LMFDB - Embedded newform 110.4.g.a.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(31,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.31"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 26x^{6} - 51x^{5} + 301x^{4} - 125x^{3} + 250x^{2} + 3125x + 15625 $ x^8 - x^7 + 26x^6 - 51x^5 + 301x^4 - 125x^3 + 250x^2 + 3125x + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.2
Root			$2.56926 + 1.86668i$ of defining polynomial
Character	$\chi$	$=$	110.31
Dual form			110.4.g.a.71.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.618034 + 1.90211i) q^{2} +(1.56926 - 1.14014i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(1.54508 + 4.75528i) q^{5} +(1.19881 + 3.68956i) q^{6} +(2.32355 + 1.68816i) q^{7} +(6.47214 - 4.70228i) q^{8} +(-7.18078 + 22.1002i) q^{9} -10.0000 q^{10} +(32.9286 + 15.7068i) q^{11} -7.75887 q^{12} +(-9.69990 + 29.8532i) q^{13} +(-4.64710 + 3.37632i) q^{14} +(7.84632 + 5.70069i) q^{15} +(4.94427 + 15.2169i) q^{16} +(24.7342 + 76.1240i) q^{17} +(-37.5991 - 27.3173i) q^{18} +(-22.8513 + 16.6024i) q^{19} +(6.18034 - 19.0211i) q^{20} +5.57100 q^{21} +(-50.2272 + 52.9267i) q^{22} -11.0833 q^{23} +(4.79525 - 14.7583i) q^{24} +(-20.2254 + 14.6946i) q^{25} +(-50.7893 - 36.9006i) q^{26} +(30.1126 + 92.6772i) q^{27} +(-3.55007 - 10.9260i) q^{28} +(-120.709 - 87.7006i) q^{29} +(-15.6926 + 11.4014i) q^{30} +(-1.30501 + 4.01639i) q^{31} -32.0000 q^{32} +(69.5817 - 12.8950i) q^{33} -160.083 q^{34} +(-4.43759 + 13.6575i) q^{35} +(75.1981 - 54.6346i) q^{36} +(95.6389 + 69.4857i) q^{37} +(-17.4568 - 53.7266i) q^{38} +(18.8151 + 57.9068i) q^{39} +(32.3607 + 23.5114i) q^{40} +(178.364 - 129.589i) q^{41} +(-3.44307 + 10.5967i) q^{42} +305.021 q^{43} +(-69.6304 - 128.248i) q^{44} -116.187 q^{45} +(6.84983 - 21.0816i) q^{46} +(395.602 - 287.422i) q^{47} +(25.1082 + 18.2422i) q^{48} +(-103.444 - 318.367i) q^{49} +(-15.4508 - 47.5528i) q^{50} +(125.606 + 91.2583i) q^{51} +(101.579 - 73.8012i) q^{52} +(135.112 - 415.832i) q^{53} -194.893 q^{54} +(-23.8128 + 180.853i) q^{55} +22.9765 q^{56} +(-16.9307 + 52.1072i) q^{57} +(241.419 - 175.401i) q^{58} +(-339.772 - 246.859i) q^{59} +(-11.9881 - 36.8956i) q^{60} +(74.1097 + 228.086i) q^{61} +(-6.83310 - 4.96454i) q^{62} +(-53.9935 + 39.2286i) q^{63} +(19.7771 - 60.8676i) q^{64} -156.948 q^{65} +(-18.4760 + 140.322i) q^{66} -382.944 q^{67} +(98.9367 - 304.496i) q^{68} +(-17.3926 + 12.6364i) q^{69} +(-23.2355 - 16.8816i) q^{70} +(-126.799 - 390.246i) q^{71} +(57.4462 + 176.801i) q^{72} +(364.465 + 264.800i) q^{73} +(-191.278 + 138.971i) q^{74} +(-14.9851 + 46.1195i) q^{75} +112.983 q^{76} +(49.9958 + 92.0844i) q^{77} -121.774 q^{78} +(-150.166 + 462.163i) q^{79} +(-64.7214 + 47.0228i) q^{80} +(-354.668 - 257.681i) q^{81} +(136.258 + 419.358i) q^{82} +(372.213 + 1145.55i) q^{83} +(-18.0281 - 13.0982i) q^{84} +(-323.775 + 235.236i) q^{85} +(-188.514 + 580.185i) q^{86} -289.416 q^{87} +(286.977 - 53.1832i) q^{88} -1533.91 q^{89} +(71.8078 - 221.002i) q^{90} +(-72.9352 + 52.9905i) q^{91} +(35.8662 + 26.0583i) q^{92} +(2.53134 + 7.79067i) q^{93} +(302.213 + 930.117i) q^{94} +(-114.256 - 83.0121i) q^{95} +(-50.2165 + 36.4844i) q^{96} +(317.163 - 976.128i) q^{97} +669.502 q^{98} +(-583.577 + 614.942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 10 q^{5} - 26 q^{6} - 15 q^{7} + 16 q^{8} - 41 q^{9} - 80 q^{10} + 23 q^{11} - 48 q^{12} - 32 q^{13} + 30 q^{14} - 35 q^{15} - 32 q^{16} + 81 q^{17} - 138 q^{18} + 157 q^{19}+ \cdots - 2906 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 10 * q^5 - 26 * q^6 - 15 * q^7 + 16 * q^8 - 41 * q^9 - 80 * q^10 + 23 * q^11 - 48 * q^12 - 32 * q^13 + 30 * q^14 - 35 * q^15 - 32 * q^16 + 81 * q^17 - 138 * q^18 + 157 * q^19 - 40 * q^20 + 140 * q^21 - 76 * q^22 - 518 * q^23 - 104 * q^24 - 50 * q^25 + 54 * q^26 + 152 * q^27 - 40 * q^28 - 73 * q^29 + 70 * q^30 + 460 * q^31 - 256 * q^32 - 67 * q^33 - 92 * q^34 - 50 * q^35 + 276 * q^36 + 46 * q^38 + 1063 * q^39 + 80 * q^40 - 564 * q^41 - 50 * q^42 - 294 * q^43 - 428 * q^44 - 280 * q^45 + 146 * q^46 + 1652 * q^47 - 112 * q^48 + 641 * q^49 + 100 * q^50 + 675 * q^51 - 108 * q^52 + 679 * q^53 + 636 * q^54 - 285 * q^55 - 400 * q^56 - 1585 * q^57 + 146 * q^58 - 143 * q^59 + 260 * q^60 + 826 * q^61 + 110 * q^62 + 105 * q^63 - 128 * q^64 + 590 * q^65 - 1376 * q^66 - 1378 * q^67 + 324 * q^68 + 1435 * q^69 + 150 * q^70 - 8 * q^71 + 328 * q^72 + 2017 * q^73 + 325 * q^75 - 1072 * q^76 - 360 * q^77 + 1164 * q^78 - 1763 * q^79 - 160 * q^80 - 360 * q^81 - 862 * q^82 + 581 * q^83 - 380 * q^84 - 520 * q^85 + 448 * q^86 - 4054 * q^87 - 824 * q^88 - 3368 * q^89 + 410 * q^90 - 2010 * q^91 + 1328 * q^92 - 3737 * q^93 + 2846 * q^94 + 785 * q^95 + 224 * q^96 + 3604 * q^97 + 3828 * q^98 - 2906 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.618034	+	1.90211i	−0.218508	+	0.672499i
$2$	−0.618034	+	1.90211i	−0.218508	+	0.672499i
$3$	1.56926	−	1.14014i	0.302005	−	0.219420i	−0.426453	−	0.904510i	$-0.640237\pi$
$3$	1.56926	−	1.14014i	0.302005	−	0.219420i	0.728458	+	0.685090i	$0.240237\pi$
$4$	−3.23607	−	2.35114i	−0.404508	−	0.293893i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$6$	1.19881	+	3.68956i	0.0815688	+	0.251043i
$7$	2.32355	+	1.68816i	0.125460	+	0.0911520i	0.648746	−	0.761005i	$-0.275294\pi$
$7$	2.32355	+	1.68816i	0.125460	+	0.0911520i	−0.523286	+	0.852157i	$0.675294\pi$
$8$	6.47214	−	4.70228i	0.286031	−	0.207813i
$9$	−7.18078	+	22.1002i	−0.265955	+	0.818525i
$10$	−10.0000			−0.316228
$11$	32.9286	+	15.7068i	0.902578	+	0.430526i
$11$	32.9286	+	15.7068i	0.902578	+	0.430526i
$12$	−7.75887			−0.186649
$13$	−9.69990	+	29.8532i	−0.206944	+	0.636907i	0.792684	+	0.609632i	$0.208683\pi$
$13$	−9.69990	+	29.8532i	−0.206944	+	0.636907i	−0.999628	+	0.0272749i	$0.991317\pi$
$14$	−4.64710	+	3.37632i	−0.0887136	+	0.0644542i
$15$	7.84632	+	5.70069i	0.135061	+	0.0981274i
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	24.7342	+	76.1240i	0.352878	+	1.08605i	0.957230	+	0.289329i	$0.0934320\pi$
$17$	24.7342	+	76.1240i	0.352878	+	1.08605i	−0.604352	+	0.796717i	$0.706568\pi$
$18$	−37.5991	−	27.3173i	−0.492343	−	0.357708i
$19$	−22.8513	+	16.6024i	−0.275918	+	0.200466i	−0.717135	−	0.696934i	$-0.754547\pi$
$19$	−22.8513	+	16.6024i	−0.275918	+	0.200466i	0.441217	+	0.897400i	$0.354547\pi$
$20$	6.18034	−	19.0211i	0.0690983	−	0.212663i
$21$	5.57100			0.0578901
$22$	−50.2272	+	52.9267i	−0.486748	+	0.512909i
$23$	−11.0833			−0.100479			−0.0502395	−	0.998737i	$-0.515998\pi$
$23$	−11.0833			−0.100479			−0.0502395	+	0.998737i	$0.515998\pi$
$24$	4.79525	−	14.7583i	0.0407844	−	0.125521i
$25$	−20.2254	+	14.6946i	−0.161803	+	0.117557i
$26$	−50.7893	−	36.9006i	−0.383100	−	0.278339i
$27$	30.1126	+	92.6772i	0.214636	+	0.660583i
$28$	−3.55007	−	10.9260i	−0.0239607	−	0.0737435i
$29$	−120.709	−	87.7006i	−0.772937	−	0.561572i	0.129914	−	0.991525i	$-0.458530\pi$
$29$	−120.709	−	87.7006i	−0.772937	−	0.561572i	−0.902851	+	0.429953i	$0.858530\pi$
$30$	−15.6926	+	11.4014i	−0.0955024	+	0.0693866i
$31$	−1.30501	+	4.01639i	−0.00756084	+	0.0232699i	−0.954766	−	0.297359i	$-0.903894\pi$
$31$	−1.30501	+	4.01639i	−0.00756084	+	0.0232699i	0.947205	+	0.320629i	$0.103894\pi$
$32$	−32.0000			−0.176777
$33$	69.5817	−	12.8950i	0.367049	−	0.0680224i
$34$	−160.083			−0.807471
$35$	−4.43759	+	13.6575i	−0.0214311	+	0.0659582i
$36$	75.1981	−	54.6346i	0.348139	−	0.252938i
$37$	95.6389	+	69.4857i	0.424944	+	0.308740i	0.779624	−	0.626248i	$-0.215410\pi$
$37$	95.6389	+	69.4857i	0.424944	+	0.308740i	−0.354680	+	0.934988i	$0.615410\pi$
$38$	−17.4568	−	53.7266i	−0.0745229	−	0.229358i
$39$	18.8151	+	57.9068i	0.0772519	+	0.237757i
$40$	32.3607	+	23.5114i	0.127917	+	0.0929370i
$41$	178.364	−	129.589i	0.679408	−	0.493619i	−0.193753	−	0.981050i	$-0.562066\pi$
$41$	178.364	−	129.589i	0.679408	−	0.493619i	0.873161	+	0.487431i	$0.162066\pi$
$42$	−3.44307	+	10.5967i	−0.0126494	+	0.0389310i
$43$	305.021			1.08175			0.540876	−	0.841102i	$-0.318093\pi$
$43$	305.021			1.08175			0.540876	+	0.841102i	$0.318093\pi$
$44$	−69.6304	−	128.248i	−0.238572	−	0.439412i
$45$	−116.187			−0.384893
$46$	6.84983	−	21.0816i	0.0219555	−	0.0675720i
$47$	395.602	−	287.422i	1.22776	−	0.892017i	0.231036	−	0.972945i	$-0.425789\pi$
$47$	395.602	−	287.422i	1.22776	−	0.892017i	0.996720	+	0.0809287i	$0.0257886\pi$
$48$	25.1082	+	18.2422i	0.0755013	+	0.0548549i
$49$	−103.444	−	318.367i	−0.301585	−	0.928185i
$50$	−15.4508	−	47.5528i	−0.0437016	−	0.134500i
$51$	125.606	+	91.2583i	0.344871	+	0.250563i
$52$	101.579	−	73.8012i	0.270893	−	0.196815i
$53$	135.112	−	415.832i	0.350171	−	1.07772i	−0.608585	−	0.793488i	$-0.708263\pi$
$53$	135.112	−	415.832i	0.350171	−	1.07772i	0.958757	−	0.284228i	$-0.0917373\pi$
$54$	−194.893			−0.491141
$55$	−23.8128	+	180.853i	−0.0583803	+	0.443387i
$56$	22.9765			0.0548280
$57$	−16.9307	+	52.1072i	−0.0393425	+	0.121084i
$58$	241.419	−	175.401i	0.546549	−	0.397091i
$59$	−339.772	−	246.859i	−0.749738	−	0.544717i	0.146007	−	0.989283i	$-0.453358\pi$
$59$	−339.772	−	246.859i	−0.749738	−	0.544717i	−0.895746	+	0.444567i	$0.853358\pi$
$60$	−11.9881	−	36.8956i	−0.0257943	−	0.0793867i
$61$	74.1097	+	228.086i	0.155554	+	0.478745i	0.998217	−	0.0596966i	$-0.0190133\pi$
$61$	74.1097	+	228.086i	0.155554	+	0.478745i	−0.842663	+	0.538441i	$0.819013\pi$
$62$	−6.83310	−	4.96454i	−0.0139968	−	0.0101693i
$63$	−53.9935	+	39.2286i	−0.107977	+	0.0784498i
$64$	19.7771	−	60.8676i	0.0386271	−	0.118882i
$65$	−156.948			−0.299492
$66$	−18.4760	+	140.322i	−0.0344582	+	0.261703i
$67$	−382.944			−0.698270			−0.349135	−	0.937073i	$-0.613524\pi$
$67$	−382.944			−0.698270			−0.349135	+	0.937073i	$0.613524\pi$
$68$	98.9367	−	304.496i	0.176439	−	0.543023i
$69$	−17.3926	+	12.6364i	−0.0303452	+	0.0220471i
$70$	−23.2355	−	16.8816i	−0.0396739	−	0.0288248i
$71$	−126.799	−	390.246i	−0.211947	−	0.652306i	−0.999356	−	0.0358754i	$-0.988578\pi$
$71$	−126.799	−	390.246i	−0.211947	−	0.652306i	0.787409	−	0.616431i	$-0.211422\pi$
$72$	57.4462	+	176.801i	0.0940292	+	0.289392i
$73$	364.465	+	264.800i	0.584349	+	0.424554i	0.840289	−	0.542138i	$-0.182385\pi$
$73$	364.465	+	264.800i	0.584349	+	0.424554i	−0.255941	+	0.966693i	$0.582385\pi$
$74$	−191.278	+	138.971i	−0.300481	+	0.218312i
$75$	−14.9851	+	46.1195i	−0.0230711	+	0.0710057i
$76$	112.983			0.170527
$77$	49.9958	+	92.0844i	0.0739942	+	0.136286i
$78$	−121.774			−0.176771
$79$	−150.166	+	462.163i	−0.213860	+	0.658194i	0.785372	+	0.619024i	$0.212472\pi$
$79$	−150.166	+	462.163i	−0.213860	+	0.658194i	−0.999233	+	0.0391706i	$0.987528\pi$
$80$	−64.7214	+	47.0228i	−0.0904508	+	0.0657164i
$81$	−354.668	−	257.681i	−0.486513	−	0.353472i
$82$	136.258	+	419.358i	0.183502	+	0.564761i
$83$	372.213	+	1145.55i	0.492237	+	1.51495i	0.821219	+	0.570613i	$0.193294\pi$
$83$	372.213	+	1145.55i	0.492237	+	1.51495i	−0.328982	+	0.944336i	$0.606706\pi$
$84$	−18.0281	−	13.0982i	−0.0234170	−	0.0170135i
$85$	−323.775	+	235.236i	−0.413156	+	0.300176i
$86$	−188.514	+	580.185i	−0.236371	+	0.727477i
$87$	−289.416			−0.356651
$88$	286.977	−	53.1832i	0.347634	−	0.0644244i
$89$	−1533.91			−1.82689			−0.913447	−	0.406957i	$-0.866590\pi$
$89$	−1533.91			−1.82689			−0.913447	+	0.406957i	$0.866590\pi$
$90$	71.8078	−	221.002i	0.0841023	−	0.258840i
$91$	−72.9352	+	52.9905i	−0.0840185	+	0.0610430i
$92$	35.8662	+	26.0583i	0.0406446	+	0.0295301i
$93$	2.53134	+	7.79067i	0.00282245	+	0.00868661i
$94$	302.213	+	930.117i	0.331605	+	1.02058i
$95$	−114.256	−	83.0121i	−0.123394	−	0.0896512i
$96$	−50.2165	+	36.4844i	−0.0533875	+	0.0387883i
$97$	317.163	−	976.128i	0.331990	−	1.02176i	−0.636196	−	0.771528i	$-0.719493\pi$
$97$	317.163	−	976.128i	0.331990	−	1.02176i	0.968186	−	0.250233i	$-0.0805071\pi$
$98$	669.502			0.690102
$99$	−583.577	+	614.942i	−0.592441	+	0.624282i
$100$	100.000			0.100000
$101$	465.025	−	1431.20i	0.458136	−	1.41000i	−0.409278	−	0.912410i	$-0.634219\pi$
$101$	465.025	−	1431.20i	0.458136	−	1.41000i	0.867414	−	0.497588i	$-0.165781\pi$
$102$	−251.213	+	182.517i	−0.243860	+	0.177175i
$103$	949.546	+	689.885i	0.908364	+	0.659965i	0.940601	−	0.339515i	$-0.110263\pi$
$103$	949.546	+	689.885i	0.908364	+	0.659965i	−0.0322362	+	0.999480i	$0.510263\pi$
$104$	77.5992	+	238.826i	0.0731657	+	0.225181i
$105$	8.60767	+	26.4917i	0.00800021	+	0.0246221i
$106$	707.456	+	513.997i	0.648247	+	0.470979i
$107$	152.328	−	110.673i	0.137627	−	0.0999918i	−0.516842	−	0.856081i	$-0.672892\pi$
$107$	152.328	−	110.673i	0.137627	−	0.0999918i	0.654469	+	0.756089i	$0.272892\pi$
$108$	120.451	−	370.709i	0.107318	−	0.330291i
$109$	−670.930			−0.589572			−0.294786	−	0.955563i	$-0.595248\pi$
$109$	−670.930			−0.589572			−0.294786	+	0.955563i	$0.595248\pi$
$110$	−329.286	−	157.068i	−0.285420	−	0.136144i
$111$	229.306			0.196079
$112$	−14.2003	+	43.7040i	−0.0119804	+	0.0368718i
$113$	−321.668	+	233.705i	−0.267787	+	0.194559i	−0.713573	−	0.700581i	$-0.752924\pi$
$113$	−321.668	+	233.705i	−0.267787	+	0.194559i	0.445786	+	0.895140i	$0.352924\pi$
$114$	−88.6501	−	64.4080i	−0.0728319	−	0.0529155i
$115$	−17.1246	−	52.7040i	−0.0138859	−	0.0427363i
$116$	184.428	+	567.610i	0.147618	+	0.454321i
$117$	−590.108	−	428.739i	−0.466287	−	0.338777i
$118$	679.544	−	493.718i	0.530145	−	0.385173i
$119$	−71.0382	+	218.633i	−0.0547232	+	0.168421i
$120$	77.5887			0.0590237
$121$	837.592	+	1034.41i	0.629295	+	0.777166i
$122$	−479.648			−0.355945
$123$	132.151	−	406.718i	0.0968751	−	0.298151i
$124$	13.6662	−	9.92907i	0.00989726	−	0.00719078i
$125$	−101.127	−	73.4732i	−0.0723607	−	0.0525731i
$126$	−41.2474	−	126.946i	−0.0291636	−	0.0897562i
$127$	513.360	+	1579.96i	0.358688	+	1.10393i	0.953840	+	0.300314i	$0.0970916\pi$
$127$	513.360	+	1579.96i	0.358688	+	1.10393i	−0.595153	+	0.803613i	$0.702908\pi$
$128$	103.554	+	75.2365i	0.0715077	+	0.0519534i
$129$	478.659	−	347.766i	0.326695	−	0.237358i
$130$	96.9990	−	298.532i	0.0654413	−	0.201408i
$131$	−442.249			−0.294958			−0.147479	−	0.989065i	$-0.547116\pi$
$131$	−442.249			−0.294958			−0.147479	+	0.989065i	$0.547116\pi$
$132$	−255.489	−	121.867i	−0.168466	−	0.0803574i
$133$	−81.1236			−0.0528896
$134$	236.672	−	728.403i	0.152577	−	0.469585i
$135$	−394.180	+	286.388i	−0.251301	+	0.182581i
$136$	518.040	+	376.378i	0.326629	+	0.237310i
$137$	−881.478	−	2712.91i	−0.549706	−	1.69182i	−0.709529	−	0.704677i	$-0.751092\pi$
$137$	−881.478	−	2712.91i	−0.549706	−	1.69182i	0.159822	−	0.987146i	$-0.448908\pi$
$138$	−13.2867	−	40.8924i	−0.00819596	−	0.0252246i
$139$	1272.62	+	924.609i	0.776560	+	0.564204i	0.903945	−	0.427650i	$-0.140658\pi$
$139$	1272.62	+	924.609i	0.776560	+	0.564204i	−0.127385	+	0.991853i	$0.540658\pi$
$140$	46.4710	−	33.7632i	0.0280537	−	0.0203822i
$141$	293.104	−	902.082i	0.175063	−	0.538787i
$142$	820.659			0.484987
$143$	−788.304	+	830.672i	−0.460988	+	0.485764i
$144$	−371.800			−0.215162
$145$	230.535	−	709.512i	0.132033	−	0.406357i
$146$	−728.931	+	529.599i	−0.413197	+	0.300205i
$147$	−525.313	−	381.662i	−0.294742	−	0.214143i
$148$	−146.123	−	449.721i	−0.0811571	−	0.249776i
$149$	−114.189	−	351.437i	−0.0627834	−	0.193227i	0.914745	−	0.404032i	$-0.132392\pi$
$149$	−114.189	−	351.437i	−0.0627834	−	0.193227i	−0.977528	+	0.210805i	$0.932392\pi$
$150$	−78.4632	−	57.0069i	−0.0427100	−	0.0310306i
$151$	1547.13	−	1124.06i	0.833799	−	0.605790i	−0.0868326	−	0.996223i	$-0.527675\pi$
$151$	1547.13	−	1124.06i	0.833799	−	0.605790i	0.920632	+	0.390433i	$0.127675\pi$
$152$	−69.8273	+	214.906i	−0.0372615	+	0.114679i
$153$	−1859.96			−0.982805
$154$	−206.054	+	38.1864i	−0.107820	+	0.0199815i
$155$	−21.1154			−0.0109421
$156$	75.2603	−	231.627i	0.0386259	−	0.118878i
$157$	928.671	−	674.719i	0.472076	−	0.342984i	−0.326174	−	0.945310i	$-0.605759\pi$
$157$	928.671	−	674.719i	0.472076	−	0.342984i	0.798250	+	0.602326i	$0.205759\pi$
$158$	−786.278	−	571.264i	−0.395905	−	0.287642i
$159$	−262.079	−	806.598i	−0.130719	−	0.402310i
$160$	−49.4427	−	152.169i	−0.0244299	−	0.0751876i
$161$	−25.7525	−	18.7103i	−0.0126061	−	0.00915887i
$162$	709.336	−	515.362i	0.344016	−	0.249943i
$163$	−269.044	+	828.033i	−0.129283	+	0.397893i	−0.994657	−	0.103234i	$-0.967081\pi$
$163$	−269.044	+	828.033i	−0.129283	+	0.397893i	0.865374	+	0.501127i	$0.167081\pi$
$164$	−881.879			−0.419897
$165$	168.829	+	310.957i	0.0796566	+	0.146715i
$166$	−2409.01			−1.12636
$167$	13.6235	−	41.9290i	0.00631271	−	0.0194285i	−0.947851	−	0.318715i	$-0.896749\pi$
$167$	13.6235	−	41.9290i	0.00631271	−	0.0194285i	0.954163	+	0.299287i	$0.0967487\pi$
$168$	36.0563	−	26.1964i	0.0165583	−	0.0120303i
$169$	980.283	+	712.218i	0.446192	+	0.324177i
$170$	−247.342	−	761.240i	−0.111590	−	0.343438i
$171$	−202.826	−	624.236i	−0.0907048	−	0.279161i
$172$	−987.070	−	717.148i	−0.437578	−	0.317919i
$173$	1205.36	−	875.748i	0.529723	−	0.384866i	−0.290531	−	0.956866i	$-0.593832\pi$
$173$	1205.36	−	875.748i	0.529723	−	0.384866i	0.820254	+	0.571999i	$0.193832\pi$
$174$	178.869	−	550.502i	0.0779311	−	0.239847i
$175$	−71.8017			−0.0310154
$176$	−76.2009	+	578.731i	−0.0326356	+	0.247861i
$177$	−814.645			−0.345946
$178$	948.006	−	2917.66i	0.399191	−	1.22858i
$179$	2001.39	−	1454.10i	0.835705	−	0.607175i	−0.0854628	−	0.996341i	$-0.527237\pi$
$179$	2001.39	−	1454.10i	0.835705	−	0.607175i	0.921167	+	0.389166i	$0.127237\pi$
$180$	375.991	+	273.173i	0.155693	+	0.113117i
$181$	−1059.02	−	3259.32i	−0.434895	−	1.33847i	−0.893194	−	0.449672i	$-0.851541\pi$
$181$	−1059.02	−	3259.32i	−0.434895	−	1.33847i	0.458298	−	0.888798i	$-0.348459\pi$
$182$	−55.7175	−	171.481i	−0.0226926	−	0.0698407i
$183$	376.347	+	273.432i	0.152024	+	0.110452i
$184$	−71.7323	+	52.1166i	−0.0287401	+	0.0208809i
$185$	−182.654	+	562.151i	−0.0725891	+	0.223406i
$186$	−16.3832			−0.00645846
$187$	−381.202	+	2895.16i	−0.149071	+	1.13216i
$188$	−1955.96			−0.758795
$189$	−86.4855	+	266.175i	−0.0332852	+	0.102441i
$190$	228.513	−	166.024i	0.0872529	−	0.0633930i
$191$	2502.85	+	1818.43i	0.948166	+	0.688883i	0.950372	−	0.311115i	$-0.100702\pi$
$191$	2502.85	+	1818.43i	0.948166	+	0.688883i	−0.00220633	+	0.999998i	$0.500702\pi$
$192$	−38.3620	−	118.066i	−0.0144195	−	0.0443785i
$193$	874.704	+	2692.06i	0.326231	+	1.00404i	0.970882	+	0.239558i	$0.0770027\pi$
$193$	874.704	+	2692.06i	0.326231	+	1.00404i	−0.644651	+	0.764477i	$0.722997\pi$
$194$	1660.69	+	1206.56i	0.614590	+	0.446526i
$195$	−246.292	+	178.942i	−0.0904480	+	0.0657144i
$196$	−413.775	+	1273.47i	−0.150793	+	0.464092i
$197$	3173.44			1.14771			0.573854	−	0.818957i	$-0.305448\pi$
$197$	3173.44			1.14771			0.573854	+	0.818957i	$0.305448\pi$
$198$	−809.018	−	1490.08i	−0.290376	−	0.534826i
$199$	1815.07			0.646569			0.323284	−	0.946302i	$-0.395213\pi$
$199$	1815.07			0.646569			0.323284	+	0.946302i	$0.395213\pi$
$200$	−61.8034	+	190.211i	−0.0218508	+	0.0672499i
$201$	−600.941	+	436.609i	−0.210881	+	0.153214i
$202$	2434.90	+	1769.06i	0.848115	+	0.616192i
$203$	−132.422	−	407.553i	−0.0457843	−	0.140910i
$204$	−191.909	−	590.636i	−0.0658644	−	0.202710i
$205$	891.819	+	647.944i	0.303841	+	0.220753i
$206$	−1899.09	+	1379.77i	−0.642311	+	0.466666i
$207$	79.5864	−	244.942i	0.0267229	−	0.0822446i
$208$	−502.233			−0.167421
$209$	−1013.23	+	187.775i	−0.335343	+	0.0621466i
$210$	−55.7100			−0.0183065
$211$	−117.772	+	362.464i	−0.0384253	+	0.118261i	−0.968429	−	0.249289i	$-0.919803\pi$
$211$	−117.772	+	362.464i	−0.0384253	+	0.118261i	0.930004	+	0.367550i	$0.119803\pi$
$212$	−1414.91	+	1027.99i	−0.458380	+	0.333033i
$213$	−643.915	−	467.832i	−0.207138	−	0.150494i
$214$	116.368	+	358.144i	0.0371718	+	0.114403i
$215$	471.284	+	1450.46i	0.149494	+	0.460097i
$216$	630.687	+	458.221i	0.198671	+	0.144343i
$217$	−9.81256	+	7.12924i	−0.00306968	+	0.00223025i
$218$	414.657	−	1276.18i	0.128826	−	0.396487i
$219$	873.851			0.269632
$220$	502.272	−	529.267i	0.153923	−	0.162196i
$221$	−2512.47			−0.764736
$222$	−141.719	+	436.166i	−0.0428448	+	0.131863i
$223$	−3165.65	+	2299.98i	−0.950617	+	0.690664i	−0.950953	−	0.309336i	$-0.899893\pi$
$223$	−3165.65	+	2299.98i	−0.950617	+	0.690664i	0.000335732		1.00000i	$0.499893\pi$
$224$	−74.3536	−	54.0211i	−0.0221784	−	0.0161136i
$225$	−179.520	−	552.504i	−0.0531910	−	0.163705i
$226$	−245.732	−	756.286i	−0.0723268	−	0.222599i
$227$	−296.703	−	215.567i	−0.0867527	−	0.0630295i	0.543563	−	0.839368i	$-0.317075\pi$
$227$	−296.703	−	215.567i	−0.0867527	−	0.0630295i	−0.630316	+	0.776339i	$0.717075\pi$
$228$	177.300	−	128.816i	0.0514999	−	0.0374169i
$229$	−537.357	+	1653.81i	−0.155063	+	0.477236i	−0.998167	−	0.0605146i	$-0.980726\pi$
$229$	−537.357	+	1653.81i	−0.155063	+	0.477236i	0.843104	+	0.537751i	$0.180726\pi$
$230$	110.833			0.0317743
$231$	183.446	+	87.5027i	0.0522503	+	0.0249232i
$232$	−1193.64			−0.337786
$233$	−1519.32	+	4675.98i	−0.427183	+	1.31474i	0.473705	+	0.880684i	$0.342916\pi$
$233$	−1519.32	+	4675.98i	−0.427183	+	1.31474i	−0.900888	+	0.434051i	$0.857084\pi$
$234$	1180.22	−	857.478i	0.329715	−	0.239552i
$235$	1978.01	+	1437.11i	0.549069	+	0.398922i
$236$	519.126	+	1597.70i	0.143187	+	0.440685i
$237$	291.279	+	896.465i	0.0798338	+	0.245703i
$238$	−371.961	−	270.246i	−0.101305	−	0.0736026i
$239$	5869.70	−	4264.59i	1.58862	−	1.15420i	0.682736	−	0.730666i	$-0.260790\pi$
$239$	5869.70	−	4264.59i	1.58862	−	1.15420i	0.905881	−	0.423532i	$-0.139210\pi$
$240$	−47.9525	+	147.583i	−0.0128972	+	0.0396934i
$241$	−2416.59			−0.645918			−0.322959	−	0.946413i	$-0.604678\pi$
$241$	−2416.59			−0.645918			−0.322959	+	0.946413i	$0.604678\pi$
$242$	−2485.22	+	953.895i	−0.660149	+	0.253383i
$243$	−3481.42			−0.919066
$244$	296.439	−	912.344i	0.0777768	−	0.239372i
$245$	1354.10	−	983.809i	0.353102	−	0.256544i
$246$	691.951	+	502.732i	0.179338	+	0.130297i
$247$	−273.981	−	843.226i	−0.0705789	−	0.217219i
$248$	10.4400	+	32.1311i	0.00267316	+	0.00822714i
$249$	1890.19	+	1373.30i	0.481068	+	0.349516i
$250$	202.254	−	146.946i	0.0511667	−	0.0371748i
$251$	−1342.96	+	4133.21i	−0.337717	+	1.03939i	0.627651	+	0.778495i	$0.284017\pi$
$251$	−1342.96	+	4133.21i	−0.337717	+	1.03939i	−0.965368	+	0.260892i	$0.915983\pi$
$252$	266.959			0.0667334
$253$	−364.957	−	174.083i	−0.0906902	−	0.0432588i
$254$	−3322.54			−0.820765
$255$	−239.887	+	738.295i	−0.0589109	+	0.181309i
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$	1722.57	+	1251.52i	0.418098	+	0.303766i	0.776872	−	0.629659i	$-0.216805\pi$
$257$	1722.57	+	1251.52i	0.418098	+	0.303766i	−0.358774	+	0.933424i	$0.616805\pi$
$258$	365.663	+	1125.40i	0.0882372	+	0.271566i
$259$	104.919	+	322.907i	0.0251712	+	0.0774690i
$260$	507.893	+	369.006i	0.121147	+	0.0880184i
$261$	2804.99	−	2037.94i	0.665227	−	0.483316i
$262$	273.325	−	841.207i	0.0644506	−	0.198359i
$263$	−5969.13			−1.39952			−0.699758	−	0.714380i	$-0.746709\pi$
$263$	−5969.13			−1.39952			−0.699758	+	0.714380i	$0.746709\pi$
$264$	389.706	−	410.651i	0.0908513	−	0.0957342i
$265$	2186.16			0.506773
$266$	50.1372	−	154.306i	0.0115568	−	0.0355682i
$267$	−2407.10	+	1748.86i	−0.551732	+	0.400857i
$268$	1239.23	+	900.355i	0.282456	+	0.205216i
$269$	−1290.89	−	3972.94i	−0.292590	−	0.900499i	−0.984020	−	0.178056i	$-0.943019\pi$
$269$	−1290.89	−	3972.94i	−0.292590	−	0.900499i	0.691431	−	0.722443i	$-0.256981\pi$
$270$	−301.126	−	926.772i	−0.0678740	−	0.208895i
$271$	−6437.30	−	4676.97i	−1.44295	−	1.04836i	−0.987417	−	0.158140i	$-0.949450\pi$
$271$	−6437.30	−	4676.97i	−1.44295	−	1.04836i	−0.455528	−	0.890221i	$-0.650550\pi$
$272$	−1036.08	+	752.755i	−0.230961	+	0.167803i
$273$	−54.0381	+	166.312i	−0.0119800	+	0.0368706i
$274$	5705.05			1.25786
$275$	−896.802	+	166.197i	−0.196652	+	0.0364439i
$276$	85.9936			0.0187544
$277$	−553.488	+	1703.46i	−0.120057	+	0.369499i	−0.992968	−	0.118381i	$-0.962230\pi$
$277$	−553.488	+	1703.46i	−0.120057	+	0.369499i	0.872911	+	0.487880i	$0.162230\pi$
$278$	−2545.23	+	1849.22i	−0.549111	+	0.398952i
$279$	−79.3920	−	57.6817i	−0.0170361	−	0.0123775i
$280$	35.5007	+	109.260i	0.00757705	+	0.0233197i
$281$	358.047	+	1101.95i	0.0760116	+	0.233940i	0.981842	−	0.189701i	$-0.0607519\pi$
$281$	358.047	+	1101.95i	0.0760116	+	0.233940i	−0.905830	+	0.423641i	$0.860752\pi$
$282$	1534.71	+	1115.03i	0.324081	+	0.235459i
$283$	5873.31	−	4267.21i	1.23368	−	0.896323i	0.236522	−	0.971626i	$-0.423992\pi$
$283$	5873.31	−	4267.21i	1.23368	−	0.896323i	0.997161	+	0.0753032i	$0.0239925\pi$
$284$	−507.195	+	1560.99i	−0.105974	+	0.326153i
$285$	−273.944			−0.0569369
$286$	−1092.83	−	2012.83i	−0.225946	−	0.416157i
$287$	633.204			0.130233
$288$	229.785	−	707.205i	0.0470146	−	0.144696i
$289$	−1208.38	+	877.941i	−0.245956	+	0.178698i
$290$	1207.09	+	877.006i	0.244424	+	0.177585i
$291$	−615.207	−	1893.41i	−0.123931	−	0.381422i
$292$	−556.854	−	1713.82i	−0.111601	−	0.343471i
$293$	−1899.19	−	1379.84i	−0.378676	−	0.275124i	0.382123	−	0.924111i	$-0.375193\pi$
$293$	−1899.19	−	1379.84i	−0.378676	−	0.275124i	−0.760799	+	0.648987i	$0.775193\pi$
$294$	1050.63	−	763.325i	0.208414	−	0.151422i
$295$	648.907	−	1997.13i	0.128071	−	0.394161i
$296$	945.729			0.185707
$297$	−464.095	+	3524.71i	−0.0906717	+	0.688634i
$298$	739.046			0.143664
$299$	107.506	−	330.871i	0.0207935	−	0.0639959i
$300$	156.926	−	114.014i	0.0302005	−	0.0219420i
$301$	708.733	+	514.925i	0.135717	+	0.0986039i
$302$	1181.90	+	3637.52i	0.225201	+	0.693099i
$303$	−902.018	−	2776.12i	−0.171022	−	0.526351i
$304$	−365.620	−	265.639i	−0.0689795	−	0.0501165i
$305$	−970.108	+	704.825i	−0.182125	+	0.132322i
$306$	1149.52	−	3537.86i	0.214751	−	0.660935i
$307$	−1382.74			−0.257059			−0.128529	−	0.991706i	$-0.541026\pi$
$307$	−1382.74			−0.257059			−0.128529	+	0.991706i	$0.541026\pi$
$308$	54.7135	−	415.538i	0.0101221	−	0.0768750i
$309$	2276.65			0.419140
$310$	13.0501	−	40.1639i	0.00239095	−	0.00735858i
$311$	3797.08	−	2758.74i	0.692324	−	0.503003i	−0.185099	−	0.982720i	$-0.559261\pi$
$311$	3797.08	−	2758.74i	0.692324	−	0.503003i	0.877423	+	0.479717i	$0.159261\pi$
$312$	394.068	+	286.307i	0.0715055	+	0.0519518i
$313$	−85.9171	−	264.426i	−0.0155154	−	0.0477515i	0.942999	−	0.332795i	$-0.107992\pi$
$313$	−85.9171	−	264.426i	−0.0155154	−	0.0477515i	−0.958514	+	0.285044i	$0.907992\pi$
$314$	709.441	+	2183.44i	0.127503	+	0.392415i
$315$	−269.968	−	196.143i	−0.0482887	−	0.0350838i
$316$	1572.56	−	1142.53i	0.279947	−	0.203393i
$317$	2555.85	−	7866.09i	0.452841	−	1.39370i	−0.420810	−	0.907149i	$-0.638254\pi$
$317$	2555.85	−	7866.09i	0.452841	−	1.39370i	0.873651	−	0.486553i	$-0.161746\pi$
$318$	1696.21			0.299116
$319$	−2597.30	−	4783.82i	−0.455865	−	0.839632i
$320$	320.000			0.0559017
$321$	112.861	−	347.349i	0.0196239	−	0.0603961i
$322$	51.5050	−	37.4206i	0.00891386	−	0.00647630i
$323$	−1829.05	−	1328.88i	−0.315081	−	0.228920i
$324$	541.884	+	1667.75i	0.0929157	+	0.285965i
$325$	−242.498	−	746.331i	−0.0413887	−	0.127381i
$326$	−1408.73	−	1023.51i	−0.239333	−	0.173886i
$327$	−1052.87	+	764.952i	−0.178054	+	0.129364i
$328$	545.031	−	1677.43i	0.0917510	−	0.282380i
$329$	1404.42			0.235343
$330$	−695.817	+	128.950i	−0.116071	+	0.0215106i
$331$	−702.849			−0.116713			−0.0583566	−	0.998296i	$-0.518586\pi$
$331$	−702.849			−0.116713			−0.0583566	+	0.998296i	$0.518586\pi$
$332$	1488.85	−	4582.21i	0.246118	−	0.757475i
$333$	−2222.41	+	1614.67i	−0.365727	+	0.265717i
$334$	71.3338	+	51.8271i	0.0116863	+	0.00849057i
$335$	−591.681	−	1821.01i	−0.0964985	−	0.296992i
$336$	27.5445	+	84.7734i	0.00447226	+	0.0137642i
$337$	−3207.13	−	2330.11i	−0.518407	−	0.376645i	0.297596	−	0.954692i	$-0.403815\pi$
$337$	−3207.13	−	2330.11i	−0.518407	−	0.376645i	−0.816004	+	0.578047i	$0.803815\pi$
$338$	−1960.57	+	1424.44i	−0.315505	+	0.229228i
$339$	−238.326	+	733.491i	−0.0381831	+	0.117515i
$340$	1600.83			0.255345
$341$	−106.057	+	111.757i	−0.0168425	+	0.0177477i
$342$	1312.72			0.207555
$343$	601.516	−	1851.28i	0.0946904	−	0.291427i
$344$	1974.14	−	1434.30i	0.309414	−	0.224803i
$345$	−86.9628	−	63.1822i	−0.0135708	−	0.00985975i
$346$	920.816	+	2833.98i	0.143073	+	0.440335i
$347$	−2696.34	−	8298.48i	−0.417138	−	1.28382i	−0.910324	−	0.413896i	$-0.864168\pi$
$347$	−2696.34	−	8298.48i	−0.417138	−	1.28382i	0.493186	−	0.869924i	$-0.335832\pi$
$348$	936.569	+	680.457i	0.144268	+	0.104817i
$349$	−1172.32	+	851.740i	−0.179807	+	0.130638i	−0.674048	−	0.738687i	$-0.735446\pi$
$349$	−1172.32	+	851.740i	−0.179807	+	0.130638i	0.494241	+	0.869325i	$0.335446\pi$
$350$	44.3759	−	136.575i	0.00677712	−	0.0208578i
$351$	−3058.80			−0.465148
$352$	−1053.72	−	502.618i	−0.159555	−	0.0761069i
$353$	6713.24			1.01221			0.506104	−	0.862472i	$-0.331085\pi$
$353$	6713.24			1.01221			0.506104	+	0.862472i	$0.331085\pi$
$354$	503.479	−	1549.55i	0.0755920	−	0.232648i
$355$	1659.82	−	1205.93i	0.248152	−	0.180293i
$356$	4963.82	+	3606.43i	0.738994	+	0.536911i
$357$	137.794	+	424.087i	0.0204281	+	0.0628713i
$358$	1528.93	+	4705.56i	0.225716	+	0.694683i
$359$	10476.8	+	7611.84i	1.54024	+	1.11905i	0.950188	+	0.311678i	$0.100891\pi$
$359$	10476.8	+	7611.84i	1.54024	+	1.11905i	0.590048	+	0.807368i	$0.299109\pi$
$360$	−751.981	+	546.346i	−0.110091	+	0.0799860i
$361$	−1873.01	+	5764.52i	−0.273073	+	0.840432i
$362$	6854.10			0.995148
$363$	2493.77	+	668.291i	0.360576	+	0.0966285i
$364$	360.611			0.0519263
$365$	−696.067	+	2142.27i	−0.0998187	+	0.307210i
$366$	−752.694	+	546.865i	−0.107497	+	0.0781013i
$367$	−3884.64	−	2822.36i	−0.552525	−	0.401433i	0.276191	−	0.961103i	$-0.410928\pi$
$367$	−3884.64	−	2822.36i	−0.552525	−	0.401433i	−0.828715	+	0.559670i	$0.810928\pi$
$368$	−54.7986	−	168.653i	−0.00776244	−	0.0238903i
$369$	1583.14	+	4872.42i	0.223348	+	0.687393i
$370$	−956.389	−	694.857i	−0.134379	−	0.0976322i
$371$	1015.93	−	738.117i	0.142168	−	0.103291i
$372$	10.1254	−	31.1627i	0.00141123	−	0.00434331i
$373$	−4200.11			−0.583039			−0.291519	−	0.956565i	$-0.594161\pi$
$373$	−4200.11			−0.583039			−0.291519	+	0.956565i	$0.594161\pi$
$374$	−5271.32	−	2514.39i	−0.728806	−	0.347637i
$375$	−242.465			−0.0333889
$376$	1208.85	−	3720.47i	0.165803	−	0.510288i
$377$	3789.01	−	2752.88i	0.517624	−	0.376076i
$378$	−452.844	−	329.011i	−0.0616185	−	0.0447685i
$379$	−1887.82	−	5810.10i	−0.255859	−	0.787453i	−0.993659	−	0.112434i	$-0.964135\pi$
$379$	−1887.82	−	5810.10i	−0.255859	−	0.787453i	0.737800	−	0.675019i	$-0.235865\pi$
$380$	174.568	+	537.266i	0.0235662	+	0.0725294i
$381$	2606.97	+	1894.07i	0.350549	+	0.254689i
$382$	−5005.70	+	3636.85i	−0.670455	+	0.487114i
$383$	1645.94	−	5065.69i	0.219592	−	0.675834i	−0.779204	−	0.626771i	$-0.784376\pi$
$383$	1645.94	−	5065.69i	0.219592	−	0.675834i	0.998796	−	0.0490637i	$-0.0156237\pi$
$384$	248.284			0.0329953
$385$	−360.639	+	380.022i	−0.0477400	+	0.0503058i
$386$	−5661.20			−0.746496
$387$	−2190.29	+	6741.03i	−0.287697	+	0.885441i
$388$	−3321.37	+	2413.12i	−0.434581	+	0.315741i
$389$	−9823.78	−	7137.39i	−1.28042	−	0.930283i	−0.280859	−	0.959749i	$-0.590619\pi$
$389$	−9823.78	−	7137.39i	−1.28042	−	0.930283i	−0.999566	+	0.0294661i	$0.990619\pi$
$390$	−188.151	−	579.068i	−0.0244292	−	0.0751853i
$391$	−274.135	−	843.702i	−0.0354568	−	0.109125i
$392$	−2166.56	−	1574.09i	−0.279152	−	0.202816i
$393$	−694.005	+	504.224i	−0.0890787	+	0.0647195i
$394$	−1961.30	+	6036.25i	−0.250784	+	0.771832i
$395$	−2429.73			−0.309502
$396$	3334.31	−	617.922i	0.423119	−	0.0784135i
$397$	3856.36			0.487519			0.243759	−	0.969836i	$-0.421619\pi$
$397$	3856.36			0.487519			0.243759	+	0.969836i	$0.421619\pi$
$398$	−1121.78	+	3452.48i	−0.141280	+	0.434816i
$399$	−127.304	+	92.4921i	−0.0159729	+	0.0116050i
$400$	−323.607	−	235.114i	−0.0404508	−	0.0293893i
$401$	3735.26	+	11495.9i	0.465161	+	1.43162i	0.858779	+	0.512346i	$0.171223\pi$
$401$	3735.26	+	11495.9i	0.465161	+	1.43162i	−0.393618	+	0.919274i	$0.628777\pi$
$402$	−459.078	−	1412.90i	−0.0569570	−	0.175296i
$403$	−107.244	−	77.9172i	−0.0132561	−	0.00963110i
$404$	−4869.81	+	3538.12i	−0.599708	+	0.435713i
$405$	677.355	−	2084.68i	0.0831063	−	0.255775i
$406$	857.054			0.104766
$407$	2057.86	+	3790.25i	0.250625	+	0.461612i
$408$	1242.06			0.150714
$409$	−4189.09	+	12892.7i	−0.506448	+	1.55869i	0.291874	+	0.956457i	$0.405721\pi$
$409$	−4189.09	+	12892.7i	−0.506448	+	1.55869i	−0.798322	+	0.602230i	$0.794279\pi$
$410$	−1783.64	+	1295.89i	−0.214848	+	0.156096i
$411$	−4476.37	−	3252.27i	−0.537233	−	0.390323i
$412$	−1450.78	−	4465.03i	−0.173482	−	0.533923i
$413$	−372.741	−	1147.18i	−0.0444101	−	0.136680i
$414$	416.720	+	302.765i	0.0494702	+	0.0359422i
$415$	−4872.33	+	3539.95i	−0.576321	+	0.418722i
$416$	310.397	−	955.303i	0.0365828	−	0.112590i
$417$	3051.25			0.358322
$418$	269.044	−	2043.33i	0.0314817	−	0.239098i
$419$	5570.74			0.649519			0.324759	−	0.945797i	$-0.394717\pi$
$419$	5570.74			0.649519			0.324759	+	0.945797i	$0.394717\pi$
$420$	34.4307	−	105.967i	0.00400011	−	0.0123111i
$421$	−6102.80	+	4433.94i	−0.706490	+	0.513295i	−0.882039	−	0.471176i	$-0.843830\pi$
$421$	−6102.80	+	4433.94i	−0.706490	+	0.513295i	0.175549	+	0.984471i	$0.443830\pi$
$422$	−616.660	−	448.030i	−0.0711340	−	0.0516819i
$423$	3511.34	+	10806.8i	0.403610	+	1.24218i
$424$	−1080.90	−	3326.66i	−0.123804	−	0.381030i
$425$	−1618.87	−	1176.18i	−0.184769	−	0.134243i
$426$	1287.83	−	935.664i	0.146469	−	0.106416i
$427$	−212.848	+	655.079i	−0.0241228	+	0.0742423i
$428$	−753.150			−0.0850581
$429$	−289.977	+	2202.32i	−0.0326345	+	0.247853i
$430$	−3050.21			−0.342080
$431$	−3361.73	+	10346.3i	−0.375705	+	1.15630i	0.567297	+	0.823513i	$0.307989\pi$
$431$	−3361.73	+	10346.3i	−0.375705	+	1.15630i	−0.943002	+	0.332787i	$0.892011\pi$
$432$	−1261.37	+	916.442i	−0.140481	+	0.102066i
$433$	271.965	+	197.594i	0.0301843	+	0.0219301i	0.602775	−	0.797911i	$-0.294062\pi$
$433$	271.965	+	197.594i	0.0301843	+	0.0219301i	−0.572591	+	0.819841i	$0.694062\pi$
$434$	−7.49613	−	23.0707i	−0.000829091	−	0.00255168i
$435$	−447.172	−	1376.25i	−0.0492879	−	0.151693i
$436$	2171.17	+	1577.45i	0.238487	+	0.173271i
$437$	253.267	−	184.009i	0.0277240	−	0.0201427i
$438$	−540.069	+	1662.16i	−0.0589167	+	0.181327i
$439$	−9150.35			−0.994811			−0.497406	−	0.867518i	$-0.665714\pi$
$439$	−9150.35			−0.994811			−0.497406	+	0.867518i	$0.665714\pi$
$440$	696.304	+	1282.48i	0.0754432	+	0.138954i
$441$	7778.78			0.839950
$442$	1552.79	−	4778.99i	0.167101	−	0.514284i
$443$	9199.44	−	6683.78i	0.986633	−	0.716831i	0.0274521	−	0.999623i	$-0.491261\pi$
$443$	9199.44	−	6683.78i	0.986633	−	0.716831i	0.959181	+	0.282792i	$0.0912606\pi$
$444$	−742.050	−	539.131i	−0.0793156	−	0.0576262i
$445$	−2370.01	−	7294.15i	−0.252471	−	0.777025i
$446$	−2418.34	−	7442.89i	−0.256753	−	0.790204i
$447$	−579.880	−	421.307i	−0.0613588	−	0.0445798i
$448$	148.707	−	108.042i	0.0156825	−	0.0113940i
$449$	−5688.80	+	17508.3i	−0.597931	+	1.84024i	−0.0583718	+	0.998295i	$0.518591\pi$
$449$	−5688.80	+	17508.3i	−0.597931	+	1.84024i	−0.539559	+	0.841948i	$0.681409\pi$
$450$	1161.87			0.121714
$451$	7908.71	−	1465.66i	0.825735	−	0.153027i
$452$	1590.41			0.165502
$453$	1146.28	−	3527.88i	0.118889	−	0.365904i
$454$	593.406	−	431.134i	0.0613434	−	0.0445686i
$455$	−364.676	−	264.953i	−0.0375742	−	0.0272993i
$456$	135.445	+	416.858i	0.0139097	+	0.0428095i
$457$	2147.54	+	6609.44i	0.219820	+	0.676535i	0.998776	+	0.0494573i	$0.0157492\pi$
$457$	2147.54	+	6609.44i	0.219820	+	0.676535i	−0.778957	+	0.627078i	$0.784251\pi$
$458$	−2813.64	−	2044.23i	−0.287058	−	0.208560i
$459$	−6310.15	+	4584.59i	−0.641683	+	0.466210i
$460$	−68.4983	+	210.816i	−0.00694293	+	0.0213682i
$461$	10094.3			1.01982			0.509911	−	0.860227i	$-0.329678\pi$
$461$	10094.3			1.01982			0.509911	+	0.860227i	$0.329678\pi$
$462$	−279.816	+	294.854i	−0.0281779	+	0.0296924i
$463$	8936.31			0.896988			0.448494	−	0.893786i	$-0.351961\pi$
$463$	8936.31			0.896988			0.448494	+	0.893786i	$0.351961\pi$
$464$	737.711	−	2270.44i	0.0738090	−	0.227161i
$465$	−33.1357	+	24.0745i	−0.00330458	+	0.00240092i
$466$	−7955.24	−	5779.82i	−0.790815	−	0.574560i
$467$	−744.092	−	2290.08i	−0.0737312	−	0.226921i	0.907399	−	0.420271i	$-0.138065\pi$
$467$	−744.092	−	2290.08i	−0.0737312	−	0.226921i	−0.981130	+	0.193349i	$0.938065\pi$
$468$	901.605	+	2774.86i	0.0890528	+	0.274076i
$469$	−889.790	−	646.470i	−0.0876049	−	0.0636487i
$470$	−3956.02	+	2874.22i	−0.388250	+	0.282080i
$471$	688.058	−	2117.62i	0.0673122	−	0.207166i
$472$	−3359.85			−0.327648
$473$	10043.9	+	4790.92i	0.976366	+	0.465722i
$474$	−1885.20			−0.182679
$475$	218.210	−	671.582i	0.0210783	−	0.0648722i
$476$	743.922	−	540.491i	0.0716336	−	0.0520449i
$477$	8219.76	+	5972.00i	0.789008	+	0.573248i
$478$	4484.05	+	13800.5i	0.429071	+	1.32054i
$479$	−3013.21	−	9273.72i	−0.287426	−	0.884607i	−0.985661	−	0.168738i	$-0.946031\pi$
$479$	−3013.21	−	9273.72i	−0.287426	−	0.884607i	0.698234	−	0.715869i	$-0.253969\pi$
$480$	−251.082	−	182.422i	−0.0238756	−	0.0173466i
$481$	−3002.06	+	2181.12i	−0.284578	+	0.206758i
$482$	1493.53	−	4596.63i	0.141138	−	0.434379i
$483$	−61.7448			−0.00581674
$484$	−278.465	−	5316.71i	−0.0261518	−	0.499316i
$485$	5131.81			0.480460
$486$	2151.63	−	6622.05i	0.200823	−	0.618070i
$487$	−12492.9	+	9076.59i	−1.16243	+	0.844558i	−0.990084	−	0.140478i	$-0.955136\pi$
$487$	−12492.9	+	9076.59i	−1.16243	+	0.844558i	−0.172350	+	0.985036i	$0.555136\pi$
$488$	1552.17	+	1127.72i	0.143983	+	0.104610i
$489$	521.870	+	1606.15i	0.0482613	+	0.148533i
$490$	1034.44	+	3183.67i	0.0953697	+	0.293518i
$491$	4955.37	+	3600.28i	0.455463	+	0.330914i	0.791749	−	0.610847i	$-0.209171\pi$
$491$	4955.37	+	3600.28i	0.455463	+	0.330914i	−0.336286	+	0.941760i	$0.609171\pi$
$492$	−1383.90	+	1005.46i	−0.126811	+	0.0921337i
$493$	3690.47	−	11358.1i	0.337140	−	1.03761i
$494$	1773.24			0.161502
$495$	−3825.90	−	1824.94i	−0.347396	−	0.165707i
$496$	−67.5694			−0.00611684
$497$	364.175	−	1120.81i	0.0328681	−	0.101158i
$498$	−3780.38	+	2746.60i	−0.340166	+	0.247145i
$499$	−13051.8	−	9482.70i	−1.17090	−	0.850709i	−0.179784	−	0.983706i	$-0.557540\pi$
$499$	−13051.8	−	9482.70i	−1.17090	−	0.850709i	−0.991116	+	0.132997i	$0.957540\pi$
$500$	154.508	+	475.528i	0.0138197	+	0.0425325i
$501$	−26.4258	−	81.3304i	−0.00235653	−	0.00725264i
$502$	−7031.84	−	5108.93i	−0.625192	−	0.454229i
$503$	12878.4	−	9356.70i	1.14159	−	0.829413i	0.154249	−	0.988032i	$-0.450704\pi$
$503$	12878.4	−	9356.70i	1.14159	−	0.829413i	0.987340	+	0.158619i	$0.0507042\pi$
$504$	−164.989	+	507.785i	−0.0145818	+	0.0448781i
$505$	7524.27			0.663021
$506$	556.681	−	586.600i	0.0489080	−	0.0515366i
$507$	2350.35			0.205883
$508$	2053.44	−	6319.84i	0.179344	−	0.551963i
$509$	15539.1	−	11289.8i	1.35316	−	0.983126i	0.354309	−	0.935128i	$-0.384716\pi$
$509$	15539.1	−	11289.8i	1.35316	−	0.983126i	0.998847	−	0.0479977i	$-0.0152840\pi$
$510$	−1256.06	−	912.583i	−0.109058	−	0.0792350i
$511$	399.830	+	1230.55i	0.0346134	+	0.106529i
$512$	−158.217	−	486.941i	−0.0136568	−	0.0420312i
$513$	−2226.78	−	1617.85i	−0.191647	−	0.139239i
$514$	−3445.15	+	2503.05i	−0.295640	+	0.214795i
$515$	−1813.47	+	5581.29i	−0.155167	+	0.477555i
$516$	−2366.62			−0.201908
$517$	17541.1	−	3250.76i	1.49218	−	0.276535i
$518$	−679.050			−0.0575979
$519$	893.062	−	2748.56i	0.0755319	−	0.232463i
$520$	−1015.79	+	738.012i	−0.0856638	+	0.0622384i
$521$	−6479.75	−	4707.81i	−0.544881	−	0.395879i	0.281014	−	0.959704i	$-0.409329\pi$
$521$	−6479.75	−	4707.81i	−0.544881	−	0.395879i	−0.825894	+	0.563825i	$0.809329\pi$
$522$	2142.82	+	6594.92i	0.179672	+	0.552973i
$523$	−1961.39	−	6036.53i	−0.163988	−	0.504702i	0.834973	−	0.550291i	$-0.185483\pi$
$523$	−1961.39	−	6036.53i	−0.163988	−	0.504702i	−0.998960	+	0.0455895i	$0.985483\pi$
$524$	1431.15	+	1039.79i	0.119313	+	0.0866859i
$525$	−112.676	+	81.8638i	−0.00936681	+	0.00680539i
$526$	3689.13	−	11354.0i	0.305805	−	0.941172i
$527$	−338.022			−0.0279402
$528$	540.253	+	995.061i	0.0445294	+	0.0820161i
$529$	−12044.2			−0.989904
$530$	−1351.12	+	4158.32i	−0.110734	+	0.340804i
$531$	7895.45	−	5736.38i	0.645261	−	0.468809i
$532$	262.522	+	190.733i	0.0213943	+	0.0155439i
$533$	2138.53	+	6581.73i	0.173790	+	0.534871i
$534$	−1838.86	−	5659.44i	−0.149018	−	0.458629i
$535$	761.639	+	553.363i	0.0615486	+	0.0447177i
$536$	−2478.47	+	1800.71i	−0.199727	+	0.145110i
$537$	1482.84	−	4563.73i	0.119161	−	0.366740i
$538$	8354.79			0.669517
$539$	1594.27	−	12108.2i	0.127403	−	0.967600i
$540$	1948.93			0.155312
$541$	2634.27	−	8107.44i	0.209346	−	0.644300i	−0.790161	−	0.612899i	$-0.790003\pi$
$541$	2634.27	−	8107.44i	0.209346	−	0.644300i	0.999507	−	0.0314006i	$-0.00999677\pi$
$542$	12874.6	−	9353.94i	1.02032	−	0.741303i
$543$	−5377.95	−	3907.31i	−0.425027	−	0.308800i
$544$	−791.494	−	2435.97i	−0.0623806	−	0.191988i
$545$	−1036.64	−	3190.46i	−0.0814769	−	0.250760i
$546$	−282.947	−	205.573i	−0.0221777	−	0.0161131i
$547$	−17047.2	+	12385.5i	−1.33252	+	0.968129i	−0.332832	+	0.942986i	$0.608004\pi$
$547$	−17047.2	+	12385.5i	−1.33252	+	0.968129i	−0.999684	+	0.0251428i	$0.991996\pi$
$548$	−3525.91	+	10851.6i	−0.274853	+	0.845911i
$549$	−5572.91			−0.433235
$550$	238.128	−	1808.53i	0.0184615	−	0.140211i
$551$	4214.41			0.325844
$552$	−53.1469	+	163.569i	−0.00409798	+	0.0126123i
$553$	−1129.12	+	820.355i	−0.0868267	+	0.0630833i
$554$	−2898.10	−	2105.59i	−0.222254	−	0.161477i
$555$	354.297	+	1090.42i	0.0270974	+	0.0833974i
$556$	−1944.38	−	5984.19i	−0.148310	−	0.456450i
$557$	−16098.2	−	11696.0i	−1.22460	−	0.889725i	−0.228127	−	0.973631i	$-0.573260\pi$
$557$	−16098.2	−	11696.0i	−1.22460	−	0.889725i	−0.996474	+	0.0839066i	$0.973260\pi$
$558$	158.784	−	115.363i	0.0120464	−	0.00875219i
$559$	−2958.68	+	9105.87i	−0.223862	+	0.688976i
$560$	−229.765			−0.0173381
$561$	2702.67	+	4977.89i	0.203399	+	0.374629i
$562$	−2317.33			−0.173933
$563$	3664.27	−	11277.5i	0.274299	−	0.844206i	−0.715105	−	0.699017i	$-0.753621\pi$
$563$	3664.27	−	11277.5i	0.274299	−	0.844206i	0.989404	−	0.145189i	$-0.0463790\pi$
$564$	−3069.43	+	2230.07i	−0.229160	+	0.166494i
$565$	−1608.34	−	1168.53i	−0.119758	−	0.0870093i
$566$	4486.81	+	13809.0i	0.333206	+	1.02550i
$567$	−389.082	−	1197.47i	−0.0288182	−	0.0886932i
$568$	−2655.71	−	1929.48i	−0.196181	−	0.142534i
$569$	−21642.6	+	15724.3i	−1.59456	+	1.15852i	−0.697525	+	0.716560i	$0.745715\pi$
$569$	−21642.6	+	15724.3i	−1.59456	+	1.15852i	−0.897036	+	0.441957i	$0.854285\pi$
$570$	169.307	−	521.072i	0.0124412	−	0.0382900i
$571$	−7238.07			−0.530480			−0.265240	−	0.964182i	$-0.585451\pi$
$571$	−7238.07			−0.530480			−0.265240	+	0.964182i	$0.585451\pi$
$572$	4504.03	−	834.697i	0.329236	−	0.0610148i
$573$	6000.89			0.437505
$574$	−391.342	+	1204.43i	−0.0284569	+	0.0875814i
$575$	224.164	−	162.864i	0.0162579	−	0.0118120i
$576$	1203.17	+	874.154i	0.0870349	+	0.0632345i
$577$	112.542	+	346.370i	0.00811993	+	0.0249906i	0.955034	−	0.296495i	$-0.0958178\pi$
$577$	112.542	+	346.370i	0.00811993	+	0.0249906i	−0.946914	+	0.321486i	$0.895818\pi$
$578$	−923.122	−	2841.08i	−0.0664305	−	0.204452i
$579$	4441.96	+	3227.27i	0.318828	+	0.231642i
$580$	−2414.19	+	1754.01i	−0.172834	+	0.125571i
$581$	−1069.02	+	3290.11i	−0.0763346	+	0.234934i
$582$	3981.70			0.283586
$583$	10980.5	−	11570.6i	0.780042	−	0.821966i
$584$	3604.03			0.255370
$585$	1127.01	−	3468.57i	0.0796513	−	0.245141i
$586$	3798.39	−	2759.69i	0.267764	−	0.194542i
$587$	5732.74	+	4165.08i	0.403093	+	0.292864i	0.770800	−	0.637078i	$-0.219857\pi$
$587$	5732.74	+	4165.08i	0.403093	+	0.292864i	−0.367707	+	0.929942i	$0.619857\pi$
$588$	802.607	+	2470.17i	0.0562908	+	0.173245i
$589$	−36.8608	−	113.446i	−0.00257865	−	0.00793627i
$590$	3397.72	+	2468.59i	0.237088	+	0.172255i
$591$	4979.98	−	3618.16i	0.346614	−	0.251830i
$592$	−584.493	+	1798.88i	−0.0405786	+	0.124888i
$593$	−23897.0			−1.65486			−0.827431	−	0.561567i	$-0.810199\pi$
$593$	−23897.0			−1.65486			−0.827431	+	0.561567i	$0.810199\pi$
$594$	−6417.57	−	3061.15i	−0.443293	−	0.211449i
$595$	−1149.42			−0.0791962
$596$	−456.756	+	1405.75i	−0.0313917	+	0.0966137i
$597$	2848.33	−	2069.43i	0.195267	−	0.141870i
$598$	562.911	+	408.979i	0.0384936	+	0.0279672i
$599$	−3744.71	−	11525.0i	−0.255434	−	0.786144i	−0.993744	−	0.111683i	$-0.964376\pi$
$599$	−3744.71	−	11525.0i	−0.255434	−	0.786144i	0.738310	−	0.674461i	$-0.235624\pi$
$600$	119.881	+	368.956i	0.00815688	+	0.0251043i
$601$	−16956.8	−	12319.8i	−1.15089	−	0.836168i	−0.162288	−	0.986744i	$-0.551887\pi$
$601$	−16956.8	−	12319.8i	−1.15089	−	0.836168i	−0.988598	+	0.150576i	$0.951887\pi$
$602$	−1417.47	+	1029.85i	−0.0959661	+	0.0697235i
$603$	2749.84	−	8463.13i	0.185708	−	0.571551i
$604$	−7649.43			−0.515316
$605$	−3624.75	+	5581.24i	−0.243582	+	0.375057i
$606$	5837.98			0.391340
$607$	−6828.48	+	21015.9i	−0.456605	+	1.40529i	0.412635	+	0.910897i	$0.364609\pi$
$607$	−6828.48	+	21015.9i	−0.456605	+	1.40529i	−0.869240	+	0.494390i	$0.835391\pi$
$608$	731.241	−	531.278i	0.0487759	−	0.0354378i
$609$	−672.472	−	488.580i	−0.0447454	−	0.0325094i
$610$	−741.097	−	2280.86i	−0.0491904	−	0.151392i
$611$	4743.17	+	14598.0i	0.314056	+	0.966564i
$612$	6018.97	+	4373.04i	0.397553	+	0.288839i
$613$	750.817	−	545.500i	0.0494702	−	0.0359422i	−0.562775	−	0.826610i	$-0.690266\pi$
$613$	750.817	−	545.500i	0.0494702	−	0.0359422i	0.612246	+	0.790668i	$0.290266\pi$
$614$	854.580	−	2630.13i	0.0561694	−	0.172872i
$615$	2138.25			0.140199
$616$	756.586	+	360.888i	0.0494866	+	0.0236049i
$617$	12800.1			0.835191			0.417596	−	0.908633i	$-0.362873\pi$
$617$	12800.1			0.835191			0.417596	+	0.908633i	$0.362873\pi$
$618$	−1407.05	+	4330.45i	−0.0915855	+	0.281871i
$619$	15837.5	−	11506.6i	1.02837	−	0.747155i	0.0603884	−	0.998175i	$-0.480766\pi$
$619$	15837.5	−	11506.6i	1.02837	−	0.747155i	0.967982	+	0.251020i	$0.0807661\pi$
$620$	68.3310	+	49.6454i	0.00442619	+	0.00321582i
$621$	−333.746	−	1027.17i	−0.0215665	−	0.0663747i
$622$	2900.71	+	8927.48i	0.186990	+	0.575497i
$623$	−3564.11	−	2589.48i	−0.229202	−	0.166525i
$624$	−788.136	+	572.614i	−0.0505620	+	0.0367354i
$625$	193.136	−	594.410i	0.0123607	−	0.0380423i
$626$	556.067			0.0355030
$627$	−1375.94	+	1449.89i	−0.0876393	+	0.0923495i
$628$	−4591.60			−0.291759
$629$	−2923.98	+	8999.09i	−0.185353	+	0.570456i
$630$	539.935	−	392.286i	0.0341453	−	0.0248080i
$631$	−9684.98	−	7036.55i	−0.611019	−	0.443931i	0.238754	−	0.971080i	$-0.423261\pi$
$631$	−9684.98	−	7036.55i	−0.611019	−	0.443931i	−0.849773	+	0.527149i	$0.823261\pi$
$632$	1201.33	+	3697.30i	0.0756110	+	0.232707i
$633$	228.444	+	703.077i	0.0143441	+	0.0441466i
$634$	13382.6	+	9723.02i	0.838313	+	0.609070i
$635$	−6719.97	+	4882.34i	−0.419959	+	0.305118i
$636$	−1048.32	+	3226.39i	−0.0653593	+	0.201155i
$637$	10507.7			0.653579
$638$	10704.6	−	1983.80i	0.664262	−	0.123102i
$639$	9535.03			0.590297
$640$	−197.771	+	608.676i	−0.0122150	+	0.0375938i
$641$	−21566.4	+	15668.9i	−1.32889	+	0.965498i	−0.329118	+	0.944289i	$0.606752\pi$
$641$	−21566.4	+	15668.9i	−1.32889	+	0.965498i	−0.999775	+	0.0212090i	$0.993248\pi$
$642$	590.946	+	429.347i	0.0363283	+	0.0263941i
$643$	8832.08	+	27182.3i	0.541684	+	1.66713i	0.728745	+	0.684785i	$0.240104\pi$
$643$	8832.08	+	27182.3i	0.541684	+	1.66713i	−0.187061	+	0.982348i	$0.559896\pi$
$644$	39.3463	+	121.096i	0.00240755	+	0.00740968i
$645$	2393.30	+	1738.83i	0.146102	+	0.106150i
$646$	3658.10	−	2657.77i	0.222796	−	0.161871i
$647$	−4267.14	+	13132.9i	−0.259287	+	0.798003i	0.733668	+	0.679508i	$0.237807\pi$
$647$	−4267.14	+	13132.9i	−0.259287	+	0.798003i	−0.992955	+	0.118495i	$0.962193\pi$
$648$	−3507.15			−0.212614
$649$	−7310.87	−	13465.5i	−0.442183	−	0.814431i
$650$	1569.48			0.0947076
$651$	−7.27019	+	22.3753i	−0.000437697	+	0.00134709i
$652$	2817.47	−	2047.01i	0.169234	−	0.122956i
$653$	−3543.63	−	2574.60i	−0.212363	−	0.154291i	0.476519	−	0.879164i	$-0.341898\pi$
$653$	−3543.63	−	2574.60i	−0.212363	−	0.154291i	−0.688882	+	0.724873i	$0.741898\pi$
$654$	−804.318	−	2475.44i	−0.0480907	−	0.148008i
$655$	−683.312	−	2103.02i	−0.0407621	−	0.125453i
$656$	2853.82	+	2073.42i	0.169852	+	0.123405i
$657$	−8469.26	+	6153.28i	−0.502918	+	0.365392i
$658$	−867.977	+	2671.36i	−0.0514244	+	0.158268i
$659$	17328.6			1.02432			0.512161	−	0.858889i	$-0.328845\pi$
$659$	17328.6			1.02432			0.512161	+	0.858889i	$0.328845\pi$
$660$	184.760	−	1403.22i	0.0108966	−	0.0827579i
$661$	20384.7			1.19950			0.599752	−	0.800186i	$-0.295266\pi$
$661$	20384.7			1.19950			0.599752	+	0.800186i	$0.295266\pi$
$662$	434.384	−	1336.90i	0.0255028	−	0.0784894i
$663$	−3942.72	+	2864.56i	−0.230954	+	0.167798i
$664$	7795.72	+	5663.93i	0.455622	+	0.331029i
$665$	−125.343	−	385.766i	−0.00730916	−	0.0224953i
$666$	−1697.77	−	5225.20i	−0.0987796	−	0.304012i
$667$	1337.85	+	972.008i	0.0776640	+	0.0564262i
$668$	−142.668	+	103.654i	−0.00826344	+	0.00600374i
$669$	−2345.45	+	7218.55i	−0.135546	+	0.417168i
$670$	3829.44			0.220812
$671$	−1142.17	+	8674.59i	−0.0657126	+	0.499074i
$672$	−178.272			−0.0102336
$673$	−2003.17	+	6165.13i	−0.114735	+	0.353118i	−0.991892	−	0.127086i	$-0.959437\pi$
$673$	−2003.17	+	6165.13i	−0.114735	+	0.353118i	0.877157	+	0.480204i	$0.159437\pi$
$674$	6414.25	−	4660.23i	0.366569	−	0.266328i
$675$	−1970.90	−	1431.94i	−0.112385	−	0.0816525i
$676$	−1497.74	−	4609.57i	−0.0852151	−	0.262265i
$677$	−9194.56	−	28297.9i	−0.521973	−	1.60647i	−0.770225	−	0.637772i	$-0.779856\pi$
$677$	−9194.56	−	28297.9i	−0.521973	−	1.60647i	0.248252	−	0.968695i	$-0.420144\pi$
$678$	−1247.89	−	906.644i	−0.0706857	−	0.0513561i
$679$	2384.80	−	1732.66i	0.134787	−	0.0979285i
$680$	−989.367	+	3044.96i	−0.0557949	+	0.171719i
$681$	−711.382			−0.0400297
$682$	−147.028	−	270.802i	−0.00825510	−	0.0152046i
$683$	−26343.9			−1.47587			−0.737937	−	0.674870i	$-0.764200\pi$
$683$	−26343.9			−1.47587			−0.737937	+	0.674870i	$0.764200\pi$
$684$	−811.306	+	2496.94i	−0.0453524	+	0.139580i
$685$	11538.7	−	8383.36i	0.643608	−	0.467608i
$686$	3149.58	+	2288.30i	0.175294	+	0.127358i
$687$	1042.32	+	3207.93i	0.0578850	+	0.178152i
$688$	1508.11	+	4641.48i	0.0835699	+	0.257202i
$689$	11103.4	+	8067.07i	0.613940	+	0.446053i
$690$	173.926	−	126.364i	0.00959599	−	0.00697190i
$691$	2152.30	−	6624.11i	0.118491	−	0.364679i	−0.874168	−	0.485624i	$-0.838592\pi$
$691$	2152.30	−	6624.11i	0.118491	−	0.364679i	0.992659	+	0.120945i	$0.0385925\pi$
$692$	−5959.65			−0.327387
$693$	−2394.09	+	443.678i	−0.131232	+	0.0243203i
$694$	17451.1			0.954515
$695$	−2430.48	+	7480.24i	−0.132652	+	0.408262i
$696$	−1873.14	+	1360.91i	−0.102013	+	0.0741169i
$697$	14276.5	+	10372.5i	0.775841	+	0.563682i
$698$	−895.572	−	2756.29i	−0.0485643	−	0.149466i
$699$	2947.05	+	9070.07i	0.159467	+	0.490789i
$700$	232.355	+	168.816i	0.0125460	+	0.00911520i
$701$	−13116.0	+	9529.32i	−0.706682	+	0.513435i	−0.882102	−	0.471059i	$-0.843872\pi$
$701$	−13116.0	+	9529.32i	−0.706682	+	0.513435i	0.175420	+	0.984494i	$0.443872\pi$
$702$	1890.44	−	5818.19i	0.101638	−	0.312811i
$703$	−3339.10			−0.179142
$704$	1607.27	−	1693.65i	0.0860458	−	0.0906704i
$705$	4742.52			0.253353
$706$	−4149.01	+	12769.3i	−0.221176	+	0.680709i
$707$	3496.60	−	2540.43i	0.186002	−	0.135138i
$708$	2636.25	+	1915.35i	0.139938	+	0.101671i
$709$	−6780.97	−	20869.7i	−0.359188	−	1.10547i	−0.953541	−	0.301264i	$-0.902592\pi$
$709$	−6780.97	−	20869.7i	−0.359188	−	1.10547i	0.594352	−	0.804205i	$-0.297408\pi$
$710$	1267.99	+	3902.46i	0.0670236	+	0.206277i
$711$	−9135.57	−	6637.38i	−0.481871	−	0.350100i
$712$	−9927.64	+	7212.86i	−0.522548	+	0.379653i
$713$	14.4637	−	44.5147i	0.000759706	−	0.00233813i
$714$	−891.822			−0.0467446
$715$	−5168.08	−	2465.15i	−0.270315	−	0.128939i
$716$	−9895.43			−0.516494
$717$	4348.90	−	13384.5i	0.226517	−	0.697147i
$718$	−20953.6	+	15223.7i	−1.08911	+	0.791285i
$719$	6461.80	+	4694.77i	0.335166	+	0.243512i	0.742620	−	0.669714i	$-0.233583\pi$
$719$	6461.80	+	4694.77i	0.335166	+	0.243512i	−0.407453	+	0.913226i	$0.633583\pi$
$720$	−574.462	−	1768.01i	−0.0297347	−	0.0915139i
$721$	1041.68	+	3205.97i	0.0538062	+	0.165598i
$722$	−9807.19	−	7125.34i	−0.505521	−	0.367282i
$723$	−3792.27	+	2755.25i	−0.195071	+	0.141727i
$724$	−4236.07	+	13037.3i	−0.217448	+	0.669235i
$725$	3730.13			0.191081
$726$	−2812.40	+	4330.41i	−0.143771	+	0.221373i
$727$	4693.26			0.239427			0.119714	−	0.992808i	$-0.461802\pi$
$727$	4693.26			0.239427			0.119714	+	0.992808i	$0.461802\pi$
$728$	−222.870	+	685.924i	−0.0113463	+	0.0349204i
$729$	4112.77	−	2988.10i	0.208950	−	0.151811i
$730$	−3644.65	−	2648.00i	−0.184787	−	0.134256i
$731$	7544.46	+	23219.5i	0.381726	+	1.17483i
$732$	−575.007	−	1769.69i	−0.0290340	−	0.0893574i
$733$	−17479.8	−	12699.8i	−0.880808	−	0.639945i	0.0526570	−	0.998613i	$-0.483231\pi$
$733$	−17479.8	−	12699.8i	−0.880808	−	0.639945i	−0.933465	+	0.358668i	$0.883231\pi$
$734$	7769.28	−	5644.71i	0.390694	−	0.283856i
$735$	1003.26	−	3087.71i	0.0503480	−	0.154955i
$736$	354.664			0.0177624
$737$	−12609.8	−	6014.83i	−0.630243	−	0.300623i
$738$	−10246.3			−0.511074
$739$	−2328.58	+	7166.63i	−0.115911	+	0.356737i	−0.992136	−	0.125165i	$-0.960054\pi$
$739$	−2328.58	+	7166.63i	−0.115911	+	0.356737i	0.876225	+	0.481902i	$0.160054\pi$
$740$	1912.78	−	1389.71i	0.0950204	−	0.0690364i
$741$	−1391.34	−	1010.87i	−0.0689774	−	0.0501150i
$742$	776.102	+	2388.60i	0.0383984	+	0.118178i
$743$	−3113.63	−	9582.76i	−0.153739	−	0.473159i	0.844292	−	0.535883i	$-0.180021\pi$
$743$	−3113.63	−	9582.76i	−0.153739	−	0.473159i	−0.998031	+	0.0627238i	$0.980021\pi$
$744$	53.0171	+	38.5192i	0.00261250	+	0.00189809i
$745$	1494.75	−	1086.00i	0.0735081	−	0.0534067i
$746$	2595.81	−	7989.08i	0.127399	−	0.392093i
$747$	−27989.7			−1.37094
$748$	8040.52	−	8472.66i	0.393035	−	0.414159i
$749$	540.774			0.0263811
$750$	149.851	−	461.195i	0.00729574	−	0.0224540i
$751$	−14093.6	+	10239.6i	−0.684797	+	0.497534i	−0.874946	−	0.484221i	$-0.839103\pi$
$751$	−14093.6	+	10239.6i	−0.684797	+	0.497534i	0.190149	+	0.981755i	$0.439103\pi$
$752$	6329.63	+	4598.75i	0.306939	+	0.223004i
$753$	2604.97	+	8017.27i	0.126069	+	0.388002i
$754$	2894.55	+	8908.51i	0.139805	+	0.430277i
$755$	7735.65	+	5620.28i	0.372886	+	0.270918i
$756$	905.688	−	658.021i	0.0435709	−	0.0316561i
$757$	6895.77	−	21223.0i	0.331085	−	1.01897i	−0.637534	−	0.770422i	$-0.720046\pi$
$757$	6895.77	−	21223.0i	0.331085	−	1.01897i	0.968619	−	0.248551i	$-0.0799545\pi$
$758$	12218.2			0.585468
$759$	−771.192	+	142.919i	−0.0368808	+	0.00683483i
$760$	−1129.83			−0.0539253
$761$	−3432.03	+	10562.7i	−0.163483	+	0.503150i	−0.998921	−	0.0464345i	$-0.985214\pi$
$761$	−3432.03	+	10562.7i	−0.163483	+	0.503150i	0.835438	+	0.549585i	$0.185214\pi$
$762$	−5213.94	+	3788.15i	−0.247875	+	0.180092i
$763$	−1558.94	−	1132.64i	−0.0739677	−	0.0537407i
$764$	−3824.01	−	11769.1i	−0.181084	−	0.557318i
$765$	−2873.80	−	8844.65i	−0.135820	−	0.418012i
$766$	8618.26	+	6261.53i	0.406515	+	0.295350i
$767$	10665.3	−	7748.79i	0.502088	−	0.364788i
$768$	−153.448	+	472.264i	−0.00720973	+	0.0221893i
$769$	38068.8			1.78517			0.892585	−	0.450879i	$-0.148889\pi$
$769$	38068.8			1.78517			0.892585	+	0.450879i	$0.148889\pi$
$770$	−499.958	−	920.844i	−0.0233990	−	0.0430973i
$771$	4130.08			0.192920
$772$	3498.81	−	10768.2i	0.163115	−	0.502018i
$773$	−20989.5	+	15249.8i	−0.976638	+	0.709569i	−0.956955	−	0.290237i	$-0.906266\pi$
$773$	−20989.5	+	15249.8i	−0.976638	+	0.709569i	−0.0196831	+	0.999806i	$0.506266\pi$
$774$	−11468.5	−	8332.37i	−0.532594	−	0.386952i
$775$	−32.6251	−	100.410i	−0.00151217	−	0.00465397i
$776$	−2537.30	−	7809.02i	−0.117376	−	0.361247i
$777$	532.804	+	387.105i	0.0246001	+	0.0178730i
$778$	19647.6	−	14274.8i	0.905397	−	0.657809i
$779$	−1924.35	+	5922.54i	−0.0885071	+	0.272397i
$780$	1217.74			0.0559000
$781$	1954.22	−	14841.9i	0.0895357	−	0.680006i
$782$	1774.24			0.0811339
$783$	4492.96	−	13827.9i	0.205064	−	0.631123i
$784$	4333.11	−	3148.19i	0.197390	−	0.143412i
$785$	4643.35	+	3373.59i	0.211119	+	0.153387i
$786$	−530.173	−	1631.70i	−0.0240593	−	0.0740470i
$787$	6510.15	+	20036.2i	0.294869	+	0.907514i	0.983265	+	0.182179i	$0.0583150\pi$
$787$	6510.15	+	20036.2i	0.294869	+	0.907514i	−0.688396	+	0.725335i	$0.741685\pi$
$788$	−10269.5	−	7461.22i	−0.464258	−	0.337303i
$789$	−9367.15	+	6805.63i	−0.422661	+	0.307081i
$790$	1501.66	−	4621.63i	0.0676286	−	0.208139i
$791$	−1141.94			−0.0513310
$792$	−885.359	+	6724.13i	−0.0397220	+	0.301681i
$793$	−7527.96			−0.337107
$794$	−2383.36	+	7335.23i	−0.106527	+	0.327856i
$795$	3430.66	−	2492.52i	0.153048	−	0.111196i
$796$	−5873.70	−	4267.49i	−0.261543	−	0.190022i
$797$	−6378.63	−	19631.4i	−0.283491	−	0.872497i	−0.986847	−	0.161658i	$-0.948316\pi$
$797$	−6378.63	−	19631.4i	−0.283491	−	0.872497i	0.703355	−	0.710838i	$-0.251684\pi$
$798$	−97.2520	−	299.311i	−0.00431414	−	0.0132776i
$799$	31664.6	+	23005.7i	1.40202	+	1.01863i
$800$	647.214	−	470.228i	0.0286031	−	0.0207813i
$801$	11014.6	−	33899.6i	0.485872	−	1.49536i
$802$	−24175.1			−1.06440
$803$	7842.19	+	14444.1i	0.344639	+	0.634770i
$804$	2971.21			0.130332
$805$	49.1829	−	151.369i	0.00215338	−	0.00662742i
$806$	214.488	−	155.834i	0.00937346	−	0.00681022i
$807$	−6555.44	−	4762.80i	−0.285951	−	0.207755i
$808$	−3720.20	−	11449.6i	−0.161976	−	0.498509i
$809$	−5434.69	−	16726.3i	−0.236185	−	0.726903i	−0.996962	−	0.0778893i	$-0.975182\pi$
$809$	−5434.69	−	16726.3i	−0.236185	−	0.726903i	0.760777	−	0.649013i	$-0.224818\pi$
$810$	3546.68	+	2576.81i	0.153849	+	0.111778i
$811$	35540.9	−	25822.0i	1.53885	−	1.11804i	0.587801	−	0.809005i	$-0.299994\pi$
$811$	35540.9	−	25822.0i	1.53885	−	1.11804i	0.951050	−	0.309036i	$-0.100006\pi$
$812$	−529.689	+	1630.21i	−0.0228922	+	0.0704548i
$813$	−15434.2			−0.665808
$814$	−8481.32	+	1571.78i	−0.365197	+	0.0676791i
$815$	−4353.23			−0.187101
$816$	−767.637	+	2362.55i	−0.0329322	+	0.101355i
$817$	−6970.13	+	5064.10i	−0.298475	+	0.216855i
$818$	−21934.4	−	15936.3i	−0.937552	−	0.681171i
$819$	−647.368	−	1992.39i	−0.0276201	−	0.0850059i
$820$	−1362.58	−	4193.58i	−0.0580284	−	0.178593i
$821$	−22619.7	−	16434.2i	−0.961551	−	0.698608i	−0.00804086	−	0.999968i	$-0.502560\pi$
$821$	−22619.7	−	16434.2i	−0.961551	−	0.698608i	−0.953511	+	0.301360i	$0.902560\pi$
$822$	8952.73	−	6504.54i	0.379881	−	0.276000i
$823$	−2774.43	+	8538.83i	−0.117510	+	0.361658i	−0.992462	−	0.122551i	$-0.960893\pi$
$823$	−2774.43	+	8538.83i	−0.117510	+	0.361658i	0.874952	+	0.484209i	$0.160893\pi$
$824$	9389.63			0.396970
$825$	−1217.83	+	1283.29i	−0.0513933	+	0.0541555i
$826$	2412.43			0.101621
$827$	6767.14	−	20827.1i	0.284542	−	0.875732i	−0.701993	−	0.712184i	$-0.747706\pi$
$827$	6767.14	−	20827.1i	0.284542	−	0.875732i	0.986535	−	0.163548i	$-0.0522938\pi$
$828$	−833.440	+	605.530i	−0.0349807	+	0.0254150i
$829$	16864.4	+	12252.7i	0.706542	+	0.513333i	0.882056	−	0.471144i	$-0.156159\pi$
$829$	16864.4	+	12252.7i	0.706542	+	0.513333i	−0.175514	+	0.984477i	$0.556159\pi$
$830$	−3722.13	−	11455.5i	−0.155659	−	0.479069i
$831$	1073.61	+	3304.24i	0.0448173	+	0.137933i
$832$	1625.26	+	1180.82i	0.0677232	+	0.0492038i
$833$	21676.8	−	15749.1i	0.901628	−	0.655071i
$834$	−1885.78	+	5803.83i	−0.0782963	+	0.240971i
$835$	220.434			0.00913583
$836$	3720.38	+	1774.60i	0.153914	+	0.0734161i
$837$	−411.525			−0.0169945
$838$	−3442.90	+	10596.2i	−0.141925	+	0.436800i
$839$	26466.6	−	19229.1i	1.08907	−	0.791255i	0.109827	−	0.993951i	$-0.464970\pi$
$839$	26466.6	−	19229.1i	1.08907	−	0.791255i	0.979242	+	0.202696i	$0.0649703\pi$
$840$	180.281	+	130.982i	0.00740512	+	0.00538013i
$841$	−657.229	−	2022.74i	−0.0269477	−	0.0829366i
$842$	−4662.12	−	14348.5i	−0.190816	−	0.587273i
$843$	1818.25	+	1321.04i	0.0742869	+	0.0539726i
$844$	1233.32	−	896.060i	0.0502993	−	0.0365446i
$845$	−1872.17	+	5761.96i	−0.0762187	+	0.234577i
$846$	−22725.9			−0.923559
$847$	199.942	+	3817.49i	0.00811109	+	0.154865i
$848$	6995.71			0.283295
$849$	4351.57	−	13392.8i	0.175908	−	0.541388i
$850$	3237.75	−	2352.36i	0.130652	−	0.0949239i
$851$	−1059.99	−	770.128i	−0.0426980	−	0.0310219i
$852$	983.815	+	3027.87i	0.0395598	+	0.121753i
$853$	−3789.26	−	11662.1i	−0.152101	−	0.468117i	0.845755	−	0.533571i	$-0.179150\pi$
$853$	−3789.26	−	11662.1i	−0.152101	−	0.468117i	−0.997856	+	0.0654540i	$0.979150\pi$
$854$	−1114.49	−	809.722i	−0.0446568	−	0.0324451i
$855$	2655.03	−	1928.99i	0.106199	−	0.0771581i
$856$	465.472	−	1432.58i	0.0185859	−	0.0572015i
$857$	16771.7			0.668508			0.334254	−	0.942483i	$-0.391516\pi$
$857$	16771.7			0.668508			0.334254	+	0.942483i	$0.391516\pi$
$858$	−4009.84	−	1912.68i	−0.159550	−	0.0761046i
$859$	22891.0			0.909232			0.454616	−	0.890688i	$-0.349776\pi$
$859$	22891.0			0.909232			0.454616	+	0.890688i	$0.349776\pi$
$860$	1885.14	−	5801.85i	0.0747472	−	0.230048i
$861$	993.665	−	721.940i	0.0393310	−	0.0285757i
$862$	−17602.2	−	12788.8i	−0.695516	−	0.505322i
$863$	14422.5	+	44387.8i	0.568883	+	1.75084i	0.656121	+	0.754656i	$0.272196\pi$
$863$	14422.5	+	44387.8i	0.568883	+	1.75084i	−0.0872374	+	0.996188i	$0.527804\pi$
$864$	−963.605	−	2965.67i	−0.0379427	−	0.116776i
$865$	6026.82	+	4378.74i	0.236899	+	0.172118i
$866$	−543.929	+	395.188i	−0.0213435	+	0.0155070i
$867$	−895.298	+	2755.44i	−0.0350703	+	0.107935i
$868$	48.5160			0.00189716
$869$	−12203.9	+	12859.8i	−0.476395	+	0.502000i
$870$	2894.16			0.112783
$871$	3714.52	−	11432.1i	0.144502	−	0.444733i
$872$	−4342.35	+	3154.90i	−0.168636	+	0.122521i
$873$	19295.1	+	14018.7i	0.748042	+	0.543484i
$874$	193.478	+	595.465i	0.00748799	+	0.0230457i
$875$	−110.940	−	341.437i	−0.00428622	−	0.0131916i
$876$	−2827.84	−	2054.55i	−0.109068	−	0.0792428i
$877$	16555.2	−	12028.1i	0.637434	−	0.463123i	−0.221533	−	0.975153i	$-0.571106\pi$
$877$	16555.2	−	12028.1i	0.637434	−	0.463123i	0.858968	+	0.512030i	$0.171106\pi$
$878$	5655.23	−	17405.0i	0.217374	−	0.669009i
$879$	−4553.55			−0.174730
$880$	−2869.77	+	531.832i	−0.109932	+	0.0203728i
$881$	−36028.5			−1.37779			−0.688894	−	0.724862i	$-0.741904\pi$
$881$	−36028.5			−1.37779			−0.688894	+	0.724862i	$0.741904\pi$
$882$	−4807.55	+	14796.1i	−0.183536	+	0.564865i
$883$	−27451.5	+	19944.7i	−1.04622	+	0.760126i	−0.971491	−	0.237077i	$-0.923810\pi$
$883$	−27451.5	+	19944.7i	−1.04622	+	0.760126i	−0.0747331	+	0.997204i	$0.523810\pi$
$884$	8130.51	+	5907.16i	0.309342	+	0.224750i
$885$	−1258.70	−	3873.87i	−0.0478086	−	0.147140i
$886$	7027.75	+	21629.2i	0.266481	+	0.820143i
$887$	−3452.05	−	2508.06i	−0.130675	−	0.0949408i	0.520528	−	0.853845i	$-0.325735\pi$
$887$	−3452.05	−	2508.06i	−0.130675	−	0.0949408i	−0.651203	+	0.758904i	$0.725735\pi$
$888$	1484.10	−	1078.26i	0.0560846	−	0.0407479i
$889$	−1474.40	+	4537.75i	−0.0556242	+	0.171194i
$890$	15339.1			0.577715
$891$	−7631.38	−	14055.8i	−0.286937	−	0.528493i
$892$	15651.8			0.587514
$893$	−4268.12	+	13135.9i	−0.159941	+	0.492247i
$894$	1159.76	−	842.615i	0.0433872	−	0.0315226i
$895$	10007.0	+	7270.49i	0.373739	+	0.271537i
$896$	113.602	+	349.632i	0.00423570	+	0.0130361i
$897$	−208.532	−	641.796i	−0.00776220	−	0.0238896i
$898$	−29786.9	−	21641.5i	−1.10691	−	0.804215i
$899$	509.766	−	370.367i	0.0189118	−	0.0137402i
$900$	−718.078	+	2210.02i	−0.0265955	+	0.0818525i
$901$	34996.7			1.29402
$902$	−2100.00	+	15949.1i	−0.0775192	+	0.588743i
$903$	1699.27			0.0626227
$904$	−982.929	+	3025.14i	−0.0361634	+	0.111300i
$905$	13862.7	−	10071.8i	0.509184	−	0.369944i
$906$	6001.99	+	4360.70i	0.220091	+	0.159906i
$907$	2316.40	+	7129.13i	0.0848012	+	0.260991i	0.984462	−	0.175599i	$-0.0561861\pi$
$907$	2316.40	+	7129.13i	0.0848012	+	0.260991i	−0.899661	+	0.436590i	$0.856186\pi$
$908$	453.322	+	1395.18i	0.0165683	+	0.0509919i
$909$	28290.5	+	20554.3i	1.03227	+	0.749991i
$910$	729.352	−	529.905i	0.0265690	−	0.0193035i
$911$	−10333.1	+	31802.2i	−0.375798	+	1.15659i	0.567140	+	0.823621i	$0.308050\pi$
$911$	−10333.1	+	31802.2i	−0.375798	+	1.15659i	−0.942938	+	0.332967i	$0.891950\pi$
$912$	−876.620			−0.0318287
$913$	−5736.53	+	43567.8i	−0.207942	+	1.57928i
$914$	−13899.1			−0.503001
$915$	−718.759	+	2212.11i	−0.0259688	+	0.0799237i
$916$	5627.27	−	4088.45i	0.202981	−	0.147474i
$917$	−1027.59	−	746.586i	−0.0370054	−	0.0268860i
$918$	−4820.52	−	14836.0i	−0.173313	−	0.533401i
$919$	3442.39	+	10594.6i	0.123562	+	0.380286i	0.993636	−	0.112635i	$-0.0359291\pi$
$919$	3442.39	+	10594.6i	0.123562	+	0.380286i	−0.870074	+	0.492921i	$0.835929\pi$
$920$	−358.662	−	260.583i	−0.0128530	−	0.00933822i
$921$	−2169.88	+	1576.51i	−0.0776331	+	0.0564038i
$922$	−6238.61	+	19200.5i	−0.222839	+	0.685828i
$923$	12880.0			0.459320
$924$	−387.911	−	714.471i	−0.0138110	−	0.0254376i
$925$	−2955.40			−0.105052
$926$	−5522.94	+	16997.9i	−0.195999	+	0.603223i
$927$	−22065.1	+	16031.2i	−0.781782	+	0.567998i
$928$	3862.70	+	2806.42i	0.136637	+	0.0992728i
$929$	−11367.1	−	34984.2i	−0.401444	−	1.23552i	−0.923828	−	0.382807i	$-0.874958\pi$
$929$	−11367.1	−	34984.2i	−0.401444	−	1.23552i	0.522385	−	0.852710i	$-0.325042\pi$
$930$	−25.3134	−	77.9067i	−0.000892537	−	0.00274695i
$931$	7649.49	+	5557.68i	0.269283	+	0.195645i
$932$	15910.5	−	11559.6i	0.559190	−	0.406276i
$933$	2813.28	−	8658.40i	0.0987168	−	0.303819i
$934$	4815.87			0.168715
$935$	−14356.3	+	2660.54i	−0.502139	+	0.0930576i
$936$	−5835.31			−0.203775
$937$	329.826	−	1015.10i	0.0114994	−	0.0353915i	−0.945142	−	0.326659i	$-0.894077\pi$
$937$	329.826	−	1015.10i	0.0114994	−	0.0353915i	0.956642	+	0.291268i	$0.0940771\pi$
$938$	1779.58	−	1292.94i	0.0619460	−	0.0450064i
$939$	−436.308	−	316.996i	−0.0151633	−	0.0110168i
$940$	−3022.13	−	9301.17i	−0.104863	−	0.322735i
$941$	−15.6920	−	48.2950i	−0.000543618	−	0.00167309i	0.950784	−	0.309853i	$-0.100280\pi$
$941$	−15.6920	−	48.2950i	−0.000543618	−	0.00167309i	−0.951328	+	0.308180i	$0.900280\pi$
$942$	3602.72	+	2617.53i	0.124610	+	0.0905347i
$943$	−1976.85	+	1436.27i	−0.0682663	+	0.0495984i
$944$	2076.50	−	6390.82i	0.0715936	−	0.220343i
$945$	−1399.37			−0.0481708
$946$	−15320.4	+	16143.8i	−0.526541	+	0.554841i
$947$	−49011.4			−1.68179			−0.840895	−	0.541198i	$-0.817971\pi$
$947$	−49011.4			−1.68179			−0.840895	+	0.541198i	$0.817971\pi$
$948$	1165.12	−	3585.86i	0.0399169	−	0.122852i
$949$	−11440.4	+	8311.94i	−0.391329	+	0.284317i
$950$	1142.56	+	830.121i	0.0390207	+	0.0283502i
$951$	−4957.62	−	15258.0i	−0.169045	−	0.520267i
$952$	568.306	+	1749.07i	0.0193476	+	0.0595457i
$953$	−14374.9	−	10444.0i	−0.488614	−	0.354999i	0.316037	−	0.948747i	$-0.397648\pi$
$953$	−14374.9	−	10444.0i	−0.488614	−	0.354999i	−0.804651	+	0.593748i	$0.797648\pi$
$954$	−16439.5	+	11944.0i	−0.557913	+	0.405347i
$955$	−4780.01	+	14711.4i	−0.161966	+	0.498480i
$956$	−29021.4			−0.981819
$957$	−9530.07	−	4545.80i	−0.321905	−	0.153547i
$958$	19501.9			0.657702
$959$	2531.67	−	7791.66i	0.0852469	−	0.262363i
$960$	502.165	−	364.844i	0.0168826	−	0.0122659i
$961$	24087.0	+	17500.2i	0.808533	+	0.587433i
$962$	−2293.37	−	7058.27i	−0.0768620	−	0.236557i
$963$	1352.05	+	4161.19i	0.0452432	+	0.139244i
$964$	7820.25	+	5681.74i	0.261279	+	0.189831i
$965$	−11450.0	+	8318.93i	−0.381958	+	0.277509i
$966$	38.1604	−	117.446i	0.00127100	−	0.00391175i
$967$	31017.2			1.03148			0.515742	−	0.856744i	$-0.327516\pi$
$967$	31017.2			1.03148			0.515742	+	0.856744i	$0.327516\pi$
$968$	10285.1	+	2756.24i	0.341503	+	0.0915174i
$969$	−4385.37			−0.145385
$970$	−3171.63	+	9761.28i	−0.104984	+	0.323109i
$971$	−23080.8	+	16769.2i	−0.762821	+	0.554222i	−0.899774	−	0.436356i	$-0.856269\pi$
$971$	−23080.8	+	16769.2i	−0.762821	+	0.554222i	0.136953	+	0.990577i	$0.456269\pi$
$972$	11266.1	+	8185.30i	0.371770	+	0.270107i
$973$	1396.10	+	4296.75i	0.0459989	+	0.141570i
$974$	−9543.69	−	29372.5i	−0.313963	−	0.966278i
$975$	−1231.46	−	894.710i	−0.0404496	−	0.0293884i
$976$	−3104.35	+	2255.44i	−0.101811	+	0.0739701i
$977$	−2552.71	+	7856.45i	−0.0835912	+	0.257267i	−0.984113	−	0.177544i	$-0.943185\pi$
$977$	−2552.71	+	7856.45i	−0.0835912	+	0.257267i	0.900522	+	0.434811i	$0.143185\pi$
$978$	−3377.61			−0.110434
$979$	−50509.4	−	24092.8i	−1.64892	−	0.786525i
$980$	−6695.02			−0.218229
$981$	4817.80	−	14827.7i	0.156800	−	0.482580i
$982$	−9910.73	+	7200.57i	−0.322061	+	0.233991i
$983$	18502.9	+	13443.2i	0.600358	+	0.436186i	0.846006	−	0.533173i	$-0.179001\pi$
$983$	18502.9	+	13443.2i	0.600358	+	0.436186i	−0.245648	+	0.969359i	$0.579001\pi$
$984$	−1057.21	−	3253.75i	−0.0342505	−	0.105412i
$985$	4903.24	+	15090.6i	0.158609	+	0.488150i
$986$	19323.5	+	14039.4i	0.624124	+	0.453453i
$987$	2203.90	−	1601.23i	0.0710749	−	0.0516389i
$988$	−1095.92	+	3372.90i	−0.0352894	+	0.108610i
$989$	−3380.63			−0.108693
$990$	5835.77	−	6149.42i	0.187346	−	0.197415i
$991$	−26496.6			−0.849337			−0.424668	−	0.905349i	$-0.639609\pi$
$991$	−26496.6			−0.849337			−0.424668	+	0.905349i	$0.639609\pi$
$992$	41.7602	−	128.525i	0.00133658	−	0.00411357i
$993$	−1102.96	+	801.344i	−0.0352480	+	0.0256092i
$994$	1906.84	+	1385.40i	0.0608465	+	0.0442075i
$995$	2804.44	+	8631.19i	0.0893536	+	0.275002i
$996$	−2887.95	−	8888.20i	−0.0918757	−	0.282764i
$997$	30148.6	+	21904.3i	0.957690	+	0.695803i	0.952613	−	0.304184i	$-0.0983839\pi$
$997$	30148.6	+	21904.3i	0.957690	+	0.695803i	0.00507718	+	0.999987i	$0.498384\pi$
$998$	26103.6	−	18965.4i	0.827952	−	0.601542i
$999$	−3559.80	+	10955.9i	−0.112740	+	0.346978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.g.a.31.2	✓	8
11.4	even	5		1210.4.a.y.1.2		4
11.5	even	5	inner	110.4.g.a.71.2	yes	8
11.7	odd	10		1210.4.a.ba.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.g.a.31.2	✓	8	1.1	even	1	trivial
110.4.g.a.71.2	yes	8	11.5	even	5	inner
1210.4.a.y.1.2		4	11.4	even	5
1210.4.a.ba.1.2		4	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 + 1.90211i) q^{2} +(1.56926 - 1.14014i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(1.54508 + 4.75528i) q^{5} +(1.19881 + 3.68956i) q^{6} +(2.32355 + 1.68816i) q^{7} +(6.47214 - 4.70228i) q^{8} +(-7.18078 + 22.1002i) q^{9} -10.0000 q^{10} +(32.9286 + 15.7068i) q^{11} -7.75887 q^{12} +(-9.69990 + 29.8532i) q^{13} +(-4.64710 + 3.37632i) q^{14} +(7.84632 + 5.70069i) q^{15} +(4.94427 + 15.2169i) q^{16} +(24.7342 + 76.1240i) q^{17} +(-37.5991 - 27.3173i) q^{18} +(-22.8513 + 16.6024i) q^{19} +(6.18034 - 19.0211i) q^{20} +5.57100 q^{21} +(-50.2272 + 52.9267i) q^{22} -11.0833 q^{23} +(4.79525 - 14.7583i) q^{24} +(-20.2254 + 14.6946i) q^{25} +(-50.7893 - 36.9006i) q^{26} +(30.1126 + 92.6772i) q^{27} +(-3.55007 - 10.9260i) q^{28} +(-120.709 - 87.7006i) q^{29} +(-15.6926 + 11.4014i) q^{30} +(-1.30501 + 4.01639i) q^{31} -32.0000 q^{32} +(69.5817 - 12.8950i) q^{33} -160.083 q^{34} +(-4.43759 + 13.6575i) q^{35} +(75.1981 - 54.6346i) q^{36} +(95.6389 + 69.4857i) q^{37} +(-17.4568 - 53.7266i) q^{38} +(18.8151 + 57.9068i) q^{39} +(32.3607 + 23.5114i) q^{40} +(178.364 - 129.589i) q^{41} +(-3.44307 + 10.5967i) q^{42} +305.021 q^{43} +(-69.6304 - 128.248i) q^{44} -116.187 q^{45} +(6.84983 - 21.0816i) q^{46} +(395.602 - 287.422i) q^{47} +(25.1082 + 18.2422i) q^{48} +(-103.444 - 318.367i) q^{49} +(-15.4508 - 47.5528i) q^{50} +(125.606 + 91.2583i) q^{51} +(101.579 - 73.8012i) q^{52} +(135.112 - 415.832i) q^{53} -194.893 q^{54} +(-23.8128 + 180.853i) q^{55} +22.9765 q^{56} +(-16.9307 + 52.1072i) q^{57} +(241.419 - 175.401i) q^{58} +(-339.772 - 246.859i) q^{59} +(-11.9881 - 36.8956i) q^{60} +(74.1097 + 228.086i) q^{61} +(-6.83310 - 4.96454i) q^{62} +(-53.9935 + 39.2286i) q^{63} +(19.7771 - 60.8676i) q^{64} -156.948 q^{65} +(-18.4760 + 140.322i) q^{66} -382.944 q^{67} +(98.9367 - 304.496i) q^{68} +(-17.3926 + 12.6364i) q^{69} +(-23.2355 - 16.8816i) q^{70} +(-126.799 - 390.246i) q^{71} +(57.4462 + 176.801i) q^{72} +(364.465 + 264.800i) q^{73} +(-191.278 + 138.971i) q^{74} +(-14.9851 + 46.1195i) q^{75} +112.983 q^{76} +(49.9958 + 92.0844i) q^{77} -121.774 q^{78} +(-150.166 + 462.163i) q^{79} +(-64.7214 + 47.0228i) q^{80} +(-354.668 - 257.681i) q^{81} +(136.258 + 419.358i) q^{82} +(372.213 + 1145.55i) q^{83} +(-18.0281 - 13.0982i) q^{84} +(-323.775 + 235.236i) q^{85} +(-188.514 + 580.185i) q^{86} -289.416 q^{87} +(286.977 - 53.1832i) q^{88} -1533.91 q^{89} +(71.8078 - 221.002i) q^{90} +(-72.9352 + 52.9905i) q^{91} +(35.8662 + 26.0583i) q^{92} +(2.53134 + 7.79067i) q^{93} +(302.213 + 930.117i) q^{94} +(-114.256 - 83.0121i) q^{95} +(-50.2165 + 36.4844i) q^{96} +(317.163 - 976.128i) q^{97} +669.502 q^{98} +(-583.577 + 614.942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 10 q^{5} - 26 q^{6} - 15 q^{7} + 16 q^{8} - 41 q^{9} - 80 q^{10} + 23 q^{11} - 48 q^{12} - 32 q^{13} + 30 q^{14} - 35 q^{15} - 32 q^{16} + 81 q^{17} - 138 q^{18} + 157 q^{19}+ \cdots - 2906 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 10 * q^5 - 26 * q^6 - 15 * q^7 + 16 * q^8 - 41 * q^9 - 80 * q^10 + 23 * q^11 - 48 * q^12 - 32 * q^13 + 30 * q^14 - 35 * q^15 - 32 * q^16 + 81 * q^17 - 138 * q^18 + 157 * q^19 - 40 * q^20 + 140 * q^21 - 76 * q^22 - 518 * q^23 - 104 * q^24 - 50 * q^25 + 54 * q^26 + 152 * q^27 - 40 * q^28 - 73 * q^29 + 70 * q^30 + 460 * q^31 - 256 * q^32 - 67 * q^33 - 92 * q^34 - 50 * q^35 + 276 * q^36 + 46 * q^38 + 1063 * q^39 + 80 * q^40 - 564 * q^41 - 50 * q^42 - 294 * q^43 - 428 * q^44 - 280 * q^45 + 146 * q^46 + 1652 * q^47 - 112 * q^48 + 641 * q^49 + 100 * q^50 + 675 * q^51 - 108 * q^52 + 679 * q^53 + 636 * q^54 - 285 * q^55 - 400 * q^56 - 1585 * q^57 + 146 * q^58 - 143 * q^59 + 260 * q^60 + 826 * q^61 + 110 * q^62 + 105 * q^63 - 128 * q^64 + 590 * q^65 - 1376 * q^66 - 1378 * q^67 + 324 * q^68 + 1435 * q^69 + 150 * q^70 - 8 * q^71 + 328 * q^72 + 2017 * q^73 + 325 * q^75 - 1072 * q^76 - 360 * q^77 + 1164 * q^78 - 1763 * q^79 - 160 * q^80 - 360 * q^81 - 862 * q^82 + 581 * q^83 - 380 * q^84 - 520 * q^85 + 448 * q^86 - 4054 * q^87 - 824 * q^88 - 3368 * q^89 + 410 * q^90 - 2010 * q^91 + 1328 * q^92 - 3737 * q^93 + 2846 * q^94 + 785 * q^95 + 224 * q^96 + 3604 * q^97 + 3828 * q^98 - 2906 * q^99

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