LMFDB - Embedded newform 45.3.i.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(11,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.22616118962$
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} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Root			$1.83391i$ of defining polynomial
Character	$\chi$	$=$	45.11
Dual form			45.3.i.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58822 + 0.916957i) q^{2} +(0.822398 + 2.88508i) q^{3} +(-0.318381 - 0.551452i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.33934 + 5.33623i) q^{6} +(3.23398 - 5.60142i) q^{7} -8.50342i q^{8} +(-7.64732 + 4.74536i) q^{9} +O(q^{10})$	\(q+(1.58822 + 0.916957i) q^{2} +(0.822398 + 2.88508i) q^{3} +(-0.318381 - 0.551452i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.33934 + 5.33623i) q^{6} +(3.23398 - 5.60142i) q^{7} -8.50342i q^{8} +(-7.64732 + 4.74536i) q^{9} -4.10076 q^{10} +(9.24701 + 5.33876i) q^{11} +(1.32914 - 1.37207i) q^{12} +(-5.53374 - 9.58473i) q^{13} +(10.2725 - 5.93084i) q^{14} +(-4.81818 - 4.66746i) q^{15} +(6.52374 - 11.2995i) q^{16} +12.6328i q^{17} +(-16.4969 + 0.524391i) q^{18} -32.1403 q^{19} +(1.23308 + 0.711921i) q^{20} +(18.8201 + 4.72368i) q^{21} +(9.79083 + 16.9582i) q^{22} +(-9.82266 + 5.67112i) q^{23} +(24.5330 - 6.99319i) q^{24} +(2.50000 - 4.33013i) q^{25} -20.2968i q^{26} +(-19.9799 - 18.1605i) q^{27} -4.11855 q^{28} +(35.2234 + 20.3362i) q^{29} +(-3.37245 - 11.8310i) q^{30} +(15.9429 + 27.6139i) q^{31} +(-8.73448 + 5.04286i) q^{32} +(-7.79801 + 31.0689i) q^{33} +(-11.5837 + 20.0635i) q^{34} +14.4628i q^{35} +(5.05160 + 2.70630i) q^{36} +45.4499 q^{37} +(-51.0457 - 29.4713i) q^{38} +(23.1017 - 23.8477i) q^{39} +(9.50711 + 16.4668i) q^{40} +(-25.4781 + 14.7098i) q^{41} +(25.5590 + 24.7595i) q^{42} +(18.8093 - 32.5786i) q^{43} -6.79904i q^{44} +(9.50350 - 17.7393i) q^{45} -20.8007 q^{46} +(-49.8119 - 28.7589i) q^{47} +(37.9649 + 9.52885i) q^{48} +(3.58274 + 6.20548i) q^{49} +(7.94108 - 4.58478i) q^{50} +(-36.4465 + 10.3891i) q^{51} +(-3.52368 + 6.10319i) q^{52} -33.3940i q^{53} +(-15.0799 - 47.1635i) q^{54} -23.8757 q^{55} +(-47.6312 - 27.4999i) q^{56} +(-26.4321 - 92.7272i) q^{57} +(37.2949 + 64.5966i) q^{58} +(3.54909 - 2.04907i) q^{59} +(-1.03986 + 4.14302i) q^{60} +(33.1195 - 57.3647i) q^{61} +58.4757i q^{62} +(1.84945 + 58.1823i) q^{63} -70.6863 q^{64} +(21.4321 + 12.3738i) q^{65} +(-40.8738 + 42.1937i) q^{66} +(-35.4890 - 61.4687i) q^{67} +(6.96635 - 4.02203i) q^{68} +(-24.4397 - 23.6752i) q^{69} +(-13.2618 + 22.9700i) q^{70} +13.1123i q^{71} +(40.3518 + 65.0284i) q^{72} +109.273 q^{73} +(72.1842 + 41.6756i) q^{74} +(14.5487 + 3.65160i) q^{75} +(10.2328 + 17.7238i) q^{76} +(59.8093 - 34.5309i) q^{77} +(58.5579 - 16.6921i) q^{78} +(-49.8891 + 86.4104i) q^{79} +29.1751i q^{80} +(35.9631 - 72.5786i) q^{81} -53.9530 q^{82} +(74.2472 + 42.8667i) q^{83} +(-3.38709 - 11.8823i) q^{84} +(-14.1238 - 24.4632i) q^{85} +(59.7463 - 34.4945i) q^{86} +(-29.7039 + 118.347i) q^{87} +(45.3977 - 78.6312i) q^{88} +63.6372i q^{89} +(31.3598 - 19.4596i) q^{90} -71.5841 q^{91} +(6.25469 + 3.61115i) q^{92} +(-66.5567 + 68.7060i) q^{93} +(-52.7414 - 91.3507i) q^{94} +(62.2394 - 35.9339i) q^{95} +(-21.7322 - 21.0524i) q^{96} +(-43.2064 + 74.8357i) q^{97} +13.1409i q^{98} +(-96.0492 + 3.05314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9	$ 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9} - 18 q^{11} - 22 q^{12} - 10 q^{13} - 54 q^{14} + 10 q^{15} - 32 q^{16} - 8 q^{18} - 52 q^{19} + 72 q^{21} - 24 q^{22} - 54 q^{23} + 108 q^{24} + 40 q^{25} + 34 q^{27} + 32 q^{28} - 54 q^{29} - 100 q^{30} + 32 q^{31} + 216 q^{32} + 62 q^{33} + 54 q^{34} - 86 q^{36} + 44 q^{37} + 252 q^{38} + 160 q^{39} - 30 q^{40} + 144 q^{41} - 270 q^{42} - 124 q^{43} + 140 q^{45} - 108 q^{46} - 216 q^{47} - 172 q^{48} - 54 q^{49} - 106 q^{51} + 62 q^{52} - 316 q^{54} - 18 q^{56} - 236 q^{57} + 90 q^{58} - 486 q^{59} - 10 q^{60} + 62 q^{61} - 132 q^{63} + 256 q^{64} - 90 q^{65} + 208 q^{66} + 14 q^{67} - 288 q^{68} + 90 q^{69} - 60 q^{70} + 804 q^{72} - 268 q^{73} + 540 q^{74} - 20 q^{75} - 106 q^{76} + 702 q^{77} + 290 q^{78} - 40 q^{79} - 112 q^{81} - 204 q^{82} + 522 q^{83} + 714 q^{84} + 30 q^{85} + 54 q^{86} + 106 q^{87} + 144 q^{88} + 250 q^{90} + 136 q^{91} - 1332 q^{92} + 90 q^{93} - 150 q^{94} + 180 q^{95} + 166 q^{96} - 142 q^{97} - 824 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9 - 18 * q^11 - 22 * q^12 - 10 * q^13 - 54 * q^14 + 10 * q^15 - 32 * q^16 - 8 * q^18 - 52 * q^19 + 72 * q^21 - 24 * q^22 - 54 * q^23 + 108 * q^24 + 40 * q^25 + 34 * q^27 + 32 * q^28 - 54 * q^29 - 100 * q^30 + 32 * q^31 + 216 * q^32 + 62 * q^33 + 54 * q^34 - 86 * q^36 + 44 * q^37 + 252 * q^38 + 160 * q^39 - 30 * q^40 + 144 * q^41 - 270 * q^42 - 124 * q^43 + 140 * q^45 - 108 * q^46 - 216 * q^47 - 172 * q^48 - 54 * q^49 - 106 * q^51 + 62 * q^52 - 316 * q^54 - 18 * q^56 - 236 * q^57 + 90 * q^58 - 486 * q^59 - 10 * q^60 + 62 * q^61 - 132 * q^63 + 256 * q^64 - 90 * q^65 + 208 * q^66 + 14 * q^67 - 288 * q^68 + 90 * q^69 - 60 * q^70 + 804 * q^72 - 268 * q^73 + 540 * q^74 - 20 * q^75 - 106 * q^76 + 702 * q^77 + 290 * q^78 - 40 * q^79 - 112 * q^81 - 204 * q^82 + 522 * q^83 + 714 * q^84 + 30 * q^85 + 54 * q^86 + 106 * q^87 + 144 * q^88 + 250 * q^90 + 136 * q^91 - 1332 * q^92 + 90 * q^93 - 150 * q^94 + 180 * q^95 + 166 * q^96 - 142 * q^97 - 824 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.58822	+	0.916957i	0.794108	+	0.458478i	0.841407	−	0.540402i	$-0.181728\pi$
$2$	1.58822	+	0.916957i	0.794108	+	0.458478i	−0.0472989	+	0.998881i	$0.515061\pi$
$3$	0.822398	+	2.88508i	0.274133	+	0.961692i
$3$	0.822398	+	2.88508i	0.274133	+	0.961692i
$4$	−0.318381	−	0.551452i	−0.0795952	−	0.137863i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$	−1.33934	+	5.33623i	−0.223224	+	0.889371i
$7$	3.23398	−	5.60142i	0.461997	−	0.800203i	−0.537063	−	0.843542i	$-0.680466\pi$
$7$	3.23398	−	5.60142i	0.461997	−	0.800203i	0.999060	+	0.0433393i	$0.0137997\pi$
$8$		−	8.50342i		−	1.06293i
$9$	−7.64732	+	4.74536i	−0.849703	+	0.527262i
$10$	−4.10076			−0.410076
$11$	9.24701	+	5.33876i	0.840637	+	0.485342i	0.857481	−	0.514516i	$-0.172028\pi$
$11$	9.24701	+	5.33876i	0.840637	+	0.485342i	−0.0168436	+	0.999858i	$0.505362\pi$
$12$	1.32914	−	1.37207i	0.110762	−	0.114339i
$13$	−5.53374	−	9.58473i	−0.425673	−	0.737287i	0.570810	−	0.821082i	$-0.306629\pi$
$13$	−5.53374	−	9.58473i	−0.425673	−	0.737287i	−0.996483	+	0.0837952i	$0.973296\pi$
$14$	10.2725	−	5.93084i	0.733751	−	0.423631i
$15$	−4.81818	−	4.66746i	−0.321212	−	0.311164i
$16$	6.52374	−	11.2995i	0.407734	−	0.706216i
$17$			12.6328i			0.743103i	0.928412	+	0.371552i	$0.121174\pi$
$17$			12.6328i			0.743103i	−0.928412	+	0.371552i	$0.878826\pi$
$18$	−16.4969	+	0.524391i	−0.916494	+	0.0291328i
$19$	−32.1403			−1.69159			−0.845797	−	0.533505i	$-0.820875\pi$
$19$	−32.1403			−1.69159			−0.845797	+	0.533505i	$0.820875\pi$
$20$	1.23308	+	0.711921i	0.0616542	+	0.0355961i
$21$	18.8201	+	4.72368i	0.896197	+	0.224937i
$22$	9.79083	+	16.9582i	0.445038	+	0.770828i
$23$	−9.82266	+	5.67112i	−0.427072	+	0.246570i	−0.698099	−	0.716002i	$-0.745970\pi$
$23$	−9.82266	+	5.67112i	−0.427072	+	0.246570i	0.271026	+	0.962572i	$0.412637\pi$
$24$	24.5330	−	6.99319i	1.02221	−	0.291383i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		−	20.2968i		−	0.780647i
$27$	−19.9799	−	18.1605i	−0.739995	−	0.672612i
$28$	−4.11855			−0.147091
$29$	35.2234	+	20.3362i	1.21460	+	0.701249i	0.963758	−	0.266779i	$-0.0859594\pi$
$29$	35.2234	+	20.3362i	1.21460	+	0.701249i	0.250841	+	0.968028i	$0.419293\pi$
$30$	−3.37245	−	11.8310i	−0.112415	−	0.394366i
$31$	15.9429	+	27.6139i	0.514286	+	0.890770i	0.999863	+	0.0165759i	$0.00527652\pi$
$31$	15.9429	+	27.6139i	0.514286	+	0.890770i	−0.485576	+	0.874194i	$0.661390\pi$
$32$	−8.73448	+	5.04286i	−0.272953	+	0.157589i
$33$	−7.79801	+	31.0689i	−0.236303	+	0.941482i
$34$	−11.5837	+	20.0635i	−0.340697	+	0.590104i
$35$			14.4628i			0.413223i
$36$	5.05160	+	2.70630i	0.140322	+	0.0751749i
$37$	45.4499			1.22837			0.614187	−	0.789160i	$-0.289484\pi$
$37$	45.4499			1.22837			0.614187	+	0.789160i	$0.289484\pi$
$38$	−51.0457	−	29.4713i	−1.34331	−	0.775559i
$39$	23.1017	−	23.8477i	0.592352	−	0.611480i
$40$	9.50711	+	16.4668i	0.237678	+	0.411670i
$41$	−25.4781	+	14.7098i	−0.621418	+	0.358776i	−0.777421	−	0.628981i	$-0.783472\pi$
$41$	−25.4781	+	14.7098i	−0.621418	+	0.358776i	0.156003	+	0.987757i	$0.450139\pi$
$42$	25.5590	+	24.7595i	0.608548	+	0.589511i
$43$	18.8093	−	32.5786i	0.437424	−	0.757641i	−0.560066	−	0.828448i	$-0.689224\pi$
$43$	18.8093	−	32.5786i	0.437424	−	0.757641i	0.997490	+	0.0708069i	$0.0225574\pi$
$44$		−	6.79904i		−	0.154524i
$45$	9.50350	−	17.7393i	0.211189	−	0.394207i
$46$	−20.8007			−0.452188
$47$	−49.8119	−	28.7589i	−1.05983	−	0.611892i	−0.134443	−	0.990921i	$-0.542925\pi$
$47$	−49.8119	−	28.7589i	−1.05983	−	0.611892i	−0.925385	+	0.379029i	$0.876258\pi$
$48$	37.9649	+	9.52885i	0.790935	+	0.198518i
$49$	3.58274	+	6.20548i	0.0731171	+	0.126642i
$50$	7.94108	−	4.58478i	0.158822	−	0.0916957i
$51$	−36.4465	+	10.3891i	−0.714636	+	0.203709i
$52$	−3.52368	+	6.10319i	−0.0677630	+	0.117369i
$53$		−	33.3940i		−	0.630075i	−0.949079	−	0.315038i	$-0.897983\pi$
$53$		−	33.3940i		−	0.630075i	0.949079	−	0.315038i	$-0.102017\pi$
$54$	−15.0799	−	47.1635i	−0.279258	−	0.873398i
$55$	−23.8757			−0.434103
$56$	−47.6312	−	27.4999i	−0.850557	−	0.491070i
$57$	−26.4321	−	92.7272i	−0.463721	−	1.62679i
$58$	37.2949	+	64.5966i	0.643015	+	1.11373i
$59$	3.54909	−	2.04907i	0.0601541	−	0.0347300i	−0.469621	−	0.882868i	$-0.655610\pi$
$59$	3.54909	−	2.04907i	0.0601541	−	0.0347300i	0.529775	+	0.848138i	$0.322276\pi$
$60$	−1.03986	+	4.14302i	−0.0173310	+	0.0690504i
$61$	33.1195	−	57.3647i	0.542943	−	0.940404i	−0.455791	−	0.890087i	$-0.650643\pi$
$61$	33.1195	−	57.3647i	0.542943	−	0.940404i	0.998733	−	0.0503172i	$-0.0160232\pi$
$62$			58.4757i			0.943157i
$63$	1.84945	+	58.1823i	0.0293564	+	0.923528i
$64$	−70.6863			−1.10447
$65$	21.4321	+	12.3738i	0.329725	+	0.190367i
$66$	−40.8738	+	42.1937i	−0.619300	+	0.639298i
$67$	−35.4890	−	61.4687i	−0.529686	−	0.917444i	−0.999400	−	0.0346251i	$-0.988976\pi$
$67$	−35.4890	−	61.4687i	−0.529686	−	0.917444i	0.469714	−	0.882819i	$-0.344357\pi$
$68$	6.96635	−	4.02203i	0.102446	−	0.0591474i
$69$	−24.4397	−	23.6752i	−0.354199	−	0.343119i
$70$	−13.2618	+	22.9700i	−0.189454	+	0.328144i
$71$			13.1123i			0.184680i	0.995728	+	0.0923400i	$0.0294347\pi$
$71$			13.1123i			0.184680i	−0.995728	+	0.0923400i	$0.970565\pi$
$72$	40.3518	+	65.0284i	0.560441	+	0.903172i
$73$	109.273			1.49688			0.748442	−	0.663200i	$-0.230802\pi$
$73$	109.273			1.49688			0.748442	+	0.663200i	$0.230802\pi$
$74$	72.1842	+	41.6756i	0.975462	+	0.563183i
$75$	14.5487	+	3.65160i	0.193983	+	0.0486880i
$76$	10.2328	+	17.7238i	0.134643	+	0.233208i
$77$	59.8093	−	34.5309i	0.776744	−	0.448453i
$78$	58.5579	−	16.6921i	0.750742	−	0.214001i
$79$	−49.8891	+	86.4104i	−0.631507	+	1.09380i	0.355736	+	0.934586i	$0.384230\pi$
$79$	−49.8891	+	86.4104i	−0.631507	+	1.09380i	−0.987244	+	0.159217i	$0.949103\pi$
$80$			29.1751i			0.364688i
$81$	35.9631	−	72.5786i	0.443989	−	0.896032i
$82$	−53.9530			−0.657964
$83$	74.2472	+	42.8667i	0.894545	+	0.516466i	0.875426	−	0.483351i	$-0.160581\pi$
$83$	74.2472	+	42.8667i	0.894545	+	0.516466i	0.0191187	+	0.999817i	$0.493914\pi$
$84$	−3.38709	−	11.8823i	−0.0403225	−	0.141456i
$85$	−14.1238	−	24.4632i	−0.166163	−	0.287803i
$86$	59.7463	−	34.4945i	0.694724	−	0.401099i
$87$	−29.7039	+	118.347i	−0.341424	+	1.36031i
$88$	45.3977	−	78.6312i	0.515883	−	0.893536i
$89$			63.6372i			0.715025i	0.933908	+	0.357513i	$0.116375\pi$
$89$			63.6372i			0.715025i	−0.933908	+	0.357513i	$0.883625\pi$
$90$	31.3598	−	19.4596i	0.348442	−	0.216217i
$91$	−71.5841			−0.786638
$92$	6.25469	+	3.61115i	0.0679858	+	0.0392516i
$93$	−66.5567	+	68.7060i	−0.715664	+	0.738774i
$94$	−52.7414	−	91.3507i	−0.561078	−	0.971816i
$95$	62.2394	−	35.9339i	0.655152	−	0.378252i
$96$	−21.7322	−	21.0524i	−0.226378	−	0.219296i
$97$	−43.2064	+	74.8357i	−0.445427	+	0.771503i	−0.998082	−	0.0619078i	$-0.980282\pi$
$97$	−43.2064	+	74.8357i	−0.445427	+	0.771503i	0.552655	+	0.833410i	$0.313615\pi$
$98$			13.1409i			0.134090i
$99$	−96.0492	+	3.05314i	−0.970194	+	0.0308398i
$100$	−3.18381			−0.0318381
$101$	−38.1796	−	22.0430i	−0.378015	−	0.218247i	0.298939	−	0.954272i	$-0.403367\pi$
$101$	−38.1796	−	22.0430i	−0.378015	−	0.218247i	−0.676954	+	0.736025i	$0.736701\pi$
$102$	−67.4112	−	16.9196i	−0.660894	−	0.165879i
$103$	−46.9358	−	81.2952i	−0.455688	−	0.789274i	0.543040	−	0.839707i	$-0.317273\pi$
$103$	−46.9358	−	81.2952i	−0.455688	−	0.789274i	−0.998727	+	0.0504329i	$0.983940\pi$
$104$	−81.5030	+	47.0558i	−0.783682	+	0.452459i
$105$	−41.7263	+	11.8942i	−0.397393	+	0.113278i
$106$	30.6208	−	53.0369i	0.288876	−	0.500348i
$107$		−	138.518i		−	1.29456i	−0.762252	−	0.647280i	$-0.775906\pi$
$107$		−	138.518i		−	1.29456i	0.762252	−	0.647280i	$-0.224094\pi$
$108$	−3.65345	+	16.7999i	−0.0338282	+	0.155555i
$109$	176.733			1.62140			0.810700	−	0.585461i	$-0.199087\pi$
$109$	176.733			1.62140			0.810700	+	0.585461i	$0.199087\pi$
$110$	−37.9197	−	21.8930i	−0.344725	−	0.199027i
$111$	37.3779	+	131.126i	0.336738	+	1.18132i
$112$	−42.1953	−	73.0845i	−0.376744	−	0.652540i
$113$	−76.8430	+	44.3653i	−0.680026	+	0.392613i	−0.799865	−	0.600180i	$-0.795096\pi$
$113$	−76.8430	+	44.3653i	−0.680026	+	0.392613i	0.119839	+	0.992793i	$0.461762\pi$
$114$	43.0469	−	171.508i	0.377604	−	1.50445i
$115$	12.6810	−	21.9641i	0.110270	−	0.190992i
$116$		−	25.8986i		−	0.223264i
$117$	87.8013	+	47.0379i	0.750439	+	0.402033i
$118$	7.51564			0.0636918
$119$	70.7613	+	40.8541i	0.594633	+	0.343312i
$120$	−39.6893	+	40.9710i	−0.330744	+	0.341425i
$121$	−3.49522	−	6.05390i	−0.0288861	−	0.0500323i
$122$	105.202	−	60.7383i	0.862310	−	0.497855i
$123$	−63.3921	−	61.4090i	−0.515383	−	0.499260i
$124$	10.1518	−	17.5835i	0.0818695	−	0.141802i
$125$			11.1803i			0.0894427i
$126$	−50.4133	+	94.1019i	−0.400105	+	0.746840i
$127$	92.0203			0.724569			0.362285	−	0.932068i	$-0.381997\pi$
$127$	92.0203			0.724569			0.362285	+	0.932068i	$0.381997\pi$
$128$	−77.3271	−	44.6448i	−0.604118	−	0.348788i
$129$	109.460	+	27.4736i	0.848530	+	0.212973i
$130$	22.6925	+	39.3046i	0.174558	+	0.302343i
$131$	−138.979	+	80.2398i	−1.06091	+	0.612518i	−0.925684	−	0.378297i	$-0.876510\pi$
$131$	−138.979	+	80.2398i	−1.06091	+	0.612518i	−0.135228	+	0.990815i	$0.543177\pi$
$132$	19.6157	−	5.59151i	0.148604	−	0.0423600i
$133$	−103.941	+	180.031i	−0.781512	+	1.35362i
$134$		−	130.167i		−	0.971399i
$135$	58.9949	+	12.8296i	0.437000	+	0.0950337i
$136$	107.422			0.789865
$137$	−78.6907	−	45.4321i	−0.574385	−	0.331621i	0.184514	−	0.982830i	$-0.440929\pi$
$137$	−78.6907	−	45.4321i	−0.574385	−	0.331621i	−0.758899	+	0.651209i	$0.774262\pi$
$138$	−17.1064	−	60.0115i	−0.123960	−	0.434866i
$139$	32.4865	+	56.2682i	0.233716	+	0.404807i	0.958899	−	0.283749i	$-0.0915782\pi$
$139$	32.4865	+	56.2682i	0.233716	+	0.404807i	−0.725183	+	0.688556i	$0.758245\pi$
$140$	7.97554	−	4.60468i	0.0569681	−	0.0328906i
$141$	42.0065	−	167.362i	0.297918	−	1.18697i
$142$	−12.0234	+	20.8251i	−0.0846718	+	0.146656i
$143$		−	118.173i		−	0.826387i
$144$	3.73081	+	117.368i	0.0259084	+	0.815056i
$145$	−90.9464			−0.627216
$146$	173.548	+	100.198i	1.18869	+	0.686289i
$147$	−14.9568	+	15.4398i	−0.101747	+	0.105033i
$148$	−14.4704	−	25.0634i	−0.0977727	−	0.169347i
$149$	−124.965	+	72.1483i	−0.838688	+	0.484217i	−0.856818	−	0.515619i	$-0.827562\pi$
$149$	−124.965	+	72.1483i	−0.838688	+	0.484217i	0.0181301	+	0.999836i	$0.494229\pi$
$150$	19.7582	+	19.1401i	0.131721	+	0.127601i
$151$	−68.3876	+	118.451i	−0.452898	+	0.784442i	−0.998565	−	0.0535600i	$-0.982943\pi$
$151$	−68.3876	+	118.451i	−0.452898	+	0.784442i	0.545667	+	0.838002i	$0.316276\pi$
$152$			273.302i			1.79804i
$153$	−59.9470	−	96.6068i	−0.391810	−	0.631417i
$154$	126.653			0.822425
$155$	−61.7465	−	35.6494i	−0.398365	−	0.229996i
$156$	−20.5060	−	5.14682i	−0.131449	−	0.0329925i
$157$	26.0965	+	45.2004i	0.166220	+	0.287901i	0.937088	−	0.349094i	$-0.113511\pi$
$157$	26.0965	+	45.2004i	0.166220	+	0.287901i	−0.770868	+	0.636995i	$0.780177\pi$
$158$	−158.469	+	91.4923i	−1.00297	+	0.579065i
$159$	96.3442	−	27.4631i	0.605938	−	0.172724i
$160$	11.2762	−	19.5309i	0.0704761	−	0.122068i
$161$			73.3611i			0.455659i
$162$	123.669	−	82.2939i	0.763387	−	0.507987i
$163$	−103.226			−0.633287			−0.316643	−	0.948545i	$-0.602556\pi$
$163$	−103.226			−0.633287			−0.316643	+	0.948545i	$0.602556\pi$
$164$	16.2235	+	9.36664i	0.0989238	+	0.0571137i
$165$	−19.6353	−	68.8831i	−0.119002	−	0.417473i
$166$	78.6138	+	136.163i	0.473577	+	0.820259i
$167$	97.7044	−	56.4096i	0.585056	−	0.337782i	−0.178084	−	0.984015i	$-0.556990\pi$
$167$	97.7044	−	56.4096i	0.585056	−	0.337782i	0.763140	+	0.646233i	$0.223657\pi$
$168$	40.1675	−	160.036i	0.239092	−	0.952592i
$169$	23.2553	−	40.2794i	0.137606	−	0.238340i
$170$		−	51.8038i		−	0.304728i
$171$	245.787	−	152.517i	1.43735	−	0.891914i
$172$	−23.9540			−0.139268
$173$	113.723	+	65.6580i	0.657359	+	0.379526i	0.791270	−	0.611467i	$-0.209420\pi$
$173$	113.723	+	65.6580i	0.657359	+	0.379526i	−0.133911	+	0.990993i	$0.542754\pi$
$174$	−155.695	+	160.723i	−0.894798	+	0.923693i
$175$	−16.1699	−	28.0071i	−0.0923995	−	0.160041i
$176$	120.650	−	69.6574i	0.685513	−	0.395781i
$177$	8.83049	+	8.55425i	0.0498898	+	0.0483291i
$178$	−58.3526	+	101.070i	−0.327824	+	0.567807i
$179$		−	297.076i		−	1.65964i	−0.558028	−	0.829822i	$-0.688442\pi$
$179$		−	297.076i		−	1.65964i	0.558028	−	0.829822i	$-0.311558\pi$
$180$	−12.8081	+	0.407135i	−0.0711562	+	0.00226186i
$181$	28.1168			0.155342			0.0776708	−	0.996979i	$-0.475252\pi$
$181$	28.1168			0.155342			0.0776708	+	0.996979i	$0.475252\pi$
$182$	−113.691	−	65.6395i	−0.624676	−	0.360657i
$183$	192.739	+	48.3757i	1.05322	+	0.264348i
$184$	48.2239	+	83.5262i	0.262086	+	0.453947i
$185$	−88.0133	+	50.8145i	−0.475748	+	0.274673i
$186$	−168.707	+	48.0903i	−0.907026	+	0.258550i
$187$	−67.4433	+	116.815i	−0.360659	+	0.624680i
$188$			36.6252i			0.194815i
$189$	−166.339	+	53.1848i	−0.880102	+	0.281401i
$190$	131.799			0.693681
$191$	7.94176	+	4.58518i	0.0415799	+	0.0240062i	0.520646	−	0.853773i	$-0.325691\pi$
$191$	7.94176	+	4.58518i	0.0415799	+	0.0240062i	−0.479066	+	0.877779i	$0.659025\pi$
$192$	−58.1322	−	203.935i	−0.302772	−	1.06216i
$193$	−47.3830	−	82.0697i	−0.245508	−	0.425232i	0.716767	−	0.697313i	$-0.245621\pi$
$193$	−47.3830	−	82.0697i	−0.245508	−	0.425232i	−0.962274	+	0.272082i	$0.912288\pi$
$194$	−137.242	+	79.2369i	−0.707434	+	0.408437i
$195$	−18.0737	+	72.0094i	−0.0926857	+	0.369279i
$196$	2.28135	−	3.95141i	0.0116395	−	0.0201603i
$197$			267.330i			1.35701i	0.734597	+	0.678504i	$0.237371\pi$
$197$			267.330i			1.35701i	−0.734597	+	0.678504i	$0.762629\pi$
$198$	−155.346	−	83.2239i	−0.784578	−	0.420323i
$199$	−158.327			−0.795615			−0.397808	−	0.917469i	$-0.630229\pi$
$199$	−158.327			−0.795615			−0.397808	+	0.917469i	$0.630229\pi$
$200$	−36.8209	−	21.2585i	−0.184104	−	0.106293i
$201$	148.156	−	152.940i	0.737094	−	0.760896i
$202$	−40.4249	−	70.0180i	−0.200123	−	0.346624i
$203$	227.823	−	131.534i	1.12228	−	0.647950i
$204$	17.3330	+	16.7907i	0.0849655	+	0.0823076i
$205$	32.8921	−	56.9708i	0.160449	−	0.277907i
$206$		−	172.152i		−	0.835692i
$207$	48.2056	−	89.9809i	0.232877	−	0.434690i
$208$	−144.403			−0.694245
$209$	−297.202	−	171.589i	−1.42202	−	0.821002i
$210$	−77.1768	−	19.3707i	−0.367508	−	0.0922413i
$211$	−158.786	−	275.026i	−0.752542	−	1.30344i	−0.946587	−	0.322448i	$-0.895494\pi$
$211$	−158.786	−	275.026i	−0.752542	−	1.30344i	0.194045	−	0.980993i	$-0.437839\pi$
$212$	−18.4152	+	10.6320i	−0.0868640	+	0.0501510i
$213$	−37.8299	+	10.7835i	−0.177605	+	0.0506268i
$214$	127.015	−	219.996i	0.593528	−	1.02802i
$215$			84.1175i			0.391244i
$216$	−154.427	+	169.897i	−0.714938	+	0.786561i
$217$	206.236			0.950396
$218$	280.690	+	162.056i	1.28757	+	0.743377i
$219$	89.8656	+	315.260i	0.410345	+	1.43954i
$220$	7.60155	+	13.1663i	0.0345525	+	0.0598467i
$221$	121.081	−	69.9064i	0.547880	−	0.316319i
$222$	−60.8730	+	242.531i	−0.274203	+	1.09248i
$223$	61.9955	−	107.379i	0.278007	−	0.481522i	−0.692883	−	0.721050i	$-0.743660\pi$
$223$	61.9955	−	107.379i	0.278007	−	0.481522i	0.970889	+	0.239529i	$0.0769929\pi$
$224$			65.2340i			0.291223i
$225$	1.42970	+	44.9773i	0.00635424	+	0.199899i
$226$	−162.724			−0.720019
$227$	−188.341	−	108.739i	−0.829695	−	0.479025i	0.0240532	−	0.999711i	$-0.492343\pi$
$227$	−188.341	−	108.739i	−0.829695	−	0.479025i	−0.853748	+	0.520686i	$0.825676\pi$
$228$	−42.7191	+	44.0986i	−0.187364	+	0.193415i
$229$	−37.4773	−	64.9126i	−0.163656	−	0.283461i	0.772521	−	0.634989i	$-0.218995\pi$
$229$	−37.4773	−	64.9126i	−0.163656	−	0.283461i	−0.936177	+	0.351528i	$0.885662\pi$
$230$	40.2803	−	23.2559i	0.175132	−	0.101112i
$231$	148.811	+	144.156i	0.644205	+	0.624053i
$232$	172.927	−	299.519i	0.745377	−	1.29103i
$233$			142.781i			0.612792i	0.951904	+	0.306396i	$0.0991232\pi$
$233$			142.781i			0.612792i	−0.951904	+	0.306396i	$0.900877\pi$
$234$	96.3157	+	155.216i	0.411606	+	0.663318i
$235$	128.614			0.547293
$236$	−2.25993	−	1.30477i	−0.00957596	−	0.00552868i
$237$	−290.329	−	72.8700i	−1.22502	−	0.307469i
$238$	74.9229	+	129.770i	0.314802	+	0.545253i
$239$	173.362	−	100.090i	0.725363	−	0.418789i	−0.0913604	−	0.995818i	$-0.529122\pi$
$239$	173.362	−	100.090i	0.725363	−	0.418789i	0.816723	+	0.577029i	$0.195788\pi$
$240$	−84.1723	+	23.9935i	−0.350718	+	0.0999730i
$241$	−96.9600	+	167.940i	−0.402324	+	0.696845i	−0.994006	−	0.109326i	$-0.965131\pi$
$241$	−96.9600	+	167.940i	−0.402324	+	0.696845i	0.591682	+	0.806171i	$0.298464\pi$
$242$		−	12.8199i		−	0.0529747i
$243$	238.971	+	44.0678i	0.983419	+	0.181349i
$244$	−42.1784			−0.172862
$245$	−13.8759	−	8.01124i	−0.0566362	−	0.0326989i
$246$	−44.3709	−	155.659i	−0.180369	−	0.632758i
$247$	177.856	+	308.056i	0.720065	+	1.24719i
$248$	234.812	−	135.569i	0.946824	−	0.546649i
$249$	−62.6128	+	249.462i	−0.251457	+	1.00186i
$250$	−10.2519	+	17.7568i	−0.0410076	+	0.0710272i
$251$			301.288i			1.20035i	0.799868	+	0.600176i	$0.204903\pi$
$251$			301.288i			1.20035i	−0.799868	+	0.600176i	$0.795097\pi$
$252$	31.4959	−	19.5440i	0.124984	−	0.0775556i
$253$	−121.107			−0.478684
$254$	146.148	+	84.3786i	0.575386	+	0.332199i
$255$	58.9628	−	60.8669i	0.231227	−	0.238694i
$256$	59.4978	+	103.053i	0.232413	+	0.402552i
$257$	181.874	−	105.005i	0.707679	−	0.408579i	−0.102522	−	0.994731i	$-0.532691\pi$
$257$	181.874	−	105.005i	0.707679	−	0.408579i	0.810201	+	0.586152i	$0.199358\pi$
$258$	148.655	+	144.004i	0.576181	+	0.558156i
$259$	146.984	−	254.584i	0.567506	−	0.982949i
$260$		−	15.7584i		−	0.0606091i
$261$	−365.867	+	11.6299i	−1.40179	+	0.0445591i
$262$	−294.306			−1.12330
$263$	131.132	+	75.7092i	0.498601	+	0.287868i	0.728136	−	0.685433i	$-0.240387\pi$
$263$	131.132	+	75.7092i	0.498601	+	0.287868i	−0.229534	+	0.973301i	$0.573720\pi$
$264$	264.192	+	66.3098i	1.00073	+	0.251173i
$265$	37.3356	+	64.6672i	0.140889	+	0.244027i
$266$	−330.162	+	190.619i	−1.24121	+	0.716613i
$267$	−183.598	+	52.3351i	−0.687634	+	0.196012i
$268$	−22.5980	+	39.1409i	−0.0843210	+	0.146048i
$269$		−	411.264i		−	1.52886i	−0.644706	−	0.764431i	$-0.723020\pi$
$269$		−	411.264i		−	1.52886i	0.644706	−	0.764431i	$-0.276980\pi$
$270$	81.9325	+	74.4719i	0.303454	+	0.275822i
$271$	−255.156			−0.941534			−0.470767	−	0.882257i	$-0.656023\pi$
$271$	−255.156			−0.941534			−0.470767	+	0.882257i	$0.656023\pi$
$272$	142.743	+	82.4129i	0.524791	+	0.302988i
$273$	−58.8706	−	206.526i	−0.215643	−	0.756504i
$274$	−83.3186	−	144.312i	−0.304082	−	0.526686i
$275$	46.2350	−	26.6938i	0.168127	−	0.0970684i
$276$	−5.27459	+	21.0151i	−0.0191108	+	0.0761415i
$277$	92.7798	−	160.699i	0.334945	−	0.580142i	−0.648529	−	0.761190i	$-0.724615\pi$
$277$	92.7798	−	160.699i	0.334945	−	0.580142i	0.983474	+	0.181048i	$0.0579488\pi$
$278$			119.155i			0.428614i
$279$	−252.958	−	135.518i	−0.906660	−	0.485726i
$280$	122.983			0.439226
$281$	90.1892	+	52.0708i	0.320958	+	0.185305i	0.651820	−	0.758374i	$-0.274006\pi$
$281$	90.1892	+	52.0708i	0.320958	+	0.185305i	−0.330862	+	0.943679i	$0.607339\pi$
$282$	220.179	−	227.290i	0.780778	−	0.805991i
$283$	25.9282	+	44.9089i	0.0916189	+	0.158689i	0.908192	−	0.418553i	$-0.137463\pi$
$283$	25.9282	+	44.9089i	0.0916189	+	0.158689i	−0.816574	+	0.577241i	$0.804129\pi$
$284$	7.23079	−	4.17470i	0.0254605	−	0.0146996i
$285$	154.858	+	150.013i	0.543360	+	0.526363i
$286$	108.360	−	187.685i	0.378881	−	0.656241i
$287$			190.285i			0.663014i
$288$	42.8652	−	80.0126i	0.148838	−	0.277822i
$289$	129.414			0.447798
$290$	−144.442	−	83.3939i	−0.498077	−	0.287565i
$291$	−251.440	−	63.1091i	−0.864054	−	0.216870i
$292$	−34.7903	−	60.2586i	−0.119145	−	0.206365i
$293$	−287.235	+	165.835i	−0.980323	+	0.565990i	−0.902368	−	0.430967i	$-0.858172\pi$
$293$	−287.235	+	165.835i	−0.980323	+	0.565990i	−0.0779553	+	0.996957i	$0.524839\pi$
$294$	−37.9124	+	10.8070i	−0.128954	+	0.0367585i
$295$	−4.58186	+	7.93602i	−0.0155317	+	0.0269017i
$296$		−	386.479i		−	1.30567i
$297$	−87.7992	−	274.598i	−0.295620	−	0.924574i
$298$	−264.627			−0.888012
$299$	108.712	+	62.7650i	0.363586	+	0.209916i
$300$	−2.61836	−	9.18553i	−0.00872786	−	0.0306184i
$301$	−121.658	−	210.717i	−0.404178	−	0.700057i
$302$	−217.228	+	125.417i	−0.719300	+	0.415288i
$303$	32.1969	−	128.279i	0.106260	−	0.423363i
$304$	−209.675	+	363.168i	−0.689720	+	1.19463i
$305$			148.115i			0.485623i
$306$	−6.62450	−	208.401i	−0.0216487	−	0.681049i
$307$	−292.274			−0.952031			−0.476016	−	0.879437i	$-0.657919\pi$
$307$	−292.274			−0.952031			−0.476016	+	0.879437i	$0.657919\pi$
$308$	−38.0843	−	21.9880i	−0.123650	−	0.0713895i
$309$	195.943	−	202.270i	0.634120	−	0.654597i
$310$	−65.3778	−	113.238i	−0.210896	−	0.365283i
$311$	171.292	−	98.8956i	0.550779	−	0.317992i	−0.198657	−	0.980069i	$-0.563658\pi$
$311$	171.292	−	98.8956i	0.550779	−	0.317992i	0.749436	+	0.662077i	$0.230325\pi$
$312$	−202.787	−	196.444i	−0.649959	−	0.629627i
$313$	−107.849	+	186.800i	−0.344565	+	0.596804i	−0.985275	−	0.170979i	$-0.945307\pi$
$313$	−107.849	+	186.800i	−0.344565	+	0.596804i	0.640710	+	0.767783i	$0.278640\pi$
$314$			95.7173i			0.304832i
$315$	−68.6312	−	110.602i	−0.217877	−	0.351117i
$316$	63.5349			0.201060
$317$	−176.354	−	101.818i	−0.556321	−	0.321192i	0.195346	−	0.980734i	$-0.437417\pi$
$317$	−176.354	−	101.818i	−0.556321	−	0.321192i	−0.751668	+	0.659542i	$0.770750\pi$
$318$	178.198	+	44.7261i	0.560371	+	0.140648i
$319$	217.141	+	376.098i	0.680691	+	1.17899i
$320$	136.883	−	79.0297i	0.427761	−	0.246968i
$321$	399.635	−	113.917i	1.24497	−	0.354881i
$322$	−67.2690	+	116.513i	−0.208910	+	0.361842i
$323$		−	406.020i		−	1.25703i
$324$	−51.4736	+	3.27572i	−0.158869	+	0.0101102i
$325$	−55.3374			−0.170269
$326$	−163.945	−	94.6536i	−0.502898	−	0.290348i
$327$	145.345	+	509.887i	0.444479	+	1.55929i
$328$	125.084	+	216.651i	0.381353	+	0.660522i
$329$	−322.182	+	186.012i	−0.979275	+	0.565385i
$330$	31.9777	−	127.406i	0.0969023	−	0.386079i
$331$	−47.0115	+	81.4264i	−0.142029	+	0.246001i	−0.928260	−	0.371931i	$-0.878696\pi$
$331$	−47.0115	+	81.4264i	−0.142029	+	0.246001i	0.786232	+	0.617932i	$0.212029\pi$
$332$		−	54.5917i		−	0.164433i
$333$	−347.570	+	215.676i	−1.04375	+	0.647676i
$334$	206.901			0.619464
$335$	137.448	+	79.3558i	0.410293	+	0.236883i
$336$	176.153	−	181.841i	0.524264	−	0.541194i
$337$	168.068	+	291.103i	0.498719	+	0.863807i	0.999999	−	0.00147845i	$-0.000470606\pi$
$337$	168.068	+	291.103i	0.498719	+	0.863807i	−0.501280	+	0.865285i	$0.667137\pi$
$338$	73.8690	−	42.6483i	0.218547	−	0.126178i
$339$	−191.193	−	185.212i	−0.563990	−	0.546348i
$340$	−8.99352	+	15.5772i	−0.0264515	+	0.0458154i
$341$			340.461i			0.998419i
$342$	530.215	−	16.8541i	1.55034	−	0.0492809i
$343$	363.276			1.05911
$344$	−277.029	−	159.943i	−0.805318	−	0.464950i
$345$	73.7970	+	18.5224i	0.213904	+	0.0536881i
$346$	120.411	+	208.558i	0.348009	+	0.602769i
$347$	54.1469	−	31.2617i	0.156043	−	0.0900914i	−0.419945	−	0.907549i	$-0.637951\pi$
$347$	54.1469	−	31.2617i	0.156043	−	0.0900914i	0.575988	+	0.817458i	$0.304617\pi$
$348$	74.7196	−	21.2990i	0.214711	−	0.0612040i
$349$	160.475	−	277.951i	0.459815	−	0.796422i	−0.539136	−	0.842219i	$-0.681249\pi$
$349$	160.475	−	277.951i	0.459815	−	0.796422i	0.998951	+	0.0457962i	$0.0145825\pi$
$350$		−	59.3084i		−	0.169453i
$351$	−63.5003	+	291.997i	−0.180912	+	0.831901i
$352$	−107.690			−0.305939
$353$	−143.945	−	83.1067i	−0.407776	−	0.235430i	0.282058	−	0.959397i	$-0.408983\pi$
$353$	−143.945	−	83.1067i	−0.407776	−	0.235430i	−0.689834	+	0.723968i	$0.742316\pi$
$354$	6.18084	+	21.6832i	0.0174600	+	0.0612519i
$355$	−14.6600	−	25.3918i	−0.0412957	−	0.0715263i
$356$	35.0929	−	20.2609i	0.0985754	−	0.0569126i
$357$	−59.6731	+	237.750i	−0.167152	+	0.665967i
$358$	272.406	−	471.821i	0.760911	−	1.31794i
$359$			199.670i			0.556183i	0.960555	+	0.278091i	$0.0897018\pi$
$359$			199.670i			0.556183i	−0.960555	+	0.278091i	$0.910298\pi$
$360$	−150.845	−	80.8123i	−0.419013	−	0.224479i
$361$	671.998			1.86149
$362$	44.6556	+	25.7819i	0.123358	+	0.0712208i
$363$	14.5915	−	15.0627i	0.0401970	−	0.0414950i
$364$	22.7910	+	39.4752i	0.0626126	+	0.108448i
$365$	−211.605	+	122.170i	−0.579741	+	0.334714i
$366$	261.752	+	253.564i	0.715170	+	0.692798i
$367$	80.3209	−	139.120i	0.218858	−	0.379073i	−0.735601	−	0.677415i	$-0.763100\pi$
$367$	80.3209	−	139.120i	0.218858	−	0.379073i	0.954459	+	0.298342i	$0.0964335\pi$
$368$			147.988i			0.402140i
$369$	125.036	−	233.394i	0.338852	−	0.632503i
$370$	−186.379			−0.503726
$371$	−187.054	−	107.996i	−0.504188	−	0.291093i
$372$	59.0784	+	14.8282i	0.158813	+	0.0398606i
$373$	85.6188	+	148.296i	0.229541	+	0.397577i	0.957672	−	0.287861i	$-0.0929442\pi$
$373$	85.6188	+	148.296i	0.229541	+	0.397577i	−0.728131	+	0.685438i	$0.759611\pi$
$374$	−214.229	+	123.685i	−0.572805	+	0.330709i
$375$	−32.2561	+	9.19469i	−0.0860163	+	0.0245192i
$376$	−244.549	+	423.572i	−0.650397	+	1.12652i
$377$		−	450.142i		−	1.19401i
$378$	−312.951	−	68.0570i	−0.827912	−	0.180045i
$379$	−297.486			−0.784922			−0.392461	−	0.919769i	$-0.628376\pi$
$379$	−297.486			−0.784922			−0.392461	+	0.919769i	$0.628376\pi$
$380$	−39.6317	−	22.8813i	−0.104294	−	0.0602141i
$381$	75.6773	+	265.485i	0.198628	+	0.696812i
$382$	8.40882	+	14.5645i	0.0220126	+	0.0381270i
$383$	−416.340	+	240.374i	−1.08705	+	0.627608i	−0.932789	−	0.360423i	$-0.882632\pi$
$383$	−416.340	+	240.374i	−1.08705	+	0.627608i	−0.154259	+	0.988030i	$0.549299\pi$
$384$	65.2101	−	259.810i	0.169818	−	0.676590i
$385$	−77.2135	+	133.738i	−0.200554	+	0.347371i
$386$		−	173.793i		−	0.450240i
$387$	10.7567	+	338.396i	0.0277950	+	0.874407i
$388$	55.0244			0.141815
$389$	514.801	+	297.220i	1.32340	+	0.764062i	0.984269	−	0.176678i	$-0.0565352\pi$
$389$	514.801	+	297.220i	1.32340	+	0.764062i	0.339126	+	0.940741i	$0.389869\pi$
$390$	−94.7345	+	97.7937i	−0.242909	+	0.250753i
$391$	−71.6418	−	124.087i	−0.183227	−	0.317359i
$392$	52.7678	−	30.4655i	0.134612	−	0.0777181i
$393$	−345.794	−	334.977i	−0.879884	−	0.852359i
$394$	−245.130	+	424.578i	−0.622158	+	1.07761i
$395$		−	223.111i		−	0.564837i
$396$	32.2639	+	51.9944i	0.0814745	+	0.131299i
$397$	−106.303			−0.267765			−0.133883	−	0.990997i	$-0.542745\pi$
$397$	−106.303			−0.267765			−0.133883	+	0.990997i	$0.542745\pi$
$398$	−251.458	−	145.179i	−0.631804	−	0.364772i
$399$	−604.885	−	151.821i	−1.51600	−	0.380503i
$400$	−32.6187	−	56.4973i	−0.0815468	−	0.141243i
$401$	−26.3207	+	15.1963i	−0.0656376	+	0.0378959i	−0.532460	−	0.846455i	$-0.678732\pi$
$401$	−26.3207	+	15.1963i	−0.0656376	+	0.0378959i	0.466822	+	0.884351i	$0.345399\pi$
$402$	375.543	−	107.049i	0.934187	−	0.266292i
$403$	176.448	−	305.616i	0.437835	−	0.758353i
$404$			28.0722i			0.0694857i
$405$	11.5031	+	180.756i	0.0284027	+	0.446311i
$406$	482.444			1.18828
$407$	420.275	+	242.646i	1.03262	+	0.596182i
$408$	88.3433	+	309.919i	0.216528	+	0.759606i
$409$	−36.7195	−	63.6000i	−0.0897787	−	0.155501i	0.817639	−	0.575732i	$-0.195283\pi$
$409$	−36.7195	−	63.6000i	−0.0897787	−	0.155501i	−0.907418	+	0.420230i	$0.861949\pi$
$410$	104.480	−	60.3213i	0.254828	−	0.147125i
$411$	66.3600	−	264.392i	0.161460	−	0.643290i
$412$	−29.8869	+	51.7657i	−0.0725411	+	0.125645i
$413$		−	26.5066i		−	0.0641807i
$414$	159.069	−	98.7067i	0.384226	−	0.238422i
$415$	−191.706			−0.461941
$416$	96.6688	+	55.8118i	0.232377	+	0.134163i
$417$	−135.621	+	140.001i	−0.325231	+	0.335733i
$418$	−314.680	−	545.042i	−0.752823	−	1.30393i
$419$	144.551	−	83.4568i	0.344992	−	0.199181i	−0.317486	−	0.948263i	$-0.602838\pi$
$419$	144.551	−	83.4568i	0.344992	−	0.199181i	0.662477	+	0.749082i	$0.269505\pi$
$420$	19.8439	+	19.2231i	0.0472474	+	0.0457694i
$421$	152.746	−	264.563i	0.362816	−	0.628416i	−0.625607	−	0.780138i	$-0.715149\pi$
$421$	152.746	−	264.563i	0.362816	−	0.628416i	0.988423	+	0.151722i	$0.0484820\pi$
$422$		−	582.401i		−	1.38010i
$423$	517.399	−	16.4467i	1.22317	−	0.0388811i
$424$	−283.963			−0.669724
$425$	54.7014	+	31.5819i	0.128709	+	0.0743103i
$426$	−69.9701	−	17.5619i	−0.164249	−	0.0412250i
$427$	−214.216	−	371.032i	−0.501676	−	0.868928i
$428$	−76.3859	+	44.1014i	−0.178472	+	0.103041i
$429$	340.939	−	97.1856i	0.794730	−	0.226540i
$430$	−77.1321	+	133.597i	−0.179377	+	0.310690i
$431$			221.026i			0.512820i	0.966568	+	0.256410i	$0.0825398\pi$
$431$			221.026i			0.512820i	−0.966568	+	0.256410i	$0.917460\pi$
$432$	−335.548	+	107.287i	−0.776731	+	0.248349i
$433$	194.055			0.448164			0.224082	−	0.974570i	$-0.428062\pi$
$433$	194.055			0.448164			0.224082	+	0.974570i	$0.428062\pi$
$434$	327.547	+	189.109i	0.754717	+	0.435736i
$435$	−74.7941	−	262.387i	−0.171940	−	0.603189i
$436$	−56.2683	−	97.4595i	−0.129056	−	0.223531i
$437$	315.703	−	182.271i	0.722433	−	0.417097i
$438$	−146.354	+	583.103i	−0.334141	+	1.33129i
$439$	77.3450	−	133.965i	0.176184	−	0.305160i	−0.764386	−	0.644759i	$-0.776958\pi$
$439$	77.3450	−	133.965i	0.176184	−	0.305160i	0.940571	+	0.339598i	$0.110291\pi$
$440$			203.025i			0.461420i
$441$	−56.8456	−	30.4539i	−0.128902	−	0.0690566i
$442$	256.405			0.580101
$443$	−418.418	−	241.573i	−0.944509	−	0.545313i	−0.0531381	−	0.998587i	$-0.516922\pi$
$443$	−418.418	−	241.573i	−0.944509	−	0.545313i	−0.891371	+	0.453275i	$0.850256\pi$
$444$	60.4094	−	62.3602i	0.136057	−	0.140451i
$445$	−71.1486	−	123.233i	−0.159884	−	0.276928i
$446$	196.924	−	113.694i	0.441535	−	0.254920i
$447$	−310.924	−	301.197i	−0.695579	−	0.673820i
$448$	−228.598	+	395.943i	−0.510264	+	0.883802i
$449$			679.146i			1.51257i	0.654240	+	0.756287i	$0.272989\pi$
$449$			679.146i			1.51257i	−0.654240	+	0.756287i	$0.727011\pi$
$450$	−38.9715	+	72.7446i	−0.0866034	+	0.161655i
$451$	−314.129			−0.696516
$452$	48.9306	+	28.2501i	0.108254	+	0.0625003i
$453$	−397.981	−	99.8897i	−0.878546	−	0.220507i
$454$	−199.417	−	345.401i	−0.439245	−	0.760794i
$455$	138.622	−	80.0335i	0.304664	−	0.175898i
$456$	−788.498	+	224.763i	−1.72916	+	0.492902i
$457$	40.2569	−	69.7270i	0.0880896	−	0.152576i	−0.818614	−	0.574344i	$-0.805257\pi$
$457$	40.2569	−	69.7270i	0.0880896	−	0.152576i	0.906704	+	0.421768i	$0.138590\pi$
$458$		−	137.460i		−	0.300131i
$459$	229.418	−	252.401i	0.499820	−	0.549893i
$460$	−16.1495			−0.0351077
$461$	535.846	+	309.371i	1.16236	+	0.671087i	0.951868	−	0.306510i	$-0.0991612\pi$
$461$	535.846	+	309.371i	1.16236	+	0.671087i	0.210489	+	0.977596i	$0.432495\pi$
$462$	104.159	+	365.405i	0.225453	+	0.790919i
$463$	−164.729	−	285.318i	−0.355785	−	0.616238i	0.631467	−	0.775403i	$-0.282453\pi$
$463$	−164.729	−	285.318i	−0.355785	−	0.616238i	−0.987252	+	0.159165i	$0.949120\pi$
$464$	459.577	−	265.337i	0.990467	−	0.571846i
$465$	52.0709	−	207.461i	0.111980	−	0.446153i
$466$	−130.924	+	226.766i	−0.280952	+	0.486623i
$467$			216.349i			0.463275i	0.972802	+	0.231637i	$0.0744083\pi$
$467$			216.349i			0.463275i	−0.972802	+	0.231637i	$0.925592\pi$
$468$	−2.01513	−	63.3941i	−0.00430582	−	0.135458i
$469$	−459.083			−0.978855
$470$	204.266	+	117.933i	0.434610	+	0.250922i
$471$	−108.945	+	112.463i	−0.231306	+	0.238775i
$472$	−17.4241	−	30.1794i	−0.0369155	−	0.0639395i
$473$	347.859	−	200.836i	0.735430	−	0.424601i
$474$	−394.287	−	381.953i	−0.831829	−	0.805808i
$475$	−80.3507	+	139.172i	−0.169159	+	0.292993i
$476$		−	52.0286i		−	0.109304i
$477$	158.467	+	255.375i	0.332215	+	0.535377i
$478$	367.114			0.768022
$479$	−119.965	−	69.2617i	−0.250448	−	0.144596i	0.369521	−	0.929222i	$-0.379522\pi$
$479$	−119.965	−	69.2617i	−0.250448	−	0.144596i	−0.619970	+	0.784626i	$0.712855\pi$
$480$	65.6216	+	16.4704i	0.136712	+	0.0343134i
$481$	−251.508	−	435.625i	−0.522886	−	0.905665i
$482$	−307.987	+	177.816i	−0.638977	+	0.368913i
$483$	−211.652	+	60.3320i	−0.438204	+	0.124911i
$484$	−2.22562	+	3.85489i	−0.00459840	+	0.00796466i
$485$		−	193.225i		−	0.398402i
$486$	339.129	+	289.115i	0.697796	+	0.594887i
$487$	93.0290			0.191025			0.0955123	−	0.995428i	$-0.469551\pi$
$487$	93.0290			0.191025			0.0955123	+	0.995428i	$0.469551\pi$
$488$	−487.796	−	281.629i	−0.999581	−	0.577109i
$489$	−84.8927	−	297.814i	−0.173605	−	0.609027i
$490$	−14.6919	−	25.4472i	−0.0299835	−	0.0519330i
$491$	−203.168	+	117.299i	−0.413783	+	0.238898i	−0.692414	−	0.721501i	$-0.743453\pi$
$491$	−203.168	+	117.299i	−0.413783	+	0.238898i	0.278631	+	0.960398i	$0.410119\pi$
$492$	−13.6813	+	54.5091i	−0.0278075	+	0.110791i
$493$	−256.902	+	444.968i	−0.521100	+	0.902572i
$494$			652.346i			1.32054i
$495$	182.585	−	113.299i	0.368859	−	0.228886i
$496$	416.029			0.838768
$497$	73.4474	+	42.4049i	0.147781	+	0.0853217i
$498$	−328.189	+	338.787i	−0.659014	+	0.680295i
$499$	330.575	+	572.573i	0.662476	+	1.14744i	0.979963	+	0.199179i	$0.0638275\pi$
$499$	330.575	+	572.573i	0.662476	+	1.14744i	−0.317487	+	0.948262i	$0.602839\pi$
$500$	6.16542	−	3.55961i	0.0123308	−	0.00711921i
$501$	243.098	+	235.493i	0.485225	+	0.470047i
$502$	−276.268	+	478.511i	−0.550336	+	0.953209i
$503$			184.352i			0.366504i	0.983066	+	0.183252i	$0.0586624\pi$
$503$			184.352i			0.366504i	−0.983066	+	0.183252i	$0.941338\pi$
$504$	494.748	−	15.7267i	0.981643	−	0.0312037i
$505$	98.5792			0.195206
$506$	−192.344	−	111.050i	−0.380126	−	0.219466i
$507$	135.334	+	33.9677i	0.266932	+	0.0669974i
$508$	−29.2975	−	50.7447i	−0.0576722	−	0.0998912i
$509$	702.274	−	405.458i	1.37971	−	0.796578i	0.387588	−	0.921833i	$-0.373308\pi$
$509$	702.274	−	405.458i	1.37971	−	0.796578i	0.992125	+	0.125255i	$0.0399749\pi$
$510$	149.458	−	42.6034i	0.293055	−	0.0835360i
$511$	353.385	−	612.082i	0.691557	−	1.19781i
$512$			575.386i			1.12380i
$513$	642.159	+	583.685i	1.25177	+	1.13779i
$514$	385.139			0.749298
$515$	181.782	+	104.952i	0.352974	+	0.203790i
$516$	−19.6997	−	69.1091i	−0.0381778	−	0.133932i
$517$	−307.074	−	531.868i	−0.593954	−	1.02876i
$518$	466.885	−	269.556i	0.901322	−	0.520378i
$519$	−95.9028	+	382.097i	−0.184784	+	0.736217i
$520$	105.220	−	182.246i	0.202346	−	0.350473i
$521$		−	787.925i		−	1.51233i	−0.654379	−	0.756167i	$-0.727070\pi$
$521$		−	787.925i		−	1.51233i	0.654379	−	0.756167i	$-0.272930\pi$
$522$	−591.740	−	317.014i	−1.13360	−	0.607306i
$523$	495.806			0.948004			0.474002	−	0.880524i	$-0.342809\pi$
$523$	495.806			0.948004			0.474002	+	0.880524i	$0.342809\pi$
$524$	88.4968	+	51.0936i	0.168887	+	0.0975070i
$525$	67.5045	−	69.6844i	0.128580	−	0.132732i
$526$	138.844	+	240.485i	0.263962	+	0.457196i
$527$	−348.839	+	201.402i	−0.661934	+	0.382168i
$528$	300.190	+	290.799i	0.568541	+	0.550756i
$529$	−200.177	+	346.717i	−0.378406	+	0.655419i
$530$			136.941i			0.258378i
$531$	−17.4175	+	32.5116i	−0.0328013	+	0.0612272i
$532$	132.371			0.248818
$533$	281.979	+	162.801i	0.529041	+	0.305442i
$534$	−339.583	−	85.2322i	−0.635922	−	0.159611i
$535$	154.868	+	268.239i	0.289472	+	0.501381i
$536$	−522.694	+	301.778i	−0.975176	+	0.563018i
$537$	857.088	−	244.315i	1.59607	−	0.454963i
$538$	377.111	−	653.175i	0.700950	−	1.21408i
$539$			76.5095i			0.141947i
$540$	−11.7080	−	36.6175i	−0.0216814	−	0.0678103i
$541$	−395.636			−0.731305			−0.365652	−	0.930751i	$-0.619154\pi$
$541$	−395.636			−0.731305			−0.365652	+	0.930751i	$0.619154\pi$
$542$	−405.242	−	233.967i	−0.747680	−	0.431673i
$543$	23.1232	+	81.1192i	0.0425842	+	0.149391i
$544$	−63.7052	−	110.341i	−0.117105	−	0.202832i
$545$	−342.241	+	197.593i	−0.627966	+	0.362556i
$546$	95.8758	−	381.989i	0.175597	−	0.699613i
$547$	−80.8992	+	140.121i	−0.147896	+	0.256164i	−0.930450	−	0.366420i	$-0.880583\pi$
$547$	−80.8992	+	140.121i	−0.147896	+	0.256164i	0.782554	+	0.622583i	$0.213917\pi$
$548$			57.8589i			0.105582i
$549$	18.9404	+	595.850i	0.0344999	+	1.08534i
$550$	97.9083			0.178015
$551$	−1132.09	−	653.612i	−2.05461	−	1.18623i
$552$	−201.320	+	207.821i	−0.364710	+	0.376488i
$553$	322.681	+	558.899i	0.583509	+	1.01067i
$554$	294.709	−	170.150i	0.531965	−	0.307130i
$555$	−218.986	−	212.135i	−0.394569	−	0.382226i
$556$	20.6861	−	35.8294i	0.0372053	−	0.0644414i
$557$		−	199.042i		−	0.357347i	−0.983908	−	0.178673i	$-0.942819\pi$
$557$		−	199.042i		−	0.357347i	0.983908	−	0.178673i	$-0.0571806\pi$
$558$	−277.488	−	447.183i	−0.497291	−	0.801403i
$559$	−416.342			−0.744799
$560$	163.422	+	94.3516i	0.291825	+	0.168485i
$561$	−392.486	−	98.5104i	−0.699618	−	0.175598i
$562$	95.4933	+	165.399i	0.169917	+	0.294305i
$563$	−785.990	+	453.792i	−1.39608	+	0.806024i	−0.993979	−	0.109573i	$-0.965052\pi$
$563$	−785.990	+	453.792i	−1.39608	+	0.806024i	−0.402096	+	0.915597i	$0.631718\pi$
$564$	−105.666	+	30.1204i	−0.187352	+	0.0534050i
$565$	99.2038	−	171.826i	0.175582	−	0.304117i
$566$			95.1000i			0.168021i
$567$	−290.239	−	436.162i	−0.511886	−	0.769246i
$568$	111.499			0.196301
$569$	−776.399	−	448.254i	−1.36450	−	0.787793i	−0.374279	−	0.927316i	$-0.622110\pi$
$569$	−776.399	−	448.254i	−1.36450	−	0.787793i	−0.990219	+	0.139523i	$0.955443\pi$
$570$	108.392	+	380.251i	0.190161	+	0.667108i
$571$	304.808	+	527.943i	0.533815	+	0.924594i	0.999220	+	0.0394965i	$0.0125754\pi$
$571$	304.808	+	527.943i	0.533815	+	0.924594i	−0.465405	+	0.885098i	$0.654091\pi$
$572$	−65.1669	+	37.6241i	−0.113928	+	0.0657765i
$573$	−6.69729	+	26.6834i	−0.0116881	+	0.0465679i
$574$	−174.483	+	302.214i	−0.303977	+	0.526504i
$575$			56.7112i			0.0986281i
$576$	540.561	−	335.432i	0.938474	−	0.582347i
$577$	477.854			0.828170			0.414085	−	0.910238i	$-0.364102\pi$
$577$	477.854			0.828170			0.414085	+	0.910238i	$0.364102\pi$
$578$	205.537	+	118.667i	0.355600	+	0.205306i
$579$	197.810	−	204.197i	0.341640	−	0.352673i
$580$	28.9556	+	50.1525i	0.0499234	+	0.0864699i
$581$	480.228	−	277.260i	0.826555	−	0.477212i
$582$	−341.472	−	330.790i	−0.586722	−	0.568368i
$583$	178.283	−	308.795i	0.305802	−	0.529665i
$584$		−	929.191i		−	1.59108i
$585$	−222.616	+	7.07637i	−0.380541	+	0.0120964i
$586$	−608.254			−1.03798
$587$	−220.698	−	127.420i	−0.375976	−	0.217070i	0.300090	−	0.953911i	$-0.402983\pi$
$587$	−220.698	−	127.420i	−0.375976	−	0.217070i	−0.676066	+	0.736841i	$0.736317\pi$
$588$	13.2763	+	3.33223i	0.0225787	+	0.00566706i
$589$	−512.409	−	887.518i	−0.869964	−	1.50682i
$590$	−14.5540	+	8.40274i	−0.0246677	+	0.0142419i
$591$	−771.268	+	219.852i	−1.30502	+	0.372000i
$592$	296.503	−	513.559i	0.500850	−	0.867498i
$593$		−	604.184i		−	1.01886i	−0.860512	−	0.509430i	$-0.829856\pi$
$593$		−	604.184i		−	1.01886i	0.860512	−	0.509430i	$-0.170144\pi$
$594$	112.351	−	516.629i	0.189143	−	0.869747i
$595$	−182.705			−0.307067
$596$	79.5726	+	45.9413i	0.133511	+	0.0770826i
$597$	−130.208	−	456.787i	−0.218104	−	0.765137i
$598$	115.106	+	199.369i	0.192484	+	0.333393i
$599$	−164.832	+	95.1657i	−0.275178	+	0.158874i	−0.631239	−	0.775589i	$-0.717453\pi$
$599$	−164.832	+	95.1657i	−0.275178	+	0.158874i	0.356060	+	0.934463i	$0.384120\pi$
$600$	31.0511	−	123.714i	0.0517518	−	0.206190i
$601$	−468.662	+	811.746i	−0.779804	+	1.35066i	0.152251	+	0.988342i	$0.451348\pi$
$601$	−468.662	+	811.746i	−0.779804	+	1.35066i	−0.932055	+	0.362318i	$0.881986\pi$
$602$		−	446.219i		−	0.741227i
$603$	563.087	+	301.663i	0.933809	+	0.500271i
$604$	87.0932			0.144194
$605$	13.5369	+	7.81556i	0.0223751	+	0.0129183i
$606$	168.762	−	174.212i	0.278485	−	0.287478i
$607$	483.997	+	838.308i	0.797360	+	1.38107i	0.921330	+	0.388781i	$0.127104\pi$
$607$	483.997	+	838.308i	0.797360	+	1.38107i	−0.123970	+	0.992286i	$0.539563\pi$
$608$	280.729	−	162.079i	0.461725	−	0.266577i
$609$	566.847	+	549.115i	0.930783	+	0.901666i
$610$	−135.815	+	235.238i	−0.222647	+	0.385637i
$611$			636.578i			1.04186i
$612$	−34.1880	+	63.8156i	−0.0558627	+	0.104274i
$613$	14.3244			0.0233677			0.0116839	−	0.999932i	$-0.496281\pi$
$613$	14.3244			0.0233677			0.0116839	+	0.999932i	$0.496281\pi$
$614$	−464.194	−	268.002i	−0.756016	−	0.436486i
$615$	191.416	+	48.0436i	0.311245	+	0.0781197i
$616$	−293.631	−	508.584i	−0.476673	−	0.825623i
$617$	−924.580	+	533.807i	−1.49851	+	0.865165i	−0.999999	−	0.00171906i	$-0.999453\pi$
$617$	−924.580	+	533.807i	−1.49851	+	0.865165i	−0.498511	+	0.866884i	$0.666119\pi$
$618$	496.673	−	141.578i	0.803678	−	0.229090i
$619$	−582.166	+	1008.34i	−0.940494	+	1.62898i	−0.175963	+	0.984397i	$0.556304\pi$
$619$	−582.166	+	1008.34i	−0.940494	+	1.62898i	−0.764531	+	0.644586i	$0.777030\pi$
$620$			45.4003i			0.0732263i
$621$	299.246	+	65.0766i	0.481877	+	0.104793i
$622$	362.732			0.583170
$623$	356.459	+	205.802i	0.572165	+	0.330340i
$624$	−118.757	−	416.613i	−0.190315	−	0.667650i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−342.574	+	197.785i	−0.547243	+	0.315951i
$627$	250.630	−	998.564i	0.399730	−	1.59261i
$628$	16.6172	−	28.7819i	0.0264605	−	0.0458310i
$629$			574.157i			0.912809i
$630$	−7.58416	−	238.591i	−0.0120383	−	0.378716i
$631$	−88.9538			−0.140973			−0.0704864	−	0.997513i	$-0.522455\pi$
$631$	−88.9538			−0.140973			−0.0704864	+	0.997513i	$0.522455\pi$
$632$	734.784	+	424.228i	1.16263	+	0.671247i
$633$	662.885	−	684.291i	1.04721	−	1.08103i
$634$	−186.725	−	323.418i	−0.294519	−	0.510123i
$635$	−178.196	+	102.882i	−0.280624	+	0.162019i
$636$	−45.8187	−	44.3854i	−0.0720420	−	0.0697884i
$637$	39.6519	−	68.6791i	0.0622479	−	0.107816i
$638$			796.434i			1.24833i
$639$	−62.2225	−	100.274i	−0.0973748	−	0.156923i
$640$	199.658			0.311965
$641$	115.362	+	66.6040i	0.179971	+	0.103906i	0.587279	−	0.809384i	$-0.300199\pi$
$641$	115.362	+	66.6040i	0.179971	+	0.103906i	−0.407308	+	0.913291i	$0.633532\pi$
$642$	739.163	+	185.523i	1.15134	+	0.288977i
$643$	241.729	+	418.686i	0.375939	+	0.651145i	0.990467	−	0.137750i	$-0.0439870\pi$
$643$	241.729	+	418.686i	0.375939	+	0.651145i	−0.614528	+	0.788895i	$0.710654\pi$
$644$	40.4551	−	23.3568i	0.0628185	−	0.0362683i
$645$	−242.685	+	69.1781i	−0.376257	+	0.107253i
$646$	372.303	−	644.848i	0.576321	−	0.998216i
$647$		−	347.759i		−	0.537495i	−0.963211	−	0.268748i	$-0.913390\pi$
$647$		−	347.759i		−	0.537495i	0.963211	−	0.268748i	$-0.0866097\pi$
$648$	−617.166	−	305.809i	−0.952417	−	0.471928i
$649$	43.7580			0.0674237
$650$	−87.8878	−	50.7420i	−0.135212	−	0.0780647i
$651$	169.608	+	595.006i	0.260534	+	0.913988i
$652$	32.8651	+	56.9240i	0.0504066	+	0.0873068i
$653$	751.488	−	433.872i	1.15082	−	0.664428i	0.201736	−	0.979440i	$-0.435342\pi$
$653$	751.488	−	433.872i	1.15082	−	0.664428i	0.949088	+	0.315011i	$0.102008\pi$
$654$	−236.706	+	943.085i	−0.361936	+	1.44203i
$655$	179.422	−	310.768i	0.273926	−	0.474454i
$656$			383.852i			0.585140i
$657$	−835.643	+	518.538i	−1.27191	+	0.789251i
$658$	−682.258			−1.03687
$659$	804.603	+	464.538i	1.22095	+	0.704913i	0.965120	−	0.261810i	$-0.0843193\pi$
$659$	804.603	+	464.538i	1.22095	+	0.704913i	0.255826	+	0.966723i	$0.417653\pi$
$660$	−31.7342	+	32.7590i	−0.0480821	+	0.0496348i
$661$	463.561	+	802.912i	0.701303	+	1.21469i	0.968009	+	0.250915i	$0.0807314\pi$
$661$	463.561	+	802.912i	0.701303	+	1.21469i	−0.266706	+	0.963778i	$0.585935\pi$
$662$	−149.329	+	86.2151i	−0.225572	+	0.130234i
$663$	301.263	+	291.838i	0.454393	+	0.440179i
$664$	364.513	−	631.355i	0.548966	−	0.950837i
$665$		−	464.839i		−	0.699005i
$666$	−749.781	+	23.8335i	−1.12580	+	0.0357860i
$667$	−461.316			−0.691629
$668$	−62.2144	−	35.9195i	−0.0931353	−	0.0537717i
$669$	360.783	+	90.5531i	0.539286	+	0.135356i
$670$	145.532	+	252.068i	0.217211	+	0.376221i
$671$	612.513	−	353.634i	0.912836	−	0.527026i
$672$	−188.205	+	53.6483i	−0.280067	+	0.0798338i
$673$	−472.996	+	819.253i	−0.702817	+	1.21732i	0.264656	+	0.964343i	$0.414742\pi$
$673$	−472.996	+	819.253i	−0.702817	+	1.21732i	−0.967473	+	0.252973i	$0.918592\pi$
$674$			616.446i			0.914608i
$675$	−128.587	+	41.1140i	−0.190499	+	0.0609097i
$676$	−29.6162			−0.0438110
$677$	532.245	+	307.292i	0.786182	+	0.453902i	0.838617	−	0.544722i	$-0.183365\pi$
$677$	532.245	+	307.292i	0.786182	+	0.453902i	−0.0524349	+	0.998624i	$0.516698\pi$
$678$	−133.824	−	469.472i	−0.197381	−	0.692436i
$679$	279.458	+	484.035i	0.411572	+	0.712864i
$680$	−208.021	+	120.101i	−0.305913	+	0.176619i
$681$	158.828	−	632.804i	0.233228	−	0.929227i
$682$	−312.188	+	540.726i	−0.457754	+	0.792853i
$683$		−	258.893i		−	0.379053i	−0.981876	−	0.189527i	$-0.939305\pi$
$683$		−	258.893i		−	0.379053i	0.981876	−	0.189527i	$-0.0606954\pi$
$684$	−162.360	−	86.9812i	−0.237368	−	0.127165i
$685$	203.179			0.296611
$686$	576.961	+	333.108i	0.841051	+	0.485581i
$687$	156.456	−	161.509i	0.227739	−	0.235093i
$688$	−245.414	−	425.069i	−0.356706	−	0.617832i
$689$	−320.072	+	184.794i	−0.464546	+	0.268206i
$690$	100.221	+	97.0862i	0.145248	+	0.140705i
$691$	485.487	−	840.888i	0.702586	−	1.21691i	−0.264969	−	0.964257i	$-0.585362\pi$
$691$	485.487	−	840.888i	0.702586	−	1.21691i	0.967556	−	0.252658i	$-0.0813048\pi$
$692$		−	83.6170i		−	0.120834i
$693$	−293.519	+	547.886i	−0.423549	+	0.790600i
$694$	114.663			0.165220
$695$	−125.820	−	72.6420i	−0.181035	−	0.104521i
$696$	1006.35	+	252.585i	1.44591	+	0.362909i
$697$	−185.825	−	321.859i	−0.266607	−	0.461778i
$698$	509.739	−	294.298i	0.730285	−	0.421630i
$699$	−411.933	+	117.422i	−0.589317	+	0.167986i
$700$	−10.2964	+	17.8338i	−0.0147091	+	0.0254769i
$701$		−	718.418i		−	1.02485i	−0.858733	−	0.512424i	$-0.828748\pi$
$701$		−	718.418i		−	1.02485i	0.858733	−	0.512424i	$-0.171252\pi$
$702$	−368.601	+	405.528i	−0.525073	+	0.577675i
$703$	−1460.77			−2.07791
$704$	−653.637	−	377.377i	−0.928461	−	0.536047i
$705$	105.772	+	371.061i	0.150031	+	0.526327i
$706$	−152.410	−	263.983i	−0.215879	−	0.373913i
$707$	−246.944	+	142.573i	−0.349284	+	0.201659i
$708$	1.90580	−	7.59310i	0.00269181	−	0.0107247i
$709$	494.222	−	856.018i	0.697070	−	1.20736i	−0.272408	−	0.962182i	$-0.587820\pi$
$709$	494.222	−	856.018i	0.697070	−	1.20736i	0.969478	−	0.245178i	$-0.0788465\pi$
$710$		−	53.7703i		−	0.0757328i
$711$	−28.5307	−	897.550i	−0.0401275	−	1.26238i
$712$	541.134			0.760020
$713$	−313.203	−	180.828i	−0.439275	−	0.253615i
$714$	−312.780	+	322.881i	−0.438068	+	0.452214i
$715$	132.122	+	228.842i	0.184786	+	0.320058i
$716$	−163.823	+	94.5834i	−0.228803	+	0.132100i
$717$	431.341	+	417.848i	0.601591	+	0.582772i
$718$	−183.088	+	317.118i	−0.254998	+	0.441669i
$719$		−	1280.53i		−	1.78099i	−0.454994	−	0.890495i	$-0.650358\pi$
$719$		−	1280.53i		−	1.78099i	0.454994	−	0.890495i	$-0.349642\pi$
$720$	−138.446	−	223.111i	−0.192286	−	0.309877i
$721$	−607.158			−0.842106
$722$	1067.28	+	616.193i	1.47822	+	0.853453i
$723$	−564.258	−	141.624i	−0.780440	−	0.195883i
$724$	−8.95186	−	15.5051i	−0.0123644	−	0.0214158i
$725$	176.117	−	101.681i	0.242920	−	0.140250i
$726$	36.9863	−	10.5430i	0.0509453	−	0.0145221i
$727$	324.824	−	562.611i	0.446800	−	0.773881i	−0.551376	−	0.834257i	$-0.685897\pi$
$727$	324.824	−	562.611i	0.446800	−	0.773881i	0.998176	+	0.0603766i	$0.0192302\pi$
$728$			608.710i			0.836140i
$729$	69.3901	+	725.690i	0.0951853	+	0.995460i
$730$	−448.100			−0.613836
$731$	411.557	+	237.613i	0.563006	+	0.325052i
$732$	−34.6875	−	121.688i	−0.0473873	−	0.166240i
$733$	−585.044	−	1013.33i	−0.798150	−	1.38244i	−0.920820	−	0.389989i	$-0.872479\pi$
$733$	−585.044	−	1013.33i	−0.798150	−	1.38244i	0.122669	−	0.992448i	$-0.460855\pi$
$734$	255.134	−	147.302i	0.347594	−	0.200683i
$735$	11.7015	−	46.6214i	0.0159205	−	0.0634305i
$736$	57.1972	−	99.0685i	0.0777136	−	0.134604i
$737$		−	757.869i		−	1.02832i
$738$	412.596	−	256.027i	0.559074	−	0.346919i
$739$	1175.25			1.59033			0.795164	−	0.606394i	$-0.207385\pi$
$739$	1175.25			1.59033			0.795164	+	0.606394i	$0.207385\pi$
$740$	56.0435	+	32.3567i	0.0757344	+	0.0437253i
$741$	−742.496	+	766.473i	−1.00202	+	1.03438i
$742$	−198.054	−	343.040i	−0.266920	−	0.462319i
$743$	−881.124	+	508.717i	−1.18590	+	0.684680i	−0.957372	−	0.288858i	$-0.906725\pi$
$743$	−881.124	+	508.717i	−1.18590	+	0.684680i	−0.228528	+	0.973537i	$0.573391\pi$
$744$	584.236	+	565.960i	0.785263	+	0.760699i
$745$	161.328	−	279.429i	0.216548	−	0.375073i
$746$			314.035i			0.420958i
$747$	−771.211	+	24.5147i	−1.03241	+	0.0328175i
$748$	85.8906			0.114827
$749$	−775.897	−	447.964i	−1.03591	−	0.598083i
$750$	−59.6608	−	14.9743i	−0.0795478	−	0.0199658i
$751$	497.229	+	861.226i	0.662089	+	1.14677i	0.980066	+	0.198673i	$0.0636633\pi$
$751$	497.229	+	861.226i	0.662089	+	1.14677i	−0.317977	+	0.948099i	$0.603003\pi$
$752$	−649.920	+	375.232i	−0.864256	+	0.498978i
$753$	−869.240	+	247.779i	−1.15437	+	0.329056i
$754$	412.761	−	714.922i	0.547428	−	0.948173i
$755$		−	305.839i		−	0.405084i
$756$	82.2881	+	74.7950i	0.108847	+	0.0989352i
$757$	−659.088			−0.870658			−0.435329	−	0.900271i	$-0.643368\pi$
$757$	−659.088			−0.870658			−0.435329	+	0.900271i	$0.643368\pi$
$758$	−472.471	−	272.781i	−0.623313	−	0.359870i
$759$	−99.5981	−	349.403i	−0.131223	−	0.460346i
$760$	−305.561	−	529.248i	−0.402054	−	0.696379i
$761$	559.677	−	323.130i	0.735450	−	0.424612i	−0.0849628	−	0.996384i	$-0.527077\pi$
$761$	559.677	−	323.130i	0.735450	−	0.424612i	0.820413	+	0.571772i	$0.193744\pi$
$762$	−123.247	+	491.041i	−0.161741	+	0.644411i
$763$	571.550	−	989.954i	0.749083	−	1.29745i
$764$		−	5.83933i		−	0.00764310i
$765$	224.096	+	120.055i	0.292937	+	0.156935i
$766$	−881.649			−1.15098
$767$	−39.2796	−	22.6781i	−0.0512119	−	0.0295672i
$768$	−248.385	+	256.406i	−0.323419	+	0.333862i
$769$	123.429	+	213.784i	0.160505	+	0.278003i	0.935050	−	0.354516i	$-0.115354\pi$
$769$	123.429	+	213.784i	0.160505	+	0.278003i	−0.774545	+	0.632519i	$0.782021\pi$
$770$	−245.263	+	141.603i	−0.318524	+	0.183900i
$771$	452.519	+	438.363i	0.586925	+	0.568565i
$772$	−30.1717	+	52.2588i	−0.0390824	+	0.0676928i
$773$			263.071i			0.340325i	0.985416	+	0.170162i	$0.0544292\pi$
$773$			263.071i			0.340325i	−0.985416	+	0.170162i	$0.945571\pi$
$774$	−293.210	+	547.309i	−0.378825	+	0.707117i
$775$	159.429			0.205715
$776$	636.360	+	367.402i	0.820051	+	0.473457i
$777$	855.373	+	214.691i	1.10087	+	0.276307i
$778$	545.076	+	944.100i	0.700612	+	1.21350i
$779$	818.875	−	472.777i	1.05119	−	0.606903i
$780$	45.4641	−	12.9596i	0.0582872	−	0.0166149i
$781$	−70.0034	+	121.249i	−0.0896330	+	0.155249i
$782$		−	262.770i		−	0.336023i
$783$	−334.442	−	1045.99i	−0.427128	−	1.33588i
$784$	93.4914			0.119249
$785$	−101.071	−	58.3535i	−0.128753	−	0.0743356i
$786$	−242.037	−	849.095i	−0.307934	−	1.08027i
$787$	−538.388	−	932.515i	−0.684102	−	1.18490i	−0.973718	−	0.227756i	$-0.926861\pi$
$787$	−538.388	−	932.515i	−0.684102	−	1.18490i	0.289617	−	0.957143i	$-0.406472\pi$
$788$	147.420	−	85.1129i	0.187081	−	0.108011i
$789$	−110.584	+	440.589i	−0.140157	+	0.558415i
$790$	204.583	−	354.348i	0.258966	−	0.448542i
$791$			573.906i			0.725545i
$792$	25.9621	+	816.747i	0.0327805	+	1.03125i
$793$	−733.100			−0.924463
$794$	−168.832	−	97.4751i	−0.212635	−	0.122765i
$795$	−155.865	+	160.898i	−0.196057	+	0.202388i
$796$	50.4084	+	87.3099i	0.0633271	+	0.109686i
$797$	791.487	−	456.965i	0.993082	−	0.573356i	0.0868882	−	0.996218i	$-0.472308\pi$
$797$	791.487	−	456.965i	0.993082	−	0.573356i	0.906194	+	0.422862i	$0.138974\pi$
$798$	−821.474	−	795.777i	−1.02942	−	0.997214i
$799$	363.304	−	629.262i	0.454699	−	0.787562i
$800$			50.4286i			0.0630357i
$801$	−301.982	−	486.654i	−0.377006	−	0.607559i
$802$	−55.7373			−0.0694978
$803$	1010.44	+	583.381i	1.25834	+	0.726501i
$804$	−131.509	−	33.0076i	−0.163569	−	0.0410542i
$805$	−82.0202	−	142.063i	−0.101888	−	0.176476i
$806$	560.474	−	323.590i	0.695377	−	0.401476i
$807$	1186.53	−	338.222i	1.47029	−	0.419111i
$808$	−187.441	+	324.657i	−0.231981	+	0.401803i
$809$			1008.67i			1.24681i	0.781897	+	0.623407i	$0.214252\pi$
$809$			1008.67i			1.24681i	−0.781897	+	0.623407i	$0.785748\pi$
$810$	−147.476	+	297.627i	−0.182069	+	0.367441i
$811$	952.468			1.17444			0.587218	−	0.809429i	$-0.300223\pi$
$811$	952.468			1.17444			0.587218	+	0.809429i	$0.300223\pi$
$812$	−145.069	−	83.7557i	−0.178657	−	0.103147i
$813$	−209.840	−	736.144i	−0.258105	−	0.905466i
$814$	444.992	+	770.749i	0.546673	+	0.946866i
$815$	199.896	−	115.410i	0.245271	−	0.141607i
$816$	−120.376	+	479.601i	−0.147519	+	0.587747i
$817$	−604.535	+	1047.08i	−0.739945	+	1.28162i
$818$		−	134.681i		−	0.164646i
$819$	547.427	−	339.692i	0.668409	−	0.414765i
$820$	−41.8889			−0.0510840
$821$	−1222.35	−	705.724i	−1.48885	−	0.859590i	−0.488935	−	0.872320i	$-0.662615\pi$
$821$	−1222.35	−	705.724i	−1.48885	−	0.859590i	−0.999919	+	0.0127295i	$0.995948\pi$
$822$	347.830	−	359.062i	0.423151	−	0.436815i
$823$	−380.867	−	659.680i	−0.462778	−	0.801556i	0.536320	−	0.844015i	$-0.319814\pi$
$823$	−380.867	−	659.680i	−0.462778	−	0.801556i	−0.999098	+	0.0424591i	$0.986481\pi$
$824$	−691.287	+	399.115i	−0.838941	+	0.484363i
$825$	115.037	+	111.439i	0.139439	+	0.135077i
$826$	24.3054	−	42.0982i	0.0294255	−	0.0509664i
$827$			718.144i			0.868373i	0.900823	+	0.434186i	$0.142964\pi$
$827$			718.144i			0.868373i	−0.900823	+	0.434186i	$0.857036\pi$
$828$	−64.9678	+	2.06515i	−0.0784636	+	0.00249414i
$829$	400.411			0.483005			0.241503	−	0.970400i	$-0.422360\pi$
$829$	400.411			0.483005			0.241503	+	0.970400i	$0.422360\pi$
$830$	−304.470	−	175.786i	−0.366831	−	0.211790i
$831$	539.932	+	135.518i	0.649738	+	0.163078i
$832$	391.160	+	677.509i	0.470144	+	0.814313i
$833$	−78.3923	+	45.2598i	−0.0941084	+	0.0543335i
$834$	−343.771	+	97.9926i	−0.412195	+	0.117497i
$835$	−126.136	+	218.474i	−0.151061	+	0.261645i
$836$			218.523i			0.261391i
$837$	182.946	−	841.253i	0.218574	−	1.00508i
$838$	306.105			0.365281
$839$	−614.302	−	354.667i	−0.732183	−	0.422726i	0.0870370	−	0.996205i	$-0.472260\pi$
$839$	−614.302	−	354.667i	−0.732183	−	0.422726i	−0.819220	+	0.573479i	$0.805593\pi$
$840$	101.141	+	354.816i	0.120406	+	0.422400i
$841$	406.624	+	704.293i	0.483500	+	0.837447i
$842$	485.186	−	280.122i	0.576230	−	0.332687i
$843$	−76.0567	+	303.026i	−0.0902214	+	0.359461i
$844$	−101.109	+	175.126i	−0.119797	+	0.207495i
$845$			104.001i			0.123078i
$846$	836.823	+	448.312i	0.989152	+	0.529919i
$847$	−45.2139			−0.0533813
$848$	−377.334	−	217.854i	−0.444969	−	0.256903i
$849$	−108.242	+	111.738i	−0.127494	+	0.131611i
$850$	57.9184	+	100.318i	0.0681393	+	0.118021i
$851$	−446.439	+	257.751i	−0.524605	+	0.302881i
$852$	17.9909	+	17.4281i	0.0211161	+	0.0204555i
$853$	−443.113	+	767.495i	−0.519476	+	0.899760i	0.480267	+	0.877122i	$0.340540\pi$
$853$	−443.113	+	767.495i	−0.519476	+	0.899760i	−0.999744	+	0.0226375i	$0.992794\pi$
$854$		−	785.706i		−	0.920030i
$855$	−305.445	+	570.147i	−0.357246	+	0.666838i
$856$	−1177.88			−1.37602
$857$	283.635	+	163.757i	0.330963	+	0.191081i	0.656268	−	0.754527i	$-0.272134\pi$
$857$	283.635	+	163.757i	0.330963	+	0.191081i	−0.325306	+	0.945609i	$0.605467\pi$
$858$	630.600	+	158.275i	0.734965	+	0.184470i
$859$	35.0835	+	60.7664i	0.0408423	+	0.0707409i	0.885724	−	0.464212i	$-0.153663\pi$
$859$	35.0835	+	60.7664i	0.0408423	+	0.0707409i	−0.844882	+	0.534953i	$0.820329\pi$
$860$	46.3868	−	26.7814i	0.0539381	−	0.0311412i
$861$	−548.987	+	156.490i	−0.637615	+	0.181754i
$862$	−202.671	+	351.036i	−0.235117	+	0.407235i
$863$			982.709i			1.13871i	0.822091	+	0.569356i	$0.192807\pi$
$863$			982.709i			1.13871i	−0.822091	+	0.569356i	$0.807193\pi$
$864$	266.095	+	57.8673i	0.307980	+	0.0669760i
$865$	−293.632			−0.339459
$866$	308.201	+	177.940i	0.355891	+	0.205474i
$867$	106.429	+	373.368i	0.122756	+	0.430643i
$868$	−65.6615	−	113.729i	−0.0756469	−	0.131024i
$869$	−922.650	+	532.692i	−1.06174	+	0.612994i
$870$	121.808	−	485.310i	0.140010	−	0.557828i
$871$	−392.774	+	680.305i	−0.450946	+	0.781062i
$872$		−	1502.83i		−	1.72343i
$873$	−24.7090	−	777.323i	−0.0283035	−	0.890405i
$874$	668.539			0.764919
$875$	62.6258	+	36.1570i	0.0715723	+	0.0413223i
$876$	145.239	−	149.929i	0.165798	−	0.171152i
$877$	−463.447	−	802.714i	−0.528446	−	0.915296i	−0.999450	−	0.0331646i	$-0.989441\pi$
$877$	−463.447	−	802.714i	−0.528446	−	0.915296i	0.471004	−	0.882131i	$-0.343892\pi$
$878$	245.681	−	141.844i	0.279819	−	0.161553i
$879$	−714.668	−	692.311i	−0.813046	−	0.787612i
$880$	−155.759	+	269.782i	−0.176999	+	0.306571i
$881$			766.920i			0.870510i	0.900307	+	0.435255i	$0.143342\pi$
$881$			766.920i			0.870510i	−0.900307	+	0.435255i	$0.856658\pi$
$882$	−62.3581	−	100.492i	−0.0707008	−	0.113937i
$883$	1206.08			1.36589			0.682946	−	0.730469i	$-0.260699\pi$
$883$	1206.08			1.36589			0.682946	+	0.730469i	$0.260699\pi$
$884$	−77.1000	−	44.5137i	−0.0872172	−	0.0503549i
$885$	−26.6641	−	6.69245i	−0.0301289	−	0.00756209i
$886$	−443.025	−	767.341i	−0.500028	−	0.866074i
$887$	651.741	−	376.283i	0.734771	−	0.424220i	−0.0853943	−	0.996347i	$-0.527215\pi$
$887$	651.741	−	376.283i	0.734771	−	0.424220i	0.820165	+	0.572127i	$0.193882\pi$
$888$	1115.02	−	317.840i	1.25566	−	0.357928i
$889$	297.592	−	515.444i	0.334749	−	0.579802i
$890$		−	260.961i		−	0.293214i
$891$	720.031	−	479.136i	0.808116	−	0.537751i
$892$	−78.9527			−0.0885120
$893$	1600.97	+	924.320i	1.79280	+	1.03507i
$894$	−217.629	−	763.470i	−0.243433	−	0.853993i
$895$	332.142	+	575.286i	0.371108	+	0.642778i
$896$	−500.149	+	288.761i	−0.558202	+	0.322278i
$897$	−91.6771	+	365.261i	−0.102204	+	0.407203i
$898$	−622.747	+	1078.63i	−0.693482	+	1.20115i
$899$			1296.87i			1.44257i
$900$	24.3476	−	15.1083i	0.0270529	−	0.0167870i
$901$	421.858			0.468211
$902$	−498.904	−	288.042i	−0.553109	−	0.319338i
$903$	507.884	−	524.284i	0.562440	−	0.580603i
$904$	377.257	+	653.428i	0.417319	+	0.722818i
$905$	−54.4480	+	31.4356i	−0.0601635	+	0.0347354i
$906$	−540.486	−	523.578i	−0.596562	−	0.577901i
$907$	177.370	−	307.213i	0.195556	−	0.338713i	−0.751526	−	0.659703i	$-0.770682\pi$
$907$	177.370	−	307.213i	0.195556	−	0.338713i	0.947083	+	0.320989i	$0.104015\pi$
$908$			138.481i			0.152512i
$909$	396.573	−	12.6060i	0.436274	−	0.0138680i
$910$	293.549			0.322581
$911$	280.940	+	162.201i	0.308387	+	0.178047i	0.646204	−	0.763164i	$-0.276355\pi$
$911$	280.940	+	162.201i	0.308387	+	0.178047i	−0.337818	+	0.941212i	$0.609689\pi$
$912$	−1220.20	−	306.260i	−1.33794	−	0.335811i
$913$	457.710	+	792.777i	0.501325	+	0.868321i
$914$	127.873	−	73.8277i	0.139905	−	0.0807743i
$915$	−427.323	+	121.809i	−0.467019	+	0.133125i
$916$	−23.8641	+	41.3338i	−0.0260525	+	0.0451243i
$917$			1037.98i			1.13193i
$918$	595.805	−	190.501i	0.649025	−	0.207517i
$919$	−604.200			−0.657453			−0.328727	−	0.944425i	$-0.606619\pi$
$919$	−604.200			−0.657453			−0.328727	+	0.944425i	$0.606619\pi$
$920$	−186.770	−	107.832i	−0.203011	−	0.117209i
$921$	−240.365	−	843.232i	−0.260983	−	0.915561i
$922$	567.360	+	982.696i	0.615357	+	1.06583i
$923$	125.678	−	72.5600i	0.136162	−	0.0786133i
$924$	32.1165	−	127.959i	0.0347581	−	0.138484i
$925$	113.625	−	196.804i	0.122837	−	0.212761i
$926$		−	604.196i		−	0.652479i
$927$	744.709	+	398.964i	0.803353	+	0.430381i
$928$	−410.211			−0.442037
$929$	−1417.48	−	818.384i	−1.52582	−	0.880930i	−0.999531	−	0.0306220i	$-0.990251\pi$
$929$	−1417.48	−	818.384i	−1.52582	−	0.880930i	−0.526285	−	0.850308i	$-0.676415\pi$
$930$	272.933	−	281.747i	0.293476	−	0.302953i
$931$	−115.150	−	199.446i	−0.123684	−	0.214228i
$932$	78.7366	−	45.4586i	0.0844813	−	0.0487753i
$933$	426.192	+	412.859i	0.456797	+	0.442507i
$934$	−198.383	+	343.609i	−0.212401	+	0.367890i
$935$		−	301.615i		−	0.322583i
$936$	399.983	−	746.611i	0.427332	−	0.797662i
$937$	−266.212			−0.284111			−0.142055	−	0.989859i	$-0.545371\pi$
$937$	−266.212			−0.284111			−0.142055	+	0.989859i	$0.545371\pi$
$938$	−729.123	−	420.959i	−0.777316	−	0.448784i
$939$	−627.626	−	157.528i	−0.668398	−	0.167762i
$940$	−40.9482	−	70.9243i	−0.0435619	−	0.0754514i
$941$	140.374	−	81.0449i	0.149175	−	0.0861264i	−0.423554	−	0.905871i	$-0.639218\pi$
$941$	140.374	−	81.0449i	0.149175	−	0.0861264i	0.572730	+	0.819744i	$0.305884\pi$
$942$	−276.152	+	78.7177i	−0.293155	+	0.0835645i
$943$	166.842	−	288.979i	0.176927	−	0.306446i
$944$		−	53.4704i		−	0.0566424i
$945$	262.652	−	288.965i	0.277939	−	0.305783i
$946$	736.633			0.778681
$947$	−690.598	−	398.717i	−0.729248	−	0.421032i	0.0888989	−	0.996041i	$-0.471665\pi$
$947$	−690.598	−	398.717i	−0.729248	−	0.421032i	−0.818147	+	0.575009i	$0.804999\pi$
$948$	52.2510	+	183.303i	0.0551171	+	0.193358i
$949$	−604.687	−	1047.35i	−0.637183	−	1.10363i
$950$	−255.229	+	147.356i	−0.268662	+	0.155112i
$951$	148.719	−	592.529i	0.156382	−	0.623059i
$952$	347.399	−	601.713i	0.364915	−	0.632052i
$953$		−	1382.90i		−	1.45110i	−0.688168	−	0.725551i	$-0.741585\pi$
$953$		−	1382.90i		−	1.45110i	0.688168	−	0.725551i	$-0.258415\pi$
$954$	17.5115	+	550.897i	0.0183559	+	0.577460i
$955$	−20.5055			−0.0214718
$956$	−110.390	−	63.7338i	−0.115471	−	0.0666671i
$957$	−906.497	+	935.769i	−0.947227	+	0.977816i
$958$	−127.020	−	220.005i	−0.132589	−	0.229650i
$959$	−508.969	+	293.853i	−0.530729	+	0.306416i
$960$	340.579	+	329.925i	0.354770	+	0.343672i
$961$	−27.8509	+	48.2391i	−0.0289811	+	0.0501968i
$962$		−	922.488i		−	0.958927i
$963$	657.317	+	1059.29i	0.682573	+	1.09999i
$964$	123.481			0.128092
$965$	183.513	+	105.952i	0.190169	+	0.109794i
$966$	−391.471	−	98.2558i	−0.405250	−	0.101714i
$967$	−184.756	−	320.006i	−0.191061	−	0.330927i	0.754541	−	0.656252i	$-0.227859\pi$
$967$	−184.756	−	320.006i	−0.191061	−	0.330927i	−0.945602	+	0.325326i	$0.894526\pi$
$968$	−51.4789	+	29.7214i	−0.0531807	+	0.0307039i
$969$	1171.40	−	333.910i	1.20887	−	0.344593i
$970$	177.179	−	306.883i	0.182659	−	0.316374i
$971$		−	961.450i		−	0.990165i	−0.868846	−	0.495082i	$-0.835138\pi$
$971$		−	961.450i		−	0.990165i	0.868846	−	0.495082i	$-0.164862\pi$
$972$	−51.7824	−	145.811i	−0.0532741	−	0.150011i
$973$	420.243			0.431904
$974$	147.750	+	85.3036i	0.151694	+	0.0875807i
$975$	−45.5094	−	159.653i	−0.0466763	−	0.163746i
$976$	−432.126	−	748.465i	−0.442752	−	0.766870i
$977$	−1487.96	+	859.076i	−1.52299	+	0.879300i	−0.523362	+	0.852110i	$0.675323\pi$
$977$	−1487.96	+	859.076i	−1.52299	+	0.879300i	−0.999630	+	0.0271901i	$0.991344\pi$
$978$	138.255	−	550.836i	0.141365	−	0.563227i
$979$	−339.744	+	588.454i	−0.347032	+	0.601077i
$980$			10.2025i			0.0104107i
$981$	−1351.53	+	838.660i	−1.37771	+	0.854903i
$982$	−430.232			−0.438118
$983$	−1109.96	−	640.833i	−1.12915	−	0.651915i	−0.185430	−	0.982658i	$-0.559368\pi$
$983$	−1109.96	−	640.833i	−1.12915	−	0.651915i	−0.943721	+	0.330742i	$0.892701\pi$
$984$	−522.187	+	539.049i	−0.530678	+	0.547814i
$985$	−298.884	−	517.683i	−0.303436	−	0.525567i
$986$	−816.033	+	471.137i	−0.827620	+	0.477826i
$987$	−801.619	−	776.543i	−0.812177	−	0.786771i
$988$	113.252	−	196.158i	0.114627	−	0.198541i
$989$			426.678i			0.431423i
$990$	393.874	−	12.5202i	0.397853	−	0.0126466i
$991$	952.926			0.961581			0.480790	−	0.876836i	$-0.340350\pi$
$991$	952.926			0.961581			0.480790	+	0.876836i	$0.340350\pi$
$992$	−278.506	−	160.795i	−0.280752	−	0.162092i
$993$	−273.583	−	68.6670i	−0.275512	−	0.0691510i
$994$	77.7669	+	134.696i	0.0782363	+	0.135509i
$995$	306.600	−	177.015i	0.308140	−	0.177905i
$996$	157.501	−	44.8961i	0.158134	−	0.0450764i
$997$	−884.833	+	1532.57i	−0.887495	+	1.53719i	−0.0446679	+	0.999002i	$0.514223\pi$
$997$	−884.833	+	1532.57i	−0.887495	+	1.53719i	−0.842827	+	0.538185i	$0.819110\pi$
$998$			1212.49i			1.21492i
$999$	−908.082	−	825.394i	−0.908991	−	0.826220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.i.a.11.6	✓	16
3.2	odd	2		135.3.i.a.116.3		16
4.3	odd	2		720.3.bs.c.641.4		16
5.2	odd	4		225.3.i.b.74.5		32
5.3	odd	4		225.3.i.b.74.12		32
5.4	even	2		225.3.j.b.101.3		16
9.2	odd	6		405.3.c.a.161.12		16
9.4	even	3		135.3.i.a.71.3		16
9.5	odd	6	inner	45.3.i.a.41.6	yes	16
9.7	even	3		405.3.c.a.161.5		16
12.11	even	2		2160.3.bs.c.1601.6		16
15.2	even	4		675.3.i.c.224.12		32
15.8	even	4		675.3.i.c.224.5		32
15.14	odd	2		675.3.j.b.251.6		16
36.23	even	6		720.3.bs.c.401.4		16
36.31	odd	6		2160.3.bs.c.881.6		16
45.4	even	6		675.3.j.b.476.6		16
45.13	odd	12		675.3.i.c.449.12		32
45.14	odd	6		225.3.j.b.176.3		16
45.22	odd	12		675.3.i.c.449.5		32
45.23	even	12		225.3.i.b.149.5		32
45.32	even	12		225.3.i.b.149.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.6	✓	16	1.1	even	1	trivial
45.3.i.a.41.6	yes	16	9.5	odd	6	inner
135.3.i.a.71.3		16	9.4	even	3
135.3.i.a.116.3		16	3.2	odd	2
225.3.i.b.74.5		32	5.2	odd	4
225.3.i.b.74.12		32	5.3	odd	4
225.3.i.b.149.5		32	45.23	even	12
225.3.i.b.149.12		32	45.32	even	12
225.3.j.b.101.3		16	5.4	even	2
225.3.j.b.176.3		16	45.14	odd	6
405.3.c.a.161.5		16	9.7	even	3
405.3.c.a.161.12		16	9.2	odd	6
675.3.i.c.224.5		32	15.8	even	4
675.3.i.c.224.12		32	15.2	even	4
675.3.i.c.449.5		32	45.22	odd	12
675.3.i.c.449.12		32	45.13	odd	12
675.3.j.b.251.6		16	15.14	odd	2
675.3.j.b.476.6		16	45.4	even	6
720.3.bs.c.401.4		16	36.23	even	6
720.3.bs.c.641.4		16	4.3	odd	2
2160.3.bs.c.881.6		16	36.31	odd	6
2160.3.bs.c.1601.6		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58822 + 0.916957i) q^{2} +(0.822398 + 2.88508i) q^{3} +(-0.318381 - 0.551452i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.33934 + 5.33623i) q^{6} +(3.23398 - 5.60142i) q^{7} -8.50342i q^{8} +(-7.64732 + 4.74536i) q^{9} +O(q^{10})\)	\(q+(1.58822 + 0.916957i) q^{2} +(0.822398 + 2.88508i) q^{3} +(-0.318381 - 0.551452i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.33934 + 5.33623i) q^{6} +(3.23398 - 5.60142i) q^{7} -8.50342i q^{8} +(-7.64732 + 4.74536i) q^{9} -4.10076 q^{10} +(9.24701 + 5.33876i) q^{11} +(1.32914 - 1.37207i) q^{12} +(-5.53374 - 9.58473i) q^{13} +(10.2725 - 5.93084i) q^{14} +(-4.81818 - 4.66746i) q^{15} +(6.52374 - 11.2995i) q^{16} +12.6328i q^{17} +(-16.4969 + 0.524391i) q^{18} -32.1403 q^{19} +(1.23308 + 0.711921i) q^{20} +(18.8201 + 4.72368i) q^{21} +(9.79083 + 16.9582i) q^{22} +(-9.82266 + 5.67112i) q^{23} +(24.5330 - 6.99319i) q^{24} +(2.50000 - 4.33013i) q^{25} -20.2968i q^{26} +(-19.9799 - 18.1605i) q^{27} -4.11855 q^{28} +(35.2234 + 20.3362i) q^{29} +(-3.37245 - 11.8310i) q^{30} +(15.9429 + 27.6139i) q^{31} +(-8.73448 + 5.04286i) q^{32} +(-7.79801 + 31.0689i) q^{33} +(-11.5837 + 20.0635i) q^{34} +14.4628i q^{35} +(5.05160 + 2.70630i) q^{36} +45.4499 q^{37} +(-51.0457 - 29.4713i) q^{38} +(23.1017 - 23.8477i) q^{39} +(9.50711 + 16.4668i) q^{40} +(-25.4781 + 14.7098i) q^{41} +(25.5590 + 24.7595i) q^{42} +(18.8093 - 32.5786i) q^{43} -6.79904i q^{44} +(9.50350 - 17.7393i) q^{45} -20.8007 q^{46} +(-49.8119 - 28.7589i) q^{47} +(37.9649 + 9.52885i) q^{48} +(3.58274 + 6.20548i) q^{49} +(7.94108 - 4.58478i) q^{50} +(-36.4465 + 10.3891i) q^{51} +(-3.52368 + 6.10319i) q^{52} -33.3940i q^{53} +(-15.0799 - 47.1635i) q^{54} -23.8757 q^{55} +(-47.6312 - 27.4999i) q^{56} +(-26.4321 - 92.7272i) q^{57} +(37.2949 + 64.5966i) q^{58} +(3.54909 - 2.04907i) q^{59} +(-1.03986 + 4.14302i) q^{60} +(33.1195 - 57.3647i) q^{61} +58.4757i q^{62} +(1.84945 + 58.1823i) q^{63} -70.6863 q^{64} +(21.4321 + 12.3738i) q^{65} +(-40.8738 + 42.1937i) q^{66} +(-35.4890 - 61.4687i) q^{67} +(6.96635 - 4.02203i) q^{68} +(-24.4397 - 23.6752i) q^{69} +(-13.2618 + 22.9700i) q^{70} +13.1123i q^{71} +(40.3518 + 65.0284i) q^{72} +109.273 q^{73} +(72.1842 + 41.6756i) q^{74} +(14.5487 + 3.65160i) q^{75} +(10.2328 + 17.7238i) q^{76} +(59.8093 - 34.5309i) q^{77} +(58.5579 - 16.6921i) q^{78} +(-49.8891 + 86.4104i) q^{79} +29.1751i q^{80} +(35.9631 - 72.5786i) q^{81} -53.9530 q^{82} +(74.2472 + 42.8667i) q^{83} +(-3.38709 - 11.8823i) q^{84} +(-14.1238 - 24.4632i) q^{85} +(59.7463 - 34.4945i) q^{86} +(-29.7039 + 118.347i) q^{87} +(45.3977 - 78.6312i) q^{88} +63.6372i q^{89} +(31.3598 - 19.4596i) q^{90} -71.5841 q^{91} +(6.25469 + 3.61115i) q^{92} +(-66.5567 + 68.7060i) q^{93} +(-52.7414 - 91.3507i) q^{94} +(62.2394 - 35.9339i) q^{95} +(-21.7322 - 21.0524i) q^{96} +(-43.2064 + 74.8357i) q^{97} +13.1409i q^{98} +(-96.0492 + 3.05314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9	\( 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9} - 18 q^{11} - 22 q^{12} - 10 q^{13} - 54 q^{14} + 10 q^{15} - 32 q^{16} - 8 q^{18} - 52 q^{19} + 72 q^{21} - 24 q^{22} - 54 q^{23} + 108 q^{24} + 40 q^{25} + 34 q^{27} + 32 q^{28} - 54 q^{29} - 100 q^{30} + 32 q^{31} + 216 q^{32} + 62 q^{33} + 54 q^{34} - 86 q^{36} + 44 q^{37} + 252 q^{38} + 160 q^{39} - 30 q^{40} + 144 q^{41} - 270 q^{42} - 124 q^{43} + 140 q^{45} - 108 q^{46} - 216 q^{47} - 172 q^{48} - 54 q^{49} - 106 q^{51} + 62 q^{52} - 316 q^{54} - 18 q^{56} - 236 q^{57} + 90 q^{58} - 486 q^{59} - 10 q^{60} + 62 q^{61} - 132 q^{63} + 256 q^{64} - 90 q^{65} + 208 q^{66} + 14 q^{67} - 288 q^{68} + 90 q^{69} - 60 q^{70} + 804 q^{72} - 268 q^{73} + 540 q^{74} - 20 q^{75} - 106 q^{76} + 702 q^{77} + 290 q^{78} - 40 q^{79} - 112 q^{81} - 204 q^{82} + 522 q^{83} + 714 q^{84} + 30 q^{85} + 54 q^{86} + 106 q^{87} + 144 q^{88} + 250 q^{90} + 136 q^{91} - 1332 q^{92} + 90 q^{93} - 150 q^{94} + 180 q^{95} + 166 q^{96} - 142 q^{97} - 824 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9 - 18 * q^11 - 22 * q^12 - 10 * q^13 - 54 * q^14 + 10 * q^15 - 32 * q^16 - 8 * q^18 - 52 * q^19 + 72 * q^21 - 24 * q^22 - 54 * q^23 + 108 * q^24 + 40 * q^25 + 34 * q^27 + 32 * q^28 - 54 * q^29 - 100 * q^30 + 32 * q^31 + 216 * q^32 + 62 * q^33 + 54 * q^34 - 86 * q^36 + 44 * q^37 + 252 * q^38 + 160 * q^39 - 30 * q^40 + 144 * q^41 - 270 * q^42 - 124 * q^43 + 140 * q^45 - 108 * q^46 - 216 * q^47 - 172 * q^48 - 54 * q^49 - 106 * q^51 + 62 * q^52 - 316 * q^54 - 18 * q^56 - 236 * q^57 + 90 * q^58 - 486 * q^59 - 10 * q^60 + 62 * q^61 - 132 * q^63 + 256 * q^64 - 90 * q^65 + 208 * q^66 + 14 * q^67 - 288 * q^68 + 90 * q^69 - 60 * q^70 + 804 * q^72 - 268 * q^73 + 540 * q^74 - 20 * q^75 - 106 * q^76 + 702 * q^77 + 290 * q^78 - 40 * q^79 - 112 * q^81 - 204 * q^82 + 522 * q^83 + 714 * q^84 + 30 * q^85 + 54 * q^86 + 106 * q^87 + 144 * q^88 + 250 * q^90 + 136 * q^91 - 1332 * q^92 + 90 * q^93 - 150 * q^94 + 180 * q^95 + 166 * q^96 - 142 * q^97 - 824 * q^99

Introduction

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