LMFDB - Embedded newform 69.5.d.a.22.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,5,Mod(22,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("69.22");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	69.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.13252745279$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5598 x^{14} + 11369517 x^{12} + 11272666128 x^{10} + 5958872960073 x^{8} + \cdots + 13\!\cdots\!52 $ x^16 + 5598x^14 + 11369517x^12 + 11272666128x^10 + 5958872960073x^8 + 1661250441139200x^6 + 215215956313867368x^4 + 8236967436040727664*x^2 + 13861812915684254052
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.5
Root			$-19.7839i$ of defining polynomial
Character	$\chi$	$=$	69.22
Dual form			69.5.d.a.22.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02014 q^{2} +5.19615 q^{3} -11.9191 q^{4} -11.8600i q^{5} -10.4969 q^{6} +49.3562i q^{7} +56.4003 q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.02014 q^{2} +5.19615 q^{3} -11.9191 q^{4} -11.8600i q^{5} -10.4969 q^{6} +49.3562i q^{7} +56.4003 q^{8} +27.0000 q^{9} +23.9589i q^{10} +138.760i q^{11} -61.9332 q^{12} +1.54329 q^{13} -99.7061i q^{14} -61.6265i q^{15} +76.7686 q^{16} +442.918i q^{17} -54.5437 q^{18} +136.903i q^{19} +141.360i q^{20} +256.462i q^{21} -280.314i q^{22} +(-111.696 + 517.074i) q^{23} +293.064 q^{24} +484.340 q^{25} -3.11765 q^{26} +140.296 q^{27} -588.279i q^{28} +799.586 q^{29} +124.494i q^{30} -1832.70 q^{31} -1057.49 q^{32} +721.019i q^{33} -894.755i q^{34} +585.366 q^{35} -321.814 q^{36} -2680.48i q^{37} -276.562i q^{38} +8.01917 q^{39} -668.909i q^{40} +1129.66 q^{41} -518.088i q^{42} -1149.16i q^{43} -1653.89i q^{44} -320.221i q^{45} +(225.641 - 1044.56i) q^{46} -1549.99 q^{47} +398.902 q^{48} -35.0313 q^{49} -978.432 q^{50} +2301.47i q^{51} -18.3945 q^{52} +1245.11i q^{53} -283.417 q^{54} +1645.70 q^{55} +2783.70i q^{56} +711.368i q^{57} -1615.27 q^{58} -272.245 q^{59} +734.530i q^{60} +6172.94i q^{61} +3702.31 q^{62} +1332.62i q^{63} +907.970 q^{64} -18.3035i q^{65} -1456.56i q^{66} -653.333i q^{67} -5279.17i q^{68} +(-580.389 + 2686.79i) q^{69} -1182.52 q^{70} +1628.32 q^{71} +1522.81 q^{72} -830.928 q^{73} +5414.92i q^{74} +2516.70 q^{75} -1631.75i q^{76} -6848.67 q^{77} -16.1998 q^{78} -4359.86i q^{79} -910.478i q^{80} +729.000 q^{81} -2282.07 q^{82} +5180.44i q^{83} -3056.79i q^{84} +5253.03 q^{85} +2321.47i q^{86} +4154.77 q^{87} +7826.11i q^{88} +4715.91i q^{89} +646.889i q^{90} +76.1709i q^{91} +(1331.31 - 6163.03i) q^{92} -9523.01 q^{93} +3131.18 q^{94} +1623.67 q^{95} -5494.87 q^{96} -7546.72i q^{97} +70.7680 q^{98} +3746.52i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9	$ 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9} + 104 q^{13} + 680 q^{16} + 324 q^{18} - 732 q^{23} - 1764 q^{24} - 2984 q^{25} + 1800 q^{26} - 3528 q^{29} - 400 q^{31} + 5244 q^{32} + 912 q^{35} + 3888 q^{36} + 2016 q^{39} + 1008 q^{41} - 1168 q^{46} - 8664 q^{47} - 2016 q^{48} + 7240 q^{49} - 18852 q^{50} - 20952 q^{52} - 972 q^{54} + 6816 q^{55} - 13352 q^{58} + 20112 q^{59} + 4248 q^{62} - 896 q^{64} - 10044 q^{69} - 10680 q^{70} + 40368 q^{71} + 10044 q^{72} - 9568 q^{73} + 7560 q^{75} + 2952 q^{77} - 6912 q^{78} + 11664 q^{81} + 71800 q^{82} + 42744 q^{85} + 8352 q^{87} - 9876 q^{92} - 10008 q^{93} + 73720 q^{94} + 33312 q^{95} - 24948 q^{96} - 59052 q^{98}+O(q^{100}) $ 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9 + 104 * q^13 + 680 * q^16 + 324 * q^18 - 732 * q^23 - 1764 * q^24 - 2984 * q^25 + 1800 * q^26 - 3528 * q^29 - 400 * q^31 + 5244 * q^32 + 912 * q^35 + 3888 * q^36 + 2016 * q^39 + 1008 * q^41 - 1168 * q^46 - 8664 * q^47 - 2016 * q^48 + 7240 * q^49 - 18852 * q^50 - 20952 * q^52 - 972 * q^54 + 6816 * q^55 - 13352 * q^58 + 20112 * q^59 + 4248 * q^62 - 896 * q^64 - 10044 * q^69 - 10680 * q^70 + 40368 * q^71 + 10044 * q^72 - 9568 * q^73 + 7560 * q^75 + 2952 * q^77 - 6912 * q^78 + 11664 * q^81 + 71800 * q^82 + 42744 * q^85 + 8352 * q^87 - 9876 * q^92 - 10008 * q^93 + 73720 * q^94 + 33312 * q^95 - 24948 * q^96 - 59052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.02014			−0.505034			−0.252517	−	0.967592i	$-0.581258\pi$
$2$	−2.02014			−0.505034			−0.252517	+	0.967592i	$0.581258\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−11.9191			−0.744941
$5$		−	11.8600i		−	0.474401i	−0.971461	−	0.237201i	$-0.923770\pi$
$5$		−	11.8600i		−	0.474401i	0.971461	−	0.237201i	$-0.0762299\pi$
$6$	−10.4969			−0.291581
$7$			49.3562i			1.00727i	0.863917	+	0.503634i	$0.168004\pi$
$7$			49.3562i			1.00727i	−0.863917	+	0.503634i	$0.831996\pi$
$8$	56.4003			0.881254
$9$	27.0000			0.333333
$10$			23.9589i			0.239589i
$11$			138.760i			1.14678i	0.819283	+	0.573389i	$0.194372\pi$
$11$			138.760i			1.14678i	−0.819283	+	0.573389i	$0.805628\pi$
$12$	−61.9332			−0.430092
$13$	1.54329			0.00913189			0.00456595	−	0.999990i	$-0.498547\pi$
$13$	1.54329			0.00913189			0.00456595	+	0.999990i	$0.498547\pi$
$14$		−	99.7061i		−	0.508705i
$15$		−	61.6265i		−	0.273896i
$16$	76.7686			0.299878
$17$			442.918i			1.53259i	0.642489	+	0.766295i	$0.277902\pi$
$17$			442.918i			1.53259i	−0.642489	+	0.766295i	$0.722098\pi$
$18$	−54.5437			−0.168345
$19$			136.903i			0.379232i	0.981858	+	0.189616i	$0.0607244\pi$
$19$			136.903i			0.379232i	−0.981858	+	0.189616i	$0.939276\pi$
$20$			141.360i			0.353401i
$21$			256.462i			0.581547i
$22$		−	280.314i		−	0.579162i
$23$	−111.696	+	517.074i	−0.211145	+	0.977455i
$23$	−111.696	+	517.074i	−0.211145	+	0.977455i
$24$	293.064			0.508792
$25$	484.340			0.774943
$26$	−3.11765			−0.00461191
$27$	140.296			0.192450
$28$		−	588.279i		−	0.750356i
$29$	799.586			0.950756			0.475378	−	0.879782i	$-0.342311\pi$
$29$	799.586			0.950756			0.475378	+	0.879782i	$0.342311\pi$
$30$			124.494i			0.138327i
$31$	−1832.70			−1.90708			−0.953540	−	0.301265i	$-0.902591\pi$
$31$	−1832.70			−1.90708			−0.953540	+	0.301265i	$0.902591\pi$
$32$	−1057.49			−1.03270
$33$			721.019i			0.662092i
$34$		−	894.755i		−	0.774010i
$35$	585.366			0.477850
$36$	−321.814			−0.248314
$37$		−	2680.48i		−	1.95798i	−0.203906	−	0.978990i	$-0.565364\pi$
$37$		−	2680.48i		−	1.95798i	0.203906	−	0.978990i	$-0.434636\pi$
$38$		−	276.562i		−	0.191525i
$39$	8.01917			0.00527230
$40$		−	668.909i		−	0.418068i
$41$	1129.66			0.672017			0.336009	−	0.941859i	$-0.390923\pi$
$41$	1129.66			0.672017			0.336009	+	0.941859i	$0.390923\pi$
$42$		−	518.088i		−	0.293701i
$43$		−	1149.16i		−	0.621506i	−0.950491	−	0.310753i	$-0.899419\pi$
$43$		−	1149.16i		−	0.621506i	0.950491	−	0.310753i	$-0.100581\pi$
$44$		−	1653.89i		−	0.854281i
$45$		−	320.221i		−	0.158134i
$46$	225.641	−	1044.56i	0.106636	−	0.493648i
$47$	−1549.99			−0.701669			−0.350834	−	0.936438i	$-0.614102\pi$
$47$	−1549.99			−0.701669			−0.350834	+	0.936438i	$0.614102\pi$
$48$	398.902			0.173134
$49$	−35.0313			−0.0145903
$50$	−978.432			−0.391373
$51$			2301.47i			0.884841i
$52$	−18.3945			−0.00680272
$53$			1245.11i			0.443258i	0.975131	+	0.221629i	$0.0711374\pi$
$53$			1245.11i			0.443258i	−0.975131	+	0.221629i	$0.928863\pi$
$54$	−283.417			−0.0971938
$55$	1645.70			0.544033
$56$			2783.70i			0.887660i
$57$			711.368i			0.218950i
$58$	−1615.27			−0.480164
$59$	−272.245			−0.0782087			−0.0391044	−	0.999235i	$-0.512450\pi$
$59$	−272.245			−0.0782087			−0.0391044	+	0.999235i	$0.512450\pi$
$60$			734.530i			0.204036i
$61$			6172.94i			1.65895i	0.558546	+	0.829474i	$0.311359\pi$
$61$			6172.94i			1.65895i	−0.558546	+	0.829474i	$0.688641\pi$
$62$	3702.31			0.963140
$63$			1332.62i			0.335756i
$64$	907.970			0.221672
$65$		−	18.3035i		−	0.00433218i
$66$		−	1456.56i		−	0.334379i
$67$		−	653.333i		−	0.145541i	−0.997349	−	0.0727705i	$-0.976816\pi$
$67$		−	653.333i		−	0.145541i	0.997349	−	0.0727705i	$-0.0231840\pi$
$68$		−	5279.17i		−	1.14169i
$69$	−580.389	+	2686.79i	−0.121905	+	0.564334i
$70$	−1182.52			−0.241330
$71$	1628.32			0.323016			0.161508	−	0.986871i	$-0.448364\pi$
$71$	1628.32			0.323016			0.161508	+	0.986871i	$0.448364\pi$
$72$	1522.81			0.293751
$73$	−830.928			−0.155926			−0.0779628	−	0.996956i	$-0.524842\pi$
$73$	−830.928			−0.155926			−0.0779628	+	0.996956i	$0.524842\pi$
$74$			5414.92i			0.988847i
$75$	2516.70			0.447414
$76$		−	1631.75i		−	0.282506i
$77$	−6848.67			−1.15511
$78$	−16.1998			−0.00266269
$79$		−	4359.86i		−	0.698584i	−0.937014	−	0.349292i	$-0.886422\pi$
$79$		−	4359.86i		−	0.698584i	0.937014	−	0.349292i	$-0.113578\pi$
$80$		−	910.478i		−	0.142262i
$81$	729.000			0.111111
$82$	−2282.07			−0.339391
$83$			5180.44i			0.751987i	0.926622	+	0.375994i	$0.122699\pi$
$83$			5180.44i			0.751987i	−0.926622	+	0.375994i	$0.877301\pi$
$84$		−	3056.79i		−	0.433218i
$85$	5253.03			0.727062
$86$			2321.47i			0.313882i
$87$	4154.77			0.548920
$88$			7826.11i			1.01060i
$89$			4715.91i			0.595367i	0.954665	+	0.297684i	$0.0962141\pi$
$89$			4715.91i			0.595367i	−0.954665	+	0.297684i	$0.903786\pi$
$90$			646.889i			0.0798629i
$91$			76.1709i			0.00919827i
$92$	1331.31	−	6163.03i	0.157291	−	0.728146i
$93$	−9523.01			−1.10105
$94$	3131.18			0.354366
$95$	1623.67			0.179908
$96$	−5494.87			−0.596231
$97$		−	7546.72i		−	0.802075i	−0.916062	−	0.401037i	$-0.868650\pi$
$97$		−	7546.72i		−	0.802075i	0.916062	−	0.401037i	$-0.131350\pi$
$98$	70.7680			0.00736860
$99$			3746.52i			0.382259i
$100$	−5772.87			−0.577287
$101$	12320.4			1.20776			0.603880	−	0.797075i	$-0.293621\pi$
$101$	12320.4			1.20776			0.603880	+	0.797075i	$0.293621\pi$
$102$		−	4649.28i		−	0.446875i
$103$			15454.2i			1.45671i	0.685200	+	0.728355i	$0.259715\pi$
$103$			15454.2i			1.45671i	−0.685200	+	0.728355i	$0.740285\pi$
$104$	87.0419			0.00804752
$105$	3041.65			0.275887
$106$		−	2515.30i		−	0.223860i
$107$		−	8600.42i		−	0.751194i	−0.926783	−	0.375597i	$-0.877438\pi$
$107$		−	8600.42i		−	0.751194i	0.926783	−	0.375597i	$-0.122562\pi$
$108$	−1672.20			−0.143364
$109$		−	1914.39i		−	0.161131i	−0.996749	−	0.0805653i	$-0.974327\pi$
$109$		−	1914.39i		−	0.161131i	0.996749	−	0.0805653i	$-0.0256726\pi$
$110$	−3324.53			−0.274755
$111$		−	13928.2i		−	1.13044i
$112$			3789.01i			0.302057i
$113$		−	8842.41i		−	0.692490i	−0.938144	−	0.346245i	$-0.887457\pi$
$113$		−	8842.41i		−	0.692490i	0.938144	−	0.346245i	$-0.112543\pi$
$114$		−	1437.06i		−	0.110577i
$115$	6132.51	+	1324.72i	0.463706	+	0.100168i
$116$	−9530.31			−0.708257
$117$	41.6688			0.00304396
$118$	549.971			0.0394981
$119$	−21860.8			−1.54373
$120$		−	3475.75i		−	0.241372i
$121$	−4613.36			−0.315099
$122$		−	12470.2i		−	0.837825i
$123$	5869.89			0.387989
$124$	21844.1			1.42066
$125$		−	13156.8i		−	0.842035i
$126$		−	2692.07i		−	0.169568i
$127$	−16086.6			−0.997372			−0.498686	−	0.866783i	$-0.666184\pi$
$127$	−16086.6			−0.997372			−0.498686	+	0.866783i	$0.666184\pi$
$128$	15085.6			0.920751
$129$		−	5971.23i		−	0.358827i
$130$			36.9755i			0.00218790i
$131$	9411.82			0.548443			0.274221	−	0.961667i	$-0.411580\pi$
$131$	9411.82			0.548443			0.274221	+	0.961667i	$0.411580\pi$
$132$		−	8593.86i		−	0.493220i
$133$	−6757.00			−0.381989
$134$			1319.82i			0.0735031i
$135$		−	1663.92i		−	0.0912986i
$136$			24980.7i			1.35060i
$137$			20606.2i			1.09788i	0.835860	+	0.548942i	$0.184969\pi$
$137$			20606.2i			1.09788i	−0.835860	+	0.548942i	$0.815031\pi$
$138$	1172.46	−	5427.69i	0.0615661	−	0.285008i
$139$	−9481.33			−0.490727			−0.245363	−	0.969431i	$-0.578907\pi$
$139$	−9481.33			−0.490727			−0.245363	+	0.969431i	$0.578907\pi$
$140$	−6977.00			−0.355970
$141$	−8053.96			−0.405109
$142$	−3289.43			−0.163134
$143$			214.147i			0.0104722i
$144$	2072.75			0.0999592
$145$		−	9483.12i		−	0.451040i
$146$	1678.59			0.0787478
$147$	−182.028			−0.00842371
$148$			31948.7i			1.45858i
$149$		−	34843.6i		−	1.56946i	−0.619838	−	0.784730i	$-0.712802\pi$
$149$		−	34843.6i		−	1.56946i	0.619838	−	0.784730i	$-0.287198\pi$
$150$	−5084.08			−0.225959
$151$	19394.8			0.850613			0.425307	−	0.905049i	$-0.360166\pi$
$151$	19394.8			0.850613			0.425307	+	0.905049i	$0.360166\pi$
$152$			7721.36i			0.334200i
$153$			11958.8i			0.510863i
$154$	13835.2			0.583371
$155$			21735.9i			0.904721i
$156$	−95.5809			−0.00392755
$157$		−	22896.2i		−	0.928891i	−0.885602	−	0.464446i	$-0.846254\pi$
$157$		−	22896.2i		−	0.928891i	0.885602	−	0.464446i	$-0.153746\pi$
$158$			8807.51i			0.352808i
$159$			6469.79i			0.255915i
$160$			12541.8i			0.489915i
$161$	−25520.8	−	5512.88i	−0.984560	−	0.212680i
$162$	−1472.68			−0.0561149
$163$	34238.6			1.28867			0.644333	−	0.764745i	$-0.277135\pi$
$163$	34238.6			1.28867			0.644333	+	0.764745i	$0.277135\pi$
$164$	−13464.5			−0.500613
$165$	8551.30			0.314097
$166$		−	10465.2i		−	0.379779i
$167$	44643.0			1.60074			0.800370	−	0.599506i	$-0.204636\pi$
$167$	44643.0			1.60074			0.800370	+	0.599506i	$0.204636\pi$
$168$			14464.5i			0.512491i
$169$	−28558.6			−0.999917
$170$	−10611.8			−0.367191
$171$			3696.38i			0.126411i
$172$			13696.9i			0.462985i
$173$	26121.0			0.872765			0.436383	−	0.899761i	$-0.356259\pi$
$173$	26121.0			0.872765			0.436383	+	0.899761i	$0.356259\pi$
$174$	−8393.20			−0.277223
$175$			23905.2i			0.780576i
$176$			10652.4i			0.343893i
$177$	−1414.62			−0.0451538
$178$		−	9526.77i		−	0.300681i
$179$	−18435.7			−0.575379			−0.287689	−	0.957724i	$-0.592887\pi$
$179$	−18435.7			−0.575379			−0.287689	+	0.957724i	$0.592887\pi$
$180$			3816.73i			0.117800i
$181$		−	19820.1i		−	0.604992i	−0.953151	−	0.302496i	$-0.902180\pi$
$181$		−	19820.1i		−	0.604992i	0.953151	−	0.302496i	$-0.0978199\pi$
$182$		−	153.875i		−	0.00464544i
$183$			32075.6i			0.957794i
$184$	−6299.68	+	29163.1i	−0.186073	+	0.861386i
$185$	−31790.5			−0.928869
$186$	19237.8			0.556069
$187$	−61459.4			−1.75754
$188$	18474.4			0.522702
$189$			6924.48i			0.193849i
$190$	−3280.04			−0.0908598
$191$			6762.97i			0.185383i	0.995695	+	0.0926916i	$0.0295471\pi$
$191$			6762.97i			0.185383i	−0.995695	+	0.0926916i	$0.970453\pi$
$192$	4717.95			0.127983
$193$	54646.4			1.46706			0.733528	−	0.679659i	$-0.237872\pi$
$193$	54646.4			1.46706			0.733528	+	0.679659i	$0.237872\pi$
$194$			15245.4i			0.405075i
$195$		−	95.1076i		−	0.00250119i
$196$	417.540			0.0108689
$197$	34881.1			0.898789			0.449395	−	0.893333i	$-0.351640\pi$
$197$	34881.1			0.898789			0.449395	+	0.893333i	$0.351640\pi$
$198$		−	7568.48i		−	0.193054i
$199$		−	56991.5i		−	1.43914i	−0.694418	−	0.719572i	$-0.744338\pi$
$199$		−	56991.5i		−	1.43914i	0.694418	−	0.719572i	$-0.255662\pi$
$200$	27316.9			0.682922
$201$		−	3394.82i		−	0.0840281i
$202$	−24888.8			−0.609960
$203$			39464.5i			0.957667i
$204$		−	27431.4i		−	0.659154i
$205$		−	13397.8i		−	0.318806i
$206$		−	31219.6i		−	0.735688i
$207$	−3015.79	+	13961.0i	−0.0703818	+	0.325818i
$208$	118.476			0.00273845
$209$	−18996.7			−0.434895
$210$	−6144.54			−0.139332
$211$	16055.7			0.360631			0.180316	−	0.983609i	$-0.442288\pi$
$211$	16055.7			0.360631			0.180316	+	0.983609i	$0.442288\pi$
$212$		−	14840.6i		−	0.330201i
$213$	8461.01			0.186493
$214$			17374.0i			0.379379i
$215$	−13629.1			−0.294843
$216$	7912.74			0.169597
$217$		−	90455.3i		−	1.92094i
$218$			3867.33i			0.0813764i
$219$	−4317.63			−0.0900237
$220$	−19615.2			−0.405272
$221$			683.551i			0.0139954i
$222$			28136.8i			0.570911i
$223$	−49350.5			−0.992389			−0.496195	−	0.868211i	$-0.665270\pi$
$223$	−49350.5			−0.992389			−0.496195	+	0.868211i	$0.665270\pi$
$224$		−	52193.5i		−	1.04021i
$225$	13077.2			0.258314
$226$			17862.9i			0.349731i
$227$			32093.6i			0.622826i	0.950275	+	0.311413i	$0.100802\pi$
$227$			32093.6i			0.622826i	−0.950275	+	0.311413i	$0.899198\pi$
$228$		−	8478.84i		−	0.163105i
$229$		−	98532.0i		−	1.87891i	−0.342669	−	0.939456i	$-0.611331\pi$
$229$		−	98532.0i		−	1.87891i	0.342669	−	0.939456i	$-0.388669\pi$
$230$	−12388.5	−	2676.11i	−0.234187	−	0.0505880i
$231$	−35586.7			−0.666905
$232$	45096.9			0.837858
$233$	−82075.6			−1.51183			−0.755913	−	0.654672i	$-0.772807\pi$
$233$	−82075.6			−1.51183			−0.755913	+	0.654672i	$0.772807\pi$
$234$	−84.1767			−0.00153730
$235$			18382.9i			0.332872i
$236$	3244.90			0.0582609
$237$		−	22654.5i		−	0.403327i
$238$	44161.7			0.779636
$239$	56560.3			0.990183			0.495092	−	0.868841i	$-0.335134\pi$
$239$	56560.3			0.990183			0.495092	+	0.868841i	$0.335134\pi$
$240$		−	4730.98i		−	0.0821352i
$241$		−	26464.4i		−	0.455647i	−0.973702	−	0.227824i	$-0.926839\pi$
$241$		−	26464.4i		−	0.455647i	0.973702	−	0.227824i	$-0.0731610\pi$
$242$	9319.61			0.159135
$243$	3788.00			0.0641500
$244$		−	73575.6i		−	1.23582i
$245$			415.472i			0.00692166i
$246$	−11858.0			−0.195948
$247$			211.281i			0.00346311i
$248$	−103365.			−1.68062
$249$			26918.3i			0.434160i
$250$			26578.5i			0.425256i
$251$		−	34816.3i		−	0.552631i	−0.961067	−	0.276315i	$-0.910887\pi$
$251$		−	34816.3i		−	0.552631i	0.961067	−	0.276315i	$-0.0891135\pi$
$252$		−	15883.5i		−	0.250119i
$253$	−71749.2	−	15498.9i	−1.12092	−	0.242137i
$254$	32497.1			0.503706
$255$	27295.5			0.419770
$256$	−45002.4			−0.686682
$257$	50347.6			0.762277			0.381138	−	0.924518i	$-0.375532\pi$
$257$	50347.6			0.762277			0.381138	+	0.924518i	$0.375532\pi$
$258$			12062.7i			0.181220i
$259$	132298.			1.97221
$260$			218.160i			0.00322722i
$261$	21588.8			0.316919
$262$	−19013.2			−0.276982
$263$			91707.4i			1.32584i	0.748688	+	0.662922i	$0.230684\pi$
$263$			91707.4i			1.32584i	−0.748688	+	0.662922i	$0.769316\pi$
$264$			40665.6i			0.583472i
$265$	14767.1			0.210282
$266$	13650.1			0.192917
$267$			24504.6i			0.343736i
$268$			7787.11i			0.108419i
$269$	104021.			1.43753			0.718764	−	0.695254i	$-0.244708\pi$
$269$	104021.			1.43753			0.718764	+	0.695254i	$0.244708\pi$
$270$			3361.34i			0.0461089i
$271$	−71982.7			−0.980143			−0.490072	−	0.871682i	$-0.663029\pi$
$271$	−71982.7			−0.980143			−0.490072	+	0.871682i	$0.663029\pi$
$272$			34002.2i			0.459589i
$273$			395.795i			0.00531062i
$274$		−	41627.3i		−	0.554469i
$275$			67207.0i			0.888688i
$276$	6917.69	−	32024.0i	0.0908119	−	0.420395i
$277$	−74174.4			−0.966707			−0.483353	−	0.875425i	$-0.660581\pi$
$277$	−74174.4			−0.966707			−0.483353	+	0.875425i	$0.660581\pi$
$278$	19153.6			0.247834
$279$	−49483.0			−0.635694
$280$	33014.8			0.421107
$281$			42936.8i			0.543773i	0.962329	+	0.271886i	$0.0876475\pi$
$281$			42936.8i			0.543773i	−0.962329	+	0.271886i	$0.912353\pi$
$282$	16270.1			0.204594
$283$			128674.i			1.60664i	0.595550	+	0.803318i	$0.296934\pi$
$283$			128674.i			1.60664i	−0.595550	+	0.803318i	$0.703066\pi$
$284$	−19408.1			−0.240627
$285$	8436.85			0.103870
$286$		−	432.606i		−	0.00528884i
$287$			55755.7i			0.676902i
$288$	−28552.2			−0.344234
$289$	−112656.			−1.34883
$290$			19157.2i			0.227790i
$291$		−	39213.9i		−	0.463078i
$292$	9903.87			0.116155
$293$			55591.2i			0.647546i	0.946135	+	0.323773i	$0.104951\pi$
$293$			55591.2i			0.647546i	−0.946135	+	0.323773i	$0.895049\pi$
$294$	367.721			0.00425426
$295$			3228.83i			0.0371023i
$296$		−	151180.i		−	1.72548i
$297$			19467.5i			0.220697i
$298$			70388.8i			0.792630i
$299$	−172.379	+	797.994i	−0.00192816	+	0.00892601i
$300$	−29996.7			−0.333297
$301$	56718.3			0.626023
$302$	−39180.2			−0.429588
$303$	64018.4			0.697300
$304$			10509.9i			0.113723i
$305$	73211.3			0.787007
$306$		−	24158.4i		−	0.258003i
$307$	162102.			1.71993			0.859967	−	0.510350i	$-0.170484\pi$
$307$	162102.			1.71993			0.859967	+	0.510350i	$0.170484\pi$
$308$	81629.6			0.860491
$309$			80302.5i			0.841031i
$310$		−	43909.5i		−	0.456915i
$311$	−14298.7			−0.147834			−0.0739171	−	0.997264i	$-0.523550\pi$
$311$	−14298.7			−0.147834			−0.0739171	+	0.997264i	$0.523550\pi$
$312$	452.283			0.00464624
$313$			49552.0i			0.505793i	0.967493	+	0.252896i	$0.0813831\pi$
$313$			49552.0i			0.505793i	−0.967493	+	0.252896i	$0.918617\pi$
$314$			46253.5i			0.469122i
$315$	15804.9			0.159283
$316$			51965.4i			0.520403i
$317$	−193612.			−1.92670			−0.963349	−	0.268250i	$-0.913555\pi$
$317$	−193612.			−1.92670			−0.963349	+	0.268250i	$0.913555\pi$
$318$		−	13069.9i		−	0.129246i
$319$			110951.i			1.09031i
$320$		−	10768.5i		−	0.105162i
$321$		−	44689.1i		−	0.433702i
$322$	51555.4	+	11136.8i	0.497236	+	0.107411i
$323$	−60636.8			−0.581208
$324$	−8688.99			−0.0827712
$325$	747.476			0.00707670
$326$	−69166.6			−0.650820
$327$		−	9947.48i		−	0.0930288i
$328$	63713.2			0.592218
$329$		−	76501.4i		−	0.706769i
$330$	−17274.8			−0.158630
$331$	154717.			1.41215			0.706075	−	0.708137i	$-0.250464\pi$
$331$	154717.			1.41215			0.706075	+	0.708137i	$0.250464\pi$
$332$		−	61745.9i		−	0.560186i
$333$		−	72372.8i		−	0.652660i
$334$	−90185.0			−0.808428
$335$	−7748.55			−0.0690448
$336$			19688.3i			0.174393i
$337$			123315.i			1.08582i	0.839791	+	0.542909i	$0.182677\pi$
$337$			123315.i			1.08582i	−0.839791	+	0.542909i	$0.817323\pi$
$338$	57692.3			0.504992
$339$		−	45946.5i		−	0.399809i
$340$	−62611.1			−0.541618
$341$		−	254306.i		−	2.18700i
$342$		−	7467.19i		−	0.0638417i
$343$			116775.i			0.992572i
$344$		−	64813.2i		−	0.547705i
$345$	31865.4	+	6883.43i	0.267721	+	0.0578318i
$346$	−52767.9			−0.440776
$347$	−156697.			−1.30137			−0.650685	−	0.759348i	$-0.725518\pi$
$347$	−156697.			−1.30137			−0.650685	+	0.759348i	$0.725518\pi$
$348$	−49520.9			−0.408913
$349$	−160116.			−1.31457			−0.657287	−	0.753640i	$-0.728296\pi$
$349$	−160116.			−1.31457			−0.657287	+	0.753640i	$0.728296\pi$
$350$		−	48291.6i		−	0.394218i
$351$	216.518			0.00175743
$352$		−	146737.i		−	1.18428i
$353$	216727.			1.73925			0.869627	−	0.493709i	$-0.164359\pi$
$353$	216727.			1.73925			0.869627	+	0.493709i	$0.164359\pi$
$354$	2857.73			0.0228042
$355$		−	19311.9i		−	0.153239i
$356$		−	56209.1i		−	0.443513i
$357$	−113592.			−0.891273
$358$	37242.6			0.290586
$359$		−	158846.i		−	1.23250i	−0.787550	−	0.616250i	$-0.788651\pi$
$359$		−	158846.i		−	1.23250i	0.787550	−	0.616250i	$-0.211349\pi$
$360$		−	18060.5i		−	0.139356i
$361$	111579.			0.856183
$362$			40039.4i			0.305541i
$363$	−23971.7			−0.181922
$364$		−	907.884i		−	0.00685216i
$365$			9854.83i			0.0739713i
$366$		−	64797.0i		−	0.483718i
$367$			63218.6i			0.469367i	0.972072	+	0.234684i	$0.0754054\pi$
$367$			63218.6i			0.469367i	−0.972072	+	0.234684i	$0.924595\pi$
$368$	−8574.74	+	39695.0i	−0.0633177	+	0.293117i
$369$	30500.8			0.224006
$370$	64221.2			0.469110
$371$	−61454.0			−0.446480
$372$	113505.			0.820220
$373$		−	35956.2i		−	0.258438i	−0.991616	−	0.129219i	$-0.958753\pi$
$373$		−	35956.2i		−	0.258438i	0.991616	−	0.129219i	$-0.0412470\pi$
$374$	124156.			0.887617
$375$		−	68364.8i		−	0.486149i
$376$	−87419.6			−0.618348
$377$	1233.99			0.00868220
$378$		−	13988.4i		−	0.0979003i
$379$			92556.1i			0.644357i	0.946679	+	0.322179i	$0.104415\pi$
$379$			92556.1i			0.644357i	−0.946679	+	0.322179i	$0.895585\pi$
$380$	−19352.6			−0.134021
$381$	−83588.5			−0.575833
$382$		−	13662.1i		−	0.0936248i
$383$		−	94193.3i		−	0.642129i	−0.947057	−	0.321065i	$-0.895959\pi$
$383$		−	94193.3i		−	0.642129i	0.947057	−	0.321065i	$-0.104041\pi$
$384$	78387.0			0.531596
$385$			81225.4i			0.547987i
$386$	−110393.			−0.740913
$387$		−	31027.4i		−	0.207169i
$388$			89949.8i			0.597498i
$389$			255864.i			1.69087i	0.534077	+	0.845436i	$0.320659\pi$
$389$			255864.i			1.69087i	−0.534077	+	0.845436i	$0.679341\pi$
$390$			192.130i			0.00126318i
$391$	−229021.	−	49472.2i	−1.49804	−	0.323599i
$392$	−1975.78			−0.0128578
$393$	48905.3			0.316643
$394$	−70464.6			−0.453919
$395$	−51708.1			−0.331409
$396$		−	44655.0i		−	0.284760i
$397$	209181.			1.32721			0.663607	−	0.748081i	$-0.269025\pi$
$397$	209181.			1.32721			0.663607	+	0.748081i	$0.269025\pi$
$398$			115131.i			0.726816i
$399$	−35110.4			−0.220541
$400$	37182.1			0.232388
$401$		−	130365.i		−	0.810725i	−0.914156	−	0.405363i	$-0.867145\pi$
$401$		−	130365.i		−	0.810725i	0.914156	−	0.405363i	$-0.132855\pi$
$402$			6857.99i			0.0424370i
$403$	−2828.39			−0.0174153
$404$	−146847.			−0.899709
$405$		−	8645.96i		−	0.0527112i
$406$		−	79723.7i		−	0.483654i
$407$	371943.			2.24537
$408$			129804.i			0.779770i
$409$	41308.2			0.246939			0.123469	−	0.992348i	$-0.460598\pi$
$409$	41308.2			0.246939			0.123469	+	0.992348i	$0.460598\pi$
$410$			27065.4i			0.161008i
$411$			107073.i			0.633864i
$412$		−	184200.i		−	1.08516i
$413$		−	13437.0i		−	0.0787772i
$414$	6092.30	−	28203.1i	0.0355452	−	0.164549i
$415$	61440.2			0.356744
$416$	−1632.01			−0.00943053
$417$	−49266.4			−0.283321
$418$	38375.8			0.219637
$419$		−	81532.1i		−	0.464409i	−0.972667	−	0.232204i	$-0.925406\pi$
$419$		−	81532.1i		−	0.464409i	0.972667	−	0.232204i	$-0.0745938\pi$
$420$	−36253.6			−0.205519
$421$		−	190672.i		−	1.07578i	−0.843016	−	0.537889i	$-0.819222\pi$
$421$		−	190672.i		−	1.07578i	0.843016	−	0.537889i	$-0.180778\pi$
$422$	−32434.6			−0.182131
$423$	−41849.6			−0.233890
$424$			70224.7i			0.390623i
$425$			214523.i			1.18767i
$426$	−17092.4			−0.0941854
$427$	−304673.			−1.67101
$428$			102509.i			0.559595i
$429$			1112.74i			0.00604615i
$430$	27532.7			0.148906
$431$		−	329168.i		−	1.77200i	−0.463685	−	0.886000i	$-0.653473\pi$
$431$		−	329168.i		−	1.77200i	0.463685	−	0.886000i	$-0.346527\pi$
$432$	10770.3			0.0577115
$433$			58185.4i			0.310341i	0.987888	+	0.155170i	$0.0495926\pi$
$433$			58185.4i			0.310341i	−0.987888	+	0.155170i	$0.950407\pi$
$434$			182732.i			0.970141i
$435$		−	49275.7i		−	0.260408i
$436$			22817.7i			0.120033i
$437$	−70788.9	−	15291.5i	−0.370683	−	0.0800732i
$438$	8722.20			0.0454650
$439$	196906.			1.02172			0.510858	−	0.859665i	$-0.329328\pi$
$439$	196906.			1.02172			0.510858	+	0.859665i	$0.329328\pi$
$440$	92817.9			0.479431
$441$	−945.845			−0.00486343
$442$		−	1380.87i		−	0.00706817i
$443$	−6730.75			−0.0342970			−0.0171485	−	0.999853i	$-0.505459\pi$
$443$	−6730.75			−0.0342970			−0.0171485	+	0.999853i	$0.505459\pi$
$444$			166010.i			0.842111i
$445$	55930.8			0.282443
$446$	99694.8			0.501190
$447$		−	181053.i		−	0.906128i
$448$			44813.9i			0.223284i
$449$	−253160.			−1.25575			−0.627874	−	0.778315i	$-0.716075\pi$
$449$	−253160.			−1.25575			−0.627874	+	0.778315i	$0.716075\pi$
$450$	−26417.7			−0.130458
$451$			156752.i			0.770654i
$452$			105393.i			0.515864i
$453$	100778.			0.491102
$454$		−	64833.5i		−	0.314548i
$455$	903.389			0.00436367
$456$			40121.4i			0.192951i
$457$		−	386298.i		−	1.84965i	−0.380388	−	0.924827i	$-0.624210\pi$
$457$		−	386298.i		−	1.84965i	0.380388	−	0.924827i	$-0.375790\pi$
$458$			199048.i			0.948914i
$459$			62139.7i			0.294947i
$460$	−73093.7	−	15789.4i	−0.345433	−	0.0746189i
$461$	−215298.			−1.01307			−0.506535	−	0.862220i	$-0.669074\pi$
$461$	−215298.			−1.01307			−0.506535	+	0.862220i	$0.669074\pi$
$462$	71890.0			0.336810
$463$	−58694.1			−0.273800			−0.136900	−	0.990585i	$-0.543714\pi$
$463$	−58694.1			−0.273800			−0.136900	+	0.990585i	$0.543714\pi$
$464$	61383.1			0.285110
$465$			112943.i			0.522341i
$466$	165804.			0.763524
$467$			201704.i			0.924868i	0.886654	+	0.462434i	$0.153024\pi$
$467$			201704.i			0.924868i	−0.886654	+	0.462434i	$0.846976\pi$
$468$	−496.653			−0.00226757
$469$	32246.0			0.146599
$470$		−	37135.9i		−	0.168112i
$471$		−	118972.i		−	0.536296i
$472$	−15354.7			−0.0689218
$473$	159458.			0.712729
$474$			45765.2i			0.203694i
$475$			66307.5i			0.293884i
$476$	260559.			1.14999
$477$			33618.0i			0.147753i
$478$	−114259.			−0.500076
$479$			151028.i			0.658242i	0.944288	+	0.329121i	$0.106752\pi$
$479$			151028.i			0.658242i	−0.944288	+	0.329121i	$0.893248\pi$
$480$			65169.3i			0.282853i
$481$		−	4136.75i		−	0.0178801i
$482$			53461.8i			0.230117i
$483$	−132610.	−	28645.8i	−0.568436	−	0.122791i
$484$	54986.9			0.234730
$485$	−89504.4			−0.380505
$486$	−7652.26			−0.0323979
$487$	−167922.			−0.708026			−0.354013	−	0.935240i	$-0.615183\pi$
$487$	−167922.			−0.708026			−0.354013	+	0.935240i	$0.615183\pi$
$488$			348156.i			1.46195i
$489$	177909.			0.744012
$490$		−	839.311i		−	0.00349567i
$491$	143884.			0.596827			0.298414	−	0.954437i	$-0.403543\pi$
$491$	143884.			0.596827			0.298414	+	0.954437i	$0.403543\pi$
$492$	−69963.5			−0.289029
$493$			354151.i			1.45712i
$494$		−	426.816i		−	0.00174899i
$495$	44433.9			0.181344
$496$	−140694.			−0.571891
$497$			80367.7i			0.325364i
$498$		−	54378.7i		−	0.219265i
$499$	101117.			0.406089			0.203045	−	0.979169i	$-0.434916\pi$
$499$	101117.			0.406089			0.203045	+	0.979169i	$0.434916\pi$
$500$			156817.i			0.627266i
$501$	231972.			0.924188
$502$			70333.6i			0.279097i
$503$		−	240661.i		−	0.951195i	−0.879663	−	0.475597i	$-0.842232\pi$
$503$		−	240661.i		−	0.951195i	0.879663	−	0.475597i	$-0.157768\pi$
$504$			75159.9i			0.295887i
$505$		−	146120.i		−	0.572963i
$506$	144943.	+	31309.9i	0.566104	+	0.122287i
$507$	−148395.			−0.577302
$508$	191737.			0.742983
$509$	−59313.3			−0.228937			−0.114469	−	0.993427i	$-0.536517\pi$
$509$	−59313.3			−0.228937			−0.114469	+	0.993427i	$0.536517\pi$
$510$	−55140.6			−0.211998
$511$		−	41011.4i		−	0.157059i
$512$	−150458.			−0.573953
$513$			19206.9i			0.0729833i
$514$	−101709.			−0.384976
$515$	183288.			0.691065
$516$			71171.4i			0.267305i
$517$		−	215076.i		−	0.804658i
$518$	−267260.			−0.996034
$519$	135729.			0.503891
$520$		−	1032.32i		−	0.00381775i
$521$			90521.5i			0.333485i	0.986000	+	0.166742i	$0.0533248\pi$
$521$			90521.5i			0.333485i	−0.986000	+	0.166742i	$0.946675\pi$
$522$	−43612.4			−0.160055
$523$		−	198379.i		−	0.725258i	−0.931934	−	0.362629i	$-0.881879\pi$
$523$		−	198379.i		−	0.725258i	0.931934	−	0.362629i	$-0.118121\pi$
$524$	−112180.			−0.408557
$525$			124215.i			0.450666i
$526$		−	185261.i		−	0.669597i
$527$		−	811739.i		−	2.92277i
$528$			55351.6i			0.198547i
$529$	−254889.	−	115510.i	−0.910835	−	0.412770i
$530$	−29831.5			−0.106200
$531$	−7350.60			−0.0260696
$532$	80537.1			0.284559
$533$	1743.39			0.00613679
$534$		−	49502.5i		−	0.173598i
$535$	−102001.			−0.356368
$536$		−	36848.2i		−	0.128259i
$537$	−95794.8			−0.332195
$538$	−210137.			−0.726001
$539$		−	4860.95i		−	0.0167318i
$540$			19832.3i			0.0680120i
$541$	−104556.			−0.357234			−0.178617	−	0.983919i	$-0.557162\pi$
$541$	−104556.			−0.357234			−0.178617	+	0.983919i	$0.557162\pi$
$542$	145415.			0.495006
$543$		−	102988.i		−	0.349292i
$544$		−	468381.i		−	1.58271i
$545$	−22704.8			−0.0764405
$546$		−	799.560i		−	0.00268204i
$547$	77964.8			0.260570			0.130285	−	0.991477i	$-0.458411\pi$
$547$	77964.8			0.260570			0.130285	+	0.991477i	$0.458411\pi$
$548$		−	245606.i		−	0.817859i
$549$			166669.i			0.552982i
$550$		−	135767.i		−	0.448817i
$551$			109466.i			0.360558i
$552$	−32734.1	+	151536.i	−0.107429	+	0.497321i
$553$	215186.			0.703661
$554$	149842.			0.488220
$555$	−165188.			−0.536282
$556$	113008.			0.365562
$557$		−	336204.i		−	1.08366i	−0.840488	−	0.541830i	$-0.817732\pi$
$557$		−	336204.i		−	1.08366i	0.840488	−	0.541830i	$-0.182268\pi$
$558$	99962.4			0.321047
$559$		−	1773.49i		−	0.00567552i
$560$	44937.7			0.143296
$561$	−319352.			−1.01472
$562$		−	86738.2i		−	0.274624i
$563$		−	168359.i		−	0.531153i	−0.964090	−	0.265576i	$-0.914438\pi$
$563$		−	168359.i		−	0.531153i	0.964090	−	0.265576i	$-0.0855622\pi$
$564$	95995.6			0.301782
$565$	−104871.			−0.328518
$566$		−	259939.i		−	0.811406i
$567$			35980.6i			0.111919i
$568$	91837.8			0.284659
$569$			165559.i			0.511361i	0.966761	+	0.255681i	$0.0822996\pi$
$569$			165559.i			0.511361i	−0.966761	+	0.255681i	$0.917700\pi$
$570$	−17043.6			−0.0524579
$571$			41362.8i			0.126864i	0.997986	+	0.0634318i	$0.0202045\pi$
$571$			41362.8i			0.126864i	−0.997986	+	0.0634318i	$0.979795\pi$
$572$		−	2552.43i		−	0.00780120i
$573$			35141.4i			0.107031i
$574$		−	112634.i		−	0.341858i
$575$	−54098.8	+	250439.i	−0.163626	+	0.757472i
$576$	24515.2			0.0738908
$577$	302679.			0.909139			0.454569	−	0.890711i	$-0.349793\pi$
$577$	302679.			0.909139			0.454569	+	0.890711i	$0.349793\pi$
$578$	227580.			0.681205
$579$	283951.			0.847005
$580$			113030.i			0.335998i
$581$	−255687.			−0.757453
$582$			79217.4i			0.233870i
$583$	−172772.			−0.508318
$584$	−46864.6			−0.137410
$585$		−	494.193i		−	0.00144406i
$586$		−	112302.i		−	0.327033i
$587$	75857.9			0.220153			0.110076	−	0.993923i	$-0.464890\pi$
$587$	75857.9			0.220153			0.110076	+	0.993923i	$0.464890\pi$
$588$	2169.60			0.00627517
$589$		−	250903.i		−	0.723227i
$590$		−	6522.67i		−	0.0187379i
$591$	181248.			0.518916
$592$		−	205777.i		−	0.587154i
$593$	−204326.			−0.581050			−0.290525	−	0.956867i	$-0.593830\pi$
$593$	−204326.			−0.581050			−0.290525	+	0.956867i	$0.593830\pi$
$594$		−	39327.0i		−	0.111460i
$595$			259269.i			0.732347i
$596$			415302.i			1.16915i
$597$		−	296137.i		−	0.830890i
$598$	348.229	−	1612.06i	0.000973784	−	0.00450794i
$599$	−485028.			−1.35180			−0.675901	−	0.736992i	$-0.736245\pi$
$599$	−485028.			−1.35180			−0.675901	+	0.736992i	$0.736245\pi$
$600$	141943.			0.394285
$601$	172356.			0.477175			0.238588	−	0.971121i	$-0.423316\pi$
$601$	172356.			0.477175			0.238588	+	0.971121i	$0.423316\pi$
$602$	−114579.			−0.316163
$603$		−	17640.0i		−	0.0485136i
$604$	−231168.			−0.633656
$605$			54714.6i			0.149483i
$606$	−129326.			−0.352160
$607$	182994.			0.496660			0.248330	−	0.968675i	$-0.420118\pi$
$607$	182994.			0.496660			0.248330	+	0.968675i	$0.420118\pi$
$608$		−	144773.i		−	0.391634i
$609$			205064.i			0.552909i
$610$	−147897.			−0.397465
$611$	−2392.08			−0.00640756
$612$		−	142538.i		−	0.380563i
$613$			556006.i			1.47965i	0.672800	+	0.739824i	$0.265091\pi$
$613$			556006.i			1.47965i	−0.672800	+	0.739824i	$0.734909\pi$
$614$	−327468.			−0.868625
$615$		−	69617.1i		−	0.184063i
$616$	−386267.			−1.01795
$617$			648584.i			1.70371i	0.523776	+	0.851856i	$0.324523\pi$
$617$			648584.i			1.70371i	−0.523776	+	0.851856i	$0.675477\pi$
$618$		−	162222.i		−	0.424749i
$619$			565911.i			1.47695i	0.674279	+	0.738477i	$0.264455\pi$
$619$			565911.i			1.47695i	−0.674279	+	0.738477i	$0.735545\pi$
$620$		−	259072.i		−	0.673964i
$621$	−15670.5	+	72543.4i	−0.0406349	+	0.188111i
$622$	28885.2			0.0746612
$623$	−232759.			−0.599695
$624$	615.621			0.00158104
$625$	146672.			0.375481
$626$		−	100102.i		−	0.255442i
$627$	−98709.5			−0.251087
$628$			272901.i			0.691969i
$629$	1.18723e6			3.00078
$630$	−31928.0			−0.0804434
$631$			126414.i			0.317494i	0.987319	+	0.158747i	$0.0507455\pi$
$631$			126414.i			0.317494i	−0.987319	+	0.158747i	$0.949255\pi$
$632$		−	245897.i		−	0.615630i
$633$	83427.7			0.208211
$634$	391123.			0.973048
$635$			190788.i			0.473154i
$636$		−	77113.8i		−	0.190642i
$637$	−54.0635			−0.000133237
$638$		−	224135.i		−	0.550642i
$639$	43964.7			0.107672
$640$		−	178915.i		−	0.436805i
$641$			321370.i			0.782148i	0.920359	+	0.391074i	$0.127896\pi$
$641$			321370.i			0.782148i	−0.920359	+	0.391074i	$0.872104\pi$
$642$			90278.1i			0.219034i
$643$			417589.i			1.01001i	0.863115	+	0.505007i	$0.168510\pi$
$643$			417589.i			1.01001i	−0.863115	+	0.505007i	$0.831490\pi$
$644$	304183.	+	65708.3i	0.733439	+	0.158434i
$645$	−70819.0			−0.170228
$646$	122495.			0.293530
$647$	558983.			1.33534			0.667668	−	0.744460i	$-0.267293\pi$
$647$	558983.			1.33534			0.667668	+	0.744460i	$0.267293\pi$
$648$	41115.8			0.0979171
$649$		−	37776.7i		−	0.0896880i
$650$	−1510.00			−0.00357397
$651$		−	470019.i		−	1.10906i
$652$	−408091.			−0.959980
$653$	481380.			1.12892			0.564458	−	0.825462i	$-0.309085\pi$
$653$	481380.			1.12892			0.564458	+	0.825462i	$0.309085\pi$
$654$			20095.2i			0.0469827i
$655$		−	111624.i		−	0.260182i
$656$	86722.5			0.201523
$657$	−22435.1			−0.0519752
$658$			154543.i			0.356942i
$659$		−	622949.i		−	1.43444i	−0.696848	−	0.717218i	$-0.745415\pi$
$659$		−	622949.i		−	1.43444i	0.696848	−	0.717218i	$-0.254585\pi$
$660$	−101923.			−0.233984
$661$			529511.i			1.21191i	0.795497	+	0.605957i	$0.207210\pi$
$661$			529511.i			1.21191i	−0.795497	+	0.605957i	$0.792790\pi$
$662$	−312549.			−0.713184
$663$			3551.84i			0.00808027i
$664$			292178.i			0.662692i
$665$			80138.3i			0.181216i
$666$			146203.i			0.329616i
$667$	−89310.5	+	413445.i	−0.200748	+	0.929321i
$668$	−532103.			−1.19246
$669$	−256433.			−0.572956
$670$	15653.1			0.0348700
$671$	−856558.			−1.90244
$672$		−	271206.i		−	0.600565i
$673$	−506899.			−1.11916			−0.559579	−	0.828777i	$-0.689037\pi$
$673$	−506899.			−1.11916			−0.559579	+	0.828777i	$0.689037\pi$
$674$		−	249114.i		−	0.548375i
$675$	67951.0			0.149138
$676$	340392.			0.744879
$677$			547712.i			1.19502i	0.801862	+	0.597510i	$0.203843\pi$
$677$			547712.i			1.19502i	−0.801862	+	0.597510i	$0.796157\pi$
$678$			92818.1i			0.201917i
$679$	372477.			0.807905
$680$	296272.			0.640727
$681$			166763.i			0.359589i
$682$			513733.i			1.10451i
$683$	−368670.			−0.790308			−0.395154	−	0.918615i	$-0.629309\pi$
$683$	−368670.			−0.790308			−0.395154	+	0.918615i	$0.629309\pi$
$684$		−	44057.3i		−	0.0941686i
$685$	244390.			0.520838
$686$		−	235902.i		−	0.501283i
$687$		−	511988.i		−	1.08479i
$688$		−	88219.8i		−	0.186376i
$689$			1921.57i			0.00404778i
$690$	−64372.5	−	13905.5i	−0.135208	−	0.0292070i
$691$	744240.			1.55868			0.779340	−	0.626601i	$-0.215555\pi$
$691$	744240.			1.55868			0.779340	+	0.626601i	$0.215555\pi$
$692$	−311337.			−0.650158
$693$	−184914.			−0.385038
$694$	316549.			0.657236
$695$			112449.i			0.232801i
$696$	234330.			0.483738
$697$			500348.i			1.02993i
$698$	323457.			0.663905
$699$	−426477.			−0.872854
$700$		−	284927.i		−	0.581483i
$701$			523105.i			1.06452i	0.846582	+	0.532258i	$0.178657\pi$
$701$			523105.i			1.06452i	−0.846582	+	0.532258i	$0.821343\pi$
$702$	−437.395			−0.000887563
$703$	366965.			0.742530
$704$			125990.i			0.254209i
$705$			95520.3i			0.192184i
$706$	−437817.			−0.878383
$707$			608086.i			1.21654i
$708$	16861.0			0.0336369
$709$		−	344738.i		−	0.685798i	−0.939372	−	0.342899i	$-0.888591\pi$
$709$		−	344738.i		−	0.685798i	0.939372	−	0.342899i	$-0.111409\pi$
$710$			39012.7i			0.0773909i
$711$		−	117716.i		−	0.232861i
$712$			265978.i			0.524670i
$713$	204706.	−	947643.i	0.402671	−	1.86409i
$714$	229471.			0.450123
$715$	2539.79			0.00496805
$716$	219736.			0.428623
$717$	293896.			0.571683
$718$			320890.i			0.622455i
$719$	−811269.			−1.56930			−0.784652	−	0.619937i	$-0.787158\pi$
$719$	−811269.			−1.56930			−0.784652	+	0.619937i	$0.787158\pi$
$720$		−	24582.9i		−	0.0474208i
$721$	−762761.			−1.46730
$722$	−225404.			−0.432401
$723$		−	137513.i		−	0.263068i
$724$			236237.i			0.450683i
$725$	387271.			0.736783
$726$	48426.1			0.0918769
$727$		−	339414.i		−	0.642186i	−0.947048	−	0.321093i	$-0.895950\pi$
$727$		−	339414.i		−	0.642186i	0.947048	−	0.321093i	$-0.104050\pi$
$728$			4296.06i			0.00810601i
$729$	19683.0			0.0370370
$730$		−	19908.1i		−	0.0373580i
$731$	508986.			0.952513
$732$		−	382310.i		−	0.713500i
$733$		−	372296.i		−	0.692917i	−0.938065	−	0.346458i	$-0.887384\pi$
$733$		−	372296.i		−	0.692917i	0.938065	−	0.346458i	$-0.112616\pi$
$734$		−	127710.i		−	0.237046i
$735$			2158.86i			0.00399622i
$736$	118117.	−	546799.i	0.218050	−	1.00942i
$737$	90656.6			0.166903
$738$	−61615.8			−0.113130
$739$	−641928.			−1.17543			−0.587716	−	0.809067i	$-0.699973\pi$
$739$	−641928.			−1.17543			−0.587716	+	0.809067i	$0.699973\pi$
$740$	378913.			0.691952
$741$			1097.85i			0.00199943i
$742$	124145.			0.225488
$743$		−	866593.i		−	1.56978i	−0.619638	−	0.784888i	$-0.712721\pi$
$743$		−	866593.i		−	1.56978i	0.619638	−	0.784888i	$-0.287279\pi$
$744$	−537101.			−0.970308
$745$	−413246.			−0.744554
$746$			72636.4i			0.130520i
$747$			139872.i			0.250662i
$748$	732538.			1.30926
$749$	424484.			0.756655
$750$			138106.i			0.245522i
$751$		−	516803.i		−	0.916316i	−0.888871	−	0.458158i	$-0.848509\pi$
$751$		−	516803.i		−	0.916316i	0.888871	−	0.458158i	$-0.151491\pi$
$752$	−118990.			−0.210415
$753$		−	180911.i		−	0.319062i
$754$	−2492.83			−0.00438481
$755$		−	230023.i		−	0.403532i
$756$		−	82533.2i		−	0.144406i
$757$		−	520664.i		−	0.908586i	−0.890852	−	0.454293i	$-0.849892\pi$
$757$		−	520664.i		−	0.908586i	0.890852	−	0.454293i	$-0.150108\pi$
$758$		−	186976.i		−	0.325422i
$759$	−372820.	−	80534.8i	−0.647165	−	0.139798i
$760$	91575.6			0.158545
$761$	−700906.			−1.21029			−0.605146	−	0.796114i	$-0.706885\pi$
$761$	−700906.			−1.21029			−0.605146	+	0.796114i	$0.706885\pi$
$762$	168860.			0.290815
$763$	94487.1			0.162302
$764$		−	80608.2i		−	0.138100i
$765$	141832.			0.242354
$766$			190283.i			0.324297i
$767$	−420.152			−0.000714194
$768$	−233839.			−0.396456
$769$		−	1.03699e6i		−	1.75357i	−0.480886	−	0.876783i	$-0.659685\pi$
$769$		−	1.03699e6i		−	1.75357i	0.480886	−	0.876783i	$-0.340315\pi$
$770$		−	164086.i		−	0.276752i
$771$	261614.			0.440101
$772$	−651333.			−1.09287
$773$			90854.6i			0.152050i	0.997106	+	0.0760252i	$0.0242230\pi$
$773$			90854.6i			0.152050i	−0.997106	+	0.0760252i	$0.975777\pi$
$774$			62679.6i			0.104627i
$775$	−887652.			−1.47788
$776$		−	425637.i		−	0.706832i
$777$	687441.			1.13866
$778$		−	516881.i		−	0.853948i
$779$			154654.i			0.254851i
$780$			1133.59i			0.00186323i
$781$			225946.i			0.370427i
$782$	462654.	+	99940.5i	0.756559	+	0.163429i
$783$	112179.			0.182973
$784$	−2689.31			−0.00437530
$785$	−271550.			−0.440667
$786$	−98795.3			−0.159916
$787$			672862.i			1.08637i	0.839614	+	0.543183i	$0.182781\pi$
$787$			672862.i			1.08637i	−0.839614	+	0.543183i	$0.817219\pi$
$788$	−415750.			−0.669545
$789$			476525.i			0.765477i
$790$	104457.			0.167373
$791$	436427.			0.697524
$792$			211305.i			0.336868i
$793$			9526.64i			0.0151493i
$794$	−422574.			−0.670288
$795$	76731.9			0.121406
$796$			679285.i			1.07208i
$797$			505332.i			0.795537i	0.917486	+	0.397769i	$0.130215\pi$
$797$			505332.i			0.795537i	−0.917486	+	0.397769i	$0.869785\pi$
$798$	70927.8			0.111381
$799$		−	686517.i		−	1.07537i
$800$	−512183.			−0.800286
$801$			127329.i			0.198456i
$802$			263356.i			0.409444i
$803$		−	115300.i		−	0.178812i
$804$			40463.0i			0.0625959i
$805$	−65382.9	+	302677.i	−0.100896	+	0.467076i
$806$	5713.74			0.00879529
$807$	540509.			0.829958
$808$	694871.			1.06434
$809$	−9994.35			−0.0152707			−0.00763533	−	0.999971i	$-0.502430\pi$
$809$	−9994.35			−0.0152707			−0.00763533	+	0.999971i	$0.502430\pi$
$810$			17466.0i			0.0266210i
$811$	682250.			1.03729			0.518647	−	0.854988i	$-0.326436\pi$
$811$	682250.			1.03729			0.518647	+	0.854988i	$0.326436\pi$
$812$		−	470380.i		−	0.713405i
$813$	−374033.			−0.565886
$814$	−751375.			−1.13399
$815$		−	406071.i		−	0.611345i
$816$			176681.i			0.265344i
$817$	157324.			0.235695
$818$	−83448.1			−0.124712
$819$			2056.61i			0.00306609i
$820$			159689.i			0.237491i
$821$	−514646.			−0.763523			−0.381762	−	0.924261i	$-0.624682\pi$
$821$	−514646.			−0.763523			−0.381762	+	0.924261i	$0.624682\pi$
$822$		−	216302.i		−	0.320123i
$823$	992478.			1.46528			0.732641	−	0.680615i	$-0.238287\pi$
$823$	992478.			1.46528			0.732641	+	0.680615i	$0.238287\pi$
$824$			871623.i			1.28373i
$825$			349218.i			0.513084i
$826$			27144.5i			0.0397852i
$827$		−	68379.1i		−	0.0999798i	−0.998750	−	0.0499899i	$-0.984081\pi$
$827$		−	68379.1i		−	0.0999798i	0.998750	−	0.0499899i	$-0.0159189\pi$
$828$	35945.3	−	166402.i	0.0524303	−	0.242715i
$829$	548249.			0.797754			0.398877	−	0.917004i	$-0.369400\pi$
$829$	548249.			0.797754			0.398877	+	0.917004i	$0.369400\pi$
$830$	−124117.			−0.180168
$831$	−385422.			−0.558128
$832$	1401.26			0.00202429
$833$		−	15516.0i		−	0.0223609i
$834$	99524.9			0.143087
$835$		−	529468.i		−	0.759393i
$836$	226422.			0.323971
$837$	−257121.			−0.367018
$838$			164706.i			0.234542i
$839$		−	404909.i		−	0.575220i	−0.957748	−	0.287610i	$-0.907139\pi$
$839$		−	404909.i		−	0.575220i	0.957748	−	0.287610i	$-0.0928607\pi$
$840$	171550.			0.243126
$841$	−67942.9			−0.0960621
$842$			385183.i			0.543304i
$843$			223106.i			0.313947i
$844$	−191368.			−0.268649
$845$			338706.i			0.474362i
$846$	84541.9			0.118122
$847$		−	227698.i		−	0.317389i
$848$			95585.6i			0.132923i
$849$			668609.i			0.927592i
$850$		−	433365.i		−	0.599814i
$851$	1.38600e6	+	299398.i	1.91384	+	0.413419i
$852$	−100847.			−0.138926
$853$	−662146.			−0.910030			−0.455015	−	0.890484i	$-0.650366\pi$
$853$	−662146.			−0.910030			−0.455015	+	0.890484i	$0.650366\pi$
$854$	615480.			0.843915
$855$	43839.2			0.0599694
$856$		−	485066.i		−	0.661993i
$857$	−644207.			−0.877130			−0.438565	−	0.898700i	$-0.644513\pi$
$857$	−644207.			−0.877130			−0.438565	+	0.898700i	$0.644513\pi$
$858$		−	2247.89i		−	0.00305351i
$859$	−439207.			−0.595228			−0.297614	−	0.954686i	$-0.596191\pi$
$859$	−439207.			−0.595228			−0.297614	+	0.954686i	$0.596191\pi$
$860$	162446.			0.219641
$861$			289715.i			0.390810i
$862$			664965.i			0.894920i
$863$	−523440.			−0.702823			−0.351411	−	0.936221i	$-0.614298\pi$
$863$	−523440.			−0.702823			−0.351411	+	0.936221i	$0.614298\pi$
$864$	−148361.			−0.198744
$865$		−	309796.i		−	0.414041i
$866$		−	117542.i		−	0.156733i
$867$	−585376.			−0.778748
$868$			1.07814e6i			1.43099i
$869$	604975.			0.801120
$870$			99543.6i			0.131515i
$871$		−	1008.28i		−	0.00132906i
$872$		−	107972.i		−	0.141997i
$873$		−	203762.i		−	0.267358i
$874$	143003.	+	30890.9i	0.187207	+	0.0404397i
$875$	649369.			0.848156
$876$	51462.0			0.0670624
$877$	−328707.			−0.427376			−0.213688	−	0.976902i	$-0.568548\pi$
$877$	−328707.			−0.427376			−0.213688	+	0.976902i	$0.568548\pi$
$878$	−397777.			−0.516001
$879$			288860.i			0.373861i
$880$	126338.			0.163143
$881$			1.45433e6i			1.87375i	0.349663	+	0.936875i	$0.386296\pi$
$881$			1.45433e6i			1.87375i	−0.349663	+	0.936875i	$0.613704\pi$
$882$	1910.74			0.00245620
$883$	−342671.			−0.439497			−0.219748	−	0.975557i	$-0.570524\pi$
$883$	−342671.			−0.439497			−0.219748	+	0.975557i	$0.570524\pi$
$884$		−	8147.28i		−	0.0104258i
$885$			16777.5i			0.0214210i
$886$	13597.0			0.0173211
$887$	819987.			1.04222			0.521111	−	0.853489i	$-0.325518\pi$
$887$	819987.			1.04222			0.521111	+	0.853489i	$0.325518\pi$
$888$		−	785552.i		−	0.996206i
$889$		−	793973.i		−	1.00462i
$890$	−112988.			−0.142643
$891$			101156.i			0.127420i
$892$	588211.			0.739271
$893$		−	212198.i		−	0.266096i
$894$			365751.i			0.457625i
$895$			218648.i			0.272960i
$896$			744566.i			0.927443i
$897$	−895.708	+	4146.50i	−0.00111322	+	0.00515343i
$898$	511417.			0.634195
$899$	−1.46541e6			−1.81317
$900$	−155867.			−0.192429
$901$	−551483.			−0.679333
$902$		−	316660.i		−	0.389206i
$903$	294717.			0.361435
$904$		−	498714.i		−	0.610260i
$905$	−235068.			−0.287009
$906$	−203586.			−0.248023
$907$			645547.i			0.784718i	0.919812	+	0.392359i	$0.128341\pi$
$907$			645547.i			0.784718i	−0.919812	+	0.392359i	$0.871659\pi$
$908$		−	382525.i		−	0.463969i
$909$	332650.			0.402587
$910$	−1824.97			−0.00220380
$911$		−	594043.i		−	0.715782i	−0.933763	−	0.357891i	$-0.883496\pi$
$911$		−	594043.i		−	0.715782i	0.933763	−	0.357891i	$-0.116504\pi$
$912$			54610.8i			0.0656582i
$913$	−718838.			−0.862362
$914$			780375.i			0.934138i
$915$	380417.			0.454378
$916$			1.17441e6i			1.39968i
$917$			464531.i			0.552429i
$918$		−	125531.i		−	0.148958i
$919$		−	1.36511e6i		−	1.61636i	−0.588938	−	0.808178i	$-0.700454\pi$
$919$		−	1.36511e6i		−	1.61636i	0.588938	−	0.808178i	$-0.299546\pi$
$920$	345875.	+	74714.4i	0.408643	+	0.0882731i
$921$	842307.			0.993004
$922$	434932.			0.511634
$923$	2512.97			0.00294974
$924$	424160.			0.496805
$925$		−	1.29826e6i		−	1.51732i
$926$	118570.			0.138278
$927$			417264.i			0.485570i
$928$	−845552.			−0.981849
$929$	1.05613e6			1.22374			0.611868	−	0.790960i	$-0.290418\pi$
$929$	1.05613e6			1.22374			0.611868	+	0.790960i	$0.290418\pi$
$930$		−	228161.i		−	0.263800i
$931$		−	4795.89i		−	0.00553312i
$932$	978263.			1.12622
$933$	−74298.0			−0.0853521
$934$		−	407469.i		−	0.467090i
$935$			728910.i			0.833779i
$936$	2350.13			0.00268251
$937$		−	683295.i		−	0.778268i	−0.921181	−	0.389134i	$-0.872774\pi$
$937$		−	683295.i		−	0.778268i	0.921181	−	0.389134i	$-0.127226\pi$
$938$	−65141.3			−0.0740374
$939$			257480.i			0.292019i
$940$		−	219107.i		−	0.247970i
$941$		−	110797.i		−	0.125126i	−0.998041	−	0.0625631i	$-0.980073\pi$
$941$		−	110797.i		−	0.125126i	0.998041	−	0.0625631i	$-0.0199275\pi$
$942$			240340.i			0.270847i
$943$	−126178.	+	584118.i	−0.141893	+	0.656866i
$944$	−20899.8			−0.0234530
$945$	82124.5			0.0919622
$946$	−322127.			−0.359952
$947$	−1.07809e6			−1.20214			−0.601071	−	0.799195i	$-0.705259\pi$
$947$	−1.07809e6			−1.20214			−0.601071	+	0.799195i	$0.705259\pi$
$948$			270020.i			0.300455i
$949$	−1282.36			−0.00142390
$950$		−	133950.i		−	0.148421i
$951$	−1.00604e6			−1.11238
$952$	−1.23295e6			−1.36042
$953$			828193.i			0.911897i	0.890006	+	0.455948i	$0.150700\pi$
$953$			828193.i			0.911897i	−0.890006	+	0.455948i	$0.849300\pi$
$954$		−	67913.0i		−	0.0746201i
$955$	80209.0			0.0879461
$956$	−674145.			−0.737628
$957$			576516.i			0.629489i
$958$		−	305096.i		−	0.332434i
$959$	−1.01704e6			−1.10586
$960$		−	55955.0i		−	0.0607151i
$961$	2.43529e6			2.63696
$962$			8356.80i			0.00903004i
$963$		−	232211.i		−	0.250398i
$964$			315431.i			0.339430i
$965$		−	648108.i		−	0.695973i
$966$	267890.	+	57868.3i	0.287079	+	0.0620136i
$967$	464748.			0.497010			0.248505	−	0.968631i	$-0.420061\pi$
$967$	464748.			0.497010			0.248505	+	0.968631i	$0.420061\pi$
$968$	−260195.			−0.277682
$969$	−315078.			−0.335560
$970$	180811.			0.192168
$971$			1.21507e6i			1.28873i	0.764719	+	0.644364i	$0.222878\pi$
$971$			1.21507e6i			1.28873i	−0.764719	+	0.644364i	$0.777122\pi$
$972$	−45149.3			−0.0477880
$973$		−	467962.i		−	0.494294i
$974$	339225.			0.357577
$975$	3884.00			0.00408573
$976$			473888.i			0.497481i
$977$		−	565350.i		−	0.592282i	−0.955144	−	0.296141i	$-0.904300\pi$
$977$		−	565350.i		−	0.592282i	0.955144	−	0.296141i	$-0.0956997\pi$
$978$	−359400.			−0.375751
$979$	−654379.			−0.682754
$980$		−	4952.04i		−	0.00515622i
$981$		−	51688.6i		−	0.0537102i
$982$	−290665.			−0.301418
$983$		−	977831.i		−	1.01195i	−0.862550	−	0.505973i	$-0.831134\pi$
$983$		−	977831.i		−	1.01195i	0.862550	−	0.505973i	$-0.168866\pi$
$984$	331063.			0.341917
$985$		−	413691.i		−	0.426387i
$986$		−	715434.i		−	0.735895i
$987$		−	397513.i		−	0.408053i
$988$		−	2518.27i		−	0.00257981i
$989$	594202.	+	128357.i	0.607494	+	0.131228i
$990$	−89762.4			−0.0915850
$991$	−204101.			−0.207825			−0.103913	−	0.994586i	$-0.533136\pi$
$991$	−204101.			−0.207825			−0.103913	+	0.994586i	$0.533136\pi$
$992$	1.93806e6			1.96945
$993$	803931.			0.815306
$994$		−	162354.i		−	0.164320i
$995$	−675921.			−0.682731
$996$		−	320841.i		−	0.323423i
$997$	−171468.			−0.172502			−0.0862508	−	0.996273i	$-0.527489\pi$
$997$	−171468.			−0.172502			−0.0862508	+	0.996273i	$0.527489\pi$
$998$	−204269.			−0.205089
$999$		−	376060.i		−	0.376814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.5.d.a.22.5	✓	16
3.2	odd	2		207.5.d.c.91.12		16
4.3	odd	2		1104.5.c.c.1057.4		16
23.22	odd	2	inner	69.5.d.a.22.6	yes	16
69.68	even	2		207.5.d.c.91.11		16
92.91	even	2		1104.5.c.c.1057.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.5.d.a.22.5	✓	16	1.1	even	1	trivial
69.5.d.a.22.6	yes	16	23.22	odd	2	inner
207.5.d.c.91.11		16	69.68	even	2
207.5.d.c.91.12		16	3.2	odd	2
1104.5.c.c.1057.4		16	4.3	odd	2
1104.5.c.c.1057.5		16	92.91	even	2

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	69.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.02014 q^{2} +5.19615 q^{3} -11.9191 q^{4} -11.8600i q^{5} -10.4969 q^{6} +49.3562i q^{7} +56.4003 q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.02014 q^{2} +5.19615 q^{3} -11.9191 q^{4} -11.8600i q^{5} -10.4969 q^{6} +49.3562i q^{7} +56.4003 q^{8} +27.0000 q^{9} +23.9589i q^{10} +138.760i q^{11} -61.9332 q^{12} +1.54329 q^{13} -99.7061i q^{14} -61.6265i q^{15} +76.7686 q^{16} +442.918i q^{17} -54.5437 q^{18} +136.903i q^{19} +141.360i q^{20} +256.462i q^{21} -280.314i q^{22} +(-111.696 + 517.074i) q^{23} +293.064 q^{24} +484.340 q^{25} -3.11765 q^{26} +140.296 q^{27} -588.279i q^{28} +799.586 q^{29} +124.494i q^{30} -1832.70 q^{31} -1057.49 q^{32} +721.019i q^{33} -894.755i q^{34} +585.366 q^{35} -321.814 q^{36} -2680.48i q^{37} -276.562i q^{38} +8.01917 q^{39} -668.909i q^{40} +1129.66 q^{41} -518.088i q^{42} -1149.16i q^{43} -1653.89i q^{44} -320.221i q^{45} +(225.641 - 1044.56i) q^{46} -1549.99 q^{47} +398.902 q^{48} -35.0313 q^{49} -978.432 q^{50} +2301.47i q^{51} -18.3945 q^{52} +1245.11i q^{53} -283.417 q^{54} +1645.70 q^{55} +2783.70i q^{56} +711.368i q^{57} -1615.27 q^{58} -272.245 q^{59} +734.530i q^{60} +6172.94i q^{61} +3702.31 q^{62} +1332.62i q^{63} +907.970 q^{64} -18.3035i q^{65} -1456.56i q^{66} -653.333i q^{67} -5279.17i q^{68} +(-580.389 + 2686.79i) q^{69} -1182.52 q^{70} +1628.32 q^{71} +1522.81 q^{72} -830.928 q^{73} +5414.92i q^{74} +2516.70 q^{75} -1631.75i q^{76} -6848.67 q^{77} -16.1998 q^{78} -4359.86i q^{79} -910.478i q^{80} +729.000 q^{81} -2282.07 q^{82} +5180.44i q^{83} -3056.79i q^{84} +5253.03 q^{85} +2321.47i q^{86} +4154.77 q^{87} +7826.11i q^{88} +4715.91i q^{89} +646.889i q^{90} +76.1709i q^{91} +(1331.31 - 6163.03i) q^{92} -9523.01 q^{93} +3131.18 q^{94} +1623.67 q^{95} -5494.87 q^{96} -7546.72i q^{97} +70.7680 q^{98} +3746.52i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9	\( 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9} + 104 q^{13} + 680 q^{16} + 324 q^{18} - 732 q^{23} - 1764 q^{24} - 2984 q^{25} + 1800 q^{26} - 3528 q^{29} - 400 q^{31} + 5244 q^{32} + 912 q^{35} + 3888 q^{36} + 2016 q^{39} + 1008 q^{41} - 1168 q^{46} - 8664 q^{47} - 2016 q^{48} + 7240 q^{49} - 18852 q^{50} - 20952 q^{52} - 972 q^{54} + 6816 q^{55} - 13352 q^{58} + 20112 q^{59} + 4248 q^{62} - 896 q^{64} - 10044 q^{69} - 10680 q^{70} + 40368 q^{71} + 10044 q^{72} - 9568 q^{73} + 7560 q^{75} + 2952 q^{77} - 6912 q^{78} + 11664 q^{81} + 71800 q^{82} + 42744 q^{85} + 8352 q^{87} - 9876 q^{92} - 10008 q^{93} + 73720 q^{94} + 33312 q^{95} - 24948 q^{96} - 59052 q^{98}+O(q^{100}) \) 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9 + 104 * q^13 + 680 * q^16 + 324 * q^18 - 732 * q^23 - 1764 * q^24 - 2984 * q^25 + 1800 * q^26 - 3528 * q^29 - 400 * q^31 + 5244 * q^32 + 912 * q^35 + 3888 * q^36 + 2016 * q^39 + 1008 * q^41 - 1168 * q^46 - 8664 * q^47 - 2016 * q^48 + 7240 * q^49 - 18852 * q^50 - 20952 * q^52 - 972 * q^54 + 6816 * q^55 - 13352 * q^58 + 20112 * q^59 + 4248 * q^62 - 896 * q^64 - 10044 * q^69 - 10680 * q^70 + 40368 * q^71 + 10044 * q^72 - 9568 * q^73 + 7560 * q^75 + 2952 * q^77 - 6912 * q^78 + 11664 * q^81 + 71800 * q^82 + 42744 * q^85 + 8352 * q^87 - 9876 * q^92 - 10008 * q^93 + 73720 * q^94 + 33312 * q^95 - 24948 * q^96 - 59052 * q^98

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