LMFDB - Embedded newform 18.6.c.b.13.3

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			13.3
Root			$0.500000 + 5.23712i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.6.c.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(15.5145 - 1.51695i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(33.0434 - 57.2329i) q^{5} +(-36.2838 - 50.7098i) q^{6} +(-57.0952 - 98.8918i) q^{7} +64.0000 q^{8} +(238.398 - 47.0695i) q^{9} -264.347 q^{10} +(192.812 + 333.961i) q^{11} +(-103.096 + 227.110i) q^{12} +(-516.287 + 894.236i) q^{13} +(-228.381 + 395.567i) q^{14} +(425.832 - 938.063i) q^{15} +(-128.000 - 221.703i) q^{16} +959.020 q^{17} +(-639.849 - 731.695i) q^{18} -464.576 q^{19} +(528.695 + 915.726i) q^{20} +(-1035.82 - 1447.64i) q^{21} +(771.249 - 1335.84i) q^{22} +(-1151.70 + 1994.81i) q^{23} +(992.926 - 97.0850i) q^{24} +(-621.235 - 1076.01i) q^{25} +4130.30 q^{26} +(3627.21 - 1091.90i) q^{27} +1827.05 q^{28} +(-3549.13 - 6147.28i) q^{29} +(-4101.21 + 401.003i) q^{30} +(-3881.53 + 6723.00i) q^{31} +(-512.000 + 886.810i) q^{32} +(3497.98 + 4888.74i) q^{33} +(-1918.04 - 3322.14i) q^{34} -7546.48 q^{35} +(-1254.97 + 3679.89i) q^{36} +9317.57 q^{37} +(929.153 + 1609.34i) q^{38} +(-6653.41 + 14656.8i) q^{39} +(2114.78 - 3662.90i) q^{40} +(6661.64 - 11538.3i) q^{41} +(-2943.15 + 6483.46i) q^{42} +(1056.29 + 1829.55i) q^{43} -6169.99 q^{44} +(5183.55 - 15199.5i) q^{45} +9213.62 q^{46} +(-1247.40 - 2160.56i) q^{47} +(-2322.16 - 3245.43i) q^{48} +(1883.78 - 3262.80i) q^{49} +(-2484.94 + 4304.04i) q^{50} +(14878.7 - 1454.79i) q^{51} +(-8260.60 - 14307.8i) q^{52} -10044.2 q^{53} +(-11036.9 - 10381.2i) q^{54} +25484.7 q^{55} +(-3654.09 - 6329.07i) q^{56} +(-7207.66 + 704.741i) q^{57} +(-14196.5 + 24589.1i) q^{58} +(-2720.33 + 4711.75i) q^{59} +(9591.53 + 13405.0i) q^{60} +(-17094.4 - 29608.4i) q^{61} +31052.2 q^{62} +(-18266.1 - 20888.1i) q^{63} +4096.00 q^{64} +(34119.8 + 59097.2i) q^{65} +(9939.11 - 21894.8i) q^{66} +(-26792.6 + 46406.2i) q^{67} +(-7672.16 + 13288.6i) q^{68} +(-14842.0 + 32695.5i) q^{69} +(15093.0 + 26141.8i) q^{70} -970.010 q^{71} +(15257.5 - 3012.45i) q^{72} -72400.3 q^{73} +(-18635.1 - 32277.0i) q^{74} +(-11270.4 - 15751.3i) q^{75} +(3716.61 - 6437.36i) q^{76} +(22017.3 - 38135.1i) q^{77} +(64079.4 - 6265.47i) q^{78} +(-16098.9 - 27884.0i) q^{79} -16918.2 q^{80} +(54617.9 - 22442.5i) q^{81} -53293.1 q^{82} +(18046.6 + 31257.6i) q^{83} +(28345.7 - 2771.54i) q^{84} +(31689.3 - 54887.5i) q^{85} +(4225.17 - 7318.21i) q^{86} +(-64388.1 - 89987.9i) q^{87} +(12340.0 + 21373.5i) q^{88} +42622.2 q^{89} +(-63019.8 + 12442.7i) q^{90} +117910. q^{91} +(-18427.2 - 31916.9i) q^{92} +(-50021.4 + 110192. i) q^{93} +(-4989.60 + 8642.25i) q^{94} +(-15351.2 + 26589.0i) q^{95} +(-6598.16 + 14535.1i) q^{96} +(21926.9 + 37978.6i) q^{97} -15070.2 q^{98} +(61685.4 + 70539.9i) 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} + 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}+ \cdots + 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

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
$3$	15.5145	−	1.51695i	0.995254	−	0.0973126i
$3$	15.5145	−	1.51695i	0.995254	−	0.0973126i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	33.0434	−	57.2329i	0.591099	−	1.02381i	−0.402986	−	0.915206i	$-0.632028\pi$
$5$	33.0434	−	57.2329i	0.591099	−	1.02381i	0.994085	−	0.108607i	$-0.0346389\pi$
$6$	−36.2838	−	50.7098i	−0.411467	−	0.575061i
$7$	−57.0952	−	98.8918i	−0.440407	−	0.762808i	0.557312	−	0.830303i	$-0.311833\pi$
$7$	−57.0952	−	98.8918i	−0.440407	−	0.762808i	−0.997720	+	0.0674952i	$0.978499\pi$
$8$	64.0000			0.353553
$9$	238.398	−	47.0695i	0.981061	−	0.193702i
$10$	−264.347			−0.835940
$11$	192.812	+	333.961i	0.480455	+	0.832173i	0.999749	−	0.0224231i	$-0.00713811\pi$
$11$	192.812	+	333.961i	0.480455	+	0.832173i	−0.519293	+	0.854596i	$0.673805\pi$
$12$	−103.096	+	227.110i	−0.206676	+	0.455286i
$13$	−516.287	+	894.236i	−0.847292	+	1.46755i	0.0363242	+	0.999340i	$0.488435\pi$
$13$	−516.287	+	894.236i	−0.847292	+	1.46755i	−0.883616	+	0.468212i	$0.844898\pi$
$14$	−228.381	+	395.567i	−0.311415	+	0.539386i
$15$	425.832	−	938.063i	0.488663	−	1.07648i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	959.020			0.804832			0.402416	−	0.915457i	$-0.368171\pi$
$17$	959.020			0.804832			0.402416	+	0.915457i	$0.368171\pi$
$18$	−639.849	−	731.695i	−0.465475	−	0.532291i
$19$	−464.576			−0.295239			−0.147619	−	0.989044i	$-0.547161\pi$
$19$	−464.576			−0.295239			−0.147619	+	0.989044i	$0.547161\pi$
$20$	528.695	+	915.726i	0.295549	+	0.511906i
$21$	−1035.82	−	1447.64i	−0.512548	−	0.716330i
$22$	771.249	−	1335.84i	0.339733	−	0.588435i
$23$	−1151.70	+	1994.81i	−0.453963	+	0.786288i	−0.998628	−	0.0523662i	$-0.983324\pi$
$23$	−1151.70	+	1994.81i	−0.453963	+	0.786288i	0.544664	+	0.838654i	$0.316657\pi$
$24$	992.926	−	97.0850i	0.351875	−	0.0344052i
$25$	−621.235	−	1076.01i	−0.198795	−	0.344323i
$26$	4130.30			1.19825
$27$	3627.21	−	1091.90i	0.957555	−	0.288252i
$28$	1827.05			0.440407
$29$	−3549.13	−	6147.28i	−0.783659	−	1.35734i	−0.929797	−	0.368073i	$-0.880018\pi$
$29$	−3549.13	−	6147.28i	−0.783659	−	1.35734i	0.146138	−	0.989264i	$-0.453316\pi$
$30$	−4101.21	+	401.003i	−0.831972	+	0.0813475i
$31$	−3881.53	+	6723.00i	−0.725435	+	1.25649i	0.233360	+	0.972391i	$0.425028\pi$
$31$	−3881.53	+	6723.00i	−0.725435	+	1.25649i	−0.958795	+	0.284100i	$0.908305\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	3497.98	+	4888.74i	0.559156	+	0.781469i
$34$	−1918.04	−	3322.14i	−0.284551	−	0.492857i
$35$	−7546.48			−1.04130
$36$	−1254.97	+	3679.89i	−0.161390	+	0.473237i
$37$	9317.57			1.11892			0.559459	−	0.828858i	$-0.311009\pi$
$37$	9317.57			1.11892			0.559459	+	0.828858i	$0.311009\pi$
$38$	929.153	+	1609.34i	0.104383	+	0.180796i
$39$	−6653.41	+	14656.8i	−0.700459	+	1.54304i
$40$	2114.78	−	3662.90i	0.208985	−	0.361972i
$41$	6661.64	−	11538.3i	0.618901	−	1.07197i	−0.370785	−	0.928719i	$-0.620911\pi$
$41$	6661.64	−	11538.3i	0.618901	−	1.07197i	0.989687	−	0.143250i	$-0.0457552\pi$
$42$	−2943.15	+	6483.46i	−0.257448	+	0.567131i
$43$	1056.29	+	1829.55i	0.0871190	+	0.150895i	0.906292	−	0.422652i	$-0.138901\pi$
$43$	1056.29	+	1829.55i	0.0871190	+	0.150895i	−0.819173	+	0.573546i	$0.805567\pi$
$44$	−6169.99			−0.480455
$45$	5183.55	−	15199.5i	0.381589	−	1.11892i
$46$	9213.62			0.642001
$47$	−1247.40	−	2160.56i	−0.0823686	−	0.142667i	0.821898	−	0.569634i	$-0.192915\pi$
$47$	−1247.40	−	2160.56i	−0.0823686	−	0.142667i	−0.904267	+	0.426968i	$0.859582\pi$
$48$	−2322.16	−	3245.43i	−0.145476	−	0.203315i
$49$	1883.78	−	3262.80i	0.112083	−	0.194133i
$50$	−2484.94	+	4304.04i	−0.140569	+	0.243473i
$51$	14878.7	−	1454.79i	0.801012	−	0.0783203i
$52$	−8260.60	−	14307.8i	−0.423646	−	0.733776i
$53$	−10044.2			−0.491163			−0.245582	−	0.969376i	$-0.578979\pi$
$53$	−10044.2			−0.491163			−0.245582	+	0.969376i	$0.578979\pi$
$54$	−11036.9	−	10381.2i	−0.515064	−	0.484468i
$55$	25484.7			1.13599
$56$	−3654.09	−	6329.07i	−0.155707	−	0.269693i
$57$	−7207.66	+	704.741i	−0.293837	+	0.0287304i
$58$	−14196.5	+	24589.1i	−0.554131	+	0.959783i
$59$	−2720.33	+	4711.75i	−0.101740	+	0.176219i	−0.912402	−	0.409296i	$-0.865774\pi$
$59$	−2720.33	+	4711.75i	−0.101740	+	0.176219i	0.810662	+	0.585515i	$0.199108\pi$
$60$	9591.53	+	13405.0i	0.343962	+	0.480716i
$61$	−17094.4	−	29608.4i	−0.588206	−	1.01880i	−0.994467	−	0.105046i	$-0.966501\pi$
$61$	−17094.4	−	29608.4i	−0.588206	−	1.01880i	0.406261	−	0.913757i	$-0.366832\pi$
$62$	31052.2			1.02592
$63$	−18266.1	−	20888.1i	−0.579823	−	0.663053i
$64$	4096.00			0.125000
$65$	34119.8	+	59097.2i	1.00167	+	1.73494i
$66$	9939.11	−	21894.8i	0.280859	−	0.618703i
$67$	−26792.6	+	46406.2i	−0.729169	+	1.26296i	0.228066	+	0.973646i	$0.426760\pi$
$67$	−26792.6	+	46406.2i	−0.729169	+	1.26296i	−0.957235	+	0.289311i	$0.906574\pi$
$68$	−7672.16	+	13288.6i	−0.201208	+	0.348503i
$69$	−14842.0	+	32695.5i	−0.375293	+	0.826732i
$70$	15093.0	+	26141.8i	0.368154	+	0.637661i
$71$	−970.010			−0.0228365			−0.0114183	−	0.999935i	$-0.503635\pi$
$71$	−970.010			−0.0228365			−0.0114183	+	0.999935i	$0.503635\pi$
$72$	15257.5	−	3012.45i	0.346857	−	0.0684838i
$73$	−72400.3			−1.59013			−0.795066	−	0.606523i	$-0.792564\pi$
$73$	−72400.3			−1.59013			−0.795066	+	0.606523i	$0.792564\pi$
$74$	−18635.1	−	32277.0i	−0.395597	−	0.685195i
$75$	−11270.4	−	15751.3i	−0.231359	−	0.323344i
$76$	3716.61	−	6437.36i	0.0738097	−	0.127842i
$77$	22017.3	−	38135.1i	0.423192	−	0.732990i
$78$	64079.4	−	6265.47i	1.19256	−	0.116605i
$79$	−16098.9	−	27884.0i	−0.290220	−	0.502676i	0.683642	−	0.729818i	$-0.260395\pi$
$79$	−16098.9	−	27884.0i	−0.290220	−	0.502676i	−0.973862	+	0.227142i	$0.927062\pi$
$80$	−16918.2			−0.295549
$81$	54617.9	−	22442.5i	0.924959	−	0.380066i
$82$	−53293.1			−0.875258
$83$	18046.6	+	31257.6i	0.287541	+	0.498036i	0.973222	−	0.229866i	$-0.0738289\pi$
$83$	18046.6	+	31257.6i	0.287541	+	0.498036i	−0.685681	+	0.727902i	$0.740496\pi$
$84$	28345.7	−	2771.54i	0.438317	−	0.0428572i
$85$	31689.3	−	54887.5i	0.475735	−	0.823998i
$86$	4225.17	−	7318.21i	0.0616024	−	0.106699i
$87$	−64388.1	−	89987.9i	−0.912026	−	1.27464i
$88$	12340.0	+	21373.5i	0.169867	+	0.294218i
$89$	42622.2			0.570375			0.285188	−	0.958472i	$-0.407944\pi$
$89$	42622.2			0.570375			0.285188	+	0.958472i	$0.407944\pi$
$90$	−63019.8	+	12442.7i	−0.820107	+	0.161923i
$91$	117910.			1.49261
$92$	−18427.2	−	31916.9i	−0.226982	−	0.393144i
$93$	−50021.4	+	110192.i	−0.599720	+	1.32112i
$94$	−4989.60	+	8642.25i	−0.0582434	+	0.100880i
$95$	−15351.2	+	26589.0i	−0.174515	+	0.302269i
$96$	−6598.16	+	14535.1i	−0.0730710	+	0.160968i
$97$	21926.9	+	37978.6i	0.236618	+	0.409835i	0.959742	−	0.280884i	$-0.0906275\pi$
$97$	21926.9	+	37978.6i	0.236618	+	0.409835i	−0.723123	+	0.690719i	$0.757294\pi$
$98$	−15070.2			−0.158509
$99$	61685.4	+	70539.9i	0.632549	+	0.723347i
$100$	19879.5			0.198795
$101$	−12056.7	−	20882.8i	−0.117604	−	0.203697i	0.801213	−	0.598379i	$-0.204188\pi$
$101$	−12056.7	−	20882.8i	−0.117604	−	0.203697i	−0.918818	+	0.394682i	$0.870855\pi$
$102$	−34796.9	−	48631.7i	−0.331162	−	0.462827i
$103$	68610.4	−	118837.i	0.637231	−	1.10372i	−0.348807	−	0.937195i	$-0.613413\pi$
$103$	68610.4	−	118837.i	0.637231	−	1.10372i	0.986038	−	0.166522i	$-0.0532536\pi$
$104$	−33042.4	+	57231.1i	−0.299563	+	0.518858i
$105$	−117080.	+	11447.7i	−1.03635	+	0.101331i
$106$	20088.4	+	34794.2i	0.173652	+	0.300775i
$107$	−167979.			−1.41839			−0.709195	−	0.705012i	$-0.750941\pi$
$107$	−167979.			−1.41839			−0.709195	+	0.705012i	$0.750941\pi$
$108$	−13887.9	+	58995.3i	−0.114572	+	0.486696i
$109$	−21224.0			−0.171104			−0.0855521	−	0.996334i	$-0.527265\pi$
$109$	−21224.0			−0.171104			−0.0855521	+	0.996334i	$0.527265\pi$
$110$	−50969.4	−	88281.6i	−0.401632	−	0.695646i
$111$	144557.	−	14134.3i	1.11361	−	0.108885i
$112$	−14616.4	+	25316.3i	−0.110102	+	0.190702i
$113$	14420.8	−	24977.5i	0.106241	−	0.184015i	−0.808003	−	0.589178i	$-0.799452\pi$
$113$	14420.8	−	24977.5i	0.106241	−	0.184015i	0.914245	+	0.405163i	$0.132785\pi$
$114$	16856.6	+	23558.6i	0.121481	+	0.169780i
$115$	76112.4	+	131831.i	0.536674	+	0.929547i
$116$	113572.			0.783659
$117$	−80990.5	+	237485.i	−0.546977	+	1.60388i
$118$	21762.6			0.143882
$119$	−54755.4	−	94839.2i	−0.354454	−	0.613932i
$120$	27253.2	−	60036.0i	0.172769	−	0.380591i
$121$	6172.35	−	10690.8i	0.0383255	−	0.0663816i
$122$	−68377.6	+	118434.i	−0.415925	+	0.720402i
$123$	85848.7	−	189116.i	0.511648	−	1.12711i
$124$	−62104.5	−	107568.i	−0.362718	−	0.628245i
$125$	124410.			0.712167
$126$	−35826.3	+	105052.i	−0.201037	+	0.589492i
$127$	−215062.			−1.18319			−0.591594	−	0.806236i	$-0.701501\pi$
$127$	−215062.			−1.18319			−0.591594	+	0.806236i	$0.701501\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	19163.2	+	26782.2i	0.101389	+	0.141701i
$130$	136479.	−	236389.i	0.708285	−	1.22679i
$131$	94654.7	−	163947.i	0.481908	−	0.834688i	−0.517877	−	0.855455i	$-0.673277\pi$
$131$	94654.7	−	163947.i	0.481908	−	0.834688i	0.999784	+	0.0207668i	$0.00661075\pi$
$132$	−95724.2	+	9359.59i	−0.478175	+	0.0467544i
$133$	26525.1	+	45942.8i	0.130025	+	0.225210i
$134$	214341.			1.03120
$135$	57363.1	−	243676.i	0.270893	−	1.15074i
$136$	61377.3			0.284551
$137$	1809.78	+	3134.63i	0.00823805	+	0.0142687i	0.870115	−	0.492849i	$-0.164044\pi$
$137$	1809.78	+	3134.63i	0.00823805	+	0.0142687i	−0.861877	+	0.507117i	$0.830711\pi$
$138$	142945.	−	13976.6i	0.638954	−	0.0624748i
$139$	−60440.1	+	104685.i	−0.265331	+	0.459567i	−0.967650	−	0.252295i	$-0.918815\pi$
$139$	−60440.1	+	104685.i	−0.265331	+	0.459567i	0.702319	+	0.711862i	$0.252148\pi$
$140$	60371.8	−	104567.i	0.260324	−	0.450895i
$141$	−22630.2	−	31627.7i	−0.0958609	−	0.133974i
$142$	1940.02	+	3360.21i	0.00807394	+	0.0139845i
$143$	−398186.			−1.62834
$144$	−40950.3	−	46828.5i	−0.164570	−	0.188193i
$145$	−469102.			−1.85288
$146$	144801.	+	250802.i	0.562197	+	0.973753i
$147$	24276.3	−	53478.2i	0.0926594	−	0.204119i
$148$	−74540.6	+	129108.i	−0.279730	+	0.484506i
$149$	−37408.2	+	64792.9i	−0.138039	+	0.239090i	−0.926754	−	0.375668i	$-0.877413\pi$
$149$	−37408.2	+	64792.9i	−0.138039	+	0.239090i	0.788715	+	0.614758i	$0.210746\pi$
$150$	−32023.5	+	70544.5i	−0.116209	+	0.255997i
$151$	179976.	+	311728.i	0.642352	+	1.11259i	0.984906	+	0.173088i	$0.0553745\pi$
$151$	179976.	+	311728.i	0.642352	+	1.11259i	−0.342554	+	0.939498i	$0.611292\pi$
$152$	−29732.9			−0.104383
$153$	228628.	−	45140.6i	0.789589	−	0.155897i
$154$	−176138.			−0.598484
$155$	256518.	+	444302.i	0.857607	+	1.48542i
$156$	−149863.	−	209447.i	−0.493041	−	0.689068i
$157$	−23983.3	+	41540.3i	−0.0776533	+	0.134499i	−0.902237	−	0.431241i	$-0.858076\pi$
$157$	−23983.3	+	41540.3i	−0.0776533	+	0.134499i	0.824584	+	0.565740i	$0.191409\pi$
$158$	−64395.4	+	111536.i	−0.205217	+	0.355446i
$159$	−155831.	+	15236.6i	−0.488832	+	0.0477964i
$160$	33836.5	+	58606.5i	0.104492	+	0.180986i
$161$	263027.			0.799715
$162$	−186979.	−	144317.i	−0.559764	−	0.432046i
$163$	361063.			1.06442			0.532212	−	0.846611i	$-0.321361\pi$
$163$	361063.			1.06442			0.532212	+	0.846611i	$0.321361\pi$
$164$	106586.	+	184613.i	0.309451	+	0.535984i
$165$	395382.	−	38659.1i	1.13059	−	0.110546i
$166$	72186.3	−	125030.i	0.203322	−	0.352164i
$167$	−58233.2	+	100863.i	−0.161577	+	0.279860i	−0.935434	−	0.353500i	$-0.884991\pi$
$167$	−58233.2	+	100863.i	−0.161577	+	0.279860i	0.773857	+	0.633360i	$0.218325\pi$
$168$	−66292.2	−	92649.1i	−0.181213	−	0.253261i
$169$	−347458.	−	601816.i	−0.935807	−	1.62086i
$170$	−253514.			−0.672791
$171$	−110754.	+	21867.4i	−0.289647	+	0.0571882i
$172$	−33801.4			−0.0871190
$173$	−51762.9	−	89656.0i	−0.131493	−	0.227753i	0.792759	−	0.609535i	$-0.208644\pi$
$173$	−51762.9	−	89656.0i	−0.131493	−	0.227753i	−0.924252	+	0.381782i	$0.875311\pi$
$174$	−182951.	+	403023.i	−0.458102	+	1.00915i
$175$	−70939.0	+	122870.i	−0.175102	+	0.303285i
$176$	49359.9	−	85493.9i	0.120114	−	0.208043i
$177$	−35057.0	+	77226.9i	−0.0841088	+	0.185283i
$178$	−85244.4	−	147648.i	−0.201658	−	0.349282i
$179$	−78941.2			−0.184150			−0.0920748	−	0.995752i	$-0.529350\pi$
$179$	−78941.2			−0.184150			−0.0920748	+	0.995752i	$0.529350\pi$
$180$	169142.	+	193422.i	0.389109	+	0.444963i
$181$	586108.			1.32978			0.664892	−	0.746940i	$-0.268478\pi$
$181$	586108.			1.32978			0.664892	+	0.746940i	$0.268478\pi$
$182$	−235820.	−	408452.i	−0.527719	−	0.914035i
$183$	−310125.	−	433427.i	−0.684557	−	0.956728i
$184$	−73709.0	+	127668.i	−0.160500	+	0.277995i
$185$	307884.	−	533271.i	0.661391	−	1.14556i
$186$	481759.	−	47104.8i	1.02105	−	0.0998350i
$187$	184911.	+	320275.i	0.386686	+	0.669760i
$188$	39916.8			0.0823686
$189$	−315076.	−	296359.i	−0.641595	−	0.603482i
$190$	122810.			0.246802
$191$	−386026.	−	668617.i	−0.765656	−	1.32615i	−0.939899	−	0.341452i	$-0.889081\pi$
$191$	−386026.	−	668617.i	−0.765656	−	1.32615i	0.174243	−	0.984703i	$-0.444252\pi$
$192$	63547.3	−	6213.44i	0.124407	−	0.0121641i
$193$	8719.67	−	15102.9i	0.0168503	−	0.0291855i	−0.857477	−	0.514522i	$-0.827969\pi$
$193$	8719.67	−	15102.9i	0.0168503	−	0.0291855i	0.874328	+	0.485336i	$0.161303\pi$
$194$	87707.8	−	151914.i	0.167315	−	0.289797i
$195$	618998.	+	865104.i	1.16574	+	1.62923i
$196$	30140.5	+	52204.8i	0.0560415	+	0.0970667i
$197$	340729.			0.625524			0.312762	−	0.949832i	$-0.398746\pi$
$197$	340729.			0.625524			0.312762	+	0.949832i	$0.398746\pi$
$198$	120987.	−	354764.i	0.219318	−	0.643097i
$199$	14239.7			0.0254899			0.0127450	−	0.999919i	$-0.495943\pi$
$199$	14239.7			0.0254899			0.0127450	+	0.999919i	$0.495943\pi$
$200$	−39759.0	−	68864.7i	−0.0702847	−	0.121737i
$201$	−345277.	+	760610.i	−0.602806	+	1.32792i
$202$	−48226.7	+	83531.1i	−0.0831589	+	0.144036i
$203$	−405277.	+	701960.i	−0.690258	+	1.19556i
$204$	−98871.4	+	217803.i	−0.166339	+	0.366429i
$205$	−440246.	−	762529.i	−0.731663	−	1.26728i
$206$	−548883.			−0.901181
$207$	−180669.	+	529768.i	−0.293061	+	0.859329i
$208$	264339.			0.423646
$209$	−89576.0	−	155150.i	−0.141849	−	0.245690i
$210$	273815.	+	382681.i	0.428459	+	0.598809i
$211$	24049.2	−	41654.4i	0.0371873	−	0.0644102i	−0.846833	−	0.531859i	$-0.821494\pi$
$211$	24049.2	−	41654.4i	0.0371873	−	0.0644102i	0.884020	+	0.467449i	$0.154827\pi$
$212$	80353.7	−	139177.i	0.122791	−	0.212680i
$213$	−15049.2	+	1471.46i	−0.0227282	+	0.00222228i
$214$	335958.	+	581897.i	0.501477	+	0.868583i
$215$	139614.			0.205984
$216$	232142.	−	69881.4i	0.338547	−	0.101912i
$217$	886466.			1.27795
$218$	42448.0	+	73522.1i	0.0604945	+	0.104780i
$219$	−1.12325e6	+	109828.i	−1.58258	+	0.154740i
$220$	−203878.	+	353126.i	−0.283996	+	0.491896i
$221$	−495130.	+	857590.i	−0.681928	+	1.18113i
$222$	−338077.	−	472492.i	−0.460398	−	0.643446i
$223$	−391988.	−	678944.i	−0.527851	−	0.914264i	−0.999473	−	0.0324633i	$-0.989665\pi$
$223$	−391988.	−	678944.i	−0.527851	−	0.914264i	0.471622	−	0.881801i	$-0.343669\pi$
$224$	116931.			0.155707
$225$	−198748.	−	227277.i	−0.261726	−	0.299295i
$226$	−115366.			−0.150248
$227$	277898.	+	481334.i	0.357949	+	0.619986i	0.987618	−	0.156878i	$-0.0501428\pi$
$227$	277898.	+	481334.i	0.357949	+	0.619986i	−0.629669	+	0.776863i	$0.716810\pi$
$228$	47896.1	−	105510.i	0.0610187	−	0.134418i
$229$	−57346.2	+	99326.6i	−0.0722630	+	0.125163i	−0.899893	−	0.436111i	$-0.856355\pi$
$229$	−57346.2	+	99326.6i	−0.0722630	+	0.125163i	0.827630	+	0.561274i	$0.189689\pi$
$230$	304450.	−	527322.i	0.379486	−	0.657289i
$231$	283738.	−	625045.i	0.349854	−	0.770693i
$232$	−227144.	−	393426.i	−0.277065	−	0.479891i
$233$	−111177.			−0.134161			−0.0670805	−	0.997748i	$-0.521368\pi$
$233$	−111177.			−0.134161			−0.0670805	+	0.997748i	$0.521368\pi$
$234$	984653.	−	194411.i	1.17556	−	0.232103i
$235$	−164874.			−0.194752
$236$	−43525.3	−	75388.0i	−0.0508700	−	0.0881094i
$237$	−292064.	−	408185.i	−0.337759	−	0.472048i
$238$	−219022.	+	379357.i	−0.250637	+	0.434116i
$239$	369523.	−	640033.i	0.418453	−	0.724782i	−0.577331	−	0.816510i	$-0.695906\pi$
$239$	369523.	−	640033.i	0.418453	−	0.724782i	0.995784	+	0.0917279i	$0.0292390\pi$
$240$	−262477.	+	25664.2i	−0.294147	+	0.0287607i
$241$	645180.	+	1.11748e6i	0.715547	+	1.23936i	0.962748	+	0.270400i	$0.0871559\pi$
$241$	645180.	+	1.11748e6i	0.715547	+	1.23936i	−0.247201	+	0.968964i	$0.579511\pi$
$242$	−49378.8			−0.0542004
$243$	813324.	−	431036.i	0.883584	−	0.468272i
$244$	547021.			0.588206
$245$	−124493.	−	215628.i	−0.132504	−	0.229504i
$246$	−826814.	+	80843.1i	−0.871104	+	0.0851737i
$247$	239855.	−	415441.i	0.250153	−	0.433278i
$248$	−248418.	+	430272.i	−0.256480	+	0.444236i
$249$	327400.	+	457569.i	0.334641	+	0.467690i
$250$	−248821.	−	430971.i	−0.251789	−	0.436111i
$251$	1.29383e6			1.29626			0.648129	−	0.761530i	$-0.275552\pi$
$251$	1.29383e6			1.29626			0.648129	+	0.761530i	$0.275552\pi$
$252$	435564.	−	85998.1i	0.432066	−	0.0853075i
$253$	−888250.			−0.872437
$254$	430123.	+	744996.i	0.418320	+	0.724552i
$255$	408381.	−	899621.i	0.393292	−	0.866382i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−312181.	+	540713.i	−0.294831	+	0.510663i	−0.974946	−	0.222443i	$-0.928597\pi$
$257$	−312181.	+	540713.i	−0.294831	+	0.510663i	0.680114	+	0.733106i	$0.261930\pi$
$258$	54449.9	−	119948.i	0.0509270	−	0.112187i
$259$	−531988.	−	921431.i	−0.492780	−	0.853519i
$260$	−1.09183e6			−1.00167
$261$	−1.13545e6	−	1.29844e6i	−1.03174	−	1.17983i
$262$	−757237.			−0.681520
$263$	582495.	+	1.00891e6i	0.519281	+	0.899421i	0.999749	+	0.0224089i	$0.00713358\pi$
$263$	582495.	+	1.00891e6i	0.519281	+	0.899421i	−0.480468	+	0.877012i	$0.659533\pi$
$264$	223871.	+	312879.i	0.197691	+	0.276291i
$265$	−331895.	+	574859.i	−0.290326	+	0.502859i
$266$	106100.	−	183771.i	0.0919417	−	0.159248i
$267$	661261.	−	64655.9i	0.567668	−	0.0555047i
$268$	−428682.	−	742498.i	−0.364584	−	0.631479i
$269$	1.58951e6			1.33932			0.669659	−	0.742669i	$-0.266440\pi$
$269$	1.58951e6			1.33932			0.669659	+	0.742669i	$0.266440\pi$
$270$	−958844.	+	288640.i	−0.800458	+	0.240961i
$271$	−977878.			−0.808837			−0.404419	−	0.914574i	$-0.632526\pi$
$271$	−977878.			−0.808837			−0.404419	+	0.914574i	$0.632526\pi$
$272$	−122755.	−	212617.i	−0.100604	−	0.174251i
$273$	1.82931e6	−	178864.i	1.48553	−	0.145250i
$274$	7239.12	−	12538.5i	0.00582518	−	0.0100895i
$275$	239563.	−	414936.i	0.191024	−	0.330864i
$276$	−334306.	−	467221.i	−0.264162	−	0.369190i
$277$	645243.	+	1.11759e6i	0.505271	+	0.875154i	0.999981	+	0.00609677i	$0.00194067\pi$
$277$	645243.	+	1.11759e6i	0.505271	+	0.875154i	−0.494711	+	0.869058i	$0.664726\pi$
$278$	483521.			0.375235
$279$	−608899.	+	1.78545e6i	−0.468312	+	1.37321i
$280$	−482975.			−0.368154
$281$	−833662.	−	1.44395e6i	−0.629831	−	1.09090i	−0.987585	−	0.157084i	$-0.949791\pi$
$281$	−833662.	−	1.44395e6i	−0.629831	−	1.09090i	0.357754	−	0.933816i	$-0.383543\pi$
$282$	−64301.2	+	141649.i	−0.0481500	+	0.106069i
$283$	−564568.	+	977861.i	−0.419035	+	0.725790i	−0.995843	−	0.0910901i	$-0.970965\pi$
$283$	−564568.	+	977861.i	−0.419035	+	0.725790i	0.576808	+	0.816880i	$0.304298\pi$
$284$	7760.08	−	13440.9i	0.00570914	−	0.00988852i
$285$	−197831.	+	435802.i	−0.144272	+	0.317817i
$286$	796372.	+	1.37936e6i	0.575706	+	0.997152i
$287$	−1.52139e6			−1.09027
$288$	−80318.0	+	235513.i	−0.0570600	+	0.167315i
$289$	−500138.			−0.352245
$290$	938204.	+	1.62502e6i	0.655092	+	1.13465i
$291$	397797.	+	555955.i	0.275378	+	0.384864i
$292$	579202.	−	1.00321e6i	0.397533	−	0.688547i
$293$	−1.02815e6	+	1.78081e6i	−0.699663	+	1.21185i	0.268921	+	0.963162i	$0.413333\pi$
$293$	−1.02815e6	+	1.78081e6i	−0.699663	+	1.21185i	−0.968583	+	0.248689i	$0.920000\pi$
$294$	−233807.	+	22860.8i	−0.157757	+	0.0154249i
$295$	179778.	+	311385.i	0.120277	+	0.208325i
$296$	596324.			0.395597
$297$	1.06402e6	+	1.00082e6i	0.699937	+	0.658359i
$298$	299265.			0.195216
$299$	−1.18922e6	−	2.05979e6i	−0.769279	−	1.33243i
$300$	308420.	−	30156.3i	0.197852	−	0.0193453i
$301$	120618.	−	208917.i	0.0767357	−	0.132910i
$302$	719905.	−	1.24691e6i	0.454211	−	0.786717i
$303$	−218731.	−	305696.i	−0.136869	−	0.191286i
$304$	59465.8	+	102998.i	0.0369048	+	0.0639210i
$305$	−2.25943e6			−1.39075
$306$	−613628.	−	701710.i	−0.374629	−	0.428405i
$307$	1.52149e6			0.921346			0.460673	−	0.887570i	$-0.347608\pi$
$307$	1.52149e6			0.921346			0.460673	+	0.887570i	$0.347608\pi$
$308$	352277.	+	610162.i	0.211596	+	0.366495i
$309$	884184.	−	1.94777e6i	0.526801	−	1.16049i
$310$	1.02607e6	−	1.77721e6i	0.606420	−	1.05035i
$311$	1.35420e6	−	2.34554e6i	0.793928	−	1.37512i	−0.129589	−	0.991568i	$-0.541366\pi$
$311$	1.35420e6	−	2.34554e6i	0.793928	−	1.37512i	0.923517	−	0.383556i	$-0.125301\pi$
$312$	−425818.	+	938034.i	−0.247650	+	0.545547i
$313$	325583.	+	563926.i	0.187845	+	0.325358i	0.944532	−	0.328420i	$-0.106516\pi$
$313$	325583.	+	563926.i	0.187845	+	0.325358i	−0.756686	+	0.653778i	$0.773183\pi$
$314$	191866.			0.109818
$315$	−1.79906e6	+	355209.i	−1.02157	+	0.201701i
$316$	515164.			0.290220
$317$	58055.3	+	100555.i	0.0324484	+	0.0562024i	0.881794	−	0.471636i	$-0.156336\pi$
$317$	58055.3	+	100555.i	0.0324484	+	0.0562024i	−0.849345	+	0.527838i	$0.823003\pi$
$318$	364442.	+	509340.i	0.202098	+	0.282449i
$319$	1.36863e6	−	2.37054e6i	0.753026	−	1.30428i
$320$	135346.	−	234426.i	0.0738873	−	0.127977i
$321$	−2.60611e6	+	254816.i	−1.41166	+	0.138027i
$322$	−526054.	−	911152.i	−0.282742	−	0.489724i
$323$	−445538.			−0.237618
$324$	−125971.	+	936348.i	−0.0666666	+	0.495536i
$325$	1.28294e6			0.673750
$326$	−722127.	−	1.25076e6i	−0.376331	−	0.651824i
$327$	−329279.	+	32195.8i	−0.170292	+	0.0166506i
$328$	426345.	−	738451.i	0.218815	−	0.378998i
$329$	−142441.	+	246715.i	−0.0725514	+	0.125663i
$330$	−924683.	−	1.29232e6i	−0.467421	−	0.653261i
$331$	−158828.	−	275099.i	−0.0796816	−	0.138013i	0.823431	−	0.567416i	$-0.192057\pi$
$331$	−158828.	−	275099.i	−0.0796816	−	0.138013i	−0.903113	+	0.429404i	$0.858724\pi$
$332$	−577491.			−0.287541
$333$	2.22129e6	−	438573.i	1.09773	−	0.216736i
$334$	465866.			0.228504
$335$	1.77064e6	+	3.06684e6i	0.862021	+	1.49306i
$336$	−188362.	+	414941.i	−0.0910215	+	0.200511i
$337$	−215275.	+	372867.i	−0.103257	+	0.178846i	−0.913025	−	0.407904i	$-0.866260\pi$
$337$	−215275.	+	372867.i	−0.103257	+	0.178846i	0.809768	+	0.586750i	$0.199593\pi$
$338$	−1.38983e6	+	2.40726e6i	−0.661715	+	1.14612i
$339$	185841.	−	409389.i	0.0878299	−	0.193480i
$340$	507029.	+	878200.i	0.237868	+	0.411999i
$341$	−2.99363e6			−1.39416
$342$	297259.	+	339928.i	0.137426	+	0.157153i
$343$	−2.34942e6			−1.07826
$344$	67602.7	+	117091.i	0.0308012	+	0.0533493i
$345$	1.38082e6	+	1.92982e6i	0.624584	+	0.872910i
$346$	−207052.	+	358624.i	−0.0929798	+	0.161046i
$347$	2.07020e6	−	3.58569e6i	0.922971	−	1.59863i	0.128178	−	0.991751i	$-0.459087\pi$
$347$	2.07020e6	−	3.58569e6i	0.922971	−	1.59863i	0.794793	−	0.606881i	$-0.207580\pi$
$348$	1.76201e6	−	172284.i	0.779940	−	0.0762599i
$349$	1.73048e6	+	2.99727e6i	0.760505	+	1.31723i	0.942590	+	0.333951i	$0.108382\pi$
$349$	1.73048e6	+	2.99727e6i	0.760505	+	1.31723i	−0.182085	+	0.983283i	$0.558285\pi$
$350$	567512.			0.247631
$351$	−896271.	+	3.80731e6i	−0.388304	+	1.64949i
$352$	−394880.			−0.169867
$353$	−1.32229e6	−	2.29027e6i	−0.564792	−	0.978249i	−0.997069	−	0.0765076i	$-0.975623\pi$
$353$	−1.32229e6	−	2.29027e6i	−0.564792	−	0.978249i	0.432277	−	0.901741i	$-0.357710\pi$
$354$	337636.	−	33012.9i	0.143199	−	0.0140015i
$355$	−32052.5	+	55516.5i	−0.0134987	+	0.0233804i
$356$	−340977.	+	590590.i	−0.142594	+	0.246980i
$357$	−993368.	−	1.38832e6i	−0.412515	−	0.576526i
$358$	157882.	+	273460.i	0.0651067	+	0.112768i
$359$	2.13123e6			0.872761			0.436380	−	0.899762i	$-0.356260\pi$
$359$	2.13123e6			0.872761			0.436380	+	0.899762i	$0.356260\pi$
$360$	331747.	−	972769.i	0.134912	−	0.395598i
$361$	−2.26027e6			−0.912834
$362$	−1.17222e6	−	2.03034e6i	−0.470149	−	0.814323i
$363$	79543.3	−	175226.i	0.0316838	−	0.0697961i
$364$	−943281.	+	1.63381e6i	−0.373153	+	0.646321i
$365$	−2.39235e6	+	4.14368e6i	−0.939925	+	1.62800i
$366$	−881185.	+	1.94116e6i	−0.343846	+	0.757458i
$367$	640035.	+	1.10857e6i	0.248049	+	0.429634i	0.962985	−	0.269557i	$-0.0868771\pi$
$367$	640035.	+	1.10857e6i	0.248049	+	0.429634i	−0.714935	+	0.699191i	$0.753544\pi$
$368$	589672.			0.226982
$369$	1.04502e6	−	3.06426e6i	0.399538	−	1.17155i
$370$	−2.46307e6			−0.935348
$371$	573476.	+	993289.i	0.216312	+	0.374663i
$372$	−1.12669e6	−	1.57465e6i	−0.422132	−	0.589966i
$373$	1.94733e6	−	3.37288e6i	0.724716	−	1.25524i	−0.234375	−	0.972146i	$-0.575304\pi$
$373$	1.94733e6	−	3.37288e6i	0.724716	−	1.25524i	0.959091	−	0.283099i	$-0.0913623\pi$
$374$	739643.	−	1.28110e6i	0.273428	−	0.473592i
$375$	1.93016e6	−	188725.i	0.708787	−	0.0693028i
$376$	−79833.7	−	138276.i	−0.0291217	−	0.0504402i
$377$	7.32949e6			2.65595
$378$	−396467.	+	1.68417e6i	−0.142718	+	0.606258i
$379$	−2.83335e6			−1.01322			−0.506609	−	0.862176i	$-0.669101\pi$
$379$	−2.83335e6			−1.01322			−0.506609	+	0.862176i	$0.669101\pi$
$380$	−245619.	−	425425.i	−0.0872576	−	0.151135i
$381$	−3.33657e6	+	326239.i	−1.17757	+	0.115139i
$382$	−1.54411e6	+	2.67447e6i	−0.541400	+	0.937733i
$383$	−1.18249e6	+	2.04814e6i	−0.411909	+	0.713448i	−0.995099	−	0.0988883i	$-0.968471\pi$
$383$	−1.18249e6	+	2.04814e6i	−0.411909	+	0.713448i	0.583189	+	0.812336i	$0.301805\pi$
$384$	−148619.	−	207707.i	−0.0514334	−	0.0718826i
$385$	−1.45505e6	−	2.52023e6i	−0.500296	−	0.866539i
$386$	−69757.3			−0.0238299
$387$	337934.	+	386442.i	0.114698	+	0.131162i
$388$	−701662.			−0.236618
$389$	871692.	+	1.50981e6i	0.292071	+	0.505882i	0.974299	−	0.225257i	$-0.0723222\pi$
$389$	871692.	+	1.50981e6i	0.292071	+	0.505882i	−0.682228	+	0.731139i	$0.738989\pi$
$390$	1.75881e6	−	3.87448e6i	0.585542	−	1.28989i
$391$	−1.10451e6	+	1.91306e6i	−0.365364	+	0.632830i
$392$	120562.	−	208819.i	0.0396273	−	0.0686365i
$393$	1.21982e6	−	2.68713e6i	0.398395	−	0.877623i
$394$	−681458.	−	1.18032e6i	−0.221156	−	0.383053i
$395$	−2.12785e6			−0.686195
$396$	−1.47091e6	+	290418.i	−0.471356	+	0.0930649i
$397$	4.81109e6			1.53203			0.766015	−	0.642823i	$-0.222237\pi$
$397$	4.81109e6			1.53203			0.766015	+	0.642823i	$0.222237\pi$
$398$	−28479.4	−	49327.8i	−0.00901205	−	0.0156093i
$399$	481216.	+	672541.i	0.151324	+	0.211488i
$400$	−159036.	+	275459.i	−0.0496988	+	0.0860808i
$401$	2.27703e6	−	3.94394e6i	0.707145	−	1.22481i	−0.258767	−	0.965940i	$-0.583316\pi$
$401$	2.27703e6	−	3.94394e6i	0.707145	−	1.22481i	0.965912	−	0.258871i	$-0.0833506\pi$
$402$	3.32539e6	−	325145.i	1.02631	−	0.100349i
$403$	−4.00797e6	−	6.94200e6i	−1.22931	−	2.12923i
$404$	385813.			0.117604
$405$	520314.	−	3.86752e6i	0.157626	−	1.17164i
$406$	3.24221e6			0.976173
$407$	1.79654e6	+	3.11170e6i	0.537590	+	0.931133i
$408$	952236.	−	93106.5i	0.283201	−	0.0276904i
$409$	−956414.	+	1.65656e6i	−0.282708	+	0.489664i	−0.972051	−	0.234771i	$-0.924566\pi$
$409$	−956414.	+	1.65656e6i	−0.282708	+	0.489664i	0.689343	+	0.724435i	$0.257899\pi$
$410$	−1.76099e6	+	3.05012e6i	−0.517364	+	0.896101i
$411$	32832.9	+	45886.8i	0.00958748	+	0.0133993i
$412$	1.09777e6	+	1.90139e6i	0.318615	+	0.551858i
$413$	621271.			0.179228
$414$	2.19651e6	−	433680.i	0.629842	−	0.124357i
$415$	2.38528e6			0.679860
$416$	−528678.	−	915697.i	−0.149781	−	0.259429i
$417$	−778894.	+	1.71582e6i	−0.219350	+	0.483206i
$418$	−358304.	+	620601.i	−0.100302	+	0.173729i
$419$	−2.20697e6	+	3.82259e6i	−0.614132	+	1.06371i	0.376404	+	0.926456i	$0.377161\pi$
$419$	−2.20697e6	+	3.82259e6i	−0.614132	+	1.06371i	−0.990536	+	0.137252i	$0.956173\pi$
$420$	778014.	−	1.71388e6i	0.215211	−	0.474087i
$421$	872253.	+	1.51079e6i	0.239848	+	0.415430i	0.960671	−	0.277690i	$-0.0895689\pi$
$421$	872253.	+	1.51079e6i	0.239848	+	0.415430i	−0.720822	+	0.693120i	$0.756236\pi$
$422$	−192393.			−0.0525907
$423$	−399074.	−	456359.i	−0.108443	−	0.124010i
$424$	−642829.			−0.173652
$425$	−595777.	−	1.03192e6i	−0.159997	−	0.277122i
$426$	35195.7	+	49189.0i	0.00939648	+	0.0131324i
$427$	−1.95202e6	+	3.38099e6i	−0.518100	+	0.897376i
$428$	1.34383e6	−	2.32759e6i	0.354598	−	0.614181i
$429$	−6.17765e6	+	604030.i	−1.62061	+	0.158458i
$430$	−279228.	−	483637.i	−0.0728262	−	0.126139i
$431$	−2.21740e6			−0.574976			−0.287488	−	0.957784i	$-0.592820\pi$
$431$	−2.21740e6			−0.574976			−0.287488	+	0.957784i	$0.592820\pi$
$432$	−706359.	−	664399.i	−0.182103	−	0.171285i
$433$	−3.63511e6			−0.931746			−0.465873	−	0.884851i	$-0.654260\pi$
$433$	−3.63511e6			−0.931746			−0.465873	+	0.884851i	$0.654260\pi$
$434$	−1.77293e6	−	3.07081e6i	−0.451823	−	0.782580i
$435$	−7.27787e6	+	711606.i	−1.84409	+	0.180309i
$436$	169792.	−	294088.i	0.0427761	−	0.0740903i
$437$	535054.	−	926741.i	0.134028	−	0.232143i
$438$	2.62696e6	+	3.67140e6i	0.654287	+	0.914423i
$439$	1.54413e6	+	2.67452e6i	0.382405	+	0.662345i	0.991405	−	0.130825i	$-0.0417626\pi$
$439$	1.54413e6	+	2.67452e6i	0.382405	+	0.662345i	−0.609001	+	0.793170i	$0.708429\pi$
$440$	1.63102e6			0.401632
$441$	295510.	−	866512.i	0.0723562	−	0.212167i
$442$	3.96104e6			0.964391
$443$	3.50048e6	+	6.06302e6i	0.847459	+	1.46784i	0.883468	+	0.468491i	$0.155202\pi$
$443$	3.50048e6	+	6.06302e6i	0.847459	+	1.46784i	−0.0360092	+	0.999351i	$0.511465\pi$
$444$	−960607.	+	2.11612e6i	−0.231253	+	0.509427i
$445$	1.40838e6	−	2.43939e6i	0.337148	−	0.583958i
$446$	−1.56795e6	+	2.71577e6i	−0.373247	+	0.646482i
$447$	−482080.	+	1.06197e6i	−0.114117	+	0.251388i
$448$	−233862.	−	405061.i	−0.0550509	−	0.0953510i
$449$	−5.00196e6			−1.17091			−0.585456	−	0.810704i	$-0.699084\pi$
$449$	−5.00196e6			−1.17091			−0.585456	+	0.810704i	$0.699084\pi$
$450$	−389815.	+	1.14304e6i	−0.0907459	+	0.266091i
$451$	5.13778e6			1.18942
$452$	230733.	+	399641.i	0.0531206	+	0.0920076i
$453$	3.26511e6	+	4.56328e6i	0.747572	+	1.04480i
$454$	1.11159e6	−	1.92534e6i	0.253108	−	0.438396i
$455$	3.89615e6	−	6.74833e6i	0.882282	−	1.52816i
$456$	−461290.	+	45103.4i	−0.103887	+	0.0101577i
$457$	−1.78581e6	−	3.09311e6i	−0.399985	−	0.692795i	0.593738	−	0.804658i	$-0.297651\pi$
$457$	−1.78581e6	−	3.09311e6i	−0.399985	−	0.692795i	−0.993724	+	0.111863i	$0.964318\pi$
$458$	458770.			0.102195
$459$	3.47857e6	−	1.04715e6i	0.770671	−	0.231994i
$460$	−2.43560e6			−0.536674
$461$	−2.75061e6	−	4.76420e6i	−0.602805	−	1.04409i	−0.992394	−	0.123100i	$-0.960716\pi$
$461$	−2.75061e6	−	4.76420e6i	−0.602805	−	1.04409i	0.389589	−	0.920989i	$-0.372617\pi$
$462$	−2.73270e6	+	267194.i	−0.595643	+	0.0582400i
$463$	1.42708e6	−	2.47177e6i	0.309382	−	0.535866i	−0.668845	−	0.743402i	$-0.733211\pi$
$463$	1.42708e6	−	2.47177e6i	0.309382	−	0.535866i	0.978227	+	0.207536i	$0.0665444\pi$
$464$	−908578.	+	1.57370e6i	−0.195915	+	0.339334i
$465$	4.65373e6	+	6.50399e6i	0.998087	+	1.39491i
$466$	222355.	+	385130.i	0.0474331	+	0.0821566i
$467$	−7.16552e6			−1.52039			−0.760196	−	0.649694i	$-0.774897\pi$
$467$	−7.16552e6			−1.52039			−0.760196	+	0.649694i	$0.774897\pi$
$468$	−2.64277e6	−	3.02212e6i	−0.557756	−	0.637818i
$469$	6.11892e6			1.28452
$470$	329747.	+	571139.i	0.0688551	+	0.119261i
$471$	−309074.	+	680857.i	−0.0641962	+	0.141418i
$472$	−174101.	+	301552.i	−0.0359705	+	0.0623027i
$473$	−407332.	+	705520.i	−0.0837136	+	0.144996i
$474$	−829866.	+	1.82811e6i	−0.169653	+	0.373729i
$475$	288611.	+	499889.i	0.0586920	+	0.101658i
$476$	1.75217e6			0.354454
$477$	−2.39452e6	+	472775.i	−0.481861	+	0.0951391i
$478$	−2.95619e6			−0.591782
$479$	−1.64185e6	−	2.84377e6i	−0.326961	−	0.566312i	0.654947	−	0.755675i	$-0.272691\pi$
$479$	−1.64185e6	−	2.84377e6i	−0.326961	−	0.566312i	−0.981907	+	0.189363i	$0.939358\pi$
$480$	613858.	+	857920.i	0.121609	+	0.169959i
$481$	−4.81054e6	+	8.33210e6i	−0.948050	+	1.64207i
$482$	2.58072e6	−	4.46994e6i	0.505968	−	0.876363i
$483$	4.08072e6	−	398999.i	0.795920	−	0.0778224i
$484$	98757.6	+	171053.i	0.0191627	+	0.0331908i
$485$	2.89816e6			0.559459
$486$	−3.11980e6	−	1.95536e6i	−0.599151	−	0.375523i
$487$	2.18097e6			0.416704			0.208352	−	0.978054i	$-0.433190\pi$
$487$	2.18097e6			0.416704			0.208352	+	0.978054i	$0.433190\pi$
$488$	−1.09404e6	−	1.89494e6i	−0.207962	−	0.360201i
$489$	5.60171e6	−	547716.i	1.05937	−	0.103582i
$490$	−497972.	+	862512.i	−0.0936946	+	0.162284i
$491$	4.96974e6	−	8.60785e6i	0.930315	−	1.61135i	0.147534	−	0.989057i	$-0.452866\pi$
$491$	4.96974e6	−	8.60785e6i	0.930315	−	1.61135i	0.782782	−	0.622297i	$-0.213800\pi$
$492$	1.93368e6	+	2.70248e6i	0.360140	+	0.503327i
$493$	−3.40369e6	−	5.89536e6i	−0.630714	−	1.09243i
$494$	−1.91884e6			−0.353770
$495$	6.07550e6	−	1.19955e6i	1.11447	−	0.220042i
$496$	1.98734e6			0.362718
$497$	55382.9	+	95926.0i	0.0100574	+	0.0174199i
$498$	930267.	−	2.04928e6i	0.168087	−	0.370279i
$499$	2.26386e6	−	3.92112e6i	0.407004	−	0.704951i	−0.587549	−	0.809189i	$-0.699907\pi$
$499$	2.26386e6	−	3.92112e6i	0.407004	−	0.704951i	0.994552	+	0.104238i	$0.0332403\pi$
$500$	−995284.	+	1.72388e6i	−0.178042	+	0.308377i
$501$	−750453.	+	1.65317e6i	−0.133576	+	0.294255i
$502$	−2.58765e6	−	4.48194e6i	−0.458297	−	0.793793i
$503$	−4.40282e6			−0.775909			−0.387955	−	0.921679i	$-0.626818\pi$
$503$	−4.40282e6			−0.775909			−0.387955	+	0.921679i	$0.626818\pi$
$504$	−1.16903e6	−	1.33684e6i	−0.204998	−	0.234425i
$505$	−1.59357e6			−0.278063
$506$	1.77650e6	+	3.07699e6i	0.308453	+	0.534256i
$507$	−6.30356e6	−	8.80977e6i	−1.08910	−	1.52211i
$508$	1.72049e6	−	2.97998e6i	0.295797	−	0.512335i
$509$	−2.91063e6	+	5.04135e6i	−0.497957	+	0.862487i	−0.999997	−	0.00235703i	$-0.999250\pi$
$509$	−2.91063e6	+	5.04135e6i	−0.497957	+	0.862487i	0.502040	+	0.864844i	$0.332583\pi$
$510$	−3.93314e6	+	384570.i	−0.669598	+	0.0654711i
$511$	4.13371e6	+	7.15979e6i	0.700306	+	1.21296i
$512$	262144.			0.0441942
$513$	−1.68512e6	+	507269.i	−0.282707	+	0.0851030i
$514$	2.49745e6			0.416954
$515$	−4.53424e6	−	7.85354e6i	−0.753333	−	1.30481i
$516$	−524410.	+	51275.1i	−0.0867055	+	0.00847778i
$517$	481028.	−	833166.i	0.0791488	−	0.137090i
$518$	−2.12795e6	+	3.68572e6i	−0.348448	+	0.603529i
$519$	−939078.	−	1.31244e6i	−0.153032	−	0.213876i
$520$	2.18367e6	+	3.78222e6i	0.354142	+	0.613393i
$521$	1.09649e7			1.76975			0.884875	−	0.465829i	$-0.154244\pi$
$521$	1.09649e7			1.76975			0.884875	+	0.465829i	$0.154244\pi$
$522$	−2.22702e6	+	6.53021e6i	−0.357724	+	1.04894i
$523$	−3.83705e6			−0.613399			−0.306700	−	0.951806i	$-0.599225\pi$
$523$	−3.83705e6			−0.613399			−0.306700	+	0.951806i	$0.599225\pi$
$524$	1.51447e6	+	2.62315e6i	0.240954	+	0.417344i
$525$	−914194.	+	2.01387e6i	−0.144757	+	0.318885i
$526$	2.32998e6	−	4.03564e6i	0.367187	−	0.635987i
$527$	−3.72246e6	+	6.44750e6i	−0.583854	+	1.01126i
$528$	636103.	−	1.40127e6i	0.0992985	−	0.218744i
$529$	565332.	+	979183.i	0.0878343	+	0.152133i
$530$	2.65516e6			0.410583
$531$	−426741.	+	1.25131e6i	−0.0656792	+	0.192588i
$532$	−848803.			−0.130025
$533$	6.87864e6	+	1.19141e7i	1.04878	+	1.81654i
$534$	−1.54650e6	−	2.16136e6i	−0.234691	−	0.328000i
$535$	−5.55060e6	+	9.61392e6i	−0.838408	+	1.45217i
$536$	−1.71473e6	+	2.96999e6i	−0.257800	+	0.446523i
$537$	−1.22473e6	+	119750.i	−0.183276	+	0.0179201i
$538$	−3.17903e6	−	5.50623e6i	−0.473520	−	0.820161i
$539$	1.45286e6			0.215403
$540$	2.91757e6	+	2.74425e6i	0.430563	+	0.404986i
$541$	−4.88767e6			−0.717974			−0.358987	−	0.933343i	$-0.616878\pi$
$541$	−4.88767e6			−0.717974			−0.358987	+	0.933343i	$0.616878\pi$
$542$	1.95576e6	+	3.38747e6i	0.285967	+	0.495310i
$543$	9.09315e6	−	889098.i	1.32347	−	0.129405i
$544$	−491018.	+	850469.i	−0.0711378	+	0.123214i
$545$	−701313.	+	1.21471e6i	−0.101139	+	0.175179i
$546$	−4.27823e6	−	5.97920e6i	−0.614161	−	0.858344i
$547$	3.46672e6	+	6.00454e6i	0.495394	+	0.858047i	0.999986	−	0.00531061i	$-0.00169043\pi$
$547$	3.46672e6	+	6.00454e6i	0.495394	+	0.858047i	−0.504592	+	0.863358i	$0.668357\pi$
$548$	−57913.0			−0.00823805
$549$	−5.46892e6	−	6.25395e6i	−0.774410	−	0.885571i
$550$	−1.91651e6			−0.270149
$551$	1.64884e6	+	2.85588e6i	0.231366	+	0.400739i
$552$	−949890.	+	2.09251e6i	−0.132686	+	0.292294i
$553$	−1.83834e6	+	3.18409e6i	−0.255630	+	0.442764i
$554$	2.58097e6	−	4.47038e6i	0.357280	−	0.618828i
$555$	3.96772e6	−	8.74047e6i	0.546774	−	1.20449i
$556$	−967042.	−	1.67497e6i	−0.132666	−	0.229784i
$557$	−9.83771e6			−1.34356			−0.671778	−	0.740752i	$-0.734469\pi$
$557$	−9.83771e6			−1.34356			−0.671778	+	0.740752i	$0.734469\pi$
$558$	7.40278e6	−	1.46161e6i	1.00649	−	0.198722i
$559$	−2.18140e6			−0.295261
$560$	965950.	+	1.67307e6i	0.130162	+	0.225447i
$561$	3.35464e6	+	4.68840e6i	0.450027	+	0.628951i
$562$	−3.33465e6	+	5.77578e6i	−0.445358	+	0.771383i
$563$	−1.36609e6	+	2.36613e6i	−0.181638	+	0.314607i	−0.942439	−	0.334379i	$-0.891473\pi$
$563$	−1.36609e6	+	2.36613e6i	−0.181638	+	0.314607i	0.760800	+	0.648986i	$0.224807\pi$
$564$	619289.	−	60552.0i	0.0819776	−	0.00801550i
$565$	−953024.	−	1.65069e6i	−0.125598	−	0.217542i
$566$	4.51654e6			0.592605
$567$	−5.33780e6	−	4.11990e6i	−0.697276	−	0.538182i
$568$	−62080.7			−0.00807394
$569$	−4.71998e6	−	8.17525e6i	−0.611167	−	1.05857i	−0.991044	−	0.133535i	$-0.957367\pi$
$569$	−4.71998e6	−	8.17525e6i	−0.611167	−	1.05857i	0.379877	−	0.925037i	$-0.375966\pi$
$570$	1.90533e6	−	186296.i	0.245630	−	0.0240169i
$571$	6.33948e6	−	1.09803e7i	0.813698	−	1.40937i	−0.0965611	−	0.995327i	$-0.530784\pi$
$571$	6.33948e6	−	1.09803e7i	0.813698	−	1.40937i	0.910259	−	0.414039i	$-0.135882\pi$
$572$	3.18549e6	−	5.51743e6i	0.407086	−	0.705093i
$573$	−7.00326e6	−	9.78766e6i	−0.891073	−	1.24535i
$574$	3.04278e6	+	5.27025e6i	0.385470	+	0.667654i
$575$	2.86191e6			0.360983
$576$	976477.	−	192797.i	0.122633	−	0.0242127i
$577$	−1.51657e7			−1.89637			−0.948187	−	0.317712i	$-0.897086\pi$
$577$	−1.51657e7			−1.89637			−0.948187	+	0.317712i	$0.897086\pi$
$578$	1.00028e6	+	1.73253e6i	0.124537	+	0.215705i
$579$	112371.	−	247541.i	0.0139302	−	0.0306867i
$580$	3.75282e6	−	6.50007e6i	0.463220	−	0.802320i
$581$	2.06075e6	−	3.56932e6i	0.253270	−	0.438677i
$582$	1.13029e6	−	2.48992e6i	0.138320	−	0.304704i
$583$	−1.93665e6	−	3.35437e6i	−0.235982	−	0.408733i
$584$	−4.63362e6			−0.562197
$585$	1.09158e7	+	1.24826e7i	1.31875	+	1.50805i
$586$	8.22522e6			0.989472
$587$	−911702.	−	1.57911e6i	−0.109209	−	0.189155i	0.806241	−	0.591587i	$-0.201498\pi$
$587$	−911702.	−	1.57911e6i	−0.109209	−	0.189155i	−0.915450	+	0.402432i	$0.868165\pi$
$588$	546806.	+	764208.i	0.0652213	+	0.0911525i
$589$	1.80327e6	−	3.12335e6i	0.214176	−	0.370965i
$590$	719112.	−	1.24554e6i	0.0850485	−	0.147308i
$591$	5.28623e6	−	516870.i	0.622555	−	0.0608713i
$592$	−1.19265e6	−	2.06573e6i	−0.139865	−	0.242253i
$593$	1.27957e7			1.49427			0.747133	−	0.664674i	$-0.231430\pi$
$593$	1.27957e7			1.49427			0.747133	+	0.664674i	$0.231430\pi$
$594$	1.33888e6	−	5.68751e6i	0.155696	−	0.661387i
$595$	−7.23723e6			−0.838069
$596$	−598531.	−	1.03669e6i	−0.0690193	−	0.119545i
$597$	220922.	−	21601.0i	0.0253689	−	0.00248049i
$598$	−4.75688e6	+	8.23915e6i	−0.543962	+	0.942171i
$599$	−4.38212e6	+	7.59006e6i	−0.499020	+	0.864327i	−0.999999	−	0.00113166i	$-0.999640\pi$
$599$	−4.38212e6	+	7.59006e6i	−0.499020	+	0.864327i	0.500980	+	0.865459i	$0.332973\pi$
$600$	−721305.	−	1.00809e6i	−0.0817976	−	0.114319i
$601$	−834793.	−	1.44590e6i	−0.0942741	−	0.163288i	0.815031	−	0.579417i	$-0.196720\pi$
$601$	−834793.	−	1.44590e6i	−0.0942741	−	0.163288i	−0.909305	+	0.416129i	$0.863386\pi$
$602$	−964947.			−0.108521
$603$	−4.20298e6	+	1.23242e7i	−0.470722	+	1.38028i
$604$	−5.75924e6			−0.642352
$605$	−407911.	−	706523.i	−0.0453082	−	0.0784762i
$606$	−621499.	+	1.36910e6i	−0.0687478	+	0.151444i
$607$	5.08535e6	−	8.80809e6i	0.560208	−	0.970308i	−0.437270	−	0.899330i	$-0.644055\pi$
$607$	5.08535e6	−	8.80809e6i	0.560208	−	0.970308i	0.997478	−	0.0709782i	$-0.0226121\pi$
$608$	237863.	−	411991.i	0.0260957	−	0.0451990i
$609$	−5.22282e6	+	1.15053e7i	−0.570639	+	1.25706i
$610$	4.51886e6	+	7.82690e6i	0.491705	+	0.851658i
$611$	2.57607e6			0.279161
$612$	−1.20354e6	+	3.52909e6i	−0.129892	+	0.380876i
$613$	1.37829e7			1.48146			0.740730	−	0.671803i	$-0.234480\pi$
$613$	1.37829e7			1.48146			0.740730	+	0.671803i	$0.234480\pi$
$614$	−3.04298e6	−	5.27059e6i	−0.325745	−	0.564207i
$615$	−7.98691e6	−	1.11624e7i	−0.851513	−	1.19006i
$616$	1.40911e6	−	2.44065e6i	0.149621	−	0.259151i
$617$	6.05409e6	−	1.04860e7i	0.640230	−	1.10891i	−0.345152	−	0.938547i	$-0.612173\pi$
$617$	6.05409e6	−	1.04860e7i	0.640230	−	1.10891i	0.985381	−	0.170363i	$-0.0544942\pi$
$618$	−8.51563e6	+	832630.i	−0.896903	+	0.0876962i
$619$	8.48665e6	+	1.46993e7i	0.890245	+	1.54195i	0.839581	+	0.543234i	$0.182800\pi$
$619$	8.48665e6	+	1.46993e7i	0.890245	+	1.54195i	0.0506641	+	0.998716i	$0.483866\pi$
$620$	−8.20857e6			−0.857607
$621$	−1.99935e6	+	8.49313e6i	−0.208046	+	0.883769i
$622$	−1.08336e7			−1.12278
$623$	−2.43352e6	−	4.21498e6i	−0.251197	−	0.435087i
$624$	4.10108e6	−	400990.i	0.421635	−	0.0412261i
$625$	6.05231e6	−	1.04829e7i	0.619756	−	1.07345i
$626$	1.30233e6	−	2.25570e6i	0.132827	−	0.230063i
$627$	−1.62508e6	−	2.27119e6i	−0.165084	−	0.230720i
$628$	−383733.	−	664645.i	−0.0388266	−	0.0672497i
$629$	8.93574e6			0.900541
$630$	4.82861e6	+	5.52172e6i	0.484697	+	0.554272i
$631$	7.90092e6			0.789958			0.394979	−	0.918690i	$-0.370752\pi$
$631$	7.90092e6			0.789958			0.394979	+	0.918690i	$0.370752\pi$
$632$	−1.03033e6	−	1.78458e6i	−0.102608	−	0.177723i
$633$	309923.	−	682728.i	0.0307428	−	0.0677233i
$634$	232221.	−	402219.i	0.0229445	−	0.0397411i
$635$	−7.10637e6	+	1.23086e7i	−0.699381	+	1.21136i
$636$	1.03552e6	−	2.28114e6i	0.101512	−	0.223620i
$637$	1.94514e6	+	3.36908e6i	0.189934	+	0.328975i
$638$	−1.09491e7			−1.06494
$639$	−231248.	+	45657.9i	−0.0224040	+	0.00442347i
$640$	−1.08277e6			−0.104492
$641$	−5.33807e6	−	9.24581e6i	−0.513144	−	0.888792i	−0.999884	−	0.0152446i	$-0.995147\pi$
$641$	−5.33807e6	−	9.24581e6i	−0.513144	−	0.888792i	0.486740	−	0.873547i	$-0.338186\pi$
$642$	6.09492e6	+	8.51818e6i	0.583621	+	0.815661i
$643$	−4.68885e6	+	8.12132e6i	−0.447238	+	0.774639i	−0.998205	−	0.0598882i	$-0.980926\pi$
$643$	−4.68885e6	+	8.12132e6i	−0.447238	+	0.774639i	0.550967	+	0.834527i	$0.314259\pi$
$644$	−2.10421e6	+	3.64461e6i	−0.199929	+	0.346287i
$645$	2.16604e6	−	211788.i	0.205006	−	0.0200448i
$646$	891076.	+	1.54339e6i	0.0840105	+	0.145510i
$647$	−9.44013e6			−0.886579			−0.443289	−	0.896379i	$-0.646189\pi$
$647$	−9.44013e6			−0.886579			−0.443289	+	0.896379i	$0.646189\pi$
$648$	3.49555e6	−	1.43632e6i	0.327023	−	0.134374i
$649$	−2.09805e6			−0.195526
$650$	−2.56588e6	−	4.44424e6i	−0.238207	−	0.412586i
$651$	1.37531e7	−	1.34473e6i	1.27188	−	0.124360i
$652$	−2.88851e6	+	5.00304e6i	−0.266106	+	0.460909i
$653$	−7.44455e6	+	1.28943e7i	−0.683212	+	1.18336i	0.290783	+	0.956789i	$0.406084\pi$
$653$	−7.44455e6	+	1.28943e7i	−0.683212	+	1.18336i	−0.973995	+	0.226569i	$0.927249\pi$
$654$	770087.	+	1.07626e6i	0.0704037	+	0.0983953i
$655$	−6.25543e6	−	1.08347e7i	−0.569710	−	0.986766i
$656$	−3.41076e6			−0.309451
$657$	−1.72601e7	+	3.40784e6i	−1.56002	+	0.308011i
$658$	1.13953e6			0.102603
$659$	3.82391e6	+	6.62320e6i	0.343000	+	0.594093i	0.984988	−	0.172621i	$-0.0552237\pi$
$659$	3.82391e6	+	6.62320e6i	0.343000	+	0.594093i	−0.641989	+	0.766714i	$0.721890\pi$
$660$	−2.62738e6	+	5.78784e6i	−0.234781	+	0.517198i
$661$	2.50269e6	−	4.33479e6i	0.222794	−	0.385891i	−0.732861	−	0.680378i	$-0.761816\pi$
$661$	2.50269e6	−	4.33479e6i	0.222794	−	0.385891i	0.955655	+	0.294487i	$0.0951489\pi$
$662$	−635313.	+	1.10039e6i	−0.0563434	+	0.0975896i
$663$	−6.38075e6	+	1.40561e7i	−0.563752	+	1.24189i
$664$	1.15498e6	+	2.00049e6i	0.101661	+	0.176082i
$665$	3.50592e6			0.307431
$666$	−5.96184e6	−	6.81762e6i	−0.520828	−	0.595590i
$667$	1.63502e7			1.42301
$668$	−931732.	−	1.61381e6i	−0.0807885	−	0.139930i
$669$	−7.11142e6	−	9.93882e6i	−0.614315	−	0.858558i
$670$	7.08255e6	−	1.22673e7i	0.609541	−	1.05576i
$671$	6.59202e6	−	1.14177e7i	0.565214	−	0.978979i
$672$	1.81412e6	−	177379.i	0.154968	−	0.0151523i
$673$	−1.07220e6	−	1.85710e6i	−0.0912511	−	0.158051i	0.816787	−	0.576940i	$-0.195753\pi$
$673$	−1.07220e6	−	1.85710e6i	−0.0912511	−	0.158051i	−0.908038	+	0.418888i	$0.862420\pi$
$674$	1.72220e6			0.146027
$675$	−3.42824e6	−	3.22459e6i	−0.289609	−	0.272405i
$676$	1.11187e7			0.935807
$677$	4.75463e6	+	8.23526e6i	0.398699	+	0.690567i	0.993566	−	0.113257i	$-0.0361285\pi$
$677$	4.75463e6	+	8.23526e6i	0.398699	+	0.690567i	−0.594867	+	0.803824i	$0.702795\pi$
$678$	−1.78985e6	+	175005.i	−0.149535	+	0.0146210i
$679$	2.50385e6	−	4.33679e6i	0.208417	−	0.360989i
$680$	2.02812e6	−	3.51280e6i	0.168198	−	0.291327i
$681$	5.04161e6	+	7.04608e6i	0.416583	+	0.582210i
$682$	5.98725e6	+	1.03702e7i	0.492909	+	0.853743i
$683$	−5.47266e6			−0.448897			−0.224449	−	0.974486i	$-0.572058\pi$
$683$	−5.47266e6			−0.448897			−0.224449	+	0.974486i	$0.572058\pi$
$684$	583029.	−	1.70959e6i	0.0476485	−	0.139718i
$685$	239205.			0.0194780
$686$	4.69883e6	+	8.13862e6i	0.381224	+	0.660299i
$687$	−739023.	+	1.62799e6i	−0.0597401	+	0.131601i
$688$	270411.	−	468365.i	0.0217798	−	0.0377236i
$689$	5.18570e6	−	8.98189e6i	0.416159	−	0.720808i
$690$	3.92345e6	−	8.64296e6i	0.313722	−	0.691098i
$691$	−3.44084e6	−	5.95970e6i	−0.274138	−	0.474821i	0.695779	−	0.718255i	$-0.255059\pi$
$691$	−3.44084e6	−	5.95970e6i	−0.274138	−	0.474821i	−0.969917	+	0.243435i	$0.921726\pi$
$692$	1.65641e6			0.131493
$693$	3.45388e6	−	1.01277e7i	0.273196	−	0.801080i
$694$	−1.65616e7			−1.30528
$695$	3.99430e6	+	6.91832e6i	0.313674	+	0.543299i
$696$	−4.12084e6	−	5.75923e6i	−0.322450	−	0.450652i
$697$	6.38864e6	−	1.10655e7i	0.498112	−	0.862755i
$698$	6.92191e6	−	1.19891e7i	0.537758	−	0.931425i
$699$	−1.72486e6	+	168651.i	−0.133524	+	0.0130556i
$700$	−1.13502e6	−	1.96592e6i	−0.0875508	−	0.151642i
$701$	5.19615e6			0.399380			0.199690	−	0.979859i	$-0.436006\pi$
$701$	5.19615e6			0.399380			0.199690	+	0.979859i	$0.436006\pi$
$702$	1.49815e7	−	4.50986e6i	1.14739	−	0.345398i
$703$	−4.32872e6			−0.330348
$704$	789759.	+	1.36790e6i	0.0600569	+	0.104022i
$705$	−2.55793e6	+	250106.i	−0.193827	+	0.0189518i
$706$	−5.28914e6	+	9.16106e6i	−0.399368	+	0.691726i
$707$	−1.37676e6	+	2.38461e6i	−0.103588	+	0.179419i
$708$	−789632.	−	1.10358e6i	−0.0592027	−	0.0827409i
$709$	−287410.	−	497809.i	−0.0214727	−	0.0371918i	0.855089	−	0.518481i	$-0.173502\pi$
$709$	−287410.	−	497809.i	−0.0214727	−	0.0371918i	−0.876562	+	0.481289i	$0.840169\pi$
$710$	256420.			0.0190900
$711$	−5.15042e6	−	5.88973e6i	−0.382093	−	0.436939i
$712$	2.72782e6			0.201658
$713$	−8.94074e6	−	1.54858e7i	−0.658642	−	1.14080i
$714$	−2.82254e6	+	6.21777e6i	−0.207202	+	0.456445i
$715$	−1.31574e7	+	2.27893e7i	−0.962511	+	1.66712i
$716$	631529.	−	1.09384e6i	0.0460374	−	0.0797391i
$717$	4.76206e6	−	1.04903e7i	0.345937	−	0.762063i
$718$	−4.26247e6	−	7.38281e6i	−0.308567	−	0.534455i
$719$	−400906.			−0.0289215			−0.0144607	−	0.999895i	$-0.504603\pi$
$719$	−400906.			−0.0289215			−0.0144607	+	0.999895i	$0.504603\pi$
$720$	−4.03327e6	+	796332.i	−0.289952	+	0.0572483i
$721$	−1.56693e7			−1.12256
$722$	4.52054e6	+	7.82980e6i	0.322736	+	0.558994i
$723$	1.17048e7	+	1.63585e7i	0.832757	+	1.16385i
$724$	−4.68886e6	+	8.12134e6i	−0.332446	+	0.575813i
$725$	−4.40969e6	+	7.63781e6i	−0.311575	+	0.539664i
$726$	−766086.	+	74905.4i	−0.0539431	+	0.00527438i
$727$	−5.27154e6	−	9.13058e6i	−0.369915	−	0.640711i	0.619637	−	0.784889i	$-0.287280\pi$
$727$	−5.27154e6	−	9.13058e6i	−0.369915	−	0.640711i	−0.989552	+	0.144177i	$0.953946\pi$
$728$	7.54624e6			0.527719
$729$	1.19644e7	−	7.92108e6i	0.833822	−	0.552034i
$730$	1.91388e7			1.32925
$731$	1.01301e6	+	1.75458e6i	0.0701162	+	0.121445i
$732$	8.48675e6	−	829806.i	0.585414	−	0.0572399i
$733$	−6.96868e6	+	1.20701e7i	−0.479061	+	0.829758i	−0.999712	−	0.0240119i	$-0.992356\pi$
$733$	−6.96868e6	+	1.20701e7i	−0.479061	+	0.829758i	0.520651	+	0.853770i	$0.325689\pi$
$734$	2.56014e6	−	4.43429e6i	0.175397	−	0.303797i
$735$	−2.25854e6	−	3.15651e6i	−0.154209	−	0.215520i
$736$	−1.17934e6	−	2.04268e6i	−0.0802502	−	0.138997i
$737$	−2.06638e7			−1.40133
$738$	−1.27050e7	+	2.50848e6i	−0.858681	+	0.169539i
$739$	−9.88034e6			−0.665519			−0.332760	−	0.943012i	$-0.607980\pi$
$739$	−9.88034e6			−0.665519			−0.332760	+	0.943012i	$0.607980\pi$
$740$	4.92615e6	+	8.53234e6i	0.330695	+	0.572781i
$741$	3.09102e6	−	6.80919e6i	0.206803	−	0.455565i
$742$	2.29390e6	−	3.97316e6i	0.152956	−	0.264927i
$743$	4.66695e6	−	8.08339e6i	0.310142	−	0.537182i	−0.668251	−	0.743936i	$-0.732957\pi$
$743$	4.66695e6	−	8.08339e6i	0.310142	−	0.537182i	0.978393	+	0.206754i	$0.0662899\pi$
$744$	−3.20137e6	+	7.05229e6i	−0.212033	+	0.467087i
$745$	2.47219e6	+	4.28195e6i	0.163189	+	0.282652i
$746$	−1.55787e7			−1.02490
$747$	5.77354e6	+	6.60230e6i	0.378565	+	0.432906i
$748$	−5.91715e6			−0.386686
$749$	9.59080e6	+	1.66117e7i	0.624669	+	1.08196i
$750$	−4.51409e6	−	6.30883e6i	−0.293033	−	0.409539i
$751$	−1.43761e7	+	2.49001e7i	−0.930124	+	1.61102i	−0.147018	+	0.989134i	$0.546968\pi$
$751$	−1.43761e7	+	2.49001e7i	−0.930124	+	1.61102i	−0.783106	+	0.621888i	$0.786366\pi$
$752$	−319335.	+	553104.i	−0.0205921	+	0.0356666i
$753$	2.00730e7	−	1.96267e6i	1.29011	−	0.126142i
$754$	−1.46590e7	−	2.53901e7i	−0.939021	−	1.62643i
$755$	2.37881e7			1.51877
$756$	6.62708e6	−	1.99494e6i	0.421714	−	0.126948i
$757$	−4.94587e6			−0.313691			−0.156846	−	0.987623i	$-0.550133\pi$
$757$	−4.94587e6			−0.313691			−0.156846	+	0.987623i	$0.550133\pi$
$758$	5.66671e6	+	9.81503e6i	0.358227	+	0.620467i
$759$	−1.37807e7	+	1.34743e6i	−0.868296	+	0.0848991i
$760$	−982476.	+	1.70170e6i	−0.0617004	+	0.106868i
$761$	−4.56829e6	+	7.91251e6i	−0.285951	+	0.495282i	−0.972839	−	0.231481i	$-0.925643\pi$
$761$	−4.56829e6	+	7.91251e6i	−0.285951	+	0.495282i	0.686888	+	0.726763i	$0.258976\pi$
$762$	7.80326e6	+	1.09057e7i	0.486843	+	0.680405i
$763$	1.21179e6	+	2.09888e6i	0.0753555	+	0.130520i
$764$	1.23528e7			0.765656
$765$	4.97113e6	−	1.45766e7i	0.307115	−	0.900542i
$766$	9.45995e6			0.582528
$767$	−2.80894e6	−	4.86523e6i	−0.172407	−	0.298617i
$768$	−422282.	+	930244.i	−0.0258345	+	0.0569107i
$769$	−8.26221e6	+	1.43106e7i	−0.503826	+	0.872652i	0.496164	+	0.868229i	$0.334741\pi$
$769$	−8.26221e6	+	1.43106e7i	−0.503826	+	0.872652i	−0.999990	+	0.00442349i	$0.998592\pi$
$770$	−5.82022e6	+	1.00809e7i	−0.353763	+	0.612735i
$771$	−4.02309e6	+	8.86244e6i	−0.243738	+	0.536930i
$772$	139515.	+	241647.i	0.00842513	+	0.0145928i
$773$	1.01763e7			0.612550			0.306275	−	0.951943i	$-0.400917\pi$
$773$	1.01763e7			0.612550			0.306275	+	0.951943i	$0.400917\pi$
$774$	662806.	−	1.94352e6i	0.0397681	−	0.116610i
$775$	9.64536e6			0.576852
$776$	1.40332e6	+	2.43063e6i	0.0836573	+	0.144899i
$777$	−9.65129e6	−	1.34885e7i	−0.573499	−	0.801515i
$778$	3.48677e6	−	6.03926e6i	0.206526	−	0.357713i
$779$	−3.09484e6	+	5.36042e6i	−0.182724	+	0.316486i
$780$	−1.69392e7	+	1.65626e6i	−0.996912	+	0.0974747i
$781$	−187030.	−	323945.i	−0.0109719	−	0.0190040i
$782$	8.83605e6			0.516703
$783$	−1.95856e7	−	1.84222e7i	−1.14165	−	1.07383i
$784$	−964495.			−0.0560415
$785$	1.58498e6	+	2.74527e6i	0.0918015	+	0.159005i
$786$	−1.17481e7	+	1.14869e6i	−0.678286	+	0.0663205i
$787$	9.38173e6	−	1.62496e7i	0.539941	−	0.935205i	−0.458966	−	0.888454i	$-0.651780\pi$
$787$	9.38173e6	−	1.62496e7i	0.539941	−	0.935205i	0.998907	−	0.0467507i	$-0.0148866\pi$
$788$	−2.72583e6	+	4.72128e6i	−0.156381	+	0.270860i
$789$	1.05676e7	+	1.47691e7i	0.604342	+	0.844620i
$790$	4.25569e6	+	7.37107e6i	0.242606	+	0.420207i
$791$	−3.29343e6			−0.187158
$792$	3.94786e6	+	4.51455e6i	0.223640	+	0.255742i
$793$	3.53025e7			1.99353
$794$	−9.62218e6	−	1.66661e7i	−0.541654	−	0.938173i
$795$	−4.27714e6	+	9.42210e6i	−0.240014	+	0.528725i
$796$	−113918.	+	197311.i	−0.00637248	+	0.0110375i
$797$	1.23982e6	−	2.14744e6i	0.0691376	−	0.119750i	−0.829384	−	0.558678i	$-0.811309\pi$
$797$	1.23982e6	−	2.14744e6i	0.0691376	−	0.119750i	0.898522	+	0.438929i	$0.144642\pi$
$798$	1.36732e6	−	3.01206e6i	0.0760085	−	0.167439i
$799$	−1.19628e6	−	2.07202e6i	−0.0662929	−	0.114823i
$800$	1.27229e6			0.0702847
$801$	1.01610e7	−	2.00620e6i	0.559573	−	0.110483i
$802$	−1.82163e7			−1.00005
$803$	−1.39597e7	−	2.41788e7i	−0.763987	−	1.32326i
$804$	−7.77711e6	−	1.08692e7i	−0.424305	−	0.593003i
$805$	8.69130e6	−	1.50538e7i	0.472711	−	0.818759i
$806$	−1.60319e7	+	2.77680e7i	−0.869254	+	1.50559i
$807$	2.46605e7	−	2.41122e6i	1.33296	−	0.130332i
$808$	−771627.	−	1.33650e6i	−0.0415795	−	0.0720178i
$809$	−2.50880e7			−1.34770			−0.673852	−	0.738867i	$-0.735361\pi$
$809$	−2.50880e7			−1.34770			−0.673852	+	0.738867i	$0.735361\pi$
$810$	−1.44381e7	+	5.93262e6i	−0.773210	+	0.317712i
$811$	−4.28465e6			−0.228751			−0.114376	−	0.993438i	$-0.536487\pi$
$811$	−4.28465e6			−0.228751			−0.114376	+	0.993438i	$0.536487\pi$
$812$	−6.48443e6	−	1.12314e7i	−0.345129	−	0.597781i
$813$	−1.51713e7	+	1.48339e6i	−0.804999	+	0.0787101i
$814$	7.18617e6	−	1.24468e7i	0.380134	−	0.658411i
$815$	1.19308e7	−	2.06647e7i	0.629179	−	1.08977i
$816$	−2.22700e6	−	3.11243e6i	−0.117083	−	0.163634i
$817$	−490728.	−	849967.i	−0.0257209	−	0.0445499i
$818$	7.65132e6			0.399809
$819$	2.81095e7	−	5.54996e6i	1.46434	−	0.289121i
$820$	1.40879e7			0.731663
$821$	−1.01563e7	−	1.75913e7i	−0.525871	−	0.910836i	−0.999546	−	0.0301356i	$-0.990406\pi$
$821$	−1.01563e7	−	1.75913e7i	−0.525871	−	0.910836i	0.473675	−	0.880700i	$-0.342927\pi$
$822$	93290.8	−	205510.i	0.00481570	−	0.0106085i
$823$	6.58313e6	−	1.14023e7i	0.338792	−	0.586804i	−0.645414	−	0.763833i	$-0.723315\pi$
$823$	6.58313e6	−	1.14023e7i	0.338792	−	0.586804i	0.984206	+	0.177029i	$0.0566485\pi$
$824$	4.39107e6	−	7.60555e6i	0.225295	−	0.390223i
$825$	3.08726e6	−	6.80092e6i	0.157920	−	0.347883i
$826$	−1.24254e6	−	2.15215e6i	−0.0633667	−	0.109754i
$827$	2.82859e7			1.43816			0.719079	−	0.694928i	$-0.244564\pi$
$827$	2.82859e7			1.43816			0.719079	+	0.694928i	$0.244564\pi$
$828$	−5.89533e6	−	6.74156e6i	−0.298835	−	0.341731i
$829$	1.36608e7			0.690381			0.345190	−	0.938533i	$-0.387814\pi$
$829$	1.36608e7			0.690381			0.345190	+	0.938533i	$0.387814\pi$
$830$	−4.77057e6	−	8.26286e6i	−0.240367	−	0.416328i
$831$	1.17059e7	+	1.63601e7i	0.588036	+	0.821832i
$832$	−2.11471e6	+	3.66279e6i	−0.105911	+	0.183444i
$833$	1.80658e6	−	3.12909e6i	0.0902080	−	0.156245i
$834$	7.50157e6	−	733479.i	0.373454	−	0.0365151i
$835$	3.84845e6	+	6.66571e6i	0.191016	+	0.330849i
$836$	2.86643e6			0.141849
$837$	−6.73831e6	+	2.86240e7i	−0.332458	+	1.41227i
$838$	1.76558e7			0.868514
$839$	75641.6	+	131015.i	0.00370984	+	0.00642564i	0.867874	−	0.496784i	$-0.165486\pi$
$839$	75641.6	+	131015.i	0.00370984	+	0.00642564i	−0.864165	+	0.503209i	$0.832152\pi$
$840$	−7.49310e6	+	732650.i	−0.366407	+	0.0358260i
$841$	−1.49371e7	+	2.58718e7i	−0.728244	+	1.26135i
$842$	3.48901e6	−	6.04314e6i	0.169598	−	0.293753i
$843$	−1.51242e7	−	2.11374e7i	−0.733000	−	1.02443i
$844$	384787.	+	666470.i	0.0185936	+	0.0322051i
$845$	−4.59249e7			−2.21262
$846$	−782724.	+	2.29515e6i	−0.0375996	+	0.110252i
$847$	−1.40965e6			−0.0675152
$848$	1.28566e6	+	2.22683e6i	0.0613954	+	0.106340i
$849$	−7.27561e6	+	1.60274e7i	−0.346418	+	0.763123i
$850$	−2.38311e6	+	4.12766e6i	−0.113135	+	0.195955i
$851$	−1.07311e7	+	1.85868e7i	−0.507948	+	0.879792i
$852$	100004.	−	220299.i	0.00471976	−	0.0103972i
$853$	1.38831e7	+	2.40462e7i	0.653301	+	1.13155i	0.982317	+	0.187226i	$0.0599498\pi$
$853$	1.38831e7	+	2.40462e7i	0.653301	+	1.13155i	−0.329015	+	0.944325i	$0.606717\pi$
$854$	1.56161e7			0.732705
$855$	−2.40816e6	+	7.06134e6i	−0.112660	+	0.330348i
$856$	−1.07507e7			−0.501477
$857$	1.76136e7	+	3.05077e7i	0.819212	+	1.41892i	0.906263	+	0.422713i	$0.138922\pi$
$857$	1.76136e7	+	3.05077e7i	0.819212	+	1.41892i	−0.0870512	+	0.996204i	$0.527744\pi$
$858$	1.44477e7	+	2.01919e7i	0.670009	+	0.936396i
$859$	2.02341e7	−	3.50464e7i	0.935622	−	1.62054i	0.162100	−	0.986774i	$-0.448173\pi$
$859$	2.02341e7	−	3.50464e7i	0.935622	−	1.62054i	0.773522	−	0.633770i	$-0.218493\pi$
$860$	−1.11691e6	+	1.93455e6i	−0.0514959	+	0.0891936i
$861$	−2.36036e7	+	2.30788e6i	−1.08510	+	0.106097i
$862$	4.43479e6	+	7.68128e6i	0.203285	+	0.352100i
$863$	−1.96865e7			−0.899789			−0.449895	−	0.893082i	$-0.648538\pi$
$863$	−1.96865e7			−0.899789			−0.449895	+	0.893082i	$0.648538\pi$
$864$	−888828.	+	3.77570e6i	−0.0405073	+	0.172073i
$865$	−6.84170e6			−0.310902
$866$	7.27022e6	+	1.25924e7i	0.329422	+	0.570576i
$867$	−7.75937e6	+	758686.i	−0.350573	+	0.0342779i
$868$	−7.09173e6	+	1.22832e7i	−0.319487	+	0.553367i
$869$	6.20812e6	−	1.07528e7i	0.278876	−	0.483027i
$870$	1.70208e7	+	2.37881e7i	0.762399	+	1.06552i
$871$	−2.76654e7	−	4.79178e7i	−1.23564	−	2.14019i
$872$	−1.35834e6			−0.0604945
$873$	7.01496e6	+	8.02191e6i	0.311523	+	0.356240i
$874$	−4.28043e6			−0.189544
$875$	−7.10324e6	−	1.23032e7i	−0.313644	−	0.543247i
$876$	7.46420e6	−	1.64429e7i	0.328642	−	0.723964i
$877$	−1.31221e7	+	2.27282e7i	−0.576109	+	0.997850i	0.419811	+	0.907611i	$0.362096\pi$
$877$	−1.31221e7	+	2.27282e7i	−0.576109	+	0.997850i	−0.995920	+	0.0902384i	$0.971237\pi$
$878$	6.17653e6	−	1.06981e7i	0.270401	−	0.468348i
$879$	−1.32498e7	+	2.91880e7i	−0.578414	+	1.27419i
$880$	−3.26204e6	−	5.65002e6i	−0.141998	−	0.245948i
$881$	−1.29423e7			−0.561786			−0.280893	−	0.959739i	$-0.590631\pi$
$881$	−1.29423e7			−0.561786			−0.280893	+	0.959739i	$0.590631\pi$
$882$	−3.59271e6	+	709348.i	−0.155507	+	0.0307035i
$883$	3.39097e6			0.146360			0.0731800	−	0.997319i	$-0.476685\pi$
$883$	3.39097e6			0.146360			0.0731800	+	0.997319i	$0.476685\pi$
$884$	−7.92208e6	−	1.37214e7i	−0.340964	−	0.590567i
$885$	3.26152e6	+	4.55825e6i	0.139979	+	0.195632i
$886$	1.40019e7	−	2.42521e7i	0.599244	−	1.03792i
$887$	−3.83796e6	+	6.64753e6i	−0.163791	+	0.283695i	−0.936225	−	0.351400i	$-0.885706\pi$
$887$	−3.83796e6	+	6.64753e6i	−0.163791	+	0.283695i	0.772434	+	0.635095i	$0.219039\pi$
$888$	9.25166e6	−	904596.i	0.393720	−	0.0384966i
$889$	1.22790e7	+	2.12678e7i	0.521085	+	0.902545i
$890$	−1.12671e7			−0.476799
$891$	1.80259e7	+	1.39130e7i	0.760682	+	0.587122i
$892$	1.25436e7			0.527851
$893$	579513.	+	1.00375e6i	0.0243184	+	0.0421207i
$894$	4.64294e6	−	453972.i	0.194290	−	0.0189970i
$895$	−2.60849e6	+	4.51803e6i	−0.108851	+	0.188535i
$896$	−935448.	+	1.62024e6i	−0.0389269	+	0.0674233i
$897$	−2.15747e7	−	3.01525e7i	−0.895290	−	1.25125i
$898$	1.00039e7	+	1.73273e7i	0.413980	+	0.717034i
$899$	5.51042e7			2.27398
$900$	4.73923e6	−	935718.i	0.195030	−	0.0385069i
$901$	−9.63260e6			−0.395304
$902$	−1.02756e7	−	1.77978e7i	−0.420523	−	0.728366i
$903$	1.55441e6	−	3.42421e6i	0.0634377	−	0.139747i
$904$	922930.	−	1.59856e6i	0.0375619	−	0.0650592i
$905$	1.93670e7	−	3.35446e7i	0.786033	−	1.36145i
$906$	9.27744e6	−	2.04373e7i	0.375498	−	0.827184i
$907$	−5.44435e6	−	9.42990e6i	−0.219750	−	0.380618i	0.734982	−	0.678087i	$-0.237191\pi$
$907$	−5.44435e6	−	9.42990e6i	−0.219750	−	0.380618i	−0.954731	+	0.297469i	$0.903857\pi$
$908$	−8.89274e6			−0.357949
$909$	−3.85722e6	−	4.41090e6i	−0.154834	−	0.177059i
$910$	−3.11692e7			−1.24773
$911$	90239.2	+	156299.i	0.00360246	+	0.00623964i	0.867821	−	0.496877i	$-0.165520\pi$
$911$	90239.2	+	156299.i	0.00360246	+	0.00623964i	−0.864219	+	0.503117i	$0.832187\pi$
$912$	1.07882e6	+	1.50775e6i	0.0429500	+	0.0600264i
$913$	−6.95920e6	+	1.20537e7i	−0.276301	+	0.478568i
$914$	−7.14323e6	+	1.23724e7i	−0.282832	+	0.489880i
$915$	−3.50539e7	+	3.42745e6i	−1.38415	+	0.135338i
$916$	−917540.	−	1.58923e6i	−0.0361315	−	0.0625816i
$917$	−2.16173e7			−0.848942
$918$	−1.05846e7	−	9.95582e6i	−0.414540	−	0.389915i
$919$	−2.24831e7			−0.878148			−0.439074	−	0.898451i	$-0.644693\pi$
$919$	−2.24831e7			−0.878148			−0.439074	+	0.898451i	$0.644693\pi$
$920$	4.87119e6	+	8.43716e6i	0.189743	+	0.328645i
$921$	2.36051e7	−	2.30803e6i	0.916973	−	0.0896586i
$922$	−1.10024e7	+	1.90568e7i	−0.426248	+	0.738282i
$923$	500804.	−	867418.i	0.0193492	−	0.0335138i
$924$	6.39098e6	+	8.93195e6i	0.246256	+	0.344165i
$925$	−5.78840e6	−	1.00258e7i	−0.222436	−	0.385270i
$926$	−1.14166e7			−0.437533
$927$	1.07630e7	−	3.15598e7i	0.411371	−	1.20625i
$928$	7.26862e6			0.277065
$929$	2.06620e7	+	3.57877e7i	0.785477	+	1.36049i	0.928714	+	0.370797i	$0.120916\pi$
$929$	2.06620e7	+	3.57877e7i	0.785477	+	1.36049i	−0.143237	+	0.989688i	$0.545751\pi$
$930$	1.32230e7	−	2.91290e7i	0.501329	−	1.10438i
$931$	−875159.	+	1.51582e6i	−0.0330912	+	0.0573157i
$932$	889419.	−	1.54052e6i	0.0335403	−	0.0580935i
$933$	1.74516e7	−	3.84441e7i	0.656343	−	1.44586i
$934$	1.43310e7	+	2.48221e7i	0.537539	+	0.931046i
$935$	2.44403e7			0.914278
$936$	−5.18339e6	+	1.51990e7i	−0.193386	+	0.567057i
$937$	2.56470e7			0.954305			0.477153	−	0.878820i	$-0.341669\pi$
$937$	2.56470e7			0.954305			0.477153	+	0.878820i	$0.341669\pi$
$938$	−1.22378e7	−	2.11965e7i	−0.454148	−	0.786607i
$939$	5.90670e6	+	8.25512e6i	0.218615	+	0.305534i
$940$	1.31899e6	−	2.28456e6i	0.0486879	−	0.0843300i
$941$	−8.99880e6	+	1.55864e7i	−0.331292	+	0.573814i	−0.982765	−	0.184857i	$-0.940818\pi$
$941$	−8.99880e6	+	1.55864e7i	−0.331292	+	0.573814i	0.651474	+	0.758671i	$0.274151\pi$
$942$	2.97671e6	−	291052.i	0.109297	−	0.0106867i
$943$	1.53445e7	+	2.65774e7i	0.561917	+	0.973269i
$944$	1.39281e6			0.0508700
$945$	−2.73727e7	+	8.23997e6i	−0.997098	+	0.300155i
$946$	3.25866e6			0.118389
$947$	2.25398e7	+	3.90400e7i	0.816723	+	1.41461i	0.908084	+	0.418788i	$0.137545\pi$
$947$	2.25398e7	+	3.90400e7i	0.816723	+	1.41461i	−0.0913614	+	0.995818i	$0.529122\pi$
$948$	7.99249e6	−	781479.i	0.288843	−	0.0282421i
$949$	3.73793e7	−	6.47429e7i	1.34731	−	2.33360i
$950$	1.15444e6	−	1.99956e6i	0.0415015	−	0.0718827i
$951$	1.05323e6	+	1.47199e6i	0.0377636	+	0.0527780i
$952$	−3.50435e6	−	6.06971e6i	−0.125318	−	0.217058i
$953$	2.21374e7			0.789577			0.394788	−	0.918772i	$-0.370818\pi$
$953$	2.21374e7			0.789577			0.394788	+	0.918772i	$0.370818\pi$
$954$	6.42677e6	+	7.34930e6i	0.228624	+	0.261442i
$955$	−5.10225e7			−1.81031
$956$	5.91237e6	+	1.02405e7i	0.209227	+	0.362391i
$957$	1.76376e7	−	3.88539e7i	0.622530	−	1.37137i
$958$	−6.56741e6	+	1.13751e7i	−0.231196	+	0.400443i
$959$	206660.	−	357945.i	0.00725619	−	0.0125681i
$960$	1.74421e6	−	3.84231e6i	0.0610829	−	0.134559i
$961$	−1.58180e7	−	2.73975e7i	−0.552512	−	0.956979i
$962$	3.84843e7			1.34075
$963$	−4.00458e7	+	7.90668e6i	−1.39153	+	0.274744i
$964$	−2.06458e7			−0.715547
$965$	−576255.	−	998103.i	−0.0199203	−	0.0345030i
$966$	−9.54362e6	−	1.33380e7i	−0.329056	−	0.459885i
$967$	9.81614e6	−	1.70020e7i	0.337578	−	0.584703i	−0.646398	−	0.763000i	$-0.723726\pi$
$967$	9.81614e6	−	1.70020e7i	0.337578	−	0.584703i	0.983977	+	0.178297i	$0.0570589\pi$
$968$	395031.	−	684213.i	0.0135501	−	0.0234695i
$969$	−6.91229e6	+	675861.i	−0.236490	+	0.0231232i
$970$	−5.79633e6	−	1.00395e7i	−0.197799	−	0.342598i
$971$	−3.46539e7			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$971$	−3.46539e7			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$972$	−533977.	+	1.47180e7i	−0.0181283	+	0.499671i
$973$	1.38034e7			0.467415
$974$	−4.36194e6	−	7.55511e6i	−0.147327	−	0.255178i
$975$	1.99042e7	−	1.94616e6i	0.670552	−	0.0655644i
$976$	−4.37617e6	+	7.57975e6i	−0.147052	+	0.254701i
$977$	−1.34006e7	+	2.32106e7i	−0.449148	+	0.777947i	−0.998331	−	0.0577553i	$-0.981606\pi$
$977$	−1.34006e7	+	2.32106e7i	−0.449148	+	0.777947i	0.549183	+	0.835702i	$0.314939\pi$
$978$	−1.31008e7	−	1.83095e7i	−0.437975	−	0.612108i
$979$	8.21808e6	+	1.42341e7i	0.274040	+	0.474651i
$980$	3.98377e6			0.132504
$981$	−5.05975e6	+	999002.i	−0.167864	+	0.0331431i
$982$	−3.97579e7			−1.31566
$983$	1.19040e7	+	2.06183e7i	0.392924	+	0.680565i	0.992834	−	0.119503i	$-0.0381301\pi$
$983$	1.19040e7	+	2.06183e7i	0.392924	+	0.680565i	−0.599910	+	0.800068i	$0.704797\pi$
$984$	5.49432e6	−	1.21034e7i	0.180895	−	0.398493i
$985$	1.12589e7	−	1.95009e7i	0.369746	−	0.640419i
$986$	−1.36148e7	+	2.35815e7i	−0.445982	+	0.772464i
$987$	−1.83564e6	+	4.04374e6i	−0.0599785	+	0.132126i
$988$	3.83768e6	+	6.64705e6i	0.125077	+	0.216639i
$989$	−4.86614e6			−0.158195
$990$	−1.63064e7	−	1.86470e7i	−0.528773	−	0.604675i
$991$	−2.37156e7			−0.767096			−0.383548	−	0.923521i	$-0.625298\pi$
$991$	−2.37156e7			−0.767096			−0.383548	+	0.923521i	$0.625298\pi$
$992$	−3.97469e6	−	6.88436e6i	−0.128240	−	0.222118i
$993$	−2.88145e6	−	4.02708e6i	−0.0927338	−	0.129603i
$994$	221532.	−	383704.i	0.00711164	−	0.0123177i
$995$	470529.	−	814980.i	0.0150671	−	0.0260969i
$996$	−8.95946e6	+	876026.i	−0.286176	+	0.0279814i
$997$	2.04170e7	+	3.53633e7i	0.650511	+	1.12672i	0.982999	+	0.183610i	$0.0587785\pi$
$997$	2.04170e7	+	3.53633e7i	0.650511	+	1.12672i	−0.332488	+	0.943107i	$0.607888\pi$
$998$	−1.81109e7			−0.575590
$999$	3.37968e7	−	1.01738e7i	1.07143	−	0.322530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.b.13.3	yes	6
3.2	odd	2		54.6.c.b.37.1		6
4.3	odd	2		144.6.i.b.49.1		6
9.2	odd	6		54.6.c.b.19.1		6
9.4	even	3		162.6.a.j.1.1		3
9.5	odd	6		162.6.a.i.1.3		3
9.7	even	3	inner	18.6.c.b.7.3	✓	6
12.11	even	2		432.6.i.b.145.1		6
36.7	odd	6		144.6.i.b.97.1		6
36.11	even	6		432.6.i.b.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.3	✓	6	9.7	even	3	inner
18.6.c.b.13.3	yes	6	1.1	even	1	trivial
54.6.c.b.19.1		6	9.2	odd	6
54.6.c.b.37.1		6	3.2	odd	2
144.6.i.b.49.1		6	4.3	odd	2
144.6.i.b.97.1		6	36.7	odd	6
162.6.a.i.1.3		3	9.5	odd	6
162.6.a.j.1.1		3	9.4	even	3
432.6.i.b.145.1		6	12.11	even	2
432.6.i.b.289.1		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} +(15.5145 - 1.51695i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(33.0434 - 57.2329i) q^{5} +(-36.2838 - 50.7098i) q^{6} +(-57.0952 - 98.8918i) q^{7} +64.0000 q^{8} +(238.398 - 47.0695i) q^{9} -264.347 q^{10} +(192.812 + 333.961i) q^{11} +(-103.096 + 227.110i) q^{12} +(-516.287 + 894.236i) q^{13} +(-228.381 + 395.567i) q^{14} +(425.832 - 938.063i) q^{15} +(-128.000 - 221.703i) q^{16} +959.020 q^{17} +(-639.849 - 731.695i) q^{18} -464.576 q^{19} +(528.695 + 915.726i) q^{20} +(-1035.82 - 1447.64i) q^{21} +(771.249 - 1335.84i) q^{22} +(-1151.70 + 1994.81i) q^{23} +(992.926 - 97.0850i) q^{24} +(-621.235 - 1076.01i) q^{25} +4130.30 q^{26} +(3627.21 - 1091.90i) q^{27} +1827.05 q^{28} +(-3549.13 - 6147.28i) q^{29} +(-4101.21 + 401.003i) q^{30} +(-3881.53 + 6723.00i) q^{31} +(-512.000 + 886.810i) q^{32} +(3497.98 + 4888.74i) q^{33} +(-1918.04 - 3322.14i) q^{34} -7546.48 q^{35} +(-1254.97 + 3679.89i) q^{36} +9317.57 q^{37} +(929.153 + 1609.34i) q^{38} +(-6653.41 + 14656.8i) q^{39} +(2114.78 - 3662.90i) q^{40} +(6661.64 - 11538.3i) q^{41} +(-2943.15 + 6483.46i) q^{42} +(1056.29 + 1829.55i) q^{43} -6169.99 q^{44} +(5183.55 - 15199.5i) q^{45} +9213.62 q^{46} +(-1247.40 - 2160.56i) q^{47} +(-2322.16 - 3245.43i) q^{48} +(1883.78 - 3262.80i) q^{49} +(-2484.94 + 4304.04i) q^{50} +(14878.7 - 1454.79i) q^{51} +(-8260.60 - 14307.8i) q^{52} -10044.2 q^{53} +(-11036.9 - 10381.2i) q^{54} +25484.7 q^{55} +(-3654.09 - 6329.07i) q^{56} +(-7207.66 + 704.741i) q^{57} +(-14196.5 + 24589.1i) q^{58} +(-2720.33 + 4711.75i) q^{59} +(9591.53 + 13405.0i) q^{60} +(-17094.4 - 29608.4i) q^{61} +31052.2 q^{62} +(-18266.1 - 20888.1i) q^{63} +4096.00 q^{64} +(34119.8 + 59097.2i) q^{65} +(9939.11 - 21894.8i) q^{66} +(-26792.6 + 46406.2i) q^{67} +(-7672.16 + 13288.6i) q^{68} +(-14842.0 + 32695.5i) q^{69} +(15093.0 + 26141.8i) q^{70} -970.010 q^{71} +(15257.5 - 3012.45i) q^{72} -72400.3 q^{73} +(-18635.1 - 32277.0i) q^{74} +(-11270.4 - 15751.3i) q^{75} +(3716.61 - 6437.36i) q^{76} +(22017.3 - 38135.1i) q^{77} +(64079.4 - 6265.47i) q^{78} +(-16098.9 - 27884.0i) q^{79} -16918.2 q^{80} +(54617.9 - 22442.5i) q^{81} -53293.1 q^{82} +(18046.6 + 31257.6i) q^{83} +(28345.7 - 2771.54i) q^{84} +(31689.3 - 54887.5i) q^{85} +(4225.17 - 7318.21i) q^{86} +(-64388.1 - 89987.9i) q^{87} +(12340.0 + 21373.5i) q^{88} +42622.2 q^{89} +(-63019.8 + 12442.7i) q^{90} +117910. q^{91} +(-18427.2 - 31916.9i) q^{92} +(-50021.4 + 110192. i) q^{93} +(-4989.60 + 8642.25i) q^{94} +(-15351.2 + 26589.0i) q^{95} +(-6598.16 + 14535.1i) q^{96} +(21926.9 + 37978.6i) q^{97} -15070.2 q^{98} +(61685.4 + 70539.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18}+ \cdots + 282168 q^{99}+O(q^{100}) \) 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

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