LMFDB - Embedded newform 150.4.g.b.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,4,Mod(31,150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("150.31"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.85028650086$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 66 x^{14} + 116 x^{13} - 15174 x^{12} + 66830 x^{11} - 253085 x^{10} + \cdots + 48733788520125 $ x^16 - 4x^15 + 66x^14 + 116x^13 - 15174x^12 + 66830x^11 - 253085x^10 - 2763760x^9 + 83790040x^8 - 245751650x^7 + 550471825x^6 + 10129042700x^5 - 118334390050x^4 + 286942998000x^3 + 664960189500x^2 - 7593598503000*x + 48733788520125
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.2
Root			$8.63398 + 2.08603i$ of defining polynomial
Character	$\chi$	$=$	150.31
Dual form			150.4.g.b.121.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.618034 + 1.90211i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-2.17298 - 10.9671i) q^{5} +(-4.85410 - 3.52671i) q^{6} +31.0680 q^{7} +(-6.47214 - 4.70228i) q^{8} +(2.78115 - 8.55951i) q^{9} +(19.5178 - 10.9113i) q^{10} +(3.19233 + 9.82498i) q^{11} +(3.70820 - 11.4127i) q^{12} +(5.33415 - 16.4168i) q^{13} +(19.2011 + 59.0949i) q^{14} +(24.6129 + 22.7861i) q^{15} +(4.94427 - 15.2169i) q^{16} +(51.8935 + 37.7028i) q^{17} +18.0000 q^{18} +(115.722 + 84.0771i) q^{19} +(32.8172 + 30.3814i) q^{20} +(-75.4037 + 54.7840i) q^{21} +(-16.7152 + 12.1443i) q^{22} +(-12.9904 - 39.9803i) q^{23} +24.0000 q^{24} +(-115.556 + 47.6628i) q^{25} +34.5233 q^{26} +(8.34346 + 25.6785i) q^{27} +(-100.538 + 73.0454i) q^{28} +(47.8512 - 34.7659i) q^{29} +(-28.1300 + 60.8991i) q^{30} +(71.2923 + 51.7969i) q^{31} +32.0000 q^{32} +(-25.0729 - 18.2165i) q^{33} +(-39.6431 + 122.009i) q^{34} +(-67.5104 - 340.728i) q^{35} +(11.1246 + 34.2380i) q^{36} +(26.0285 - 80.1076i) q^{37} +(-88.4039 + 272.079i) q^{38} +(16.0024 + 49.2505i) q^{39} +(-37.5067 + 81.1988i) q^{40} +(108.390 - 333.590i) q^{41} +(-150.807 - 109.568i) q^{42} +351.309 q^{43} +(-33.4305 - 24.2887i) q^{44} +(-99.9167 - 11.9016i) q^{45} +(68.0185 - 49.4183i) q^{46} +(-60.1750 + 43.7197i) q^{47} +(14.8328 + 45.6507i) q^{48} +622.223 q^{49} +(-162.078 - 190.344i) q^{50} -192.432 q^{51} +(21.3366 + 65.6673i) q^{52} +(-446.823 + 324.636i) q^{53} +(-43.6869 + 31.7404i) q^{54} +(100.815 - 56.3602i) q^{55} +(-201.077 - 146.091i) q^{56} -429.122 q^{57} +(95.7024 + 69.5319i) q^{58} +(201.457 - 620.020i) q^{59} +(-133.222 - 15.8688i) q^{60} +(4.14535 + 12.7581i) q^{61} +(-54.4625 + 167.618i) q^{62} +(86.4050 - 265.927i) q^{63} +(19.7771 + 60.8676i) q^{64} +(-191.637 - 22.8269i) q^{65} +(19.1540 - 58.9499i) q^{66} +(-664.765 - 482.980i) q^{67} -256.575 q^{68} +(102.028 + 74.1275i) q^{69} +(606.379 - 338.994i) q^{70} +(-114.085 + 82.8873i) q^{71} +(-58.2492 + 42.3205i) q^{72} +(180.182 + 554.544i) q^{73} +168.460 q^{74} +(196.414 - 319.447i) q^{75} -572.162 q^{76} +(99.1794 + 305.243i) q^{77} +(-83.7899 + 60.8769i) q^{78} +(347.955 - 252.804i) q^{79} +(-177.630 - 21.1584i) q^{80} +(-65.5304 - 47.6106i) q^{81} +701.514 q^{82} +(-961.871 - 698.840i) q^{83} +(115.207 - 354.570i) q^{84} +(300.728 - 651.051i) q^{85} +(217.121 + 668.229i) q^{86} +(-54.8326 + 168.757i) q^{87} +(25.5386 - 78.5998i) q^{88} +(423.539 + 1303.52i) q^{89} +(-39.1137 - 197.409i) q^{90} +(165.722 - 510.039i) q^{91} +(136.037 + 98.8367i) q^{92} -264.367 q^{93} +(-120.350 - 87.4393i) q^{94} +(670.623 - 1451.84i) q^{95} +(-77.6656 + 56.4274i) q^{96} +(-72.9866 + 53.0279i) q^{97} +(384.555 + 1183.54i) q^{98} +92.9753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$3$	−2.42705	+	1.76336i	−0.467086	+	0.339358i
$3$	−2.42705	+	1.76336i	−0.467086	+	0.339358i
$4$	−3.23607	+	2.35114i	−0.404508	+	0.293893i
$5$	−2.17298	−	10.9671i	−0.194358	−	0.980931i
$5$	−2.17298	−	10.9671i	−0.194358	−	0.980931i
$6$	−4.85410	−	3.52671i	−0.330280	−	0.239962i
$7$	31.0680			1.67752			0.838758	−	0.544504i	$-0.183282\pi$
$7$	31.0680			1.67752			0.838758	+	0.544504i	$0.183282\pi$
$8$	−6.47214	−	4.70228i	−0.286031	−	0.207813i
$9$	2.78115	−	8.55951i	0.103006	−	0.317019i
$10$	19.5178	−	10.9113i	0.617206	−	0.345046i
$11$	3.19233	+	9.82498i	0.0875021	+	0.269304i	0.985227	−	0.171252i	$-0.0547813\pi$
$11$	3.19233	+	9.82498i	0.0875021	+	0.269304i	−0.897725	+	0.440556i	$0.854781\pi$
$12$	3.70820	−	11.4127i	0.0892055	−	0.274546i
$13$	5.33415	−	16.4168i	0.113802	−	0.350247i	−0.877893	−	0.478856i	$-0.841051\pi$
$13$	5.33415	−	16.4168i	0.113802	−	0.350247i	0.991695	+	0.128610i	$0.0410514\pi$
$14$	19.2011	+	59.0949i	0.366551	+	1.12813i
$15$	24.6129	+	22.7861i	0.423668	+	0.392222i
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	51.8935	+	37.7028i	0.740354	+	0.537899i	0.892822	−	0.450410i	$-0.148722\pi$
$17$	51.8935	+	37.7028i	0.740354	+	0.537899i	−0.152468	+	0.988308i	$0.548722\pi$
$18$	18.0000			0.235702
$19$	115.722	+	84.0771i	1.39729	+	1.01519i	0.995021	+	0.0996684i	$0.0317782\pi$
$19$	115.722	+	84.0771i	1.39729	+	1.01519i	0.402269	+	0.915522i	$0.368222\pi$
$20$	32.8172	+	30.3814i	0.366908	+	0.339675i
$21$	−75.4037	+	54.7840i	−0.783545	+	0.569279i
$22$	−16.7152	+	12.1443i	−0.161987	+	0.117690i
$23$	−12.9904	−	39.9803i	−0.117769	−	0.362455i	0.874746	−	0.484582i	$-0.161028\pi$
$23$	−12.9904	−	39.9803i	−0.117769	−	0.362455i	−0.992514	+	0.122127i	$0.961028\pi$
$24$	24.0000			0.204124
$25$	−115.556	+	47.6628i	−0.924450	+	0.381303i
$26$	34.5233			0.260407
$27$	8.34346	+	25.6785i	0.0594703	+	0.183031i
$28$	−100.538	+	73.0454i	−0.678570	+	0.493010i
$29$	47.8512	−	34.7659i	0.306405	−	0.222616i	−0.423947	−	0.905687i	$-0.639356\pi$
$29$	47.8512	−	34.7659i	0.306405	−	0.222616i	0.730352	+	0.683071i	$0.239356\pi$
$30$	−28.1300	+	60.8991i	−0.171194	+	0.370620i
$31$	71.2923	+	51.7969i	0.413048	+	0.300097i	0.774835	−	0.632164i	$-0.217833\pi$
$31$	71.2923	+	51.7969i	0.413048	+	0.300097i	−0.361787	+	0.932261i	$0.617833\pi$
$32$	32.0000			0.176777
$33$	−25.0729	−	18.2165i	−0.132261	−	0.0960936i
$34$	−39.6431	+	122.009i	−0.199963	+	0.615422i
$35$	−67.5104	−	340.728i	−0.326038	−	1.64553i
$36$	11.1246	+	34.2380i	0.0515028	+	0.158509i
$37$	26.0285	−	80.1076i	0.115650	−	0.355935i	−0.876432	−	0.481526i	$-0.840083\pi$
$37$	26.0285	−	80.1076i	0.115650	−	0.355935i	0.992082	+	0.125591i	$0.0400827\pi$
$38$	−88.4039	+	272.079i	−0.377395	+	1.16150i
$39$	16.0024	+	49.2505i	0.0657037	+	0.202215i
$40$	−37.5067	+	81.1988i	−0.148258	+	0.320966i
$41$	108.390	−	333.590i	0.412870	−	1.27068i	−0.501272	−	0.865290i	$-0.667135\pi$
$41$	108.390	−	333.590i	0.412870	−	1.27068i	0.914142	−	0.405393i	$-0.132865\pi$
$42$	−150.807	−	109.568i	−0.554050	−	0.402541i
$43$	351.309			1.24591			0.622954	−	0.782258i	$-0.285932\pi$
$43$	351.309			1.24591			0.622954	+	0.782258i	$0.285932\pi$
$44$	−33.4305	−	24.2887i	−0.114542	−	0.0832195i
$45$	−99.9167	−	11.9016i	−0.330993	−	0.0394264i
$46$	68.0185	−	49.4183i	0.218017	−	0.158399i
$47$	−60.1750	+	43.7197i	−0.186754	+	0.135684i	−0.677234	−	0.735768i	$-0.736821\pi$
$47$	−60.1750	+	43.7197i	−0.186754	+	0.135684i	0.490480	+	0.871452i	$0.336821\pi$
$48$	14.8328	+	45.6507i	0.0446028	+	0.137273i
$49$	622.223			1.81406
$50$	−162.078	−	190.344i	−0.458425	−	0.538374i
$51$	−192.432			−0.528349
$52$	21.3366	+	65.6673i	0.0569010	+	0.175123i
$53$	−446.823	+	324.636i	−1.15804	+	0.841362i	−0.989528	−	0.144338i	$-0.953895\pi$
$53$	−446.823	+	324.636i	−1.15804	+	0.841362i	−0.168507	+	0.985700i	$0.553895\pi$
$54$	−43.6869	+	31.7404i	−0.110093	+	0.0799874i
$55$	100.815	−	56.3602i	0.247162	−	0.138175i
$56$	−201.077	−	146.091i	−0.479821	−	0.348611i
$57$	−429.122			−0.997167
$58$	95.7024	+	69.5319i	0.216661	+	0.157413i
$59$	201.457	−	620.020i	0.444533	−	1.36813i	−0.438462	−	0.898750i	$-0.644477\pi$
$59$	201.457	−	620.020i	0.444533	−	1.36813i	0.882995	−	0.469382i	$-0.155523\pi$
$60$	−133.222	−	15.8688i	−0.286649	−	0.0341443i
$61$	4.14535	+	12.7581i	0.00870096	+	0.0267788i	0.955313	−	0.295597i	$-0.0955185\pi$
$61$	4.14535	+	12.7581i	0.00870096	+	0.0267788i	−0.946612	+	0.322376i	$0.895519\pi$
$62$	−54.4625	+	167.618i	−0.111560	+	0.343348i
$63$	86.4050	−	265.927i	0.172794	−	0.531804i
$64$	19.7771	+	60.8676i	0.0386271	+	0.118882i
$65$	−191.637	−	22.8269i	−0.365686	−	0.0435588i
$66$	19.1540	−	58.9499i	0.0357226	−	0.109943i
$67$	−664.765	−	482.980i	−1.21215	−	0.880677i	−0.216724	−	0.976233i	$-0.569537\pi$
$67$	−664.765	−	482.980i	−1.21215	−	0.880677i	−0.995424	+	0.0955558i	$0.969537\pi$
$68$	−256.575			−0.457564
$69$	102.028	+	74.1275i	0.178010	+	0.129332i
$70$	606.379	−	338.994i	1.03537	−	0.578821i
$71$	−114.085	+	82.8873i	−0.190695	+	0.138548i	−0.679036	−	0.734105i	$-0.737602\pi$
$71$	−114.085	+	82.8873i	−0.190695	+	0.138548i	0.488341	+	0.872653i	$0.337602\pi$
$72$	−58.2492	+	42.3205i	−0.0953436	+	0.0692712i
$73$	180.182	+	554.544i	0.288887	+	0.889103i	0.985207	+	0.171371i	$0.0548197\pi$
$73$	180.182	+	554.544i	0.288887	+	0.889103i	−0.696320	+	0.717732i	$0.745180\pi$
$74$	168.460			0.264636
$75$	196.414	−	319.447i	0.302400	−	0.491821i
$76$	−572.162			−0.863572
$77$	99.1794	+	305.243i	0.146786	+	0.451762i
$78$	−83.7899	+	60.8769i	−0.121633	+	0.0883712i
$79$	347.955	−	252.804i	0.495545	−	0.360034i	−0.311768	−	0.950158i	$-0.600921\pi$
$79$	347.955	−	252.804i	0.495545	−	0.360034i	0.807313	+	0.590124i	$0.200921\pi$
$80$	−177.630	−	21.1584i	−0.248245	−	0.0295698i
$81$	−65.5304	−	47.6106i	−0.0898908	−	0.0653095i
$82$	701.514			0.944748
$83$	−961.871	−	698.840i	−1.27204	−	0.924189i	−0.272755	−	0.962084i	$-0.587935\pi$
$83$	−961.871	−	698.840i	−1.27204	−	0.924189i	−0.999282	+	0.0378949i	$0.987935\pi$
$84$	115.207	−	354.570i	0.149644	−	0.460556i
$85$	300.728	−	651.051i	0.383748	−	0.830781i
$86$	217.121	+	668.229i	0.272241	+	0.837872i
$87$	−54.8326	+	168.757i	−0.0675709	+	0.207962i
$88$	25.5386	−	78.5998i	0.0309367	−	0.0952133i
$89$	423.539	+	1303.52i	0.504439	+	1.55250i	0.801711	+	0.597712i	$0.203923\pi$
$89$	423.539	+	1303.52i	0.504439	+	1.55250i	−0.297272	+	0.954793i	$0.596077\pi$
$90$	−39.1137	−	197.409i	−0.0458105	−	0.231208i
$91$	165.722	−	510.039i	0.190905	−	0.587545i
$92$	136.037	+	98.8367i	0.154161	+	0.112005i
$93$	−264.367			−0.294769
$94$	−120.350	−	87.4393i	−0.132055	−	0.0959434i
$95$	670.623	−	1451.84i	0.724257	−	1.56795i
$96$	−77.6656	+	56.4274i	−0.0825700	+	0.0599906i
$97$	−72.9866	+	53.0279i	−0.0763986	+	0.0555068i	−0.625329	−	0.780361i	$-0.715035\pi$
$97$	−72.9866	+	53.0279i	−0.0763986	+	0.0555068i	0.548930	+	0.835868i	$0.315035\pi$
$98$	384.555	+	1183.54i	0.396387	+	1.21995i
$99$	92.9753			0.0943876
$100$	261.886	−	425.929i	0.261886	−	0.425929i
$101$	−1429.95			−1.40877			−0.704383	−	0.709820i	$-0.748776\pi$
$101$	−1429.95			−1.40877			−0.704383	+	0.709820i	$0.748776\pi$
$102$	−118.929	−	366.027i	−0.115449	−	0.355314i
$103$	−1275.13	+	926.434i	−1.21983	+	0.886255i	−0.996086	−	0.0883935i	$-0.971827\pi$
$103$	−1275.13	+	926.434i	−1.21983	+	0.886255i	−0.223740	+	0.974649i	$0.571827\pi$
$104$	−111.720	+	81.1692i	−0.105337	+	0.0765317i
$105$	764.675	+	707.918i	0.710711	+	0.657960i
$106$	−893.646	−	649.272i	−0.818855	−	0.594933i
$107$	−1797.42			−1.62395			−0.811976	−	0.583691i	$-0.801608\pi$
$107$	−1797.42			−1.62395			−0.811976	+	0.583691i	$0.801608\pi$
$108$	−87.3738	−	63.4808i	−0.0778477	−	0.0565597i
$109$	−462.243	+	1422.64i	−0.406191	+	1.25013i	0.513706	+	0.857967i	$0.328272\pi$
$109$	−462.243	+	1422.64i	−0.406191	+	1.25013i	−0.919897	+	0.392161i	$0.871728\pi$
$110$	169.511	+	156.929i	0.146929	+	0.136024i
$111$	78.0856	+	240.323i	0.0667708	+	0.205499i
$112$	153.609	−	472.759i	0.129595	−	0.398853i
$113$	179.033	−	551.007i	0.149044	−	0.458711i	−0.848465	−	0.529252i	$-0.822473\pi$
$113$	179.033	−	551.007i	0.149044	−	0.458711i	0.997509	+	0.0705408i	$0.0224725\pi$
$114$	−265.212	−	816.238i	−0.217889	−	0.670594i
$115$	−410.241	+	229.344i	−0.332654	+	0.185969i
$116$	−73.1101	+	225.010i	−0.0585182	+	0.180100i
$117$	−125.685	−	91.3154i	−0.0993126	−	0.0721548i
$118$	1303.86			1.01720
$119$	1612.23	+	1171.35i	1.24196	+	0.902334i
$120$	−52.1516	−	263.211i	−0.0396731	−	0.200232i
$121$	990.462	−	719.613i	0.744149	−	0.540656i
$122$	−21.7054	+	15.7699i	−0.0161075	+	0.0117028i
$123$	325.170	+	1000.77i	0.238371	+	0.733629i
$124$	−352.489			−0.255278
$125$	773.827	+	1163.75i	0.553706	+	0.832713i
$126$	559.225			0.395395
$127$	781.261	+	2404.47i	0.545872	+	1.68002i	0.718908	+	0.695105i	$0.244642\pi$
$127$	781.261	+	2404.47i	0.545872	+	1.68002i	−0.173037	+	0.984915i	$0.555358\pi$
$128$	−103.554	+	75.2365i	−0.0715077	+	0.0519534i
$129$	−852.644	+	619.482i	−0.581947	+	0.422809i
$130$	−75.0187	−	378.622i	−0.0506121	−	0.255441i
$131$	−492.954	−	358.152i	−0.328775	−	0.238869i	0.411135	−	0.911574i	$-0.365132\pi$
$131$	−492.954	−	358.152i	−0.328775	−	0.238869i	−0.739911	+	0.672705i	$0.765132\pi$
$132$	123.967			0.0817421
$133$	3595.26	+	2612.11i	2.34398	+	1.70300i
$134$	507.835	−	1562.96i	0.327390	−	1.00760i
$135$	263.490	−	147.303i	0.167982	−	0.0939097i
$136$	−158.572	−	488.035i	−0.0999814	−	0.307711i
$137$	137.012	−	421.679i	0.0854431	−	0.262967i	−0.899202	−	0.437533i	$-0.855852\pi$
$137$	137.012	−	421.679i	0.0854431	−	0.262967i	0.984645	+	0.174566i	$0.0558523\pi$
$138$	−77.9423	+	239.882i	−0.0480789	+	0.147972i
$139$	−402.137	−	1237.65i	−0.245387	−	0.755224i	−0.995573	−	0.0939965i	$-0.970036\pi$
$139$	−402.137	−	1237.65i	−0.245387	−	0.755224i	0.750185	−	0.661228i	$-0.229964\pi$
$140$	1019.57	+	943.891i	0.615494	+	0.569810i
$141$	68.9544	−	212.220i	0.0411844	−	0.126753i
$142$	−228.169	−	165.775i	−0.134842	−	0.0979683i
$143$	178.323			0.104281
$144$	−116.498	−	84.6411i	−0.0674181	−	0.0489821i
$145$	−485.263	−	449.245i	−0.277923	−	0.257295i
$146$	−943.447	+	685.455i	−0.534796	+	0.388552i
$147$	−1510.17	+	1097.20i	−0.847324	+	0.615617i
$148$	104.114	+	320.430i	0.0578252	+	0.177968i
$149$	1291.79			0.710251			0.355125	−	0.934819i	$-0.384438\pi$
$149$	1291.79			0.710251			0.355125	+	0.934819i	$0.384438\pi$
$150$	729.015	+	176.173i	0.396826	+	0.0958966i
$151$	2025.45			1.09158			0.545790	−	0.837922i	$-0.316230\pi$
$151$	2025.45			1.09158			0.545790	+	0.837922i	$0.316230\pi$
$152$	−353.616	−	1088.32i	−0.188697	−	0.580751i
$153$	467.041	−	339.325i	0.246785	−	0.179300i
$154$	−519.310	+	377.301i	−0.271735	+	0.197427i
$155$	413.147	−	894.427i	0.214095	−	0.463497i
$156$	−167.580	−	121.754i	−0.0860072	−	0.0624879i
$157$	−2945.18			−1.49714			−0.748571	−	0.663055i	$-0.769260\pi$
$157$	−2945.18			−1.49714			−0.748571	+	0.663055i	$0.769260\pi$
$158$	695.911	+	505.609i	0.350403	+	0.254583i
$159$	512.014	−	1575.82i	0.255379	−	0.785977i
$160$	−69.5355	−	350.948i	−0.0343579	−	0.173406i
$161$	−403.586	−	1242.11i	−0.197559	−	0.608024i
$162$	50.0608	−	154.071i	0.0242787	−	0.0747221i
$163$	312.846	−	962.840i	0.150331	−	0.462672i	−0.847327	−	0.531072i	$-0.821789\pi$
$163$	312.846	−	962.840i	0.150331	−	0.462672i	0.997658	+	0.0684001i	$0.0217894\pi$
$164$	433.560	+	1334.36i	0.206435	+	0.635341i
$165$	−145.300	+	314.562i	−0.0685551	+	0.148416i
$166$	734.804	−	2261.49i	0.343565	−	1.05739i
$167$	−108.852	−	79.0857i	−0.0504385	−	0.0366457i	0.562280	−	0.826947i	$-0.309924\pi$
$167$	−108.852	−	79.0857i	−0.0504385	−	0.0366457i	−0.612719	+	0.790301i	$0.709924\pi$
$168$	745.633			0.342422
$169$	1536.35	+	1116.22i	0.699295	+	0.508068i
$170$	1424.23	+	169.648i	0.642551	+	0.0765376i
$171$	1041.50	−	756.694i	0.465763	−	0.338397i
$172$	−1136.86	+	825.976i	−0.503981	+	0.366163i
$173$	−232.794	−	716.466i	−0.102306	−	0.314867i	0.886782	−	0.462187i	$-0.152935\pi$
$173$	−232.794	−	716.466i	−0.102306	−	0.314867i	−0.989089	+	0.147320i	$0.952935\pi$
$174$	−354.884			−0.154619
$175$	−3590.11	+	1480.79i	−1.55078	+	0.639642i
$176$	165.289			0.0707907
$177$	604.370	+	1860.06i	0.256651	+	0.789891i
$178$	−2217.68	+	1611.24i	−0.933833	+	0.678469i
$179$	1365.16	−	991.847i	0.570039	−	0.414157i	−0.265081	−	0.964226i	$-0.585399\pi$
$179$	1365.16	−	991.847i	0.570039	−	0.414157i	0.835119	+	0.550069i	$0.185399\pi$
$180$	351.320	−	196.404i	0.145477	−	0.0813282i
$181$	−2819.67	−	2048.61i	−1.15792	−	0.841280i	−0.168409	−	0.985717i	$-0.553863\pi$
$181$	−2819.67	−	2048.61i	−1.15792	−	0.841280i	−0.989514	+	0.144437i	$0.953863\pi$
$182$	1072.57			0.436837
$183$	−32.5580	−	23.6548i	−0.0131517	−	0.00955526i
$184$	−103.923	+	319.842i	−0.0416375	+	0.128147i
$185$	−935.110	−	111.386i	−0.371625	−	0.0442663i
$186$	−163.387	−	502.855i	−0.0644094	−	0.198232i
$187$	−204.768	+	630.212i	−0.0800756	+	0.246447i
$188$	91.9392	−	282.960i	0.0356668	−	0.109771i
$189$	259.215	+	797.782i	0.0997625	+	0.307037i
$190$	3176.03	+	378.314i	1.21270	+	0.144451i
$191$	−907.862	+	2794.11i	−0.343930	+	1.05851i	0.618225	+	0.786001i	$0.287852\pi$
$191$	−907.862	+	2794.11i	−0.343930	+	1.05851i	−0.962154	+	0.272505i	$0.912148\pi$
$192$	−155.331	−	112.855i	−0.0583858	−	0.0424197i
$193$	239.871			0.0894627			0.0447314	−	0.998999i	$-0.485757\pi$
$193$	239.871			0.0894627			0.0447314	+	0.998999i	$0.485757\pi$
$194$	−145.973	−	106.056i	−0.0540220	−	0.0392493i
$195$	505.364	−	282.522i	0.185589	−	0.103753i
$196$	−2013.56	+	1462.94i	−0.733804	+	0.533140i
$197$	94.4095	−	68.5925i	0.0341442	−	0.0248072i	−0.570582	−	0.821240i	$-0.693282\pi$
$197$	94.4095	−	68.5925i	0.0341442	−	0.0248072i	0.604726	+	0.796433i	$0.293282\pi$
$198$	57.4619	+	176.850i	0.0206244	+	0.0634755i
$199$	−3252.65			−1.15866			−0.579332	−	0.815092i	$-0.696686\pi$
$199$	−3252.65			−1.15866			−0.579332	+	0.815092i	$0.696686\pi$
$200$	972.020	+	234.898i	0.343661	+	0.0830489i
$201$	2465.08			0.865042
$202$	−883.758	−	2719.93i	−0.307827	−	0.947393i
$203$	1486.64	−	1080.11i	0.514000	−	0.373443i
$204$	622.722	−	452.434i	0.213722	−	0.155278i
$205$	−3894.06	−	463.842i	−1.32670	−	0.158030i
$206$	−2550.26	−	1852.87i	−0.862547	−	0.626677i
$207$	−378.340			−0.127036
$208$	−223.440	−	162.338i	−0.0744844	−	0.0541161i
$209$	−456.632	+	1405.37i	−0.151129	+	0.465127i
$210$	−873.946	+	1892.02i	−0.287181	+	0.621721i
$211$	−1686.50	−	5190.51i	−0.550253	−	1.69350i	−0.708161	−	0.706051i	$-0.750475\pi$
$211$	−1686.50	−	5190.51i	−0.550253	−	1.69350i	0.157908	−	0.987454i	$-0.449525\pi$
$212$	682.685	−	2101.09i	0.221165	−	0.680676i
$213$	130.729	−	402.344i	0.0420537	−	0.129428i
$214$	−1110.86	−	3418.89i	−0.354846	−	1.09211i
$215$	−763.388	−	3852.85i	−0.242152	−	1.22215i
$216$	66.7477	−	205.428i	0.0210259	−	0.0647112i
$217$	2214.91	+	1609.23i	0.692895	+	0.503417i
$218$	−2991.70			−0.929465
$219$	−1415.17	−	1028.18i	−0.436659	−	0.317252i
$220$	−193.733	+	419.416i	−0.0593705	+	0.128532i
$221$	895.768	−	650.814i	0.272651	−	0.198093i
$222$	−408.861	+	297.055i	−0.123608	+	0.0898065i
$223$	−1793.19	−	5518.87i	−0.538480	−	1.65727i	−0.736008	−	0.676972i	$-0.763292\pi$
$223$	−1793.19	−	5518.87i	−0.538480	−	1.65727i	0.197529	−	0.980297i	$-0.436708\pi$
$224$	994.177			0.296546
$225$	86.5908	+	1121.66i	0.0256565	+	0.332344i
$226$	1158.73			0.341050
$227$	1423.25	+	4380.31i	0.416143	+	1.28076i	0.911225	+	0.411909i	$0.135138\pi$
$227$	1423.25	+	4380.31i	0.416143	+	1.28076i	−0.495082	+	0.868846i	$0.664862\pi$
$228$	1388.67	−	1008.93i	0.403363	−	0.293060i
$229$	−4126.43	+	2998.03i	−1.19075	+	0.865132i	−0.993344	−	0.115190i	$-0.963252\pi$
$229$	−4126.43	+	2998.03i	−1.19075	+	0.865132i	−0.197408	+	0.980321i	$0.563252\pi$
$230$	−689.781	−	638.583i	−0.197751	−	0.183074i
$231$	−778.965	−	565.951i	−0.221871	−	0.161199i
$232$	−473.179			−0.133904
$233$	−4619.55	−	3356.30i	−1.29887	−	0.943684i	−0.298926	−	0.954276i	$-0.596628\pi$
$233$	−4619.55	−	3356.30i	−1.29887	−	0.943684i	−0.999944	+	0.0105926i	$0.996628\pi$
$234$	96.0147	−	295.503i	0.0268234	−	0.0825540i
$235$	610.239	+	564.945i	0.169394	+	0.156821i
$236$	805.827	+	2480.08i	0.222266	+	0.684066i
$237$	−398.721	+	1227.14i	−0.109282	+	0.336334i
$238$	−1231.63	+	3790.58i	−0.335441	+	1.03238i
$239$	325.692	+	1002.38i	0.0881476	+	0.271291i	0.985407	−	0.170213i	$-0.0544454\pi$
$239$	325.692	+	1002.38i	0.0881476	+	0.271291i	−0.897260	+	0.441503i	$0.854445\pi$
$240$	468.426	−	261.872i	0.125987	−	0.0704323i
$241$	−1132.05	+	3484.10i	−0.302580	+	0.931246i	0.677989	+	0.735072i	$0.262852\pi$
$241$	−1132.05	+	3484.10i	−0.302580	+	0.931246i	−0.980569	+	0.196174i	$0.937148\pi$
$242$	1980.92	+	1439.23i	0.526193	+	0.382301i
$243$	243.000			0.0641500
$244$	−43.4107	−	31.5397i	−0.0113897	−	0.00827510i
$245$	−1352.08	−	6824.01i	−0.352577	−	1.77947i
$246$	−1702.61	+	1237.02i	−0.441279	+	0.320608i
$247$	1997.56	−	1451.31i	0.514581	−	0.373865i
$248$	−217.850	−	670.473i	−0.0557802	−	0.171674i
$249$	3566.81			0.907782
$250$	−1735.33	+	2191.14i	−0.439009	+	0.554321i
$251$	7359.63			1.85074			0.925370	−	0.379065i	$-0.123754\pi$
$251$	7359.63			1.85074			0.925370	+	0.379065i	$0.123754\pi$
$252$	345.620	+	1063.71i	0.0863969	+	0.265902i
$253$	351.336	−	255.260i	0.0873055	−	0.0634312i
$254$	−4090.74	+	2972.09i	−1.01053	+	0.734196i
$255$	418.151	+	2110.42i	0.102689	+	0.518274i
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$	961.910			0.233472			0.116736	−	0.993163i	$-0.462757\pi$
$257$	961.910			0.233472			0.116736	+	0.993163i	$0.462757\pi$
$258$	−1705.29	−	1238.96i	−0.411499	−	0.298971i
$259$	808.655	−	2488.79i	0.194005	−	0.597087i
$260$	673.818	−	376.695i	0.160725	−	0.0898525i
$261$	−164.498	−	506.272i	−0.0390121	−	0.120067i
$262$	376.583	−	1159.00i	0.0887992	−	0.273296i
$263$	523.490	−	1611.14i	0.122737	−	0.377745i	−0.870745	−	0.491734i	$-0.836363\pi$
$263$	523.490	−	1611.14i	0.122737	−	0.377745i	0.993482	+	0.113990i	$0.0363631\pi$
$264$	76.6159	+	235.799i	0.0178613	+	0.0549714i
$265$	4531.27	+	4194.94i	1.05039	+	0.972428i
$266$	−2746.54	+	8452.97i	−0.633086	+	1.94844i
$267$	−3326.52	−	2416.86i	−0.762471	−	0.553968i
$268$	3286.78			0.749149
$269$	2512.15	+	1825.18i	0.569400	+	0.413693i	0.834887	−	0.550421i	$-0.185533\pi$
$269$	2512.15	+	1825.18i	0.569400	+	0.413693i	−0.265487	+	0.964114i	$0.585533\pi$
$270$	443.032	+	410.149i	0.0998596	+	0.0924477i
$271$	1636.76	−	1189.18i	0.366886	−	0.266558i	−0.389032	−	0.921224i	$-0.627191\pi$
$271$	1636.76	−	1189.18i	0.366886	−	0.266558i	0.755918	+	0.654666i	$0.227191\pi$
$272$	830.296	−	603.245i	0.185088	−	0.134475i
$273$	497.165	+	1530.12i	0.110219	+	0.339219i
$274$	886.759			0.195515
$275$	−837.180	−	983.182i	−0.183578	−	0.215593i
$276$	−504.453			−0.110016
$277$	329.863	+	1015.21i	0.0715507	+	0.220210i	0.980437	−	0.196834i	$-0.0630660\pi$
$277$	329.863	+	1015.21i	0.0715507	+	0.220210i	−0.908886	+	0.417044i	$0.863066\pi$
$278$	2105.62	−	1529.82i	0.454268	−	0.330045i
$279$	641.631	−	466.172i	0.137683	−	0.100032i
$280$	−1165.26	+	2522.69i	−0.248706	+	0.538427i
$281$	2118.66	+	1539.30i	0.449782	+	0.326786i	0.789510	−	0.613738i	$-0.210335\pi$
$281$	2118.66	+	1539.30i	0.449782	+	0.326786i	−0.339728	+	0.940524i	$0.610335\pi$
$282$	446.282			0.0942401
$283$	−579.584	−	421.092i	−0.121741	−	0.0884500i	0.525249	−	0.850949i	$-0.323972\pi$
$283$	−579.584	−	421.092i	−0.121741	−	0.0884500i	−0.646990	+	0.762499i	$0.723972\pi$
$284$	174.306	−	536.458i	0.0364195	−	0.112088i
$285$	932.474	+	4706.24i	0.193807	+	0.978152i
$286$	110.210	+	339.191i	0.0227862	+	0.0701286i
$287$	3367.46	−	10364.0i	0.692596	−	2.13159i
$288$	88.9969	−	273.904i	0.0182090	−	0.0560415i
$289$	−246.770	−	759.481i	−0.0502280	−	0.154586i
$290$	554.606	−	1200.67i	0.112302	−	0.243124i
$291$	83.6352	−	257.403i	0.0168480	−	0.0518530i
$292$	−1886.89	−	1370.91i	−0.378158	−	0.274748i
$293$	−7930.75			−1.58129			−0.790647	−	0.612272i	$-0.790256\pi$
$293$	−7930.75			−1.58129			−0.790647	+	0.612272i	$0.790256\pi$
$294$	−3020.34	−	2194.40i	−0.599148	−	0.435307i
$295$	−7237.61	−	862.110i	−1.42844	−	0.170149i
$296$	−545.148	+	396.074i	−0.107048	+	0.0777747i
$297$	−225.656	+	163.949i	−0.0440871	+	0.0320312i
$298$	798.369	+	2457.13i	0.155195	+	0.477643i
$299$	−725.642			−0.140351
$300$	115.454	+	1495.55i	0.0222192	+	0.287819i
$301$	10914.5			2.09003
$302$	1251.80	+	3852.63i	0.238519	+	0.734086i
$303$	3470.56	−	2521.51i	0.658015	−	0.478076i
$304$	1851.56	−	1345.23i	0.349322	−	0.253798i
$305$	130.912	−	73.1858i	0.0245770	−	0.0137397i
$306$	934.083	+	678.651i	0.174503	+	0.126784i
$307$	−2059.86			−0.382940			−0.191470	−	0.981498i	$-0.561325\pi$
$307$	−2059.86			−0.382940			−0.191470	+	0.981498i	$0.561325\pi$
$308$	−1038.62	−	754.602i	−0.192146	−	0.139602i
$309$	1461.17	−	4497.01i	0.269006	−	0.827915i
$310$	1956.64	+	233.066i	0.358483	+	0.0427008i
$311$	2870.80	+	8835.41i	0.523434	+	1.61096i	0.767392	+	0.641179i	$0.221554\pi$
$311$	2870.80	+	8835.41i	0.523434	+	1.61096i	−0.243957	+	0.969786i	$0.578446\pi$
$312$	128.020	−	394.004i	0.0232298	−	0.0714938i
$313$	2633.55	−	8105.23i	0.475581	−	1.46369i	−0.369591	−	0.929195i	$-0.620502\pi$
$313$	2633.55	−	8105.23i	0.475581	−	1.46369i	0.845172	−	0.534494i	$-0.179498\pi$
$314$	−1820.22	−	5602.07i	−0.327138	−	1.00683i
$315$	−3104.22	−	369.760i	−0.555247	−	0.0661384i
$316$	−531.628	+	1636.18i	−0.0946406	+	0.291274i
$317$	5346.81	+	3884.69i	0.947341	+	0.688283i	0.950176	−	0.311713i	$-0.100903\pi$
$317$	5346.81	+	3884.69i	0.947341	+	0.688283i	−0.00283571	+	0.999996i	$0.500903\pi$
$318$	3313.82			0.584371
$319$	494.331	+	359.153i	0.0867625	+	0.0630367i
$320$	624.568	−	349.162i	0.109108	−	0.0609962i
$321$	4362.42	−	3169.49i	0.758525	−	0.551101i
$322$	2113.20	−	1535.33i	0.365727	−	0.265716i
$323$	2835.28	+	8726.11i	0.488419	+	1.50320i
$324$	324.000			0.0555556
$325$	166.078	+	2151.31i	0.0283457	+	0.367179i
$326$	2024.78			0.343995
$327$	−1386.73	−	4267.91i	−0.234515	−	0.721761i
$328$	−2270.15	+	1649.36i	−0.382158	+	0.277654i
$329$	−1869.52	+	1358.28i	−0.313282	+	0.227613i
$330$	−688.133	−	81.9671i	−0.114789	−	0.0136732i
$331$	−435.257	−	316.233i	−0.0722776	−	0.0525127i	0.551060	−	0.834466i	$-0.314224\pi$
$331$	−435.257	−	316.233i	−0.0722776	−	0.0525127i	−0.623337	+	0.781953i	$0.714224\pi$
$332$	4755.75			0.786162
$333$	−613.292	−	445.583i	−0.100926	−	0.0733267i
$334$	83.1557	−	255.927i	0.0136230	−	0.0419272i
$335$	−3852.38	+	8340.07i	−0.628293	+	1.36020i
$336$	460.827	+	1418.28i	0.0748219	+	0.230278i
$337$	509.711	−	1568.73i	0.0823909	−	0.253573i	−0.901372	−	0.433045i	$-0.857439\pi$
$337$	509.711	−	1568.73i	0.0823909	−	0.253573i	0.983763	+	0.179472i	$0.0574390\pi$
$338$	−1173.67	+	3612.18i	−0.188873	+	0.581292i
$339$	537.099	+	1653.02i	0.0860508	+	0.264837i
$340$	557.534	+	2813.90i	0.0889310	+	0.448838i
$341$	−281.315	+	865.798i	−0.0446747	+	0.137494i
$342$	2083.00	+	1513.39i	0.329344	+	0.239283i
$343$	8674.93			1.36560
$344$	−2273.72	−	1651.95i	−0.356368	−	0.258917i
$345$	591.262	−	1280.03i	0.0922680	−	0.199752i
$346$	1218.93	−	885.601i	0.189393	−	0.137602i
$347$	4083.39	−	2966.75i	0.631722	−	0.458973i	−0.225274	−	0.974295i	$-0.572328\pi$
$347$	4083.39	−	2966.75i	0.631722	−	0.458973i	0.856996	+	0.515322i	$0.172328\pi$
$348$	−219.330	−	675.030i	−0.0337855	−	0.103981i
$349$	−7436.29			−1.14056			−0.570280	−	0.821450i	$-0.693165\pi$
$349$	−7436.29			−1.14056			−0.570280	+	0.821450i	$0.693165\pi$
$350$	−5035.44	−	5913.61i	−0.769016	−	0.903131i
$351$	466.065			0.0708738
$352$	102.155	+	314.399i	0.0154683	+	0.0476066i
$353$	−9564.97	+	6949.36i	−1.44219	+	1.04781i	−0.454608	+	0.890692i	$0.650221\pi$
$353$	−9564.97	+	6949.36i	−1.44219	+	1.04781i	−0.987580	+	0.157119i	$0.949779\pi$
$354$	−3164.52	+	2299.16i	−0.475120	+	0.345195i
$355$	1156.94	+	1071.07i	0.172969	+	0.160131i
$356$	−4435.36	−	3222.48i	−0.660320	−	0.479750i
$357$	−5978.47			−0.886315
$358$	2730.32	+	1983.69i	0.403078	+	0.292853i
$359$	−2923.84	+	8998.64i	−0.429845	+	1.32293i	0.468434	+	0.883499i	$0.344818\pi$
$359$	−2923.84	+	8998.64i	−0.429845	+	1.32293i	−0.898278	+	0.439427i	$0.855182\pi$
$360$	590.710	+	546.865i	0.0864810	+	0.0800621i
$361$	4203.12	+	12935.9i	0.612789	+	1.88597i
$362$	2154.03	−	6629.43i	0.312744	−	0.962528i
$363$	−1134.97	+	3493.08i	−0.164106	+	0.505066i
$364$	662.886	+	2040.15i	0.0954524	+	0.293772i
$365$	5690.23	−	3181.10i	0.816001	−	0.456182i
$366$	24.8721	−	76.5485i	0.00355215	−	0.0109324i
$367$	9103.50	+	6614.08i	1.29482	+	0.940742i	0.999891	−	0.0147774i	$-0.00470395\pi$
$367$	9103.50	+	6614.08i	1.29482	+	0.940742i	0.294929	+	0.955519i	$0.404704\pi$
$368$	−672.604			−0.0952769
$369$	−2553.92	−	1855.53i	−0.360302	−	0.261775i
$370$	−366.061	−	1847.53i	−0.0514341	−	0.259590i
$371$	−13881.9	+	10085.8i	−1.94262	+	1.41140i
$372$	855.508	−	621.563i	0.119237	−	0.0866305i
$373$	−3115.81	−	9589.47i	−0.432521	−	1.33116i	−0.895606	−	0.444849i	$-0.853257\pi$
$373$	−3115.81	−	9589.47i	−0.432521	−	1.33116i	0.463084	−	0.886314i	$-0.346743\pi$
$374$	−1325.29			−0.183233
$375$	−3930.22	−	1459.95i	−0.541216	−	0.201044i
$376$	595.043			0.0816143
$377$	−315.501	−	971.012i	−0.0431011	−	0.132652i
$378$	−1357.27	+	986.112i	−0.184683	+	0.134180i
$379$	10248.4	−	7445.91i	1.38899	−	1.00916i	0.393010	−	0.919534i	$-0.371434\pi$
$379$	10248.4	−	7445.91i	1.38899	−	1.00916i	0.995976	−	0.0896226i	$-0.0285661\pi$
$380$	1243.30	+	6274.98i	0.167842	+	0.847105i
$381$	−6136.10	−	4458.14i	−0.825097	−	0.599468i
$382$	−5875.80			−0.786996
$383$	−7164.02	−	5204.96i	−0.955781	−	0.694415i	−0.00361387	−	0.999993i	$-0.501150\pi$
$383$	−7164.02	−	5204.96i	−0.955781	−	0.694415i	−0.952167	+	0.305578i	$0.901150\pi$
$384$	118.663	−	365.206i	0.0157695	−	0.0485334i
$385$	3132.13	−	1751.00i	0.414618	−	0.231790i
$386$	148.249	+	456.262i	0.0195483	+	0.0601635i
$387$	977.043	−	3007.03i	0.128336	−	0.394977i
$388$	111.514	−	343.204i	0.0145908	−	0.0449060i
$389$	2368.70	+	7290.12i	0.308735	+	0.950190i	0.978257	+	0.207397i	$0.0664993\pi$
$389$	2368.70	+	7290.12i	0.308735	+	0.950190i	−0.669521	+	0.742793i	$0.733501\pi$
$390$	849.720	+	786.651i	0.110326	+	0.102137i
$391$	833.253	−	2564.49i	0.107773	−	0.331693i
$392$	−4027.11	−	2925.87i	−0.518878	−	0.376987i
$393$	1827.97			0.234629
$394$	188.819	+	137.185i	0.0241436	+	0.0175413i
$395$	−3528.64	−	3266.73i	−0.449482	−	0.416120i
$396$	−300.874	+	218.598i	−0.0381806	+	0.0277398i
$397$	3101.05	−	2253.04i	0.392033	−	0.284829i	−0.374255	−	0.927326i	$-0.622102\pi$
$397$	3101.05	−	2253.04i	0.392033	−	0.284829i	0.766288	+	0.642497i	$0.222102\pi$
$398$	−2010.25	−	6186.90i	−0.253177	−	0.779199i
$399$	−13332.0			−1.67277
$400$	153.939	+	1994.07i	0.0192424	+	0.249258i
$401$	−6953.87			−0.865984			−0.432992	−	0.901398i	$-0.642542\pi$
$401$	−6953.87			−0.865984			−0.432992	+	0.901398i	$0.642542\pi$
$402$	1523.50	+	4688.87i	0.189019	+	0.581740i
$403$	1230.62	−	894.101i	0.152114	−	0.110517i
$404$	4627.42	−	3362.01i	0.569858	−	0.414026i
$405$	−379.756	+	822.138i	−0.0465931	+	0.100870i
$406$	2973.29	+	2160.22i	0.363453	+	0.264064i
$407$	870.146			0.105974
$408$	1245.44	+	904.868i	0.151124	+	0.109798i
$409$	−1587.53	+	4885.92i	−0.191928	+	0.590692i	0.808071	+	0.589085i	$0.200512\pi$
$409$	−1587.53	+	4885.92i	−0.191928	+	0.590692i	−0.999999	+	0.00160745i	$0.999488\pi$
$410$	−1524.38	−	7693.61i	−0.183619	−	0.926732i
$411$	411.035	+	1265.04i	0.0493306	+	0.151824i
$412$	1948.22	−	5996.01i	0.232966	−	0.716996i
$413$	6258.87	−	19262.8i	0.745711	−	2.29506i
$414$	−233.827	−	719.645i	−0.0277584	−	0.0854315i
$415$	−5574.15	+	12067.5i	−0.659335	+	1.42740i
$416$	170.693	−	525.338i	0.0201176	−	0.0619155i
$417$	3158.43	+	2294.73i	0.370908	+	0.269481i
$418$	−2955.39			−0.345820
$419$	9079.94	+	6596.96i	1.05867	+	0.769171i	0.973842	−	0.227225i	$-0.0729651\pi$
$419$	9079.94	+	6596.96i	1.05867	+	0.769171i	0.0848304	+	0.996395i	$0.472965\pi$
$420$	−4138.96	−	493.013i	−0.480858	−	0.0572776i
$421$	−8881.63	+	6452.88i	−1.02818	+	0.747017i	−0.967944	−	0.251167i	$-0.919186\pi$
$421$	−8881.63	+	6452.88i	−1.02818	+	0.747017i	−0.0602371	+	0.998184i	$0.519186\pi$
$422$	8830.63	−	6415.82i	1.01864	−	0.740089i
$423$	206.863	+	636.659i	0.0237778	+	0.0731807i
$424$	4418.43			0.506080
$425$	−7793.64	−	1883.41i	−0.889523	−	0.214962i
$426$	846.098			0.0962291
$427$	128.788	+	396.369i	0.0145960	+	0.0449219i
$428$	5816.56	−	4225.98i	0.656902	−	0.477267i
$429$	−432.800	+	314.447i	−0.0487081	+	0.0353885i
$430$	6856.76	−	3833.24i	0.768982	−	0.429896i
$431$	275.595	+	200.232i	0.0308003	+	0.0223778i	0.603079	−	0.797682i	$-0.293940\pi$
$431$	275.595	+	200.232i	0.0308003	+	0.0223778i	−0.572279	+	0.820059i	$0.693940\pi$
$432$	432.000			0.0481125
$433$	3073.54	+	2233.06i	0.341120	+	0.247838i	0.745134	−	0.666914i	$-0.232385\pi$
$433$	3073.54	+	2233.06i	0.341120	+	0.247838i	−0.404014	+	0.914753i	$0.632385\pi$
$434$	−1692.04	+	5207.57i	−0.187144	+	0.575971i
$435$	1969.94	+	234.650i	0.217129	+	0.0258634i
$436$	−1848.97	−	5690.55i	−0.203096	−	0.625064i
$437$	1858.15	−	5718.80i	0.203404	−	0.626012i
$438$	1081.09	−	3327.27i	0.117938	−	0.362975i
$439$	−4739.41	−	14586.4i	−0.515261	−	1.58581i	−0.782806	−	0.622266i	$-0.786212\pi$
$439$	−4739.41	−	14586.4i	−0.515261	−	1.58581i	0.267545	−	0.963545i	$-0.413788\pi$
$440$	−917.510	−	109.290i	−0.0994104	−	0.0118413i
$441$	1730.50	−	5325.93i	0.186859	−	0.575092i
$442$	1791.54	+	1301.63i	0.192793	+	0.140073i
$443$	−881.571			−0.0945479			−0.0472739	−	0.998882i	$-0.515053\pi$
$443$	−881.571			−0.0945479			−0.0472739	+	0.998882i	$0.515053\pi$
$444$	−817.723	−	594.110i	−0.0874041	−	0.0635028i
$445$	13375.5	−	7477.55i	1.42486	−	0.796561i
$446$	9389.27	−	6821.70i	0.996849	−	0.724253i
$447$	−3135.23	+	2277.88i	−0.331748	+	0.241029i
$448$	614.435	+	1891.04i	0.0647977	+	0.199427i
$449$	−3652.80			−0.383934			−0.191967	−	0.981401i	$-0.561487\pi$
$449$	−3652.80			−0.383934			−0.191967	+	0.981401i	$0.561487\pi$
$450$	−2080.01	+	857.931i	−0.217895	+	0.0898739i
$451$	3623.53			0.378327
$452$	716.132	+	2204.03i	0.0745222	+	0.229356i
$453$	−4915.87	+	3571.59i	−0.509862	+	0.370437i
$454$	−7452.23	+	5414.36i	−0.770376	+	0.559711i
$455$	−5953.78	−	709.186i	−0.613445	−	0.0730707i
$456$	2777.33	+	2017.85i	0.285220	+	0.207225i
$457$	−8995.51			−0.920770			−0.460385	−	0.887719i	$-0.652289\pi$
$457$	−8995.51			−0.920770			−0.460385	+	0.887719i	$0.652289\pi$
$458$	−8252.86	−	5996.05i	−0.841989	−	0.611741i
$459$	−535.182	+	1647.12i	−0.0544230	+	0.167497i
$460$	788.349	−	1706.71i	0.0799065	−	0.172991i
$461$	766.245	+	2358.26i	0.0774134	+	0.238254i	0.982273	−	0.187456i	$-0.0600243\pi$
$461$	766.245	+	2358.26i	0.0774134	+	0.238254i	−0.904860	+	0.425710i	$0.860024\pi$
$462$	595.076	−	1831.46i	0.0599252	−	0.184431i
$463$	−1671.26	+	5143.61i	−0.167754	+	0.516293i	−0.999229	−	0.0392693i	$-0.987497\pi$
$463$	−1671.26	+	5143.61i	−0.167754	+	0.516293i	0.831475	+	0.555562i	$0.187497\pi$
$464$	−292.441	−	900.040i	−0.0292591	−	0.0900502i
$465$	574.464	+	2899.34i	0.0572906	+	0.289148i
$466$	3529.02	−	10861.2i	0.350813	−	1.07969i
$467$	1132.44	+	822.764i	0.112212	+	0.0815267i	0.642476	−	0.766306i	$-0.277907\pi$
$467$	1132.44	+	822.764i	0.112212	+	0.0815267i	−0.530264	+	0.847832i	$0.677907\pi$
$468$	621.420			0.0613785
$469$	−20652.9	−	15005.2i	−2.03340	−	1.47735i
$470$	−697.441	+	1509.90i	−0.0684480	+	0.148184i
$471$	7148.11	−	5193.41i	0.699294	−	0.508067i
$472$	−4219.37	+	3065.55i	−0.411466	+	0.298948i
$473$	1121.49	+	3451.60i	0.109020	+	0.335528i
$474$	−2580.58			−0.250063
$475$	−17379.8	−	4199.99i	−1.67882	−	0.405703i
$476$	−7971.30			−0.767571
$477$	1536.04	+	4727.45i	0.147443	+	0.453784i
$478$	−1705.35	+	1239.01i	−0.163182	+	0.118558i
$479$	7396.85	−	5374.13i	0.705576	−	0.512631i	−0.176167	−	0.984360i	$-0.556370\pi$
$479$	7396.85	−	5374.13i	0.705576	−	0.512631i	0.881743	+	0.471729i	$0.156370\pi$
$480$	787.613	+	729.154i	0.0748947	+	0.0693358i
$481$	−1176.27	−	854.611i	−0.111504	−	0.0810123i
$482$	−7326.79			−0.692378
$483$	3169.80	+	2303.00i	0.298615	+	0.216956i
$484$	−1513.29	+	4657.43i	−0.142120	+	0.437400i
$485$	740.163	+	685.225i	0.0692970	+	0.0641536i
$486$	150.182	+	462.213i	0.0140173	+	0.0431408i
$487$	151.314	−	465.697i	0.0140795	−	0.0433322i	−0.943770	−	0.330603i	$-0.892748\pi$
$487$	151.314	−	465.697i	0.0140795	−	0.0433322i	0.957849	+	0.287271i	$0.0927479\pi$
$488$	33.1628	−	102.065i	0.00307625	−	0.00946773i
$489$	938.537	+	2888.52i	0.0867937	+	0.267124i
$490$	12144.4	−	6789.28i	1.11965	−	0.625936i
$491$	4056.57	−	12484.8i	0.372852	−	1.14752i	−0.572065	−	0.820208i	$-0.693857\pi$
$491$	4056.57	−	12484.8i	0.372852	−	1.14752i	0.944917	−	0.327311i	$-0.106143\pi$
$492$	−3405.22	−	2474.04i	−0.312031	−	0.226704i
$493$	3793.94			0.346593
$494$	3995.12	+	2902.62i	0.363864	+	0.264363i
$495$	−202.034	−	1019.67i	−0.0183449	−	0.0925877i
$496$	1140.68	−	828.751i	0.103262	−	0.0750242i
$497$	−3544.39	+	2575.15i	−0.319894	+	0.232417i
$498$	2204.41	+	6784.48i	0.198358	+	0.610482i
$499$	6333.86			0.568222			0.284111	−	0.958791i	$-0.408302\pi$
$499$	6333.86			0.568222			0.284111	+	0.958791i	$0.408302\pi$
$500$	−5240.30	−	1946.60i	−0.468707	−	0.174109i
$501$	403.646			0.0359952
$502$	4548.50	+	13998.8i	0.404402	+	1.24462i
$503$	4957.19	−	3601.61i	0.439424	−	0.319260i	−0.345982	−	0.938241i	$-0.612454\pi$
$503$	4957.19	−	3601.61i	0.439424	−	0.319260i	0.785406	+	0.618981i	$0.212454\pi$
$504$	−1809.69	+	1314.82i	−0.159940	+	0.116204i
$505$	3107.26	+	15682.5i	0.273804	+	1.38190i
$506$	702.672	+	510.521i	0.0617343	+	0.0448526i
$507$	−5697.10			−0.499048
$508$	−8181.47	−	5944.19i	−0.714555	−	0.519155i
$509$	2103.71	−	6474.56i	0.183193	−	0.563811i	−0.816719	−	0.577035i	$-0.804209\pi$
$509$	2103.71	−	6474.56i	0.183193	−	0.563811i	0.999913	+	0.0132241i	$0.00420950\pi$
$510$	−3755.83	+	2099.68i	−0.326100	+	0.182305i
$511$	5597.91	+	17228.6i	0.484613	+	1.49148i
$512$	158.217	−	486.941i	0.0136568	−	0.0420312i
$513$	−1193.45	+	3673.07i	−0.102714	+	0.316121i
$514$	594.493	+	1829.66i	0.0510155	+	0.157009i
$515$	12931.2	+	11971.4i	1.10644	+	1.02431i
$516$	1302.72	−	4009.37i	0.111142	−	0.342060i
$517$	−621.643	−	451.650i	−0.0528817	−	0.0384208i
$518$	5233.73			0.443932
$519$	1828.39	+	1328.40i	0.154638	+	0.112351i
$520$	1132.96	+	1048.87i	0.0955454	+	0.0884537i
$521$	−4859.84	+	3530.88i	−0.408663	+	0.296911i	−0.773060	−	0.634332i	$-0.781275\pi$
$521$	−4859.84	+	3530.88i	−0.408663	+	0.296911i	0.364397	+	0.931244i	$0.381275\pi$
$522$	861.322	−	625.787i	0.0722204	−	0.0524712i
$523$	2402.78	+	7394.99i	0.200891	+	0.618280i	0.999857	+	0.0169036i	$0.00538083\pi$
$523$	2402.78	+	7394.99i	0.200891	+	0.618280i	−0.798966	+	0.601377i	$0.794619\pi$
$524$	2437.30			0.203194
$525$	6102.21	−	9924.59i	0.507281	−	0.825038i
$526$	3388.10			0.280852
$527$	1746.72	+	5375.84i	0.144380	+	0.444356i
$528$	−401.166	+	291.464i	−0.0330654	+	0.0240234i
$529$	8413.64	−	6112.87i	0.691513	−	0.502414i
$530$	−5178.78	+	11211.6i	−0.424437	+	0.918870i
$531$	−4746.79	−	3448.74i	−0.387934	−	0.281851i
$532$	−17776.0			−1.44866
$533$	−4898.32	−	3558.84i	−0.398067	−	0.289213i
$534$	2541.24	−	7821.12i	0.205936	−	0.633807i
$535$	3905.76	+	19712.5i	0.315627	+	1.59298i
$536$	2031.34	+	6251.82i	0.163695	+	0.503801i
$537$	−1564.34	+	4814.53i	−0.125710	+	0.386894i
$538$	−1919.11	+	5906.42i	−0.153790	+	0.473316i
$539$	1986.34	+	6113.33i	0.158734	+	0.488534i
$540$	−506.341	+	1096.18i	−0.0403508	+	0.0873560i
$541$	4230.01	−	13018.6i	0.336159	−	1.03459i	−0.629989	−	0.776604i	$-0.716940\pi$
$541$	4230.01	−	13018.6i	0.336159	−	1.03459i	0.966148	−	0.257988i	$-0.0830596\pi$
$542$	3273.52	+	2378.35i	0.259428	+	0.188485i
$543$	10455.9			0.826345
$544$	1660.59	+	1206.49i	0.130877	+	0.0950879i
$545$	16606.7	+	1978.11i	1.30523	+	0.155473i
$546$	−2603.19	+	1891.33i	−0.204041	+	0.148244i
$547$	−4629.18	+	3363.29i	−0.361845	+	0.262896i	−0.753821	−	0.657079i	$-0.771792\pi$
$547$	−4629.18	+	3363.29i	−0.361845	+	0.262896i	0.391976	+	0.919975i	$0.371792\pi$
$548$	548.047	+	1686.72i	0.0427215	+	0.131483i
$549$	120.732			0.00938563
$550$	1352.72	−	2200.05i	0.104873	−	0.170565i
$551$	8460.47			0.654134
$552$	−311.769	−	959.527i	−0.0240394	−	0.0739858i
$553$	10810.3	−	7854.14i	0.831285	−	0.603964i
$554$	−1727.18	+	1254.87i	−0.132457	+	0.0962354i
$555$	2465.97	−	1378.59i	0.188603	−	0.105438i
$556$	4211.23	+	3059.64i	0.321216	+	0.233377i
$557$	−10858.4			−0.826009			−0.413005	−	0.910729i	$-0.635521\pi$
$557$	−10858.4			−0.826009			−0.413005	+	0.910729i	$0.635521\pi$
$558$	1283.26	+	932.344i	0.0973563	+	0.0707335i
$559$	1873.93	−	5767.37i	0.141787	−	0.436376i
$560$	−5518.61	−	657.351i	−0.416435	−	0.0496038i
$561$	−614.305	−	1890.64i	−0.0462317	−	0.142286i
$562$	−1618.51	+	4981.27i	−0.121482	+	0.373883i
$563$	−6339.53	+	19511.1i	−0.474563	+	1.46056i	0.371982	+	0.928240i	$0.378678\pi$
$563$	−6339.53	+	19511.1i	−0.474563	+	1.46056i	−0.846546	+	0.532316i	$0.821322\pi$
$564$	275.817	+	848.879i	0.0205922	+	0.0633763i
$565$	−6432.01	−	766.151i	−0.478932	−	0.0570482i
$566$	442.763	−	1362.68i	0.0328811	−	0.101198i
$567$	−2035.90	−	1479.17i	−0.150793	−	0.109558i
$568$	1128.13			0.0833368
$569$	2277.79	+	1654.91i	0.167821	+	0.121929i	0.668526	−	0.743689i	$-0.266926\pi$
$569$	2277.79	+	1654.91i	0.167821	+	0.121929i	−0.500705	+	0.865618i	$0.666926\pi$
$570$	−8375.49	+	4682.29i	−0.615457	+	0.344069i
$571$	−2904.54	+	2110.27i	−0.212874	+	0.154662i	−0.689113	−	0.724654i	$-0.742000\pi$
$571$	−2904.54	+	2110.27i	−0.212874	+	0.154662i	0.476239	+	0.879316i	$0.342000\pi$
$572$	−577.066	+	419.263i	−0.0421824	+	0.0306473i
$573$	−2723.59	−	8382.33i	−0.198568	−	0.611129i
$574$	21794.7			1.58483
$575$	3406.69	+	4000.81i	0.247076	+	0.290166i
$576$	576.000			0.0416667
$577$	1898.69	+	5843.57i	0.136991	+	0.421614i	0.995894	−	0.0905234i	$-0.0288540\pi$
$577$	1898.69	+	5843.57i	0.136991	+	0.421614i	−0.858904	+	0.512137i	$0.828854\pi$
$578$	1292.11	−	938.770i	0.0929836	−	0.0675565i
$579$	−582.180	+	422.978i	−0.0417868	+	0.0303599i
$580$	2626.58	+	312.866i	0.188039	+	0.0223984i
$581$	−29883.4	−	21711.6i	−2.13386	−	1.55034i
$582$	541.298			0.0385525
$583$	−4615.95	−	3353.68i	−0.327913	−	0.238242i
$584$	1441.46	−	4436.35i	0.102137	−	0.314345i
$585$	−728.357	+	1576.83i	−0.0514767	+	0.111443i
$586$	−4901.47	−	15085.2i	−0.345525	−	1.06342i
$587$	−2804.60	+	8631.68i	−0.197203	+	0.606929i	0.802741	+	0.596328i	$0.203374\pi$
$587$	−2804.60	+	8631.68i	−0.197203	+	0.606929i	−0.999944	+	0.0106007i	$0.996626\pi$
$588$	2307.33	−	7101.24i	0.161824	−	0.498044i
$589$	3895.17	+	11988.1i	0.272492	+	0.838644i
$590$	−2833.26	−	14299.6i	−0.197701	−	0.997803i
$591$	−108.184	+	332.955i	−0.00752975	+	0.0231742i
$592$	−1090.30	−	792.147i	−0.0756941	−	0.0549950i
$593$	−3825.98			−0.264948			−0.132474	−	0.991186i	$-0.542292\pi$
$593$	−3825.98			−0.264948			−0.132474	+	0.991186i	$0.542292\pi$
$594$	−451.312	−	327.897i	−0.0311743	−	0.0226495i
$595$	9343.04	−	20226.9i	0.643743	−	1.39365i
$596$	−4180.31	+	3037.17i	−0.287302	+	0.208737i
$597$	7894.34	−	5735.57i	0.541196	−	0.393202i
$598$	−448.471	−	1380.25i	−0.0306678	−	0.0943858i
$599$	1554.05			0.106005			0.0530024	−	0.998594i	$-0.483121\pi$
$599$	1554.05			0.106005			0.0530024	+	0.998594i	$0.483121\pi$
$600$	−2773.35	+	1143.91i	−0.188703	+	0.0778331i
$601$	−6695.89			−0.454461			−0.227230	−	0.973841i	$-0.572967\pi$
$601$	−6695.89			−0.454461			−0.227230	+	0.973841i	$0.572967\pi$
$602$	6745.52	+	20760.6i	0.456689	+	1.40554i
$603$	−5982.88	+	4346.82i	−0.404049	+	0.293559i
$604$	−6554.49	+	4762.11i	−0.441554	+	0.320807i
$605$	−10044.4	−	9298.83i	−0.674977	−	0.624878i
$606$	6941.12	+	5043.02i	0.465287	+	0.338051i
$607$	−27340.9			−1.82823			−0.914113	−	0.405460i	$-0.867111\pi$
$607$	−27340.9			−1.82823			−0.914113	+	0.405460i	$0.867111\pi$
$608$	3703.11	+	2690.47i	0.247008	+	0.179462i
$609$	−1703.54	+	5242.96i	−0.113351	+	0.348860i
$610$	220.116	+	203.778i	0.0146102	+	0.0135258i
$611$	396.756	+	1221.09i	0.0262701	+	0.0808510i
$612$	−713.576	+	2196.16i	−0.0471317	+	0.145056i
$613$	−1043.59	+	3211.83i	−0.0687602	+	0.211622i	−0.979532	−	0.201287i	$-0.935487\pi$
$613$	−1043.59	+	3211.83i	−0.0687602	+	0.211622i	0.910772	+	0.412910i	$0.135487\pi$
$614$	−1273.07	−	3918.09i	−0.0836755	−	0.257527i
$615$	10269.0	−	5740.84i	0.673310	−	0.376411i
$616$	793.435	−	2441.94i	0.0518968	−	0.159722i
$617$	18155.6	+	13190.8i	1.18463	+	0.860686i	0.992687	−	0.120720i	$-0.0385203\pi$
$617$	18155.6	+	13190.8i	1.18463	+	0.860686i	0.191946	+	0.981406i	$0.438520\pi$
$618$	9456.87			0.615552
$619$	−10692.2	−	7768.33i	−0.694274	−	0.504420i	0.183788	−	0.982966i	$-0.441164\pi$
$619$	−10692.2	−	7768.33i	−0.694274	−	0.504420i	−0.878062	+	0.478546i	$0.841164\pi$
$620$	765.952	+	3865.79i	0.0496151	+	0.250410i
$621$	918.250	−	667.148i	0.0593367	−	0.0431106i
$622$	−15031.7	+	10921.2i	−0.968997	+	0.704017i
$623$	13158.5	+	40497.8i	0.846205	+	2.60435i
$624$	828.560			0.0531554
$625$	11081.5	−	11015.5i	0.709216	−	0.704991i
$626$	17044.7			1.08825
$627$	−1369.90	−	4216.11i	−0.0872543	−	0.268541i
$628$	9530.82	−	6924.54i	0.605607	−	0.439999i
$629$	4370.99	−	3175.71i	0.277079	−	0.201310i
$630$	−1215.19	−	6133.10i	−0.0768479	−	0.387855i
$631$	−837.540	−	608.508i	−0.0528398	−	0.0383904i	0.561052	−	0.827781i	$-0.310397\pi$
$631$	−837.540	−	608.508i	−0.0528398	−	0.0383904i	−0.613892	+	0.789390i	$0.710397\pi$
$632$	−3440.77			−0.216561
$633$	13245.9	+	9623.74i	0.831720	+	0.604280i
$634$	−4084.60	+	12571.1i	−0.255868	+	0.787481i
$635$	24672.5	−	13793.1i	1.54189	−	0.861987i
$636$	2048.06	+	6303.27i	0.127690	+	0.392989i
$637$	3319.03	−	10214.9i	0.206444	−	0.635370i
$638$	−377.636	+	1162.24i	−0.0234338	+	0.0721217i
$639$	392.188	+	1207.03i	0.0242797	+	0.0747252i
$640$	1050.15	+	972.205i	0.0648607	+	0.0600465i
$641$	7463.26	−	22969.5i	0.459877	−	1.41535i	−0.405437	−	0.914123i	$-0.632881\pi$
$641$	7463.26	−	22969.5i	0.459877	−	1.41535i	0.865313	−	0.501231i	$-0.167119\pi$
$642$	8724.84	+	6338.97i	0.536358	+	0.389687i
$643$	−28451.5			−1.74497			−0.872486	−	0.488639i	$-0.837493\pi$
$643$	−28451.5			−1.74497			−0.872486	+	0.488639i	$0.837493\pi$
$644$	4226.40	+	3070.66i	0.258608	+	0.187890i
$645$	8646.73	+	8004.94i	0.527852	+	0.488673i
$646$	−14845.7	+	10786.1i	−0.904176	+	0.656922i
$647$	23248.8	−	16891.2i	1.41268	−	1.02637i	0.419752	−	0.907639i	$-0.362117\pi$
$647$	23248.8	−	16891.2i	1.41268	−	1.02637i	0.992926	−	0.118732i	$-0.0378828\pi$
$648$	200.243	+	616.285i	0.0121393	+	0.0373610i
$649$	6734.80			0.407341
$650$	−3989.39	+	1645.48i	−0.240733	+	0.0992939i
$651$	−8213.35			−0.494480
$652$	1251.38	+	3851.36i	0.0751656	+	0.231336i
$653$	−10424.9	+	7574.17i	−0.624747	+	0.453905i	−0.854576	−	0.519326i	$-0.826183\pi$
$653$	−10424.9	+	7574.17i	−0.624747	+	0.453905i	0.229829	+	0.973231i	$0.426183\pi$
$654$	7261.00	−	5275.43i	0.434140	−	0.315421i
$655$	−2856.72	+	6184.55i	−0.170414	+	0.368932i
$656$	−4540.30	−	3298.72i	−0.270227	−	0.196331i
$657$	5247.74			0.311619
$658$	−3739.04	−	2716.57i	−0.221524	−	0.160947i
$659$	−4235.85	+	13036.6i	−0.250388	+	0.770614i	0.744316	+	0.667828i	$0.232776\pi$
$659$	−4235.85	+	13036.6i	−0.250388	+	0.770614i	−0.994704	+	0.102786i	$0.967224\pi$
$660$	−269.379	−	1359.56i	−0.0158872	−	0.0801833i
$661$	−4891.48	−	15054.4i	−0.287831	−	0.885853i	−0.985536	−	0.169467i	$-0.945795\pi$
$661$	−4891.48	−	15054.4i	−0.287831	−	0.885853i	0.697705	−	0.716385i	$-0.254205\pi$
$662$	332.507	−	1023.35i	0.0195215	−	0.0600810i
$663$	−1026.46	+	3159.12i	−0.0601272	+	0.185053i
$664$	2939.22	+	9045.98i	0.171783	+	0.528693i
$665$	20834.9	−	45105.8i	1.21495	−	2.63027i
$666$	468.513	−	1441.94i	0.0272590	−	0.0838947i
$667$	−2011.56	−	1461.48i	−0.116773	−	0.0848408i
$668$	538.195			0.0311727
$669$	14083.9	+	10232.6i	0.813924	+	0.591350i
$670$	−18244.7	−	2173.22i	−1.05202	−	0.125312i
$671$	−112.115	+	81.4560i	−0.00645028	+	0.00468640i
$672$	−2412.92	+	1753.09i	−0.138512	+	0.100635i
$673$	−2131.78	−	6560.95i	−0.122101	−	0.375789i	0.871261	−	0.490821i	$-0.163303\pi$
$673$	−2131.78	−	6560.95i	−0.122101	−	0.375789i	−0.993362	+	0.115032i	$0.963303\pi$
$674$	3298.92			0.188531
$675$	−2188.05	−	2569.64i	−0.124768	−	0.146527i
$676$	−7596.14			−0.432188
$677$	−4981.71	−	15332.1i	−0.282810	−	0.870401i	−0.987046	−	0.160435i	$-0.948710\pi$
$677$	−4981.71	−	15332.1i	−0.282810	−	0.870401i	0.704236	−	0.709966i	$-0.251290\pi$
$678$	−2812.29	+	2043.25i	−0.159300	+	0.115738i
$679$	−2267.55	+	1647.47i	−0.128160	+	0.0931137i
$680$	−5007.78	+	2799.58i	−0.282411	+	0.157881i
$681$	−11178.3	−	8121.54i	−0.629009	−	0.457002i
$682$	−1820.71			−0.102227
$683$	17087.8	+	12415.0i	0.957314	+	0.695529i	0.952525	−	0.304459i	$-0.0984758\pi$
$683$	17087.8	+	12415.0i	0.957314	+	0.695529i	0.00478844	+	0.999989i	$0.498476\pi$
$684$	−1591.27	+	4897.43i	−0.0889528	+	0.273769i
$685$	−4922.33	−	586.325i	−0.274559	−	0.0327042i
$686$	5361.40	+	16500.7i	0.298395	+	0.918366i
$687$	4728.47	−	14552.7i	0.262594	−	0.808182i
$688$	1736.97	−	5345.83i	0.0962518	−	0.296232i
$689$	2946.07	+	9067.08i	0.162898	+	0.501347i
$690$	2800.18	+	333.545i	0.154494	+	0.0184027i
$691$	−4723.73	+	14538.2i	−0.260057	+	0.800373i	0.732734	+	0.680515i	$0.238244\pi$
$691$	−4723.73	+	14538.2i	−0.260057	+	0.800373i	−0.992791	+	0.119858i	$0.961756\pi$
$692$	2437.85	+	1771.20i	0.133921	+	0.0972991i
$693$	2888.56			0.158337
$694$	8166.77	+	5933.51i	0.446695	+	0.324543i
$695$	−12699.6	+	7099.69i	−0.693130	+	0.387491i
$696$	1148.43	−	834.383i	0.0625447	−	0.0454414i
$697$	18202.0	−	13224.5i	0.989168	−	0.718673i
$698$	−4595.88	−	14144.7i	−0.249221	−	0.767025i
$699$	17130.2			0.926931
$700$	8136.28	−	13232.8i	0.439318	−	0.714504i
$701$	−3364.83			−0.181295			−0.0906476	−	0.995883i	$-0.528894\pi$
$701$	−3364.83			−0.181295			−0.0906476	+	0.995883i	$0.528894\pi$
$702$	288.044	+	886.509i	0.0154865	+	0.0476625i
$703$	9747.29	−	7081.82i	0.522939	−	0.379937i
$704$	−534.888	+	388.619i	−0.0286354	+	0.0208049i
$705$	−2477.28	−	295.082i	−0.132340	−	0.0157637i
$706$	−19129.9	−	13898.7i	−1.01978	−	0.740914i
$707$	−44425.8			−2.36323
$708$	−6329.05	−	4598.32i	−0.335961	−	0.244090i
$709$	6431.24	−	19793.3i	0.340663	−	1.04845i	−0.623201	−	0.782062i	$-0.714168\pi$
$709$	6431.24	−	19793.3i	0.340663	−	1.04845i	0.963865	−	0.266393i	$-0.0858318\pi$
$710$	−1322.27	+	2862.59i	−0.0698926	+	0.151311i
$711$	−1196.16	−	3681.41i	−0.0630938	−	0.194183i
$712$	3388.32	−	10428.2i	0.178346	−	0.548893i
$713$	1144.74	−	3523.15i	0.0601274	−	0.185053i
$714$	−3694.90	−	11371.7i	−0.193667	−	0.596045i
$715$	−387.494	−	1955.70i	−0.0202678	−	0.102292i
$716$	−2085.78	+	6419.37i	−0.108868	+	0.335060i
$717$	−2558.02	−	1858.51i	−0.133237	−	0.0968024i
$718$	−18923.5			−0.983590
$719$	−10152.9	−	7376.52i	−0.526619	−	0.382611i	0.292472	−	0.956274i	$-0.405522\pi$
$719$	−10152.9	−	7376.52i	−0.526619	−	0.382611i	−0.819092	+	0.573663i	$0.805522\pi$
$720$	−675.121	+	1461.58i	−0.0349448	+	0.0756525i
$721$	−39615.7	+	28782.5i	−2.04628	+	1.48671i
$722$	−22007.8	+	15989.6i	−1.13441	+	0.824200i
$723$	−3396.15	−	10452.3i	−0.174695	−	0.537655i
$724$	13941.2			0.715636
$725$	−3872.46	+	6298.15i	−0.198372	+	0.322631i
$726$	−7345.67			−0.375514
$727$	−2417.86	−	7441.41i	−0.123347	−	0.379624i	0.870249	−	0.492612i	$-0.163958\pi$
$727$	−2417.86	−	7441.41i	−0.123347	−	0.379624i	−0.993596	+	0.112988i	$0.963958\pi$
$728$	−3470.92	+	2521.77i	−0.176704	+	0.128383i
$729$	−589.773	+	428.495i	−0.0299636	+	0.0217698i
$730$	9567.57	+	8857.44i	0.485085	+	0.449080i
$731$	18230.6	+	13245.3i	0.922413	+	0.670173i
$732$	160.976			0.00812819
$733$	24239.7	+	17611.2i	1.22144	+	0.887426i	0.996219	−	0.0868826i	$-0.0276905\pi$
$733$	24239.7	+	17611.2i	1.22144	+	0.887426i	0.225218	+	0.974308i	$0.427691\pi$
$734$	−6954.46	+	21403.6i	−0.349719	+	1.07632i
$735$	15314.7	+	14178.0i	0.768561	+	0.711516i
$736$	−415.692	−	1279.37i	−0.0208188	−	0.0640736i
$737$	2623.12	−	8073.13i	0.131104	−	0.403497i
$738$	1951.02	−	6004.62i	0.0973144	−	0.299503i
$739$	−3054.91	−	9402.03i	−0.152066	−	0.468010i	0.845786	−	0.533522i	$-0.179132\pi$
$739$	−3054.91	−	9402.03i	−0.152066	−	0.468010i	−0.997852	+	0.0655121i	$0.979132\pi$
$740$	3287.96	−	1838.12i	0.163335	−	0.0913118i
$741$	−2289.00	+	7044.81i	−0.113480	+	0.349255i
$742$	−27763.8	−	20171.6i	−1.37364	−	0.998010i
$743$	−5223.21			−0.257902			−0.128951	−	0.991651i	$-0.541161\pi$
$743$	−5223.21			−0.257902			−0.128951	+	0.991651i	$0.541161\pi$
$744$	1711.02	+	1243.13i	0.0843130	+	0.0612570i
$745$	−2807.03	−	14167.2i	−0.138043	−	0.696707i
$746$	16314.6	−	11853.2i	0.800696	−	0.581740i
$747$	−8656.84	+	6289.56i	−0.424012	+	0.308063i
$748$	−819.073	−	2520.85i	−0.0400378	−	0.123224i
$749$	−55842.2			−2.72421
$750$	347.980	−	8378.03i	0.0169419	−	0.407897i
$751$	17608.0			0.855561			0.427781	−	0.903883i	$-0.359296\pi$
$751$	17608.0			0.855561			0.427781	+	0.903883i	$0.359296\pi$
$752$	367.757	+	1131.84i	0.0178334	+	0.0548855i
$753$	−17862.2	+	12977.6i	−0.864455	+	0.628063i
$754$	1651.98	−	1200.24i	0.0797901	−	0.0579709i
$755$	−4401.27	−	22213.4i	−0.212157	−	1.07076i
$756$	−2714.53	−	1972.22i	−0.130591	−	0.0948798i
$757$	6215.88			0.298441			0.149221	−	0.988804i	$-0.452324\pi$
$757$	6215.88			0.298441			0.149221	+	0.988804i	$0.452324\pi$
$758$	20496.8	+	14891.8i	0.982161	+	0.713582i
$759$	−402.595	+	1239.06i	−0.0192533	+	0.0592556i
$760$	−11167.3	+	6243.05i	−0.533002	+	0.297973i
$761$	−5814.21	−	17894.3i	−0.276958	−	0.852389i	−0.988695	−	0.149943i	$-0.952091\pi$
$761$	−5814.21	−	17894.3i	−0.276958	−	0.852389i	0.711737	−	0.702446i	$-0.247909\pi$
$762$	4687.57	−	14426.8i	0.222851	−	0.685865i
$763$	−14361.0	+	44198.5i	−0.681392	+	2.09711i
$764$	−3631.45	−	11176.4i	−0.171965	−	0.529253i
$765$	−4736.30	−	4384.76i	−0.223845	−	0.207230i
$766$	5472.82	−	16843.6i	0.258148	−	0.794497i
$767$	−9104.16	−	6614.56i	−0.428595	−	0.311392i
$768$	768.000			0.0360844
$769$	3201.41	+	2325.96i	0.150125	+	0.109072i	0.660312	−	0.750991i	$-0.270424\pi$
$769$	3201.41	+	2325.96i	0.150125	+	0.109072i	−0.510187	+	0.860063i	$0.670424\pi$
$770$	5266.36	+	4875.48i	0.246476	+	0.228182i
$771$	−2334.60	+	1696.19i	−0.109051	+	0.0792305i
$772$	−776.239	+	563.971i	−0.0361884	+	0.0262924i
$773$	−5893.62	−	18138.7i	−0.274229	−	0.843990i	−0.989422	−	0.145063i	$-0.953661\pi$
$773$	−5893.62	−	18138.7i	−0.274229	−	0.843990i	0.715194	−	0.698926i	$-0.246339\pi$
$774$	6323.56			0.293664
$775$	−10707.1	−	2587.46i	−0.496270	−	0.119928i
$776$	721.731			0.0333874
$777$	2425.97	+	7466.36i	0.112009	+	0.344728i
$778$	−12402.7	+	9011.09i	−0.571540	+	0.415248i
$779$	40590.4	−	29490.7i	1.86688	−	1.35637i
$780$	−971.143	+	2102.44i	−0.0445801	+	0.0965121i
$781$	−1178.56	−	856.275i	−0.0539978	−	0.0392317i
$782$	5392.93			0.246612
$783$	1291.98	+	938.680i	0.0589677	+	0.0428425i
$784$	3076.44	−	9468.32i	0.140144	−	0.431319i
$785$	6399.84	+	32300.2i	0.290981	+	1.46859i
$786$	1129.75	+	3477.01i	0.0512682	+	0.157787i
$787$	1877.25	−	5777.58i	0.0850275	−	0.261688i	−0.899499	−	0.436922i	$-0.856068\pi$
$787$	1877.25	−	5777.58i	0.0850275	−	0.261688i	0.984527	+	0.175235i	$0.0560684\pi$
$788$	−144.245	+	443.940i	−0.00652095	+	0.0200694i
$789$	1570.47	+	4833.41i	0.0708621	+	0.218091i
$790$	4032.88	−	8730.83i	0.181625	−	0.393201i
$791$	5562.21	−	17118.7i	0.250024	−	0.769496i
$792$	−601.749	−	437.196i	−0.0269978	−	0.0196150i
$793$	231.559			0.0103694
$794$	6202.09	+	4506.08i	0.277209	+	0.201404i
$795$	−18394.8	−	2191.10i	−0.820624	−	0.0977489i
$796$	10525.8	−	7647.43i	0.468689	−	0.340523i
$797$	−13134.2	+	9542.54i	−0.583735	+	0.424108i	−0.840069	−	0.542480i	$-0.817485\pi$
$797$	−13134.2	+	9542.54i	−0.583735	+	0.424108i	0.256334	+	0.966588i	$0.417485\pi$
$798$	−8239.61	−	25358.9i	−0.365513	−	1.12493i
$799$	−4771.04			−0.211248
$800$	−3697.80	+	1525.21i	−0.163421	+	0.0674054i
$801$	12335.4			0.544133
$802$	−4297.73	−	13227.0i	−0.189224	−	0.582373i
$803$	−4873.18	+	3540.58i	−0.214161	+	0.155597i
$804$	−7977.17	+	5795.76i	−0.349917	+	0.254230i
$805$	−12745.4	+	7125.26i	−0.558033	+	0.311966i
$806$	2461.25	+	1788.20i	0.107561	+	0.0781473i
$807$	−9315.56			−0.406349
$808$	9254.83	+	6724.03i	0.402950	+	0.292761i
$809$	5251.67	−	16163.0i	0.228231	−	0.702422i	−0.769717	−	0.638386i	$-0.779603\pi$
$809$	5251.67	−	16163.0i	0.228231	−	0.702422i	0.997948	−	0.0640366i	$-0.0203974\pi$
$810$	−1798.50	−	214.229i	−0.0780159	−	0.00929289i
$811$	−4175.17	−	12849.9i	−0.180777	−	0.556374i	0.819073	−	0.573689i	$-0.194488\pi$
$811$	−4175.17	−	12849.9i	−0.180777	−	0.556374i	−0.999850	+	0.0173150i	$0.994488\pi$
$812$	−2271.39	+	6990.62i	−0.0981652	+	0.302121i
$813$	−1875.56	+	5772.38i	−0.0809087	+	0.249011i
$814$	537.780	+	1655.12i	0.0231562	+	0.0712676i
$815$	−11239.4	−	1338.79i	−0.483067	−	0.0575407i
$816$	−951.434	+	2928.21i	−0.0408172	+	0.125622i
$817$	40654.2	+	29537.0i	1.74090	+	1.26483i
$818$	−10274.7			−0.439177
$819$	−3904.78	−	2836.99i	−0.166599	−	0.121041i
$820$	13692.0	−	7654.45i	0.583104	−	0.325982i
$821$	−20749.3	+	15075.2i	−0.882040	+	0.640839i	−0.933790	−	0.357821i	$-0.883520\pi$
$821$	−20749.3	+	15075.2i	−0.882040	+	0.640839i	0.0517507	+	0.998660i	$0.483520\pi$
$822$	−2152.21	+	1563.67i	−0.0913223	+	0.0663495i
$823$	−255.873	−	787.495i	−0.0108374	−	0.0333540i	0.945492	−	0.325646i	$-0.105582\pi$
$823$	−255.873	−	787.495i	−0.0108374	−	0.0333540i	−0.956329	+	0.292292i	$0.905582\pi$
$824$	12609.2			0.533083
$825$	3765.58	+	909.988i	0.158910	+	0.0384021i
$826$	40508.3			1.70637
$827$	−2671.96	−	8223.46i	−0.112350	−	0.345777i	0.879035	−	0.476757i	$-0.158188\pi$
$827$	−2671.96	−	8223.46i	−0.112350	−	0.345777i	−0.991385	+	0.130980i	$0.958188\pi$
$828$	1224.33	−	889.530i	0.0513871	−	0.0373349i
$829$	−34587.5	+	25129.3i	−1.44906	+	1.05281i	−0.463014	+	0.886351i	$0.653232\pi$
$829$	−34587.5	+	25129.3i	−1.44906	+	1.05281i	−0.986049	+	0.166455i	$0.946768\pi$
$830$	−26398.8	−	3144.51i	−1.10400	−	0.131503i
$831$	−2590.78	−	1882.31i	−0.108150	−	0.0785759i
$832$	1104.75			0.0460339
$833$	32289.3	+	23459.6i	1.34305	+	0.975782i
$834$	−2412.82	+	7425.90i	−0.100179	+	0.308319i
$835$	−630.810	+	1365.65i	−0.0261438	+	0.0565991i
$836$	−1826.53	−	5621.48i	−0.0755644	−	0.232563i
$837$	−735.244	+	2262.85i	−0.0303629	+	0.0934474i
$838$	−6936.45	+	21348.2i	−0.285938	+	0.880026i
$839$	−5792.51	−	17827.5i	−0.238355	−	0.733581i	−0.996659	−	0.0816793i	$-0.973972\pi$
$839$	−5792.51	−	17827.5i	−0.238355	−	0.733581i	0.758304	−	0.651901i	$-0.226028\pi$
$840$	−1620.25	−	8177.46i	−0.0665523	−	0.335892i
$841$	−6455.55	+	19868.1i	−0.264691	+	0.814635i
$842$	−17763.3	−	12905.8i	−0.727034	−	0.528221i
$843$	−7856.43			−0.320984
$844$	17661.3	+	12831.6i	0.720291	+	0.523322i
$845$	8903.32	−	19274.9i	0.362466	−	0.784707i
$846$	−1083.15	+	786.954i	−0.0440182	+	0.0319811i
$847$	30771.7	−	22357.0i	1.24832	−	0.906959i
$848$	2730.74	+	8404.35i	0.110583	+	0.340338i
$849$	2149.22			0.0868797
$850$	−1234.28	−	15988.4i	−0.0498065	−	0.645173i
$851$	−3540.84			−0.142630
$852$	522.918	+	1609.37i	0.0210268	+	0.0647139i
$853$	17808.3	−	12938.5i	0.714822	−	0.519349i	−0.169904	−	0.985461i	$-0.554346\pi$
$853$	17808.3	−	12938.5i	0.714822	−	0.519349i	0.884726	+	0.466112i	$0.154346\pi$
$854$	−674.343	+	489.939i	−0.0270205	+	0.0196316i
$855$	−10561.9	−	9777.99i	−0.422468	−	0.391111i
$856$	11633.1	+	8451.96i	0.464500	+	0.337479i
$857$	317.031			0.0126366			0.00631830	−	0.999980i	$-0.497989\pi$
$857$	317.031			0.0126366			0.00631830	+	0.999980i	$0.497989\pi$
$858$	−865.599	−	628.895i	−0.0344418	−	0.0250234i
$859$	10488.2	−	32279.4i	0.416592	−	1.28214i	−0.494226	−	0.869333i	$-0.664549\pi$
$859$	10488.2	−	32279.4i	0.416592	−	1.28214i	0.910819	−	0.412806i	$-0.135451\pi$
$860$	11529.0	+	10673.3i	0.457133	+	0.423204i
$861$	10102.4	+	31092.0i	0.399871	+	1.23068i
$862$	−210.536	+	647.963i	−0.00831889	+	0.0256029i
$863$	2748.95	−	8460.41i	0.108430	−	0.333715i	−0.882090	−	0.471081i	$-0.843864\pi$
$863$	2748.95	−	8460.41i	0.108430	−	0.333715i	0.990520	+	0.137367i	$0.0438638\pi$
$864$	266.991	+	821.713i	0.0105130	+	0.0323556i
$865$	−7351.73	+	4109.95i	−0.288978	+	0.161552i
$866$	−2347.98	+	7226.33i	−0.0921334	+	0.283557i
$867$	1938.16	+	1408.15i	0.0759208	+	0.0551597i
$868$	−10951.1			−0.428232
$869$	3594.59	+	2611.62i	0.140320	+	0.101948i
$870$	771.158	+	3892.06i	0.0300514	+	0.151670i
$871$	−11474.9	+	8337.04i	−0.446399	+	0.324328i
$872$	9681.34	−	7033.90i	0.375976	−	0.273163i
$873$	250.906	+	772.208i	0.00972722	+	0.0299373i
$874$	12026.2			0.465438
$875$	24041.3	+	36155.5i	0.928850	+	1.39689i
$876$	6996.99			0.269870
$877$	12421.4	+	38229.1i	0.478267	+	1.47196i	0.841500	+	0.540257i	$0.181673\pi$
$877$	12421.4	+	38229.1i	0.478267	+	1.47196i	−0.363233	+	0.931698i	$0.618327\pi$
$878$	24815.9	−	18029.8i	0.953867	−	0.693025i
$879$	19248.3	−	13984.7i	0.738601	−	0.536625i
$880$	−359.171	−	1812.75i	−0.0137587	−	0.0694408i
$881$	1253.22	+	910.520i	0.0479253	+	0.0348198i	0.611490	−	0.791252i	$-0.290570\pi$
$881$	1253.22	+	910.520i	0.0479253	+	0.0348198i	−0.563565	+	0.826072i	$0.690570\pi$
$882$	11200.0			0.427579
$883$	−4541.44	−	3299.55i	−0.173082	−	0.125751i	0.497872	−	0.867251i	$-0.334115\pi$
$883$	−4541.44	−	3299.55i	−0.173082	−	0.125751i	−0.670954	+	0.741499i	$0.734115\pi$
$884$	−1368.61	+	4212.15i	−0.0520717	+	0.160260i
$885$	19086.3	−	10670.1i	0.724946	−	0.405278i
$886$	−544.841	−	1676.85i	−0.0206595	−	0.0635833i
$887$	5397.43	−	16611.6i	0.204316	−	0.628819i	−0.795425	−	0.606052i	$-0.792752\pi$
$887$	5397.43	−	16611.6i	0.204316	−	0.628819i	0.999741	−	0.0227672i	$-0.00724766\pi$
$888$	624.685	−	1922.58i	0.0236070	−	0.0726550i
$889$	24272.3	+	74702.3i	0.915709	+	2.81826i
$890$	22489.7	+	20820.4i	0.847029	+	0.784160i
$891$	258.579	−	795.823i	0.00972246	−	0.0299226i
$892$	18778.5	+	13643.4i	0.704879	+	0.512124i
$893$	−10639.4			−0.398694
$894$	−6270.47	−	4555.76i	−0.234581	−	0.170433i
$895$	−13844.2	−	12816.6i	−0.517051	−	0.478674i
$896$	−3217.23	+	2337.45i	−0.119955	+	0.0871526i
$897$	1761.17	−	1279.56i	0.0655560	−	0.0476292i
$898$	−2257.55	−	6948.04i	−0.0838926	−	0.258195i
$899$	5212.19			0.193366
$900$	−2917.40	−	3426.19i	−0.108052	−	0.126896i
$901$	−35426.9			−1.30992
$902$	2239.46	+	6892.36i	0.0826674	+	0.254424i
$903$	−26490.0	+	19246.1i	−0.976226	+	0.709269i
$904$	−3749.72	+	2724.33i	−0.137958	+	0.100232i
$905$	−16340.3	+	35375.3i	−0.600187	+	1.29935i
$906$	−9831.73	−	7143.17i	−0.360527	−	0.261938i
$907$	8642.23			0.316384			0.158192	−	0.987408i	$-0.449433\pi$
$907$	8642.23			0.316384			0.158192	+	0.987408i	$0.449433\pi$
$908$	−14904.5	−	10828.7i	−0.544738	−	0.395775i
$909$	−3976.91	+	12239.7i	−0.145111	+	0.446605i
$910$	−2330.68	−	11763.1i	−0.0849027	−	0.428507i
$911$	7503.71	+	23094.0i	0.272897	+	0.839890i	0.989768	+	0.142685i	$0.0455734\pi$
$911$	7503.71	+	23094.0i	0.272897	+	0.839890i	−0.716871	+	0.697205i	$0.754427\pi$
$912$	−2121.69	+	6529.90i	−0.0770354	+	0.237091i
$913$	3795.48	−	11681.3i	0.137582	−	0.423433i
$914$	−5559.53	−	17110.5i	−0.201196	−	0.619217i
$915$	−188.677	+	408.470i	−0.00681692	+	0.0147580i
$916$	6304.62	−	19403.6i	0.227413	−	0.699906i
$917$	−15315.1	−	11127.1i	−0.551526	−	0.400707i
$918$	−3463.77			−0.124533
$919$	−4790.29	−	3480.35i	−0.171945	−	0.124925i	0.498485	−	0.866898i	$-0.333890\pi$
$919$	−4790.29	−	3480.35i	−0.171945	−	0.124925i	−0.670429	+	0.741973i	$0.733890\pi$
$920$	3733.58	+	444.726i	0.133796	+	0.0159372i
$921$	4999.39	−	3632.27i	0.178866	−	0.129954i
$922$	−4012.11	+	2914.97i	−0.143310	+	0.104121i
$923$	752.203	+	2315.04i	0.0268245	+	0.0825574i
$924$	3851.42			0.137124
$925$	810.394	+	10497.5i	0.0288061	+	0.373142i
$926$	−10816.6			−0.383862
$927$	4383.50	+	13491.0i	0.155311	+	0.477997i
$928$	1531.24	−	1112.51i	0.0541653	−	0.0393534i
$929$	−4060.94	+	2950.45i	−0.143418	+	0.104199i	−0.657181	−	0.753733i	$-0.728251\pi$
$929$	−4060.94	+	2950.45i	−0.143418	+	0.104199i	0.513763	+	0.857932i	$0.328251\pi$
$930$	−5159.84	+	2884.59i	−0.181933	+	0.101709i
$931$	72005.1	+	52314.8i	2.53477	+	1.84162i
$932$	22840.3			0.802745
$933$	−22547.5	−	16381.7i	−0.791183	−	0.574828i
$934$	−865.105	+	2662.52i	−0.0303074	+	0.0932765i
$935$	7356.58	+	876.282i	0.257311	+	0.0306497i
$936$	384.059	+	1182.01i	0.0134117	+	0.0412770i
$937$	−3244.52	+	9985.59i	−0.113120	+	0.348148i	−0.991550	−	0.129722i	$-0.958591\pi$
$937$	−3244.52	+	9985.59i	−0.113120	+	0.348148i	0.878430	+	0.477871i	$0.158591\pi$
$938$	15777.4	−	48558.0i	0.549202	−	1.69027i
$939$	7900.64	+	24315.7i	0.274577	+	0.845061i
$940$	−3303.04	−	393.443i	−0.114610	−	0.0136518i
$941$	−1713.73	+	5274.31i	−0.0593687	+	0.182718i	−0.976343	−	0.216229i	$-0.930624\pi$
$941$	−1713.73	+	5274.31i	−0.0593687	+	0.182718i	0.916974	+	0.398947i	$0.130624\pi$
$942$	14296.2	+	10386.8i	0.494476	+	0.359258i
$943$	−14745.0			−0.509188
$944$	−8438.73	−	6131.10i	−0.290951	−	0.211388i
$945$	8186.11	−	4576.41i	0.281793	−	0.157535i
$946$	−5872.21	+	4266.41i	−0.201820	+	0.146631i
$947$	−10133.9	+	7362.72i	−0.347738	+	0.252647i	−0.747920	−	0.663789i	$-0.768947\pi$
$947$	−10133.9	+	7362.72i	−0.347738	+	0.252647i	0.400181	+	0.916436i	$0.368947\pi$
$948$	−1594.89	−	4908.55i	−0.0546408	−	0.168167i
$949$	10065.0			0.344281
$950$	−2752.44	−	35654.0i	−0.0940011	−	1.21765i
$951$	−19827.1			−0.676064
$952$	−4926.53	−	15162.3i	−0.167720	−	0.516190i
$953$	35158.6	−	25544.2i	1.19507	−	0.868267i	0.201276	−	0.979534i	$-0.435491\pi$
$953$	35158.6	−	25544.2i	1.19507	−	0.868267i	0.993790	+	0.111268i	$0.0354911\pi$
$954$	−8042.82	+	5843.45i	−0.272952	+	0.198311i
$955$	32616.2	+	3885.09i	1.10517	+	0.131642i
$956$	−3410.69	−	2478.01i	−0.115387	−	0.0838334i
$957$	−1833.08			−0.0619176
$958$	14793.7	+	10748.3i	0.498918	+	0.362485i
$959$	4256.69	−	13100.7i	0.143332	−	0.441131i
$960$	−900.162	+	1948.77i	−0.0302631	+	0.0655170i
$961$	−6806.25	−	20947.5i	−0.228467	−	0.703148i
$962$	898.592	−	2765.58i	0.0301162	−	0.0926880i
$963$	−4998.89	+	15385.0i	−0.167276	+	0.514823i
$964$	−4528.21	−	13936.4i	−0.151290	−	0.465623i
$965$	−521.236	−	2630.70i	−0.0173878	−	0.0877567i
$966$	−2421.51	+	7452.65i	−0.0806531	+	0.248225i
$967$	29009.3	+	21076.5i	0.964713	+	0.700905i	0.954241	−	0.299040i	$-0.0966665\pi$
$967$	29009.3	+	21076.5i	0.964713	+	0.700905i	0.0104724	+	0.999945i	$0.496666\pi$
$968$	−9794.23			−0.325205
$969$	−22268.6	−	16179.1i	−0.738257	−	0.536375i
$970$	−845.930	+	1831.37i	−0.0280012	+	0.0606202i
$971$	41325.4	−	30024.7i	1.36580	−	0.992315i	0.367752	−	0.929924i	$-0.380127\pi$
$971$	41325.4	−	30024.7i	1.36580	−	0.992315i	0.998052	−	0.0623911i	$-0.0198726\pi$
$972$	−786.365	+	571.327i	−0.0259492	+	0.0188532i
$973$	−12493.6	−	38451.4i	−0.411641	−	1.26690i
$974$	979.326			0.0322173
$975$	−4196.60	−	4928.48i	−0.137845	−	0.161885i
$976$	214.634			0.00703922
$977$	7236.22	+	22270.8i	0.236957	+	0.729279i	0.996856	+	0.0792374i	$0.0252485\pi$
$977$	7236.22	+	22270.8i	0.236957	+	0.729279i	−0.759899	+	0.650042i	$0.774751\pi$
$978$	−4914.25	+	3570.41i	−0.160675	+	0.116737i
$979$	−11455.0	+	8322.53i	−0.373956	+	0.271695i
$980$	20419.6	+	18904.0i	0.665593	+	0.616191i
$981$	10891.5	+	7913.14i	0.354474	+	0.257540i
$982$	26254.6			0.853176
$983$	−30535.6	−	22185.4i	−0.990776	−	0.719841i	−0.0306852	−	0.999529i	$-0.509769\pi$
$983$	−30535.6	−	22185.4i	−0.990776	−	0.719841i	−0.960091	+	0.279688i	$0.909769\pi$
$984$	2601.36	−	8006.16i	0.0842767	−	0.259377i
$985$	−957.414	−	886.352i	−0.0309703	−	0.0286716i
$986$	2344.78	+	7216.50i	0.0757334	+	0.233083i
$987$	2142.28	−	6593.25i	0.0690876	−	0.212630i
$988$	−3052.00	+	9393.09i	−0.0982763	+	0.302463i
$989$	−4563.63	−	14045.4i	−0.146729	−	0.451586i
$990$	1814.67	−	1014.48i	0.0582566	−	0.0325681i
$991$	9658.59	−	29726.1i	0.309602	−	0.952856i	−0.668318	−	0.743876i	$-0.732985\pi$
$991$	9658.59	−	29726.1i	0.309602	−	0.952856i	0.977920	−	0.208981i	$-0.0670145\pi$
$992$	2281.35	+	1657.50i	0.0730172	+	0.0530501i
$993$	1614.02			0.0515805
$994$	−7088.77	−	5150.30i	−0.226199	−	0.164344i
$995$	7067.95	+	35672.2i	0.225195	+	1.13657i
$996$	−11542.4	+	8386.08i	−0.367205	+	0.266790i
$997$	9559.34	−	6945.26i	0.303658	−	0.220621i	−0.425512	−	0.904953i	$-0.639906\pi$
$997$	9559.34	−	6945.26i	0.303658	−	0.220621i	0.729171	+	0.684332i	$0.239906\pi$
$998$	3914.54	+	12047.7i	0.124161	+	0.382128i
$999$	2274.21			0.0720249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.g.b.31.2	✓	16
25.21	even	5	inner	150.4.g.b.121.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.4.g.b.31.2	✓	16	1.1	even	1	trivial
150.4.g.b.121.2	yes	16	25.21	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 + 1.90211i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-2.17298 - 10.9671i) q^{5} +(-4.85410 - 3.52671i) q^{6} +31.0680 q^{7} +(-6.47214 - 4.70228i) q^{8} +(2.78115 - 8.55951i) q^{9} +(19.5178 - 10.9113i) q^{10} +(3.19233 + 9.82498i) q^{11} +(3.70820 - 11.4127i) q^{12} +(5.33415 - 16.4168i) q^{13} +(19.2011 + 59.0949i) q^{14} +(24.6129 + 22.7861i) q^{15} +(4.94427 - 15.2169i) q^{16} +(51.8935 + 37.7028i) q^{17} +18.0000 q^{18} +(115.722 + 84.0771i) q^{19} +(32.8172 + 30.3814i) q^{20} +(-75.4037 + 54.7840i) q^{21} +(-16.7152 + 12.1443i) q^{22} +(-12.9904 - 39.9803i) q^{23} +24.0000 q^{24} +(-115.556 + 47.6628i) q^{25} +34.5233 q^{26} +(8.34346 + 25.6785i) q^{27} +(-100.538 + 73.0454i) q^{28} +(47.8512 - 34.7659i) q^{29} +(-28.1300 + 60.8991i) q^{30} +(71.2923 + 51.7969i) q^{31} +32.0000 q^{32} +(-25.0729 - 18.2165i) q^{33} +(-39.6431 + 122.009i) q^{34} +(-67.5104 - 340.728i) q^{35} +(11.1246 + 34.2380i) q^{36} +(26.0285 - 80.1076i) q^{37} +(-88.4039 + 272.079i) q^{38} +(16.0024 + 49.2505i) q^{39} +(-37.5067 + 81.1988i) q^{40} +(108.390 - 333.590i) q^{41} +(-150.807 - 109.568i) q^{42} +351.309 q^{43} +(-33.4305 - 24.2887i) q^{44} +(-99.9167 - 11.9016i) q^{45} +(68.0185 - 49.4183i) q^{46} +(-60.1750 + 43.7197i) q^{47} +(14.8328 + 45.6507i) q^{48} +622.223 q^{49} +(-162.078 - 190.344i) q^{50} -192.432 q^{51} +(21.3366 + 65.6673i) q^{52} +(-446.823 + 324.636i) q^{53} +(-43.6869 + 31.7404i) q^{54} +(100.815 - 56.3602i) q^{55} +(-201.077 - 146.091i) q^{56} -429.122 q^{57} +(95.7024 + 69.5319i) q^{58} +(201.457 - 620.020i) q^{59} +(-133.222 - 15.8688i) q^{60} +(4.14535 + 12.7581i) q^{61} +(-54.4625 + 167.618i) q^{62} +(86.4050 - 265.927i) q^{63} +(19.7771 + 60.8676i) q^{64} +(-191.637 - 22.8269i) q^{65} +(19.1540 - 58.9499i) q^{66} +(-664.765 - 482.980i) q^{67} -256.575 q^{68} +(102.028 + 74.1275i) q^{69} +(606.379 - 338.994i) q^{70} +(-114.085 + 82.8873i) q^{71} +(-58.2492 + 42.3205i) q^{72} +(180.182 + 554.544i) q^{73} +168.460 q^{74} +(196.414 - 319.447i) q^{75} -572.162 q^{76} +(99.1794 + 305.243i) q^{77} +(-83.7899 + 60.8769i) q^{78} +(347.955 - 252.804i) q^{79} +(-177.630 - 21.1584i) q^{80} +(-65.5304 - 47.6106i) q^{81} +701.514 q^{82} +(-961.871 - 698.840i) q^{83} +(115.207 - 354.570i) q^{84} +(300.728 - 651.051i) q^{85} +(217.121 + 668.229i) q^{86} +(-54.8326 + 168.757i) q^{87} +(25.5386 - 78.5998i) q^{88} +(423.539 + 1303.52i) q^{89} +(-39.1137 - 197.409i) q^{90} +(165.722 - 510.039i) q^{91} +(136.037 + 98.8367i) q^{92} -264.367 q^{93} +(-120.350 - 87.4393i) q^{94} +(670.623 - 1451.84i) q^{95} +(-77.6656 + 56.4274i) q^{96} +(-72.9866 + 53.0279i) q^{97} +(384.555 + 1183.54i) q^{98} +92.9753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Introduction

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