LMFDB - Embedded newform 18.6.c.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, 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:	$2.88690875663$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.1
Root			$0.500000 + 4.03013i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.6.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-8.58066 - 13.0143i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-39.2420 + 67.9691i) q^{5} +(-27.9216 + 55.7529i) q^{6} +(-110.566 - 191.505i) q^{7} +64.0000 q^{8} +(-95.7446 + 223.343i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.58066 - 13.0143i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-39.2420 + 67.9691i) q^{5} +(-27.9216 + 55.7529i) q^{6} +(-110.566 - 191.505i) q^{7} +64.0000 q^{8} +(-95.7446 + 223.343i) q^{9} +313.936 q^{10} +(-115.144 - 199.436i) q^{11} +(248.977 - 14.7826i) q^{12} +(385.793 - 668.213i) q^{13} +(-442.262 + 766.020i) q^{14} +(1221.29 - 72.5123i) q^{15} +(-128.000 - 221.703i) q^{16} -769.880 q^{17} +(965.171 - 115.016i) q^{18} -383.367 q^{19} +(-627.872 - 1087.51i) q^{20} +(-1543.58 + 3082.17i) q^{21} +(-460.577 + 797.743i) q^{22} +(-193.178 + 334.594i) q^{23} +(-549.162 - 832.916i) q^{24} +(-1517.37 - 2628.15i) q^{25} -3086.34 q^{26} +(3728.20 - 670.377i) q^{27} +3538.10 q^{28} +(394.883 + 683.958i) q^{29} +(-2693.78 - 4085.66i) q^{30} +(-1609.97 + 2788.54i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1607.51 + 3209.82i) q^{33} +(1539.76 + 2666.94i) q^{34} +17355.2 q^{35} +(-2328.77 - 3113.42i) q^{36} +2465.33 q^{37} +(766.733 + 1328.02i) q^{38} +(-12006.7 + 712.877i) q^{39} +(-2511.49 + 4350.02i) q^{40} +(4621.73 - 8005.07i) q^{41} +(13764.1 - 817.223i) q^{42} +(-5315.76 - 9207.16i) q^{43} +3684.62 q^{44} +(-11423.2 - 15272.1i) q^{45} +1545.42 q^{46} +(-976.032 - 1690.54i) q^{47} +(-1786.98 + 3568.19i) q^{48} +(-16046.0 + 27792.4i) q^{49} +(-6069.46 + 10512.6i) q^{50} +(6606.08 + 10019.5i) q^{51} +(6172.68 + 10691.4i) q^{52} -32589.2 q^{53} +(-9778.66 - 11574.1i) q^{54} +18074.0 q^{55} +(-7076.19 - 12256.3i) q^{56} +(3289.54 + 4989.25i) q^{57} +(1579.53 - 2735.83i) q^{58} +(11916.1 - 20639.2i) q^{59} +(-8765.58 + 17502.8i) q^{60} +(-18804.4 - 32570.2i) q^{61} +12879.7 q^{62} +(53357.3 - 6358.42i) q^{63} +4096.00 q^{64} +(30278.5 + 52444.0i) q^{65} +(14334.1 - 851.066i) q^{66} +(11525.6 - 19962.9i) q^{67} +(6159.04 - 10667.8i) q^{68} +(6012.10 - 356.959i) q^{69} +(-34710.5 - 60120.3i) q^{70} -66050.4 q^{71} +(-6127.65 + 14293.9i) q^{72} +65130.0 q^{73} +(-4930.66 - 8540.16i) q^{74} +(-21183.6 + 42298.8i) q^{75} +(3066.93 - 5312.08i) q^{76} +(-25462.0 + 44101.5i) q^{77} +(26482.8 + 40166.6i) q^{78} +(35433.7 + 61373.0i) q^{79} +20091.9 q^{80} +(-40714.9 - 42767.7i) q^{81} -36973.8 q^{82} +(-27643.5 - 47880.0i) q^{83} +(-30359.2 - 46045.9i) q^{84} +(30211.6 - 52328.0i) q^{85} +(-21263.0 + 36828.6i) q^{86} +(5512.88 - 11007.9i) q^{87} +(-7369.24 - 12763.9i) q^{88} +10598.6 q^{89} +(-30057.7 + 70115.3i) q^{90} -170622. q^{91} +(-3090.85 - 5353.50i) q^{92} +(50105.6 - 2974.94i) q^{93} +(-3904.13 + 6762.15i) q^{94} +(15044.1 - 26057.1i) q^{95} +(15934.5 - 946.086i) q^{96} +(41409.9 + 71724.1i) q^{97} +128368. q^{98} +(55567.0 - 6621.74i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9}+O(q^{10}) $ 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9	\( 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18} + 2262 q^{19} - 864 q^{20} - 11076 q^{21} - 1260 q^{22} - 3168 q^{23} + 576 q^{24} - 2883 q^{25} + 5952 q^{26} + 18144 q^{27} + 4224 q^{28} - 5148 q^{29} - 14400 q^{30} - 8610 q^{31} - 3072 q^{32} + 17469 q^{33} - 5796 q^{34} + 2700 q^{35} - 1392 q^{36} + 39936 q^{37} - 4524 q^{38} - 49026 q^{39} - 3456 q^{40} + 5049 q^{41} + 41352 q^{42} - 31389 q^{43} + 10080 q^{44} + 2538 q^{45} + 25344 q^{46} + 12924 q^{47} - 768 q^{48} - 52857 q^{49} - 11532 q^{50} + 36837 q^{51} - 11904 q^{52} - 96048 q^{53} - 71892 q^{54} + 126252 q^{55} - 8448 q^{56} - 17469 q^{57} - 20592 q^{58} + 62955 q^{59} + 21024 q^{60} - 75966 q^{61} + 68880 q^{62} + 49578 q^{63} + 24576 q^{64} + 108702 q^{65} + 2952 q^{66} - 32991 q^{67} - 23184 q^{68} - 29250 q^{69} - 5400 q^{70} - 129672 q^{71} - 11328 q^{72} - 8466 q^{73} - 79872 q^{74} - 105483 q^{75} - 18096 q^{76} + 88740 q^{77} + 171720 q^{78} + 89202 q^{79} + 27648 q^{80} + 123435 q^{81} - 40392 q^{82} + 32634 q^{83} + 11808 q^{84} + 71388 q^{85} - 125556 q^{86} - 151524 q^{87} - 20160 q^{88} + 66132 q^{89} - 263088 q^{90} - 301836 q^{91} - 50688 q^{92} + 57678 q^{93} + 51696 q^{94} - 82944 q^{95} - 6144 q^{96} + 46245 q^{97} + 422856 q^{98} + 282168 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 + 432 * q^10 - 315 * q^11 - 96 * q^12 - 744 * q^13 - 528 * q^14 + 2286 * q^15 - 768 * q^16 + 2898 * q^17 + 1056 * q^18 + 2262 * q^19 - 864 * q^20 - 11076 * q^21 - 1260 * q^22 - 3168 * q^23 + 576 * q^24 - 2883 * q^25 + 5952 * q^26 + 18144 * q^27 + 4224 * q^28 - 5148 * q^29 - 14400 * q^30 - 8610 * q^31 - 3072 * q^32 + 17469 * q^33 - 5796 * q^34 + 2700 * q^35 - 1392 * q^36 + 39936 * q^37 - 4524 * q^38 - 49026 * q^39 - 3456 * q^40 + 5049 * q^41 + 41352 * q^42 - 31389 * q^43 + 10080 * q^44 + 2538 * q^45 + 25344 * q^46 + 12924 * q^47 - 768 * q^48 - 52857 * q^49 - 11532 * q^50 + 36837 * q^51 - 11904 * q^52 - 96048 * q^53 - 71892 * q^54 + 126252 * q^55 - 8448 * q^56 - 17469 * q^57 - 20592 * q^58 + 62955 * q^59 + 21024 * q^60 - 75966 * q^61 + 68880 * q^62 + 49578 * q^63 + 24576 * q^64 + 108702 * q^65 + 2952 * q^66 - 32991 * q^67 - 23184 * q^68 - 29250 * q^69 - 5400 * q^70 - 129672 * q^71 - 11328 * q^72 - 8466 * q^73 - 79872 * q^74 - 105483 * q^75 - 18096 * q^76 + 88740 * q^77 + 171720 * q^78 + 89202 * q^79 + 27648 * q^80 + 123435 * q^81 - 40392 * q^82 + 32634 * q^83 + 11808 * q^84 + 71388 * q^85 - 125556 * q^86 - 151524 * q^87 - 20160 * q^88 + 66132 * q^89 - 263088 * q^90 - 301836 * q^91 - 50688 * q^92 + 57678 * q^93 + 51696 * q^94 - 82944 * q^95 - 6144 * q^96 + 46245 * q^97 + 422856 * q^98 + 282168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	−8.58066	−	13.0143i	−0.550449	−	0.834868i
$3$	−8.58066	−	13.0143i	−0.550449	−	0.834868i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−39.2420	+	67.9691i	−0.701982	+	1.21587i	0.265788	+	0.964032i	$0.414368\pi$
$5$	−39.2420	+	67.9691i	−0.701982	+	1.21587i	−0.967770	+	0.251837i	$0.918965\pi$
$6$	−27.9216	+	55.7529i	−0.316637	+	0.632251i
$7$	−110.566	−	191.505i	−0.852854	−	1.47719i	−0.878622	−	0.477518i	$-0.841536\pi$
$7$	−110.566	−	191.505i	−0.852854	−	1.47719i	0.0257678	−	0.999668i	$-0.491797\pi$
$8$	64.0000			0.353553
$9$	−95.7446	+	223.343i	−0.394011	+	0.919106i
$10$	313.936			0.992752
$11$	−115.144	−	199.436i	−0.286920	−	0.496960i	0.686153	−	0.727457i	$-0.259298\pi$
$11$	−115.144	−	199.436i	−0.286920	−	0.496960i	−0.973073	+	0.230497i	$0.925965\pi$
$12$	248.977	−	14.7826i	0.499121	−	0.0296345i
$13$	385.793	−	668.213i	0.633134	−	1.09662i	−0.353773	−	0.935331i	$-0.615101\pi$
$13$	385.793	−	668.213i	0.633134	−	1.09662i	0.986907	−	0.161289i	$-0.0515652\pi$
$14$	−442.262	+	766.020i	−0.603059	+	1.04453i
$15$	1221.29	−	72.5123i	1.40150	−	0.0832115i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−769.880			−0.646101			−0.323051	−	0.946382i	$-0.604708\pi$
$17$	−769.880			−0.646101			−0.323051	+	0.946382i	$0.604708\pi$
$18$	965.171	−	115.016i	0.702139	−	0.0836717i
$19$	−383.367			−0.243630			−0.121815	−	0.992553i	$-0.538871\pi$
$19$	−383.367			−0.243630			−0.121815	+	0.992553i	$0.538871\pi$
$20$	−627.872	−	1087.51i	−0.350991	−	0.607934i
$21$	−1543.58	+	3082.17i	−0.763803	+	1.52514i
$22$	−460.577	+	797.743i	−0.202883	+	0.351404i
$23$	−193.178	+	334.594i	−0.0761444	+	0.131886i	−0.901583	−	0.432605i	$-0.857594\pi$
$23$	−193.178	+	334.594i	−0.0761444	+	0.131886i	0.825439	+	0.564491i	$0.190928\pi$
$24$	−549.162	−	832.916i	−0.194613	−	0.295171i
$25$	−1517.37	−	2628.15i	−0.485557	−	0.841009i
$26$	−3086.34			−0.895387
$27$	3728.20	−	670.377i	0.984215	−	0.176974i
$28$	3538.10			0.852854
$29$	394.883	+	683.958i	0.0871914	+	0.151020i	0.906323	−	0.422586i	$-0.138877\pi$
$29$	394.883	+	683.958i	0.0871914	+	0.151020i	−0.819131	+	0.573606i	$0.805544\pi$
$30$	−2693.78	−	4085.66i	−0.546460	−	0.828817i
$31$	−1609.97	+	2788.54i	−0.300893	+	0.521163i	−0.976339	−	0.216247i	$-0.930618\pi$
$31$	−1609.97	+	2788.54i	−0.300893	+	0.521163i	0.675445	+	0.737410i	$0.263952\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−1607.51	+	3209.82i	−0.256961	+	0.513092i
$34$	1539.76	+	2666.94i	0.228431	+	0.395655i
$35$	17355.2			2.39475
$36$	−2328.77	−	3113.42i	−0.299482	−	0.400388i
$37$	2465.33			0.296054			0.148027	−	0.988983i	$-0.452708\pi$
$37$	2465.33			0.296054			0.148027	+	0.988983i	$0.452708\pi$
$38$	766.733	+	1328.02i	0.0861361	+	0.149192i
$39$	−12006.7	+	712.877i	−1.26404	+	0.0750505i
$40$	−2511.49	+	4350.02i	−0.248188	+	0.429874i
$41$	4621.73	−	8005.07i	0.429383	−	0.743713i	−0.567436	−	0.823418i	$-0.692064\pi$
$41$	4621.73	−	8005.07i	0.429383	−	0.743713i	0.996819	+	0.0797047i	$0.0253977\pi$
$42$	13764.1	−	817.223i	1.20400	−	0.0714854i
$43$	−5315.76	−	9207.16i	−0.438424	−	0.759372i	0.559145	−	0.829070i	$-0.311130\pi$
$43$	−5315.76	−	9207.16i	−0.438424	−	0.759372i	−0.997568	+	0.0696983i	$0.977796\pi$
$44$	3684.62			0.286920
$45$	−11423.2	−	15272.1i	−0.840923	−	1.12426i
$46$	1545.42			0.107684
$47$	−976.032	−	1690.54i	−0.0644495	−	0.111630i	0.832000	−	0.554775i	$-0.187196\pi$
$47$	−976.032	−	1690.54i	−0.0644495	−	0.111630i	−0.896450	+	0.443146i	$0.853862\pi$
$48$	−1786.98	+	3568.19i	−0.111948	+	0.223534i
$49$	−16046.0	+	27792.4i	−0.954720	+	1.65362i
$50$	−6069.46	+	10512.6i	−0.343341	+	0.594683i
$51$	6606.08	+	10019.5i	0.355646	+	0.539410i
$52$	6172.68	+	10691.4i	0.316567	+	0.548310i
$53$	−32589.2			−1.59362			−0.796809	−	0.604231i	$-0.793480\pi$
$53$	−32589.2			−1.59362			−0.796809	+	0.604231i	$0.793480\pi$
$54$	−9778.66	−	11574.1i	−0.456347	−	0.540137i
$55$	18074.0			0.805651
$56$	−7076.19	−	12256.3i	−0.301529	−	0.522264i
$57$	3289.54	+	4989.25i	0.134106	+	0.203399i
$58$	1579.53	−	2735.83i	0.0616537	−	0.106787i
$59$	11916.1	−	20639.2i	0.445659	−	0.771903i	−0.552439	−	0.833553i	$-0.686303\pi$
$59$	11916.1	−	20639.2i	0.445659	−	0.771903i	0.998098	+	0.0616498i	$0.0196362\pi$
$60$	−8765.58	+	17502.8i	−0.314342	+	0.627668i
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	−0.983825	−	0.179133i	$-0.942671\pi$
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	0.336779	−	0.941584i	$-0.390663\pi$
$62$	12879.7			0.425528
$63$	53357.3	−	6358.42i	1.69372	−	0.201836i
$64$	4096.00			0.125000
$65$	30278.5	+	52444.0i	0.888897	+	1.53962i
$66$	14334.1	−	851.066i	0.405053	−	0.0240494i
$67$	11525.6	−	19962.9i	0.313672	−	0.543295i	−0.665483	−	0.746413i	$-0.731774\pi$
$67$	11525.6	−	19962.9i	0.313672	−	0.543295i	0.979154	+	0.203118i	$0.0651075\pi$
$68$	6159.04	−	10667.8i	0.161525	−	0.279770i
$69$	6012.10	−	356.959i	0.152021	−	0.00902600i
$70$	−34710.5	−	60120.3i	−0.846673	−	1.46648i
$71$	−66050.4			−1.55500			−0.777498	−	0.628885i	$-0.783511\pi$
$71$	−66050.4			−1.55500			−0.777498	+	0.628885i	$0.783511\pi$
$72$	−6127.65	+	14293.9i	−0.139304	+	0.324953i
$73$	65130.0			1.43045			0.715227	−	0.698893i	$-0.246324\pi$
$73$	65130.0			1.43045			0.715227	+	0.698893i	$0.246324\pi$
$74$	−4930.66	−	8540.16i	−0.104671	−	0.181295i
$75$	−21183.6	+	42298.8i	−0.434858	+	0.868309i
$76$	3066.93	−	5312.08i	0.0609074	−	0.105495i
$77$	−25462.0	+	44101.5i	−0.489402	+	0.847669i
$78$	26482.8	+	40166.6i	0.492865	+	0.747530i
$79$	35433.7	+	61373.0i	0.638776	+	1.10639i	0.985702	+	0.168500i	$0.0538924\pi$
$79$	35433.7	+	61373.0i	0.638776	+	1.10639i	−0.346925	+	0.937893i	$0.612774\pi$
$80$	20091.9			0.350991
$81$	−40714.9	−	42767.7i	−0.689511	−	0.724275i
$82$	−36973.8			−0.607239
$83$	−27643.5	−	47880.0i	−0.440451	−	0.762884i	0.557272	−	0.830330i	$-0.311848\pi$
$83$	−27643.5	−	47880.0i	−0.440451	−	0.762884i	−0.997723	+	0.0674462i	$0.978515\pi$
$84$	−30359.2	−	46045.9i	−0.469453	−	0.712021i
$85$	30211.6	−	52328.0i	0.453551	−	0.785574i
$86$	−21263.0	+	36828.6i	−0.310012	+	0.536957i
$87$	5512.88	−	11007.9i	0.0780873	−	0.155922i
$88$	−7369.24	−	12763.9i	−0.101442	−	0.175702i
$89$	10598.6			0.141831			0.0709156	−	0.997482i	$-0.477408\pi$
$89$	10598.6			0.141831			0.0709156	+	0.997482i	$0.477408\pi$
$90$	−30057.7	+	70115.3i	−0.391155	+	0.912444i
$91$	−170622.			−2.15988
$92$	−3090.85	−	5353.50i	−0.0380722	−	0.0659430i
$93$	50105.6	−	2974.94i	0.600729	−	0.0356673i
$94$	−3904.13	+	6762.15i	−0.0455727	+	0.0789342i
$95$	15044.1	−	26057.1i	0.171024	−	0.296222i
$96$	15934.5	−	946.086i	0.176466	−	0.0104774i
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	0.998180	−	0.0603057i	$-0.0192076\pi$
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	−0.551316	+	0.834296i	$0.685874\pi$
$98$	128368.			1.35018
$99$	55567.0	−	6621.74i	0.569809	−	0.0679023i
$100$	48555.7			0.485557
$101$	−10604.1	−	18366.9i	−0.103436	−	0.179156i	0.809662	−	0.586896i	$-0.199650\pi$
$101$	−10604.1	−	18366.9i	−0.103436	−	0.179156i	−0.913098	+	0.407740i	$0.866317\pi$
$102$	21496.3	−	42923.0i	0.204580	−	0.408498i
$103$	−65877.4	+	114103.i	−0.611848	+	1.05975i	0.379081	+	0.925363i	$0.376240\pi$
$103$	−65877.4	+	114103.i	−0.611848	+	1.05975i	−0.990929	+	0.134388i	$0.957093\pi$
$104$	24690.7	−	42765.6i	0.223847	−	0.387714i
$105$	−148919.	−	225866.i	−1.31819	−	1.99930i
$106$	65178.4	+	112892.i	0.563429	+	0.975888i
$107$	54796.5			0.462693			0.231347	−	0.972871i	$-0.425687\pi$
$107$	54796.5			0.462693			0.231347	+	0.972871i	$0.425687\pi$
$108$	−20536.6	+	57022.5i	−0.169422	+	0.470421i
$109$	160570.			1.29448			0.647242	−	0.762284i	$-0.275922\pi$
$109$	160570.			1.29448			0.647242	+	0.762284i	$0.275922\pi$
$110$	−36147.9	−	62610.1i	−0.284840	−	0.493358i
$111$	−21154.2	−	32084.6i	−0.162963	−	0.247166i
$112$	−28304.8	+	49025.3i	−0.213213	+	0.369297i
$113$	33217.8	−	57534.9i	0.244723	−	0.423873i	−0.717331	−	0.696733i	$-0.754636\pi$
$113$	33217.8	−	57534.9i	0.244723	−	0.423873i	0.962054	+	0.272860i	$0.0879696\pi$
$114$	10704.2	−	21373.8i	0.0771422	−	0.154035i
$115$	−15161.4	−	26260.3i	−0.106904	−	0.185163i
$116$	−12636.3			−0.0871914
$117$	112303.	+	150142.i	0.758449	+	1.01400i
$118$	−95328.4			−0.630256
$119$	85122.2	+	147436.i	0.551030	+	0.954412i
$120$	78162.7	−	4640.79i	0.495503	−	0.0294197i
$121$	54009.1	−	93546.4i	0.335354	−	0.580850i
$122$	−75217.7	+	130281.i	−0.457531	+	0.792467i
$123$	−143838.	+	8540.15i	−0.857256	+	0.0508982i
$124$	−25759.5	−	44616.7i	−0.150447	−	0.260581i
$125$	−7084.72			−0.0405553
$126$	−128741.	−	172118.i	−0.722421	−	0.965830i
$127$	−299603.			−1.64830			−0.824152	−	0.566368i	$-0.808348\pi$
$127$	−299603.			−1.64830			−0.824152	+	0.566368i	$0.808348\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−74212.1	+	148184.i	−0.392646	+	0.784022i
$130$	121114.	−	209776.i	0.628545	−	1.08867i
$131$	166224.	−	287909.i	0.846283	−	1.46581i	−0.0382189	−	0.999269i	$-0.512168\pi$
$131$	166224.	−	287909.i	0.846283	−	1.46581i	0.884502	−	0.466536i	$-0.154498\pi$
$132$	−31616.5	−	47952.8i	−0.157935	−	0.239541i
$133$	42387.1	+	73416.7i	0.207781	+	0.359887i
$134$	−92204.5			−0.443599
$135$	−100737.	+	279710.i	−0.475724	+	1.32091i
$136$	−49272.3			−0.228431
$137$	93601.3	+	162122.i	0.426070	+	0.737974i	0.996520	−	0.0833580i	$-0.0265645\pi$
$137$	93601.3	+	162122.i	0.426070	+	0.737974i	−0.570450	+	0.821332i	$0.693231\pi$
$138$	−13260.7	−	20112.6i	−0.0592748	−	0.0899023i
$139$	105285.	−	182358.i	0.462198	−	0.800550i	−0.536872	−	0.843664i	$-0.680394\pi$
$139$	105285.	−	182358.i	0.462198	−	0.800550i	0.999070	+	0.0431133i	$0.0137276\pi$
$140$	−138842.	+	240481.i	−0.598688	+	1.03696i
$141$	−13626.2	+	27208.3i	−0.0577200	+	0.115253i
$142$	132101.	+	228805.i	0.549774	+	0.952237i
$143$	−177687.			−0.726635
$144$	61770.9	−	7361.05i	0.248244	−	0.0295824i
$145$	−61984.0			−0.244827
$146$	−130260.	−	225617.i	−0.505742	−	0.875970i
$147$	499385.	−	29650.1i	1.90608	−	0.113171i
$148$	−19722.7	+	34160.6i	−0.0740135	+	0.128195i
$149$	−242872.	+	420667.i	−0.896215	+	1.55229i	−0.0639212	+	0.997955i	$0.520361\pi$
$149$	−242872.	+	420667.i	−0.896215	+	1.55229i	−0.832294	+	0.554335i	$0.812973\pi$
$150$	188894.	−	11215.3i	0.685474	−	0.0406989i
$151$	−105105.	−	182047.i	−0.375130	−	0.649744i	0.615217	−	0.788358i	$-0.289069\pi$
$151$	−105105.	−	182047.i	−0.375130	−	0.649744i	−0.990346	+	0.138614i	$0.955735\pi$
$152$	−24535.5			−0.0861361
$153$	73711.8	−	171947.i	0.254571	−	0.593835i
$154$	203696.			0.692119
$155$	−126357.	−	218856.i	−0.422443	−	0.731694i
$156$	86175.6	−	172073.i	0.283513	−	0.566109i
$157$	196123.	−	339696.i	0.635009	−	1.09987i	−0.351504	−	0.936186i	$-0.614330\pi$
$157$	196123.	−	339696.i	0.635009	−	1.09987i	0.986513	−	0.163682i	$-0.0523371\pi$
$158$	141735.	−	245492.i	0.451683	−	0.782338i
$159$	279637.	+	424126.i	0.877206	+	1.33046i
$160$	−40183.8	−	69600.4i	−0.124094	−	0.214937i
$161$	85435.3			0.259760
$162$	−66721.9	+	226576.i	−0.199747	+	0.678308i
$163$	190208.			0.560738			0.280369	−	0.959892i	$-0.409543\pi$
$163$	190208.			0.560738			0.280369	+	0.959892i	$0.409543\pi$
$164$	73947.7	+	128081.i	0.214692	+	0.371857i
$165$	−155087.	−	235220.i	−0.443470	−	0.672612i
$166$	−110574.	+	191520.i	−0.311446	+	0.539440i
$167$	200619.	−	347483.i	0.556650	−	0.964145i	−0.441123	−	0.897446i	$-0.645420\pi$
$167$	200619.	−	347483.i	0.556650	−	0.964145i	0.997773	−	0.0666991i	$-0.0212467\pi$
$168$	−98789.3	+	197259.i	−0.270045	+	0.539217i
$169$	−112026.	−	194034.i	−0.301718	−	0.522590i
$170$	−241693.			−0.641418
$171$	36705.3	−	85622.1i	0.0959927	−	0.223922i
$172$	170104.			0.438424
$173$	−47391.9	−	82085.1i	−0.120389	−	0.208521i	0.799532	−	0.600624i	$-0.205081\pi$
$173$	−47391.9	−	82085.1i	−0.120389	−	0.208521i	−0.919921	+	0.392103i	$0.871748\pi$
$174$	−49158.4	+	2918.70i	−0.123091	+	0.00730830i
$175$	−335537.	+	581166.i	−0.828218	+	1.43452i
$176$	−29477.0	+	51055.6i	−0.0717300	+	0.124240i
$177$	−370853.	+	22018.8i	−0.889750	+	0.0528275i
$178$	−21197.1	−	36714.5i	−0.0501449	−	0.0868536i
$179$	−218816.			−0.510442			−0.255221	−	0.966883i	$-0.582148\pi$
$179$	−218816.			−0.510442			−0.255221	+	0.966883i	$0.582148\pi$
$180$	303002.	−	36107.8i	0.697050	−	0.0830652i
$181$	−344513.			−0.781645			−0.390823	−	0.920466i	$-0.627809\pi$
$181$	−344513.			−0.781645			−0.390823	+	0.920466i	$0.627809\pi$
$182$	341243.	+	591050.i	0.763634	+	1.32265i
$183$	−262525.	+	524200.i	−0.579485	+	1.15710i
$184$	−12363.4	+	21414.0i	−0.0269211	+	0.0466287i
$185$	−96744.5	+	167566.i	−0.207825	+	0.359963i
$186$	−110517.	−	167621.i	−0.234231	−	0.355260i
$187$	88647.3	+	153542.i	0.185379	+	0.321087i
$188$	31233.0			0.0644495
$189$	−540592.	−	639849.i	−1.10082	−	1.30294i
$190$	−120353.			−0.241864
$191$	67476.5	+	116873.i	0.133835	+	0.231809i	0.925152	−	0.379597i	$-0.123938\pi$
$191$	67476.5	+	116873.i	0.133835	+	0.231809i	−0.791317	+	0.611406i	$0.790604\pi$
$192$	−35146.4	−	53306.6i	−0.0688062	−	0.104359i
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	−0.954707	−	0.297546i	$-0.903832\pi$
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	0.735036	+	0.678028i	$0.237165\pi$
$194$	165640.	−	286896.i	0.315980	−	0.547294i
$195$	422712.	−	844058.i	0.796083	−	1.58959i
$196$	−256736.	−	444679.i	−0.477360	−	0.826811i
$197$	430437.			0.790213			0.395107	−	0.918635i	$-0.370708\pi$
$197$	430437.			0.790213			0.395107	+	0.918635i	$0.370708\pi$
$198$	−134072.	−	179246.i	−0.243039	−	0.324928i
$199$	719704.			1.28831			0.644156	−	0.764894i	$-0.277209\pi$
$199$	719704.			1.28831			0.644156	+	0.764894i	$0.277209\pi$
$200$	−97111.4	−	168202.i	−0.171670	−	0.297342i
$201$	−358700.	+	21297.2i	−0.626241	+	0.0371820i
$202$	−42416.5	+	73467.5i	−0.0731402	+	0.126683i
$203$	87321.0	−	151244.i	0.148723	−	0.257596i
$204$	−191682.	+	11380.8i	−0.322483	+	0.0191469i
$205$	362732.	+	628269.i	0.602838	+	1.04415i
$206$	527019.			0.865283
$207$	−56233.4	−	75180.4i	−0.0912154	−	0.121949i
$208$	−197526.			−0.316567
$209$	44142.5	+	76457.1i	0.0699023	+	0.121074i
$210$	−484586.	+	967605.i	−0.758267	+	1.51408i
$211$	−30700.0	+	53174.0i	−0.0474715	+	0.0822230i	−0.888785	−	0.458325i	$-0.848450\pi$
$211$	−30700.0	+	53174.0i	−0.0474715	+	0.0822230i	0.841313	+	0.540548i	$0.181783\pi$
$212$	260714.	−	451569.i	0.398405	−	0.690057i
$213$	566756.	+	859600.i	0.855947	+	1.29822i
$214$	−109593.	−	189821.i	−0.163587	−	0.283341i
$215$	834403.			1.23106
$216$	238605.	−	42904.2i	0.347973	−	0.0625698i
$217$	712027.			1.02647
$218$	−321139.	−	556229.i	−0.457670	−	0.792707i
$219$	−558858.	−	847621.i	−0.787392	−	1.19424i
$220$	−144592.	+	250440.i	−0.201413	+	0.348857i
$221$	−297014.	+	514443.i	−0.409069	+	0.708528i
$222$	−68835.9	+	137449.i	−0.0937417	+	0.187180i
$223$	−329013.	−	569868.i	−0.443049	−	0.767383i	0.554865	−	0.831940i	$-0.312770\pi$
$223$	−329013.	−	569868.i	−0.443049	−	0.767383i	−0.997914	+	0.0645574i	$0.979436\pi$
$224$	226438.			0.301529
$225$	732259.	−	87260.9i	0.964291	−	0.114912i
$226$	−265742.			−0.346091
$227$	5067.16	+	8776.57i	0.00652679	+	0.0113047i	0.869270	−	0.494337i	$-0.164589\pi$
$227$	5067.16	+	8776.57i	0.00652679	+	0.0113047i	−0.862744	+	0.505642i	$0.831256\pi$
$228$	−95449.4	+	5667.15i	−0.121601	+	0.00721985i
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	0.166659	+	0.986015i	$0.446702\pi$
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	−0.937243	+	0.348677i	$0.886631\pi$
$230$	−60645.5	+	105041.i	−0.0755925	+	0.130930i
$231$	792431.	−	47049.3i	0.977083	−	0.0580127i
$232$	25272.5	+	43773.3i	0.0308268	+	0.0533936i
$233$	−1.16513e6			−1.40599			−0.702996	−	0.711194i	$-0.748155\pi$
$233$	−1.16513e6			−1.40599			−0.702996	+	0.711194i	$0.748155\pi$
$234$	295501.	−	689312.i	0.352792	−	0.822955i
$235$	153206.			0.180969
$236$	190657.	+	330227.i	0.222829	+	0.385952i
$237$	494683.	−	987766.i	0.572079	−	1.14231i
$238$	340489.	−	589744.i	0.389637	−	0.674871i
$239$	−659760.	+	1.14274e6i	−0.747122	+	1.29405i	0.202075	+	0.979370i	$0.435231\pi$
$239$	−659760.	+	1.14274e6i	−0.747122	+	1.29405i	−0.949197	+	0.314683i	$0.898102\pi$
$240$	−172402.	−	261482.i	−0.193203	−	0.293031i
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	0.680057	−	0.733159i	$-0.261955\pi$
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	−0.974963	+	0.222367i	$0.928622\pi$
$242$	−432072.			−0.474262
$243$	−207231.	+	896852.i	−0.225133	+	0.974328i
$244$	601741.			0.647046
$245$	−1.25935e6	−	2.18126e6i	−1.34039	−	2.32163i
$246$	317260.	+	481189.i	0.334255	+	0.506965i
$247$	−147900.	+	256170.i	−0.154250	+	0.267169i
$248$	−103038.	+	178467.i	−0.106382	+	0.184259i
$249$	−385925.	+	770603.i	−0.394462	+	0.787648i
$250$	14169.4	+	24542.2i	0.0143385	+	0.0248349i
$251$	475.750			0.000476644			0.000238322	−	1.00000i	$-0.499924\pi$
$251$	475.750			0.000476644			0.000238322		1.00000i	$0.499924\pi$
$252$	−338754.	+	790208.i	−0.336034	+	0.783863i
$253$	88973.4			0.0873894
$254$	599207.	+	1.03786e6i	0.582764	+	1.00938i
$255$	−940249.	+	55825.7i	−0.905508	+	0.0537631i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	13603.3	−	23561.6i	0.0128473	−	0.0222522i	−0.859530	−	0.511085i	$-0.829244\pi$
$257$	13603.3	−	23561.6i	0.0128473	−	0.0222522i	0.872378	+	0.488833i	$0.162577\pi$
$258$	661750.	−	39290.3i	0.618935	−	0.0367482i
$259$	−272581.	−	472124.i	−0.252491	−	0.437327i
$260$	−968913.			−0.888897
$261$	−190565.	+	22709.0i	−0.173158	+	0.0206347i
$262$	−1.32979e6			−1.19683
$263$	69991.2	+	121228.i	0.0623956	+	0.108072i	0.895536	−	0.444990i	$-0.146793\pi$
$263$	69991.2	+	121228.i	0.0623956	+	0.108072i	−0.833140	+	0.553062i	$0.813459\pi$
$264$	−102880.	+	205428.i	−0.0908495	+	0.181405i
$265$	1.27887e6	−	2.21506e6i	1.11869	−	1.93763i
$266$	169549.	−	293667.i	0.146923	−	0.254478i
$267$	−90942.6	−	137933.i	−0.0780709	−	0.118410i
$268$	184409.	+	319406.i	0.156836	+	0.271648i
$269$	1.63842e6			1.38053			0.690263	−	0.723558i	$-0.257495\pi$
$269$	1.63842e6			1.38053			0.690263	+	0.723558i	$0.257495\pi$
$270$	1.17042e6	−	210455.i	0.977082	−	0.175692i
$271$	−280791.			−0.232252			−0.116126	−	0.993234i	$-0.537048\pi$
$271$	−280791.			−0.232252			−0.116126	+	0.993234i	$0.537048\pi$
$272$	98544.6	+	170684.i	0.0807627	+	0.139885i
$273$	1.46405e6	+	2.22052e6i	1.18891	+	1.80322i
$274$	374405.	−	648489.i	0.301277	−	0.521827i
$275$	−349432.	+	605234.i	−0.278632	+	0.482605i
$276$	−43150.7	+	86161.8i	−0.0340969	+	0.0680835i
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	0.697926	−	0.716170i	$-0.254107\pi$
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	−0.969184	+	0.246336i	$0.920773\pi$
$278$	−842277.			−0.653647
$279$	−468656.	−	626563.i	−0.360449	−	0.481897i
$280$	1.11074e6			0.846673
$281$	1.05464e6	+	1.82670e6i	0.796782	+	1.38007i	0.921701	+	0.387901i	$0.126800\pi$
$281$	1.05464e6	+	1.82670e6i	0.796782	+	1.38007i	−0.124919	+	0.992167i	$0.539867\pi$
$282$	121505.	−	7214.14i	0.0909851	−	0.00540209i
$283$	731346.	−	1.26673e6i	0.542821	−	0.940193i	−0.455920	−	0.890021i	$-0.650690\pi$
$283$	731346.	−	1.26673e6i	0.542821	−	0.940193i	0.998741	−	0.0501725i	$-0.0159771\pi$
$284$	528403.	−	915221.i	0.388749	−	0.673333i
$285$	−468203.	+	27798.8i	−0.341446	+	0.0202728i
$286$	355375.	+	615527.i	0.256904	+	0.444972i
$287$	−2.04402e6			−1.46480
$288$	−149041.	−	199259.i	−0.105883	−	0.141559i
$289$	−827142.			−0.582553
$290$	123968.	+	214719.i	0.0865595	+	0.149925i
$291$	578115.	−	1.15436e6i	0.400204	−	0.799115i
$292$	−521040.	+	902467.i	−0.357613	+	0.619404i
$293$	1.27745e6	−	2.21261e6i	0.869313	−	1.50569i	0.00661216	−	0.999978i	$-0.497895\pi$
$293$	1.27745e6	−	2.21261e6i	0.869313	−	1.50569i	0.862700	−	0.505715i	$-0.168771\pi$
$294$	−1.10148e6	−	1.67062e6i	−0.743205	−	1.12722i
$295$	935219.	+	1.61985e6i	0.625688	+	1.08372i
$296$	157781.			0.104671
$297$	−562979.	−	666347.i	−0.370340	−	0.438338i
$298$	1.94298e6			1.26744
$299$	149053.	+	258168.i	0.0964192	+	0.167003i
$300$	−416640.	−	631919.i	−0.267275	−	0.405376i
$301$	−1.17548e6	+	2.03599e6i	−0.747822	+	1.29527i
$302$	−420421.	+	728190.i	−0.265257	+	0.459438i
$303$	−148042.	+	295605.i	−0.0926357	+	0.184972i
$304$	49070.9	+	84993.3i	0.0304537	+	0.0527474i
$305$	2.95169e6			1.81686
$306$	−743066.	+	88548.8i	−0.453653	+	0.0540604i
$307$	−2.14982e6			−1.30183			−0.650917	−	0.759149i	$-0.725615\pi$
$307$	−2.14982e6			−1.30183			−0.650917	+	0.759149i	$0.725615\pi$
$308$	−407392.	−	705623.i	−0.244701	−	0.423834i
$309$	2.05024e6	−	121730.i	1.22154	−	0.0725272i
$310$	−505426.	+	875424.i	−0.298713	+	0.517385i
$311$	183809.	−	318367.i	0.107762	−	0.186650i	−0.807101	−	0.590413i	$-0.798965\pi$
$311$	183809.	−	318367.i	0.107762	−	0.186650i	0.914863	+	0.403763i	$0.132298\pi$
$312$	−768428.	+	45624.2i	−0.446906	+	0.0265343i
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	0.838463	−	0.544959i	$-0.183455\pi$
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	−0.891180	+	0.453650i	$0.850121\pi$
$314$	−1.56899e6			−0.898039
$315$	−1.66167e6	+	3.87617e6i	−0.943558	+	2.20103i
$316$	−1.13388e6			−0.638776
$317$	−432482.	−	749081.i	−0.241724	−	0.418679i	0.719481	−	0.694512i	$-0.244380\pi$
$317$	−432482.	−	749081.i	−0.241724	−	0.418679i	−0.961206	+	0.275833i	$0.911046\pi$
$318$	909942.	−	1.81694e6i	0.504599	−	1.00757i
$319$	90937.2	−	157508.i	0.0500339	−	0.0866613i
$320$	−160735.	+	278401.i	−0.0877477	+	0.151984i
$321$	−470190.	−	713139.i	−0.254689	−	0.386288i
$322$	−170871.	−	295956.i	−0.0918391	−	0.159070i
$323$	295146.			0.157409
$324$	918326.	−	222021.i	0.485998	−	0.117498i
$325$	−2.34155e6			−1.22969
$326$	−380416.	−	658900.i	−0.198251	−	0.343381i
$327$	−1.37779e6	−	2.08970e6i	−0.712549	−	1.08072i
$328$	295791.	−	512324.i	0.151810	−	0.262942i
$329$	−215831.	+	373830.i	−0.109932	+	0.190408i
$330$	−504654.	+	1.00768e6i	−0.255099	+	0.509373i
$331$	1.49880e6	+	2.59600e6i	0.751923	+	1.30237i	0.946890	+	0.321559i	$0.104207\pi$
$331$	1.49880e6	+	2.59600e6i	0.751923	+	1.30237i	−0.194967	+	0.980810i	$0.562460\pi$
$332$	884592.			0.440451
$333$	−236042.	+	550614.i	−0.116648	+	0.272105i
$334$	−1.60496e6			−0.787221
$335$	904572.	+	1.56676e6i	0.440384	+	0.762767i
$336$	880904.	−	52302.3i	0.425677	−	0.0252739i
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	−0.939210	−	0.343343i	$-0.888441\pi$
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	0.766949	+	0.641708i	$0.221774\pi$
$338$	−448103.	+	776136.i	−0.213347	+	0.369527i
$339$	−1.03381e6	+	61380.7i	−0.488586	+	0.0290090i
$340$	483386.	+	837249.i	0.226776	+	0.392787i
$341$	741514.			0.345329
$342$	−370014.	+	44093.4i	−0.171062	+	0.0203849i
$343$	3.37998e6			1.55124
$344$	−340208.	−	589258.i	−0.155006	−	0.268478i
$345$	−211665.	+	422645.i	−0.0957416	+	0.191174i
$346$	−189567.	+	328340.i	−0.0851282	+	0.147446i
$347$	1.87463e6	−	3.24695e6i	0.835779	−	1.44761i	−0.0576157	−	0.998339i	$-0.518350\pi$
$347$	1.87463e6	−	3.24695e6i	0.835779	−	1.44761i	0.893395	−	0.449273i	$-0.148317\pi$
$348$	108427.	+	164452.i	0.0479945	+	0.0727934i
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	0.999890	+	0.0148181i	$0.00471692\pi$
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	−0.487112	+	0.873339i	$0.661950\pi$
$350$	2.68429e6			1.17128
$351$	990359.	−	2.74986e6i	0.429067	−	1.19136i
$352$	235816.			0.101442
$353$	−2.17285e6	−	3.76348e6i	−0.928094	−	1.60751i	−0.786508	−	0.617580i	$-0.788113\pi$
$353$	−2.17285e6	−	3.76348e6i	−0.928094	−	1.60751i	−0.141586	−	0.989926i	$-0.545220\pi$
$354$	817980.	+	1.24063e6i	0.346924	+	0.526181i
$355$	2.59195e6	−	4.48938e6i	1.09158	−	1.89067i
$356$	−84788.5	+	146858.i	−0.0354578	+	0.0614147i
$357$	1.18837e6	−	2.37290e6i	0.493494	−	0.985393i
$358$	437632.	+	758001.i	0.180469	+	0.312581i
$359$	−2.71281e6			−1.11092			−0.555461	−	0.831542i	$-0.687458\pi$
$359$	−2.71281e6			−1.11092			−0.555461	+	0.831542i	$0.687458\pi$
$360$	−731084.	−	977413.i	−0.297311	−	0.397486i
$361$	−2.32913e6			−0.940645
$362$	689027.	+	1.19343e6i	0.276353	+	0.478658i
$363$	−1.68088e6	+	99799.3i	−0.669528	+	0.0397522i
$364$	1.36497e6	−	2.36420e6i	0.539971	−	0.935257i
$365$	−2.55583e6	+	4.42682e6i	−1.00415	+	1.73924i
$366$	2.34093e6	−	138989.i	0.913453	−	0.0542348i
$367$	−1.95814e6	−	3.39160e6i	−0.758889	−	1.31443i	−0.943417	−	0.331608i	$-0.892409\pi$
$367$	−1.95814e6	−	3.39160e6i	−0.758889	−	1.31443i	0.184528	−	0.982827i	$-0.440924\pi$
$368$	98907.1			0.0380722
$369$	1.34537e6	+	1.79867e6i	0.514370	+	0.687679i
$370$	773956.			0.293908
$371$	3.60324e6	+	6.24100e6i	1.35912	+	2.35407i
$372$	−359623.	+	718083.i	−0.134738	+	0.269040i
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	−0.982775	−	0.184806i	$-0.940834\pi$
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	0.651434	+	0.758705i	$0.274168\pi$
$374$	354589.	−	614167.i	0.131083	−	0.227042i
$375$	60791.5	+	92202.7i	0.0223236	+	0.0338583i
$376$	−62466.1	−	108194.i	−0.0227863	−	0.0394671i
$377$	609373.			0.220815
$378$	−1.13532e6	+	3.15236e6i	−0.408685	+	1.13477i
$379$	−631740.			−0.225912			−0.112956	−	0.993600i	$-0.536032\pi$
$379$	−631740.			−0.225912			−0.112956	+	0.993600i	$0.536032\pi$
$380$	240705.	+	416913.i	0.0855118	+	0.148111i
$381$	2.57079e6	+	3.89913e6i	0.907308	+	1.37612i
$382$	269906.	−	467491.i	0.0946355	−	0.163914i
$383$	−66803.0	+	115706.i	−0.0232701	+	0.0403050i	−0.877426	−	0.479712i	$-0.840741\pi$
$383$	−66803.0	+	115706.i	−0.0232701	+	0.0403050i	0.854156	+	0.520017i	$0.174074\pi$
$384$	−114367.	+	228364.i	−0.0395796	+	0.0790313i
$385$	−1.99836e6	−	3.46126e6i	−0.687102	−	1.19010i
$386$	909404.			0.310662
$387$	2.56531e6	−	305700.i	0.870687	−	0.103757i
$388$	−1.32512e6			−0.446864
$389$	−2.79735e6	−	4.84515e6i	−0.937286	−	1.62343i	−0.770505	−	0.637434i	$-0.779996\pi$
$389$	−2.79735e6	−	4.84515e6i	−0.937286	−	1.62343i	−0.166781	−	0.985994i	$-0.553337\pi$
$390$	−3.76933e6	+	223798.i	−1.25488	+	0.0745065i
$391$	148724.	−	257597.i	0.0491970	−	0.0852117i
$392$	−1.02694e6	+	1.77872e6i	−0.337544	+	0.584644i
$393$	−5.17324e6	+	307153.i	−1.68959	+	0.100317i
$394$	−860875.	−	1.49108e6i	−0.279383	−	0.483905i
$395$	−5.56195e6			−1.79364
$396$	−352782.	+	822933.i	−0.113050	+	0.263710i
$397$	4.19051e6			1.33441			0.667206	−	0.744873i	$-0.267490\pi$
$397$	4.19051e6			1.33441			0.667206	+	0.744873i	$0.267490\pi$
$398$	−1.43941e6	−	2.49313e6i	−0.455487	−	0.788927i
$399$	591758.	−	1.18160e6i	0.186085	−	0.371569i
$400$	−388445.	+	672807.i	−0.121389	+	0.210252i
$401$	229109.	−	396829.i	0.0711511	−	0.123237i	−0.828255	−	0.560351i	$-0.810666\pi$
$401$	229109.	−	396829.i	0.0711511	−	0.123237i	0.899406	+	0.437114i	$0.143999\pi$
$402$	791176.	+	1.19998e6i	0.244179	+	0.370347i
$403$	1.24223e6	+	2.15160e6i	0.381012	+	0.659932i
$404$	339332.			0.103436
$405$	4.50462e6	−	1.08907e6i	1.36465	−	0.329927i
$406$	−698568.			−0.210326
$407$	−283869.	−	491675.i	−0.0849438	−	0.147127i
$408$	422789.	+	641245.i	0.125740	+	0.190710i
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	−0.867274	−	0.497831i	$-0.834130\pi$
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	0.864771	+	0.502166i	$0.167463\pi$
$410$	1.45093e6	−	2.51308e6i	0.426271	−	0.738323i
$411$	1.30675e6	−	2.60927e6i	0.381582	−	0.761930i
$412$	−1.05404e6	−	1.82565e6i	−0.305924	−	0.529876i
$413$	−5.27002e6			−1.52033
$414$	−147966.	+	345159.i	−0.0424288	+	0.0989734i
$415$	4.33914e6			1.23676
$416$	395052.	+	684250.i	0.111923	+	0.193857i
$417$	−3.27668e6	+	194548.i	−0.922771	+	0.0547880i
$418$	176570.	−	305828.i	0.0494284	−	0.0856124i
$419$	−2.24889e6	+	3.89520e6i	−0.625798	+	1.08391i	0.362588	+	0.931949i	$0.381893\pi$
$419$	−2.24889e6	+	3.89520e6i	−0.625798	+	1.08391i	−0.988386	+	0.151964i	$0.951440\pi$
$420$	4.32105e6	−	256556.i	1.19527	−	0.0709673i
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	0.894348	−	0.447372i	$-0.147640\pi$
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	−0.834610	+	0.550842i	$0.814307\pi$
$422$	245600.			0.0671348
$423$	471019.	−	56129.8i	0.127993	−	0.0152526i
$424$	−2.08571e6			−0.563429
$425$	1.16819e6	+	2.02336e6i	0.313719	+	0.543377i
$426$	1.84423e6	−	3.68250e6i	0.492370	−	0.983147i
$427$	−4.15824e6	+	7.20229e6i	−1.10367	+	1.91162i
$428$	−438372.	+	759282.i	−0.115673	+	0.200352i
$429$	1.52468e6	+	2.31248e6i	0.399976	+	0.606645i
$430$	−1.66881e6	−	2.89046e6i	−0.435246	−	0.753868i
$431$	5.16700e6			1.33982			0.669908	−	0.742444i	$-0.266334\pi$
$431$	5.16700e6			1.33982			0.669908	+	0.742444i	$0.266334\pi$
$432$	−625834.	−	740744.i	−0.161343	−	0.190967i
$433$	3.95066e6			1.01263			0.506314	−	0.862349i	$-0.331008\pi$
$433$	3.95066e6			1.01263			0.506314	+	0.862349i	$0.331008\pi$
$434$	−1.42405e6	−	2.46654e6i	−0.362913	−	0.628584i
$435$	531864.	+	806679.i	0.134765	+	0.204398i
$436$	−1.28456e6	+	2.22492e6i	−0.323621	+	0.560528i
$437$	74058.0	−	128272.i	0.0185510	−	0.0321313i
$438$	−1.81853e6	+	3.63118e6i	−0.452935	+	0.904405i
$439$	243803.	+	422279.i	0.0603778	+	0.104577i	0.894634	−	0.446799i	$-0.147436\pi$
$439$	243803.	+	422279.i	0.0603778	+	0.104577i	−0.834257	+	0.551377i	$0.814103\pi$
$440$	1.15673e6			0.284840
$441$	−4.67092e6	−	6.24473e6i	−1.14368	−	1.52903i
$442$	2.37611e6			0.578511
$443$	4027.52	+	6975.87i	0.000975053	+	0.00168884i	0.866513	−	0.499155i	$-0.166356\pi$
$443$	4027.52	+	6975.87i	0.000975053	+	0.00168884i	−0.865537	+	0.500844i	$0.833023\pi$
$444$	613810.	−	36444.0i	0.147767	−	0.00877341i
$445$	−415909.	+	720375.i	−0.0995630	+	0.172448i
$446$	−1.31605e6	+	2.27947e6i	−0.313283	+	0.542622i
$447$	7.55870e6	−	448785.i	1.78928	−	0.106236i
$448$	−452876.	−	784405.i	−0.106607	−	0.184648i
$449$	6.79644e6			1.59098			0.795492	−	0.605964i	$-0.207212\pi$
$449$	6.79644e6			1.59098			0.795492	+	0.605964i	$0.207212\pi$
$450$	−1.76680e6	−	2.36210e6i	−0.411297	−	0.549878i
$451$	−2.12866e6			−0.492794
$452$	531485.	+	920559.i	0.122362	+	0.211936i
$453$	−1.46735e6	+	2.92996e6i	−0.335961	+	0.670835i
$454$	20268.6	−	35106.3i	0.00461514	−	0.00799365i
$455$	6.69553e6	−	1.15970e7i	1.51620	−	2.62613i
$456$	210530.	+	319312.i	0.0474136	+	0.0719123i
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	0.842872	−	0.538115i	$-0.180863\pi$
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	−0.887457	+	0.460891i	$0.847530\pi$
$458$	4.89214e6			1.08977
$459$	−2.87027e6	+	516110.i	−0.635903	+	0.114343i
$460$	485164.			0.106904
$461$	620959.	+	1.07553e6i	0.136085	+	0.235706i	0.926011	−	0.377495i	$-0.123215\pi$
$461$	620959.	+	1.07553e6i	0.136085	+	0.235706i	−0.789926	+	0.613202i	$0.789881\pi$
$462$	−1.74785e6	−	2.65096e6i	−0.380976	−	0.577828i
$463$	1.21707e6	−	2.10802e6i	0.263853	−	0.457007i	−0.703409	−	0.710785i	$-0.748340\pi$
$463$	1.21707e6	−	2.10802e6i	0.263853	−	0.457007i	0.967263	+	0.253778i	$0.0816732\pi$
$464$	101090.	−	175093.i	0.0217979	−	0.0377550i
$465$	−1.76404e6	+	3.52237e6i	−0.378334	+	0.755445i
$466$	2.33025e6	+	4.03611e6i	0.497093	+	0.860991i
$467$	−1.08309e6			−0.229811			−0.114906	−	0.993376i	$-0.536657\pi$
$467$	−1.08309e6			−0.229811			−0.114906	+	0.993376i	$0.536657\pi$
$468$	−2.97885e6	+	354980.i	−0.628686	+	0.0749185i
$469$	−5.09732e6			−1.07006
$470$	−306411.	−	530720.i	−0.0639824	−	0.110821i
$471$	−6.10377e6	+	362402.i	−1.26779	+	0.0752727i
$472$	762627.	−	1.32091e6i	0.157564	−	0.272909i
$473$	−1.22416e6	+	2.12030e6i	−0.251585	+	0.435758i
$474$	−4.41109e6	+	261901.i	−0.901778	+	0.0535416i
$475$	581707.	+	1.00755e6i	0.118296	+	0.204895i
$476$	−2.72391e6			−0.551030
$477$	3.12024e6	−	7.27856e6i	0.627903	−	1.46470i
$478$	5.27808e6			1.05659
$479$	1.66906e6	+	2.89090e6i	0.332379	+	0.575698i	0.982978	−	0.183724i	$-0.0588153\pi$
$479$	1.66906e6	+	2.89090e6i	0.332379	+	0.575698i	−0.650599	+	0.759422i	$0.725482\pi$
$480$	−560997.	+	1.12018e6i	−0.111137	+	0.221914i
$481$	951107.	−	1.64737e6i	0.187442	−	0.324659i
$482$	−1.06362e6	+	1.84224e6i	−0.208530	+	0.361184i
$483$	−733091.	−	1.11188e6i	−0.142985	−	0.216866i
$484$	864145.	+	1.49674e6i	0.167677	+	0.290425i
$485$	−6.50003e6			−1.25476
$486$	3.52125e6	−	1.07583e6i	0.676248	−	0.206611i
$487$	−5.17210e6			−0.988198			−0.494099	−	0.869406i	$-0.664502\pi$
$487$	−5.17210e6			−0.988198			−0.494099	+	0.869406i	$0.664502\pi$
$488$	−1.20348e6	−	2.08449e6i	−0.228765	−	0.396233i
$489$	−1.63211e6	−	2.47543e6i	−0.308658	−	0.468143i
$490$	−5.03741e6	+	8.72504e6i	−0.947800	+	1.64164i
$491$	−303947.	+	526452.i	−0.0568977	+	0.0985497i	−0.893071	−	0.449915i	$-0.851454\pi$
$491$	−303947.	+	526452.i	−0.0568977	+	0.0985497i	0.836174	+	0.548465i	$0.184788\pi$
$492$	1.03237e6	−	2.06140e6i	0.192275	−	0.383927i
$493$	−304013.	−	526565.i	−0.0563345	−	0.0975742i
$494$	1.18320e6			0.218143
$495$	−1.73048e6	+	4.03669e6i	−0.317435	+	0.740478i
$496$	824303.			0.150447
$497$	7.30289e6	+	1.26490e7i	1.32618	+	2.29702i
$498$	3.44130e6	−	204321.i	0.621797	−	0.0369182i
$499$	−1.75645e6	+	3.04226e6i	−0.315780	+	0.546947i	−0.979603	−	0.200943i	$-0.935599\pi$
$499$	−1.75645e6	+	3.04226e6i	−0.315780	+	0.546947i	0.663823	+	0.747890i	$0.268933\pi$
$500$	56677.7	−	98168.7i	0.0101388	−	0.0175610i
$501$	−6.24370e6	+	370710.i	−1.11134	+	0.0659841i
$502$	−951.500	−	1648.05i	−0.000168519	−	0.000291884i
$503$	−8.23500e6			−1.45125			−0.725627	−	0.688088i	$-0.758450\pi$
$503$	−8.23500e6			−1.45125			−0.725627	+	0.688088i	$0.758450\pi$
$504$	3.41487e6	−	406939.i	0.598822	−	0.0713597i
$505$	1.66451e6			0.290440
$506$	−177947.	−	308213.i	−0.0308968	−	0.0535149i
$507$	−1.56397e6	+	3.12288e6i	−0.270214	+	0.539554i
$508$	2.39683e6	−	4.15143e6i	0.412076	−	0.713737i
$509$	5.30292e6	−	9.18492e6i	0.907236	−	1.57138i	0.0893495	−	0.996000i	$-0.471521\pi$
$509$	5.30292e6	−	9.18492e6i	0.907236	−	1.57138i	0.817887	−	0.575379i	$-0.195145\pi$
$510$	2.07388e6	+	3.14547e6i	0.353068	+	0.535500i
$511$	−7.20113e6	−	1.24727e7i	−1.21997	−	2.11305i
$512$	262144.			0.0441942
$513$	−1.42927e6	+	257000.i	−0.239784	+	0.0431162i
$514$	−108826.			−0.0181688
$515$	−5.17032e6	−	8.95525e6i	−0.859012	−	1.48785i
$516$	−1.45961e6	−	2.21379e6i	−0.241330	−	0.366026i
$517$	−224769.	+	389312.i	−0.0369837	+	0.0640576i
$518$	−1.09032e6	+	1.88849e6i	−0.178538	+	0.309237i
$519$	−661628.	+	1.32112e6i	−0.107819	+	0.215289i
$520$	1.93783e6	+	3.35641e6i	0.314273	+	0.544336i
$521$	1.03709e7			1.67388			0.836939	−	0.547297i	$-0.184343\pi$
$521$	1.03709e7			1.67388			0.836939	+	0.547297i	$0.184343\pi$
$522$	459796.	+	614718.i	0.0738566	+	0.0987416i
$523$	8.86641e6			1.41740			0.708702	−	0.705508i	$-0.249281\pi$
$523$	8.86641e6			1.41740			0.708702	+	0.705508i	$0.249281\pi$
$524$	2.65959e6	+	4.60654e6i	0.423142	+	0.732903i
$525$	1.04426e7	−	620013.i	1.65352	−	0.0981753i
$526$	279965.	−	484913.i	0.0441204	−	0.0764187i
$527$	1.23948e6	−	2.14684e6i	0.194408	−	0.336724i
$528$	917385.	−	54468.2i	0.143208	−	0.00850273i
$529$	3.14354e6	+	5.44476e6i	0.488404	+	0.845941i
$530$	−1.02309e7			−1.58207
$531$	3.46872e6	+	4.63746e6i	0.533867	+	0.713746i
$532$	−1.35639e6			−0.207781
$533$	−3.56606e6	−	6.17660e6i	−0.543714	−	0.941740i
$534$	−295929.	+	590901.i	−0.0449090	+	0.0896729i
$535$	−2.15032e6	+	3.72447e6i	−0.324802	+	0.562574i
$536$	737636.	−	1.27762e6i	0.110900	−	0.192084i
$537$	1.87759e6	+	2.84774e6i	0.280973	+	0.426152i
$538$	−3.27684e6	−	5.67566e6i	−0.488090	−	0.845397i
$539$	7.39041e6			1.09571
$540$	−3.06987e6	−	3.63353e6i	−0.453039	−	0.536222i
$541$	−1.22530e6			−0.179990			−0.0899949	−	0.995942i	$-0.528685\pi$
$541$	−1.22530e6			−0.179990			−0.0899949	+	0.995942i	$0.528685\pi$
$542$	561582.	+	972688.i	0.0821135	+	0.142225i
$543$	2.95615e6	+	4.48360e6i	0.430256	+	0.652571i
$544$	394178.	−	682737.i	0.0571078	−	0.0989137i
$545$	−6.30107e6	+	1.09138e7i	−0.908705	+	1.57392i
$546$	4.76402e6	−	9.51264e6i	0.683899	−	1.36559i
$547$	−1.34505e6	−	2.32969e6i	−0.192207	−	0.332913i	0.753774	−	0.657134i	$-0.228231\pi$
$547$	−1.34505e6	−	2.32969e6i	−0.192207	−	0.332913i	−0.945981	+	0.324221i	$0.894898\pi$
$548$	−2.99524e6			−0.426070
$549$	9.07474e6	−	1.08141e6i	1.28500	−	0.153129i
$550$	2.79546e6			0.394045
$551$	−151385.	−	262207.i	−0.0212424	−	0.0367930i
$552$	384775.	−	22845.4i	0.0537476	−	0.00319117i
$553$	7.83549e6	−	1.35715e7i	1.08957	−	1.88718i
$554$	−1.38562e6	+	2.39996e6i	−0.191809	+	0.332223i
$555$	3.01089e6	−	178767.i	0.414918	−	0.0246351i
$556$	1.68455e6	+	2.91773e6i	0.231099	+	0.400275i
$557$	−5.82722e6			−0.795835			−0.397918	−	0.917421i	$-0.630267\pi$
$557$	−5.82722e6			−0.795835			−0.397918	+	0.917421i	$0.630267\pi$
$558$	−1.23317e6	+	2.87660e6i	−0.167662	+	0.391105i
$559$	−8.20312e6			−1.11032
$560$	−2.22147e6	−	3.84770e6i	−0.299344	−	0.518479i
$561$	1.23759e6	−	2.47117e6i	0.166023	−	0.331509i
$562$	4.21857e6	−	7.30678e6i	0.563410	−	0.975855i
$563$	−4.66117e6	+	8.07338e6i	−0.619760	+	1.07346i	0.369769	+	0.929124i	$0.379437\pi$
$563$	−4.66117e6	+	8.07338e6i	−0.619760	+	1.07346i	−0.989529	+	0.144333i	$0.953896\pi$
$564$	−268000.	−	406476.i	−0.0354762	−	0.0538068i
$565$	2.60707e6	+	4.51557e6i	0.343582	+	0.595102i
$566$	−5.85076e6			−0.767665
$567$	−3.68857e6	+	1.25258e7i	−0.481837	+	1.63624i
$568$	−4.22722e6			−0.549774
$569$	−5.38674e6	−	9.33011e6i	−0.697502	−	1.20811i	−0.969330	−	0.245763i	$-0.920961\pi$
$569$	−5.38674e6	−	9.33011e6i	−0.697502	−	1.20811i	0.271828	−	0.962346i	$-0.412372\pi$
$570$	1.03270e6	+	1.56631e6i	0.133134	+	0.201925i
$571$	1.66600e6	−	2.88559e6i	0.213838	−	0.370378i	−0.739075	−	0.673623i	$-0.764737\pi$
$571$	1.66600e6	−	2.88559e6i	0.213838	−	0.370378i	0.952912	+	0.303246i	$0.0980703\pi$
$572$	1.42150e6	−	2.46211e6i	0.181659	−	0.314642i
$573$	942025.	−	1.88101e6i	0.119860	−	0.239333i
$574$	4.08803e6	+	7.08068e6i	0.517886	+	0.897006i
$575$	1.17249e6			0.147890
$576$	−392170.	+	914812.i	−0.0492513	+	0.114888i
$577$	3.94388e6			0.493156			0.246578	−	0.969123i	$-0.420694\pi$
$577$	3.94388e6			0.493156			0.246578	+	0.969123i	$0.420694\pi$
$578$	1.65428e6	+	2.86530e6i	0.205964	+	0.356739i
$579$	3.53782e6	−	210052.i	0.438570	−	0.0260394i
$580$	495872.	−	858876.i	0.0612068	−	0.106013i
$581$	−6.11284e6	+	1.05877e7i	−0.751281	+	1.30126i
$582$	−5.15506e6	+	306073.i	−0.630850	+	0.0374557i
$583$	3.75246e6	+	6.49946e6i	0.457241	+	0.791965i
$584$	4.16832e6			0.505742
$585$	−1.46120e7	+	1.74126e6i	−1.76530	+	0.210366i
$586$	−1.02196e7			−1.22939
$587$	817286.	+	1.41558e6i	0.0978991	+	0.169566i	0.910815	−	0.412815i	$-0.135454\pi$
$587$	817286.	+	1.41558e6i	0.0978991	+	0.169566i	−0.812916	+	0.582381i	$0.802121\pi$
$588$	−3.58423e6	+	7.15688e6i	−0.427516	+	0.853651i
$589$	617208.	−	1.06904e6i	0.0733066	−	0.126971i
$590$	3.74087e6	−	6.47939e6i	0.442429	−	0.766309i
$591$	−3.69344e6	−	5.60185e6i	−0.434973	−	0.659724i
$592$	−315562.	−	546570.i	−0.0370068	−	0.0640976i
$593$	9.45304e6			1.10391			0.551957	−	0.833873i	$-0.313881\pi$
$593$	9.45304e6			1.10391			0.551957	+	0.833873i	$0.313881\pi$
$594$	−1.18234e6	+	3.28291e6i	−0.137491	+	0.381762i
$595$	−1.33614e7			−1.54725
$596$	−3.88596e6	−	6.73067e6i	−0.448107	−	0.776145i
$597$	−6.17553e6	−	9.36645e6i	−0.709151	−	1.07557i
$598$	596213.	−	1.03267e6i	0.0681787	−	0.118089i
$599$	1.03628e6	−	1.79489e6i	0.118008	−	0.204395i	−0.800970	−	0.598704i	$-0.795683\pi$
$599$	1.03628e6	−	1.79489e6i	0.118008	−	0.204395i	0.918978	+	0.394309i	$0.129016\pi$
$600$	−1.35575e6	+	2.70712e6i	−0.153745	+	0.306994i
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	−0.992952	−	0.118517i	$-0.962186\pi$
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	0.393838	−	0.919180i	$-0.371147\pi$
$602$	9.40383e6			1.05758
$603$	3.35505e6	+	4.48549e6i	0.375756	+	0.502362i
$604$	3.36336e6			0.375130
$605$	4.23884e6	+	7.34189e6i	0.470824	+	0.815492i
$606$	1.32009e6	−	78378.2i	0.146023	−	0.00866990i
$607$	−3.67761e6	+	6.36980e6i	−0.405129	+	0.701704i	−0.994336	−	0.106278i	$-0.966107\pi$
$607$	−3.67761e6	+	6.36980e6i	−0.405129	+	0.701704i	0.589207	+	0.807982i	$0.299440\pi$
$608$	196284.	−	339973.i	0.0215340	−	0.0372980i
$609$	−2.71761e6	+	161354.i	−0.296923	+	0.0176293i
$610$	−5.90338e6	−	1.02250e7i	−0.642357	−	1.11259i
$611$	−1.50618e6			−0.163221
$612$	1.79287e6	+	2.39696e6i	0.193496	+	0.258691i
$613$	1.09586e7			1.17789			0.588946	−	0.808173i	$-0.299543\pi$
$613$	1.09586e7			1.17789			0.588946	+	0.808173i	$0.299543\pi$
$614$	4.29963e6	+	7.44718e6i	0.460268	+	0.797207i
$615$	5.06402e6	−	1.01117e7i	0.539893	−	1.07804i
$616$	−1.62957e6	+	2.82249e6i	−0.173030	+	0.299696i
$617$	−1.88984e6	+	3.27330e6i	−0.199854	+	0.346157i	−0.948481	−	0.316835i	$-0.897380\pi$
$617$	−1.88984e6	+	3.27330e6i	−0.199854	+	0.346157i	0.748627	+	0.662991i	$0.230713\pi$
$618$	−4.52217e6	−	6.85879e6i	−0.476295	−	0.722398i
$619$	246460.	+	426881.i	0.0258535	+	0.0447796i	0.878663	−	0.477443i	$-0.158436\pi$
$619$	246460.	+	426881.i	0.0258535	+	0.0447796i	−0.852809	+	0.522223i	$0.825103\pi$
$620$	4.04341e6			0.422443
$621$	−495902.	+	1.37694e6i	−0.0516021	+	0.143280i
$622$	−1.47048e6			−0.152399
$623$	−1.17184e6	−	2.02968e6i	−0.120961	−	0.209511i
$624$	1.69490e6	+	2.57066e6i	0.174254	+	0.264292i
$625$	5.01978e6	−	8.69452e6i	0.514026	−	0.890319i
$626$	−365487.	+	633042.i	−0.0372766	+	0.0645649i
$627$	616264.	−	1.23054e6i	0.0626034	−	0.125004i
$628$	3.13797e6	+	5.43513e6i	0.317505	+	0.549934i
$629$	−1.89801e6			−0.191281
$630$	1.67508e7	−	1.99614e6i	1.68145	−	0.200373i
$631$	−1.31134e6			−0.131112			−0.0655558	−	0.997849i	$-0.520882\pi$
$631$	−1.31134e6			−0.131112			−0.0655558	+	0.997849i	$0.520882\pi$
$632$	2.26776e6	+	3.92787e6i	0.225842	+	0.391169i
$633$	955450.	−	56728.3i	0.0947761	−	0.00562718i
$634$	−1.72993e6	+	2.99632e6i	−0.170925	+	0.296050i
$635$	1.17570e7	−	2.03638e7i	1.15708	−	2.00412i
$636$	−8.11396e6	+	481753.i	−0.795408	+	0.0472261i
$637$	1.23808e7	+	2.14442e7i	1.20893	+	2.09393i
$638$	−727497.			−0.0707587
$639$	6.32397e6	−	1.47519e7i	0.612685	−	1.42921i
$640$	1.28588e6			0.124094
$641$	−692306.	−	1.19911e6i	−0.0665508	−	0.115269i	0.830830	−	0.556526i	$-0.187866\pi$
$641$	−692306.	−	1.19911e6i	−0.0665508	−	0.115269i	−0.897381	+	0.441257i	$0.854533\pi$
$642$	−1.53000e6	+	3.05506e6i	−0.146506	+	0.292538i
$643$	−3.97132e6	+	6.87852e6i	−0.378797	+	0.656096i	−0.990888	−	0.134692i	$-0.956996\pi$
$643$	−3.97132e6	+	6.87852e6i	−0.378797	+	0.656096i	0.612090	+	0.790788i	$0.290329\pi$
$644$	−683482.	+	1.18383e6i	−0.0649400	+	0.112479i
$645$	−7.15973e6	−	1.08592e7i	−0.677637	−	1.02777i
$646$	−590292.	−	1.02242e6i	−0.0556527	−	0.0963932i
$647$	−2.30348e6			−0.216334			−0.108167	−	0.994133i	$-0.534498\pi$
$647$	−2.30348e6			−0.216334			−0.108167	+	0.994133i	$0.534498\pi$
$648$	−2.60576e6	−	2.73713e6i	−0.243779	−	0.256070i
$649$	−5.48826e6			−0.511474
$650$	4.68311e6	+	8.11138e6i	0.434761	+	0.753029i
$651$	−6.10966e6	−	9.26655e6i	−0.565021	−	0.856970i
$652$	−1.52166e6	+	2.63560e6i	−0.140185	+	0.242807i
$653$	3.96246e6	−	6.86318e6i	0.363649	−	0.629858i	−0.624910	−	0.780697i	$-0.714864\pi$
$653$	3.96246e6	−	6.86318e6i	0.363649	−	0.629858i	0.988558	+	0.150839i	$0.0481975\pi$
$654$	−4.48336e6	+	8.95222e6i	−0.409882	+	0.818439i
$655$	1.30459e7	+	2.25962e7i	1.18815	+	2.05794i
$656$	−2.36633e6			−0.214692
$657$	−6.23584e6	+	1.45463e7i	−0.563614	+	1.31474i
$658$	1.72665e6			0.155467
$659$	−4.75895e6	−	8.24275e6i	−0.426872	−	0.739364i	0.569721	−	0.821838i	$-0.307051\pi$
$659$	−4.75895e6	−	8.24275e6i	−0.426872	−	0.739364i	−0.996593	+	0.0824739i	$0.973718\pi$
$660$	4.50000e6	−	267180.i	0.402117	−	0.0238751i
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	0.424161	+	0.905587i	$0.360569\pi$
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	−0.996342	+	0.0854592i	$0.972764\pi$
$662$	5.99520e6	−	1.03840e7i	0.531690	−	0.920914i
$663$	9.24370e6	−	548830.i	0.816699	−	0.0484902i
$664$	−1.76918e6	−	3.06432e6i	−0.155723	−	0.269720i
$665$	−6.65342e6			−0.583433
$666$	2.37947e6	−	283554.i	0.207871	−	0.0247713i
$667$	−305131.			−0.0265565
$668$	3.20991e6	+	5.55973e6i	0.278325	+	0.482073i
$669$	−4.59329e6	+	9.17172e6i	−0.396788	+	0.792293i
$670$	3.61829e6	−	6.26706e6i	0.311398	−	0.539358i
$671$	−4.33045e6	+	7.50055e6i	−0.371301	+	0.643112i
$672$	−1.94299e6	−	2.94694e6i	−0.165977	−	0.251737i
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	0.692313	−	0.721598i	$-0.256592\pi$
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	−0.971078	+	0.238762i	$0.923259\pi$
$674$	2.87311e6			0.243614
$675$	−7.41890e6	−	8.78108e6i	−0.626730	−	0.741803i
$676$	3.58482e6			0.301718
$677$	−4.58192e6	−	7.93613e6i	−0.384217	−	0.665483i	0.607443	−	0.794363i	$-0.292195\pi$
$677$	−4.58192e6	−	7.93613e6i	−0.384217	−	0.665483i	−0.991660	+	0.128880i	$0.958862\pi$
$678$	2.28025e6	+	3.45846e6i	0.190505	+	0.288940i
$679$	9.15702e6	−	1.58604e7i	0.762219	−	1.32020i
$680$	1.93354e6	−	3.34899e6i	0.160355	−	0.277742i
$681$	70741.5	−	141254.i	0.00584530	−	0.0116717i
$682$	−1.48303e6	−	2.56868e6i	−0.122092	−	0.211470i
$683$	8.96737e6			0.735552			0.367776	−	0.929914i	$-0.380119\pi$
$683$	8.96737e6			0.735552			0.367776	+	0.929914i	$0.380119\pi$
$684$	892773.	+	1.19358e6i	0.0729627	+	0.0975465i
$685$	−1.46924e7			−1.19637
$686$	−6.75995e6	−	1.17086e7i	−0.548445	−	0.949935i
$687$	1.90317e7	−	1.12998e6i	1.53846	−	0.0913435i
$688$	−1.36083e6	+	2.35703e6i	−0.109606	+	0.189843i
$689$	−1.25727e7	+	2.17765e7i	−1.00897	+	1.74759i
$690$	1.88741e6	−	112062.i	0.150919	−	0.00896058i
$691$	−6.85931e6	−	1.18807e7i	−0.546494	−	0.946555i	−0.998511	−	0.0545458i	$-0.982629\pi$
$691$	−6.85931e6	−	1.18807e7i	−0.546494	−	0.946555i	0.452018	−	0.892009i	$-0.350704\pi$
$692$	1.51654e6			0.120389
$693$	−7.41189e6	−	9.90923e6i	−0.586268	−	0.783803i
$694$	−1.49970e7			−1.18197
$695$	8.26315e6	+	1.43122e7i	0.648909	+	1.12394i
$696$	352825.	−	704508.i	0.0276080	−	0.0551268i
$697$	−3.55818e6	+	6.16294e6i	−0.277425	+	0.480514i
$698$	4.66716e6	−	8.08376e6i	0.362589	−	0.628022i
$699$	9.99754e6	+	1.51633e7i	0.773927	+	1.17382i
$700$	−5.36859e6	−	9.29866e6i	−0.414109	−	0.717258i
$701$	3.42100e6			0.262941			0.131470	−	0.991320i	$-0.458030\pi$
$701$	3.42100e6			0.262941			0.131470	+	0.991320i	$0.458030\pi$
$702$	−1.15065e7	+	2.06901e6i	−0.881254	+	0.158460i
$703$	−945126.			−0.0721276
$704$	−471631.	−	816889.i	−0.0358650	−	0.0621200i
$705$	−1.31461e6	−	1.99387e6i	−0.0996145	−	0.151086i
$706$	−8.69138e6	+	1.50539e7i	−0.656262	+	1.13668i
$707$	−2.34490e6	+	4.06149e6i	−0.176431	+	0.305588i
$708$	2.66172e6	−	5.31483e6i	0.199563	−	0.398480i
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	0.506043	−	0.862508i	$-0.331108\pi$
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	−0.999976	+	0.00699191i	$0.997774\pi$
$710$	−2.07356e7			−1.54373
$711$	−1.70998e7	+	2.03773e6i	−1.26858	+	0.151172i
$712$	678308.			0.0501449
$713$	−622020.	−	1.07737e6i	−0.0458227	−	0.0793672i
$714$	−1.05967e7	+	629163.i	−0.777904	+	0.0461868i
$715$	6.97281e6	−	1.20773e7i	0.510085	−	0.883493i
$716$	1.75053e6	−	3.03201e6i	0.127611	−	0.221028i
$717$	2.05331e7	−	1.21912e6i	1.49162	−	0.0885623i
$718$	5.42563e6	+	9.39746e6i	0.392770	+	0.680298i
$719$	−6.17969e6			−0.445804			−0.222902	−	0.974841i	$-0.571553\pi$
$719$	−6.17969e6			−0.445804			−0.222902	+	0.974841i	$0.571553\pi$
$720$	−1.92369e6	+	4.48738e6i	−0.138294	+	0.322598i
$721$	2.91351e7			2.08727
$722$	4.65826e6	+	8.06834e6i	0.332568	+	0.576025i
$723$	−3.71224e6	+	7.41248e6i	−0.264113	+	0.527373i
$724$	2.75611e6	−	4.77372e6i	0.195411	−	0.338462i
$725$	1.19836e6	−	2.07563e6i	0.0846728	−	0.146658i
$726$	3.70747e6	+	5.62313e6i	0.261057	+	0.395946i
$727$	4.83384e6	+	8.37245e6i	0.339200	+	0.587512i	0.984282	−	0.176601i	$-0.0565103\pi$
$727$	4.83384e6	+	8.37245e6i	0.339200	+	0.587512i	−0.645082	+	0.764113i	$0.723177\pi$
$728$	−1.09198e7			−0.763634
$729$	1.34501e7	−	4.99861e6i	0.937360	−	0.348362i
$730$	2.04466e7			1.42009
$731$	4.09249e6	+	7.08841e6i	0.283266	+	0.490631i
$732$	−5.16334e6	−	7.83125e6i	−0.356166	−	0.540199i
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	0.149608	+	0.988745i	$0.452199\pi$
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	−0.931082	+	0.364809i	$0.881134\pi$
$734$	−7.83256e6	+	1.35664e7i	−0.536616	+	0.929446i
$735$	−1.75815e7	+	3.51062e7i	−1.20043	+	2.39699i
$736$	−197814.	−	342624.i	−0.0134606	−	0.0233144i
$737$	−5.30842e6			−0.359995
$738$	3.54005e6	−	8.25784e6i	0.239259	−	0.558117i
$739$	2.13860e7			1.44052			0.720260	−	0.693704i	$-0.244022\pi$
$739$	2.13860e7			1.44052			0.720260	+	0.693704i	$0.244022\pi$
$740$	−1.54791e6	−	2.68106e6i	−0.103912	−	0.179981i
$741$	4.60296e6	−	273293.i	0.307958	−	0.0182845i
$742$	1.44130e7	−	2.49640e7i	0.961045	−	1.66458i
$743$	−4.30567e6	+	7.45765e6i	−0.286134	+	0.495598i	−0.972884	−	0.231296i	$-0.925704\pi$
$743$	−4.30567e6	+	7.45765e6i	−0.286134	+	0.495598i	0.686750	+	0.726894i	$0.259037\pi$
$744$	3.20676e6	−	190396.i	0.212390	−	0.0126103i
$745$	−1.90616e7	−	3.30156e7i	−1.25825	−	2.17936i
$746$	7.12257e6			0.468587
$747$	1.33404e7	−	1.58973e6i	0.874714	−	0.104237i
$748$	−2.83671e6			−0.185379
$749$	−6.05860e6	−	1.04938e7i	−0.394610	−	0.683484i
$750$	197816.	−	394993.i	0.0128413	−	0.0256411i
$751$	3.62736e6	−	6.28277e6i	0.234688	−	0.406491i	−0.724494	−	0.689281i	$-0.757927\pi$
$751$	3.62736e6	−	6.28277e6i	0.234688	−	0.406491i	0.959182	+	0.282790i	$0.0912599\pi$
$752$	−249864.	+	432777.i	−0.0161124	+	0.0279074i
$753$	−4082.25	−	6191.56i	−0.000262369	−	0.000397935i
$754$	−1.21875e6	−	2.11093e6i	−0.0780701	−	0.135221i
$755$	1.64981e7			1.05334
$756$	1.31907e7	−	2.37186e6i	0.839392	−	0.150933i
$757$	−3.04305e6			−0.193005			−0.0965027	−	0.995333i	$-0.530766\pi$
$757$	−3.04305e6			−0.193005			−0.0965027	+	0.995333i	$0.530766\pi$
$758$	1.26348e6	+	2.18841e6i	0.0798721	+	0.138343i
$759$	−763450.	−	1.15793e6i	−0.0481034	−	0.0729586i
$760$	962820.	−	1.66765e6i	0.0604660	−	0.104730i
$761$	1.33530e7	−	2.31282e7i	0.835832	−	1.44770i	−0.0575199	−	0.998344i	$-0.518319\pi$
$761$	1.33530e7	−	2.31282e7i	0.835832	−	1.44770i	0.893352	−	0.449359i	$-0.148347\pi$
$762$	8.36540e6	−	1.67038e7i	0.521914	−	1.04214i
$763$	−1.77535e7	−	3.07499e7i	−1.10401	−	1.91220i
$764$	−2.15925e6			−0.133835
$765$	8.79449e6	+	1.17577e7i	0.543322	+	0.726386i
$766$	534424.			0.0329089
$767$	−9.19425e6	−	1.59249e7i	−0.564323	−	0.977437i
$768$	1.01981e6	−	60549.5i	0.0623901	−	0.00370431i
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	−0.931020	−	0.364968i	$-0.881080\pi$
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	0.781581	+	0.623803i	$0.214413\pi$
$770$	−7.99343e6	+	1.38450e7i	−0.485855	+	0.841525i
$771$	−423363.	+	25136.5i	−0.0256494	+	0.00152289i
$772$	−1.81881e6	−	3.15027e6i	−0.109836	−	0.190241i
$773$	5.22612e6			0.314579			0.157290	−	0.987552i	$-0.449724\pi$
$773$	5.22612e6			0.314579			0.157290	+	0.987552i	$0.449724\pi$
$774$	−6.18959e6	−	8.27508e6i	−0.371372	−	0.496501i
$775$	9.77163e6			0.584404
$776$	2.65024e6	+	4.59034e6i	0.157990	+	0.273647i
$777$	−3.80544e6	+	7.59858e6i	−0.226127	+	0.451523i
$778$	−1.11894e7	+	1.93806e7i	−0.662762	+	1.14794i
$779$	−1.77182e6	+	3.06888e6i	−0.104610	+	0.181191i
$780$	8.31391e6	+	1.26097e7i	0.489293	+	0.742112i
$781$	7.60532e6	+	1.31728e7i	0.446160	+	0.772771i
$782$	−1.18979e6			−0.0695750
$783$	1.93072e6	+	2.28521e6i	0.112542	+	0.133206i
$784$	8.21554e6			0.477360
$785$	1.53925e7	+	2.66607e7i	0.891530	+	1.54418i
$786$	1.14105e7	+	1.73063e7i	0.658792	+	0.999192i
$787$	272112.	−	471312.i	0.0156607	−	0.0271251i	−0.858089	−	0.513501i	$-0.828348\pi$
$787$	272112.	−	471312.i	0.0156607	−	0.0271251i	0.873750	+	0.486376i	$0.161682\pi$
$788$	−3.44350e6	+	5.96432e6i	−0.197553	+	0.342172i
$789$	977132.	−	1.95111e6i	0.0558806	−	0.111580i
$790$	1.11239e7	+	1.92672e7i	0.634147	+	1.09837i
$791$	−1.46910e7			−0.834852
$792$	3.55629e6	−	423792.i	0.201458	−	0.0240071i
$793$	−2.90184e7			−1.63867
$794$	−8.38101e6	−	1.45163e7i	−0.471786	−	0.817158i
$795$	−3.98010e7	+	2.36312e6i	−2.23345	+	0.132607i
$796$	−5.75763e6	+	9.97251e6i	−0.322078	+	0.557855i
$797$	8.60486e6	−	1.49041e7i	0.479842	−	0.831110i	−0.519891	−	0.854233i	$-0.674027\pi$
$797$	8.60486e6	−	1.49041e7i	0.479842	−	0.831110i	0.999733	+	0.0231224i	$0.00736074\pi$
$798$	−5.27671e6	+	313296.i	−0.293330	+	0.0174160i
$799$	751427.	+	1.30151e6i	0.0416409	+	0.0721241i
$800$	3.10756e6			0.171670
$801$	−1.01476e6	+	2.36711e6i	−0.0558830	+	0.130358i
$802$	−1.83287e6			−0.100623
$803$	−7.49935e6	−	1.29892e7i	−0.410426	−	0.710878i
$804$	2.57450e6	−	5.14067e6i	0.140460	−	0.280466i
$805$	−3.35265e6	+	5.80696e6i	−0.182347	+	0.315834i
$806$	4.96891e6	−	8.60640e6i	0.269416	−	0.466642i
$807$	−1.40587e7	−	2.13229e7i	−0.759910	−	1.15256i
$808$	−678664.	−	1.17548e6i	−0.0365701	−	0.0633413i
$809$	−9.72387e6			−0.522357			−0.261179	−	0.965290i	$-0.584111\pi$
$809$	−9.72387e6			−0.522357			−0.261179	+	0.965290i	$0.584111\pi$
$810$	−1.27819e7	−	1.34263e7i	−0.684514	−	0.719026i
$811$	1.04900e6			0.0560045			0.0280023	−	0.999608i	$-0.491085\pi$
$811$	1.04900e6			0.0560045			0.0280023	+	0.999608i	$0.491085\pi$
$812$	1.39714e6	+	2.41991e6i	0.0743616	+	0.128798i
$813$	2.40937e6	+	3.65430e6i	0.127843	+	0.193900i
$814$	−1.13548e6	+	1.96670e6i	−0.0600644	+	0.104035i
$815$	−7.46414e6	+	1.29283e7i	−0.393628	+	0.681784i
$816$	1.37576e6	−	2.74707e6i	0.0723298	−	0.144426i
$817$	2.03788e6	+	3.52972e6i	0.106813	+	0.185006i
$818$	67743.6			0.00353985
$819$	1.63361e7	−	3.81071e7i	0.851017	−	1.98516i
$820$	−1.16074e7			−0.602838
$821$	2.86412e6	+	4.96080e6i	0.148297	+	0.256858i	0.930598	−	0.366042i	$-0.119287\pi$
$821$	2.86412e6	+	4.96080e6i	0.148297	+	0.256858i	−0.782301	+	0.622901i	$0.785954\pi$
$822$	−1.16523e7	+	691836.i	−0.601494	+	0.0357128i
$823$	−1.60427e7	+	2.77868e7i	−0.825617	+	1.43001i	0.0758307	+	0.997121i	$0.475839\pi$
$823$	−1.60427e7	+	2.77868e7i	−0.825617	+	1.43001i	−0.901447	+	0.432889i	$0.857494\pi$
$824$	−4.21615e6	+	7.30259e6i	−0.216321	+	0.374679i
$825$	1.08751e7	−	645689.i	0.556284	−	0.0330285i
$826$	1.05400e7	+	1.82559e7i	0.537517	+	0.931006i
$827$	−5.90474e6			−0.300218			−0.150109	−	0.988669i	$-0.547963\pi$
$827$	−5.90474e6			−0.300218			−0.150109	+	0.988669i	$0.547963\pi$
$828$	1.49160e6	−	177749.i	0.0756094	−	0.00901013i
$829$	−1.24236e6			−0.0627859			−0.0313929	−	0.999507i	$-0.509994\pi$
$829$	−1.24236e6			−0.0627859			−0.0313929	+	0.999507i	$0.509994\pi$
$830$	−8.67829e6	−	1.50312e7i	−0.437259	−	0.757355i
$831$	−4.83607e6	+	9.65652e6i	−0.242935	+	0.485085i
$832$	1.58021e6	−	2.73700e6i	0.0791418	−	0.137078i
$833$	1.23535e7	−	2.13968e7i	0.616846	−	1.06841i
$834$	7.22729e6	+	1.09617e7i	0.359799	+	0.545709i
$835$	1.57454e7	+	2.72718e7i	0.781516	+	1.35363i
$836$	−1.41256e6			−0.0699023
$837$	−4.13291e6	+	1.14755e7i	−0.203912	+	0.566187i
$838$	1.79912e7			0.885012
$839$	9.84453e6	+	1.70512e7i	0.482825	+	0.836278i	0.999806	−	0.0197194i	$-0.00627728\pi$
$839$	9.84453e6	+	1.70512e7i	0.482825	+	0.836278i	−0.516980	+	0.855997i	$0.672944\pi$
$840$	−9.53084e6	−	1.44555e7i	−0.466050	−	0.706860i
$841$	9.94371e6	−	1.72230e7i	0.484795	−	0.839690i
$842$	868994.	−	1.50514e6i	0.0422412	−	0.0731639i
$843$	1.47237e7	−	2.93997e7i	0.713586	−	1.42487i
$844$	−491201.	−	850785.i	−0.0237357	−	0.0411115i
$845$	1.75844e7			0.847201
$846$	−1.13648e6	−	1.51940e6i	−0.0545927	−	0.0729870i
$847$	−2.38862e7			−1.14403
$848$	4.17142e6	+	7.22511e6i	0.199202	+	0.345028i
$849$	−2.27610e7	+	1.35140e6i	−1.08373	+	0.0643449i
$850$	4.67276e6	−	8.09345e6i	0.221833	−	0.384226i
$851$	−476247.	+	824885.i	−0.0225428	+	0.0390454i
$852$	−1.64450e7	+	976396.i	−0.776131	+	0.0460815i
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	−0.976665	−	0.214767i	$-0.931101\pi$
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	0.302339	−	0.953201i	$-0.402233\pi$
$854$	3.32659e7			1.56083
$855$	4.37927e6	+	5.85481e6i	0.204874	+	0.273903i
$856$	3.50698e6			0.163587
$857$	−3.69269e6	−	6.39594e6i	−0.171748	−	0.297476i	0.767283	−	0.641308i	$-0.221608\pi$
$857$	−3.69269e6	−	6.39594e6i	−0.171748	−	0.297476i	−0.939031	+	0.343832i	$0.888275\pi$
$858$	4.96131e6	−	9.90659e6i	0.230080	−	0.459416i
$859$	−3.84152e6	+	6.65370e6i	−0.177631	+	0.307667i	−0.941069	−	0.338215i	$-0.890177\pi$
$859$	−3.84152e6	+	6.65370e6i	−0.177631	+	0.307667i	0.763437	+	0.645882i	$0.223510\pi$
$860$	−6.67522e6	+	1.15618e7i	−0.307765	+	0.533065i
$861$	1.75390e7	+	2.66015e7i	0.806301	+	1.22292i
$862$	−1.03340e7	−	1.78990e7i	−0.473696	−	0.820466i
$863$	3.40976e7			1.55846			0.779232	−	0.626735i	$-0.215609\pi$
$863$	3.40976e7			1.55846			0.779232	+	0.626735i	$0.215609\pi$
$864$	−1.31434e6	+	3.64944e6i	−0.0598996	+	0.166319i
$865$	7.43900e6			0.338045
$866$	−7.90133e6	−	1.36855e7i	−0.358018	−	0.620106i
$867$	7.09742e6	+	1.07647e7i	0.320666	+	0.486355i
$868$	−5.69622e6	+	9.86614e6i	−0.256618	+	0.444476i
$869$	8.15998e6	−	1.41335e7i	0.366556	−	0.634893i
$870$	1.73069e6	−	3.45579e6i	0.0775214	−	0.154792i
$871$	−8.89296e6	−	1.54031e7i	−0.397193	−	0.687958i
$872$	1.02765e7			0.457670
$873$	−1.99838e7	+	2.38141e6i	−0.887448	+	0.105754i
$874$	−592464.			−0.0262351
$875$	783325.	+	1.35676e6i	0.0345877	+	0.0599077i
$876$	1.62159e7	−	962790.i	0.713969	−	0.0423908i
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	−0.851822	−	0.523832i	$-0.824502\pi$
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	0.879562	+	0.475784i	$0.157835\pi$
$878$	975211.	−	1.68912e6i	0.0426936	−	0.0739474i
$879$	−3.97570e7	+	2.36051e6i	−1.73557	+	0.103047i
$880$	−2.31347e6	−	4.00704e6i	−0.100706	−	0.174428i
$881$	1.89395e7			0.822108			0.411054	−	0.911611i	$-0.365161\pi$
$881$	1.89395e7			0.822108			0.411054	+	0.911611i	$0.365161\pi$
$882$	−1.22905e7	+	2.86700e7i	−0.531984	+	1.24096i
$883$	3.16414e7			1.36570			0.682848	−	0.730560i	$-0.260741\pi$
$883$	3.16414e7			1.36570			0.682848	+	0.730560i	$0.260741\pi$
$884$	−4.75223e6	−	8.23110e6i	−0.204534	−	0.354264i
$885$	1.30564e7	−	2.60706e7i	0.560357	−	1.11890i
$886$	16110.1	−	27903.5i	0.000689467	−	0.00119419i
$887$	−1.39213e7	+	2.41124e7i	−0.594116	+	1.02904i	0.399555	+	0.916709i	$0.369165\pi$
$887$	−1.39213e7	+	2.41124e7i	−0.594116	+	1.02904i	−0.993671	+	0.112330i	$0.964169\pi$
$888$	−1.35387e6	−	2.05341e6i	−0.0576160	−	0.0873864i
$889$	3.31258e7	+	5.73756e7i	1.40576	+	2.43485i
$890$	3.32727e6			0.140803
$891$	−3.84132e6	+	1.30445e7i	−0.162101	+	0.550469i
$892$	1.05284e7			0.443049
$893$	374178.	+	648096.i	0.0157018	+	0.0271963i
$894$	−1.66720e7	−	2.52865e7i	−0.697661	−	1.05815i
$895$	8.58678e6	−	1.48727e7i	0.358321	−	0.620631i
$896$	−1.81151e6	+	3.13762e6i	−0.0753824	+	0.130566i
$897$	2.08090e6	−	4.15508e6i	0.0863516	−	0.172424i
$898$	−1.35929e7	−	2.35436e7i	−0.562498	−	0.974275i
$899$	−2.54300e6			−0.104941
$900$	−4.64895e6	+	1.08446e7i	−0.191315	+	0.446278i
$901$	2.50898e7			1.02964
$902$	4.25733e6	+	7.37391e6i	0.174229	+	0.301774i
$903$	3.65834e7	−	2.17208e6i	1.49302	−	0.0886454i
$904$	2.12594e6	−	3.68224e6i	0.0865227	−	0.149862i
$905$	1.35194e7	−	2.34163e7i	0.548701	−	0.950377i
$906$	1.30844e7	−	776864.i	0.529581	−	0.0314430i
$907$	4.48735e6	+	7.77232e6i	0.181122	+	0.313713i	0.942263	−	0.334874i	$-0.108694\pi$
$907$	4.48735e6	+	7.77232e6i	0.181122	+	0.313713i	−0.761141	+	0.648587i	$0.775360\pi$
$908$	−162149.			−0.00652679
$909$	5.11740e6	−	609824.i	0.205418	−	0.0244791i
$910$	−5.35642e7			−2.14423
$911$	4.43865e6	+	7.68797e6i	0.177196	+	0.306913i	0.940919	−	0.338631i	$-0.109964\pi$
$911$	4.43865e6	+	7.68797e6i	0.177196	+	0.306913i	−0.763723	+	0.645544i	$0.776631\pi$
$912$	685069.	−	1.36792e6i	0.0272739	−	0.0544596i
$913$	−6.36599e6	+	1.10262e7i	−0.252749	+	0.437773i
$914$	−796235.	+	1.37912e6i	−0.0315265	+	0.0546055i
$915$	−2.53274e7	−	3.84142e7i	−1.00009	−	1.51684i
$916$	−9.78428e6	−	1.69469e7i	−0.385292	−	0.667346i
$917$	−7.35146e7			−2.88702
$918$	7.52839e6	+	8.91068e6i	0.294846	+	0.348983i
$919$	−1.48072e7			−0.578343			−0.289172	−	0.957277i	$-0.593380\pi$
$919$	−1.48072e7			−0.578343			−0.289172	+	0.957277i	$0.593380\pi$
$920$	−970327.	−	1.68066e6i	−0.0377962	−	0.0654650i
$921$	1.84468e7	+	2.79784e7i	0.716594	+	1.08686i
$922$	2.48384e6	−	4.30213e6i	0.0962268	−	0.166670i
$923$	−2.54818e7	+	4.41357e7i	−0.984521	+	1.70524i
$924$	−5.68751e6	+	1.13566e7i	−0.219150	+	0.437592i
$925$	−3.74081e6	−	6.47927e6i	−0.143751	−	0.248984i
$926$	−9.73654e6			−0.373145
$927$	−1.91767e7	−	2.56380e7i	−0.732949	−	0.979906i
$928$	−808721.			−0.0308268
$929$	7.13029e6	+	1.23500e7i	0.271062	+	0.469492i	0.969134	−	0.246535i	$-0.0792920\pi$
$929$	7.13029e6	+	1.23500e7i	0.271062	+	0.469492i	−0.698072	+	0.716027i	$0.745959\pi$
$930$	1.57299e7	−	933939.i	0.596375	−	0.0354088i
$931$	6.15149e6	−	1.06547e7i	0.232598	−	0.402872i
$932$	9.32100e6	−	1.61444e7i	0.351498	−	0.608812i
$933$	−5.72054e6	+	339648.i	−0.215146	+	0.0127739i
$934$	2.16618e6	+	3.75193e6i	0.0812506	+	0.140730i
$935$	−1.39148e7			−0.520532
$936$	7.18738e6	+	9.60907e6i	0.268152	+	0.358502i
$937$	−3.54753e7			−1.32001			−0.660006	−	0.751261i	$-0.729446\pi$
$937$	−3.54753e7			−1.32001			−0.660006	+	0.751261i	$0.729446\pi$
$938$	1.01946e7	+	1.76576e7i	0.378325	+	0.655278i
$939$	−1.27562e6	+	2.54712e6i	−0.0472126	+	0.0942726i
$940$	−1.22565e6	+	2.12288e6i	−0.0452424	+	0.0783621i
$941$	−1.30008e7	+	2.25180e7i	−0.478624	+	0.829001i	−0.999700	−	0.0245095i	$-0.992198\pi$
$941$	−1.30008e7	+	2.25180e7i	−0.478624	+	0.829001i	0.521076	+	0.853511i	$0.325531\pi$
$942$	1.34629e7	+	2.04193e7i	0.494325	+	0.749744i
$943$	1.78563e6	+	3.09280e6i	0.0653902	+	0.113259i
$944$	−6.10102e6			−0.222829
$945$	6.47039e7	−	1.16346e7i	2.35695	−	0.423809i
$946$	9.79327e6			0.355795
$947$	−1.11889e7	−	1.93797e7i	−0.405426	−	0.702218i	0.588945	−	0.808173i	$-0.299543\pi$
$947$	−1.11889e7	−	1.93797e7i	−0.405426	−	0.702218i	−0.994371	+	0.105955i	$0.966210\pi$
$948$	9.72942e6	+	1.47566e7i	0.351614	+	0.533294i
$949$	2.51267e7	−	4.35207e7i	0.905669	−	1.56866i
$950$	2.32683e6	−	4.03019e6i	0.0836480	−	0.144883i
$951$	−6.03779e6	+	1.20561e7i	−0.216485	+	0.432269i
$952$	5.44782e6	+	9.43590e6i	0.194819	+	0.337436i
$953$	−4.62557e7			−1.64981			−0.824903	−	0.565275i	$-0.808770\pi$
$953$	−4.62557e7			−1.64981			−0.824903	+	0.565275i	$0.808770\pi$
$954$	−3.14542e7	+	3.74829e6i	−1.11894	+	0.133341i
$955$	−1.05916e7			−0.375798
$956$	−1.05562e7	−	1.82838e7i	−0.373561	−	0.647026i
$957$	−2.83016e6	+	168036.i	−0.0998920	+	0.00593092i
$958$	6.67625e6	−	1.15636e7i	0.235028	−	0.407080i
$959$	2.06982e7	−	3.58503e7i	0.726750	−	1.25877i
$960$	5.00242e6	−	297010.i	0.175187	−	0.0104014i
$961$	9.13059e6	+	1.58146e7i	0.318926	+	0.552396i
$962$	−7.60886e6			−0.265083
$963$	−5.24647e6	+	1.22384e7i	−0.182306	+	0.425264i
$964$	8.50895e6			0.294906
$965$	−8.92170e6	−	1.54528e7i	−0.308411	−	0.534183i
$966$	−2.38549e6	+	4.76326e6i	−0.0822497	+	0.164234i
$967$	2.04313e7	−	3.53880e7i	0.702634	−	1.21700i	−0.264905	−	0.964274i	$-0.585341\pi$
$967$	2.04313e7	−	3.53880e7i	0.702634	−	1.21700i	0.967539	−	0.252723i	$-0.0813260\pi$
$968$	3.45658e6	−	5.98697e6i	0.118565	−	0.205361i
$969$	−2.53255e6	−	3.84112e6i	−0.0866460	−	0.131416i
$970$	1.30001e7	+	2.25168e7i	0.443625	+	0.768381i
$971$	−3.69663e7			−1.25822			−0.629112	−	0.777315i	$-0.716581\pi$
$971$	−3.69663e7			−1.25822			−0.629112	+	0.777315i	$0.716581\pi$
$972$	−1.07693e7	−	1.00463e7i	−0.365613	−	0.341068i
$973$	−4.65634e7			−1.57675
$974$	1.03442e7	+	1.79167e7i	0.349381	+	0.605145i
$975$	2.00921e7	+	3.04737e7i	0.676882	+	1.02663i
$976$	−4.81393e6	+	8.33797e6i	−0.161762	+	0.280179i
$977$	2.95829e7	−	5.12390e7i	0.991525	−	1.71737i	0.383253	−	0.923643i	$-0.374804\pi$
$977$	2.95829e7	−	5.12390e7i	0.991525	−	1.71737i	0.608272	−	0.793729i	$-0.291863\pi$
$978$	−5.31091e6	+	1.06047e7i	−0.177551	+	0.354527i
$979$	−1.22036e6	−	2.11373e6i	−0.0406942	−	0.0704845i
$980$	4.02992e7			1.34039
$981$	−1.53737e7	+	3.58620e7i	−0.510041	+	1.18977i
$982$	2.43158e6			0.0804655
$983$	9.12629e6	+	1.58072e7i	0.301238	+	0.521760i	0.976417	−	0.215894i	$-0.0692667\pi$
$983$	9.12629e6	+	1.58072e7i	0.301238	+	0.521760i	−0.675178	+	0.737655i	$0.735933\pi$
$984$	−9.20563e6	+	546569.i	−0.303086	+	0.0179952i
$985$	−1.68912e7	+	2.92564e7i	−0.554715	+	0.960795i
$986$	−1.21605e6	+	2.10626e6i	−0.0398345	+	0.0689954i
$987$	6.71712e6	−	398818.i	0.219477	−	0.0130311i
$988$	−2.36640e6	−	4.09873e6i	−0.0771252	−	0.133585i
$989$	4.10755e6			0.133534
$990$	1.74445e7	−	2.07880e6i	0.565679	−	0.0674101i
$991$	4.10661e7			1.32831			0.664154	−	0.747596i	$-0.268792\pi$
$991$	4.10661e7			1.32831			0.664154	+	0.747596i	$0.268792\pi$
$992$	−1.64861e6	−	2.85547e6i	−0.0531910	−	0.0921294i
$993$	2.09244e7	−	4.17812e7i	0.673411	−	1.34465i
$994$	2.92116e7	−	5.05959e7i	0.937754	−	1.62424i
$995$	−2.82426e7	+	4.89176e7i	−0.904372	+	1.56642i
$996$	−7.59038e6	−	1.15124e7i	−0.242446	−	0.367719i
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	0.677732	−	0.735309i	$-0.262963\pi$
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	−0.975662	+	0.219279i	$0.929629\pi$
$998$	1.40516e7			0.446580
$999$	9.19126e6	−	1.65270e6i	0.291381	−	0.0523939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.b.13.1	yes	6
3.2	odd	2		54.6.c.b.37.3		6
4.3	odd	2		144.6.i.b.49.3		6
9.2	odd	6		54.6.c.b.19.3		6
9.4	even	3		162.6.a.j.1.3		3
9.5	odd	6		162.6.a.i.1.1		3
9.7	even	3	inner	18.6.c.b.7.1	✓	6
12.11	even	2		432.6.i.b.145.3		6
36.7	odd	6		144.6.i.b.97.3		6
36.11	even	6		432.6.i.b.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.1	✓	6	9.7	even	3	inner
18.6.c.b.13.1	yes	6	1.1	even	1	trivial
54.6.c.b.19.3		6	9.2	odd	6
54.6.c.b.37.3		6	3.2	odd	2
144.6.i.b.49.3		6	4.3	odd	2
144.6.i.b.97.3		6	36.7	odd	6
162.6.a.i.1.1		3	9.5	odd	6
162.6.a.j.1.3		3	9.4	even	3
432.6.i.b.145.3		6	12.11	even	2
432.6.i.b.289.3		6	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.58066 - 13.0143i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-39.2420 + 67.9691i) q^{5} +(-27.9216 + 55.7529i) q^{6} +(-110.566 - 191.505i) q^{7} +64.0000 q^{8} +(-95.7446 + 223.343i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.58066 - 13.0143i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-39.2420 + 67.9691i) q^{5} +(-27.9216 + 55.7529i) q^{6} +(-110.566 - 191.505i) q^{7} +64.0000 q^{8} +(-95.7446 + 223.343i) q^{9} +313.936 q^{10} +(-115.144 - 199.436i) q^{11} +(248.977 - 14.7826i) q^{12} +(385.793 - 668.213i) q^{13} +(-442.262 + 766.020i) q^{14} +(1221.29 - 72.5123i) q^{15} +(-128.000 - 221.703i) q^{16} -769.880 q^{17} +(965.171 - 115.016i) q^{18} -383.367 q^{19} +(-627.872 - 1087.51i) q^{20} +(-1543.58 + 3082.17i) q^{21} +(-460.577 + 797.743i) q^{22} +(-193.178 + 334.594i) q^{23} +(-549.162 - 832.916i) q^{24} +(-1517.37 - 2628.15i) q^{25} -3086.34 q^{26} +(3728.20 - 670.377i) q^{27} +3538.10 q^{28} +(394.883 + 683.958i) q^{29} +(-2693.78 - 4085.66i) q^{30} +(-1609.97 + 2788.54i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1607.51 + 3209.82i) q^{33} +(1539.76 + 2666.94i) q^{34} +17355.2 q^{35} +(-2328.77 - 3113.42i) q^{36} +2465.33 q^{37} +(766.733 + 1328.02i) q^{38} +(-12006.7 + 712.877i) q^{39} +(-2511.49 + 4350.02i) q^{40} +(4621.73 - 8005.07i) q^{41} +(13764.1 - 817.223i) q^{42} +(-5315.76 - 9207.16i) q^{43} +3684.62 q^{44} +(-11423.2 - 15272.1i) q^{45} +1545.42 q^{46} +(-976.032 - 1690.54i) q^{47} +(-1786.98 + 3568.19i) q^{48} +(-16046.0 + 27792.4i) q^{49} +(-6069.46 + 10512.6i) q^{50} +(6606.08 + 10019.5i) q^{51} +(6172.68 + 10691.4i) q^{52} -32589.2 q^{53} +(-9778.66 - 11574.1i) q^{54} +18074.0 q^{55} +(-7076.19 - 12256.3i) q^{56} +(3289.54 + 4989.25i) q^{57} +(1579.53 - 2735.83i) q^{58} +(11916.1 - 20639.2i) q^{59} +(-8765.58 + 17502.8i) q^{60} +(-18804.4 - 32570.2i) q^{61} +12879.7 q^{62} +(53357.3 - 6358.42i) q^{63} +4096.00 q^{64} +(30278.5 + 52444.0i) q^{65} +(14334.1 - 851.066i) q^{66} +(11525.6 - 19962.9i) q^{67} +(6159.04 - 10667.8i) q^{68} +(6012.10 - 356.959i) q^{69} +(-34710.5 - 60120.3i) q^{70} -66050.4 q^{71} +(-6127.65 + 14293.9i) q^{72} +65130.0 q^{73} +(-4930.66 - 8540.16i) q^{74} +(-21183.6 + 42298.8i) q^{75} +(3066.93 - 5312.08i) q^{76} +(-25462.0 + 44101.5i) q^{77} +(26482.8 + 40166.6i) q^{78} +(35433.7 + 61373.0i) q^{79} +20091.9 q^{80} +(-40714.9 - 42767.7i) q^{81} -36973.8 q^{82} +(-27643.5 - 47880.0i) q^{83} +(-30359.2 - 46045.9i) q^{84} +(30211.6 - 52328.0i) q^{85} +(-21263.0 + 36828.6i) q^{86} +(5512.88 - 11007.9i) q^{87} +(-7369.24 - 12763.9i) q^{88} +10598.6 q^{89} +(-30057.7 + 70115.3i) q^{90} -170622. q^{91} +(-3090.85 - 5353.50i) q^{92} +(50105.6 - 2974.94i) q^{93} +(-3904.13 + 6762.15i) q^{94} +(15044.1 - 26057.1i) q^{95} +(15934.5 - 946.086i) q^{96} +(41409.9 + 71724.1i) q^{97} +128368. q^{98} +(55567.0 - 6621.74i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9}+O(q^{10}) \) 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9	\( 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18} + 2262 q^{19} - 864 q^{20} - 11076 q^{21} - 1260 q^{22} - 3168 q^{23} + 576 q^{24} - 2883 q^{25} + 5952 q^{26} + 18144 q^{27} + 4224 q^{28} - 5148 q^{29} - 14400 q^{30} - 8610 q^{31} - 3072 q^{32} + 17469 q^{33} - 5796 q^{34} + 2700 q^{35} - 1392 q^{36} + 39936 q^{37} - 4524 q^{38} - 49026 q^{39} - 3456 q^{40} + 5049 q^{41} + 41352 q^{42} - 31389 q^{43} + 10080 q^{44} + 2538 q^{45} + 25344 q^{46} + 12924 q^{47} - 768 q^{48} - 52857 q^{49} - 11532 q^{50} + 36837 q^{51} - 11904 q^{52} - 96048 q^{53} - 71892 q^{54} + 126252 q^{55} - 8448 q^{56} - 17469 q^{57} - 20592 q^{58} + 62955 q^{59} + 21024 q^{60} - 75966 q^{61} + 68880 q^{62} + 49578 q^{63} + 24576 q^{64} + 108702 q^{65} + 2952 q^{66} - 32991 q^{67} - 23184 q^{68} - 29250 q^{69} - 5400 q^{70} - 129672 q^{71} - 11328 q^{72} - 8466 q^{73} - 79872 q^{74} - 105483 q^{75} - 18096 q^{76} + 88740 q^{77} + 171720 q^{78} + 89202 q^{79} + 27648 q^{80} + 123435 q^{81} - 40392 q^{82} + 32634 q^{83} + 11808 q^{84} + 71388 q^{85} - 125556 q^{86} - 151524 q^{87} - 20160 q^{88} + 66132 q^{89} - 263088 q^{90} - 301836 q^{91} - 50688 q^{92} + 57678 q^{93} + 51696 q^{94} - 82944 q^{95} - 6144 q^{96} + 46245 q^{97} + 422856 q^{98} + 282168 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 + 432 * q^10 - 315 * q^11 - 96 * q^12 - 744 * q^13 - 528 * q^14 + 2286 * q^15 - 768 * q^16 + 2898 * q^17 + 1056 * q^18 + 2262 * q^19 - 864 * q^20 - 11076 * q^21 - 1260 * q^22 - 3168 * q^23 + 576 * q^24 - 2883 * q^25 + 5952 * q^26 + 18144 * q^27 + 4224 * q^28 - 5148 * q^29 - 14400 * q^30 - 8610 * q^31 - 3072 * q^32 + 17469 * q^33 - 5796 * q^34 + 2700 * q^35 - 1392 * q^36 + 39936 * q^37 - 4524 * q^38 - 49026 * q^39 - 3456 * q^40 + 5049 * q^41 + 41352 * q^42 - 31389 * q^43 + 10080 * q^44 + 2538 * q^45 + 25344 * q^46 + 12924 * q^47 - 768 * q^48 - 52857 * q^49 - 11532 * q^50 + 36837 * q^51 - 11904 * q^52 - 96048 * q^53 - 71892 * q^54 + 126252 * q^55 - 8448 * q^56 - 17469 * q^57 - 20592 * q^58 + 62955 * q^59 + 21024 * q^60 - 75966 * q^61 + 68880 * q^62 + 49578 * q^63 + 24576 * q^64 + 108702 * q^65 + 2952 * q^66 - 32991 * q^67 - 23184 * q^68 - 29250 * q^69 - 5400 * q^70 - 129672 * q^71 - 11328 * q^72 - 8466 * q^73 - 79872 * q^74 - 105483 * q^75 - 18096 * q^76 + 88740 * q^77 + 171720 * q^78 + 89202 * q^79 + 27648 * q^80 + 123435 * q^81 - 40392 * q^82 + 32634 * q^83 + 11808 * q^84 + 71388 * q^85 - 125556 * q^86 - 151524 * q^87 - 20160 * q^88 + 66132 * q^89 - 263088 * q^90 - 301836 * q^91 - 50688 * q^92 + 57678 * q^93 + 51696 * q^94 - 82944 * q^95 - 6144 * q^96 + 46245 * q^97 + 422856 * q^98 + 282168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more