LMFDB - Embedded newform 63.4.f.b.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$2.28179 + 3.95218i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28179 - 3.95218i) q^{2} +(1.09409 - 5.07966i) q^{3} +(-6.41313 + 11.1079i) q^{4} +(-10.3955 + 18.0055i) q^{5} +(-22.5722 + 7.26670i) q^{6} +(3.50000 + 6.06218i) q^{7} +22.0250 q^{8} +(-24.6060 - 11.1152i) q^{9} +O(q^{10})$	\(q+(-2.28179 - 3.95218i) q^{2} +(1.09409 - 5.07966i) q^{3} +(-6.41313 + 11.1079i) q^{4} +(-10.3955 + 18.0055i) q^{5} +(-22.5722 + 7.26670i) q^{6} +(3.50000 + 6.06218i) q^{7} +22.0250 q^{8} +(-24.6060 - 11.1152i) q^{9} +94.8813 q^{10} +(-22.6993 - 39.3163i) q^{11} +(49.4077 + 44.7295i) q^{12} +(-14.6521 + 25.3782i) q^{13} +(15.9725 - 27.6652i) q^{14} +(80.0884 + 72.5052i) q^{15} +(1.04863 + 1.81629i) q^{16} -98.0555 q^{17} +(12.2165 + 122.610i) q^{18} +31.1554 q^{19} +(-133.335 - 230.943i) q^{20} +(34.6231 - 11.1463i) q^{21} +(-103.590 + 179.423i) q^{22} +(-4.19596 + 7.26761i) q^{23} +(24.0972 - 111.879i) q^{24} +(-153.632 - 266.099i) q^{25} +133.732 q^{26} +(-83.3823 + 112.829i) q^{27} -89.7838 q^{28} +(36.1332 + 62.5845i) q^{29} +(103.808 - 481.965i) q^{30} +(15.4299 - 26.7254i) q^{31} +(92.8855 - 160.882i) q^{32} +(-224.548 + 72.2893i) q^{33} +(223.742 + 387.533i) q^{34} -145.537 q^{35} +(281.267 - 202.036i) q^{36} -196.369 q^{37} +(-71.0900 - 123.131i) q^{38} +(112.882 + 102.194i) q^{39} +(-228.961 + 396.571i) q^{40} +(-106.336 + 184.180i) q^{41} +(-123.055 - 111.403i) q^{42} +(-118.438 - 205.141i) q^{43} +582.293 q^{44} +(455.925 - 327.495i) q^{45} +38.2972 q^{46} +(110.018 + 190.557i) q^{47} +(10.3734 - 3.33953i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-701.114 + 1214.36i) q^{50} +(-107.281 + 498.089i) q^{51} +(-187.932 - 325.507i) q^{52} +55.9028 q^{53} +(636.181 + 72.0896i) q^{54} +943.880 q^{55} +(77.0874 + 133.519i) q^{56} +(34.0866 - 158.259i) q^{57} +(164.897 - 285.609i) q^{58} +(327.326 - 566.946i) q^{59} +(-1318.99 + 424.626i) q^{60} +(-174.391 - 302.055i) q^{61} -140.831 q^{62} +(-18.7387 - 188.069i) q^{63} -831.002 q^{64} +(-304.632 - 527.638i) q^{65} +(798.072 + 722.506i) q^{66} +(-105.247 + 182.293i) q^{67} +(628.842 - 1089.19i) q^{68} +(32.3263 + 29.2654i) q^{69} +(332.085 + 575.187i) q^{70} -548.252 q^{71} +(-541.946 - 244.811i) q^{72} -266.888 q^{73} +(448.073 + 776.086i) q^{74} +(-1519.78 + 489.266i) q^{75} +(-199.803 + 346.070i) q^{76} +(158.895 - 275.214i) q^{77} +(146.314 - 679.314i) q^{78} +(134.946 + 233.733i) q^{79} -43.6042 q^{80} +(481.906 + 546.999i) q^{81} +970.550 q^{82} +(-312.634 - 541.499i) q^{83} +(-98.2311 + 456.071i) q^{84} +(1019.34 - 1765.54i) q^{85} +(-540.503 + 936.178i) q^{86} +(357.441 - 115.072i) q^{87} +(-499.951 - 865.941i) q^{88} +1605.63 q^{89} +(-2334.64 - 1054.62i) q^{90} -205.129 q^{91} +(-53.8184 - 93.2162i) q^{92} +(-118.874 - 107.618i) q^{93} +(502.076 - 869.621i) q^{94} +(-323.875 + 560.969i) q^{95} +(-715.603 - 647.846i) q^{96} +(145.549 + 252.099i) q^{97} +223.615 q^{98} +(121.530 + 1219.72i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.28179	−	3.95218i	−0.806734	−	1.39730i	−0.915114	−	0.403195i	$-0.867900\pi$
$2$	−2.28179	−	3.95218i	−0.806734	−	1.39730i	0.108380	−	0.994110i	$-0.465434\pi$
$3$	1.09409	−	5.07966i	0.210557	−	0.977582i
$3$	1.09409	−	5.07966i	0.210557	−	0.977582i
$4$	−6.41313	+	11.1079i	−0.801641	+	1.38848i
$5$	−10.3955	+	18.0055i	−0.929801	+	1.61046i	−0.146149	+	0.989263i	$0.546688\pi$
$5$	−10.3955	+	18.0055i	−0.929801	+	1.61046i	−0.783652	+	0.621200i	$0.786645\pi$
$6$	−22.5722	+	7.26670i	−1.53584	+	0.494437i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	22.0250			0.973376
$9$	−24.6060	−	11.1152i	−0.911332	−	0.411673i
$10$	94.8813			3.00041
$11$	−22.6993	−	39.3163i	−0.622190	−	1.07766i	−0.989077	−	0.147399i	$-0.952910\pi$
$11$	−22.6993	−	39.3163i	−0.622190	−	1.07766i	0.366887	−	0.930265i	$-0.380423\pi$
$12$	49.4077	+	44.7295i	1.18856	+	1.07602i
$13$	−14.6521	+	25.3782i	−0.312597	+	0.541434i	−0.978924	−	0.204226i	$-0.934532\pi$
$13$	−14.6521	+	25.3782i	−0.312597	+	0.541434i	0.666327	+	0.745660i	$0.267866\pi$
$14$	15.9725	−	27.6652i	0.304917	−	0.528132i
$15$	80.0884	+	72.5052i	1.37858	+	1.24805i
$16$	1.04863	+	1.81629i	0.0163849	+	0.0283795i
$17$	−98.0555			−1.39894			−0.699469	−	0.714663i	$-0.746580\pi$
$17$	−98.0555			−1.39894			−0.699469	+	0.714663i	$0.746580\pi$
$18$	12.2165	+	122.610i	0.159970	+	1.60552i
$19$	31.1554			0.376186			0.188093	−	0.982151i	$-0.439769\pi$
$19$	31.1554			0.376186			0.188093	+	0.982151i	$0.439769\pi$
$20$	−133.335	−	230.943i	−1.49073	−	2.58202i
$21$	34.6231	−	11.1463i	0.359780	−	0.115825i
$22$	−103.590	+	179.423i	−1.00388	+	1.73878i
$23$	−4.19596	+	7.26761i	−0.0380399	+	0.0658870i	−0.884419	−	0.466695i	$-0.845445\pi$
$23$	−4.19596	+	7.26761i	−0.0380399	+	0.0658870i	0.846379	+	0.532582i	$0.178778\pi$
$24$	24.0972	−	111.879i	0.204951	−	0.951554i
$25$	−153.632	−	266.099i	−1.22906	−	2.12879i
$26$	133.732			1.00873
$27$	−83.3823	+	112.829i	−0.594331	+	0.804220i
$28$	−89.7838			−0.605983
$29$	36.1332	+	62.5845i	0.231371	+	0.400747i	0.958212	−	0.286059i	$-0.0923455\pi$
$29$	36.1332	+	62.5845i	0.231371	+	0.400747i	−0.726841	+	0.686806i	$0.759012\pi$
$30$	103.808	−	481.965i	0.631757	−	2.93315i
$31$	15.4299	−	26.7254i	0.0893965	−	0.154839i	−0.817860	−	0.575418i	$-0.804840\pi$
$31$	15.4299	−	26.7254i	0.0893965	−	0.154839i	0.907256	+	0.420578i	$0.138173\pi$
$32$	92.8855	−	160.882i	0.513125	−	0.888758i
$33$	−224.548	+	72.2893i	−1.18451	+	0.381332i
$34$	223.742	+	387.533i	1.12857	+	1.95474i
$35$	−145.537			−0.702863
$36$	281.267	−	202.036i	1.30216	−	0.935354i
$37$	−196.369			−0.872511			−0.436255	−	0.899823i	$-0.643696\pi$
$37$	−196.369			−0.872511			−0.436255	+	0.899823i	$0.643696\pi$
$38$	−71.0900	−	123.131i	−0.303482	−	0.525646i
$39$	112.882	+	102.194i	0.463477	+	0.419592i
$40$	−228.961	+	396.571i	−0.905046	+	1.56759i
$41$	−106.336	+	184.180i	−0.405048	+	0.701564i	−0.994327	−	0.106366i	$-0.966079\pi$
$41$	−106.336	+	184.180i	−0.405048	+	0.701564i	0.589279	+	0.807930i	$0.299412\pi$
$42$	−123.055	−	111.403i	−0.452089	−	0.409283i
$43$	−118.438	−	205.141i	−0.420039	−	0.727529i	0.575904	−	0.817517i	$-0.304650\pi$
$43$	−118.438	−	205.141i	−0.420039	−	0.727529i	−0.995943	+	0.0899887i	$0.971317\pi$
$44$	582.293			1.99509
$45$	455.925	−	327.495i	1.51034	−	1.08489i
$46$	38.2972			0.122752
$47$	110.018	+	190.557i	0.341442	+	0.591395i	0.984701	−	0.174254i	$-0.0557513\pi$
$47$	110.018	+	190.557i	0.341442	+	0.591395i	−0.643259	+	0.765649i	$0.722418\pi$
$48$	10.3734	−	3.33953i	0.0311932	−	0.0100421i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−701.114	+	1214.36i	−1.98305	+	3.43474i
$51$	−107.281	+	498.089i	−0.294556	+	1.36758i
$52$	−187.932	−	325.507i	−0.501181	−	0.868071i
$53$	55.9028			0.144884			0.0724419	−	0.997373i	$-0.476921\pi$
$53$	55.9028			0.144884			0.0724419	+	0.997373i	$0.476921\pi$
$54$	636.181	+	72.0896i	1.60321	+	0.181670i
$55$	943.880			2.31405
$56$	77.0874	+	133.519i	0.183951	+	0.318612i
$57$	34.0866	−	158.259i	0.0792085	−	0.367752i
$58$	164.897	−	285.609i	0.373310	−	0.646592i
$59$	327.326	−	566.946i	0.722275	−	1.25102i	−0.237810	−	0.971312i	$-0.576430\pi$
$59$	327.326	−	566.946i	0.722275	−	1.25102i	0.960086	−	0.279706i	$-0.0902370\pi$
$60$	−1318.99	+	424.626i	−2.83802	+	0.913650i
$61$	−174.391	−	302.055i	−0.366041	−	0.634002i	0.622901	−	0.782300i	$-0.285954\pi$
$61$	−174.391	−	302.055i	−0.366041	−	0.634002i	−0.988943	+	0.148298i	$0.952620\pi$
$62$	−140.831			−0.288477
$63$	−18.7387	−	188.069i	−0.0374739	−	0.376102i
$64$	−831.002			−1.62305
$65$	−304.632	−	527.638i	−0.581306	−	1.00685i
$66$	798.072	+	722.506i	1.48842	+	1.34749i
$67$	−105.247	+	182.293i	−0.191910	+	0.332398i	−0.945883	−	0.324507i	$-0.894802\pi$
$67$	−105.247	+	182.293i	−0.191910	+	0.332398i	0.753973	+	0.656905i	$0.228135\pi$
$68$	628.842	−	1089.19i	1.12145	−	1.94240i
$69$	32.3263	+	29.2654i	0.0564004	+	0.0510601i
$70$	332.085	+	575.187i	0.567024	+	0.982115i
$71$	−548.252			−0.916416			−0.458208	−	0.888845i	$-0.651508\pi$
$71$	−548.252			−0.916416			−0.458208	+	0.888845i	$0.651508\pi$
$72$	−541.946	−	244.811i	−0.887068	−	0.400713i
$73$	−266.888			−0.427902			−0.213951	−	0.976844i	$-0.568633\pi$
$73$	−266.888			−0.427902			−0.213951	+	0.976844i	$0.568633\pi$
$74$	448.073	+	776.086i	0.703884	+	1.21916i
$75$	−1519.78	+	489.266i	−2.33986	+	0.753274i
$76$	−199.803	+	346.070i	−0.301566	+	0.522328i
$77$	158.895	−	275.214i	0.235166	−	0.407319i
$78$	146.314	−	679.314i	0.212395	−	0.986117i
$79$	134.946	+	233.733i	0.192185	+	0.332874i	0.945974	−	0.324242i	$-0.105109\pi$
$79$	134.946	+	233.733i	0.192185	+	0.332874i	−0.753789	+	0.657116i	$0.771776\pi$
$80$	−43.6042			−0.0609388
$81$	481.906	+	546.999i	0.661051	+	0.750341i
$82$	970.550			1.30706
$83$	−312.634	−	541.499i	−0.413447	−	0.716111i	0.581817	−	0.813320i	$-0.302342\pi$
$83$	−312.634	−	541.499i	−0.413447	−	0.716111i	−0.995264	+	0.0972088i	$0.969009\pi$
$84$	−98.2311	+	456.071i	−0.127594	+	0.592398i
$85$	1019.34	−	1765.54i	1.30073	−	2.25294i
$86$	−540.503	+	936.178i	−0.677720	+	1.17384i
$87$	357.441	−	115.072i	0.440479	−	0.141804i
$88$	−499.951	−	865.941i	−0.605625	−	1.04897i
$89$	1605.63			1.91232			0.956162	−	0.292838i	$-0.0945996\pi$
$89$	1605.63			1.91232			0.956162	+	0.292838i	$0.0945996\pi$
$90$	−2334.64	−	1054.62i	−2.73437	−	1.23519i
$91$	−205.129			−0.236301
$92$	−53.8184	−	93.2162i	−0.0609887	−	0.105635i
$93$	−118.874	−	107.618i	−0.132545	−	0.119995i
$94$	502.076	−	869.621i	0.550906	−	0.954198i
$95$	−323.875	+	560.969i	−0.349778	+	0.605833i
$96$	−715.603	−	647.846i	−0.760791	−	0.688755i
$97$	145.549	+	252.099i	0.152354	+	0.263884i	0.932092	−	0.362221i	$-0.117981\pi$
$97$	145.549	+	252.099i	0.152354	+	0.263884i	−0.779739	+	0.626105i	$0.784648\pi$
$98$	223.615			0.230496
$99$	121.530	+	1219.72i	0.123376	+	1.23825i
$100$	3941.06			3.94106
$101$	726.307	+	1258.00i	0.715547	+	1.23936i	0.962748	+	0.270399i	$0.0871557\pi$
$101$	726.307	+	1258.00i	0.715547	+	1.23936i	−0.247201	+	0.968964i	$0.579511\pi$
$102$	2213.33	−	712.540i	2.14855	−	0.691686i
$103$	28.1341	−	48.7296i	0.0269139	−	0.0466162i	−0.852255	−	0.523127i	$-0.824765\pi$
$103$	28.1341	−	48.7296i	0.0269139	−	0.0466162i	0.879169	+	0.476511i	$0.158099\pi$
$104$	−322.712	+	558.954i	−0.304275	+	0.527019i
$105$	−159.230	+	739.278i	−0.147993	+	0.687106i
$106$	−127.558	−	220.938i	−0.116883	−	0.202447i
$107$	−300.124			−0.271160			−0.135580	−	0.990766i	$-0.543290\pi$
$107$	−300.124			−0.271160			−0.135580	+	0.990766i	$0.543290\pi$
$108$	−718.547	−	1649.79i	−0.640206	−	1.46991i
$109$	−936.906			−0.823296			−0.411648	−	0.911343i	$-0.635047\pi$
$109$	−936.906			−0.823296			−0.411648	+	0.911343i	$0.635047\pi$
$110$	−2153.74	−	3730.38i	−1.86682	−	3.23343i
$111$	−214.845	+	997.489i	−0.183713	+	0.852951i
$112$	−7.34044	+	12.7140i	−0.00619291	+	0.0107264i
$113$	−697.297	+	1207.75i	−0.580498	+	1.00545i	0.414923	+	0.909857i	$0.363809\pi$
$113$	−697.297	+	1207.75i	−0.580498	+	1.00545i	−0.995420	+	0.0955946i	$0.969525\pi$
$114$	−703.245	+	226.397i	−0.577763	+	0.186000i
$115$	−87.2381	−	151.101i	−0.0707391	−	0.122524i
$116$	−926.907			−0.741906
$117$	642.612	−	461.594i	0.507773	−	0.364738i
$118$	−2987.56			−2.33074
$119$	−343.194	−	594.430i	−0.264375	−	0.457910i
$120$	1763.95	+	1596.93i	1.34188	+	1.21482i
$121$	−365.014	+	632.222i	−0.274240	+	0.474998i
$122$	−795.849	+	1378.45i	−0.590596	+	1.02294i
$123$	819.232	+	741.662i	0.600550	+	0.543686i
$124$	197.908	+	342.786i	0.143328	+	0.248251i
$125$	3789.47			2.71152
$126$	−700.523	+	503.192i	−0.495298	+	0.355777i
$127$	−2387.37			−1.66807			−0.834034	−	0.551714i	$-0.813974\pi$
$127$	−2387.37			−1.66807			−0.834034	+	0.551714i	$0.813974\pi$
$128$	1153.09	+	1997.21i	0.796247	+	1.37914i
$129$	−1171.63	+	377.185i	−0.799661	+	0.257436i
$130$	−1390.21	+	2407.92i	−0.937920	+	1.62452i
$131$	−1060.00	+	1835.97i	−0.706963	+	1.22450i	0.259015	+	0.965873i	$0.416602\pi$
$131$	−1060.00	+	1835.97i	−0.706963	+	1.22450i	−0.965978	+	0.258623i	$0.916731\pi$
$132$	637.078	−	2957.85i	0.420080	−	1.95036i
$133$	109.044	+	188.869i	0.0710925	+	0.123136i
$134$	960.606			0.619282
$135$	−1164.74	−	2674.26i	−0.742557	−	1.70491i
$136$	−2159.67			−1.36169
$137$	32.9508	+	57.0725i	0.0205487	+	0.0355915i	0.876117	−	0.482099i	$-0.160125\pi$
$137$	32.9508	+	57.0725i	0.0205487	+	0.0355915i	−0.855568	+	0.517690i	$0.826792\pi$
$138$	41.9004	−	194.537i	0.0258463	−	0.120000i
$139$	981.641	−	1700.25i	0.599005	−	1.03751i	−0.393963	−	0.919126i	$-0.628896\pi$
$139$	981.641	−	1700.25i	0.599005	−	1.03751i	0.992968	−	0.118381i	$-0.0377705\pi$
$140$	933.346	−	1616.60i	0.563444	−	0.975914i
$141$	1088.33	−	350.369i	0.650030	−	0.209265i
$142$	1251.00	+	2166.79i	0.739304	+	1.28051i
$143$	1330.37			0.777979
$144$	−5.61429	−	56.3472i	−0.00324901	−	0.0326083i
$145$	−1502.49			−0.860517
$146$	608.982	+	1054.79i	0.345203	+	0.597910i
$147$	188.752	+	170.880i	0.105905	+	0.0958769i
$148$	1259.34	−	2181.24i	0.699440	−	1.21147i
$149$	1316.91	−	2280.95i	0.724063	−	1.25411i	−0.235296	−	0.971924i	$-0.575606\pi$
$149$	1316.91	−	2280.95i	0.724063	−	1.25411i	0.959359	−	0.282190i	$-0.0910607\pi$
$150$	5401.49	+	4890.04i	2.94020	+	2.66180i
$151$	368.737	+	638.671i	0.198724	+	0.344200i	0.948115	−	0.317927i	$-0.102987\pi$
$151$	368.737	+	638.671i	0.198724	+	0.344200i	−0.749391	+	0.662128i	$0.769654\pi$
$152$	686.197			0.366170
$153$	2412.75	+	1089.90i	1.27490	+	0.575905i
$154$	−1450.26			−0.758865
$155$	320.803	+	555.646i	0.166242	+	0.287939i
$156$	−1859.08	+	598.497i	−0.954138	+	0.307167i
$157$	−1173.36	+	2032.32i	−0.596462	+	1.03310i	0.396877	+	0.917872i	$0.370094\pi$
$157$	−1173.36	+	2032.32i	−0.596462	+	1.03310i	−0.993339	+	0.115230i	$0.963239\pi$
$158$	615.837	−	1066.66i	0.310084	−	0.537082i
$159$	61.1624	−	283.967i	0.0305063	−	0.141636i
$160$	1931.18	+	3344.90i	0.954207	+	1.65274i
$161$	−58.7434			−0.0287555
$162$	1062.23	−	3152.71i	0.515163	−	1.52902i
$163$	−572.002			−0.274863			−0.137431	−	0.990511i	$-0.543885\pi$
$163$	−572.002			−0.274863			−0.137431	+	0.990511i	$0.543885\pi$
$164$	−1363.90	−	2362.34i	−0.649406	−	1.12480i
$165$	1032.69	−	4794.59i	0.487239	−	2.26217i
$166$	−1426.73	+	2471.17i	−0.667083	+	1.15542i
$167$	−271.886	+	470.920i	−0.125983	+	0.218209i	−0.922117	−	0.386912i	$-0.873542\pi$
$167$	−271.886	+	470.920i	−0.125983	+	0.218209i	0.796134	+	0.605121i	$0.206875\pi$
$168$	762.574	−	245.497i	0.350201	−	0.112741i
$169$	669.132	+	1158.97i	0.304566	+	0.527524i
$170$	−9303.63			−4.19739
$171$	−766.608	−	346.297i	−0.342830	−	0.154866i
$172$	3038.24			1.34688
$173$	−1017.23	−	1761.89i	−0.447042	−	0.774299i	0.551150	−	0.834406i	$-0.314189\pi$
$173$	−1017.23	−	1761.89i	−0.447042	−	0.774299i	−0.998192	+	0.0601072i	$0.980856\pi$
$174$	−1270.39	−	1150.10i	−0.553494	−	0.501086i
$175$	1075.43	−	1862.69i	0.464541	−	0.804608i
$176$	47.6064	−	82.4568i	0.0203890	−	0.0353148i
$177$	−2521.77	−	2282.99i	−1.07089	−	0.969493i
$178$	−3663.72	−	6345.75i	−1.54274	−	2.67210i
$179$	−931.218			−0.388841			−0.194420	−	0.980918i	$-0.562283\pi$
$179$	−931.218			−0.388841			−0.194420	+	0.980918i	$0.562283\pi$
$180$	713.865	+	7164.62i	0.295602	+	2.96678i
$181$	1002.74			0.411785			0.205892	−	0.978575i	$-0.433990\pi$
$181$	1002.74			0.411785			0.205892	+	0.978575i	$0.433990\pi$
$182$	468.062	+	810.708i	0.190632	+	0.330185i
$183$	−1725.13	+	555.376i	−0.696861	+	0.224342i
$184$	−92.4159	+	160.069i	−0.0370271	+	0.0641328i
$185$	2041.35	−	3535.73i	0.811261	−	1.40515i
$186$	−154.081	+	715.374i	−0.0607408	+	0.282010i
$187$	2225.79	+	3855.18i	0.870405	+	1.50759i
$188$	−2822.24			−1.09486
$189$	−975.828	−	110.577i	−0.375561	−	0.0425572i
$190$	2956.06			1.12871
$191$	1921.54	+	3328.21i	0.727947	+	1.26084i	0.957750	+	0.287604i	$0.0928586\pi$
$191$	1921.54	+	3328.21i	0.727947	+	1.26084i	−0.229803	+	0.973237i	$0.573808\pi$
$192$	−909.187	+	4221.21i	−0.341745	+	1.58666i
$193$	1733.05	−	3001.73i	0.646361	−	1.11953i	−0.337624	−	0.941281i	$-0.609623\pi$
$193$	1733.05	−	3001.73i	0.646361	−	1.11953i	0.983985	−	0.178250i	$-0.0570435\pi$
$194$	664.227	−	1150.47i	0.245818	−	0.425769i
$195$	−3013.51	+	970.146i	−1.10668	+	0.356275i
$196$	−314.243	−	544.285i	−0.114520	−	0.198355i
$197$	−3691.99			−1.33525			−0.667623	−	0.744500i	$-0.732688\pi$
$197$	−3691.99			−1.33525			−0.667623	+	0.744500i	$0.732688\pi$
$198$	4543.25	−	3263.45i	1.63068	−	1.17133i
$199$	−481.783			−0.171622			−0.0858108	−	0.996311i	$-0.527348\pi$
$199$	−481.783			−0.171622			−0.0858108	+	0.996311i	$0.527348\pi$
$200$	−3383.75	−	5860.83i	−1.19634	−	2.07212i
$201$	810.839	+	734.064i	0.284538	+	0.257596i
$202$	3314.56	−	5740.98i	1.15451	−	1.99967i
$203$	−252.932	+	438.092i	−0.0874501	+	0.151468i
$204$	−4844.70	−	4385.97i	−1.66273	−	1.50529i
$205$	−2210.84	−	3829.29i	−0.753228	−	1.30463i
$206$	−256.784			−0.0868494
$207$	184.026	−	132.188i	0.0617909	−	0.0443849i
$208$	−61.4588			−0.0204875
$209$	−707.204	−	1224.91i	−0.234059	−	0.405402i
$210$	3285.09	−	1057.57i	1.07949	−	0.347521i
$211$	−574.892	+	995.742i	−0.187570	+	0.324880i	−0.944439	−	0.328686i	$-0.893394\pi$
$211$	−574.892	+	995.742i	−0.187570	+	0.324880i	0.756870	+	0.653566i	$0.226728\pi$
$212$	−358.512	+	620.960i	−0.116145	+	0.201169i
$213$	−599.834	+	2784.93i	−0.192958	+	0.895871i
$214$	684.820	+	1186.14i	0.218754	+	0.378893i
$215$	4924.90			1.56221
$216$	−1836.49	+	2485.06i	−0.578508	+	0.782809i
$217$	216.018			0.0675774
$218$	2137.82	+	3702.82i	0.664182	+	1.15040i
$219$	−291.998	+	1355.70i	−0.0900978	+	0.418309i
$220$	−6053.22	+	10484.5i	−1.85504	+	3.21302i
$221$	1436.72	−	2488.47i	0.437304	−	0.757433i
$222$	4432.48	−	1426.96i	1.34004	−	0.431401i
$223$	1007.98	+	1745.87i	0.302687	+	0.524269i	0.976744	−	0.214411i	$-0.0687830\pi$
$223$	1007.98	+	1745.87i	0.302687	+	0.524269i	−0.674057	+	0.738680i	$0.735450\pi$
$224$	1300.40			0.387886
$225$	822.534	+	8255.28i	0.243714	+	2.44601i
$226$	6364.34			1.87323
$227$	−1521.10	−	2634.62i	−0.444753	−	0.770335i	0.553282	−	0.832994i	$-0.313375\pi$
$227$	−1521.10	−	2634.62i	−0.444753	−	0.770335i	−0.998035	+	0.0626590i	$0.980042\pi$
$228$	1539.31	+	1393.56i	0.447121	+	0.404785i
$229$	−2040.67	+	3534.54i	−0.588870	+	1.01995i	0.405511	+	0.914090i	$0.367094\pi$
$229$	−2040.67	+	3534.54i	−0.588870	+	1.01995i	−0.994381	+	0.105863i	$0.966240\pi$
$230$	−398.118	+	689.560i	−0.114135	+	0.197688i
$231$	−1224.15	−	1108.24i	−0.348672	−	0.315657i
$232$	795.833	+	1378.42i	0.225211	+	0.390077i
$233$	2667.57			0.750035			0.375017	−	0.927018i	$-0.377637\pi$
$233$	2667.57			0.750035			0.375017	+	0.927018i	$0.377637\pi$
$234$	−3290.61	−	1486.46i	−0.919289	−	0.415268i
$235$	−4574.77			−1.26989
$236$	4198.37	+	7271.79i	1.15801	+	2.00573i
$237$	1334.93	−	429.756i	0.365878	−	0.117788i
$238$	−1566.19	+	2712.73i	−0.426560	+	0.738824i
$239$	2986.31	−	5172.45i	0.808237	−	1.39991i	−0.105848	−	0.994382i	$-0.533756\pi$
$239$	2986.31	−	5172.45i	0.808237	−	1.39991i	0.914084	−	0.405525i	$-0.132911\pi$
$240$	−47.7068	+	221.495i	−0.0128311	+	0.0595726i
$241$	1320.63	+	2287.40i	0.352984	+	0.611387i	0.986771	−	0.162121i	$-0.0518336\pi$
$241$	1320.63	+	2287.40i	0.352984	+	0.611387i	−0.633787	+	0.773508i	$0.718500\pi$
$242$	3331.54			0.884956
$243$	3305.82	−	1849.46i	0.872709	−	0.488241i
$244$	4473.57			1.17373
$245$	−509.379	−	882.270i	−0.132829	−	0.230066i
$246$	1061.86	−	4930.07i	0.275211	−	1.27776i
$247$	−456.492	+	790.667i	−0.117595	+	0.203680i
$248$	339.843	−	588.626i	0.0870164	−	0.150717i
$249$	−3092.68	+	995.631i	−0.787111	+	0.253396i
$250$	−8646.77	−	14976.6i	−2.18748	−	3.78882i
$251$	−7001.16			−1.76060			−0.880298	−	0.474422i	$-0.842657\pi$
$251$	−7001.16			−1.76060			−0.880298	+	0.474422i	$0.842657\pi$
$252$	2209.22	+	997.962i	0.552252	+	0.249467i
$253$	380.981			0.0946721
$254$	5447.47	+	9435.29i	1.34569	+	2.33080i
$255$	−7853.11	−	7109.53i	−1.92855	−	1.74595i
$256$	1938.20	−	3357.06i	0.473193	−	0.819595i
$257$	−2893.85	+	5012.30i	−0.702388	+	1.21657i	0.265239	+	0.964183i	$0.414549\pi$
$257$	−2893.85	+	5012.30i	−0.702388	+	1.21657i	−0.967626	+	0.252388i	$0.918784\pi$
$258$	4164.11	+	3769.83i	1.00483	+	0.909687i
$259$	−687.292	−	1190.43i	−0.164889	−	0.285596i
$260$	7814.57			1.86400
$261$	−193.454	−	1941.58i	−0.0458793	−	0.460462i
$262$	9674.74			2.28133
$263$	3743.32	+	6483.62i	0.877653	+	1.52014i	0.853909	+	0.520422i	$0.174225\pi$
$263$	3743.32	+	6483.62i	0.877653	+	1.52014i	0.0237442	+	0.999718i	$0.492441\pi$
$264$	−4945.68	+	1592.17i	−1.15297	+	0.371179i
$265$	−581.137	+	1006.56i	−0.134713	+	0.233330i
$266$	497.630	−	861.920i	0.114705	−	0.198676i
$267$	1756.70	−	8156.08i	0.402653	−	1.86945i
$268$	−1349.93	−	2338.14i	−0.307686	−	0.532928i
$269$	−3249.42			−0.736508			−0.368254	−	0.929725i	$-0.620044\pi$
$269$	−3249.42			−0.736508			−0.368254	+	0.929725i	$0.620044\pi$
$270$	−7911.42	+	10705.4i	−1.78324	+	2.41299i
$271$	−3946.32			−0.884581			−0.442291	−	0.896872i	$-0.645834\pi$
$271$	−3946.32			−0.884581			−0.442291	+	0.896872i	$0.645834\pi$
$272$	−102.824	−	178.097i	−0.0229215	−	0.0397012i
$273$	−224.429	+	1041.99i	−0.0497548	+	0.231004i
$274$	150.374	−	260.455i	0.0331547	−	0.0574257i
$275$	−6974.69	+	12080.5i	−1.52942	+	2.64903i
$276$	−532.389	+	171.393i	−0.116109	+	0.0373791i
$277$	−2327.13	−	4030.71i	−0.504779	−	0.874303i	−0.999985	−	0.00552735i	$-0.998241\pi$
$277$	−2327.13	−	4030.71i	−0.504779	−	0.874303i	0.495206	−	0.868776i	$-0.335093\pi$
$278$	−8959.60			−1.93295
$279$	−676.724	+	486.097i	−0.145213	+	0.104308i
$280$	−3205.45			−0.684150
$281$	−3223.44	−	5583.17i	−0.684322	−	1.18528i	−0.973649	−	0.228051i	$-0.926765\pi$
$281$	−3223.44	−	5583.17i	−0.684322	−	1.18528i	0.289327	−	0.957230i	$-0.406569\pi$
$282$	−3868.07	−	3501.82i	−0.816809	−	0.739469i
$283$	1819.23	−	3151.00i	0.382127	−	0.661864i	−0.609239	−	0.792987i	$-0.708525\pi$
$283$	1819.23	−	3151.00i	0.382127	−	0.661864i	0.991366	+	0.131123i	$0.0418583\pi$
$284$	3516.01	−	6089.91i	0.734636	−	1.27243i
$285$	2495.18	+	2258.93i	0.518603	+	0.469499i
$286$	−3035.62	−	5257.85i	−0.627622	−	1.08707i
$287$	−1488.71			−0.306187
$288$	−4073.77	+	2926.23i	−0.833504	+	0.598713i
$289$	4701.88			0.957029
$290$	3428.36	+	5938.10i	0.694208	+	1.20240i
$291$	1439.82	−	463.524i	0.290048	−	0.0933755i
$292$	1711.59	−	2964.55i	0.343024	−	0.594135i
$293$	−3163.73	+	5479.74i	−0.630809	+	1.09259i	0.356578	+	0.934266i	$0.383944\pi$
$293$	−3163.73	+	5479.74i	−0.630809	+	1.09259i	−0.987387	+	0.158328i	$0.949390\pi$
$294$	244.654	−	1135.89i	0.0485324	−	0.225328i
$295$	6805.43	+	11787.4i	1.34314	+	2.32639i
$296$	−4325.03			−0.849281
$297$	6328.74	+	717.148i	1.23647	+	0.140112i
$298$	−12019.6			−2.33651
$299$	−122.959	−	212.972i	−0.0237823	−	0.0411922i
$300$	4311.85	−	20019.2i	0.829817	−	3.85271i
$301$	829.068	−	1435.99i	0.158760	−	0.274980i
$302$	1682.76	−	2914.62i	0.320635	−	0.555357i
$303$	7184.86	−	2313.03i	1.36224	−	0.438549i
$304$	32.6706	+	56.5871i	0.00616377	+	0.0106760i
$305$	7251.53			1.36138
$306$	−1197.89	−	12022.5i	−0.223788	−	2.24602i
$307$	2712.80			0.504324			0.252162	−	0.967685i	$-0.418858\pi$
$307$	2712.80			0.504324			0.252162	+	0.967685i	$0.418858\pi$
$308$	2038.03	+	3529.96i	0.377037	+	0.653047i
$309$	−216.749	−	196.226i	−0.0399043	−	0.0361259i
$310$	1464.01	−	2535.74i	0.268226	−	0.464581i
$311$	−1523.04	+	2637.98i	−0.277696	+	0.480983i	−0.970812	−	0.239843i	$-0.922904\pi$
$311$	−1523.04	+	2637.98i	−0.277696	+	0.480983i	0.693116	+	0.720826i	$0.256237\pi$
$312$	2486.22	+	2250.81i	0.451137	+	0.408421i
$313$	−2190.26	−	3793.65i	−0.395531	−	0.685079i	0.597638	−	0.801766i	$-0.296106\pi$
$313$	−2190.26	−	3793.65i	−0.395531	−	0.685079i	−0.993169	+	0.116687i	$0.962773\pi$
$314$	10709.5			1.92475
$315$	3581.07	+	1617.67i	0.640542	+	0.289350i
$316$	−3461.70			−0.616253
$317$	−3453.12	−	5980.99i	−0.611820	−	1.05970i	−0.990934	−	0.134353i	$-0.957105\pi$
$317$	−3453.12	−	5980.99i	−0.611820	−	1.05970i	0.379114	−	0.925350i	$-0.376229\pi$
$318$	−1261.85	+	406.229i	−0.222519	+	0.0716358i
$319$	1640.39	−	2841.25i	0.287914	−	0.498681i
$320$	8638.67	−	14962.6i	1.50911	−	2.61386i
$321$	−328.361	+	1524.53i	−0.0570945	+	0.265081i
$322$	134.040	+	232.164i	0.0231980	+	0.0401801i
$323$	−3054.96			−0.526261
$324$	−9166.51	+	1844.97i	−1.57176	+	0.316353i
$325$	9004.16			1.53680
$326$	1305.19	+	2260.65i	0.221741	+	0.384067i
$327$	−1025.06	+	4759.17i	−0.173351	+	0.804839i
$328$	−2342.06	+	4056.57i	−0.394264	+	0.682885i
$329$	−770.126	+	1333.90i	−0.129053	+	0.223526i
$330$	−21305.4	+	6858.90i	−3.55402	+	1.14415i
$331$	−2851.26	−	4938.52i	−0.473472	−	0.820078i	0.526067	−	0.850443i	$-0.323666\pi$
$331$	−2851.26	−	4938.52i	−0.473472	−	0.820078i	−0.999539	+	0.0303654i	$0.990333\pi$
$332$	8019.85			1.32574
$333$	4831.85	+	2182.68i	0.795147	+	0.359189i
$334$	2481.54			0.406539
$335$	−2188.19	−	3790.06i	−0.356876	−	0.618128i
$336$	56.5518	+	51.1972i	0.00918201	+	0.00831260i
$337$	−614.807	+	1064.88i	−0.0993788	+	0.172129i	−0.911428	−	0.411460i	$-0.865019\pi$
$337$	−614.807	+	1064.88i	−0.0993788	+	0.172129i	0.812049	+	0.583589i	$0.198352\pi$
$338$	3053.63	−	5289.05i	0.491408	−	0.851143i
$339$	5372.08	+	4863.42i	0.860683	+	0.779188i
$340$	13074.3	+	22645.3i	2.08544	+	3.61209i
$341$	−1400.99			−0.222486
$342$	380.610	+	3819.95i	0.0601784	+	0.603974i
$343$	−343.000			−0.0539949
$344$	−2608.60	−	4518.23i	−0.408856	−	0.708159i
$345$	−862.987	+	277.823i	−0.134671	+	0.0433550i
$346$	−4642.19	+	8040.50i	−0.721288	+	1.24931i
$347$	−2192.74	+	3797.94i	−0.339229	+	0.587562i	−0.984288	−	0.176571i	$-0.943500\pi$
$347$	−2192.74	+	3797.94i	−0.339229	+	0.587562i	0.645059	+	0.764133i	$0.276833\pi$
$348$	−1014.12	+	4708.37i	−0.156213	+	0.725274i
$349$	−1460.02	−	2528.82i	−0.223934	−	0.387865i	0.732065	−	0.681235i	$-0.238557\pi$
$349$	−1460.02	−	2528.82i	−0.223934	−	0.387865i	−0.955999	+	0.293370i	$0.905223\pi$
$350$	−9815.59			−1.49904
$351$	−1641.67	−	3769.28i	−0.249646	−	0.573188i
$352$	−8433.73			−1.27704
$353$	−5565.95	−	9640.52i	−0.839223	−	1.45358i	−0.890545	−	0.454895i	$-0.849677\pi$
$353$	−5565.95	−	9640.52i	−0.839223	−	1.45358i	0.0513214	−	0.998682i	$-0.483657\pi$
$354$	−3268.64	+	15175.8i	−0.490753	+	2.27849i
$355$	5699.35	−	9871.56i	0.852084	−	1.47585i
$356$	−10297.1	+	17835.2i	−1.53300	+	2.65523i
$357$	−3394.99	+	1092.95i	−0.503310	+	0.162032i
$358$	2124.84	+	3680.34i	0.313691	+	0.543329i
$359$	7640.81			1.12330			0.561652	−	0.827373i	$-0.310166\pi$
$359$	7640.81			1.12330			0.561652	+	0.827373i	$0.310166\pi$
$360$	10041.7	−	7213.08i	1.47013	−	1.05601i
$361$	−5888.34			−0.858484
$362$	−2288.04	−	3963.00i	−0.332201	−	0.575389i
$363$	2812.12	+	2545.85i	0.406606	+	0.368106i
$364$	1315.52	−	2278.55i	0.189429	−	0.328100i
$365$	2774.43	−	4805.45i	0.397864	−	0.689121i
$366$	6131.34	+	5550.78i	0.875656	+	0.792744i
$367$	−2204.25	−	3817.87i	−0.313518	−	0.543028i	0.665604	−	0.746305i	$-0.268174\pi$
$367$	−2204.25	−	3817.87i	−0.313518	−	0.543028i	−0.979121	+	0.203277i	$0.934841\pi$
$368$	−17.6001			−0.00249312
$369$	4663.70	−	3349.98i	0.657948	−	0.472610i
$370$	−18631.8			−2.61789
$371$	195.660	+	338.893i	0.0273804	+	0.0474243i
$372$	1957.77	−	630.267i	0.272864	−	0.0878436i
$373$	−2302.17	+	3987.47i	−0.319575	+	0.553521i	−0.980399	−	0.197020i	$-0.936874\pi$
$373$	−2302.17	+	3987.47i	−0.319575	+	0.553521i	0.660824	+	0.750541i	$0.270207\pi$
$374$	10157.6	−	17593.4i	1.40437	−	2.43244i
$375$	4146.00	−	19249.2i	0.570930	−	2.65073i
$376$	2423.15	+	4197.01i	0.332352	+	0.575650i
$377$	−2117.71			−0.289304
$378$	1789.61	+	4108.96i	0.243513	+	0.559106i
$379$	14679.5			1.98954			0.994770	−	0.102143i	$-0.0325700\pi$
$379$	14679.5			1.98954			0.994770	+	0.102143i	$0.0325700\pi$
$380$	−4154.11	−	7195.13i	−0.560793	−	0.971321i
$381$	−2611.98	+	12127.0i	−0.351223	+	1.63067i
$382$	8769.10	−	15188.5i	1.17452	−	2.03433i
$383$	−911.873	+	1579.41i	−0.121657	+	0.210716i	−0.920421	−	0.390928i	$-0.872154\pi$
$383$	−911.873	+	1579.41i	−0.121657	+	0.210716i	0.798764	+	0.601644i	$0.205487\pi$
$384$	11406.7	−	3672.18i	1.51588	−	0.488009i
$385$	3303.58	+	5721.97i	0.437314	+	0.757451i
$386$	−15817.8			−2.08577
$387$	634.108	+	6364.16i	0.0832908	+	0.835939i
$388$	−3733.71			−0.488532
$389$	−4306.80	−	7459.59i	−0.561345	−	0.972278i	−0.997379	−	0.0723480i	$-0.976951\pi$
$389$	−4306.80	−	7459.59i	−0.561345	−	0.972278i	0.436035	−	0.899930i	$-0.356383\pi$
$390$	10710.4	+	9696.27i	1.39062	+	1.25895i
$391$	411.437	−	712.629i	0.0532155	−	0.0921719i
$392$	−539.612	+	934.636i	−0.0695269	+	0.120424i
$393$	8166.36	+	7393.12i	1.04819	+	0.948941i
$394$	8424.34	+	14591.4i	1.07719	+	1.86575i
$395$	−5611.32			−0.714775
$396$	−14327.9	−	6472.29i	−1.81819	−	0.821325i
$397$	−5497.04			−0.694933			−0.347467	−	0.937692i	$-0.612958\pi$
$397$	−5497.04			−0.694933			−0.347467	+	0.937692i	$0.612958\pi$
$398$	1099.33	+	1904.09i	0.138453	+	0.239808i
$399$	1078.70	−	347.267i	0.135344	−	0.0435716i
$400$	322.208	−	558.081i	0.0402760	−	0.0697602i
$401$	4310.52	−	7466.04i	0.536801	−	0.929767i	−0.462273	−	0.886738i	$-0.652966\pi$
$401$	4310.52	−	7466.04i	0.536801	−	0.929767i	0.999074	−	0.0430288i	$-0.0137007\pi$
$402$	1050.99	−	4879.56i	0.130394	−	0.605398i
$403$	452.161	+	783.165i	0.0558902	+	0.0968046i
$404$	−18631.6			−2.29445
$405$	−14858.6	+	2990.64i	−1.82304	+	0.366929i
$406$	2308.55			0.282196
$407$	4457.44	+	7720.51i	0.542867	+	0.940274i
$408$	−2362.87	+	10970.4i	−0.286714	+	1.33117i
$409$	−4699.45	+	8139.69i	−0.568149	+	0.984063i	0.428600	+	0.903494i	$0.359007\pi$
$409$	−4699.45	+	8139.69i	−0.568149	+	0.984063i	−0.996749	+	0.0805684i	$0.974326\pi$
$410$	−10089.3	+	17475.3i	−1.21531	+	2.10498i
$411$	325.960	−	104.937i	0.0391202	−	0.0125940i
$412$	360.854	+	625.018i	0.0431505	+	0.0747389i
$413$	4582.57			0.545989
$414$	−942.338	−	425.680i	−0.111868	−	0.0505338i
$415$	13000.0			1.53769
$416$	2721.94	+	4714.53i	0.320803	+	0.555646i
$417$	−7562.71	−	6846.63i	−0.888124	−	0.804031i
$418$	−3227.38	+	5589.99i	−0.377647	+	0.654104i
$419$	297.363	−	515.048i	0.0346710	−	0.0600519i	−0.848169	−	0.529725i	$-0.822295\pi$
$419$	297.363	−	515.048i	0.0346710	−	0.0600519i	0.882840	+	0.469673i	$0.155628\pi$
$420$	−7190.64	−	6509.79i	−0.835398	−	0.756298i
$421$	−1558.89	−	2700.07i	−0.180464	−	0.312574i	0.761574	−	0.648078i	$-0.224427\pi$
$421$	−1558.89	−	2700.07i	−0.180464	−	0.312574i	−0.942039	+	0.335504i	$0.891093\pi$
$422$	5247.13			0.605276
$423$	−589.027	−	5911.70i	−0.0677056	−	0.679520i
$424$	1231.26			0.141026
$425$	15064.5	+	26092.5i	1.71938	+	2.97805i
$426$	12375.2	−	3983.98i	1.40747	−	0.453109i
$427$	1220.74	−	2114.38i	0.138351	−	0.239630i
$428$	1924.73	−	3333.73i	0.217373	−	0.376500i
$429$	1455.54	−	6757.82i	0.163809	−	0.760538i
$430$	−11237.6	−	19464.1i	−1.26029	−	2.18288i
$431$	−8465.93			−0.946148			−0.473074	−	0.881023i	$-0.656856\pi$
$431$	−8465.93			−0.946148			−0.473074	+	0.881023i	$0.656856\pi$
$432$	−292.367	−	33.1300i	−0.0325614	−	0.00368974i
$433$	5368.98			0.595881			0.297941	−	0.954584i	$-0.403700\pi$
$433$	5368.98			0.595881			0.297941	+	0.954584i	$0.403700\pi$
$434$	−492.909	−	853.743i	−0.0545170	−	0.0944262i
$435$	−1643.85	+	7632.14i	−0.181188	+	0.841225i
$436$	6008.50	−	10407.0i	0.659988	−	1.14313i
$437$	−130.727	+	226.425i	−0.0143101	+	0.0247858i
$438$	6024.24	−	1939.40i	0.657191	−	0.211571i
$439$	8896.36	+	15408.9i	0.967198	+	1.67524i	0.703589	+	0.710607i	$0.251580\pi$
$439$	8896.36	+	15408.9i	0.967198	+	1.67524i	0.263609	+	0.964630i	$0.415087\pi$
$440$	20788.9			2.25244
$441$	1074.52	−	771.838i	0.116026	−	0.0833428i
$442$	−13113.2			−1.41115
$443$	−4431.80	−	7676.10i	−0.475307	−	0.823256i	0.524293	−	0.851538i	$-0.324330\pi$
$443$	−4431.80	−	7676.10i	−0.475307	−	0.823256i	−0.999600	+	0.0282821i	$0.990996\pi$
$444$	−9702.15	−	8783.49i	−1.03703	−	0.938842i
$445$	−16691.4	+	28910.3i	−1.77808	+	3.07973i
$446$	4599.99	−	7967.41i	0.488376	−	0.845892i
$447$	−10145.7	−	9185.01i	−1.07354	−	0.971893i
$448$	−2908.51	−	5037.68i	−0.306728	−	0.531268i
$449$	114.115			0.0119943			0.00599714	−	0.999982i	$-0.498091\pi$
$449$	114.115			0.0119943			0.00599714	+	0.999982i	$0.498091\pi$
$450$	30749.5	−	22087.6i	3.22121	−	2.31382i
$451$	9655.04			1.00807
$452$	−8943.71	−	15491.0i	−0.930701	−	1.61202i
$453$	3647.66	−	1174.30i	0.378327	−	0.121795i
$454$	−6941.66	+	12023.3i	−0.717595	+	1.24291i
$455$	2132.42	−	3693.46i	0.219713	−	0.380554i
$456$	750.758	−	3485.65i	0.0770997	−	0.357961i
$457$	−4031.28	−	6982.39i	−0.412638	−	0.714710i	0.582540	−	0.812802i	$-0.302059\pi$
$457$	−4031.28	−	6982.39i	−0.412638	−	0.714710i	−0.995177	+	0.0980929i	$0.968726\pi$
$458$	18625.5			1.90025
$459$	8176.10	−	11063.5i	0.831433	−	1.12505i
$460$	2237.87			0.226829
$461$	−2064.94	−	3576.57i	−0.208620	−	0.361340i	0.742660	−	0.669668i	$-0.233564\pi$
$461$	−2064.94	−	3576.57i	−0.208620	−	0.361340i	−0.951280	+	0.308329i	$0.900230\pi$
$462$	−1586.71	+	7366.83i	−0.159784	+	0.741852i
$463$	−5909.24	+	10235.1i	−0.593144	+	1.02736i	0.400662	+	0.916226i	$0.368780\pi$
$463$	−5909.24	+	10235.1i	−0.593144	+	1.02736i	−0.993806	+	0.111130i	$0.964553\pi$
$464$	−75.7810	+	131.256i	−0.00758199	+	0.0131324i
$465$	3173.48	−	1021.64i	0.316488	−	0.101887i
$466$	−6086.83	−	10542.7i	−0.605079	−	1.04803i
$467$	1590.26			0.157577			0.0787884	−	0.996891i	$-0.474895\pi$
$467$	1590.26			0.157577			0.0787884	+	0.996891i	$0.474895\pi$
$468$	1006.17	+	10098.3i	0.0993807	+	0.997424i
$469$	−1473.46			−0.145070
$470$	10438.7	+	18080.3i	1.02447	+	1.77443i
$471$	9039.76	+	8183.82i	0.884353	+	0.800617i
$472$	7209.35	−	12487.0i	0.703045	−	1.21771i
$473$	−5376.93	+	9313.11i	−0.522688	+	0.905322i
$474$	−4744.50	−	4295.26i	−0.459751	−	0.416219i
$475$	−4786.48	−	8290.42i	−0.462355	−	0.800822i
$476$	8803.79			0.847734
$477$	−1375.54	−	621.369i	−0.132037	−	0.0596447i
$478$	−27256.6			−2.60813
$479$	−6567.28	−	11374.9i	−0.626444	−	1.08503i	−0.988260	−	0.152783i	$-0.951177\pi$
$479$	−6567.28	−	11374.9i	−0.626444	−	1.08503i	0.361816	−	0.932249i	$-0.382157\pi$
$480$	19103.8	−	6150.13i	1.81660	−	0.584821i
$481$	2877.22	−	4983.50i	0.272744	−	0.472407i
$482$	6026.80	−	10438.7i	0.569529	−	0.986453i
$483$	−64.2703	+	298.397i	−0.00605466	+	0.0281108i
$484$	−4681.76	−	8109.04i	−0.439684	−	0.761555i
$485$	−6052.23			−0.566635
$486$	−14852.6	−	8845.09i	−1.38627	−	0.825559i
$487$	−18337.9			−1.70631			−0.853153	−	0.521661i	$-0.825313\pi$
$487$	−18337.9			−1.70631			−0.853153	+	0.521661i	$0.825313\pi$
$488$	−3840.97	−	6652.75i	−0.356296	−	0.617122i
$489$	−625.819	+	2905.58i	−0.0578743	+	0.268701i
$490$	−2324.59	+	4026.31i	−0.214315	+	0.371204i
$491$	4048.59	−	7012.36i	0.372119	−	0.644528i	−0.617773	−	0.786357i	$-0.711965\pi$
$491$	4048.59	−	7012.36i	0.372119	−	0.644528i	0.989891	+	0.141828i	$0.0452981\pi$
$492$	−13492.1	+	4343.54i	−1.23632	+	0.398012i
$493$	−3543.06	−	6136.76i	−0.323674	−	0.560620i
$494$	4166.47			0.379471
$495$	−23225.1	−	10491.4i	−2.10887	−	0.952632i
$496$	64.7212			0.00585901
$497$	−1918.88	−	3323.60i	−0.173186	−	0.299968i
$498$	10991.8	+	9950.99i	0.989061	+	0.895411i
$499$	301.177	−	521.655i	0.0270191	−	0.0467985i	−0.852200	−	0.523217i	$-0.824732\pi$
$499$	301.177	−	521.655i	0.0270191	−	0.0467985i	0.879219	+	0.476418i	$0.158065\pi$
$500$	−24302.3	+	42092.9i	−2.17367	+	3.76490i
$501$	2094.65	+	1896.32i	0.186790	+	0.169104i
$502$	15975.2	+	27669.8i	1.42033	+	2.46009i
$503$	11416.3			1.01198			0.505992	−	0.862538i	$-0.331126\pi$
$503$	11416.3			1.01198			0.505992	+	0.862538i	$0.331126\pi$
$504$	−412.719	−	4142.21i	−0.0364761	−	0.366089i
$505$	−30201.3			−2.66126
$506$	−869.317	−	1505.70i	−0.0763752	−	0.132286i
$507$	6619.26	−	2130.95i	0.579826	−	0.186664i
$508$	15310.5	−	26518.5i	1.33719	−	2.31608i
$509$	−6406.07	+	11095.6i	−0.557847	+	0.966220i	0.439829	+	0.898082i	$0.355039\pi$
$509$	−6406.07	+	11095.6i	−0.557847	+	0.966220i	−0.997676	+	0.0681380i	$0.978294\pi$
$510$	−10179.0	+	47259.3i	−0.883789	+	4.10329i
$511$	−934.108	−	1617.92i	−0.0808659	−	0.140064i
$512$	759.150			0.0655273
$513$	−2597.81	+	3515.23i	−0.223579	+	0.302536i
$514$	26412.7			2.26656
$515$	584.935	+	1013.14i	0.0500491	+	0.0866876i
$516$	3324.09	−	15433.2i	0.283595	−	1.31669i
$517$	4994.66	−	8651.00i	0.424884	−	0.735920i
$518$	−3136.51	+	5432.60i	−0.266043	+	0.460801i
$519$	−10062.7	+	3239.51i	−0.851068	+	0.273986i
$520$	−6709.51	−	11621.2i	−0.565830	−	0.980046i
$521$	3033.32			0.255071			0.127536	−	0.991834i	$-0.459293\pi$
$521$	3033.32			0.255071			0.127536	+	0.991834i	$0.459293\pi$
$522$	−7232.04	+	5194.84i	−0.606394	+	0.435578i
$523$	12789.3			1.06928			0.534642	−	0.845078i	$-0.320446\pi$
$523$	12789.3			1.06928			0.534642	+	0.845078i	$0.320446\pi$
$524$	−13595.8	−	23548.6i	−1.13346	−	1.96321i
$525$	−8285.25	−	7500.76i	−0.688758	−	0.623543i
$526$	17082.9	−	29588.5i	1.41607	−	2.45270i
$527$	−1512.99	+	2620.57i	−0.125060	+	0.216611i
$528$	−366.767	−	332.039i	−0.0302301	−	0.0273677i
$529$	6048.29	+	10475.9i	0.497106	+	0.861013i
$530$	5304.13			0.434711
$531$	−14355.9	+	10312.0i	−1.17324	+	0.842751i
$532$	−2797.25			−0.227962
$533$	−3116.11	−	5397.25i	−0.253234	−	0.438614i
$534$	−36242.7	+	11667.7i	−2.93703	+	0.945523i
$535$	3119.94	−	5403.89i	0.252124	−	0.436692i
$536$	−2318.06	+	4015.01i	−0.186801	+	0.323548i
$537$	−1018.83	+	4730.28i	−0.0818731	+	0.380124i
$538$	7414.49	+	12842.3i	0.594166	+	1.02913i
$539$	2224.53			0.177768
$540$	37174.9	+	4212.52i	2.96251	+	0.335700i
$541$	3836.05			0.304851			0.152426	−	0.988315i	$-0.451292\pi$
$541$	3836.05			0.304851			0.152426	+	0.988315i	$0.451292\pi$
$542$	9004.66	+	15596.5i	0.713622	+	1.23603i
$543$	1097.08	−	5093.58i	0.0867041	−	0.402553i
$544$	−9107.93	+	15775.4i	−0.717830	+	1.24332i
$545$	9739.60	−	16869.5i	0.765502	−	1.32589i
$546$	4630.22	−	1490.62i	0.362922	−	0.116836i
$547$	−2438.27	−	4223.20i	−0.190590	−	0.330112i	0.754856	−	0.655891i	$-0.227707\pi$
$547$	−2438.27	−	4223.20i	−0.190590	−	0.330112i	−0.945446	+	0.325779i	$0.894373\pi$
$548$	−845.271			−0.0658908
$549$	933.676	+	9370.73i	0.0725834	+	0.728476i
$550$	63659.1			4.93533
$551$	1125.74	+	1949.84i	0.0870386	+	0.150755i
$552$	711.986	+	644.571i	0.0548988	+	0.0497006i
$553$	−944.622	+	1636.13i	−0.0726391	+	0.125815i
$554$	−10620.1	+	18394.5i	−0.814445	+	1.41066i
$555$	−15726.9	−	14237.8i	−1.20283	−	1.08894i
$556$	12590.8	+	21807.9i	0.960374	+	1.66342i
$557$	26004.6			1.97819			0.989095	−	0.147276i	$-0.0470506\pi$
$557$	26004.6			1.97819			0.989095	+	0.147276i	$0.0470506\pi$
$558$	3465.28	+	1565.36i	0.262898	+	0.118758i
$559$	6941.48			0.525212
$560$	−152.615	−	264.337i	−0.0115163	−	0.0199469i
$561$	22018.2	−	7088.36i	1.65706	−	0.533460i
$562$	−14710.4	+	25479.2i	−1.10413	+	1.91241i
$563$	−7675.11	+	13293.7i	−0.574542	+	0.995137i	0.421549	+	0.906806i	$0.361487\pi$
$563$	−7675.11	+	13293.7i	−0.574542	+	0.995137i	−0.996091	+	0.0883309i	$0.971847\pi$
$564$	−3087.77	+	14336.0i	−0.230529	+	1.07031i
$565$	−14497.5	−	25110.4i	−1.07949	−	1.86974i
$566$	−16604.4			−1.23310
$567$	−1629.33	+	4835.90i	−0.120680	+	0.358181i
$568$	−12075.2			−0.892017
$569$	10436.7	+	18077.0i	0.768947	+	1.33186i	0.938134	+	0.346272i	$0.112552\pi$
$569$	10436.7	+	18077.0i	0.768947	+	1.33186i	−0.169187	+	0.985584i	$0.554114\pi$
$570$	3234.18	−	15015.8i	0.237658	−	1.10341i
$571$	3.53471	−	6.12229i	0.000259059	−	0.000448704i	−0.865896	−	0.500224i	$-0.833251\pi$
$571$	3.53471	−	6.12229i	0.000259059	−	0.000448704i	0.866155	+	0.499776i	$0.166584\pi$
$572$	−8531.82	+	14777.5i	−0.623660	+	1.08021i
$573$	19008.5	−	6119.44i	1.38585	−	0.446149i
$574$	3396.92	+	5883.64i	0.247012	+	0.427837i
$575$	2578.54			0.187013
$576$	20447.6	+	9236.73i	1.47914	+	0.668166i
$577$	−13121.5			−0.946715			−0.473357	−	0.880870i	$-0.656958\pi$
$577$	−13121.5			−0.946715			−0.473357	+	0.880870i	$0.656958\pi$
$578$	−10728.7	−	18582.7i	−0.772068	−	1.33726i
$579$	−13351.7	−	12087.5i	−0.958337	−	0.867596i
$580$	9635.65	−	16689.4i	0.689825	−	1.19481i
$581$	2188.44	−	3790.49i	0.156268	−	0.270664i
$582$	−5117.30	−	4632.76i	−0.364466	−	0.329956i
$583$	−1268.95	−	2197.89i	−0.0901452	−	0.156136i
$584$	−5878.20			−0.416510
$585$	1630.97	+	16369.1i	0.115269	+	1.15688i
$586$	28875.9			2.03558
$587$	1918.15	+	3322.34i	0.134873	+	0.233607i	0.925549	−	0.378628i	$-0.123604\pi$
$587$	1918.15	+	3322.34i	0.134873	+	0.233607i	−0.790676	+	0.612235i	$0.790271\pi$
$588$	−3108.59	+	1000.75i	−0.218021	+	0.0701878i
$589$	480.724	−	832.638i	0.0336297	−	0.0582483i
$590$	31057.1	−	53792.5i	2.16712	−	3.75357i
$591$	−4039.35	+	18754.1i	−0.281145	+	1.30531i
$592$	−205.919	−	356.663i	−0.0142960	−	0.0247614i
$593$	2999.00			0.207680			0.103840	−	0.994594i	$-0.466887\pi$
$593$	2999.00			0.207680			0.103840	+	0.994594i	$0.466887\pi$
$594$	−11606.5	−	26648.7i	−0.801721	−	1.84075i
$595$	14270.7			0.983263
$596$	16891.0	+	29256.1i	1.16088	+	2.01070i
$597$	−527.112	+	2447.30i	−0.0361361	+	0.167774i
$598$	−561.134	+	971.913i	−0.0383720	+	0.0664623i
$599$	−4181.01	+	7241.73i	−0.285195	+	0.493972i	−0.972656	−	0.232249i	$-0.925392\pi$
$599$	−4181.01	+	7241.73i	−0.285195	+	0.493972i	0.687462	+	0.726221i	$0.258725\pi$
$600$	−33473.2	+	10776.1i	−2.27756	+	0.733219i
$601$	7265.07	+	12583.5i	0.493092	+	0.854061i	0.999968	−	0.00795794i	$-0.00253312\pi$
$601$	7265.07	+	12583.5i	0.493092	+	0.854061i	−0.506876	+	0.862019i	$0.669200\pi$
$602$	−7567.04			−0.512308
$603$	4615.92	−	3315.66i	0.311733	−	0.223921i
$604$	−9459.02			−0.637222
$605$	−7588.99	−	13144.5i	−0.509977	−	0.883307i
$606$	−25535.9	−	23118.0i	−1.71175	−	1.54968i
$607$	6504.64	−	11266.4i	0.434951	−	0.753357i	−0.562341	−	0.826906i	$-0.690099\pi$
$607$	6504.64	−	11266.4i	0.434951	−	0.753357i	0.997292	+	0.0735487i	$0.0234324\pi$
$608$	2893.88	−	5012.35i	0.193030	−	0.334338i
$609$	1948.63	+	1764.12i	0.129659	+	0.117382i
$610$	−16546.5	−	28659.3i	−1.09827	−	1.90227i
$611$	−6447.98			−0.426935
$612$	−27579.8	+	19810.8i	−1.82164	+	1.30850i
$613$	3740.67			0.246467			0.123233	−	0.992378i	$-0.460674\pi$
$613$	3740.67			0.246467			0.123233	+	0.992378i	$0.460674\pi$
$614$	−6190.03	−	10721.5i	−0.406856	−	0.704695i
$615$	−21870.3	+	7040.75i	−1.43398	+	0.461643i
$616$	3499.66	−	6061.58i	0.228905	−	0.396474i
$617$	−11342.8	+	19646.3i	−0.740104	+	1.28190i	0.212344	+	0.977195i	$0.431890\pi$
$617$	−11342.8	+	19646.3i	−0.740104	+	1.28190i	−0.952448	+	0.304703i	$0.901443\pi$
$618$	−280.944	+	1304.38i	−0.0182867	+	0.0849024i
$619$	594.523	+	1029.74i	0.0386040	+	0.0668641i	0.884682	−	0.466195i	$-0.154376\pi$
$619$	594.523	+	1029.74i	0.0386040	+	0.0668641i	−0.846078	+	0.533059i	$0.821042\pi$
$620$	−8229.39			−0.533065
$621$	−470.128	−	1079.42i	−0.0303794	−	0.0697512i
$622$	13901.0			0.896107
$623$	5619.72	+	9733.64i	0.361395	+	0.625955i
$624$	−67.2412	+	312.190i	−0.00431378	+	0.0200282i
$625$	−20189.3	+	34968.9i	−1.29212	+	2.23801i
$626$	−9995.45	+	17312.6i	−0.638176	+	1.10535i
$627$	−6995.89	+	2252.20i	−0.445596	+	0.143452i
$628$	−15049.8	−	26067.1i	−0.956296	−	1.65635i
$629$	19255.1			1.22059
$630$	−1777.95	−	17844.2i	−0.112437	−	1.12846i
$631$	23574.4			1.48729			0.743646	−	0.668574i	$-0.233095\pi$
$631$	23574.4			1.48729			0.743646	+	0.668574i	$0.233095\pi$
$632$	2972.18	+	5147.97i	0.187068	+	0.324012i
$633$	4429.05	+	4009.69i	0.278103	+	0.251770i
$634$	−15758.6	+	27294.7i	−0.987152	+	1.70980i
$635$	24817.8	−	42985.8i	1.55097	−	2.68636i
$636$	2762.03	+	2500.50i	0.172204	+	0.155898i
$637$	−717.953	−	1243.53i	−0.0446567	−	0.0773477i
$638$	−14972.1			−0.929079
$639$	13490.3	+	6093.91i	0.835159	+	0.377264i
$640$	−47947.7			−2.96140
$641$	6996.33	+	12118.0i	0.431105	+	0.746696i	0.996969	−	0.0778026i	$-0.0247904\pi$
$641$	6996.33	+	12118.0i	0.431105	+	0.746696i	−0.565863	+	0.824499i	$0.691457\pi$
$642$	6774.45	−	2180.91i	0.416459	−	0.134071i
$643$	−5948.33	+	10302.8i	−0.364820	+	0.631886i	−0.988747	−	0.149596i	$-0.952203\pi$
$643$	−5948.33	+	10302.8i	−0.364820	+	0.631886i	0.623927	+	0.781482i	$0.285536\pi$
$644$	376.729	−	652.513i	0.0230515	−	0.0399264i
$645$	5388.26	−	25016.8i	0.328934	−	1.52719i
$646$	6970.77	+	12073.7i	0.424553	+	0.735347i
$647$	−5011.63			−0.304525			−0.152262	−	0.988340i	$-0.548656\pi$
$647$	−5011.63			−0.304525			−0.152262	+	0.988340i	$0.548656\pi$
$648$	10614.0	+	12047.6i	0.643451	+	0.730364i
$649$	−29720.3			−1.79757
$650$	−20545.6	−	35586.0i	−1.23979	−	2.14738i
$651$	236.343	−	1097.30i	0.0142289	−	0.0660624i
$652$	3668.32	−	6353.72i	0.220341	−	0.381642i
$653$	6238.61	−	10805.6i	0.373868	−	0.647558i	−0.616289	−	0.787520i	$-0.711365\pi$
$653$	6238.61	−	10805.6i	0.373868	−	0.647558i	0.990157	+	0.139962i	$0.0446981\pi$
$654$	21148.0	−	6808.22i	1.26445	−	0.407068i
$655$	−22038.3	−	38171.5i	−1.31467	−	2.27708i
$656$	−446.032			−0.0265467
$657$	6567.03	+	2966.50i	0.389961	+	0.176156i
$658$	7029.06			0.416446
$659$	−14463.6	−	25051.6i	−0.854962	−	1.48084i	−0.876680	−	0.481073i	$-0.840247\pi$
$659$	−14463.6	−	25051.6i	−0.854962	−	1.48084i	0.0217183	−	0.999764i	$-0.493086\pi$
$660$	46634.9	+	42219.3i	2.75040	+	2.48997i
$661$	12339.9	−	21373.3i	0.726121	−	1.25768i	−0.232389	−	0.972623i	$-0.574654\pi$
$661$	12339.9	−	21373.3i	0.726121	−	1.25768i	0.958511	−	0.285056i	$-0.0920123\pi$
$662$	−13011.9	+	22537.3i	−0.763933	+	1.32317i
$663$	−11068.7	−	10020.7i	−0.648375	−	0.586983i
$664$	−6885.77	−	11926.5i	−0.402439	−	0.697045i
$665$	−4534.26			−0.264407
$666$	−2398.94	−	24076.7i	−0.139575	−	1.40083i
$667$	−606.453			−0.0352053
$668$	−3487.28	−	6040.14i	−0.201986	−	0.349850i
$669$	9971.24	−	3210.06i	0.576249	−	0.185513i
$670$	−9985.98	+	17296.2i	−0.575809	+	0.997330i
$671$	−7917.11	+	13712.8i	−0.455494	+	0.788939i
$672$	1422.74	−	6605.58i	0.0816720	−	0.379190i
$673$	537.810	+	931.515i	0.0308040	+	0.0533540i	0.881016	−	0.473086i	$-0.156860\pi$
$673$	537.810	+	931.515i	0.0308040	+	0.0533540i	−0.850212	+	0.526440i	$0.823527\pi$
$674$	5611.44			0.320689
$675$	42833.9	+	4853.78i	2.44249	+	0.276774i
$676$	−17164.9			−0.976610
$677$	−11518.6	−	19950.8i	−0.653908	−	1.13260i	−0.982166	−	0.188013i	$-0.939795\pi$
$677$	−11518.6	−	19950.8i	−0.653908	−	1.13260i	0.328259	−	0.944588i	$-0.393538\pi$
$678$	6963.14	−	32328.7i	0.394421	−	1.83123i
$679$	−1018.85	+	1764.69i	−0.0575843	+	0.0997389i
$680$	22450.8	−	38886.0i	1.26610	−	2.19296i
$681$	−15047.2	+	4844.17i	−0.846711	+	0.272583i
$682$	3196.76	+	5536.95i	0.179487	+	0.310881i
$683$	−1233.44			−0.0691015			−0.0345508	−	0.999403i	$-0.511000\pi$
$683$	−1233.44			−0.0691015			−0.0345508	+	0.999403i	$0.511000\pi$
$684$	8762.97	−	6294.52i	0.489855	−	0.351867i
$685$	−1370.16			−0.0764249
$686$	782.654	+	1355.60i	0.0435596	+	0.0754474i
$687$	15721.6	+	14233.0i	0.873097	+	0.790427i
$688$	248.397	−	430.236i	0.0137646	−	0.0238410i
$689$	−819.093	+	1418.71i	−0.0452902	+	0.0784450i
$690$	3067.16	+	2776.74i	0.169224	+	0.153201i
$691$	15214.0	+	26351.4i	0.837578	+	1.45073i	0.891914	+	0.452205i	$0.149363\pi$
$691$	15214.0	+	26351.4i	0.837578	+	1.45073i	−0.0543356	+	0.998523i	$0.517304\pi$
$692$	26094.4			1.43347
$693$	−6968.81	+	5005.76i	−0.381996	+	0.274391i
$694$	20013.5			1.09467
$695$	20409.3	+	35349.9i	1.11391	+	1.92935i
$696$	7872.63	−	2534.45i	0.428752	−	0.138029i
$697$	10426.9	−	18059.9i	0.566637	−	0.981444i
$698$	−6662.90	+	11540.5i	−0.361310	+	0.625808i
$699$	2918.55	−	13550.3i	0.157925	−	0.733220i
$700$	13793.7	+	23891.4i	0.744790	+	1.29001i
$701$	359.627			0.0193765			0.00968825	−	0.999953i	$-0.496916\pi$
$701$	359.627			0.0193765			0.00968825	+	0.999953i	$0.496916\pi$
$702$	−11150.9	+	15088.9i	−0.599521	+	0.811242i
$703$	−6117.96			−0.328226
$704$	18863.1	+	32671.9i	1.00985	+	1.74910i
$705$	−5005.19	+	23238.3i	−0.267385	+	1.24142i
$706$	−25400.7	+	43995.3i	−1.35406	+	2.34530i
$707$	−5084.15	+	8806.00i	−0.270451	+	0.468435i
$708$	41531.6	−	13370.3i	2.20460	−	0.709729i
$709$	−16634.0	−	28810.9i	−0.881103	−	1.52611i	−0.850116	−	0.526595i	$-0.823469\pi$
$709$	−16634.0	−	28810.9i	−0.881103	−	1.52611i	−0.0309861	−	0.999520i	$-0.509865\pi$
$710$	−52018.8			−2.74962
$711$	−722.489	−	7251.18i	−0.0381089	−	0.382476i
$712$	35364.1			1.86141
$713$	129.486	+	224.277i	0.00680126	+	0.0117801i
$714$	12066.2	+	10923.7i	0.632445	+	0.572562i
$715$	−13829.8	+	23954.0i	−0.723366	+	1.25291i
$716$	5972.02	−	10343.8i	0.311711	−	0.539899i
$717$	−23007.0	−	20828.6i	−1.19834	−	1.08488i
$718$	−17434.7	−	30197.8i	−0.906209	−	1.56960i
$719$	−8882.66			−0.460733			−0.230367	−	0.973104i	$-0.573993\pi$
$719$	−8882.66			−0.460733			−0.230367	+	0.973104i	$0.573993\pi$
$720$	1072.92	+	484.669i	0.0555354	+	0.0250869i
$721$	393.877			0.0203450
$722$	13436.0	+	23271.8i	0.692569	+	1.19956i
$723$	13064.1	−	4205.74i	0.672004	−	0.216339i
$724$	−6430.69	+	11138.3i	−0.330103	+	0.571756i
$725$	11102.5	−	19230.0i	0.568738	−	0.985083i
$726$	3644.99	−	16923.1i	0.186333	−	0.865116i
$727$	8494.42	+	14712.8i	0.433343	+	0.750573i	0.997159	−	0.0753280i	$-0.0240004\pi$
$727$	8494.42	+	14712.8i	0.433343	+	0.750573i	−0.563815	+	0.825901i	$0.690667\pi$
$728$	−4517.97			−0.230010
$729$	−5777.77	−	18815.9i	−0.293541	−	0.955946i
$730$	−25322.7			−1.28388
$731$	11613.5	+	20115.2i	0.587609	+	1.01777i
$732$	4894.47	−	22724.2i	0.247138	−	1.14742i
$733$	10991.9	−	19038.5i	0.553882	−	0.959351i	−0.444108	−	0.895973i	$-0.646479\pi$
$733$	10991.9	−	19038.5i	0.553882	−	0.959351i	0.997990	−	0.0633778i	$-0.0201873\pi$
$734$	−10059.3	+	17423.2i	−0.505851	+	0.876159i
$735$	−5038.94	+	1622.19i	−0.252876	+	0.0814089i
$736$	779.487	+	1350.11i	0.0390384	+	0.0676165i
$737$	9556.12			0.477618
$738$	−23881.3	−	10787.8i	−1.19117	−	0.538083i
$739$	18909.8			0.941284			0.470642	−	0.882324i	$-0.344022\pi$
$739$	18909.8			0.941284			0.470642	+	0.882324i	$0.344022\pi$
$740$	26182.9	+	45350.2i	1.30068	+	2.25284i
$741$	3516.88	+	3183.88i	0.174353	+	0.157845i
$742$	892.909	−	1546.56i	0.0441775	−	0.0765177i
$743$	5004.66	−	8668.33i	0.247111	−	0.428008i	−0.715612	−	0.698498i	$-0.753852\pi$
$743$	5004.66	−	8668.33i	0.247111	−	0.428008i	0.962723	+	0.270489i	$0.0871855\pi$
$744$	−2618.20	−	2370.30i	−0.129016	−	0.116800i
$745$	27379.8	+	47423.2i	1.34647	+	2.33215i
$746$	21012.2			1.03125
$747$	1673.82	+	16799.1i	0.0819836	+	0.822819i
$748$	−57097.0			−2.79101
$749$	−1050.43	−	1819.40i	−0.0512443	−	0.0887578i
$750$	−85536.6	+	27536.9i	−4.16447	+	1.34068i
$751$	14626.9	−	25334.5i	0.710708	−	1.23098i	−0.253884	−	0.967235i	$-0.581708\pi$
$751$	14626.9	−	25334.5i	0.710708	−	1.23098i	0.964592	−	0.263747i	$-0.0849585\pi$
$752$	−230.737	+	399.649i	−0.0111890	+	0.0193799i
$753$	−7659.87	+	35563.5i	−0.370705	+	1.72113i
$754$	4832.17	+	8369.56i	0.233391	+	0.404246i
$755$	−15332.8			−0.739096
$756$	7486.38	−	10130.2i	0.360155	−	0.487344i
$757$	−20805.2			−0.998912			−0.499456	−	0.866339i	$-0.666467\pi$
$757$	−20805.2			−0.998912			−0.499456	+	0.866339i	$0.666467\pi$
$758$	−33495.5	−	58016.0i	−1.60503	−	2.77999i
$759$	416.825	−	1935.25i	0.0199339	−	0.0925497i
$760$	−7133.35	+	12355.3i	−0.340466	+	0.589704i
$761$	−5062.52	+	8768.54i	−0.241151	+	0.417687i	−0.961043	−	0.276400i	$-0.910858\pi$
$761$	−5062.52	+	8768.54i	−0.241151	+	0.417687i	0.719891	+	0.694087i	$0.244192\pi$
$762$	53888.1	−	17348.3i	2.56189	−	0.824753i
$763$	−3279.17	−	5679.69i	−0.155588	−	0.269487i
$764$	−49292.3			−2.33421
$765$	−44706.0	+	32112.7i	−2.11287	+	1.51770i
$766$	8322.81			0.392579
$767$	9592.04	+	16613.9i	0.451562	+	0.782129i
$768$	−14932.2	−	13518.3i	−0.701587	−	0.635157i
$769$	18632.4	−	32272.3i	0.873735	−	1.51335i	0.0156305	−	0.999878i	$-0.495024\pi$
$769$	18632.4	−	32272.3i	0.873735	−	1.51335i	0.858104	−	0.513475i	$-0.171642\pi$
$770$	15076.2	−	26112.7i	0.705593	−	1.22212i
$771$	22294.7	+	20183.7i	1.04140	+	0.942798i
$772$	22228.6	+	38501.0i	1.03630	+	1.79492i
$773$	16637.3			0.774130			0.387065	−	0.922052i	$-0.373489\pi$
$773$	16637.3			0.774130			0.387065	+	0.922052i	$0.373489\pi$
$774$	23705.4	−	17027.8i	1.10087	−	0.790763i
$775$	−9482.13			−0.439494
$776$	3205.73	+	5552.48i	0.148297	+	0.256859i
$777$	−6798.91	+	2188.79i	−0.313912	+	0.101058i
$778$	−19654.4	+	34042.4i	−0.905713	+	1.56874i
$779$	−3312.95	+	5738.20i	−0.152373	+	0.263918i
$780$	8549.80	−	39695.4i	0.392477	−	1.82221i
$781$	12444.9	+	21555.2i	0.570185	+	0.987589i
$782$	−3755.25			−0.171723
$783$	−10074.2	−	1141.57i	−0.459800	−	0.0521028i
$784$	−102.766			−0.00468140
$785$	−24395.4	−	42254.0i	−1.10918	−	1.92116i
$786$	10585.0	−	49144.4i	0.480349	−	2.23018i
$787$	−6559.92	+	11362.1i	−0.297123	+	0.514633i	−0.975477	−	0.220103i	$-0.929361\pi$
$787$	−6559.92	+	11362.1i	−0.297123	+	0.514633i	0.678353	+	0.734736i	$0.262694\pi$
$788$	23677.2	−	41010.1i	1.07039	−	1.85397i
$789$	37030.1	−	11921.2i	1.67086	−	0.537902i
$790$	12803.9	+	22176.9i	0.576634	+	0.998759i
$791$	−9762.16			−0.438815
$792$	2676.69	+	26864.3i	0.120091	+	1.20528i
$793$	10220.8			0.457694
$794$	12543.1	+	21725.3i	0.560626	+	0.971033i
$795$	4477.16	+	4053.24i	0.199734	+	0.180822i
$796$	3089.74	−	5351.58i	0.137579	−	0.238294i
$797$	191.253	−	331.260i	0.00850004	−	0.0147225i	−0.861744	−	0.507343i	$-0.830628\pi$
$797$	191.253	−	331.260i	0.00850004	−	0.0147225i	0.870244	+	0.492621i	$0.163961\pi$
$798$	−3833.82	−	3470.81i	−0.170070	−	0.153966i
$799$	−10787.9	−	18685.1i	−0.477657	−	0.827325i
$800$	−57080.9			−2.52264
$801$	−39508.2	−	17846.9i	−1.74276	−	0.787252i
$802$	−39342.8			−1.73222
$803$	6058.16	+	10493.0i	0.266236	+	0.461135i
$804$	−13353.9	+	4299.04i	−0.585766	+	0.188576i
$805$	610.666	−	1057.71i	0.0267368	−	0.0463096i
$806$	2063.47	−	3574.04i	0.0901770	−	0.156191i
$807$	−3555.14	+	16506.0i	−0.155077	+	0.719997i
$808$	15996.9	+	27707.4i	0.696496	+	1.20637i
$809$	2590.19			0.112566			0.0562831	−	0.998415i	$-0.482075\pi$
$809$	2590.19			0.112566			0.0562831	+	0.998415i	$0.482075\pi$
$810$	45723.9	+	51900.0i	1.98342	+	2.25133i
$811$	−20167.1			−0.873199			−0.436599	−	0.899656i	$-0.643817\pi$
$811$	−20167.1			−0.873199			−0.436599	+	0.899656i	$0.643817\pi$
$812$	−3244.17	−	5619.07i	−0.140207	−	0.242846i
$813$	−4317.61	+	20046.0i	−0.186255	+	0.864751i
$814$	20341.9	−	35233.1i	0.875899	−	1.51710i
$815$	5946.24	−	10299.2i	0.255568	−	0.442656i
$816$	−1017.17	+	327.460i	−0.0436374	+	0.0140483i
$817$	−3689.99	−	6391.25i	−0.158013	−	0.273686i
$818$	42892.6			1.83338
$819$	5047.41	+	2280.05i	0.215349	+	0.0972788i
$820$	56713.6			2.41527
$821$	−14806.3	−	25645.2i	−0.629407	−	1.09016i	−0.987671	−	0.156544i	$-0.949965\pi$
$821$	−14806.3	−	25645.2i	−0.629407	−	1.09016i	0.358264	−	0.933620i	$-0.383369\pi$
$822$	−1158.50	−	1048.81i	−0.0491573	−	0.0445028i
$823$	−5118.30	+	8865.16i	−0.216784	+	0.375480i	−0.953823	−	0.300370i	$-0.902890\pi$
$823$	−5118.30	+	8865.16i	−0.216784	+	0.375480i	0.737039	+	0.675850i	$0.236223\pi$
$824$	619.652	−	1073.27i	0.0261973	−	0.0453751i
$825$	53734.0	+	48646.2i	2.26761	+	2.05290i
$826$	−10456.5	−	18111.1i	−0.440468	−	0.762913i
$827$	−8733.00			−0.367202			−0.183601	−	0.983001i	$-0.558775\pi$
$827$	−8733.00			−0.367202			−0.183601	+	0.983001i	$0.558775\pi$
$828$	288.139	+	2891.87i	0.0120936	+	0.121376i
$829$	10394.4			0.435481			0.217741	−	0.976007i	$-0.430131\pi$
$829$	10394.4			0.435481			0.217741	+	0.976007i	$0.430131\pi$
$830$	−29663.1	−	51378.1i	−1.24051	−	2.14863i
$831$	−23020.7	+	7411.11i	−0.960987	+	0.309372i
$832$	12175.9	−	21089.3i	0.507361	−	0.878775i
$833$	2402.36	−	4161.01i	0.0999242	−	0.173074i
$834$	−9802.57	+	45511.7i	−0.406997	+	1.88962i
$835$	−5652.77	−	9790.89i	−0.234278	−	0.405782i
$836$	18141.6			0.750525
$837$	1728.81	+	3969.36i	0.0713938	+	0.163920i
$838$	−2714.08			−0.111881
$839$	14344.8	+	24846.0i	0.590272	+	1.02238i	0.994196	+	0.107588i	$0.0343128\pi$
$839$	14344.8	+	24846.0i	0.590272	+	1.02238i	−0.403924	+	0.914793i	$0.632354\pi$
$840$	−3507.03	+	16282.6i	−0.144053	+	0.668813i
$841$	9583.28	−	16598.7i	0.392935	−	0.680583i
$842$	−7114.11	+	12322.0i	−0.291174	+	0.504328i
$843$	−31887.3	+	10265.5i	−1.30280	+	0.419412i
$844$	−7373.71	−	12771.6i	−0.300727	−	0.520874i
$845$	−27823.8			−1.13274
$846$	−22020.0	+	15817.2i	−0.894876	+	0.642797i
$847$	−5110.19			−0.207306
$848$	58.6215	+	101.535i	0.00237391	+	0.00411172i
$849$	−14015.6	−	12688.5i	−0.566566	−	0.512920i
$850$	68748.1	−	119075.i	2.77416	−	4.80499i
$851$	823.957	−	1427.13i	0.0331902	−	0.0574871i
$852$	−27087.9	−	24523.0i	−1.08922	−	0.986085i
$853$	−11064.3	−	19163.9i	−0.444120	−	0.769239i	0.553870	−	0.832603i	$-0.313150\pi$
$853$	−11064.3	−	19163.9i	−0.444120	−	0.769239i	−0.997990	+	0.0633642i	$0.979817\pi$
$854$	−11141.9			−0.446449
$855$	14204.5	−	10203.2i	0.568169	−	0.408121i
$856$	−6610.22			−0.263940
$857$	−2393.76	−	4146.11i	−0.0954132	−	0.165261i	0.814368	−	0.580349i	$-0.197084\pi$
$857$	−2393.76	−	4146.11i	−0.0954132	−	0.165261i	−0.909781	+	0.415089i	$0.863751\pi$
$858$	−30029.3	+	9667.39i	−1.19485	+	0.384661i
$859$	−5787.93	+	10025.0i	−0.229897	+	0.398194i	−0.957777	−	0.287511i	$-0.907172\pi$
$859$	−5787.93	+	10025.0i	−0.229897	+	0.398194i	0.727880	+	0.685704i	$0.240506\pi$
$860$	−31584.0	+	54705.1i	−1.25233	+	2.16910i
$861$	−1628.78	+	7562.15i	−0.0644699	+	0.299323i
$862$	19317.5	+	33458.8i	0.763290	+	1.32206i
$863$	4683.61			0.184741			0.0923707	−	0.995725i	$-0.470556\pi$
$863$	4683.61			0.184741			0.0923707	+	0.995725i	$0.470556\pi$
$864$	10407.2	+	23894.9i	0.409791	+	0.940882i
$865$	42298.2			1.66264
$866$	−12250.9	−	21219.1i	−0.480718	−	0.832628i
$867$	5144.26	−	23884.0i	0.201509	−	0.935574i
$868$	−1385.35	+	2399.50i	−0.0541728	+	0.0938300i
$869$	6126.35	−	10611.2i	0.239151	−	0.414222i
$870$	33914.5	−	10918.1i	1.32162	−	0.425471i
$871$	−3084.18	−	5341.96i	−0.119981	−	0.207813i
$872$	−20635.3			−0.801377
$873$	−779.259	−	7820.95i	−0.0302107	−	0.303206i
$874$	1193.16			0.0461777
$875$	13263.1	+	22972.4i	0.512429	+	0.887554i
$876$	−13186.3	−	11937.8i	−0.508589	−	0.460433i
$877$	11435.6	−	19807.1i	0.440313	−	0.762644i	−0.557400	−	0.830244i	$-0.688201\pi$
$877$	11435.6	−	19807.1i	0.440313	−	0.762644i	0.997712	+	0.0676002i	$0.0215342\pi$
$878$	40599.2	−	70319.9i	1.56054	−	2.70294i
$879$	24373.8	+	22066.0i	0.935278	+	0.846720i
$880$	989.785	+	1714.36i	0.0379155	+	0.0656716i
$881$	−20712.8			−0.792091			−0.396045	−	0.918231i	$-0.629618\pi$
$881$	−20712.8			−0.792091			−0.396045	+	0.918231i	$0.629618\pi$
$882$	−5502.27	−	2485.52i	−0.210058	−	0.0948888i
$883$	−21641.0			−0.824775			−0.412388	−	0.911008i	$-0.635305\pi$
$883$	−21641.0			−0.824775			−0.412388	+	0.911008i	$0.635305\pi$
$884$	18427.7	+	31917.8i	0.701122	+	1.21438i
$885$	67321.5	−	21672.9i	2.55705	−	0.823195i
$886$	−20224.9	+	35030.5i	−0.766893	+	1.32830i
$887$	−13479.5	+	23347.1i	−0.510255	+	0.883787i	0.489675	+	0.871905i	$0.337116\pi$
$887$	−13479.5	+	23347.1i	−0.510255	+	0.883787i	−0.999929	+	0.0118818i	$0.996218\pi$
$888$	−4731.95	+	21969.7i	−0.178822	+	0.830242i
$889$	−8355.78	−	14472.6i	−0.315235	−	0.546003i
$890$	152345.			5.73776
$891$	10567.1	−	31363.2i	0.397317	−	1.17925i
$892$	−25857.1			−0.970585
$893$	3427.65	+	5936.87i	0.128446	+	0.222475i
$894$	−13150.5	+	61055.7i	−0.491967	+	2.28412i
$895$	9680.47	−	16767.1i	0.361545	−	0.626214i
$896$	−8071.62	+	13980.5i	−0.300953	+	0.521266i
$897$	−1216.35	+	391.582i	−0.0452763	+	0.0145759i
$898$	−260.387	−	451.003i	−0.00967620	−	0.0167597i
$899$	2230.12			0.0827351
$900$	−96973.5	−	43805.5i	−3.59161	−	1.62243i
$901$	−5481.58			−0.202683
$902$	−22030.8	−	38158.4i	−0.813242	−	1.40858i
$903$	−6387.26	−	5782.48i	−0.235387	−	0.213100i
$904$	−15358.0	+	26600.8i	−0.565042	+	0.978682i
$905$	−10424.0	+	18054.8i	−0.382878	+	0.663164i
$906$	−12964.2	−	11736.7i	−0.475395	−	0.430381i
$907$	10184.2	+	17639.5i	0.372833	+	0.645765i	0.990000	−	0.141067i	$-0.0450532\pi$
$907$	10184.2	+	17639.5i	0.372833	+	0.645765i	−0.617167	+	0.786832i	$0.711720\pi$
$908$	39020.0			1.42613
$909$	−3888.58	−	39027.3i	−0.141888	−	1.42404i
$910$	−19462.9			−0.709001
$911$	−10750.9	−	18621.1i	−0.390991	−	0.677217i	0.601589	−	0.798806i	$-0.294534\pi$
$911$	−10750.9	−	18621.1i	−0.390991	−	0.677217i	−0.992581	+	0.121589i	$0.961201\pi$
$912$	323.188	−	104.044i	0.0117344	−	0.00377769i
$913$	−14193.1	+	24583.2i	−0.514485	+	0.891113i
$914$	−18397.1	+	31864.7i	−0.665778	+	1.15316i
$915$	7933.80	−	36835.3i	0.286648	−	1.33086i
$916$	−26174.2	−	45335.0i	−0.944125	−	1.63527i
$917$	−14839.9			−0.534414
$918$	−62381.1	−	7068.79i	−2.24279	−	0.254145i
$919$	−2461.02			−0.0883369			−0.0441685	−	0.999024i	$-0.514064\pi$
$919$	−2461.02			−0.0883369			−0.0441685	+	0.999024i	$0.514064\pi$
$920$	−1921.42	−	3327.99i	−0.0688557	−	0.119262i
$921$	2968.03	−	13780.1i	0.106189	−	0.493018i
$922$	−9423.50	+	16322.0i	−0.336601	+	0.583010i
$923$	8033.04	−	13913.6i	0.286469	−	0.496179i
$924$	20160.8	−	6490.40i	0.717794	−	0.231081i
$925$	30168.7	+	52253.7i	1.07237	+	1.85740i
$926$	53934.6			1.91404
$927$	−1233.90	+	886.324i	−0.0437181	+	0.0314031i
$928$	13425.0			0.474889
$929$	−866.047	−	1500.04i	−0.0305857	−	0.0529759i	0.850327	−	0.526254i	$-0.176404\pi$
$929$	−866.047	−	1500.04i	−0.0305857	−	0.0529759i	−0.880913	+	0.473278i	$0.843071\pi$
$930$	−11278.9	−	10211.0i	−0.397689	−	0.360034i
$931$	−763.307	+	1322.09i	−0.0268704	+	0.0465409i
$932$	−17107.4	+	29631.0i	−0.601259	+	1.04141i
$933$	11733.7	+	10622.7i	0.411730	+	0.372745i
$934$	−3628.63	−	6284.97i	−0.127123	−	0.220183i
$935$	−92552.7			−3.23721
$936$	14153.5	−	10166.6i	0.494255	−	0.355027i
$937$	35120.9			1.22449			0.612247	−	0.790667i	$-0.290266\pi$
$937$	35120.9			1.22449			0.612247	+	0.790667i	$0.290266\pi$
$938$	3362.12	+	5823.37i	0.117033	+	0.202708i
$939$	−21666.8	+	6975.23i	−0.753002	+	0.242415i
$940$	29338.6	−	50815.9i	1.01800	−	1.76322i
$941$	6463.99	−	11196.0i	0.223932	−	0.387862i	−0.732066	−	0.681233i	$-0.761444\pi$
$941$	6463.99	−	11196.0i	0.223932	−	0.387862i	0.955999	+	0.293371i	$0.0947773\pi$
$942$	11717.1	−	54400.5i	0.405268	−	1.88160i
$943$	−892.366	−	1545.62i	−0.0308160	−	0.0533748i
$944$	1372.98			0.0473376
$945$	12135.2	−	16420.8i	0.417734	−	0.565257i
$946$	49076.1			1.68668
$947$	1601.47	+	2773.83i	0.0549533	+	0.0951819i	0.892193	−	0.451654i	$-0.149166\pi$
$947$	1601.47	+	2773.83i	0.0549533	+	0.0951819i	−0.837240	+	0.546835i	$0.815832\pi$
$948$	−3787.40	+	17584.3i	−0.129756	+	0.602438i
$949$	3910.47	−	6773.13i	0.133761	−	0.231681i
$950$	−21843.5	+	37834.0i	−0.745995	+	1.29210i
$951$	−34159.4	+	10997.0i	−1.16477	+	0.374976i
$952$	−7558.85	−	13092.3i	−0.257336	−	0.445719i
$953$	−36827.2			−1.25178			−0.625891	−	0.779910i	$-0.715265\pi$
$953$	−36827.2			−1.25178			−0.625891	+	0.779910i	$0.715265\pi$
$954$	682.936	+	6854.21i	0.0231770	+	0.232614i
$955$	−79901.5			−2.70738
$956$	38303.2	+	66343.1i	1.29583	+	2.24444i
$957$	−12637.8	−	11441.2i	−0.426879	−	0.386460i
$958$	−29970.3	+	51910.1i	−1.01075	+	1.75067i
$959$	−230.656	+	399.507i	−0.00776669	+	0.0134523i
$960$	−66553.6	−	60251.9i	−2.23751	−	2.02565i
$961$	14419.3	+	24975.0i	0.484017	+	0.838341i
$962$	−26260.9			−0.880129
$963$	7384.84	+	3335.93i	0.247116	+	0.111629i
$964$	−33877.5			−1.13187
$965$	36031.8	+	62409.0i	1.20197	+	2.08188i
$966$	1325.97	−	426.871i	0.0441639	−	0.0142177i
$967$	−490.524	+	849.612i	−0.0163125	+	0.0282541i	−0.874066	−	0.485806i	$-0.838526\pi$
$967$	−490.524	+	849.612i	−0.0163125	+	0.0282541i	0.857754	+	0.514061i	$0.171859\pi$
$968$	−8039.42	+	13924.7i	−0.266939	+	0.462351i
$969$	−3342.38	+	15518.1i	−0.110808	+	0.514463i
$970$	13809.9	+	23919.5i	0.457124	+	0.791761i
$971$	35299.7			1.16666			0.583328	−	0.812237i	$-0.301750\pi$
$971$	35299.7			1.16666			0.583328	+	0.812237i	$0.301750\pi$
$972$	−657.116	+	48581.3i	−0.0216841	+	1.60313i
$973$	13743.0			0.452805
$974$	41843.3	+	72474.7i	1.37654	+	2.38423i
$975$	9851.32	−	45738.1i	0.323584	−	1.50235i
$976$	365.745	−	633.489i	0.0119951	−	0.0207761i
$977$	19802.8	−	34299.4i	0.648462	−	1.12317i	−0.335029	−	0.942208i	$-0.608746\pi$
$977$	19802.8	−	34299.4i	0.648462	−	1.12317i	0.983490	−	0.180961i	$-0.0579207\pi$
$978$	12911.3	−	4156.57i	0.422146	−	0.135902i
$979$	−36446.7	−	63127.6i	−1.18983	−	2.06084i
$980$	13066.8			0.425924
$981$	23053.5	+	10413.9i	0.750296	+	0.338929i
$982$	−36952.1			−1.20080
$983$	5834.71	+	10106.0i	0.189317	+	0.327906i	0.945023	−	0.327005i	$-0.106039\pi$
$983$	5834.71	+	10106.0i	0.189317	+	0.327906i	−0.755706	+	0.654911i	$0.772706\pi$
$984$	18043.6	+	16335.1i	0.584561	+	0.529211i
$985$	38380.0	−	66476.2i	1.24151	−	2.15036i
$986$	−16169.0	+	28005.6i	−0.522238	+	0.904543i
$987$	5933.17	+	5371.38i	0.191342	+	0.173225i
$988$	−5855.08	−	10141.3i	−0.188537	−	0.326556i
$989$	1987.85			0.0639129
$990$	11530.9	+	115729.i	0.370178	+	3.71525i
$991$	37428.6			1.19976			0.599879	−	0.800091i	$-0.295215\pi$
$991$	37428.6			1.19976			0.599879	+	0.800091i	$0.295215\pi$
$992$	−2866.42	−	4964.79i	−0.0917430	−	0.158904i
$993$	−28205.6	+	9080.26i	−0.901386	+	0.290185i
$994$	−8756.97	+	15167.5i	−0.279431	+	0.483988i
$995$	5008.37	−	8674.76i	0.159574	−	0.276390i
$996$	8774.41	−	40738.2i	0.279144	−	1.29602i
$997$	−5306.23	−	9190.66i	−0.168556	−	0.291947i	0.769357	−	0.638820i	$-0.220577\pi$
$997$	−5306.23	−	9190.66i	−0.168556	−	0.291947i	−0.937912	+	0.346873i	$0.887244\pi$
$998$	−2748.89			−0.0871891
$999$	16373.7	−	22156.1i	0.518560	−	0.701691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.b.22.2	✓	16
3.2	odd	2		189.4.f.b.64.7		16
9.2	odd	6		189.4.f.b.127.7		16
9.4	even	3		567.4.a.i.1.7		8
9.5	odd	6		567.4.a.g.1.2		8
9.7	even	3	inner	63.4.f.b.43.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.2	✓	16	1.1	even	1	trivial
63.4.f.b.43.2	yes	16	9.7	even	3	inner
189.4.f.b.64.7		16	3.2	odd	2
189.4.f.b.127.7		16	9.2	odd	6
567.4.a.g.1.2		8	9.5	odd	6
567.4.a.i.1.7		8	9.4	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28179 - 3.95218i) q^{2} +(1.09409 - 5.07966i) q^{3} +(-6.41313 + 11.1079i) q^{4} +(-10.3955 + 18.0055i) q^{5} +(-22.5722 + 7.26670i) q^{6} +(3.50000 + 6.06218i) q^{7} +22.0250 q^{8} +(-24.6060 - 11.1152i) q^{9} +O(q^{10})\)	\(q+(-2.28179 - 3.95218i) q^{2} +(1.09409 - 5.07966i) q^{3} +(-6.41313 + 11.1079i) q^{4} +(-10.3955 + 18.0055i) q^{5} +(-22.5722 + 7.26670i) q^{6} +(3.50000 + 6.06218i) q^{7} +22.0250 q^{8} +(-24.6060 - 11.1152i) q^{9} +94.8813 q^{10} +(-22.6993 - 39.3163i) q^{11} +(49.4077 + 44.7295i) q^{12} +(-14.6521 + 25.3782i) q^{13} +(15.9725 - 27.6652i) q^{14} +(80.0884 + 72.5052i) q^{15} +(1.04863 + 1.81629i) q^{16} -98.0555 q^{17} +(12.2165 + 122.610i) q^{18} +31.1554 q^{19} +(-133.335 - 230.943i) q^{20} +(34.6231 - 11.1463i) q^{21} +(-103.590 + 179.423i) q^{22} +(-4.19596 + 7.26761i) q^{23} +(24.0972 - 111.879i) q^{24} +(-153.632 - 266.099i) q^{25} +133.732 q^{26} +(-83.3823 + 112.829i) q^{27} -89.7838 q^{28} +(36.1332 + 62.5845i) q^{29} +(103.808 - 481.965i) q^{30} +(15.4299 - 26.7254i) q^{31} +(92.8855 - 160.882i) q^{32} +(-224.548 + 72.2893i) q^{33} +(223.742 + 387.533i) q^{34} -145.537 q^{35} +(281.267 - 202.036i) q^{36} -196.369 q^{37} +(-71.0900 - 123.131i) q^{38} +(112.882 + 102.194i) q^{39} +(-228.961 + 396.571i) q^{40} +(-106.336 + 184.180i) q^{41} +(-123.055 - 111.403i) q^{42} +(-118.438 - 205.141i) q^{43} +582.293 q^{44} +(455.925 - 327.495i) q^{45} +38.2972 q^{46} +(110.018 + 190.557i) q^{47} +(10.3734 - 3.33953i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-701.114 + 1214.36i) q^{50} +(-107.281 + 498.089i) q^{51} +(-187.932 - 325.507i) q^{52} +55.9028 q^{53} +(636.181 + 72.0896i) q^{54} +943.880 q^{55} +(77.0874 + 133.519i) q^{56} +(34.0866 - 158.259i) q^{57} +(164.897 - 285.609i) q^{58} +(327.326 - 566.946i) q^{59} +(-1318.99 + 424.626i) q^{60} +(-174.391 - 302.055i) q^{61} -140.831 q^{62} +(-18.7387 - 188.069i) q^{63} -831.002 q^{64} +(-304.632 - 527.638i) q^{65} +(798.072 + 722.506i) q^{66} +(-105.247 + 182.293i) q^{67} +(628.842 - 1089.19i) q^{68} +(32.3263 + 29.2654i) q^{69} +(332.085 + 575.187i) q^{70} -548.252 q^{71} +(-541.946 - 244.811i) q^{72} -266.888 q^{73} +(448.073 + 776.086i) q^{74} +(-1519.78 + 489.266i) q^{75} +(-199.803 + 346.070i) q^{76} +(158.895 - 275.214i) q^{77} +(146.314 - 679.314i) q^{78} +(134.946 + 233.733i) q^{79} -43.6042 q^{80} +(481.906 + 546.999i) q^{81} +970.550 q^{82} +(-312.634 - 541.499i) q^{83} +(-98.2311 + 456.071i) q^{84} +(1019.34 - 1765.54i) q^{85} +(-540.503 + 936.178i) q^{86} +(357.441 - 115.072i) q^{87} +(-499.951 - 865.941i) q^{88} +1605.63 q^{89} +(-2334.64 - 1054.62i) q^{90} -205.129 q^{91} +(-53.8184 - 93.2162i) q^{92} +(-118.874 - 107.618i) q^{93} +(502.076 - 869.621i) q^{94} +(-323.875 + 560.969i) q^{95} +(-715.603 - 647.846i) q^{96} +(145.549 + 252.099i) q^{97} +223.615 q^{98} +(121.530 + 1219.72i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

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