LMFDB - Embedded newform 36.3.f.c.31.5

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			31.5
Root			$-0.523926 + 1.93016i$ of defining polynomial
Character	$\chi$	$=$	36.31
Dual form			36.3.f.c.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.523926 - 1.93016i) q^{2} +(2.76570 - 1.16229i) q^{3} +(-3.45100 - 2.02252i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(-0.794388 - 5.94718i) q^{6} +(3.90254 - 2.25313i) q^{7} +(-5.71184 + 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +O(q^{10})$	\(q+(0.523926 - 1.93016i) q^{2} +(2.76570 - 1.16229i) q^{3} +(-3.45100 - 2.02252i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(-0.794388 - 5.94718i) 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} +(-11.8952 - 1.58259i) q^{12} +(-3.52605 + 6.10730i) q^{13} +(-2.30426 - 8.71299i) q^{14} +(-3.03354 + 23.9953i) q^{15} +(7.81885 + 13.9594i) q^{16} +0.517890 q^{17} +(-9.10940 - 15.5248i) q^{18} -16.4164i q^{19} +(28.0323 - 15.9420i) q^{20} +(8.17444 - 10.7674i) q^{21} +(1.92394 + 7.27490i) q^{22} +(-27.7049 - 15.9954i) q^{23} +(-9.28684 + 22.1304i) 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} +(44.7253 + 18.4270i) q^{30} +(13.1355 + 7.58377i) q^{31} +(31.0404 - 7.77790i) q^{32} +(-6.82524 + 8.99021i) q^{33} +(0.271336 - 0.999608i) q^{34} +36.3299i q^{35} +(-34.7379 + 9.44873i) q^{36} +0.592061 q^{37} +(-31.6863 - 8.60099i) q^{38} +(-2.65351 + 20.9892i) q^{39} +(-16.0836 - 62.4591i) q^{40} +(12.3766 - 21.4369i) q^{41} +(-16.4999 - 21.4193i) 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} +(37.8495 + 29.5197i) q^{48} +(-14.3468 + 24.8493i) q^{49} +(-77.3358 + 20.4524i) q^{50} +(1.43233 - 0.601940i) q^{51} +(24.5205 - 13.9448i) q^{52} -0.664765 q^{53} +(-43.2382 - 32.3490i) q^{54} -30.3336i q^{55} +(-9.67017 + 34.7290i) q^{56} +(-19.0807 - 45.4029i) q^{57} +(36.6749 - 9.69913i) q^{58} +(30.5921 + 17.6623i) q^{59} +(58.9996 - 76.6724i) 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} +(13.7766 + 17.8840i) q^{66} +(74.4692 + 42.9948i) q^{67} +(-1.78724 - 1.04744i) q^{68} +(-95.2148 - 12.0373i) q^{69} +(70.1224 + 19.0342i) q^{70} -56.4434i q^{71} +(0.0374515 + 72.0000i) q^{72} +131.921 q^{73} +(0.310196 - 1.14277i) q^{74} +(-95.5705 - 72.5557i) q^{75} +(-33.2025 + 56.6532i) q^{76} +(-8.47743 + 14.6833i) q^{77} +(39.1222 + 16.1185i) 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} +(-49.9873 + 20.6253i) q^{84} +(-2.08764 + 3.61589i) q^{85} +(16.4550 + 62.2207i) q^{86} +(45.3223 + 34.4081i) q^{87} +(8.07410 - 28.9969i) q^{88} -25.8362 q^{89} +(145.114 - 1.02053i) q^{90} +31.7786i q^{91} +(63.2587 + 111.234i) q^{92} +(45.1433 + 5.70713i) q^{93} +(-30.9798 - 117.143i) q^{94} +(114.619 + 66.1754i) q^{95} +(76.8080 - 57.5893i) 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 $

$2$	0.523926	−	1.93016i	0.261963	−	0.965078i
$2$	0.523926	−	1.93016i	0.261963	−	0.965078i
$3$	2.76570	−	1.16229i	0.921899	−	0.387431i
$3$	2.76570	−	1.16229i	0.921899	−	0.387431i
$4$	−3.45100	−	2.02252i	−0.862751	−	0.505629i
$5$	−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	$0.868182\pi$
$6$	−0.794388	−	5.94718i	−0.132398	−	0.991197i
$7$	3.90254	−	2.25313i	0.557506	−	0.321876i	−0.194638	−	0.980875i	$-0.562353\pi$
$7$	3.90254	−	2.25313i	0.557506	−	0.321876i	0.752144	+	0.658999i	$0.229020\pi$
$8$	−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	−0.640744	−	0.767755i	$-0.721374\pi$
$11$	−3.25842	+	1.88125i	−0.296220	+	0.171023i	0.344523	+	0.938778i	$0.388041\pi$
$12$	−11.8952	−	1.58259i	−0.991265	−	0.131882i
$13$	−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	$0.254099\pi$
$14$	−2.30426	−	8.71299i	−0.164590	−	0.622357i
$15$	−3.03354	+	23.9953i	−0.202236	+	1.59968i
$16$	7.81885	+	13.9594i	0.488678	+	0.872464i
$17$	0.517890			0.0304641			0.0152321	−	0.999884i	$-0.495151\pi$
$17$	0.517890			0.0304641			0.0152321	+	0.999884i	$0.495151\pi$
$18$	−9.10940	−	15.5248i	−0.506078	−	0.862488i
$19$		−	16.4164i		−	0.864023i	−0.901868	−	0.432012i	$-0.857804\pi$
$19$		−	16.4164i		−	0.864023i	0.901868	−	0.432012i	$-0.142196\pi$
$20$	28.0323	−	15.9420i	1.40162	−	0.797098i
$21$	8.17444	−	10.7674i	0.389259	−	0.512733i
$22$	1.92394	+	7.27490i	0.0874517	+	0.330677i
$23$	−27.7049	−	15.9954i	−1.20456	−	0.695454i	−0.242996	−	0.970027i	$-0.578130\pi$
$23$	−27.7049	−	15.9954i	−1.20456	−	0.695454i	−0.961566	+	0.274573i	$0.911463\pi$
$24$	−9.28684	+	22.1304i	−0.386951	+	0.922100i
$25$	−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	$0.727285\pi$
$30$	44.7253	+	18.4270i	1.49084	+	0.614232i
$31$	13.1355	+	7.58377i	0.423725	+	0.244638i	0.696670	−	0.717392i	$-0.254664\pi$
$31$	13.1355	+	7.58377i	0.423725	+	0.244638i	−0.272945	+	0.962030i	$0.587998\pi$
$32$	31.0404	−	7.77790i	0.970011	−	0.243059i
$33$	−6.82524	+	8.99021i	−0.206826	+	0.272431i
$34$	0.271336	−	0.999608i	0.00798047	−	0.0294002i
$35$			36.3299i			1.03800i
$36$	−34.7379	+	9.44873i	−0.964942	+	0.262465i
$37$	0.592061			0.0160017			0.00800083	−	0.999968i	$-0.497453\pi$
$37$	0.592061			0.0160017			0.00800083	+	0.999968i	$0.497453\pi$
$38$	−31.6863	−	8.60099i	−0.833850	−	0.226342i
$39$	−2.65351	+	20.9892i	−0.0680387	+	0.538185i
$40$	−16.0836	−	62.4591i	−0.402091	−	1.56148i
$41$	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	$0.0690565\pi$
$42$	−16.4999	−	21.4193i	−0.392855	−	0.509982i
$43$	−27.8686	+	16.0900i	−0.648107	+	0.374185i	−0.787731	−	0.616020i	$-0.788744\pi$
$43$	−27.8686	+	16.0900i	−0.648107	+	0.374185i	0.139623	+	0.990205i	$0.455411\pi$
$44$	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	0.175879	−	0.984412i	$-0.443723\pi$
$47$	52.4682	−	30.2925i	1.11634	−	0.644521i	0.940465	+	0.339890i	$0.110390\pi$
$48$	37.8495	+	29.5197i	0.788532	+	0.614994i
$49$	−14.3468	+	24.8493i	−0.292791	+	0.507129i
$50$	−77.3358	+	20.4524i	−1.54672	+	0.409048i
$51$	1.43233	−	0.601940i	0.0280848	−	0.0118027i
$52$	24.5205	−	13.9448i	0.471548	−	0.268169i
$53$	−0.664765			−0.0125427			−0.00627137	−	0.999980i	$-0.501996\pi$
$53$	−0.664765			−0.0125427			−0.00627137	+	0.999980i	$0.501996\pi$
$54$	−43.2382	−	32.3490i	−0.800707	−	0.599056i
$55$		−	30.3336i		−	0.551521i
$56$	−9.67017	+	34.7290i	−0.172682	+	0.620160i
$57$	−19.0807	−	45.4029i	−0.334749	−	0.796542i
$58$	36.6749	−	9.69913i	0.632326	−	0.167226i
$59$	30.5921	+	17.6623i	0.518510	+	0.299362i	0.736325	−	0.676628i	$-0.236560\pi$
$59$	30.5921	+	17.6623i	0.518510	+	0.299362i	−0.217815	+	0.975990i	$0.569893\pi$
$60$	58.9996	−	76.6724i	0.983327	−	1.27787i
$61$	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
$66$	13.7766	+	17.8840i	0.208736	+	0.270970i
$67$	74.4692	+	42.9948i	1.11148	+	0.641714i	0.939213	−	0.343336i	$-0.111557\pi$
$67$	74.4692	+	42.9948i	1.11148	+	0.641714i	0.172269	+	0.985050i	$0.444890\pi$
$68$	−1.78724	−	1.04744i	−0.0262829	−	0.0154035i
$69$	−95.2148	−	12.0373i	−1.37992	−	0.174454i
$70$	70.1224	+	19.0342i	1.00175	+	0.271917i
$71$		−	56.4434i		−	0.794977i	−0.917607	−	0.397489i	$-0.869882\pi$
$71$		−	56.4434i		−	0.794977i	0.917607	−	0.397489i	$-0.130118\pi$
$72$	0.0374515	+	72.0000i	0.000520160	+	1.00000i
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$	0.310196	−	1.14277i	0.00419184	−	0.0154429i
$75$	−95.5705	−	72.5557i	−1.27427	−	0.967410i
$76$	−33.2025	+	56.6532i	−0.436875	+	0.745437i
$77$	−8.47743	+	14.6833i	−0.110096	+	0.190693i
$78$	39.1222	+	16.1185i	0.501567	+	0.206647i
$79$	−126.869	+	73.2481i	−1.60594	+	0.927191i	−0.615677	+	0.787999i	$0.711117\pi$
$79$	−126.869	+	73.2481i	−1.60594	+	0.927191i	−0.990265	+	0.139192i	$0.955549\pi$
$80$	−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	−0.922491	−	0.386020i	$-0.873850\pi$
$83$	−87.1029	+	50.2889i	−1.04943	+	0.605890i	−0.126942	+	0.991910i	$0.540516\pi$
$84$	−49.9873	+	20.6253i	−0.595086	+	0.245540i
$85$	−2.08764	+	3.61589i	−0.0245604	+	0.0425399i
$86$	16.4550	+	62.2207i	0.191338	+	0.723497i
$87$	45.3223	+	34.4081i	0.520946	+	0.395495i
$88$	8.07410	−	28.9969i	0.0917511	−	0.329510i
$89$	−25.8362			−0.290295			−0.145147	−	0.989410i	$-0.546366\pi$
$89$	−25.8362			−0.290295			−0.145147	+	0.989410i	$0.546366\pi$
$90$	145.114	−	1.02053i	1.61238	−	0.0113392i
$91$			31.7786i			0.349216i
$92$	63.2587	+	111.234i	0.687595	+	1.20907i
$93$	45.1433	+	5.70713i	0.485412	+	0.0613670i
$94$	−30.9798	−	117.143i	−0.329573	−	1.24620i
$95$	114.619	+	66.1754i	1.20652	+	0.696583i
$96$	76.8080	−	57.5893i	0.800083	−	0.599889i
$97$	−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	$0.902131\pi$
$102$	−0.411406	−	3.07999i	−0.00403339	−	0.0301959i
$103$	−125.439	−	72.4223i	−1.21786	−	0.703129i	−0.253397	−	0.967362i	$-0.581548\pi$
$103$	−125.439	−	72.4223i	−1.21786	−	0.703129i	−0.964459	+	0.264233i	$0.914881\pi$
$104$	−14.0687	−	54.6345i	−0.135276	−	0.525331i
$105$	42.2260	+	100.478i	0.402153	+	0.956929i
$106$	−0.348288	+	1.28310i	−0.00328573	+	0.0121047i
$107$		−	54.9861i		−	0.513889i	−0.966426	−	0.256944i	$-0.917284\pi$
$107$		−	54.9861i		−	0.513889i	0.966426	−	0.256944i	$-0.0827158\pi$
$108$	−85.0923	+	66.5079i	−0.787891	+	0.615814i
$109$	−63.9235			−0.586454			−0.293227	−	0.956043i	$-0.594729\pi$
$109$	−63.9235			−0.586454			−0.293227	+	0.956043i	$0.594729\pi$
$110$	−58.5487	−	15.8926i	−0.532261	−	0.144478i
$111$	1.63746	−	0.688149i	0.0147519	−	0.00619954i
$112$	61.9659	+	36.8603i	0.553267	+	0.329110i
$113$	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	$0.116248\pi$
$114$	−97.6315	+	13.0410i	−0.856417	+	0.114395i
$115$	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
$120$	−117.078	−	154.049i	−0.975652	−	1.28374i
$121$	−53.4218	+	92.5292i	−0.441502	+	0.764704i
$122$	130.610	−	34.5413i	1.07057	−	0.283126i
$123$	9.31394	−	73.6731i	0.0757231	−	0.598968i
$124$	−29.9923	−	52.7383i	−0.241873	−	0.425309i
$125$	120.909			0.967276
$126$	−70.5292	−	40.0614i	−0.559756	−	0.317948i
$127$			9.81219i			0.0772613i	0.999254	+	0.0386307i	$0.0122996\pi$
$127$			9.81219i			0.0772613i	−0.999254	+	0.0386307i	$0.987700\pi$
$128$	−122.851	−	35.9381i	−0.959776	−	0.280766i
$129$	−58.3749	+	76.8914i	−0.452518	+	0.596057i
$130$	−109.930	+	29.0723i	−0.845615	+	0.223633i
$131$	−101.561	−	58.6365i	−0.775278	−	0.447607i	0.0594761	−	0.998230i	$-0.481057\pi$
$131$	−101.561	−	58.6365i	−0.775278	−	0.447607i	−0.834754	+	0.550623i	$0.814390\pi$
$132$	41.7368	−	17.2211i	0.316188	−	0.130463i
$133$	−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	$0.464071\pi$
$138$	−73.1193	+	177.473i	−0.529850	+	1.28603i
$139$	133.073	+	76.8298i	0.957361	+	0.552732i	0.895360	−	0.445344i	$-0.146919\pi$
$139$	133.073	+	76.8298i	0.957361	+	0.552732i	0.0620009	+	0.998076i	$0.480252\pi$
$140$	73.4779	−	125.375i	0.524842	−	0.895534i
$141$	109.902	−	144.763i	0.779448	−	1.02669i
$142$	−108.945	−	29.5721i	−0.767215	−	0.208255i
$143$		−	26.5335i		−	0.185549i
$144$	138.991	+	37.6504i	0.965214	+	0.261461i
$145$	−152.921			−1.05463
$146$	69.1167	−	254.628i	0.473402	−	1.74403i
$147$	−10.7966	+	85.4009i	−0.0734462	+	0.580958i
$148$	−2.04321	−	1.19745i	−0.0138054	−	0.00809091i
$149$	−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	$0.266264\pi$
$150$	−190.116	+	146.452i	−1.26744	+	0.976347i
$151$	−36.0215	+	20.7970i	−0.238553	+	0.137729i	−0.614512	−	0.788908i	$-0.710647\pi$
$151$	−36.0215	+	20.7970i	−0.238553	+	0.137729i	0.375958	+	0.926637i	$0.377314\pi$
$152$	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
$156$	51.6083	−	67.0671i	0.330823	−	0.429918i
$157$	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	$-0.0888099\pi$
$158$	74.9101	+	283.254i	0.474114	+	1.79275i
$159$	−1.83854	+	0.772652i	−0.0115631	+	0.00485945i
$160$	−70.8200	+	248.076i	−0.442625	+	1.55048i
$161$	−144.160			−0.895401
$162$	−157.183	−	39.2121i	−0.970264	−	0.242050i
$163$		−	125.175i		−	0.767945i	−0.923344	−	0.383973i	$-0.874556\pi$
$163$		−	125.175i		−	0.767945i	0.923344	−	0.383973i	$-0.125444\pi$
$164$	−86.0681	+	48.9469i	−0.524805	+	0.298457i
$165$	−35.2566	−	83.8936i	−0.213676	−	0.508446i
$166$	51.4299	+	194.470i	0.309819	+	1.17151i
$167$	−154.373	−	89.1274i	−0.924390	−	0.533697i	−0.0393573	−	0.999225i	$-0.512531\pi$
$167$	−154.373	−	89.1274i	−0.924390	−	0.533697i	−0.885033	+	0.465528i	$0.845864\pi$
$168$	13.6205	+	107.289i	0.0810743	+	0.638627i
$169$	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	$0.977271\pi$
$174$	90.1584	−	69.4519i	0.518152	−	0.399149i
$175$	−156.091	−	90.1193i	−0.891949	−	0.514967i
$176$	−51.7383	−	30.7765i	−0.293968	−	0.174866i
$177$	105.137	+	13.2917i	0.593995	+	0.0750944i
$178$	−13.5363	+	49.8680i	−0.0760465	+	0.280157i
$179$			276.827i			1.54652i	0.634088	+	0.773261i	$0.281376\pi$
$179$			276.827i			1.54652i	−0.634088	+	0.773261i	$0.718624\pi$
$180$	74.0592	−	280.627i	0.411440	−	1.55904i
$181$	−104.729			−0.578612			−0.289306	−	0.957237i	$-0.593425\pi$
$181$	−104.729			−0.578612			−0.289306	+	0.957237i	$0.593425\pi$
$182$	61.3377	+	16.6497i	0.337021	+	0.0914816i
$183$	161.405	+	122.537i	0.881997	+	0.669600i
$184$	247.842	−	63.8209i	1.34697	−	0.346852i
$185$	−2.38663	+	4.13376i	−0.0129007	+	0.0223446i
$186$	34.6674	−	84.1435i	0.186384	−	0.452384i
$187$	−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	0.0990389	−	0.995084i	$-0.468423\pi$
$191$	192.972	−	111.413i	1.01033	−	0.583312i	0.911287	+	0.411772i	$0.135090\pi$
$192$	−70.9147	−	178.424i	−0.369347	−	0.929291i
$193$	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	$0.0717888\pi$
$194$	−186.598	+	49.3482i	−0.961847	+	0.254372i
$195$	−135.850	−	103.135i	−0.696666	−	0.528899i
$196$	99.7690	−	56.7386i	0.509025	−	0.289482i
$197$	−120.998			−0.614201			−0.307100	−	0.951677i	$-0.599359\pi$
$197$	−120.998			−0.614201			−0.307100	+	0.951677i	$0.599359\pi$
$198$	58.8883	+	33.4492i	0.297416	+	0.168936i
$199$			82.2364i			0.413248i	0.978420	+	0.206624i	$0.0662477\pi$
$199$			82.2364i			0.413248i	−0.978420	+	0.206624i	$0.933752\pi$
$200$	308.252	+	85.8317i	1.54126	+	0.429158i
$201$	255.932	+	32.3556i	1.27329	+	0.160973i
$202$	−83.7605	+	22.1515i	−0.414656	+	0.109661i
$203$	74.0230	+	42.7372i	0.364645	+	0.210528i
$204$	−6.16040	−	0.819607i	−0.0301980	−	0.00401768i
$205$	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
$210$	216.061	−	28.8601i	1.02886	−	0.137429i
$211$	−93.5819	−	54.0295i	−0.443516	−	0.256064i	0.261572	−	0.965184i	$-0.415759\pi$
$211$	−93.5819	−	54.0295i	−0.443516	−	0.256064i	−0.705088	+	0.709120i	$0.749093\pi$
$212$	2.29411	+	1.34450i	0.0108213	+	0.00634198i
$213$	−65.6038	−	156.105i	−0.307999	−	0.732889i
$214$	−106.132	−	28.8086i	−0.495943	−	0.134620i
$215$		−	259.437i		−	1.20668i
$216$	83.7887	+	199.087i	0.387911	+	0.921697i
$217$	68.3490			0.314972
$218$	−33.4912	+	123.382i	−0.153629	+	0.565974i
$219$	364.853	−	153.331i	1.66599	−	0.700140i
$220$	−61.3503	+	104.682i	−0.278865	+	0.475825i
$221$	−1.82611	+	3.16291i	−0.00826292	+	0.0143118i
$222$	−0.470326	−	3.52110i	−0.00211859	−	0.0158608i
$223$	141.400	−	81.6371i	0.634079	−	0.366086i	−0.148251	−	0.988950i	$-0.547364\pi$
$223$	141.400	−	81.6371i	0.634079	−	0.366086i	0.782330	+	0.622864i	$0.214031\pi$
$224$	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	−0.520925	−	0.853602i	$-0.674413\pi$
$227$	−9.56722	+	5.52364i	−0.0421463	+	0.0243332i	0.478779	+	0.877936i	$0.341080\pi$
$228$	−25.9805	+	195.277i	−0.113949	+	0.856476i
$229$	−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	$0.189165\pi$
$230$	−131.883	−	498.683i	−0.573403	−	2.16818i
$231$	−6.37965	+	50.4629i	−0.0276175	+	0.218454i
$232$	−146.182	−	40.7039i	−0.630094	−	0.175448i
$233$	181.049			0.777036			0.388518	−	0.921441i	$-0.372987\pi$
$233$	181.049			0.777036			0.388518	+	0.921441i	$0.372987\pi$
$234$	126.935	−	0.892680i	0.542456	−	0.00381487i
$235$			488.442i			2.07848i
$236$	−69.8510	−	122.826i	−0.295979	−	0.520448i
$237$	−265.746	+	350.041i	−1.12129	+	1.47697i
$238$	−1.19335	−	4.51237i	−0.00501408	−	0.0189595i
$239$	39.6432	+	22.8880i	0.165871	+	0.0957658i	0.580638	−	0.814162i	$-0.302803\pi$
$239$	39.6432	+	22.8880i	0.165871	+	0.0957658i	−0.414766	+	0.909928i	$0.636137\pi$
$240$	−358.679	+	145.269i	−1.49450	+	0.605287i
$241$	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
$246$	−137.321	−	56.5766i	−0.558214	−	0.229986i
$247$	100.260	+	57.8852i	0.405911	+	0.234353i
$248$	−117.507	+	30.2588i	−0.473818	+	0.122011i
$249$	−182.450	+	240.323i	−0.732730	+	0.965152i
$250$	63.3476	−	233.374i	0.253390	−	0.933496i
$251$			282.587i			1.12585i	0.826510	+	0.562923i	$0.190323\pi$
$251$			282.587i			1.12585i	−0.826510	+	0.562923i	$0.809677\pi$
$252$	−114.277	+	115.143i	−0.453480	+	0.456918i
$253$	120.366			0.475754
$254$	18.9391	+	5.14086i	0.0745632	+	0.0202396i
$255$	−1.57104	+	12.4269i	−0.00616095	+	0.0487330i
$256$	−133.731	+	218.293i	−0.522387	+	0.852708i
$257$	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	$0.118314\pi$
$258$	117.828	+	152.958i	0.456699	+	0.592860i
$259$	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	−0.0806619	−	0.996742i	$-0.525703\pi$
$263$	195.201	−	112.700i	0.742211	−	0.428516i	0.822873	+	0.568226i	$0.192370\pi$
$264$	−11.3724	−	89.5811i	−0.0430773	−	0.339322i
$265$	2.67970	−	4.64138i	0.0101121	−	0.0175146i
$266$	−143.036	+	37.8277i	−0.537730	+	0.142209i
$267$	−71.4552	+	30.0293i	−0.267622	+	0.112469i
$268$	−170.036	−	298.991i	−0.634462	−	1.11564i
$269$	425.808			1.58293			0.791465	−	0.611214i	$-0.209319\pi$
$269$	425.808			1.58293			0.791465	+	0.611214i	$0.209319\pi$
$270$	400.155	−	171.488i	1.48206	−	0.635139i
$271$		−	56.3665i		−	0.207995i	−0.994578	−	0.103997i	$-0.966837\pi$
$271$		−	56.3665i		−	0.207995i	0.994578	−	0.103997i	$-0.0331633\pi$
$272$	4.04931	+	7.22945i	0.0148872	+	0.0265788i
$273$	36.9361	+	87.8901i	0.135297	+	0.321942i
$274$	485.725	−	128.456i	1.77272	−	0.468817i
$275$	130.328	+	75.2450i	0.473920	+	0.273618i
$276$	304.241	+	234.114i	1.10232	+	0.848240i
$277$	−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	$0.918117\pi$
$282$	−221.835	−	287.974i	−0.786649	−	1.02118i
$283$	−229.852	−	132.705i	−0.812198	−	0.468923i	0.0355207	−	0.999369i	$-0.488691\pi$
$283$	−229.852	−	132.705i	−0.812198	−	0.468923i	−0.847719	+	0.530446i	$0.822024\pi$
$284$	−114.158	+	194.786i	−0.401964	+	0.685867i
$285$	393.917	+	49.8000i	1.38216	+	0.174737i
$286$	−51.2139	−	13.9016i	−0.179070	−	0.0486070i
$287$		−	111.544i		−	0.388656i
$288$	145.492	−	248.548i	0.505180	−	0.863014i
$289$	−288.732			−0.999072
$290$	−80.1191	+	295.161i	−0.276273	+	1.01780i
$291$	−230.595	−	175.065i	−0.792424	−	0.601597i
$292$	−455.259	−	266.812i	−1.55911	−	0.913740i
$293$	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	$0.0265581\pi$
$294$	159.180	+	65.5828i	0.541430	+	0.223071i
$295$	−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
$300$	183.069	+	443.683i	0.610229	+	1.47894i
$301$	−72.5056	+	125.583i	−0.240883	+	0.417221i
$302$	21.2689	+	80.4232i	0.0704269	+	0.266302i
$303$	−103.510	−	78.5833i	−0.341617	−	0.259351i
$304$	229.164	−	128.358i	0.753829	−	0.422229i
$305$	−544.594			−1.78555
$306$	−4.71767	−	8.04013i	−0.0154172	−	0.0262749i
$307$		−	259.968i		−	0.846801i	−0.905943	−	0.423401i	$-0.860836\pi$
$307$		−	259.968i		−	0.846801i	0.905943	−	0.423401i	$-0.139164\pi$
$308$	58.9529	−	33.5265i	0.191406	−	0.108852i
$309$	−431.102	−	54.5010i	−1.39515	−	0.176379i
$310$	62.5283	+	236.436i	0.201704	+	0.762695i
$311$	16.5959	+	9.58164i	0.0533630	+	0.0308091i	0.526444	−	0.850210i	$-0.323525\pi$
$311$	16.5959	+	9.58164i	0.0533630	+	0.0308091i	−0.473081	+	0.881019i	$0.656858\pi$
$312$	−102.411	−	134.750i	−0.328241	−	0.431892i
$313$	−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	$0.763521\pi$
$318$	0.528082	+	3.95348i	0.00166063	+	0.0124323i
$319$	−61.8054	−	35.6834i	−0.193747	−	0.111860i
$320$	441.721	+	266.667i	1.38038	+	0.833335i
$321$	−63.9100	−	152.075i	−0.199097	−	0.473754i
$322$	−75.5289	+	278.250i	−0.234562	+	0.864132i
$323$		−	8.50191i		−	0.0263217i
$324$	−158.038	+	282.843i	−0.487770	+	0.872972i
$325$	282.065			0.867892
$326$	−241.607	−	65.5824i	−0.741127	−	0.201173i
$327$	−176.793	+	74.2978i	−0.540651	+	0.227211i
$328$	49.3818	+	191.769i	0.150554	+	0.584662i
$329$	136.506	−	236.436i	0.414912	−	0.718649i
$330$	−180.400	+	24.0967i	−0.546666	+	0.0730202i
$331$	51.7490	−	29.8773i	0.156341	−	0.0902638i	−0.419788	−	0.907622i	$-0.637896\pi$
$331$	51.7490	−	29.8773i	0.156341	−	0.0902638i	0.576130	+	0.817358i	$0.304562\pi$
$332$	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
$336$	214.221	+	29.9220i	0.637563	+	0.0890535i
$337$	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	$-0.0652188\pi$
$338$	230.608	−	60.9870i	0.682271	−	0.180435i
$339$	13.4133	−	106.099i	0.0395673	−	0.312977i
$340$	14.5177	−	8.25618i	0.0426990	−	0.0242829i
$341$	−57.0679			−0.167355
$342$	−254.862	+	149.544i	−0.745209	+	0.437263i
$343$			350.108i			1.02072i
$344$	69.0561	−	248.004i	0.200744	−	0.720943i
$345$	467.859	−	616.264i	1.35611	−	1.78627i
$346$	−292.312	+	77.3056i	−0.844833	+	0.223426i
$347$	−500.441	−	288.930i	−1.44219	−	0.832651i	−0.444198	−	0.895929i	$-0.646511\pi$
$347$	−500.441	−	288.930i	−1.44219	−	0.832651i	−0.997996	+	0.0632779i	$0.979845\pi$
$348$	−86.8166	−	210.407i	−0.249473	−	0.604619i
$349$	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	$0.555347\pi$
$354$	80.7391	−	195.967i	0.228077	−	0.553580i
$355$	394.086	+	227.526i	1.11010	+	0.640918i
$356$	89.1609	+	52.2542i	0.250452	+	0.146782i
$357$	4.23346	−	5.57632i	0.0118584	−	0.0156199i
$358$	534.320	+	145.037i	1.49251	+	0.405131i
$359$			292.754i			0.815470i	0.913100	+	0.407735i	$0.133681\pi$
$359$			292.754i			0.815470i	−0.913100	+	0.407735i	$0.866319\pi$
$360$	−502.853	−	289.974i	−1.39681	−	0.805482i
$361$	91.5006			0.253464
$362$	−54.8701	+	202.143i	−0.151575	+	0.558406i
$363$	−40.2023	+	318.000i	−0.110750	+	0.876032i
$364$	64.2728	−	109.668i	0.176574	−	0.301286i
$365$	−531.779	+	921.067i	−1.45693	+	2.52347i
$366$	321.079	−	247.338i	0.877266	−	0.675786i
$367$	378.870	−	218.741i	1.03234	−	0.596024i	0.114689	−	0.993401i	$-0.463413\pi$
$367$	378.870	−	218.741i	1.03234	−	0.596024i	0.917655	+	0.397377i	$0.130080\pi$
$368$	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
$372$	−144.247	−	110.998i	−0.387760	−	0.298383i
$373$	−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	$0.771433\pi$
$374$	0.996388	+	3.76760i	0.00266414	+	0.0100738i
$375$	334.399	−	140.532i	0.891730	−	0.374753i
$376$	−130.012	+	466.917i	−0.345776	+	1.24180i
$377$	−133.763			−0.354810
$378$	−241.626	−	28.8220i	−0.639221	−	0.0762488i
$379$		−	541.432i		−	1.42858i	−0.699850	−	0.714290i	$-0.746750\pi$
$379$		−	541.432i		−	1.42858i	0.699850	−	0.714290i	$-0.253250\pi$
$380$	−261.710	−	460.191i	−0.688711	−	1.21103i
$381$	11.4046	+	27.1375i	0.0299334	+	0.0712271i
$382$	−113.941	−	430.838i	−0.298274	−	1.12785i
$383$	311.941	+	180.099i	0.814467	+	0.470233i	0.848505	−	0.529188i	$-0.177503\pi$
$383$	311.941	+	180.099i	0.814467	+	0.470233i	−0.0340377	+	0.999421i	$0.510837\pi$
$384$	−381.540	+	43.3954i	−0.993594	+	0.113009i
$385$	−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	$0.869337\pi$
$390$	−270.242	+	208.176i	−0.692929	+	0.533785i
$391$	−14.3481	−	8.28388i	−0.0366959	−	0.0211864i
$392$	−57.2428	−	222.296i	−0.146027	−	0.567083i
$393$	−349.041	−	44.1266i	−0.888145	−	0.112281i
$394$	−63.3937	+	233.544i	−0.160898	+	0.592751i
$395$		−	1181.07i		−	2.99004i
$396$	95.4153	−	96.1387i	0.240948	−	0.242775i
$397$	−48.4128			−0.121947			−0.0609733	−	0.998139i	$-0.519420\pi$
$397$	−48.4128			−0.121947			−0.0609733	+	0.998139i	$0.519420\pi$
$398$	158.729	+	43.0858i	0.398817	+	0.108256i
$399$	−176.762	−	134.195i	−0.443013	−	0.336329i
$400$	327.169	−	550.004i	0.817924	−	1.37501i
$401$	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	$-0.0161548\pi$
$402$	196.541	−	477.037i	0.488907	−	1.18666i
$403$	−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
$408$	−4.80956	+	11.4611i	−0.0117881	+	0.0280910i
$409$	−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	$0.187784\pi$
$410$	385.859	−	102.045i	0.941119	−	0.248891i
$411$	600.251	+	455.702i	1.46047	+	1.10876i
$412$	286.415	+	503.632i	0.695183	+	1.22241i
$413$	159.182			0.385430
$414$	4.04952	+	575.822i	0.00978146	+	1.39087i
$415$		−	810.867i		−	1.95390i
$416$	−61.9479	+	216.998i	−0.148913	+	0.521630i
$417$	457.339	+	57.8179i	1.09674	+	0.138652i
$418$	119.428	−	31.5842i	0.285713	−	0.0755603i
$419$	552.029	+	318.714i	1.31749	+	0.760655i	0.983325	−	0.181859i	$-0.0582114\pi$
$419$	552.029	+	318.714i	1.31749	+	0.760655i	0.334168	+	0.942514i	$0.391545\pi$
$420$	57.4953	−	432.151i	0.136894	−	1.02893i
$421$	−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
$426$	−335.679	+	44.8379i	−0.787979	+	0.105253i
$427$	263.617	+	152.199i	0.617369	+	0.356438i
$428$	−111.210	+	189.757i	−0.259837	+	0.443358i
$429$	−30.8398	−	73.3837i	−0.0718876	−	0.171058i
$430$	−500.754	−	135.926i	−1.16454	−	0.316107i
$431$			481.190i			1.11645i	0.829689	+	0.558225i	$0.188518\pi$
$431$			481.190i			1.11645i	−0.829689	+	0.558225i	$0.811482\pi$
$432$	428.167	−	57.4186i	0.991128	−	0.132914i
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$	35.8098	−	131.924i	0.0825110	−	0.303973i
$435$	−422.932	+	177.739i	−0.972258	+	0.408595i
$436$	220.600	+	129.286i	0.505964	+	0.296528i
$437$	−262.588	+	454.816i	−0.600888	+	1.04077i
$438$	−104.796	−	784.557i	−0.239261	−	1.79123i
$439$	−488.267	+	281.901i	−1.11223	+	0.642144i	−0.939405	−	0.342809i	$-0.888622\pi$
$439$	−488.267	+	281.901i	−1.11223	+	0.642144i	−0.172821	+	0.984953i	$0.555288\pi$
$440$	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	−0.978027	−	0.208478i	$-0.933149\pi$
$443$	−569.917	+	329.042i	−1.28649	+	0.742757i	−0.308467	+	0.951235i	$0.599816\pi$
$444$	−7.04268	−	0.936990i	−0.0158619	−	0.00211034i
$445$	104.147	−	180.388i	0.234038	−	0.405366i
$446$	−83.4895	−	315.695i	−0.187196	−	0.707837i
$447$	−34.5150	+	273.013i	−0.0772147	+	0.610767i
$448$	−139.294	−	252.532i	−0.310924	−	0.563688i
$449$	227.569			0.506836			0.253418	−	0.967357i	$-0.418445\pi$
$449$	227.569			0.506836			0.253418	+	0.967357i	$0.418445\pi$
$450$	−355.582	+	626.012i	−0.790182	+	1.39114i
$451$			93.1339i			0.206505i
$452$	−123.950	+	70.4901i	−0.274225	+	0.155951i
$453$	−75.4523	+	99.3858i	−0.166561	+	0.219395i
$454$	5.64897	+	21.3602i	0.0124427	+	0.0470489i
$455$	−221.878	−	128.101i	−0.487643	−	0.281541i
$456$	363.302	+	152.457i	0.796716	+	0.334335i
$457$	−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	$0.976844\pi$
$462$	94.0588	+	38.7525i	0.203590	+	0.0838799i
$463$	396.754	+	229.066i	0.856920	+	0.494743i	0.862980	−	0.505239i	$-0.168595\pi$
$463$	396.754	+	229.066i	0.856920	+	0.494743i	−0.00605956	+	0.999982i	$0.501929\pi$
$464$	−155.153	+	260.828i	−0.334382	+	0.562129i
$465$	−221.822	+	292.184i	−0.477036	+	0.628352i
$466$	94.8565	−	349.454i	0.203555	−	0.749900i
$467$			204.395i			0.437677i	0.975761	+	0.218838i	$0.0702267\pi$
$467$			204.395i			0.437677i	−0.975761	+	0.218838i	$0.929773\pi$
$468$	64.7813	−	245.471i	0.138422	−	0.524511i
$469$	387.493			0.826210
$470$	942.769	+	255.907i	2.00589	+	0.544483i
$471$	84.9693	−	672.106i	0.180402	−	1.42698i
$472$	−273.670	+	70.4717i	−0.579808	+	0.149304i
$473$	60.5385	−	104.856i	0.127988	−	0.221682i
$474$	536.403	+	696.328i	1.13165	+	1.46905i
$475$	−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	−0.579654	−	0.814863i	$-0.696812\pi$
$479$	−78.4548	+	45.2959i	−0.163789	+	0.0945634i	0.415865	+	0.909426i	$0.363479\pi$
$480$	92.4706	+	768.417i	0.192647	+	1.60087i
$481$	−2.08764	+	3.61589i	−0.00434020	+	0.00751745i
$482$	654.367	−	173.055i	1.35761	−	0.359036i
$483$	−398.701	+	167.556i	−0.825469	+	0.346906i
$484$	371.501	−	211.272i	0.767563	−	0.436513i
$485$	778.046			1.60422
$486$	−480.296	+	74.2436i	−0.988263	+	0.152765i
$487$			301.289i			0.618663i	0.950954	+	0.309332i	$0.100105\pi$
$487$			301.289i			0.618663i	−0.950954	+	0.309332i	$0.899895\pi$
$488$	−520.595	−	144.958i	−1.06679	−	0.297045i
$489$	−145.490	−	346.196i	−0.297526	−	0.707968i
$490$	−447.283	+	118.289i	−0.912822	+	0.241407i
$491$	−389.556	−	224.911i	−0.793394	−	0.458066i	0.0477620	−	0.998859i	$-0.484791\pi$
$491$	−389.556	−	224.911i	−0.793394	−	0.458066i	−0.841156	+	0.540792i	$0.818124\pi$
$492$	−181.147	+	235.408i	−0.368186	+	0.478473i
$493$	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
$498$	368.271	+	478.068i	0.739499	+	0.959976i
$499$	−552.630	−	319.061i	−1.10748	−	0.639401i	−0.169301	−	0.985564i	$-0.554151\pi$
$499$	−552.630	−	319.061i	−1.10748	−	0.639401i	−0.938174	+	0.346163i	$0.887484\pi$
$500$	−417.259	−	244.541i	−0.834518	−	0.489083i
$501$	−530.541	−	67.0724i	−1.05897	−	0.133877i
$502$	545.437	+	148.055i	1.08653	+	0.294930i
$503$		−	182.179i		−	0.362185i	−0.983466	−	0.181093i	$-0.942037\pi$
$503$		−	182.179i		−	0.362185i	0.983466	−	0.181093i	$-0.0579634\pi$
$504$	162.372	+	280.899i	0.322166	+	0.557339i
$505$	349.250			0.691585
$506$	63.0628	−	232.325i	0.124630	−	0.459140i
$507$	284.982	+	216.354i	0.562094	+	0.426734i
$508$	19.8453	−	33.8619i	0.0390656	−	0.0666573i
$509$	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	$-0.209760\pi$
$510$	23.1628	+	9.54313i	0.0454172	+	0.0187120i
$511$	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
$516$	356.966	−	147.288i	0.691795	−	0.285443i
$517$	−113.976	+	197.412i	−0.220456	+	0.381841i
$518$	−1.36426	−	5.15863i	−0.00263371	−	0.00995874i
$519$	−361.235	−	274.245i	−0.696021	−	0.528409i
$520$	438.168	+	122.007i	0.842631	+	0.234628i
$521$	−634.330			−1.21752			−0.608762	−	0.793353i	$-0.708334\pi$
$521$	−634.330			−1.21752			−0.608762	+	0.793353i	$0.708334\pi$
$522$	168.627	−	296.873i	0.323041	−	0.568723i
$523$			534.777i			1.02252i	0.859426	+	0.511259i	$0.170821\pi$
$523$			534.777i			1.02252i	−0.859426	+	0.511259i	$0.829179\pi$
$524$	231.896	+	407.765i	0.442549	+	0.778177i
$525$	−536.446	−	67.8188i	−1.02180	−	0.129179i
$526$	−115.257	−	435.815i	−0.219119	−	0.828546i
$527$	6.80273	+	3.92756i	0.0129084	+	0.00745267i
$528$	−178.864	−	24.9833i	−0.338757	−	0.0473169i
$529$	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
$534$	20.5240	+	153.653i	0.0384344	+	0.287739i
$535$	383.912	+	221.652i	0.717592	+	0.414302i
$536$	−666.185	+	171.547i	−1.24288	+	0.320050i
$537$	321.755	+	765.620i	0.599170	+	1.42574i
$538$	223.092	−	821.876i	0.414669	−	1.52765i
$539$		−	107.960i		−	0.200296i
$540$	−121.346	−	862.208i	−0.224715	−	1.59668i
$541$	−61.0097			−0.112772			−0.0563860	−	0.998409i	$-0.517958\pi$
$541$	−61.0097			−0.112772			−0.0563860	+	0.998409i	$0.517958\pi$
$542$	−108.796	−	29.5319i	−0.200731	−	0.0544869i
$543$	−289.648	+	121.726i	−0.533422	+	0.224172i
$544$	16.0755	−	4.02810i	0.0295505	−	0.00740459i
$545$	257.678	−	446.312i	0.472805	−	0.818921i
$546$	188.993	−	25.2446i	0.346142	−	0.0462355i
$547$	−104.430	+	60.2925i	−0.190914	+	0.110224i	−0.592410	−	0.805637i	$-0.701823\pi$
$547$	−104.430	+	60.2925i	−0.190914	+	0.110224i	0.401497	+	0.915861i	$0.368490\pi$
$548$	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
$552$	611.277	−	464.574i	1.10739	−	0.841620i
$553$	−330.076	+	571.708i	−0.596882	+	1.03383i
$554$	−810.694	+	214.398i	−1.46335	+	0.387000i
$555$	−1.79604	+	14.2067i	−0.00323611	+	0.0255976i
$556$	−303.846	−	534.283i	−0.546486	−	0.960940i
$557$	−527.461			−0.946968			−0.473484	−	0.880802i	$-0.657004\pi$
$557$	−527.461			−0.946968			−0.473484	+	0.880802i	$0.657004\pi$
$558$	−1.91996	−	273.009i	−0.00344079	−	0.489263i
$559$		−	226.936i		−	0.405967i
$560$	−507.145	+	284.058i	−0.905616	+	0.507247i
$561$	−3.53473	+	4.65594i	−0.00630076	+	0.00829936i
$562$	−286.022	+	75.6420i	−0.508936	+	0.134594i
$563$	595.478	+	343.800i	1.05769	+	0.610656i	0.924792	−	0.380474i	$-0.124239\pi$
$563$	595.478	+	343.800i	1.05769	+	0.610656i	0.132896	+	0.991130i	$0.457572\pi$
$564$	−672.059	+	277.299i	−1.19159	+	0.491666i
$565$	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	$0.660706\pi$
$570$	302.505	−	734.230i	0.530710	−	1.28812i
$571$	−742.245	−	428.535i	−1.29990	−	0.750500i	−0.319517	−	0.947581i	$-0.603521\pi$
$571$	−742.245	−	428.535i	−1.29990	−	0.750500i	−0.980387	+	0.197081i	$0.936854\pi$
$572$	−53.6645	+	91.5674i	−0.0938191	+	0.160083i
$573$	404.209	−	532.424i	0.705425	−	0.929186i
$574$	−215.298	−	58.4410i	−0.375084	−	0.101814i
$575$			1279.55i			2.22530i
$576$	−403.509	−	411.043i	−0.700537	−	0.713616i
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$	−151.274	+	557.297i	−0.261720	+	0.964182i
$579$	42.6535	−	337.388i	0.0736675	−	0.582709i
$580$	527.730	+	309.285i	0.909880	+	0.533250i
$581$	−226.615	+	392.509i	−0.390044	+	0.675575i
$582$	−458.717	+	353.364i	−0.788174	+	0.607155i
$583$	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	0.233725	−	0.972303i	$-0.424909\pi$
$587$	700.071	−	404.186i	1.19263	−	0.688563i	0.958901	+	0.283740i	$0.0915753\pi$
$588$	209.984	−	272.882i	0.357115	−	0.464086i
$589$	124.498	−	215.638i	0.211373	−	0.366108i
$590$	145.626	+	550.651i	0.246824	+	0.933306i
$591$	−334.642	+	140.635i	−0.566231	+	0.237960i
$592$	4.62924	+	8.26484i	0.00781966	+	0.0139609i
$593$	−445.123			−0.750628			−0.375314	−	0.926898i	$-0.622465\pi$
$593$	−445.123			−0.750628			−0.375314	+	0.926898i	$0.622465\pi$
$594$	201.745	+	24.0649i	0.339638	+	0.0405133i
$595$			18.8149i			0.0316217i
$596$	318.945	−	181.384i	0.535143	−	0.304336i
$597$	95.5828	+	227.441i	0.160105	+	0.380973i
$598$	−115.361	−	436.209i	−0.192911	−	0.729447i
$599$	−684.932	−	395.445i	−1.14346	−	0.660176i	−0.196174	−	0.980569i	$-0.562852\pi$
$599$	−684.932	−	395.445i	−1.14346	−	0.660176i	−0.947285	+	0.320393i	$0.896185\pi$
$600$	952.292	−	120.894i	1.58715	−	0.201491i
$601$	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
$606$	−205.910	+	158.619i	−0.339785	+	0.261747i
$607$	902.512	+	521.066i	1.48684	+	0.858428i	0.999887	−	0.0150003i	$-0.00477491\pi$
$607$	902.512	+	521.066i	1.48684	+	0.858428i	0.486953	+	0.873428i	$0.338108\pi$
$608$	−127.685	−	509.572i	−0.210009	−	0.838112i
$609$	254.398	+	32.1617i	0.417731	+	0.0528106i
$610$	−285.327	+	1051.15i	−0.467749	+	1.72320i
$611$			427.251i			0.699266i
$612$	−17.9904	+	4.89341i	−0.0293961	+	0.00799576i
$613$	256.336			0.418166			0.209083	−	0.977898i	$-0.432952\pi$
$613$	256.336			0.418166			0.209083	+	0.977898i	$0.432952\pi$
$614$	−501.779	−	136.204i	−0.817229	−	0.221831i
$615$	476.839	+	362.009i	0.775347	+	0.588633i
$616$	−33.8244	−	131.354i	−0.0549098	−	0.213237i
$617$	−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	$0.301449\pi$
$618$	−331.061	+	803.540i	−0.535698	+	1.30023i
$619$	−662.787	+	382.660i	−1.07074	+	0.618191i	−0.928383	−	0.371624i	$-0.878801\pi$
$619$	−662.787	+	382.660i	−1.07074	+	0.618191i	−0.142355	+	0.989816i	$0.545468\pi$
$620$	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
$624$	−313.745	+	127.070i	−0.502796	+	0.203638i
$625$	12.5746	−	21.7799i	0.0201194	−	0.0348479i
$626$	−84.8268	+	22.4335i	−0.135506	+	0.0358362i
$627$	147.587	+	112.046i	0.235386	+	0.178702i
$628$	−785.183	+	446.533i	−1.25029	+	0.711040i
$629$	0.306623			0.000487477
$630$	564.014	−	330.944i	0.895261	−	0.525308i
$631$			719.756i			1.14066i	0.821416	+	0.570330i	$0.193185\pi$
$631$			719.756i			1.14066i	−0.821416	+	0.570330i	$0.806815\pi$
$632$	314.372	−	1129.02i	0.497423	−	1.78642i
$633$	−321.617	−	40.6597i	−0.508084	−	0.0642333i
$634$	266.707	−	70.5338i	0.420673	−	0.111252i
$635$	−68.5084	−	39.5534i	−0.107887	−	0.0622888i
$636$	7.90751	+	1.05205i	0.0124332	+	0.00165417i
$637$	−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	$0.648575\pi$
$642$	−327.012	+	43.6803i	−0.509365	+	0.0680379i
$643$	−507.224	−	292.846i	−0.788841	−	0.455437i	0.0507136	−	0.998713i	$-0.483850\pi$
$643$	−507.224	−	292.846i	−0.788841	−	0.455437i	−0.839554	+	0.543276i	$0.817184\pi$
$644$	497.495	+	291.565i	0.772508	+	0.452741i
$645$	−301.542	−	717.525i	−0.467507	−	1.11244i
$646$	−16.4100	−	4.45437i	−0.0254025	−	0.00689531i
$647$		−	791.553i		−	1.22342i	−0.791082	−	0.611710i	$-0.790482\pi$
$647$		−	791.553i		−	1.22342i	0.791082	−	0.611710i	$-0.209518\pi$
$648$	463.131	+	453.226i	0.714708	+	0.699423i
$649$	−132.909			−0.204791
$650$	147.781	−	544.429i	0.227355	−	0.837583i
$651$	189.033	−	79.4416i	0.290373	−	0.122030i
$652$	−253.169	+	431.980i	−0.388296	+	0.662545i
$653$	−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	$0.263901\pi$
$654$	50.7800	+	380.165i	0.0776453	+	0.581291i
$655$	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	−0.755285	−	0.655397i	$-0.772501\pi$
$659$	−372.557	+	215.096i	−0.565337	+	0.326398i	0.189948	+	0.981794i	$0.439168\pi$
$660$	−48.0057	+	360.824i	−0.0727359	+	0.546703i
$661$	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	$-0.0742456\pi$
$662$	−30.5552	−	115.537i	−0.0461559	−	0.174527i
$663$	−1.37423	+	10.8701i	−0.00207274	+	0.0163953i
$664$	215.834	−	775.134i	0.325051	−	1.16737i
$665$	596.408			0.896854
$666$	−5.39333	−	9.19162i	−0.00809809	−	0.0138012i
$667$		−	606.799i		−	0.909744i
$668$	352.481	+	619.801i	0.527666	+	0.927846i
$669$	296.182	−	390.131i	0.442724	−	0.583156i
$670$	354.493	+	1340.43i	0.529094	+	2.00064i
$671$	−220.106	−	127.078i	−0.328027	−	0.189387i
$672$	169.990	−	397.804i	0.252961	−	0.591970i
$673$	−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	$0.901802\pi$
$678$	−197.760	−	81.4778i	−0.291682	−	0.120174i
$679$	−376.622	−	217.443i	−0.554671	−	0.320239i
$680$	−8.32955	−	32.3470i	−0.0122493	−	0.0475691i
$681$	−20.0399	+	26.3966i	−0.0294272	+	0.0387616i
$682$	−29.8993	+	110.150i	−0.0438407	+	0.161510i
$683$		−	522.729i		−	0.765343i	−0.923884	−	0.382672i	$-0.875004\pi$
$683$		−	522.729i		−	0.765343i	0.923884	−	0.382672i	$-0.124996\pi$
$684$	155.115	+	570.273i	0.226776	+	0.833732i
$685$	−2025.29			−2.95663
$686$	675.763	+	183.431i	0.985077	+	0.267392i
$687$	−12.1705	+	96.2687i	−0.0177155	+	0.140129i
$688$	−442.507	−	263.225i	−0.643179	−	0.382594i
$689$	2.34400	−	4.05992i	0.00340203	−	0.00589248i
$690$	−944.363	−	1225.92i	−1.36864	−	1.77669i
$691$	485.917	−	280.544i	0.703208	−	0.405997i	−0.105333	−	0.994437i	$-0.533591\pi$
$691$	485.917	−	280.544i	0.703208	−	0.405997i	0.808541	+	0.588440i	$0.200258\pi$
$692$	−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
$696$	−451.605	+	57.3317i	−0.648857	+	0.0823731i
$697$	6.40971	−	11.1019i	0.00919614	−	0.0159282i
$698$	255.733	−	67.6316i	0.366379	−	0.0968934i
$699$	500.728	−	210.433i	0.716349	−	0.301048i
$700$	356.403	+	626.699i	0.509148	+	0.895284i
$701$	1203.11			1.71627			0.858137	−	0.513421i	$-0.171622\pi$
$701$	1203.11			1.71627			0.858137	+	0.513421i	$0.171622\pi$
$702$	350.025	−	150.004i	0.498611	−	0.213681i
$703$		−	9.71954i		−	0.0138258i
$704$	116.303	+	210.851i	0.165203	+	0.299505i
$705$	567.713	+	1350.88i	0.805266	+	1.91614i
$706$	1046.28	−	276.701i	1.48198	−	0.391928i
$707$	−169.058	−	97.6059i	−0.239121	−	0.138056i
$708$	−335.946	−	258.511i	−0.474500	−	0.365129i
$709$	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
$714$	−8.54515	−	11.0928i	−0.0119680	−	0.0155362i
$715$	185.257	+	106.958i	0.259100	+	0.149591i
$716$	559.888	−	955.332i	0.781966	−	1.33426i
$717$	136.244	+	17.2243i	0.190019	+	0.0240227i
$718$	565.061	+	153.381i	0.786993	+	0.213623i
$719$			53.0278i			0.0737521i	0.999320	+	0.0368760i	$0.0117407\pi$
$719$			53.0278i			0.0737521i	−0.999320	+	0.0368760i	$0.988259\pi$
$720$	−823.152	+	818.660i	−1.14327	+	1.13703i
$721$	−652.709			−0.905282
$722$	47.9395	−	176.610i	0.0663982	−	0.244613i
$723$	808.656	+	613.920i	1.11847	+	0.849129i
$724$	361.419	+	211.816i	0.499198	+	0.292563i
$725$	379.332	−	657.022i	0.523216	−	0.906238i
$726$	592.726	+	244.205i	0.816427	+	0.336370i
$727$	436.956	−	252.277i	0.601041	−	0.347011i	−0.168410	−	0.985717i	$-0.553863\pi$
$727$	436.956	−	252.277i	0.601041	−	0.347011i	0.769451	+	0.638706i	$0.220530\pi$
$728$	−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
$732$	−309.178	−	749.320i	−0.422375	−	1.02366i
$733$	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	$-0.0227860\pi$
$734$	−223.704	−	845.883i	−0.304774	−	1.15243i
$735$	−552.745	−	419.636i	−0.752034	−	0.570934i
$736$	−984.382	−	281.018i	−1.33748	−	0.381818i
$737$	−323.536			−0.438991
$738$	−445.546	+	3.13335i	−0.603721	+	0.00424573i
$739$		−	190.298i		−	0.257507i	−0.991677	−	0.128754i	$-0.958902\pi$
$739$		−	190.298i		−	0.257507i	0.991677	−	0.128754i	$-0.0410977\pi$
$740$	16.5969	−	9.43862i	0.0224282	−	0.0127549i
$741$	344.568	+	43.5612i	0.465005	+	0.0587870i
$742$	1.53179	+	5.79210i	0.00206441	+	0.00780606i
$743$	664.128	+	383.435i	0.893847	+	0.516063i	0.875199	−	0.483763i	$-0.160730\pi$
$743$	664.128	+	383.435i	0.893847	+	0.516063i	0.0186481	+	0.999826i	$0.494064\pi$
$744$	−289.819	+	220.264i	−0.389541	+	0.296054i
$745$	−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
$750$	−96.0490	−	719.070i	−0.128065	−	0.958760i
$751$	−519.601	−	299.992i	−0.691879	−	0.399456i	0.112437	−	0.993659i	$-0.464134\pi$
$751$	−519.601	−	299.992i	−0.691879	−	0.399456i	−0.804315	+	0.594202i	$0.797468\pi$
$752$	833.107	+	495.573i	1.10785	+	0.659006i
$753$	328.449	+	781.550i	0.436188	+	1.03792i
$754$	−70.0821	+	258.184i	−0.0929471	+	0.342419i
$755$		−	335.335i		−	0.444152i
$756$	−182.225	+	451.274i	−0.241038	+	0.596924i
$757$	−343.082			−0.453213			−0.226606	−	0.973986i	$-0.572763\pi$
$757$	−343.082			−0.453213			−0.226606	+	0.973986i	$0.572763\pi$
$758$	−1045.05	−	283.670i	−1.37869	−	0.374235i
$759$	332.895	−	139.900i	0.438597	−	0.184322i
$760$	−1025.36	+	264.036i	−1.34915	+	0.347416i
$761$	−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	$0.229551\pi$
$762$	58.3549	−	7.79468i	0.0765812	−	0.0102292i
$763$	−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
$768$	−116.139	+	759.168i	−0.151222	+	0.988500i
$769$	−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	$0.959322\pi$
$770$	−264.297	+	69.8965i	−0.343243	+	0.0907747i
$771$	29.2662	−	231.495i	0.0379588	−	0.300253i
$772$	−394.152	+	224.154i	−0.510559	+	0.290355i
$773$	−173.239			−0.224113			−0.112056	−	0.993702i	$-0.535744\pi$
$773$	−173.239			−0.224113			−0.112056	+	0.993702i	$0.535744\pi$
$774$	503.659	+	286.084i	0.650723	+	0.369618i
$775$		−	606.660i		−	0.782787i
$776$	743.759	+	207.097i	0.958452	+	0.266878i
$777$	4.83977	−	6.37495i	0.00622880	−	0.00820457i
$778$	−169.786	+	44.9019i	−0.218233	+	0.0577145i
$779$	−351.917	−	203.179i	−0.451755	−	0.260821i
$780$	260.225	+	630.679i	0.333622	+	0.808562i
$781$	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
$786$	−268.043	+	650.584i	−0.341021	+	0.827715i
$787$	43.1896	+	24.9355i	0.0548788	+	0.0316843i	0.527188	−	0.849748i	$-0.323246\pi$
$787$	43.1896	+	24.9355i	0.0548788	+	0.0316843i	−0.472310	+	0.881433i	$0.656580\pi$
$788$	417.563	+	244.719i	0.529902	+	0.310558i
$789$	408.878	−	538.574i	0.518223	−	0.682603i
$790$	−2279.64	−	618.791i	−2.88562	−	0.783279i
$791$		−	160.639i		−	0.203083i
$792$	−135.572	−	234.536i	−0.171177	−	0.296131i
$793$	−476.369			−0.600717
$794$	−25.3647	+	93.4443i	−0.0319455	+	0.117688i
$795$	2.01659	−	15.9512i	0.00253660	−	0.0200644i
$796$	166.324	−	283.798i	0.208950	−	0.356530i
$797$	−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	$0.943687\pi$
$798$	−351.628	+	270.870i	−0.440637	+	0.339436i
$799$	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
$804$	−817.782	−	629.286i	−1.01714	−	0.782694i
$805$	581.114	−	1006.52i	0.721880	−	1.25033i
$806$	54.6950	+	206.816i	0.0678598	+	0.256595i
$807$	1177.66	−	494.914i	1.45930	−	0.613277i
$808$	333.860	+	92.9621i	0.413193	+	0.115052i
$809$	−637.363			−0.787841			−0.393920	−	0.919145i	$-0.628881\pi$
$809$	−637.363			−0.787841			−0.393920	+	0.919145i	$0.628881\pi$
$810$	907.389	−	939.380i	1.12023	−	1.15973i
$811$			1486.54i			1.83298i	0.400061	+	0.916489i	$0.368989\pi$
$811$			1486.54i			1.83298i	−0.400061	+	0.916489i	$0.631011\pi$
$812$	−169.017	−	297.199i	−0.208149	−	0.366009i
$813$	−65.5144	−	155.893i	−0.0805836	−	0.191750i
$814$	1.13909	+	4.30719i	0.00139937	+	0.00529139i
$815$	873.969	+	504.586i	1.07235	+	0.619124i
$816$	19.6019	+	15.2880i	0.0240219	+	0.0187353i
$817$	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	$0.616071\pi$
$822$	1194.06	−	919.825i	1.45263	−	1.11901i
$823$	278.230	+	160.636i	0.338068	+	0.195184i	0.659417	−	0.751777i	$-0.270803\pi$
$823$	278.230	+	160.636i	0.338068	+	0.195184i	−0.321349	+	0.946961i	$0.604136\pi$
$824$	1122.15	−	288.961i	1.36183	−	0.350680i
$825$	447.905	+	56.6252i	0.542915	+	0.0686366i
$826$	83.3998	−	307.247i	0.100968	−	0.371970i
$827$		−	119.865i		−	0.144939i	−0.997371	−	0.0724695i	$-0.976912\pi$
$827$		−	119.865i		−	0.144939i	0.997371	−	0.0724695i	$-0.0230880\pi$
$828$	1113.55	+	293.872i	1.34486	+	0.354917i
$829$	810.947			0.978223			0.489112	−	0.872221i	$-0.337321\pi$
$829$	810.947			0.978223			0.489112	+	0.872221i	$0.337321\pi$
$830$	−1565.10	−	424.834i	−1.88566	−	0.511848i
$831$	−1001.84	−	760.585i	−1.20559	−	0.915265i
$832$	386.384	+	233.260i	0.464404	+	0.280361i
$833$	−7.43005	+	12.8692i	−0.00891963	+	0.0154492i
$834$	351.209	−	852.442i	0.421114	−	1.02211i
$835$	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	−0.469086	−	0.883152i	$-0.655417\pi$
$839$	51.3491	−	29.6464i	0.0612027	−	0.0353354i	0.530289	+	0.847817i	$0.322083\pi$
$840$	−803.996	−	337.390i	−0.957138	−	0.401655i
$841$	240.610	−	416.748i	0.286100	−	0.495539i
$842$	−370.370	+	97.9488i	−0.439869	+	0.116329i
$843$	−353.462	−	268.343i	−0.419290	−	0.318319i
$844$	213.676	+	375.727i	0.253170	+	0.445174i
$845$	−961.549			−1.13793
$846$	−948.238	−	538.610i	−1.12085	−	0.636655i
$847$			481.466i			0.568437i
$848$	−5.19770	−	9.27974i	−0.00612937	−	0.0109431i
$849$	−789.943	−	99.8666i	−0.930439	−	0.117628i
$850$	−40.0515	+	10.5921i	−0.0471194	+	0.0124613i
$851$	−16.4030	−	9.47029i	−0.0192750	−	0.0111284i
$852$	−89.3267	+	671.405i	−0.104843	+	0.788033i
$853$	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	$-0.465932\pi$
$858$	−157.800	+	21.0779i	−0.183916	+	0.0245663i
$859$	414.983	+	239.591i	0.483101	+	0.278918i	0.721708	−	0.692198i	$-0.243357\pi$
$859$	414.983	+	239.591i	0.483101	+	0.278918i	−0.238607	+	0.971116i	$0.576691\pi$
$860$	−524.716	+	895.319i	−0.610135	+	1.04107i
$861$	−129.647	−	308.498i	−0.150578	−	0.358302i
$862$	928.772	+	252.108i	1.07746	+	0.292469i
$863$		−	4.93230i		−	0.00571530i	−0.999996	−	0.00285765i	$-0.999090\pi$
$863$		−	4.93230i		−	0.00571530i	0.999996	−	0.00285765i	$-0.000909619\pi$
$864$	113.501	−	856.512i	0.131367	−	0.991334i
$865$	1218.83			1.40906
$866$	−188.795	+	695.525i	−0.218008	+	0.803147i
$867$	−798.544	+	335.591i	−0.921043	+	0.387072i
$868$	−235.873	−	138.237i	−0.271743	−	0.159259i
$869$	275.596	−	477.347i	0.317142	−	0.549306i
$870$	121.478	+	909.447i	0.139630	+	1.04534i
$871$	−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
$876$	−1569.22	−	208.776i	−1.79135	−	0.238329i
$877$	−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	$0.760095\pi$
$878$	288.298	+	1090.13i	0.328357	+	1.24160i
$879$	93.9506	−	743.147i	0.106883	−	0.845446i
$880$	423.440	−	237.174i	0.481182	−	0.269516i
$881$	830.879			0.943109			0.471555	−	0.881837i	$-0.343693\pi$
$881$	830.879			0.943109			0.471555	+	0.881837i	$0.343693\pi$
$882$	516.471	−	3.63213i	0.585568	−	0.00411807i
$883$		−	1228.46i		−	1.39123i	−0.718414	−	0.695615i	$-0.755132\pi$
$883$		−	1228.46i		−	1.39123i	0.718414	−	0.695615i	$-0.244868\pi$
$884$	12.6989	−	7.22188i	0.0143653	−	0.00816954i
$885$	−516.615	+	680.486i	−0.583746	+	0.768910i
$886$	336.507	+	1272.42i	0.379805	+	1.43614i
$887$	−660.079	−	381.097i	−0.744170	−	0.429647i	0.0794134	−	0.996842i	$-0.474695\pi$
$887$	−660.079	−	381.097i	−0.744170	−	0.429647i	−0.823584	+	0.567195i	$0.808029\pi$
$888$	−5.49838	+	13.1026i	−0.00619187	+	0.0147551i
$889$	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
$894$	508.874	+	209.658i	0.569210	+	0.234516i
$895$	−1932.80	−	1115.90i	−2.15955	−	1.24682i
$896$	−560.406	+	136.551i	−0.625453	+	0.152400i
$897$	409.247	−	539.061i	0.456240	−	0.600960i
$898$	119.229	−	439.244i	0.132772	−	0.489136i
$899$			287.696i			0.320018i
$900$	1022.00	+	1014.31i	1.13556	+	1.12701i
$901$	−0.344275			−0.000382104
$902$	179.763	+	48.7952i	0.199294	+	0.0540967i
$903$	−54.5638	+	431.598i	−0.0604250	+	0.477961i
$904$	71.1164	+	276.173i	0.0786686	+	0.305502i
$905$	422.166	−	731.214i	0.466482	−	0.807971i
$906$	152.299	+	197.705i	0.168100	+	0.218218i
$907$	−324.076	+	187.106i	−0.357306	+	0.206291i	−0.667898	−	0.744253i	$-0.732806\pi$
$907$	−324.076	+	187.106i	−0.357306	+	0.206291i	0.310592	+	0.950543i	$0.399473\pi$
$908$	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	0.395918	−	0.918286i	$-0.370426\pi$
$911$	1265.50	−	730.639i	1.38914	−	0.802018i	0.993218	+	0.116268i	$0.0370930\pi$
$912$	484.609	−	621.354i	0.531369	−	0.681309i
$913$	189.212	−	327.725i	0.207242	−	0.358954i
$914$	−1387.80	+	367.021i	−1.51838	+	0.401555i
$915$	−1506.18	+	632.978i	−1.64610	+	0.691779i
$916$	112.465	−	63.9589i	0.122779	−	0.0698241i
$917$	−528.464			−0.576296
$918$	−22.3926	−	16.7532i	−0.0243928	−	0.0182497i
$919$			1112.72i			1.21080i	0.795923	+	0.605398i	$0.206986\pi$
$919$			1112.72i			1.21080i	−0.795923	+	0.605398i	$0.793014\pi$
$920$	−553.466	+	1987.69i	−0.601593	+	2.16053i
$921$	−302.159	−	718.993i	−0.328077	−	0.780665i
$922$	−776.787	+	205.431i	−0.842502	+	0.222810i
$923$	344.717	+	199.022i	0.373474	+	0.215625i
$924$	124.078	−	161.245i	0.134284	−	0.174507i
$925$	−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	$-0.350914\pi$
$930$	447.742	+	581.233i	0.481443	+	0.624981i
$931$	407.938	+	235.523i	0.438171	+	0.252978i
$932$	−624.802	−	366.175i	−0.670389	−	0.392892i
$933$	57.0358	+	7.21061i	0.0611317	+	0.00772842i
$934$	394.514	+	107.088i	0.422392	+	0.114655i
$935$		−	15.7095i		−	0.0168016i
$936$	−439.857	−	253.647i	−0.469933	−	0.270990i
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$	203.017	−	747.921i	0.216436	−	0.797357i
$939$	−104.828	−	79.5837i	−0.111638	−	0.0847537i
$940$	987.882	−	1685.61i	1.05094	−	1.79321i
$941$	−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	$0.217943\pi$
$942$	−1252.75	−	516.138i	−1.32989	−	0.547917i
$943$	−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	−0.833238	−	0.552914i	$-0.813516\pi$
$947$	−730.155	+	421.555i	−0.771019	+	0.445148i	0.0622189	+	0.998063i	$0.480182\pi$
$948$	1625.06	−	670.517i	1.71419	−	0.707297i
$949$	−465.159	+	805.679i	−0.490157	+	0.848977i
$950$	335.756	+	1269.58i	0.353427	+	1.33640i
$951$	329.592	+	250.222i	0.346574	+	0.263114i
$952$	−5.00808	+	17.9858i	−0.00526059	+	0.0188926i
$953$	306.171			0.321270			0.160635	−	0.987014i	$-0.448646\pi$
$953$	306.171			0.321270			0.160635	+	0.987014i	$0.448646\pi$
$954$	6.05562	+	10.3203i	0.00634761	+	0.0108180i
$955$			1796.44i			1.88109i
$956$	−90.5175	−	159.166i	−0.0946835	−	0.166491i
$957$	−212.409	−	26.8533i	−0.221953	−	0.0280599i
$958$	46.3236	+	175.162i	0.0483545	+	0.182841i
$959$	980.365	+	566.014i	1.02228	+	0.590213i
$960$	1531.61	+	224.111i	1.59543	+	0.233449i
$961$	−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
$966$	114.519	+	857.343i	0.118549	+	0.887518i
$967$	103.822	+	59.9417i	0.107365	+	0.0619873i	0.552721	−	0.833366i	$-0.313590\pi$
$967$	103.822	+	59.9417i	0.107365	+	0.0619873i	−0.445356	+	0.895354i	$0.646923\pi$
$968$	−213.150	−	827.745i	−0.220196	−	0.855109i
$969$	−9.88171	−	23.5137i	−0.0101978	−	0.0242659i
$970$	407.638	−	1501.75i	0.420246	−	1.54820i
$971$			62.7602i			0.0646346i	0.999478	+	0.0323173i	$0.0102887\pi$
$971$			62.7602i			0.0646346i	−0.999478	+	0.0323173i	$0.989711\pi$
$972$	−108.337	+	965.944i	−0.111458	+	0.993769i
$973$	692.431			0.711646
$974$	581.535	+	157.853i	0.597058	+	0.162067i
$975$	780.105	−	327.842i	0.800108	−	0.336248i
$976$	−552.545	+	928.882i	−0.566132	+	0.951723i
$977$	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	$-0.0513728\pi$
$978$	−744.439	+	99.4376i	−0.761185	+	0.101674i
$979$	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	−0.728343	−	0.685213i	$-0.759709\pi$
$983$	−490.618	+	283.258i	−0.499103	+	0.288157i	0.229240	+	0.973370i	$0.426376\pi$
$984$	359.467	+	472.979i	0.365312	+	0.480670i
$985$	487.746	−	844.801i	0.495174	−	0.857666i
$986$	18.9936	−	5.02308i	0.0192633	−	0.00509441i
$987$	102.727	−	812.569i	0.104080	−	0.823272i
$988$	−228.924	−	402.540i	−0.231705	−	0.407429i
$989$	1029.46			1.04091
$990$	−470.923	+	276.321i	−0.475680	+	0.279112i
$991$		−	457.774i		−	0.461931i	−0.972962	−	0.230966i	$-0.925812\pi$
$991$		−	457.774i		−	0.461931i	0.972962	−	0.230966i	$-0.0741885\pi$
$992$	466.716	+	133.237i	0.470479	+	0.134311i
$993$	108.396	−	142.779i	0.109160	−	0.143786i
$994$	−491.791	+	130.060i	−0.494759	+	0.130845i
$995$	−574.172	−	331.498i	−0.577057	−	0.333164i
$996$	1115.69	−	460.348i	1.12017	−	0.462196i
$997$	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.31.5	yes	16
3.2	odd	2		108.3.f.c.91.4		16
4.3	odd	2	inner	36.3.f.c.31.1	yes	16
8.3	odd	2		576.3.o.g.319.8		16
8.5	even	2		576.3.o.g.319.1		16
9.2	odd	6		108.3.f.c.19.8		16
9.4	even	3		324.3.d.i.163.6		8
9.5	odd	6		324.3.d.g.163.3		8
9.7	even	3	inner	36.3.f.c.7.1	✓	16
12.11	even	2		108.3.f.c.91.8		16
24.5	odd	2		1728.3.o.g.1279.2		16
24.11	even	2		1728.3.o.g.1279.1		16
36.7	odd	6	inner	36.3.f.c.7.5	yes	16
36.11	even	6		108.3.f.c.19.4		16
36.23	even	6		324.3.d.g.163.4		8
36.31	odd	6		324.3.d.i.163.5		8
72.11	even	6		1728.3.o.g.127.2		16
72.29	odd	6		1728.3.o.g.127.1		16
72.43	odd	6		576.3.o.g.511.1		16
72.61	even	6		576.3.o.g.511.8		16

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

\(f(q)\)	\(=\)	\(q+(0.523926 - 1.93016i) q^{2} +(2.76570 - 1.16229i) q^{3} +(-3.45100 - 2.02252i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(-0.794388 - 5.94718i) q^{6} +(3.90254 - 2.25313i) q^{7} +(-5.71184 + 5.60133i) q^{8} +(6.29815 - 6.42910i) q^{9} +O(q^{10})\)	\(q+(0.523926 - 1.93016i) q^{2} +(2.76570 - 1.16229i) q^{3} +(-3.45100 - 2.02252i) q^{4} +(-4.03104 + 6.98197i) q^{5} +(-0.794388 - 5.94718i) 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} +(-11.8952 - 1.58259i) q^{12} +(-3.52605 + 6.10730i) q^{13} +(-2.30426 - 8.71299i) q^{14} +(-3.03354 + 23.9953i) q^{15} +(7.81885 + 13.9594i) q^{16} +0.517890 q^{17} +(-9.10940 - 15.5248i) q^{18} -16.4164i q^{19} +(28.0323 - 15.9420i) q^{20} +(8.17444 - 10.7674i) q^{21} +(1.92394 + 7.27490i) q^{22} +(-27.7049 - 15.9954i) q^{23} +(-9.28684 + 22.1304i) 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} +(44.7253 + 18.4270i) q^{30} +(13.1355 + 7.58377i) q^{31} +(31.0404 - 7.77790i) q^{32} +(-6.82524 + 8.99021i) q^{33} +(0.271336 - 0.999608i) q^{34} +36.3299i q^{35} +(-34.7379 + 9.44873i) q^{36} +0.592061 q^{37} +(-31.6863 - 8.60099i) q^{38} +(-2.65351 + 20.9892i) q^{39} +(-16.0836 - 62.4591i) q^{40} +(12.3766 - 21.4369i) q^{41} +(-16.4999 - 21.4193i) 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} +(37.8495 + 29.5197i) q^{48} +(-14.3468 + 24.8493i) q^{49} +(-77.3358 + 20.4524i) q^{50} +(1.43233 - 0.601940i) q^{51} +(24.5205 - 13.9448i) q^{52} -0.664765 q^{53} +(-43.2382 - 32.3490i) q^{54} -30.3336i q^{55} +(-9.67017 + 34.7290i) q^{56} +(-19.0807 - 45.4029i) q^{57} +(36.6749 - 9.69913i) q^{58} +(30.5921 + 17.6623i) q^{59} +(58.9996 - 76.6724i) 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} +(13.7766 + 17.8840i) q^{66} +(74.4692 + 42.9948i) q^{67} +(-1.78724 - 1.04744i) q^{68} +(-95.2148 - 12.0373i) q^{69} +(70.1224 + 19.0342i) q^{70} -56.4434i q^{71} +(0.0374515 + 72.0000i) q^{72} +131.921 q^{73} +(0.310196 - 1.14277i) q^{74} +(-95.5705 - 72.5557i) q^{75} +(-33.2025 + 56.6532i) q^{76} +(-8.47743 + 14.6833i) q^{77} +(39.1222 + 16.1185i) 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} +(-49.9873 + 20.6253i) q^{84} +(-2.08764 + 3.61589i) q^{85} +(16.4550 + 62.2207i) q^{86} +(45.3223 + 34.4081i) q^{87} +(8.07410 - 28.9969i) q^{88} -25.8362 q^{89} +(145.114 - 1.02053i) q^{90} +31.7786i q^{91} +(63.2587 + 111.234i) q^{92} +(45.1433 + 5.70713i) q^{93} +(-30.9798 - 117.143i) q^{94} +(114.619 + 66.1754i) q^{95} +(76.8080 - 57.5893i) 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

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