LMFDB - Embedded newform 201.4.e.a.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48985 + 2.58049i) q^{2} +3.00000 q^{3} +(-0.439276 + 0.760849i) q^{4} -11.6804 q^{5} +(4.46954 + 7.74146i) q^{6} +(9.08077 - 15.7283i) q^{7} +21.2197 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.48985 + 2.58049i) q^{2} +3.00000 q^{3} +(-0.439276 + 0.760849i) q^{4} -11.6804 q^{5} +(4.46954 + 7.74146i) q^{6} +(9.08077 - 15.7283i) q^{7} +21.2197 q^{8} +9.00000 q^{9} +(-17.4019 - 30.1410i) q^{10} +(32.7080 - 56.6519i) q^{11} +(-1.31783 + 2.28255i) q^{12} +(18.0138 + 31.2008i) q^{13} +54.1157 q^{14} -35.0411 q^{15} +(35.1283 + 60.8440i) q^{16} +(16.7119 + 28.9458i) q^{17} +(13.4086 + 23.2244i) q^{18} +(46.3021 + 80.1977i) q^{19} +(5.13091 - 8.88700i) q^{20} +(27.2423 - 47.1850i) q^{21} +194.919 q^{22} +(-53.5007 - 92.6660i) q^{23} +63.6591 q^{24} +11.4310 q^{25} +(-53.6756 + 92.9688i) q^{26} +27.0000 q^{27} +(7.97793 + 13.8182i) q^{28} +(98.1994 - 170.086i) q^{29} +(-52.2058 - 90.4231i) q^{30} +(-44.0290 + 76.2605i) q^{31} +(-19.7926 + 34.2818i) q^{32} +(98.1239 - 169.956i) q^{33} +(-49.7963 + 86.2496i) q^{34} +(-106.067 + 183.713i) q^{35} +(-3.95349 + 6.84764i) q^{36} +(33.4886 + 58.0040i) q^{37} +(-137.966 + 238.964i) q^{38} +(54.0414 + 93.6025i) q^{39} -247.854 q^{40} +(31.4044 - 54.3940i) q^{41} +162.347 q^{42} -420.590 q^{43} +(28.7357 + 49.7716i) q^{44} -105.123 q^{45} +(159.416 - 276.116i) q^{46} +(57.7766 - 100.072i) q^{47} +(105.385 + 182.532i) q^{48} +(6.57940 + 11.3959i) q^{49} +(17.0304 + 29.4975i) q^{50} +(50.1357 + 86.8375i) q^{51} -31.6522 q^{52} +431.391 q^{53} +(40.2258 + 69.6732i) q^{54} +(-382.041 + 661.714i) q^{55} +(192.691 - 333.751i) q^{56} +(138.906 + 240.593i) q^{57} +585.208 q^{58} -294.175 q^{59} +(15.3927 - 26.6610i) q^{60} +(169.739 + 293.997i) q^{61} -262.386 q^{62} +(81.7269 - 141.555i) q^{63} +444.101 q^{64} +(-210.408 - 364.437i) q^{65} +584.758 q^{66} +(-527.580 - 149.742i) q^{67} -29.3646 q^{68} +(-160.502 - 277.998i) q^{69} -632.092 q^{70} +(-114.265 + 197.912i) q^{71} +190.977 q^{72} +(-85.3246 - 147.786i) q^{73} +(-99.7857 + 172.834i) q^{74} +34.2929 q^{75} -81.3578 q^{76} +(-594.027 - 1028.88i) q^{77} +(-161.027 + 278.906i) q^{78} +(-450.361 + 780.048i) q^{79} +(-410.311 - 710.680i) q^{80} +81.0000 q^{81} +187.151 q^{82} +(497.911 + 862.407i) q^{83} +(23.9338 + 41.4546i) q^{84} +(-195.201 - 338.098i) q^{85} +(-626.614 - 1085.33i) q^{86} +(294.598 - 510.259i) q^{87} +(694.053 - 1202.14i) q^{88} -1494.11 q^{89} +(-156.617 - 271.269i) q^{90} +654.317 q^{91} +94.0065 q^{92} +(-132.087 + 228.782i) q^{93} +344.313 q^{94} +(-540.826 - 936.738i) q^{95} +(-59.3777 + 102.845i) q^{96} +(-243.129 - 421.112i) q^{97} +(-19.6046 + 33.9561i) q^{98} +(294.372 - 509.867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.48985	+	2.58049i	0.526740	+	0.912340i	0.999515	+	0.0311567i	$0.00991910\pi$
$2$	1.48985	+	2.58049i	0.526740	+	0.912340i	−0.472775	+	0.881183i	$0.656748\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−0.439276	+	0.760849i	−0.0549096	+	0.0951061i
$5$	−11.6804			−1.04472			−0.522362	−	0.852724i	$-0.674949\pi$
$5$	−11.6804			−1.04472			−0.522362	+	0.852724i	$0.674949\pi$
$6$	4.46954	+	7.74146i	0.304113	+	0.526740i
$7$	9.08077	−	15.7283i	0.490315	−	0.849251i	−0.509623	−	0.860398i	$-0.670215\pi$
$7$	9.08077	−	15.7283i	0.490315	−	0.849251i	0.999938	+	0.0111471i	$0.00354832\pi$
$8$	21.2197			0.937787
$9$	9.00000			0.333333
$10$	−17.4019	−	30.1410i	−0.550298	−	0.953143i
$11$	32.7080	−	56.6519i	0.896529	−	1.55283i	0.0646287	−	0.997909i	$-0.479414\pi$
$11$	32.7080	−	56.6519i	0.896529	−	1.55283i	0.831900	−	0.554925i	$-0.187253\pi$
$12$	−1.31783	+	2.28255i	−0.0317020	+	0.0549096i
$13$	18.0138	+	31.2008i	0.384318	+	0.665658i	0.991674	−	0.128771i	$-0.0411033\pi$
$13$	18.0138	+	31.2008i	0.384318	+	0.665658i	−0.607356	+	0.794429i	$0.707770\pi$
$14$	54.1157			1.03307
$15$	−35.0411			−0.603172
$16$	35.1283	+	60.8440i	0.548879	+	0.950687i
$17$	16.7119	+	28.9458i	0.238425	+	0.412965i	0.960263	−	0.279098i	$-0.0900355\pi$
$17$	16.7119	+	28.9458i	0.238425	+	0.412965i	−0.721837	+	0.692063i	$0.756702\pi$
$18$	13.4086	+	23.2244i	0.175580	+	0.304113i
$19$	46.3021	+	80.1977i	0.559076	+	0.968348i	0.997574	+	0.0696157i	$0.0221773\pi$
$19$	46.3021	+	80.1977i	0.559076	+	0.968348i	−0.438498	+	0.898732i	$0.644489\pi$
$20$	5.13091	−	8.88700i	0.0573653	−	0.0993596i
$21$	27.2423	−	47.1850i	0.283084	−	0.490315i
$22$	194.919			1.88895
$23$	−53.5007	−	92.6660i	−0.485029	−	0.840095i	0.514823	−	0.857297i	$-0.327858\pi$
$23$	−53.5007	−	92.6660i	−0.485029	−	0.840095i	−0.999852	+	0.0172012i	$0.994524\pi$
$24$	63.6591			0.541432
$25$	11.4310			0.0914478
$26$	−53.6756	+	92.9688i	−0.404871	+	0.701257i
$27$	27.0000			0.192450
$28$	7.97793	+	13.8182i	0.0538460	+	0.0932640i
$29$	98.1994	−	170.086i	0.628799	−	1.08911i	−0.358994	−	0.933340i	$-0.616880\pi$
$29$	98.1994	−	170.086i	0.628799	−	1.08911i	0.987793	−	0.155772i	$-0.0497866\pi$
$30$	−52.2058	−	90.4231i	−0.317714	−	0.550298i
$31$	−44.0290	+	76.2605i	−0.255092	+	0.441832i	−0.964920	−	0.262542i	$-0.915439\pi$
$31$	−44.0290	+	76.2605i	−0.255092	+	0.441832i	0.709829	+	0.704374i	$0.248772\pi$
$32$	−19.7926	+	34.2818i	−0.109340	+	0.189382i
$33$	98.1239	−	169.956i	0.517611	−	0.896529i
$34$	−49.7963	+	86.2496i	−0.251176	+	0.435050i
$35$	−106.067	+	183.713i	−0.512244	+	0.887233i
$36$	−3.95349	+	6.84764i	−0.0183032	+	0.0317020i
$37$	33.4886	+	58.0040i	0.148797	+	0.257724i	0.930783	−	0.365572i	$-0.119127\pi$
$37$	33.4886	+	58.0040i	0.148797	+	0.257724i	−0.781986	+	0.623296i	$0.785793\pi$
$38$	−137.966	+	238.964i	−0.588975	+	1.02013i
$39$	54.0414	+	93.6025i	0.221886	+	0.384318i
$40$	−247.854			−0.979729
$41$	31.4044	−	54.3940i	0.119623	−	0.207193i	−0.799995	−	0.600006i	$-0.795165\pi$
$41$	31.4044	−	54.3940i	0.119623	−	0.207193i	0.919618	+	0.392813i	$0.128498\pi$
$42$	162.347			0.596446
$43$	−420.590			−1.49161			−0.745807	−	0.666162i	$-0.767936\pi$
$43$	−420.590			−1.49161			−0.745807	+	0.666162i	$0.767936\pi$
$44$	28.7357	+	49.7716i	0.0984560	+	0.170531i
$45$	−105.123			−0.348241
$46$	159.416	−	276.116i	0.510968	−	0.885023i
$47$	57.7766	−	100.072i	0.179310	−	0.310575i	−0.762334	−	0.647184i	$-0.775947\pi$
$47$	57.7766	−	100.072i	0.179310	−	0.310575i	0.941645	+	0.336609i	$0.109280\pi$
$48$	105.385	+	182.532i	0.316896	+	0.548879i
$49$	6.57940	+	11.3959i	0.0191819	+	0.0332241i
$50$	17.0304	+	29.4975i	0.0481692	+	0.0834315i
$51$	50.1357	+	86.8375i	0.137655	+	0.238425i
$52$	−31.6522			−0.0844109
$53$	431.391			1.11804			0.559020	−	0.829154i	$-0.311178\pi$
$53$	431.391			1.11804			0.559020	+	0.829154i	$0.311178\pi$
$54$	40.2258	+	69.6732i	0.101371	+	0.175580i
$55$	−382.041	+	661.714i	−0.936625	+	1.62228i
$56$	192.691	−	333.751i	0.459811	−	0.796417i
$57$	138.906	+	240.593i	0.322783	+	0.559076i
$58$	585.208			1.32485
$59$	−294.175			−0.649125			−0.324562	−	0.945864i	$-0.605217\pi$
$59$	−294.175			−0.649125			−0.324562	+	0.945864i	$0.605217\pi$
$60$	15.3927	−	26.6610i	0.0331199	−	0.0573653i
$61$	169.739	+	293.997i	0.356277	+	0.617090i	0.987336	−	0.158645i	$-0.0507127\pi$
$61$	169.739	+	293.997i	0.356277	+	0.617090i	−0.631059	+	0.775735i	$0.717379\pi$
$62$	−262.386			−0.537468
$63$	81.7269	−	141.555i	0.163438	−	0.283084i
$64$	444.101			0.867385
$65$	−210.408	−	364.437i	−0.401506	−	0.695429i
$66$	584.758			1.09059
$67$	−527.580	−	149.742i	−0.962002	−	0.273044i
$67$	−527.580	−	149.742i	−0.962002	−	0.273044i
$68$	−29.3646			−0.0523673
$69$	−160.502	−	277.998i	−0.280032	−	0.485029i
$70$	−632.092			−1.07928
$71$	−114.265	+	197.912i	−0.190996	+	0.330815i	−0.945581	−	0.325388i	$-0.894505\pi$
$71$	−114.265	+	197.912i	−0.190996	+	0.330815i	0.754585	+	0.656203i	$0.227838\pi$
$72$	190.977			0.312596
$73$	−85.3246	−	147.786i	−0.136801	−	0.236947i	0.789483	−	0.613773i	$-0.210349\pi$
$73$	−85.3246	−	147.786i	−0.136801	−	0.236947i	−0.926284	+	0.376826i	$0.877015\pi$
$74$	−99.7857	+	172.834i	−0.156755	+	0.271507i
$75$	34.2929			0.0527974
$76$	−81.3578			−0.122794
$77$	−594.027	−	1028.88i	−0.879164	−	1.52276i
$78$	−161.027	+	278.906i	−0.233752	+	0.404871i
$79$	−450.361	+	780.048i	−0.641387	+	1.11091i	0.343737	+	0.939066i	$0.388307\pi$
$79$	−450.361	+	780.048i	−0.641387	+	1.11091i	−0.985123	+	0.171848i	$0.945026\pi$
$80$	−410.311	−	710.680i	−0.573427	−	0.993205i
$81$	81.0000			0.111111
$82$	187.151			0.252041
$83$	497.911	+	862.407i	0.658468	+	1.14050i	0.981012	+	0.193945i	$0.0621284\pi$
$83$	497.911	+	862.407i	0.658468	+	1.14050i	−0.322545	+	0.946554i	$0.604538\pi$
$84$	23.9338	+	41.4546i	0.0310880	+	0.0538460i
$85$	−195.201	−	338.098i	−0.249088	−	0.431434i
$86$	−626.614	−	1085.33i	−0.785693	−	1.36086i
$87$	294.598	−	510.259i	0.363037	−	0.628799i
$88$	694.053	−	1202.14i	0.840754	−	1.45623i
$89$	−1494.11			−1.77950			−0.889750	−	0.456449i	$-0.849121\pi$
$89$	−1494.11			−1.77950			−0.889750	+	0.456449i	$0.849121\pi$
$90$	−156.617	−	271.269i	−0.183433	−	0.317714i
$91$	654.317			0.753748
$92$	94.0065			0.106531
$93$	−132.087	+	228.782i	−0.147277	+	0.255092i
$94$	344.313			0.377800
$95$	−540.826	−	936.738i	−0.584080	−	1.01166i
$96$	−59.3777	+	102.845i	−0.0631272	+	0.109340i
$97$	−243.129	−	421.112i	−0.254495	−	0.440799i	0.710263	−	0.703936i	$-0.248576\pi$
$97$	−243.129	−	421.112i	−0.254495	−	0.440799i	−0.964758	+	0.263138i	$0.915243\pi$
$98$	−19.6046	+	33.9561i	−0.0202078	+	0.0350009i
$99$	294.372	−	509.867i	0.298843	−	0.517611i
$100$	−5.02136	+	8.69725i	−0.00502136	+	0.00869725i
$101$	20.3590	−	35.2627i	0.0200573	−	0.0347403i	−0.855823	−	0.517270i	$-0.826948\pi$
$101$	20.3590	−	35.2627i	0.0200573	−	0.0347403i	0.875880	+	0.482529i	$0.160282\pi$
$102$	−149.389	+	258.749i	−0.145017	+	0.251176i
$103$	183.964	−	318.636i	0.175986	−	0.304817i	−0.764516	−	0.644605i	$-0.777022\pi$
$103$	183.964	−	318.636i	0.175986	−	0.304817i	0.940502	+	0.339788i	$0.110355\pi$
$104$	382.248	+	662.073i	0.360408	+	0.624246i
$105$	−318.200	+	551.139i	−0.295744	+	0.512244i
$106$	642.705	+	1113.20i	0.588916	+	1.02003i
$107$	−1035.48			−0.935546			−0.467773	−	0.883849i	$-0.654944\pi$
$107$	−1035.48			−0.935546			−0.467773	+	0.883849i	$0.654944\pi$
$108$	−11.8605	+	20.5429i	−0.0105673	+	0.0183032i
$109$	1088.26			0.956294			0.478147	−	0.878280i	$-0.341309\pi$
$109$	1088.26			0.956294			0.478147	+	0.878280i	$0.341309\pi$
$110$	−2276.73			−1.97343
$111$	100.466	+	174.012i	0.0859081	+	0.148797i
$112$	1275.97			1.07650
$113$	−468.348	+	811.203i	−0.389898	+	0.675323i	−0.992435	−	0.122767i	$-0.960823\pi$
$113$	−468.348	+	811.203i	−0.389898	+	0.675323i	0.602537	+	0.798091i	$0.294156\pi$
$114$	−413.898	+	716.893i	−0.340045	+	0.588975i
$115$	624.908	+	1082.37i	0.506722	+	0.877668i
$116$	86.2734	+	149.430i	0.0690542	+	0.119605i
$117$	162.124	+	280.808i	0.128106	+	0.221886i
$118$	−438.276	−	759.116i	−0.341920	−	0.592223i
$119$	607.027			0.467614
$120$	−743.562			−0.565647
$121$	−1474.12	−	2553.25i	−1.10753	−	1.91830i
$122$	−505.770	+	876.020i	−0.375330	+	0.650091i
$123$	94.2132	−	163.182i	0.0690644	−	0.119623i
$124$	−38.6818	−	66.9989i	−0.0280140	−	0.0485216i
$125$	1326.53			0.949186
$126$	487.042			0.344358
$127$	−260.012	+	450.355i	−0.181672	+	0.314666i	−0.942450	−	0.334347i	$-0.891484\pi$
$127$	−260.012	+	450.355i	−0.181672	+	0.314666i	0.760778	+	0.649012i	$0.224818\pi$
$128$	819.982	+	1420.25i	0.566226	+	0.980732i
$129$	−1261.77			−0.861184
$130$	626.950	−	1085.91i	0.422978	−	0.732620i
$131$	−1478.81			−0.986290			−0.493145	−	0.869947i	$-0.664153\pi$
$131$	−1478.81			−0.986290			−0.493145	+	0.869947i	$0.664153\pi$
$132$	86.2070	+	149.315i	0.0568436	+	0.0984560i
$133$	1681.84			1.09649
$134$	−399.604	−	1584.51i	−0.257616	−	1.02150i
$135$	−315.370			−0.201057
$136$	354.621	+	614.222i	0.223592	+	0.387273i
$137$	1014.93			0.632932			0.316466	−	0.948604i	$-0.397504\pi$
$137$	1014.93			0.632932			0.316466	+	0.948604i	$0.397504\pi$
$138$	478.247	−	828.348i	0.295008	−	0.510968i
$139$	−539.324			−0.329100			−0.164550	−	0.986369i	$-0.552617\pi$
$139$	−539.324			−0.329100			−0.164550	+	0.986369i	$0.552617\pi$
$140$	−93.1852	−	161.401i	−0.0562542	−	0.0974351i
$141$	173.330	−	300.216i	0.103525	−	0.179310i
$142$	−680.947			−0.402421
$143$	2356.78			1.37821
$144$	316.155	+	547.596i	0.182960	+	0.316896i
$145$	−1147.01	+	1986.67i	−0.656922	+	1.13782i
$146$	254.241	−	440.358i	0.144117	−	0.249618i
$147$	19.7382	+	34.1876i	0.0110747	+	0.0191819i
$148$	−58.8431			−0.0326816
$149$	−2390.28			−1.31423			−0.657113	−	0.753792i	$-0.728222\pi$
$149$	−2390.28			−1.31423			−0.657113	+	0.753792i	$0.728222\pi$
$150$	51.0911	+	88.4925i	0.0278105	+	0.0481692i
$151$	1211.45	+	2098.29i	0.652888	+	1.13084i	0.982419	+	0.186691i	$0.0597762\pi$
$151$	1211.45	+	2098.29i	0.652888	+	1.13084i	−0.329531	+	0.944145i	$0.606890\pi$
$152$	982.518	+	1701.77i	0.524294	+	0.908104i
$153$	150.407	+	260.513i	0.0794751	+	0.137655i
$154$	1770.02	−	3065.76i	0.926181	−	1.60419i
$155$	514.275	−	890.751i	0.266501	−	0.461592i
$156$	−94.9565			−0.0487347
$157$	315.673	+	546.761i	0.160468	+	0.277938i	0.935037	−	0.354551i	$-0.115366\pi$
$157$	315.673	+	546.761i	0.160468	+	0.277938i	−0.774569	+	0.632490i	$0.782033\pi$
$158$	−2683.87			−1.35138
$159$	1294.17			0.645500
$160$	231.185	−	400.423i	0.114230	−	0.197852i
$161$	−1943.31			−0.951269
$162$	120.677	+	209.019i	0.0585266	+	0.101371i
$163$	−1044.40	+	1808.96i	−0.501864	+	0.869254i	0.498134	+	0.867100i	$0.334019\pi$
$163$	−1044.40	+	1808.96i	−0.501864	+	0.869254i	−0.999998	+	0.00215361i	$0.999314\pi$
$164$	27.5904	+	47.7880i	0.0131369	+	0.0227538i
$165$	−1146.12	+	1985.14i	−0.540761	+	0.936625i
$166$	−1483.62	+	2569.71i	−0.693682	+	1.20149i
$167$	−1237.99	+	2144.27i	−0.573645	+	0.993583i	0.422542	+	0.906343i	$0.361138\pi$
$167$	−1237.99	+	2144.27i	−0.573645	+	0.993583i	−0.996187	+	0.0872393i	$0.972196\pi$
$168$	578.073	−	1001.25i	0.265472	−	0.459811i
$169$	449.505	−	778.566i	0.204600	−	0.354377i
$170$	581.638	−	1007.43i	0.262410	−	0.454507i
$171$	416.719	+	721.779i	0.186359	+	0.322783i
$172$	184.755	−	320.006i	0.0819039	−	0.141862i
$173$	2109.39	+	3653.56i	0.927015	+	1.60564i	0.788288	+	0.615307i	$0.210968\pi$
$173$	2109.39	+	3653.56i	0.927015	+	1.60564i	0.138728	+	0.990331i	$0.455699\pi$
$174$	1755.62			0.764905
$175$	103.802	−	179.790i	0.0448382	−	0.0776621i
$176$	4595.90			1.96835
$177$	−882.526			−0.374772
$178$	−2225.99	−	3855.53i	−0.937333	−	1.62351i
$179$	622.052			0.259745			0.129873	−	0.991531i	$-0.458543\pi$
$179$	622.052			0.259745			0.129873	+	0.991531i	$0.458543\pi$
$180$	46.1782	−	79.9830i	0.0191218	−	0.0331199i
$181$	−1569.65	+	2718.72i	−0.644594	+	1.11647i	0.339801	+	0.940497i	$0.389640\pi$
$181$	−1569.65	+	2718.72i	−0.644594	+	1.11647i	−0.984395	+	0.175972i	$0.943693\pi$
$182$	974.831	+	1688.46i	0.397029	+	0.687674i
$183$	509.218	+	881.991i	0.205697	+	0.356277i
$184$	−1135.27	−	1966.35i	−0.454854	−	0.787831i
$185$	−391.159	−	677.508i	−0.155452	−	0.269251i
$186$	−787.157			−0.310307
$187$	2186.45			0.855021
$188$	50.7598	+	87.9186i	0.0196917	+	0.0341070i
$189$	245.181	−	424.665i	0.0943612	−	0.163438i
$190$	1611.49	−	2791.19i	0.615316	−	1.06576i
$191$	−2037.52	−	3529.08i	−0.771883	−	1.33694i	−0.936530	−	0.350588i	$-0.885982\pi$
$191$	−2037.52	−	3529.08i	−0.771883	−	1.33694i	0.164647	−	0.986353i	$-0.447352\pi$
$192$	1332.30			0.500785
$193$	5290.03			1.97298			0.986488	−	0.163832i	$-0.0523856\pi$
$193$	5290.03			1.97298			0.986488	+	0.163832i	$0.0523856\pi$
$194$	724.450	−	1254.78i	0.268106	−	0.464373i
$195$	−631.224	−	1093.31i	−0.231810	−	0.401506i
$196$	−11.5607			−0.00421309
$197$	669.777	−	1160.09i	0.242232	−	0.419558i	−0.719118	−	0.694888i	$-0.755454\pi$
$197$	669.777	−	1160.09i	0.242232	−	0.419558i	0.961350	+	0.275330i	$0.0887873\pi$
$198$	1754.27			0.629650
$199$	186.115	+	322.360i	0.0662981	+	0.114832i	0.897269	−	0.441484i	$-0.145548\pi$
$199$	186.115	+	322.360i	0.0662981	+	0.114832i	−0.830971	+	0.556316i	$0.812215\pi$
$200$	242.562			0.0857586
$201$	−1582.74	−	449.227i	−0.555412	−	0.157642i
$202$	121.327			0.0422600
$203$	−1783.45	−	3089.03i	−0.616620	−	1.06802i
$204$	−88.0937			−0.0302343
$205$	−366.815	+	635.342i	−0.124973	+	0.216460i
$206$	1096.31			0.370795
$207$	−481.507	−	833.994i	−0.161676	−	0.280032i
$208$	−1265.59	+	2192.06i	−0.421888	+	0.730732i
$209$	6057.80			2.00491
$210$	−1896.27			−0.623121
$211$	418.450	+	724.776i	0.136527	+	0.236472i	0.926180	−	0.377082i	$-0.123072\pi$
$211$	418.450	+	724.776i	0.136527	+	0.236472i	−0.789653	+	0.613554i	$0.789739\pi$
$212$	−189.500	+	328.223i	−0.0613910	+	0.106332i
$213$	−342.794	+	593.737i	−0.110272	+	0.190996i
$214$	−1542.70	−	2672.04i	−0.492789	−	0.853536i
$215$	4912.65			1.55833
$216$	572.932			0.180477
$217$	799.635	+	1385.01i	0.250151	+	0.433274i
$218$	1621.33	+	2808.23i	0.503718	+	0.872465i
$219$	−255.974	−	443.359i	−0.0789822	−	0.136801i
$220$	−335.643	−	581.351i	−0.102859	−	0.178158i
$221$	−602.090	+	1042.85i	−0.183262	+	0.317419i
$222$	−299.357	+	518.502i	−0.0905024	+	0.156755i
$223$	3110.25			0.933980			0.466990	−	0.884263i	$-0.345338\pi$
$223$	3110.25			0.933980			0.466990	+	0.884263i	$0.345338\pi$
$224$	359.464	+	622.609i	0.107222	+	0.185713i
$225$	102.879			0.0304826
$226$	−2791.06			−0.821499
$227$	1579.35	−	2735.52i	0.461785	−	0.799835i	−0.537265	−	0.843413i	$-0.680543\pi$
$227$	1579.35	−	2735.52i	0.461785	−	0.799835i	0.999050	+	0.0435785i	$0.0138759\pi$
$228$	−244.073			−0.0708954
$229$	−214.930	−	372.270i	−0.0620218	−	0.107425i	0.833347	−	0.552750i	$-0.186422\pi$
$229$	−214.930	−	372.270i	−0.0620218	−	0.107425i	−0.895369	+	0.445325i	$0.853088\pi$
$230$	−1862.03	+	3225.14i	−0.533821	+	0.924605i
$231$	−1782.08	−	3086.65i	−0.507586	−	0.879164i
$232$	2083.76	−	3609.18i	0.589680	−	1.02136i
$233$	135.626	−	234.911i	0.0381337	−	0.0660494i	−0.846329	−	0.532661i	$-0.821192\pi$
$233$	135.626	−	234.911i	0.0381337	−	0.0660494i	0.884462	+	0.466612i	$0.154525\pi$
$234$	−483.080	+	836.719i	−0.134957	+	0.233752i
$235$	−674.852	+	1168.88i	−0.187330	+	0.324465i
$236$	129.224	−	223.823i	0.0356432	−	0.0617358i
$237$	−1351.08	+	2340.14i	−0.370305	+	0.641387i
$238$	904.376	+	1566.43i	0.246311	+	0.426623i
$239$	−3484.63	+	6035.55i	−0.943104	+	1.63350i	−0.183601	+	0.983001i	$0.558775\pi$
$239$	−3484.63	+	6035.55i	−0.943104	+	1.63350i	−0.759503	+	0.650504i	$0.774558\pi$
$240$	−1230.93	−	2132.04i	−0.331068	−	0.573427i
$241$	−4280.66			−1.14416			−0.572078	−	0.820199i	$-0.693863\pi$
$241$	−4280.66			−1.14416			−0.572078	+	0.820199i	$0.693863\pi$
$242$	4392.43	−	7607.90i	1.16676	−	2.02089i
$243$	243.000			0.0641500
$244$	−298.250			−0.0782520
$245$	−76.8499	−	133.108i	−0.0200398	−	0.0347100i
$246$	561.452			0.145516
$247$	−1668.16	+	2889.33i	−0.429726	+	0.744307i
$248$	−934.283	+	1618.23i	−0.239222	+	0.414345i
$249$	1493.73	+	2587.22i	0.380167	+	0.658468i
$250$	1976.32	+	3423.09i	0.499974	+	0.865980i
$251$	−3748.08	−	6491.87i	−0.942537	−	1.63252i	−0.760610	−	0.649209i	$-0.775100\pi$
$251$	−3748.08	−	6491.87i	−0.942537	−	1.63252i	−0.181927	−	0.983312i	$-0.558233\pi$
$252$	71.8014	+	124.364i	0.0179487	+	0.0310880i
$253$	−6999.60			−1.73937
$254$	−1549.51			−0.382776
$255$	−585.603	−	1014.29i	−0.143811	−	0.249088i
$256$	−666.889	+	1155.09i	−0.162815	+	0.282003i
$257$	−692.413	+	1199.29i	−0.168060	+	0.291089i	−0.937738	−	0.347344i	$-0.887084\pi$
$257$	−692.413	+	1199.29i	−0.168060	+	0.291089i	0.769677	+	0.638433i	$0.220417\pi$
$258$	−1879.84	−	3255.98i	−0.453620	−	0.785693i
$259$	1216.41			0.291830
$260$	369.709			0.0881861
$261$	883.795	−	1530.78i	0.209600	−	0.363037i
$262$	−2203.19	−	3816.04i	−0.519518	−	0.899832i
$263$	−3607.01			−0.845694			−0.422847	−	0.906201i	$-0.638969\pi$
$263$	−3607.01			−0.845694			−0.422847	+	0.906201i	$0.638969\pi$
$264$	2082.16	−	3606.41i	0.485409	−	0.840754i
$265$	−5038.80			−1.16804
$266$	2505.67	+	4339.96i	0.577567	+	1.00038i
$267$	−4482.33			−1.02739
$268$	345.685	−	335.630i	0.0787912	−	0.0764995i
$269$	8226.38			1.86458			0.932288	−	0.361717i	$-0.117809\pi$
$269$	8226.38			1.86458			0.932288	+	0.361717i	$0.117809\pi$
$270$	−469.852	−	813.808i	−0.105905	−	0.183433i
$271$	−1351.93			−0.303040			−0.151520	−	0.988454i	$-0.548417\pi$
$271$	−1351.93			−0.303040			−0.151520	+	0.988454i	$0.548417\pi$
$272$	−1174.12	+	2033.64i	−0.261733	+	0.453336i
$273$	1962.95			0.435176
$274$	1512.10	+	2619.03i	0.333391	+	0.577449i
$275$	373.884	−	647.586i	0.0819856	−	0.142003i
$276$	282.019			0.0615057
$277$	−1615.51			−0.350420			−0.175210	−	0.984531i	$-0.556060\pi$
$277$	−1615.51			−0.350420			−0.175210	+	0.984531i	$0.556060\pi$
$278$	−803.509	−	1391.72i	−0.173350	−	0.300251i
$279$	−396.261	+	686.345i	−0.0850306	+	0.147277i
$280$	−2250.70	+	3898.33i	−0.480376	+	0.832036i
$281$	3804.05	+	6588.82i	0.807583	+	1.39878i	0.914533	+	0.404511i	$0.132558\pi$
$281$	3804.05	+	6588.82i	0.807583	+	1.39878i	−0.106950	+	0.994264i	$0.534108\pi$
$282$	1032.94			0.218123
$283$	−7854.81			−1.64989			−0.824947	−	0.565209i	$-0.808795\pi$
$283$	−7854.81			−1.64989			−0.824947	+	0.565209i	$0.808795\pi$
$284$	−100.388	−	173.876i	−0.0209750	−	0.0363298i
$285$	−1622.48	−	2810.21i	−0.337219	−	0.584080i
$286$	3511.24	+	6081.64i	0.725957	+	1.25740i
$287$	−570.352	−	987.879i	−0.117306	−	0.203180i
$288$	−178.133	+	308.536i	−0.0364465	+	0.0631272i
$289$	1897.93	−	3287.30i	0.386307	−	0.669103i
$290$	−6835.44			−1.38411
$291$	−729.388	−	1263.34i	−0.146933	−	0.254495i
$292$	149.924			0.0300468
$293$	9052.97			1.80505			0.902526	−	0.430635i	$-0.141710\pi$
$293$	9052.97			1.80505			0.902526	+	0.430635i	$0.141710\pi$
$294$	−58.8138	+	101.868i	−0.0116670	+	0.0202078i
$295$	3436.08			0.678156
$296$	710.619	+	1230.83i	0.139540	+	0.241691i
$297$	883.115	−	1529.60i	0.172537	−	0.298843i
$298$	−3561.15	−	6168.09i	−0.692255	−	1.19902i
$299$	1927.50	−	3338.54i	0.372811	−	0.645727i
$300$	−15.0641	+	26.0917i	−0.00289908	+	0.00502136i
$301$	−3819.28	+	6615.19i	−0.731361	+	1.26676i
$302$	−3609.73	+	6252.24i	−0.687804	+	1.19131i
$303$	61.0769	−	105.788i	0.0115801	−	0.0200573i
$304$	−3253.03	+	5634.41i	−0.613730	+	1.06301i
$305$	−1982.62	−	3433.99i	−0.372211	−	0.644688i
$306$	−448.166	+	776.247i	−0.0837254	+	0.145017i
$307$	−4346.25	−	7527.93i	−0.807992	−	1.39948i	−0.914252	−	0.405145i	$-0.867221\pi$
$307$	−4346.25	−	7527.93i	−0.807992	−	1.39948i	0.106260	−	0.994338i	$-0.466112\pi$
$308$	1043.77			0.193098
$309$	551.893	−	955.908i	0.101606	−	0.175986i
$310$	3064.76			0.561506
$311$	4410.72			0.804209			0.402105	−	0.915594i	$-0.368279\pi$
$311$	4410.72			0.804209			0.402105	+	0.915594i	$0.368279\pi$
$312$	1146.74	+	1986.22i	0.208082	+	0.360408i
$313$	5419.27			0.978644			0.489322	−	0.872103i	$-0.337244\pi$
$313$	5419.27			0.978644			0.489322	+	0.872103i	$0.337244\pi$
$314$	−940.607	+	1629.18i	−0.169050	+	0.292802i
$315$	−954.600	+	1653.42i	−0.170748	+	0.295744i
$316$	−395.666	−	685.313i	−0.0704365	−	0.122000i
$317$	−5284.23	−	9152.56i	−0.936252	−	1.62164i	−0.772385	−	0.635154i	$-0.780936\pi$
$317$	−5284.23	−	9152.56i	−0.936252	−	1.62164i	−0.163867	−	0.986482i	$-0.552397\pi$
$318$	1928.12	+	3339.60i	0.340011	+	0.588916i
$319$	−6423.81	−	11126.4i	−1.12747	−	1.95284i
$320$	−5187.26			−0.906178
$321$	−3106.43			−0.540138
$322$	−2895.23	−	5014.69i	−0.501071	−	0.867881i
$323$	−1547.59	+	2680.51i	−0.266596	+	0.461757i
$324$	−35.5814	+	61.6288i	−0.00610106	+	0.0105673i
$325$	205.915	+	356.656i	0.0351450	+	0.0608730i
$326$	−6223.98			−1.05741
$327$	3264.77			0.552116
$328$	666.392	−	1154.22i	0.112181	−	0.194303i
$329$	−1049.31	−	1817.46i	−0.175837	−	0.304559i
$330$	−6830.18			−1.13936
$331$	−743.407	+	1287.62i	−0.123448	+	0.213818i	−0.921125	−	0.389266i	$-0.872729\pi$
$331$	−743.407	+	1287.62i	−0.123448	+	0.213818i	0.797677	+	0.603085i	$0.206062\pi$
$332$	−874.882			−0.144625
$333$	301.398	+	522.036i	0.0495991	+	0.0859081i
$334$	−7377.67			−1.20865
$335$	6162.32	+	1749.04i	1.00503	+	0.285255i
$336$	3827.90			0.621515
$337$	−355.867	−	616.380i	−0.0575232	−	0.0996331i	0.835830	−	0.548989i	$-0.184987\pi$
$337$	−355.867	−	616.380i	−0.0575232	−	0.0996331i	−0.893353	+	0.449356i	$0.851654\pi$
$338$	2678.77			0.431083
$339$	−1405.04	+	2433.61i	−0.225108	+	0.389898i
$340$	342.989			0.0547094
$341$	2880.20	+	4988.65i	0.457395	+	0.792231i
$342$	−1241.69	+	2150.68i	−0.196325	+	0.340045i
$343$	6468.39			1.01825
$344$	−8924.80			−1.39882
$345$	1874.72	+	3247.12i	0.292556	+	0.506722i
$346$	−6285.32	+	10886.5i	−0.976592	+	1.69151i
$347$	4395.20	−	7612.72i	0.679962	−	1.17773i	−0.295029	−	0.955488i	$-0.595329\pi$
$347$	4395.20	−	7612.72i	0.679962	−	1.17773i	0.974992	−	0.222241i	$-0.0713372\pi$
$348$	258.820	+	448.290i	0.0398685	+	0.0690542i
$349$	−6771.64			−1.03862			−0.519309	−	0.854587i	$-0.673811\pi$
$349$	−6771.64			−1.03862			−0.519309	+	0.854587i	$0.673811\pi$
$350$	618.596			0.0944724
$351$	486.373	+	842.423i	0.0739620	+	0.128106i
$352$	1294.75	+	2242.57i	0.196052	+	0.339572i
$353$	3892.90	+	6742.70i	0.586964	+	1.01665i	0.994627	+	0.103519i	$0.0330103\pi$
$353$	3892.90	+	6742.70i	0.586964	+	1.01665i	−0.407664	+	0.913132i	$0.633656\pi$
$354$	−1314.83	−	2277.35i	−0.197408	−	0.341920i
$355$	1334.65	−	2311.69i	0.199538	−	0.345610i
$356$	656.328	−	1136.79i	0.0977115	−	0.169241i
$357$	1821.08			0.269977
$358$	926.761	+	1605.20i	0.136818	+	0.236976i
$359$	10967.7			1.61240			0.806199	−	0.591644i	$-0.201521\pi$
$359$	10967.7			1.61240			0.806199	+	0.591644i	$0.201521\pi$
$360$	−2230.69			−0.326576
$361$	−858.278	+	1486.58i	−0.125132	+	0.216734i
$362$	−9354.17			−1.35813
$363$	−4422.36	−	7659.76i	−0.639432	−	1.10753i
$364$	−287.426	+	497.836i	−0.0413879	+	0.0716860i
$365$	996.622	+	1726.20i	0.142919	+	0.247544i
$366$	−1517.31	+	2628.06i	−0.216697	+	0.375330i
$367$	4895.35	−	8479.00i	0.696282	−	1.20600i	−0.273465	−	0.961882i	$-0.588170\pi$
$367$	4895.35	−	8479.00i	0.696282	−	1.20600i	0.969747	−	0.244113i	$-0.0784969\pi$
$368$	3758.78	−	6510.39i	0.532445	−	0.922222i
$369$	282.640	−	489.546i	0.0398743	−	0.0690644i
$370$	1165.53	−	2018.76i	0.163765	−	0.283650i
$371$	3917.36	−	6785.06i	0.548192	−	0.949496i
$372$	−116.046	−	200.997i	−0.0161739	−	0.0280140i
$373$	2157.54	−	3736.96i	0.299499	−	0.518747i	−0.676523	−	0.736422i	$-0.736514\pi$
$373$	2157.54	−	3736.96i	0.299499	−	0.518747i	0.976021	+	0.217675i	$0.0698473\pi$
$374$	3257.47	+	5642.10i	0.450373	+	0.780070i
$375$	3979.58			0.548013
$376$	1226.00	−	2123.50i	0.168155	−	0.291253i
$377$	7075.79			0.966635
$378$	1461.12			0.198815
$379$	4493.61	+	7783.17i	0.609027	+	1.05487i	0.991401	+	0.130859i	$0.0417734\pi$
$379$	4493.61	+	7783.17i	0.609027	+	1.05487i	−0.382374	+	0.924008i	$0.624893\pi$
$380$	950.289			0.128286
$381$	−780.037	+	1351.06i	−0.104889	+	0.181672i
$382$	6071.17	−	10515.6i	0.813163	−	1.40844i
$383$	−3045.10	−	5274.28i	−0.406260	−	0.703663i	0.588207	−	0.808710i	$-0.299834\pi$
$383$	−3045.10	−	5274.28i	−0.406260	−	0.703663i	−0.994467	+	0.105047i	$0.966501\pi$
$384$	2459.95	+	4260.75i	0.326911	+	0.566226i
$385$	6938.45	+	12017.7i	0.918483	+	1.59086i
$386$	7881.32	+	13650.8i	1.03925	+	1.80003i
$387$	−3785.31			−0.497205
$388$	427.204			0.0558969
$389$	−1004.95	−	1740.63i	−0.130985	−	0.226873i	0.793071	−	0.609129i	$-0.208481\pi$
$389$	−1004.95	−	1740.63i	−0.130985	−	0.226873i	−0.924057	+	0.382256i	$0.875147\pi$
$390$	1880.85	−	3257.73i	0.244207	−	0.422978i
$391$	1788.20	−	3097.25i	0.231286	−	0.400600i
$392$	139.613	+	241.817i	0.0179886	+	0.0311571i
$393$	−4436.42			−0.569435
$394$	3991.46			0.510372
$395$	5260.38	−	9111.24i	0.670072	−	1.16060i
$396$	258.621	+	447.945i	0.0328187	+	0.0568436i
$397$	6160.17			0.778766			0.389383	−	0.921076i	$-0.372688\pi$
$397$	6160.17			0.778766			0.389383	+	0.921076i	$0.372688\pi$
$398$	−554.564	+	960.533i	−0.0698437	+	0.120973i
$399$	5045.51			0.633061
$400$	401.551	+	695.506i	0.0501938	+	0.0869382i
$401$	−7811.25			−0.972756			−0.486378	−	0.873748i	$-0.661682\pi$
$401$	−7811.25			−0.972756			−0.486378	+	0.873748i	$0.661682\pi$
$402$	−1198.81	−	4753.52i	−0.148735	−	0.589761i
$403$	−3172.52			−0.392145
$404$	17.8864	+	30.9802i	0.00220268	+	0.00381515i
$405$	−946.110			−0.116080
$406$	5314.14	−	9204.35i	0.649596	−	1.12513i
$407$	4381.38			0.533604
$408$	1063.86	+	1842.67i	0.129091	+	0.223592i
$409$	484.628	−	839.401i	0.0585901	−	0.101481i	−0.835243	−	0.549882i	$-0.814673\pi$
$409$	484.628	−	839.401i	0.0585901	−	0.101481i	0.893833	+	0.448401i	$0.148006\pi$
$410$	−2185.99			−0.263313
$411$	3044.80			0.365424
$412$	161.623	+	279.938i	0.0193266	+	0.0334747i
$413$	−2671.34	+	4626.89i	−0.318276	+	0.551270i
$414$	1434.74	−	2485.04i	0.170323	−	0.295008i
$415$	−5815.78	−	10073.2i	−0.687917	−	1.19151i
$416$	−1426.16			−0.168085
$417$	−1617.97			−0.190006
$418$	9025.18	+	15632.1i	1.05607	+	1.82916i
$419$	−323.531	−	560.372i	−0.0377220	−	0.0653364i	0.846548	−	0.532312i	$-0.178677\pi$
$419$	−323.531	−	560.372i	−0.0377220	−	0.0653364i	−0.884270	+	0.466976i	$0.845343\pi$
$420$	−279.556	−	484.204i	−0.0324784	−	0.0562542i
$421$	−2384.92	−	4130.80i	−0.276090	−	0.478202i	0.694320	−	0.719667i	$-0.255705\pi$
$421$	−2384.92	−	4130.80i	−0.276090	−	0.478202i	−0.970410	+	0.241465i	$0.922372\pi$
$422$	−1246.85	+	2159.61i	−0.143829	+	0.249119i
$423$	519.990	−	900.648i	0.0597701	−	0.103525i
$424$	9153.99			1.04848
$425$	191.033	+	330.879i	0.0218035	+	0.0377647i
$426$	−2042.84			−0.232338
$427$	6165.45			0.698752
$428$	454.861	−	787.843i	0.0513704	−	0.0889762i
$429$	7070.34			0.795709
$430$	7319.09	+	12677.0i	0.820832	+	1.42172i
$431$	−2828.25	+	4898.68i	−0.316084	+	0.547473i	−0.979667	−	0.200629i	$-0.935701\pi$
$431$	−2828.25	+	4898.68i	−0.316084	+	0.547473i	0.663584	+	0.748102i	$0.269035\pi$
$432$	948.464	+	1642.79i	0.105632	+	0.182960i
$433$	8472.27	−	14674.4i	0.940303	−	1.62865i	0.175409	−	0.984496i	$-0.443875\pi$
$433$	8472.27	−	14674.4i	0.940303	−	1.62865i	0.764894	−	0.644157i	$-0.222792\pi$
$434$	−2382.66	+	4126.89i	−0.263529	+	0.456445i
$435$	−3441.02	+	5960.02i	−0.379274	+	0.656922i
$436$	−478.045	+	827.999i	−0.0525097	+	0.0909494i
$437$	4954.40	−	8581.27i	0.542336	−	0.939354i
$438$	762.722	−	1321.07i	0.0832061	−	0.144117i
$439$	7587.02	+	13141.1i	0.824849	+	1.42868i	0.902035	+	0.431663i	$0.142073\pi$
$439$	7587.02	+	13141.1i	0.824849	+	1.42868i	−0.0771862	+	0.997017i	$0.524594\pi$
$440$	−8106.80	+	14041.4i	−0.878355	+	1.52136i
$441$	59.2146	+	102.563i	0.00639398	+	0.0110747i
$442$	−3588.08			−0.386126
$443$	−888.970	+	1539.74i	−0.0953414	+	0.165136i	−0.909751	−	0.415154i	$-0.863728\pi$
$443$	−888.970	+	1539.74i	−0.0953414	+	0.165136i	0.814410	+	0.580290i	$0.197061\pi$
$444$	−176.529			−0.0188687
$445$	17451.8			1.85909
$446$	4633.78	+	8025.95i	0.491964	+	0.852107i
$447$	−7170.85			−0.758768
$448$	4032.78	−	6984.98i	0.425292	−	0.736627i
$449$	1645.69	−	2850.42i	0.172973	−	0.299598i	−0.766485	−	0.642262i	$-0.777996\pi$
$449$	1645.69	−	2850.42i	0.172973	−	0.299598i	0.939458	+	0.342664i	$0.111329\pi$
$450$	153.273	+	265.477i	0.0160564	+	0.0278105i
$451$	−2054.35	−	3558.23i	−0.214491	−	0.371509i
$452$	−411.469	−	712.685i	−0.0428183	−	0.0741634i
$453$	3634.34	+	6294.86i	0.376945	+	0.652888i
$454$	9411.95			0.972962
$455$	−7642.66			−0.787458
$456$	2947.55	+	5105.31i	0.302701	+	0.524294i
$457$	−8173.96	+	14157.7i	−0.836677	+	1.44917i	0.0559803	+	0.998432i	$0.482172\pi$
$457$	−8173.96	+	14157.7i	−0.836677	+	1.44917i	−0.892657	+	0.450736i	$0.851162\pi$
$458$	640.426	−	1109.25i	0.0653387	−	0.113170i
$459$	451.221	+	781.538i	0.0458850	+	0.0794751i
$460$	−1098.03			−0.111295
$461$	−15289.4			−1.54468			−0.772342	−	0.635207i	$-0.780915\pi$
$461$	−15289.4			−1.54468			−0.772342	+	0.635207i	$0.780915\pi$
$462$	5310.05	−	9197.27i	0.534731	−	0.926181i
$463$	−8246.41	−	14283.2i	−0.827739	−	1.43369i	−0.899808	−	0.436286i	$-0.856294\pi$
$463$	−8246.41	−	14283.2i	−0.827739	−	1.43369i	0.0720690	−	0.997400i	$-0.477040\pi$
$464$	13798.3			1.38054
$465$	1542.83	−	2672.25i	0.153864	−	0.266501i
$466$	808.246			0.0803461
$467$	−8327.04	−	14422.9i	−0.825116	−	1.42914i	−0.901830	−	0.432090i	$-0.857776\pi$
$467$	−8327.04	−	14422.9i	−0.825116	−	1.42914i	0.0767140	−	0.997053i	$-0.475557\pi$
$468$	−284.870			−0.0281370
$469$	−7146.03	+	6938.18i	−0.703567	+	0.683103i
$470$	−4021.70			−0.394696
$471$	947.019	+	1640.28i	0.0926461	+	0.160468i
$472$	−6242.31			−0.608741
$473$	−13756.7	+	23827.2i	−1.33728	+	2.31623i
$474$	−8051.61			−0.780217
$475$	529.279	+	916.738i	0.0511263	+	0.0885533i
$476$	−266.653	+	461.856i	−0.0256765	+	0.0444730i
$477$	3882.52			0.372680
$478$	−20766.2			−1.98708
$479$	−3512.83	−	6084.41i	−0.335084	−	0.580383i	0.648417	−	0.761286i	$-0.275432\pi$
$479$	−3512.83	−	6084.41i	−0.335084	−	0.580383i	−0.983501	+	0.180902i	$0.942098\pi$
$480$	693.554	−	1201.27i	0.0659505	−	0.114230i
$481$	−1206.52	+	2089.75i	−0.114371	+	0.198096i
$482$	−6377.52	−	11046.2i	−0.602673	−	1.04386i
$483$	−5829.93			−0.549215
$484$	2590.19			0.243256
$485$	2839.84	+	4918.75i	0.265877	+	0.460513i
$486$	362.032	+	627.058i	0.0337904	+	0.0585266i
$487$	−130.465	−	225.973i	−0.0121395	−	0.0210263i	0.859892	−	0.510476i	$-0.170531\pi$
$487$	−130.465	−	225.973i	−0.0121395	−	0.0210263i	−0.872031	+	0.489450i	$0.837198\pi$
$488$	3601.82	+	6238.53i	0.334112	+	0.578699i
$489$	−3133.20	+	5426.87i	−0.289751	+	0.501864i
$490$	228.989	−	396.620i	0.0211115	−	0.0365663i
$491$	−18982.8			−1.74477			−0.872383	−	0.488822i	$-0.837427\pi$
$491$	−18982.8			−1.74477			−0.872383	+	0.488822i	$0.837427\pi$
$492$	82.7713	+	143.364i	0.00758459	+	0.0131369i
$493$	6564.39			0.599686
$494$	−9941.18			−0.905414
$495$	−3438.37	+	5955.43i	−0.312208	+	0.540761i
$496$	−6186.66			−0.560059
$497$	2075.22	+	3594.39i	0.187297	+	0.324407i
$498$	−4450.86	+	7709.12i	−0.400498	+	0.693682i
$499$	2841.19	+	4921.08i	0.254888	+	0.441479i	0.964865	−	0.262746i	$-0.0846281\pi$
$499$	2841.19	+	4921.08i	0.254888	+	0.441479i	−0.709977	+	0.704225i	$0.751295\pi$
$500$	−582.712	+	1009.29i	−0.0521194	+	0.0902734i
$501$	−3713.98	+	6432.80i	−0.331194	+	0.573645i
$502$	11168.1	−	19343.7i	0.992943	−	1.71983i
$503$	6872.62	−	11903.7i	0.609215	−	1.05519i	−0.382155	−	0.924098i	$-0.624818\pi$
$503$	6872.62	−	11903.7i	0.609215	−	1.05519i	0.991370	−	0.131093i	$-0.0418487\pi$
$504$	1734.22	−	3003.76i	0.153270	−	0.265472i
$505$	−237.800	+	411.882i	−0.0209544	+	0.0362941i
$506$	−10428.3	−	18062.4i	−0.916196	−	1.58690i
$507$	1348.52	−	2335.70i	0.118126	−	0.204600i
$508$	−228.435	−	395.660i	−0.0199511	−	0.0345563i
$509$	9876.27			0.860035			0.430018	−	0.902820i	$-0.358507\pi$
$509$	9876.27			0.860035			0.430018	+	0.902820i	$0.358507\pi$
$510$	1744.92	−	3022.28i	0.151502	−	0.262410i
$511$	−3099.25			−0.268303
$512$	9145.47			0.789407
$513$	1250.16	+	2165.34i	0.107594	+	0.186359i
$514$	−4126.35			−0.354096
$515$	−2148.77	+	3721.78i	−0.183857	+	0.318449i
$516$	554.266	−	960.017i	0.0472872	−	0.0819039i
$517$	−3779.51	−	6546.30i	−0.321514	−	0.556878i
$518$	1812.26	+	3138.93i	0.153719	+	0.266248i
$519$	6328.16	+	10960.7i	0.535213	+	0.927015i
$520$	−4464.79	−	7733.25i	−0.376527	−	0.652164i
$521$	4257.29			0.357995			0.178997	−	0.983850i	$-0.442715\pi$
$521$	4257.29			0.357995			0.178997	+	0.983850i	$0.442715\pi$
$522$	5266.87			0.441618
$523$	4949.89	+	8573.45i	0.413850	+	0.716809i	0.995307	−	0.0967683i	$-0.0308506\pi$
$523$	4949.89	+	8573.45i	0.413850	+	0.716809i	−0.581457	+	0.813577i	$0.697517\pi$
$524$	649.605	−	1125.15i	0.0541568	−	0.0938023i
$525$	311.406	−	539.371i	0.0258874	−	0.0448382i
$526$	−5373.88	−	9307.83i	−0.445461	−	0.771560i
$527$	−2943.23			−0.243281
$528$	13787.7			1.13643
$529$	358.842	−	621.533i	0.0294931	−	0.0510835i
$530$	−7507.04	−	13002.6i	−0.615254	−	1.06565i
$531$	−2647.58			−0.216375
$532$	−738.791	+	1279.62i	−0.0602080	+	0.104283i
$533$	2262.85			0.183893
$534$	−6677.98	−	11566.6i	−0.541170	−	0.937333i
$535$	12094.8			0.977387
$536$	−11195.1	−	3177.49i	−0.902153	−	0.256057i
$537$	1866.16			0.149964
$538$	12256.0	+	21228.1i	0.982146	+	1.70113i
$539$	860.796			0.0687887
$540$	138.535	−	239.949i	0.0110400	−	0.0191218i
$541$	−318.786			−0.0253339			−0.0126670	−	0.999920i	$-0.504032\pi$
$541$	−318.786			−0.0253339			−0.0126670	+	0.999920i	$0.504032\pi$
$542$	−2014.16	−	3488.63i	−0.159623	−	0.276475i
$543$	−4708.96	+	8156.16i	−0.372156	+	0.644594i
$544$	−1323.09			−0.104277
$545$	−12711.2			−0.999063
$546$	2924.49	+	5065.37i	0.229225	+	0.397029i
$547$	−12638.6	+	21890.8i	−0.987915	+	1.71112i	−0.359725	+	0.933058i	$0.617130\pi$
$547$	−12638.6	+	21890.8i	−0.987915	+	1.71112i	−0.628190	+	0.778060i	$0.716204\pi$
$548$	−445.837	+	772.212i	−0.0347540	+	0.0601957i
$549$	1527.65	+	2645.97i	0.118759	+	0.205697i
$550$	2228.12			0.172740
$551$	18187.4			1.40619
$552$	−3405.81	−	5899.04i	−0.262610	−	0.454854i
$553$	8179.24	+	14166.9i	0.628963	+	1.08940i
$554$	−2406.85	−	4168.79i	−0.184580	−	0.319702i
$555$	−1173.48	−	2032.52i	−0.0897502	−	0.155452i
$556$	236.912	−	410.344i	0.0180707	−	0.0312994i
$557$	3376.06	−	5847.51i	0.256819	−	0.444824i	−0.708569	−	0.705642i	$-0.750659\pi$
$557$	3376.06	−	5847.51i	0.256819	−	0.444824i	0.965388	+	0.260818i	$0.0839921\pi$
$558$	−2361.47			−0.179156
$559$	−7576.44	−	13122.8i	−0.573254	−	0.992905i
$560$	−14903.8			−1.12464
$561$	6559.34			0.493646
$562$	−11334.9	+	19632.6i	−0.850772	+	1.47358i
$563$	−9942.01			−0.744237			−0.372119	−	0.928185i	$-0.621369\pi$
$563$	−9942.01			−0.744237			−0.372119	+	0.928185i	$0.621369\pi$
$564$	152.279	+	263.756i	0.0113690	+	0.0196917i
$565$	5470.48	−	9475.15i	0.407336	−	0.705526i
$566$	−11702.5	−	20269.2i	−0.869065	−	1.50527i
$567$	735.542	−	1274.00i	0.0544795	−	0.0943612i
$568$	−2424.66	+	4199.64i	−0.179114	+	0.310234i
$569$	−1578.58	+	2734.18i	−0.116305	+	0.201446i	−0.918301	−	0.395884i	$-0.870438\pi$
$569$	−1578.58	+	2734.18i	−0.116305	+	0.201446i	0.801996	+	0.597330i	$0.203772\pi$
$570$	4834.48	−	8373.57i	0.355253	−	0.615316i
$571$	−6261.13	+	10844.6i	−0.458879	+	0.794802i	−0.998902	−	0.0468483i	$-0.985082\pi$
$571$	−6261.13	+	10844.6i	−0.458879	+	0.794802i	0.540023	+	0.841650i	$0.318416\pi$
$572$	−1035.28	+	1793.15i	−0.0756768	+	0.131076i
$573$	−6112.55	−	10587.3i	−0.445647	−	0.771883i
$574$	1699.47	−	2943.57i	0.123579	−	0.214046i
$575$	−611.566	−	1059.26i	−0.0443549	−	0.0768249i
$576$	3996.91			0.289128
$577$	−6644.01	+	11507.8i	−0.479365	+	0.830285i	−0.999720	−	0.0236651i	$-0.992466\pi$
$577$	−6644.01	+	11507.8i	−0.479365	+	0.830285i	0.520355	+	0.853950i	$0.325800\pi$
$578$	11310.5			0.813933
$579$	15870.1			1.13910
$580$	−1007.71	−	1745.40i	−0.0721425	−	0.124955i
$581$	18085.6			1.29143
$582$	2173.35	−	3764.35i	0.154791	−	0.268106i
$583$	14109.9	−	24439.1i	1.00235	−	1.73613i
$584$	−1810.56	−	3135.99i	−0.128290	−	0.222205i
$585$	−1893.67	−	3279.94i	−0.133835	−	0.231810i
$586$	13487.5	+	23361.1i	0.950793	+	1.64682i
$587$	−9472.93	−	16407.6i	−0.666081	−	1.15369i	−0.978991	−	0.203903i	$-0.934637\pi$
$587$	−9472.93	−	16407.6i	−0.666081	−	1.15369i	0.312910	−	0.949783i	$-0.398696\pi$
$588$	−34.6821			−0.00243243
$589$	−8154.56			−0.570463
$590$	5119.22	+	8866.75i	0.357212	+	0.618709i
$591$	2009.33	−	3480.26i	0.139853	−	0.242232i
$592$	−2352.80	+	4075.16i	−0.163343	+	0.282919i
$593$	−1664.38	−	2882.79i	−0.115258	−	0.199632i	0.802625	−	0.596484i	$-0.203436\pi$
$593$	−1664.38	−	2882.79i	−0.115258	−	0.199632i	−0.917883	+	0.396852i	$0.870103\pi$
$594$	5262.82			0.363529
$595$	−7090.30			−0.488528
$596$	1050.00	−	1818.64i	0.0721635	−	0.124991i
$597$	558.344	+	967.080i	0.0382772	+	0.0662981i
$598$	11486.7			0.785497
$599$	−4667.89	+	8085.03i	−0.318406	+	0.551495i	−0.980156	−	0.198230i	$-0.936481\pi$
$599$	−4667.89	+	8085.03i	−0.318406	+	0.551495i	0.661750	+	0.749725i	$0.269814\pi$
$600$	727.686			0.0495127
$601$	−5885.61	−	10194.2i	−0.399466	−	0.691895i	0.594194	−	0.804322i	$-0.297471\pi$
$601$	−5885.61	−	10194.2i	−0.399466	−	0.691895i	−0.993660	+	0.112426i	$0.964138\pi$
$602$	−22760.6			−1.54095
$603$	−4748.22	−	1347.68i	−0.320667	−	0.0910146i
$604$	−2128.64			−0.143399
$605$	17218.3	+	29822.9i	1.15706	+	2.00409i
$606$	363.980			0.0243988
$607$	−4667.50	+	8084.35i	−0.312106	+	0.540583i	−0.978818	−	0.204732i	$-0.934368\pi$
$607$	−4667.50	+	8084.35i	−0.312106	+	0.540583i	0.666712	+	0.745315i	$0.267701\pi$
$608$	−3665.76			−0.244516
$609$	−5350.36	−	9267.09i	−0.356006	−	0.616620i
$610$	5907.58	−	10232.2i	0.392117	−	0.679166i
$611$	4163.11			0.275649
$612$	−264.281			−0.0174558
$613$	−11775.7	−	20396.0i	−0.775880	−	1.34386i	−0.934299	−	0.356491i	$-0.883973\pi$
$613$	−11775.7	−	20396.0i	−0.775880	−	1.34386i	0.158419	−	0.987372i	$-0.449360\pi$
$614$	12950.5	−	22430.9i	0.851203	−	1.47433i
$615$	−1100.44	+	1906.03i	−0.0721532	+	0.124973i
$616$	−12605.1	−	21832.6i	−0.824469	−	1.42802i
$617$	−10556.9			−0.688824			−0.344412	−	0.938819i	$-0.611922\pi$
$617$	−10556.9			−0.688824			−0.344412	+	0.938819i	$0.611922\pi$
$618$	3288.94			0.214079
$619$	−4743.49	−	8215.97i	−0.308008	−	0.533486i	0.669918	−	0.742435i	$-0.266329\pi$
$619$	−4743.49	−	8215.97i	−0.308008	−	0.533486i	−0.977927	+	0.208949i	$0.932996\pi$
$620$	451.818	+	782.572i	0.0292669	+	0.0506917i
$621$	−1444.52	−	2501.98i	−0.0933439	−	0.161676i
$622$	6571.29	+	11381.8i	0.423609	+	0.733712i
$623$	−13567.7	+	23499.9i	−0.872516	+	1.51124i
$624$	−3796.77	+	6576.19i	−0.243577	+	0.421888i
$625$	−16923.2			−1.08309
$626$	8073.88	+	13984.4i	0.515491	+	0.892856i
$627$	18173.4			1.15754
$628$	−554.671			−0.0352449
$629$	−1119.32	+	1938.71i	−0.0709540	+	0.122896i
$630$	−5688.82			−0.359759
$631$	−3630.79	−	6288.72i	−0.229064	−	0.396751i	0.728467	−	0.685081i	$-0.240233\pi$
$631$	−3630.79	−	6288.72i	−0.229064	−	0.396751i	−0.957531	+	0.288330i	$0.906900\pi$
$632$	−9556.52	+	16552.4i	−0.601484	+	1.04180i
$633$	1255.35	+	2174.33i	0.0788241	+	0.136527i
$634$	15745.4	−	27271.8i	0.986323	−	1.70836i
$635$	3037.04	−	5260.31i	0.189797	−	0.328739i
$636$	−568.499	+	984.670i	−0.0354441	+	0.0613910i
$637$	−237.040	+	410.566i	−0.0147439	+	0.0255372i
$638$	19141.0	−	33153.1i	1.18777	−	2.05728i
$639$	−1028.38	+	1781.21i	−0.0636654	+	0.110272i
$640$	−9577.69	−	16589.1i	−0.591549	−	1.02459i
$641$	−2318.16	+	4015.16i	−0.142842	+	0.247409i	−0.928566	−	0.371168i	$-0.878957\pi$
$641$	−2318.16	+	4015.16i	−0.142842	+	0.247409i	0.785724	+	0.618577i	$0.212291\pi$
$642$	−4628.11	−	8016.11i	−0.284512	−	0.492789i
$643$	−8129.37			−0.498586			−0.249293	−	0.968428i	$-0.580198\pi$
$643$	−8129.37			−0.498586			−0.249293	+	0.968428i	$0.580198\pi$
$644$	853.651	−	1478.57i	0.0522338	−	0.0904715i
$645$	14737.9			0.899700
$646$	−9222.69			−0.561706
$647$	722.529	+	1251.46i	0.0439035	+	0.0760430i	0.887142	−	0.461496i	$-0.152687\pi$
$647$	722.529	+	1251.46i	0.0439035	+	0.0760430i	−0.843239	+	0.537539i	$0.819354\pi$
$648$	1718.80			0.104199
$649$	−9621.87	+	16665.6i	−0.581959	+	1.00798i
$650$	−613.564	+	1062.72i	−0.0370246	+	0.0641284i
$651$	2398.90	+	4155.02i	0.144425	+	0.250151i
$652$	−917.562	−	1589.26i	−0.0551143	−	0.0954607i
$653$	−6618.94	−	11464.3i	−0.396660	−	0.687035i	0.596651	−	0.802501i	$-0.296498\pi$
$653$	−6618.94	−	11464.3i	−0.396660	−	0.687035i	−0.993312	+	0.115465i	$0.963164\pi$
$654$	4864.00	+	8424.69i	0.290822	+	0.503718i
$655$	17273.0			1.03040
$656$	4412.73			0.262634
$657$	−767.921	−	1330.08i	−0.0456004	−	0.0789822i
$658$	3126.62	−	5415.47i	0.185241	−	0.320847i
$659$	12365.9	−	21418.4i	0.730969	−	1.26608i	−0.225501	−	0.974243i	$-0.572402\pi$
$659$	12365.9	−	21418.4i	0.730969	−	1.26608i	0.956470	−	0.291832i	$-0.0942648\pi$
$660$	−1006.93	−	1744.05i	−0.0593859	−	0.102859i
$661$	−15545.1			−0.914730			−0.457365	−	0.889279i	$-0.651207\pi$
$661$	−15545.1			−0.914730			−0.457365	+	0.889279i	$0.651207\pi$
$662$	−4430.24			−0.260100
$663$	−1806.27	+	3128.55i	−0.105806	+	0.183262i
$664$	10565.5	+	18300.0i	0.617503	+	1.06955i
$665$	−19644.5			−1.14553
$666$	−898.072	+	1555.51i	−0.0522516	+	0.0905024i
$667$	−21015.0			−1.21994
$668$	−1087.64	−	1883.85i	−0.0629972	−	0.109114i
$669$	9330.74			0.539233
$670$	4667.52	+	18507.6i	0.269137	+	1.06718i
$671$	22207.3			1.27765
$672$	1078.39	+	1867.83i	0.0619045	+	0.107222i
$673$	28232.1			1.61704			0.808520	−	0.588469i	$-0.200269\pi$
$673$	28232.1			1.61704			0.808520	+	0.588469i	$0.200269\pi$
$674$	1060.37	−	1836.62i	0.0605995	−	0.104961i
$675$	308.636			0.0175991
$676$	394.914	+	684.011i	0.0224689	+	0.0389173i
$677$	−2791.86	+	4835.65i	−0.158493	+	0.274519i	−0.934326	−	0.356421i	$-0.883997\pi$
$677$	−2791.86	+	4835.65i	−0.158493	+	0.274519i	0.775832	+	0.630939i	$0.217330\pi$
$678$	−8373.19			−0.474293
$679$	−8831.20			−0.499132
$680$	−4142.11	−	7174.34i	−0.233592	−	0.404593i
$681$	4738.05	−	8206.55i	0.266612	−	0.461785i
$682$	−8582.10	+	14864.6i	−0.481856	+	0.834599i
$683$	7236.84	+	12534.6i	0.405432	+	0.702228i	0.994372	−	0.105948i	$-0.0337879\pi$
$683$	7236.84	+	12534.6i	0.405432	+	0.702228i	−0.588940	+	0.808177i	$0.700455\pi$
$684$	−732.220			−0.0409315
$685$	−11854.8			−0.661239
$686$	9636.90	+	16691.6i	0.536353	+	0.928991i
$687$	−644.791	−	1116.81i	−0.0358083	−	0.0620218i
$688$	−14774.6	−	25590.4i	−0.818717	−	1.41806i
$689$	7770.99	+	13459.8i	0.429682	+	0.744232i
$690$	−5586.10	+	9675.41i	−0.308202	+	0.533821i
$691$	6164.86	−	10677.9i	0.339396	−	0.587850i	−0.644924	−	0.764247i	$-0.723111\pi$
$691$	6164.86	−	10677.9i	0.339396	−	0.587850i	0.984319	+	0.176397i	$0.0564442\pi$
$692$	−3706.41			−0.203608
$693$	−5346.24	−	9259.96i	−0.293055	−	0.507586i
$694$	26192.7			1.43265
$695$	6299.50			0.343818
$696$	6251.29	−	10827.6i	0.340452	−	0.589680i
$697$	2099.31			0.114085
$698$	−10088.7	−	17474.1i	−0.547081	−	0.947572i
$699$	406.877	−	704.732i	0.0220165	−	0.0381337i
$700$	91.1955	+	157.955i	0.00492410	+	0.00852879i
$701$	−12515.3	+	21677.1i	−0.674316	+	1.16795i	0.302352	+	0.953196i	$0.402228\pi$
$701$	−12515.3	+	21677.1i	−0.674316	+	1.16795i	−0.976668	+	0.214754i	$0.931105\pi$
$702$	−1449.24	+	2510.16i	−0.0779175	+	0.134957i
$703$	−3101.19	+	5371.42i	−0.166378	+	0.288175i
$704$	14525.6	−	25159.1i	0.777636	−	1.34690i
$705$	−2024.56	+	3506.63i	−0.108155	+	0.187330i
$706$	−11599.6	+	20091.2i	−0.618354	+	1.07102i
$707$	−369.750	−	640.425i	−0.0196688	−	0.0340674i
$708$	387.673	−	671.469i	0.0205786	−	0.0356432i
$709$	4000.32	+	6928.76i	0.211897	+	0.367017i	0.952308	−	0.305138i	$-0.0987024\pi$
$709$	4000.32	+	6928.76i	0.211897	+	0.367017i	−0.740411	+	0.672154i	$0.765369\pi$
$710$	7953.71			0.420419
$711$	−4053.25	+	7020.43i	−0.213796	+	0.370305i
$712$	−31704.6			−1.66879
$713$	9422.34			0.494908
$714$	2713.13	+	4699.28i	0.142208	+	0.246311i
$715$	−27528.1			−1.43985
$716$	−273.253	+	473.288i	−0.0142625	+	0.0247033i
$717$	−10453.9	+	18106.7i	−0.544501	+	0.943104i
$718$	16340.1	+	28301.9i	0.849314	+	1.47106i
$719$	−1365.29	−	2364.75i	−0.0708160	−	0.122657i	0.828443	−	0.560073i	$-0.189227\pi$
$719$	−1365.29	−	2364.75i	−0.0708160	−	0.122657i	−0.899259	+	0.437416i	$0.855894\pi$
$720$	−3692.80	−	6396.12i	−0.191142	−	0.331068i
$721$	−3341.08	−	5786.91i	−0.172577	−	0.298913i
$722$	−5114.80			−0.263647
$723$	−12842.0			−0.660579
$724$	−1379.02	−	2388.54i	−0.0707887	−	0.122610i
$725$	1122.52	−	1944.25i	0.0575023	−	0.0995969i
$726$	13177.3	−	22823.7i	0.673629	−	1.16676i
$727$	13627.0	+	23602.7i	0.695183	+	1.20409i	0.970119	+	0.242630i	$0.0780100\pi$
$727$	13627.0	+	23602.7i	0.695183	+	1.20409i	−0.274936	+	0.961462i	$0.588657\pi$
$728$	13884.4			0.706855
$729$	729.000			0.0370370
$730$	−2969.63	+	5143.54i	−0.150563	+	0.260782i
$731$	−7028.86	−	12174.3i	−0.355639	−	0.615984i
$732$	−894.749			−0.0451788
$733$	−7212.07	+	12491.7i	−0.363416	+	0.629455i	−0.988521	−	0.151086i	$-0.951723\pi$
$733$	−7212.07	+	12491.7i	−0.363416	+	0.629455i	0.625105	+	0.780541i	$0.285056\pi$
$734$	29173.3			1.46704
$735$	−230.550	−	399.324i	−0.0115700	−	0.0200398i
$736$	4235.67			0.212132
$737$	−25739.2	+	24990.6i	−1.28645	+	1.24904i
$738$	1684.36			0.0840136
$739$	18121.2	+	31386.8i	0.902029	+	1.56236i	0.824857	+	0.565342i	$0.191256\pi$
$739$	18121.2	+	31386.8i	0.902029	+	1.56236i	0.0771720	+	0.997018i	$0.475411\pi$
$740$	687.309			0.0341432
$741$	−5004.47	+	8667.99i	−0.248102	+	0.429726i
$742$	23345.0			1.15502
$743$	1596.12	+	2764.57i	0.0788104	+	0.136504i	0.902737	−	0.430193i	$-0.141554\pi$
$743$	1596.12	+	2764.57i	0.0788104	+	0.136504i	−0.823927	+	0.566697i	$0.808221\pi$
$744$	−2802.85	+	4854.68i	−0.138115	+	0.239222i
$745$	27919.4			1.37300
$746$	12857.6			0.631031
$747$	4481.20	+	7761.66i	0.219489	+	0.380167i
$748$	−960.455	+	1663.56i	−0.0469488	+	0.0813177i
$749$	−9402.93	+	16286.4i	−0.458713	+	0.794513i
$750$	5928.96	+	10269.3i	0.288660	+	0.499974i
$751$	11510.7			0.559298			0.279649	−	0.960102i	$-0.409782\pi$
$751$	11510.7			0.559298			0.279649	+	0.960102i	$0.409782\pi$
$752$	8118.37			0.393679
$753$	−11244.2	−	19475.6i	−0.544174	−	0.942537i
$754$	10541.8	+	18259.0i	0.509165	+	0.881900i
$755$	−14150.1	−	24508.8i	−0.682088	−	1.18141i
$756$	215.404	+	373.091i	0.0103627	+	0.0179487i
$757$	2783.78	−	4821.66i	0.133657	−	0.231501i	−0.791427	−	0.611264i	$-0.790661\pi$
$757$	2783.78	−	4821.66i	0.133657	−	0.231501i	0.925084	+	0.379763i	$0.123995\pi$
$758$	−13389.6	+	23191.4i	−0.641598	+	1.11128i
$759$	−20998.8			−1.00423
$760$	−11476.2	−	19877.3i	−0.547743	−	0.948718i
$761$	18881.5			0.899415			0.449708	−	0.893176i	$-0.351528\pi$
$761$	18881.5			0.899415			0.449708	+	0.893176i	$0.351528\pi$
$762$	−4648.54			−0.220996
$763$	9882.20	−	17116.5i	0.468885	−	0.812133i
$764$	3580.13			0.169535
$765$	−1756.81	−	3042.88i	−0.0830295	−	0.143811i
$766$	9073.47	−	15715.7i	0.427987	−	0.741294i
$767$	−5299.22	−	9178.52i	−0.249470	−	0.432095i
$768$	−2000.67	+	3465.26i	−0.0940011	+	0.162815i
$769$	1447.22	−	2506.65i	0.0678647	−	0.117545i	−0.830096	−	0.557620i	$-0.811715\pi$
$769$	1447.22	−	2506.65i	0.0678647	−	0.117545i	0.897961	+	0.440075i	$0.145048\pi$
$770$	−20674.4	+	35809.2i	−0.967603	+	1.67594i
$771$	−2077.24	+	3597.88i	−0.0970297	+	0.168060i
$772$	−2323.78	+	4024.91i	−0.108335	+	0.187642i
$773$	18477.1	−	32003.3i	0.859734	−	1.48910i	−0.0124477	−	0.999923i	$-0.503962\pi$
$773$	18477.1	−	32003.3i	0.859734	−	1.48910i	0.872182	−	0.489181i	$-0.162704\pi$
$774$	−5639.53	−	9767.95i	−0.261898	−	0.453620i
$775$	−503.295	+	871.732i	−0.0233276	+	0.0404046i
$776$	−5159.13	−	8935.88i	−0.238663	−	0.413376i
$777$	3649.23			0.168488
$778$	2994.45	−	5186.54i	0.137990	−	0.239006i
$779$	5816.36			0.267513
$780$	1109.13			0.0509143
$781$	7474.73	+	12946.6i	0.342467	+	0.593171i
$782$	10656.5			0.487311
$783$	2651.39	−	4592.33i	0.121012	−	0.209600i
$784$	−462.246	+	800.634i	−0.0210571	+	0.0364720i
$785$	−3687.18	−	6386.37i	−0.167644	−	0.290369i
$786$	−6609.58	−	11448.1i	−0.299944	−	0.519518i
$787$	6858.50	+	11879.3i	0.310647	+	0.538056i	0.978503	−	0.206235i	$-0.0661210\pi$
$787$	6858.50	+	11879.3i	0.310647	+	0.538056i	−0.667856	+	0.744291i	$0.732788\pi$
$788$	588.435	+	1019.20i	0.0266017	+	0.0460754i
$789$	−10821.0			−0.488262
$790$	31348.6			1.41181
$791$	8505.92	+	14732.7i	0.382346	+	0.662243i
$792$	6246.48	−	10819.2i	0.280251	−	0.485409i
$793$	−6115.30	+	10592.0i	−0.273847	+	0.474317i
$794$	9177.70	+	15896.3i	0.410207	+	0.710500i
$795$	−15116.4			−0.674369
$796$	−327.023			−0.0145616
$797$	−17705.9	+	30667.5i	−0.786920	+	1.36299i	0.140925	+	0.990020i	$0.454992\pi$
$797$	−17705.9	+	30667.5i	−0.786920	+	1.36299i	−0.927845	+	0.372966i	$0.878341\pi$
$798$	7517.02	+	13019.9i	0.333458	+	0.577567i
$799$	3862.23			0.171008
$800$	−226.248	+	391.874i	−0.00999886	+	0.0173185i
$801$	−13447.0			−0.593167
$802$	−11637.6	−	20156.8i	−0.512389	−	0.887484i
$803$	−11163.2			−0.490585
$804$	1037.05	−	1006.89i	0.0454901	−	0.0441670i
$805$	22698.6			0.993813
$806$	−4726.57	−	8186.65i	−0.206559	−	0.357770i
$807$	24679.1			1.07651
$808$	432.011	−	748.265i	0.0188095	−	0.0325790i
$809$	26134.1			1.13576			0.567878	−	0.823113i	$-0.307765\pi$
$809$	26134.1			1.13576			0.567878	+	0.823113i	$0.307765\pi$
$810$	−1409.56	−	2441.42i	−0.0611442	−	0.105905i
$811$	−3092.04	+	5355.57i	−0.133879	+	0.231886i	−0.925169	−	0.379556i	$-0.876077\pi$
$811$	−3092.04	+	5355.57i	−0.133879	+	0.231886i	0.791289	+	0.611442i	$0.209410\pi$
$812$	3133.71			0.135433
$813$	−4055.78			−0.174960
$814$	6527.58	+	11306.1i	0.281071	+	0.486828i
$815$	12199.0	−	21129.3i	0.524309	−	0.908130i
$816$	−3522.36	+	6100.91i	−0.151112	+	0.261733i
$817$	−19474.2	−	33730.4i	−0.833926	−	1.44440i
$818$	2888.08			0.123447
$819$	5888.85			0.251249
$820$	−322.266	−	558.182i	−0.0137244	−	0.0237714i
$821$	3544.09	+	6138.54i	0.150657	+	0.260946i	0.931469	−	0.363820i	$-0.118528\pi$
$821$	3544.09	+	6138.54i	0.150657	+	0.260946i	−0.780812	+	0.624766i	$0.785194\pi$
$822$	4536.29	+	7857.08i	0.192483	+	0.333391i
$823$	−12114.1	−	20982.3i	−0.513088	−	0.888695i	−0.999885	−	0.0151797i	$-0.995168\pi$
$823$	−12114.1	−	20982.3i	−0.513088	−	0.888695i	0.486796	−	0.873515i	$-0.338165\pi$
$824$	3903.67	−	6761.36i	0.165037	−	0.285853i
$825$	1121.65	−	1942.76i	0.0473344	−	0.0819856i
$826$	−15919.5			−0.670594
$827$	−15848.8	−	27451.0i	−0.666406	−	1.15425i	−0.978902	−	0.204331i	$-0.934498\pi$
$827$	−15848.8	−	27451.0i	−0.666406	−	1.15425i	0.312495	−	0.949919i	$-0.398835\pi$
$828$	846.058			0.0355103
$829$	44771.7			1.87574			0.937868	−	0.346992i	$-0.112797\pi$
$829$	44771.7			1.87574			0.937868	+	0.346992i	$0.112797\pi$
$830$	17329.2	−	30015.1i	0.724706	−	1.25523i
$831$	−4846.52			−0.202315
$832$	7999.95	+	13856.3i	0.333352	+	0.577382i
$833$	−219.909	+	380.893i	−0.00914692	+	0.0158429i
$834$	−2410.53	−	4175.16i	−0.100084	−	0.173350i
$835$	14460.2	−	25045.8i	0.599301	−	1.03802i
$836$	−2661.05	+	4609.07i	−0.110089	+	0.190679i
$837$	−1188.78	+	2059.03i	−0.0490925	+	0.0850306i
$838$	964.021	−	1669.73i	0.0397393	−	0.0688305i
$839$	−11366.5	+	19687.3i	−0.467716	+	0.810108i	−0.999319	−	0.0368857i	$-0.988256\pi$
$839$	−11366.5	+	19687.3i	−0.467716	+	0.810108i	0.531604	+	0.846993i	$0.321590\pi$
$840$	−6752.11	+	11695.0i	−0.277345	+	0.480376i
$841$	−7091.76	−	12283.3i	−0.290777	−	0.503641i
$842$	7106.32	−	12308.5i	0.290855	−	0.503776i
$843$	11412.2	+	19766.4i	0.466258	+	0.807583i
$844$	−735.261			−0.0299866
$845$	−5250.39	+	9093.93i	−0.213750	+	0.370226i
$846$	3098.82			0.125933
$847$	−53544.6			−2.17215
$848$	15154.0	+	26247.5i	0.613669	+	1.06291i
$849$	−23564.4			−0.952567
$850$	−569.220	+	985.917i	−0.0229695	+	0.0397843i
$851$	3583.33	−	6206.51i	0.144342	−	0.250008i
$852$	−301.163	−	521.629i	−0.0121099	−	0.0209750i
$853$	5678.94	+	9836.22i	0.227952	+	0.394825i	0.957201	−	0.289424i	$-0.0934636\pi$
$853$	5678.94	+	9836.22i	0.227952	+	0.394825i	−0.729249	+	0.684249i	$0.760130\pi$
$854$	9185.56	+	15909.9i	0.368060	+	0.637499i
$855$	−4867.43	−	8430.64i	−0.194693	−	0.337219i
$856$	−21972.5			−0.877343
$857$	3408.40			0.135856			0.0679280	−	0.997690i	$-0.478361\pi$
$857$	3408.40			0.135856			0.0679280	+	0.997690i	$0.478361\pi$
$858$	10533.7	+	18244.9i	0.419132	+	0.725957i
$859$	12168.2	−	21076.0i	0.483324	−	0.837141i	−0.516493	−	0.856291i	$-0.672763\pi$
$859$	12168.2	−	21076.0i	0.483324	−	0.837141i	0.999817	+	0.0191503i	$0.00609609\pi$
$860$	−2158.01	+	3737.79i	−0.0855670	+	0.148206i
$861$	−1711.06	−	2963.64i	−0.0677266	−	0.117306i
$862$	−16854.6			−0.665976
$863$	−17488.7			−0.689830			−0.344915	−	0.938634i	$-0.612092\pi$
$863$	−17488.7			−0.689830			−0.344915	+	0.938634i	$0.612092\pi$
$864$	−534.400	+	925.607i	−0.0210424	+	0.0364465i
$865$	−24638.4	−	42675.0i	−0.968475	−	1.67745i
$866$	50489.5			1.98118
$867$	5693.78	−	9861.91i	0.223034	−	0.386307i
$868$	−1405.04			−0.0549427
$869$	29460.8	+	51027.5i	1.15004	+	1.99193i
$870$	−20506.3			−0.799114
$871$	−4831.63	−	19158.4i	−0.187961	−	0.745300i
$872$	23092.5			0.896800
$873$	−2188.16	−	3790.01i	−0.0848318	−	0.146933i
$874$	29525.1			1.14268
$875$	12045.9	−	20864.1i	0.465400	−	0.806097i
$876$	449.773			0.0173475
$877$	−4894.13	−	8476.89i	−0.188441	−	0.326390i	0.756289	−	0.654237i	$-0.227010\pi$
$877$	−4894.13	−	8476.89i	−0.188441	−	0.326390i	−0.944731	+	0.327847i	$0.893677\pi$
$878$	−22607.0	+	39156.4i	−0.868961	+	1.50508i
$879$	27158.9			1.04215
$880$	−53681.8			−2.05638
$881$	5799.48	+	10045.0i	0.221781	+	0.384136i	0.955349	−	0.295480i	$-0.0954796\pi$
$881$	5799.48	+	10045.0i	0.221781	+	0.384136i	−0.733568	+	0.679616i	$0.762146\pi$
$882$	−176.441	+	305.605i	−0.00673593	+	0.0116670i
$883$	8111.09	−	14048.8i	0.309128	−	0.535425i	−0.669044	−	0.743223i	$-0.733296\pi$
$883$	8111.09	−	14048.8i	0.309128	−	0.535425i	0.978172	+	0.207798i	$0.0666295\pi$
$884$	−528.968	−	916.199i	−0.0201257	−	0.0348587i
$885$	10308.2			0.391534
$886$	−5297.71			−0.200880
$887$	2802.86	+	4854.70i	0.106100	+	0.183771i	0.914187	−	0.405292i	$-0.132830\pi$
$887$	2802.86	+	4854.70i	0.106100	+	0.183771i	−0.808087	+	0.589063i	$0.799497\pi$
$888$	2131.86	+	3692.48i	0.0805635	+	0.139540i
$889$	4722.22	+	8179.13i	0.178153	+	0.308571i
$890$	26000.4	+	45034.1i	0.979254	+	1.69612i
$891$	2649.34	−	4588.80i	0.0996144	−	0.172537i
$892$	−1366.26	+	2366.43i	−0.0512844	+	0.0888272i
$893$	10700.7			0.400992
$894$	−10683.5	−	18504.3i	−0.399674	−	0.692255i
$895$	−7265.80			−0.271362
$896$	29784.3			1.11052
$897$	5782.51	−	10015.6i	0.215242	−	0.372811i
$898$	9807.29			0.364447
$899$	8647.25	+	14977.5i	0.320803	+	0.555647i
$900$	−45.1922	+	78.2752i	−0.00167379	+	0.00289908i
$901$	7209.35	+	12487.0i	0.266569	+	0.461711i
$902$	6121.32	−	10602.4i	0.225962	−	0.391378i
$903$	−11457.8	+	19845.6i	−0.422252	+	0.731361i
$904$	−9938.21	+	17213.5i	−0.365641	+	0.633310i
$905$	18334.1	−	31755.7i	0.673422	−	1.16640i
$906$	−10829.2	+	18756.7i	−0.397104	+	0.687804i
$907$	23407.9	−	40543.6i	0.856941	−	1.48426i	−0.0178921	−	0.999840i	$-0.505696\pi$
$907$	23407.9	−	40543.6i	0.856941	−	1.48426i	0.874833	−	0.484425i	$-0.160971\pi$
$908$	1387.54	+	2403.29i	0.0507128	+	0.0878372i
$909$	183.231	−	317.365i	0.00668578	−	0.0115801i
$910$	−11386.4	−	19721.8i	−0.414785	−	0.718430i
$911$	24714.6			0.898825			0.449413	−	0.893324i	$-0.351633\pi$
$911$	24714.6			0.898825			0.449413	+	0.893324i	$0.351633\pi$
$912$	−9759.09	+	16903.2i	−0.354337	+	0.613730i
$913$	65142.6			2.36134
$914$	−48711.7			−1.76284
$915$	−5947.85	−	10302.0i	−0.214896	−	0.372211i
$916$	377.655			0.0136224
$917$	−13428.7	+	23259.2i	−0.483593	+	0.837608i
$918$	−1344.50	+	2328.74i	−0.0483389	+	0.0837254i
$919$	1817.71	+	3148.36i	0.0652455	+	0.113009i	0.896803	−	0.442430i	$-0.145884\pi$
$919$	1817.71	+	3148.36i	0.0652455	+	0.113009i	−0.831557	+	0.555439i	$0.812550\pi$
$920$	13260.4	+	22967.6i	0.475197	+	0.823066i
$921$	−13038.8	−	22583.8i	−0.466495	−	0.807992i
$922$	−22778.9	−	39454.2i	−0.813647	−	1.40928i
$923$	−8233.37			−0.293613
$924$	3131.30			0.111485
$925$	382.808	+	663.042i	0.0136072	+	0.0235683i
$926$	24571.7	−	42559.5i	0.872006	−	1.51036i
$927$	1655.68	−	2867.72i	0.0586620	−	0.101606i
$928$	3887.24	+	6732.90i	0.137505	+	0.238166i
$929$	−34125.2			−1.20518			−0.602590	−	0.798051i	$-0.705865\pi$
$929$	−34125.2			−1.20518			−0.602590	+	0.798051i	$0.705865\pi$
$930$	9194.29			0.324185
$931$	−609.281	+	1055.31i	−0.0214483	+	0.0371496i
$932$	119.154	+	206.382i	0.00418780	+	0.00725349i
$933$	13232.2			0.464310
$934$	24812.0	−	42975.6i	0.869243	−	1.50557i
$935$	−25538.5			−0.893260
$936$	3440.23	+	5958.65i	0.120136	+	0.208082i
$937$	−47016.8			−1.63925			−0.819623	−	0.572904i	$-0.805817\pi$
$937$	−47016.8			−1.63925			−0.819623	+	0.572904i	$0.805817\pi$
$938$	−28550.4	−	8103.41i	−0.993819	−	0.282074i
$939$	16257.8			0.565020
$940$	−592.893	−	1026.92i	−0.0205724	−	0.0356324i
$941$	11331.5			0.392558			0.196279	−	0.980548i	$-0.437114\pi$
$941$	11331.5			0.392558			0.196279	+	0.980548i	$0.437114\pi$
$942$	−2821.82	+	4887.54i	−0.0976008	+	0.169050i
$943$	−6720.63			−0.232083
$944$	−10333.9	−	17898.8i	−0.356291	−	0.617115i
$945$	−2863.80	+	4960.25i	−0.0985814	+	0.170748i
$946$	−81981.1			−2.81759
$947$	60.9441			0.00209125			0.00104563	−	0.999999i	$-0.499667\pi$
$947$	60.9441			0.00209125			0.00104563	+	0.999999i	$0.499667\pi$
$948$	−1187.00	−	2055.94i	−0.0406665	−	0.0704365i
$949$	3074.04	−	5324.40i	0.105150	−	0.182126i
$950$	−1577.09	+	2731.59i	−0.0538605	+	0.0932891i
$951$	−15852.7	−	27457.7i	−0.540546	−	0.936252i
$952$	12880.9			0.438523
$953$	−44413.4			−1.50964			−0.754822	−	0.655930i	$-0.772277\pi$
$953$	−44413.4			−1.50964			−0.754822	+	0.655930i	$0.772277\pi$
$954$	5784.35	+	10018.8i	0.196305	+	0.340011i
$955$	23799.0	+	41221.0i	0.806404	+	1.39673i
$956$	−3061.43	−	5302.55i	−0.103571	−	0.179390i
$957$	−19271.4	−	33379.1i	−0.650947	−	1.12747i
$958$	10467.2	−	18129.6i	0.353005	−	0.611422i
$959$	9216.38	−	15963.2i	0.310336	−	0.537518i
$960$	−15561.8			−0.523182
$961$	11018.4	+	19084.4i	0.369856	+	0.640610i
$962$	−7190.09			−0.240975
$963$	−9319.30			−0.311849
$964$	1880.39	−	3256.94i	0.0628251	−	0.108816i
$965$	−61789.5			−2.06122
$966$	−8685.69	−	15044.1i	−0.289294	−	0.501071i
$967$	15388.4	−	26653.5i	0.511745	−	0.886369i	−0.488162	−	0.872753i	$-0.662332\pi$
$967$	15388.4	−	26653.5i	0.511745	−	0.886369i	0.999907	−	0.0136158i	$-0.00433417\pi$
$968$	−31280.4	−	54179.3i	−1.03863	−	1.79895i
$969$	−4642.78	+	8041.53i	−0.153919	+	0.266596i
$970$	−8461.84	+	14656.3i	−0.280096	+	0.485141i
$971$	−5517.72	+	9556.97i	−0.182360	+	0.315857i	−0.942684	−	0.333687i	$-0.891707\pi$
$971$	−5517.72	+	9556.97i	−0.182360	+	0.315857i	0.760323	+	0.649545i	$0.225040\pi$
$972$	−106.744	+	184.886i	−0.00352245	+	0.00610106i
$973$	−4897.47	+	8482.68i	−0.161363	+	0.279488i
$974$	388.747	−	673.329i	0.0127888	−	0.0221508i
$975$	617.746	+	1069.97i	0.0202910	+	0.0351450i
$976$	−11925.3	+	20655.2i	−0.391106	+	0.677415i
$977$	−29469.2	−	51042.2i	−0.964999	−	1.67143i	−0.709617	−	0.704587i	$-0.751132\pi$
$977$	−29469.2	−	51042.2i	−0.964999	−	1.67143i	−0.255382	−	0.966840i	$-0.582201\pi$
$978$	−18672.0			−0.610494
$979$	−48869.3	+	84644.2i	−1.59537	+	2.76327i
$980$	135.033			0.00440151
$981$	9794.30			0.318765
$982$	−28281.4	−	48984.8i	−0.919038	−	1.59182i
$983$	10187.6			0.330554			0.165277	−	0.986247i	$-0.447148\pi$
$983$	10187.6			0.330554			0.165277	+	0.986247i	$0.447148\pi$
$984$	1999.18	−	3462.67i	0.0647677	−	0.112181i
$985$	−7823.24	+	13550.3i	−0.253065	+	0.438322i
$986$	9779.93	+	16939.3i	0.315879	+	0.547118i
$987$	−3147.94	−	5452.38i	−0.101520	−	0.175837i
$988$	−1465.56	−	2538.43i	−0.0471921	−	0.0817391i
$989$	22501.9	+	38974.4i	0.723477	+	1.25310i
$990$	−20490.5			−0.657810
$991$	−12329.6			−0.395220			−0.197610	−	0.980281i	$-0.563318\pi$
$991$	−12329.6			−0.395220			−0.197610	+	0.980281i	$0.563318\pi$
$992$	−1742.90	−	3018.78i	−0.0557833	−	0.0966195i
$993$	−2230.22	+	3862.86i	−0.0712728	+	0.123448i
$994$	−6183.52	+	10710.2i	−0.197313	+	0.341756i
$995$	−2173.89	−	3765.28i	−0.0692632	−	0.119967i
$996$	−2624.65			−0.0834991
$997$	−25686.9			−0.815959			−0.407980	−	0.912991i	$-0.633767\pi$
$997$	−25686.9			−0.815959			−0.407980	+	0.912991i	$0.633767\pi$
$998$	−8465.86	+	14663.3i	−0.268519	+	0.465089i
$999$	904.193	+	1566.11i	0.0286360	+	0.0495991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.12	✓	32
67.29	even	3	inner	201.4.e.a.163.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.12	✓	32	1.1	even	1	trivial
201.4.e.a.163.12	yes	32	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48985 + 2.58049i) q^{2} +3.00000 q^{3} +(-0.439276 + 0.760849i) q^{4} -11.6804 q^{5} +(4.46954 + 7.74146i) q^{6} +(9.08077 - 15.7283i) q^{7} +21.2197 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.48985 + 2.58049i) q^{2} +3.00000 q^{3} +(-0.439276 + 0.760849i) q^{4} -11.6804 q^{5} +(4.46954 + 7.74146i) q^{6} +(9.08077 - 15.7283i) q^{7} +21.2197 q^{8} +9.00000 q^{9} +(-17.4019 - 30.1410i) q^{10} +(32.7080 - 56.6519i) q^{11} +(-1.31783 + 2.28255i) q^{12} +(18.0138 + 31.2008i) q^{13} +54.1157 q^{14} -35.0411 q^{15} +(35.1283 + 60.8440i) q^{16} +(16.7119 + 28.9458i) q^{17} +(13.4086 + 23.2244i) q^{18} +(46.3021 + 80.1977i) q^{19} +(5.13091 - 8.88700i) q^{20} +(27.2423 - 47.1850i) q^{21} +194.919 q^{22} +(-53.5007 - 92.6660i) q^{23} +63.6591 q^{24} +11.4310 q^{25} +(-53.6756 + 92.9688i) q^{26} +27.0000 q^{27} +(7.97793 + 13.8182i) q^{28} +(98.1994 - 170.086i) q^{29} +(-52.2058 - 90.4231i) q^{30} +(-44.0290 + 76.2605i) q^{31} +(-19.7926 + 34.2818i) q^{32} +(98.1239 - 169.956i) q^{33} +(-49.7963 + 86.2496i) q^{34} +(-106.067 + 183.713i) q^{35} +(-3.95349 + 6.84764i) q^{36} +(33.4886 + 58.0040i) q^{37} +(-137.966 + 238.964i) q^{38} +(54.0414 + 93.6025i) q^{39} -247.854 q^{40} +(31.4044 - 54.3940i) q^{41} +162.347 q^{42} -420.590 q^{43} +(28.7357 + 49.7716i) q^{44} -105.123 q^{45} +(159.416 - 276.116i) q^{46} +(57.7766 - 100.072i) q^{47} +(105.385 + 182.532i) q^{48} +(6.57940 + 11.3959i) q^{49} +(17.0304 + 29.4975i) q^{50} +(50.1357 + 86.8375i) q^{51} -31.6522 q^{52} +431.391 q^{53} +(40.2258 + 69.6732i) q^{54} +(-382.041 + 661.714i) q^{55} +(192.691 - 333.751i) q^{56} +(138.906 + 240.593i) q^{57} +585.208 q^{58} -294.175 q^{59} +(15.3927 - 26.6610i) q^{60} +(169.739 + 293.997i) q^{61} -262.386 q^{62} +(81.7269 - 141.555i) q^{63} +444.101 q^{64} +(-210.408 - 364.437i) q^{65} +584.758 q^{66} +(-527.580 - 149.742i) q^{67} -29.3646 q^{68} +(-160.502 - 277.998i) q^{69} -632.092 q^{70} +(-114.265 + 197.912i) q^{71} +190.977 q^{72} +(-85.3246 - 147.786i) q^{73} +(-99.7857 + 172.834i) q^{74} +34.2929 q^{75} -81.3578 q^{76} +(-594.027 - 1028.88i) q^{77} +(-161.027 + 278.906i) q^{78} +(-450.361 + 780.048i) q^{79} +(-410.311 - 710.680i) q^{80} +81.0000 q^{81} +187.151 q^{82} +(497.911 + 862.407i) q^{83} +(23.9338 + 41.4546i) q^{84} +(-195.201 - 338.098i) q^{85} +(-626.614 - 1085.33i) q^{86} +(294.598 - 510.259i) q^{87} +(694.053 - 1202.14i) q^{88} -1494.11 q^{89} +(-156.617 - 271.269i) q^{90} +654.317 q^{91} +94.0065 q^{92} +(-132.087 + 228.782i) q^{93} +344.313 q^{94} +(-540.826 - 936.738i) q^{95} +(-59.3777 + 102.845i) q^{96} +(-243.129 - 421.112i) q^{97} +(-19.6046 + 33.9561i) q^{98} +(294.372 - 509.867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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