LMFDB - Embedded newform 42.5.h.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,5,Mod(11,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("42.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	42.h (of order $6$, 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:	$4.34153844952$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} - 684 x^{17} - 3593 x^{16} - 62280 x^{15} + 1340206 x^{14} + 6921828 x^{13} + \cdots + 81\!\cdots\!09 $ x^20 - 20x^18 - 684x^17 - 3593x^16 - 62280x^15 + 1340206x^14 + 6921828x^13 + 37679467x^12 - 380890548x^11 - 2077817540x^10 - 73982451888x^9 + 507364948243x^8 + 687686868324x^7 + 27986581473280x^6 - 42677138798460x^5 - 1338007627265483x^4 - 14348052126267588x^3 + 52054868201143878x^2 - 406604690130980484x + 8145239244704821809
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Root			$6.90852 + 4.56068i$ of defining polynomial
Character	$\chi$	$=$	42.11
Dual form			42.5.h.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(-8.13327 + 3.85357i) q^{3} +(4.00000 - 6.92820i) q^{4} +(30.1838 - 17.4266i) q^{5} +(-14.4726 + 20.9415i) q^{6} +(31.6264 - 37.4269i) q^{7} -22.6274i q^{8} +(51.3000 - 62.6842i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.41421i) q^{2} +(-8.13327 + 3.85357i) q^{3} +(4.00000 - 6.92820i) q^{4} +(30.1838 - 17.4266i) q^{5} +(-14.4726 + 20.9415i) q^{6} +(31.6264 - 37.4269i) q^{7} -22.6274i q^{8} +(51.3000 - 62.6842i) q^{9} +(49.2899 - 85.3727i) q^{10} +(119.285 + 68.8691i) q^{11} +(-5.83475 + 71.7632i) q^{12} -238.320 q^{13} +(24.5390 - 136.403i) q^{14} +(-178.338 + 258.051i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-198.234 - 114.451i) q^{17} +(37.0100 - 226.093i) q^{18} +(258.940 + 448.497i) q^{19} -278.826i q^{20} +(-112.999 + 426.277i) q^{21} +389.582 q^{22} +(187.697 - 108.367i) q^{23} +(87.1963 + 184.035i) q^{24} +(294.875 - 510.738i) q^{25} +(-583.763 + 337.036i) q^{26} +(-175.679 + 707.515i) q^{27} +(-132.795 - 368.822i) q^{28} -565.551i q^{29} +(-71.8986 + 884.301i) q^{30} +(-737.320 + 1277.08i) q^{31} +(-156.767 - 90.5097i) q^{32} +(-1235.57 - 100.458i) q^{33} -647.430 q^{34} +(302.382 - 1680.83i) q^{35} +(-229.089 - 606.154i) q^{36} +(410.451 + 710.922i) q^{37} +(1268.54 + 732.393i) q^{38} +(1938.32 - 918.383i) q^{39} +(-394.320 - 682.982i) q^{40} +747.708i q^{41} +(326.057 + 1203.97i) q^{42} -984.000 q^{43} +(954.278 - 550.953i) q^{44} +(456.055 - 2786.03i) q^{45} +(306.508 - 530.887i) q^{46} +(254.566 - 146.973i) q^{47} +(473.851 + 327.477i) q^{48} +(-400.540 - 2367.35i) q^{49} -1668.06i q^{50} +(2053.33 + 166.947i) q^{51} +(-953.281 + 1651.13i) q^{52} +(2707.93 + 1563.43i) q^{53} +(570.255 + 1981.50i) q^{54} +4800.62 q^{55} +(-846.873 - 715.624i) q^{56} +(-3834.34 - 2649.91i) q^{57} +(-799.810 - 1385.31i) q^{58} +(-3251.78 - 1877.42i) q^{59} +(1074.48 + 2267.77i) q^{60} +(1137.12 + 1969.54i) q^{61} +4170.91i q^{62} +(-723.638 - 3902.47i) q^{63} -512.000 q^{64} +(-7193.41 + 4153.12i) q^{65} +(-3168.58 + 1501.28i) q^{66} +(-1378.19 + 2387.09i) q^{67} +(-1585.87 + 915.604i) q^{68} +(-1108.99 + 1604.68i) q^{69} +(-1636.37 - 4544.80i) q^{70} +5478.18i q^{71} +(-1418.38 - 1160.79i) q^{72} +(1241.69 - 2150.67i) q^{73} +(2010.79 + 1160.93i) q^{74} +(-430.130 + 5290.29i) q^{75} +4143.04 q^{76} +(6350.10 - 2286.37i) q^{77} +(3449.11 - 4990.77i) q^{78} +(2969.71 + 5143.70i) q^{79} +(-1931.76 - 1115.30i) q^{80} +(-1297.62 - 6431.40i) q^{81} +(1057.42 + 1831.50i) q^{82} -3543.33i q^{83} +(2501.34 + 2487.99i) q^{84} -7977.95 q^{85} +(-2410.30 + 1391.59i) q^{86} +(2179.39 + 4599.78i) q^{87} +(1558.33 - 2699.11i) q^{88} +(-7546.88 + 4357.19i) q^{89} +(-2822.94 - 7469.32i) q^{90} +(-7537.21 + 8919.57i) q^{91} -1733.87i q^{92} +(1075.52 - 13228.1i) q^{93} +(415.704 - 720.020i) q^{94} +(15631.6 + 9024.91i) q^{95} +(1623.82 + 132.025i) q^{96} +5480.25 q^{97} +(-4329.06 - 5232.36i) q^{98} +(10436.3 - 3944.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$3$	−8.13327	+	3.85357i	−0.903696	+	0.428174i
$3$	−8.13327	+	3.85357i	−0.903696	+	0.428174i
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	30.1838	−	17.4266i	1.20735	−	0.697065i	0.245172	−	0.969480i	$-0.421156\pi$
$5$	30.1838	−	17.4266i	1.20735	−	0.697065i	0.962180	+	0.272414i	$0.0878222\pi$
$6$	−14.4726	+	20.9415i	−0.402016	+	0.581707i
$7$	31.6264	−	37.4269i	0.645437	−	0.763813i
$7$	31.6264	−	37.4269i	0.645437	−	0.763813i
$8$		−	22.6274i		−	0.353553i
$9$	51.3000	−	62.6842i	0.633333	−	0.773879i
$10$	49.2899	−	85.3727i	0.492899	−	0.853727i
$11$	119.285	+	68.8691i	0.985824	+	0.569166i	0.904023	−	0.427483i	$-0.140600\pi$
$11$	119.285	+	68.8691i	0.985824	+	0.569166i	0.0818007	+	0.996649i	$0.473933\pi$
$12$	−5.83475	+	71.7632i	−0.0405191	+	0.498355i
$13$	−238.320			−1.41018			−0.705089	−	0.709119i	$-0.749093\pi$
$13$	−238.320			−1.41018			−0.705089	+	0.709119i	$0.749093\pi$
$14$	24.5390	−	136.403i	0.125199	−	0.695935i
$15$	−178.338	+	258.051i	−0.792614	+	1.14689i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−198.234	−	114.451i	−0.685931	−	0.396023i	0.116155	−	0.993231i	$-0.462943\pi$
$17$	−198.234	−	114.451i	−0.685931	−	0.396023i	−0.802086	+	0.597209i	$0.796276\pi$
$18$	37.0100	−	226.093i	0.114228	−	0.697819i
$19$	258.940	+	448.497i	0.717286	+	1.24238i	0.962071	+	0.272798i	$0.0879491\pi$
$19$	258.940	+	448.497i	0.717286	+	1.24238i	−0.244786	+	0.969577i	$0.578718\pi$
$20$		−	278.826i		−	0.697065i
$21$	−112.999	+	426.277i	−0.256234	+	0.966615i
$22$	389.582			0.804922
$23$	187.697	−	108.367i	0.354814	−	0.204852i	−0.311989	−	0.950086i	$-0.600995\pi$
$23$	187.697	−	108.367i	0.354814	−	0.204852i	0.666804	+	0.745233i	$0.267662\pi$
$24$	87.1963	+	184.035i	0.151383	+	0.319505i
$25$	294.875	−	510.738i	0.471800	−	0.817181i
$26$	−583.763	+	337.036i	−0.863554	+	0.498573i
$27$	−175.679	+	707.515i	−0.240986	+	0.970529i
$28$	−132.795	−	368.822i	−0.169382	−	0.470436i
$29$		−	565.551i		−	0.672474i	−0.941777	−	0.336237i	$-0.890846\pi$
$29$		−	565.551i		−	0.672474i	0.941777	−	0.336237i	$-0.109154\pi$
$30$	−71.8986	+	884.301i	−0.0798874	+	0.982557i
$31$	−737.320	+	1277.08i	−0.767242	+	1.32890i	0.171810	+	0.985130i	$0.445038\pi$
$31$	−737.320	+	1277.08i	−0.767242	+	1.32890i	−0.939053	+	0.343773i	$0.888295\pi$
$32$	−156.767	−	90.5097i	−0.153093	−	0.0883883i
$33$	−1235.57	−	100.458i	−1.13459	−	0.0922483i
$34$	−647.430			−0.560060
$35$	302.382	−	1680.83i	0.246842	−	1.37210i
$36$	−229.089	−	606.154i	−0.176766	−	0.467711i
$37$	410.451	+	710.922i	0.299818	+	0.519300i	0.976094	−	0.217348i	$-0.0697407\pi$
$37$	410.451	+	710.922i	0.299818	+	0.519300i	−0.676276	+	0.736648i	$0.736407\pi$
$38$	1268.54	+	732.393i	0.878492	+	0.507198i
$39$	1938.32	−	918.383i	1.27437	−	0.603802i
$40$	−394.320	−	682.982i	−0.246450	−	0.426863i
$41$			747.708i			0.444800i	0.974956	+	0.222400i	$0.0713890\pi$
$41$			747.708i			0.444800i	−0.974956	+	0.222400i	$0.928611\pi$
$42$	326.057	+	1203.97i	0.184840	+	0.682521i
$43$	−984.000			−0.532180			−0.266090	−	0.963948i	$-0.585732\pi$
$43$	−984.000			−0.532180			−0.266090	+	0.963948i	$0.585732\pi$
$44$	954.278	−	550.953i	0.492912	−	0.284583i
$45$	456.055	−	2786.03i	0.225212	−	1.37582i
$46$	306.508	−	530.887i	0.144852	−	0.250892i
$47$	254.566	−	146.973i	0.115240	−	0.0665339i	−0.441272	−	0.897373i	$-0.645473\pi$
$47$	254.566	−	146.973i	0.115240	−	0.0665339i	0.556512	+	0.830839i	$0.312139\pi$
$48$	473.851	+	327.477i	0.205664	+	0.142134i
$49$	−400.540	−	2367.35i	−0.166822	−	0.985987i
$50$		−	1668.06i		−	0.667225i
$51$	2053.33	+	166.947i	0.789440	+	0.0641859i
$52$	−953.281	+	1651.13i	−0.352545	+	0.610625i
$53$	2707.93	+	1563.43i	0.964020	+	0.556577i	0.897408	−	0.441202i	$-0.145448\pi$
$53$	2707.93	+	1563.43i	0.964020	+	0.556577i	0.0666122	+	0.997779i	$0.478781\pi$
$54$	570.255	+	1981.50i	0.195561	+	0.679526i
$55$	4800.62			1.58698
$56$	−846.873	−	715.624i	−0.270049	−	0.228196i
$57$	−3834.34	−	2649.91i	−1.18016	−	0.815606i
$58$	−799.810	−	1385.31i	−0.237756	−	0.411805i
$59$	−3251.78	−	1877.42i	−0.934153	−	0.539333i	−0.0460300	−	0.998940i	$-0.514657\pi$
$59$	−3251.78	−	1877.42i	−0.934153	−	0.539333i	−0.888122	+	0.459607i	$0.847990\pi$
$60$	1074.48	+	2267.77i	0.298465	+	0.629935i
$61$	1137.12	+	1969.54i	0.305595	+	0.529305i	0.977394	−	0.211428i	$-0.0678115\pi$
$61$	1137.12	+	1969.54i	0.305595	+	0.529305i	−0.671799	+	0.740733i	$0.734478\pi$
$62$			4170.91i			1.08504i
$63$	−723.638	−	3902.47i	−0.182322	−	0.983239i
$64$	−512.000			−0.125000
$65$	−7193.41	+	4153.12i	−1.70258	+	0.982986i
$66$	−3168.58	+	1501.28i	−0.727405	+	0.344647i
$67$	−1378.19	+	2387.09i	−0.307014	+	0.531765i	−0.977708	−	0.209970i	$-0.932663\pi$
$67$	−1378.19	+	2387.09i	−0.307014	+	0.531765i	0.670693	+	0.741735i	$0.265997\pi$
$68$	−1585.87	+	915.604i	−0.342966	+	0.198011i
$69$	−1108.99	+	1604.68i	−0.232932	+	0.337046i
$70$	−1636.37	−	4544.80i	−0.333953	−	0.927510i
$71$			5478.18i			1.08672i	0.839498	+	0.543362i	$0.182849\pi$
$71$			5478.18i			1.08672i	−0.839498	+	0.543362i	$0.817151\pi$
$72$	−1418.38	−	1160.79i	−0.273608	−	0.223917i
$73$	1241.69	−	2150.67i	0.233006	−	0.403578i	−0.725685	−	0.688027i	$-0.758477\pi$
$73$	1241.69	−	2150.67i	0.233006	−	0.403578i	0.958691	+	0.284449i	$0.0918105\pi$
$74$	2010.79	+	1160.93i	0.367201	+	0.212003i
$75$	−430.130	+	5290.29i	−0.0764675	+	0.940496i
$76$	4143.04			0.717286
$77$	6350.10	−	2286.37i	1.07102	−	0.385625i
$78$	3449.11	−	4990.77i	0.566914	−	0.820311i
$79$	2969.71	+	5143.70i	0.475840	+	0.824178i	0.999617	−	0.0276769i	$-0.00881096\pi$
$79$	2969.71	+	5143.70i	0.475840	+	0.824178i	−0.523777	+	0.851855i	$0.675478\pi$
$80$	−1931.76	−	1115.30i	−0.301838	−	0.174266i
$81$	−1297.62	−	6431.40i	−0.197778	−	0.980247i
$82$	1057.42	+	1831.50i	0.157260	+	0.272383i
$83$		−	3543.33i		−	0.514346i	−0.966365	−	0.257173i	$-0.917209\pi$
$83$		−	3543.33i		−	0.514346i	0.966365	−	0.257173i	$-0.0827909\pi$
$84$	2501.34	+	2487.99i	0.354498	+	0.352606i
$85$	−7977.95			−1.10421
$86$	−2410.30	+	1391.59i	−0.325892	+	0.188154i
$87$	2179.39	+	4599.78i	0.287936	+	0.607713i
$88$	1558.33	−	2699.11i	0.201231	−	0.348541i
$89$	−7546.88	+	4357.19i	−0.952769	+	0.550081i	−0.893940	−	0.448187i	$-0.852070\pi$
$89$	−7546.88	+	4357.19i	−0.952769	+	0.550081i	−0.0588288	+	0.998268i	$0.518737\pi$
$90$	−2822.94	−	7469.32i	−0.348512	−	0.922138i
$91$	−7537.21	+	8919.57i	−0.910181	+	1.07711i
$92$		−	1733.87i		−	0.204852i
$93$	1075.52	−	13228.1i	0.124352	−	1.52944i
$94$	415.704	−	720.020i	0.0470466	−	0.0814871i
$95$	15631.6	+	9024.91i	1.73203	+	0.999990i
$96$	1623.82	+	132.025i	0.176195	+	0.0143257i
$97$	5480.25			0.582448			0.291224	−	0.956655i	$-0.405938\pi$
$97$	5480.25			0.582448			0.291224	+	0.956655i	$0.405938\pi$
$98$	−4329.06	−	5232.36i	−0.450756	−	0.544811i
$99$	10436.3	−	3944.28i	1.06482	−	0.402437i
$100$	−2359.00	−	4085.90i	−0.235900	−	0.408590i
$101$	−4782.56	−	2761.21i	−0.468833	−	0.270681i	0.246918	−	0.969036i	$-0.420582\pi$
$101$	−4782.56	−	2761.21i	−0.468833	−	0.270681i	−0.715751	+	0.698356i	$0.753915\pi$
$102$	5265.72	−	2494.92i	0.506124	−	0.239804i
$103$	−5703.26	−	9878.34i	−0.537587	−	0.931129i	−0.999033	−	0.0439602i	$-0.986003\pi$
$103$	−5703.26	−	9878.34i	−0.537587	−	0.931129i	0.461446	−	0.887168i	$-0.347331\pi$
$104$			5392.57i			0.498573i
$105$	4017.83	+	14835.9i	0.364429	+	1.34566i
$106$	8844.07			0.787119
$107$	7496.68	−	4328.21i	0.654789	−	0.378042i	−0.135500	−	0.990777i	$-0.543264\pi$
$107$	7496.68	−	4328.21i	0.654789	−	0.378042i	0.790288	+	0.612735i	$0.209931\pi$
$108$	4199.10	+	4047.20i	0.360005	+	0.346982i
$109$	2955.62	−	5119.28i	0.248768	−	0.430879i	−0.714416	−	0.699721i	$-0.753308\pi$
$109$	2955.62	−	5119.28i	0.248768	−	0.430879i	0.963184	+	0.268842i	$0.0866409\pi$
$110$	11759.1	−	6789.10i	0.971824	−	0.561083i
$111$	−6077.89	−	4200.41i	−0.493295	−	0.340915i
$112$	−3086.45	−	555.254i	−0.246050	−	0.0442645i
$113$		−	7001.56i		−	0.548325i	−0.961683	−	0.274163i	$-0.911599\pi$
$113$		−	7001.56i		−	0.548325i	0.961683	−	0.274163i	$-0.0884006\pi$
$114$	−13139.7	−	1068.33i	−1.01106	−	0.0822047i
$115$	3776.93	−	6541.84i	0.285591	−	0.494657i
$116$	−3918.25	−	2262.20i	−0.291190	−	0.168119i
$117$	−12225.8	+	14938.9i	−0.893113	+	1.09131i
$118$	−10620.3			−0.762732
$119$	−10553.0	+	3799.62i	−0.745213	+	0.268316i
$120$	5839.02	+	4035.33i	0.405488	+	0.280231i
$121$	2165.40	+	3750.58i	0.147899	+	0.256169i
$122$	5570.71	+	3216.25i	0.374275	+	0.216088i
$123$	−2881.34	−	6081.31i	−0.190452	−	0.401964i
$124$	5898.56	+	10216.6i	0.383621	+	0.664451i
$125$			1228.60i			0.0786303i
$126$	−7291.48	−	8535.69i	−0.459277	−	0.537648i
$127$	−26391.8			−1.63629			−0.818147	−	0.575009i	$-0.804998\pi$
$127$	−26391.8			−1.63629			−0.818147	+	0.575009i	$0.804998\pi$
$128$	−1254.14	+	724.077i	−0.0765466	+	0.0441942i
$129$	8003.14	−	3791.91i	0.480929	−	0.227866i
$130$	−11746.8	+	20346.0i	−0.695076	+	1.20391i
$131$	24305.6	−	14032.8i	1.41633	−	0.817717i	0.420354	−	0.907360i	$-0.361906\pi$
$131$	24305.6	−	14032.8i	1.41633	−	0.817717i	0.995974	+	0.0896427i	$0.0285725\pi$
$132$	−5638.26	+	8158.42i	−0.323592	+	0.468229i
$133$	24975.2	+	4493.05i	1.41191	+	0.254003i
$134$			7796.21i			0.434184i
$135$	7026.96	+	24417.0i	0.385567	+	1.33975i
$136$	−2589.72	+	4485.53i	−0.140015	+	0.242513i
$137$	−25614.4	−	14788.5i	−1.36472	−	0.787922i	−0.374472	−	0.927238i	$-0.622176\pi$
$137$	−25614.4	−	14788.5i	−1.36472	−	0.787922i	−0.990248	+	0.139316i	$0.955509\pi$
$138$	−447.099	+	5498.99i	−0.0234771	+	0.288752i
$139$	17792.7			0.920901			0.460451	−	0.887685i	$-0.347688\pi$
$139$	17792.7			0.920901			0.460451	+	0.887685i	$0.347688\pi$
$140$	−10435.6	−	8818.27i	−0.532428	−	0.449912i
$141$	−1504.08	+	2176.36i	−0.0756540	+	0.109469i
$142$	7747.32	+	13418.7i	0.384215	+	0.665480i
$143$	−28427.9	−	16412.9i	−1.39019	−	0.802625i
$144$	−5115.91	−	837.440i	−0.246716	−	0.0403858i
$145$	−9855.65	−	17070.5i	−0.468758	−	0.811913i
$146$		−	7024.05i		−	0.329520i
$147$	12380.5	+	17710.8i	0.572931	+	0.819604i
$148$	6567.21			0.299818
$149$	12676.3	−	7318.67i	0.570979	−	0.329655i	−0.186561	−	0.982443i	$-0.559734\pi$
$149$	12676.3	−	7318.67i	0.570979	−	0.329655i	0.757540	+	0.652788i	$0.226401\pi$
$150$	6428.00	+	13566.8i	0.285689	+	0.602969i
$151$	1773.08	−	3071.07i	0.0777633	−	0.134690i	−0.824521	−	0.565831i	$-0.808555\pi$
$151$	1773.08	−	3071.07i	0.0777633	−	0.134690i	0.902285	+	0.431141i	$0.141889\pi$
$152$	10148.3	−	5859.15i	0.439246	−	0.253599i
$153$	−17343.6	+	6554.83i	−0.740897	+	0.280013i
$154$	12321.1	−	14580.8i	0.519526	−	0.614810i
$155$			51396.0i			2.13927i
$156$	1390.54	−	17102.6i	0.0571391	−	0.702770i
$157$	2735.50	−	4738.03i	0.110978	−	0.192220i	−0.805187	−	0.593021i	$-0.797935\pi$
$157$	2735.50	−	4738.03i	0.110978	−	0.192220i	0.916165	+	0.400801i	$0.131268\pi$
$158$	14548.6	+	8399.62i	0.582782	+	0.336469i
$159$	−28049.1	−	2280.55i	−1.10949	−	0.0902080i
$160$	−6309.11			−0.246450
$161$	1880.35	−	10452.2i	0.0725415	−	0.403231i
$162$	−12273.9	−	13918.5i	−0.467683	−	0.530351i
$163$	−8748.94	−	15153.6i	−0.329291	−	0.570349i	0.653080	−	0.757289i	$-0.273476\pi$
$163$	−8748.94	−	15153.6i	−0.329291	−	0.570349i	−0.982371	+	0.186940i	$0.940143\pi$
$164$	5180.27	+	2990.83i	0.192604	+	0.111200i
$165$	−39044.7	+	18499.5i	−1.43415	+	0.679505i
$166$	−5011.02	−	8679.34i	−0.181849	−	0.314971i
$167$		−	14138.1i		−	0.506941i	−0.967343	−	0.253471i	$-0.918428\pi$
$167$		−	14138.1i		−	0.506941i	0.967343	−	0.253471i	$-0.0815721\pi$
$168$	9645.55	+	2556.88i	0.341750	+	0.0905923i
$169$	28235.5			0.988603
$170$	−19541.9	+	11282.5i	−0.676190	+	0.390399i
$171$	41397.3	+	6776.47i	1.41573	+	0.231745i
$172$	−3936.00	+	6817.35i	−0.133045	+	0.230441i
$173$	50974.9	−	29430.3i	1.70319	−	0.983339i	0.760705	−	0.649097i	$-0.224853\pi$
$173$	50974.9	−	29430.3i	1.70319	−	0.983339i	0.942487	−	0.334241i	$-0.108480\pi$
$174$	11843.5	+	8184.98i	0.391183	+	0.270346i
$175$	−9789.49	−	27189.0i	−0.319657	−	0.887806i
$176$		−	8815.24i		−	0.284583i
$177$	33682.4	+	2738.57i	1.07512	+	0.0874132i
$178$	−12324.0	+	21345.8i	−0.388966	+	0.673709i
$179$	−26712.9	−	15422.7i	−0.833709	−	0.481342i	0.0214119	−	0.999771i	$-0.493184\pi$
$179$	−26712.9	−	15422.7i	−0.833709	−	0.481342i	−0.855121	+	0.518429i	$0.826517\pi$
$180$	−17478.0	−	14303.8i	−0.539444	−	0.441475i
$181$	−16622.6			−0.507390			−0.253695	−	0.967284i	$-0.581646\pi$
$181$	−16622.6			−0.507390			−0.253695	+	0.967284i	$0.581646\pi$
$182$	−5848.14	+	32507.6i	−0.176553	+	0.981392i
$183$	−16838.3	−	11636.9i	−0.502799	−	0.347483i
$184$	−2452.06	−	4247.09i	−0.0724262	−	0.125446i
$185$	24777.9	+	14305.6i	0.723972	+	0.417985i
$186$	−16072.9	−	33923.1i	−0.464588	−	0.980551i
$187$	−15764.2	−	27304.4i	−0.450805	−	0.780817i
$188$		−	2351.58i		−	0.0665339i
$189$	20924.0	+	28951.3i	0.585762	+	0.810483i
$190$	51052.6			1.41420
$191$	3237.41	−	1869.12i	0.0887423	−	0.0512354i	−0.454972	−	0.890506i	$-0.650351\pi$
$191$	3237.41	−	1869.12i	0.0887423	−	0.0512354i	0.543714	+	0.839270i	$0.317017\pi$
$192$	4164.23	−	1973.03i	0.112962	−	0.0535218i
$193$	−17397.2	+	30132.9i	−0.467052	+	0.808958i	−0.999292	−	0.0376357i	$-0.988017\pi$
$193$	−17397.2	+	30132.9i	−0.467052	+	0.808958i	0.532239	+	0.846594i	$0.321351\pi$
$194$	13423.8	−	7750.25i	0.356675	−	0.205926i
$195$	42501.6	−	61498.7i	1.11773	−	1.61732i
$196$	−18003.7	−	6694.40i	−0.468650	−	0.174261i
$197$			56798.6i			1.46354i	0.681551	+	0.731771i	$0.261306\pi$
$197$			56798.6i			1.46354i	−0.681551	+	0.731771i	$0.738694\pi$
$198$	19985.6	−	24420.7i	0.509784	−	0.622912i
$199$	−11490.6	+	19902.2i	−0.290159	+	0.502569i	−0.973847	−	0.227205i	$-0.927041\pi$
$199$	−11490.6	+	19902.2i	−0.290159	+	0.502569i	0.683689	+	0.729774i	$0.260375\pi$
$200$	−11556.7	−	6672.25i	−0.288917	−	0.166806i
$201$	2010.35	−	24725.8i	0.0497598	−	0.612009i
$202$	−15619.8			−0.382800
$203$	−21166.8	−	17886.4i	−0.513645	−	0.434040i
$204$	9369.98	−	13558.1i	0.225153	−	0.325791i
$205$	13030.0	+	22568.7i	0.310054	+	0.537030i
$206$	−27940.2	−	16131.3i	−0.658407	−	0.380132i
$207$	2835.96	−	17324.8i	0.0661850	−	0.404323i
$208$	7626.24	+	13209.0i	0.176272	+	0.305313i
$209$			71331.9i			1.63302i
$210$	30822.7	+	30658.2i	0.698928	+	0.695197i
$211$	2751.12			0.0617937			0.0308969	−	0.999523i	$-0.490164\pi$
$211$	2751.12			0.0617937			0.0308969	+	0.999523i	$0.490164\pi$
$212$	21663.5	−	12507.4i	0.482010	−	0.278289i
$213$	−21110.5	−	44555.5i	−0.465308	−	0.982069i
$214$	12242.0	−	21203.8i	0.267316	−	0.463006i
$215$	−29700.9	+	17147.8i	−0.642528	+	0.370964i
$216$	16009.2	+	3975.15i	0.343134	+	0.0852013i
$217$	24478.1	+	67984.9i	0.519827	+	1.44375i
$218$		−	16719.5i		−	0.351811i
$219$	−1811.24	+	22276.9i	−0.0377648	+	0.464479i
$220$	19202.5	−	33259.7i	0.396746	−	0.687184i
$221$	47243.2	+	27275.9i	0.967285	+	0.558462i
$222$	−20828.0	−	1693.43i	−0.422612	−	0.0343607i
$223$	−75430.8			−1.51684			−0.758418	−	0.651768i	$-0.774028\pi$
$223$	−75430.8			−1.51684			−0.758418	+	0.651768i	$0.774028\pi$
$224$	−8345.48	+	3004.81i	−0.166324	+	0.0598855i
$225$	−16888.1	−	44684.8i	−0.333593	−	0.882664i
$226$	−9901.71	−	17150.3i	−0.193862	−	0.335779i
$227$	−17904.3	−	10337.0i	−0.347461	−	0.200606i	0.316106	−	0.948724i	$-0.397625\pi$
$227$	−17904.3	−	10337.0i	−0.347461	−	0.200606i	−0.663566	+	0.748118i	$0.730958\pi$
$228$	−33696.5	+	15965.5i	−0.648208	+	0.307123i
$229$	34509.0	+	59771.3i	0.658054	+	1.13978i	0.981119	+	0.193406i	$0.0619534\pi$
$229$	34509.0	+	59771.3i	0.658054	+	1.13978i	−0.323065	+	0.946377i	$0.604713\pi$
$230$		−	21365.6i		−	0.403886i
$231$	−42836.4	+	43066.2i	−0.802765	+	0.807073i
$232$	−12797.0			−0.237756
$233$	−82098.9	+	47399.8i	−1.51226	+	0.873101i	−0.512359	+	0.858772i	$0.671228\pi$
$233$	−82098.9	+	47399.8i	−1.51226	+	0.873101i	−0.999897	+	0.0143297i	$0.995439\pi$
$234$	−8820.23	+	53882.6i	−0.161082	+	0.984050i
$235$	5122.50	−	8872.44i	0.0927570	−	0.160660i
$236$	−26014.3	+	15019.4i	−0.467076	+	0.269667i
$237$	−43975.1	−	30391.0i	−0.782906	−	0.541064i
$238$	−20475.9	+	24231.3i	−0.361484	+	0.427782i
$239$			71289.7i			1.24805i	0.781405	+	0.624024i	$0.214503\pi$
$239$			71289.7i			1.24805i	−0.781405	+	0.624024i	$0.785497\pi$
$240$	20009.4	+	1626.88i	0.347386	+	0.0282444i
$241$	2541.14	−	4401.39i	0.0437517	−	0.0757802i	−0.843320	−	0.537411i	$-0.819402\pi$
$241$	2541.14	−	4401.39i	0.0437517	−	0.0757802i	0.887072	+	0.461631i	$0.152736\pi$
$242$	10608.2	+	6124.66i	0.181139	+	0.104581i
$243$	35337.7	+	47307.8i	0.598447	+	0.801162i
$244$	18193.9			0.305595
$245$	−53344.8	−	64475.7i	−0.888710	−	1.07415i
$246$	−15658.1	−	10821.3i	−0.258743	−	0.178817i
$247$	−61710.6	−	106886.i	−1.01150	−	1.75197i
$248$	28896.9	+	16683.6i	0.469838	+	0.271261i
$249$	13654.5	+	28818.8i	0.220230	+	0.464812i
$250$	1737.50	+	3009.44i	0.0278000	+	0.0481510i
$251$		−	54998.3i		−	0.872975i	−0.899710	−	0.436488i	$-0.856222\pi$
$251$		−	54998.3i		−	0.872975i	0.899710	−	0.436488i	$-0.143778\pi$
$252$	−29931.7	−	10596.4i	−0.471335	−	0.166862i
$253$	29852.5			0.466379
$254$	−64646.4	+	37323.6i	−1.00202	+	0.578517i
$255$	64886.7	−	30743.6i	0.997874	−	0.472796i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	100541.	−	58047.3i	1.52222	−	0.878852i	0.522561	−	0.852602i	$-0.324977\pi$
$257$	100541.	−	58047.3i	1.52222	−	0.878852i	0.999655	−	0.0262503i	$-0.00835668\pi$
$258$	14241.0	−	20606.4i	0.213945	−	0.309573i
$259$	39588.7	+	7122.02i	0.590162	+	0.106170i
$260$			66449.9i			0.982986i
$261$	−35451.1	−	29012.8i	−0.520414	−	0.425901i
$262$	39690.9	−	68746.6i	0.578214	−	1.00150i
$263$	22951.3	+	13250.9i	0.331814	+	0.191573i	0.656646	−	0.754199i	$-0.271974\pi$
$263$	22951.3	+	13250.9i	0.331814	+	0.191573i	−0.324832	+	0.945772i	$0.605308\pi$
$264$	−2273.11	+	27957.7i	−0.0326147	+	0.401137i
$265$	108981.			1.55188
$266$	67530.6	−	24314.6i	0.954416	−	0.343640i
$267$	44590.0	−	64520.6i	0.625483	−	0.905058i
$268$	11025.5	+	19096.7i	0.153507	+	0.265882i
$269$	−41926.3	−	24206.2i	−0.579405	−	0.334520i	0.181492	−	0.983392i	$-0.441907\pi$
$269$	−41926.3	−	24206.2i	−0.579405	−	0.334520i	−0.760897	+	0.648873i	$0.775241\pi$
$270$	51743.3	+	49871.6i	0.709785	+	0.684109i
$271$	43320.4	+	75033.1i	0.589867	+	1.02168i	0.994249	+	0.107089i	$0.0341530\pi$
$271$	43320.4	+	75033.1i	0.589867	+	1.02168i	−0.404383	+	0.914590i	$0.632514\pi$
$272$			14649.7i			0.198011i
$273$	26929.9	−	101590.i	0.361335	−	1.36310i
$274$	−83656.4			−1.11429
$275$	70348.1	−	40615.5i	0.930223	−	0.537064i
$276$	6681.58	+	14102.0i	0.0877124	+	0.185124i
$277$	49742.0	−	86155.7i	0.648282	−	1.12286i	−0.335251	−	0.942129i	$-0.608821\pi$
$277$	49742.0	−	86155.7i	0.648282	−	1.12286i	0.983533	−	0.180728i	$-0.0578455\pi$
$278$	43583.1	−	25162.7i	0.563934	−	0.325588i
$279$	42228.0	+	111732.i	0.542490	+	1.43539i
$280$	−38032.8	−	6842.11i	−0.485112	−	0.0872719i
$281$		−	142701.i		−	1.80723i	−0.428347	−	0.903614i	$-0.640904\pi$
$281$		−	142701.i		−	1.80723i	0.428347	−	0.903614i	$-0.359096\pi$
$282$	−606.382	+	7458.06i	−0.00762514	+	0.0937837i
$283$	−24035.9	+	41631.3i	−0.300114	+	0.519813i	−0.976162	−	0.217045i	$-0.930358\pi$
$283$	−24035.9	+	41631.3i	−0.300114	+	0.519813i	0.676047	+	0.736858i	$0.263692\pi$
$284$	37953.9	+	21912.7i	0.470566	+	0.271681i
$285$	−161914.	−	13164.5i	−1.99340	−	0.162075i
$286$	−92845.3			−1.13508
$287$	27984.4	+	23647.3i	0.339744	+	0.287090i
$288$	−13715.7	+	5183.69i	−0.165361	+	0.0624963i
$289$	−15562.7	−	26955.3i	−0.186332	−	0.322737i
$290$	−48282.6	−	27876.0i	−0.574110	−	0.331462i
$291$	−44572.4	+	21118.5i	−0.526356	+	0.249389i
$292$	−9933.51	−	17205.3i	−0.116503	−	0.201789i
$293$		−	24090.1i		−	0.280610i	−0.990108	−	0.140305i	$-0.955192\pi$
$293$		−	24090.1i		−	0.280610i	0.990108	−	0.140305i	$-0.0448083\pi$
$294$	55372.7	+	25873.8i	0.640621	+	0.299341i
$295$	−130868.			−1.50380
$296$	16086.3	−	9287.44i	0.183600	−	0.106002i
$297$	−69681.7	+	72296.9i	−0.789961	+	0.819610i
$298$	20700.3	−	35854.0i	0.233101	−	0.403743i
$299$	−44731.9	+	25826.0i	−0.500351	+	0.288878i
$300$	34931.7	+	24141.2i	0.388130	+	0.268235i
$301$	−31120.4	+	36828.0i	−0.343489	+	0.406486i
$302$		−	10030.1i		−	0.109974i
$303$	49538.4	+	4027.75i	0.539581	+	0.0438709i
$304$	16572.2	−	28703.8i	0.179321	−	0.310594i
$305$	68645.0	+	39632.2i	0.737920	+	0.426039i
$306$	−33213.2	+	40583.6i	−0.354705	+	0.433419i
$307$	88298.0			0.936859			0.468430	−	0.883501i	$-0.344820\pi$
$307$	88298.0			0.936859			0.468430	+	0.883501i	$0.344820\pi$
$308$	9559.96	−	53140.3i	0.100775	−	0.560173i
$309$	84453.0	+	58365.3i	0.884501	+	0.611276i
$310$	72684.9	+	125894.i	0.756347	+	1.31003i
$311$	19374.6	+	11185.9i	0.200314	+	0.115651i	0.596802	−	0.802389i	$-0.296438\pi$
$311$	19374.6	+	11185.9i	0.200314	+	0.115651i	−0.396488	+	0.918040i	$0.629771\pi$
$312$	−20780.6	−	43859.2i	−0.213476	−	0.450559i
$313$	−56997.2	−	98722.1i	−0.581789	−	1.00769i	−0.995267	−	0.0971736i	$-0.969020\pi$
$313$	−56997.2	−	98722.1i	−0.581789	−	1.00769i	0.413479	−	0.910514i	$-0.364314\pi$
$314$		−	15474.4i		−	0.156947i
$315$	−89849.1	−	105181.i	−0.905509	−	1.06002i
$316$	47515.4			0.475840
$317$	−36944.1	+	21329.7i	−0.367643	+	0.212259i	−0.672428	−	0.740162i	$-0.734749\pi$
$317$	−36944.1	+	21329.7i	−0.367643	+	0.212259i	0.304785	+	0.952421i	$0.401415\pi$
$318$	−71931.2	+	34081.2i	−0.711317	+	0.337024i
$319$	38949.0	−	67461.6i	0.382749	−	0.662941i
$320$	−15454.1	+	8922.43i	−0.150919	+	0.0871331i
$321$	−44293.4	+	64091.4i	−0.429862	+	0.621999i
$322$	−10175.7	−	28261.7i	−0.0981413	−	0.272575i
$323$		−	118543.i		−	1.13625i
$324$	−49748.5	−	16735.4i	−0.473904	−	0.159422i
$325$	−70274.6	+	121719.i	−0.665321	+	1.15237i
$326$	−42860.9	−	24745.7i	−0.403298	−	0.232844i
$327$	−4311.32	+	53026.1i	−0.0403194	+	0.495900i
$328$	16918.7			0.157260
$329$	2550.24	−	14175.8i	0.0235608	−	0.130965i
$330$	−69477.4	+	100532.i	−0.637993	+	0.923159i
$331$	99415.2	+	172192.i	0.907396	+	1.57166i	0.817668	+	0.575689i	$0.195266\pi$
$331$	99415.2	+	172192.i	0.907396	+	1.57166i	0.0897275	+	0.995966i	$0.471400\pi$
$332$	−24548.9	−	14173.3i	−0.222718	−	0.128586i
$333$	65619.7	+	10741.5i	0.591760	+	0.0968672i
$334$	−19994.3	−	34631.1i	−0.179231	−	0.310437i
$335$			96068.7i			0.856036i
$336$	27242.6	−	7377.83i	0.241307	−	0.0653507i
$337$	113097.			0.995846			0.497923	−	0.867221i	$-0.334096\pi$
$337$	113097.			0.995846			0.497923	+	0.867221i	$0.334096\pi$
$338$	69162.5	−	39931.0i	0.605393	−	0.349524i
$339$	26981.0	+	56945.6i	0.234779	+	0.495519i
$340$	−31911.8	+	55272.8i	−0.276053	+	0.478139i
$341$	−175902.	+	101557.i	−1.51273	+	0.873376i
$342$	110986.	−	41945.8i	0.948888	−	0.358621i
$343$	−101270.	−	59880.0i	−0.860783	−	0.508972i
$344$			22265.4i			0.188154i
$345$	−5509.37	+	67761.2i	−0.0462875	+	0.569302i
$346$	83241.6	−	144179.i	0.695326	−	1.20434i
$347$	−24493.7	−	14141.5i	−0.203421	−	0.117445i	0.394829	−	0.918755i	$-0.370804\pi$
$347$	−24493.7	−	14141.5i	−0.203421	−	0.117445i	−0.598250	+	0.801309i	$0.704137\pi$
$348$	40585.7	+	3299.85i	0.335131	+	0.0272481i
$349$	−101598.			−0.834131			−0.417066	−	0.908876i	$-0.636942\pi$
$349$	−101598.			−0.834131			−0.417066	+	0.908876i	$0.636942\pi$
$350$	−62430.4	−	52754.9i	−0.509636	−	0.430652i
$351$	41867.8	−	168615.i	0.339833	−	1.36862i
$352$	−12466.6	−	21592.8i	−0.100615	−	0.174271i
$353$	−48105.1	−	27773.5i	−0.386048	−	0.222885i	0.294398	−	0.955683i	$-0.404881\pi$
$353$	−48105.1	−	27773.5i	−0.386048	−	0.222885i	−0.680446	+	0.732798i	$0.738214\pi$
$354$	86377.6	−	40926.0i	0.689278	−	0.326582i
$355$	95466.2	+	165352.i	0.757518	+	1.31206i
$356$			69715.1i			0.550081i
$357$	71187.9	−	71569.9i	0.558560	−	0.561557i
$358$	−87243.9			−0.680721
$359$	−28547.0	+	16481.6i	−0.221499	+	0.127883i	−0.606644	−	0.794973i	$-0.707485\pi$
$359$	−28547.0	+	16481.6i	−0.221499	+	0.127883i	0.385145	+	0.922856i	$0.374151\pi$
$360$	−63040.7	−	10319.3i	−0.486426	−	0.0796246i
$361$	−68939.5	+	119407.i	−0.528998	+	0.916251i
$362$	−40716.9	+	23507.9i	−0.310712	+	0.179389i
$363$	−32064.8	−	22159.9i	−0.243341	−	0.168172i
$364$	31647.8	+	87897.6i	0.238858	+	0.663398i
$365$		−	86553.8i		−	0.649681i
$366$	−57702.1	−	4691.51i	−0.430754	−	0.0350227i
$367$	−95898.9	+	166102.i	−0.712003	+	1.23323i	0.252101	+	0.967701i	$0.418878\pi$
$367$	−95898.9	+	166102.i	−0.712003	+	1.23323i	−0.964104	+	0.265524i	$0.914455\pi$
$368$	−12012.6	−	6935.47i	−0.0887036	−	0.0512130i
$369$	46869.5	+	38357.4i	0.344221	+	0.281706i
$370$	80924.4			0.591121
$371$	144156.	−	51903.9i	1.04734	−	0.377096i
$372$	−87345.0	−	60363.9i	−0.631178	−	0.436205i
$373$	−110920.	−	192119.i	−0.797247	−	1.38087i	−0.921403	−	0.388609i	$-0.872956\pi$
$373$	−110920.	−	192119.i	−0.797247	−	1.38087i	0.124156	−	0.992263i	$-0.460378\pi$
$374$	−77228.5	−	44587.9i	−0.552121	−	0.318767i
$375$	−4734.49	−	9992.52i	−0.0336675	−	0.0710579i
$376$	−3325.63	−	5760.16i	−0.0235233	−	0.0407435i
$377$			134782.i			0.948309i
$378$	92196.4	+	41324.9i	0.645253	+	0.289220i
$379$	−120825.			−0.841158			−0.420579	−	0.907256i	$-0.638173\pi$
$379$	−120825.			−0.841158			−0.420579	+	0.907256i	$0.638173\pi$
$380$	125053.	−	72199.3i	0.866016	−	0.499995i
$381$	214651.	−	101703.i	1.47871	−	0.700619i
$382$	5286.67	−	9156.77i	0.0362289	−	0.0627503i
$383$	122682.	−	70830.7i	0.836343	−	0.482863i	−0.0196766	−	0.999806i	$-0.506264\pi$
$383$	122682.	−	70830.7i	0.836343	−	0.482863i	0.856019	+	0.516944i	$0.172930\pi$
$384$	7409.96	−	10722.0i	0.0502520	−	0.0727134i
$385$	151826.	−	179672.i	1.02430	−	1.21216i
$386$			98413.6i			0.660512i
$387$	−50479.2	+	61681.3i	−0.337047	+	0.411843i
$388$	21921.0	−	37968.3i	0.145612	−	0.252207i
$389$	160536.	+	92685.8i	1.06090	+	0.612511i	0.925681	−	0.378305i	$-0.123493\pi$
$389$	160536.	+	92685.8i	1.06090	+	0.612511i	0.135219	+	0.990816i	$0.456826\pi$
$390$	17134.9	−	210747.i	0.112655	−	1.38558i
$391$	−49610.5			−0.324504
$392$	−53567.1	+	9063.18i	−0.348599	+	0.0589805i
$393$	−143607.	+	207796.i	−0.929805	+	1.34540i
$394$	80325.3	+	139128.i	0.517440	+	0.896232i
$395$	179275.	+	103504.i	1.14901	+	0.663382i
$396$	14418.4	−	88082.0i	0.0919449	−	0.561690i
$397$	−72914.1	−	126291.i	−0.462627	−	0.801293i	0.536464	−	0.843923i	$-0.319760\pi$
$397$	−72914.1	−	126291.i	−0.462627	−	0.801293i	−0.999091	+	0.0426300i	$0.986426\pi$
$398$			65000.5i			0.410346i
$399$	−220444.	+	59700.5i	−1.38469	+	0.375001i
$400$	−37744.0			−0.235900
$401$	−20846.4	+	12035.7i	−0.129641	+	0.0748483i	−0.563418	−	0.826172i	$-0.690514\pi$
$401$	−20846.4	+	12035.7i	−0.129641	+	0.0748483i	0.433777	+	0.901020i	$0.357181\pi$
$402$	−30043.2	−	63408.6i	−0.185906	−	0.392370i
$403$	175718.	−	304353.i	1.08195	−	1.87399i
$404$	−38260.5	+	22089.7i	−0.234416	+	0.135340i
$405$	−151245.	−	171511.i	−0.922083	−	1.04564i
$406$	−77143.0	−	13878.1i	−0.467998	−	0.0841931i
$407$			113069.i			0.682585i
$408$	3777.59	−	46461.6i	0.0226931	−	0.279109i
$409$	55546.3	−	96209.0i	0.332054	−	0.575134i	−0.650861	−	0.759197i	$-0.725592\pi$
$409$	55546.3	−	96209.0i	0.332054	−	0.575134i	0.982914	+	0.184063i	$0.0589251\pi$
$410$	63833.8	+	36854.5i	0.379737	+	0.219241i
$411$	265318.	+	21571.8i	1.57066	+	0.127703i
$412$	−91252.2			−0.537587
$413$	−173108.	+	62328.1i	−1.01489	+	0.365413i
$414$	−17554.4	−	46447.7i	−0.102420	−	0.270996i
$415$	−61748.2	−	106951.i	−0.358532	−	0.620996i
$416$	37360.8	+	21570.3i	0.215889	+	0.124643i
$417$	−144713.	+	68565.5i	−0.832215	+	0.394306i
$418$	100878.	+	174727.i	0.577359	+	1.00002i
$419$		−	175440.i		−	0.999314i	−0.866223	−	0.499657i	$-0.833459\pi$
$419$		−	175440.i		−	0.999314i	0.866223	−	0.499657i	$-0.166541\pi$
$420$	118857.	+	31507.1i	0.673794	+	0.178612i
$421$	211361.			1.19251			0.596254	−	0.802796i	$-0.296655\pi$
$421$	211361.			1.19251			0.596254	+	0.802796i	$0.296655\pi$
$422$	6738.83	−	3890.67i	0.0378408	−	0.0218474i
$423$	3846.30	−	23497.0i	0.0214962	−	0.131320i
$424$	35376.3	−	61273.5i	0.196780	−	0.340833i
$425$	−116908.	+	67497.1i	−0.647244	+	0.373686i
$426$	−114721.	−	79283.4i	−0.632155	−	0.436881i
$427$	109677.	+	19730.9i	0.601532	+	0.108216i
$428$		−	69251.3i		−	0.378042i
$429$	294460.	+	23941.3i	1.59997	+	0.130087i
$430$	−48501.3	+	84006.8i	−0.262311	+	0.454336i
$431$	−200611.	−	115823.i	−1.07994	−	0.623503i	−0.149059	−	0.988828i	$-0.547624\pi$
$431$	−200611.	−	115823.i	−1.07994	−	0.623503i	−0.930880	+	0.365325i	$0.880958\pi$
$432$	44836.2	−	12903.4i	0.240249	−	0.0691411i
$433$	13584.6			0.0724556			0.0362278	−	0.999344i	$-0.488466\pi$
$433$	13584.6			0.0724556			0.0362278	+	0.999344i	$0.488466\pi$
$434$	156104.	+	131911.i	0.828772	+	0.700328i
$435$	145941.	+	100859.i	0.771256	+	0.533013i
$436$	−23644.9	−	40954.2i	−0.124384	−	0.215440i
$437$	97204.5	+	56121.0i	0.509006	+	0.293875i
$438$	27067.7	+	57128.5i	0.141092	+	0.297786i
$439$	−16938.8	−	29338.8i	−0.0878926	−	0.152234i	0.818728	−	0.574182i	$-0.194680\pi$
$439$	−16938.8	−	29338.8i	−0.0878926	−	0.152234i	−0.906620	+	0.421948i	$0.861347\pi$
$440$		−	108626.i		−	0.561083i
$441$	−168943.	−	96337.8i	−0.868689	−	0.495358i
$442$	154296.			0.789785
$443$	−194989.	+	112577.i	−0.993581	+	0.573644i	−0.906343	−	0.422543i	$-0.861138\pi$
$443$	−194989.	+	112577.i	−0.993581	+	0.573644i	−0.0872385	+	0.996187i	$0.527804\pi$
$444$	−53412.9	+	25307.2i	−0.270944	+	0.128374i
$445$	−151862.	+	263033.i	−0.766885	+	1.32828i
$446$	−184767.	+	106675.i	−0.928869	+	0.536283i
$447$	−74896.8	+	108374.i	−0.374842	+	0.542387i
$448$	−16192.7	+	19162.6i	−0.0806796	+	0.0954767i
$449$		−	218947.i		−	1.08604i	−0.839719	−	0.543021i	$-0.817280\pi$
$449$		−	218947.i		−	1.08604i	0.839719	−	0.543021i	$-0.182720\pi$
$450$	−104561.	−	85571.7i	−0.516352	−	0.422576i
$451$	−51493.9	+	89190.1i	−0.253165	+	0.438494i
$452$	−48508.3	−	28006.3i	−0.237432	−	0.137081i
$453$	−2586.37	+	31810.5i	−0.0126036	+	0.155015i
$454$	−58475.2			−0.283700
$455$	−72063.6	+	400575.i	−0.348091	+	1.93491i
$456$	−59960.5	+	86761.3i	−0.288360	+	0.417250i
$457$	−118919.	−	205973.i	−0.569401	−	0.986231i	−0.996625	−	0.0820853i	$-0.973842\pi$
$457$	−118919.	−	205973.i	−0.569401	−	0.986231i	0.427225	−	0.904145i	$-0.359491\pi$
$458$	169059.	+	97606.2i	0.805948	+	0.465314i
$459$	115801.	−	120147.i	0.549651	−	0.570280i
$460$	−30215.5	−	52334.7i	−0.142795	−	0.247329i
$461$		−	111930.i		−	0.526677i	−0.964703	−	0.263339i	$-0.915176\pi$
$461$		−	111930.i		−	0.526677i	0.964703	−	0.263339i	$-0.0848236\pi$
$462$	−44022.4	+	166070.i	−0.206248	+	0.778050i
$463$	174147.			0.812369			0.406184	−	0.913791i	$-0.366859\pi$
$463$	174147.			0.812369			0.406184	+	0.913791i	$0.366859\pi$
$464$	−31346.0	+	18097.6i	−0.145595	+	0.0840593i
$465$	−198058.	−	418017.i	−0.915981	−	1.93325i
$466$	−134067.	+	232211.i	−0.617376	+	1.06933i
$467$	159407.	−	92033.9i	0.730928	−	0.422002i	−0.0878335	−	0.996135i	$-0.527994\pi$
$467$	159407.	−	92033.9i	0.730928	−	0.422002i	0.818762	+	0.574134i	$0.194661\pi$
$468$	54596.5	+	144459.i	0.249272	+	0.659556i
$469$	45754.2	+	127076.i	0.208010	+	0.577722i
$470$		−	28977.3i		−	0.131178i
$471$	−3990.25	+	49077.1i	−0.0179870	+	0.221227i
$472$	−42481.1	+	73579.5i	−0.190683	+	0.330273i
$473$	−117376.	−	67767.2i	−0.524636	−	0.302898i
$474$	−150696.	−	12252.4i	−0.670725	−	0.0545337i
$475$	305420.			1.35366
$476$	−15887.3	+	88311.5i	−0.0701190	+	0.389766i
$477$	236919.	−	89540.9i	1.04127	−	0.393536i
$478$	100819.	+	174623.i	0.441251	+	0.764270i
$479$	−260275.	−	150270.i	−1.13439	−	0.654940i	−0.189354	−	0.981909i	$-0.560639\pi$
$479$	−260275.	−	150270.i	−1.13439	−	0.654940i	−0.945035	+	0.326969i	$0.893973\pi$
$480$	51313.7	−	24312.6i	0.222716	−	0.105523i
$481$	−97818.7	−	169427.i	−0.422797	−	0.732306i
$482$		−	14374.9i		−	0.0618743i
$483$	24984.7	+	92256.2i	0.107098	+	0.395459i
$484$	34646.3			0.147899
$485$	165415.	−	95502.3i	0.703220	−	0.406004i
$486$	153463.	+	65904.9i	0.649726	+	0.279026i
$487$	−154480.	+	267567.i	−0.651348	+	1.12817i	0.331448	+	0.943474i	$0.392463\pi$
$487$	−154480.	+	267567.i	−0.651348	+	1.12817i	−0.982796	+	0.184695i	$0.940870\pi$
$488$	44565.7	−	25730.0i	0.187138	−	0.108044i
$489$	129553.	+	89533.7i	0.541788	+	0.374428i
$490$	−221850.	−	82491.6i	−0.923990	−	0.343572i
$491$			324955.i			1.34791i	0.738774	+	0.673953i	$0.235405\pi$
$491$			324955.i			1.34791i	−0.738774	+	0.673953i	$0.764595\pi$
$492$	−53657.9	−	4362.69i	−0.221668	−	0.0180229i
$493$	−64727.6	+	112111.i	−0.266315	+	0.461271i
$494$	−302319.	−	174544.i	−1.23883	−	0.715239i
$495$	246272.	−	300923.i	1.00509	−	1.22813i
$496$	94377.0			0.383621
$497$	205031.	+	173255.i	0.830055	+	0.701412i
$498$	74202.4	+	51281.1i	0.299198	+	0.206775i
$499$	−126197.	−	218580.i	−0.506813	−	0.877826i	−0.999969	−	0.00788500i	$-0.997490\pi$
$499$	−126197.	−	218580.i	−0.506813	−	0.877826i	0.493156	−	0.869941i	$-0.335843\pi$
$500$	8511.98	+	4914.39i	0.0340479	+	0.0196576i
$501$	54482.1	+	114989.i	0.217059	+	0.458121i
$502$	−77779.4	−	134718.i	−0.308643	−	0.534586i
$503$		−	148148.i		−	0.585544i	−0.956182	−	0.292772i	$-0.905422\pi$
$503$		−	148148.i		−	0.585544i	0.956182	−	0.292772i	$-0.0945777\pi$
$504$	−88302.9	+	16374.0i	−0.347627	+	0.0644607i
$505$	−192475.			−0.754728
$506$	73123.3	−	42217.8i	0.285598	−	0.164890i
$507$	−229647.	+	108807.i	−0.893397	+	0.423294i
$508$	−105567.	+	182848.i	−0.409073	+	0.708536i
$509$	−140858.	+	81324.2i	−0.543682	+	0.313895i	−0.746570	−	0.665307i	$-0.768301\pi$
$509$	−140858.	+	81324.2i	−0.543682	+	0.313895i	0.202888	+	0.979202i	$0.434967\pi$
$510$	115461.	−	167070.i	0.443912	−	0.642329i
$511$	−41222.6	−	114490.i	−0.157868	−	0.438457i
$512$			11585.2i			0.0441942i
$513$	−362809.	+	104413.i	−1.37862	+	0.396752i
$514$	164183.	−	284373.i	0.621442	−	1.07637i
$515$	−344292.	−	198777.i	−1.29811	−	0.749467i
$516$	5741.39	−	70615.0i	0.0215634	−	0.265215i
$517$	40487.7			0.151475
$518$	107044.	−	38541.5i	0.398936	−	0.143638i
$519$	−301180.	+	435800.i	−1.11813	+	1.61790i
$520$	93974.3	+	162768.i	0.347538	+	0.601954i
$521$	331921.	+	191635.i	1.22281	+	0.705991i	0.965517	−	0.260342i	$-0.0838353\pi$
$521$	331921.	+	191635.i	1.22281	+	0.705991i	0.257296	+	0.966333i	$0.417169\pi$
$522$	−127867.	−	20931.0i	−0.469266	−	0.0768156i
$523$	−39274.9	−	68026.0i	−0.143586	−	0.248698i	0.785259	−	0.619168i	$-0.212530\pi$
$523$	−39274.9	−	68026.0i	−0.143586	−	0.248698i	−0.928844	+	0.370470i	$0.879197\pi$
$524$		−	224526.i		−	0.817717i
$525$	184395.	+	183411.i	0.669008	+	0.665438i
$526$	74958.5			0.270925
$527$	292324.	−	168773.i	1.05255	−	0.607691i
$528$	33970.1	+	71696.7i	0.121851	+	0.257176i
$529$	−116434.	+	201669.i	−0.416071	+	0.720656i
$530$	266948.	−	154122.i	0.950330	−	0.548673i
$531$	−284501.	+	107524.i	−1.00901	+	0.381343i
$532$	131030.	−	155061.i	0.462963	−	0.547872i
$533$		−	178194.i		−	0.627247i
$534$	17976.9	−	221103.i	0.0630422	−	0.775374i
$535$	150852.	−	261284.i	0.527040	−	0.912861i
$536$	54013.7	+	31184.8i	0.188007	+	0.108546i
$537$	276695.	+	22496.9i	0.959518	+	0.0780142i
$538$	−136931.			−0.473082
$539$	115259.	−	309974.i	0.396733	−	1.06696i
$540$	197274.	+	48983.8i	0.676522	+	0.167983i
$541$	209640.	+	363106.i	0.716273	+	1.24062i	0.962466	+	0.271401i	$0.0874869\pi$
$541$	209640.	+	363106.i	0.716273	+	1.24062i	−0.246193	+	0.969221i	$0.579180\pi$
$542$	212226.	+	122529.i	0.722436	+	0.417099i
$543$	135196.	−	64056.3i	0.458526	−	0.217251i
$544$	20717.8	+	35884.2i	0.0700076	+	0.121257i
$545$		−	206026.i		−	0.693631i
$546$	−77705.9	−	286929.i	−0.260657	−	0.962476i
$547$	−281900.			−0.942150			−0.471075	−	0.882093i	$-0.656134\pi$
$547$	−281900.			−0.942150			−0.471075	+	0.882093i	$0.656134\pi$
$548$	−204915.	+	118308.i	−0.682360	+	0.393961i
$549$	181793.	+	29758.4i	0.603161	+	0.0987335i
$550$	114878.	−	198974.i	0.379762	−	0.657767i
$551$	253648.	−	146444.i	0.835466	−	0.482356i
$552$	36309.7	+	25093.5i	0.119164	+	0.0823539i
$553$	286434.	+	51529.6i	0.936643	+	0.168503i
$554$		−	281383.i		−	0.916809i
$555$	−256653.	−	20867.3i	−0.833221	−	0.0677456i
$556$	71170.9	−	123272.i	0.230225	−	0.398762i
$557$	257277.	+	148539.i	0.829260	+	0.478773i	0.853599	−	0.520930i	$-0.174415\pi$
$557$	257277.	+	148539.i	0.829260	+	0.478773i	−0.0243393	+	0.999704i	$0.507748\pi$
$558$	261450.	+	213968.i	0.839693	+	0.687195i
$559$	234507.			0.750468
$560$	−102837.	+	37026.8i	−0.327924	+	0.118070i
$561$	233434.	+	161325.i	0.741717	+	0.512598i
$562$	−201809.	−	349544.i	−0.638952	−	1.10670i
$563$	108374.	+	62569.7i	0.341907	+	0.197400i	0.661115	−	0.750285i	$-0.270084\pi$
$563$	108374.	+	62569.7i	0.341907	+	0.197400i	−0.319208	+	0.947685i	$0.603417\pi$
$564$	9061.96	+	19126.0i	0.0284881	+	0.0601265i
$565$	−122014.	−	211334.i	−0.382218	−	0.662022i
$566$			135967.i			0.424426i
$567$	−281746.	−	154836.i	−0.876379	−	0.481623i
$568$	123957.			0.384215
$569$	333841.	−	192743.i	1.03113	−	0.595326i	0.113825	−	0.993501i	$-0.463690\pi$
$569$	333841.	−	192743.i	1.03113	−	0.595326i	0.917309	+	0.398175i	$0.130356\pi$
$570$	−415224.	+	196735.i	−1.27801	+	0.605524i
$571$	85863.9	−	148721.i	0.263353	−	0.456141i	−0.703778	−	0.710420i	$-0.748505\pi$
$571$	85863.9	−	148721.i	0.263353	−	0.456141i	0.967131	+	0.254279i	$0.0818383\pi$
$572$	−227424.	+	131303.i	−0.695094	+	0.401313i
$573$	−19127.9	+	27677.6i	−0.0582584	+	0.0842984i
$574$	101990.	+	18348.0i	0.309551	+	0.0556885i
$575$		−	127818.i		−	0.386597i
$576$	−26265.6	+	32094.3i	−0.0791667	+	0.0967349i
$577$	−52749.2	+	91364.3i	−0.158440	+	0.274426i	−0.934306	−	0.356472i	$-0.883980\pi$
$577$	−52749.2	+	91364.3i	−0.158440	+	0.274426i	0.775866	+	0.630897i	$0.217313\pi$
$578$	−76241.2	−	44017.9i	−0.228210	−	0.131757i
$579$	25377.1	−	312120.i	0.0756981	−	0.931032i
$580$	−157690.			−0.468758
$581$	−132616.	−	112063.i	−0.392864	−	0.331978i
$582$	−79313.4	+	114764.i	−0.234153	+	0.338814i
$583$	215343.	+	372986.i	0.633570	+	1.09737i
$584$	−48664.1	−	28096.2i	−0.142686	−	0.0823800i
$585$	−108687.	+	663968.i	−0.317590	+	1.94015i
$586$	−34068.5	−	59008.4i	−0.0992105	−	0.171838i
$587$			331052.i			0.960771i	0.877058	+	0.480385i	$0.159503\pi$
$587$			331052.i			0.960771i	−0.877058	+	0.480385i	$0.840497\pi$
$588$	172226.	−	14931.1i	0.498132	−	0.0431854i
$589$	−763687.			−2.20133
$590$	−320561.	+	185076.i	−0.920887	+	0.531674i
$591$	−218877.	−	461958.i	−0.626651	−	1.32260i
$592$	26268.9	−	45499.0i	0.0749545	−	0.129825i
$593$	−504120.	+	291054.i	−1.43359	+	0.827683i	−0.997392	−	0.0721680i	$-0.977008\pi$
$593$	−504120.	+	291054.i	−1.43359	+	0.827683i	−0.436197	+	0.899851i	$0.643675\pi$
$594$	−68441.3	+	275635.i	−0.193975	+	0.781200i
$595$	−252314.	+	298589.i	−0.712701	+	0.843413i
$596$		−	117099.i		−	0.329655i
$597$	16761.1	−	206150.i	0.0470278	−	0.578408i
$598$	−73046.9	+	126521.i	−0.204268	+	0.353802i
$599$	−501114.	−	289318.i	−1.39664	−	0.806348i	−0.402597	−	0.915377i	$-0.631892\pi$
$599$	−501114.	−	289318.i	−1.39664	−	0.806348i	−0.994039	+	0.109029i	$0.965226\pi$
$600$	119706.	+	9732.73i	0.332515	+	0.0270354i
$601$	18618.8			0.0515471			0.0257735	−	0.999668i	$-0.491795\pi$
$601$	18618.8			0.0515471			0.0257735	+	0.999668i	$0.491795\pi$
$602$	−24146.4	+	134221.i	−0.0666284	+	0.370362i
$603$	78931.9	+	208848.i	0.217079	+	0.574376i
$604$	−14184.7	−	24568.5i	−0.0388817	−	0.0673450i
$605$	130720.	+	75471.1i	0.357133	+	0.206191i
$606$	127040.	−	60191.9i	0.345935	−	0.163905i
$607$	202367.	+	350510.i	0.549241	+	0.951313i	0.998327	+	0.0578247i	$0.0184164\pi$
$607$	202367.	+	350510.i	0.549241	+	0.951313i	−0.449086	+	0.893489i	$0.648250\pi$
$608$		−	93746.3i		−	0.253599i
$609$	241081.	+	63906.7i	0.650024	+	0.172311i
$610$	224194.			0.602509
$611$	−60668.1	+	35026.7i	−0.162509	+	0.0938247i
$612$	−23961.4	+	146380.i	−0.0639748	+	0.390821i
$613$	77668.8	−	134526.i	0.206693	−	0.358003i	−0.743978	−	0.668204i	$-0.767063\pi$
$613$	77668.8	−	134526.i	0.206693	−	0.358003i	0.950671	+	0.310202i	$0.100397\pi$
$614$	216285.	−	124872.i	0.573707	−	0.331230i
$615$	−192947.	−	133345.i	−0.510137	−	0.352554i
$616$	−51734.7	−	143686.i	−0.136339	−	0.378664i
$617$			80571.2i			0.211646i	0.994385	+	0.105823i	$0.0337476\pi$
$617$			80571.2i			0.211646i	−0.994385	+	0.105823i	$0.966252\pi$
$618$	289408.	+	23530.5i	0.757763	+	0.0616104i
$619$	59508.8	−	103072.i	0.155310	−	0.269005i	−0.777862	−	0.628435i	$-0.783696\pi$
$619$	59508.8	−	103072.i	0.155310	−	0.269005i	0.933172	+	0.359430i	$0.117029\pi$
$620$	356082.	+	205584.i	0.926332	+	0.534818i
$621$	43696.9	+	151836.i	0.113310	+	0.393724i
$622$	63277.1			0.163556
$623$	−75604.7	+	420259.i	−0.194793	+	1.08278i
$624$	−112928.	−	78044.4i	−0.290024	−	0.200434i
$625$	205707.	+	356295.i	0.526610	+	0.912115i
$626$	−279228.	−	161213.i	−0.712543	−	0.411387i
$627$	−274882.	−	580161.i	−0.699216	−	1.47575i
$628$	−21884.0	−	37904.3i	−0.0554892	−	0.0961101i
$629$		−	187905.i		−	0.474939i
$630$	−368833.	−	130574.i	−0.929284	−	0.328984i
$631$	333974.			0.838790			0.419395	−	0.907804i	$-0.362242\pi$
$631$	333974.			0.838790			0.419395	+	0.907804i	$0.362242\pi$
$632$	116389.	−	67197.0i	0.291391	−	0.168235i
$633$	−22375.6	+	10601.6i	−0.0558427	+	0.0264585i
$634$	−60329.4	+	104494.i	−0.150090	+	0.259963i
$635$	−796604.	+	459920.i	−1.97558	+	1.14060i
$636$	−127997.	+	185208.i	−0.316435	+	0.457873i
$637$	95456.7	+	564188.i	0.235249	+	1.39042i
$638$		−	220329.i		−	0.541289i
$639$	343395.	+	281031.i	0.840994	+	0.688259i
$640$	−25236.5	+	43710.8i	−0.0616124	+	0.106716i
$641$	−78742.6	−	45462.1i	−0.191643	−	0.110645i	0.401108	−	0.916031i	$-0.368625\pi$
$641$	−78742.6	−	45462.1i	−0.191643	−	0.110645i	−0.592752	+	0.805385i	$0.701958\pi$
$642$	−17857.3	+	219632.i	−0.0433257	+	0.532874i
$643$	11665.1			0.0282140			0.0141070	−	0.999900i	$-0.495509\pi$
$643$	11665.1			0.0282140			0.0141070	+	0.999900i	$0.495509\pi$
$644$	−64893.2	−	54836.0i	−0.156469	−	0.132219i
$645$	175485.	−	253922.i	0.421813	−	0.610353i
$646$	−167646.	−	290371.i	−0.401723	−	0.695805i
$647$	258017.	+	148966.i	0.616367	+	0.355860i	0.775453	−	0.631405i	$-0.217521\pi$
$647$	258017.	+	148966.i	0.616367	+	0.355860i	−0.159086	+	0.987265i	$0.550855\pi$
$648$	−145526.	+	29361.8i	−0.346570	+	0.0699249i
$649$	−258592.	−	447895.i	−0.613940	−	1.06338i
$650$			397533.i			0.940907i
$651$	−461072.	−	458611.i	−1.08794	−	1.08214i
$652$	−139983.			−0.329291
$653$	−251233.	+	145049.i	−0.589182	+	0.340165i	−0.764774	−	0.644298i	$-0.777149\pi$
$653$	−251233.	+	145049.i	−0.589182	+	0.340165i	0.175592	+	0.984463i	$0.443816\pi$
$654$	64429.7	+	135984.i	0.150637	+	0.317931i
$655$	489090.	−	847129.i	1.14000	−	1.97455i
$656$	41442.2	−	23926.7i	0.0963019	−	0.0555999i
$657$	−71114.3	−	188164.i	−0.164750	−	0.435918i
$658$	−13800.9	−	38330.1i	−0.0318753	−	0.0885296i
$659$		−	274180.i		−	0.631341i	−0.948869	−	0.315671i	$-0.897771\pi$
$659$		−	274180.i		−	0.631341i	0.948869	−	0.315671i	$-0.102229\pi$
$660$	−28010.4	+	344508.i	−0.0643031	+	0.790881i
$661$	33358.6	−	57778.8i	0.0763493	−	0.132241i	−0.825323	−	0.564661i	$-0.809007\pi$
$661$	33358.6	−	57778.8i	0.0763493	−	0.132241i	0.901672	+	0.432420i	$0.142340\pi$
$662$	487033.	+	281189.i	1.11133	+	0.641626i
$663$	−489351.	−	39786.9i	−1.11325	−	0.0905135i
$664$	−80176.3			−0.181849
$665$	832145.	−	299616.i	1.88172	−	0.677520i
$666$	175926.	−	66489.1i	0.396625	−	0.149900i
$667$	−61286.9	−	106152.i	−0.137758	−	0.238604i
$668$	−97951.5	−	56552.3i	−0.219512	−	0.126735i
$669$	613498.	−	290678.i	1.37076	−	0.649471i
$670$	135862.	+	235319.i	0.302655	+	0.524213i
$671$			313249.i			0.695736i
$672$	56296.8	−	56598.8i	0.124665	−	0.125334i
$673$	798822.			1.76368			0.881840	−	0.471549i	$-0.156305\pi$
$673$	798822.			1.76368			0.881840	+	0.471549i	$0.156305\pi$
$674$	277030.	−	159944.i	0.609828	−	0.352085i
$675$	309552.	+	298354.i	0.679400	+	0.654824i
$676$	112942.	−	195621.i	0.247151	−	0.428078i
$677$	−120303.	+	69457.0i	−0.262482	+	0.151544i	−0.625466	−	0.780251i	$-0.715091\pi$
$677$	−120303.	+	69457.0i	−0.262482	+	0.151544i	0.362984	+	0.931795i	$0.381758\pi$
$678$	146623.	+	101331.i	0.318965	+	0.220436i
$679$	173321.	−	205109.i	0.375934	−	0.444882i
$680$			180520.i			0.390399i
$681$	185455.	+	15078.5i	0.399893	+	0.0325136i
$682$	−287247.	+	497526.i	−0.617570	+	1.06966i
$683$	618158.	+	356894.i	1.32513	+	0.765063i	0.984542	−	0.175150i	$-0.0560410\pi$
$683$	618158.	+	356894.i	1.32513	+	0.765063i	0.340587	+	0.940213i	$0.389374\pi$
$684$	212538.	−	259703.i	0.454281	−	0.555092i
$685$	−1.03085e6			−2.19693
$686$	−332744.	−	3457.65i	−0.707069	−	0.00734738i
$687$	−511004.	−	353153.i	−1.08271	−	0.748255i
$688$	31488.0	+	54538.8i	0.0665225	+	0.115220i
$689$	−645355.	−	372596.i	−1.35944	−	0.784873i
$690$	82333.7	+	173772.i	0.172934	+	0.364990i
$691$	375952.	+	651168.i	0.787366	+	1.36376i	0.927575	+	0.373636i	$0.121889\pi$
$691$	375952.	+	651168.i	0.787366	+	1.36376i	−0.140209	+	0.990122i	$0.544778\pi$
$692$		−	470886.i		−	0.983339i
$693$	182441.	−	515342.i	0.379888	−	1.07307i
$694$	−79996.1			−0.166093
$695$	537052.	−	310067.i	1.11185	−	0.641928i
$696$	104081.	−	49314.0i	0.214859	−	0.101801i
$697$	85575.6	−	148221.i	0.176151	−	0.305102i
$698$	−248863.	+	143681.i	−0.510799	+	0.294910i
$699$	485073.	−	701889.i	0.992780	−	1.43653i
$700$	−227529.	−	40932.6i	−0.464345	−	0.0835360i
$701$			437453.i			0.890215i	0.895477	+	0.445107i	$0.146835\pi$
$701$			437453.i			0.890215i	−0.895477	+	0.445107i	$0.853165\pi$
$702$	−135903.	−	472231.i	−0.275775	−	0.958253i
$703$	−212564.	+	368172.i	−0.430110	+	0.744973i
$704$	−61073.8	−	35261.0i	−0.123228	−	0.0711457i
$705$	−7472.13	+	91901.8i	−0.0150337	+	0.184904i
$706$	−157110.			−0.315207
$707$	−254599.	+	91669.0i	−0.509352	+	0.183393i
$708$	153703.	−	222404.i	0.306631	−	0.443687i
$709$	−210009.	−	363746.i	−0.417778	−	0.723612i	0.577938	−	0.816081i	$-0.303858\pi$
$709$	−210009.	−	363746.i	−0.417778	−	0.723612i	−0.995716	+	0.0924687i	$0.970524\pi$
$710$	467687.	+	270019.i	0.927766	+	0.535646i
$711$	474775.	+	77717.5i	0.939179	+	0.153737i
$712$	98592.0	+	170766.i	0.194483	+	0.336855i
$713$			319604.i			0.628685i
$714$	73158.9	−	275985.i	0.143506	−	0.541363i
$715$	−1.14408e6			−2.23793
$716$	−213703.	+	123381.i	−0.416854	+	0.240671i
$717$	−274720.	−	579818.i	−0.534382	−	1.12786i
$718$	−46617.1	+	80743.2i	−0.0904267	+	0.156624i
$719$	62932.5	−	36334.1i	0.121736	−	0.0702841i	−0.437896	−	0.899026i	$-0.644276\pi$
$719$	62932.5	−	36334.1i	0.121736	−	0.0702841i	0.559631	+	0.828742i	$0.310943\pi$
$720$	−169011.	+	63875.9i	−0.326025	+	0.123217i
$721$	−550089.	−	98961.3i	−1.05819	−	0.190368i
$722$			389981.i			0.748116i
$723$	−3706.73	+	45590.2i	−0.00709112	+	0.0872157i
$724$	−66490.4	+	115165.i	−0.126847	+	0.219706i
$725$	−288848.	−	166767.i	−0.549533	−	0.317273i
$726$	−109881.	−	8933.97i	−0.208473	−	0.0169501i
$727$	536454.			1.01499			0.507497	−	0.861653i	$-0.330571\pi$
$727$	536454.			1.01499			0.507497	+	0.861653i	$0.330571\pi$
$728$	201827.	+	170548.i	0.380817	+	0.321798i
$729$	−469715.	−	248591.i	−0.883852	−	0.467767i
$730$	−122406.	−	212013.i	−0.229697	−	0.397847i
$731$	195062.	+	112619.i	0.365039	+	0.210755i
$732$	−147976.	+	70111.4i	−0.276165	+	0.130848i
$733$	5398.70	+	9350.82i	0.0100480	+	0.0174037i	0.871006	−	0.491273i	$-0.163468\pi$
$733$	5398.70	+	9350.82i	0.0100480	+	0.0174037i	−0.860958	+	0.508677i	$0.830135\pi$
$734$			542486.i			1.00692i
$735$	682329.	+	318830.i	1.26305	+	0.590180i
$736$	−39233.0			−0.0724262
$737$	−328794.	+	189829.i	−0.605325	+	0.349484i
$738$	169052.	+	27672.7i	0.310390	+	0.0508087i
$739$	−177420.	+	307300.i	−0.324873	+	0.562696i	−0.981487	−	0.191531i	$-0.938655\pi$
$739$	−177420.	+	307300.i	−0.324873	+	0.562696i	0.656614	+	0.754227i	$0.271988\pi$
$740$	198224.	−	114444.i	0.361986	−	0.208993i
$741$	913802.	+	631526.i	1.66424	+	1.15015i
$742$	279706.	−	331006.i	0.508036	−	0.601212i
$743$		−	487992.i		−	0.883966i	−0.897024	−	0.441983i	$-0.854275\pi$
$743$		−	487992.i		−	0.883966i	0.897024	−	0.441983i	$-0.145725\pi$
$744$	−299318.	−	24336.2i	−0.540738	−	0.0439650i
$745$	255080.	−	441811.i	0.459582	−	0.796019i
$746$	−543395.	−	313729.i	−0.976424	−	0.563738i
$747$	−222111.	−	181773.i	−0.398041	−	0.325752i
$748$	−252227.			−0.450805
$749$	75101.8	−	417463.i	0.133871	−	0.744139i
$750$	−25728.6	−	17781.0i	−0.0457398	−	0.0316107i
$751$	35273.5	+	61095.6i	0.0625416	+	0.108325i	0.895601	−	0.444859i	$-0.146746\pi$
$751$	35273.5	+	61095.6i	0.0625416	+	0.108325i	−0.833059	+	0.553184i	$0.813413\pi$
$752$	−16292.2	−	9406.30i	−0.0288100	−	0.0166335i
$753$	211940.	+	447316.i	0.373786	+	0.788904i
$754$	190611.	+	330148.i	0.335278	+	0.580718i
$755$		−	123595.i		−	0.216824i
$756$	284276.	−	29160.6i	0.497390	−	0.0510214i
$757$	486142.			0.848343			0.424172	−	0.905582i	$-0.360565\pi$
$757$	486142.			0.848343			0.424172	+	0.905582i	$0.360565\pi$
$758$	−295959.	+	170872.i	−0.515102	+	0.297394i
$759$	−242798.	+	115039.i	−0.421465	+	0.199692i
$760$	204210.	−	353703.i	0.353550	−	0.612366i
$761$	232358.	−	134152.i	0.401225	−	0.231647i	−0.285788	−	0.958293i	$-0.592255\pi$
$761$	232358.	−	134152.i	0.401225	−	0.231647i	0.687012	+	0.726646i	$0.258922\pi$
$762$	381957.	−	552682.i	0.657816	−	0.951843i
$763$	−98122.9	−	272524.i	−0.168547	−	0.468118i
$764$		−	29905.9i		−	0.0512354i
$765$	−409269.	+	500091.i	−0.699336	+	0.854528i
$766$	200339.	−	346998.i	0.341436	−	0.591384i
$767$	774966.	+	447427.i	1.31732	+	0.760556i
$768$	2987.39	−	36742.8i	0.00506489	−	0.0622944i
$769$	588792.			0.995657			0.497828	−	0.867276i	$-0.334131\pi$
$769$	588792.			0.995657			0.497828	+	0.867276i	$0.334131\pi$
$770$	117803.	−	654820.i	0.198689	−	1.10444i
$771$	−594036.	+	859555.i	−0.999319	+	1.44599i
$772$	139178.	+	241063.i	0.233526	+	0.404479i
$773$	−745360.	−	430334.i	−1.24740	−	0.720189i	−0.276813	−	0.960924i	$-0.589278\pi$
$773$	−745360.	−	430334.i	−1.24740	−	0.720189i	−0.970591	+	0.240735i	$0.922612\pi$
$774$	−36417.8	+	222476.i	−0.0607900	+	0.371365i
$775$	434834.	+	753155.i	0.723969	+	1.25395i
$776$		−	124004.i		−	0.205926i
$777$	−349430.	+	94632.4i	−0.578787	+	0.156746i
$778$	524310.			0.866221
$779$	−335345.	+	193612.i	−0.552608	+	0.319048i
$780$	−256069.	−	540454.i	−0.420889	−	0.888321i
$781$	−377277.	+	653463.i	−0.618527	+	1.07132i
$782$	−121520.	+	70159.9i	−0.198717	+	0.114730i
$783$	400136.	+	99355.2i	0.652656	+	0.162057i
$784$	−118395.	+	97955.5i	−0.192620	+	0.159366i
$785$		−	190682.i		−	0.309436i
$786$	−57896.6	+	712086.i	−0.0937147	+	1.15262i
$787$	182229.	−	315630.i	0.294217	−	0.509599i	−0.680585	−	0.732669i	$-0.738274\pi$
$787$	182229.	−	315630.i	0.294217	−	0.509599i	0.974802	+	0.223070i	$0.0716078\pi$
$788$	393512.	+	227194.i	0.633732	+	0.365885i
$789$	−237732.	−	19328.9i	−0.381886	−	0.0310495i
$790$	585508.			0.938164
$791$	−262047.	−	221434.i	−0.418818	−	0.353909i
$792$	−89249.0	−	236147.i	−0.142283	−	0.376471i
$793$	−270998.	−	469382.i	−0.430943	−	0.746415i
$794$	−357205.	−	206232.i	−0.566600	−	0.327127i
$795$	−886371.	+	419966.i	−1.40243	+	0.664476i
$796$	91924.5	+	159218.i	0.145079	+	0.251285i
$797$			926552.i			1.45866i	0.684164	+	0.729328i	$0.260167\pi$
$797$			926552.i			1.45866i	−0.684164	+	0.729328i	$0.739833\pi$
$798$	−455547.	+	457991.i	−0.715364	+	0.719202i
$799$	−67284.7			−0.105396
$800$	−92453.4	+	53378.0i	−0.144459	+	0.0834032i
$801$	−114028.	+	696594.i	−0.177724	+	1.08571i
$802$	−34042.1	+	58962.6i	−0.0529258	+	0.0916701i
$803$	296229.	−	171028.i	0.459406	−	0.265238i
$804$	−163264.	−	112831.i	−0.252568	−	0.174549i
$805$	−125390.	−	348254.i	−0.193495	−	0.537408i
$806$		−	994012.i		−	1.53011i
$807$	434278.	+	35309.2i	0.666839	+	0.0542177i
$808$	−62479.1	+	108217.i	−0.0957001	+	0.165757i
$809$	500564.	+	289001.i	0.764826	+	0.441572i	0.831026	−	0.556234i	$-0.187754\pi$
$809$	500564.	+	289001.i	0.764826	+	0.441572i	−0.0662001	+	0.997806i	$0.521088\pi$
$810$	−613025.	−	206222.i	−0.934348	−	0.314315i
$811$	−182213.			−0.277037			−0.138519	−	0.990360i	$-0.544234\pi$
$811$	−182213.			−0.277037			−0.138519	+	0.990360i	$0.544234\pi$
$812$	−208587.	+	75102.5i	−0.316356	+	0.113905i
$813$	−641482.	−	443326.i	−0.970517	−	0.670722i
$814$	159904.	+	276963.i	0.241330	+	0.417996i
$815$	−528153.	−	304929.i	−0.795141	−	0.459075i
$816$	−56453.5	−	119150.i	−0.0847833	−	0.178942i
$817$	−254797.	−	441322.i	−0.381725	−	0.661167i
$818$		−	314217.i		−	0.469595i
$819$	172457.	+	930038.i	0.257107	+	1.38654i
$820$	208480.			0.310054
$821$	194176.	−	112108.i	0.288078	−	0.166322i	−0.348997	−	0.937124i	$-0.613478\pi$
$821$	194176.	−	112108.i	0.288078	−	0.166322i	0.637075	+	0.770802i	$0.280144\pi$
$822$	680400.	−	322376.i	1.00698	−	0.477110i
$823$	−173272.	+	300116.i	−0.255817	+	0.443087i	−0.965117	−	0.261819i	$-0.915678\pi$
$823$	−173272.	+	300116.i	−0.255817	+	0.443087i	0.709300	+	0.704906i	$0.249011\pi$
$824$	−223521.	+	129050.i	−0.329204	+	0.190066i
$825$	−415645.	+	601428.i	−0.610681	+	0.883640i
$826$	−335882.	+	397484.i	−0.492296	+	0.582585i
$827$			136354.i			0.199369i	0.995019	+	0.0996846i	$0.0317834\pi$
$827$			136354.i			0.199369i	−0.995019	+	0.0996846i	$0.968217\pi$
$828$	−108686.	−	88947.5i	−0.158531	−	0.129740i
$829$	−319608.	+	553578.i	−0.465060	+	0.805508i	−0.999204	−	0.0398855i	$-0.987301\pi$
$829$	−319608.	+	553578.i	−0.465060	+	0.805508i	0.534144	+	0.845394i	$0.320634\pi$
$830$	−302503.	−	174650.i	−0.439111	−	0.253521i
$831$	−72558.0	+	892411.i	−0.105071	+	1.29230i
$832$	122020.			0.176272
$833$	−191544.	+	515132.i	−0.276045	+	0.742384i
$834$	−257507.	+	372606.i	−0.370217	+	0.535695i
$835$	−246379.	−	426741.i	−0.353371	−	0.612056i
$836$	494202.	+	285327.i	0.707118	+	0.408254i
$837$	−774019.	−	746020.i	−1.10484	−	1.06488i
$838$	−248110.	−	429740.i	−0.353311	−	0.611952i
$839$		−	1.00288e6i		−	1.42471i	−0.701819	−	0.712355i	$-0.747629\pi$
$839$		−	1.00288e6i		−	1.42471i	0.701819	−	0.712355i	$-0.252371\pi$
$840$	335697.	−	90913.2i	0.475761	−	0.128845i
$841$	387433.			0.547778
$842$	517727.	−	298910.i	0.730259	−	0.421615i
$843$	549907.	+	1.16062e6i	0.773809	+	1.63319i
$844$	11004.5	−	19060.3i	0.0154484	−	0.0267575i
$845$	852254.	−	492049.i	1.19359	−	0.689121i
$846$	−23808.3	−	62995.1i	−0.0332650	−	0.0880169i
$847$	208856.	+	37573.3i	0.291125	+	0.0523736i
$848$		−	200118.i		−	0.278289i
$849$	35060.8	−	431223.i	0.0486415	−	0.598255i
$850$	−190911.	+	330667.i	−0.264236	+	0.457671i
$851$	154081.	+	88958.5i	0.212759	+	0.122837i
$852$	−393132.	−	31963.8i	−0.541575	−	0.0440331i
$853$	−564453.			−0.775764			−0.387882	−	0.921709i	$-0.626793\pi$
$853$	−564453.			−0.775764			−0.387882	+	0.921709i	$0.626793\pi$
$854$	296556.	−	106776.i	0.406622	−	0.146405i
$855$	1.36762e6	−	516876.i	1.87083	−	0.707057i
$856$	−97936.2	−	169630.i	−0.133658	−	0.231503i
$857$	−333385.	−	192480.i	−0.453926	−	0.262074i	0.255561	−	0.966793i	$-0.417740\pi$
$857$	−333385.	−	192480.i	−0.453926	−	0.262074i	−0.709487	+	0.704719i	$0.751073\pi$
$858$	755135.	−	357786.i	1.02577	−	0.486014i
$859$	−182016.	−	315261.i	−0.246674	−	0.427252i	0.715927	−	0.698175i	$-0.246004\pi$
$859$	−182016.	−	315261.i	−0.246674	−	0.427252i	−0.962601	+	0.270923i	$0.912671\pi$
$860$			274365.i			0.370964i
$861$	−318731.	−	84490.3i	−0.429950	−	0.113973i
$862$	−655191.			−0.881766
$863$	−435468.	+	251418.i	−0.584702	+	0.337578i	−0.763000	−	0.646399i	$-0.776274\pi$
$863$	−435468.	+	251418.i	−0.584702	+	0.337578i	0.178298	+	0.983977i	$0.442941\pi$
$864$	91577.7	−	95014.7i	0.122677	−	0.127281i
$865$	1.02574e6	−	1.77664e6i	1.37090	−	2.37447i
$866$	33275.4	−	19211.6i	0.0443698	−	0.0256169i
$867$	230449.	+	159263.i	0.306576	+	0.211874i
$868$	568926.	+	102350.i	0.755120	+	0.135847i
$869$			818086.i			1.08333i
$870$	500117.	+	40662.3i	0.660744	+	0.0537222i
$871$	328450.	−	568892.i	0.432945	−	0.749883i
$872$	−115836.	−	66877.9i	−0.152339	−	0.0879529i
$873$	281137.	−	343525.i	0.368884	−	0.450744i
$874$	317468.			0.415602
$875$	45982.6	+	38856.2i	0.0600589	+	0.0507509i
$876$	147094.	+	101656.i	0.191684	+	0.132472i
$877$	254267.	+	440403.i	0.330591	+	0.572600i	0.982628	−	0.185587i	$-0.0594187\pi$
$877$	254267.	+	440403.i	0.330591	+	0.572600i	−0.652037	+	0.758187i	$0.726085\pi$
$878$	−82982.6	−	47910.0i	−0.107646	−	0.0621495i
$879$	92832.7	+	195931.i	0.120150	+	0.253586i
$880$	−153620.	−	266077.i	−0.198373	−	0.343592i
$881$		−	1.00766e6i		−	1.29826i	−0.760678	−	0.649129i	$-0.775134\pi$
$881$		−	1.00766e6i		−	1.29826i	0.760678	−	0.649129i	$-0.224866\pi$
$882$	−550067.	+	2943.63i	−0.707097	+	0.00378395i
$883$	273904.			0.351300			0.175650	−	0.984453i	$-0.443797\pi$
$883$	273904.			0.351300			0.175650	+	0.984453i	$0.443797\pi$
$884$	377945.	−	218207.i	0.483643	−	0.279231i
$885$	1.06439e6	−	504310.i	1.35898	−	0.643889i
$886$	−318416.	+	551513.i	−0.405628	+	0.702568i
$887$	1.17917e6	−	680796.i	1.49875	−	0.865305i	0.498754	−	0.866744i	$-0.333791\pi$
$887$	1.17917e6	−	680796.i	1.49875	−	0.865305i	0.999999	+	0.00143802i	$0.000457737\pi$
$888$	−95044.5	+	137527.i	−0.120532	+	0.174406i
$889$	−834677.	+	987761.i	−1.05612	+	1.24982i
$890$			859063.i			1.08454i
$891$	288138.	−	856534.i	0.362949	−	1.07892i
$892$	−301723.	+	522600.i	−0.379209	+	0.656810i
$893$	131834.	+	76114.7i	0.165320	+	0.0954477i
$894$	−30195.3	+	371380.i	−0.0377802	+	0.464669i
$895$	−1.07506e6			−1.34211
$896$	−12564.0	+	69838.4i	−0.0156499	+	0.0869918i
$897$	264294.	−	382427.i	0.328475	−	0.475296i
$898$	−309638.	−	536309.i	−0.383974	−	0.665062i
$899$	722251.	+	416992.i	0.893653	+	0.515951i
$900$	−377138.	−	61735.0i	−0.465603	−	0.0762160i
$901$	−357870.	−	619849.i	−0.440834	−	0.763547i
$902$			291294.i			0.358029i
$903$	111191.	−	419457.i	0.136362	−	0.514413i
$904$	−158427.			−0.193862
$905$	−501733.	+	289676.i	−0.612598	+	0.353684i
$906$	38651.5	+	81577.2i	0.0470880	+	0.0993830i
$907$	−267393.	+	463139.i	−0.325040	+	0.562985i	−0.981520	−	0.191358i	$-0.938711\pi$
$907$	−267393.	+	463139.i	−0.325040	+	0.562985i	0.656481	+	0.754343i	$0.272044\pi$
$908$	−143234.	+	82696.4i	−0.173730	+	0.100303i
$909$	−418430.	+	158141.i	−0.506402	+	0.191389i
$910$	389979.	+	1.08312e6i	0.470933	+	1.30795i
$911$		−	37566.0i		−	0.0452646i	−0.999744	−	0.0226323i	$-0.992795\pi$
$911$		−	37566.0i		−	0.0452646i	0.999744	−	0.0226323i	$-0.00720470\pi$
$912$	−24173.6	+	297318.i	−0.0290638	+	0.357463i
$913$	244026.	−	422665.i	0.292748	−	0.507054i
$914$	−582580.	−	336353.i	−0.697370	−	0.402627i
$915$	−711034.	−	57811.0i	−0.849275	−	0.0690508i
$916$	552144.			0.658054
$917$	243494.	−	1.35349e6i	0.289567	−	1.60960i
$918$	113740.	−	458067.i	0.134967	−	0.543555i
$919$	603074.	+	1.04455e6i	0.714068	+	1.23680i	0.963318	+	0.268363i	$0.0864827\pi$
$919$	603074.	+	1.04455e6i	0.714068	+	1.23680i	−0.249250	+	0.968439i	$0.580184\pi$
$920$	−148025.	−	85462.3i	−0.174888	−	0.100972i
$921$	−718151.	+	340263.i	−0.846636	+	0.401139i
$922$	−158293.	−	274171.i	−0.186209	−	0.322523i
$923$		−	1.30556e6i		−	1.53248i
$924$	127026.	+	469044.i	0.148781	+	0.549376i
$925$	484126.			0.565816
$926$	426570.	−	246281.i	0.497472	−	0.287216i
$927$	−911794.	−	149254.i	−1.06105	−	0.173687i
$928$	−51187.8	+	88659.9i	−0.0594389	+	0.102951i
$929$	−110152.	+	63596.5i	−0.127633	+	0.0736889i	−0.562457	−	0.826826i	$-0.690144\pi$
$929$	−110152.	+	63596.5i	−0.127633	+	0.0736889i	0.434824	+	0.900515i	$0.356811\pi$
$930$	−1.07631e6	−	743833.i	−1.24443	−	0.860022i
$931$	958037.	−	792644.i	1.10531	−	0.914490i
$932$			758397.i			0.873101i
$933$	−200684.	−	16316.8i	−0.230542	−	0.0187444i
$934$	260311.	−	450872.i	0.298400	−	0.516844i
$935$	−951647.	−	549434.i	−1.08856	−	0.628481i
$936$	338029.	+	276639.i	0.385835	+	0.315763i
$937$	443919.			0.505620			0.252810	−	0.967516i	$-0.418645\pi$
$937$	443919.			0.505620			0.252810	+	0.967516i	$0.418645\pi$
$938$	291788.	+	246566.i	0.331636	+	0.280238i
$939$	844006.	+	583290.i	0.957226	+	0.661536i
$940$	−40980.0	−	70979.5i	−0.0463785	−	0.0803299i
$941$	656825.	+	379218.i	0.741772	+	0.428262i	0.822713	−	0.568456i	$-0.192459\pi$
$941$	656825.	+	379218.i	0.741772	+	0.428262i	−0.0809411	+	0.996719i	$0.525793\pi$
$942$	59631.5	+	125857.i	0.0672007	+	0.141832i
$943$	81026.7	+	140342.i	0.0911181	+	0.157821i
$944$			240310.i			0.269667i
$945$	1.13609e6	+	509225.i	1.27218	+	0.570225i
$946$	−383349.			−0.428363
$947$	−679981.	+	392587.i	−0.758223	+	0.437760i	−0.828657	−	0.559756i	$-0.810895\pi$
$947$	−679981.	+	392587.i	−0.758223	+	0.437760i	0.0704344	+	0.997516i	$0.477561\pi$
$948$	−386456.	+	183104.i	−0.430014	+	0.203742i
$949$	−295919.	+	512547.i	−0.328580	+	0.569117i
$950$	748122.	−	431929.i	0.828944	−	0.478591i
$951$	218280.	−	315846.i	0.241354	−	0.349233i
$952$	85975.6	+	238786.i	0.0948640	+	0.263472i
$953$			1.35750e6i			1.49471i	0.664428	+	0.747353i	$0.268675\pi$
$953$			1.35750e6i			1.49471i	−0.664428	+	0.747353i	$0.731325\pi$
$954$	453701.	−	554384.i	0.498509	−	0.609135i
$955$	65144.9	−	112834.i	0.0714288	−	0.123718i
$956$	493910.	+	285159.i	0.540420	+	0.312012i
$957$	−56814.4	+	698776.i	−0.0620346	+	0.762981i
$958$	−850056.			−0.926225
$959$	−1.36358e6	+	490961.i	−1.48267	+	0.533838i
$960$	91309.1	−	132122.i	0.0990768	−	0.143362i
$961$	−625521.	−	1.08343e6i	−0.677322	−	1.17316i
$962$	−479212.	−	276673.i	−0.517818	−	0.298963i
$963$	113269.	−	691960.i	0.122140	−	0.746154i
$964$	−20329.2	−	35211.1i	−0.0218759	−	0.0378901i
$965$			1.21270e6i			1.30226i
$966$	191670.	+	190647.i	0.205400	+	0.204303i
$967$	−468442.			−0.500960			−0.250480	−	0.968122i	$-0.580588\pi$
$967$	−468442.			−0.500960			−0.250480	+	0.968122i	$0.580588\pi$
$968$	84865.8	−	48997.3i	0.0905695	−	0.0522903i
$969$	456815.	+	964144.i	0.486511	+	1.02682i
$970$	270121.	−	467864.i	0.287088	−	0.497252i
$971$	−277659.	+	160306.i	−0.294492	+	0.170025i	−0.639966	−	0.768403i	$-0.721051\pi$
$971$	−277659.	+	160306.i	−0.294492	+	0.170025i	0.345474	+	0.938428i	$0.387718\pi$
$972$	469109.	−	55595.7i	0.496525	−	0.0588448i
$973$	562720.	−	665926.i	0.594384	−	0.703397i
$974$			873869.i			0.921146i
$975$	102509.	−	1.26078e6i	0.107833	−	1.32627i
$976$	72775.5	−	126051.i	0.0763986	−	0.132326i
$977$	−661667.	−	382014.i	−0.693187	−	0.400212i	0.111618	−	0.993751i	$-0.464397\pi$
$977$	−661667.	−	382014.i	−0.693187	−	0.400212i	−0.804805	+	0.593539i	$0.797730\pi$
$978$	443958.	+	36096.3i	0.464156	+	0.0377385i
$979$	−1.20030e6			−1.25235
$980$	−660080.	+	111681.i	−0.687297	+	0.116286i
$981$	−169275.	−	447889.i	−0.175895	−	0.465407i
$982$	459555.	+	795973.i	0.476557	+	0.825421i
$983$	−103488.	−	59748.8i	−0.107098	−	0.0618333i	0.445494	−	0.895285i	$-0.353028\pi$
$983$	−103488.	−	59748.8i	−0.107098	−	0.0618333i	−0.552592	+	0.833452i	$0.686361\pi$
$984$	−137604.	+	65197.4i	−0.142116	+	0.0673349i
$985$	989807.	+	1.71440e6i	1.02018	+	1.76701i
$986$			366155.i			0.376626i
$987$	33885.8	+	125123.i	0.0347843	+	0.128441i
$988$	−987370.			−1.01150
$989$	−184694.	+	106633.i	−0.188825	+	0.109018i
$990$	177671.	−	1.08539e6i	0.181278	−	1.10743i
$991$	−429293.	+	743557.i	−0.437125	+	0.757123i	−0.997466	−	0.0711386i	$-0.977337\pi$
$991$	−429293.	+	743557.i	−0.437125	+	0.757123i	0.560341	+	0.828262i	$0.310670\pi$
$992$	231175.	−	133469.i	0.234919	−	0.135631i
$993$	−1.47212e6	−	1.01738e6i	−1.49295	−	1.03178i
$994$	747241.	+	134429.i	0.756290	+	0.136057i
$995$			800967.i			0.809038i
$996$	254280.	+	20674.4i	0.256327	+	0.0208408i
$997$	−177749.	+	307870.i	−0.178820	+	0.309725i	−0.941477	−	0.337078i	$-0.890561\pi$
$997$	−177749.	+	307870.i	−0.178820	+	0.309725i	0.762657	+	0.646804i	$0.223895\pi$
$998$	−618236.	−	356939.i	−0.620717	−	0.358371i
$999$	−575096.	+	165507.i	−0.576247	+	0.165838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.5.h.a.11.7	yes	20
3.2	odd	2	inner	42.5.h.a.11.3	✓	20
7.2	even	3	inner	42.5.h.a.23.3	yes	20
7.3	odd	6		294.5.b.f.197.6		10
7.4	even	3		294.5.b.e.197.10		10
21.2	odd	6	inner	42.5.h.a.23.7	yes	20
21.11	odd	6		294.5.b.e.197.5		10
21.17	even	6		294.5.b.f.197.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.h.a.11.3	✓	20	3.2	odd	2	inner
42.5.h.a.11.7	yes	20	1.1	even	1	trivial
42.5.h.a.23.3	yes	20	7.2	even	3	inner
42.5.h.a.23.7	yes	20	21.2	odd	6	inner
294.5.b.e.197.5		10	21.11	odd	6
294.5.b.e.197.10		10	7.4	even	3
294.5.b.f.197.1		10	21.17	even	6
294.5.b.f.197.6		10	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(-8.13327 + 3.85357i) q^{3} +(4.00000 - 6.92820i) q^{4} +(30.1838 - 17.4266i) q^{5} +(-14.4726 + 20.9415i) q^{6} +(31.6264 - 37.4269i) q^{7} -22.6274i q^{8} +(51.3000 - 62.6842i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{2} +(-8.13327 + 3.85357i) q^{3} +(4.00000 - 6.92820i) q^{4} +(30.1838 - 17.4266i) q^{5} +(-14.4726 + 20.9415i) q^{6} +(31.6264 - 37.4269i) q^{7} -22.6274i q^{8} +(51.3000 - 62.6842i) q^{9} +(49.2899 - 85.3727i) q^{10} +(119.285 + 68.8691i) q^{11} +(-5.83475 + 71.7632i) q^{12} -238.320 q^{13} +(24.5390 - 136.403i) q^{14} +(-178.338 + 258.051i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-198.234 - 114.451i) q^{17} +(37.0100 - 226.093i) q^{18} +(258.940 + 448.497i) q^{19} -278.826i q^{20} +(-112.999 + 426.277i) q^{21} +389.582 q^{22} +(187.697 - 108.367i) q^{23} +(87.1963 + 184.035i) q^{24} +(294.875 - 510.738i) q^{25} +(-583.763 + 337.036i) q^{26} +(-175.679 + 707.515i) q^{27} +(-132.795 - 368.822i) q^{28} -565.551i q^{29} +(-71.8986 + 884.301i) q^{30} +(-737.320 + 1277.08i) q^{31} +(-156.767 - 90.5097i) q^{32} +(-1235.57 - 100.458i) q^{33} -647.430 q^{34} +(302.382 - 1680.83i) q^{35} +(-229.089 - 606.154i) q^{36} +(410.451 + 710.922i) q^{37} +(1268.54 + 732.393i) q^{38} +(1938.32 - 918.383i) q^{39} +(-394.320 - 682.982i) q^{40} +747.708i q^{41} +(326.057 + 1203.97i) q^{42} -984.000 q^{43} +(954.278 - 550.953i) q^{44} +(456.055 - 2786.03i) q^{45} +(306.508 - 530.887i) q^{46} +(254.566 - 146.973i) q^{47} +(473.851 + 327.477i) q^{48} +(-400.540 - 2367.35i) q^{49} -1668.06i q^{50} +(2053.33 + 166.947i) q^{51} +(-953.281 + 1651.13i) q^{52} +(2707.93 + 1563.43i) q^{53} +(570.255 + 1981.50i) q^{54} +4800.62 q^{55} +(-846.873 - 715.624i) q^{56} +(-3834.34 - 2649.91i) q^{57} +(-799.810 - 1385.31i) q^{58} +(-3251.78 - 1877.42i) q^{59} +(1074.48 + 2267.77i) q^{60} +(1137.12 + 1969.54i) q^{61} +4170.91i q^{62} +(-723.638 - 3902.47i) q^{63} -512.000 q^{64} +(-7193.41 + 4153.12i) q^{65} +(-3168.58 + 1501.28i) q^{66} +(-1378.19 + 2387.09i) q^{67} +(-1585.87 + 915.604i) q^{68} +(-1108.99 + 1604.68i) q^{69} +(-1636.37 - 4544.80i) q^{70} +5478.18i q^{71} +(-1418.38 - 1160.79i) q^{72} +(1241.69 - 2150.67i) q^{73} +(2010.79 + 1160.93i) q^{74} +(-430.130 + 5290.29i) q^{75} +4143.04 q^{76} +(6350.10 - 2286.37i) q^{77} +(3449.11 - 4990.77i) q^{78} +(2969.71 + 5143.70i) q^{79} +(-1931.76 - 1115.30i) q^{80} +(-1297.62 - 6431.40i) q^{81} +(1057.42 + 1831.50i) q^{82} -3543.33i q^{83} +(2501.34 + 2487.99i) q^{84} -7977.95 q^{85} +(-2410.30 + 1391.59i) q^{86} +(2179.39 + 4599.78i) q^{87} +(1558.33 - 2699.11i) q^{88} +(-7546.88 + 4357.19i) q^{89} +(-2822.94 - 7469.32i) q^{90} +(-7537.21 + 8919.57i) q^{91} -1733.87i q^{92} +(1075.52 - 13228.1i) q^{93} +(415.704 - 720.020i) q^{94} +(15631.6 + 9024.91i) q^{95} +(1623.82 + 132.025i) q^{96} +5480.25 q^{97} +(-4329.06 - 5232.36i) q^{98} +(10436.3 - 3944.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

Introduction

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