LMFDB - Embedded newform 11.7.d.a.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,7,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

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("11.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, 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:	$2.53059491982$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			6.3
Root			$-0.868969i$ of defining polynomial
Character	$\chi$	$=$	11.6
Dual form			11.7.d.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.291595 - 0.0947451i) q^{2} +(-33.5534 - 24.3780i) q^{3} +(-51.7010 + 37.5630i) q^{4} +(29.6861 - 91.3645i) q^{5} +(-12.0937 - 3.92948i) q^{6} +(-91.4937 - 125.930i) q^{7} +(-23.0507 + 31.7266i) q^{8} +(306.271 + 942.605i) q^{9} +O(q^{10})$	\(q+(0.291595 - 0.0947451i) q^{2} +(-33.5534 - 24.3780i) q^{3} +(-51.7010 + 37.5630i) q^{4} +(29.6861 - 91.3645i) q^{5} +(-12.0937 - 3.92948i) q^{6} +(-91.4937 - 125.930i) q^{7} +(-23.0507 + 31.7266i) q^{8} +(306.271 + 942.605i) q^{9} -29.4541i q^{10} +(941.710 - 940.608i) q^{11} +2650.45 q^{12} +(-2700.81 + 877.547i) q^{13} +(-38.6104 - 28.0521i) q^{14} +(-3223.35 + 2341.90i) q^{15} +(1260.16 - 3878.37i) q^{16} +(-6339.53 - 2059.84i) q^{17} +(178.614 + 245.842i) q^{18} +(4994.15 - 6873.86i) q^{19} +(1897.12 + 5838.74i) q^{20} +6455.82i q^{21} +(185.480 - 363.499i) q^{22} -2379.19 q^{23} +(1546.86 - 502.604i) q^{24} +(5174.68 + 3759.63i) q^{25} +(-704.401 + 511.777i) q^{26} +(3359.32 - 10338.9i) q^{27} +(9460.64 + 3073.95i) q^{28} +(24050.1 + 33102.1i) q^{29} +(-718.031 + 988.284i) q^{30} +(-14101.5 - 43399.9i) q^{31} -3760.14i q^{32} +(-54527.7 + 8603.59i) q^{33} -2043.74 q^{34} +(-14221.7 + 4620.90i) q^{35} +(-51241.6 - 37229.2i) q^{36} +(-115.988 + 84.2706i) q^{37} +(805.008 - 2477.56i) q^{38} +(112014. + 36395.6i) q^{39} +(2214.40 + 3047.85i) q^{40} +(958.842 - 1319.73i) q^{41} +(611.657 + 1882.49i) q^{42} -53698.0i q^{43} +(-13355.4 + 84003.9i) q^{44} +95212.7 q^{45} +(-693.761 + 225.417i) q^{46} +(-35134.9 - 25527.0i) q^{47} +(-136829. + 99412.3i) q^{48} +(28868.2 - 88847.2i) q^{49} +(1865.12 + 606.014i) q^{50} +(162498. + 223659. i) q^{51} +(106671. - 146821. i) q^{52} +(-27885.3 - 85822.2i) q^{53} -3333.06i q^{54} +(-57982.4 - 113962. i) q^{55} +6104.33 q^{56} +(-335142. + 108894. i) q^{57} +(10149.1 + 7373.79i) q^{58} +(-97523.6 + 70855.0i) q^{59} +(78681.7 - 242157. i) q^{60} +(-246917. - 80228.2i) q^{61} +(-8223.85 - 11319.2i) q^{62} +(90680.7 - 124811. i) q^{63} +(80293.9 + 247119. i) q^{64} +272809. i q^{65} +(-15084.9 + 7674.99i) q^{66} +163882. q^{67} +(405134. - 131636. i) q^{68} +(79829.9 + 57999.8i) q^{69} +(-3709.16 + 2694.86i) q^{70} +(50757.5 - 156215. i) q^{71} +(-36965.4 - 12010.8i) q^{72} +(161041. + 221654. i) q^{73} +(-25.8375 + 35.5623i) q^{74} +(-81976.0 - 252296. i) q^{75} +542981. i q^{76} +(-204612. - 32530.2i) q^{77} +36111.1 q^{78} +(-309907. + 100695. i) q^{79} +(-316936. - 230268. i) q^{80} +(219775. - 159676. i) q^{81} +(154.556 - 475.674i) q^{82} +(603906. + 196221. i) q^{83} +(-242500. - 333772. i) q^{84} +(-376392. + 518060. i) q^{85} +(-5087.62 - 15658.1i) q^{86} -1.69698e6i q^{87} +(8135.16 + 51558.9i) q^{88} -578895. q^{89} +(27763.6 - 9020.93i) q^{90} +(357617. + 259824. i) q^{91} +(123007. - 89369.6i) q^{92} +(-584848. + 1.79998e6i) q^{93} +(-12663.7 - 4114.69i) q^{94} +(-479770. - 660347. i) q^{95} +(-91664.6 + 126166. i) q^{96} +(-96430.6 - 296783. i) q^{97} -28642.6i q^{98} +(1.17504e6 + 599580. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.291595	−	0.0947451i	0.0364494	−	0.0118431i	−0.290736	−	0.956803i	$-0.593900\pi$
$2$	0.291595	−	0.0947451i	0.0364494	−	0.0118431i	0.327185	+	0.944960i	$0.393900\pi$
$3$	−33.5534	−	24.3780i	−1.24272	−	0.902887i	−0.244941	−	0.969538i	$-0.578769\pi$
$3$	−33.5534	−	24.3780i	−1.24272	−	0.902887i	−0.997776	+	0.0666507i	$0.978769\pi$
$4$	−51.7010	+	37.5630i	−0.807829	+	0.586922i
$5$	29.6861	−	91.3645i	0.237489	−	0.730916i	−0.759292	−	0.650750i	$-0.774455\pi$
$5$	29.6861	−	91.3645i	0.237489	−	0.730916i	0.996781	−	0.0801666i	$-0.0255452\pi$
$6$	−12.0937	−	3.92948i	−0.0559894	−	0.0181920i
$7$	−91.4937	−	125.930i	−0.266746	−	0.367144i	0.654542	−	0.756026i	$-0.272861\pi$
$7$	−91.4937	−	125.930i	−0.266746	−	0.367144i	−0.921288	+	0.388882i	$0.872861\pi$
$8$	−23.0507	+	31.7266i	−0.0450209	+	0.0619659i
$9$	306.271	+	942.605i	0.420125	+	1.29301i
$10$		−	29.4541i		−	0.0294541i
$11$	941.710	−	940.608i	0.707521	−	0.706692i
$11$	941.710	−	940.608i	0.707521	−	0.706692i
$12$	2650.45			1.53383
$13$	−2700.81	+	877.547i	−1.22932	+	0.399430i	−0.850467	−	0.526028i	$-0.823681\pi$
$13$	−2700.81	+	877.547i	−1.22932	+	0.399430i	−0.378851	+	0.925458i	$0.623681\pi$
$14$	−38.6104	−	28.0521i	−0.0140709	−	0.0102231i
$15$	−3223.35	+	2341.90i	−0.955067	+	0.693897i
$16$	1260.16	−	3878.37i	0.307656	−	0.946868i
$17$	−6339.53	−	2059.84i	−1.29036	−	0.419263i	−0.418141	−	0.908382i	$-0.637318\pi$
$17$	−6339.53	−	2059.84i	−1.29036	−	0.419263i	−0.872217	+	0.489119i	$0.837318\pi$
$18$	178.614	+	245.842i	0.0306266	+	0.0421539i
$19$	4994.15	−	6873.86i	0.728117	−	1.00217i	−0.271098	−	0.962552i	$-0.587387\pi$
$19$	4994.15	−	6873.86i	0.728117	−	1.00217i	0.999215	−	0.0396154i	$-0.0126133\pi$
$20$	1897.12	+	5838.74i	0.237140	+	0.729843i
$21$			6455.82i			0.697097i
$22$	185.480	−	363.499i	0.0174193	−	0.0341378i
$23$	−2379.19			−0.195545			−0.0977723	−	0.995209i	$-0.531172\pi$
$23$	−2379.19			−0.195545			−0.0977723	+	0.995209i	$0.531172\pi$
$24$	1546.86	−	502.604i	0.111896	−	0.0363574i
$25$	5174.68	+	3759.63i	0.331180	+	0.240616i
$26$	−704.401	+	511.777i	−0.0400774	+	0.0291180i
$27$	3359.32	−	10338.9i	0.170671	−	0.525271i
$28$	9460.64	+	3073.95i	0.430969	+	0.140030i
$29$	24050.1	+	33102.1i	0.986103	+	1.35725i	0.933476	+	0.358640i	$0.116759\pi$
$29$	24050.1	+	33102.1i	0.986103	+	1.35725i	0.0526272	+	0.998614i	$0.483241\pi$
$30$	−718.031	+	988.284i	−0.0265937	+	0.0366031i
$31$	−14101.5	−	43399.9i	−0.473347	−	1.45681i	−0.848174	−	0.529717i	$-0.822298\pi$
$31$	−14101.5	−	43399.9i	−0.473347	−	1.45681i	0.374828	−	0.927095i	$-0.377702\pi$
$32$		−	3760.14i		−	0.114751i
$33$	−54527.7	+	8603.59i	−1.51731	+	0.239408i
$34$	−2043.74			−0.0519982
$35$	−14221.7	+	4620.90i	−0.331700	+	0.107776i
$36$	−51241.6	−	37229.2i	−1.09829	−	0.797951i
$37$	−115.988	+	84.2706i	−0.00228986	+	0.00166368i	−0.588930	−	0.808184i	$-0.700450\pi$
$37$	−115.988	+	84.2706i	−0.00228986	+	0.00166368i	0.586640	+	0.809848i	$0.300450\pi$
$38$	805.008	−	2477.56i	0.0146706	−	0.0451516i
$39$	112014.	+	36395.6i	1.88833	+	0.613557i
$40$	2214.40	+	3047.85i	0.0345999	+	0.0476227i
$41$	958.842	−	1319.73i	0.0139122	−	0.0191485i	−0.802004	−	0.597318i	$-0.796233\pi$
$41$	958.842	−	1319.73i	0.0139122	−	0.0191485i	0.815916	+	0.578170i	$0.196233\pi$
$42$	611.657	+	1882.49i	0.00825582	+	0.0254088i
$43$		−	53698.0i		−	0.675387i	−0.941256	−	0.337693i	$-0.890353\pi$
$43$		−	53698.0i		−	0.675387i	0.941256	−	0.337693i	$-0.109647\pi$
$44$	−13355.4	+	84003.9i	−0.156782	+	0.986146i
$45$	95212.7			1.04486
$46$	−693.761	+	225.417i	−0.00712749	+	0.00231586i
$47$	−35134.9	−	25527.0i	−0.338411	−	0.245870i	0.405580	−	0.914060i	$-0.367070\pi$
$47$	−35134.9	−	25527.0i	−0.338411	−	0.245870i	−0.743991	+	0.668189i	$0.767070\pi$
$48$	−136829.	+	99412.3i	−1.23724	+	0.898911i
$49$	28868.2	−	88847.2i	0.245376	−	0.755189i
$50$	1865.12	+	606.014i	0.0149210	+	0.00484811i
$51$	162498.	+	223659.i	1.22500	+	1.68607i
$52$	106671.	−	146821.i	0.758644	−	1.04418i
$53$	−27885.3	−	85822.2i	−0.187305	−	0.576464i	0.812676	−	0.582716i	$-0.198010\pi$
$53$	−27885.3	−	85822.2i	−0.187305	−	0.576464i	−0.999980	+	0.00625184i	$0.998010\pi$
$54$		−	3333.06i		−	0.0211671i
$55$	−57982.4	−	113962.i	−0.348504	−	0.684970i
$56$	6104.33			0.0347595
$57$	−335142.	+	108894.i	−1.80969	+	0.588003i
$58$	10149.1	+	7373.79i	0.0520170	+	0.0377926i
$59$	−97523.6	+	70855.0i	−0.474847	+	0.344997i	−0.799327	−	0.600896i	$-0.794811\pi$
$59$	−97523.6	+	70855.0i	−0.474847	+	0.344997i	0.324480	+	0.945892i	$0.394811\pi$
$60$	78681.7	−	242157.i	0.364267	−	1.12110i
$61$	−246917.	−	80228.2i	−1.08783	−	0.353458i	−0.290423	−	0.956898i	$-0.593796\pi$
$61$	−246917.	−	80228.2i	−1.08783	−	0.353458i	−0.797408	+	0.603440i	$0.793796\pi$
$62$	−8223.85	−	11319.2i	−0.0345064	−	0.0474940i
$63$	90680.7	−	124811.i	0.362655	−	0.499151i
$64$	80293.9	+	247119.i	0.306297	+	0.942685i
$65$			272809.i			0.993388i
$66$	−15084.9	+	7674.99i	−0.0524698	+	0.0266960i
$67$	163882.			0.544886			0.272443	−	0.962172i	$-0.412168\pi$
$67$	163882.			0.544886			0.272443	+	0.962172i	$0.412168\pi$
$68$	405134.	−	131636.i	1.28846	−	0.418647i
$69$	79829.9	+	57999.8i	0.243007	+	0.176555i
$70$	−3709.16	+	2694.86i	−0.0108139	+	0.00785675i
$71$	50757.5	−	156215.i	0.141816	−	0.436464i	−0.854772	−	0.519004i	$-0.826303\pi$
$71$	50757.5	−	156215.i	0.141816	−	0.436464i	0.996588	+	0.0825395i	$0.0263030\pi$
$72$	−36965.4	−	12010.8i	−0.0990370	−	0.0321791i
$73$	161041.	+	221654.i	0.413969	+	0.569779i	0.964181	−	0.265246i	$-0.0854532\pi$
$73$	161041.	+	221654.i	0.413969	+	0.569779i	−0.550212	+	0.835025i	$0.685453\pi$
$74$	−25.8375	+	35.5623i	−6.37610e−5	+	8.77595e-5i
$75$	−81976.0	−	252296.i	−0.194314	−	0.598036i
$76$			542981.i			1.23693i
$77$	−204612.	−	32530.2i	−0.448186	−	0.0712548i
$78$	36111.1			0.0760952
$79$	−309907.	+	100695.i	−0.628565	+	0.204233i	−0.605939	−	0.795511i	$-0.707203\pi$
$79$	−309907.	+	100695.i	−0.628565	+	0.204233i	−0.0226258	+	0.999744i	$0.507203\pi$
$80$	−316936.	−	230268.i	−0.619016	−	0.449741i
$81$	219775.	−	159676.i	0.413545	−	0.300458i
$82$	154.556	−	475.674i	0.000280313	−	0.000862715i
$83$	603906.	+	196221.i	1.05617	+	0.343172i	0.785088	−	0.619384i	$-0.212617\pi$
$83$	603906.	+	196221.i	1.05617	+	0.343172i	0.271085	+	0.962555i	$0.412617\pi$
$84$	−242500.	−	333772.i	−0.409142	−	0.563135i
$85$	−376392.	+	518060.i	−0.612892	+	0.843573i
$86$	−5087.62	−	15658.1i	−0.00799870	−	0.0246175i
$87$		−	1.69698e6i		−	2.57702i
$88$	8135.16	+	51558.9i	0.0119376	+	0.0756581i
$89$	−578895.			−0.821163			−0.410582	−	0.911824i	$-0.634674\pi$
$89$	−578895.			−0.821163			−0.410582	+	0.911824i	$0.634674\pi$
$90$	27763.6	−	9020.93i	0.0380845	−	0.0123744i
$91$	357617.	+	259824.i	0.474563	+	0.344790i
$92$	123007.	−	89369.6i	0.157967	−	0.114769i
$93$	−584848.	+	1.79998e6i	−0.727100	+	2.23778i
$94$	−12663.7	−	4114.69i	−0.0152468	−	0.00495398i
$95$	−479770.	−	660347.i	−0.559580	−	0.770196i
$96$	−91664.6	+	126166.i	−0.103607	+	0.142602i
$97$	−96430.6	−	296783.i	−0.105657	−	0.325180i	0.884227	−	0.467058i	$-0.154686\pi$
$97$	−96430.6	−	296783.i	−0.105657	−	0.325180i	−0.989884	+	0.141878i	$0.954686\pi$
$98$		−	28642.6i		−	0.0304322i
$99$	1.17504e6	+	599580.i	1.21101	+	0.617934i
$100$	−408759.			−0.408759
$101$	1.43910e6	−	467593.i	1.39678	−	0.453842i	0.488632	−	0.872490i	$-0.337496\pi$
$101$	1.43910e6	−	467593.i	1.39678	−	0.453842i	0.908149	+	0.418648i	$0.137496\pi$
$102$	68574.3	+	49822.1i	0.0646191	+	0.0469485i
$103$	577405.	−	419509.i	0.528407	−	0.383910i	−0.291355	−	0.956615i	$-0.594106\pi$
$103$	577405.	−	419509.i	0.528407	−	0.383910i	0.819762	+	0.572705i	$0.194106\pi$
$104$	34414.0	−	105915.i	0.0305939	−	0.0941585i
$105$	589833.	+	191648.i	0.509520	+	0.165553i
$106$	−16262.5	−	22383.4i	−0.0136543	−	0.0187935i
$107$	−112009.	+	154167.i	−0.0914328	+	0.125846i	−0.852283	−	0.523082i	$-0.824782\pi$
$107$	−112009.	+	154167.i	−0.0914328	+	0.125846i	0.760850	+	0.648928i	$0.224782\pi$
$108$	214680.	+	660718.i	0.170420	+	0.524500i
$109$			816031.i			0.630125i	0.949071	+	0.315063i	$0.102026\pi$
$109$			816031.i			0.630125i	−0.949071	+	0.315063i	$0.897974\pi$
$110$	−27704.7	−	27737.2i	−0.0208150	−	0.0208394i
$111$	5946.15			0.00434777
$112$	−603701.	+	196154.i	−0.429703	+	0.139619i
$113$	−60201.2	−	43738.7i	−0.0417224	−	0.0303131i	0.566729	−	0.823905i	$-0.308209\pi$
$113$	−60201.2	−	43738.7i	−0.0417224	−	0.0303131i	−0.608451	+	0.793591i	$0.708209\pi$
$114$	−87408.6	+	63506.0i	−0.0589983	+	0.0428648i
$115$	−70629.0	+	217374.i	−0.0464397	+	0.142927i
$116$	−2.48683e6	−	808019.i	−1.59320	−	0.517664i
$117$	−1.65436e6	−	2.27703e6i	−1.03293	−	1.42171i
$118$	−21724.3	+	29900.9i	−0.0132221	+	0.0181986i
$119$	320631.	+	986801.i	0.190268	+	0.585584i
$120$		−	156248.i		−	0.0904214i
$121$	2075.76	−	1.77156e6i	0.00117171	−	0.999999i
$122$	−79601.1			−0.0438369
$123$	−64344.8	+	20906.9i	−0.0345778	+	0.0112350i
$124$	2.35929e6	+	1.71412e6i	1.23742	+	0.899037i
$125$	1.71148e6	−	1.24346e6i	0.876276	−	0.636652i
$126$	14616.8	−	44986.0i	0.00730704	−	0.0224887i
$127$	−2.21398e6	−	719365.i	−1.08084	−	0.351187i	−0.286141	−	0.958188i	$-0.592373\pi$
$127$	−2.21398e6	−	719365.i	−1.08084	−	0.351187i	−0.794701	+	0.607001i	$0.792373\pi$
$128$	188277.	+	259141.i	0.0897774	+	0.123568i
$129$	−1.30905e6	+	1.80175e6i	−0.609798	+	0.839315i
$130$	25847.3	+	79549.9i	0.0117648	+	0.0362084i
$131$			3.47975e6i			1.54787i	0.633265	+	0.773935i	$0.281714\pi$
$131$			3.47975e6i			1.54787i	−0.633265	+	0.773935i	$0.718286\pi$
$132$	2.49596e6	−	2.49304e6i	1.08521	−	1.08394i
$133$	−1.32256e6			−0.562161
$134$	47787.1	−	15527.0i	0.0198608	−	0.00645316i
$135$	−844885.	−	613845.i	−0.343397	−	0.249492i
$136$	211482.	−	153651.i	0.0840731	−	0.0610827i
$137$	428650.	−	1.31925e6i	0.166702	−	0.513057i	−0.832455	−	0.554092i	$-0.813066\pi$
$137$	428650.	−	1.31925e6i	0.166702	−	0.513057i	0.999158	+	0.0410352i	$0.0130656\pi$
$138$	28773.2	+	9348.99i	0.0109484	+	0.00355736i
$139$	339066.	+	466685.i	0.126253	+	0.173772i	0.867464	−	0.497500i	$-0.165748\pi$
$139$	339066.	+	466685.i	0.126253	+	0.173772i	−0.741212	+	0.671272i	$0.765748\pi$
$140$	561700.	−	773113.i	0.204701	−	0.281747i
$141$	556598.	+	1.71303e6i	0.198557	+	0.611094i
$142$		−	50360.7i		−	0.0175884i
$143$	−1.71795e6	+	3.36680e6i	−0.587494	+	1.15135i
$144$	4.04172e6			1.35356
$145$	3.73831e6	−	1.21465e6i	1.22623	−	0.398426i
$146$	67959.4	+	49375.4i	0.0218369	+	0.0158654i
$147$	−3.13454e6	+	2.27738e6i	−0.986783	+	0.716940i
$148$	2831.27	−	8713.75i	0.000873366	−	0.00268794i
$149$	3.10439e6	+	1.00868e6i	0.938464	+	0.304925i	0.738019	−	0.674780i	$-0.235761\pi$
$149$	3.10439e6	+	1.00868e6i	0.938464	+	0.304925i	0.200445	+	0.979705i	$0.435761\pi$
$150$	−47807.7	−	65801.6i	−0.0141652	−	0.0194968i
$151$	1.68851e6	−	2.32403e6i	0.490424	−	0.675011i	−0.490042	−	0.871699i	$-0.663019\pi$
$151$	1.68851e6	−	2.32403e6i	0.490424	−	0.675011i	0.980466	+	0.196688i	$0.0630185\pi$
$152$	102965.	+	316895.i	0.0293197	+	0.0902369i
$153$		−	6.60654e6i		−	1.84459i
$154$	−62745.9	+	9900.29i	−0.0171800	+	0.00271073i
$155$	−4.38383e6			−1.17722
$156$	−7.15837e6	+	2.32590e6i	−1.88556	+	0.612656i
$157$	−2.54683e6	−	1.85038e6i	−0.658115	−	0.478148i	0.207911	−	0.978148i	$-0.433334\pi$
$157$	−2.54683e6	−	1.85038e6i	−0.658115	−	0.478148i	−0.866026	+	0.500000i	$0.833334\pi$
$158$	−80827.2	+	58724.4i	−0.0204921	+	0.0148884i
$159$	−1.15652e6	+	3.55941e6i	−0.287715	+	0.885497i
$160$	−343544.	−	111624.i	−0.0838730	−	0.0272520i
$161$	217681.	+	299612.i	0.0521607	+	0.0717930i
$162$	48956.8	−	67383.3i	0.0115151	−	0.0158492i
$163$	−2.61371e6	−	8.04419e6i	−0.603525	−	1.85746i	−0.506628	−	0.862165i	$-0.669108\pi$
$163$	−2.61371e6	−	8.04419e6i	−0.603525	−	1.85746i	−0.0968971	−	0.995294i	$-0.530892\pi$
$164$			104249.i			0.0236341i
$165$	−832652.	+	5.23730e6i	−0.185358	+	1.16588i
$166$	194687.			0.0425612
$167$	2.63060e6	−	854735.i	0.564814	−	0.183519i	−0.0126719	−	0.999920i	$-0.504034\pi$
$167$	2.63060e6	−	854735.i	0.564814	−	0.183519i	0.577486	+	0.816400i	$0.304034\pi$
$168$	−204821.	−	148811.i	−0.0431963	−	0.0313839i
$169$	2.61932e6	−	1.90305e6i	0.542661	−	0.394266i
$170$	−60670.7	+	186725.i	−0.0123490	+	0.0380063i
$171$	8.00891e6	+	2.60225e6i	1.60171	+	0.520428i
$172$	2.01706e6	+	2.77624e6i	0.396399	+	0.545597i
$173$	−1.67349e6	+	2.30336e6i	−0.323210	+	0.444861i	−0.939444	−	0.342702i	$-0.888658\pi$
$173$	−1.67349e6	+	2.30336e6i	−0.323210	+	0.444861i	0.616234	+	0.787563i	$0.288658\pi$
$174$	−160780.	−	494831.i	−0.0305200	−	0.0939310i
$175$		−	995631.i		−	0.185774i
$176$	−2.46132e6	−	4.83762e6i	−0.451471	−	0.887347i
$177$	4.99955e6			0.901594
$178$	−168803.	+	54847.4i	−0.0299309	+	0.00972515i
$179$	−1.61456e6	−	1.17305e6i	−0.281511	−	0.204530i	0.438065	−	0.898943i	$-0.355664\pi$
$179$	−1.61456e6	−	1.17305e6i	−0.281511	−	0.204530i	−0.719576	+	0.694413i	$0.755664\pi$
$180$	−4.92259e6	+	3.57647e6i	−0.844066	+	0.613250i
$181$	1.07974e6	−	3.32311e6i	0.182090	−	0.560414i	−0.817797	−	0.575507i	$-0.804805\pi$
$181$	1.07974e6	−	3.32311e6i	0.182090	−	0.560414i	0.999886	+	0.0150934i	$0.00480456\pi$
$182$	128897.	+	41881.0i	0.0213810	+	0.00694709i
$183$	6.32910e6	+	8.71126e6i	1.03273	+	1.42144i
$184$	54842.0	−	75483.5i	0.00880359	−	0.0121171i
$185$	4256.09	+	13098.9i	0.000672196	+	0.00206881i
$186$			580277.i			0.0901771i
$187$	−7.90750e6	+	4.02324e6i	−1.20925	+	0.615249i
$188$	2.77538e6			0.417685
$189$	−1.60934e6	+	522906.i	−0.238376	+	0.0774530i
$190$	−202463.	−	147098.i	−0.0295179	−	0.0214460i
$191$	−1.00105e6	+	727308.i	−0.143667	+	0.104380i	−0.657297	−	0.753631i	$-0.728300\pi$
$191$	−1.00105e6	+	727308.i	−0.143667	+	0.104380i	0.513630	+	0.858012i	$0.328300\pi$
$192$	3.33013e6	−	1.02491e7i	0.470498	−	1.44804i
$193$	5.77268e6	+	1.87566e6i	0.802981	+	0.260904i	0.681622	−	0.731704i	$-0.261275\pi$
$193$	5.77268e6	+	1.87566e6i	0.802981	+	0.260904i	0.121359	+	0.992609i	$0.461275\pi$
$194$	−56237.5	−	77404.2i	−0.00770230	−	0.0106013i
$195$	6.65053e6	−	9.15367e6i	0.896918	−	1.23450i
$196$	1.84485e6	+	5.67787e6i	0.245015	+	0.754079i
$197$			7.91788e6i			1.03564i	0.855489	+	0.517821i	$0.173257\pi$
$197$			7.91788e6i			1.03564i	−0.855489	+	0.517821i	$0.826743\pi$
$198$	399444.	+	63505.6i	0.0514588	+	0.00818119i
$199$	−5.93743e6			−0.753423			−0.376712	−	0.926331i	$-0.622945\pi$
$199$	−5.93743e6			−0.753423			−0.376712	+	0.926331i	$0.622945\pi$
$200$	−238560.	+	77512.8i	−0.0298200	+	0.00968910i
$201$	−5.49878e6	−	3.99510e6i	−0.677140	−	0.491971i
$202$	375334.	−	272696.i	0.0455370	−	0.0330845i
$203$	1.96812e6	−	6.05727e6i	0.235269	−	0.724083i
$204$	−1.68026e7	−	5.45951e6i	−1.97919	−	0.643077i
$205$	−92112.4	−	126782.i	−0.0106919	−	0.0147162i
$206$	128622.	−	177033.i	0.0147134	−	0.0202513i
$207$	−728677.	−	2.24264e6i	−0.0821531	−	0.252841i
$208$			1.15806e7i			1.28689i
$209$	−1.76256e6	−	1.11707e7i	−0.193066	−	1.22361i
$210$	190150.			0.0205324
$211$	−4.76819e6	+	1.54928e6i	−0.507582	+	0.164923i	−0.551602	−	0.834107i	$-0.685983\pi$
$211$	−4.76819e6	+	1.54928e6i	−0.507582	+	0.164923i	0.0440202	+	0.999031i	$0.485983\pi$
$212$	4.66544e6	+	3.38964e6i	0.489649	+	0.355751i
$213$	−5.51130e6	+	4.00419e6i	−0.570315	+	0.414358i
$214$	−18054.7	+	55566.8i	−0.00184226	+	0.00566988i
$215$	−4.90609e6	−	1.59409e6i	−0.493651	−	0.160397i
$216$	250583.	+	344899.i	0.0248652	+	0.0342239i
$217$	−4.17516e6	+	5.74662e6i	−0.408596	+	0.562384i
$218$	77314.9	+	237951.i	0.00746266	+	0.0229677i
$219$		−	1.13631e7i		−	1.08184i
$220$	7.27850e6	+	3.71396e6i	0.683556	+	0.348794i
$221$	1.89295e7			1.75373
$222$	1733.87	−	563.369i	0.000158474	−	5.14913e-5i
$223$	8.08452e6	+	5.87375e6i	0.729020	+	0.529664i	0.889253	−	0.457415i	$-0.151225\pi$
$223$	8.08452e6	+	5.87375e6i	0.729020	+	0.529664i	−0.160233	+	0.987079i	$0.551225\pi$
$224$	−473516.	+	344030.i	−0.0421299	+	0.0306092i
$225$	−1.95899e6	+	6.02915e6i	−0.171983	+	0.529308i
$226$	−21698.4	−	7050.24i	−0.00187976	−	0.000610771i
$227$	4.35860e6	+	5.99909e6i	0.372623	+	0.512871i	0.953611	−	0.301041i	$-0.0973340\pi$
$227$	4.35860e6	+	5.99909e6i	0.372623	+	0.512871i	−0.580989	+	0.813912i	$0.697334\pi$
$228$	1.32368e7	−	1.82189e7i	1.11681	−	1.53715i
$229$	−463739.	−	1.42724e6i	−0.0386160	−	0.118848i	0.929890	−	0.367837i	$-0.119902\pi$
$229$	−463739.	−	1.42724e6i	−0.0386160	−	0.118848i	−0.968506	+	0.248989i	$0.919902\pi$
$230$			70076.9i			0.00575959i
$231$	6.07239e6	+	6.07951e6i	0.492633	+	0.493211i
$232$	−1.60459e6			−0.128499
$233$	−1.69204e7	+	5.49777e6i	−1.33765	+	0.434629i	−0.888521	−	0.458837i	$-0.848266\pi$
$233$	−1.69204e7	+	5.49777e6i	−1.33765	+	0.434629i	−0.449131	+	0.893466i	$0.648266\pi$
$234$	−698141.	−	507229.i	−0.0544874	−	0.0395874i
$235$	−3.37528e6	+	2.45228e6i	−0.260079	+	0.188959i
$236$	2.38054e6	−	7.32656e6i	0.181109	−	0.557396i
$237$	1.28532e7	+	4.17625e6i	0.965529	+	0.313719i
$238$	186989.	+	257369.i	0.0138703	+	0.0190908i
$239$	−7.57190e6	+	1.04218e7i	−0.554640	+	0.763396i	−0.990633	−	0.136554i	$-0.956397\pi$
$239$	−7.57190e6	+	1.04218e7i	−0.554640	+	0.763396i	0.435993	+	0.899950i	$0.356397\pi$
$240$	5.02083e6	+	1.54525e7i	0.363196	+	1.11780i
$241$		−	1.47841e7i		−	1.05620i	−0.849184	−	0.528098i	$-0.822905\pi$
$241$		−	1.47841e7i		−	1.05620i	0.849184	−	0.528098i	$-0.177095\pi$
$242$	−167241.	−	516775.i	−0.0118004	−	0.0364633i
$243$	−1.91917e7			−1.33750
$244$	1.57795e7	−	5.12706e6i	1.08623	−	0.352939i
$245$	−7.26049e6	−	5.27506e6i	−0.493705	−	0.358698i
$246$	−16781.8	+	12192.7i	−0.00112728	+	0.000819020i
$247$	−7.45613e6	+	2.29476e7i	−0.494792	+	1.52281i
$248$	1.70198e6	+	553006.i	0.111583	+	0.0362556i
$249$	−1.54796e7	−	2.13059e7i	−1.00268	−	1.38007i
$250$	381247.	−	524742.i	0.0243998	−	0.0335835i
$251$	−4.37040e6	−	1.34507e7i	−0.276376	−	0.850597i	−0.988852	−	0.148901i	$-0.952426\pi$
$251$	−4.37040e6	−	1.34507e7i	−0.276376	−	0.850597i	0.712476	−	0.701696i	$-0.247574\pi$
$252$			9.85911e6i			0.616079i
$253$	−2.24051e6	+	2.23789e6i	−0.138352	+	0.138190i
$254$	−713743.			−0.0435552
$255$	2.52585e7	−	8.20697e6i	1.52330	−	0.494951i
$256$	−1.33741e7	−	9.71687e6i	−0.797160	−	0.579171i
$257$	2.35760e7	−	1.71290e7i	1.38890	−	1.00909i	0.392915	−	0.919575i	$-0.371467\pi$
$257$	2.35760e7	−	1.71290e7i	1.38890	−	1.00909i	0.995985	−	0.0895200i	$-0.0285333\pi$
$258$	−211005.	+	649408.i	−0.0122867	+	0.0378145i
$259$	21224.4	+	6896.24i	0.00122162	+	0.000396929i
$260$	−1.02475e7	−	1.41045e7i	−0.583041	−	0.802488i
$261$	−2.38364e7	+	3.28079e7i	−1.34066	+	1.84526i
$262$	329689.	+	1.01468e6i	0.0183316	+	0.0564190i
$263$		−	1.87830e7i		−	1.03252i	−0.856432	−	0.516260i	$-0.827324\pi$
$263$		−	1.87830e7i		−	1.03252i	0.856432	−	0.516260i	$-0.172676\pi$
$264$	983938.	−	1.92829e6i	0.0534756	−	0.104800i
$265$	−8.66892e6			−0.465830
$266$	−385653.	+	125306.i	−0.0204905	+	0.00665776i
$267$	1.94239e7	+	1.41123e7i	1.02047	+	0.741418i
$268$	−8.47285e6	+	6.15589e6i	−0.440175	+	0.319806i
$269$	−6.76508e6	+	2.08208e7i	−0.347549	+	1.06965i	0.612656	+	0.790350i	$0.290101\pi$
$269$	−6.76508e6	+	2.08208e7i	−0.347549	+	1.06965i	−0.960205	+	0.279296i	$0.909899\pi$
$270$	−304523.	−	98945.6i	−0.0154714	−	0.00502696i
$271$	116773.	+	160724.i	0.00586725	+	0.00807557i	0.811941	−	0.583740i	$-0.198411\pi$
$271$	116773.	+	160724.i	0.00586725	+	0.00807557i	−0.806073	+	0.591816i	$0.798411\pi$
$272$	−1.59776e7	+	2.19913e7i	−0.793973	+	1.09281i
$273$	−5.66528e6	−	1.74359e7i	−0.278441	−	0.856954i
$274$		−	425300.i		−	0.0206749i
$275$	8.40938e6	−	1.32687e6i	0.404358	−	0.0638012i
$276$	−6.30594e6			−0.299932
$277$	−1.64577e6	+	534744.i	−0.0774338	+	0.0251598i	−0.347478	−	0.937688i	$-0.612962\pi$
$277$	−1.64577e6	+	534744.i	−0.0774338	+	0.0251598i	0.270044	+	0.962848i	$0.412962\pi$
$278$	143086.	+	103958.i	0.00665984	+	0.00483866i
$279$	3.65901e7	−	2.65842e7i	1.68481	−	1.22409i
$280$	181214.	−	557719.i	0.00825501	−	0.0254063i
$281$	2.03407e7	+	6.60910e6i	0.916742	+	0.297868i	0.729130	−	0.684376i	$-0.239925\pi$
$281$	2.03407e7	+	6.60910e6i	0.916742	+	0.297868i	0.187612	+	0.982243i	$0.439925\pi$
$282$	324603.	+	446777.i	0.0144745	+	0.0199225i
$283$	2.52375e7	−	3.47365e7i	1.11349	−	1.53259i	0.297325	−	0.954776i	$-0.403906\pi$
$283$	2.52375e7	−	3.47365e7i	1.11349	−	1.53259i	0.816168	−	0.577815i	$-0.196094\pi$
$284$	3.24371e6	+	9.98310e6i	0.141608	+	0.435823i
$285$			3.38527e7i			1.46237i
$286$	−181960.	+	1.14451e6i	−0.00777818	+	0.0489240i
$287$	−253922.			−0.0107413
$288$	3.54433e6	−	1.15162e6i	0.148374	−	0.0482095i
$289$	1.64190e7	+	1.19291e7i	0.680226	+	0.494213i
$290$	974992.	−	708373.i	0.0399767	−	0.0290448i
$291$	−3.99939e6	+	1.23089e7i	−0.162299	+	0.499504i
$292$	−1.66520e7	−	5.41055e6i	−0.668831	−	0.217316i
$293$	3.82489e6	+	5.26450e6i	0.152060	+	0.209293i	0.878251	−	0.478201i	$-0.158711\pi$
$293$	3.82489e6	+	5.26450e6i	0.152060	+	0.209293i	−0.726190	+	0.687494i	$0.758711\pi$
$294$	−698247.	+	961054.i	−0.0274769	+	0.0378186i
$295$	3.57854e6	+	1.10136e7i	0.139393	+	0.429006i
$296$		−	5622.41i		−	0.000216794i
$297$	−6.56136e6	−	1.28961e7i	−0.250452	−	0.492252i
$298$	1.00079e6			0.0378177
$299$	6.42575e6	−	2.08785e6i	0.240386	−	0.0781063i
$300$	1.37153e7	+	9.96471e6i	0.507972	+	0.369063i
$301$	−6.76221e6	+	4.91303e6i	−0.247964	+	0.180156i
$302$	272170.	−	837654.i	0.00988144	−	0.0304119i
$303$	−5.96858e7	−	1.93931e7i	−2.14557	−	0.697139i
$304$	−2.03660e7	−	2.80313e7i	−0.724910	−	0.997753i
$305$	−1.46600e7	+	2.01778e7i	−0.516696	+	0.711171i
$306$	−625938.	−	1.92644e6i	−0.0218457	−	0.0672343i
$307$		−	8.80217e6i		−	0.304211i	−0.988364	−	0.152105i	$-0.951395\pi$
$307$		−	8.80217e6i		−	0.304211i	0.988364	−	0.152105i	$-0.0486053\pi$
$308$	1.18006e7	−	6.00398e6i	0.403878	−	0.205488i
$309$	−2.96006e7			−1.00329
$310$	−1.27830e6	+	415346.i	−0.0429091	+	0.0139420i
$311$	−1.64883e7	−	1.19794e7i	−0.548144	−	0.398250i	0.278957	−	0.960304i	$-0.410011\pi$
$311$	−1.64883e7	−	1.19794e7i	−0.548144	−	0.398250i	−0.827101	+	0.562054i	$0.810011\pi$
$312$	−3.73671e6	+	2.71488e6i	−0.123034	+	0.0893895i
$313$	1.09436e7	−	3.36810e7i	0.356884	−	1.09838i	−0.598025	−	0.801478i	$-0.704048\pi$
$313$	1.09436e7	−	3.36810e7i	0.356884	−	1.09838i	0.954909	−	0.296899i	$-0.0959525\pi$
$314$	−917960.	−	298263.i	−0.0296507	−	0.00963409i
$315$	−8.71136e6	−	1.19902e7i	−0.278711	−	0.383613i
$316$	1.22401e7	−	1.68471e7i	0.387904	−	0.533904i
$317$	1.33091e7	+	4.09612e7i	0.417802	+	1.28586i	0.909721	+	0.415221i	$0.136296\pi$
$317$	1.33091e7	+	4.09612e7i	0.417802	+	1.28586i	−0.491919	+	0.870641i	$0.663704\pi$
$318$			1.14748e6i			0.0356833i
$319$	5.37843e7	+	8.55089e6i	1.65685	+	0.263414i
$320$	2.49615e7			0.761766
$321$	7.51656e6	−	2.44228e6i	0.227250	−	0.0738381i
$322$	91861.6	+	66741.4i	0.00275148	+	0.00199907i
$323$	−4.58196e7	+	3.32899e7i	−1.35970	+	0.987882i
$324$	−5.36468e6	+	1.65108e7i	−0.157728	+	0.485437i
$325$	−1.72751e7	−	5.61301e6i	−0.503234	−	0.163511i
$326$	−1.52429e6	−	2.09801e6i	−0.0439963	−	0.0605557i
$327$	1.98932e7	−	2.73806e7i	0.568932	−	0.783068i
$328$	19768.6	+	60841.5i	0.000560215	+	0.00172416i
$329$			6.76010e6i			0.189830i
$330$	253411.	+	1.60606e6i	0.00705153	+	0.0446911i
$331$	2.55492e7			0.704520			0.352260	−	0.935902i	$-0.385413\pi$
$331$	2.55492e7			0.704520			0.352260	+	0.935902i	$0.385413\pi$
$332$	−3.85932e7	+	1.25397e7i	−1.05462	+	0.342668i
$333$	−114958.	−	83521.7i	−0.00311319	−	0.00226187i
$334$	686090.	−	498473.i	0.0184137	−	0.0133783i
$335$	4.86501e6	−	1.49730e7i	0.129405	−	0.398266i
$336$	2.50381e7	+	8.13536e6i	0.660059	+	0.214466i
$337$	1.43978e7	+	1.98168e7i	0.376188	+	0.517778i	0.954570	−	0.297988i	$-0.0963155\pi$
$337$	1.43978e7	+	1.98168e7i	0.376188	+	0.517778i	−0.578382	+	0.815766i	$0.696316\pi$
$338$	583477.	−	803088.i	0.0151103	−	0.0207976i
$339$	953692.	+	2.93516e6i	0.0244799	+	0.0753413i
$340$		−	4.09226e7i		−	1.04118i
$341$	−5.41018e7	−	2.76062e7i	−1.36442	−	0.696214i
$342$	2.58191e6			0.0645450
$343$	−3.12466e7	+	1.01526e7i	−0.774319	+	0.251592i
$344$	1.70365e6	+	1.23778e6i	0.0418510	+	0.0304065i
$345$	7.66897e6	−	5.57183e6i	0.186758	−	0.135688i
$346$	−269750.	+	830206.i	−0.00651229	+	0.0200428i
$347$	6.04267e7	+	1.96338e7i	1.44624	+	0.469912i	0.923837	−	0.382786i	$-0.125035\pi$
$347$	6.04267e7	+	1.96338e7i	1.44624	+	0.469912i	0.522404	+	0.852698i	$0.325035\pi$
$348$	6.37436e7	+	8.77355e7i	1.51251	+	2.08179i
$349$	−1.38623e7	+	1.90798e7i	−0.326106	+	0.448846i	−0.940319	−	0.340294i	$-0.889473\pi$
$349$	−1.38623e7	+	1.90798e7i	−0.326106	+	0.448846i	0.614213	+	0.789140i	$0.289473\pi$
$350$	−94331.2	−	290322.i	−0.00220014	−	0.00677135i
$351$			3.08714e7i			0.713896i
$352$	−3.53682e6	−	3.54097e6i	−0.0810933	−	0.0811884i
$353$	7.24035e7			1.64602			0.823011	−	0.568025i	$-0.192292\pi$
$353$	7.24035e7			1.64602			0.823011	+	0.568025i	$0.192292\pi$
$354$	1.45785e6	−	473683.i	0.0328626	−	0.0106777i
$355$	−1.27658e7	−	9.27486e6i	−0.285339	−	0.207311i
$356$	2.99294e7	−	2.17450e7i	0.663359	−	0.481959i
$357$	1.32979e7	−	4.09269e7i	0.292267	−	0.899505i
$358$	−581940.	−	189084.i	−0.0126832	−	0.00412102i
$359$	−5.02332e7	−	6.91400e7i	−1.08569	−	1.49433i	−0.853095	−	0.521755i	$-0.825277\pi$
$359$	−5.02332e7	−	6.91400e7i	−1.08569	−	1.49433i	−0.232598	−	0.972573i	$-0.574723\pi$
$360$	−2.19472e6	+	3.02077e6i	−0.0470404	+	0.0647456i
$361$	−7.77045e6	−	2.39150e7i	−0.165168	−	0.508333i
$362$		−	1.07130e6i		−	0.0225833i
$363$	−4.32567e7	+	5.93912e7i	−0.904343	+	1.24166i
$364$	−2.82489e7			−0.585731
$365$	2.50320e7	−	8.13338e6i	0.514774	−	0.167260i
$366$	2.67089e6	+	1.94051e6i	0.0544769	+	0.0395798i
$367$	−4.15661e7	+	3.01995e7i	−0.840893	+	0.610945i	−0.922620	−	0.385710i	$-0.873956\pi$
$367$	−4.15661e7	+	3.01995e7i	−0.840893	+	0.610945i	0.0817270	+	0.996655i	$0.473956\pi$
$368$	−2.99816e6	+	9.22738e6i	−0.0601605	+	0.185155i
$369$	1.53765e6	+	499613.i	0.0306041	+	0.00994386i
$370$	2482.11	+	3416.34i	4.90023e−5	+	6.74459e-5i
$371$	−8.25629e6	+	1.13638e7i	−0.161683	+	0.222537i
$372$	−3.73753e7	−	1.15029e8i	−0.726032	−	2.23450i
$373$		−	5.84663e6i		−	0.112662i	−0.998412	−	0.0563312i	$-0.982060\pi$
$373$		−	5.84663e6i		−	0.112662i	0.998412	−	0.0563312i	$-0.0179403\pi$
$374$	−1.92461e6	+	1.92236e6i	−0.0367898	+	0.0367467i
$375$	−8.77389e7			−1.66379
$376$	1.61977e6	−	526294.i	0.0304711	−	0.00990067i
$377$	−9.40033e7	−	6.82974e7i	−1.75436	−	1.27462i
$378$	−419733.	+	304954.i	−0.00777137	+	0.00564623i
$379$	−1.06139e7	+	3.26663e7i	−0.194966	+	0.600044i	0.805011	+	0.593260i	$0.202159\pi$
$379$	−1.06139e7	+	3.26663e7i	−0.194966	+	0.600044i	−0.999977	+	0.00678382i	$0.997841\pi$
$380$	4.96092e7	+	1.61190e7i	0.904090	+	0.293757i
$381$	5.67498e7	+	7.81094e7i	1.02610	+	1.41231i
$382$	−222994.	+	306925.i	−0.00400039	+	0.00550607i
$383$	8.50650e6	+	2.61803e7i	0.151410	+	0.465992i	0.997779	−	0.0666042i	$-0.0212165\pi$
$383$	8.50650e6	+	2.61803e7i	0.151410	+	0.465992i	−0.846369	+	0.532596i	$0.821216\pi$
$384$		−	1.32848e7i		−	0.234619i
$385$	−9.04623e6	+	1.77285e7i	−0.158521	+	0.310664i
$386$	1.86100e6			0.0323581
$387$	5.06160e7	−	1.64461e7i	0.873283	−	0.283747i
$388$	1.61336e7	+	1.17218e7i	0.276208	+	0.200677i
$389$	321613.	−	233666.i	0.00546368	−	0.00396960i	−0.585050	−	0.810997i	$-0.698925\pi$
$389$	321613.	−	233666.i	0.00546368	−	0.00396960i	0.590514	+	0.807028i	$0.298925\pi$
$390$	1.07200e6	−	3.29927e6i	0.0180718	−	0.0556192i
$391$	1.50830e7	+	4.90075e6i	0.252323	+	0.0819846i
$392$	2.15338e6	+	2.96388e6i	0.0357489	+	0.0492042i
$393$	8.48292e7	−	1.16757e8i	1.39755	−	1.92356i
$394$	750180.	+	2.30882e6i	0.0122653	+	0.0377486i
$395$			3.13038e7i			0.507932i
$396$	−8.32728e7	+	1.31391e7i	−1.34097	+	0.211583i
$397$	2.90058e7			0.463567			0.231784	−	0.972767i	$-0.425544\pi$
$397$	2.90058e7			0.463567			0.231784	+	0.972767i	$0.425544\pi$
$398$	−1.73133e6	+	562542.i	−0.0274618	+	0.00892290i
$399$	4.43764e7	+	3.22414e7i	0.698608	+	0.507568i
$400$	2.11021e7	−	1.53316e7i	0.329721	−	0.239556i
$401$	3.37396e7	−	1.03840e8i	0.523247	−	1.61039i	−0.244510	−	0.969647i	$-0.578627\pi$
$401$	3.37396e7	−	1.03840e8i	0.523247	−	1.61039i	0.767757	−	0.640741i	$-0.221373\pi$
$402$	−1.98194e6	−	643970.i	−0.0305078	−	0.00991260i
$403$	7.61708e7	+	1.04840e8i	1.16379	+	1.60182i
$404$	−5.68390e7	+	7.82322e7i	−0.861990	+	1.18643i
$405$	−8.06443e6	−	2.48198e7i	−0.121397	−	0.373622i
$406$		−	1.95274e6i		−	0.0291787i
$407$	−29962.0	+	188458.i	−0.000444414	+	0.00279532i
$408$	−1.08416e7			−0.159630
$409$	−7.03465e7	+	2.28570e7i	−1.02819	+	0.334079i	−0.774074	−	0.633095i	$-0.781784\pi$
$409$	−7.03465e7	+	2.28570e7i	−1.02819	+	0.334079i	−0.254115	+	0.967174i	$0.581784\pi$
$410$	−38871.5	−	28241.8i	−0.000564001	−	0.000409771i
$411$	−4.65433e7	+	3.38157e7i	−0.670396	+	0.487071i
$412$	−1.40944e7	+	4.33781e7i	−0.201537	+	0.620267i
$413$	1.78456e7	+	5.79839e6i	0.253327	+	0.0823108i
$414$	−424958.	−	584904.i	−0.00598887	−	0.00824297i
$415$	3.58553e7	−	4.93506e7i	0.501659	−	0.690475i
$416$	3.29970e6	+	1.01554e7i	0.0458347	+	0.141065i
$417$		−	2.39246e7i		−	0.329941i
$418$	−1.57233e6	−	3.09034e6i	−0.0215285	−	0.0423133i
$419$	5.77137e7			0.784579			0.392289	−	0.919842i	$-0.371683\pi$
$419$	5.77137e7			0.784579			0.392289	+	0.919842i	$0.371683\pi$
$420$	−3.76938e7	+	1.22475e7i	−0.508771	+	0.165310i
$421$	5.48349e7	+	3.98399e7i	0.734871	+	0.533915i	0.891101	−	0.453806i	$-0.149934\pi$
$421$	5.48349e7	+	3.98399e7i	0.734871	+	0.533915i	−0.156230	+	0.987721i	$0.549934\pi$
$422$	−1.24360e6	+	903526.i	−0.0165479	+	0.0120227i
$423$	1.33011e7	−	4.09365e7i	0.175738	−	0.540866i
$424$	3.36562e6	+	1.09356e6i	0.0441537	+	0.0143464i
$425$	−2.50608e7	−	3.44933e7i	−0.326459	−	0.449332i
$426$	−1.22769e6	+	1.68977e6i	−0.0158804	+	0.0218574i
$427$	1.24882e7	+	3.84347e7i	0.160404	+	0.493674i
$428$		−	1.21780e7i		−	0.155326i
$429$	1.39719e8	−	7.10872e7i	1.76963	−	0.900367i
$430$	−1.58163e6			−0.0198929
$431$	−9.15376e6	+	2.97424e6i	−0.114332	+	0.0371487i	−0.365624	−	0.930763i	$-0.619144\pi$
$431$	−9.15376e6	+	2.97424e6i	−0.114332	+	0.0371487i	0.251292	+	0.967911i	$0.419144\pi$
$432$	−3.58649e7	−	2.60573e7i	−0.444854	−	0.323206i
$433$	−6.80347e7	+	4.94301e7i	−0.838043	+	0.608874i	−0.921823	−	0.387610i	$-0.873301\pi$
$433$	−6.80347e7	+	4.94301e7i	−0.838043	+	0.608874i	0.0837800	+	0.996484i	$0.473301\pi$
$434$	−672995.	+	2.07126e6i	−0.00823270	+	0.0253377i
$435$	−1.55044e8	−	5.03767e7i	−1.88359	−	0.612015i
$436$	−3.06526e7	−	4.21896e7i	−0.369834	−	0.509033i
$437$	−1.18820e7	+	1.63542e7i	−0.142379	+	0.195968i
$438$	−1.07660e6	−	3.31342e6i	−0.0128124	−	0.0394325i
$439$			1.83741e7i			0.217176i	0.994087	+	0.108588i	$0.0346330\pi$
$439$			1.83741e7i			0.217176i	−0.994087	+	0.108588i	$0.965367\pi$
$440$	4.95215e6	+	787318.i	0.0581348	+	0.00924256i
$441$	9.25893e7			1.07956
$442$	5.51975e6	−	1.79348e6i	0.0639223	−	0.0207696i
$443$	−9.80420e7	−	7.12317e7i	−1.12772	−	0.819336i	−0.142358	−	0.989815i	$-0.545468\pi$
$443$	−9.80420e7	−	7.12317e7i	−1.12772	−	0.819336i	−0.985361	+	0.170479i	$0.945468\pi$
$444$	−307422.	+	223355.i	−0.00351226	+	0.00255180i
$445$	−1.71851e7	+	5.28904e7i	−0.195017	+	0.600201i
$446$	2.91392e6	+	946789.i	0.0328453	+	0.0106721i
$447$	−7.95733e7	−	1.09523e8i	−0.890932	−	1.22626i
$448$	2.37734e7	−	3.27213e7i	0.264398	−	0.363912i
$449$	4.22362e7	+	1.29990e8i	0.466601	+	1.43605i	0.856958	+	0.515387i	$0.172352\pi$
$449$	4.22362e7	+	1.29990e8i	0.466601	+	1.43605i	−0.390356	+	0.920664i	$0.627648\pi$
$450$			1.94368e6i			0.0213298i
$451$	−338399.	−	2.14470e6i	−0.00368892	−	0.0233796i
$452$	4.75542e6			0.0514960
$453$	−1.13310e8	+	3.68167e7i	−1.21892	+	0.396050i
$454$	1.83933e6	+	1.33635e6i	0.0196559	+	0.0142808i
$455$	3.43550e7	−	2.49603e7i	0.364716	−	0.264982i
$456$	4.27041e6	−	1.31430e7i	0.0450376	−	0.138611i
$457$	−9.99528e7	−	3.24766e7i	−1.04724	−	0.340269i	−0.265656	−	0.964068i	$-0.585588\pi$
$457$	−9.99528e7	−	3.24766e7i	−1.04724	−	0.340269i	−0.781585	+	0.623799i	$0.785588\pi$
$458$	−270448.	−	372240.i	−0.00281506	−	0.00387460i
$459$	−4.25930e7	+	5.86242e7i	−0.440453	+	0.606232i
$460$	−4.51362e6	−	1.38915e7i	−0.0463715	−	0.142717i
$461$			7.65517e7i			0.781362i	0.920526	+	0.390681i	$0.127760\pi$
$461$			7.65517e7i			0.781362i	−0.920526	+	0.390681i	$0.872240\pi$
$462$	2.34669e6	+	1.19743e6i	0.0237974	+	0.0121429i
$463$	−3.95543e7			−0.398521			−0.199261	−	0.979947i	$-0.563854\pi$
$463$	−3.95543e7			−0.398521			−0.199261	+	0.979947i	$0.563854\pi$
$464$	1.58689e8	−	5.15612e7i	1.58852	−	0.516142i
$465$	1.47092e8	+	1.06869e8i	1.46295	+	1.06290i
$466$	−4.41302e6	+	3.20625e6i	−0.0436092	+	0.0316840i
$467$	4.63425e7	−	1.42627e8i	0.455018	−	1.40040i	−0.416096	−	0.909321i	$-0.636602\pi$
$467$	4.63425e7	−	1.42627e8i	0.455018	−	1.40040i	0.871114	−	0.491081i	$-0.163398\pi$
$468$	1.71064e8	+	5.55821e7i	1.66887	+	0.542248i
$469$	−1.49941e7	−	2.06377e7i	−0.145346	−	0.200052i
$470$	−751874.	+	1.03487e6i	−0.00724188	+	0.00996759i
$471$	4.03463e7	+	1.24173e8i	0.386137	+	1.18841i
$472$		−	4.72735e6i		−	0.0449564i
$473$	−5.05087e7	−	5.05680e7i	−0.477291	−	0.477850i
$474$	4.14360e6			0.0389084
$475$	5.16863e7	−	1.67939e7i	0.482275	−	0.156701i
$476$	−5.36442e7	−	3.89748e7i	−0.497395	−	0.361379i
$477$	7.23560e7	−	5.25697e7i	0.666683	−	0.484374i
$478$	−1.22051e6	+	3.75636e6i	−0.0111753	+	0.0343940i
$479$	−2.14571e7	−	6.97183e6i	−0.195238	−	0.0634366i	0.209766	−	0.977752i	$-0.432730\pi$
$479$	−2.14571e7	−	6.97183e6i	−0.195238	−	0.0634366i	−0.405004	+	0.914315i	$0.632730\pi$
$480$	8.80589e6	+	1.21203e7i	0.0796250	+	0.109594i
$481$	239312.	−	329384.i	0.00215045	−	0.00295984i
$482$	−1.40072e6	−	4.31098e6i	−0.0125087	−	0.0384977i
$483$		−	1.53596e7i		−	0.136314i
$484$	6.64378e7	+	9.16694e7i	0.585975	+	0.808516i
$485$	−2.99781e7			−0.262772
$486$	−5.59621e6	+	1.81832e6i	−0.0487512	+	0.0158402i
$487$	6.54258e7	+	4.75346e7i	0.566450	+	0.411550i	0.833814	−	0.552045i	$-0.186152\pi$
$487$	6.54258e7	+	4.75346e7i	0.566450	+	0.411550i	−0.267364	+	0.963596i	$0.586152\pi$
$488$	8.23697e6	−	5.98451e6i	0.0708775	−	0.0514955i
$489$	−1.08402e8	+	3.33627e8i	−0.927065	+	2.85321i
$490$	−2.61691e6	−	850287.i	−0.0222434	−	0.00722732i
$491$	−6.08731e6	−	8.37847e6i	−0.0514258	−	0.0707816i	0.782530	−	0.622613i	$-0.213929\pi$
$491$	−6.08731e6	−	8.37847e6i	−0.0514258	−	0.0707816i	−0.833955	+	0.551832i	$0.813929\pi$
$492$	2.54137e6	−	3.49789e6i	0.0213389	−	0.0293705i
$493$	−8.42812e7	−	2.59391e8i	−0.703380	−	2.16478i
$494$			7.39785e6i			0.0613656i
$495$	8.96628e7	−	8.95578e7i	0.739259	−	0.738393i
$496$	−1.86091e8			−1.52504
$497$	−2.43162e7	+	7.90083e6i	−0.198074	+	0.0643581i
$498$	−6.53242e6	−	4.74608e6i	−0.0528915	−	0.0384279i
$499$	1.81132e8	−	1.31600e8i	1.45778	−	1.05914i	0.473850	−	0.880605i	$-0.342864\pi$
$499$	1.81132e8	−	1.31600e8i	1.45778	−	1.05914i	0.983933	−	0.178537i	$-0.0571363\pi$
$500$	−4.17770e7	+	1.28576e8i	−0.334216	+	1.02861i
$501$	−1.09102e8	−	3.54495e7i	−0.867602	−	0.281901i
$502$	−2.54878e6	−	3.50809e6i	−0.0201475	−	0.0277306i
$503$	−1.41546e8	+	1.94821e8i	−1.11223	+	1.53085i	−0.294134	+	0.955764i	$0.595031\pi$
$503$	−1.41546e8	+	1.94821e8i	−1.11223	+	1.53085i	−0.818094	+	0.575085i	$0.804969\pi$
$504$	1.86958e6	+	5.75397e6i	0.0146033	+	0.0449445i
$505$		−	1.45364e8i		−	1.12871i
$506$	−441293.	+	864834.i	−0.00340625	+	0.00667546i
$507$	−1.34279e8			−1.03035
$508$	1.41487e8	−	4.59718e7i	1.07925	−	0.350671i
$509$	1.02067e8	+	7.41562e7i	0.773986	+	0.562334i	0.903168	−	0.429287i	$-0.141235\pi$
$509$	1.02067e8	+	7.41562e7i	0.773986	+	0.562334i	−0.129182	+	0.991621i	$0.541235\pi$
$510$	6.58768e6	−	4.78623e6i	0.0496618	−	0.0360814i
$511$	1.31787e7	−	4.05598e7i	0.0987665	−	0.303972i
$512$	−2.43173e7	−	7.90117e6i	−0.181178	−	0.0588683i
$513$	−5.42913e7	−	7.47256e7i	−0.402141	−	0.553500i
$514$	5.25177e6	−	7.22844e6i	0.0386738	−	0.0532299i
$515$	−2.11873e7	−	6.52079e7i	−0.155115	−	0.477396i
$516$		−	1.42324e8i		−	1.03593i
$517$	−5.70977e7	+	9.00910e6i	−0.413188	+	0.0651944i
$518$	6842.33			4.92283e−5
$519$	1.12303e8	−	3.64893e7i	0.803319	−	0.261014i
$520$	−8.65530e6	−	6.28844e6i	−0.0615562	−	0.0447232i
$521$	3.75793e7	−	2.73030e7i	0.265727	−	0.193062i	−0.446941	−	0.894563i	$-0.647487\pi$
$521$	3.75793e7	−	2.73030e7i	0.265727	−	0.193062i	0.712668	+	0.701501i	$0.247487\pi$
$522$	−3.84218e6	+	1.18250e7i	−0.0270126	+	0.0831362i
$523$	1.50748e8	+	4.89809e7i	1.05377	+	0.342391i	0.784147	−	0.620575i	$-0.213101\pi$
$523$	1.50748e8	+	4.89809e7i	1.05377	+	0.342391i	0.269623	+	0.962966i	$0.413101\pi$
$524$	−1.30710e8	−	1.79907e8i	−0.908478	−	1.25041i
$525$	−2.42715e7	+	3.34068e7i	−0.167733	+	0.230864i
$526$	−1.77960e6	−	5.47704e6i	−0.0122283	−	0.0376347i
$527$			3.04182e8i			2.07827i
$528$	−3.53456e7	+	2.22320e8i	−0.240123	+	1.51035i
$529$	−1.42375e8			−0.961762
$530$	−2.52782e6	+	821337.i	−0.0169792	+	0.00551689i
$531$	−9.66570e7	−	7.02254e7i	−0.645579	−	0.469041i
$532$	6.83778e7	−	4.96794e7i	0.454130	−	0.329945i
$533$	−1.43152e6	+	4.40578e6i	−0.00945403	+	0.0290965i
$534$	7.00098e6	+	2.27476e6i	0.0459764	+	0.0149386i
$535$	1.07603e7	+	1.48103e7i	0.0702689	+	0.0967168i
$536$	−3.77759e6	+	5.19940e6i	−0.0245313	+	0.0337644i
$537$	2.55775e7	+	7.87195e7i	0.165172	+	0.508346i
$538$			6.71220e6i			0.0431040i
$539$	−5.63848e7	−	1.10822e8i	−0.360078	−	0.707717i
$540$	6.67392e7			0.423838
$541$	−5.28153e7	+	1.71607e7i	−0.333555	+	0.108379i	−0.471006	−	0.882130i	$-0.656109\pi$
$541$	−5.28153e7	+	1.71607e7i	−0.333555	+	0.108379i	0.137451	+	0.990509i	$0.456109\pi$
$542$	49278.3	+	35802.8i	0.000309498	+	0.000224863i
$543$	−1.17240e8	+	8.51796e7i	−0.732277	+	0.532030i
$544$	−7.74529e6	+	2.38376e7i	−0.0481106	+	0.148069i
$545$	7.45563e7	+	2.42248e7i	0.460569	+	0.149648i
$546$	−3.30394e6	−	4.54748e6i	−0.0202980	−	0.0279379i
$547$	9.93540e7	−	1.36749e8i	0.607048	−	0.835531i	−0.389282	−	0.921119i	$-0.627277\pi$
$547$	9.93540e7	−	1.36749e8i	0.607048	−	0.835531i	0.996331	+	0.0855880i	$0.0272769\pi$
$548$	2.73933e7	+	8.43080e7i	0.166457	+	0.512303i
$549$		−	2.57317e8i		−	1.55507i
$550$	2.32642e6	−	1.18366e6i	0.0139830	−	0.00711439i
$551$	3.47649e8			2.07819
$552$	−3.68027e6	+	1.19579e6i	−0.0218808	+	0.00710949i
$553$	4.10351e7	+	2.98138e7i	0.242650	+	0.176296i
$554$	−429235.	+	311858.i	−0.00252445	+	0.00183412i
$555$	176518.	−	543267.i	0.00103255	−	0.00317786i
$556$	−3.50602e7	−	1.13917e7i	−0.203981	−	0.0662774i
$557$	1.10518e8	+	1.52114e8i	0.639537	+	0.880248i	0.998591	−	0.0530694i	$-0.0169005\pi$
$557$	1.10518e8	+	1.52114e8i	0.639537	+	0.880248i	−0.359054	+	0.933317i	$0.616900\pi$
$558$	8.15077e6	−	1.12186e7i	0.0469133	−	0.0645706i
$559$	4.71225e7	+	1.45028e8i	0.269769	+	0.830265i
$560$			6.09799e7i			0.347234i
$561$	3.63402e8	+	5.77754e7i	2.05825	+	0.327231i
$562$	6.55744e6			0.0369424
$563$	−5.60393e7	+	1.82083e7i	−0.314027	+	0.102034i	−0.461790	−	0.886989i	$-0.652793\pi$
$563$	−5.60393e7	+	1.82083e7i	−0.314027	+	0.102034i	0.147763	+	0.989023i	$0.452793\pi$
$564$	−9.31233e7	−	6.76581e7i	−0.519064	−	0.377122i
$565$	−5.78331e6	+	4.20182e6i	−0.0320650	+	0.0232966i
$566$	4.06804e6	−	1.25201e7i	0.0224355	−	0.0690493i
$567$	−4.02160e7	−	1.30670e7i	−0.220622	−	0.0716846i
$568$	3.78618e6	+	5.21123e6i	0.0206612	+	0.0284378i
$569$	−6.37227e7	+	8.77068e7i	−0.345906	+	0.476098i	−0.946155	−	0.323715i	$-0.895068\pi$
$569$	−6.37227e7	+	8.77068e7i	−0.345906	+	0.476098i	0.600249	+	0.799813i	$0.295068\pi$
$570$	3.20738e6	+	9.87129e6i	0.0173191	+	0.0533027i
$571$			7.34263e7i			0.394406i	0.980363	+	0.197203i	$0.0631858\pi$
$571$			7.34263e7i			0.394406i	−0.980363	+	0.197203i	$0.936814\pi$
$572$	−3.76470e7	−	2.38598e8i	−0.201160	−	1.27491i
$573$	5.13190e7			0.272781
$574$	−74042.6	+	24057.9i	−0.000391513	+	0.000127210i
$575$	−1.23116e7	−	8.94487e6i	−0.0647604	−	0.0470512i
$576$	−2.08344e8	+	1.51371e8i	−1.09022	+	0.792091i
$577$	6.03560e6	−	1.85757e7i	0.0314190	−	0.0966978i	−0.934117	−	0.356966i	$-0.883811\pi$
$577$	6.03560e6	−	1.85757e7i	0.0314190	−	0.0966978i	0.965536	+	0.260269i	$0.0838111\pi$
$578$	5.91793e6	+	1.92285e6i	0.0306469	+	0.00995778i
$579$	−1.47968e8	−	2.03661e8i	−0.762312	−	1.04923i
$580$	−1.47649e8	+	2.03221e8i	−0.756737	+	1.04156i
$581$	−3.05435e7	−	9.40031e7i	−0.155736	−	0.479307i
$582$			3.96813e6i			0.0201287i
$583$	−1.06985e8	−	5.45905e7i	−0.539905	−	0.275494i
$584$	−1.07444e7			−0.0539441
$585$	−2.57151e8	+	8.35536e7i	−1.28446	+	0.417347i
$586$	1.61411e6	+	1.17272e6i	0.00802119	+	0.00582774i
$587$	1.94678e7	−	1.41442e7i	0.0962506	−	0.0699301i	−0.538619	−	0.842549i	$-0.681054\pi$
$587$	1.94678e7	−	1.41442e7i	0.0962506	−	0.0699301i	0.634870	+	0.772619i	$0.281054\pi$
$588$	7.65138e7	−	2.35485e8i	0.376364	−	1.15833i
$589$	−3.68750e8	−	1.19814e8i	−1.80462	−	0.586357i
$590$	2.08697e6	+	2.87247e6i	0.0101616	+	0.0139862i
$591$	1.93022e8	−	2.65672e8i	0.935069	−	1.28701i
$592$	180669.	+	556041.i	0.000870798	+	0.00268004i
$593$		−	4.45741e7i		−	0.213756i	−0.994272	−	0.106878i	$-0.965915\pi$
$593$		−	4.45741e7i		−	0.213756i	0.994272	−	0.106878i	$-0.0340855\pi$
$594$	−3.13510e6	−	3.13877e6i	−0.0149586	−	0.0149762i
$595$	9.96769e7			0.473199
$596$	−1.98389e8	+	6.44606e7i	−0.937086	+	0.304478i
$597$	1.99221e8	+	1.44742e8i	0.936292	+	0.680256i
$598$	1.67590e6	−	1.21762e6i	0.00783692	−	0.00569386i
$599$	8.66460e7	−	2.66669e8i	0.403151	−	1.24077i	−0.519278	−	0.854605i	$-0.673799\pi$
$599$	8.66460e7	−	2.66669e8i	0.403151	−	1.24077i	0.922429	−	0.386166i	$-0.126201\pi$
$600$	9.89410e6	+	3.21479e6i	0.0458060	+	0.0148833i
$601$	1.50631e8	+	2.07326e8i	0.693891	+	0.955060i	0.999995	+	0.00306146i	$0.000974495\pi$
$601$	1.50631e8	+	2.07326e8i	0.693891	+	0.955060i	−0.306104	+	0.951998i	$0.599026\pi$
$602$	−1.50634e6	+	2.07330e6i	−0.00690453	+	0.00950327i
$603$	5.01922e7	+	1.54476e8i	0.228920	+	0.704544i
$604$			1.83580e8i			0.833134i
$605$	−1.61796e8	−	5.27804e7i	−0.730637	−	0.238345i
$606$	−1.92415e7			−0.0864612
$607$	1.85710e8	−	6.03408e7i	0.830365	−	0.269802i	0.137166	−	0.990548i	$-0.456201\pi$
$607$	1.85710e8	−	6.03408e7i	0.830365	−	0.269802i	0.693199	+	0.720746i	$0.256201\pi$
$608$	−2.58467e7	−	1.87787e7i	−0.114999	−	0.0835518i
$609$	−2.13701e8	+	1.55263e8i	−0.946138	+	0.687410i
$610$	−2.36305e6	+	7.27272e6i	−0.0104108	+	0.0320411i
$611$	1.17294e8	+	3.81110e7i	0.514223	+	0.167081i
$612$	2.48162e8	+	3.41565e8i	1.08263	+	1.49011i
$613$	1.78869e8	−	2.46193e8i	0.776524	−	1.06879i	−0.219133	−	0.975695i	$-0.570323\pi$
$613$	1.78869e8	−	2.46193e8i	0.776524	−	1.06879i	0.995657	−	0.0930984i	$-0.0296771\pi$
$614$	−833963.	−	2.56667e6i	−0.00360281	−	0.0110883i
$615$			6.49947e6i			0.0279417i
$616$	5.74851e6	−	5.74178e6i	0.0245931	−	0.0245643i
$617$	−2.59209e8			−1.10356			−0.551779	−	0.833991i	$-0.686051\pi$
$617$	−2.59209e8			−1.10356			−0.551779	+	0.833991i	$0.686051\pi$
$618$	−8.63141e6	+	2.80452e6i	−0.0365693	+	0.0118821i
$619$	−2.84851e8	−	2.06957e8i	−1.20101	−	0.872584i	−0.206625	−	0.978420i	$-0.566248\pi$
$619$	−2.84851e8	−	2.06957e8i	−1.20101	−	0.872584i	−0.994384	+	0.105836i	$0.966248\pi$
$620$	2.26648e8	−	1.64670e8i	0.950994	−	0.690937i
$621$	−7.99245e6	+	2.45982e7i	−0.0333738	+	0.102714i
$622$	−5.94290e6	−	1.93097e6i	−0.0246960	−	0.00802423i
$623$	5.29652e7	+	7.29004e7i	0.219042	+	0.301485i
$624$	2.82311e8	−	3.88568e8i	1.16191	−	1.59924i
$625$	−3.19174e7	−	9.82318e7i	−0.130734	−	0.402357i
$626$		−	1.08581e7i		−	0.0442618i
$627$	−2.13180e8	+	4.17783e8i	−0.864855	+	1.69492i
$628$	2.01180e8			0.812279
$629$	908896.	−	295318.i	0.00365227	−	0.00118669i
$630$	−3.67620e6	−	2.67092e6i	−0.0147020	−	0.0106817i
$631$	−3.31399e8	+	2.40776e8i	−1.31906	+	0.958351i	−0.319113	+	0.947717i	$0.603385\pi$
$631$	−3.31399e8	+	2.40776e8i	−1.31906	+	0.958351i	−0.999943	+	0.0106344i	$0.996615\pi$
$632$	3.94887e6	−	1.21534e7i	0.0156431	−	0.0481444i
$633$	1.97757e8	+	6.42552e7i	0.779689	+	0.253336i
$634$	7.76174e6	+	1.06831e7i	0.0304573	+	0.0419209i
$635$	−1.31449e8	+	1.80924e8i	−0.513376	+	0.706602i
$636$	−7.39088e7	−	2.27468e8i	−0.287293	−	0.884196i
$637$			2.65293e8i			1.02638i
$638$	1.64934e7	−	2.60239e6i	0.0635109	−	0.0100210i
$639$	1.62795e8			0.623934
$640$	2.92655e7	−	9.50893e6i	0.111639	−	0.0362737i
$641$	4.00500e7	+	2.90980e7i	0.152065	+	0.110481i	0.661216	−	0.750196i	$-0.270041\pi$
$641$	4.00500e7	+	2.90980e7i	0.152065	+	0.110481i	−0.509151	+	0.860677i	$0.670041\pi$
$642$	1.96040e6	−	1.42432e6i	0.00740867	−	0.00538271i
$643$	5.21264e7	−	1.60428e8i	0.196076	−	0.603460i	−0.803886	−	0.594783i	$-0.797238\pi$
$643$	5.21264e7	−	1.60428e8i	0.196076	−	0.603460i	0.999962	−	0.00867692i	$-0.00276199\pi$
$644$	−2.25087e7	−	7.31351e6i	−0.0842738	−	0.0273822i
$645$	1.25755e8	+	1.73087e8i	0.468649	+	0.645040i
$646$	−1.02067e7	+	1.40484e7i	−0.0378608	+	0.0521109i
$647$	−5.04658e7	−	1.55318e8i	−0.186330	−	0.573466i	0.813638	−	0.581371i	$-0.197484\pi$
$647$	−5.04658e7	−	1.55318e8i	−0.186330	−	0.573466i	−0.999969	+	0.00790517i	$0.997484\pi$
$648$			1.06533e7i			0.0391526i
$649$	−2.51922e7	+	1.58456e8i	−0.0921578	+	0.579663i
$650$	−5.56914e6			−0.0202791
$651$	2.80182e8	−	9.10365e7i	1.01554	−	0.329969i
$652$	4.37296e8	+	3.17714e8i	1.57773	+	1.14629i
$653$	2.63901e8	−	1.91735e8i	0.947767	−	0.688593i	−0.00251085	−	0.999997i	$-0.500799\pi$
$653$	2.63901e8	−	1.91735e8i	0.947767	−	0.688593i	0.950278	+	0.311404i	$0.100799\pi$
$654$	3.20658e6	−	9.86883e6i	0.0114633	−	0.0352803i
$655$	3.17926e8	+	1.03300e8i	1.13136	+	0.367602i
$656$	−3.91012e6	−	5.38182e6i	−0.0138509	−	0.0190641i
$657$	−1.59610e8	+	2.19684e8i	−0.562812	+	0.774644i
$658$	640487.	+	1.97122e6i	0.00224819	+	0.00691921i
$659$		−	3.08695e8i		−	1.07863i	−0.842103	−	0.539317i	$-0.818683\pi$
$659$		−	3.08695e8i		−	1.07863i	0.842103	−	0.539317i	$-0.181317\pi$
$660$	−1.53680e8	−	3.02051e8i	−0.534546	−	1.05063i
$661$	−3.52705e8			−1.22126			−0.610629	−	0.791917i	$-0.709083\pi$
$661$	−3.52705e8			−1.22126			−0.610629	+	0.791917i	$0.709083\pi$
$662$	7.45003e6	−	2.42066e6i	0.0256794	−	0.00834373i
$663$	−6.35148e8	−	4.61462e8i	−2.17939	−	1.58342i
$664$	−2.01459e7	+	1.46368e7i	−0.0688148	+	0.0499969i
$665$	−3.92617e7	+	1.20835e8i	−0.133507	+	0.410893i
$666$	−41434.4	−	13462.9i	−0.000140262	−	4.55738e-5i
$667$	−5.72197e7	−	7.87562e7i	−0.192827	−	0.265404i
$668$	−1.03898e8	+	1.43004e8i	−0.348562	+	0.479754i
$669$	−1.28073e8	−	3.94168e8i	−0.427739	−	1.31645i
$670$		−	4.82698e6i		−	0.0160491i
$671$	−3.07988e8	+	1.56700e8i	−1.01945	+	0.518683i
$672$	2.42748e7			0.0799923
$673$	−2.09460e8	+	6.80578e7i	−0.687158	+	0.223271i	−0.631727	−	0.775191i	$-0.717653\pi$
$673$	−2.09460e8	+	6.80578e7i	−0.687158	+	0.223271i	−0.0554317	+	0.998462i	$0.517653\pi$
$674$	6.07586e6	+	4.41437e6i	0.0198440	+	0.0144175i
$675$	5.62538e7	−	4.08708e7i	0.182911	−	0.132893i
$676$	−6.39374e7	+	1.96779e8i	−0.206974	+	0.636999i
$677$	2.45691e8	+	7.98298e7i	0.791813	+	0.257276i	0.676876	−	0.736097i	$-0.263333\pi$
$677$	2.45691e8	+	7.98298e7i	0.791813	+	0.257276i	0.114937	+	0.993373i	$0.463333\pi$
$678$	556185.	+	765522.i	0.00178455	+	0.00245623i
$679$	−2.85512e7	+	3.92973e7i	−0.0912042	+	0.125532i
$680$	−7.76014e6	−	2.38833e7i	−0.0246799	−	0.0759568i
$681$		−	3.07544e8i		−	0.973790i
$682$	−1.83914e7	−	2.92395e6i	−0.0579777	−	0.00921759i
$683$	1.46302e8			0.459184			0.229592	−	0.973287i	$-0.426261\pi$
$683$	1.46302e8			0.459184			0.229592	+	0.973287i	$0.426261\pi$
$684$	−5.11817e8	+	1.66299e8i	−1.59936	+	0.519664i
$685$	−1.07808e8	−	7.83269e7i	−0.335412	−	0.243691i
$686$	−8.14944e6	+	5.92092e6i	−0.0252439	+	0.0183407i
$687$	−1.92332e7	+	5.91938e7i	−0.0593174	+	0.182560i
$688$	−2.08261e8	−	6.76680e7i	−0.639502	−	0.207787i
$689$	1.50626e8	+	2.07319e8i	0.460514	+	0.633842i
$690$	1.70833e6	−	2.35132e6i	0.00520026	−	0.00715754i
$691$	1.09483e8	+	3.36955e8i	0.331829	+	1.02126i	0.968263	+	0.249933i	$0.0804085\pi$
$691$	1.09483e8	+	3.36955e8i	0.331829	+	1.02126i	−0.636435	+	0.771331i	$0.719591\pi$
$692$		−	1.81948e8i		−	0.549071i
$693$	−3.20035e7	−	2.02831e8i	−0.0961607	−	0.609445i
$694$	1.94804e7			0.0582799
$695$	5.27040e7	−	1.71246e7i	0.156996	−	0.0510112i
$696$	5.38393e7	+	3.91165e7i	0.159688	+	0.116020i
$697$	−8.79704e6	+	6.39143e6i	−0.0259800	+	0.0188755i
$698$	−2.23446e6	+	6.87696e6i	−0.00657062	+	0.0202223i
$699$	7.01761e8	+	2.28016e8i	2.05474	+	0.667627i
$700$	3.73989e7	+	5.14752e7i	0.109035	+	0.150073i
$701$	2.80266e8	−	3.85753e8i	0.813610	−	1.11984i	−0.177147	−	0.984184i	$-0.556687\pi$
$701$	2.80266e8	−	3.85753e8i	0.813610	−	1.11984i	0.990756	−	0.135653i	$-0.0433133\pi$
$702$	2.92491e6	+	9.00196e6i	0.00845477	+	0.0260211i
$703$			1.21815e6i			0.00350618i
$704$	3.08056e8	+	1.57190e8i	0.882900	+	0.450512i
$705$	1.73034e8			0.493814
$706$	2.11125e7	−	6.85988e6i	0.0599966	−	0.0194941i
$707$	−1.90553e8	−	1.38445e8i	−0.539210	−	0.391759i
$708$	−2.58482e8	+	1.87798e8i	−0.728333	+	0.529165i
$709$	6.73306e7	−	2.07222e8i	0.188918	−	0.581430i	−0.811076	−	0.584941i	$-0.801118\pi$
$709$	6.73306e7	−	2.07222e8i	0.188918	−	0.581430i	0.999994	+	0.00351095i	$0.00111757\pi$
$710$	−4.60118e6	−	1.49501e6i	−0.0128557	−	0.00417706i
$711$	−1.89831e8	−	2.61280e8i	−0.528152	−	0.726939i
$712$	1.33439e7	−	1.83663e7i	0.0369695	−	0.0508841i
$713$	3.35501e7	+	1.03257e8i	0.0925604	+	0.284872i
$714$		−	1.31940e7i		−	0.0362478i
$715$	2.56606e8	+	2.56907e8i	0.702020	+	0.702843i
$716$	1.27538e8			0.347456
$717$	5.08125e8	−	1.65100e8i	1.37852	−	0.447909i
$718$	−2.11984e7	−	1.54016e7i	−0.0572704	−	0.0416094i
$719$	−3.67403e8	+	2.66934e8i	−0.988453	+	0.718153i	−0.959582	−	0.281430i	$-0.909191\pi$
$719$	−3.67403e8	+	2.66934e8i	−0.988453	+	0.718153i	−0.0288714	+	0.999583i	$0.509191\pi$
$720$	1.19983e8	−	3.69270e8i	0.321457	−	0.989342i
$721$	−1.05658e8	−	3.43303e7i	−0.281900	−	0.0915950i
$722$	−4.53166e6	−	6.23729e6i	−0.0120405	−	0.0165724i
$723$	−3.60407e8	+	4.96057e8i	−0.953625	+	1.31255i
$724$	6.90021e7	+	2.12367e8i	0.181822	+	0.559591i
$725$			2.61712e8i			0.686767i
$726$	−6.98642e6	+	2.14166e7i	−0.0182576	+	0.0559680i
$727$	−4.52587e7			−0.117787			−0.0588937	−	0.998264i	$-0.518757\pi$
$727$	−4.52587e7			−0.117787			−0.0588937	+	0.998264i	$0.518757\pi$
$728$	−1.64866e7	+	5.35683e6i	−0.0427305	+	0.0138840i
$729$	4.83730e8	+	3.51451e8i	1.24859	+	0.907155i
$730$	6.52861e6	−	4.74331e6i	0.0167823	−	0.0121931i
$731$	−1.10609e8	+	3.40420e8i	−0.283165	+	0.871491i
$732$	−6.54442e8	−	2.12641e8i	−1.66855	−	0.542143i
$733$	−2.57116e8	−	3.53890e8i	−0.652856	−	0.898579i	0.346363	−	0.938101i	$-0.387417\pi$
$733$	−2.57116e8	−	3.53890e8i	−0.652856	−	0.898579i	−0.999219	+	0.0395213i	$0.987417\pi$
$734$	−9.25922e6	+	1.27442e7i	−0.0234146	+	0.0322274i
$735$	1.15019e8	+	3.53992e8i	0.289673	+	0.891521i
$736$			8.94610e6i			0.0224388i
$737$	1.54329e8	−	1.54148e8i	0.385518	−	0.385067i
$738$	495708.			0.00123327
$739$	1.35247e8	−	4.39446e7i	0.335117	−	0.108886i	−0.136625	−	0.990623i	$-0.543626\pi$
$739$	1.35247e8	−	4.39446e7i	0.335117	−	0.108886i	0.471742	+	0.881737i	$0.343626\pi$
$740$	−712078.	−	517355.i	−0.00175725	−	0.00127671i
$741$	8.09594e8	−	5.88205e8i	1.98982	−	1.44569i
$742$	−1.33083e6	+	4.09588e6i	−0.00325770	+	0.0100262i
$743$	−6.79453e8	−	2.20768e8i	−1.65651	−	0.538232i	−0.676371	−	0.736561i	$-0.736448\pi$
$743$	−6.79453e8	−	2.20768e8i	−1.65651	−	0.538232i	−0.980135	+	0.198330i	$0.936448\pi$
$744$	−4.36259e7	−	6.00459e7i	−0.105932	−	0.145802i
$745$	1.84315e8	−	2.53687e8i	0.445750	−	0.613522i
$746$	−553939.	−	1.70485e6i	−0.00133428	−	0.00410648i
$747$			6.29342e8i			1.50982i
$748$	2.57701e8	−	5.05035e8i	0.615760	−	1.20675i
$749$	2.96625e7			0.0705930
$750$	−2.55842e7	+	8.31283e6i	−0.0606441	+	0.0197045i
$751$	1.55197e8	+	1.12757e8i	0.366407	+	0.266210i	0.755720	−	0.654895i	$-0.227287\pi$
$751$	1.55197e8	+	1.12757e8i	0.366407	+	0.266210i	−0.389312	+	0.921106i	$0.627287\pi$
$752$	−1.43279e8	+	1.04098e8i	−0.336921	+	0.244787i
$753$	−1.81259e8	+	5.57858e8i	−0.424536	+	1.30659i
$754$	−3.38818e7	−	1.10089e7i	−0.0790409	−	0.0256820i
$755$	−1.62209e8	−	2.23261e8i	−0.376906	−	0.518767i
$756$	6.35626e7	−	8.74864e7i	0.147108	−	0.202477i
$757$	−1.83535e8	−	5.64863e8i	−0.423089	−	1.30213i	−0.904812	−	0.425810i	$-0.859989\pi$
$757$	−1.83535e8	−	5.64863e8i	−0.423089	−	1.30213i	0.481723	−	0.876323i	$-0.340011\pi$
$758$			1.05310e7i			0.0241803i
$759$	1.29732e8	−	2.04696e7i	0.296702	−	0.0468148i
$760$	3.20096e7			0.0729187
$761$	−2.90720e8	+	9.44606e7i	−0.659661	+	0.214337i	−0.619669	−	0.784863i	$-0.712733\pi$
$761$	−2.90720e8	+	9.44606e7i	−0.659661	+	0.214337i	−0.0399917	+	0.999200i	$0.512733\pi$
$762$	2.39485e7	+	1.73996e7i	0.0541269	+	0.0393255i
$763$	1.02763e8	−	7.46617e7i	0.231347	−	0.168083i
$764$	2.44356e7	−	7.52051e7i	0.0547953	−	0.168643i
$765$	−6.03604e8	−	1.96123e8i	−1.34824	−	0.438070i
$766$	4.96091e6	+	6.82811e6i	0.0110376	+	0.0151920i
$767$	2.01214e8	−	2.76948e8i	0.445936	−	0.613778i
$768$	2.11870e8	+	6.52068e8i	0.467719	+	1.43949i
$769$		−	7.35192e8i		−	1.61667i	−0.588722	−	0.808335i	$-0.700369\pi$
$769$		−	7.35192e8i		−	1.61667i	0.588722	−	0.808335i	$-0.299631\pi$
$770$	−958147.	+	6.02665e6i	−0.00209875	+	0.0132009i
$771$	−1.20862e9			−2.63711
$772$	−3.68909e8	+	1.19866e8i	−0.801802	+	0.260521i
$773$	5.93832e8	+	4.31444e8i	1.28566	+	0.934084i	0.999708	−	0.0241609i	$-0.00769142\pi$
$773$	5.93832e8	+	4.31444e8i	1.28566	+	0.934084i	0.285948	+	0.958245i	$0.407691\pi$
$774$	1.32012e7	−	9.59124e6i	0.0284702	−	0.0206848i
$775$	9.01967e7	−	2.77597e8i	0.193769	−	0.596361i
$776$	1.16387e7	+	3.78164e6i	0.0249069	+	0.00809273i
$777$	−544035.	−	748801.i	−0.00115975	−	0.00159626i
$778$	71642.3	−	98607.2i	0.000152136	−	0.000209397i
$779$	−4.28306e6	−	1.31819e7i	−0.00906028	−	0.0278847i
$780$			7.23068e8i			1.52369i
$781$	−9.91386e7	−	1.94852e8i	−0.208108	−	0.409028i
$782$	4.86244e6			0.0101680
$783$	4.23031e8	−	1.37451e8i	0.881226	−	0.286328i
$784$	−3.08204e8	−	2.23923e8i	−0.639572	−	0.464677i
$785$	−2.44665e8	+	1.77759e8i	−0.505781	+	0.367472i
$786$	1.36736e7	−	4.20831e7i	0.0281589	−	0.0866642i
$787$	−4.72141e7	−	1.53408e7i	−0.0968606	−	0.0314719i	0.260186	−	0.965559i	$-0.416216\pi$
$787$	−4.72141e7	−	1.53408e7i	−0.0968606	−	0.0314719i	−0.357046	+	0.934087i	$0.616216\pi$
$788$	−2.97419e8	−	4.09362e8i	−0.607842	−	0.836622i
$789$	−4.57892e8	+	6.30234e8i	−0.932248	+	1.28313i
$790$	2.96588e6	+	9.12804e6i	0.00601550	+	0.0185138i
$791$			1.15830e7i			0.0234040i
$792$	−4.61081e7	+	2.34592e7i	−0.0928115	+	0.0472213i
$793$	7.37280e8			1.47847
$794$	8.45795e6	−	2.74815e6i	0.0168968	−	0.00549009i
$795$	2.90871e8	+	2.11330e8i	0.578895	+	0.420592i
$796$	3.06971e8	−	2.23028e8i	0.608637	−	0.442201i
$797$	−6.52749e7	+	2.00896e8i	−0.128935	+	0.396822i	−0.994597	−	0.103807i	$-0.966898\pi$
$797$	−6.52749e7	+	2.00896e8i	−0.128935	+	0.396822i	0.865662	+	0.500628i	$0.166898\pi$
$798$	1.59947e7	+	5.19698e6i	0.0314751	+	0.0102269i
$799$	1.70157e8	+	2.34201e8i	0.333587	+	0.459144i
$800$	1.41367e7	−	1.94575e7i	0.0276108	−	0.0380030i
$801$	−1.77299e8	−	5.45669e8i	−0.344991	−	1.06177i
$802$		−	3.34759e7i		−	0.0648946i
$803$	3.60143e8	+	5.72573e7i	0.695550	+	0.110582i
$804$	4.34361e8			0.835761
$805$	3.38360e7	−	1.09940e7i	0.0648622	−	0.0210750i
$806$	3.21442e7	+	2.33541e7i	0.0613899	+	0.0446024i
$807$	7.34559e8	−	5.33688e8i	1.39767	−	1.01547i
$808$	−1.83372e7	+	5.64362e7i	−0.0347616	+	0.106985i
$809$	7.50549e8	+	2.43868e8i	1.41753	+	0.460585i	0.914818	−	0.403867i	$-0.132334\pi$
$809$	7.50549e8	+	2.43868e8i	1.41753	+	0.460585i	0.502716	+	0.864452i	$0.332334\pi$
$810$	−4.70310e6	−	6.47326e6i	−0.00884971	−	0.0121806i
$811$	−4.49227e8	+	6.18308e8i	−0.842177	+	1.15916i	0.143355	+	0.989671i	$0.454211\pi$
$811$	−4.49227e8	+	6.18308e8i	−0.842177	+	1.15916i	−0.985533	+	0.169486i	$0.945789\pi$
$812$	1.25775e8	+	3.87096e8i	0.234923	+	0.723020i
$813$		−	8.23953e6i		−	0.0153331i
$814$	9118.69	+	57792.3i	1.69067e−5	+	0.000107151i
$815$	−8.12544e8			−1.50098
$816$	1.07221e9	−	3.48381e8i	1.97337	−	0.641186i
$817$	−3.69113e8	−	2.68176e8i	−0.676851	−	0.491761i
$818$	−1.83471e7	+	1.33300e7i	−0.0335203	+	0.0243540i
$819$	−1.35384e8	+	4.16668e8i	−0.246442	+	0.758470i
$820$	9.52462e6	+	3.09474e6i	0.0172745	+	0.00561283i
$821$	4.38855e7	+	6.04033e7i	0.0793034	+	0.109152i	0.846826	−	0.531870i	$-0.178511\pi$
$821$	4.38855e7	+	6.04033e7i	0.0793034	+	0.109152i	−0.767522	+	0.641022i	$0.778511\pi$
$822$	−1.03679e7	+	1.42702e7i	−0.0186671	+	0.0256931i
$823$	1.01276e8	+	3.11696e8i	0.181680	+	0.559155i	0.999875	−	0.0157860i	$-0.00502506\pi$
$823$	1.01276e8	+	3.11696e8i	0.181680	+	0.559155i	−0.818195	+	0.574941i	$0.805025\pi$
$824$			2.79890e7i			0.0500272i
$825$	−3.14509e8	−	1.60483e8i	−0.560108	−	0.285803i
$826$	5.75306e6			0.0102084
$827$	7.65418e8	−	2.48699e8i	1.35326	−	0.439702i	0.459475	−	0.888191i	$-0.348038\pi$
$827$	7.65418e8	−	2.48699e8i	1.35326	−	0.439702i	0.893788	+	0.448489i	$0.148038\pi$
$828$	1.21914e8	+	8.85754e7i	0.214764	+	0.156035i
$829$	−1.06973e8	+	7.77203e7i	−0.187763	+	0.136418i	−0.677696	−	0.735342i	$-0.737021\pi$
$829$	−1.06973e8	+	7.77203e7i	−0.187763	+	0.136418i	0.489933	+	0.871760i	$0.337021\pi$
$830$	5.77951e6	−	1.77875e7i	0.0101078	−	0.0311086i
$831$	6.82572e7	+	2.21781e7i	0.118945	+	0.0386475i
$832$	−4.33717e8	−	5.96961e8i	−0.753073	−	1.03652i
$833$	−3.66022e8	+	5.03786e8i	−0.633245	+	0.871587i
$834$	−2.26674e6	−	6.97630e6i	−0.00390754	−	0.0120262i
$835$		−	2.65717e8i		−	0.456416i
$836$	5.10732e8	+	5.11331e8i	0.874127	+	0.875152i
$837$	−4.96079e8			−0.846008
$838$	1.68290e7	−	5.46809e6i	0.0285975	−	0.00929188i
$839$	−5.96574e8	−	4.33436e8i	−1.01013	−	0.733904i	−0.0458959	−	0.998946i	$-0.514614\pi$
$839$	−5.96574e8	−	4.33436e8i	−1.01013	−	0.733904i	−0.964237	+	0.265042i	$0.914614\pi$
$840$	−1.96764e7	+	1.42957e7i	−0.0331977	+	0.0241195i
$841$	−3.33531e8	+	1.02650e9i	−0.560723	+	1.72573i
$842$	1.97642e7	+	6.42179e6i	0.0331088	+	0.0107577i
$843$	−5.21383e8	−	7.17623e8i	−0.870311	−	1.19788i
$844$	1.88325e8	−	2.59207e8i	0.313242	−	0.431141i
$845$	−9.61136e7	−	2.95807e8i	−0.159300	−	0.490274i
$846$		−	1.31971e7i		−	0.0217955i
$847$	−2.23283e8	+	1.61825e8i	−0.367456	+	0.266315i
$848$	−3.67990e8			−0.603461
$849$	−1.69361e9	+	5.50287e8i	−2.76751	+	0.899220i
$850$	−1.05757e7	−	7.68369e6i	−0.0172207	−	0.0125116i
$851$	275959.	−	200496.i	0.000447771	−	0.000325324i
$852$	1.34530e8	−	4.14042e8i	0.217521	−	0.669461i
$853$	1.16094e9	+	3.77213e8i	1.87052	+	0.607770i	0.991346	+	0.131275i	$0.0419071\pi$
$853$	1.16094e9	+	3.77213e8i	1.87052	+	0.607770i	0.879177	+	0.476495i	$0.158093\pi$
$854$	7.28300e6	+	1.00242e7i	0.0116933	+	0.0160944i
$855$	4.75507e8	−	6.54479e8i	0.760779	−	1.04712i
$856$	−2.30931e6	−	7.10732e6i	−0.00368181	−	0.0113314i
$857$		−	1.07720e9i		−	1.71141i	−0.517461	−	0.855707i	$-0.673123\pi$
$857$		−	1.07720e9i		−	1.71141i	0.517461	−	0.855707i	$-0.326877\pi$
$858$	3.40062e7	−	3.39664e7i	0.0538389	−	0.0537759i
$859$	7.26527e8			1.14623			0.573116	−	0.819474i	$-0.305735\pi$
$859$	7.26527e8			1.14623			0.573116	+	0.819474i	$0.305735\pi$
$860$	3.13529e8	−	1.01872e8i	0.492926	−	0.160161i
$861$	8.51995e6	+	6.19011e6i	0.0133484	+	0.00969815i
$862$	−2.38740e6	+	1.73455e6i	−0.00372738	+	0.00270810i
$863$	−8.88294e7	+	2.73389e8i	−0.138205	+	0.425352i	−0.996075	−	0.0885157i	$-0.971788\pi$
$863$	−8.88294e7	+	2.73389e8i	−0.138205	+	0.425352i	0.857870	+	0.513867i	$0.171788\pi$
$864$	−3.88758e7	−	1.26315e7i	−0.0602751	−	0.0195846i
$865$	1.60766e8	+	2.21276e8i	0.248397	+	0.341889i
$866$	−1.51553e7	+	2.08595e7i	−0.0233352	+	0.0321182i
$867$	−2.60106e8	−	8.00524e8i	−0.399110	−	1.22834i
$868$		−	4.53938e8i		−	0.694124i
$869$	−1.97128e8	+	3.86327e8i	−0.300393	+	0.588702i
$870$	−4.99829e7			−0.0759039
$871$	−4.42613e8	+	1.43814e8i	−0.669838	+	0.217644i
$872$	−2.58898e7	−	1.88101e7i	−0.0390463	−	0.0283688i
$873$	2.50215e8	−	1.81792e8i	0.376072	−	0.273232i
$874$	−1.91527e6	+	5.89459e6i	−0.00286877	+	0.00882915i
$875$	−3.13179e8	−	1.01758e8i	−0.467486	−	0.151895i
$876$	4.26831e8	+	5.87483e8i	0.634956	+	0.873942i
$877$	−5.89449e8	+	8.11307e8i	−0.873871	+	1.20278i	0.104210	+	0.994555i	$0.466769\pi$
$877$	−5.89449e8	+	8.11307e8i	−0.873871	+	1.20278i	−0.978081	+	0.208225i	$0.933231\pi$
$878$	1.74086e6	+	5.35780e6i	0.00257205	+	0.00791595i
$879$		−	2.69885e8i		−	0.397385i
$880$	−5.15054e8	+	8.12672e7i	−0.755796	+	0.119252i
$881$	1.02246e9			1.49527			0.747636	−	0.664109i	$-0.231189\pi$
$881$	1.02246e9			1.49527			0.747636	+	0.664109i	$0.231189\pi$
$882$	2.69986e7	−	8.77238e6i	0.0393492	−	0.0127853i
$883$	3.90625e8	+	2.83806e8i	0.567385	+	0.412230i	0.834155	−	0.551531i	$-0.185956\pi$
$883$	3.90625e8	+	2.83806e8i	0.567385	+	0.412230i	−0.266769	+	0.963760i	$0.585956\pi$
$884$	−9.78674e8	+	7.11048e8i	−1.41671	+	1.02930i
$885$	1.48417e8	−	4.56781e8i	0.214119	−	0.658989i
$886$	−3.53375e7	−	1.14818e7i	−0.0508082	−	0.0165086i
$887$	3.35409e8	+	4.61651e8i	0.480622	+	0.661520i	0.978624	−	0.205656i	$-0.0659329\pi$
$887$	3.35409e8	+	4.61651e8i	0.480622	+	0.661520i	−0.498002	+	0.867176i	$0.665933\pi$
$888$	−137063.	+	188651.i	−0.000195741	+	0.000269414i
$889$	1.11975e8	+	3.44625e8i	0.159374	+	0.490502i
$890$			1.70508e7i			0.0241866i
$891$	5.67720e7	−	3.57090e8i	0.0802603	−	0.504829i
$892$	−6.38613e8			−0.899795
$893$	−3.50938e8	+	1.14027e8i	−0.492806	+	0.160122i
$894$	−3.35800e7	−	2.43973e7i	−0.0469968	−	0.0341452i
$895$	−1.55105e8	+	1.12690e8i	−0.216350	+	0.157188i
$896$	1.54075e7	−	4.74195e7i	0.0214195	−	0.0659224i
$897$	−2.66503e8	−	8.65921e7i	−0.369254	−	0.119978i
$898$	2.46318e7	+	3.39027e7i	0.0340147	+	0.0468172i
$899$	1.09748e9	−	1.51056e9i	1.51050	−	2.07902i
$900$	−1.25191e8	−	3.85299e8i	−0.171730	−	0.528530i
$901$			6.01512e8i			0.822375i
$902$	−301875.	−	593323.i	−0.000411347	−	0.000808484i
$903$	3.46664e8			0.470810
$904$	2.77536e6	−	901768.i	0.00375676	−	0.00122065i
$905$	−2.71561e8	−	1.97301e8i	−0.366371	−	0.266184i
$906$	−2.95525e7	+	2.14712e7i	−0.0397384	+	0.0288716i
$907$	1.50312e8	−	4.62613e8i	0.201452	−	0.620006i	−0.798388	−	0.602143i	$-0.794314\pi$
$907$	1.50312e8	−	4.62613e8i	0.201452	−	0.620006i	0.999840	−	0.0178629i	$-0.00568623\pi$
$908$	−4.50688e8	−	1.46437e8i	−0.602030	−	0.195612i
$909$	8.81512e8	+	1.21330e9i	1.17364	+	1.61538i
$910$	7.65288e6	−	1.05333e7i	0.0101555	−	0.0139778i
$911$	4.83124e7	+	1.48690e8i	0.0639004	+	0.196665i	0.977910	−	0.209028i	$-0.0670301\pi$
$911$	4.83124e7	+	1.48690e8i	0.0639004	+	0.196665i	−0.914009	+	0.405693i	$0.867030\pi$
$912$			1.43703e9i			1.89444i
$913$	7.53272e8	−	3.83255e8i	0.989782	−	0.503589i
$914$	−3.22228e7			−0.0422012
$915$	9.83787e8	−	3.19652e8i	1.28421	−	0.417267i
$916$	7.75873e7	+	5.63704e7i	0.100949	+	0.0733441i
$917$	4.38206e8	−	3.18375e8i	0.568291	−	0.412887i
$918$	−6.86556e6	+	2.11300e7i	−0.00887458	+	0.0273132i
$919$	4.36639e8	+	1.41873e8i	0.562569	+	0.182790i	0.576477	−	0.817114i	$-0.304427\pi$
$919$	4.36639e8	+	1.41873e8i	0.562569	+	0.182790i	−0.0139077	+	0.999903i	$0.504427\pi$
$920$	−5.26847e6	−	7.25143e6i	−0.00676583	−	0.00931237i
$921$	−2.14579e8	+	2.95343e8i	−0.274668	+	0.378048i
$922$	7.25290e6	+	2.23221e7i	0.00925378	+	0.0284802i
$923$			4.66450e8i			0.593199i
$924$	−5.42314e8	−	8.62197e7i	−0.687440	−	0.109293i
$925$	−917029.			−0.00115867
$926$	−1.15339e7	+	3.74758e6i	−0.0145259	+	0.00471974i
$927$	5.72274e8	+	4.15781e8i	0.718397	+	0.521946i
$928$	1.24469e8	−	9.04317e7i	0.155746	−	0.113156i
$929$	3.15413e8	−	9.70741e8i	0.393398	−	1.21076i	−0.536804	−	0.843707i	$-0.680368\pi$
$929$	3.15413e8	−	9.70741e8i	0.393398	−	1.21076i	0.930202	−	0.367048i	$-0.119632\pi$
$930$	5.30167e7	+	1.72262e7i	0.0659119	+	0.0214161i
$931$	−4.66551e8	−	6.42153e8i	−0.578163	−	0.795773i
$932$	6.68289e8	−	9.19822e8i	0.825500	−	1.13620i
$933$	2.61203e8	+	8.03901e8i	0.321613	+	0.989824i
$934$		−	4.59802e7i		−	0.0564327i
$935$	1.32838e8	+	8.41899e8i	0.162513	+	1.02997i
$936$	1.10377e8			0.134601
$937$	−4.06435e8	+	1.32059e8i	−0.494052	+	0.160527i	−0.545437	−	0.838152i	$-0.683636\pi$
$937$	−4.06435e8	+	1.32059e8i	−0.494052	+	0.160527i	0.0513852	+	0.998679i	$0.483636\pi$
$938$	−6.32754e6	−	4.59723e6i	−0.00766702	−	0.00557041i
$939$	−1.18827e9	+	8.63327e8i	−1.43522	+	1.04275i
$940$	8.23903e7	−	2.53571e8i	0.0991956	−	0.305293i
$941$	−1.28284e9	−	4.16820e8i	−1.53958	−	0.500241i	−0.588323	−	0.808626i	$-0.700212\pi$
$941$	−1.28284e9	−	4.16820e8i	−1.53958	−	0.500241i	−0.951262	+	0.308385i	$0.900212\pi$
$942$	2.35296e7	+	3.23857e7i	0.0281489	+	0.0387437i
$943$	−2.28127e6	+	3.13990e6i	−0.00272045	+	0.00374438i
$944$	1.51907e8	+	4.67521e8i	0.180577	+	0.555758i
$945$			1.62560e8i			0.192627i
$946$	−1.95192e7	−	9.95993e6i	−0.0230562	−	0.0117648i
$947$	−1.02227e9			−1.20369			−0.601845	−	0.798613i	$-0.705567\pi$
$947$	−1.02227e9			−1.20369			−0.601845	+	0.798613i	$0.705567\pi$
$948$	−8.21395e8	+	2.66887e8i	−0.964111	+	0.313259i
$949$	−6.29452e8	−	4.57324e8i	−0.736485	−	0.535088i
$950$	1.34804e7	−	9.79405e6i	0.0157228	−	0.0114233i
$951$	5.51984e8	−	1.69883e9i	0.641779	−	1.97519i
$952$	−3.86986e7	−	1.25739e7i	−0.0448522	−	0.0145734i
$953$	1.28340e8	+	1.76645e8i	0.148281	+	0.204091i	0.876696	−	0.481045i	$-0.159743\pi$
$953$	1.28340e8	+	1.76645e8i	0.148281	+	0.204091i	−0.728415	+	0.685136i	$0.759743\pi$
$954$	1.61180e7	−	2.21845e7i	0.0185637	−	0.0255508i
$955$	3.67327e7	+	1.13052e8i	0.0421738	+	0.129798i
$956$		−	8.23242e8i		−	0.942224i
$957$	−1.59619e9	−	1.59806e9i	−1.82116	−	1.82330i
$958$	−6.91733e6			−0.00786760
$959$	−2.05352e8	+	6.67231e7i	−0.232833	+	0.0756519i
$960$	−8.37544e8	−	6.08512e8i	−0.946660	−	0.687789i
$961$	−9.66692e8	+	7.02343e8i	−1.08923	+	0.791369i
$962$	38574.6	−	118721.i	4.33288e−5	−	0.000133352i
$963$	−1.79624e8	−	5.83634e7i	−0.201134	−	0.0653524i
$964$	5.55336e8	+	7.64354e8i	0.619904	+	0.853225i
$965$	3.42737e8	−	4.71737e8i	0.381398	−	0.524950i
$966$	−1.45525e6	−	4.47880e6i	−0.00161438	−	0.00496855i
$967$			1.10324e9i			1.22009i	0.792366	+	0.610046i	$0.208849\pi$
$967$			1.10324e9i			1.22009i	−0.792366	+	0.610046i	$0.791151\pi$
$968$	5.61576e7	+	4.09015e7i	0.0619131	+	0.0450935i
$969$	2.34894e9			2.58167
$970$	−8.74147e6	+	2.84028e6i	−0.00957788	+	0.00311204i
$971$	5.56804e8	+	4.04542e8i	0.608197	+	0.441881i	0.848779	−	0.528748i	$-0.177338\pi$
$971$	5.56804e8	+	4.04542e8i	0.608197	+	0.441881i	−0.240582	+	0.970629i	$0.577338\pi$
$972$	9.92230e8	−	7.20897e8i	1.08047	−	0.785009i
$973$	2.77473e7	−	8.53975e7i	0.0301219	−	0.0927057i
$974$	2.35815e7	+	7.66210e6i	0.0255208	+	0.00829222i
$975$	4.42804e8	+	6.09467e8i	0.477746	+	0.657561i
$976$	−6.22310e8	+	8.56536e8i	−0.669356	+	0.921289i
$977$	−2.32188e8	−	7.14603e8i	−0.248976	−	0.766268i	−0.994957	−	0.100302i	$-0.968019\pi$
$977$	−2.32188e8	−	7.14603e8i	−0.248976	−	0.766268i	0.745981	−	0.665967i	$-0.231981\pi$
$978$			1.07555e8i			0.114977i
$979$	−5.45151e8	+	5.44513e8i	−0.580990	+	0.580310i
$980$	5.73522e8			0.609357
$981$	−7.69195e8	+	2.49927e8i	−0.814759	+	0.264731i
$982$	−2.56885e6	−	1.86638e6i	−0.00271272	−	0.00197090i
$983$	−1.33414e8	+	9.69311e7i	−0.140456	+	0.102048i	−0.655795	−	0.754939i	$-0.727666\pi$
$983$	−1.33414e8	+	9.69311e7i	−0.140456	+	0.102048i	0.515338	+	0.856987i	$0.327666\pi$
$984$	819888.	−	2.52336e6i	0.000860536	−	0.00264846i
$985$	7.23413e8	+	2.35051e8i	0.756968	+	0.245954i
$986$	−4.91520e7	−	6.76520e7i	−0.0512756	−	0.0705748i
$987$	1.64797e8	−	2.26824e8i	0.171395	−	0.235905i
$988$	−4.76491e8	−	1.46649e9i	−0.494065	−	1.52058i
$989$			1.27758e8i			0.132068i
$990$	1.76601e7	−	3.46097e7i	0.0182007	−	0.0356692i
$991$	1.28296e8			0.131823			0.0659116	−	0.997825i	$-0.479004\pi$
$991$	1.28296e8			0.131823			0.0659116	+	0.997825i	$0.479004\pi$
$992$	−1.63190e8	+	5.30236e7i	−0.167170	+	0.0543168i
$993$	−8.57262e8	−	6.22838e8i	−0.875520	−	0.636102i
$994$	−6.34194e6	+	4.60769e6i	−0.00645748	+	0.00469163i
$995$	−1.76259e8	+	5.42470e8i	−0.178930	+	0.550689i
$996$	1.60063e9	+	5.20075e8i	1.61999	+	0.526366i
$997$	5.34588e8	+	7.35797e8i	0.539428	+	0.742459i	0.988531	−	0.151021i	$-0.0482562\pi$
$997$	5.34588e8	+	7.35797e8i	0.539428	+	0.742459i	−0.449103	+	0.893480i	$0.648256\pi$
$998$	4.03488e7	−	5.55353e7i	0.0405918	−	0.0558698i
$999$	481624.	+	1.48229e6i	0.000483072	+	0.00148674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.6.3	yes	20
3.2	odd	2		99.7.k.a.28.3		20
11.2	odd	10	inner	11.7.d.a.2.3	✓	20
11.3	even	5		121.7.b.c.120.10		20
11.8	odd	10		121.7.b.c.120.11		20
33.2	even	10		99.7.k.a.46.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.2.3	✓	20	11.2	odd	10	inner
11.7.d.a.6.3	yes	20	1.1	even	1	trivial
99.7.k.a.28.3		20	3.2	odd	2
99.7.k.a.46.3		20	33.2	even	10
121.7.b.c.120.10		20	11.3	even	5
121.7.b.c.120.11		20	11.8	odd	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.291595 - 0.0947451i) q^{2} +(-33.5534 - 24.3780i) q^{3} +(-51.7010 + 37.5630i) q^{4} +(29.6861 - 91.3645i) q^{5} +(-12.0937 - 3.92948i) q^{6} +(-91.4937 - 125.930i) q^{7} +(-23.0507 + 31.7266i) q^{8} +(306.271 + 942.605i) q^{9} +O(q^{10})\)	\(q+(0.291595 - 0.0947451i) q^{2} +(-33.5534 - 24.3780i) q^{3} +(-51.7010 + 37.5630i) q^{4} +(29.6861 - 91.3645i) q^{5} +(-12.0937 - 3.92948i) q^{6} +(-91.4937 - 125.930i) q^{7} +(-23.0507 + 31.7266i) q^{8} +(306.271 + 942.605i) q^{9} -29.4541i q^{10} +(941.710 - 940.608i) q^{11} +2650.45 q^{12} +(-2700.81 + 877.547i) q^{13} +(-38.6104 - 28.0521i) q^{14} +(-3223.35 + 2341.90i) q^{15} +(1260.16 - 3878.37i) q^{16} +(-6339.53 - 2059.84i) q^{17} +(178.614 + 245.842i) q^{18} +(4994.15 - 6873.86i) q^{19} +(1897.12 + 5838.74i) q^{20} +6455.82i q^{21} +(185.480 - 363.499i) q^{22} -2379.19 q^{23} +(1546.86 - 502.604i) q^{24} +(5174.68 + 3759.63i) q^{25} +(-704.401 + 511.777i) q^{26} +(3359.32 - 10338.9i) q^{27} +(9460.64 + 3073.95i) q^{28} +(24050.1 + 33102.1i) q^{29} +(-718.031 + 988.284i) q^{30} +(-14101.5 - 43399.9i) q^{31} -3760.14i q^{32} +(-54527.7 + 8603.59i) q^{33} -2043.74 q^{34} +(-14221.7 + 4620.90i) q^{35} +(-51241.6 - 37229.2i) q^{36} +(-115.988 + 84.2706i) q^{37} +(805.008 - 2477.56i) q^{38} +(112014. + 36395.6i) q^{39} +(2214.40 + 3047.85i) q^{40} +(958.842 - 1319.73i) q^{41} +(611.657 + 1882.49i) q^{42} -53698.0i q^{43} +(-13355.4 + 84003.9i) q^{44} +95212.7 q^{45} +(-693.761 + 225.417i) q^{46} +(-35134.9 - 25527.0i) q^{47} +(-136829. + 99412.3i) q^{48} +(28868.2 - 88847.2i) q^{49} +(1865.12 + 606.014i) q^{50} +(162498. + 223659. i) q^{51} +(106671. - 146821. i) q^{52} +(-27885.3 - 85822.2i) q^{53} -3333.06i q^{54} +(-57982.4 - 113962. i) q^{55} +6104.33 q^{56} +(-335142. + 108894. i) q^{57} +(10149.1 + 7373.79i) q^{58} +(-97523.6 + 70855.0i) q^{59} +(78681.7 - 242157. i) q^{60} +(-246917. - 80228.2i) q^{61} +(-8223.85 - 11319.2i) q^{62} +(90680.7 - 124811. i) q^{63} +(80293.9 + 247119. i) q^{64} +272809. i q^{65} +(-15084.9 + 7674.99i) q^{66} +163882. q^{67} +(405134. - 131636. i) q^{68} +(79829.9 + 57999.8i) q^{69} +(-3709.16 + 2694.86i) q^{70} +(50757.5 - 156215. i) q^{71} +(-36965.4 - 12010.8i) q^{72} +(161041. + 221654. i) q^{73} +(-25.8375 + 35.5623i) q^{74} +(-81976.0 - 252296. i) q^{75} +542981. i q^{76} +(-204612. - 32530.2i) q^{77} +36111.1 q^{78} +(-309907. + 100695. i) q^{79} +(-316936. - 230268. i) q^{80} +(219775. - 159676. i) q^{81} +(154.556 - 475.674i) q^{82} +(603906. + 196221. i) q^{83} +(-242500. - 333772. i) q^{84} +(-376392. + 518060. i) q^{85} +(-5087.62 - 15658.1i) q^{86} -1.69698e6i q^{87} +(8135.16 + 51558.9i) q^{88} -578895. q^{89} +(27763.6 - 9020.93i) q^{90} +(357617. + 259824. i) q^{91} +(123007. - 89369.6i) q^{92} +(-584848. + 1.79998e6i) q^{93} +(-12663.7 - 4114.69i) q^{94} +(-479770. - 660347. i) q^{95} +(-91664.6 + 126166. i) q^{96} +(-96430.6 - 296783. i) q^{97} -28642.6i q^{98} +(1.17504e6 + 599580. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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