LMFDB - Embedded newform 110.5.h.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,5,Mod(41,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("110.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	110.h (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:	$11.3706959392$
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			41.2
Character	$\chi$	$=$	110.41
Dual form			110.5.h.a.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.66251 - 2.28825i) q^{2} +(-2.06757 - 6.36334i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-9.04508 - 6.57164i) q^{5} +(-11.1235 + 15.3102i) q^{6} +(87.9902 + 28.5898i) q^{7} +(21.5200 - 6.99226i) q^{8} +(29.3131 - 21.2972i) q^{9} +31.6228i q^{10} +(114.486 - 39.1662i) q^{11} +53.5265 q^{12} +(-177.682 - 244.558i) q^{13} +(-80.8640 - 248.874i) q^{14} +(-23.1162 + 71.1443i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(-235.598 + 324.273i) q^{17} +(-97.4666 - 31.6688i) q^{18} +(272.156 - 88.4288i) q^{19} +(72.3607 - 52.5731i) q^{20} -619.023i q^{21} +(-279.956 - 196.858i) q^{22} +73.4505 q^{23} +(-88.9882 - 122.482i) q^{24} +(38.6271 + 118.882i) q^{25} +(-264.211 + 813.158i) q^{26} +(-634.580 - 461.049i) q^{27} +(-435.048 + 598.792i) q^{28} +(-1041.18 - 338.300i) q^{29} +(201.227 - 65.3825i) q^{30} +(878.032 - 637.927i) q^{31} +181.019i q^{32} +(-485.936 - 647.533i) q^{33} +1133.70 q^{34} +(-607.997 - 836.837i) q^{35} +(89.5730 + 275.677i) q^{36} +(677.221 - 2084.27i) q^{37} +(-654.808 - 475.746i) q^{38} +(-1188.83 + 1636.29i) q^{39} +(-240.600 - 78.1758i) q^{40} +(216.819 - 70.4489i) q^{41} +(-1416.48 + 1029.13i) q^{42} -1761.82i q^{43} +(14.9699 + 967.884i) q^{44} -405.098 q^{45} +(-122.112 - 168.073i) q^{46} +(19.7383 + 60.7483i) q^{47} +(-132.325 + 407.254i) q^{48} +(4982.45 + 3619.97i) q^{49} +(207.813 - 286.031i) q^{50} +(2550.58 + 828.733i) q^{51} +(2299.96 - 747.302i) q^{52} +(1409.64 - 1024.17i) q^{53} +2218.57i q^{54} +(-1292.92 - 398.098i) q^{55} +2093.45 q^{56} +(-1125.41 - 1548.99i) q^{57} +(956.856 + 2944.90i) q^{58} +(-1106.19 + 3404.51i) q^{59} +(-484.152 - 351.757i) q^{60} +(278.692 - 383.586i) q^{61} +(-2919.47 - 948.593i) q^{62} +(3188.15 - 1035.89i) q^{63} +(414.217 - 300.946i) q^{64} +3379.70i q^{65} +(-673.843 + 2188.47i) q^{66} -3530.45 q^{67} +(-1884.79 - 2594.19i) q^{68} +(-151.864 - 467.391i) q^{69} +(-904.087 + 2782.50i) q^{70} +(-2192.87 - 1593.21i) q^{71} +(481.901 - 663.281i) q^{72} +(1253.05 + 407.142i) q^{73} +(-5895.21 + 1915.47i) q^{74} +(676.623 - 491.595i) q^{75} +2289.29i q^{76} +(11193.4 - 173.124i) q^{77} +5720.68 q^{78} +(1918.34 + 2640.36i) q^{79} +(221.115 + 680.521i) q^{80} +(-714.847 + 2200.07i) q^{81} +(-521.668 - 379.014i) q^{82} +(-4253.74 + 5854.77i) q^{83} +(4709.81 + 1530.31i) q^{84} +(4262.01 - 1384.81i) q^{85} +(-4031.47 + 2929.04i) q^{86} +7324.84i q^{87} +(2189.87 - 1643.37i) q^{88} +8326.12 q^{89} +(673.478 + 926.963i) q^{90} +(-8642.40 - 26598.6i) q^{91} +(-181.580 + 558.845i) q^{92} +(-5874.75 - 4268.25i) q^{93} +(106.192 - 146.161i) q^{94} +(-3042.79 - 988.664i) q^{95} +(1151.89 - 374.271i) q^{96} +(-9421.98 + 6845.47i) q^{97} -17419.3i q^{98} +(2521.81 - 3586.32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) $ 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.66251	−	2.28825i	−0.415627	−	0.572061i
$2$	−1.66251	−	2.28825i	−0.415627	−	0.572061i
$3$	−2.06757	−	6.36334i	−0.229731	−	0.707038i	−0.997777	−	0.0666436i	$-0.978771\pi$
$3$	−2.06757	−	6.36334i	−0.229731	−	0.707038i	0.768046	−	0.640394i	$-0.221229\pi$
$4$	−2.47214	+	7.60845i	−0.154508	+	0.475528i
$5$	−9.04508	−	6.57164i	−0.361803	−	0.262866i
$5$	−9.04508	−	6.57164i	−0.361803	−	0.262866i
$6$	−11.1235	+	15.3102i	−0.308987	+	0.425284i
$7$	87.9902	+	28.5898i	1.79572	+	0.583464i	0.999760	−	0.0218870i	$-0.00696741\pi$
$7$	87.9902	+	28.5898i	1.79572	+	0.583464i	0.795958	+	0.605351i	$0.206967\pi$
$8$	21.5200	−	6.99226i	0.336249	−	0.109254i
$9$	29.3131	−	21.2972i	0.361891	−	0.262929i
$10$			31.6228i			0.316228i
$11$	114.486	−	39.1662i	0.946164	−	0.323688i
$11$	114.486	−	39.1662i	0.946164	−	0.323688i
$12$	53.5265			0.371712
$13$	−177.682	−	244.558i	−1.05137	−	1.44709i	−0.887615	−	0.460586i	$-0.847639\pi$
$13$	−177.682	−	244.558i	−1.05137	−	1.44709i	−0.163755	−	0.986501i	$-0.552361\pi$
$14$	−80.8640	−	248.874i	−0.412572	−	1.26976i
$15$	−23.1162	+	71.1443i	−0.102739	+	0.316197i
$16$	−51.7771	−	37.6183i	−0.202254	−	0.146946i
$17$	−235.598	+	324.273i	−0.815219	+	1.12205i	0.175278	+	0.984519i	$0.443918\pi$
$17$	−235.598	+	324.273i	−0.815219	+	1.12205i	−0.990497	+	0.137534i	$0.956082\pi$
$18$	−97.4666	−	31.6688i	−0.300823	−	0.0977433i
$19$	272.156	−	88.4288i	0.753894	−	0.244955i	0.0932382	−	0.995644i	$-0.470278\pi$
$19$	272.156	−	88.4288i	0.753894	−	0.244955i	0.660656	+	0.750689i	$0.270278\pi$
$20$	72.3607	−	52.5731i	0.180902	−	0.131433i
$21$		−	619.023i		−	1.40368i
$22$	−279.956	−	196.858i	−0.578421	−	0.406730i
$23$	73.4505			0.138848			0.0694239	−	0.997587i	$-0.477884\pi$
$23$	73.4505			0.138848			0.0694239	+	0.997587i	$0.477884\pi$
$24$	−88.9882	−	122.482i	−0.154493	−	0.212642i
$25$	38.6271	+	118.882i	0.0618034	+	0.190211i
$26$	−264.211	+	813.158i	−0.390845	+	1.20290i
$27$	−634.580	−	461.049i	−0.870480	−	0.632441i
$28$	−435.048	+	598.792i	−0.554908	+	0.763765i
$29$	−1041.18	−	338.300i	−1.23803	−	0.402259i	−0.384410	−	0.923163i	$-0.625595\pi$
$29$	−1041.18	−	338.300i	−1.23803	−	0.402259i	−0.853615	+	0.520904i	$0.825595\pi$
$30$	201.227	−	65.3825i	0.223585	−	0.0726472i
$31$	878.032	−	637.927i	0.913665	−	0.663816i	−0.0282744	−	0.999600i	$-0.509001\pi$
$31$	878.032	−	637.927i	0.913665	−	0.663816i	0.941939	+	0.335784i	$0.109001\pi$
$32$			181.019i			0.176777i
$33$	−485.936	−	647.533i	−0.446222	−	0.594613i
$34$	1133.70			0.980710
$35$	−607.997	−	836.837i	−0.496324	−	0.683132i
$36$	89.5730	+	275.677i	0.0691149	+	0.212714i
$37$	677.221	−	2084.27i	0.494683	−	1.52248i	−0.322767	−	0.946478i	$-0.604613\pi$
$37$	677.221	−	2084.27i	0.494683	−	1.52248i	0.817450	−	0.575999i	$-0.195387\pi$
$38$	−654.808	−	475.746i	−0.453468	−	0.329464i
$39$	−1188.83	+	1636.29i	−0.781614	+	1.07580i
$40$	−240.600	−	78.1758i	−0.150375	−	0.0488599i
$41$	216.819	−	70.4489i	0.128982	−	0.0419089i	−0.243815	−	0.969822i	$-0.578399\pi$
$41$	216.819	−	70.4489i	0.128982	−	0.0419089i	0.372797	+	0.927913i	$0.378399\pi$
$42$	−1416.48	+	1029.13i	−0.802992	+	0.583408i
$43$		−	1761.82i		−	0.952849i	−0.879215	−	0.476425i	$-0.841932\pi$
$43$		−	1761.82i		−	0.952849i	0.879215	−	0.476425i	$-0.158068\pi$
$44$	14.9699	+	967.884i	0.00773237	+	0.499940i
$45$	−405.098			−0.200048
$46$	−122.112	−	168.073i	−0.0577089	−	0.0794295i
$47$	19.7383	+	60.7483i	0.00893542	+	0.0275004i	0.955425	−	0.295235i	$-0.0953978\pi$
$47$	19.7383	+	60.7483i	0.00893542	+	0.0275004i	−0.946489	+	0.322735i	$0.895398\pi$
$48$	−132.325	+	407.254i	−0.0574326	+	0.176759i
$49$	4982.45	+	3619.97i	2.07516	+	1.50769i
$50$	207.813	−	286.031i	0.0831254	−	0.114412i
$51$	2550.58	+	828.733i	0.980615	+	0.318621i
$52$	2299.96	−	747.302i	0.850577	−	0.276369i
$53$	1409.64	−	1024.17i	0.501832	−	0.364602i	−0.307885	−	0.951424i	$-0.599621\pi$
$53$	1409.64	−	1024.17i	0.501832	−	0.364602i	0.809716	+	0.586822i	$0.199621\pi$
$54$			2218.57i			0.760828i
$55$	−1292.92	−	398.098i	−0.427412	−	0.131603i
$56$	2093.45			0.667555
$57$	−1125.41	−	1548.99i	−0.346385	−	0.476758i
$58$	956.856	+	2944.90i	0.284440	+	0.875416i
$59$	−1106.19	+	3404.51i	−0.317780	+	0.978026i	0.656815	+	0.754052i	$0.271903\pi$
$59$	−1106.19	+	3404.51i	−0.317780	+	0.978026i	−0.974595	+	0.223974i	$0.928097\pi$
$60$	−484.152	−	351.757i	−0.134487	−	0.0977102i
$61$	278.692	−	383.586i	0.0748970	−	0.103087i	−0.769925	−	0.638135i	$-0.779706\pi$
$61$	278.692	−	383.586i	0.0748970	−	0.103087i	0.844822	+	0.535048i	$0.179706\pi$
$62$	−2919.47	−	948.593i	−0.759487	−	0.246772i
$63$	3188.15	−	1035.89i	0.803263	−	0.260996i
$64$	414.217	−	300.946i	0.101127	−	0.0734732i
$65$			3379.70i			0.799930i
$66$	−673.843	+	2188.47i	−0.154693	+	0.502404i
$67$	−3530.45			−0.786466			−0.393233	−	0.919439i	$-0.628643\pi$
$67$	−3530.45			−0.786466			−0.393233	+	0.919439i	$0.628643\pi$
$68$	−1884.79	−	2594.19i	−0.407610	−	0.561027i
$69$	−151.864	−	467.391i	−0.0318976	−	0.0981707i
$70$	−904.087	+	2782.50i	−0.184508	+	0.567856i
$71$	−2192.87	−	1593.21i	−0.435006	−	0.316051i	0.348641	−	0.937256i	$-0.386643\pi$
$71$	−2192.87	−	1593.21i	−0.435006	−	0.316051i	−0.783648	+	0.621206i	$0.786643\pi$
$72$	481.901	−	663.281i	0.0929594	−	0.127948i
$73$	1253.05	+	407.142i	0.235139	+	0.0764011i	0.424216	−	0.905561i	$-0.360550\pi$
$73$	1253.05	+	407.142i	0.235139	+	0.0764011i	−0.189077	+	0.981962i	$0.560550\pi$
$74$	−5895.21	+	1915.47i	−1.07655	+	0.349794i
$75$	676.623	−	491.595i	0.120288	−	0.0873947i
$76$			2289.29i			0.396346i
$77$	11193.4	−	173.124i	1.88790	−	0.0291994i
$78$	5720.68			0.940283
$79$	1918.34	+	2640.36i	0.307376	+	0.423067i	0.934561	−	0.355804i	$-0.115793\pi$
$79$	1918.34	+	2640.36i	0.307376	+	0.423067i	−0.627184	+	0.778871i	$0.715793\pi$
$80$	221.115	+	680.521i	0.0345492	+	0.106331i
$81$	−714.847	+	2200.07i	−0.108954	+	0.335326i
$82$	−521.668	−	379.014i	−0.0775830	−	0.0563674i
$83$	−4253.74	+	5854.77i	−0.617468	+	0.849872i	−0.997166	−	0.0752384i	$-0.976028\pi$
$83$	−4253.74	+	5854.77i	−0.617468	+	0.849872i	0.379697	+	0.925111i	$0.376028\pi$
$84$	4709.81	+	1530.31i	0.667490	+	0.216881i
$85$	4262.01	−	1384.81i	0.589898	−	0.191670i
$86$	−4031.47	+	2929.04i	−0.545088	+	0.396030i
$87$			7324.84i			0.967742i
$88$	2189.87	−	1643.37i	0.282783	−	0.212212i
$89$	8326.12			1.05114			0.525572	−	0.850749i	$-0.323851\pi$
$89$	8326.12			1.05114			0.525572	+	0.850749i	$0.323851\pi$
$90$	673.478	+	926.963i	0.0831454	+	0.114440i
$91$	−8642.40	−	26598.6i	−1.04364	−	3.21200i
$92$	−181.580	+	558.845i	−0.0214532	+	0.0660261i
$93$	−5874.75	−	4268.25i	−0.679240	−	0.493497i
$94$	106.192	−	146.161i	0.0120181	−	0.0165415i
$95$	−3042.79	−	988.664i	−0.337152	−	0.109547i
$96$	1151.89	−	374.271i	0.124988	−	0.0406110i
$97$	−9421.98	+	6845.47i	−1.00138	+	0.727544i	−0.962383	−	0.271695i	$-0.912416\pi$
$97$	−9421.98	+	6845.47i	−1.00138	+	0.727544i	−0.0389956	+	0.999239i	$0.512416\pi$
$98$		−	17419.3i		−	1.81375i
$99$	2521.81	−	3586.32i	0.257301	−	0.365913i
$100$	−1000.00			−0.100000
$101$	9409.75	+	12951.4i	0.922434	+	1.26962i	0.962739	+	0.270434i	$0.0871671\pi$
$101$	9409.75	+	12951.4i	0.922434	+	1.26962i	−0.0403048	+	0.999187i	$0.512833\pi$
$102$	−2344.01	−	7214.13i	−0.225299	−	0.693399i
$103$	−1529.82	+	4708.31i	−0.144201	+	0.443804i	−0.996907	−	0.0785861i	$-0.974959\pi$
$103$	−1529.82	+	4708.31i	−0.144201	+	0.443804i	0.852707	+	0.522390i	$0.174959\pi$
$104$	−5533.71	−	4020.48i	−0.511623	−	0.371716i
$105$	−4068.00	+	5599.12i	−0.368979	+	0.507856i
$106$	−4687.09	−	1522.93i	−0.417149	−	0.135540i
$107$	6058.42	−	1968.50i	0.529166	−	0.171936i	−0.0322352	−	0.999480i	$-0.510263\pi$
$107$	6058.42	−	1968.50i	0.529166	−	0.171936i	0.561401	+	0.827544i	$0.310263\pi$
$108$	5076.64	−	3688.40i	0.435240	−	0.316220i
$109$			6127.95i			0.515777i	0.966175	+	0.257889i	$0.0830268\pi$
$109$			6127.95i			0.515777i	−0.966175	+	0.257889i	$0.916973\pi$
$110$	1238.55	+	3620.36i	0.102359	+	0.299203i
$111$	−14663.1			−1.19009
$112$	−3480.38	−	4790.33i	−0.277454	−	0.381882i
$113$	−5531.44	−	17024.0i	−0.433193	−	1.33323i	−0.894927	−	0.446212i	$-0.852773\pi$
$113$	−5531.44	−	17024.0i	−0.433193	−	1.33323i	0.461734	−	0.887018i	$-0.347227\pi$
$114$	−1673.47	+	5150.41i	−0.128768	+	0.396307i
$115$	−664.366	−	482.690i	−0.0502356	−	0.0364983i
$116$	5147.87	−	7085.44i	0.382571	−	0.526564i
$117$	−10416.8	−	3384.63i	−0.760962	−	0.247252i
$118$	9629.41	−	3128.78i	0.691569	−	0.224704i
$119$	−30001.3	+	21797.2i	−2.11858	+	1.53924i
$120$			1692.66i			0.117546i
$121$	11573.0	−	8967.96i	0.790452	−	0.612524i
$122$	−1341.07			−0.0901012
$123$	−896.581	−	1234.04i	−0.0592624	−	0.0815677i
$124$	2683.03	+	8257.51i	0.174494	+	0.537039i
$125$	431.864	−	1329.14i	0.0276393	−	0.0850651i
$126$	−7670.71	−	5573.09i	−0.483164	−	0.351039i
$127$	5788.56	−	7967.27i	0.358892	−	0.493972i	−0.590948	−	0.806710i	$-0.701246\pi$
$127$	5788.56	−	7967.27i	0.358892	−	0.493972i	0.949840	+	0.312738i	$0.101246\pi$
$128$	−1377.28	−	447.504i	−0.0840623	−	0.0273135i
$129$	−11211.1	+	3642.69i	−0.673701	+	0.218899i
$130$	7733.59	−	5618.79i	0.457609	−	0.332473i
$131$		−	7862.65i		−	0.458170i	−0.973406	−	0.229085i	$-0.926427\pi$
$131$		−	7862.65i		−	0.458170i	0.973406	−	0.229085i	$-0.0735733\pi$
$132$	6128.03	−	2096.43i	0.351700	−	0.120319i
$133$	26475.2			1.49670
$134$	5869.40	+	8078.53i	0.326877	+	0.449907i
$135$	2709.98	+	8340.46i	0.148696	+	0.457639i
$136$	−2802.66	+	8625.71i	−0.151528	+	0.466356i
$137$	−22242.9	−	16160.4i	−1.18509	−	0.861016i	−0.192350	−	0.981326i	$-0.561611\pi$
$137$	−22242.9	−	16160.4i	−1.18509	−	0.861016i	−0.992736	+	0.120311i	$0.961611\pi$
$138$	−817.029	+	1124.54i	−0.0429022	+	0.0590498i
$139$	33824.7	+	10990.3i	1.75067	+	0.568827i	0.996167	−	0.0874721i	$-0.0278789\pi$
$139$	33824.7	+	10990.3i	1.75067	+	0.568827i	0.754501	+	0.656299i	$0.227879\pi$
$140$	7870.08	−	2557.15i	0.401535	−	0.130467i
$141$	345.752	−	251.203i	0.0173911	−	0.0126354i
$142$			7666.55i			0.380210i
$143$	−29920.4	−	21039.3i	−1.46317	−	1.02887i
$144$	−2318.91			−0.111830
$145$	7194.37	+	9902.20i	0.342182	+	0.470973i
$146$	−1151.57	−	3544.17i	−0.0540238	−	0.166268i
$147$	12733.5	−	39189.6i	0.589267	−	1.81358i
$148$	14183.9	+	10305.2i	0.647548	+	0.470471i
$149$	−6652.18	+	9155.94i	−0.299634	+	0.412411i	−0.932114	−	0.362166i	$-0.882037\pi$
$149$	−6652.18	+	9155.94i	−0.299634	+	0.412411i	0.632479	+	0.774577i	$0.282037\pi$
$150$	−2249.78	−	730.998i	−0.0999903	−	0.0324888i
$151$	11524.7	−	3744.62i	0.505449	−	0.164230i	−0.0451824	−	0.998979i	$-0.514387\pi$
$151$	11524.7	−	3744.62i	0.505449	−	0.164230i	0.550632	+	0.834748i	$0.314387\pi$
$152$	5238.46	−	3805.97i	0.226734	−	0.164732i
$153$			14523.1i			0.620405i
$154$	−19005.2	−	25325.4i	−0.801368	−	1.06786i
$155$	−12134.1			−0.505061
$156$	−9510.67	−	13090.3i	−0.390807	−	0.537899i
$157$	8817.90	+	27138.7i	0.357739	+	1.10101i	0.954404	+	0.298516i	$0.0964918\pi$
$157$	8817.90	+	27138.7i	0.357739	+	1.10101i	−0.596666	+	0.802490i	$0.703508\pi$
$158$	2852.55	−	8779.25i	0.114267	−	0.351676i
$159$	−9431.67	−	6852.51i	−0.373073	−	0.271054i
$160$	1189.59	−	1637.34i	0.0464685	−	0.0639584i
$161$	6462.93	+	2099.93i	0.249332	+	0.0810128i
$162$	6222.74	−	2021.89i	0.237111	−	0.0770421i
$163$	10243.8	−	7442.59i	0.385556	−	0.280123i	−0.378076	−	0.925775i	$-0.623414\pi$
$163$	10243.8	−	7442.59i	0.385556	−	0.280123i	0.763632	+	0.645652i	$0.223414\pi$
$164$			1823.82i			0.0678101i
$165$	139.979	+	9050.39i	0.00514155	+	0.332429i
$166$	20469.0			0.742816
$167$	31226.4	+	42979.4i	1.11967	+	1.54109i	0.806349	+	0.591441i	$0.201441\pi$
$167$	31226.4	+	42979.4i	1.11967	+	1.54109i	0.313318	+	0.949648i	$0.398559\pi$
$168$	−4328.37	−	13321.4i	−0.153358	−	0.471987i
$169$	−19411.9	+	59743.7i	−0.679665	+	2.09179i
$170$	−10254.4	−	7450.28i	−0.354824	−	0.257795i
$171$	6094.45	−	8388.29i	0.208421	−	0.286867i
$172$	13404.7	+	4355.45i	0.453107	+	0.147223i
$173$	−18240.8	+	5926.78i	−0.609468	+	0.198028i	−0.597459	−	0.801900i	$-0.703823\pi$
$173$	−18240.8	+	5926.78i	−0.609468	+	0.198028i	−0.0120092	+	0.999928i	$0.503823\pi$
$174$	16761.0	−	12177.6i	0.553608	−	0.402220i
$175$			11564.8i			0.377626i
$176$	−7401.11	−	2278.84i	−0.238930	−	0.0735680i
$177$	23951.2			0.764505
$178$	−13842.2	−	19052.2i	−0.436884	−	0.601319i
$179$	349.000	+	1074.11i	0.0108923	+	0.0335230i	0.956355	−	0.292207i	$-0.0943898\pi$
$179$	349.000	+	1074.11i	0.0108923	+	0.0335230i	−0.945463	+	0.325731i	$0.894390\pi$
$180$	1001.46	−	3082.17i	0.0309091	−	0.0951286i
$181$	26356.0	+	19148.7i	0.804493	+	0.584498i	0.912229	−	0.409681i	$-0.134360\pi$
$181$	26356.0	+	19148.7i	0.804493	+	0.584498i	−0.107736	+	0.994180i	$0.534360\pi$
$182$	−46496.0	+	63996.2i	−1.40369	+	1.93202i
$183$	−3017.11	−	980.317i	−0.0900925	−	0.0292728i
$184$	1580.65	−	513.585i	0.0466875	−	0.0151697i
$185$	−19822.6	+	14402.0i	−0.579185	+	0.420802i
$186$			20538.9i			0.593677i
$187$	−14272.1	+	46352.2i	−0.408136	+	1.32552i
$188$	−510.997			−0.0144578
$189$	−42655.6	−	58710.3i	−1.19413	−	1.64358i
$190$	2796.36	+	8606.32i	0.0774616	+	0.238402i
$191$	4552.19	−	14010.2i	0.124783	−	0.384041i	−0.869079	−	0.494674i	$-0.835288\pi$
$191$	4552.19	−	14010.2i	0.124783	−	0.384041i	0.993861	+	0.110632i	$0.0352876\pi$
$192$	−2771.45	−	2013.57i	−0.0751803	−	0.0546217i
$193$	7083.25	−	9749.26i	0.190160	−	0.261732i	−0.703283	−	0.710910i	$-0.748283\pi$
$193$	7083.25	−	9749.26i	0.190160	−	0.261732i	0.893442	+	0.449178i	$0.148283\pi$
$194$	31328.2	+	10179.2i	0.832400	+	0.270463i
$195$	21506.2	−	6987.79i	0.565581	−	0.183768i
$196$	−39859.6	+	28959.7i	−1.03758	+	0.753845i
$197$			10613.1i			0.273470i	0.990608	+	0.136735i	$0.0436608\pi$
$197$			10613.1i			0.273470i	−0.990608	+	0.136735i	$0.956339\pi$
$198$	−12398.9	+	191.769i	−0.316266	+	0.00489156i
$199$	16206.1			0.409234			0.204617	−	0.978842i	$-0.434405\pi$
$199$	16206.1			0.409234			0.204617	+	0.978842i	$0.434405\pi$
$200$	1662.51	+	2288.25i	0.0415627	+	0.0572061i
$201$	7299.46	+	22465.4i	0.180675	+	0.556062i
$202$	13992.2	−	43063.6i	0.342913	−	1.05538i
$203$	−81941.7	−	59534.1i	−1.98844	−	1.44469i
$204$	−12610.8	+	17357.2i	−0.303027	+	0.417080i
$205$	−2424.12	−	787.643i	−0.0576827	−	0.0187422i
$206$	13317.1	−	4327.00i	0.313817	−	0.101965i
$207$	2153.06	−	1564.29i	0.0502477	−	0.0365071i
$208$			19346.6i			0.447175i
$209$	27694.6	−	20783.2i	0.634019	−	0.475794i
$210$	19575.2			0.443883
$211$	−10585.7	−	14569.9i	−0.237768	−	0.327259i	0.673413	−	0.739267i	$-0.264828\pi$
$211$	−10585.7	−	14569.9i	−0.237768	−	0.327259i	−0.911180	+	0.412008i	$0.864828\pi$
$212$	4307.49	+	13257.1i	0.0958413	+	0.294969i
$213$	−5604.23	+	17248.0i	−0.123526	+	0.380173i
$214$	−14576.6	−	10590.5i	−0.318294	−	0.231254i
$215$	−11578.0	+	15935.8i	−0.250471	+	0.344744i
$216$	−16879.9	−	5484.62i	−0.361795	−	0.117554i
$217$	95496.4	−	31028.7i	2.02800	−	0.658936i
$218$	14022.3	−	10187.8i	0.295056	−	0.214371i
$219$		−	8815.40i		−	0.183804i
$220$	6225.18	−	8852.97i	0.128619	−	0.182913i
$221$	121165.			2.48081
$222$	24377.6	+	33552.9i	0.494635	+	0.680806i
$223$	4324.10	+	13308.2i	0.0869533	+	0.267615i	0.985073	−	0.172136i	$-0.0550668\pi$
$223$	4324.10	+	13308.2i	0.0869533	+	0.267615i	−0.898120	+	0.439751i	$0.855067\pi$
$224$	−5175.30	+	15927.9i	−0.103143	+	0.317441i
$225$	3664.14	+	2662.15i	0.0723781	+	0.0525858i
$226$	−29759.1	+	40959.9i	−0.582643	+	0.801939i
$227$	−36407.6	−	11829.5i	−0.706545	−	0.229570i	−0.0663652	−	0.997795i	$-0.521140\pi$
$227$	−36407.6	−	11829.5i	−0.706545	−	0.229570i	−0.640180	+	0.768225i	$0.721140\pi$
$228$	14567.5	−	4733.28i	0.280231	−	0.0910527i
$229$	−36426.6	+	26465.5i	−0.694621	+	0.504672i	−0.878176	−	0.478338i	$-0.841240\pi$
$229$	−36426.6	+	26465.5i	−0.694621	+	0.504672i	0.183555	+	0.983010i	$0.441240\pi$
$230$			2322.71i			0.0439075i
$231$	−24244.8	−	70869.4i	−0.454354	−	1.32811i
$232$	−24771.6			−0.460233
$233$	45632.8	+	62808.2i	0.840553	+	1.15692i	0.985866	+	0.167537i	$0.0535813\pi$
$233$	45632.8	+	62808.2i	0.840553	+	1.15692i	−0.145312	+	0.989386i	$0.546419\pi$
$234$	9573.17	+	29463.2i	0.174833	+	0.538081i
$235$	220.681	−	679.187i	0.00399604	−	0.0122985i
$236$	−23168.4	−	16832.8i	−0.415979	−	0.302227i
$237$	12835.2	−	17666.2i	0.228511	−	0.314518i
$238$	99754.6	+	32412.2i	1.76108	+	0.572210i
$239$	33059.0	−	10741.5i	0.578754	−	0.188049i	−0.00498823	−	0.999988i	$-0.501588\pi$
$239$	33059.0	−	10741.5i	0.578754	−	0.188049i	0.583742	+	0.811939i	$0.301588\pi$
$240$	3873.21	−	2814.05i	0.0672433	−	0.0488551i
$241$			7612.22i			0.131062i	0.997851	+	0.0655311i	$0.0208741\pi$
$241$			7612.22i			0.131062i	−0.997851	+	0.0655311i	$0.979126\pi$
$242$	−39761.1	−	11572.6i	−0.678934	−	0.197606i
$243$	−48057.3			−0.813855
$244$	2229.53	+	3068.69i	0.0374485	+	0.0515434i
$245$	−21277.6	−	65485.8i	−0.354479	−	1.09098i
$246$	−1333.21	+	4103.19i	−0.0220307	+	0.0678035i
$247$	−69983.0	−	50845.6i	−1.14709	−	0.833412i
$248$	14434.6	−	19867.6i	0.234694	−	0.323029i
$249$	46050.8	+	14962.8i	0.742743	+	0.241332i
$250$	−3759.38	+	1221.50i	−0.0601501	+	0.0195440i
$251$	−57712.5	+	41930.6i	−0.916057	+	0.665554i	−0.942539	−	0.334095i	$-0.891569\pi$
$251$	−57712.5	+	41930.6i	−0.916057	+	0.665554i	0.0264824	+	0.999649i	$0.491569\pi$
$252$			26817.8i			0.422300i
$253$	8409.04	−	2876.78i	0.131373	−	0.0449434i
$254$	−27854.6			−0.431747
$255$	−17624.1	−	24257.5i	−0.271035	−	0.373048i
$256$	1265.73	+	3895.53i	0.0193136	+	0.0594410i
$257$	39685.4	−	122139.i	0.600848	−	1.84922i	0.0776991	−	0.996977i	$-0.475243\pi$
$257$	39685.4	−	122139.i	0.600848	−	1.84922i	0.523148	−	0.852242i	$-0.324757\pi$
$258$	26973.8	+	19597.6i	0.405232	+	0.294418i
$259$	119178.	−	164034.i	1.77662	−	2.44531i
$260$	−25714.3	−	8355.09i	−0.380389	−	0.123596i
$261$	−37725.1	+	12257.6i	−0.553795	+	0.179939i
$262$	−17991.7	+	13071.7i	−0.262101	+	0.190428i
$263$			37584.7i			0.543375i	0.962386	+	0.271688i	$0.0875817\pi$
$263$			37584.7i			0.543375i	−0.962386	+	0.271688i	$0.912418\pi$
$264$	−14985.0	−	10537.1i	−0.215006	−	0.151187i
$265$	−19480.8			−0.277406
$266$	−44015.2	−	60581.8i	−0.622071	−	0.856207i
$267$	−17214.9	−	52981.9i	−0.241480	−	0.743199i
$268$	8727.75	−	26861.2i	0.121516	−	0.373987i
$269$	6957.45	+	5054.88i	0.0961492	+	0.0698565i	0.634821	−	0.772659i	$-0.281074\pi$
$269$	6957.45	+	5054.88i	0.0961492	+	0.0698565i	−0.538672	+	0.842516i	$0.681074\pi$
$270$	14579.7	−	20067.2i	0.199995	−	0.275270i
$271$	28698.0	+	9324.54i	0.390762	+	0.126966i	0.497807	−	0.867288i	$-0.334139\pi$
$271$	28698.0	+	9324.54i	0.390762	+	0.126966i	−0.107045	+	0.994254i	$0.534139\pi$
$272$	24397.2	−	7927.13i	0.329763	−	0.107147i
$273$	−151387.	+	109989.i	−2.03125	+	1.47579i
$274$			77764.0i			1.03580i
$275$	9078.42	+	12097.4i	0.120045	+	0.159966i
$276$	3931.55			0.0516114
$277$	−32409.2	−	44607.4i	−0.422385	−	0.581363i	0.543799	−	0.839215i	$-0.316985\pi$
$277$	−32409.2	−	44607.4i	−0.422385	−	0.581363i	−0.966184	+	0.257852i	$0.916985\pi$
$278$	−31085.3	−	95670.6i	−0.402221	−	1.23791i
$279$	12151.8	−	37399.3i	0.156110	−	0.480458i
$280$	−18935.5	−	13757.4i	−0.241524	−	0.175477i
$281$	−74008.4	+	101864.i	−0.937278	+	1.29005i	0.0196743	+	0.999806i	$0.493737\pi$
$281$	−74008.4	+	101864.i	−0.937278	+	1.29005i	−0.956952	+	0.290246i	$0.906263\pi$
$282$	−1149.63	−	373.538i	−0.0144564	−	0.00469717i
$283$	−128822.	+	41856.8i	−1.60849	+	0.522628i	−0.969186	−	0.246330i	$-0.920775\pi$
$283$	−128822.	+	41856.8i	−1.60849	+	0.522628i	−0.639299	+	0.768958i	$0.720775\pi$
$284$	17542.9	−	12745.7i	0.217503	−	0.158025i
$285$			21406.5i			0.263545i
$286$	1599.91	+	103443.i	0.0195598	+	1.26465i
$287$	21092.1			0.256069
$288$	3855.21	+	5306.24i	0.0464797	+	0.0639738i
$289$	−23837.2	−	73363.4i	−0.285404	−	0.878382i
$290$	10698.0	−	32925.0i	0.127205	−	0.391498i
$291$	63040.7	+	45801.7i	0.744449	+	0.540874i
$292$	−6195.44	+	8527.29i	−0.0726618	+	0.100010i
$293$	139015.	+	45168.6i	1.61929	+	0.526140i	0.971775	−	0.235911i	$-0.0758074\pi$
$293$	139015.	+	45168.6i	1.61929	+	0.526140i	0.647517	+	0.762051i	$0.275807\pi$
$294$	−110845.	+	36015.7i	−1.28239	+	0.416675i
$295$	32378.8	−	23524.6i	0.372063	−	0.270320i
$296$		−	49588.7i		−	0.565978i
$297$	−90708.0	−	27929.5i	−1.02833	−	0.316629i
$298$	32010.4			0.360461
$299$	−13050.8	−	17962.9i	−0.145980	−	0.200925i
$300$	2067.57	+	6363.34i	0.0229731	+	0.0707038i
$301$	50370.0	−	155023.i	0.555954	−	1.71105i
$302$	−27728.6	−	20146.0i	−0.304028	−	0.220889i
$303$	62958.9	−	86655.4i	0.685759	−	0.943866i
$304$	−17418.0	−	5659.44i	−0.188474	−	0.0612388i
$305$	−5041.58	+	1638.11i	−0.0541960	+	0.0176093i
$306$	33232.3	−	24144.7i	0.354910	−	0.257857i
$307$			114638.i			1.21633i	0.793811	+	0.608164i	$0.208094\pi$
$307$			114638.i			1.21633i	−0.793811	+	0.608164i	$0.791906\pi$
$308$	−26354.4	+	85592.3i	−0.277812	+	0.902264i
$309$	33123.6			0.346913
$310$	20173.0	+	27765.8i	0.209917	+	0.288926i
$311$	−6840.10	−	21051.7i	−0.0707199	−	0.217653i	0.909450	−	0.415814i	$-0.136503\pi$
$311$	−6840.10	−	21051.7i	−0.0707199	−	0.217653i	−0.980170	+	0.198161i	$0.936503\pi$
$312$	−14142.3	+	43525.5i	−0.145282	+	0.447131i
$313$	63670.0	+	46259.0i	0.649899	+	0.472180i	0.863237	−	0.504799i	$-0.168433\pi$
$313$	63670.0	+	46259.0i	0.649899	+	0.472180i	−0.213338	+	0.976979i	$0.568433\pi$
$314$	47440.2	−	65295.8i	0.481157	−	0.662256i
$315$	−35644.6	−	11581.6i	−0.359230	−	0.116721i
$316$	−24831.5	+	8068.23i	−0.248673	+	0.0807987i
$317$	−103601.	+	75270.4i	−1.03097	+	0.749041i	−0.968502	−	0.249006i	$-0.919896\pi$
$317$	−103601.	+	75270.4i	−1.03097	+	0.749041i	−0.0624649	+	0.998047i	$0.519896\pi$
$318$			32974.3i			0.326078i
$319$	−132450.	+	2048.55i	−1.30158	+	0.0201310i
$320$	−5724.33			−0.0559017
$321$	−25052.5	−	34481.8i	−0.243131	−	0.334641i
$322$	−5939.50	−	18279.9i	−0.0572847	−	0.176304i
$323$	−35444.4	+	109087.i	−0.339737	+	1.04560i
$324$	−14971.9	−	10877.8i	−0.142623	−	0.103621i
$325$	22210.2	−	30569.7i	0.210274	−	0.289417i
$326$	−34060.9	−	11067.1i	−0.320495	−	0.104135i
$327$	38994.2	−	12670.0i	0.364674	−	0.118490i
$328$	4173.35	−	3032.11i	0.0387915	−	0.0281837i
$329$			5909.57i			0.0545964i
$330$	20476.8	−	15366.6i	0.188033	−	0.141108i
$331$	24781.4			0.226188			0.113094	−	0.993584i	$-0.463924\pi$
$331$	24781.4			0.226188			0.113094	+	0.993584i	$0.463924\pi$
$332$	−34029.9	−	46838.2i	−0.308734	−	0.424936i
$333$	−24537.8	−	75519.5i	−0.221282	−	0.681037i
$334$	46433.4	−	142907.i	0.416234	−	1.28104i
$335$	31933.2	+	23200.8i	0.284546	+	0.206735i
$336$	−23286.6	+	32051.2i	−0.206266	+	0.283900i
$337$	−33661.0	−	10937.1i	−0.296392	−	0.0963037i	0.157046	−	0.987591i	$-0.449803\pi$
$337$	−33661.0	−	10937.1i	−0.296392	−	0.0963037i	−0.453438	+	0.891288i	$0.649803\pi$
$338$	168981.	−	54905.2i	1.47912	−	0.480596i
$339$	−96893.0	+	70396.9i	−0.843127	+	0.612568i
$340$			35850.8i			0.310128i
$341$	75537.0	−	107423.i	0.649607	−	0.923821i
$342$	−29326.5			−0.250731
$343$	204345.	+	281256.i	1.73690	+	2.39064i
$344$	−12319.1	−	37914.3i	−0.104103	−	0.320395i
$345$	−1697.90	+	5225.59i	−0.0142650	+	0.0439033i
$346$	43887.3	+	31886.0i	0.366595	+	0.266347i
$347$	−30919.4	+	42556.9i	−0.256786	+	0.353436i	−0.917874	−	0.396873i	$-0.870095\pi$
$347$	−30919.4	+	42556.9i	−0.256786	+	0.353436i	0.661087	+	0.750309i	$0.270095\pi$
$348$	−55730.7	−	18108.0i	−0.460189	−	0.149524i
$349$	159177.	−	51719.9i	1.30686	−	0.424626i	0.428900	−	0.903352i	$-0.358901\pi$
$349$	159177.	−	51719.9i	1.30686	−	0.424626i	0.877965	+	0.478726i	$0.158901\pi$
$350$	26463.1	−	19226.6i	0.216025	−	0.156952i
$351$			237111.i			1.92459i
$352$	7089.85	+	20724.1i	0.0572205	+	0.167260i
$353$	27790.2			0.223019			0.111510	−	0.993763i	$-0.464431\pi$
$353$	27790.2			0.223019			0.111510	+	0.993763i	$0.464431\pi$
$354$	−39819.0	−	54806.2i	−0.317749	−	0.437344i
$355$	9364.66	+	28821.5i	0.0743080	+	0.228696i
$356$	−20583.3	+	63348.9i	−0.162411	+	0.499849i
$357$	200733.	+	145841.i	1.57500	+	1.14431i
$358$	1877.62	−	2584.32i	0.0146501	−	0.0201641i
$359$	−15536.5	−	5048.13i	−0.120549	−	0.0391689i	0.248121	−	0.968729i	$-0.420187\pi$
$359$	−15536.5	−	5048.13i	−0.120549	−	0.0391689i	−0.368670	+	0.929560i	$0.620187\pi$
$360$	−8717.68	+	2832.55i	−0.0672660	+	0.0218561i
$361$	−39182.8	+	28467.9i	−0.300663	+	0.218445i
$362$		−	92143.9i		−	0.703152i
$363$	−80994.2	−	55101.1i	−0.614668	−	0.418164i
$364$	223739.			1.68865
$365$	−8658.38	−	11917.2i	−0.0649907	−	0.0894520i
$366$	2772.76	+	8533.67i	0.0206990	+	0.0637050i
$367$	−27192.5	+	83689.8i	−0.201891	+	0.621356i	0.797936	+	0.602742i	$0.205925\pi$
$367$	−27192.5	+	83689.8i	−0.201891	+	0.621356i	−0.999827	+	0.0186136i	$0.994075\pi$
$368$	−3803.05	−	2763.08i	−0.0280826	−	0.0204032i
$369$	4855.29	−	6682.73i	0.0356584	−	0.0490796i
$370$	65910.5	+	21415.6i	0.481450	+	0.156432i
$371$	153316.	−	49815.3i	1.11388	−	0.361922i
$372$	46998.0	−	34146.0i	0.339620	−	0.246748i
$373$			123464.i			0.887410i	0.896173	+	0.443705i	$0.146336\pi$
$373$			123464.i			0.887410i	−0.896173	+	0.443705i	$0.853664\pi$
$374$	129793.	−	44402.8i	0.927913	−	0.317444i
$375$	−9350.69			−0.0664938
$376$	849.536	+	1169.29i	0.00600905	+	0.00827075i
$377$	102265.	+	314738.i	0.719520	+	2.21445i
$378$	−63428.5	+	195213.i	−0.443916	+	1.36623i
$379$	60075.6	+	43647.5i	0.418235	+	0.303865i	0.776927	−	0.629591i	$-0.216777\pi$
$379$	60075.6	+	43647.5i	0.418235	+	0.303865i	−0.358693	+	0.933456i	$0.616777\pi$
$380$	15044.4	−	20706.8i	0.104186	−	0.143399i
$381$	−62666.8	−	20361.7i	−0.431705	−	0.140270i
$382$	−39626.9	+	12875.5i	−0.271558	+	0.0882346i
$383$	99412.1	−	72227.1i	0.677707	−	0.492383i	−0.194890	−	0.980825i	$-0.562435\pi$
$383$	99412.1	−	72227.1i	0.677707	−	0.492383i	0.872596	+	0.488443i	$0.162435\pi$
$384$			9689.33i			0.0657100i
$385$	−102383.	−	71993.0i	−0.690726	−	0.485701i
$386$	−34084.7			−0.228762
$387$	−37521.9	−	51644.4i	−0.250532	−	0.344827i
$388$	−28791.0	−	88609.6i	−0.191246	−	0.588596i
$389$	−6055.66	+	18637.4i	−0.0400187	+	0.123165i	−0.969070	−	0.246786i	$-0.920625\pi$
$389$	−6055.66	+	18637.4i	−0.0400187	+	0.123165i	0.929051	+	0.369951i	$0.120625\pi$
$390$	−51744.0	−	37594.2i	−0.340197	−	0.247168i
$391$	−17304.8	+	23818.0i	−0.113191	+	0.155795i
$392$	132534.	+	43062.9i	0.862492	+	0.280241i
$393$	−50032.7	+	16256.6i	−0.323943	+	0.105256i
$394$	24285.3	−	17644.3i	0.156441	−	0.113661i
$395$		−	36488.9i		−	0.233866i
$396$	21052.1	+	28052.9i	0.134247	+	0.178891i
$397$	−26285.6			−0.166777			−0.0833886	−	0.996517i	$-0.526574\pi$
$397$	−26285.6			−0.166777			−0.0833886	+	0.996517i	$0.526574\pi$
$398$	−26942.7	−	37083.4i	−0.170089	−	0.234107i
$399$	−54739.5	−	168471.i	−0.343839	−	1.05823i
$400$	2472.14	−	7608.45i	0.0154508	−	0.0475528i
$401$	−84829.3	−	61632.1i	−0.527542	−	0.383282i	0.291895	−	0.956450i	$-0.405714\pi$
$401$	−84829.3	−	61632.1i	−0.527542	−	0.383282i	−0.819438	+	0.573168i	$0.805714\pi$
$402$	39271.0	−	54051.9i	0.243008	−	0.334472i
$403$	−312020.	−	101381.i	−1.92120	−	0.624236i
$404$	−121802.	+	39576.0i	−0.746265	+	0.242476i
$405$	20923.9	−	15202.1i	0.127565	−	0.0926818i
$406$			286479.i			1.73796i
$407$	−4100.87	−	265144.i	−0.0247564	−	1.60064i
$408$	60683.1			0.364542
$409$	53141.7	+	73143.3i	0.317679	+	0.437248i	0.937757	−	0.347293i	$-0.112899\pi$
$409$	53141.7	+	73143.3i	0.317679	+	0.437248i	−0.620078	+	0.784540i	$0.712899\pi$
$410$	2227.79	+	6856.43i	0.0132528	+	0.0407878i
$411$	−56845.3	+	174952.i	−0.336520	+	1.03570i
$412$	−32041.1	−	23279.2i	−0.188761	−	0.137143i
$413$	−194668.	+	267938.i	−1.14129	+	1.57085i
$414$	−7158.97	−	2326.09i	−0.0417686	−	0.0135714i
$415$	76950.9	−	25002.9i	0.446804	−	0.145176i
$416$	44269.7	−	32163.8i	0.255811	−	0.185858i
$417$		−	237961.i		−	1.36847i
$418$	−93599.4	−	28819.8i	−0.535699	−	0.164945i
$419$	−66155.3			−0.376822			−0.188411	−	0.982090i	$-0.560334\pi$
$419$	−66155.3			−0.376822			−0.188411	+	0.982090i	$0.560334\pi$
$420$	−32544.0	−	44792.9i	−0.184490	−	0.253928i
$421$	−18838.9	−	57980.2i	−0.106290	−	0.327127i	0.883741	−	0.467976i	$-0.155017\pi$
$421$	−18838.9	−	57980.2i	−0.106290	−	0.327127i	−0.990031	+	0.140849i	$0.955017\pi$
$422$	−15740.8	+	48445.2i	−0.0883897	+	0.272035i
$423$	1872.36	+	1360.35i	0.0104643	+	0.00760275i
$424$	23174.3	−	31896.6i	0.128906	−	0.177424i
$425$	−47650.8	−	15482.7i	−0.263811	−	0.0857172i
$426$	48784.8	−	15851.2i	0.268823	−	0.0873458i
$427$	35488.8	−	25784.1i	0.194641	−	0.141415i
$428$			50961.6i			0.278199i
$429$	−72017.4	+	233894.i	−0.391312	+	1.27088i
$430$	55713.6			0.301317
$431$	−12080.4	−	16627.2i	−0.0650318	−	0.0895085i	0.775262	−	0.631639i	$-0.217618\pi$
$431$	−12080.4	−	16627.2i	−0.0650318	−	0.0895085i	−0.840294	+	0.542131i	$0.817618\pi$
$432$	15512.8	+	47743.6i	0.0831235	+	0.255828i
$433$	88410.1	−	272098.i	0.471548	−	1.45128i	−0.379009	−	0.925393i	$-0.623735\pi$
$433$	88410.1	−	272098.i	0.471548	−	1.45128i	0.850557	−	0.525883i	$-0.176265\pi$
$434$	−229765.	−	166934.i	−1.21984	−	0.886268i
$435$	48136.2	−	66253.8i	0.254386	−	0.350132i
$436$	−46624.2	−	15149.1i	−0.245267	−	0.0796920i
$437$	19990.0	−	6495.14i	0.104677	−	0.0340115i
$438$	−20171.8	+	14655.7i	−0.105147	+	0.0763937i
$439$		−	76816.3i		−	0.398588i	−0.979940	−	0.199294i	$-0.936135\pi$
$439$		−	76816.3i		−	0.398588i	0.979940	−	0.199294i	$-0.0638649\pi$
$440$	−30607.2	+	473.389i	−0.158095	+	0.00244519i
$441$	223147.			1.14740
$442$	−201438.	−	277255.i	−1.03109	−	1.41917i
$443$	46843.1	+	144168.i	0.238692	+	0.734619i	0.996610	+	0.0822693i	$0.0262168\pi$
$443$	46843.1	+	144168.i	0.238692	+	0.734619i	−0.757918	+	0.652350i	$0.773783\pi$
$444$	36249.3	−	111564.i	0.183879	−	0.565923i
$445$	−75310.4	−	54716.2i	−0.380308	−	0.276310i
$446$	23263.6	−	32019.6i	0.116952	−	0.160971i
$447$	72016.3	+	23399.5i	0.360426	+	0.117109i
$448$	45051.0	−	14638.0i	0.224465	−	0.0729331i
$449$	−115255.	+	83737.8i	−0.571700	+	0.415364i	−0.835722	−	0.549152i	$-0.814951\pi$
$449$	−115255.	+	83737.8i	−0.571700	+	0.415364i	0.264023	+	0.964517i	$0.414951\pi$
$450$		−	12810.3i		−	0.0632608i
$451$	22063.5	−	16557.4i	0.108473	−	0.0814028i
$452$	143201.			0.700921
$453$	−47656.6	−	65593.6i	−0.232234	−	0.319643i
$454$	33459.0	+	102976.i	0.162331	+	0.499603i
$455$	−96624.9	+	297381.i	−0.466731	+	1.43645i
$456$	−35049.6	−	25465.0i	−0.168559	−	0.122466i
$457$	−90389.3	+	124410.i	−0.432797	+	0.595694i	−0.968592	−	0.248654i	$-0.920012\pi$
$457$	−90389.3	+	124410.i	−0.432797	+	0.595694i	0.535795	+	0.844348i	$0.320012\pi$
$458$	121119.	+	39354.0i	0.577407	+	0.187611i
$459$	299012.	−	97154.9i	1.41926	−	0.461147i
$460$	5314.93	−	3861.52i	0.0251178	−	0.0182492i
$461$		−	85879.0i		−	0.404097i	−0.979376	−	0.202048i	$-0.935240\pi$
$461$		−	85879.0i		−	0.404097i	0.979376	−	0.202048i	$-0.0647598\pi$
$462$	−121859.	+	173299.i	−0.570920	+	0.811918i
$463$	−206292.			−0.962322			−0.481161	−	0.876632i	$-0.659785\pi$
$463$	−206292.			−0.962322			−0.481161	+	0.876632i	$0.659785\pi$
$464$	41183.0	+	56683.5i	0.191285	+	0.263282i
$465$	25088.2	+	77213.4i	0.116028	+	0.357098i
$466$	67855.6	−	208838.i	0.312474	−	0.961696i
$467$	208088.	+	151185.i	0.954144	+	0.693226i	0.951783	−	0.306771i	$-0.0992486\pi$
$467$	208088.	+	151185.i	0.954144	+	0.693226i	0.00236059	+	0.999997i	$0.499249\pi$
$468$	51503.5	−	70888.5i	0.235150	−	0.323656i
$469$	−310645.	−	100935.i	−1.41227	−	0.458875i
$470$	−1921.03	+	624.181i	−0.00869638	+	0.00282563i
$471$	154461.	−	112223.i	0.696270	−	0.505869i
$472$			80999.6i			0.363579i
$473$	−69003.8	−	201703.i	−0.308426	−	0.901552i
$474$	−61763.2			−0.274899
$475$	21025.2	+	28938.7i	0.0931865	+	0.128260i
$476$	−91675.7	−	282149.i	−0.404613	−	1.24527i
$477$	19509.2	−	60043.1i	0.0857437	−	0.263892i
$478$	−79540.1	−	57789.3i	−0.348121	−	0.252925i
$479$	−41829.3	+	57573.1i	−0.182310	+	0.250928i	−0.890384	−	0.455210i	$-0.849564\pi$
$479$	−41829.3	+	57573.1i	−0.182310	+	0.250928i	0.708074	+	0.706138i	$0.249564\pi$
$480$	−12878.5	−	4184.48i	−0.0558963	−	0.0181618i
$481$	−630054.	+	204717.i	−2.72325	+	0.884838i
$482$	17418.6	−	12655.4i	0.0749756	−	0.0544730i
$483$		−	45467.6i		−	0.194898i
$484$	39622.2	+	110223.i	0.169141	+	0.470523i
$485$	130209.			0.553549
$486$	79895.7	+	109967.i	0.338260	+	0.465575i
$487$	7971.40	+	24533.4i	0.0336106	+	0.103443i	0.966454	−	0.256838i	$-0.0826808\pi$
$487$	7971.40	+	24533.4i	0.0336106	+	0.103443i	−0.932844	+	0.360281i	$0.882681\pi$
$488$	3315.30	−	10203.4i	0.0139214	−	0.0428457i
$489$	−68539.6	−	49797.0i	−0.286632	−	0.208250i
$490$	−114473.	+	157559.i	−0.476774	+	0.656223i
$491$	−148898.	−	48379.9i	−0.617627	−	0.200679i	−0.0165404	−	0.999863i	$-0.505265\pi$
$491$	−148898.	−	48379.9i	−0.617627	−	0.200679i	−0.601086	+	0.799184i	$0.705265\pi$
$492$	11605.6	−	3770.88i	0.0479443	−	0.0155780i
$493$	355002.	−	257924.i	1.46062	−	1.06120i
$494$			244670.i			1.00260i
$495$	−46377.9	+	15866.1i	−0.189278	+	0.0647532i
$496$	−69459.6			−0.282338
$497$	−147401.	−	202881.i	−0.596745	−	0.821349i
$498$	−42321.3	−	130251.i	−0.170647	−	0.525199i
$499$	108018.	−	332446.i	0.433806	−	1.33512i	−0.460499	−	0.887660i	$-0.652329\pi$
$499$	108018.	−	332446.i	0.433806	−	1.33512i	0.894305	−	0.447458i	$-0.147671\pi$
$500$	9045.08	+	6571.64i	0.0361803	+	0.0262866i
$501$	208930.	−	287567.i	0.832387	−	1.14568i
$502$	191895.	+	62350.5i	0.761476	+	0.247419i
$503$	191436.	−	62201.3i	0.756637	−	0.245846i	0.0948022	−	0.995496i	$-0.469778\pi$
$503$	191436.	−	62201.3i	0.756637	−	0.245846i	0.661835	+	0.749650i	$0.269778\pi$
$504$	61365.6	−	44584.8i	0.241582	−	0.175519i
$505$		−	178984.i		−	0.701829i
$506$	−20562.9	−	14459.3i	−0.0803124	−	0.0564736i
$507$	420305.			1.63512
$508$	46308.5	+	63738.2i	0.179446	+	0.246986i
$509$	−64202.3	−	197594.i	−0.247808	−	0.762674i	−0.995162	−	0.0982483i	$-0.968676\pi$
$509$	−64202.3	−	197594.i	−0.247808	−	0.762674i	0.747354	−	0.664426i	$-0.231324\pi$
$510$	−26206.9	+	80656.4i	−0.100757	+	0.310098i
$511$	98616.3	+	71649.0i	0.377665	+	0.274390i
$512$	6809.63	−	9372.65i	0.0259767	−	0.0357538i
$513$	−213475.	−	69362.1i	−0.811170	−	0.263565i
$514$	−345461.	+	112247.i	−1.30759	+	0.424863i
$515$	44778.7	−	32533.7i	0.168833	−	0.122664i
$516$		−	94304.0i		−	0.354185i
$517$	4639.04	+	6181.75i	0.0173559	+	0.0231276i
$518$	−573484.			−2.13728
$519$	75428.3	+	103818.i	0.280027	+	0.385424i
$520$	23631.8	+	72731.1i	0.0873956	+	0.268976i
$521$	34982.0	−	107664.i	0.128875	−	0.396637i	−0.865712	−	0.500542i	$-0.833134\pi$
$521$	34982.0	−	107664.i	0.128875	−	0.396637i	0.994587	+	0.103905i	$0.0331339\pi$
$522$	90766.7	+	65945.8i	0.333108	+	0.242017i
$523$	258188.	−	355365.i	0.943913	−	1.29918i	−0.0102656	−	0.999947i	$-0.503268\pi$
$523$	258188.	−	355365.i	0.943913	−	1.29918i	0.954179	−	0.299238i	$-0.0967323\pi$
$524$	59822.6	+	19437.5i	0.217873	+	0.0707911i
$525$	73590.8	−	23911.1i	0.266996	−	0.0867522i
$526$	86003.1	−	62484.9i	0.310844	−	0.225841i
$527$			435017.i			1.56634i
$528$	801.285	+	51807.5i	0.00287421	+	0.185834i
$529$	−274446.			−0.980721
$530$	32387.0	+	44576.9i	0.115297	+	0.158693i
$531$	40080.7	+	123356.i	0.142150	+	0.437492i
$532$	−65450.3	+	201435.i	−0.231254	+	0.711725i
$533$	−55753.7	−	40507.4i	−0.196254	−	0.142587i
$534$	−92615.8	+	127475.i	−0.324790	+	0.447035i
$535$	−67735.2	−	22008.5i	−0.236650	−	0.0768923i
$536$	−75975.1	+	24685.8i	−0.264449	+	0.0859246i
$537$	6113.35	−	4441.61i	0.0211998	−	0.0154025i
$538$		−	24324.1i		−	0.0840375i
$539$	712201.	+	219291.i	2.45146	+	0.754819i
$540$	−70157.5			−0.240595
$541$	115863.	+	159472.i	0.395868	+	0.544866i	0.959701	−	0.281023i	$-0.0906738\pi$
$541$	115863.	+	159472.i	0.395868	+	0.544866i	−0.563833	+	0.825889i	$0.690674\pi$
$542$	−26373.8	−	81170.1i	−0.0897788	−	0.276311i
$543$	67357.0	−	207304.i	0.228446	−	0.703084i
$544$	−58699.7	−	42647.9i	−0.198353	−	0.144112i
$545$	40270.7	−	55427.8i	0.135580	−	0.186610i
$546$	503364.	+	163553.i	1.68848	+	0.548621i
$547$	−301175.	+	97857.6i	−1.00657	+	0.327054i	−0.765488	−	0.643451i	$-0.777502\pi$
$547$	−301175.	+	97857.6i	−1.00657	+	0.327054i	−0.241082	+	0.970505i	$0.577502\pi$
$548$	177943.	−	129283.i	0.592543	−	0.430508i
$549$		−	17179.5i		−	0.0569988i
$550$	12589.0	−	40885.7i	0.0416164	−	0.135159i
$551$	−313278.			−1.03188
$552$	−6536.23	−	8996.35i	−0.0214511	−	0.0295249i
$553$	93307.5	+	287171.i	0.305117	+	0.939053i
$554$	−48192.2	+	148320.i	−0.157021	+	0.483261i
$555$	132629.	+	96360.8i	0.430580	+	0.312834i
$556$	−167238.	+	230184.i	−0.540986	+	0.744604i
$557$	−3626.91	−	1178.45i	−0.0116903	−	0.00379842i	0.303166	−	0.952938i	$-0.401956\pi$
$557$	−3626.91	−	1178.45i	−0.0116903	−	0.00379842i	−0.314856	+	0.949139i	$0.601956\pi$
$558$	−105781.	+	34370.4i	−0.339735	+	0.110387i
$559$	−430866.	+	313043.i	−1.37886	+	1.00180i
$560$			66200.8i			0.211099i
$561$	324464.	−	5018.34i	1.03096	−	0.0159454i
$562$	356129.			1.12755
$563$	86393.0	+	118910.i	0.272560	+	0.375147i	0.923252	−	0.384195i	$-0.125521\pi$
$563$	86393.0	+	118910.i	0.272560	+	0.375147i	−0.650692	+	0.759342i	$0.725521\pi$
$564$	1056.52	+	3251.65i	0.00332140	+	0.0102222i
$565$	−61843.4	+	190334.i	−0.193730	+	0.596239i
$566$	309946.	+	225189.i	0.967505	+	0.702934i
$567$	−125799.	+	173148.i	−0.391301	+	0.538580i
$568$	−58330.5	−	18952.7i	−0.180800	−	0.0587456i
$569$	13849.8	−	4500.09i	0.0427780	−	0.0138994i	−0.287550	−	0.957766i	$-0.592841\pi$
$569$	13849.8	−	4500.09i	0.0427780	−	0.0138994i	0.330328	+	0.943866i	$0.392841\pi$
$570$	48983.3	−	35588.4i	0.150764	−	0.109537i
$571$		−	446577.i		−	1.36970i	−0.728686	−	0.684848i	$-0.759869\pi$
$571$		−	446577.i		−	1.36970i	0.728686	−	0.684848i	$-0.240131\pi$
$572$	234044.	−	175636.i	0.715327	−	0.536812i
$573$	−98563.7			−0.300198
$574$	−35065.8	−	48263.9i	−0.106429	−	0.146487i
$575$	2837.18	+	8731.95i	0.00858127	+	0.0264104i
$576$	5732.67	−	17643.3i	0.0172787	−	0.0531785i
$577$	−389383.	−	282903.i	−1.16957	−	0.849740i	−0.178610	−	0.983920i	$-0.557160\pi$
$577$	−389383.	−	282903.i	−1.16957	−	0.849740i	−0.990957	+	0.134180i	$0.957160\pi$
$578$	−128244.	+	176513.i	−0.383867	+	0.528348i
$579$	−76683.0	−	24915.8i	−0.228740	−	0.0743221i
$580$	−93125.9	+	30258.4i	−0.276831	+	0.0899478i
$581$	−541674.	+	393549.i	−1.60467	+	1.16586i
$582$		−	220398.i		−	0.650672i
$583$	121272.	−	172463.i	0.356798	−	0.507410i
$584$	29812.5			0.0874123
$585$	71978.4	+	99069.7i	0.210325	+	0.289487i
$586$	−127756.	−	393193.i	−0.372037	−	1.14501i
$587$	−49752.6	+	153123.i	−0.144391	+	0.444390i	−0.996932	−	0.0782704i	$-0.975060\pi$
$587$	−49752.6	+	153123.i	−0.144391	+	0.444390i	0.852541	+	0.522660i	$0.175060\pi$
$588$	266693.	+	193764.i	0.771361	+	0.560426i
$589$	182550.	−	251259.i	0.526201	−	0.724254i
$590$	−107660.	−	34980.9i	−0.309279	−	0.100491i
$591$	67534.6	−	21943.3i	0.193353	−	0.0628243i
$592$	−113471.	+	82441.6i	−0.323774	+	0.235236i
$593$		−	190657.i		−	0.542181i	−0.962554	−	0.271090i	$-0.912616\pi$
$593$		−	190657.i		−	0.542181i	0.962554	−	0.271090i	$-0.0873842\pi$
$594$	86893.2	+	253995.i	0.246271	+	0.719868i
$595$	414607.			1.17112
$596$	−53217.5	−	73247.5i	−0.149817	−	0.206206i
$597$	−33507.2	−	103125.i	−0.0940135	−	0.289344i
$598$	−19406.4	+	59726.9i	−0.0542680	+	0.167020i
$599$	60239.8	+	43766.8i	0.167892	+	0.121981i	0.668558	−	0.743660i	$-0.266912\pi$
$599$	60239.8	+	43766.8i	0.167892	+	0.121981i	−0.500666	+	0.865640i	$0.666912\pi$
$600$	11123.5	−	15310.2i	0.0308987	−	0.0425284i
$601$	−21597.1	−	7017.33i	−0.0597926	−	0.0194278i	0.278968	−	0.960300i	$-0.410008\pi$
$601$	−21597.1	−	7017.33i	−0.0597926	−	0.0194278i	−0.338761	+	0.940873i	$0.610008\pi$
$602$	−438471.	+	142468.i	−1.20989	+	0.393119i
$603$	−103488.	+	75188.8i	−0.284615	+	0.206785i
$604$			96942.7i			0.265730i
$605$	−163613.	+	5062.28i	−0.447000	+	0.0138304i
$606$	−302958.			−0.824969
$607$	69915.3	+	96230.1i	0.189756	+	0.261176i	0.893286	−	0.449489i	$-0.148394\pi$
$607$	69915.3	+	96230.1i	0.189756	+	0.261176i	−0.703530	+	0.710665i	$0.748394\pi$
$608$	16007.3	+	49265.5i	0.0433024	+	0.133271i
$609$	−209415.	+	644514.i	−0.564643	+	1.73779i
$610$	12130.1	+	8813.01i	0.0325989	+	0.0236845i
$611$	11349.3	−	15621.0i	0.0304010	−	0.0418434i
$612$	−110498.	−	35903.0i	−0.295020	−	0.0958579i
$613$	647333.	−	210331.i	1.72269	−	0.559735i	0.730327	−	0.683098i	$-0.239368\pi$
$613$	647333.	−	210331.i	1.72269	−	0.559735i	0.992362	+	0.123363i	$0.0393679\pi$
$614$	262319.	−	190586.i	0.695814	−	0.505539i
$615$			17054.0i			0.0450895i
$616$	239671.	−	81992.6i	0.631616	−	0.216079i
$617$	−243543.			−0.639744			−0.319872	−	0.947461i	$-0.603640\pi$
$617$	−243543.			−0.639744			−0.319872	+	0.947461i	$0.603640\pi$
$618$	−55068.3	−	75795.0i	−0.144187	−	0.198456i
$619$	150590.	+	463469.i	0.393021	+	1.20959i	0.930492	+	0.366312i	$0.119380\pi$
$619$	150590.	+	463469.i	0.393021	+	1.20959i	−0.537472	+	0.843282i	$0.680620\pi$
$620$	29997.1	−	92321.7i	0.0780363	−	0.240171i
$621$	−46610.2	−	33864.3i	−0.120864	−	0.0878131i
$622$	−36799.6	+	50650.4i	−0.0951180	+	0.130919i
$623$	732617.	+	238042.i	1.88756	+	0.613305i
$624$	123109.	−	40000.5i	0.316169	−	0.102730i
$625$	−12640.9	+	9184.14i	−0.0323607	+	0.0235114i
$626$		−	222598.i		−	0.568033i
$627$	−189511.	−	133259.i	−0.482058	−	0.338971i
$628$	−228283.			−0.578833
$629$	516322.	+	710656.i	1.30503	+	1.79621i
$630$	32757.8	+	100818.i	0.0825342	+	0.254014i
$631$	−40941.8	+	126006.i	−0.102827	+	0.316470i	−0.989214	−	0.146475i	$-0.953207\pi$
$631$	−40941.8	+	126006.i	−0.102827	+	0.316470i	0.886387	+	0.462945i	$0.153207\pi$
$632$	59744.6	+	43407.0i	0.149577	+	0.108674i
$633$	−70826.6	+	97484.5i	−0.176762	+	0.243292i
$634$	344474.	+	111927.i	0.856995	+	0.278455i
$635$	−104716.	+	34024.3i	−0.259696	+	0.0843805i
$636$	75453.4	−	54820.1i	0.186537	−	0.135527i
$637$		−	1.86170e6i		−	4.58808i
$638$	224887.	+	299673.i	0.552488	+	0.736217i
$639$	−98210.8			−0.240524
$640$	9516.75	+	13098.7i	0.0232343	+	0.0319792i
$641$	136282.	+	419433.i	0.331683	+	1.02081i	0.968333	+	0.249662i	$0.0803195\pi$
$641$	136282.	+	419433.i	0.331683	+	1.02081i	−0.636650	+	0.771153i	$0.719680\pi$
$642$	−37252.8	+	114652.i	−0.0903835	+	0.278172i
$643$	−96457.3	−	70080.4i	−0.233299	−	0.169502i	0.464994	−	0.885314i	$-0.346057\pi$
$643$	−96457.3	−	70080.4i	−0.233299	−	0.169502i	−0.698293	+	0.715812i	$0.746057\pi$
$644$	−31954.5	+	43981.5i	−0.0770477	+	0.106047i
$645$	125343.	+	40726.5i	0.301288	+	0.0978944i
$646$	308543.	−	100252.i	0.739352	−	0.240230i
$647$	44319.5	−	32200.0i	0.105873	−	0.0769213i	−0.533589	−	0.845744i	$-0.679157\pi$
$647$	44319.5	−	32200.0i	0.105873	−	0.0769213i	0.639462	+	0.768823i	$0.279157\pi$
$648$			52343.8i			0.124657i
$649$	6698.48	+	433093.i	0.0159033	+	1.02823i
$650$	−106876.			−0.252960
$651$	−394892.	−	543522.i	−0.931786	−	1.28249i
$652$	31302.4	+	96338.9i	0.0736347	+	0.226624i
$653$	62505.6	−	192373.i	0.146586	−	0.451146i	−0.850625	−	0.525772i	$-0.823776\pi$
$653$	62505.6	−	192373.i	0.146586	−	0.451146i	0.997212	+	0.0746265i	$0.0237765\pi$
$654$	−93820.3	−	68164.4i	−0.219352	−	0.159368i
$655$	−51670.5	+	71118.3i	−0.120437	+	0.165767i
$656$	−13876.4	−	4508.73i	−0.0322456	−	0.0104772i
$657$	45401.9	−	14752.0i	0.105182	−	0.0341759i
$658$	13522.6	−	9824.71i	0.0312325	−	0.0226918i
$659$			366949.i			0.844957i	0.906373	+	0.422478i	$0.138840\pi$
$659$			366949.i			0.844957i	−0.906373	+	0.422478i	$0.861160\pi$
$660$	−69205.5	−	21308.8i	−0.158874	−	0.0489182i
$661$	−90276.2			−0.206619			−0.103310	−	0.994649i	$-0.532943\pi$
$661$	−90276.2			−0.206619			−0.103310	+	0.994649i	$0.532943\pi$
$662$	−41199.2	−	56705.9i	−0.0940098	−	0.129393i
$663$	−250518.	−	771015.i	−0.569917	−	1.75402i
$664$	−50602.2	+	155738.i	−0.114771	+	0.353230i
$665$	−239471.	−	173986.i	−0.541513	−	0.393432i
$666$	−132013.	+	181700.i	−0.297624	+	0.409644i
$667$	−76475.1	−	24848.3i	−0.171897	−	0.0558528i
$668$	−404203.	+	131333.i	−0.905829	+	0.294322i
$669$	75744.3	−	55031.5i	0.169238	−	0.122959i
$670$		−	111643.i		−	0.248703i
$671$	16882.6	−	54830.5i	0.0374969	−	0.121780i
$672$	112055.			0.248138
$673$	391035.	+	538213.i	0.863347	+	1.18830i	0.980761	+	0.195212i	$0.0625396\pi$
$673$	391035.	+	538213.i	0.863347	+	1.18830i	−0.117414	+	0.993083i	$0.537460\pi$
$674$	30934.8	+	95207.6i	0.0680970	+	0.209581i
$675$	30298.5	−	93249.2i	0.0664988	−	0.204662i
$676$	−406568.	−	295389.i	−0.889693	−	0.646400i
$677$	−25794.6	+	35503.2i	−0.0562796	+	0.0774622i	−0.836229	−	0.548380i	$-0.815245\pi$
$677$	−25794.6	+	35503.2i	−0.0562796	+	0.0774622i	0.779950	+	0.625842i	$0.215245\pi$
$678$	322171.	+	104680.i	0.700852	+	0.227721i
$679$	−1.02475e6	+	332962.i	−2.22269	+	0.722196i
$680$	82035.4	−	59602.2i	0.177412	−	0.128897i
$681$			256132.i			0.552294i
$682$	−371391.	+	5744.15i	−0.798477	+	0.0123497i
$683$	−575521.			−1.23373			−0.616864	−	0.787070i	$-0.711597\pi$
$683$	−575521.			−1.23373			−0.616864	+	0.787070i	$0.711597\pi$
$684$	48755.6	+	67106.3i	0.104211	+	0.143434i
$685$	94988.5	+	292344.i	0.202437	+	0.623037i
$686$	303859.	−	935182.i	0.645690	−	1.98723i
$687$	243724.	+	177076.i	0.516398	+	0.375185i
$688$	−66276.5	+	91221.8i	−0.140018	+	0.192718i
$689$	−500936.	−	162764.i	−1.05522	−	0.342862i
$690$	14780.2	−	4802.37i	0.0310443	−	0.0100869i
$691$	−89788.3	+	65235.0i	−0.188046	+	0.136623i	−0.677825	−	0.735223i	$-0.737077\pi$
$691$	−89788.3	+	65235.0i	−0.188046	+	0.136623i	0.489779	+	0.871846i	$0.337077\pi$
$692$		−	153436.i		−	0.320416i
$693$	324426.	−	243463.i	0.675537	−	0.506952i
$694$	148784.			0.308915
$695$	−233723.	−	321692.i	−0.483873	−	0.665994i
$696$	51217.1	+	157630.i	0.105730	+	0.325402i
$697$	−28237.6	+	86906.4i	−0.0581249	+	0.178890i
$698$	−382982.	−	278252.i	−0.786080	−	0.571121i
$699$	305321.	−	420238.i	0.624887	−	0.860084i
$700$	−87990.2	−	28589.8i	−0.179572	−	0.0583464i
$701$	497922.	−	161785.i	1.01327	−	0.329231i	0.245114	−	0.969494i	$-0.421175\pi$
$701$	497922.	−	161785.i	1.01327	−	0.329231i	0.768156	+	0.640263i	$0.221175\pi$
$702$	542569.	−	394200.i	1.10098	−	0.799912i
$703$		−	627132.i		−	1.26896i
$704$	35635.0	−	50677.4i	0.0719005	−	0.102251i
$705$	−4778.17			−0.00961355
$706$	−46201.4	−	63590.8i	−0.0926928	−	0.127581i
$707$	457688.	+	1.40862e6i	0.915653	+	2.81809i
$708$	−59210.6	+	182231.i	−0.118123	+	0.363544i
$709$	169840.	+	123396.i	0.337868	+	0.245476i	0.743762	−	0.668445i	$-0.233040\pi$
$709$	169840.	+	123396.i	0.337868	+	0.245476i	−0.405894	+	0.913920i	$0.633040\pi$
$710$	50381.8	−	69344.6i	0.0999440	−	0.137561i
$711$	112465.	+	36542.1i	0.222473	+	0.0722859i
$712$	179178.	−	58218.3i	0.353447	−	0.114842i
$713$	64491.9	−	46856.1i	0.126860	−	0.0921694i
$714$		−	701787.i		−	1.37660i
$715$	132370.	+	386928.i	0.258928	+	0.756865i
$716$	−9035.10			−0.0176241
$717$	−136704.	−	188157.i	−0.265915	−	0.366001i
$718$	14278.3	+	43944.0i	0.0276966	+	0.0852413i
$719$	131630.	−	405116.i	0.254623	−	0.783650i	−0.739280	−	0.673398i	$-0.764834\pi$
$719$	131630.	−	405116.i	0.254623	−	0.783650i	0.993904	−	0.110252i	$-0.0351658\pi$
$720$	20974.8	+	15239.1i	0.0404606	+	0.0293963i
$721$	−269219.	+	370548.i	−0.517887	+	0.712811i
$722$	130283.	+	42331.6i	0.249928	+	0.0812064i
$723$	48439.2	−	15738.8i	0.0926659	−	0.0301090i
$724$	−210848.	+	153190.i	−0.402246	+	0.292249i
$725$		−	136845.i		−	0.260347i
$726$	8568.71	+	276941.i	0.0162571	+	0.525428i
$727$	−871304.			−1.64855			−0.824273	−	0.566193i	$-0.808416\pi$
$727$	−871304.			−1.64855			−0.824273	+	0.566193i	$0.808416\pi$
$728$	−371968.	−	511970.i	−0.701847	−	0.966010i
$729$	157265.	+	484011.i	0.295921	+	0.910752i
$730$	−12874.9	+	39625.0i	−0.0241602	+	0.0743573i
$731$	571311.	+	415082.i	1.06915	+	0.776781i
$732$	14917.4	−	20532.0i	0.0278401	−	0.0383186i
$733$	−249327.	−	81011.3i	−0.464047	−	0.150778i	0.0676566	−	0.997709i	$-0.478448\pi$
$733$	−249327.	−	81011.3i	−0.464047	−	0.150778i	−0.531703	+	0.846931i	$0.678448\pi$
$734$	236710.	−	76911.9i	0.439365	−	0.142758i
$735$	−372715.	+	270794.i	−0.689926	+	0.501261i
$736$			13296.0i			0.0245451i
$737$	−404186.	+	138274.i	−0.744126	+	0.254570i
$738$	−23363.7			−0.0428972
$739$	−617435.	−	849827.i	−1.13058	−	1.55611i	−0.786957	−	0.617008i	$-0.788345\pi$
$739$	−617435.	−	849827.i	−1.13058	−	1.55611i	−0.343626	−	0.939107i	$-0.611655\pi$
$740$	−60572.5	−	186423.i	−0.110614	−	0.340436i
$741$	−178853.	+	550453.i	−0.325732	+	1.00250i
$742$	−368878.	−	268006.i	−0.670000	−	0.486784i
$743$	227706.	−	313411.i	0.412475	−	0.567723i	−0.551345	−	0.834277i	$-0.685885\pi$
$743$	227706.	−	313411.i	0.412475	−	0.567723i	0.963820	+	0.266554i	$0.0858852\pi$
$744$	−156269.	−	50774.9i	−0.282310	−	0.0917282i
$745$	120339.	−	39100.5i	0.216817	−	0.0704483i
$746$	282517.	−	205261.i	0.507653	−	0.368832i
$747$			262215.i			0.469911i
$748$	−317386.	−	223178.i	−0.567263	−	0.398885i
$749$	589360.			1.05055
$750$	15545.6	+	21396.7i	0.0276366	+	0.0380386i
$751$	113954.	+	350714.i	0.202045	+	0.621832i	0.999822	+	0.0188785i	$0.00600956\pi$
$751$	113954.	+	350714.i	0.202045	+	0.621832i	−0.797776	+	0.602954i	$0.793990\pi$
$752$	1263.25	−	3887.89i	0.00223385	−	0.00687510i
$753$	386144.	+	280550.i	0.681018	+	0.494789i
$754$	550182.	−	757261.i	0.967752	−	1.33200i
$755$	−128851.	−	41866.1i	−0.226044	−	0.0734461i
$756$	552145.	−	179403.i	0.966072	−	0.313896i
$757$	592544.	−	430508.i	1.03402	−	0.751259i	0.0649104	−	0.997891i	$-0.479324\pi$
$757$	592544.	−	430508.i	1.03402	−	0.751259i	0.969109	+	0.246632i	$0.0793239\pi$
$758$		−	210032.i		−	0.365550i
$759$	−35692.3	−	47561.6i	−0.0619570	−	0.0825607i
$760$	−72393.8			−0.125336
$761$	−228316.	−	314250.i	−0.394246	−	0.542634i	0.565042	−	0.825062i	$-0.308860\pi$
$761$	−228316.	−	314250.i	−0.394246	−	0.542634i	−0.959288	+	0.282429i	$0.908860\pi$
$762$	57591.5	+	177248.i	0.0991856	+	0.305262i
$763$	−175197.	+	539200.i	−0.300938	+	0.926191i
$764$	95342.4	+	69270.3i	0.163343	+	0.118675i
$765$	95440.3	−	131362.i	0.163083	−	0.224465i
$766$	−330547.	−	107401.i	−0.563346	−	0.183042i
$767$	1.02915e6	−	334391.i	1.74939	−	0.568412i
$768$	22171.6	−	16108.6i	0.0375901	−	0.0273108i
$769$		−	342544.i		−	0.579247i	−0.957141	−	0.289624i	$-0.906470\pi$
$769$		−	342544.i		−	0.579247i	0.957141	−	0.289624i	$-0.0935301\pi$
$770$	5474.65	+	353966.i	0.00923368	+	0.597008i
$771$	−859265.			−1.44550
$772$	56666.0	+	77994.1i	0.0950798	+	0.130866i
$773$	−289221.	−	890131.i	−0.484029	−	1.48969i	−0.833383	−	0.552696i	$-0.813599\pi$
$773$	−289221.	−	890131.i	−0.484029	−	1.48969i	0.349354	−	0.936991i	$-0.386401\pi$
$774$	−55794.7	+	171719.i	−0.0931346	+	0.286639i
$775$	109754.	+	79740.9i	0.182733	+	0.132763i
$776$	−154895.	+	213195.i	−0.257226	+	0.354041i
$777$	−1.29021e6	−	419215.i	−2.13707	−	0.694377i
$778$	52714.6	−	17128.0i	0.0870907	−	0.0282975i
$779$	52779.0	−	38346.2i	0.0869733	−	0.0631898i
$780$			180904.i			0.297343i
$781$	−313452.	−	96513.8i	−0.513889	−	0.158229i
$782$	83270.9			0.136170
$783$	504739.	+	694713.i	0.823272	+	1.13314i
$784$	−121800.	−	374863.i	−0.198160	−	0.609874i
$785$	98587.1	−	303420.i	0.159986	−	0.492385i
$786$	120379.	+	87460.4i	0.194852	+	0.141568i
$787$	−580576.	+	799094.i	−0.937366	+	1.29017i	0.0195496	+	0.999809i	$0.493777\pi$
$787$	−580576.	+	799094.i	−0.937366	+	1.29017i	−0.956916	+	0.290365i	$0.906223\pi$
$788$	−80749.1	−	26237.0i	−0.130042	−	0.0422534i
$789$	239164.	−	77709.2i	0.384187	−	0.124830i
$790$	−83495.6	+	60663.1i	−0.133786	+	0.0972009i
$791$		−	1.65609e6i		−	2.64686i
$792$	29192.7	−	94810.5i	0.0465397	−	0.151149i
$793$	−143327.			−0.227920
$794$	43700.0	+	60147.9i	0.0693171	+	0.0954068i
$795$	40278.0	+	123963.i	0.0637285	+	0.196136i
$796$	−40063.6	+	123303.i	−0.0632301	+	0.194602i
$797$	750507.	+	545275.i	1.18151	+	0.858419i	0.992341	−	0.123525i	$-0.0394200\pi$
$797$	750507.	+	545275.i	1.18151	+	0.858419i	0.189171	+	0.981944i	$0.439420\pi$
$798$	−294498.	+	405341.i	−0.462462	+	0.636524i
$799$	−24349.4	−	7911.60i	−0.0381412	−	0.0123928i
$800$	−21520.0	+	6992.26i	−0.0336249	+	0.0109254i
$801$	244065.	−	177323.i	0.380399	−	0.276376i
$802$			296574.i			0.461089i
$803$	159403.	−	2465.42i	0.247210	−	0.00382349i
$804$	−188973.			−0.292339
$805$	−44657.7	−	61466.1i	−0.0689136	−	0.0948514i
$806$	286750.	+	882526.i	0.441401	+	1.35849i
$807$	17780.9	−	54724.0i	0.0273028	−	0.0840293i
$808$	293057.	+	212918.i	0.448879	+	0.326130i
$809$	274386.	−	377660.i	0.419242	−	0.577037i	−0.546200	−	0.837655i	$-0.683926\pi$
$809$	274386.	−	377660.i	0.419242	−	0.577037i	0.965442	+	0.260617i	$0.0839261\pi$
$810$	−69572.4	−	22605.4i	−0.106039	−	0.0344543i
$811$	−1.15778e6	+	376187.i	−1.76030	+	0.571955i	−0.997231	−	0.0743659i	$-0.976307\pi$
$811$	−1.15778e6	+	376187.i	−1.76030	+	0.571955i	−0.763066	+	0.646321i	$0.776307\pi$
$812$	655533.	−	476273.i	0.994221	−	0.722344i
$813$		−	201894.i		−	0.305452i
$814$	−599896.	+	450187.i	−0.905373	+	0.679430i
$815$	−141566.			−0.213130
$816$	−100886.	−	138858.i	−0.151513	−	0.208540i
$817$	−155795.	−	479489.i	−0.233405	−	0.718348i
$818$	79021.3	−	243202.i	0.118097	−	0.363464i
$819$	−819812.	−	595628.i	−1.22221	−	0.887988i
$820$	11985.5	−	16496.6i	0.0178249	−	0.0245339i
$821$	168444.	+	54730.8i	0.249902	+	0.0811981i	0.431289	−	0.902214i	$-0.358059\pi$
$821$	168444.	+	54730.8i	0.249902	+	0.0811981i	−0.181387	+	0.983412i	$0.558059\pi$
$822$	494839.	−	160783.i	0.732352	−	0.237956i
$823$	299404.	−	217530.i	0.442036	−	0.321158i	−0.344407	−	0.938820i	$-0.611920\pi$
$823$	299404.	−	217530.i	0.442036	−	0.321158i	0.786444	+	0.617662i	$0.211920\pi$
$824$			112020.i			0.164983i
$825$	58209.8	−	82781.4i	0.0855240	−	0.121626i
$826$	936745.			1.37297
$827$	493900.	+	679795.i	0.722151	+	0.993956i	0.999450	+	0.0331718i	$0.0105609\pi$
$827$	493900.	+	679795.i	0.722151	+	0.993956i	−0.277299	+	0.960784i	$0.589439\pi$
$828$	6579.18	+	20248.6i	0.00959646	+	0.0295349i
$829$	−253010.	+	778685.i	−0.368153	+	1.13306i	0.579829	+	0.814738i	$0.303119\pi$
$829$	−253010.	+	778685.i	−0.368153	+	1.13306i	−0.947983	+	0.318322i	$0.896881\pi$
$830$	−185144.	−	134515.i	−0.268753	−	0.195261i
$831$	−216844.	+	298460.i	−0.314011	+	0.432199i
$832$	−147197.	−	47827.3i	−0.212644	−	0.0690923i
$833$	−2.34772e6	+	762819.i	−3.38342	+	1.09934i
$834$	−544513.	+	395612.i	−0.782846	+	0.568771i
$835$		−	593961.i		−	0.851893i
$836$	89663.0	+	262092.i	0.128292	+	0.375008i
$837$	−851298.			−1.21515
$838$	109984.	+	151380.i	0.156617	+	0.215565i
$839$	−107487.	−	330810.i	−0.152697	−	0.469953i	0.845223	−	0.534413i	$-0.179467\pi$
$839$	−107487.	−	330810.i	−0.152697	−	0.469953i	−0.997920	+	0.0644603i	$0.979467\pi$
$840$	−48392.6	+	148937.i	−0.0685837	+	0.211079i
$841$	397405.	+	288732.i	0.561877	+	0.408228i
$842$	−101353.	+	139501.i	−0.142960	+	0.196767i
$843$	801212.	+	260330.i	1.12744	+	0.366327i
$844$	137024.	−	44521.7i	0.192358	−	0.0625009i
$845$	568196.	−	412819.i	0.795765	−	0.578157i
$846$		−	6546.03i		−	0.00914612i
$847$	1.27470e6	−	458223.i	1.77682	−	0.638719i
$848$	−111515.			−0.155074
$849$	532698.	+	733196.i	0.739036	+	1.01720i
$850$	43791.6	+	134777.i	0.0606112	+	0.186542i
$851$	49742.2	−	153091.i	0.0686856	−	0.211393i
$852$	−117377.	−	85279.0i	−0.161697	−	0.117480i
$853$	−532493.	+	732913.i	−0.731839	+	1.00729i	0.267208	+	0.963639i	$0.413899\pi$
$853$	−532493.	+	732913.i	−0.731839	+	1.00729i	−0.999047	+	0.0436510i	$0.986101\pi$
$854$	−118001.	−	38340.8i	−0.161796	−	0.0525709i
$855$	−110250.	+	35822.3i	−0.150815	+	0.0490028i
$856$	116613.	−	84724.0i	0.159147	−	0.115627i
$857$			1.19368e6i			1.62527i	0.582772	+	0.812636i	$0.301968\pi$
$857$			1.19368e6i			1.62527i	−0.582772	+	0.812636i	$0.698032\pi$
$858$	654937.	−	224057.i	0.889662	−	0.304358i
$859$	782260.			1.06014			0.530072	−	0.847952i	$-0.322165\pi$
$859$	782260.			1.06014			0.530072	+	0.847952i	$0.322165\pi$
$860$	−92624.3	−	127486.i	−0.125236	−	0.172372i
$861$	−43609.5	−	134216.i	−0.0588268	−	0.181050i
$862$	−17963.4	+	55285.7i	−0.0241754	+	0.0744043i
$863$	729120.	+	529737.i	0.978988	+	0.711277i	0.957482	−	0.288492i	$-0.0931539\pi$
$863$	729120.	+	529737.i	0.978988	+	0.711277i	0.0215061	+	0.999769i	$0.493154\pi$
$864$	83458.9	−	114871.i	0.111801	−	0.153881i
$865$	203938.	+	66263.4i	0.272562	+	0.0885609i
$866$	−769610.	+	250062.i	−1.02621	+	0.333435i
$867$	−417551.	+	303369.i	−0.555484	+	0.403583i
$868$			803287.i			1.06618i
$869$	323035.	+	227150.i	0.427770	+	0.300797i
$870$	−231632.			−0.306027
$871$	627296.	+	863398.i	0.826867	+	1.13809i
$872$	42848.2	+	131873.i	0.0563507	+	0.173430i
$873$	−130398.	+	401324.i	−0.171097	+	0.526583i
$874$	−48096.0	−	34943.8i	−0.0629631	−	0.0457453i
$875$	75999.7	−	104605.i	0.0992649	−	0.136626i
$876$	67071.5	+	21792.9i	0.0874038	+	0.0283992i
$877$	1.27205e6	−	413316.i	1.65389	−	0.537381i	0.674312	−	0.738447i	$-0.264440\pi$
$877$	1.27205e6	−	413316.i	1.65389	−	0.537381i	0.979578	+	0.201065i	$0.0644404\pi$
$878$	−175774.	+	127708.i	−0.228017	+	0.165664i
$879$		−	977987.i		−	1.26577i
$880$	51967.9	+	69249.7i	0.0671073	+	0.0894237i
$881$	54448.3			0.0701508			0.0350754	−	0.999385i	$-0.488833\pi$
$881$	54448.3			0.0701508			0.0350754	+	0.999385i	$0.488833\pi$
$882$	−370983.	−	510614.i	−0.476888	−	0.656381i
$883$	−150752.	−	463968.i	−0.193349	−	0.595068i	−0.999992	−	0.00402855i	$-0.998718\pi$
$883$	−150752.	−	463968.i	−0.193349	−	0.595068i	0.806643	−	0.591040i	$-0.201282\pi$
$884$	−299536.	+	921879.i	−0.383306	+	1.17969i
$885$	−216641.	−	157399.i	−0.276601	−	0.200962i
$886$	252015.	−	346869.i	0.321040	−	0.441874i
$887$	−417678.	−	135712.i	−0.530877	−	0.172492i	0.0312989	−	0.999510i	$-0.490036\pi$
$887$	−417678.	−	135712.i	−0.530877	−	0.172492i	−0.562176	+	0.827018i	$0.690036\pi$
$888$	−315550.	+	102528.i	−0.400168	+	0.130022i
$889$	737119.	−	535549.i	0.932684	−	0.677634i
$890$			263295.i			0.332401i
$891$	4328.71	+	279875.i	0.00545259	+	0.352540i
$892$	−111945.			−0.140693
$893$	10743.8	+	14787.6i	0.0134727	+	0.0185436i
$894$	−66183.8	−	203693.i	−0.0828088	−	0.254859i
$895$	3901.94	−	12008.9i	0.00487118	−	0.0149920i
$896$	−108393.	−	78752.0i	−0.135016	−	0.0980947i
$897$	−87320.5	+	120186.i	−0.108525	+	0.149372i
$898$	383225.	+	124518.i	0.475228	+	0.154411i
$899$	−1.13000e6	+	367159.i	−1.39817	+	0.454292i
$900$	−29313.1	+	21297.2i	−0.0361891	+	0.0262929i
$901$			698402.i			0.860312i
$902$	−74568.2	−	22960.0i	−0.0916517	−	0.0282201i
$903$	−1.09061e6			−1.33750
$904$	−238073.	−	327679.i	−0.291322	−	0.400970i
$905$	−112553.	−	346404.i	−0.137424	−	0.422947i
$906$	−70864.9	+	218100.i	−0.0863326	+	0.265704i
$907$	−1.15109e6	−	836314.i	−1.39924	−	1.01661i	−0.994778	−	0.102058i	$-0.967457\pi$
$907$	−1.15109e6	−	836314.i	−1.39924	−	1.01661i	−0.404466	−	0.914553i	$-0.632543\pi$
$908$	180009.	−	247761.i	0.218334	−	0.300512i
$909$	551658.	+	179245.i	0.667640	+	0.216929i
$910$	841120.	−	273297.i	1.01572	−	0.330028i
$911$	174766.	−	126975.i	0.210582	−	0.152997i	−0.477495	−	0.878634i	$-0.658455\pi$
$911$	174766.	−	126975.i	0.210582	−	0.152997i	0.688077	+	0.725638i	$0.258455\pi$
$912$			122538.i			0.147326i
$913$	−257684.	+	836891.i	−0.309133	+	1.00399i
$914$	434954.			0.520656
$915$	20847.7	+	28694.4i	0.0249009	+	0.0342732i
$916$	−111310.	−	342577.i	−0.132661	−	0.408288i
$917$	224791.	−	691836.i	0.267326	−	0.822744i
$918$	−719424.	−	522692.i	−0.853689	−	0.620241i
$919$	916870.	−	1.26196e6i	1.08562	−	1.49422i	0.232435	−	0.972612i	$-0.425331\pi$
$919$	916870.	−	1.26196e6i	1.08562	−	1.49422i	0.853183	−	0.521612i	$-0.174669\pi$
$920$	−17672.2	−	5742.05i	−0.0208793	−	0.00678409i
$921$	729479.	−	237022.i	0.859990	−	0.279428i
$922$	−196512.	+	142775.i	−0.231168	+	0.167954i
$923$			819367.i			0.961779i
$924$	599143.	−	9266.70i	0.701756	−	0.0108538i
$925$	273942.			0.320166
$926$	342962.	+	472047.i	0.399967	+	0.550507i
$927$	55430.2	+	170596.i	0.0645040	+	0.198523i
$928$	61238.8	−	188474.i	0.0711100	−	0.218854i
$929$	−564650.	−	410242.i	−0.654256	−	0.475345i	0.210462	−	0.977602i	$-0.432503\pi$
$929$	−564650.	−	410242.i	−0.654256	−	0.475345i	−0.864718	+	0.502257i	$0.832503\pi$
$930$	134974.	−	185776.i	0.156057	−	0.214795i
$931$	1.67611e6	+	544602.i	1.93377	+	0.628319i
$932$	−590683.	+	191925.i	−0.680022	+	0.220953i
$933$	−119816.	+	87051.8i	−0.137643	+	0.100003i
$934$		−	727503.i		−	0.833952i
$935$	433702.	−	325468.i	0.496099	−	0.372294i
$936$	−247835.			−0.282886
$937$	637690.	+	877704.i	0.726324	+	0.999699i	0.999290	+	0.0376750i	$0.0119952\pi$
$937$	637690.	+	877704.i	0.726324	+	0.999699i	−0.272967	+	0.962024i	$0.588005\pi$
$938$	285486.	+	878636.i	0.324474	+	0.998627i
$939$	162719.	−	500798.i	0.184547	−	0.567978i
$940$	4622.01	+	3358.09i	0.00523088	+	0.00380046i
$941$	−1340.91	+	1845.60i	−0.00151433	+	0.00208429i	−0.809773	−	0.586743i	$-0.800410\pi$
$941$	−1340.91	+	1845.60i	−0.00151433	+	0.00208429i	0.808259	+	0.588827i	$0.200410\pi$
$942$	−513586.	−	166874.i	−0.578777	−	0.188056i
$943$	15925.5	−	5174.51i	0.0179089	−	0.00581896i
$944$	185347.	−	134663.i	0.207990	−	0.151113i
$945$			811357.i			0.908549i
$946$	−346827.	+	493231.i	−0.387553	+	0.551148i
$947$	553824.			0.617549			0.308775	−	0.951135i	$-0.400081\pi$
$947$	553824.			0.617549			0.308775	+	0.951135i	$0.400081\pi$
$948$	102682.	+	141329.i	0.114255	+	0.157259i
$949$	−123075.	−	378785.i	−0.136659	−	0.420592i
$950$	31264.3	−	96221.6i	0.0346419	−	0.106617i
$951$	693174.	+	503620.i	0.766445	+	0.556855i
$952$	−493214.	+	678851.i	−0.544204	+	0.749032i
$953$	1.04371e6	+	339120.i	1.14919	+	0.373395i	0.820838	−	0.571161i	$-0.193507\pi$
$953$	1.04371e6	+	339120.i	1.14919	+	0.373395i	0.328352	+	0.944555i	$0.393507\pi$
$954$	−169827.	+	55180.3i	−0.186600	+	0.0606300i
$955$	−133245.	+	96808.2i	−0.146098	+	0.106146i
$956$			278082.i			0.304269i
$957$	286886.	+	838590.i	0.313246	+	0.915642i
$958$	201283.			0.219319
$959$	−1.49513e6	−	2.05788e6i	−1.62571	−	2.23760i
$960$	11835.5	+	36425.9i	0.0128423	+	0.0395246i
$961$	78604.7	−	241920.i	0.0851141	−	0.261954i
$962$	1.51591e6	+	1.10138e6i	1.63804	+	1.19011i
$963$	135668.	−	186730.i	0.146293	−	0.201355i
$964$	−57917.2	−	18818.4i	−0.0623238	−	0.0202502i
$965$	−128137.	+	41634.3i	−0.137601	+	0.0447092i
$966$	−104041.	+	75590.2i	−0.111494	+	0.0810049i
$967$			1.49378e6i			1.59747i	0.601684	+	0.798734i	$0.294497\pi$
$967$			1.49378e6i			1.59747i	−0.601684	+	0.798734i	$0.705503\pi$
$968$	186344.	−	273911.i	0.198868	−	0.292321i
$969$	767439.			0.817328
$970$	−216473.	−	297949.i	−0.230070	−	0.316664i
$971$	−562911.	−	1.73246e6i	−0.597037	−	1.83749i	−0.544314	−	0.838881i	$-0.683210\pi$
$971$	−562911.	−	1.73246e6i	−0.597037	−	1.83749i	−0.0527227	−	0.998609i	$-0.516790\pi$
$972$	118804.	−	365642.i	0.125747	−	0.387011i
$973$	2.66203e6	+	1.93408e6i	2.81182	+	2.04291i
$974$	42886.0	−	59027.5i	0.0452062	−	0.0622210i
$975$	−240447.	−	78125.9i	−0.252935	−	0.0821837i
$976$	−28859.7	+	9377.08i	−0.0302965	+	0.00984392i
$977$	891347.	−	647602.i	0.933808	−	0.678451i	−0.0131140	−	0.999914i	$-0.504174\pi$
$977$	891347.	−	647602.i	0.933808	−	0.678451i	0.946922	+	0.321463i	$0.104174\pi$
$978$			239623.i			0.250525i
$979$	953222.	−	326103.i	0.994555	−	0.340243i
$980$	550847.			0.573560
$981$	130508.	+	179629.i	0.135613	+	0.186655i
$982$	136839.	+	421147.i	0.141902	+	0.436728i
$983$	452660.	−	1.39315e6i	0.468452	−	1.44175i	−0.386136	−	0.922442i	$-0.626191\pi$
$983$	452660.	−	1.39315e6i	0.468452	−	1.44175i	0.854588	−	0.519306i	$-0.173809\pi$
$984$	−27923.1	−	20287.3i	−0.0288385	−	0.0209524i
$985$	69745.3	−	95996.2i	0.0718857	−	0.0989422i
$986$	−1.18039e6	−	383531.i	−1.21414	−	0.394499i
$987$	37604.6	−	12218.5i	0.0386018	−	0.0125425i
$988$	559864.	−	406765.i	0.573547	−	0.416706i
$989$		−	129406.i		−	0.132301i
$990$	113409.	+	79746.5i	0.115712	+	0.0813657i
$991$	−1.48539e6			−1.51249			−0.756247	−	0.654286i	$-0.772969\pi$
$991$	−1.48539e6			−1.51249			−0.756247	+	0.654286i	$0.772969\pi$
$992$	115477.	+	158941.i	0.117347	+	0.161515i
$993$	−51237.4	−	157692.i	−0.0519623	−	0.159923i
$994$	−219185.	+	674581.i	−0.221839	+	0.682750i
$995$	−146585.	−	106500.i	−0.148062	−	0.107573i
$996$	−227688.	+	313385.i	−0.229520	+	0.315908i
$997$	−812049.	−	263851.i	−0.816943	−	0.265441i	−0.129407	−	0.991592i	$-0.541308\pi$
$997$	−812049.	−	263851.i	−0.816943	−	0.265441i	−0.687536	+	0.726151i	$0.741308\pi$
$998$	−940298.	+	305521.i	−0.944071	+	0.306747i
$999$	−1.39070e6	+	1.01041e6i	−1.39349	+	1.01243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.5.h.a.41.2	✓	32
11.7	odd	10	inner	110.5.h.a.51.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.5.h.a.41.2	✓	32	1.1	even	1	trivial
110.5.h.a.51.2	yes	32	11.7	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	110.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66251 - 2.28825i) q^{2} +(-2.06757 - 6.36334i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-9.04508 - 6.57164i) q^{5} +(-11.1235 + 15.3102i) q^{6} +(87.9902 + 28.5898i) q^{7} +(21.5200 - 6.99226i) q^{8} +(29.3131 - 21.2972i) q^{9} +31.6228i q^{10} +(114.486 - 39.1662i) q^{11} +53.5265 q^{12} +(-177.682 - 244.558i) q^{13} +(-80.8640 - 248.874i) q^{14} +(-23.1162 + 71.1443i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(-235.598 + 324.273i) q^{17} +(-97.4666 - 31.6688i) q^{18} +(272.156 - 88.4288i) q^{19} +(72.3607 - 52.5731i) q^{20} -619.023i q^{21} +(-279.956 - 196.858i) q^{22} +73.4505 q^{23} +(-88.9882 - 122.482i) q^{24} +(38.6271 + 118.882i) q^{25} +(-264.211 + 813.158i) q^{26} +(-634.580 - 461.049i) q^{27} +(-435.048 + 598.792i) q^{28} +(-1041.18 - 338.300i) q^{29} +(201.227 - 65.3825i) q^{30} +(878.032 - 637.927i) q^{31} +181.019i q^{32} +(-485.936 - 647.533i) q^{33} +1133.70 q^{34} +(-607.997 - 836.837i) q^{35} +(89.5730 + 275.677i) q^{36} +(677.221 - 2084.27i) q^{37} +(-654.808 - 475.746i) q^{38} +(-1188.83 + 1636.29i) q^{39} +(-240.600 - 78.1758i) q^{40} +(216.819 - 70.4489i) q^{41} +(-1416.48 + 1029.13i) q^{42} -1761.82i q^{43} +(14.9699 + 967.884i) q^{44} -405.098 q^{45} +(-122.112 - 168.073i) q^{46} +(19.7383 + 60.7483i) q^{47} +(-132.325 + 407.254i) q^{48} +(4982.45 + 3619.97i) q^{49} +(207.813 - 286.031i) q^{50} +(2550.58 + 828.733i) q^{51} +(2299.96 - 747.302i) q^{52} +(1409.64 - 1024.17i) q^{53} +2218.57i q^{54} +(-1292.92 - 398.098i) q^{55} +2093.45 q^{56} +(-1125.41 - 1548.99i) q^{57} +(956.856 + 2944.90i) q^{58} +(-1106.19 + 3404.51i) q^{59} +(-484.152 - 351.757i) q^{60} +(278.692 - 383.586i) q^{61} +(-2919.47 - 948.593i) q^{62} +(3188.15 - 1035.89i) q^{63} +(414.217 - 300.946i) q^{64} +3379.70i q^{65} +(-673.843 + 2188.47i) q^{66} -3530.45 q^{67} +(-1884.79 - 2594.19i) q^{68} +(-151.864 - 467.391i) q^{69} +(-904.087 + 2782.50i) q^{70} +(-2192.87 - 1593.21i) q^{71} +(481.901 - 663.281i) q^{72} +(1253.05 + 407.142i) q^{73} +(-5895.21 + 1915.47i) q^{74} +(676.623 - 491.595i) q^{75} +2289.29i q^{76} +(11193.4 - 173.124i) q^{77} +5720.68 q^{78} +(1918.34 + 2640.36i) q^{79} +(221.115 + 680.521i) q^{80} +(-714.847 + 2200.07i) q^{81} +(-521.668 - 379.014i) q^{82} +(-4253.74 + 5854.77i) q^{83} +(4709.81 + 1530.31i) q^{84} +(4262.01 - 1384.81i) q^{85} +(-4031.47 + 2929.04i) q^{86} +7324.84i q^{87} +(2189.87 - 1643.37i) q^{88} +8326.12 q^{89} +(673.478 + 926.963i) q^{90} +(-8642.40 - 26598.6i) q^{91} +(-181.580 + 558.845i) q^{92} +(-5874.75 - 4268.25i) q^{93} +(106.192 - 146.161i) q^{94} +(-3042.79 - 988.664i) q^{95} +(1151.89 - 374.271i) q^{96} +(-9421.98 + 6845.47i) q^{97} -17419.3i q^{98} +(2521.81 - 3586.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) \) 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Introduction

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