LMFDB - Embedded newform 105.3.t.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(11,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("105.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.t (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Root			$-0.178197 - 1.72286i$ of defining polynomial
Character	$\chi$	$=$	105.11
Dual form			105.3.t.a.86.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16124 - 1.82514i) q^{2} +(0.0335498 + 2.99981i) q^{3} +(4.66228 - 8.07530i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.58114 + 9.42188i) q^{6} +7.00000 q^{7} -19.4361i q^{8} +(-8.99775 + 0.201286i) q^{9} +O(q^{10})$	\(q+(3.16124 - 1.82514i) q^{2} +(0.0335498 + 2.99981i) q^{3} +(4.66228 - 8.07530i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.58114 + 9.42188i) q^{6} +7.00000 q^{7} -19.4361i q^{8} +(-8.99775 + 0.201286i) q^{9} +(-4.08114 + 7.06874i) q^{10} +(-2.13524 - 1.23278i) q^{11} +(24.3808 + 13.7150i) q^{12} -14.8114 q^{13} +(22.1287 - 12.7760i) q^{14} +(-3.41886 - 5.77160i) q^{15} +(-16.8246 - 29.1410i) q^{16} +(-14.2672 - 8.23717i) q^{17} +(-28.0766 + 17.0585i) q^{18} +(15.5680 + 26.9645i) q^{19} +20.8503i q^{20} +(0.234849 + 20.9987i) q^{21} -9.00000 q^{22} +(-21.5324 + 12.4317i) q^{23} +(58.3047 - 0.652079i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-46.8223 + 27.0329i) q^{26} +(-0.905694 - 26.9848i) q^{27} +(32.6359 - 56.5271i) q^{28} -24.9596i q^{29} +(-21.3418 - 12.0055i) q^{30} +(14.0680 - 24.3664i) q^{31} +(-39.0441 - 22.5421i) q^{32} +(3.62648 - 6.44668i) q^{33} -60.1359 q^{34} +(-13.5554 + 7.82624i) q^{35} +(-40.3246 + 73.5980i) q^{36} +(19.0548 + 33.0039i) q^{37} +(98.4281 + 56.8275i) q^{38} +(-0.496919 - 44.4314i) q^{39} +(21.7302 + 37.6379i) q^{40} -20.1246i q^{41} +(39.0680 + 65.9532i) q^{42} +21.8114 q^{43} +(-19.9102 + 11.4951i) q^{44} +(17.1990 - 10.4496i) q^{45} +(-45.3794 + 78.5994i) q^{46} +(6.66897 - 3.85033i) q^{47} +(86.8530 - 51.4482i) q^{48} +49.0000 q^{49} -18.2514i q^{50} +(24.2313 - 43.0752i) q^{51} +(-69.0548 + 119.606i) q^{52} +(68.4380 + 39.5127i) q^{53} +(-52.1142 - 83.6523i) q^{54} +5.51317 q^{55} -136.053i q^{56} +(-80.3662 + 47.6056i) q^{57} +(-45.5548 - 78.9032i) q^{58} +(-67.1622 - 38.7761i) q^{59} +(-62.5471 + 0.699525i) q^{60} +(10.8641 + 18.8171i) q^{61} -102.704i q^{62} +(-62.9842 + 1.40900i) q^{63} -29.9737 q^{64} +(28.6821 - 16.5596i) q^{65} +(-0.301948 - 26.9983i) q^{66} +(42.3246 - 73.3083i) q^{67} +(-133.035 + 76.8079i) q^{68} +(-38.0153 - 64.1761i) q^{69} +(-28.5680 + 49.4812i) q^{70} -5.61961i q^{71} +(3.91223 + 174.881i) q^{72} +(-24.9320 + 43.1835i) q^{73} +(120.473 + 69.5554i) q^{74} +(13.0734 + 7.35426i) q^{75} +290.329 q^{76} +(-14.9467 - 8.62947i) q^{77} +(-82.6644 - 139.551i) q^{78} +(-38.2566 - 66.2623i) q^{79} +(65.1612 + 37.6208i) q^{80} +(80.9190 - 3.62225i) q^{81} +(-36.7302 - 63.6187i) q^{82} +1.56922i q^{83} +(170.666 + 96.0052i) q^{84} +36.8377 q^{85} +(68.9510 - 39.8089i) q^{86} +(74.8742 - 0.837391i) q^{87} +(-23.9605 + 41.5008i) q^{88} +(1.19249 - 0.688486i) q^{89} +(35.2982 - 64.4242i) q^{90} -103.680 q^{91} +231.841i q^{92} +(73.5667 + 41.3838i) q^{93} +(14.0548 - 24.3436i) q^{94} +(-60.2945 - 34.8110i) q^{95} +(66.3122 - 117.881i) q^{96} -71.8114 q^{97} +(154.901 - 89.4319i) q^{98} +(19.4605 + 10.6625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	3.16124	−	1.82514i	1.58062	−	0.912570i	0.585849	−	0.810420i	$-0.300761\pi$
$2$	3.16124	−	1.82514i	1.58062	−	0.912570i	0.994769	−	0.102150i	$-0.0325723\pi$
$3$	0.0335498	+	2.99981i	0.0111833	+	0.999937i
$3$	0.0335498	+	2.99981i	0.0111833	+	0.999937i
$4$	4.66228	−	8.07530i	1.16557	−	2.01883i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$	5.58114	+	9.42188i	0.930190	+	1.57031i
$7$	7.00000			1.00000
$7$	7.00000			1.00000
$8$		−	19.4361i		−	2.42952i
$9$	−8.99775	+	0.201286i	−0.999750	+	0.0223651i
$10$	−4.08114	+	7.06874i	−0.408114	+	0.706874i
$11$	−2.13524	−	1.23278i	−0.194113	−	0.112071i	0.399794	−	0.916605i	$-0.369082\pi$
$11$	−2.13524	−	1.23278i	−0.194113	−	0.112071i	−0.593906	+	0.804534i	$0.702415\pi$
$12$	24.3808	+	13.7150i	2.03173	+	1.14292i
$13$	−14.8114			−1.13934			−0.569669	−	0.821874i	$-0.692929\pi$
$13$	−14.8114			−1.13934			−0.569669	+	0.821874i	$0.692929\pi$
$14$	22.1287	−	12.7760i	1.58062	−	0.912570i
$15$	−3.41886	−	5.77160i	−0.227924	−	0.384773i
$16$	−16.8246	−	29.1410i	−1.05153	−	1.82131i
$17$	−14.2672	−	8.23717i	−0.839246	−	0.484539i	0.0177616	−	0.999842i	$-0.494346\pi$
$17$	−14.2672	−	8.23717i	−0.839246	−	0.484539i	−0.857008	+	0.515303i	$0.827679\pi$
$18$	−28.0766	+	17.0585i	−1.55981	+	0.947693i
$19$	15.5680	+	26.9645i	0.819367	+	1.41919i	0.906149	+	0.422958i	$0.139008\pi$
$19$	15.5680	+	26.9645i	0.819367	+	1.41919i	−0.0867824	+	0.996227i	$0.527658\pi$
$20$			20.8503i			1.04252i
$21$	0.234849	+	20.9987i	0.0111833	+	0.999937i
$22$	−9.00000			−0.409091
$23$	−21.5324	+	12.4317i	−0.936192	+	0.540511i	−0.888764	−	0.458364i	$-0.848436\pi$
$23$	−21.5324	+	12.4317i	−0.936192	+	0.540511i	−0.0474272	+	0.998875i	$0.515102\pi$
$24$	58.3047	−	0.652079i	2.42936	−	0.0271699i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−46.8223	+	27.0329i	−1.80086	+	1.03973i
$27$	−0.905694	−	26.9848i	−0.0335442	−	0.999437i
$28$	32.6359	−	56.5271i	1.16557	−	2.01883i
$29$		−	24.9596i		−	0.860676i	−0.902668	−	0.430338i	$-0.858394\pi$
$29$		−	24.9596i		−	0.860676i	0.902668	−	0.430338i	$-0.141606\pi$
$30$	−21.3418	−	12.0055i	−0.711394	−	0.400183i
$31$	14.0680	−	24.3664i	0.453806	−	0.786014i	−0.544813	−	0.838557i	$-0.683399\pi$
$31$	14.0680	−	24.3664i	0.453806	−	0.786014i	0.998619	+	0.0525432i	$0.0167327\pi$
$32$	−39.0441	−	22.5421i	−1.22013	−	0.704441i
$33$	3.62648	−	6.44668i	0.109893	−	0.195354i
$34$	−60.1359			−1.76870
$35$	−13.5554	+	7.82624i	−0.387298	+	0.223607i
$36$	−40.3246	+	73.5980i	−1.12013	+	2.04439i
$37$	19.0548	+	33.0039i	0.514995	+	0.891997i	0.999849	+	0.0174018i	$0.00553946\pi$
$37$	19.0548	+	33.0039i	0.514995	+	0.891997i	−0.484854	+	0.874595i	$0.661127\pi$
$38$	98.4281	+	56.8275i	2.59021	+	1.49546i
$39$	−0.496919	−	44.4314i	−0.0127415	−	1.13927i
$40$	21.7302	+	37.6379i	0.543256	+	0.940947i
$41$		−	20.1246i		−	0.490844i	−0.969416	−	0.245422i	$-0.921073\pi$
$41$		−	20.1246i		−	0.490844i	0.969416	−	0.245422i	$-0.0789266\pi$
$42$	39.0680	+	65.9532i	0.930190	+	1.57031i
$43$	21.8114			0.507242			0.253621	−	0.967304i	$-0.418378\pi$
$43$	21.8114			0.507242			0.253621	+	0.967304i	$0.418378\pi$
$44$	−19.9102	+	11.4951i	−0.452504	+	0.261253i
$45$	17.1990	−	10.4496i	0.382200	−	0.232213i
$46$	−45.3794	+	78.5994i	−0.986508	+	1.70868i
$47$	6.66897	−	3.85033i	0.141893	−	0.0819220i	−0.427373	−	0.904075i	$-0.640561\pi$
$47$	6.66897	−	3.85033i	0.141893	−	0.0819220i	0.569266	+	0.822153i	$0.307227\pi$
$48$	86.8530	−	51.4482i	1.80944	−	1.07184i
$49$	49.0000			1.00000
$50$		−	18.2514i		−	0.365028i
$51$	24.2313	−	43.0752i	0.475123	−	0.844613i
$52$	−69.0548	+	119.606i	−1.32798	+	2.30012i
$53$	68.4380	+	39.5127i	1.29128	+	0.745522i	0.978882	−	0.204428i	$-0.0655335\pi$
$53$	68.4380	+	39.5127i	1.29128	+	0.745522i	0.312401	+	0.949950i	$0.398867\pi$
$54$	−52.1142	−	83.6523i	−0.965077	−	1.54912i
$55$	5.51317			0.100239
$56$		−	136.053i		−	2.42952i
$57$	−80.3662	+	47.6056i	−1.40993	+	0.835187i
$58$	−45.5548	−	78.9032i	−0.785428	−	1.36040i
$59$	−67.1622	−	38.7761i	−1.13834	−	0.657222i	−0.192323	−	0.981332i	$-0.561602\pi$
$59$	−67.1622	−	38.7761i	−1.13834	−	0.657222i	−0.946020	+	0.324109i	$0.894935\pi$
$60$	−62.5471	+	0.699525i	−1.04245	+	0.0116588i
$61$	10.8641	+	18.8171i	0.178099	+	0.308477i	0.941229	−	0.337768i	$-0.109672\pi$
$61$	10.8641	+	18.8171i	0.178099	+	0.308477i	−0.763130	+	0.646245i	$0.776339\pi$
$62$		−	102.704i		−	1.65652i
$63$	−62.9842	+	1.40900i	−0.999750	+	0.0223651i
$64$	−29.9737			−0.468339
$65$	28.6821	−	16.5596i	0.441264	−	0.254764i
$66$	−0.301948	−	26.9983i	−0.00457498	−	0.409065i
$67$	42.3246	−	73.3083i	0.631710	−	1.09415i	−0.355492	−	0.934679i	$-0.615687\pi$
$67$	42.3246	−	73.3083i	0.631710	−	1.09415i	0.987202	−	0.159474i	$-0.0509799\pi$
$68$	−133.035	+	76.8079i	−1.95640	+	1.12953i
$69$	−38.0153	−	64.1761i	−0.550946	−	0.930089i
$70$	−28.5680	+	49.4812i	−0.408114	+	0.706874i
$71$		−	5.61961i		−	0.0791495i	−0.999217	−	0.0395747i	$-0.987400\pi$
$71$		−	5.61961i		−	0.0791495i	0.999217	−	0.0395747i	$-0.0126003\pi$
$72$	3.91223	+	174.881i	0.0543365	+	2.42891i
$73$	−24.9320	+	43.1835i	−0.341535	+	0.591555i	−0.984718	−	0.174157i	$-0.944280\pi$
$73$	−24.9320	+	43.1835i	−0.341535	+	0.591555i	0.643183	+	0.765712i	$0.277613\pi$
$74$	120.473	+	69.5554i	1.62802	+	0.939938i
$75$	13.0734	+	7.35426i	0.174313	+	0.0980567i
$76$	290.329			3.82012
$77$	−14.9467	−	8.62947i	−0.194113	−	0.112071i
$78$	−82.6644	−	139.551i	−1.05980	−	1.78912i
$79$	−38.2566	−	66.2623i	−0.484261	−	0.838764i	0.515576	−	0.856844i	$-0.327578\pi$
$79$	−38.2566	−	66.2623i	−0.484261	−	0.838764i	−0.999837	+	0.0180800i	$0.994245\pi$
$80$	65.1612	+	37.6208i	0.814515	+	0.470261i
$81$	80.9190	−	3.62225i	0.999000	−	0.0447191i
$82$	−36.7302	−	63.6187i	−0.447930	−	0.775837i
$83$			1.56922i			0.0189063i	0.999955	+	0.00945316i	$0.00300908\pi$
$83$			1.56922i			0.0189063i	−0.999955	+	0.00945316i	$0.996991\pi$
$84$	170.666	+	96.0052i	2.03173	+	1.14292i
$85$	36.8377			0.433385
$86$	68.9510	−	39.8089i	0.801755	−	0.462894i
$87$	74.8742	−	0.837391i	0.860622	−	0.00962518i
$88$	−23.9605	+	41.5008i	−0.272278	+	0.471600i
$89$	1.19249	−	0.688486i	0.0133988	−	0.00773580i	−0.493286	−	0.869867i	$-0.664204\pi$
$89$	1.19249	−	0.688486i	0.0133988	−	0.00773580i	0.506684	+	0.862132i	$0.330871\pi$
$90$	35.2982	−	64.4242i	0.392202	−	0.715825i
$91$	−103.680			−1.13934
$92$			231.841i			2.52001i
$93$	73.5667	+	41.3838i	0.791040	+	0.444987i
$94$	14.0548	−	24.3436i	0.149519	−	0.258975i
$95$	−60.2945	−	34.8110i	−0.634679	−	0.366432i
$96$	66.3122	−	117.881i	0.690752	−	1.22793i
$97$	−71.8114			−0.740324			−0.370162	−	0.928967i	$-0.620698\pi$
$97$	−71.8114			−0.740324			−0.370162	+	0.928967i	$0.620698\pi$
$98$	154.901	−	89.4319i	1.58062	−	0.912570i
$99$	19.4605	+	10.6625i	0.196571	+	0.107702i
$100$	−23.3114	−	40.3765i	−0.233114	−	0.403765i
$101$	53.6578	+	30.9793i	0.531265	+	0.306726i	0.741531	−	0.670918i	$-0.234100\pi$
$101$	53.6578	+	30.9793i	0.531265	+	0.306726i	−0.210266	+	0.977644i	$0.567433\pi$
$102$	−2.01755	−	180.397i	−0.0197799	−	1.76859i
$103$	40.9210	+	70.8772i	0.397291	+	0.688129i	0.993391	−	0.114782i	$-0.0366169\pi$
$103$	40.9210	+	70.8772i	0.397291	+	0.688129i	−0.596099	+	0.802911i	$0.703284\pi$
$104$			287.876i			2.76804i
$105$	−23.9320	−	40.4012i	−0.227924	−	0.384773i
$106$	288.465			2.72137
$107$	−157.992	+	91.2168i	−1.47656	+	0.852493i	−0.999650	−	0.0264580i	$-0.991577\pi$
$107$	−157.992	+	91.2168i	−1.47656	+	0.852493i	−0.476912	+	0.878951i	$0.658244\pi$
$108$	−222.133	−	118.497i	−2.05679	−	1.09719i
$109$	22.8530	−	39.5826i	0.209661	−	0.363143i	−0.741947	−	0.670459i	$-0.766097\pi$
$109$	22.8530	−	39.5826i	0.209661	−	0.363143i	0.951608	+	0.307316i	$0.0994307\pi$
$110$	17.4284	−	10.0623i	0.158440	−	0.0914755i
$111$	−98.3662	+	58.2681i	−0.886182	+	0.524938i
$112$	−117.772	−	203.987i	−1.05153	−	1.82131i
$113$			195.627i			1.73121i	0.500729	+	0.865604i	$0.333065\pi$
$113$			195.627i			1.73121i	−0.500729	+	0.865604i	$0.666935\pi$
$114$	−167.170	+	297.172i	−1.46640	+	2.60677i
$115$	27.7982	−	48.1479i	0.241724	−	0.418678i
$116$	−201.556	−	116.369i	−1.73756	−	1.00318i
$117$	133.269	−	2.98133i	1.13905	−	0.0254815i
$118$	−283.088			−2.39905
$119$	−99.8703	−	57.6602i	−0.839246	−	0.484539i
$120$	−112.178	+	66.4494i	−0.934813	+	0.553745i
$121$	−57.4605	−	99.5245i	−0.474880	−	0.822517i
$122$	68.6877	+	39.6569i	0.563014	+	0.325056i
$123$	60.3701	−	0.675177i	0.490813	−	0.00548925i
$124$	−131.178	−	227.206i	−1.05788	−	1.83231i
$125$			11.1803i			0.0894427i
$126$	−196.536	+	119.409i	−1.55981	+	0.947693i
$127$	−26.1317			−0.205761			−0.102881	−	0.994694i	$-0.532806\pi$
$127$	−26.1317			−0.205761			−0.102881	+	0.994694i	$0.532806\pi$
$128$	61.4225	−	35.4623i	0.479863	−	0.277049i
$129$	0.731768	+	65.4301i	0.00567262	+	0.507210i
$130$	60.4473	−	104.698i	0.464979	−	0.805368i
$131$	99.7173	−	57.5718i	0.761201	−	0.439480i	−0.0685258	−	0.997649i	$-0.521830\pi$
$131$	99.7173	−	57.5718i	0.761201	−	0.439480i	0.829727	+	0.558170i	$0.188496\pi$
$132$	−35.1512	−	59.3411i	−0.266297	−	0.449554i
$133$	108.976	+	188.752i	0.819367	+	1.41919i
$134$		−	308.993i		−	2.30592i
$135$	31.9238	+	51.2433i	0.236473	+	0.379580i
$136$	−160.099	+	277.299i	−1.17720	+	2.03896i
$137$	−99.3708	−	57.3718i	−0.725335	−	0.418772i	0.0913784	−	0.995816i	$-0.470873\pi$
$137$	−99.3708	−	57.3718i	−0.725335	−	0.418772i	−0.816713	+	0.577044i	$0.804206\pi$
$138$	−237.306	−	133.493i	−1.71961	−	0.967337i
$139$	−0.377223			−0.00271384			−0.00135692	−	0.999999i	$-0.500432\pi$
$139$	−0.377223			−0.00271384			−0.00135692	+	0.999999i	$0.500432\pi$
$140$			145.952i			1.04252i
$141$	11.7740	+	19.8765i	0.0835037	+	0.140968i
$142$	−10.2566	−	17.7649i	−0.0722295	−	0.125105i
$143$	31.6259	+	18.2592i	0.221160	+	0.127687i
$144$	157.249	+	258.817i	1.09201	+	1.79734i
$145$	27.9057	+	48.3341i	0.192453	+	0.333338i
$146$			182.018i			1.24670i
$147$	1.64394	+	146.991i	0.0111833	+	0.999937i
$148$	355.355			2.40105
$149$	148.425	−	85.6933i	0.996142	−	0.575123i	0.0890373	−	0.996028i	$-0.471621\pi$
$149$	148.425	−	85.6933i	0.996142	−	0.575123i	0.907104	+	0.420906i	$0.138288\pi$
$150$	54.7508	−	0.612331i	0.365005	−	0.00408221i
$151$	−114.434	+	198.206i	−0.757842	+	1.31262i	0.186107	+	0.982530i	$0.440413\pi$
$151$	−114.434	+	198.206i	−0.757842	+	1.31262i	−0.943949	+	0.330092i	$0.892920\pi$
$152$	524.086	−	302.581i	3.44793	−	1.99066i
$153$	130.031	+	71.2442i	0.849873	+	0.465648i
$154$	−63.0000			−0.409091
$155$			62.9139i			0.405896i
$156$	−361.114	−	203.139i	−2.31483	−	1.30217i
$157$	−86.8399	+	150.411i	−0.553120	+	0.958032i	0.444927	+	0.895567i	$0.353230\pi$
$157$	−86.8399	+	150.411i	−0.553120	+	0.958032i	−0.998047	+	0.0624653i	$0.980104\pi$
$158$	−241.876	−	139.647i	−1.53086	−	0.883844i
$159$	−116.235	+	206.627i	−0.731035	+	1.29954i
$160$	100.811			0.630071
$161$	−150.727	+	87.0222i	−0.936192	+	0.540511i
$162$	249.193	−	159.139i	1.53823	−	0.982341i
$163$	−25.2719	−	43.7722i	−0.155042	−	0.268541i	0.778032	−	0.628224i	$-0.216218\pi$
$163$	−25.2719	−	43.7722i	−0.155042	−	0.268541i	−0.933074	+	0.359683i	$0.882885\pi$
$164$	−162.512	−	93.8265i	−0.990929	−	0.572113i
$165$	0.184966	+	16.5385i	0.00112100	+	0.100233i
$166$	2.86406	+	4.96069i	0.0172534	+	0.0298837i
$167$		−	58.8046i		−	0.352123i	−0.984379	−	0.176062i	$-0.943664\pi$
$167$		−	58.8046i		−	0.352123i	0.984379	−	0.176062i	$-0.0563358\pi$
$168$	408.133	−	4.56455i	2.42936	−	0.0271699i
$169$	50.3772			0.298090
$170$	116.453	−	67.2340i	0.685016	−	0.395494i
$171$	−145.504	−	239.486i	−0.850902	−	1.40050i
$172$	101.691	−	176.134i	0.591225	−	1.02403i
$173$	−72.3484	+	41.7704i	−0.418199	+	0.241447i	−0.694306	−	0.719679i	$-0.744289\pi$
$173$	−72.3484	+	41.7704i	−0.418199	+	0.241447i	0.276107	+	0.961127i	$0.410955\pi$
$174$	235.167	−	139.303i	1.35153	−	0.800592i
$175$	17.5000	−	30.3109i	0.100000	−	0.173205i
$176$			82.9640i			0.471386i
$177$	114.068	−	202.775i	0.644451	−	1.14562i
$178$	2.51317	−	4.35293i	0.0141189	−	0.0244547i
$179$	183.961	+	106.210i	1.02772	+	0.593353i	0.916330	−	0.400424i	$-0.131137\pi$
$179$	183.961	+	106.210i	1.02772	+	0.593353i	0.111388	+	0.993777i	$0.464470\pi$
$180$	−4.19689	−	187.606i	−0.0233160	−	1.04226i
$181$	−187.057			−1.03346			−0.516732	−	0.856147i	$-0.672852\pi$
$181$	−187.057			−1.03346			−0.516732	+	0.856147i	$0.672852\pi$
$182$	−327.756	+	189.230i	−1.80086	+	1.03973i
$183$	−56.0833	+	33.2214i	−0.306466	+	0.181538i
$184$	241.625	+	418.507i	1.31318	+	2.27449i
$185$	−73.7989	−	42.6078i	−0.398913	−	0.230313i
$186$	308.093	−	3.44570i	1.65641	−	0.0185253i
$187$	20.3093	+	35.1767i	0.108606	+	0.188110i
$188$		−	71.8053i		−	0.381943i
$189$	−6.33986	−	188.894i	−0.0335442	−	0.999437i
$190$	−254.140			−1.33758
$191$	−67.0925	+	38.7359i	−0.351270	+	0.202806i	−0.665244	−	0.746626i	$-0.731673\pi$
$191$	−67.0925	+	38.7359i	−0.351270	+	0.202806i	0.313975	+	0.949431i	$0.398339\pi$
$192$	−1.00561	−	89.9154i	−0.00523756	−	0.468309i
$193$	76.7740	−	132.977i	0.397793	−	0.688997i	−0.595660	−	0.803236i	$-0.703110\pi$
$193$	76.7740	−	132.977i	0.397793	−	0.688997i	0.993453	+	0.114239i	$0.0364429\pi$
$194$	−227.013	+	131.066i	−1.17017	+	0.675597i
$195$	50.6381	+	85.4854i	0.259682	+	0.438387i
$196$	228.452	−	395.690i	1.16557	−	2.01883i
$197$			43.5150i			0.220888i	0.993882	+	0.110444i	$0.0352273\pi$
$197$			43.5150i			0.220888i	−0.993882	+	0.110444i	$0.964773\pi$
$198$	80.9797	−	1.81158i	0.408989	−	0.00914938i
$199$	44.5658	−	77.1903i	0.223949	−	0.387891i	−0.732055	−	0.681246i	$-0.761438\pi$
$199$	44.5658	−	77.1903i	0.223949	−	0.387891i	0.956004	+	0.293355i	$0.0947718\pi$
$200$	−84.1609	−	48.5903i	−0.420804	−	0.242952i
$201$	221.331	+	124.506i	1.10115	+	0.619434i
$202$	226.167			1.11964
$203$		−	174.717i		−	0.860676i
$204$	−234.873	−	396.504i	−1.15134	−	1.94365i
$205$	22.5000	+	38.9711i	0.109756	+	0.190103i
$206$	258.722	+	149.373i	1.25593	+	0.725112i
$207$	191.241	−	116.192i	0.923869	−	0.561313i
$208$	249.195	+	431.618i	1.19805	+	2.07509i
$209$		−	76.7676i		−	0.367309i
$210$	−149.393	−	84.0385i	−0.711394	−	0.400183i
$211$	−22.0569			−0.104535			−0.0522676	−	0.998633i	$-0.516645\pi$
$211$	−22.0569			−0.104535			−0.0522676	+	0.998633i	$0.516645\pi$
$212$	638.154	−	368.438i	3.01016	−	1.73792i
$213$	16.8578	−	0.188537i	0.0791445	−	0.000885150i
$214$	−332.967	+	576.716i	−1.55592	+	2.69493i
$215$	−42.2376	+	24.3859i	−0.196454	+	0.113423i
$216$	−524.480	+	17.6032i	−2.42815	+	0.0814962i
$217$	98.4758	−	170.565i	0.453806	−	0.786014i
$218$		−	166.840i		−	0.765321i
$219$	−130.379	−	73.3426i	−0.595338	−	0.334898i
$220$	25.7039	−	44.5205i	0.116836	−	0.202366i
$221$	211.317	+	122.004i	0.956185	+	0.552054i
$222$	−204.611	+	363.731i	−0.921672	+	1.63843i
$223$	−382.114			−1.71352			−0.856758	−	0.515719i	$-0.827525\pi$
$223$	−382.114			−1.71352			−0.856758	+	0.515719i	$0.827525\pi$
$224$	−273.309	−	157.795i	−1.22013	−	0.704441i
$225$	−21.6228	+	39.4646i	−0.0961012	+	0.175398i
$226$	357.046	+	618.422i	1.57985	+	2.73638i
$227$	−9.40046	−	5.42736i	−0.0414117	−	0.0239091i	0.479151	−	0.877732i	$-0.340945\pi$
$227$	−9.40046	−	5.42736i	−0.0414117	−	0.0239091i	−0.520563	+	0.853823i	$0.674278\pi$
$228$	9.74048	+	870.932i	0.0427214	+	3.81988i
$229$	−107.314	−	185.872i	−0.468618	−	0.811670i	0.530739	−	0.847536i	$-0.321915\pi$
$229$	−107.314	−	185.872i	−0.468618	−	0.811670i	−0.999357	+	0.0358653i	$0.988581\pi$
$230$		−	202.943i		−	0.882359i
$231$	25.3853	−	45.1268i	0.109893	−	0.195354i
$232$	−485.118			−2.09103
$233$	58.5942	−	33.8294i	0.251477	−	0.145191i	−0.368963	−	0.929444i	$-0.620287\pi$
$233$	58.5942	−	33.8294i	0.251477	−	0.145191i	0.620441	+	0.784253i	$0.286954\pi$
$234$	415.854	−	252.660i	1.77715	−	1.07974i
$235$	−8.60961	+	14.9123i	−0.0366366	+	0.0634565i
$236$	−626.258	+	361.570i	−2.65363	+	1.53208i
$237$	197.491	−	116.986i	0.833296	−	0.493610i
$238$	−420.952			−1.76870
$239$			182.161i			0.762179i	0.924538	+	0.381089i	$0.124451\pi$
$239$			182.161i			0.762179i	−0.924538	+	0.381089i	$0.875549\pi$
$240$	−110.669	+	196.734i	−0.461122	+	0.819723i
$241$	166.610	−	288.576i	0.691326	−	1.19741i	−0.280077	−	0.959977i	$-0.590360\pi$
$241$	166.610	−	288.576i	0.691326	−	1.19741i	0.971404	−	0.237435i	$-0.0763066\pi$
$242$	−363.292	−	209.747i	−1.50121	−	0.866723i
$243$	13.5809	+	242.620i	0.0558884	+	0.998437i
$244$	202.605			0.830348
$245$	−94.8881	+	54.7837i	−0.387298	+	0.223607i
$246$	189.612	−	112.318i	0.770779	−	0.456578i
$247$	−230.583	−	399.382i	−0.933536	−	1.61693i
$248$	−473.589	−	273.427i	−1.90963	−	1.10253i
$249$	−4.70738	+	0.0526472i	−0.0189051	+	0.000211435i
$250$	20.4057	+	35.3437i	0.0816228	+	0.141375i
$251$		−	273.771i		−	1.09072i	−0.838201	−	0.545361i	$-0.816393\pi$
$251$		−	273.771i		−	1.09072i	0.838201	−	0.545361i	$-0.183607\pi$
$252$	−282.272	+	515.186i	−1.12013	+	2.04439i
$253$	61.3025			0.242302
$254$	−82.6084	+	47.6940i	−0.325230	+	0.187772i
$255$	1.23590	+	110.506i	0.00484666	+	0.433358i
$256$	189.395	−	328.041i	0.739823	−	1.28141i
$257$	102.186	−	58.9969i	0.397609	−	0.229560i	−0.287843	−	0.957678i	$-0.592938\pi$
$257$	102.186	−	58.9969i	0.397609	−	0.229560i	0.685452	+	0.728118i	$0.259605\pi$
$258$	121.732	+	205.504i	0.471831	+	0.796529i
$259$	133.384	+	231.027i	0.514995	+	0.891997i
$260$		−	308.822i		−	1.18778i
$261$	5.02403	+	224.580i	0.0192492	+	0.860461i
$262$	210.153	−	363.996i	0.802112	−	1.38930i
$263$	−108.675	−	62.7433i	−0.413211	−	0.238568i	0.278957	−	0.960303i	$-0.410011\pi$
$263$	−108.675	−	62.7433i	−0.413211	−	0.238568i	−0.692169	+	0.721736i	$0.743345\pi$
$264$	−125.298	−	70.4847i	−0.474615	−	0.266987i
$265$	−176.706			−0.666815
$266$	688.997	+	397.792i	2.59021	+	1.49546i
$267$	2.10534	+	3.55415i	0.00788515	+	0.0133114i
$268$	−394.658	−	683.567i	−1.47260	−	2.55062i
$269$	273.032	+	157.635i	1.01499	+	0.586004i	0.912648	−	0.408746i	$-0.134034\pi$
$269$	273.032	+	157.635i	1.01499	+	0.586004i	0.102340	+	0.994749i	$0.467367\pi$
$270$	194.445	+	103.727i	0.720166	+	0.384173i
$271$	−138.706	−	240.246i	−0.511830	−	0.886516i	−0.999906	−	0.0137149i	$-0.995634\pi$
$271$	−138.706	−	240.246i	−0.511830	−	0.886516i	0.488075	−	0.872801i	$-0.337699\pi$
$272$			554.347i			2.03804i
$273$	−3.47844	−	311.020i	−0.0127415	−	1.13927i
$274$	−418.846			−1.52864
$275$	−10.6762	+	6.16391i	−0.0388226	+	0.0224142i
$276$	−695.479	+	7.77822i	−2.51985	+	0.0281820i
$277$	−222.842	+	385.974i	−0.804484	+	1.39341i	0.112155	+	0.993691i	$0.464225\pi$
$277$	−222.842	+	385.974i	−0.804484	+	1.39341i	−0.916639	+	0.399716i	$0.869109\pi$
$278$	−1.19249	+	0.688486i	−0.00428954	+	0.00247657i
$279$	−121.675	+	222.075i	−0.436113	+	0.795967i
$280$	152.112	+	263.465i	0.543256	+	0.940947i
$281$		−	303.693i		−	1.08076i	−0.841422	−	0.540379i	$-0.818281\pi$
$281$		−	303.693i		−	1.08076i	0.841422	−	0.540379i	$-0.181719\pi$
$282$	73.4979	+	41.3451i	0.260631	+	0.146614i
$283$	156.053	−	270.291i	0.551423	−	0.955092i	−0.446749	−	0.894659i	$-0.647418\pi$
$283$	156.053	−	270.291i	0.551423	−	0.955092i	0.998172	−	0.0604333i	$-0.0192482\pi$
$284$	−45.3801	−	26.2002i	−0.159789	−	0.0922542i
$285$	102.404	−	182.040i	0.359311	−	0.638737i
$286$	133.302			0.466093
$287$		−	140.872i		−	0.490844i
$288$	355.846	+	194.969i	1.23558	+	0.676976i
$289$	−8.79822	−	15.2390i	−0.0304437	−	0.0527300i
$290$	176.433	+	101.864i	0.608390	+	0.351254i
$291$	−2.40926	−	215.421i	−0.00827924	−	0.740277i
$292$	232.480	+	402.667i	0.796165	+	1.37900i
$293$			304.350i			1.03874i	0.854550	+	0.519369i	$0.173833\pi$
$293$			304.350i			1.03874i	−0.854550	+	0.519369i	$0.826167\pi$
$294$	273.476	+	461.672i	0.930190	+	1.57031i
$295$	173.412			0.587838
$296$	641.468	−	370.352i	2.16712	−	1.25119i
$297$	−31.3325	+	58.7356i	−0.105497	+	0.197763i
$298$	312.805	−	541.794i	1.04968	−	1.81810i
$299$	318.925	−	184.131i	1.06664	−	0.615824i
$300$	120.340	−	71.2844i	0.401133	−	0.237615i
$301$	152.680			0.507242
$302$			835.434i			2.76634i
$303$	−91.1320	+	162.003i	−0.300766	+	0.534662i
$304$	523.848	−	907.332i	1.72319	−	2.98464i
$305$	−42.0763	−	24.2928i	−0.137955	−	0.0796484i
$306$	541.088	−	12.1045i	1.76826	−	0.0395573i
$307$	452.794			1.47490			0.737449	−	0.675403i	$-0.236030\pi$
$307$	452.794			1.47490			0.737449	+	0.675403i	$0.236030\pi$
$308$	−139.371	+	80.4660i	−0.452504	+	0.261253i
$309$	−211.246	+	125.133i	−0.683643	+	0.404962i
$310$	114.827	+	198.886i	0.370409	+	0.641567i
$311$	−395.625	−	228.414i	−1.27211	−	0.734451i	−0.296722	−	0.954964i	$-0.595893\pi$
$311$	−395.625	−	228.414i	−1.27211	−	0.734451i	−0.975384	+	0.220513i	$0.929227\pi$
$312$	−863.574	+	9.65819i	−2.76787	+	0.0309557i
$313$	0.539501	+	0.934443i	0.00172365	+	0.00298544i	0.866886	−	0.498507i	$-0.166118\pi$
$313$	0.539501	+	0.934443i	0.00172365	+	0.00298544i	−0.865162	+	0.501492i	$0.832785\pi$
$314$			633.980i			2.01904i
$315$	120.393	−	73.1470i	0.382200	−	0.232213i
$316$	−713.451			−2.25776
$317$	−359.328	+	207.458i	−1.13353	+	0.654442i	−0.944819	−	0.327591i	$-0.893763\pi$
$317$	−359.328	+	207.458i	−1.13353	+	0.654442i	−0.188707	+	0.982033i	$0.560430\pi$
$318$	9.67794	+	865.340i	0.0304338	+	2.72120i
$319$	−30.7698	+	53.2948i	−0.0964569	+	0.167068i
$320$	58.0438	−	33.5116i	0.181387	−	0.104724i
$321$	−278.934	−	470.886i	−0.868953	−	1.46694i
$322$	−317.656	+	550.196i	−0.986508	+	1.70868i
$323$		−	512.944i		−	1.58806i
$324$	348.016	−	670.333i	1.07412	−	2.06893i
$325$	−37.0285	+	64.1352i	−0.113934	+	0.197339i
$326$	−159.781	−	92.2495i	−0.490125	−	0.282974i
$327$	119.507	+	67.2268i	0.365465	+	0.205587i
$328$	−391.144			−1.19251
$329$	46.6828	−	26.9523i	0.141893	−	0.0819220i
$330$	30.7698	+	51.9444i	0.0932417	+	0.157407i
$331$	84.4320	+	146.241i	0.255082	+	0.441814i	0.964918	−	0.262553i	$-0.0845643\pi$
$331$	84.4320	+	146.241i	0.255082	+	0.441814i	−0.709836	+	0.704367i	$0.751231\pi$
$332$	12.6720	+	7.31616i	0.0381686	+	0.0220366i
$333$	−178.094	−	293.125i	−0.534816	−	0.880256i
$334$	−107.327	−	185.895i	−0.321337	−	0.556573i
$335$			189.281i			0.565018i
$336$	607.971	−	360.137i	1.80944	−	1.07184i
$337$	−209.925			−0.622924			−0.311462	−	0.950259i	$-0.600819\pi$
$337$	−209.925			−0.622924			−0.311462	+	0.950259i	$0.600819\pi$
$338$	159.254	−	91.9455i	0.471167	−	0.272028i
$339$	−586.843	+	6.56323i	−1.73110	+	0.0193606i
$340$	171.748	−	297.476i	0.505140	−	0.874929i
$341$	−60.0770	+	34.6855i	−0.176179	+	0.101717i
$342$	−897.070	−	491.507i	−2.62301	−	1.43716i
$343$	343.000			1.00000
$344$		−	423.929i		−	1.23235i
$345$	145.367	+	81.7741i	0.421355	+	0.237026i
$346$	−152.474	+	264.092i	−0.440675	+	0.763272i
$347$	−65.8730	−	38.0318i	−0.189836	−	0.109602i	0.402070	−	0.915609i	$-0.368291\pi$
$347$	−65.8730	−	38.0318i	−0.189836	−	0.109602i	−0.591906	+	0.806007i	$0.701624\pi$
$348$	342.322	−	608.536i	0.983684	−	1.74867i
$349$	75.6975			0.216898			0.108449	−	0.994102i	$-0.465412\pi$
$349$	75.6975			0.216898			0.108449	+	0.994102i	$0.465412\pi$
$350$		−	127.760i		−	0.365028i
$351$	13.4146	+	399.682i	0.0382182	+	1.13870i
$352$	55.5790	+	96.2657i	0.157895	+	0.273482i
$353$	−5.46297	−	3.15405i	−0.0154758	−	0.00893498i	0.492242	−	0.870458i	$-0.336177\pi$
$353$	−5.46297	−	3.15405i	−0.0154758	−	0.00893498i	−0.507718	+	0.861523i	$0.669511\pi$
$354$	−9.49754	−	849.210i	−0.0268292	−	2.39890i
$355$	6.28292	+	10.8823i	0.0176984	+	0.0306545i
$356$		−	12.8396i		−	0.0360664i
$357$	169.619	−	301.527i	0.475123	−	0.844613i
$358$	775.394			2.16591
$359$	−189.271	+	109.276i	−0.527219	+	0.304390i	−0.739883	−	0.672736i	$-0.765119\pi$
$359$	−189.271	+	109.276i	−0.527219	+	0.304390i	0.212665	+	0.977125i	$0.431786\pi$
$360$	−203.099	−	334.282i	−0.564165	−	0.928562i
$361$	−304.223	+	526.931i	−0.842724	+	1.45964i
$362$	−591.331	+	341.405i	−1.63351	+	0.943108i
$363$	296.627	−	175.710i	0.817154	−	0.484049i
$364$	−483.384	+	837.245i	−1.32798	+	2.30012i
$365$		−	111.499i		−	0.305478i
$366$	−116.659	+	207.381i	−0.318740	+	0.566614i
$367$	−25.1754	+	43.6051i	−0.0685979	+	0.118815i	−0.898284	−	0.439415i	$-0.855186\pi$
$367$	−25.1754	+	43.6051i	−0.0685979	+	0.118815i	0.829686	+	0.558230i	$0.188519\pi$
$368$	724.546	+	418.317i	1.96888	+	1.13673i
$369$	4.05081	+	181.076i	0.0109778	+	0.490721i
$370$	−311.061			−0.840706
$371$	479.066	+	276.589i	1.29128	+	0.745522i
$372$	677.175	−	401.131i	1.82036	−	1.07831i
$373$	287.329	+	497.668i	0.770319	+	1.33423i	0.937388	+	0.348286i	$0.113236\pi$
$373$	287.329	+	497.668i	0.770319	+	1.33423i	−0.167070	+	0.985945i	$0.553431\pi$
$374$	128.405	+	74.1345i	0.343328	+	0.198221i
$375$	−33.5389	+	0.375098i	−0.0894371	+	0.00100026i
$376$	−74.8356	−	129.619i	−0.199031	−	0.344731i
$377$			369.686i			0.980601i
$378$	−364.799	−	585.566i	−0.965077	−	1.54912i
$379$	−89.3025			−0.235627			−0.117813	−	0.993036i	$-0.537588\pi$
$379$	−89.3025			−0.235627			−0.117813	+	0.993036i	$0.537588\pi$
$380$	−562.219	+	324.597i	−1.47952	+	0.854204i
$381$	−0.876713	−	78.3901i	−0.00230108	−	0.205748i
$382$	−141.397	+	244.906i	−0.370149	+	0.641116i
$383$	229.481	−	132.491i	0.599167	−	0.345929i	−0.169547	−	0.985522i	$-0.554230\pi$
$383$	229.481	−	132.491i	0.599167	−	0.345929i	0.768714	+	0.639593i	$0.220897\pi$
$384$	108.441	+	183.066i	0.282398	+	0.476735i
$385$	38.5922			0.100239
$386$		−	560.494i		−	1.45206i
$387$	−196.253	+	4.39033i	−0.507115	+	0.0113445i
$388$	−334.805	+	579.899i	−0.862899	+	1.49458i
$389$	554.035	+	319.872i	1.42426	+	0.822294i	0.996659	−	0.0816755i	$-0.0260271\pi$
$389$	554.035	+	319.872i	1.42426	+	0.822294i	0.427596	+	0.903970i	$0.359360\pi$
$390$	316.102	+	177.818i	0.810518	+	0.455944i
$391$	409.609			1.04759
$392$		−	952.370i		−	2.42952i
$393$	176.050	+	297.202i	0.447965	+	0.756239i
$394$	79.4210	+	137.561i	0.201576	+	0.349140i
$395$	148.167	+	85.5443i	0.375107	+	0.216568i
$396$	176.833	−	107.438i	0.446548	−	0.271308i
$397$	−183.355	−	317.580i	−0.461852	−	0.799951i	0.537201	−	0.843454i	$-0.319481\pi$
$397$	−183.355	−	317.580i	−0.461852	−	0.799951i	−0.999053	+	0.0435032i	$0.986148\pi$
$398$		−	325.356i		−	0.817477i
$399$	−562.563	+	333.240i	−1.40993	+	0.835187i
$400$	−168.246			−0.420614
$401$	−306.903	+	177.191i	−0.765345	+	0.441872i	−0.831211	−	0.555956i	$-0.812352\pi$
$401$	−306.903	+	177.191i	−0.765345	+	0.441872i	0.0658668	+	0.997828i	$0.479019\pi$
$402$	926.921	−	10.3667i	2.30577	−	0.0257877i
$403$	−208.366	+	360.901i	−0.517038	+	0.895536i
$404$	500.335	−	288.868i	1.23845	−	0.715021i
$405$	−152.649	+	97.4846i	−0.376911	+	0.240703i
$406$	−318.884	−	552.323i	−0.785428	−	1.36040i
$407$		−	93.9617i		−	0.230864i
$408$	−837.216	−	470.962i	−2.05200	−	1.15432i
$409$	99.9473	−	173.114i	0.244370	−	0.423261i	−0.717584	−	0.696472i	$-0.754752\pi$
$409$	99.9473	−	173.114i	0.244370	−	0.423261i	0.961954	+	0.273210i	$0.0880855\pi$
$410$	142.256	+	82.1313i	0.346965	+	0.200320i
$411$	168.771	−	300.019i	0.410634	−	0.729972i
$412$	763.140			1.85228
$413$	−470.136	−	271.433i	−1.13834	−	0.657222i
$414$	392.491	−	716.352i	0.948046	−	1.73032i
$415$	−1.75445	−	3.03879i	−0.00422758	−	0.00732239i
$416$	578.297	+	333.880i	1.39014	+	0.802596i
$417$	−0.0126558	−	1.13160i	−3.03496e−5	−	0.00271367i
$418$	−140.112	−	242.681i	−0.335196	−	0.580576i
$419$		−	378.572i		−	0.903513i	−0.892141	−	0.451756i	$-0.850798\pi$
$419$		−	378.572i		−	0.903513i	0.892141	−	0.451756i	$-0.149202\pi$
$420$	−437.830	+	4.89668i	−1.04245	+	0.0116588i
$421$	244.719			0.581280			0.290640	−	0.956832i	$-0.406132\pi$
$421$	244.719			0.581280			0.290640	+	0.956832i	$0.406132\pi$
$422$	−69.7272	+	40.2570i	−0.165230	+	0.0953958i
$423$	−59.2307	+	35.9867i	−0.140025	+	0.0850750i
$424$	767.973	−	1330.17i	1.81126	−	3.13719i
$425$	−71.3359	+	41.1858i	−0.167849	+	0.0969078i
$426$	52.9473	−	31.3638i	0.124290	−	0.0736240i
$427$	76.0484	+	131.720i	0.178099	+	0.308477i
$428$			1701.11i			3.97456i
$429$	−53.7132	+	95.4843i	−0.125205	+	0.222574i
$430$	−89.0153	+	154.179i	−0.207012	+	0.358556i
$431$	222.506	+	128.464i	0.516255	+	0.298060i	0.735401	−	0.677632i	$-0.236994\pi$
$431$	222.506	+	128.464i	0.516255	+	0.298060i	−0.219146	+	0.975692i	$0.570327\pi$
$432$	−771.126	+	480.400i	−1.78501	+	1.11204i
$433$	69.2456			0.159920			0.0799602	−	0.996798i	$-0.474521\pi$
$433$	69.2456			0.159920			0.0799602	+	0.996798i	$0.474521\pi$
$434$		−	718.929i		−	1.65652i
$435$	−144.057	+	85.3334i	−0.331165	+	0.196169i
$436$	−213.094	−	369.090i	−0.488748	−	0.846537i
$437$	−670.432	−	387.074i	−1.53417	−	0.885753i
$438$	−546.019	+	6.10667i	−1.24662	+	0.0139422i
$439$	162.042	+	280.664i	0.369115	+	0.639327i	0.989427	−	0.145029i	$-0.0463274\pi$
$439$	162.042	+	280.664i	0.369115	+	0.639327i	−0.620312	+	0.784355i	$0.712994\pi$
$440$		−	107.155i		−	0.243533i
$441$	−440.890	+	9.86303i	−0.999750	+	0.0223651i
$442$	890.697			2.01515
$443$	583.027	−	336.611i	1.31609	−	0.759843i	0.332990	−	0.942930i	$-0.391942\pi$
$443$	583.027	−	336.611i	1.31609	−	0.759843i	0.983097	+	0.183087i	$0.0586090\pi$
$444$	11.9221	+	1066.00i	0.0268516	+	2.40090i
$445$	−1.53950	+	2.66649i	−0.00345955	+	0.00599212i
$446$	−1207.95	+	697.412i	−2.70841	+	1.56370i
$447$	262.043	+	442.373i	0.586227	+	0.989648i
$448$	−209.816			−0.468339
$449$			482.461i			1.07452i	0.843416	+	0.537261i	$0.180541\pi$
$449$			482.461i			1.07452i	−0.843416	+	0.537261i	$0.819459\pi$
$450$	3.67376	+	164.222i	0.00816391	+	0.364937i
$451$	−24.8093	+	42.9709i	−0.0550094	+	0.0952791i
$452$	1579.74	+	912.065i	3.49501	+	2.01784i
$453$	−598.419	−	336.631i	−1.32101	−	0.743115i
$454$	−39.6228			−0.0872748
$455$	200.775	−	115.917i	0.441264	−	0.254764i
$456$	925.269	+	1562.01i	2.02910	+	3.42545i
$457$	287.228	+	497.493i	0.628507	+	1.08861i	0.987851	+	0.155401i	$0.0496670\pi$
$457$	287.228	+	497.493i	0.628507	+	1.08861i	−0.359344	+	0.933205i	$0.617000\pi$
$458$	−678.487	−	391.725i	−1.48141	−	0.855294i
$459$	−209.357	+	392.458i	−0.456115	+	0.855028i
$460$	−259.206	−	448.958i	−0.563491	−	0.975996i
$461$			153.808i			0.333640i	0.985987	+	0.166820i	$0.0533499\pi$
$461$			153.808i			0.333640i	−0.985987	+	0.166820i	$0.946650\pi$
$462$	−2.11364	−	188.988i	−0.00457498	−	0.409065i
$463$	−382.509			−0.826153			−0.413077	−	0.910696i	$-0.635546\pi$
$463$	−382.509			−0.826153			−0.413077	+	0.910696i	$0.635546\pi$
$464$	−727.348	+	419.934i	−1.56756	+	0.905031i
$465$	−188.730	+	2.11075i	−0.405871	+	0.00453925i
$466$	123.487	−	213.885i	0.264993	−	0.458982i
$467$	624.469	−	360.537i	1.33719	−	0.772029i	0.350803	−	0.936449i	$-0.385909\pi$
$467$	624.469	−	360.537i	1.33719	−	0.772029i	0.986390	+	0.164421i	$0.0525755\pi$
$468$	597.263	−	1090.09i	1.27620	−	2.32925i
$469$	296.272	−	513.158i	0.631710	−	1.09415i
$470$			62.8550i			0.133734i
$471$	−454.118	−	255.457i	−0.964158	−	0.542372i
$472$	−753.658	+	1305.37i	−1.59673	+	2.76562i
$473$	−46.5726	−	26.8887i	−0.0984621	−	0.0568471i
$474$	410.801	−	730.268i	0.866668	−	1.54065i
$475$	155.680			0.327747
$476$	−931.246	+	537.655i	−1.95640	+	1.12953i
$477$	−623.741	−	341.749i	−1.30763	−	0.716456i
$478$	332.469	+	575.853i	0.695542	+	1.20471i
$479$	544.522	+	314.380i	1.13679	+	0.656326i	0.945634	−	0.325234i	$-0.105443\pi$
$479$	544.522	+	314.380i	1.13679	+	0.656326i	0.191156	+	0.981560i	$0.438776\pi$
$480$	3.38220	+	302.415i	0.00704626	+	0.630032i
$481$	−282.228	−	488.833i	−0.586753	−	1.01629i
$482$		−	1216.34i		−	2.52354i
$483$	−266.107	−	449.233i	−0.550946	−	0.930089i
$484$	−1071.59			−2.21402
$485$	139.062	−	80.2876i	0.286726	−	0.165541i
$486$	485.748	+	742.193i	0.999482	+	1.52715i
$487$	10.1053	−	17.5030i	0.0207502	−	0.0359404i	−0.855464	−	0.517863i	$-0.826728\pi$
$487$	10.1053	−	17.5030i	0.0207502	−	0.0359404i	0.876214	+	0.481922i	$0.160061\pi$
$488$	365.731	−	211.155i	0.749450	−	0.432695i
$489$	130.460	−	77.2795i	0.266790	−	0.158036i
$490$	−199.976	+	346.368i	−0.408114	+	0.706874i
$491$		−	304.223i		−	0.619599i	−0.950802	−	0.309799i	$-0.899738\pi$
$491$		−	304.223i		−	0.619599i	0.950802	−	0.309799i	$-0.100262\pi$
$492$	276.010	−	490.654i	0.560995	−	0.997265i
$493$	−205.596	+	356.103i	−0.417031	+	0.722319i
$494$	−1457.86	−	841.694i	−2.95113	−	1.70383i
$495$	−49.6061	+	1.10973i	−0.100214	+	0.00224187i
$496$	−946.749			−1.90877
$497$		−	39.3373i		−	0.0791495i
$498$	−14.7851	+	8.75806i	−0.0296889	+	0.0175865i
$499$	−5.30249	−	9.18419i	−0.0106262	−	0.0184052i	0.860663	−	0.509174i	$-0.170049\pi$
$499$	−5.30249	−	9.18419i	−0.0106262	−	0.0184052i	−0.871290	+	0.490769i	$0.836716\pi$
$500$	90.2846	+	52.1258i	0.180569	+	0.104252i
$501$	176.403	−	1.97288i	0.352101	−	0.00393789i
$502$	−499.671	−	865.455i	−0.995360	−	1.72401i
$503$			836.073i			1.66217i	0.556143	+	0.831086i	$0.312281\pi$
$503$			836.073i			1.66217i	−0.556143	+	0.831086i	$0.687719\pi$
$504$	27.3856	+	1224.17i	0.0543365	+	2.42891i
$505$	−138.544			−0.274344
$506$	193.792	−	111.886i	0.382988	−	0.221118i
$507$	1.69015	+	151.122i	0.00333362	+	0.298071i
$508$	−121.833	+	211.021i	−0.239829	+	0.415396i
$509$	−286.257	+	165.271i	−0.562392	+	0.324697i	−0.754105	−	0.656754i	$-0.771929\pi$
$509$	−286.257	+	165.271i	−0.562392	+	0.324697i	0.191713	+	0.981451i	$0.438596\pi$
$510$	205.596	+	347.081i	0.403130	+	0.680550i
$511$	−174.524	+	302.285i	−0.341535	+	0.591555i
$512$		−	1098.99i		−	2.14646i
$513$	713.532	−	444.520i	1.39090	−	0.866511i
$514$	215.355	−	373.006i	0.418979	−	0.725693i
$515$	−158.486	−	91.5021i	−0.307740	−	0.177674i
$516$	531.779	+	299.144i	1.03058	+	0.579736i
$517$	−18.9865			−0.0367243
$518$	843.314	+	486.888i	1.62802	+	0.939938i
$519$	−127.731	−	215.630i	−0.246109	−	0.415473i
$520$	−321.855	−	557.469i	−0.618952	−	1.07206i
$521$	644.406	+	372.048i	1.23686	+	0.714104i	0.968452	−	0.249200i	$-0.0801677\pi$
$521$	644.406	+	372.048i	1.23686	+	0.714104i	0.268412	+	0.963304i	$0.413501\pi$
$522$	425.773	+	700.782i	0.815657	+	1.34249i
$523$	−158.427	−	274.404i	−0.302920	−	0.524674i	0.673876	−	0.738845i	$-0.264628\pi$
$523$	−158.427	−	274.404i	−0.302920	−	0.524674i	−0.976796	+	0.214171i	$0.931295\pi$
$524$		−	1073.66i		−	2.04898i
$525$	91.5141	+	51.4798i	0.174313	+	0.0980567i
$526$	−458.061			−0.870839
$527$	−401.421	+	231.760i	−0.761709	+	0.439773i
$528$	−248.876	+	2.78343i	−0.471357	+	0.00527164i
$529$	44.5964	−	77.2433i	0.0843033	−	0.146018i
$530$	−558.610	+	322.513i	−1.05398	+	0.608516i
$531$	612.114	+	335.379i	1.15276	+	0.631599i
$532$	2032.30			3.82012
$533$			298.073i			0.559237i
$534$	13.1423	+	7.39299i	0.0246110	+	0.0138445i
$535$	203.967	−	353.281i	0.381247	−	0.660338i
$536$	−1424.83	−	822.625i	−2.65826	−	1.53475i
$537$	−312.439	+	555.413i	−0.581823	+	1.03429i
$538$	1150.82			2.13908
$539$	−104.627	−	60.4063i	−0.194113	−	0.112071i
$540$	562.642	−	18.8840i	1.04193	−	0.0349704i
$541$	−246.015	−	426.111i	−0.454742	−	0.787636i	0.543932	−	0.839130i	$-0.316935\pi$
$541$	−246.015	−	426.111i	−0.454742	−	0.787636i	−0.998673	+	0.0514937i	$0.983602\pi$
$542$	−876.965	−	506.316i	−1.61802	−	0.934163i
$543$	−6.27573	−	561.136i	−0.0115575	−	1.03340i
$544$	371.366	+	643.225i	0.682658	+	1.18240i
$545$			102.202i			0.187526i
$546$	−578.651	−	976.858i	−1.05980	−	1.78912i
$547$	390.754			0.714359			0.357180	−	0.934036i	$-0.383738\pi$
$547$	390.754			0.714359			0.357180	+	0.934036i	$0.383738\pi$
$548$	−926.589	+	534.966i	−1.69086	+	0.976216i
$549$	−101.540	−	167.125i	−0.184954	−	0.304417i
$550$	−22.5000	+	38.9711i	−0.0409091	+	0.0708566i
$551$	673.024	−	388.571i	1.22146	−	0.705210i
$552$	−1247.33	+	738.870i	−2.25966	+	1.33853i
$553$	−267.796	−	463.836i	−0.484261	−	0.838764i
$554$			1626.87i			2.93659i
$555$	125.340	−	222.812i	0.225837	−	0.401464i
$556$	−1.75872	+	3.04619i	−0.00316317	+	0.00547876i
$557$	156.399	+	90.2970i	0.280788	+	0.162113i	0.633780	−	0.773513i	$-0.281502\pi$
$557$	156.399	+	90.2970i	0.280788	+	0.162113i	−0.352992	+	0.935626i	$0.614836\pi$
$558$	20.6729	+	924.106i	0.0370483	+	1.65610i
$559$	−323.057			−0.577919
$560$	456.129	+	263.346i	0.814515	+	0.470261i
$561$	−104.842	+	62.1041i	−0.186884	+	0.110703i
$562$	−554.283	−	960.046i	−0.986268	−	1.70827i
$563$	601.355	+	347.192i	1.06813	+	0.616683i	0.927669	−	0.373404i	$-0.121809\pi$
$563$	601.355	+	347.192i	1.06813	+	0.616683i	0.140457	+	0.990087i	$0.455143\pi$
$564$	215.402	−	2.40906i	0.381919	−	0.00427138i
$565$	−218.717	−	378.829i	−0.387110	−	0.670494i
$566$		−	1139.27i		−	2.01285i
$567$	566.433	−	25.3557i	0.999000	−	0.0447191i
$568$	−109.223			−0.192295
$569$	−158.161	+	91.3142i	−0.277963	+	0.160482i	−0.632501	−	0.774560i	$-0.717971\pi$
$569$	−158.161	+	91.3142i	−0.277963	+	0.160482i	0.354538	+	0.935042i	$0.384638\pi$
$570$	−8.52636	−	762.373i	−0.0149585	−	1.33750i
$571$	−404.088	+	699.900i	−0.707684	+	1.22574i	0.258030	+	0.966137i	$0.416927\pi$
$571$	−404.088	+	699.900i	−0.707684	+	1.22574i	−0.965714	+	0.259608i	$0.916407\pi$
$572$	294.897	−	170.259i	0.515555	−	0.297656i
$573$	−118.451	−	199.965i	−0.206721	−	0.348980i
$574$	−257.112	−	445.331i	−0.447930	−	0.775837i
$575$			124.317i			0.216204i
$576$	269.696	−	6.03329i	0.468221	−	0.0104745i
$577$	146.160	−	253.156i	0.253310	−	0.438746i	−0.711125	−	0.703065i	$-0.751814\pi$
$577$	146.160	−	253.156i	0.253310	−	0.438746i	0.964435	+	0.264320i	$0.0851474\pi$
$578$	−55.6265	−	32.1160i	−0.0962396	−	0.0555640i
$579$	401.480	+	225.846i	0.693403	+	0.390063i
$580$	520.416			0.897270
$581$			10.9846i			0.0189063i
$582$	−400.789	−	676.599i	−0.688641	−	1.16254i
$583$	−97.4210	−	168.738i	−0.167103	−	0.289431i
$584$	839.321	+	484.582i	1.43719	+	0.829764i
$585$	−254.741	+	154.773i	−0.435455	+	0.264569i
$586$	555.482	+	962.123i	0.947922	+	1.64185i
$587$			736.637i			1.25492i	0.778649	+	0.627459i	$0.215905\pi$
$587$			736.637i			1.25492i	−0.778649	+	0.627459i	$0.784095\pi$
$588$	1194.66	+	672.037i	2.03173	+	1.14292i
$589$	876.039			1.48733
$590$	548.197	−	316.502i	0.929147	−	0.536443i
$591$	−130.537	+	1.45992i	−0.220875	+	0.00247025i
$592$	641.177	−	1110.55i	1.08307	−	1.87593i
$593$	124.231	−	71.7248i	0.209496	−	0.120952i	−0.391581	−	0.920144i	$-0.628072\pi$
$593$	124.231	−	71.7248i	0.209496	−	0.120952i	0.601077	+	0.799191i	$0.294738\pi$
$594$	8.15125	+	242.863i	0.0137226	+	0.408861i
$595$	257.864			0.433385
$596$		−	1598.10i		−	2.68138i
$597$	233.052	+	131.099i	0.390371	+	0.219597i
$598$	672.131	−	1164.17i	1.12397	−	1.94677i
$599$	−528.676	−	305.231i	−0.882597	−	0.509568i	−0.0110833	−	0.999939i	$-0.503528\pi$
$599$	−528.676	−	305.231i	−0.882597	−	0.509568i	−0.871514	+	0.490371i	$0.836861\pi$
$600$	142.938	−	254.097i	0.238230	−	0.423495i
$601$	563.623			0.937808			0.468904	−	0.883249i	$-0.344649\pi$
$601$	563.623			0.937808			0.468904	+	0.883249i	$0.344649\pi$
$602$	482.657	−	278.662i	0.801755	−	0.462894i
$603$	−366.070	+	668.129i	−0.607081	+	1.10801i
$604$	1067.05	+	1848.18i	1.76664	+	3.05990i
$605$	222.544	+	128.486i	0.367841	+	0.212373i
$606$	7.58785	+	678.457i	0.0125212	+	1.11957i
$607$	−6.63167	−	11.4864i	−0.0109253	−	0.0189232i	0.860511	−	0.509432i	$-0.170144\pi$
$607$	−6.63167	−	11.4864i	−0.0109253	−	0.0189232i	−0.871436	+	0.490509i	$0.836811\pi$
$608$		−	1403.74i		−	2.30878i
$609$	524.119	−	5.86173i	0.860622	−	0.00962518i
$610$	−177.351			−0.290739
$611$	−98.7768	+	57.0288i	−0.161664	+	0.0933368i
$612$	1181.56	−	717.876i	1.93065	−	1.17300i
$613$	157.735	−	273.204i	0.257316	−	0.445684i	−0.708206	−	0.706006i	$-0.750495\pi$
$613$	157.735	−	273.204i	0.257316	−	0.445684i	0.965522	+	0.260322i	$0.0838286\pi$
$614$	1431.39	−	826.412i	2.33125	−	1.34595i
$615$	−116.151	+	68.8033i	−0.188864	+	0.111875i
$616$	−167.723	+	290.506i	−0.272278	+	0.471600i
$617$		−	366.039i		−	0.593256i	−0.954993	−	0.296628i	$-0.904138\pi$
$617$		−	366.039i		−	0.593256i	0.954993	−	0.296628i	$-0.0958621\pi$
$618$	−439.411	+	781.129i	−0.711022	+	1.26396i
$619$	−33.8705	+	58.6654i	−0.0547180	+	0.0947744i	−0.892087	−	0.451864i	$-0.850759\pi$
$619$	−33.8705	+	58.6654i	−0.0547180	+	0.0947744i	0.837369	+	0.546638i	$0.184093\pi$
$620$	508.049	+	293.322i	0.819433	+	0.473100i
$621$	354.970	+	569.789i	0.571610	+	0.917534i
$622$	−1667.55			−2.68095
$623$	8.34745	−	4.81940i	0.0133988	−	0.00773580i
$624$	−1286.41	+	762.019i	−2.06156	+	1.22118i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	3.41098	+	1.96933i	0.00544885	+	0.00314590i
$627$	230.289	−	2.57554i	0.367286	−	0.00410772i
$628$	809.743	+	1402.52i	1.28940	+	2.23331i
$629$		−	627.830i		−	0.998140i
$630$	247.088	−	450.970i	0.392202	−	0.715825i
$631$	625.662			0.991540			0.495770	−	0.868454i	$-0.334886\pi$
$631$	625.662			0.991540			0.495770	+	0.868454i	$0.334886\pi$
$632$	−1287.88	+	743.560i	−2.03779	+	1.17652i
$633$	−0.740006	−	66.1667i	−0.00116905	−	0.104529i
$634$	−757.280	+	1311.65i	−1.19445	+	2.06885i
$635$	50.6038	−	29.2161i	0.0796910	−	0.0460096i
$636$	1126.66	+	1901.98i	1.77147	+	2.99053i
$637$	−725.758			−1.13934
$638$			224.637i			0.352095i
$639$	1.13115	+	50.5639i	0.00177019	+	0.0791297i
$640$	−79.2961	+	137.345i	−0.123900	+	0.214601i
$641$	−982.076	−	567.002i	−1.53210	−	0.884558i	−0.999265	−	0.0383388i	$-0.987793\pi$
$641$	−982.076	−	567.002i	−1.53210	−	0.884558i	−0.532835	−	0.846219i	$-0.678873\pi$
$642$	−1741.21	−	979.490i	−2.71216	−	1.52568i
$643$	−1185.10			−1.84307			−0.921537	−	0.388291i	$-0.873065\pi$
$643$	−1185.10			−1.84307			−0.921537	+	0.388291i	$0.873065\pi$
$644$			1622.89i			2.52001i
$645$	−74.5701	−	125.887i	−0.115613	−	0.195173i
$646$	−936.195	−	1621.54i	−1.44922	−	2.51012i
$647$	193.405	+	111.662i	0.298925	+	0.172585i	0.641960	−	0.766738i	$-0.278122\pi$
$647$	193.405	+	111.662i	0.298925	+	0.172585i	−0.343035	+	0.939323i	$0.611455\pi$
$648$	−70.4025	−	1572.75i	−0.108646	−	2.42709i
$649$	95.6050	+	165.593i	0.147311	+	0.255151i
$650$			270.329i			0.415890i
$651$	514.967	+	289.687i	0.791040	+	0.444987i
$652$	−471.298			−0.722850
$653$	609.840	−	352.091i	0.933905	−	0.539190i	0.0458602	−	0.998948i	$-0.485397\pi$
$653$	609.840	−	352.091i	0.933905	−	0.539190i	0.888044	+	0.459758i	$0.152064\pi$
$654$	500.489	−	5.59745i	0.765273	−	0.00855879i
$655$	−128.735	+	222.975i	−0.196541	+	0.340419i
$656$	−586.451	+	338.588i	−0.893980	+	0.516140i
$657$	215.640	−	393.573i	0.328219	−	0.599046i
$658$	98.3836	−	170.405i	0.149519	−	0.258975i
$659$		−	1214.01i		−	1.84220i	−0.389329	−	0.921099i	$-0.627293\pi$
$659$		−	1214.01i		−	1.84220i	0.389329	−	0.921099i	$-0.372707\pi$
$660$	134.415	+	75.6133i	0.203660	+	0.114566i
$661$	140.816	−	243.900i	0.213034	−	0.368986i	−0.739628	−	0.673015i	$-0.764999\pi$
$661$	140.816	−	243.900i	0.213034	−	0.368986i	0.952663	+	0.304029i	$0.0983321\pi$
$662$	533.819	+	308.201i	0.806373	+	0.465560i
$663$	−358.899	+	638.004i	−0.541326	+	0.962299i
$664$	30.4997			0.0459332
$665$	−422.061	−	243.677i	−0.634679	−	0.366432i
$666$	−1097.99	−	601.592i	−1.64863	−	0.903292i
$667$	310.291	+	537.441i	0.465205	+	0.805758i
$668$	−474.865	−	274.163i	−0.710876	−	0.410424i
$669$	−12.8199	−	1146.27i	−0.0191627	−	1.71341i
$670$	345.465	+	598.363i	0.515619	+	0.893078i
$671$		−	53.5720i		−	0.0798391i
$672$	464.185	−	825.168i	0.690752	−	1.22793i
$673$	−895.512			−1.33063			−0.665314	−	0.746564i	$-0.731702\pi$
$673$	−895.512			−1.33063			−0.665314	+	0.746564i	$0.731702\pi$
$674$	−663.623	+	383.143i	−0.984605	+	0.568462i
$675$	−119.112	−	63.5402i	−0.176462	−	0.0941337i
$676$	234.873	−	406.811i	0.347445	−	0.601792i
$677$	−724.756	+	418.438i	−1.07054	+	0.618077i	−0.928329	−	0.371760i	$-0.878755\pi$
$677$	−724.756	+	418.438i	−1.07054	+	0.618077i	−0.142211	+	0.989836i	$0.545421\pi$
$678$	−1843.17	+	1091.82i	−2.71854	+	1.61035i
$679$	−502.680			−0.740324
$680$		−	715.983i		−	1.05292i
$681$	15.9657	−	28.3817i	0.0234445	−	0.0416765i
$682$	−126.612	+	219.298i	−0.185648	+	0.321551i
$683$	−1104.57	−	637.726i	−1.61724	−	0.933713i	−0.987630	−	0.156801i	$-0.949882\pi$
$683$	−1104.57	−	637.726i	−1.61724	−	0.933713i	−0.629609	−	0.776912i	$-0.716785\pi$
$684$	−2612.31	+	58.4392i	−3.81916	+	0.0854375i
$685$	256.574			0.374561
$686$	1084.30	−	626.023i	1.58062	−	0.912570i
$687$	553.982	−	328.156i	0.806379	−	0.477666i
$688$	−366.967	−	635.605i	−0.533382	−	0.923845i
$689$	−1013.66	−	585.238i	−1.47121	−	0.849401i
$690$	608.790	−	6.80869i	0.882304	−	0.00986767i
$691$	597.438	+	1034.79i	0.864600	+	1.49753i	0.867444	+	0.497535i	$0.165761\pi$
$691$	597.438	+	1034.79i	0.864600	+	1.49753i	−0.00284427	+	0.999996i	$0.500905\pi$
$692$			778.981i			1.12569i
$693$	136.223	+	74.6373i	0.196571	+	0.107702i
$694$	−277.653			−0.400077
$695$	0.730490	−	0.421749i	0.00105106	−	0.000606832i
$696$	−16.2756	−	1455.26i	−0.0233845	−	2.09090i
$697$	−165.770	+	287.122i	−0.237833	+	0.411939i
$698$	239.298	−	138.159i	0.342833	−	0.197935i
$699$	103.448	+	174.637i	0.147994	+	0.249838i
$700$	−163.180	−	282.636i	−0.233114	−	0.403765i
$701$			901.684i			1.28628i	0.765747	+	0.643142i	$0.222369\pi$
$701$			901.684i			1.28628i	−0.765747	+	0.643142i	$0.777631\pi$
$702$	771.883	+	1239.01i	1.09955	+	1.76497i
$703$	−593.289	+	1027.61i	−0.843939	+	1.46175i
$704$	64.0010	+	36.9510i	0.0909105	+	0.0524872i
$705$	−45.0229	−	25.3269i	−0.0638623	−	0.0359247i
$706$	−23.0263			−0.0326152
$707$	375.604	+	216.855i	0.531265	+	0.306726i
$708$	−1105.65	−	1866.53i	−1.56166	−	2.63634i
$709$	−38.7214	−	67.0674i	−0.0546140	−	0.0945943i	0.837426	−	0.546551i	$-0.184060\pi$
$709$	−38.7214	−	67.0674i	−0.0546140	−	0.0945943i	−0.892040	+	0.451957i	$0.850726\pi$
$710$	39.7236	+	22.9344i	0.0559487	+	0.0323020i
$711$	357.561	+	588.511i	0.502899	+	0.827724i
$712$	−13.3815	−	23.1774i	−0.0187942	−	0.0325526i
$713$			699.558i			0.981147i
$714$	−14.1229	−	1262.78i	−0.0197799	−	1.76859i
$715$	−81.6577			−0.114207
$716$	1715.36	−	990.363i	2.39575	−	1.38319i
$717$	−546.448	+	6.11146i	−0.762131	+	0.00852366i
$718$	−398.888	+	690.894i	−0.555554	+	0.962248i
$719$	−194.487	+	112.287i	−0.270496	+	0.156171i	−0.629113	−	0.777314i	$-0.716582\pi$
$719$	−194.487	+	112.287i	−0.270496	+	0.156171i	0.358617	+	0.933485i	$0.383248\pi$
$720$	−593.877	−	325.387i	−0.824829	−	0.451926i
$721$	286.447	+	496.141i	0.397291	+	0.688129i
$722$			2221.00i			3.07618i
$723$	871.265	+	490.116i	1.20507	+	0.677892i
$724$	−872.111	+	1510.54i	−1.20457	+	2.08638i
$725$	−108.078	−	62.3990i	−0.149074	−	0.0860676i
$726$	617.013	−	1096.85i	0.849881	−	1.51081i
$727$	61.7189			0.0848953			0.0424476	−	0.999099i	$-0.486484\pi$
$727$	61.7189			0.0848953			0.0424476	+	0.999099i	$0.486484\pi$
$728$			2015.13i			2.76804i
$729$	−727.359	+	48.8800i	−0.997750	+	0.0670507i
$730$	−203.502	−	352.476i	−0.278770	−	0.482844i
$731$	−311.187	−	179.664i	−0.425701	−	0.245778i
$732$	6.79736	+	607.777i	0.00928601	+	0.830296i
$733$	−261.836	−	453.513i	−0.357211	−	0.618707i	0.630283	−	0.776366i	$-0.282939\pi$
$733$	−261.836	−	453.513i	−0.357211	−	0.618707i	−0.987494	+	0.157658i	$0.949606\pi$
$734$			183.795i			0.250402i
$735$	−167.524	−	282.808i	−0.227924	−	0.384773i
$736$	1120.95			1.52303
$737$	−180.746	+	104.354i	−0.245246	+	0.141593i
$738$	343.295	+	565.031i	0.465170	+	0.765625i
$739$	445.270	−	771.230i	0.602530	−	1.04361i	−0.389906	−	0.920854i	$-0.627493\pi$
$739$	445.270	−	771.230i	0.602530	−	1.04361i	0.992437	−	0.122758i	$-0.0391740\pi$
$740$	−688.142	+	397.299i	−0.929922	+	0.536891i
$741$	1190.33	−	705.106i	1.60639	−	0.951560i
$742$	2019.25			2.72137
$743$		−	284.098i		−	0.382367i	−0.981554	−	0.191183i	$-0.938768\pi$
$743$		−	284.098i		−	0.382367i	0.981554	−	0.191183i	$-0.0612325\pi$
$744$	804.340	−	1429.85i	1.08110	−	1.92184i
$745$	−191.616	+	331.889i	−0.257203	+	0.445488i
$746$	1816.63	+	1048.83i	2.43516	+	1.40594i
$747$	−0.315864	−	14.1195i	−0.000422843	−	0.0189016i
$748$	378.749			0.506350
$749$	−1105.94	+	638.517i	−1.47656	+	0.852493i
$750$	−105.340	+	62.3990i	−0.140453	+	0.0831987i
$751$	−569.302	−	986.061i	−0.758059	−	1.31300i	−0.943839	−	0.330406i	$-0.892814\pi$
$751$	−569.302	−	986.061i	−0.758059	−	1.31300i	0.185780	−	0.982591i	$-0.440519\pi$
$752$	−224.405	−	129.560i	−0.298411	−	0.172288i
$753$	821.262	−	9.18497i	1.09065	−	0.0121978i
$754$	674.730	+	1168.67i	0.894867	+	1.54996i
$755$		−	511.765i		−	0.677835i
$756$	−1554.93	−	829.478i	−2.05679	−	1.09719i
$757$	−510.605			−0.674511			−0.337256	−	0.941413i	$-0.609499\pi$
$757$	−510.605			−0.674511			−0.337256	+	0.941413i	$0.609499\pi$
$758$	−282.306	+	162.990i	−0.372436	+	0.215026i
$759$	2.05669	+	183.896i	0.00270973	+	0.242287i
$760$	−676.592	+	1171.89i	−0.890252	+	1.54196i
$761$	−241.266	+	139.295i	−0.317039	+	0.183042i	−0.650072	−	0.759873i	$-0.725261\pi$
$761$	−241.266	+	139.295i	−0.317039	+	0.183042i	0.333033	+	0.942915i	$0.391928\pi$
$762$	−145.844	−	246.210i	−0.191397	−	0.323110i
$763$	159.971	−	277.078i	0.209661	−	0.363143i
$764$			722.389i			0.945536i
$765$	−331.457	+	7.41493i	−0.433277	+	0.00969272i
$766$	483.629	−	837.670i	0.631370	−	1.09356i
$767$	994.766	+	574.328i	1.29696	+	0.748798i
$768$	990.416	+	557.143i	1.28960	+	0.725446i
$769$	1252.21			1.62836			0.814181	−	0.580612i	$-0.197186\pi$
$769$	1252.21			1.62836			0.814181	+	0.580612i	$0.197186\pi$
$770$	121.999	−	70.4361i	0.158440	−	0.0914755i
$771$	180.408	+	304.558i	0.233992	+	0.395017i
$772$	−715.884	−	1239.95i	−0.927310	−	1.60615i
$773$	730.939	+	422.008i	0.945587	+	0.545935i	0.891707	−	0.452613i	$-0.149508\pi$
$773$	730.939	+	422.008i	0.945587	+	0.545935i	0.0538796	+	0.998547i	$0.482841\pi$
$774$	−612.390	+	372.069i	−0.791202	+	0.480709i
$775$	−70.3399	−	121.832i	−0.0907611	−	0.157203i
$776$			1395.74i			1.79863i
$777$	−688.563	+	407.877i	−0.886182	+	0.524938i
$778$	2335.25			3.00161
$779$	542.650	−	313.299i	0.696599	−	0.402182i
$780$	926.409	−	10.3609i	1.18770	−	0.0132833i
$781$	−6.92775	+	11.9992i	−0.00887036	+	0.0153639i
$782$	1294.87	−	747.595i	1.65585	−	0.956003i
$783$	−673.530	+	22.6058i	−0.860192	+	0.0288707i
$784$	−824.403	−	1427.91i	−1.05153	−	1.82131i
$785$		−	388.360i		−	0.494726i
$786$	1098.97	+	618.209i	1.39818	+	0.786525i
$787$	715.390	−	1239.09i	0.909009	−	1.57445i	0.0935654	−	0.995613i	$-0.470174\pi$
$787$	715.390	−	1239.09i	0.909009	−	1.57445i	0.815444	−	0.578837i	$-0.196493\pi$
$788$	351.397	+	202.879i	0.445935	+	0.257461i
$789$	184.572	−	328.108i	0.233932	−	0.415853i
$790$	624.522			0.790534
$791$			1369.39i			1.73121i
$792$	207.237	−	378.237i	0.261663	−	0.477572i
$793$	−160.912	−	278.707i	−0.202915	−	0.351459i
$794$	−1159.26	−	669.298i	−1.46002	−	0.842945i
$795$	−5.92846	−	530.085i	−0.00745718	−	0.666774i
$796$	−415.557	−	719.765i	−0.522056	−	0.904228i
$797$		−	1579.90i		−	1.98231i	−0.132719	−	0.991154i	$-0.542371\pi$
$797$		−	1579.90i		−	1.98231i	0.132719	−	0.991154i	$-0.457629\pi$
$798$	−1170.19	+	2080.21i	−1.46640	+	2.60677i
$799$	−126.863			−0.158778
$800$	−195.220	+	112.711i	−0.244026	+	0.140888i
$801$	−10.5912	+	6.43485i	−0.0132224	+	0.00803353i
$802$	−646.796	+	1120.28i	−0.806478	+	1.39686i
$803$	106.472	−	61.4715i	0.132592	−	0.0765523i
$804$	2037.33	−	1206.83i	2.53400	−	1.50104i
$805$	194.588	−	337.036i	0.241724	−	0.418678i
$806$			1521.19i			1.88733i
$807$	−463.715	+	824.333i	−0.574616	+	1.02148i
$808$	602.118	−	1042.90i	0.745196	−	1.29072i
$809$	1290.44	+	745.034i	1.59510	+	0.920932i	0.992412	+	0.122956i	$0.0392375\pi$
$809$	1290.44	+	745.034i	1.59510	+	0.920932i	0.602689	+	0.797976i	$0.294096\pi$
$810$	−304.637	+	586.778i	−0.376095	+	0.724417i
$811$	−1193.42			−1.47154			−0.735768	−	0.677233i	$-0.763179\pi$
$811$	−1193.42			−1.47154			−0.735768	+	0.677233i	$0.763179\pi$
$812$	−1410.89	−	814.580i	−1.73756	−	1.00318i
$813$	716.039	−	424.152i	0.880737	−	0.521713i
$814$	−171.493	−	297.035i	−0.210680	−	0.364908i
$815$	97.8776	+	56.5097i	0.120095	+	0.0693370i
$816$	−1662.94	+	18.5982i	−2.03791	+	0.0227919i
$817$	339.559	+	588.134i	0.415617	+	0.719870i
$818$		−	729.672i		−	0.892019i
$819$	932.884	−	20.8693i	1.13905	−	0.0254815i
$820$	419.605			0.511713
$821$	−1159.98	+	669.714i	−1.41288	+	0.815729i	−0.995659	−	0.0930739i	$-0.970331\pi$
$821$	−1159.98	+	669.714i	−1.41288	+	0.815729i	−0.417225	+	0.908803i	$0.636997\pi$
$822$	−14.0522	−	1256.46i	−0.0170952	−	1.52854i
$823$	−149.065	+	258.189i	−0.181125	+	0.313717i	−0.942264	−	0.334872i	$-0.891307\pi$
$823$	−149.065	+	258.189i	−0.181125	+	0.313717i	0.761139	+	0.648589i	$0.224640\pi$
$824$	1377.58	−	795.346i	1.67182	−	0.965225i
$825$	−18.8488	−	31.8198i	−0.0228470	−	0.0385695i
$826$	−1981.61			−2.39905
$827$		−	723.426i		−	0.874759i	−0.899277	−	0.437380i	$-0.855907\pi$
$827$		−	723.426i		−	0.874759i	0.899277	−	0.437380i	$-0.144093\pi$
$828$	−46.6664	−	2086.05i	−0.0563604	−	2.51938i
$829$	−153.028	+	265.052i	−0.184594	+	0.319726i	−0.943440	−	0.331545i	$-0.892430\pi$
$829$	−153.028	+	265.052i	−0.184594	+	0.319726i	0.758846	+	0.651270i	$0.225764\pi$
$830$	−11.0924	−	6.40422i	−0.0133644	−	0.00771593i
$831$	−1165.32	−	655.535i	−1.40232	−	0.788851i
$832$	443.952			0.533596
$833$	−699.092	−	403.621i	−0.839246	−	0.484539i
$834$	−2.10534	−	3.55415i	−0.00252438	−	0.00426158i
$835$	65.7456	+	113.875i	0.0787372	+	0.136377i
$836$	−619.922	−	357.912i	−0.741533	−	0.428124i
$837$	−670.265	−	357.553i	−0.800794	−	0.427184i
$838$	−690.947	−	1196.76i	−0.824519	−	1.42811i
$839$		−	551.338i		−	0.657137i	−0.944480	−	0.328569i	$-0.893434\pi$
$839$		−	551.338i		−	0.657137i	0.944480	−	0.328569i	$-0.106566\pi$
$840$	−785.243	+	465.146i	−0.934813	+	0.553745i
$841$	218.018			0.259236
$842$	773.614	−	446.646i	0.918782	−	0.530459i
$843$	911.022	−	10.1888i	1.08069	−	0.0120864i
$844$	−102.836	+	178.116i	−0.121843	+	0.211038i
$845$	−97.5551	+	56.3234i	−0.115450	+	0.0666550i
$846$	−121.562	+	221.867i	−0.143690	+	0.262254i
$847$	−402.223	−	696.672i	−0.474880	−	0.822517i
$848$		−	2659.13i		−	3.13577i
$849$	816.058	+	459.061i	0.961199	+	0.540707i
$850$	−150.340	+	260.396i	−0.176870	+	0.306349i
$851$	−820.592	−	473.769i	−0.964268	−	0.556720i
$852$	77.0732	−	137.011i	0.0904615	−	0.160811i
$853$	219.530			0.257363			0.128681	−	0.991686i	$-0.458926\pi$
$853$	219.530			0.257363			0.128681	+	0.991686i	$0.458926\pi$
$854$	480.814	+	277.598i	0.563014	+	0.325056i
$855$	549.522	+	301.085i	0.642715	+	0.352146i
$856$	1772.90	+	3070.75i	2.07115	+	3.58733i
$857$	399.589	+	230.703i	0.466265	+	0.269198i	0.714675	−	0.699457i	$-0.246575\pi$
$857$	399.589	+	230.703i	0.466265	+	0.269198i	−0.248410	+	0.968655i	$0.579908\pi$
$858$	4.47228	+	399.882i	0.00521244	+	0.466063i
$859$	−440.157	−	762.375i	−0.512407	−	0.887514i	−0.999897	−	0.0143857i	$-0.995421\pi$
$859$	−440.157	−	762.375i	−0.512407	−	0.887514i	0.487490	−	0.873129i	$-0.337913\pi$
$860$			454.775i			0.528808i
$861$	422.590	−	4.72624i	0.490813	−	0.00548925i
$862$	937.859			1.08800
$863$	−795.399	+	459.224i	−0.921667	+	0.532125i	−0.884166	−	0.467172i	$-0.845273\pi$
$863$	−795.399	+	459.224i	−0.921667	+	0.532125i	−0.0375005	+	0.999297i	$0.511940\pi$
$864$	−572.932	+	1074.01i	−0.663116	+	1.24307i
$865$	93.4014	−	161.776i	0.107979	−	0.187024i
$866$	218.902	−	126.383i	0.252773	−	0.145939i
$867$	45.4189	−	26.9043i	0.0523862	−	0.0310315i
$868$	−918.243	−	1590.44i	−1.05788	−	1.83231i
$869$			188.648i			0.217086i
$870$	−299.653	+	532.683i	−0.344428	+	0.612280i
$871$	−626.885	+	1085.80i	−0.719731	+	1.24661i
$872$	−769.332	−	444.174i	−0.882262	−	0.509374i
$873$	646.141	−	14.4547i	0.740138	−	0.0165574i
$874$	−2825.86			−3.23325
$875$			78.2624i			0.0894427i
$876$	−1200.13	+	710.906i	−1.37001	+	0.811537i
$877$	108.625	+	188.144i	0.123860	+	0.214531i	0.921287	−	0.388884i	$-0.127139\pi$
$877$	108.625	+	188.144i	0.123860	+	0.214531i	−0.797427	+	0.603415i	$0.793806\pi$
$878$	1024.50	+	591.498i	1.16686	+	0.673687i
$879$	−912.994	+	10.2109i	−1.03867	+	0.0116165i
$880$	−92.7566	−	160.659i	−0.105405	−	0.182567i
$881$		−	1138.45i		−	1.29223i	−0.763242	−	0.646113i	$-0.776393\pi$
$881$		−	1138.45i		−	1.29223i	0.763242	−	0.646113i	$-0.223607\pi$
$882$	−1375.76	+	835.865i	−1.55981	+	0.947693i
$883$	406.943			0.460864			0.230432	−	0.973088i	$-0.425986\pi$
$883$	406.943			0.460864			0.230432	+	0.973088i	$0.425986\pi$
$884$	1970.44	−	1137.63i	2.22900	−	1.28691i
$885$	5.81795	+	520.204i	0.00657395	+	0.587801i
$886$	1228.72	−	2128.21i	1.38682	−	2.40204i
$887$	369.948	−	213.590i	0.417078	−	0.240800i	−0.276749	−	0.960942i	$-0.589257\pi$
$887$	369.948	−	213.590i	0.417078	−	0.240800i	0.693826	+	0.720142i	$0.255924\pi$
$888$	1132.51	+	1911.86i	1.27535	+	2.15299i
$889$	−182.922			−0.205761
$890$			11.2392i			0.0126283i
$891$	−177.247	−	92.0210i	−0.198930	−	0.103278i
$892$	−1781.52	+	3085.68i	−1.99722	+	3.45929i
$893$	207.645	+	119.884i	0.232525	+	0.134248i
$894$	1635.77	+	920.178i	1.82972	+	1.02928i
$895$	−474.986			−0.530711
$896$	429.957	−	248.236i	0.479863	−	0.277049i
$897$	563.059	+	950.537i	0.627714	+	1.05968i
$898$	880.559	+	1525.17i	0.980578	+	1.69841i
$899$	−608.177	−	351.131i	−0.676504	−	0.390580i
$900$	217.877	+	358.605i	0.242086	+	0.398450i
$901$	−650.945	−	1127.47i	−0.722469	−	1.25135i
$902$			181.122i			0.200800i
$903$	5.12238	+	458.011i	0.00567262	+	0.507210i
$904$	3802.22			4.20600
$905$	362.234	−	209.136i	0.400259	−	0.231090i
$906$	−2506.14	+	28.0287i	−2.76616	+	0.0309367i
$907$	868.719	−	1504.67i	0.957794	−	1.65895i	0.229952	−	0.973202i	$-0.426143\pi$
$907$	868.719	−	1504.67i	0.957794	−	1.65895i	0.727842	−	0.685745i	$-0.240524\pi$
$908$	−87.6551	+	50.6077i	−0.0965365	+	0.0557354i
$909$	−489.035	−	267.944i	−0.537992	−	0.294767i
$910$	423.131	−	732.885i	0.464979	−	0.805368i
$911$		−	190.007i		−	0.208570i	−0.994547	−	0.104285i	$-0.966745\pi$
$911$		−	190.007i		−	0.208570i	0.994547	−	0.104285i	$-0.0332553\pi$
$912$	2739.40	+	1541.01i	3.00373	+	1.68970i
$913$	1.93451	−	3.35067i	0.00211885	−	0.00366996i
$914$	1815.99	+	1048.46i	1.98686	+	1.14711i
$915$	71.4621	−	127.036i	0.0781007	−	0.138837i
$916$	−2001.30			−2.18483
$917$	698.021	−	403.003i	0.761201	−	0.439480i
$918$	54.4648	+	1622.76i	0.0593298	+	1.76771i
$919$	−168.423	−	291.717i	−0.183268	−	0.317429i	0.759724	−	0.650246i	$-0.225334\pi$
$919$	−168.423	−	291.717i	−0.183268	−	0.317429i	−0.942991	+	0.332817i	$0.892001\pi$
$920$	−935.809	−	540.290i	−1.01718	−	0.587271i
$921$	15.1911	+	1358.30i	0.0164942	+	1.47481i
$922$	280.721	+	486.224i	0.304470	+	0.527358i
$923$			83.2343i			0.0901780i
$924$	−246.059	−	415.388i	−0.266297	−	0.449554i
$925$	190.548			0.205998
$926$	−1209.20	+	698.133i	−1.30583	+	0.753923i
$927$	−382.463	−	629.499i	−0.412582	−	0.679071i
$928$	−562.642	+	974.525i	−0.606296	+	1.05013i
$929$	−1190.50	+	687.334i	−1.28148	+	0.739864i	−0.977119	−	0.212692i	$-0.931777\pi$
$929$	−1190.50	+	687.334i	−1.28148	+	0.739864i	−0.304363	+	0.952556i	$0.598444\pi$
$930$	−592.767	+	351.131i	−0.637384	+	0.377560i
$931$	762.831	+	1321.26i	0.819367	+	1.41919i
$932$		−	630.888i		−	0.676919i
$933$	671.926	−	1194.46i	0.720178	−	1.28024i
$934$	1316.06	−	2279.49i	1.40906	−	2.44057i
$935$	−78.6574	−	45.4129i	−0.0841256	−	0.0485699i
$936$	−57.9455	−	2590.24i	−0.0619076	−	2.76735i
$937$	−1063.74			−1.13526			−0.567631	−	0.823283i	$-0.692140\pi$
$937$	−1063.74			−1.13526			−0.567631	+	0.823283i	$0.692140\pi$
$938$		−	2162.95i		−	2.30592i
$939$	−2.78505	+	1.64975i	−0.00296598	+	0.00175692i
$940$	80.2808	+	139.050i	0.0854051	+	0.147926i
$941$	1261.99	+	728.608i	1.34111	+	0.774291i	0.986971	−	0.160901i	$-0.0514400\pi$
$941$	1261.99	+	728.608i	1.34111	+	0.774291i	0.354141	+	0.935192i	$0.384773\pi$
$942$	−1901.82	+	21.2699i	−2.01892	+	0.0225795i
$943$	250.184	+	433.331i	0.265306	+	0.459524i
$944$			2609.56i			2.76437i
$945$	223.467	+	358.703i	0.236473	+	0.379580i
$946$	−196.302			−0.207508
$947$	627.059	−	362.033i	0.662153	−	0.382294i	−0.130944	−	0.991390i	$-0.541801\pi$
$947$	627.059	−	362.033i	0.662153	−	0.382294i	0.793097	+	0.609096i	$0.208467\pi$
$948$	−23.9362	−	2140.22i	−0.0252491	−	2.25762i
$949$	369.278	−	639.608i	0.389123	−	0.673981i
$950$	492.140	−	284.137i	0.518043	−	0.299092i
$951$	−634.391	−	1070.96i	−0.667078	−	1.12614i
$952$	−1120.69	+	1941.09i	−1.17720	+	2.03896i
$953$		−	1061.11i		−	1.11344i	−0.830699	−	0.556722i	$-0.812059\pi$
$953$		−	1061.11i		−	1.11344i	0.830699	−	0.556722i	$-0.187941\pi$
$954$	−2595.53	+	58.0640i	−2.72069	+	0.0608638i
$955$	86.6160	−	150.023i	0.0906974	−	0.157093i
$956$	1471.00	+	849.284i	1.53871	+	0.888372i
$957$	−160.907	−	90.5154i	−0.168137	−	0.0945825i
$958$	2295.15			2.39577
$959$	−695.596	−	401.602i	−0.725335	−	0.418772i
$960$	102.476	+	172.996i	0.106746	+	0.180204i
$961$	84.6843	+	146.678i	0.0881211	+	0.152630i
$962$	−1784.38	−	1030.21i	−1.85486	−	1.07091i
$963$	1403.21	−	852.547i	1.45713	−	0.885304i
$964$	−1553.56	−	2690.85i	−1.61158	−	2.79133i
$965$			343.344i			0.355797i
$966$	−1661.14	−	934.448i	−1.71961	−	0.967337i
$967$	486.192			0.502784			0.251392	−	0.967885i	$-0.419112\pi$
$967$	486.192			0.502784			0.251392	+	0.967885i	$0.419112\pi$
$968$	−1934.37	+	1116.81i	−1.99832	+	1.15373i
$969$	1538.74	−	17.2092i	1.58796	−	0.0177597i
$970$	293.072	−	507.616i	0.302136	−	0.523315i
$971$	−435.110	+	251.211i	−0.448105	+	0.258714i	−0.707030	−	0.707184i	$-0.749965\pi$
$971$	−435.110	+	251.211i	−0.448105	+	0.258714i	0.258925	+	0.965898i	$0.416632\pi$
$972$	2022.55	+	1021.49i	2.08081	+	1.05092i
$973$	−2.64056			−0.00271384
$974$		−	73.7746i		−	0.0757440i
$975$	−193.636	−	108.927i	−0.198601	−	0.111720i
$976$	365.566	−	633.179i	0.374555	−	0.648749i
$977$	1218.49	+	703.494i	1.24717	+	0.720055i	0.970544	−	0.240922i	$-0.0774499\pi$
$977$	1218.49	+	703.494i	1.24717	+	0.720055i	0.276627	+	0.960977i	$0.410783\pi$
$978$	271.371	−	482.407i	0.277475	−	0.493259i
$979$	−3.39501			−0.00346784
$980$			1021.67i			1.04252i
$981$	−197.658	+	360.754i	−0.201487	+	0.367741i
$982$	−555.250	−	961.721i	−0.565428	−	0.979349i
$983$	−395.445	−	228.310i	−0.402284	−	0.232259i	0.285185	−	0.958472i	$-0.407945\pi$
$983$	−395.445	−	228.310i	−0.402284	−	0.232259i	−0.687469	+	0.726214i	$0.741278\pi$
$984$	−13.1228	−	1173.36i	−0.0133362	−	1.19244i
$985$	−48.6512	−	84.2664i	−0.0493921	−	0.0855497i
$986$			1500.97i			1.52228i
$987$	82.4182	+	139.135i	0.0835037	+	0.140968i
$988$	−4300.17			−4.35240
$989$	−469.652	+	271.154i	−0.474875	+	0.274169i
$990$	−154.791	+	94.0462i	−0.156355	+	0.0949962i
$991$	909.339	−	1575.02i	0.917598	−	1.58933i	0.114544	−	0.993418i	$-0.463459\pi$
$991$	909.339	−	1575.02i	0.917598	−	1.58933i	0.803053	−	0.595907i	$-0.203207\pi$
$992$	−1098.54	+	634.244i	−1.10740	+	0.639358i
$993$	−435.862	+	258.187i	−0.438934	+	0.260007i
$994$	−71.7961	−	124.354i	−0.0722295	−	0.125105i
$995$			199.304i			0.200306i
$996$	−21.5220	+	38.2590i	−0.0216084	+	0.0384126i
$997$	−739.645	+	1281.10i	−0.741870	+	1.28496i	0.209772	+	0.977750i	$0.432728\pi$
$997$	−739.645	+	1281.10i	−0.741870	+	1.28496i	−0.951643	+	0.307207i	$0.900606\pi$
$998$	−33.5249	−	19.3556i	−0.0335921	−	0.0193944i
$999$	873.346	−	544.082i	0.874220	−	0.544626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.t.a.11.4	yes	8
3.2	odd	2	inner	105.3.t.a.11.1	✓	8
7.2	even	3	inner	105.3.t.a.86.1	yes	8
21.2	odd	6	inner	105.3.t.a.86.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.t.a.11.1	✓	8	3.2	odd	2	inner
105.3.t.a.11.4	yes	8	1.1	even	1	trivial
105.3.t.a.86.1	yes	8	7.2	even	3	inner
105.3.t.a.86.4	yes	8	21.2	odd	6	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.16124 - 1.82514i) q^{2} +(0.0335498 + 2.99981i) q^{3} +(4.66228 - 8.07530i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.58114 + 9.42188i) q^{6} +7.00000 q^{7} -19.4361i q^{8} +(-8.99775 + 0.201286i) q^{9} +O(q^{10})\)	\(q+(3.16124 - 1.82514i) q^{2} +(0.0335498 + 2.99981i) q^{3} +(4.66228 - 8.07530i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(5.58114 + 9.42188i) q^{6} +7.00000 q^{7} -19.4361i q^{8} +(-8.99775 + 0.201286i) q^{9} +(-4.08114 + 7.06874i) q^{10} +(-2.13524 - 1.23278i) q^{11} +(24.3808 + 13.7150i) q^{12} -14.8114 q^{13} +(22.1287 - 12.7760i) q^{14} +(-3.41886 - 5.77160i) q^{15} +(-16.8246 - 29.1410i) q^{16} +(-14.2672 - 8.23717i) q^{17} +(-28.0766 + 17.0585i) q^{18} +(15.5680 + 26.9645i) q^{19} +20.8503i q^{20} +(0.234849 + 20.9987i) q^{21} -9.00000 q^{22} +(-21.5324 + 12.4317i) q^{23} +(58.3047 - 0.652079i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-46.8223 + 27.0329i) q^{26} +(-0.905694 - 26.9848i) q^{27} +(32.6359 - 56.5271i) q^{28} -24.9596i q^{29} +(-21.3418 - 12.0055i) q^{30} +(14.0680 - 24.3664i) q^{31} +(-39.0441 - 22.5421i) q^{32} +(3.62648 - 6.44668i) q^{33} -60.1359 q^{34} +(-13.5554 + 7.82624i) q^{35} +(-40.3246 + 73.5980i) q^{36} +(19.0548 + 33.0039i) q^{37} +(98.4281 + 56.8275i) q^{38} +(-0.496919 - 44.4314i) q^{39} +(21.7302 + 37.6379i) q^{40} -20.1246i q^{41} +(39.0680 + 65.9532i) q^{42} +21.8114 q^{43} +(-19.9102 + 11.4951i) q^{44} +(17.1990 - 10.4496i) q^{45} +(-45.3794 + 78.5994i) q^{46} +(6.66897 - 3.85033i) q^{47} +(86.8530 - 51.4482i) q^{48} +49.0000 q^{49} -18.2514i q^{50} +(24.2313 - 43.0752i) q^{51} +(-69.0548 + 119.606i) q^{52} +(68.4380 + 39.5127i) q^{53} +(-52.1142 - 83.6523i) q^{54} +5.51317 q^{55} -136.053i q^{56} +(-80.3662 + 47.6056i) q^{57} +(-45.5548 - 78.9032i) q^{58} +(-67.1622 - 38.7761i) q^{59} +(-62.5471 + 0.699525i) q^{60} +(10.8641 + 18.8171i) q^{61} -102.704i q^{62} +(-62.9842 + 1.40900i) q^{63} -29.9737 q^{64} +(28.6821 - 16.5596i) q^{65} +(-0.301948 - 26.9983i) q^{66} +(42.3246 - 73.3083i) q^{67} +(-133.035 + 76.8079i) q^{68} +(-38.0153 - 64.1761i) q^{69} +(-28.5680 + 49.4812i) q^{70} -5.61961i q^{71} +(3.91223 + 174.881i) q^{72} +(-24.9320 + 43.1835i) q^{73} +(120.473 + 69.5554i) q^{74} +(13.0734 + 7.35426i) q^{75} +290.329 q^{76} +(-14.9467 - 8.62947i) q^{77} +(-82.6644 - 139.551i) q^{78} +(-38.2566 - 66.2623i) q^{79} +(65.1612 + 37.6208i) q^{80} +(80.9190 - 3.62225i) q^{81} +(-36.7302 - 63.6187i) q^{82} +1.56922i q^{83} +(170.666 + 96.0052i) q^{84} +36.8377 q^{85} +(68.9510 - 39.8089i) q^{86} +(74.8742 - 0.837391i) q^{87} +(-23.9605 + 41.5008i) q^{88} +(1.19249 - 0.688486i) q^{89} +(35.2982 - 64.4242i) q^{90} -103.680 q^{91} +231.841i q^{92} +(73.5667 + 41.3838i) q^{93} +(14.0548 - 24.3436i) q^{94} +(-60.2945 - 34.8110i) q^{95} +(66.3122 - 117.881i) q^{96} -71.8114 q^{97} +(154.901 - 89.4319i) q^{98} +(19.4605 + 10.6625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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