LMFDB - Embedded newform 126.4.e.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(25,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	126.121
Dual form			126.4.e.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-5.17368 + 0.482721i) q^{3} +4.00000 q^{4} +(-1.28937 - 2.23325i) q^{5} +(-10.3474 + 0.965443i) q^{6} +(-3.69263 + 18.1484i) q^{7} +8.00000 q^{8} +(26.5340 - 4.99489i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-5.17368 + 0.482721i) q^{3} +4.00000 q^{4} +(-1.28937 - 2.23325i) q^{5} +(-10.3474 + 0.965443i) q^{6} +(-3.69263 + 18.1484i) q^{7} +8.00000 q^{8} +(26.5340 - 4.99489i) q^{9} +(-2.57874 - 4.46651i) q^{10} +(-16.7695 + 29.0455i) q^{11} +(-20.6947 + 1.93089i) q^{12} +(-39.4185 + 68.2749i) q^{13} +(-7.38526 + 36.2968i) q^{14} +(7.74883 + 10.9317i) q^{15} +16.0000 q^{16} +(17.3059 + 29.9747i) q^{17} +(53.0679 - 9.98979i) q^{18} +(-24.3463 + 42.1691i) q^{19} +(-5.15748 - 8.93301i) q^{20} +(10.3439 - 95.6766i) q^{21} +(-33.5389 + 58.0911i) q^{22} +(13.5657 + 23.4965i) q^{23} +(-41.3895 + 3.86177i) q^{24} +(59.1751 - 102.494i) q^{25} +(-78.8370 + 136.550i) q^{26} +(-134.867 + 38.6505i) q^{27} +(-14.7705 + 72.5936i) q^{28} +(37.3798 + 64.7438i) q^{29} +(15.4977 + 21.8635i) q^{30} -118.252 q^{31} +32.0000 q^{32} +(72.7389 - 158.367i) q^{33} +(34.6118 + 59.9495i) q^{34} +(45.2911 - 15.1534i) q^{35} +(106.136 - 19.9796i) q^{36} +(92.0173 - 159.379i) q^{37} +(-48.6927 + 84.3382i) q^{38} +(170.981 - 372.261i) q^{39} +(-10.3150 - 17.8660i) q^{40} +(208.135 - 360.500i) q^{41} +(20.6877 - 191.353i) q^{42} +(89.9002 + 155.712i) q^{43} +(-67.0778 + 116.182i) q^{44} +(-45.3669 - 52.8168i) q^{45} +(27.1314 + 46.9930i) q^{46} -200.604 q^{47} +(-82.7789 + 7.72354i) q^{48} +(-315.729 - 134.031i) q^{49} +(118.350 - 204.988i) q^{50} +(-104.005 - 146.726i) q^{51} +(-157.674 + 273.099i) q^{52} +(184.672 + 319.862i) q^{53} +(-269.734 + 77.3010i) q^{54} +86.4881 q^{55} +(-29.5410 + 145.187i) q^{56} +(105.604 - 229.922i) q^{57} +(74.7597 + 129.488i) q^{58} +574.408 q^{59} +(30.9953 + 43.7269i) q^{60} -684.198 q^{61} -236.504 q^{62} +(-7.33074 + 499.993i) q^{63} +64.0000 q^{64} +203.300 q^{65} +(145.478 - 316.735i) q^{66} +16.8078 q^{67} +(69.2237 + 119.899i) q^{68} +(-81.5269 - 115.015i) q^{69} +(90.5823 - 30.3068i) q^{70} +724.856 q^{71} +(212.272 - 39.9591i) q^{72} +(-271.325 - 469.949i) q^{73} +(184.035 - 318.757i) q^{74} +(-256.677 + 558.837i) q^{75} +(-97.3853 + 168.676i) q^{76} +(-465.207 - 411.593i) q^{77} +(341.962 - 744.521i) q^{78} -1184.20 q^{79} +(-20.6299 - 35.7321i) q^{80} +(679.102 - 265.069i) q^{81} +(416.269 - 721.000i) q^{82} +(658.882 + 1141.22i) q^{83} +(41.3755 - 382.706i) q^{84} +(44.6275 - 77.2970i) q^{85} +(179.800 + 311.424i) q^{86} +(-224.645 - 316.920i) q^{87} +(-134.156 + 232.364i) q^{88} +(-49.8758 + 86.3875i) q^{89} +(-90.7339 - 105.634i) q^{90} +(-1093.52 - 967.497i) q^{91} +(54.2628 + 93.9859i) q^{92} +(611.798 - 57.0828i) q^{93} -401.208 q^{94} +125.566 q^{95} +(-165.558 + 15.4471i) q^{96} +(136.196 + 235.899i) q^{97} +(-631.458 - 268.061i) q^{98} +(-299.881 + 854.455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{2} + 2 q^{3} + 96 q^{4} + 10 q^{5} + 4 q^{6} + 17 q^{7} + 192 q^{8} + 32 q^{9}+O(q^{10}) $ 24 * q + 48 * q^2 + 2 * q^3 + 96 * q^4 + 10 * q^5 + 4 * q^6 + 17 * q^7 + 192 * q^8 + 32 * q^9	\( 24 q + 48 q^{2} + 2 q^{3} + 96 q^{4} + 10 q^{5} + 4 q^{6} + 17 q^{7} + 192 q^{8} + 32 q^{9} + 20 q^{10} - 4 q^{11} + 8 q^{12} + 80 q^{13} + 34 q^{14} - 126 q^{15} + 384 q^{16} + 92 q^{17} + 64 q^{18} + 54 q^{19} + 40 q^{20} + 230 q^{21} - 8 q^{22} + 131 q^{23} + 16 q^{24} - 178 q^{25} + 160 q^{26} + 92 q^{27} + 68 q^{28} - 278 q^{29} - 252 q^{30} - 220 q^{31} + 768 q^{32} - 396 q^{33} + 184 q^{34} - 493 q^{35} + 128 q^{36} - 21 q^{37} + 108 q^{38} - 17 q^{39} + 80 q^{40} + 465 q^{41} + 460 q^{42} + 159 q^{43} - 16 q^{44} - 870 q^{45} + 262 q^{46} - 678 q^{47} + 32 q^{48} - 207 q^{49} - 356 q^{50} - 444 q^{51} + 320 q^{52} - 78 q^{53} + 184 q^{54} - 1532 q^{55} + 136 q^{56} - 1970 q^{57} - 556 q^{58} - 1622 q^{59} - 504 q^{60} - 1978 q^{61} - 440 q^{62} - 3784 q^{63} + 1536 q^{64} - 624 q^{65} - 792 q^{66} - 80 q^{67} + 368 q^{68} - 2049 q^{69} - 986 q^{70} + 980 q^{71} + 256 q^{72} + 1510 q^{73} - 42 q^{74} - 43 q^{75} + 216 q^{76} - 350 q^{77} - 34 q^{78} + 812 q^{79} + 160 q^{80} + 1292 q^{81} + 930 q^{82} - 7 q^{83} + 920 q^{84} - 581 q^{85} + 318 q^{86} + 3336 q^{87} - 32 q^{88} + 675 q^{89} - 1740 q^{90} - 232 q^{91} + 524 q^{92} - 443 q^{93} - 1356 q^{94} + 2438 q^{95} + 64 q^{96} + 2836 q^{97} - 414 q^{98} + 6429 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 2 * q^3 + 96 * q^4 + 10 * q^5 + 4 * q^6 + 17 * q^7 + 192 * q^8 + 32 * q^9 + 20 * q^10 - 4 * q^11 + 8 * q^12 + 80 * q^13 + 34 * q^14 - 126 * q^15 + 384 * q^16 + 92 * q^17 + 64 * q^18 + 54 * q^19 + 40 * q^20 + 230 * q^21 - 8 * q^22 + 131 * q^23 + 16 * q^24 - 178 * q^25 + 160 * q^26 + 92 * q^27 + 68 * q^28 - 278 * q^29 - 252 * q^30 - 220 * q^31 + 768 * q^32 - 396 * q^33 + 184 * q^34 - 493 * q^35 + 128 * q^36 - 21 * q^37 + 108 * q^38 - 17 * q^39 + 80 * q^40 + 465 * q^41 + 460 * q^42 + 159 * q^43 - 16 * q^44 - 870 * q^45 + 262 * q^46 - 678 * q^47 + 32 * q^48 - 207 * q^49 - 356 * q^50 - 444 * q^51 + 320 * q^52 - 78 * q^53 + 184 * q^54 - 1532 * q^55 + 136 * q^56 - 1970 * q^57 - 556 * q^58 - 1622 * q^59 - 504 * q^60 - 1978 * q^61 - 440 * q^62 - 3784 * q^63 + 1536 * q^64 - 624 * q^65 - 792 * q^66 - 80 * q^67 + 368 * q^68 - 2049 * q^69 - 986 * q^70 + 980 * q^71 + 256 * q^72 + 1510 * q^73 - 42 * q^74 - 43 * q^75 + 216 * q^76 - 350 * q^77 - 34 * q^78 + 812 * q^79 + 160 * q^80 + 1292 * q^81 + 930 * q^82 - 7 * q^83 + 920 * q^84 - 581 * q^85 + 318 * q^86 + 3336 * q^87 - 32 * q^88 + 675 * q^89 - 1740 * q^90 - 232 * q^91 + 524 * q^92 - 443 * q^93 - 1356 * q^94 + 2438 * q^95 + 64 * q^96 + 2836 * q^97 - 414 * q^98 + 6429 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.00000			0.707107
$2$	2.00000			0.707107
$3$	−5.17368	+	0.482721i	−0.995675	+	0.0928998i
$3$	−5.17368	+	0.482721i	−0.995675	+	0.0928998i
$4$	4.00000			0.500000
$5$	−1.28937	−	2.23325i	−0.115325	−	0.199748i	0.802585	−	0.596538i	$-0.203458\pi$
$5$	−1.28937	−	2.23325i	−0.115325	−	0.199748i	−0.917910	+	0.396790i	$0.870124\pi$
$6$	−10.3474	+	0.965443i	−0.704049	+	0.0656901i
$7$	−3.69263	+	18.1484i	−0.199383	+	0.979922i
$7$	−3.69263	+	18.1484i	−0.199383	+	0.979922i
$8$	8.00000			0.353553
$9$	26.5340	−	4.99489i	0.982739	−	0.184996i
$10$	−2.57874	−	4.46651i	−0.0815469	−	0.141243i
$11$	−16.7695	+	29.0455i	−0.459653	+	0.796142i	−0.998942	−	0.0459783i	$-0.985359\pi$
$11$	−16.7695	+	29.0455i	−0.459653	+	0.796142i	0.539290	+	0.842120i	$0.318693\pi$
$12$	−20.6947	+	1.93089i	−0.497838	+	0.0464499i
$13$	−39.4185	+	68.2749i	−0.840979	+	1.45662i	0.0480887	+	0.998843i	$0.484687\pi$
$13$	−39.4185	+	68.2749i	−0.840979	+	1.45662i	−0.889068	+	0.457775i	$0.848646\pi$
$14$	−7.38526	+	36.2968i	−0.140985	+	0.692909i
$15$	7.74883	+	10.9317i	0.133383	+	0.188171i
$16$	16.0000			0.250000
$17$	17.3059	+	29.9747i	0.246900	+	0.427644i	0.962664	−	0.270699i	$-0.0872547\pi$
$17$	17.3059	+	29.9747i	0.246900	+	0.427644i	−0.715764	+	0.698342i	$0.753921\pi$
$18$	53.0679	−	9.98979i	0.694902	−	0.130812i
$19$	−24.3463	+	42.1691i	−0.293970	+	0.509171i	−0.974745	−	0.223322i	$-0.928310\pi$
$19$	−24.3463	+	42.1691i	−0.293970	+	0.509171i	0.680775	+	0.732493i	$0.261643\pi$
$20$	−5.15748	−	8.93301i	−0.0576624	−	0.0998741i
$21$	10.3439	−	95.6766i	0.107486	−	0.994207i
$22$	−33.5389	+	58.0911i	−0.325024	+	0.562957i
$23$	13.5657	+	23.4965i	0.122985	+	0.213015i	0.920943	−	0.389697i	$-0.127420\pi$
$23$	13.5657	+	23.4965i	0.122985	+	0.213015i	−0.797959	+	0.602712i	$0.794087\pi$
$24$	−41.3895	+	3.86177i	−0.352024	+	0.0328450i
$25$	59.1751	−	102.494i	0.473400	−	0.819954i
$26$	−78.8370	+	136.550i	−0.594662	+	1.02998i
$27$	−134.867	+	38.6505i	−0.961303	+	0.275492i
$28$	−14.7705	+	72.5936i	−0.0996916	+	0.489961i
$29$	37.3798	+	64.7438i	0.239354	+	0.414573i	0.960529	−	0.278180i	$-0.0897311\pi$
$29$	37.3798	+	64.7438i	0.239354	+	0.414573i	−0.721175	+	0.692753i	$0.756398\pi$
$30$	15.4977	+	21.8635i	0.0943157	+	0.133057i
$31$	−118.252			−0.685119			−0.342559	−	0.939496i	$-0.611294\pi$
$31$	−118.252			−0.685119			−0.342559	+	0.939496i	$0.611294\pi$
$32$	32.0000			0.176777
$33$	72.7389	−	158.367i	0.383704	−	0.835401i
$34$	34.6118	+	59.9495i	0.174585	+	0.302390i
$35$	45.2911	−	15.1534i	0.218731	−	0.0731827i
$36$	106.136	−	19.9796i	0.491370	−	0.0924980i
$37$	92.0173	−	159.379i	0.408853	−	0.708154i	−0.585909	−	0.810377i	$-0.699262\pi$
$37$	92.0173	−	159.379i	0.408853	−	0.708154i	0.994761	+	0.102223i	$0.0325956\pi$
$38$	−48.6927	+	84.3382i	−0.207868	+	0.360038i
$39$	170.981	−	372.261i	0.702023	−	1.52845i
$40$	−10.3150	−	17.8660i	−0.0407734	−	0.0706217i
$41$	208.135	−	360.500i	0.792809	−	1.37319i	−0.131412	−	0.991328i	$-0.541951\pi$
$41$	208.135	−	360.500i	0.792809	−	1.37319i	0.924221	−	0.381858i	$-0.124716\pi$
$42$	20.6877	−	191.353i	0.0760044	−	0.703010i
$43$	89.9002	+	155.712i	0.318829	+	0.552228i	0.980244	−	0.197792i	$-0.0633770\pi$
$43$	89.9002	+	155.712i	0.318829	+	0.552228i	−0.661415	+	0.750020i	$0.730044\pi$
$44$	−67.0778	+	116.182i	−0.229826	+	0.398071i
$45$	−45.3669	−	52.8168i	−0.150287	−	0.174966i
$46$	27.1314	+	46.9930i	0.0869632	+	0.150625i
$47$	−200.604			−0.622577			−0.311289	−	0.950315i	$-0.600761\pi$
$47$	−200.604			−0.622577			−0.311289	+	0.950315i	$0.600761\pi$
$48$	−82.7789	+	7.72354i	−0.248919	+	0.0232249i
$49$	−315.729	−	134.031i	−0.920493	−	0.390760i
$50$	118.350	−	204.988i	0.334745	−	0.579795i
$51$	−104.005	−	146.726i	−0.285560	−	0.402857i
$52$	−157.674	+	273.099i	−0.420490	+	0.728309i
$53$	184.672	+	319.862i	0.478617	+	0.828989i	0.999699	−	0.0245173i	$-0.00780488\pi$
$53$	184.672	+	319.862i	0.478617	+	0.828989i	−0.521082	+	0.853506i	$0.674472\pi$
$54$	−269.734	+	77.3010i	−0.679744	+	0.194802i
$55$	86.4881			0.212037
$56$	−29.5410	+	145.187i	−0.0704926	+	0.346455i
$57$	105.604	−	229.922i	0.245397	−	0.534279i
$58$	74.7597	+	129.488i	0.169249	+	0.293147i
$59$	574.408			1.26748			0.633742	−	0.773544i	$-0.281518\pi$
$59$	574.408			1.26748			0.633742	+	0.773544i	$0.281518\pi$
$60$	30.9953	+	43.7269i	0.0666913	+	0.0940854i
$61$	−684.198			−1.43611			−0.718054	−	0.695987i	$-0.754967\pi$
$61$	−684.198			−1.43611			−0.718054	+	0.695987i	$0.754967\pi$
$62$	−236.504			−0.484452
$63$	−7.33074	+	499.993i	−0.0146601	+	0.999893i
$64$	64.0000			0.125000
$65$	203.300			0.387943
$66$	145.478	−	316.735i	0.271319	−	0.590718i
$67$	16.8078			0.0306477			0.0153239	−	0.999883i	$-0.495122\pi$
$67$	16.8078			0.0306477			0.0153239	+	0.999883i	$0.495122\pi$
$68$	69.2237	+	119.899i	0.123450	+	0.213822i
$69$	−81.5269	−	115.015i	−0.142242	−	0.200669i
$70$	90.5823	−	30.3068i	0.154666	−	0.0517480i
$71$	724.856			1.21161			0.605807	−	0.795612i	$-0.292850\pi$
$71$	724.856			1.21161			0.605807	+	0.795612i	$0.292850\pi$
$72$	212.272	−	39.9591i	0.347451	−	0.0654060i
$73$	−271.325	−	469.949i	−0.435017	−	0.753471i	0.562280	−	0.826947i	$-0.309924\pi$
$73$	−271.325	−	469.949i	−0.435017	−	0.753471i	−0.997297	+	0.0734755i	$0.976591\pi$
$74$	184.035	−	318.757i	0.289103	−	0.500740i
$75$	−256.677	+	558.837i	−0.395180	+	0.860386i
$76$	−97.3853	+	168.676i	−0.146985	+	0.254586i
$77$	−465.207	−	411.593i	−0.688510	−	0.609161i
$78$	341.962	−	744.521i	0.496405	−	1.08077i
$79$	−1184.20			−1.68649			−0.843247	−	0.537527i	$-0.819359\pi$
$79$	−1184.20			−1.68649			−0.843247	+	0.537527i	$0.819359\pi$
$80$	−20.6299	−	35.7321i	−0.0288312	−	0.0499371i
$81$	679.102	−	265.069i	0.931553	−	0.363606i
$82$	416.269	−	721.000i	0.560601	−	0.970989i
$83$	658.882	+	1141.22i	0.871345	+	1.50921i	0.860606	+	0.509272i	$0.170085\pi$
$83$	658.882	+	1141.22i	0.871345	+	1.50921i	0.0107393	+	0.999942i	$0.496582\pi$
$84$	41.3755	−	382.706i	0.0537432	−	0.497103i
$85$	44.6275	−	77.2970i	0.0569474	−	0.0986358i
$86$	179.800	+	311.424i	0.225446	+	0.390484i
$87$	−224.645	−	316.920i	−0.276833	−	0.390544i
$88$	−134.156	+	232.364i	−0.162512	+	0.281479i
$89$	−49.8758	+	86.3875i	−0.0594025	+	0.102888i	−0.894197	−	0.447673i	$-0.852253\pi$
$89$	−49.8758	+	86.3875i	−0.0594025	+	0.102888i	0.834795	+	0.550561i	$0.185586\pi$
$90$	−90.7339	−	105.634i	−0.106269	−	0.123720i
$91$	−1093.52	−	967.497i	−1.25969	−	1.11452i
$92$	54.2628	+	93.9859i	0.0614923	+	0.106508i
$93$	611.798	−	57.0828i	0.682156	−	0.0636474i
$94$	−401.208			−0.440229
$95$	125.566			0.135608
$96$	−165.558	+	15.4471i	−0.176012	+	0.0164225i
$97$	136.196	+	235.899i	0.142563	+	0.246927i	0.928461	−	0.371430i	$-0.121132\pi$
$97$	136.196	+	235.899i	0.142563	+	0.246927i	−0.785898	+	0.618356i	$0.787799\pi$
$98$	−631.458	−	268.061i	−0.650887	−	0.276309i
$99$	−299.881	+	854.455i	−0.304436	+	0.867434i
$100$	236.700	−	409.977i	0.236700	−	0.409977i
$101$	656.961	−	1137.89i	0.647228	−	1.12103i	−0.336554	−	0.941664i	$-0.609261\pi$
$101$	656.961	−	1137.89i	0.647228	−	1.12103i	0.983782	−	0.179368i	$-0.0574053\pi$
$102$	−208.010	−	293.452i	−0.201922	−	0.284863i
$103$	764.704	+	1324.51i	0.731539	+	1.26706i	0.956225	+	0.292632i	$0.0945310\pi$
$103$	764.704	+	1324.51i	0.731539	+	1.26706i	−0.224686	+	0.974431i	$0.572136\pi$
$104$	−315.348	+	546.199i	−0.297331	+	0.514992i
$105$	−227.007	+	100.262i	−0.210987	+	0.0931863i
$106$	369.345	+	639.724i	0.338433	+	0.586184i
$107$	−120.048	+	207.929i	−0.108462	+	0.187862i	−0.915147	−	0.403119i	$-0.867926\pi$
$107$	−120.048	+	207.929i	−0.108462	+	0.187862i	0.806685	+	0.590981i	$0.201259\pi$
$108$	−539.468	+	154.602i	−0.480652	+	0.137746i
$109$	813.194	+	1408.49i	0.714586	+	1.23770i	0.963119	+	0.269076i	$0.0867182\pi$
$109$	813.194	+	1408.49i	0.714586	+	1.23770i	−0.248533	+	0.968623i	$0.579948\pi$
$110$	172.976			0.149933
$111$	−399.133	+	868.993i	−0.341297	+	0.743074i
$112$	−59.0821	+	290.374i	−0.0498458	+	0.244980i
$113$	558.113	−	966.681i	0.464627	−	0.804758i	−0.534557	−	0.845132i	$-0.679522\pi$
$113$	558.113	−	966.681i	0.464627	−	0.804758i	0.999185	+	0.0403741i	$0.0128550\pi$
$114$	211.208	−	459.844i	0.173522	−	0.377792i
$115$	34.9824	−	60.5913i	0.0283663	−	0.0491319i
$116$	149.519	+	258.975i	0.119677	+	0.207287i
$117$	−704.904	+	2008.49i	−0.556995	+	1.58705i
$118$	1148.82			0.896247
$119$	−607.898	+	203.389i	−0.468285	+	0.156678i
$120$	61.9906	+	87.4539i	0.0471579	+	0.0665284i
$121$	103.071	+	178.524i	0.0774385	+	0.134127i
$122$	−1368.40			−1.01548
$123$	−902.802	+	1965.58i	−0.661812	+	1.44090i
$124$	−473.008			−0.342559
$125$	−627.536			−0.449028
$126$	−14.6615	+	999.987i	−0.0103663	+	0.707031i
$127$	−1021.67			−0.713846			−0.356923	−	0.934134i	$-0.616174\pi$
$127$	−1021.67			−0.713846			−0.356923	+	0.934134i	$0.616174\pi$
$128$	128.000			0.0883883
$129$	−540.281	−	762.206i	−0.368752	−	0.520221i
$130$	406.600			0.274317
$131$	1168.82	+	2024.46i	0.779544	+	1.35021i	0.932205	+	0.361932i	$0.117883\pi$
$131$	1168.82	+	2024.46i	0.779544	+	1.35021i	−0.152660	+	0.988279i	$0.548784\pi$
$132$	290.956	−	633.470i	0.191852	−	0.417700i
$133$	−675.399	−	597.562i	−0.440335	−	0.389588i
$134$	33.6156			0.0216712
$135$	260.210	+	251.358i	0.165891	+	0.160248i
$136$	138.447	+	239.798i	0.0872924	+	0.151195i
$137$	−1317.88	+	2282.63i	−0.821853	+	1.42349i	0.0824474	+	0.996595i	$0.473726\pi$
$137$	−1317.88	+	2282.63i	−0.821853	+	1.42349i	−0.904301	+	0.426896i	$0.859607\pi$
$138$	−163.054	−	230.030i	−0.100580	−	0.141894i
$139$	464.555	−	804.632i	0.283475	−	0.490993i	−0.688763	−	0.724986i	$-0.741846\pi$
$139$	464.555	−	804.632i	0.283475	−	0.490993i	0.972238	+	0.233993i	$0.0751794\pi$
$140$	181.165	−	60.6137i	0.109366	−	0.0365914i
$141$	1037.86	−	96.8359i	0.619885	−	0.0578373i
$142$	1449.71			0.856740
$143$	−1322.05	−	2289.86i	−0.773117	−	1.33908i
$144$	424.543	−	79.9183i	0.245685	−	0.0462490i
$145$	96.3929	−	166.957i	0.0552068	−	0.0956210i
$146$	−542.651	−	939.899i	−0.307603	−	0.532785i
$147$	1698.18	+	541.023i	0.952813	+	0.303556i
$148$	368.069	−	637.515i	0.204426	−	0.354077i
$149$	−889.460	−	1540.59i	−0.489043	−	0.847047i	0.510878	−	0.859653i	$-0.329320\pi$
$149$	−889.460	−	1540.59i	−0.489043	−	0.847047i	−0.999921	+	0.0126064i	$0.995987\pi$
$150$	−513.353	+	1117.67i	−0.279434	+	0.608385i
$151$	188.503	−	326.497i	0.101590	−	0.175960i	−0.810750	−	0.585393i	$-0.800940\pi$
$151$	188.503	−	326.497i	0.101590	−	0.175960i	0.912340	+	0.409433i	$0.134274\pi$
$152$	−194.771	+	337.353i	−0.103934	+	0.180019i
$153$	608.915	+	708.907i	0.321751	+	0.374587i
$154$	−930.414	−	823.187i	−0.486850	−	0.430742i
$155$	152.470	+	264.087i	0.0790111	+	0.136851i
$156$	683.924	−	1489.04i	0.351011	−	0.764223i
$157$	2586.80			1.31496			0.657482	−	0.753470i	$-0.271622\pi$
$157$	2586.80			1.31496			0.657482	+	0.753470i	$0.271622\pi$
$158$	−2368.40			−1.19253
$159$	−1109.84	−	1565.72i	−0.553560	−	0.780941i
$160$	−41.2598	−	71.4641i	−0.0203867	−	0.0353108i
$161$	−476.517	+	159.432i	−0.233260	+	0.0780435i
$162$	1358.20	−	530.137i	0.658707	−	0.257108i
$163$	1284.26	−	2224.40i	0.617121	−	1.06889i	−0.372887	−	0.927877i	$-0.621632\pi$
$163$	1284.26	−	2224.40i	0.617121	−	1.06889i	0.990008	−	0.141008i	$-0.0450345\pi$
$164$	832.539	−	1442.00i	0.396405	−	0.686593i
$165$	−447.462	+	41.7497i	−0.211120	+	0.0196982i
$166$	1317.76	+	2282.43i	0.616134	+	1.06718i
$167$	1156.75	−	2003.54i	0.535998	−	0.928376i	−0.463116	−	0.886298i	$-0.653269\pi$
$167$	1156.75	−	2003.54i	0.535998	−	0.928376i	0.999114	−	0.0420782i	$-0.0133979\pi$
$168$	82.7509	−	765.412i	0.0380022	−	0.351505i
$169$	−2009.14	−	3479.93i	−0.914492	−	1.58395i
$170$	89.2549	−	154.594i	0.0402679	−	0.0697460i
$171$	−435.374	+	1240.52i	−0.194701	+	0.554766i
$172$	359.601	+	622.847i	0.159415	+	0.276114i
$173$	762.517			0.335105			0.167552	−	0.985863i	$-0.446414\pi$
$173$	762.517			0.335105			0.167552	+	0.985863i	$0.446414\pi$
$174$	−449.289	−	633.839i	−0.195750	−	0.276157i
$175$	1641.59	+	1452.41i	0.709102	+	0.627380i
$176$	−268.311	+	464.729i	−0.114913	+	0.199036i
$177$	−2971.81	+	277.279i	−1.26200	+	0.117749i
$178$	−99.7516	+	172.775i	−0.0420039	+	0.0727530i
$179$	−1487.53	−	2576.48i	−0.621136	−	1.07584i	−0.989274	−	0.146069i	$-0.953338\pi$
$179$	−1487.53	−	2576.48i	−0.621136	−	1.07584i	0.368138	−	0.929771i	$-0.379995\pi$
$180$	−181.468	−	211.267i	−0.0751434	−	0.0874829i
$181$	2374.38			0.975060			0.487530	−	0.873106i	$-0.337898\pi$
$181$	2374.38			0.975060			0.487530	+	0.873106i	$0.337898\pi$
$182$	−2187.04	−	1934.99i	−0.890739	−	0.788084i
$183$	3539.82	−	330.277i	1.42990	−	0.133414i
$184$	108.526	+	187.972i	0.0434816	+	0.0753123i
$185$	−474.577			−0.188603
$186$	1223.60	−	114.166i	0.482357	−	0.0450055i
$187$	−1160.84			−0.453953
$188$	−802.417			−0.311289
$189$	−203.431	−	2590.34i	−0.0782931	−	0.996930i
$190$	251.131			0.0958894
$191$	−1387.67			−0.525696			−0.262848	−	0.964837i	$-0.584662\pi$
$191$	−1387.67			−0.525696			−0.262848	+	0.964837i	$0.584662\pi$
$192$	−331.116	+	30.8942i	−0.124459	+	0.0116125i
$193$	4645.17			1.73247			0.866235	−	0.499637i	$-0.166533\pi$
$193$	4645.17			1.73247			0.866235	+	0.499637i	$0.166533\pi$
$194$	272.392	+	471.797i	0.100807	+	0.174603i
$195$	−1051.81	+	98.1373i	−0.386265	+	0.0360398i
$196$	−1262.92	−	536.122i	−0.460246	−	0.195380i
$197$	2838.00			1.02639			0.513195	−	0.858272i	$-0.328462\pi$
$197$	2838.00			1.02639			0.513195	+	0.858272i	$0.328462\pi$
$198$	−599.761	+	1708.91i	−0.215269	+	0.613368i
$199$	−729.065	−	1262.78i	−0.259709	−	0.449829i	0.706455	−	0.707758i	$-0.250293\pi$
$199$	−729.065	−	1262.78i	−0.259709	−	0.449829i	−0.966164	+	0.257929i	$0.916960\pi$
$200$	473.400	−	819.954i	0.167372	−	0.289897i
$201$	−86.9581	+	8.11348i	−0.0305152	+	0.00284717i
$202$	1313.92	−	2275.78i	0.457659	−	0.792689i
$203$	−1313.03	+	439.310i	−0.453972	+	0.151889i
$204$	−416.019	−	586.903i	−0.142780	−	0.201429i
$205$	−1073.45			−0.365722
$206$	1529.41	+	2649.01i	0.517276	+	0.895949i
$207$	477.314	+	555.696i	0.160269	+	0.186587i
$208$	−630.696	+	1092.40i	−0.210245	+	0.364155i
$209$	−816.549	−	1414.30i	−0.270248	−	0.468084i
$210$	−454.014	+	200.524i	−0.149190	+	0.0658927i
$211$	−2879.08	+	4986.72i	−0.939356	+	1.62701i	−0.172681	+	0.984978i	$0.555243\pi$
$211$	−2879.08	+	4986.72i	−0.939356	+	1.62701i	−0.766675	+	0.642035i	$0.778090\pi$
$212$	738.690	+	1279.45i	0.239309	+	0.414495i
$213$	−3750.17	+	349.903i	−1.20637	+	0.112559i
$214$	−240.096	+	415.858i	−0.0766944	+	0.132839i
$215$	231.829	−	401.540i	0.0735378	−	0.127371i
$216$	−1078.94	+	309.204i	−0.339872	+	0.0974012i
$217$	436.661	−	2146.08i	0.136601	−	0.671363i
$218$	1626.39	+	2816.99i	0.505289	+	0.875185i
$219$	1630.61	+	2300.39i	0.503133	+	0.709800i
$220$	345.952			0.106019
$221$	−2728.69			−0.830552
$222$	−798.266	+	1737.99i	−0.241334	+	0.525433i
$223$	725.209	+	1256.10i	0.217774	+	0.377195i	0.954127	−	0.299402i	$-0.0967871\pi$
$223$	725.209	+	1256.10i	0.217774	+	0.377195i	−0.736353	+	0.676597i	$0.763454\pi$
$224$	−118.164	+	580.749i	−0.0352463	+	0.173227i
$225$	1058.20	−	3015.15i	0.313541	−	0.893378i
$226$	1116.23	−	1933.36i	0.328541	−	0.569050i
$227$	1151.44	−	1994.35i	0.336669	−	0.583127i	−0.647135	−	0.762375i	$-0.724033\pi$
$227$	1151.44	−	1994.35i	0.336669	−	0.583127i	0.983804	+	0.179248i	$0.0573664\pi$
$228$	422.417	−	919.687i	0.122698	−	0.267139i
$229$	−526.482	−	911.894i	−0.151925	−	0.263143i	0.780010	−	0.625767i	$-0.215214\pi$
$229$	−526.482	−	911.894i	−0.151925	−	0.263143i	−0.931935	+	0.362625i	$0.881881\pi$
$230$	69.9648	−	121.183i	0.0200580	−	0.0347415i
$231$	2605.52	+	1904.89i	0.742123	+	0.542564i
$232$	299.039	+	517.950i	0.0846244	+	0.146574i
$233$	175.012	−	303.130i	0.0492079	−	0.0852305i	−0.840372	−	0.542010i	$-0.817664\pi$
$233$	175.012	−	303.130i	0.0492079	−	0.0852305i	0.889580	+	0.456779i	$0.150997\pi$
$234$	−1409.81	+	4016.99i	−0.393855	+	1.12222i
$235$	258.653	+	448.000i	0.0717985	+	0.124359i
$236$	2297.63			0.633742
$237$	6126.68	−	571.639i	1.67920	−	0.156675i
$238$	−1215.80	+	406.779i	−0.331127	+	0.110788i
$239$	108.529	−	187.978i	0.0293730	−	0.0508756i	−0.850965	−	0.525222i	$-0.823982\pi$
$239$	108.529	−	187.978i	0.0293730	−	0.0508756i	0.880338	+	0.474346i	$0.157316\pi$
$240$	123.981	+	174.908i	0.0333456	+	0.0470427i
$241$	512.979	−	888.506i	0.137112	−	0.237484i	−0.789291	−	0.614020i	$-0.789551\pi$
$241$	512.979	−	888.506i	0.137112	−	0.237484i	0.926402	+	0.376536i	$0.122885\pi$
$242$	206.141	+	357.047i	0.0547573	+	0.0948424i
$243$	−3385.50	+	1699.20i	−0.893746	+	0.448574i
$244$	−2736.79			−0.718054
$245$	107.767	+	877.918i	0.0281020	+	0.228931i
$246$	−1805.60	+	3931.16i	−0.467972	+	1.01887i
$247$	−1919.39	−	3324.48i	−0.494445	−	0.856404i
$248$	−946.016			−0.242226
$249$	−3959.73	−	5586.23i	−1.00778	−	1.42174i
$250$	−1255.07			−0.317511
$251$	−1525.73			−0.383678			−0.191839	−	0.981426i	$-0.561445\pi$
$251$	−1525.73			−0.383678			−0.191839	+	0.981426i	$0.561445\pi$
$252$	−29.3230	+	1999.97i	−0.00733005	+	0.499946i
$253$	−909.958			−0.226121
$254$	−2043.34			−0.504765
$255$	−193.575	+	421.453i	−0.0475379	+	0.103500i
$256$	256.000			0.0625000
$257$	1679.12	+	2908.31i	0.407550	+	0.705897i	0.994615	−	0.103643i	$-0.0330499\pi$
$257$	1679.12	+	2908.31i	0.407550	+	0.705897i	−0.587065	+	0.809540i	$0.699717\pi$
$258$	−1080.56	−	1524.41i	−0.260747	−	0.367852i
$259$	2552.68	+	2258.49i	0.612417	+	0.541838i
$260$	813.200			0.193971
$261$	1315.22	+	1531.20i	0.311917	+	0.363138i
$262$	2337.64	+	4048.91i	0.551221	+	0.954743i
$263$	726.468	−	1258.28i	0.170327	−	0.295015i	−0.768207	−	0.640201i	$-0.778851\pi$
$263$	726.468	−	1258.28i	0.170327	−	0.295015i	0.938534	+	0.345186i	$0.112184\pi$
$264$	581.911	−	1266.94i	0.135660	−	0.295359i
$265$	476.222	−	824.841i	0.110393	−	0.191206i
$266$	−1350.80	−	1195.12i	−0.311364	−	0.275480i
$267$	216.341	−	471.017i	0.0495874	−	0.107962i
$268$	67.2311			0.0153239
$269$	−2863.26	−	4959.32i	−0.648982	−	1.12407i	−0.983366	−	0.181633i	$-0.941862\pi$
$269$	−2863.26	−	4959.32i	−0.648982	−	1.12407i	0.334384	−	0.942437i	$-0.391472\pi$
$270$	520.420	+	502.715i	0.117303	+	0.113312i
$271$	457.750	−	792.846i	0.102606	−	0.177719i	−0.810151	−	0.586221i	$-0.800615\pi$
$271$	457.750	−	792.846i	0.102606	−	0.177719i	0.912758	+	0.408501i	$0.133948\pi$
$272$	276.895	+	479.596i	0.0617250	+	0.106911i
$273$	6124.56	+	4477.65i	1.35779	+	0.992674i
$274$	−2635.76	+	4565.26i	−0.581138	+	1.00656i
$275$	1984.67	+	3437.54i	0.435200	+	0.753788i
$276$	−326.108	−	460.060i	−0.0711209	−	0.100335i
$277$	−3884.89	+	6728.82i	−0.842673	+	1.45955i	0.0449544	+	0.998989i	$0.485686\pi$
$277$	−3884.89	+	6728.82i	−0.842673	+	1.45955i	−0.887627	+	0.460563i	$0.847648\pi$
$278$	929.109	−	1609.26i	0.200447	−	0.347184i
$279$	−3137.69	+	590.656i	−0.673293	+	0.126744i
$280$	362.329	−	121.227i	0.0773332	−	0.0258740i
$281$	2345.92	+	4063.26i	0.498029	+	0.862611i	0.999997	−	0.00227455i	$-0.000724014\pi$
$281$	2345.92	+	4063.26i	0.498029	+	0.862611i	−0.501969	+	0.864886i	$0.667391\pi$
$282$	2075.72	−	193.672i	0.438325	−	0.0408971i
$283$	−3055.58			−0.641821			−0.320911	−	0.947109i	$-0.603989\pi$
$283$	−3055.58			−0.641821			−0.320911	+	0.947109i	$0.603989\pi$
$284$	2899.42			0.605807
$285$	−649.637	+	60.6132i	−0.135022	+	0.0125980i
$286$	−2644.11	−	4579.73i	−0.546676	−	0.946871i
$287$	5773.93	+	5108.50i	1.18754	+	1.05068i
$288$	849.087	−	159.837i	0.173725	−	0.0327030i
$289$	1857.51	−	3217.30i	0.378081	−	0.654855i
$290$	192.786	−	333.915i	0.0390371	−	0.0676143i
$291$	−818.509	−	1154.72i	−0.164886	−	0.232615i
$292$	−1085.30	−	1879.80i	−0.217508	−	0.376736i
$293$	−3982.91	+	6898.61i	−0.794144	+	1.37550i	0.129237	+	0.991614i	$0.458747\pi$
$293$	−3982.91	+	6898.61i	−0.794144	+	1.37550i	−0.923381	+	0.383884i	$0.874586\pi$
$294$	3396.36	+	1082.05i	0.673741	+	0.214647i
$295$	−740.625	−	1282.80i	−0.146172	−	0.253178i
$296$	736.139	−	1275.03i	0.144551	−	0.250370i
$297$	1139.02	−	4565.44i	0.222535	−	0.891965i
$298$	−1778.92	−	3081.18i	−0.345806	−	0.598953i
$299$	−2138.96			−0.413710
$300$	−1026.71	+	2235.35i	−0.197590	+	0.430193i
$301$	−3157.89	+	1056.56i	−0.604710	+	0.202323i
$302$	377.006	−	652.994i	0.0718353	−	0.124422i
$303$	−2849.62	+	6204.21i	−0.540286	+	1.17631i
$304$	−389.541	+	674.705i	−0.0734925	+	0.127293i
$305$	882.184	+	1527.99i	0.165619	+	0.286860i
$306$	1217.83	+	1417.81i	0.227512	+	0.264873i
$307$	−2417.10			−0.449352			−0.224676	−	0.974434i	$-0.572132\pi$
$307$	−2417.10			−0.449352			−0.224676	+	0.974434i	$0.572132\pi$
$308$	−1860.83	−	1646.37i	−0.344255	−	0.304581i
$309$	−4595.70	−	6483.44i	−0.846085	−	1.19362i
$310$	304.941	+	528.173i	0.0558693	+	0.0967685i
$311$	9211.34			1.67951			0.839754	−	0.542967i	$-0.182699\pi$
$311$	9211.34			1.67951			0.839754	+	0.542967i	$0.182699\pi$
$312$	1367.85	−	2978.08i	0.248203	−	0.540387i
$313$	2436.87			0.440064			0.220032	−	0.975493i	$-0.429384\pi$
$313$	2436.87			0.440064			0.220032	+	0.975493i	$0.429384\pi$
$314$	5173.60			0.929820
$315$	1126.06	−	628.305i	0.201417	−	0.112384i
$316$	−4736.80			−0.843247
$317$	−7990.45			−1.41574			−0.707868	−	0.706344i	$-0.750343\pi$
$317$	−7990.45			−1.41574			−0.707868	+	0.706344i	$0.750343\pi$
$318$	−2219.68	−	3131.44i	−0.391426	−	0.552208i
$319$	−2507.36			−0.440079
$320$	−82.5196	−	142.928i	−0.0144156	−	0.0249685i
$321$	520.718	−	1133.71i	0.0905409	−	0.197126i
$322$	−953.034	+	318.864i	−0.164939	+	0.0551851i
$323$	−1685.34			−0.290325
$324$	2716.41	−	1060.27i	0.465776	−	0.181803i
$325$	4665.19	+	8080.34i	0.796240	+	1.37913i
$326$	2568.51	−	4448.80i	0.436371	−	0.755816i
$327$	−4887.12	−	6894.55i	−0.826478	−	1.16596i
$328$	1665.08	−	2884.00i	0.280300	−	0.485494i
$329$	740.757	−	3640.65i	0.124131	−	0.610077i
$330$	−894.924	+	83.4993i	−0.149285	+	0.0139287i
$331$	−3157.11			−0.524261			−0.262131	−	0.965032i	$-0.584425\pi$
$331$	−3157.11			−0.524261			−0.262131	+	0.965032i	$0.584425\pi$
$332$	2635.53	+	4564.87i	0.435673	+	0.754607i
$333$	1645.50	−	4688.56i	0.270790	−	0.771567i
$334$	2313.49	−	4007.08i	0.379008	−	0.656461i
$335$	−21.6714	−	37.5360i	−0.00353444	−	0.00612183i
$336$	165.502	−	1530.82i	0.0268716	−	0.248552i
$337$	−2810.48	+	4867.90i	−0.454293	+	0.786859i	−0.998647	−	0.0519966i	$-0.983442\pi$
$337$	−2810.48	+	4867.90i	−0.454293	+	0.786859i	0.544354	+	0.838856i	$0.316775\pi$
$338$	−4018.28	−	6959.86i	−0.646643	−	1.12002i
$339$	−2420.86	+	5270.71i	−0.387856	+	0.844442i
$340$	178.510	−	309.188i	0.0284737	−	0.0493179i
$341$	1983.02	−	3434.69i	0.314917	−	0.545452i
$342$	−870.749	+	2481.04i	−0.137675	+	0.392279i
$343$	3598.31	−	5235.05i	0.566445	−	0.824100i
$344$	719.202	+	1245.69i	0.112723	+	0.195242i
$345$	−151.739	+	330.367i	−0.0236793	+	0.0515546i
$346$	1525.03			0.236955
$347$	10111.4			1.56429			0.782145	−	0.623096i	$-0.214126\pi$
$347$	10111.4			1.56429			0.782145	+	0.623096i	$0.214126\pi$
$348$	−898.578	−	1267.68i	−0.138416	−	0.195272i
$349$	6426.40	+	11130.9i	0.985666	+	1.70722i	0.638939	+	0.769258i	$0.279374\pi$
$349$	6426.40	+	11130.9i	0.985666	+	1.70722i	0.346727	+	0.937966i	$0.387293\pi$
$350$	3283.19	+	2904.81i	0.501411	+	0.443625i
$351$	2677.40	−	10731.6i	0.407149	−	1.63194i
$352$	−536.623	+	929.458i	−0.0812559	+	0.140739i
$353$	2552.20	−	4420.55i	0.384816	−	0.666521i	−0.606927	−	0.794757i	$-0.707598\pi$
$353$	2552.20	−	4420.55i	0.384816	−	0.666521i	0.991744	+	0.128236i	$0.0409315\pi$
$354$	−5943.61	+	554.558i	−0.892371	+	0.0832611i
$355$	−934.607	−	1618.79i	−0.139729	−	0.242018i
$356$	−199.503	+	345.550i	−0.0297013	+	0.0514441i
$357$	3046.89	−	1345.72i	0.451705	−	0.199504i
$358$	−2975.07	−	5152.96i	−0.439210	−	0.760734i
$359$	−4090.93	+	7085.71i	−0.601424	+	1.04170i	0.391182	+	0.920313i	$0.372066\pi$
$359$	−4090.93	+	7085.71i	−0.601424	+	1.04170i	−0.992606	+	0.121383i	$0.961267\pi$
$360$	−362.936	−	422.534i	−0.0531344	−	0.0618598i
$361$	2244.01	+	3886.74i	0.327163	+	0.566663i
$362$	4748.75			0.689472
$363$	−619.432	−	873.870i	−0.0895641	−	0.126353i
$364$	−4374.09	−	3869.99i	−0.629847	−	0.557259i
$365$	−699.677	+	1211.88i	−0.100336	+	0.173788i
$366$	7079.65	−	660.554i	1.01109	−	0.0943380i
$367$	850.146	−	1472.50i	0.120919	−	0.209438i	−0.799211	−	0.601050i	$-0.794749\pi$
$367$	850.146	−	1472.50i	0.120919	−	0.209438i	0.920130	+	0.391612i	$0.128083\pi$
$368$	217.051	+	375.944i	0.0307461	+	0.0532539i
$369$	3721.98	−	10605.1i	0.525091	−	1.49615i
$370$	−949.155			−0.133363
$371$	−6486.91	+	2170.38i	−0.907773	+	0.303721i
$372$	2447.19	−	228.331i	0.341078	−	0.0318237i
$373$	94.4747	+	163.635i	0.0131145	+	0.0227150i	0.872508	−	0.488599i	$-0.162492\pi$
$373$	94.4747	+	163.635i	0.0131145	+	0.0227150i	−0.859394	+	0.511315i	$0.829159\pi$
$374$	−2321.69			−0.320994
$375$	3246.67	−	302.925i	0.447087	−	0.0417146i
$376$	−1604.83			−0.220114
$377$	−5893.83			−0.805166
$378$	−406.861	−	5180.69i	−0.0553616	−	0.704936i
$379$	−11511.6			−1.56019			−0.780095	−	0.625660i	$-0.784830\pi$
$379$	−11511.6			−1.56019			−0.780095	+	0.625660i	$0.784830\pi$
$380$	502.263			0.0678040
$381$	5285.79	−	493.181i	0.710759	−	0.0663161i
$382$	−2775.33			−0.371723
$383$	−1840.68	−	3188.16i	−0.245573	−	0.425346i	0.716719	−	0.697362i	$-0.245643\pi$
$383$	−1840.68	−	3188.16i	−0.245573	−	0.425346i	−0.962293	+	0.272016i	$0.912310\pi$
$384$	−662.231	+	61.7883i	−0.0880061	+	0.00821126i
$385$	−319.368	+	1569.62i	−0.0422767	+	0.207780i
$386$	9290.34			1.22504
$387$	3163.17	+	3682.61i	0.415486	+	0.483714i
$388$	544.785	+	943.595i	0.0712816	+	0.123463i
$389$	−6621.52	+	11468.8i	−0.863044	+	1.49484i	0.00593146	+	0.999982i	$0.498112\pi$
$389$	−6621.52	+	11468.8i	−0.863044	+	1.49484i	−0.868976	+	0.494854i	$0.835221\pi$
$390$	−2103.62	+	196.275i	−0.273131	+	0.0254840i
$391$	−469.534	+	813.257i	−0.0607298	+	0.105187i
$392$	−2525.83	−	1072.24i	−0.325443	−	0.138154i
$393$	−7024.35	−	9909.68i	−0.901608	−	1.27195i
$394$	5676.00			0.725768
$395$	1526.87	+	2644.62i	0.194494	+	0.336874i
$396$	−1199.52	+	3417.82i	−0.152218	+	0.433717i
$397$	−3707.77	+	6422.04i	−0.468734	+	0.811871i	−0.999361	−	0.0357341i	$-0.988623\pi$
$397$	−3707.77	+	6422.04i	−0.468734	+	0.811871i	0.530627	+	0.847605i	$0.321956\pi$
$398$	−1458.13	−	2525.55i	−0.183642	−	0.318077i
$399$	3782.76	+	2765.56i	0.474623	+	0.346996i
$400$	946.801	−	1639.91i	0.118350	−	0.204988i
$401$	−382.786	−	663.004i	−0.0476693	−	0.0825657i	0.841206	−	0.540714i	$-0.181846\pi$
$401$	−382.786	−	663.004i	−0.0476693	−	0.0825657i	−0.888876	+	0.458149i	$0.848513\pi$
$402$	−173.916	+	16.2270i	−0.0215775	+	0.00201325i
$403$	4661.32	−	8073.64i	0.576171	−	0.997957i
$404$	2627.84	−	4551.56i	0.323614	−	0.560516i
$405$	−1467.58	−	1174.84i	−0.180061	−	0.144143i
$406$	−2626.05	+	878.619i	−0.321007	+	0.107402i
$407$	3086.16	+	5345.39i	0.375861	+	0.651010i
$408$	−832.038	−	1173.81i	−0.100961	−	0.142432i
$409$	3070.58			0.371224			0.185612	−	0.982623i	$-0.440573\pi$
$409$	3070.58			0.371224			0.185612	+	0.982623i	$0.440573\pi$
$410$	−2146.90			−0.258604
$411$	5716.40	−	12445.8i	0.686057	−	1.49369i
$412$	3058.82	+	5298.03i	0.365770	+	0.633532i
$413$	−2121.08	+	10424.6i	−0.252715	+	1.24204i
$414$	954.628	+	1111.39i	0.113327	+	0.131937i
$415$	1699.08	−	2942.90i	0.200975	−	0.348099i
$416$	−1261.39	+	2184.80i	−0.148666	+	0.257496i
$417$	−2015.04	+	4387.16i	−0.236636	+	0.515204i
$418$	−1633.10	−	2828.61i	−0.191094	−	0.330985i
$419$	3713.82	−	6432.52i	0.433012	−	0.749998i	−0.564119	−	0.825693i	$-0.690784\pi$
$419$	3713.82	−	6432.52i	0.433012	−	0.749998i	0.997131	+	0.0756950i	$0.0241175\pi$
$420$	−908.028	+	401.048i	−0.105493	+	0.0465932i
$421$	−226.041	−	391.514i	−0.0261676	−	0.0453235i	0.852645	−	0.522491i	$-0.174997\pi$
$421$	−226.041	−	391.514i	−0.0261676	−	0.0453235i	−0.878813	+	0.477167i	$0.841664\pi$
$422$	−5758.16	+	9973.43i	−0.664225	+	1.15047i
$423$	−5322.82	+	1002.00i	−0.611831	+	0.115174i
$424$	1477.38	+	2558.90i	0.169217	+	0.293092i
$425$	4096.32			0.467531
$426$	−7500.35	+	699.807i	−0.853035	+	0.0795910i
$427$	2526.49	−	12417.1i	0.286336	−	1.40727i
$428$	−480.192	+	831.716i	−0.0542312	+	0.0939311i
$429$	7945.25	+	11208.8i	0.894174	+	1.26146i
$430$	463.658	−	803.080i	0.0519991	−	0.0900650i
$431$	−4951.13	−	8575.62i	−0.553336	−	0.958406i	−0.998031	−	0.0627238i	$-0.980021\pi$
$431$	−4951.13	−	8575.62i	−0.553336	−	0.958406i	0.444695	−	0.895682i	$-0.353312\pi$
$432$	−2157.87	+	618.408i	−0.240326	+	0.0688731i
$433$	267.061			0.0296401			0.0148200	−	0.999890i	$-0.495282\pi$
$433$	267.061			0.0296401			0.0148200	+	0.999890i	$0.495282\pi$
$434$	873.321	−	4292.17i	0.0965916	−	0.474725i
$435$	−418.112	+	910.315i	−0.0460849	+	0.100336i
$436$	3252.78	+	5633.97i	0.357293	+	0.618850i
$437$	−1321.10			−0.144615
$438$	3261.21	+	4600.79i	0.355769	+	0.501904i
$439$	2635.51			0.286528			0.143264	−	0.989684i	$-0.454240\pi$
$439$	2635.51			0.286528			0.143264	+	0.989684i	$0.454240\pi$
$440$	691.905			0.0749665
$441$	−9047.01	−	1979.33i	−0.976893	−	0.213728i
$442$	−5457.39			−0.587289
$443$	1799.39			0.192984			0.0964918	−	0.995334i	$-0.469238\pi$
$443$	1799.39			0.192984			0.0964918	+	0.995334i	$0.469238\pi$
$444$	−1596.53	+	3475.97i	−0.170649	+	0.371537i
$445$	257.233			0.0274023
$446$	1450.42	+	2512.20i	0.153989	+	0.266717i
$447$	5345.46	+	7541.16i	0.565618	+	0.797952i
$448$	−236.328	+	1161.50i	−0.0249229	+	0.122490i
$449$	−17046.9			−1.79175			−0.895874	−	0.444307i	$-0.853450\pi$
$449$	−17046.9			−1.79175			−0.895874	+	0.444307i	$0.853450\pi$
$450$	2116.40	−	6030.30i	0.221707	−	0.631713i
$451$	6980.61	+	12090.8i	0.728834	+	1.26238i
$452$	2232.45	−	3866.72i	0.232314	−	0.402379i
$453$	−817.648	+	1780.19i	−0.0848045	+	0.184637i
$454$	2302.88	−	3988.71i	0.238061	−	0.412333i
$455$	−750.712	+	3689.57i	−0.0773493	+	0.380153i
$456$	844.834	−	1839.37i	0.0867609	−	0.188896i
$457$	7727.95			0.791024			0.395512	−	0.918461i	$-0.370567\pi$
$457$	7727.95			0.791024			0.395512	+	0.918461i	$0.370567\pi$
$458$	−1052.96	−	1823.79i	−0.107427	−	0.186070i
$459$	−3492.54	−	3373.72i	−0.355158	−	0.343076i
$460$	139.930	−	242.365i	0.0141832	−	0.0245659i
$461$	−1912.38	−	3312.35i	−0.193207	−	0.334645i	0.753104	−	0.657901i	$-0.228556\pi$
$461$	−1912.38	−	3312.35i	−0.193207	−	0.334645i	−0.946311	+	0.323256i	$0.895222\pi$
$462$	5211.03	+	3809.77i	0.524760	+	0.383651i
$463$	−4746.91	+	8221.89i	−0.476475	+	0.825278i	−0.999637	−	0.0269550i	$-0.991419\pi$
$463$	−4746.91	+	8221.89i	−0.476475	+	0.825278i	0.523162	+	0.852233i	$0.324752\pi$
$464$	598.077	+	1035.90i	0.0598385	+	0.103643i
$465$	−916.314	−	1292.70i	−0.0913829	−	0.128919i
$466$	350.024	−	606.260i	0.0347952	−	0.0602671i
$467$	7872.72	−	13635.9i	0.780098	−	1.35117i	−0.151786	−	0.988413i	$-0.548502\pi$
$467$	7872.72	−	13635.9i	0.780098	−	1.35117i	0.931884	−	0.362756i	$-0.118164\pi$
$468$	−2819.61	+	8033.98i	−0.278497	+	0.793527i
$469$	−62.0649	+	305.034i	−0.00611064	+	0.0300324i
$470$	517.306	+	896.000i	0.0507692	+	0.0879349i
$471$	−13383.3	+	1248.70i	−1.30928	+	0.122160i
$472$	4595.27			0.448124
$473$	−6030.31			−0.586203
$474$	12253.4	−	1143.28i	1.18737	−	0.110786i
$475$	2881.39	+	4990.71i	0.278331	+	0.482084i
$476$	−2431.59	+	813.557i	−0.234142	+	0.0783389i
$477$	6497.77	+	7564.79i	0.623716	+	0.726138i
$478$	217.058	−	375.955i	0.0207699	−	0.0359745i
$479$	8023.21	−	13896.6i	0.765323	−	1.32558i	−0.174753	−	0.984612i	$-0.555913\pi$
$479$	8023.21	−	13896.6i	0.765323	−	1.32558i	0.940076	−	0.340966i	$-0.110754\pi$
$480$	247.962	+	349.816i	0.0235789	+	0.0332642i
$481$	7254.37	+	12564.9i	0.687673	+	1.19109i
$482$	1025.96	−	1777.01i	0.0969525	−	0.167927i
$483$	2388.38	−	1054.88i	0.225001	−	0.0993758i
$484$	412.283	+	714.095i	0.0387193	+	0.0670637i
$485$	351.214	−	608.321i	0.0328821	−	0.0569535i
$486$	−6771.01	+	3398.40i	−0.631974	+	0.317190i
$487$	−3354.77	−	5810.64i	−0.312154	−	0.540667i	0.666674	−	0.745349i	$-0.267717\pi$
$487$	−3354.77	−	5810.64i	−0.312154	−	0.540667i	−0.978829	+	0.204682i	$0.934384\pi$
$488$	−5473.58			−0.507741
$489$	−5570.57	+	12128.3i	−0.515153	+	1.12159i
$490$	215.534	+	1755.84i	0.0198711	+	0.161879i
$491$	1642.85	−	2845.50i	0.150999	−	0.261539i	−0.780596	−	0.625036i	$-0.785084\pi$
$491$	1642.85	−	2845.50i	0.150999	−	0.261539i	0.931595	+	0.363498i	$0.118418\pi$
$492$	−3611.21	+	7862.33i	−0.330906	+	0.720450i
$493$	−1293.79	+	2240.90i	−0.118193	+	0.204716i
$494$	−3838.78	−	6648.97i	−0.349626	−	0.605569i
$495$	2294.87	−	431.999i	0.208377	−	0.0392261i
$496$	−1892.03			−0.171280
$497$	−2676.62	+	13155.0i	−0.241575	+	1.18729i
$498$	−7919.47	−	11172.5i	−0.712610	−	1.00532i
$499$	−9745.99	−	16880.6i	−0.874330	−	1.51438i	−0.857475	−	0.514525i	$-0.827968\pi$
$499$	−9745.99	−	16880.6i	−0.874330	−	1.51438i	−0.0168545	−	0.999858i	$-0.505365\pi$
$500$	−2510.15			−0.224514
$501$	−5017.48	+	10924.1i	−0.447434	+	0.974155i
$502$	−3051.46			−0.271302
$503$	−9809.64			−0.869563			−0.434782	−	0.900536i	$-0.643174\pi$
$503$	−9809.64			−0.869563			−0.434782	+	0.900536i	$0.643174\pi$
$504$	−58.6459	+	3999.95i	−0.00518313	+	0.353515i
$505$	−3388.26			−0.298566
$506$	−1819.92			−0.159892
$507$	12074.5	+	17034.2i	1.05769	+	1.49214i
$508$	−4086.67			−0.356923
$509$	7.08745	+	12.2758i	0.000617182	+	0.00106899i	0.866334	−	0.499465i	$-0.166470\pi$
$509$	7.08745	+	12.2758i	0.000617182	+	0.00106899i	−0.865717	+	0.500534i	$0.833137\pi$
$510$	−387.151	+	842.906i	−0.0336144	+	0.0731853i
$511$	9530.73	−	3188.77i	0.825078	−	0.276053i
$512$	512.000			0.0441942
$513$	1653.66	−	6628.22i	0.142322	−	0.570454i
$514$	3358.23	+	5816.63i	0.288181	+	0.499145i
$515$	1971.97	−	3415.56i	0.168729	−	0.292247i
$516$	−2161.12	−	3048.83i	−0.184376	−	0.260111i
$517$	3364.02	−	5826.66i	0.286169	−	0.495660i
$518$	5105.37	+	4516.99i	0.433044	+	0.383137i
$519$	−3945.02	+	368.083i	−0.333656	+	0.0311312i
$520$	1626.40			0.137158
$521$	−9621.27	−	16664.5i	−0.809051	−	1.40132i	−0.913522	−	0.406789i	$-0.866648\pi$
$521$	−9621.27	−	16664.5i	−0.809051	−	1.40132i	0.104471	−	0.994528i	$-0.466685\pi$
$522$	2630.45	+	3062.40i	0.220559	+	0.256777i
$523$	3009.79	−	5213.11i	0.251642	−	0.435857i	−0.712336	−	0.701839i	$-0.752363\pi$
$523$	3009.79	−	5213.11i	0.251642	−	0.435857i	0.963978	+	0.265982i	$0.0856960\pi$
$524$	4675.28	+	8097.83i	0.389772	+	0.675105i
$525$	−9194.19	−	6721.85i	−0.764319	−	0.558792i
$526$	1452.94	−	2516.56i	0.120439	−	0.208607i
$527$	−2046.46	−	3544.57i	−0.169156	−	0.292987i
$528$	1163.82	−	2533.88i	0.0959259	−	0.208850i
$529$	5715.44	−	9899.44i	0.469750	−	0.813630i
$530$	952.444	−	1649.68i	0.0780595	−	0.135203i
$531$	15241.3	−	2869.11i	1.24561	−	0.234480i
$532$	−2701.60	−	2390.25i	−0.220167	−	0.194794i
$533$	16408.7	+	28420.7i	1.33347	+	2.30964i
$534$	432.681	−	942.035i	0.0350636	−	0.0763405i
$535$	619.144			0.0500335
$536$	134.462			0.0108356
$537$	8939.74	+	12611.8i	0.718396	+	1.01348i
$538$	−5726.53	−	9918.63i	−0.458900	−	0.794838i
$539$	9187.60	−	6922.90i	0.734207	−	0.553229i
$540$	1040.84	+	1005.43i	0.0829456	+	0.0801238i
$541$	−434.072	+	751.835i	−0.0344958	+	0.0597485i	−0.882758	−	0.469828i	$-0.844316\pi$
$541$	−434.072	+	751.835i	−0.0344958	+	0.0597485i	0.848262	+	0.529577i	$0.177649\pi$
$542$	915.499	−	1585.69i	0.0725536	−	0.125667i
$543$	−12284.3	+	1146.16i	−0.970844	+	0.0905829i
$544$	553.790	+	959.192i	0.0436462	+	0.0755974i
$545$	2097.02	−	3632.14i	0.164819	−	0.285475i
$546$	12249.1	+	8955.31i	0.960100	+	0.701926i
$547$	−2706.55	−	4687.88i	−0.211561	−	0.366434i	0.740642	−	0.671899i	$-0.234521\pi$
$547$	−2706.55	−	4687.88i	−0.211561	−	0.366434i	−0.952203	+	0.305465i	$0.901188\pi$
$548$	−5271.51	+	9130.52i	−0.410927	+	0.711746i
$549$	−18154.5	+	3417.50i	−1.41132	+	0.265674i
$550$	3969.33	+	6875.09i	0.307733	+	0.533009i
$551$	−3640.25			−0.281451
$552$	−652.215	−	920.119i	−0.0502901	−	0.0709472i
$553$	4372.81	−	21491.4i	0.336259	−	1.65263i
$554$	−7769.78	+	13457.6i	−0.595860	+	1.03206i
$555$	2455.31	−	229.089i	0.187788	−	0.0175212i
$556$	1858.22	−	3218.53i	0.141737	−	0.245496i
$557$	1088.75	+	1885.77i	0.0828220	+	0.143452i	0.904461	−	0.426556i	$-0.140273\pi$
$557$	1088.75	+	1885.77i	0.0828220	+	0.143452i	−0.821639	+	0.570008i	$0.806940\pi$
$558$	−6275.39	+	1181.31i	−0.476090	+	0.0896217i
$559$	−14174.9			−1.07251
$560$	724.658	−	242.455i	0.0546829	−	0.0182957i
$561$	6005.84	−	560.364i	0.451990	−	0.0421722i
$562$	4691.85	+	8126.52i	0.352160	+	0.609958i
$563$	24.3719			0.00182443			0.000912214	−	1.00000i	$-0.499710\pi$
$563$	24.3719			0.00182443			0.000912214		1.00000i	$0.499710\pi$
$564$	4151.45	−	387.344i	0.309942	−	0.0289186i
$565$	−2878.46			−0.214332
$566$	−6111.16			−0.453836
$567$	2302.90	+	13303.4i	0.170569	+	0.985346i
$568$	5798.85			0.428370
$569$	13982.9			1.03022			0.515110	−	0.857124i	$-0.327751\pi$
$569$	13982.9			1.03022			0.515110	+	0.857124i	$0.327751\pi$
$570$	−1299.27	+	121.226i	−0.0954747	+	0.00890810i
$571$	724.477			0.0530970			0.0265485	−	0.999648i	$-0.491548\pi$
$571$	724.477			0.0530970			0.0265485	+	0.999648i	$0.491548\pi$
$572$	−5288.22	−	9159.46i	−0.386558	−	0.669539i
$573$	7179.34	−	669.856i	0.523423	−	0.0488370i
$574$	11547.9	+	10217.0i	0.839719	+	0.742944i
$575$	3211.00			0.232884
$576$	1698.17	−	319.673i	0.122842	−	0.0231245i
$577$	10110.1	+	17511.2i	0.729443	+	1.26343i	0.957119	+	0.289695i	$0.0935540\pi$
$577$	10110.1	+	17511.2i	0.729443	+	1.26343i	−0.227676	+	0.973737i	$0.573113\pi$
$578$	3715.02	−	6434.60i	0.267343	−	0.463052i
$579$	−24032.6	+	2242.32i	−1.72498	+	0.160946i
$580$	385.571	−	667.829i	0.0276034	−	0.0478105i
$581$	−23144.3	+	7743.56i	−1.65264	+	0.552938i
$582$	−1637.02	−	2309.44i	−0.116592	−	0.164483i
$583$	−12387.4			−0.879991
$584$	−2170.60	−	3759.59i	−0.153802	−	0.266392i
$585$	5394.36	−	1015.46i	0.381247	−	0.0717679i
$586$	−7965.83	+	13797.2i	−0.561545	+	0.972624i
$587$	−12733.7	−	22055.4i	−0.895358	−	1.55081i	−0.833361	−	0.552730i	$-0.813586\pi$
$587$	−12733.7	−	22055.4i	−0.895358	−	1.55081i	−0.0619978	−	0.998076i	$-0.519747\pi$
$588$	6792.72	+	2164.09i	0.476407	+	0.151778i
$589$	2879.00	−	4986.58i	0.201404	−	0.348843i
$590$	−1481.25	−	2565.60i	−0.103359	−	0.179024i
$591$	−14682.9	+	1369.96i	−1.02195	+	0.0953515i
$592$	1472.28	−	2550.06i	0.102213	−	0.177038i
$593$	265.863	−	460.487i	0.0184109	−	0.0318886i	−0.856673	−	0.515860i	$-0.827473\pi$
$593$	265.863	−	460.487i	0.0184109	−	0.0318886i	0.875084	+	0.483971i	$0.160806\pi$
$594$	2278.05	−	9130.87i	0.157356	−	0.630714i
$595$	1238.02	+	1095.35i	0.0853010	+	0.0754703i
$596$	−3557.84	−	6162.36i	−0.244521	−	0.423524i
$597$	4381.52	+	6181.27i	0.300374	+	0.423756i
$598$	−4277.92			−0.292537
$599$	15005.5			1.02355			0.511776	−	0.859119i	$-0.328988\pi$
$599$	15005.5			1.02355			0.511776	+	0.859119i	$0.328988\pi$
$600$	−2053.41	+	4470.70i	−0.139717	+	0.304193i
$601$	−8175.79	−	14160.9i	−0.554904	−	0.961123i	−0.997911	−	0.0646042i	$-0.979422\pi$
$601$	−8175.79	−	14160.9i	−0.554904	−	0.961123i	0.443007	−	0.896518i	$-0.353912\pi$
$602$	−6315.78	+	2113.12i	−0.427594	+	0.143064i
$603$	445.977	−	83.9531i	0.0301187	−	0.00566971i
$604$	754.012	−	1305.99i	0.0507952	−	0.0879799i
$605$	265.792	−	460.366i	0.0178612	−	0.0309364i
$606$	−5699.25	+	12408.4i	−0.382040	+	0.831778i
$607$	331.885	+	574.841i	0.0221924	+	0.0384383i	0.876908	−	0.480658i	$-0.159602\pi$
$607$	331.885	+	574.841i	0.0221924	+	0.0384383i	−0.854716	+	0.519096i	$0.826269\pi$
$608$	−779.082	+	1349.41i	−0.0519670	+	0.0900096i
$609$	6581.11	−	2906.67i	0.437899	−	0.193406i
$610$	1764.37	+	3055.98i	0.117110	+	0.202841i
$611$	7907.52	−	13696.2i	0.523574	−	0.906858i
$612$	2435.66	+	2835.63i	0.160875	+	0.187293i
$613$	2552.17	+	4420.48i	0.168158	+	0.291259i	0.937772	−	0.347251i	$-0.112885\pi$
$613$	2552.17	+	4420.48i	0.168158	+	0.291259i	−0.769614	+	0.638509i	$0.779551\pi$
$614$	−4834.20			−0.317740
$615$	5553.69	−	518.177i	0.364140	−	0.0339755i
$616$	−3721.66	−	3292.75i	−0.243425	−	0.215371i
$617$	10449.3	−	18098.7i	0.681804	−	1.18092i	−0.292626	−	0.956227i	$-0.594529\pi$
$617$	10449.3	−	18098.7i	0.681804	−	1.18092i	0.974430	−	0.224692i	$-0.0721374\pi$
$618$	−9191.41	−	12966.9i	−0.598273	−	0.844019i
$619$	8645.50	−	14974.4i	0.561377	−	0.972333i	−0.436000	−	0.899947i	$-0.643605\pi$
$619$	8645.50	−	14974.4i	0.561377	−	0.972333i	0.997377	−	0.0723861i	$-0.0230614\pi$
$620$	609.882	+	1056.35i	0.0395056	+	0.0684256i
$621$	−2737.72	−	2644.58i	−0.176910	−	0.170891i
$622$	18422.7			1.18759
$623$	−1383.62	−	1224.16i	−0.0889785	−	0.0787240i
$624$	2735.70	−	5956.17i	0.175506	−	0.382112i
$625$	−6587.76	−	11410.3i	−0.421616	−	0.730261i
$626$	4873.74			0.311172
$627$	4907.28	+	6923.00i	0.312564	+	0.440954i
$628$	10347.2			0.657482
$629$	6369.78			0.403783
$630$	2252.13	−	1256.61i	0.142424	−	0.0794675i
$631$	−7500.16			−0.473180			−0.236590	−	0.971610i	$-0.576030\pi$
$631$	−7500.16			−0.473180			−0.236590	+	0.971610i	$0.576030\pi$
$632$	−9473.61			−0.596266
$633$	12488.3	−	27189.5i	0.784145	−	1.70724i
$634$	−15980.9			−1.00108
$635$	1317.31	+	2281.65i	0.0823241	+	0.142589i
$636$	−4439.36	−	6262.88i	−0.276780	−	0.390470i
$637$	21596.5	−	16273.1i	1.34330	−	1.01219i
$638$	−5014.72			−0.311183
$639$	19233.3	−	3620.58i	1.19070	−	0.224144i
$640$	−165.039	−	285.856i	−0.0101934	−	0.0176554i
$641$	8767.89	−	15186.4i	0.540266	−	0.935769i	−0.458622	−	0.888631i	$-0.651657\pi$
$641$	8767.89	−	15186.4i	0.540266	−	0.935769i	0.998888	−	0.0471374i	$-0.0150099\pi$
$642$	1041.44	−	2267.42i	0.0640221	−	0.139389i
$643$	923.122	−	1598.89i	0.0566164	−	0.0980626i	−0.836328	−	0.548229i	$-0.815302\pi$
$643$	923.122	−	1598.89i	0.0566164	−	0.0980626i	0.892945	+	0.450167i	$0.148635\pi$
$644$	−1906.07	+	637.728i	−0.116630	+	0.0390217i
$645$	−1005.58	+	2189.35i	−0.0613870	+	0.133652i
$646$	−3370.69			−0.205291
$647$	6971.31	+	12074.7i	0.423602	+	0.733700i	0.996289	−	0.0860745i	$-0.0274323\pi$
$647$	6971.31	+	12074.7i	0.423602	+	0.733700i	−0.572687	+	0.819774i	$0.694099\pi$
$648$	5432.82	−	2120.55i	0.329354	−	0.128554i
$649$	−9632.52	+	16684.0i	−0.582603	+	1.00910i
$650$	9330.37	+	16160.7i	0.563027	+	0.975191i
$651$	−1223.18	+	11313.9i	−0.0736410	+	0.681150i
$652$	5137.03	−	8897.59i	0.308561	−	0.534443i
$653$	−3858.51	−	6683.13i	−0.231233	−	0.400507i	0.726938	−	0.686703i	$-0.240943\pi$
$653$	−3858.51	−	6683.13i	−0.231233	−	0.400507i	−0.958171	+	0.286196i	$0.907609\pi$
$654$	−9774.23	−	13789.1i	−0.584408	−	0.824459i
$655$	3014.08	−	5220.55i	0.179801	−	0.311425i
$656$	3330.15	−	5768.00i	0.198202	−	0.343296i
$657$	−9546.68	−	11114.4i	−0.566897	−	0.659989i
$658$	1481.51	−	7281.29i	0.0877742	−	0.431389i
$659$	1019.94	+	1766.58i	0.0602899	+	0.104425i	0.894595	−	0.446878i	$-0.147464\pi$
$659$	1019.94	+	1766.58i	0.0602899	+	0.104425i	−0.834305	+	0.551303i	$0.814131\pi$
$660$	−1789.85	+	166.999i	−0.105560	+	0.00984911i
$661$	−19521.3			−1.14870			−0.574349	−	0.818611i	$-0.694745\pi$
$661$	−19521.3			−1.14870			−0.574349	+	0.818611i	$0.694745\pi$
$662$	−6314.22			−0.370709
$663$	14117.4	−	1317.20i	0.826960	−	0.0771580i
$664$	5271.05	+	9129.73i	0.308067	+	0.533588i
$665$	−463.667	+	2278.82i	−0.0270380	+	0.132885i
$666$	3291.01	−	9377.13i	0.191478	−	0.545580i
$667$	−1014.17	+	1756.59i	−0.0588737	+	0.101972i
$668$	4626.98	−	8014.17i	0.267999	−	0.464188i
$669$	−4358.35	−	6148.58i	−0.251873	−	0.355333i
$670$	−43.3429	−	75.0721i	−0.00249923	−	0.00432879i
$671$	11473.6	−	19872.9i	0.660111	−	1.14335i
$672$	331.004	−	3061.65i	0.0190011	−	0.175753i
$673$	8294.49	+	14366.5i	0.475081	+	0.822864i	0.999593	−	0.0285393i	$-0.00908558\pi$
$673$	8294.49	+	14366.5i	0.475081	+	0.822864i	−0.524512	+	0.851403i	$0.675752\pi$
$674$	−5620.97	+	9735.80i	−0.321234	+	0.556393i
$675$	−4019.32	+	16110.2i	−0.229191	+	0.918642i
$676$	−8036.55	−	13919.7i	−0.457246	−	0.791973i
$677$	−29134.2			−1.65394			−0.826969	−	0.562247i	$-0.809937\pi$
$677$	−29134.2			−1.65394			−0.826969	+	0.562247i	$0.809937\pi$
$678$	−4841.73	+	10541.4i	−0.274256	+	0.597110i
$679$	−4784.11	+	1600.66i	−0.270393	+	0.0904677i
$680$	357.020	−	618.376i	0.0201339	−	0.0348730i
$681$	−4994.47	+	10874.0i	−0.281040	+	0.611882i
$682$	3966.04	−	6869.39i	0.222680	−	0.385693i
$683$	4154.73	+	7196.21i	0.232762	+	0.403156i	0.958620	−	0.284689i	$-0.0918904\pi$
$683$	4154.73	+	7196.21i	0.232762	+	0.403156i	−0.725858	+	0.687845i	$0.758557\pi$
$684$	−1741.50	+	4962.08i	−0.0973506	+	0.277383i
$685$	6796.93			0.379120
$686$	7196.62	−	10470.1i	0.400537	−	0.582726i
$687$	3164.04	+	4463.70i	0.175714	+	0.247891i
$688$	1438.40	+	2491.39i	0.0797073	+	0.138057i
$689$	−29118.0			−1.61003
$690$	−303.478	+	660.734i	−0.0167438	+	0.0364546i
$691$	−432.606			−0.0238164			−0.0119082	−	0.999929i	$-0.503791\pi$
$691$	−432.606			−0.0238164			−0.0119082	+	0.999929i	$0.503791\pi$
$692$	3050.07			0.167552
$693$	−14399.6	−	8597.54i	−0.789318	−	0.471275i
$694$	20222.8			1.10612
$695$	−2395.93			−0.130767
$696$	−1797.16	−	2535.36i	−0.0978751	−	0.138078i
$697$	14407.9			0.782979
$698$	12852.8	+	22261.7i	0.696971	+	1.20719i
$699$	−759.130	+	1652.78i	−0.0410772	+	0.0894333i
$700$	6566.38	+	5809.62i	0.354551	+	0.313690i
$701$	19136.7			1.03107			0.515536	−	0.856868i	$-0.327593\pi$
$701$	19136.7			1.03107			0.515536	+	0.856868i	$0.327593\pi$
$702$	5354.81	−	21463.2i	0.287898	−	1.15395i
$703$	4480.57	+	7760.57i	0.240381	+	0.416352i
$704$	−1073.25	+	1858.92i	−0.0574566	+	0.0995178i
$705$	−1554.45	−	2192.95i	−0.0830409	−	0.117151i
$706$	5104.41	−	8841.10i	0.272106	−	0.471302i
$707$	18225.0	+	16124.6i	0.969477	+	0.857748i
$708$	−11887.2	+	1109.12i	−0.631002	+	0.0588745i
$709$	−29342.4			−1.55427			−0.777133	−	0.629336i	$-0.783327\pi$
$709$	−29342.4			−1.55427			−0.777133	+	0.629336i	$0.783327\pi$
$710$	−1869.21	−	3237.57i	−0.0988033	−	0.171132i
$711$	−31421.5	+	5914.96i	−1.65738	+	0.311995i
$712$	−399.007	+	691.100i	−0.0210020	+	0.0363765i
$713$	−1604.17	−	2778.51i	−0.0842590	−	0.145941i
$714$	6093.78	−	2691.43i	0.319403	−	0.141071i
$715$	−3409.23	+	5904.96i	−0.178319	+	0.308857i
$716$	−5950.13	−	10305.9i	−0.310568	−	0.537920i
$717$	−470.753	+	1024.93i	−0.0245197	+	0.0533843i
$718$	−8181.87	+	14171.4i	−0.425271	+	0.736591i
$719$	−8657.83	+	14995.8i	−0.449072	+	0.777815i	−0.998326	−	0.0578403i	$-0.981579\pi$
$719$	−8657.83	+	14995.8i	−0.449072	+	0.777815i	0.549254	+	0.835655i	$0.314912\pi$
$720$	−725.871	−	845.069i	−0.0375717	−	0.0437415i
$721$	−26861.4	+	8987.25i	−1.38748	+	0.464220i
$722$	4488.03	+	7773.49i	0.231339	+	0.400692i
$723$	−2225.09	+	4844.47i	−0.114456	+	0.249195i
$724$	9497.50			0.487530
$725$	8847.82			0.453241
$726$	−1238.86	−	1747.74i	−0.0633314	−	0.0893454i
$727$	10848.3	+	18789.8i	0.553428	+	0.958565i	0.998024	+	0.0628340i	$0.0200139\pi$
$727$	10848.3	+	18789.8i	0.553428	+	0.958565i	−0.444596	+	0.895731i	$0.646653\pi$
$728$	−8748.17	−	7739.97i	−0.445369	−	0.394042i
$729$	16695.3	−	10425.4i	0.848208	−	0.529663i
$730$	−1399.35	+	2423.75i	−0.0709485	+	0.122886i
$731$	−3111.61	+	5389.47i	−0.157438	+	0.272691i
$732$	14159.3	−	1321.11i	0.714949	−	0.0667070i
$733$	11107.6	+	19238.9i	0.559712	+	0.969449i	0.997520	+	0.0703810i	$0.0224215\pi$
$733$	11107.6	+	19238.9i	0.559712	+	0.969449i	−0.437808	+	0.899068i	$0.644245\pi$
$734$	1700.29	−	2944.99i	0.0855026	−	0.148095i
$735$	−981.342	−	4490.05i	−0.0492481	−	0.225330i
$736$	434.102	+	751.888i	0.0217408	+	0.0376562i
$737$	−281.857	+	488.191i	−0.0140873	+	0.0243999i
$738$	7443.96	−	21210.2i	0.371295	−	1.05794i
$739$	−16123.6	−	27927.0i	−0.802595	−	1.39013i	−0.917903	−	0.396805i	$-0.870119\pi$
$739$	−16123.6	−	27927.0i	−0.802595	−	1.39013i	0.115308	−	0.993330i	$-0.463214\pi$
$740$	−1898.31			−0.0943017
$741$	11535.1	+	16273.3i	0.571867	+	0.806767i
$742$	−12973.8	+	4340.75i	−0.641892	+	0.214763i
$743$	−16125.5	+	27930.2i	−0.796215	+	1.37908i	0.125850	+	0.992049i	$0.459834\pi$
$743$	−16125.5	+	27930.2i	−0.796215	+	1.37908i	−0.922065	+	0.387036i	$0.873499\pi$
$744$	4894.38	−	456.662i	0.241179	−	0.0225027i
$745$	−2293.68	+	3972.78i	−0.112797	+	0.195371i
$746$	188.949	+	327.270i	0.00927336	+	0.0160619i
$747$	23183.0	+	26989.9i	1.13550	+	1.32197i
$748$	−4643.37			−0.226977
$749$	−3330.29	−	2946.48i	−0.162465	−	0.143741i
$750$	6493.35	−	605.850i	0.316138	−	0.0294967i
$751$	19541.5	+	33846.9i	0.949508	+	1.64460i	0.746463	+	0.665427i	$0.231751\pi$
$751$	19541.5	+	33846.9i	0.949508	+	1.64460i	0.203046	+	0.979169i	$0.434916\pi$
$752$	−3209.67			−0.155644
$753$	7893.64	−	736.503i	0.382019	−	0.0356436i
$754$	−11787.7			−0.569339
$755$	−972.201			−0.0468636
$756$	−813.722	−	10361.4i	−0.0391465	−	0.498465i
$757$	21547.5			1.03455			0.517277	−	0.855818i	$-0.326946\pi$
$757$	21547.5			1.03455			0.517277	+	0.855818i	$0.326946\pi$
$758$	−23023.2			−1.10322
$759$	4707.83	−	439.256i	0.225143	−	0.0210066i
$760$	1004.53			0.0479447
$761$	4991.90	+	8646.22i	0.237787	+	0.411860i	0.960079	−	0.279729i	$-0.0902445\pi$
$761$	4991.90	+	8646.22i	0.237787	+	0.411860i	−0.722292	+	0.691589i	$0.756911\pi$
$762$	10571.6	−	986.363i	0.502582	−	0.0468926i
$763$	−28564.7	+	9557.13i	−1.35532	+	0.453462i
$764$	−5550.66			−0.262848
$765$	798.053	−	2273.91i	0.0377172	−	0.107468i
$766$	−3681.37	−	6376.32i	−0.173647	−	0.300765i
$767$	−22642.3	+	39217.7i	−1.06593	+	1.84624i
$768$	−1324.46	+	123.577i	−0.0622297	+	0.00580624i
$769$	−7062.99	+	12233.5i	−0.331207	+	0.573667i	−0.982749	−	0.184946i	$-0.940789\pi$
$769$	−7062.99	+	12233.5i	−0.331207	+	0.573667i	0.651542	+	0.758613i	$0.274122\pi$
$770$	−638.737	+	3139.24i	−0.0298941	+	0.146923i
$771$	−10091.1	−	14236.1i	−0.471365	−	0.664983i
$772$	18580.7			0.866235
$773$	19727.1	+	34168.3i	0.917895	+	1.58984i	0.802607	+	0.596508i	$0.203446\pi$
$773$	19727.1	+	34168.3i	0.917895	+	1.58984i	0.115288	+	0.993332i	$0.463221\pi$
$774$	6326.35	+	7365.22i	0.293793	+	0.342038i
$775$	−6997.57	+	12120.1i	−0.324336	+	0.561766i
$776$	1089.57	+	1887.19i	0.0504037	+	0.0873017i
$777$	−14297.0	−	10452.5i	−0.660105	−	0.482601i
$778$	−13243.0	+	22937.6i	−0.610265	+	1.05701i
$779$	10134.6	+	17553.7i	0.466124	+	0.807351i
$780$	−4207.24	+	392.549i	−0.193133	+	0.0180199i
$781$	−12155.4	+	21053.8i	−0.556922	+	0.964616i
$782$	−939.068	+	1626.51i	−0.0429425	+	0.0743785i
$783$	−7543.69	−	7287.06i	−0.344303	−	0.332590i
$784$	−5051.66	−	2144.49i	−0.230123	−	0.0976900i
$785$	−3335.34	−	5776.98i	−0.151648	−	0.262662i
$786$	−14048.7	−	19819.4i	−0.637533	−	0.899406i
$787$	−36533.5			−1.65474			−0.827369	−	0.561659i	$-0.810163\pi$
$787$	−36533.5			−1.65474			−0.827369	+	0.561659i	$0.810163\pi$
$788$	11352.0			0.513195
$789$	−3151.12	+	6860.62i	−0.142183	+	0.309562i
$790$	3053.74	+	5289.24i	0.137528	+	0.238206i
$791$	15482.8	+	13698.5i	0.695961	+	0.615754i
$792$	−2399.05	+	6835.64i	−0.107634	+	0.306684i
$793$	26970.1	−	46713.5i	1.20774	−	2.09186i
$794$	−7415.53	+	12844.1i	−0.331445	+	0.574080i
$795$	−2065.65	+	4497.34i	−0.0921524	+	0.200634i
$796$	−2916.26	−	5051.11i	−0.129854	−	0.224914i
$797$	−807.427	+	1398.50i	−0.0358852	+	0.0621550i	−0.883410	−	0.468600i	$-0.844758\pi$
$797$	−807.427	+	1398.50i	−0.0358852	+	0.0621550i	0.847525	+	0.530755i	$0.178092\pi$
$798$	7565.51	+	5531.13i	0.335609	+	0.245363i
$799$	−3471.64	−	6013.06i	−0.153714	−	0.266241i
$800$	1893.60	−	3279.81i	0.0836862	−	0.144949i
$801$	−891.907	+	2541.33i	−0.0393433	+	0.112102i
$802$	−765.571	−	1326.01i	−0.0337073	−	0.0583828i
$803$	18199.9			0.799827
$804$	−347.832	+	32.4539i	−0.0152576	+	0.00142358i
$805$	970.458	+	858.616i	0.0424896	+	0.0375928i
$806$	9322.63	−	16147.3i	0.407414	−	0.705662i
$807$	17207.6	+	24275.8i	0.750602	+	1.05892i
$808$	5255.69	−	9103.12i	0.228830	−	0.396345i
$809$	6807.51	+	11791.0i	0.295846	+	0.512420i	0.975181	−	0.221408i	$-0.0710651\pi$
$809$	6807.51	+	11791.0i	0.295846	+	0.512420i	−0.679335	+	0.733828i	$0.737732\pi$
$810$	−2935.16	−	2349.67i	−0.127322	−	0.101925i
$811$	−26337.5			−1.14036			−0.570181	−	0.821519i	$-0.693127\pi$
$811$	−26337.5			−1.14036			−0.570181	+	0.821519i	$0.693127\pi$
$812$	−5252.10	+	1757.24i	−0.226986	+	0.0759446i
$813$	−1985.53	+	4322.90i	−0.0856525	+	0.186483i
$814$	6172.32	+	10690.8i	0.265774	+	0.460334i
$815$	−6623.53			−0.284677
$816$	−1664.08	−	2347.61i	−0.0713901	−	0.100714i
$817$	−8754.96			−0.374905
$818$	6141.17			0.262495
$819$	−33848.0	−	20209.5i	−1.44413	−	0.862243i
$820$	−4293.80			−0.182861
$821$	37900.7			1.61114			0.805569	−	0.592502i	$-0.201860\pi$
$821$	37900.7			1.61114			0.805569	+	0.592502i	$0.201860\pi$
$822$	11432.8	−	24891.5i	0.485116	−	1.05620i
$823$	15694.9			0.664749			0.332374	−	0.943148i	$-0.392150\pi$
$823$	15694.9			0.664749			0.332374	+	0.943148i	$0.392150\pi$
$824$	6117.63	+	10596.1i	0.258638	+	0.447974i
$825$	−11927.4	−	16826.7i	−0.503344	−	0.710098i
$826$	−4242.15	+	20849.2i	−0.178697	+	0.878252i
$827$	5640.64			0.237176			0.118588	−	0.992944i	$-0.462163\pi$
$827$	5640.64			0.237176			0.118588	+	0.992944i	$0.462163\pi$
$828$	1909.26	+	2222.78i	0.0801344	+	0.0932935i
$829$	−12318.7	−	21336.6i	−0.516098	−	0.893909i	−0.999825	−	0.0186896i	$-0.994051\pi$
$829$	−12318.7	−	21336.6i	−0.516098	−	0.893909i	0.483727	−	0.875219i	$-0.339283\pi$
$830$	3398.17	−	5885.80i	0.142111	−	0.246143i
$831$	16851.0	−	36688.1i	0.703436	−	1.53152i
$832$	−2522.78	+	4369.59i	−0.105122	+	0.182077i
$833$	−1446.45	−	11783.4i	−0.0601638	−	0.490121i
$834$	−4030.09	+	8774.32i	−0.167327	+	0.364305i
$835$	−5965.89			−0.247255
$836$	−3266.20	−	5657.22i	−0.135124	−	0.234042i
$837$	15948.3	−	4570.50i	0.658607	−	0.188745i
$838$	7427.64	−	12865.0i	0.306186	−	0.530329i
$839$	−7818.70	−	13542.4i	−0.321730	−	0.557253i	0.659115	−	0.752042i	$-0.270931\pi$
$839$	−7818.70	−	13542.4i	−0.321730	−	0.557253i	−0.980845	+	0.194789i	$0.937598\pi$
$840$	−1816.06	+	802.096i	−0.0745951	+	0.0329463i
$841$	9399.99	−	16281.3i	0.385419	−	0.667566i
$842$	−452.081	−	783.027i	−0.0185033	−	0.0320486i
$843$	−14098.5	−	19889.6i	−0.576012	−	0.812614i
$844$	−11516.3	+	19946.9i	−0.469678	+	0.813506i
$845$	−5181.04	+	8973.83i	−0.210927	+	0.365336i
$846$	−10645.6	+	2003.99i	−0.432630	+	0.0814405i
$847$	−3620.52	+	1211.35i	−0.146874	+	0.0491409i
$848$	2954.76	+	5117.79i	0.119654	+	0.207247i
$849$	15808.6	−	1474.99i	0.639046	−	0.0596250i
$850$	8192.63			0.330594
$851$	4993.12			0.201130
$852$	−15000.7	+	1399.61i	−0.603187	+	0.0562793i
$853$	9722.22	+	16839.4i	0.390249	+	0.675932i	0.992482	−	0.122389i	$-0.0390555\pi$
$853$	9722.22	+	16839.4i	0.390249	+	0.675932i	−0.602233	+	0.798320i	$0.705722\pi$
$854$	5052.98	−	24834.2i	0.202470	−	0.995092i
$855$	3331.75	−	627.187i	0.133267	−	0.0250869i
$856$	−960.383	+	1663.43i	−0.0383472	+	0.0664193i
$857$	16045.1	−	27790.9i	0.639545	−	1.10773i	−0.345987	−	0.938239i	$-0.612456\pi$
$857$	16045.1	−	27790.9i	0.639545	−	1.10773i	0.985533	−	0.169486i	$-0.0542107\pi$
$858$	15890.5	+	22417.7i	0.632276	+	0.891990i
$859$	−8936.33	−	15478.2i	−0.354952	−	0.614795i	0.632158	−	0.774840i	$-0.282169\pi$
$859$	−8936.33	−	15478.2i	−0.354952	−	0.614795i	−0.987110	+	0.160045i	$0.948836\pi$
$860$	927.317	−	1606.16i	0.0367689	−	0.0636856i
$861$	−32338.5	−	23642.6i	−1.28001	−	0.935815i
$862$	−9902.27	−	17151.2i	−0.391268	−	0.677695i
$863$	19053.2	−	33001.1i	0.751539	−	1.30170i	−0.195538	−	0.980696i	$-0.562645\pi$
$863$	19053.2	−	33001.1i	0.751539	−	1.30170i	0.947077	−	0.321007i	$-0.104021\pi$
$864$	−4315.75	+	1236.82i	−0.169936	+	0.0487006i
$865$	−983.167	−	1702.89i	−0.0386459	−	0.0669366i
$866$	534.123			0.0209587
$867$	−8057.11	+	17542.0i	−0.315610	+	0.687147i
$868$	1746.64	−	8584.34i	0.0683006	−	0.335681i
$869$	19858.4	−	34395.8i	0.775202	−	1.34269i
$870$	−836.224	+	1820.63i	−0.0325870	+	0.0709484i
$871$	−662.538	+	1147.55i	−0.0257741	+	0.0446420i
$872$	6505.55	+	11267.9i	0.252644	+	0.437593i
$873$	4792.11	+	5579.04i	0.185783	+	0.216291i
$874$	−2642.20			−0.102258
$875$	2317.26	−	11388.8i	0.0895287	−	0.440013i
$876$	6522.42	+	9201.57i	0.251566	+	0.354900i
$877$	−1535.91	−	2660.28i	−0.0591381	−	0.102430i	0.834941	−	0.550340i	$-0.185502\pi$
$877$	−1535.91	−	2660.28i	−0.0591381	−	0.102430i	−0.894079	+	0.447910i	$0.852169\pi$
$878$	5271.02			0.202606
$879$	17276.2	−	37613.8i	0.662926	−	1.44333i
$880$	1383.81			0.0530093
$881$	25679.5			0.982026			0.491013	−	0.871152i	$-0.336627\pi$
$881$	25679.5			0.982026			0.491013	+	0.871152i	$0.336627\pi$
$882$	−18094.0	−	3958.66i	−0.690768	−	0.151128i
$883$	44463.9			1.69460			0.847299	−	0.531117i	$-0.178227\pi$
$883$	44463.9			1.69460			0.847299	+	0.531117i	$0.178227\pi$
$884$	−10914.8			−0.415276
$885$	4450.99	+	6279.28i	0.169060	+	0.238504i
$886$	3598.79			0.136460
$887$	−2243.77	−	3886.33i	−0.0849363	−	0.147114i	0.820428	−	0.571750i	$-0.193735\pi$
$887$	−2243.77	−	3886.33i	−0.0849363	−	0.147114i	−0.905364	+	0.424636i	$0.860402\pi$
$888$	−3193.06	+	6951.95i	−0.120667	+	0.262716i
$889$	3772.64	−	18541.7i	0.142329	−	0.699513i
$890$	514.467			0.0193764
$891$	−3689.11	+	24169.9i	−0.138709	+	0.908781i
$892$	2900.84	+	5024.39i	0.108887	+	0.188598i
$893$	4883.98	−	8459.29i	0.183019	−	0.316998i
$894$	10690.9	+	15082.3i	0.399953	+	0.564237i
$895$	−3835.96	+	6644.08i	−0.143265	+	0.248142i
$896$	−472.656	+	2323.00i	−0.0176232	+	0.0866137i
$897$	11066.3	−	1032.52i	0.411921	−	0.0384335i
$898$	−34093.9			−1.26696
$899$	−4420.24	−	7656.08i	−0.163986	−	0.284032i
$900$	4232.80	−	12060.6i	0.156771	−	0.446689i
$901$	−6391.85	+	11071.0i	−0.236341	+	0.409355i
$902$	13961.2	+	24181.5i	0.515363	+	0.892636i
$903$	15827.9	−	6990.68i	0.583299	−	0.257625i
$904$	4464.91	−	7733.45i	0.164271	−	0.284525i
$905$	−3061.45	−	5302.58i	−0.112449	−	0.194767i
$906$	−1635.30	+	3560.37i	−0.0599659	+	0.130558i
$907$	−14663.3	+	25397.5i	−0.536809	+	0.929781i	0.462264	+	0.886742i	$0.347037\pi$
$907$	−14663.3	+	25397.5i	−0.536809	+	0.929781i	−0.999073	+	0.0430386i	$0.986296\pi$
$908$	4605.76	−	7977.42i	0.168334	−	0.291564i
$909$	11748.1	−	33474.2i	0.428670	−	1.22142i
$910$	−1501.42	+	7379.14i	−0.0546942	+	0.268809i
$911$	−17532.1	−	30366.5i	−0.637612	−	1.10438i	−0.985955	−	0.167009i	$-0.946589\pi$
$911$	−17532.1	−	30366.5i	−0.637612	−	1.10438i	0.348344	−	0.937367i	$-0.386744\pi$
$912$	1689.67	−	3678.75i	0.0613492	−	0.133570i
$913$	−44196.3			−1.60207
$914$	15455.9			0.559339
$915$	−5301.73	−	7479.47i	−0.191552	−	0.270234i
$916$	−2105.93	−	3647.58i	−0.0759627	−	0.131571i
$917$	−41056.7	+	13736.7i	−1.47853	+	0.494683i
$918$	−6985.08	−	6747.45i	−0.251135	−	0.242591i
$919$	14407.9	−	24955.3i	0.517165	−	0.895755i	−0.482637	−	0.875821i	$-0.660321\pi$
$919$	14407.9	−	24955.3i	0.517165	−	0.895755i	0.999801	−	0.0199346i	$-0.00634580\pi$
$920$	279.859	−	484.730i	0.0100290	−	0.0173707i
$921$	12505.3	−	1166.79i	0.447409	−	0.0417447i
$922$	−3824.77	−	6624.69i	−0.136618	−	0.236630i
$923$	−28572.7	+	49489.4i	−1.01894	+	1.76486i
$924$	10422.1	+	7619.55i	0.371062	+	0.271282i
$925$	−10890.3	−	18862.5i	−0.387102	−	0.670481i
$926$	−9493.83	+	16443.8i	−0.336918	+	0.583560i
$927$	26906.4	+	31324.8i	0.953314	+	1.10986i
$928$	1196.15	+	2071.80i	0.0423122	+	0.0732869i
$929$	−40635.2			−1.43509			−0.717544	−	0.696513i	$-0.754734\pi$
$929$	−40635.2			−1.43509			−0.717544	+	0.696513i	$0.754734\pi$
$930$	−1832.63	−	2585.40i	−0.0646175	−	0.0911597i
$931$	13338.8	−	10050.8i	0.469561	−	0.353817i
$932$	700.049	−	1212.52i	0.0246039	−	0.0426153i
$933$	−47656.5	+	4446.51i	−1.67225	+	0.156026i
$934$	15745.4	−	27271.9i	0.551613	−	0.955421i
$935$	1496.76	+	2592.46i	0.0523520	+	0.0906764i
$936$	−5639.23	+	16068.0i	−0.196927	+	0.561108i
$937$	−32623.9			−1.13743			−0.568717	−	0.822533i	$-0.692560\pi$
$937$	−32623.9			−1.13743			−0.568717	+	0.822533i	$0.692560\pi$
$938$	−124.130	+	610.069i	−0.00432088	+	0.0212361i
$939$	−12607.6	+	1176.33i	−0.438161	+	0.0408818i
$940$	1034.61	+	1792.00i	0.0358993	+	0.0621794i
$941$	7436.20			0.257612			0.128806	−	0.991670i	$-0.458886\pi$
$941$	7436.20			0.257612			0.128806	+	0.991670i	$0.458886\pi$
$942$	−26766.6	+	2497.41i	−0.925799	+	0.0863800i
$943$	11294.0			0.390013
$944$	9190.53			0.316871
$945$	−5522.60	+	3794.22i	−0.190106	+	0.130610i
$946$	−12060.6			−0.414508
$947$	39607.3			1.35910			0.679548	−	0.733631i	$-0.262176\pi$
$947$	39607.3			1.35910			0.679548	+	0.733631i	$0.262176\pi$
$948$	24506.7	−	2286.56i	0.839600	−	0.0783374i
$949$	42781.0			1.46336
$950$	5762.78	+	9981.43i	0.196810	+	0.340885i
$951$	41340.1	−	3857.16i	1.40961	−	0.131522i
$952$	−4863.18	+	1627.11i	−0.165564	+	0.0553940i
$953$	15868.8			0.539392			0.269696	−	0.962946i	$-0.413077\pi$
$953$	15868.8			0.539392			0.269696	+	0.962946i	$0.413077\pi$
$954$	12995.5	+	15129.6i	0.441033	+	0.513457i
$955$	1789.21	+	3099.01i	0.0606258	+	0.105007i
$956$	434.116	−	751.910i	0.0146865	−	0.0254378i
$957$	12972.3	−	1210.36i	0.438176	−	0.0408832i
$958$	16046.4	−	27793.2i	0.541165	−	0.937325i
$959$	−36559.7	−	32346.3i	−1.23105	−	1.08917i
$960$	495.925	+	699.631i	0.0166728	+	0.0235213i
$961$	−15807.5			−0.530612
$962$	14508.7	+	25129.9i	0.486259	+	0.842225i
$963$	−2146.76	+	6116.81i	−0.0718364	+	0.204685i
$964$	2051.92	−	3554.02i	0.0685558	−	0.118742i
$965$	−5989.34	−	10373.8i	−0.199797	−	0.346058i
$966$	4776.77	−	2109.75i	0.159099	−	0.0702693i
$967$	−3095.14	+	5360.94i	−0.102930	+	0.178279i	−0.912890	−	0.408205i	$-0.866155\pi$
$967$	−3095.14	+	5360.94i	−0.102930	+	0.178279i	0.809961	+	0.586484i	$0.199488\pi$
$968$	824.566	+	1428.19i	0.0273787	+	0.0474212i
$969$	8719.43	−	813.551i	0.289069	−	0.0269711i
$970$	702.429	−	1216.64i	0.0232512	−	0.0402722i
$971$	9880.98	−	17114.4i	0.326566	−	0.565629i	−0.655262	−	0.755402i	$-0.727442\pi$
$971$	9880.98	−	17114.4i	0.326566	−	0.565629i	0.981828	+	0.189773i	$0.0607751\pi$
$972$	−13542.0	+	6796.79i	−0.446873	+	0.224287i
$973$	12887.4	+	11402.1i	0.424614	+	0.375679i
$974$	−6709.54	−	11621.3i	−0.220727	−	0.382310i
$975$	−28036.7	−	39553.1i	−0.920917	−	1.29919i
$976$	−10947.2			−0.359027
$977$	−12406.0			−0.406248			−0.203124	−	0.979153i	$-0.565110\pi$
$977$	−12406.0			−0.406248			−0.203124	+	0.979153i	$0.565110\pi$
$978$	−11141.1	+	24256.5i	−0.364268	+	0.793086i
$979$	−1672.78	−	2897.34i	−0.0546091	−	0.0945857i
$980$	431.068	+	3511.67i	0.0140510	+	0.114466i
$981$	28612.5	+	33311.1i	0.931221	+	1.08414i
$982$	3285.70	−	5690.99i	0.106773	−	0.184936i
$983$	−21460.3	+	37170.3i	−0.696314	+	1.20605i	0.273422	+	0.961894i	$0.411844\pi$
$983$	−21460.3	+	37170.3i	−0.696314	+	1.20605i	−0.969736	+	0.244157i	$0.921489\pi$
$984$	−7222.41	+	15724.7i	−0.233986	+	0.509435i
$985$	−3659.23	−	6337.97i	−0.118368	−	0.205020i
$986$	−2587.57	+	4481.80i	−0.0835751	+	0.144756i
$987$	−2075.02	+	19193.1i	−0.0669186	+	0.618970i
$988$	−7677.57	−	13297.9i	−0.247223	−	0.428202i
$989$	−2439.12	+	4224.68i	−0.0784221	+	0.135831i
$990$	4589.74	−	863.998i	0.147345	−	0.0277370i
$991$	15135.4	+	26215.2i	0.485157	+	0.840316i	0.999855	−	0.0170556i	$-0.00542922\pi$
$991$	15135.4	+	26215.2i	0.485157	+	0.840316i	−0.514698	+	0.857372i	$0.672096\pi$
$992$	−3784.06			−0.121113
$993$	16333.9	−	1524.01i	0.521994	−	0.0487038i
$994$	−5353.25	+	26309.9i	−0.170820	+	0.839538i
$995$	−1880.07	+	3256.37i	−0.0599016	+	0.103753i
$996$	−15838.9	−	22344.9i	−0.503891	−	0.710870i
$997$	2284.30	−	3956.52i	0.0725621	−	0.125681i	−0.827461	−	0.561523i	$-0.810216\pi$
$997$	2284.30	−	3956.52i	0.0725621	−	0.125681i	0.900024	+	0.435841i	$0.143549\pi$
$998$	−19492.0	−	33761.1i	−0.618244	−	1.07083i
$999$	−6250.05	+	25051.5i	−0.197941	+	0.793387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.e.b.121.1	yes	24
3.2	odd	2		378.4.e.a.37.7		24
7.4	even	3		126.4.h.a.67.9	yes	24
9.2	odd	6		378.4.h.b.289.6		24
9.7	even	3		126.4.h.a.79.9	yes	24
21.11	odd	6		378.4.h.b.361.6		24
63.11	odd	6		378.4.e.a.235.7		24
63.25	even	3	inner	126.4.e.b.25.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.e.b.25.1	✓	24	63.25	even	3	inner
126.4.e.b.121.1	yes	24	1.1	even	1	trivial
126.4.h.a.67.9	yes	24	7.4	even	3
126.4.h.a.79.9	yes	24	9.7	even	3
378.4.e.a.37.7		24	3.2	odd	2
378.4.e.a.235.7		24	63.11	odd	6
378.4.h.b.289.6		24	9.2	odd	6
378.4.h.b.361.6		24	21.11	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-5.17368 + 0.482721i) q^{3} +4.00000 q^{4} +(-1.28937 - 2.23325i) q^{5} +(-10.3474 + 0.965443i) q^{6} +(-3.69263 + 18.1484i) q^{7} +8.00000 q^{8} +(26.5340 - 4.99489i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-5.17368 + 0.482721i) q^{3} +4.00000 q^{4} +(-1.28937 - 2.23325i) q^{5} +(-10.3474 + 0.965443i) q^{6} +(-3.69263 + 18.1484i) q^{7} +8.00000 q^{8} +(26.5340 - 4.99489i) q^{9} +(-2.57874 - 4.46651i) q^{10} +(-16.7695 + 29.0455i) q^{11} +(-20.6947 + 1.93089i) q^{12} +(-39.4185 + 68.2749i) q^{13} +(-7.38526 + 36.2968i) q^{14} +(7.74883 + 10.9317i) q^{15} +16.0000 q^{16} +(17.3059 + 29.9747i) q^{17} +(53.0679 - 9.98979i) q^{18} +(-24.3463 + 42.1691i) q^{19} +(-5.15748 - 8.93301i) q^{20} +(10.3439 - 95.6766i) q^{21} +(-33.5389 + 58.0911i) q^{22} +(13.5657 + 23.4965i) q^{23} +(-41.3895 + 3.86177i) q^{24} +(59.1751 - 102.494i) q^{25} +(-78.8370 + 136.550i) q^{26} +(-134.867 + 38.6505i) q^{27} +(-14.7705 + 72.5936i) q^{28} +(37.3798 + 64.7438i) q^{29} +(15.4977 + 21.8635i) q^{30} -118.252 q^{31} +32.0000 q^{32} +(72.7389 - 158.367i) q^{33} +(34.6118 + 59.9495i) q^{34} +(45.2911 - 15.1534i) q^{35} +(106.136 - 19.9796i) q^{36} +(92.0173 - 159.379i) q^{37} +(-48.6927 + 84.3382i) q^{38} +(170.981 - 372.261i) q^{39} +(-10.3150 - 17.8660i) q^{40} +(208.135 - 360.500i) q^{41} +(20.6877 - 191.353i) q^{42} +(89.9002 + 155.712i) q^{43} +(-67.0778 + 116.182i) q^{44} +(-45.3669 - 52.8168i) q^{45} +(27.1314 + 46.9930i) q^{46} -200.604 q^{47} +(-82.7789 + 7.72354i) q^{48} +(-315.729 - 134.031i) q^{49} +(118.350 - 204.988i) q^{50} +(-104.005 - 146.726i) q^{51} +(-157.674 + 273.099i) q^{52} +(184.672 + 319.862i) q^{53} +(-269.734 + 77.3010i) q^{54} +86.4881 q^{55} +(-29.5410 + 145.187i) q^{56} +(105.604 - 229.922i) q^{57} +(74.7597 + 129.488i) q^{58} +574.408 q^{59} +(30.9953 + 43.7269i) q^{60} -684.198 q^{61} -236.504 q^{62} +(-7.33074 + 499.993i) q^{63} +64.0000 q^{64} +203.300 q^{65} +(145.478 - 316.735i) q^{66} +16.8078 q^{67} +(69.2237 + 119.899i) q^{68} +(-81.5269 - 115.015i) q^{69} +(90.5823 - 30.3068i) q^{70} +724.856 q^{71} +(212.272 - 39.9591i) q^{72} +(-271.325 - 469.949i) q^{73} +(184.035 - 318.757i) q^{74} +(-256.677 + 558.837i) q^{75} +(-97.3853 + 168.676i) q^{76} +(-465.207 - 411.593i) q^{77} +(341.962 - 744.521i) q^{78} -1184.20 q^{79} +(-20.6299 - 35.7321i) q^{80} +(679.102 - 265.069i) q^{81} +(416.269 - 721.000i) q^{82} +(658.882 + 1141.22i) q^{83} +(41.3755 - 382.706i) q^{84} +(44.6275 - 77.2970i) q^{85} +(179.800 + 311.424i) q^{86} +(-224.645 - 316.920i) q^{87} +(-134.156 + 232.364i) q^{88} +(-49.8758 + 86.3875i) q^{89} +(-90.7339 - 105.634i) q^{90} +(-1093.52 - 967.497i) q^{91} +(54.2628 + 93.9859i) q^{92} +(611.798 - 57.0828i) q^{93} -401.208 q^{94} +125.566 q^{95} +(-165.558 + 15.4471i) q^{96} +(136.196 + 235.899i) q^{97} +(-631.458 - 268.061i) q^{98} +(-299.881 + 854.455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{2} + 2 q^{3} + 96 q^{4} + 10 q^{5} + 4 q^{6} + 17 q^{7} + 192 q^{8} + 32 q^{9}+O(q^{10}) \) 24 * q + 48 * q^2 + 2 * q^3 + 96 * q^4 + 10 * q^5 + 4 * q^6 + 17 * q^7 + 192 * q^8 + 32 * q^9	\( 24 q + 48 q^{2} + 2 q^{3} + 96 q^{4} + 10 q^{5} + 4 q^{6} + 17 q^{7} + 192 q^{8} + 32 q^{9} + 20 q^{10} - 4 q^{11} + 8 q^{12} + 80 q^{13} + 34 q^{14} - 126 q^{15} + 384 q^{16} + 92 q^{17} + 64 q^{18} + 54 q^{19} + 40 q^{20} + 230 q^{21} - 8 q^{22} + 131 q^{23} + 16 q^{24} - 178 q^{25} + 160 q^{26} + 92 q^{27} + 68 q^{28} - 278 q^{29} - 252 q^{30} - 220 q^{31} + 768 q^{32} - 396 q^{33} + 184 q^{34} - 493 q^{35} + 128 q^{36} - 21 q^{37} + 108 q^{38} - 17 q^{39} + 80 q^{40} + 465 q^{41} + 460 q^{42} + 159 q^{43} - 16 q^{44} - 870 q^{45} + 262 q^{46} - 678 q^{47} + 32 q^{48} - 207 q^{49} - 356 q^{50} - 444 q^{51} + 320 q^{52} - 78 q^{53} + 184 q^{54} - 1532 q^{55} + 136 q^{56} - 1970 q^{57} - 556 q^{58} - 1622 q^{59} - 504 q^{60} - 1978 q^{61} - 440 q^{62} - 3784 q^{63} + 1536 q^{64} - 624 q^{65} - 792 q^{66} - 80 q^{67} + 368 q^{68} - 2049 q^{69} - 986 q^{70} + 980 q^{71} + 256 q^{72} + 1510 q^{73} - 42 q^{74} - 43 q^{75} + 216 q^{76} - 350 q^{77} - 34 q^{78} + 812 q^{79} + 160 q^{80} + 1292 q^{81} + 930 q^{82} - 7 q^{83} + 920 q^{84} - 581 q^{85} + 318 q^{86} + 3336 q^{87} - 32 q^{88} + 675 q^{89} - 1740 q^{90} - 232 q^{91} + 524 q^{92} - 443 q^{93} - 1356 q^{94} + 2438 q^{95} + 64 q^{96} + 2836 q^{97} - 414 q^{98} + 6429 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 2 * q^3 + 96 * q^4 + 10 * q^5 + 4 * q^6 + 17 * q^7 + 192 * q^8 + 32 * q^9 + 20 * q^10 - 4 * q^11 + 8 * q^12 + 80 * q^13 + 34 * q^14 - 126 * q^15 + 384 * q^16 + 92 * q^17 + 64 * q^18 + 54 * q^19 + 40 * q^20 + 230 * q^21 - 8 * q^22 + 131 * q^23 + 16 * q^24 - 178 * q^25 + 160 * q^26 + 92 * q^27 + 68 * q^28 - 278 * q^29 - 252 * q^30 - 220 * q^31 + 768 * q^32 - 396 * q^33 + 184 * q^34 - 493 * q^35 + 128 * q^36 - 21 * q^37 + 108 * q^38 - 17 * q^39 + 80 * q^40 + 465 * q^41 + 460 * q^42 + 159 * q^43 - 16 * q^44 - 870 * q^45 + 262 * q^46 - 678 * q^47 + 32 * q^48 - 207 * q^49 - 356 * q^50 - 444 * q^51 + 320 * q^52 - 78 * q^53 + 184 * q^54 - 1532 * q^55 + 136 * q^56 - 1970 * q^57 - 556 * q^58 - 1622 * q^59 - 504 * q^60 - 1978 * q^61 - 440 * q^62 - 3784 * q^63 + 1536 * q^64 - 624 * q^65 - 792 * q^66 - 80 * q^67 + 368 * q^68 - 2049 * q^69 - 986 * q^70 + 980 * q^71 + 256 * q^72 + 1510 * q^73 - 42 * q^74 - 43 * q^75 + 216 * q^76 - 350 * q^77 - 34 * q^78 + 812 * q^79 + 160 * q^80 + 1292 * q^81 + 930 * q^82 - 7 * q^83 + 920 * q^84 - 581 * q^85 + 318 * q^86 + 3336 * q^87 - 32 * q^88 + 675 * q^89 - 1740 * q^90 - 232 * q^91 + 524 * q^92 - 443 * q^93 - 1356 * q^94 + 2438 * q^95 + 64 * q^96 + 2836 * q^97 - 414 * q^98 + 6429 * q^99

Introduction

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