LMFDB - Embedded newform 833.2.t.d.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(48,833)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("833.48");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.t (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			146.2
Character	$\chi$	$=$	833.146
Dual form			833.2.t.d.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.684321 + 1.65210i) q^{2} +(0.302826 - 0.453212i) q^{3} +(-0.846919 - 0.846919i) q^{4} +(0.523006 + 2.62933i) q^{5} +(0.541520 + 0.810442i) q^{6} +(-1.32544 + 0.549014i) q^{8} +(1.03435 + 2.49715i) q^{9} +O(q^{10})$	\(q+(-0.684321 + 1.65210i) q^{2} +(0.302826 - 0.453212i) q^{3} +(-0.846919 - 0.846919i) q^{4} +(0.523006 + 2.62933i) q^{5} +(0.541520 + 0.810442i) q^{6} +(-1.32544 + 0.549014i) q^{8} +(1.03435 + 2.49715i) q^{9} +(-4.70181 - 0.935249i) q^{10} +(-2.78572 - 4.16913i) q^{11} +(-0.640303 + 0.127364i) q^{12} +(-4.70535 - 4.70535i) q^{13} +(1.35002 + 0.559198i) q^{15} -4.96091i q^{16} +(-2.09362 + 3.55201i) q^{17} -4.83337 q^{18} +(-4.91367 - 2.03531i) q^{19} +(1.78388 - 2.66977i) q^{20} +(8.79414 - 1.74926i) q^{22} +(-3.40111 + 2.27255i) q^{23} +(-0.152558 + 0.766960i) q^{24} +(-2.02043 + 0.836891i) q^{25} +(10.9937 - 4.55373i) q^{26} +(3.04877 + 0.606437i) q^{27} +(1.90098 + 9.55688i) q^{29} +(-1.84770 + 1.84770i) q^{30} +(-0.638820 - 0.426846i) q^{31} +(5.54503 + 2.29683i) q^{32} -2.73309 q^{33} +(-4.43555 - 5.88958i) q^{34} +(1.23887 - 2.99090i) q^{36} +(4.93349 + 3.29645i) q^{37} +(6.72506 - 6.72506i) q^{38} +(-3.55742 + 0.707616i) q^{39} +(-2.13675 - 3.19787i) q^{40} +(0.0510695 - 0.256744i) q^{41} +(0.397620 + 0.959941i) q^{43} +(-1.17163 + 5.89020i) q^{44} +(-6.02485 + 4.02568i) q^{45} +(-1.42702 - 7.17412i) q^{46} +(-6.07130 - 6.07130i) q^{47} +(-2.24834 - 1.50229i) q^{48} -3.91066i q^{50} +(0.975807 + 2.02450i) q^{51} +7.97010i q^{52} +(-0.700266 + 1.69059i) q^{53} +(-3.08823 + 4.62186i) q^{54} +(9.50506 - 9.50506i) q^{55} +(-2.41041 + 1.61059i) q^{57} +(-17.0898 - 3.39937i) q^{58} +(-2.28490 - 5.51623i) q^{59} +(-0.669765 - 1.61696i) q^{60} +(1.48687 + 0.295757i) q^{61} +(1.14235 - 0.763294i) q^{62} +(-0.573383 + 0.573383i) q^{64} +(9.91098 - 14.8328i) q^{65} +(1.87031 - 4.51533i) q^{66} +12.3675i q^{67} +(4.78139 - 1.23513i) q^{68} +2.22961i q^{69} +(-3.95416 - 2.64209i) q^{71} +(-2.74194 - 2.74194i) q^{72} +(-0.221196 - 1.11203i) q^{73} +(-8.82216 + 5.89478i) q^{74} +(-0.232552 + 1.16912i) q^{75} +(2.43774 + 5.88522i) q^{76} +(1.26537 - 6.36145i) q^{78} +(-6.72273 - 10.0613i) q^{79} +(13.0438 - 2.59458i) q^{80} +(-4.53561 + 4.53561i) q^{81} +(0.389218 + 0.260067i) q^{82} +(-5.11069 + 12.3383i) q^{83} +(-10.4344 - 3.64710i) q^{85} -1.85802 q^{86} +(4.90696 + 2.03253i) q^{87} +(5.98122 + 3.99652i) q^{88} +(-1.38538 + 1.38538i) q^{89} +(-2.52788 - 12.7085i) q^{90} +(4.80513 + 0.955800i) q^{92} +(-0.386903 + 0.160261i) q^{93} +(14.1851 - 5.87566i) q^{94} +(2.78161 - 13.9841i) q^{95} +(2.72013 - 1.81753i) q^{96} +(-9.84825 + 1.95894i) q^{97} +(7.52952 - 11.2687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9}+O(q^{10}) $ 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9	$ 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{13} - 40 q^{18} + 24 q^{19} + 24 q^{22} + 8 q^{23} - 24 q^{24} + 8 q^{25} + 8 q^{27} + 80 q^{31} - 40 q^{32} - 80 q^{33} + 120 q^{36} + 48 q^{37} - 56 q^{38} - 16 q^{39} - 32 q^{40} + 24 q^{41} + 24 q^{43} + 32 q^{44} - 48 q^{45} - 40 q^{47} - 40 q^{51} - 24 q^{53} + 200 q^{54} - 48 q^{57} + 32 q^{58} + 8 q^{59} - 80 q^{60} + 128 q^{62} - 24 q^{65} - 8 q^{66} - 40 q^{68} - 48 q^{73} - 32 q^{74} + 128 q^{75} + 72 q^{76} - 48 q^{78} - 32 q^{79} + 256 q^{80} + 16 q^{81} - 152 q^{82} - 32 q^{85} - 80 q^{86} - 64 q^{87} + 56 q^{88} - 64 q^{89} - 376 q^{90} - 216 q^{92} - 32 q^{93} - 128 q^{94} + 32 q^{95} + 32 q^{96} - 8 q^{97} + 40 q^{99}+O(q^{100}) $ 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^13 - 40 * q^18 + 24 * q^19 + 24 * q^22 + 8 * q^23 - 24 * q^24 + 8 * q^25 + 8 * q^27 + 80 * q^31 - 40 * q^32 - 80 * q^33 + 120 * q^36 + 48 * q^37 - 56 * q^38 - 16 * q^39 - 32 * q^40 + 24 * q^41 + 24 * q^43 + 32 * q^44 - 48 * q^45 - 40 * q^47 - 40 * q^51 - 24 * q^53 + 200 * q^54 - 48 * q^57 + 32 * q^58 + 8 * q^59 - 80 * q^60 + 128 * q^62 - 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 - 32 * q^74 + 128 * q^75 + 72 * q^76 - 48 * q^78 - 32 * q^79 + 256 * q^80 + 16 * q^81 - 152 * q^82 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 56 * q^88 - 64 * q^89 - 376 * q^90 - 216 * q^92 - 32 * q^93 - 128 * q^94 + 32 * q^95 + 32 * q^96 - 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.684321	+	1.65210i	−0.483888	+	1.16821i	0.473859	+	0.880601i	$0.342860\pi$
$2$	−0.684321	+	1.65210i	−0.483888	+	1.16821i	−0.957748	+	0.287609i	$0.907140\pi$
$3$	0.302826	−	0.453212i	0.174837	−	0.261662i	−0.733694	−	0.679481i	$-0.762205\pi$
$3$	0.302826	−	0.453212i	0.174837	−	0.261662i	0.908530	+	0.417819i	$0.137205\pi$
$4$	−0.846919	−	0.846919i	−0.423460	−	0.423460i
$5$	0.523006	+	2.62933i	0.233895	+	1.17587i	0.901977	+	0.431784i	$0.142116\pi$
$5$	0.523006	+	2.62933i	0.233895	+	1.17587i	−0.668082	+	0.744088i	$0.732884\pi$
$6$	0.541520	+	0.810442i	0.221075	+	0.330861i
$7$		0			0
$7$		0			0
$8$	−1.32544	+	0.549014i	−0.468613	+	0.194106i
$9$	1.03435	+	2.49715i	0.344784	+	0.832383i
$10$	−4.70181	−	0.935249i	−1.48684	−	0.295752i
$11$	−2.78572	−	4.16913i	−0.839927	−	1.25704i	−0.964302	−	0.264805i	$-0.914693\pi$
$11$	−2.78572	−	4.16913i	−0.839927	−	1.25704i	0.124375	−	0.992235i	$-0.460307\pi$
$12$	−0.640303	+	0.127364i	−0.184840	+	0.0367669i
$13$	−4.70535	−	4.70535i	−1.30503	−	1.30503i	−0.924957	−	0.380072i	$-0.875899\pi$
$13$	−4.70535	−	4.70535i	−1.30503	−	1.30503i	−0.380072	−	0.924957i	$-0.624101\pi$
$14$		0			0
$15$	1.35002	+	0.559198i	0.348574	+	0.144384i
$16$		−	4.96091i		−	1.24023i
$17$	−2.09362	+	3.55201i	−0.507778	+	0.861488i
$17$	−2.09362	+	3.55201i	−0.507778	+	0.861488i
$18$	−4.83337			−1.13924
$19$	−4.91367	−	2.03531i	−1.12727	−	0.466932i	−0.260420	−	0.965495i	$-0.583861\pi$
$19$	−4.91367	−	2.03531i	−1.12727	−	0.466932i	−0.866853	+	0.498564i	$0.833861\pi$
$20$	1.78388	−	2.66977i	0.398889	−	0.596979i
$21$		0			0
$22$	8.79414	−	1.74926i	1.87492	−	0.372944i
$23$	−3.40111	+	2.27255i	−0.709180	+	0.473859i	−0.857107	−	0.515139i	$-0.827740\pi$
$23$	−3.40111	+	2.27255i	−0.709180	+	0.473859i	0.147926	+	0.988998i	$0.452740\pi$
$24$	−0.152558	+	0.766960i	−0.0311407	+	0.156555i
$25$	−2.02043	+	0.836891i	−0.404087	+	0.167378i
$26$	10.9937	−	4.55373i	2.15604	−	0.893059i
$27$	3.04877	+	0.606437i	0.586735	+	0.116709i
$28$		0			0
$29$	1.90098	+	9.55688i	0.353004	+	1.77467i	0.594327	+	0.804224i	$0.297419\pi$
$29$	1.90098	+	9.55688i	0.353004	+	1.77467i	−0.241323	+	0.970445i	$0.577581\pi$
$30$	−1.84770	+	1.84770i	−0.337342	+	0.337342i
$31$	−0.638820	−	0.426846i	−0.114735	−	0.0766638i	0.496879	−	0.867820i	$-0.334479\pi$
$31$	−0.638820	−	0.426846i	−0.114735	−	0.0766638i	−0.611614	+	0.791156i	$0.709479\pi$
$32$	5.54503	+	2.29683i	0.980231	+	0.406025i
$33$	−2.73309			−0.475770
$34$	−4.43555	−	5.88958i	−0.760691	−	1.01006i
$35$		0			0
$36$	1.23887	−	2.99090i	0.206478	−	0.498483i
$37$	4.93349	+	3.29645i	0.811061	+	0.541934i	0.890541	−	0.454903i	$-0.150326\pi$
$37$	4.93349	+	3.29645i	0.811061	+	0.541934i	−0.0794800	+	0.996836i	$0.525326\pi$
$38$	6.72506	−	6.72506i	1.09095	−	1.09095i
$39$	−3.55742	+	0.707616i	−0.569644	+	0.113309i
$40$	−2.13675	−	3.19787i	−0.337850	−	0.505628i
$41$	0.0510695	−	0.256744i	0.00797571	−	0.0400966i	−0.976593	−	0.215098i	$-0.930993\pi$
$41$	0.0510695	−	0.256744i	0.00797571	−	0.0400966i	0.984568	+	0.175001i	$0.0559930\pi$
$42$		0			0
$43$	0.397620	+	0.959941i	0.0606365	+	0.146390i	0.951294	−	0.308286i	$-0.0997553\pi$
$43$	0.397620	+	0.959941i	0.0606365	+	0.146390i	−0.890657	+	0.454675i	$0.849755\pi$
$44$	−1.17163	+	5.89020i	−0.176630	+	0.887981i
$45$	−6.02485	+	4.02568i	−0.898132	+	0.600113i
$46$	−1.42702	−	7.17412i	−0.210403	−	1.05777i
$47$	−6.07130	−	6.07130i	−0.885590	−	0.885590i	0.108506	−	0.994096i	$-0.465393\pi$
$47$	−6.07130	−	6.07130i	−0.885590	−	0.885590i	−0.994096	+	0.108506i	$0.965393\pi$
$48$	−2.24834	−	1.50229i	−0.324520	−	0.216837i
$49$		0			0
$50$		−	3.91066i		−	0.553050i
$51$	0.975807	+	2.02450i	0.136640	+	0.283486i
$52$			7.97010i			1.10525i
$53$	−0.700266	+	1.69059i	−0.0961890	+	0.232221i	−0.964649	−	0.263539i	$-0.915110\pi$
$53$	−0.700266	+	1.69059i	−0.0961890	+	0.232221i	0.868460	+	0.495760i	$0.165110\pi$
$54$	−3.08823	+	4.62186i	−0.420255	+	0.628956i
$55$	9.50506	−	9.50506i	1.28166	−	1.28166i
$56$		0			0
$57$	−2.41041	+	1.61059i	−0.319267	+	0.213327i
$58$	−17.0898	−	3.39937i	−2.24400	−	0.446359i
$59$	−2.28490	−	5.51623i	−0.297468	−	0.718151i	−0.999979	−	0.00647849i	$-0.997938\pi$
$59$	−2.28490	−	5.51623i	−0.297468	−	0.718151i	0.702511	−	0.711673i	$-0.252062\pi$
$60$	−0.669765	−	1.61696i	−0.0864663	−	0.208748i
$61$	1.48687	+	0.295757i	0.190374	+	0.0378677i	0.289356	−	0.957221i	$-0.406559\pi$
$61$	1.48687	+	0.295757i	0.190374	+	0.0378677i	−0.0989824	+	0.995089i	$0.531559\pi$
$62$	1.14235	−	0.763294i	0.145079	−	0.0969384i
$63$		0			0
$64$	−0.573383	+	0.573383i	−0.0716728	+	0.0716728i
$65$	9.91098	−	14.8328i	1.22931	−	1.83979i
$66$	1.87031	−	4.51533i	0.230219	−	0.555799i
$67$			12.3675i			1.51093i	0.655186	+	0.755467i	$0.272590\pi$
$67$			12.3675i			1.51093i	−0.655186	+	0.755467i	$0.727410\pi$
$68$	4.78139	−	1.23513i	0.579829	−	0.149782i
$69$			2.22961i			0.268414i
$70$		0			0
$71$	−3.95416	−	2.64209i	−0.469273	−	0.313558i	0.298354	−	0.954455i	$-0.403562\pi$
$71$	−3.95416	−	2.64209i	−0.469273	−	0.313558i	−0.767627	+	0.640897i	$0.778562\pi$
$72$	−2.74194	−	2.74194i	−0.323141	−	0.323141i
$73$	−0.221196	−	1.11203i	−0.0258890	−	0.130153i	0.965679	−	0.259737i	$-0.0836358\pi$
$73$	−0.221196	−	1.11203i	−0.0258890	−	0.130153i	−0.991568	+	0.129584i	$0.958636\pi$
$74$	−8.82216	+	5.89478i	−1.02556	+	0.685254i
$75$	−0.232552	+	1.16912i	−0.0268528	+	0.134998i
$76$	2.43774	+	5.88522i	0.279628	+	0.675081i
$77$		0			0
$78$	1.26537	−	6.36145i	0.143275	−	0.720292i
$79$	−6.72273	−	10.0613i	−0.756367	−	1.13198i	−0.987277	−	0.159008i	$-0.949171\pi$
$79$	−6.72273	−	10.0613i	−0.756367	−	1.13198i	0.230911	−	0.972975i	$-0.425829\pi$
$80$	13.0438	−	2.59458i	1.45835	−	0.290083i
$81$	−4.53561	+	4.53561i	−0.503957	+	0.503957i
$82$	0.389218	+	0.260067i	0.0429819	+	0.0287196i
$83$	−5.11069	+	12.3383i	−0.560971	+	1.35430i	0.348019	+	0.937488i	$0.386854\pi$
$83$	−5.11069	+	12.3383i	−0.560971	+	1.35430i	−0.908990	+	0.416817i	$0.863146\pi$
$84$		0			0
$85$	−10.4344	−	3.64710i	−1.13177	−	0.395583i
$86$	−1.85802			−0.200355
$87$	4.90696	+	2.03253i	0.526081	+	0.217910i
$88$	5.98122	+	3.99652i	0.637600	+	0.426031i
$89$	−1.38538	+	1.38538i	−0.146849	+	0.146849i	−0.776709	−	0.629860i	$-0.783112\pi$
$89$	−1.38538	+	1.38538i	−0.146849	+	0.146849i	0.629860	+	0.776709i	$0.283112\pi$
$90$	−2.52788	−	12.7085i	−0.266462	−	1.33959i
$91$		0			0
$92$	4.80513	+	0.955800i	0.500969	+	0.0996490i
$93$	−0.386903	+	0.160261i	−0.0401200	+	0.0166182i
$94$	14.1851	−	5.87566i	1.46308	−	0.606028i
$95$	2.78161	−	13.9841i	0.285388	−	1.43474i
$96$	2.72013	−	1.81753i	0.277622	−	0.185501i
$97$	−9.84825	+	1.95894i	−0.999938	+	0.198900i	−0.667808	−	0.744334i	$-0.732767\pi$
$97$	−9.84825	+	1.95894i	−0.999938	+	0.198900i	−0.332130	+	0.943234i	$0.607767\pi$
$98$		0			0
$99$	7.52952	−	11.2687i	0.756745	−	1.13255i
$100$	2.41992	+	1.00236i	0.241992	+	0.100236i
$101$	5.20889			0.518304			0.259152	−	0.965837i	$-0.416557\pi$
$101$	5.20889			0.518304			0.259152	+	0.965837i	$0.416557\pi$
$102$	−4.01243	+	0.226723i	−0.397290	+	0.0224489i
$103$			6.41077i			0.631672i	0.948814	+	0.315836i	$0.102285\pi$
$103$			6.41077i			0.631672i	−0.948814	+	0.315836i	$0.897715\pi$
$104$	8.81995	+	3.65334i	0.864867	+	0.358240i
$105$		0			0
$106$	−2.31382	−	2.31382i	−0.224738	−	0.224738i
$107$	5.31426	−	1.05707i	0.513749	−	0.102191i	0.0685944	−	0.997645i	$-0.478149\pi$
$107$	5.31426	−	1.05707i	0.513749	−	0.102191i	0.445155	+	0.895454i	$0.353149\pi$
$108$	−2.06846	−	3.09566i	−0.199037	−	0.297880i
$109$	2.29235	+	0.455976i	0.219567	+	0.0436746i	0.303648	−	0.952784i	$-0.401795\pi$
$109$	2.29235	+	0.455976i	0.219567	+	0.0436746i	−0.0840808	+	0.996459i	$0.526795\pi$
$110$	9.19878	+	22.2078i	0.877069	+	2.11743i
$111$	2.98798	−	1.23766i	0.283607	−	0.117474i
$112$		0			0
$113$	10.3160	+	15.4390i	0.970451	+	1.45238i	0.890180	+	0.455610i	$0.150579\pi$
$113$	10.3160	+	15.4390i	0.970451	+	1.45238i	0.0802713	+	0.996773i	$0.474421\pi$
$114$	−1.01135	−	5.08440i	−0.0947216	−	0.476198i
$115$	−7.75408	−	7.75408i	−0.723071	−	0.723071i
$116$	6.48393	−	9.70388i	0.602018	−	0.900983i
$117$	6.88297	−	16.6170i	0.636331	−	1.53624i
$118$	10.6769			0.982893
$119$		0			0
$120$	−2.09638			−0.191372
$121$	−5.41187	+	13.0654i	−0.491988	+	1.18776i
$122$	−1.50611	+	2.25406i	−0.136357	+	0.204073i
$123$	−0.100894	−	0.100894i	−0.00909731	−	0.00909731i
$124$	0.179525	+	0.902533i	0.0161218	+	0.0810498i
$125$	4.18982	+	6.27050i	0.374748	+	0.560851i
$126$		0			0
$127$	1.38122	−	0.572121i	0.122564	−	0.0507675i	−0.320559	−	0.947229i	$-0.603871\pi$
$127$	1.38122	−	0.572121i	0.122564	−	0.0507675i	0.443122	+	0.896461i	$0.353871\pi$
$128$	4.03874	+	9.75039i	0.356978	+	0.861821i
$129$	0.555466	+	0.110489i	0.0489061	+	0.00972803i
$130$	17.7230	+	26.5243i	1.55441	+	2.32634i
$131$	3.52084	−	0.700339i	0.307617	−	0.0611889i	−0.0388678	−	0.999244i	$-0.512375\pi$
$131$	3.52084	−	0.700339i	0.307617	−	0.0611889i	0.346485	+	0.938055i	$0.387375\pi$
$132$	2.31471	+	2.31471i	0.201469	+	0.201469i
$133$		0			0
$134$	−20.4324	−	8.46337i	−1.76509	−	0.731124i
$135$			8.33338i			0.717223i
$136$	0.824863	−	5.85739i	0.0707315	−	0.502267i
$137$	4.88115			0.417025			0.208512	−	0.978020i	$-0.433138\pi$
$137$	4.88115			0.417025			0.208512	+	0.978020i	$0.433138\pi$
$138$	−3.68354	−	1.52577i	−0.313563	−	0.129882i
$139$	−2.96540	+	4.43803i	−0.251522	+	0.376429i	−0.935648	−	0.352935i	$-0.885184\pi$
$139$	−2.96540	+	4.43803i	−0.251522	+	0.376429i	0.684126	+	0.729364i	$0.260184\pi$
$140$		0			0
$141$	−4.59013	+	0.913034i	−0.386559	+	0.0768914i
$142$	7.07091	−	4.72463i	0.593377	−	0.396482i
$143$	−6.50941	+	32.7250i	−0.544344	+	2.73660i
$144$	12.3881	−	5.13133i	1.03234	−	0.427611i
$145$	−24.1340	+	9.99661i	−2.00422	+	0.830173i
$146$	1.98854	+	0.395546i	0.164573	+	0.0327356i
$147$		0			0
$148$	−1.38644	−	6.97010i	−0.113965	−	0.572939i
$149$	5.31090	−	5.31090i	0.435086	−	0.435086i	−0.455268	−	0.890354i	$-0.650457\pi$
$149$	5.31090	−	5.31090i	0.435086	−	0.435086i	0.890354	+	0.455268i	$0.150457\pi$
$150$	−1.77236	−	1.18425i	−0.144712	−	0.0966936i
$151$	−5.31362	−	2.20097i	−0.432416	−	0.179113i	0.155849	−	0.987781i	$-0.450189\pi$
$151$	−5.31362	−	2.20097i	−0.432416	−	0.179113i	−0.588265	+	0.808668i	$0.700189\pi$
$152$	7.63017			0.618889
$153$	−11.0354	−	1.55406i	−0.892162	−	0.125638i
$154$		0			0
$155$	0.788211	−	1.90291i	0.0633107	−	0.152845i
$156$	3.61214	+	2.41356i	0.289203	+	0.193239i
$157$	−4.89744	+	4.89744i	−0.390858	+	0.390858i	−0.874993	−	0.484135i	$-0.839134\pi$
$157$	−4.89744	+	4.89744i	−0.390858	+	0.390858i	0.484135	+	0.874993i	$0.339134\pi$
$158$	21.2227	−	4.22146i	1.68839	−	0.335842i
$159$	0.554137	+	0.829325i	0.0439459	+	0.0657697i
$160$	−3.13903	+	15.7809i	−0.248162	+	1.24759i
$161$		0			0
$162$	−4.38946	−	10.5971i	−0.344869	−	0.832587i
$163$	2.46110	−	12.3728i	0.192769	−	0.969113i	−0.756344	−	0.654175i	$-0.773016\pi$
$163$	2.46110	−	12.3728i	0.192769	−	0.969113i	0.949112	−	0.314938i	$-0.101984\pi$
$164$	−0.260693	+	0.174189i	−0.0203567	+	0.0136019i
$165$	−1.42942	−	7.18619i	−0.111280	−	0.559444i
$166$	−16.8867	−	16.8867i	−1.31066	−	1.31066i
$167$	−11.1181	−	7.42888i	−0.860345	−	0.574864i	0.0452651	−	0.998975i	$-0.485587\pi$
$167$	−11.1181	−	7.42888i	−0.860345	−	0.574864i	−0.905610	+	0.424111i	$0.860587\pi$
$168$		0			0
$169$			31.2806i			2.40620i
$170$	13.1658	−	14.7428i	1.00977	−	1.13072i
$171$		−	14.3754i		−	1.09931i
$172$	0.476240	−	1.14974i	0.0363129	−	0.0876672i
$173$	1.97005	−	2.94838i	0.149780	−	0.224161i	−0.748991	−	0.662580i	$-0.769461\pi$
$173$	1.97005	−	2.94838i	0.149780	−	0.224161i	0.898771	+	0.438419i	$0.144461\pi$
$174$	−6.71588	+	6.71588i	−0.509129	+	0.509129i
$175$		0			0
$176$	−20.6827	+	13.8197i	−1.55901	+	1.04170i
$177$	−3.19195	−	0.634917i	−0.239921	−	0.0477233i
$178$	−1.34073	−	3.23682i	−0.100492	−	0.242610i
$179$	−3.28072	−	7.92036i	−0.245213	−	0.591996i	0.752573	−	0.658509i	$-0.228813\pi$
$179$	−3.28072	−	7.92036i	−0.245213	−	0.591996i	−0.997786	+	0.0665132i	$0.978813\pi$
$180$	8.51199	+	1.69314i	0.634446	+	0.126199i
$181$	4.23355	−	2.82877i	0.314677	−	0.210261i	−0.388194	−	0.921578i	$-0.626901\pi$
$181$	4.23355	−	2.82877i	0.314677	−	0.210261i	0.702871	+	0.711317i	$0.251901\pi$
$182$		0			0
$183$	0.584303	−	0.584303i	0.0431930	−	0.0431930i
$184$	3.26030	−	4.87938i	0.240352	−	0.359713i
$185$	−6.08721	+	14.6958i	−0.447541	+	1.08046i
$186$		−	0.748872i		−	0.0549100i
$187$	20.6410	−	1.16633i	1.50942	−	0.0852902i
$188$			10.2838i			0.750023i
$189$		0			0
$190$	21.1996	+	14.1651i	1.53798	+	1.02765i
$191$	17.4411	+	17.4411i	1.26200	+	1.26200i	0.950124	+	0.311872i	$0.100956\pi$
$191$	17.4411	+	17.4411i	1.26200	+	1.26200i	0.311872	+	0.950124i	$0.399044\pi$
$192$	0.0862284	+	0.433499i	0.00622300	+	0.0312851i
$193$	−16.9790	+	11.3450i	−1.22218	+	0.816633i	−0.987833	−	0.155520i	$-0.950295\pi$
$193$	−16.9790	+	11.3450i	−1.22218	+	0.816633i	−0.234345	+	0.972153i	$0.575295\pi$
$194$	3.50301	−	17.6108i	0.251501	−	1.26438i
$195$	−3.72111	−	8.98355i	−0.266474	−	0.643325i
$196$		0			0
$197$	1.66733	−	8.38222i	0.118792	−	0.597208i	−0.874828	−	0.484433i	$-0.839026\pi$
$197$	1.66733	−	8.38222i	0.118792	−	0.597208i	0.993621	−	0.112775i	$-0.0359740\pi$
$198$	13.4644	+	20.1509i	0.956875	+	1.43206i
$199$	−15.9403	+	3.17072i	−1.12998	+	0.224766i	−0.724457	−	0.689320i	$-0.757909\pi$
$199$	−15.9403	+	3.17072i	−1.12998	+	0.224766i	−0.405519	+	0.914087i	$0.632909\pi$
$200$	2.21849	−	2.21849i	0.156871	−	0.156871i
$201$	5.60511	+	3.74522i	0.395354	+	0.264167i
$202$	−3.56456	+	8.60560i	−0.250801	+	0.605488i
$203$		0			0
$204$	0.888154	−	2.54101i	0.0621832	−	0.177907i
$205$	0.701772			0.0490139
$206$	−10.5912	−	4.38703i	−0.737925	−	0.305659i
$207$	−9.19284	−	6.14246i	−0.638947	−	0.426931i
$208$	−23.3428	+	23.3428i	−1.61853	+	1.61853i
$209$	5.20266	+	26.1555i	0.359875	+	1.80922i
$210$		0			0
$211$	−9.74454	−	1.93831i	−0.670842	−	0.133439i	−0.152094	−	0.988366i	$-0.548602\pi$
$211$	−9.74454	−	1.93831i	−0.670842	−	0.133439i	−0.518748	+	0.854927i	$0.673602\pi$
$212$	2.02486	−	0.838726i	0.139068	−	0.0576039i
$213$	−2.39485	+	0.991979i	−0.164092	+	0.0679693i
$214$	−1.89028	+	9.50307i	−0.129217	+	0.649616i
$215$	−2.31604	+	1.54753i	−0.157953	+	0.105541i
$216$	−4.37389	+	0.870022i	−0.297606	+	0.0591975i
$217$		0			0
$218$	−2.32202	+	3.47515i	−0.157267	+	0.235367i
$219$	−0.570967	−	0.236502i	−0.0385824	−	0.0159813i
$220$	−16.1000			−1.08546
$221$	26.5646	−	6.86221i	1.78693	−	0.461602i
$222$			5.78340i			0.388157i
$223$	−1.88077	−	0.779040i	−0.125946	−	0.0521684i	0.318821	−	0.947815i	$-0.396713\pi$
$223$	−1.88077	−	0.779040i	−0.125946	−	0.0521684i	−0.444766	+	0.895647i	$0.646713\pi$
$224$		0			0
$225$	−4.17968	−	4.17968i	−0.278645	−	0.278645i
$226$	−32.5663	+	6.47784i	−2.16628	+	0.430899i
$227$	0.793816	+	1.18803i	0.0526874	+	0.0788523i	0.856878	−	0.515519i	$-0.172401\pi$
$227$	0.793816	+	1.18803i	0.0526874	+	0.0788523i	−0.804191	+	0.594371i	$0.797401\pi$
$228$	3.40546	+	0.677389i	0.225532	+	0.0448612i
$229$	3.45831	+	8.34911i	0.228532	+	0.551724i	0.995999	−	0.0893636i	$-0.0284833\pi$
$229$	3.45831	+	8.34911i	0.228532	+	0.551724i	−0.767467	+	0.641088i	$0.778483\pi$
$230$	18.1168	−	7.50422i	1.19459	−	0.494813i
$231$		0			0
$232$	−7.76650	−	11.6234i	−0.509896	−	0.763113i
$233$	−0.354571	−	1.78255i	−0.0232287	−	0.116779i	0.967431	−	0.253134i	$-0.0814612\pi$
$233$	−0.354571	−	1.78255i	−0.0232287	−	0.116779i	−0.990660	+	0.136355i	$0.956461\pi$
$234$	22.7427	+	22.7427i	1.48674	+	1.48674i
$235$	12.7881	−	19.1388i	0.834204	−	1.24848i
$236$	−2.73668	+	6.60692i	−0.178142	+	0.430074i
$237$	−6.59571			−0.428438
$238$		0			0
$239$	−4.77316			−0.308750			−0.154375	−	0.988012i	$-0.549336\pi$
$239$	−4.77316			−0.308750			−0.154375	+	0.988012i	$0.549336\pi$
$240$	2.77413	−	6.69733i	0.179069	−	0.432311i
$241$	8.03495	−	12.0252i	0.517577	−	0.774608i	−0.476968	−	0.878921i	$-0.658264\pi$
$241$	8.03495	−	12.0252i	0.517577	−	0.774608i	0.994545	+	0.104313i	$0.0332642\pi$
$242$	−17.8819	−	17.8819i	−1.14949	−	1.14949i
$243$	2.50140	+	12.5754i	0.160465	+	0.806712i
$244$	−1.00878	−	1.50974i	−0.0645802	−	0.0966512i
$245$		0			0
$246$	0.235731	−	0.0976429i	0.0150296	−	0.00622548i
$247$	13.5437	+	32.6974i	0.861764	+	2.08048i
$248$	1.08106	+	0.215036i	0.0686474	+	0.0136548i
$249$	4.04421	+	6.05259i	0.256292	+	0.383567i
$250$	−13.2267	+	2.63095i	−0.836528	+	0.166396i
$251$	22.0951	+	22.0951i	1.39463	+	1.39463i	0.814589	+	0.580038i	$0.196963\pi$
$251$	22.0951	+	22.0951i	1.39463	+	1.39463i	0.580038	+	0.814589i	$0.303037\pi$
$252$		0			0
$253$	18.9491	+	7.84898i	1.19132	+	0.493461i
$254$			2.67343i			0.167746i
$255$	−4.81271	+	3.62454i	−0.301384	+	0.226977i
$256$	−20.4942			−1.28089
$257$	−20.6564	−	8.55615i	−1.28851	−	0.533718i	−0.369969	−	0.929044i	$-0.620632\pi$
$257$	−20.6564	−	8.55615i	−1.28851	−	0.533718i	−0.918541	+	0.395326i	$0.870632\pi$
$258$	−0.562657	+	0.842075i	−0.0350295	+	0.0524253i
$259$		0			0
$260$	−20.9560	+	4.16841i	−1.29964	+	0.258514i
$261$	−21.8987	+	14.6322i	−1.35549	+	0.905712i
$262$	−1.25236	+	6.29603i	−0.0773710	+	0.388970i
$263$	−6.50189	+	2.69317i	−0.400924	+	0.166068i	−0.574028	−	0.818835i	$-0.694620\pi$
$263$	−6.50189	+	2.69317i	−0.400924	+	0.166068i	0.173105	+	0.984903i	$0.444620\pi$
$264$	3.62254	−	1.50051i	0.222952	−	0.0923497i
$265$	−4.81136	−	0.957040i	−0.295560	−	0.0587905i
$266$		0			0
$267$	0.208340	+	1.04740i	0.0127502	+	0.0640996i
$268$	10.4743	−	10.4743i	0.639820	−	0.639820i
$269$	−3.49544	−	2.33558i	−0.213121	−	0.142403i	0.444429	−	0.895814i	$-0.353407\pi$
$269$	−3.49544	−	2.33558i	−0.213121	−	0.142403i	−0.657549	+	0.753412i	$0.728407\pi$
$270$	−13.7676	−	5.70271i	−0.837867	−	0.347056i
$271$	4.29597			0.260961			0.130481	−	0.991451i	$-0.458348\pi$
$271$	4.29597			0.260961			0.130481	+	0.991451i	$0.458348\pi$
$272$	17.6212	+	10.3863i	1.06844	+	0.629759i
$273$		0			0
$274$	−3.34027	+	8.06414i	−0.201793	+	0.487172i
$275$	9.11747	+	6.09210i	0.549804	+	0.367367i
$276$	1.88830	−	1.88830i	0.113662	−	0.113662i
$277$	−12.2433	+	2.43534i	−0.735627	+	0.146325i	−0.548666	−	0.836042i	$-0.684864\pi$
$277$	−12.2433	+	2.43534i	−0.735627	+	0.146325i	−0.186962	+	0.982367i	$0.559864\pi$
$278$	−5.30278	−	7.93617i	−0.318040	−	0.475980i
$279$	0.405133	−	2.03674i	0.0242546	−	0.121936i
$280$		0			0
$281$	−2.91965	−	7.04865i	−0.174172	−	0.420487i	0.812554	−	0.582887i	$-0.198077\pi$
$281$	−2.91965	−	7.04865i	−0.174172	−	0.420487i	−0.986725	+	0.162399i	$0.948077\pi$
$282$	1.63270	−	8.20816i	0.0972262	−	0.488789i
$283$	−5.96002	+	3.98236i	−0.354286	+	0.236727i	−0.719958	−	0.694017i	$-0.755839\pi$
$283$	−5.96002	+	3.98236i	−0.354286	+	0.236727i	0.365672	+	0.930744i	$0.380839\pi$
$284$	1.11122	+	5.58649i	0.0659389	+	0.331497i
$285$	−5.49542	−	5.49542i	−0.325521	−	0.325521i
$286$	−49.6104	−	33.1486i	−2.93352	−	1.96012i
$287$		0			0
$288$			16.2225i			0.955919i
$289$	−8.23349	−	14.8731i	−0.484323	−	0.874889i
$290$		−	46.7126i		−	2.74306i
$291$	−2.09450	+	5.05656i	−0.122782	+	0.296421i
$292$	−0.754461	+	1.12913i	−0.0441515	+	0.0660774i
$293$	4.15110	−	4.15110i	0.242510	−	0.242510i	−0.575378	−	0.817888i	$-0.695145\pi$
$293$	4.15110	−	4.15110i	0.242510	−	0.242510i	0.817888	+	0.575378i	$0.195145\pi$
$294$		0			0
$295$	13.3090	−	8.89276i	0.774877	−	0.517756i
$296$	−8.34884	−	1.66069i	−0.485266	−	0.0965255i
$297$	−5.96470	−	14.4001i	−0.346107	−	0.835577i
$298$	5.13976	+	12.4085i	0.297739	+	0.718804i
$299$	26.6965	+	5.31027i	1.54390	+	0.307101i
$300$	1.18710	−	0.793195i	0.0685372	−	0.0457951i
$301$		0			0
$302$	7.27245	−	7.27245i	0.418482	−	0.418482i
$303$	1.57739	−	2.36073i	0.0906187	−	0.135620i
$304$	−10.0970	+	24.3762i	−0.579101	+	1.39807i
$305$			4.06415i			0.232712i
$306$	10.1192	−	17.1681i	0.578479	−	0.981438i
$307$			24.0844i			1.37457i	0.726387	+	0.687286i	$0.241198\pi$
$307$			24.0844i			1.37457i	−0.726387	+	0.687286i	$0.758802\pi$
$308$		0			0
$309$	2.90544	+	1.94135i	0.165284	+	0.110440i
$310$	2.60440	+	2.60440i	0.147920	+	0.147920i
$311$	0.631126	+	3.17289i	0.0357879	+	0.179918i	0.994545	−	0.104309i	$-0.0332631\pi$
$311$	0.631126	+	3.17289i	0.0357879	+	0.179918i	−0.958757	+	0.284227i	$0.908263\pi$
$312$	4.32665	−	2.89098i	0.244949	−	0.163669i
$313$	−1.29305	+	6.50060i	−0.0730875	+	0.367436i	−0.999969	−	0.00791932i	$-0.997479\pi$
$313$	−1.29305	+	6.50060i	−0.0730875	+	0.367436i	0.926881	+	0.375355i	$0.122479\pi$
$314$	−4.73963	−	11.4425i	−0.267473	−	0.645737i
$315$		0			0
$316$	−2.82748	+	14.2147i	−0.159058	+	0.799639i
$317$	6.30432	+	9.43509i	0.354086	+	0.529927i	0.965165	−	0.261643i	$-0.0842641\pi$
$317$	6.30432	+	9.43509i	0.354086	+	0.529927i	−0.611079	+	0.791570i	$0.709264\pi$
$318$	−1.74933	+	0.347964i	−0.0980978	+	0.0195129i
$319$	34.5483	−	34.5483i	1.93433	−	1.93433i
$320$	−1.80749	−	1.20773i	−0.101042	−	0.0675141i
$321$	1.13022	−	2.72860i	0.0630828	−	0.152295i
$322$		0			0
$323$	17.5168	−	13.1922i	0.974660	−	0.734034i
$324$	7.68260			0.426811
$325$	13.4447	+	5.56898i	0.745778	+	0.308911i
$326$	18.7569	+	12.5330i	1.03885	+	0.694137i
$327$	0.900837	−	0.900837i	0.0498164	−	0.0498164i
$328$	0.0732665	+	0.368335i	0.00404546	+	0.0203379i
$329$		0			0
$330$	12.8505	+	2.55612i	0.707395	+	0.140710i
$331$	22.6983	−	9.40193i	1.24761	−	0.516777i	0.341524	−	0.939873i	$-0.389057\pi$
$331$	22.6983	−	9.40193i	1.24761	−	0.516777i	0.906085	+	0.423096i	$0.139057\pi$
$332$	14.7779	−	6.12120i	0.811042	−	0.335945i
$333$	−3.12877	+	15.7294i	−0.171455	+	0.861964i
$334$	19.8816	−	13.2845i	1.08787	−	0.726894i
$335$	−32.5183	+	6.46829i	−1.77666	+	0.353401i
$336$		0			0
$337$	2.83989	−	4.25020i	0.154699	−	0.231523i	−0.746022	−	0.665921i	$-0.768039\pi$
$337$	2.83989	−	4.25020i	0.154699	−	0.231523i	0.900721	+	0.434398i	$0.143039\pi$
$338$	−51.6787	−	21.4060i	−2.81095	−	1.16433i
$339$	10.1211			0.549704
$340$	5.74827	+	11.9259i	0.311744	+	0.646771i
$341$			3.85240i			0.208619i
$342$	23.7496	+	9.83739i	1.28423	+	0.531945i
$343$		0			0
$344$	−1.05404	−	1.05404i	−0.0568302	−	0.0568302i
$345$	−5.86238	+	1.16610i	−0.315620	+	0.0627807i
$346$	3.52287	+	5.27235i	0.189391	+	0.283443i
$347$	−20.6231	−	4.10219i	−1.10711	−	0.220217i	−0.392505	−	0.919750i	$-0.628392\pi$
$347$	−20.6231	−	4.10219i	−1.10711	−	0.220217i	−0.714601	+	0.699533i	$0.753392\pi$
$348$	−2.43441	−	5.87719i	−0.130498	−	0.315050i
$349$	26.1712	−	10.8405i	1.40091	−	0.580276i	0.450923	−	0.892563i	$-0.351095\pi$
$349$	26.1712	−	10.8405i	1.40091	−	0.580276i	0.949988	+	0.312287i	$0.101095\pi$
$350$		0			0
$351$	−11.4920	−	17.1990i	−0.613398	−	0.918015i
$352$	−5.87115	−	29.5163i	−0.312933	−	1.57322i
$353$	4.04792	+	4.04792i	0.215449	+	0.215449i	0.806577	−	0.591128i	$-0.201317\pi$
$353$	4.04792	+	4.04792i	0.215449	+	0.215449i	−0.591128	+	0.806577i	$0.701317\pi$
$354$	3.23326	−	4.83892i	0.171846	−	0.257186i
$355$	4.87886	−	11.7786i	0.258943	−	0.625144i
$356$	2.34660			0.124370
$357$		0			0
$358$	15.3303			0.810231
$359$	−8.48019	+	20.4730i	−0.447567	+	1.08052i	0.525663	+	0.850693i	$0.323817\pi$
$359$	−8.48019	+	20.4730i	−0.447567	+	1.08052i	−0.973231	+	0.229831i	$0.926183\pi$
$360$	5.77541	−	8.64352i	0.304391	−	0.455553i
$361$	6.56663	+	6.56663i	0.345612	+	0.345612i
$362$	1.77629	+	8.93003i	0.0933599	+	0.469352i
$363$	4.28254	+	6.40927i	0.224775	+	0.336400i
$364$		0			0
$365$	2.80819	−	1.16319i	0.146988	−	0.0608843i
$366$	0.565475	+	1.36518i	0.0295579	+	0.0713590i
$367$	27.1486	+	5.40020i	1.41715	+	0.281888i	0.843462	−	0.537188i	$-0.180514\pi$
$367$	27.1486	+	5.40020i	1.41715	+	0.281888i	0.573684	+	0.819076i	$0.305514\pi$
$368$	11.2739	+	16.8726i	0.587693	+	0.879544i
$369$	0.693951	−	0.138035i	0.0361256	−	0.00718584i
$370$	−20.1134	−	20.1134i	−1.04564	−	1.04564i
$371$		0			0
$372$	0.463403	+	0.191948i	0.0240264	+	0.00995204i
$373$		−	26.1076i		−	1.35180i	−0.736994	−	0.675899i	$-0.763756\pi$
$373$		−	26.1076i		−	1.35180i	0.736994	−	0.675899i	$-0.236244\pi$
$374$	−12.1982	+	34.8991i	−0.630755	+	1.80459i
$375$	4.11065			0.212273
$376$	11.3804	+	4.71390i	0.586897	+	0.243101i
$377$	36.0237	−	53.9132i	1.85531	−	2.77667i
$378$		0			0
$379$	6.55946	−	1.30476i	0.336937	−	0.0670209i	−0.0237224	−	0.999719i	$-0.507552\pi$
$379$	6.55946	−	1.30476i	0.336937	−	0.0670209i	0.360659	+	0.932698i	$0.382552\pi$
$380$	−14.1992	+	9.48762i	−0.728405	+	0.486705i
$381$	0.158979	−	0.799240i	0.00814472	−	0.0409463i
$382$	−40.7498	+	16.8791i	−2.08494	+	0.863611i
$383$	−13.4919	+	5.58852i	−0.689403	+	0.285560i	−0.699751	−	0.714386i	$-0.746706\pi$
$383$	−13.4919	+	5.58852i	−0.689403	+	0.285560i	0.0103486	+	0.999946i	$0.496706\pi$
$384$	5.64203	+	1.12227i	0.287919	+	0.0572706i
$385$		0			0
$386$	−7.12399	−	35.8147i	−0.362601	−	1.82292i
$387$	−1.98584	+	1.98584i	−0.100946	+	0.100946i
$388$	9.99973	+	6.68161i	0.507660	+	0.339207i
$389$	−11.6682	−	4.83312i	−0.591601	−	0.245049i	0.0667382	−	0.997771i	$-0.478741\pi$
$389$	−11.6682	−	4.83312i	−0.591601	−	0.245049i	−0.658339	+	0.752721i	$0.728741\pi$
$390$	17.3881			0.880482
$391$	−0.951470	−	16.8386i	−0.0481179	−	0.851566i
$392$		0			0
$393$	0.748802	−	1.80777i	0.0377721	−	0.0911898i
$394$	12.7073	+	8.49072i	0.640182	+	0.427756i
$395$	22.9384	−	22.9384i	1.15416	−	1.15416i
$396$	−15.9206	+	3.16680i	−0.800040	+	0.159138i
$397$	2.12684	+	3.18304i	0.106743	+	0.159752i	0.880996	−	0.473125i	$-0.156874\pi$
$397$	2.12684	+	3.18304i	0.106743	+	0.159752i	−0.774253	+	0.632877i	$0.781874\pi$
$398$	5.66993	−	28.5047i	0.284208	−	1.42881i
$399$		0			0
$400$	4.15174	+	10.0232i	0.207587	+	0.501159i
$401$	2.31756	−	11.6512i	0.115733	−	0.581831i	−0.878781	−	0.477226i	$-0.841642\pi$
$401$	2.31756	−	11.6512i	0.115733	−	0.581831i	0.994514	−	0.104605i	$-0.0333577\pi$
$402$	−10.0232	+	6.69726i	−0.499910	+	0.334029i
$403$	0.997412	+	5.01433i	0.0496846	+	0.249782i
$404$	−4.41151	−	4.41151i	−0.219481	−	0.219481i
$405$	−14.2978	−	9.55347i	−0.710462	−	0.474716i
$406$		0			0
$407$		−	29.7514i		−	1.47472i
$408$	−2.40485	−	2.14761i	−0.119058	−	0.106323i
$409$			2.45600i			0.121441i	0.998155	+	0.0607207i	$0.0193399\pi$
$409$			2.45600i			0.121441i	−0.998155	+	0.0607207i	$0.980660\pi$
$410$	−0.480238	+	1.15940i	−0.0237173	+	0.0572585i
$411$	1.47814	−	2.21219i	0.0729113	−	0.109119i
$412$	5.42940	−	5.42940i	0.267487	−	0.267487i
$413$		0			0
$414$	16.4388	−	10.9841i	0.807924	−	0.539837i
$415$	−35.1144	−	6.98468i	−1.72370	−	0.342865i
$416$	−15.2839	−	36.8986i	−0.749356	−	1.80911i
$417$	1.11337	+	2.68791i	0.0545219	+	0.131627i
$418$	−46.7718	−	9.30349i	−2.28768	−	0.455048i
$419$	28.3283	−	18.9283i	1.38393	−	0.924710i	0.383927	−	0.923363i	$-0.374571\pi$
$419$	28.3283	−	18.9283i	1.38393	−	0.924710i	0.999999	−	0.00134678i	$-0.000428695\pi$
$420$		0			0
$421$	−0.501993	+	0.501993i	−0.0244656	+	0.0244656i	−0.719234	−	0.694768i	$-0.755507\pi$
$421$	−0.501993	+	0.501993i	−0.0244656	+	0.0244656i	0.694768	+	0.719234i	$0.255507\pi$
$422$	9.87067	−	14.7725i	0.480497	−	0.719114i
$423$	8.88107	−	21.4408i	0.431813	−	1.04249i
$424$		−	2.62523i		−	0.127492i
$425$	1.25738	−	8.92872i	0.0609920	−	0.433107i
$426$		−	4.63536i		−	0.224584i
$427$		0			0
$428$	−5.39601	−	3.60550i	−0.260826	−	0.174278i
$429$	12.8601	+	12.8601i	0.620893	+	0.620893i
$430$	−0.971754	−	4.88533i	−0.0468621	−	0.235592i
$431$	−9.35137	+	6.24839i	−0.450440	+	0.300974i	−0.760021	−	0.649899i	$-0.774811\pi$
$431$	−9.35137	+	6.24839i	−0.450440	+	0.300974i	0.309581	+	0.950873i	$0.399811\pi$
$432$	3.00848	−	15.1246i	0.144745	−	0.727685i
$433$	2.47687	+	5.97968i	0.119031	+	0.287365i	0.972154	−	0.234345i	$-0.0752944\pi$
$433$	2.47687	+	5.97968i	0.119031	+	0.287365i	−0.853123	+	0.521710i	$0.825294\pi$
$434$		0			0
$435$	−2.77782	+	13.9650i	−0.133186	+	0.669572i
$436$	−1.55526	−	2.32761i	−0.0744833	−	0.111472i
$437$	21.3373	−	4.24425i	1.02070	−	0.203030i
$438$	0.781450	−	0.781450i	0.0373391	−	0.0373391i
$439$	−17.9030	−	11.9624i	−0.854463	−	0.570934i	0.0493888	−	0.998780i	$-0.484273\pi$
$439$	−17.9030	−	11.9624i	−0.854463	−	0.570934i	−0.903852	+	0.427846i	$0.859273\pi$
$440$	−7.37995	+	17.8168i	−0.351825	+	0.849382i
$441$		0			0
$442$	−6.84172	+	48.5834i	−0.325427	+	2.31088i
$443$	−32.3242			−1.53577			−0.767886	−	0.640587i	$-0.778691\pi$
$443$	−32.3242			−1.53577			−0.767886	+	0.640587i	$0.778691\pi$
$444$	−3.57878	−	1.48238i	−0.169841	−	0.0703506i
$445$	−4.36717	−	2.91805i	−0.207023	−	0.138329i
$446$	2.57410	−	2.57410i	0.121887	−	0.121887i
$447$	−0.798681	−	4.01524i	−0.0377763	−	0.189914i
$448$		0			0
$449$	−21.1303	−	4.20309i	−0.997203	−	0.198356i	−0.330601	−	0.943770i	$-0.607252\pi$
$449$	−21.1303	−	4.20309i	−0.997203	−	0.198356i	−0.666601	+	0.745415i	$0.732252\pi$
$450$	9.76549	−	4.04500i	0.460350	−	0.190683i
$451$	−1.21266	+	0.502301i	−0.0571020	+	0.0236524i
$452$	4.33877	−	21.8125i	0.204079	−	1.02597i
$453$	−2.60661	+	1.74168i	−0.122469	+	0.0818314i
$454$	−2.50597	+	0.498468i	−0.117611	+	0.0233943i
$455$		0			0
$456$	2.31062	−	3.45809i	0.108205	−	0.161940i
$457$	3.91001	+	1.61958i	0.182903	+	0.0757608i	0.472255	−	0.881462i	$-0.343440\pi$
$457$	3.91001	+	1.61958i	0.182903	+	0.0757608i	−0.289353	+	0.957223i	$0.593440\pi$
$458$	−16.1601			−0.755114
$459$	−8.53703	+	9.55959i	−0.398475	+	0.446203i
$460$			13.1342i			0.612383i
$461$	−33.5138	−	13.8819i	−1.56089	−	0.646544i	−0.575650	−	0.817696i	$-0.695251\pi$
$461$	−33.5138	−	13.8819i	−1.56089	−	0.646544i	−0.985245	+	0.171152i	$0.945251\pi$
$462$		0			0
$463$	9.81782	+	9.81782i	0.456273	+	0.456273i	0.897430	−	0.441157i	$-0.145432\pi$
$463$	9.81782	+	9.81782i	0.456273	+	0.456273i	−0.441157	+	0.897430i	$0.645432\pi$
$464$	47.4108	−	9.43059i	2.20099	−	0.437804i
$465$	−0.623730	−	0.933478i	−0.0289248	−	0.0432890i
$466$	3.18759	+	0.634051i	0.147662	+	0.0293718i
$467$	13.5691	+	32.7586i	0.627901	+	1.51589i	0.842225	+	0.539125i	$0.181245\pi$
$467$	13.5691	+	32.7586i	0.627901	+	1.51589i	−0.214324	+	0.976763i	$0.568755\pi$
$468$	−19.9025	+	8.24390i	−0.919995	+	0.381074i
$469$		0			0
$470$	22.8679	+	34.2243i	1.05482	+	1.57865i
$471$	0.736504	+	3.70265i	0.0339363	+	0.170609i
$472$	6.05697	+	6.05697i	0.278795	+	0.278795i
$473$	2.89446	−	4.33186i	0.133087	−	0.199179i
$474$	4.51359	−	10.8968i	0.207316	−	0.500505i
$475$	11.6311			0.533670
$476$		0			0
$477$	−4.94598			−0.226461
$478$	3.26637	−	7.88572i	0.149400	−	0.360685i
$479$	6.42831	−	9.62065i	0.293717	−	0.439579i	−0.655036	−	0.755598i	$-0.727346\pi$
$479$	6.42831	−	9.62065i	0.293717	−	0.439579i	0.948753	+	0.316019i	$0.102346\pi$
$480$	6.20153	+	6.20153i	0.283060	+	0.283060i
$481$	−7.70284	−	38.7248i	−0.351219	−	1.76570i
$482$	14.3682	+	21.5036i	0.654456	+	0.979462i
$483$		0			0
$484$	15.6488	−	6.48193i	0.711307	−	0.294633i
$485$	−10.3014	−	24.8697i	−0.467762	−	1.12928i
$486$	−22.4876	−	4.47305i	−1.02006	−	0.202902i
$487$	15.0011	+	22.4507i	0.679765	+	1.01734i	0.997603	+	0.0691955i	$0.0220432\pi$
$487$	15.0011	+	22.4507i	0.679765	+	1.01734i	−0.317838	+	0.948145i	$0.602957\pi$
$488$	−2.13313	+	0.424305i	−0.0965621	+	0.0192074i
$489$	−4.86221	−	4.86221i	−0.219877	−	0.219877i
$490$		0			0
$491$	−5.96262	−	2.46980i	−0.269089	−	0.111460i	0.244059	−	0.969760i	$-0.421521\pi$
$491$	−5.96262	−	2.46980i	−0.269089	−	0.111460i	−0.513148	+	0.858300i	$0.671521\pi$
$492$			0.170898i			0.00770468i
$493$	−37.9260	−	13.2562i	−1.70810	−	0.597029i
$494$	−63.2875			−2.84744
$495$	33.5671	+	13.9040i	1.50873	+	0.624937i
$496$	−2.11754	+	3.16913i	−0.0950804	+	0.142298i
$497$		0			0
$498$	−12.7670	+	2.53952i	−0.572104	+	0.113798i
$499$	−26.9971	+	18.0389i	−1.20856	+	0.807532i	−0.985895	−	0.167364i	$-0.946474\pi$
$499$	−26.9971	+	18.0389i	−1.20856	+	0.807532i	−0.222661	+	0.974896i	$0.571474\pi$
$500$	1.76217	−	8.85904i	0.0788068	−	0.396188i
$501$	−6.73372	+	2.78920i	−0.300840	+	0.124612i
$502$	−51.6233	+	21.3831i	−2.30406	+	0.954374i
$503$	−27.8736	−	5.54441i	−1.24282	−	0.247213i	−0.470476	−	0.882413i	$-0.655918\pi$
$503$	−27.8736	−	5.54441i	−1.24282	−	0.247213i	−0.772348	+	0.635200i	$0.780918\pi$
$504$		0			0
$505$	2.72428	+	13.6959i	0.121229	+	0.609459i
$506$	−25.9346	+	25.9346i	−1.15293	+	1.15293i
$507$	14.1767	+	9.47260i	0.629611	+	0.420693i
$508$	−1.65432	−	0.685243i	−0.0733988	−	0.0304028i
$509$	36.2754			1.60788			0.803939	−	0.594711i	$-0.202734\pi$
$509$	36.2754			1.60788			0.803939	+	0.594711i	$0.202734\pi$
$510$	−2.69465	−	10.4314i	−0.119321	−	0.461911i
$511$		0			0
$512$	5.94712	−	14.3576i	0.262828	−	0.634523i
$513$	−13.7463	−	9.18501i	−0.606916	−	0.405528i
$514$	28.2712	−	28.2712i	1.24699	−	1.24699i
$515$	−16.8560	+	3.35287i	−0.742765	+	0.147745i
$516$	−0.376860	−	0.564011i	−0.0165903	−	0.0248292i
$517$	−8.39907	+	42.2250i	−0.369391	+	1.85705i
$518$		0			0
$519$	−0.739659	−	1.78570i	−0.0324674	−	0.0783834i
$520$	−4.99295	+	25.1013i	−0.218955	+	1.10076i
$521$	−22.0440	+	14.7294i	−0.965767	+	0.645305i	−0.935160	−	0.354226i	$-0.884744\pi$
$521$	−22.0440	+	14.7294i	−0.965767	+	0.645305i	−0.0306076	+	0.999531i	$0.509744\pi$
$522$	−9.18814	−	46.1919i	−0.402154	−	2.02177i
$523$	14.7577	+	14.7577i	0.645308	+	0.645308i	0.951856	−	0.306547i	$-0.0991737\pi$
$523$	14.7577	+	14.7577i	0.645308	+	0.645308i	−0.306547	+	0.951856i	$0.599174\pi$
$524$	−3.57500	−	2.38874i	−0.156174	−	0.104352i
$525$		0			0
$526$		−	12.5848i		−	0.548721i
$527$	2.85361	−	1.37544i	0.124305	−	0.0599151i
$528$			13.5586i			0.590062i
$529$	−2.39865	+	5.79085i	−0.104289	+	0.251776i
$530$	4.87364	−	7.29392i	0.211698	−	0.316828i
$531$	11.4115	−	11.4115i	0.495215	−	0.495215i
$532$		0			0
$533$	−1.44837	+	0.967768i	−0.0627358	+	0.0419187i
$534$	−1.87297	−	0.372558i	−0.0810515	−	0.0161221i
$535$	5.55878	+	13.4201i	0.240327	+	0.580201i
$536$	−6.78995	−	16.3924i	−0.293281	−	0.708044i
$537$	−4.58309	−	0.911634i	−0.197775	−	0.0393399i
$538$	6.25061	−	4.17652i	0.269483	−	0.180063i
$539$		0			0
$540$	7.05770	−	7.05770i	0.303715	−	0.303715i
$541$	19.3927	−	29.0232i	0.833757	−	1.24780i	−0.132746	−	0.991150i	$-0.542380\pi$
$541$	19.3927	−	29.0232i	0.833757	−	1.24780i	0.966503	−	0.256655i	$-0.0826204\pi$
$542$	−2.93982	+	7.09736i	−0.126276	+	0.304858i
$543$		−	2.77532i		−	0.119100i
$544$	−19.7675	+	14.8873i	−0.847526	+	0.638287i
$545$			6.26581i			0.268398i
$546$		0			0
$547$	3.70359	+	2.47466i	0.158354	+	0.105809i	0.632223	−	0.774787i	$-0.282143\pi$
$547$	3.70359	+	2.47466i	0.158354	+	0.105809i	−0.473869	+	0.880596i	$0.657143\pi$
$548$	−4.13394	−	4.13394i	−0.176593	−	0.176593i
$549$	0.799399	+	4.01885i	0.0341175	+	0.171520i
$550$	−16.3040	+	10.8940i	−0.695206	+	0.464522i
$551$	10.1104	−	50.8284i	0.430718	−	2.16536i
$552$	−1.22409	−	2.95521i	−0.0521007	−	0.125782i
$553$		0			0
$554$	4.35492	−	21.8937i	0.185023	−	0.930172i
$555$	4.81696	+	7.20908i	0.204468	+	0.306009i
$556$	6.27011	−	1.24720i	0.265912	−	0.0528932i
$557$	−5.88222	+	5.88222i	−0.249238	+	0.249238i	−0.820658	−	0.571420i	$-0.806393\pi$
$557$	−5.88222	+	5.88222i	−0.249238	+	0.249238i	0.571420	+	0.820658i	$0.306393\pi$
$558$	3.08765	+	2.06310i	0.130711	+	0.0873381i
$559$	2.64591	−	6.38780i	0.111910	−	0.270175i
$560$		0			0
$561$	5.72206	−	9.70795i	0.241585	−	0.409870i
$562$	13.6430			0.575497
$563$	33.3865	+	13.8291i	1.40707	+	0.582829i	0.951577	−	0.307409i	$-0.0994621\pi$
$563$	33.3865	+	13.8291i	1.40707	+	0.582829i	0.455496	+	0.890238i	$0.349462\pi$
$564$	4.66074	+	3.11421i	0.196253	+	0.131132i
$565$	−35.1989	+	35.1989i	−1.48083	+	1.48083i
$566$	−2.50068	−	12.5718i	−0.105111	−	0.528430i
$567$		0			0
$568$	6.69154	+	1.33103i	0.280771	+	0.0558488i
$569$	7.83649	−	3.24598i	0.328523	−	0.136079i	−0.212325	−	0.977199i	$-0.568103\pi$
$569$	7.83649	−	3.24598i	0.328523	−	0.136079i	0.540848	+	0.841120i	$0.318103\pi$
$570$	12.8396	−	5.31834i	0.537792	−	0.222761i
$571$	3.94479	−	19.8318i	0.165084	−	0.829935i	−0.806132	−	0.591736i	$-0.798443\pi$
$571$	3.94479	−	19.8318i	0.165084	−	0.829935i	0.971216	−	0.238199i	$-0.0765572\pi$
$572$	33.2284	−	22.2025i	1.38935	−	0.928333i
$573$	13.1862	−	2.62289i	0.550860	−	0.109573i
$574$		0			0
$575$	4.96984	−	7.43789i	0.207257	−	0.310181i
$576$	−2.02490	−	0.838742i	−0.0843710	−	0.0349476i
$577$	−36.0093			−1.49909			−0.749543	−	0.661956i	$-0.769727\pi$
$577$	−36.0093			−1.49909			−0.749543	+	0.661956i	$0.769727\pi$
$578$	30.2062	−	3.42455i	1.25641	−	0.142442i
$579$			11.1307i			0.462575i
$580$	28.9058	+	11.9732i	1.20025	+	0.497159i
$581$		0			0
$582$	−6.92063	−	6.92063i	−0.286869	−	0.286869i
$583$	8.99904	−	1.79002i	0.372702	−	0.0741351i
$584$	0.903699	+	1.35248i	0.0373953	+	0.0559661i
$585$	47.2913	+	9.40681i	1.95525	+	0.388924i
$586$	4.01734	+	9.69871i	0.165955	+	0.400650i
$587$	−18.6945	+	7.74352i	−0.771605	+	0.319609i	−0.733522	−	0.679666i	$-0.762125\pi$
$587$	−18.6945	+	7.74352i	−0.771605	+	0.319609i	−0.0380824	+	0.999275i	$0.512125\pi$
$588$		0			0
$589$	2.27019	+	3.39757i	0.0935414	+	0.139995i
$590$	5.58411	+	28.0732i	0.229894	+	1.15576i
$591$	−3.29401	−	3.29401i	−0.135497	−	0.135497i
$592$	16.3534	−	24.4746i	0.672120	−	1.00590i
$593$	−9.53650	+	23.0231i	−0.391617	+	0.945447i	0.597971	+	0.801518i	$0.295974\pi$
$593$	−9.53650	+	23.0231i	−0.391617	+	0.945447i	−0.989588	+	0.143929i	$0.954026\pi$
$594$	27.8721			1.14361
$595$		0			0
$596$	−8.99580			−0.368482
$597$	−3.39013	+	8.18449i	−0.138749	+	0.334969i
$598$	−27.0421	+	40.4714i	−1.10583	+	1.65500i
$599$	−8.05216	−	8.05216i	−0.329002	−	0.329002i	0.523205	−	0.852207i	$-0.324736\pi$
$599$	−8.05216	−	8.05216i	−0.329002	−	0.329002i	−0.852207	+	0.523205i	$0.824736\pi$
$600$	−0.333629	−	1.67727i	−0.0136203	−	0.0684741i
$601$	10.4548	+	15.6467i	0.426460	+	0.638243i	0.981021	−	0.193900i	$-0.0621138\pi$
$601$	10.4548	+	15.6467i	0.426460	+	0.638243i	−0.554561	+	0.832143i	$0.687114\pi$
$602$		0			0
$603$	−30.8836	+	12.7924i	−1.25768	+	0.520947i
$604$	2.63616	+	6.36425i	0.107264	+	0.258958i
$605$	−37.1837	−	7.39629i	−1.51173	−	0.300702i
$606$	2.82072	+	4.22150i	0.114584	+	0.171487i
$607$	35.7964	−	7.12034i	1.45293	−	0.289006i	0.595396	−	0.803432i	$-0.296995\pi$
$607$	35.7964	−	7.12034i	1.45293	−	0.289006i	0.857535	+	0.514426i	$0.171995\pi$
$608$	−22.5717	−	22.5717i	−0.915402	−	0.915402i
$609$		0			0
$610$	−6.71437	−	2.78118i	−0.271857	−	0.112607i
$611$			57.1352i			2.31144i
$612$	8.02996	+	10.6623i	0.324592	+	0.430997i
$613$	−3.48685			−0.140832			−0.0704162	−	0.997518i	$-0.522433\pi$
$613$	−3.48685			−0.140832			−0.0704162	+	0.997518i	$0.522433\pi$
$614$	−39.7899	−	16.4815i	−1.60579	−	0.665139i
$615$	0.212515	−	0.318052i	0.00856944	−	0.0128251i
$616$		0			0
$617$	46.2155	−	9.19283i	1.86057	−	0.370089i	0.868487	−	0.495712i	$-0.165093\pi$
$617$	46.2155	−	9.19283i	1.86057	−	0.370089i	0.992078	+	0.125622i	$0.0400928\pi$
$618$	−5.19555	+	3.47156i	−0.208996	+	0.139647i
$619$	−0.779629	+	3.91946i	−0.0313359	+	0.157536i	−0.993285	−	0.115692i	$-0.963091\pi$
$619$	−0.779629	+	3.91946i	−0.0313359	+	0.157536i	0.961949	+	0.273228i	$0.0880915\pi$
$620$	−2.27916	+	0.944060i	−0.0915334	+	0.0379144i
$621$	−11.7473	+	4.86591i	−0.471405	+	0.195262i
$622$	−5.67381	−	1.12859i	−0.227499	−	0.0452524i
$623$		0			0
$624$	3.51041	+	17.6480i	0.140529	+	0.706487i
$625$	−22.0278	+	22.0278i	−0.881111	+	0.881111i
$626$	−9.85477	−	6.58475i	−0.393876	−	0.263179i
$627$	13.4295	+	5.56268i	0.536322	+	0.222152i
$628$	8.29548			0.331026
$629$	−22.0379	+	10.6223i	−0.878708	+	0.423537i
$630$		0			0
$631$	−1.89828	+	4.58286i	−0.0755694	+	0.182441i	−0.957150	−	0.289593i	$-0.906480\pi$
$631$	−1.89828	+	4.58286i	−0.0755694	+	0.182441i	0.881580	+	0.472034i	$0.156480\pi$
$632$	14.4344	+	9.64473i	0.574168	+	0.383647i
$633$	−3.82937	+	3.82937i	−0.152204	+	0.152204i
$634$	−19.9019	+	3.95873i	−0.790404	+	0.157221i
$635$	2.22668	+	3.33246i	0.0883632	+	0.132245i
$636$	0.233062	−	1.17168i	0.00924150	−	0.0464602i
$637$		0			0
$638$	33.4350	+	80.7193i	1.32370	+	3.19571i
$639$	2.50769	−	12.6070i	0.0992025	−	0.498725i
$640$	−23.5247	+	15.7187i	−0.929895	+	0.621336i
$641$	−6.50339	−	32.6948i	−0.256869	−	1.29137i	−0.866698	−	0.498833i	$-0.833762\pi$
$641$	−6.50339	−	32.6948i	−0.256869	−	1.29137i	0.609830	−	0.792533i	$-0.291238\pi$
$642$	3.73448	+	3.73448i	0.147388	+	0.147388i
$643$	27.9715	+	18.6900i	1.10309	+	0.737061i	0.967289	−	0.253675i	$-0.0816394\pi$
$643$	27.9715	+	18.6900i	1.10309	+	0.737061i	0.135800	+	0.990736i	$0.456639\pi$
$644$		0			0
$645$			1.51829i			0.0597826i
$646$	9.80772	+	37.9672i	0.385879	+	1.49380i
$647$			34.7391i			1.36574i	0.730542	+	0.682868i	$0.239268\pi$
$647$			34.7391i			1.36574i	−0.730542	+	0.682868i	$0.760732\pi$
$648$	3.52156	−	8.50179i	0.138340	−	0.333982i
$649$	−16.6328	+	24.8927i	−0.652893	+	0.977124i
$650$	−18.4010	+	18.4010i	−0.721747	+	0.721747i
$651$		0			0
$652$	−12.5631	+	8.39441i	−0.492010	+	0.328750i
$653$	35.1878	+	6.99928i	1.37700	+	0.273903i	0.827442	−	0.561551i	$-0.189795\pi$
$653$	35.1878	+	6.99928i	1.37700	+	0.273903i	0.549561	+	0.835454i	$0.314795\pi$
$654$	0.871809	+	2.10473i	0.0340904	+	0.0823016i
$655$	3.68284	+	8.89116i	0.143900	+	0.347406i
$656$	−1.27368	−	0.253351i	−0.0497289	−	0.00989168i
$657$	2.54810	−	1.70259i	0.0994109	−	0.0664242i
$658$		0			0
$659$	−4.30369	+	4.30369i	−0.167648	+	0.167648i	−0.785945	−	0.618297i	$-0.787823\pi$
$659$	−4.30369	+	4.30369i	−0.167648	+	0.167648i	0.618297	+	0.785945i	$0.287823\pi$
$660$	−4.87552	+	7.29673i	−0.189779	+	0.284025i
$661$	12.6534	−	30.5481i	0.492161	−	1.18818i	−0.461457	−	0.887163i	$-0.652673\pi$
$661$	12.6534	−	30.5481i	0.492161	−	1.18818i	0.953618	−	0.301019i	$-0.0973269\pi$
$662$			43.9337i			1.70753i
$663$	4.93445	−	14.1175i	0.191638	−	0.548277i
$664$		−	19.1595i		−	0.743533i
$665$		0			0
$666$	−23.8454	−	15.9330i	−0.923990	−	0.617390i
$667$	−28.1839	−	28.1839i	−1.09129	−	1.09129i
$668$	3.12448	+	15.7078i	0.120890	+	0.607753i
$669$	−0.922617	+	0.616473i	−0.0356704	+	0.0238342i
$670$	11.5667	−	58.1498i	0.446861	−	2.24652i
$671$	−2.90896	−	7.02284i	−0.112299	−	0.271114i
$672$		0			0
$673$	−3.94208	+	19.8182i	−0.151956	+	0.763934i	0.827372	+	0.561654i	$0.189835\pi$
$673$	−3.94208	+	19.8182i	−0.151956	+	0.763934i	−0.979328	+	0.202279i	$0.935165\pi$
$674$	5.07834	+	7.60028i	0.195611	+	0.292752i
$675$	−6.66735	+	1.32622i	−0.256626	+	0.0510462i
$676$	26.4922	−	26.4922i	1.01893	−	1.01893i
$677$	−21.3826	−	14.2874i	−0.821798	−	0.549108i	0.0720898	−	0.997398i	$-0.477033\pi$
$677$	−21.3826	−	14.2874i	−0.821798	−	0.549108i	−0.893888	+	0.448290i	$0.852033\pi$
$678$	−6.92610	+	16.7211i	−0.265995	+	0.642170i
$679$		0			0
$680$	15.8324	−	0.894614i	0.607145	−	0.0343069i
$681$	0.778817			0.0298443
$682$	−6.36454	−	2.63628i	−0.243711	−	0.100948i
$683$	21.7925	+	14.5613i	0.833866	+	0.557171i	0.897608	−	0.440795i	$-0.145304\pi$
$683$	21.7925	+	14.5613i	0.833866	+	0.557171i	−0.0637421	+	0.997966i	$0.520304\pi$
$684$	−12.1748	+	12.1748i	−0.465515	+	0.465515i
$685$	2.55287	+	12.8341i	0.0975401	+	0.490367i
$686$		0			0
$687$	4.83118	+	0.960982i	0.184321	+	0.0366637i
$688$	4.76217	−	1.97256i	0.181556	−	0.0752030i
$689$	11.2498	−	4.65983i	0.428584	−	0.177525i
$690$	2.08524	−	10.4832i	0.0793838	−	0.399089i
$691$	33.0199	−	22.0632i	1.25614	−	0.839324i	0.264005	−	0.964521i	$-0.414956\pi$
$691$	33.0199	−	22.0632i	1.25614	−	0.839324i	0.992132	+	0.125198i	$0.0399565\pi$
$692$	−4.16551	+	0.828572i	−0.158349	+	0.0314976i
$693$		0			0
$694$	20.8901	−	31.2642i	0.792975	−	1.18677i
$695$	−13.2200	−	5.47589i	−0.501462	−	0.207712i
$696$	−7.61976			−0.288826
$697$	0.805034	+	0.718923i	0.0304929	+	0.0272311i
$698$			50.6557i			1.91735i
$699$	−0.915246	−	0.379107i	−0.0346178	−	0.0143392i
$700$		0			0
$701$	9.39878	+	9.39878i	0.354987	+	0.354987i	0.861961	−	0.506974i	$-0.169236\pi$
$701$	9.39878	+	9.39878i	0.354987	+	0.354987i	−0.506974	+	0.861961i	$0.669236\pi$
$702$	36.2787	−	7.21628i	1.36925	−	0.272361i
$703$	−17.5322	−	26.2389i	−0.661241	−	0.989617i
$704$	3.98779	+	0.793221i	0.150296	+	0.0298957i
$705$	−4.80133	−	11.5914i	−0.180829	−	0.436559i
$706$	−9.45764	+	3.91748i	−0.355943	+	0.147436i
$707$		0			0
$708$	2.16560	+	3.24104i	0.0813881	+	0.121806i
$709$	−8.28893	−	41.6713i	−0.311297	−	1.56500i	−0.746949	−	0.664882i	$-0.768482\pi$
$709$	−8.28893	−	41.6713i	−0.311297	−	1.56500i	0.435651	−	0.900115i	$-0.356518\pi$
$710$	16.1207	+	16.1207i	0.605000	+	0.605000i
$711$	18.1708	−	27.1946i	0.681460	−	1.01988i
$712$	1.07564	−	2.59682i	0.0403112	−	0.0973199i
$713$	3.14273			0.117696
$714$		0			0
$715$	−89.4492			−3.34521
$716$	−3.92940	+	9.48641i	−0.146849	+	0.354524i
$717$	−1.44544	+	2.16325i	−0.0539809	+	0.0807881i
$718$	−28.0202	−	28.0202i	−1.04571	−	1.04571i
$719$	−3.92972	−	19.7560i	−0.146554	−	0.736775i	−0.982249	−	0.187582i	$-0.939935\pi$
$719$	−3.92972	−	19.7560i	−0.146554	−	0.736775i	0.835695	−	0.549193i	$-0.185065\pi$
$720$	19.9710	+	29.8887i	0.744275	+	1.11389i
$721$		0			0
$722$	−15.3424	+	6.35503i	−0.570985	+	0.236510i
$723$	−3.01675	−	7.28307i	−0.112194	−	0.270860i
$724$	−5.98121	−	1.18974i	−0.222290	−	0.0442162i
$725$	−11.8389	−	17.7181i	−0.439685	−	0.658035i
$726$	−13.5194	+	2.68917i	−0.501751	+	0.0998046i
$727$	−15.6585	−	15.6585i	−0.580743	−	0.580743i	0.354364	−	0.935107i	$-0.384697\pi$
$727$	−15.6585	−	15.6585i	−0.580743	−	0.580743i	−0.935107	+	0.354364i	$0.884697\pi$
$728$		0			0
$729$	−11.3214	−	4.68947i	−0.419311	−	0.173684i
$730$			5.43541i			0.201174i
$731$	−4.24218	−	0.597403i	−0.156903	−	0.0220957i
$732$	−0.989716			−0.0365809
$733$	−30.4919	−	12.6302i	−1.12624	−	0.466505i	−0.259741	−	0.965678i	$-0.583637\pi$
$733$	−30.4919	−	12.6302i	−1.12624	−	0.466505i	−0.866502	+	0.499173i	$0.833637\pi$
$734$	−27.5000	+	41.1567i	−1.01505	+	1.51912i
$735$		0			0
$736$	−24.0789	+	4.78959i	−0.887560	+	0.176547i
$737$	51.5618	−	34.4525i	1.89930	−	1.26907i
$738$	−0.246837	+	1.24094i	−0.00908621	+	0.0456795i
$739$	21.3775	−	8.85484i	0.786383	−	0.325731i	0.0468947	−	0.998900i	$-0.485067\pi$
$739$	21.3775	−	8.85484i	0.786383	−	0.325731i	0.739488	+	0.673169i	$0.235067\pi$
$740$	17.6016	−	7.29081i	0.647046	−	0.268015i
$741$	18.9202	+	3.76346i	0.695051	+	0.138254i
$742$		0			0
$743$	−4.30776	−	21.6566i	−0.158037	−	0.794503i	−0.975752	−	0.218880i	$-0.929760\pi$
$743$	−4.30776	−	21.6566i	−0.158037	−	0.794503i	0.817715	−	0.575623i	$-0.195240\pi$
$744$	0.424831	−	0.424831i	0.0155751	−	0.0155751i
$745$	16.7417	+	11.1865i	0.613369	+	0.409840i
$746$	43.1322	+	17.8660i	1.57918	+	0.654119i
$747$	−36.0969			−1.32071
$748$	−18.4691	−	16.4935i	−0.675296	−	0.603062i
$749$		0			0
$750$	−2.81301	+	6.79120i	−0.102717	+	0.247980i
$751$	−2.11608	−	1.41392i	−0.0772170	−	0.0515947i	0.516362	−	0.856370i	$-0.327286\pi$
$751$	−2.11608	−	1.41392i	−0.0772170	−	0.0515947i	−0.593579	+	0.804775i	$0.702286\pi$
$752$	−30.1191	+	30.1191i	−1.09833	+	1.09833i
$753$	16.7047	−	3.32277i	0.608753	−	0.121089i
$754$	64.4182	+	96.4087i	2.34597	+	3.51100i
$755$	3.00803	−	15.1224i	0.109473	−	0.550360i
$756$		0			0
$757$	−14.2277	−	34.3488i	−0.517115	−	1.24843i	−0.939668	−	0.342089i	$-0.888866\pi$
$757$	−14.2277	−	34.3488i	−0.517115	−	1.24843i	0.422552	−	0.906339i	$-0.361134\pi$
$758$	−2.33319	+	11.7297i	−0.0847453	+	0.426043i
$759$	9.29554	−	6.21108i	0.337407	−	0.225448i
$760$	3.99063	+	20.0622i	0.144755	+	0.727734i
$761$	2.05410	+	2.05410i	0.0744609	+	0.0744609i	0.743356	−	0.668896i	$-0.233233\pi$
$761$	2.05410	+	2.05410i	0.0744609	+	0.0744609i	−0.668896	+	0.743356i	$0.733233\pi$
$762$	1.21163	+	0.809585i	0.0438927	+	0.0293282i
$763$		0			0
$764$		−	29.5425i		−	1.06881i
$765$	−1.68547	−	29.8286i	−0.0609383	−	1.07845i
$766$		−	26.1143i		−	0.943546i
$767$	−15.2045	+	36.7070i	−0.549004	+	1.32541i
$768$	−6.20618	+	9.28820i	−0.223946	+	0.335159i
$769$	−22.1893	+	22.1893i	−0.800166	+	0.800166i	−0.983121	−	0.182955i	$-0.941434\pi$
$769$	−22.1893	+	22.1893i	−0.800166	+	0.800166i	0.182955	+	0.983121i	$0.441434\pi$
$770$		0			0
$771$	−10.1330	+	6.77069i	−0.364933	+	0.243840i
$772$	23.9882	+	4.77155i	0.863354	+	0.171732i
$773$	1.36515	+	3.29576i	0.0491010	+	0.118540i	0.946527	−	0.322625i	$-0.104565\pi$
$773$	1.36515	+	3.29576i	0.0491010	+	0.118540i	−0.897426	+	0.441165i	$0.854565\pi$
$774$	−1.92185	−	4.63975i	−0.0690793	−	0.166772i
$775$	1.64792	+	0.327791i	0.0591949	+	0.0117746i
$776$	11.9778	−	8.00328i	0.429976	−	0.287301i
$777$		0			0
$778$	15.9696	−	15.9696i	0.572538	−	0.572538i
$779$	−0.773490	+	1.15761i	−0.0277132	+	0.0414757i
$780$	−4.45686	+	10.7598i	−0.159581	+	0.385263i
$781$			23.8455i			0.853261i
$782$	28.4702	+	9.95111i	1.01809	+	0.355851i
$783$			30.2895i			1.08246i
$784$		0			0
$785$	−15.4384	−	10.3156i	−0.551019	−	0.368179i
$786$	2.47419	+	2.47419i	0.0882514	+	0.0882514i
$787$	−8.39050	−	42.1819i	−0.299089	−	1.50362i	−0.779401	−	0.626525i	$-0.784477\pi$
$787$	−8.39050	−	42.1819i	−0.299089	−	1.50362i	0.480312	−	0.877098i	$-0.340523\pi$
$788$	−8.51115	+	5.68697i	−0.303197	+	0.202590i
$789$	−0.748367	+	3.76230i	−0.0266426	+	0.133941i
$790$	22.1992	+	53.5937i	0.789813	+	1.90678i
$791$		0			0
$792$	−3.79322	+	19.0698i	−0.134786	+	0.677616i
$793$	−5.60460	−	8.38787i	−0.199025	−	0.297862i
$794$	−6.71413	+	1.33552i	−0.238276	+	0.0473960i
$795$	−1.89075	+	1.89075i	−0.0670580	+	0.0670580i
$796$	16.1855	+	10.8148i	0.573678	+	0.383320i
$797$	−4.78470	+	11.5513i	−0.169483	+	0.409168i	−0.985685	−	0.168599i	$-0.946076\pi$
$797$	−4.78470	+	11.5513i	−0.169483	+	0.409168i	0.816202	+	0.577767i	$0.196076\pi$
$798$		0			0
$799$	34.2763	−	8.85429i	1.21261	−	0.313242i
$800$	−13.1255			−0.464058
$801$	−4.89246	−	2.02652i	−0.172866	−	0.0716036i
$802$	17.6629	+	11.8020i	0.623698	+	0.416742i
$803$	−4.01999	+	4.01999i	−0.141862	+	0.141862i
$804$	−1.57518	−	7.91897i	−0.0555524	−	0.279281i
$805$		0			0
$806$	−8.96672	−	1.78359i	−0.315839	−	0.0628243i
$807$	−2.11702	+	0.876899i	−0.0745227	+	0.0308683i
$808$	−6.90406	+	2.85976i	−0.242884	+	0.100606i
$809$	−8.88319	+	44.6588i	−0.312316	+	1.57012i	0.431737	+	0.902000i	$0.357901\pi$
$809$	−8.88319	+	44.6588i	−0.312316	+	1.57012i	−0.744053	+	0.668120i	$0.767099\pi$
$810$	25.5675	−	17.0837i	0.898352	−	0.600259i
$811$	22.1324	−	4.40241i	0.777174	−	0.154590i	0.209462	−	0.977817i	$-0.432829\pi$
$811$	22.1324	−	4.40241i	0.777174	−	0.154590i	0.567712	+	0.823227i	$0.307829\pi$
$812$		0			0
$813$	1.30093	−	1.94698i	0.0456257	−	0.0682836i
$814$	49.1522	+	20.3595i	1.72278	+	0.713600i
$815$	33.8193			1.18464
$816$	10.0433	−	4.84089i	0.351587	−	0.169465i
$817$		−	5.52611i		−	0.193334i
$818$	−4.05755	−	1.68069i	−0.141869	−	0.0587641i
$819$		0			0
$820$	−0.594345	−	0.594345i	−0.0207554	−	0.0207554i
$821$	−41.4807	+	8.25103i	−1.44769	+	0.287963i	−0.855485	−	0.517827i	$-0.826741\pi$
$821$	−41.4807	+	8.25103i	−1.44769	+	0.287963i	−0.592202	+	0.805790i	$0.701741\pi$
$822$	2.64324	+	3.95589i	0.0921935	+	0.137977i
$823$	−27.9541	−	5.56042i	−0.974419	−	0.193824i	−0.317892	−	0.948127i	$-0.602975\pi$
$823$	−27.9541	−	5.56042i	−0.974419	−	0.193824i	−0.656526	+	0.754303i	$0.727975\pi$
$824$	−3.51960	−	8.49707i	−0.122611	−	0.296010i
$825$	5.52202	−	2.28730i	0.192252	−	0.0796335i
$826$		0			0
$827$	−5.50470	−	8.23837i	−0.191417	−	0.286476i	0.723330	−	0.690502i	$-0.242610\pi$
$827$	−5.50470	−	8.23837i	−0.191417	−	0.286476i	−0.914747	+	0.404026i	$0.867610\pi$
$828$	2.58343	+	12.9878i	0.0897803	+	0.451356i
$829$	28.5355	+	28.5355i	0.991079	+	0.991079i	0.999961	−	0.00888175i	$-0.00282719\pi$
$829$	28.5355	+	28.5355i	0.991079	+	0.991079i	−0.00888175	+	0.999961i	$0.502827\pi$
$830$	35.5689	−	53.2326i	1.23461	−	1.84773i
$831$	−2.60386	+	6.28628i	−0.0903270	+	0.218069i
$832$	5.39593			0.187070
$833$		0			0
$834$	−5.20259			−0.180151
$835$	13.7181	−	33.1185i	0.474736	−	1.14611i
$836$	17.7454	−	26.5578i	0.613737	−	0.918522i
$837$	−1.68876	−	1.68876i	−0.0583720	−	0.0583720i
$838$	11.8858	+	59.7542i	0.410590	+	2.06417i
$839$	−26.4350	−	39.5628i	−0.912637	−	1.36586i	−0.930607	−	0.366020i	$-0.880720\pi$
$839$	−26.4350	−	39.5628i	−0.912637	−	1.36586i	0.0179698	−	0.999839i	$-0.494280\pi$
$840$		0			0
$841$	−60.9278	+	25.2371i	−2.10096	+	0.870245i
$842$	−0.485817	−	1.17287i	−0.0167424	−	0.0404196i
$843$	−4.07868	−	0.811300i	−0.140477	−	0.0279427i
$844$	6.61124	+	9.89442i	0.227568	+	0.340580i
$845$	−82.2470	+	16.3599i	−2.82938	+	0.562799i
$846$	29.3448	+	29.3448i	1.00890	+	1.00890i
$847$		0			0
$848$	8.38687	+	3.47395i	0.288006	+	0.119296i
$849$			3.90711i			0.134092i
$850$	13.8907	+	8.18743i	0.476446	+	0.280827i
$851$	−24.2707			−0.831989
$852$	2.86837	+	1.18812i	0.0982688	+	0.0407043i
$853$	2.30560	−	3.45057i	0.0789422	−	0.118145i	−0.789897	−	0.613239i	$-0.789866\pi$
$853$	2.30560	−	3.45057i	0.0789422	−	0.118145i	0.868840	+	0.495094i	$0.164866\pi$
$854$		0			0
$855$	37.7976	−	7.51841i	1.29265	−	0.257124i
$856$	−6.46338	+	4.31869i	−0.220914	+	0.147610i
$857$	4.07401	−	20.4814i	0.139165	−	0.699632i	−0.846697	−	0.532075i	$-0.821412\pi$
$857$	4.07401	−	20.4814i	0.139165	−	0.699632i	0.985862	−	0.167557i	$-0.0535877\pi$
$858$	−30.0467	+	12.4457i	−1.02578	+	0.424891i
$859$	12.4145	−	5.14224i	0.423576	−	0.175451i	−0.160705	−	0.987003i	$-0.551377\pi$
$859$	12.4145	−	5.14224i	0.423576	−	0.175451i	0.584281	+	0.811552i	$0.301377\pi$
$860$	3.27213	+	0.650867i	0.111579	+	0.0221944i
$861$		0			0
$862$	−3.92361	−	19.7253i	−0.133639	−	0.671846i
$863$	18.3763	−	18.3763i	0.625537	−	0.625537i	−0.321405	−	0.946942i	$-0.604155\pi$
$863$	18.3763	−	18.3763i	0.625537	−	0.625537i	0.946942	+	0.321405i	$0.104155\pi$
$864$	15.5126	+	10.3652i	0.527750	+	0.352631i
$865$	8.78261	+	3.63788i	0.298618	+	0.123691i
$866$	−11.5740			−0.393300
$867$	−9.23399	−	0.772456i	−0.313603	−	0.0262340i
$868$		0			0
$869$	−23.2191	+	56.0559i	−0.787654	+	1.90157i
$870$	−21.1707	−	14.1458i	−0.717753	−	0.479587i
$871$	58.1936	−	58.1936i	1.97181	−	1.97181i
$872$	−3.28870	+	0.654163i	−0.111369	+	0.0221528i
$873$	−15.0783	−	22.5663i	−0.510324	−	0.763754i
$874$	−7.58964	+	38.1557i	−0.256723	+	1.29064i
$875$		0			0
$876$	0.283265	+	0.683861i	0.00957063	+	0.0231055i
$877$	5.54597	−	27.8815i	0.187274	−	0.941490i	−0.766793	−	0.641895i	$-0.778148\pi$
$877$	5.54597	−	27.8815i	0.187274	−	0.941490i	0.954067	−	0.299595i	$-0.0968515\pi$
$878$	32.0144	−	21.3914i	1.08044	−	0.721924i
$879$	−0.624265	−	3.13839i	−0.0210559	−	0.105855i
$880$	−47.1537	−	47.1537i	−1.58955	−	1.58955i
$881$	2.44242	+	1.63198i	0.0822873	+	0.0549826i	0.596033	−	0.802960i	$-0.296743\pi$
$881$	2.44242	+	1.63198i	0.0822873	+	0.0549826i	−0.513746	+	0.857942i	$0.671743\pi$
$882$		0			0
$883$			17.1609i			0.577509i	0.957403	+	0.288755i	$0.0932411\pi$
$883$			17.1609i			0.577509i	−0.957403	+	0.288755i	$0.906759\pi$
$884$	−28.3098	−	16.6864i	−0.952163	−	0.561224i
$885$		−	8.72474i		−	0.293279i
$886$	22.1202	−	53.4028i	0.743142	−	1.79410i
$887$	4.24508	−	6.35321i	0.142536	−	0.213320i	−0.753332	−	0.657640i	$-0.771555\pi$
$887$	4.24508	−	6.35321i	0.142536	−	0.213320i	0.895868	+	0.444320i	$0.146555\pi$
$888$	−3.28089	+	3.28089i	−0.110100	+	0.110100i
$889$		0			0
$890$	7.80944	−	5.21810i	0.261773	−	0.174911i
$891$	31.5445	+	6.27460i	1.05678	+	0.210207i
$892$	0.933075	+	2.25264i	0.0312417	+	0.0754241i
$893$	17.4754	+	42.1893i	0.584791	+	1.41181i
$894$	7.18013	+	1.42822i	0.240139	+	0.0477667i
$895$	19.1094	−	12.7685i	0.638757	−	0.426804i
$896$		0			0
$897$	10.4911	−	10.4911i	0.350288	−	0.350288i
$898$	21.4039	−	32.0331i	0.714256	−	1.06896i
$899$	2.86493	−	6.91655i	0.0955508	−	0.230680i
$900$			7.07971i			0.235990i
$901$	−4.53890	−	6.02681i	−0.151213	−	0.200782i
$902$		−	2.34717i		−	0.0781523i
$903$		0			0
$904$	−22.1495	−	14.7998i	−0.736682	−	0.492235i
$905$	9.65193	+	9.65193i	0.320841	+	0.320841i
$906$	−1.09367	−	5.49825i	−0.0363348	−	0.182667i
$907$	25.1433	−	16.8002i	0.834869	−	0.557842i	−0.0630460	−	0.998011i	$-0.520081\pi$
$907$	25.1433	−	16.8002i	0.834869	−	0.557842i	0.897915	+	0.440169i	$0.145081\pi$
$908$	0.333867	−	1.67846i	0.0110798	−	0.0557017i
$909$	5.38783	+	13.0074i	0.178703	+	0.431428i
$910$		0			0
$911$	0.758034	−	3.81090i	0.0251148	−	0.126261i	−0.966194	−	0.257816i	$-0.916997\pi$
$911$	0.758034	−	3.81090i	0.0251148	−	0.126261i	0.991309	+	0.131555i	$0.0419971\pi$
$912$	7.98997	+	11.9578i	0.264574	+	0.395964i
$913$	65.6770	−	13.0640i	2.17359	−	0.432354i
$914$	−5.35141	+	5.35141i	−0.177009	+	0.177009i
$915$	1.84192	+	1.23073i	0.0608920	+	0.0406867i
$916$	4.14211	−	9.99993i	0.136859	−	0.330407i
$917$		0			0
$918$	−9.95130	−	20.6458i	−0.328442	−	0.681415i
$919$	2.67414			0.0882118			0.0441059	−	0.999027i	$-0.485956\pi$
$919$	2.67414			0.0882118			0.0441059	+	0.999027i	$0.485956\pi$
$920$	14.5346	+	6.02045i	0.479193	+	0.198488i
$921$	10.9154	+	7.29341i	0.359673	+	0.240326i
$922$	45.8685	−	45.8685i	1.51060	−	1.51060i
$923$	6.17377	+	31.0377i	0.203212	+	1.02162i
$924$		0			0
$925$	−12.7266	−	2.53147i	−0.418447	−	0.0832342i
$926$	−22.9386	+	9.50146i	−0.753808	+	0.312237i
$927$	−16.0086	+	6.63100i	−0.525793	+	0.217791i
$928$	−11.4095	+	57.3594i	−0.374535	+	1.88291i
$929$	6.15442	−	4.11225i	0.201920	−	0.134919i	−0.450499	−	0.892777i	$-0.648754\pi$
$929$	6.15442	−	4.11225i	0.201920	−	0.134919i	0.652420	+	0.757858i	$0.273754\pi$
$930$	1.96903	−	0.391664i	0.0645670	−	0.0128432i
$931$		0			0
$932$	−1.20938	+	1.80997i	−0.0396146	+	0.0592875i
$933$	1.62911	+	0.674800i	0.0533347	+	0.0220920i
$934$	−63.4061			−2.07471
$935$	13.8620	+	53.6620i	0.453337	+	1.75494i
$936$			25.8036i			0.843417i
$937$	−8.20064	−	3.39682i	−0.267903	−	0.110969i	0.244688	−	0.969602i	$-0.421314\pi$
$937$	−8.20064	−	3.39682i	−0.267903	−	0.110969i	−0.512591	+	0.858633i	$0.671314\pi$
$938$		0			0
$939$	2.55458	+	2.55458i	0.0833655	+	0.0833655i
$940$	−27.0395	+	5.37849i	−0.881931	+	0.175427i
$941$	−19.8675	−	29.7338i	−0.647662	−	0.969294i	−0.999448	−	0.0332140i	$-0.989426\pi$
$941$	−19.8675	−	29.7338i	−0.647662	−	0.969294i	0.351787	−	0.936080i	$-0.385574\pi$
$942$	−6.62115	−	1.31703i	−0.215729	−	0.0429111i
$943$	0.409769	+	0.989271i	0.0133439	+	0.0322151i
$944$	−27.3655	+	11.3351i	−0.890670	+	0.368928i
$945$		0			0
$946$	5.17592	+	7.74631i	0.168284	+	0.251854i
$947$	3.99355	+	20.0769i	0.129773	+	0.652413i	0.989835	+	0.142223i	$0.0454249\pi$
$947$	3.99355	+	20.0769i	0.129773	+	0.652413i	−0.860062	+	0.510190i	$0.829575\pi$
$948$	5.58604	+	5.58604i	0.181426	+	0.181426i
$949$	−4.19167	+	6.27327i	−0.136067	+	0.203639i
$950$	−7.95939	+	19.2157i	−0.258237	+	0.623438i
$951$	6.18521			0.200569
$952$		0			0
$953$	25.8889			0.838625			0.419312	−	0.907842i	$-0.362271\pi$
$953$	25.8889			0.838625			0.419312	+	0.907842i	$0.362271\pi$
$954$	3.38464	−	8.17125i	0.109582	−	0.264554i
$955$	−36.7366	+	54.9803i	−1.18877	+	1.77912i
$956$	4.04248	+	4.04248i	0.130743	+	0.130743i
$957$	−5.19555	−	26.1198i	−0.167948	−	0.844334i
$958$	11.4952	+	17.2038i	0.371394	+	0.555830i
$959$		0			0
$960$	−1.09471	+	0.453445i	−0.0353317	+	0.0146349i
$961$	−11.6373	−	28.0949i	−0.375397	−	0.906287i
$962$	69.2483	+	13.7744i	2.23266	+	0.444103i
$963$	8.13650	+	12.1771i	0.262195	+	0.392402i
$964$	−16.9893	+	3.37938i	−0.547188	+	0.108842i
$965$	−38.7099	−	38.7099i	−1.24612	−	1.24612i
$966$		0			0
$967$	28.4678	+	11.7917i	0.915462	+	0.379197i	0.790145	−	0.612920i	$-0.210005\pi$
$967$	28.4678	+	11.7917i	0.915462	+	0.379197i	0.125317	+	0.992117i	$0.460005\pi$
$968$		−	20.2886i		−	0.652100i
$969$	−0.674320	−	11.9338i	−0.0216623	−	0.383368i
$970$	48.1367			1.54558
$971$	55.0899	+	22.8190i	1.76792	+	0.732296i	0.995235	+	0.0975065i	$0.0310867\pi$
$971$	55.0899	+	22.8190i	1.76792	+	0.732296i	0.772685	+	0.634790i	$0.218913\pi$
$972$	8.53186	−	12.7688i	0.273660	−	0.409560i
$973$		0			0
$974$	−47.3564	+	9.41978i	−1.51740	+	0.301829i
$975$	6.59534	−	4.40686i	0.211220	−	0.141133i
$976$	1.46722	−	7.37621i	0.0469646	−	0.236107i
$977$	−50.1000	+	20.7521i	−1.60284	+	0.663919i	−0.991814	−	0.127691i	$-0.959244\pi$
$977$	−50.1000	+	20.7521i	−1.60284	+	0.663919i	−0.611028	+	0.791609i	$0.709244\pi$
$978$	11.3602	−	4.70554i	0.363258	−	0.150467i
$979$	9.63508	+	1.91654i	0.307939	+	0.0612528i
$980$		0			0
$981$	1.23246	+	6.19597i	0.0393493	+	0.197822i
$982$	8.16069	−	8.16069i	0.260418	−	0.260418i
$983$	−30.4564	−	20.3503i	−0.971408	−	0.649074i	−0.0347783	−	0.999395i	$-0.511072\pi$
$983$	−30.4564	−	20.3503i	−0.971408	−	0.649074i	−0.936630	+	0.350321i	$0.886072\pi$
$984$	0.189121	+	0.0783365i	0.00602896	+	0.00249728i
$985$	22.9116			0.730025
$986$	47.8541	−	53.5860i	1.52399	−	1.70653i
$987$		0			0
$988$	16.2216	−	39.1624i	0.516078	−	1.24592i
$989$	−3.53386	−	2.36125i	−0.112370	−	0.0750834i
$990$	−45.9414	+	45.9414i	−1.46011	+	1.46011i
$991$	42.4220	−	8.43825i	1.34758	−	0.268050i	0.532023	−	0.846730i	$-0.321432\pi$
$991$	42.4220	−	8.43825i	1.34758	−	0.268050i	0.815555	+	0.578680i	$0.196432\pi$
$992$	−2.56188	−	3.83413i	−0.0813399	−	0.121734i
$993$	2.61257	−	13.1343i	0.0829074	−	0.416803i
$994$		0			0
$995$	−16.6737	−	40.2539i	−0.528592	−	1.27613i
$996$	1.70093	−	8.55118i	0.0538962	−	0.270954i
$997$	−30.4788	+	20.3653i	−0.965272	+	0.644974i	−0.935030	−	0.354568i	$-0.884628\pi$
$997$	−30.4788	+	20.3653i	−0.965272	+	0.644974i	−0.0302423	+	0.999543i	$0.509628\pi$
$998$	−11.3273	−	56.9463i	−0.358560	−	1.80260i
$999$	13.0420	+	13.0420i	0.412630	+	0.412630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.t.d.146.2	yes	72
7.2	even	3		833.2.bc.a.129.8		144
7.3	odd	6		833.2.bc.d.656.2		144
7.4	even	3		833.2.bc.a.656.2		144
7.5	odd	6		833.2.bc.d.129.8		144
7.6	odd	2		833.2.t.a.146.2	yes	72
17.12	odd	16		833.2.t.a.97.2	✓	72
119.12	even	48		833.2.bc.a.80.2		144
119.46	odd	48		833.2.bc.d.607.8		144
119.80	even	48		833.2.bc.a.607.8		144
119.97	even	16	inner	833.2.t.d.97.2	yes	72
119.114	odd	48		833.2.bc.d.80.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.a.97.2	✓	72	17.12	odd	16
833.2.t.a.146.2	yes	72	7.6	odd	2
833.2.t.d.97.2	yes	72	119.97	even	16	inner
833.2.t.d.146.2	yes	72	1.1	even	1	trivial
833.2.bc.a.80.2		144	119.12	even	48
833.2.bc.a.129.8		144	7.2	even	3
833.2.bc.a.607.8		144	119.80	even	48
833.2.bc.a.656.2		144	7.4	even	3
833.2.bc.d.80.2		144	119.114	odd	48
833.2.bc.d.129.8		144	7.5	odd	6
833.2.bc.d.607.8		144	119.46	odd	48
833.2.bc.d.656.2		144	7.3	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.684321 + 1.65210i) q^{2} +(0.302826 - 0.453212i) q^{3} +(-0.846919 - 0.846919i) q^{4} +(0.523006 + 2.62933i) q^{5} +(0.541520 + 0.810442i) q^{6} +(-1.32544 + 0.549014i) q^{8} +(1.03435 + 2.49715i) q^{9} +O(q^{10})\)	\(q+(-0.684321 + 1.65210i) q^{2} +(0.302826 - 0.453212i) q^{3} +(-0.846919 - 0.846919i) q^{4} +(0.523006 + 2.62933i) q^{5} +(0.541520 + 0.810442i) q^{6} +(-1.32544 + 0.549014i) q^{8} +(1.03435 + 2.49715i) q^{9} +(-4.70181 - 0.935249i) q^{10} +(-2.78572 - 4.16913i) q^{11} +(-0.640303 + 0.127364i) q^{12} +(-4.70535 - 4.70535i) q^{13} +(1.35002 + 0.559198i) q^{15} -4.96091i q^{16} +(-2.09362 + 3.55201i) q^{17} -4.83337 q^{18} +(-4.91367 - 2.03531i) q^{19} +(1.78388 - 2.66977i) q^{20} +(8.79414 - 1.74926i) q^{22} +(-3.40111 + 2.27255i) q^{23} +(-0.152558 + 0.766960i) q^{24} +(-2.02043 + 0.836891i) q^{25} +(10.9937 - 4.55373i) q^{26} +(3.04877 + 0.606437i) q^{27} +(1.90098 + 9.55688i) q^{29} +(-1.84770 + 1.84770i) q^{30} +(-0.638820 - 0.426846i) q^{31} +(5.54503 + 2.29683i) q^{32} -2.73309 q^{33} +(-4.43555 - 5.88958i) q^{34} +(1.23887 - 2.99090i) q^{36} +(4.93349 + 3.29645i) q^{37} +(6.72506 - 6.72506i) q^{38} +(-3.55742 + 0.707616i) q^{39} +(-2.13675 - 3.19787i) q^{40} +(0.0510695 - 0.256744i) q^{41} +(0.397620 + 0.959941i) q^{43} +(-1.17163 + 5.89020i) q^{44} +(-6.02485 + 4.02568i) q^{45} +(-1.42702 - 7.17412i) q^{46} +(-6.07130 - 6.07130i) q^{47} +(-2.24834 - 1.50229i) q^{48} -3.91066i q^{50} +(0.975807 + 2.02450i) q^{51} +7.97010i q^{52} +(-0.700266 + 1.69059i) q^{53} +(-3.08823 + 4.62186i) q^{54} +(9.50506 - 9.50506i) q^{55} +(-2.41041 + 1.61059i) q^{57} +(-17.0898 - 3.39937i) q^{58} +(-2.28490 - 5.51623i) q^{59} +(-0.669765 - 1.61696i) q^{60} +(1.48687 + 0.295757i) q^{61} +(1.14235 - 0.763294i) q^{62} +(-0.573383 + 0.573383i) q^{64} +(9.91098 - 14.8328i) q^{65} +(1.87031 - 4.51533i) q^{66} +12.3675i q^{67} +(4.78139 - 1.23513i) q^{68} +2.22961i q^{69} +(-3.95416 - 2.64209i) q^{71} +(-2.74194 - 2.74194i) q^{72} +(-0.221196 - 1.11203i) q^{73} +(-8.82216 + 5.89478i) q^{74} +(-0.232552 + 1.16912i) q^{75} +(2.43774 + 5.88522i) q^{76} +(1.26537 - 6.36145i) q^{78} +(-6.72273 - 10.0613i) q^{79} +(13.0438 - 2.59458i) q^{80} +(-4.53561 + 4.53561i) q^{81} +(0.389218 + 0.260067i) q^{82} +(-5.11069 + 12.3383i) q^{83} +(-10.4344 - 3.64710i) q^{85} -1.85802 q^{86} +(4.90696 + 2.03253i) q^{87} +(5.98122 + 3.99652i) q^{88} +(-1.38538 + 1.38538i) q^{89} +(-2.52788 - 12.7085i) q^{90} +(4.80513 + 0.955800i) q^{92} +(-0.386903 + 0.160261i) q^{93} +(14.1851 - 5.87566i) q^{94} +(2.78161 - 13.9841i) q^{95} +(2.72013 - 1.81753i) q^{96} +(-9.84825 + 1.95894i) q^{97} +(7.52952 - 11.2687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9}+O(q^{10}) \) 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9	\( 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{13} - 40 q^{18} + 24 q^{19} + 24 q^{22} + 8 q^{23} - 24 q^{24} + 8 q^{25} + 8 q^{27} + 80 q^{31} - 40 q^{32} - 80 q^{33} + 120 q^{36} + 48 q^{37} - 56 q^{38} - 16 q^{39} - 32 q^{40} + 24 q^{41} + 24 q^{43} + 32 q^{44} - 48 q^{45} - 40 q^{47} - 40 q^{51} - 24 q^{53} + 200 q^{54} - 48 q^{57} + 32 q^{58} + 8 q^{59} - 80 q^{60} + 128 q^{62} - 24 q^{65} - 8 q^{66} - 40 q^{68} - 48 q^{73} - 32 q^{74} + 128 q^{75} + 72 q^{76} - 48 q^{78} - 32 q^{79} + 256 q^{80} + 16 q^{81} - 152 q^{82} - 32 q^{85} - 80 q^{86} - 64 q^{87} + 56 q^{88} - 64 q^{89} - 376 q^{90} - 216 q^{92} - 32 q^{93} - 128 q^{94} + 32 q^{95} + 32 q^{96} - 8 q^{97} + 40 q^{99}+O(q^{100}) \) 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^13 - 40 * q^18 + 24 * q^19 + 24 * q^22 + 8 * q^23 - 24 * q^24 + 8 * q^25 + 8 * q^27 + 80 * q^31 - 40 * q^32 - 80 * q^33 + 120 * q^36 + 48 * q^37 - 56 * q^38 - 16 * q^39 - 32 * q^40 + 24 * q^41 + 24 * q^43 + 32 * q^44 - 48 * q^45 - 40 * q^47 - 40 * q^51 - 24 * q^53 + 200 * q^54 - 48 * q^57 + 32 * q^58 + 8 * q^59 - 80 * q^60 + 128 * q^62 - 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 - 32 * q^74 + 128 * q^75 + 72 * q^76 - 48 * q^78 - 32 * q^79 + 256 * q^80 + 16 * q^81 - 152 * q^82 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 56 * q^88 - 64 * q^89 - 376 * q^90 - 216 * q^92 - 32 * q^93 - 128 * q^94 + 32 * q^95 + 32 * q^96 - 8 * q^97 + 40 * q^99

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