LMFDB - Embedded newform 42.5.h.a.23.6

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			23.6
Root			$7.75666 - 1.28530i$ of defining polynomial
Character	$\chi$	$=$	42.23
Dual form			42.5.h.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 + 1.41421i) q^{2} +(-8.98141 - 0.578196i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-35.7395 - 20.6342i) q^{5} +(-21.1822 - 14.1179i) q^{6} +(-9.50910 - 48.0685i) q^{7} +22.6274i q^{8} +(80.3314 + 10.3860i) q^{9} +O(q^{10})$	\(q+(2.44949 + 1.41421i) q^{2} +(-8.98141 - 0.578196i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-35.7395 - 20.6342i) q^{5} +(-21.1822 - 14.1179i) q^{6} +(-9.50910 - 48.0685i) q^{7} +22.6274i q^{8} +(80.3314 + 10.3860i) q^{9} +(-58.3624 - 101.087i) q^{10} +(-127.299 + 73.4961i) q^{11} +(-31.9198 - 64.5378i) q^{12} -89.0960 q^{13} +(44.6866 - 131.191i) q^{14} +(309.061 + 205.989i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(41.5038 - 23.9622i) q^{17} +(182.083 + 139.046i) q^{18} +(30.9933 - 53.6820i) q^{19} -330.148i q^{20} +(57.6122 + 437.221i) q^{21} -415.757 q^{22} +(-127.669 - 73.7096i) q^{23} +(13.0831 - 203.226i) q^{24} +(539.043 + 933.649i) q^{25} +(-218.240 - 126.001i) q^{26} +(-715.484 - 139.728i) q^{27} +(294.992 - 258.155i) q^{28} -1075.61i q^{29} +(465.729 + 941.645i) q^{30} +(524.925 + 909.196i) q^{31} +(-156.767 + 90.5097i) q^{32} +(1185.82 - 586.495i) q^{33} +135.551 q^{34} +(-652.005 + 1914.16i) q^{35} +(249.369 + 598.096i) q^{36} +(1052.67 - 1823.28i) q^{37} +(151.836 - 87.6623i) q^{38} +(800.208 + 51.5149i) q^{39} +(466.899 - 808.693i) q^{40} -1695.63i q^{41} +(-477.203 + 1152.44i) q^{42} -3636.45 q^{43} +(-1018.39 - 587.969i) q^{44} +(-2656.70 - 2028.77i) q^{45} +(-208.482 - 361.102i) q^{46} +(-1913.88 - 1104.98i) q^{47} +(319.452 - 479.298i) q^{48} +(-2220.15 + 914.176i) q^{49} +3049.29i q^{50} +(-386.618 + 191.217i) q^{51} +(-356.384 - 617.275i) q^{52} +(2856.74 - 1649.34i) q^{53} +(-1554.96 - 1354.11i) q^{54} +6066.14 q^{55} +(1087.67 - 215.166i) q^{56} +(-309.402 + 464.220i) q^{57} +(1521.15 - 2634.71i) q^{58} +(-1289.36 + 744.410i) q^{59} +(-190.890 + 2965.19i) q^{60} +(-1516.02 + 2625.82i) q^{61} +2969.42i q^{62} +(-264.639 - 3960.17i) q^{63} -512.000 q^{64} +(3184.25 + 1838.43i) q^{65} +(3734.08 + 240.389i) q^{66} +(2270.71 + 3932.99i) q^{67} +(332.030 + 191.698i) q^{68} +(1104.03 + 735.834i) q^{69} +(-4304.11 + 3766.63i) q^{70} +155.944i q^{71} +(-235.009 + 1817.69i) q^{72} +(-2317.15 - 4013.42i) q^{73} +(5157.02 - 2977.41i) q^{74} +(-4301.53 - 8697.16i) q^{75} +495.893 q^{76} +(4743.34 + 5420.18i) q^{77} +(1887.25 + 1257.85i) q^{78} +(-2357.21 + 4082.81i) q^{79} +(2287.33 - 1320.59i) q^{80} +(6345.26 + 1668.65i) q^{81} +(2397.98 - 4153.43i) q^{82} +2608.10i q^{83} +(-2798.70 + 2148.03i) q^{84} -1977.77 q^{85} +(-8907.45 - 5142.72i) q^{86} +(-621.916 + 9660.53i) q^{87} +(-1663.03 - 2880.45i) q^{88} +(6521.76 + 3765.34i) q^{89} +(-3638.44 - 8726.58i) q^{90} +(847.223 + 4282.71i) q^{91} -1179.35i q^{92} +(-4188.87 - 8469.37i) q^{93} +(-3125.36 - 5413.28i) q^{94} +(-2215.37 + 1279.05i) q^{95} +(1460.32 - 722.262i) q^{96} +5570.35 q^{97} +(-6731.08 - 900.507i) q^{98} +(-10989.4 + 4581.91i) 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 $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$3$	−8.98141	−	0.578196i	−0.997934	−	0.0642440i
$3$	−8.98141	−	0.578196i	−0.997934	−	0.0642440i
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	−35.7395	−	20.6342i	−1.42958	−	0.825369i	−0.432494	−	0.901637i	$-0.642366\pi$
$5$	−35.7395	−	20.6342i	−1.42958	−	0.825369i	−0.997087	+	0.0762679i	$0.975700\pi$
$6$	−21.1822	−	14.1179i	−0.588394	−	0.392164i
$7$	−9.50910	−	48.0685i	−0.194063	−	0.980989i
$7$	−9.50910	−	48.0685i	−0.194063	−	0.980989i
$8$			22.6274i			0.353553i
$9$	80.3314	+	10.3860i	0.991745	+	0.128223i
$10$	−58.3624	−	101.087i	−0.583624	−	1.01087i
$11$	−127.299	+	73.4961i	−1.05206	+	0.607406i	−0.923225	−	0.384260i	$-0.874456\pi$
$11$	−127.299	+	73.4961i	−1.05206	+	0.607406i	−0.128833	+	0.991666i	$0.541123\pi$
$12$	−31.9198	−	64.5378i	−0.221665	−	0.448179i
$13$	−89.0960			−0.527195			−0.263598	−	0.964633i	$-0.584909\pi$
$13$	−89.0960			−0.527195			−0.263598	+	0.964633i	$0.584909\pi$
$14$	44.6866	−	131.191i	0.227993	−	0.669342i
$15$	309.061	+	205.989i	1.37360	+	0.915506i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	41.5038	−	23.9622i	0.143612	−	0.0829143i	−0.426472	−	0.904501i	$-0.640244\pi$
$17$	41.5038	−	23.9622i	0.143612	−	0.0829143i	0.570084	+	0.821586i	$0.306911\pi$
$18$	182.083	+	139.046i	0.561984	+	0.429155i
$19$	30.9933	−	53.6820i	0.0858540	−	0.148704i	−0.819901	−	0.572506i	$-0.805971\pi$
$19$	30.9933	−	53.6820i	0.0858540	−	0.148704i	0.905755	+	0.423802i	$0.139305\pi$
$20$		−	330.148i		−	0.825369i
$21$	57.6122	+	437.221i	0.130640	+	0.991430i
$22$	−415.757			−0.859002
$23$	−127.669	−	73.7096i	−0.241340	−	0.139338i	0.374453	−	0.927246i	$-0.377831\pi$
$23$	−127.669	−	73.7096i	−0.241340	−	0.139338i	−0.615792	+	0.787908i	$0.711164\pi$
$24$	13.0831	−	203.226i	0.0227137	−	0.352823i
$25$	539.043	+	933.649i	0.862468	+	1.49384i
$26$	−218.240	−	126.001i	−0.322840	−	0.186392i
$27$	−715.484	−	139.728i	−0.981459	−	0.191671i
$28$	294.992	−	258.155i	0.376265	−	0.329279i
$29$		−	1075.61i		−	1.27897i	−0.768803	−	0.639486i	$-0.779147\pi$
$29$		−	1075.61i		−	1.27897i	0.768803	−	0.639486i	$-0.220853\pi$
$30$	465.729	+	941.645i	0.517476	+	1.04627i
$31$	524.925	+	909.196i	0.546227	+	0.946094i	0.998529	+	0.0542284i	$0.0172699\pi$
$31$	524.925	+	909.196i	0.546227	+	0.946094i	−0.452301	+	0.891865i	$0.649397\pi$
$32$	−156.767	+	90.5097i	−0.153093	+	0.0883883i
$33$	1185.82	−	586.495i	1.08891	−	0.538563i
$34$	135.551			0.117259
$35$	−652.005	+	1914.16i	−0.532249	+	1.56258i
$36$	249.369	+	598.096i	0.192414	+	0.461494i
$37$	1052.67	−	1823.28i	0.768936	−	1.33184i	−0.169205	−	0.985581i	$-0.554120\pi$
$37$	1052.67	−	1823.28i	0.768936	−	1.33184i	0.938141	−	0.346255i	$-0.112547\pi$
$38$	151.836	−	87.6623i	0.105149	−	0.0607080i
$39$	800.208	+	51.5149i	0.526106	+	0.0338691i
$40$	466.899	−	808.693i	0.291812	−	0.505433i
$41$		−	1695.63i		−	1.00870i	−0.863499	−	0.504351i	$-0.831732\pi$
$41$		−	1695.63i		−	1.00870i	0.863499	−	0.504351i	$-0.168268\pi$
$42$	−477.203	+	1152.44i	−0.270523	+	0.653312i
$43$	−3636.45			−1.96671			−0.983357	−	0.181686i	$-0.941845\pi$
$43$	−3636.45			−1.96671			−0.983357	+	0.181686i	$0.941845\pi$
$44$	−1018.39	−	587.969i	−0.526029	−	0.303703i
$45$	−2656.70	−	2028.77i	−1.31195	−	1.00186i
$46$	−208.482	−	361.102i	−0.0985266	−	0.170653i
$47$	−1913.88	−	1104.98i	−0.866402	−	0.500218i	−0.000251398	−	1.00000i	$-0.500080\pi$
$47$	−1913.88	−	1104.98i	−0.866402	−	0.500218i	−0.866151	+	0.499782i	$0.833413\pi$
$48$	319.452	−	479.298i	0.138651	−	0.208029i
$49$	−2220.15	+	914.176i	−0.924679	+	0.380748i
$50$			3049.29i			1.21971i
$51$	−386.618	+	191.217i	−0.148642	+	0.0735168i
$52$	−356.384	−	617.275i	−0.131799	−	0.228282i
$53$	2856.74	−	1649.34i	1.01699	−	0.587162i	0.103763	−	0.994602i	$-0.466912\pi$
$53$	2856.74	−	1649.34i	1.01699	−	0.587162i	0.913232	+	0.407440i	$0.133578\pi$
$54$	−1554.96	−	1354.11i	−0.533252	−	0.464372i
$55$	6066.14			2.00534
$56$	1087.67	−	215.166i	0.346832	−	0.0686118i
$57$	−309.402	+	464.220i	−0.0952300	+	0.142881i
$58$	1521.15	−	2634.71i	0.452185	−	0.783207i
$59$	−1289.36	+	744.410i	−0.370398	+	0.213850i	−0.673632	−	0.739066i	$-0.735267\pi$
$59$	−1289.36	+	744.410i	−0.370398	+	0.213850i	0.303234	+	0.952916i	$0.401934\pi$
$60$	−190.890	+	2965.19i	−0.0530250	+	0.823664i
$61$	−1516.02	+	2625.82i	−0.407422	+	0.705675i	−0.994600	−	0.103783i	$-0.966905\pi$
$61$	−1516.02	+	2625.82i	−0.407422	+	0.705675i	0.587178	+	0.809458i	$0.300239\pi$
$62$			2969.42i			0.772482i
$63$	−264.639	−	3960.17i	−0.0666765	−	0.997775i
$64$	−512.000			−0.125000
$65$	3184.25	+	1838.43i	0.753668	+	0.435131i
$66$	3734.08	+	240.389i	0.857227	+	0.0551857i
$67$	2270.71	+	3932.99i	0.505839	+	0.876140i	0.999977	+	0.00675596i	$0.00215050\pi$
$67$	2270.71	+	3932.99i	0.505839	+	0.876140i	−0.494138	+	0.869384i	$0.664516\pi$
$68$	332.030	+	191.698i	0.0718059	+	0.0414572i
$69$	1104.03	+	735.834i	0.231890	+	0.154554i
$70$	−4304.11	+	3766.63i	−0.878389	+	0.768701i
$71$			155.944i			0.0309351i	0.999880	+	0.0154675i	$0.00492367\pi$
$71$			155.944i			0.0309351i	−0.999880	+	0.0154675i	$0.995076\pi$
$72$	−235.009	+	1817.69i	−0.0453335	+	0.350635i
$73$	−2317.15	−	4013.42i	−0.434819	−	0.753129i	0.562462	−	0.826823i	$-0.309854\pi$
$73$	−2317.15	−	4013.42i	−0.434819	−	0.753129i	−0.997281	+	0.0736944i	$0.976521\pi$
$74$	5157.02	−	2977.41i	0.941750	−	0.543720i
$75$	−4301.53	−	8697.16i	−0.764716	−	1.54616i
$76$	495.893			0.0858540
$77$	4743.34	+	5420.18i	0.800024	+	0.914182i
$78$	1887.25	+	1257.85i	0.310198	+	0.206747i
$79$	−2357.21	+	4082.81i	−0.377697	+	0.654191i	−0.990727	−	0.135869i	$-0.956617\pi$
$79$	−2357.21	+	4082.81i	−0.377697	+	0.654191i	0.613029	+	0.790060i	$0.289951\pi$
$80$	2287.33	−	1320.59i	0.357395	−	0.206342i
$81$	6345.26	+	1668.65i	0.967118	+	0.254328i
$82$	2397.98	−	4153.43i	0.356630	−	0.617702i
$83$			2608.10i			0.378589i	0.981920	+	0.189295i	$0.0606201\pi$
$83$			2608.10i			0.378589i	−0.981920	+	0.189295i	$0.939380\pi$
$84$	−2798.70	+	2148.03i	−0.396642	+	0.304426i
$85$	−1977.77			−0.273740
$86$	−8907.45	−	5142.72i	−1.20436	−	0.695338i
$87$	−621.916	+	9660.53i	−0.0821662	+	1.27633i
$88$	−1663.03	−	2880.45i	−0.214750	−	0.371959i
$89$	6521.76	+	3765.34i	0.823350	+	0.475361i	0.851570	−	0.524240i	$-0.175651\pi$
$89$	6521.76	+	3765.34i	0.823350	+	0.475361i	−0.0282202	+	0.999602i	$0.508984\pi$
$90$	−3638.44	−	8726.58i	−0.449191	−	1.07736i
$91$	847.223	+	4282.71i	0.102309	+	0.517173i
$92$		−	1179.35i		−	0.139338i
$93$	−4188.87	−	8469.37i	−0.484318	−	0.979231i
$94$	−3125.36	−	5413.28i	−0.353707	−	0.612639i
$95$	−2215.37	+	1279.05i	−0.245471	+	0.141723i
$96$	1460.32	−	722.262i	0.158455	−	0.0783704i
$97$	5570.35			0.592024			0.296012	−	0.955184i	$-0.404343\pi$
$97$	5570.35			0.592024			0.296012	+	0.955184i	$0.404343\pi$
$98$	−6731.08	−	900.507i	−0.700863	−	0.0937638i
$99$	−10989.4	+	4581.91i	−1.12126	+	0.467494i
$100$	−4312.34	+	7469.19i	−0.431234	+	0.746919i
$101$	−13863.0	+	8003.79i	−1.35898	+	0.784609i	−0.989487	−	0.144624i	$-0.953803\pi$
$101$	−13863.0	+	8003.79i	−1.35898	+	0.784609i	−0.369496	+	0.929232i	$0.620470\pi$
$102$	−1217.44	−	78.3750i	−0.117016	−	0.00753316i
$103$	8179.83	−	14167.9i	0.771027	−	1.33546i	−0.165974	−	0.986130i	$-0.553077\pi$
$103$	8179.83	−	14167.9i	0.771027	−	1.33546i	0.937001	−	0.349328i	$-0.113590\pi$
$104$		−	2016.01i		−	0.186392i
$105$	6962.68	−	16814.8i	0.631535	−	1.52516i
$106$	9330.07			0.830373
$107$	990.170	+	571.675i	0.0864853	+	0.0499323i	0.542619	−	0.839979i	$-0.317433\pi$
$107$	990.170	+	571.675i	0.0864853	+	0.0499323i	−0.456134	+	0.889911i	$0.650766\pi$
$108$	−1893.87	−	5515.93i	−0.162369	−	0.472902i
$109$	−2551.54	−	4419.39i	−0.214758	−	0.371971i	0.738440	−	0.674319i	$-0.235563\pi$
$109$	−2551.54	−	4419.39i	−0.214758	−	0.371971i	−0.953198	+	0.302348i	$0.902229\pi$
$110$	14859.0	+	8578.82i	1.22801	+	0.708993i
$111$	−10508.7	+	15767.0i	−0.852910	+	1.27968i
$112$	2968.52	+	1011.14i	0.236648	+	0.0806077i
$113$		−	14607.1i		−	1.14395i	−0.820270	−	0.571976i	$-0.806177\pi$
$113$		−	14607.1i		−	1.14395i	0.820270	−	0.571976i	$-0.193823\pi$
$114$	−1414.38	+	699.540i	−0.108832	+	0.0538274i
$115$	3041.88	+	5268.69i	0.230010	+	0.398389i
$116$	7452.08	−	4302.46i	0.553811	−	0.319743i
$117$	−7157.20	−	925.353i	−0.522844	−	0.0675983i
$118$	−4211.02			−0.302429
$119$	−1546.49	−	1767.16i	−0.109208	−	0.124791i
$120$	−4661.00	+	6993.24i	−0.323680	+	0.485642i
$121$	3482.85	−	6032.48i	0.237884	−	0.412027i
$122$	−7426.93	+	4287.94i	−0.498988	+	0.288091i
$123$	−980.406	+	15229.1i	−0.0648031	+	1.00662i
$124$	−4199.40	+	7273.57i	−0.273114	+	0.473047i
$125$		−	18698.1i		−	1.19668i
$126$	4952.29	−	10074.6i	0.311936	−	0.634583i
$127$	−1857.78			−0.115182			−0.0575912	−	0.998340i	$-0.518342\pi$
$127$	−1857.78			−0.115182			−0.0575912	+	0.998340i	$0.518342\pi$
$128$	−1254.14	−	724.077i	−0.0765466	−	0.0441942i
$129$	32660.5	+	2102.58i	1.96265	+	0.126349i
$130$	5199.86	+	9006.42i	0.307684	+	0.532924i
$131$	−12917.4	−	7457.89i	−0.752721	−	0.434584i	0.0739551	−	0.997262i	$-0.476438\pi$
$131$	−12917.4	−	7457.89i	−0.752721	−	0.434584i	−0.826676	+	0.562678i	$0.809771\pi$
$132$	8806.63	+	5869.62i	0.505431	+	0.336870i
$133$	−2875.13	−	979.333i	−0.162538	−	0.0553640i
$134$			12845.1i			0.715365i
$135$	22687.9	+	19757.3i	1.24488	+	1.08408i
$136$	542.204	+	939.124i	0.0293146	+	0.0507744i
$137$	−7337.66	+	4236.40i	−0.390946	+	0.225713i	−0.682570	−	0.730820i	$-0.739138\pi$
$137$	−7337.66	+	4236.40i	−0.390946	+	0.225713i	0.291624	+	0.956533i	$0.405804\pi$
$138$	1663.68	+	3363.75i	0.0873596	+	0.176630i
$139$	−11916.2			−0.616748			−0.308374	−	0.951265i	$-0.599785\pi$
$139$	−11916.2			−0.616748			−0.308374	+	0.951265i	$0.599785\pi$
$140$	−15869.7	+	3139.41i	−0.809678	+	0.160174i
$141$	16550.5	+	11030.9i	0.832477	+	0.554846i
$142$	−220.538	+	381.982i	−0.0109372	+	0.0189438i
$143$	11341.8	−	6548.21i	0.554640	−	0.320221i
$144$	−3146.26	+	4120.06i	−0.151729	+	0.198691i
$145$	−22194.5	+	38442.0i	−1.05562	+	1.82839i
$146$		−	13107.8i		−	0.614927i
$147$	20468.7	−	6926.90i	0.947229	−	0.320556i
$148$	16842.8			0.768936
$149$	3006.80	+	1735.98i	0.135435	+	0.0781936i	0.566187	−	0.824277i	$-0.308418\pi$
$149$	3006.80	+	1735.98i	0.135435	+	0.0781936i	−0.430751	+	0.902471i	$0.641751\pi$
$150$	1763.08	−	27386.9i	0.0783593	−	1.21719i
$151$	−18186.7	−	31500.4i	−0.797629	−	1.38153i	−0.921156	−	0.389193i	$-0.872754\pi$
$151$	−18186.7	−	31500.4i	−0.797629	−	1.38153i	0.123527	−	0.992341i	$-0.460580\pi$
$152$	1214.68	+	701.299i	0.0525746	+	0.0303540i
$153$	3582.93	−	1493.86i	0.153058	−	0.0638156i
$154$	3953.47	+	19984.8i	0.166701	+	0.842671i
$155$		−	43325.7i		−	1.80336i
$156$	2843.92	+	5750.06i	0.116861	+	0.236278i
$157$	−1000.68	−	1733.23i	−0.0405972	−	0.0703164i	0.845013	−	0.534746i	$-0.179593\pi$
$157$	−1000.68	−	1733.23i	−0.0405972	−	0.0703164i	−0.885610	+	0.464430i	$0.846259\pi$
$158$	−11547.9	+	6667.20i	−0.462583	+	0.267072i
$159$	−26611.2	+	13161.6i	−1.05262	+	0.520613i
$160$	7470.39			0.291812
$161$	−2329.09	+	6837.76i	−0.0898535	+	0.263792i
$162$	13182.8	+	13060.9i	0.502318	+	0.497671i
$163$	16529.1	−	28629.2i	0.622119	−	1.07754i	−0.366971	−	0.930232i	$-0.619605\pi$
$163$	16529.1	−	28629.2i	0.622119	−	1.07754i	0.989090	−	0.147309i	$-0.0470613\pi$
$164$	11747.7	−	6782.52i	0.436781	−	0.252176i
$165$	−54482.5	−	3507.42i	−2.00119	−	0.128831i
$166$	−3688.41	+	6388.51i	−0.133851	+	0.231837i
$167$			36645.4i			1.31397i	0.753902	+	0.656987i	$0.228169\pi$
$167$			36645.4i			1.31397i	−0.753902	+	0.656987i	$0.771831\pi$
$168$	−9893.17	+	1303.61i	−0.350523	+	0.0461881i
$169$	−20622.9			−0.722065
$170$	−4844.52	−	2796.99i	−0.167631	−	0.0967816i
$171$	3047.28	−	3990.45i	0.104213	−	0.136468i
$172$	−14545.8	−	25194.1i	−0.491678	−	0.851612i
$173$	35464.5	+	20475.4i	1.18495	+	0.684134i	0.957156	−	0.289574i	$-0.0935137\pi$
$173$	35464.5	+	20475.4i	1.18495	+	0.684134i	0.227799	+	0.973708i	$0.426847\pi$
$174$	−15185.4	+	22783.9i	−0.501567	+	0.752539i
$175$	39753.3	−	34789.1i	1.29807	−	1.13597i
$176$		−	9407.50i		−	0.303703i
$177$	12010.7	−	5940.35i	0.383372	−	0.189612i
$178$	10650.0	+	18446.3i	0.336131	+	0.582197i
$179$	23082.1	−	13326.5i	0.720394	−	0.415919i	−0.0945039	−	0.995524i	$-0.530126\pi$
$179$	23082.1	−	13326.5i	0.720394	−	0.415919i	0.814898	+	0.579605i	$0.196793\pi$
$180$	3428.92	−	26521.2i	0.105831	−	0.818556i
$181$	15250.8			0.465518			0.232759	−	0.972534i	$-0.425225\pi$
$181$	15250.8			0.465518			0.232759	+	0.972534i	$0.425225\pi$
$182$	−3981.40	+	11688.6i	−0.120197	+	0.352874i
$183$	15134.2	−	22707.0i	0.451915	−	0.678043i
$184$	1667.86	−	2888.82i	0.0492633	−	0.0853265i
$185$	−75244.1	+	43442.2i	−2.19851	+	1.26931i
$186$	1716.91	−	26669.6i	0.0496273	−	0.770887i
$187$	−3522.26	+	6100.74i	−0.100725	+	0.174461i
$188$		−	17679.7i		−	0.500218i
$189$	87.0797	+	35720.9i	0.00243777	+	0.999997i
$190$	−7235.38			−0.200426
$191$	4739.91	+	2736.59i	0.129928	+	0.0750140i	0.563555	−	0.826078i	$-0.309433\pi$
$191$	4739.91	+	2736.59i	0.129928	+	0.0750140i	−0.433627	+	0.901092i	$0.642767\pi$
$192$	4598.48	+	296.036i	0.124742	+	0.00803050i
$193$	3213.74	+	5566.36i	0.0862772	+	0.149436i	0.905935	−	0.423417i	$-0.139170\pi$
$193$	3213.74	+	5566.36i	0.0862772	+	0.149436i	−0.819658	+	0.572854i	$0.805836\pi$
$194$	13644.5	+	7877.66i	0.362539	+	0.209312i
$195$	−27536.1	−	18352.8i	−0.724157	−	0.482650i
$196$	−15214.2	−	11725.0i	−0.396038	−	0.305211i
$197$		−	43125.8i		−	1.11123i	−0.831439	−	0.555615i	$-0.812483\pi$
$197$		−	43125.8i		−	1.11123i	0.831439	−	0.555615i	$-0.187517\pi$
$198$	−33398.3	−	4318.06i	−0.851911	−	0.110143i
$199$	−7021.44	−	12161.5i	−0.177305	−	0.307101i	0.763652	−	0.645628i	$-0.223404\pi$
$199$	−7021.44	−	12161.5i	−0.177305	−	0.307101i	−0.940956	+	0.338528i	$0.890071\pi$
$200$	−21126.1	+	12197.1i	−0.528152	+	0.304929i
$201$	−18120.2	−	36636.7i	−0.448508	−	0.906827i
$202$	−45276.3			−1.10960
$203$	−51703.1	+	10228.1i	−1.25466	+	0.248201i
$204$	−2871.26	−	1913.70i	−0.0689942	−	0.0459846i
$205$	−34988.0	+	60601.0i	−0.832552	+	1.44202i
$206$	40072.8	−	23136.0i	0.944311	−	0.545198i
$207$	−9490.26	−	7247.17i	−0.221481	−	0.169133i
$208$	2851.07	−	4938.20i	0.0658994	−	0.114141i
$209$			9111.55i			0.208593i
$210$	40834.8	−	31341.1i	0.925959	−	0.710682i
$211$	5524.96			0.124098			0.0620489	−	0.998073i	$-0.480237\pi$
$211$	5524.96			0.124098			0.0620489	+	0.998073i	$0.480237\pi$
$212$	22853.9	+	13194.7i	0.508497	+	0.293581i
$213$	90.1660	−	1400.59i	0.00198739	−	0.0308712i
$214$	1616.94	+	2800.62i	0.0353075	+	0.0611543i
$215$	129965.	+	75035.4i	2.81158	+	1.62326i
$216$	3161.69	−	16189.5i	0.0677661	−	0.346998i
$217$	38712.1	−	33878.0i	0.822105	−	0.719445i
$218$		−	14433.7i		−	0.303713i
$219$	18490.7	+	37386.0i	0.385537	+	0.779508i
$220$	24264.6	+	42027.5i	0.501334	+	0.868336i
$221$	−3697.82	+	2134.94i	−0.0757115	+	0.0437120i
$222$	−48038.9	+	23759.6i	−0.974735	+	0.482095i
$223$	38437.9			0.772947			0.386473	−	0.922301i	$-0.373693\pi$
$223$	38437.9			0.772947			0.386473	+	0.922301i	$0.373693\pi$
$224$	5841.38	+	6674.90i	0.116418	+	0.133030i
$225$	33605.1	+	80599.8i	0.663805	+	1.59210i
$226$	20657.6	−	35780.0i	0.404448	−	0.700525i
$227$	22075.4	−	12745.3i	0.428408	−	0.247341i	−0.270260	−	0.962787i	$-0.587110\pi$
$227$	22075.4	−	12745.3i	0.428408	−	0.247341i	0.698668	+	0.715446i	$0.253776\pi$
$228$	−4453.82	−	286.723i	−0.0856767	−	0.00551561i
$229$	−14043.0	+	24323.2i	−0.267787	+	0.463820i	−0.968290	−	0.249829i	$-0.919626\pi$
$229$	−14043.0	+	24323.2i	−0.267787	+	0.463820i	0.700503	+	0.713649i	$0.252959\pi$
$230$			17207.5i			0.325283i
$231$	−39468.0	−	51423.5i	−0.739641	−	0.963690i
$232$	24338.4			0.452185
$233$	−40928.8	−	23630.3i	−0.753906	−	0.435268i	0.0731973	−	0.997317i	$-0.476680\pi$
$233$	−40928.8	−	23630.3i	−0.753906	−	0.435268i	−0.827104	+	0.562049i	$0.810013\pi$
$234$	−16222.9	−	12388.5i	−0.296275	−	0.226248i
$235$	45600.9	+	78983.0i	0.825728	+	1.43020i
$236$	−10314.9	−	5955.28i	−0.185199	−	0.106925i
$237$	23531.7	−	35306.4i	0.418945	−	0.628575i
$238$	−1288.97	−	6515.72i	−0.0227556	−	0.115029i
$239$			16631.0i			0.291153i	0.989347	+	0.145577i	$0.0465038\pi$
$239$			16631.0i			0.291153i	−0.989347	+	0.145577i	$0.953496\pi$
$240$	−21307.0	+	10538.2i	−0.369913	+	0.182956i
$241$	25998.5	+	45030.7i	0.447624	+	0.775308i	0.998231	−	0.0594569i	$-0.0189369\pi$
$241$	25998.5	+	45030.7i	0.447624	+	0.775308i	−0.550607	+	0.834765i	$0.685604\pi$
$242$	17062.4	−	9851.00i	0.291347	−	0.168209i
$243$	−56024.6	−	18655.6i	−0.948781	−	0.315934i
$244$	−24256.3			−0.407422
$245$	98210.6	+	13138.9i	1.63616	+	0.218891i
$246$	−23938.7	+	35917.1i	−0.395577	+	0.593514i
$247$	−2761.38	+	4782.85i	−0.0452618	+	0.0783958i
$248$	−20572.8	+	11877.7i	−0.334495	+	0.193121i
$249$	1507.99	−	23424.4i	0.0243221	−	0.377807i
$250$	26443.1	−	45800.9i	0.423090	−	0.732814i
$251$			15839.9i			0.251423i	0.992067	+	0.125712i	$0.0401214\pi$
$251$			15839.9i			0.251423i	−0.992067	+	0.125712i	$0.959879\pi$
$252$	26378.3	−	17674.1i	0.415380	−	0.278315i
$253$	21669.5			0.338538
$254$	−4550.60	−	2627.29i	−0.0705345	−	0.0407231i
$255$	17763.1	+	1143.54i	0.273174	+	0.0175861i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−73719.7	−	42562.1i	−1.11614	−	0.644402i	−0.175725	−	0.984439i	$-0.556227\pi$
$257$	−73719.7	−	42562.1i	−1.11614	−	0.644402i	−0.940412	+	0.340037i	$0.889560\pi$
$258$	77028.0	+	51339.1i	1.15720	+	0.771275i
$259$	−97652.4	−	33262.6i	−1.45574	−	0.495857i
$260$			29414.8i			0.435131i
$261$	11171.4	−	86405.6i	0.163993	−	1.26841i
$262$	−21094.1	−	36536.1i	−0.307297	−	0.532254i
$263$	35078.7	−	20252.7i	0.507145	−	0.292800i	−0.224514	−	0.974471i	$-0.572080\pi$
$263$	35078.7	−	20252.7i	0.507145	−	0.292800i	0.731659	+	0.681671i	$0.238746\pi$
$264$	13270.9	+	26832.0i	0.190411	+	0.384987i
$265$	−136131.			−1.93850
$266$	−5657.61	−	6464.91i	−0.0799595	−	0.0913691i
$267$	−56397.5	−	37588.9i	−0.791110	−	0.527275i
$268$	−18165.7	+	31463.9i	−0.252920	+	0.438070i
$269$	9132.25	−	5272.51i	0.126204	−	0.0728639i	−0.435569	−	0.900155i	$-0.643453\pi$
$269$	9132.25	−	5272.51i	0.126204	−	0.0728639i	0.561773	+	0.827291i	$0.310119\pi$
$270$	27632.7	+	80480.7i	0.379049	+	1.10399i
$271$	46807.6	−	81073.2i	0.637350	−	1.10392i	−0.348662	−	0.937249i	$-0.613364\pi$
$271$	46807.6	−	81073.2i	0.637350	−	1.10392i	0.986012	−	0.166674i	$-0.0533029\pi$
$272$			3067.17i			0.0414572i
$273$	−5133.01	−	38954.6i	−0.0688727	−	0.522677i
$274$	−23964.7			−0.319206
$275$	−137239.	−	79235.1i	−1.81473	−	1.04774i
$276$	−681.897	+	10592.3i	−0.00895161	+	0.139050i
$277$	−23815.8	−	41250.1i	−0.310388	−	0.537608i	0.668058	−	0.744109i	$-0.267126\pi$
$277$	−23815.8	−	41250.1i	−0.310388	−	0.537608i	−0.978446	+	0.206501i	$0.933792\pi$
$278$	−29188.6	−	16852.0i	−0.377680	−	0.218053i
$279$	32725.0	+	78488.9i	0.420408	+	1.00832i
$280$	−43312.4	−	14753.2i	−0.552454	−	0.188178i
$281$			23522.0i			0.297894i	0.988845	+	0.148947i	$0.0475883\pi$
$281$			23522.0i			0.297894i	−0.988845	+	0.148947i	$0.952412\pi$
$282$	24940.2	+	50425.9i	0.313618	+	0.634097i
$283$	−54327.0	−	94097.2i	−0.678333	−	1.17491i	−0.975483	−	0.220077i	$-0.929369\pi$
$283$	−54327.0	−	94097.2i	−0.678333	−	1.17491i	0.297149	−	0.954831i	$-0.403964\pi$
$284$	−1080.41	+	623.775i	−0.0133953	+	0.00773377i
$285$	20636.7	−	10206.7i	0.254068	−	0.125660i
$286$	37042.3			0.452862
$287$	−81506.3	+	16123.9i	−0.989526	+	0.195752i
$288$	−13533.4	+	5642.58i	−0.163163	+	0.0680288i
$289$	−40612.1	+	70342.3i	−0.486250	+	0.842210i
$290$	−108730.	+	62775.5i	−1.29287	+	0.746438i
$291$	−50029.6	−	3220.75i	−0.590801	−	0.0380340i
$292$	18537.2	−	32107.4i	0.217410	−	0.376564i
$293$		−	57127.2i		−	0.665438i	−0.943026	−	0.332719i	$-0.892034\pi$
$293$		−	57127.2i		−	0.665438i	0.943026	−	0.332719i	$-0.107966\pi$
$294$	59933.9	+	11979.7i	0.693391	+	0.138596i
$295$	61441.3			0.706019
$296$	41256.2	+	23819.3i	0.470875	+	0.271860i
$297$	101350.	−	34798.0i	1.14897	−	0.394495i
$298$	4910.08	+	8504.51i	0.0552912	+	0.0957672i
$299$	11374.8	+	6567.23i	0.127233	+	0.0734581i
$300$	43049.5	−	64590.5i	0.478328	−	0.717672i
$301$	34579.4	+	174799.i	0.381667	+	1.92932i
$302$		−	102880.i		−	1.12802i
$303$	129137.	−	63869.8i	1.40658	−	0.695682i
$304$	1983.57	+	3435.65i	0.0214635	+	0.0371759i
$305$	108363.	−	62563.6i	1.16488	−	0.672547i
$306$	10889.0	+	1407.83i	0.116291	+	0.0150352i
$307$	80592.6			0.855103			0.427551	−	0.903991i	$-0.359376\pi$
$307$	80592.6			0.855103			0.427551	+	0.903991i	$0.359376\pi$
$308$	−18578.8	+	54543.6i	−0.195846	+	0.574966i
$309$	−81658.2	+	122518.i	−0.855229	+	1.28317i
$310$	61271.7	−	106126.i	0.637583	−	1.10433i
$311$	−24072.3	+	13898.2i	−0.248884	+	0.143693i	−0.619253	−	0.785191i	$-0.712565\pi$
$311$	−24072.3	+	13898.2i	−0.248884	+	0.143693i	0.370369	+	0.928885i	$0.379231\pi$
$312$	−1165.65	+	18106.6i	−0.0119745	+	0.186007i
$313$	61861.1	−	107147.i	0.631435	−	1.09368i	−0.355823	−	0.934553i	$-0.615799\pi$
$313$	61861.1	−	107147.i	0.631435	−	1.09368i	0.987259	−	0.159125i	$-0.0508672\pi$
$314$		−	5660.70i		−	0.0574131i
$315$	−72256.9	+	146995.i	−0.728213	+	1.48143i
$316$	−37715.4			−0.377697
$317$	42654.4	+	24626.5i	0.424468	+	0.245067i	0.696987	−	0.717084i	$-0.254523\pi$
$317$	42654.4	+	24626.5i	0.424468	+	0.245067i	−0.272519	+	0.962150i	$0.587857\pi$
$318$	−83797.1	−	5394.61i	−0.828657	−	0.0533464i
$319$	79053.5	+	136925.i	0.776855	+	1.34555i
$320$	18298.6	+	10564.7i	0.178698	+	0.103171i
$321$	−8562.58	−	5706.96i	−0.0830987	−	0.0553853i
$322$	−15375.1	+	13455.2i	−0.148288	+	0.129771i
$323$		−	2970.68i		−	0.0284741i
$324$	13820.3	+	50635.8i	0.131652	+	0.482356i
$325$	−48026.5	−	83184.4i	−0.454689	−	0.787545i
$326$	80975.6	−	46751.3i	0.761937	−	0.439905i
$327$	20361.1	+	41167.6i	0.190417	+	0.385000i
$328$	38367.7			0.356630
$329$	−34915.4	+	102505.i	−0.322571	+	0.947005i
$330$	−128494.	−	85641.3i	−1.17993	−	0.786421i
$331$	−60472.3	+	104741.i	−0.551951	+	0.956007i	0.446183	+	0.894942i	$0.352783\pi$
$331$	−60472.3	+	104741.i	−0.551951	+	0.956007i	−0.998134	+	0.0610651i	$0.980550\pi$
$332$	−18069.4	+	10432.4i	−0.163934	+	0.0946473i
$333$	103499.	−	135534.i	0.933360	−	1.22225i
$334$	−51824.5	+	89762.6i	−0.464560	+	0.804642i
$335$		−	187418.i		−	1.67002i
$336$	−26076.8	−	10797.9i	−0.230981	−	0.0956444i
$337$	−99404.2			−0.875276			−0.437638	−	0.899151i	$-0.644185\pi$
$337$	−99404.2			−0.875276			−0.437638	+	0.899151i	$0.644185\pi$
$338$	−50515.6	−	29165.2i	−0.442173	−	0.255289i
$339$	−8445.78	+	131193.i	−0.0734921	+	1.14159i
$340$	−7911.08	−	13702.4i	−0.0684349	−	0.118533i
$341$	−133645.	−	77159.8i	−1.14933	−	0.663564i
$342$	13107.6	−	5465.07i	0.112065	−	0.0467243i
$343$	65054.7	+	98026.4i	0.552956	+	0.833211i
$344$		−	82283.5i		−	0.695338i
$345$	−24274.0	−	49079.1i	−0.203941	−	0.412343i
$346$	57913.3	+	100309.i	0.483756	+	0.837889i
$347$	−117959.	+	68103.7i	−0.979653	+	0.565603i	−0.902165	−	0.431390i	$-0.858023\pi$
$347$	−117959.	+	68103.7i	−0.979653	+	0.565603i	−0.0774877	+	0.996993i	$0.524690\pi$
$348$	−69417.8	+	34333.4i	−0.573208	+	0.283503i
$349$	178669.			1.46689			0.733444	−	0.679750i	$-0.237912\pi$
$349$	178669.			1.46689			0.733444	+	0.679750i	$0.237912\pi$
$350$	146574.	−	28996.0i	1.19653	−	0.236702i
$351$	63746.7	+	12449.2i	0.517421	+	0.101048i
$352$	13304.2	−	23043.6i	0.107375	−	0.185979i
$353$	67959.1	−	39236.2i	0.545379	−	0.314875i	−0.201877	−	0.979411i	$-0.564704\pi$
$353$	67959.1	−	39236.2i	0.545379	−	0.314875i	0.747256	+	0.664536i	$0.231371\pi$
$354$	37820.9	+	2434.80i	0.301804	+	0.0194292i
$355$	3217.78	−	5573.35i	0.0255328	−	0.0442242i
$356$			60245.4i			0.475361i
$357$	12867.9	+	16765.8i	0.100965	+	0.131549i
$358$	75385.9			0.588199
$359$	155968.	+	90048.3i	1.21017	+	0.698693i	0.962797	−	0.270226i	$-0.0870986\pi$
$359$	155968.	+	90048.3i	1.21017	+	0.698693i	0.247375	+	0.968920i	$0.420432\pi$
$360$	45905.8	−	60114.2i	0.354211	−	0.463844i
$361$	63239.3	+	109534.i	0.485258	+	0.840492i
$362$	37356.7	+	21567.9i	0.285070	+	0.164585i
$363$	−34768.9	+	52166.4i	−0.263862	+	0.395893i
$364$	−26282.6	+	23000.6i	−0.198365	+	0.173594i
$365$			191251.i			1.43555i
$366$	69183.6	−	34217.5i	0.516465	−	0.255439i
$367$	−86519.3	−	149856.i	−0.642364	−	1.11261i	−0.984904	−	0.173103i	$-0.944621\pi$
$367$	−86519.3	−	149856.i	−0.642364	−	1.11261i	0.342540	−	0.939503i	$-0.388713\pi$
$368$	8170.80	−	4717.42i	0.0603350	−	0.0348344i
$369$	17610.8	−	136212.i	0.129338	−	1.00038i
$370$	−245746.			−1.79508
$371$	−106446.	−	121635.i	−0.773361	−	0.883714i
$372$	41922.0	−	62898.8i	0.302940	−	0.454524i
$373$	47674.5	−	82574.7i	0.342664	−	0.593512i	−0.642262	−	0.766485i	$-0.722004\pi$
$373$	47674.5	−	82574.7i	0.342664	−	0.593512i	0.984927	+	0.172973i	$0.0553373\pi$
$374$	−17255.5	+	9962.46i	−0.123363	+	0.0712235i
$375$	−10811.2	+	167935.i	−0.0768795	+	1.19421i
$376$	25002.9	−	43306.2i	0.176854	−	0.306320i
$377$			95833.0i			0.674268i
$378$	−50303.7	+	87621.1i	−0.352060	+	0.613232i
$379$	−82652.9			−0.575413			−0.287707	−	0.957719i	$-0.592893\pi$
$379$	−82652.9			−0.575413			−0.287707	+	0.957719i	$0.592893\pi$
$380$	−17723.0	−	10232.4i	−0.122735	−	0.0708613i
$381$	16685.4	+	1074.16i	0.114944	+	0.00739977i
$382$	7740.24	+	13406.5i	0.0530429	+	0.0918731i
$383$	−6176.04	−	3565.74i	−0.0421029	−	0.0243081i	0.478801	−	0.877924i	$-0.341072\pi$
$383$	−6176.04	−	3565.74i	−0.0421029	−	0.0243081i	−0.520904	+	0.853615i	$0.674405\pi$
$384$	10845.3	+	7228.37i	0.0735492	+	0.0490205i
$385$	−57683.6	−	291590.i	−0.389162	−	1.96721i
$386$			18179.7i			0.122014i
$387$	−292121.	−	37768.3i	−1.95048	−	0.252177i
$388$	22281.4	+	38592.5i	0.148006	+	0.256354i
$389$	−19509.6	+	11263.9i	−0.128929	+	0.0744370i	−0.563077	−	0.826404i	$-0.690383\pi$
$389$	−19509.6	+	11263.9i	−0.128929	+	0.0744370i	0.434149	+	0.900841i	$0.357049\pi$
$390$	−41494.6	−	83896.8i	−0.272811	−	0.551590i
$391$	−7064.99			−0.0462123
$392$	−20685.4	−	50236.3i	−0.134615	−	0.326923i
$393$	111705.	+	74451.2i	0.723247	+	0.482044i
$394$	60989.0	−	105636.i	0.392879	−	0.680487i
$395$	168491.	−	97278.4i	1.07990	−	0.623480i
$396$	−75702.2	−	57809.4i	−0.482745	−	0.368645i
$397$	−81601.3	+	141338.i	−0.517745	+	0.896761i	0.482042	+	0.876148i	$0.339895\pi$
$397$	−81601.3	+	141338.i	−0.517745	+	0.896761i	−0.999788	+	0.0206129i	$0.993438\pi$
$398$		−	39719.3i		−	0.250747i
$399$	25256.5	+	10458.2i	0.158645	+	0.0656917i
$400$	−68997.5			−0.431234
$401$	163248.	+	94251.2i	1.01522	+	0.586136i	0.912715	−	0.408597i	$-0.133982\pi$
$401$	163248.	+	94251.2i	1.01522	+	0.586136i	0.102502	+	0.994733i	$0.467315\pi$
$402$	7426.98	−	115367.i	0.0459579	−	0.713887i
$403$	−46768.7	−	81005.7i	−0.287969	−	0.498776i
$404$	−110904.	−	64030.4i	−0.679491	−	0.392304i
$405$	−192345.	−	190566.i	−1.17266	−	1.16181i
$406$	−141111.	−	48065.6i	−0.856070	−	0.291596i
$407$			309469.i			1.86822i
$408$	−4326.75	−	8748.16i	−0.0259921	−	0.0525528i
$409$	−55086.2	−	95412.2i	−0.329304	−	0.570371i	0.653070	−	0.757297i	$-0.273481\pi$
$409$	−55086.2	−	95412.2i	−0.329304	−	0.570371i	−0.982374	+	0.186927i	$0.940147\pi$
$410$	−171405.	+	98961.0i	−1.01966	+	0.588703i
$411$	68352.0	−	33806.2i	0.404639	−	0.200130i
$412$	130877.			0.771027
$413$	48043.3	+	54898.7i	0.281665	+	0.321856i
$414$	−12997.3	−	31173.1i	−0.0758317	−	0.181878i
$415$	53816.1	−	93212.3i	0.312476	−	0.541224i
$416$	13967.3	−	8064.05i	0.0807100	−	0.0465979i
$417$	107024.	+	6889.89i	0.615474	+	0.0396224i
$418$	−12885.7	+	22318.6i	−0.0737488	+	0.127737i
$419$		−	9764.42i		−	0.0556184i	−0.999613	−	0.0278092i	$-0.991147\pi$
$419$		−	9764.42i		−	0.0556184i	0.999613	−	0.0278092i	$-0.00885308\pi$
$420$	144347.	−	19020.5i	0.818296	−	0.107826i
$421$	75461.7			0.425757			0.212879	−	0.977079i	$-0.431716\pi$
$421$	75461.7			0.425757			0.212879	+	0.977079i	$0.431716\pi$
$422$	13533.3	+	7813.47i	0.0759940	+	0.0438752i
$423$	−142269.	−	108642.i	−0.795112	−	0.607181i
$424$	37320.3	+	64640.6i	0.207593	+	0.359562i
$425$	44744.6	+	25833.3i	0.247721	+	0.143022i
$426$	2201.60	−	3303.23i	0.0121316	−	0.0182020i
$427$	140635.	+	47903.4i	0.771325	+	0.262731i
$428$			9146.80i			0.0499323i
$429$	−105652.	+	52254.3i	−0.574066	+	0.283928i
$430$	212232.	+	367597.i	1.14782	+	1.98808i
$431$	−178279.	+	102930.i	−0.959725	+	0.554097i	−0.896088	−	0.443876i	$-0.853603\pi$
$431$	−178279.	+	102930.i	−0.959725	+	0.554097i	−0.0636366	+	0.997973i	$0.520270\pi$
$432$	30640.0	−	35184.8i	0.164180	−	0.188533i
$433$	−139798.			−0.745633			−0.372816	−	0.927905i	$-0.621608\pi$
$433$	−139798.			−0.745633			−0.372816	+	0.927905i	$0.621608\pi$
$434$	142736.	−	28236.5i	0.757797	−	0.149911i
$435$	221565.	−	332430.i	1.17091	−	1.75680i
$436$	20412.3	−	35355.1i	0.107379	−	0.185986i
$437$	−7913.76	+	4569.01i	−0.0414400	+	0.0239254i
$438$	−7578.87	+	117726.i	−0.0395054	+	0.613657i
$439$	5029.05	−	8710.56i	0.0260950	−	0.0451978i	−0.852683	−	0.522429i	$-0.825026\pi$
$439$	5029.05	−	8710.56i	0.0260950	−	0.0451978i	0.878778	+	0.477231i	$0.158359\pi$
$440$			137261.i			0.708993i
$441$	−187843.	+	50378.4i	−0.965866	+	0.259040i
$442$	−12077.0			−0.0618182
$443$	−102064.	−	58926.9i	−0.520076	−	0.300266i	0.216890	−	0.976196i	$-0.430409\pi$
$443$	−102064.	−	58926.9i	−0.520076	−	0.300266i	−0.736966	+	0.675930i	$0.763742\pi$
$444$	−151272.	−	9738.42i	−0.767347	−	0.0493995i
$445$	−155390.	−	269143.i	−0.784697	−	1.35914i
$446$	94153.2	+	54359.3i	0.473331	+	0.273278i
$447$	−26001.6	−	17330.0i	−0.130132	−	0.0867330i
$448$	4868.66	+	24611.1i	0.0242579	+	0.122624i
$449$		−	364373.i		−	1.80739i	−0.428172	−	0.903697i	$-0.640842\pi$
$449$		−	364373.i		−	1.80739i	0.428172	−	0.903697i	$-0.359158\pi$
$450$	−31670.0	+	244953.i	−0.156395	+	1.20965i
$451$	124622.	+	215852.i	0.612692	+	1.06121i
$452$	101201.	−	58428.5i	0.495346	−	0.285988i
$453$	145129.	+	293433.i	0.707226	+	1.42992i
$454$	72098.1			0.349794
$455$	58091.0	−	170544.i	0.280599	−	0.823783i
$456$	−10504.1	−	7000.97i	−0.0505160	−	0.0336689i
$457$	−148425.	+	257080.i	−0.710683	+	1.23094i	0.253919	+	0.967226i	$0.418280\pi$
$457$	−148425.	+	257080.i	−0.710683	+	1.23094i	−0.964601	+	0.263713i	$0.915053\pi$
$458$	−68796.4	+	39719.6i	−0.327970	+	0.189354i
$459$	−33043.5	+	11345.3i	−0.156841	+	0.0538507i
$460$	−24335.1	+	42149.6i	−0.115005	+	0.199194i
$461$		−	37525.9i		−	0.176575i	−0.996095	−	0.0882876i	$-0.971861\pi$
$461$		−	37525.9i		−	0.176575i	0.996095	−	0.0882876i	$-0.0281395\pi$
$462$	−23952.6	−	181777.i	−0.112220	−	0.851640i
$463$	−361028.			−1.68414			−0.842070	−	0.539368i	$-0.818663\pi$
$463$	−361028.			−1.68414			−0.842070	+	0.539368i	$0.818663\pi$
$464$	59616.6	+	34419.7i	0.276905	+	0.159871i
$465$	−25050.7	+	389125.i	−0.115855	+	1.79963i
$466$	−66836.5	−	115764.i	−0.307781	−	0.533092i
$467$	232635.	+	134312.i	1.06670	+	0.615858i	0.927277	−	0.374375i	$-0.122143\pi$
$467$	232635.	+	134312.i	1.06670	+	0.615858i	0.139420	+	0.990233i	$0.455476\pi$
$468$	−22217.8	−	53288.0i	−0.101440	−	0.243297i
$469$	167460.	−	146549.i	0.761318	−	0.666249i
$470$			257957.i			1.16776i
$471$	7985.37	+	16145.4i	0.0359959	+	0.0727792i
$472$	−16844.1	−	29174.8i	−0.0756072	−	0.130956i
$473$	462917.	−	267265.i	2.06910	−	1.19459i
$474$	107572.	−	53203.8i	0.478785	−	0.236803i
$475$	66826.9			0.296186
$476$	6057.31	−	17783.1i	0.0267341	−	0.0784861i
$477$	246616.	−	102823.i	1.08389	−	0.451914i
$478$	−23519.8	+	40737.4i	−0.102938	+	0.178294i
$479$	9931.11	−	5733.73i	0.0432839	−	0.0249900i	−0.478202	−	0.878250i	$-0.658711\pi$
$479$	9931.11	−	5733.73i	0.0432839	−	0.0249900i	0.521486	+	0.853260i	$0.325378\pi$
$480$	−67094.6	−	4319.35i	−0.291209	−	0.0187472i
$481$	−93788.9	+	162447.i	−0.405379	+	0.702137i
$482$			147070.i			0.633036i
$483$	24872.1	−	60066.0i	0.106615	−	0.257475i
$484$	55725.7			0.237884
$485$	−199082.	−	114940.i	−0.846346	−	0.488638i
$486$	−110849.	−	124927.i	−0.469308	−	0.528914i
$487$	−57717.7	−	99970.1i	−0.243361	−	0.421514i	0.718308	−	0.695725i	$-0.244917\pi$
$487$	−57717.7	−	99970.1i	−0.243361	−	0.421514i	−0.961670	+	0.274211i	$0.911583\pi$
$488$	−59415.5	−	34303.5i	−0.249494	−	0.144045i
$489$	−165008.	+	247574.i	−0.690059	+	1.03535i
$490$	221985.	+	171074.i	0.924550	+	0.712513i
$491$		−	34353.8i		−	0.142499i	−0.997459	−	0.0712495i	$-0.977301\pi$
$491$		−	34353.8i		−	0.142499i	0.997459	−	0.0712495i	$-0.0226987\pi$
$492$	−109432.	+	54124.1i	−0.452079	+	0.223594i
$493$	−25774.1	−	44642.1i	−0.106045	−	0.183675i
$494$	−13527.9	+	7810.36i	−0.0554342	+	0.0320050i
$495$	487301.	+	63003.1i	1.98878	+	0.257129i
$496$	−67190.4			−0.273114
$497$	7495.97	−	1482.88i	0.0303470	−	0.00600336i
$498$	36820.9	−	55245.2i	0.148469	−	0.222759i
$499$	15203.2	−	26332.8i	0.0610570	−	0.105754i	−0.833881	−	0.551944i	$-0.813886\pi$
$499$	15203.2	−	26332.8i	0.0610570	−	0.105754i	0.894938	+	0.446190i	$0.147220\pi$
$500$	129544.	−	74792.5i	0.518178	−	0.299170i
$501$	21188.2	−	329128.i	0.0844149	−	1.31126i
$502$	−22401.0	+	38799.7i	−0.0888915	+	0.153965i
$503$			227366.i			0.898649i	0.893369	+	0.449324i	$0.148335\pi$
$503$			227366.i			0.898649i	−0.893369	+	0.449324i	$0.851665\pi$
$504$	89608.4	−	5988.10i	0.352767	−	0.0235737i
$505$	660608.			2.59037
$506$	53079.2	+	30645.3i	0.207311	+	0.119691i
$507$	185223.	+	11924.1i	0.720574	+	0.0463883i
$508$	−7431.11	−	12871.1i	−0.0287956	−	0.0498754i
$509$	−437421.	−	252545.i	−1.68836	−	0.974773i	−0.955777	−	0.294092i	$-0.904983\pi$
$509$	−437421.	−	252545.i	−1.68836	−	0.974773i	−0.732579	−	0.680682i	$-0.761684\pi$
$510$	41893.4	+	27922.0i	0.161067	+	0.107351i
$511$	−170885.	+	149546.i	−0.654429	+	0.572708i
$512$		−	11585.2i		−	0.0441942i
$513$	−29676.1	+	34077.9i	−0.112764	+	0.129491i
$514$	−120384.	−	208511.i	−0.455661	−	0.789228i
$515$	−584686.	+	337569.i	−2.20449	+	1.27276i
$516$	116075.	+	234689.i	0.435952	+	0.881440i
$517$	324847.			1.21534
$518$	−192158.	−	219578.i	−0.716142	−	0.818330i
$519$	−306682.	−	204404.i	−1.13856	−	0.758847i
$520$	−41598.9	+	72051.3i	−0.153842	+	0.266462i
$521$	−74406.5	+	42958.6i	−0.274117	+	0.158261i	−0.630757	−	0.775980i	$-0.717256\pi$
$521$	−74406.5	+	42958.6i	−0.274117	+	0.158261i	0.356640	+	0.934242i	$0.383922\pi$
$522$	149560.	−	195851.i	0.548877	−	0.718761i
$523$	−34823.6	+	60316.2i	−0.127312	+	0.220511i	−0.922634	−	0.385676i	$-0.873968\pi$
$523$	−34823.6	+	60316.2i	−0.127312	+	0.220511i	0.795322	+	0.606187i	$0.207302\pi$
$524$		−	119326.i		−	0.434584i
$525$	−377155.	+	289470.i	−1.36836	+	1.05023i
$526$	114567.			0.414082
$527$	43572.7	+	25156.7i	0.156889	+	0.0905802i
$528$	−5439.38	+	84492.6i	−0.0195111	+	0.303076i
$529$	−129054.	−	223529.i	−0.461170	−	0.798770i
$530$	−333452.	−	192519.i	−1.18709	−	0.685364i
$531$	−111307.	+	46408.2i	−0.394761	+	0.164591i
$532$	−4715.50	−	23836.8i	−0.0166611	−	0.0842219i
$533$			151074.i			0.531783i
$534$	−84986.3	−	171832.i	−0.298034	−	0.602588i
$535$	−23592.1	−	40862.8i	−0.0824251	−	0.142765i
$536$	−88993.4	+	51380.4i	−0.309762	+	0.178841i
$537$	−215015.	+	106345.i	−0.745626	+	0.368779i
$538$	29825.8			0.103045
$539$	215435.	−	279546.i	0.741547	−	0.962224i
$540$	−46131.0	+	236215.i	−0.158200	+	0.810066i
$541$	168889.	−	292525.i	0.577042	−	0.999467i	−0.418774	−	0.908090i	$-0.637540\pi$
$541$	168889.	−	292525.i	0.577042	−	0.999467i	0.995816	−	0.0913763i	$-0.0291266\pi$
$542$	229310.	−	132392.i	0.780591	−	0.450675i
$543$	−136974.	−	8817.96i	−0.464556	−	0.0299067i
$544$	−4337.63	+	7512.99i	−0.0146573	+	0.0253872i
$545$			210596.i			0.709017i
$546$	42516.9	−	102678.i	0.142619	−	0.344423i
$547$	−293444.			−0.980734			−0.490367	−	0.871516i	$-0.663137\pi$
$547$	−293444.			−0.980734			−0.490367	+	0.871516i	$0.663137\pi$
$548$	−58701.3	−	33891.2i	−0.195473	−	0.112856i
$549$	−149055.	+	195190.i	−0.494542	+	0.647609i
$550$	−224111.	−	388171.i	−0.740861	−	1.28321i
$551$	−57741.1	−	33336.9i	−0.190188	−	0.109805i
$552$	−16650.0	+	24981.3i	−0.0546432	+	0.0819854i
$553$	218669.	+	74483.6i	0.715052	+	0.243563i
$554$		−	134722.i		−	0.438955i
$555$	700916.	−	346666.i	2.27552	−	1.12545i
$556$	−47664.8	−	82557.8i	−0.154187	−	0.267060i
$557$	−466787.	+	269499.i	−1.50456	+	0.868655i	−0.504569	+	0.863371i	$0.668349\pi$
$557$	−466787.	+	269499.i	−1.50456	+	0.868655i	−0.999986	+	0.00528411i	$0.998318\pi$
$558$	−30840.5	+	238538.i	−0.0990496	+	0.766106i
$559$	323993.			1.03684
$560$	−85229.2	−	97390.8i	−0.271777	−	0.310557i
$561$	35162.3	−	52756.6i	0.111725	−	0.167630i
$562$	−33265.1	+	57616.8i	−0.105321	+	0.182422i
$563$	478363.	−	276183.i	1.50918	−	0.871325i	0.509236	−	0.860627i	$-0.329928\pi$
$563$	478363.	−	276183.i	1.50918	−	0.871325i	0.999943	−	0.0106975i	$-0.00340517\pi$
$564$	−10222.3	+	158789.i	−0.0321360	+	0.499184i
$565$	−301407.	+	522052.i	−0.944183	+	1.63537i
$566$		−	307320.i		−	0.959308i
$567$	19871.6	−	320874.i	0.0618111	−	0.998088i
$568$	−3528.60			−0.0109372
$569$	−59579.1	−	34398.0i	−0.184022	−	0.106245i	0.405159	−	0.914246i	$-0.367216\pi$
$569$	−59579.1	−	34398.0i	−0.184022	−	0.106245i	−0.589181	+	0.808001i	$0.700549\pi$
$570$	64983.9	+	4183.46i	0.200012	+	0.0128762i
$571$	−46754.7	−	80981.4i	−0.143401	−	0.248378i	0.785374	−	0.619021i	$-0.212471\pi$
$571$	−46754.7	−	80981.4i	−0.143401	−	0.248378i	−0.928775	+	0.370643i	$0.879137\pi$
$572$	90734.6	+	52385.7i	0.277320	+	0.160111i
$573$	−40988.8	−	27319.0i	−0.124841	−	0.0832062i
$574$	−222451.	−	75771.9i	−0.675167	−	0.229977i
$575$		−	158930.i		−	0.480697i
$576$	−41129.7	−	5317.65i	−0.123968	−	0.0160278i
$577$	−130588.	−	226184.i	−0.392239	−	0.679377i	0.600506	−	0.799620i	$-0.294966\pi$
$577$	−130588.	−	226184.i	−0.392239	−	0.679377i	−0.992744	+	0.120243i	$0.961633\pi$
$578$	−198958.	+	114868.i	−0.595533	+	0.343831i
$579$	−25645.5	−	51851.9i	−0.0764986	−	0.154671i
$580$	−355112.			−1.05562
$581$	125367.	−	24800.7i	0.371392	−	0.0734703i
$582$	−117992.	−	78641.7i	−0.348343	−	0.232170i
$583$	−242440.	+	419918.i	−0.713291	+	1.23546i
$584$	90813.4	−	52431.2i	0.266271	−	0.153732i
$585$	236701.	+	180755.i	0.691654	+	0.528176i
$586$	80790.0	−	139932.i	0.235268	−	0.407496i
$587$			235249.i			0.682733i	0.939930	+	0.341366i	$0.110890\pi$
$587$			235249.i			0.682733i	−0.939930	+	0.341366i	$0.889110\pi$
$588$	129866.	+	114104.i	0.375612	+	0.330023i
$589$	65076.6			0.187583
$590$	150500.	+	86891.2i	0.432347	+	0.249616i
$591$	−24935.1	+	387330.i	−0.0713899	+	1.10894i
$592$	67371.1	+	116690.i	0.192234	+	0.332959i
$593$	−261396.	−	150917.i	−0.743343	−	0.429169i	0.0799404	−	0.996800i	$-0.474527\pi$
$593$	−261396.	−	150917.i	−0.743343	−	0.429169i	−0.823284	+	0.567630i	$0.807860\pi$
$594$	297467.	+	58093.0i	0.843075	+	0.164646i
$595$	18806.8	+	95068.3i	0.0531228	+	0.268536i
$596$			27775.6i			0.0781936i
$597$	56030.7	+	113287.i	0.157209	+	0.317857i
$598$	18574.9	+	32172.7i	0.0519428	+	0.0899675i
$599$	407551.	−	235300.i	1.13587	−	0.655794i	0.190464	−	0.981694i	$-0.439001\pi$
$599$	407551.	−	235300.i	1.13587	−	0.655794i	0.945404	+	0.325900i	$0.105667\pi$
$600$	196794.	−	97332.5i	0.546651	−	0.270368i
$601$	−399788.			−1.10683			−0.553415	−	0.832906i	$-0.686676\pi$
$601$	−399788.			−1.10683			−0.553415	+	0.832906i	$0.686676\pi$
$602$	−162501.	+	477070.i	−0.448397	+	1.31640i
$603$	141561.	+	339526.i	0.389323	+	0.933767i
$604$	145494.	−	252003.i	0.398815	−	0.690767i
$605$	−248951.	+	143732.i	−0.680148	+	0.392684i
$606$	406645.	+	26178.6i	1.10731	+	0.0712854i
$607$	230869.	−	399877.i	0.626597	−	1.08530i	−0.361633	−	0.932321i	$-0.617781\pi$
$607$	230869.	−	399877.i	0.626597	−	1.08530i	0.988230	−	0.152977i	$-0.0488860\pi$
$608$			11220.8i			0.0303540i
$609$	470281.	−	61968.5i	1.26801	−	0.167085i
$610$	353913.			0.951124
$611$	170519.	+	98449.4i	0.456763	+	0.263712i
$612$	24681.5	+	18847.8i	0.0658974	+	0.0503221i
$613$	353101.	+	611590.i	0.939677	+	1.62757i	0.766074	+	0.642752i	$0.222207\pi$
$613$	353101.	+	611590.i	0.939677	+	1.62757i	0.173602	+	0.984816i	$0.444459\pi$
$614$	197411.	+	113975.i	0.523641	+	0.302325i
$615$	349281.	−	524052.i	0.923473	−	1.38556i
$616$	−122645.	+	107330.i	−0.323212	+	0.282851i
$617$			524911.i			1.37884i	0.724360	+	0.689422i	$0.242135\pi$
$617$			524911.i			1.37884i	−0.724360	+	0.689422i	$0.757865\pi$
$618$	−373287.	+	184624.i	−0.977386	+	0.483406i
$619$	−7637.19	−	13228.0i	−0.0199321	−	0.0345233i	0.855887	−	0.517162i	$-0.173012\pi$
$619$	−7637.19	−	13228.0i	−0.0199321	−	0.0345233i	−0.875819	+	0.482639i	$0.839678\pi$
$620$	300169.	−	173303.i	0.780877	−	0.450839i
$621$	81045.6	+	70577.0i	0.210158	+	0.183012i
$622$	−78619.8			−0.203213
$623$	118978.	−	349296.i	0.306542	−	0.899948i
$624$	−28461.9	+	42703.5i	−0.0730962	+	0.109672i
$625$	−48919.7	+	84731.4i	−0.125234	+	0.216912i
$626$	303056.	−	174970.i	0.773347	−	0.446492i
$627$	5268.26	−	81834.5i	0.0134008	−	0.208162i
$628$	8005.44	−	13865.8i	0.0202986	−	0.0351582i
$629$		−	100898.i		−	0.255023i
$630$	−384875.	+	257876.i	−0.969703	+	0.649726i
$631$	−37126.6			−0.0932451			−0.0466226	−	0.998913i	$-0.514846\pi$
$631$	−37126.6			−0.0932451			−0.0466226	+	0.998913i	$0.514846\pi$
$632$	−92383.4	−	53337.6i	−0.231291	−	0.133536i
$633$	−49621.9	−	3194.51i	−0.123841	−	0.00797253i
$634$	69654.3	+	120645.i	0.173288	+	0.300144i
$635$	66396.1	+	38333.8i	0.164663	+	0.0950680i
$636$	−197631.	−	131721.i	−0.488586	−	0.325643i
$637$	197807.	−	81449.4i	0.487486	−	0.200729i
$638$			447194.i			1.09864i
$639$	−1619.64	+	12527.2i	−0.00396657	+	0.0306797i
$640$	29881.6	+	51756.4i	0.0729530	+	0.126358i
$641$	213562.	−	123300.i	0.519767	−	0.300087i	−0.217073	−	0.976155i	$-0.569651\pi$
$641$	213562.	−	123300.i	0.519767	−	0.300087i	0.736839	+	0.676068i	$0.236317\pi$
$642$	−12903.1	−	26088.4i	−0.0313057	−	0.0632963i
$643$	−546903.			−1.32278			−0.661391	−	0.750041i	$-0.730034\pi$
$643$	−546903.			−1.32278			−0.661391	+	0.750041i	$0.730034\pi$
$644$	−56689.7	+	11214.6i	−0.136689	+	0.0270403i
$645$	−1.12388e6	−	749069.i	−2.70148	−	1.80054i
$646$	4201.17	−	7276.64i	0.0100671	−	0.0174368i
$647$	−273352.	+	157820.i	−0.653001	+	0.377010i	−0.789605	−	0.613616i	$-0.789714\pi$
$647$	−273352.	+	157820.i	−0.653001	+	0.377010i	0.136604	+	0.990626i	$0.456381\pi$
$648$	−37757.2	+	143577.i	−0.0899186	+	0.341928i
$649$	109423.	−	189525.i	0.259787	−	0.449964i
$650$		−	271679.i		−	0.643028i
$651$	−367277.	+	281889.i	−0.866627	+	0.665144i
$652$	264465.			0.622119
$653$	445043.	+	256945.i	1.04370	+	0.602580i	0.920879	−	0.389849i	$-0.127473\pi$
$653$	445043.	+	256945.i	1.04370	+	0.602580i	0.122820	+	0.992429i	$0.460806\pi$
$654$	−8345.48	+	129635.i	−0.0195117	+	0.303086i
$655$	307776.	+	533083.i	0.717384	+	1.24255i
$656$	93981.3	+	54260.1i	0.218390	+	0.126088i
$657$	−144456.	−	346470.i	−0.334662	−	0.802666i
$658$	−230489.	+	201707.i	−0.532351	+	0.465874i
$659$		−	682838.i		−	1.57234i	−0.618009	−	0.786171i	$-0.712060\pi$
$659$		−	682838.i		−	1.57234i	0.618009	−	0.786171i	$-0.287940\pi$
$660$	−193630.	−	391495.i	−0.444513	−	0.898750i
$661$	278301.	+	482031.i	0.636959	+	1.10325i	0.986096	+	0.166174i	$0.0531414\pi$
$661$	278301.	+	482031.i	0.636959	+	1.10325i	−0.349137	+	0.937072i	$0.613525\pi$
$662$	−296252.	+	171041.i	−0.675999	+	0.390288i
$663$	34446.1	−	17036.7i	0.0783633	−	0.0387577i
$664$	−59014.6			−0.133851
$665$	82548.0	+	94327.0i	0.186665	+	0.213301i
$666$	445194.	−	185618.i	1.00369	−	0.418478i
$667$	−79283.1	+	137322.i	−0.178209	+	0.308667i
$668$	−253887.	+	146582.i	−0.568968	+	0.328494i
$669$	−345226.	−	22224.6i	−0.771350	−	0.0496572i
$670$	265049.	−	459078.i	0.590440	−	1.02267i
$671$		−	445685.i		−	0.989881i
$672$	−48604.4	−	63327.5i	−0.107631	−	0.140234i
$673$	−425992.			−0.940528			−0.470264	−	0.882526i	$-0.655841\pi$
$673$	−425992.			−0.940528			−0.470264	+	0.882526i	$0.655841\pi$
$674$	−243490.	−	140579.i	−0.535995	−	0.309457i
$675$	−255219.	−	743330.i	−0.560151	−	1.63145i
$676$	−82491.6	−	142880.i	−0.180516	−	0.312663i
$677$	−118967.	−	68685.5i	−0.259566	−	0.149861i	0.364570	−	0.931176i	$-0.381216\pi$
$677$	−118967.	−	68685.5i	−0.259566	−	0.149861i	−0.624137	+	0.781315i	$0.714549\pi$
$678$	−206222.	+	309411.i	−0.448617	+	0.673095i
$679$	−52969.0	−	267758.i	−0.114890	−	0.580769i
$680$		−	44751.8i		−	0.0967816i
$681$	−205638.	+	101706.i	−0.443413	+	0.219308i
$682$	−218241.	−	378004.i	−0.469210	−	0.812696i
$683$	−353022.	+	203818.i	−0.756765	+	0.436918i	−0.828133	−	0.560532i	$-0.810597\pi$
$683$	−353022.	+	203818.i	−0.756765	+	0.436918i	0.0713683	+	0.997450i	$0.477263\pi$
$684$	39835.8	+	5150.36i	0.0851454	+	0.0110084i
$685$	349659.			0.745185
$686$	20720.6	+	332116.i	0.0440305	+	0.705735i
$687$	140190.	−	210337.i	0.297031	−	0.445658i
$688$	116366.	−	201553.i	0.245839	−	0.425806i
$689$	−254524.	+	146949.i	−0.536155	+	0.309549i
$690$	9949.29	−	154547.i	0.0208975	−	0.324611i
$691$	214925.	−	372260.i	0.450122	−	0.779634i	−0.548271	−	0.836301i	$-0.684714\pi$
$691$	214925.	−	372260.i	0.450122	−	0.779634i	0.998393	+	0.0566666i	$0.0180472\pi$
$692$			327607.i			0.684134i
$693$	324745.	+	484675.i	0.676202	+	1.00922i
$694$	−385253.			−0.799883
$695$	425879.	+	245881.i	0.881692	+	0.509045i
$696$	−218593.	−	14072.4i	−0.451250	−	0.0290501i
$697$	−40631.1	−	70375.1i	−0.0836359	−	0.144862i
$698$	437647.	+	252675.i	0.898282	+	0.518623i
$699$	353936.	+	235898.i	0.724386	+	0.482803i
$700$	400039.	+	136262.i	0.816406	+	0.278086i
$701$			788356.i			1.60430i	0.597121	+	0.802152i	$0.296311\pi$
$701$			788356.i			1.60430i	−0.597121	+	0.802152i	$0.703689\pi$
$702$	138541.	+	120646.i	0.281128	+	0.244815i
$703$	−65251.6	−	113019.i	−0.132032	−	0.228687i
$704$	65177.1	−	37630.0i	0.131507	−	0.0759257i
$705$	−363892.	−	735745.i	−0.732141	−	1.48030i
$706$	221953.			0.445300
$707$	516555.	+	590263.i	1.03342	+	1.18088i
$708$	89198.6	+	59450.8i	0.177947	+	0.118602i
$709$	441178.	−	764143.i	0.877651	−	1.52014i	0.0237392	−	0.999718i	$-0.492443\pi$
$709$	441178.	−	764143.i	0.877651	−	1.52014i	0.853912	−	0.520418i	$-0.174224\pi$
$710$	15763.8	−	9101.25i	0.0312712	−	0.0180545i
$711$	−231762.	+	303495.i	−0.458462	+	0.600362i
$712$	−85199.9	+	147571.i	−0.168066	+	0.291098i
$713$		−	154768.i		−	0.304440i
$714$	7809.38	+	59265.6i	0.0153186	+	0.116254i
$715$	−540469.			−1.05720
$716$	184657.	+	106612.i	0.360197	+	0.207960i
$717$	9615.96	−	149370.i	0.0187049	−	0.290552i
$718$	254695.	+	441145.i	0.494051	+	0.855721i
$719$	−704513.	−	406751.i	−1.36280	−	0.786811i	−0.372802	−	0.927911i	$-0.621603\pi$
$719$	−704513.	−	406751.i	−1.36280	−	0.786811i	−0.989995	+	0.141100i	$0.954936\pi$
$720$	197460.	−	82328.6i	0.380903	−	0.158813i
$721$	−758811.	−	258468.i	−1.45970	−	0.497206i
$722$			357736.i			0.686259i
$723$	−207466.	−	419471.i	−0.396891	−	0.802463i
$724$	61003.3	+	105661.i	0.116379	+	0.201575i
$725$	1.00425e6	−	579802.i	1.91058	−	1.10307i
$726$	−158940.	+	78610.4i	−0.301551	+	0.149144i
$727$	142261.			0.269164			0.134582	−	0.990902i	$-0.457031\pi$
$727$	142261.			0.269164			0.134582	+	0.990902i	$0.457031\pi$
$728$	−96906.6	+	19170.5i	−0.182848	+	0.0361718i
$729$	492393.	+	199947.i	0.926524	+	0.376235i
$730$	−270469.	+	468466.i	−0.507542	+	0.879088i
$731$	−150927.	+	87137.5i	−0.282443	+	0.163069i
$732$	217855.	+	14024.9i	0.406580	+	0.0261744i
$733$	356035.	−	616671.i	0.662651	−	1.14774i	−0.317266	−	0.948337i	$-0.602765\pi$
$733$	356035.	−	616671.i	0.662651	−	1.14774i	0.979917	−	0.199408i	$-0.0639019\pi$
$734$		−	489427.i		−	0.908440i
$735$	−874472.	−	174791.i	−1.61872	−	0.323552i
$736$	26685.7			0.0492633
$737$	−578119.	−	333777.i	−1.06434	−	0.614500i
$738$	235771.	−	308745.i	0.432890	−	0.566875i
$739$	223153.	+	386512.i	0.408614	+	0.707741i	0.994735	−	0.102483i	$-0.0326787\pi$
$739$	223153.	+	386512.i	0.408614	+	0.707741i	−0.586120	+	0.810224i	$0.699345\pi$
$740$	−601953.	−	347537.i	−1.09926	−	0.634656i
$741$	27566.5	−	41360.1i	0.0502048	−	0.0753261i
$742$	−88720.6	−	448482.i	−0.161145	−	0.814586i
$743$		−	118160.i		−	0.214038i	−0.994257	−	0.107019i	$-0.965869\pi$
$743$		−	118160.i		−	0.214038i	0.994257	−	0.107019i	$-0.0341306\pi$
$744$	191640.	−	94783.3i	0.346211	−	0.171232i
$745$	−71641.1	−	124086.i	−0.129077	−	0.223568i
$746$	233557.	−	134844.i	0.419676	−	0.242300i
$747$	−27087.8	+	209512.i	−0.0485436	+	0.375464i
$748$	−56356.2			−0.100725
$749$	18063.9	−	53032.0i	0.0321994	−	0.0945311i
$750$	−263979.	+	396067.i	−0.469295	+	0.704119i
$751$	−177742.	+	307858.i	−0.315144	+	0.545846i	−0.979468	−	0.201599i	$-0.935386\pi$
$751$	−177742.	+	307858.i	−0.315144	+	0.545846i	0.664324	+	0.747445i	$0.268720\pi$
$752$	122489.	−	70718.8i	0.216601	−	0.125054i
$753$	9158.57	−	142265.i	0.0161524	−	0.250904i
$754$	−135528.	+	234742.i	−0.238390	+	0.412903i
$755$			1.50108e6i			2.63335i
$756$	−247133.	+	143487.i	−0.432402	+	0.251055i
$757$	84343.5			0.147184			0.0735919	−	0.997288i	$-0.476554\pi$
$757$	84343.5			0.147184			0.0735919	+	0.997288i	$0.476554\pi$
$758$	−202457.	−	116889.i	−0.352367	−	0.203439i
$759$	−194622.	−	12529.2i	−0.337839	−	0.0217490i
$760$	−28941.5	−	50128.2i	−0.0501065	−	0.0867870i
$761$	99471.3	+	57429.8i	0.171763	+	0.0991671i	0.583417	−	0.812173i	$-0.301715\pi$
$761$	99471.3	+	57429.8i	0.171763	+	0.0991671i	−0.411654	+	0.911340i	$0.635049\pi$
$762$	39351.7	+	26227.9i	0.0677726	+	0.0451704i
$763$	−188170.	+	164673.i	−0.323223	+	0.282861i
$764$			43785.4i			0.0750140i
$765$	−158877.	−	20541.2i	−0.271480	−	0.0350996i
$766$	−10085.4	−	17468.5i	−0.0171885	−	0.0297713i
$767$	114877.	−	66324.0i	0.195272	−	0.112740i
$768$	16342.9	+	33043.4i	0.0277081	+	0.0560224i
$769$	391724.			0.662410			0.331205	−	0.943559i	$-0.392545\pi$
$769$	391724.			0.662410			0.331205	+	0.943559i	$0.392545\pi$
$770$	271075.	−	795824.i	0.457202	−	1.34226i
$771$	637498.	+	424892.i	1.07243	+	0.714776i
$772$	−25709.9	+	44530.9i	−0.0431386	+	0.0747182i
$773$	874179.	−	504708.i	1.46299	−	0.844658i	0.463842	−	0.885918i	$-0.346470\pi$
$773$	874179.	−	504708.i	1.46299	−	0.844658i	0.999148	+	0.0412599i	$0.0131372\pi$
$774$	−662136.	−	505635.i	−1.10526	−	0.844025i
$775$	−565913.	+	980191.i	−0.942208	+	1.63195i
$776$			126043.i			0.209312i
$777$	857824.	+	355207.i	1.42088	+	0.588355i
$778$	−63718.1			−0.105270
$779$	−91024.7	−	52553.1i	−0.149998	−	0.0866012i
$780$	17007.5	−	264187.i	0.0279545	−	0.434232i
$781$	−11461.3	−	19851.5i	−0.0187901	−	0.0325455i
$782$	−17305.6	−	9991.40i	−0.0282992	−	0.0163385i
$783$	−150294.	+	769585.i	−0.245142	+	1.25526i
$784$	20376.1	−	152307.i	0.0331505	−	0.247792i
$785$			82593.0i			0.134031i
$786$	168330.	+	340342.i	0.272468	+	0.550897i
$787$	387305.	+	670832.i	0.625322	+	1.08309i	0.988479	+	0.151361i	$0.0483655\pi$
$787$	387305.	+	670832.i	0.625322	+	1.08309i	−0.363157	+	0.931728i	$0.618301\pi$
$788$	298784.	−	172503.i	0.481177	−	0.277808i
$789$	−326766.	+	161615.i	−0.524908	+	0.259614i
$790$	550290.			0.881733
$791$	−702142.	+	138901.i	−1.12220	+	0.221999i
$792$	−103677.	−	248663.i	−0.165284	−	0.396424i
$793$	135071.	−	233950.i	0.214791	−	0.372029i
$794$	−399763.	+	230803.i	−0.634106	+	0.366101i
$795$	1.22265e6	+	78710.6i	1.93450	+	0.124537i
$796$	56171.5	−	97291.9i	0.0886523	−	0.153550i
$797$		−	1.05721e6i		−	1.66434i	−0.554517	−	0.832172i	$-0.687097\pi$
$797$		−	1.05721e6i		−	1.66434i	0.554517	−	0.832172i	$-0.312903\pi$
$798$	47075.3	+	61335.2i	0.0739244	+	0.0963173i
$799$	−105911.			−0.165901
$800$	−169009.	−	97577.1i	−0.264076	−	0.152464i
$801$	484795.	+	370210.i	0.755602	+	0.577010i
$802$	266583.	+	461735.i	0.414460	+	0.717867i
$803$	589942.	+	340603.i	0.914910	+	0.528223i
$804$	181346.	−	272087.i	0.280541	−	0.420916i
$805$	224332.	−	196319.i	0.346179	−	0.302950i
$806$		−	264564.i		−	0.407249i
$807$	−85069.0	+	42074.3i	−0.130624	+	0.0646055i
$808$	−181105.	−	313683.i	−0.277401	−	0.480473i
$809$	−442408.	+	255424.i	−0.675968	+	0.390270i	−0.798334	−	0.602215i	$-0.794285\pi$
$809$	−442408.	+	255424.i	−0.675968	+	0.390270i	0.122366	+	0.992485i	$0.460952\pi$
$810$	−201647.	−	738807.i	−0.307341	−	1.12606i
$811$	437547.			0.665247			0.332623	−	0.943060i	$-0.392066\pi$
$811$	437547.			0.665247			0.332623	+	0.943060i	$0.392066\pi$
$812$	−277675.	−	317297.i	−0.421139	−	0.481232i
$813$	−467275.	+	701088.i	−0.706954	+	1.06070i
$814$	−437656.	+	758042.i	−0.660517	+	1.14405i
$815$	−1.18148e6	+	682130.i	−1.77874	+	1.02696i
$816$	1773.42	−	27547.5i	0.00266337	−	0.0413715i
$817$	−112706.	+	195212.i	−0.168850	+	0.292457i
$818$		−	311615.i		−	0.465706i
$819$	23578.3	+	352835.i	0.0351516	+	0.526022i
$820$	−559808.			−0.832552
$821$	125695.	+	72570.0i	0.186480	+	0.107664i	0.590334	−	0.807159i	$-0.298996\pi$
$821$	125695.	+	72570.0i	0.186480	+	0.107664i	−0.403854	+	0.914824i	$0.632330\pi$
$822$	215237.	+	13856.3i	0.318547	+	0.0205071i
$823$	−72522.9	−	125613.i	−0.107072	−	0.185454i	0.807511	−	0.589853i	$-0.200814\pi$
$823$	−72522.9	−	125613.i	−0.107072	−	0.185454i	−0.914583	+	0.404399i	$0.867481\pi$
$824$	320582.	+	185088.i	0.472156	+	0.272599i
$825$	1.18679e6	+	790994.i	1.74367	+	1.16216i
$826$	40043.0	+	202417.i	0.0586904	+	0.296680i
$827$		−	1.09628e6i		−	1.60291i	−0.598053	−	0.801457i	$-0.704059\pi$
$827$		−	1.09628e6i		−	1.60291i	0.598053	−	0.801457i	$-0.295941\pi$
$828$	12248.8	−	94739.1i	0.0178662	−	0.138187i
$829$	119101.	+	206289.i	0.173303	+	0.300170i	0.939573	−	0.342349i	$-0.111223\pi$
$829$	119101.	+	206289.i	0.173303	+	0.300170i	−0.766269	+	0.642519i	$0.777889\pi$
$830$	263644.	−	152215.i	0.382703	−	0.220954i
$831$	190049.	+	384254.i	0.275209	+	0.556438i
$832$	45617.2			0.0658994
$833$	−70239.1	+	91141.6i	−0.101225	+	0.131349i
$834$	252411.	+	168232.i	0.362891	+	0.241867i
$835$	756150.	−	1.30969e6i	1.08451	−	1.87843i
$836$	−63126.7	+	36446.2i	−0.0903234	+	0.0521482i
$837$	−248535.	−	723862.i	−0.354761	−	1.03325i
$838$	13809.0	−	23917.8i	0.0196641	−	0.0340592i
$839$		−	439815.i		−	0.624808i	−0.949949	−	0.312404i	$-0.898866\pi$
$839$		−	439815.i		−	0.624808i	0.949949	−	0.312404i	$-0.101134\pi$
$840$	380476.	+	157547.i	0.539224	+	0.223281i
$841$	−449666.			−0.635767
$842$	184843.	+	106719.i	0.260722	+	0.150528i
$843$	13600.3	−	211260.i	0.0191379	−	0.297278i
$844$	22099.8	+	38278.0i	0.0310244	+	0.0537359i
$845$	737053.	+	425538.i	1.03225	+	0.595970i
$846$	−194842.	−	467316.i	−0.272233	−	0.652935i
$847$	−323091.	−	110052.i	−0.450358	−	0.153402i
$848$			211115.i			0.293581i
$849$	433527.	+	876537.i	0.601451	+	1.21606i
$850$	73067.7	+	126557.i	0.101132	+	0.175165i
$851$	−268787.	+	155184.i	−0.371150	+	0.214283i
$852$	10064.3	−	4977.69i	0.0138645	−	0.00685722i
$853$	−1.27599e6			−1.75368			−0.876839	−	0.480785i	$-0.840352\pi$
$853$	−1.27599e6			−1.75368			−0.876839	+	0.480785i	$0.840352\pi$
$854$	276738.	+	316227.i	0.379449	+	0.433594i
$855$	−191248.	+	79738.6i	−0.261616	+	0.109078i
$856$	−12935.5	+	22405.0i	−0.0176537	+	0.0305772i
$857$	−690542.	+	398685.i	−0.940218	+	0.542835i	−0.890029	−	0.455905i	$-0.849316\pi$
$857$	−690542.	+	398685.i	−0.940218	+	0.542835i	−0.0501893	+	0.998740i	$0.515982\pi$
$858$	−332692.	−	21417.7i	−0.451926	−	0.0290936i
$859$	689547.	−	1.19433e6i	0.934496	−	1.61860i	0.158967	−	0.987284i	$-0.449184\pi$
$859$	689547.	−	1.19433e6i	0.934496	−	1.61860i	0.775530	−	0.631311i	$-0.217483\pi$
$860$			1.20057e6i			1.62326i
$861$	741364.	−	97688.8i	1.00006	−	0.131777i
$862$	−582258.			−0.783612
$863$	−1.01989e6	−	588832.i	−1.36940	−	0.790623i	−0.378548	−	0.925582i	$-0.623577\pi$
$863$	−1.01989e6	−	588832.i	−1.36940	−	0.790623i	−0.990851	+	0.134958i	$0.956910\pi$
$864$	124811.	−	42853.3i	0.167196	−	0.0574060i
$865$	−844990.	−	1.46357e6i	−1.12933	−	1.95605i
$866$	−342434.	−	197704.i	−0.456605	−	0.263621i
$867$	405426.	−	608291.i	0.539353	−	0.809232i
$868$	389562.	+	132693.i	0.517055	+	0.176121i
$869$		−	692983.i		−	0.917662i
$870$	1.01285e6	−	500945.i	1.33815	−	0.661837i
$871$	−202311.	−	350414.i	−0.266676	−	0.461897i
$872$	99999.4	−	57734.7i	0.131512	−	0.0759283i
$873$	447474.	+	57853.8i	0.587137	+	0.0759108i
$874$	−25846.2			−0.0338356
$875$	−898790.	+	177802.i	−1.17393	+	0.232232i
$876$	−185055.	+	277651.i	−0.241152	+	0.361819i
$877$	−711631.	+	1.23258e6i	−0.925242	+	1.60257i	−0.134071	+	0.990972i	$0.542805\pi$
$877$	−711631.	+	1.23258e6i	−0.925242	+	1.60257i	−0.791171	+	0.611595i	$0.790528\pi$
$878$	24637.2	−	14224.3i	0.0319597	−	0.0184519i
$879$	−33030.7	+	513082.i	−0.0427504	+	0.664063i
$880$	−194117.	+	336220.i	−0.250667	+	0.434168i
$881$		−	811986.i		−	1.04616i	−0.852285	−	0.523078i	$-0.824784\pi$
$881$		−	811986.i		−	1.04616i	0.852285	−	0.523078i	$-0.175216\pi$
$882$	−531365.	−	142248.i	−0.683055	−	0.182856i
$883$	1.27343e6			1.63326			0.816630	−	0.577162i	$-0.195840\pi$
$883$	1.27343e6			1.63326			0.816630	+	0.577162i	$0.195840\pi$
$884$	−29582.6	−	17079.5i	−0.0378557	−	0.0218560i
$885$	−551830.	−	35525.1i	−0.704561	−	0.0453575i
$886$	−166670.	−	288682.i	−0.212320	−	0.367749i
$887$	285560.	+	164868.i	0.362953	+	0.209551i	0.670375	−	0.742022i	$-0.266133\pi$
$887$	285560.	+	164868.i	0.362953	+	0.209551i	−0.307423	+	0.951573i	$0.599467\pi$
$888$	−356766.	−	237785.i	−0.452437	−	0.301549i
$889$	17665.8	+	89300.5i	0.0223527	+	0.112993i
$890$		−	879017.i		−	1.10973i
$891$	−930384.	+	253935.i	−1.17194	+	0.319865i
$892$	153751.	+	266305.i	0.193237	+	0.334696i
$893$	−118635.	+	68494.0i	−0.148768	+	0.0858914i
$894$	−39182.2	−	79221.5i	−0.0490246	−	0.0991215i
$895$	−1.09993e6			−1.37315
$896$	−22879.5	+	67169.8i	−0.0284991	+	0.0836678i
$897$	−98364.4	−	65559.8i	−0.122251	−	0.0814804i
$898$	515301.	−	892527.i	0.639011	−	1.10680i
$899$	977945.	−	564617.i	1.21003	−	0.698609i
$900$	−423992.	+	555223.i	−0.523446	+	0.685460i
$901$	79043.7	−	136908.i	0.0973683	−	0.168647i
$902$			704969.i			0.866477i
$903$	−209504.	−	1.58993e6i	−0.256931	−	1.94986i
$904$	330522.			0.404448
$905$	−545057.	−	314689.i	−0.665495	−	0.384224i
$906$	−59484.7	+	924005.i	−0.0724684	+	1.12569i
$907$	297220.	+	514800.i	0.361296	+	0.625784i	0.988174	−	0.153334i	$-0.0490009\pi$
$907$	297220.	+	514800.i	0.361296	+	0.625784i	−0.626878	+	0.779117i	$0.715668\pi$
$908$	176603.	+	101962.i	0.214204	+	0.123671i
$909$	−1.19676e6	+	498975.i	−1.44837	+	0.603880i
$910$	383479.	−	335592.i	0.463082	−	0.405255i
$911$		−	368003.i		−	0.443419i	−0.975113	−	0.221710i	$-0.928836\pi$
$911$		−	368003.i		−	0.443419i	0.975113	−	0.221710i	$-0.0711637\pi$
$912$	−15828.8	−	32003.8i	−0.0190308	−	0.0384780i
$913$	−191685.	−	332008.i	−0.229957	−	0.398298i
$914$	−727133.	+	419810.i	−0.870405	+	0.502529i
$915$	−1.00943e6	+	499254.i	−1.20569	+	0.596320i
$916$	−224688.			−0.267787
$917$	−235656.	+	691840.i	−0.280246	+	0.822748i
$918$	−96984.4	−	18940.3i	−0.115084	−	0.0224751i
$919$	−221890.	+	384324.i	−0.262728	+	0.455058i	−0.966966	−	0.254906i	$-0.917955\pi$
$919$	−221890.	+	384324.i	−0.262728	+	0.455058i	0.704238	+	0.709964i	$0.251289\pi$
$920$	−119217.	+	68829.9i	−0.140852	+	0.0813208i
$921$	−723835.	−	46598.3i	−0.853336	−	0.0549352i
$922$	53069.7	−	91919.4i	0.0624288	−	0.108130i
$923$		−	13894.0i		−	0.0163088i
$924$	198400.	−	479136.i	0.232380	−	0.561196i
$925$	2.26974e6			2.65273
$926$	−884333.	−	510570.i	−1.03132	−	0.595434i
$927$	804245.	−	1.05317e6i	0.935898	−	1.22557i
$928$	97353.5	+	168621.i	0.113046	+	0.195802i
$929$	1.00442e6	+	579903.i	1.16382	+	0.671930i	0.952216	−	0.305426i	$-0.0987990\pi$
$929$	1.00442e6	+	579903.i	1.16382	+	0.671930i	0.211601	+	0.977356i	$0.432132\pi$
$930$	−611668.	+	917732.i	−0.707212	+	1.06108i
$931$	−19735.1	+	147516.i	−0.0227688	+	0.170192i
$932$		−	378084.i		−	0.435268i
$933$	224239.	−	110906.i	0.257601	−	0.127407i
$934$	379891.	+	657991.i	0.435477	+	0.754269i
$935$	251768.	−	145358.i	0.287990	−	0.166271i
$936$	20938.4	−	161949.i	0.0238996	−	0.184853i
$937$	132676.			0.151117			0.0755587	−	0.997141i	$-0.475926\pi$
$937$	132676.			0.151117			0.0755587	+	0.997141i	$0.475926\pi$
$938$	617444.	−	122145.i	0.701765	−	0.138826i
$939$	−617551.	+	926559.i	−0.700393	+	1.05085i
$940$	−364807.	+	631864.i	−0.412864	+	0.715102i
$941$	746126.	−	430776.i	0.842622	−	0.486488i	−0.0155327	−	0.999879i	$-0.504944\pi$
$941$	746126.	−	430776.i	0.842622	−	0.486488i	0.858155	+	0.513391i	$0.171611\pi$
$942$	−3272.99	+	50841.0i	−0.00368844	+	0.0572945i
$943$	−124984.	+	216479.i	−0.140550	+	0.243440i
$944$		−	95284.5i		−	0.106925i
$945$	733961.	−	1.27844e6i	0.821882	−	1.43159i
$946$	1.51188e6			1.68941
$947$	1.31201e6	+	757487.i	1.46297	+	0.844647i	0.999148	−	0.0412804i	$-0.0131437\pi$
$947$	1.31201e6	+	757487.i	1.46297	+	0.844647i	0.463824	+	0.885927i	$0.346477\pi$
$948$	338737.	+	21806.9i	0.376917	+	0.0242648i
$949$	206449.	+	357580.i	0.229235	+	0.397046i
$950$	163692.	+	94507.4i	0.181376	+	0.104717i
$951$	−368858.	−	245843.i	−0.407847	−	0.271830i
$952$	39986.4	−	34993.1i	0.0441203	−	0.0386108i
$953$			438895.i			0.483253i	0.970369	+	0.241626i	$0.0776809\pi$
$953$			438895.i			0.483253i	−0.970369	+	0.241626i	$0.922319\pi$
$954$	749497.	+	96902.3i	0.823518	+	0.106472i
$955$	−112935.	−	195609.i	−0.123829	−	0.214477i
$956$	−115223.	+	66523.9i	−0.126073	+	0.0727884i
$957$	−630842.	−	1.27548e6i	−0.688806	−	1.39268i
$958$	32434.9			0.0353412
$959$	273412.	+	312426.i	0.297290	+	0.339711i
$960$	−158239.	−	105466.i	−0.171700	−	0.114438i
$961$	−89331.2	+	154726.i	−0.0967289	+	0.167539i
$962$	−459470.	+	265275.i	−0.496486	+	0.286646i
$963$	73604.3	+	56207.3i	0.0793689	+	0.0606095i
$964$	−207988.	+	360245.i	−0.223812	+	0.387654i
$965$		−	265252.i		−	0.284842i
$966$	145870.	−	111957.i	0.156319	−	0.119976i
$967$	96984.3			0.103717			0.0518583	−	0.998654i	$-0.483486\pi$
$967$	96984.3			0.103717			0.0518583	+	0.998654i	$0.483486\pi$
$968$	136499.	+	78808.0i	0.145673	+	0.0841046i
$969$	−1717.63	+	26680.9i	−0.00182929	+	0.0284153i
$970$	−325099.	−	563088.i	−0.345519	−	0.598457i
$971$	306668.	+	177055.i	0.325259	+	0.187788i	0.653734	−	0.756724i	$-0.273201\pi$
$971$	306668.	+	177055.i	0.325259	+	0.187788i	−0.328475	+	0.944513i	$0.606535\pi$
$972$	−94848.4	−	462772.i	−0.100392	−	0.489818i
$973$	113312.	+	572793.i	0.119688	+	0.605023i
$974$		−	326501.i		−	0.344165i
$975$	383249.	+	774882.i	0.403155	+	0.815129i
$976$	−97025.0	−	168052.i	−0.101855	−	0.176419i
$977$	−535196.	+	308995.i	−0.560691	+	0.323715i	−0.753423	−	0.657536i	$-0.771599\pi$
$977$	−535196.	+	308995.i	−0.560691	+	0.323715i	0.192732	+	0.981251i	$0.438265\pi$
$978$	−754306.	+	373073.i	−0.788624	+	0.390046i
$979$	−1.10695e6			−1.15495
$980$	301813.	+	732979.i	0.314258	+	0.763201i
$981$	−159068.	−	381516.i	−0.165290	−	0.396437i
$982$	48583.6	−	84149.3i	0.0503810	−	0.0872625i
$983$	−661848.	+	382118.i	−0.684938	+	0.395449i	−0.801713	−	0.597709i	$-0.796078\pi$
$983$	−661848.	+	382118.i	−0.684938	+	0.395449i	0.116775	+	0.993158i	$0.462744\pi$
$984$	−344596.	−	22184.0i	−0.355893	−	0.0229113i
$985$	−889867.	+	1.54129e6i	−0.917176	+	1.58859i
$986$		−	145801.i		−	0.149970i
$987$	372857.	−	900449.i	0.382744	−	0.924326i
$988$	−44182.1			−0.0452618
$989$	464262.	+	268042.i	0.474646	+	0.274037i
$990$	1.10454e6	+	843474.i	1.12697	+	0.860600i
$991$	−617539.	−	1.06961e6i	−0.628807	−	1.08913i	−0.987791	−	0.155782i	$-0.950210\pi$
$991$	−617539.	−	1.06961e6i	−0.628807	−	1.08913i	0.358985	−	0.933344i	$-0.383123\pi$
$992$	−164582.	−	95021.5i	−0.167247	−	0.0965603i
$993$	603687.	−	905757.i	0.612228	−	0.918572i
$994$	20458.4	+	6968.60i	0.0207062	+	0.00705298i
$995$			579528.i			0.585367i
$996$	168321.	−	83250.0i	0.169676	−	0.0839200i
$997$	−514450.	−	891054.i	−0.517551	−	0.896425i	−0.999792	−	0.0203861i	$-0.993510\pi$
$997$	−514450.	−	891054.i	−0.517551	−	0.896425i	0.482241	−	0.876038i	$-0.339823\pi$
$998$	74480.4	−	43001.3i	0.0747792	−	0.0431738i
$999$	−1.00793e6	+	1.15744e6i	−1.00995	+	1.15976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.5.h.a.23.6	yes	20
3.2	odd	2	inner	42.5.h.a.23.4	yes	20
7.2	even	3		294.5.b.e.197.4		10
7.4	even	3	inner	42.5.h.a.11.4	✓	20
7.5	odd	6		294.5.b.f.197.2		10
21.2	odd	6		294.5.b.e.197.9		10
21.5	even	6		294.5.b.f.197.7		10
21.11	odd	6	inner	42.5.h.a.11.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.h.a.11.4	✓	20	7.4	even	3	inner
42.5.h.a.11.6	yes	20	21.11	odd	6	inner
42.5.h.a.23.4	yes	20	3.2	odd	2	inner
42.5.h.a.23.6	yes	20	1.1	even	1	trivial
294.5.b.e.197.4		10	7.2	even	3
294.5.b.e.197.9		10	21.2	odd	6
294.5.b.f.197.2		10	7.5	odd	6
294.5.b.f.197.7		10	21.5	even	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)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(-8.98141 - 0.578196i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-35.7395 - 20.6342i) q^{5} +(-21.1822 - 14.1179i) q^{6} +(-9.50910 - 48.0685i) q^{7} +22.6274i q^{8} +(80.3314 + 10.3860i) q^{9} +O(q^{10})\)	\(q+(2.44949 + 1.41421i) q^{2} +(-8.98141 - 0.578196i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-35.7395 - 20.6342i) q^{5} +(-21.1822 - 14.1179i) q^{6} +(-9.50910 - 48.0685i) q^{7} +22.6274i q^{8} +(80.3314 + 10.3860i) q^{9} +(-58.3624 - 101.087i) q^{10} +(-127.299 + 73.4961i) q^{11} +(-31.9198 - 64.5378i) q^{12} -89.0960 q^{13} +(44.6866 - 131.191i) q^{14} +(309.061 + 205.989i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(41.5038 - 23.9622i) q^{17} +(182.083 + 139.046i) q^{18} +(30.9933 - 53.6820i) q^{19} -330.148i q^{20} +(57.6122 + 437.221i) q^{21} -415.757 q^{22} +(-127.669 - 73.7096i) q^{23} +(13.0831 - 203.226i) q^{24} +(539.043 + 933.649i) q^{25} +(-218.240 - 126.001i) q^{26} +(-715.484 - 139.728i) q^{27} +(294.992 - 258.155i) q^{28} -1075.61i q^{29} +(465.729 + 941.645i) q^{30} +(524.925 + 909.196i) q^{31} +(-156.767 + 90.5097i) q^{32} +(1185.82 - 586.495i) q^{33} +135.551 q^{34} +(-652.005 + 1914.16i) q^{35} +(249.369 + 598.096i) q^{36} +(1052.67 - 1823.28i) q^{37} +(151.836 - 87.6623i) q^{38} +(800.208 + 51.5149i) q^{39} +(466.899 - 808.693i) q^{40} -1695.63i q^{41} +(-477.203 + 1152.44i) q^{42} -3636.45 q^{43} +(-1018.39 - 587.969i) q^{44} +(-2656.70 - 2028.77i) q^{45} +(-208.482 - 361.102i) q^{46} +(-1913.88 - 1104.98i) q^{47} +(319.452 - 479.298i) q^{48} +(-2220.15 + 914.176i) q^{49} +3049.29i q^{50} +(-386.618 + 191.217i) q^{51} +(-356.384 - 617.275i) q^{52} +(2856.74 - 1649.34i) q^{53} +(-1554.96 - 1354.11i) q^{54} +6066.14 q^{55} +(1087.67 - 215.166i) q^{56} +(-309.402 + 464.220i) q^{57} +(1521.15 - 2634.71i) q^{58} +(-1289.36 + 744.410i) q^{59} +(-190.890 + 2965.19i) q^{60} +(-1516.02 + 2625.82i) q^{61} +2969.42i q^{62} +(-264.639 - 3960.17i) q^{63} -512.000 q^{64} +(3184.25 + 1838.43i) q^{65} +(3734.08 + 240.389i) q^{66} +(2270.71 + 3932.99i) q^{67} +(332.030 + 191.698i) q^{68} +(1104.03 + 735.834i) q^{69} +(-4304.11 + 3766.63i) q^{70} +155.944i q^{71} +(-235.009 + 1817.69i) q^{72} +(-2317.15 - 4013.42i) q^{73} +(5157.02 - 2977.41i) q^{74} +(-4301.53 - 8697.16i) q^{75} +495.893 q^{76} +(4743.34 + 5420.18i) q^{77} +(1887.25 + 1257.85i) q^{78} +(-2357.21 + 4082.81i) q^{79} +(2287.33 - 1320.59i) q^{80} +(6345.26 + 1668.65i) q^{81} +(2397.98 - 4153.43i) q^{82} +2608.10i q^{83} +(-2798.70 + 2148.03i) q^{84} -1977.77 q^{85} +(-8907.45 - 5142.72i) q^{86} +(-621.916 + 9660.53i) q^{87} +(-1663.03 - 2880.45i) q^{88} +(6521.76 + 3765.34i) q^{89} +(-3638.44 - 8726.58i) q^{90} +(847.223 + 4282.71i) q^{91} -1179.35i q^{92} +(-4188.87 - 8469.37i) q^{93} +(-3125.36 - 5413.28i) q^{94} +(-2215.37 + 1279.05i) q^{95} +(1460.32 - 722.262i) q^{96} +5570.35 q^{97} +(-6731.08 - 900.507i) q^{98} +(-10989.4 + 4581.91i) 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

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