LMFDB - Embedded newform 120.4.b.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165720 - 2.82357i) q^{2} +(3.31357 + 4.00253i) q^{3} +(-7.94507 - 0.935845i) q^{4} +5.00000 q^{5} +(11.8505 - 8.69280i) q^{6} +30.8728i q^{7} +(-3.95908 + 22.2784i) q^{8} +(-5.04045 + 26.5253i) q^{9} +O(q^{10})$	\(q+(0.165720 - 2.82357i) q^{2} +(3.31357 + 4.00253i) q^{3} +(-7.94507 - 0.935845i) q^{4} +5.00000 q^{5} +(11.8505 - 8.69280i) q^{6} +30.8728i q^{7} +(-3.95908 + 22.2784i) q^{8} +(-5.04045 + 26.5253i) q^{9} +(0.828601 - 14.1178i) q^{10} -45.8002i q^{11} +(-22.5808 - 34.9014i) q^{12} +76.8279i q^{13} +(87.1715 + 5.11625i) q^{14} +(16.5679 + 20.0126i) q^{15} +(62.2484 + 14.8707i) q^{16} -13.8879i q^{17} +(74.0608 + 18.6279i) q^{18} +45.8869 q^{19} +(-39.7254 - 4.67922i) q^{20} +(-123.569 + 102.299i) q^{21} +(-129.320 - 7.59002i) q^{22} +74.3371 q^{23} +(-102.288 + 57.9747i) q^{24} +25.0000 q^{25} +(216.929 + 12.7319i) q^{26} +(-122.870 + 67.7191i) q^{27} +(28.8922 - 245.287i) q^{28} +85.8680 q^{29} +(59.2527 - 43.4640i) q^{30} -227.728i q^{31} +(52.3043 - 173.298i) q^{32} +(183.317 - 151.762i) q^{33} +(-39.2134 - 2.30151i) q^{34} +154.364i q^{35} +(64.8704 - 206.029i) q^{36} -5.58615i q^{37} +(7.60439 - 129.565i) q^{38} +(-307.506 + 254.575i) q^{39} +(-19.7954 + 111.392i) q^{40} +61.0663i q^{41} +(268.371 + 365.860i) q^{42} +65.1565 q^{43} +(-42.8619 + 363.886i) q^{44} +(-25.2023 + 132.627i) q^{45} +(12.3192 - 209.896i) q^{46} -529.167 q^{47} +(146.744 + 298.426i) q^{48} -610.132 q^{49} +(4.14300 - 70.5892i) q^{50} +(55.5867 - 46.0186i) q^{51} +(71.8990 - 610.403i) q^{52} +22.7454 q^{53} +(170.847 + 358.155i) q^{54} -229.001i q^{55} +(-687.796 - 122.228i) q^{56} +(152.050 + 183.664i) q^{57} +(14.2301 - 242.454i) q^{58} -384.963i q^{59} +(-112.904 - 174.507i) q^{60} +588.386i q^{61} +(-643.005 - 37.7391i) q^{62} +(-818.912 - 155.613i) q^{63} +(-480.651 - 176.404i) q^{64} +384.139i q^{65} +(-398.132 - 542.757i) q^{66} +369.398 q^{67} +(-12.9969 + 110.340i) q^{68} +(246.321 + 297.536i) q^{69} +(435.858 + 25.5813i) q^{70} -102.090 q^{71} +(-570.986 - 217.309i) q^{72} +897.637 q^{73} +(-15.7729 - 0.925739i) q^{74} +(82.8394 + 100.063i) q^{75} +(-364.575 - 42.9430i) q^{76} +1413.98 q^{77} +(667.850 + 910.452i) q^{78} -1020.54i q^{79} +(311.242 + 74.3535i) q^{80} +(-678.188 - 267.400i) q^{81} +(172.425 + 10.1199i) q^{82} +588.935i q^{83} +(1077.50 - 697.135i) q^{84} -69.4395i q^{85} +(10.7978 - 183.974i) q^{86} +(284.530 + 343.689i) q^{87} +(1020.35 + 181.327i) q^{88} -1260.99i q^{89} +(370.304 + 93.1393i) q^{90} -2371.89 q^{91} +(-590.613 - 69.5679i) q^{92} +(911.486 - 754.593i) q^{93} +(-87.6936 + 1494.14i) q^{94} +229.435 q^{95} +(866.945 - 364.887i) q^{96} +936.527 q^{97} +(-101.111 + 1722.75i) q^{98} +(1214.87 + 230.854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.165720	−	2.82357i	0.0585909	−	0.998282i
$2$	0.165720	−	2.82357i	0.0585909	−	0.998282i
$3$	3.31357	+	4.00253i	0.637698	+	0.770287i
$3$	3.31357	+	4.00253i	0.637698	+	0.770287i
$4$	−7.94507	−	0.935845i	−0.993134	−	0.116981i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	11.8505	−	8.69280i	0.806327	−	0.591470i
$7$			30.8728i			1.66698i	0.552537	+	0.833488i	$0.313660\pi$
$7$			30.8728i			1.66698i	−0.552537	+	0.833488i	$0.686340\pi$
$8$	−3.95908	+	22.2784i	−0.174968	+	0.984574i
$9$	−5.04045	+	26.5253i	−0.186683	+	0.982420i
$10$	0.828601	−	14.1178i	0.0262027	−	0.446445i
$11$		−	45.8002i		−	1.25539i	−0.778459	−	0.627695i	$-0.783999\pi$
$11$		−	45.8002i		−	1.25539i	0.778459	−	0.627695i	$-0.216001\pi$
$12$	−22.5808	−	34.9014i	−0.543211	−	0.839596i
$13$			76.8279i			1.63909i	0.573012	+	0.819547i	$0.305775\pi$
$13$			76.8279i			1.63909i	−0.573012	+	0.819547i	$0.694225\pi$
$14$	87.1715	+	5.11625i	1.66411	+	0.0976697i
$15$	16.5679	+	20.0126i	0.285187	+	0.344483i
$16$	62.2484	+	14.8707i	0.972631	+	0.232355i
$17$		−	13.8879i		−	0.198136i	−0.995081	−	0.0990679i	$-0.968414\pi$
$17$		−	13.8879i		−	0.198136i	0.995081	−	0.0990679i	$-0.0315861\pi$
$18$	74.0608	+	18.6279i	0.969794	+	0.243924i
$19$	45.8869			0.554062			0.277031	−	0.960861i	$-0.410650\pi$
$19$	45.8869			0.554062			0.277031	+	0.960861i	$0.410650\pi$
$20$	−39.7254	−	4.67922i	−0.444143	−	0.0523153i
$21$	−123.569	+	102.299i	−1.28405	+	1.06303i
$22$	−129.320	−	7.59002i	−1.25323	−	0.0735545i
$23$	74.3371			0.673928			0.336964	−	0.941517i	$-0.390600\pi$
$23$	74.3371			0.673928			0.336964	+	0.941517i	$0.390600\pi$
$24$	−102.288	+	57.9747i	−0.869981	+	0.493085i
$25$	25.0000			0.200000
$26$	216.929	+	12.7319i	1.63628	+	0.0960361i
$27$	−122.870	+	67.7191i	−0.875793	+	0.482687i
$28$	28.8922	−	245.287i	0.195004	−	1.65553i
$29$	85.8680			0.549838			0.274919	−	0.961467i	$-0.411349\pi$
$29$	85.8680			0.549838			0.274919	+	0.961467i	$0.411349\pi$
$30$	59.2527	−	43.4640i	0.360600	−	0.264514i
$31$		−	227.728i		−	1.31939i	−0.751533	−	0.659695i	$-0.770685\pi$
$31$		−	227.728i		−	1.31939i	0.751533	−	0.659695i	$-0.229315\pi$
$32$	52.3043	−	173.298i	0.288943	−	0.957346i
$33$	183.317	−	151.762i	0.967010	−	0.800559i
$34$	−39.2134	−	2.30151i	−0.197795	−	0.0116090i
$35$			154.364i			0.745494i
$36$	64.8704	−	206.029i	0.300326	−	0.953837i
$37$		−	5.58615i		−	0.0248205i	−0.999923	−	0.0124102i	$-0.996050\pi$
$37$		−	5.58615i		−	0.0248205i	0.999923	−	0.0124102i	$-0.00395041\pi$
$38$	7.60439	−	129.565i	0.0324630	−	0.553110i
$39$	−307.506	+	254.575i	−1.26257	+	1.04525i
$40$	−19.7954	+	111.392i	−0.0782482	+	0.440315i
$41$			61.0663i			0.232609i	0.993214	+	0.116304i	$0.0371048\pi$
$41$			61.0663i			0.232609i	−0.993214	+	0.116304i	$0.962895\pi$
$42$	268.371	+	365.860i	0.985967	+	1.34413i
$43$	65.1565			0.231076			0.115538	−	0.993303i	$-0.463141\pi$
$43$	65.1565			0.231076			0.115538	+	0.993303i	$0.463141\pi$
$44$	−42.8619	+	363.886i	−0.146856	+	1.24677i
$45$	−25.2023	+	132.627i	−0.0834874	+	0.439352i
$46$	12.3192	−	209.896i	0.0394861	−	0.672771i
$47$	−529.167			−1.64228			−0.821138	−	0.570730i	$-0.806660\pi$
$47$	−529.167			−1.64228			−0.821138	+	0.570730i	$0.806660\pi$
$48$	146.744	+	298.426i	0.441265	+	0.897377i
$49$	−610.132			−1.77881
$50$	4.14300	−	70.5892i	0.0117182	−	0.199656i
$51$	55.5867	−	46.0186i	0.152621	−	0.126351i
$52$	71.8990	−	610.403i	0.191742	−	1.62784i
$53$	22.7454			0.0589496			0.0294748	−	0.999566i	$-0.490617\pi$
$53$	22.7454			0.0589496			0.0294748	+	0.999566i	$0.490617\pi$
$54$	170.847	+	358.155i	0.430544	+	0.902569i
$55$		−	229.001i		−	0.561427i
$56$	−687.796	−	122.228i	−1.64126	−	0.291668i
$57$	152.050	+	183.664i	0.353324	+	0.426787i
$58$	14.2301	−	242.454i	0.0322155	−	0.548893i
$59$		−	384.963i		−	0.849456i	−0.905321	−	0.424728i	$-0.860370\pi$
$59$		−	384.963i		−	0.849456i	0.905321	−	0.424728i	$-0.139630\pi$
$60$	−112.904	−	174.507i	−0.242931	−	0.375479i
$61$			588.386i			1.23500i	0.786571	+	0.617500i	$0.211855\pi$
$61$			588.386i			1.23500i	−0.786571	+	0.617500i	$0.788145\pi$
$62$	−643.005	−	37.7391i	−1.31712	−	0.0773043i
$63$	−818.912	−	155.613i	−1.63767	−	0.311197i
$64$	−480.651	−	176.404i	−0.938772	−	0.344538i
$65$			384.139i			0.733025i
$66$	−398.132	−	542.757i	−0.742526	−	1.01225i
$67$	369.398			0.673570			0.336785	−	0.941582i	$-0.390660\pi$
$67$	369.398			0.673570			0.336785	+	0.941582i	$0.390660\pi$
$68$	−12.9969	+	110.340i	−0.0231780	+	0.196776i
$69$	246.321	+	297.536i	0.429762	+	0.519118i
$70$	435.858	+	25.5813i	0.744214	+	0.0436792i
$71$	−102.090			−0.170646			−0.0853229	−	0.996353i	$-0.527192\pi$
$71$	−102.090			−0.170646			−0.0853229	+	0.996353i	$0.527192\pi$
$72$	−570.986	−	217.309i	−0.934602	−	0.355696i
$73$	897.637			1.43918			0.719592	−	0.694397i	$-0.244329\pi$
$73$	897.637			1.43918			0.719592	+	0.694397i	$0.244329\pi$
$74$	−15.7729	−	0.925739i	−0.0247778	−	0.00145426i
$75$	82.8394	+	100.063i	0.127540	+	0.154057i
$76$	−364.575	−	42.9430i	−0.550258	−	0.0648145i
$77$	1413.98			2.09271
$78$	667.850	+	910.452i	0.969476	+	1.32165i
$79$		−	1020.54i		−	1.45341i	−0.686951	−	0.726704i	$-0.741051\pi$
$79$		−	1020.54i		−	1.45341i	0.686951	−	0.726704i	$-0.258949\pi$
$80$	311.242	+	74.3535i	0.434974	+	0.103912i
$81$	−678.188	−	267.400i	−0.930299	−	0.366803i
$82$	172.425	+	10.1199i	0.232209	+	0.0136288i
$83$			588.935i			0.778844i	0.921059	+	0.389422i	$0.127325\pi$
$83$			588.935i			0.778844i	−0.921059	+	0.389422i	$0.872675\pi$
$84$	1077.50	−	697.135i	1.39959	−	0.905519i
$85$		−	69.4395i		−	0.0886091i
$86$	10.7978	−	183.974i	0.0135390	−	0.230679i
$87$	284.530	+	343.689i	0.350630	+	0.423533i
$88$	1020.35	+	181.327i	1.23602	+	0.219653i
$89$		−	1260.99i		−	1.50185i	−0.660387	−	0.750925i	$-0.729608\pi$
$89$		−	1260.99i		−	1.50185i	0.660387	−	0.750925i	$-0.270392\pi$
$90$	370.304	+	93.1393i	0.433705	+	0.109086i
$91$	−2371.89			−2.73233
$92$	−590.613	−	69.5679i	−0.669301	−	0.0788365i
$93$	911.486	−	754.593i	1.01631	−	0.841372i
$94$	−87.6936	+	1494.14i	−0.0962224	+	1.63945i
$95$	229.435			0.247784
$96$	866.945	−	364.887i	0.921689	−	0.387928i
$97$	936.527			0.980308			0.490154	−	0.871636i	$-0.336941\pi$
$97$	936.527			0.980308			0.490154	+	0.871636i	$0.336941\pi$
$98$	−101.111	+	1722.75i	−0.104222	+	1.77575i
$99$	1214.87	+	230.854i	1.23332	+	0.234361i
$100$	−198.627	−	23.3961i	−0.198627	−	0.0233961i
$101$	1632.64			1.60845			0.804227	−	0.594322i	$-0.202579\pi$
$101$	1632.64			1.60845			0.804227	+	0.594322i	$0.202579\pi$
$102$	−120.725	−	164.579i	−0.117191	−	0.159762i
$103$		−	524.863i		−	0.502100i	−0.967974	−	0.251050i	$-0.919224\pi$
$103$		−	524.863i		−	0.502100i	0.967974	−	0.251050i	$-0.0807759\pi$
$104$	−1711.60	−	304.168i	−1.61381	−	0.286789i
$105$	−617.847	+	511.497i	−0.574244	+	0.475400i
$106$	3.76938	−	64.2233i	0.00345391	−	0.0588483i
$107$		−	1358.24i		−	1.22716i	−0.789633	−	0.613580i	$-0.789729\pi$
$107$		−	1358.24i		−	1.22716i	0.789633	−	0.613580i	$-0.210271\pi$
$108$	1039.59	−	423.046i	0.926245	−	0.376922i
$109$			188.470i			0.165616i	0.996566	+	0.0828080i	$0.0263888\pi$
$109$			188.470i			0.165616i	−0.996566	+	0.0828080i	$0.973611\pi$
$110$	−646.600	−	37.9501i	−0.560463	−	0.0328946i
$111$	22.3587	−	18.5101i	0.0191189	−	0.0158280i
$112$	−459.101	+	1921.78i	−0.387330	+	1.62135i
$113$			663.242i			0.552146i	0.961137	+	0.276073i	$0.0890332\pi$
$113$			663.242i			0.552146i	−0.961137	+	0.276073i	$0.910967\pi$
$114$	543.785	−	398.886i	0.446755	−	0.327711i
$115$	371.685			0.301390
$116$	−682.228	−	80.3591i	−0.546062	−	0.0643203i
$117$	−2037.89	−	387.247i	−1.61028	−	0.305992i
$118$	−1086.97	−	63.7962i	−0.847997	−	0.0497705i
$119$	428.759			0.330288
$120$	−511.442	+	289.873i	−0.389067	+	0.220514i
$121$	−766.661			−0.576004
$122$	1661.35	+	97.5074i	1.23288	+	0.0723599i
$123$	−244.420	+	202.348i	−0.179175	+	0.148334i
$124$	−213.118	+	1809.31i	−0.154343	+	1.31033i
$125$	125.000			0.0894427
$126$	−575.094	+	2286.47i	−0.406615	+	1.61662i
$127$		−	1963.64i		−	1.37200i	−0.727600	−	0.686002i	$-0.759364\pi$
$127$		−	1963.64i		−	1.37200i	0.727600	−	0.686002i	$-0.240636\pi$
$128$	−577.741	+	1327.92i	−0.398950	+	0.916973i
$129$	215.901	+	260.791i	0.147357	+	0.177995i
$130$	1084.64	+	63.6597i	0.731766	+	0.0429486i
$131$			2280.27i			1.52082i	0.649441	+	0.760412i	$0.275003\pi$
$131$			2280.27i			1.52082i	−0.649441	+	0.760412i	$0.724997\pi$
$132$	−1598.49	+	1034.21i	−1.05402	+	0.681941i
$133$			1416.66i			0.923608i
$134$	61.2168	−	1043.02i	0.0394651	−	0.672413i
$135$	−614.352	+	338.596i	−0.391666	+	0.215864i
$136$	309.400	+	54.9833i	0.195079	+	0.0346675i
$137$		−	1285.92i		−	0.801926i	−0.916094	−	0.400963i	$-0.868676\pi$
$137$		−	1285.92i		−	0.801926i	0.916094	−	0.400963i	$-0.131324\pi$
$138$	880.934	−	646.197i	0.543406	−	0.398609i
$139$	3056.74			1.86525			0.932623	−	0.360853i	$-0.117514\pi$
$139$	3056.74			1.86525			0.932623	+	0.360853i	$0.117514\pi$
$140$	144.461	−	1226.43i	0.0872084	−	0.740376i
$141$	−1753.43	−	2118.01i	−1.04727	−	1.26502i
$142$	−16.9184	+	288.258i	−0.00999830	+	0.170353i
$143$	3518.74			2.05770
$144$	−708.211	+	1576.20i	−0.409844	+	0.912156i
$145$	429.340			0.245895
$146$	148.757	−	2534.54i	0.0843232	−	1.43671i
$147$	−2021.72	−	2442.07i	−1.13434	−	1.37019i
$148$	−5.22777	+	44.3824i	−0.00290351	+	0.0246501i
$149$	−213.268			−0.117259			−0.0586296	−	0.998280i	$-0.518673\pi$
$149$	−213.268			−0.117259			−0.0586296	+	0.998280i	$0.518673\pi$
$150$	296.263	−	217.320i	0.161265	−	0.118294i
$151$			1145.23i			0.617202i	0.951192	+	0.308601i	$0.0998608\pi$
$151$			1145.23i			0.617202i	−0.951192	+	0.308601i	$0.900139\pi$
$152$	−181.670	+	1022.29i	−0.0969433	+	0.545515i
$153$	368.381	+	70.0013i	0.194653	+	0.0369887i
$154$	234.325	−	3992.48i	0.122614	−	2.08911i
$155$		−	1138.64i		−	0.590049i
$156$	2681.40	−	1734.84i	1.37618	−	0.890374i
$157$			1821.66i			0.926016i	0.886354	+	0.463008i	$0.153230\pi$
$157$			1821.66i			0.926016i	−0.886354	+	0.463008i	$0.846770\pi$
$158$	−2881.55	−	169.123i	−1.45091	−	0.0851565i
$159$	75.3687	+	91.0393i	0.0375920	+	0.0454081i
$160$	261.521	−	866.491i	0.129219	−	0.428138i
$161$			2295.00i			1.12342i
$162$	−867.410	+	1870.60i	−0.420680	+	0.907209i
$163$	45.0906			0.0216673			0.0108336	−	0.999941i	$-0.496551\pi$
$163$	45.0906			0.0216673			0.0108336	+	0.999941i	$0.496551\pi$
$164$	57.1486	−	485.176i	0.0272107	−	0.231012i
$165$	916.583	−	758.812i	0.432460	−	0.358021i
$166$	1662.90	+	97.5985i	0.777506	+	0.0456332i
$167$	1273.78			0.590226			0.295113	−	0.955462i	$-0.404643\pi$
$167$	1273.78			0.590226			0.295113	+	0.955462i	$0.404643\pi$
$168$	−1789.84	−	3157.94i	−0.821961	−	1.45024i
$169$	−3705.53			−1.68663
$170$	−196.067	−	11.5075i	−0.0884568	−	0.00519169i
$171$	−231.291	+	1217.17i	−0.103434	+	0.544322i
$172$	−517.673	−	60.9764i	−0.229490	−	0.0270314i
$173$	−2464.79			−1.08321			−0.541603	−	0.840634i	$-0.682183\pi$
$173$	−2464.79			−1.08321			−0.541603	+	0.840634i	$0.682183\pi$
$174$	1017.58	−	746.434i	0.443349	−	0.325213i
$175$			771.821i			0.333395i
$176$	681.082	−	2850.99i	0.291696	−	1.22103i
$177$	1540.83	−	1275.60i	0.654325	−	0.541696i
$178$	−3560.49	−	208.972i	−1.49927	−	0.0879948i
$179$		−	940.520i		−	0.392725i	−0.980531	−	0.196362i	$-0.937087\pi$
$179$		−	940.520i		−	0.392725i	0.980531	−	0.196362i	$-0.0629129\pi$
$180$	324.352	−	1030.14i	0.134310	−	0.426569i
$181$			72.3126i			0.0296959i	0.999890	+	0.0148479i	$0.00472642\pi$
$181$			72.3126i			0.0296959i	−0.999890	+	0.0148479i	$0.995274\pi$
$182$	−393.071	+	6697.21i	−0.160090	+	2.72764i
$183$	−2355.03	+	1949.66i	−0.951305	+	0.787557i
$184$	−294.306	+	1656.11i	−0.117916	+	0.663532i
$185$		−	27.9308i		−	0.0111001i
$186$	−1979.59	−	2698.70i	−0.780380	−	1.06386i
$187$	−636.069			−0.248738
$188$	4204.27	+	495.218i	1.63100	+	0.192114i
$189$	−2090.68	−	3793.35i	−0.804628	−	1.45993i
$190$	38.0219	−	647.824i	0.0145179	−	0.247358i
$191$	−2309.87			−0.875060			−0.437530	−	0.899204i	$-0.644147\pi$
$191$	−2309.87			−0.875060			−0.437530	+	0.899204i	$0.644147\pi$
$192$	−886.613	−	2508.35i	−0.333259	−	0.942835i
$193$	−73.8936			−0.0275595			−0.0137797	−	0.999905i	$-0.504386\pi$
$193$	−73.8936			−0.0275595			−0.0137797	+	0.999905i	$0.504386\pi$
$194$	155.201	−	2644.35i	0.0574372	−	0.978624i
$195$	−1537.53	+	1272.87i	−0.564640	+	0.467448i
$196$	4847.54	+	570.988i	1.76660	+	0.208086i
$197$	−3741.28			−1.35307			−0.676536	−	0.736409i	$-0.736520\pi$
$197$	−3741.28			−1.35307			−0.676536	+	0.736409i	$0.736520\pi$
$198$	853.160	−	3392.00i	0.306219	−	1.21747i
$199$			1758.41i			0.626382i	0.949690	+	0.313191i	$0.101398\pi$
$199$			1758.41i			0.626382i	−0.949690	+	0.313191i	$0.898602\pi$
$200$	−98.9770	+	556.959i	−0.0349937	+	0.196915i
$201$	1224.03	+	1478.53i	0.429534	+	0.518842i
$202$	270.562	−	4609.88i	0.0942409	−	1.60569i
$203$			2650.99i			0.916566i
$204$	−484.707	+	313.600i	−0.166354	+	0.107630i
$205$			305.332i			0.104026i
$206$	−1481.99	−	86.9805i	−0.501238	−	0.0294185i
$207$	−374.693	+	1971.82i	−0.125811	+	0.662081i
$208$	−1142.49	+	4782.41i	−0.380851	+	1.59423i
$209$		−	2101.63i		−	0.695564i
$210$	1341.86	+	1829.30i	0.440938	+	0.601112i
$211$	327.697			0.106917			0.0534587	−	0.998570i	$-0.482975\pi$
$211$	327.697			0.106917			0.0534587	+	0.998570i	$0.482975\pi$
$212$	−180.714	−	21.2862i	−0.0585448	−	0.00689595i
$213$	−338.283	−	408.618i	−0.108820	−	0.131446i
$214$	−3835.08	−	225.088i	−1.22505	−	0.0719004i
$215$	325.783			0.103340
$216$	−1022.22	−	3005.46i	−0.322005	−	0.946738i
$217$	7030.60			2.19939
$218$	532.157	+	31.2333i	0.165331	+	0.00970359i
$219$	2974.39	+	3592.82i	0.917764	+	1.10858i
$220$	−214.309	+	1819.43i	−0.0656761	+	0.557573i
$221$	1066.98			0.324763
$222$	−48.5593	−	66.1989i	−0.0146806	−	0.0200134i
$223$		−	724.529i		−	0.217570i	−0.994065	−	0.108785i	$-0.965304\pi$
$223$		−	724.529i		−	0.217570i	0.994065	−	0.108785i	$-0.0346959\pi$
$224$	5350.21	+	1614.78i	1.59587	+	0.481661i
$225$	−126.011	+	663.134i	−0.0373367	+	0.196484i
$226$	1872.71	+	109.913i	0.551198	+	0.0323508i
$227$		−	4049.18i		−	1.18394i	−0.805961	−	0.591968i	$-0.798351\pi$
$227$		−	4049.18i		−	1.18394i	0.805961	−	0.591968i	$-0.201649\pi$
$228$	−1036.17	−	1601.52i	−0.300972	−	0.465189i
$229$			5915.98i			1.70716i	0.520965	+	0.853578i	$0.325572\pi$
$229$			5915.98i			1.70716i	−0.520965	+	0.853578i	$0.674428\pi$
$230$	61.5958	−	1049.48i	0.0176587	−	0.300872i
$231$	4685.34	+	5659.50i	1.33451	+	1.61198i
$232$	−339.958	+	1913.00i	−0.0962041	+	0.541356i
$233$		−	2260.11i		−	0.635471i	−0.948179	−	0.317736i	$-0.897078\pi$
$233$		−	2260.11i		−	0.635471i	0.948179	−	0.317736i	$-0.102922\pi$
$234$	−1431.14	+	5689.94i	−0.399814	+	1.58958i
$235$	−2645.83			−0.734448
$236$	−360.266	+	3058.56i	−0.0993699	+	0.843624i
$237$	4084.72	−	3381.62i	1.11954	−	0.926834i
$238$	71.0540	−	1210.63i	0.0193519	−	0.329720i
$239$	−928.002			−0.251161			−0.125581	−	0.992083i	$-0.540079\pi$
$239$	−928.002			−0.251161			−0.125581	+	0.992083i	$0.540079\pi$
$240$	733.721	+	1492.13i	0.197340	+	0.401319i
$241$	−5101.54			−1.36357			−0.681783	−	0.731554i	$-0.738795\pi$
$241$	−5101.54			−1.36357			−0.681783	+	0.731554i	$0.738795\pi$
$242$	−127.051	+	2164.72i	−0.0337486	+	0.575014i
$243$	−1176.95	−	3600.51i	−0.310705	−	0.950506i
$244$	550.637	−	4674.77i	0.144471	−	1.22652i
$245$	−3050.66			−0.795508
$246$	530.837	+	723.669i	0.137581	+	0.187559i
$247$			3525.40i			0.908160i
$248$	5073.40	+	901.592i	1.29904	+	0.230851i
$249$	−2357.23	+	1951.48i	−0.599933	+	0.496667i
$250$	20.7150	−	352.946i	0.00524053	−	0.0892891i
$251$			396.163i			0.0996238i	0.998759	+	0.0498119i	$0.0158622\pi$
$251$			396.163i			0.0996238i	−0.998759	+	0.0498119i	$0.984138\pi$
$252$	6360.69	+	2002.73i	1.59002	+	0.500636i
$253$		−	3404.65i		−	0.846043i
$254$	−5544.46	−	325.414i	−1.36965	−	0.0803870i
$255$	277.933	−	230.093i	0.0682544	−	0.0565058i
$256$	3653.72	+	1851.36i	0.892022	+	0.451991i
$257$			4197.44i			1.01879i	0.860532	+	0.509396i	$0.170131\pi$
$257$			4197.44i			1.01879i	−0.860532	+	0.509396i	$0.829869\pi$
$258$	772.140	−	566.393i	0.186323	−	0.136675i
$259$	172.460			0.0413752
$260$	359.495	−	3052.02i	0.0857497	−	0.727992i
$261$	−432.814	+	2277.68i	−0.102646	+	0.540171i
$262$	6438.49	+	377.886i	1.51821	+	0.0891065i
$263$	−4060.33			−0.951981			−0.475990	−	0.879450i	$-0.657910\pi$
$263$	−4060.33			−0.951981			−0.475990	+	0.879450i	$0.657910\pi$
$264$	2655.25	+	4684.84i	0.619014	+	1.09217i
$265$	113.727			0.0263631
$266$	4000.03	+	234.769i	0.922022	+	0.0541151i
$267$	5047.15	−	4178.38i	1.15686	−	0.957726i
$268$	−2934.90	−	345.699i	−0.668945	−	0.0787946i
$269$	−166.812			−0.0378094			−0.0189047	−	0.999821i	$-0.506018\pi$
$269$	−166.812			−0.0378094			−0.0189047	+	0.999821i	$0.506018\pi$
$270$	854.237	+	1790.78i	0.192545	+	0.403641i
$271$		−	6388.24i		−	1.43195i	−0.698127	−	0.715974i	$-0.745983\pi$
$271$		−	6388.24i		−	1.43195i	0.698127	−	0.715974i	$-0.254017\pi$
$272$	206.523	−	864.499i	0.0460378	−	0.192713i
$273$	−7859.45	−	9493.57i	−1.74240	−	2.10468i
$274$	−3630.89	−	213.103i	−0.800548	−	0.0469856i
$275$		−	1145.01i		−	0.251078i
$276$	−1678.59	−	2594.47i	−0.366085	−	0.565828i
$277$		−	3245.23i		−	0.703924i	−0.936014	−	0.351962i	$-0.885515\pi$
$277$		−	3245.23i		−	0.703924i	0.936014	−	0.351962i	$-0.114485\pi$
$278$	506.563	−	8630.91i	0.109286	−	1.86204i
$279$	6040.56	+	1147.85i	1.29620	+	0.246308i
$280$	−3438.98	−	611.140i	−0.733994	−	0.130438i
$281$			6182.32i			1.31248i	0.754553	+	0.656239i	$0.227854\pi$
$281$			6182.32i			1.31248i	−0.754553	+	0.656239i	$0.772146\pi$
$282$	−6270.91	+	4599.94i	−1.32421	+	0.971357i
$283$	5095.93			1.07039			0.535197	−	0.844727i	$-0.320237\pi$
$283$	5095.93			1.07039			0.535197	+	0.844727i	$0.320237\pi$
$284$	811.113	+	95.5404i	0.169474	+	0.0199622i
$285$	760.248	+	918.318i	0.158011	+	0.190865i
$286$	583.126	−	9935.39i	0.120563	−	2.05417i
$287$	−1885.29			−0.387753
$288$	4333.16	+	2260.89i	0.886575	+	0.462584i
$289$	4720.13			0.960742
$290$	71.1503	−	1212.27i	0.0144072	−	0.245472i
$291$	3103.25	+	3748.47i	0.625140	+	0.755118i
$292$	−7131.79	−	840.049i	−1.42930	−	0.168357i
$293$	−304.740			−0.0607614			−0.0303807	−	0.999538i	$-0.509672\pi$
$293$	−304.740			−0.0607614			−0.0303807	+	0.999538i	$0.509672\pi$
$294$	−7230.39	+	5303.75i	−1.43430	+	1.05211i
$295$		−	1924.82i		−	0.379888i
$296$	124.450	+	22.1160i	0.0244376	+	0.00434280i
$297$	3101.55	+	5627.49i	0.605961	+	1.09946i
$298$	−35.3429	+	602.178i	−0.00687033	+	0.117058i
$299$			5711.16i			1.10463i
$300$	−564.521	−	872.534i	−0.108642	−	0.167919i
$301$			2011.57i			0.385199i
$302$	3233.64	+	189.788i	0.616142	+	0.0361625i
$303$	5409.88	+	6534.69i	1.02571	+	1.23897i
$304$	2856.39	+	682.371i	0.538898	+	0.128739i
$305$			2941.93i			0.552309i
$306$	258.702	−	1028.55i	0.0483300	−	0.192151i
$307$	−9307.57			−1.73033			−0.865165	−	0.501488i	$-0.832786\pi$
$307$	−9307.57			−1.73033			−0.865165	+	0.501488i	$0.832786\pi$
$308$	−11234.2	−	1323.27i	−2.07834	−	0.244806i
$309$	2100.78	−	1739.17i	0.386761	−	0.320188i
$310$	−3215.02	−	188.695i	−0.589036	−	0.0345715i
$311$	6574.29			1.19869			0.599347	−	0.800490i	$-0.295427\pi$
$311$	6574.29			1.19869			0.599347	+	0.800490i	$0.295427\pi$
$312$	−4454.07	−	7858.61i	−0.808212	−	1.42598i
$313$	−1809.44			−0.326759			−0.163380	−	0.986563i	$-0.552240\pi$
$313$	−1809.44			−0.326759			−0.163380	+	0.986563i	$0.552240\pi$
$314$	5143.59	+	301.886i	0.924425	+	0.0542562i
$315$	−4094.56	−	778.065i	−0.732389	−	0.139171i
$316$	−955.062	+	8108.23i	−0.170020	+	1.44343i
$317$	2060.25			0.365031			0.182516	−	0.983203i	$-0.441576\pi$
$317$	2060.25			0.365031			0.182516	+	0.983203i	$0.441576\pi$
$318$	269.546	−	197.722i	0.0475326	−	0.0348669i
$319$		−	3932.77i		−	0.690261i
$320$	−2403.26	−	882.018i	−0.419832	−	0.154082i
$321$	5436.39	−	4500.63i	0.945264	−	0.782556i
$322$	6480.08	+	380.327i	1.12149	+	0.0658224i
$323$		−	637.273i		−	0.109780i
$324$	5138.01	+	2759.19i	0.881002	+	0.473112i
$325$			1920.70i			0.327819i
$326$	7.47242	−	127.316i	0.00126951	−	0.0216301i
$327$	−754.356	+	624.509i	−0.127572	+	0.105613i
$328$	−1360.46	−	241.766i	−0.229021	−	0.0406991i
$329$		−	16336.9i		−	2.73763i
$330$	−1990.66	−	2713.79i	−0.332068	−	0.452694i
$331$	474.742			0.0788343			0.0394172	−	0.999223i	$-0.487450\pi$
$331$	474.742			0.0788343			0.0394172	+	0.999223i	$0.487450\pi$
$332$	551.152	−	4679.13i	0.0911096	−	0.773497i
$333$	148.175	+	28.1568i	0.0243841	+	0.00463358i
$334$	211.090	−	3596.59i	0.0345819	−	0.589212i
$335$	1846.99			0.301230
$336$	−9213.26	+	4530.41i	−1.49591	+	0.735578i
$337$	1554.93			0.251342			0.125671	−	0.992072i	$-0.459892\pi$
$337$	1554.93			0.251342			0.125671	+	0.992072i	$0.459892\pi$
$338$	−614.081	+	10462.8i	−0.0988212	+	1.68373i
$339$	−2654.64	+	2197.70i	−0.425311	+	0.352102i
$340$	−64.9846	+	551.702i	−0.0103655	+	0.0880007i
$341$	−10430.0			−1.65635
$342$	3398.42	+	854.775i	0.537326	+	0.135149i
$343$		−	8247.11i		−	1.29826i
$344$	−257.960	+	1451.58i	−0.0404310	+	0.227512i
$345$	1231.61	+	1487.68i	0.192196	+	0.232157i
$346$	−408.466	+	6959.51i	−0.0634661	+	1.08135i
$347$		−	227.214i		−	0.0351512i	−0.999846	−	0.0175756i	$-0.994405\pi$
$347$		−	227.214i		−	0.0351512i	0.999846	−	0.0175756i	$-0.00559478\pi$
$348$	−1938.97	−	2996.91i	−0.298678	−	0.461642i
$349$		−	11005.7i		−	1.68802i	−0.536327	−	0.844010i	$-0.680189\pi$
$349$		−	11005.7i		−	1.68802i	0.536327	−	0.844010i	$-0.319811\pi$
$350$	2179.29	+	127.906i	0.332822	+	0.0195339i
$351$	−5202.72	−	9439.87i	−0.791170	−	1.43551i
$352$	−7937.10	−	2395.55i	−1.20184	−	0.362736i
$353$			3366.22i			0.507551i	0.967263	+	0.253776i	$0.0816725\pi$
$353$			3366.22i			0.507551i	−0.967263	+	0.253776i	$0.918327\pi$
$354$	−3346.41	−	4562.02i	−0.502428	−	0.684940i
$355$	−510.450			−0.0763151
$356$	−1180.09	+	10018.7i	−0.175687	+	1.49154i
$357$	1420.72	+	1716.12i	0.210624	+	0.254416i
$358$	−2655.62	−	155.863i	−0.392050	−	0.0230101i
$359$	−7235.65			−1.06374			−0.531870	−	0.846826i	$-0.678511\pi$
$359$	−7235.65			−1.06374			−0.531870	+	0.846826i	$0.678511\pi$
$360$	−2854.93	−	1086.55i	−0.417967	−	0.159072i
$361$	−4753.39			−0.693015
$362$	204.179	+	11.9837i	0.0296448	+	0.00173991i
$363$	−2540.39	−	3068.58i	−0.367316	−	0.443688i
$364$	18844.9	+	2219.72i	2.71357	+	0.319630i
$365$	4488.18			0.643623
$366$	5114.72	+	6972.68i	0.730466	+	0.995814i
$367$		−	8609.76i		−	1.22459i	−0.790628	−	0.612297i	$-0.790246\pi$
$367$		−	8609.76i		−	1.22459i	0.790628	−	0.612297i	$-0.209754\pi$
$368$	4627.36	+	1105.44i	0.655484	+	0.156590i
$369$	−1619.81	−	307.802i	−0.228519	−	0.0434242i
$370$	−78.8644	−	4.62869i	−0.0110810	−	0.000650363i
$371$			702.216i			0.0982675i
$372$	−7948.01	+	5142.28i	−1.10776	+	0.716707i
$373$			8108.93i			1.12564i	0.826579	+	0.562821i	$0.190284\pi$
$373$			8108.93i			1.12564i	−0.826579	+	0.562821i	$0.809716\pi$
$374$	−105.409	+	1795.98i	−0.0145738	+	0.248310i
$375$	414.197	+	500.316i	0.0570374	+	0.0688965i
$376$	2095.01	−	11789.0i	0.287346	−	1.61694i
$377$			6597.06i			0.901236i
$378$	−11057.3	+	5274.55i	−1.50456	+	0.717707i
$379$	−699.156			−0.0947578			−0.0473789	−	0.998877i	$-0.515087\pi$
$379$	−699.156			−0.0947578			−0.0473789	+	0.998877i	$0.515087\pi$
$380$	−1822.87	−	214.715i	−0.246083	−	0.0289859i
$381$	7859.51	−	6506.65i	1.05684	−	0.874924i
$382$	−382.792	+	6522.08i	−0.0512706	+	0.873556i
$383$	−464.645			−0.0619902			−0.0309951	−	0.999520i	$-0.509868\pi$
$383$	−464.645			−0.0619902			−0.0309951	+	0.999520i	$0.509868\pi$
$384$	−7229.42	+	2087.73i	−0.960741	+	0.277445i
$385$	7069.91			0.935886
$386$	−12.2457	+	208.644i	−0.00161474	+	0.0275121i
$387$	−328.419	+	1728.30i	−0.0431381	+	0.227014i
$388$	−7440.77	−	876.443i	−0.973577	−	0.114677i
$389$	−2826.36			−0.368386			−0.184193	−	0.982890i	$-0.558967\pi$
$389$	−2826.36			−0.368386			−0.184193	+	0.982890i	$0.558967\pi$
$390$	3339.25	+	4552.26i	0.433563	+	0.591058i
$391$		−	1032.39i		−	0.133529i
$392$	2415.56	−	13592.7i	0.311235	−	1.75137i
$393$	−9126.84	+	7555.84i	−1.17147	+	0.969826i
$394$	−620.006	+	10563.8i	−0.0792778	+	1.35075i
$395$		−	5102.68i		−	0.649983i
$396$	−9436.16	−	2971.08i	−1.19744	−	0.377026i
$397$			1121.59i			0.141791i	0.997484	+	0.0708957i	$0.0225857\pi$
$397$			1121.59i			0.141791i	−0.997484	+	0.0708957i	$0.977414\pi$
$398$	4964.98	+	291.403i	0.625306	+	0.0367003i
$399$	−5670.22	+	4694.20i	−0.711443	+	0.588983i
$400$	1556.21	+	371.768i	0.194526	+	0.0464710i
$401$		−	3167.14i		−	0.394412i	−0.980362	−	0.197206i	$-0.936813\pi$
$401$		−	3167.14i		−	0.394412i	0.980362	−	0.197206i	$-0.0631868\pi$
$402$	4377.57	−	3211.11i	0.543118	−	0.398397i
$403$	17495.8			2.16261
$404$	−12971.5	−	1527.90i	−1.59741	−	0.188158i
$405$	−3390.94	−	1337.00i	−0.416042	−	0.164039i
$406$	7485.25	+	439.322i	0.914991	+	0.0537025i
$407$	−255.847			−0.0311594
$408$	805.147	+	1420.57i	0.0976978	+	0.172375i
$409$	−6367.99			−0.769870			−0.384935	−	0.922944i	$-0.625776\pi$
$409$	−6367.99			−0.769870			−0.384935	+	0.922944i	$0.625776\pi$
$410$	862.125	+	50.5996i	0.103847	+	0.00609497i
$411$	5146.94	−	4261.00i	0.617713	−	0.511386i
$412$	−491.191	+	4170.08i	−0.0587360	+	0.498653i
$413$	11884.9			1.41602
$414$	5505.46	+	1384.74i	0.653572	+	0.164387i
$415$			2944.68i			0.348310i
$416$	13314.1	+	4018.43i	1.56918	+	0.473605i
$417$	10128.7	+	12234.7i	1.18946	+	1.43677i
$418$	−5934.10	−	348.283i	−0.694369	−	0.0407537i
$419$		−	5043.53i		−	0.588049i	−0.955798	−	0.294025i	$-0.905005\pi$
$419$		−	5043.53i		−	0.588049i	0.955798	−	0.294025i	$-0.0949948\pi$
$420$	5387.52	−	3485.67i	0.625914	−	0.404961i
$421$			7446.89i			0.862089i	0.902331	+	0.431044i	$0.141855\pi$
$421$			7446.89i			0.862089i	−0.902331	+	0.431044i	$0.858145\pi$
$422$	54.3060	−	925.274i	0.00626439	−	0.106734i
$423$	2667.24	−	14036.3i	0.306586	−	1.61340i
$424$	−90.0510	+	506.731i	−0.0103143	+	0.0580402i
$425$		−	347.197i		−	0.0396272i
$426$	−1209.82	+	887.448i	−0.137596	+	0.100932i
$427$	−18165.1			−2.05872
$428$	−1271.10	+	10791.3i	−0.143554	+	1.21873i
$429$	11659.6	+	14083.8i	1.31219	+	1.58502i
$430$	53.9888	−	919.870i	0.00605481	−	0.103163i
$431$	−8372.86			−0.935746			−0.467873	−	0.883796i	$-0.654980\pi$
$431$	−8372.86			−0.935746			−0.467873	+	0.883796i	$0.654980\pi$
$432$	−8655.51	+	2388.24i	−0.963978	+	0.265982i
$433$	−4694.85			−0.521063			−0.260531	−	0.965465i	$-0.583898\pi$
$433$	−4694.85			−0.521063			−0.260531	+	0.965465i	$0.583898\pi$
$434$	1165.11	−	19851.4i	0.128864	−	2.19561i
$435$	1422.65	+	1718.45i	0.156807	+	0.189410i
$436$	176.378	−	1497.41i	0.0193738	−	0.164479i
$437$	3411.10			0.373398
$438$	10637.5	−	7802.98i	1.16045	−	0.851235i
$439$		−	5414.00i		−	0.588602i	−0.955713	−	0.294301i	$-0.904913\pi$
$439$		−	5414.00i		−	0.588602i	0.955713	−	0.294301i	$-0.0950868\pi$
$440$	5101.77	+	906.634i	0.552767	+	0.0982320i
$441$	3075.34	−	16183.9i	0.332074	−	1.74754i
$442$	176.820	−	3012.69i	0.0190282	−	0.324205i
$443$			8147.10i			0.873771i	0.899517	+	0.436886i	$0.143919\pi$
$443$			8147.10i			0.873771i	−0.899517	+	0.436886i	$0.856081\pi$
$444$	−194.964	+	126.140i	−0.0208392	+	0.0134828i
$445$		−	6304.95i		−	0.671648i
$446$	−2045.76	−	120.069i	−0.217196	−	0.0127476i
$447$	−706.680	−	853.612i	−0.0747759	−	0.0903232i
$448$	5446.08	−	14839.1i	0.574337	−	1.56491i
$449$		−	2592.32i		−	0.272470i	−0.990677	−	0.136235i	$-0.956500\pi$
$449$		−	2592.32i		−	0.272470i	0.990677	−	0.136235i	$-0.0435002\pi$
$450$	1851.52	+	465.696i	0.193959	+	0.0487847i
$451$	2796.85			0.292015
$452$	620.691	−	5269.51i	0.0645904	−	0.548356i
$453$	−4583.82	+	3794.81i	−0.475423	+	0.393588i
$454$	−11433.1	−	671.031i	−1.18190	−	0.0693679i
$455$	−11859.5			−1.22194
$456$	−4693.70	+	2660.28i	−0.482024	+	0.273200i
$457$	−5102.14			−0.522249			−0.261125	−	0.965305i	$-0.584093\pi$
$457$	−5102.14			−0.522249			−0.261125	+	0.965305i	$0.584093\pi$
$458$	16704.2	+	980.397i	1.70422	+	0.100024i
$459$	940.476	+	1706.41i	0.0956376	+	0.173526i
$460$	−2953.07	−	347.840i	−0.299321	−	0.0352568i
$461$	15229.7			1.53865			0.769326	−	0.638857i	$-0.220592\pi$
$461$	15229.7			1.53865			0.769326	+	0.638857i	$0.220592\pi$
$462$	16756.5	−	12291.5i	1.68740	−	1.23777i
$463$			14047.2i			1.41000i	0.709206	+	0.705001i	$0.249053\pi$
$463$			14047.2i			1.41000i	−0.709206	+	0.705001i	$0.750947\pi$
$464$	5345.15	+	1276.92i	0.534789	+	0.127757i
$465$	4557.43	−	3772.96i	0.454507	−	0.376273i
$466$	−6381.58	−	374.546i	−0.634380	−	0.0372329i
$467$			12290.1i			1.21781i	0.793242	+	0.608906i	$0.208392\pi$
$467$			12290.1i			1.21781i	−0.793242	+	0.608906i	$0.791608\pi$
$468$	15828.8	+	4983.85i	1.56343	+	0.492262i
$469$			11404.4i			1.12283i
$470$	−438.468	+	7470.69i	−0.0430320	+	0.733186i
$471$	−7291.26	+	6036.22i	−0.713298	+	0.590518i
$472$	8576.35	+	1524.10i	0.836353	+	0.148628i
$473$		−	2984.18i		−	0.290091i
$474$	−8871.31	−	12093.9i	−0.859647	−	1.17192i
$475$	1147.17			0.110812
$476$	−3406.52	−	401.251i	−0.328020	−	0.0386373i
$477$	−114.647	+	603.331i	−0.0110049	+	0.0579132i
$478$	−153.789	+	2620.28i	−0.0147158	+	0.250730i
$479$	9853.78			0.939939			0.469970	−	0.882683i	$-0.344265\pi$
$479$	9853.78			0.939939			0.469970	+	0.882683i	$0.344265\pi$
$480$	4334.72	−	1824.44i	0.412192	−	0.173487i
$481$	429.172			0.0406831
$482$	−845.429	+	14404.6i	−0.0798926	+	1.36122i
$483$	−9185.78	+	7604.64i	−0.865357	+	0.716404i
$484$	6091.18	+	717.476i	0.572049	+	0.0673813i
$485$	4682.63			0.438407
$486$	−10361.3	+	2726.52i	−0.967078	+	0.254481i
$487$			10068.4i			0.936845i	0.883505	+	0.468423i	$0.155177\pi$
$487$			10068.4i			0.936845i	−0.883505	+	0.468423i	$0.844823\pi$
$488$	−13108.3	−	2329.47i	−1.21595	−	0.216086i
$489$	149.411	+	180.476i	0.0138172	+	0.0166900i
$490$	−505.556	+	8613.74i	−0.0466095	+	0.794141i
$491$		−	15664.3i		−	1.43975i	−0.694102	−	0.719877i	$-0.744198\pi$
$491$		−	15664.3i		−	1.43975i	0.694102	−	0.719877i	$-0.255802\pi$
$492$	2131.30	−	1378.93i	0.195297	−	0.126356i
$493$		−	1192.53i		−	0.108943i
$494$	9954.19	+	584.229i	0.906600	+	0.0532099i
$495$	6074.33	+	1154.27i	0.551558	+	0.104809i
$496$	3386.47	−	14175.7i	0.306567	−	1.28328i
$497$		−	3151.81i		−	0.284463i
$498$	5119.50	+	6979.20i	0.460663	+	0.628003i
$499$	12529.3			1.12403			0.562013	−	0.827128i	$-0.310027\pi$
$499$	12529.3			1.12403			0.562013	+	0.827128i	$0.310027\pi$
$500$	−993.134	−	116.981i	−0.0888286	−	0.0104631i
$501$	4220.75	+	5098.32i	0.376386	+	0.454643i
$502$	1118.59	+	65.6522i	0.0994526	+	0.00583705i
$503$	−21913.7			−1.94251			−0.971256	−	0.238036i	$-0.923496\pi$
$503$	−21913.7			−1.94251			−0.971256	+	0.238036i	$0.923496\pi$
$504$	6708.95	−	17627.9i	0.592937	−	1.55796i
$505$	8163.21			0.719323
$506$	−9613.27	−	564.220i	−0.844589	−	0.0495704i
$507$	−12278.5	−	14831.5i	−1.07556	−	1.29919i
$508$	−1837.66	+	15601.2i	−0.160498	+	1.36258i
$509$	−3965.77			−0.345344			−0.172672	−	0.984979i	$-0.555240\pi$
$509$	−3965.77			−0.345344			−0.172672	+	0.984979i	$0.555240\pi$
$510$	−603.624	−	822.895i	−0.0524096	−	0.0714479i
$511$			27712.6i			2.39909i
$512$	5832.92	−	10009.7i	0.503479	−	0.864007i
$513$	−5638.14	+	3107.42i	−0.485244	+	0.267439i
$514$	11851.8	+	695.601i	1.01704	+	0.0596919i
$515$		−	2624.32i		−	0.224546i
$516$	−1471.29	−	2274.05i	−0.125523	−	0.194011i
$517$			24236.0i			2.06170i
$518$	28.5802	−	486.954i	0.00242421	−	0.0413041i
$519$	−8167.27	−	9865.40i	−0.690758	−	0.834380i
$520$	−8558.00	−	1520.84i	−0.721718	−	0.128256i
$521$			5250.21i			0.441489i	0.975332	+	0.220745i	$0.0708488\pi$
$521$			5250.21i			0.441489i	−0.975332	+	0.220745i	$0.929151\pi$
$522$	6359.45	+	1599.54i	0.533229	+	0.134118i
$523$	12458.4			1.04162			0.520809	−	0.853673i	$-0.325630\pi$
$523$	12458.4			1.04162			0.520809	+	0.853673i	$0.325630\pi$
$524$	2133.98	−	18116.9i	0.177907	−	1.51038i
$525$	−3089.23	+	2557.49i	−0.256810	+	0.212605i
$526$	−672.879	+	11464.6i	−0.0557774	+	0.950345i
$527$	−3162.66			−0.261419
$528$	13668.0	−	6720.92i	1.12656	−	0.553959i
$529$	−6641.00			−0.545821
$530$	18.8469	−	321.117i	0.00154464	−	0.0263178i
$531$	10211.3	+	1940.39i	0.834523	+	0.158579i
$532$	1325.77	−	11255.5i	0.108044	−	0.917267i
$533$	−4691.60			−0.381268
$534$	−10961.5	−	14943.4i	−0.888300	−	1.21098i
$535$		−	6791.20i		−	0.548802i
$536$	−1462.48	+	8229.59i	−0.117853	+	0.663180i
$537$	3764.46	−	3116.48i	0.302511	−	0.250440i
$538$	−27.6442	+	471.006i	−0.00221529	+	0.0377445i
$539$			27944.2i			2.23310i
$540$	5197.94	−	2115.23i	0.414229	−	0.168565i
$541$		−	17111.4i		−	1.35984i	−0.733285	−	0.679922i	$-0.762014\pi$
$541$		−	17111.4i		−	1.35984i	0.733285	−	0.679922i	$-0.237986\pi$
$542$	−18037.6	−	1058.66i	−1.42949	−	0.0838992i
$543$	−289.433	+	239.613i	−0.0228743	+	0.0189370i
$544$	−2406.75	−	726.396i	−0.189685	−	0.0572500i
$545$			942.349i			0.0740657i
$546$	−28108.2	+	20618.4i	−2.20315	+	1.61609i
$547$	−8732.92			−0.682619			−0.341310	−	0.939951i	$-0.610870\pi$
$547$	−8732.92			−0.682619			−0.341310	+	0.939951i	$0.610870\pi$
$548$	−1203.42	+	10216.8i	−0.0938097	+	0.796420i
$549$	−15607.1	−	2965.73i	−1.21329	−	0.230554i
$550$	−3233.00	−	189.751i	−0.250647	−	0.0147109i
$551$	3940.22			0.304644
$552$	−7603.83	+	4309.67i	−0.586305	+	0.332304i
$553$	31506.8			2.42279
$554$	−9163.13	−	537.800i	−0.702715	−	0.0412436i
$555$	111.794	−	92.5507i	0.00855023	−	0.00707848i
$556$	−24286.0	−	2860.63i	−1.85244	−	0.218197i
$557$	−9911.76			−0.753994			−0.376997	−	0.926214i	$-0.623043\pi$
$557$	−9911.76			−0.753994			−0.376997	+	0.926214i	$0.623043\pi$
$558$	4242.08	−	16865.7i	0.321831	−	1.27954i
$559$			5005.84i			0.378756i
$560$	−2295.50	+	9608.92i	−0.173219	+	0.725091i
$561$	−2107.66	−	2545.88i	−0.158619	−	0.191599i
$562$	17456.2	+	1024.54i	1.31022	+	0.0768993i
$563$			11569.0i			0.866028i	0.901387	+	0.433014i	$0.142550\pi$
$563$			11569.0i			0.866028i	−0.901387	+	0.433014i	$0.857450\pi$
$564$	11949.0	+	18468.6i	0.892101	+	1.37885i
$565$			3316.21i			0.246927i
$566$	844.498	−	14388.7i	0.0627154	−	1.06855i
$567$	8255.38	−	20937.6i	0.611452	−	1.55079i
$568$	404.183	−	2274.40i	0.0298576	−	0.168013i
$569$			16691.6i			1.22978i	0.788611	+	0.614892i	$0.210800\pi$
$569$			16691.6i			1.22978i	−0.788611	+	0.614892i	$0.789200\pi$
$570$	2718.92	−	1994.43i	0.199795	−	0.146557i
$571$	−17494.0			−1.28214			−0.641068	−	0.767484i	$-0.721508\pi$
$571$	−17494.0			−1.28214			−0.641068	+	0.767484i	$0.721508\pi$
$572$	−27956.6	−	3292.99i	−2.04357	−	0.240711i
$573$	−7653.93	−	9245.32i	−0.558023	−	0.674047i
$574$	−312.431	+	5323.25i	−0.0227188	+	0.387087i
$575$	1858.43			0.134786
$576$	7101.87	−	11860.3i	0.513735	−	0.857949i
$577$	−15697.4			−1.13257			−0.566285	−	0.824210i	$-0.691620\pi$
$577$	−15697.4			−1.13257			−0.566285	+	0.824210i	$0.691620\pi$
$578$	782.220	−	13327.6i	0.0562908	−	0.959092i
$579$	−244.852	−	295.761i	−0.0175746	−	0.0212287i
$580$	−3411.14	−	401.796i	−0.244207	−	0.0287649i
$581$	−18182.1			−1.29831
$582$	11098.3	−	8141.04i	0.790449	−	0.579823i
$583$		−	1041.75i		−	0.0740047i
$584$	−3553.82	+	19997.9i	−0.251812	+	1.41698i
$585$	−10189.4	−	1936.24i	−0.720139	−	0.136844i
$586$	−50.5015	+	860.453i	−0.00356007	+	0.0606570i
$587$		−	20677.6i		−	1.45393i	−0.686676	−	0.726964i	$-0.740931\pi$
$587$		−	20677.6i		−	1.45393i	0.686676	−	0.726964i	$-0.259069\pi$
$588$	13777.3	+	21294.4i	0.966268	+	1.49348i
$589$		−	10449.7i		−	0.731024i
$590$	−5434.85	−	318.981i	−0.379236	−	0.0222580i
$591$	−12397.0	−	14974.6i	−0.862851	−	1.04225i
$592$	83.0701	−	347.729i	0.00576716	−	0.0241412i
$593$		−	6.94591i		−	0.000481002i	−1.00000		0.000240501i	$-0.999923\pi$
$593$		−	6.94591i		−	0.000481002i	1.00000		0.000240501i	$-7.65539e-5\pi$
$594$	16403.6	−	7824.85i	1.13308	−	0.540501i
$595$	2143.79			0.147709
$596$	1694.43	+	199.586i	0.116454	+	0.0137170i
$597$	−7038.07	+	5826.61i	−0.482494	+	0.399443i
$598$	16125.9	+	946.455i	1.10273	+	0.0647214i
$599$	19963.5			1.36174			0.680872	−	0.732402i	$-0.261601\pi$
$599$	19963.5			1.36174			0.680872	+	0.732402i	$0.261601\pi$
$600$	−2557.21	+	1449.37i	−0.173996	+	0.0986170i
$601$	−2588.32			−0.175674			−0.0878369	−	0.996135i	$-0.527995\pi$
$601$	−2588.32			−0.175674			−0.0878369	+	0.996135i	$0.527995\pi$
$602$	5679.80	+	333.357i	0.384537	+	0.0225691i
$603$	−1861.94	+	9798.42i	−0.125744	+	0.661729i
$604$	1071.76	−	9098.94i	0.0722007	−	0.612965i
$605$	−3833.31			−0.257597
$606$	19347.7	−	14192.2i	1.29694	−	0.951353i
$607$			10641.9i			0.711599i	0.934562	+	0.355800i	$0.115791\pi$
$607$			10641.9i			0.711599i	−0.934562	+	0.355800i	$0.884209\pi$
$608$	2400.08	−	7952.12i	0.160092	−	0.530429i
$609$	−10610.7	+	8784.25i	−0.706019	+	0.584492i
$610$	8306.73	+	487.537i	0.551360	+	0.0323603i
$611$		−	40654.8i		−	2.69184i
$612$	−2861.31	−	900.913i	−0.188989	−	0.0595053i
$613$		−	18486.2i		−	1.21802i	−0.793161	−	0.609012i	$-0.791566\pi$
$613$		−	18486.2i		−	1.21802i	0.793161	−	0.609012i	$-0.208434\pi$
$614$	−1542.45	+	26280.6i	−0.101382	+	1.72736i
$615$	−1222.10	+	1011.74i	−0.0801297	+	0.0663370i
$616$	−5598.07	+	31501.2i	−0.366157	+	2.06042i
$617$			1293.82i			0.0844201i	0.999109	+	0.0422101i	$0.0134399\pi$
$617$			1293.82i			0.0844201i	−0.999109	+	0.0422101i	$0.986560\pi$
$618$	−4562.53	−	6219.91i	−0.296977	−	0.404857i
$619$	−2590.13			−0.168184			−0.0840922	−	0.996458i	$-0.526799\pi$
$619$	−2590.13			−0.168184			−0.0840922	+	0.996458i	$0.526799\pi$
$620$	−1065.59	+	9046.57i	−0.0690243	+	0.585998i
$621$	−9133.82	+	5034.04i	−0.590222	+	0.325297i
$622$	1089.49	−	18562.9i	0.0702326	−	1.19663i
$623$	38930.3			2.50355
$624$	−22927.4	+	11274.1i	−1.47089	+	0.723274i
$625$	625.000			0.0400000
$626$	−299.861	+	5109.08i	−0.0191451	+	0.326198i
$627$	8411.84	−	6963.91i	0.535784	−	0.443560i
$628$	1704.79	−	14473.2i	0.108326	−	0.919658i
$629$	−77.5799			−0.00491783
$630$	−2875.47	+	11432.3i	−0.181844	+	0.722976i
$631$		−	20155.5i		−	1.27160i	−0.771854	−	0.635800i	$-0.780670\pi$
$631$		−	20155.5i		−	1.27160i	0.771854	−	0.635800i	$-0.219330\pi$
$632$	22735.9	+	4040.38i	1.43099	+	0.254300i
$633$	1085.85	+	1311.62i	0.0681810	+	0.0823571i
$634$	341.424	−	5817.25i	0.0213875	−	0.364404i
$635$		−	9818.18i		−	0.613579i
$636$	−513.611	−	793.847i	−0.0320220	−	0.0494939i
$637$		−	46875.1i		−	2.91564i
$638$	−11104.5	−	651.740i	−0.689075	−	0.0404430i
$639$	514.580	−	2707.97i	0.0318568	−	0.167646i
$640$	−2888.71	+	6639.59i	−0.178416	+	0.410083i
$641$		−	22915.7i		−	1.41204i	−0.708193	−	0.706019i	$-0.750489\pi$
$641$		−	22915.7i		−	1.41204i	0.708193	−	0.706019i	$-0.249511\pi$
$642$	−11806.9	−	16095.9i	−0.725828	−	0.989491i
$643$	−7306.88			−0.448142			−0.224071	−	0.974573i	$-0.571935\pi$
$643$	−7306.88			−0.448142			−0.224071	+	0.974573i	$0.571935\pi$
$644$	2147.76	−	18233.9i	0.131419	−	1.11571i
$645$	1079.51	+	1303.95i	0.0659000	+	0.0796018i
$646$	−1799.38	−	105.609i	−0.109591	−	0.00643209i
$647$	12065.5			0.733146			0.366573	−	0.930389i	$-0.380531\pi$
$647$	12065.5			0.733146			0.366573	+	0.930389i	$0.380531\pi$
$648$	8642.22	−	14050.3i	0.523918	−	0.851769i
$649$	−17631.4			−1.06640
$650$	5423.22	+	318.298i	0.327256	+	0.0192072i
$651$	23296.4	+	28140.2i	1.40255	+	1.69416i
$652$	−358.248	−	42.1978i	−0.0215185	−	0.00253465i
$653$	17110.6			1.02540			0.512701	−	0.858567i	$-0.328645\pi$
$653$	17110.6			1.02540			0.512701	+	0.858567i	$0.328645\pi$
$654$	1638.33	+	2233.47i	0.0979569	+	0.133541i
$655$			11401.3i			0.680133i
$656$	−908.099	+	3801.28i	−0.0540478	+	0.226242i
$657$	−4524.50	+	23810.1i	−0.268672	+	1.41388i
$658$	−46128.3	−	2707.35i	−2.73293	−	0.160401i
$659$			6115.63i			0.361504i	0.983529	+	0.180752i	$0.0578531\pi$
$659$			6115.63i			0.361504i	−0.983529	+	0.180752i	$0.942147\pi$
$660$	−7992.45	+	5171.04i	−0.471372	+	0.304973i
$661$		−	6240.95i		−	0.367239i	−0.982997	−	0.183619i	$-0.941219\pi$
$661$		−	6240.95i		−	0.367239i	0.982997	−	0.183619i	$-0.0587814\pi$
$662$	78.6743	−	1340.47i	0.00461898	−	0.0786989i
$663$	3535.51	+	4270.61i	0.207101	+	0.250161i
$664$	−13120.5	−	2331.64i	−0.766830	−	0.136273i
$665$			7083.29i			0.413050i
$666$	104.058	−	413.715i	0.00605431	−	0.0240708i
$667$	6383.18			0.370551
$668$	−10120.2	−	1192.06i	−0.586173	−	0.0690449i
$669$	2899.95	−	2400.78i	0.167591	−	0.138744i
$670$	306.084	−	5215.11i	0.0176493	−	0.300712i
$671$	26948.2			1.55041
$672$	11265.1	+	26765.0i	0.646667	+	1.53643i
$673$	22328.5			1.27890			0.639450	−	0.768833i	$-0.279162\pi$
$673$	22328.5			1.27890			0.639450	+	0.768833i	$0.279162\pi$
$674$	257.683	−	4390.44i	0.0147264	−	0.250910i
$675$	−3071.76	+	1692.98i	−0.175159	+	0.0965374i
$676$	29440.7	+	3467.80i	1.67505	+	0.197303i
$677$	10294.2			0.584398			0.292199	−	0.956358i	$-0.405613\pi$
$677$	10294.2			0.584398			0.292199	+	0.956358i	$0.405613\pi$
$678$	5765.43	+	7859.77i	0.326578	+	0.445210i
$679$			28913.2i			1.63415i
$680$	1547.00	+	274.916i	0.0872422	+	0.0155038i
$681$	16207.0	−	13417.3i	0.911970	−	0.754993i
$682$	−1728.46	+	29449.8i	−0.0970471	+	1.65350i
$683$		−	5988.48i		−	0.335495i	−0.985830	−	0.167747i	$-0.946351\pi$
$683$		−	5988.48i		−	0.335495i	0.985830	−	0.167747i	$-0.0536493\pi$
$684$	2976.70	−	9454.02i	0.166399	−	0.528485i
$685$		−	6429.61i		−	0.358632i
$686$	−23286.3	−	1366.71i	−1.29603	−	0.0760661i
$687$	−23678.9	+	19603.0i	−1.31500	+	1.08865i
$688$	4055.89	+	968.924i	0.224752	+	0.0536917i
$689$			1747.48i			0.0966239i
$690$	4404.67	−	3230.99i	0.243019	−	0.178263i
$691$	−17513.5			−0.964176			−0.482088	−	0.876123i	$-0.660121\pi$
$691$	−17513.5			−0.964176			−0.482088	+	0.876123i	$0.660121\pi$
$692$	19583.0	+	2306.66i	1.07577	+	0.126714i
$693$	−7127.12	+	37506.4i	−0.390673	+	2.05592i
$694$	−641.553	−	37.6539i	−0.0350908	−	0.00205954i
$695$	15283.7			0.834163
$696$	−8783.31	+	4978.17i	−0.478348	+	0.271117i
$697$	848.083			0.0460881
$698$	−31075.2	−	1823.86i	−1.68512	−	0.0989027i
$699$	9046.16	−	7489.05i	0.489495	−	0.405239i
$700$	722.304	−	6132.17i	0.0390008	−	0.331106i
$701$	−11644.9			−0.627422			−0.313711	−	0.949519i	$-0.601572\pi$
$701$	−11644.9			−0.627422			−0.313711	+	0.949519i	$0.601572\pi$
$702$	−27516.3	+	13125.9i	−1.47940	+	0.705703i
$703$		−	256.331i		−	0.0137521i
$704$	−8079.33	+	22013.9i	−0.432530	+	1.17853i
$705$	−8767.17	−	10590.0i	−0.468356	−	0.565735i
$706$	9504.74	+	557.850i	0.506679	+	0.0297379i
$707$			50404.3i			2.68126i
$708$	−13435.7	+	8692.79i	−0.713201	+	0.461434i
$709$		−	6434.79i		−	0.340852i	−0.985371	−	0.170426i	$-0.945486\pi$
$709$		−	6434.79i		−	0.340852i	0.985371	−	0.170426i	$-0.0545143\pi$
$710$	−84.5919	+	1441.29i	−0.00447138	+	0.0761840i
$711$	27070.0	+	5143.96i	1.42786	+	0.271327i
$712$	28092.8	+	4992.36i	1.47868	+	0.262776i
$713$		−	16928.6i		−	0.889174i
$714$	5081.02	−	3727.11i	0.266320	−	0.195355i
$715$	17593.7			0.920233
$716$	−880.181	+	7472.50i	−0.0459412	+	0.390029i
$717$	−3075.00	−	3714.35i	−0.160165	−	0.193466i
$718$	−1199.09	+	20430.3i	−0.0623255	+	1.06191i
$719$	−14776.3			−0.766432			−0.383216	−	0.923659i	$-0.625183\pi$
$719$	−14776.3			−0.766432			−0.383216	+	0.923659i	$0.625183\pi$
$720$	−3541.05	+	7881.02i	−0.183288	+	0.407928i
$721$	16204.0			0.836989
$722$	−787.733	+	13421.5i	−0.0406044	+	0.691825i
$723$	−16904.3	−	20419.1i	−0.869543	−	1.05034i
$724$	67.6733	−	574.529i	0.00347384	−	0.0294920i
$725$	2146.70			0.109968
$726$	−9085.35	+	6664.43i	−0.464447	+	0.340689i
$727$			13213.0i			0.674060i	0.941494	+	0.337030i	$0.109422\pi$
$727$			13213.0i			0.674060i	−0.941494	+	0.337030i	$0.890578\pi$
$728$	9390.52	−	52841.9i	0.478071	−	2.69018i
$729$	10511.2	−	16641.3i	0.534026	−	0.845468i
$730$	743.783	−	12672.7i	0.0377105	−	0.642517i
$731$		−	904.887i		−	0.0457845i
$732$	20535.5	−	13286.2i	1.03690	−	0.670866i
$733$		−	7834.21i		−	0.394766i	−0.980326	−	0.197383i	$-0.936756\pi$
$733$		−	7834.21i		−	0.394766i	0.980326	−	0.197383i	$-0.0632442\pi$
$734$	−24310.2	−	1426.81i	−1.22249	−	0.0717501i
$735$	−10108.6	−	12210.3i	−0.507293	−	0.612769i
$736$	3888.15	−	12882.5i	0.194727	−	0.645183i
$737$		−	16918.5i		−	0.845593i
$738$	−1137.53	+	4522.62i	−0.0567388	+	0.225583i
$739$	−7534.72			−0.375060			−0.187530	−	0.982259i	$-0.560048\pi$
$739$	−7534.72			−0.375060			−0.187530	+	0.982259i	$0.560048\pi$
$740$	−26.1389	+	221.912i	−0.00129849	+	0.0110238i
$741$	−14110.5	+	11681.7i	−0.699544	+	0.579131i
$742$	1982.76	+	116.371i	0.0980987	+	0.00575759i
$743$	−196.228			−0.00968896			−0.00484448	−	0.999988i	$-0.501542\pi$
$743$	−196.228			−0.00968896			−0.00484448	+	0.999988i	$0.501542\pi$
$744$	13202.4	+	23293.9i	0.650571	+	1.14784i
$745$	−1066.34			−0.0524399
$746$	22896.1	+	1343.81i	1.12371	+	0.0659524i
$747$	−15621.7	−	2968.50i	−0.765152	−	0.145397i
$748$	5053.61	+	595.262i	0.247030	+	0.0290975i
$749$	41932.7			2.04564
$750$	1481.32	−	1086.60i	0.0721201	−	0.0529027i
$751$		−	6242.17i		−	0.303302i	−0.988434	−	0.151651i	$-0.951541\pi$
$751$		−	6242.17i		−	0.303302i	0.988434	−	0.151651i	$-0.0484590\pi$
$752$	−32939.8	−	7869.09i	−1.59733	−	0.381591i
$753$	−1585.65	+	1312.71i	−0.0767389	+	0.0635298i
$754$	18627.2	+	1093.27i	0.899687	+	0.0528042i
$755$			5726.15i			0.276021i
$756$	13060.6	+	32095.0i	0.628321	+	1.54403i
$757$		−	12861.5i		−	0.617517i	−0.951141	−	0.308758i	$-0.900087\pi$
$757$		−	12861.5i		−	0.617517i	0.951141	−	0.308758i	$-0.0999134\pi$
$758$	−115.864	+	1974.11i	−0.00555195	+	0.0945950i
$759$	13627.2	−	11281.6i	0.651696	−	0.539519i
$760$	−908.350	+	5111.43i	−0.0433544	+	0.243962i
$761$			33111.2i			1.57724i	0.614879	+	0.788621i	$0.289205\pi$
$761$			33111.2i			1.57724i	−0.614879	+	0.788621i	$0.710795\pi$
$762$	−17069.5	−	23270.1i	−0.811500	−	1.10628i
$763$	−5818.60			−0.276078
$764$	18352.1	+	2161.68i	0.869052	+	0.102365i
$765$	1841.91	+	350.007i	0.0870513	+	0.0165418i
$766$	−77.0010	+	1311.96i	−0.00363206	+	0.0618837i
$767$	29575.9			1.39234
$768$	4696.79	+	20758.7i	0.220678	+	0.975347i
$769$	−31567.2			−1.48029			−0.740145	−	0.672448i	$-0.765243\pi$
$769$	−31567.2			−1.48029			−0.740145	+	0.672448i	$0.765243\pi$
$770$	1171.63	−	19962.4i	0.0548344	−	0.934278i
$771$	−16800.4	+	13908.5i	−0.784761	+	0.649681i
$772$	587.090	+	69.1529i	0.0273702	+	0.00322392i
$773$	−30856.5			−1.43575			−0.717873	−	0.696174i	$-0.754884\pi$
$773$	−30856.5			−1.43575			−0.717873	+	0.696174i	$0.754884\pi$
$774$	4825.55	+	1213.73i	0.224096	+	0.0563650i
$775$		−	5693.19i		−	0.263878i
$776$	−3707.78	+	20864.3i	−0.171523	+	0.965186i
$777$	571.460	+	690.277i	0.0263848	+	0.0318707i
$778$	−468.385	+	7980.42i	−0.0215841	+	0.367753i
$779$			2802.15i			0.128880i
$780$	13407.0	−	8674.19i	0.615445	−	0.398187i
$781$			4675.75i			0.214227i
$782$	−2915.01	−	171.087i	−0.133300	−	0.00782361i
$783$	−10550.6	+	5814.91i	−0.481544	+	0.265400i
$784$	−37979.7	−	9073.09i	−1.73013	−	0.413315i
$785$			9108.32i			0.414127i
$786$	19821.9	+	27022.4i	0.899522	+	1.22628i
$787$	22387.1			1.01399			0.506996	−	0.861948i	$-0.330756\pi$
$787$	22387.1			1.01399			0.506996	+	0.861948i	$0.330756\pi$
$788$	29724.8	+	3501.26i	1.34378	+	0.158283i
$789$	−13454.2	−	16251.6i	−0.607076	−	0.733298i
$790$	−14407.8	−	845.616i	−0.648867	−	0.0380831i
$791$	−20476.2			−0.920415
$792$	−9952.80	+	26151.3i	−0.446537	+	1.17329i
$793$	−45204.4			−2.02428
$794$	3166.90	+	185.871i	0.141548	+	0.00830769i
$795$	376.844	+	455.196i	0.0168117	+	0.0203071i
$796$	1645.59	−	13970.7i	0.0732746	−	0.622082i
$797$	22479.6			0.999083			0.499541	−	0.866290i	$-0.333502\pi$
$797$	22479.6			0.999083			0.499541	+	0.866290i	$0.333502\pi$
$798$	12314.7	+	16788.2i	0.546287	+	0.744730i
$799$			7349.02i			0.325394i
$800$	1307.61	−	4332.45i	0.0577886	−	0.191469i
$801$	33448.2	+	6355.96i	1.47545	+	0.280371i
$802$	−8942.63	−	524.859i	−0.393735	−	0.0231090i
$803$		−	41112.0i		−	1.80674i
$804$	−8341.33	−	12892.5i	−0.365890	−	0.565527i
$805$			11475.0i			0.502410i
$806$	2899.41	−	49400.7i	0.126709	−	2.15889i
$807$	−552.745	−	667.671i	−0.0241110	−	0.0291241i
$808$	−6463.76	+	36372.6i	−0.281429	+	1.58364i
$809$			6314.08i			0.274402i	0.990543	+	0.137201i	$0.0438106\pi$
$809$			6314.08i			0.274402i	−0.990543	+	0.137201i	$0.956189\pi$
$810$	−4337.05	+	9352.98i	−0.188134	+	0.405716i
$811$	33274.4			1.44072			0.720359	−	0.693601i	$-0.243977\pi$
$811$	33274.4			1.44072			0.720359	+	0.693601i	$0.243977\pi$
$812$	2480.91	−	21062.3i	0.107220	−	0.910273i
$813$	25569.1	−	21167.9i	1.10301	−	0.913150i
$814$	−42.3990	+	722.402i	−0.00182566	+	0.0311059i
$815$	225.453			0.00968990
$816$	4144.51	−	2037.97i	0.177803	−	0.0874304i
$817$	2989.83			0.128031
$818$	−1055.30	+	17980.5i	−0.0451074	+	0.768548i
$819$	11955.4	−	62915.3i	0.510081	−	2.68430i
$820$	285.743	−	2425.88i	0.0121690	−	0.103312i
$821$	40381.8			1.71661			0.858304	−	0.513141i	$-0.171518\pi$
$821$	40381.8			1.71661			0.858304	+	0.513141i	$0.171518\pi$
$822$	−11178.3	−	15238.9i	−0.474315	−	0.646614i
$823$		−	2147.64i		−	0.0909625i	−0.998965	−	0.0454812i	$-0.985518\pi$
$823$		−	2147.64i		−	0.0909625i	0.998965	−	0.0454812i	$-0.0144821\pi$
$824$	11693.1	+	2077.98i	0.494355	+	0.0878516i
$825$	4582.92	−	3794.06i	0.193402	−	0.160112i
$826$	1969.57	−	33557.8i	0.0829662	−	1.41359i
$827$			15402.2i			0.647625i	0.946121	+	0.323812i	$0.104965\pi$
$827$			15402.2i			0.647625i	−0.946121	+	0.323812i	$0.895035\pi$
$828$	4822.27	−	15315.6i	0.202398	−	0.642817i
$829$		−	19592.3i		−	0.820832i	−0.911898	−	0.410416i	$-0.865383\pi$
$829$		−	19592.3i		−	0.820832i	0.911898	−	0.410416i	$-0.134617\pi$
$830$	8314.49	+	487.992i	0.347711	+	0.0204078i
$831$	12989.1	−	10753.3i	0.542224	−	0.448891i
$832$	13552.7	−	36927.4i	0.564731	−	1.53874i
$833$			8473.45i			0.352446i
$834$	36224.0	−	26571.6i	1.50400	−	1.10324i
$835$	6368.88			0.263957
$836$	−1966.80	+	16697.6i	−0.0813675	+	0.690788i
$837$	15421.5	+	27981.0i	0.636853	+	1.15551i
$838$	−14240.8	−	835.815i	−0.587039	−	0.0344544i
$839$	−30637.0			−1.26068			−0.630338	−	0.776320i	$-0.717084\pi$
$839$	−30637.0			−1.26068			−0.630338	+	0.776320i	$0.717084\pi$
$840$	−8949.21	−	15789.7i	−0.367592	−	0.648566i
$841$	−17015.7			−0.697679
$842$	21026.8	+	1234.10i	0.860608	+	0.0505106i
$843$	−24744.9	+	20485.6i	−1.01098	+	0.836964i
$844$	−2603.58	−	306.673i	−0.106183	−	0.0125073i
$845$	−18527.6			−0.754284
$846$	−39190.5	−	9857.24i	−1.59267	−	0.400590i
$847$		−	23669.0i		−	0.960185i
$848$	1415.87	+	338.241i	0.0573362	+	0.0136972i
$849$	16885.7	+	20396.6i	0.682587	+	0.824510i
$850$	−980.336	−	57.5376i	−0.0395591	−	0.00232179i
$851$		−	415.258i		−	0.0167272i
$852$	2305.28	+	3563.08i	0.0926967	+	0.143274i
$853$		−	39184.1i		−	1.57285i	−0.617687	−	0.786424i	$-0.711930\pi$
$853$		−	39184.1i		−	1.57285i	0.617687	−	0.786424i	$-0.288070\pi$
$854$	−3010.33	+	51290.5i	−0.120622	+	2.05518i
$855$	−1156.45	+	6085.83i	−0.0462572	+	0.243428i
$856$	30259.4	+	5377.38i	1.20823	+	0.214714i
$857$		−	40181.7i		−	1.60161i	−0.598924	−	0.800806i	$-0.704405\pi$
$857$		−	40181.7i		−	1.60161i	0.598924	−	0.800806i	$-0.295595\pi$
$858$	41698.9	−	30587.7i	1.65918	−	1.21707i
$859$	17782.5			0.706323			0.353162	−	0.935562i	$-0.385107\pi$
$859$	17782.5			0.706323			0.353162	+	0.935562i	$0.385107\pi$
$860$	−2588.37	−	304.882i	−0.102631	−	0.0120888i
$861$	−6247.05	−	7545.93i	−0.247269	−	0.298681i
$862$	−1387.55	+	23641.3i	−0.0548262	+	0.934138i
$863$	−40594.3			−1.60121			−0.800607	−	0.599190i	$-0.795489\pi$
$863$	−40594.3			−1.60121			−0.800607	+	0.599190i	$0.795489\pi$
$864$	5308.96	+	24835.2i	0.209045	+	0.977906i
$865$	−12324.0			−0.484425
$866$	−778.032	+	13256.2i	−0.0305295	+	0.520167i
$867$	15640.5	+	18892.4i	0.612663	+	0.740047i
$868$	−55858.6	−	6579.55i	−2.18429	−	0.257286i
$869$	−46740.7			−1.82459
$870$	5087.91	−	3732.17i	0.198272	−	0.145439i
$871$			28380.1i			1.10404i
$872$	−4198.80	−	746.167i	−0.163061	−	0.0289775i
$873$	−4720.52	+	24841.7i	−0.183007	+	0.963074i
$874$	565.288	−	9631.47i	0.0218777	−	0.372757i
$875$			3859.10i			0.149099i
$876$	−20269.4	−	31328.8i	−0.781780	−	1.20833i
$877$			20000.2i			0.770079i	0.922900	+	0.385039i	$0.125812\pi$
$877$			20000.2i			0.770079i	−0.922900	+	0.385039i	$0.874188\pi$
$878$	−15286.8	−	897.210i	−0.587591	−	0.0344867i
$879$	−1009.78	−	1219.73i	−0.0387474	−	0.0468037i
$880$	3405.41	−	14255.0i	0.130450	−	0.546062i
$881$			23868.5i			0.912770i	0.889782	+	0.456385i	$0.150856\pi$
$881$			23868.5i			0.912770i	−0.889782	+	0.456385i	$0.849144\pi$
$882$	−45186.8	−	11365.4i	−1.72508	−	0.433894i
$883$	−31165.4			−1.18777			−0.593885	−	0.804550i	$-0.702406\pi$
$883$	−31165.4			−1.18777			−0.593885	+	0.804550i	$0.702406\pi$
$884$	−8477.22	−	998.526i	−0.322534	−	0.0379910i
$885$	7704.13	−	6378.02i	0.292623	−	0.242254i
$886$	23003.9	+	1350.14i	0.872270	+	0.0511951i
$887$	−45311.6			−1.71523			−0.857617	−	0.514288i	$-0.828056\pi$
$887$	−45311.6			−1.71523			−0.857617	+	0.514288i	$0.828056\pi$
$888$	323.856	+	571.399i	0.0122386	+	0.0215934i
$889$	60623.0			2.28710
$890$	−17802.5	−	1044.86i	−0.670494	−	0.0393525i
$891$	−12247.0	+	31061.2i	−0.460481	+	1.16789i
$892$	−678.046	+	5756.43i	−0.0254514	+	0.216076i
$893$	−24281.8			−0.909922
$894$	−2527.34	+	1853.90i	−0.0945492	+	0.0693553i
$895$		−	4702.60i		−	0.175632i
$896$	−40996.6	−	17836.5i	−1.52857	−	0.665040i
$897$	−22859.1	+	18924.4i	−0.850883	+	0.704421i
$898$	−7319.58	−	429.599i	−0.272002	−	0.0159643i
$899$		−	19554.5i		−	0.725450i
$900$	1621.76	−	5150.72i	0.0600652	−	0.190767i
$901$		−	315.886i		−	0.0116800i
$902$	463.495	−	7897.10i	0.0171094	−	0.291513i
$903$	−8051.35	+	6665.48i	−0.296713	+	0.245640i
$904$	−14775.9	−	2625.83i	−0.543629	−	0.0966081i
$905$			361.563i			0.0132804i
$906$	9955.26	+	13571.6i	0.365057	+	0.497667i
$907$	2344.08			0.0858146			0.0429073	−	0.999079i	$-0.486338\pi$
$907$	2344.08			0.0858146			0.0429073	+	0.999079i	$0.486338\pi$
$908$	−3789.40	+	32171.0i	−0.138497	+	1.17581i
$909$	−8229.26	+	43306.4i	−0.300272	+	1.58018i
$910$	−1965.35	+	33486.0i	−0.0715943	+	1.21984i
$911$	−35403.8			−1.28757			−0.643787	−	0.765205i	$-0.722638\pi$
$911$	−35403.8			−1.28757			−0.643787	+	0.765205i	$0.722638\pi$
$912$	6733.64	+	13693.9i	0.244488	+	0.497203i
$913$	26973.4			0.977753
$914$	−845.527	+	14406.2i	−0.0305991	+	0.521352i
$915$	−11775.1	+	9748.30i	−0.425436	+	0.352206i
$916$	5536.44	−	47002.9i	0.199704	−	1.69544i
$917$	−70398.3			−2.53518
$918$	4974.02	−	2372.71i	0.178831	−	0.0853063i
$919$		−	23879.3i		−	0.857132i	−0.903510	−	0.428566i	$-0.859019\pi$
$919$		−	23879.3i		−	0.857132i	0.903510	−	0.428566i	$-0.140981\pi$
$920$	−1471.53	+	8280.54i	−0.0527337	+	0.296741i
$921$	−30841.3	−	37253.8i	−1.10343	−	1.33285i
$922$	2523.87	−	43002.1i	0.0901510	−	1.53601i
$923$		−	7843.36i		−	0.279705i
$924$	−31928.9	−	49349.9i	−1.13678	−	1.75703i
$925$		−	139.654i		−	0.00496410i
$926$	39663.4	+	2327.91i	1.40758	+	0.0826133i
$927$	13922.2	+	2645.55i	0.493273	+	0.0937338i
$928$	4491.26	−	14880.8i	0.158872	−	0.526385i
$929$		−	23794.9i		−	0.840350i	−0.907443	−	0.420175i	$-0.861969\pi$
$929$		−	23794.9i		−	0.840350i	0.907443	−	0.420175i	$-0.138031\pi$
$930$	−9897.96	−	13493.5i	−0.348997	−	0.475773i
$931$	−27997.1			−0.985571
$932$	−2115.11	+	17956.8i	−0.0743378	+	0.631108i
$933$	21784.4	+	26313.8i	0.764404	+	0.923337i
$934$	34702.0	+	2036.72i	1.21572	+	0.0713528i
$935$	−3180.34			−0.111239
$936$	16695.4	−	43867.6i	0.583019	−	1.53190i
$937$	30230.7			1.05400			0.526999	−	0.849866i	$-0.323317\pi$
$937$	30230.7			1.05400			0.526999	+	0.849866i	$0.323317\pi$
$938$	32201.0	+	1889.93i	1.12090	+	0.0657874i
$939$	−5995.72	−	7242.34i	−0.208374	−	0.251698i
$940$	21021.4	+	2476.09i	0.729405	+	0.0859161i
$941$	17271.7			0.598343			0.299172	−	0.954199i	$-0.403290\pi$
$941$	17271.7			0.598343			0.299172	+	0.954199i	$0.403290\pi$
$942$	15835.4	+	21587.7i	0.547711	+	0.746672i
$943$			4539.49i			0.156762i
$944$	5724.67	−	23963.3i	0.197375	−	0.826208i
$945$	−10453.4	−	18966.8i	−0.359841	−	0.652899i
$946$	−8426.05	−	494.540i	−0.289592	−	0.0169967i
$947$			46463.0i			1.59434i	0.603752	+	0.797172i	$0.293672\pi$
$947$			46463.0i			1.59434i	−0.603752	+	0.797172i	$0.706328\pi$
$948$	−35618.1	+	23044.5i	−1.22028	+	0.789506i
$949$			68963.6i			2.35896i
$950$	190.110	−	3239.12i	0.00649260	−	0.110622i
$951$	6826.78	+	8246.19i	0.232780	+	0.281179i
$952$	−1697.49	+	9552.04i	−0.0577899	+	0.325193i
$953$		−	38846.0i		−	1.32040i	−0.751088	−	0.660202i	$-0.770471\pi$
$953$		−	38846.0i		−	1.32040i	0.751088	−	0.660202i	$-0.229529\pi$
$954$	1684.55	+	423.699i	0.0571690	+	0.0143792i
$955$	−11549.4			−0.391339
$956$	7373.05	+	868.466i	0.249437	+	0.0293810i
$957$	15741.0	−	13031.5i	0.531699	−	0.440177i
$958$	1632.97	−	27822.8i	0.0550719	−	0.938325i
$959$	39700.1			1.33679
$960$	−4433.07	−	12541.7i	−0.149038	−	0.421649i
$961$	−22068.9			−0.740791
$962$	71.1226	−	1211.80i	0.00238366	−	0.0406132i
$963$	36027.8	+	6846.15i	1.20559	+	0.229090i
$964$	40532.1	+	4774.25i	1.35420	+	0.159511i
$965$	−369.468			−0.0123250
$966$	19949.9	+	27196.9i	0.664471	+	0.905846i
$967$		−	9489.48i		−	0.315575i	−0.987473	−	0.157787i	$-0.949564\pi$
$967$		−	9489.48i		−	0.315575i	0.987473	−	0.157787i	$-0.0504361\pi$
$968$	3035.27	−	17080.0i	0.100782	−	0.567119i
$969$	2550.70	−	2111.65i	0.0845618	−	0.0700062i
$970$	776.007	−	13221.7i	0.0256867	−	0.437654i
$971$			14606.1i			0.482732i	0.970434	+	0.241366i	$0.0775954\pi$
$971$			14606.1i			0.482732i	−0.970434	+	0.241366i	$0.922405\pi$
$972$	5981.44	+	29707.8i	0.197381	+	0.980327i
$973$			94370.1i			3.10932i
$974$	28428.9	+	1668.54i	0.935236	+	0.0548906i
$975$	−7687.64	+	6364.37i	−0.252515	+	0.209049i
$976$	−8749.71	+	36626.1i	−0.286958	+	1.20120i
$977$		−	30617.5i		−	1.00260i	−0.865273	−	0.501300i	$-0.832855\pi$
$977$		−	30617.5i		−	1.00260i	0.865273	−	0.501300i	$-0.167145\pi$
$978$	534.347	−	391.963i	0.0174709	−	0.0128155i
$979$	−57753.6			−1.88541
$980$	24237.7	+	2854.94i	0.790046	+	0.0930589i
$981$	−4999.23	−	949.974i	−0.162704	−	0.0309178i
$982$	−44229.2	−	2595.89i	−1.43728	−	0.0843565i
$983$	52367.2			1.69914			0.849571	−	0.527475i	$-0.176861\pi$
$983$	52367.2			1.69914			0.849571	+	0.527475i	$0.176861\pi$
$984$	−3540.30	−	6246.38i	−0.114696	−	0.202365i
$985$	−18706.4			−0.605113
$986$	−3367.18	−	197.626i	−0.108755	−	0.00638305i
$987$	65388.8	−	54133.5i	2.10876	−	1.74578i
$988$	3299.22	−	28009.5i	0.106237	−	0.901925i
$989$	4843.55			0.155729
$990$	4265.80	−	16960.0i	0.136945	−	0.544469i
$991$			19821.2i			0.635360i	0.948198	+	0.317680i	$0.102904\pi$
$991$			19821.2i			0.635360i	−0.948198	+	0.317680i	$0.897096\pi$
$992$	−39464.8	−	11911.1i	−1.26311	−	0.381229i
$993$	1573.09	+	1900.17i	0.0502725	+	0.0607250i
$994$	−8899.34	−	522.318i	−0.283974	−	0.0166669i
$995$			8792.03i			0.280127i
$996$	20554.6	−	13298.7i	0.653915	−	0.423076i
$997$			27175.1i			0.863233i	0.902057	+	0.431616i	$0.142057\pi$
$997$			27175.1i			0.863233i	−0.902057	+	0.431616i	$0.857943\pi$
$998$	2076.36	−	35377.4i	0.0658578	−	1.12210i
$999$	378.290	+	686.373i	0.0119805	+	0.0217376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.a.11.13	✓	24
3.2	odd	2		120.4.b.b.11.12	yes	24
4.3	odd	2		480.4.b.b.431.7		24
8.3	odd	2		120.4.b.b.11.11	yes	24
8.5	even	2		480.4.b.a.431.7		24
12.11	even	2		480.4.b.a.431.8		24
24.5	odd	2		480.4.b.b.431.8		24
24.11	even	2	inner	120.4.b.a.11.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.13	✓	24	1.1	even	1	trivial
120.4.b.a.11.14	yes	24	24.11	even	2	inner
120.4.b.b.11.11	yes	24	8.3	odd	2
120.4.b.b.11.12	yes	24	3.2	odd	2
480.4.b.a.431.7		24	8.5	even	2
480.4.b.a.431.8		24	12.11	even	2
480.4.b.b.431.7		24	4.3	odd	2
480.4.b.b.431.8		24	24.5	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.165720 - 2.82357i) q^{2} +(3.31357 + 4.00253i) q^{3} +(-7.94507 - 0.935845i) q^{4} +5.00000 q^{5} +(11.8505 - 8.69280i) q^{6} +30.8728i q^{7} +(-3.95908 + 22.2784i) q^{8} +(-5.04045 + 26.5253i) q^{9} +O(q^{10})\)	\(q+(0.165720 - 2.82357i) q^{2} +(3.31357 + 4.00253i) q^{3} +(-7.94507 - 0.935845i) q^{4} +5.00000 q^{5} +(11.8505 - 8.69280i) q^{6} +30.8728i q^{7} +(-3.95908 + 22.2784i) q^{8} +(-5.04045 + 26.5253i) q^{9} +(0.828601 - 14.1178i) q^{10} -45.8002i q^{11} +(-22.5808 - 34.9014i) q^{12} +76.8279i q^{13} +(87.1715 + 5.11625i) q^{14} +(16.5679 + 20.0126i) q^{15} +(62.2484 + 14.8707i) q^{16} -13.8879i q^{17} +(74.0608 + 18.6279i) q^{18} +45.8869 q^{19} +(-39.7254 - 4.67922i) q^{20} +(-123.569 + 102.299i) q^{21} +(-129.320 - 7.59002i) q^{22} +74.3371 q^{23} +(-102.288 + 57.9747i) q^{24} +25.0000 q^{25} +(216.929 + 12.7319i) q^{26} +(-122.870 + 67.7191i) q^{27} +(28.8922 - 245.287i) q^{28} +85.8680 q^{29} +(59.2527 - 43.4640i) q^{30} -227.728i q^{31} +(52.3043 - 173.298i) q^{32} +(183.317 - 151.762i) q^{33} +(-39.2134 - 2.30151i) q^{34} +154.364i q^{35} +(64.8704 - 206.029i) q^{36} -5.58615i q^{37} +(7.60439 - 129.565i) q^{38} +(-307.506 + 254.575i) q^{39} +(-19.7954 + 111.392i) q^{40} +61.0663i q^{41} +(268.371 + 365.860i) q^{42} +65.1565 q^{43} +(-42.8619 + 363.886i) q^{44} +(-25.2023 + 132.627i) q^{45} +(12.3192 - 209.896i) q^{46} -529.167 q^{47} +(146.744 + 298.426i) q^{48} -610.132 q^{49} +(4.14300 - 70.5892i) q^{50} +(55.5867 - 46.0186i) q^{51} +(71.8990 - 610.403i) q^{52} +22.7454 q^{53} +(170.847 + 358.155i) q^{54} -229.001i q^{55} +(-687.796 - 122.228i) q^{56} +(152.050 + 183.664i) q^{57} +(14.2301 - 242.454i) q^{58} -384.963i q^{59} +(-112.904 - 174.507i) q^{60} +588.386i q^{61} +(-643.005 - 37.7391i) q^{62} +(-818.912 - 155.613i) q^{63} +(-480.651 - 176.404i) q^{64} +384.139i q^{65} +(-398.132 - 542.757i) q^{66} +369.398 q^{67} +(-12.9969 + 110.340i) q^{68} +(246.321 + 297.536i) q^{69} +(435.858 + 25.5813i) q^{70} -102.090 q^{71} +(-570.986 - 217.309i) q^{72} +897.637 q^{73} +(-15.7729 - 0.925739i) q^{74} +(82.8394 + 100.063i) q^{75} +(-364.575 - 42.9430i) q^{76} +1413.98 q^{77} +(667.850 + 910.452i) q^{78} -1020.54i q^{79} +(311.242 + 74.3535i) q^{80} +(-678.188 - 267.400i) q^{81} +(172.425 + 10.1199i) q^{82} +588.935i q^{83} +(1077.50 - 697.135i) q^{84} -69.4395i q^{85} +(10.7978 - 183.974i) q^{86} +(284.530 + 343.689i) q^{87} +(1020.35 + 181.327i) q^{88} -1260.99i q^{89} +(370.304 + 93.1393i) q^{90} -2371.89 q^{91} +(-590.613 - 69.5679i) q^{92} +(911.486 - 754.593i) q^{93} +(-87.6936 + 1494.14i) q^{94} +229.435 q^{95} +(866.945 - 364.887i) q^{96} +936.527 q^{97} +(-101.111 + 1722.75i) q^{98} +(1214.87 + 230.854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

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Database

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