LMFDB - Embedded newform 36.3.f.c.7.7

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			7.7
Root			$-1.26364 + 1.55023i$ of defining polynomial
Character	$\chi$	$=$	36.7
Dual form			36.3.f.c.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26364 - 1.55023i) q^{2} +(-2.32245 - 1.89900i) q^{3} +(-0.806428 - 3.91787i) q^{4} +(1.35609 + 2.34881i) q^{5} +(-5.87864 + 1.20068i) q^{6} +(10.0431 + 5.79837i) q^{7} +(-7.09263 - 3.70062i) q^{8} +(1.78756 + 8.82069i) q^{9} +O(q^{10})$	\(q+(1.26364 - 1.55023i) q^{2} +(-2.32245 - 1.89900i) q^{3} +(-0.806428 - 3.91787i) q^{4} +(1.35609 + 2.34881i) q^{5} +(-5.87864 + 1.20068i) q^{6} +(10.0431 + 5.79837i) q^{7} +(-7.09263 - 3.70062i) q^{8} +(1.78756 + 8.82069i) q^{9} +(5.35481 + 0.865806i) q^{10} +(-8.54822 - 4.93532i) q^{11} +(-5.56715 + 10.6305i) q^{12} +(0.296185 + 0.513008i) q^{13} +(21.6796 - 8.24203i) q^{14} +(1.31096 - 8.03023i) q^{15} +(-14.6993 + 6.31895i) q^{16} -8.87968 q^{17} +(15.9329 + 8.37504i) q^{18} +14.0989i q^{19} +(8.10875 - 7.20712i) q^{20} +(-12.3134 - 32.5383i) q^{21} +(-18.4528 + 7.01525i) q^{22} +(-18.2754 + 10.5513i) q^{23} +(9.44479 + 22.0635i) q^{24} +(8.82205 - 15.2802i) q^{25} +(1.16955 + 0.189102i) q^{26} +(12.5990 - 23.8802i) q^{27} +(14.6182 - 44.0234i) q^{28} +(10.1764 - 17.6260i) q^{29} +(-10.7921 - 12.1796i) q^{30} +(14.3357 - 8.27670i) q^{31} +(-8.77885 + 30.7723i) q^{32} +(10.4806 + 27.6952i) q^{33} +(-11.2207 + 13.7655i) q^{34} +31.4524i q^{35} +(33.1167 - 14.1167i) q^{36} -40.6557 q^{37} +(21.8565 + 17.8159i) q^{38} +(0.286328 - 1.75389i) q^{39} +(-0.926156 - 21.6776i) q^{40} +(21.2177 + 36.7502i) q^{41} +(-66.0016 - 22.0280i) q^{42} +(-32.2385 - 18.6129i) q^{43} +(-12.4424 + 37.4708i) q^{44} +(-18.2941 + 16.1603i) q^{45} +(-6.73658 + 41.6642i) q^{46} +(1.57134 + 0.907211i) q^{47} +(46.1382 + 13.2387i) q^{48} +(42.7423 + 74.0318i) q^{49} +(-12.5400 - 32.9849i) q^{50} +(20.6226 + 16.8625i) q^{51} +(1.77105 - 1.57412i) q^{52} -21.1005 q^{53} +(-21.0992 - 49.7074i) q^{54} -26.7709i q^{55} +(-49.7742 - 78.2914i) q^{56} +(26.7738 - 32.7440i) q^{57} +(-14.4651 - 38.0487i) q^{58} +(76.6879 - 44.2758i) q^{59} +(-32.5185 + 1.33964i) q^{60} +(36.4925 - 63.2069i) q^{61} +(5.28433 - 32.6823i) q^{62} +(-33.1930 + 98.9519i) q^{63} +(36.6108 + 52.4943i) q^{64} +(-0.803307 + 1.39137i) q^{65} +(56.1776 + 18.7493i) q^{66} +(-38.3110 + 22.1189i) q^{67} +(7.16082 + 34.7894i) q^{68} +(62.4808 + 10.2002i) q^{69} +(48.7585 + 39.7446i) q^{70} -111.798i q^{71} +(19.9635 - 69.1770i) q^{72} -76.2003 q^{73} +(-51.3742 + 63.0257i) q^{74} +(-49.5060 + 18.7345i) q^{75} +(55.2375 - 11.3697i) q^{76} +(-57.2337 - 99.1316i) q^{77} +(-2.35712 - 2.66017i) q^{78} +(-8.30434 - 4.79451i) q^{79} +(-34.7757 - 25.9570i) q^{80} +(-74.6092 + 31.5351i) q^{81} +(83.7828 + 13.5466i) q^{82} +(73.6244 + 42.5070i) q^{83} +(-117.551 + 74.4821i) q^{84} +(-12.0416 - 20.8567i) q^{85} +(-69.5921 + 26.4571i) q^{86} +(-57.1060 + 21.6106i) q^{87} +(42.3656 + 66.6381i) q^{88} +64.7845 q^{89} +(1.93506 + 48.7808i) q^{90} +6.86958i q^{91} +(56.0765 + 63.0918i) q^{92} +(-49.0114 - 8.00125i) q^{93} +(3.39199 - 1.28954i) q^{94} +(-33.1157 + 19.1193i) q^{95} +(78.8251 - 54.7960i) q^{96} +(-3.59139 + 6.22047i) q^{97} +(168.777 + 27.2892i) q^{98} +(28.2524 - 84.2235i) 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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.26364	−	1.55023i	0.631820	−	0.775115i
$2$	1.26364	−	1.55023i	0.631820	−	0.775115i
$3$	−2.32245	−	1.89900i	−0.774151	−	0.633001i
$3$	−2.32245	−	1.89900i	−0.774151	−	0.633001i
$4$	−0.806428	−	3.91787i	−0.201607	−	0.979467i
$5$	1.35609	+	2.34881i	0.271218	+	0.469763i	0.969174	−	0.246378i	$-0.0792403\pi$
$5$	1.35609	+	2.34881i	0.271218	+	0.469763i	−0.697956	+	0.716140i	$0.745907\pi$
$6$	−5.87864	+	1.20068i	−0.979773	+	0.200113i
$7$	10.0431	+	5.79837i	1.43473	+	0.828339i	0.997476	−	0.0710013i	$-0.0226195\pi$
$7$	10.0431	+	5.79837i	1.43473	+	0.828339i	0.437249	+	0.899340i	$0.355953\pi$
$8$	−7.09263	−	3.70062i	−0.886579	−	0.462578i
$9$	1.78756	+	8.82069i	0.198618	+	0.980077i
$10$	5.35481	+	0.865806i	0.535481	+	0.0865806i
$11$	−8.54822	−	4.93532i	−0.777111	−	0.448665i	0.0582943	−	0.998299i	$-0.481434\pi$
$11$	−8.54822	−	4.93532i	−0.777111	−	0.448665i	−0.835406	+	0.549634i	$0.814767\pi$
$12$	−5.56715	+	10.6305i	−0.463930	+	0.885872i
$13$	0.296185	+	0.513008i	0.0227835	+	0.0394622i	0.877192	−	0.480139i	$-0.159414\pi$
$13$	0.296185	+	0.513008i	0.0227835	+	0.0394622i	−0.854409	+	0.519601i	$0.826080\pi$
$14$	21.6796	−	8.24203i	1.54855	−	0.588716i
$15$	1.31096	−	8.03023i	0.0873972	−	0.535348i
$16$	−14.6993	+	6.31895i	−0.918709	+	0.394935i
$17$	−8.87968			−0.522334			−0.261167	−	0.965294i	$-0.584107\pi$
$17$	−8.87968			−0.522334			−0.261167	+	0.965294i	$0.584107\pi$
$18$	15.9329	+	8.37504i	0.885163	+	0.465280i
$19$			14.0989i			0.742046i	0.928624	+	0.371023i	$0.120993\pi$
$19$			14.0989i			0.742046i	−0.928624	+	0.371023i	$0.879007\pi$
$20$	8.10875	−	7.20712i	0.405438	−	0.360356i
$21$	−12.3134	−	32.5383i	−0.586354	−	1.54944i
$22$	−18.4528	+	7.01525i	−0.838762	+	0.318875i
$23$	−18.2754	+	10.5513i	−0.794583	+	0.458753i	−0.841574	−	0.540142i	$-0.818370\pi$
$23$	−18.2754	+	10.5513i	−0.794583	+	0.458753i	0.0469902	+	0.998895i	$0.485037\pi$
$24$	9.44479	+	22.0635i	0.393533	+	0.919311i
$25$	8.82205	−	15.2802i	0.352882	−	0.611209i
$26$	1.16955	+	0.189102i	0.0449828	+	0.00727316i
$27$	12.5990	−	23.8802i	0.466630	−	0.884453i
$28$	14.6182	−	44.0234i	0.522080	−	1.57226i
$29$	10.1764	−	17.6260i	0.350910	−	0.607793i	−0.635499	−	0.772101i	$-0.719206\pi$
$29$	10.1764	−	17.6260i	0.350910	−	0.607793i	0.986409	+	0.164308i	$0.0525391\pi$
$30$	−10.7921	−	12.1796i	−0.359737	−	0.405987i
$31$	14.3357	−	8.27670i	0.462441	−	0.266990i	−0.250629	−	0.968083i	$-0.580638\pi$
$31$	14.3357	−	8.27670i	0.462441	−	0.266990i	0.713070	+	0.701093i	$0.247304\pi$
$32$	−8.77885	+	30.7723i	−0.274339	+	0.961633i
$33$	10.4806	+	27.6952i	0.317595	+	0.839247i
$34$	−11.2207	+	13.7655i	−0.330021	+	0.404869i
$35$			31.4524i			0.898641i
$36$	33.1167	−	14.1167i	0.919910	−	0.392130i
$37$	−40.6557			−1.09880			−0.549401	−	0.835559i	$-0.685144\pi$
$37$	−40.6557			−1.09880			−0.549401	+	0.835559i	$0.685144\pi$
$38$	21.8565	+	17.8159i	0.575171	+	0.468840i
$39$	0.286328	−	1.75389i	0.00734176	−	0.0449716i
$40$	−0.926156	−	21.6776i	−0.0231539	−	0.541941i
$41$	21.2177	+	36.7502i	0.517506	+	0.896346i	0.999793	+	0.0203330i	$0.00647263\pi$
$41$	21.2177	+	36.7502i	0.517506	+	0.896346i	−0.482288	+	0.876013i	$0.660194\pi$
$42$	−66.0016	−	22.0280i	−1.57147	−	0.524477i
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	0.0758649	−	0.997118i	$-0.475828\pi$
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	−0.825597	+	0.564260i	$0.809162\pi$
$44$	−12.4424	+	37.4708i	−0.282782	+	0.851609i
$45$	−18.2941	+	16.1603i	−0.406535	+	0.359118i
$46$	−6.73658	+	41.6642i	−0.146447	+	0.905743i
$47$	1.57134	+	0.907211i	0.0334327	+	0.0193024i	0.516623	−	0.856213i	$-0.327189\pi$
$47$	1.57134	+	0.907211i	0.0334327	+	0.0193024i	−0.483191	+	0.875515i	$0.660522\pi$
$48$	46.1382	+	13.2387i	0.961213	+	0.275805i
$49$	42.7423	+	74.0318i	0.872291	+	1.51085i
$50$	−12.5400	−	32.9849i	−0.250800	−	0.659698i
$51$	20.6226	+	16.8625i	0.404365	+	0.330638i
$52$	1.77105	−	1.57412i	0.0340586	−	0.0302715i
$53$	−21.1005			−0.398122			−0.199061	−	0.979987i	$-0.563789\pi$
$53$	−21.1005			−0.398122			−0.199061	+	0.979987i	$0.563789\pi$
$54$	−21.0992	−	49.7074i	−0.390727	−	0.920507i
$55$		−	26.7709i		−	0.486744i
$56$	−49.7742	−	78.2914i	−0.888826	−	1.39806i
$57$	26.7738	−	32.7440i	0.469716	−	0.574456i
$58$	−14.4651	−	38.0487i	−0.249398	−	0.656011i
$59$	76.6879	−	44.2758i	1.29980	−	0.750437i	0.319427	−	0.947611i	$-0.396510\pi$
$59$	76.6879	−	44.2758i	1.29980	−	0.750437i	0.980369	+	0.197174i	$0.0631764\pi$
$60$	−32.5185	+	1.33964i	−0.541976	+	0.0223273i
$61$	36.4925	−	63.2069i	0.598238	−	1.03618i	−0.394843	−	0.918749i	$-0.629201\pi$
$61$	36.4925	−	63.2069i	0.598238	−	1.03618i	0.993081	−	0.117431i	$-0.0374657\pi$
$62$	5.28433	−	32.6823i	0.0852311	−	0.527134i
$63$	−33.1930	+	98.9519i	−0.526873	+	1.57066i
$64$	36.6108	+	52.4943i	0.572043	+	0.820223i
$65$	−0.803307	+	1.39137i	−0.0123586	+	0.0214057i
$66$	56.1776	+	18.7493i	0.851176	+	0.284080i
$67$	−38.3110	+	22.1189i	−0.571807	+	0.330133i	−0.757871	−	0.652405i	$-0.773760\pi$
$67$	−38.3110	+	22.1189i	−0.571807	+	0.330133i	0.186064	+	0.982538i	$0.440427\pi$
$68$	7.16082	+	34.7894i	0.105306	+	0.511609i
$69$	62.4808	+	10.2002i	0.905519	+	0.147829i
$70$	48.7585	+	39.7446i	0.696550	+	0.567779i
$71$		−	111.798i		−	1.57462i	−0.616557	−	0.787310i	$-0.711473\pi$
$71$		−	111.798i		−	1.57462i	0.616557	−	0.787310i	$-0.288527\pi$
$72$	19.9635	−	69.1770i	0.277271	−	0.960792i
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$	−51.3742	+	63.0257i	−0.694246	+	0.851699i
$75$	−49.5060	+	18.7345i	−0.660080	+	0.249793i
$76$	55.2375	−	11.3697i	0.726810	−	0.149602i
$77$	−57.2337	−	99.1316i	−0.743294	−	1.28742i
$78$	−2.35712	−	2.66017i	−0.0302195	−	0.0341047i
$79$	−8.30434	−	4.79451i	−0.105118	−	0.0606901i	0.446519	−	0.894774i	$-0.352663\pi$
$79$	−8.30434	−	4.79451i	−0.105118	−	0.0606901i	−0.551637	+	0.834084i	$0.685997\pi$
$80$	−34.7757	−	25.9570i	−0.434696	−	0.324462i
$81$	−74.6092	+	31.5351i	−0.921102	+	0.389322i
$82$	83.7828	+	13.5466i	1.02174	+	0.165203i
$83$	73.6244	+	42.5070i	0.887041	+	0.512133i	0.872973	−	0.487768i	$-0.162189\pi$
$83$	73.6244	+	42.5070i	0.887041	+	0.512133i	0.0140672	+	0.999901i	$0.495522\pi$
$84$	−117.551	+	74.4821i	−1.39941	+	0.886692i
$85$	−12.0416	−	20.8567i	−0.141666	−	0.245373i
$86$	−69.5921	+	26.4571i	−0.809211	+	0.307640i
$87$	−57.1060	+	21.6106i	−0.656391	+	0.248397i
$88$	42.3656	+	66.6381i	0.481428	+	0.757252i
$89$	64.7845			0.727916			0.363958	−	0.931415i	$-0.381425\pi$
$89$	64.7845			0.727916			0.363958	+	0.931415i	$0.381425\pi$
$90$	1.93506	+	48.7808i	0.0215007	+	0.542009i
$91$			6.86958i			0.0754898i
$92$	56.0765	+	63.0918i	0.609527	+	0.685780i
$93$	−49.0114	−	8.00125i	−0.527004	−	0.0860350i
$94$	3.39199	−	1.28954i	0.0360850	−	0.0137186i
$95$	−33.1157	+	19.1193i	−0.348586	+	0.201256i
$96$	78.8251	−	54.7960i	0.821095	−	0.570792i
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	−0.883944	−	0.467593i	$-0.845121\pi$
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	0.846919	+	0.531721i	$0.178455\pi$
$98$	168.777	+	27.2892i	1.72222	+	0.278461i
$99$	28.2524	−	84.2235i	0.285378	−	0.850742i
$100$	−66.9803	−	22.2412i	−0.669803	−	0.222412i
$101$	−55.5037	+	96.1353i	−0.549542	+	0.951834i	0.448764	+	0.893650i	$0.351864\pi$
$101$	−55.5037	+	96.1353i	−0.549542	+	0.951834i	−0.998306	+	0.0581840i	$0.981469\pi$
$102$	52.2004	−	10.6616i	0.511769	−	0.104526i
$103$	79.6133	−	45.9648i	0.772945	−	0.446260i	−0.0609793	−	0.998139i	$-0.519422\pi$
$103$	79.6133	−	45.9648i	0.772945	−	0.446260i	0.833924	+	0.551879i	$0.186089\pi$
$104$	−0.202283	−	4.73465i	−0.00194503	−	0.0455255i
$105$	59.7283	−	73.0468i	0.568841	−	0.695683i
$106$	−26.6634	+	32.7106i	−0.251541	+	0.308590i
$107$			107.741i			1.00693i	0.864016	+	0.503465i	$0.167942\pi$
$107$			107.741i			1.00693i	−0.864016	+	0.503465i	$0.832058\pi$
$108$	−103.720	−	30.1035i	−0.960368	−	0.278736i
$109$	86.5562			0.794093			0.397047	−	0.917798i	$-0.370035\pi$
$109$	86.5562			0.794093			0.397047	+	0.917798i	$0.370035\pi$
$110$	−41.5011	−	33.8288i	−0.377283	−	0.307535i
$111$	94.4209	+	77.2054i	0.850639	+	0.695544i
$112$	−184.266	−	21.7706i	−1.64524	−	0.194380i
$113$	−2.35198	−	4.07376i	−0.0208140	−	0.0360509i	0.855431	−	0.517917i	$-0.173292\pi$
$113$	−2.35198	−	4.07376i	−0.0208140	−	0.0360509i	−0.876245	+	0.481866i	$0.839959\pi$
$114$	−16.9282	−	82.8822i	−0.148493	−	0.727037i
$115$	−49.5662	−	28.6170i	−0.431010	−	0.248844i
$116$	−77.2628	−	25.6556i	−0.666059	−	0.221169i
$117$	−3.99564	+	3.52960i	−0.0341507	+	0.0301675i
$118$	28.2682	−	174.833i	0.239561	−	1.48163i
$119$	−89.1793	−	51.4877i	−0.749406	−	0.432670i
$120$	−39.0150	+	52.1041i	−0.325125	+	0.434200i
$121$	−11.7852	−	20.4126i	−0.0973987	−	0.168700i
$122$	−51.8719	−	136.443i	−0.425179	−	1.11838i
$123$	20.5116	−	125.643i	0.166761	−	1.02149i
$124$	−43.9877	−	49.4906i	−0.354739	−	0.399118i
$125$	115.658			0.925267
$126$	111.454	+	176.496i	0.884557	+	1.40076i
$127$			8.37118i			0.0659148i	0.999457	+	0.0329574i	$0.0104926\pi$
$127$			8.37118i			0.0659148i	−0.999457	+	0.0329574i	$0.989507\pi$
$128$	127.641	+	9.57876i	0.997196	+	0.0748341i
$129$	39.5264	+	104.449i	0.306406	+	0.809679i
$130$	1.14185	+	3.00350i	0.00878347	+	0.0231039i
$131$	−115.067	+	66.4338i	−0.878372	+	0.507129i	−0.870121	−	0.492837i	$-0.835960\pi$
$131$	−115.067	+	66.4338i	−0.878372	+	0.507129i	−0.00825098	+	0.999966i	$0.502626\pi$
$132$	100.054	−	63.3959i	0.757985	−	0.480272i
$133$	−81.7506	+	141.596i	−0.614666	+	1.06463i
$134$	−14.1220	+	87.3413i	−0.105388	+	0.651800i
$135$	73.1756	−	2.79099i	0.542041	−	0.0206740i
$136$	62.9803	+	32.8603i	0.463090	+	0.241620i
$137$	22.5579	−	39.0715i	0.164656	−	0.285193i	−0.771877	−	0.635772i	$-0.780682\pi$
$137$	22.5579	−	39.0715i	0.164656	−	0.285193i	0.936533	+	0.350579i	$0.114015\pi$
$138$	94.7658	−	83.9702i	0.686709	−	0.608480i
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.890149	−	0.455670i	$-0.849400\pi$
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.0504522	+	0.998726i	$0.516066\pi$
$140$	123.226	−	25.3641i	0.880189	−	0.181172i
$141$	−1.92655	−	5.09093i	−0.0136635	−	0.0361059i
$142$	−173.313	−	141.273i	−1.22051	−	0.994877i
$143$		−	5.84708i		−	0.0408887i
$144$	−82.0136	−	118.363i	−0.569539	−	0.821965i
$145$	55.2003			0.380692
$146$	−96.2897	+	118.128i	−0.659519	+	0.809096i
$147$	41.3198	−	253.103i	0.281087	−	1.72179i
$148$	32.7859	+	159.284i	0.221526	+	1.07624i
$149$	71.3914	+	123.653i	0.479137	+	0.829889i	0.999714	−	0.0239255i	$-0.00761646\pi$
$149$	71.3914	+	123.653i	0.479137	+	0.829889i	−0.520577	+	0.853815i	$0.674283\pi$
$150$	−33.5150	+	100.419i	−0.223433	+	0.669463i
$151$	220.027	+	127.033i	1.45713	+	0.841276i	0.998869	−	0.0475407i	$-0.0151384\pi$
$151$	220.027	+	127.033i	1.45713	+	0.841276i	0.458263	+	0.888817i	$0.348472\pi$
$152$	52.1746	−	99.9981i	0.343254	−	0.657882i
$153$	−15.8730	−	78.3249i	−0.103745	−	0.511927i
$154$	−226.000	−	36.5413i	−1.46753	−	0.237281i
$155$	38.8808	+	22.4479i	0.250844	+	0.144825i
$156$	−7.10243	+	0.292593i	−0.0455284	+	0.00187559i
$157$	2.65361	+	4.59618i	0.0169020	+	0.0292751i	0.874353	−	0.485291i	$-0.161286\pi$
$157$	2.65361	+	4.59618i	0.0169020	+	0.0292751i	−0.857451	+	0.514566i	$0.827953\pi$
$158$	−17.9263	+	6.81510i	−0.113458	+	0.0431336i
$159$	49.0048	+	40.0698i	0.308206	+	0.252012i
$160$	−84.1832	+	21.1100i	−0.526145	+	0.131938i
$161$	−244.722			−1.52001
$162$	−45.3925	+	155.511i	−0.280201	+	0.959941i
$163$			59.5534i			0.365359i	0.983173	+	0.182679i	$0.0584770\pi$
$163$			59.5534i			0.365359i	−0.983173	+	0.182679i	$0.941523\pi$
$164$	126.872	−	112.765i	0.773608	−	0.687589i
$165$	−50.8381	+	62.1742i	−0.308110	+	0.376813i
$166$	158.930	−	60.4211i	0.957412	−	0.363983i
$167$	−85.7434	+	49.5040i	−0.513434	+	0.296431i	−0.734244	−	0.678886i	$-0.762463\pi$
$167$	−85.7434	+	49.5040i	−0.513434	+	0.296431i	0.220810	+	0.975317i	$0.429130\pi$
$168$	−33.0774	+	276.349i	−0.196889	+	1.64494i
$169$	84.3245	−	146.054i	0.498962	−	0.864227i
$170$	−47.5490	−	7.68808i	−0.279700	−	0.0452240i
$171$	−124.362	+	25.2027i	−0.727263	+	0.147384i
$172$	−46.9248	+	141.316i	−0.272819	+	0.821605i
$173$	19.2965	−	33.4225i	0.111540	−	0.193193i	−0.804851	−	0.593477i	$-0.797755\pi$
$173$	19.2965	−	33.4225i	0.111540	−	0.193193i	0.916391	+	0.400283i	$0.131088\pi$
$174$	−38.6601	+	115.835i	−0.222184	+	0.665721i
$175$	177.201	−	102.307i	1.01258	−	0.584612i
$176$	156.839	+	18.5302i	0.891133	+	0.105285i
$177$	−262.184	−	42.8023i	−1.48126	−	0.241821i
$178$	81.8643	−	100.431i	0.459912	−	0.564219i
$179$			36.4264i			0.203499i	0.994810	+	0.101750i	$0.0324441\pi$
$179$			36.4264i			0.203499i	−0.994810	+	0.101750i	$0.967556\pi$
$180$	78.0667	+	58.6416i	0.433704	+	0.325787i
$181$	−18.5921			−0.102719			−0.0513594	−	0.998680i	$-0.516355\pi$
$181$	−18.5921			−0.102719			−0.0513594	+	0.998680i	$0.516355\pi$
$182$	10.6494	+	8.68067i	0.0585133	+	0.0476960i
$183$	−204.782	+	77.4956i	−1.11903	+	0.423473i
$184$	168.667	−	7.20614i	0.916670	−	0.0391638i
$185$	−55.1327	−	95.4927i	−0.298015	−	0.516177i
$186$	−74.3365	+	65.8682i	−0.399659	+	0.354130i
$187$	75.9055	+	43.8240i	0.405912	+	0.234353i
$188$	2.28716	−	6.88788i	0.0121658	−	0.0366377i
$189$	264.999	−	166.777i	1.40211	−	0.882419i
$190$	−12.2069	+	75.4968i	−0.0642468	+	0.397352i
$191$	−244.973	−	141.435i	−1.28258	−	0.740497i	−0.305260	−	0.952269i	$-0.598743\pi$
$191$	−244.973	−	141.435i	−1.28258	−	0.740497i	−0.977319	+	0.211772i	$0.932077\pi$
$192$	14.6601	−	191.439i	0.0763549	−	0.997081i
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	−0.928884	−	0.370372i	$-0.879230\pi$
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	0.143691	−	0.989623i	$-0.454103\pi$
$194$	5.10493	+	13.4279i	0.0263141	+	0.0692160i
$195$	4.50786	−	1.70590i	0.0231172	−	0.00874822i
$196$	255.578	−	227.160i	1.30397	−	1.15898i
$197$	139.184			0.706520			0.353260	−	0.935525i	$-0.385073\pi$
$197$	139.184			0.706520			0.353260	+	0.935525i	$0.385073\pi$
$198$	−94.8649	−	150.226i	−0.479115	−	0.758717i
$199$			11.2337i			0.0564505i	0.999602	+	0.0282253i	$0.00898558\pi$
$199$			11.2337i			0.0564505i	−0.999602	+	0.0282253i	$0.991014\pi$
$200$	−119.118	+	75.7300i	−0.595590	+	0.378650i
$201$	130.979	+	21.3828i	0.651639	+	0.106382i
$202$	78.8951	+	207.524i	0.390570	+	1.02735i
$203$	204.404	−	118.013i	1.00692	−	0.581344i
$204$	49.4345	−	94.3951i	0.242326	−	0.462721i
$205$	−57.5462	+	99.6730i	−0.280713	+	0.486210i
$206$	29.3466	−	181.502i	0.142459	−	0.881077i
$207$	−125.738	−	142.341i	−0.607432	−	0.687636i
$208$	−7.59541	−	5.66930i	−0.0365164	−	0.0272563i
$209$	69.5825	−	120.520i	0.332931	−	0.576653i
$210$	−37.7642	−	184.897i	−0.179830	−	0.880464i
$211$	−112.017	+	64.6728i	−0.530884	+	0.306506i	−0.741376	−	0.671090i	$-0.765827\pi$
$211$	−112.017	+	64.6728i	−0.530884	+	0.306506i	0.210492	+	0.977595i	$0.432493\pi$
$212$	17.0160	+	82.6687i	0.0802641	+	0.389947i
$213$	−212.305	+	259.646i	−0.996737	+	1.21899i
$214$	167.024	+	136.146i	0.780486	+	0.636198i
$215$		−	100.963i		−	0.469595i
$216$	−177.732	+	122.749i	−0.822832	+	0.568284i
$217$	191.966			0.884634
$218$	109.376	−	134.182i	0.501724	−	0.615514i
$219$	176.971	+	144.705i	0.808089	+	0.660752i
$220$	−104.885	+	21.5888i	−0.476749	+	0.0981310i
$221$	−2.63003	−	4.55535i	−0.0119006	−	0.0206124i
$222$	239.000	−	48.8144i	1.07658	−	0.219885i
$223$	−209.210	−	120.787i	−0.938159	−	0.541647i	−0.0487765	−	0.998810i	$-0.515532\pi$
$223$	−209.210	−	120.787i	−0.938159	−	0.541647i	−0.889383	+	0.457163i	$0.848866\pi$
$224$	−266.596	+	258.145i	−1.19016	+	1.15243i
$225$	150.552	+	50.5022i	0.669121	+	0.224454i
$226$	−9.28732	−	1.50164i	−0.0410943	−	0.00664444i
$227$	330.710	+	190.936i	1.45687	+	0.841126i	0.998856	−	0.0478181i	$-0.0152268\pi$
$227$	330.710	+	190.936i	1.45687	+	0.841126i	0.458016	+	0.888944i	$0.348560\pi$
$228$	−149.878	−	78.4907i	−0.657358	−	0.344257i
$229$	74.6642	+	129.322i	0.326044	+	0.564725i	0.981723	−	0.190315i	$-0.0609508\pi$
$229$	74.6642	+	129.322i	0.326044	+	0.564725i	−0.655679	+	0.755040i	$0.727617\pi$
$230$	−106.997	+	40.6773i	−0.465204	+	0.176858i
$231$	−55.3289	+	338.915i	−0.239519	+	1.46717i
$232$	−137.404	+	87.3558i	−0.592261	+	0.376534i
$233$	−218.934			−0.939631			−0.469816	−	0.882765i	$-0.655680\pi$
$233$	−218.934			−0.939631			−0.469816	+	0.882765i	$0.655680\pi$
$234$	0.422640	+	10.6543i	0.00180615	+	0.0455312i
$235$			4.92103i			0.0209406i
$236$	−235.310	−	264.748i	−0.997076	−	1.12181i
$237$	10.1816	+	26.9050i	0.0429605	+	0.113523i
$238$	−192.508	+	73.1865i	−0.808858	+	0.307506i
$239$	218.254	−	126.009i	0.913197	−	0.527235i	0.0317388	−	0.999496i	$-0.489896\pi$
$239$	218.254	−	126.009i	0.913197	−	0.527235i	0.881458	+	0.472262i	$0.156562\pi$
$240$	31.4724	+	126.323i	0.131135	+	0.526346i
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.168282	+	0.985739i	$0.553822\pi$
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.769534	+	0.638606i	$0.779511\pi$
$242$	−46.5366	−	7.52439i	−0.192300	−	0.0310925i
$243$	233.162	+	68.4445i	0.959513	+	0.281664i
$244$	−277.065	−	92.0011i	−1.13551	−	0.377053i
$245$	−115.925	+	200.787i	−0.473162	+	0.819540i
$246$	−168.856	−	190.565i	−0.686408	−	0.774656i
$247$	−7.23284	+	4.17588i	−0.0292828	+	0.0169064i
$248$	−132.306	+	5.65266i	−0.533494	+	0.0227930i
$249$	−90.2680	−	238.534i	−0.362522	−	0.957966i
$250$	146.151	−	179.297i	0.584602	−	0.717188i
$251$		−	139.429i		−	0.555492i	−0.960655	−	0.277746i	$-0.910413\pi$
$251$		−	139.429i		−	0.555492i	0.960655	−	0.277746i	$-0.0895874\pi$
$252$	414.448	+	50.2483i	1.64463	+	0.199398i
$253$	208.297			0.823306
$254$	12.9773	+	10.5782i	0.0510916	+	0.0416463i
$255$	−11.6409	+	71.3058i	−0.0456505	+	0.279631i
$256$	176.142	−	185.769i	0.688053	−	0.725660i
$257$	235.308	+	407.565i	0.915594	+	1.58586i	0.806029	+	0.591875i	$0.201612\pi$
$257$	235.308	+	407.565i	0.915594	+	1.58586i	0.109564	+	0.993980i	$0.465054\pi$
$258$	211.866	+	70.7105i	0.821188	+	0.274072i
$259$	−408.308	−	235.737i	−1.57648	−	0.910181i
$260$	6.09901	+	2.02521i	0.0234577	+	0.00778928i
$261$	173.665	+	58.2551i	0.665381	+	0.223200i
$262$	−42.4152	+	262.328i	−0.161890	+	1.00125i
$263$	22.2028	+	12.8188i	0.0844214	+	0.0487407i	0.541616	−	0.840626i	$-0.317813\pi$
$263$	22.2028	+	12.8188i	0.0844214	+	0.0487407i	−0.457195	+	0.889366i	$0.651146\pi$
$264$	28.1540	−	235.216i	0.106644	−	0.890971i
$265$	−28.6141	−	49.5610i	−0.107978	−	0.187023i
$266$	116.203	+	305.659i	0.436855	+	1.14909i
$267$	−150.459	−	123.026i	−0.563517	−	0.460772i
$268$	117.554	+	132.260i	0.438634	+	0.493508i
$269$	8.15075			0.0303002			0.0151501	−	0.999885i	$-0.495177\pi$
$269$	8.15075			0.0303002			0.0151501	+	0.999885i	$0.495177\pi$
$270$	88.1409	−	116.966i	0.326448	−	0.433207i
$271$		−	401.979i		−	1.48332i	−0.670777	−	0.741659i	$-0.734039\pi$
$271$		−	401.979i		−	1.48332i	0.670777	−	0.741659i	$-0.265961\pi$
$272$	130.525	−	56.1103i	0.479873	−	0.206288i
$273$	13.0454	−	15.9543i	0.0477852	−	0.0584405i
$274$	−32.0647	−	84.3423i	−0.117024	−	0.307819i
$275$	−150.826	+	87.0792i	−0.548457	+	0.316652i
$276$	−10.4233	−	253.017i	−0.0377657	−	0.916728i
$277$	56.2021	−	97.3449i	0.202896	−	0.351426i	−0.746565	−	0.665313i	$-0.768298\pi$
$277$	56.2021	−	97.3449i	0.202896	−	0.351426i	0.949460	+	0.313887i	$0.101631\pi$
$278$	−48.1939	+	298.068i	−0.173359	+	1.07219i
$279$	98.6321	+	111.655i	0.353520	+	0.400198i
$280$	116.394	−	223.080i	0.415691	−	0.796716i
$281$	268.867	−	465.692i	0.956823	−	1.65727i	0.226681	−	0.973969i	$-0.427212\pi$
$281$	268.867	−	465.692i	0.956823	−	1.65727i	0.730141	−	0.683296i	$-0.239454\pi$
$282$	−10.3266	−	3.44650i	−0.0366191	−	0.0122216i
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	−0.700268	−	0.713880i	$-0.746936\pi$
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	0.268104	+	0.963390i	$0.413603\pi$
$284$	−438.010	+	90.1571i	−1.54229	+	0.317454i
$285$	113.217	+	18.4830i	0.397253	+	0.0648528i
$286$	−9.06432	−	7.38860i	−0.0316934	−	0.0258343i
$287$			492.113i			1.71468i
$288$	−287.125	−	22.4282i	−0.996963	−	0.0778755i
$289$	−210.151			−0.727167
$290$	69.7533	−	85.5732i	0.240529	−	0.295080i
$291$	20.1535	−	7.62667i	0.0692561	−	0.0262085i
$292$	61.4500	+	298.543i	0.210445	+	1.02241i
$293$	−230.291	−	398.875i	−0.785975	−	1.36135i	−0.928415	−	0.371545i	$-0.878828\pi$
$293$	−230.291	−	398.875i	−0.785975	−	1.36135i	0.142440	−	0.989803i	$-0.454505\pi$
$294$	−340.155	−	383.886i	−1.15699	−	1.30574i
$295$	207.991	+	120.084i	0.705055	+	0.407064i
$296$	288.356	+	150.451i	0.974175	+	0.508282i
$297$	−225.556	+	141.953i	−0.759447	+	0.477958i
$298$	281.904	+	45.5804i	0.945988	+	0.152954i
$299$	−10.8258	−	6.25029i	−0.0362068	−	0.0209040i
$300$	113.322	+	178.850i	0.377741	+	0.596166i
$301$	−215.849	−	373.862i	−0.717107	−	1.24206i
$302$	474.965	−	180.569i	1.57273	−	0.597911i
$303$	311.466	−	117.868i	1.02794	−	0.389002i
$304$	−89.0902	−	207.244i	−0.293060	−	0.681725i
$305$	197.948			0.649011
$306$	−141.479	−	74.3677i	−0.462351	−	0.243032i
$307$		−	210.322i		−	0.685089i	−0.939502	−	0.342545i	$-0.888711\pi$
$307$		−	210.322i		−	0.685089i	0.939502	−	0.342545i	$-0.111289\pi$
$308$	−342.229	+	304.176i	−1.11113	+	0.987585i
$309$	−272.185	−	44.4351i	−0.880859	−	0.143803i
$310$	83.9308	−	31.9082i	0.270744	−	0.102930i
$311$	110.993	−	64.0821i	0.356892	−	0.206052i	−0.310824	−	0.950467i	$-0.600605\pi$
$311$	110.993	−	64.0821i	0.356892	−	0.206052i	0.667717	+	0.744416i	$0.267272\pi$
$312$	−8.52132	+	11.3801i	−0.0273119	+	0.0364748i
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	−0.871752	−	0.489947i	$-0.837016\pi$
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	0.860182	+	0.509986i	$0.170350\pi$
$314$	10.4784	+	1.69422i	0.0333705	+	0.00539560i
$315$	−277.432	+	56.2233i	−0.880737	+	0.178487i
$316$	−12.0874	+	36.4017i	−0.0382513	+	0.115195i
$317$	−120.145	+	208.098i	−0.379007	+	0.656460i	−0.990918	−	0.134467i	$-0.957068\pi$
$317$	−120.145	+	208.098i	−0.379007	+	0.656460i	0.611911	+	0.790927i	$0.290401\pi$
$318$	124.042	−	25.3348i	0.390069	−	0.0796693i
$319$	−173.980	+	100.447i	−0.545392	+	0.314882i
$320$	−73.6519	+	157.179i	−0.230162	+	0.491184i
$321$	204.602	−	250.224i	0.637388	−	0.779515i
$322$	−309.240	+	379.375i	−0.960374	+	1.17818i
$323$		−	125.194i		−	0.387596i
$324$	183.717	+	266.878i	0.567029	+	0.823698i
$325$	10.4518			0.0321595
$326$	92.3216	+	75.2541i	0.283195	+	0.230841i
$327$	−201.023	−	164.371i	−0.614748	−	0.502662i
$328$	−14.4909	−	339.174i	−0.0441795	−	1.03407i
$329$	10.5207	+	18.2224i	0.0319778	+	0.0553872i
$330$	32.1432	+	157.377i	0.0974037	+	0.476899i
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.941142	−	0.338011i	$-0.109754\pi$
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.177845	+	0.984058i	$0.443087\pi$
$332$	107.164	−	322.729i	0.322784	−	0.972076i
$333$	−72.6747	−	358.612i	−0.218242	−	1.07691i
$334$	−31.6062	+	195.477i	−0.0946295	+	0.585261i
$335$	−103.906	−	59.9904i	−0.310168	−	0.179076i
$336$	386.607	+	400.484i	1.15062	+	1.19192i
$337$	152.442	+	264.037i	0.452349	+	0.783492i	0.998531	−	0.0541746i	$-0.0172528\pi$
$337$	152.442	+	264.037i	0.452349	+	0.783492i	−0.546182	+	0.837666i	$0.683919\pi$
$338$	−119.862	−	315.283i	−0.354622	−	0.932789i
$339$	−2.27371	+	13.9275i	−0.00670711	+	0.0410842i
$340$	−72.0031	+	63.9969i	−0.211774	+	0.188226i
$341$	−163.393			−0.479157
$342$	−118.079	+	224.637i	−0.345259	+	0.656832i
$343$			423.102i			1.23353i
$344$	159.776	+	251.317i	0.464466	+	0.730572i
$345$	60.7712	+	160.588i	0.176148	+	0.465473i
$346$	−27.4287	−	72.1480i	−0.0792738	−	0.208520i
$347$	−146.406	+	84.5276i	−0.421919	+	0.243595i	−0.695898	−	0.718140i	$-0.744994\pi$
$347$	−146.406	+	84.5276i	−0.421919	+	0.243595i	0.273979	+	0.961736i	$0.411660\pi$
$348$	130.719	+	206.306i	0.375630	+	0.592834i
$349$	107.298	−	185.846i	0.307444	−	0.532509i	−0.670358	−	0.742037i	$-0.733860\pi$
$349$	107.298	−	185.846i	0.307444	−	0.532509i	0.977802	+	0.209529i	$0.0671930\pi$
$350$	65.3188	−	403.982i	0.186625	−	1.15423i
$351$	15.9824	−	0.609584i	0.0455339	−	0.00173671i
$352$	226.915	−	219.722i	0.644644	−	0.624209i
$353$	−275.895	+	477.865i	−0.781574	+	1.35373i	0.149451	+	0.988769i	$0.452249\pi$
$353$	−275.895	+	477.865i	−0.781574	+	1.35373i	−0.931025	+	0.364956i	$0.881084\pi$
$354$	−397.659	+	352.359i	−1.12333	+	0.995364i
$355$	262.593	−	151.608i	0.739698	−	0.427065i
$356$	−52.2441	−	253.817i	−0.146753	−	0.712970i
$357$	109.339	+	288.930i	0.306272	+	0.809326i
$358$	56.4693	+	46.0299i	0.157736	+	0.128575i
$359$		−	554.828i		−	1.54548i	−0.634721	−	0.772741i	$-0.718885\pi$
$359$		−	554.828i		−	1.54548i	0.634721	−	0.772741i	$-0.281115\pi$
$360$	189.556	−	46.9195i	0.526545	−	0.130332i
$361$	162.222			0.449367
$362$	−23.4937	+	28.8220i	−0.0648998	+	0.0796189i
$363$	−11.3930	+	69.7876i	−0.0313858	+	0.192252i
$364$	26.9141	−	5.53982i	0.0739398	−	0.0152193i
$365$	−103.334	−	178.980i	−0.283108	−	0.490357i
$366$	−138.635	+	415.386i	−0.378785	+	1.13494i
$367$	145.642	+	84.0864i	0.396845	+	0.229118i	0.685122	−	0.728429i	$-0.259749\pi$
$367$	145.642	+	84.0864i	0.396845	+	0.229118i	−0.288277	+	0.957547i	$0.593082\pi$
$368$	201.963	−	270.579i	0.548814	−	0.735269i
$369$	−286.234	+	252.848i	−0.775702	+	0.685226i
$370$	−217.704	−	35.2000i	−0.588388	−	0.0951350i
$371$	−211.913	−	122.348i	−0.571195	−	0.329780i
$372$	8.17630	+	198.472i	0.0219793	+	0.533528i
$373$	171.699	+	297.391i	0.460318	+	0.797295i	0.998977	−	0.0452296i	$-0.0144020\pi$
$373$	171.699	+	297.391i	0.460318	+	0.797295i	−0.538658	+	0.842524i	$0.681069\pi$
$374$	163.855	−	62.2931i	0.438114	−	0.166559i
$375$	−268.611	−	219.636i	−0.716296	−	0.585695i
$376$	−7.78765	−	12.2494i	−0.0207118	−	0.0325783i
$377$	12.0564			0.0319798
$378$	76.3205	−	621.556i	0.201906	−	1.64433i
$379$			602.392i			1.58943i	0.606986	+	0.794713i	$0.292379\pi$
$379$			602.392i			1.58943i	−0.606986	+	0.794713i	$0.707621\pi$
$380$	101.612	+	114.324i	0.267401	+	0.300854i
$381$	15.8969	−	19.4417i	0.0417242	−	0.0510280i
$382$	−528.814	+	201.041i	−1.38433	+	0.526285i
$383$	−315.762	+	182.305i	−0.824443	+	0.475992i	−0.851946	−	0.523630i	$-0.824578\pi$
$383$	−315.762	+	182.305i	−0.824443	+	0.475992i	0.0275035	+	0.999622i	$0.491244\pi$
$384$	−278.250	−	264.637i	−0.724610	−	0.689159i
$385$	155.228	−	268.862i	0.403189	−	0.698344i
$386$	−598.398	−	96.7534i	−1.55025	−	0.250657i
$387$	106.550	−	317.638i	0.275324	−	0.820769i
$388$	27.2672	+	9.05422i	0.0702762	+	0.0233356i
$389$	107.326	−	185.893i	0.275901	−	0.477875i	−0.694461	−	0.719530i	$-0.744357\pi$
$389$	107.326	−	185.893i	0.275901	−	0.477875i	0.970362	+	0.241656i	$0.0776904\pi$
$390$	3.05177	−	9.14387i	0.00782504	−	0.0234458i
$391$	162.280	−	93.6923i	0.415038	−	0.239622i
$392$	−29.1913	−	683.253i	−0.0744677	−	1.74299i
$393$	393.395	+	64.2229i	1.00101	+	0.163417i
$394$	175.879	−	215.768i	0.446393	−	0.547634i
$395$		−	26.0071i		−	0.0658409i
$396$	−352.760	−	42.7691i	−0.890807	−	0.108003i
$397$	−684.628			−1.72450			−0.862251	−	0.506480i	$-0.830946\pi$
$397$	−684.628			−1.72450			−0.862251	+	0.506480i	$0.830946\pi$
$398$	17.4148	+	14.1953i	0.0437557	+	0.0356666i
$399$	458.754	−	173.606i	1.14976	−	0.435102i
$400$	−33.1233	+	280.356i	−0.0828082	+	0.700889i
$401$	95.1918	+	164.877i	0.237386	+	0.411164i	0.959963	−	0.280125i	$-0.0903761\pi$
$401$	95.1918	+	164.877i	0.237386	+	0.411164i	−0.722577	+	0.691290i	$0.757043\pi$
$402$	198.659	−	176.028i	0.494177	−	0.437881i
$403$	8.49203	+	4.90287i	0.0210720	+	0.0121659i
$404$	421.405	+	139.930i	1.04308	+	0.346361i
$405$	−175.247	−	132.479i	−0.432708	−	0.327108i
$406$	75.3463	−	466.000i	0.185582	−	1.14778i
$407$	347.534	+	200.649i	0.853892	+	0.492995i
$408$	−83.8667	−	195.916i	−0.205556	−	0.480187i
$409$	188.978	+	327.320i	0.462049	+	0.800293i	0.999063	−	0.0432806i	$-0.0137809\pi$
$409$	188.978	+	327.320i	0.462049	+	0.800293i	−0.537014	+	0.843574i	$0.680448\pi$
$410$	81.7984	+	215.161i	0.199508	+	0.524782i
$411$	−126.587	+	47.9040i	−0.307997	+	0.116555i
$412$	−244.286	−	274.847i	−0.592928	−	0.667104i
$413$	1026.91			2.48647
$414$	−379.549	+	15.0561i	−0.916785	+	0.0363675i
$415$			230.573i			0.555598i
$416$	−18.3866	+	4.61067i	−0.0441985	+	0.0110833i
$417$	446.991	+	72.9727i	1.07192	+	0.174994i
$418$	−98.9072	−	260.163i	−0.236620	−	0.622400i
$419$	−267.326	+	154.341i	−0.638009	+	0.368355i	−0.783847	−	0.620954i	$-0.786745\pi$
$419$	−267.326	+	154.341i	−0.638009	+	0.368355i	0.145838	+	0.989308i	$0.453412\pi$
$420$	−334.354	−	175.101i	−0.796081	−	0.416906i
$421$	176.834	−	306.286i	0.420034	−	0.727521i	−0.575908	−	0.817514i	$-0.695351\pi$
$421$	176.834	−	306.286i	0.420034	−	0.727521i	0.995942	+	0.0899938i	$0.0286847\pi$
$422$	−41.2909	+	255.374i	−0.0978457	+	0.605153i
$423$	−5.19337	+	15.4820i	−0.0122775	+	0.0366004i
$424$	149.658	+	78.0848i	0.352966	+	0.184162i
$425$	−78.3369	+	135.684i	−0.184322	+	0.319255i
$426$	134.233	+	657.220i	0.315102	+	1.54277i
$427$	732.995	−	423.195i	1.71662	−	0.991088i
$428$	422.117	−	86.8857i	0.986254	−	0.203004i
$429$	−11.1036	+	13.5796i	−0.0258826	+	0.0316540i
$430$	−156.516	−	127.581i	−0.363990	−	0.296700i
$431$			472.777i			1.09693i	0.836174	+	0.548465i	$0.184787\pi$
$431$			472.777i			1.09693i	−0.836174	+	0.548465i	$0.815213\pi$
$432$	−34.2991	+	430.636i	−0.0793960	+	0.996843i
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$	242.575	−	297.591i	0.558929	−	0.685693i
$435$	−128.200	−	104.826i	−0.294713	−	0.240978i
$436$	−69.8013	−	339.116i	−0.160095	−	0.777788i
$437$	−148.762	−	257.663i	−0.340416	−	0.589618i
$438$	447.954	−	91.4919i	1.02273	−	0.208886i
$439$	−354.347	−	204.582i	−0.807169	−	0.466019i	0.0388030	−	0.999247i	$-0.487646\pi$
$439$	−354.347	−	204.582i	−0.807169	−	0.466019i	−0.845972	+	0.533228i	$0.820979\pi$
$440$	−99.0691	+	189.876i	−0.225157	+	0.431537i
$441$	−576.607	+	509.353i	−1.30750	+	1.15500i
$442$	−10.3853	−	1.67917i	−0.0234960	−	0.00379902i
$443$	−668.806	−	386.136i	−1.50972	−	0.871638i	−0.999936	−	0.0113360i	$-0.996392\pi$
$443$	−668.806	−	386.136i	−1.50972	−	0.871638i	−0.509785	−	0.860302i	$-0.670275\pi$
$444$	226.337	−	432.189i	0.509767	−	0.973399i
$445$	87.8536	+	152.167i	0.197424	+	0.341948i
$446$	−451.613	+	171.691i	−1.01259	+	0.384958i
$447$	69.0155	−	422.752i	0.154397	−	0.945753i
$448$	63.3033	+	739.487i	0.141302	+	1.65064i
$449$	−789.037			−1.75732			−0.878660	−	0.477448i	$-0.841562\pi$
$449$	−789.037			−1.75732			−0.878660	+	0.477448i	$0.841562\pi$
$450$	268.534	−	169.574i	0.596742	−	0.376831i
$451$		−	418.865i		−	0.928747i
$452$	−14.0637	+	12.4999i	−0.0311144	+	0.0276548i
$453$	−269.767	−	712.859i	−0.595511	−	1.57364i
$454$	713.892	−	271.403i	1.57245	−	0.597804i
$455$	−16.1354	+	9.31575i	−0.0354623	+	0.0204742i
$456$	−311.070	+	133.161i	−0.682171	+	0.292020i
$457$	138.165	−	239.309i	0.302331	−	0.523653i	−0.674332	−	0.738428i	$-0.735568\pi$
$457$	138.165	−	239.309i	0.302331	−	0.523653i	0.976664	+	0.214775i	$0.0689018\pi$
$458$	294.828	+	47.6700i	0.643728	+	0.104083i
$459$	−111.875	+	212.049i	−0.243737	+	0.461980i
$460$	−72.1462	+	217.271i	−0.156840	+	0.472329i
$461$	−294.041	+	509.295i	−0.637834	+	1.10476i	0.348073	+	0.937467i	$0.386836\pi$
$461$	−294.041	+	509.295i	−0.637834	+	1.10476i	−0.985907	+	0.167293i	$0.946497\pi$
$462$	455.481	+	514.040i	0.985889	+	1.11264i
$463$	−677.285	+	391.031i	−1.46282	+	0.844558i	−0.999141	−	0.0414459i	$-0.986804\pi$
$463$	−677.285	+	391.031i	−1.46282	+	0.844558i	−0.463677	+	0.886004i	$0.653470\pi$
$464$	−38.2082	+	323.395i	−0.0823454	+	0.696972i
$465$	−47.6703	−	125.969i	−0.102517	−	0.270901i
$466$	−276.654	+	339.398i	−0.593678	+	0.728322i
$467$			663.203i			1.42014i	0.704133	+	0.710068i	$0.251336\pi$
$467$			663.203i			1.42014i	−0.704133	+	0.710068i	$0.748664\pi$
$468$	17.0507	+	12.8080i	0.0364331	+	0.0273675i
$469$	−513.014			−1.09385
$470$	7.62874	+	6.21842i	0.0162314	+	0.0132307i
$471$	2.56530	−	15.7136i	0.00544649	−	0.0333623i
$472$	−707.767	+	30.2387i	−1.49951	+	0.0640649i
$473$	183.721	+	318.214i	0.388417	+	0.672758i
$474$	54.5749	+	18.2144i	0.115137	+	0.0384270i
$475$	215.434	+	124.381i	0.453546	+	0.261855i
$476$	−129.805	+	390.914i	−0.272700	+	0.821247i
$477$	−37.7184	−	186.121i	−0.0790743	−	0.390190i
$478$	80.4516	−	497.574i	0.168309	−	1.04095i
$479$	562.018	+	324.481i	1.17331	+	0.677414i	0.954459	−	0.298344i	$-0.0964341\pi$
$479$	562.018	+	324.481i	1.17331	+	0.677414i	0.218856	+	0.975757i	$0.429767\pi$
$480$	235.599	+	110.837i	0.490832	+	0.230911i
$481$	−12.0416	−	20.8567i	−0.0250346	−	0.0433611i
$482$	321.264	+	845.047i	0.666524	+	1.75321i
$483$	568.355	+	464.728i	1.17672	+	0.962170i
$484$	−70.4700	+	62.6343i	−0.145599	+	0.129410i
$485$	−19.4810			−0.0401669
$486$	400.737	−	274.965i	0.824562	−	0.565772i
$487$		−	282.104i		−	0.579269i	−0.957137	−	0.289635i	$-0.906466\pi$
$487$		−	282.104i		−	0.579269i	0.957137	−	0.289635i	$-0.0935338\pi$
$488$	−492.733	+	313.258i	−1.00970	+	0.641923i
$489$	113.092	−	138.310i	0.231272	−	0.282843i
$490$	164.780	+	433.433i	0.336285	+	0.884557i
$491$	652.933	−	376.971i	1.32980	−	0.767762i	0.344534	−	0.938774i	$-0.388037\pi$
$491$	652.933	−	376.971i	1.32980	−	0.767762i	0.985269	+	0.171012i	$0.0547036\pi$
$492$	−508.794	+	20.9604i	−1.03413	+	0.0426023i
$493$	−90.3630	+	156.513i	−0.183292	+	0.317471i
$494$	−2.66613	+	16.4894i	−0.00539702	+	0.0333793i
$495$	236.138	−	47.8548i	0.477047	−	0.0966763i
$496$	−158.425	+	212.248i	−0.319405	+	0.427920i
$497$	648.247	−	1122.80i	1.30432	−	2.25915i
$498$	−483.848	−	161.484i	−0.971583	−	0.324266i
$499$	−446.169	+	257.596i	−0.894126	+	0.516224i	−0.875290	−	0.483599i	$-0.839329\pi$
$499$	−446.169	+	257.596i	−0.894126	+	0.516224i	−0.0188362	+	0.999823i	$0.505996\pi$
$500$	−93.2701	−	453.134i	−0.186540	−	0.906268i
$501$	293.143	+	47.8565i	0.585116	+	0.0955220i
$502$	−216.146	−	176.187i	−0.430570	−	0.350971i
$503$		−	523.660i		−	1.04107i	−0.853839	−	0.520537i	$-0.825732\pi$
$503$		−	523.660i		−	1.04107i	0.853839	−	0.520537i	$-0.174268\pi$
$504$	601.609	−	578.994i	1.19367	−	1.14880i
$505$	−301.072			−0.596182
$506$	263.212	−	322.908i	0.520181	−	0.638157i
$507$	−473.198	+	179.072i	−0.933329	+	0.353198i
$508$	32.7972	−	6.75075i	0.0645613	−	0.0132889i
$509$	−267.685	−	463.645i	−0.525905	−	0.910893i	−0.999545	−	0.0301749i	$-0.990394\pi$
$509$	−267.685	−	463.645i	−0.525905	−	0.910893i	0.473640	−	0.880719i	$-0.342940\pi$
$510$	95.8305	+	108.151i	0.187903	+	0.212061i
$511$	−765.285	−	441.838i	−1.49762	−	0.864653i
$512$	−65.4050	−	507.805i	−0.127744	−	0.991807i
$513$	336.684	+	177.632i	0.656305	+	0.346261i
$514$	929.163	+	150.234i	1.80771	+	0.292284i
$515$	215.925	+	124.665i	0.419273	+	0.242067i
$516$	377.340	−	239.089i	0.731280	−	0.463351i
$517$	−8.95475	−	15.5101i	−0.0173206	−	0.0300002i
$518$	−881.402	+	335.085i	−1.70155	+	0.646883i
$519$	−108.285	+	40.9780i	−0.208641	+	0.0789557i
$520$	10.8465	−	6.89573i	0.0208586	−	0.0132610i
$521$	177.268			0.340246			0.170123	−	0.985423i	$-0.445584\pi$
$521$	177.268			0.340246			0.170123	+	0.985423i	$0.445584\pi$
$522$	309.758	−	195.607i	0.593407	−	0.374725i
$523$		−	444.206i		−	0.849343i	−0.905347	−	0.424672i	$-0.860390\pi$
$523$		−	444.206i		−	0.849343i	0.905347	−	0.424672i	$-0.139610\pi$
$524$	353.072	+	397.242i	0.673801	+	0.758096i
$525$	−605.822	−	98.9023i	−1.15395	−	0.188385i
$526$	47.9285	−	18.2211i	0.0911188	−	0.0346409i
$527$	−127.296	+	73.4944i	−0.241548	+	0.139458i
$528$	−329.063	−	340.874i	−0.623225	−	0.645595i
$529$	−41.8394	+	72.4679i	−0.0790914	+	0.136990i
$530$	−112.989	−	18.2689i	−0.213187	−	0.0344696i
$531$	527.628	+	597.295i	0.993649	+	1.12485i
$532$	620.681	+	206.101i	1.16669	+	0.387407i
$533$	−12.5688	+	21.7697i	−0.0235812	+	0.0408438i
$534$	−380.845	+	77.7853i	−0.713193	+	0.145665i
$535$	−253.065	+	146.107i	−0.473018	+	0.273097i
$536$	353.580	−	15.1064i	0.659664	−	0.0281835i
$537$	69.1739	−	84.5986i	0.128815	−	0.157539i
$538$	10.2996	−	12.6355i	0.0191443	−	0.0234861i
$539$		−	843.787i		−	1.56547i
$540$	−69.9455	−	284.441i	−0.129529	−	0.526743i
$541$	571.163			1.05575			0.527877	−	0.849321i	$-0.322988\pi$
$541$	571.163			1.05575			0.527877	+	0.849321i	$0.322988\pi$
$542$	−623.160	−	507.957i	−1.14974	−	0.937190i
$543$	43.1793	+	35.3065i	0.0795198	+	0.0650211i
$544$	77.9534	−	273.248i	0.143297	−	0.502294i
$545$	117.378	+	203.304i	0.215372	+	0.373036i
$546$	−8.24814	−	40.3837i	−0.0151065	−	0.0739629i
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	0.622377	−	0.782717i	$-0.286167\pi$
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	−0.366664	+	0.930353i	$0.619500\pi$
$548$	−171.268	−	56.8706i	−0.312533	−	0.103779i
$549$	622.762	+	208.903i	1.13436	+	0.380515i
$550$	−55.5965	+	343.851i	−0.101085	+	0.625184i
$551$	248.507	+	143.476i	0.451011	+	0.260391i
$552$	−405.406	−	303.564i	−0.734431	−	0.549935i
$553$	−55.6008	−	96.3034i	−0.100544	−	0.174147i
$554$	−79.8878	−	210.135i	−0.144202	−	0.379305i
$555$	−53.2979	+	326.475i	−0.0960323	+	0.588242i
$556$	401.175	+	451.363i	0.721537	+	0.811803i
$557$	−568.917			−1.02139			−0.510697	−	0.859761i	$-0.670613\pi$
$557$	−568.917			−1.02139			−0.510697	+	0.859761i	$0.670613\pi$
$558$	297.727	−	11.8104i	0.533561	−	0.0211655i
$559$		−	22.0515i		−	0.0394481i
$560$	−198.746	−	462.330i	−0.354904	−	0.825590i
$561$	−93.0647	−	245.924i	−0.165891	−	0.438367i
$562$	−382.178	−	1005.27i	−0.680032	−	1.78874i
$563$	250.527	−	144.642i	0.444985	−	0.256912i	−0.260725	−	0.965413i	$-0.583962\pi$
$563$	250.527	−	144.642i	0.444985	−	0.256912i	0.705710	+	0.708501i	$0.250628\pi$
$564$	−18.3919	+	11.6534i	−0.0326098	+	0.0206621i
$565$	6.37900	−	11.0487i	0.0112903	−	0.0195553i
$566$	−45.0824	+	278.824i	−0.0796510	+	0.492623i
$567$	−932.159	−	115.903i	−1.64402	−	0.204414i
$568$	−413.723	+	792.942i	−0.728385	+	1.39603i
$569$	−223.117	+	386.450i	−0.392121	+	0.679174i	−0.992729	−	0.120370i	$-0.961592\pi$
$569$	−223.117	+	386.450i	−0.392121	+	0.679174i	0.600608	+	0.799544i	$0.294925\pi$
$570$	171.719	−	152.157i	0.301261	−	0.266942i
$571$	372.386	−	214.997i	0.652164	−	0.376527i	−0.137121	−	0.990554i	$-0.543785\pi$
$571$	372.386	−	214.997i	0.652164	−	0.376527i	0.789285	+	0.614027i	$0.210451\pi$
$572$	−22.9081	+	4.71525i	−0.0400491	+	0.00824344i
$573$	300.351	+	793.680i	0.524173	+	1.38513i
$574$	762.889	+	621.854i	1.32907	+	1.08337i
$575$			372.337i			0.647542i
$576$	−397.592	+	416.769i	−0.690264	+	0.723558i
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$	−265.556	+	325.783i	−0.459439	+	0.563638i
$579$	−146.499	+	897.374i	−0.253021	+	1.54987i
$580$	−44.5150	−	216.267i	−0.0767501	−	0.372875i
$581$	492.943	+	853.803i	0.848440	+	1.46954i
$582$	13.6437	−	40.8800i	0.0234428	−	0.0702405i
$583$	180.371	+	104.137i	0.309385	+	0.178623i
$584$	540.460	+	281.989i	0.925446	+	0.482857i
$585$	−13.7088	−	4.59856i	−0.0234339	−	0.00786079i
$586$	−909.353	−	147.031i	−1.55180	−	0.250906i
$587$	−643.771	−	371.681i	−1.09671	−	0.633188i	−0.161358	−	0.986896i	$-0.551587\pi$
$587$	−643.771	−	371.681i	−1.09671	−	0.633188i	−0.935356	+	0.353708i	$0.884921\pi$
$588$	−1024.95	+	42.2238i	−1.74310	+	0.0718092i
$589$	116.692	+	202.117i	0.198119	+	0.343152i
$590$	448.983	−	170.692i	0.760989	−	0.289308i
$591$	−323.249	−	264.312i	−0.546953	−	0.447228i
$592$	597.612	−	256.902i	1.00948	−	0.433955i
$593$	−382.547			−0.645104			−0.322552	−	0.946552i	$-0.604541\pi$
$593$	−382.547			−0.645104			−0.322552	+	0.946552i	$0.604541\pi$
$594$	−64.9606	+	529.041i	−0.109361	+	0.890642i
$595$		−	279.287i		−	0.469391i
$596$	426.886	−	379.419i	0.716251	−	0.636610i
$597$	21.3328	−	26.0896i	0.0357333	−	0.0437012i
$598$	−23.3693	+	8.88440i	−0.0390792	+	0.0148569i
$599$	856.248	−	494.355i	1.42946	−	0.825301i	0.432384	−	0.901689i	$-0.357672\pi$
$599$	856.248	−	494.355i	1.42946	−	0.825301i	0.997078	+	0.0763888i	$0.0243390\pi$
$600$	420.457	+	50.3262i	0.700762	+	0.0838771i
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	−0.997541	−	0.0700905i	$-0.977671\pi$
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	0.559470	+	0.828850i	$0.311005\pi$
$602$	−852.327	−	137.811i	−1.41583	−	0.228921i
$603$	−263.587	−	298.391i	−0.437127	−	0.494844i
$604$	320.261	−	964.479i	0.530233	−	1.59682i
$605$	31.9637	−	55.3627i	0.0528325	−	0.0915086i
$606$	210.859	−	631.786i	0.347952	−	1.04255i
$607$	447.631	−	258.440i	0.737448	−	0.425766i	−0.0836928	−	0.996492i	$-0.526671\pi$
$607$	447.631	−	258.440i	0.737448	−	0.425766i	0.821141	+	0.570726i	$0.193338\pi$
$608$	−433.854	−	123.772i	−0.713576	−	0.203572i
$609$	−698.826	−	114.085i	−1.14750	−	0.187332i
$610$	250.136	−	306.866i	0.410058	−	0.503059i
$611$			1.07481i			0.00175910i
$612$	−294.066	+	125.352i	−0.480500	+	0.204823i
$613$	762.957			1.24463			0.622314	−	0.782768i	$-0.286193\pi$
$613$	762.957			1.24463			0.622314	+	0.782768i	$0.286193\pi$
$614$	−326.048	−	265.772i	−0.531023	−	0.432853i
$615$	322.928	−	122.205i	0.525086	−	0.198708i
$616$	39.0884	+	914.904i	0.0634552	+	1.48523i
$617$	60.9168	+	105.511i	0.0987307	+	0.171007i	0.911160	−	0.412054i	$-0.135188\pi$
$617$	60.9168	+	105.511i	0.0987307	+	0.171007i	−0.812429	+	0.583060i	$0.801855\pi$
$618$	−412.829	+	365.800i	−0.668008	+	0.591910i
$619$	265.675	+	153.388i	0.429200	+	0.247799i	0.699006	−	0.715116i	$-0.253626\pi$
$619$	265.675	+	153.388i	0.429200	+	0.247799i	−0.269806	+	0.962915i	$0.586959\pi$
$620$	56.5931	−	170.433i	0.0912793	−	0.274891i
$621$	21.7158	+	569.357i	0.0349692	+	0.916839i
$622$	40.9138	−	253.042i	0.0657778	−	0.406820i
$623$	650.636	+	375.645i	1.04436	+	0.602961i
$624$	6.87393	+	27.5904i	0.0110159	+	0.0442154i
$625$	−63.7082	−	110.346i	−0.101933	−	0.176553i
$626$	5.14760	+	13.5401i	0.00822300	+	0.0216296i
$627$	−390.471	+	147.765i	−0.622760	+	0.235670i
$628$	15.8673	−	14.1030i	0.0252664	−	0.0224570i
$629$	361.010			0.573942
$630$	−263.415	+	501.130i	−0.418120	+	0.795444i
$631$			1071.11i			1.69749i	0.528805	+	0.848744i	$0.322640\pi$
$631$			1071.11i			1.69749i	−0.528805	+	0.848744i	$0.677360\pi$
$632$	41.1569	+	64.7370i	0.0651217	+	0.102432i
$633$	382.967	+	62.5205i	0.605003	+	0.0987685i
$634$	170.779	+	449.214i	0.269368	+	0.708539i
$635$	−19.6623	+	11.3521i	−0.0309643	+	0.0178773i
$636$	117.469	−	224.308i	0.184700	−	0.352685i
$637$	−25.3193	+	43.8543i	−0.0397477	+	0.0688450i
$638$	−64.1315	+	396.638i	−0.100520	+	0.621690i
$639$	986.136	−	199.846i	1.54325	−	0.312748i
$640$	150.594	+	312.795i	0.235303	+	0.488742i
$641$	527.259	−	913.240i	0.822557	−	1.42471i	−0.0812143	−	0.996697i	$-0.525880\pi$
$641$	527.259	−	913.240i	0.822557	−	1.42471i	0.903772	−	0.428015i	$-0.140787\pi$
$642$	−129.363	−	633.373i	−0.201500	−	0.986562i
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	−0.532355	−	0.846521i	$-0.678693\pi$
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	0.466931	+	0.884294i	$0.345360\pi$
$644$	197.351	+	958.788i	0.306445	+	1.48880i
$645$	−191.729	+	234.482i	−0.297254	+	0.363537i
$646$	−194.079	−	158.200i	−0.300432	−	0.244891i
$647$			539.373i			0.833653i	0.908986	+	0.416826i	$0.136858\pi$
$647$			539.373i			0.833653i	−0.908986	+	0.416826i	$0.863142\pi$
$648$	645.875	+	52.4338i	0.996721	+	0.0809163i
$649$	−874.061			−1.34678
$650$	13.2074	−	16.2028i	0.0203190	−	0.0249273i
$651$	−445.831	−	364.543i	−0.684840	−	0.559974i
$652$	233.322	−	48.0256i	0.357856	−	0.0736588i
$653$	−276.457	−	478.838i	−0.423365	−	0.733290i	0.572901	−	0.819624i	$-0.305818\pi$
$653$	−276.457	−	478.838i	−0.423365	−	0.733290i	−0.996266	+	0.0863348i	$0.972485\pi$
$654$	−508.832	+	103.926i	−0.778031	+	0.158908i
$655$	−312.081	−	180.180i	−0.476460	−	0.275084i
$656$	−544.109	−	406.130i	−0.829435	−	0.619100i
$657$	−136.213	−	672.139i	−0.207326	−	1.02304i
$658$	41.5433	+	6.71703i	0.0631357	+	0.0102082i
$659$	−734.162	−	423.869i	−1.11406	−	0.643200i	−0.174178	−	0.984714i	$-0.555727\pi$
$659$	−734.162	−	423.869i	−1.11406	−	0.643200i	−0.939877	+	0.341514i	$0.889060\pi$
$660$	284.587	+	149.038i	0.431193	+	0.225815i
$661$	−359.447	−	622.580i	−0.543792	−	0.941876i	−0.998682	−	0.0513280i	$-0.983655\pi$
$661$	−359.447	−	622.580i	−0.543792	−	0.941876i	0.454890	−	0.890548i	$-0.349679\pi$
$662$	799.537	−	303.963i	1.20776	−	0.459158i
$663$	−2.54250	+	15.5740i	−0.00383485	+	0.0234902i
$664$	−364.888	−	573.943i	−0.549530	−	0.864372i
$665$	−443.444			−0.666833
$666$	−647.765	−	340.493i	−0.972620	−	0.511251i
$667$			429.497i			0.643923i
$668$	263.096	+	296.010i	0.393856	+	0.443129i
$669$	256.504	+	677.812i	0.383414	+	1.01317i
$670$	−224.299	+	85.2725i	−0.334775	+	0.127272i
$671$	−623.893	+	360.205i	−0.929796	+	0.536818i
$672$	1109.37	−	93.2631i	1.65085	−	0.138784i
$673$	288.488	−	499.675i	0.428659	−	0.742460i	−0.568095	−	0.822963i	$-0.692319\pi$
$673$	288.488	−	499.675i	0.428659	−	0.742460i	0.996754	+	0.0805033i	$0.0256528\pi$
$674$	601.949	+	97.3277i	0.893100	+	0.144403i
$675$	−253.746	−	403.188i	−0.375921	−	0.597316i
$676$	−640.223	−	212.590i	−0.947076	−	0.314482i
$677$	−101.021	+	174.974i	−0.149219	+	0.258454i	−0.930939	−	0.365175i	$-0.881009\pi$
$677$	−101.021	+	174.974i	−0.149219	+	0.258454i	0.781720	+	0.623629i	$0.214343\pi$
$678$	18.7177	+	21.1242i	0.0276073	+	0.0311566i
$679$	−72.1372	+	41.6484i	−0.106240	+	0.0613379i
$680$	8.22397	+	192.490i	0.0120941	+	0.283074i
$681$	−405.471	−	1071.46i	−0.595405	−	1.57336i
$682$	−206.469	+	253.296i	−0.302741	+	0.371402i
$683$		−	568.249i		−	0.831990i	−0.909367	−	0.415995i	$-0.863433\pi$
$683$		−	568.249i		−	0.831990i	0.909367	−	0.415995i	$-0.136567\pi$
$684$	199.030	+	466.909i	0.290979	+	0.682616i
$685$	122.362			0.178631
$686$	655.906	+	534.649i	0.956131	+	0.779371i
$687$	72.1793	−	442.132i	0.105065	−	0.643569i
$688$	591.499	+	69.8840i	0.859737	+	0.101576i
$689$	−6.24965	−	10.8247i	−0.00907060	−	0.0157107i
$690$	325.741	+	108.716i	0.472089	+	0.157560i
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	0.223714	−	0.974655i	$-0.428182\pi$
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	−0.732218	+	0.681070i	$0.761515\pi$
$692$	−146.506	−	48.6482i	−0.211714	−	0.0703008i
$693$	772.100	−	682.045i	1.11414	−	0.984191i
$694$	−53.9673	+	333.775i	−0.0777627	+	0.480945i
$695$	−354.600	−	204.728i	−0.510215	−	0.294573i
$696$	485.004	+	58.0522i	0.696845	+	0.0834083i
$697$	−188.407	−	326.330i	−0.270311	−	0.468192i
$698$	−152.517	−	401.178i	−0.218506	−	0.574754i
$699$	508.464	+	415.757i	0.727416	+	0.594788i
$700$	−543.725	−	611.747i	−0.776750	−	0.873924i
$701$	83.5164			0.119139			0.0595695	−	0.998224i	$-0.481027\pi$
$701$	83.5164			0.119139			0.0595695	+	0.998224i	$0.481027\pi$
$702$	19.2510	−	25.5467i	0.0274231	−	0.0363913i
$703$		−	573.200i		−	0.815363i
$704$	−53.8810	−	629.419i	−0.0765355	−	0.894061i
$705$	9.34506	−	11.4289i	0.0132554	−	0.0162112i
$706$	392.168	+	1031.55i	0.555479	+	1.46112i
$707$	−1114.86	+	643.663i	−1.57688	+	0.910414i
$708$	43.7387	+	1061.72i	0.0617778	+	1.49960i
$709$	−173.908	+	301.217i	−0.245286	+	0.424848i	−0.962212	−	0.272302i	$-0.912215\pi$
$709$	−173.908	+	301.217i	−0.245286	+	0.424848i	0.716926	+	0.697149i	$0.245548\pi$
$710$	96.7955	−	598.657i	0.136332	−	0.843180i
$711$	27.4464	−	81.8205i	0.0386025	−	0.115078i
$712$	−459.493	−	239.743i	−0.645355	−	0.336718i
$713$	−174.660	+	302.520i	−0.244965	+	0.424292i
$714$	586.073	+	195.602i	0.820830	+	0.273952i
$715$	13.7337	−	7.92916i	0.0192080	−	0.0110897i
$716$	142.714	−	29.3753i	0.199321	−	0.0410269i
$717$	−746.177	−	121.816i	−1.04069	−	0.169896i
$718$	−860.112	−	701.103i	−1.19793	−	0.976467i
$719$			536.277i			0.745865i	0.927858	+	0.372933i	$0.121648\pi$
$719$			536.277i			0.745865i	−0.927858	+	0.372933i	$0.878352\pi$
$720$	166.795	−	353.145i	0.231659	−	0.490479i
$721$	1066.08			1.47862
$722$	204.990	−	251.481i	0.283919	−	0.348311i
$723$	1268.30	−	479.963i	1.75422	−	0.663849i
$724$	14.9932	+	72.8414i	0.0207088	+	0.100610i
$725$	−179.553	−	310.995i	−0.247659	−	0.428959i
$726$	93.7902	+	105.848i	0.129188	+	0.145796i
$727$	815.055	+	470.573i	1.12112	+	0.647280i	0.941687	−	0.336490i	$-0.109240\pi$
$727$	815.055	+	470.573i	1.12112	+	0.647280i	0.179435	+	0.983770i	$0.442573\pi$
$728$	25.4217	−	48.7233i	0.0349199	−	0.0669277i
$729$	−411.530	−	601.734i	−0.564514	−	0.825424i
$730$	−408.038	−	65.9747i	−0.558956	−	0.0903763i
$731$	286.267	+	165.277i	0.391611	+	0.226096i
$732$	468.759	+	739.815i	0.640382	+	1.01068i
$733$	311.063	+	538.777i	0.424370	+	0.735030i	0.996361	−	0.0852294i	$-0.0271623\pi$
$733$	311.063	+	538.777i	0.424370	+	0.735030i	−0.571991	+	0.820260i	$0.693829\pi$
$734$	314.392	−	119.524i	0.428327	−	0.162839i
$735$	650.525	−	246.178i	0.885068	−	0.334935i
$736$	−164.251	−	655.004i	−0.223167	−	0.889952i
$737$	436.655			0.592477
$738$	30.2765	+	763.238i	0.0410250	+	1.03420i
$739$		−	444.439i		−	0.601406i	−0.953718	−	0.300703i	$-0.902779\pi$
$739$		−	444.439i		−	0.601406i	0.953718	−	0.300703i	$-0.0972213\pi$
$740$	−329.667	+	293.011i	−0.445496	+	0.395960i
$741$	24.7279	+	4.03691i	0.0333710	+	0.00544792i
$742$	−457.450	+	173.910i	−0.616510	+	0.234381i
$743$	−66.2270	+	38.2362i	−0.0891346	+	0.0514619i	−0.543905	−	0.839147i	$-0.683055\pi$
$743$	−66.2270	+	38.2362i	−0.0891346	+	0.0514619i	0.454770	+	0.890609i	$0.349721\pi$
$744$	318.010	+	238.122i	0.427433	+	0.320057i
$745$	−193.626	+	335.370i	−0.259901	+	0.450161i
$746$	677.990	+	109.622i	0.908833	+	0.146947i
$747$	−243.333	+	725.402i	−0.325747	+	0.971087i
$748$	110.484	−	332.728i	0.147706	−	0.444824i
$749$	−624.725	+	1082.06i	−0.834079	+	1.44467i
$750$	−679.913	+	138.868i	−0.906551	+	0.185158i
$751$	−949.025	+	547.920i	−1.26368	+	0.729587i	−0.973785	−	0.227471i	$-0.926954\pi$
$751$	−949.025	+	547.920i	−1.26368	+	0.729587i	−0.289897	+	0.957058i	$0.593621\pi$
$752$	−28.8302	−	3.40622i	−0.0383381	−	0.00452954i
$753$	−264.775	+	323.816i	−0.351627	+	0.430034i
$754$	15.2349	−	18.6902i	0.0202055	−	0.0247880i
$755$			689.070i			0.912676i
$756$	−867.114	−	903.738i	−1.14698	−	1.19542i
$757$	−346.346			−0.457525			−0.228762	−	0.973482i	$-0.573468\pi$
$757$	−346.346			−0.457525			−0.228762	+	0.973482i	$0.573468\pi$
$758$	933.847	+	761.207i	1.23199	+	1.00423i
$759$	−483.759	−	395.556i	−0.637363	−	0.521154i
$760$	305.630	−	13.0578i	0.402145	−	0.0171813i
$761$	−106.565	−	184.576i	−0.140033	−	0.242544i	0.787476	−	0.616345i	$-0.211387\pi$
$761$	−106.565	−	184.576i	−0.140033	−	0.242544i	−0.927509	+	0.373802i	$0.878054\pi$
$762$	−10.0511	−	49.2111i	−0.0131904	−	0.0645815i
$763$	869.291	+	501.885i	1.13931	+	0.657779i
$764$	−356.571	+	1073.83i	−0.466715	+	1.40553i
$765$	162.445	−	143.498i	0.212347	−	0.187579i
$766$	−116.394	+	719.871i	−0.151951	+	0.939779i
$767$	45.4277	+	26.2277i	0.0592277	+	0.0341952i
$768$	−761.857	+	96.9457i	−0.992001	+	0.126231i
$769$	−270.786	−	469.015i	−0.352127	−	0.609902i	0.634495	−	0.772927i	$-0.281208\pi$
$769$	−270.786	−	469.015i	−0.352127	−	0.609902i	−0.986622	+	0.163025i	$0.947875\pi$
$770$	−220.647	−	580.384i	−0.286554	−	0.753746i
$771$	227.477	−	1393.40i	0.295041	−	1.80726i
$772$	−906.149	+	805.393i	−1.17377	+	1.04325i
$773$	1255.73			1.62449			0.812245	−	0.583317i	$-0.198245\pi$
$773$	1255.73			1.62449			0.812245	+	0.583317i	$0.198245\pi$
$774$	−357.770	−	566.557i	−0.462235	−	0.731986i
$775$		−	292.070i		−	0.376864i
$776$	48.4920	−	30.8291i	0.0624897	−	0.0397282i
$777$	500.611	+	1322.87i	0.644287	+	1.70253i
$778$	−152.557	−	401.281i	−0.196088	−	0.515786i
$779$	−518.136	+	299.146i	−0.665130	+	0.384013i
$780$	−10.3188	−	16.2855i	−0.0132292	−	0.0208788i
$781$	−551.759	+	955.675i	−0.706478	+	1.22366i
$782$	59.8186	−	369.964i	0.0764944	−	0.473100i
$783$	−292.701	−	465.084i	−0.373820	−	0.593977i
$784$	−1096.09	−	818.133i	−1.39807	−	1.04354i
$785$	−7.19706	+	12.4657i	−0.00916822	+	0.0158798i
$786$	596.670	−	528.698i	0.759122	−	0.672644i
$787$	859.448	−	496.202i	1.09206	−	0.630499i	0.157933	−	0.987450i	$-0.449517\pi$
$787$	859.448	−	496.202i	1.09206	−	0.630499i	0.934123	+	0.356951i	$0.116184\pi$
$788$	−112.242	−	545.306i	−0.142439	−	0.692012i
$789$	−27.2220	−	71.9343i	−0.0345019	−	0.0911715i
$790$	−40.3171	−	32.8637i	−0.0510343	−	0.0415996i
$791$		−	54.5507i		−	0.0689643i
$792$	−512.063	+	492.814i	−0.646545	+	0.622240i
$793$	43.2342			0.0545198
$794$	−865.123	+	1061.33i	−1.08958	+	1.33669i
$795$	−27.6618	+	169.441i	−0.0347947	+	0.213134i
$796$	44.0120	−	9.05914i	0.0552914	−	0.0113808i
$797$	319.262	+	552.978i	0.400580	+	0.693824i	0.993796	−	0.111219i	$-0.0354754\pi$
$797$	319.262	+	552.978i	0.400580	+	0.693824i	−0.593216	+	0.805043i	$0.702142\pi$
$798$	310.571	−	930.548i	0.389186	−	1.16610i
$799$	−13.9530	−	8.05574i	−0.0174630	−	0.0100823i
$800$	392.760	+	405.617i	0.490950	+	0.507022i
$801$	115.807	+	571.445i	0.144577	+	0.713414i
$802$	375.885	+	60.7760i	0.468685	+	0.0757805i
$803$	651.377	+	376.073i	0.811179	+	0.468335i
$804$	−21.8506	−	530.404i	−0.0271773	−	0.659706i
$805$	−331.865	−	574.806i	−0.412254	−	0.714045i
$806$	18.3314	−	6.96913i	0.0227437	−	0.00864656i
$807$	−18.9297	−	15.4783i	−0.0234569	−	0.0191801i
$808$	749.428	−	476.453i	0.927509	−	0.589670i
$809$	−174.260			−0.215401			−0.107701	−	0.994183i	$-0.534349\pi$
$809$	−174.260			−0.215401			−0.107701	+	0.994183i	$0.534349\pi$
$810$	−426.822	+	104.267i	−0.526940	+	0.128725i
$811$			1182.19i			1.45770i	0.684675	+	0.728849i	$0.259944\pi$
$811$			1182.19i			1.45770i	−0.684675	+	0.728849i	$0.740056\pi$
$812$	−627.196	−	705.660i	−0.772409	−	0.869039i
$813$	−763.360	+	933.577i	−0.938942	+	1.14831i
$814$	750.210	−	285.210i	0.921634	−	0.350381i
$815$	−139.880	+	80.7597i	−0.171632	+	0.0990917i
$816$	−409.693	−	117.555i	−0.502074	−	0.144063i
$817$	262.421	−	454.527i	0.321201	−	0.556336i
$818$	746.222	+	120.655i	0.912251	+	0.147500i
$819$	−60.5944	+	12.2798i	−0.0739858	+	0.0149937i
$820$	436.912	+	145.079i	0.532820	+	0.176926i
$821$	293.955	−	509.144i	0.358045	−	0.620151i	−0.629590	−	0.776928i	$-0.716777\pi$
$821$	293.955	−	509.144i	0.358045	−	0.620151i	0.987634	+	0.156777i	$0.0501103\pi$
$822$	−85.6977	+	256.772i	−0.104255	+	0.312375i
$823$	98.0750	−	56.6236i	0.119168	−	0.0688015i	−0.439231	−	0.898374i	$-0.644749\pi$
$823$	98.0750	−	56.6236i	0.119168	−	0.0688015i	0.558399	+	0.829573i	$0.311416\pi$
$824$	−734.766	+	31.3922i	−0.891706	+	0.0380973i
$825$	515.649	+	84.1813i	0.625029	+	0.102038i
$826$	1297.64	−	1591.95i	1.57100	−	1.92730i
$827$		−	800.560i		−	0.968030i	−0.875060	−	0.484015i	$-0.839178\pi$
$827$		−	800.560i		−	0.968030i	0.875060	−	0.484015i	$-0.160822\pi$
$828$	−456.273	+	607.414i	−0.551054	+	0.733592i
$829$	1162.87			1.40274			0.701369	−	0.712798i	$-0.252573\pi$
$829$	1162.87			1.40274			0.701369	+	0.712798i	$0.252573\pi$
$830$	357.442	+	291.362i	0.430653	+	0.351038i
$831$	−315.385	+	119.351i	−0.379525	+	0.143623i
$832$	−16.0864	+	34.3297i	−0.0193346	+	0.0412616i
$833$	−379.538	−	657.378i	−0.455627	−	0.789170i
$834$	677.961	−	600.729i	0.812903	−	0.720298i
$835$	−232.551	−	134.264i	−0.278505	−	0.160795i
$836$	−528.296	−	175.424i	−0.631933	−	0.209837i
$837$	−17.0344	−	446.617i	−0.0203517	−	0.533592i
$838$	−98.5400	+	609.447i	−0.117590	+	0.727264i
$839$	−1355.92	−	782.842i	−1.61612	−	0.933065i	−0.987912	−	0.155017i	$-0.950457\pi$
$839$	−1355.92	−	782.842i	−1.61612	−	0.933065i	−0.628205	−	0.778048i	$-0.716210\pi$
$840$	−693.949	+	297.062i	−0.826130	+	0.353645i
$841$	213.383	+	369.590i	0.253725	+	0.439464i
$842$	−251.359	−	661.170i	−0.298526	−	0.785237i
$843$	−1508.78	+	570.966i	−1.78978	+	0.677303i
$844$	343.712	+	386.712i	0.407242	+	0.458189i
$845$	457.406			0.541309
$846$	17.4381	+	27.6145i	0.0206124	+	0.0326413i
$847$		−	273.341i		−	0.322717i
$848$	310.163	−	133.333i	0.365758	−	0.157232i
$849$	418.133	+	68.2615i	0.492501	+	0.0804022i
$850$	111.351	+	292.895i	0.131001	+	0.344583i
$851$	743.000	−	428.971i	0.873091	−	0.504079i
$852$	1188.47	+	622.397i	1.39491	+	0.730513i
$853$	−68.8088	+	119.180i	−0.0806668	+	0.139719i	−0.903537	−	0.428511i	$-0.859038\pi$
$853$	−68.8088	+	119.180i	−0.0806668	+	0.139719i	0.822870	+	0.568230i	$0.192372\pi$
$854$	270.192	−	1671.08i	0.316384	−	1.95676i
$855$	−227.842	−	257.926i	−0.266482	−	0.301668i
$856$	398.711	−	764.170i	0.465783	−	0.892722i
$857$	−384.489	+	665.955i	−0.448646	+	0.777077i	−0.998298	−	0.0583164i	$-0.981427\pi$
$857$	−384.489	+	665.955i	−0.448646	+	0.777077i	0.549653	+	0.835393i	$0.314760\pi$
$858$	7.02045	+	34.3729i	0.00818235	+	0.0400616i
$859$	178.353	−	102.972i	0.207629	−	0.119875i	−0.392580	−	0.919718i	$-0.628417\pi$
$859$	178.353	−	102.972i	0.207629	−	0.119875i	0.600209	+	0.799843i	$0.295084\pi$
$860$	−395.559	+	81.4193i	−0.459953	+	0.0946736i
$861$	934.525	−	1142.91i	1.08540	−	1.32742i
$862$	732.912	+	597.419i	0.850246	+	0.693062i
$863$		−	772.757i		−	0.895431i	−0.894176	−	0.447716i	$-0.852238\pi$
$863$		−	772.757i		−	0.895431i	0.894176	−	0.447716i	$-0.147762\pi$
$864$	624.244	+	597.341i	0.722504	+	0.691366i
$865$	104.671			0.121007
$866$	77.6112	−	95.2133i	0.0896204	−	0.109946i
$867$	488.066	+	399.078i	0.562937	+	0.460298i
$868$	−154.806	−	752.095i	−0.178348	−	0.866469i
$869$	47.3249	+	81.9692i	0.0544591	+	0.0943258i
$870$	−324.502	+	66.2777i	−0.372991	+	0.0761813i
$871$	−22.6943	−	13.1026i	−0.0260555	−	0.0150432i
$872$	−613.911	−	320.312i	−0.704026	−	0.367330i
$873$	−61.2887	−	20.5590i	−0.0702047	−	0.0235499i
$874$	−587.418	−	94.9782i	−0.672103	−	0.108671i
$875$	1161.57	+	670.630i	1.32750	+	0.766435i
$876$	424.219	−	810.044i	0.484268	−	0.924708i
$877$	−200.096	−	346.577i	−0.228160	−	0.395185i	0.729103	−	0.684404i	$-0.239938\pi$
$877$	−200.096	−	346.577i	−0.228160	−	0.395185i	−0.957263	+	0.289219i	$0.906604\pi$
$878$	−764.917	+	290.801i	−0.871204	+	0.331209i
$879$	−222.627	+	1363.69i	−0.253273	+	1.55141i
$880$	169.164	+	393.515i	0.192232	+	0.447176i
$881$	−728.323			−0.826700			−0.413350	−	0.910572i	$-0.635641\pi$
$881$	−728.323			−0.826700			−0.413350	+	0.910572i	$0.635641\pi$
$882$	60.9908	+	1537.51i	0.0691506	+	1.74321i
$883$		−	383.413i		−	0.434216i	−0.976148	−	0.217108i	$-0.930338\pi$
$883$		−	383.413i		−	0.434216i	0.976148	−	0.217108i	$-0.0696625\pi$
$884$	−15.7263	+	13.9777i	−0.0177899	+	0.0158118i
$885$	−255.010	−	673.865i	−0.288147	−	0.761429i
$886$	−1443.73	+	548.868i	−1.62949	+	0.619489i
$887$	1255.91	−	725.098i	1.41590	−	0.817473i	0.419968	−	0.907539i	$-0.362041\pi$
$887$	1255.91	−	725.098i	1.41590	−	0.817473i	0.995936	+	0.0900662i	$0.0287079\pi$
$888$	−383.985	−	897.005i	−0.432415	−	1.01014i
$889$	−48.5392	+	84.0724i	−0.0545998	+	0.0945696i
$890$	346.909	+	56.0909i	0.389785	+	0.0630234i
$891$	793.412	+	98.6511i	0.890474	+	0.110720i
$892$	−304.516	+	917.061i	−0.341385	+	1.02810i
$893$	−12.7907	+	22.1541i	−0.0143232	+	0.0248086i
$894$	−568.152	−	641.196i	−0.635517	−	0.717221i
$895$	−85.5589	+	49.3974i	−0.0955965	+	0.0551927i
$896$	1226.37	+	836.311i	1.36871	+	0.933383i
$897$	13.2731	+	35.0743i	0.0147972	+	0.0391018i
$898$	−997.059	+	1223.19i	−1.11031	+	1.36213i
$899$		−	336.907i		−	0.374758i
$900$	76.4512	−	630.570i	0.0849458	−	0.700633i
$901$	187.365			0.207952
$902$	−649.337	−	529.295i	−0.719886	−	0.586801i
$903$	−208.666	+	1278.17i	−0.231080	+	1.41547i
$904$	1.60631	+	37.5974i	0.00177690	+	0.0415901i
$905$	−25.2125	−	43.6694i	−0.0278592	−	0.0482535i
$906$	−1445.98	−	482.597i	−1.59601	−	0.532668i
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	0.176324	−	0.984332i	$-0.443580\pi$
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	−0.764295	+	0.644867i	$0.776913\pi$
$908$	481.366	−	1449.65i	0.530139	−	1.59653i
$909$	−947.196	−	317.733i	−1.04202	−	0.349541i
$910$	−5.94772	+	36.7853i	−0.00653596	+	0.0404234i
$911$	227.031	+	131.076i	0.249211	+	0.143882i	0.619403	−	0.785073i	$-0.287375\pi$
$911$	227.031	+	131.076i	0.249211	+	0.143882i	−0.370192	+	0.928955i	$0.620708\pi$
$912$	−186.650	+	650.498i	−0.204660	+	0.713265i
$913$	−419.572	−	726.720i	−0.459553	−	0.795969i
$914$	−196.393	−	516.589i	−0.214872	−	0.565196i
$915$	−459.726	−	375.905i	−0.502433	−	0.410825i
$916$	446.455	−	396.813i	0.487397	−	0.433202i
$917$	−1540.83			−1.68030
$918$	187.355	+	441.385i	0.204090	+	0.480812i
$919$			566.458i			0.616385i	0.951324	+	0.308193i	$0.0997241\pi$
$919$			566.458i			0.616385i	−0.951324	+	0.308193i	$0.900276\pi$
$920$	245.654	+	386.396i	0.267015	+	0.419995i
$921$	−399.403	+	488.464i	−0.433663	+	0.530362i
$922$	417.961	+	1099.40i	0.453320	+	1.19240i
$923$	57.3533	−	33.1130i	0.0621379	−	0.0358754i
$924$	1372.44	−	56.5394i	1.48533	−	0.0611898i
$925$	−358.667	+	621.229i	−0.387748	+	0.671599i
$926$	−249.657	+	1544.07i	−0.269608	+	1.66746i
$927$	547.755	+	620.080i	0.590890	+	0.668910i
$928$	453.055	+	467.886i	0.488206	+	0.504188i
$929$	298.745	−	517.442i	0.321577	−	0.556988i	−0.659236	−	0.751936i	$-0.729120\pi$
$929$	298.745	−	517.442i	0.321577	−	0.556988i	0.980814	+	0.194948i	$0.0624537\pi$
$930$	−255.519	−	85.2795i	−0.274752	−	0.0916984i
$931$	−1043.77	+	602.618i	−1.12112	+	0.647281i
$932$	176.555	+	857.754i	0.189436	+	0.920337i
$933$	−379.469	−	61.9495i	−0.406719	−	0.0663982i
$934$	1028.12	+	838.050i	1.10077	+	0.897270i
$935$			237.717i			0.254243i
$936$	41.4013	−	10.2478i	0.0442321	−	0.0109485i
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$	−648.265	+	795.290i	−0.691115	+	0.847858i
$939$	20.3220	−	7.69041i	0.0216421	−	0.00819000i
$940$	19.2800	−	3.96846i	0.0205106	−	0.00422176i
$941$	−677.858	−	1174.09i	−0.720360	−	1.24770i	−0.960856	−	0.277049i	$-0.910643\pi$
$941$	−677.858	−	1174.09i	−0.720360	−	1.24770i	0.240496	−	0.970650i	$-0.422690\pi$
$942$	−21.1181	−	23.8332i	−0.0224184	−	0.0253006i
$943$	−775.526	−	447.750i	−0.822403	−	0.474814i
$944$	−847.486	+	1135.41i	−0.897760	+	1.20277i
$945$	751.091	+	396.269i	0.794805	+	0.419332i
$946$	725.463	+	117.298i	0.766874	+	0.123994i
$947$	−567.925	−	327.891i	−0.599709	−	0.346242i	0.169218	−	0.985579i	$-0.445876\pi$
$947$	−567.925	−	327.891i	−0.599709	−	0.346242i	−0.768927	+	0.639336i	$0.779209\pi$
$948$	97.1995	−	61.5872i	0.102531	−	0.0649654i
$949$	−22.5694	−	39.0914i	−0.0237823	−	0.0411922i
$950$	465.050	−	176.800i	0.489527	−	0.186105i
$951$	674.210	−	255.141i	0.708949	−	0.268287i
$952$	441.979	+	695.202i	0.464264	+	0.730254i
$953$	554.778			0.582139			0.291069	−	0.956702i	$-0.405989\pi$
$953$	554.778			0.582139			0.291069	+	0.956702i	$0.405989\pi$
$954$	−336.192	−	176.717i	−0.352403	−	0.185238i
$955$		−	767.193i		−	0.803344i
$956$	−669.693	−	753.473i	−0.700516	−	0.788152i
$957$	594.810	+	97.1045i	0.621536	+	0.101468i
$958$	1213.21	−	461.230i	1.26640	−	0.481451i
$959$	453.102	−	261.599i	0.472474	−	0.272783i
$960$	469.536	−	225.175i	0.489100	−	0.234557i
$961$	−343.493	+	594.947i	−0.357432	+	0.619091i
$962$	−47.5490	−	7.68808i	−0.0494272	−	0.00799177i
$963$	−950.354	+	192.595i	−0.986869	+	0.199995i
$964$	1715.98	+	569.801i	1.78006	+	0.591080i
$965$	411.009	−	711.889i	0.425917	−	0.737709i
$966$	1438.63	−	293.832i	1.48927	−	0.304174i
$967$	502.000	−	289.830i	0.519131	−	0.299720i	−0.217448	−	0.976072i	$-0.569773\pi$
$967$	502.000	−	289.830i	0.519131	−	0.299720i	0.736579	+	0.676351i	$0.236440\pi$
$968$	8.04887	+	188.392i	0.00831495	+	0.194620i
$969$	−237.743	+	290.756i	−0.245349	+	0.300058i
$970$	−24.6169	+	30.2000i	−0.0253783	+	0.0311340i
$971$			260.660i			0.268445i	0.990951	+	0.134223i	$0.0428537\pi$
$971$			260.660i			0.268445i	−0.990951	+	0.134223i	$0.957146\pi$
$972$	80.1282	−	968.692i	0.0824364	−	0.996596i
$973$	−1750.76			−1.79934
$974$	−437.326	−	356.478i	−0.449000	−	0.365994i
$975$	−24.2739	−	19.8481i	−0.0248963	−	0.0203570i
$976$	−137.015	+	1159.70i	−0.140384	+	1.18821i
$977$	638.953	+	1106.70i	0.653995	+	1.13275i	0.982145	+	0.188127i	$0.0602417\pi$
$977$	638.953	+	1106.70i	0.653995	+	1.13275i	−0.328149	+	0.944626i	$0.606425\pi$
$978$	−71.5045	−	350.093i	−0.0731129	−	0.357968i
$979$	−553.793	−	319.732i	−0.565672	−	0.326591i
$980$	880.143	+	292.257i	0.898105	+	0.298221i
$981$	154.725	+	763.486i	0.157721	+	0.778273i
$982$	240.680	−	1488.55i	0.245092	−	1.51584i
$983$	378.325	+	218.426i	0.384868	+	0.222204i	0.679934	−	0.733273i	$-0.262008\pi$
$983$	378.325	+	218.426i	0.384868	+	0.222204i	−0.295066	+	0.955477i	$0.595342\pi$
$984$	−610.439	+	815.234i	−0.620365	+	0.828490i
$985$	188.746	+	326.918i	0.191621	+	0.331897i
$986$	128.445	+	337.860i	0.130269	+	0.342657i
$987$	10.1706	−	62.2994i	0.0103045	−	0.0631200i
$988$	22.1933	+	24.9698i	0.0224629	+	0.0252730i
$989$	785.562			0.794300
$990$	224.208	−	426.540i	0.226472	−	0.430848i
$991$		−	1344.50i		−	1.35671i	−0.734734	−	0.678356i	$-0.762693\pi$
$991$		−	1344.50i		−	1.35671i	0.734734	−	0.678356i	$-0.237307\pi$
$992$	128.842	+	513.800i	0.129881	+	0.517944i
$993$	−454.114	−	1200.00i	−0.457316	−	1.20846i
$994$	−921.443	−	2423.74i	−0.927005	−	2.43837i
$995$	−26.3858	+	15.2338i	−0.0265184	+	0.0153104i
$996$	−861.748	+	546.018i	−0.865209	+	0.548211i
$997$	942.397	−	1632.28i	0.945233	−	1.63719i	0.189949	−	0.981794i	$-0.439168\pi$
$997$	942.397	−	1632.28i	0.945233	−	1.63719i	0.755284	−	0.655398i	$-0.227499\pi$
$998$	−164.464	+	1017.17i	−0.164794	+	1.01921i
$999$	−512.221	+	970.868i	−0.512734	+	0.971839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.f.c.7.7	yes	16
3.2	odd	2		108.3.f.c.19.2		16
4.3	odd	2	inner	36.3.f.c.7.6	✓	16
8.3	odd	2		576.3.o.g.511.3		16
8.5	even	2		576.3.o.g.511.6		16
9.2	odd	6		324.3.d.g.163.8		8
9.4	even	3	inner	36.3.f.c.31.6	yes	16
9.5	odd	6		108.3.f.c.91.3		16
9.7	even	3		324.3.d.i.163.1		8
12.11	even	2		108.3.f.c.19.3		16
24.5	odd	2		1728.3.o.g.127.6		16
24.11	even	2		1728.3.o.g.127.5		16
36.7	odd	6		324.3.d.i.163.2		8
36.11	even	6		324.3.d.g.163.7		8
36.23	even	6		108.3.f.c.91.2		16
36.31	odd	6	inner	36.3.f.c.31.7	yes	16
72.5	odd	6		1728.3.o.g.1279.5		16
72.13	even	6		576.3.o.g.319.3		16
72.59	even	6		1728.3.o.g.1279.6		16
72.67	odd	6		576.3.o.g.319.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	4.3	odd	2	inner
36.3.f.c.7.7	yes	16	1.1	even	1	trivial
36.3.f.c.31.6	yes	16	9.4	even	3	inner
36.3.f.c.31.7	yes	16	36.31	odd	6	inner
108.3.f.c.19.2		16	3.2	odd	2
108.3.f.c.19.3		16	12.11	even	2
108.3.f.c.91.2		16	36.23	even	6
108.3.f.c.91.3		16	9.5	odd	6
324.3.d.g.163.7		8	36.11	even	6
324.3.d.g.163.8		8	9.2	odd	6
324.3.d.i.163.1		8	9.7	even	3
324.3.d.i.163.2		8	36.7	odd	6
576.3.o.g.319.3		16	72.13	even	6
576.3.o.g.319.6		16	72.67	odd	6
576.3.o.g.511.3		16	8.3	odd	2
576.3.o.g.511.6		16	8.5	even	2
1728.3.o.g.127.5		16	24.11	even	2
1728.3.o.g.127.6		16	24.5	odd	2
1728.3.o.g.1279.5		16	72.5	odd	6
1728.3.o.g.1279.6		16	72.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.26364 - 1.55023i) q^{2} +(-2.32245 - 1.89900i) q^{3} +(-0.806428 - 3.91787i) q^{4} +(1.35609 + 2.34881i) q^{5} +(-5.87864 + 1.20068i) q^{6} +(10.0431 + 5.79837i) q^{7} +(-7.09263 - 3.70062i) q^{8} +(1.78756 + 8.82069i) q^{9} +O(q^{10})\)	\(q+(1.26364 - 1.55023i) q^{2} +(-2.32245 - 1.89900i) q^{3} +(-0.806428 - 3.91787i) q^{4} +(1.35609 + 2.34881i) q^{5} +(-5.87864 + 1.20068i) q^{6} +(10.0431 + 5.79837i) q^{7} +(-7.09263 - 3.70062i) q^{8} +(1.78756 + 8.82069i) q^{9} +(5.35481 + 0.865806i) q^{10} +(-8.54822 - 4.93532i) q^{11} +(-5.56715 + 10.6305i) q^{12} +(0.296185 + 0.513008i) q^{13} +(21.6796 - 8.24203i) q^{14} +(1.31096 - 8.03023i) q^{15} +(-14.6993 + 6.31895i) q^{16} -8.87968 q^{17} +(15.9329 + 8.37504i) q^{18} +14.0989i q^{19} +(8.10875 - 7.20712i) q^{20} +(-12.3134 - 32.5383i) q^{21} +(-18.4528 + 7.01525i) q^{22} +(-18.2754 + 10.5513i) q^{23} +(9.44479 + 22.0635i) q^{24} +(8.82205 - 15.2802i) q^{25} +(1.16955 + 0.189102i) q^{26} +(12.5990 - 23.8802i) q^{27} +(14.6182 - 44.0234i) q^{28} +(10.1764 - 17.6260i) q^{29} +(-10.7921 - 12.1796i) q^{30} +(14.3357 - 8.27670i) q^{31} +(-8.77885 + 30.7723i) q^{32} +(10.4806 + 27.6952i) q^{33} +(-11.2207 + 13.7655i) q^{34} +31.4524i q^{35} +(33.1167 - 14.1167i) q^{36} -40.6557 q^{37} +(21.8565 + 17.8159i) q^{38} +(0.286328 - 1.75389i) q^{39} +(-0.926156 - 21.6776i) q^{40} +(21.2177 + 36.7502i) q^{41} +(-66.0016 - 22.0280i) q^{42} +(-32.2385 - 18.6129i) q^{43} +(-12.4424 + 37.4708i) q^{44} +(-18.2941 + 16.1603i) q^{45} +(-6.73658 + 41.6642i) q^{46} +(1.57134 + 0.907211i) q^{47} +(46.1382 + 13.2387i) q^{48} +(42.7423 + 74.0318i) q^{49} +(-12.5400 - 32.9849i) q^{50} +(20.6226 + 16.8625i) q^{51} +(1.77105 - 1.57412i) q^{52} -21.1005 q^{53} +(-21.0992 - 49.7074i) q^{54} -26.7709i q^{55} +(-49.7742 - 78.2914i) q^{56} +(26.7738 - 32.7440i) q^{57} +(-14.4651 - 38.0487i) q^{58} +(76.6879 - 44.2758i) q^{59} +(-32.5185 + 1.33964i) q^{60} +(36.4925 - 63.2069i) q^{61} +(5.28433 - 32.6823i) q^{62} +(-33.1930 + 98.9519i) q^{63} +(36.6108 + 52.4943i) q^{64} +(-0.803307 + 1.39137i) q^{65} +(56.1776 + 18.7493i) q^{66} +(-38.3110 + 22.1189i) q^{67} +(7.16082 + 34.7894i) q^{68} +(62.4808 + 10.2002i) q^{69} +(48.7585 + 39.7446i) q^{70} -111.798i q^{71} +(19.9635 - 69.1770i) q^{72} -76.2003 q^{73} +(-51.3742 + 63.0257i) q^{74} +(-49.5060 + 18.7345i) q^{75} +(55.2375 - 11.3697i) q^{76} +(-57.2337 - 99.1316i) q^{77} +(-2.35712 - 2.66017i) q^{78} +(-8.30434 - 4.79451i) q^{79} +(-34.7757 - 25.9570i) q^{80} +(-74.6092 + 31.5351i) q^{81} +(83.7828 + 13.5466i) q^{82} +(73.6244 + 42.5070i) q^{83} +(-117.551 + 74.4821i) q^{84} +(-12.0416 - 20.8567i) q^{85} +(-69.5921 + 26.4571i) q^{86} +(-57.1060 + 21.6106i) q^{87} +(42.3656 + 66.6381i) q^{88} +64.7845 q^{89} +(1.93506 + 48.7808i) q^{90} +6.86958i q^{91} +(56.0765 + 63.0918i) q^{92} +(-49.0114 - 8.00125i) q^{93} +(3.39199 - 1.28954i) q^{94} +(-33.1157 + 19.1193i) q^{95} +(78.8251 - 54.7960i) q^{96} +(-3.59139 + 6.22047i) q^{97} +(168.777 + 27.2892i) q^{98} +(28.2524 - 84.2235i) 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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