LMFDB - Embedded newform 231.2.p.a.208.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (of order $6$, degree $2$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			208.4
Character	$\chi$	$=$	231.208
Dual form			231.2.p.a.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49489 - 0.863074i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.489794 + 0.848348i) q^{4} +(1.43342 + 0.827587i) q^{5} +1.72615 q^{6} +(-2.00786 - 1.72293i) q^{7} +1.76138i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.49489 - 0.863074i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.489794 + 0.848348i) q^{4} +(1.43342 + 0.827587i) q^{5} +1.72615 q^{6} +(-2.00786 - 1.72293i) q^{7} +1.76138i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.42854 - 2.47430i) q^{10} +(3.00374 + 1.40625i) q^{11} +(-0.848348 - 0.489794i) q^{12} +2.97508 q^{13} +(1.51451 + 4.30852i) q^{14} -1.65517 q^{15} +(2.49979 - 4.32977i) q^{16} +(0.747692 + 1.29504i) q^{17} +(-1.49489 + 0.863074i) q^{18} +(2.75805 - 4.77708i) q^{19} +1.62139i q^{20} +(2.60032 + 0.488171i) q^{21} +(-3.27656 - 4.69464i) q^{22} +(4.31421 - 7.47244i) q^{23} +(-0.880692 - 1.52540i) q^{24} +(-1.13020 - 1.95756i) q^{25} +(-4.44742 - 2.56772i) q^{26} +1.00000i q^{27} +(0.478206 - 2.54725i) q^{28} +8.02774i q^{29} +(2.47430 + 1.42854i) q^{30} +(7.67855 - 4.43321i) q^{31} +(-4.42301 + 2.55363i) q^{32} +(-3.30444 + 0.284023i) q^{33} -2.58126i q^{34} +(-1.45224 - 4.13137i) q^{35} +0.979587 q^{36} +(-4.11387 + 7.12543i) q^{37} +(-8.24595 + 4.76080i) q^{38} +(-2.57650 + 1.48754i) q^{39} +(-1.45770 + 2.52481i) q^{40} +8.12983 q^{41} +(-3.46587 - 2.97403i) q^{42} +5.03560i q^{43} +(0.278226 + 3.23699i) q^{44} +(1.43342 - 0.827587i) q^{45} +(-12.8985 + 7.44697i) q^{46} +(-6.38129 - 3.68424i) q^{47} +4.99958i q^{48} +(1.06302 + 6.91881i) q^{49} +3.90179i q^{50} +(-1.29504 - 0.747692i) q^{51} +(1.45718 + 2.52390i) q^{52} +(0.630245 + 1.09162i) q^{53} +(0.863074 - 1.49489i) q^{54} +(3.14184 + 4.50161i) q^{55} +(3.03474 - 3.53661i) q^{56} +5.51610i q^{57} +(6.92854 - 12.0006i) q^{58} +(-4.30283 + 2.48424i) q^{59} +(-0.810694 - 1.40416i) q^{60} +(1.82951 - 3.16880i) q^{61} -15.3048 q^{62} +(-2.49603 + 0.877394i) q^{63} -1.18329 q^{64} +(4.26455 + 2.46214i) q^{65} +(5.18490 + 2.42739i) q^{66} +(5.36799 + 9.29763i) q^{67} +(-0.732430 + 1.26861i) q^{68} +8.62843i q^{69} +(-1.39474 + 7.42932i) q^{70} -1.05369 q^{71} +(1.52540 + 0.880692i) q^{72} +(-4.92537 - 8.53099i) q^{73} +(12.2996 - 7.10115i) q^{74} +(1.95756 + 1.13020i) q^{75} +5.40350 q^{76} +(-3.60823 - 7.99879i) q^{77} +5.13544 q^{78} +(-3.41161 - 1.96969i) q^{79} +(7.16651 - 4.13759i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-12.1532 - 7.01665i) q^{82} -10.2146 q^{83} +(0.859484 + 2.44508i) q^{84} +2.47512i q^{85} +(4.34610 - 7.52766i) q^{86} +(-4.01387 - 6.95223i) q^{87} +(-2.47694 + 5.29074i) q^{88} +(-4.47304 - 2.58251i) q^{89} -2.85707 q^{90} +(-5.97356 - 5.12586i) q^{91} +8.45230 q^{92} +(-4.43321 + 7.67855i) q^{93} +(6.35954 + 11.0150i) q^{94} +(7.90690 - 4.56505i) q^{95} +(2.55363 - 4.42301i) q^{96} -3.35986i q^{97} +(4.38235 - 11.2603i) q^{98} +(2.71972 - 1.89819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.49489	−	0.863074i	−1.05705	−	0.610286i	−0.132432	−	0.991192i	$-0.542279\pi$
$2$	−1.49489	−	0.863074i	−1.05705	−	0.610286i	−0.924614	+	0.380907i	$0.875612\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.489794	+	0.848348i	0.244897	+	0.424174i
$5$	1.43342	+	0.827587i	0.641046	+	0.370108i	0.785017	−	0.619474i	$-0.212654\pi$
$5$	1.43342	+	0.827587i	0.641046	+	0.370108i	−0.143971	+	0.989582i	$0.545987\pi$
$6$	1.72615			0.704697
$7$	−2.00786	−	1.72293i	−0.758900	−	0.651207i
$7$	−2.00786	−	1.72293i	−0.758900	−	0.651207i
$8$			1.76138i			0.622743i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.42854	−	2.47430i	−0.451743	−	0.782442i
$11$	3.00374	+	1.40625i	0.905662	+	0.424000i
$11$	3.00374	+	1.40625i	0.905662	+	0.424000i
$12$	−0.848348	−	0.489794i	−0.244897	−	0.141391i
$13$	2.97508			0.825140			0.412570	−	0.910926i	$-0.364631\pi$
$13$	2.97508			0.825140			0.412570	+	0.910926i	$0.364631\pi$
$14$	1.51451	+	4.30852i	0.404770	+	1.15150i
$15$	−1.65517			−0.427364
$16$	2.49979	−	4.32977i	0.624948	−	1.08244i
$17$	0.747692	+	1.29504i	0.181342	+	0.314094i	0.942338	−	0.334663i	$-0.108623\pi$
$17$	0.747692	+	1.29504i	0.181342	+	0.314094i	−0.760996	+	0.648757i	$0.775289\pi$
$18$	−1.49489	+	0.863074i	−0.352349	+	0.203429i
$19$	2.75805	−	4.77708i	0.632740	−	1.09594i	−0.354249	−	0.935151i	$-0.615264\pi$
$19$	2.75805	−	4.77708i	0.632740	−	1.09594i	0.986989	−	0.160786i	$-0.0514031\pi$
$20$			1.62139i			0.362553i
$21$	2.60032	+	0.488171i	0.567437	+	0.106528i
$22$	−3.27656	−	4.69464i	−0.698565	−	1.00090i
$23$	4.31421	−	7.47244i	0.899576	−	1.55811i	0.0715389	−	0.997438i	$-0.477209\pi$
$23$	4.31421	−	7.47244i	0.899576	−	1.55811i	0.828037	−	0.560673i	$-0.189458\pi$
$24$	−0.880692	−	1.52540i	−0.179770	−	0.311372i
$25$	−1.13020	−	1.95756i	−0.226040	−	0.391513i
$26$	−4.44742	−	2.56772i	−0.872210	−	0.503571i
$27$			1.00000i			0.192450i
$28$	0.478206	−	2.54725i	0.0903725	−	0.481384i
$29$			8.02774i			1.49071i	0.666665	+	0.745357i	$0.267721\pi$
$29$			8.02774i			1.49071i	−0.666665	+	0.745357i	$0.732279\pi$
$30$	2.47430	+	1.42854i	0.451743	+	0.260814i
$31$	7.67855	−	4.43321i	1.37911	−	0.796229i	0.387056	−	0.922056i	$-0.373492\pi$
$31$	7.67855	−	4.43321i	1.37911	−	0.796229i	0.992052	+	0.125827i	$0.0401585\pi$
$32$	−4.42301	+	2.55363i	−0.781886	+	0.451422i
$33$	−3.30444	+	0.284023i	−0.575229	+	0.0494421i
$34$		−	2.58126i		−	0.442682i
$35$	−1.45224	−	4.13137i	−0.245473	−	0.698329i
$36$	0.979587			0.163265
$37$	−4.11387	+	7.12543i	−0.676316	+	1.17141i	0.299766	+	0.954013i	$0.403091\pi$
$37$	−4.11387	+	7.12543i	−0.676316	+	1.17141i	−0.976082	+	0.217401i	$0.930242\pi$
$38$	−8.24595	+	4.76080i	−1.33767	+	0.772304i
$39$	−2.57650	+	1.48754i	−0.412570	+	0.238197i
$40$	−1.45770	+	2.52481i	−0.230482	+	0.399207i
$41$	8.12983			1.26967			0.634833	−	0.772649i	$-0.281069\pi$
$41$	8.12983			1.26967			0.634833	+	0.772649i	$0.281069\pi$
$42$	−3.46587	−	2.97403i	−0.534795	−	0.458903i
$43$			5.03560i			0.767922i	0.923349	+	0.383961i	$0.125440\pi$
$43$			5.03560i			0.767922i	−0.923349	+	0.383961i	$0.874560\pi$
$44$	0.278226	+	3.23699i	0.0419441	+	0.487994i
$45$	1.43342	−	0.827587i	0.213682	−	0.123369i
$46$	−12.8985	+	7.44697i	−1.90179	+	1.09800i
$47$	−6.38129	−	3.68424i	−0.930806	−	0.537401i	−0.0437397	−	0.999043i	$-0.513927\pi$
$47$	−6.38129	−	3.68424i	−0.930806	−	0.537401i	−0.887066	+	0.461642i	$0.847261\pi$
$48$			4.99958i			0.721628i
$49$	1.06302	+	6.91881i	0.151860	+	0.988402i
$50$			3.90179i			0.551796i
$51$	−1.29504	−	0.747692i	−0.181342	−	0.104698i
$52$	1.45718	+	2.52390i	0.202074	+	0.350003i
$53$	0.630245	+	1.09162i	0.0865708	+	0.149945i	0.906059	−	0.423150i	$-0.139076\pi$
$53$	0.630245	+	1.09162i	0.0865708	+	0.149945i	−0.819489	+	0.573095i	$0.805742\pi$
$54$	0.863074	−	1.49489i	0.117450	−	0.203429i
$55$	3.14184	+	4.50161i	0.423645	+	0.606996i
$56$	3.03474	−	3.53661i	0.405534	−	0.472600i
$57$			5.51610i			0.730625i
$58$	6.92854	−	12.0006i	0.909762	−	1.57575i
$59$	−4.30283	+	2.48424i	−0.560181	+	0.323421i	−0.753218	−	0.657771i	$-0.771499\pi$
$59$	−4.30283	+	2.48424i	−0.560181	+	0.323421i	0.193037	+	0.981191i	$0.438166\pi$
$60$	−0.810694	−	1.40416i	−0.104660	−	0.181277i
$61$	1.82951	−	3.16880i	0.234244	−	0.405723i	−0.724808	−	0.688951i	$-0.758072\pi$
$61$	1.82951	−	3.16880i	0.234244	−	0.405723i	0.959053	+	0.283227i	$0.0914050\pi$
$62$	−15.3048			−1.94371
$63$	−2.49603	+	0.877394i	−0.314471	+	0.110541i
$64$	−1.18329			−0.147911
$65$	4.26455	+	2.46214i	0.528952	+	0.305391i
$66$	5.18490	+	2.42739i	0.638217	+	0.298792i
$67$	5.36799	+	9.29763i	0.655804	+	1.13589i	0.981692	+	0.190478i	$0.0610037\pi$
$67$	5.36799	+	9.29763i	0.655804	+	1.13589i	−0.325887	+	0.945409i	$0.605663\pi$
$68$	−0.732430	+	1.26861i	−0.0888202	+	0.153841i
$69$			8.62843i			1.03874i
$70$	−1.39474	+	7.42932i	−0.166703	+	0.887974i
$71$	−1.05369			−0.125050			−0.0625250	−	0.998043i	$-0.519915\pi$
$71$	−1.05369			−0.125050			−0.0625250	+	0.998043i	$0.519915\pi$
$72$	1.52540	+	0.880692i	0.179770	+	0.103791i
$73$	−4.92537	−	8.53099i	−0.576471	−	0.998477i	−0.995880	−	0.0906797i	$-0.971096\pi$
$73$	−4.92537	−	8.53099i	−0.576471	−	0.998477i	0.419409	−	0.907797i	$-0.362237\pi$
$74$	12.2996	−	7.10115i	1.42979	−	0.825492i
$75$	1.95756	+	1.13020i	0.226040	+	0.130504i
$76$	5.40350			0.619824
$77$	−3.60823	−	7.99879i	−0.411196	−	0.911547i
$78$	5.13544			0.581474
$79$	−3.41161	−	1.96969i	−0.383836	−	0.221608i	0.295650	−	0.955296i	$-0.404464\pi$
$79$	−3.41161	−	1.96969i	−0.383836	−	0.221608i	−0.679486	+	0.733689i	$0.737797\pi$
$80$	7.16651	−	4.13759i	0.801241	−	0.462597i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−12.1532	−	7.01665i	−1.34210	−	0.774859i
$83$	−10.2146			−1.12120			−0.560600	−	0.828087i	$-0.689429\pi$
$83$	−10.2146			−1.12120			−0.560600	+	0.828087i	$0.689429\pi$
$84$	0.859484	+	2.44508i	0.0937774	+	0.266780i
$85$			2.47512i			0.268465i
$86$	4.34610	−	7.52766i	0.468652	−	0.811728i
$87$	−4.01387	−	6.95223i	−0.430332	−	0.745357i
$88$	−2.47694	+	5.29074i	−0.264043	+	0.563995i
$89$	−4.47304	−	2.58251i	−0.474142	−	0.273746i	0.243830	−	0.969818i	$-0.421596\pi$
$89$	−4.47304	−	2.58251i	−0.474142	−	0.273746i	−0.717972	+	0.696072i	$0.754929\pi$
$90$	−2.85707			−0.301162
$91$	−5.97356	−	5.12586i	−0.626199	−	0.537336i
$92$	8.45230			0.881213
$93$	−4.43321	+	7.67855i	−0.459703	+	0.796229i
$94$	6.35954	+	11.0150i	0.655936	+	1.13612i
$95$	7.90690	−	4.56505i	0.811231	−	0.468364i
$96$	2.55363	−	4.42301i	0.260629	−	0.451422i
$97$		−	3.35986i		−	0.341142i	−0.985345	−	0.170571i	$-0.945439\pi$
$97$		−	3.35986i		−	0.341142i	0.985345	−	0.170571i	$-0.0545613\pi$
$98$	4.38235	−	11.2603i	0.442685	−	1.13746i
$99$	2.71972	−	1.89819i	0.273342	−	0.190775i
$100$	1.10713	−	1.91761i	0.110713	−	0.191761i
$101$	4.17003	+	7.22271i	0.414934	+	0.718687i	0.995422	−	0.0955825i	$-0.0304714\pi$
$101$	4.17003	+	7.22271i	0.414934	+	0.718687i	−0.580488	+	0.814269i	$0.697138\pi$
$102$	1.29063	+	2.23543i	0.127791	+	0.221341i
$103$	3.61980	+	2.08989i	0.356669	+	0.205923i	0.667619	−	0.744503i	$-0.267314\pi$
$103$	3.61980	+	2.08989i	0.356669	+	0.205923i	−0.310950	+	0.950426i	$0.600647\pi$
$104$			5.24026i			0.513850i
$105$	3.32336	+	2.85175i	0.324327	+	0.278302i
$106$		−	2.17579i		−	0.211332i
$107$	−2.47468	−	1.42876i	−0.239236	−	0.138123i	0.375589	−	0.926786i	$-0.377440\pi$
$107$	−2.47468	−	1.42876i	−0.239236	−	0.138123i	−0.614826	+	0.788663i	$0.710774\pi$
$108$	−0.848348	+	0.489794i	−0.0816323	+	0.0471304i
$109$	7.10543	−	4.10232i	0.680576	−	0.392931i	−0.119496	−	0.992835i	$-0.538128\pi$
$109$	7.10543	−	4.10232i	0.680576	−	0.392931i	0.800072	+	0.599904i	$0.204794\pi$
$110$	−0.811476	−	9.44103i	−0.0773712	−	0.900167i
$111$		−	8.22774i		−	0.780943i
$112$	−12.4791	+	4.38660i	−1.17917	+	0.414495i
$113$	−2.03684			−0.191609			−0.0958047	−	0.995400i	$-0.530542\pi$
$113$	−2.03684			−0.191609			−0.0958047	+	0.995400i	$0.530542\pi$
$114$	4.76080	−	8.24595i	0.445890	−	0.772304i
$115$	12.3682	−	7.14077i	1.15334	−	0.665881i
$116$	−6.81032	+	3.93194i	−0.632322	+	0.365071i
$117$	1.48754	−	2.57650i	0.137523	−	0.238197i
$118$	8.57633			0.789515
$119$	0.730003	−	3.88849i	0.0669193	−	0.356457i
$120$		−	2.91540i		−	0.266138i
$121$	7.04493	+	8.44802i	0.640448	+	0.768002i
$122$	−5.46982	+	3.15800i	−0.495214	+	0.285912i
$123$	−7.04064	+	4.06492i	−0.634833	+	0.366521i
$124$	7.52181	+	4.34272i	0.675479	+	0.389988i
$125$		−	12.0172i		−	1.07485i
$126$	4.48855	+	0.842655i	0.399871	+	0.0750697i
$127$		−	14.2795i		−	1.26710i	−0.773703	−	0.633549i	$-0.781598\pi$
$127$		−	14.2795i		−	1.26710i	0.773703	−	0.633549i	$-0.218402\pi$
$128$	10.6149	+	6.12852i	0.938234	+	0.541690i
$129$	−2.51780	−	4.36096i	−0.221680	−	0.383961i
$130$	−4.25002	−	7.36125i	−0.372751	−	0.645624i
$131$	0.300186	−	0.519937i	0.0262273	−	0.0454271i	−0.852614	−	0.522542i	$-0.824984\pi$
$131$	0.300186	−	0.519937i	0.0262273	−	0.0454271i	0.878841	+	0.477114i	$0.158317\pi$
$132$	−1.85944	−	2.66420i	−0.161844	−	0.231889i
$133$	−13.7684	+	4.83979i	−1.19387	+	0.419663i
$134$		−	18.5319i		−	1.60091i
$135$	−0.827587	+	1.43342i	−0.0712273	+	0.123369i
$136$	−2.28106	+	1.31697i	−0.195600	+	0.112930i
$137$	7.14793	+	12.3806i	0.610689	+	1.05774i	0.991124	+	0.132937i	$0.0424408\pi$
$137$	7.14793	+	12.3806i	0.610689	+	1.05774i	−0.380435	+	0.924807i	$0.624226\pi$
$138$	7.44697	−	12.8985i	0.633928	−	1.09800i
$139$	1.20134			0.101896			0.0509482	−	0.998701i	$-0.483776\pi$
$139$	1.20134			0.101896			0.0509482	+	0.998701i	$0.483776\pi$
$140$	2.79354	−	3.25552i	0.236097	−	0.275142i
$141$	7.36847			0.620537
$142$	1.57515	+	0.909412i	0.132183	+	0.0763162i
$143$	8.93638	+	4.18371i	0.747298	+	0.349859i
$144$	−2.49979	−	4.32977i	−0.208316	−	0.360814i
$145$	−6.64365	+	11.5071i	−0.551725	+	0.955617i
$146$			17.0038i			1.40725i
$147$	−4.38001	−	5.46036i	−0.361257	−	0.450363i
$148$	−8.05979			−0.662511
$149$	−15.0715	−	8.70151i	−1.23470	−	0.712856i	−0.266696	−	0.963781i	$-0.585932\pi$
$149$	−15.0715	−	8.70151i	−1.23470	−	0.712856i	−0.968006	+	0.250925i	$0.919265\pi$
$150$	−1.95089	−	3.37905i	−0.159290	−	0.275898i
$151$	7.02803	−	4.05764i	0.571933	−	0.330206i	−0.185988	−	0.982552i	$-0.559549\pi$
$151$	7.02803	−	4.05764i	0.571933	−	0.330206i	0.757921	+	0.652346i	$0.226215\pi$
$152$	8.41427	+	4.85798i	0.682487	+	0.394034i
$153$	1.49538			0.120895
$154$	−1.50965	+	15.0715i	−0.121651	+	1.21449i
$155$	14.6755			1.17876
$156$	−2.52390	−	1.45718i	−0.202074	−	0.116668i
$157$	6.99748	−	4.04000i	0.558460	−	0.322427i	−0.194067	−	0.980988i	$-0.562168\pi$
$157$	6.99748	−	4.04000i	0.558460	−	0.322427i	0.752527	+	0.658561i	$0.228835\pi$
$158$	3.39998	+	5.88894i	0.270488	+	0.468499i
$159$	−1.09162	−	0.630245i	−0.0865708	−	0.0499817i
$160$	−8.45339			−0.668299
$161$	−21.5368	+	7.57053i	−1.69734	+	0.596642i
$162$			1.72615i			0.135619i
$163$	−6.36643	+	11.0270i	−0.498657	+	0.863699i	−0.999999	−	0.00155000i	$-0.999507\pi$
$163$	−6.36643	+	11.0270i	−0.498657	+	0.863699i	0.501342	+	0.865249i	$0.332840\pi$
$164$	3.98194	+	6.89692i	0.310937	+	0.538559i
$165$	−4.97171	−	2.32759i	−0.387047	−	0.181202i
$166$	15.2697	+	8.81597i	1.18516	+	0.684252i
$167$	−19.0316			−1.47271			−0.736356	−	0.676594i	$-0.763455\pi$
$167$	−19.0316			−1.47271			−0.736356	+	0.676594i	$0.763455\pi$
$168$	−0.859856	+	4.58017i	−0.0663393	+	0.353368i
$169$	−4.14888			−0.319144
$170$	2.13621	−	3.70003i	0.163840	−	0.283779i
$171$	−2.75805	−	4.77708i	−0.210913	−	0.365312i
$172$	−4.27194	+	2.46641i	−0.325732	+	0.188062i
$173$	1.41953	−	2.45869i	0.107925	−	0.186931i	−0.807005	−	0.590545i	$-0.798913\pi$
$173$	1.41953	−	2.45869i	0.107925	−	0.186931i	0.914929	+	0.403614i	$0.132246\pi$
$174$			13.8571i			1.05050i
$175$	−1.10346	+	5.87778i	−0.0834139	+	0.444318i
$176$	13.5975	−	9.49017i	1.02495	−	0.715348i
$177$	2.48424	−	4.30283i	0.186727	−	0.323421i
$178$	4.45780	+	7.72113i	0.334126	+	0.578723i
$179$	1.47898	+	2.56166i	0.110544	+	0.191468i	0.915990	−	0.401202i	$-0.131407\pi$
$179$	1.47898	+	2.56166i	0.110544	+	0.191468i	−0.805446	+	0.592669i	$0.798074\pi$
$180$	1.40416	+	0.810694i	0.104660	+	0.0604255i
$181$		−	16.1267i		−	1.19869i	−0.800492	−	0.599343i	$-0.795429\pi$
$181$		−	16.1267i		−	1.19869i	0.800492	−	0.599343i	$-0.204571\pi$
$182$	4.50580	+	12.8182i	0.333992	+	0.950149i
$183$			3.65902i			0.270482i
$184$	13.1618	+	7.59899i	0.970303	+	0.560205i
$185$	−11.7938	+	6.80917i	−0.867099	+	0.500620i
$186$	13.2543	−	7.65238i	0.971854	−	0.561100i
$187$	0.424724	+	4.94141i	0.0310589	+	0.361352i
$188$		−	7.21806i		−	0.526431i
$189$	1.72293	−	2.00786i	0.125325	−	0.146050i
$190$	−15.7599			−1.14334
$191$	−7.56148	+	13.0969i	−0.547130	+	0.947657i	0.451340	+	0.892352i	$0.350946\pi$
$191$	−7.56148	+	13.0969i	−0.547130	+	0.947657i	−0.998470	+	0.0553044i	$0.982387\pi$
$192$	1.02476	−	0.591644i	0.0739555	−	0.0426982i
$193$	−5.53124	+	3.19346i	−0.398147	+	0.229870i	−0.685684	−	0.727899i	$-0.740497\pi$
$193$	−5.53124	+	3.19346i	−0.398147	+	0.229870i	0.287537	+	0.957770i	$0.407164\pi$
$194$	−2.89981	+	5.02262i	−0.208194	+	0.360603i
$195$	−4.92428			−0.352635
$196$	−5.34890	+	4.29060i	−0.382064	+	0.306471i
$197$			22.4207i			1.59741i	0.601721	+	0.798706i	$0.294482\pi$
$197$			22.4207i			1.59741i	−0.601721	+	0.798706i	$0.705518\pi$
$198$	−5.70395	+	0.490266i	−0.405362	+	0.0348417i
$199$	−20.9450	+	12.0926i	−1.48475	+	0.857222i	−0.999850	−	0.0173466i	$-0.994478\pi$
$199$	−20.9450	+	12.0926i	−1.48475	+	0.857222i	−0.484902	+	0.874568i	$0.661145\pi$
$200$	3.44802	−	1.99072i	0.243812	−	0.140765i
$201$	−9.29763	−	5.36799i	−0.655804	−	0.378629i
$202$		−	14.3962i		−	1.01291i
$203$	13.8312	−	16.1186i	0.970763	−	1.13130i
$204$		−	1.46486i		−	0.102561i
$205$	11.6535	+	6.72814i	0.813914	+	0.469914i
$206$	−3.60746	−	6.24830i	−0.251344	−	0.435340i
$207$	−4.31421	−	7.47244i	−0.299859	−	0.519370i
$208$	7.43709	−	12.8814i	0.515669	−	0.893166i
$209$	15.0022	−	10.4706i	1.03773	−	0.724267i
$210$	−2.50678	−	7.13135i	−0.172984	−	0.492110i
$211$			3.05467i			0.210292i	0.994457	+	0.105146i	$0.0335311\pi$
$211$			3.05467i			0.210292i	−0.994457	+	0.105146i	$0.966469\pi$
$212$	−0.617380	+	1.06933i	−0.0424018	+	0.0734422i
$213$	0.912522	−	0.526845i	0.0625250	−	0.0360988i
$214$	2.46625	+	4.27166i	0.168589	+	0.292005i
$215$	−4.16740	+	7.21814i	−0.284214	+	0.492273i
$216$	−1.76138			−0.119847
$217$	−23.0556	−	4.32833i	−1.56512	−	0.293826i
$218$	−14.1624			−0.959200
$219$	8.53099	+	4.92537i	0.576471	+	0.332826i
$220$	−2.28007	+	4.87023i	−0.153723	+	0.328351i
$221$	2.22445	+	3.85286i	0.149633	+	0.259171i
$222$	−7.10115	+	12.2996i	−0.476598	+	0.825492i
$223$		−	9.90928i		−	0.663575i	−0.943354	−	0.331787i	$-0.892348\pi$
$223$		−	9.90928i		−	0.663575i	0.943354	−	0.331787i	$-0.107652\pi$
$224$	13.2805	+	2.49321i	0.887342	+	0.166585i
$225$	−2.26040			−0.150693
$226$	3.04484	+	1.75794i	0.202540	+	0.116936i
$227$	−6.64550	−	11.5103i	−0.441077	−	0.763969i	0.556692	−	0.830719i	$-0.312070\pi$
$227$	−6.64550	−	11.5103i	−0.441077	−	0.763969i	−0.997770	+	0.0667503i	$0.978737\pi$
$228$	−4.67957	+	2.70175i	−0.309912	+	0.178928i
$229$	7.45825	+	4.30602i	0.492855	+	0.284550i	0.725758	−	0.687950i	$-0.241489\pi$
$229$	7.45825	+	4.30602i	0.492855	+	0.284550i	−0.232903	+	0.972500i	$0.574822\pi$
$230$	−24.6521			−1.62551
$231$	7.12421	+	5.12304i	0.468739	+	0.337072i
$232$	−14.1399			−0.928332
$233$	0.354673	+	0.204771i	0.0232354	+	0.0134150i	0.511573	−	0.859240i	$-0.329063\pi$
$233$	0.354673	+	0.204771i	0.0232354	+	0.0134150i	−0.488337	+	0.872655i	$0.662396\pi$
$234$	−4.44742	+	2.56772i	−0.290737	+	0.167857i
$235$	−6.09805	−	10.5621i	−0.397793	−	0.688998i
$236$	−4.21500	−	2.43353i	−0.274373	−	0.158409i
$237$	3.93938			0.255891
$238$	−4.44733	+	5.18281i	−0.288277	+	0.335951i
$239$			0.631535i			0.0408506i	0.999791	+	0.0204253i	$0.00650203\pi$
$239$			0.631535i			0.0408506i	−0.999791	+	0.0204253i	$0.993498\pi$
$240$	−4.13759	+	7.16651i	−0.267080	+	0.462597i
$241$	2.97320	+	5.14973i	0.191520	+	0.331723i	0.945754	−	0.324883i	$-0.105325\pi$
$241$	2.97320	+	5.14973i	0.191520	+	0.331723i	−0.754234	+	0.656606i	$0.771992\pi$
$242$	−3.24011	−	18.7091i	−0.208282	−	1.20267i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.58433			0.229463
$245$	−4.20216	+	10.7973i	−0.268466	+	0.689816i
$246$	14.0333			0.894730
$247$	8.20543	−	14.2122i	0.522099	−	0.904302i
$248$	7.80859	+	13.5249i	0.495846	+	0.858830i
$249$	8.84612	−	5.10731i	0.560600	−	0.323662i
$250$	−10.3718	+	17.9644i	−0.655967	+	1.13617i
$251$		−	0.396714i		−	0.0250404i	−0.999922	−	0.0125202i	$-0.996015\pi$
$251$		−	0.396714i		−	0.0250404i	0.999922	−	0.0125202i	$-0.00398540\pi$
$252$	−1.96688	−	1.68776i	−0.123902	−	0.106319i
$253$	23.4669	−	16.3784i	1.47535	−	1.02970i
$254$	−12.3242	+	21.3462i	−0.773291	+	1.33938i
$255$	−1.23756	−	2.14352i	−0.0774991	−	0.134232i
$256$	−9.39545	−	16.2734i	−0.587215	−	1.01709i
$257$	−15.6290	−	9.02343i	−0.974912	−	0.562866i	−0.0741820	−	0.997245i	$-0.523635\pi$
$257$	−15.6290	−	9.02343i	−0.974912	−	0.562866i	−0.900730	+	0.434379i	$0.856968\pi$
$258$			8.69219i			0.541152i
$259$	20.5367	−	7.21897i	1.27609	−	0.448565i
$260$			4.82376i			0.299157i
$261$	6.95223	+	4.01387i	0.430332	+	0.248452i
$262$	−0.897488	+	0.518165i	−0.0554470	+	0.0320123i
$263$	0.484812	−	0.279906i	0.0298948	−	0.0172598i	−0.484978	−	0.874526i	$-0.661172\pi$
$263$	0.484812	−	0.279906i	0.0298948	−	0.0172598i	0.514873	+	0.857267i	$0.327839\pi$
$264$	−0.500274	−	5.82039i	−0.0307897	−	0.358220i
$265$			2.08633i			0.128162i
$266$	24.7593	+	4.64817i	1.51809	+	0.284998i
$267$	5.16502			0.316094
$268$	−5.25842	+	9.10784i	−0.321209	+	0.556350i
$269$	1.45713	−	0.841274i	0.0888427	−	0.0512934i	−0.454920	−	0.890532i	$-0.650332\pi$
$269$	1.45713	−	0.841274i	0.0888427	−	0.0512934i	0.543763	+	0.839239i	$0.316999\pi$
$270$	2.47430	−	1.42854i	0.150581	−	0.0869380i
$271$	−13.7119	+	23.7496i	−0.832936	+	1.44269i	0.0627633	+	0.998028i	$0.480009\pi$
$271$	−13.7119	+	23.7496i	−0.832936	+	1.44269i	−0.895700	+	0.444660i	$0.853325\pi$
$272$	7.47630			0.453317
$273$	7.73618	+	1.45235i	0.468215	+	0.0879002i
$274$		−	24.6768i		−	1.49078i
$275$	−0.642007	−	7.46936i	−0.0387145	−	0.450419i
$276$	−7.31991	+	4.22615i	−0.440607	+	0.254384i
$277$	3.50799	−	2.02534i	0.210775	−	0.121691i	−0.390897	−	0.920435i	$-0.627835\pi$
$277$	3.50799	−	2.02534i	0.210775	−	0.121691i	0.601671	+	0.798744i	$0.294502\pi$
$278$	−1.79587	−	1.03685i	−0.107709	−	0.0621860i
$279$		−	8.86643i		−	0.530819i
$280$	7.27692	−	2.55795i	0.434879	−	0.152867i
$281$			1.37565i			0.0820646i	0.999158	+	0.0410323i	$0.0130647\pi$
$281$			1.37565i			0.0820646i	−0.999158	+	0.0410323i	$0.986935\pi$
$282$	−11.0150	−	6.35954i	−0.655936	−	0.378705i
$283$	−7.44347	−	12.8925i	−0.442469	−	0.766378i	0.555403	−	0.831581i	$-0.312564\pi$
$283$	−7.44347	−	12.8925i	−0.442469	−	0.766378i	−0.997872	+	0.0652030i	$0.979231\pi$
$284$	−0.516090	−	0.893895i	−0.0306243	−	0.0530429i
$285$	−4.56505	+	7.90690i	−0.270410	+	0.468364i
$286$	−9.74804	−	13.9669i	−0.576414	−	0.825882i
$287$	−16.3236	−	14.0071i	−0.963550	−	0.826815i
$288$			5.10725i			0.300948i
$289$	7.38191	−	12.7858i	0.434230	−	0.752109i
$290$	19.8630	−	11.4679i	1.16640	−	0.673420i
$291$	1.67993	+	2.90973i	0.0984793	+	0.170571i
$292$	4.82483	−	8.35685i	0.282352	−	0.489048i
$293$	23.7041			1.38481			0.692403	−	0.721511i	$-0.256552\pi$
$293$	23.7041			1.38481			0.692403	+	0.721511i	$0.256552\pi$
$294$	1.83493	+	11.9429i	0.107015	+	0.696524i
$295$	−8.22370			−0.478802
$296$	−12.5506	−	7.24610i	−0.729490	−	0.421171i
$297$	−1.40625	+	3.00374i	−0.0815988	+	0.174295i
$298$	15.0201	+	26.0156i	0.870091	+	1.50704i
$299$	12.8351	−	22.2311i	0.742276	−	1.28566i
$300$			2.21426i			0.127840i
$301$	8.67599	−	10.1108i	0.500076	−	0.582776i
$302$	−14.0082			−0.806079
$303$	−7.22271	−	4.17003i	−0.414934	−	0.239562i
$304$	−13.7891	−	23.8834i	−0.790859	−	1.36981i
$305$	5.24491	−	3.02815i	0.300323	−	0.173392i
$306$	−2.23543	−	1.29063i	−0.127791	−	0.0737803i
$307$	29.9744			1.71073			0.855364	−	0.518028i	$-0.173334\pi$
$307$	29.9744			1.71073			0.855364	+	0.518028i	$0.173334\pi$
$308$	5.01847	−	6.97879i	0.285954	−	0.397653i
$309$	−4.17978			−0.237779
$310$	−21.9382	−	12.6660i	−1.24601	−	0.719382i
$311$	−7.96340	+	4.59767i	−0.451563	+	0.260710i	−0.708490	−	0.705721i	$-0.750623\pi$
$311$	−7.96340	+	4.59767i	−0.451563	+	0.260710i	0.256927	+	0.966431i	$0.417290\pi$
$312$	−2.62013	−	4.53820i	−0.148336	−	0.256925i
$313$	16.1748	+	9.33853i	0.914254	+	0.527845i	0.881798	−	0.471628i	$-0.156334\pi$
$313$	16.1748	+	9.33853i	0.914254	+	0.527845i	0.0324568	+	0.999473i	$0.489667\pi$
$314$	−13.9473			−0.787090
$315$	−4.30399	−	0.808008i	−0.242502	−	0.0455261i
$316$		−	3.85897i		−	0.217084i
$317$	−4.72329	+	8.18097i	−0.265286	+	0.459489i	−0.967639	−	0.252340i	$-0.918800\pi$
$317$	−4.72329	+	8.18097i	−0.265286	+	0.459489i	0.702352	+	0.711829i	$0.252133\pi$
$318$	1.08790	+	1.88429i	0.0610062	+	0.105666i
$319$	−11.2890	+	24.1133i	−0.632063	+	1.35008i
$320$	−1.69615	−	0.979274i	−0.0948178	−	0.0547431i
$321$	2.85751			0.159491
$322$	38.7291	+	7.27079i	2.15829	+	0.405185i
$323$	8.24869			0.458969
$324$	0.489794	−	0.848348i	0.0272108	−	0.0471304i
$325$	−3.36244	−	5.82392i	−0.186515	−	0.323053i
$326$	19.0342	−	10.9894i	1.05421	−	0.608646i
$327$	−4.10232	+	7.10543i	−0.226859	+	0.392931i
$328$			14.3197i			0.790676i
$329$	6.46505	+	18.3920i	0.356430	+	1.01398i
$330$	5.42328	+	7.77044i	0.298542	+	0.427749i
$331$	−12.3977	+	21.4734i	−0.681438	+	1.18029i	0.293104	+	0.956081i	$0.405312\pi$
$331$	−12.3977	+	21.4734i	−0.681438	+	1.18029i	−0.974542	+	0.224205i	$0.928022\pi$
$332$	−5.00305	−	8.66554i	−0.274578	−	0.475584i
$333$	4.11387	+	7.12543i	0.225439	+	0.390471i
$334$	28.4502	+	16.4257i	1.55672	+	0.898775i
$335$			17.7699i			0.970874i
$336$	8.61394	−	10.0385i	0.469929	−	0.547644i
$337$			19.2924i			1.05093i	0.850816	+	0.525463i	$0.176108\pi$
$337$			19.2924i			1.05093i	−0.850816	+	0.525463i	$0.823892\pi$
$338$	6.20211	+	3.58079i	0.337350	+	0.194769i
$339$	1.76395	−	1.01842i	0.0958047	−	0.0553129i
$340$	−2.09976	+	1.21230i	−0.113876	+	0.0657461i
$341$	29.2986	−	2.51827i	1.58661	−	0.136372i
$342$			9.52160i			0.514869i
$343$	9.78624	−	15.7235i	0.528407	−	0.848991i
$344$	−8.86962			−0.478218
$345$	−7.14077	+	12.3682i	−0.384446	+	0.665881i
$346$	−4.24407	+	2.45032i	−0.228163	+	0.131730i
$347$	−29.9259	+	17.2777i	−1.60651	+	0.927518i	−0.616365	+	0.787461i	$0.711395\pi$
$347$	−29.9259	+	17.2777i	−1.60651	+	0.927518i	−0.990143	+	0.140057i	$0.955271\pi$
$348$	3.93194	−	6.81032i	0.210774	−	0.365071i
$349$	−13.4656			−0.720796			−0.360398	−	0.932799i	$-0.617359\pi$
$349$	−13.4656			−0.720796			−0.360398	+	0.932799i	$0.617359\pi$
$350$	6.72251	−	7.83425i	0.359333	−	0.418758i
$351$			2.97508i			0.158798i
$352$	−16.8766	+	1.45058i	−0.899527	+	0.0773162i
$353$	−6.71783	+	3.87854i	−0.357554	+	0.206434i	−0.668007	−	0.744155i	$-0.732853\pi$
$353$	−6.71783	+	3.87854i	−0.357554	+	0.206434i	0.310453	+	0.950589i	$0.399519\pi$
$354$	−7.42732	+	4.28817i	−0.394758	+	0.227913i
$355$	−1.51038	−	0.872019i	−0.0801627	−	0.0462820i
$356$		−	5.05959i		−	0.268158i
$357$	1.31204	+	3.73253i	0.0694406	+	0.197546i
$358$		−	5.10586i		−	0.269853i
$359$	−18.2433	−	10.5328i	−0.962847	−	0.555900i	−0.0657990	−	0.997833i	$-0.520960\pi$
$359$	−18.2433	−	10.5328i	−0.962847	−	0.555900i	−0.897048	+	0.441933i	$0.854293\pi$
$360$	1.45770	+	2.52481i	0.0768274	+	0.133069i
$361$	−5.71367	−	9.89636i	−0.300719	−	0.520861i
$362$	−13.9185	+	24.1076i	−0.731540	+	1.26707i
$363$	−10.3251	−	3.79373i	−0.541927	−	0.199119i
$364$	1.42270	−	7.57827i	0.0745699	−	0.397209i
$365$		−	16.3047i		−	0.853426i
$366$	3.15800	−	5.46982i	0.165071	−	0.285912i
$367$	19.6490	−	11.3444i	1.02567	−	0.592171i	0.109929	−	0.993939i	$-0.464938\pi$
$367$	19.6490	−	11.3444i	1.02567	−	0.592171i	0.915741	+	0.401768i	$0.131604\pi$
$368$	−21.5693	−	37.3591i	−1.12438	−	1.94748i
$369$	4.06492	−	7.04064i	0.211611	−	0.366521i
$370$	23.5073			1.22208
$371$	0.615335	−	3.27768i	0.0319466	−	0.170169i
$372$	−8.68544			−0.450319
$373$	−26.3693	−	15.2243i	−1.36535	−	0.788287i	−0.375022	−	0.927016i	$-0.622365\pi$
$373$	−26.3693	−	15.2243i	−1.36535	−	0.788287i	−0.990330	+	0.138729i	$0.955698\pi$
$374$	3.62989	−	7.75343i	0.187697	−	0.400920i
$375$	6.00861	+	10.4072i	0.310283	+	0.537427i
$376$	6.48935	−	11.2399i	0.334663	−	0.579653i
$377$			23.8832i			1.23005i
$378$	−4.30852	+	1.51451i	−0.221606	+	0.0778981i
$379$	−11.7721			−0.604695			−0.302347	−	0.953198i	$-0.597770\pi$
$379$	−11.7721			−0.604695			−0.302347	+	0.953198i	$0.597770\pi$
$380$	7.74550	+	4.47186i	0.397336	+	0.229402i
$381$	7.13973	+	12.3664i	0.365780	+	0.633549i
$382$	22.6071	−	13.0522i	1.15668	−	0.667811i
$383$	19.1772	+	11.0720i	0.979908	+	0.565750i	0.902243	−	0.431229i	$-0.141920\pi$
$383$	19.1772	+	11.0720i	0.979908	+	0.565750i	0.0776660	+	0.996979i	$0.475253\pi$
$384$	−12.2570			−0.625489
$385$	1.44758	−	14.4518i	0.0737755	−	0.736530i
$386$	11.0248			0.561146
$387$	4.36096	+	2.51780i	0.221680	+	0.127987i
$388$	2.85033	−	1.64564i	0.144704	−	0.0835447i
$389$	−1.39068	−	2.40874i	−0.0705105	−	0.122128i	0.828615	−	0.559819i	$-0.189129\pi$
$389$	−1.39068	−	2.40874i	−0.0705105	−	0.122128i	−0.899125	+	0.437692i	$0.855796\pi$
$390$	7.36125	+	4.25002i	0.372751	+	0.215208i
$391$	12.9028			0.652524
$392$	−12.1867	+	1.87238i	−0.615521	+	0.0945697i
$393$			0.600371i			0.0302847i
$394$	19.3508	−	33.5165i	0.974878	−	1.68854i
$395$	−3.26018	−	5.64680i	−0.164038	−	0.284121i
$396$	2.94243	+	1.37754i	0.147863	+	0.0692242i
$397$	2.70831	+	1.56364i	0.135926	+	0.0784770i	0.566421	−	0.824116i	$-0.308328\pi$
$397$	2.70831	+	1.56364i	0.135926	+	0.0784770i	−0.430495	+	0.902593i	$0.641661\pi$
$398$	41.7472			2.09260
$399$	9.50385	−	11.0756i	0.475788	−	0.554472i
$400$	−11.3011			−0.565053
$401$	−4.34142	+	7.51956i	−0.216800	+	0.375509i	−0.953828	−	0.300353i	$-0.902895\pi$
$401$	−4.34142	+	7.51956i	−0.216800	+	0.375509i	0.737028	+	0.675862i	$0.236229\pi$
$402$	9.26595	+	16.0491i	0.462143	+	0.800456i
$403$	22.8443	−	13.1892i	1.13796	−	0.657000i
$404$	−4.08491	+	7.07528i	−0.203232	+	0.352008i
$405$		−	1.65517i		−	0.0822462i
$406$	−34.5877	+	12.1581i	−1.71656	+	0.603397i
$407$	−22.3771	+	15.6178i	−1.10919	+	0.774147i
$408$	1.31697	−	2.28106i	0.0651999	−	0.112930i
$409$	12.4882	+	21.6302i	0.617503	+	1.06955i	0.989940	+	0.141489i	$0.0451890\pi$
$409$	12.4882	+	21.6302i	0.617503	+	1.06955i	−0.372437	+	0.928058i	$0.621478\pi$
$410$	−11.6138	−	20.1156i	−0.573563	−	0.993440i
$411$	−12.3806	−	7.14793i	−0.610689	−	0.352581i
$412$			4.09446i			0.201720i
$413$	12.9197	+	2.42547i	0.635735	+	0.119349i
$414$			14.8939i			0.731998i
$415$	−14.6419	−	8.45348i	−0.718741	−	0.414965i
$416$	−13.1588	+	7.59726i	−0.645165	+	0.372486i
$417$	−1.04039	+	0.600671i	−0.0509482	+	0.0294150i
$418$	−31.4636	+	2.70436i	−1.53893	+	0.132274i
$419$		−	5.05059i		−	0.246738i	−0.992361	−	0.123369i	$-0.960630\pi$
$419$		−	5.05059i		−	0.246738i	0.992361	−	0.123369i	$-0.0393698\pi$
$420$	−0.791514	+	4.21613i	−0.0386219	+	0.205726i
$421$	−26.8136			−1.30682			−0.653408	−	0.757006i	$-0.726661\pi$
$421$	−26.8136			−1.30682			−0.653408	+	0.757006i	$0.726661\pi$
$422$	2.63641	−	4.56640i	0.128338	−	0.222289i
$423$	−6.38129	+	3.68424i	−0.310269	+	0.179134i
$424$	−1.92276	+	1.11010i	−0.0933773	+	0.0539114i
$425$	1.69008	−	2.92731i	0.0819811	−	0.141996i
$426$	−1.81882			−0.0881223
$427$	−9.13302	+	3.21040i	−0.441978	+	0.155362i
$428$		−	2.79918i		−	0.135304i
$429$	−9.83099	+	0.844993i	−0.474645	+	0.0407967i
$430$	12.4596	−	7.19354i	0.600854	−	0.346903i
$431$	−3.91116	+	2.25811i	−0.188394	+	0.108769i	−0.591231	−	0.806503i	$-0.701358\pi$
$431$	−3.91116	+	2.25811i	−0.188394	+	0.108769i	0.402836	+	0.915272i	$0.368024\pi$
$432$	4.32977	+	2.49979i	0.208316	+	0.120271i
$433$		−	0.625010i		−	0.0300361i	−0.999887	−	0.0150180i	$-0.995219\pi$
$433$		−	0.625010i		−	0.0300361i	0.999887	−	0.0150180i	$-0.00478057\pi$
$434$	30.7299	+	26.3691i	1.47508	+	1.26576i
$435$		−	13.2873i		−	0.637078i
$436$	6.96039	+	4.01858i	0.333342	+	0.192455i
$437$	−23.7976	−	41.2187i	−1.13839	−	1.97176i
$438$	−8.50192	−	14.7258i	−0.406237	−	0.703624i
$439$	10.8134	−	18.7294i	0.516096	−	0.893904i	−0.483729	−	0.875218i	$-0.660718\pi$
$439$	10.8134	−	18.7294i	0.516096	−	0.893904i	0.999825	−	0.0186867i	$-0.00594852\pi$
$440$	−7.92905	+	5.53398i	−0.378003	+	0.263822i
$441$	6.52338	+	2.53881i	0.310637	+	0.120896i
$442$		−	7.67945i		−	0.365274i
$443$	11.2798	−	19.5371i	0.535917	−	0.928236i	−0.463201	−	0.886253i	$-0.653299\pi$
$443$	11.2798	−	19.5371i	0.535917	−	0.928236i	0.999118	−	0.0419829i	$-0.0133675\pi$
$444$	6.97998	−	4.02990i	0.331255	−	0.191250i
$445$	−4.27451	−	7.40366i	−0.202631	−	0.350967i
$446$	−8.55245	+	14.8133i	−0.404970	+	0.701429i
$447$	17.4030			0.823135
$448$	2.37588	+	2.03872i	0.112250	+	0.0963207i
$449$	−1.18995			−0.0561571			−0.0280785	−	0.999606i	$-0.508939\pi$
$449$	−1.18995			−0.0561571			−0.0280785	+	0.999606i	$0.508939\pi$
$450$	3.37905	+	1.95089i	0.159290	+	0.0919660i
$451$	24.4199	+	11.4326i	1.14989	+	0.538339i
$452$	−0.997629	−	1.72794i	−0.0469245	−	0.0812757i
$453$	−4.05764	+	7.02803i	−0.190644	+	0.330206i
$454$			22.9422i			1.07673i
$455$	−4.32053	−	12.2912i	−0.202550	−	0.576219i
$456$	−9.71596			−0.454992
$457$	−6.31402	−	3.64540i	−0.295357	−	0.170525i	0.344998	−	0.938603i	$-0.387880\pi$
$457$	−6.31402	−	3.64540i	−0.295357	−	0.170525i	−0.640355	+	0.768079i	$0.721213\pi$
$458$	−7.43284	−	12.8740i	−0.347314	−	0.601565i
$459$	−1.29504	+	0.747692i	−0.0604474	+	0.0348993i
$460$	12.1157	+	6.99501i	0.564898	+	0.326144i
$461$	9.97446			0.464557			0.232279	−	0.972649i	$-0.425382\pi$
$461$	9.97446			0.464557			0.232279	+	0.972649i	$0.425382\pi$
$462$	−6.22834	−	13.8071i	−0.289768	−	0.642364i
$463$	10.9915			0.510818			0.255409	−	0.966833i	$-0.417790\pi$
$463$	10.9915			0.510818			0.255409	+	0.966833i	$0.417790\pi$
$464$	34.7583	+	20.0677i	1.61361	+	0.931619i
$465$	−12.7093	+	7.33774i	−0.589381	+	0.340279i
$466$	−0.353464	−	0.612218i	−0.0163739	−	0.0283605i
$467$	−21.7021	−	12.5297i	−1.00425	−	0.579806i	−0.0947495	−	0.995501i	$-0.530205\pi$
$467$	−21.7021	−	12.5297i	−1.00425	−	0.579806i	−0.909504	+	0.415695i	$0.863538\pi$
$468$	2.91435			0.134716
$469$	5.24099	−	27.9170i	0.242007	−	1.28909i
$470$			21.0523i			0.971069i
$471$	−4.04000	+	6.99748i	−0.186153	+	0.322427i
$472$	−4.37570	−	7.57893i	−0.201408	−	0.348849i
$473$	−7.08131	+	15.1256i	−0.325599	+	0.695478i
$474$	−5.88894	−	3.39998i	−0.270488	−	0.156166i
$475$	−12.4686			−0.572098
$476$	3.65634	−	1.28526i	0.167588	−	0.0589098i
$477$	1.26049			0.0577139
$478$	0.545062	−	0.944075i	0.0249306	−	0.0431810i
$479$	12.2025	+	21.1353i	0.557544	+	0.965695i	0.997701	+	0.0677741i	$0.0215897\pi$
$479$	12.2025	+	21.1353i	0.557544	+	0.965695i	−0.440156	+	0.897921i	$0.645077\pi$
$480$	7.32085	−	4.22670i	0.334150	−	0.192921i
$481$	−12.2391	+	21.1988i	−0.558055	+	0.966580i
$482$		−	10.2644i		−	0.467528i
$483$	14.8662	−	17.3247i	0.676435	−	0.788301i
$484$	−3.71629	+	10.1143i	−0.168922	+	0.459742i
$485$	2.78058	−	4.81610i	0.126260	−	0.218688i
$486$	−0.863074	−	1.49489i	−0.0391498	−	0.0678095i
$487$	3.84742	+	6.66393i	0.174343	+	0.301972i	0.939934	−	0.341357i	$-0.110886\pi$
$487$	3.84742	+	6.66393i	0.174343	+	0.301972i	−0.765590	+	0.643328i	$0.777553\pi$
$488$	5.58147	+	3.22246i	0.252661	+	0.145874i
$489$		−	12.7329i		−	0.575800i
$490$	15.6007	−	12.5140i	0.704766	−	0.565325i
$491$			12.2135i			0.551190i	0.961274	+	0.275595i	$0.0888748\pi$
$491$			12.2135i			0.551190i	−0.961274	+	0.275595i	$0.911125\pi$
$492$	−6.89692	−	3.98194i	−0.310937	−	0.179520i
$493$	−10.3963	+	6.00228i	−0.468224	+	0.270329i
$494$	−24.5324	+	14.1638i	−1.10376	+	0.637259i
$495$	5.46942	−	0.470108i	0.245832	−	0.0211298i
$496$		−	44.3284i		−	1.99041i
$497$	2.11566	+	1.81543i	0.0949004	+	0.0814333i
$498$	−17.6319			−0.790106
$499$	−12.7481	+	22.0803i	−0.570683	+	0.988452i	0.425813	+	0.904811i	$0.359988\pi$
$499$	−12.7481	+	22.0803i	−0.570683	+	0.988452i	−0.996496	+	0.0836409i	$0.973345\pi$
$500$	10.1948	−	5.88596i	0.455924	−	0.263228i
$501$	16.4819	−	9.51582i	0.736356	−	0.425136i
$502$	−0.342393	+	0.593043i	−0.0152818	+	0.0264688i
$503$	13.6574			0.608953			0.304477	−	0.952520i	$-0.401518\pi$
$503$	13.6574			0.608953			0.304477	+	0.952520i	$0.401518\pi$
$504$	−1.54543	−	4.39647i	−0.0688388	−	0.195834i
$505$			13.8043i			0.614281i
$506$	−49.2162	+	4.23023i	−2.18793	+	0.188057i
$507$	3.59303	−	2.07444i	0.159572	−	0.0921291i
$508$	12.1139	−	6.99399i	0.537470	−	0.310308i
$509$	23.9307	+	13.8164i	1.06071	+	0.612400i	0.925628	−	0.378435i	$-0.123538\pi$
$509$	23.9307	+	13.8164i	1.06071	+	0.612400i	0.135080	+	0.990835i	$0.456871\pi$
$510$			4.27243i			0.189186i
$511$	−4.80885	+	25.6151i	−0.212731	+	1.13315i
$512$			7.92178i			0.350097i
$513$	4.77708	+	2.75805i	0.210913	+	0.121771i
$514$	15.5758	+	26.9780i	0.687018	+	1.18995i
$515$	3.45913	+	5.99139i	0.152428	+	0.264012i
$516$	2.46641	−	4.27194i	0.108577	−	0.188062i
$517$	−13.9868	−	20.0402i	−0.615138	−	0.881366i
$518$	−36.9306	−	6.93315i	−1.62264	−	0.304625i
$519$			2.83906i			0.124621i
$520$	−4.33677	+	7.51151i	−0.190180	+	0.329401i
$521$	−31.1122	+	17.9626i	−1.36305	+	0.786957i	−0.990029	−	0.140866i	$-0.955011\pi$
$521$	−31.1122	+	17.9626i	−1.36305	+	0.786957i	−0.373021	+	0.927823i	$0.621678\pi$
$522$	−6.92854	−	12.0006i	−0.303254	−	0.525251i
$523$	−21.0025	+	36.3774i	−0.918375	+	1.59067i	−0.116491	+	0.993192i	$0.537165\pi$
$523$	−21.0025	+	36.3774i	−0.918375	+	1.59067i	−0.801884	+	0.597480i	$0.796169\pi$
$524$	0.588116			0.0256920
$525$	−1.98326	−	5.64203i	−0.0865566	−	0.246239i
$526$	−0.966320			−0.0421335
$527$	11.4824	+	6.62936i	0.500181	+	0.288780i
$528$	−7.03066	+	15.0175i	−0.305970	+	0.653551i
$529$	−25.7249	−	44.5568i	−1.11847	−	1.93725i
$530$	1.80066	−	3.11883i	0.0782156	−	0.135473i
$531$			4.96848i			0.215614i
$532$	−10.8495	−	9.30986i	−0.470385	−	0.403633i
$533$	24.1869			1.04765
$534$	−7.72113	−	4.45780i	−0.334126	−	0.192908i
$535$	−2.36484	−	4.09602i	−0.102241	−	0.177087i
$536$	−16.3767	+	9.45509i	−0.707365	+	0.408398i
$537$	−2.56166	−	1.47898i	−0.110544	−	0.0638225i
$538$	−2.90433			−0.125214
$539$	−6.53654	+	22.2772i	−0.281549	+	0.959547i
$540$	−1.62139			−0.0697734
$541$	−2.32014	−	1.33954i	−0.0997507	−	0.0575911i	0.449295	−	0.893384i	$-0.351675\pi$
$541$	−2.32014	−	1.33954i	−0.0997507	−	0.0575911i	−0.549045	+	0.835792i	$0.685009\pi$
$542$	40.9954	−	23.6687i	1.76090	−	1.01666i
$543$	8.06333	+	13.9661i	0.346031	+	0.599343i
$544$	−6.61411	−	3.81866i	−0.283577	−	0.163724i
$545$	13.5801			0.581708
$546$	−10.3112	−	8.84800i	−0.441281	−	0.378659i
$547$			29.7261i			1.27100i	0.772103	+	0.635498i	$0.219205\pi$
$547$			29.7261i			1.27100i	−0.772103	+	0.635498i	$0.780795\pi$
$548$	−7.00202	+	12.1279i	−0.299112	+	0.518077i
$549$	−1.82951	−	3.16880i	−0.0780815	−	0.135241i
$550$	−5.48688	+	11.7200i	−0.233961	+	0.499741i
$551$	38.3492	+	22.1409i	1.63373	+	0.943234i
$552$	−15.1980			−0.646869
$553$	3.45639	+	9.83283i	0.146981	+	0.418135i
$554$	−6.99208			−0.297065
$555$	6.80917	−	11.7938i	0.289033	−	0.500620i
$556$	0.588410	+	1.01916i	0.0249541	+	0.0432218i
$557$	20.7005	−	11.9515i	0.877110	−	0.506400i	0.00740546	−	0.999973i	$-0.497643\pi$
$557$	20.7005	−	11.9515i	0.877110	−	0.506400i	0.869704	+	0.493573i	$0.164309\pi$
$558$	−7.65238	+	13.2543i	−0.323951	+	0.561100i
$559$			14.9813i			0.633643i
$560$	−21.5182	−	4.03970i	−0.909308	−	0.170709i
$561$	−2.83853	−	4.06703i	−0.119843	−	0.171710i
$562$	1.18729	−	2.05645i	0.0500829	−	0.0867460i
$563$	−2.58699	−	4.48080i	−0.109029	−	0.188843i	0.806348	−	0.591441i	$-0.201441\pi$
$563$	−2.58699	−	4.48080i	−0.109029	−	0.188843i	−0.915377	+	0.402598i	$0.868107\pi$
$564$	3.60903	+	6.25103i	0.151968	+	0.263216i
$565$	−2.91965	−	1.68566i	−0.122830	−	0.0709162i
$566$			25.6971i			1.08013i
$567$	−0.488171	+	2.60032i	−0.0205013	+	0.109203i
$568$		−	1.85595i		−	0.0778740i
$569$	8.10585	+	4.67991i	0.339815	+	0.196192i	0.660190	−	0.751099i	$-0.270476\pi$
$569$	8.10585	+	4.67991i	0.339815	+	0.196192i	−0.320375	+	0.947291i	$0.603809\pi$
$570$	13.6485	−	7.87995i	0.571672	−	0.330055i
$571$	0.746099	−	0.430760i	0.0312233	−	0.0180268i	−0.484307	−	0.874898i	$-0.660928\pi$
$571$	0.746099	−	0.430760i	0.0312233	−	0.0180268i	0.515530	+	0.856871i	$0.327595\pi$
$572$	0.827745	+	9.63031i	0.0346098	+	0.402664i
$573$		−	15.1230i		−	0.631771i
$574$	12.3127	+	35.0276i	0.513923	+	1.46202i
$575$	−19.5037			−0.813361
$576$	−0.591644	+	1.02476i	−0.0246518	+	0.0426982i
$577$	8.00594	−	4.62223i	0.333292	−	0.192426i	−0.324010	−	0.946054i	$-0.605031\pi$
$577$	8.00594	−	4.62223i	0.333292	−	0.192426i	0.657302	+	0.753628i	$0.271698\pi$
$578$	−22.0703	+	12.7423i	−0.918002	+	0.530009i
$579$	3.19346	−	5.53124i	0.132716	−	0.229870i
$580$	−13.0161			−0.540463
$581$	20.5095	+	17.5991i	0.850879	+	0.730133i
$582$		−	5.79962i		−	0.240402i
$583$	0.358009	+	4.16522i	0.0148272	+	0.172506i
$584$	15.0263	−	8.67547i	0.621795	−	0.358993i
$585$	4.26455	−	2.46214i	0.176317	−	0.101797i
$586$	−35.4349	−	20.4584i	−1.46380	−	0.845127i
$587$			9.19283i			0.379429i	0.981839	+	0.189714i	$0.0607562\pi$
$587$			9.19283i			0.379429i	−0.981839	+	0.189714i	$0.939244\pi$
$588$	2.48698	−	6.39022i	0.102561	−	0.263528i
$589$		−	48.9081i		−	2.01522i
$590$	12.2935	+	7.09766i	0.506116	+	0.292206i
$591$	−11.2104	−	19.4169i	−0.461133	−	0.798706i
$592$	20.5676	+	35.6242i	0.845325	+	1.46415i
$593$	−18.1728	+	31.4763i	−0.746269	+	1.29258i	0.203331	+	0.979110i	$0.434823\pi$
$593$	−18.1728	+	31.4763i	−0.746269	+	1.29258i	−0.949600	+	0.313465i	$0.898510\pi$
$594$	4.69464	−	3.27656i	0.192623	−	0.134439i
$595$	4.26446	−	4.96970i	0.174826	−	0.203738i
$596$		−	17.0478i		−	0.698304i
$597$	12.0926	−	20.9450i	0.494917	−	0.857222i
$598$	−38.3742	+	22.1554i	−1.56924	+	0.906000i
$599$	−5.33146	−	9.23435i	−0.217837	−	0.377305i	0.736309	−	0.676645i	$-0.236567\pi$
$599$	−5.33146	−	9.23435i	−0.217837	−	0.377305i	−0.954147	+	0.299340i	$0.903234\pi$
$600$	−1.99072	+	3.44802i	−0.0812706	+	0.140765i
$601$	−27.8885			−1.13760			−0.568798	−	0.822477i	$-0.692592\pi$
$601$	−27.8885			−1.13760			−0.568798	+	0.822477i	$0.692592\pi$
$602$	−21.6960	+	7.62648i	−0.884263	+	0.310832i
$603$	10.7360			0.437203
$604$	6.88457	+	3.97481i	0.280129	+	0.161733i
$605$	3.10689	+	17.9399i	0.126313	+	0.729359i
$606$	7.19810	+	12.4675i	0.292403	+	0.506456i
$607$	24.3692	−	42.2087i	0.989116	−	1.71320i	0.367134	−	0.930168i	$-0.380339\pi$
$607$	24.3692	−	42.2087i	0.989116	−	1.71320i	0.621982	−	0.783031i	$-0.286328\pi$
$608$			28.1721i			1.14253i
$609$	−3.91891	+	20.8747i	−0.158802	+	0.845887i
$610$	−10.4541			−0.423273
$611$	−18.9849	−	10.9609i	−0.768045	−	0.443431i
$612$	0.732430	+	1.26861i	0.0296067	+	0.0512804i
$613$	−13.3681	+	7.71806i	−0.539931	+	0.311729i	−0.745051	−	0.667008i	$-0.767575\pi$
$613$	−13.3681	+	7.71806i	−0.539931	+	0.311729i	0.205120	+	0.978737i	$0.434242\pi$
$614$	−44.8083	−	25.8701i	−1.80832	−	1.04403i
$615$	−13.4563			−0.542610
$616$	14.0889	−	6.35547i	0.567660	−	0.256069i
$617$	40.0745			1.61334			0.806669	−	0.591004i	$-0.201268\pi$
$617$	40.0745			1.61334			0.806669	+	0.591004i	$0.201268\pi$
$618$	6.24830	+	3.60746i	0.251344	+	0.145113i
$619$	−10.8714	+	6.27659i	−0.436958	+	0.252278i	−0.702306	−	0.711875i	$-0.747846\pi$
$619$	−10.8714	+	6.27659i	−0.436958	+	0.252278i	0.265349	+	0.964153i	$0.414513\pi$
$620$	7.18796	+	12.4499i	0.288675	+	0.500000i
$621$	7.47244	+	4.31421i	0.299859	+	0.173123i
$622$	15.8725			0.636430
$623$	4.53176	+	12.8921i	0.181561	+	0.516510i
$624$			14.8742i			0.595444i
$625$	4.29429	−	7.43793i	0.171772	−	0.297517i
$626$	−16.1197	−	27.9201i	−0.644272	−	1.11591i
$627$	−7.75701	+	16.5689i	−0.309785	+	0.661699i
$628$	6.85464	+	3.95753i	0.273530	+	0.157923i
$629$	−12.3036			−0.490578
$630$	5.73661	+	4.92254i	0.228552	+	0.196119i
$631$	29.4070			1.17067			0.585337	−	0.810790i	$-0.300962\pi$
$631$	29.4070			1.17067			0.585337	+	0.810790i	$0.300962\pi$
$632$	3.46938	−	6.00915i	0.138005	−	0.239031i
$633$	−1.52734	−	2.64543i	−0.0607062	−	0.105146i
$634$	14.1216	−	8.15309i	0.560839	−	0.323801i
$635$	11.8175	−	20.4685i	0.468963	−	0.812268i
$636$		−	1.23476i		−	0.0489614i
$637$	3.16257	+	20.5841i	0.125306	+	0.815570i
$638$	37.6873	−	26.3034i	1.49206	−	1.04136i
$639$	−0.526845	+	0.912522i	−0.0208417	+	0.0360988i
$640$	10.1438	+	17.5695i	0.400967	+	0.694496i
$641$	−23.4934	−	40.6917i	−0.927933	−	1.60723i	−0.786775	−	0.617240i	$-0.788251\pi$
$641$	−23.4934	−	40.6917i	−0.927933	−	1.60723i	−0.141159	−	0.989987i	$-0.545083\pi$
$642$	−4.27166	−	2.46625i	−0.168589	−	0.0973350i
$643$			43.4205i			1.71234i	0.516697	+	0.856168i	$0.327161\pi$
$643$			43.4205i			1.71234i	−0.516697	+	0.856168i	$0.672839\pi$
$644$	−16.9711	−	14.5627i	−0.668753	−	0.573852i
$645$		−	8.33479i		−	0.328182i
$646$	−12.3309	−	7.11923i	−0.485151	−	0.280102i
$647$	31.7244	−	18.3161i	1.24722	−	0.720081i	0.276663	−	0.960967i	$-0.410771\pi$
$647$	31.7244	−	18.3161i	1.24722	−	0.720081i	0.970553	+	0.240886i	$0.0774381\pi$
$648$	1.52540	−	0.880692i	0.0599235	−	0.0345968i
$649$	−16.4181	+	1.41116i	−0.644465	+	0.0553931i
$650$			11.6081i			0.455309i
$651$	22.1309	−	7.77935i	0.867378	−	0.304897i
$652$	−12.4729			−0.488478
$653$	9.04493	−	15.6663i	0.353956	−	0.613069i	−0.632983	−	0.774166i	$-0.718170\pi$
$653$	9.04493	−	15.6663i	0.353956	−	0.613069i	0.986939	+	0.161097i	$0.0515031\pi$
$654$	12.2650	−	7.08121i	0.479600	−	0.276897i
$655$	0.860585	−	0.496859i	0.0336259	−	0.0194139i
$656$	20.3229	−	35.2003i	0.793475	−	1.37434i
$657$	−9.85074			−0.384314
$658$	6.20908	−	33.0737i	0.242055	−	1.28935i
$659$		−	42.0600i		−	1.63842i	−0.573490	−	0.819212i	$-0.694411\pi$
$659$		−	42.0600i		−	1.63842i	0.573490	−	0.819212i	$-0.305589\pi$
$660$	−0.460512	−	5.35778i	−0.0179254	−	0.208551i
$661$	−6.73314	+	3.88738i	−0.261889	+	0.151201i	−0.625196	−	0.780468i	$-0.714981\pi$
$661$	−6.73314	+	3.88738i	−0.261889	+	0.151201i	0.363307	+	0.931669i	$0.381648\pi$
$662$	37.0663	−	21.4002i	1.44062	−	0.831744i
$663$	−3.85286	−	2.22445i	−0.149633	−	0.0863904i
$664$		−	17.9919i		−	0.698219i
$665$	−23.7412	−	4.45705i	−0.920645	−	0.172837i
$666$		−	14.2023i		−	0.550328i
$667$	59.9868	+	34.6334i	2.32270	+	1.34101i
$668$	−9.32158	−	16.1455i	−0.360663	−	0.624686i
$669$	4.95464	+	8.58169i	0.191558	+	0.331787i
$670$	15.3367	−	26.5640i	0.592510	−	1.02626i
$671$	9.95149	−	6.94551i	0.384173	−	0.268129i
$672$	−12.7479	+	4.48107i	−0.491760	+	0.172861i
$673$			29.5062i			1.13738i	0.822552	+	0.568690i	$0.192550\pi$
$673$			29.5062i			1.13738i	−0.822552	+	0.568690i	$0.807450\pi$
$674$	16.6508	−	28.8400i	0.641365	−	1.11088i
$675$	1.95756	−	1.13020i	0.0753467	−	0.0435014i
$676$	−2.03209	−	3.51969i	−0.0781575	−	0.135373i
$677$	18.1014	−	31.3525i	0.695692	−	1.20497i	−0.274255	−	0.961657i	$-0.588431\pi$
$677$	18.1014	−	31.3525i	0.695692	−	1.20497i	0.969947	−	0.243317i	$-0.0782355\pi$
$678$	−3.51588			−0.135027
$679$	−5.78881	+	6.74614i	−0.222154	+	0.258893i
$680$	−4.35964			−0.167184
$681$	11.5103	+	6.64550i	0.441077	+	0.254656i
$682$	−45.9716	−	21.5223i	−1.76034	−	0.824132i
$683$	−8.31889	−	14.4087i	−0.318313	−	0.551335i	0.661823	−	0.749660i	$-0.269783\pi$
$683$	−8.31889	−	14.4087i	−0.318313	−	0.551335i	−0.980136	+	0.198325i	$0.936450\pi$
$684$	2.70175	−	4.67957i	0.103304	−	0.178928i
$685$			23.6621i			0.904084i
$686$	−28.1999	+	15.0587i	−1.07668	+	0.574943i
$687$	−8.61205			−0.328570
$688$	21.8030	+	12.5880i	0.831230	+	0.479911i
$689$	1.87503	+	3.24765i	0.0714330	+	0.123726i
$690$	21.3493	−	12.3260i	0.812755	−	0.469244i
$691$	−25.4559	−	14.6970i	−0.968388	−	0.559099i	−0.0696433	−	0.997572i	$-0.522186\pi$
$691$	−25.4559	−	14.6970i	−0.968388	−	0.559099i	−0.898744	+	0.438473i	$0.855519\pi$
$692$	2.78110			0.105722
$693$	−8.73127	−	0.874579i	−0.331674	−	0.0332225i
$694$	59.6479			2.26420
$695$	1.72203	+	0.994215i	0.0653203	+	0.0377127i
$696$	12.2455	−	7.06997i	0.464166	−	0.267986i
$697$	6.07861	+	10.5285i	0.230244	+	0.398794i
$698$	20.1295	+	11.6218i	0.761914	+	0.439891i
$699$	−0.409541			−0.0154903
$700$	−5.52687	+	1.94278i	−0.208896	+	0.0734301i
$701$		−	2.65658i		−	0.100338i	−0.998741	−	0.0501688i	$-0.984024\pi$
$701$		−	2.65658i		−	0.100338i	0.998741	−	0.0501688i	$-0.0159759\pi$
$702$	2.56772	−	4.44742i	0.0969123	−	0.167857i
$703$	22.6925	+	39.3046i	0.855864	+	1.48240i
$704$	−3.55429	−	1.66400i	−0.133957	−	0.0627143i
$705$	10.5621	+	6.09805i	0.397793	+	0.229666i
$706$	13.3899			0.503935
$707$	4.07138	−	21.6869i	0.153120	−	0.815619i
$708$	4.86706			0.182915
$709$	10.0076	−	17.3337i	0.375844	−	0.650981i	−0.614609	−	0.788832i	$-0.710686\pi$
$709$	10.0076	−	17.3337i	0.375844	−	0.650981i	0.990453	+	0.137851i	$0.0440195\pi$
$710$	1.50523	+	2.60714i	0.0564904	+	0.0978443i
$711$	−3.41161	+	1.96969i	−0.127945	+	0.0738692i
$712$	4.54879	−	7.87874i	0.170473	−	0.295268i
$713$		−	76.5033i		−	2.86507i
$714$	1.26009	−	6.71210i	0.0471578	−	0.251194i
$715$	9.34723	+	13.3927i	0.349567	+	0.500857i
$716$	−1.44879	+	2.50937i	−0.0541437	+	0.0937796i
$717$	−0.315768	−	0.546926i	−0.0117926	−	0.0204253i
$718$	18.1812	+	31.4907i	0.678516	+	1.17522i
$719$	−6.47463	−	3.73813i	−0.241463	−	0.139409i	0.374386	−	0.927273i	$-0.377854\pi$
$719$	−6.47463	−	3.73813i	−0.241463	−	0.139409i	−0.615849	+	0.787864i	$0.711187\pi$
$720$		−	8.27518i		−	0.308398i
$721$	−3.66731	−	10.4329i	−0.136578	−	0.388540i
$722$			19.7253i			0.734098i
$723$	−5.14973	−	2.97320i	−0.191520	−	0.110574i
$724$	13.6810	−	7.89874i	0.508451	−	0.293554i
$725$	15.7148	−	9.07296i	0.583634	−	0.336961i
$726$	12.1606	+	14.5825i	0.451322	+	0.541208i
$727$		−	36.4649i		−	1.35241i	−0.736714	−	0.676204i	$-0.763624\pi$
$727$		−	36.4649i		−	1.35241i	0.736714	−	0.676204i	$-0.236376\pi$
$728$	9.02861	−	10.5217i	0.334623	−	0.389961i
$729$	−1.00000			−0.0370370
$730$	−14.0722	+	24.3737i	−0.520834	+	0.902110i
$731$	−6.52131	+	3.76508i	−0.241199	+	0.139257i
$732$	−3.10412	+	1.79216i	−0.114731	+	0.0662402i
$733$	−8.56710	+	14.8387i	−0.316433	+	0.548078i	−0.979741	−	0.200268i	$-0.935819\pi$
$733$	−8.56710	+	14.8387i	−0.316433	+	0.548078i	0.663308	+	0.748347i	$0.269152\pi$
$734$	−39.1641			−1.44557
$735$	−1.75948	−	11.4518i	−0.0648994	−	0.422407i
$736$			44.0676i			1.62435i
$737$	3.04927	+	35.4764i	0.112321	+	1.30679i
$738$	−12.1532	+	7.01665i	−0.447365	+	0.258286i
$739$	−7.28034	+	4.20331i	−0.267812	+	0.154621i	−0.627893	−	0.778300i	$-0.716082\pi$
$739$	−7.28034	+	4.20331i	−0.267812	+	0.154621i	0.360081	+	0.932921i	$0.382749\pi$
$740$	−11.5531	−	6.67018i	−0.424700	−	0.245201i
$741$			16.4109i			0.602868i
$742$	−3.74874	+	4.36869i	−0.137621	+	0.160380i
$743$		−	27.0887i		−	0.993790i	−0.867811	−	0.496895i	$-0.834473\pi$
$743$		−	27.0887i		−	0.993790i	0.867811	−	0.496895i	$-0.165527\pi$
$744$	−13.5249	−	7.80859i	−0.495846	−	0.286277i
$745$	−14.4025	−	24.9459i	−0.527667	−	0.913946i
$746$	26.2795	+	45.5174i	0.962160	+	1.66651i
$747$	−5.10731	+	8.84612i	−0.186867	+	0.323662i
$748$	−3.98401	+	2.78059i	−0.145670	+	0.101668i
$749$	2.50717	+	7.13245i	0.0916098	+	0.260614i
$750$		−	20.7435i		−	0.757446i
$751$	−20.3019	+	35.1639i	−0.740825	+	1.28315i	0.211294	+	0.977422i	$0.432232\pi$
$751$	−20.3019	+	35.1639i	−0.740825	+	1.28315i	−0.952120	+	0.305725i	$0.901101\pi$
$752$	−31.9038	+	18.4197i	−1.16341	+	0.671696i
$753$	0.198357	+	0.343564i	0.00722853	+	0.0125202i
$754$	20.6130	−	35.7027i	0.750680	−	1.30022i
$755$	13.4322			0.488847
$756$	2.54725	+	0.478206i	0.0926424	+	0.0173922i
$757$	27.7043			1.00693			0.503465	−	0.864016i	$-0.332058\pi$
$757$	27.7043			1.00693			0.503465	+	0.864016i	$0.332058\pi$
$758$	17.5980	+	10.1602i	0.639190	+	0.369036i
$759$	−12.1337	+	25.9176i	−0.440426	+	0.940748i
$760$	8.04080	+	13.9271i	0.291671	+	0.505188i
$761$	6.68794	−	11.5839i	0.242438	−	0.419914i	−0.718970	−	0.695041i	$-0.755386\pi$
$761$	6.68794	−	11.5839i	0.242438	−	0.419914i	0.961408	+	0.275126i	$0.0887197\pi$
$762$		−	24.6485i		−	0.892920i
$763$	−21.3347	−	4.00527i	−0.772369	−	0.145000i
$764$	−14.8143			−0.535961
$765$	2.14352	+	1.23756i	0.0774991	+	0.0447441i
$766$	−19.1118	−	33.1027i	−0.690539	−	1.19605i
$767$	−12.8013	+	7.39082i	−0.462227	+	0.266867i
$768$	16.2734	+	9.39545i	0.587215	+	0.339029i
$769$	−32.4856			−1.17146			−0.585731	−	0.810506i	$-0.699192\pi$
$769$	−32.4856			−1.17146			−0.585731	+	0.810506i	$0.699192\pi$
$770$	−14.6369	+	20.3544i	−0.527478	+	0.733522i
$771$	18.0469			0.649941
$772$	−5.41833	−	3.12827i	−0.195010	−	0.112589i
$773$	22.1160	−	12.7687i	0.795456	−	0.459256i	−0.0464241	−	0.998922i	$-0.514783\pi$
$773$	22.1160	−	12.7687i	0.795456	−	0.459256i	0.841880	+	0.539665i	$0.181449\pi$
$774$	−4.34610	−	7.52766i	−0.156217	−	0.270576i
$775$	−17.3566	−	10.0208i	−0.623468	−	0.359959i
$776$	5.91801			0.212444
$777$	−14.1758	+	16.5202i	−0.508555	+	0.592658i
$778$			4.80105i			0.172126i
$779$	22.4225	−	38.8369i	0.803368	−	1.39147i
$780$	−2.41188	−	4.17750i	−0.0863592	−	0.149579i
$781$	−3.16501	−	1.48175i	−0.113253	−	0.0530212i
$782$	−19.2883	−	11.1361i	−0.689747	−	0.398226i
$783$	−8.02774			−0.286888
$784$	32.6142	+	12.6930i	1.16479	+	0.453320i
$785$	13.3738			0.477331
$786$	0.518165	−	0.897488i	0.0184823	−	0.0320123i
$787$	22.5556	+	39.0675i	0.804021	+	1.39261i	0.916950	+	0.399003i	$0.130644\pi$
$787$	22.5556	+	39.0675i	0.804021	+	1.39261i	−0.112929	+	0.993603i	$0.536023\pi$
$788$	−19.0206	+	10.9815i	−0.677580	+	0.391201i
$789$	−0.279906	+	0.484812i	−0.00996493	+	0.0172598i
$790$			11.2551i			0.400439i
$791$	4.08968	+	3.50933i	0.145412	+	0.124777i
$792$	3.34344	+	4.79047i	0.118804	+	0.170222i
$793$	5.44294	−	9.42745i	0.193284	−	0.334778i
$794$	−2.69908	−	4.67494i	−0.0957867	−	0.165907i
$795$	−1.04317	−	1.80682i	−0.0369973	−	0.0640811i
$796$	−20.5175	−	11.8458i	−0.727222	−	0.419862i
$797$			6.70198i			0.237396i	0.992930	+	0.118698i	$0.0378721\pi$
$797$			6.70198i			0.237396i	−0.992930	+	0.118698i	$0.962128\pi$
$798$	−23.7662	+	8.35420i	−0.841315	+	0.295735i
$799$		−	11.0187i		−	0.389814i
$800$	9.99778	+	5.77222i	0.353475	+	0.204079i
$801$	−4.47304	+	2.58251i	−0.158047	+	0.0912486i
$802$	12.9799	−	7.49394i	0.458335	−	0.264620i
$803$	−2.79784	−	32.5512i	−0.0987337	−	1.14871i
$804$		−	10.5168i		−	0.370900i
$805$	−37.1367	−	6.97184i	−1.30890	−	0.245725i
$806$	−45.5330			−1.60383
$807$	−0.841274	+	1.45713i	−0.0296142	+	0.0512934i
$808$	−12.7220	+	7.34503i	−0.447557	+	0.258397i
$809$	−13.0181	+	7.51598i	−0.457691	+	0.264248i	−0.711073	−	0.703118i	$-0.751790\pi$
$809$	−13.0181	+	7.51598i	−0.457691	+	0.264248i	0.253382	+	0.967366i	$0.418457\pi$
$810$	−1.42854	+	2.47430i	−0.0501937	+	0.0869380i
$811$	−38.8505			−1.36423			−0.682113	−	0.731247i	$-0.738939\pi$
$811$	−38.8505			−1.36423			−0.682113	+	0.731247i	$0.738939\pi$
$812$	20.4486	+	3.83892i	0.717606	+	0.134720i
$813$		−	27.4237i		−	0.961792i
$814$	46.9307	−	4.03379i	1.64492	−	0.141384i
$815$	−18.2516	+	10.5375i	−0.639324	+	0.369114i
$816$	−6.47467	+	3.73815i	−0.226659	+	0.130861i
$817$	24.0555	+	13.8884i	0.841594	+	0.485895i
$818$		−	43.1131i		−	1.50741i
$819$	−7.42591	+	2.61032i	−0.259482	+	0.0912120i
$820$			13.1816i			0.460322i
$821$	−22.8357	−	13.1842i	−0.796973	−	0.460133i	0.0454387	−	0.998967i	$-0.485531\pi$
$821$	−22.8357	−	13.1842i	−0.796973	−	0.460133i	−0.842412	+	0.538835i	$0.818865\pi$
$822$	12.3384	+	21.3707i	0.430351	+	0.745389i
$823$	−13.9030	−	24.0807i	−0.484629	−	0.839402i	0.515215	−	0.857061i	$-0.327712\pi$
$823$	−13.9030	−	24.0807i	−0.484629	−	0.839402i	−0.999844	+	0.0176589i	$0.994379\pi$
$824$	−3.68110	+	6.37585i	−0.128237	+	0.222113i
$825$	4.29067	+	6.14765i	0.149382	+	0.214034i
$826$	−17.2201	−	14.7764i	−0.599164	−	0.514138i
$827$		−	6.14673i		−	0.213743i	−0.994273	−	0.106871i	$-0.965917\pi$
$827$		−	6.14673i		−	0.213743i	0.994273	−	0.106871i	$-0.0340833\pi$
$828$	4.22615	−	7.31991i	0.146869	−	0.254384i
$829$	39.6857	−	22.9126i	1.37834	−	0.795786i	0.386382	−	0.922339i	$-0.373725\pi$
$829$	39.6857	−	22.9126i	1.37834	−	0.795786i	0.991960	+	0.126553i	$0.0403914\pi$
$830$	14.5920	+	25.2740i	0.506494	+	0.877274i
$831$	−2.02534	+	3.50799i	−0.0702583	+	0.121691i
$832$	−3.52038			−0.122047
$833$	−8.16534	+	6.54980i	−0.282912	+	0.226937i
$834$	2.07369			0.0718062
$835$	−27.2804	−	15.7503i	−0.944077	−	0.545063i
$836$	16.2307	+	7.59867i	0.561351	+	0.262805i
$837$	4.43321	+	7.67855i	0.153234	+	0.265410i
$838$	−4.35904	+	7.55007i	−0.150580	+	0.260813i
$839$			16.5099i			0.569984i	0.958530	+	0.284992i	$0.0919909\pi$
$839$			16.5099i			0.569984i	−0.958530	+	0.284992i	$0.908009\pi$
$840$	−5.02302	+	5.85371i	−0.173311	+	0.201972i
$841$	−35.4447			−1.22223
$842$	40.0833	+	23.1421i	1.38136	+	0.797530i
$843$	−0.687827	−	1.19135i	−0.0236900	−	0.0410323i
$844$	−2.59143	+	1.49616i	−0.0892005	+	0.0515000i
$845$	−5.94709	−	3.43356i	−0.204586	−	0.118118i
$846$	12.7191			0.437291
$847$	0.410109	−	29.1004i	0.0140915	−	0.999901i
$848$	6.30193			0.216409
$849$	12.8925	+	7.44347i	0.442469	+	0.255459i
$850$	−5.05297	+	2.91734i	−0.173316	+	0.100064i
$851$	35.4962	+	61.4813i	1.21680	+	2.10755i
$852$	0.893895	+	0.516090i	0.0306243	+	0.0176810i
$853$	−31.2895			−1.07133			−0.535666	−	0.844430i	$-0.679940\pi$
$853$	−31.2895			−1.07133			−0.535666	+	0.844430i	$0.679940\pi$
$854$	16.4237	+	3.08329i	0.562006	+	0.105508i
$855$		−	9.13010i		−	0.312243i
$856$	2.51659	−	4.35886i	0.0860152	−	0.148983i
$857$	−2.20428	−	3.81793i	−0.0752968	−	0.130418i	0.825919	−	0.563790i	$-0.190657\pi$
$857$	−2.20428	−	3.81793i	−0.0752968	−	0.130418i	−0.901215	+	0.433372i	$0.857324\pi$
$858$	15.4255	+	7.22170i	0.526619	+	0.246545i
$859$	−28.9668	−	16.7240i	−0.988333	−	0.570614i	−0.0835573	−	0.996503i	$-0.526628\pi$
$859$	−28.9668	−	16.7240i	−0.988333	−	0.570614i	−0.904776	+	0.425889i	$0.859961\pi$
$860$	−8.16466			−0.278412
$861$	21.1402	+	3.96875i	0.720456	+	0.135255i
$862$	7.79567			0.265522
$863$	−1.74877	+	3.02897i	−0.0595290	+	0.103107i	−0.894254	−	0.447560i	$-0.852293\pi$
$863$	−1.74877	+	3.02897i	−0.0595290	+	0.103107i	0.834725	+	0.550667i	$0.185627\pi$
$864$	−2.55363	−	4.42301i	−0.0868762	−	0.150474i
$865$	4.06957	−	2.34957i	0.138369	−	0.0798876i
$866$	−0.539430	+	0.934320i	−0.0183306	+	0.0317495i
$867$			14.7638i			0.501406i
$868$	−7.62055	−	21.6791i	−0.258658	−	0.735838i
$869$	−7.47771	−	10.7140i	−0.253664	−	0.363448i
$870$	−11.4679	+	19.8630i	−0.388799	+	0.673420i
$871$	15.9702	+	27.6612i	0.541130	+	0.937265i
$872$	7.22576	+	12.5154i	0.244695	+	0.423824i
$873$	−2.90973	−	1.67993i	−0.0984793	−	0.0568571i
$874$			82.1565i			2.77898i
$875$	−20.7048	+	24.1289i	−0.699951	+	0.815707i
$876$			9.64966i			0.326032i
$877$	−2.38486	−	1.37690i	−0.0805311	−	0.0464946i	0.459194	−	0.888336i	$-0.348138\pi$
$877$	−2.38486	−	1.37690i	−0.0805311	−	0.0464946i	−0.539725	+	0.841842i	$0.681472\pi$
$878$	−32.3297	+	18.6655i	−1.09107	+	0.629932i
$879$	−20.5283	+	11.8520i	−0.692403	+	0.399759i
$880$	27.3448	−	2.35034i	0.921794	−	0.0792301i
$881$			1.11529i			0.0375752i	0.999823	+	0.0187876i	$0.00598063\pi$
$881$			1.11529i			0.0375752i	−0.999823	+	0.0187876i	$0.994019\pi$
$882$	−7.56054	−	9.42539i	−0.254577	−	0.317369i
$883$	17.3039			0.582323			0.291161	−	0.956674i	$-0.405958\pi$
$883$	17.3039			0.582323			0.291161	+	0.956674i	$0.405958\pi$
$884$	−2.17904	+	3.77421i	−0.0732891	+	0.126940i
$885$	7.12193	−	4.11185i	0.239401	−	0.138218i
$886$	−33.7239	+	19.4705i	−1.13298	+	0.654125i
$887$	−19.2938	+	33.4178i	−0.647822	+	1.12206i	0.335820	+	0.941926i	$0.390987\pi$
$887$	−19.2938	+	33.4178i	−0.647822	+	1.12206i	−0.983642	+	0.180135i	$0.942347\pi$
$888$	14.4922			0.486327
$889$	−24.6025	+	28.6712i	−0.825142	+	0.961601i
$890$			14.7569i			0.494651i
$891$	−0.284023	−	3.30444i	−0.00951514	−	0.110703i
$892$	8.40652	−	4.85350i	0.281471	−	0.162507i
$893$	−35.1998	+	20.3226i	−1.17792	+	0.680070i
$894$	−26.0156	−	15.0201i	−0.870091	−	0.502347i
$895$			4.89592i			0.163653i
$896$	−10.7543	−	30.5940i	−0.359274	−	1.02207i
$897$			25.6703i			0.857106i
$898$	1.77884	+	1.02701i	0.0593606	+	0.0342718i
$899$	35.5887	+	61.6414i	1.18695	+	2.05586i
$900$	−1.10713	−	1.91761i	−0.0369043	−	0.0639202i
$901$	−0.942459	+	1.63239i	−0.0313979	+	0.0543827i
$902$	−26.6379	−	38.1666i	−0.886945	−	1.27081i
$903$	−2.45823	+	13.0942i	−0.0818049	+	0.435748i
$904$		−	3.58765i		−	0.119323i
$905$	13.3462	−	23.1163i	0.443643	−	0.768413i
$906$	12.1314	−	7.00408i	0.403039	−	0.232695i
$907$	14.4016	+	24.9444i	0.478198	+	0.828264i	0.999688	−	0.0249939i	$-0.00795662\pi$
$907$	14.4016	+	24.9444i	0.478198	+	0.828264i	−0.521489	+	0.853258i	$0.674623\pi$
$908$	6.50985	−	11.2754i	0.216037	−	0.374187i
$909$	8.34007			0.276623
$910$	−4.14947	+	22.1029i	−0.137554	+	0.732703i
$911$	−30.2528			−1.00232			−0.501161	−	0.865354i	$-0.667093\pi$
$911$	−30.2528			−1.00232			−0.501161	+	0.865354i	$0.667093\pi$
$912$	23.8834	+	13.7891i	0.790859	+	0.456603i
$913$	−30.6821	−	14.3643i	−1.01543	−	0.475389i
$914$	6.29250	+	10.8989i	0.208138	+	0.360505i
$915$	−3.02815	+	5.24491i	−0.100108	+	0.173392i
$916$			8.43625i			0.278742i
$917$	−1.49855	+	0.526762i	−0.0494863	+	0.0173952i
$918$	2.58126			0.0851941
$919$	−25.0505	−	14.4629i	−0.826340	−	0.477087i	0.0262580	−	0.999655i	$-0.491641\pi$
$919$	−25.0505	−	14.4629i	−0.826340	−	0.477087i	−0.852598	+	0.522568i	$0.824974\pi$
$920$	12.5776	+	21.7851i	0.414673	+	0.718234i
$921$	−25.9586	+	14.9872i	−0.855364	+	0.493845i
$922$	−14.9107	−	8.60870i	−0.491058	−	0.283512i
$923$	−3.13481			−0.103184
$924$	−0.856726	+	8.55304i	−0.0281842	+	0.281374i
$925$	18.5980			0.611498
$926$	−16.4311	−	9.48647i	−0.539958	−	0.311745i
$927$	3.61980	−	2.08989i	0.118890	−	0.0686410i
$928$	−20.4999	−	35.5068i	−0.672941	−	1.16557i
$929$	−10.4417	−	6.02854i	−0.342583	−	0.197790i	0.318831	−	0.947812i	$-0.396710\pi$
$929$	−10.4417	−	6.02854i	−0.342583	−	0.197790i	−0.661413	+	0.750021i	$0.730043\pi$
$930$	25.3320			0.830671
$931$	35.9836	+	14.0043i	1.17931	+	0.458972i
$932$			0.401181i			0.0131411i
$933$	4.59767	−	7.96340i	0.150521	−	0.260710i
$934$	21.6281	+	37.4610i	0.707694	+	1.22576i
$935$	−3.48064	+	7.43463i	−0.113829	+	0.243138i
$936$	4.53820	+	2.62013i	0.148336	+	0.0856417i
$937$	32.2826			1.05463			0.527314	−	0.849671i	$-0.323199\pi$
$937$	32.2826			1.05463			0.527314	+	0.849671i	$0.323199\pi$
$938$	−31.9292	+	37.2095i	−1.04252	+	1.21493i
$939$	−18.6771			−0.609503
$940$	5.97357	−	10.3465i	0.194837	−	0.337467i
$941$	0.124050	+	0.214862i	0.00404393	+	0.00700429i	0.868040	−	0.496494i	$-0.165379\pi$
$941$	0.124050	+	0.214862i	0.00404393	+	0.00700429i	−0.863996	+	0.503498i	$0.832046\pi$
$942$	12.0787	−	6.97363i	0.393545	−	0.227213i
$943$	35.0738	−	60.7497i	1.14216	−	1.97828i
$944$			24.8403i			0.808484i
$945$	4.13137	−	1.45224i	0.134393	−	0.0472413i
$946$	23.6403	−	16.4994i	0.768613	−	0.536443i
$947$	−19.4577	+	33.7018i	−0.632292	+	1.09516i	0.354790	+	0.934946i	$0.384552\pi$
$947$	−19.4577	+	33.7018i	−0.632292	+	1.09516i	−0.987082	+	0.160215i	$0.948781\pi$
$948$	1.92949	+	3.34197i	0.0626668	+	0.108542i
$949$	−14.6534	−	25.3804i	−0.475669	−	0.823883i
$950$	18.6391	+	10.7613i	0.604734	+	0.349143i
$951$		−	9.44657i		−	0.306326i
$952$	6.84912	+	1.28582i	0.221981	+	0.0416735i
$953$			2.04695i			0.0663073i	0.999450	+	0.0331537i	$0.0105551\pi$
$953$			2.04695i			0.0663073i	−0.999450	+	0.0331537i	$0.989445\pi$
$954$	−1.88429	−	1.08790i	−0.0610062	−	0.0352220i
$955$	−21.6776	+	12.5156i	−0.701471	+	0.404994i
$956$	−0.535762	+	0.309322i	−0.0173278	+	0.0100042i
$957$	−2.28007	−	26.5272i	−0.0737041	−	0.857503i
$958$		−	42.1265i		−	1.36105i
$959$	6.97882	−	37.1739i	0.225358	−	1.20041i
$960$	1.95855			0.0632119
$961$	23.8068	−	41.2345i	0.767960	−	1.33015i
$962$	36.5922	−	21.1265i	1.17978	−	0.681146i
$963$	−2.47468	+	1.42876i	−0.0797454	+	0.0460410i
$964$	−2.91250	+	5.04461i	−0.0938055	+	0.162476i
$965$	−10.5715			−0.340308
$966$	−37.1758	+	13.0679i	−1.19611	+	0.420451i
$967$		−	21.7478i		−	0.699361i	−0.936869	−	0.349681i	$-0.886290\pi$
$967$		−	21.7478i		−	0.699361i	0.936869	−	0.349681i	$-0.113710\pi$
$968$	−14.8802	+	12.4088i	−0.478268	+	0.398835i
$969$	−7.14357	+	4.12434i	−0.229485	+	0.132493i
$970$	−8.31331	+	4.79969i	−0.266924	+	0.154109i
$971$	1.38049	+	0.797024i	0.0443019	+	0.0255777i	0.521987	−	0.852953i	$-0.325191\pi$
$971$	1.38049	+	0.797024i	0.0443019	+	0.0255777i	−0.477685	+	0.878531i	$0.658524\pi$
$972$			0.979587i			0.0314203i
$973$	−2.41213	−	2.06983i	−0.0773293	−	0.0663557i
$974$		−	13.2824i		−	0.425597i
$975$	5.82392	+	3.36244i	0.186515	+	0.107684i
$976$	−9.14678	−	15.8427i	−0.292781	−	0.507112i
$977$	8.79118	+	15.2268i	0.281255	+	0.487147i	0.971694	−	0.236243i	$-0.0759161\pi$
$977$	8.79118	+	15.2268i	0.281255	+	0.487147i	−0.690439	+	0.723390i	$0.742583\pi$
$978$	−10.9894	+	19.0342i	−0.351402	+	0.608646i
$979$	−9.80421	−	14.0474i	−0.313344	−	0.448957i
$980$	−11.2181	+	1.72356i	−0.358348	+	0.0550573i
$981$		−	8.20464i		−	0.261954i
$982$	10.5412	−	18.2579i	0.336383	−	0.582632i
$983$	11.5990	−	6.69671i	0.369952	−	0.213592i	−0.303485	−	0.952836i	$-0.598150\pi$
$983$	11.5990	−	6.69671i	0.369952	−	0.213592i	0.673438	+	0.739244i	$0.264817\pi$
$984$	−7.15987	−	12.4013i	−0.228248	−	0.395338i
$985$	−18.5551	+	32.1384i	−0.591215	+	1.02401i
$986$	20.7217			0.659912
$987$	−14.7949	−	12.6954i	−0.470926	−	0.404098i
$988$	16.0759			0.511441
$989$	37.6282	+	21.7247i	1.19651	+	0.690804i
$990$	−8.58191	−	4.01776i	−0.272751	−	0.127693i
$991$	6.39096	+	11.0695i	0.203016	+	0.351633i	0.949499	−	0.313771i	$-0.101592\pi$
$991$	6.39096	+	11.0695i	0.203016	+	0.351633i	−0.746483	+	0.665404i	$0.768259\pi$
$992$	−22.6416	+	39.2163i	−0.718870	+	1.24512i
$993$		−	24.7954i		−	0.786857i
$994$	−1.59583	−	4.53984i	−0.0506165	−	0.143995i
$995$	−40.0307			−1.26906
$996$	8.66554	+	5.00305i	0.274578	+	0.158528i
$997$	−24.8450	−	43.0328i	−0.786849	−	1.36286i	−0.927888	−	0.372859i	$-0.878378\pi$
$997$	−24.8450	−	43.0328i	−0.786849	−	1.36286i	0.141039	−	0.990004i	$-0.454956\pi$
$998$	38.1140	−	22.0051i	1.20648	−	0.696559i
$999$	−7.12543	−	4.11387i	−0.225439	−	0.130157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.208.4	yes	32
3.2	odd	2		693.2.bg.b.208.13		32
7.2	even	3		1617.2.c.a.538.25		32
7.3	odd	6	inner	231.2.p.a.10.13	yes	32
7.5	odd	6		1617.2.c.a.538.26		32
11.10	odd	2	inner	231.2.p.a.208.13	yes	32
21.17	even	6		693.2.bg.b.10.4		32
33.32	even	2		693.2.bg.b.208.4		32
77.10	even	6	inner	231.2.p.a.10.4	✓	32
77.54	even	6		1617.2.c.a.538.8		32
77.65	odd	6		1617.2.c.a.538.7		32
231.164	odd	6		693.2.bg.b.10.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.4	✓	32	77.10	even	6	inner
231.2.p.a.10.13	yes	32	7.3	odd	6	inner
231.2.p.a.208.4	yes	32	1.1	even	1	trivial
231.2.p.a.208.13	yes	32	11.10	odd	2	inner
693.2.bg.b.10.4		32	21.17	even	6
693.2.bg.b.10.13		32	231.164	odd	6
693.2.bg.b.208.4		32	33.32	even	2
693.2.bg.b.208.13		32	3.2	odd	2
1617.2.c.a.538.7		32	77.65	odd	6
1617.2.c.a.538.8		32	77.54	even	6
1617.2.c.a.538.25		32	7.2	even	3
1617.2.c.a.538.26		32	7.5	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49489 - 0.863074i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.489794 + 0.848348i) q^{4} +(1.43342 + 0.827587i) q^{5} +1.72615 q^{6} +(-2.00786 - 1.72293i) q^{7} +1.76138i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.49489 - 0.863074i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.489794 + 0.848348i) q^{4} +(1.43342 + 0.827587i) q^{5} +1.72615 q^{6} +(-2.00786 - 1.72293i) q^{7} +1.76138i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.42854 - 2.47430i) q^{10} +(3.00374 + 1.40625i) q^{11} +(-0.848348 - 0.489794i) q^{12} +2.97508 q^{13} +(1.51451 + 4.30852i) q^{14} -1.65517 q^{15} +(2.49979 - 4.32977i) q^{16} +(0.747692 + 1.29504i) q^{17} +(-1.49489 + 0.863074i) q^{18} +(2.75805 - 4.77708i) q^{19} +1.62139i q^{20} +(2.60032 + 0.488171i) q^{21} +(-3.27656 - 4.69464i) q^{22} +(4.31421 - 7.47244i) q^{23} +(-0.880692 - 1.52540i) q^{24} +(-1.13020 - 1.95756i) q^{25} +(-4.44742 - 2.56772i) q^{26} +1.00000i q^{27} +(0.478206 - 2.54725i) q^{28} +8.02774i q^{29} +(2.47430 + 1.42854i) q^{30} +(7.67855 - 4.43321i) q^{31} +(-4.42301 + 2.55363i) q^{32} +(-3.30444 + 0.284023i) q^{33} -2.58126i q^{34} +(-1.45224 - 4.13137i) q^{35} +0.979587 q^{36} +(-4.11387 + 7.12543i) q^{37} +(-8.24595 + 4.76080i) q^{38} +(-2.57650 + 1.48754i) q^{39} +(-1.45770 + 2.52481i) q^{40} +8.12983 q^{41} +(-3.46587 - 2.97403i) q^{42} +5.03560i q^{43} +(0.278226 + 3.23699i) q^{44} +(1.43342 - 0.827587i) q^{45} +(-12.8985 + 7.44697i) q^{46} +(-6.38129 - 3.68424i) q^{47} +4.99958i q^{48} +(1.06302 + 6.91881i) q^{49} +3.90179i q^{50} +(-1.29504 - 0.747692i) q^{51} +(1.45718 + 2.52390i) q^{52} +(0.630245 + 1.09162i) q^{53} +(0.863074 - 1.49489i) q^{54} +(3.14184 + 4.50161i) q^{55} +(3.03474 - 3.53661i) q^{56} +5.51610i q^{57} +(6.92854 - 12.0006i) q^{58} +(-4.30283 + 2.48424i) q^{59} +(-0.810694 - 1.40416i) q^{60} +(1.82951 - 3.16880i) q^{61} -15.3048 q^{62} +(-2.49603 + 0.877394i) q^{63} -1.18329 q^{64} +(4.26455 + 2.46214i) q^{65} +(5.18490 + 2.42739i) q^{66} +(5.36799 + 9.29763i) q^{67} +(-0.732430 + 1.26861i) q^{68} +8.62843i q^{69} +(-1.39474 + 7.42932i) q^{70} -1.05369 q^{71} +(1.52540 + 0.880692i) q^{72} +(-4.92537 - 8.53099i) q^{73} +(12.2996 - 7.10115i) q^{74} +(1.95756 + 1.13020i) q^{75} +5.40350 q^{76} +(-3.60823 - 7.99879i) q^{77} +5.13544 q^{78} +(-3.41161 - 1.96969i) q^{79} +(7.16651 - 4.13759i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-12.1532 - 7.01665i) q^{82} -10.2146 q^{83} +(0.859484 + 2.44508i) q^{84} +2.47512i q^{85} +(4.34610 - 7.52766i) q^{86} +(-4.01387 - 6.95223i) q^{87} +(-2.47694 + 5.29074i) q^{88} +(-4.47304 - 2.58251i) q^{89} -2.85707 q^{90} +(-5.97356 - 5.12586i) q^{91} +8.45230 q^{92} +(-4.43321 + 7.67855i) q^{93} +(6.35954 + 11.0150i) q^{94} +(7.90690 - 4.56505i) q^{95} +(2.55363 - 4.42301i) q^{96} -3.35986i q^{97} +(4.38235 - 11.2603i) q^{98} +(2.71972 - 1.89819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more