LMFDB - Embedded newform 87.4.i.a.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,4,Mod(4,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("87.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	87.i (of order $14$, degree $6$, 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:	$5.13316617050$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			67.2
Character	$\chi$	$=$	87.67
Dual form			87.4.i.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22145 - 4.61288i) q^{2} +(2.34549 - 1.87047i) q^{3} +(-11.3559 + 14.2399i) q^{4} +(-10.0741 + 4.85142i) q^{5} +(-13.8386 - 6.66434i) q^{6} +(21.3564 + 26.7801i) q^{7} +(50.9810 + 11.6361i) q^{8} +(2.00269 - 8.77435i) q^{9} +O(q^{10})$	\(q+(-2.22145 - 4.61288i) q^{2} +(2.34549 - 1.87047i) q^{3} +(-11.3559 + 14.2399i) q^{4} +(-10.0741 + 4.85142i) q^{5} +(-13.8386 - 6.66434i) q^{6} +(21.3564 + 26.7801i) q^{7} +(50.9810 + 11.6361i) q^{8} +(2.00269 - 8.77435i) q^{9} +(44.7580 + 35.6933i) q^{10} +(-63.1079 + 14.4040i) q^{11} +54.6404i q^{12} +(6.16044 + 26.9906i) q^{13} +(76.0911 - 158.005i) q^{14} +(-14.5543 + 30.2222i) q^{15} +(-27.1526 - 118.963i) q^{16} +5.34309i q^{17} +(-44.9239 + 10.2536i) q^{18} +(-75.4691 - 60.1846i) q^{19} +(45.3168 - 198.546i) q^{20} +(100.183 + 22.8660i) q^{21} +(206.635 + 259.112i) q^{22} +(134.000 + 64.5312i) q^{23} +(141.341 - 68.0660i) q^{24} +(0.0144936 - 0.0181744i) q^{25} +(110.819 - 88.3756i) q^{26} +(-11.7149 - 24.3262i) q^{27} -623.866 q^{28} +(-56.5979 + 145.553i) q^{29} +171.743 q^{30} +(-19.6457 - 40.7947i) q^{31} +(-161.377 + 128.694i) q^{32} +(-121.077 + 151.826i) q^{33} +(24.6470 - 11.8694i) q^{34} +(-345.067 - 166.176i) q^{35} +(102.203 + 128.159i) q^{36} +(18.9557 + 4.32651i) q^{37} +(-109.974 + 481.826i) q^{38} +(64.9344 + 51.7835i) q^{39} +(-570.038 + 130.107i) q^{40} +109.949i q^{41} +(-117.072 - 512.926i) q^{42} +(-118.670 + 246.421i) q^{43} +(511.538 - 1062.22i) q^{44} +(22.3928 + 98.1094i) q^{45} -761.480i q^{46} +(200.679 - 45.8038i) q^{47} +(-286.204 - 228.240i) q^{48} +(-184.752 + 809.451i) q^{49} +(-0.116033 - 0.0264837i) q^{50} +(9.99409 + 12.5322i) q^{51} +(-454.300 - 218.780i) q^{52} +(-232.380 + 111.908i) q^{53} +(-86.1897 + 108.078i) q^{54} +(565.874 - 451.270i) q^{55} +(777.155 + 1613.78i) q^{56} -289.586 q^{57} +(797.148 - 62.2590i) q^{58} -353.732 q^{59} +(-265.084 - 550.452i) q^{60} +(430.847 - 343.589i) q^{61} +(-144.539 + 181.247i) q^{62} +(277.748 - 133.756i) q^{63} +(72.6311 + 34.9773i) q^{64} +(-193.004 - 242.019i) q^{65} +(969.321 + 221.241i) q^{66} +(86.5961 - 379.402i) q^{67} +(-76.0849 - 60.6757i) q^{68} +(435.001 - 99.2861i) q^{69} +1960.90i q^{70} +(79.2572 + 347.248i) q^{71} +(204.198 - 424.022i) q^{72} +(341.302 - 708.721i) q^{73} +(-22.1513 - 97.0513i) q^{74} -0.0697377i q^{75} +(1714.04 - 391.219i) q^{76} +(-1733.50 - 1382.42i) q^{77} +(94.6226 - 414.569i) q^{78} +(-584.596 - 133.430i) q^{79} +(850.679 + 1066.72i) q^{80} +(-72.9785 - 35.1446i) q^{81} +(507.182 - 244.246i) q^{82} +(211.805 - 265.595i) q^{83} +(-1463.27 + 1166.92i) q^{84} +(-25.9216 - 53.8267i) q^{85} +1400.33 q^{86} +(139.502 + 447.258i) q^{87} -3384.91 q^{88} +(-64.5251 - 133.988i) q^{89} +(402.822 - 321.240i) q^{90} +(-591.246 + 741.399i) q^{91} +(-2440.61 + 1175.34i) q^{92} +(-122.384 - 58.9371i) q^{93} +(-657.086 - 823.959i) q^{94} +(1052.26 + 240.172i) q^{95} +(-137.791 + 603.703i) q^{96} +(-207.741 - 165.668i) q^{97} +(4144.31 - 945.913i) q^{98} +582.578i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9}+O(q^{10}) $ 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9} - 140 q^{11} + 304 q^{13} - 294 q^{15} - 692 q^{16} + 800 q^{20} - 528 q^{22} + 324 q^{23} - 54 q^{24} - 170 q^{25} - 1288 q^{26} - 956 q^{28} - 478 q^{29} + 1056 q^{30} - 616 q^{31} - 406 q^{32} + 72 q^{33} + 34 q^{34} + 1032 q^{35} - 468 q^{36} + 1792 q^{37} + 1912 q^{38} + 2688 q^{40} + 762 q^{42} - 1092 q^{43} + 1750 q^{44} + 630 q^{45} + 2772 q^{47} + 1848 q^{48} - 1304 q^{49} - 882 q^{50} - 192 q^{51} + 1304 q^{52} - 3066 q^{53} - 108 q^{54} - 1974 q^{55} - 4704 q^{56} - 1752 q^{57} - 6092 q^{58} - 640 q^{59} - 7812 q^{60} - 252 q^{61} - 532 q^{62} - 18 q^{63} - 454 q^{64} - 8346 q^{65} + 5628 q^{66} + 744 q^{67} + 5530 q^{68} + 2100 q^{69} + 3216 q^{71} + 2142 q^{72} + 6510 q^{73} + 5090 q^{74} + 6594 q^{76} - 8876 q^{77} - 2118 q^{78} + 7092 q^{80} - 1296 q^{81} - 10590 q^{82} + 572 q^{83} - 2520 q^{85} + 12680 q^{86} - 2238 q^{87} + 6472 q^{88} - 2800 q^{89} + 1576 q^{91} - 10418 q^{92} + 60 q^{93} - 17564 q^{94} + 1374 q^{96} + 11690 q^{97} + 22554 q^{98}+O(q^{100}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9 - 140 * q^11 + 304 * q^13 - 294 * q^15 - 692 * q^16 + 800 * q^20 - 528 * q^22 + 324 * q^23 - 54 * q^24 - 170 * q^25 - 1288 * q^26 - 956 * q^28 - 478 * q^29 + 1056 * q^30 - 616 * q^31 - 406 * q^32 + 72 * q^33 + 34 * q^34 + 1032 * q^35 - 468 * q^36 + 1792 * q^37 + 1912 * q^38 + 2688 * q^40 + 762 * q^42 - 1092 * q^43 + 1750 * q^44 + 630 * q^45 + 2772 * q^47 + 1848 * q^48 - 1304 * q^49 - 882 * q^50 - 192 * q^51 + 1304 * q^52 - 3066 * q^53 - 108 * q^54 - 1974 * q^55 - 4704 * q^56 - 1752 * q^57 - 6092 * q^58 - 640 * q^59 - 7812 * q^60 - 252 * q^61 - 532 * q^62 - 18 * q^63 - 454 * q^64 - 8346 * q^65 + 5628 * q^66 + 744 * q^67 + 5530 * q^68 + 2100 * q^69 + 3216 * q^71 + 2142 * q^72 + 6510 * q^73 + 5090 * q^74 + 6594 * q^76 - 8876 * q^77 - 2118 * q^78 + 7092 * q^80 - 1296 * q^81 - 10590 * q^82 + 572 * q^83 - 2520 * q^85 + 12680 * q^86 - 2238 * q^87 + 6472 * q^88 - 2800 * q^89 + 1576 * q^91 - 10418 * q^92 + 60 * q^93 - 17564 * q^94 + 1374 * q^96 + 11690 * q^97 + 22554 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$1$

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 $

$2$	−2.22145	−	4.61288i	−0.785400	−	1.63090i	−0.775828	−	0.630945i	$-0.782667\pi$
$2$	−2.22145	−	4.61288i	−0.785400	−	1.63090i	−0.00957188	−	0.999954i	$-0.503047\pi$
$3$	2.34549	−	1.87047i	0.451391	−	0.359972i
$3$	2.34549	−	1.87047i	0.451391	−	0.359972i
$4$	−11.3559	+	14.2399i	−1.41949	+	1.77998i
$5$	−10.0741	+	4.85142i	−0.901053	+	0.433924i	−0.826269	−	0.563276i	$-0.809541\pi$
$5$	−10.0741	+	4.85142i	−0.901053	+	0.433924i	−0.0747836	+	0.997200i	$0.523827\pi$
$6$	−13.8386	−	6.66434i	−0.941600	−	0.453451i
$7$	21.3564	+	26.7801i	1.15314	+	1.44599i	0.874126	+	0.485700i	$0.161435\pi$
$7$	21.3564	+	26.7801i	1.15314	+	1.44599i	0.279011	+	0.960288i	$0.409993\pi$
$8$	50.9810	+	11.6361i	2.25306	+	0.514247i
$9$	2.00269	−	8.77435i	0.0741736	−	0.324976i
$10$	44.7580	+	35.6933i	1.41537	+	1.12872i
$11$	−63.1079	+	14.4040i	−1.72980	+	0.394815i	−0.967591	−	0.252521i	$-0.918740\pi$
$11$	−63.1079	+	14.4040i	−1.72980	+	0.394815i	−0.762205	+	0.647336i	$0.775883\pi$
$12$			54.6404i			1.31444i
$13$	6.16044	+	26.9906i	0.131431	+	0.575835i	0.997159	+	0.0753215i	$0.0239983\pi$
$13$	6.16044	+	26.9906i	0.131431	+	0.575835i	−0.865729	+	0.500514i	$0.833145\pi$
$14$	76.0911	−	158.005i	1.45259	−	3.01633i
$15$	−14.5543	+	30.2222i	−0.250526	+	0.520223i
$16$	−27.1526	−	118.963i	−0.424260	−	1.85880i
$17$			5.34309i			0.0762288i	0.999273	+	0.0381144i	$0.0121351\pi$
$17$			5.34309i			0.0762288i	−0.999273	+	0.0381144i	$0.987865\pi$
$18$	−44.9239	+	10.2536i	−0.588259	+	0.134266i
$19$	−75.4691	−	60.1846i	−0.911252	−	0.726699i	0.0510459	−	0.998696i	$-0.483745\pi$
$19$	−75.4691	−	60.1846i	−0.911252	−	0.726699i	−0.962298	+	0.271997i	$0.912316\pi$
$20$	45.3168	−	198.546i	0.506657	−	2.21981i
$21$	100.183	+	22.8660i	1.04103	+	0.237608i
$22$	206.635	+	259.112i	2.00248	+	2.51104i
$23$	134.000	+	64.5312i	1.21483	+	0.585030i	0.927866	−	0.372913i	$-0.121641\pi$
$23$	134.000	+	64.5312i	1.21483	+	0.585030i	0.286960	+	0.957942i	$0.407355\pi$
$24$	141.341	−	68.0660i	1.20213	−	0.578913i
$25$	0.0144936	−	0.0181744i	0.000115949	−	0.000145395i
$26$	110.819	−	88.3756i	0.835903	−	0.666611i
$27$	−11.7149	−	24.3262i	−0.0835010	−	0.173392i
$28$	−623.866			−4.21070
$29$	−56.5979	+	145.553i	−0.362412	+	0.932018i
$29$	−56.5979	+	145.553i	−0.362412	+	0.932018i
$30$	171.743			1.04519
$31$	−19.6457	−	40.7947i	−0.113822	−	0.236353i	0.836274	−	0.548312i	$-0.184729\pi$
$31$	−19.6457	−	40.7947i	−0.113822	−	0.236353i	−0.950096	+	0.311959i	$0.899015\pi$
$32$	−161.377	+	128.694i	−0.891492	+	0.710941i
$33$	−121.077	+	151.826i	−0.638691	+	0.800894i
$34$	24.6470	−	11.8694i	0.124321	−	0.0598701i
$35$	−345.067	−	166.176i	−1.66649	−	0.802537i
$36$	102.203	+	128.159i	0.473163	+	0.593328i
$37$	18.9557	+	4.32651i	0.0842241	+	0.0192236i	0.264425	−	0.964406i	$-0.414818\pi$
$37$	18.9557	+	4.32651i	0.0842241	+	0.0192236i	−0.180201	+	0.983630i	$0.557675\pi$
$38$	−109.974	+	481.826i	−0.469476	+	2.05691i
$39$	64.9344	+	51.7835i	0.266611	+	0.212615i
$40$	−570.038	+	130.107i	−2.25327	+	0.514295i
$41$			109.949i			0.418809i	0.977829	+	0.209404i	$0.0671525\pi$
$41$			109.949i			0.418809i	−0.977829	+	0.209404i	$0.932847\pi$
$42$	−117.072	−	512.926i	−0.430109	−	1.88443i
$43$	−118.670	+	246.421i	−0.420860	+	0.873925i	0.577484	+	0.816402i	$0.304035\pi$
$43$	−118.670	+	246.421i	−0.420860	+	0.873925i	−0.998344	+	0.0575231i	$0.981680\pi$
$44$	511.538	−	1062.22i	1.75266	−	3.63944i
$45$	22.3928	+	98.1094i	0.0741805	+	0.325006i
$46$		−	761.480i		−	2.44074i
$47$	200.679	−	45.8038i	0.622811	−	0.142152i	0.100541	−	0.994933i	$-0.467943\pi$
$47$	200.679	−	45.8038i	0.622811	−	0.142152i	0.522270	+	0.852780i	$0.325085\pi$
$48$	−286.204	−	228.240i	−0.860624	−	0.686325i
$49$	−184.752	+	809.451i	−0.538635	+	2.35991i
$50$	−0.116033	−	0.0264837i	−0.000328190	−	7.49073e-5i
$51$	9.99409	+	12.5322i	0.0274402	+	0.0344090i
$52$	−454.300	−	218.780i	−1.21154	−	0.583447i
$53$	−232.380	+	111.908i	−0.602261	+	0.290033i	−0.710062	−	0.704139i	$-0.751333\pi$
$53$	−232.380	+	111.908i	−0.602261	+	0.290033i	0.107802	+	0.994172i	$0.465619\pi$
$54$	−86.1897	+	108.078i	−0.217202	+	0.272363i
$55$	565.874	−	451.270i	1.38732	−	1.10635i
$56$	777.155	+	1613.78i	1.85449	+	3.85090i
$57$	−289.586			−0.672922
$58$	797.148	−	62.2590i	1.80467	−	0.140948i
$59$	−353.732			−0.780543			−0.390272	−	0.920700i	$-0.627619\pi$
$59$	−353.732			−0.780543			−0.390272	+	0.920700i	$0.627619\pi$
$60$	−265.084	−	550.452i	−0.570369	−	1.18438i
$61$	430.847	−	343.589i	0.904334	−	0.721182i	−0.0564721	−	0.998404i	$-0.517985\pi$
$61$	430.847	−	343.589i	0.904334	−	0.721182i	0.960806	+	0.277222i	$0.0894138\pi$
$62$	−144.539	+	181.247i	−0.296073	+	0.371263i
$63$	277.748	−	133.756i	0.555444	−	0.267488i
$64$	72.6311	+	34.9773i	0.141858	+	0.0683151i
$65$	−193.004	−	242.019i	−0.368295	−	0.461827i
$66$	969.321	+	221.241i	1.80780	+	0.412620i
$67$	86.5961	−	379.402i	0.157901	−	0.691811i	−0.832550	−	0.553950i	$-0.813120\pi$
$67$	86.5961	−	379.402i	0.157901	−	0.691811i	0.990452	−	0.137861i	$-0.0440229\pi$
$68$	−76.0849	−	60.6757i	−0.135686	−	0.108206i
$69$	435.001	−	99.2861i	0.758956	−	0.173227i
$70$			1960.90i			3.34818i
$71$	79.2572	+	347.248i	0.132480	+	0.580434i	0.996970	+	0.0777838i	$0.0247844\pi$
$71$	79.2572	+	347.248i	0.132480	+	0.580434i	−0.864490	+	0.502650i	$0.832358\pi$
$72$	204.198	−	424.022i	0.334236	−	0.694048i
$73$	341.302	−	708.721i	0.547211	−	1.13629i	−0.425647	−	0.904889i	$-0.639953\pi$
$73$	341.302	−	708.721i	0.547211	−	1.13629i	0.972857	−	0.231405i	$-0.0743324\pi$
$74$	−22.1513	−	97.0513i	−0.0347978	−	0.152459i
$75$		−	0.0697377i		−	0.000107368i
$76$	1714.04	−	391.219i	2.58703	−	0.590472i
$77$	−1733.50	−	1382.42i	−2.56559	−	2.04599i
$78$	94.6226	−	414.569i	0.137358	−	0.601804i
$79$	−584.596	−	133.430i	−0.832560	−	0.190026i	−0.215063	−	0.976600i	$-0.568996\pi$
$79$	−584.596	−	133.430i	−0.832560	−	0.190026i	−0.617496	+	0.786574i	$0.711853\pi$
$80$	850.679	+	1066.72i	1.18886	+	1.49078i
$81$	−72.9785	−	35.1446i	−0.100108	−	0.0482093i
$82$	507.182	−	244.246i	0.683035	−	0.328932i
$83$	211.805	−	265.595i	0.280103	−	0.351239i	−0.621800	−	0.783176i	$-0.713598\pi$
$83$	211.805	−	265.595i	0.280103	−	0.351239i	0.901904	+	0.431937i	$0.142170\pi$
$84$	−1463.27	+	1166.92i	−1.90067	+	1.51573i
$85$	−25.9216	−	53.8267i	−0.0330775	−	0.0686862i
$86$	1400.33			1.75583
$87$	139.502	+	447.258i	0.171911	+	0.551162i
$88$	−3384.91			−4.10037
$89$	−64.5251	−	133.988i	−0.0768500	−	0.159581i	0.859004	−	0.511969i	$-0.171084\pi$
$89$	−64.5251	−	133.988i	−0.0768500	−	0.159581i	−0.935854	+	0.352389i	$0.885370\pi$
$90$	402.822	−	321.240i	0.471791	−	0.376241i
$91$	−591.246	+	741.399i	−0.681093	+	0.854063i
$92$	−2440.61	+	1175.34i	−2.76578	+	1.33193i
$93$	−122.384	−	58.9371i	−0.136459	−	0.0657150i
$94$	−657.086	−	823.959i	−0.720992	−	0.904095i
$95$	1052.26	+	240.172i	1.13642	+	0.259380i
$96$	−137.791	+	603.703i	−0.146492	+	0.641824i
$97$	−207.741	−	165.668i	−0.217453	−	0.173413i	0.508705	−	0.860941i	$-0.330124\pi$
$97$	−207.741	−	165.668i	−0.217453	−	0.173413i	−0.726158	+	0.687528i	$0.758696\pi$
$98$	4144.31	−	945.913i	4.27183	−	0.975016i
$99$			582.578i			0.591427i
$100$	0.0942128	+	0.412773i	9.42128e−5	+	0.000412773i
$101$	−86.6558	+	179.943i	−0.0853721	+	0.177277i	−0.939284	−	0.343140i	$-0.888509\pi$
$101$	−86.6558	+	179.943i	−0.0853721	+	0.177277i	0.853912	+	0.520417i	$0.174224\pi$
$102$	35.6081	−	73.9411i	0.0345660	−	0.0717770i
$103$	416.403	+	1824.38i	0.398343	+	1.74526i	0.633918	+	0.773400i	$0.281446\pi$
$103$	416.403	+	1824.38i	0.398343	+	1.74526i	−0.235575	+	0.971856i	$0.575697\pi$
$104$			1447.69i			1.36498i
$105$	−1120.18	+	255.674i	−1.04113	+	0.237630i
$106$	1032.44	+	823.342i	0.946031	+	0.754434i
$107$	202.137	−	885.620i	0.182629	−	0.800151i	−0.797743	−	0.602997i	$-0.793973\pi$
$107$	202.137	−	885.620i	0.182629	−	0.800151i	0.980373	−	0.197154i	$-0.0631698\pi$
$108$	479.434	+	109.428i	0.427163	+	0.0974971i
$109$	78.9897	+	99.0499i	0.0694114	+	0.0870391i	0.815325	−	0.579004i	$-0.196558\pi$
$109$	78.9897	+	99.0499i	0.0694114	+	0.0870391i	−0.745914	+	0.666043i	$0.767987\pi$
$110$	−3338.71	−	1607.84i	−2.89394	−	1.39365i
$111$	52.5530	−	25.3082i	0.0449379	−	0.0216410i
$112$	2605.97	−	3267.78i	2.19858	−	2.75693i
$113$	−114.377	+	91.2125i	−0.0952183	+	0.0759340i	−0.669942	−	0.742414i	$-0.733681\pi$
$113$	−114.377	+	91.2125i	−0.0952183	+	0.0759340i	0.574724	+	0.818348i	$0.305110\pi$
$114$	643.299	+	1335.82i	0.528513	+	1.09747i
$115$	−1663.00			−1.34848
$116$	−1429.94	−	2458.83i	−1.14454	−	1.96808i
$117$	249.163			0.196881
$118$	785.797	+	1631.73i	0.613038	+	1.27299i
$119$	−143.088	+	114.109i	−0.110226	+	0.0879022i
$120$	−1093.66	+	1371.40i	−0.831974	+	1.04326i
$121$	2575.95	−	1240.51i	1.93535	−	0.932014i
$122$	−2542.04	−	1224.18i	−1.88644	−	0.908461i
$123$	205.656	+	257.885i	0.150759	+	0.189046i
$124$	804.007	+	183.509i	0.582274	+	0.132900i
$125$	310.954	−	1362.38i	0.222500	−	0.974837i
$126$	−1234.00	−	984.085i	−0.872490	−	0.695788i
$127$	−42.0478	+	9.59714i	−0.0293791	+	0.00670558i	−0.237185	−	0.971464i	$-0.576225\pi$
$127$	−42.0478	+	9.59714i	−0.0293791	+	0.00670558i	0.207806	+	0.978170i	$0.433368\pi$
$128$			1238.54i			0.855251i
$129$	182.583	+	799.946i	0.124616	+	0.545979i
$130$	−687.657	+	1427.93i	−0.463934	+	0.963370i
$131$	−884.127	+	1835.91i	−0.589668	+	1.22446i	0.366165	+	0.930550i	$0.380671\pi$
$131$	−884.127	+	1835.91i	−0.589668	+	1.22446i	−0.955833	+	0.293909i	$0.905044\pi$
$132$	−787.039	−	3448.24i	−0.518962	−	2.27372i
$133$		−	3306.39i		−	2.15564i
$134$	−1942.50	+	443.364i	−1.25229	+	0.285827i
$135$	236.033	+	188.230i	0.150478	+	0.120002i
$136$	−62.1726	+	272.396i	−0.0392004	+	0.171748i
$137$	2628.09	+	599.844i	1.63893	+	0.374074i	0.940014	−	0.341135i	$-0.110811\pi$
$137$	2628.09	+	599.844i	1.63893	+	0.374074i	0.698911	+	0.715209i	$0.253668\pi$
$138$	−1424.33	−	1786.05i	−0.878599	−	1.10173i
$139$	380.873	+	183.419i	0.232412	+	0.111924i	0.546466	−	0.837482i	$-0.315973\pi$
$139$	380.873	+	183.419i	0.232412	+	0.111924i	−0.314054	+	0.949405i	$0.601687\pi$
$140$	6284.87	−	3026.63i	3.79406	−	1.82712i
$141$	385.018	−	482.797i	0.229960	−	0.288361i
$142$	1425.75	−	1137.00i	0.842579	−	0.671934i
$143$	−777.545	−	1614.59i	−0.454696	−	0.944186i
$144$	−1098.21			−0.635536
$145$	−135.968	−	1740.89i	−0.0778723	−	0.997057i
$146$	−4027.43			−2.28296
$147$	1080.72	+	2244.13i	0.606368	+	1.25914i
$148$	−276.868	+	220.795i	−0.153773	+	0.122630i
$149$	−250.268	+	313.826i	−0.137602	+	0.172548i	−0.845858	−	0.533408i	$-0.820911\pi$
$149$	−250.268	+	313.826i	−0.137602	+	0.172548i	0.708256	+	0.705956i	$0.249482\pi$
$150$	−0.321691	+	0.154918i	−0.000175107	+	8.43269e-5i
$151$	1061.69	+	511.281i	0.572178	+	0.275546i	0.697518	−	0.716568i	$-0.254288\pi$
$151$	1061.69	+	511.281i	0.572178	+	0.275546i	−0.125340	+	0.992114i	$0.540002\pi$
$152$	−3147.18	−	3946.43i	−1.67941	−	2.10591i
$153$	46.8821	+	10.7005i	0.0247725	+	0.00565417i
$154$	−2526.06	+	11067.4i	−1.32179	+	5.79113i
$155$	395.825	+	315.660i	0.205119	+	0.163577i
$156$	−1474.78	+	336.609i	−0.756903	+	0.172758i
$157$			1560.58i			0.793297i	0.917971	+	0.396648i	$0.129827\pi$
$157$			1560.58i			0.793297i	−0.917971	+	0.396648i	$0.870173\pi$
$158$	683.151	+	2993.08i	0.343978	+	1.50707i
$159$	−335.725	+	697.139i	−0.167451	+	0.347715i
$160$	1001.38	−	2079.38i	0.494787	−	1.02744i
$161$	1133.62	+	4966.69i	0.554916	+	2.43124i
$162$			414.713i			0.201129i
$163$	862.724	−	196.911i	0.414563	−	0.0946213i	−0.0101519	−	0.999948i	$-0.503232\pi$
$163$	862.724	−	196.911i	0.414563	−	0.0946213i	0.424715	+	0.905327i	$0.360374\pi$
$164$	−1565.66	−	1248.57i	−0.745473	−	0.594495i
$165$	483.169	−	2116.90i	0.227968	−	0.998791i
$166$	−1695.67	−	387.025i	−0.792828	−	0.180958i
$167$	383.763	+	481.224i	0.177823	+	0.222983i	0.862753	−	0.505626i	$-0.168738\pi$
$167$	383.763	+	481.224i	0.177823	+	0.222983i	−0.684929	+	0.728609i	$0.740167\pi$
$168$	4841.34	+	2331.46i	2.22332	+	1.07069i
$169$	1288.89	−	620.694i	0.586657	−	0.282519i
$170$	−190.713	+	239.146i	−0.0860411	+	0.107892i
$171$	−679.222	+	541.661i	−0.303751	+	0.242233i
$172$	−2161.39	−	4488.17i	−0.958166	−	1.98965i
$173$	−538.655			−0.236724			−0.118362	−	0.992971i	$-0.537764\pi$
$173$	−538.655			−0.236724			−0.118362	+	0.992971i	$0.537764\pi$
$174$	1753.25	−	1637.07i	0.763872	−	0.713252i
$175$	0.796241			0.000343944
$176$	3427.09	+	7116.43i	1.46777	+	3.04785i
$177$	−829.678	+	661.646i	−0.352330	+	0.280974i
$178$	−474.730	+	595.293i	−0.199902	+	0.250669i
$179$	−1891.61	+	910.950i	−0.789862	+	0.380377i	−0.784910	−	0.619610i	$-0.787291\pi$
$179$	−1891.61	+	910.950i	−0.789862	+	0.380377i	−0.00495234	+	0.999988i	$0.501576\pi$
$180$	−1651.36	−	795.251i	−0.683804	−	0.329303i
$181$	−644.932	−	808.719i	−0.264847	−	0.332108i	0.631570	−	0.775319i	$-0.282411\pi$
$181$	−644.932	−	808.719i	−0.264847	−	0.332108i	−0.896417	+	0.443211i	$0.853839\pi$
$182$	4733.41	+	1080.37i	1.92782	+	0.440013i
$183$	367.877	−	1611.77i	0.148602	−	0.651070i
$184$	6080.58	+	4849.10i	2.43623	+	1.94283i
$185$	−211.950	+	48.3763i	−0.0842319	+	0.0192254i
$186$			695.469i			0.274163i
$187$	−76.9617	−	337.191i	−0.0300962	−	0.131860i
$188$	−1626.66	+	3377.79i	−0.631044	+	1.31038i
$189$	401.269	−	833.244i	0.154434	−	0.320685i
$190$	−1229.66	−	5387.48i	−0.469520	−	2.05710i
$191$		−	986.174i		−	0.373597i	−0.982398	−	0.186799i	$-0.940189\pi$
$191$		−	986.174i		−	0.373597i	0.982398	−	0.186799i	$-0.0598112\pi$
$192$	235.780	−	53.8152i	0.0886247	−	0.0202280i
$193$	−2802.77	−	2235.14i	−1.04533	−	0.833620i	−0.0589722	−	0.998260i	$-0.518782\pi$
$193$	−2802.77	−	2235.14i	−1.04533	−	0.833620i	−0.986354	+	0.164640i	$0.947354\pi$
$194$	−302.721	+	1326.31i	−0.112032	+	0.490843i
$195$	−905.378	−	206.647i	−0.332489	−	0.0758885i
$196$	−9428.44	−	11822.9i	−3.43602	−	4.30864i
$197$	4193.42	+	2019.44i	1.51659	+	0.730352i	0.992607	−	0.121375i	$-0.0387304\pi$
$197$	4193.42	+	2019.44i	1.51659	+	0.730352i	0.523985	+	0.851727i	$0.324445\pi$
$198$	2687.36	−	1294.16i	0.964558	−	0.464507i
$199$	579.914	−	727.190i	0.206578	−	0.259041i	−0.667739	−	0.744395i	$-0.732738\pi$
$199$	579.914	−	727.190i	0.206578	−	0.259041i	0.874318	+	0.485354i	$0.161309\pi$
$200$	0.950375	−	0.757899i	0.000336008	−	0.000267958i
$201$	−506.549	−	1051.86i	−0.177757	−	0.369117i
$202$	1022.56			0.356172
$203$	−5106.65	+	1592.79i	−1.76560	+	0.550700i
$204$	−291.949			−0.100199
$205$	−533.409	−	1107.64i	−0.181731	−	0.377369i
$206$	7490.62	−	5973.57i	2.53348	−	2.02038i
$207$	834.581	−	1046.53i	0.280229	−	0.351396i
$208$	3043.63	−	1465.73i	1.01460	−	0.488607i
$209$	5629.59	+	2711.07i	1.86319	+	0.897266i
$210$	3667.81	+	4599.29i	1.20525	+	1.51134i
$211$	4976.99	+	1135.97i	1.62384	+	0.370631i	0.935102	−	0.354378i	$-0.115308\pi$
$211$	4976.99	+	1135.97i	1.62384	+	0.370631i	0.688739	+	0.725010i	$0.258165\pi$
$212$	1045.33	−	4579.88i	0.338648	−	1.48371i
$213$	835.415	+	666.221i	0.268740	+	0.214313i
$214$	−4534.30	+	1034.92i	−1.44840	+	0.330588i
$215$		−	3058.18i		−	0.970074i
$216$	−314.174	−	1376.49i	−0.0989668	−	0.433602i
$217$	672.924	−	1397.34i	0.210512	−	0.437132i
$218$	281.434	−	584.404i	0.0874363	−	0.181563i
$219$	−525.119	−	2300.70i	−0.162029	−	0.709893i
$220$			13182.6i			4.03985i
$221$	−144.213	+	32.9158i	−0.0438952	+	0.0100188i
$222$	−233.487	−	186.200i	−0.0705885	−	0.0562924i
$223$	−894.360	+	3918.45i	−0.268569	+	1.17668i	0.643111	+	0.765773i	$0.277643\pi$
$223$	−894.360	+	3918.45i	−0.268569	+	1.17668i	−0.911679	+	0.410902i	$0.865214\pi$
$224$	−6892.87	−	1573.25i	−2.05602	−	0.469274i
$225$	−0.130442	−	0.163569i	−3.86495e−5	−	4.84650e-5i
$226$	674.834	+	324.983i	0.198625	+	0.0956528i
$227$	1501.76	−	723.212i	0.439100	−	0.211459i	−0.201255	−	0.979539i	$-0.564502\pi$
$227$	1501.76	−	723.212i	0.439100	−	0.211459i	0.640354	+	0.768080i	$0.278788\pi$
$228$	3288.51	−	4123.66i	0.955206	−	1.19779i
$229$	−218.730	+	174.432i	−0.0631184	+	0.0503353i	−0.654541	−	0.756027i	$-0.727138\pi$
$229$	−218.730	+	174.432i	−0.0631184	+	0.0503353i	0.591422	+	0.806362i	$0.298567\pi$
$230$	3694.26	+	7671.21i	1.05910	+	2.19924i
$231$	−6651.68			−1.89458
$232$	−4579.08	+	6761.86i	−1.29583	+	1.91353i
$233$	−6149.65			−1.72909			−0.864543	−	0.502559i	$-0.832392\pi$
$233$	−6149.65			−1.72909			−0.864543	+	0.502559i	$0.832392\pi$
$234$	−553.501	−	1149.36i	−0.154630	−	0.321093i
$235$	−1799.45	+	1435.01i	−0.499502	+	0.398339i
$236$	4016.96	−	5037.10i	1.10797	−	1.38935i
$237$	−1620.74	+	780.510i	−0.444214	+	0.213922i
$238$	844.234	+	406.562i	0.229931	+	0.110729i
$239$	1569.16	+	1967.66i	0.424688	+	0.532542i	0.947436	−	0.319946i	$-0.103665\pi$
$239$	1569.16	+	1967.66i	0.424688	+	0.532542i	−0.522748	+	0.852487i	$0.675093\pi$
$240$	3990.53	+	910.812i	1.07328	+	0.244969i
$241$	864.217	−	3786.38i	0.230992	−	1.01204i	−0.717827	−	0.696222i	$-0.754863\pi$
$241$	864.217	−	3786.38i	0.230992	−	1.01204i	0.948819	−	0.315821i	$-0.102280\pi$
$242$	−11444.6	−	9126.80i	−3.04004	−	2.42435i
$243$	−236.907	+	54.0726i	−0.0625417	+	0.0142747i
$244$			10037.0i			2.63341i
$245$	−2065.78	−	9050.78i	−0.538685	−	2.36013i
$246$	732.738	−	1521.55i	0.189909	−	0.394350i
$247$	1159.50	−	2407.72i	0.298693	−	0.620241i
$248$	−526.867	−	2308.35i	−0.134904	−	0.591051i
$249$		−	1019.13i		−	0.259375i
$250$	−6975.24	+	1592.05i	−1.76461	+	0.402761i
$251$	6131.92	+	4890.05i	1.54201	+	1.22971i	0.874412	+	0.485184i	$0.161247\pi$
$251$	6131.92	+	4890.05i	1.54201	+	1.22971i	0.667594	+	0.744526i	$0.267324\pi$
$252$	−1249.41	+	5474.02i	−0.312323	+	1.36838i
$253$	−9385.99	−	2142.29i	−2.33238	−	0.532351i
$254$	137.677	+	172.642i	0.0340104	+	0.0426477i
$255$	−161.480	−	77.7647i	−0.0396560	−	0.0190973i
$256$	6294.26	−	3031.16i	1.53669	−	0.740029i
$257$	2039.20	−	2557.08i	0.494949	−	0.620646i	−0.470133	−	0.882596i	$-0.655794\pi$
$257$	2039.20	−	2557.08i	0.494949	−	0.620646i	0.965082	+	0.261949i	$0.0843654\pi$
$258$	3284.46	−	2619.27i	0.792564	−	0.632049i
$259$	288.960	+	600.032i	0.0693248	+	0.143954i
$260$	5638.05			1.34483
$261$	1163.79	+	788.107i	0.276002	+	0.186906i
$262$	10432.9			2.46009
$263$	1422.99	+	2954.86i	0.333632	+	0.692794i	0.998534	−	0.0541373i	$-0.0172409\pi$
$263$	1422.99	+	2954.86i	0.333632	+	0.692794i	−0.664902	+	0.746931i	$0.731527\pi$
$264$	−7939.29	+	6331.37i	−1.85087	+	1.47602i
$265$	1798.10	−	2254.74i	0.416816	−	0.522671i
$266$	−15252.0	+	7344.97i	−3.51564	+	1.69304i
$267$	−401.963	−	193.575i	−0.0921339	−	0.0443693i
$268$	4419.26	+	5541.57i	1.00727	+	1.26308i
$269$	−6050.15	−	1380.91i	−1.37132	−	0.312994i	−0.527467	−	0.849575i	$-0.676858\pi$
$269$	−6050.15	−	1380.91i	−1.37132	−	0.312994i	−0.843849	+	0.536581i	$0.819715\pi$
$270$	343.948	−	1506.93i	0.0775259	−	0.339663i
$271$	−3280.40	−	2616.03i	−0.735313	−	0.586393i	0.182594	−	0.983188i	$-0.441551\pi$
$271$	−3280.40	−	2616.03i	−0.735313	−	0.586393i	−0.917907	+	0.396796i	$0.870122\pi$
$272$	635.632	−	145.079i	0.141694	−	0.0323408i
$273$			2844.86i			0.630691i
$274$	−3071.15	−	13455.6i	−0.677134	−	2.96672i
$275$	−0.652876	+	1.35571i	−0.000143163	+	0.000297282i
$276$	−3526.01	+	7321.84i	−0.768989	+	1.59682i
$277$	40.4126	+	177.059i	0.00876592	+	0.0384060i	0.979122	−	0.203275i	$-0.0651585\pi$
$277$	40.4126	+	177.059i	0.00876592	+	0.0384060i	−0.970356	+	0.241681i	$0.922301\pi$
$278$		−	2164.38i		−	0.466945i
$279$	−397.292	+	90.6792i	−0.0852517	+	0.0194581i
$280$	−15658.2	−	12487.0i	−3.34199	−	2.66515i
$281$	943.315	−	4132.93i	0.200261	−	0.877403i	−0.770516	−	0.637421i	$-0.780001\pi$
$281$	943.315	−	4132.93i	0.200261	−	0.877403i	0.970777	−	0.239982i	$-0.0771416\pi$
$282$	−3082.38	−	703.533i	−0.650898	−	0.148563i
$283$	5803.62	+	7277.51i	1.21904	+	1.52863i	0.774084	+	0.633083i	$0.218211\pi$
$283$	5803.62	+	7277.51i	1.21904	+	1.52863i	0.444960	+	0.895550i	$0.353218\pi$
$284$	−5844.81	−	2814.71i	−1.22122	−	0.588107i
$285$	2917.31	−	1404.90i	0.606338	−	0.291997i
$286$	−5720.63	+	7173.44i	−1.18275	+	1.48313i
$287$	−2944.44	+	2348.12i	−0.605592	+	0.482944i
$288$	806.019	+	1673.72i	0.164914	+	0.342447i
$289$	4884.45			0.994189
$290$	−7728.48	+	4494.50i	−1.56494	+	0.910090i
$291$	−797.134			−0.160580
$292$	6216.30	+	12908.3i	1.24583	+	2.58698i
$293$	6219.22	−	4959.67i	1.24004	−	0.988897i	0.240203	−	0.970723i	$-0.422786\pi$
$293$	6219.22	−	4959.67i	1.24004	−	0.988897i	0.999835	−	0.0181741i	$-0.00578531\pi$
$294$	7951.17	−	9970.45i	1.57728	−	1.97785i
$295$	3563.53	−	1716.10i	0.703310	−	0.338696i
$296$	916.035	+	441.139i	0.179876	+	0.0866240i
$297$	1089.69	+	1366.43i	0.212897	+	0.266965i
$298$	2003.60	+	457.308i	0.389481	+	0.0888964i
$299$	−916.237	+	4014.30i	−0.177215	+	0.776431i
$300$	0.993055	+	0.791935i	0.000191114	+	0.000152408i
$301$	−9133.52	+	2084.67i	−1.74899	+	0.399196i
$302$		−	6033.22i		−	1.14958i
$303$	133.327	+	584.142i	0.0252786	+	0.110753i
$304$	−5110.58	+	10612.2i	−0.964184	+	2.00215i
$305$	−2673.49	+	5551.57i	−0.501914	+	1.04224i
$306$	−54.7858	−	240.032i	−0.0102350	−	0.0448423i
$307$			8039.13i			1.49452i	0.664532	+	0.747260i	$0.268631\pi$
$307$			8039.13i			1.49452i	−0.664532	+	0.747260i	$0.731369\pi$
$308$	39370.9	−	8986.15i	7.28365	−	1.66245i
$309$	4389.12	+	3500.20i	0.808052	+	0.644400i
$310$	576.797	−	2527.11i	0.105677	−	0.463001i
$311$	−975.192	−	222.581i	−0.177807	−	0.0405833i	0.132690	−	0.991158i	$-0.457638\pi$
$311$	−975.192	−	222.581i	−0.177807	−	0.0405833i	−0.310497	+	0.950574i	$0.600496\pi$
$312$	2707.86	+	3395.55i	0.491355	+	0.616139i
$313$	−6318.30	−	3042.73i	−1.14099	−	0.549474i	−0.234678	−	0.972073i	$-0.575404\pi$
$313$	−6318.30	−	3042.73i	−1.14099	−	0.549474i	−0.906317	+	0.422599i	$0.861118\pi$
$314$	7198.75	−	3466.74i	1.29379	−	0.623055i
$315$	−2149.15	+	2694.94i	−0.384415	+	0.482041i
$316$	8538.66	−	6809.35i	1.52005	−	1.21220i
$317$	−541.034	−	1123.47i	−0.0958597	−	0.199055i	0.847525	−	0.530756i	$-0.178092\pi$
$317$	−541.034	−	1123.47i	−0.0958597	−	0.199055i	−0.943385	+	0.331701i	$0.892378\pi$
$318$	3961.61			0.698604
$319$	1475.23	−	10000.8i	0.258925	−	1.75529i
$320$	−901.381			−0.157465
$321$	−1182.41	−	2455.31i	−0.205595	−	0.426922i
$322$	20392.5	−	16262.5i	3.52928	−	2.81451i
$323$	321.572	−	403.238i	0.0553954	−	0.0694637i
$324$	1329.19	−	640.105i	0.227914	−	0.109757i
$325$	0.579824	+	0.279229i	9.89627e−5	+	4.76579e-5i
$326$	−2824.82	−	3542.21i	−0.479915	−	0.601795i
$327$	370.540	+	84.5733i	0.0626633	+	0.0143025i
$328$	−1279.38	+	5605.31i	−0.215371	+	0.943603i
$329$	5512.42	+	4396.00i	0.923736	+	0.736655i
$330$	−10838.3	+	2473.78i	−1.80797	+	0.412658i
$331$		−	6359.61i		−	1.05606i	−0.849226	−	0.528030i	$-0.822931\pi$
$331$		−	6359.61i		−	1.05606i	0.849226	−	0.528030i	$-0.177069\pi$
$332$	1376.80	+	6032.14i	0.227595	+	0.997159i
$333$	75.9246	−	157.659i	0.0124944	−	0.0259449i
$334$	1367.32	−	2839.27i	0.224001	−	0.465143i
$335$	968.263	+	4242.24i	0.157916	+	0.691875i
$336$		−	12538.9i		−	2.03588i
$337$	−11714.6	+	2673.77i	−1.89357	+	0.432195i	−0.999865	−	0.0164610i	$-0.994760\pi$
$337$	−11714.6	+	2673.77i	−1.89357	+	0.432195i	−0.893705	+	0.448656i	$0.851903\pi$
$338$	−5726.38	−	4566.63i	−0.921520	−	0.734888i
$339$	−97.6600	+	427.877i	−0.0156465	+	0.0685518i
$340$	1060.85	+	242.132i	0.169213	+	0.0386219i
$341$	1827.41	+	2291.49i	0.290204	+	0.363904i
$342$	4007.47	+	1929.90i	0.633623	+	0.305137i
$343$	−15037.5	+	7241.68i	−2.36720	+	1.13998i
$344$	−8917.28	+	11181.9i	−1.39764	+	1.75258i
$345$	−3900.55	+	3110.59i	−0.608692	+	0.485416i
$346$	1196.59	+	2484.75i	0.185923	+	0.386073i
$347$	3798.55			0.587657			0.293828	−	0.955858i	$-0.405071\pi$
$347$	3798.55			0.587657			0.293828	+	0.955858i	$0.405071\pi$
$348$	−7953.08	−	3092.53i	−1.22509	−	0.476371i
$349$	2344.37			0.359573			0.179787	−	0.983706i	$-0.442459\pi$
$349$	2344.37			0.359573			0.179787	+	0.983706i	$0.442459\pi$
$350$	−1.76881	−	3.67296i	−0.000270133	−	0.000560938i
$351$	584.410	−	466.051i	0.0888703	−	0.0708717i
$352$	8330.48	−	10446.1i	1.26141	−	1.58176i
$353$	3889.83	−	1873.24i	0.586500	−	0.282444i	−0.117008	−	0.993131i	$-0.537330\pi$
$353$	3889.83	−	1873.24i	0.586500	−	0.282444i	0.703508	+	0.710687i	$0.251616\pi$
$354$	4895.18	+	2357.39i	0.734959	+	0.353938i
$355$	−2483.09	−	3113.70i	−0.371236	−	0.465515i
$356$	2640.71	+	602.725i	0.393139	+	0.0897313i
$357$	−122.175	+	535.285i	−0.0181126	+	0.0793565i
$358$	8404.20	+	6702.13i	1.24071	+	0.989437i
$359$	−8966.40	+	2046.52i	−1.31819	+	0.300867i	−0.823060	−	0.567954i	$-0.807735\pi$
$359$	−8966.40	+	2046.52i	−1.31819	+	0.300867i	−0.495125	+	0.868822i	$0.664878\pi$
$360$			5262.28i			0.770406i
$361$	547.126	+	2397.12i	0.0797677	+	0.349485i
$362$	−2297.84	+	4771.52i	−0.333624	+	0.692777i
$363$	3721.53	−	7727.84i	0.538098	−	1.11737i
$364$	−3843.29	−	16838.5i	−0.553415	−	2.42467i
$365$			8795.51i			1.26131i
$366$	−8252.14	+	1883.50i	−1.17854	+	0.268994i
$367$	9493.58	+	7570.88i	1.35030	+	1.07683i	0.989553	+	0.144167i	$0.0460501\pi$
$367$	9493.58	+	7570.88i	1.35030	+	1.07683i	0.360748	+	0.932663i	$0.382521\pi$
$368$	4038.39	−	17693.3i	0.572053	−	2.50633i
$369$	964.732	+	220.194i	0.136103	+	0.0310646i
$370$	693.990	+	870.236i	0.0975104	+	0.122274i
$371$	−7959.70	−	3833.19i	−1.11387	−	0.536413i
$372$	2229.04	−	1073.45i	0.310673	−	0.149612i
$373$	−29.7246	+	37.2735i	−0.00412622	+	0.00517412i	−0.783890	−	0.620899i	$-0.786768\pi$
$373$	−29.7246	+	37.2735i	−0.00412622	+	0.00517412i	0.779764	+	0.626073i	$0.215339\pi$
$374$	−1384.46	+	1104.07i	−0.191413	+	0.152647i
$375$	−1818.94	−	3777.08i	−0.250480	−	0.520126i
$376$	10763.8			1.47633
$377$	−4277.24	−	630.942i	−0.584321	−	0.0861941i
$378$	−4735.05			−0.644298
$379$	3689.06	+	7660.41i	0.499985	+	1.03823i	0.986379	+	0.164489i	$0.0525976\pi$
$379$	3689.06	+	7660.41i	0.499985	+	1.03823i	−0.486394	+	0.873739i	$0.661688\pi$
$380$	−15369.4	+	12256.7i	−2.07483	+	1.65462i
$381$	−80.6718	+	101.159i	−0.0108476	+	0.0136025i
$382$	−4549.10	+	2190.73i	−0.609299	+	0.293423i
$383$	−351.947	−	169.489i	−0.0469547	−	0.0226122i	0.410259	−	0.911969i	$-0.365438\pi$
$383$	−351.947	−	169.489i	−0.0469547	−	0.0226122i	−0.457214	+	0.889357i	$0.651153\pi$
$384$	2316.64	+	2904.98i	0.307866	+	0.386052i
$385$	24170.1	+	5516.66i	3.19953	+	0.730273i
$386$	−4084.21	+	17894.1i	−0.538551	+	2.35955i
$387$	1924.52	+	1534.75i	0.252788	+	0.201592i
$388$	4718.19	−	1076.90i	0.617345	−	0.140905i
$389$			227.916i			0.0297064i	0.999890	+	0.0148532i	$0.00472809\pi$
$389$			227.916i			0.0297064i	−0.999890	+	0.0148532i	$0.995272\pi$
$390$	1058.01	+	4635.45i	0.137370	+	0.601859i
$391$	−344.796	+	715.976i	−0.0445961	+	0.0926048i
$392$	−18837.7	+	39116.8i	−2.42716	+	5.04004i
$393$	1360.30	+	5959.85i	0.174600	+	0.764973i
$394$		−	23829.8i		−	3.04703i
$395$	6536.59	−	1491.93i	0.832637	−	0.190044i
$396$	−8295.83	−	6615.70i	−1.05273	−	0.839524i
$397$	−1345.28	+	5894.04i	−0.170069	+	0.745122i	0.815900	+	0.578194i	$0.196242\pi$
$397$	−1345.28	+	5894.04i	−0.170069	+	0.745122i	−0.985969	+	0.166929i	$0.946615\pi$
$398$	−4642.69	−	1059.66i	−0.584716	−	0.133458i
$399$	−6184.50	−	7755.12i	−0.775971	−	0.973037i
$400$	−2.55562	−	1.23072i	−0.000319453	−	0.000153840i
$401$	2455.09	−	1182.31i	0.305739	−	0.147236i	−0.274723	−	0.961523i	$-0.588586\pi$
$401$	2455.09	−	1182.31i	0.305739	−	0.147236i	0.580462	+	0.814287i	$0.302872\pi$
$402$	−3726.83	+	4673.30i	−0.462382	+	0.579809i
$403$	980.050	−	781.563i	0.121141	−	0.0966066i
$404$	−1578.30	−	3277.38i	−0.194365	−	0.403604i
$405$	905.692			0.111121
$406$	18691.5	+	20018.0i	2.28484	+	2.44699i
$407$	−1258.57			−0.153280
$408$	363.683	+	755.195i	0.0441299	+	0.0916366i
$409$	−3778.05	+	3012.89i	−0.456754	+	0.364249i	−0.824674	−	0.565608i	$-0.808642\pi$
$409$	−3778.05	+	3012.89i	−0.456754	+	0.364249i	0.367920	+	0.929858i	$0.380070\pi$
$410$	−3924.45	+	4921.10i	−0.472719	+	0.592771i
$411$	7286.16	−	3508.83i	0.874452	−	0.421114i
$412$	−30707.5	−	14788.0i	−3.67197	−	1.76833i
$413$	−7554.45	−	9472.98i	−0.900073	−	1.12866i
$414$	−6681.50	−	1525.01i	−0.793183	−	0.181039i
$415$	−845.225	+	3703.17i	−0.0999771	+	0.438028i
$416$	−4467.69	−	3562.86i	−0.526554	−	0.419913i
$417$	1236.41	−	282.204i	0.145198	−	0.0331405i
$418$		−	31991.1i		−	3.74339i
$419$	−472.059	−	2068.23i	−0.0550396	−	0.241144i	0.939924	−	0.341385i	$-0.110896\pi$
$419$	−472.059	−	2068.23i	−0.0550396	−	0.241144i	−0.994963	+	0.100240i	$0.968039\pi$
$420$	9079.90	−	18854.6i	1.05489	−	2.19050i
$421$	−820.559	+	1703.91i	−0.0949919	+	0.197253i	−0.943050	−	0.332650i	$-0.892057\pi$
$421$	−820.559	+	1703.91i	−0.0949919	+	0.197253i	0.848058	+	0.529903i	$0.177772\pi$
$422$	−5816.05	−	25481.8i	−0.670902	−	2.93941i
$423$		−	1852.56i		−	0.212942i
$424$	−13149.1	+	3001.20i	−1.50608	+	0.343753i
$425$	0.0971073	+	0.0774405i	1.10833e−5	+	8.83862e-6i
$426$	1217.37	−	5333.64i	0.138455	−	0.606610i
$427$	18402.7	+	4200.29i	2.08564	+	0.476034i
$428$	10315.7	+	12935.4i	1.16502	+	1.46088i
$429$	−4843.76	−	2332.63i	−0.545126	−	0.262519i
$430$	−14107.0	+	6793.57i	−1.58209	+	0.761896i
$431$	5510.89	−	6910.44i	0.615894	−	0.772307i	−0.371866	−	0.928286i	$-0.621282\pi$
$431$	5510.89	−	6910.44i	0.615894	−	0.772307i	0.987760	+	0.155980i	$0.0498534\pi$
$432$	−2575.83	+	2054.16i	−0.286875	+	0.228775i
$433$	363.217	+	754.228i	0.0403120	+	0.0837087i	0.920152	−	0.391561i	$-0.128065\pi$
$433$	363.217	+	754.228i	0.0403120	+	0.0837087i	−0.879840	+	0.475270i	$0.842351\pi$
$434$	−7940.63			−0.878255
$435$	−3575.20	−	3828.93i	−0.394063	−	0.422030i
$436$	−2307.46			−0.253457
$437$	−6229.10	−	12934.9i	−0.681873	−	1.41592i
$438$	−9446.31	+	7533.18i	−1.03051	+	0.821802i
$439$	−9883.14	+	12393.1i	−1.07448	+	1.34736i	−0.140479	+	0.990084i	$0.544864\pi$
$439$	−9883.14	+	12393.1i	−1.07448	+	1.34736i	−0.934001	+	0.357271i	$0.883707\pi$
$440$	34099.8	−	16421.6i	3.69465	−	1.77925i
$441$	6732.40	+	3242.16i	0.726963	+	0.350087i
$442$	472.199	+	592.118i	0.0508149	+	0.0637199i
$443$	−15260.9	−	3483.20i	−1.63672	−	0.373571i	−0.697419	−	0.716664i	$-0.745668\pi$
$443$	−15260.9	−	3483.20i	−1.63672	−	0.373571i	−0.939301	+	0.343093i	$0.888525\pi$
$444$	−236.402	+	1035.75i	−0.0252684	+	0.110708i
$445$	1300.06	+	1036.76i	0.138492	+	0.110443i
$446$	20062.1	−	4579.04i	2.12997	−	0.486152i
$447$			1204.19i			0.127419i
$448$	614.444	+	2692.06i	0.0647986	+	0.283901i
$449$	−4267.71	+	8861.99i	−0.448565	+	0.931455i	0.546978	+	0.837147i	$0.315778\pi$
$449$	−4267.71	+	8861.99i	−0.448565	+	0.931455i	−0.995543	+	0.0943079i	$0.969936\pi$
$450$	−0.464755	+	0.965074i	−4.86862e−5	+	0.000101098i
$451$	−1583.70	−	6938.66i	−0.165352	−	0.724454i
$452$		−	2664.51i		−	0.277274i
$453$	3446.52	−	786.645i	0.357465	−	0.0815890i
$454$	−6672.18	−	5320.88i	−0.689737	−	0.550047i
$455$	2359.42	−	10337.3i	0.243102	−	1.06510i
$456$	−14763.4	−	3369.64i	−1.51614	−	0.346048i
$457$	−6504.45	−	8156.32i	−0.665788	−	0.834872i	0.328171	−	0.944618i	$-0.393568\pi$
$457$	−6504.45	−	8156.32i	−0.665788	−	0.834872i	−0.993960	+	0.109746i	$0.964996\pi$
$458$	1290.53	+	621.487i	0.131665	+	0.0634065i
$459$	129.977	−	62.5936i	0.0132174	−	0.00636518i
$460$	18884.9	−	23680.9i	1.91416	−	2.40027i
$461$	−1492.79	+	1190.46i	−0.150816	+	0.120271i	−0.695991	−	0.718051i	$-0.745035\pi$
$461$	−1492.79	+	1190.46i	−0.150816	+	0.120271i	0.545175	+	0.838322i	$0.316463\pi$
$462$	14776.3	+	30683.4i	1.48800	+	3.08987i
$463$	4046.07			0.406128			0.203064	−	0.979166i	$-0.434910\pi$
$463$	4046.07			0.406128			0.203064	+	0.979166i	$0.434910\pi$
$464$	18852.3	+	2780.93i	1.88620	+	0.278236i
$465$	1518.84			0.151472
$466$	13661.1	+	28367.6i	1.35802	+	2.81997i
$467$	5767.11	−	4599.12i	0.571456	−	0.455721i	−0.294633	−	0.955610i	$-0.595197\pi$
$467$	5767.11	−	4599.12i	0.571456	−	0.455721i	0.866089	+	0.499889i	$0.166626\pi$
$468$	−2829.47	+	3548.04i	−0.279471	+	0.350445i
$469$	12009.8	−	5783.61i	1.18243	−	0.569429i
$470$	10616.9	+	5112.83i	1.04196	+	0.501781i
$471$	2919.01	+	3660.32i	0.285565	+	0.358087i
$472$	−18033.6	−	4116.06i	−1.75861	−	0.401392i
$473$	3939.58	−	17260.4i	0.382964	−	1.67787i
$474$	7200.79	+	5742.44i	0.697771	+	0.556454i
$475$	−2.18763	+	0.499313i	−0.000211317	+	4.82317e-5i
$476$		−	3333.37i		−	0.320977i
$477$	516.538	+	2263.10i	0.0495820	+	0.217233i
$478$	5590.79	−	11609.4i	0.534972	−	1.11088i
$479$	−1309.75	+	2719.72i	−0.124935	+	0.259430i	−0.954050	−	0.299648i	$-0.903131\pi$
$479$	−1309.75	+	2719.72i	−0.124935	+	0.259430i	0.829115	+	0.559079i	$0.188845\pi$
$480$	−1540.70	−	6750.23i	−0.146506	−	0.641884i
$481$			538.279i			0.0510258i
$482$	−19385.9	+	4424.71i	−1.83196	+	0.418133i
$483$	11948.9	+	9528.96i	1.12566	+	0.897687i
$484$	−11587.5	+	50768.3i	−1.08823	+	4.76787i
$485$	2896.53	+	661.114i	0.271185	+	0.0618962i
$486$	775.707	+	972.706i	0.0724008	+	0.0907878i
$487$	−10347.7	−	4983.20i	−0.962835	−	0.463677i	−0.114667	−	0.993404i	$-0.536580\pi$
$487$	−10347.7	−	4983.20i	−0.962835	−	0.463677i	−0.848168	+	0.529727i	$0.822294\pi$
$488$	25963.1	−	12503.2i	2.40839	−	1.15982i
$489$	1655.20	−	2075.55i	0.153069	−	0.191942i
$490$	−37161.1	+	29635.0i	−3.42606	+	2.73219i
$491$	4001.28	+	8308.73i	0.367770	+	0.763682i	0.999938	−	0.0111493i	$-0.00354900\pi$
$491$	4001.28	+	8308.73i	0.367770	+	0.763682i	−0.632168	+	0.774831i	$0.717835\pi$
$492$	−6007.66			−0.550501
$493$	−777.703	−	302.407i	−0.0710466	−	0.0276263i
$494$	−13682.3			−1.24614
$495$	−2826.33	−	5868.93i	−0.256634	−	0.532907i
$496$	−4319.65	+	3444.81i	−0.391044	+	0.311847i
$497$	−7606.69	+	9538.48i	−0.686532	+	0.860884i
$498$	−4701.10	+	2263.93i	−0.423015	+	0.203713i
$499$	−12347.1	−	5946.07i	−1.10768	−	0.533432i	−0.211617	−	0.977353i	$-0.567873\pi$
$499$	−12347.1	−	5946.07i	−1.10768	−	0.533432i	−0.896066	+	0.443921i	$0.853587\pi$
$500$	15868.9	+	19899.0i	1.41936	+	1.77982i
$501$	1800.23	+	410.891i	0.160536	+	0.0366412i
$502$	8935.46	−	39148.8i	0.794440	−	3.48067i
$503$	2411.85	+	1923.38i	0.213795	+	0.170496i	0.724532	−	0.689241i	$-0.242056\pi$
$503$	2411.85	+	1923.38i	0.213795	+	0.170496i	−0.510737	+	0.859737i	$0.670627\pi$
$504$	15716.3	−	3587.13i	1.38900	−	0.317031i
$505$		−	2233.16i		−	0.196781i
$506$	10968.3	+	48055.4i	0.963641	+	4.22199i
$507$	1862.08	−	3866.66i	0.163112	−	0.338707i
$508$	340.830	−	707.740i	0.0297675	−	0.0618128i
$509$	1090.32	+	4777.01i	0.0949462	+	0.415987i	0.999956	−	0.00940465i	$-0.00299364\pi$
$509$	1090.32	+	4777.01i	0.0949462	+	0.415987i	−0.905010	+	0.425391i	$0.860136\pi$
$510$			917.638i			0.0796739i
$511$	26268.6	−	5995.63i	2.27408	−	0.519043i
$512$	−20218.1	−	16123.4i	−1.74516	−	1.39172i
$513$	−579.950	+	2540.93i	−0.0499131	+	0.218684i
$514$	−16325.5	−	3726.18i	−1.40094	−	0.319756i
$515$	−13045.7	−	16358.8i	−1.11624	−	1.39972i
$516$	−13464.5	−	6484.17i	−1.14873	−	0.553197i
$517$	−12004.7	+	5781.16i	−1.02121	+	0.491790i
$518$	2125.97	−	2665.88i	0.180327	−	0.226124i
$519$	−1263.41	+	1007.54i	−0.106855	+	0.0852139i
$520$	−7023.36	−	14584.2i	−0.592298	−	1.22992i
$521$	12885.7			1.08356			0.541779	−	0.840521i	$-0.317751\pi$
$521$	12885.7			1.08356			0.541779	+	0.840521i	$0.317751\pi$
$522$	1050.16	−	7119.14i	0.0880538	−	0.596928i
$523$	−15535.1			−1.29886			−0.649430	−	0.760422i	$-0.724992\pi$
$523$	−15535.1			−1.29886			−0.649430	+	0.760422i	$0.724992\pi$
$524$	−16103.0	−	33438.3i	−1.34249	−	2.78771i
$525$	1.86758	−	1.48934i	0.000155253	−	0.000123810i
$526$	10469.3	−	13128.1i	0.867842	−	1.08824i
$527$	217.970	−	104.969i	0.0180169	−	0.00867649i
$528$	21349.3	+	10281.3i	1.75968	+	0.847415i
$529$	6205.84	+	7781.87i	0.510055	+	0.639588i
$530$	−14395.2	−	3285.62i	−1.17979	−	0.269279i
$531$	−708.416	+	3103.77i	−0.0578957	+	0.253658i
$532$	47082.6	+	37547.1i	3.83701	+	3.05991i
$533$	−2967.60	+	677.334i	−0.241165	+	0.0550443i
$534$			2284.22i			0.185109i
$535$	2260.17	+	9902.46i	0.182646	+	0.800225i
$536$	8829.50	−	18334.7i	0.711523	−	1.47749i
$537$	−2732.85	+	5674.82i	−0.219611	+	0.456027i
$538$	7070.12	+	30976.2i	0.566569	+	2.48230i
$539$		−	53743.9i		−	4.29483i
$540$	−5360.74	+	1223.55i	−0.427202	+	0.0975062i
$541$	−3709.28	−	2958.05i	−0.294777	−	0.235077i	0.464922	−	0.885352i	$-0.346082\pi$
$541$	−3709.28	−	2958.05i	−0.294777	−	0.235077i	−0.759699	+	0.650275i	$0.774654\pi$
$542$	−4780.20	+	20943.4i	−0.378833	+	1.65977i
$543$	−3025.37	−	690.520i	−0.239099	−	0.0545728i
$544$	−687.624	−	862.253i	−0.0541942	−	0.0679574i
$545$	−1276.28	−	614.624i	−0.100312	−	0.0483075i
$546$	13123.0	−	6319.69i	1.02859	−	0.495344i
$547$	4519.63	−	5667.44i	0.353283	−	0.443002i	−0.573157	−	0.819445i	$-0.694282\pi$
$547$	4519.63	−	5667.44i	0.353283	−	0.443002i	0.926440	+	0.376443i	$0.122853\pi$
$548$	−38386.0	+	30611.9i	−2.99228	+	2.38627i
$549$	−2151.92	−	4468.51i	−0.167289	−	0.347379i
$550$	7.70406			0.000597277
$551$	13031.4	−	7578.43i	1.00755	−	0.585938i
$552$	23332.1			1.79906
$553$	−8911.59	−	18505.1i	−0.685279	−	1.42300i
$554$	726.978	−	579.746i	0.0557515	−	0.0444604i
$555$	−406.642	+	509.913i	−0.0311009	+	0.0389993i
$556$	−6937.02	+	3340.69i	−0.529128	+	0.254815i
$557$	15338.7	+	7386.74i	1.16683	+	0.561914i	0.914047	−	0.405609i	$-0.132941\pi$
$557$	15338.7	+	7386.74i	1.16683	+	0.561914i	0.252781	+	0.967524i	$0.418655\pi$
$558$	1300.85	+	1631.22i	0.0986909	+	0.123754i
$559$	−7382.10	−	1684.92i	−0.558551	−	0.127486i
$560$	−10399.3	+	45562.5i	−0.784736	+	3.43815i
$561$	−811.219	−	646.926i	−0.0610512	−	0.0486867i
$562$	−21160.3	+	4829.69i	−1.58824	+	0.362506i
$563$			4500.06i			0.336865i	0.985713	+	0.168432i	$0.0538705\pi$
$563$			4500.06i			0.336865i	−0.985713	+	0.168432i	$0.946130\pi$
$564$	2502.74	+	10965.2i	0.186851	+	0.818650i
$565$	709.731	−	1473.77i	0.0528471	−	0.109738i
$566$	20677.9	−	42938.0i	1.53561	−	3.18873i
$567$	−617.383	−	2704.93i	−0.0457277	−	0.200346i
$568$			18625.3i			1.37588i
$569$	−20664.0	+	4716.42i	−1.52246	+	0.347492i	−0.900255	−	0.435363i	$-0.856620\pi$
$569$	−20664.0	+	4716.42i	−1.52246	+	0.347492i	−0.622205	+	0.782854i	$0.713763\pi$
$570$	−12961.3	−	10336.3i	−0.952436	−	0.759542i
$571$	−4587.85	+	20100.7i	−0.336244	+	1.47318i	0.470563	+	0.882366i	$0.344051\pi$
$571$	−4587.85	+	20100.7i	−0.336244	+	1.47318i	−0.806807	+	0.590815i	$0.798806\pi$
$572$	31821.3	+	7262.99i	2.32607	+	0.530911i
$573$	−1844.61	−	2313.07i	−0.134484	−	0.168638i
$574$	17372.5	+	8366.15i	1.26326	+	0.608356i
$575$	3.11496	−	1.50009i	0.000225918	−	0.000108796i
$576$	452.361	−	567.242i	0.0327229	−	0.0410332i
$577$	12247.1	−	9766.75i	0.883629	−	0.704671i	−0.0725775	−	0.997363i	$-0.523122\pi$
$577$	12247.1	−	9766.75i	0.883629	−	0.704671i	0.956207	+	0.292692i	$0.0945510\pi$
$578$	−10850.5	−	22531.4i	−0.780836	−	1.62142i
$579$	−10754.6			−0.771930
$580$	26334.1	+	17833.3i	1.88528	+	1.27670i
$581$	11636.0			0.830884
$582$	1770.79	+	3677.08i	0.126120	+	0.261890i
$583$	13053.1	−	10409.5i	0.927279	−	0.739480i
$584$	25646.6	−	32159.9i	1.81724	−	2.27874i
$585$	−2510.08	+	1208.79i	−0.177400	+	0.0854315i
$586$	−36694.0	−	17670.9i	−2.58672	−	1.24570i
$587$	5159.53	+	6469.85i	0.362788	+	0.454922i	0.929406	−	0.369059i	$-0.120320\pi$
$587$	5159.53	+	6469.85i	0.362788	+	0.454922i	−0.566618	+	0.823981i	$0.691748\pi$
$588$	−44228.7	−	10094.9i	−3.10198	−	0.708006i
$589$	−972.570	+	4261.11i	−0.0680375	+	0.298092i
$590$	−15832.4	−	12625.9i	−1.10476	−	0.881016i
$591$	13612.9	−	3107.07i	0.947482	−	0.216257i
$592$		−	2372.51i		−	0.164712i
$593$	3487.47	+	15279.6i	0.241506	+	1.05811i	0.939646	+	0.342147i	$0.111154\pi$
$593$	3487.47	+	15279.6i	0.241506	+	1.05811i	−0.698140	+	0.715961i	$0.745989\pi$
$594$	3882.49	−	8062.08i	0.268183	−	0.556888i
$595$	887.891	−	1843.72i	0.0611764	−	0.127034i
$596$	−1626.82	−	7127.56i	−0.111807	−	0.489859i
$597$		−	2790.33i		−	0.191291i
$598$	20552.8	−	4691.05i	1.40546	−	0.320788i
$599$	17968.5	+	14329.4i	1.22566	+	0.977433i	0.999995	+	0.00322849i	$0.00102766\pi$
$599$	17968.5	+	14329.4i	1.22566	+	0.977433i	0.225667	+	0.974204i	$0.427544\pi$
$600$	0.811473	−	3.55529i	5.52137e−5	−	0.000241907i
$601$	9775.57	+	2231.21i	0.663484	+	0.151436i	0.540984	−	0.841033i	$-0.318052\pi$
$601$	9775.57	+	2231.21i	0.663484	+	0.151436i	0.122500	+	0.992469i	$0.460909\pi$
$602$	29905.9	+	37500.8i	2.02471	+	2.53890i
$603$	−3155.58	−	1519.65i	−0.213110	−	0.102628i
$604$	−19337.0	+	9312.21i	−1.30267	+	0.627332i
$605$	−19932.0	+	24994.0i	−1.33943	+	1.67959i
$606$	2398.40	−	1912.66i	0.160773	−	0.128212i
$607$	12068.9	+	25061.2i	0.807018	+	1.67579i	0.734684	+	0.678410i	$0.237330\pi$
$607$	12068.9	+	25061.2i	0.807018	+	1.67579i	0.0723340	+	0.997380i	$0.476955\pi$
$608$	19924.4			1.32901
$609$	−8998.34	+	13287.7i	−0.598737	+	0.884146i
$610$	31547.7			2.09398
$611$	2472.55	+	5134.29i	0.163713	+	0.339953i
$612$	−684.764	+	546.081i	−0.0452287	+	0.0360687i
$613$	755.963	−	947.947i	0.0498092	−	0.0624588i	−0.756303	−	0.654222i	$-0.772996\pi$
$613$	755.963	−	947.947i	0.0498092	−	0.0624588i	0.806112	+	0.591763i	$0.201568\pi$
$614$	37083.5	−	17858.5i	2.43741	−	1.17380i
$615$	−3322.91	−	1600.23i	−0.217874	−	0.104923i
$616$	−72289.5	−	90648.1i	−4.72829	−	5.92909i
$617$	−3660.24	−	835.426i	−0.238826	−	0.0545105i	0.101432	−	0.994842i	$-0.467657\pi$
$617$	−3660.24	−	835.426i	−0.238826	−	0.0545105i	−0.340259	+	0.940332i	$0.610515\pi$
$618$	6395.83	−	28022.0i	0.416308	−	1.82396i
$619$	11610.9	+	9259.38i	0.753928	+	0.601238i	0.923195	−	0.384333i	$-0.125568\pi$
$619$	11610.9	+	9259.38i	0.753928	+	0.601238i	−0.169267	+	0.985570i	$0.554140\pi$
$620$	−8989.90	+	2051.89i	−0.582328	+	0.132912i
$621$		−	4015.69i		−	0.259491i
$622$	1139.60	+	4992.89i	0.0734624	+	0.321860i
$623$	2210.18	−	4589.48i	0.142133	−	0.295142i
$624$	4397.20	−	9130.88i	0.282098	−	0.585782i
$625$	3477.54	+	15236.1i	0.222562	+	0.975109i
$626$			35904.8i			2.29240i
$627$	18275.2	−	4171.18i	1.16402	−	0.265680i
$628$	−22222.4	−	17721.8i	−1.41205	−	1.12608i
$629$	−23.1169	+	101.282i	−0.00146539	+	0.00642030i
$630$	17205.7	+	3927.08i	1.08808	+	0.248347i
$631$	−2051.09	−	2571.99i	−0.129402	−	0.162265i	0.712909	−	0.701256i	$-0.247377\pi$
$631$	−2051.09	−	2571.99i	−0.129402	−	0.162265i	−0.842311	+	0.538991i	$0.818806\pi$
$632$	−28250.7	−	13604.8i	−1.77809	−	0.856282i
$633$	13798.3	−	6644.91i	0.866403	−	0.417238i
$634$	−3980.55	+	4991.45i	−0.249350	+	0.312675i
$635$	377.033	−	300.674i	0.0235624	−	0.0187904i
$636$	−6114.71	−	12697.3i	−0.381233	−	0.791638i
$637$	−22985.7			−1.42971
$638$	−49409.6	+	15411.1i	−3.06605	+	0.956320i
$639$	3205.61			0.198454
$640$	−6008.66	−	12477.1i	−0.371114	−	0.770626i
$641$	5089.47	−	4058.72i	0.313607	−	0.250093i	−0.454018	−	0.890992i	$-0.650010\pi$
$641$	5089.47	−	4058.72i	0.313607	−	0.250093i	0.767625	+	0.640899i	$0.221438\pi$
$642$	−8699.37	+	10908.7i	−0.534793	+	0.670609i
$643$	−11569.7	+	5571.65i	−0.709584	+	0.341718i	−0.753618	−	0.657312i	$-0.771693\pi$
$643$	−11569.7	+	5571.65i	−0.709584	+	0.341718i	0.0440341	+	0.999030i	$0.485979\pi$
$644$	−83598.3	−	40258.8i	−5.11527	−	2.46338i
$645$	−5720.22	−	7172.94i	−0.349199	−	0.437882i
$646$	−2574.44	−	587.600i	−0.156796	−	0.0357876i
$647$	6589.38	−	28870.0i	0.400395	−	1.75424i	−0.225411	−	0.974264i	$-0.572372\pi$
$647$	6589.38	−	28870.0i	0.400395	−	1.75424i	0.625805	−	0.779979i	$-0.284770\pi$
$648$	−3311.57	−	2640.89i	−0.200757	−	0.160099i
$649$	22323.3	−	5095.15i	1.35018	−	0.308170i
$650$		−	3.29495i		−	0.000198829i
$651$	−1035.34	−	4536.14i	−0.0623323	−	0.273096i
$652$	−6993.03	+	14521.2i	−0.420043	+	0.872229i
$653$	−3241.70	+	6731.46i	−0.194269	+	0.403403i	−0.975235	−	0.221170i	$-0.929013\pi$
$653$	−3241.70	+	6731.46i	−0.194269	+	0.403403i	0.780967	+	0.624573i	$0.214727\pi$
$654$	−433.007	−	1897.13i	−0.0258898	−	0.113431i
$655$		−	22784.4i		−	1.35917i
$656$	13079.9	−	2985.41i	0.778484	−	0.177684i
$657$	−5535.05	−	4414.05i	−0.328680	−	0.262113i
$658$	8032.71	−	35193.6i	0.475908	−	2.08509i
$659$	−18368.6	−	4192.52i	−1.08580	−	0.247826i	−0.358072	−	0.933694i	$-0.616566\pi$
$659$	−18368.6	−	4192.52i	−1.08580	−	0.247826i	−0.727726	+	0.685868i	$0.759423\pi$
$660$	24657.6	+	30919.6i	1.45423	+	1.82355i
$661$	−25199.8	−	12135.6i	−1.48284	−	0.714099i	−0.494904	−	0.868948i	$-0.664797\pi$
$661$	−25199.8	−	12135.6i	−1.48284	−	0.714099i	−0.987938	+	0.154848i	$0.950511\pi$
$662$	−29336.1	+	14127.5i	−1.72233	+	0.829429i
$663$	−276.684	+	346.950i	−0.0162074	+	0.0203234i
$664$	13888.5	−	11075.7i	0.811714	−	0.647320i
$665$	16040.7	+	33308.8i	0.935385	+	1.94235i
$666$	−895.924			−0.0521267
$667$	−16976.8	+	15851.8i	−0.985527	+	0.920218i
$668$	−11210.6			−0.649325
$669$	5231.62	+	10863.6i	0.302341	+	0.627817i
$670$	17418.0	−	13890.4i	1.00435	−	0.800944i
$671$	−22240.8	+	27889.1i	−1.27958	+	1.60454i
$672$	−19109.9	+	9202.85i	−1.09700	+	0.528285i
$673$	5702.13	+	2746.00i	0.326599	+	0.157282i	0.589997	−	0.807406i	$-0.299129\pi$
$673$	5702.13	+	2746.00i	0.326599	+	0.157282i	−0.263398	+	0.964687i	$0.584843\pi$
$674$	38357.0	+	48098.2i	2.19207	+	2.74877i
$675$	−0.611903	−	0.139663i	−3.48921e−5	−	7.96389e-6i
$676$	−5797.87	+	25402.1i	−0.329874	+	1.44527i
$677$	10391.0	+	8286.57i	0.589896	+	0.470426i	0.872368	−	0.488849i	$-0.162583\pi$
$677$	10391.0	+	8286.57i	0.589896	+	0.470426i	−0.282472	+	0.959275i	$0.591155\pi$
$678$	2190.69	−	500.011i	0.124090	−	0.0283227i
$679$		−	9101.41i		−	0.514403i
$680$	−695.175	−	3045.76i	−0.0392041	−	0.171764i
$681$	2169.64	−	4505.29i	0.122086	−	0.253514i
$682$	6510.91	−	13520.0i	0.365565	−	0.759104i
$683$	−1637.28	−	7173.38i	−0.0917257	−	0.401877i	0.908133	−	0.418682i	$-0.137508\pi$
$683$	−1637.28	−	7173.38i	−0.0917257	−	0.401877i	−0.999859	+	0.0168050i	$0.994651\pi$
$684$		−	15823.1i		−	0.884519i
$685$	−29385.7	+	6707.08i	−1.63908	+	0.374109i
$686$	66809.9	+	53279.2i	3.71839	+	2.96532i
$687$	−186.762	+	818.257i	−0.0103718	+	0.0454417i
$688$	32537.2	+	7426.41i	1.80301	+	0.411525i
$689$	−4452.03	−	5582.67i	−0.246167	−	0.308684i
$690$	23013.6	+	11082.8i	1.26973	+	0.611470i
$691$	6845.15	−	3296.45i	0.376848	−	0.181480i	−0.235865	−	0.971786i	$-0.575792\pi$
$691$	6845.15	−	3296.45i	0.376848	−	0.181480i	0.612713	+	0.790305i	$0.290078\pi$
$692$	6116.93	−	7670.38i	0.336027	−	0.421364i
$693$	−15601.5	+	12441.8i	−0.855196	+	0.681996i
$694$	−8438.28	−	17522.3i	−0.461545	−	0.958409i
$695$	−4726.78			−0.257982
$696$	1907.64	+	24424.9i	0.103892	+	1.33021i
$697$	−587.468			−0.0319253
$698$	−5207.88	−	10814.3i	−0.282409	−	0.586428i
$699$	−14424.0	+	11502.7i	−0.780493	+	0.622423i
$700$	−9.04205	+	11.3384i	−0.000488225	+	0.000612214i
$701$	2878.96	−	1386.43i	0.155117	−	0.0747003i	−0.354715	−	0.934975i	$-0.615422\pi$
$701$	2878.96	−	1386.43i	0.155117	−	0.0747003i	0.509831	+	0.860274i	$0.329708\pi$
$702$	−3448.07	−	1660.50i	−0.185383	−	0.0892759i
$703$	−1170.18	−	1467.36i	−0.0627796	−	0.0787232i
$704$	−5087.41	−	1161.17i	−0.272357	−	0.0621636i
$705$	−1536.45	+	6731.62i	−0.0820794	+	0.359613i
$706$	−17282.1	−	13782.0i	−0.921274	−	0.734692i
$707$	−6669.53	+	1522.28i	−0.354786	+	0.0809776i
$708$		−	19328.1i		−	1.02598i
$709$	150.054	+	657.428i	0.00794835	+	0.0348240i	0.978747	−	0.205073i	$-0.0657433\pi$
$709$	150.054	+	657.428i	0.00794835	+	0.0348240i	−0.970798	+	0.239897i	$0.922886\pi$
$710$	−8847.06	+	18371.1i	−0.467640	+	0.971064i
$711$	−2341.53	+	4862.23i	−0.123508	+	0.256467i
$712$	−1730.46	−	7581.65i	−0.0910840	−	0.399065i
$713$		−	6734.27i		−	0.353717i
$714$	2740.61	−	625.526i	0.143648	−	0.0327867i
$715$	15666.1	+	12493.3i	0.819410	+	0.653458i
$716$	8509.12	−	37280.9i	0.444135	−	1.94588i
$717$	7360.90	+	1680.08i	0.383400	+	0.0875086i
$718$	29358.7	+	36814.7i	1.52599	+	1.91353i
$719$	9776.92	+	4708.32i	0.507118	+	0.244215i	0.669906	−	0.742446i	$-0.266334\pi$
$719$	9776.92	+	4708.32i	0.507118	+	0.244215i	−0.162788	+	0.986661i	$0.552049\pi$
$720$	11063.4	−	5327.85i	0.572651	−	0.275774i
$721$	−39964.1	+	50113.4i	−2.06427	+	2.58852i
$722$	9842.20	−	7848.89i	0.507325	−	0.404578i
$723$	−5055.30	−	10497.4i	−0.260039	−	0.539977i
$724$	18839.8			0.967095
$725$	1.82503	+	3.13821i	9.34895e−5	+	0.000160759i
$726$	−43914.8			−2.24494
$727$	−10311.9	−	21412.9i	−0.526063	−	1.09238i	−0.979565	−	0.201126i	$-0.935540\pi$
$727$	−10311.9	−	21412.9i	−0.526063	−	1.09238i	0.453502	−	0.891255i	$-0.350174\pi$
$728$	−38769.3	+	30917.5i	−1.97374	+	1.57401i
$729$	−454.524	+	569.955i	−0.0230922	+	0.0289567i
$730$	40572.6	−	19538.7i	2.05707	−	0.990632i
$731$	−1316.65	−	634.064i	−0.0666183	−	0.0320817i
$732$	18773.9	+	23541.7i	0.947954	+	1.18870i
$733$	15624.7	+	3566.23i	0.787327	+	0.179702i	0.597237	−	0.802065i	$-0.296265\pi$
$733$	15624.7	+	3566.23i	0.787327	+	0.179702i	0.190089	+	0.981767i	$0.439122\pi$
$734$	13834.1	−	60611.0i	0.695674	−	3.04795i
$735$	−21774.5	−	17364.6i	−1.09274	−	0.871431i
$736$	−29929.4	+	6831.19i	−1.49893	+	0.342121i
$737$			25190.6i			1.25903i
$738$	−1127.37	−	4939.34i	−0.0562319	−	0.246368i
$739$	−7770.29	+	16135.2i	−0.386786	+	0.803170i	0.613127	+	0.789984i	$0.289911\pi$
$739$	−7770.29	+	16135.2i	−0.386786	+	0.803170i	−0.999913	+	0.0131852i	$0.995803\pi$
$740$	1718.02	−	3567.50i	0.0853455	−	0.177222i
$741$	−1783.97	−	7816.10i	−0.0884425	−	0.387492i
$742$			45232.4i			2.23791i
$743$	−132.623	+	30.2704i	−0.00654843	+	0.00149464i	−0.225794	−	0.974175i	$-0.572498\pi$
$743$	−132.623	+	30.2704i	−0.00654843	+	0.00149464i	0.219245	+	0.975670i	$0.429640\pi$
$744$	−5553.47	−	4428.74i	−0.273656	−	0.218233i
$745$	998.715	−	4375.66i	0.0491142	−	0.215183i
$746$	237.970	+	54.3150i	0.0116792	+	0.00266570i
$747$	−1906.24	−	2390.35i	−0.0933678	−	0.117080i
$748$	5675.53	+	2733.19i	0.277430	+	0.133603i
$749$	28033.9	−	13500.4i	1.36760	−	0.658604i
$750$	−13382.5	+	16781.1i	−0.651547	+	0.817014i
$751$	5048.57	−	4026.10i	0.245306	−	0.195625i	−0.493117	−	0.869963i	$-0.664142\pi$
$751$	5048.57	−	4026.10i	0.245306	−	0.195625i	0.738423	+	0.674338i	$0.235571\pi$
$752$	−10897.9	−	22629.8i	−0.528467	−	1.09737i
$753$	23529.1			1.13871
$754$	6591.19	+	21132.0i	0.318351	+	1.02066i
$755$	−13176.0			−0.635129
$756$	7308.50	+	15176.3i	0.351597	+	0.730100i
$757$	14378.6	−	11466.6i	0.690356	−	0.550540i	−0.214256	−	0.976778i	$-0.568733\pi$
$757$	14378.6	−	11466.6i	0.690356	−	0.550540i	0.904611	+	0.426237i	$0.140161\pi$
$758$	27141.5	−	34034.4i	1.30056	−	1.63085i
$759$	−26021.9	+	12531.5i	−1.24445	+	0.599294i
$760$	50850.7	+	24488.4i	2.42704	+	1.16880i
$761$	23805.2	+	29850.8i	1.13395	+	1.42193i	0.892228	+	0.451586i	$0.149141\pi$
$761$	23805.2	+	29850.8i	1.13395	+	1.42193i	0.241724	+	0.970345i	$0.422287\pi$
$762$	645.843	+	147.410i	0.0307040	+	0.00700798i
$763$	−965.629	+	4230.70i	−0.0458167	+	0.200736i
$764$	14043.0	+	11198.9i	0.664996	+	0.530317i
$765$	−524.207	+	119.647i	−0.0247748	+	0.00565469i
$766$			2000.00i			0.0943379i
$767$	−2179.15	−	9547.46i	−0.102587	−	0.449464i
$768$	9093.47	−	18882.8i	0.427256	−	0.887206i
$769$	6294.88	−	13071.4i	0.295187	−	0.612963i	−0.699645	−	0.714490i	$-0.746659\pi$
$769$	6294.88	−	13071.4i	0.295187	−	0.612963i	0.994833	+	0.101527i	$0.0323729\pi$
$770$	−28244.8	−	123749.i	−1.32191	−	5.79167i
$771$		−	9811.87i		−	0.458322i
$772$	63656.1	−	14529.1i	2.96766	−	0.677349i
$773$	−7991.08	−	6372.68i	−0.371823	−	0.296519i	0.419694	−	0.907665i	$-0.362137\pi$
$773$	−7991.08	−	6372.68i	−0.371823	−	0.296519i	−0.791518	+	0.611146i	$0.790709\pi$
$774$	2804.42	−	12287.0i	0.130236	−	0.570602i
$775$	−1.02615	−	0.234213i	−4.75620e−5	−	1.08557e-5i
$776$	−8663.14	−	10863.2i	−0.400758	−	0.502535i
$777$	1800.10	+	866.881i	0.0831121	+	0.0400247i
$778$	1051.35	−	506.302i	0.0484481	−	0.0233314i
$779$	6617.24	−	8297.76i	0.304348	−	0.381640i
$780$	13224.0	−	10545.8i	0.607046	−	0.484103i
$781$	−10003.5	−	20772.5i	−0.458328	−	0.951727i
$782$	4068.66			0.186055
$783$	4203.78	−	328.325i	0.191866	−	0.0149851i
$784$	101312.			4.61514
$785$	−7571.01	−	15721.4i	−0.344231	−	0.714802i
$786$	24470.2	−	19514.4i	1.11046	−	0.885565i
$787$	15561.8	−	19513.8i	0.704850	−	0.883854i	−0.292525	−	0.956258i	$-0.594496\pi$
$787$	15561.8	−	19513.8i	0.704850	−	0.883854i	0.997375	+	0.0724036i	$0.0230670\pi$
$788$	−76376.7	+	36781.1i	−3.45280	+	1.66278i
$789$	8864.59	+	4268.96i	0.399985	+	0.192622i
$790$	−21402.8	−	26838.3i	−0.963895	−	1.20869i
$791$	−4885.35	−	1115.05i	−0.219599	−	0.0501221i
$792$	−6778.92	+	29700.4i	−0.304139	+	1.33252i
$793$	11927.9	+	9512.19i	0.534139	+	0.425962i
$794$	30177.0	−	6887.70i	1.34879	−	0.307853i
$795$		−	8651.77i		−	0.385971i
$796$	3769.63	+	16515.8i	0.167853	+	0.735411i
$797$	3631.03	−	7539.91i	0.161377	−	0.335103i	−0.804564	−	0.593867i	$-0.797601\pi$
$797$	3631.03	−	7539.91i	0.161377	−	0.335103i	0.965941	+	0.258763i	$0.0833150\pi$
$798$	−22034.9	+	45756.0i	−0.977478	+	2.02975i
$799$	244.734	+	1072.25i	0.0108361	+	0.0474761i
$800$			4.79817i			0.000212051i
$801$	−1304.88	+	297.830i	−0.0575601	+	0.0131377i
$802$	−10907.7	−	8698.59i	−0.480254	−	0.382990i
$803$	−11330.5	+	49642.0i	−0.497937	+	2.18161i
$804$	20730.7	+	4731.64i	0.909347	+	0.207553i
$805$	−35515.6	−	44535.2i	−1.55498	−	1.94989i
$806$	−5782.38	−	2784.65i	−0.252700	−	0.121694i
$807$	−16773.5	+	8077.71i	−0.731668	+	0.352353i
$808$	−6511.63	+	8165.32i	−0.283513	+	0.355514i
$809$	18138.3	−	14464.8i	0.788268	−	0.628623i	−0.144334	−	0.989529i	$-0.546104\pi$
$809$	18138.3	−	14464.8i	0.788268	−	0.628623i	0.932602	+	0.360906i	$0.117533\pi$
$810$	−2011.94	−	4177.85i	−0.0872747	−	0.181228i
$811$	−3835.43			−0.166067			−0.0830334	−	0.996547i	$-0.526461\pi$
$811$	−3835.43			−0.166067			−0.0830334	+	0.996547i	$0.526461\pi$
$812$	35309.5	−	90805.6i	1.52601	−	3.92445i
$813$	−12587.4			−0.542999
$814$	2795.85	+	5805.64i	0.120386	+	0.249985i
$815$	−7735.85	+	6169.13i	−0.332485	+	0.265148i
$816$	1219.51	−	1529.21i	0.0523177	−	0.0656044i
$817$	23786.6	−	11455.0i	1.01859	−	0.490527i
$818$	22290.8	+	10734.7i	0.952789	+	0.458839i
$819$	5321.22	+	6672.59i	0.227031	+	0.284688i
$820$	21829.9	+	4982.54i	0.929676	+	0.212192i
$821$	−1891.17	+	8285.76i	−0.0803926	+	0.352223i	−0.999086	−	0.0427488i	$-0.986388\pi$
$821$	−1891.17	+	8285.76i	−0.0803926	+	0.352223i	0.918693	+	0.394972i	$0.129246\pi$
$822$	−32371.6	−	25815.5i	−1.37359	−	1.09540i
$823$	−28864.7	+	6588.19i	−1.22255	+	0.279040i	−0.784626	−	0.619970i	$-0.787145\pi$
$823$	−28864.7	+	6588.19i	−1.22255	+	0.279040i	−0.437928	+	0.899010i	$0.644288\pi$
$824$			97853.9i			4.13702i
$825$	1.00450	+	4.40100i	4.23905e−5	+	0.000185725i
$826$	−26915.9	+	55891.5i	−1.13381	+	2.35437i
$827$	−10389.5	+	21574.1i	−0.436856	+	0.907141i	0.560044	+	0.828463i	$0.310784\pi$
$827$	−10389.5	+	21574.1i	−0.436856	+	0.907141i	−0.996900	+	0.0786778i	$0.974930\pi$
$828$	5425.03	+	23768.6i	0.227697	+	0.997605i
$829$		−	1915.36i		−	0.0802451i	−0.999195	−	0.0401225i	$-0.987225\pi$
$829$		−	1915.36i		−	0.0802451i	0.999195	−	0.0401225i	$-0.0127748\pi$
$830$	18959.9	−	4327.48i	0.792902	−	0.180975i
$831$	425.971	+	339.701i	0.0177819	+	0.0141806i
$832$	−496.620	+	2175.84i	−0.0206938	+	0.0906653i
$833$	−4324.97	−	987.146i	−0.179893	−	0.0410595i
$834$	−4048.40	−	5076.53i	−0.168087	−	0.210774i
$835$	−6200.68	−	2986.09i	−0.256986	−	0.123758i
$836$	−102534.	+	49378.0i	−4.24190	+	2.04279i
$837$	−762.232	+	955.809i	−0.0314774	+	0.0394714i
$838$	−8491.82	+	6772.00i	−0.350054	+	0.279159i
$839$	−9809.59	−	20369.8i	−0.403653	−	0.838194i	−0.999387	−	0.0350120i	$-0.988853\pi$
$839$	−9809.59	−	20369.8i	−0.403653	−	0.838194i	0.595734	−	0.803182i	$-0.296861\pi$
$840$	−60082.9			−2.46792
$841$	−17982.4	−	16476.0i	−0.737314	−	0.675550i
$842$	9682.75			0.396306
$843$	−5517.99	−	11458.2i	−0.225444	−	0.468140i
$844$	−72694.3	+	57971.8i	−2.96474	+	2.36430i
$845$	−9973.08	+	12505.8i	−0.406017	+	0.509129i
$846$	−8545.65	+	4115.37i	−0.347288	+	0.167245i
$847$	88233.9	+	42491.2i	3.57940	+	1.72375i
$848$	19622.7	+	24606.1i	0.794630	+	0.996435i
$849$	27224.7	+	6213.87i	1.10053	+	0.251189i
$850$	0.141505	−	0.619974i	5.71010e−6	−	2.50176e-5i
$851$	2260.87	+	1802.99i	0.0910713	+	0.0726270i
$852$	−18973.8	+	4330.65i	−0.762948	+	0.174138i
$853$		−	34534.3i		−	1.38621i	−0.720839	−	0.693103i	$-0.756243\pi$
$853$		−	34534.3i		−	1.38621i	0.720839	−	0.693103i	$-0.243757\pi$
$854$	−21505.1	−	94220.1i	−0.861698	−	3.77535i
$855$	4214.70	−	8751.92i	0.168585	−	0.350070i
$856$	20610.3	−	42797.7i	0.822950	−	1.70887i
$857$	6968.41	+	30530.6i	0.277755	+	1.21693i	0.900624	+	0.434599i	$0.143110\pi$
$857$	6968.41	+	30530.6i	0.277755	+	1.21693i	−0.622869	+	0.782326i	$0.714033\pi$
$858$			27525.5i			1.09523i
$859$	−3751.81	+	856.327i	−0.149022	+	0.0340134i	−0.296381	−	0.955070i	$-0.595780\pi$
$859$	−3751.81	+	856.327i	−0.149022	+	0.0340134i	0.147359	+	0.989083i	$0.452923\pi$
$860$	43548.0	+	34728.4i	1.72672	+	1.37701i
$861$	−2514.10	+	11015.0i	−0.0995125	+	0.435993i
$862$	−44119.2	−	10069.9i	−1.74328	−	0.397892i
$863$	−11596.8	−	14541.9i	−0.457426	−	0.573594i	0.498616	−	0.866823i	$-0.333842\pi$
$863$	−11596.8	−	14541.9i	−0.457426	−	0.573594i	−0.956042	+	0.293229i	$0.905270\pi$
$864$	5021.15	+	2418.06i	0.197712	+	0.0952129i
$865$	5426.46	−	2613.24i	0.213301	−	0.102720i
$866$	2672.29	−	3350.95i	0.104859	−	0.131490i
$867$	11456.5	−	9136.22i	0.448768	−	0.357880i
$868$	12256.3	+	25450.4i	0.479269	+	0.995212i
$869$	38814.6			1.51518
$870$	−9720.28	+	24997.7i	−0.378791	+	0.974140i
$871$	10773.8			0.419122
$872$	2874.42	+	5968.79i	0.111629	+	0.231799i
$873$	−1869.67	+	1491.01i	−0.0724844	+	0.0578044i
$874$	−45829.4	+	57468.2i	−1.77369	+	2.22413i
$875$	43125.4	−	20768.1i	1.66618	−	0.802388i
$876$	38724.8	+	18648.9i	1.49360	+	0.719278i
$877$	−26352.6	−	33045.1i	−1.01467	−	1.27235i	−0.961800	−	0.273751i	$-0.911735\pi$
$877$	−26352.6	−	33045.1i	−1.01467	−	1.27235i	−0.0528672	−	0.998602i	$-0.516836\pi$
$878$	79122.6	+	18059.2i	3.04130	+	0.694156i
$879$	5310.25	−	23265.7i	0.203766	−	0.892758i
$880$	−69049.6	−	55065.2i	−2.64507	−	2.10937i
$881$	−18919.1	+	4318.15i	−0.723495	+	0.165133i	−0.568383	−	0.822764i	$-0.692431\pi$
$881$	−18919.1	+	4318.15i	−0.723495	+	0.165133i	−0.155112	+	0.987897i	$0.549574\pi$
$882$		−	38258.0i		−	1.46056i
$883$	−11545.4	−	50583.7i	−0.440015	−	1.92783i	−0.366122	−	0.930567i	$-0.619315\pi$
$883$	−11545.4	−	50583.7i	−0.440015	−	1.92783i	−0.0738934	−	0.997266i	$-0.523542\pi$
$884$	1168.96	−	2427.37i	0.0444755	−	0.0923543i
$885$	5148.31	−	10690.6i	0.195547	−	0.406056i
$886$	17833.7	+	78134.4i	0.676223	+	2.96273i
$887$		−	18264.1i		−	0.691375i	−0.938350	−	0.345688i	$-0.887646\pi$
$887$		−	18264.1i		−	0.691375i	0.938350	−	0.345688i	$-0.112354\pi$
$888$	2973.69	−	678.726i	0.112377	−	0.0256493i
$889$	−1155.00	−	921.083i	−0.0435743	−	0.0347493i
$890$	1894.45	−	8300.14i	0.0713508	−	0.312608i
$891$	5111.74	+	1166.72i	0.192200	+	0.0438683i
$892$	−45641.9	−	57233.1i	−1.71323	−	2.14833i
$893$	−17901.8	−	8621.04i	−0.670840	−	0.323059i
$894$	5554.80	−	2675.05i	0.207808	−	0.100075i
$895$	14636.8	−	18353.9i	0.546652	−	0.685480i
$896$	−33168.1	+	26450.7i	−1.23668	+	0.986221i
$897$	5359.59	+	11129.3i	0.199500	+	0.414266i
$898$	50359.8			1.87141
$899$	7049.70	−	550.597i	0.261536	−	0.0204265i
$900$	3.81050			0.000141129
$901$	−597.935	−	1241.63i	−0.0221089	−	0.0459096i
$902$	−28489.1	+	22719.3i	−1.05164	+	0.838658i
$903$	−17523.3	+	21973.5i	−0.645780	+	0.809782i
$904$	−6892.40	+	3319.20i	−0.253582	+	0.122118i
$905$	10420.5	+	5018.26i	0.382751	+	0.184323i
$906$	−11284.9	−	14150.9i	−0.413816	−	0.518909i
$907$	−47020.5	−	10732.1i	−1.72138	−	0.392894i	−0.756171	−	0.654374i	$-0.772932\pi$
$907$	−47020.5	−	10732.1i	−1.72138	−	0.392894i	−0.965209	+	0.261481i	$0.915789\pi$
$908$	−6755.47	+	29597.7i	−0.246903	+	1.08175i
$909$	1405.34	+	1120.72i	0.0512784	+	0.0408931i
$910$	−52926.0	+	12080.0i	−1.92800	+	0.440054i
$911$		−	28548.5i		−	1.03826i	−0.854695	−	0.519130i	$-0.826256\pi$
$911$		−	28548.5i		−	1.03826i	0.854695	−	0.519130i	$-0.173744\pi$
$912$	7863.01	+	34450.1i	0.285494	+	1.25083i
$913$	−9540.94	+	19812.0i	−0.345848	+	0.718160i
$914$	−23174.8	+	48123.0i	−0.838682	+	1.74154i
$915$	4113.37	+	18021.9i	0.148616	+	0.651130i
$916$		−	5095.52i		−	0.183800i
$917$	−68047.5	+	15531.4i	−2.45052	+	0.559315i
$918$	−577.473	−	460.519i	−0.0207619	−	0.0165571i
$919$	−8081.39	+	35406.9i	−0.290077	+	1.27091i	0.594341	+	0.804213i	$0.297413\pi$
$919$	−8081.39	+	35406.9i	−0.290077	+	1.27091i	−0.884418	+	0.466696i	$0.845444\pi$
$920$	−84781.3	−	19350.8i	−3.03821	−	0.693452i
$921$	15037.0	+	18855.7i	0.537985	+	0.674612i
$922$	8807.58	+	4241.51i	0.314601	+	0.151504i
$923$	−8884.20	+	4278.40i	−0.316822	+	0.152574i
$924$	75535.9	−	94719.0i	2.68934	−	3.37232i
$925$	0.353367	−	0.281801i	1.25607e−5	−	1.00168e-5i
$926$	−8988.13	−	18664.1i	−0.318972	−	0.662353i
$927$	16841.7			0.596713
$928$	−9598.20	−	30772.8i	−0.339522	−	1.08854i
$929$	11543.4			0.407673			0.203836	−	0.979005i	$-0.434659\pi$
$929$	11543.4			0.407673			0.203836	+	0.979005i	$0.434659\pi$
$930$	−3374.01	−	7006.21i	−0.118966	−	0.247035i
$931$	62659.5	−	49969.3i	2.20578	−	1.75905i
$932$	69834.9	−	87570.2i	2.45442	−	3.07774i
$933$	−2703.64	+	1302.00i	−0.0948694	+	0.0456867i
$934$	−34026.5	−	16386.3i	−1.19206	−	0.574064i
$935$	2411.17	+	3023.52i	0.0843356	+	0.105754i
$936$	12702.6	+	2899.28i	0.443586	+	0.101246i
$937$	−6936.88	+	30392.5i	−0.241855	+	1.05964i	0.697472	+	0.716612i	$0.254308\pi$
$937$	−6936.88	+	30392.5i	−0.241855	+	1.05964i	−0.939327	+	0.343024i	$0.888549\pi$
$938$	−53358.2	−	42551.7i	−1.85736	−	1.48120i
$939$	−20510.9	+	4681.47i	−0.712830	+	0.162699i
$940$		−	41919.7i		−	1.45454i
$941$	−12175.1	−	53342.5i	−0.421782	−	1.84795i	−0.521951	−	0.852976i	$-0.674796\pi$
$941$	−12175.1	−	53342.5i	−0.421782	−	1.84795i	0.100169	−	0.994970i	$-0.468062\pi$
$942$	10400.2	−	21596.3i	0.359721	−	0.746968i
$943$	−7095.15	+	14733.2i	−0.245016	+	0.508780i
$944$	9604.77	+	42081.2i	0.331153	+	1.45088i
$945$			10340.9i			0.355967i
$946$	−88371.7	+	20170.3i	−3.03722	+	0.693226i
$947$	−21243.8	−	16941.4i	−0.728966	−	0.581331i	0.187109	−	0.982339i	$-0.440088\pi$
$947$	−21243.8	−	16941.4i	−0.728966	−	0.581331i	−0.916074	+	0.401009i	$0.868660\pi$
$948$	7290.69	−	31942.6i	0.249779	−	1.09435i
$949$	21231.4	+	4845.93i	0.726239	+	0.165759i
$950$	7.16298	+	8.98209i	0.000244629	+	0.000306755i
$951$	−3370.41	−	1623.10i	−0.114924	−	0.0553446i
$952$	−8622.56	+	4152.41i	−0.293549	+	0.141366i
$953$	−5364.19	+	6726.49i	−0.182333	+	0.228638i	−0.864595	−	0.502469i	$-0.832425\pi$
$953$	−5364.19	+	6726.49i	−0.182333	+	0.228638i	0.682262	+	0.731108i	$0.260996\pi$
$954$	9291.94	−	7410.08i	0.315344	−	0.251478i
$955$	4784.34	+	9934.79i	0.162113	+	0.336631i
$956$	−45838.5			−1.55075
$957$	−15246.0	−	26216.2i	−0.514978	−	0.885526i
$958$	15455.3			0.521229
$959$	40062.6	+	83190.9i	1.34900	+	2.80122i
$960$	−2114.18	+	1686.01i	−0.0710781	+	0.0566829i
$961$	17296.1	−	21688.7i	0.580582	−	0.728027i
$962$	2483.01	−	1195.76i	0.0832179	−	0.0400756i
$963$	−7365.93	−	3547.24i	−0.246484	−	0.118700i
$964$	44103.6	+	55304.2i	1.47353	+	1.84775i
$965$	39078.9	+	8919.51i	1.30362	+	0.297543i
$966$	17412.0	−	76287.1i	0.579941	−	2.54089i
$967$	28155.8	+	22453.5i	0.936327	+	0.746696i	0.967514	−	0.252818i	$-0.0813573\pi$
$967$	28155.8	+	22453.5i	0.936327	+	0.746696i	−0.0311870	+	0.999514i	$0.509929\pi$
$968$	145759.	−	33268.5i	4.83974	−	1.10464i
$969$		−	1547.28i		−	0.0512960i
$970$	−3384.84	−	14830.0i	−0.112042	−	0.490888i
$971$	1070.73	−	2223.38i	0.0353875	−	0.0734828i	−0.882526	−	0.470264i	$-0.844159\pi$
$971$	1070.73	−	2223.38i	0.0353875	−	0.0734828i	0.917913	+	0.396781i	$0.129873\pi$
$972$	1920.31	−	3987.57i	0.0633684	−	0.131586i
$973$	3222.11	+	14117.0i	0.106162	+	0.465128i
$974$			58802.8i			1.93446i
$975$	1.88226	−	0.429614i	6.18263e−5	−	1.41115e-5i
$976$	−52573.2	−	41925.7i	−1.72421	−	1.37501i
$977$	−5605.39	+	24558.8i	−0.183554	+	0.804203i	0.796366	+	0.604815i	$0.206753\pi$
$977$	−5605.39	+	24558.8i	−0.183554	+	0.804203i	−0.979920	+	0.199389i	$0.936104\pi$
$978$	−13251.2	−	3024.50i	−0.433258	−	0.0988884i
$979$	6002.00	+	7526.27i	0.195940	+	0.245700i
$980$	152341.	+	73363.4i	4.96566	+	2.39133i
$981$	1027.29	−	494.717i	0.0334341	−	0.0161010i
$982$	29438.6	−	36914.8i	0.956642	−	1.19959i
$983$	1122.87	−	895.461i	0.0364334	−	0.0290547i	−0.605104	−	0.796147i	$-0.706868\pi$
$983$	1122.87	−	895.461i	0.0364334	−	0.0290547i	0.641537	+	0.767092i	$0.278297\pi$
$984$	7483.80	+	15540.3i	0.242454	+	0.503461i
$985$	−52042.0			−1.68345
$986$	332.655	+	4259.23i	0.0107443	+	0.137567i
$987$	21151.9			0.682141
$988$	21118.5	+	43853.0i	0.680029	+	1.41209i
$989$	−31803.6	+	25362.5i	−1.02254	+	0.815452i
$990$	−20794.1	+	26075.0i	−0.667557	+	0.837090i
$991$	−22833.7	+	10996.1i	−0.731923	+	0.352475i	−0.762440	−	0.647059i	$-0.775999\pi$
$991$	−22833.7	+	10996.1i	−0.731923	+	0.352475i	0.0305174	+	0.999534i	$0.490284\pi$
$992$	8420.41	+	4055.06i	0.269504	+	0.129786i
$993$	−11895.5	−	14916.4i	−0.380152	−	0.476696i
$994$	60897.7	+	13899.5i	1.94322	+	0.443527i
$995$	−2314.20	+	10139.2i	−0.0737337	+	0.323049i
$996$	14512.2	+	11573.1i	0.461684	+	0.368180i
$997$	8917.23	−	2035.30i	0.283261	−	0.0646526i	−0.0785297	−	0.996912i	$-0.525023\pi$
$997$	8917.23	−	2035.30i	0.283261	−	0.0646526i	0.361791	+	0.932259i	$0.382165\pi$
$998$			70164.7i			2.22548i
$999$	−116.816	−	511.803i	−0.00369958	−	0.0162089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.4.i.a.67.2	yes	96
29.13	even	14	inner	87.4.i.a.13.2	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.4.i.a.13.2	✓	96	29.13	even	14	inner
87.4.i.a.67.2	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	87.i (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22145 - 4.61288i) q^{2} +(2.34549 - 1.87047i) q^{3} +(-11.3559 + 14.2399i) q^{4} +(-10.0741 + 4.85142i) q^{5} +(-13.8386 - 6.66434i) q^{6} +(21.3564 + 26.7801i) q^{7} +(50.9810 + 11.6361i) q^{8} +(2.00269 - 8.77435i) q^{9} +O(q^{10})\)	\(q+(-2.22145 - 4.61288i) q^{2} +(2.34549 - 1.87047i) q^{3} +(-11.3559 + 14.2399i) q^{4} +(-10.0741 + 4.85142i) q^{5} +(-13.8386 - 6.66434i) q^{6} +(21.3564 + 26.7801i) q^{7} +(50.9810 + 11.6361i) q^{8} +(2.00269 - 8.77435i) q^{9} +(44.7580 + 35.6933i) q^{10} +(-63.1079 + 14.4040i) q^{11} +54.6404i q^{12} +(6.16044 + 26.9906i) q^{13} +(76.0911 - 158.005i) q^{14} +(-14.5543 + 30.2222i) q^{15} +(-27.1526 - 118.963i) q^{16} +5.34309i q^{17} +(-44.9239 + 10.2536i) q^{18} +(-75.4691 - 60.1846i) q^{19} +(45.3168 - 198.546i) q^{20} +(100.183 + 22.8660i) q^{21} +(206.635 + 259.112i) q^{22} +(134.000 + 64.5312i) q^{23} +(141.341 - 68.0660i) q^{24} +(0.0144936 - 0.0181744i) q^{25} +(110.819 - 88.3756i) q^{26} +(-11.7149 - 24.3262i) q^{27} -623.866 q^{28} +(-56.5979 + 145.553i) q^{29} +171.743 q^{30} +(-19.6457 - 40.7947i) q^{31} +(-161.377 + 128.694i) q^{32} +(-121.077 + 151.826i) q^{33} +(24.6470 - 11.8694i) q^{34} +(-345.067 - 166.176i) q^{35} +(102.203 + 128.159i) q^{36} +(18.9557 + 4.32651i) q^{37} +(-109.974 + 481.826i) q^{38} +(64.9344 + 51.7835i) q^{39} +(-570.038 + 130.107i) q^{40} +109.949i q^{41} +(-117.072 - 512.926i) q^{42} +(-118.670 + 246.421i) q^{43} +(511.538 - 1062.22i) q^{44} +(22.3928 + 98.1094i) q^{45} -761.480i q^{46} +(200.679 - 45.8038i) q^{47} +(-286.204 - 228.240i) q^{48} +(-184.752 + 809.451i) q^{49} +(-0.116033 - 0.0264837i) q^{50} +(9.99409 + 12.5322i) q^{51} +(-454.300 - 218.780i) q^{52} +(-232.380 + 111.908i) q^{53} +(-86.1897 + 108.078i) q^{54} +(565.874 - 451.270i) q^{55} +(777.155 + 1613.78i) q^{56} -289.586 q^{57} +(797.148 - 62.2590i) q^{58} -353.732 q^{59} +(-265.084 - 550.452i) q^{60} +(430.847 - 343.589i) q^{61} +(-144.539 + 181.247i) q^{62} +(277.748 - 133.756i) q^{63} +(72.6311 + 34.9773i) q^{64} +(-193.004 - 242.019i) q^{65} +(969.321 + 221.241i) q^{66} +(86.5961 - 379.402i) q^{67} +(-76.0849 - 60.6757i) q^{68} +(435.001 - 99.2861i) q^{69} +1960.90i q^{70} +(79.2572 + 347.248i) q^{71} +(204.198 - 424.022i) q^{72} +(341.302 - 708.721i) q^{73} +(-22.1513 - 97.0513i) q^{74} -0.0697377i q^{75} +(1714.04 - 391.219i) q^{76} +(-1733.50 - 1382.42i) q^{77} +(94.6226 - 414.569i) q^{78} +(-584.596 - 133.430i) q^{79} +(850.679 + 1066.72i) q^{80} +(-72.9785 - 35.1446i) q^{81} +(507.182 - 244.246i) q^{82} +(211.805 - 265.595i) q^{83} +(-1463.27 + 1166.92i) q^{84} +(-25.9216 - 53.8267i) q^{85} +1400.33 q^{86} +(139.502 + 447.258i) q^{87} -3384.91 q^{88} +(-64.5251 - 133.988i) q^{89} +(402.822 - 321.240i) q^{90} +(-591.246 + 741.399i) q^{91} +(-2440.61 + 1175.34i) q^{92} +(-122.384 - 58.9371i) q^{93} +(-657.086 - 823.959i) q^{94} +(1052.26 + 240.172i) q^{95} +(-137.791 + 603.703i) q^{96} +(-207.741 - 165.668i) q^{97} +(4144.31 - 945.913i) q^{98} +582.578i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9}+O(q^{10}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9} - 140 q^{11} + 304 q^{13} - 294 q^{15} - 692 q^{16} + 800 q^{20} - 528 q^{22} + 324 q^{23} - 54 q^{24} - 170 q^{25} - 1288 q^{26} - 956 q^{28} - 478 q^{29} + 1056 q^{30} - 616 q^{31} - 406 q^{32} + 72 q^{33} + 34 q^{34} + 1032 q^{35} - 468 q^{36} + 1792 q^{37} + 1912 q^{38} + 2688 q^{40} + 762 q^{42} - 1092 q^{43} + 1750 q^{44} + 630 q^{45} + 2772 q^{47} + 1848 q^{48} - 1304 q^{49} - 882 q^{50} - 192 q^{51} + 1304 q^{52} - 3066 q^{53} - 108 q^{54} - 1974 q^{55} - 4704 q^{56} - 1752 q^{57} - 6092 q^{58} - 640 q^{59} - 7812 q^{60} - 252 q^{61} - 532 q^{62} - 18 q^{63} - 454 q^{64} - 8346 q^{65} + 5628 q^{66} + 744 q^{67} + 5530 q^{68} + 2100 q^{69} + 3216 q^{71} + 2142 q^{72} + 6510 q^{73} + 5090 q^{74} + 6594 q^{76} - 8876 q^{77} - 2118 q^{78} + 7092 q^{80} - 1296 q^{81} - 10590 q^{82} + 572 q^{83} - 2520 q^{85} + 12680 q^{86} - 2238 q^{87} + 6472 q^{88} - 2800 q^{89} + 1576 q^{91} - 10418 q^{92} + 60 q^{93} - 17564 q^{94} + 1374 q^{96} + 11690 q^{97} + 22554 q^{98}+O(q^{100}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9 - 140 * q^11 + 304 * q^13 - 294 * q^15 - 692 * q^16 + 800 * q^20 - 528 * q^22 + 324 * q^23 - 54 * q^24 - 170 * q^25 - 1288 * q^26 - 956 * q^28 - 478 * q^29 + 1056 * q^30 - 616 * q^31 - 406 * q^32 + 72 * q^33 + 34 * q^34 + 1032 * q^35 - 468 * q^36 + 1792 * q^37 + 1912 * q^38 + 2688 * q^40 + 762 * q^42 - 1092 * q^43 + 1750 * q^44 + 630 * q^45 + 2772 * q^47 + 1848 * q^48 - 1304 * q^49 - 882 * q^50 - 192 * q^51 + 1304 * q^52 - 3066 * q^53 - 108 * q^54 - 1974 * q^55 - 4704 * q^56 - 1752 * q^57 - 6092 * q^58 - 640 * q^59 - 7812 * q^60 - 252 * q^61 - 532 * q^62 - 18 * q^63 - 454 * q^64 - 8346 * q^65 + 5628 * q^66 + 744 * q^67 + 5530 * q^68 + 2100 * q^69 + 3216 * q^71 + 2142 * q^72 + 6510 * q^73 + 5090 * q^74 + 6594 * q^76 - 8876 * q^77 - 2118 * q^78 + 7092 * q^80 - 1296 * q^81 - 10590 * q^82 + 572 * q^83 - 2520 * q^85 + 12680 * q^86 - 2238 * q^87 + 6472 * q^88 - 2800 * q^89 + 1576 * q^91 - 10418 * q^92 + 60 * q^93 - 17564 * q^94 + 1374 * q^96 + 11690 * q^97 + 22554 * q^98

Introduction

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