
$588$	10.7745	−	22.3735i	0.444334	−	0.922670i
$589$	−14.7153	−	7.08652i	−0.606334	−	0.291995i
$590$	−4.78165	+	1.09138i	−0.196857	+	0.0449314i
$591$	−11.6506	−	24.1927i	−0.479242	−	0.995156i
$592$			14.7501i			0.606227i
$593$	−9.19662	+	4.42886i	−0.377660	+	0.181871i	−0.613077	−	0.790023i	$-0.710069\pi$
$593$	−9.19662	+	4.42886i	−0.377660	+	0.181871i	0.235417	+	0.971894i	$0.424354\pi$
$594$	6.73741	−	5.37290i	0.276439	−	0.220453i
$595$	−3.08832	+	2.46285i	−0.126609	+	0.100967i
$596$	−32.5941	+	15.6965i	−1.33511	+	0.642953i
$597$			59.7483i			2.44534i
$598$	−0.602312	−	1.25071i	−0.0246304	−	0.0511455i
$599$	−18.3035	+	4.17765i	−0.747860	+	0.170694i	−0.579433	−	0.815020i	$-0.696726\pi$
$599$	−18.3035	+	4.17765i	−0.747860	+	0.170694i	−0.168427	+	0.985714i	$0.553869\pi$
$600$	−0.664008	−	0.319770i	−0.0271080	−	0.0130545i
$601$	17.7072	−	36.7693i	0.722290	−	1.49985i	−0.138211	−	0.990403i	$-0.544135\pi$
$601$	17.7072	−	36.7693i	0.722290	−	1.49985i	0.860501	−	0.509448i	$-0.170151\pi$
$602$	−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
$606$	1.30787	+	0.298512i	0.0531284	+	0.0121262i
$607$	9.15041	+	7.29721i	0.371404	+	0.296185i	0.791349	−	0.611365i	$-0.209379\pi$
$607$	9.15041	+	7.29721i	0.371404	+	0.296185i	−0.419945	+	0.907550i	$0.637951\pi$
$608$	30.3616			1.23133
$609$		0			0
$610$	−6.12419			−0.247961
$611$	7.05704	+	5.62781i	0.285497	+	0.227677i
$612$	9.91644	+	2.26336i	0.400848	+	0.0914910i
$613$	3.08627	+	13.5218i	0.124653	+	0.546142i	0.998231	+	0.0594571i	$0.0189369\pi$
$613$	3.08627	+	13.5218i	0.124653	+	0.546142i	−0.873577	+	0.486685i	$0.838206\pi$
$614$	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
$617$	−10.9470	+	22.7317i	−0.440709	+	0.915142i	0.555773	+	0.831334i	$0.312422\pi$
$617$	−10.9470	+	22.7317i	−0.440709	+	0.915142i	−0.996482	+	0.0838079i	$0.973292\pi$
$618$	−9.64572	−	4.64514i	−0.388008	−	0.186855i
$619$	−28.1788	+	6.43162i	−1.13260	+	0.258509i	−0.747432	−	0.664338i	$-0.768714\pi$
$619$	−28.1788	+	6.43162i	−1.13260	+	0.258509i	−0.385168	+	0.922847i	$0.625856\pi$
$620$	−4.56180	−	9.47268i	−0.183206	−	0.380432i
$621$			2.91215i			0.116860i
$622$	−10.0451	+	4.83748i	−0.402773	+	0.193965i
$623$	−12.1475	+	9.68732i	−0.486680	+	0.388114i
$624$	−16.5140	+	13.1694i	−0.661088	+	0.527200i
$625$	21.8606	−	10.5275i	0.874426	−	0.421101i
$626$			12.2331i			0.488934i
$627$	34.8277	+	72.3205i	1.39088	+	2.88820i
$628$	−19.9832	+	4.56104i	−0.797417	+	0.182005i
$629$	7.31752	+	3.52393i	0.291769	+	0.140508i
$630$	2.70516	−	5.61733i	0.107776	−	0.223800i
$631$	3.49292	−	15.3035i	0.139051	−	0.609222i	−0.856594	−	0.515992i	$-0.827424\pi$
$631$	3.49292	−	15.3035i	0.139051	−	0.609222i	0.995645	−	0.0932302i	$-0.0297193\pi$
$632$	−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
$635$	−11.8518	−	2.70510i	−0.470326	−	0.107349i
$636$	21.2391	+	16.9376i	0.842186	+	0.671621i
$637$	16.6450			0.659499
$638$		0			0
$639$	−66.2544			−2.62098
$640$	19.6852	+	15.6984i	0.778125	+	0.620534i
$641$	−31.7296	−	7.24207i	−1.25324	−	0.286045i	−0.456152	−	0.889902i	$-0.650772\pi$
$641$	−31.7296	−	7.24207i	−1.25324	−	0.286045i	−0.797092	+	0.603857i	$0.793630\pi$
$642$	−1.66923	−	7.31339i	−0.0658794	−	0.288636i
$643$	−15.3163	+	19.2061i	−0.604017	+	0.757413i	−0.985998	−	0.166757i	$-0.946671\pi$
$643$	−15.3163	+	19.2061i	−0.604017	+	0.757413i	0.381981	+	0.924170i	$0.375242\pi$
$644$	−1.22137	−	1.53155i	−0.0481286	−	0.0603514i
$645$	−14.5434	+	63.7189i	−0.572647	+	2.50893i
$646$	1.81757	−	3.77422i	0.0715112	−	0.148495i
$647$	11.7322	+	5.64994i	0.461242	+	0.222122i	0.650050	−	0.759892i	$-0.274748\pi$
$647$	11.7322	+	5.64994i	0.461242	+	0.222122i	−0.188808	+	0.982014i	$0.560462\pi$
$648$	6.87283	−	1.56868i	0.269990	−	0.0616235i
$649$	−9.45968	−	19.6432i	−0.371325	−	0.771064i
$650$		−	0.229729i		−	0.00901071i
$651$	−8.66742	+	4.17401i	−0.339703	+	0.163592i
$652$	3.40726	−	2.71720i	0.133439	−	0.106414i
$653$	23.4230	−	18.6792i	0.916612	−	0.730974i	−0.0468264	−	0.998903i	$-0.514911\pi$
$653$	23.4230	−	18.6792i	0.916612	−	0.730974i	0.963439	+	0.267929i	$0.0863393\pi$
$654$	9.78753	−	4.71343i	0.382723	−	0.184310i
$655$			0.0623513i			0.00243627i
$656$	2.07040	+	4.29923i	0.0808355	+	0.167857i
$657$	−14.0726	+	3.21198i	−0.549024	+	0.125311i
$658$	−1.72528	−	0.830853i	−0.0672586	−	0.0323900i
$659$	−6.16174	+	12.7950i	−0.240027	+	0.498422i	−0.985830	−	0.167745i	$-0.946352\pi$
$659$	−6.16174	+	12.7950i	−0.240027	+	0.498422i	0.745803	+	0.666166i	$0.232066\pi$
$660$	−11.4981	+	50.3764i	−0.447563	+	1.96090i
$661$	25.1774	+	31.5715i	0.979288	+	1.22799i	0.973660	+	0.228004i	$0.0732200\pi$
$661$	25.1774	+	31.5715i	0.979288	+	1.22799i	0.00562783	+	0.999984i	$0.498209\pi$
$662$	−3.26648	+	4.09604i	−0.126955	+	0.159197i
$663$	2.58802	+	11.3389i	0.100510	+	0.440365i
$664$	11.8499	+	2.70466i	0.459865	+	0.104961i
$665$	13.3535	+	10.6491i	0.517826	+	0.412953i
$666$	−12.8193			−0.496739
$667$		0			0
$668$	4.64368			0.179669
$669$	−11.5785	−	9.23357i	−0.447652	−	0.356990i
$670$	−2.59543	−	0.592389i	−0.100270	−	0.0228860i
$671$	−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	0.973320	+	0.229454i	$0.0736939\pi$
$673$	25.4347	+	31.8941i	0.980436	+	1.22943i	0.00711674	+	0.999975i	$0.497735\pi$
$674$	1.81382	−	7.94687i	0.0698658	−	0.306102i
$675$	−0.209100	+	0.434201i	−0.00804826	+	0.0167124i
$676$	4.94067	+	2.37930i	0.190026	+	0.0915116i
$677$	20.0725	−	4.58142i	0.771449	−	0.176078i	0.181360	−	0.983417i	$-0.441950\pi$
$677$	20.0725	−	4.58142i	0.771449	−	0.176078i	0.590088	+	0.807339i	$0.299093\pi$
$678$	−10.3335	−	21.4577i	−0.396854	−	0.824076i
$679$			14.8742i			0.570818i
$680$	5.22441	−	2.51594i	0.200347	−	0.0964820i
$681$	33.1579	−	26.4425i	1.27061	−	1.01328i
$682$	−5.49345	+	4.38088i	−0.210355	+	0.167753i
$683$	−11.3859	+	5.48315i	−0.435668	+	0.209807i	−0.638845	−	0.769335i	$-0.720588\pi$
$683$	−11.3859	+	5.48315i	−0.435668	+	0.209807i	0.203177	+	0.979142i	$0.434873\pi$
$684$		−	43.9801i		−	1.68162i
$685$	−5.88509	−	12.2205i	−0.224858	−	0.466922i
$686$	−7.98566	+	1.82267i	−0.304894	+	0.0695900i
$687$	−35.9816	−	17.3278i	−1.37278	−	0.661098i
$688$	−11.9474	+	24.8090i	−0.455490	+	0.945836i
$689$	−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	−0.971578	−	0.236722i	$-0.923927\pi$
$691$	−13.7900	+	17.2921i	−0.524595	+	0.657821i	0.446983	+	0.894543i	$0.352499\pi$
$692$	9.12966	+	39.9997i	0.347058	+	1.52056i
$693$	27.0203	+	6.16721i	1.02642	+	0.234273i
$694$	14.7065	+	11.7281i	0.558253	+	0.445192i
$695$	−27.3453			−1.03726
$696$		0			0
$697$	2.62748			0.0995229
$698$	−12.9865	−	10.3564i	−0.491546	−	0.391995i
$699$	−41.7035	−	9.51856i	−1.57737	−	0.360025i
$700$	−0.0721366	−	0.316051i	−0.00272651	−	0.0119456i
$701$	−1.36403	+	1.71044i	−0.0515187	+	0.0646024i	−0.806923	−	0.590656i	$-0.798869\pi$
$701$	−1.36403	+	1.71044i	−0.0515187	+	0.0646024i	0.755405	+	0.655259i	$0.227440\pi$
$702$	−3.36610	−	4.22095i	−0.127045	−	0.159310i
$703$	7.81444	−	34.2373i	0.294727	−	1.29128i
$704$	−5.19849	+	10.7948i	−0.195925	+	0.406843i
$705$	−15.3791	−	7.40619i	−0.579211	−	0.278933i
$706$	−5.98976	+	1.36712i	−0.225428	+	0.0514524i
$707$	0.550544	+	1.14322i	0.0207053	+	0.0429951i
$708$			20.3780i			0.765852i
$709$	26.8470	−	12.9288i	1.00826	−	0.485552i	0.144525	−	0.989501i	$-0.453834\pi$
$709$	26.8470	−	12.9288i	1.00826	−	0.485552i	0.863733	+	0.503949i	$0.168120\pi$
$710$	−13.7330	+	10.9517i	−0.515390	+	0.411010i
$711$	−7.03122	+	5.60721i	−0.263691	+	0.210287i
$712$	20.5495	−	9.89613i	0.770126	−	0.370873i
$713$		−	2.37446i		−	0.0889244i
$714$	−1.07056	−	2.22304i	−0.0400647	−	0.0831952i
$715$	−33.7665	+	7.70699i	−1.26280	+	0.288225i
$716$	−32.8301	−	15.8101i	−1.22692	−	0.590853i
$717$	−10.9816	+	22.8034i	−0.410114	+	0.851610i
$718$	0.444663	−	1.94820i	0.0165947	−	0.0727060i
$719$	5.06984	+	6.35738i	0.189073	+	0.237090i	0.867329	−	0.497736i	$-0.165835\pi$
$719$	5.06984	+	6.35738i	0.189073	+	0.237090i	−0.678255	+	0.734826i	$0.737264\pi$
$720$	14.5991	−	18.3067i	0.544075	−	0.682249i
$721$	−2.25333	−	9.87246i	−0.0839182	−	0.367670i
$722$	−8.18852	−	1.86898i	−0.304745	−	0.0695561i
$723$	−21.9781	−	17.5270i	−0.817376	−	0.651836i
$724$	15.8108			0.587604
$725$		0			0
$726$	19.3898			0.719621
$727$	−7.97784	−	6.36211i	−0.295882	−	0.235958i	0.464285	−	0.885686i	$-0.346311\pi$
$727$	−7.97784	−	6.36211i	−0.295882	−	0.235958i	−0.760167	+	0.649728i	$0.774883\pi$
$728$	7.61344	+	1.73772i	0.282173	+	0.0644041i
$729$	−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
$733$	−10.6995	+	22.2177i	−0.395194	+	0.820629i	0.604517	+	0.796592i	$0.293366\pi$
$733$	−10.6995	+	22.2177i	−0.395194	+	0.820629i	−0.999711	+	0.0240365i	$0.992348\pi$
$734$	−5.89018	−	2.83656i	−0.217410	−	0.104699i
$735$	−30.6880	+	7.00433i	−1.13194	+	0.258359i
$736$	1.91516	+	3.97687i	0.0705937	+	0.146589i
$737$		−	11.8341i		−	0.435913i
$738$	−3.73646	+	1.79938i	−0.137541	+	0.0662362i
$739$	−3.26153	+	2.60098i	−0.119977	+	0.0956786i	−0.681640	−	0.731687i	$-0.738733\pi$
$739$	−3.26153	+	2.60098i	−0.119977	+	0.0956786i	0.561663	+	0.827366i	$0.310162\pi$
$740$	17.6743	−	14.0948i	0.649722	−	0.518136i
$741$	45.3084	−	21.8194i	1.66445	−	0.801555i
$742$		−	3.86299i		−	0.141815i
$743$	1.21424	+	2.52140i	0.0445462	+	0.0925010i	0.922054	−	0.387061i	$-0.126510\pi$
$743$	1.21424	+	2.52140i	0.0445462	+	0.0925010i	−0.877508	+	0.479562i	$0.840795\pi$
$744$	13.7680	−	3.14245i	0.504759	−	0.115208i
$745$	41.3152	+	19.8963i	1.51367	+	0.728945i
$746$	−5.54264	+	11.5094i	−0.202930	+	0.421389i
$747$	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
$751$	14.3322	+	3.27124i	0.522991	+	0.119369i	0.475863	−	0.879520i	$-0.342136\pi$
$751$	14.3322	+	3.27124i	0.522991	+	0.119369i	0.0471282	+	0.998889i	$0.484993\pi$
$752$	−5.62263	−	4.48390i	−0.205036	−	0.163511i
$753$	−39.8019			−1.45046
$754$		0			0
$755$	44.1387			1.60637
$756$	−5.95634	−	4.75003i	−0.216630	−	0.172757i
$757$	22.3609	+	5.10374i	0.812722	+	0.185499i	0.608631	−	0.793453i	$-0.291719\pi$
$757$	22.3609	+	5.10374i	0.812722	+	0.185499i	0.204091	+	0.978952i	$0.434576\pi$
$758$	−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	−0.898164	−	0.439660i	$-0.855099\pi$
$761$	2.80870	−	12.3057i	0.101815	−	0.446081i	0.999979	−	0.00642120i	$-0.00204395\pi$
$762$	3.29469	−	6.84149i	0.119354	−	0.247841i
$763$	9.25766	+	4.45825i	0.335150	+	0.161400i
$764$	−32.6631	+	7.45515i	−1.18171	+	0.269718i
$765$	−5.59407	−	11.6162i	−0.202254	−	0.419985i
$766$			12.2880i			0.443985i
$767$	−12.3064	+	5.92644i	−0.444358	+	0.213991i
$768$	−2.22444	+	1.77393i	−0.0802677	+	0.0640113i
$769$	−2.75784	+	2.19931i	−0.0994503	+	0.0793090i	−0.671953	−	0.740594i	$-0.734544\pi$
$769$	−2.75784	+	2.19931i	−0.0994503	+	0.0793090i	0.572502	+	0.819903i	$0.305973\pi$
$770$	6.62010	−	3.18807i	0.238572	−	0.114890i
$771$		−	4.65956i		−	0.167810i
$772$	4.01172	+	8.33042i	0.144385	+	0.299818i
$773$	25.5505	−	5.83174i	0.918989	−	0.209753i	0.263238	−	0.964731i	$-0.415209\pi$
$773$	25.5505	−	5.83174i	0.918989	−	0.209753i	0.655751	+	0.754978i	$0.272352\pi$
$774$	−21.5615	−	10.3835i	−0.775012	−	0.373226i
$775$	0.170493	−	0.354032i	0.00612429	−	0.0127172i
$776$	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
$780$	31.5606	+	7.20350i	1.13005	+	0.257927i
$781$	−61.0468	−	48.6832i	−2.18442	−	1.74202i
$782$	0.609008			0.0217781
$783$		0			0
$784$	−13.2617			−0.473634
$785$	20.3131	+	16.1992i	0.725006	+	0.578173i
$786$	−0.0379705	−	0.00866651i	−0.00135436	−	0.000309124i
$787$	−4.00807	−	17.5605i	−0.142872	−	0.625964i	−0.994760	−	0.102239i	$-0.967399\pi$
$787$	−4.00807	−	17.5605i	−0.142872	−	0.625964i	0.851888	−	0.523724i	$-0.175458\pi$
$788$	−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
$791$	9.77404	−	20.2960i	0.347525	−	0.721642i
$792$	−36.6560	−	17.6526i	−1.30251	−	0.627258i
$793$	−16.6279	+	3.79520i	−0.590473	+	0.134772i
$794$	6.71079	+	13.9351i	0.238157	+	0.494538i
$795$		−	34.4345i		−	1.22127i
$796$	34.7596	−	16.7393i	1.23202	−	0.593310i
$797$	−27.3437	+	21.8058i	−0.968562	+	0.772402i	−0.973758	−	0.227584i	$-0.926917\pi$
$797$	−27.3437	+	21.8058i	−0.968562	+	0.772402i	0.00519652	+	0.999986i	$0.498346\pi$
$798$	−8.34110	+	6.65180i	−0.295272	+	0.235471i
$799$	−3.56775	+	1.71814i	−0.126218	+	0.0607834i
$800$			0.730464i			0.0258258i
$801$	−22.0035	−	45.6908i	−0.777456	−	1.61440i
$802$	6.15932	−	1.40582i	0.217493	−	0.0496414i
$803$	−15.3266	−	7.38090i	−0.540864	−	0.260466i
$804$	−4.79917	+	9.96558i	−0.169254	+	0.351459i
$805$	−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
$809$	37.3023	+	8.51401i	1.31148	+	0.299337i	0.820406	−	0.571781i	$-0.193747\pi$
$809$	37.3023	+	8.51401i	1.31148	+	0.299337i	0.491074	+	0.871118i	$0.336605\pi$
$810$	−3.24893	−	2.59093i	−0.114156	−	0.0910362i
$811$	−31.7116			−1.11354			−0.556772	−	0.830665i	$-0.687960\pi$
$811$	−31.7116			−1.11354			−0.556772	+	0.830665i	$0.687960\pi$
$812$		0			0
$813$	25.2130			0.884260
$814$	−11.8117	−	9.41952i	−0.414000	−	0.330154i
$815$	−5.38562	−	1.22923i	−0.188650	−	0.0430581i
$816$	−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
$820$	3.17314	−	6.58908i	0.110811	−	0.230101i
$821$	−19.3601	−	9.32331i	−0.675671	−	0.325386i	0.0643911	−	0.997925i	$-0.479489\pi$
$821$	−19.3601	−	9.32331i	−0.675671	−	0.325386i	−0.740062	+	0.672539i	$0.765204\pi$
$822$	8.26000	−	1.88529i	0.288101	−	0.0657571i
$823$	3.86280	+	8.02119i	0.134649	+	0.279601i	0.957381	−	0.288828i	$-0.0932656\pi$
$823$	3.86280	+	8.02119i	0.134649	+	0.279601i	−0.822732	+	0.568429i	$0.807551\pi$
$824$			14.8652i			0.517854i
$825$	−1.73994	+	0.837912i	−0.0605770	+	0.0291724i
$826$	2.26556	−	1.80672i	0.0788288	−	0.0628639i
$827$	−21.4488	+	17.1049i	−0.745848	+	0.594794i	−0.920916	−	0.389762i	$-0.872557\pi$
$827$	−21.4488	+	17.1049i	−0.745848	+	0.594794i	0.175067	+	0.984557i	$0.443986\pi$
$828$	5.76065	−	2.77418i	0.200197	−	0.0964096i
$829$		−	40.4211i		−	1.40388i	−0.712234	−	0.701942i	$-0.752317\pi$
$829$		−	40.4211i		−	1.40388i	0.712234	−	0.701942i	$-0.247683\pi$
$830$	−3.10870	−	6.45529i	−0.107905	−	0.224066i
$831$	−58.8594	+	13.4343i	−2.04181	+	0.466030i
$832$	6.76287	+	3.25683i	0.234460	+	0.112910i
$833$	−3.16834	+	6.57913i	−0.109777	+	0.227953i
$834$	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
$838$	−5.78560	−	1.32052i	−0.199860	−	0.0456168i
$839$	−6.33704	−	5.05362i	−0.218779	−	0.174470i	0.507968	−	0.861376i	$-0.330397\pi$
$839$	−6.33704	−	5.05362i	−0.218779	−	0.174470i	−0.726746	+	0.686906i	$0.758968\pi$
$840$	−14.7680			−0.509543
$841$		0			0
$842$	10.3717			0.357432
$843$	18.3400	+	14.6256i	0.631662	+	0.503734i
$844$	−12.3912	−	2.82821i	−0.426523	−	0.0973511i
$845$	−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
$849$	−16.8908	+	35.0740i	−0.579690	+	1.20374i
$850$	0.0908030	+	0.0437284i	0.00311452	+	0.00149987i
$851$	4.97743	−	1.13607i	0.170624	−	0.0389439i
$852$	31.6652	+	65.7534i	1.08483	+	2.25267i
$853$			12.7043i			0.434988i	0.976062	+	0.217494i	$0.0697883\pi$
$853$			12.7043i			0.434988i	−0.976062	+	0.217494i	$0.930212\pi$
$854$	3.25998	−	1.56992i	0.111554	−	0.0537217i
$855$	−43.5853	+	34.7581i	−1.49059	+	1.18870i
$856$	−8.14339	+	6.49413i	−0.278335	+	0.221965i
$857$	41.6417	−	20.0536i	1.42245	−	0.685018i	0.444877	−	0.895592i	$-0.353248\pi$
$857$	41.6417	−	20.0536i	1.42245	−	0.685018i	0.977578	+	0.210574i	$0.0675332\pi$
$858$		−	21.6343i		−	0.738581i
$859$	−2.62599	−	5.45292i	−0.0895975	−	0.186051i	0.851355	−	0.524590i	$-0.175782\pi$
$859$	−2.62599	−	5.45292i	−0.0895975	−	0.186051i	−0.940952	+	0.338539i	$0.890067\pi$
$860$	41.1440	−	9.39086i	1.40300	−	0.320226i
$861$	−6.02896	−	2.90339i	−0.205466	−	0.0989474i
$862$	−3.76742	+	7.82313i	−0.128319	+	0.266457i
$863$	−2.92205	+	12.8023i	−0.0994677	+	0.435796i	0.900532	+	0.434790i	$0.143177\pi$
$863$	−2.92205	+	12.8023i	−0.0994677	+	0.435796i	−0.999999	+	0.00100628i	$0.999680\pi$
$864$	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
$867$	39.6514	+	9.05018i	1.34663	+	0.307360i
$868$	4.85660	+	3.87301i	0.164844	+	0.131458i
$869$	−10.5987			−0.359536
$870$		0			0
$871$	−7.41398			−0.251213
$872$	−11.7929	−	9.40456i	−0.399360	−	0.318479i
$873$	−47.3315	−	10.8031i	−1.60193	−	0.365630i
$874$	−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	0.717356	+	0.696707i	$0.245352\pi$
$877$	−6.84826	+	30.0042i	−0.231249	+	1.01317i	−0.948605	+	0.316462i	$0.897505\pi$
$878$	−1.19864	+	2.48900i	−0.0404521	+	0.0839996i
$879$	79.4631	+	38.2674i	2.68022	+	1.29073i
$880$	26.9031	−	6.14046i	0.906904	−	0.206995i
$881$	12.8085	+	26.5971i	0.431530	+	0.896080i	0.997433	+	0.0716088i	$0.0228133\pi$
$881$	12.8085	+	26.5971i	0.431530	+	0.896080i	−0.565903	+	0.824472i	$0.691472\pi$
$882$		−	11.5258i		−	0.388093i
$883$	32.4541	−	15.6291i	1.09217	−	0.525960i	0.200980	−	0.979595i	$-0.435587\pi$
$883$	32.4541	−	15.6291i	1.09217	−	0.525960i	0.891187	+	0.453635i	$0.149873\pi$
$884$	5.87150	−	4.68236i	0.197480	−	0.157485i
$885$	20.1951	−	16.1050i	0.678851	−	0.541365i
$886$	−8.77555	+	4.22608i	−0.294820	+	0.141978i
$887$			14.2942i			0.479952i	0.970779	+	0.239976i	$0.0771396\pi$
$887$			14.2942i			0.479952i	−0.970779	+	0.239976i	$0.922860\pi$
$888$	13.1746	+	27.3574i	0.442112	+	0.918055i
$889$	7.00232	−	1.59823i	0.234850	−	0.0536030i
$890$	−12.1134	−	5.83350i	−0.406042	−	0.195539i
$891$	8.01490	−	16.6431i	0.268509	−	0.557565i
$892$	−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
$896$	−14.5029	−	3.31019i	−0.484508	−	0.110586i
$897$	5.71595	+	4.55832i	0.190850	+	0.152198i
$898$	−9.04279			−0.301762
$899$		0			0
$900$	1.05811			0.0352702
$901$	−6.24554	−	4.98066i	−0.208069	−	0.165930i
$902$	−4.76494	−	1.08757i	−0.158655	−	0.0362120i
$903$	−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
$907$	−8.74258	+	18.1541i	−0.290292	+	0.602798i	−0.994207	−	0.107487i	$-0.965720\pi$
$907$	−8.74258	+	18.1541i	−0.290292	+	0.602798i	0.703914	+	0.710285i	$0.251434\pi$
$908$	−24.6730	−	11.8819i	−0.818803	−	0.394315i
$909$	−4.03772	+	0.921582i	−0.133923	+	0.0305670i
$910$	−1.99731	−	4.14746i	−0.0662102	−	0.137487i
$911$		−	18.4045i		−	0.609769i	−0.952389	−	0.304885i	$-0.901382\pi$
$911$		−	18.4045i		−	0.609769i	0.952389	−	0.304885i	$-0.0986179\pi$
$912$	−36.0990	+	17.3844i	−1.19536	+	0.575654i
$913$	24.9010	−	19.8579i	0.824102	−	0.657199i
$914$	6.03491	−	4.81268i	0.199617	−	0.159189i
$915$	29.0593	−	13.9942i	0.960672	−	0.462635i
$916$			25.7875i			0.852044i
$917$	−0.0159836	−	0.0331903i	−0.000527825	−	0.00109604i
$918$	2.30911	−	0.527040i	0.0762120	−	0.0173949i
$919$	−4.79102	−	2.30724i	−0.158041	−	0.0761087i	0.353191	−	0.935551i	$-0.385097\pi$
$919$	−4.79102	−	2.30724i	−0.158041	−	0.0761087i	−0.511232	+	0.859443i	$0.670811\pi$
$920$	1.58154	−	3.28409i	0.0521417	−	0.108273i
$921$	−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
$925$	0.823707	+	0.188006i	0.0270833	+	0.00618159i
$926$	−10.6880	−	8.52341i	−0.351230	−	0.280097i
$927$	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	$0.509959\pi$
$930$	−6.50841	−	5.19029i	−0.213419	−	0.170196i
$931$	30.7825	+	7.02591i	1.00886	+	0.230265i
$932$	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
$936$	−11.0593	+	22.9648i	−0.361484	+	0.750629i
$937$	−3.03904	−	1.46353i	−0.0992812	−	0.0478113i	0.383584	−	0.923506i	$-0.374690\pi$
$937$	−3.03904	−	1.46353i	−0.0992812	−	0.0478113i	−0.482865	+	0.875695i	$0.660404\pi$
$938$	1.53343	−	0.349996i	0.0500684	−	0.0114278i
$939$	−27.9536	−	58.0463i	−0.912232	−	1.89427i
$940$			11.0220i			0.359498i
$941$	−17.8667	+	8.60413i	−0.582437	+	0.280487i	−0.701812	−	0.712363i	$-0.747625\pi$
$941$	−17.8667	+	8.60413i	−0.582437	+	0.280487i	0.119375	+	0.992849i	$0.461911\pi$
$942$	−12.6883	+	10.1186i	−0.413409	+	0.329682i
$943$	1.29131	−	1.02979i	0.0420509	−	0.0335345i
$944$	9.80499	−	4.72183i	0.319125	−	0.153683i
$945$			9.65689i			0.314139i
$946$	−12.2371	−	25.4105i	−0.397861	−	0.826167i
$947$	−39.4989	+	9.01536i	−1.28354	+	0.292960i	−0.809279	−	0.587424i	$-0.800142\pi$
$947$	−39.4989	+	9.01536i	−1.28354	+	0.292960i	−0.474262	+	0.880384i	$0.657285\pi$
$948$	8.92525	+	4.29817i	0.289879	+	0.139598i
$949$	−4.62410	+	9.60204i	−0.150105	+	0.311696i
$950$	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	0.982667	−	0.185381i	$-0.0593518\pi$
$953$	0.521127	+	2.28321i	0.0168810	+	0.0739604i	−0.965786	+	0.259341i	$0.916495\pi$
$954$	12.2925	+	2.80568i	0.397985	+	0.0908374i
$955$	33.2024	+	26.4780i	1.07440	+	0.856809i
$956$	16.3429			0.528567
$957$		0			0
$958$	12.4378			0.401848
$959$	6.26540	+	4.99649i	0.202320	+	0.161345i
$960$	−13.8390	−	3.15867i	−0.446653	−	0.101946i
$961$	−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
$965$	5.08512	−	10.5594i	0.163696	−	0.339918i
$966$	−1.39742	−	0.672961i	−0.0449612	−	0.0216522i
$967$	12.8970	−	2.94367i	0.414741	−	0.0946619i	−0.0100585	−	0.999949i	$-0.503202\pi$
$967$	12.8970	−	2.94367i	0.414741	−	0.0946619i	0.424799	+	0.905287i	$0.360345\pi$
$968$	−11.6813	−	24.2565i	−0.375451	−	0.779633i
$969$			22.0620i			0.708732i
$970$	−11.5964	+	5.58455i	−0.372339	+	0.179309i
$971$	16.1371	−	12.8689i	0.517865	−	0.412983i	−0.329371	−	0.944201i	$-0.606837\pi$
$971$	16.1371	−	12.8689i	0.517865	−	0.412983i	0.847236	+	0.531217i	$0.178265\pi$
$972$	−27.2225	+	21.7092i	−0.873162	+	0.696323i
$973$	14.5562	−	7.00990i	0.466650	−	0.224727i
$974$		−	0.657928i		−	0.0210814i
$975$	0.524948	+	1.09007i	0.0168118	+	0.0349100i
$976$	13.2481	−	3.02379i	0.424061	−	0.0967891i
$977$	2.43493	+	1.17260i	0.0779004	+	0.0375149i	0.472428	−	0.881369i	$-0.343378\pi$
$977$	2.43493	+	1.17260i	0.0779004	+	0.0375149i	−0.394528	+	0.918884i	$0.629092\pi$
$978$	1.49715	−	3.10886i	0.0478735	−	0.0994104i
$979$	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
$983$	−14.2199	−	3.24559i	−0.453543	−	0.103518i	−0.0103539	−	0.999946i	$-0.503296\pi$
$983$	−14.2199	−	3.24559i	−0.453543	−	0.103518i	−0.443189	+	0.896428i	$0.646153\pi$
$984$	7.68004	+	6.12463i	0.244831	+	0.195246i
$985$	21.9778			0.700272
$986$		0			0
$987$	10.0850			0.321011
$988$	−25.3876	−	20.2459i	−0.807686	−	0.644108i
$989$	9.29201	+	2.12084i	0.295469	+	0.0674388i
$990$	5.33667	+	23.3815i	0.169611	+	0.743112i
$991$	−13.9345	+	17.4733i	−0.442644	+	0.555058i	−0.952238	−	0.305357i	$-0.901224\pi$
$991$	−13.9345	+	17.4733i	−0.442644	+	0.555058i	0.509594	+	0.860415i	$0.329796\pi$
$992$	−8.72695	−	10.9433i	−0.277081	−	0.347449i
$993$	6.13973	−	26.8999i	0.194838	−	0.853642i
$994$	4.50279	−	9.35014i	0.142820	−	0.296568i
$995$	−44.0601	−	21.2182i	−1.39680	−	0.672663i
$996$	−29.0225	+	6.62419i	−0.919612	+	0.209896i
$997$	−23.6110	−	49.0288i	−0.747768	−	1.55276i	−0.831029	−	0.556229i	$-0.812248\pi$
$997$	−23.6110	−	49.0288i	−0.747768	−	1.55276i	0.0832607	−	0.996528i	$-0.473467\pi$
$998$		−	5.35958i		−	0.169655i
$999$	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.e.l.267.6		72
29.2	odd	28		841.2.d.o.778.4		36
29.3	odd	28		841.2.d.o.605.3		36
29.4	even	14	inner	841.2.e.l.270.6		72
29.5	even	14	inner	841.2.e.l.63.6		72
29.6	even	14	inner	841.2.e.l.651.7		72
29.7	even	7	inner	841.2.e.l.236.7		72
29.8	odd	28		841.2.d.n.645.4		36
29.9	even	14	inner	841.2.e.l.196.7		72
29.10	odd	28		841.2.d.n.571.4		36
29.11	odd	28		841.2.a.g.1.4	✓	6
29.12	odd	4		841.2.d.n.574.3		36
29.13	even	14		841.2.b.d.840.7		12
29.14	odd	28		841.2.d.o.190.3		36
29.15	odd	28		841.2.d.n.190.4		36
29.16	even	7		841.2.b.d.840.6		12
29.17	odd	4		841.2.d.o.574.4		36
29.18	odd	28		841.2.a.h.1.3	yes	6
29.19	odd	28		841.2.d.o.571.3		36
29.20	even	7	inner	841.2.e.l.196.6		72
29.21	odd	28		841.2.d.o.645.3		36
29.22	even	14	inner	841.2.e.l.236.6		72
29.23	even	7	inner	841.2.e.l.651.6		72
29.24	even	7	inner	841.2.e.l.63.7		72
29.25	even	7	inner	841.2.e.l.270.7		72
29.26	odd	28		841.2.d.n.605.4		36
29.27	odd	28		841.2.d.n.778.3		36
29.28	even	2	inner	841.2.e.l.267.7		72
87.11	even	28		7569.2.a.bc.1.3		6
87.47	even	28		7569.2.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.4	✓	6	29.11	odd	28
841.2.a.h.1.3	yes	6	29.18	odd	28
841.2.b.d.840.6		12	29.16	even	7
841.2.b.d.840.7		12	29.13	even	14
841.2.d.n.190.4		36	29.15	odd	28
841.2.d.n.571.4		36	29.10	odd	28
841.2.d.n.574.3		36	29.12	odd	4
841.2.d.n.605.4		36	29.26	odd	28
841.2.d.n.645.4		36	29.8	odd	28
841.2.d.n.778.3		36	29.27	odd	28
841.2.d.o.190.3		36	29.14	odd	28
841.2.d.o.571.3		36	29.19	odd	28
841.2.d.o.574.4		36	29.17	odd	4
841.2.d.o.605.3		36	29.3	odd	28
841.2.d.o.645.3		36	29.21	odd	28
841.2.d.o.778.4		36	29.2	odd	28
841.2.e.l.63.6		72	29.5	even	14	inner
841.2.e.l.63.7		72	29.24	even	7	inner
841.2.e.l.196.6		72	29.20	even	7	inner
841.2.e.l.196.7		72	29.9	even	14	inner
841.2.e.l.236.6		72	29.22	even	14	inner
841.2.e.l.236.7		72	29.7	even	7	inner
841.2.e.l.267.6		72	1.1	even	1	trivial
841.2.e.l.267.7		72	29.28	even	2	inner
841.2.e.l.270.6		72	29.4	even	14	inner
841.2.e.l.270.7		72	29.25	even	7	inner
841.2.e.l.651.6		72	29.23	even	7	inner
841.2.e.l.651.7		72	29.6	even	14	inner
7569.2.a.y.1.4		6	87.47	even	28
7569.2.a.bc.1.3		6	87.11	even	28

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.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.399716 - 0.318763i) q^{2} +(2.62505 + 0.599151i) 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} +(-0.829321 + 1.72210i) q^{8} +(3.82900 + 1.84395i) q^{9} +(1.09846 - 0.250717i) q^{10} +(2.17312 + 4.51253i) q^{11} -4.68133i q^{12} +(2.82708 - 1.36145i) q^{13} +(-0.520454 + 0.415048i) q^{14} +(-4.63931 + 3.69973i) q^{15} +(-2.25245 + 1.08472i) q^{16} +1.37659i q^{17} +(-0.942730 - 1.95760i) q^{18} +(5.80294 - 1.32448i) q^{19} +(3.45214 + 1.66246i) q^{20} +(1.52114 - 3.15868i) 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} +(-1.56401 - 0.356974i) q^{26} +(2.63114 + 2.09827i) q^{27} -2.26379 q^{28} +3.03374 q^{30} +(-2.14534 - 1.71085i) q^{31} +(4.97304 + 1.13506i) 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} +(2.55991 - 5.31570i) q^{37} +(-2.74172 - 1.32034i) q^{38} +(8.23694 - 1.88003i) q^{39} +(-1.82767 - 3.79519i) q^{40} -1.90869i q^{41} +(-1.61489 + 0.777692i) q^{42} +(8.61130 - 6.86728i) q^{43} +(6.80813 - 5.42930i) q^{44} +(-8.43841 + 4.06373i) q^{45} -0.442405i q^{46} +(1.24812 + 2.59174i) q^{47} +(-6.56270 + 1.49789i) q^{48} +(4.77931 + 2.30160i) q^{49} +(0.0317659 - 0.0659625i) 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} +(-10.7611 - 2.45616i) q^{55} +(1.94578 + 1.55171i) q^{56} +16.0266 q^{57} -4.35304 q^{59} +(8.06599 + 6.43241i) q^{60} +(-5.29918 - 1.20950i) 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} +(2.99149 - 6.21189i) q^{66} +(-2.12879 - 1.02517i) q^{67} +(2.33335 - 0.532572i) q^{68} +(1.01093 + 2.09921i) q^{69} -1.46705i q^{70} +(-14.0459 + 6.76414i) q^{71} +(-6.35094 + 5.06471i) q^{72} +(-2.65545 + 2.11765i) q^{73} +(-2.71768 + 1.30877i) q^{74} +0.385580i q^{75} +(-4.49007 - 9.32373i) q^{76} +(6.35791 - 1.45115i) q^{77} +(-3.89172 - 1.87415i) q^{78} +(-0.918152 + 1.90656i) 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} +(-5.94255 - 1.35635i) q^{84} +(-2.37187 - 1.89151i) q^{85} -5.63110 q^{86} -9.57325 q^{88} +(-9.32945 - 7.43999i) q^{89} +(4.66833 + 1.06552i) 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} +(-5.69146 + 11.8184i) q^{95} +(12.3744 + 5.95920i) q^{96} +(-11.1372 + 2.54198i) q^{97} +(-1.17670 - 2.44345i) q^{98} +21.2856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{4} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 12 q^{9} - 12 q^{13} - 8 q^{16} + 10 q^{20} - 8 q^{22} + 10 q^{23} + 20 q^{24} - 12 q^{25} + 60 q^{28} + 312 q^{30} + 54 q^{33} - 8 q^{35} + 42 q^{36} + 82 q^{38}+ \cdots - 74 q^{96}+O(q^{100}) \) 72 * q + 16 * q^4 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 12 * q^9 - 12 * q^13 - 8 * q^16 + 10 * q^20 - 8 * q^22 + 10 * q^23 + 20 * q^24 - 12 * q^25 + 60 * q^28 + 312 * q^30 + 54 * q^33 - 8 * q^35 + 42 * q^36 + 82 * q^38 - 42 * q^42 - 32 * q^45 + 24 * q^49 - 46 * q^51 + 26 * q^53 - 38 * q^54 + 192 * q^57 - 204 * q^59 - 18 * q^63 + 2 * q^64 - 64 * q^65 - 18 * q^67 + 72 * q^74 + 10 * q^80 + 44 * q^81 - 38 * q^82 + 48 * q^83 - 204 * q^86 + 252 * q^88 + 32 * q^91 - 46 * q^92 - 24 * q^93 + 74 * q^94 - 74 * q^96

Introduction

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