LMFDB - Embedded newform 9.7.d.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,7,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	9.d (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:	$2.07048675258$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.4
Root			$-2.32209 - 4.02197i$ of defining polynomial
Character	$\chi$	$=$	9.2
Dual form			9.7.d.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.96626 + 4.02197i) q^{2} +(0.282380 + 26.9985i) q^{3} +(0.352523 + 0.610587i) q^{4} +(80.3236 - 46.3749i) q^{5} +(-106.620 + 189.214i) q^{6} +(60.0074 - 103.936i) q^{7} -509.141i q^{8} +(-728.841 + 15.2477i) q^{9} +O(q^{10})$	\(q+(6.96626 + 4.02197i) q^{2} +(0.282380 + 26.9985i) q^{3} +(0.352523 + 0.610587i) q^{4} +(80.3236 - 46.3749i) q^{5} +(-106.620 + 189.214i) q^{6} +(60.0074 - 103.936i) q^{7} -509.141i q^{8} +(-728.841 + 15.2477i) q^{9} +746.074 q^{10} +(-1299.95 - 750.527i) q^{11} +(-16.3854 + 9.69001i) q^{12} +(2142.08 + 3710.18i) q^{13} +(836.055 - 482.697i) q^{14} +(1274.73 + 2155.52i) q^{15} +(2070.31 - 3585.89i) q^{16} +940.477i q^{17} +(-5138.62 - 2825.16i) q^{18} -8397.07 q^{19} +(56.6318 + 32.6964i) q^{20} +(2823.06 + 1590.76i) q^{21} +(-6037.20 - 10456.7i) q^{22} +(7822.55 - 4516.35i) q^{23} +(13746.1 - 143.771i) q^{24} +(-3511.24 + 6081.65i) q^{25} +34461.5i q^{26} +(-617.476 - 19673.3i) q^{27} +84.6160 q^{28} +(-11618.5 - 6707.92i) q^{29} +(210.677 + 20142.9i) q^{30} +(6751.04 + 11693.1i) q^{31} +(625.213 - 360.967i) q^{32} +(19896.0 - 35308.7i) q^{33} +(-3782.57 + 6551.61i) q^{34} -11131.3i q^{35} +(-266.243 - 439.646i) q^{36} +39037.3 q^{37} +(-58496.2 - 33772.8i) q^{38} +(-99564.6 + 58880.5i) q^{39} +(-23611.4 - 40896.1i) q^{40} +(95285.0 - 55012.8i) q^{41} +(13268.2 + 22435.9i) q^{42} +(-5770.09 + 9994.09i) q^{43} -1058.31i q^{44} +(-57836.0 + 35024.6i) q^{45} +72658.5 q^{46} +(22839.5 + 13186.4i) q^{47} +(97398.3 + 54882.8i) q^{48} +(51622.7 + 89413.2i) q^{49} +(-48920.5 + 28244.2i) q^{50} +(-25391.5 + 265.572i) q^{51} +(-1510.26 + 2615.85i) q^{52} +12963.7i q^{53} +(74824.0 - 139533. i) q^{54} -139222. q^{55} +(-52918.1 - 30552.3i) q^{56} +(-2371.17 - 226709. i) q^{57} +(-53958.1 - 93458.2i) q^{58} +(-160987. + 92945.8i) q^{59} +(-866.763 + 1538.21i) q^{60} +(48707.2 - 84363.3i) q^{61} +108610. i q^{62} +(-42151.1 + 76667.7i) q^{63} -259193. q^{64} +(344118. + 198677. i) q^{65} +(280611. - 165948. i) q^{66} +(48333.5 + 83716.1i) q^{67} +(-574.243 + 331.540i) q^{68} +(124144. + 209922. i) q^{69} +(44770.0 - 77543.9i) q^{70} -264450. i q^{71} +(7763.23 + 371083. i) q^{72} -154006. q^{73} +(271944. + 157007. i) q^{74} +(-165187. - 93081.1i) q^{75} +(-2960.16 - 5127.15i) q^{76} +(-156013. + 90074.4i) q^{77} +(-930409. + 9731.24i) q^{78} +(43195.7 - 74817.2i) q^{79} -384042. i q^{80} +(530976. - 22226.3i) q^{81} +885040. q^{82} +(-543967. - 314059. i) q^{83} +(23.8939 + 2284.51i) q^{84} +(43614.5 + 75542.5i) q^{85} +(-80391.9 + 46414.3i) q^{86} +(177823. - 315575. i) q^{87} +(-382124. + 661858. i) q^{88} -874390. i q^{89} +(-543769. + 11375.9i) q^{90} +514162. q^{91} +(5515.25 + 3184.23i) q^{92} +(-313791. + 185570. i) q^{93} +(106070. + 183719. i) q^{94} +(-674483. + 389413. i) q^{95} +(9922.12 + 16777.9i) q^{96} +(95150.6 - 164806. i) q^{97} +830500. i q^{98} +(958900. + 527193. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9	\( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} - 132 q^{10} + 483 q^{11} - 1830 q^{12} - 841 q^{13} + 12174 q^{14} + 7965 q^{15} - 1985 q^{16} - 7884 q^{18} + 6176 q^{19} - 63186 q^{20} - 25845 q^{21} + 3471 q^{22} + 53565 q^{23} + 111519 q^{24} + 8452 q^{25} - 101034 q^{27} - 22660 q^{28} - 80679 q^{29} - 37782 q^{30} - 24601 q^{31} + 218295 q^{32} + 229995 q^{33} + 7425 q^{34} - 274977 q^{36} + 12764 q^{37} - 371877 q^{38} - 112749 q^{39} + 54150 q^{40} + 232251 q^{41} + 270540 q^{42} - 93271 q^{43} + 63801 q^{45} + 112512 q^{46} - 142887 q^{47} - 143283 q^{48} + 86238 q^{49} + 318459 q^{50} + 57078 q^{51} + 186920 q^{52} + 13851 q^{54} - 419982 q^{55} + 342546 q^{56} - 1086 q^{57} - 380658 q^{58} - 995061 q^{59} - 1011402 q^{60} - 59305 q^{61} + 526455 q^{63} + 403066 q^{64} + 1642029 q^{65} + 1610586 q^{66} + 158513 q^{67} - 1693791 q^{68} - 851715 q^{69} - 304788 q^{70} + 1469907 q^{72} + 933896 q^{73} + 595182 q^{74} - 757524 q^{75} + 666641 q^{76} - 2198883 q^{77} - 3481884 q^{78} + 468707 q^{79} + 1774548 q^{81} - 2038470 q^{82} + 3008337 q^{83} + 1543746 q^{84} - 1189944 q^{85} + 1905549 q^{86} - 615591 q^{87} - 349773 q^{88} + 84294 q^{90} - 211778 q^{91} - 973788 q^{92} - 2954553 q^{93} + 809124 q^{94} - 2562954 q^{95} - 1022112 q^{96} + 336029 q^{97} - 432567 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9 - 132 * q^10 + 483 * q^11 - 1830 * q^12 - 841 * q^13 + 12174 * q^14 + 7965 * q^15 - 1985 * q^16 - 7884 * q^18 + 6176 * q^19 - 63186 * q^20 - 25845 * q^21 + 3471 * q^22 + 53565 * q^23 + 111519 * q^24 + 8452 * q^25 - 101034 * q^27 - 22660 * q^28 - 80679 * q^29 - 37782 * q^30 - 24601 * q^31 + 218295 * q^32 + 229995 * q^33 + 7425 * q^34 - 274977 * q^36 + 12764 * q^37 - 371877 * q^38 - 112749 * q^39 + 54150 * q^40 + 232251 * q^41 + 270540 * q^42 - 93271 * q^43 + 63801 * q^45 + 112512 * q^46 - 142887 * q^47 - 143283 * q^48 + 86238 * q^49 + 318459 * q^50 + 57078 * q^51 + 186920 * q^52 + 13851 * q^54 - 419982 * q^55 + 342546 * q^56 - 1086 * q^57 - 380658 * q^58 - 995061 * q^59 - 1011402 * q^60 - 59305 * q^61 + 526455 * q^63 + 403066 * q^64 + 1642029 * q^65 + 1610586 * q^66 + 158513 * q^67 - 1693791 * q^68 - 851715 * q^69 - 304788 * q^70 + 1469907 * q^72 + 933896 * q^73 + 595182 * q^74 - 757524 * q^75 + 666641 * q^76 - 2198883 * q^77 - 3481884 * q^78 + 468707 * q^79 + 1774548 * q^81 - 2038470 * q^82 + 3008337 * q^83 + 1543746 * q^84 - 1189944 * q^85 + 1905549 * q^86 - 615591 * q^87 - 349773 * q^88 + 84294 * q^90 - 211778 * q^91 - 973788 * q^92 - 2954553 * q^93 + 809124 * q^94 - 2562954 * q^95 - 1022112 * q^96 + 336029 * q^97 - 432567 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	6.96626	+	4.02197i	0.870783	+	0.502747i	0.867608	−	0.497248i	$-0.165656\pi$
$2$	6.96626	+	4.02197i	0.870783	+	0.502747i	0.00317434	+	0.999995i	$0.498990\pi$
$3$	0.282380	+	26.9985i	0.0104585	+	0.999945i
$3$	0.282380	+	26.9985i	0.0104585	+	0.999945i
$4$	0.352523	+	0.610587i	0.00550817	+	0.00954043i
$5$	80.3236	−	46.3749i	0.642589	−	0.370999i	−0.143022	−	0.989719i	$-0.545682\pi$
$5$	80.3236	−	46.3749i	0.642589	−	0.370999i	0.785611	+	0.618721i	$0.212349\pi$
$6$	−106.620	+	189.214i	−0.493612	+	0.875993i
$7$	60.0074	−	103.936i	0.174949	−	0.303020i	−0.765195	−	0.643799i	$-0.777357\pi$
$7$	60.0074	−	103.936i	0.174949	−	0.303020i	0.940144	+	0.340779i	$0.110691\pi$
$8$		−	509.141i		−	0.994416i
$9$	−728.841	+	15.2477i	−0.999781	+	0.0209159i
$10$	746.074			0.746074
$11$	−1299.95	−	750.527i	−0.976672	−	0.563882i	−0.0754083	−	0.997153i	$-0.524026\pi$
$11$	−1299.95	−	750.527i	−0.976672	−	0.563882i	−0.901264	+	0.433271i	$0.857359\pi$
$12$	−16.3854	+	9.69001i	−0.00948230	+	0.00560765i
$13$	2142.08	+	3710.18i	0.975000	+	1.68875i	0.679935	+	0.733273i	$0.262008\pi$
$13$	2142.08	+	3710.18i	0.975000	+	1.68875i	0.295065	+	0.955477i	$0.404659\pi$
$14$	836.055	−	482.697i	0.304685	−	0.175910i
$15$	1274.73	+	2155.52i	0.377699	+	0.638674i
$16$	2070.31	−	3585.89i	0.505447	−	0.875461i
$17$			940.477i			0.191426i	0.995409	+	0.0957131i	$0.0305131\pi$
$17$			940.477i			0.191426i	−0.995409	+	0.0957131i	$0.969487\pi$
$18$	−5138.62	−	2825.16i	−0.881107	−	0.484423i
$19$	−8397.07			−1.22424			−0.612121	−	0.790764i	$-0.709683\pi$
$19$	−8397.07			−1.22424			−0.612121	+	0.790764i	$0.709683\pi$
$20$	56.6318	+	32.6964i	0.00707898	+	0.00408705i
$21$	2823.06	+	1590.76i	0.304833	+	0.171770i
$22$	−6037.20	−	10456.7i	−0.566979	−	0.982037i
$23$	7822.55	−	4516.35i	0.642932	−	0.371197i	−0.142811	−	0.989750i	$-0.545614\pi$
$23$	7822.55	−	4516.35i	0.642932	−	0.371197i	0.785743	+	0.618553i	$0.212281\pi$
$24$	13746.1	−	143.771i	0.994362	−	0.0104001i
$25$	−3511.24	+	6081.65i	−0.224720	+	0.389226i
$26$			34461.5i			1.96071i
$27$	−617.476	−	19673.3i	−0.0313710	−	0.999508i
$28$	84.6160			0.00385459
$29$	−11618.5	−	6707.92i	−0.476381	−	0.275039i	0.242526	−	0.970145i	$-0.422024\pi$
$29$	−11618.5	−	6707.92i	−0.476381	−	0.275039i	−0.718907	+	0.695106i	$0.755357\pi$
$30$	210.677	+	20142.9i	0.00780284	+	0.746033i
$31$	6751.04	+	11693.1i	0.226613	+	0.392506i	0.956802	−	0.290740i	$-0.0939013\pi$
$31$	6751.04	+	11693.1i	0.226613	+	0.392506i	−0.730189	+	0.683245i	$0.760568\pi$
$32$	625.213	−	360.967i	0.0190800	−	0.0110158i
$33$	19896.0	−	35308.7i	0.553637	−	0.982516i
$34$	−3782.57	+	6551.61i	−0.0962389	+	0.166691i
$35$		−	11131.3i		−	0.259623i
$36$	−266.243	−	439.646i	−0.00570651	−	0.00942313i
$37$	39037.3			0.770681			0.385341	−	0.922774i	$-0.374084\pi$
$37$	39037.3			0.770681			0.385341	+	0.922774i	$0.374084\pi$
$38$	−58496.2	−	33772.8i	−1.06605	−	0.615483i
$39$	−99564.6	+	58880.5i	−1.67846	+	0.992609i
$40$	−23611.4	−	40896.1i	−0.368927	−	0.639001i
$41$	95285.0	−	55012.8i	1.38253	−	0.798201i	0.390067	−	0.920786i	$-0.372452\pi$
$41$	95285.0	−	55012.8i	1.38253	−	0.798201i	0.992458	+	0.122585i	$0.0391184\pi$
$42$	13268.2	+	22435.9i	0.179087	+	0.302828i
$43$	−5770.09	+	9994.09i	−0.0725734	+	0.125701i	−0.900028	−	0.435831i	$-0.856454\pi$
$43$	−5770.09	+	9994.09i	−0.0725734	+	0.125701i	0.827455	+	0.561532i	$0.189788\pi$
$44$		−	1058.31i		−	0.0124238i
$45$	−57836.0	+	35024.6i	−0.634689	+	0.384358i
$46$	72658.5			0.746471
$47$	22839.5	+	13186.4i	0.219985	+	0.127008i	0.605943	−	0.795508i	$-0.292796\pi$
$47$	22839.5	+	13186.4i	0.219985	+	0.127008i	−0.385959	+	0.922516i	$0.626129\pi$
$48$	97398.3	+	54882.8i	0.880699	+	0.496264i
$49$	51622.7	+	89413.2i	0.438786	+	0.759999i
$50$	−48920.5	+	28244.2i	−0.391364	+	0.225954i
$51$	−25391.5	+	265.572i	−0.191416	+	0.00200204i
$52$	−1510.26	+	2615.85i	−0.0107409	+	0.0186038i
$53$			12963.7i			0.0870766i	0.999052	+	0.0435383i	$0.0138631\pi$
$53$			12963.7i			0.0870766i	−0.999052	+	0.0435383i	$0.986137\pi$
$54$	74824.0	−	139533.i	0.475182	−	0.886126i
$55$	−139222.			−0.836798
$56$	−52918.1	−	30552.3i	−0.301328	−	0.173972i
$57$	−2371.17	−	226709.i	−0.0128038	−	1.22417i
$58$	−53958.1	−	93458.2i	−0.276550	−	0.478998i
$59$	−160987.	+	92945.8i	−0.783853	+	0.452557i	−0.837794	−	0.545987i	$-0.816155\pi$
$59$	−160987.	+	92945.8i	−0.783853	+	0.452557i	0.0539413	+	0.998544i	$0.482822\pi$
$60$	−866.763	+	1538.21i	−0.00401279	+	0.00712133i
$61$	48707.2	−	84363.3i	0.214587	−	0.371676i	−0.738558	−	0.674190i	$-0.764493\pi$
$61$	48707.2	−	84363.3i	0.214587	−	0.371676i	0.953145	+	0.302515i	$0.0978261\pi$
$62$			108610.i			0.455716i
$63$	−42151.1	+	76667.7i	−0.168573	+	0.306613i
$64$	−259193.			−0.988742
$65$	344118.	+	198677.i	1.25305	+	0.723448i
$66$	280611.	−	165948.i	0.976054	−	0.577219i
$67$	48333.5	+	83716.1i	0.160703	+	0.278346i	0.935121	−	0.354329i	$-0.115291\pi$
$67$	48333.5	+	83716.1i	0.160703	+	0.278346i	−0.774418	+	0.632674i	$0.781957\pi$
$68$	−574.243	+	331.540i	−0.00182629	+	0.00105441i
$69$	124144.	+	209922.i	0.377900	+	0.639014i
$70$	44770.0	−	77543.9i	0.130525	−	0.226075i
$71$		−	264450.i		−	0.738871i	−0.929256	−	0.369435i	$-0.879551\pi$
$71$		−	264450.i		−	0.738871i	0.929256	−	0.369435i	$-0.120449\pi$
$72$	7763.23	+	371083.i	0.0207991	+	0.994199i
$73$	−154006.			−0.395885			−0.197942	−	0.980214i	$-0.563426\pi$
$73$	−154006.			−0.395885			−0.197942	+	0.980214i	$0.563426\pi$
$74$	271944.	+	157007.i	0.671096	+	0.387457i
$75$	−165187.	−	93081.1i	−0.391555	−	0.220637i
$76$	−2960.16	−	5127.15i	−0.00674333	−	0.0116798i
$77$	−156013.	+	90074.4i	−0.341735	+	0.197301i
$78$	−930409.	+	9731.24i	−1.96060	+	0.0205062i
$79$	43195.7	−	74817.2i	0.0876112	−	0.151747i	−0.818890	−	0.573951i	$-0.805410\pi$
$79$	43195.7	−	74817.2i	0.0876112	−	0.151747i	0.906501	+	0.422204i	$0.138743\pi$
$80$		−	384042.i		−	0.750082i
$81$	530976.	−	22226.3i	0.999125	−	0.0418227i
$82$	885040.			1.60517
$83$	−543967.	−	314059.i	−0.951345	−	0.549259i	−0.0578467	−	0.998325i	$-0.518423\pi$
$83$	−543967.	−	314059.i	−0.951345	−	0.549259i	−0.893499	+	0.449066i	$0.851757\pi$
$84$	23.8939	+	2284.51i	4.03133e−5	+	0.00385438i
$85$	43614.5	+	75542.5i	0.0710189	+	0.123008i
$86$	−80391.9	+	46414.3i	−0.126391	+	0.0729720i
$87$	177823.	−	315575.i	0.270041	−	0.479232i
$88$	−382124.	+	661858.i	−0.560733	+	0.971219i
$89$		−	874390.i		−	1.24032i	−0.784474	−	0.620162i	$-0.787067\pi$
$89$		−	874390.i		−	1.24032i	0.784474	−	0.620162i	$-0.212933\pi$
$90$	−543769.	+	11375.9i	−0.745911	+	0.0156048i
$91$	514162.			0.682300
$92$	5515.25	+	3184.23i	0.00708275	+	0.00408923i
$93$	−313791.	+	185570.i	−0.390114	+	0.230706i
$94$	106070.	+	183719.i	0.127706	+	0.221193i
$95$	−674483.	+	389413.i	−0.786684	+	0.454192i
$96$	9922.12	+	16777.9i	0.0112148	+	0.0189637i
$97$	95150.6	−	164806.i	0.104255	−	0.180575i	−0.809179	−	0.587563i	$-0.800088\pi$
$97$	95150.6	−	164806.i	0.104255	−	0.180575i	0.913434	+	0.406988i	$0.133421\pi$
$98$			830500.i			0.882392i
$99$	958900.	+	527193.i	0.988253	+	0.543331i
$100$	−4951.17			−0.00495117
$101$	983657.	+	567915.i	0.954728	+	0.551213i	0.894547	−	0.446975i	$-0.147499\pi$
$101$	983657.	+	567915.i	0.954728	+	0.551213i	0.0601817	+	0.998187i	$0.480832\pi$
$102$	−177952.	−	100274.i	−0.167688	−	0.0944903i
$103$	−555871.	−	962798.i	−0.508701	−	0.881096i	−0.999949	−	0.0100765i	$-0.996792\pi$
$103$	−555871.	−	962798.i	−0.508701	−	0.881096i	0.491248	−	0.871020i	$-0.336541\pi$
$104$	1.88901e6	−	1.09062e6i	1.67932	−	0.969556i
$105$	300530.	−	3143.27i	0.259609	−	0.00271528i
$106$	−52139.6	+	90308.5i	−0.0437775	+	0.0758248i
$107$			1.27312e6i			1.03924i	0.854396	+	0.519622i	$0.173927\pi$
$107$			1.27312e6i			1.03924i	−0.854396	+	0.519622i	$0.826073\pi$
$108$	11794.6	−	7312.31i	0.00936293	−	0.00580475i
$109$	−1.87984e6			−1.45158			−0.725792	−	0.687915i	$-0.758526\pi$
$109$	−1.87984e6			−1.45158			−0.725792	+	0.687915i	$0.758526\pi$
$110$	−969859.	−	559948.i	−0.728669	−	0.420697i
$111$	11023.4	+	1.05395e6i	0.00806019	+	0.770639i
$112$	−248468.	−	430360.i	−0.176855	−	0.306322i
$113$	−1.21138e6	+	699388.i	−0.839544	+	0.484711i	−0.857109	−	0.515135i	$-0.827742\pi$
$113$	−1.21138e6	+	699388.i	−0.839544	+	0.484711i	0.0175650	+	0.999846i	$0.494409\pi$
$114$	895297.	−	1.58885e6i	0.604300	−	1.07243i
$115$	418890.	−	725539.i	0.275427	−	0.477054i
$116$		−	9458.78i		−	0.00605984i
$117$	−1.61780e6	−	2.67147e6i	−1.01011	−	1.66799i
$118$	−1.49530e6			−0.910087
$119$	97749.4	+	56435.6i	0.0580060	+	0.0334898i
$120$	1.09747e6	−	649020.i	0.635108	−	0.375590i
$121$	240800.	+	417079.i	0.135926	+	0.235430i
$122$	678614.	−	391798.i	0.373717	−	0.215766i
$123$	1.51217e6	+	2.55702e6i	0.812617	+	1.37410i
$124$	−4759.79	+	8244.19i	−0.00249645	+	0.00432397i
$125$			2.10055e6i			1.07548i
$126$	−601991.	+	364557.i	−0.300939	+	0.182244i
$127$	2.84521e6			1.38900			0.694501	−	0.719491i	$-0.255625\pi$
$127$	2.84521e6			1.38900			0.694501	+	0.719491i	$0.255625\pi$
$128$	−1.84562e6	−	1.06557e6i	−0.880060	−	0.508103i
$129$	−271455.	−	152962.i	−0.126453	−	0.0712547i
$130$	1.59815e6	+	2.76807e6i	0.727422	+	1.25993i
$131$	1.24280e6	−	717533.i	0.552827	−	0.319175i	−0.197435	−	0.980316i	$-0.563261\pi$
$131$	1.24280e6	−	717533.i	0.552827	−	0.319175i	0.750261	+	0.661141i	$0.229928\pi$
$132$	28572.8	−	298.846i	0.0124231	−	0.000129935i
$133$	−503887.	+	872757.i	−0.214180	+	0.370970i
$134$			777584.i			0.323172i
$135$	−961945.	−	1.55160e6i	−0.390975	−	0.630634i
$136$	478836.			0.190357
$137$	−485772.	−	280461.i	−0.188917	−	0.109071i	0.402558	−	0.915394i	$-0.368121\pi$
$137$	−485772.	−	280461.i	−0.188917	−	0.109071i	−0.591475	+	0.806323i	$0.701454\pi$
$138$	20517.3	+	1.96167e6i	0.00780699	+	0.746431i
$139$	−409282.	−	708898.i	−0.152398	−	0.263961i	0.779711	−	0.626140i	$-0.215366\pi$
$139$	−409282.	−	708898.i	−0.152398	−	0.263961i	−0.932108	+	0.362179i	$0.882033\pi$
$140$	6796.66	−	3924.05i	0.00247692	−	0.00143005i
$141$	−349563.	+	620355.i	−0.124700	+	0.221301i
$142$	1.06361e6	−	1.84223e6i	0.371465	−	0.643396i
$143$		−	6.43074e6i		−	2.19914i
$144$	−1.45425e6	+	2.64511e6i	−0.487026	+	0.885841i
$145$	−1.24432e6			−0.408156
$146$	−1.07284e6	−	619407.i	−0.344729	−	0.199030i
$147$	−2.39945e6	+	1.41899e6i	−0.755369	+	0.446710i
$148$	13761.5	+	23835.7i	0.00424504	+	0.00735263i
$149$	2.45815e6	−	1.41921e6i	0.743104	−	0.429032i	−0.0800926	−	0.996787i	$-0.525522\pi$
$149$	2.45815e6	−	1.41921e6i	0.743104	−	0.429032i	0.823197	+	0.567756i	$0.192188\pi$
$150$	−776367.	−	1.31280e6i	−0.230035	−	0.388979i
$151$	881580.	−	1.52694e6i	0.256054	−	0.443498i	−0.709127	−	0.705080i	$-0.750911\pi$
$151$	881580.	−	1.52694e6i	0.256054	−	0.443498i	0.965181	+	0.261582i	$0.0842443\pi$
$152$			4.27529e6i			1.21741i
$153$	−14340.1	−	685458.i	−0.00400386	−	0.191384i
$154$	−1.44911e6			−0.396769
$155$	1.08454e6	+	626157.i	0.291238	+	0.168147i
$156$	−71050.5	−	40036.1i	−0.0187152	−	0.0105458i
$157$	215379.	+	373048.i	0.0556551	+	0.0963974i	0.892511	−	0.451026i	$-0.148942\pi$
$157$	215379.	+	373048.i	0.0556551	+	0.0963974i	−0.836856	+	0.547424i	$0.815609\pi$
$158$	601825.	−	347464.i	0.152581	−	0.0880924i
$159$	−350001.	+	3660.69i	−0.0870718	+	0.000910693i
$160$	33479.6	−	57988.3i	0.00817373	−	0.0141573i
$161$		−	1.08406e6i		−	0.259762i
$162$	3.78831e6	+	1.98074e6i	0.891047	+	0.465888i
$163$	4.87338e6			1.12530			0.562649	−	0.826696i	$-0.309782\pi$
$163$	4.87338e6			1.12530			0.562649	+	0.826696i	$0.309782\pi$
$164$	67180.3	+	38786.6i	0.0152304	+	0.00879325i
$165$	−39313.6	−	3.75880e6i	−0.00875168	−	0.836753i
$166$	−2.52628e6	−	4.37564e6i	−0.552277	−	0.956571i
$167$	−6.72564e6	+	3.88305e6i	−1.44406	+	0.833726i	−0.998117	−	0.0613369i	$-0.980464\pi$
$167$	−6.72564e6	+	3.88305e6i	−1.44406	+	0.833726i	−0.445939	+	0.895063i	$0.647130\pi$
$168$	809923.	−	1.43734e6i	0.170811	−	0.303131i
$169$	−6.76357e6	+	1.17148e7i	−1.40125	+	2.42704i
$170$			701665.i			0.142818i
$171$	6.12013e6	−	128036.i	1.22397	−	0.0256061i
$172$	−8136.35			−0.00159898
$173$	6.09924e6	+	3.52140e6i	1.17798	+	0.680106i	0.955546	−	0.294842i	$-0.0952671\pi$
$173$	6.09924e6	+	3.52140e6i	1.17798	+	0.680106i	0.222432	+	0.974948i	$0.428600\pi$
$174$	2.50800e6	−	1.48318e6i	0.476079	−	0.281544i
$175$	421401.	+	729889.i	0.0786289	+	0.136189i
$176$	−5.38261e6	+	3.10765e6i	−0.987313	+	0.570025i
$177$	−2.55486e6	−	4.32016e6i	−0.460731	−	0.779077i
$178$	3.51677e6	−	6.09123e6i	0.623568	−	1.08005i
$179$		−	352194.i		−	0.0614077i	−0.999529	−	0.0307039i	$-0.990225\pi$
$179$		−	352194.i		−	0.0614077i	0.999529	−	0.0307039i	$-0.00977488\pi$
$180$	−41774.1	−	22966.9i	−0.00716291	−	0.00393809i
$181$	−503263.			−0.0848710			−0.0424355	−	0.999099i	$-0.513512\pi$
$181$	−503263.			−0.0848710			−0.0424355	+	0.999099i	$0.513512\pi$
$182$	3.58179e6	+	2.06794e6i	0.594135	+	0.343024i
$183$	2.29144e6	+	1.29120e6i	0.373900	+	0.210688i
$184$	−2.29946e6	−	3.98278e6i	−0.369124	−	0.639342i
$185$	3.13562e6	−	1.81035e6i	0.495231	−	0.285922i
$186$	−2.93231e6	+	30669.3i	−0.455691	+	0.00476612i
$187$	705853.	−	1.22257e6i	0.107942	−	0.186961i
$188$			18594.0i			0.00279833i
$189$	−2.08182e6	−	1.11637e6i	−0.308359	−	0.165357i
$190$	−6.26483e6			−0.913374
$191$	−5.51607e6	−	3.18470e6i	−0.791643	−	0.457055i	0.0488977	−	0.998804i	$-0.484429\pi$
$191$	−5.51607e6	−	3.18470e6i	−0.791643	−	0.457055i	−0.840541	+	0.541749i	$0.817763\pi$
$192$	−73191.0	−	6.99782e6i	−0.0103408	−	0.988688i
$193$	−1.35056e6	−	2.33925e6i	−0.187864	−	0.325390i	0.756674	−	0.653792i	$-0.226823\pi$
$193$	−1.35056e6	−	2.33925e6i	−0.187864	−	0.325390i	−0.944538	+	0.328403i	$0.893490\pi$
$194$	1.32569e6	−	765386.i	0.181567	−	0.104827i
$195$	−5.26681e6	+	9.34679e6i	−0.710303	+	1.26055i
$196$	−36396.4	+	63040.3i	−0.00483381	+	0.00837241i
$197$		−	5.74167e6i		−	0.750999i	−0.926823	−	0.375499i	$-0.877471\pi$
$197$		−	5.74167e6i		−	0.750999i	0.926823	−	0.375499i	$-0.122529\pi$
$198$	4.55959e6	+	7.52924e6i	0.587396	+	0.969963i
$199$	−7.52739e6			−0.955180			−0.477590	−	0.878583i	$-0.658490\pi$
$199$	−7.52739e6			−0.955180			−0.477590	+	0.878583i	$0.658490\pi$
$200$	3.09642e6	+	1.78772e6i	0.387052	+	0.223465i
$201$	−2.24656e6	+	1.32857e6i	−0.276650	+	0.163605i
$202$	4.56828e6	+	7.91249e6i	0.554240	+	0.959973i
$203$	−1.39439e6	+	805050.i	−0.166685	+	0.0962354i
$204$	−9113.23	−	15410.1i	−0.00107345	−	0.00181516i
$205$	5.10243e6	−	8.83766e6i	0.592264	−	1.02583i
$206$		−	8.94280e6i		−	1.02299i
$207$	−5.63253e6	+	3.41097e6i	−0.635027	+	0.384563i
$208$	1.77391e7			1.97125
$209$	1.09158e7	+	6.30223e6i	1.19568	+	0.690328i
$210$	2.10621e6	+	1.18683e6i	0.227428	+	0.128153i
$211$	6.34178e6	+	1.09843e7i	0.675094	+	1.16930i	0.976441	+	0.215782i	$0.0692302\pi$
$211$	6.34178e6	+	1.09843e7i	0.675094	+	1.16930i	−0.301348	+	0.953514i	$0.597437\pi$
$212$	−7915.47	+	4570.00i	−0.000830748	+	0.000479632i
$213$	7.13976e6	−	74675.5i	0.738831	−	0.00772750i
$214$	−5.12045e6	+	8.86888e6i	−0.522477	+	0.904956i
$215$			1.07035e6i			0.107699i
$216$	−1.00165e7	+	314382.i	−0.993927	+	0.0311958i
$217$	1.62045e6			0.158583
$218$	−1.30955e7	−	7.56068e6i	−1.26401	−	0.729779i
$219$	−43488.2	−	4.15793e6i	−0.00414037	−	0.395863i
$220$	−49079.0	−	85007.4i	−0.00460923	−	0.00798341i
$221$	−3.48934e6	+	2.01457e6i	−0.323271	+	0.186641i
$222$	−4.16216e6	+	7.38642e6i	−0.380417	+	0.675111i
$223$	6.60263e6	−	1.14361e7i	0.595392	−	1.03125i	−0.398100	−	0.917342i	$-0.630330\pi$
$223$	6.60263e6	−	1.14361e7i	0.595392	−	1.03125i	0.993491	−	0.113906i	$-0.0363364\pi$
$224$		−	86642.8i		−	0.00770883i
$225$	2.46641e6	−	4.48609e6i	0.216529	−	0.393841i
$226$	−1.12517e7			−0.974747
$227$	−1.37632e7	−	7.94620e6i	−1.17664	−	0.679332i	−0.221403	−	0.975182i	$-0.571064\pi$
$227$	−1.37632e7	−	7.94620e6i	−1.17664	−	0.679332i	−0.955234	+	0.295851i	$0.904397\pi$
$228$	137589.	−	81367.7i	0.0116086	−	0.00686511i
$229$	1.57241e6	+	2.72350e6i	0.130936	+	0.226788i	0.924038	−	0.382301i	$-0.124868\pi$
$229$	1.57241e6	+	2.72350e6i	0.130936	+	0.226788i	−0.793102	+	0.609089i	$0.791535\pi$
$230$	5.83620e6	−	3.36953e6i	0.479674	−	0.276940i
$231$	−2.47593e6	−	4.18670e6i	−0.200864	−	0.339653i
$232$	−3.41528e6	+	5.91544e6i	−0.273503	+	0.473721i
$233$			6.95409e6i			0.549759i	0.961479	+	0.274880i	$0.0886380\pi$
$233$			6.95409e6i			0.549759i	−0.961479	+	0.274880i	$0.911362\pi$
$234$	−525458.	−	2.51169e7i	−0.0410101	−	1.96028i
$235$	2.44606e6			0.188480
$236$	−113503.	−	65531.0i	−0.00863518	−	0.00498553i
$237$	2.03215e6	+	1.14509e6i	0.152655	+	0.0860193i
$238$	453965.	+	786290.i	0.0336738	+	0.0583247i
$239$	2.35289e6	−	1.35844e6i	0.172349	−	0.0995057i	−0.411344	−	0.911480i	$-0.634941\pi$
$239$	2.35289e6	−	1.35844e6i	0.172349	−	0.0995057i	0.583693	+	0.811974i	$0.301607\pi$
$240$	1.03686e7	−	108446.i	0.750041	−	0.00784476i
$241$	1.35533e6	−	2.34750e6i	0.0968266	−	0.167709i	−0.813543	−	0.581505i	$-0.802464\pi$
$241$	1.35533e6	−	2.34750e6i	0.0968266	−	0.167709i	0.910369	+	0.413796i	$0.135797\pi$
$242$			3.87397e6i			0.273344i
$243$	750014.	+	1.43293e7i	0.0522698	+	0.998633i
$244$	68681.6			0.00472793
$245$	8.29305e6	+	4.78799e6i	0.563918	+	0.325578i
$246$	249918.	+	2.38948e7i	0.0167877	+	1.60508i
$247$	−1.79872e7	−	3.11547e7i	−1.19364	−	2.06744i
$248$	5.95346e6	−	3.43723e6i	0.390314	−	0.225348i
$249$	8.32553e6	−	1.47750e7i	0.539280	−	0.957038i
$250$	−8.44835e6	+	1.46330e7i	−0.540694	+	0.936510i
$251$			2.84107e7i			1.79664i	0.439342	+	0.898320i	$0.355212\pi$
$251$			2.84107e7i			1.79664i	−0.439342	+	0.898320i	$0.644788\pi$
$252$	−61671.5	+	1290.20i	−0.00385375	+	8.06223e-5i
$253$	−1.35586e7			−0.837244
$254$	1.98205e7	+	1.14434e7i	1.20952	+	0.698316i
$255$	−2.02722e6	+	1.19886e6i	−0.122259	+	0.0723015i
$256$	−277202.	−	480127.i	−0.0165225	−	0.0286178i
$257$	9.70883e6	−	5.60539e6i	0.571962	−	0.330223i	−0.185970	−	0.982555i	$-0.559543\pi$
$257$	9.70883e6	−	5.60539e6i	0.571962	−	0.330223i	0.757933	+	0.652333i	$0.226210\pi$
$258$	−1.27582e6	−	2.15736e6i	−0.0742899	−	0.125621i
$259$	2.34253e6	−	4.05738e6i	0.134830	−	0.233532i
$260$			280153.i			0.0159395i
$261$	8.57028e6	+	4.71185e6i	0.482030	+	0.265015i
$262$	1.15436e7			0.641856
$263$	−2.41287e7	−	1.39307e7i	−1.32638	−	0.765784i	−0.341639	−	0.939831i	$-0.610982\pi$
$263$	−2.41287e7	−	1.39307e7i	−1.32638	−	0.765784i	−0.984737	+	0.174047i	$0.944315\pi$
$264$	−1.79771e7	−	1.01299e7i	−0.977030	−	0.550545i
$265$	601190.	+	1.04129e6i	0.0323053	+	0.0559545i
$266$	−7.02041e6	+	4.05324e6i	−0.373008	+	0.215356i
$267$	2.36072e7	−	246910.i	1.24026	−	0.0129720i
$268$	−34077.3	+	59023.7i	−0.00177036	+	0.00306635i
$269$			7.85279e6i			0.403429i	0.979444	+	0.201714i	$0.0646513\pi$
$269$			7.85279e6i			0.403429i	−0.979444	+	0.201714i	$0.935349\pi$
$270$	−460682.	−	1.46777e7i	−0.0234051	−	0.745707i
$271$	2.02821e6			0.101907			0.0509535	−	0.998701i	$-0.483774\pi$
$271$	2.02821e6			0.101907			0.0509535	+	0.998701i	$0.483774\pi$
$272$	3.37244e6	+	1.94708e6i	0.167586	+	0.0967559i
$273$	145189.	+	1.38816e7i	0.00713586	+	0.682263i
$274$	−2.25601e6	−	3.90753e6i	−0.109670	−	0.189955i
$275$	9.12889e6	−	5.27056e6i	0.438955	−	0.253431i
$276$	−84412.2	+	149803.i	−0.00401493	+	0.00712513i
$277$	−1.40017e7	+	2.42517e7i	−0.658782	+	1.14104i	0.322149	+	0.946689i	$0.395595\pi$
$277$	−1.40017e7	+	2.42517e7i	−0.658782	+	1.14104i	−0.980931	+	0.194355i	$0.937739\pi$
$278$		−	6.58449e6i		−	0.306470i
$279$	−5.09872e6	−	8.41949e6i	−0.234773	−	0.387680i
$280$	−5.66743e6			−0.258174
$281$	−3.01460e7	−	1.74048e7i	−1.35866	−	0.784423i	−0.369217	−	0.929343i	$-0.620374\pi$
$281$	−3.01460e7	−	1.74048e7i	−1.35866	−	0.784423i	−0.989443	+	0.144921i	$0.953707\pi$
$282$	−4.93020e6	+	2.91562e6i	−0.219845	+	0.130012i
$283$	1.54784e7	+	2.68093e7i	0.682914	+	1.18284i	0.974088	+	0.226171i	$0.0726208\pi$
$283$	1.54784e7	+	2.68093e7i	0.682914	+	1.18284i	−0.291174	+	0.956670i	$0.594046\pi$
$284$	161470.	−	93224.7i	0.00704914	−	0.00406983i
$285$	−1.07040e7	−	1.81001e7i	−0.462395	−	0.781891i
$286$	2.58643e7	−	4.47982e7i	1.10561	−	1.91497i
$287$		−	1.32047e7i		−	0.558578i
$288$	−450177.	+	272620.i	−0.0188454	+	0.0114125i
$289$	2.32531e7			0.963356
$290$	−8.66823e6	−	5.00460e6i	−0.355415	−	0.205199i
$291$	4.47638e6	+	2.52239e6i	0.181655	+	0.102361i
$292$	−54290.6	−	94034.0i	−0.00218060	−	0.00377691i
$293$	−2.14339e7	+	1.23749e7i	−0.852116	+	0.491969i	−0.861364	−	0.507988i	$-0.830389\pi$
$293$	−2.14339e7	+	1.23749e7i	−0.852116	+	0.491969i	0.00924835	+	0.999957i	$0.497056\pi$
$294$	−2.24223e7	+	234517.i	−0.882344	+	0.00922853i
$295$	−8.62070e6	+	1.49315e7i	−0.335797	+	0.581617i
$296$		−	1.98755e7i		−	0.766378i
$297$	−1.39627e7	+	2.60378e7i	−0.532965	+	0.993881i
$298$	2.28322e7			0.862776
$299$	3.35130e7	+	1.93487e7i	1.25372	+	0.723834i
$300$	−1398.11	−	133674.i	−5.17820e−5	−	0.00495090i
$301$	692497.	+	1.19944e6i	0.0253932	+	0.0439824i
$302$	1.22826e7	−	7.09138e6i	0.445934	−	0.257460i
$303$	−1.50551e7	+	2.67177e7i	−0.541197	+	0.960441i
$304$	−1.73846e7	+	3.01109e7i	−0.618790	+	1.07178i
$305$		−	9.03516e6i		−	0.318446i
$306$	2.65700e6	−	4.83275e6i	0.0927313	−	0.168667i
$307$	−1.90164e7			−0.657222			−0.328611	−	0.944465i	$-0.606581\pi$
$307$	−1.90164e7			−0.657222			−0.328611	+	0.944465i	$0.606581\pi$
$308$	−109997.	−	63506.5i	−0.00376467	−	0.00217353i
$309$	2.58371e7	−	1.52796e7i	0.875728	−	0.517888i
$310$	5.03677e6	+	8.72394e6i	0.169070	+	0.292838i
$311$	2.49630e7	−	1.44124e7i	0.829879	−	0.479131i	−0.0239322	−	0.999714i	$-0.507619\pi$
$311$	2.49630e7	−	1.44124e7i	0.829879	−	0.479131i	0.853811	+	0.520583i	$0.174285\pi$
$312$	2.99785e7	+	5.06924e7i	0.987066	+	1.66909i
$313$	2.40307e7	−	4.16225e7i	0.783672	−	1.35736i	−0.146118	−	0.989267i	$-0.546678\pi$
$313$	2.40307e7	−	4.16225e7i	0.783672	−	1.35736i	0.929789	−	0.368092i	$-0.119989\pi$
$314$			3.46500e6i			0.111922i
$315$	169728.	+	8.11298e6i	0.00543026	+	0.259566i
$316$	60909.9			0.00193031
$317$	−3.07478e6	−	1.77522e6i	−0.0965242	−	0.0557282i	0.450961	−	0.892544i	$-0.351081\pi$
$317$	−3.07478e6	−	1.77522e6i	−0.0965242	−	0.0557282i	−0.547485	+	0.836815i	$0.684415\pi$
$318$	−2.45292e6	−	1.38219e6i	−0.0762785	−	0.0429820i
$319$	1.00689e7	+	1.74399e7i	0.310179	+	0.537245i
$320$	−2.08193e7	+	1.20200e7i	−0.635355	+	0.366822i
$321$	−3.43723e7	+	359504.i	−1.03919	+	0.0108690i
$322$	4.36005e6	−	7.55183e6i	0.130594	−	0.226196i
$323$		−	7.89725e6i		−	0.234352i
$324$	200752.	+	316372.i	0.00590235	+	0.00930171i
$325$	−3.00854e7			−0.876406
$326$	3.39492e7	+	1.96006e7i	0.979890	+	0.565740i
$327$	−530831.	−	5.07530e7i	−0.0151814	−	1.45150i
$328$	−2.80093e7	−	4.85135e7i	−0.793744	−	1.37481i
$329$	2.74107e6	−	1.58256e6i	0.0769721	−	0.0444398i
$330$	1.48439e7	−	2.63429e7i	0.413054	−	0.733029i
$331$	4.51963e6	−	7.82823e6i	0.124629	−	0.215864i	−0.796959	−	0.604034i	$-0.793559\pi$
$331$	4.51963e6	−	7.82823e6i	0.124629	−	0.215864i	0.921588	+	0.388170i	$0.126893\pi$
$332$		−	442852.i		−	0.0121017i
$333$	−2.84520e7	+	595229.i	−0.770512	+	0.0161195i
$334$	−6.24701e7			−1.67661
$335$	7.76465e6	+	4.48292e6i	0.206532	+	0.119241i
$336$	1.15489e7	−	6.82980e6i	0.304455	−	0.180049i
$337$	82154.7	+	142296.i	0.00214656	+	0.00371795i	0.867097	−	0.498140i	$-0.165983\pi$
$337$	82154.7	+	142296.i	0.00214656	+	0.00371795i	−0.864950	+	0.501858i	$0.832650\pi$
$338$	−9.42335e7	+	5.44058e7i	−2.44037	+	1.40895i
$339$	−1.92245e7	−	3.25079e7i	−0.493465	−	0.834429i
$340$	−30750.2	+	53260.9i	−0.000782368	+	0.00135510i
$341$		−	2.02673e7i		−	0.511132i
$342$	4.31493e7	+	2.37230e7i	1.07869	+	0.593051i
$343$	2.65106e7			0.656958
$344$	5.08840e6	+	2.93779e6i	0.124999	+	0.0721681i
$345$	1.97068e7	+	1.11045e7i	0.479908	+	0.270423i
$346$	2.83259e7	+	4.90619e7i	0.683842	+	1.18445i
$347$	2.59533e7	−	1.49841e7i	0.621160	−	0.358627i	−0.156160	−	0.987732i	$-0.549912\pi$
$347$	2.59533e7	−	1.49841e7i	0.621160	−	0.358627i	0.777321	+	0.629105i	$0.216578\pi$
$348$	255373.	−	2670.97i	0.00605951	−	6.33770e-5i
$349$	−1.24435e7	+	2.15528e7i	−0.292729	+	0.507022i	−0.974454	−	0.224587i	$-0.927897\pi$
$349$	−1.24435e7	+	2.15528e7i	−0.292729	+	0.507022i	0.681725	+	0.731609i	$0.261230\pi$
$350$			6.77946e6i			0.158122i
$351$	7.16689e7	−	4.44327e7i	1.65733	−	1.02750i
$352$	−1.08366e6			−0.0248465
$353$	1.88005e7	+	1.08545e7i	0.427410	+	0.246765i	0.698243	−	0.715861i	$-0.253966\pi$
$353$	1.88005e7	+	1.08545e7i	0.427410	+	0.246765i	−0.270833	+	0.962626i	$0.587299\pi$
$354$	−422244.	−	4.03709e7i	−0.00951817	−	0.910037i
$355$	−1.22638e7	−	2.12416e7i	−0.274120	−	0.474790i
$356$	533891.	−	308242.i	0.0118332	−	0.00683191i
$357$	−1.49608e6	+	2.65502e6i	−0.0328813	+	0.0583531i
$358$	1.41651e6	−	2.45348e6i	0.0308725	−	0.0534728i
$359$			7.81560e7i			1.68919i	0.535404	+	0.844596i	$0.320159\pi$
$359$			7.81560e7i			1.68919i	−0.535404	+	0.844596i	$0.679841\pi$
$360$	1.78325e7	+	2.94467e7i	0.382212	+	0.631145i
$361$	2.34649e7			0.498767
$362$	−3.50586e6	−	2.02411e6i	−0.0739042	−	0.0426686i
$363$	−1.11925e7	+	6.61903e6i	−0.233996	+	0.138380i
$364$	181254.	+	313941.i	0.00375823	+	0.00650944i
$365$	−1.23703e7	+	7.14200e6i	−0.254391	+	0.146873i
$366$	1.07696e7	+	1.82109e7i	0.219663	+	0.371440i
$367$	−2.43155e7	+	4.21157e7i	−0.491910	+	0.852012i	−0.999957	−	0.00931702i	$-0.997034\pi$
$367$	−2.43155e7	+	4.21157e7i	−0.491910	+	0.852012i	0.508047	+	0.861329i	$0.330368\pi$
$368$		−	3.74010e7i		−	0.750482i
$369$	−6.86088e7	+	4.15485e7i	−1.36553	+	0.826944i
$370$	2.91247e7			0.574985
$371$	1.34739e6	+	777919.i	0.0263860	+	0.0152339i
$372$	−223925.	−	126179.i	−0.00434985	−	0.00245109i
$373$	−2.28561e7	−	3.95878e7i	−0.440428	−	0.762843i	0.557293	−	0.830316i	$-0.311840\pi$
$373$	−2.28561e7	−	3.95878e7i	−0.440428	−	0.762843i	−0.997721	+	0.0674723i	$0.978507\pi$
$374$	9.83431e6	−	5.67784e6i	0.187988	−	0.108535i
$375$	−5.67117e7	+	593154.i	−1.07542	+	0.0112479i
$376$	6.71372e6	−	1.16285e7i	0.126299	−	0.218756i
$377$		−	5.74755e7i		−	1.07265i
$378$	−1.00125e7	−	1.61499e7i	−0.185382	−	0.299016i
$379$	2.09916e7			0.385593			0.192796	−	0.981239i	$-0.438244\pi$
$379$	2.09916e7			0.385593			0.192796	+	0.981239i	$0.438244\pi$
$380$	−475541.	−	274554.i	−0.00866638	−	0.00500353i
$381$	803431.	+	7.68165e7i	0.0145269	+	1.38893i
$382$	−2.56176e7	−	4.43709e7i	−0.459566	−	0.795991i
$383$	5.34458e7	−	3.08569e7i	0.951299	−	0.549233i	0.0578149	−	0.998327i	$-0.481587\pi$
$383$	5.34458e7	−	3.08569e7i	0.951299	−	0.549233i	0.893484	+	0.449095i	$0.148253\pi$
$384$	2.82476e7	−	5.01299e7i	0.498871	−	0.885325i
$385$	−8.35438e6	+	1.44702e7i	−0.146397	+	0.253567i
$386$		−	2.17277e7i		−	0.377792i
$387$	4.05309e6	−	7.37208e6i	0.0699283	−	0.127191i
$388$	134171.			0.00229701
$389$	−1.24081e7	−	7.16380e6i	−0.210793	−	0.121701i	0.390887	−	0.920439i	$-0.372168\pi$
$389$	−1.24081e7	−	7.16380e6i	−0.210793	−	0.121701i	−0.601680	+	0.798737i	$0.705502\pi$
$390$	−7.42825e7	+	4.39292e7i	−1.25226	+	0.740559i
$391$	4.24752e6	+	7.35693e6i	0.0710568	+	0.123074i
$392$	4.55239e7	−	2.62832e7i	0.755756	−	0.436336i
$393$	1.97233e7	+	3.33513e7i	0.324939	+	0.549458i
$394$	2.30928e7	−	3.99979e7i	0.377562	−	0.653957i
$395$		−	8.01278e6i		−	0.130015i
$396$	16136.8	+	771340.i	0.000259856	+	0.0124211i
$397$	7.70168e7			1.23088			0.615438	−	0.788186i	$-0.288979\pi$
$397$	7.70168e7			1.23088			0.615438	+	0.788186i	$0.288979\pi$
$398$	−5.24378e7	−	3.02750e7i	−0.831754	−	0.480213i
$399$	−2.37055e7	−	1.33577e7i	−0.373190	−	0.210288i
$400$	1.45387e7	+	2.51818e7i	0.227168	+	0.393466i
$401$	−7.57065e7	+	4.37092e7i	−1.17409	+	0.677859i	−0.954639	−	0.297765i	$-0.903759\pi$
$401$	−7.57065e7	+	4.37092e7i	−1.17409	+	0.677859i	−0.219448	+	0.975624i	$0.570426\pi$
$402$	−2.09936e7	+	219575.i	−0.323154	+	0.00337990i
$403$	−2.89225e7	+	5.00952e7i	−0.441896	+	0.765386i
$404$			800812.i			0.0121447i
$405$	4.16192e7	−	2.64092e7i	0.626511	−	0.397549i
$406$	−1.29516e7			−0.193528
$407$	−5.07466e7	−	2.92985e7i	−0.752703	−	0.434573i
$408$	135214.	+	1.29279e7i	0.00199086	+	0.190347i
$409$	2.56830e7	+	4.44842e7i	0.375384	+	0.650183i	0.990384	−	0.138343i	$-0.0441777\pi$
$409$	2.56830e7	+	4.44842e7i	0.375384	+	0.650183i	−0.615001	+	0.788526i	$0.710844\pi$
$410$	7.10897e7	−	4.10436e7i	1.03147	−	0.595517i
$411$	7.43485e6	−	1.31943e7i	0.107090	−	0.190047i
$412$	391915.	−	678816.i	0.00560402	−	0.00970645i
$413$			2.23098e7i			0.316698i
$414$	−5.29565e7	+	1.10788e6i	−0.746308	+	0.0156131i
$415$	−5.82579e7			−0.815099
$416$	2.67851e6	+	1.54644e6i	0.0372060	+	0.0214809i
$417$	1.90236e7	−	1.12502e7i	0.262352	−	0.155150i
$418$	5.06948e7	+	8.78059e7i	0.694120	+	1.20225i
$419$	1.15800e7	−	6.68574e6i	0.157423	−	0.0908881i	−0.419219	−	0.907885i	$-0.637696\pi$
$419$	1.15800e7	−	6.68574e6i	0.157423	−	0.0908881i	0.576642	+	0.816997i	$0.304363\pi$
$420$	107863.	+	182392.i	0.00145588	+	0.00246183i
$421$	5.48660e7	−	9.50307e7i	0.735287	−	1.27355i	−0.219310	−	0.975655i	$-0.570381\pi$
$421$	5.48660e7	−	9.50307e7i	0.735287	−	1.27355i	0.954597	−	0.297899i	$-0.0962860\pi$
$422$			1.02026e8i			1.35760i
$423$	−1.68474e7	−	9.26251e6i	−0.222593	−	0.122379i
$424$	6.60035e6			0.0865904
$425$	−5.71965e6	−	3.30224e6i	−0.0745080	−	0.0430172i
$426$	5.00378e7	+	2.81957e7i	0.647246	+	0.364716i
$427$	−5.84559e6	−	1.01249e7i	−0.0750835	−	0.130048i
$428$	−777350.	+	448803.i	−0.00991483	+	0.00572433i
$429$	1.73620e8	−	1.81591e6i	2.19902	−	0.0229998i
$430$	−4.30491e6	+	7.45633e6i	−0.0541451	+	0.0937820i
$431$			6.35161e7i			0.793327i	0.917964	+	0.396664i	$0.129832\pi$
$431$			6.35161e7i			0.793327i	−0.917964	+	0.396664i	$0.870168\pi$
$432$	−7.18246e7	−	3.85157e7i	−0.890886	−	0.477735i
$433$	−1.45827e7			−0.179628			−0.0898142	−	0.995959i	$-0.528627\pi$
$433$	−1.45827e7			−0.179628			−0.0898142	+	0.995959i	$0.528627\pi$
$434$	1.12885e7	+	6.51740e6i	0.138091	+	0.0797270i
$435$	−351370.	−	3.35947e7i	−0.00426872	−	0.408134i
$436$	−662687.	−	1.14781e6i	−0.00799557	−	0.0138487i
$437$	−6.56865e7	+	3.79241e7i	−0.787103	+	0.454434i
$438$	1.64201e7	−	2.91401e7i	0.195413	−	0.346792i
$439$	−2.80070e7	+	4.85095e7i	−0.331034	+	0.573367i	−0.982715	−	0.185126i	$-0.940731\pi$
$439$	−2.80070e7	+	4.85095e7i	−0.331034	+	0.573367i	0.651681	+	0.758493i	$0.274064\pi$
$440$			7.08838e7i			0.832126i
$441$	−3.89881e7	−	6.43808e7i	−0.454586	−	0.750655i
$442$	−3.24102e7			−0.375332
$443$	−1.15568e7	−	6.67232e6i	−0.132931	−	0.0767478i	0.432060	−	0.901845i	$-0.357787\pi$
$443$	−1.15568e7	−	6.67232e6i	−0.132931	−	0.0767478i	−0.564991	+	0.825097i	$0.691120\pi$
$444$	−639642.	+	378272.i	−0.00730783	+	0.00432171i
$445$	−4.05497e7	−	7.02341e7i	−0.460159	−	0.797018i
$446$	9.19913e7	−	5.31112e7i	1.03691	−	0.598662i
$447$	3.90108e7	+	6.59657e7i	0.436780	+	0.738577i
$448$	−1.55535e7	+	2.69395e7i	−0.172979	+	0.299609i
$449$		−	9.37897e7i		−	1.03613i	−0.855340	−	0.518067i	$-0.826652\pi$
$449$		−	9.37897e7i		−	1.03613i	0.855340	−	0.518067i	$-0.173348\pi$
$450$	3.52246e7	−	2.13315e7i	0.386552	−	0.234090i
$451$	−1.65154e8			−1.80037
$452$	−854075.	−	493101.i	−0.00924870	−	0.00533974i
$453$	4.14741e7	+	2.33702e7i	0.446152	+	0.251401i
$454$	−6.39188e7	−	1.10711e8i	−0.683063	−	1.18310i
$455$	4.12993e7	−	2.38442e7i	0.438439	−	0.253133i
$456$	−1.15427e8	+	1.20726e6i	−1.21734	+	0.0127323i
$457$	5.76767e7	−	9.98990e7i	0.604299	−	1.04668i	−0.387863	−	0.921717i	$-0.626787\pi$
$457$	5.76767e7	−	9.98990e7i	0.604299	−	1.04668i	0.992162	−	0.124959i	$-0.0398800\pi$
$458$			2.52968e7i			0.263311i
$459$	1.85023e7	−	580722.i	0.191332	−	0.00600524i
$460$	590673.			0.00606840
$461$	1.60801e7	+	9.28384e6i	0.164129	+	0.0947600i	0.579815	−	0.814748i	$-0.303125\pi$
$461$	1.60801e7	+	9.28384e6i	0.164129	+	0.0947600i	−0.415686	+	0.909508i	$0.636458\pi$
$462$	−409199.	−	3.91237e7i	−0.00414963	−	0.396748i
$463$	−3.53162e7	−	6.11695e7i	−0.355821	−	0.616300i	0.631437	−	0.775427i	$-0.282465\pi$
$463$	−3.53162e7	−	6.11695e7i	−0.355821	−	0.616300i	−0.987258	+	0.159127i	$0.949132\pi$
$464$	−4.81077e7	+	2.77750e7i	−0.481571	+	0.278035i
$465$	−1.65991e7	+	2.94577e7i	−0.165091	+	0.292981i
$466$	−2.79692e7	+	4.84440e7i	−0.276390	+	0.478721i
$467$			8.13433e7i			0.798677i	0.916804	+	0.399338i	$0.130760\pi$
$467$			8.13433e7i			0.798677i	−0.916804	+	0.399338i	$0.869240\pi$
$468$	1.06085e6	−	1.92956e6i	0.0103495	−	0.0188244i
$469$	1.16015e7			0.112459
$470$	1.70399e7	+	9.83800e6i	0.164125	+	0.0947574i
$471$	−1.00109e7	+	5.92026e6i	−0.0958101	+	0.0566602i
$472$	4.73225e7	+	8.19650e7i	0.450031	+	0.779476i
$473$	1.50017e7	−	8.66121e6i	0.141761	−	0.0818456i
$474$	9.55096e6	+	1.61503e7i	0.0896834	+	0.151651i
$475$	2.94842e7	−	5.10681e7i	0.275111	−	0.476506i
$476$			79579.4i			0.000737870i
$477$	−197667.	−	9.44847e6i	−0.00182129	−	0.0870575i
$478$	2.18545e7			0.200105
$479$	9.72480e7	+	5.61461e7i	0.884859	+	0.510874i	0.872257	−	0.489047i	$-0.162655\pi$
$479$	9.72480e7	+	5.61461e7i	0.884859	+	0.510874i	0.0126015	+	0.999921i	$0.495989\pi$
$480$	1.57505e6	+	887525.i	0.0142420	+	0.00802522i
$481$	8.36208e7	+	1.44836e8i	0.751414	+	1.30149i
$482$	1.88832e7	−	1.09022e7i	0.168630	−	0.0973585i
$483$	2.92680e7	−	306117.i	0.259747	−	0.00271673i
$484$	−169775.	+	294059.i	−0.00149740	+	0.00259358i
$485$		−	1.76504e7i		−	0.154714i
$486$	−5.24072e7	+	1.02838e8i	−0.456544	+	0.895871i
$487$	1.17703e8			1.01907			0.509533	−	0.860451i	$-0.329818\pi$
$487$	1.17703e8			1.01907			0.509533	+	0.860451i	$0.329818\pi$
$488$	−4.29528e7	−	2.47988e7i	−0.369600	−	0.213389i
$489$	1.37615e6	+	1.31574e8i	0.0117690	+	1.12524i
$490$	3.85143e7	+	6.67088e7i	0.327367	+	0.567016i
$491$	−1.17596e8	+	6.78940e7i	−0.993453	+	0.573571i	−0.906305	−	0.422625i	$-0.861109\pi$
$491$	−1.17596e8	+	6.78940e7i	−0.993453	+	0.573571i	−0.0871486	+	0.996195i	$0.527775\pi$
$492$	−1.02821e6	+	1.82472e6i	−0.00863349	+	0.0153215i
$493$	6.30865e6	−	1.09269e7i	0.0526496	−	0.0911918i
$494$		−	2.89375e8i		−	2.40038i
$495$	1.01471e8	−	2.12282e6i	0.836615	−	0.0175024i
$496$	5.59070e7			0.458164
$497$	−2.74859e7	−	1.58690e7i	−0.223893	−	0.129265i
$498$	1.17422e8	−	6.94413e7i	0.950743	−	0.562251i
$499$	−2.40967e7	−	4.17367e7i	−0.193935	−	0.335905i	0.752616	−	0.658460i	$-0.228792\pi$
$499$	−2.40967e7	−	4.17367e7i	−0.193935	−	0.335905i	−0.946551	+	0.322555i	$0.895458\pi$
$500$	−1.28257e6	+	740491.i	−0.0102605	+	0.00592393i
$501$	−1.06736e8	−	1.80486e8i	−0.848783	−	1.43526i
$502$	−1.14267e8	+	1.97916e8i	−0.903255	+	1.56448i
$503$		−	1.99031e7i		−	0.156393i	−0.996938	−	0.0781963i	$-0.975084\pi$
$503$		−	1.99031e7i		−	0.156393i	0.996938	−	0.0781963i	$-0.0249161\pi$
$504$	3.90347e7	+	2.14608e7i	0.304901	+	0.167631i
$505$	1.05348e8			0.817997
$506$	−9.44525e7	−	5.45322e7i	−0.729058	−	0.420922i
$507$	−3.18193e8	−	1.79298e8i	−2.44156	−	1.37579i
$508$	1.00300e6	+	1.73725e6i	0.00765086	+	0.0132517i
$509$	−4.74516e7	+	2.73962e7i	−0.359830	+	0.207748i	−0.669006	−	0.743257i	$-0.733280\pi$
$509$	−4.74516e7	+	2.73962e7i	−0.359830	+	0.207748i	0.309176	+	0.951005i	$0.399947\pi$
$510$	−1.89439e7	+	198136.i	−0.142810	+	0.00149367i
$511$	−9.24150e6	+	1.60067e7i	−0.0692595	+	0.119961i
$512$			1.31933e8i			0.982979i
$513$	5.18499e6	+	1.65198e8i	0.0384057	+	1.22364i
$514$	9.01790e7			0.664073
$515$	−8.92992e7	−	5.15569e7i	−0.653772	−	0.377455i
$516$	−2297.55	−	219669.i	−1.67230e−5	−	0.00159890i
$517$	−1.97934e7	−	3.42832e7i	−0.143235	−	0.248091i
$518$	3.26373e7	−	1.88432e7i	0.234815	−	0.135570i
$519$	−9.33502e7	+	1.65665e8i	−0.667749	+	1.18503i
$520$	1.01155e8	−	1.75205e8i	0.719408	−	1.24605i
$521$		−	2.09737e8i		−	1.48307i	−0.670912	−	0.741537i	$-0.734097\pi$
$521$		−	2.09737e8i		−	1.48307i	0.670912	−	0.741537i	$-0.265903\pi$
$522$	4.07519e7	+	6.72934e7i	0.286508	+	0.473109i
$523$	1.69217e7			0.118287			0.0591436	−	0.998249i	$-0.481163\pi$
$523$	1.69217e7			0.118287			0.0591436	+	0.998249i	$0.481163\pi$
$524$	876234.	+	505894.i	0.00609012	+	0.00351613i
$525$	−1.95869e7	+	1.15833e7i	−0.135359	+	0.0800489i
$526$	−1.12058e8	−	1.94090e8i	−0.769990	−	1.33366i
$527$	−1.09971e7	+	6.34919e6i	−0.0751359	+	0.0433797i
$528$	−8.54219e7	−	1.44445e8i	−0.580320	−	0.981297i
$529$	−3.32231e7	+	5.75441e7i	−0.224426	+	0.388717i
$530$			9.67188e6i			0.0649656i
$531$	1.15917e8	−	7.01973e7i	0.774215	−	0.468853i
$532$	−710526.			−0.00471895
$533$	4.08215e8	+	2.35683e8i	2.69592	+	1.55649i
$534$	1.65447e8	+	9.32276e7i	1.08651	+	0.612238i
$535$	5.90407e7	+	1.02262e8i	0.385559	+	0.667807i
$536$	4.26233e7	−	2.46086e7i	0.276792	−	0.159806i
$537$	9.50872e6	−	99452.7i	0.0614044	−	0.000642234i
$538$	−3.15837e7	+	5.47046e7i	−0.202822	+	0.351299i
$539$		−	1.54977e8i		−	0.989694i
$540$	608278.	−	1.13432e6i	0.00386296	−	0.00720371i
$541$	−2.96138e8			−1.87026			−0.935132	−	0.354299i	$-0.884719\pi$
$541$	−2.96138e8			−1.87026			−0.935132	+	0.354299i	$0.884719\pi$
$542$	1.41290e7	+	8.15739e6i	0.0887388	+	0.0512334i
$543$	−142112.	−	1.35874e7i	−0.000887626	−	0.0848663i
$544$	339481.	+	587999.i	0.00210872	+	0.00365241i
$545$	−1.50996e8	+	8.71775e7i	−0.932772	+	0.538536i
$546$	−5.48200e7	+	9.72869e7i	−0.336792	+	0.597690i
$547$	2.32052e7	−	4.01926e7i	0.141783	−	0.245575i	−0.786385	−	0.617736i	$-0.788050\pi$
$547$	2.32052e7	−	4.01926e7i	0.141783	−	0.245575i	0.928168	+	0.372161i	$0.121383\pi$
$548$		−	395475.i		−	0.00240313i
$549$	−3.42134e7	+	6.22301e7i	−0.206766	+	0.376083i
$550$	8.47923e7			0.509645
$551$	9.75610e7	+	5.63269e7i	0.583205	+	0.336714i
$552$	1.06880e8	−	6.32067e7i	0.635446	−	0.375790i
$553$	−5.18413e6	−	8.97917e6i	−0.0306549	−	0.0530959i
$554$	−1.95079e8	+	1.12629e8i	−1.14731	+	0.662401i
$555$	4.97622e7	+	8.41459e7i	0.291086	+	0.492214i
$556$	288563.	−	499805.i	0.00167886	−	0.00290788i
$557$			1.93358e8i			1.11892i	0.828859	+	0.559458i	$0.188991\pi$
$557$			1.93358e8i			1.11892i	−0.828859	+	0.559458i	$0.811009\pi$
$558$	−1.65605e6	−	7.91593e7i	−0.00953172	−	0.455616i
$559$	−4.94399e7			−0.283036
$560$	−3.99158e7	−	2.30454e7i	−0.227290	−	0.131226i
$561$	3.32070e7	+	1.87118e7i	0.188079	+	0.105981i
$562$	−1.40003e8	−	2.42493e8i	−0.788732	−	1.36612i
$563$	2.78735e8	−	1.60928e8i	1.56195	−	0.901790i	0.564885	−	0.825169i	$-0.308920\pi$
$563$	2.78735e8	−	1.60928e8i	1.56195	−	0.901790i	0.997060	−	0.0766203i	$-0.0244129\pi$
$564$	−502010.	+	5250.57i	−0.00279818	+	2.92664e-5i
$565$	−6.48681e7	+	1.12355e8i	−0.359655	+	0.622940i
$566$			2.49014e8i			1.37333i
$567$	2.95524e7	−	5.65212e7i	0.162123	−	0.310072i
$568$	−1.34642e8			−0.734745
$569$	−1.32578e8	−	7.65442e7i	−0.719674	−	0.415504i	0.0949586	−	0.995481i	$-0.469728\pi$
$569$	−1.32578e8	−	7.65442e7i	−0.719674	−	0.415504i	−0.814633	+	0.579977i	$0.803061\pi$
$570$	−1.76907e6	−	1.69141e8i	−0.00955255	−	0.913324i
$571$	1.23735e8	+	2.14315e8i	0.664635	+	1.15118i	0.979384	+	0.202007i	$0.0647465\pi$
$571$	1.23735e8	+	2.14315e8i	0.664635	+	1.15118i	−0.314749	+	0.949175i	$0.601920\pi$
$572$	3.92653e6	−	2.26698e6i	0.0209807	−	0.0121132i
$573$	8.44246e7	−	1.49825e8i	0.448751	−	0.796380i
$574$	5.31090e7	−	9.19875e7i	0.280823	−	0.486400i
$575$			6.34320e7i			0.333661i
$576$	1.88910e8	−	3.95210e6i	0.988526	−	0.0206805i
$577$	1.55274e8			0.808296			0.404148	−	0.914694i	$-0.367568\pi$
$577$	1.55274e8			0.808296			0.404148	+	0.914694i	$0.367568\pi$
$578$	1.61987e8	+	9.35232e7i	0.838874	+	0.484324i
$579$	6.27748e7	−	3.71238e7i	0.323407	−	0.191257i
$580$	−438650.	−	759763.i	−0.00224819	−	0.00389399i
$581$	−6.52841e7	+	3.76918e7i	−0.332873	+	0.192185i
$582$	2.10386e7	+	3.55755e7i	0.106721	+	0.180460i
$583$	9.72960e6	−	1.68522e7i	0.0491009	−	0.0850453i
$584$			7.84107e7i			0.393674i
$585$	−2.53837e8	−	1.39557e8i	−1.26791	−	0.697081i
$586$	−1.99086e8			−0.989343
$587$	−2.78742e8	−	1.60932e8i	−1.37812	−	0.795659i	−0.386189	−	0.922420i	$-0.626209\pi$
$587$	−2.78742e8	−	1.60932e8i	−1.37812	−	0.795659i	−0.991933	+	0.126760i	$0.959542\pi$
$588$	−1.71227e6	−	964847.i	−0.00842250	−	0.00474598i
$589$	−5.66889e7	−	9.81881e7i	−0.277429	−	0.480522i
$590$	−1.20108e8	+	6.93444e7i	−0.584812	+	0.337641i
$591$	1.55017e8	−	1.62133e6i	0.750958	−	0.00785435i
$592$	8.08194e7	−	1.39983e8i	0.389539	−	0.674701i
$593$		−	3.82156e8i		−	1.83264i	−0.400448	−	0.916319i	$-0.631146\pi$
$593$		−	3.82156e8i		−	1.83264i	0.400448	−	0.916319i	$-0.368854\pi$
$594$	−2.01991e8	+	1.25228e8i	−0.963767	+	0.597508i
$595$	1.04688e7			0.0496987
$596$	1.73311e6	+	1.00061e6i	0.00818629	+	0.00472636i
$597$	−2.12559e6	−	2.03228e8i	−0.00998978	−	0.955128i
$598$	1.55640e8	+	2.69576e8i	0.727810	+	1.26060i
$599$	−7.30381e7	+	4.21685e7i	−0.339835	+	0.196204i	−0.660199	−	0.751090i	$-0.729528\pi$
$599$	−7.30381e7	+	4.21685e7i	−0.339835	+	0.196204i	0.320364	+	0.947295i	$0.396195\pi$
$600$	−4.73914e7	+	8.41036e7i	−0.219405	+	0.389368i
$601$	−4.80447e7	+	8.32159e7i	−0.221321	+	0.383339i	−0.955209	−	0.295931i	$-0.904370\pi$
$601$	−4.80447e7	+	8.32159e7i	−0.221321	+	0.383339i	0.733889	+	0.679270i	$0.237703\pi$
$602$			1.11408e7i			0.0510655i
$603$	−3.65039e7	−	6.02787e7i	−0.166490	−	0.274924i
$604$	1.24311e6			0.00564155
$605$	3.86839e7	+	2.23342e7i	0.174689	+	0.100857i
$606$	−2.12335e8	+	1.25571e8i	−0.954124	+	0.564250i
$607$	4.97861e7	+	8.62320e7i	0.222609	+	0.385569i	0.955599	−	0.294669i	$-0.0952095\pi$
$607$	4.97861e7	+	8.62320e7i	0.222609	+	0.385569i	−0.732991	+	0.680239i	$0.761876\pi$
$608$	−5.24996e6	+	3.03106e6i	−0.0233585	+	0.0134860i
$609$	−2.21289e7	−	3.74191e7i	−0.0979734	−	0.165669i
$610$	3.63391e7	−	6.29412e7i	0.160098	−	0.277297i
$611$			1.12985e8i			0.495332i
$612$	413477.	−	250395.i	0.00180383	−	0.00109238i
$613$	−2.79460e8			−1.21322			−0.606609	−	0.795000i	$-0.707471\pi$
$613$	−2.79460e8			−1.21322			−0.606609	+	0.795000i	$0.707471\pi$
$614$	−1.32473e8	−	7.64833e7i	−0.572298	−	0.330416i
$615$	2.40045e8	+	1.35262e8i	1.03197	+	0.581503i
$616$	4.58606e7	+	7.94328e7i	0.196199	+	0.339827i
$617$	3.17031e8	−	1.83038e8i	1.34973	−	0.779265i	0.361516	−	0.932366i	$-0.382259\pi$
$617$	3.17031e8	−	1.83038e8i	1.34973	−	0.779265i	0.988211	+	0.153101i	$0.0489260\pi$
$618$	2.41442e8	−	2.52527e6i	1.02293	−	0.0106990i
$619$	1.53497e8	−	2.65865e8i	0.647186	−	1.12096i	−0.336606	−	0.941645i	$-0.609279\pi$
$619$	1.53497e8	−	2.65865e8i	0.647186	−	1.12096i	0.983792	−	0.179313i	$-0.0573875\pi$
$620$			882938.i			0.00370472i
$621$	−9.36818e7	−	1.51107e8i	−0.391183	−	0.630970i
$622$	2.31865e8			0.963526
$623$	−9.08805e7	−	5.24699e7i	−0.375843	−	0.216993i
$624$	5.00916e6	+	4.78929e8i	0.0206163	+	1.97114i
$625$	4.25495e7	+	7.36978e7i	0.174283	+	0.301866i
$626$	3.34809e8	−	1.93302e8i	1.36482	−	0.787976i
$627$	−1.67068e8	+	2.96489e8i	−0.677785	+	1.20284i
$628$	−151852.	+	263016.i	−0.000613115	+	0.00106195i
$629$			3.67137e7i			0.147529i
$630$	−3.14478e7	+	5.71998e7i	−0.125768	+	0.228756i
$631$	4.69076e8			1.86705			0.933523	−	0.358518i	$-0.116718\pi$
$631$	4.69076e8			1.86705			0.933523	+	0.358518i	$0.116718\pi$
$632$	−3.80925e7	−	2.19927e7i	−0.150900	−	0.0871220i
$633$	−2.94769e8	+	1.74321e8i	−1.16217	+	0.687286i
$634$	−1.42798e7	−	2.47333e7i	−0.0560344	−	0.0970544i
$635$	2.28538e8	−	1.31946e8i	0.892558	−	0.515319i
$636$	−125618.	−	212416.i	−0.000488295	−	0.000825686i
$637$	−2.21159e8	+	3.83059e8i	−0.855632	+	1.48200i
$638$			1.61988e8i			0.623765i
$639$	4.03226e6	+	1.92742e8i	0.0154542	+	0.738709i
$640$	−1.97662e8			−0.754022
$641$	1.78248e8	+	1.02911e8i	0.676784	+	0.390742i	0.798642	−	0.601806i	$-0.205552\pi$
$641$	1.78248e8	+	1.02911e8i	0.676784	+	0.390742i	−0.121858	+	0.992548i	$0.538885\pi$
$642$	−2.40893e8	−	1.35740e8i	−0.910371	−	0.512983i
$643$	−1.50649e8	−	2.60932e8i	−0.566676	−	0.981511i	−0.996892	−	0.0787851i	$-0.974896\pi$
$643$	−1.50649e8	−	2.60932e8i	−0.566676	−	0.981511i	0.430216	−	0.902726i	$-0.358437\pi$
$644$	661912.	−	382155.i	0.00247824	−	0.00143081i
$645$	−2.88978e7	+	302245.i	−0.107693	+	0.00112637i
$646$	3.17625e7	−	5.50143e7i	0.117820	−	0.204070i
$647$			1.33959e8i			0.494604i	0.968938	+	0.247302i	$0.0795440\pi$
$647$			1.33959e8i			0.494604i	−0.968938	+	0.247302i	$0.920456\pi$
$648$	−1.13163e7	−	2.70342e8i	−0.0415892	−	0.993546i
$649$	2.79033e8			1.02076
$650$	−2.09583e8	−	1.21003e8i	−0.763159	−	0.440610i
$651$	457583.	+	4.37497e7i	0.00165854	+	0.158574i
$652$	1.71798e6	+	2.97562e6i	0.00619833	+	0.0107358i
$653$	−3.13278e8	+	1.80871e8i	−1.12510	+	0.649576i	−0.942698	−	0.333649i	$-0.891720\pi$
$653$	−3.13278e8	+	1.80871e8i	−1.12510	+	0.649576i	−0.182401	+	0.983224i	$0.558387\pi$
$654$	2.00429e8	−	3.55693e8i	0.716519	−	1.27158i
$655$	6.65510e7	−	1.15270e8i	0.236827	−	0.410196i
$656$		−	4.55575e8i		−	1.61380i
$657$	1.12246e8	−	2.34824e6i	0.395798	−	0.00828029i
$658$	2.54601e7			0.0893679
$659$	−3.64863e8	−	2.10654e8i	−1.27489	−	0.736060i	−0.298989	−	0.954257i	$-0.596649\pi$
$659$	−3.64863e8	−	2.10654e8i	−1.27489	−	0.736060i	−0.975905	+	0.218196i	$0.929983\pi$
$660$	2.28121e6	−	1.34907e6i	0.00793477	−	0.00469247i
$661$	−1.67487e8	−	2.90095e8i	−0.579930	−	1.00447i	−0.995487	−	0.0949012i	$-0.969746\pi$
$661$	−1.67487e8	−	2.90095e8i	−0.579930	−	1.00447i	0.415557	−	0.909567i	$-0.363587\pi$
$662$	6.29699e7	−	3.63557e7i	0.217049	−	0.125314i
$663$	−5.53758e7	−	9.36382e7i	−0.190011	−	0.321301i
$664$	−1.59901e8	+	2.76956e8i	−0.546193	+	0.946033i
$665$			9.34707e7i			0.317842i
$666$	−2.00598e8	−	1.10287e8i	−0.679053	−	0.373336i
$667$	−1.21181e8			−0.408374
$668$	−4.74188e6	−	2.73773e6i	−0.0159082	−	0.00918461i
$669$	3.10622e8	+	1.75032e8i	1.03742	+	0.584574i
$670$	3.60604e7	+	6.24584e7i	0.119896	+	0.207666i
$671$	−1.26634e8	+	7.31121e7i	−0.419162	+	0.242003i
$672$	2.33923e6	−	24466.2i	0.00770841	−	8.06230e-5i
$673$	−1.42359e8	+	2.46572e8i	−0.467024	+	0.808908i	−0.999290	−	0.0376682i	$-0.988007\pi$
$673$	−1.42359e8	+	2.46572e8i	−0.467024	+	0.808908i	0.532267	+	0.846577i	$0.321340\pi$
$674$			1.32170e6i			0.00431670i
$675$	1.21814e8	+	6.53225e7i	0.396084	+	0.212399i
$676$	−9.53725e6			−0.0308733
$677$	1.29812e8	+	7.49471e7i	0.418359	+	0.241540i	0.694375	−	0.719613i	$-0.255681\pi$
$677$	1.29812e8	+	7.49471e7i	0.418359	+	0.241540i	−0.276016	+	0.961153i	$0.589014\pi$
$678$	−3.17725e6	−	3.03779e8i	−0.0101944	−	0.974694i
$679$	−1.14195e7	−	1.97791e7i	−0.0364785	−	0.0631826i
$680$	3.84618e7	−	2.22059e7i	0.122322	−	0.0706224i
$681$	2.10649e8	−	3.73830e8i	0.666989	−	1.18368i
$682$	8.15147e7	−	1.41188e8i	0.256970	−	0.445085i
$683$			5.60477e8i			1.75912i	0.475787	+	0.879560i	$0.342163\pi$
$683$			5.60477e8i			1.75912i	−0.475787	+	0.879560i	$0.657837\pi$
$684$	2.23566e6	+	3.69174e6i	0.00698614	+	0.0115362i
$685$	−5.20253e7			−0.161861
$686$	1.84680e8	+	1.06625e8i	0.572067	+	0.330283i
$687$	−7.30863e7	+	4.32218e7i	−0.225406	+	0.133301i
$688$	2.38918e7	+	4.13818e7i	0.0733640	+	0.127070i
$689$	−4.80977e7	+	2.77692e7i	−0.147051	+	0.0848997i
$690$	9.26204e7	+	1.56617e8i	0.281942	+	0.476752i
$691$	−8.08334e6	+	1.40008e7i	−0.0244995	+	0.0424343i	−0.878015	−	0.478633i	$-0.841133\pi$
$691$	−8.08334e6	+	1.40008e7i	−0.0244995	+	0.0424343i	0.853516	+	0.521067i	$0.174466\pi$
$692$			4.96549e6i			0.0149846i
$693$	1.12335e8	−	6.80287e7i	0.337534	−	0.204405i
$694$	2.41063e8			0.721194
$695$	−6.57501e7	−	3.79608e7i	−0.195858	−	0.113079i
$696$	−1.60672e8	−	9.05371e7i	−0.476556	−	0.268534i
$697$	5.17383e7	+	8.96134e7i	0.152797	+	0.264652i
$698$	−1.73369e8	+	1.00095e8i	−0.509807	+	0.294337i
$699$	−1.87750e8	+	1.96370e6i	−0.549729	+	0.00574968i
$700$	−297107.	+	514605.i	−0.000866202	+	0.00150031i
$701$			5.37669e8i			1.56085i	0.625249	+	0.780425i	$0.284997\pi$
$701$			5.37669e8i			1.56085i	−0.625249	+	0.780425i	$0.715003\pi$
$702$	6.77971e8	−	2.12791e7i	1.95975	−	0.0615095i
$703$	−3.27799e8			−0.943500
$704$	3.36938e8	+	1.94531e8i	0.965677	+	0.557534i
$705$	690720.	+	6.60401e7i	0.00197122	+	0.188469i
$706$	8.73127e7	+	1.51230e8i	0.248121	+	0.429758i
$707$	1.18054e8	−	6.81582e7i	0.334057	−	0.192868i
$708$	1.73719e6	−	3.08292e6i	0.00489494	−	0.00868685i
$709$	2.93468e8	−	5.08302e8i	0.823422	−	1.42621i	−0.0796974	−	0.996819i	$-0.525395\pi$
$709$	2.93468e8	−	5.08302e8i	0.823422	−	1.42621i	0.903119	−	0.429390i	$-0.141271\pi$
$710$		−	1.97299e8i		−	0.551252i
$711$	−3.03420e7	+	5.51884e7i	−0.0844181	+	0.153546i
$712$	−4.45188e8			−1.23340
$713$	1.05621e8	+	6.09801e7i	0.291394	+	0.168236i
$714$	−2.11005e7	+	1.24784e7i	−0.0579693	+	0.0342819i
$715$	−2.98225e8	−	5.16540e8i	−0.815878	−	1.41314i
$716$	215045.	−	124156.i	0.000585856	−	0.000338244i
$717$	3.73404e7	+	6.31410e7i	0.101303	+	0.171299i
$718$	−3.14341e8	+	5.44455e8i	−0.849236	+	1.47092i
$719$		−	4.52832e8i		−	1.21829i	−0.793059	−	0.609144i	$-0.791513\pi$
$719$		−	4.52832e8i		−	1.21829i	0.793059	−	0.609144i	$-0.208487\pi$
$720$	5.85576e6	+	2.79905e8i	0.0156887	+	0.749918i
$721$	−1.33426e8			−0.355987
$722$	1.63463e8	+	9.43753e7i	0.434317	+	0.250753i
$723$	6.37619e7	+	3.59291e7i	0.168712	+	0.0950673i
$724$	−177412.	−	307286.i	−0.000467484	−	0.000809705i
$725$	8.15905e7	−	4.71063e7i	0.214104	−	0.123613i
$726$	−1.04592e8	+	1.09393e6i	−0.273330	+	0.00285878i
$727$	8.62458e7	−	1.49382e8i	0.224458	−	0.388772i	−0.731699	−	0.681628i	$-0.761272\pi$
$727$	8.62458e7	−	1.49382e8i	0.224458	−	0.388772i	0.956157	+	0.292856i	$0.0946056\pi$
$728$		−	2.61781e8i		−	0.678491i
$729$	−3.86658e8	+	2.42956e7i	−0.998032	+	0.0627112i
$730$	−1.14900e8			−0.295359
$731$	−9.39921e6	−	5.42664e6i	−0.0240624	−	0.0138924i
$732$	19394.3	+	1.85430e6i	4.94472e−5	+	0.00472767i
$733$	8.58050e7	+	1.48619e8i	0.217872	+	0.377365i	0.954157	−	0.299306i	$-0.0967552\pi$
$733$	8.58050e7	+	1.48619e8i	0.217872	+	0.377365i	−0.736285	+	0.676671i	$0.763422\pi$
$734$	−3.38776e8	+	1.95593e8i	−0.856692	+	0.494612i
$735$	−1.26927e8	+	2.25252e8i	−0.319663	+	0.567292i
$736$	3.26051e6	−	5.64736e6i	0.00817808	−	0.0141649i
$737$		−	1.45102e8i		−	0.362470i
$738$	−6.45053e8	+	1.34948e7i	−1.60482	+	0.0335736i
$739$	5.61249e8			1.39066			0.695332	−	0.718688i	$-0.255257\pi$
$739$	5.61249e8			1.39066			0.695332	+	0.718688i	$0.255257\pi$
$740$	2.21075e6	+	1.27638e6i	0.00545563	+	0.00314981i
$741$	8.36051e8	−	4.94424e8i	2.05484	−	1.21519i
$742$	6.25753e6	+	1.08384e7i	0.0153176	+	0.0265309i
$743$	−1.02996e8	+	5.94646e7i	−0.251103	+	0.144975i	−0.620269	−	0.784389i	$-0.712977\pi$
$743$	−1.02996e8	+	5.94646e7i	−0.251103	+	0.144975i	0.369166	+	0.929363i	$0.379643\pi$
$744$	9.44813e7	+	1.59764e8i	0.229418	+	0.387936i
$745$	1.31632e8	−	2.27993e8i	0.318340	−	0.551382i
$746$		−	3.67706e8i		−	0.885694i
$747$	4.01254e8	+	2.20605e8i	0.962625	+	0.529241i
$748$	995317.			0.00237825
$749$	1.32323e8	+	7.63966e7i	0.314912	+	0.181815i
$750$	−3.97454e8	−	2.23961e8i	−0.942114	−	0.530870i
$751$	−1.22156e7	−	2.11581e7i	−0.0288400	−	0.0499524i	0.851245	−	0.524768i	$-0.175848\pi$
$751$	−1.22156e7	−	2.11581e7i	−0.0288400	−	0.0499524i	−0.880085	+	0.474816i	$0.842515\pi$
$752$	9.45696e7	−	5.45998e7i	0.222381	−	0.128392i
$753$	−7.67048e8	+	8.02263e6i	−1.79654	+	0.0187902i
$754$	2.31165e8	−	4.00389e8i	0.539272	−	0.934046i
$755$		−	1.63533e8i		−	0.379983i
$756$	−52248.3	−	1.66468e6i	−0.000120922	−	0.00385269i
$757$	−2.95715e8			−0.681688			−0.340844	−	0.940120i	$-0.610713\pi$
$757$	−2.95715e8			−0.681688			−0.340844	+	0.940120i	$0.610713\pi$
$758$	1.46233e8	+	8.44278e7i	0.335767	+	0.193855i
$759$	−3.82867e6	−	3.66061e8i	−0.00875635	−	0.837199i
$760$	1.98266e8	+	3.43407e8i	0.451656	+	0.782291i
$761$	2.26182e8	−	1.30586e8i	0.513220	−	0.296308i	−0.220936	−	0.975288i	$-0.570911\pi$
$761$	2.26182e8	−	1.30586e8i	0.513220	−	0.296308i	0.734156	+	0.678981i	$0.237578\pi$
$762$	−3.03357e8	+	5.38355e8i	−0.685628	+	1.21676i
$763$	−1.12805e8	+	1.95383e8i	−0.253953	+	0.439859i
$764$		−	4.49072e6i		−	0.0100701i
$765$	−3.29399e7	−	5.43934e7i	−0.0735762	−	0.121496i
$766$	4.96423e8			1.10450
$767$	−6.89692e8	−	3.98194e8i	−1.52851	−	0.882487i
$768$	1.28845e7	−	7.61961e6i	0.0284435	−	0.0168209i
$769$	2.50506e8	+	4.33889e8i	0.550857	+	0.954112i	0.998213	+	0.0597559i	$0.0190322\pi$
$769$	2.50506e8	+	4.33889e8i	0.550857	+	0.954112i	−0.447356	+	0.894356i	$0.647634\pi$
$770$	−1.16398e8	+	6.72021e7i	−0.254960	+	0.147201i
$771$	1.54079e8	+	2.60541e8i	0.336186	+	0.568477i
$772$	952210.	−	1.64928e6i	0.00206957	−	0.00358460i
$773$		−	4.17209e8i		−	0.903265i	−0.892204	−	0.451633i	$-0.850842\pi$
$773$		−	4.17209e8i		−	0.903265i	0.892204	−	0.451633i	$-0.149158\pi$
$774$	5.78852e7	−	3.50544e7i	0.124837	−	0.0755996i
$775$	−9.48181e7			−0.203698
$776$	−8.39093e7	−	4.84451e7i	−0.179566	−	0.103673i
$777$	1.10205e8	+	6.20991e7i	0.234929	+	0.132380i
$778$	−5.76252e7	−	9.98098e7i	−0.122370	−	0.211951i
$779$	−8.00115e8	+	4.61947e8i	−1.69254	+	0.977191i
$780$	−7.56370e6	+	79109.6i	−0.0159386	+	0.000166704i
$781$	−1.98477e8	+	3.43772e8i	−0.416636	+	0.721635i
$782$			6.83337e7i			0.142894i
$783$	−1.24793e8	+	2.32716e8i	−0.259959	+	0.484775i
$784$	4.27501e8			0.887133
$785$	3.46001e7	+	1.99764e7i	0.0715267	+	0.0412959i
$786$	3.25969e6	+	3.11660e8i	0.00671287	+	0.641821i
$787$	4.21601e8	+	7.30234e8i	0.864922	+	1.49809i	0.867124	+	0.498092i	$0.165966\pi$
$787$	4.21601e8	+	7.30234e8i	0.864922	+	1.49809i	−0.00220161	+	0.999998i	$0.500701\pi$
$788$	3.50579e6	−	2.02407e6i	0.00716485	−	0.00413663i
$789$	3.69295e8	−	6.55373e8i	0.751870	−	1.33431i
$790$	3.22272e7	−	5.58191e7i	0.0653644	−	0.113214i
$791$			1.67874e8i			0.339199i
$792$	2.68416e8	−	4.88216e8i	0.540297	−	0.982734i
$793$	4.17338e8			0.836889
$794$	5.36519e8	+	3.09759e8i	1.07182	+	0.618818i
$795$	−2.79436e7	+	1.65253e7i	−0.0556135	+	0.0328888i
$796$	−2.65358e6	−	4.59613e6i	−0.00526129	−	0.00911282i
$797$	6.47167e8	−	3.73642e8i	1.27833	−	0.738042i	0.301786	−	0.953376i	$-0.402417\pi$
$797$	6.47167e8	−	3.73642e8i	1.27833	−	0.738042i	0.976540	+	0.215334i	$0.0690840\pi$
$798$	−1.11414e8	−	1.88396e8i	−0.219245	−	0.370735i
$799$	−1.24015e7	+	2.14800e7i	−0.0243127	+	0.0421108i
$800$			5.06977e6i			0.00990190i
$801$	1.33324e7	+	6.37291e8i	0.0259425	+	1.24005i
$802$	−7.03189e8			−1.36317
$803$	2.00200e8	+	1.15586e8i	0.386649	+	0.223232i
$804$	−1.60317e6	−	903370.i	−0.00308470	−	0.00173819i
$805$	−5.02731e7	−	8.70755e7i	−0.0963713	−	0.166920i
$806$	−4.02963e8	+	2.32651e8i	−0.769590	+	0.444323i
$807$	−2.12014e8	+	2.21747e6i	−0.403407	+	0.00421927i
$808$	2.89149e8	−	5.00820e8i	0.548135	−	0.949397i
$809$		−	4.29916e8i		−	0.811967i	−0.913880	−	0.405984i	$-0.866929\pi$
$809$		−	4.29916e8i		−	0.811967i	0.913880	−	0.405984i	$-0.133071\pi$
$810$	3.96147e8	−	1.65825e7i	0.745421	−	0.0312028i
$811$	−2.17167e8			−0.407128			−0.203564	−	0.979062i	$-0.565252\pi$
$811$	−2.17167e8			−0.407128			−0.203564	+	0.979062i	$0.565252\pi$
$812$	−983107.	−	567597.i	−0.00183625	−	0.00106016i
$813$	572725.	+	5.47585e7i	0.00106580	+	0.101901i
$814$	−2.35676e8	−	4.08203e8i	−0.436960	−	0.756837i
$815$	3.91448e8	−	2.26002e8i	0.723104	−	0.417484i
$816$	−5.16160e7	+	9.16008e7i	−0.0949979	+	0.168589i
$817$	4.84519e7	−	8.39211e7i	0.0888473	−	0.153888i
$818$			4.13185e8i			0.754891i
$819$	−3.74742e8	+	7.83979e6i	−0.682151	+	0.0142709i
$820$	7.19489e6			0.0130492
$821$	9.93226e7	+	5.73439e7i	0.179481	+	0.103623i	0.587049	−	0.809552i	$-0.300290\pi$
$821$	9.93226e7	+	5.73439e7i	0.179481	+	0.103623i	−0.407568	+	0.913175i	$0.633623\pi$
$822$	1.04860e8	−	6.20124e7i	0.188797	−	0.111651i
$823$	−3.31550e8	−	5.74262e8i	−0.594771	−	1.03017i	−0.993579	−	0.113139i	$-0.963909\pi$
$823$	−3.31550e8	−	5.74262e8i	−0.594771	−	1.03017i	0.398808	−	0.917034i	$-0.369424\pi$
$824$	−4.90200e8	+	2.83017e8i	−0.876176	+	0.505861i
$825$	1.44875e8	+	2.44978e8i	0.258008	+	0.436280i
$826$	−8.97292e7	+	1.55416e8i	−0.159219	+	0.275775i
$827$			7.09882e7i			0.125508i	0.998029	+	0.0627538i	$0.0199883\pi$
$827$			7.09882e7i			0.125508i	−0.998029	+	0.0627538i	$0.980012\pi$
$828$	−4.06829e6	−	2.23670e6i	−0.00716673	−	0.00394019i
$829$	−9.23151e8			−1.62035			−0.810176	−	0.586187i	$-0.800629\pi$
$829$	−9.23151e8			−1.62035			−0.810176	+	0.586187i	$0.800629\pi$
$830$	−4.05839e8	−	2.34311e8i	−0.709774	−	0.409788i
$831$	−6.58713e8	−	3.71177e8i	−1.14787	−	0.646813i
$832$	−5.55211e8	−	9.61653e8i	−0.964024	−	1.66974i
$833$	−8.40910e7	+	4.85500e7i	−0.145484	+	0.0839951i
$834$	1.77771e8	−	1.85933e6i	0.306453	−	0.00320522i
$835$	−3.60152e8	+	6.23801e8i	−0.618623	+	1.07149i
$836$			8.88671e6i			0.0152098i
$837$	2.25874e8	−	1.40035e8i	0.385203	−	0.238815i
$838$	1.07559e8			0.182775
$839$	5.54532e8	+	3.20159e8i	0.938946	+	0.542101i	0.889630	−	0.456682i	$-0.150962\pi$
$839$	5.54532e8	+	3.20159e8i	0.938946	+	0.542101i	0.0493163	+	0.998783i	$0.484296\pi$
$840$	−1.60037e6	−	1.53012e8i	−0.00270012	−	0.258159i
$841$	−2.07419e8	−	3.59261e8i	−0.348707	−	0.603979i
$842$	7.64421e8	−	4.41339e8i	1.28055	−	0.739326i
$843$	4.61391e8	−	8.18812e8i	0.770170	−	1.36679i
$844$	−4.47125e6	+	7.74443e6i	−0.00743706	+	0.0128814i
$845$			1.25464e9i			2.07945i
$846$	−8.01097e7	−	1.32285e8i	−0.132304	−	0.218473i
$847$	5.77993e7			0.0951201
$848$	4.64864e7	+	2.68389e7i	0.0762321	+	0.0440126i
$849$	−7.19441e8	+	4.25463e8i	−1.17563	+	0.695247i
$850$	−2.65631e7	−	4.60086e7i	−0.0432535	−	0.0749173i
$851$	3.05371e8	−	1.76306e8i	0.495495	−	0.286074i
$852$	2.56252e6	+	4.33312e6i	0.00414333	+	0.00700619i
$853$	1.17026e8	−	2.02694e8i	0.188553	−	0.326584i	−0.756215	−	0.654323i	$-0.772954\pi$
$853$	1.17026e8	−	2.02694e8i	0.188553	−	0.326584i	0.944768	+	0.327740i	$0.106287\pi$
$854$		−	9.40432e7i		−	0.150992i
$855$	4.85653e8	−	2.94104e8i	0.777012	−	0.470547i
$856$	6.48197e8			1.03344
$857$	−7.81860e8	−	4.51407e8i	−1.24219	−	0.717177i	−0.272647	−	0.962114i	$-0.587899\pi$
$857$	−7.81860e8	−	4.51407e8i	−1.24219	−	0.717177i	−0.969539	+	0.244937i	$0.921233\pi$
$858$	1.21679e9	+	6.85647e8i	1.92643	+	1.08552i
$859$	3.87666e8	+	6.71458e8i	0.611616	+	1.05935i	0.990968	+	0.134097i	$0.0428135\pi$
$859$	3.87666e8	+	6.71458e8i	0.611616	+	1.05935i	−0.379352	+	0.925252i	$0.623853\pi$
$860$	−653541.	+	377322.i	−0.00102749	+	0.000593222i
$861$	3.56508e8	−	3.72875e6i	0.558547	−	0.00584190i
$862$	−2.55460e8	+	4.42470e8i	−0.398842	+	0.690815i
$863$			1.80225e6i			0.00280402i	0.999999	+	0.00140201i	$0.000446274\pi$
$863$			1.80225e6i			0.00280402i	−0.999999	+	0.00140201i	$0.999554\pi$
$864$	−7.48747e6	−	1.20771e7i	−0.0116090	−	0.0187250i
$865$	6.53217e8			1.00927
$866$	−1.01587e8	−	5.86513e7i	−0.156417	−	0.0903075i
$867$	6.56621e6	+	6.27799e8i	0.0100753	+	0.963303i
$868$	571245.	+	989426.i	0.000873501	+	0.00151295i
$869$	−1.12305e8	+	6.48391e7i	−0.171135	+	0.0988047i
$870$	1.32669e8	−	2.35443e8i	0.201471	−	0.357542i
$871$	−2.07068e8	+	3.58652e8i	−0.313371	+	0.542774i
$872$			9.57105e8i			1.44348i
$873$	−6.68367e7	+	1.21568e8i	−0.100455	+	0.182716i
$874$	−6.10119e8			−0.913861
$875$	2.18322e8	+	1.26049e8i	0.325892	+	0.188154i
$876$	2.52345e6	−	1.49232e6i	0.00375390	−	0.00221998i
$877$	1.32637e8	+	2.29734e8i	0.196637	+	0.340585i	0.947436	−	0.319945i	$-0.103665\pi$
$877$	1.32637e8	+	2.29734e8i	0.196637	+	0.340585i	−0.750799	+	0.660531i	$0.770331\pi$
$878$	−3.90208e8	+	2.25286e8i	−0.576517	+	0.332852i
$879$	−3.40156e8	−	5.75190e8i	−0.500854	−	0.846924i
$880$	−2.88234e8	+	4.99236e8i	−0.422958	+	0.732584i
$881$		−	1.59497e6i		−	0.00233251i	−0.999999	−	0.00116626i	$-0.999629\pi$
$881$		−	1.59497e6i		−	0.00233251i	0.999999	−	0.00116626i	$-0.000371231\pi$
$882$	−1.26632e7	−	6.05302e8i	−0.0184560	−	0.882199i
$883$	7.55655e8			1.09759			0.548796	−	0.835956i	$-0.315086\pi$
$883$	7.55655e8			1.09759			0.548796	+	0.835956i	$0.315086\pi$
$884$	−2.46014e6	−	1.42037e6i	−0.00356126	−	0.00205610i
$885$	−4.05562e8	−	2.28530e8i	−0.585097	−	0.329695i
$886$	−5.36718e7	−	9.29623e7i	−0.0771694	−	0.133661i
$887$	3.65191e8	−	2.10843e8i	0.523298	−	0.302127i	−0.214985	−	0.976617i	$-0.568970\pi$
$887$	3.65191e8	−	2.10843e8i	0.523298	−	0.302127i	0.738283	+	0.674491i	$0.235637\pi$
$888$	5.36609e8	−	5.61245e6i	0.766336	−	0.00801519i
$889$	1.70734e8	−	2.95720e8i	0.243004	−	0.420896i
$890$		−	6.52359e8i		−	0.925373i
$891$	−7.06924e8	−	3.69619e8i	−0.999401	−	0.522541i
$892$	9.31032e6			0.0131181
$893$	−1.91785e8	−	1.10727e8i	−0.269314	−	0.155489i
$894$	6.44735e6	+	6.16435e8i	0.00902337	+	0.862729i
$895$	−1.63330e7	−	2.82895e7i	−0.0227822	−	0.0394599i
$896$	−2.21502e8	+	1.27884e8i	−0.307931	+	0.177784i
$897$	−5.12924e8	+	9.10264e8i	−0.710682	+	1.26122i
$898$	3.77220e8	−	6.53364e8i	0.520913	−	0.902248i
$899$		−	1.81142e8i		−	0.249310i
$900$	3.60862e6	−	75494.0i	0.00495009	−	0.000103558i
$901$	−1.21921e7			−0.0166687
$902$	−1.15051e9	−	6.64247e8i	−1.56773	−	0.905127i
$903$	−3.21875e7	+	1.90351e7i	−0.0437144	+	0.0258518i
$904$	3.56087e8	+	6.16761e8i	0.482005	+	0.834857i
$905$	−4.04239e7	+	2.33388e7i	−0.0545372	+	0.0314870i
$906$	1.94925e8	+	3.29611e8i	0.262110	+	0.443217i
$907$	5.00053e8	−	8.66117e8i	0.670184	−	1.16079i	−0.307668	−	0.951494i	$-0.599549\pi$
$907$	5.00053e8	−	8.66117e8i	0.670184	−	1.16079i	0.977852	−	0.209299i	$-0.0671180\pi$
$908$		−	1.12049e7i		−	0.0149675i
$909$	−7.25589e8	−	3.98921e8i	−0.966048	−	0.531123i
$910$	3.83603e8			0.509046
$911$	−1.24689e8	−	7.19891e7i	−0.164920	−	0.0952164i	0.415268	−	0.909699i	$-0.363688\pi$
$911$	−1.24689e8	−	7.19891e7i	−0.164920	−	0.0952164i	−0.580188	+	0.814482i	$0.697021\pi$
$912$	−8.17860e8	−	4.60855e8i	−1.07819	−	0.607547i
$913$	4.71420e8	+	8.16523e8i	0.619435	+	1.07289i
$914$	8.03582e8	−	4.63948e8i	1.05243	−	0.607618i
$915$	2.43936e8	−	2.55135e6i	0.318429	−	0.00333048i
$916$	−1.10862e6	+	1.92019e6i	−0.00144244	+	0.00249837i
$917$		−	1.72229e8i		−	0.223357i
$918$	1.31227e8	+	7.03703e7i	0.169628	+	0.0909623i
$919$	−1.25483e9			−1.61673			−0.808365	−	0.588682i	$-0.799647\pi$
$919$	−1.25483e9			−1.61673			−0.808365	+	0.588682i	$0.799647\pi$
$920$	−3.69402e8	−	2.13274e8i	−0.474390	−	0.273889i
$921$	−5.36985e6	−	5.13414e8i	−0.00687358	−	0.657187i
$922$	7.46787e7	+	1.29347e8i	0.0952805	+	0.165031i
$923$	9.81158e8	−	5.66472e8i	1.24777	−	0.720399i
$924$	1.68352e6	−	2.98768e6i	0.00213404	−	0.00378720i
$925$	−1.37069e8	+	2.37411e8i	−0.173187	+	0.299969i
$926$		−	5.68164e8i		−	0.715551i
$927$	4.19822e8	+	6.93250e8i	0.527019	+	0.870264i
$928$	−9.68535e6			−0.0121191
$929$	−3.98994e7	−	2.30359e7i	−0.0497644	−	0.0287315i	0.474911	−	0.880034i	$-0.342480\pi$
$929$	−3.98994e7	−	2.30359e7i	−0.0497644	−	0.0287315i	−0.524676	+	0.851302i	$0.675813\pi$
$930$	−2.34111e8	+	1.38449e8i	−0.291054	+	0.172124i
$931$	−4.33480e8	−	7.50809e8i	−0.537180	−	0.930423i
$932$	−4.24608e6	+	2.45148e6i	−0.00524494	+	0.00302817i
$933$	3.96162e8	+	6.69893e8i	0.487784	+	0.824823i
$934$	−3.27160e8	+	5.66658e8i	−0.401532	+	0.695474i
$935$		−	1.30935e8i		−	0.160185i
$936$	−1.36016e9	+	8.23690e8i	−1.65867	+	1.00447i
$937$	5.55499e8			0.675250			0.337625	−	0.941281i	$-0.390376\pi$
$937$	5.55499e8			0.675250			0.337625	+	0.941281i	$0.390376\pi$
$938$	8.08190e7	+	4.66608e7i	0.0979275	+	0.0565385i
$939$	1.13053e9	+	6.37041e8i	1.36548	+	0.769433i
$940$	862293.	+	1.49354e6i	0.00103818	+	0.00179818i
$941$	−7.36911e8	+	4.25456e8i	−0.884394	+	0.510605i	−0.872105	−	0.489319i	$-0.837245\pi$
$941$	−7.36911e8	+	4.25456e8i	−0.884394	+	0.510605i	−0.0122896	+	0.999924i	$0.503912\pi$
$942$	−9.35498e7	+	978447.i	−0.111915	+	0.00117054i
$943$	4.96914e8	−	8.60681e8i	0.592579	−	1.02638i
$944$			7.69708e8i			0.914976i
$945$	−2.18990e8	+	6.87334e6i	−0.259496	+	0.00814465i
$946$	1.39341e8			0.164590
$947$	1.09931e9	+	6.34686e8i	1.29440	+	0.747325i	0.979432	−	0.201776i	$-0.0646713\pi$
$947$	1.09931e9	+	6.34686e8i	1.29440	+	0.747325i	0.314973	+	0.949101i	$0.398005\pi$
$948$	17199.8	+	1.64448e6i	2.01882e−5	+	0.00193020i
$949$	−3.29892e8	−	5.71390e8i	−0.385988	−	0.668550i
$950$	4.10789e8	−	2.37169e8i	0.479124	−	0.276622i
$951$	4.70602e7	−	8.35158e7i	0.0547157	−	0.0971017i
$952$	2.87337e7	−	4.97682e7i	0.0333028	−	0.0576821i
$953$		−	1.54351e9i		−	1.78333i	−0.452694	−	0.891666i	$-0.649537\pi$
$953$		−	1.54351e9i		−	1.78333i	0.452694	−	0.891666i	$-0.350463\pi$
$954$	3.66245e7	−	6.66155e7i	0.0421819	−	0.0767238i
$955$	−5.90761e8			−0.678268
$956$	1.65890e6	+	957764.i	0.00189865	+	0.00109619i
$957$	−4.68009e8	+	2.76771e8i	−0.533972	+	0.315781i
$958$	4.51636e8	+	7.82257e8i	0.513680	+	0.889720i
$959$	−5.82999e7	+	3.36595e7i	−0.0661016	+	0.0381638i
$960$	−3.30402e8	−	5.58696e8i	−0.373447	−	0.631484i
$961$	3.52599e8	−	6.10719e8i	0.397293	−	0.688131i
$962$			1.34528e9i			1.51108i
$963$	−1.94121e7	−	9.27901e8i	−0.0217367	−	1.03902i
$964$	1.91114e6			0.00213335
$965$	−2.16965e8	−	1.25265e8i	−0.241439	−	0.139395i
$966$	2.05120e8	+	1.15583e8i	0.227549	+	0.128221i
$967$	5.94735e8	+	1.03011e9i	0.657724	+	1.13921i	0.981203	+	0.192977i	$0.0618142\pi$
$967$	5.94735e8	+	1.03011e9i	0.657724	+	1.13921i	−0.323479	+	0.946235i	$0.604852\pi$
$968$	2.12352e8	−	1.22601e8i	0.234115	−	0.135167i
$969$	2.13214e8	−	2.23003e6i	0.234339	−	0.00245098i
$970$	7.09893e7	−	1.22957e8i	0.0777818	−	0.134722i
$971$			8.11000e8i			0.885856i	0.896557	+	0.442928i	$0.146060\pi$
$971$			8.11000e8i			0.885856i	−0.896557	+	0.442928i	$0.853940\pi$
$972$	−8.48489e6	+	5.50935e6i	−0.00923947	+	0.00599931i
$973$	−9.82399e7			−0.106647
$974$	8.19952e8	+	4.73400e8i	0.887384	+	0.512331i
$975$	−8.49552e6	−	8.12261e8i	−0.00916592	−	0.876359i
$976$	−2.01678e8	−	3.49317e8i	−0.216925	−	0.375725i
$977$	−1.17951e9	+	6.80992e8i	−1.26479	+	0.730228i	−0.973998	−	0.226558i	$-0.927253\pi$
$977$	−1.17951e9	+	6.80992e8i	−1.26479	+	0.730228i	−0.290794	+	0.956786i	$0.593919\pi$
$978$	−5.19601e8	+	9.22114e8i	−0.555460	+	0.985753i
$979$	−6.56253e8	+	1.13666e9i	−0.699396	+	1.21139i
$980$			6.75151e6i			0.00717336i
$981$	1.37011e9	−	2.86633e7i	1.45127	−	0.0303612i
$982$	−1.09227e9			−1.15344
$983$	−1.09347e8	−	6.31316e7i	−0.115119	−	0.0664640i	0.441335	−	0.897342i	$-0.354505\pi$
$983$	−1.09347e8	−	6.31316e7i	−0.115119	−	0.0664640i	−0.556454	+	0.830878i	$0.687838\pi$
$984$	1.30188e9	−	7.69909e8i	1.36643	−	0.808079i
$985$	−2.66269e8	−	4.61191e8i	−0.278620	−	0.482584i
$986$	8.78953e7	−	5.07464e7i	0.0916928	−	0.0529388i
$987$	4.35008e7	+	7.35581e7i	0.0452424	+	0.0765031i
$988$	1.26818e7	−	2.19655e7i	0.0131495	−	0.0227756i
$989$			1.04239e8i			0.107756i
$990$	7.15410e8	+	3.93325e8i	0.737309	+	0.405365i
$991$	−1.97170e8			−0.202590			−0.101295	−	0.994856i	$-0.532299\pi$
$991$	−1.97170e8			−0.202590			−0.101295	+	0.994856i	$0.532299\pi$
$992$	8.44167e6	+	4.87380e6i	0.00864756	+	0.00499267i
$993$	2.12627e8	+	1.19813e8i	0.217155	+	0.122365i
$994$	−1.27649e8	−	2.21095e8i	−0.129975	−	0.225123i
$995$	−6.04627e8	+	3.49082e8i	−0.613788	+	0.354371i
$996$	1.19564e7	−	125053.i	0.0121010	−	0.000126566i
$997$	−4.53174e7	+	7.84920e7i	−0.0457277	+	0.0792026i	−0.887983	−	0.459876i	$-0.847894\pi$
$997$	−4.53174e7	+	7.84920e7i	−0.0457277	+	0.0792026i	0.842256	+	0.539078i	$0.181227\pi$
$998$		−	3.87665e8i		−	0.390000i
$999$	−2.41046e7	−	7.67993e8i	−0.0241770	−	0.770302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.7.d.a.2.4	✓	10
3.2	odd	2		27.7.d.a.8.2		10
4.3	odd	2		144.7.q.a.65.4		10
9.2	odd	6		81.7.b.a.80.8		10
9.4	even	3		27.7.d.a.17.2		10
9.5	odd	6	inner	9.7.d.a.5.4	yes	10
9.7	even	3		81.7.b.a.80.3		10
12.11	even	2		432.7.q.a.305.2		10
36.23	even	6		144.7.q.a.113.4		10
36.31	odd	6		432.7.q.a.17.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.4	✓	10	1.1	even	1	trivial
9.7.d.a.5.4	yes	10	9.5	odd	6	inner
27.7.d.a.8.2		10	3.2	odd	2
27.7.d.a.17.2		10	9.4	even	3
81.7.b.a.80.3		10	9.7	even	3
81.7.b.a.80.8		10	9.2	odd	6
144.7.q.a.65.4		10	4.3	odd	2
144.7.q.a.113.4		10	36.23	even	6
432.7.q.a.17.2		10	36.31	odd	6
432.7.q.a.305.2		10	12.11	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.96626 + 4.02197i) q^{2} +(0.282380 + 26.9985i) q^{3} +(0.352523 + 0.610587i) q^{4} +(80.3236 - 46.3749i) q^{5} +(-106.620 + 189.214i) q^{6} +(60.0074 - 103.936i) q^{7} -509.141i q^{8} +(-728.841 + 15.2477i) q^{9} +O(q^{10})\)	\(q+(6.96626 + 4.02197i) q^{2} +(0.282380 + 26.9985i) q^{3} +(0.352523 + 0.610587i) q^{4} +(80.3236 - 46.3749i) q^{5} +(-106.620 + 189.214i) q^{6} +(60.0074 - 103.936i) q^{7} -509.141i q^{8} +(-728.841 + 15.2477i) q^{9} +746.074 q^{10} +(-1299.95 - 750.527i) q^{11} +(-16.3854 + 9.69001i) q^{12} +(2142.08 + 3710.18i) q^{13} +(836.055 - 482.697i) q^{14} +(1274.73 + 2155.52i) q^{15} +(2070.31 - 3585.89i) q^{16} +940.477i q^{17} +(-5138.62 - 2825.16i) q^{18} -8397.07 q^{19} +(56.6318 + 32.6964i) q^{20} +(2823.06 + 1590.76i) q^{21} +(-6037.20 - 10456.7i) q^{22} +(7822.55 - 4516.35i) q^{23} +(13746.1 - 143.771i) q^{24} +(-3511.24 + 6081.65i) q^{25} +34461.5i q^{26} +(-617.476 - 19673.3i) q^{27} +84.6160 q^{28} +(-11618.5 - 6707.92i) q^{29} +(210.677 + 20142.9i) q^{30} +(6751.04 + 11693.1i) q^{31} +(625.213 - 360.967i) q^{32} +(19896.0 - 35308.7i) q^{33} +(-3782.57 + 6551.61i) q^{34} -11131.3i q^{35} +(-266.243 - 439.646i) q^{36} +39037.3 q^{37} +(-58496.2 - 33772.8i) q^{38} +(-99564.6 + 58880.5i) q^{39} +(-23611.4 - 40896.1i) q^{40} +(95285.0 - 55012.8i) q^{41} +(13268.2 + 22435.9i) q^{42} +(-5770.09 + 9994.09i) q^{43} -1058.31i q^{44} +(-57836.0 + 35024.6i) q^{45} +72658.5 q^{46} +(22839.5 + 13186.4i) q^{47} +(97398.3 + 54882.8i) q^{48} +(51622.7 + 89413.2i) q^{49} +(-48920.5 + 28244.2i) q^{50} +(-25391.5 + 265.572i) q^{51} +(-1510.26 + 2615.85i) q^{52} +12963.7i q^{53} +(74824.0 - 139533. i) q^{54} -139222. q^{55} +(-52918.1 - 30552.3i) q^{56} +(-2371.17 - 226709. i) q^{57} +(-53958.1 - 93458.2i) q^{58} +(-160987. + 92945.8i) q^{59} +(-866.763 + 1538.21i) q^{60} +(48707.2 - 84363.3i) q^{61} +108610. i q^{62} +(-42151.1 + 76667.7i) q^{63} -259193. q^{64} +(344118. + 198677. i) q^{65} +(280611. - 165948. i) q^{66} +(48333.5 + 83716.1i) q^{67} +(-574.243 + 331.540i) q^{68} +(124144. + 209922. i) q^{69} +(44770.0 - 77543.9i) q^{70} -264450. i q^{71} +(7763.23 + 371083. i) q^{72} -154006. q^{73} +(271944. + 157007. i) q^{74} +(-165187. - 93081.1i) q^{75} +(-2960.16 - 5127.15i) q^{76} +(-156013. + 90074.4i) q^{77} +(-930409. + 9731.24i) q^{78} +(43195.7 - 74817.2i) q^{79} -384042. i q^{80} +(530976. - 22226.3i) q^{81} +885040. q^{82} +(-543967. - 314059. i) q^{83} +(23.8939 + 2284.51i) q^{84} +(43614.5 + 75542.5i) q^{85} +(-80391.9 + 46414.3i) q^{86} +(177823. - 315575. i) q^{87} +(-382124. + 661858. i) q^{88} -874390. i q^{89} +(-543769. + 11375.9i) q^{90} +514162. q^{91} +(5515.25 + 3184.23i) q^{92} +(-313791. + 185570. i) q^{93} +(106070. + 183719. i) q^{94} +(-674483. + 389413. i) q^{95} +(9922.12 + 16777.9i) q^{96} +(95150.6 - 164806. i) q^{97} +830500. i q^{98} +(958900. + 527193. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9	\( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} - 132 q^{10} + 483 q^{11} - 1830 q^{12} - 841 q^{13} + 12174 q^{14} + 7965 q^{15} - 1985 q^{16} - 7884 q^{18} + 6176 q^{19} - 63186 q^{20} - 25845 q^{21} + 3471 q^{22} + 53565 q^{23} + 111519 q^{24} + 8452 q^{25} - 101034 q^{27} - 22660 q^{28} - 80679 q^{29} - 37782 q^{30} - 24601 q^{31} + 218295 q^{32} + 229995 q^{33} + 7425 q^{34} - 274977 q^{36} + 12764 q^{37} - 371877 q^{38} - 112749 q^{39} + 54150 q^{40} + 232251 q^{41} + 270540 q^{42} - 93271 q^{43} + 63801 q^{45} + 112512 q^{46} - 142887 q^{47} - 143283 q^{48} + 86238 q^{49} + 318459 q^{50} + 57078 q^{51} + 186920 q^{52} + 13851 q^{54} - 419982 q^{55} + 342546 q^{56} - 1086 q^{57} - 380658 q^{58} - 995061 q^{59} - 1011402 q^{60} - 59305 q^{61} + 526455 q^{63} + 403066 q^{64} + 1642029 q^{65} + 1610586 q^{66} + 158513 q^{67} - 1693791 q^{68} - 851715 q^{69} - 304788 q^{70} + 1469907 q^{72} + 933896 q^{73} + 595182 q^{74} - 757524 q^{75} + 666641 q^{76} - 2198883 q^{77} - 3481884 q^{78} + 468707 q^{79} + 1774548 q^{81} - 2038470 q^{82} + 3008337 q^{83} + 1543746 q^{84} - 1189944 q^{85} + 1905549 q^{86} - 615591 q^{87} - 349773 q^{88} + 84294 q^{90} - 211778 q^{91} - 973788 q^{92} - 2954553 q^{93} + 809124 q^{94} - 2562954 q^{95} - 1022112 q^{96} + 336029 q^{97} - 432567 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9 - 132 * q^10 + 483 * q^11 - 1830 * q^12 - 841 * q^13 + 12174 * q^14 + 7965 * q^15 - 1985 * q^16 - 7884 * q^18 + 6176 * q^19 - 63186 * q^20 - 25845 * q^21 + 3471 * q^22 + 53565 * q^23 + 111519 * q^24 + 8452 * q^25 - 101034 * q^27 - 22660 * q^28 - 80679 * q^29 - 37782 * q^30 - 24601 * q^31 + 218295 * q^32 + 229995 * q^33 + 7425 * q^34 - 274977 * q^36 + 12764 * q^37 - 371877 * q^38 - 112749 * q^39 + 54150 * q^40 + 232251 * q^41 + 270540 * q^42 - 93271 * q^43 + 63801 * q^45 + 112512 * q^46 - 142887 * q^47 - 143283 * q^48 + 86238 * q^49 + 318459 * q^50 + 57078 * q^51 + 186920 * q^52 + 13851 * q^54 - 419982 * q^55 + 342546 * q^56 - 1086 * q^57 - 380658 * q^58 - 995061 * q^59 - 1011402 * q^60 - 59305 * q^61 + 526455 * q^63 + 403066 * q^64 + 1642029 * q^65 + 1610586 * q^66 + 158513 * q^67 - 1693791 * q^68 - 851715 * q^69 - 304788 * q^70 + 1469907 * q^72 + 933896 * q^73 + 595182 * q^74 - 757524 * q^75 + 666641 * q^76 - 2198883 * q^77 - 3481884 * q^78 + 468707 * q^79 + 1774548 * q^81 - 2038470 * q^82 + 3008337 * q^83 + 1543746 * q^84 - 1189944 * q^85 + 1905549 * q^86 - 615591 * q^87 - 349773 * q^88 + 84294 * q^90 - 211778 * q^91 - 973788 * q^92 - 2954553 * q^93 + 809124 * q^94 - 2562954 * q^95 - 1022112 * q^96 + 336029 * q^97 - 432567 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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