LMFDB - Embedded newform 32.3.h.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,3,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	32.11
Dual form			32.3.h.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96275 + 0.384217i) q^{2} +(-1.10785 - 2.67458i) q^{3} +(3.70475 - 1.50824i) q^{4} +(2.95565 - 7.13556i) q^{5} +(3.20204 + 4.82387i) q^{6} +(-4.18452 + 4.18452i) q^{7} +(-6.69200 + 4.38373i) q^{8} +(0.437918 - 0.437918i) q^{9} +O(q^{10})$	\(q+(-1.96275 + 0.384217i) q^{2} +(-1.10785 - 2.67458i) q^{3} +(3.70475 - 1.50824i) q^{4} +(2.95565 - 7.13556i) q^{5} +(3.20204 + 4.82387i) q^{6} +(-4.18452 + 4.18452i) q^{7} +(-6.69200 + 4.38373i) q^{8} +(0.437918 - 0.437918i) q^{9} +(-3.05958 + 15.1409i) q^{10} +(1.42655 - 3.44399i) q^{11} +(-8.13821 - 8.23775i) q^{12} +(8.39996 + 20.2793i) q^{13} +(6.60538 - 9.82091i) q^{14} -22.3590 q^{15} +(11.4504 - 11.1753i) q^{16} -1.73115i q^{17} +(-0.691266 + 1.02778i) q^{18} +(14.2459 - 5.90085i) q^{19} +(0.187785 - 30.8933i) q^{20} +(15.8276 + 6.55601i) q^{21} +(-1.47671 + 7.30779i) q^{22} +(15.1565 + 15.1565i) q^{23} +(19.1383 + 13.0418i) q^{24} +(-24.5027 - 24.5027i) q^{25} +(-24.2787 - 36.5757i) q^{26} +(-25.7276 - 10.6567i) q^{27} +(-9.19134 + 21.8139i) q^{28} +(-6.74107 + 2.79224i) q^{29} +(43.8851 - 8.59072i) q^{30} +31.1695i q^{31} +(-18.1805 + 26.3338i) q^{32} -10.7916 q^{33} +(0.665136 + 3.39780i) q^{34} +(17.4909 + 42.2268i) q^{35} +(0.961891 - 2.28286i) q^{36} +(5.30038 - 12.7962i) q^{37} +(-25.6939 + 17.0554i) q^{38} +(44.9327 - 44.9327i) q^{39} +(11.5012 + 60.7079i) q^{40} +(-18.5776 + 18.5776i) q^{41} +(-33.5845 - 6.78655i) q^{42} +(31.0691 - 75.0074i) q^{43} +(0.0906349 - 14.9107i) q^{44} +(-1.83046 - 4.41911i) q^{45} +(-35.5718 - 23.9250i) q^{46} -16.2824 q^{47} +(-42.5746 - 18.2445i) q^{48} +13.9797i q^{49} +(57.5069 + 38.6782i) q^{50} +(-4.63009 + 1.91784i) q^{51} +(61.7059 + 62.4607i) q^{52} +(-29.0670 - 12.0399i) q^{53} +(54.5913 + 11.0315i) q^{54} +(-20.3584 - 20.3584i) q^{55} +(9.65901 - 46.3466i) q^{56} +(-31.5646 - 31.5646i) q^{57} +(12.1582 - 8.07050i) q^{58} +(34.1002 + 14.1248i) q^{59} +(-82.8346 + 33.7228i) q^{60} +(-68.7647 + 28.4833i) q^{61} +(-11.9758 - 61.1778i) q^{62} +3.66495i q^{63} +(25.5658 - 58.6719i) q^{64} +169.531 q^{65} +(21.1812 - 4.14633i) q^{66} +(10.5147 + 25.3846i) q^{67} +(-2.61099 - 6.41347i) q^{68} +(23.7462 - 57.3284i) q^{69} +(-50.5545 - 76.1602i) q^{70} +(-32.2012 + 32.2012i) q^{71} +(-1.01083 + 4.85026i) q^{72} +(-28.5494 + 28.5494i) q^{73} +(-5.48676 + 27.1523i) q^{74} +(-38.3891 + 92.6796i) q^{75} +(43.8777 - 43.3475i) q^{76} +(8.44203 + 20.3809i) q^{77} +(-70.9276 + 105.455i) q^{78} +22.4049 q^{79} +(-45.8989 - 114.735i) q^{80} +75.0427i q^{81} +(29.3252 - 43.6009i) q^{82} +(-123.286 + 51.0669i) q^{83} +(68.5255 + 0.416532i) q^{84} +(-12.3527 - 5.11665i) q^{85} +(-32.1616 + 159.158i) q^{86} +(14.9361 + 14.9361i) q^{87} +(5.55106 + 29.3008i) q^{88} +(61.0281 + 61.0281i) q^{89} +(5.29063 + 7.97031i) q^{90} +(-120.009 - 49.7093i) q^{91} +(79.0109 + 33.2915i) q^{92} +(83.3652 - 34.5310i) q^{93} +(31.9583 - 6.25599i) q^{94} -119.093i q^{95} +(90.5730 + 19.4514i) q^{96} -69.9064 q^{97} +(-5.37122 - 27.4385i) q^{98} +(-0.883474 - 2.13290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−1.96275	+	0.384217i	−0.981374	+	0.192109i
$2$	−1.96275	+	0.384217i	−0.981374	+	0.192109i
$3$	−1.10785	−	2.67458i	−0.369282	−	0.891526i	−0.993868	−	0.110570i	$-0.964732\pi$
$3$	−1.10785	−	2.67458i	−0.369282	−	0.891526i	0.624586	−	0.780956i	$-0.285268\pi$
$4$	3.70475	−	1.50824i	0.926189	−	0.377061i
$5$	2.95565	−	7.13556i	0.591129	−	1.42711i	−0.291284	−	0.956637i	$-0.594083\pi$
$5$	2.95565	−	7.13556i	0.591129	−	1.42711i	0.882413	−	0.470475i	$-0.155917\pi$
$6$	3.20204	+	4.82387i	0.533674	+	0.803978i
$7$	−4.18452	+	4.18452i	−0.597788	+	0.597788i	−0.939723	−	0.341935i	$-0.888918\pi$
$7$	−4.18452	+	4.18452i	−0.597788	+	0.597788i	0.341935	+	0.939723i	$0.388918\pi$
$8$	−6.69200	+	4.38373i	−0.836500	+	0.547966i
$9$	0.437918	−	0.437918i	0.0486575	−	0.0486575i
$10$	−3.05958	+	15.1409i	−0.305958	+	1.51409i
$11$	1.42655	−	3.44399i	0.129686	−	0.313090i	−0.845677	−	0.533695i	$-0.820803\pi$
$11$	1.42655	−	3.44399i	0.129686	−	0.313090i	0.975363	+	0.220605i	$0.0708031\pi$
$12$	−8.13821	−	8.23775i	−0.678184	−	0.686479i
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	0.818247	+	0.574866i	$0.194946\pi$
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	−0.172096	+	0.985080i	$0.555054\pi$
$14$	6.60538	−	9.82091i	0.471813	−	0.701494i
$15$	−22.3590			−1.49060
$16$	11.4504	−	11.1753i	0.715651	−	0.698459i
$17$		−	1.73115i		−	0.101832i	−0.998703	−	0.0509161i	$-0.983786\pi$
$17$		−	1.73115i		−	0.101832i	0.998703	−	0.0509161i	$-0.0162141\pi$
$18$	−0.691266	+	1.02778i	−0.0384037	+	0.0570987i
$19$	14.2459	−	5.90085i	0.749785	−	0.310571i	0.0251314	−	0.999684i	$-0.492000\pi$
$19$	14.2459	−	5.90085i	0.749785	−	0.310571i	0.724654	+	0.689113i	$0.242000\pi$
$20$	0.187785	−	30.8933i	0.00938926	−	1.54467i
$21$	15.8276	+	6.55601i	0.753696	+	0.312191i
$22$	−1.47671	+	7.30779i	−0.0671233	+	0.332172i
$23$	15.1565	+	15.1565i	0.658979	+	0.658979i	0.955139	−	0.296159i	$-0.0957059\pi$
$23$	15.1565	+	15.1565i	0.658979	+	0.658979i	−0.296159	+	0.955139i	$0.595706\pi$
$24$	19.1383	+	13.0418i	0.797431	+	0.543408i
$25$	−24.5027	−	24.5027i	−0.980107	−	0.980107i
$26$	−24.2787	−	36.5757i	−0.933795	−	1.40676i
$27$	−25.7276	−	10.6567i	−0.952874	−	0.394693i
$28$	−9.19134	+	21.8139i	−0.328262	+	0.779067i
$29$	−6.74107	+	2.79224i	−0.232451	+	0.0962842i	−0.495869	−	0.868398i	$-0.665150\pi$
$29$	−6.74107	+	2.79224i	−0.232451	+	0.0962842i	0.263418	+	0.964682i	$0.415150\pi$
$30$	43.8851	−	8.59072i	1.46284	−	0.286357i
$31$			31.1695i			1.00547i	0.864442	+	0.502733i	$0.167672\pi$
$31$			31.1695i			1.00547i	−0.864442	+	0.502733i	$0.832328\pi$
$32$	−18.1805	+	26.3338i	−0.568141	+	0.822931i
$33$	−10.7916			−0.327019
$34$	0.665136	+	3.39780i	0.0195628	+	0.0999354i
$35$	17.4909	+	42.2268i	0.499740	+	1.20648i
$36$	0.961891	−	2.28286i	0.0267192	−	0.0634129i
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	−0.835926	−	0.548843i	$-0.815069\pi$
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	0.979179	+	0.202998i	$0.0650686\pi$
$38$	−25.6939	+	17.0554i	−0.676156	+	0.448827i
$39$	44.9327	−	44.9327i	1.15212	−	1.15212i
$40$	11.5012	+	60.7079i	0.287529	+	1.51770i
$41$	−18.5776	+	18.5776i	−0.453111	+	0.453111i	−0.896386	−	0.443275i	$-0.853817\pi$
$41$	−18.5776	+	18.5776i	−0.453111	+	0.453111i	0.443275	+	0.896386i	$0.353817\pi$
$42$	−33.5845	−	6.78655i	−0.799632	−	0.161585i
$43$	31.0691	−	75.0074i	0.722537	−	1.74436i	0.0565443	−	0.998400i	$-0.481992\pi$
$43$	31.0691	−	75.0074i	0.722537	−	1.74436i	0.665993	−	0.745958i	$-0.268008\pi$
$44$	0.0906349	−	14.9107i	0.00205988	−	0.338880i
$45$	−1.83046	−	4.41911i	−0.0406768	−	0.0982026i
$46$	−35.5718	−	23.9250i	−0.773301	−	0.520109i
$47$	−16.2824			−0.346435			−0.173217	−	0.984884i	$-0.555416\pi$
$47$	−16.2824			−0.346435			−0.173217	+	0.984884i	$0.555416\pi$
$48$	−42.5746	−	18.2445i	−0.886971	−	0.380093i
$49$			13.9797i			0.285299i
$50$	57.5069	+	38.6782i	1.15014	+	0.773565i
$51$	−4.63009	+	1.91784i	−0.0907860	+	0.0376048i
$52$	61.7059	+	62.4607i	1.18665	+	1.20117i
$53$	−29.0670	−	12.0399i	−0.548434	−	0.227169i	0.0912216	−	0.995831i	$-0.470923\pi$
$53$	−29.0670	−	12.0399i	−0.548434	−	0.227169i	−0.639655	+	0.768662i	$0.720923\pi$
$54$	54.5913	+	11.0315i	1.01095	+	0.204286i
$55$	−20.3584	−	20.3584i	−0.370153	−	0.370153i
$56$	9.65901	−	46.3466i	0.172482	−	0.827618i
$57$	−31.5646	−	31.5646i	−0.553765	−	0.553765i
$58$	12.1582	−	8.07050i	0.209624	−	0.139147i
$59$	34.1002	+	14.1248i	0.577969	+	0.239403i	0.652465	−	0.757819i	$-0.273735\pi$
$59$	34.1002	+	14.1248i	0.577969	+	0.239403i	−0.0744962	+	0.997221i	$0.523735\pi$
$60$	−82.8346	+	33.7228i	−1.38058	+	0.562047i
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.866859	−	0.498553i	$-0.833865\pi$
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.260432	+	0.965492i	$0.583865\pi$
$62$	−11.9758	−	61.1778i	−0.193159	−	0.986739i
$63$			3.66495i			0.0581737i
$64$	25.5658	−	58.6719i	0.399466	−	0.916748i
$65$	169.531			2.60818
$66$	21.1812	−	4.14633i	0.320928	−	0.0628231i
$67$	10.5147	+	25.3846i	0.156935	+	0.378875i	0.982717	−	0.185115i	$-0.0592657\pi$
$67$	10.5147	+	25.3846i	0.156935	+	0.378875i	−0.825782	+	0.563990i	$0.809266\pi$
$68$	−2.61099	−	6.41347i	−0.0383969	−	0.0943158i
$69$	23.7462	−	57.3284i	0.344148	−	0.830847i
$70$	−50.5545	−	76.1602i	−0.722207	−	1.08800i
$71$	−32.2012	+	32.2012i	−0.453538	+	0.453538i	−0.896527	−	0.442989i	$-0.853918\pi$
$71$	−32.2012	+	32.2012i	−0.453538	+	0.453538i	0.442989	+	0.896527i	$0.353918\pi$
$72$	−1.01083	+	4.85026i	−0.0140394	+	0.0673647i
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	−0.875075	−	0.483987i	$-0.839188\pi$
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	0.483987	+	0.875075i	$0.339188\pi$
$74$	−5.48676	+	27.1523i	−0.0741455	+	0.366923i
$75$	−38.3891	+	92.6796i	−0.511855	+	1.23573i
$76$	43.8777	−	43.3475i	0.577338	−	0.570362i
$77$	8.44203	+	20.3809i	0.109637	+	0.264686i
$78$	−70.9276	+	105.455i	−0.909329	+	1.35199i
$79$	22.4049			0.283606			0.141803	−	0.989895i	$-0.454710\pi$
$79$	22.4049			0.283606			0.141803	+	0.989895i	$0.454710\pi$
$80$	−45.8989	−	114.735i	−0.573737	−	1.43419i
$81$			75.0427i			0.926453i
$82$	29.3252	−	43.6009i	0.357625	−	0.531718i
$83$	−123.286	+	51.0669i	−1.48538	+	0.615264i	−0.970306	−	0.241882i	$-0.922235\pi$
$83$	−123.286	+	51.0669i	−1.48538	+	0.615264i	−0.515073	+	0.857146i	$0.672235\pi$
$84$	68.5255	+	0.416532i	0.815780	+	0.00495872i
$85$	−12.3527	−	5.11665i	−0.145326	−	0.0601959i
$86$	−32.1616	+	159.158i	−0.373972	+	1.85067i
$87$	14.9361	+	14.9361i	0.171680	+	0.171680i
$88$	5.55106	+	29.3008i	0.0630803	+	0.332964i
$89$	61.0281	+	61.0281i	0.685709	+	0.685709i	0.961280	−	0.275572i	$-0.0888672\pi$
$89$	61.0281	+	61.0281i	0.685709	+	0.685709i	−0.275572	+	0.961280i	$0.588867\pi$
$90$	5.29063	+	7.97031i	0.0587847	+	0.0885590i
$91$	−120.009	−	49.7093i	−1.31878	−	0.546256i
$92$	79.0109	+	33.2915i	0.858814	+	0.361864i
$93$	83.3652	−	34.5310i	0.896400	−	0.371301i
$94$	31.9583	−	6.25599i	0.339982	−	0.0665531i
$95$		−	119.093i		−	1.25362i
$96$	90.5730	+	19.4514i	0.943469	+	0.202618i
$97$	−69.9064			−0.720684			−0.360342	−	0.932820i	$-0.617340\pi$
$97$	−69.9064			−0.720684			−0.360342	+	0.932820i	$0.617340\pi$
$98$	−5.37122	−	27.4385i	−0.0548084	−	0.279985i
$99$	−0.883474	−	2.13290i	−0.00892398	−	0.0215444i
$100$	−127.732	−	53.8204i	−1.27732	−	0.538204i
$101$	−10.4825	+	25.3069i	−0.103787	+	0.250564i	−0.967239	−	0.253867i	$-0.918298\pi$
$101$	−10.4825	+	25.3069i	−0.103787	+	0.250564i	0.863452	+	0.504431i	$0.168298\pi$
$102$	8.35082	−	5.54320i	0.0818708	−	0.0543451i
$103$	116.721	−	116.721i	1.13322	−	1.13322i	0.143579	−	0.989639i	$-0.454139\pi$
$103$	116.721	−	116.721i	1.13322	−	1.13322i	0.989639	−	0.143579i	$-0.0458612\pi$
$104$	−145.112	−	98.8860i	−1.39530	−	0.950827i
$105$	93.5616	−	93.5616i	0.891063	−	0.891063i
$106$	61.6771	+	12.4633i	0.581859	+	0.117579i
$107$	−21.6236	+	52.2039i	−0.202090	+	0.487887i	−0.992137	−	0.125159i	$-0.960056\pi$
$107$	−21.6236	+	52.2039i	−0.202090	+	0.487887i	0.790047	+	0.613046i	$0.210056\pi$
$108$	−111.387	−	0.677068i	−1.03136	−	0.00626915i
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	0.734725	−	0.678366i	$-0.237311\pi$
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	−0.999206	+	0.0398518i	$0.987311\pi$
$110$	47.7805	+	32.1364i	0.434369	+	0.292149i
$111$	−40.0965			−0.361230
$112$	−1.15104	+	94.6778i	−0.0102772	+	0.845337i
$113$		−	130.141i		−	1.15169i	−0.817559	−	0.575845i	$-0.804673\pi$
$113$		−	130.141i		−	1.15169i	0.817559	−	0.575845i	$-0.195327\pi$
$114$	74.0810	+	49.8257i	0.649833	+	0.437067i
$115$	152.948	−	63.3530i	1.32998	−	0.550895i
$116$	−20.7626	+	20.5117i	−0.178988	+	0.176825i
$117$	12.5592	+	5.20217i	0.107343	+	0.0444630i
$118$	−72.3570	−	14.6214i	−0.613195	−	0.123911i
$119$	7.24401	+	7.24401i	0.0608740	+	0.0608740i
$120$	149.627	−	98.0158i	1.24689	−	0.816799i
$121$	75.7339	+	75.7339i	0.625900	+	0.625900i
$122$	124.024	−	82.3261i	1.01659	−	0.674804i
$123$	70.2682	+	29.1060i	0.571286	+	0.236635i
$124$	47.0111	+	115.475i	0.379122	+	0.931252i
$125$	−68.8726	+	28.5280i	−0.550981	+	0.228224i
$126$	−1.40814	−	7.19336i	−0.0111757	−	0.0570902i
$127$			56.3580i			0.443764i	0.975074	+	0.221882i	$0.0712200\pi$
$127$			56.3580i			0.443764i	−0.975074	+	0.221882i	$0.928780\pi$
$128$	−27.6365	+	124.981i	−0.215910	+	0.976413i
$129$	−235.033			−1.82196
$130$	−332.747	+	65.1369i	−2.55960	+	0.501053i
$131$	−39.2631	−	94.7895i	−0.299718	−	0.723584i	−0.999953	−	0.00967128i	$-0.996921\pi$
$131$	−39.2631	−	94.7895i	−0.299718	−	0.723584i	0.700235	−	0.713912i	$-0.253079\pi$
$132$	−39.9803	+	16.2764i	−0.302881	+	0.123306i
$133$	−34.9201	+	84.3045i	−0.262557	+	0.633868i
$134$	−30.3908	−	45.7837i	−0.226797	−	0.341670i
$135$	−152.083	+	152.083i	−1.12654	+	1.12654i
$136$	7.58888	+	11.5848i	0.0558006	+	0.0851826i
$137$	62.6423	−	62.6423i	0.457243	−	0.457243i	−0.440506	−	0.897750i	$-0.645201\pi$
$137$	62.6423	−	62.6423i	0.457243	−	0.457243i	0.897750	+	0.440506i	$0.145201\pi$
$138$	−24.5812	+	121.645i	−0.178125	+	0.881485i
$139$	11.6343	−	28.0877i	0.0837000	−	0.202070i	−0.876488	−	0.481423i	$-0.840120\pi$
$139$	11.6343	−	28.0877i	0.0837000	−	0.202070i	0.960188	+	0.279353i	$0.0901201\pi$
$140$	128.488	+	130.059i	0.917770	+	0.928996i
$141$	18.0384	+	43.5487i	0.127932	+	0.308856i
$142$	50.8306	−	75.5751i	0.357962	−	0.532219i
$143$	81.8247			0.572201
$144$	0.120459	−	9.90821i	0.000836518	−	0.0688070i
$145$			56.3542i			0.388649i
$146$	45.0661	−	67.0044i	0.308672	−	0.458935i
$147$	37.3897	−	15.4873i	0.254352	−	0.105356i
$148$	0.336756	−	55.4012i	0.00227538	−	0.374332i
$149$	−52.6977	−	21.8281i	−0.353676	−	0.146497i	0.198770	−	0.980046i	$-0.436305\pi$
$149$	−52.6977	−	21.8281i	−0.353676	−	0.146497i	−0.552446	+	0.833549i	$0.686305\pi$
$150$	39.7391	−	196.656i	0.264927	−	1.31104i
$151$	−48.5998	−	48.5998i	−0.321853	−	0.321853i	0.527625	−	0.849478i	$-0.323083\pi$
$151$	−48.5998	−	48.5998i	−0.321853	−	0.321853i	−0.849478	+	0.527625i	$0.823083\pi$
$152$	−69.4660	+	101.939i	−0.457013	+	0.670650i
$153$	−0.758099	−	0.758099i	−0.00495490	−	0.00495490i
$154$	−24.4002	−	36.7589i	−0.158443	−	0.238694i
$155$	222.412	+	92.1259i	1.43491	+	0.594361i
$156$	98.6952	−	234.234i	0.632662	−	1.50150i
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.0399023	−	0.999204i	$-0.487295\pi$
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.734759	+	0.678328i	$0.237295\pi$
$158$	−43.9751	+	8.60834i	−0.278323	+	0.0544832i
$159$			91.0803i			0.572832i
$160$	134.171	+	207.561i	0.838571	+	1.29726i
$161$	−126.845			−0.787860
$162$	−28.8327	−	147.290i	−0.177980	−	0.909196i
$163$	−13.0161	−	31.4236i	−0.0798533	−	0.192783i	0.878911	−	0.476986i	$-0.158271\pi$
$163$	−13.0161	−	31.4236i	−0.0798533	−	0.192783i	−0.958764	+	0.284203i	$0.908271\pi$
$164$	−40.8058	+	96.8448i	−0.248816	+	0.590517i
$165$	−31.8962	+	77.0043i	−0.193310	+	0.466692i
$166$	222.359	−	147.600i	1.33951	−	0.889158i
$167$	−138.734	+	138.734i	−0.830744	+	0.830744i	−0.987619	−	0.156875i	$-0.949858\pi$
$167$	−138.734	+	138.734i	−0.830744	+	0.830744i	0.156875	+	0.987619i	$0.449858\pi$
$168$	−134.658	+	25.5111i	−0.801537	+	0.151852i
$169$	−221.190	+	221.190i	−1.30881	+	1.30881i
$170$	26.2111	+	5.29658i	0.154183	+	0.0311564i
$171$	3.65445	−	8.82263i	0.0213711	−	0.0515943i
$172$	1.97396	−	324.744i	0.0114765	−	1.88805i
$173$	−69.7574	−	168.409i	−0.403222	−	0.973464i	−0.986879	−	0.161464i	$-0.948379\pi$
$173$	−69.7574	−	168.409i	−0.403222	−	0.973464i	0.583656	−	0.812001i	$-0.301621\pi$
$174$	−35.0546	−	23.5771i	−0.201463	−	0.135501i
$175$	205.064			1.17179
$176$	−22.1532	−	55.3773i	−0.125871	−	0.314644i
$177$		−	106.852i		−	0.603682i
$178$	−143.231	−	96.3346i	−0.804667	−	0.541206i
$179$	45.0027	−	18.6407i	0.251411	−	0.104138i	−0.253419	−	0.967357i	$-0.581555\pi$
$179$	45.0027	−	18.6407i	0.251411	−	0.104138i	0.504830	+	0.863219i	$0.331555\pi$
$180$	−13.4465	−	13.6110i	−0.0747027	−	0.0756165i
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	0.686201	−	0.727412i	$-0.259277\pi$
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	−0.0291408	+	0.999575i	$0.509277\pi$
$182$	254.646	+	51.4573i	1.39915	+	0.282732i
$183$	152.362	+	152.362i	0.832577	+	0.832577i
$184$	−167.870	−	34.9854i	−0.912335	−	0.190138i
$185$	−75.6423	−	75.6423i	−0.408877	−	0.408877i
$186$	−150.357	+	99.8059i	−0.808373	+	0.536591i
$187$	−5.96206	−	2.46956i	−0.0318827	−	0.0132062i
$188$	−60.3224	+	24.5579i	−0.320864	+	0.130627i
$189$	152.251	−	63.0643i	0.805559	−	0.333674i
$190$	45.7577	+	233.750i	0.240830	+	1.23026i
$191$		−	179.282i		−	0.938649i	−0.883026	−	0.469325i	$-0.844497\pi$
$191$		−	179.282i		−	0.938649i	0.883026	−	0.469325i	$-0.155503\pi$
$192$	−185.246	−	3.37838i	−0.964820	−	0.0175957i
$193$	179.924			0.932249			0.466125	−	0.884719i	$-0.345650\pi$
$193$	179.924			0.932249			0.466125	+	0.884719i	$0.345650\pi$
$194$	137.209	−	26.8592i	0.707260	−	0.138450i
$195$	−187.815	−	453.425i	−0.963153	−	2.32526i
$196$	21.0847	+	51.7912i	0.107575	+	0.264241i
$197$	−93.2938	+	225.231i	−0.473573	+	1.14331i	0.489000	+	0.872284i	$0.337362\pi$
$197$	−93.2938	+	225.231i	−0.473573	+	1.14331i	−0.962573	+	0.271022i	$0.912638\pi$
$198$	2.55353	+	3.84689i	0.0128966	+	0.0194287i
$199$	−131.782	+	131.782i	−0.662220	+	0.662220i	−0.955903	−	0.293683i	$-0.905119\pi$
$199$	−131.782	+	131.782i	−0.662220	+	0.662220i	0.293683	+	0.955903i	$0.405119\pi$
$200$	271.385	+	56.5589i	1.35693	+	0.282795i
$201$	56.2446	−	56.2446i	0.279824	−	0.279824i
$202$	10.8511	−	53.6987i	0.0537183	−	0.265835i
$203$	16.5239	−	39.8923i	0.0813987	−	0.196514i
$204$	−14.2608	+	14.0884i	−0.0699057	+	0.0690610i
$205$	77.6526	+	187.470i	0.378793	+	0.914487i
$206$	−184.248	+	273.941i	−0.894409	+	1.32981i
$207$	13.2746			0.0641286
$208$	322.811	+	138.334i	1.55198	+	0.665067i
$209$		−	57.4807i		−	0.275027i
$210$	−147.690	+	219.586i	−0.703285	+	1.04565i
$211$	−182.694	+	75.6743i	−0.865848	+	0.358646i	−0.770992	−	0.636845i	$-0.780239\pi$
$211$	−182.694	+	75.6743i	−0.865848	+	0.358646i	−0.0948559	+	0.995491i	$0.530239\pi$
$212$	−125.845	−	0.764951i	−0.593609	−	0.00360826i
$213$	121.799	+	50.4506i	0.571824	+	0.236857i
$214$	22.3840	−	110.771i	0.104598	−	0.517623i
$215$	−443.391	−	443.391i	−2.06228	−	2.06228i
$216$	218.885	−	41.4680i	1.01336	−	0.191982i
$217$	−130.429	−	130.429i	−0.601056	−	0.601056i
$218$	83.3237	+	125.527i	0.382219	+	0.575812i
$219$	107.986	+	44.7293i	0.493087	+	0.204243i
$220$	−106.128	−	44.7176i	−0.482402	−	0.203262i
$221$	35.1064	−	14.5416i	0.158853	−	0.0657989i
$222$	78.6994	−	15.4058i	0.354502	−	0.0693954i
$223$			175.414i			0.786612i	0.919408	+	0.393306i	$0.128669\pi$
$223$			175.414i			0.786612i	−0.919408	+	0.393306i	$0.871331\pi$
$224$	−34.1176	−	186.271i	−0.152311	−	0.831566i
$225$	−21.4603			−0.0953792
$226$	50.0024	+	255.434i	0.221250	+	1.13024i
$227$	157.825	+	381.024i	0.695265	+	1.67852i	0.733893	+	0.679265i	$0.237701\pi$
$227$	157.825	+	381.024i	0.695265	+	1.67852i	−0.0386277	+	0.999254i	$0.512299\pi$
$228$	−164.546	−	69.3320i	−0.721693	−	0.304088i
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	−0.748965	−	0.662610i	$-0.769449\pi$
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	0.998134	+	0.0610623i	$0.0194488\pi$
$230$	−275.856	+	183.111i	−1.19937	+	0.796135i
$231$	45.1577	−	45.1577i	0.195488	−	0.195488i
$232$	32.8708	−	48.2367i	0.141685	−	0.207917i
$233$	275.512	−	275.512i	1.18246	−	1.18246i	0.203349	−	0.979106i	$-0.434817\pi$
$233$	275.512	−	275.512i	1.18246	−	1.18246i	0.979106	−	0.203349i	$-0.0651826\pi$
$234$	−26.6492	−	5.38511i	−0.113886	−	0.0230133i
$235$	−48.1251	+	116.184i	−0.204788	+	0.494401i
$236$	147.636	+	0.897408i	0.625578	+	0.00380258i
$237$	−24.8212	−	59.9236i	−0.104731	−	0.252842i
$238$	−17.0014	−	11.4349i	−0.0714346	−	0.0480457i
$239$	−63.0374			−0.263755			−0.131877	−	0.991266i	$-0.542101\pi$
$239$	−63.0374			−0.263755			−0.131877	+	0.991266i	$0.542101\pi$
$240$	−256.020	+	249.869i	−1.06675	+	1.04112i
$241$		−	194.368i		−	0.806507i	−0.915088	−	0.403253i	$-0.867879\pi$
$241$		−	194.368i		−	0.806507i	0.915088	−	0.403253i	$-0.132121\pi$
$242$	−177.745	−	119.548i	−0.734482	−	0.494001i
$243$	−30.8408	+	12.7747i	−0.126917	+	0.0525708i
$244$	−211.797	+	209.238i	−0.868020	+	0.857531i
$245$	99.7526	+	41.3189i	0.407154	+	0.168649i
$246$	−149.102	−	30.1296i	−0.606105	−	0.122478i
$247$	239.330	+	239.330i	0.968949	+	0.968949i
$248$	−136.639	−	208.586i	−0.550962	−	0.841073i
$249$	273.165	+	273.165i	1.09705	+	1.09705i
$250$	124.219	−	82.4553i	0.496875	−	0.329821i
$251$	−317.091	−	131.343i	−1.26331	−	0.523281i	−0.352387	−	0.935854i	$-0.614630\pi$
$251$	−317.091	−	131.343i	−1.26331	−	0.523281i	−0.910924	+	0.412574i	$0.864630\pi$
$252$	5.52763	+	13.5777i	0.0219350	+	0.0538799i
$253$	73.8205	−	30.5774i	0.291781	−	0.120859i
$254$	−21.6537	−	110.617i	−0.0852509	−	0.435498i
$255$			38.7067i			0.151791i
$256$	6.22370	−	255.924i	0.0243113	−	0.999704i
$257$	−180.756			−0.703330			−0.351665	−	0.936126i	$-0.614384\pi$
$257$	−180.756			−0.703330			−0.351665	+	0.936126i	$0.614384\pi$
$258$	461.310	−	90.3037i	1.78802	−	0.350014i
$259$	31.3666	+	75.7256i	0.121106	+	0.292377i
$260$	628.072	−	255.695i	2.41566	−	0.983441i
$261$	−1.72926	+	4.17480i	−0.00662552	+	0.0159954i
$262$	113.483	+	170.962i	0.433142	+	0.652527i
$263$	266.626	−	266.626i	1.01379	−	1.01379i	0.0138830	−	0.999904i	$-0.495581\pi$
$263$	266.626	−	266.626i	1.01379	−	1.01379i	0.999904	−	0.0138830i	$-0.00441924\pi$
$264$	72.2176	−	47.3076i	0.273551	−	0.179195i
$265$	−171.823	+	171.823i	−0.648390	+	0.648390i
$266$	36.1480	−	178.885i	0.135895	−	0.672501i
$267$	95.6146	−	230.834i	0.358107	−	0.864547i
$268$	77.2404	+	78.1852i	0.288211	+	0.291736i
$269$	−156.911	−	378.816i	−0.583311	−	1.40824i	−0.889794	−	0.456362i	$-0.849152\pi$
$269$	−156.911	−	378.816i	−0.583311	−	1.40824i	0.306483	−	0.951876i	$-0.400848\pi$
$270$	240.068	−	356.934i	0.889141	−	1.32198i
$271$	−323.931			−1.19532			−0.597659	−	0.801750i	$-0.703902\pi$
$271$	−323.931			−1.19532			−0.597659	+	0.801750i	$0.703902\pi$
$272$	−19.3461	−	19.8223i	−0.0711255	−	0.0728762i
$273$			376.043i			1.37745i
$274$	−98.8828	+	147.019i	−0.360886	+	0.536567i
$275$	−119.341	+	49.4328i	−0.433969	+	0.179756i
$276$	1.50870	−	248.203i	0.00546631	−	0.899285i
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.207864	−	0.978158i	$-0.566651\pi$
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.838644	+	0.544680i	$0.816651\pi$
$278$	−12.0434	+	59.5991i	−0.0433216	+	0.214385i
$279$	13.6497	+	13.6497i	0.0489235	+	0.0489235i
$280$	−302.160	−	205.906i	−1.07914	−	0.735380i
$281$	297.826	+	297.826i	1.05988	+	1.05988i	0.998089	+	0.0617901i	$0.0196809\pi$
$281$	297.826	+	297.826i	1.05988	+	1.05988i	0.0617901	+	0.998089i	$0.480319\pi$
$282$	−52.1370	−	78.5443i	−0.184883	−	0.278526i
$283$	−132.389	−	54.8372i	−0.467804	−	0.193771i	0.136314	−	0.990666i	$-0.456474\pi$
$283$	−132.389	−	54.8372i	−0.467804	−	0.193771i	−0.604118	+	0.796895i	$0.706474\pi$
$284$	−70.7303	+	167.865i	−0.249050	+	0.591073i
$285$	−318.525	+	131.937i	−1.11763	+	0.462938i
$286$	−160.601	+	31.4385i	−0.561543	+	0.109925i
$287$		−	155.476i		−	0.541729i
$288$	3.57048	+	19.4936i	0.0123975	+	0.0676861i
$289$	286.003			0.989630
$290$	−21.6522	−	110.609i	−0.0746629	−	0.381410i
$291$	77.4455	+	186.970i	0.266136	+	0.642509i
$292$	−62.7091	+	148.828i	−0.214757	+	0.509685i
$293$	18.1180	−	43.7407i	0.0618361	−	0.149286i	−0.889941	−	0.456075i	$-0.849255\pi$
$293$	18.1180	−	43.7407i	0.0618361	−	0.149286i	0.951777	+	0.306790i	$0.0992548\pi$
$294$	−67.4360	+	44.7634i	−0.229374	+	0.152257i
$295$	201.576	−	201.576i	0.683309	−	0.683309i
$296$	20.6251	+	108.868i	0.0696795	+	0.367797i
$297$	−73.4033	+	73.4033i	−0.247149	+	0.247149i
$298$	111.819	+	22.5957i	0.375231	+	0.0758244i
$299$	−180.050	+	434.678i	−0.602172	+	1.45377i
$300$	−2.43903	+	401.255i	−0.00813010	+	1.33752i
$301$	183.861	+	443.879i	0.610833	+	1.47468i
$302$	114.062	+	76.7162i	0.377689	+	0.254027i
$303$	79.2984			0.261711
$304$	97.1776	−	226.770i	0.319663	−	0.745954i
$305$			574.861i			1.88479i
$306$	1.77923	+	1.19668i	0.00581449	+	0.00391073i
$307$	532.332	−	220.499i	1.73398	−	0.718239i	0.734779	−	0.678307i	$-0.237286\pi$
$307$	532.332	−	220.499i	1.73398	−	0.718239i	0.999202	−	0.0399320i	$-0.0127141\pi$
$308$	62.0149	+	62.7734i	0.201347	+	0.203810i
$309$	−441.490	−	182.871i	−1.42877	−	0.591816i
$310$	−471.934	−	95.3655i	−1.52237	−	0.307631i
$311$	383.582	+	383.582i	1.23338	+	1.23338i	0.962657	+	0.270725i	$0.0872634\pi$
$311$	383.582	+	383.582i	1.23338	+	1.23338i	0.270725	+	0.962657i	$0.412737\pi$
$312$	−103.717	+	497.663i	−0.332426	+	1.59507i
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.985101	−	0.171974i	$-0.944985\pi$
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.171974	−	0.985101i	$-0.555015\pi$
$314$	−219.357	+	145.607i	−0.698589	+	0.463718i
$315$	26.1514	+	10.8323i	0.0830204	+	0.0343882i
$316$	83.0046	−	33.7920i	0.262673	−	0.106937i
$317$	−487.277	+	201.837i	−1.53715	+	0.636709i	−0.980936	−	0.194329i	$-0.937747\pi$
$317$	−487.277	+	201.837i	−1.53715	+	0.636709i	−0.556215	+	0.831038i	$0.687747\pi$
$318$	−34.9946	−	178.768i	−0.110046	−	0.562162i
$319$			27.1995i			0.0852648i
$320$	−343.093	−	355.840i	−1.07217	−	1.11200i
$321$	163.579			0.509592
$322$	248.966	−	48.7362i	0.773185	−	0.151355i
$323$	−10.2152	−	24.6618i	−0.0316261	−	0.0763523i
$324$	113.183	+	278.015i	0.349329	+	0.858070i
$325$	291.076	−	702.719i	0.895618	−	2.16221i
$326$	37.6208	+	56.6756i	0.115401	+	0.173852i
$327$	−154.208	+	154.208i	−0.471584	+	0.471584i
$328$	42.8821	−	205.760i	0.130738	−	0.627317i
$329$	68.1341	−	68.1341i	0.207095	−	0.207095i
$330$	33.0178	−	163.395i	0.100054	−	0.495136i
$331$	20.5475	−	49.6062i	0.0620772	−	0.149868i	−0.889797	−	0.456356i	$-0.849154\pi$
$331$	20.5475	−	49.6062i	0.0620772	−	0.149868i	0.951874	+	0.306489i	$0.0991542\pi$
$332$	−379.725	+	375.136i	−1.14375	+	1.12993i
$333$	−3.28257	−	7.92483i	−0.00985757	−	0.0237983i
$334$	218.996	−	325.604i	0.655677	−	0.974863i
$335$	212.211			0.633466
$336$	254.498	−	101.810i	0.757435	−	0.303006i
$337$		−	627.680i		−	1.86255i	−0.364315	−	0.931276i	$-0.618697\pi$
$337$		−	627.680i		−	1.86255i	0.364315	−	0.931276i	$-0.381303\pi$
$338$	349.155	−	519.124i	1.03300	−	1.53587i
$339$	−348.072	+	144.176i	−1.02676	+	0.425299i
$340$	−53.4809	−	0.325084i	−0.157297	−	0.000956128i
$341$	107.347	+	44.4648i	0.314802	+	0.130395i
$342$	−3.78296	+	18.7207i	−0.0110613	+	0.0547389i
$343$	−263.539	−	263.539i	−0.768336	−	0.768336i
$344$	120.898	+	638.148i	0.351447	+	1.85508i
$345$	−338.885	−	338.885i	−0.982275	−	0.982275i
$346$	201.622	+	303.743i	0.582722	+	0.877870i
$347$	320.625	+	132.807i	0.923992	+	0.382730i	0.793396	−	0.608706i	$-0.208311\pi$
$347$	320.625	+	132.807i	0.923992	+	0.382730i	0.130596	+	0.991436i	$0.458311\pi$
$348$	77.8620	+	32.8074i	0.223741	+	0.0942741i
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	−0.361741	−	0.932279i	$-0.617818\pi$
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	0.403431	+	0.915010i	$0.367818\pi$
$350$	−402.488	+	78.7890i	−1.14997	+	0.225112i
$351$		−	611.254i		−	1.74146i
$352$	64.7581	+	100.180i	0.183972	+	0.284602i
$353$	283.828			0.804045			0.402023	−	0.915630i	$-0.368307\pi$
$353$	283.828			0.804045			0.402023	+	0.915630i	$0.368307\pi$
$354$	41.0542	+	209.723i	0.115972	+	0.592437i
$355$	134.598	+	324.949i	0.379150	+	0.915349i
$356$	318.139	+	134.049i	0.893649	+	0.376542i
$357$	11.3494	−	27.3999i	0.0317911	−	0.0767505i
$358$	−81.1668	+	53.8778i	−0.226723	+	0.150497i
$359$	388.417	−	388.417i	1.08194	−	1.08194i	0.0856121	−	0.996329i	$-0.472715\pi$
$359$	388.417	−	388.417i	1.08194	−	1.08194i	0.996329	−	0.0856121i	$-0.0272846\pi$
$360$	31.6216	+	21.5485i	0.0878379	+	0.0598570i
$361$	−87.1393	+	87.1393i	−0.241383	+	0.241383i
$362$	−252.352	−	50.9938i	−0.697106	−	0.140867i
$363$	118.655	−	286.458i	0.326872	−	0.789140i
$364$	−519.577	−	3.15825i	−1.42741	−	0.00867651i
$365$	119.334	+	288.098i	0.326943	+	0.789309i
$366$	−357.587	−	240.507i	−0.977014	−	0.657124i
$367$	−529.617			−1.44310			−0.721548	−	0.692364i	$-0.756569\pi$
$367$	−529.617			−1.44310			−0.721548	+	0.692364i	$0.756569\pi$
$368$	342.928	+	4.16913i	0.931869	+	0.0113292i
$369$			16.2709i			0.0440945i
$370$	177.530	+	119.404i	0.479810	+	0.322713i
$371$	172.013	−	71.2499i	0.463646	−	0.192048i
$372$	256.766	−	253.664i	0.690232	−	0.681892i
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	0.332737	−	0.943020i	$-0.392028\pi$
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	−0.431535	+	0.902096i	$0.642028\pi$
$374$	12.6509	+	2.55641i	0.0338258	+	0.00683531i
$375$	152.601	+	152.601i	0.406935	+	0.406935i
$376$	108.962	−	71.3778i	0.289793	−	0.189835i
$377$	−113.249	−	113.249i	−0.300396	−	0.300396i
$378$	−274.599	+	182.277i	−0.726453	+	0.482213i
$379$	−463.955	−	192.176i	−1.22415	−	0.507061i	−0.325426	−	0.945567i	$-0.605508\pi$
$379$	−463.955	−	192.176i	−1.22415	−	0.507061i	−0.898728	+	0.438506i	$0.855508\pi$
$380$	−179.622	−	441.212i	−0.472689	−	1.16108i
$381$	150.734	−	62.4361i	0.395627	−	0.163874i
$382$	68.8832	+	351.885i	0.180323	+	0.921165i
$383$			304.650i			0.795432i	0.917509	+	0.397716i	$0.130197\pi$
$383$			304.650i			0.795432i	−0.917509	+	0.397716i	$0.869803\pi$
$384$	364.888	−	64.5436i	0.950230	−	0.168082i
$385$	170.380			0.442547
$386$	−353.145	+	69.1299i	−0.914885	+	0.179093i
$387$	−19.2414	−	46.4528i	−0.0497193	−	0.120033i
$388$	−258.986	+	105.436i	−0.667489	+	0.271742i
$389$	−72.6039	+	175.281i	−0.186642	+	0.450594i	−0.989309	−	0.145833i	$-0.953414\pi$
$389$	−72.6039	+	175.281i	−0.186642	+	0.450594i	0.802667	+	0.596428i	$0.203414\pi$
$390$	542.847	+	817.797i	1.39191	+	2.09692i
$391$	26.2382	−	26.2382i	0.0671053	−	0.0671053i
$392$	−61.2830	−	93.5519i	−0.156334	−	0.238653i
$393$	−210.024	+	210.024i	−0.534413	+	0.534413i
$394$	96.5745	−	477.917i	0.245113	−	1.21299i
$395$	66.2209	−	159.871i	0.167648	−	0.404737i
$396$	−6.48998	−	6.56936i	−0.0163888	−	0.0165893i
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	0.991796	−	0.127829i	$-0.0408007\pi$
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	−0.791694	+	0.610917i	$0.790801\pi$
$398$	208.021	−	309.287i	0.522667	−	0.777103i
$399$	264.165			0.662068
$400$	−554.392	−	6.73999i	−1.38598	−	0.0168500i
$401$			58.9969i			0.147124i	0.997291	+	0.0735622i	$0.0234368\pi$
$401$			58.9969i			0.147124i	−0.997291	+	0.0735622i	$0.976563\pi$
$402$	−88.7838	+	132.004i	−0.220855	+	0.328368i
$403$	−632.095	+	261.822i	−1.56847	+	0.649683i
$404$	−0.665998	+	109.566i	−0.00164851	+	0.271203i
$405$	535.471	+	221.800i	1.32215	+	0.547653i
$406$	−17.1050	+	84.6473i	−0.0421305	+	0.208491i
$407$	−36.5089	−	36.5089i	−0.0897025	−	0.0897025i
$408$	22.5772	−	33.1313i	0.0553364	−	0.0812041i
$409$	110.309	+	110.309i	0.269704	+	0.269704i	0.828981	−	0.559277i	$-0.188921\pi$
$409$	110.309	+	110.309i	0.269704	+	0.269704i	−0.559277	+	0.828981i	$0.688921\pi$
$410$	−224.442	−	338.121i	−0.547418	−	0.824685i
$411$	−236.940	−	98.1437i	−0.576496	−	0.238792i
$412$	256.380	−	608.469i	0.622282	−	1.47687i
$413$	−201.798	+	83.5875i	−0.488615	+	0.202391i
$414$	−26.0547	+	5.10034i	−0.0629341	+	0.0123197i
$415$			1030.65i			2.48350i
$416$	−686.747	−	147.485i	−1.65083	−	0.354531i
$417$	−88.0117			−0.211059
$418$	22.0851	+	112.820i	0.0528351	+	0.269905i
$419$	4.61960	+	11.1527i	0.0110253	+	0.0266174i	0.929296	−	0.369335i	$-0.120415\pi$
$419$	4.61960	+	11.1527i	0.0110253	+	0.0266174i	−0.918271	+	0.395952i	$0.870415\pi$
$420$	205.509	−	487.736i	0.489308	−	1.16128i
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	−0.880506	−	0.474036i	$-0.842797\pi$
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	0.957805	+	0.287418i	$0.0927967\pi$
$422$	329.506	−	218.724i	0.780821	−	0.518302i
$423$	−7.13037	+	7.13037i	−0.0168567	+	0.0168567i
$424$	247.296	−	46.8505i	0.583246	−	0.110496i
$425$	−42.4177	+	42.4177i	−0.0998064	+	0.0998064i
$426$	−258.444	−	52.2247i	−0.606676	−	0.122593i
$427$	168.558	−	406.936i	0.394750	−	0.953012i
$428$	−1.37384	+	226.016i	−0.00320991	+	0.528076i
$429$	−90.6492	−	218.847i	−0.211304	−	0.510132i
$430$	1040.62	+	699.905i	2.42005	+	1.62769i
$431$	−201.982			−0.468636			−0.234318	−	0.972160i	$-0.575286\pi$
$431$	−201.982			−0.468636			−0.234318	+	0.972160i	$0.575286\pi$
$432$	−413.684	+	165.491i	−0.957601	+	0.383080i
$433$			643.404i			1.48592i	0.669334	+	0.742961i	$0.266579\pi$
$433$			643.404i			1.48592i	−0.669334	+	0.742961i	$0.733421\pi$
$434$	306.113	+	205.886i	0.705328	+	0.474392i
$435$	150.724	−	62.4318i	0.346491	−	0.143521i
$436$	−211.773	−	214.363i	−0.485718	−	0.491659i
$437$	305.355	+	126.482i	0.698753	+	0.289433i
$438$	−229.135	−	46.3022i	−0.523139	−	0.105713i
$439$	−218.953	−	218.953i	−0.498753	−	0.498753i	0.412296	−	0.911050i	$-0.364727\pi$
$439$	−218.953	−	218.953i	−0.498753	−	0.498753i	−0.911050	+	0.412296i	$0.864727\pi$
$440$	225.485	+	46.9929i	0.512465	+	0.106802i
$441$	6.12194	+	6.12194i	0.0138819	+	0.0138819i
$442$	−63.3180	+	42.0299i	−0.143253	+	0.0950903i
$443$	275.767	+	114.227i	0.622499	+	0.257848i	0.671562	−	0.740948i	$-0.265624\pi$
$443$	275.767	+	114.227i	0.622499	+	0.257848i	−0.0490630	+	0.998796i	$0.515624\pi$
$444$	−148.548	+	60.4753i	−0.334567	+	0.136206i
$445$	615.847	−	255.092i	1.38392	−	0.573240i
$446$	−67.3972	−	344.294i	−0.151115	−	0.771960i
$447$			165.126i			0.369410i
$448$	138.533	+	352.494i	0.309225	+	0.786817i
$449$	−264.162			−0.588334			−0.294167	−	0.955754i	$-0.595042\pi$
$449$	−264.162			−0.588334			−0.294167	+	0.955754i	$0.595042\pi$
$450$	42.1212	−	8.24542i	0.0936026	−	0.0183232i
$451$	37.4792	+	90.4828i	0.0831024	+	0.200627i
$452$	−196.284	−	482.140i	−0.434257	−	1.06668i
$453$	−76.1428	+	183.825i	−0.168086	+	0.405795i
$454$	−456.167	−	687.214i	−1.00477	−	1.51369i
$455$	−709.407	+	709.407i	−1.55914	+	1.55914i
$456$	349.601	+	72.8597i	0.766669	+	0.159780i
$457$	324.484	−	324.484i	0.710030	−	0.710030i	−0.256511	−	0.966541i	$-0.582573\pi$
$457$	324.484	−	324.484i	0.710030	−	0.710030i	0.966541	+	0.256511i	$0.0825731\pi$
$458$	−59.0662	+	292.300i	−0.128966	+	0.638210i
$459$	−18.4483	+	44.5382i	−0.0401925	+	0.0970332i
$460$	471.082	−	465.389i	1.02409	−	1.01172i
$461$	−46.5472	−	112.375i	−0.100970	−	0.243763i	0.865320	−	0.501220i	$-0.167115\pi$
$461$	−46.5472	−	112.375i	−0.100970	−	0.243763i	−0.966290	+	0.257457i	$0.917115\pi$
$462$	−71.2828	+	105.984i	−0.154292	+	0.229402i
$463$	−602.217			−1.30069			−0.650343	−	0.759641i	$-0.725375\pi$
$463$	−602.217			−1.30069			−0.650343	+	0.759641i	$0.725375\pi$
$464$	−45.9837	+	107.306i	−0.0991029	+	0.231263i
$465$		−	696.918i		−	1.49875i
$466$	−434.904	+	646.617i	−0.933271	+	1.38759i
$467$	327.171	−	135.519i	0.700580	−	0.290190i	−0.00382006	−	0.999993i	$-0.501216\pi$
$467$	327.171	−	135.519i	0.700580	−	0.290190i	0.704400	+	0.709803i	$0.251216\pi$
$468$	54.3747	+	0.330517i	0.116185	+	0.000706233i
$469$	−150.221	−	62.2237i	−0.320301	−	0.132673i
$470$	49.8174	−	246.531i	0.105995	−	0.524534i
$471$	−269.477	−	269.477i	−0.572137	−	0.572137i
$472$	−290.118	+	54.9630i	−0.614656	+	0.116447i
$473$	−214.003	−	214.003i	−0.452439	−	0.452439i
$474$	71.7413	+	108.078i	0.151353	+	0.228013i
$475$	−493.650	−	204.477i	−1.03926	−	0.430477i
$476$	37.7630	+	15.9116i	0.0793340	+	0.0334276i
$477$	−18.0014	+	7.45644i	−0.0377389	+	0.0156320i
$478$	123.726	−	24.2201i	0.258842	−	0.0506696i
$479$		−	151.023i		−	0.315289i	−0.987496	−	0.157644i	$-0.949610\pi$
$479$		−	151.023i		−	0.315289i	0.987496	−	0.157644i	$-0.0503900\pi$
$480$	406.498	−	588.798i	0.846871	−	1.22666i
$481$	304.022			0.632062
$482$	74.6796	+	381.495i	0.154937	+	0.791484i
$483$	140.525	+	339.258i	0.290943	+	0.702398i
$484$	394.800	+	166.350i	0.815703	+	0.343699i
$485$	−206.618	+	498.821i	−0.426017	+	1.02850i
$486$	55.6245	−	36.9231i	0.114454	−	0.0759734i
$487$	382.894	−	382.894i	0.786231	−	0.786231i	−0.194643	−	0.980874i	$-0.562355\pi$
$487$	382.894	−	382.894i	0.786231	−	0.786231i	0.980874	+	0.194643i	$0.0623549\pi$
$488$	335.311	−	492.056i	0.687112	−	1.00831i
$489$	−69.6251	+	69.6251i	−0.142383	+	0.142383i
$490$	−211.665	−	42.7719i	−0.431969	−	0.0872895i
$491$	205.776	−	496.786i	0.419095	−	1.01178i	−0.563516	−	0.826105i	$-0.690552\pi$
$491$	205.776	−	496.786i	0.419095	−	1.01178i	0.982610	−	0.185679i	$-0.0594484\pi$
$492$	304.225	+	1.84924i	0.618344	+	0.00375861i
$493$	4.83378	+	11.6698i	0.00980483	+	0.0236709i
$494$	−561.700	−	377.790i	−1.13704	−	0.764758i
$495$	−17.8306			−0.0360215
$496$	348.329	+	356.903i	0.702277	+	0.719563i
$497$		−	269.493i		−	0.542239i
$498$	−641.108	−	431.199i	−1.28737	−	0.865861i
$499$	604.867	−	250.544i	1.21216	−	0.502093i	0.317250	−	0.948342i	$-0.397240\pi$
$499$	604.867	−	250.544i	1.21216	−	0.502093i	0.894909	+	0.446249i	$0.147240\pi$
$500$	−212.129	+	209.566i	−0.424258	+	0.419132i
$501$	524.752	+	217.359i	1.04741	+	0.433851i
$502$	672.834	+	135.962i	1.34031	+	0.270841i
$503$	324.203	+	324.203i	0.644539	+	0.644539i	0.951668	−	0.307129i	$-0.0993682\pi$
$503$	324.203	+	324.203i	0.644539	+	0.644539i	−0.307129	+	0.951668i	$0.599368\pi$
$504$	−16.0661	−	24.5258i	−0.0318772	−	0.0486624i
$505$	149.597	+	149.597i	0.296231	+	0.296231i
$506$	−133.143	+	88.3789i	−0.263128	+	0.174662i
$507$	836.633	+	346.545i	1.65016	+	0.683521i
$508$	85.0016	+	208.793i	0.167326	+	0.411009i
$509$	734.614	−	304.287i	1.44325	−	0.597813i	0.482666	−	0.875805i	$-0.339669\pi$
$509$	734.614	−	304.287i	1.44325	−	0.597813i	0.960584	+	0.277991i	$0.0896686\pi$
$510$	−14.8718	−	75.9715i	−0.0291604	−	0.148964i
$511$		−	238.931i		−	0.467575i
$512$	86.1150	+	504.706i	0.168193	+	0.985754i
$513$	−429.397			−0.837031
$514$	354.778	−	69.4495i	0.690229	−	0.135116i
$515$	−487.886	−	1177.86i	−0.947351	−	2.28711i
$516$	−870.739	+	354.487i	−1.68748	+	0.686990i
$517$	−23.2277	+	56.0766i	−0.0449278	+	0.108465i
$518$	−90.6597	−	136.579i	−0.175019	−	0.263665i
$519$	−373.143	+	373.143i	−0.718966	+	0.718966i
$520$	−1134.51	+	743.180i	−2.18174	+	1.42919i
$521$	−16.7805	+	16.7805i	−0.0322082	+	0.0322082i	−0.723027	−	0.690819i	$-0.757250\pi$
$521$	−16.7805	+	16.7805i	−0.0322082	+	0.0322082i	0.690819	+	0.723027i	$0.257250\pi$
$522$	1.79007	−	8.85850i	0.00342925	−	0.0169703i
$523$	−250.400	+	604.519i	−0.478776	+	1.15587i	0.481407	+	0.876497i	$0.340126\pi$
$523$	−250.400	+	604.519i	−0.478776	+	1.15587i	−0.960183	+	0.279371i	$0.909874\pi$
$524$	−288.426	−	291.953i	−0.550430	−	0.557163i
$525$	−227.179	−	548.459i	−0.432722	−	1.04468i
$526$	−420.877	+	625.762i	−0.800146	+	1.18966i
$527$	53.9589			0.102389
$528$	−123.568	+	120.600i	−0.234031	+	0.228409i
$529$		−	69.5595i		−	0.131492i
$530$	271.228	−	403.263i	0.511752	−	0.760874i
$531$	21.1185	−	8.74759i	0.0397713	−	0.0164738i
$532$	−2.21863	+	364.995i	−0.00417035	+	0.686082i
$533$	−532.791	−	220.689i	−0.999607	−	0.414051i
$534$	−98.9769	+	489.806i	−0.185350	+	0.917239i
$535$	308.593	+	308.593i	0.576809	+	0.576809i
$536$	−181.644	−	123.781i	−0.338887	−	0.230934i
$537$	−99.7121	−	99.7121i	−0.185684	−	0.185684i
$538$	453.524	+	683.232i	0.842981	+	1.26995i
$539$	48.1458	+	19.9427i	0.0893244	+	0.0369994i
$540$	−334.053	+	792.810i	−0.618616	+	1.46817i
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.992781	−	0.119939i	$-0.961730\pi$
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.617192	+	0.786812i	$0.711730\pi$
$542$	635.795	−	124.460i	1.17305	−	0.229631i
$543$		−	372.656i		−	0.686291i
$544$	45.5877	+	31.4731i	0.0838009	+	0.0578550i
$545$	−581.827			−1.06757
$546$	−144.482	−	738.078i	−0.264620	−	1.35179i
$547$	36.1835	+	87.3546i	0.0661489	+	0.159698i	0.953497	−	0.301403i	$-0.0974548\pi$
$547$	36.1835	+	87.3546i	0.0661489	+	0.159698i	−0.887348	+	0.461100i	$0.847455\pi$
$548$	137.595	−	326.554i	0.251085	−	0.595902i
$549$	−17.6400	+	42.5866i	−0.0321311	+	0.0775713i
$550$	215.244	−	142.877i	0.391353	−	0.259777i
$551$	−79.5561	+	79.5561i	−0.144385	+	0.144385i
$552$	92.4026	+	487.739i	0.167396	+	0.883585i
$553$	−93.7536	+	93.7536i	−0.169536	+	0.169536i
$554$	615.101	+	124.296i	1.11029	+	0.224360i
$555$	−118.511	+	286.111i	−0.213534	+	0.515516i
$556$	0.739178	−	121.605i	0.00132946	−	0.218715i
$557$	288.342	+	696.118i	0.517669	+	1.24976i	0.939332	+	0.343010i	$0.111447\pi$
$557$	288.342	+	696.118i	0.517669	+	1.24976i	−0.421663	+	0.906753i	$0.638553\pi$
$558$	−32.0353	−	21.5464i	−0.0574109	−	0.0386136i
$559$	1782.08			3.18797
$560$	672.177	+	288.047i	1.20032	+	0.514370i
$561$			18.6819i			0.0333010i
$562$	−698.987	−	470.127i	−1.24375	−	0.836526i
$563$	−609.320	+	252.389i	−1.08227	+	0.448293i	−0.851306	−	0.524669i	$-0.824189\pi$
$563$	−609.320	+	252.389i	−1.08227	+	0.448293i	−0.230968	+	0.972961i	$0.574189\pi$
$564$	132.510	+	134.131i	0.234947	+	0.237820i
$565$	−928.629	−	384.651i	−1.64359	−	0.680797i
$566$	280.915	+	56.7655i	0.496316	+	0.100292i
$567$	−314.017	−	314.017i	−0.553822	−	0.553822i
$568$	74.3292	−	356.652i	0.130861	−	0.627908i
$569$	256.311	+	256.311i	0.450459	+	0.450459i	0.895507	−	0.445047i	$-0.146813\pi$
$569$	256.311	+	256.311i	0.450459	+	0.450459i	−0.445047	+	0.895507i	$0.646813\pi$
$570$	574.491	−	381.342i	1.00788	−	0.669021i
$571$	346.136	+	143.374i	0.606193	+	0.251094i	0.664600	−	0.747199i	$-0.268602\pi$
$571$	346.136	+	143.374i	0.606193	+	0.251094i	−0.0584066	+	0.998293i	$0.518602\pi$
$572$	303.141	−	123.412i	0.529966	−	0.215754i
$573$	−479.504	+	198.617i	−0.836830	+	0.346626i
$574$	59.7366	+	305.160i	0.104071	+	0.531638i
$575$		−	742.751i		−	1.29174i
$576$	−14.4977	−	36.8892i	−0.0251696	−	0.0640437i
$577$	−354.659			−0.614661			−0.307330	−	0.951603i	$-0.599436\pi$
$577$	−354.659			−0.614661			−0.307330	+	0.951603i	$0.599436\pi$
$578$	−561.352	+	109.887i	−0.971197	+	0.190116i
$579$	−199.328	−	481.221i	−0.344263	−	0.831124i
$580$	84.9958	+	208.778i	0.146544	+	0.359963i
$581$	302.204	−	729.584i	0.520144	−	1.25574i
$582$	−223.843	−	337.219i	−0.384610	−	0.579414i
$583$	−82.9309	+	82.9309i	−0.142249	+	0.142249i
$584$	65.8999	−	316.206i	0.112842	−	0.541448i
$585$	74.2408	−	74.2408i	0.126907	−	0.126907i
$586$	−18.7551	+	92.8132i	−0.0320053	+	0.158384i
$587$	−230.018	+	555.312i	−0.391853	+	0.946018i	0.597683	+	0.801733i	$0.296088\pi$
$587$	−230.018	+	555.312i	−0.391853	+	0.946018i	−0.989536	+	0.144285i	$0.953912\pi$
$588$	115.161	−	113.769i	0.195852	−	0.193485i
$589$	183.926	+	444.038i	0.312269	+	0.753884i
$590$	−318.194	+	473.092i	−0.539312	+	0.801850i
$591$	705.754			1.19417
$592$	−82.3108	−	205.756i	−0.139039	−	0.347560i
$593$			458.661i			0.773460i	0.922193	+	0.386730i	$0.126395\pi$
$593$			458.661i			0.773460i	−0.922193	+	0.386730i	$0.873605\pi$
$594$	115.869	−	172.275i	0.195066	−	0.290025i
$595$	73.1008	−	30.2793i	0.122858	−	0.0508896i
$596$	−228.154	−	1.38683i	−0.382809	−	0.00232690i
$597$	498.454	+	206.467i	0.834932	+	0.345840i
$598$	186.381	−	922.341i	0.311674	−	1.54238i
$599$	265.583	+	265.583i	0.443377	+	0.443377i	0.893145	−	0.449768i	$-0.148493\pi$
$599$	265.583	+	265.583i	0.443377	+	0.443377i	−0.449768	+	0.893145i	$0.648493\pi$
$600$	−149.382	−	788.500i	−0.248970	−	1.31417i
$601$	466.600	+	466.600i	0.776373	+	0.776373i	0.979212	−	0.202839i	$-0.0650168\pi$
$601$	466.600	+	466.600i	0.776373	+	0.776373i	−0.202839	+	0.979212i	$0.565017\pi$
$602$	−531.418	−	800.579i	−0.882754	−	1.32987i
$603$	15.7209	+	6.51182i	0.0260712	+	0.0107990i
$604$	−253.351	−	106.750i	−0.419455	−	0.176738i
$605$	764.246	−	316.561i	1.26322	−	0.523241i
$606$	−155.643	+	30.4678i	−0.256836	+	0.0502769i
$607$		−	90.4302i		−	0.148979i	−0.997222	−	0.0744894i	$-0.976267\pi$
$607$		−	90.4302i		−	0.148979i	0.997222	−	0.0744894i	$-0.0237327\pi$
$608$	−103.606	+	482.430i	−0.170405	+	0.793470i
$609$	−125.001			−0.205256
$610$	−220.872	−	1128.31i	−0.362085	−	1.84968i
$611$	−136.772	−	330.197i	−0.223849	−	0.540420i
$612$	−3.95197	−	1.66517i	−0.00645747	−	0.00272087i
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	−0.863542	−	0.504277i	$-0.831759\pi$
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	0.967194	+	0.254038i	$0.0817589\pi$
$614$	−960.114	+	637.316i	−1.56370	+	1.03797i
$615$	415.376	−	415.376i	0.675408	−	0.675408i
$616$	−145.838	−	99.3812i	−0.236750	−	0.161333i
$617$	181.842	−	181.842i	0.294720	−	0.294720i	−0.544221	−	0.838942i	$-0.683175\pi$
$617$	181.842	−	181.842i	0.294720	−	0.294720i	0.838942	+	0.544221i	$0.183175\pi$
$618$	936.796	+	189.302i	1.51585	+	0.306314i
$619$	−388.636	+	938.250i	−0.627844	+	1.51575i	0.214451	+	0.976735i	$0.431204\pi$
$619$	−388.636	+	938.250i	−0.627844	+	1.51575i	−0.842296	+	0.539016i	$0.818796\pi$
$620$	962.928	+	5.85316i	1.55311	+	0.00944059i
$621$	−228.422	−	551.460i	−0.367829	−	0.888019i
$622$	−900.253	−	605.495i	−1.44735	−	0.973465i
$623$	−510.746			−0.819817
$624$	12.3597	−	1016.64i	0.0198072	−	1.62922i
$625$		−	290.538i		−	0.464860i
$626$	849.988	+	571.688i	1.35781	+	0.913239i
$627$	−153.737	+	63.6798i	−0.245194	+	0.101563i
$628$	374.598	−	370.071i	0.596493	−	0.589285i
$629$	−22.1522	−	9.17573i	−0.0352181	−	0.0145878i
$630$	−55.4906	−	11.2132i	−0.0880803	−	0.0177987i
$631$	−241.593	−	241.593i	−0.382873	−	0.382873i	0.489263	−	0.872136i	$-0.337266\pi$
$631$	−241.593	−	241.593i	−0.382873	−	0.382873i	−0.872136	+	0.489263i	$0.837266\pi$
$632$	−149.934	+	98.2169i	−0.237237	+	0.155407i
$633$	404.793	+	404.793i	0.639484	+	0.639484i
$634$	878.853	−	583.375i	1.38620	−	0.920150i
$635$	402.146	+	166.574i	0.633301	+	0.262322i
$636$	137.371	+	337.430i	0.215992	+	0.530551i
$637$	−283.498	+	117.429i	−0.445051	+	0.184346i
$638$	−10.4505	−	53.3857i	−0.0163801	−	0.0836766i
$639$			28.2029i			0.0441361i
$640$	810.125	+	566.601i	1.26582	+	0.885314i
$641$	−385.038			−0.600684			−0.300342	−	0.953832i	$-0.597101\pi$
$641$	−385.038			−0.600684			−0.300342	+	0.953832i	$0.597101\pi$
$642$	−321.064	+	62.8499i	−0.500100	+	0.0978971i
$643$	144.485	+	348.818i	0.224705	+	0.542486i	0.995518	−	0.0945760i	$-0.0301495\pi$
$643$	144.485	+	348.818i	0.224705	+	0.542486i	−0.770813	+	0.637062i	$0.780150\pi$
$644$	−469.931	+	191.314i	−0.729707	+	0.297071i
$645$	−694.674	+	1677.09i	−1.07701	+	2.60014i
$646$	29.5254	+	44.4800i	0.0457050	+	0.0688544i
$647$	−580.537	+	580.537i	−0.897276	+	0.897276i	−0.995194	−	0.0979186i	$-0.968782\pi$
$647$	−580.537	+	580.537i	−0.897276	+	0.897276i	0.0979186	+	0.995194i	$0.468782\pi$
$648$	−328.967	−	502.186i	−0.507665	−	0.774978i
$649$	97.2911	−	97.2911i	0.149909	−	0.149909i
$650$	−301.311	+	1491.10i	−0.463556	+	2.29399i
$651$	−204.347	+	493.338i	−0.313898	+	0.757816i
$652$	−95.6158	−	96.7853i	−0.146650	−	0.148444i
$653$	−467.055	−	1127.57i	−0.715246	−	1.72676i	−0.686457	−	0.727170i	$-0.740835\pi$
$653$	−467.055	−	1127.57i	−0.715246	−	1.72676i	−0.0287882	−	0.999586i	$-0.509165\pi$
$654$	243.422	−	361.920i	0.372204	−	0.553395i
$655$	−792.423			−1.20981
$656$	−5.11016	+	420.331i	−0.00778988	+	0.640749i
$657$			25.0046i			0.0380587i
$658$	−107.552	+	159.908i	−0.163453	+	0.243022i
$659$	−287.435	+	119.060i	−0.436169	+	0.180667i	−0.589953	−	0.807437i	$-0.700854\pi$
$659$	−287.435	+	119.060i	−0.436169	+	0.180667i	0.153784	+	0.988104i	$0.450854\pi$
$660$	−2.02651	+	333.389i	−0.00307047	+	0.505135i
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.00997082	−	0.999950i	$-0.503174\pi$
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.714122	+	0.700021i	$0.753174\pi$
$662$	−21.2701	+	105.259i	−0.0321301	+	0.159002i
$663$	−77.7851	−	77.7851i	−0.117323	−	0.117323i
$664$	601.170	−	882.194i	0.905376	−	1.32861i
$665$	498.348	+	498.348i	0.749396	+	0.749396i
$666$	9.48771	+	14.2932i	0.0142458	+	0.0214613i
$667$	−144.492	−	59.8505i	−0.216629	−	0.0897309i
$668$	−304.731	+	723.221i	−0.456185	+	1.08267i
$669$	469.160	−	194.332i	0.701285	−	0.290482i
$670$	−416.517	+	81.5352i	−0.621667	+	0.121694i
$671$			277.458i			0.413499i
$672$	−460.399	+	297.610i	−0.685117	+	0.442872i
$673$	831.026			1.23481			0.617405	−	0.786646i	$-0.288184\pi$
$673$	831.026			1.23481			0.617405	+	0.786646i	$0.288184\pi$
$674$	241.165	+	1231.98i	0.357812	+	1.82786i
$675$	369.277	+	891.513i	0.547077	+	1.32076i
$676$	−485.846	+	1153.06i	−0.718707	+	1.70571i
$677$	−16.6301	+	40.1487i	−0.0245644	+	0.0593038i	−0.935686	−	0.352834i	$-0.885218\pi$
$677$	−16.6301	+	40.1487i	−0.0245644	+	0.0593038i	0.911121	+	0.412138i	$0.135218\pi$
$678$	627.783	−	416.717i	0.925933	−	0.614627i
$679$	292.524	−	292.524i	0.430816	−	0.430816i
$680$	105.094	−	19.9102i	0.154550	−	0.0292797i
$681$	844.232	−	844.232i	1.23969	−	1.23969i
$682$	−227.780	−	46.0284i	−0.333988	−	0.0674903i
$683$	411.955	−	994.547i	0.603155	−	1.45614i	−0.267162	−	0.963652i	$-0.586086\pi$
$683$	411.955	−	994.547i	0.603155	−	1.45614i	0.870317	−	0.492493i	$-0.163914\pi$
$684$	0.232183	−	38.1975i	0.000339449	−	0.0558442i
$685$	−261.839	−	632.136i	−0.382247	−	0.922827i
$686$	618.518	+	416.005i	0.901629	+	0.606421i
$687$	−431.648			−0.628309
$688$	−482.479	−	1206.07i	−0.701278	−	1.75301i
$689$		−	690.593i		−	1.00231i
$690$	795.351	+	534.940i	1.15268	+	0.775275i
$691$	657.136	−	272.195i	0.950993	−	0.393914i	0.147389	−	0.989079i	$-0.452913\pi$
$691$	657.136	−	272.195i	0.950993	−	0.393914i	0.803604	+	0.595164i	$0.202913\pi$
$692$	−512.436	−	518.704i	−0.740515	−	0.749572i
$693$	12.6220	+	5.22822i	0.0182136	+	0.00754433i
$694$	−680.333	−	137.478i	−0.980307	−	0.198094i
$695$	−166.034	−	166.034i	−0.238898	−	0.238898i
$696$	−165.429	−	34.4767i	−0.237685	−	0.0495355i
$697$	32.1605	+	32.1605i	0.0461413	+	0.0461413i
$698$	−26.2421	+	17.4193i	−0.0375961	+	0.0249560i
$699$	−1042.10	−	431.653i	−1.49085	−	0.617530i
$700$	759.711	−	309.286i	1.08530	−	0.441837i
$701$	57.0623	−	23.6360i	0.0814012	−	0.0337175i	−0.341611	−	0.939841i	$-0.610973\pi$
$701$	57.0623	−	23.6360i	0.0814012	−	0.0337175i	0.423013	+	0.906124i	$0.360973\pi$
$702$	234.854	+	1199.74i	0.334550	+	1.70903i
$703$		−	213.571i		−	0.303799i
$704$	−165.595	−	171.747i	−0.235220	−	0.243959i
$705$	364.059			0.516396
$706$	−557.083	+	109.052i	−0.789069	+	0.154464i
$707$	−62.0332	−	149.761i	−0.0877414	−	0.211827i
$708$	−161.158	−	395.859i	−0.227625	−	0.559123i
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	−0.996930	−	0.0783041i	$-0.975049\pi$
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	0.760305	+	0.649566i	$0.225049\pi$
$710$	−389.033	−	586.078i	−0.547934	−	0.825461i
$711$	9.81149	−	9.81149i	0.0137996	−	0.0137996i
$712$	−675.931	−	140.869i	−0.949341	−	0.197850i
$713$	−472.421	+	472.421i	−0.662582	+	0.662582i
$714$	−11.7485	+	58.1398i	−0.0164545	+	0.0814282i
$715$	241.845	−	583.865i	0.338245	−	0.816595i
$716$	138.609	−	136.934i	0.193588	−	0.191249i
$717$	69.8358	+	168.598i	0.0973999	+	0.235144i
$718$	−613.127	+	911.600i	−0.853938	+	1.26964i
$719$	1154.30			1.60542			0.802712	−	0.596367i	$-0.203390\pi$
$719$	1154.30			1.60542			0.802712	+	0.596367i	$0.203390\pi$
$720$	−70.3446	−	30.1447i	−0.0977008	−	0.0418676i
$721$			976.846i			1.35485i
$722$	137.552	−	204.513i	0.190515	−	0.283259i
$723$	−519.853	+	215.330i	−0.719022	+	0.297829i
$724$	514.897	+	3.12980i	0.711183	+	0.00432293i
$725$	233.592	+	96.7569i	0.322195	+	0.133458i
$726$	−122.827	+	607.833i	−0.169183	+	0.837236i
$727$	−644.722	−	644.722i	−0.886825	−	0.886825i	0.107392	−	0.994217i	$-0.465750\pi$
$727$	−644.722	−	644.722i	−0.886825	−	0.886825i	−0.994217	+	0.107392i	$0.965750\pi$
$728$	1021.01	−	193.432i	1.40249	−	0.265703i
$729$	545.902	+	545.902i	0.748837	+	0.748837i
$730$	−344.915	−	519.613i	−0.472486	−	0.711799i
$731$	−129.849	−	53.7851i	−0.177632	−	0.0735775i
$732$	794.260	+	334.664i	1.08506	+	0.457191i
$733$	508.297	−	210.544i	0.693448	−	0.287235i	−0.00798801	−	0.999968i	$-0.502543\pi$
$733$	508.297	−	210.544i	0.693448	−	0.287235i	0.701436	+	0.712733i	$0.252543\pi$
$734$	1039.50	−	203.488i	1.41622	−	0.277231i
$735$		−	312.571i		−	0.425267i
$736$	−674.682	+	123.576i	−0.916688	+	0.167902i
$737$	102.424			0.138974
$738$	−6.25155	−	31.9356i	−0.00847094	−	0.0432732i
$739$	−479.243	−	1157.00i	−0.648503	−	1.56562i	−0.814923	−	0.579569i	$-0.803221\pi$
$739$	−479.243	−	1157.00i	−0.648503	−	1.56562i	0.166421	−	0.986055i	$-0.446779\pi$
$740$	−394.323	−	166.149i	−0.532869	−	0.224526i
$741$	374.967	−	905.249i	0.506028	−	1.22166i
$742$	−310.242	+	205.936i	−0.418116	+	0.277542i
$743$	−106.350	+	106.350i	−0.143136	+	0.143136i	−0.775044	−	0.631908i	$-0.782272\pi$
$743$	−106.350	+	106.350i	−0.143136	+	0.143136i	0.631908	+	0.775044i	$0.282272\pi$
$744$	−406.506	+	596.532i	−0.546378	+	0.801790i
$745$	−311.511	+	311.511i	−0.418136	+	0.418136i
$746$	78.1950	+	15.8012i	0.104819	+	0.0211812i
$747$	−31.6262	+	76.3524i	−0.0423376	+	0.102212i
$748$	−25.8127	−	0.156902i	−0.0345089	−	0.000209762i
$749$	−127.964	−	308.932i	−0.170846	−	0.412460i
$750$	−358.148	−	240.885i	−0.477531	−	0.321180i
$751$	−186.540			−0.248389			−0.124195	−	0.992258i	$-0.539635\pi$
$751$	−186.540			−0.248389			−0.124195	+	0.992258i	$0.539635\pi$
$752$	−186.441	+	181.962i	−0.247926	+	0.241970i
$753$			993.594i			1.31951i
$754$	265.792	+	178.768i	0.352510	+	0.237092i
$755$	−490.430	+	203.143i	−0.649577	+	0.269064i
$756$	468.935	−	463.269i	0.620285	−	0.612789i
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.987244	−	0.159214i	$-0.0508959\pi$
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.585506	+	0.810668i	$0.300896\pi$
$758$	984.463	+	198.934i	1.29876	+	0.262446i
$759$	−163.564	−	163.564i	−0.215499	−	0.215499i
$760$	522.073	+	796.974i	0.686939	+	1.04865i
$761$	−1042.65	−	1042.65i	−1.37010	−	1.37010i	−0.860279	−	0.509823i	$-0.829711\pi$
$761$	−1042.65	−	1042.65i	−1.37010	−	1.37010i	−0.509823	−	0.860279i	$-0.670289\pi$
$762$	−271.864	+	180.461i	−0.356777	+	0.236825i
$763$	411.867	+	170.601i	0.539800	+	0.223592i
$764$	−270.401	−	664.196i	−0.353928	−	0.869366i
$765$	−7.65014	+	3.16879i	−0.0100002	+	0.00414221i
$766$	−117.052	−	597.952i	−0.152809	−	0.780616i
$767$			810.175i			1.05629i
$768$	−691.384	+	266.879i	−0.900240	+	0.347499i
$769$	362.542			0.471446			0.235723	−	0.971820i	$-0.424254\pi$
$769$	362.542			0.471446			0.235723	+	0.971820i	$0.424254\pi$
$770$	−334.414	+	65.4631i	−0.434304	+	0.0850170i
$771$	200.250	+	483.445i	0.259727	+	0.627037i
$772$	666.574	−	271.369i	0.863438	−	0.351514i
$773$	259.669	−	626.896i	0.335924	−	0.810991i	−0.662175	−	0.749350i	$-0.730366\pi$
$773$	259.669	−	626.896i	0.335924	−	0.810991i	0.998098	−	0.0616419i	$-0.0196337\pi$
$774$	55.6139	+	83.7822i	0.0718526	+	0.108246i
$775$	763.736	−	763.736i	0.985465	−	0.985465i
$776$	467.814	−	306.451i	0.602853	−	0.394910i
$777$	167.785	−	167.785i	0.215939	−	0.215939i
$778$	75.1570	−	371.928i	0.0966028	−	0.478057i
$779$	−155.031	+	374.278i	−0.199013	+	0.480459i
$780$	−1379.68	−	1396.56i	−1.76882	−	1.79046i
$781$	64.9641	+	156.837i	0.0831807	+	0.200816i
$782$	−41.4177	+	61.5800i	−0.0529639	+	0.0787469i
$783$	203.188			0.259499
$784$	156.227	+	160.073i	0.199270	+	0.204174i
$785$		−	1016.74i		−	1.29521i
$786$	331.530	−	492.920i	0.421794	−	0.627124i
$787$	−148.037	+	61.3188i	−0.188103	+	0.0779147i	−0.474747	−	0.880122i	$-0.657460\pi$
$787$	−148.037	+	61.3188i	−0.188103	+	0.0779147i	0.286644	+	0.958037i	$0.407460\pi$
$788$	−5.92737	+	975.136i	−0.00752204	+	1.23748i
$789$	−1008.49	−	417.731i	−1.27819	−	0.529444i
$790$	−68.5495	+	339.230i	−0.0867715	+	0.429405i
$791$	544.577	+	544.577i	0.688466	+	0.688466i
$792$	15.2622	+	10.4004i	0.0192705	+	0.0131319i
$793$	−1155.24	−	1155.24i	−1.45680	−	1.45680i
$794$	−229.609	−	345.906i	−0.289180	−	0.435649i
$795$	649.909	+	269.201i	0.817495	+	0.338618i
$796$	−289.460	+	686.978i	−0.363643	+	0.863037i
$797$	−173.793	+	71.9875i	−0.218059	+	0.0903231i	−0.489039	−	0.872262i	$-0.662652\pi$
$797$	−173.793	+	71.9875i	−0.218059	+	0.0903231i	0.270980	+	0.962585i	$0.412652\pi$
$798$	−518.489	+	101.497i	−0.649736	+	0.127189i
$799$			28.1873i			0.0352782i
$800$	1090.72	−	199.778i	1.36340	−	0.249722i
$801$	53.4505			0.0667297
$802$	−22.6676	−	115.796i	−0.0282639	−	0.144384i
$803$	57.5968	+	139.051i	0.0717271	+	0.173164i
$804$	123.542	−	293.203i	0.153659	−	0.364680i
$805$	−374.910	+	905.113i	−0.465727	+	1.12436i
$806$	1140.05	−	756.753i	1.41445	−	0.938899i
$807$	−839.340	+	839.340i	−1.04007	+	1.04007i
$808$	−40.7900	−	215.307i	−0.0504827	−	0.266468i
$809$	−679.446	+	679.446i	−0.839859	+	0.839859i	−0.988840	−	0.148981i	$-0.952401\pi$
$809$	−679.446	+	679.446i	−0.839859	+	0.839859i	0.148981	+	0.988840i	$0.452401\pi$
$810$	−1136.21	−	229.599i	−1.40273	−	0.283456i
$811$	4.19630	−	10.1308i	0.00517422	−	0.0124917i	−0.921271	−	0.388921i	$-0.872848\pi$
$811$	4.19630	−	10.1308i	0.00517422	−	0.0124917i	0.926446	+	0.376429i	$0.122848\pi$
$812$	1.04984	−	172.713i	0.00129290	−	0.212701i
$813$	358.866	+	866.379i	0.441410	+	1.06566i
$814$	85.6851	+	57.6304i	0.105264	+	0.0707990i
$815$	−262.696			−0.322326
$816$	−31.5838	+	73.7029i	−0.0387057	+	0.0903222i
$817$		−	1251.88i		−	1.53229i
$818$	−258.891	−	174.126i	−0.316493	−	0.212868i
$819$	−74.3225	+	30.7854i	−0.0907479	+	0.0375890i
$820$	570.434	+	577.411i	0.695651	+	0.704160i
$821$	114.507	+	47.4303i	0.139472	+	0.0577714i	0.451328	−	0.892358i	$-0.350950\pi$
$821$	114.507	+	47.4303i	0.139472	+	0.0577714i	−0.311855	+	0.950130i	$0.600950\pi$
$822$	502.762	+	101.595i	0.611632	+	0.123595i
$823$	701.981	+	701.981i	0.852954	+	0.852954i	0.990496	−	0.137542i	$-0.0439202\pi$
$823$	701.981	+	701.981i	0.852954	+	0.852954i	−0.137542	+	0.990496i	$0.543920\pi$
$824$	−269.425	+	1292.78i	−0.326972	+	1.56890i
$825$	264.424	+	264.424i	0.320514	+	0.320514i
$826$	363.963	−	241.595i	0.440633	−	0.292488i
$827$	−420.620	−	174.226i	−0.508609	−	0.210673i	0.113596	−	0.993527i	$-0.463763\pi$
$827$	−420.620	−	174.226i	−0.508609	−	0.210673i	−0.622205	+	0.782854i	$0.713763\pi$
$828$	49.1792	−	20.0213i	0.0593952	−	0.0241804i
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.859893	−	0.510475i	$-0.829470\pi$
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.247076	+	0.968996i	$0.579470\pi$
$830$	−395.995	−	2022.91i	−0.477102	−	2.43724i
$831$			908.337i			1.09306i
$832$	1404.58	+	25.6157i	1.68819	+	0.0307881i
$833$	24.2008			0.0290526
$834$	172.745	−	33.8156i	0.207128	−	0.0405463i
$835$	579.897	+	1400.00i	0.694487	+	1.67664i
$836$	−86.6949	−	212.952i	−0.103702	−	0.254727i
$837$	332.164	−	801.915i	0.396851	−	0.958083i
$838$	−13.3522	−	20.1150i	−0.0159334	−	0.0240036i
$839$	125.592	−	125.592i	0.149693	−	0.149693i	−0.628288	−	0.777981i	$-0.716244\pi$
$839$	125.592	−	125.592i	0.149693	−	0.149693i	0.777981	+	0.628288i	$0.216244\pi$
$840$	−215.966	+	1036.26i	−0.257102	+	1.23365i
$841$	−557.031	+	557.031i	−0.662344	+	0.662344i
$842$	−33.6876	+	166.709i	−0.0400090	+	0.197992i
$843$	466.613	−	1126.50i	0.553515	−	1.33630i
$844$	−562.701	+	555.901i	−0.666707	+	0.658651i
$845$	924.554	+	2232.07i	1.09415	+	2.64150i
$846$	11.2555	−	16.7347i	0.0133044	−	0.0197810i
$847$	−633.819			−0.748311
$848$	−467.379	+	186.971i	−0.551155	+	0.220485i
$849$			414.835i			0.488616i
$850$	66.9577	−	99.5529i	0.0787737	−	0.117121i
$851$	274.282	−	113.611i	0.322305	−	0.133503i
$852$	527.326	+	3.20535i	0.618927	+	0.00376215i
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.827659	−	0.561232i	$-0.189672\pi$
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.188392	+	0.982094i	$0.439672\pi$
$854$	−174.486	+	863.475i	−0.204316	+	1.01110i
$855$	−52.1531	−	52.1531i	−0.0609978	−	0.0609978i
$856$	−84.1429	−	444.141i	−0.0982977	−	0.518856i
$857$	−559.264	−	559.264i	−0.652584	−	0.652584i	0.301031	−	0.953614i	$-0.402669\pi$
$857$	−559.264	−	559.264i	−0.652584	−	0.652584i	−0.953614	+	0.301031i	$0.902669\pi$
$858$	262.006	+	394.712i	0.305369	+	0.460037i
$859$	552.858	+	229.001i	0.643607	+	0.266591i	0.680522	−	0.732728i	$-0.261753\pi$
$859$	552.858	+	229.001i	0.643607	+	0.266591i	−0.0369150	+	0.999318i	$0.511753\pi$
$860$	−2311.39	−	973.913i	−2.68767	−	1.13246i
$861$	−415.833	+	172.244i	−0.482965	+	0.200051i
$862$	396.440	−	77.6051i	0.459907	−	0.0900291i
$863$		−	106.004i		−	0.122833i	−0.998112	−	0.0614163i	$-0.980438\pi$
$863$		−	106.004i		−	0.122833i	0.998112	−	0.0614163i	$-0.0195617\pi$
$864$	748.372	−	483.761i	0.866172	−	0.559909i
$865$	−1407.87			−1.62760
$866$	−247.207	−	1262.84i	−0.285458	−	1.45825i
$867$	−316.848	−	764.938i	−0.365453	−	0.882281i
$868$	−679.927	−	286.489i	−0.783326	−	0.330057i
$869$	31.9616	−	77.1622i	0.0367798	−	0.0887943i
$870$	−271.845	+	180.448i	−0.312466	+	0.207412i
$871$	−426.460	+	426.460i	−0.489621	+	0.489621i
$872$	498.019	+	339.374i	0.571123	+	0.389190i
$873$	−30.6132	+	30.6132i	−0.0350667	+	0.0350667i
$874$	−647.932	−	130.930i	−0.741340	−	0.149805i
$875$	168.823	−	407.574i	0.192940	−	0.465799i
$876$	467.524	+	2.84185i	0.533703	+	0.00324412i
$877$	135.124	+	326.217i	0.154075	+	0.371969i	0.982003	−	0.188864i	$-0.0604807\pi$
$877$	135.124	+	326.217i	0.154075	+	0.371969i	−0.827928	+	0.560834i	$0.810481\pi$
$878$	513.874	+	345.623i	0.585278	+	0.393649i
$879$	−137.060			−0.155927
$880$	−460.625	−	5.60003i	−0.523437	−	0.00636367i
$881$			628.648i			0.713562i	0.934188	+	0.356781i	$0.116126\pi$
$881$			628.648i			0.713562i	−0.934188	+	0.356781i	$0.883874\pi$
$882$	−14.3680	−	9.66366i	−0.0162902	−	0.0109565i
$883$	816.843	−	338.347i	0.925077	−	0.383179i	0.131268	−	0.991347i	$-0.458095\pi$
$883$	816.843	−	338.347i	0.925077	−	0.383179i	0.793809	+	0.608167i	$0.208095\pi$
$884$	108.129	−	106.822i	0.122317	−	0.120839i
$885$	−762.446	−	315.815i	−0.861521	−	0.356854i
$886$	−585.149	−	118.243i	−0.660439	−	0.133457i
$887$	22.4622	+	22.4622i	0.0253238	+	0.0253238i	0.719655	−	0.694332i	$-0.244300\pi$
$887$	22.4622	+	22.4622i	0.0253238	+	0.0253238i	−0.694332	+	0.719655i	$0.744300\pi$
$888$	268.326	−	175.772i	0.302169	−	0.197942i
$889$	−235.831	−	235.831i	−0.265277	−	0.265277i
$890$	−1110.74	+	737.300i	−1.24802	+	0.828427i
$891$	258.446	+	107.052i	0.290063	+	0.120148i
$892$	264.568	+	649.867i	0.296600	+	0.728551i
$893$	−231.958	+	96.0803i	−0.259752	+	0.107593i
$894$	−63.4443	−	324.101i	−0.0709668	−	0.362529i
$895$		−	376.214i		−	0.420351i
$896$	−407.339	−	638.630i	−0.454619	−	0.712757i
$897$	1362.05			1.51845
$898$	518.483	−	101.496i	0.577376	−	0.113024i
$899$	−87.0327	−	210.116i	−0.0968106	−	0.233721i
$900$	−79.5052	+	32.3674i	−0.0883391	+	0.0359637i
$901$	−20.8429	+	50.3192i	−0.0231331	+	0.0558482i
$902$	−108.327	−	163.195i	−0.120097	−	0.180925i
$903$	983.499	−	983.499i	1.08915	−	1.08915i
$904$	570.503	+	870.904i	0.631087	+	0.963389i
$905$	703.017	−	703.017i	0.776814	−	0.776814i
$906$	78.8204	−	390.058i	0.0869982	−	0.430527i
$907$	554.178	−	1337.90i	0.611001	−	1.47509i	−0.250902	−	0.968012i	$-0.580727\pi$
$907$	554.178	−	1337.90i	0.611001	−	1.47509i	0.861903	−	0.507074i	$-0.169273\pi$
$908$	1159.38	+	1173.56i	1.27685	+	1.29247i
$909$	6.49189	+	15.6728i	0.00714180	+	0.0172418i
$910$	1119.82	−	1664.95i	1.23057	−	1.82962i
$911$	−267.709			−0.293863			−0.146931	−	0.989147i	$-0.546940\pi$
$911$	−267.709			−0.293863			−0.146931	+	0.989147i	$0.546940\pi$
$912$	−714.172	−	8.68252i	−0.783084	−	0.00952031i
$913$			497.447i			0.544849i
$914$	−512.207	+	761.551i	−0.560402	+	0.833207i
$915$	1537.51	−	636.858i	1.68034	−	0.696020i
$916$	3.62526	−	596.406i	0.00395770	−	0.651098i
$917$	560.945	+	232.351i	0.611717	+	0.253382i
$918$	19.0971	−	94.5055i	0.0208029	−	0.102947i
$919$	−191.361	−	191.361i	−0.208227	−	0.208227i	0.595286	−	0.803514i	$-0.297039\pi$
$919$	−191.361	−	191.361i	−0.208227	−	0.208227i	−0.803514	+	0.595286i	$0.797039\pi$
$920$	−745.803	+	1094.44i	−0.810656	+	1.18961i
$921$	−1179.48	−	1179.48i	−1.28066	−	1.28066i
$922$	134.537	+	202.679i	0.145918	+	0.219826i
$923$	−923.507	−	382.529i	−1.00055	−	0.414441i
$924$	99.1895	−	235.407i	0.107348	−	0.254770i
$925$	−443.416	+	183.669i	−0.479368	+	0.198561i
$926$	1182.00	−	231.382i	1.27646	−	0.249873i
$927$		−	102.229i		−	0.110279i
$928$	49.0256	−	228.282i	0.0528294	−	0.245994i
$929$	−459.352			−0.494458			−0.247229	−	0.968957i	$-0.579520\pi$
$929$	−459.352			−0.494458			−0.247229	+	0.968957i	$0.579520\pi$
$930$	267.768	+	1367.87i	0.287923	+	1.47083i
$931$	82.4919	+	199.153i	0.0886057	+	0.213913i
$932$	605.165	−	1436.24i	0.649319	−	1.54103i
$933$	600.970	−	1450.87i	0.644126	−	1.55506i
$934$	−590.085	+	391.694i	−0.631783	+	0.419372i
$935$	−35.2434	+	35.2434i	−0.0376935	+	0.0376935i
$936$	−106.851	+	20.2430i	−0.114157	+	0.0216271i
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	−0.775796	−	0.630984i	$-0.782651\pi$
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	0.630984	+	0.775796i	$0.282651\pi$
$938$	318.754	+	64.4118i	0.339823	+	0.0686692i
$939$	−567.415	+	1369.86i	−0.604276	+	1.45885i
$940$	−3.05760	+	503.019i	−0.00325277	+	0.535126i
$941$	−471.321	−	1137.87i	−0.500873	−	1.20921i	−0.949009	−	0.315249i	$-0.897912\pi$
$941$	−471.321	−	1137.87i	−0.500873	−	1.20921i	0.448136	−	0.893965i	$-0.352088\pi$
$942$	632.452	+	425.377i	0.671393	+	0.451568i
$943$	−563.142			−0.597182
$944$	548.310	−	219.347i	0.580837	−	0.232359i
$945$		−	1272.79i		−	1.34687i
$946$	502.258	+	337.811i	0.530929	+	0.357094i
$947$	300.223	−	124.357i	0.317026	−	0.131316i	−0.218496	−	0.975838i	$-0.570115\pi$
$947$	300.223	−	124.357i	0.317026	−	0.131316i	0.535522	+	0.844521i	$0.320115\pi$
$948$	−182.336	−	184.566i	−0.192337	−	0.194690i
$949$	−818.776	−	339.148i	−0.862778	−	0.357374i
$950$	1047.47	+	211.667i	1.10260	+	0.222807i
$951$	1079.66	+	1079.66i	1.13529	+	1.13529i
$952$	−80.2327	−	16.7212i	−0.0842781	−	0.0175642i
$953$	362.517	+	362.517i	0.380395	+	0.380395i	0.871245	−	0.490849i	$-0.163313\pi$
$953$	362.517	+	362.517i	0.380395	+	0.380395i	−0.490849	+	0.871245i	$0.663313\pi$
$954$	32.4674	−	21.5516i	0.0340329	−	0.0225907i
$955$	−1279.28	−	529.894i	−1.33956	−	0.554863i
$956$	−233.538	+	95.0757i	−0.244287	+	0.0994516i
$957$	72.7471	−	30.1328i	0.0760158	−	0.0314868i
$958$	58.0258	+	296.421i	0.0605697	+	0.309416i
$959$			524.256i			0.546669i
$960$	−571.627	+	1311.84i	−0.595444	+	1.36651i
$961$	−10.5357			−0.0109633
$962$	−596.718	+	116.810i	−0.620289	+	0.121425i
$963$	13.3917	+	32.3304i	0.0139062	+	0.0335725i
$964$	−293.154	−	720.086i	−0.304102	−	0.746977i
$965$	531.792	−	1283.86i	0.551079	−	1.33042i
$966$	−406.164	−	611.886i	−0.420460	−	0.633422i
$967$	642.315	−	642.315i	0.664235	−	0.664235i	−0.292141	−	0.956375i	$-0.594368\pi$
$967$	642.315	−	642.315i	0.664235	−	0.664235i	0.956375	+	0.292141i	$0.0943675\pi$
$968$	−838.808	−	174.815i	−0.866537	−	0.180594i
$969$	−54.6429	+	54.6429i	−0.0563910	+	0.0563910i
$970$	213.884	−	1058.45i	0.220499	−	1.09118i
$971$	114.682	−	276.867i	0.118107	−	0.285136i	−0.853760	−	0.520667i	$-0.825683\pi$
$971$	114.682	−	276.867i	0.118107	−	0.285136i	0.971867	+	0.235532i	$0.0756832\pi$
$972$	−94.9904	+	93.8426i	−0.0977267	+	0.0965458i
$973$	68.8494	+	166.217i	0.0707599	+	0.170830i
$974$	−604.410	+	898.640i	−0.620545	+	0.922628i
$975$	−2201.94			−2.25840
$976$	−469.074	+	1094.61i	−0.480609	+	1.12153i
$977$			1952.32i			1.99828i	0.0414975	+	0.999139i	$0.486787\pi$
$977$			1952.32i			1.99828i	−0.0414975	+	0.999139i	$0.513213\pi$
$978$	109.905	−	163.408i	0.112378	−	0.167083i
$979$	297.240	−	123.121i	0.303616	−	0.125762i
$980$	431.878	+	2.62517i	0.440692	+	0.00267875i
$981$	−43.1027	−	17.8537i	−0.0439375	−	0.0181995i
$982$	−213.012	+	1054.13i	−0.216916	+	1.07345i
$983$	437.102	+	437.102i	0.444661	+	0.444661i	0.893575	−	0.448914i	$-0.148189\pi$
$983$	437.102	+	437.102i	0.444661	+	0.444661i	−0.448914	+	0.893575i	$0.648189\pi$
$984$	−597.828	+	113.259i	−0.607549	+	0.115101i
$985$	1331.41	+	1331.41i	1.35168	+	1.35168i
$986$	−13.9712	−	21.0476i	−0.0141696	−	0.0213465i
$987$	−257.712	−	106.748i	−0.261107	−	0.108154i
$988$	1247.63	+	525.692i	1.26278	+	0.532077i
$989$	1607.75	−	665.952i	1.62563	−	0.673359i
$990$	34.9970	−	6.85084i	0.0353505	−	0.00692004i
$991$			238.251i			0.240415i	0.992749	+	0.120208i	$0.0383560\pi$
$991$			238.251i			0.240415i	−0.992749	+	0.120208i	$0.961644\pi$
$992$	−820.811	−	566.677i	−0.827430	−	0.571247i
$993$	−155.439			−0.156535
$994$	103.544	+	528.946i	0.104169	+	0.532139i
$995$	550.836	+	1329.84i	0.553604	+	1.33652i
$996$	1424.01	+	600.010i	1.42973	+	0.602419i
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	−0.999161	−	0.0409509i	$-0.986961\pi$
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	0.735470	+	0.677557i	$0.236961\pi$
$998$	−1090.94	+	724.156i	−1.09312	+	0.725607i
$999$	−272.732	+	272.732i	−0.273005	+	0.273005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.11.1	yes	28
3.2	odd	2		288.3.u.a.235.7		28
4.3	odd	2		128.3.h.a.79.5		28
8.3	odd	2		256.3.h.a.159.3		28
8.5	even	2		256.3.h.b.159.5		28
32.3	odd	8	inner	32.3.h.a.3.1	✓	28
32.13	even	8		256.3.h.a.95.3		28
32.19	odd	8		256.3.h.b.95.5		28
32.29	even	8		128.3.h.a.47.5		28
96.35	even	8		288.3.u.a.163.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.1	✓	28	32.3	odd	8	inner
32.3.h.a.11.1	yes	28	1.1	even	1	trivial
128.3.h.a.47.5		28	32.29	even	8
128.3.h.a.79.5		28	4.3	odd	2
256.3.h.a.95.3		28	32.13	even	8
256.3.h.a.159.3		28	8.3	odd	2
256.3.h.b.95.5		28	32.19	odd	8
256.3.h.b.159.5		28	8.5	even	2
288.3.u.a.163.7		28	96.35	even	8
288.3.u.a.235.7		28	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96275 + 0.384217i) q^{2} +(-1.10785 - 2.67458i) q^{3} +(3.70475 - 1.50824i) q^{4} +(2.95565 - 7.13556i) q^{5} +(3.20204 + 4.82387i) q^{6} +(-4.18452 + 4.18452i) q^{7} +(-6.69200 + 4.38373i) q^{8} +(0.437918 - 0.437918i) q^{9} +O(q^{10})\)	\(q+(-1.96275 + 0.384217i) q^{2} +(-1.10785 - 2.67458i) q^{3} +(3.70475 - 1.50824i) q^{4} +(2.95565 - 7.13556i) q^{5} +(3.20204 + 4.82387i) q^{6} +(-4.18452 + 4.18452i) q^{7} +(-6.69200 + 4.38373i) q^{8} +(0.437918 - 0.437918i) q^{9} +(-3.05958 + 15.1409i) q^{10} +(1.42655 - 3.44399i) q^{11} +(-8.13821 - 8.23775i) q^{12} +(8.39996 + 20.2793i) q^{13} +(6.60538 - 9.82091i) q^{14} -22.3590 q^{15} +(11.4504 - 11.1753i) q^{16} -1.73115i q^{17} +(-0.691266 + 1.02778i) q^{18} +(14.2459 - 5.90085i) q^{19} +(0.187785 - 30.8933i) q^{20} +(15.8276 + 6.55601i) q^{21} +(-1.47671 + 7.30779i) q^{22} +(15.1565 + 15.1565i) q^{23} +(19.1383 + 13.0418i) q^{24} +(-24.5027 - 24.5027i) q^{25} +(-24.2787 - 36.5757i) q^{26} +(-25.7276 - 10.6567i) q^{27} +(-9.19134 + 21.8139i) q^{28} +(-6.74107 + 2.79224i) q^{29} +(43.8851 - 8.59072i) q^{30} +31.1695i q^{31} +(-18.1805 + 26.3338i) q^{32} -10.7916 q^{33} +(0.665136 + 3.39780i) q^{34} +(17.4909 + 42.2268i) q^{35} +(0.961891 - 2.28286i) q^{36} +(5.30038 - 12.7962i) q^{37} +(-25.6939 + 17.0554i) q^{38} +(44.9327 - 44.9327i) q^{39} +(11.5012 + 60.7079i) q^{40} +(-18.5776 + 18.5776i) q^{41} +(-33.5845 - 6.78655i) q^{42} +(31.0691 - 75.0074i) q^{43} +(0.0906349 - 14.9107i) q^{44} +(-1.83046 - 4.41911i) q^{45} +(-35.5718 - 23.9250i) q^{46} -16.2824 q^{47} +(-42.5746 - 18.2445i) q^{48} +13.9797i q^{49} +(57.5069 + 38.6782i) q^{50} +(-4.63009 + 1.91784i) q^{51} +(61.7059 + 62.4607i) q^{52} +(-29.0670 - 12.0399i) q^{53} +(54.5913 + 11.0315i) q^{54} +(-20.3584 - 20.3584i) q^{55} +(9.65901 - 46.3466i) q^{56} +(-31.5646 - 31.5646i) q^{57} +(12.1582 - 8.07050i) q^{58} +(34.1002 + 14.1248i) q^{59} +(-82.8346 + 33.7228i) q^{60} +(-68.7647 + 28.4833i) q^{61} +(-11.9758 - 61.1778i) q^{62} +3.66495i q^{63} +(25.5658 - 58.6719i) q^{64} +169.531 q^{65} +(21.1812 - 4.14633i) q^{66} +(10.5147 + 25.3846i) q^{67} +(-2.61099 - 6.41347i) q^{68} +(23.7462 - 57.3284i) q^{69} +(-50.5545 - 76.1602i) q^{70} +(-32.2012 + 32.2012i) q^{71} +(-1.01083 + 4.85026i) q^{72} +(-28.5494 + 28.5494i) q^{73} +(-5.48676 + 27.1523i) q^{74} +(-38.3891 + 92.6796i) q^{75} +(43.8777 - 43.3475i) q^{76} +(8.44203 + 20.3809i) q^{77} +(-70.9276 + 105.455i) q^{78} +22.4049 q^{79} +(-45.8989 - 114.735i) q^{80} +75.0427i q^{81} +(29.3252 - 43.6009i) q^{82} +(-123.286 + 51.0669i) q^{83} +(68.5255 + 0.416532i) q^{84} +(-12.3527 - 5.11665i) q^{85} +(-32.1616 + 159.158i) q^{86} +(14.9361 + 14.9361i) q^{87} +(5.55106 + 29.3008i) q^{88} +(61.0281 + 61.0281i) q^{89} +(5.29063 + 7.97031i) q^{90} +(-120.009 - 49.7093i) q^{91} +(79.0109 + 33.2915i) q^{92} +(83.3652 - 34.5310i) q^{93} +(31.9583 - 6.25599i) q^{94} -119.093i q^{95} +(90.5730 + 19.4514i) q^{96} -69.9064 q^{97} +(-5.37122 - 27.4385i) q^{98} +(-0.883474 - 2.13290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Introduction

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