LMFDB - Embedded newform 36.3.f.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,3,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	36.f (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:	$0.980928951697$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$1.93353 + 0.511345i$ of defining polynomial
Character	$\chi$	$=$	36.31
Dual form			36.3.f.c.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93353 - 0.511345i) q^{2} +(-2.76570 + 1.16229i) q^{3} +(3.47705 + 1.97740i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(5.94188 - 0.833101i) q^{6} +(-3.90254 + 2.25313i) q^{7} +(-5.71184 - 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +O(q^{10})$	\(q+(-1.93353 - 0.511345i) q^{2} +(-2.76570 + 1.16229i) q^{3} +(3.47705 + 1.97740i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(5.94188 - 0.833101i) q^{6} +(-3.90254 + 2.25313i) q^{7} +(-5.71184 - 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +(11.3643 - 11.4386i) q^{10} +(3.25842 - 1.88125i) q^{11} +(-11.9148 - 1.42753i) q^{12} +(-3.52605 + 6.10730i) q^{13} +(8.69780 - 2.36095i) q^{14} +(3.03354 - 23.9953i) q^{15} +(8.17979 + 13.7510i) q^{16} +0.517890 q^{17} +(-15.4651 + 9.21031i) q^{18} +16.4164i q^{19} +(-27.8223 + 16.3057i) q^{20} +(8.17444 - 10.7674i) q^{21} +(-7.26222 + 1.97127i) q^{22} +(27.7049 + 15.9954i) q^{23} +(22.3076 + 8.85273i) q^{24} +(-19.9986 - 34.6387i) q^{25} +(9.94065 - 10.0056i) q^{26} +(-9.94627 + 25.1012i) q^{27} +(-18.0247 + 0.117384i) q^{28} +(9.48394 + 16.4267i) q^{29} +(-18.1353 + 44.8443i) q^{30} +(-13.1355 - 7.58377i) q^{31} +(-8.78432 - 30.7707i) q^{32} +(-6.82524 + 8.99021i) q^{33} +(-1.00135 - 0.264820i) q^{34} -36.3299i q^{35} +(34.6119 - 9.90037i) q^{36} +0.592061 q^{37} +(8.39446 - 31.7416i) q^{38} +(2.65351 - 20.9892i) q^{39} +(62.1330 - 17.3007i) q^{40} +(12.3766 - 21.4369i) q^{41} +(-21.3114 + 16.6391i) q^{42} +(27.8686 - 16.0900i) q^{43} +(15.0497 - 0.0980099i) q^{44} +(19.4997 + 69.8895i) q^{45} +(-45.3890 - 45.0944i) q^{46} +(-52.4682 + 30.2925i) q^{47} +(-38.6056 - 28.5239i) q^{48} +(-14.3468 + 24.8493i) q^{49} +(20.9556 + 77.2010i) q^{50} +(-1.43233 + 0.601940i) q^{51} +(-24.3368 + 14.2630i) q^{52} -0.664765 q^{53} +(32.0668 - 43.4479i) q^{54} +30.3336i q^{55} +(34.9113 + 8.98987i) q^{56} +(-19.0807 - 45.4029i) q^{57} +(-9.93776 - 36.6110i) q^{58} +(-30.5921 - 17.6623i) q^{59} +(57.9960 - 77.4343i) q^{60} +(33.7750 + 58.5000i) q^{61} +(21.5199 + 21.3802i) q^{62} +(-10.0932 + 39.2804i) q^{63} +(1.25029 + 63.9878i) q^{64} +(-28.4273 - 49.2376i) q^{65} +(17.7939 - 13.8928i) q^{66} +(-74.4692 - 42.9948i) q^{67} +(1.80073 + 1.02407i) q^{68} +(-95.2148 - 12.0373i) q^{69} +(-18.5771 + 70.2449i) q^{70} +56.4434i q^{71} +(-71.9855 + 1.44402i) q^{72} +131.921 q^{73} +(-1.14477 - 0.302748i) q^{74} +(95.5705 + 72.5557i) q^{75} +(-32.4618 + 57.0808i) q^{76} +(-8.47743 + 14.6833i) q^{77} +(-15.8634 + 39.2264i) q^{78} +(126.869 - 73.2481i) q^{79} +(-128.982 + 1.68005i) q^{80} +(-1.66664 - 80.9829i) q^{81} +(-34.8921 + 35.1201i) q^{82} +(87.1029 - 50.2889i) q^{83} +(49.7144 - 21.2746i) q^{84} +(-2.08764 + 3.61589i) q^{85} +(-62.1122 + 16.8599i) q^{86} +(-45.3223 - 34.4081i) q^{87} +(-29.1491 - 7.50608i) q^{88} -25.8362 q^{89} +(-1.96553 - 145.104i) q^{90} -31.7786i q^{91} +(64.7021 + 110.401i) q^{92} +(45.1433 + 5.70713i) q^{93} +(116.939 - 31.7420i) q^{94} +(-114.619 - 66.1754i) q^{95} +(60.0593 + 74.8924i) q^{96} +(-48.2534 - 83.5773i) q^{97} +(40.4465 - 40.7107i) q^{98} +(8.42728 - 32.7971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.93353	−	0.511345i	−0.966763	−	0.255672i
$2$	−1.93353	−	0.511345i	−0.966763	−	0.255672i
$3$	−2.76570	+	1.16229i	−0.921899	+	0.387431i
$3$	−2.76570	+	1.16229i	−0.921899	+	0.387431i
$4$	3.47705	+	1.97740i	0.869263	+	0.494350i
$5$	−4.03104	+	6.98197i	−0.806209	+	1.39639i	0.109263	+	0.994013i	$0.465151\pi$
$5$	−4.03104	+	6.98197i	−0.806209	+	1.39639i	−0.915472	+	0.402382i	$0.868182\pi$
$6$	5.94188	−	0.833101i	0.990313	−	0.138850i
$7$	−3.90254	+	2.25313i	−0.557506	+	0.321876i	−0.752144	−	0.658999i	$-0.770980\pi$
$7$	−3.90254	+	2.25313i	−0.557506	+	0.321876i	0.194638	+	0.980875i	$0.437647\pi$
$8$	−5.71184	−	5.60133i	−0.713980	−	0.700166i
$9$	6.29815	−	6.42910i	0.699794	−	0.714344i
$10$	11.3643	−	11.4386i	1.13643	−	1.14386i
$11$	3.25842	−	1.88125i	0.296220	−	0.171023i	−0.344523	−	0.938778i	$-0.611959\pi$
$11$	3.25842	−	1.88125i	0.296220	−	0.171023i	0.640744	+	0.767755i	$0.278626\pi$
$12$	−11.9148	−	1.42753i	−0.992899	−	0.118961i
$13$	−3.52605	+	6.10730i	−0.271235	+	0.469792i	−0.969178	−	0.246361i	$-0.920765\pi$
$13$	−3.52605	+	6.10730i	−0.271235	+	0.469792i	0.697944	+	0.716153i	$0.254099\pi$
$14$	8.69780	−	2.36095i	0.621271	−	0.168639i
$15$	3.03354	−	23.9953i	0.202236	−	1.59968i
$16$	8.17979	+	13.7510i	0.511237	+	0.859440i
$17$	0.517890			0.0304641			0.0152321	−	0.999884i	$-0.495151\pi$
$17$	0.517890			0.0304641			0.0152321	+	0.999884i	$0.495151\pi$
$18$	−15.4651	+	9.21031i	−0.859174	+	0.511684i
$19$			16.4164i			0.864023i	0.901868	+	0.432012i	$0.142196\pi$
$19$			16.4164i			0.864023i	−0.901868	+	0.432012i	$0.857804\pi$
$20$	−27.8223	+	16.3057i	−1.39111	+	0.815286i
$21$	8.17444	−	10.7674i	0.389259	−	0.512733i
$22$	−7.26222	+	1.97127i	−0.330101	+	0.0896033i
$23$	27.7049	+	15.9954i	1.20456	+	0.695454i	0.961566	−	0.274573i	$-0.0885366\pi$
$23$	27.7049	+	15.9954i	1.20456	+	0.695454i	0.242996	+	0.970027i	$0.421870\pi$
$24$	22.3076	+	8.85273i	0.929483	+	0.368864i
$25$	−19.9986	−	34.6387i	−0.799946	−	1.38555i
$26$	9.94065	−	10.0056i	0.382333	−	0.384831i
$27$	−9.94627	+	25.1012i	−0.368380	+	0.929675i
$28$	−18.0247	+	0.117384i	−0.643739	+	0.00419230i
$29$	9.48394	+	16.4267i	0.327032	+	0.566437i	0.981922	−	0.189288i	$-0.0606180\pi$
$29$	9.48394	+	16.4267i	0.327032	+	0.566437i	−0.654889	+	0.755725i	$0.727285\pi$
$30$	−18.1353	+	44.8443i	−0.604510	+	1.49481i
$31$	−13.1355	−	7.58377i	−0.423725	−	0.244638i	0.272945	−	0.962030i	$-0.412002\pi$
$31$	−13.1355	−	7.58377i	−0.423725	−	0.244638i	−0.696670	+	0.717392i	$0.745336\pi$
$32$	−8.78432	−	30.7707i	−0.274510	−	0.961584i
$33$	−6.82524	+	8.99021i	−0.206826	+	0.272431i
$34$	−1.00135	−	0.264820i	−0.0294516	−	0.00778884i
$35$		−	36.3299i		−	1.03800i
$36$	34.6119	−	9.90037i	0.961441	−	0.275010i
$37$	0.592061			0.0160017			0.00800083	−	0.999968i	$-0.497453\pi$
$37$	0.592061			0.0160017			0.00800083	+	0.999968i	$0.497453\pi$
$38$	8.39446	−	31.7416i	0.220907	−	0.835306i
$39$	2.65351	−	20.9892i	0.0680387	−	0.538185i
$40$	62.1330	−	17.3007i	1.55333	−	0.432518i
$41$	12.3766	−	21.4369i	0.301868	−	0.522850i	−0.674691	−	0.738100i	$-0.735723\pi$
$41$	12.3766	−	21.4369i	0.301868	−	0.522850i	0.976559	+	0.215250i	$0.0690565\pi$
$42$	−21.3114	+	16.6391i	−0.507413	+	0.396168i
$43$	27.8686	−	16.0900i	0.648107	−	0.374185i	−0.139623	−	0.990205i	$-0.544589\pi$
$43$	27.8686	−	16.0900i	0.648107	−	0.374185i	0.787731	+	0.616020i	$0.211256\pi$
$44$	15.0497	−	0.0980099i	0.342039	−	0.00222750i
$45$	19.4997	+	69.8895i	0.433326	+	1.55310i
$46$	−45.3890	−	45.0944i	−0.986718	−	0.980313i
$47$	−52.4682	+	30.2925i	−1.11634	+	0.644521i	−0.940465	−	0.339890i	$-0.889610\pi$
$47$	−52.4682	+	30.2925i	−1.11634	+	0.644521i	−0.175879	+	0.984412i	$0.556277\pi$
$48$	−38.6056	−	28.5239i	−0.804282	−	0.594247i
$49$	−14.3468	+	24.8493i	−0.292791	+	0.507129i
$50$	20.9556	+	77.2010i	0.419112	+	1.54402i
$51$	−1.43233	+	0.601940i	−0.0280848	+	0.0118027i
$52$	−24.3368	+	14.2630i	−0.468016	+	0.274288i
$53$	−0.664765			−0.0125427			−0.00627137	−	0.999980i	$-0.501996\pi$
$53$	−0.664765			−0.0125427			−0.00627137	+	0.999980i	$0.501996\pi$
$54$	32.0668	−	43.4479i	0.593829	−	0.804591i
$55$			30.3336i			0.551521i
$56$	34.9113	+	8.98987i	0.623415	+	0.160533i
$57$	−19.0807	−	45.4029i	−0.334749	−	0.796542i
$58$	−9.93776	−	36.6110i	−0.171341	−	0.631224i
$59$	−30.5921	−	17.6623i	−0.518510	−	0.299362i	0.217815	−	0.975990i	$-0.430107\pi$
$59$	−30.5921	−	17.6623i	−0.518510	−	0.299362i	−0.736325	+	0.676628i	$0.763440\pi$
$60$	57.9960	−	77.4343i	0.966600	−	1.29057i
$61$	33.7750	+	58.5000i	0.553688	+	0.959016i	0.998004	+	0.0631460i	$0.0201134\pi$
$61$	33.7750	+	58.5000i	0.553688	+	0.959016i	−0.444316	+	0.895870i	$0.646553\pi$
$62$	21.5199	+	21.3802i	0.347095	+	0.344842i
$63$	−10.0932	+	39.2804i	−0.160209	+	0.623499i
$64$	1.25029	+	63.9878i	0.0195357	+	0.999809i
$65$	−28.4273	−	49.2376i	−0.437343	−	0.757501i
$66$	17.7939	−	13.8928i	0.269604	−	0.210496i
$67$	−74.4692	−	42.9948i	−1.11148	−	0.641714i	−0.172269	−	0.985050i	$-0.555110\pi$
$67$	−74.4692	−	42.9948i	−1.11148	−	0.641714i	−0.939213	+	0.343336i	$0.888443\pi$
$68$	1.80073	+	1.02407i	0.0264813	+	0.0150599i
$69$	−95.2148	−	12.0373i	−1.37992	−	0.174454i
$70$	−18.5771	+	70.2449i	−0.265388	+	1.00350i
$71$			56.4434i			0.794977i	0.917607	+	0.397489i	$0.130118\pi$
$71$			56.4434i			0.794977i	−0.917607	+	0.397489i	$0.869882\pi$
$72$	−71.9855	+	1.44402i	−0.999799	+	0.0200558i
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$	−1.14477	−	0.302748i	−0.0154698	−	0.00409118i
$75$	95.5705	+	72.5557i	1.27427	+	0.967410i
$76$	−32.4618	+	57.0808i	−0.427129	+	0.751063i
$77$	−8.47743	+	14.6833i	−0.110096	+	0.190693i
$78$	−15.8634	+	39.2264i	−0.203377	+	0.502902i
$79$	126.869	−	73.2481i	1.60594	−	0.927191i	0.615677	−	0.787999i	$-0.288883\pi$
$79$	126.869	−	73.2481i	1.60594	−	0.927191i	0.990265	−	0.139192i	$-0.0444505\pi$
$80$	−128.982	+	1.68005i	−1.61228	+	0.0210006i
$81$	−1.66664	−	80.9829i	−0.0205758	−	0.999788i
$82$	−34.8921	+	35.1201i	−0.425513	+	0.428293i
$83$	87.1029	−	50.2889i	1.04943	−	0.605890i	0.126942	−	0.991910i	$-0.459484\pi$
$83$	87.1029	−	50.2889i	1.04943	−	0.605890i	0.922491	+	0.386020i	$0.126150\pi$
$84$	49.7144	−	21.2746i	0.591838	−	0.253269i
$85$	−2.08764	+	3.61589i	−0.0245604	+	0.0425399i
$86$	−62.1122	+	16.8599i	−0.722235	+	0.196045i
$87$	−45.3223	−	34.4081i	−0.520946	−	0.395495i
$88$	−29.1491	−	7.50608i	−0.331240	−	0.0852964i
$89$	−25.8362			−0.290295			−0.145147	−	0.989410i	$-0.546366\pi$
$89$	−25.8362			−0.290295			−0.145147	+	0.989410i	$0.546366\pi$
$90$	−1.96553	−	145.104i	−0.0218392	−	1.61227i
$91$		−	31.7786i		−	0.349216i
$92$	64.7021	+	110.401i	0.703284	+	1.20001i
$93$	45.1433	+	5.70713i	0.485412	+	0.0613670i
$94$	116.939	−	31.7420i	1.24403	−	0.337681i
$95$	−114.619	−	66.1754i	−1.20652	−	0.696583i
$96$	60.0593	+	74.8924i	0.625618	+	0.780129i
$97$	−48.2534	−	83.5773i	−0.497457	−	0.861621i	0.502538	−	0.864555i	$-0.332400\pi$
$97$	−48.2534	−	83.5773i	−0.497457	−	0.861621i	−0.999996	+	0.00293363i	$0.999066\pi$
$98$	40.4465	−	40.7107i	0.412719	−	0.415415i
$99$	8.42728	−	32.7971i	0.0851241	−	0.331284i
$100$	−1.04189	−	159.986i	−0.0104189	−	1.59986i
$101$	−21.6600	−	37.5163i	−0.214456	−	0.371448i	0.738648	−	0.674091i	$-0.235464\pi$
$101$	−21.6600	−	37.5163i	−0.214456	−	0.371448i	−0.953104	+	0.302643i	$0.902131\pi$
$102$	3.07724	−	0.431455i	0.0301690	−	0.00422995i
$103$	125.439	+	72.4223i	1.21786	+	0.703129i	0.964459	−	0.264233i	$-0.0851189\pi$
$103$	125.439	+	72.4223i	1.21786	+	0.703129i	0.253397	+	0.967362i	$0.418452\pi$
$104$	54.3492	−	15.1334i	0.522588	−	0.145513i
$105$	42.2260	+	100.478i	0.402153	+	0.956929i
$106$	1.28534	+	0.339924i	0.0121259	+	0.00320683i
$107$			54.9861i			0.513889i	0.966426	+	0.256944i	$0.0827158\pi$
$107$			54.9861i			0.513889i	−0.966426	+	0.256944i	$0.917284\pi$
$108$	−84.2188	+	67.6106i	−0.779804	+	0.626024i
$109$	−63.9235			−0.586454			−0.293227	−	0.956043i	$-0.594729\pi$
$109$	−63.9235			−0.586454			−0.293227	+	0.956043i	$0.594729\pi$
$110$	15.5110	−	58.6509i	0.141009	−	0.533190i
$111$	−1.63746	+	0.688149i	−0.0147519	+	0.00619954i
$112$	−62.9049	−	35.2338i	−0.561651	−	0.314588i
$113$	17.8239	−	30.8720i	0.157734	−	0.273203i	−0.776317	−	0.630342i	$-0.782914\pi$
$113$	17.8239	−	30.8720i	0.157734	−	0.273203i	0.934051	+	0.357139i	$0.116248\pi$
$114$	13.6765	+	97.5445i	0.119970	+	0.855654i
$115$	−223.360	+	128.957i	−1.94226	+	1.12136i
$116$	0.494097	+	75.8699i	0.00425945	+	0.654051i
$117$	17.0568	+	61.1340i	0.145785	+	0.522513i
$118$	50.1190	+	49.7937i	0.424738	+	0.421981i
$119$	−2.02109	+	1.16688i	−0.0169839	+	0.00980568i
$120$	−151.732	+	120.065i	−1.26444	+	1.00054i
$121$	−53.4218	+	92.5292i	−0.441502	+	0.764704i
$122$	−35.3912	−	130.382i	−0.290091	−	1.06870i
$123$	−9.31394	+	73.6731i	−0.0757231	+	0.598968i
$124$	−30.6766	−	52.3432i	−0.247392	−	0.422123i
$125$	120.909			0.967276
$126$	39.6013	−	70.7886i	0.314296	−	0.561815i
$127$		−	9.81219i		−	0.0772613i	−0.999254	−	0.0386307i	$-0.987700\pi$
$127$		−	9.81219i		−	0.0772613i	0.999254	−	0.0386307i	$-0.0122996\pi$
$128$	30.3024	−	124.361i	0.236737	−	0.971574i
$129$	−58.3749	+	76.8914i	−0.452518	+	0.596057i
$130$	29.7876	+	109.738i	0.229135	+	0.844141i
$131$	101.561	+	58.6365i	0.775278	+	0.447607i	0.834754	−	0.550623i	$-0.185610\pi$
$131$	101.561	+	58.6365i	0.775278	+	0.447607i	−0.0594761	+	0.998230i	$0.518943\pi$
$132$	−41.5090	+	17.7632i	−0.314462	+	0.134570i
$133$	−36.9884	−	64.0659i	−0.278109	−	0.481698i
$134$	122.003	+	121.211i	0.910471	+	0.904561i
$135$	−135.162	−	170.629i	−1.00120	−	1.26392i
$136$	−2.95811	−	2.90087i	−0.0217508	−	0.0213299i
$137$	125.606	+	217.556i	0.916831	+	1.58800i	0.804198	+	0.594362i	$0.202595\pi$
$137$	125.606	+	217.556i	0.916831	+	1.58800i	0.112634	+	0.993637i	$0.464071\pi$
$138$	177.945	+	71.9620i	1.28946	+	0.521464i
$139$	−133.073	−	76.8298i	−0.957361	−	0.552732i	−0.0620009	−	0.998076i	$-0.519748\pi$
$139$	−133.073	−	76.8298i	−0.957361	−	0.552732i	−0.895360	+	0.445344i	$0.853081\pi$
$140$	71.8388	−	126.321i	0.513134	−	0.902294i
$141$	109.902	−	144.763i	0.779448	−	1.02669i
$142$	28.8620	−	109.135i	0.203254	−	0.768555i
$143$			26.5335i			0.185549i
$144$	139.924	+	34.0174i	0.971697	+	0.236232i
$145$	−152.921			−1.05463
$146$	−255.072	−	67.4570i	−1.74707	−	0.462034i
$147$	10.7966	−	85.4009i	0.0734462	−	0.580958i
$148$	2.05863	+	1.17074i	0.0139097	+	0.00791041i
$149$	−45.8643	+	79.4393i	−0.307814	+	0.533150i	−0.977884	−	0.209148i	$-0.932931\pi$
$149$	−45.8643	+	79.4393i	−0.307814	+	0.533150i	0.670070	+	0.742298i	$0.266264\pi$
$150$	−147.687	−	189.158i	−0.984580	−	1.26105i
$151$	36.0215	−	20.7970i	0.238553	−	0.137729i	−0.375958	−	0.926637i	$-0.622686\pi$
$151$	36.0215	−	20.7970i	0.238553	−	0.137729i	0.614512	+	0.788908i	$0.289353\pi$
$152$	91.9538	−	93.7681i	0.604959	−	0.616895i
$153$	3.26175	−	3.32957i	0.0213186	−	0.0217619i
$154$	23.8996	−	24.0557i	0.155192	−	0.156206i
$155$	105.899	−	61.1410i	0.683222	−	0.394458i
$156$	50.7305	−	67.7336i	0.325195	−	0.434190i
$157$	112.909	−	195.565i	0.719167	−	1.24563i	−0.242163	−	0.970236i	$-0.577857\pi$
$157$	112.909	−	195.565i	0.719167	−	1.24563i	0.961330	−	0.275399i	$-0.0888099\pi$
$158$	−282.760	+	76.7531i	−1.78962	+	0.485779i
$159$	1.83854	−	0.772652i	0.0115631	−	0.00485945i
$160$	250.250	+	62.7061i	1.56406	+	0.391913i
$161$	−144.160			−0.895401
$162$	−38.1877	+	157.435i	−0.235726	+	0.971819i
$163$			125.175i			0.767945i	0.923344	+	0.383973i	$0.125444\pi$
$163$			125.175i			0.767945i	−0.923344	+	0.383973i	$0.874556\pi$
$164$	85.4233	−	50.0637i	0.520874	−	0.305266i
$165$	−35.2566	−	83.8936i	−0.213676	−	0.508446i
$166$	−194.131	+	52.6953i	−1.16946	+	0.317442i
$167$	154.373	+	89.1274i	0.924390	+	0.533697i	0.885033	−	0.465528i	$-0.154136\pi$
$167$	154.373	+	89.1274i	0.924390	+	0.533697i	0.0393573	+	0.999225i	$0.487469\pi$
$168$	−107.003	+	15.7139i	−0.636921	+	0.0935349i
$169$	59.6340	+	103.289i	0.352864	+	0.611178i
$170$	5.88547	−	5.92393i	0.0346204	−	0.0348466i
$171$	105.543	+	103.393i	0.617210	+	0.604638i
$172$	128.717	−	0.838258i	0.748354	−	0.00487359i
$173$	−75.5904	−	130.926i	−0.436939	−	0.756800i	0.560513	−	0.828146i	$-0.310604\pi$
$173$	−75.5904	−	130.926i	−0.436939	−	0.756800i	−0.997452	+	0.0713455i	$0.977271\pi$
$174$	70.0375	+	89.7042i	0.402514	+	0.515542i
$175$	156.091	+	90.1193i	0.891949	+	0.514967i
$176$	52.5224	+	29.4185i	0.298423	+	0.167150i
$177$	105.137	+	13.2917i	0.593995	+	0.0750944i
$178$	49.9551	+	13.2112i	0.280646	+	0.0742204i
$179$		−	276.827i		−	1.54652i	−0.634088	−	0.773261i	$-0.718624\pi$
$179$		−	276.827i		−	1.54652i	0.634088	−	0.773261i	$-0.281376\pi$
$180$	−70.3979	+	281.568i	−0.391100	+	1.56427i
$181$	−104.729			−0.578612			−0.289306	−	0.957237i	$-0.593425\pi$
$181$	−104.729			−0.578612			−0.289306	+	0.957237i	$0.593425\pi$
$182$	−16.2499	+	61.4449i	−0.0892849	+	0.337609i
$183$	−161.405	−	122.537i	−0.881997	−	0.669600i
$184$	−68.6504	−	246.548i	−0.373100	−	1.33993i
$185$	−2.38663	+	4.13376i	−0.0129007	+	0.0223446i
$186$	−84.3674	−	34.1187i	−0.453588	−	0.183434i
$187$	1.68751	−	0.974282i	0.00902409	−	0.00521006i
$188$	−242.335	+	1.57819i	−1.28902	+	0.00839461i
$189$	−17.7407	−	120.369i	−0.0938662	−	0.636873i
$190$	187.781	+	186.562i	0.988320	+	0.981904i
$191$	−192.972	+	111.413i	−1.01033	+	0.583312i	−0.911287	−	0.411772i	$-0.864910\pi$
$191$	−192.972	+	111.413i	−1.01033	+	0.583312i	−0.0990389	+	0.995084i	$0.531577\pi$
$192$	−77.8305	−	175.518i	−0.405367	−	0.914154i
$193$	56.6790	−	98.1709i	0.293674	−	0.508657i	−0.681002	−	0.732282i	$-0.738455\pi$
$193$	56.6790	−	98.1709i	0.293674	−	0.508657i	0.974675	+	0.223624i	$0.0717888\pi$
$194$	50.5623	+	186.273i	0.260631	+	0.960170i
$195$	135.850	+	103.135i	0.696666	+	0.528899i
$196$	−99.0215	+	58.0332i	−0.505212	+	0.296088i
$197$	−120.998			−0.614201			−0.307100	−	0.951677i	$-0.599359\pi$
$197$	−120.998			−0.614201			−0.307100	+	0.951677i	$0.599359\pi$
$198$	−33.0650	+	59.1049i	−0.166995	+	0.298510i
$199$		−	82.2364i		−	0.413248i	−0.978420	−	0.206624i	$-0.933752\pi$
$199$		−	82.2364i		−	0.413248i	0.978420	−	0.206624i	$-0.0662477\pi$
$200$	−79.7934	+	309.870i	−0.398967	+	1.54935i
$201$	255.932	+	32.3556i	1.27329	+	0.160973i
$202$	22.6965	+	83.6145i	0.112359	+	0.413933i
$203$	−74.0230	−	42.7372i	−0.364645	−	0.210528i
$204$	−6.17055	−	0.739302i	−0.0302478	−	0.00362403i
$205$	99.7811	+	172.826i	0.486737	+	0.843053i
$206$	−205.507	−	204.173i	−0.997607	−	0.991132i
$207$	277.326	−	77.3760i	1.33974	−	0.373797i
$208$	−112.824	+	1.46958i	−0.542423	+	0.00706527i
$209$	30.8835	+	53.4917i	0.147768	+	0.255941i
$210$	−30.2665	−	215.868i	−0.144126	−	1.02794i
$211$	93.5819	+	54.0295i	0.443516	+	0.256064i	0.705088	−	0.709120i	$-0.250907\pi$
$211$	93.5819	+	54.0295i	0.443516	+	0.256064i	−0.261572	+	0.965184i	$0.584241\pi$
$212$	−2.31142	−	1.31451i	−0.0109029	−	0.00620050i
$213$	−65.6038	−	156.105i	−0.307999	−	0.732889i
$214$	28.1169	−	106.317i	0.131387	−	0.496809i
$215$			259.437i			1.20668i
$216$	197.412	−	87.6620i	0.913943	−	0.405843i
$217$	68.3490			0.314972
$218$	123.598	+	32.6870i	0.566962	+	0.149940i
$219$	−364.853	+	153.331i	−1.66599	+	0.700140i
$220$	−59.9817	+	105.472i	−0.272644	+	0.479417i
$221$	−1.82611	+	3.16291i	−0.00826292	+	0.0143118i
$222$	3.51796	−	0.493247i	0.0158467	−	0.00222183i
$223$	−141.400	+	81.6371i	−0.634079	+	0.366086i	−0.782330	−	0.622864i	$-0.785969\pi$
$223$	−141.400	+	81.6371i	−0.634079	+	0.366086i	0.148251	+	0.988950i	$0.452636\pi$
$224$	103.612	+	100.292i	0.462552	+	0.447731i
$225$	−348.650	−	89.5862i	−1.54955	−	0.398161i
$226$	−50.2493	+	50.5776i	−0.222342	+	0.223795i
$227$	9.56722	−	5.52364i	0.0421463	−	0.0243332i	−0.478779	−	0.877936i	$-0.658920\pi$
$227$	9.56722	−	5.52364i	0.0421463	−	0.0243332i	0.520925	+	0.853602i	$0.325587\pi$
$228$	23.4349	−	195.598i	0.102785	−	0.857888i
$229$	−16.1725	+	28.0116i	−0.0706222	+	0.122321i	−0.899174	−	0.437591i	$-0.855832\pi$
$229$	−16.1725	+	28.0116i	−0.0706222	+	0.122321i	0.828552	+	0.559912i	$0.189165\pi$
$230$	497.813	−	135.127i	2.16440	−	0.587511i
$231$	6.37965	−	50.4629i	0.0276175	−	0.218454i
$232$	37.8404	−	146.949i	0.163105	−	0.633402i
$233$	181.049			0.777036			0.388518	−	0.921441i	$-0.372987\pi$
$233$	181.049			0.777036			0.388518	+	0.921441i	$0.372987\pi$
$234$	−1.71930	−	126.926i	−0.00734742	−	0.542419i
$235$		−	488.442i		−	2.07848i
$236$	−71.4448	−	121.906i	−0.302732	−	0.516549i
$237$	−265.746	+	350.041i	−1.12129	+	1.47697i
$238$	4.50450	−	1.22271i	0.0189265	−	0.00513745i
$239$	−39.6432	−	22.8880i	−0.165871	−	0.0957658i	0.414766	−	0.909928i	$-0.363863\pi$
$239$	−39.6432	−	22.8880i	−0.165871	−	0.0957658i	−0.580638	+	0.814162i	$0.697197\pi$
$240$	354.774	−	154.562i	1.47822	−	0.644008i
$241$	169.216	+	293.090i	0.702140	+	1.21614i	0.967714	+	0.252052i	$0.0811054\pi$
$241$	169.216	+	293.090i	0.702140	+	1.21614i	−0.265573	+	0.964091i	$0.585561\pi$
$242$	150.607	−	151.591i	0.622342	−	0.626408i
$243$	98.7353	+	222.037i	0.406318	+	0.913732i
$244$	1.75962	+	270.194i	0.00721154	+	1.10735i
$245$	−115.665	−	200.338i	−0.472102	−	0.817704i
$246$	55.6811	−	137.686i	0.226346	−	0.559700i
$247$	−100.260	−	57.8852i	−0.405911	−	0.234353i
$248$	32.5486	+	116.893i	0.131244	+	0.471344i
$249$	−182.450	+	240.323i	−0.732730	+	0.965152i
$250$	−233.782	−	61.8264i	−0.935127	−	0.247306i
$251$		−	282.587i		−	1.12585i	−0.826510	−	0.562923i	$-0.809677\pi$
$251$		−	282.587i		−	1.12585i	0.826510	−	0.562923i	$-0.190323\pi$
$252$	−112.768	+	116.622i	−0.447490	+	0.462785i
$253$	120.366			0.475754
$254$	−5.01741	+	18.9721i	−0.0197536	+	0.0746934i
$255$	1.57104	−	12.4269i	0.00616095	−	0.0487330i
$256$	−122.182	+	224.961i	−0.477274	+	0.878755i
$257$	38.8897	−	67.3589i	0.151322	−	0.262097i	−0.780392	−	0.625291i	$-0.784980\pi$
$257$	38.8897	−	67.3589i	0.151322	−	0.262097i	0.931714	+	0.363194i	$0.118314\pi$
$258$	152.187	−	118.822i	0.589874	−	0.460550i
$259$	−2.31055	+	1.33399i	−0.00892102	+	0.00515056i
$260$	−1.48101	−	227.414i	−0.00569620	−	0.874668i
$261$	165.340	+	42.4844i	0.633486	+	0.162775i
$262$	−166.388	−	165.308i	−0.635070	−	0.630947i
$263$	−195.201	+	112.700i	−0.742211	+	0.428516i	−0.822873	−	0.568226i	$-0.807630\pi$
$263$	−195.201	+	112.700i	−0.742211	+	0.428516i	0.0806619	+	0.996742i	$0.474297\pi$
$264$	89.3418	−	13.1203i	0.338416	−	0.0496980i
$265$	2.67970	−	4.64138i	0.0101121	−	0.0175146i
$266$	38.7584	+	142.787i	0.145708	+	0.536793i
$267$	71.4552	−	30.0293i	0.267622	−	0.112469i
$268$	−173.916	−	296.751i	−0.648939	−	1.10728i
$269$	425.808			1.58293			0.791465	−	0.611214i	$-0.209319\pi$
$269$	425.808			1.58293			0.791465	+	0.611214i	$0.209319\pi$
$270$	174.090	+	399.030i	0.644777	+	1.47789i
$271$			56.3665i			0.207995i	0.994578	+	0.103997i	$0.0331633\pi$
$271$			56.3665i			0.207995i	−0.994578	+	0.103997i	$0.966837\pi$
$272$	4.23623	+	7.12152i	0.0155744	+	0.0261821i
$273$	36.9361	+	87.8901i	0.135297	+	0.321942i
$274$	−131.616	−	484.878i	−0.480352	−	1.76963i
$275$	−130.328	−	75.2450i	−0.473920	−	0.273618i
$276$	−307.264	−	230.132i	−1.11328	−	0.833811i
$277$	−209.641	−	363.109i	−0.756828	−	1.31086i	−0.944461	−	0.328625i	$-0.893415\pi$
$277$	−209.641	−	363.109i	−0.756828	−	1.31086i	0.187633	−	0.982239i	$-0.439918\pi$
$278$	218.014	+	216.599i	0.784223	+	0.779132i
$279$	−131.486	+	36.6856i	−0.471276	+	0.131489i
$280$	−203.496	+	207.511i	−0.726771	+	0.741110i
$281$	−73.9638	−	128.109i	−0.263216	−	0.455904i	0.703878	−	0.710320i	$-0.251450\pi$
$281$	−73.9638	−	128.109i	−0.263216	−	0.455904i	−0.967095	+	0.254416i	$0.918117\pi$
$282$	−286.523	+	223.706i	−1.01604	+	0.793283i
$283$	229.852	+	132.705i	0.812198	+	0.468923i	0.847719	−	0.530446i	$-0.177976\pi$
$283$	229.852	+	132.705i	0.812198	+	0.468923i	−0.0355207	+	0.999369i	$0.511309\pi$
$284$	−111.611	+	196.257i	−0.392997	+	0.691045i
$285$	393.917	+	49.8000i	1.38216	+	0.174737i
$286$	13.5678	−	51.3033i	0.0474398	−	0.179382i
$287$			111.544i			0.388656i
$288$	−253.153	−	137.323i	−0.879003	−	0.476816i
$289$	−288.732			−0.999072
$290$	295.676	+	78.1953i	1.01957	+	0.269639i
$291$	230.595	+	175.065i	0.792424	+	0.601597i
$292$	458.695	+	260.860i	1.57087	+	0.893356i
$293$	124.844	−	216.236i	0.426088	−	0.738006i	−0.570433	−	0.821344i	$-0.693225\pi$
$293$	124.844	−	216.236i	0.426088	−	0.738006i	0.996521	+	0.0833379i	$0.0265581\pi$
$294$	−64.5448	+	159.604i	−0.219540	+	0.542871i
$295$	246.636	−	142.395i	0.836054	−	0.482696i
$296$	−3.38176	−	3.31633i	−0.0114249	−	0.0112038i
$297$	14.8126	+	100.502i	0.0498740	+	0.338390i
$298$	129.301	−	130.146i	0.433895	−	0.436730i
$299$	−195.378	+	112.801i	−0.653438	+	0.377262i
$300$	188.832	+	441.261i	0.629440	+	1.47087i
$301$	−72.5056	+	125.583i	−0.240883	+	0.417221i
$302$	−80.2830	+	21.7922i	−0.265838	+	0.0721596i
$303$	103.510	+	78.5833i	0.341617	+	0.259351i
$304$	−225.743	+	134.283i	−0.742576	+	0.441721i
$305$	−544.594			−1.78555
$306$	−8.00924	+	4.76993i	−0.0261740	+	0.0155880i
$307$			259.968i			0.846801i	0.905943	+	0.423401i	$0.139164\pi$
$307$			259.968i			0.846801i	−0.905943	+	0.423401i	$0.860836\pi$
$308$	−58.5113	+	34.2915i	−0.189972	+	0.111336i
$309$	−431.102	−	54.5010i	−1.39515	−	0.176379i
$310$	−236.023	+	64.0667i	−0.761366	+	0.206667i
$311$	−16.5959	−	9.58164i	−0.0533630	−	0.0308091i	0.473081	−	0.881019i	$-0.343142\pi$
$311$	−16.5959	−	9.58164i	−0.0533630	−	0.0308091i	−0.526444	+	0.850210i	$0.676475\pi$
$312$	−132.724	+	105.024i	−0.425397	+	0.336615i
$313$	−21.9358	−	37.9939i	−0.0700823	−	0.121386i	0.828855	−	0.559464i	$-0.188993\pi$
$313$	−21.9358	−	37.9939i	−0.0700823	−	0.121386i	−0.898937	+	0.438078i	$0.855660\pi$
$314$	−318.314	+	320.394i	−1.01374	+	1.02036i
$315$	−233.569	−	228.811i	−0.741488	−	0.726385i
$316$	585.972	−	3.81610i	1.85434	−	0.0120763i
$317$	68.9690	+	119.458i	0.217568	+	0.376838i	0.954064	−	0.299603i	$-0.0968544\pi$
$317$	68.9690	+	119.458i	0.217568	+	0.376838i	−0.736496	+	0.676442i	$0.763521\pi$
$318$	−3.94996	+	0.553817i	−0.0124212	+	0.00174156i
$319$	61.8054	+	35.6834i	0.193747	+	0.111860i
$320$	−451.801	−	249.208i	−1.41188	−	0.778775i
$321$	−63.9100	−	152.075i	−0.199097	−	0.473754i
$322$	278.736	+	73.7152i	0.865641	+	0.228929i
$323$			8.50191i			0.0263217i
$324$	154.340	−	284.877i	0.476359	−	0.879251i
$325$	282.065			0.867892
$326$	64.0076	−	242.029i	0.196342	−	0.742421i
$327$	176.793	−	74.2978i	0.540651	−	0.227211i
$328$	−190.768	+	53.1187i	−0.581610	+	0.161947i
$329$	136.506	−	236.436i	0.414912	−	0.718649i
$330$	25.2710	+	180.239i	0.0765787	+	0.546178i
$331$	−51.7490	+	29.8773i	−0.156341	+	0.0902638i	−0.576130	−	0.817358i	$-0.695438\pi$
$331$	−51.7490	+	29.8773i	−0.156341	+	0.0902638i	0.419788	+	0.907622i	$0.362104\pi$
$332$	402.303	−	2.61996i	1.21176	−	0.00789145i
$333$	3.72889	−	3.80642i	0.0111979	−	0.0114307i
$334$	−252.910	−	251.268i	−0.757215	−	0.752300i
$335$	600.378	−	346.628i	1.79217	−	1.03471i
$336$	214.928	+	24.3321i	0.639667	+	0.0724171i
$337$	224.356	−	388.595i	0.665743	−	1.15310i	−0.313340	−	0.949641i	$-0.601448\pi$
$337$	224.356	−	388.595i	0.665743	−	1.15310i	0.979083	−	0.203460i	$-0.0652188\pi$
$338$	−62.4875	−	230.206i	−0.184874	−	0.681082i
$339$	−13.4133	+	106.099i	−0.0395673	+	0.312977i
$340$	−14.4089	+	8.44457i	−0.0423791	+	0.0248370i
$341$	−57.0679			−0.167355
$342$	−151.200	−	253.882i	−0.442107	−	0.742346i
$343$		−	350.108i		−	1.02072i
$344$	−249.306	−	64.1979i	−0.724727	−	0.186622i
$345$	467.859	−	616.264i	1.35611	−	1.78627i
$346$	79.2075	+	291.803i	0.228924	+	0.843360i
$347$	500.441	+	288.930i	1.44219	+	0.832651i	0.997996	−	0.0632779i	$-0.0201555\pi$
$347$	500.441	+	288.930i	1.44219	+	0.832651i	0.444198	+	0.895929i	$0.353489\pi$
$348$	−89.5496	−	209.259i	−0.257327	−	0.601319i
$349$	66.1311	+	114.542i	0.189487	+	0.328202i	0.945079	−	0.326841i	$-0.105984\pi$
$349$	66.1311	+	114.542i	0.189487	+	0.328202i	−0.755592	+	0.655042i	$0.772651\pi$
$350$	−255.724	−	254.064i	−0.730641	−	0.725898i
$351$	−118.230	−	149.253i	−0.336837	−	0.425222i
$352$	−86.5105	−	83.7384i	−0.245768	−	0.237893i
$353$	270.562	+	468.628i	0.766465	+	1.32756i	0.939468	+	0.342636i	$0.111320\pi$
$353$	270.562	+	468.628i	0.766465	+	1.32756i	−0.173003	+	0.984921i	$0.555347\pi$
$354$	−196.489	−	79.4612i	−0.555053	−	0.224467i
$355$	−394.086	−	227.526i	−1.11010	−	0.640918i
$356$	−89.8339	−	51.0885i	−0.252343	−	0.143507i
$357$	4.23346	−	5.57632i	0.0118584	−	0.0156199i
$358$	−141.554	+	535.253i	−0.395403	+	1.49512i
$359$		−	292.754i		−	0.815470i	−0.913100	−	0.407735i	$-0.866319\pi$
$359$		−	292.754i		−	0.815470i	0.913100	−	0.407735i	$-0.133681\pi$
$360$	280.095	−	508.422i	0.778041	−	1.41228i
$361$	91.5006			0.253464
$362$	202.496	+	53.5525i	0.559381	+	0.147935i
$363$	40.2023	−	318.000i	0.110750	−	0.876032i
$364$	62.8390	−	110.496i	0.172635	−	0.303561i
$365$	−531.779	+	921.067i	−1.45693	+	2.52347i
$366$	249.423	+	319.462i	0.681484	+	0.872847i
$367$	−378.870	+	218.741i	−1.03234	+	0.596024i	−0.917655	−	0.397377i	$-0.869920\pi$
$367$	−378.870	+	218.741i	−1.03234	+	0.596024i	−0.114689	+	0.993401i	$0.536587\pi$
$368$	6.66653	+	511.811i	0.0181156	+	1.39079i
$369$	−59.8702	−	214.583i	−0.162250	−	0.581525i
$370$	6.72838	−	6.77234i	0.0181848	−	0.0183036i
$371$	2.59428	−	1.49781i	0.00699266	−	0.00403721i
$372$	145.680	+	109.110i	0.391614	+	0.293307i
$373$	−352.979	+	611.377i	−0.946323	+	1.63908i	−0.193243	+	0.981151i	$0.561901\pi$
$373$	−352.979	+	611.377i	−0.946323	+	1.63908i	−0.753080	+	0.657929i	$0.771433\pi$
$374$	−3.76103	+	1.02090i	−0.0100562	+	0.00272969i
$375$	−334.399	+	140.532i	−0.891730	+	0.374753i
$376$	469.368	+	120.865i	1.24832	+	0.321450i
$377$	−133.763			−0.354810
$378$	−27.2479	+	241.808i	−0.0720844	+	0.639704i
$379$			541.432i			1.42858i	0.699850	+	0.714290i	$0.253250\pi$
$379$			541.432i			1.42858i	−0.699850	+	0.714290i	$0.746750\pi$
$380$	−267.682	−	456.743i	−0.704426	−	1.20196i
$381$	11.4046	+	27.1375i	0.0299334	+	0.0712271i
$382$	430.087	−	116.744i	1.12588	−	0.305612i
$383$	−311.941	−	180.099i	−0.814467	−	0.470233i	0.0340377	−	0.999421i	$-0.489163\pi$
$383$	−311.941	−	180.099i	−0.814467	−	0.470233i	−0.848505	+	0.529188i	$0.822497\pi$
$384$	60.7373	+	379.166i	0.158170	+	0.987412i
$385$	−68.3458	−	118.378i	−0.177521	−	0.307476i
$386$	−159.790	+	160.834i	−0.413963	+	0.416667i
$387$	72.0768	−	280.507i	0.186245	−	0.724824i
$388$	−2.51391	−	386.019i	−0.00647916	−	0.994893i
$389$	−43.9057	−	76.0468i	−0.112868	−	0.195493i	0.804057	−	0.594552i	$-0.202670\pi$
$389$	−43.9057	−	76.0468i	−0.112868	−	0.195493i	−0.916926	+	0.399058i	$0.869337\pi$
$390$	−209.932	−	268.881i	−0.538286	−	0.689438i
$391$	14.3481	+	8.28388i	0.0366959	+	0.0211864i
$392$	221.136	−	61.5745i	0.564122	−	0.157078i
$393$	−349.041	−	44.1266i	−0.888145	−	0.112281i
$394$	233.952	+	61.8715i	0.593787	+	0.157034i
$395$			1181.07i			2.99004i
$396$	94.1551	−	97.3733i	0.237765	−	0.245892i
$397$	−48.4128			−0.121947			−0.0609733	−	0.998139i	$-0.519420\pi$
$397$	−48.4128			−0.121947			−0.0609733	+	0.998139i	$0.519420\pi$
$398$	−42.0512	+	159.006i	−0.105656	+	0.399513i
$399$	176.762	+	134.195i	0.443013	+	0.336329i
$400$	312.733	−	558.339i	0.781832	−	1.39585i
$401$	217.859	−	377.343i	0.543290	−	0.941005i	−0.455423	−	0.890275i	$-0.650512\pi$
$401$	217.859	−	377.343i	0.543290	−	0.941005i	0.998712	−	0.0507299i	$-0.0161548\pi$
$402$	−478.306	−	193.430i	−1.18982	−	0.481169i
$403$	92.6326	−	53.4815i	0.229858	−	0.132708i
$404$	−1.12845	−	173.277i	−0.00279319	−	0.428902i
$405$	572.138	+	314.809i	1.41269	+	0.777306i
$406$	121.272	+	120.485i	0.298699	+	0.296761i
$407$	1.92919	−	1.11382i	0.00474002	−	0.00273665i
$408$	11.5529	+	4.58474i	0.0283159	+	0.0112371i
$409$	−27.1145	+	46.9636i	−0.0662945	+	0.114825i	−0.897267	−	0.441487i	$-0.854451\pi$
$409$	−27.1145	+	46.9636i	−0.0662945	+	0.114825i	0.830973	+	0.556313i	$0.187784\pi$
$410$	−104.556	−	385.186i	−0.255014	−	0.939479i
$411$	−600.251	−	455.702i	−1.46047	−	1.10876i
$412$	292.951	+	499.859i	0.711045	+	1.21325i
$413$	159.182			0.385430
$414$	−575.783	+	7.79935i	−1.39078	+	0.0188390i
$415$			810.867i			1.95390i
$416$	218.900	+	54.8505i	0.526201	+	0.131852i
$417$	457.339	+	57.8179i	1.09674	+	0.138652i
$418$	−32.3613	−	119.220i	−0.0774193	−	0.285215i
$419$	−552.029	−	318.714i	−1.31749	−	0.760655i	−0.334168	−	0.942514i	$-0.608455\pi$
$419$	−552.029	−	318.714i	−1.31749	−	0.760655i	−0.983325	+	0.181859i	$0.941789\pi$
$420$	−51.8620	+	432.864i	−0.123481	+	1.03063i
$421$	−95.7757	−	165.888i	−0.227496	−	0.394034i	0.729570	−	0.683907i	$-0.239720\pi$
$421$	−95.7757	−	165.888i	−0.227496	−	0.394034i	−0.957065	+	0.289873i	$0.906387\pi$
$422$	−153.315	−	152.320i	−0.363307	−	0.360948i
$423$	−135.699	+	528.110i	−0.320801	+	1.24849i
$424$	3.79704	+	3.72357i	0.00895527	+	0.00878200i
$425$	−10.3571	−	17.9390i	−0.0243696	−	0.0422095i
$426$	47.0230	+	335.380i	0.110383	+	0.787277i
$427$	−263.617	−	152.199i	−0.617369	−	0.356438i
$428$	−108.729	+	191.190i	−0.254041	+	0.446705i
$429$	−30.8398	−	73.3837i	−0.0718876	−	0.171058i
$430$	132.662	−	501.629i	0.308516	−	1.16658i
$431$		−	481.190i		−	1.11645i	−0.829689	−	0.558225i	$-0.811482\pi$
$431$		−	481.190i		−	1.11645i	0.829689	−	0.558225i	$-0.188518\pi$
$432$	−426.526	+	68.5514i	−0.987329	+	0.158684i
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$	−132.155	−	34.9499i	−0.304504	−	0.0805297i
$435$	422.932	−	177.739i	0.972258	−	0.408595i
$436$	−222.265	−	126.402i	−0.509783	−	0.289913i
$437$	−262.588	+	454.816i	−0.600888	+	1.04077i
$438$	783.857	−	109.903i	1.78963	−	0.250921i
$439$	488.267	−	281.901i	1.11223	−	0.642144i	0.172821	−	0.984953i	$-0.444712\pi$
$439$	488.267	−	281.901i	1.11223	−	0.642144i	0.939405	+	0.342809i	$0.111378\pi$
$440$	169.909	−	173.261i	0.386156	−	0.393775i
$441$	69.4008	+	248.742i	0.157371	+	0.564040i
$442$	5.14816	−	5.18180i	0.0116474	−	0.0117235i
$443$	569.917	−	329.042i	1.28649	−	0.742757i	0.308467	−	0.951235i	$-0.400184\pi$
$443$	569.917	−	329.042i	1.28649	−	0.742757i	0.978027	+	0.208478i	$0.0668509\pi$
$444$	−7.05429	−	0.845184i	−0.0158880	−	0.00190357i
$445$	104.147	−	180.388i	0.234038	−	0.405366i
$446$	315.145	−	85.5436i	0.706603	−	0.191802i
$447$	34.5150	−	273.013i	0.0772147	−	0.610767i
$448$	−149.052	−	246.898i	−0.332706	−	0.551112i
$449$	227.569			0.506836			0.253418	−	0.967357i	$-0.418445\pi$
$449$	227.569			0.506836			0.253418	+	0.967357i	$0.418445\pi$
$450$	628.314	+	351.498i	1.39625	+	0.781106i
$451$		−	93.1339i		−	0.206505i
$452$	123.021	−	72.0984i	0.272170	−	0.159510i
$453$	−75.4523	+	99.3858i	−0.166561	+	0.219395i
$454$	−21.3230	+	5.78795i	−0.0469669	+	0.0127488i
$455$	221.878	+	128.101i	0.487643	+	0.281541i
$456$	−145.330	+	366.211i	−0.318707	+	0.803095i
$457$	−358.879	−	621.596i	−0.785292	−	1.36017i	−0.928824	−	0.370520i	$-0.879179\pi$
$457$	−358.879	−	621.596i	−0.785292	−	1.36017i	0.143532	−	0.989646i	$-0.454154\pi$
$458$	45.5935	−	45.8914i	0.0995492	−	0.100200i
$459$	−5.15107	+	12.9997i	−0.0112224	+	0.0283217i
$460$	−1031.63	+	6.71842i	−2.24268	+	0.0146053i
$461$	−200.873	−	347.922i	−0.435733	−	0.754712i	0.561622	−	0.827394i	$-0.310178\pi$
$461$	−200.873	−	347.922i	−0.435733	−	0.754712i	−0.997355	+	0.0726819i	$0.976844\pi$
$462$	−38.1392	+	94.3092i	−0.0825523	+	0.204132i
$463$	−396.754	−	229.066i	−0.856920	−	0.494743i	0.00605956	−	0.999982i	$-0.498071\pi$
$463$	−396.754	−	229.066i	−0.856920	−	0.494743i	−0.862980	+	0.505239i	$0.831405\pi$
$464$	−148.307	+	264.781i	−0.319627	+	0.570648i
$465$	−221.822	+	292.184i	−0.477036	+	0.628352i
$466$	−350.064	−	92.5787i	−0.751210	−	0.198667i
$467$		−	204.395i		−	0.437677i	−0.975761	−	0.218838i	$-0.929773\pi$
$467$		−	204.395i		−	0.437677i	0.975761	−	0.218838i	$-0.0702267\pi$
$468$	−61.5787	+	246.294i	−0.131578	+	0.526270i
$469$	387.493			0.826210
$470$	−249.762	+	944.415i	−0.531409	+	2.00939i
$471$	−84.9693	+	672.106i	−0.180402	+	1.42698i
$472$	75.8045	+	272.241i	0.160603	+	0.576781i
$473$	60.5385	−	104.856i	0.127988	−	0.221682i
$474$	692.820	−	540.926i	1.46165	−	1.14119i
$475$	568.643	−	328.306i	1.19714	−	0.691172i
$476$	−9.33481	+	0.0607922i	−0.0196109	+	0.000127715i
$477$	−4.18679	+	4.27384i	−0.00877734	+	0.00895984i
$478$	64.9475	+	64.5259i	0.135874	+	0.134992i
$479$	78.4548	−	45.2959i	0.163789	−	0.0945634i	−0.415865	−	0.909426i	$-0.636521\pi$
$479$	78.4548	−	45.2959i	0.163789	−	0.0945634i	0.579654	+	0.814863i	$0.303188\pi$
$480$	−764.999	+	117.438i	−1.59375	+	0.244663i
$481$	−2.08764	+	3.61589i	−0.00434020	+	0.00751745i
$482$	−177.313	−	653.226i	−0.367869	−	1.35524i
$483$	398.701	−	167.556i	0.825469	−	0.346906i
$484$	−368.718	+	216.093i	−0.761813	+	0.446473i
$485$	778.046			1.60422
$486$	−77.3699	−	479.802i	−0.159197	−	0.987247i
$487$		−	301.289i		−	0.618663i	−0.950954	−	0.309332i	$-0.899895\pi$
$487$		−	301.289i		−	0.618663i	0.950954	−	0.309332i	$-0.100105\pi$
$488$	134.760	−	523.327i	0.276148	−	1.07239i
$489$	−145.490	−	346.196i	−0.297526	−	0.707968i
$490$	121.200	+	446.503i	0.247346	+	0.911230i
$491$	389.556	+	224.911i	0.793394	+	0.458066i	0.841156	−	0.540792i	$-0.181876\pi$
$491$	389.556	+	224.911i	0.793394	+	0.458066i	−0.0477620	+	0.998859i	$0.515209\pi$
$492$	−178.066	+	237.748i	−0.361923	+	0.483227i
$493$	4.91164	+	8.50721i	0.00996276	+	0.0172560i
$494$	164.256	+	163.190i	0.332502	+	0.330344i
$495$	195.018	+	191.046i	0.393976	+	0.385951i
$496$	−3.16074	−	242.660i	−0.00637246	−	0.489234i
$497$	−127.175	−	220.273i	−0.255884	−	0.443205i
$498$	475.659	−	371.376i	0.955140	−	0.745735i
$499$	552.630	+	319.061i	1.10748	+	0.639401i	0.938174	−	0.346163i	$-0.112516\pi$
$499$	552.630	+	319.061i	1.10748	+	0.639401i	0.169301	+	0.985564i	$0.445849\pi$
$500$	420.409	+	239.086i	0.840817	+	0.478172i
$501$	−530.541	−	67.0724i	−1.05897	−	0.133877i
$502$	−144.500	+	546.390i	−0.287848	+	1.08843i
$503$			182.179i			0.362185i	0.983466	+	0.181093i	$0.0579634\pi$
$503$			182.179i			0.362185i	−0.983466	+	0.181093i	$0.942037\pi$
$504$	277.673	−	167.828i	0.550939	−	0.332993i
$505$	349.250			0.691585
$506$	−232.731	−	61.5485i	−0.459942	−	0.121637i
$507$	−284.982	−	216.354i	−0.562094	−	0.426734i
$508$	19.4026	−	34.1175i	0.0381941	−	0.0671604i
$509$	471.123	−	816.009i	0.925585	−	1.60316i	0.134968	−	0.990850i	$-0.456907\pi$
$509$	471.123	−	816.009i	0.925585	−	1.60316i	0.790617	−	0.612311i	$-0.209760\pi$
$510$	−9.39209	+	23.2244i	−0.0184159	+	0.0455381i
$511$	−514.827	+	297.235i	−1.00749	+	0.581674i
$512$	351.275	−	372.491i	0.686084	−	0.727522i
$513$	−412.073	−	163.282i	−0.803261	−	0.318289i
$514$	−109.638	+	110.354i	−0.213303	+	0.214697i
$515$	−1011.30	+	583.875i	−1.96369	+	1.13374i
$516$	−355.017	+	151.925i	−0.688018	+	0.294429i
$517$	−113.976	+	197.412i	−0.220456	+	0.381841i
$518$	5.14963	−	1.39783i	0.00994138	−	0.00269851i
$519$	361.235	+	274.245i	0.696021	+	0.528409i
$520$	−113.423	+	440.468i	−0.218122	+	0.847054i
$521$	−634.330			−1.21752			−0.608762	−	0.793353i	$-0.708334\pi$
$521$	−634.330			−1.21752			−0.608762	+	0.793353i	$0.708334\pi$
$522$	−297.965	−	166.690i	−0.570814	−	0.319330i
$523$		−	534.777i		−	1.02252i	−0.859426	−	0.511259i	$-0.829179\pi$
$523$		−	534.777i		−	1.02252i	0.859426	−	0.511259i	$-0.170821\pi$
$524$	237.187	+	404.710i	0.452646	+	0.772347i
$525$	−536.446	−	67.8188i	−1.02180	−	0.129179i
$526$	435.056	−	118.092i	0.827102	−	0.224510i
$527$	−6.80273	−	3.92756i	−0.0129084	−	0.00745267i
$528$	−179.454	−	20.3161i	−0.339875	−	0.0384775i
$529$	247.208	+	428.178i	0.467313	+	0.809409i
$530$	−7.55461	+	7.60397i	−0.0142540	+	0.0143471i
$531$	−306.226	+	85.4394i	−0.576697	+	0.160903i
$532$	−1.92703	−	295.901i	−0.00362224	−	0.556205i
$533$	87.2809	+	151.175i	0.163754	+	0.283630i
$534$	−153.516	+	21.5242i	−0.287483	+	0.0403075i
$535$	−383.912	−	221.652i	−0.717592	−	0.414302i
$536$	184.528	+	662.706i	0.344270	+	1.23639i
$537$	321.755	+	765.620i	0.599170	+	1.42574i
$538$	−823.312	−	217.735i	−1.53032	−	0.404712i
$539$			107.960i			0.200296i
$540$	−132.565	−	860.555i	−0.245492	−	1.59362i
$541$	−61.0097			−0.112772			−0.0563860	−	0.998409i	$-0.517958\pi$
$541$	−61.0097			−0.112772			−0.0563860	+	0.998409i	$0.517958\pi$
$542$	28.8227	−	108.986i	0.0531785	−	0.201082i
$543$	289.648	−	121.726i	0.533422	−	0.224172i
$544$	−4.54931	−	15.9358i	−0.00836271	−	0.0292938i
$545$	257.678	−	446.312i	0.472805	−	0.818921i
$546$	−26.4748	−	188.825i	−0.0484887	−	0.345833i
$547$	104.430	−	60.2925i	0.190914	−	0.110224i	−0.401497	−	0.915861i	$-0.631510\pi$
$547$	104.430	−	60.2925i	0.190914	−	0.110224i	0.592410	+	0.805637i	$0.298177\pi$
$548$	6.54385	+	1004.83i	0.0119413	+	1.83362i
$549$	588.822	+	151.299i	1.07254	+	0.275590i
$550$	213.517	+	212.131i	0.388212	+	0.385692i
$551$	−269.667	+	155.693i	−0.489415	+	0.282564i
$552$	476.427	+	602.084i	0.863092	+	1.09073i
$553$	−330.076	+	571.708i	−0.596882	+	1.03383i
$554$	219.673	+	809.281i	0.396521	+	1.46080i
$555$	1.79604	−	14.2067i	0.00323611	−	0.0255976i
$556$	−310.779	−	530.280i	−0.558955	−	0.953741i
$557$	−527.461			−0.946968			−0.473484	−	0.880802i	$-0.657004\pi$
$557$	−527.461			−0.946968			−0.473484	+	0.880802i	$0.657004\pi$
$558$	272.991	−	3.69783i	0.489230	−	0.00662694i
$559$			226.936i			0.405967i
$560$	499.574	−	297.171i	0.892097	−	0.530663i
$561$	−3.53473	+	4.65594i	−0.00630076	+	0.00829936i
$562$	77.5031	+	285.523i	0.137906	+	0.508049i
$563$	−595.478	−	343.800i	−1.05769	−	0.610656i	−0.132896	−	0.991130i	$-0.542428\pi$
$563$	−595.478	−	343.800i	−1.05769	−	0.610656i	−0.924792	+	0.380474i	$0.875761\pi$
$564$	668.390	−	286.029i	1.18509	−	0.507144i
$565$	143.698	+	248.893i	0.254333	+	0.440518i
$566$	−376.567	−	374.123i	−0.665313	−	0.660994i
$567$	188.969	+	312.284i	0.333279	+	0.550765i
$568$	316.158	−	322.396i	0.556616	−	0.567598i
$569$	293.677	+	508.664i	0.516128	+	0.893961i	0.999825	+	0.0187248i	$0.00596063\pi$
$569$	293.677	+	508.664i	0.516128	+	0.893961i	−0.483696	+	0.875236i	$0.660706\pi$
$570$	−736.184	−	297.717i	−1.29155	−	0.522311i
$571$	742.245	+	428.535i	1.29990	+	0.750500i	0.980387	−	0.197081i	$-0.0631461\pi$
$571$	742.245	+	428.535i	1.29990	+	0.750500i	0.319517	+	0.947581i	$0.396479\pi$
$572$	−52.4674	+	92.2585i	−0.0917262	+	0.161291i
$573$	404.209	−	532.424i	0.705425	−	0.929186i
$574$	57.0377	−	215.674i	0.0993688	−	0.375739i
$575$		−	1279.55i		−	2.22530i
$576$	419.258	+	394.966i	0.727879	+	0.685706i
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$	558.271	+	147.642i	0.965866	+	0.255435i
$579$	−42.6535	+	337.388i	−0.0736675	+	0.582709i
$580$	−531.714	−	302.385i	−0.916748	−	0.521354i
$581$	−226.615	+	392.509i	−0.390044	+	0.675575i
$582$	−356.344	−	456.406i	−0.612275	−	0.784203i
$583$	−2.16609	+	1.25059i	−0.00371542	+	0.00214510i
$584$	−753.511	−	738.931i	−1.29026	−	1.26529i
$585$	−495.593	−	127.343i	−0.847167	−	0.217681i
$586$	−351.960	+	354.259i	−0.600614	+	0.604538i
$587$	−700.071	+	404.186i	−1.19263	+	0.688563i	−0.958901	−	0.283740i	$-0.908425\pi$
$587$	−700.071	+	404.186i	−1.19263	+	0.688563i	−0.233725	+	0.972303i	$0.575091\pi$
$588$	206.412	−	275.594i	0.351041	−	0.468698i
$589$	124.498	−	215.638i	0.211373	−	0.366108i
$590$	−549.690	+	149.209i	−0.931679	+	0.252897i
$591$	334.642	−	140.635i	0.566231	−	0.237960i
$592$	4.84294	+	8.14146i	0.00818064	+	0.0137525i
$593$	−445.123			−0.750628			−0.375314	−	0.926898i	$-0.622465\pi$
$593$	−445.123			−0.750628			−0.375314	+	0.926898i	$0.622465\pi$
$594$	22.7506	−	201.897i	0.0383007	−	0.339895i
$595$		−	18.8149i		−	0.0316217i
$596$	−316.556	+	185.523i	−0.531134	+	0.311280i
$597$	95.5828	+	227.441i	0.160105	+	0.380973i
$598$	435.449	−	118.199i	0.728175	−	0.197657i
$599$	684.932	+	395.445i	1.14346	+	0.660176i	0.947285	−	0.320393i	$-0.103815\pi$
$599$	684.932	+	395.445i	1.14346	+	0.660176i	0.196174	+	0.980569i	$0.437148\pi$
$600$	−139.475	−	949.748i	−0.232458	−	1.58291i
$601$	193.532	+	335.208i	0.322017	+	0.557750i	0.980904	−	0.194492i	$-0.0623057\pi$
$601$	193.532	+	335.208i	0.322017	+	0.557750i	−0.658887	+	0.752242i	$0.728972\pi$
$602$	204.408	−	205.744i	0.339548	−	0.341767i
$603$	−745.436	+	207.982i	−1.23621	+	0.344913i
$604$	166.373	−	1.08349i	0.275451	−	0.00179385i
$605$	−430.691	−	745.979i	−0.711886	−	1.23302i
$606$	−159.956	−	204.872i	−0.263954	−	0.338073i
$607$	−902.512	−	521.066i	−1.48684	−	0.858428i	−0.486953	−	0.873428i	$-0.661892\pi$
$607$	−902.512	−	521.066i	−1.48684	−	0.858428i	−0.999887	+	0.0150003i	$0.995225\pi$
$608$	505.145	−	144.207i	0.830831	−	0.237183i
$609$	254.398	+	32.1617i	0.417731	+	0.0528106i
$610$	1052.99	+	278.475i	1.72621	+	0.456517i
$611$		−	427.251i		−	0.699266i
$612$	17.9252	−	5.12730i	0.0292895	−	0.00837794i
$613$	256.336			0.418166			0.209083	−	0.977898i	$-0.432952\pi$
$613$	256.336			0.418166			0.209083	+	0.977898i	$0.432952\pi$
$614$	132.933	−	502.655i	0.216504	−	0.818657i
$615$	−476.839	−	362.009i	−0.775347	−	0.588633i
$616$	130.668	−	36.3841i	0.212123	−	0.0590650i
$617$	−253.519	+	439.108i	−0.410890	+	0.711683i	−0.994987	−	0.100001i	$-0.968115\pi$
$617$	−253.519	+	439.108i	−0.410890	+	0.711683i	0.584097	+	0.811684i	$0.301449\pi$
$618$	805.679	+	325.821i	1.30369	+	0.527219i
$619$	662.787	−	382.660i	1.07074	−	0.618191i	0.142355	−	0.989816i	$-0.454532\pi$
$619$	662.787	−	382.660i	1.07074	−	0.618191i	0.928383	+	0.371624i	$0.121199\pi$
$620$	489.118	−	3.18534i	0.788900	−	0.00513764i
$621$	−677.066	+	536.333i	−1.09028	+	0.863660i
$622$	27.1891	+	27.0126i	0.0437123	+	0.0434286i
$623$	100.827	−	58.2125i	0.161841	−	0.0934390i
$624$	310.329	−	135.199i	0.497322	−	0.216665i
$625$	12.5746	−	21.7799i	0.0201194	−	0.0348479i
$626$	22.9854	+	84.6789i	0.0367179	+	0.135270i
$627$	−147.587	−	112.046i	−0.235386	−	0.178702i
$628$	779.301	−	456.722i	1.24092	−	0.727264i
$629$	0.306623			0.000487477
$630$	334.610	+	561.847i	0.531127	+	0.891821i
$631$		−	719.756i		−	1.14066i	−0.821416	−	0.570330i	$-0.806815\pi$
$631$		−	719.756i		−	1.14066i	0.821416	−	0.570330i	$-0.193185\pi$
$632$	−1134.94	−	292.255i	−1.79580	−	0.462429i
$633$	−321.617	−	40.6597i	−0.508084	−	0.0642333i
$634$	−72.2692	−	266.242i	−0.113989	−	0.419940i
$635$	68.5084	+	39.5534i	0.107887	+	0.0622888i
$636$	7.92054	+	0.948971i	0.0124537	+	0.00149209i
$637$	−101.175	−	175.240i	−0.158830	−	0.275102i
$638$	−101.256	−	100.599i	−0.158708	−	0.157678i
$639$	362.880	+	355.489i	0.567888	+	0.556321i
$640$	746.138	+	712.877i	1.16584	+	1.11387i
$641$	351.516	+	608.844i	0.548388	+	0.949835i	0.998385	+	0.0568054i	$0.0180915\pi$
$641$	351.516	+	608.844i	0.548388	+	0.949835i	−0.449998	+	0.893030i	$0.648575\pi$
$642$	45.8090	+	326.721i	0.0713535	+	0.508911i
$643$	507.224	+	292.846i	0.788841	+	0.455437i	0.839554	−	0.543276i	$-0.182816\pi$
$643$	507.224	+	292.846i	0.788841	+	0.455437i	−0.0507136	+	0.998713i	$0.516150\pi$
$644$	−501.250	−	285.061i	−0.778339	−	0.442641i
$645$	−301.542	−	717.525i	−0.467507	−	1.11244i
$646$	4.34741	−	16.4387i	0.00672973	−	0.0254469i
$647$			791.553i			1.22342i	0.791082	+	0.611710i	$0.209518\pi$
$647$			791.553i			1.22342i	−0.791082	+	0.611710i	$0.790482\pi$
$648$	−444.092	+	471.897i	−0.685327	+	0.728236i
$649$	−132.909			−0.204791
$650$	−545.380	−	144.232i	−0.839046	−	0.221896i
$651$	−189.033	+	79.4416i	−0.290373	+	0.122030i
$652$	−247.521	+	435.240i	−0.379633	+	0.667547i
$653$	−196.385	+	340.148i	−0.300742	+	0.520901i	−0.976304	−	0.216402i	$-0.930568\pi$
$653$	−196.385	+	340.148i	−0.300742	+	0.520901i	0.675562	+	0.737303i	$0.263901\pi$
$654$	−379.826	+	53.2547i	−0.580773	+	0.0814292i
$655$	−818.797	+	472.733i	−1.25007	+	0.721730i
$656$	396.017	−	5.15827i	0.603685	−	0.00786322i
$657$	830.857	−	848.132i	1.26462	−	1.29092i
$658$	−384.838	+	387.353i	−0.584861	+	0.588682i
$659$	372.557	−	215.096i	0.565337	−	0.326398i	−0.189948	−	0.981794i	$-0.560832\pi$
$659$	372.557	−	215.096i	0.565337	−	0.326398i	0.755285	+	0.655397i	$0.227499\pi$
$660$	43.3021	−	361.419i	0.0656093	−	0.547604i
$661$	453.865	−	786.117i	0.686633	−	1.18928i	−0.286287	−	0.958144i	$-0.592421\pi$
$661$	453.865	−	786.117i	0.686633	−	1.18928i	0.972920	−	0.231140i	$-0.0742456\pi$
$662$	115.336	−	31.3070i	0.174223	−	0.0472915i
$663$	1.37423	−	10.8701i	0.00207274	−	0.0163953i
$664$	−779.203	−	200.650i	−1.17350	−	0.302183i
$665$	596.408			0.896854
$666$	−9.15631	+	5.45307i	−0.0137482	+	0.00818779i
$667$			606.799i			0.909744i
$668$	360.523	+	615.158i	0.539706	+	0.920895i
$669$	296.182	−	390.131i	0.442724	−	0.583156i
$670$	−1338.09	+	363.215i	−1.99715	+	0.542112i
$671$	220.106	+	127.078i	0.328027	+	0.189387i
$672$	−403.127	−	156.949i	−0.599891	−	0.233555i
$673$	−34.8528	−	60.3668i	−0.0517872	−	0.0896980i	0.838970	−	0.544178i	$-0.183158\pi$
$673$	−34.8528	−	60.3668i	−0.0517872	−	0.0896980i	−0.890757	+	0.454480i	$0.849825\pi$
$674$	−632.504	+	636.636i	−0.938433	+	0.944564i
$675$	1068.38	−	157.465i	1.58279	−	0.233282i
$676$	3.10682	+	477.062i	0.00459589	+	0.705712i
$677$	−144.502	−	250.285i	−0.213444	−	0.369697i	0.739346	−	0.673326i	$-0.235135\pi$
$677$	−144.502	−	250.285i	−0.213444	−	0.369697i	−0.952790	+	0.303629i	$0.901802\pi$
$678$	80.1883	−	198.287i	0.118272	−	0.292458i
$679$	376.622	+	217.443i	0.554671	+	0.320239i
$680$	32.1781	−	8.95988i	0.0473207	−	0.0131763i
$681$	−20.0399	+	26.3966i	−0.0294272	+	0.0387616i
$682$	110.342	+	29.1814i	0.161792	+	0.0427880i
$683$			522.729i			0.765343i	0.923884	+	0.382672i	$0.124996\pi$
$683$			522.729i			0.765343i	−0.923884	+	0.382672i	$0.875004\pi$
$684$	162.529	+	568.204i	0.237615	+	0.830707i
$685$	−2025.29			−2.95663
$686$	−179.026	+	676.943i	−0.260971	+	0.986798i
$687$	12.1705	−	96.2687i	0.0177155	−	0.140129i
$688$	449.213	+	251.610i	0.652926	+	0.365712i
$689$	2.34400	−	4.05992i	0.00340203	−	0.00589248i
$690$	−1219.74	+	952.326i	−1.76774	+	1.38018i
$691$	−485.917	+	280.544i	−0.703208	+	0.405997i	−0.808541	−	0.588440i	$-0.799742\pi$
$691$	−485.917	+	280.544i	−0.703208	+	0.405997i	0.105333	+	0.994437i	$0.466409\pi$
$692$	−3.93813	−	604.711i	−0.00569093	−	0.873859i
$693$	41.0085	+	146.980i	0.0591753	+	0.212092i
$694$	−819.874	−	814.552i	−1.18137	−	1.17371i
$695$	1072.85	−	619.409i	1.54367	−	0.891236i
$696$	66.1431	+	450.398i	0.0950333	+	0.647124i
$697$	6.40971	−	11.1019i	0.00919614	−	0.0159282i
$698$	−69.2956	−	255.287i	−0.0992773	−	0.365740i
$699$	−500.728	+	210.433i	−0.716349	+	0.301048i
$700$	364.535	+	622.004i	0.520765	+	0.888577i
$701$	1203.11			1.71627			0.858137	−	0.513421i	$-0.171622\pi$
$701$	1203.11			1.71627			0.858137	+	0.513421i	$0.171622\pi$
$702$	152.280	+	349.041i	0.216924	+	0.497209i
$703$			9.71954i			0.0138258i
$704$	124.451	+	206.147i	0.176777	+	0.292823i
$705$	567.713	+	1350.88i	0.805266	+	1.91614i
$706$	−283.509	−	1044.45i	−0.401571	−	1.47940i
$707$	169.058	+	97.6059i	0.239121	+	0.138056i
$708$	339.285	+	254.114i	0.479215	+	0.358918i
$709$	89.2724	+	154.624i	0.125913	+	0.218088i	0.922090	−	0.386977i	$-0.126481\pi$
$709$	89.2724	+	154.624i	0.125913	+	0.218088i	−0.796176	+	0.605065i	$0.793147\pi$
$710$	645.632	+	641.441i	0.909341	+	0.903439i
$711$	328.123	−	1276.98i	0.461495	−	1.79604i
$712$	147.572	+	144.717i	0.207265	+	0.203254i
$713$	−242.611	−	420.215i	−0.340269	−	0.589362i
$714$	−11.0369	+	8.61721i	−0.0154579	+	0.0120689i
$715$	−185.257	−	106.958i	−0.259100	−	0.149591i
$716$	547.398	−	962.543i	0.764522	−	1.34433i
$717$	136.244	+	17.2243i	0.190019	+	0.0240227i
$718$	−149.698	+	566.048i	−0.208493	+	0.788367i
$719$		−	53.0278i		−	0.0737521i	−0.999320	−	0.0368760i	$-0.988259\pi$
$719$		−	53.0278i		−	0.0737521i	0.999320	−	0.0368760i	$-0.0117407\pi$
$720$	−801.550	+	839.822i	−1.11326	+	1.16642i
$721$	−652.709			−0.905282
$722$	−176.919	−	46.7884i	−0.245040	−	0.0648038i
$723$	−808.656	−	613.920i	−1.11847	−	0.849129i
$724$	−364.148	−	207.091i	−0.502966	−	0.286037i
$725$	379.332	−	657.022i	0.523216	−	0.906238i
$726$	−240.340	+	594.303i	−0.331046	+	0.818600i
$727$	−436.956	+	252.277i	−0.601041	+	0.347011i	−0.769451	−	0.638706i	$-0.779470\pi$
$727$	−436.956	+	252.277i	−0.601041	+	0.347011i	0.168410	+	0.985717i	$0.446137\pi$
$728$	−178.003	+	181.515i	−0.244509	+	0.249333i
$729$	−531.144	−	499.327i	−0.728592	−	0.684948i
$730$	1499.19	−	1508.99i	2.05369	−	2.06710i
$731$	14.4329	−	8.33283i	0.0197440	−	0.0113992i
$732$	−318.911	−	745.230i	−0.435671	−	1.01807i
$733$	410.964	−	711.811i	0.560660	−	0.971092i	−0.436779	−	0.899569i	$-0.643881\pi$
$733$	410.964	−	711.811i	0.560660	−	0.971092i	0.997439	−	0.0715233i	$-0.0227860\pi$
$734$	844.408	−	229.208i	1.15042	−	0.312272i
$735$	552.745	+	419.636i	0.752034	+	0.570934i
$736$	248.822	−	993.009i	0.338073	−	1.34920i
$737$	−323.536			−0.438991
$738$	6.03480	+	445.516i	0.00817723	+	0.603680i
$739$			190.298i			0.257507i	0.991677	+	0.128754i	$0.0410977\pi$
$739$			190.298i			0.257507i	−0.991677	+	0.128754i	$0.958902\pi$
$740$	−16.4725	+	9.65398i	−0.0222602	+	0.0130459i
$741$	344.568	+	43.5612i	0.465005	+	0.0587870i
$742$	−5.78200	+	1.56948i	−0.00779245	+	0.00211520i
$743$	−664.128	−	383.435i	−0.893847	−	0.516063i	−0.0186481	−	0.999826i	$-0.505936\pi$
$743$	−664.128	−	383.435i	−0.893847	−	0.516063i	−0.875199	+	0.483763i	$0.839270\pi$
$744$	−225.884	−	285.460i	−0.303607	−	0.383683i
$745$	−369.762	−	640.447i	−0.496325	−	0.859660i
$746$	995.118	−	1001.62i	1.33394	−	1.34265i
$747$	225.275	−	876.720i	0.301573	−	1.17366i
$748$	7.79409	−	0.0507583i	0.0104199	−	6.78587e-5i
$749$	−123.891	−	214.586i	−0.165409	−	0.286496i
$750$	718.430	−	100.730i	0.957906	−	0.134306i
$751$	519.601	+	299.992i	0.691879	+	0.399456i	0.804315	−	0.594202i	$-0.202532\pi$
$751$	519.601	+	299.992i	0.691879	+	0.399456i	−0.112437	+	0.993659i	$0.535866\pi$
$752$	−845.732	−	473.705i	−1.12464	−	0.629927i
$753$	328.449	+	781.550i	0.436188	+	1.03792i
$754$	258.635	+	68.3992i	0.343017	+	0.0907152i
$755$			335.335i			0.444152i
$756$	176.332	−	453.609i	0.233243	−	0.600013i
$757$	−343.082			−0.453213			−0.226606	−	0.973986i	$-0.572763\pi$
$757$	−343.082			−0.453213			−0.226606	+	0.973986i	$0.572763\pi$
$758$	276.858	−	1046.87i	0.365249	−	1.38110i
$759$	−332.895	+	139.900i	−0.438597	+	0.184322i
$760$	284.017	+	1020.00i	0.373706	+	1.34211i
$761$	−149.365	+	258.708i	−0.196275	+	0.339958i	−0.947318	−	0.320295i	$-0.896218\pi$
$761$	−149.365	+	258.708i	−0.196275	+	0.339958i	0.751043	+	0.660253i	$0.229551\pi$
$762$	−8.17454	−	58.3029i	−0.0107277	−	0.0765129i
$763$	249.464	−	144.028i	0.326952	−	0.188766i
$764$	−891.282	+	5.80440i	−1.16660	+	0.00759738i
$765$	10.0987	+	36.1951i	0.0132009	+	0.0473138i
$766$	511.053	+	507.736i	0.667171	+	0.662841i
$767$	215.738	−	124.557i	0.281275	−	0.162394i
$768$	76.4475	−	764.186i	0.0995410	−	0.995033i
$769$	−466.241	+	807.553i	−0.606295	+	1.05013i	0.385550	+	0.922687i	$0.374012\pi$
$769$	−466.241	+	807.553i	−0.606295	+	1.05013i	−0.991845	+	0.127447i	$0.959322\pi$
$770$	71.6162	+	263.836i	0.0930081	+	0.342644i
$771$	−29.2662	+	231.495i	−0.0379588	+	0.300253i
$772$	391.199	−	229.268i	0.506734	−	0.296980i
$773$	−173.239			−0.224113			−0.112056	−	0.993702i	$-0.535744\pi$
$773$	−173.239			−0.224113			−0.112056	+	0.993702i	$0.535744\pi$
$774$	−282.798	+	505.512i	−0.365372	+	0.653116i
$775$			606.660i			0.782787i
$776$	−192.528	+	747.663i	−0.248103	+	0.963483i
$777$	4.83977	−	6.37495i	0.00622880	−	0.00820457i
$778$	46.0066	+	169.490i	0.0591345	+	0.217853i
$779$	351.917	+	203.179i	0.451755	+	0.260821i
$780$	268.418	+	627.236i	0.344125	+	0.804149i
$781$	106.184	+	183.916i	0.135959	+	0.235488i
$782$	−23.5065	−	23.3539i	−0.0300595	−	0.0298644i
$783$	−506.659	+	74.6746i	−0.647075	+	0.0953699i
$784$	−459.058	+	5.97940i	−0.585533	+	0.00762679i
$785$	910.285	+	1576.66i	1.15960	+	2.00848i
$786$	652.316	+	263.800i	0.829919	+	0.335624i
$787$	−43.1896	−	24.9355i	−0.0548788	−	0.0316843i	0.472310	−	0.881433i	$-0.343420\pi$
$787$	−43.1896	−	24.9355i	−0.0548788	−	0.0316843i	−0.527188	+	0.849748i	$0.676754\pi$
$788$	−420.715	−	239.260i	−0.533902	−	0.303630i
$789$	408.878	−	538.574i	0.518223	−	0.682603i
$790$	603.932	−	2283.62i	0.764471	−	2.89066i
$791$			160.639i			0.203083i
$792$	−231.843	+	140.128i	−0.292731	+	0.176929i
$793$	−476.369			−0.600717
$794$	93.6075	+	24.7557i	0.117894	+	0.0311784i
$795$	−2.01659	+	15.9512i	−0.00253660	+	0.0200644i
$796$	162.614	−	285.940i	0.204289	−	0.359221i
$797$	−513.753	+	889.846i	−0.644608	+	1.11649i	0.339784	+	0.940504i	$0.389646\pi$
$797$	−513.753	+	889.846i	−0.644608	+	1.11649i	−0.984392	+	0.175991i	$0.943687\pi$
$798$	−273.154	−	349.857i	−0.342298	−	0.438417i
$799$	−27.1727	+	15.6882i	−0.0340084	+	0.0196348i
$800$	−890.181	+	919.649i	−1.11273	+	1.14956i
$801$	−162.720	+	166.104i	−0.203147	+	0.207370i
$802$	−614.189	+	618.202i	−0.765822	+	0.770825i
$803$	429.854	−	248.176i	0.535310	−	0.309061i
$804$	825.909	+	618.581i	1.02725	+	0.769380i
$805$	581.114	−	1006.52i	0.721880	−	1.25033i
$806$	−206.455	+	56.0406i	−0.256148	+	0.0695293i
$807$	−1177.66	+	494.914i	−1.45930	+	0.613277i
$808$	−86.4222	+	335.612i	−0.106958	+	0.415361i
$809$	−637.363			−0.787841			−0.393920	−	0.919145i	$-0.628881\pi$
$809$	−637.363			−0.787841			−0.393920	+	0.919145i	$0.628881\pi$
$810$	−945.269	−	901.252i	−1.16700	−	1.11266i
$811$		−	1486.54i		−	1.83298i	−0.400061	−	0.916489i	$-0.631011\pi$
$811$		−	1486.54i		−	1.83298i	0.400061	−	0.916489i	$-0.368989\pi$
$812$	−172.873	−	294.972i	−0.212898	−	0.363266i
$813$	−65.5144	−	155.893i	−0.0805836	−	0.191750i
$814$	−4.29968	+	1.16711i	−0.00528216	+	0.00143380i
$815$	−873.969	−	504.586i	−1.07235	−	0.619124i
$816$	−19.9934	−	14.7722i	−0.0245018	−	0.0181032i
$817$	264.140	+	457.503i	0.323304	+	0.559980i
$818$	76.4412	−	76.9406i	0.0934488	−	0.0940594i
$819$	−204.308	−	200.147i	−0.249460	−	0.244379i
$820$	5.19842	+	798.232i	0.00633954	+	0.973454i
$821$	517.865	+	896.969i	0.630773	+	1.09253i	0.987394	+	0.158282i	$0.0505956\pi$
$821$	517.865	+	896.969i	0.630773	+	1.09253i	−0.356620	+	0.934249i	$0.616071\pi$
$822$	927.581	+	1188.05i	1.12844	+	1.44531i
$823$	−278.230	−	160.636i	−0.338068	−	0.195184i	0.321349	−	0.946961i	$-0.395864\pi$
$823$	−278.230	−	160.636i	−0.338068	−	0.195184i	−0.659417	+	0.751777i	$0.729197\pi$
$824$	−310.827	−	1116.29i	−0.377218	−	1.35472i
$825$	447.905	+	56.6252i	0.542915	+	0.0686366i
$826$	−307.784	−	81.3972i	−0.372619	−	0.0985438i
$827$			119.865i			0.144939i	0.997371	+	0.0724695i	$0.0230880\pi$
$827$			119.865i			0.144939i	−0.997371	+	0.0724695i	$0.976912\pi$
$828$	1117.28	+	279.344i	1.34937	+	0.337371i
$829$	810.947			0.978223			0.489112	−	0.872221i	$-0.337321\pi$
$829$	810.947			0.978223			0.489112	+	0.872221i	$0.337321\pi$
$830$	414.633	−	1567.83i	0.499558	−	1.88896i
$831$	1001.84	+	760.585i	1.20559	+	0.915265i
$832$	−395.201	−	217.988i	−0.475001	−	0.262005i
$833$	−7.43005	+	12.8692i	−0.00891963	+	0.0154492i
$834$	−854.712	−	345.650i	−1.02483	−	0.414449i
$835$	−1244.57	+	718.553i	−1.49050	+	0.860543i
$836$	1.60897	+	247.062i	0.00192461	+	0.295529i
$837$	321.011	−	254.286i	0.383525	−	0.303807i
$838$	904.391	+	898.520i	1.07923	+	1.07222i
$839$	−51.3491	+	29.6464i	−0.0612027	+	0.0353354i	−0.530289	−	0.847817i	$-0.677917\pi$
$839$	−51.3491	+	29.6464i	−0.0612027	+	0.0353354i	0.469086	+	0.883152i	$0.344583\pi$
$840$	321.619	−	810.434i	0.382880	−	0.964802i
$841$	240.610	−	416.748i	0.286100	−	0.495539i
$842$	100.359	+	369.724i	0.119191	+	0.439102i
$843$	353.462	+	268.343i	0.419290	+	0.318319i
$844$	218.551	+	372.912i	0.258947	+	0.441839i
$845$	−961.549			−1.13793
$846$	532.423	−	951.725i	0.629342	−	1.12497i
$847$		−	481.466i		−	0.568437i
$848$	−5.43764	−	9.14121i	−0.00641231	−	0.0107797i
$849$	−789.943	−	99.8666i	−0.930439	−	0.117628i
$850$	10.8527	+	39.9816i	0.0127679	+	0.0470372i
$851$	16.4030	+	9.47029i	0.0192750	+	0.0111284i
$852$	80.5745	−	672.511i	0.0945710	−	0.789332i
$853$	547.729	+	948.694i	0.642121	+	1.11219i	0.984959	+	0.172791i	$0.0552785\pi$
$853$	547.729	+	948.694i	0.642121	+	1.11219i	−0.342838	+	0.939395i	$0.611388\pi$
$854$	431.884	+	429.080i	0.505718	+	0.502436i
$855$	−1147.34	+	320.115i	−1.34191	+	0.374404i
$856$	307.995	−	314.072i	0.359807	−	0.366907i
$857$	−692.162	−	1198.86i	−0.807658	−	1.39890i	−0.914482	−	0.404626i	$-0.867402\pi$
$857$	−692.162	−	1198.86i	−0.807658	−	1.39890i	0.106825	−	0.994278i	$-0.465932\pi$
$858$	22.1051	+	157.659i	0.0257635	+	0.183752i
$859$	−414.983	−	239.591i	−0.483101	−	0.278918i	0.238607	−	0.971116i	$-0.423309\pi$
$859$	−414.983	−	239.591i	−0.483101	−	0.278918i	−0.721708	+	0.692198i	$0.756643\pi$
$860$	−513.011	+	902.077i	−0.596524	+	1.04893i
$861$	−129.647	−	308.498i	−0.150578	−	0.358302i
$862$	−246.054	+	930.394i	−0.285446	+	1.07934i
$863$			4.93230i			0.00571530i	0.999996	+	0.00285765i	$0.000909619\pi$
$863$			4.93230i			0.00571530i	−0.999996	+	0.00285765i	$0.999090\pi$
$864$	859.754	+	85.5562i	0.995085	+	0.0990234i
$865$	1218.83			1.40906
$866$	696.740	+	184.261i	0.804550	+	0.212773i
$867$	798.544	−	335.591i	0.921043	−	0.387072i
$868$	237.653	+	135.153i	0.273794	+	0.155706i
$869$	275.596	−	477.347i	0.317142	−	0.549306i
$870$	−908.637	+	127.398i	−1.04441	+	0.146435i
$871$	525.164	−	303.204i	0.602944	−	0.348110i
$872$	365.121	+	358.056i	0.418717	+	0.410615i
$873$	−841.233	−	216.156i	−0.963612	−	0.247602i
$874$	740.289	−	745.126i	0.847013	−	0.852547i
$875$	−471.854	+	272.425i	−0.539262	+	0.311343i
$876$	−1571.81	−	188.321i	−1.79430	−	0.214978i
$877$	−839.494	+	1454.05i	−0.957234	+	1.65798i	−0.228062	+	0.973647i	$0.573239\pi$
$877$	−839.494	+	1454.05i	−0.957234	+	1.65798i	−0.729172	+	0.684331i	$0.760095\pi$
$878$	−1088.23	+	295.391i	−1.23944	+	0.336436i
$879$	−93.9506	+	743.147i	−0.106883	+	0.845446i
$880$	−417.119	+	248.123i	−0.473999	+	0.281958i
$881$	830.879			0.943109			0.471555	−	0.881837i	$-0.343693\pi$
$881$	830.879			0.943109			0.471555	+	0.881837i	$0.343693\pi$
$882$	−6.99546	−	516.436i	−0.00793136	−	0.585529i
$883$			1228.46i			1.39123i	0.718414	+	0.695615i	$0.244868\pi$
$883$			1228.46i			1.39123i	−0.718414	+	0.695615i	$0.755132\pi$
$884$	−12.6038	+	7.38666i	−0.0142577	+	0.00835595i
$885$	−516.615	+	680.486i	−0.583746	+	0.768910i
$886$	−1270.20	+	344.787i	−1.43364	+	0.389150i
$887$	660.079	+	381.097i	0.744170	+	0.429647i	0.823584	−	0.567195i	$-0.191971\pi$
$887$	660.079	+	381.097i	0.744170	+	0.429647i	−0.0794134	+	0.996842i	$0.525305\pi$
$888$	13.2075	+	5.24136i	0.0148733	+	0.00590243i
$889$	22.1082	+	38.2925i	0.0248686	+	0.0430737i
$890$	−293.612	+	295.530i	−0.329901	+	0.332056i
$891$	−157.780	−	260.741i	−0.177082	−	0.292639i
$892$	−653.083	+	4.25315i	−0.732156	+	0.00476810i
$893$	−497.295	−	861.340i	−0.556881	−	0.964547i
$894$	−206.339	+	510.229i	−0.230805	+	0.570726i
$895$	1932.80	+	1115.90i	2.15955	+	1.24682i
$896$	161.947	+	553.601i	0.180744	+	0.617858i
$897$	409.247	−	539.061i	0.456240	−	0.600960i
$898$	−440.011	−	116.366i	−0.489990	−	0.129584i
$899$		−	287.696i		−	0.320018i
$900$	−1035.13	−	1000.92i	−1.15014	−	1.11213i
$901$	−0.344275			−0.000382104
$902$	−47.6235	+	180.077i	−0.0527977	+	0.199642i
$903$	54.5638	−	431.598i	0.0604250	−	0.477961i
$904$	−274.731	+	76.4981i	−0.303907	+	0.0846218i
$905$	422.166	−	731.214i	0.466482	−	0.807971i
$906$	196.709	−	153.583i	0.217119	−	0.169518i
$907$	324.076	−	187.106i	0.357306	−	0.206291i	−0.310592	−	0.950543i	$-0.600527\pi$
$907$	324.076	−	187.106i	0.357306	−	0.206291i	0.667898	+	0.744253i	$0.267194\pi$
$908$	44.1882	−	0.287772i	0.0486654	−	0.000316929i
$909$	−377.614	−	97.0286i	−0.415417	−	0.106742i
$910$	−363.503	−	361.143i	−0.399453	−	0.396861i
$911$	−1265.50	+	730.639i	−1.38914	+	0.802018i	−0.993218	−	0.116268i	$-0.962907\pi$
$911$	−1265.50	+	730.639i	−1.38914	+	0.802018i	−0.395918	+	0.918286i	$0.629574\pi$
$912$	468.260	−	633.766i	0.513443	−	0.694918i
$913$	189.212	−	327.725i	0.207242	−	0.358954i
$914$	376.051	+	1385.38i	0.411435	+	1.51574i
$915$	1506.18	−	632.978i	1.64610	−	0.691779i
$916$	−111.623	+	65.4183i	−0.121859	+	0.0714173i
$917$	−528.464			−0.576296
$918$	16.6071	−	22.5013i	0.0180905	−	0.0245112i
$919$		−	1112.72i		−	1.21080i	−0.795923	−	0.605398i	$-0.793014\pi$
$919$		−	1112.72i		−	1.21080i	0.795923	−	0.605398i	$-0.206986\pi$
$920$	1998.12	+	514.529i	2.17187	+	0.559271i
$921$	−302.159	−	718.993i	−0.328077	−	0.780665i
$922$	210.485	+	775.432i	0.228292	+	0.841033i
$923$	−344.717	−	199.022i	−0.373474	−	0.215625i
$924$	121.968	−	162.847i	0.132000	−	0.176241i
$925$	−11.8404	−	20.5082i	−0.0128005	−	0.0221710i
$926$	650.003	+	645.784i	0.701947	+	0.697390i
$927$	1255.64	−	350.334i	1.35452	−	0.377922i
$928$	422.150	−	436.125i	0.454903	−	0.469962i
$929$	−508.204	−	880.234i	−0.547044	−	0.947507i	−0.998475	−	0.0552017i	$-0.982420\pi$
$929$	−508.204	−	880.234i	−0.547044	−	0.947507i	0.451432	−	0.892306i	$-0.350914\pi$
$930$	578.305	−	451.517i	0.621833	−	0.485503i
$931$	−407.938	−	235.523i	−0.438171	−	0.252978i
$932$	629.518	+	358.007i	0.675449	+	0.384127i
$933$	57.0358	+	7.21061i	0.0611317	+	0.00772842i
$934$	−104.516	+	395.203i	−0.111902	+	0.423130i
$935$			15.7095i			0.0168016i
$936$	245.005	−	444.729i	0.261758	−	0.475137i
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$	−749.227	−	198.142i	−0.798750	−	0.211239i
$939$	104.828	+	79.5837i	0.111638	+	0.0847537i
$940$	965.844	−	1698.34i	1.02749	−	1.80674i
$941$	−150.929	+	261.417i	−0.160392	+	0.277808i	−0.935009	−	0.354623i	$-0.884609\pi$
$941$	−150.929	+	261.417i	−0.160392	+	0.277808i	0.774617	+	0.632430i	$0.217943\pi$
$942$	507.968	−	1256.09i	0.539245	−	1.33343i
$943$	685.784	−	395.938i	0.727237	−	0.419870i
$944$	−7.36126	−	565.147i	−0.00779794	−	0.598673i
$945$	911.926	+	361.347i	0.965001	+	0.382378i
$946$	−170.670	+	171.785i	−0.180413	+	0.181591i
$947$	730.155	−	421.555i	0.771019	−	0.445148i	−0.0622189	−	0.998063i	$-0.519818\pi$
$947$	730.155	−	421.555i	0.771019	−	0.445148i	0.833238	+	0.552914i	$0.186484\pi$
$948$	−1616.19	+	691.626i	−1.70484	+	0.729563i
$949$	−465.159	+	805.679i	−0.490157	+	0.848977i
$950$	−1267.37	+	344.016i	−1.33407	+	0.362123i
$951$	−329.592	−	250.222i	−0.346574	−	0.263114i
$952$	18.0802	+	4.65576i	0.0189918	+	0.00489051i
$953$	306.171			0.321270			0.160635	−	0.987014i	$-0.448646\pi$
$953$	306.171			0.321270			0.160635	+	0.987014i	$0.448646\pi$
$954$	10.2807	−	6.12270i	0.0107764	−	0.00641792i
$955$		−	1796.44i		−	1.88109i
$956$	−92.5828	−	157.973i	−0.0968439	−	0.165244i
$957$	−212.409	−	26.8533i	−0.221953	−	0.0280599i
$958$	−174.856	+	47.4634i	−0.182522	+	0.0495442i
$959$	−980.365	−	566.014i	−1.02228	−	0.590213i
$960$	1539.20	+	164.109i	1.60333	+	0.170947i
$961$	−365.473	−	633.018i	−0.380305	−	0.658707i
$962$	5.88547	−	5.92393i	0.00611796	−	0.00615793i
$963$	353.511	+	346.311i	0.367094	+	0.359617i
$964$	8.81584	+	1353.70i	0.00914507	+	1.40425i
$965$	456.951	+	791.462i	0.473524	+	0.820168i
$966$	−856.579	+	120.099i	−0.886727	+	0.124326i
$967$	−103.822	−	59.9417i	−0.107365	−	0.0619873i	0.445356	−	0.895354i	$-0.353077\pi$
$967$	−103.822	−	59.9417i	−0.107365	−	0.0619873i	−0.552721	+	0.833366i	$0.686410\pi$
$968$	823.423	−	229.280i	0.850644	−	0.236859i
$969$	−9.88171	−	23.5137i	−0.0101978	−	0.0242659i
$970$	−1504.37	−	397.850i	−1.55090	−	0.410154i
$971$		−	62.7602i		−	0.0646346i	−0.999478	−	0.0323173i	$-0.989711\pi$
$971$		−	62.7602i		−	0.0646346i	0.999478	−	0.0323173i	$-0.0102887\pi$
$972$	−95.7476	+	967.273i	−0.0985057	+	0.995136i
$973$	692.431			0.711646
$974$	−154.063	+	582.551i	−0.158175	+	0.598101i
$975$	−780.105	+	327.842i	−0.800108	+	0.336248i
$976$	−528.163	+	942.959i	−0.541151	+	0.966146i
$977$	618.115	−	1070.61i	0.632666	−	1.09581i	−0.354338	−	0.935117i	$-0.615294\pi$
$977$	618.115	−	1070.61i	0.632666	−	1.09581i	0.987004	−	0.160693i	$-0.0513728\pi$
$978$	104.283	+	743.775i	0.106629	+	0.760506i
$979$	−84.1854	+	48.6045i	−0.0859912	+	0.0496471i
$980$	−6.02594	−	925.300i	−0.00614892	−	0.944184i
$981$	−402.600	+	410.970i	−0.410397	+	0.418930i
$982$	−638.211	−	634.068i	−0.649909	−	0.645691i
$983$	490.618	−	283.258i	0.499103	−	0.288157i	−0.229240	−	0.973370i	$-0.573624\pi$
$983$	490.618	−	283.258i	0.499103	−	0.288157i	0.728343	+	0.685213i	$0.240291\pi$
$984$	465.867	−	368.639i	0.473442	−	0.374633i
$985$	487.746	−	844.801i	0.495174	−	0.857666i
$986$	−5.14667	−	18.9605i	−0.00521974	−	0.0192297i
$987$	−102.727	+	812.569i	−0.104080	+	0.823272i
$988$	−234.147	−	399.524i	−0.236991	−	0.404376i
$989$	1029.46			1.04091
$990$	−279.382	−	469.114i	−0.282204	−	0.473852i
$991$			457.774i			0.461931i	0.972962	+	0.230966i	$0.0741885\pi$
$991$			457.774i			0.461931i	−0.972962	+	0.230966i	$0.925812\pi$
$992$	−117.972	+	470.806i	−0.118923	+	0.474603i
$993$	108.396	−	142.779i	0.109160	−	0.143786i
$994$	133.260	+	490.933i	0.134064	+	0.493897i
$995$	574.172	+	331.498i	0.577057	+	0.333164i
$996$	−1109.60	+	474.840i	−1.11406	+	0.476747i
$997$	19.3798	+	33.5667i	0.0194381	+	0.0336677i	0.875581	−	0.483072i	$-0.160479\pi$
$997$	19.3798	+	33.5667i	0.0194381	+	0.0336677i	−0.856143	+	0.516739i	$0.827146\pi$
$998$	−905.375	−	899.498i	−0.907190	−	0.901301i
$999$	−5.88880	+	14.8615i	−0.00589470	+	0.0148763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.f.c.31.1	yes	16
3.2	odd	2		108.3.f.c.91.8		16
4.3	odd	2	inner	36.3.f.c.31.5	yes	16
8.3	odd	2		576.3.o.g.319.1		16
8.5	even	2		576.3.o.g.319.8		16
9.2	odd	6		108.3.f.c.19.4		16
9.4	even	3		324.3.d.i.163.5		8
9.5	odd	6		324.3.d.g.163.4		8
9.7	even	3	inner	36.3.f.c.7.5	yes	16
12.11	even	2		108.3.f.c.91.4		16
24.5	odd	2		1728.3.o.g.1279.1		16
24.11	even	2		1728.3.o.g.1279.2		16
36.7	odd	6	inner	36.3.f.c.7.1	✓	16
36.11	even	6		108.3.f.c.19.8		16
36.23	even	6		324.3.d.g.163.3		8
36.31	odd	6		324.3.d.i.163.6		8
72.11	even	6		1728.3.o.g.127.1		16
72.29	odd	6		1728.3.o.g.127.2		16
72.43	odd	6		576.3.o.g.511.8		16
72.61	even	6		576.3.o.g.511.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.1	✓	16	36.7	odd	6	inner
36.3.f.c.7.5	yes	16	9.7	even	3	inner
36.3.f.c.31.1	yes	16	1.1	even	1	trivial
36.3.f.c.31.5	yes	16	4.3	odd	2	inner
108.3.f.c.19.4		16	9.2	odd	6
108.3.f.c.19.8		16	36.11	even	6
108.3.f.c.91.4		16	12.11	even	2
108.3.f.c.91.8		16	3.2	odd	2
324.3.d.g.163.3		8	36.23	even	6
324.3.d.g.163.4		8	9.5	odd	6
324.3.d.i.163.5		8	9.4	even	3
324.3.d.i.163.6		8	36.31	odd	6
576.3.o.g.319.1		16	8.3	odd	2
576.3.o.g.319.8		16	8.5	even	2
576.3.o.g.511.1		16	72.61	even	6
576.3.o.g.511.8		16	72.43	odd	6
1728.3.o.g.127.1		16	72.11	even	6
1728.3.o.g.127.2		16	72.29	odd	6
1728.3.o.g.1279.1		16	24.5	odd	2
1728.3.o.g.1279.2		16	24.11	even	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93353 - 0.511345i) q^{2} +(-2.76570 + 1.16229i) q^{3} +(3.47705 + 1.97740i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(5.94188 - 0.833101i) q^{6} +(-3.90254 + 2.25313i) q^{7} +(-5.71184 - 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +O(q^{10})\)	\(q+(-1.93353 - 0.511345i) q^{2} +(-2.76570 + 1.16229i) q^{3} +(3.47705 + 1.97740i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(5.94188 - 0.833101i) q^{6} +(-3.90254 + 2.25313i) q^{7} +(-5.71184 - 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +(11.3643 - 11.4386i) q^{10} +(3.25842 - 1.88125i) q^{11} +(-11.9148 - 1.42753i) q^{12} +(-3.52605 + 6.10730i) q^{13} +(8.69780 - 2.36095i) q^{14} +(3.03354 - 23.9953i) q^{15} +(8.17979 + 13.7510i) q^{16} +0.517890 q^{17} +(-15.4651 + 9.21031i) q^{18} +16.4164i q^{19} +(-27.8223 + 16.3057i) q^{20} +(8.17444 - 10.7674i) q^{21} +(-7.26222 + 1.97127i) q^{22} +(27.7049 + 15.9954i) q^{23} +(22.3076 + 8.85273i) q^{24} +(-19.9986 - 34.6387i) q^{25} +(9.94065 - 10.0056i) q^{26} +(-9.94627 + 25.1012i) q^{27} +(-18.0247 + 0.117384i) q^{28} +(9.48394 + 16.4267i) q^{29} +(-18.1353 + 44.8443i) q^{30} +(-13.1355 - 7.58377i) q^{31} +(-8.78432 - 30.7707i) q^{32} +(-6.82524 + 8.99021i) q^{33} +(-1.00135 - 0.264820i) q^{34} -36.3299i q^{35} +(34.6119 - 9.90037i) q^{36} +0.592061 q^{37} +(8.39446 - 31.7416i) q^{38} +(2.65351 - 20.9892i) q^{39} +(62.1330 - 17.3007i) q^{40} +(12.3766 - 21.4369i) q^{41} +(-21.3114 + 16.6391i) q^{42} +(27.8686 - 16.0900i) q^{43} +(15.0497 - 0.0980099i) q^{44} +(19.4997 + 69.8895i) q^{45} +(-45.3890 - 45.0944i) q^{46} +(-52.4682 + 30.2925i) q^{47} +(-38.6056 - 28.5239i) q^{48} +(-14.3468 + 24.8493i) q^{49} +(20.9556 + 77.2010i) q^{50} +(-1.43233 + 0.601940i) q^{51} +(-24.3368 + 14.2630i) q^{52} -0.664765 q^{53} +(32.0668 - 43.4479i) q^{54} +30.3336i q^{55} +(34.9113 + 8.98987i) q^{56} +(-19.0807 - 45.4029i) q^{57} +(-9.93776 - 36.6110i) q^{58} +(-30.5921 - 17.6623i) q^{59} +(57.9960 - 77.4343i) q^{60} +(33.7750 + 58.5000i) q^{61} +(21.5199 + 21.3802i) q^{62} +(-10.0932 + 39.2804i) q^{63} +(1.25029 + 63.9878i) q^{64} +(-28.4273 - 49.2376i) q^{65} +(17.7939 - 13.8928i) q^{66} +(-74.4692 - 42.9948i) q^{67} +(1.80073 + 1.02407i) q^{68} +(-95.2148 - 12.0373i) q^{69} +(-18.5771 + 70.2449i) q^{70} +56.4434i q^{71} +(-71.9855 + 1.44402i) q^{72} +131.921 q^{73} +(-1.14477 - 0.302748i) q^{74} +(95.5705 + 72.5557i) q^{75} +(-32.4618 + 57.0808i) q^{76} +(-8.47743 + 14.6833i) q^{77} +(-15.8634 + 39.2264i) q^{78} +(126.869 - 73.2481i) q^{79} +(-128.982 + 1.68005i) q^{80} +(-1.66664 - 80.9829i) q^{81} +(-34.8921 + 35.1201i) q^{82} +(87.1029 - 50.2889i) q^{83} +(49.7144 - 21.2746i) q^{84} +(-2.08764 + 3.61589i) q^{85} +(-62.1122 + 16.8599i) q^{86} +(-45.3223 - 34.4081i) q^{87} +(-29.1491 - 7.50608i) q^{88} -25.8362 q^{89} +(-1.96553 - 145.104i) q^{90} -31.7786i q^{91} +(64.7021 + 110.401i) q^{92} +(45.1433 + 5.70713i) q^{93} +(116.939 - 31.7420i) q^{94} +(-114.619 - 66.1754i) q^{95} +(60.0593 + 74.8924i) q^{96} +(-48.2534 - 83.5773i) q^{97} +(40.4465 - 40.7107i) q^{98} +(8.42728 - 32.7971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more