LMFDB - Embedded newform 55.4.g.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,4,Mod(16,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("55.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$55 = 5 \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	55.g (of order $5$ , 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:	$3.24510505032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	55.31
Dual form			55.4.g.b.16.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50387 - 4.62843i) q^{2} +(4.25544 - 3.09176i) q^{3} +(-12.6886 - 9.21884i) q^{4} +(1.54508 + 4.75528i) q^{5} +(-7.91037 - 24.3456i) q^{6} +(4.59294 + 3.33697i) q^{7} +(-30.2534 + 21.9804i) q^{8} +(0.206327 - 0.635008i) q^{9} +24.3331 q^{10} +(33.8148 - 13.6951i) q^{11} -82.4981 q^{12} +(-24.4801 + 75.3419i) q^{13} +(22.3521 - 16.2398i) q^{14} +(21.2772 + 15.4588i) q^{15} +(17.4646 + 53.7504i) q^{16} +(-28.7566 - 88.5037i) q^{17} +(-2.62881 - 1.90994i) q^{18} +(6.75924 - 4.91087i) q^{19} +(24.2332 - 74.5820i) q^{20} +29.8621 q^{21} +(-12.5339 - 177.105i) q^{22} +25.5926 q^{23} +(-60.7835 + 187.072i) q^{24} +(-20.2254 + 14.6946i) q^{25} +(311.900 + 226.609i) q^{26} +(42.8014 + 131.729i) q^{27} +(-27.5152 - 84.6832i) q^{28} +(97.5933 + 70.9057i) q^{29} +(103.548 - 75.2320i) q^{30} +(50.9402 - 156.778i) q^{31} -24.1177 q^{32} +(101.555 - 162.826i) q^{33} -452.879 q^{34} +(-8.77174 + 26.9966i) q^{35} +(-8.47205 + 6.15530i) q^{36} +(89.4056 + 64.9570i) q^{37} +(-12.5646 - 38.6700i) q^{38} +(128.765 + 396.299i) q^{39} +(-151.267 - 109.902i) q^{40} +(-389.354 + 282.882i) q^{41} +(44.9087 - 138.215i) q^{42} -341.001 q^{43} +(-555.318 - 137.961i) q^{44} +3.33844 q^{45} +(38.4879 - 118.454i) q^{46} +(65.5726 - 47.6413i) q^{47} +(240.502 + 174.735i) q^{48} +(-96.0331 - 295.559i) q^{49} +(37.5967 + 115.711i) q^{50} +(-396.003 - 287.713i) q^{51} +(1005.18 - 730.309i) q^{52} +(-179.608 + 552.777i) q^{53} +674.067 q^{54} +(117.371 + 139.639i) q^{55} -212.300 q^{56} +(13.5803 - 41.7958i) q^{57} +(474.950 - 345.071i) q^{58} +(469.461 + 341.083i) q^{59} +(-127.467 - 392.302i) q^{60} +(-136.899 - 421.331i) q^{61} +(-649.029 - 471.547i) q^{62} +(3.06665 - 2.22805i) q^{63} +(-175.986 + 541.630i) q^{64} -396.096 q^{65} +(-600.904 - 714.909i) q^{66} +47.2746 q^{67} +(-451.019 + 1388.09i) q^{68} +(108.908 - 79.1260i) q^{69} +(111.761 + 81.1989i) q^{70} +(109.883 + 338.184i) q^{71} +(7.71564 + 23.7463i) q^{72} +(-401.808 - 291.930i) q^{73} +(435.103 - 316.121i) q^{74} +(-40.6358 + 125.064i) q^{75} -131.038 q^{76} +(201.010 + 49.9381i) q^{77} +2027.89 q^{78} +(-126.399 + 389.015i) q^{79} +(-228.614 + 166.098i) q^{80} +(603.997 + 438.830i) q^{81} +(723.765 + 2227.52i) q^{82} +(-363.087 - 1117.47i) q^{83} +(-378.909 - 275.294i) q^{84} +(376.429 - 273.491i) q^{85} +(-512.821 + 1578.30i) q^{86} +634.525 q^{87} +(-721.990 + 1157.59i) q^{88} +1148.29 q^{89} +(5.02057 - 15.4517i) q^{90} +(-363.849 + 264.352i) q^{91} +(-324.735 - 235.934i) q^{92} +(-267.946 - 824.653i) q^{93} +(-121.892 - 375.145i) q^{94} +(33.7962 + 24.5544i) q^{95} +(-102.631 + 74.5659i) q^{96} +(370.588 - 1140.55i) q^{97} -1512.40 q^{98} +(-1.71962 - 24.2984i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q + 6 q^{2} + 4 q^{3} - 36 q^{4} - 30 q^{5} + 30 q^{6} + 81 q^{7} - 10 q^{8} - 48 q^{9} - 70 q^{10} - 72 q^{11} + 10 q^{12} + 65 q^{13} - 47 q^{14} + 20 q^{15} - 60 q^{16} - 142 q^{17} + 283 q^{18} - 17 q^{19}+ \cdots + 5980 q^{99}+O(q^{100})$ 24 * q + 6 * q^2 + 4 * q^3 - 36 * q^4 - 30 * q^5 + 30 * q^6 + 81 * q^7 - 10 * q^8 - 48 * q^9 - 70 * q^10 - 72 * q^11 + 10 * q^12 + 65 * q^13 - 47 * q^14 + 20 * q^15 - 60 * q^16 - 142 * q^17 + 283 * q^18 - 17 * q^19 - 55 * q^20 - 200 * q^21 + 87 * q^22 - 182 * q^23 + 70 * q^24 - 150 * q^25 + 736 * q^26 + 643 * q^27 - 52 * q^28 + 80 * q^29 - 210 * q^31 - 504 * q^32 + 993 * q^33 + 1046 * q^34 + 80 * q^35 - 2242 * q^36 + 560 * q^37 + 187 * q^38 - 1294 * q^39 - 50 * q^40 + 293 * q^41 - 2231 * q^42 - 3658 * q^43 + 1293 * q^44 + 1310 * q^45 - 57 * q^46 - 1824 * q^47 + 1977 * q^48 + 73 * q^49 + 150 * q^50 - 1769 * q^51 + 3342 * q^52 + 838 * q^53 + 2784 * q^54 + 290 * q^55 + 8652 * q^56 + 273 * q^57 - 3896 * q^58 + 1653 * q^59 - 875 * q^60 - 888 * q^61 - 2200 * q^62 + 3149 * q^63 - 4644 * q^64 - 2050 * q^65 - 4497 * q^66 + 3966 * q^67 - 3783 * q^68 - 3384 * q^69 - 235 * q^70 + 1664 * q^71 - 4264 * q^72 - 2210 * q^73 + 1552 * q^74 - 25 * q^75 + 3048 * q^76 - 1304 * q^77 + 10064 * q^78 + 12 * q^79 - 275 * q^80 + 5005 * q^81 + 4099 * q^82 + 1945 * q^83 - 7584 * q^84 + 1865 * q^85 - 5156 * q^86 - 3844 * q^87 + 619 * q^88 + 4568 * q^89 - 210 * q^90 - 4885 * q^91 + 3390 * q^92 + 2844 * q^93 - 8932 * q^94 - 85 * q^95 - 1249 * q^96 - 3255 * q^97 - 7778 * q^98 + 5980 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$ .

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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

)

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

$2$	1.50387	−	4.62843i	0.531698	−	1.63640i	−0.218979	−	0.975730i	$-0.570273\pi$
$2$	1.50387	−	4.62843i	0.531698	−	1.63640i	0.750677	−	0.660669i	$-0.229727\pi$
$3$	4.25544	−	3.09176i	0.818959	−	0.595009i	−0.0974551	−	0.995240i	$-0.531070\pi$
$3$	4.25544	−	3.09176i	0.818959	−	0.595009i	0.916414	+	0.400231i	$0.131070\pi$
$4$	−12.6886	−	9.21884i	−1.58608	−	1.15235i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$6$	−7.91037	−	24.3456i	−0.538232	−	1.65651i
$7$	4.59294	+	3.33697i	0.247996	+	0.180179i	0.704838	−	0.709368i	$-0.251020\pi$
$7$	4.59294	+	3.33697i	0.247996	+	0.180179i	−0.456842	+	0.889548i	$0.651020\pi$
$8$	−30.2534	+	21.9804i	−1.33702	+	0.971405i
$9$	0.206327	−	0.635008i	0.00764173	−	0.0235188i
$10$	24.3331			0.769481
$11$	33.8148	−	13.6951i	0.926869	−	0.375385i
$11$	33.8148	−	13.6951i	0.926869	−	0.375385i
$12$	−82.4981			−1.98460
$13$	−24.4801	+	75.3419i	−0.522273	+	1.60739i	0.247373	+	0.968920i	$0.420433\pi$
$13$	−24.4801	+	75.3419i	−0.522273	+	1.60739i	−0.769646	+	0.638471i	$0.779567\pi$
$14$	22.3521	−	16.2398i	0.426704	−	0.310019i
$15$	21.2772	+	15.4588i	0.366250	+	0.266096i
$16$	17.4646	+	53.7504i	0.272884	+	0.839850i
$17$	−28.7566	−	88.5037i	−0.410264	−	1.26266i	−0.916419	−	0.400221i	$-0.868933\pi$
$17$	−28.7566	−	88.5037i	−0.410264	−	1.26266i	0.506154	−	0.862443i	$-0.331067\pi$
$18$	−2.62881	−	1.90994i	−0.0344231	−	0.0250098i
$19$	6.75924	−	4.91087i	0.0816145	−	0.0592964i	−0.546230	−	0.837635i	$-0.683937\pi$
$19$	6.75924	−	4.91087i	0.0816145	−	0.0592964i	0.627844	+	0.778339i	$0.283937\pi$
$20$	24.2332	−	74.5820i	0.270935	−	0.833852i
$21$	29.8621			0.310307
$22$	−12.5339	−	177.105i	−0.121466	−	1.71632i
$23$	25.5926			0.232018			0.116009	−	0.993248i	$-0.462990\pi$
$23$	25.5926			0.232018			0.116009	+	0.993248i	$0.462990\pi$
$24$	−60.7835	+	187.072i	−0.516974	+	1.59108i
$25$	−20.2254	+	14.6946i	−0.161803	+	0.117557i
$26$	311.900	+	226.609i	2.35264	+	1.70929i
$27$	42.8014	+	131.729i	0.305079	+	0.938936i
$28$	−27.5152	−	84.6832i	−0.185710	−	0.571558i
$29$	97.5933	+	70.9057i	0.624918	+	0.454029i	0.854636	−	0.519228i	$-0.173780\pi$
$29$	97.5933	+	70.9057i	0.624918	+	0.454029i	−0.229718	+	0.973257i	$0.573780\pi$
$30$	103.548	−	75.2320i	0.630173	−	0.457848i
$31$	50.9402	−	156.778i	0.295133	−	0.908327i	−0.688043	−	0.725670i	$-0.741530\pi$
$31$	50.9402	−	156.778i	0.295133	−	0.908327i	0.983177	−	0.182657i	$-0.0584699\pi$
$32$	−24.1177			−0.133233
$33$	101.555	−	162.826i	0.535710	−	0.858920i
$34$	−452.879			−2.28436
$35$	−8.77174	+	26.9966i	−0.0423627	+	0.130379i
$36$	−8.47205	+	6.15530i	−0.0392224	+	0.0284968i
$37$	89.4056	+	64.9570i	0.397248	+	0.288618i	0.768419	−	0.639947i	$-0.221044\pi$
$37$	89.4056	+	64.9570i	0.397248	+	0.288618i	−0.371171	+	0.928565i	$0.621044\pi$
$38$	−12.5646	−	38.6700i	−0.0536383	−	0.165082i
$39$	128.765	+	396.299i	0.528691	+	1.62714i
$40$	−151.267	−	109.902i	−0.597935	−	0.434426i
$41$	−389.354	+	282.882i	−1.48310	+	1.07753i	−0.506553	+	0.862209i	$0.669081\pi$
$41$	−389.354	+	282.882i	−1.48310	+	1.07753i	−0.976543	+	0.215324i	$0.930919\pi$
$42$	44.9087	−	138.215i	0.164989	−	0.507785i
$43$	−341.001			−1.20935			−0.604677	−	0.796471i	$-0.706698\pi$
$43$	−341.001			−1.20935			−0.604677	+	0.796471i	$0.706698\pi$
$44$	−555.318	−	137.961i	−1.90267	−	0.472691i
$45$	3.33844			0.0110592
$46$	38.4879	−	118.454i	0.123364	−	0.379674i
$47$	65.5726	−	47.6413i	0.203505	−	0.147855i	−0.481365	−	0.876520i	$-0.659859\pi$
$47$	65.5726	−	47.6413i	0.203505	−	0.147855i	0.684870	+	0.728665i	$0.259859\pi$
$48$	240.502	+	174.735i	0.723198	+	0.525434i
$49$	−96.0331	−	295.559i	−0.279980	−	0.861689i
$50$	37.5967	+	115.711i	0.106340	+	0.327280i
$51$	−396.003	−	287.713i	−1.08729	−	0.789959i
$52$	1005.18	−	730.309i	2.68065	−	1.94761i
$53$	−179.608	+	552.777i	−0.465492	+	1.43264i	0.392871	+	0.919594i	$0.371482\pi$
$53$	−179.608	+	552.777i	−0.465492	+	1.43264i	−0.858363	+	0.513043i	$0.828518\pi$
$54$	674.067			1.69868
$55$	117.371	+	139.639i	0.287751	+	0.342344i
$56$	−212.300			−0.506603
$57$	13.5803	−	41.7958i	0.0315571	−	0.0971227i
$58$	474.950	−	345.071i	1.07524	−	0.781208i
$59$	469.461	+	341.083i	1.03591	+	0.752632i	0.969483	−	0.245160i	$-0.0788404\pi$
$59$	469.461	+	341.083i	1.03591	+	0.752632i	0.0664259	+	0.997791i	$0.478840\pi$
$60$	−127.467	−	392.302i	−0.274264	−	0.844099i
$61$	−136.899	−	421.331i	−0.287346	−	0.884359i	−0.985686	−	0.168593i	$-0.946078\pi$
$61$	−136.899	−	421.331i	−0.287346	−	0.884359i	0.698340	−	0.715766i	$-0.253922\pi$
$62$	−649.029	−	471.547i	−1.32946	−	0.965912i
$63$	3.06665	−	2.22805i	0.00613272	−	0.00445568i
$64$	−175.986	+	541.630i	−0.343723	+	1.05787i
$65$	−396.096			−0.755841
$66$	−600.904	−	714.909i	−1.12070	−	1.33332i
$67$	47.2746			0.0862017			0.0431008	−	0.999071i	$-0.486276\pi$
$67$	47.2746			0.0862017			0.0431008	+	0.999071i	$0.486276\pi$
$68$	−451.019	+	1388.09i	−0.804325	+	2.47546i
$69$	108.908	−	79.1260i	0.190014	−	0.138053i
$70$	111.761	+	81.1989i	0.190828	+	0.138645i
$71$	109.883	+	338.184i	0.183671	+	0.565282i	0.999923	−	0.0124142i	$-0.00395167\pi$
$71$	109.883	+	338.184i	0.183671	+	0.565282i	−0.816252	+	0.577697i	$0.803952\pi$
$72$	7.71564	+	23.7463i	0.0126291	+	0.0388685i
$73$	−401.808	−	291.930i	−0.644220	−	0.468053i	0.217078	−	0.976154i	$-0.430348\pi$
$73$	−401.808	−	291.930i	−0.644220	−	0.468053i	−0.861297	+	0.508101i	$0.830348\pi$
$74$	435.103	−	316.121i	0.683510	−	0.496599i
$75$	−40.6358	+	125.064i	−0.0625629	+	0.192549i
$76$	−131.038			−0.197778
$77$	201.010	+	49.9381i	0.297496	+	0.0739087i
$78$	2027.89			2.94376
$79$	−126.399	+	389.015i	−0.180012	+	0.554021i	−0.999827	−	0.0186083i	$-0.994076\pi$
$79$	−126.399	+	389.015i	−0.180012	+	0.554021i	0.819815	+	0.572629i	$0.194076\pi$
$80$	−228.614	+	166.098i	−0.319498	+	0.232129i
$81$	603.997	+	438.830i	0.828529	+	0.601961i
$82$	723.765	+	2227.52i	0.974713	+	2.99986i
$83$	−363.087	−	1117.47i	−0.480168	−	1.47780i	−0.838859	−	0.544348i	$-0.816777\pi$
$83$	−363.087	−	1117.47i	−0.480168	−	1.47780i	0.358692	−	0.933456i	$-0.383223\pi$
$84$	−378.909	−	275.294i	−0.492171	−	0.357583i
$85$	376.429	−	273.491i	0.480346	−	0.348992i
$86$	−512.821	+	1578.30i	−0.643011	+	1.97898i
$87$	634.525			0.781934
$88$	−721.990	+	1157.59i	−0.874595	+	1.40226i
$89$	1148.29			1.36763			0.683813	−	0.729657i	$-0.260320\pi$
$89$	1148.29			1.36763			0.683813	+	0.729657i	$0.260320\pi$
$90$	5.02057	−	15.4517i	0.00588016	−	0.0180973i
$91$	−363.849	+	264.352i	−0.419140	+	0.304523i
$92$	−324.735	−	235.934i	−0.368000	−	0.267367i
$93$	−267.946	−	824.653i	−0.298760	−	0.919490i
$94$	−121.892	−	375.145i	−0.133747	−	0.411630i
$95$	33.7962	+	24.5544i	0.0364991	+	0.0265182i
$96$	−102.631	+	74.5659i	−0.109112	+	0.0792745i
$97$	370.588	−	1140.55i	0.387913	−	1.19387i	−0.546432	−	0.837503i	$-0.684014\pi$
$97$	370.588	−	1140.55i	0.387913	−	1.19387i	0.934345	−	0.356370i	$-0.115986\pi$
$98$	−1512.40			−1.55893
$99$	−1.71962	−	24.2984i	−0.00174574	−	0.0246675i
$100$	392.101			0.392101
$101$	521.188	−	1604.05i	0.513467	−	1.58029i	−0.272587	−	0.962131i	$-0.587879\pi$
$101$	521.188	−	1604.05i	0.513467	−	1.58029i	0.786054	−	0.618158i	$-0.212121\pi$
$102$	−1927.20	+	1400.19i	−1.87080	+	1.35921i
$103$	−1518.47	−	1103.23i	−1.45261	−	1.05539i	−0.985212	−	0.171340i	$-0.945190\pi$
$103$	−1518.47	−	1103.23i	−1.45261	−	1.05539i	−0.467401	−	0.884045i	$-0.654810\pi$
$104$	−915.439	−	2817.43i	−0.863136	−	2.65646i
$105$	46.1394	+	142.003i	0.0428833	+	0.131981i
$106$	2288.38	+	1662.61i	2.09686	+	1.52346i
$107$	−1019.53	+	740.734i	−0.921139	+	0.669247i	−0.943807	−	0.330496i	$-0.892784\pi$
$107$	−1019.53	+	740.734i	−0.921139	+	0.669247i	0.0226680	+	0.999743i	$0.492784\pi$
$108$	671.298	−	2066.04i	0.598108	−	1.84079i
$109$	743.082			0.652976			0.326488	−	0.945201i	$-0.394135\pi$
$109$	743.082			0.652976			0.326488	+	0.945201i	$0.394135\pi$
$110$	822.820	−	333.245i	0.713208	−	0.288852i
$111$	581.291			0.497060
$112$	−99.1496	+	305.151i	−0.0836496	+	0.257447i
$113$	646.345	−	469.597i	0.538080	−	0.390938i	−0.285292	−	0.958441i	$-0.592090\pi$
$113$	646.345	−	469.597i	0.538080	−	0.390938i	0.823371	+	0.567503i	$0.192090\pi$
$114$	−173.026	−	125.711i	−0.142153	−	0.103280i
$115$	39.5427	+	121.700i	0.0320641	+	0.0986833i
$116$	−584.659	−	1799.39i	−0.467967	−	1.44025i
$117$	42.7919	+	31.0901i	0.0338129	+	0.0245665i
$118$	2284.69	−	1659.92i	1.78240	−	1.29499i
$119$	163.257	−	502.452i	0.125762	−	0.387056i
$120$	−983.497			−0.748172
$121$	955.887	−	926.198i	0.718172	−	0.695866i
$122$	−2155.98			−1.59994
$123$	−782.269	+	2407.58i	−0.573454	+	1.76491i
$124$	−2091.67	+	1519.69i	−1.51482	+	1.10058i
$125$	−101.127	−	73.4732i	−0.0723607	−	0.0525731i
$126$	−5.70055	−	17.5445i	−0.00403052	−	0.0124047i
$127$	−209.033	−	643.337i	−0.146053	−	0.449504i	0.851092	−	0.525016i	$-0.175941\pi$
$127$	−209.033	−	643.337i	−0.146053	−	0.449504i	−0.997145	+	0.0755125i	$0.975941\pi$
$128$	2086.15	+	1515.67i	1.44055	+	1.04662i
$129$	−1451.11	+	1054.29i	−0.990411	+	0.719575i
$130$	−595.677	+	1833.30i	−0.401879	+	1.23686i
$131$	−19.1565			−0.0127764			−0.00638822	−	0.999980i	$-0.502033\pi$
$131$	−19.1565			−0.0127764			−0.00638822	+	0.999980i	$0.502033\pi$
$132$	−2789.66	+	1129.82i	−1.83946	+	0.744988i
$133$	47.4322			0.0309240
$134$	71.0948	−	218.807i	0.0458333	−	0.141060i
$135$	−560.277	+	407.065i	−0.357193	+	0.259516i
$136$	2815.33	+	2045.46i	1.77509	+	1.28968i
$137$	−139.219	−	428.473i	−0.0868199	−	0.267204i	0.898216	−	0.439555i	$-0.144864\pi$
$137$	−139.219	−	428.473i	−0.0868199	−	0.267204i	−0.985036	+	0.172351i	$0.944864\pi$
$138$	−202.447	−	623.067i	−0.124880	−	0.384340i
$139$	316.358	+	229.847i	0.193044	+	0.140255i	0.680109	−	0.733111i	$-0.261932\pi$
$139$	316.358	+	229.847i	0.193044	+	0.140255i	−0.487065	+	0.873366i	$0.661932\pi$
$140$	360.179	−	261.686i	0.217434	−	0.157975i
$141$	131.745	−	405.469i	0.0786874	−	0.242175i
$142$	1730.51			1.02269
$143$	204.028	+	2882.93i	0.119312	+	1.68589i
$144$	37.7353			0.0218376
$145$	−186.387	+	573.639i	−0.106749	+	0.328539i
$146$	−1955.45	+	1420.72i	−1.10845	+	0.805337i
$147$	−1322.46	−	960.823i	−0.742004	−	0.539098i
$148$	−535.608	−	1648.43i	−0.297478	−	0.915542i
$149$	−610.566	−	1879.13i	−0.335702	−	1.03318i	−0.966375	−	0.257135i	$-0.917221\pi$
$149$	−610.566	−	1879.13i	−0.335702	−	1.03318i	0.630674	−	0.776048i	$-0.282779\pi$
$150$	517.740	+	376.160i	0.281822	+	0.204756i
$151$	377.960	−	274.604i	0.203695	−	0.147993i	−0.481261	−	0.876577i	$-0.659821\pi$
$151$	377.960	−	274.604i	0.203695	−	0.147993i	0.684956	+	0.728584i	$0.259821\pi$
$152$	−96.5471	+	297.141i	−0.0515198	+	0.158562i
$153$	−62.1338			−0.0328315
$154$	533.428	−	855.261i	0.279122	−	0.447525i
$155$	824.230			0.427121
$156$	2019.56	−	6215.57i	1.03650	−	3.19002i
$157$	−185.411	+	134.709i	−0.0942512	+	0.0684775i	−0.633913	−	0.773405i	$-0.718552\pi$
$157$	−185.411	+	134.709i	−0.0942512	+	0.0684775i	0.539662	+	0.841882i	$0.318552\pi$
$158$	1610.44	+	1170.06i	0.810887	+	0.589144i
$159$	944.740	+	2907.61i	0.471212	+	1.45024i
$160$	−37.2639	−	114.686i	−0.0184123	−	0.0566672i
$161$	117.545	+	85.4016i	0.0575395	+	0.0418049i
$162$	2939.43	−	2135.62i	1.42558	−	1.03574i
$163$	−401.061	+	1234.34i	−0.192721	+	0.593134i	0.807275	+	0.590176i	$0.200942\pi$
$163$	−401.061	+	1234.34i	−0.192721	+	0.593134i	−0.999996	+	0.00295819i	$0.999058\pi$
$164$	7548.23			3.59401
$165$	931.194	+	231.342i	0.439354	+	0.109151i
$166$	−5718.15			−2.67358
$167$	−1049.77	+	3230.85i	−0.486427	+	1.49707i	0.343476	+	0.939161i	$0.388396\pi$
$167$	−1049.77	+	3230.85i	−0.486427	+	1.49707i	−0.829903	+	0.557908i	$0.811604\pi$
$168$	−903.429	+	656.380i	−0.414887	+	0.301433i
$169$	−3299.72	−	2397.39i	−1.50192	−	1.09121i
$170$	−699.737	−	2153.57i	−0.315691	−	0.971596i
$171$	−1.72383	−	5.30542i	−0.000770906	−	0.00237261i
$172$	4326.84	+	3143.63i	1.91813	+	1.39360i
$173$	−1314.11	+	954.754i	−0.577513	+	0.419587i	−0.837827	−	0.545937i	$-0.816174\pi$
$173$	−1314.11	+	954.754i	−0.577513	+	0.419587i	0.260314	+	0.965524i	$0.416174\pi$
$174$	954.243	−	2936.86i	0.415753	−	1.27956i
$175$	−141.930			−0.0613079
$176$	1326.68	+	1578.38i	0.568195	+	0.675994i
$177$	3052.31			1.29619
$178$	1726.88	−	5314.80i	0.727164	−	2.23798i
$179$	−346.759	+	251.935i	−0.144793	+	0.105198i	−0.657824	−	0.753172i	$-0.728523\pi$
$179$	−346.759	+	251.935i	−0.144793	+	0.105198i	0.513031	+	0.858370i	$0.328523\pi$
$180$	−42.3602	−	30.7765i	−0.0175408	−	0.0127441i
$181$	381.146	+	1173.05i	0.156521	+	0.481723i	0.998312	−	0.0580811i	$-0.0184982\pi$
$181$	381.146	+	1173.05i	0.156521	+	0.481723i	−0.841790	+	0.539804i	$0.818498\pi$
$182$	676.354	+	2081.60i	0.275465	+	0.847795i
$183$	−1885.22	−	1369.69i	−0.761525	−	0.553280i
$184$	−774.263	+	562.535i	−0.310214	+	0.225384i
$185$	−170.749	+	525.513i	−0.0678581	+	0.208846i
$186$	−4219.81			−1.66350
$187$	−2184.47	−	2598.91i	−0.854247	−	1.01632i
$188$	−1271.23			−0.493158
$189$	−242.992	+	747.851i	−0.0935187	+	0.287821i
$190$	164.473	−	119.497i	0.0628008	−	0.0456275i
$191$	1320.87	+	959.669i	0.500392	+	0.363556i	0.809167	−	0.587579i	$-0.199919\pi$
$191$	1320.87	+	959.669i	0.500392	+	0.363556i	−0.308775	+	0.951135i	$0.599919\pi$
$192$	925.689	+	2848.98i	0.347947	+	1.07087i
$193$	271.324	+	835.048i	0.101193	+	0.311441i	0.988818	−	0.149126i	$-0.0476461\pi$
$193$	271.324	+	835.048i	0.101193	+	0.311441i	−0.887625	+	0.460567i	$0.847646\pi$
$194$	−4721.66	−	3430.49i	−1.74740	−	1.26956i
$195$	−1685.56	+	1224.63i	−0.619003	+	0.449732i
$196$	−1506.19	+	4635.56i	−0.548901	+	1.68934i
$197$	2810.78			1.01655			0.508274	−	0.861195i	$-0.330284\pi$
$197$	2810.78			1.01655			0.508274	+	0.861195i	$0.330284\pi$
$198$	−115.050	−	28.5824i	−0.0412940	−	0.0102589i
$199$	3287.10			1.17094			0.585468	−	0.810696i	$-0.300911\pi$
$199$	3287.10			1.17094			0.585468	+	0.810696i	$0.300911\pi$
$200$	288.894	−	889.125i	0.102140	−	0.314353i
$201$	201.174	−	146.162i	0.0705956	−	0.0512907i
$202$	−6640.45	−	4824.57i	−2.31297	−	1.68047i
$203$	211.630	+	651.332i	0.0731702	+	0.225195i
$204$	2372.36	+	7301.38i	0.814209	+	2.50588i
$205$	−1946.77	−	1414.41i	−0.663261	−	0.481887i
$206$	−7389.81	+	5369.01i	−2.49938	+	1.81591i
$207$	5.28043	−	16.2515i	0.00177302	−	0.00545680i
$208$	−4477.19			−1.49249
$209$	161.307	−	258.629i	0.0533869	−	0.0855969i
$210$	726.637			0.238775
$211$	249.885	−	769.065i	0.0815297	−	0.250923i	−0.901980	−	0.431778i	$-0.857887\pi$
$211$	249.885	−	769.065i	0.0815297	−	0.250923i	0.983510	+	0.180855i	$0.0578865\pi$
$212$	7374.95	−	5358.21i	2.38921	−	1.73587i
$213$	1513.18	+	1099.39i	0.486767	+	0.353657i
$214$	1895.19	+	5832.80i	0.605387	+	1.86319i
$215$	−526.876	−	1621.56i	−0.167128	−	0.514369i
$216$	−4190.34	−	3044.46i	−1.31999	−	0.959025i
$217$	757.128	−	550.086i	0.236854	−	0.172084i
$218$	1117.50	−	3439.31i	0.347186	−	1.06853i
$219$	−2612.44			−0.806085
$220$	−201.970	−	2853.85i	−0.0618947	−	0.874576i
$221$	7372.00			2.24387
$222$	874.185	−	2690.47i	0.264286	−	0.813389i
$223$	2067.69	−	1502.27i	0.620911	−	0.451118i	−0.232329	−	0.972637i	$-0.574635\pi$
$223$	2067.69	−	1502.27i	0.620911	−	0.451118i	0.853239	+	0.521519i	$0.174635\pi$
$224$	−110.771	−	80.4799i	−0.0330411	−	0.0240058i
$225$	5.15817	+	15.8752i	0.00152835	+	0.00470377i
$226$	−1201.48	−	3697.78i	−0.353634	−	1.08837i
$227$	2270.90	+	1649.91i	0.663987	+	0.482415i	0.868007	−	0.496552i	$-0.165401\pi$
$227$	2270.90	+	1649.91i	0.663987	+	0.482415i	−0.204020	+	0.978967i	$0.565401\pi$
$228$	−557.624	+	405.138i	−0.161972	+	0.117679i
$229$	643.027	−	1979.03i	0.185556	−	0.571084i	−0.814401	−	0.580302i	$-0.802934\pi$
$229$	643.027	−	1979.03i	0.185556	−	0.571084i	0.999958	+	0.00921862i	$0.00293442\pi$
$230$	622.747			0.178534
$231$	1009.78	−	408.965i	0.287613	−	0.116485i
$232$	−4511.06			−1.27658
$233$	−966.037	+	2973.16i	−0.271619	+	0.835957i	0.718475	+	0.695552i	$0.244840\pi$
$233$	−966.037	+	2973.16i	−0.271619	+	0.835957i	−0.990094	+	0.140404i	$0.955160\pi$
$234$	208.252	−	151.304i	0.0581788	−	0.0422694i
$235$	327.863	+	238.207i	0.0910104	+	0.0661229i
$236$	−2812.43	−	8655.77i	−0.775736	−	2.38747i
$237$	664.858	+	2046.22i	0.182224	+	0.560829i
$238$	−2080.05	−	1511.24i	−0.566511	−	0.411594i
$239$	3266.47	−	2373.23i	0.884060	−	0.642307i	−0.0502627	−	0.998736i	$-0.516006\pi$
$239$	3266.47	−	2373.23i	0.884060	−	0.642307i	0.934322	+	0.356429i	$0.116006\pi$
$240$	−459.319	+	1413.64i	−0.123537	+	0.380208i
$241$	−5286.33			−1.41296			−0.706478	−	0.707735i	$-0.749717\pi$
$241$	−5286.33			−1.41296			−0.706478	+	0.707735i	$0.749717\pi$
$242$	−2849.32	−	5817.14i	−0.756864	−	1.54521i
$243$	187.305			0.0494471
$244$	−2147.12	+	6608.16i	−0.563342	+	1.73379i
$245$	1257.09	−	913.329i	0.327806	−	0.238165i
$246$	9966.88	+	7241.36i	2.58319	+	1.87680i
$247$	204.528	+	629.473i	0.0526875	+	0.162155i
$248$	1904.92	+	5862.75i	0.487753	+	1.50115i
$249$	−5000.02	−	3632.73i	−1.27254	−	0.924557i
$250$	−492.148	+	357.566i	−0.124505	+	0.0904579i
$251$	−487.246	+	1499.59i	−0.122529	+	0.377105i	−0.993443	−	0.114331i	$-0.963528\pi$
$251$	−487.246	+	1499.59i	−0.122529	+	0.377105i	0.870914	+	0.491435i	$0.163528\pi$
$252$	−59.4517			−0.0148615
$253$	865.409	−	350.494i	0.215051	−	0.0870963i
$254$	−3292.00			−0.813223
$255$	756.299	−	2327.65i	0.185731	−	0.571620i
$256$	6466.58	−	4698.25i	1.57876	−	1.14703i
$257$	−3376.92	−	2453.48i	−0.819636	−	0.595500i	0.0969723	−	0.995287i	$-0.469084\pi$
$257$	−3376.92	−	2453.48i	−0.819636	−	0.595500i	−0.916608	+	0.399787i	$0.869084\pi$
$258$	2697.44	+	8301.88i	0.650913	+	2.00330i
$259$	193.875	+	596.687i	0.0465129	+	0.143152i
$260$	5025.92	+	3651.54i	1.19882	+	0.870997i
$261$	65.1618	−	47.3428i	0.0154537	−	0.0112278i
$262$	−28.8089	+	88.6648i	−0.00679321	+	0.0209074i
$263$	3203.13			0.751001			0.375500	−	0.926822i	$-0.377471\pi$
$263$	3203.13			0.751001			0.375500	+	0.926822i	$0.377471\pi$
$264$	506.597	+	7158.26i	0.118102	+	1.66879i
$265$	−2906.12			−0.673666
$266$	71.3319	−	219.537i	0.0164423	−	0.0506040i
$267$	4886.48	−	3550.24i	1.12003	−	0.813749i
$268$	−599.851	−	435.817i	−0.136723	−	0.0993349i
$269$	−759.218	−	2336.63i	−0.172083	−	0.529617i	0.827405	−	0.561605i	$-0.189816\pi$
$269$	−759.218	−	2336.63i	−0.172083	−	0.529617i	−0.999488	+	0.0319883i	$0.989816\pi$
$270$	1041.49	+	3205.38i	0.234752	+	0.722493i
$271$	252.038	+	183.116i	0.0564952	+	0.0410462i	0.615674	−	0.788001i	$-0.288884\pi$
$271$	252.038	+	183.116i	0.0564952	+	0.0410462i	−0.559179	+	0.829047i	$0.688884\pi$
$272$	4254.88	−	3091.35i	0.948493	−	0.689121i
$273$	−731.026	+	2249.87i	−0.162065	+	0.498784i
$274$	−2192.53			−0.483414
$275$	−482.674	+	773.887i	−0.105841	+	0.169699i
$276$	−2111.34			−0.460463
$277$	−1394.19	+	4290.87i	−0.302414	+	0.930735i	0.678215	+	0.734863i	$0.262754\pi$
$277$	−1394.19	+	4290.87i	−0.302414	+	0.930735i	−0.980630	+	0.195872i	$0.937246\pi$
$278$	1539.59	−	1118.58i	0.332154	−	0.241324i
$279$	−89.0449	−	64.6949i	−0.0191075	−	0.0138824i
$280$	−328.022	−	1009.55i	−0.0700109	−	0.215471i
$281$	2018.78	+	6213.17i	0.428578	+	1.31903i	0.899526	+	0.436867i	$0.143912\pi$
$281$	2018.78	+	6213.17i	0.428578	+	1.31903i	−0.470948	+	0.882161i	$0.656088\pi$
$282$	−1678.56	−	1219.54i	−0.354457	−	0.257528i
$283$	−1170.46	+	850.389i	−0.245854	+	0.178623i	−0.703887	−	0.710312i	$-0.748554\pi$
$283$	−1170.46	+	850.389i	−0.245854	+	0.178623i	0.458033	+	0.888935i	$0.348554\pi$
$284$	1723.40	−	5304.09i	0.360088	−	1.10824i
$285$	219.734			0.0456698
$286$	13650.3	+	3391.22i	2.82223	+	0.701144i
$287$	−2732.25			−0.561950
$288$	−4.97612	+	15.3149i	−0.00101813	+	0.00313347i
$289$	−3031.26	+	2202.34i	−0.616987	+	0.448267i
$290$	2374.75	+	1725.36i	0.480862	+	0.349367i
$291$	−1949.30	−	5999.32i	−0.392680	−	1.20854i
$292$	2407.14	+	7408.40i	0.482421	+	1.48474i
$293$	1203.41	+	874.327i	0.239945	+	0.174330i	0.701259	−	0.712907i	$-0.252622\pi$
$293$	1203.41	+	874.327i	0.239945	+	0.174330i	−0.461314	+	0.887237i	$0.652622\pi$
$294$	−6435.91	+	4675.97i	−1.27670	+	0.927578i
$295$	−896.591	+	2759.42i	−0.176954	+	0.544609i
$296$	−4132.60			−0.811495
$297$	3251.37	+	3868.23i	0.635231	+	0.755749i
$298$	−9615.64			−1.86919
$299$	−626.508	+	1928.19i	−0.121177	+	0.372944i
$300$	1668.56	−	1212.28i	0.321114	−	0.233303i
$301$	−1566.20	−	1137.91i	−0.299914	−	0.217900i
$302$	−702.584	−	2162.33i	−0.133871	−	0.412014i
$303$	−2741.45	−	8437.33i	−0.519777	−	1.59971i
$304$	382.008	+	277.545i	0.0720713	+	0.0523629i
$305$	1792.03	−	1301.98i	0.336430	−	0.244431i
$306$	−93.4411	+	287.582i	−0.0174565	+	0.0537254i
$307$	−9022.24			−1.67729			−0.838643	−	0.544682i	$-0.816650\pi$
$307$	−9022.24			−1.67729			−0.838643	+	0.544682i	$0.816650\pi$
$308$	−2090.17	−	2486.72i	−0.386684	−	0.460046i
$309$	−9872.67			−1.81759
$310$	1239.53	−	3814.89i	0.227099	−	0.698940i
$311$	1313.76	−	954.504i	0.239539	−	0.174035i	−0.461539	−	0.887120i	$-0.652703\pi$
$311$	1313.76	−	954.504i	0.239539	−	0.174035i	0.701078	+	0.713085i	$0.252703\pi$
$312$	−12606.4	−	9159.09i	−2.28749	−	1.66196i
$313$	939.967	+	2892.92i	0.169745	+	0.522420i	0.999355	−	0.0359231i	$-0.0114371\pi$
$313$	939.967	+	2892.92i	0.169745	+	0.522420i	−0.829610	+	0.558343i	$0.811437\pi$
$314$	344.658	+	1060.75i	0.0619433	+	0.190642i
$315$	15.3333	+	11.1403i	0.00274264	+	0.00199264i
$316$	5190.10	−	3770.83i	0.923943	−	0.671284i
$317$	1655.49	−	5095.08i	0.293318	−	0.902739i	−0.690464	−	0.723367i	$-0.742593\pi$
$317$	1655.49	−	5095.08i	0.293318	−	0.902739i	0.983781	−	0.179372i	$-0.0574066\pi$
$318$	14878.5			2.62372
$319$	4271.16	+	1061.11i	0.749653	+	0.186241i
$320$	−2847.52			−0.497441
$321$	−2048.39	+	6304.29i	−0.356168	+	1.09617i
$322$	572.049	−	415.618i	0.0990032	−	0.0719300i
$323$	−629.003	−	456.997i	−0.108355	−	0.0787245i
$324$	−3618.41	−	11136.3i	−0.620440	−	1.90952i
$325$	−612.002	−	1883.55i	−0.104455	−	0.321478i
$326$	5109.91	+	3712.57i	0.868134	+	0.630737i
$327$	3162.14	−	2297.43i	0.534761	−	0.388526i
$328$	5561.43	−	17116.3i	0.936215	−	2.88137i
$329$	460.149			0.0771089
$330$	2471.15	−	3962.06i	0.412219	−	0.660923i
$331$	7332.86			1.21768			0.608838	−	0.793295i	$-0.291636\pi$
$331$	7332.86			1.21768			0.608838	+	0.793295i	$0.291636\pi$
$332$	−5694.66	+	17526.4i	−0.941371	+	2.89724i
$333$	59.6950	−	43.3709i	0.00982362	−	0.00713728i
$334$	13375.1	+	9717.55i	2.19117	+	1.59198i
$335$	73.0433	+	224.804i	0.0119128	+	0.0366638i
$336$	521.528	+	1605.10i	0.0846776	+	0.260611i
$337$	1655.35	+	1202.68i	0.267575	+	0.194405i	0.713480	−	0.700676i	$-0.247118\pi$
$337$	1655.35	+	1202.68i	0.267575	+	0.194405i	−0.445905	+	0.895080i	$0.647118\pi$
$338$	−16058.5	+	11667.2i	−2.58422	+	1.87755i
$339$	1298.60	−	3996.68i	0.208054	−	0.640324i
$340$	−7297.64			−1.16403
$341$	−424.559	−	5999.05i	−0.0674228	−	0.952689i
$342$	−27.1482			−0.00429242
$343$	1146.94	−	3529.92i	0.180551	−	0.555678i
$344$	10316.4	−	7495.34i	1.61693	−	1.17477i
$345$	544.538	+	395.630i	0.0849766	+	0.0617391i
$346$	2442.77	+	7518.08i	0.379550	+	1.16813i
$347$	−990.450	−	3048.29i	−0.153228	−	0.471588i	0.844749	−	0.535163i	$-0.179750\pi$
$347$	−990.450	−	3048.29i	−0.153228	−	0.471588i	−0.997977	+	0.0635752i	$0.979750\pi$
$348$	−8051.26	−	5849.59i	−1.24021	−	0.901065i
$349$	3833.32	−	2785.07i	0.587946	−	0.427168i	−0.253634	−	0.967300i	$-0.581626\pi$
$349$	3833.32	−	2785.07i	0.587946	−	0.427168i	0.841580	+	0.540133i	$0.181626\pi$
$350$	−213.444	+	656.913i	−0.0325973	+	0.100324i
$351$	−10972.5			−1.66857
$352$	−815.535	+	330.295i	−0.123489	+	0.0500136i
$353$	−1082.00			−0.163141			−0.0815706	−	0.996668i	$-0.525994\pi$
$353$	−1082.00			−0.163141			−0.0815706	+	0.996668i	$0.525994\pi$
$354$	4590.27	−	14127.4i	0.689181	−	2.12108i
$355$	−1438.38	+	1045.05i	−0.215046	+	0.156240i
$356$	−14570.3	−	10585.9i	−2.16917	−	1.57599i
$357$	−858.731	−	2642.90i	−0.127308	−	0.391813i
$358$	644.585	+	1983.83i	0.0951602	+	0.292873i
$359$	3384.42	+	2458.92i	0.497556	+	0.361496i	0.808083	−	0.589069i	$-0.200505\pi$
$359$	3384.42	+	2458.92i	0.497556	+	0.361496i	−0.310527	+	0.950565i	$0.600505\pi$
$360$	−100.999	+	73.3801i	−0.0147864	+	0.0107430i
$361$	−2097.98	+	6456.91i	−0.305872	+	0.941378i
$362$	6002.57			0.871513
$363$	1204.14	−	6896.74i	0.174107	−	0.997204i
$364$	7053.77			1.01571
$365$	767.384	−	2361.77i	0.110046	−	0.338686i
$366$	−9174.63	+	6665.76i	−1.31029	+	0.951981i
$367$	2271.70	+	1650.49i	0.323112	+	0.234754i	0.737502	−	0.675345i	$-0.236005\pi$
$367$	2271.70	+	1650.49i	0.323112	+	0.234754i	−0.414390	+	0.910099i	$0.636005\pi$
$368$	446.963	+	1375.61i	0.0633140	+	0.194860i
$369$	99.2985	+	305.610i	0.0140089	+	0.0431149i
$370$	2175.52	+	1580.61i	0.305675	+	0.222086i
$371$	−2669.53	+	1939.53i	−0.373572	+	0.271416i
$372$	−4202.47	+	12933.9i	−0.585721	+	1.80266i
$373$	3221.19			0.447150			0.223575	−	0.974687i	$-0.428227\pi$
$373$	3221.19			0.447150			0.223575	+	0.974687i	$0.428227\pi$
$374$	−15314.0	+	6202.25i	−2.11730	+	0.857515i
$375$	−657.501			−0.0905419
$376$	−936.621	+	2882.62i	−0.128464	+	0.395372i
$377$	−7731.26	+	5617.09i	−1.05618	+	0.767360i
$378$	3095.95	+	2249.34i	0.421266	+	0.306068i
$379$	−292.628	−	900.617i	−0.0396604	−	0.122062i	0.929266	−	0.369411i	$-0.120441\pi$
$379$	−292.628	−	900.617i	−0.0396604	−	0.122062i	−0.968926	+	0.247349i	$0.920441\pi$
$380$	−202.465	−	623.123i	−0.0273322	−	0.0841199i
$381$	−2878.57	−	2091.40i	−0.387070	−	0.281223i
$382$	6428.18	−	4670.35i	0.860980	−	0.625539i
$383$	−3405.73	+	10481.8i	−0.454372	+	1.39841i	0.417499	+	0.908678i	$0.362907\pi$
$383$	−3405.73	+	10481.8i	−0.454372	+	1.39841i	−0.871871	+	0.489736i	$0.837093\pi$
$384$	13563.6			1.80251
$385$	73.1077	+	1033.02i	0.00967770	+	0.136747i
$386$	4273.00			0.563446
$387$	−70.3576	+	216.539i	−0.00924155	+	0.0284426i
$388$	−15216.8	+	11055.7i	−1.99103	+	1.44657i
$389$	−755.199	−	548.684i	−0.0984321	−	0.0715151i	0.537481	−	0.843276i	$-0.319376\pi$
$389$	−755.199	−	548.684i	−0.0984321	−	0.0715151i	−0.635913	+	0.771761i	$0.719376\pi$
$390$	3133.26	+	9643.19i	0.406818	+	1.25206i
$391$	−735.955	−	2265.04i	−0.0951889	−	0.292961i
$392$	9401.84	+	6830.83i	1.21139	+	0.880126i
$393$	−81.5194	+	59.2273i	−0.0104634	+	0.00760210i
$394$	4227.05	−	13009.5i	0.540497	−	1.66348i
$395$	−2045.17			−0.260516
$396$	−202.183	+	324.166i	−0.0256568	+	0.0411363i
$397$	13382.7			1.69183			0.845916	−	0.533317i	$-0.179055\pi$
$397$	13382.7			1.69183			0.845916	+	0.533317i	$0.179055\pi$
$398$	4943.37	−	15214.1i	0.622584	−	1.91612i
$399$	201.845	−	146.649i	0.0253255	−	0.0184001i
$400$	−1143.07	−	830.489i	−0.142884	−	0.103811i
$401$	−4598.70	−	14153.3i	−0.572688	−	1.76255i	−0.643920	−	0.765093i	$-0.722693\pi$
$401$	−4598.70	−	14153.3i	−0.572688	−	1.76255i	0.0712323	−	0.997460i	$-0.477307\pi$
$402$	−373.959	−	1150.93i	−0.0463965	−	0.142794i
$403$	10564.9	+	7675.87i	1.30590	+	0.948790i
$404$	−21400.7	+	15548.5i	−2.63545	+	1.91477i
$405$	−1153.53	+	3550.21i	−0.141530	+	0.435583i
$406$	3332.91			0.407413
$407$	3912.83	+	972.087i	0.476540	+	0.118390i
$408$	18304.5			2.22110
$409$	−153.388	+	472.080i	−0.0185442	+	0.0570730i	−0.959900	−	0.280341i	$-0.909552\pi$
$409$	−153.388	+	472.080i	−0.0185442	+	0.0570730i	0.941356	+	0.337414i	$0.109552\pi$
$410$	−9474.21	+	6883.41i	−1.14121	+	0.829140i
$411$	−1917.17	−	1392.91i	−0.230091	−	0.167171i
$412$	9096.79	+	27997.0i	1.08778	+	3.34785i
$413$	1018.02	+	3133.15i	0.121292	+	0.373299i
$414$	−67.2779	−	48.8803i	−0.00798679	−	0.00580274i
$415$	4752.86	−	3453.16i	0.562190	−	0.408455i
$416$	590.402	−	1817.07i	0.0695838	−	0.214157i
$417$	2056.87			0.241548
$418$	−954.463	−	1135.55i	−0.111685	−	0.132874i
$419$	11470.0			1.33734			0.668672	−	0.743558i	$-0.266863\pi$
$419$	11470.0			1.33734			0.668672	+	0.743558i	$0.266863\pi$
$420$	723.652	−	2227.17i	0.0840729	−	0.258750i
$421$	1947.36	−	1414.84i	0.225436	−	0.163789i	−0.469334	−	0.883021i	$-0.655506\pi$
$421$	1947.36	−	1414.84i	0.225436	−	0.163789i	0.694770	+	0.719232i	$0.255506\pi$
$422$	−3183.78	−	2313.15i	−0.367260	−	0.266830i
$423$	−16.7232	−	51.4688i	−0.00192225	−	0.00591608i
$424$	−6716.49	−	20671.2i	−0.769297	−	2.36765i
$425$	1882.14	+	1367.46i	0.214817	+	0.156074i
$426$	7364.08	−	5350.32i	0.837537	−	0.608506i
$427$	777.200	−	2391.98i	0.0880828	−	0.271091i
$428$	19765.2			2.23221
$429$	9781.55	+	11637.3i	1.10083	+	1.30969i
$430$	−8297.62			−0.930574
$431$	2511.96	−	7731.02i	0.280735	−	0.864014i	−0.706910	−	0.707304i	$-0.749911\pi$
$431$	2511.96	−	7731.02i	0.280735	−	0.864014i	0.987645	−	0.156710i	$-0.0500888\pi$
$432$	−6332.98	+	4601.18i	−0.705314	+	0.512441i
$433$	−5426.17	−	3942.34i	−0.602229	−	0.437545i	0.244441	−	0.969664i	$-0.421396\pi$
$433$	−5426.17	−	3942.34i	−0.602229	−	0.437545i	−0.846669	+	0.532120i	$0.821396\pi$
$434$	−1407.41	−	4331.58i	−0.155664	−	0.479084i
$435$	980.395	+	3017.35i	0.108061	+	0.332576i
$436$	−9428.71	−	6850.36i	−1.03567	−	0.752460i
$437$	172.986	−	125.682i	0.0189361	−	0.0137579i
$438$	−3928.78	+	12091.5i	−0.428594	+	1.31908i
$439$	−9060.70			−0.985066			−0.492533	−	0.870294i	$-0.663929\pi$
$439$	−9060.70			−0.985066			−0.492533	+	0.870294i	$0.663929\pi$
$440$	−6620.19	−	1644.69i	−0.717285	−	0.178199i
$441$	−207.497			−0.0224054
$442$	11086.5	−	34120.8i	1.19306	−	3.67186i
$443$	15038.0	−	10925.7i	1.61281	−	1.17178i	0.759214	−	0.650840i	$-0.225583\pi$
$443$	15038.0	−	10925.7i	1.61281	−	1.17178i	0.853596	−	0.520935i	$-0.174417\pi$
$444$	−7375.79	−	5358.83i	−0.788377	−	0.572790i
$445$	1774.21	+	5460.45i	0.189001	+	0.581686i
$446$	−3843.61	−	11829.4i	−0.408072	−	1.25592i
$447$	−8408.04	−	6108.80i	−0.889679	−	0.646390i
$448$	−2615.70	+	1900.42i	−0.275848	+	0.200416i
$449$	−3247.52	+	9994.83i	−0.341336	+	1.05052i	0.622180	+	0.782874i	$0.286247\pi$
$449$	−3247.52	+	9994.83i	−0.341336	+	1.05052i	−0.963516	+	0.267650i	$0.913753\pi$
$450$	81.2346			0.00850985
$451$	−9291.84	+	14897.9i	−0.970146	+	1.55546i
$452$	−12530.4			−1.30394
$453$	759.376	−	2337.12i	0.0787607	−	0.242400i
$454$	11051.6	−	8029.48i	1.14246	−	0.830049i
$455$	−1819.25	−	1321.76i	−0.187445	−	0.136187i
$456$	507.838	+	1562.97i	0.0521529	+	0.160510i
$457$	2612.65	+	8040.90i	0.267428	+	0.823058i	0.991124	+	0.132939i	$0.0424415\pi$
$457$	2612.65	+	8040.90i	0.267428	+	0.823058i	−0.723697	+	0.690118i	$0.757558\pi$
$458$	−8192.79	−	5952.41i	−0.835861	−	0.607288i
$459$	10427.7	−	7576.16i	1.06040	−	0.770424i
$460$	620.189	−	1908.75i	0.0628619	−	0.193469i
$461$	2027.25			0.204812			0.102406	−	0.994743i	$-0.467346\pi$
$461$	2027.25			0.204812			0.102406	+	0.994743i	$0.467346\pi$
$462$	−374.289	−	5288.74i	−0.0376916	−	0.532585i
$463$	−15889.4			−1.59491			−0.797455	−	0.603379i	$-0.793821\pi$
$463$	−15889.4			−1.59491			−0.797455	+	0.603379i	$0.793821\pi$
$464$	−2106.78	+	6484.01i	−0.210787	+	0.648734i
$465$	3507.46	−	2548.32i	0.349795	−	0.254141i
$466$	12308.3	+	8942.48i	1.22354	+	0.888953i
$467$	−676.276	−	2081.36i	−0.0670114	−	0.206240i	0.911944	−	0.410315i	$-0.134581\pi$
$467$	−676.276	−	2081.36i	−0.0670114	−	0.206240i	−0.978955	+	0.204075i	$0.934581\pi$
$468$	−256.356	−	788.983i	−0.0253206	−	0.0779289i
$469$	217.130	+	157.754i	0.0213776	+	0.0155318i
$470$	1595.59	−	1159.26i	0.156593	−	0.113772i
$471$	−372.518	+	1146.49i	−0.0364432	+	0.112161i
$472$	−21699.9			−2.11615
$473$	−11530.9	+	4670.06i	−1.12091	+	0.453973i
$474$	10470.7			1.01463
$475$	−64.5450	+	198.649i	−0.00623479	+	0.0191887i
$476$	−6703.53	+	4870.40i	−0.645495	+	0.468980i
$477$	313.960	+	228.105i	0.0301368	+	0.0218957i
$478$	−6071.99	−	18687.7i	−0.581017	−	1.78819i
$479$	1410.35	+	4340.61i	0.134531	+	0.414045i	0.995517	−	0.0945847i	$-0.0301523\pi$
$479$	1410.35	+	4340.61i	0.134531	+	0.414045i	−0.860986	+	0.508629i	$0.830152\pi$
$480$	−513.156	−	372.830i	−0.0487964	−	0.0354526i
$481$	−7082.64	+	5145.84i	−0.671394	+	0.487796i
$482$	−7949.95	+	24467.4i	−0.751266	+	2.31216i
$483$	764.247			0.0719968
$484$	−20667.4	+	2940.03i	−1.94096	+	0.276111i
$485$	5996.25			0.561393
$486$	281.683	−	866.930i	0.0262909	−	0.0809151i
$487$	−15160.7	+	11014.9i	−1.41067	+	1.02491i	−0.417447	+	0.908701i	$0.637075\pi$
$487$	−15160.7	+	11014.9i	−1.41067	+	1.02491i	−0.993224	+	0.116212i	$0.962925\pi$
$488$	13402.7	+	9737.61i	1.24326	+	0.903280i
$489$	2109.58	+	6492.63i	0.195089	+	0.600423i
$490$	−2336.78	−	7191.88i	−0.215439	−	0.663053i
$491$	9822.65	+	7136.57i	0.902831	+	0.655945i	0.939192	−	0.343393i	$-0.111576\pi$
$491$	9822.65	+	7136.57i	0.902831	+	0.655945i	−0.0363604	+	0.999339i	$0.511576\pi$
$492$	32121.0	−	23337.3i	2.94335	−	2.13847i
$493$	3468.96	−	10676.4i	0.316905	−	0.975334i
$494$	3221.06			0.293365
$495$	112.889	−	45.7203i	0.0102504	−	0.00415147i
$496$	9316.52			0.843395
$497$	−623.825	+	1919.93i	−0.0563025	+	0.173281i
$498$	−24333.2	+	17679.1i	−2.18955	+	1.59080i
$499$	6955.00	+	5053.11i	0.623945	+	0.453323i	0.854297	−	0.519785i	$-0.173988\pi$
$499$	6955.00	+	5053.11i	0.623945	+	0.453323i	−0.230352	+	0.973107i	$0.573988\pi$
$500$	605.829	+	1864.55i	0.0541870	+	0.166770i
$501$	5521.78	+	16994.3i	0.492405	+	1.51547i
$502$	6208.00	+	4510.37i	0.551945	+	0.401012i
$503$	14179.0	−	10301.6i	1.25688	−	0.913174i	0.258277	−	0.966071i	$-0.416845\pi$
$503$	14179.0	−	10301.6i	1.25688	−	0.913174i	0.998600	+	0.0528966i	$0.0168454\pi$
$504$	−43.8032	+	134.812i	−0.00387133	+	0.0119147i
$505$	8433.00			0.743096
$506$	−320.776	−	4532.59i	−0.0281823	−	0.398217i
$507$	−21453.9			−1.87929
$508$	−3278.48	+	10090.1i	−0.286337	+	0.881254i
$509$	−10579.8	+	7686.65i	−0.921297	+	0.669361i	−0.943846	−	0.330384i	$-0.892822\pi$
$509$	−10579.8	+	7686.65i	−0.921297	+	0.669361i	0.0225495	+	0.999746i	$0.492822\pi$
$510$	−9636.00	−	7000.96i	−0.836645	−	0.607859i
$511$	−871.318	−	2681.64i	−0.0754302	−	0.232150i
$512$	−5645.94	−	17376.4i	−0.487339	−	1.49988i
$513$	936.210	+	680.196i	0.0805744	+	0.0585407i
$514$	−16434.2	+	11940.1i	−1.41027	+	1.02462i
$515$	2900.02	−	8925.33i	0.248136	−	0.763684i
$516$	28131.9			2.40008
$517$	1564.87	−	2509.01i	0.133120	−	0.213435i
$518$	3053.29			0.258984
$519$	−2640.23	+	8125.79i	−0.223301	+	0.687250i
$520$	11983.3	−	8706.34i	1.01058	−	0.734228i
$521$	4324.43	+	3141.88i	0.363640	+	0.264200i	0.754569	−	0.656221i	$-0.227846\pi$
$521$	4324.43	+	3141.88i	0.363640	+	0.264200i	−0.390929	+	0.920421i	$0.627846\pi$
$522$	−121.128	−	372.795i	−0.0101564	−	0.0312582i
$523$	−1635.65	−	5034.00i	−0.136753	−	0.420882i	0.859106	−	0.511798i	$-0.171021\pi$
$523$	−1635.65	−	5034.00i	−0.136753	−	0.420882i	−0.995859	+	0.0909160i	$0.971021\pi$
$524$	243.071	+	176.601i	0.0202645	+	0.0147230i
$525$	−603.973	+	438.812i	−0.0502087	+	0.0364787i
$526$	4817.08	−	14825.5i	0.399306	−	1.22894i
$527$	−15340.3			−1.26799
$528$	10525.6	+	2614.93i	0.867550	+	0.215531i
$529$	−11512.0			−0.946167
$530$	−4370.43	+	13450.8i	−0.358187	+	1.10239i
$531$	313.453	−	227.737i	0.0256171	−	0.0186119i
$532$	−601.851	−	437.270i	−0.0490480	−	0.0356355i
$533$	−11781.5	−	36259.7i	−0.957435	−	2.94668i
$534$	−9083.41	−	27955.9i	−0.736101	−	2.26548i
$535$	−5097.66	−	3703.67i	−0.411946	−	0.299296i
$536$	−1430.22	+	1039.11i	−0.115254	+	0.0837367i
$537$	−696.688	+	2144.19i	−0.0559857	+	0.172306i
$538$	−11956.7			−0.958161
$539$	−7295.07	−	8679.11i	−0.582970	−	0.693572i
$540$	10861.8			0.865590
$541$	−4177.35	+	12856.6i	−0.331975	+	1.02171i	0.636218	+	0.771509i	$0.280498\pi$
$541$	−4177.35	+	12856.6i	−0.331975	+	1.02171i	−0.968193	+	0.250204i	$0.919502\pi$
$542$	1226.57	−	891.157i	0.0972063	−	0.0706245i
$543$	5248.72	+	3813.42i	0.414814	+	0.301380i
$544$	693.542	+	2134.50i	0.0546606	+	0.168228i
$545$	1148.13	+	3533.57i	0.0902391	+	0.277727i
$546$	9313.99	+	6767.01i	0.730040	+	0.530405i
$547$	5609.79	−	4075.75i	0.438496	−	0.318586i	−0.346541	−	0.938035i	$-0.612644\pi$
$547$	5609.79	−	4075.75i	0.438496	−	0.318586i	0.785037	+	0.619449i	$0.212644\pi$
$548$	−2183.52	+	6720.19i	−0.170211	+	0.523854i
$549$	−295.794			−0.0229949
$550$	2856.00	+	3397.85i	0.221419	+	0.263427i
$551$	1007.87			0.0779247
$552$	−1555.61	+	4787.66i	−0.119947	+	0.369160i
$553$	−1878.67	+	1364.94i	−0.144465	+	0.104960i
$554$	17763.3	+	12905.8i	1.36226	+	0.989740i
$555$	898.144	+	2764.20i	0.0686920	+	0.211412i
$556$	−1895.23	−	5832.90i	−0.144560	−	0.444910i
$557$	14838.5	+	10780.8i	1.12877	+	0.820102i	0.985516	−	0.169583i	$-0.0542422\pi$
$557$	14838.5	+	10780.8i	1.12877	+	0.820102i	0.143258	+	0.989685i	$0.454242\pi$
$558$	−433.348	+	314.846i	−0.0328765	+	0.0238862i
$559$	8347.73	−	25691.7i	0.631613	−	1.94390i
$560$	−1604.27			−0.121059
$561$	−17331.1	−	4305.66i	−1.30431	−	0.324038i
$562$	31793.2			2.38633
$563$	−2086.86	+	6422.71i	−0.156218	+	0.480790i	−0.998282	−	0.0585874i	$-0.981340\pi$
$563$	−2086.86	+	6422.71i	−0.156218	+	0.480790i	0.842064	+	0.539377i	$0.181340\pi$
$564$	−5409.62	+	3930.32i	−0.403876	+	0.293433i
$565$	3231.72	+	2347.98i	0.240637	+	0.174833i
$566$	2175.75	+	6696.27i	0.161579	+	0.497288i
$567$	1309.76	+	4031.04i	0.0970105	+	0.298568i
$568$	−10757.7	−	7815.95i	−0.794691	−	0.577377i
$569$	−2166.02	+	1573.71i	−0.159586	+	0.115946i	−0.664712	−	0.747099i	$-0.731446\pi$
$569$	−2166.02	+	1573.71i	−0.159586	+	0.115946i	0.505126	+	0.863045i	$0.331446\pi$
$570$	330.451	−	1017.02i	0.0242826	−	0.0747340i
$571$	24529.5			1.79777			0.898886	−	0.438183i	$-0.144378\pi$
$571$	24529.5			1.79777			0.898886	+	0.438183i	$0.144378\pi$
$572$	23988.5	−	38461.4i	1.75351	−	2.81146i
$573$	8587.94			0.626120
$574$	−4108.95	+	12646.1i	−0.298788	+	0.919575i
$575$	−517.621	+	376.074i	−0.0375414	+	0.0272754i
$576$	307.629	+	223.506i	0.0222533	+	0.0161679i
$577$	−4273.27	−	13151.8i	−0.308317	−	0.948901i	−0.978419	−	0.206632i	$-0.933750\pi$
$577$	−4273.27	−	13151.8i	−0.308317	−	0.948901i	0.670102	−	0.742269i	$-0.266250\pi$
$578$	5634.76	+	17342.0i	0.405493	+	1.24798i
$579$	3736.36	+	2714.63i	0.268183	+	0.194846i
$580$	7653.28	−	5560.43i	0.547905	−	0.398077i
$581$	2061.31	−	6344.06i	0.147190	−	0.453005i
$582$	−30699.0			−2.18645
$583$	1496.94	+	21151.8i	0.106341	+	1.50261i
$584$	18572.8			1.31601
$585$	−81.7252	+	251.524i	−0.00577593	+	0.0177765i
$586$	5856.54	−	4255.02i	0.412852	−	0.299955i
$587$	−6783.84	−	4928.75i	−0.477000	−	0.346561i	0.323163	−	0.946343i	$-0.395254\pi$
$587$	−6783.84	−	4928.75i	−0.477000	−	0.346561i	−0.800163	+	0.599783i	$0.795254\pi$
$588$	7922.55	+	24383.1i	0.555647	+	1.71010i
$589$	−425.599	−	1309.86i	−0.0297734	−	0.0916330i
$590$	11423.4	+	8299.62i	0.797112	+	0.579136i
$591$	11961.1	−	8690.25i	0.832511	−	0.604855i
$592$	−1930.03	+	5940.03i	−0.133993	+	0.412388i
$593$	−12692.8			−0.878970			−0.439485	−	0.898250i	$-0.644839\pi$
$593$	−12692.8			−0.878970			−0.439485	+	0.898250i	$0.644839\pi$
$594$	22793.5	−	9231.44i	1.57446	−	0.637661i
$595$	2641.55			0.182005
$596$	−9576.14	+	29472.3i	−0.658144	+	2.02556i
$597$	13988.0	−	10162.9i	0.958948	−	0.696717i
$598$	7982.33	+	5799.50i	0.545856	+	0.396588i
$599$	7039.98	+	21666.8i	0.480210	+	1.47793i	0.838800	+	0.544439i	$0.183257\pi$
$599$	7039.98	+	21666.8i	0.480210	+	1.47793i	−0.358590	+	0.933495i	$0.616743\pi$
$600$	−1519.59	−	4676.81i	−0.103395	−	0.318216i
$601$	−21236.2	−	15429.0i	−1.44133	−	1.04719i	−0.987762	−	0.155969i	$-0.950150\pi$
$601$	−21236.2	−	15429.0i	−1.44133	−	1.04719i	−0.453571	−	0.891220i	$-0.649850\pi$
$602$	−7622.10	+	5537.78i	−0.516036	+	0.374922i
$603$	9.75401	−	30.0198i	0.000658730	−	0.00202736i
$604$	−7327.32			−0.493617
$605$	5881.26	+	3114.46i	0.395218	+	0.209290i
$606$	−43174.4			−2.89413
$607$	−2697.37	+	8301.64i	−0.180367	+	0.555113i	−0.999838	−	0.0180083i	$-0.994267\pi$
$607$	−2697.37	+	8301.64i	−0.180367	+	0.555113i	0.819471	+	0.573121i	$0.194267\pi$
$608$	−163.017	+	118.439i	−0.0108737	+	0.00790021i
$609$	2914.34	+	2117.39i	0.193916	+	0.140888i
$610$	−3331.17	−	10252.3i	−0.221107	−	0.680497i
$611$	1984.16	+	6106.63i	0.131376	+	0.404334i
$612$	788.394	+	572.802i	0.0520734	+	0.0378336i
$613$	−7496.32	+	5446.40i	−0.493921	+	0.358855i	−0.806690	−	0.590974i	$-0.798743\pi$
$613$	−7496.32	+	5446.40i	−0.493921	+	0.358855i	0.312769	+	0.949829i	$0.398743\pi$
$614$	−13568.3	+	41758.9i	−0.891809	+	2.74471i
$615$	−12657.4			−0.829910
$616$	−7178.89	+	2907.48i	−0.469555	+	0.190171i
$617$	−25207.7			−1.64477			−0.822387	−	0.568929i	$-0.807358\pi$
$617$	−25207.7			−1.64477			−0.822387	+	0.568929i	$0.807358\pi$
$618$	−14847.2	+	45695.0i	−0.966411	+	2.97431i
$619$	−4918.18	+	3573.27i	−0.319351	+	0.232022i	−0.735898	−	0.677092i	$-0.763240\pi$
$619$	−4918.18	+	3573.27i	−0.319351	+	0.232022i	0.416548	+	0.909114i	$0.363240\pi$
$620$	−10458.4	−	7598.45i	−0.677448	−	0.492195i
$621$	1095.40	+	3371.29i	0.0707839	+	0.217850i
$622$	−2442.13	−	7516.11i	−0.157429	−	0.484516i
$623$	5274.04	+	3831.82i	0.339165	+	0.246418i
$624$	−19052.4	+	13842.4i	−1.22229	+	0.888042i
$625$	193.136	−	594.410i	0.0123607	−	0.0380423i
$626$	14803.3			0.945141
$627$	−113.184	−	1599.30i	−0.00720916	−	0.101866i
$628$	3594.48			0.228400
$629$	3177.93	−	9780.66i	0.201450	−	0.620001i
$630$	74.6212	−	54.2154i	0.00471901	−	0.00342856i
$631$	−22756.6	−	16533.6i	−1.43570	−	1.04310i	−0.988919	−	0.148453i	$-0.952571\pi$
$631$	−22756.6	−	16533.6i	−1.43570	−	1.04310i	−0.446780	−	0.894644i	$-0.647429\pi$
$632$	−4726.71	−	14547.3i	−0.297498	−	0.915604i
$633$	−1314.39	−	4045.29i	−0.0825316	−	0.254006i
$634$	−21092.6	−	15324.7i	−1.32128	−	0.959970i
$635$	2736.28	−	1988.02i	0.171001	−	0.124240i
$636$	14817.3	−	45603.1i	0.923814	−	2.84321i
$637$	24618.9			1.53130
$638$	11334.6	−	18173.0i	0.703353	−	1.12771i
$639$	237.421			0.0146983
$640$	−3984.18	+	12262.1i	−0.246076	+	0.757344i
$641$	2309.39	−	1677.87i	0.142302	−	0.103388i	−0.514357	−	0.857576i	$-0.671969\pi$
$641$	2309.39	−	1677.87i	0.142302	−	0.103388i	0.656659	+	0.754188i	$0.271969\pi$
$642$	26098.5	+	18961.7i	1.60440	+	1.16566i
$643$	−3239.10	−	9968.92i	−0.198659	−	0.611409i	−0.999914	−	0.0130865i	$-0.995834\pi$
$643$	−3239.10	−	9968.92i	−0.198659	−	0.611409i	0.801256	−	0.598322i	$-0.204166\pi$
$644$	−704.186	−	2167.26i	−0.0430882	−	0.132612i
$645$	−7255.54	−	5271.46i	−0.442925	−	0.321804i
$646$	−3061.12	+	2224.03i	−0.186437	+	0.135454i
$647$	−421.036	+	1295.81i	−0.0255836	+	0.0787384i	−0.963033	−	0.269383i	$-0.913180\pi$
$647$	−421.036	+	1295.81i	−0.0255836	+	0.0787384i	0.937449	+	0.348121i	$0.113180\pi$
$648$	−27918.6			−1.69251
$649$	20545.9	+	5104.35i	1.24268	+	0.308726i
$650$	−9638.25			−0.581605
$651$	1521.18	−	4681.71i	0.0915818	−	0.281860i
$652$	16468.1	−	11964.8i	0.989172	−	0.718676i
$653$	7899.31	+	5739.18i	0.473390	+	0.343938i	0.798761	−	0.601648i	$-0.205489\pi$
$653$	7899.31	+	5739.18i	0.473390	+	0.343938i	−0.325371	+	0.945586i	$0.605489\pi$
$654$	−5878.05	−	18090.8i	−0.351453	−	1.08166i
$655$	−29.5985	−	91.0948i	−0.00176566	−	0.00543415i
$656$	−22004.9	−	15987.5i	−1.30968	−	0.951537i
$657$	−268.282	+	194.918i	−0.0159310	+	0.0115746i
$658$	692.004	−	2129.77i	0.0409987	−	0.126181i
$659$	−12471.8			−0.737225			−0.368613	−	0.929583i	$-0.620167\pi$
$659$	−12471.8			−0.737225			−0.368613	+	0.929583i	$0.620167\pi$
$660$	−9682.89	−	11520.0i	−0.571070	−	0.679414i
$661$	−14284.1			−0.840523			−0.420261	−	0.907403i	$-0.638062\pi$
$661$	−14284.1			−0.840523			−0.420261	+	0.907403i	$0.638062\pi$
$662$	11027.7	−	33939.7i	0.647436	−	1.99260i
$663$	31371.1	−	22792.4i	1.83763	−	1.33512i
$664$	35546.9	+	25826.4i	2.07754	+	1.50942i
$665$	73.2868	+	225.554i	0.00427360	+	0.0131528i
$666$	−110.966	−	341.518i	−0.00645623	−	0.0198702i
$667$	2497.66	+	1814.66i	0.144992	+	0.105343i
$668$	43104.8	−	31317.5i	2.49667	−	1.81394i
$669$	4154.30	−	12785.6i	0.240081	−	0.738894i
$670$	1150.34			0.0663305
$671$	−10399.4	−	12372.4i	−0.598307	−	0.711819i
$672$	−720.204			−0.0413429
$673$	−2471.53	+	7606.60i	−0.141561	+	0.435680i	−0.996553	−	0.0829614i	$-0.973562\pi$
$673$	−2471.53	+	7606.60i	−0.141561	+	0.435680i	0.854992	+	0.518642i	$0.173562\pi$
$674$	8055.98	−	5853.01i	0.460393	−	0.334495i
$675$	−2801.39	−	2035.33i	−0.159741	−	0.116059i
$676$	19767.9	+	60839.2i	1.12471	+	3.46149i
$677$	−3422.26	−	10532.6i	−0.194281	−	0.597936i	−0.999984	−	0.00561605i	$-0.998212\pi$
$677$	−3422.26	−	10532.6i	−0.194281	−	0.597936i	0.805703	−	0.592319i	$-0.201788\pi$
$678$	−16545.4	−	12021.0i	−0.937204	−	0.680918i
$679$	5508.08	−	4001.86i	0.311312	−	0.226181i
$680$	−5376.80	+	16548.1i	−0.303222	+	0.933221i
$681$	14764.8			0.830820
$682$	−28404.7	−	7056.75i	−1.59483	−	0.396212i
$683$	22433.9			1.25682			0.628411	−	0.777882i	$-0.283706\pi$
$683$	22433.9			1.25682			0.628411	+	0.777882i	$0.283706\pi$
$684$	−27.0367	+	83.2103i	−0.00151136	+	0.00465150i
$685$	1822.41	−	1324.06i	0.101650	−	0.0738534i
$686$	−14613.1	−	10617.1i	−0.813312	−	0.590906i
$687$	−3382.33	−	10409.7i	−0.187837	−	0.578102i
$688$	−5955.43	−	18328.9i	−0.330013	−	1.01567i
$689$	−37250.5	−	27064.0i	−2.05969	−	1.49646i
$690$	2650.06	−	1925.38i	0.146212	−	0.106229i
$691$	−9780.24	+	30100.5i	−0.538434	+	1.65713i	0.197677	+	0.980267i	$0.436660\pi$
$691$	−9780.24	+	30100.5i	−0.538434	+	1.65713i	−0.736110	+	0.676862i	$0.763340\pi$
$692$	25476.0			1.39950
$693$	73.1848	−	117.339i	0.00401163	−	0.00643197i
$694$	−15598.3			−0.853176
$695$	−604.190	+	1859.50i	−0.0329759	+	0.101489i
$696$	−19196.5	+	13947.1i	−1.04546	+	0.759574i
$697$	36232.6	+	26324.6i	1.96902	+	1.43058i
$698$	−7125.71	−	21930.7i	−0.386407	−	1.18924i
$699$	5081.36	+	15638.8i	0.274957	+	0.846230i
$700$	1800.90	+	1308.43i	0.0972393	+	0.0706485i
$701$	11367.7	−	8259.11i	0.612485	−	0.444996i	−0.237804	−	0.971313i	$-0.576427\pi$
$701$	11367.7	−	8259.11i	0.612485	−	0.444996i	0.850288	+	0.526317i	$0.176427\pi$
$702$	−16501.2	+	50785.5i	−0.887177	+	2.73045i
$703$	923.309			0.0495352
$704$	1466.75	+	20725.3i	0.0785230	+	1.10954i
$705$	2131.68			0.113877
$706$	−1627.18	+	5007.95i	−0.0867418	+	0.266964i
$707$	7746.46	−	5628.13i	0.412073	−	0.299389i
$708$	−38729.6	−	28138.7i	−2.05586	−	1.49367i
$709$	−4304.63	−	13248.3i	−0.228017	−	0.701763i	−0.997971	−	0.0636644i	$-0.979721\pi$
$709$	−4304.63	−	13248.3i	−0.228017	−	0.701763i	0.769955	−	0.638098i	$-0.220279\pi$
$710$	2673.79	+	8229.07i	0.141332	+	0.434974i
$711$	220.949	+	160.529i	0.0116543	+	0.00846736i
$712$	−34739.8	+	25239.9i	−1.82855	+	1.32852i
$713$	1303.69	−	4012.35i	0.0684764	−	0.210749i
$714$	−13523.9			−0.708851
$715$	−13393.9	+	5424.59i	−0.700565	+	0.283732i
$716$	6722.45			0.350879
$717$	6562.81	−	20198.2i	0.341831	−	1.05205i
$718$	16470.7	−	11966.7i	0.856101	−	0.621994i
$719$	5452.60	+	3961.54i	0.282820	+	0.205481i	0.720146	−	0.693822i	$-0.244075\pi$
$719$	5452.60	+	3961.54i	0.282820	+	0.205481i	−0.437326	+	0.899303i	$0.644075\pi$
$720$	58.3043	+	179.442i	0.00301788	+	0.00928808i
$721$	−3292.79	−	10134.2i	−0.170083	−	0.523462i
$722$	26730.3	+	19420.7i	1.37784	+	1.00106i
$723$	−22495.6	+	16344.0i	−1.15715	+	0.840721i
$724$	5977.91	−	18398.1i	0.306861	−	0.944420i
$725$	−3015.80			−0.154488
$726$	−30110.3	−	15945.1i	−1.53925	−	0.815120i
$727$	11175.6			0.570122			0.285061	−	0.958509i	$-0.407986\pi$
$727$	11175.6			0.570122			0.285061	+	0.958509i	$0.407986\pi$
$728$	5197.12	−	15995.1i	0.264585	−	0.814310i
$729$	−15510.9	+	11269.3i	−0.788033	+	0.572540i
$730$	−9777.23	−	7103.58i	−0.495715	−	0.360158i
$731$	9806.03	+	30179.8i	0.496155	+	1.52701i
$732$	11293.9	+	34759.0i	0.570265	+	1.75509i
$733$	3176.16	+	2307.62i	0.160047	+	0.116281i	0.664926	−	0.746909i	$-0.268463\pi$
$733$	3176.16	+	2307.62i	0.160047	+	0.116281i	−0.504879	+	0.863190i	$0.668463\pi$
$734$	11055.5	−	8032.31i	0.555950	−	0.403921i
$735$	2525.67	−	7773.22i	0.126749	−	0.390095i
$736$	−617.233			−0.0309124
$737$	1598.58	−	647.432i	0.0798976	−	0.0323588i
$738$	1563.83			0.0780016
$739$	10559.0	−	32497.3i	0.525601	−	1.61763i	−0.237524	−	0.971382i	$-0.576336\pi$
$739$	10559.0	−	32497.3i	0.525601	−	1.61763i	0.763125	−	0.646251i	$-0.223664\pi$
$740$	7011.20	−	5093.93i	0.348293	−	0.253050i
$741$	2816.53	+	2046.33i	0.139633	+	0.101449i
$742$	4962.35	+	15272.5i	0.245517	+	0.755623i
$743$	7406.04	+	22793.4i	0.365681	+	1.12545i	0.949553	+	0.313606i	$0.101537\pi$
$743$	7406.04	+	22793.4i	0.365681	+	1.12545i	−0.583872	+	0.811846i	$0.698463\pi$
$744$	26232.5	+	19059.0i	1.29265	+	0.939163i
$745$	7992.42	−	5806.83i	0.393046	−	0.285565i
$746$	4844.25	−	14909.1i	0.237749	−	0.731715i
$747$	−784.514			−0.0384255
$748$	3759.00	+	53114.9i	0.183747	+	2.59636i
$749$	−7154.46			−0.349023
$750$	−988.796	+	3043.20i	−0.0481410	+	0.148163i
$751$	6387.30	−	4640.65i	0.310354	−	0.225485i	−0.421694	−	0.906738i	$-0.638564\pi$
$751$	6387.30	−	4640.65i	0.310354	−	0.225485i	0.732048	+	0.681253i	$0.238564\pi$
$752$	3705.93	+	2692.52i	0.179709	+	0.130567i
$753$	2562.92	+	7887.85i	0.124034	+	0.381739i
$754$	14371.5	+	44231.0i	0.694138	+	2.13634i
$755$	1889.80	+	1373.02i	0.0910951	+	0.0661845i
$756$	9977.55	−	7249.12i	0.480000	−	0.348741i
$757$	−4135.04	+	12726.3i	−0.198534	+	0.611026i	0.801383	+	0.598152i	$0.204098\pi$
$757$	−4135.04	+	12726.3i	−0.198534	+	0.611026i	−0.999917	+	0.0128743i	$0.995902\pi$
$758$	−4608.52			−0.220830
$759$	2599.05	−	4167.14i	0.124295	−	0.199285i
$760$	−1562.16			−0.0745601
$761$	7562.39	−	23274.7i	0.360232	−	1.10868i	−0.592681	−	0.805437i	$-0.701931\pi$
$761$	7562.39	−	23274.7i	0.360232	−	1.10868i	0.952913	−	0.303243i	$-0.0980694\pi$
$762$	−14008.9	+	10178.1i	−0.665996	+	0.483875i
$763$	3412.94	+	2479.64i	0.161935	+	0.117653i
$764$	−7913.03	−	24353.8i	−0.374716	−	1.15326i
$765$	−96.0020	−	295.464i	−0.00453720	−	0.0139641i
$766$	43392.3	+	31526.4i	2.04677	+	1.48707i
$767$	−37190.3	+	27020.3i	−1.75080	+	1.27203i
$768$	12992.3	−	39986.2i	0.610442	−	1.87875i
$769$	−5952.47			−0.279131			−0.139565	−	0.990213i	$-0.544571\pi$
$769$	−5952.47			−0.279131			−0.139565	+	0.990213i	$0.544571\pi$
$770$	4891.20	+	1215.15i	0.228918	+	0.0568713i
$771$	−21955.8			−1.02558
$772$	4255.45	−	13096.9i	0.198390	−	0.610581i
$773$	−18761.8	+	13631.2i	−0.872980	+	0.634257i	−0.931385	−	0.364036i	$-0.881399\pi$
$773$	−18761.8	+	13631.2i	−0.872980	+	0.634257i	0.0584047	+	0.998293i	$0.481399\pi$
$774$	896.426	+	651.291i	0.0416297	+	0.0302457i
$775$	1273.51	+	3919.45i	0.0590267	+	0.181665i
$776$	13858.3	+	42651.3i	0.641085	+	1.97306i
$777$	2669.84	+	1939.75i	0.123269	+	0.0895600i
$778$	−3675.27	+	2670.24i	−0.169363	+	0.123050i
$779$	−1242.54	+	3824.14i	−0.0571484	+	0.175885i
$780$	32677.2			1.50004
$781$	8347.14	+	9930.78i	0.382438	+	0.454995i
$782$	−11590.4			−0.530013
$783$	−5163.21	+	15890.7i	−0.235655	+	0.725273i
$784$	14209.3	−	10323.6i	0.647287	−	0.470282i
$785$	−927.057	−	673.546i	−0.0421504	−	0.0306241i
$786$	151.535	+	466.378i	0.00687670	+	0.0211643i
$787$	−9368.90	−	28834.5i	−0.424352	−	1.30602i	−0.903613	−	0.428349i	$-0.859095\pi$
$787$	−9368.90	−	28834.5i	−0.424352	−	1.30602i	0.479261	−	0.877672i	$-0.340905\pi$
$788$	−35665.0	−	25912.2i	−1.61233	−	1.17142i
$789$	13630.7	−	9903.28i	0.615039	−	0.446852i
$790$	−3075.68	+	9465.96i	−0.138516	+	0.426308i
$791$	4535.66			0.203880
$792$	586.112	+	697.311i	0.0262962	+	0.0312852i
$793$	35095.2			1.57158
$794$	20125.8	−	61940.8i	0.899543	−	2.76851i
$795$	−12366.8	+	8985.01i	−0.551705	+	0.400837i
$796$	−41708.8	−	30303.2i	−1.85720	−	1.34933i
$797$	−2912.97	−	8965.20i	−0.129464	−	0.398449i	0.865224	−	0.501385i	$-0.167176\pi$
$797$	−2912.97	−	8965.20i	−0.129464	−	0.398449i	−0.994688	+	0.102937i	$0.967176\pi$
$798$	−375.206	−	1154.77i	−0.0166443	−	0.0512259i
$799$	−6102.07	−	4433.42i	−0.270183	−	0.196299i
$800$	487.790	−	354.400i	0.0215575	−	0.0156624i
$801$	236.923	−	729.175i	0.0104510	−	0.0321650i
$802$	−72423.6			−3.18874
$803$	−17585.1	−	4368.77i	−0.772807	−	0.191993i
$804$	−3900.07			−0.171076
$805$	−224.491	+	690.914i	−0.00982893	+	0.0302503i
$806$	51415.5	−	37355.6i	2.24694	−	1.63250i
$807$	−10455.1	−	7596.07i	−0.456056	−	0.331344i
$808$	19490.0	+	59984.0i	0.848583	+	2.61167i
$809$	−899.741	−	2769.12i	−0.0391016	−	0.120342i	0.929600	−	0.368569i	$-0.120152\pi$
$809$	−899.741	−	2769.12i	−0.0391016	−	0.120342i	−0.968702	+	0.248227i	$0.920152\pi$
$810$	14697.1	+	10678.1i	0.637537	+	0.463198i
$811$	−3614.34	+	2625.97i	−0.156494	+	0.113700i	−0.663277	−	0.748374i	$-0.730835\pi$
$811$	−3614.34	+	2625.97i	−0.156494	+	0.113700i	0.506783	+	0.862074i	$0.330835\pi$
$812$	3319.22	−	10215.5i	0.143450	−	0.441495i
$813$	1638.68			0.0706901
$814$	10383.6	−	16648.4i	0.447108	−	0.716862i
$815$	−6489.30			−0.278908
$816$	8548.68	−	26310.1i	0.366744	−	1.12872i
$817$	−2304.91	+	1674.61i	−0.0987008	+	0.0717103i
$818$	1954.32	+	1419.89i	0.0835343	+	0.0606912i
$819$	92.7939	+	285.590i	0.00395907	+	0.0121848i
$820$	11662.7	+	35894.0i	0.496680	+	1.52862i
$821$	−9230.00	−	6705.99i	−0.392362	−	0.285068i	0.374061	−	0.927404i	$-0.377965\pi$
$821$	−9230.00	−	6705.99i	−0.392362	−	0.285068i	−0.766423	+	0.642337i	$0.777965\pi$
$822$	−9330.17	+	6778.76i	−0.395897	+	0.287636i
$823$	−4427.87	+	13627.6i	−0.187540	+	0.577190i	−0.999983	−	0.00585144i	$-0.998137\pi$
$823$	−4427.87	+	13627.6i	−0.187540	+	0.577190i	0.812443	+	0.583041i	$0.198137\pi$
$824$	70188.3			2.96739
$825$	338.677	+	4785.54i	0.0142924	+	0.201953i
$826$	16032.6			0.675356
$827$	−6223.83	+	19155.0i	−0.261698	+	0.805422i	0.730738	+	0.682658i	$0.239176\pi$
$827$	−6223.83	+	19155.0i	−0.261698	+	0.805422i	−0.992436	+	0.122764i	$0.960824\pi$
$828$	−216.822	+	157.530i	−0.00910033	+	0.00661177i
$829$	6763.38	+	4913.88i	0.283356	+	0.205870i	0.720380	−	0.693580i	$-0.243968\pi$
$829$	6763.38	+	4913.88i	0.283356	+	0.205870i	−0.437024	+	0.899450i	$0.643968\pi$
$830$	−8835.03	−	27191.4i	−0.369480	−	1.13714i
$831$	7333.45	+	22570.0i	0.306130	+	0.942173i
$832$	−36499.3	−	26518.3i	−1.52090	−	1.10500i
$833$	−23396.5	+	16998.6i	−0.973158	+	0.707041i
$834$	3093.27	−	9520.10i	0.128431	−	0.395269i
$835$	−16985.6			−0.703964
$836$	−4431.03	+	1794.59i	−0.183314	+	0.0742429i
$837$	22832.5			0.942900
$838$	17249.4	−	53088.2i	0.711063	−	2.18843i
$839$	−30657.8	+	22274.2i	−1.26153	+	0.916555i	−0.998832	−	0.0483235i	$-0.984612\pi$
$839$	−30657.8	+	22274.2i	−1.26153	+	0.916555i	−0.262698	+	0.964878i	$0.584612\pi$
$840$	−4517.15	−	3281.90i	−0.185543	−	0.134805i
$841$	−3039.78	−	9355.48i	−0.124637	−	0.383594i
$842$	−3619.92	−	11141.0i	−0.148160	−	0.455990i
$843$	27800.4	+	20198.2i	1.13582	+	0.825222i
$844$	−10260.6	+	7454.75i	−0.418464	+	0.304032i
$845$	6301.91	−	19395.3i	0.256559	−	0.789607i
$846$	−263.370			−0.0107031
$847$	7481.03	−	1064.21i	0.303484	−	0.0431720i
$848$	−32848.7			−1.33022
$849$	−2351.62	+	7237.55i	−0.0950618	+	0.292570i
$850$	9159.68	−	6654.90i	0.369617	−	0.268542i
$851$	2288.12	+	1662.42i	0.0921689	+	0.0669646i
$852$	−9065.11	−	27899.5i	−0.364514	−	1.12186i
$853$	−10853.6	−	33404.1i	−0.435664	−	1.34084i	−0.892404	−	0.451236i	$-0.850983\pi$
$853$	−10853.6	−	33404.1i	−0.435664	−	1.34084i	0.456740	−	0.889600i	$-0.349017\pi$
$854$	−9902.29	−	7194.44i	−0.396779	−	0.288277i
$855$	22.5653	−	16.3946i	0.000902593	−	0.000655772i
$856$	14562.7	−	44819.4i	0.581476	−	1.78960i
$857$	7629.45			0.304104			0.152052	−	0.988373i	$-0.451412\pi$
$857$	7629.45			0.304104			0.152052	+	0.988373i	$0.451412\pi$
$858$	68572.8	−	27772.2i	2.72848	−	1.10505i
$859$	−38905.3			−1.54532			−0.772662	−	0.634818i	$-0.781075\pi$
$859$	−38905.3			−1.54532			−0.772662	+	0.634818i	$0.781075\pi$
$860$	−8263.53	+	25432.5i	−0.327656	+	1.00842i
$861$	−11626.9	+	8447.46i	−0.460214	+	0.334365i
$862$	−32004.8	−	23252.9i	−1.26460	−	0.918789i
$863$	3990.85	+	12282.6i	0.157416	+	0.484477i	0.998398	−	0.0565870i	$-0.0180218\pi$
$863$	3990.85	+	12282.6i	0.157416	+	0.484477i	−0.840982	+	0.541064i	$0.818022\pi$
$864$	−1032.27	−	3177.00i	−0.0406464	−	0.125097i
$865$	−6570.53	−	4773.77i	−0.258272	−	0.187645i
$866$	−26407.1	+	19185.9i	−1.03620	+	0.752844i
$867$	−6090.23	+	18743.8i	−0.238564	+	0.734225i
$868$	−14678.1			−0.573971
$869$	1053.46	+	14885.5i	0.0411235	+	0.581079i
$870$	15440.0			0.601683
$871$	−1157.29	+	3561.76i	−0.0450208	+	0.138560i
$872$	−22480.8	+	16333.2i	−0.873045	+	0.634304i
$873$	−647.799	−	470.653i	−0.0251142	−	0.0182465i
$874$	−321.562	−	989.665i	−0.0124451	−	0.0383020i
$875$	−219.294	−	674.916i	−0.00847254	−	0.0260758i
$876$	33148.4	+	24083.7i	1.27852	+	0.928896i
$877$	−2936.36	+	2133.39i	−0.113060	+	0.0821431i	−0.642879	−	0.765968i	$-0.722260\pi$
$877$	−2936.36	+	2133.39i	−0.113060	+	0.0821431i	0.529818	+	0.848111i	$0.322260\pi$
$878$	−13626.1	+	41936.9i	−0.523758	+	1.61196i
$879$	7824.23			0.300233
$880$	−5455.81	+	8747.47i	−0.208995	+	0.335088i
$881$	47324.3			1.80976			0.904878	−	0.425671i	$-0.139962\pi$
$881$	47324.3			1.80976			0.904878	+	0.425671i	$0.139962\pi$
$882$	−312.048	+	960.386i	−0.0119129	+	0.0366642i
$883$	−4342.41	+	3154.94i	−0.165497	+	0.120240i	−0.667451	−	0.744654i	$-0.732615\pi$
$883$	−4342.41	+	3154.94i	−0.165497	+	0.120240i	0.501954	+	0.864894i	$0.332615\pi$
$884$	−93540.7	−	67961.3i	−3.55895	−	2.58573i
$885$	4716.07	+	14514.6i	0.179129	+	0.551302i
$886$	−27953.8	−	86033.1i	−1.05996	−	3.26223i
$887$	36734.0	+	26688.8i	1.39054	+	1.01028i	0.995806	+	0.0914864i	$0.0291618\pi$
$887$	36734.0	+	26688.8i	1.39054	+	1.01028i	0.394730	+	0.918797i	$0.370838\pi$
$888$	−17586.0	+	12777.0i	−0.664581	+	0.482847i
$889$	1186.72	−	3652.35i	0.0447709	−	0.137791i
$890$	27941.5			1.05236
$891$	26433.9	+	6567.13i	0.993905	+	0.246922i
$892$	−40085.4			−1.50466
$893$	209.261	−	644.038i	0.00784170	−	0.0241343i
$894$	−40918.7	+	29729.2i	−1.53079	+	1.11219i
$895$	−1733.79	−	1259.67i	−0.0647534	−	0.0470461i
$896$	4523.79	+	13922.8i	0.168671	+	0.519116i
$897$	3295.44	+	10142.3i	0.122666	+	0.377527i
$898$	41376.6	+	30061.8i	1.53759	+	1.11712i
$899$	16087.9	−	11688.5i	0.596841	−	0.433631i
$900$	80.9008	−	248.987i	0.00299633	−	0.00922175i
$901$	54087.7			1.99991
$902$	54980.2	+	65411.1i	2.02953	+	2.41458i
$903$	−10183.0			−0.375270
$904$	−9232.21	+	28413.8i	−0.339667	+	1.04539i
$905$	−4989.27	+	3624.91i	−0.183258	+	0.133145i
$906$	−9675.19	−	7029.44i	−0.354787	−	0.257768i
$907$	1271.28	+	3912.60i	0.0465404	+	0.143237i	0.971626	−	0.236521i	$-0.0760073\pi$
$907$	1271.28	+	3912.60i	0.0465404	+	0.143237i	−0.925086	+	0.379758i	$0.876007\pi$
$908$	−13604.4	−	41870.2i	−0.497224	−	1.53030i
$909$	−911.052	−	661.918i	−0.0332428	−	0.0241523i
$910$	−8853.59	+	6432.51i	−0.322520	+	0.234325i
$911$	−1591.06	+	4896.78i	−0.0578641	+	0.178087i	−0.975811	−	0.218616i	$-0.929846\pi$
$911$	−1591.06	+	4896.78i	−0.0578641	+	0.178087i	0.917947	+	0.396703i	$0.129846\pi$
$912$	2483.71			0.0901798
$913$	−27581.6	−	32814.4i	−0.999799	−	1.18948i
$914$	41145.8			1.48904
$915$	3600.44	−	11081.0i	0.130084	−	0.400358i
$916$	−26403.5	+	19183.3i	−0.952398	+	0.691958i
$917$	−87.9849	−	63.9248i	−0.00316850	−	0.00230205i
$918$	−19383.9	−	59657.4i	−0.696910	−	2.14487i
$919$	−9491.84	−	29212.9i	−0.340704	−	1.04858i	−0.963844	−	0.266468i	$-0.914143\pi$
$919$	−9491.84	−	29212.9i	−0.340704	−	1.04858i	0.623140	−	0.782110i	$-0.285857\pi$
$920$	−3871.31	−	2812.67i	−0.138732	−	0.100795i
$921$	−38393.6	+	27894.6i	−1.37363	+	0.997999i
$922$	3048.72	−	9382.98i	0.108898	−	0.335154i
$923$	−28169.4			−1.00456
$924$	−16582.9	−	4119.80i	−0.590410	−	0.146679i
$925$	−2762.78			−0.0982052
$926$	−23895.6	+	73543.1i	−0.848011	+	2.60991i
$927$	−1013.86	+	736.614i	−0.0359219	+	0.0260988i
$928$	−2353.72	−	1710.08i	−0.0832594	−	0.0604915i
$929$	9054.46	+	27866.7i	0.319771	+	0.984153i	0.973746	+	0.227637i	$0.0731000\pi$
$929$	9054.46	+	27866.7i	0.319771	+	0.984153i	−0.653975	+	0.756516i	$0.726900\pi$
$930$	−6519.96	−	20066.4i	−0.229890	−	0.707530i
$931$	−2100.57	−	1526.15i	−0.0739455	−	0.0537245i
$932$	39666.8	−	28819.6i	1.39413	−	1.01289i
$933$	2639.54	−	8123.66i	0.0926202	−	0.285056i
$934$	−10650.5			−0.373121
$935$	8983.37	−	14403.3i	0.314211	−	0.503784i
$936$	−1977.97			−0.0690727
$937$	5485.86	−	16883.8i	0.191265	−	0.588653i	−0.808735	−	0.588173i	$-0.799847\pi$
$937$	5485.86	−	16883.8i	0.191265	−	0.588653i	1.00000		0.000479951i	$-0.000152773\pi$
$938$	1056.69	−	767.729i	0.0367826	−	0.0267241i
$939$	12944.2	+	9404.49i	0.449859	+	0.326841i
$940$	−1964.15	−	6045.04i	−0.0681527	−	0.209752i
$941$	−4039.07	−	12431.0i	−0.139926	−	0.430647i	0.856398	−	0.516316i	$-0.172697\pi$
$941$	−4039.07	−	12431.0i	−0.139926	−	0.430647i	−0.996324	+	0.0856694i	$0.972697\pi$
$942$	4746.25	+	3448.35i	0.164163	+	0.119271i
$943$	−9964.58	+	7239.69i	−0.344105	+	0.250007i
$944$	−10134.4	+	31190.6i	−0.349415	+	1.07539i
$945$	−3931.69			−0.135342
$946$	4274.09	+	60393.2i	0.146895	+	2.07564i
$947$	−22310.6			−0.765573			−0.382787	−	0.923837i	$-0.625036\pi$
$947$	−22310.6			−0.765573			−0.382787	+	0.923837i	$0.625036\pi$
$948$	10427.7	−	32093.0i	0.357252	−	1.09951i
$949$	31830.9	−	23126.5i	1.08880	−	0.791062i
$950$	822.367	+	597.484i	0.0280854	+	0.0204052i
$951$	−8707.90	−	26800.2i	−0.296922	−	0.913833i
$952$	6105.02	+	18789.3i	0.207841	+	0.639670i
$953$	31556.7	+	22927.3i	1.07263	+	0.779315i	0.976384	−	0.216042i	$-0.0693149\pi$
$953$	31556.7	+	22927.3i	1.07263	+	0.779315i	0.0962509	+	0.995357i	$0.469315\pi$
$954$	1527.93	−	1110.10i	0.0518537	−	0.0376739i
$955$	−2522.64	+	7763.89i	−0.0854772	+	0.263072i
$956$	−63325.5			−2.14236
$957$	21456.4	−	8689.91i	0.724750	−	0.293526i
$958$	22211.2			0.749072
$959$	790.375	−	2432.53i	0.0266137	−	0.0819086i
$960$	−12117.4	+	8803.83i	−0.407384	+	0.295982i
$961$	2117.03	+	1538.11i	0.0710626	+	0.0516300i
$962$	13165.8	+	40520.2i	0.441250	+	1.35803i
$963$	260.015	+	800.245i	0.00870080	+	0.0267783i
$964$	67076.4	+	48733.8i	2.24106	+	1.62823i
$965$	−3551.67	+	2580.44i	−0.118479	+	0.0860801i
$966$	1149.33	−	3537.27i	0.0382806	−	0.117815i
$967$	16332.2			0.543132			0.271566	−	0.962420i	$-0.412459\pi$
$967$	16332.2			0.543132			0.271566	+	0.962420i	$0.412459\pi$
$968$	−8560.64	+	49031.4i	−0.284245	+	1.62803i
$969$	−4089.61			−0.135580
$970$	9017.57	−	27753.2i	0.298492	−	0.918662i
$971$	13251.0	−	9627.45i	0.437947	−	0.318187i	−0.346872	−	0.937913i	$-0.612756\pi$
$971$	13251.0	−	9627.45i	0.437947	−	0.318187i	0.784819	+	0.619726i	$0.212756\pi$
$972$	−2376.65	−	1726.74i	−0.0784270	−	0.0569806i
$973$	686.020	+	2111.35i	0.0226031	+	0.0695651i
$974$	28182.0	+	86735.3i	0.927115	+	2.85337i
$975$	−8427.80	−	6123.16i	−0.276826	−	0.201126i
$976$	20255.8	−	14716.7i	0.664316	−	0.482654i
$977$	12909.4	−	39731.2i	0.422732	−	1.30104i	−0.482417	−	0.875942i	$-0.660241\pi$
$977$	12909.4	−	39731.2i	0.422732	−	1.30104i	0.905149	−	0.425094i	$-0.139759\pi$
$978$	33223.3			1.08626
$979$	38829.3	−	15726.0i	1.26761	−	0.513387i
$980$	−24370.6			−0.794377
$981$	153.318	−	471.864i	0.00498987	−	0.0153572i
$982$	47803.2	−	34731.0i	1.55342	−	1.12863i
$983$	−10650.7	−	7738.16i	−0.345578	−	0.251077i	0.401434	−	0.915888i	$-0.368512\pi$
$983$	−10650.7	−	7738.16i	−0.345578	−	0.251077i	−0.747012	+	0.664811i	$0.768512\pi$
$984$	−29253.2	−	90032.0i	−0.947720	−	2.91678i
$985$	4342.90	+	13366.1i	0.140484	+	0.432364i
$986$	−44198.0	−	32111.7i	−1.42754	−	1.03717i
$987$	1958.13	−	1422.67i	0.0631490	−	0.0458805i
$988$	3207.82	−	9872.67i	0.103294	−	0.317906i
$989$	−8727.10			−0.280592
$990$	−41.8437	−	591.255i	−0.00134331	−	0.0189811i
$991$	5827.02			0.186782			0.0933911	−	0.995629i	$-0.470229\pi$
$991$	5827.02			0.186782			0.0933911	+	0.995629i	$0.470229\pi$
$992$	−1228.56	+	3781.12i	−0.0393214	+	0.121019i
$993$	31204.5	−	22671.4i	0.997226	−	0.724527i
$994$	7948.14	+	5774.66i	0.253621	+	0.184267i
$995$	5078.84	+	15631.1i	0.161819	+	0.498029i
$996$	29954.0	+	92188.8i	0.952939	+	2.93285i
$997$	−9001.86	−	6540.24i	−0.285950	−	0.207755i	0.435559	−	0.900160i	$-0.356551\pi$
$997$	−9001.86	−	6540.24i	−0.285950	−	0.207755i	−0.721508	+	0.692406i	$0.756551\pi$
$998$	33847.4	−	24591.6i	1.07357	−	0.779992i
$999$	−4730.04	+	14557.6i	−0.149802	+	0.461042i

Display

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a_n

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a_n

instead) (See

a_n

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a_n

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.4.g.b.31.6	yes	24
11.4	even	5		605.4.a.p.1.12		12
11.5	even	5	inner	55.4.g.b.16.6	✓	24
11.7	odd	10		605.4.a.t.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.4.g.b.16.6	✓	24	11.5	even	5	inner
55.4.g.b.31.6	yes	24	1.1	even	1	trivial
605.4.a.p.1.12		12	11.4	even	5
605.4.a.t.1.1		12	11.7	odd	10

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	55.4.g.b.31.6

Level	$55$
Weight	$4$
Character	55.31
Analytic conductor	$3.245$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$