LMFDB - Embedded newform 50.4.e.a.39.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,4,Mod(9,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	50.e (of order $10$, 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:	$2.95009550029$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.3
Character	$\chi$	$=$	50.39
Dual form			50.4.e.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17557 - 1.61803i) q^{2} +(0.234870 + 0.0763140i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(5.37427 - 9.80394i) q^{5} +(-0.152628 - 0.469741i) q^{6} -19.9138i q^{7} +(7.60845 - 2.47214i) q^{8} +(-21.7941 - 15.8344i) q^{9} +O(q^{10})$	\(q+(-1.17557 - 1.61803i) q^{2} +(0.234870 + 0.0763140i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(5.37427 - 9.80394i) q^{5} +(-0.152628 - 0.469741i) q^{6} -19.9138i q^{7} +(7.60845 - 2.47214i) q^{8} +(-21.7941 - 15.8344i) q^{9} +(-22.1809 + 2.82947i) q^{10} +(1.78841 - 1.29936i) q^{11} +(-0.580631 + 0.799170i) q^{12} +(7.23245 - 9.95462i) q^{13} +(-32.2212 + 23.4101i) q^{14} +(2.01043 - 1.89252i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(70.7939 - 23.0023i) q^{17} +53.8780i q^{18} +(15.5949 + 47.9960i) q^{19} +(30.6534 + 32.5633i) q^{20} +(1.51970 - 4.67716i) q^{21} +(-4.20481 - 1.36622i) q^{22} +(117.154 + 161.248i) q^{23} +1.97566 q^{24} +(-67.2344 - 105.378i) q^{25} -24.6092 q^{26} +(-7.82967 - 10.7766i) q^{27} +(75.7565 + 24.6148i) q^{28} +(-74.5475 + 229.434i) q^{29} +(-5.42557 - 1.02816i) q^{30} +(-15.8456 - 48.7679i) q^{31} +32.0000i q^{32} +(0.519204 - 0.168700i) q^{33} +(-120.442 - 87.5061i) q^{34} +(-195.234 - 107.022i) q^{35} +(87.1765 - 63.3374i) q^{36} +(163.473 - 225.001i) q^{37} +(59.3264 - 81.6557i) q^{38} +(2.45836 - 1.78611i) q^{39} +(16.6532 - 87.8787i) q^{40} +(-214.861 - 156.106i) q^{41} +(-9.35431 + 3.03940i) q^{42} +103.714i q^{43} +(2.73245 + 8.40961i) q^{44} +(-272.367 + 128.570i) q^{45} +(123.183 - 379.117i) q^{46} +(391.402 + 127.174i) q^{47} +(-2.32252 - 3.19668i) q^{48} -53.5589 q^{49} +(-91.4664 + 232.667i) q^{50} +18.3828 q^{51} +(28.9298 + 39.8185i) q^{52} +(-409.226 - 132.965i) q^{53} +(-8.23260 + 25.3373i) q^{54} +(-3.12741 - 24.5166i) q^{55} +(-49.2296 - 151.513i) q^{56} +12.4629i q^{57} +(458.867 - 149.095i) q^{58} +(445.750 + 323.856i) q^{59} +(4.71455 + 9.98743i) q^{60} +(413.338 - 300.308i) q^{61} +(-60.2804 + 82.9688i) q^{62} +(-315.322 + 434.003i) q^{63} +(51.7771 - 37.6183i) q^{64} +(-58.7253 - 124.405i) q^{65} +(-0.883322 - 0.641771i) q^{66} +(72.5200 - 23.5632i) q^{67} +297.748i q^{68} +(15.2104 + 46.8129i) q^{69} +(56.3455 + 441.707i) q^{70} +(-264.409 + 813.766i) q^{71} +(-204.964 - 66.5969i) q^{72} +(-303.660 - 417.952i) q^{73} -556.233 q^{74} +(-7.74955 - 29.8811i) q^{75} -201.864 q^{76} +(-25.8751 - 35.6140i) q^{77} +(-5.77996 - 1.87802i) q^{78} +(-42.1044 + 129.584i) q^{79} +(-161.768 + 76.3622i) q^{80} +(223.748 + 688.626i) q^{81} +531.166i q^{82} +(872.626 - 283.533i) q^{83} +(15.9145 + 11.5626i) q^{84} +(154.952 - 817.680i) q^{85} +(167.812 - 121.923i) q^{86} +(-35.0180 + 48.1981i) q^{87} +(10.3949 - 14.3073i) q^{88} +(1053.94 - 765.734i) q^{89} +(528.217 + 289.555i) q^{90} +(-198.234 - 144.026i) q^{91} +(-758.234 + 246.365i) q^{92} -12.6634i q^{93} +(-254.348 - 782.803i) q^{94} +(554.361 + 105.053i) q^{95} +(-2.44205 + 7.51585i) q^{96} +(-422.225 - 137.189i) q^{97} +(62.9623 + 86.6601i) q^{98} -59.5513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9} - 40 q^{10} - 106 q^{11} + 80 q^{12} + 56 q^{14} + 260 q^{15} - 128 q^{16} + 320 q^{17} + 110 q^{19} - 160 q^{20} - 36 q^{21} - 360 q^{22} - 370 q^{23} - 192 q^{24} - 1050 q^{25} + 808 q^{26} - 1200 q^{27} - 120 q^{28} - 10 q^{29} + 160 q^{30} - 486 q^{31} + 2560 q^{33} + 616 q^{34} + 340 q^{35} - 104 q^{36} + 680 q^{37} + 1012 q^{39} + 160 q^{40} - 96 q^{41} - 1020 q^{42} - 136 q^{44} - 1500 q^{45} - 832 q^{46} + 1040 q^{47} + 320 q^{48} - 2076 q^{49} + 400 q^{50} + 884 q^{51} - 2550 q^{53} - 120 q^{54} + 720 q^{55} - 224 q^{56} + 2250 q^{59} + 360 q^{60} + 934 q^{61} + 4200 q^{62} + 4660 q^{63} + 512 q^{64} + 1670 q^{65} + 16 q^{66} - 3780 q^{67} - 628 q^{69} - 2440 q^{70} - 2616 q^{71} - 600 q^{73} - 2584 q^{74} - 4500 q^{75} + 800 q^{76} - 4320 q^{77} - 6640 q^{78} - 2800 q^{79} + 160 q^{80} - 5268 q^{81} + 4050 q^{83} + 624 q^{84} - 1420 q^{85} - 692 q^{86} + 9390 q^{87} - 1680 q^{88} + 4520 q^{89} + 9220 q^{90} + 3764 q^{91} + 1280 q^{92} + 656 q^{94} - 4860 q^{95} - 192 q^{96} + 1710 q^{97} + 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9 - 40 * q^10 - 106 * q^11 + 80 * q^12 + 56 * q^14 + 260 * q^15 - 128 * q^16 + 320 * q^17 + 110 * q^19 - 160 * q^20 - 36 * q^21 - 360 * q^22 - 370 * q^23 - 192 * q^24 - 1050 * q^25 + 808 * q^26 - 1200 * q^27 - 120 * q^28 - 10 * q^29 + 160 * q^30 - 486 * q^31 + 2560 * q^33 + 616 * q^34 + 340 * q^35 - 104 * q^36 + 680 * q^37 + 1012 * q^39 + 160 * q^40 - 96 * q^41 - 1020 * q^42 - 136 * q^44 - 1500 * q^45 - 832 * q^46 + 1040 * q^47 + 320 * q^48 - 2076 * q^49 + 400 * q^50 + 884 * q^51 - 2550 * q^53 - 120 * q^54 + 720 * q^55 - 224 * q^56 + 2250 * q^59 + 360 * q^60 + 934 * q^61 + 4200 * q^62 + 4660 * q^63 + 512 * q^64 + 1670 * q^65 + 16 * q^66 - 3780 * q^67 - 628 * q^69 - 2440 * q^70 - 2616 * q^71 - 600 * q^73 - 2584 * q^74 - 4500 * q^75 + 800 * q^76 - 4320 * q^77 - 6640 * q^78 - 2800 * q^79 + 160 * q^80 - 5268 * q^81 + 4050 * q^83 + 624 * q^84 - 1420 * q^85 - 692 * q^86 + 9390 * q^87 - 1680 * q^88 + 4520 * q^89 + 9220 * q^90 + 3764 * q^91 + 1280 * q^92 + 656 * q^94 - 4860 * q^95 - 192 * q^96 + 1710 * q^97 + 3280 * q^98 - 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.17557	−	1.61803i	−0.415627	−	0.572061i
$2$	−1.17557	−	1.61803i	−0.415627	−	0.572061i
$3$	0.234870	+	0.0763140i	0.0452008	+	0.0146866i	0.331530	−	0.943445i	$-0.392435\pi$
$3$	0.234870	+	0.0763140i	0.0452008	+	0.0146866i	−0.286329	+	0.958131i	$0.592435\pi$
$4$	−1.23607	+	3.80423i	−0.154508	+	0.475528i
$5$	5.37427	−	9.80394i	0.480689	−	0.876891i
$5$	5.37427	−	9.80394i	0.480689	−	0.876891i
$6$	−0.152628	−	0.469741i	−0.0103850	−	0.0319618i
$7$		−	19.9138i		−	1.07524i	−0.843186	−	0.537622i	$-0.819323\pi$
$7$		−	19.9138i		−	1.07524i	0.843186	−	0.537622i	$-0.180677\pi$
$8$	7.60845	−	2.47214i	0.336249	−	0.109254i
$9$	−21.7941	−	15.8344i	−0.807190	−	0.586458i
$10$	−22.1809	+	2.82947i	−0.701423	+	0.0894757i
$11$	1.78841	−	1.29936i	0.0490206	−	0.0356155i	−0.563005	−	0.826453i	$-0.690355\pi$
$11$	1.78841	−	1.29936i	0.0490206	−	0.0356155i	0.612026	+	0.790838i	$0.290355\pi$
$12$	−0.580631	+	0.799170i	−0.0139678	+	0.0192250i
$13$	7.23245	−	9.95462i	0.154302	−	0.212378i	−0.724867	−	0.688889i	$-0.758099\pi$
$13$	7.23245	−	9.95462i	0.154302	−	0.212378i	0.879169	+	0.476511i	$0.158099\pi$
$14$	−32.2212	+	23.4101i	−0.615105	+	0.446900i
$15$	2.01043	−	1.89252i	0.0346061	−	0.0325765i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	70.7939	−	23.0023i	1.01000	−	0.328170i	0.243147	−	0.969989i	$-0.421820\pi$
$17$	70.7939	−	23.0023i	1.01000	−	0.328170i	0.766856	+	0.641820i	$0.221820\pi$
$18$			53.8780i			0.705510i
$19$	15.5949	+	47.9960i	0.188300	+	0.579529i	0.999990	−	0.00456072i	$-0.00145173\pi$
$19$	15.5949	+	47.9960i	0.188300	+	0.579529i	−0.811689	+	0.584089i	$0.801452\pi$
$20$	30.6534	+	32.5633i	0.342716	+	0.364068i
$21$	1.51970	−	4.67716i	0.0157917	−	0.0486019i
$22$	−4.20481	−	1.36622i	−0.0407485	−	0.0132400i
$23$	117.154	+	161.248i	1.06210	+	1.46185i	0.877829	+	0.478974i	$0.158991\pi$
$23$	117.154	+	161.248i	1.06210	+	1.46185i	0.184268	+	0.982876i	$0.441009\pi$
$24$	1.97566			0.0168033
$25$	−67.2344	−	105.378i	−0.537876	−	0.843024i
$26$	−24.6092			−0.185625
$27$	−7.82967	−	10.7766i	−0.0558082	−	0.0768133i
$28$	75.7565	+	24.6148i	0.511309	+	0.166134i
$29$	−74.5475	+	229.434i	−0.477349	+	1.46913i	0.365414	+	0.930845i	$0.380928\pi$
$29$	−74.5475	+	229.434i	−0.477349	+	1.46913i	−0.842763	+	0.538285i	$0.819072\pi$
$30$	−5.42557	−	1.02816i	−0.0330190	−	0.00625717i
$31$	−15.8456	−	48.7679i	−0.0918052	−	0.282547i	0.894603	−	0.446862i	$-0.147459\pi$
$31$	−15.8456	−	48.7679i	−0.0918052	−	0.282547i	−0.986408	+	0.164315i	$0.947459\pi$
$32$			32.0000i			0.176777i
$33$	0.519204	−	0.168700i	0.00273884	−	0.000889903i
$34$	−120.442	−	87.5061i	−0.607517	−	0.441387i
$35$	−195.234	−	107.022i	−0.942871	−	0.516858i
$36$	87.1765	−	63.3374i	0.403595	−	0.293229i
$37$	163.473	−	225.001i	0.726345	−	0.999729i	−0.272944	−	0.962030i	$-0.587997\pi$
$37$	163.473	−	225.001i	0.726345	−	0.999729i	0.999289	−	0.0376986i	$-0.0120027\pi$
$38$	59.3264	−	81.6557i	0.253263	−	0.348587i
$39$	2.45836	−	1.78611i	0.0100937	−	0.00733348i
$40$	16.6532	−	87.8787i	0.0658276	−	0.347371i
$41$	−214.861	−	156.106i	−0.818431	−	0.594625i	0.0978313	−	0.995203i	$-0.468809\pi$
$41$	−214.861	−	156.106i	−0.818431	−	0.594625i	−0.916263	+	0.400578i	$0.868809\pi$
$42$	−9.35431	+	3.03940i	−0.0343667	+	0.0111664i
$43$			103.714i			0.367818i	0.982943	+	0.183909i	$0.0588753\pi$
$43$			103.714i			0.367818i	−0.982943	+	0.183909i	$0.941125\pi$
$44$	2.73245	+	8.40961i	0.00936210	+	0.0288136i
$45$	−272.367	+	128.570i	−0.902267	+	0.425913i
$46$	123.183	−	379.117i	0.394832	−	1.21517i
$47$	391.402	+	127.174i	1.21472	+	0.394686i	0.845156	−	0.534520i	$-0.179507\pi$
$47$	391.402	+	127.174i	1.21472	+	0.394686i	0.369563	+	0.929206i	$0.379507\pi$
$48$	−2.32252	−	3.19668i	−0.00698391	−	0.00961252i
$49$	−53.5589			−0.156148
$50$	−91.4664	+	232.667i	−0.258706	+	0.658081i
$51$	18.3828			0.0504726
$52$	28.9298	+	39.8185i	0.0771508	+	0.106189i
$53$	−409.226	−	132.965i	−1.06059	−	0.344608i	−0.273776	−	0.961793i	$-0.588273\pi$
$53$	−409.226	−	132.965i	−1.06059	−	0.344608i	−0.786818	+	0.617186i	$0.788273\pi$
$54$	−8.23260	+	25.3373i	−0.0207466	+	0.0638514i
$55$	−3.12741	−	24.5166i	−0.00766727	−	0.0601057i
$56$	−49.2296	−	151.513i	−0.117475	−	0.361550i
$57$			12.4629i			0.0289607i
$58$	458.867	−	149.095i	1.03883	−	0.337537i
$59$	445.750	+	323.856i	0.983589	+	0.714619i	0.958508	−	0.285066i	$-0.0920157\pi$
$59$	445.750	+	323.856i	0.983589	+	0.714619i	0.0250809	+	0.999685i	$0.492016\pi$
$60$	4.71455	+	9.98743i	0.0101441	+	0.0214895i
$61$	413.338	−	300.308i	0.867583	−	0.630336i	−0.0623543	−	0.998054i	$-0.519861\pi$
$61$	413.338	−	300.308i	0.867583	−	0.630336i	0.929937	+	0.367718i	$0.119861\pi$
$62$	−60.2804	+	82.9688i	−0.123478	+	0.169952i
$63$	−315.322	+	434.003i	−0.630585	+	0.867925i
$64$	51.7771	−	37.6183i	0.101127	−	0.0734732i
$65$	−58.7253	−	124.405i	−0.112061	−	0.237394i
$66$	−0.883322	−	0.641771i	−0.00164742	−	0.00119692i
$67$	72.5200	−	23.5632i	0.132235	−	0.0429657i	−0.242152	−	0.970238i	$-0.577853\pi$
$67$	72.5200	−	23.5632i	0.132235	−	0.0429657i	0.374387	+	0.927273i	$0.377853\pi$
$68$			297.748i			0.530990i
$69$	15.2104	+	46.8129i	0.0265380	+	0.0816754i
$70$	56.3455	+	441.707i	0.0962082	+	0.754200i
$71$	−264.409	+	813.766i	−0.441965	+	1.36023i	0.443812	+	0.896120i	$0.353626\pi$
$71$	−264.409	+	813.766i	−0.441965	+	1.36023i	−0.885778	+	0.464110i	$0.846374\pi$
$72$	−204.964	−	66.5969i	−0.335490	−	0.109007i
$73$	−303.660	−	417.952i	−0.486859	−	0.670104i	0.492946	−	0.870060i	$-0.335920\pi$
$73$	−303.660	−	417.952i	−0.486859	−	0.670104i	−0.979805	+	0.199956i	$0.935920\pi$
$74$	−556.233			−0.873795
$75$	−7.74955	−	29.8811i	−0.0119312	−	0.0460050i
$76$	−201.864			−0.304676
$77$	−25.8751	−	35.6140i	−0.0382954	−	0.0527090i
$78$	−5.77996	−	1.87802i	−0.00839041	−	0.00272621i
$79$	−42.1044	+	129.584i	−0.0599634	+	0.184549i	−0.976551	−	0.215285i	$-0.930932\pi$
$79$	−42.1044	+	129.584i	−0.0599634	+	0.184549i	0.916588	+	0.399833i	$0.130932\pi$
$80$	−161.768	+	76.3622i	−0.226077	+	0.106719i
$81$	223.748	+	688.626i	0.306925	+	0.944617i
$82$			531.166i			0.715335i
$83$	872.626	−	283.533i	1.15401	−	0.374962i	0.331360	−	0.943504i	$-0.392493\pi$
$83$	872.626	−	283.533i	1.15401	−	0.374962i	0.822654	+	0.568543i	$0.192493\pi$
$84$	15.9145	+	11.5626i	0.0206716	+	0.0150188i
$85$	154.952	−	817.680i	0.197728	−	1.04341i
$86$	167.812	−	121.923i	0.210415	−	0.152875i
$87$	−35.0180	+	48.1981i	−0.0431531	+	0.0593952i
$88$	10.3949	−	14.3073i	0.0125920	−	0.0173314i
$89$	1053.94	−	765.734i	1.25526	−	0.911997i	0.256741	−	0.966480i	$-0.417351\pi$
$89$	1053.94	−	765.734i	1.25526	−	0.911997i	0.998515	+	0.0544837i	$0.0173513\pi$
$90$	528.217	+	289.555i	0.618655	+	0.339131i
$91$	−198.234	−	144.026i	−0.228358	−	0.165912i
$92$	−758.234	+	246.365i	−0.859254	+	0.279189i
$93$		−	12.6634i		−	0.0141197i
$94$	−254.348	−	782.803i	−0.279085	−	0.858936i
$95$	554.361	+	105.053i	0.598697	+	0.113454i
$96$	−2.44205	+	7.51585i	−0.00259625	+	0.00799045i
$97$	−422.225	−	137.189i	−0.441963	−	0.143603i	0.0795779	−	0.996829i	$-0.474643\pi$
$97$	−422.225	−	137.189i	−0.441963	−	0.143603i	−0.521541	+	0.853226i	$0.674643\pi$
$98$	62.9623	+	86.6601i	0.0648995	+	0.0893265i
$99$	−59.5513			−0.0604559
$100$	483.988	−	125.521i	0.483988	−	0.125521i
$101$	−493.360			−0.486051			−0.243025	−	0.970020i	$-0.578140\pi$
$101$	−493.360			−0.486051			−0.243025	+	0.970020i	$0.578140\pi$
$102$	−21.6103	−	29.7440i	−0.0209778	−	0.0288734i
$103$	−1637.03	−	531.904i	−1.56603	−	0.508835i	−0.607623	−	0.794226i	$-0.707877\pi$
$103$	−1637.03	−	531.904i	−1.56603	−	0.508835i	−0.958411	+	0.285391i	$0.907877\pi$
$104$	30.4186	−	93.6188i	0.0286807	−	0.0882700i
$105$	−37.6873	−	40.0353i	−0.0350276	−	0.0372100i
$106$	265.931	+	818.451i	0.243675	+	0.749953i
$107$		−	1241.00i		−	1.12124i	−0.828074	−	0.560618i	$-0.810563\pi$
$107$		−	1241.00i		−	1.12124i	0.828074	−	0.560618i	$-0.189437\pi$
$108$	50.6747	−	16.4652i	0.0451498	−	0.0146700i
$109$	142.969	+	103.873i	0.125632	+	0.0912772i	0.648827	−	0.760936i	$-0.275260\pi$
$109$	142.969	+	103.873i	0.125632	+	0.0912772i	−0.523195	+	0.852213i	$0.675260\pi$
$110$	−35.9922	+	33.8812i	−0.0311974	+	0.0293677i
$111$	55.5657	−	40.3708i	0.0475140	−	0.0345210i
$112$	−187.280	+	257.769i	−0.158003	+	0.217473i
$113$	−112.705	+	155.126i	−0.0938268	+	0.129141i	−0.853349	−	0.521339i	$-0.825433\pi$
$113$	−112.705	+	155.126i	−0.0938268	+	0.129141i	0.759523	+	0.650481i	$0.225433\pi$
$114$	20.1655	−	14.6511i	0.0165673	−	0.0120368i
$115$	2210.48	−	281.976i	1.79242	−	0.228647i
$116$	−780.672	−	567.191i	−0.624858	−	0.453986i
$117$	−315.250	+	102.431i	−0.249101	+	0.0809379i
$118$		−	1101.96i		−	0.859688i
$119$	−458.064	−	1409.77i	−0.352862	−	1.08600i
$120$	10.6177	−	19.3692i	0.00807717	−	0.0147347i
$121$	−409.792	+	1261.21i	−0.307882	+	0.947565i
$122$	−971.817	−	315.762i	−0.721182	−	0.234326i
$123$	−38.5515	−	53.0615i	−0.0282607	−	0.0388975i
$124$	205.110			0.148544
$125$	−1394.46	+	92.8324i	−0.997791	+	0.0664255i
$126$	1072.92			0.758595
$127$	−180.653	−	248.648i	−0.126224	−	0.173732i	0.741228	−	0.671253i	$-0.234244\pi$
$127$	−180.653	−	248.648i	−0.126224	−	0.173732i	−0.867452	+	0.497521i	$0.834244\pi$
$128$	−121.735	−	39.5542i	−0.0840623	−	0.0273135i
$129$	−7.91481	+	24.3593i	−0.00540201	+	0.0166257i
$130$	−132.256	+	241.267i	−0.0892280	+	0.162773i
$131$	868.243	+	2672.18i	0.579074	+	1.78221i	0.621867	+	0.783123i	$0.286374\pi$
$131$	868.243	+	2672.18i	0.579074	+	1.78221i	−0.0427928	+	0.999084i	$0.513626\pi$
$132$			2.18369i			0.00143989i
$133$	955.783	−	310.553i	0.623134	−	0.202469i
$134$	−123.378	−	89.6397i	−0.0795394	−	0.0577887i
$135$	−147.732	+	18.8452i	−0.0941833	+	0.0120143i
$136$	481.767	−	350.024i	0.303759	−	0.220694i
$137$	−1152.57	+	1586.38i	−0.718764	+	0.989293i	0.280800	+	0.959766i	$0.409400\pi$
$137$	−1152.57	+	1586.38i	−0.718764	+	0.989293i	−0.999564	+	0.0295271i	$0.990600\pi$
$138$	57.8639	−	79.6428i	0.0356935	−	0.0491279i
$139$	−1277.07	+	927.849i	−0.779281	+	0.566181i	−0.904763	−	0.425915i	$-0.859952\pi$
$139$	−1277.07	+	927.849i	−0.779281	+	0.566181i	0.125482	+	0.992096i	$0.459952\pi$
$140$	648.458	−	610.426i	0.391462	−	0.368503i
$141$	82.2234	+	59.7388i	0.0491097	+	0.0356803i
$142$	1627.53	−	528.817i	0.961828	−	0.312517i
$143$		−	27.2005i		−	0.0159064i
$144$	133.194	+	409.928i	0.0770797	+	0.237227i
$145$	1848.72	+	1963.90i	1.05881	+	1.12478i
$146$	−319.287	+	982.665i	−0.180989	+	0.557027i
$147$	−12.5794	−	4.08729i	−0.00705803	−	0.00229329i
$148$	653.892	+	900.005i	0.363173	+	0.499864i
$149$	1448.55			0.796443			0.398221	−	0.917289i	$-0.369628\pi$
$149$	1448.55			0.796443			0.398221	+	0.917289i	$0.369628\pi$
$150$	−39.2385	+	47.6664i	−0.0213587	+	0.0259463i
$151$	−1804.96			−0.972754			−0.486377	−	0.873749i	$-0.661682\pi$
$151$	−1804.96			−0.972754			−0.486377	+	0.873749i	$0.661682\pi$
$152$	237.305	+	326.623i	0.126632	+	0.174294i
$153$	−1907.12	−	619.660i	−1.00772	−	0.327428i
$154$	−27.2067	+	83.7336i	−0.0142362	+	0.0438146i
$155$	−563.276	−	106.742i	−0.291893	−	0.0553143i
$156$	3.75605	+	11.5599i	0.00192772	+	0.00593291i
$157$			1998.98i			1.01615i	0.861312	+	0.508076i	$0.169643\pi$
$157$			1998.98i			1.01615i	−0.861312	+	0.508076i	$0.830357\pi$
$158$	259.168	−	84.2087i	0.130495	−	0.0424006i
$159$	−85.9678	−	62.4593i	−0.0428786	−	0.0311531i
$160$	313.726	+	171.977i	0.155014	+	0.0849747i
$161$	3211.06	−	2332.97i	1.57185	−	1.14201i
$162$	851.188	−	1171.56i	0.412813	−	0.568188i
$163$	−288.748	+	397.428i	−0.138752	+	0.190975i	−0.872738	−	0.488189i	$-0.837658\pi$
$163$	−288.748	+	397.428i	−0.138752	+	0.190975i	0.733986	+	0.679164i	$0.237658\pi$
$164$	859.445	−	624.423i	0.409216	−	0.297313i
$165$	1.13642	−	5.99688i	0.000536183	−	0.00282943i
$166$	−1484.60	−	1078.63i	−0.694140	−	0.504323i
$167$	−323.790	+	105.206i	−0.150034	+	0.0487489i	−0.383071	−	0.923719i	$-0.625134\pi$
$167$	−323.790	+	105.206i	−0.150034	+	0.0487489i	0.233037	+	0.972468i	$0.425134\pi$
$168$		−	39.3428i		−	0.0180676i
$169$	632.124	+	1945.48i	0.287722	+	0.885516i
$170$	−1505.19	+	710.523i	−0.679076	+	0.320556i
$171$	420.110	−	1292.97i	0.187875	−	0.578220i
$172$	−394.550	−	128.197i	−0.174908	−	0.0568311i
$173$	1280.29	+	1762.17i	0.562651	+	0.774423i	0.991661	−	0.128877i	$-0.0411372\pi$
$173$	1280.29	+	1762.17i	0.562651	+	0.774423i	−0.429009	+	0.903300i	$0.641137\pi$
$174$	119.152			0.0519133
$175$	−2098.48	+	1338.89i	−0.906456	+	0.578347i
$176$	−35.3696			−0.0151482
$177$	79.9787	+	110.081i	0.0339637	+	0.0467470i
$178$	−2477.97	−	805.141i	−1.04344	−	0.339033i
$179$	1063.04	−	3271.69i	0.443884	−	1.36613i	−0.439820	−	0.898086i	$-0.644958\pi$
$179$	1063.04	−	3271.69i	0.443884	−	1.36613i	0.883703	−	0.468047i	$-0.155042\pi$
$180$	−152.446	−	1195.07i	−0.0631260	−	0.494861i
$181$	−624.898	−	1923.24i	−0.256621	−	0.789797i	−0.993506	−	0.113779i	$-0.963704\pi$
$181$	−624.898	−	1923.24i	−0.256621	−	0.789797i	0.736886	−	0.676018i	$-0.236296\pi$
$182$			490.062i			0.199592i
$183$	119.999	−	38.9899i	0.0484730	−	0.0157498i
$184$	1289.99	+	937.229i	0.516842	+	0.375508i
$185$	−1327.35	−	2811.90i	−0.527507	−	1.11748i
$186$	−20.4898	+	14.8867i	−0.00807732	+	0.00586852i
$187$	96.7204	−	133.124i	0.0378230	−	0.0520588i
$188$	−967.598	+	1331.78i	−0.375369	+	0.516651i
$189$	−214.603	+	155.918i	−0.0825930	+	0.0600074i
$190$	−481.712	−	1020.47i	−0.183932	−	0.389646i
$191$	−3904.88	−	2837.06i	−1.47930	−	1.07478i	−0.977780	−	0.209633i	$-0.932773\pi$
$191$	−3904.88	−	2837.06i	−1.47930	−	1.07478i	−0.501523	−	0.865144i	$-0.667227\pi$
$192$	15.0317	−	4.88409i	0.00565010	−	0.00183583i
$193$		−	3075.17i		−	1.14692i	−0.819233	−	0.573460i	$-0.805601\pi$
$193$		−	3075.17i		−	1.14692i	0.819233	−	0.573460i	$-0.194399\pi$
$194$	274.378	+	844.450i	0.101542	+	0.312515i
$195$	−4.29896	−	33.7007i	−0.00157874	−	0.0123762i
$196$	66.2025	−	203.750i	0.0241263	−	0.0742530i
$197$	4027.34	+	1308.56i	1.45653	+	0.473255i	0.927008	−	0.375042i	$-0.122372\pi$
$197$	4027.34	+	1308.56i	1.45653	+	0.473255i	0.529521	+	0.848297i	$0.322372\pi$
$198$	70.0068	+	96.3561i	0.0251271	+	0.0345845i
$199$	−4126.17			−1.46983			−0.734915	−	0.678159i	$-0.762778\pi$
$199$	−4126.17			−1.46983			−0.734915	+	0.678159i	$0.762778\pi$
$200$	−772.059	−	635.551i	−0.272964	−	0.224701i
$201$	18.8310			0.00660814
$202$	579.979	+	798.273i	0.202016	+	0.278051i
$203$	4568.89	+	1484.52i	1.57967	+	0.513267i
$204$	−22.7224	+	69.9322i	−0.00779845	+	0.0240012i
$205$	−2685.17	+	1267.53i	−0.914833	+	0.431845i
$206$	1063.81	+	3274.06i	0.359801	+	1.10735i
$207$		−	5369.31i		−	1.80287i
$208$	−187.238	+	60.8372i	−0.0624163	+	0.0202803i
$209$	90.2540	+	65.5734i	0.0298708	+	0.0217024i
$210$	−20.4745	+	108.044i	−0.00672798	+	0.0355034i
$211$	4109.67	−	2985.85i	1.34086	−	0.974192i	0.341449	−	0.939900i	$-0.389082\pi$
$211$	4109.67	−	2985.85i	1.34086	−	0.974192i	0.999412	−	0.0342918i	$-0.0109176\pi$
$212$	1011.66	−	1392.43i	0.327742	−	0.451098i
$213$	−124.203	+	170.951i	−0.0399544	+	0.0549925i
$214$	−2007.99	+	1458.89i	−0.641416	+	0.466016i
$215$	1016.80	+	557.386i	0.322537	+	0.176806i
$216$	−86.2129	−	62.6373i	−0.0271576	−	0.0197312i
$217$	−971.153	+	315.547i	−0.303807	+	0.0987129i
$218$		−	353.438i		−	0.109807i
$219$	−39.4251	−	121.338i	−0.0121649	−	0.0374396i
$220$	97.1323	+	18.4068i	0.0297666	+	0.00564084i
$221$	283.034	−	871.089i	0.0861490	−	0.265139i
$222$	−130.643	−	42.4484i	−0.0394962	−	0.0128331i
$223$	2900.73	+	3992.51i	0.871064	+	1.19892i	0.978816	+	0.204740i	$0.0656347\pi$
$223$	2900.73	+	3992.51i	0.871064	+	1.19892i	−0.107752	+	0.994178i	$0.534365\pi$
$224$	637.241			0.190078
$225$	−203.278	+	3361.24i	−0.0602304	+	0.995922i
$226$	383.492			0.112874
$227$	410.391	+	564.855i	0.119994	+	0.165158i	0.864788	−	0.502136i	$-0.167452\pi$
$227$	410.391	+	564.855i	0.119994	+	0.165158i	−0.744794	+	0.667294i	$0.767452\pi$
$228$	−47.4119	−	15.4050i	−0.0137716	−	0.00447467i
$229$	−1916.69	+	5898.95i	−0.553092	+	1.70224i	0.147836	+	0.989012i	$0.452769\pi$
$229$	−1916.69	+	5898.95i	−0.553092	+	1.70224i	−0.700929	+	0.713231i	$0.747231\pi$
$230$	−3054.82	−	3245.15i	−0.875779	−	0.930344i
$231$	−3.35945	−	10.3393i	−0.000956863	−	0.00294492i
$232$			1929.93i			0.546146i
$233$	2599.21	−	844.535i	0.730815	−	0.237456i	0.0801094	−	0.996786i	$-0.474473\pi$
$233$	2599.21	−	844.535i	0.730815	−	0.237456i	0.650706	+	0.759330i	$0.274473\pi$
$234$	536.335	+	389.670i	0.149835	+	0.108861i
$235$	3350.30	−	3153.81i	0.929999	−	0.875455i
$236$	−1783.00	+	1295.43i	−0.491794	+	0.357310i
$237$	−19.7781	+	27.2223i	−0.00542079	+	0.00746108i
$238$	−1742.58	+	2398.45i	−0.474599	+	0.653229i
$239$	−1197.49	+	870.027i	−0.324097	+	0.235470i	−0.737922	−	0.674886i	$-0.764193\pi$
$239$	−1197.49	+	870.027i	−0.324097	+	0.235470i	0.413825	+	0.910357i	$0.364193\pi$
$240$	−43.8219	+	5.59006i	−0.0117862	+	0.00150349i
$241$	−209.377	−	152.121i	−0.0559633	−	0.0406597i	0.559452	−	0.828863i	$-0.311012\pi$
$241$	−209.377	−	152.121i	−0.0559633	−	0.0406597i	−0.615415	+	0.788203i	$0.711012\pi$
$242$	2522.42	−	819.583i	0.670029	−	0.217706i
$243$			538.470i			0.142152i
$244$	631.525	+	1943.63i	0.165694	+	0.509952i
$245$	−287.840	+	525.088i	−0.0750589	+	0.136925i
$246$	−40.5354	+	124.755i	−0.0105059	+	0.0323337i
$247$	590.571	+	191.888i	0.152134	+	0.0494314i
$248$	−241.122	−	331.875i	−0.0617388	−	0.0849762i
$249$	226.591			0.0576693
$250$	1789.49	+	2147.15i	0.452708	+	0.543190i
$251$	−3432.35			−0.863139			−0.431570	−	0.902080i	$-0.642040\pi$
$251$	−3432.35			−0.863139			−0.431570	+	0.902080i	$0.642040\pi$
$252$	−1261.29	−	1736.01i	−0.315292	−	0.433963i
$253$	419.038	+	136.154i	0.104129	+	0.0338336i
$254$	−189.950	+	584.607i	−0.0469234	+	0.144415i
$255$	98.7940	−	180.224i	0.0242617	−	0.0442590i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$			3106.91i			0.754100i	0.926193	+	0.377050i	$0.123061\pi$
$257$			3106.91i			0.754100i	−0.926193	+	0.377050i	$0.876939\pi$
$258$	48.7185	−	15.8296i	0.0117561	−	0.00381980i
$259$	−4480.62	−	3255.36i	−1.07495	−	0.780998i
$260$	545.854	−	69.6309i	0.130202	−	0.0166089i
$261$	5257.63	−	3819.89i	1.24689	−	0.905921i
$262$	3302.99	−	4546.18i	0.778853	−	1.07200i
$263$	−2913.49	+	4010.07i	−0.683092	+	0.940195i	−0.999966	−	0.00827224i	$-0.997367\pi$
$263$	−2913.49	+	4010.07i	−0.683092	+	0.940195i	0.316874	+	0.948468i	$0.397367\pi$
$264$	3.53329	−	2.56708i	0.000823708	−	0.000598459i
$265$	−3502.88	+	3297.43i	−0.812000	+	0.764376i
$266$	−1626.07	−	1181.41i	−0.374816	−	0.272320i
$267$	305.976	−	99.4177i	0.0701327	−	0.0227875i
$268$			305.008i			0.0695200i
$269$	−740.660	−	2279.52i	−0.167877	−	0.516671i	0.831360	−	0.555734i	$-0.187563\pi$
$269$	−740.660	−	2279.52i	−0.167877	−	0.516671i	−0.999237	+	0.0390628i	$0.987563\pi$
$270$	204.162	+	216.882i	0.0460181	+	0.0488852i
$271$	−2005.70	+	6172.92i	−0.449586	+	1.38368i	0.427789	+	0.903879i	$0.359293\pi$
$271$	−2005.70	+	6172.92i	−0.449586	+	1.38368i	−0.877375	+	0.479805i	$0.840707\pi$
$272$	−1132.70	−	368.037i	−0.252501	−	0.0820424i
$273$	−35.5681	−	48.9553i	−0.00788528	−	0.0108532i
$274$	3921.74			0.864674
$275$	−257.166	−	101.098i	−0.0563917	−	0.0221688i
$276$	−196.888			−0.0429393
$277$	−2235.87	−	3077.41i	−0.484983	−	0.667521i	0.494470	−	0.869195i	$-0.335362\pi$
$277$	−2235.87	−	3077.41i	−0.484983	−	0.667521i	−0.979453	+	0.201673i	$0.935362\pi$
$278$	3002.58	+	975.598i	0.647780	+	0.210477i
$279$	−426.866	+	1313.76i	−0.0915978	+	0.281909i
$280$	−1750.00	−	331.628i	−0.373509	−	0.0707807i
$281$	78.9690	+	243.042i	0.0167647	+	0.0515966i	0.959089	−	0.283105i	$-0.0913645\pi$
$281$	78.9690	+	243.042i	0.0167647	+	0.0515966i	−0.942324	+	0.334702i	$0.891364\pi$
$282$		−	203.268i		−	0.0429234i
$283$	1949.66	−	633.484i	0.409525	−	0.133063i	−0.0970075	−	0.995284i	$-0.530927\pi$
$283$	1949.66	−	633.484i	0.409525	−	0.133063i	0.506532	+	0.862221i	$0.330927\pi$
$284$	−2768.92	−	2011.74i	−0.578540	−	0.420334i
$285$	122.186	+	66.9792i	0.0253953	+	0.0139211i
$286$	−44.0113	+	31.9761i	−0.00909945	+	0.00661114i
$287$	−3108.66	+	4278.70i	−0.639367	+	0.880013i
$288$	506.699	−	697.412i	0.103672	−	0.142692i
$289$	507.968	−	369.060i	0.103393	−	0.0751191i
$290$	1004.36	−	5299.99i	0.203372	−	1.07319i
$291$	−88.6986	−	64.4433i	−0.0178681	−	0.0129819i
$292$	1965.33	−	638.574i	0.393878	−	0.127979i
$293$		−	6743.02i		−	1.34448i	−0.740335	−	0.672238i	$-0.765333\pi$
$293$		−	6743.02i		−	1.34448i	0.740335	−	0.672238i	$-0.234667\pi$
$294$	8.17459	+	25.1588i	0.00162160	+	0.00499078i
$295$	5570.65	−	2629.62i	1.09944	−	0.518990i
$296$	687.542	−	2116.04i	0.135009	−	0.415514i
$297$	−28.0053	−	9.09948i	−0.00547150	−	0.00177780i
$298$	−1702.87	−	2343.81i	−0.331023	−	0.455614i
$299$	2452.47			0.474348
$300$	123.253	+	7.45400i	0.0237201	+	0.00143452i
$301$	2065.33			0.395494
$302$	2121.86	+	2920.49i	0.404303	+	0.556475i
$303$	−115.876	−	37.6503i	−0.0219699	−	0.00713845i
$304$	249.518	−	767.937i	0.0470751	−	0.144882i
$305$	−722.808	−	5666.28i	−0.135698	−	1.06377i
$306$	1239.32	+	3814.24i	0.231527	+	0.712566i
$307$		−	4999.71i		−	0.929474i	−0.885449	−	0.464737i	$-0.846149\pi$
$307$		−	4999.71i		−	0.929474i	0.885449	−	0.464737i	$-0.153851\pi$
$308$	167.467	−	54.4134i	0.0309816	−	0.0100665i
$309$	−343.898	−	249.857i	−0.0633129	−	0.0459995i
$310$	489.458	+	1036.88i	0.0896754	+	0.189971i
$311$	−5557.45	+	4037.73i	−1.01329	+	0.736201i	−0.964897	−	0.262627i	$-0.915411\pi$
$311$	−5557.45	+	4037.73i	−1.01329	+	0.736201i	−0.0483961	+	0.998828i	$0.515411\pi$
$312$	14.2889	−	19.6669i	0.00259278	−	0.00356865i
$313$	263.882	−	363.202i	0.0476533	−	0.0655892i	−0.784525	−	0.620097i	$-0.787093\pi$
$313$	263.882	−	363.202i	0.0476533	−	0.0655892i	0.832179	+	0.554508i	$0.187093\pi$
$314$	3234.42	−	2349.94i	0.581301	−	0.422340i
$315$	2560.32	+	5423.85i	0.457961	+	0.970156i
$316$	−440.923	−	320.349i	−0.0784932	−	0.0570286i
$317$	−6369.56	+	2069.60i	−1.12855	+	0.366688i	−0.813025	−	0.582229i	$-0.802181\pi$
$317$	−6369.56	+	2069.60i	−1.12855	+	0.366688i	−0.315525	+	0.948917i	$0.602181\pi$
$318$			212.524i			0.0374772i
$319$	164.795	+	507.186i	0.0289239	+	0.0890186i
$320$	−90.5430	−	709.790i	−0.0158172	−	0.123995i
$321$	94.7059	−	291.475i	0.0164672	−	0.0506808i
$322$	−7549.66	−	2453.03i	−1.30660	−	0.424541i
$323$	2208.04	+	3039.11i	0.380368	+	0.523531i
$324$	−2896.25			−0.496614
$325$	−1535.27	−	92.8485i	−0.262035	−	0.0158471i
$326$	982.496			0.166918
$327$	25.6521	+	35.3071i	0.00433812	+	0.00597091i
$328$	−2020.68	−	656.558i	−0.340162	−	0.110525i
$329$	2532.52	−	7794.29i	0.424384	−	1.30612i
$330$	−11.0391	+	5.21098i	−0.00184146	+	0.000869258i
$331$	−130.339	−	401.141i	−0.0216437	−	0.0666125i	0.939651	−	0.342134i	$-0.111150\pi$
$331$	−130.339	−	401.141i	−0.0216437	−	0.0666125i	−0.961295	+	0.275521i	$0.911150\pi$
$332$			3670.13i			0.606701i
$333$	−7125.50	+	2315.21i	−1.17260	+	0.381000i
$334$	550.865	+	400.227i	0.0902454	+	0.0655672i
$335$	158.730	−	837.617i	0.0258876	−	0.136609i
$336$	−63.6580	+	46.2503i	−0.0103358	+	0.00750940i
$337$	−2683.90	+	3694.07i	−0.433832	+	0.597118i	−0.968827	−	0.247737i	$-0.920313\pi$
$337$	−2683.90	+	3694.07i	−0.433832	+	0.597118i	0.534996	+	0.844855i	$0.320313\pi$
$338$	2404.74	−	3309.85i	0.386985	−	0.532639i
$339$	−38.3094	+	27.8334i	−0.00613770	+	0.00445930i
$340$	2919.11	+	1600.18i	0.465620	+	0.255241i
$341$	−91.7054	−	66.6279i	−0.0145634	−	0.0105809i
$342$	−2585.93	+	840.220i	−0.408863	+	0.132848i
$343$		−	5763.87i		−	0.907346i
$344$	256.394	+	789.101i	0.0401856	+	0.123679i
$345$	540.695	+	102.463i	0.0843770	+	0.0159896i
$346$	1346.18	−	4143.11i	0.209165	−	0.643742i
$347$	5841.24	+	1897.93i	0.903672	+	0.293621i	0.723752	−	0.690060i	$-0.242416\pi$
$347$	5841.24	+	1897.93i	0.903672	+	0.293621i	0.179920	+	0.983681i	$0.442416\pi$
$348$	−140.072	−	192.793i	−0.0215766	−	0.0296976i
$349$	7456.55			1.14367			0.571834	−	0.820369i	$-0.306232\pi$
$349$	7456.55			1.14367			0.571834	+	0.820369i	$0.306232\pi$
$350$	4633.28	+	1821.44i	0.707598	+	0.278172i
$351$	−163.905			−0.0249248
$352$	41.5794	+	57.2292i	0.00629600	+	0.00866569i
$353$	−6281.74	−	2041.06i	−0.947149	−	0.307747i	−0.205592	−	0.978638i	$-0.565912\pi$
$353$	−6281.74	−	2041.06i	−0.947149	−	0.307747i	−0.741557	+	0.670890i	$0.765912\pi$
$354$	84.0946	−	258.816i	0.0126259	−	0.0388586i
$355$	6557.11	+	6965.65i	0.980325	+	1.04140i
$356$	1610.28	+	4955.94i	0.239732	+	0.737821i
$357$		−	366.071i		−	0.0542704i
$358$	−6543.39	+	2126.08i	−0.966002	+	0.313873i
$359$	861.031	+	625.575i	0.126583	+	0.0919683i	0.649275	−	0.760553i	$-0.275072\pi$
$359$	861.031	+	625.575i	0.126583	+	0.0919683i	−0.522692	+	0.852522i	$0.675072\pi$
$360$	−1754.44	+	1651.55i	−0.256854	+	0.241789i
$361$	3488.63	−	2534.64i	0.508620	−	0.369534i
$362$	−2377.25	+	3272.01i	−0.345154	+	0.475063i
$363$	−192.496	+	264.948i	−0.0278331	+	0.0383089i
$364$	792.937	−	576.102i	0.114179	−	0.0829559i
$365$	−5729.53	+	730.877i	−0.821637	+	0.104811i
$366$	−204.154	−	148.326i	−0.0291565	−	0.0211835i
$367$	1534.79	−	498.684i	0.218298	−	0.0709295i	−0.197826	−	0.980237i	$-0.563388\pi$
$367$	1534.79	−	498.684i	0.218298	−	0.0709295i	0.416124	+	0.909308i	$0.363388\pi$
$368$		−	3189.02i		−	0.451737i
$369$	2210.88	+	6804.38i	0.311907	+	0.959951i
$370$	−2989.35	+	5453.28i	−0.420024	+	0.766223i
$371$	−2647.85	+	8149.23i	−0.370537	+	1.14040i
$372$	48.1743	+	15.6528i	0.00671430	+	0.00218161i
$373$	−4387.88	−	6039.40i	−0.609105	−	0.838360i	0.387399	−	0.921912i	$-0.373374\pi$
$373$	−4387.88	−	6039.40i	−0.609105	−	0.838360i	−0.996503	+	0.0835517i	$0.973374\pi$
$374$	−329.101			−0.0455011
$375$	−334.601	−	84.6129i	−0.0460765	−	0.0116517i
$376$	3292.35			0.451569
$377$	1744.76	+	2401.46i	0.238355	+	0.328068i
$378$	504.562	+	163.942i	0.0686558	+	0.0223076i
$379$	2315.82	−	7127.35i	0.313867	−	0.965982i	−0.662352	−	0.749193i	$-0.730442\pi$
$379$	2315.82	−	7127.35i	0.313867	−	0.965982i	0.976218	−	0.216789i	$-0.0695584\pi$
$380$	−1084.87	+	1979.06i	−0.146455	+	0.267168i
$381$	−23.4548	−	72.1864i	−0.00315387	−	0.00970662i
$382$			9653.39i			1.29296i
$383$	−4177.01	+	1357.19i	−0.557272	+	0.181069i	−0.574093	−	0.818790i	$-0.694645\pi$
$383$	−4177.01	+	1357.19i	−0.557272	+	0.181069i	0.0168213	+	0.999859i	$0.494645\pi$
$384$	−25.5734	−	18.5802i	−0.00339854	−	0.00246918i
$385$	−488.218	+	62.2786i	−0.0646283	+	0.00824418i
$386$	−4975.73	+	3615.08i	−0.656109	+	0.476691i
$387$	1642.24	−	2260.35i	0.215710	−	0.296899i
$388$	1043.80	−	1436.66i	0.136574	−	0.187978i
$389$	4663.78	−	3388.43i	0.607874	−	0.441646i	−0.240791	−	0.970577i	$-0.577407\pi$
$389$	4663.78	−	3388.43i	0.607874	−	0.441646i	0.848665	+	0.528931i	$0.177407\pi$
$390$	−49.4751	+	46.5734i	−0.00642377	+	0.00604701i
$391$	12002.8	+	8720.58i	1.55246	+	1.12792i
$392$	−407.500	+	132.405i	−0.0525048	+	0.0170598i
$393$			693.874i			0.0890618i
$394$	−2617.13	−	8054.68i	−0.334642	−	1.02992i
$395$	1044.15	+	1109.21i	0.133005	+	0.141292i
$396$	73.6095	−	226.547i	0.00934095	−	0.0287485i
$397$	1519.36	+	493.669i	0.192076	+	0.0624094i	0.403476	−	0.914990i	$-0.367802\pi$
$397$	1519.36	+	493.669i	0.192076	+	0.0624094i	−0.211399	+	0.977400i	$0.567802\pi$
$398$	4850.60	+	6676.28i	0.610901	+	0.840833i
$399$	248.184			0.0311398
$400$	−120.734	+	1996.35i	−0.0150917	+	0.249544i
$401$	−4722.70			−0.588130			−0.294065	−	0.955785i	$-0.595008\pi$
$401$	−4722.70			−0.588130			−0.294065	+	0.955785i	$0.595008\pi$
$402$	−22.1372	−	30.4692i	−0.00274652	−	0.00378026i
$403$	−600.068	−	194.974i	−0.0741725	−	0.0241001i
$404$	609.826	−	1876.85i	0.0750990	−	0.231131i
$405$	7953.72	+	1507.25i	0.975861	+	0.184928i
$406$	−2969.05	−	9137.79i	−0.362934	−	1.11700i
$407$		−	614.804i		−	0.0748764i
$408$	139.864	−	45.4447i	0.0169714	−	0.00551434i
$409$	4715.79	+	3426.22i	0.570124	+	0.414219i	0.835150	−	0.550022i	$-0.185381\pi$
$409$	4715.79	+	3426.22i	0.570124	+	0.414219i	−0.265026	+	0.964241i	$0.585381\pi$
$410$	5207.52	+	2854.63i	0.627271	+	0.343854i
$411$	−391.767	+	284.635i	−0.0470181	+	0.0341606i
$412$	4046.96	−	5570.17i	0.483931	−	0.666074i
$413$	6449.21	−	8876.57i	0.768389	−	1.05760i
$414$	−8687.73	+	6312.01i	−1.03135	+	0.749319i
$415$	1909.98	−	10079.0i	0.225922	−	1.19218i
$416$	318.548	+	231.438i	0.0375435	+	0.0272769i
$417$	−370.755	+	120.466i	−0.0435394	+	0.0141468i
$418$		−	223.120i		−	0.0261080i
$419$	−351.782	−	1082.68i	−0.0410160	−	0.126234i	0.928452	−	0.371453i	$-0.121140\pi$
$419$	−351.782	−	1082.68i	−0.0410160	−	0.126234i	−0.969468	+	0.245219i	$0.921140\pi$
$420$	198.888	−	93.8845i	0.0231065	−	0.0109074i
$421$	−317.103	+	975.942i	−0.0367094	+	0.112980i	−0.967732	−	0.251982i	$-0.918918\pi$
$421$	−317.103	+	975.942i	−0.0367094	+	0.112980i	0.931023	+	0.364961i	$0.118918\pi$
$422$	−9662.42	−	3139.51i	−1.11460	−	0.362154i
$423$	−6516.53	−	8969.24i	−0.749042	−	1.03097i
$424$	−3442.28			−0.394274
$425$	−7183.73	−	5913.57i	−0.819911	−	0.674942i
$426$	422.615			0.0480652
$427$	−5980.27	−	8231.13i	−0.677765	−	0.932863i
$428$	4721.06	+	1533.96i	0.533180	+	0.173241i
$429$	2.07578	−	6.38859i	0.000233612	−	0.000718983i
$430$	−293.455	−	2300.47i	−0.0329108	−	0.257996i
$431$	−1729.47	−	5322.77i	−0.193285	−	0.594870i	−0.999992	−	0.00391889i	$-0.998753\pi$
$431$	−1729.47	−	5322.77i	−0.193285	−	0.594870i	0.806707	−	0.590951i	$-0.201247\pi$
$432$			213.130i			0.0237366i
$433$	835.639	−	271.516i	0.0927443	−	0.0301344i	−0.262277	−	0.964993i	$-0.584474\pi$
$433$	835.639	−	271.516i	0.0927443	−	0.0301344i	0.355022	+	0.934858i	$0.384474\pi$
$434$	1652.22	+	1200.41i	0.182740	+	0.132769i
$435$	284.335	+	602.344i	0.0313399	+	0.0663912i
$436$	−571.875	+	415.491i	−0.0628161	+	0.0456386i
$437$	−5912.28	+	8137.55i	−0.647191	+	0.890782i
$438$	−149.982	+	206.433i	−0.0163617	+	0.0225199i
$439$	−5667.04	+	4117.35i	−0.616112	+	0.447632i	−0.851561	−	0.524255i	$-0.824344\pi$
$439$	−5667.04	+	4117.35i	−0.616112	+	0.447632i	0.235449	+	0.971887i	$0.424344\pi$
$440$	−84.4030	−	178.802i	−0.00914490	−	0.0193728i
$441$	1167.27	+	848.071i	0.126041	+	0.0915744i
$442$	−1742.18	+	566.068i	−0.187482	+	0.0609166i
$443$			17736.5i			1.90223i	0.308839	+	0.951114i	$0.400060\pi$
$443$			17736.5i			1.90223i	−0.308839	+	0.951114i	$0.599940\pi$
$444$	84.8968	+	261.285i	0.00907437	+	0.0279281i
$445$	−1843.04	−	14448.1i	−0.196334	−	1.53911i
$446$	3050.01	−	9386.97i	0.323816	−	0.996605i
$447$	340.222	+	110.545i	0.0359999	+	0.0116971i
$448$	−749.122	−	1031.08i	−0.0790015	−	0.108736i
$449$	−4292.26			−0.451146			−0.225573	−	0.974226i	$-0.572425\pi$
$449$	−4292.26			−0.451146			−0.225573	+	0.974226i	$0.572425\pi$
$450$	5677.56	−	3622.46i	0.594762	−	0.379476i
$451$	−587.097			−0.0612979
$452$	−450.821	−	620.502i	−0.0469134	−	0.0645707i
$453$	−423.932	−	137.744i	−0.0439692	−	0.0142865i
$454$	431.511	−	1328.05i	0.0446075	−	0.137288i
$455$	−2477.38	+	1169.44i	−0.255256	+	0.120493i
$456$	30.8101	+	94.8237i	0.00316407	+	0.00973800i
$457$		−	17409.6i		−	1.78203i	−0.453973	−	0.891015i	$-0.649994\pi$
$457$		−	17409.6i		−	1.78203i	0.453973	−	0.891015i	$-0.350006\pi$
$458$	11797.9	−	3833.37i	1.20367	−	0.391095i
$459$	−802.180	−	582.818i	−0.0815742	−	0.0592671i
$460$	−1659.61	+	8757.72i	−0.168216	+	0.887675i
$461$	−11842.5	+	8604.09i	−1.19644	+	0.869267i	−0.993930	−	0.110012i	$-0.964911\pi$
$461$	−11842.5	+	8604.09i	−1.19644	+	0.869267i	−0.202513	+	0.979279i	$0.564911\pi$
$462$	−12.7801	+	17.5903i	−0.00128698	+	0.00177137i
$463$	−4434.07	+	6102.97i	−0.445072	+	0.612590i	−0.971330	−	0.237736i	$-0.923595\pi$
$463$	−4434.07	+	6102.97i	−0.445072	+	0.612590i	0.526258	+	0.850325i	$0.323595\pi$
$464$	3122.69	−	2268.77i	0.312429	−	0.226993i
$465$	−124.151	−	68.0563i	−0.0123814	−	0.00678718i
$466$	−4422.04	−	3212.80i	−0.439586	−	0.319378i
$467$	3355.89	−	1090.40i	0.332532	−	0.108046i	−0.137992	−	0.990433i	$-0.544065\pi$
$467$	3355.89	−	1090.40i	0.332532	−	0.108046i	0.470524	+	0.882387i	$0.344065\pi$
$468$		−	1325.89i		−	0.130960i
$469$	−469.232	−	1444.15i	−0.0461986	−	0.142185i
$470$	−9041.49	−	1713.38i	−0.887347	−	0.168154i
$471$	−152.550	+	469.501i	−0.0149239	+	0.0459309i
$472$	4192.09	+	1362.09i	0.408806	+	0.132829i
$473$	134.761	+	185.483i	0.0131001	+	0.0180307i
$474$	67.2971			0.00652122
$475$	4009.22	−	4870.34i	0.387275	−	0.470456i
$476$	5929.30			0.570943
$477$	6813.29	+	9377.69i	0.654002	+	0.900157i
$478$	2815.47	+	914.801i	0.269407	+	0.0875356i
$479$	−2295.73	+	7065.53i	−0.218987	+	0.673971i	0.779860	+	0.625954i	$0.215290\pi$
$479$	−2295.73	+	7065.53i	−0.218987	+	0.673971i	−0.998847	+	0.0480172i	$0.984710\pi$
$480$	60.5607	+	64.3339i	0.00575876	+	0.00611755i
$481$	−1057.49	−	3254.62i	−0.100244	−	0.308520i
$482$			517.608i			0.0489137i
$483$	932.221	−	302.897i	0.0878210	−	0.0285348i
$484$	−4291.39	−	3117.88i	−0.403023	−	0.292814i
$485$	−3614.15	+	3402.18i	−0.338371	+	0.318526i
$486$	871.262	−	633.009i	0.0813195	−	0.0590820i
$487$	8239.35	−	11340.5i	0.766654	−	1.05521i	−0.229977	−	0.973196i	$-0.573865\pi$
$487$	8239.35	−	11340.5i	0.766654	−	1.05521i	0.996631	−	0.0820130i	$-0.0261349\pi$
$488$	2402.46	−	3306.71i	0.222857	−	0.306737i
$489$	−98.1477	+	71.3085i	−0.00907647	+	0.00659444i
$490$	1187.99	−	151.543i	0.109526	−	0.0139715i
$491$	2914.25	+	2117.33i	0.267858	+	0.194610i	0.713604	−	0.700549i	$-0.247062\pi$
$491$	2914.25	+	2117.33i	0.267858	+	0.194610i	−0.445746	+	0.895159i	$0.647062\pi$
$492$	249.510	−	81.0708i	0.0228634	−	0.00742877i
$493$			17957.3i			1.64048i
$494$	−383.776	−	1181.14i	−0.0349533	−	0.107575i
$495$	−320.045	+	583.838i	−0.0290605	+	0.0530132i
$496$	−253.530	+	780.286i	−0.0229513	+	0.0706368i
$497$	16205.2	+	5265.38i	1.46258	+	0.475220i
$498$	−266.374	−	366.633i	−0.0239689	−	0.0329904i
$499$	−4905.02			−0.440037			−0.220019	−	0.975496i	$-0.570612\pi$
$499$	−4905.02			−0.440037			−0.220019	+	0.975496i	$0.570612\pi$
$500$	1370.49	−	5419.57i	0.122580	−	0.484741i
$501$	−84.0774			−0.00749760
$502$	4034.97	+	5553.66i	0.358744	+	0.493769i
$503$	15448.4	+	5019.49i	1.36940	+	0.444946i	0.899171	−	0.437597i	$-0.144170\pi$
$503$	15448.4	+	5019.49i	1.36940	+	0.444946i	0.470232	+	0.882543i	$0.344170\pi$
$504$	−1326.20	+	4081.61i	−0.117209	+	0.360733i
$505$	−2651.45	+	4836.87i	−0.233640	+	0.426214i
$506$	−272.307	−	838.076i	−0.0239240	−	0.0736304i
$507$			505.175i			0.0442517i
$508$	1169.21	−	379.901i	0.102117	−	0.0331798i
$509$	11603.2	+	8430.21i	1.01042	+	0.734111i	0.964297	−	0.264825i	$-0.0853141\pi$
$509$	11603.2	+	8430.21i	1.01042	+	0.734111i	0.0461207	+	0.998936i	$0.485314\pi$
$510$	−407.747	+	52.0135i	−0.0354027	+	0.00451607i
$511$	−8323.01	+	6047.02i	−0.720525	+	0.523492i
$512$	300.946	−	414.217i	0.0259767	−	0.0357538i
$513$	395.132	−	543.853i	0.0340068	−	0.0468064i
$514$	5027.08	−	3652.39i	0.431391	−	0.313424i
$515$	−14012.6	+	13190.8i	−1.19897	+	1.12865i
$516$	−82.8849	−	60.2194i	−0.00707133	−	0.00513762i
$517$	865.232	−	281.131i	0.0736032	−	0.0239151i
$518$			11076.7i			0.939542i
$519$	166.224	+	511.585i	0.0140586	+	0.0432680i
$520$	−754.356	−	801.355i	−0.0636167	−	0.0675803i
$521$	3425.75	−	10543.4i	0.288071	−	0.886591i	−0.697390	−	0.716692i	$-0.745656\pi$
$521$	3425.75	−	10543.4i	0.288071	−	0.886591i	0.985461	−	0.169900i	$-0.0543444\pi$
$522$	−12361.4	−	4016.47i	−1.03649	−	0.336774i
$523$	−9.68700	−	13.3330i	−0.000809910	−	0.00111475i	0.808612	−	0.588342i	$-0.200219\pi$
$523$	−9.68700	−	13.3330i	−0.000809910	−	0.00111475i	−0.809422	+	0.587228i	$0.800219\pi$
$524$	−11238.8			−0.936962
$525$	−595.046	+	154.323i	−0.0494665	+	0.0128290i
$526$	9913.43			0.821761
$527$	−2243.55	−	3087.98i	−0.185447	−	0.255246i
$528$	−8.30726	−	2.69919i	−0.000684710	−	0.000222476i
$529$	−8516.18	+	26210.1i	−0.699941	+	2.15420i
$530$	9453.23	+	1791.41i	0.774759	+	0.146818i
$531$	−4586.67	−	14116.3i	−0.374849	−	1.15367i
$532$			4019.88i			0.327601i
$533$	−3107.95	+	1009.83i	−0.252571	+	0.0820652i
$534$	−520.558	−	378.207i	−0.0421849	−	0.0306491i
$535$	−12166.7	−	6669.49i	−0.983202	−	0.538967i
$536$	493.514	−	358.559i	0.0397697	−	0.0288944i
$537$	499.352	−	687.299i	0.0401278	−	0.0552312i
$538$	−2817.64	+	3878.15i	−0.225794	+	0.310778i
$539$	−95.7854	+	69.5921i	−0.00765448	+	0.00556131i
$540$	110.916	−	585.300i	0.00883897	−	0.0466431i
$541$	19911.1	+	14466.2i	1.58233	+	1.14963i	0.913957	+	0.405811i	$0.133011\pi$
$541$	19911.1	+	14466.2i	1.58233	+	1.14963i	0.668378	+	0.743822i	$0.266989\pi$
$542$	12345.8	−	4011.41i	0.978413	−	0.317905i
$543$		−	499.400i		−	0.0394683i
$544$	736.075	+	2265.40i	0.0580128	+	0.178545i
$545$	1786.71	−	843.415i	0.140430	−	0.0662898i
$546$	−37.3986	+	115.101i	−0.00293134	+	0.00902173i
$547$	−5056.52	−	1642.96i	−0.395249	−	0.128424i	0.104647	−	0.994509i	$-0.466629\pi$
$547$	−5056.52	−	1642.96i	−0.395249	−	0.128424i	−0.499897	+	0.866085i	$0.666629\pi$
$548$	−4610.28	−	6345.50i	−0.359382	−	0.494647i
$549$	−13763.5			−1.06997
$550$	138.738	+	534.952i	0.0107560	+	0.0414735i
$551$	−12174.5			−0.941288
$552$	231.455	+	318.571i	0.0178467	+	0.0245639i
$553$	2580.51	+	838.458i	0.198435	+	0.0644753i
$554$	−2350.93	+	7235.42i	−0.180291	+	0.554880i
$555$	−97.1681	−	761.726i	−0.00743164	−	0.0582585i
$556$	−1951.20	−	6005.17i	−0.148829	−	0.458050i
$557$		−	9362.34i		−	0.712199i	−0.934448	−	0.356100i	$-0.884106\pi$
$557$		−	9362.34i		−	0.712199i	0.934448	−	0.356100i	$-0.115894\pi$
$558$	2627.52	−	853.732i	0.199340	−	0.0647694i
$559$	1032.43	+	750.105i	0.0781166	+	0.0567550i
$560$	1520.66	+	3221.41i	0.114749	+	0.243088i
$561$	32.8760	−	23.8858i	0.00247420	−	0.00179761i
$562$	300.416	−	413.487i	0.0225485	−	0.0310354i
$563$	7137.36	−	9823.74i	0.534288	−	0.735384i	−0.453488	−	0.891262i	$-0.649821\pi$
$563$	7137.36	−	9823.74i	0.534288	−	0.735384i	0.987776	+	0.155878i	$0.0498207\pi$
$564$	−328.894	+	238.955i	−0.0245548	+	0.0178401i
$565$	915.133	+	1938.64i	0.0681415	+	0.144353i
$566$	−3316.97	−	2409.92i	−0.246330	−	0.178969i
$567$	13713.1	−	4455.67i	1.01569	−	0.330019i
$568$			6845.16i			0.505663i
$569$	−2883.62	−	8874.88i	−0.212456	−	0.653874i	−0.999324	−	0.0367524i	$-0.988299\pi$
$569$	−2883.62	−	8874.88i	−0.212456	−	0.653874i	0.786868	−	0.617121i	$-0.211701\pi$
$570$	−35.2635	−	276.440i	−0.00259128	−	0.0203137i
$571$	5676.39	−	17470.1i	0.416024	−	1.28039i	−0.495308	−	0.868717i	$-0.664945\pi$
$571$	5676.39	−	17470.1i	0.416024	−	1.28039i	0.911332	−	0.411672i	$-0.135055\pi$
$572$	103.477	+	33.6217i	0.00756396	+	0.00245768i
$573$	−700.632	−	964.337i	−0.0510809	−	0.0703068i
$574$	10577.5			0.769160
$575$	9115.25	−	23186.8i	0.661100	−	1.68167i
$576$	−1724.10			−0.124718
$577$	−169.296	−	233.016i	−0.0122147	−	0.0168121i	0.802866	−	0.596160i	$-0.203307\pi$
$577$	−169.296	−	233.016i	−0.0122147	−	0.0168121i	−0.815081	+	0.579347i	$0.803307\pi$
$578$	−1194.30	−	388.053i	−0.0859455	−	0.0279254i
$579$	234.678	−	722.266i	0.0168444	−	0.0518417i
$580$	−9756.25	+	4605.42i	−0.698459	+	0.329706i
$581$	−5646.22	−	17377.3i	−0.403175	−	1.24085i
$582$			219.275i			0.0156173i
$583$	−904.633	+	293.933i	−0.0642643	+	0.0208807i
$584$	−3343.62	−	2429.28i	−0.236918	−	0.172131i
$585$	−690.012	+	3641.18i	−0.0487666	+	0.257341i
$586$	−10910.4	+	7926.90i	−0.769123	+	0.558801i
$587$	−8906.66	+	12259.0i	−0.626264	+	0.861979i	−0.997790	−	0.0664436i	$-0.978835\pi$
$587$	−8906.66	+	12259.0i	−0.626264	+	0.861979i	0.371526	+	0.928423i	$0.378835\pi$
$588$	31.0980	−	42.8027i	0.00218105	−	0.00300196i
$589$	2093.55	−	1521.06i	0.146457	−	0.106407i
$590$	−10803.5	−	5922.20i	−0.753853	−	0.413243i
$591$	846.041	+	614.685i	0.0588858	+	0.0427830i
$592$	−4232.08	+	1375.08i	−0.293813	+	0.0954656i
$593$			8594.02i			0.595133i	0.954701	+	0.297567i	$0.0961750\pi$
$593$			8594.02i			0.595133i	−0.954701	+	0.297567i	$0.903825\pi$
$594$	18.1990	+	56.0107i	0.00125709	+	0.00386893i
$595$	−16283.1	−	3085.68i	−1.12192	−	0.212606i
$596$	−1790.51	+	5510.62i	−0.123057	+	0.378731i
$597$	−969.114	−	314.884i	−0.0664375	−	0.0215869i
$598$	−2883.05	−	3968.18i	−0.197152	−	0.271356i
$599$	12431.0			0.847942			0.423971	−	0.905676i	$-0.360636\pi$
$599$	12431.0			0.847942			0.423971	+	0.905676i	$0.360636\pi$
$600$	−132.832	−	208.191i	−0.00903809	−	0.0141656i
$601$	16440.3			1.11583			0.557913	−	0.829899i	$-0.311602\pi$
$601$	16440.3			1.11583			0.557913	+	0.829899i	$0.311602\pi$
$602$	−2427.94	−	3341.78i	−0.164378	−	0.226247i
$603$	−1953.62	−	634.769i	−0.131936	−	0.0428686i
$604$	2231.06	−	6866.49i	0.150299	−	0.462572i
$605$	10162.5	+	10795.6i	0.682915	+	0.725464i
$606$	75.3005	+	231.751i	0.00504765	+	0.0155351i
$607$			10367.1i			0.693228i	0.938008	+	0.346614i	$0.112669\pi$
$607$			10367.1i			0.693228i	−0.938008	+	0.346614i	$0.887331\pi$
$608$	−1535.87	+	499.035i	−0.102447	+	0.0332871i
$609$	959.807	+	697.341i	0.0638643	+	0.0464001i
$610$	−8318.52	+	7830.64i	−0.552143	+	0.519760i
$611$	4096.76	−	2976.47i	0.271256	−	0.197079i
$612$	4714.65	−	6489.16i	0.311403	−	0.428609i
$613$	8515.76	−	11720.9i	0.561090	−	0.772274i	−0.430375	−	0.902650i	$-0.641618\pi$
$613$	8515.76	−	11720.9i	0.561090	−	0.772274i	0.991465	+	0.130376i	$0.0416185\pi$
$614$	−8089.70	+	5877.51i	−0.531716	+	0.386314i
$615$	−727.398	+	92.7892i	−0.0476935	+	0.00608394i
$616$	−284.912	−	207.001i	−0.0186355	−	0.0135395i
$617$	2454.25	−	797.436i	0.160137	−	0.0520317i	−0.227851	−	0.973696i	$-0.573170\pi$
$617$	2454.25	−	797.436i	0.160137	−	0.0520317i	0.387988	+	0.921664i	$0.373170\pi$
$618$			850.163i			0.0553375i
$619$	−1815.76	−	5588.34i	−0.117903	−	0.362867i	0.874639	−	0.484775i	$-0.161099\pi$
$619$	−1815.76	−	5588.34i	−0.117903	−	0.362867i	−0.992541	+	0.121908i	$0.961099\pi$
$620$	1102.32	−	2010.89i	0.0714035	−	0.130257i
$621$	820.435	−	2525.04i	0.0530160	−	0.163166i
$622$	13066.4	+	4245.52i	0.842304	+	0.273681i
$623$	−15248.7	−	20988.0i	−0.980618	−	1.34971i
$624$	−48.6193			−0.00311912
$625$	−6584.06	+	14170.1i	−0.421380	+	0.906884i
$626$	−897.886			−0.0573270
$627$	16.1938	+	22.2889i	0.00103145	+	0.00141967i
$628$	−7604.57	−	2470.87i	−0.483209	−	0.157004i
$629$	6397.33	−	19689.0i	0.405530	−	1.24809i
$630$	5766.14	−	10518.8i	0.364648	−	0.665205i
$631$	−1241.27	−	3820.25i	−0.0783111	−	0.241017i	0.904235	−	0.427035i	$-0.140442\pi$
$631$	−1241.27	−	3820.25i	−0.0783111	−	0.241017i	−0.982546	+	0.186018i	$0.940442\pi$
$632$			1090.02i			0.0686055i
$633$	1193.10	−	387.662i	0.0749156	−	0.0243415i
$634$	10836.5	+	7873.21i	0.678824	+	0.493194i
$635$	−3408.61	+	434.813i	−0.213018	+	0.0271733i
$636$	343.871	−	249.837i	0.0214393	−	0.0155766i
$637$	−387.362	+	533.158i	−0.0240940	+	0.0331625i
$638$	626.916	−	862.876i	0.0389026	−	0.0535448i
$639$	18648.0	−	13548.6i	1.15447	−	0.838769i
$640$	−1042.02	+	980.910i	−0.0643588	+	0.0605842i
$641$	−3281.65	−	2384.26i	−0.202211	−	0.146915i	0.482071	−	0.876132i	$-0.339885\pi$
$641$	−3281.65	−	2384.26i	−0.202211	−	0.146915i	−0.684283	+	0.729217i	$0.739885\pi$
$642$	−582.950	+	189.412i	−0.0358367	+	0.0116441i
$643$			3520.39i			0.215911i	0.994156	+	0.107955i	$0.0344304\pi$
$643$			3520.39i			0.215911i	−0.994156	+	0.107955i	$0.965570\pi$
$644$	4906.06	+	15099.3i	0.300196	+	0.923907i
$645$	196.280	+	208.510i	0.0119822	+	0.0127288i
$646$	2321.67	−	7145.37i	0.141401	−	0.435187i
$647$	20259.4	+	6582.66i	1.23103	+	0.399986i	0.851088	−	0.525023i	$-0.175943\pi$
$647$	20259.4	+	6582.66i	1.23103	+	0.399986i	0.379944	+	0.925010i	$0.375943\pi$
$648$	3404.75	+	4686.24i	0.206406	+	0.284094i
$649$	1217.99			0.0736676
$650$	1654.58	+	2593.27i	0.0998433	+	0.156487i
$651$	−252.176			−0.0151821
$652$	−1154.99	−	1589.71i	−0.0693758	−	0.0954876i
$653$	−8463.06	−	2749.81i	−0.507175	−	0.164791i	0.0442423	−	0.999021i	$-0.485913\pi$
$653$	−8463.06	−	2749.81i	−0.507175	−	0.164791i	−0.551417	+	0.834230i	$0.685913\pi$
$654$	26.9723	−	83.0121i	0.00161269	−	0.00496335i
$655$	30864.0	+	5848.80i	1.84116	+	0.348903i
$656$	1313.12	+	4041.35i	0.0781533	+	0.240531i
$657$			13917.2i			0.826424i
$658$	−15588.6	+	5065.04i	−0.923565	+	0.300085i
$659$	−17979.8	−	13063.1i	−1.06281	−	0.772177i	−0.0882040	−	0.996102i	$-0.528113\pi$
$659$	−17979.8	−	13063.1i	−1.06281	−	0.772177i	−0.974606	+	0.223926i	$0.928113\pi$
$660$	21.4088	+	11.7358i	0.00126263	+	0.000692142i
$661$	−22654.3	+	16459.3i	−1.33306	+	0.968522i	−0.333387	+	0.942790i	$0.608192\pi$
$661$	−22654.3	+	16459.3i	−1.33306	+	0.968522i	−0.999669	+	0.0257322i	$0.991808\pi$
$662$	−495.838	+	682.463i	−0.0291107	+	0.0400675i
$663$	132.953	−	182.994i	0.00778801	−	0.0107193i
$664$	5938.40	−	4314.50i	0.347070	−	0.252161i
$665$	2092.00	−	11039.4i	0.121991	−	0.643745i
$666$	12122.6	+	8807.60i	0.705318	+	0.512444i
$667$	−45729.3	+	14858.3i	−2.65464	+	0.862545i
$668$		−	1361.81i		−	0.0788774i
$669$	376.611	+	1159.09i	0.0217648	+	0.0669850i
$670$	−1541.89	+	727.847i	−0.0889081	+	0.0419689i
$671$	349.012	−	1074.15i	0.0200797	−	0.0617989i
$672$	149.669	+	48.6304i	0.00859168	+	0.00279161i
$673$	12385.9	+	17047.7i	0.709422	+	0.976436i	0.999809	+	0.0195266i	$0.00621589\pi$
$673$	12385.9	+	17047.7i	0.709422	+	0.976436i	−0.290387	+	0.956909i	$0.593784\pi$
$674$	9132.24			0.521900
$675$	−609.195	+	1549.63i	−0.0347377	+	0.0883637i
$676$	−8182.39			−0.465543
$677$	−7311.23	−	10063.0i	−0.415057	−	0.571277i	0.549386	−	0.835569i	$-0.314862\pi$
$677$	−7311.23	−	10063.0i	−0.415057	−	0.571277i	−0.964443	+	0.264292i	$0.914862\pi$
$678$	90.0707	+	29.2658i	0.00510199	+	0.00165774i
$679$	−2731.96	+	8408.10i	−0.154408	+	0.475218i
$680$	−842.470	−	6604.34i	−0.0475107	−	0.372448i
$681$	53.2824	+	163.986i	0.00299822	+	0.00922756i
$682$			226.708i			0.0127289i
$683$	−5562.74	+	1807.44i	−0.311643	+	0.101259i	−0.460663	−	0.887575i	$-0.652388\pi$
$683$	−5562.74	+	1807.44i	−0.311643	+	0.101259i	0.149020	+	0.988834i	$0.452388\pi$
$684$	4399.45	+	3196.39i	0.245932	+	0.178680i
$685$	9358.51	+	19825.3i	0.522000	+	1.10582i
$686$	−9326.13	+	6775.83i	−0.519058	+	0.377117i
$687$	−900.345	+	1239.22i	−0.0500004	+	0.0688197i
$688$	975.382	−	1342.50i	0.0540496	−	0.0743929i
$689$	−4283.33	+	3112.02i	−0.236839	+	0.172073i
$690$	−469.837	−	995.316i	−0.0259223	−	0.0549145i
$691$	5923.87	+	4303.94i	0.326128	+	0.236946i	0.738786	−	0.673940i	$-0.235399\pi$
$691$	5923.87	+	4303.94i	0.326128	+	0.236946i	−0.412658	+	0.910886i	$0.635399\pi$
$692$	−8286.21	+	2692.35i	−0.455194	+	0.147902i
$693$			1185.89i			0.0650048i
$694$	−3795.87	−	11682.5i	−0.207621	−	0.638993i
$695$	2233.23	+	17506.9i	0.121887	+	0.955502i
$696$	−147.280	+	453.282i	−0.00802105	+	0.0246862i
$697$	−18801.7	−	6109.03i	−1.02176	−	0.331989i
$698$	−8765.70	−	12065.0i	−0.475339	−	0.654248i
$699$	674.927			0.0365209
$700$	−2499.59	−	9638.04i	−0.134965	−	0.520405i
$701$	15238.8			0.821060			0.410530	−	0.911847i	$-0.365344\pi$
$701$	15238.8			0.821060			0.410530	+	0.911847i	$0.365344\pi$
$702$	192.682	+	265.204i	0.0103594	+	0.0142585i
$703$	13348.5	+	4337.19i	0.716143	+	0.232689i
$704$	43.7192	−	134.554i	0.00234052	−	0.00720339i
$705$	1027.57	−	485.061i	0.0548942	−	0.0259127i
$706$	4082.13	+	12563.5i	0.217610	+	0.669735i
$707$			9824.66i			0.522623i
$708$	−517.633	+	168.189i	−0.0274772	+	0.00892787i
$709$	−9001.43	−	6539.92i	−0.476807	−	0.346420i	0.323281	−	0.946303i	$-0.395214\pi$
$709$	−9001.43	−	6539.92i	−0.476807	−	0.346420i	−0.800088	+	0.599883i	$0.795214\pi$
$710$	3562.31	−	18798.2i	0.188297	−	0.993641i
$711$	2969.51	−	2157.47i	0.156632	−	0.113800i
$712$	6125.88	−	8431.54i	0.322439	−	0.443800i
$713$	6007.35	−	8268.41i	0.315536	−	0.434298i
$714$	−592.315	+	430.342i	−0.0310460	+	0.0225562i
$715$	−266.672	−	146.183i	−0.0139482	−	0.00764605i
$716$	11132.3	+	8088.07i	0.581051	+	0.422158i
$717$	−347.650	+	112.958i	−0.0181077	+	0.00588355i
$718$		−	2128.59i		−	0.110638i
$719$	8073.67	+	24848.2i	0.418772	+	1.28885i	0.908833	+	0.417160i	$0.136974\pi$
$719$	8073.67	+	24848.2i	0.418772	+	1.28885i	−0.490061	+	0.871688i	$0.663026\pi$
$720$	4734.73	+	897.242i	0.245074	+	0.0464420i
$721$	−10592.2	+	32599.5i	−0.547122	+	1.68387i
$722$	−8202.26	−	2665.07i	−0.422793	−	0.137374i
$723$	−37.5674	−	51.7071i	−0.00193243	−	0.00265976i
$724$	8088.85			0.415221
$725$	29189.4	−	7570.18i	1.49527	−	0.387792i
$726$	654.986			0.0334832
$727$	2297.94	+	3162.84i	0.117229	+	0.161352i	0.863599	−	0.504179i	$-0.168205\pi$
$727$	2297.94	+	3162.84i	0.117229	+	0.161352i	−0.746370	+	0.665532i	$0.768205\pi$
$728$	−1864.31	−	605.750i	−0.0949118	−	0.0308387i
$729$	6000.10	−	18466.4i	0.304837	−	0.938191i
$730$	7918.05	+	8411.38i	0.401452	+	0.426465i
$731$	2385.66	+	7342.30i	0.120707	+	0.371498i
$732$			504.696i			0.0254837i
$733$	−4434.46	+	1440.84i	−0.223452	+	0.0726040i	−0.418603	−	0.908169i	$-0.637480\pi$
$733$	−4434.46	+	1440.84i	−0.223452	+	0.0726040i	0.195151	+	0.980773i	$0.437480\pi$
$734$	−2611.15	−	1897.11i	−0.131307	−	0.0953999i
$735$	−107.677	+	101.361i	−0.00540369	+	0.00508676i
$736$	−5159.94	+	3748.92i	−0.258421	+	0.187754i
$737$	99.0787	−	136.370i	0.00495198	−	0.00681582i
$738$	8410.67	−	11576.3i	0.419514	−	0.577411i
$739$	−14248.6	+	10352.2i	−0.709261	+	0.515308i	−0.882935	−	0.469495i	$-0.844436\pi$
$739$	−14248.6	+	10352.2i	−0.709261	+	0.515308i	0.173674	+	0.984803i	$0.444436\pi$
$740$	12337.8	−	1573.85i	0.612900	−	0.0781834i
$741$	124.064	+	90.1377i	0.00615061	+	0.00446868i
$742$	16298.5	−	5295.69i	0.806382	−	0.262009i
$743$		−	26680.2i		−	1.31737i	−0.752421	−	0.658683i	$-0.771114\pi$
$743$		−	26680.2i		−	1.31737i	0.752421	−	0.658683i	$-0.228886\pi$
$744$	−31.3056	−	96.3486i	−0.00154263	−	0.00474773i
$745$	7784.91	−	14201.5i	0.382842	−	0.698394i
$746$	−4613.69	+	14199.5i	−0.226433	+	0.696890i
$747$	−23507.7	−	7638.11i	−1.15141	−	0.374115i
$748$	386.881	+	532.497i	0.0189115	+	0.0260294i
$749$	−24713.1			−1.20560
$750$	256.440	+	640.864i	0.0124852	+	0.0312014i
$751$	8017.53			0.389566			0.194783	−	0.980846i	$-0.437600\pi$
$751$	8017.53			0.389566			0.194783	+	0.980846i	$0.437600\pi$
$752$	−3870.39	−	5327.14i	−0.187684	−	0.258325i
$753$	−806.157	−	261.936i	−0.0390146	−	0.0126766i
$754$	1834.55	−	5646.17i	0.0886081	−	0.272708i
$755$	−9700.36	+	17695.7i	−0.467592	+	0.852999i
$756$	−327.885	−	1009.12i	−0.0157739	−	0.0485470i
$757$		−	4716.28i		−	0.226441i	−0.993570	−	0.113221i	$-0.963883\pi$
$757$		−	4716.28i		−	0.226441i	0.993570	−	0.113221i	$-0.0361167\pi$
$758$	−14254.7	+	4631.63i	−0.683052	+	0.221937i
$759$	88.0291	+	63.9569i	0.00420982	+	0.00305861i
$760$	4477.53	−	571.168i	0.213707	−	0.0272611i
$761$	4294.37	−	3120.04i	0.204561	−	0.148622i	−0.480789	−	0.876837i	$-0.659650\pi$
$761$	4294.37	−	3120.04i	0.204561	−	0.148622i	0.685349	+	0.728214i	$0.259650\pi$
$762$	−89.2273	+	122.811i	−0.00424195	+	0.00583854i
$763$	2068.50	−	2847.05i	0.0981452	−	0.135085i
$764$	15619.5	−	11348.2i	0.739652	−	0.537388i
$765$	−16324.5	+	15367.0i	−0.771520	+	0.726270i
$766$	7106.35	+	5163.07i	0.335200	+	0.243537i
$767$	6447.73	−	2095.00i	0.303539	−	0.0986257i
$768$			63.2210i			0.00297043i
$769$	−12806.7	−	39415.0i	−0.600548	−	1.84830i	−0.524902	−	0.851163i	$-0.675898\pi$
$769$	−12806.7	−	39415.0i	−0.600548	−	1.84830i	−0.0756466	−	0.997135i	$-0.524102\pi$
$770$	674.703	+	716.740i	0.0315774	+	0.0335448i
$771$	−237.100	+	729.720i	−0.0110752	+	0.0340859i
$772$	11698.6	+	3801.12i	0.545393	+	0.177209i
$773$	4904.19	+	6750.04i	0.228191	+	0.314078i	0.907725	−	0.419566i	$-0.137818\pi$
$773$	4904.19	+	6750.04i	0.228191	+	0.314078i	−0.679534	+	0.733644i	$0.737818\pi$
$774$	−5587.89			−0.259499
$775$	−4073.69	+	4948.66i	−0.188814	+	0.229369i
$776$	−3551.63			−0.164299
$777$	−803.936	−	1106.52i	−0.0371184	−	0.0510892i
$778$	−10965.2	−	3562.81i	−0.505297	−	0.164181i
$779$	4141.73	−	12746.9i	0.190492	−	0.586273i
$780$	133.519	+	25.3021i	0.00612915	+	0.00116149i
$781$	584.501	+	1798.91i	0.0267799	+	0.0824201i
$782$		−	29672.7i		−	1.35690i
$783$	3056.20	−	993.020i	0.139489	−	0.0453227i
$784$	693.281	+	503.698i	0.0315817	+	0.0229454i
$785$	19597.9	+	10743.1i	0.891055	+	0.488453i
$786$	1122.71	−	815.697i	0.0509488	−	0.0370165i
$787$	−4758.50	+	6549.52i	−0.215530	+	0.296652i	−0.903069	−	0.429496i	$-0.858691\pi$
$787$	−4758.50	+	6549.52i	−0.215530	+	0.296652i	0.687539	+	0.726148i	$0.258691\pi$
$788$	−9956.14	+	13703.4i	−0.450092	+	0.619499i
$789$	−990.315	+	719.506i	−0.0446846	+	0.0324653i
$790$	567.261	−	2993.43i	0.0255471	−	0.134812i
$791$	3089.14	+	2244.39i	0.138859	+	0.100887i
$792$	−453.093	+	147.219i	−0.0203282	+	0.00660505i
$793$		−	6286.59i		−	0.281517i
$794$	−987.338	−	3038.71i	−0.0441301	−	0.135819i
$795$	−1074.36	+	507.150i	−0.0479291	+	0.0226249i
$796$	5100.22	−	15696.9i	0.227101	−	0.698946i
$797$	−19058.1	−	6192.35i	−0.847016	−	0.275212i	−0.146821	−	0.989163i	$-0.546904\pi$
$797$	−19058.1	−	6192.35i	−0.847016	−	0.275212i	−0.700196	+	0.713951i	$0.746904\pi$
$798$	−291.758	−	401.571i	−0.0129425	−	0.0178139i
$799$	30634.1			1.35639
$800$	3372.10	−	2151.50i	0.149027	−	0.0950839i
$801$	−35094.7			−1.54808
$802$	5551.86	+	7641.48i	0.244443	+	0.336447i
$803$	−1086.14	−	352.908i	−0.0477322	−	0.0155091i
$804$	−23.2764	+	71.6374i	−0.00102101	+	0.00314236i
$805$	−5615.21	−	44019.1i	−0.245851	−	1.92729i
$806$	389.948	+	1200.14i	0.0170414	+	0.0524479i
$807$		−	591.913i		−	0.0258195i
$808$	−3753.71	+	1219.65i	−0.163434	+	0.0531030i
$809$	3586.40	+	2605.67i	0.155860	+	0.113239i	0.662982	−	0.748635i	$-0.269291\pi$
$809$	3586.40	+	2605.67i	0.155860	+	0.113239i	−0.507122	+	0.861874i	$0.669291\pi$
$810$	−6911.39	−	14641.3i	−0.299804	−	0.635113i
$811$	4379.53	−	3181.92i	0.189625	−	0.137771i	−0.488922	−	0.872327i	$-0.662610\pi$
$811$	4379.53	−	3181.92i	0.189625	−	0.137771i	0.678548	+	0.734557i	$0.262610\pi$
$812$	−11294.9	+	15546.1i	−0.488146	+	0.671875i
$813$	−942.161	+	1296.77i	−0.0406433	+	0.0559407i
$814$	−994.774	+	722.746i	−0.0428339	+	0.0311207i
$815$	2344.55	+	4966.76i	0.100768	+	0.213470i
$816$	−237.952	−	172.882i	−0.0102083	−	0.00741677i
$817$	−4977.85	+	1617.40i	−0.213161	+	0.0692603i
$818$		−	11658.1i		−	0.498307i
$819$	2039.79	+	6277.82i	0.0870280	+	0.267845i
$820$	−1502.92	−	11781.8i	−0.0640051	−	0.501753i
$821$	6717.03	−	20672.9i	0.285537	−	0.878793i	−0.700700	−	0.713456i	$-0.747129\pi$
$821$	6717.03	−	20672.9i	0.285537	−	0.878793i	0.986237	−	0.165337i	$-0.0528711\pi$
$822$	921.099	+	299.283i	0.0390840	+	0.0126991i
$823$	−15129.0	−	20823.2i	−0.640780	−	0.881959i	0.357877	−	0.933769i	$-0.383501\pi$
$823$	−15129.0	−	20823.2i	−0.640780	−	0.881959i	−0.998657	+	0.0518104i	$0.983501\pi$
$824$	−13770.2			−0.582170
$825$	−52.6856	−	43.3702i	−0.00222337	−	0.00183025i
$826$	−21944.1			−0.924374
$827$	1849.15	+	2545.13i	0.0777523	+	0.107017i	0.846122	−	0.532990i	$-0.178932\pi$
$827$	1849.15	+	2545.13i	0.0777523	+	0.107017i	−0.768369	+	0.640007i	$0.778932\pi$
$828$	20426.1	+	6636.84i	0.857313	+	0.278558i
$829$	−3738.37	+	11505.5i	−0.156621	+	0.482031i	−0.998322	−	0.0579142i	$-0.981555\pi$
$829$	−3738.37	+	11505.5i	−0.156621	+	0.482031i	0.841700	+	0.539945i	$0.181555\pi$
$830$	−18553.4	+	8758.11i	−0.775902	+	0.366263i
$831$	−290.289	−	893.419i	−0.0121180	−	0.0372953i
$832$		−	787.493i		−	0.0328142i
$833$	−3791.64	+	1231.98i	−0.157710	+	0.0512432i
$834$	630.766	+	458.278i	0.0261890	+	0.0190274i
$835$	−708.705	+	3739.82i	−0.0293721	+	0.154996i
$836$	−361.016	+	262.293i	−0.0149354	+	0.0108512i
$837$	−401.486	+	552.599i	−0.0165799	+	0.0228203i
$838$	−1338.26	+	1841.96i	−0.0551664	+	0.0759300i
$839$	−1198.70	+	870.909i	−0.0493252	+	0.0358369i	−0.612175	−	0.790723i	$-0.709705\pi$
$839$	−1198.70	+	870.909i	−0.0493252	+	0.0358369i	0.562849	+	0.826559i	$0.309705\pi$
$840$	−385.715	−	211.439i	−0.0158434	−	0.00868493i
$841$	−27351.4	−	19871.9i	−1.12146	−	0.814791i
$842$	1951.88	−	634.205i	0.0798888	−	0.0259574i
$843$			63.1097i			0.00257842i
$844$	6279.02	+	19324.8i	0.256082	+	0.788138i
$845$	22470.6	+	4258.22i	0.914806	+	0.173358i
$846$	−6851.89	+	21087.9i	−0.278455	+	0.856996i
$847$	25115.4	+	8160.50i	1.01886	+	0.331049i
$848$	4046.65	+	5569.73i	0.163871	+	0.225549i
$849$	506.262			0.0204651
$850$	−1123.38	+	18575.3i	−0.0453314	+	0.749563i
$851$	55432.5			2.23290
$852$	−496.814	−	683.806i	−0.0199772	−	0.0274962i
$853$	16215.1	+	5268.61i	0.650873	+	0.211481i	0.615799	−	0.787903i	$-0.288833\pi$
$853$	16215.1	+	5268.61i	0.650873	+	0.211481i	0.0350740	+	0.999385i	$0.488833\pi$
$854$	−6288.03	+	19352.6i	−0.251958	+	0.775446i
$855$	−10418.4	−	11067.5i	−0.416726	−	0.442690i
$856$	−3067.93	−	9442.12i	−0.122500	−	0.377015i
$857$		−	5794.04i		−	0.230946i	−0.993311	−	0.115473i	$-0.963162\pi$
$857$		−	5794.04i		−	0.230946i	0.993311	−	0.115473i	$-0.0368383\pi$
$858$	−12.7772	+	4.15155i	−0.000508398	+	0.000165188i
$859$	−16171.8	−	11749.5i	−0.642346	−	0.466692i	0.218310	−	0.975880i	$-0.429946\pi$
$859$	−16171.8	−	11749.5i	−0.642346	−	0.466692i	−0.860655	+	0.509188i	$0.829946\pi$
$860$	−3377.26	+	3179.18i	−0.133911	+	0.126057i
$861$	−1056.66	+	767.706i	−0.0418243	+	0.0303872i
$862$	−6579.31	+	9055.64i	−0.259968	+	0.357815i
$863$	−28737.4	+	39553.6i	−1.13353	+	1.56016i	−0.352331	+	0.935875i	$0.614611\pi$
$863$	−28737.4	+	39553.6i	−1.13353	+	1.56016i	−0.781194	+	0.624288i	$0.785389\pi$
$864$	344.852	−	250.549i	0.0135788	−	0.00986558i
$865$	24156.8	−	3081.52i	0.949545	−	0.121127i
$866$	−1421.67	−	1032.91i	−0.0557858	−	0.0405307i
$867$	147.471	−	47.9162i	0.00577667	−	0.00187696i
$868$		−	4084.52i		−	0.159721i
$869$	93.0758	+	286.458i	0.00363335	+	0.0111823i
$870$	640.357	−	1168.16i	0.0249542	−	0.0455223i
$871$	289.935	−	892.329i	0.0112791	−	0.0347134i
$872$	1344.56	+	436.873i	0.0522161	+	0.0169661i
$873$	7029.72	+	9675.58i	0.272531	+	0.375107i
$874$	20117.1			0.778572
$875$	1848.64	+	27768.9i	0.0714235	+	1.07287i
$876$	510.330			0.0196832
$877$	3724.75	+	5126.68i	0.143416	+	0.197395i	0.874682	−	0.484697i	$-0.161070\pi$
$877$	3724.75	+	5126.68i	0.143416	+	0.197395i	−0.731266	+	0.682092i	$0.761070\pi$
$878$	13324.0	+	4329.24i	0.512146	+	0.166406i
$879$	514.587	−	1583.74i	0.0197458	−	0.0607714i
$880$	−190.086	+	346.761i	−0.00728157	+	0.0132833i
$881$	6049.04	+	18617.0i	0.231325	+	0.711945i	0.997588	+	0.0694177i	$0.0221141\pi$
$881$	6049.04	+	18617.0i	0.231325	+	0.711945i	−0.766263	+	0.642527i	$0.777886\pi$
$882$		−	2885.65i		−	0.110164i
$883$	44526.5	−	14467.5i	1.69698	−	0.551384i	0.708902	−	0.705307i	$-0.249191\pi$
$883$	44526.5	−	14467.5i	1.69698	−	0.551384i	0.988083	+	0.153924i	$0.0491910\pi$
$884$	2963.97	+	2153.45i	0.112771	+	0.0819326i
$885$	1509.06	−	192.500i	0.0573179	−	0.00731166i
$886$	28698.3	−	20850.5i	1.08819	−	0.790617i
$887$	1898.84	−	2613.54i	0.0718793	−	0.0989334i	−0.771564	−	0.636152i	$-0.780525\pi$
$887$	1898.84	−	2613.54i	0.0718793	−	0.0989334i	0.843443	+	0.537219i	$0.180525\pi$
$888$	322.966	−	444.525i	0.0122050	−	0.0167987i
$889$	−4951.53	+	3597.49i	−0.186804	+	0.135721i
$890$	−21210.8	+	19966.8i	−0.798863	+	0.752010i
$891$	1294.92	+	940.817i	0.0486886	+	0.0353744i
$892$	−18773.9	+	6100.02i	−0.704706	+	0.228973i
$893$			20769.0i			0.778284i
$894$	−221.089	−	680.443i	−0.00827107	−	0.0254557i
$895$	−26362.4	−	28004.9i	−0.984580	−	1.04592i
$896$	−787.673	+	2424.21i	−0.0293687	+	0.0903875i
$897$	576.013	+	187.158i	0.0214409	+	0.00696658i
$898$	5045.86	+	6945.03i	0.187508	+	0.258083i
$899$	12370.2			0.458922
$900$	−12535.6	−	4928.03i	−0.464283	−	0.182520i
$901$	−32029.2			−1.18429
$902$	690.174	+	949.944i	0.0254770	+	0.0350661i
$903$	485.085	+	157.614i	0.0178767	+	0.00580848i
$904$	−474.022	+	1458.89i	−0.0174400	+	0.0536747i
$905$	−22213.7	−	4209.54i	−0.815920	−	0.154619i
$906$	275.488	+	847.864i	0.0101021	+	0.0310909i
$907$			24727.7i			0.905258i	0.891699	+	0.452629i	$0.149514\pi$
$907$			24727.7i			0.905258i	−0.891699	+	0.452629i	$0.850486\pi$
$908$	−2656.11	+	863.022i	−0.0970772	+	0.0315423i
$909$	10752.3	+	7812.04i	0.392335	+	0.285048i
$910$	4804.54	+	2633.72i	0.175021	+	0.0959419i
$911$	10203.7	−	7413.45i	0.371092	−	0.269614i	−0.386572	−	0.922259i	$-0.626341\pi$
$911$	10203.7	−	7413.45i	0.371092	−	0.269614i	0.757664	+	0.652645i	$0.226341\pi$
$912$	117.209	−	161.324i	0.00425566	−	0.00585742i
$913$	1192.20	−	1640.93i	0.0432160	−	0.0594817i
$914$	−28169.4	+	20466.2i	−1.01943	+	0.740660i
$915$	262.650	−	1386.00i	0.00948956	−	0.0500763i
$916$	−20071.8	−	14583.0i	−0.724007	−	0.526022i
$917$	53213.1	−	17290.0i	1.91631	−	0.622646i
$918$			1983.10i			0.0712985i
$919$	9253.51	+	28479.4i	0.332149	+	1.02225i	0.968109	+	0.250528i	$0.0806043\pi$
$919$	9253.51	+	28479.4i	0.332149	+	1.02225i	−0.635960	+	0.771722i	$0.719396\pi$
$920$	16121.3	−	7610.01i	0.577720	−	0.272712i
$921$	381.548	−	1174.28i	0.0136508	−	0.0420130i
$922$	27843.4	+	9046.87i	0.994548	+	0.323148i
$923$	6188.41	+	8517.61i	0.220687	+	0.303749i
$924$	43.4856			0.00154824
$925$	−34701.2	−	2098.63i	−1.23348	−	0.0745972i
$926$	15087.4			0.535423
$927$	27255.3	+	37513.7i	0.965676	+	1.32914i
$928$	−7341.88	−	2385.52i	−0.259708	−	0.0843842i
$929$	−3387.87	+	10426.8i	−0.119647	+	0.368237i	−0.992888	−	0.119052i	$-0.962014\pi$
$929$	−3387.87	+	10426.8i	−0.119647	+	0.368237i	0.873240	+	0.487290i	$0.162014\pi$
$930$	35.8306	+	280.885i	0.00126337	+	0.00990386i
$931$	−835.244	−	2570.62i	−0.0294028	−	0.0904925i
$932$			10931.9i			0.384212i
$933$	−1613.42	+	524.230i	−0.0566140	+	0.0183950i
$934$	−5709.39	−	4148.11i	−0.200018	−	0.145322i
$935$	−785.340	−	1663.69i	−0.0274688	−	0.0581907i
$936$	−2145.34	+	1558.68i	−0.0749174	+	0.0544306i
$937$	28615.8	−	39386.2i	0.997691	−	1.37320i	0.0709603	−	0.997479i	$-0.477394\pi$
$937$	28615.8	−	39386.2i	0.997691	−	1.37320i	0.926731	−	0.375725i	$-0.122606\pi$
$938$	−1785.07	+	2456.93i	−0.0621370	+	0.0855242i
$939$	89.6954	−	65.1675i	0.00311725	−	0.00226482i
$940$	7856.60	+	16643.6i	0.272611	+	0.577506i
$941$	−10133.1	−	7362.13i	−0.351041	−	0.255046i	0.398265	−	0.917271i	$-0.369613\pi$
$941$	−10133.1	−	7362.13i	−0.351041	−	0.255046i	−0.749306	+	0.662224i	$0.769613\pi$
$942$	939.001	−	305.100i	0.0324780	−	0.0105528i
$943$		−	52934.3i		−	1.82797i
$944$	−2724.18	−	8384.17i	−0.0939244	−	0.289069i
$945$	375.278	+	2941.90i	0.0129183	+	0.101270i
$946$	141.696	−	436.096i	0.00486992	−	0.0149881i
$947$	−31792.8	−	10330.1i	−1.09095	−	0.354470i	−0.292335	−	0.956316i	$-0.594432\pi$
$947$	−31792.8	−	10330.1i	−1.09095	−	0.354470i	−0.798612	+	0.601846i	$0.794432\pi$
$948$	−79.1125	−	108.889i	−0.00271040	−	0.00373054i
$949$	−6356.76			−0.217439
$950$	−12593.5	−	761.618i	−0.430092	−	0.0260107i
$951$	−1653.96			−0.0563968
$952$	−6970.31	−	9593.81i	−0.237299	−	0.326615i
$953$	−33664.4	−	10938.2i	−1.14428	−	0.371799i	−0.325293	−	0.945613i	$-0.605463\pi$
$953$	−33664.4	−	10938.2i	−1.14428	−	0.371799i	−0.818985	+	0.573815i	$0.805463\pi$
$954$	7163.92	−	22048.3i	0.243124	−	0.748259i
$955$	−48800.2	+	23036.1i	−1.65355	+	0.780554i
$956$	−1829.60	−	5630.94i	−0.0618970	−	0.190499i
$957$			131.699i			0.00444851i
$958$	14131.1	−	4591.46i	0.476570	−	0.154847i
$959$	31590.7	+	22952.0i	1.06373	+	0.772846i
$960$	32.9010	−	173.618i	0.00110612	−	0.00583699i
$961$	21974.2	−	15965.2i	0.737612	−	0.535907i
$962$	−4022.93	+	5537.09i	−0.134828	+	0.185575i
$963$	−19650.5	+	27046.6i	−0.657558	+	0.905051i
$964$	837.507	−	608.485i	0.0279816	−	0.0203298i
$965$	−30148.8	−	16526.8i	−1.00572	−	0.551312i
$966$	−1585.99	−	1152.29i	−0.0528244	−	0.0383792i
$967$	21369.2	−	6943.26i	0.710637	−	0.230900i	0.0686780	−	0.997639i	$-0.478122\pi$
$967$	21369.2	−	6943.26i	0.710637	−	0.230900i	0.641959	+	0.766739i	$0.278122\pi$
$968$			10608.9i			0.352255i
$969$	286.677	+	882.301i	0.00950401	+	0.0292503i
$970$	9753.52	+	1848.31i	0.322852	+	0.0611812i
$971$	17654.3	−	54334.4i	0.583475	−	1.79575i	−0.0218342	−	0.999762i	$-0.506951\pi$
$971$	17654.3	−	54334.4i	0.583475	−	1.79575i	0.605309	−	0.795990i	$-0.293049\pi$
$972$	−2048.46	−	665.585i	−0.0675971	−	0.0219636i
$973$	18477.0	+	25431.4i	0.608782	+	0.837917i
$974$	−28035.2			−0.922287
$975$	−353.503	−	138.970i	−0.0116114	−	0.00456471i
$976$	−8174.63			−0.268098
$977$	−19204.5	−	26432.7i	−0.628870	−	0.865566i	0.369091	−	0.929393i	$-0.379669\pi$
$977$	−19204.5	−	26432.7i	−0.628870	−	0.865566i	−0.997961	+	0.0638277i	$0.979669\pi$
$978$	230.759	+	74.9782i	0.00754485	+	0.00245147i
$979$	889.921	−	2738.90i	0.0290521	−	0.0894132i
$980$	−1641.76	−	1744.05i	−0.0535145	−	0.0568487i
$981$	−1471.12	−	4527.63i	−0.0478788	−	0.147356i
$982$		−	7204.42i		−	0.234116i
$983$	−48551.3	+	15775.3i	−1.57533	+	0.511854i	−0.960847	−	0.277079i	$-0.910634\pi$
$983$	−48551.3	+	15775.3i	−1.57533	+	0.511854i	−0.614479	+	0.788933i	$0.710634\pi$
$984$	−424.492	−	308.412i	−0.0137524	−	0.00999167i
$985$	34473.1	−	32451.2i	1.11513	−	1.04973i
$986$	29055.5	−	21110.0i	0.938453	−	0.681826i
$987$	1189.63	−	1637.38i	0.0383650	−	0.0528048i
$988$	−1459.97	+	2009.48i	−0.0470121	+	0.0647065i
$989$	−16723.6	+	12150.4i	−0.537696	+	0.390659i
$990$	1320.90	−	168.499i	0.0424051	−	0.00540933i
$991$	−44985.3	−	32683.7i	−1.44198	−	1.04766i	−0.987624	−	0.156843i	$-0.949868\pi$
$991$	−44985.3	−	32683.7i	−1.44198	−	1.04766i	−0.454359	−	0.890819i	$-0.650132\pi$
$992$	1560.57	−	507.060i	0.0499478	−	0.0162290i
$993$		−	104.163i		−	0.00332881i
$994$	−10530.8	−	32410.3i	−0.336032	−	1.03420i
$995$	−22175.1	+	40452.7i	−0.706532	+	1.28888i
$996$	−280.082	+	862.005i	−0.00891039	+	0.0274234i
$997$	9524.47	+	3094.69i	0.302551	+	0.0983047i	0.456358	−	0.889796i	$-0.349154\pi$
$997$	9524.47	+	3094.69i	0.302551	+	0.0983047i	−0.153808	+	0.988101i	$0.549154\pi$
$998$	5766.19	+	7936.48i	0.182891	+	0.251728i
$999$	−3704.69			−0.117329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.4.e.a.39.3	yes	32
5.2	odd	4		250.4.d.d.51.5		32
5.3	odd	4		250.4.d.c.51.4		32
5.4	even	2		250.4.e.b.199.6		32
25.3	odd	20		1250.4.a.n.1.8		16
25.9	even	10	inner	50.4.e.a.9.3	✓	32
25.12	odd	20		250.4.d.d.201.5		32
25.13	odd	20		250.4.d.c.201.4		32
25.16	even	5		250.4.e.b.49.6		32
25.22	odd	20		1250.4.a.m.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.3	✓	32	25.9	even	10	inner
50.4.e.a.39.3	yes	32	1.1	even	1	trivial
250.4.d.c.51.4		32	5.3	odd	4
250.4.d.c.201.4		32	25.13	odd	20
250.4.d.d.51.5		32	5.2	odd	4
250.4.d.d.201.5		32	25.12	odd	20
250.4.e.b.49.6		32	25.16	even	5
250.4.e.b.199.6		32	5.4	even	2
1250.4.a.m.1.9		16	25.22	odd	20
1250.4.a.n.1.8		16	25.3	odd	20

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	50.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17557 - 1.61803i) q^{2} +(0.234870 + 0.0763140i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(5.37427 - 9.80394i) q^{5} +(-0.152628 - 0.469741i) q^{6} -19.9138i q^{7} +(7.60845 - 2.47214i) q^{8} +(-21.7941 - 15.8344i) q^{9} +O(q^{10})\)	\(q+(-1.17557 - 1.61803i) q^{2} +(0.234870 + 0.0763140i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(5.37427 - 9.80394i) q^{5} +(-0.152628 - 0.469741i) q^{6} -19.9138i q^{7} +(7.60845 - 2.47214i) q^{8} +(-21.7941 - 15.8344i) q^{9} +(-22.1809 + 2.82947i) q^{10} +(1.78841 - 1.29936i) q^{11} +(-0.580631 + 0.799170i) q^{12} +(7.23245 - 9.95462i) q^{13} +(-32.2212 + 23.4101i) q^{14} +(2.01043 - 1.89252i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(70.7939 - 23.0023i) q^{17} +53.8780i q^{18} +(15.5949 + 47.9960i) q^{19} +(30.6534 + 32.5633i) q^{20} +(1.51970 - 4.67716i) q^{21} +(-4.20481 - 1.36622i) q^{22} +(117.154 + 161.248i) q^{23} +1.97566 q^{24} +(-67.2344 - 105.378i) q^{25} -24.6092 q^{26} +(-7.82967 - 10.7766i) q^{27} +(75.7565 + 24.6148i) q^{28} +(-74.5475 + 229.434i) q^{29} +(-5.42557 - 1.02816i) q^{30} +(-15.8456 - 48.7679i) q^{31} +32.0000i q^{32} +(0.519204 - 0.168700i) q^{33} +(-120.442 - 87.5061i) q^{34} +(-195.234 - 107.022i) q^{35} +(87.1765 - 63.3374i) q^{36} +(163.473 - 225.001i) q^{37} +(59.3264 - 81.6557i) q^{38} +(2.45836 - 1.78611i) q^{39} +(16.6532 - 87.8787i) q^{40} +(-214.861 - 156.106i) q^{41} +(-9.35431 + 3.03940i) q^{42} +103.714i q^{43} +(2.73245 + 8.40961i) q^{44} +(-272.367 + 128.570i) q^{45} +(123.183 - 379.117i) q^{46} +(391.402 + 127.174i) q^{47} +(-2.32252 - 3.19668i) q^{48} -53.5589 q^{49} +(-91.4664 + 232.667i) q^{50} +18.3828 q^{51} +(28.9298 + 39.8185i) q^{52} +(-409.226 - 132.965i) q^{53} +(-8.23260 + 25.3373i) q^{54} +(-3.12741 - 24.5166i) q^{55} +(-49.2296 - 151.513i) q^{56} +12.4629i q^{57} +(458.867 - 149.095i) q^{58} +(445.750 + 323.856i) q^{59} +(4.71455 + 9.98743i) q^{60} +(413.338 - 300.308i) q^{61} +(-60.2804 + 82.9688i) q^{62} +(-315.322 + 434.003i) q^{63} +(51.7771 - 37.6183i) q^{64} +(-58.7253 - 124.405i) q^{65} +(-0.883322 - 0.641771i) q^{66} +(72.5200 - 23.5632i) q^{67} +297.748i q^{68} +(15.2104 + 46.8129i) q^{69} +(56.3455 + 441.707i) q^{70} +(-264.409 + 813.766i) q^{71} +(-204.964 - 66.5969i) q^{72} +(-303.660 - 417.952i) q^{73} -556.233 q^{74} +(-7.74955 - 29.8811i) q^{75} -201.864 q^{76} +(-25.8751 - 35.6140i) q^{77} +(-5.77996 - 1.87802i) q^{78} +(-42.1044 + 129.584i) q^{79} +(-161.768 + 76.3622i) q^{80} +(223.748 + 688.626i) q^{81} +531.166i q^{82} +(872.626 - 283.533i) q^{83} +(15.9145 + 11.5626i) q^{84} +(154.952 - 817.680i) q^{85} +(167.812 - 121.923i) q^{86} +(-35.0180 + 48.1981i) q^{87} +(10.3949 - 14.3073i) q^{88} +(1053.94 - 765.734i) q^{89} +(528.217 + 289.555i) q^{90} +(-198.234 - 144.026i) q^{91} +(-758.234 + 246.365i) q^{92} -12.6634i q^{93} +(-254.348 - 782.803i) q^{94} +(554.361 + 105.053i) q^{95} +(-2.44205 + 7.51585i) q^{96} +(-422.225 - 137.189i) q^{97} +(62.9623 + 86.6601i) q^{98} -59.5513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9} - 40 q^{10} - 106 q^{11} + 80 q^{12} + 56 q^{14} + 260 q^{15} - 128 q^{16} + 320 q^{17} + 110 q^{19} - 160 q^{20} - 36 q^{21} - 360 q^{22} - 370 q^{23} - 192 q^{24} - 1050 q^{25} + 808 q^{26} - 1200 q^{27} - 120 q^{28} - 10 q^{29} + 160 q^{30} - 486 q^{31} + 2560 q^{33} + 616 q^{34} + 340 q^{35} - 104 q^{36} + 680 q^{37} + 1012 q^{39} + 160 q^{40} - 96 q^{41} - 1020 q^{42} - 136 q^{44} - 1500 q^{45} - 832 q^{46} + 1040 q^{47} + 320 q^{48} - 2076 q^{49} + 400 q^{50} + 884 q^{51} - 2550 q^{53} - 120 q^{54} + 720 q^{55} - 224 q^{56} + 2250 q^{59} + 360 q^{60} + 934 q^{61} + 4200 q^{62} + 4660 q^{63} + 512 q^{64} + 1670 q^{65} + 16 q^{66} - 3780 q^{67} - 628 q^{69} - 2440 q^{70} - 2616 q^{71} - 600 q^{73} - 2584 q^{74} - 4500 q^{75} + 800 q^{76} - 4320 q^{77} - 6640 q^{78} - 2800 q^{79} + 160 q^{80} - 5268 q^{81} + 4050 q^{83} + 624 q^{84} - 1420 q^{85} - 692 q^{86} + 9390 q^{87} - 1680 q^{88} + 4520 q^{89} + 9220 q^{90} + 3764 q^{91} + 1280 q^{92} + 656 q^{94} - 4860 q^{95} - 192 q^{96} + 1710 q^{97} + 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9 - 40 * q^10 - 106 * q^11 + 80 * q^12 + 56 * q^14 + 260 * q^15 - 128 * q^16 + 320 * q^17 + 110 * q^19 - 160 * q^20 - 36 * q^21 - 360 * q^22 - 370 * q^23 - 192 * q^24 - 1050 * q^25 + 808 * q^26 - 1200 * q^27 - 120 * q^28 - 10 * q^29 + 160 * q^30 - 486 * q^31 + 2560 * q^33 + 616 * q^34 + 340 * q^35 - 104 * q^36 + 680 * q^37 + 1012 * q^39 + 160 * q^40 - 96 * q^41 - 1020 * q^42 - 136 * q^44 - 1500 * q^45 - 832 * q^46 + 1040 * q^47 + 320 * q^48 - 2076 * q^49 + 400 * q^50 + 884 * q^51 - 2550 * q^53 - 120 * q^54 + 720 * q^55 - 224 * q^56 + 2250 * q^59 + 360 * q^60 + 934 * q^61 + 4200 * q^62 + 4660 * q^63 + 512 * q^64 + 1670 * q^65 + 16 * q^66 - 3780 * q^67 - 628 * q^69 - 2440 * q^70 - 2616 * q^71 - 600 * q^73 - 2584 * q^74 - 4500 * q^75 + 800 * q^76 - 4320 * q^77 - 6640 * q^78 - 2800 * q^79 + 160 * q^80 - 5268 * q^81 + 4050 * q^83 + 624 * q^84 - 1420 * q^85 - 692 * q^86 + 9390 * q^87 - 1680 * q^88 + 4520 * q^89 + 9220 * q^90 + 3764 * q^91 + 1280 * q^92 + 656 * q^94 - 4860 * q^95 - 192 * q^96 + 1710 * q^97 + 3280 * q^98 - 2108 * q^99

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