LMFDB - Embedded newform 21.6.g.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$3.57071 - 2.06155i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.6.g.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.14143 - 4.12311i) q^{2} +(-8.42929 - 13.1129i) q^{3} +(18.0000 - 31.1769i) q^{4} +(-3.57071 - 6.18466i) q^{5} +(-114.263 - 58.8897i) q^{6} +(122.500 - 42.4352i) q^{7} -32.9848i q^{8} +(-100.894 + 221.064i) q^{9} +O(q^{10})$	\(q+(7.14143 - 4.12311i) q^{2} +(-8.42929 - 13.1129i) q^{3} +(18.0000 - 31.1769i) q^{4} +(-3.57071 - 6.18466i) q^{5} +(-114.263 - 58.8897i) q^{6} +(122.500 - 42.4352i) q^{7} -32.9848i q^{8} +(-100.894 + 221.064i) q^{9} +(-51.0000 - 29.4449i) q^{10} +(389.208 + 224.709i) q^{11} +(-560.546 + 26.7676i) q^{12} -523.079i q^{13} +(699.860 - 808.129i) q^{14} +(-51.0000 + 98.9545i) q^{15} +(440.000 + 762.102i) q^{16} +(-592.739 + 1026.65i) q^{17} +(190.941 + 1994.71i) q^{18} +(-471.000 + 271.932i) q^{19} -257.091 q^{20} +(-1589.04 - 1248.63i) q^{21} +3706.00 q^{22} +(-3292.20 + 1900.75i) q^{23} +(-432.526 + 278.039i) q^{24} +(1537.00 - 2662.16i) q^{25} +(-2156.71 - 3735.53i) q^{26} +(3749.25 - 540.400i) q^{27} +(882.000 - 4583.01i) q^{28} -2626.42i q^{29} +(43.7872 + 916.955i) q^{30} +(-7510.50 - 4336.19i) q^{31} +(7198.56 + 4156.09i) q^{32} +(-334.163 - 6997.77i) q^{33} +9775.69i q^{34} +(-699.860 - 606.097i) q^{35} +(5076.00 + 7124.73i) q^{36} +(3053.00 + 5287.95i) q^{37} +(-2242.41 + 3883.97i) q^{38} +(-6859.07 + 4409.19i) q^{39} +(-204.000 + 117.779i) q^{40} -199.960 q^{41} +(-16496.2 - 2365.22i) q^{42} -4744.00 q^{43} +(14011.5 - 8089.53i) q^{44} +(1727.47 - 165.360i) q^{45} +(-15674.0 + 27148.2i) q^{46} +(13068.8 + 22635.8i) q^{47} +(6284.46 - 12193.6i) q^{48} +(13205.5 - 10396.6i) q^{49} -25348.9i q^{50} +(18458.7 - 881.455i) q^{51} +(-16308.0 - 9415.43i) q^{52} +(-11908.3 - 6875.28i) q^{53} +(24546.9 - 19317.8i) q^{54} -3209.49i q^{55} +(-1399.72 - 4040.64i) q^{56} +(7536.00 + 3883.97i) q^{57} +(-10829.0 - 18756.4i) q^{58} +(-14515.0 + 25140.6i) q^{59} +(2167.10 + 3371.20i) q^{60} +(-3852.00 + 2223.95i) q^{61} -71514.3 q^{62} +(-2978.64 + 31361.8i) q^{63} +40384.0 q^{64} +(-3235.07 + 1867.77i) q^{65} +(-31238.9 - 48596.3i) q^{66} +(-691.000 + 1196.85i) q^{67} +(21338.6 + 36959.5i) q^{68} +(52675.2 + 27148.2i) q^{69} +(-7497.00 - 1442.80i) q^{70} -83237.3i q^{71} +(7291.77 + 3327.98i) q^{72} +(28158.0 + 16257.0i) q^{73} +(43605.6 + 25175.7i) q^{74} +(-47864.4 + 2285.66i) q^{75} +19579.1i q^{76} +(57213.6 + 11010.8i) q^{77} +(-30804.0 + 59768.5i) q^{78} +(-10544.5 - 18263.6i) q^{79} +(3142.23 - 5442.50i) q^{80} +(-38689.7 - 44608.2i) q^{81} +(-1428.00 + 824.456i) q^{82} +36642.7 q^{83} +(-67531.0 + 27065.9i) q^{84} +8466.00 q^{85} +(-33878.9 + 19560.0i) q^{86} +(-34439.9 + 22138.8i) q^{87} +(7412.00 - 12838.0i) q^{88} +(-30772.4 - 53299.4i) q^{89} +(11654.8 - 8303.45i) q^{90} +(-22197.0 - 64077.2i) q^{91} +136854. i q^{92} +(6448.30 + 135035. i) q^{93} +(186660. + 107768. i) q^{94} +(3363.61 + 1941.98i) q^{95} +(-6180.48 - 129427. i) q^{96} -120324. i q^{97} +(51439.7 - 128694. i) q^{98} +(-88944.0 + 63368.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 48 q^{3} + 72 q^{4} + 490 q^{7} + 282 q^{9}+O(q^{10}) $ 4 * q - 48 * q^3 + 72 * q^4 + 490 * q^7 + 282 * q^9	$ 4 q - 48 q^{3} + 72 q^{4} + 490 q^{7} + 282 q^{9} - 204 q^{10} - 1728 q^{12} - 204 q^{15} + 1760 q^{16} - 3264 q^{18} - 1884 q^{19} - 7056 q^{21} + 14824 q^{22} - 816 q^{24} + 6148 q^{25} + 3528 q^{28} + 1632 q^{30} - 30042 q^{31} + 11118 q^{33} + 20304 q^{36} + 12212 q^{37} - 14496 q^{39} - 816 q^{40} - 9996 q^{42} - 18976 q^{43} + 4896 q^{45} - 62696 q^{46} + 52822 q^{49} + 16932 q^{51} - 65232 q^{52} + 107100 q^{54} + 30144 q^{57} - 43316 q^{58} - 3672 q^{60} - 15408 q^{61} + 55272 q^{63} + 161536 q^{64} - 177888 q^{66} - 2764 q^{67} - 29988 q^{70} + 13056 q^{72} + 112632 q^{73} - 147552 q^{75} - 123216 q^{78} - 42178 q^{79} + 38574 q^{81} - 5712 q^{82} - 169344 q^{84} + 33864 q^{85} - 64974 q^{87} + 29648 q^{88} - 88788 q^{91} + 240336 q^{93} + 746640 q^{94} + 205632 q^{96} - 355776 q^{99}+O(q^{100}) $ 4 * q - 48 * q^3 + 72 * q^4 + 490 * q^7 + 282 * q^9 - 204 * q^10 - 1728 * q^12 - 204 * q^15 + 1760 * q^16 - 3264 * q^18 - 1884 * q^19 - 7056 * q^21 + 14824 * q^22 - 816 * q^24 + 6148 * q^25 + 3528 * q^28 + 1632 * q^30 - 30042 * q^31 + 11118 * q^33 + 20304 * q^36 + 12212 * q^37 - 14496 * q^39 - 816 * q^40 - 9996 * q^42 - 18976 * q^43 + 4896 * q^45 - 62696 * q^46 + 52822 * q^49 + 16932 * q^51 - 65232 * q^52 + 107100 * q^54 + 30144 * q^57 - 43316 * q^58 - 3672 * q^60 - 15408 * q^61 + 55272 * q^63 + 161536 * q^64 - 177888 * q^66 - 2764 * q^67 - 29988 * q^70 + 13056 * q^72 + 112632 * q^73 - 147552 * q^75 - 123216 * q^78 - 42178 * q^79 + 38574 * q^81 - 5712 * q^82 - 169344 * q^84 + 33864 * q^85 - 64974 * q^87 + 29648 * q^88 - 88788 * q^91 + 240336 * q^93 + 746640 * q^94 + 205632 * q^96 - 355776 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	7.14143	−	4.12311i	1.26244	−	0.728869i	0.288892	−	0.957362i	$-0.406713\pi$
$2$	7.14143	−	4.12311i	1.26244	−	0.728869i	0.973546	+	0.228493i	$0.0733797\pi$
$3$	−8.42929	−	13.1129i	−0.540739	−	0.841190i
$3$	−8.42929	−	13.1129i	−0.540739	−	0.841190i
$4$	18.0000	−	31.1769i	0.562500	−	0.974279i
$5$	−3.57071	−	6.18466i	−0.0638749	−	0.110635i	0.832319	−	0.554296i	$-0.187013\pi$
$5$	−3.57071	−	6.18466i	−0.0638749	−	0.110635i	−0.896194	+	0.443662i	$0.853679\pi$
$6$	−114.263	−	58.8897i	−1.29577	−	0.667823i
$7$	122.500	−	42.4352i	0.944911	−	0.327327i
$7$	122.500	−	42.4352i	0.944911	−	0.327327i
$8$		−	32.9848i		−	0.182217i
$9$	−100.894	+	221.064i	−0.415203	+	0.909729i
$10$	−51.0000	−	29.4449i	−0.161276	−	0.0931128i
$11$	389.208	+	224.709i	0.969840	+	0.559937i	0.899187	−	0.437564i	$-0.144159\pi$
$11$	389.208	+	224.709i	0.969840	+	0.559937i	0.0706522	+	0.997501i	$0.477492\pi$
$12$	−560.546	+	26.7676i	−1.12372	+	0.0536607i
$13$		−	523.079i		−	0.858439i	−0.903200	−	0.429219i	$-0.858789\pi$
$13$		−	523.079i		−	0.858439i	0.903200	−	0.429219i	$-0.141211\pi$
$14$	699.860	−	808.129i	0.954314	−	1.10195i
$15$	−51.0000	+	98.9545i	−0.0585251	+	0.113555i
$16$	440.000	+	762.102i	0.429688	+	0.744241i
$17$	−592.739	+	1026.65i	−0.497440	+	0.861592i	−0.999996	−	0.00295329i	$-0.999060\pi$
$17$	−592.739	+	1026.65i	−0.497440	+	0.861592i	0.502555	+	0.864545i	$0.332393\pi$
$18$	190.941	+	1994.71i	0.138905	+	1.45110i
$19$	−471.000	+	271.932i	−0.299321	+	0.172813i	−0.642138	−	0.766589i	$-0.721952\pi$
$19$	−471.000	+	271.932i	−0.299321	+	0.172813i	0.342817	+	0.939402i	$0.388619\pi$
$20$	−257.091			−0.143718
$21$	−1589.04	−	1248.63i	−0.786294	−	0.617852i
$22$	3706.00			1.63248
$23$	−3292.20	+	1900.75i	−1.29768	+	0.749214i	−0.980002	−	0.198986i	$-0.936235\pi$
$23$	−3292.20	+	1900.75i	−1.29768	+	0.749214i	−0.317674	+	0.948200i	$0.602902\pi$
$24$	−432.526	+	278.039i	−0.153279	+	0.0985320i
$25$	1537.00	−	2662.16i	0.491840	−	0.851892i
$26$	−2156.71	−	3735.53i	−0.625689	−	1.08373i
$27$	3749.25	−	540.400i	0.989772	−	0.142661i
$28$	882.000	−	4583.01i	0.212605	−	1.10473i
$29$		−	2626.42i		−	0.579921i	−0.957039	−	0.289961i	$-0.906358\pi$
$29$		−	2626.42i		−	0.579921i	0.957039	−	0.289961i	$-0.0936422\pi$
$30$	43.7872	+	916.955i	0.00888267	+	0.186014i
$31$	−7510.50	−	4336.19i	−1.40367	−	0.810409i	−0.408902	−	0.912578i	$-0.634088\pi$
$31$	−7510.50	−	4336.19i	−1.40367	−	0.810409i	−0.994767	+	0.102170i	$0.967421\pi$
$32$	7198.56	+	4156.09i	1.24271	+	0.717480i
$33$	−334.163	−	6997.77i	−0.0534162	−	1.11860i
$34$			9775.69i			1.45027i
$35$	−699.860	−	606.097i	−0.0965697	−	0.0836318i
$36$	5076.00	+	7124.73i	0.652778	+	0.916246i
$37$	3053.00	+	5287.95i	0.366625	+	0.635014i	0.989036	−	0.147677i	$-0.0471798\pi$
$37$	3053.00	+	5287.95i	0.366625	+	0.635014i	−0.622410	+	0.782691i	$0.713846\pi$
$38$	−2242.41	+	3883.97i	−0.251916	+	0.436331i
$39$	−6859.07	+	4409.19i	−0.722110	+	0.464191i
$40$	−204.000	+	117.779i	−0.0201595	+	0.0116391i
$41$	−199.960			−0.0185773			−0.00928867	−	0.999957i	$-0.502957\pi$
$41$	−199.960			−0.0185773			−0.00928867	+	0.999957i	$0.502957\pi$
$42$	−16496.2	−	2365.22i	−1.44298	−	0.206894i
$43$	−4744.00			−0.391267			−0.195634	−	0.980677i	$-0.562676\pi$
$43$	−4744.00			−0.391267			−0.195634	+	0.980677i	$0.562676\pi$
$44$	14011.5	−	8089.53i	1.09107	−	0.629929i
$45$	1727.47	−	165.360i	0.127168	−	0.0121731i
$46$	−15674.0	+	27148.2i	−1.09216	+	1.89167i
$47$	13068.8	+	22635.8i	0.862962	+	1.49469i	0.869057	+	0.494712i	$0.164726\pi$
$47$	13068.8	+	22635.8i	0.862962	+	1.49469i	−0.00609519	+	0.999981i	$0.501940\pi$
$48$	6284.46	−	12193.6i	0.393699	−	0.763889i
$49$	13205.5	−	10396.6i	0.785714	−	0.618590i
$50$		−	25348.9i		−	1.43395i
$51$	18458.7	−	881.455i	0.993748	−	0.0474542i
$52$	−16308.0	−	9415.43i	−0.836358	−	0.482872i
$53$	−11908.3	−	6875.28i	−0.582319	−	0.336202i	0.179735	−	0.983715i	$-0.442476\pi$
$53$	−11908.3	−	6875.28i	−0.582319	−	0.336202i	−0.762055	+	0.647513i	$0.775809\pi$
$54$	24546.9	−	19317.8i	1.14554	−	0.901515i
$55$		−	3209.49i		−	0.143064i
$56$	−1399.72	−	4040.64i	−0.0596446	−	0.172179i
$57$	7536.00	+	3883.97i	0.307223	+	0.158339i
$58$	−10829.0	−	18756.4i	−0.422686	−	0.732114i
$59$	−14515.0	+	25140.6i	−0.542857	+	0.940256i	0.455881	+	0.890041i	$0.349324\pi$
$59$	−14515.0	+	25140.6i	−0.542857	+	0.940256i	−0.998738	+	0.0502156i	$0.984009\pi$
$60$	2167.10	+	3371.20i	0.0777142	+	0.120895i
$61$	−3852.00	+	2223.95i	−0.132544	+	0.0765246i	−0.564806	−	0.825224i	$-0.691049\pi$
$61$	−3852.00	+	2223.95i	−0.132544	+	0.0765246i	0.432262	+	0.901748i	$0.357716\pi$
$62$	−71514.3			−2.36273
$63$	−2978.64	+	31361.8i	−0.0945511	+	0.995520i
$64$	40384.0			1.23242
$65$	−3235.07	+	1867.77i	−0.0949729	+	0.0548327i
$66$	−31238.9	−	48596.3i	−0.882747	−	1.37323i
$67$	−691.000	+	1196.85i	−0.0188058	+	0.0325725i	−0.875275	−	0.483625i	$-0.839320\pi$
$67$	−691.000	+	1196.85i	−0.0188058	+	0.0325725i	0.856469	+	0.516198i	$0.172653\pi$
$68$	21338.6	+	36959.5i	0.559620	+	0.969291i
$69$	52675.2	+	27148.2i	1.33194	+	0.686464i
$70$	−7497.00	−	1442.80i	−0.182870	−	0.0351933i
$71$		−	83237.3i		−	1.95962i	−0.199931	−	0.979810i	$-0.564072\pi$
$71$		−	83237.3i		−	1.95962i	0.199931	−	0.979810i	$-0.435928\pi$
$72$	7291.77	+	3327.98i	0.165768	+	0.0756571i
$73$	28158.0	+	16257.0i	0.618436	+	0.357054i	0.776260	−	0.630413i	$-0.217115\pi$
$73$	28158.0	+	16257.0i	0.618436	+	0.357054i	−0.157824	+	0.987467i	$0.550448\pi$
$74$	43605.6	+	25175.7i	0.925684	+	0.534444i
$75$	−47864.4	+	2285.66i	−0.982560	+	0.0469200i
$76$			19579.1i			0.388829i
$77$	57213.6	+	11010.8i	1.09969	+	0.211636i
$78$	−30804.0	+	59768.5i	−0.573285	+	1.11234i
$79$	−10544.5	−	18263.6i	−0.190090	−	0.329245i	0.755190	−	0.655506i	$-0.227545\pi$
$79$	−10544.5	−	18263.6i	−0.190090	−	0.329245i	−0.945280	+	0.326261i	$0.894211\pi$
$80$	3142.23	−	5442.50i	0.0548925	−	0.0950766i
$81$	−38689.7	−	44608.2i	−0.655213	−	0.755444i
$82$	−1428.00	+	824.456i	−0.0234527	+	0.0135404i
$83$	36642.7			0.583837			0.291919	−	0.956443i	$-0.405706\pi$
$83$	36642.7			0.583837			0.291919	+	0.956443i	$0.405706\pi$
$84$	−67531.0	+	27065.9i	−1.04425	+	0.418528i
$85$	8466.00			0.127096
$86$	−33878.9	+	19560.0i	−0.493951	+	0.285183i
$87$	−34439.9	+	22138.8i	−0.487824	+	0.313586i
$88$	7412.00	−	12838.0i	0.102030	−	0.176721i
$89$	−30772.4	−	53299.4i	−0.411800	−	0.713259i	0.583286	−	0.812267i	$-0.301767\pi$
$89$	−30772.4	−	53299.4i	−0.411800	−	0.713259i	−0.995087	+	0.0990076i	$0.968433\pi$
$90$	11654.8	−	8303.45i	0.151670	−	0.108057i
$91$	−22197.0	−	64077.2i	−0.280990	−	0.811148i
$92$			136854.i			1.68573i
$93$	6448.30	+	135035.i	0.0773104	+	1.61897i
$94$	186660.	+	107768.i	2.17887	+	1.25797i
$95$	3363.61	+	1941.98i	0.0382382	+	0.0220768i
$96$	−6180.48	−	129427.i	−0.0684454	−	1.43333i
$97$		−	120324.i		−	1.29844i	−0.760600	−	0.649221i	$-0.775095\pi$
$97$		−	120324.i		−	1.29844i	0.760600	−	0.649221i	$-0.224905\pi$
$98$	51439.7	−	128694.i	0.541045	−	1.35361i
$99$	−88944.0	+	63368.0i	−0.912071	+	0.649804i
$100$	−55332.0	−	95837.8i	−0.553320	−	0.958378i
$101$	22852.6	−	39581.8i	0.222911	−	0.386093i	−0.732780	−	0.680466i	$-0.761777\pi$
$101$	22852.6	−	39581.8i	0.222911	−	0.386093i	0.955691	+	0.294373i	$0.0951107\pi$
$102$	128187.	−	82402.1i	1.21996	−	0.784220i
$103$	−104757.	+	60481.5i	−0.972949	+	0.561732i	−0.900134	−	0.435613i	$-0.856532\pi$
$103$	−104757.	+	60481.5i	−0.972949	+	0.561732i	−0.0728149	+	0.997345i	$0.523198\pi$
$104$	−17253.7			−0.156422
$105$	−2048.34	+	14286.1i	−0.0181313	+	0.126457i
$106$	−113390.			−0.980190
$107$	−96198.6	+	55540.3i	−0.812287	+	0.468974i	−0.847749	−	0.530397i	$-0.822043\pi$
$107$	−96198.6	+	55540.3i	−0.812287	+	0.468974i	0.0354626	+	0.999371i	$0.488710\pi$
$108$	50638.5	−	126617.i	0.417755	−	1.04456i
$109$	62645.0	−	108504.i	0.505033	−	0.874744i	−0.494950	−	0.868922i	$-0.664813\pi$
$109$	62645.0	−	108504.i	0.505033	−	0.874744i	0.999983	−	0.00582195i	$-0.00185319\pi$
$110$	−13233.1	−	22920.3i	−0.104275	−	0.180609i
$111$	43605.6	−	84607.2i	0.335919	−	0.651778i
$112$	86240.0	+	74686.0i	0.649626	+	0.562593i
$113$		−	27822.7i		−	0.204976i	−0.994734	−	0.102488i	$-0.967320\pi$
$113$		−	27822.7i		−	0.204976i	0.994734	−	0.102488i	$-0.0326804\pi$
$114$	69831.8	−	3334.66i	0.503259	−	0.0240320i
$115$	23511.0	+	13574.1i	0.165778	+	0.0957119i
$116$	−81883.6	−	47275.5i	−0.565005	−	0.326206i
$117$	115634.	+	52775.7i	0.780946	+	0.356426i
$118$			239387.i			1.58269i
$119$	−29044.2	+	150918.i	−0.188015	+	0.976953i
$120$	3264.00	+	1682.23i	0.0206917	+	0.0106643i
$121$	20463.0	+	35443.0i	0.127059	+	0.220073i
$122$	−18339.2	+	31764.4i	−0.111553	+	0.193215i
$123$	1685.52	+	2622.05i	0.0100455	+	0.0156271i
$124$	−270378.	+	156103.i	−1.57913	+	0.911710i
$125$	−44269.7			−0.253415
$126$	108036.	+	236249.i	0.606239	+	1.32570i
$127$	−62011.0			−0.341161			−0.170581	−	0.985344i	$-0.554564\pi$
$127$	−62011.0			−0.341161			−0.170581	+	0.985344i	$0.554564\pi$
$128$	58045.5	−	33512.6i	0.313144	−	0.180794i
$129$	39988.5	+	62207.4i	0.211573	+	0.329130i
$130$	−15402.0	+	26677.0i	−0.0799316	+	0.138446i
$131$	70032.4	+	121300.i	0.356550	+	0.617563i	0.987382	−	0.158356i	$-0.0506195\pi$
$131$	70032.4	+	121300.i	0.356550	+	0.617563i	−0.630832	+	0.775920i	$0.717286\pi$
$132$	−224184.	−	115542.i	−1.11987	−	0.577170i
$133$	−46158.0	+	53298.7i	−0.226265	+	0.261269i
$134$			11396.3i			0.0548278i
$135$	−16729.7	−	21258.2i	−0.0790048	−	0.100390i
$136$	33864.0	+	19551.4i	0.156997	+	0.0906422i
$137$	−95216.7	−	54973.4i	−0.433423	−	0.250237i	0.267381	−	0.963591i	$-0.413842\pi$
$137$	−95216.7	−	54973.4i	−0.433423	−	0.250237i	−0.700804	+	0.713354i	$0.747175\pi$
$138$	488111.	−	23308.6i	2.18183	−	0.104188i
$139$			99721.1i			0.437774i	0.975750	+	0.218887i	$0.0702426\pi$
$139$			99721.1i			0.437774i	−0.975750	+	0.218887i	$0.929757\pi$
$140$	−31493.7	+	10909.7i	−0.135801	+	0.0470429i
$141$	186660.	−	362174.i	0.790685	−	1.53415i
$142$	−343196.	−	594433.i	−1.42831	−	2.47390i
$143$	117541.	−	203587.i	0.480672	−	0.832548i
$144$	−212867.	+	20376.4i	−0.855465	+	0.0818883i
$145$	−16243.5	+	9378.19i	−0.0641593	+	0.0370424i
$146$	268118.			1.04098
$147$	−247643.	−	85525.7i	−0.945218	−	0.326440i
$148$	219816.			0.824907
$149$	316744.	−	182872.i	1.16881	−	0.674810i	0.215407	−	0.976524i	$-0.430892\pi$
$149$	316744.	−	182872.i	1.16881	−	0.674810i	0.953399	+	0.301714i	$0.0975587\pi$
$150$	−332396.	+	213673.i	−1.20622	+	0.775391i
$151$	−22436.5	+	38861.2i	−0.0800779	+	0.138699i	−0.903283	−	0.429045i	$-0.858850\pi$
$151$	−22436.5	+	38861.2i	−0.0800779	+	0.138699i	0.823205	+	0.567744i	$0.192184\pi$
$152$	8969.63	+	15535.9i	0.0314895	+	0.0545414i
$153$	−167152.	−	234617.i	−0.577276	−	0.810271i
$154$	453985.	−	157265.i	1.54255	−	0.534356i
$155$			61933.2i			0.207059i
$156$	14001.6	+	293210.i	0.0460644	+	0.964644i
$157$	74862.0	+	43221.6i	0.242389	+	0.139943i	0.616274	−	0.787532i	$-0.288641\pi$
$157$	74862.0	+	43221.6i	0.242389	+	0.139943i	−0.373885	+	0.927475i	$0.621975\pi$
$158$	−150606.	−	86952.2i	−0.479953	−	0.277101i
$159$	10224.2	+	214106.i	0.0320726	+	0.671639i
$160$		−	59360.8i		−	0.183316i
$161$	−322635.	+	372547.i	−0.980951	+	1.13270i
$162$	−460224.	−	159045.i	−1.37779	−	0.476137i
$163$	182351.	+	315841.i	0.537575	+	0.931107i	0.999034	+	0.0439457i	$0.0139929\pi$
$163$	182351.	+	315841.i	0.537575	+	0.931107i	−0.461459	+	0.887162i	$0.652674\pi$
$164$	−3599.28	+	6234.14i	−0.0104498	+	0.0180995i
$165$	−42085.6	+	27053.7i	−0.120344	+	0.0773601i
$166$	261681.	−	151082.i	0.737059	−	0.425541i
$167$	−139072.			−0.385877			−0.192939	−	0.981211i	$-0.561802\pi$
$167$	−139072.			−0.385877			−0.192939	+	0.981211i	$0.561802\pi$
$168$	−41185.8	+	52414.1i	−0.112583	+	0.143276i
$169$	97681.0			0.263083
$170$	60459.3	−	34906.2i	0.160450	−	0.0926361i
$171$	−12593.2	−	131558.i	−0.0329341	−	0.344053i
$172$	−85392.0	+	147903.i	−0.220088	+	0.381203i
$173$	−150998.	−	261537.i	−0.383581	−	0.664382i	0.607990	−	0.793944i	$-0.291976\pi$
$173$	−150998.	−	261537.i	−0.383581	−	0.664382i	−0.991571	+	0.129563i	$0.958643\pi$
$174$	−154669.	+	300102.i	−0.387285	+	0.751443i
$175$	75313.0	−	391338.i	0.185898	−	0.965955i
$176$			395488.i			0.962392i
$177$	452016.	−	21585.0i	1.08448	−	0.0517869i
$178$	−439518.	−	253756.i	−1.03974	−	0.600297i
$179$	360542.	+	208159.i	0.841053	+	0.485582i	0.857622	−	0.514280i	$-0.171941\pi$
$179$	360542.	+	208159.i	0.841053	+	0.485582i	−0.0165689	+	0.999863i	$0.505274\pi$
$180$	25939.1	−	56833.7i	0.0596723	−	0.130745i
$181$			359595.i			0.815862i	0.913013	+	0.407931i	$0.133750\pi$
$181$			359595.i			0.815862i	−0.913013	+	0.407931i	$0.866250\pi$
$182$	−422715.	−	366082.i	−0.945953	−	0.819219i
$183$	61632.0	+	31764.4i	0.136044	+	0.0701153i
$184$	62696.0	+	108593.i	0.136520	+	0.236459i
$185$	21802.8	−	37763.5i	0.0468363	−	0.0811228i
$186$	602814.	+	937757.i	1.27762	+	1.98750i
$187$	−461397.	+	266388.i	−0.964874	+	0.557070i
$188$	940955.			1.94166
$189$	436351.	−	225299.i	0.888549	−	0.458781i
$190$	32028.0			0.0643644
$191$	−287485.	+	165980.i	−0.570207	+	0.329209i	−0.757232	−	0.653146i	$-0.773449\pi$
$191$	−287485.	+	165980.i	−0.570207	+	0.329209i	0.187025	+	0.982355i	$0.440115\pi$
$192$	−340408.	−	529550.i	−0.666418	−	1.03670i
$193$	−3788.50	+	6561.87i	−0.00732106	+	0.0126804i	−0.869663	−	0.493646i	$-0.835664\pi$
$193$	−3788.50	+	6561.87i	−0.00732106	+	0.0126804i	0.862342	+	0.506327i	$0.168997\pi$
$194$	−496108.	−	859284.i	−0.946394	−	1.63920i
$195$	51761.1	+	26677.0i	0.0974803	+	0.0502402i
$196$	−86436.0	−	598846.i	−0.160714	−	1.11346i
$197$			633169.i			1.16240i	0.813762	+	0.581198i	$0.197416\pi$
$197$			633169.i			1.16240i	−0.813762	+	0.581198i	$0.802584\pi$
$198$	−373914.	+	819264.i	−0.677812	+	1.48512i
$199$	599631.	+	346197.i	1.07337	+	0.619713i	0.929102	−	0.369825i	$-0.120582\pi$
$199$	599631.	+	346197.i	1.07337	+	0.619713i	0.144273	+	0.989538i	$0.453916\pi$
$200$	−87811.0	−	50697.7i	−0.155229	−	0.0896217i
$201$	21518.7	−	1027.58i	0.0375687	−	0.00179401i
$202$		−	376894.i		−	0.649892i
$203$	−111453.	−	321736.i	−0.189824	−	0.547974i
$204$	304776.	−	591352.i	0.512750	−	0.994880i
$205$	714.000	+	1236.68i	0.00118663	+	0.00205530i
$206$	−498743.	+	863848.i	−0.818858	+	1.41830i
$207$	−88024.0	−	919562.i	−0.142783	−	1.49161i
$208$	398640.	−	230155.i	0.638885	−	0.368860i
$209$	−244423.			−0.387058
$210$	44275.1	+	110469.i	0.0692806	+	0.172859i
$211$	1.11674e6			1.72682			0.863408	−	0.504507i	$-0.168326\pi$
$211$	1.11674e6			1.72682			0.863408	+	0.504507i	$0.168326\pi$
$212$	−428700.	+	247510.i	−0.655109	+	0.378228i
$213$	−1.09148e6	+	701631.i	−1.64841	+	1.05964i
$214$	−457997.	+	793274.i	−0.683641	+	1.18410i
$215$	16939.5	+	29340.0i	0.0249922	+	0.0432877i
$216$	−17825.0	−	123668.i	−0.0259953	−	0.180353i
$217$	−1.10404e6	−	212473.i	−1.59161	−	0.306306i
$218$		−	1.03317e6i		−	1.47241i
$219$	−24175.7	−	506267.i	−0.0340618	−	0.713295i
$220$	−100062.	−	57770.8i	−0.139384	−	0.0804733i
$221$	537021.	+	310049.i	0.739623	+	0.427022i
$222$	−37438.5	−	784007.i	−0.0509842	−	1.06767i
$223$		−	152478.i		−	0.205326i	−0.994716	−	0.102663i	$-0.967264\pi$
$223$		−	152478.i		−	0.205326i	0.994716	−	0.102663i	$-0.0327363\pi$
$224$	1.05819e6	+	203648.i	1.40910	+	0.271182i
$225$	433434.	+	608372.i	0.570777	+	0.801149i
$226$	−114716.	−	198694.i	−0.149401	−	0.258770i
$227$	474487.	−	821836.i	0.611167	−	1.05857i	−0.379877	−	0.925037i	$-0.624034\pi$
$227$	474487.	−	821836.i	0.611167	−	1.05857i	0.991044	−	0.133535i	$-0.0426329\pi$
$228$	256738.	−	165038.i	0.327079	−	0.210255i
$229$	−491640.	+	283848.i	−0.619525	+	0.357683i	−0.776684	−	0.629891i	$-0.783100\pi$
$229$	−491640.	+	283848.i	−0.619525	+	0.357683i	0.157159	+	0.987573i	$0.449766\pi$
$230$	223869.			0.279046
$231$	−337887.	−	843046.i	−0.416621	−	1.03949i
$232$	−86632.0			−0.105672
$233$	480211.	−	277250.i	0.579485	−	0.334566i	−0.181444	−	0.983401i	$-0.558077\pi$
$233$	480211.	−	277250.i	0.579485	−	0.334566i	0.760929	+	0.648835i	$0.224744\pi$
$234$	1.04339e6	−	99877.5i	1.24568	−	0.119242i
$235$	93330.0	−	161652.i	0.110243	−	0.190947i
$236$	522538.	+	905063.i	0.610714	+	1.05779i
$237$	−150606.	+	292218.i	−0.174169	+	0.337937i
$238$	414834.	+	1.19752e6i	0.474714	+	1.37038i
$239$		−	503176.i		−	0.569803i	−0.958557	−	0.284902i	$-0.908039\pi$
$239$		−	503176.i		−	0.569803i	0.958557	−	0.284902i	$-0.0919609\pi$
$240$	−97853.5	+	4672.78i	−0.109660	+	0.00523657i
$241$	−1.10136e6	−	635870.i	−1.22148	−	0.705221i	−0.256246	−	0.966612i	$-0.582486\pi$
$241$	−1.10136e6	−	635870.i	−1.22148	−	0.705221i	−0.965233	+	0.261390i	$0.915819\pi$
$242$	292270.	+	168742.i	0.320809	+	0.185219i
$243$	−258815.	+	883348.i	−0.281173	+	0.959657i
$244$			160125.i			0.172180i
$245$	−111453.	−	44548.1i	−0.118625	−	0.0474148i
$246$	22848.0	+	11775.6i	0.0240719	+	0.0124064i
$247$	142242.	+	246370.i	0.148349	+	0.256949i
$248$	−143029.	+	247733.i	−0.147670	+	0.255773i
$249$	−308872.	−	480490.i	−0.315704	−	0.491118i
$250$	−316149.	+	182529.i	−0.319920	+	0.184706i
$251$	−1.60063e6			−1.60364			−0.801819	−	0.597566i	$-0.796134\pi$
$251$	−1.60063e6			−1.60364			−0.801819	+	0.597566i	$0.796134\pi$
$252$	924150.	+	657378.i	0.916729	+	0.652099i
$253$	−1.70847e6			−1.67805
$254$	−442847.	+	255678.i	−0.430695	+	0.248662i
$255$	−71362.3	−	111013.i	−0.0687256	−	0.106912i
$256$	−369792.	+	640499.i	−0.352661	+	0.610827i
$257$	242273.	+	419629.i	0.228808	+	0.396308i	0.957455	−	0.288582i	$-0.0931837\pi$
$257$	242273.	+	419629.i	0.228808	+	0.396308i	−0.728647	+	0.684890i	$0.759850\pi$
$258$	542063.	+	279373.i	0.506991	+	0.261297i
$259$	598388.	+	518219.i	0.554285	+	0.480025i
$260$			134479.i			0.123373i
$261$	580607.	+	264991.i	0.527571	+	0.240785i
$262$	1.00026e6	+	577502.i	0.900246	+	0.519757i
$263$	−392607.	−	226672.i	−0.350001	−	0.202073i	0.314685	−	0.949196i	$-0.398101\pi$
$263$	−392607.	−	226672.i	−0.350001	−	0.202073i	−0.664686	+	0.747123i	$0.731434\pi$
$264$	−230820.	+	11022.3i	−0.203828	+	0.00973336i
$265$			98198.6i			0.0858995i
$266$	−109878.	+	570943.i	−0.0952153	+	0.494753i
$267$	−439518.	+	852790.i	−0.377310	+	0.732089i
$268$	24876.0	+	43086.5i	0.0211565	+	0.0366441i
$269$	9080.33	−	15727.6i	0.00765104	−	0.0132520i	−0.862175	−	0.506611i	$-0.830898\pi$
$269$	9080.33	−	15727.6i	0.00765104	−	0.0132520i	0.869826	+	0.493359i	$0.164231\pi$
$270$	−207124.	−	82835.8i	−0.172910	−	0.0691526i
$271$	1.58848e6	−	917111.i	1.31389	−	0.758576i	0.331153	−	0.943577i	$-0.392562\pi$
$271$	1.58848e6	−	917111.i	1.31389	−	0.758576i	0.982738	+	0.185001i	$0.0592290\pi$
$272$	−1.04322e6			−0.854975
$273$	−653131.	+	831191.i	−0.530388	+	0.674985i
$274$	−906644.			−0.729559
$275$	1.19642e6	−	690756.i	0.954012	−	0.550799i
$276$	1.79455e6	−	1.15358e6i	1.41802	−	0.911540i
$277$	778892.	−	1.34908e6i	0.609927	−	1.05642i	−0.381325	−	0.924441i	$-0.624532\pi$
$277$	778892.	−	1.34908e6i	0.609927	−	1.05642i	0.991252	−	0.131983i	$-0.0421346\pi$
$278$	411161.	+	712151.i	0.319080	+	0.552663i
$279$	1.71634e6	−	1.22281e6i	1.32006	−	0.940474i
$280$	−19992.0	+	23084.8i	−0.0152392	+	0.0175967i
$281$		−	927443.i		−	0.700683i	−0.936622	−	0.350341i	$-0.886066\pi$
$281$		−	927443.i		−	0.700683i	0.936622	−	0.350341i	$-0.113934\pi$
$282$	−160261.	−	3.35606e6i	−0.120007	−	2.51308i
$283$	784368.	+	452855.i	0.582175	+	0.336119i	0.761997	−	0.647580i	$-0.224219\pi$
$283$	784368.	+	452855.i	0.582175	+	0.336119i	−0.179822	+	0.983699i	$0.557552\pi$
$284$	−2.59508e6	−	1.49827e6i	−1.90922	−	1.10229i
$285$	−2887.90	−	60476.1i	−0.00210606	−	0.0441034i
$286$		−	1.93853e6i		−	1.40139i
$287$	−24495.1	+	8485.35i	−0.0175539	+	0.00608086i
$288$	−1.64506e6	+	1.17202e6i	−1.16869	+	0.832632i
$289$	7250.50	+	12558.2i	0.00510650	+	0.00884472i
$290$	−77334.5	+	133947.i	−0.0539981	+	0.0935274i
$291$	−1.57779e6	+	1.01424e6i	−1.09224	+	0.702118i
$292$	1.01369e6	−	585253.i	0.695740	−	0.401686i
$293$	−32143.6			−0.0218738			−0.0109369	−	0.999940i	$-0.503481\pi$
$293$	−32143.6			−0.0218738			−0.0109369	+	0.999940i	$0.503481\pi$
$294$	−2.12115e6	+	410281.i	−1.43121	+	0.276830i
$295$	207315.			0.138700
$296$	174422.	−	100703.i	0.115710	−	0.0668055i
$297$	1.58067e6	+	632163.i	1.03980	+	0.415851i
$298$	1.50800e6	−	2.61194e6i	0.983697	−	1.70381i
$299$	994244.	+	1.72208e6i	0.643154	+	1.11398i
$300$	−790299.	+	1.53341e6i	−0.506977	+	0.983680i
$301$	−581140.	+	201313.i	−0.369713	+	0.128072i
$302$			370032.i			0.233465i
$303$	−711662.	+	33983.8i	−0.445315	+	0.0212650i
$304$	−414480.	−	239300.i	−0.257229	−	0.148511i
$305$	27508.8	+	15882.2i	0.0169325	+	0.00977600i
$306$	−2.16106e6	−	986312.i	−1.31936	−	0.602158i
$307$			2.12041e6i			1.28403i	0.766692	+	0.642015i	$0.221901\pi$
$307$			2.12041e6i			1.28403i	−0.766692	+	0.642015i	$0.778099\pi$
$308$	1.37313e6	−	1.58555e6i	0.824771	−	0.952364i
$309$	1.67611e6	+	863848.i	0.998635	+	0.514685i
$310$	255357.	+	442291.i	0.150919	+	0.261399i
$311$	23652.4	−	40967.2i	0.0138667	−	0.0240179i	−0.859009	−	0.511961i	$-0.828919\pi$
$311$	23652.4	−	40967.2i	0.0138667	−	0.0240179i	0.872876	+	0.487943i	$0.162253\pi$
$312$	145436.	+	226245.i	0.0845836	+	0.131581i
$313$	330458.	−	190790.i	0.190658	−	0.110076i	−0.401633	−	0.915801i	$-0.631557\pi$
$313$	330458.	−	190790.i	0.190658	−	0.110076i	0.592291	+	0.805724i	$0.298224\pi$
$314$	712829.			0.408001
$315$	204598.	−	93562.3i	0.116178	−	0.0531281i
$316$	−759204.			−0.427702
$317$	−2.12934e6	+	1.22938e6i	−1.19014	+	0.687126i	−0.958338	−	0.285637i	$-0.907795\pi$
$317$	−2.12934e6	+	1.22938e6i	−1.19014	+	0.687126i	−0.231800	+	0.972763i	$0.574461\pi$
$318$	955797.	+	1.48687e6i	0.530027	+	0.824526i
$319$	590180.	−	1.02222e6i	0.324719	−	0.562430i
$320$	−144200.	−	249761.i	−0.0787208	−	0.136348i
$321$	1.53918e6	+	793274.i	0.833731	+	0.429695i
$322$	−768026.	+	3.99078e6i	−0.412797	+	2.14495i
$323$		−	644738.i		−	0.343856i
$324$	−2.08716e6	+	403277.i	−1.10457	+	0.213423i
$325$	−1.39252e6	−	803973.i	−0.731297	−	0.422214i
$326$	2.60449e6	+	1.50370e6i	1.35731	+	0.783644i
$327$	−1.95085e6	+	93158.7i	−1.00892	+	0.0481786i
$328$			6595.65i			0.00338511i
$329$	2.56149e6	+	2.21831e6i	1.30468	+	1.12988i
$330$	−189006.	+	366726.i	−0.0955412	+	0.185377i
$331$	510140.	+	883588.i	0.255929	+	0.443282i	0.965147	−	0.261707i	$-0.0842854\pi$
$331$	510140.	+	883588.i	0.255929	+	0.443282i	−0.709218	+	0.704989i	$0.750952\pi$
$332$	659568.	−	1.14241e6i	0.328409	−	0.568820i
$333$	−1.47701e6	+	141385.i	−0.729914	+	0.0698702i
$334$	−993174.	+	573409.i	−0.487146	+	0.281254i
$335$	9869.45			0.00480486
$336$	252406.	−	1.76040e6i	0.121970	−	0.850676i
$337$	−239587.			−0.114918			−0.0574591	−	0.998348i	$-0.518300\pi$
$337$	−239587.			−0.114918			−0.0574591	+	0.998348i	$0.518300\pi$
$338$	697582.	−	402749.i	0.332126	−	0.191753i
$339$	−364835.	+	234526.i	−0.172424	+	0.110839i
$340$	152388.	−	263944.i	0.0714913	−	0.123827i
$341$	−1.94876e6	−	3.37536e6i	−0.907556	−	1.57193i
$342$	−632359.	−	887586.i	−0.292347	−	0.410341i
$343$	1.17649e6	−	1.83397e6i	0.539949	−	0.841698i
$344$			156480.i			0.0712956i
$345$	−20185.9	−	422716.i	−0.00913061	−	0.191206i
$346$	−2.15669e6	−	1.24516e6i	−0.968494	−	0.559160i
$347$	3.34015e6	+	1.92843e6i	1.48916	+	0.859768i	0.999923	−	0.0123825i	$-0.00394159\pi$
$347$	3.34015e6	+	1.92843e6i	1.48916	+	0.859768i	0.489238	+	0.872150i	$0.337275\pi$
$348$	70302.9	+	1.47223e6i	0.0311190	+	0.651669i
$349$		−	1.90701e6i		−	0.838085i	−0.907967	−	0.419043i	$-0.862366\pi$
$349$		−	1.90701e6i		−	0.838085i	0.907967	−	0.419043i	$-0.137634\pi$
$350$	−1.07568e6	−	3.10523e6i	−0.469370	−	1.35495i
$351$	−282672.	−	1.96116e6i	−0.122466	−	0.849658i
$352$	1.86782e6	+	3.23517e6i	0.803488	+	1.39168i
$353$	−53632.1	+	92893.6i	−0.0229081	+	0.0396779i	−0.877252	−	0.480030i	$-0.840626\pi$
$353$	−53632.1	+	92893.6i	−0.0229081	+	0.0396779i	0.854344	+	0.519708i	$0.173959\pi$
$354$	3.13905e6	−	2.01786e6i	1.33134	−	0.855821i
$355$	−514794.	+	297216.i	−0.216802	+	0.125170i
$356$	−2.21561e6			−0.926550
$357$	2.22379e6	−	891279.i	0.923471	−	0.370120i
$358$	3.43305e6			1.41570
$359$	−2.64426e6	+	1.52667e6i	−1.08285	+	0.625184i	−0.931664	−	0.363321i	$-0.881643\pi$
$359$	−2.64426e6	+	1.52667e6i	−1.08285	+	0.625184i	−0.151187	+	0.988505i	$0.548310\pi$
$360$	−5454.38	−	56980.4i	−0.00221814	−	0.0231723i
$361$	−1.09016e6	+	1.88820e6i	−0.440271	+	0.762572i
$362$	1.48265e6	+	2.56802e6i	0.594656	+	1.02998i
$363$	292270.	−	567087.i	0.116417	−	0.225883i
$364$	−2.39728e6	−	461356.i	−0.948341	−	0.182508i
$365$		−	232197.i		−	0.0912271i
$366$	571109.	−	27272.0i	0.222852	−	0.0106418i
$367$	2.23348e6	+	1.28950e6i	0.865601	+	0.499755i	0.865884	−	0.500245i	$-0.166757\pi$
$367$	2.23348e6	+	1.28950e6i	0.865601	+	0.499755i	−0.000283128		1.00000i	$0.500090\pi$
$368$	−2.89713e6	−	1.67266e6i	−1.11519	−	0.643856i
$369$	20174.8	−	44204.0i	0.00771336	−	0.0169003i
$370$		−	359581.i		−	0.136550i
$371$	−1.75052e6	−	336889.i	−0.660288	−	0.127073i
$372$	4.32605e6	+	2.22959e6i	1.62082	+	0.835350i
$373$	−1.09443e6	−	1.89560e6i	−0.407301	−	0.705465i	0.587286	−	0.809380i	$-0.300197\pi$
$373$	−1.09443e6	−	1.89560e6i	−0.407301	−	0.705465i	−0.994586	+	0.103914i	$0.966863\pi$
$374$	−2.19669e6	+	3.80478e6i	−0.812063	+	1.40653i
$375$	373162.	+	580503.i	0.137031	+	0.213170i
$376$	746640.	−	431073.i	0.272359	−	0.157247i
$377$	−1.37383e6			−0.497827
$378$	2.18724e6	−	3.40808e6i	0.787347	−	1.22682i
$379$	−5.52354e6			−1.97524			−0.987620	−	0.156866i	$-0.949861\pi$
$379$	−5.52354e6			−1.97524			−0.987620	+	0.156866i	$0.949861\pi$
$380$	121090.	−	69911.4i	0.0430179	−	0.0248364i
$381$	522708.	+	813142.i	0.184479	+	0.286981i
$382$	−1.36870e6	+	2.37066e6i	−0.479900	+	0.831212i
$383$	−1.92749e6	−	3.33852e6i	−0.671422	−	1.16294i	−0.977501	−	0.210932i	$-0.932350\pi$
$383$	−1.92749e6	−	3.33852e6i	−0.671422	−	1.16294i	0.306078	−	0.952006i	$-0.400983\pi$
$384$	−928728.	−	478656.i	−0.321411	−	0.165651i
$385$	−136196.	−	393163.i	−0.0468286	−	0.135182i
$386$			62481.5i			0.0213444i
$387$	478642.	−	1.04873e6i	0.162455	−	0.355947i
$388$	−3.75133e6	−	2.16583e6i	−1.26504	−	0.730373i
$389$	−307874.	−	177751.i	−0.103157	−	0.0595578i	0.447534	−	0.894267i	$-0.352302\pi$
$389$	−307874.	−	177751.i	−0.103157	−	0.0595578i	−0.550691	+	0.834709i	$0.685636\pi$
$390$	479640.	−	22904.2i	0.159681	−	0.00762523i
$391$		−	4.50660e6i		−	1.49076i
$392$	−342931.	−	435581.i	−0.112718	−	0.143171i
$393$	1.00026e6	−	1.94080e6i	0.326688	−	0.633867i
$394$	2.61062e6	+	4.52173e6i	0.847234	+	1.46745i
$395$	−75302.8	+	130428.i	−0.0242839	+	0.0420609i
$396$	374627.	+	3.91362e6i	0.120050	+	1.25413i
$397$	3.62234e6	−	2.09136e6i	1.15349	−	0.665967i	0.203754	−	0.979022i	$-0.434686\pi$
$397$	3.62234e6	−	2.09136e6i	1.15349	−	0.665967i	0.949735	+	0.313055i	$0.101352\pi$
$398$	5.70963e6			1.80676
$399$	1.08798e6	+	155994.i	0.342127	+	0.0490541i
$400$	2.70512e6			0.845350
$401$	1.42847e6	−	824728.i	0.443619	−	0.256124i	−0.261512	−	0.965200i	$-0.584221\pi$
$401$	1.42847e6	−	824728.i	0.443619	−	0.256124i	0.705132	+	0.709076i	$0.250888\pi$
$402$	149438.	−	96062.4i	0.0461206	−	0.0296475i
$403$	−2.26817e6	+	3.92859e6i	−0.695686	+	1.20496i
$404$	−822693.	−	1.42495e6i	−0.250775	−	0.434355i
$405$	−137737.	+	398566.i	−0.0417265	+	0.120743i
$406$	−2.12248e6	−	1.83813e6i	−0.639042	−	0.553427i
$407$			2.74415e6i			0.821149i
$408$	−29074.7	−	608858.i	−0.00864698	−	0.181078i
$409$	−830920.	−	479732.i	−0.245613	−	0.141805i	0.372141	−	0.928176i	$-0.378624\pi$
$409$	−830920.	−	479732.i	−0.245613	−	0.141805i	−0.617754	+	0.786372i	$0.711957\pi$
$410$	10198.0	+	5887.79i	0.00299608	+	0.00172979i
$411$	81750.3	+	1.71195e6i	0.0238718	+	0.499904i
$412$			4.35467e6i			1.26390i
$413$	−711233.	+	3.69567e6i	−0.205181	+	1.06615i
$414$	−4.42007e6	−	6.20405e6i	−1.26744	−	1.77899i
$415$	−130840.	−	226622.i	−0.0372925	−	0.0645926i
$416$	2.17397e6	−	3.76542e6i	0.615913	−	1.06679i
$417$	1.30763e6	−	840578.i	0.368251	−	0.236721i
$418$	−1.74553e6	+	1.00778e6i	−0.488636	+	0.282114i
$419$	4.32164e6			1.20258			0.601289	−	0.799032i	$-0.294654\pi$
$419$	4.32164e6			1.20258			0.601289	+	0.799032i	$0.294654\pi$
$420$	408527.	+	321011.i	0.113005	+	0.0887967i
$421$	2.57372e6			0.707711			0.353856	−	0.935300i	$-0.384870\pi$
$421$	2.57372e6			0.707711			0.353856	+	0.935300i	$0.384870\pi$
$422$	7.97512e6	−	4.60444e6i	2.18000	−	1.25862i
$423$	−6.32254e6	+	605218.i	−1.71807	+	0.164460i
$424$	−226780.	+	392794.i	−0.0612619	+	0.106109i
$425$	1.82208e6	+	3.15593e6i	0.489322	+	0.847531i
$426$	−4.90182e6	+	9.51093e6i	−1.30868	+	2.53921i
$427$	−377496.	+	435895.i	−0.100194	+	0.115694i
$428$			3.99890e6i			1.05519i
$429$	−3.66039e6	+	174794.i	−0.960249	+	0.0458545i
$430$	241944.	+	139686.i	0.0631021	+	0.0364320i
$431$	−1.27443e6	−	735793.i	−0.330463	−	0.190793i	0.325584	−	0.945513i	$-0.394439\pi$
$431$	−1.27443e6	−	735793.i	−0.330463	−	0.190793i	−0.656047	+	0.754720i	$0.727773\pi$
$432$	2.06151e6	+	2.61954e6i	0.531467	+	0.675328i
$433$			6.94894e6i			1.78114i	0.454843	+	0.890571i	$0.349695\pi$
$433$			6.94894e6i			1.78114i	−0.454843	+	0.890571i	$0.650305\pi$
$434$	−8.76050e6	+	3.03473e6i	−2.23257	+	0.773384i
$435$	259896.	+	133947.i	0.0658531	+	0.0339399i
$436$	−2.25522e6	−	3.90616e6i	−0.568163	−	0.984087i
$437$	1.03375e6	−	1.79051e6i	0.258948	−	0.448511i
$438$	−2.26004e6	−	3.51579e6i	−0.562900	−	0.875665i
$439$	5.20874e6	−	3.00727e6i	1.28994	−	0.744750i	0.311301	−	0.950312i	$-0.399235\pi$
$439$	5.20874e6	−	3.00727e6i	1.28994	−	0.744750i	0.978644	+	0.205562i	$0.0659021\pi$
$440$	−105865.			−0.0260687
$441$	965963.	+	3.96822e6i	0.236518	+	0.971627i
$442$	5.11346e6			1.24497
$443$	−2.76057e6	+	1.59381e6i	−0.668327	+	0.385859i	−0.795442	−	0.606029i	$-0.792761\pi$
$443$	−2.76057e6	+	1.59381e6i	−0.668327	+	0.385859i	0.127116	+	0.991888i	$0.459428\pi$
$444$	−1.85289e6	−	2.88242e6i	−0.446059	−	0.693904i
$445$	−219759.	+	380634.i	−0.0526074	+	0.0911186i
$446$	−628681.	−	1.08891e6i	−0.149656	−	0.259211i
$447$	−5.06790e6	−	2.61194e6i	−1.19966	−	0.618292i
$448$	4.94704e6	−	1.71370e6i	1.16453	−	0.403405i
$449$		−	5.10328e6i		−	1.19463i	−0.802007	−	0.597315i	$-0.796234\pi$
$449$		−	5.10328e6i		−	1.19463i	0.802007	−	0.597315i	$-0.203766\pi$
$450$	5.60372e6	+	2.55755e6i	1.30450	+	0.595379i
$451$	−77826.0	−	44932.9i	−0.0180170	−	0.0104021i
$452$	−867426.	−	500809.i	−0.199704	−	0.115299i
$453$	698705.	−	33365.1i	0.159974	−	0.00763918i
$454$		−	7.82544e6i		−	1.78184i
$455$	−317037.	+	366082.i	−0.0717928	+	0.0828992i
$456$	128112.	−	248574.i	0.0288521	−	0.0559813i
$457$	−1.20269e6	−	2.08313e6i	−0.269379	−	0.466579i	0.699322	−	0.714807i	$-0.253485\pi$
$457$	−1.20269e6	−	2.08313e6i	−0.269379	−	0.466579i	−0.968702	+	0.248228i	$0.920152\pi$
$458$	−2.34067e6	+	4.05417e6i	−0.521408	+	0.903104i
$459$	−1.66752e6	+	4.16950e6i	−0.369436	+	0.923744i
$460$	846396.	−	488667.i	0.186500	−	0.107676i
$461$	6.20476e6			1.35979			0.679896	−	0.733308i	$-0.262025\pi$
$461$	6.20476e6			1.35979			0.679896	+	0.733308i	$0.262025\pi$
$462$	−5.88896e6	−	4.62741e6i	−1.28361	−	1.00863i
$463$	−5.14496e6			−1.11540			−0.557698	−	0.830044i	$-0.688315\pi$
$463$	−5.14496e6			−1.11540			−0.557698	+	0.830044i	$0.688315\pi$
$464$	2.00160e6	−	1.15562e6i	0.431601	−	0.249185i
$465$	812121.	−	522052.i	0.174176	−	0.111965i
$466$	2.28626e6	−	3.95992e6i	0.487709	−	0.844738i
$467$	−883202.	−	1.52975e6i	−0.187399	−	0.324585i	0.756983	−	0.653434i	$-0.226672\pi$
$467$	−883202.	−	1.52975e6i	−0.187399	−	0.324585i	−0.944382	+	0.328849i	$0.893339\pi$
$468$	3.72680e6	−	2.65515e6i	0.786541	−	0.560370i
$469$	−33859.0	+	175937.i	−0.00710791	+	0.0369338i
$470$		−	1.53924e6i		−	0.321411i
$471$	−64274.4	−	1.34598e6i	−0.0133501	−	0.279568i
$472$	829260.	+	478773.i	0.171331	+	0.0989179i
$473$	−1.84640e6	−	1.06602e6i	−0.379466	−	0.219085i
$474$	129306.	+	2.70781e6i	0.0264345	+	0.553571i
$475$			1.67184e6i			0.339985i
$476$	4.18236e6	+	3.62203e6i	0.846066	+	0.732715i
$477$	2.72136e6	−	1.93883e6i	0.547634	−	0.390161i
$478$	−2.07465e6	−	3.59339e6i	−0.415312	−	0.719341i
$479$	2.66802e6	−	4.62115e6i	0.531313	−	0.920262i	−0.468019	−	0.883719i	$-0.655032\pi$
$479$	2.66802e6	−	4.62115e6i	0.531313	−	0.920262i	0.999332	−	0.0365433i	$-0.0116347\pi$
$480$	−778391.	+	500370.i	−0.154204	+	0.0991260i
$481$	2.76602e6	−	1.59696e6i	0.545120	−	0.314725i
$482$	−1.04870e7			−2.05606
$483$	7.60475e6	+	1.09037e6i	1.48326	+	0.212669i
$484$	1.47334e6			0.285883
$485$	−744162.	+	429642.i	−0.143652	+	0.0829378i
$486$	1.79383e6	+	7.37549e6i	0.344501	+	1.41645i
$487$	−298272.	+	516621.i	−0.0569888	+	0.0987075i	−0.893112	−	0.449834i	$-0.851483\pi$
$487$	−298272.	+	516621.i	−0.0569888	+	0.0987075i	0.836124	+	0.548541i	$0.184817\pi$
$488$	73356.8	+	127058.i	0.0139441	+	0.0241519i
$489$	2.60449e6	−	5.05346e6i	0.492551	−	0.955689i
$490$	−979608.	+	141394.i	−0.184316	+	0.0266037i
$491$			4.61306e6i			0.863545i	0.901982	+	0.431773i	$0.142112\pi$
$491$			4.61306e6i			0.863545i	−0.901982	+	0.431773i	$0.857888\pi$
$492$	112087.	−	5352.45i	0.0208757	−	0.000996873i
$493$	2.69642e6	+	1.55678e6i	0.499655	+	0.288476i
$494$	2.03162e6	+	1.17296e6i	0.374564	+	0.216254i
$495$	709503.	+	323819.i	0.130149	+	0.0594004i
$496$		−	7.63169e6i		−	1.39289i
$497$	−3.53219e6	−	1.01966e7i	−0.641436	−	1.85167i
$498$	−4.18690e6	−	2.15788e6i	−0.756517	−	0.389900i
$499$	3.97823e6	+	6.89049e6i	0.715218	+	1.23879i	0.962876	+	0.269946i	$0.0870058\pi$
$499$	3.97823e6	+	6.89049e6i	0.715218	+	1.23879i	−0.247658	+	0.968848i	$0.579661\pi$
$500$	−796855.	+	1.38019e6i	−0.142546	+	0.246896i
$501$	1.17228e6	+	1.82363e6i	0.208659	+	0.324596i
$502$	−1.14308e7	+	6.59957e6i	−2.02449	+	1.16884i
$503$	−2.46101e6			−0.433704			−0.216852	−	0.976205i	$-0.569579\pi$
$503$	−2.46101e6			−0.433704			−0.216852	+	0.976205i	$0.569579\pi$
$504$	1.03447e6	+	98250.0i	0.181401	+	0.0172288i
$505$	−326400.			−0.0569537
$506$	−1.22009e7	+	7.04419e6i	−2.11843	+	1.22308i
$507$	−823381.	−	1.28088e6i	−0.142259	−	0.221303i
$508$	−1.11620e6	+	1.93331e6i	−0.191903	+	0.332386i
$509$	−1.32229e6	−	2.29027e6i	−0.226220	−	0.391825i	0.730464	−	0.682951i	$-0.239304\pi$
$509$	−1.32229e6	−	2.29027e6i	−0.226220	−	0.391825i	−0.956685	+	0.291125i	$0.905970\pi$
$510$	−967349.	−	498560.i	−0.164686	−	0.0848775i
$511$	4.13923e6	+	796594.i	0.701240	+	0.134954i
$512$			8.24357e6i			1.38976i
$513$	−1.61894e6	+	1.27407e6i	−0.271606	+	0.213747i
$514$	3.46035e6	+	1.99783e6i	0.577713	+	0.333543i
$515$	748115.	+	431924.i	0.124294	+	0.0717612i
$516$	2.65923e6	−	126986.i	0.439675	−	0.0209957i
$517$			1.17467e7i			1.93282i
$518$	6.41002e6	+	1.23361e6i	1.04963	+	0.202001i
$519$	−2.15669e6	+	4.18459e6i	−0.351454	+	0.681922i
$520$	61608.0	+	106708.i	0.00999146	+	0.0173057i
$521$	−2.36667e6	+	4.09919e6i	−0.381982	+	0.661613i	−0.991346	−	0.131278i	$-0.958092\pi$
$521$	−2.36667e6	+	4.09919e6i	−0.381982	+	0.661613i	0.609363	+	0.792891i	$0.291425\pi$
$522$	5.23895e6	−	501492.i	0.841526	−	0.0805541i
$523$	−9.21208e6	+	5.31860e6i	−1.47266	+	0.850242i	−0.999527	−	0.0307469i	$-0.990211\pi$
$523$	−9.21208e6	+	5.31860e6i	−1.47266	+	0.850242i	−0.473136	+	0.880989i	$0.656878\pi$
$524$	5.04233e6			0.802238
$525$	−5.76639e6	+	2.31113e6i	−0.913074	+	0.365954i
$526$	−3.73837e6			−0.589139
$527$	8.90353e6	−	5.14045e6i	1.39648	−	0.806260i
$528$	5.18598e6	−	3.33368e6i	0.809555	−	0.520403i
$529$	4.00754e6	−	6.94127e6i	0.622643	−	1.07845i
$530$	404883.	+	701278.i	0.0626095	+	0.108443i
$531$	−4.09322e6	−	5.74528e6i	−0.629982	−	0.884250i
$532$	830844.	+	2.39844e6i	0.127274	+	0.367409i
$533$			104595.i			0.0159475i
$534$	377358.	+	7.90232e6i	0.0572664	+	1.19923i
$535$	686996.	+	396637.i	0.103769	+	0.0599113i
$536$	39477.8	+	22792.5i	0.00593528	+	0.00342674i
$537$	−309551.	−	6.48237e6i	−0.0463230	−	0.970059i
$538$		−	149757.i		−	0.0223064i
$539$	7.47590e6	−	1.07905e6i	1.10839	−	0.159982i
$540$	−963900.	+	138932.i	−0.142248	+	0.0205030i
$541$	−3.09119e6	−	5.35410e6i	−0.454080	−	0.786490i	0.544554	−	0.838726i	$-0.316699\pi$
$541$	−3.09119e6	−	5.35410e6i	−0.454080	−	0.786490i	−0.998635	+	0.0522351i	$0.983365\pi$
$542$	7.56269e6	−	1.30990e7i	1.10580	−	1.91531i
$543$	4.71531e6	−	3.03113e6i	0.686295	−	0.441168i
$544$	−8.53373e6	+	4.92695e6i	−1.23635	+	0.713807i
$545$	−894750.			−0.129036
$546$	−1.23720e6	+	8.62882e6i	−0.177606	+	1.23871i
$547$	−3.13043e6			−0.447337			−0.223669	−	0.974665i	$-0.571803\pi$
$547$	−3.13043e6			−0.447337			−0.223669	+	0.974665i	$0.571803\pi$
$548$	−3.42780e6	+	1.97904e6i	−0.487600	+	0.281516i
$549$	−102991.	−	1.07592e6i	−0.0145838	−	0.152353i
$550$	5.69612e6	−	9.86597e6i	0.802921	−	1.39070i
$551$	714207.	+	1.23704e6i	0.100218	+	0.173582i
$552$	895478.	−	1.73748e6i	0.125086	−	0.242702i
$553$	−2.06672e6	−	1.78983e6i	−0.287388	−	0.248886i
$554$		−	1.28458e7i		−	1.77823i
$555$	−678970.	+	32422.7i	−0.0935660	+	0.00446803i
$556$	3.10900e6	+	1.79498e6i	0.426514	+	0.246248i
$557$	4.25099e6	+	2.45431e6i	0.580567	+	0.335190i	0.761358	−	0.648331i	$-0.224533\pi$
$557$	4.25099e6	+	2.45431e6i	0.580567	+	0.335190i	−0.180792	+	0.983521i	$0.557866\pi$
$558$	7.21538e6	−	1.58092e7i	0.981011	−	2.14944i
$559$			2.48149e6i			0.335879i
$560$	153969.	−	800047.i	0.0207474	−	0.107807i
$561$	7.38235e6	+	3.80478e6i	0.990347	+	0.510413i
$562$	−3.82395e6	−	6.62327e6i	−0.510706	−	0.884569i
$563$	−6.63164e6	+	1.14863e7i	−0.881759	+	1.52725i	−0.0323757	+	0.999476i	$0.510307\pi$
$563$	−6.63164e6	+	1.14863e7i	−0.881759	+	1.52725i	−0.849384	+	0.527776i	$0.823026\pi$
$564$	−7.93158e6	−	1.23386e7i	−1.04993	−	1.63331i
$565$	−172074.	+	99347.0i	−0.0226774	+	0.0130928i
$566$	7.46868e6			0.979947
$567$	−6.63245e6	−	3.82270e6i	−0.866395	−	0.499359i
$568$	−2.74557e6			−0.357077
$569$	−8.53029e6	+	4.92496e6i	−1.10454	+	0.637709i	−0.937411	−	0.348226i	$-0.886784\pi$
$569$	−8.53029e6	+	4.92496e6i	−1.10454	+	0.637709i	−0.167133	+	0.985934i	$0.553451\pi$
$570$	−269973.	−	419979.i	−0.0348043	−	0.0541427i
$571$	90932.0	−	157499.i	0.0116715	−	0.0202156i	−0.860131	−	0.510074i	$-0.829618\pi$
$571$	90932.0	−	157499.i	0.0116715	−	0.0202156i	0.871802	+	0.489858i	$0.162951\pi$
$572$	−4.23147e6	−	7.32912e6i	−0.540756	−	0.936616i
$573$	4.59977e6	+	2.37066e6i	0.585260	+	0.301636i
$574$	−139944.	+	161593.i	−0.0177286	+	0.0204712i
$575$			1.16858e7i			1.47397i
$576$	−4.07451e6	+	8.92745e6i	−0.511705	+	1.12117i
$577$	−1.37148e6	−	791825.i	−0.171495	−	0.0990124i	0.411796	−	0.911276i	$-0.364902\pi$
$577$	−1.37148e6	−	791825.i	−0.171495	−	0.0990124i	−0.583290	+	0.812264i	$0.698235\pi$
$578$	103558.	+	59789.2i	0.0128933	+	0.00744394i
$579$	117979.	−	5633.84i	0.0146255	−	0.000698406i
$580$			675230.i			0.0833454i
$581$	4.48873e6	−	1.55494e6i	0.551674	−	0.191106i
$582$	−7.08584e6	+	1.37485e7i	−0.867129	+	1.68248i
$583$	−3.08988e6	−	5.35182e6i	−0.376504	−	0.652124i
$584$	536236.	−	928787.i	0.0650614	−	0.112690i
$585$	−86496.5	−	903604.i	−0.0104498	−	0.109166i
$586$	−229551.	+	132531.i	−0.0276144	+	0.0159432i
$587$	−9.90757e6			−1.18678			−0.593392	−	0.804913i	$-0.702212\pi$
$587$	−9.90757e6			−1.18678			−0.593392	+	0.804913i	$0.702212\pi$
$588$	−7.12399e6	+	6.18127e6i	−0.849729	+	0.737283i
$589$	4.71659e6			0.560196
$590$	1.48053e6	−	854782.i	0.175100	−	0.101094i
$591$	8.30266e6	−	5.33716e6i	0.977796	−	0.628553i
$592$	−2.68664e6	+	4.65340e6i	−0.315069	+	0.545715i
$593$	4.40834e6	+	7.63547e6i	0.514800	+	0.891659i	0.999853	+	0.0171744i	$0.00546705\pi$
$593$	4.40834e6	+	7.63547e6i	0.514800	+	0.891659i	−0.485053	+	0.874485i	$0.661200\pi$
$594$	1.38947e7	−	2.00272e6i	1.61579	−	0.232892i
$595$	1.03708e6	−	359257.i	0.120094	−	0.0416018i
$596$		−	1.31668e7i		−	1.51832i
$597$	−514826.	−	1.07811e7i	−0.0591187	−	1.23802i
$598$	1.42006e7	+	8.19875e6i	1.62388	+	0.937550i
$599$	−1.05247e7	−	6.07646e6i	−1.19852	−	0.691964i	−0.238292	−	0.971194i	$-0.576588\pi$
$599$	−1.05247e7	−	6.07646e6i	−1.19852	−	0.691964i	−0.960224	+	0.279230i	$0.909921\pi$
$600$	75392.0	+	1.57880e6i	0.00854963	+	0.179039i
$601$			8.37919e6i			0.946272i	0.880990	+	0.473136i	$0.156878\pi$
$601$			8.37919e6i			0.946272i	−0.880990	+	0.473136i	$0.843122\pi$
$602$	−3.32014e6	+	3.83376e6i	−0.373392	+	0.431156i
$603$	−194862.	−	273510.i	−0.0218240	−	0.0306324i
$604$	807714.	+	1.39900e6i	0.0900877	+	0.156036i
$605$	146135.	−	253113.i	0.0162318	−	0.0281143i
$606$	−4.94216e6	+	3.17695e6i	−0.546683	+	0.351422i
$607$	1.28379e7	−	7.41195e6i	1.41423	−	0.816508i	0.418450	−	0.908240i	$-0.362574\pi$
$607$	1.28379e7	−	7.41195e6i	1.41423	−	0.816508i	0.995784	+	0.0917316i	$0.0292402\pi$
$608$	−4.52070e6			−0.495960
$609$	−3.27942e6	+	4.17347e6i	−0.358305	+	0.455989i
$610$	261936.			0.0285017
$611$	1.18403e7	−	6.83603e6i	1.28310	−	0.740800i
$612$	−1.03234e7	+	988192.i	−1.11415	+	0.106650i
$613$	−822841.	+	1.42520e6i	−0.0884433	+	0.153188i	−0.906853	−	0.421446i	$-0.861523\pi$
$613$	−822841.	+	1.42520e6i	−0.0884433	+	0.153188i	0.818410	+	0.574635i	$0.194856\pi$
$614$	8.74269e6	+	1.51428e7i	0.935889	+	1.62101i
$615$	10198.0	−	19786.9i	0.00108724	−	0.00210956i
$616$	363188.	−	1.88718e6i	0.0385638	−	0.200383i
$617$			3.69950e6i			0.391228i	0.980681	+	0.195614i	$0.0626700\pi$
$617$			3.69950e6i			0.391228i	−0.980681	+	0.195614i	$0.937330\pi$
$618$	1.55316e7	−	741676.i	1.63585	−	0.0781165i
$619$	1.51109e6	+	872431.i	0.158513	+	0.0915175i	0.577158	−	0.816632i	$-0.304162\pi$
$619$	1.51109e6	+	872431.i	0.158513	+	0.0915175i	−0.418645	+	0.908150i	$0.637495\pi$
$620$	1.93089e6	+	1.11480e6i	0.201733	+	0.116471i
$621$	−1.13161e7	+	8.90550e6i	−1.17752	+	0.926679i
$622$		−	390086.i		−	0.0404282i
$623$	−6.03139e6	−	5.22334e6i	−0.622583	−	0.539173i
$624$	−6.37824e6	−	3.28727e6i	−0.655752	−	0.337967i
$625$	−4.64505e6	−	8.04546e6i	−0.475653	−	0.823855i
$626$	1.57329e6	−	2.72502e6i	0.160463	−	0.277929i
$627$	2.06031e6	+	3.20508e6i	0.209297	+	0.325589i
$628$	2.69503e6	−	1.55598e6i	0.272687	−	0.157436i
$629$	−7.23852e6			−0.729497
$630$	1.07536e6	−	1.51175e6i	0.107945	−	0.151750i
$631$	−6.96509e6			−0.696391			−0.348196	−	0.937422i	$-0.613205\pi$
$631$	−6.96509e6			−0.696391			−0.348196	+	0.937422i	$0.613205\pi$
$632$	−602422.	+	347809.i	−0.0599941	+	0.0346376i
$633$	−9.41332e6	−	1.46437e7i	−0.933756	−	1.45258i
$634$	−1.01377e7	+	1.75590e7i	−1.00165	+	1.73491i
$635$	221424.	+	383517.i	0.0217916	+	0.0377442i
$636$	6.85920e6	+	3.53515e6i	0.672405	+	0.346549i
$637$	−5.43827e6	−	6.90752e6i	−0.531021	−	0.674487i
$638$		−	9.73351e6i		−	0.946711i
$639$	1.84008e7	+	8.39816e6i	1.78272	+	0.813640i
$640$	−414528.	−	239328.i	−0.0400040	−	0.0230963i
$641$	−3.62836e6	−	2.09483e6i	−0.348791	−	0.201375i	0.315362	−	0.948972i	$-0.397874\pi$
$641$	−3.62836e6	−	2.09483e6i	−0.348791	−	0.201375i	−0.664153	+	0.747597i	$0.731208\pi$
$642$	1.42627e7	−	681083.i	1.36573	−	0.0652172i
$643$		−	1.72926e7i		−	1.64942i	−0.565553	−	0.824712i	$-0.691337\pi$
$643$		−	1.72926e7i		−	1.64942i	0.565553	−	0.824712i	$-0.308663\pi$
$644$	5.80744e6	+	1.67646e7i	0.551785	+	1.59287i
$645$	241944.	−	469440.i	0.0228990	−	0.0444305i
$646$	−2.65832e6	−	4.60435e6i	−0.250626	−	0.434097i
$647$	−1.35347e6	+	2.34428e6i	−0.127113	+	0.220165i	−0.922557	−	0.385861i	$-0.873904\pi$
$647$	−1.35347e6	+	2.34428e6i	−0.127113	+	0.220165i	0.795444	+	0.606027i	$0.207238\pi$
$648$	−1.47139e6	+	1.27617e6i	−0.137655	+	0.119391i
$649$	−1.12987e7	+	6.52329e6i	−1.05297	+	0.607932i
$650$	−1.32595e7			−1.23096
$651$	6.52017e6	+	1.62682e7i	0.602985	+	1.50448i
$652$	1.31293e7			1.20954
$653$	299872.	−	173131.i	0.0275203	−	0.0158889i	−0.486177	−	0.873861i	$-0.661609\pi$
$653$	299872.	−	173131.i	0.0275203	−	0.0158889i	0.513697	+	0.857972i	$0.328276\pi$
$654$	−1.35478e7	+	8.70887e6i	−1.23858	+	0.796191i
$655$	500132.	−	866253.i	0.0455492	−	0.0788936i
$656$	−87982.4	−	152390.i	−0.00798245	−	0.0138260i
$657$	−6.43483e6	+	4.58448e6i	−0.581599	+	0.414359i
$658$	2.74390e7	+	5.28064e6i	2.47061	+	0.475469i
$659$		−	1.77258e7i		−	1.58999i	−0.606619	−	0.794993i	$-0.707474\pi$
$659$		−	1.77258e7i		−	1.58999i	0.606619	−	0.794993i	$-0.292526\pi$
$660$	85910.4	+	1.79907e6i	0.00767690	+	0.160763i
$661$	8.33971e6	+	4.81493e6i	0.742416	+	0.428634i	0.822947	−	0.568118i	$-0.192328\pi$
$661$	8.33971e6	+	4.81493e6i	0.742416	+	0.428634i	−0.0805313	+	0.996752i	$0.525662\pi$
$662$	7.28626e6	+	4.20672e6i	0.646189	+	0.373077i
$663$	−461071.	−	9.65538e6i	−0.0407365	−	0.853072i
$664$		−	1.20865e6i		−	0.106385i
$665$	494451.	+	95157.2i	0.0433580	+	0.00834425i
$666$	−9.96499e6	+	7.09954e6i	−0.870545	+	0.620219i
$667$	4.99217e6	+	8.64669e6i	0.434485	+	0.752550i
$668$	−2.50330e6	+	4.33584e6i	−0.217056	+	0.375952i
$669$	−1.99942e6	+	1.28528e6i	−0.172718	+	0.111028i
$670$	70482.0	−	40692.8i	0.00606584	−	0.00350212i
$671$	−1.99897e6			−0.171396
$672$	−6.24936e6	−	1.55925e7i	−0.533841	−	1.33196i
$673$	685799.			0.0583659			0.0291830	−	0.999574i	$-0.490709\pi$
$673$	685799.			0.0583659			0.0291830	+	0.999574i	$0.490709\pi$
$674$	−1.71099e6	+	987843.i	−0.145077	+	0.0837603i
$675$	4.32397e6	−	1.08117e7i	0.365277	−	0.913345i
$676$	1.75826e6	−	3.04539e6i	0.147984	−	0.256316i
$677$	1.05454e7	+	1.82651e7i	0.884282	+	1.53162i	0.846534	+	0.532334i	$0.178685\pi$
$677$	1.05454e7	+	1.82651e7i	0.884282	+	1.53162i	0.0377479	+	0.999287i	$0.487982\pi$
$678$	−1.63847e6	+	3.17910e6i	−0.136888	+	0.265601i
$679$	−5.10597e6	−	1.47397e7i	−0.425015	−	1.22691i
$680$		−	279250.i		−	0.0231590i
$681$	−1.47762e7	+	705605.i	−1.22094	+	0.0583034i
$682$	−2.78339e7	−	1.60699e7i	−2.29147	−	1.32298i
$683$	4.79268e6	+	2.76706e6i	0.393121	+	0.226969i	0.683512	−	0.729940i	$-0.260452\pi$
$683$	4.79268e6	+	2.76706e6i	0.393121	+	0.226969i	−0.290390	+	0.956908i	$0.593785\pi$
$684$	−4.32824e6	−	1.97542e6i	−0.353729	−	0.161443i
$685$			785177.i			0.0639353i
$686$	840182.	−	1.79479e7i	0.0681653	−	1.45614i
$687$	7.86624e6	+	4.05417e6i	0.635880	+	0.327725i
$688$	−2.08736e6	−	3.61541e6i	−0.168123	−	0.291197i
$689$	−3.59632e6	+	6.22900e6i	−0.288609	+	0.499885i
$690$	−1.88706e6	−	2.93557e6i	−0.150891	−	0.234731i
$691$	9.77690e6	−	5.64469e6i	0.778944	−	0.449723i	−0.0571122	−	0.998368i	$-0.518189\pi$
$691$	9.77690e6	−	5.64469e6i	0.778944	−	0.449723i	0.836056	+	0.548645i	$0.184856\pi$
$692$	−1.08719e7			−0.863057
$693$	−8.20660e6	+	1.15369e7i	−0.649128	+	0.912552i
$694$	3.18046e7			2.50663
$695$	616741.	−	356076.i	0.0484329	−	0.0279628i
$696$	730246.	+	1.13599e6i	0.0571408	+	0.0888900i
$697$	118524.	−	205290.i	0.00924111	−	0.0160061i
$698$	−7.86278e6	−	1.36187e7i	−0.610855	−	1.05803i
$699$	−7.68338e6	−	3.95992e6i	−0.594784	−	0.306545i
$700$	−1.08451e7	−	9.39211e6i	−0.836541	−	0.724466i
$701$		−	1.08706e7i		−	0.835525i	−0.908556	−	0.417763i	$-0.862814\pi$
$701$		−	1.08706e7i		−	0.835525i	0.908556	−	0.417763i	$-0.137186\pi$
$702$	−1.01047e7	−	1.28400e7i	−0.773895	−	0.983379i
$703$	−2.87593e6	−	1.66042e6i	−0.219477	−	0.126715i
$704$	1.57178e7	+	9.07466e6i	1.19525	+	0.690079i
$705$	−2.90643e6	+	138790.i	−0.220235	+	0.0105168i
$706$			884524.i			0.0667879i
$707$	1.11978e6	−	5.81853e6i	0.0842525	−	0.437789i
$708$	7.46334e6	−	1.44810e7i	0.559564	−	1.08571i
$709$	5.17640e6	+	8.96579e6i	0.386734	+	0.669843i	0.992008	−	0.126174i	$-0.0402698\pi$
$709$	5.17640e6	+	8.96579e6i	0.386734	+	0.669843i	−0.605274	+	0.796017i	$0.706936\pi$
$710$	−2.45091e6	+	4.24510e6i	−0.182466	+	0.316040i
$711$	5.10131e6	−	488317.i	0.378449	−	0.0362266i
$712$	−1.75807e6	+	1.01502e6i	−0.129968	+	0.0750371i
$713$	3.29681e7			2.42868
$714$	1.22062e7	−	1.55339e7i	0.896055	−	1.14034i
$715$	−1.67882e6			−0.122811
$716$	1.29795e7	−	7.49373e6i	0.946185	−	0.546280i
$717$	−6.59807e6	+	4.24141e6i	−0.479313	+	0.308115i
$718$	−1.25892e7	+	2.18052e7i	−0.911355	+	1.57851i
$719$	−5.47378e6	−	9.48087e6i	−0.394880	−	0.683953i	0.598206	−	0.801343i	$-0.295881\pi$
$719$	−5.47378e6	−	9.48087e6i	−0.394880	−	0.683953i	−0.993086	+	0.117390i	$0.962547\pi$
$720$	886108.	+	1.24375e6i	0.0637024	+	0.0894133i
$721$	−1.02662e7	+	1.18544e7i	−0.735480	+	0.849259i
$722$			1.79793e7i			1.28360i
$723$	945595.	+	1.98019e7i	0.0672759	+	1.40884i
$724$	1.12110e7	+	6.47270e6i	0.794877	+	0.458922i
$725$	−6.99195e6	−	4.03680e6i	−0.494030	−	0.285228i
$726$	−250935.	−	5.25487e6i	−0.0176693	−	0.370016i
$727$			741427.i			0.0520274i	0.999662	+	0.0260137i	$0.00828136\pi$
$727$			741427.i			0.0520274i	−0.999662	+	0.0260137i	$0.991719\pi$
$728$	−2.11358e6	+	732165.i	−0.147805	+	0.0512012i
$729$	1.37648e7	−	4.05219e6i	0.959296	−	0.282404i
$730$	−957372.	−	1.65822e6i	−0.0664926	−	0.115169i
$731$	2.81195e6	−	4.87044e6i	0.194632	−	0.337113i
$732$	2.09969e6	−	1.34974e6i	0.144836	−	0.0931046i
$733$	7.10931e6	−	4.10456e6i	0.488728	−	0.282167i	−0.235318	−	0.971918i	$-0.575613\pi$
$733$	7.10931e6	−	4.10456e6i	0.488728	−	0.282167i	0.724047	+	0.689751i	$0.242280\pi$
$734$	2.12670e7			1.45702
$735$	355314.	+	1.83697e6i	0.0242602	+	0.125425i
$736$	−3.15988e7			−2.15019
$737$	−537885.	+	310548.i	−0.0364772	+	0.0210601i
$738$	−38180.6	−	398862.i	−0.00258049	−	0.0269577i
$739$	−2.01959e6	+	3.49803e6i	−0.136035	+	0.235620i	−0.925993	−	0.377542i	$-0.876769\pi$
$739$	−2.01959e6	+	3.49803e6i	−0.136035	+	0.235620i	0.789957	+	0.613162i	$0.210103\pi$
$740$	−784900.	−	1.35949e6i	−0.0526908	−	0.0912632i
$741$	2.03162e6	−	3.94193e6i	0.135924	−	0.263732i
$742$	−1.38903e7	+	4.81173e6i	−0.926192	+	0.320842i
$743$			1.28088e7i			0.851208i	0.904909	+	0.425604i	$0.139938\pi$
$743$			1.28088e7i			0.851208i	−0.904909	+	0.425604i	$0.860062\pi$
$744$	4.45411e6	−	212696.i	0.295005	−	0.0140873i
$745$	−2.26200e6	−	1.30597e6i	−0.149315	−	0.0862069i
$746$	−1.56316e7	−	9.02488e6i	−1.02838	−	0.593738i
$747$	−3.69704e6	+	8.10038e6i	−0.242411	+	0.531134i
$748$			1.91799e7i			1.25341i
$749$	−9.42746e6	+	1.08859e7i	−0.614031	+	0.709022i
$750$	5.05838e6	+	2.60703e6i	0.328366	+	0.169236i
$751$	8.46352e6	+	1.46593e7i	0.547585	+	0.948445i	0.998439	+	0.0558471i	$0.0177860\pi$
$751$	8.46352e6	+	1.46593e7i	0.547585	+	0.948445i	−0.450855	+	0.892597i	$0.648881\pi$
$752$	−1.15006e7	+	1.99195e7i	−0.741608	+	1.28450i
$753$	1.34922e7	+	2.09888e7i	0.867150	+	1.34897i
$754$	−9.81107e6	+	5.66443e6i	−0.628475	+	0.362850i
$755$	320457.			0.0204599
$756$	830182.	−	1.76595e7i	0.0528286	−	1.12376i
$757$	1.58905e7			1.00785			0.503927	−	0.863746i	$-0.331888\pi$
$757$	1.58905e7			1.00785			0.503927	+	0.863746i	$0.331888\pi$
$758$	−3.94460e7	+	2.27742e7i	−2.49362	+	1.43969i
$759$	1.44011e7	+	2.24029e7i	0.907387	+	1.41156i
$760$	64056.0	−	110948.i	0.00402278	−	0.00696765i
$761$	−1.13990e7	−	1.97436e7i	−0.713518	−	1.23585i	−0.963528	−	0.267607i	$-0.913767\pi$
$761$	−1.13990e7	−	1.97436e7i	−0.713518	−	1.23585i	0.250010	−	0.968243i	$-0.419566\pi$
$762$	7.08555e6	+	3.65181e6i	0.442065	+	0.227835i
$763$	3.06960e6	−	1.59501e7i	0.190885	−	0.991866i
$764$			1.19505e7i			0.740720i
$765$	−854171.	+	1.87153e6i	−0.0527705	+	0.115623i
$766$	−2.75301e7	−	1.58945e7i	−1.69526	−	0.978758i
$767$	1.31505e7	+	7.59247e6i	0.807152	+	0.466010i
$768$	1.15159e7	−	549914.i	0.704519	−	0.0336428i
$769$			1.52141e7i			0.927747i	0.885901	+	0.463874i	$0.153541\pi$
$769$			1.52141e7i			0.927747i	−0.885901	+	0.463874i	$0.846459\pi$
$770$	−2.59368e6	−	2.24619e6i	−0.157648	−	0.136528i
$771$	3.46035e6	−	6.71407e6i	0.209645	−	0.406771i
$772$	136386.	+	236227.i	0.00823619	+	0.0142655i
$773$	7.82289e6	−	1.35496e7i	0.470889	−	0.815604i	−0.528557	−	0.848898i	$-0.677267\pi$
$773$	7.82289e6	−	1.35496e7i	0.470889	−	0.815604i	0.999446	+	0.0332943i	$0.0105999\pi$
$774$	−905826.	−	9.46291e6i	−0.0543491	−	0.567770i
$775$	−2.30873e7	+	1.33294e7i	−1.38076	+	0.797183i
$776$	−3.96886e6			−0.236598
$777$	1.75135e6	−	1.22148e7i	0.104069	−	0.725828i
$778$	−2.93155e6			−0.173639
$779$	94181.2	−	54375.5i	0.00556058	−	0.00321040i
$780$	1.76341e6	−	1.13356e6i	0.103781	−	0.0667128i
$781$	1.87042e7	−	3.23966e7i	1.09726	−	1.90052i
$782$	−1.85812e7	−	3.21835e7i	−1.08657	−	1.88199i
$783$	−1.41932e6	−	9.84710e6i	−0.0827322	−	0.573989i
$784$	1.37337e7	+	5.48942e6i	0.797991	+	0.318960i
$785$		−	617328.i		−	0.0357554i
$786$	−858797.	−	1.79842e7i	−0.0495832	−	1.03833i
$787$	4.76244e6	+	2.74960e6i	0.274090	+	0.158246i	0.630745	−	0.775990i	$-0.282750\pi$
$787$	4.76244e6	+	2.74960e6i	0.274090	+	0.158246i	−0.356655	+	0.934236i	$0.616083\pi$
$788$	1.97403e7	+	1.13970e7i	1.13250	+	0.653848i
$789$	337081.	+	7.05889e6i	0.0192771	+	0.403686i
$790$			1.24193e6i			0.0707991i
$791$	−1.18066e6	−	3.40828e6i	−0.0670942	−	0.193684i
$792$	2.09018e6	+	2.93380e6i	0.118405	+	0.166195i
$793$	1.16330e6	+	2.01490e6i	0.0656917	+	0.113781i
$794$	1.72458e7	−	2.98706e7i	0.970806	−	1.68148i
$795$	1.28766e6	−	827744.i	0.0722579	−	0.0464492i
$796$	2.15867e7	−	1.24631e7i	1.20755	−	0.697177i
$797$	−7.06454e6			−0.393947			−0.196974	−	0.980409i	$-0.563111\pi$
$797$	−7.06454e6			−0.393947			−0.196974	+	0.980409i	$0.563111\pi$
$798$	8.41289e6	−	3.37183e6i	0.467668	−	0.187438i
$799$	−3.09856e7			−1.71709
$800$	2.21284e7	−	1.27758e7i	1.22243	−	0.705771i
$801$	1.48873e7	−	1.42507e6i	0.819853	−	0.0784795i
$802$	6.80088e6	−	1.17795e7i	0.373361	−	0.646681i
$803$	7.30621e6	+	1.26547e7i	0.399856	+	0.692570i
$804$	355300.	−	689384.i	0.0193845	−	0.0376115i
$805$	3.45612e6	+	665130.i	0.187974	+	0.0361757i
$806$			3.74076e7i			2.02826i
$807$	−282774.	+	13503.3i	−0.0152847	+	0.000729886i
$808$	−1.30560e6	−	753789.i	−0.0703529	−	0.0406182i
$809$	−2.28941e7	−	1.32179e7i	−1.22985	−	0.710055i	−0.262852	−	0.964836i	$-0.584663\pi$
$809$	−2.28941e7	−	1.32179e7i	−1.22985	−	0.710055i	−0.966999	+	0.254782i	$0.917996\pi$
$810$	659691.	+	3.41423e6i	0.0353287	+	0.182844i
$811$		−	3.37600e7i		−	1.80240i	−0.433406	−	0.901199i	$-0.642689\pi$
$811$		−	3.37600e7i		−	1.80240i	0.433406	−	0.901199i	$-0.357311\pi$
$812$	−1.20369e7	−	2.31650e6i	−0.640655	−	0.123294i
$813$	−2.54157e7	−	1.30990e7i	−1.34858	−	0.695042i
$814$	1.13144e7	+	1.95971e7i	0.598510	+	1.03665i
$815$	1.30225e6	−	2.25556e6i	0.0686751	−	0.118949i
$816$	8.79360e6	+	1.36796e7i	0.462318	+	0.719197i
$817$	2.23442e6	−	1.29005e6i	0.117114	−	0.0676161i
$818$	−7.91195e6			−0.413428
$819$	1.64047e7	+	1.55806e6i	0.854593	+	0.0811663i
$820$	51408.0			0.00266991
$821$	−4.24377e6	+	2.45014e6i	−0.219732	+	0.126862i	−0.605826	−	0.795597i	$-0.707157\pi$
$821$	−4.24377e6	+	2.45014e6i	−0.219732	+	0.126862i	0.386094	+	0.922459i	$0.373824\pi$
$822$	7.64236e6	+	1.18887e7i	0.394501	+	0.613698i
$823$	−6.56892e6	+	1.13777e7i	−0.338061	+	0.585538i	−0.984068	−	0.177793i	$-0.943104\pi$
$823$	−6.56892e6	+	1.13777e7i	−0.338061	+	0.585538i	0.646007	+	0.763331i	$0.276438\pi$
$824$	1.99497e6	+	3.45539e6i	0.102357	+	0.177288i
$825$	−1.91428e7	−	9.86597e6i	−0.979198	−	0.504667i
$826$	1.01584e7	+	2.93249e7i	0.518056	+	1.49550i
$827$		−	5.49577e6i		−	0.279424i	−0.990192	−	0.139712i	$-0.955382\pi$
$827$		−	5.49577e6i		−	0.279424i	0.990192	−	0.139712i	$-0.0446178\pi$
$828$	−3.02535e7	−	1.38078e7i	−1.53356	−	0.699920i
$829$	−1.06198e7	−	6.13134e6i	−0.536697	−	0.309862i	0.207042	−	0.978332i	$-0.433616\pi$
$829$	−1.06198e7	−	6.13134e6i	−0.536697	−	0.309862i	−0.743739	+	0.668470i	$0.766950\pi$
$830$	−1.86878e6	−	1.07894e6i	−0.0941590	−	0.0543628i
$831$	−2.42558e7	+	1.15828e6i	−1.21847	+	0.0581851i
$832$		−	2.11240e7i		−	1.05796i
$833$	2.84633e6	+	1.97200e7i	0.142126	+	0.984676i
$834$	5.87255e6	−	1.13944e7i	0.292356	−	0.567253i
$835$	496587.	+	860114.i	0.0246479	+	0.0426913i
$836$	−4.39961e6	+	7.62034e6i	−0.217720	+	0.377102i
$837$	−3.05020e7	−	1.21988e7i	−1.50493	−	0.601870i
$838$	3.08626e7	−	1.78186e7i	1.51818	−	0.876521i
$839$	1.85278e7			0.908696			0.454348	−	0.890824i	$-0.349872\pi$
$839$	1.85278e7			0.908696			0.454348	+	0.890824i	$0.349872\pi$
$840$	471226.	+	67564.2i	0.0230426	+	0.00330383i
$841$	1.36131e7			0.663692
$842$	1.83800e7	−	1.06117e7i	0.893442	−	0.515829i
$843$	−1.21614e7	+	7.81768e6i	−0.589408	+	0.378887i
$844$	2.01013e7	−	3.48165e7i	0.971334	−	1.68240i
$845$	−348791.	−	604124.i	−0.0168044	−	0.0291061i
$846$	−4.26566e7	+	3.03906e7i	−2.04909	+	1.45987i
$847$	4.01075e6	+	3.47341e6i	0.192095	+	0.166359i
$848$		−	1.21005e7i		−	0.577848i
$849$	−673436.	−	1.41026e7i	−0.0320647	−	0.671473i
$850$	2.60245e7	+	1.50252e7i	1.23548	+	0.713303i
$851$	−2.01022e7	−	1.16060e7i	−0.951522	−	0.549362i
$852$	2.22806e6	+	4.66583e7i	0.105155	+	2.20206i
$853$			1.20060e7i			0.564970i	0.959272	+	0.282485i	$0.0911587\pi$
$853$			1.20060e7i			0.564970i	−0.959272	+	0.282485i	$0.908841\pi$
$854$	−898620.	+	4.66937e6i	−0.0421630	+	0.219085i
$855$	−768672.	+	547639.i	−0.0359605	+	0.0256200i
$856$	1.83199e6	+	3.17310e6i	0.0854551	+	0.148013i
$857$	−5.24169e6	+	9.07888e6i	−0.243792	+	0.422260i	−0.961791	−	0.273784i	$-0.911725\pi$
$857$	−5.24169e6	+	9.07888e6i	−0.243792	+	0.422260i	0.717999	+	0.696044i	$0.245058\pi$
$858$	−2.54197e7	+	1.63404e7i	−1.17883	+	0.757784i
$859$	−1.39460e7	+	8.05175e6i	−0.644864	+	0.372312i	−0.786486	−	0.617608i	$-0.788102\pi$
$859$	−1.39460e7	+	8.05175e6i	−0.644864	+	0.372312i	0.141622	+	0.989921i	$0.454768\pi$
$860$	1.21964e6			0.0562323
$861$	317743.	+	249675.i	0.0146073	+	0.0114780i
$862$	−1.21350e7			−0.556252
$863$	3.34044e6	−	1.92860e6i	0.152678	−	0.0881487i	−0.421715	−	0.906729i	$-0.638572\pi$
$863$	3.34044e6	−	1.92860e6i	0.152678	−	0.0881487i	0.574393	+	0.818580i	$0.305238\pi$
$864$	2.92352e7	+	1.16921e7i	1.33236	+	0.532855i
$865$	−1.07834e6	+	1.86775e6i	−0.0490024	+	0.0848746i
$866$	2.86512e7	+	4.96254e7i	1.29822	+	2.24858i
$867$	103558.	−	200932.i	0.00467881	−	0.00907822i
$868$	−2.64970e7	+	3.05962e7i	−1.19371	+	1.37838i
$869$		−	9.47779e6i		−	0.425753i
$870$	2.40831e6	−	115003.i	0.107873	−	0.00515125i
$871$	626046.	+	361448.i	0.0279615	+	0.0161436i
$872$	−3.57900e6	−	2.06634e6i	−0.159393	−	0.0920258i
$873$	2.65993e7	+	1.21400e7i	1.18123	+	0.539116i
$874$		−	1.70490e7i		−	0.754956i
$875$	−5.42304e6	+	1.87860e6i	−0.239454	+	0.0829494i
$876$	−1.62190e7	−	8.35909e6i	−0.714108	−	0.368043i
$877$	−5.52497e6	−	9.56952e6i	−0.242566	−	0.420137i	0.718878	−	0.695136i	$-0.244656\pi$
$877$	−5.52497e6	−	9.56952e6i	−0.242566	−	0.420137i	−0.961445	+	0.274999i	$0.911323\pi$
$878$	2.47985e7	−	4.29523e7i	1.08565	−	1.88040i
$879$	270947.	+	421494.i	0.0118280	+	0.0184001i
$880$	2.44596e6	−	1.41218e6i	0.106474	−	0.0614727i
$881$	3.62127e7			1.57188			0.785942	−	0.618300i	$-0.212178\pi$
$881$	3.62127e7			1.57188			0.785942	+	0.618300i	$0.212178\pi$
$882$	2.32598e7	+	2.43560e7i	1.00678	+	1.05423i
$883$	−9.90406e6			−0.427476			−0.213738	−	0.976891i	$-0.568564\pi$
$883$	−9.90406e6			−0.427476			−0.213738	+	0.976891i	$0.568564\pi$
$884$	1.93328e7	−	1.11618e7i	0.832076	−	0.480400i
$885$	−1.74752e6	−	2.71849e6i	−0.0750004	−	0.116673i
$886$	−1.31429e7	+	2.27642e7i	−0.562481	+	0.974245i
$887$	1.13862e7	+	1.97216e7i	0.485927	+	0.841651i	0.999869	−	0.0161741i	$-0.00514859\pi$
$887$	1.13862e7	+	1.97216e7i	0.485927	+	0.841651i	−0.513942	+	0.857825i	$0.671815\pi$
$888$	−2.79076e6	−	1.43832e6i	−0.118765	−	0.0612102i
$889$	−7.59635e6	+	2.63145e6i	−0.322367	+	0.111671i
$890$			3.62436e6i			0.153376i
$891$	−5.03445e6	−	2.60558e7i	−0.212451	−	1.09954i
$892$	−4.75378e6	−	2.74460e6i	−0.200045	−	0.115496i
$893$	−1.23108e7	−	7.10766e6i	−0.516605	−	0.298262i
$894$	−4.69613e7	+	2.24253e6i	−1.96515	+	0.0938416i
$895$		−	2.97311e6i		−	0.124066i
$896$	5.68846e6	−	6.56847e6i	0.236714	−	0.273334i
$897$	1.42006e7	−	2.75533e7i	0.589287	−	1.14338i
$898$	−2.10413e7	−	3.64447e7i	−0.870728	−	1.50815i
$899$	−1.13886e7	+	1.97257e7i	−0.469973	+	0.814017i
$900$	2.67690e7	−	2.56243e6i	1.10160	−	0.105450i
$901$	1.41171e7	−	8.15049e6i	0.579338	−	0.334481i
$902$	−741052.			−0.0303272
$903$	7.53838e6	+	5.92349e6i	0.307651	+	0.241745i
$904$	−917728.			−0.0373502
$905$	2.22397e6	−	1.28401e6i	0.0902625	−	0.0521131i
$906$	4.85218e6	−	3.11911e6i	0.196389	−	0.126244i
$907$	1.75218e6	−	3.03486e6i	0.0707229	−	0.122496i	−0.828495	−	0.559996i	$-0.810803\pi$
$907$	1.75218e6	−	3.03486e6i	0.0707229	−	0.122496i	0.899218	+	0.437500i	$0.144136\pi$
$908$	−1.70815e7	−	2.95861e7i	−0.687563	−	1.19089i
$909$	6.44443e6	+	9.04546e6i	0.258687	+	0.363096i
$910$	−754698.	+	3.92153e6i	−0.0302113	+	0.156983i
$911$			1.88564e7i			0.752771i	0.926463	+	0.376386i	$0.122833\pi$
$911$			1.88564e7i			0.752771i	−0.926463	+	0.376386i	$0.877167\pi$
$912$	355861.	+	7.45215e6i	0.0141675	+	0.296684i
$913$	1.42616e7	+	8.23395e6i	0.566229	+	0.326912i
$914$	−1.71779e7	−	9.91766e6i	−0.680150	−	0.392685i
$915$	−23618.3	−	494594.i	−0.000932599	−	0.0195297i
$916$			2.04371e7i			0.804786i
$917$	1.37264e7	+	1.18874e7i	0.539053	+	0.466834i
$918$	5.28278e6	+	3.66515e7i	0.206898	+	1.43544i
$919$	8.89002e6	+	1.53980e7i	0.347227	+	0.601416i	0.985756	−	0.168183i	$-0.0537898\pi$
$919$	8.89002e6	+	1.53980e7i	0.347227	+	0.601416i	−0.638528	+	0.769598i	$0.720457\pi$
$920$	447739.	−	775507.i	0.0174404	−	0.0302076i
$921$	2.78047e7	−	1.78736e7i	1.08011	−	0.694325i
$922$	4.43108e7	−	2.55829e7i	1.71665	−	0.991110i
$923$	−4.35397e7			−1.68221
$924$	−3.23655e7	−	4.64056e6i	−1.24710	−	0.178809i
$925$	1.87698e7			0.721284
$926$	−3.67423e7	+	2.12132e7i	−1.40812	+	0.812978i
$927$	−2.80090e6	−	2.92602e7i	−0.107053	−	1.11835i
$928$	1.09156e7	−	1.89064e7i	0.416082	−	0.720675i
$929$	−1.56120e7	−	2.70408e7i	−0.593498	−	1.02797i	−0.993757	−	0.111567i	$-0.964413\pi$
$929$	−1.56120e7	−	2.70408e7i	−0.593498	−	1.02797i	0.400259	−	0.916402i	$-0.368920\pi$
$930$	3.64723e6	−	7.07666e6i	0.138279	−	0.268300i
$931$	−3.39261e6	+	8.48781e6i	−0.128280	+	0.320938i
$932$		−	1.99620e7i		−	0.752773i
$933$	−736570.	+	35173.3i	−0.0277019	+	0.00132284i
$934$	−1.26146e7	−	7.28307e6i	−0.473160	−	0.273179i
$935$	3.29503e6	+	1.90239e6i	0.123262	+	0.0711656i
$936$	1.74080e6	−	3.81417e6i	0.0649470	−	0.142302i
$937$			2.42895e7i			0.903793i	0.892070	+	0.451897i	$0.149252\pi$
$937$			2.42895e7i			0.903793i	−0.892070	+	0.451897i	$0.850748\pi$
$938$	483603.	+	1.39604e6i	0.0179466	+	0.0518074i
$939$	−5.28732e6	−	2.72502e6i	−0.195691	−	0.100857i
$940$	−3.35988e6	−	5.81948e6i	−0.124024	−	0.214815i
$941$	−1.57875e7	+	2.73447e7i	−0.581217	+	1.00670i	0.414119	+	0.910223i	$0.364090\pi$
$941$	−1.57875e7	+	2.73447e7i	−0.581217	+	1.00670i	−0.995335	+	0.0964742i	$0.969243\pi$
$942$	−6.00864e6	−	9.34723e6i	−0.220622	−	0.343206i
$943$	658308.	−	380074.i	0.0241074	−	0.0139184i
$944$	−2.55463e7			−0.933036
$945$	−2.95148e6	−	1.89420e6i	−0.107513	−	0.0689997i
$946$	−1.75813e7			−0.638737
$947$	−1.66873e7	+	9.63442e6i	−0.604660	+	0.349101i	−0.770873	−	0.636989i	$-0.780180\pi$
$947$	−1.66873e7	+	9.63442e6i	−0.604660	+	0.349101i	0.166213	+	0.986090i	$0.446846\pi$
$948$	6.39955e6	+	9.95534e6i	0.231275	+	0.359778i
$949$	8.50372e6	−	1.47289e7i	0.306509	−	0.530889i
$950$	6.89316e6	+	1.19393e7i	0.247805	+	0.429210i
$951$	3.40695e7	+	1.75590e7i	1.22156	+	0.629577i
$952$	4.97801e6	+	958018.i	0.178018	+	0.0342595i
$953$			7.55185e6i			0.269352i	0.990890	+	0.134676i	$0.0429994\pi$
$953$			7.55185e6i			0.269352i	−0.990890	+	0.134676i	$0.957001\pi$
$954$	1.14404e7	−	2.50665e7i	0.406977	−	0.891707i
$955$	2.05306e6	+	1.18533e6i	0.0728438	+	0.0420564i
$956$	−1.56875e7	−	9.05716e6i	−0.555147	−	0.320514i
$957$	−1.83791e7	+	877651.i	−0.648699	+	0.0309772i
$958$		−	4.40022e7i		−	1.54903i
$959$	−1.39968e7	−	2.69369e6i	−0.491455	−	0.0945806i
$960$	−2.05958e6	+	3.99618e6i	−0.0721276	+	0.139948i
$961$	2.32905e7	+	4.03403e7i	0.813524	+	1.40906i
$962$	1.31689e7	−	2.28092e7i	0.458787	−	0.794642i
$963$	−2.57208e6	−	2.68698e7i	−0.0893754	−	0.933680i
$964$	−3.96489e7	+	2.28913e7i	−1.37416	+	0.793374i
$965$	54110.6			0.00187053
$966$	5.88045e7	−	2.35684e7i	2.02753	−	0.812620i
$967$	−4.08341e7			−1.40429			−0.702144	−	0.712035i	$-0.747774\pi$
$967$	−4.08341e7			−1.40429			−0.702144	+	0.712035i	$0.747774\pi$
$968$	1.16908e6	−	674969.i	0.0401011	−	0.0231524i
$969$	−8.45436e6	+	5.43468e6i	−0.289249	+	0.185937i
$970$	−3.54292e6	+	6.13652e6i	−0.120902	+	0.209408i
$971$	1.42490e7	+	2.46800e7i	0.484994	+	0.840034i	0.999851	−	0.0172418i	$-0.00548852\pi$
$971$	1.42490e7	+	2.46800e7i	0.484994	+	0.840034i	−0.514858	+	0.857276i	$0.672155\pi$
$972$	2.28814e7	+	2.39693e7i	0.776814	+	0.813748i
$973$	4.23169e6	+	1.22158e7i	0.143295	+	0.413658i
$974$			4.91922e6i			0.166149i
$975$	1.19558e6	+	2.50369e7i	0.0402779	+	0.843468i
$976$	−3.38976e6	−	1.95708e6i	−0.113905	−	0.0657633i
$977$	3.59151e7	+	2.07356e7i	1.20376	+	0.694993i	0.961390	−	0.275190i	$-0.0887408\pi$
$977$	3.59151e7	+	2.07356e7i	1.20376	+	0.694993i	0.242373	+	0.970183i	$0.422074\pi$
$978$	−2.23614e6	−	4.68275e7i	−0.0747571	−	1.56550i
$979$		−	2.76594e7i		−	0.922329i
$980$	−3.39502e6	+	2.67289e6i	−0.112922	+	0.0889028i
$981$	1.76659e7	+	2.47960e7i	0.586088	+	0.822640i
$982$	1.90201e7	+	3.29438e7i	0.629412	+	1.09017i
$983$	2.10582e7	−	3.64739e7i	0.695086	−	1.20392i	−0.275066	−	0.961425i	$-0.588700\pi$
$983$	2.10582e7	−	3.64739e7i	0.695086	−	1.20392i	0.970152	−	0.242498i	$-0.0779669\pi$
$984$	86487.8	−	55596.6i	0.00284752	−	0.00183046i
$985$	3.91593e6	−	2.26086e6i	0.128601	−	0.0742479i
$986$	2.56751e7			0.841045
$987$	7.49692e6	−	5.22872e7i	0.244957	−	1.70845i
$988$	1.02414e7			0.333786
$989$	1.56182e7	−	9.01717e6i	0.507738	−	0.293143i
$990$	6.40201e6	−	612825.i	0.207600	−	0.0198723i
$991$	−1.77226e7	+	3.06964e7i	−0.573248	+	0.992894i	0.422982	+	0.906138i	$0.360983\pi$
$991$	−1.77226e7	+	3.06964e7i	−0.573248	+	0.992894i	−0.996230	+	0.0867560i	$0.972350\pi$
$992$	−3.60432e7	−	6.24286e7i	−1.16290	−	2.01421i
$993$	7.28626e6	−	1.41374e7i	0.234494	−	0.454985i
$994$	−6.72664e7	−	5.82544e7i	−2.15940	−	1.87009i
$995$		−	4.94468e6i		−	0.158336i
$996$	−2.05399e7	+	980837.i	−0.656069	+	0.0313291i
$997$	3.85085e6	+	2.22329e6i	0.122693	+	0.0708367i	0.560090	−	0.828432i	$-0.310766\pi$
$997$	3.85085e6	+	2.22329e6i	0.122693	+	0.0708367i	−0.437398	+	0.899268i	$0.644100\pi$
$998$	5.68204e7	+	3.28053e7i	1.80584	+	1.04260i
$999$	1.43041e7	+	1.81760e7i	0.453467	+	0.576215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.g.b.17.2	yes	4
3.2	odd	2	inner	21.6.g.b.17.1	yes	4
7.3	odd	6		147.6.c.b.146.4		4
7.4	even	3		147.6.c.b.146.3		4
7.5	odd	6	inner	21.6.g.b.5.1	✓	4
21.5	even	6	inner	21.6.g.b.5.2	yes	4
21.11	odd	6		147.6.c.b.146.2		4
21.17	even	6		147.6.c.b.146.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.b.5.1	✓	4	7.5	odd	6	inner
21.6.g.b.5.2	yes	4	21.5	even	6	inner
21.6.g.b.17.1	yes	4	3.2	odd	2	inner
21.6.g.b.17.2	yes	4	1.1	even	1	trivial
147.6.c.b.146.1		4	21.17	even	6
147.6.c.b.146.2		4	21.11	odd	6
147.6.c.b.146.3		4	7.4	even	3
147.6.c.b.146.4		4	7.3	odd	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.14143 - 4.12311i) q^{2} +(-8.42929 - 13.1129i) q^{3} +(18.0000 - 31.1769i) q^{4} +(-3.57071 - 6.18466i) q^{5} +(-114.263 - 58.8897i) q^{6} +(122.500 - 42.4352i) q^{7} -32.9848i q^{8} +(-100.894 + 221.064i) q^{9} +O(q^{10})\)	\(q+(7.14143 - 4.12311i) q^{2} +(-8.42929 - 13.1129i) q^{3} +(18.0000 - 31.1769i) q^{4} +(-3.57071 - 6.18466i) q^{5} +(-114.263 - 58.8897i) q^{6} +(122.500 - 42.4352i) q^{7} -32.9848i q^{8} +(-100.894 + 221.064i) q^{9} +(-51.0000 - 29.4449i) q^{10} +(389.208 + 224.709i) q^{11} +(-560.546 + 26.7676i) q^{12} -523.079i q^{13} +(699.860 - 808.129i) q^{14} +(-51.0000 + 98.9545i) q^{15} +(440.000 + 762.102i) q^{16} +(-592.739 + 1026.65i) q^{17} +(190.941 + 1994.71i) q^{18} +(-471.000 + 271.932i) q^{19} -257.091 q^{20} +(-1589.04 - 1248.63i) q^{21} +3706.00 q^{22} +(-3292.20 + 1900.75i) q^{23} +(-432.526 + 278.039i) q^{24} +(1537.00 - 2662.16i) q^{25} +(-2156.71 - 3735.53i) q^{26} +(3749.25 - 540.400i) q^{27} +(882.000 - 4583.01i) q^{28} -2626.42i q^{29} +(43.7872 + 916.955i) q^{30} +(-7510.50 - 4336.19i) q^{31} +(7198.56 + 4156.09i) q^{32} +(-334.163 - 6997.77i) q^{33} +9775.69i q^{34} +(-699.860 - 606.097i) q^{35} +(5076.00 + 7124.73i) q^{36} +(3053.00 + 5287.95i) q^{37} +(-2242.41 + 3883.97i) q^{38} +(-6859.07 + 4409.19i) q^{39} +(-204.000 + 117.779i) q^{40} -199.960 q^{41} +(-16496.2 - 2365.22i) q^{42} -4744.00 q^{43} +(14011.5 - 8089.53i) q^{44} +(1727.47 - 165.360i) q^{45} +(-15674.0 + 27148.2i) q^{46} +(13068.8 + 22635.8i) q^{47} +(6284.46 - 12193.6i) q^{48} +(13205.5 - 10396.6i) q^{49} -25348.9i q^{50} +(18458.7 - 881.455i) q^{51} +(-16308.0 - 9415.43i) q^{52} +(-11908.3 - 6875.28i) q^{53} +(24546.9 - 19317.8i) q^{54} -3209.49i q^{55} +(-1399.72 - 4040.64i) q^{56} +(7536.00 + 3883.97i) q^{57} +(-10829.0 - 18756.4i) q^{58} +(-14515.0 + 25140.6i) q^{59} +(2167.10 + 3371.20i) q^{60} +(-3852.00 + 2223.95i) q^{61} -71514.3 q^{62} +(-2978.64 + 31361.8i) q^{63} +40384.0 q^{64} +(-3235.07 + 1867.77i) q^{65} +(-31238.9 - 48596.3i) q^{66} +(-691.000 + 1196.85i) q^{67} +(21338.6 + 36959.5i) q^{68} +(52675.2 + 27148.2i) q^{69} +(-7497.00 - 1442.80i) q^{70} -83237.3i q^{71} +(7291.77 + 3327.98i) q^{72} +(28158.0 + 16257.0i) q^{73} +(43605.6 + 25175.7i) q^{74} +(-47864.4 + 2285.66i) q^{75} +19579.1i q^{76} +(57213.6 + 11010.8i) q^{77} +(-30804.0 + 59768.5i) q^{78} +(-10544.5 - 18263.6i) q^{79} +(3142.23 - 5442.50i) q^{80} +(-38689.7 - 44608.2i) q^{81} +(-1428.00 + 824.456i) q^{82} +36642.7 q^{83} +(-67531.0 + 27065.9i) q^{84} +8466.00 q^{85} +(-33878.9 + 19560.0i) q^{86} +(-34439.9 + 22138.8i) q^{87} +(7412.00 - 12838.0i) q^{88} +(-30772.4 - 53299.4i) q^{89} +(11654.8 - 8303.45i) q^{90} +(-22197.0 - 64077.2i) q^{91} +136854. i q^{92} +(6448.30 + 135035. i) q^{93} +(186660. + 107768. i) q^{94} +(3363.61 + 1941.98i) q^{95} +(-6180.48 - 129427. i) q^{96} -120324. i q^{97} +(51439.7 - 128694. i) q^{98} +(-88944.0 + 63368.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 48 q^{3} + 72 q^{4} + 490 q^{7} + 282 q^{9}+O(q^{10}) \) 4 * q - 48 * q^3 + 72 * q^4 + 490 * q^7 + 282 * q^9	\( 4 q - 48 q^{3} + 72 q^{4} + 490 q^{7} + 282 q^{9} - 204 q^{10} - 1728 q^{12} - 204 q^{15} + 1760 q^{16} - 3264 q^{18} - 1884 q^{19} - 7056 q^{21} + 14824 q^{22} - 816 q^{24} + 6148 q^{25} + 3528 q^{28} + 1632 q^{30} - 30042 q^{31} + 11118 q^{33} + 20304 q^{36} + 12212 q^{37} - 14496 q^{39} - 816 q^{40} - 9996 q^{42} - 18976 q^{43} + 4896 q^{45} - 62696 q^{46} + 52822 q^{49} + 16932 q^{51} - 65232 q^{52} + 107100 q^{54} + 30144 q^{57} - 43316 q^{58} - 3672 q^{60} - 15408 q^{61} + 55272 q^{63} + 161536 q^{64} - 177888 q^{66} - 2764 q^{67} - 29988 q^{70} + 13056 q^{72} + 112632 q^{73} - 147552 q^{75} - 123216 q^{78} - 42178 q^{79} + 38574 q^{81} - 5712 q^{82} - 169344 q^{84} + 33864 q^{85} - 64974 q^{87} + 29648 q^{88} - 88788 q^{91} + 240336 q^{93} + 746640 q^{94} + 205632 q^{96} - 355776 q^{99}+O(q^{100}) \) 4 * q - 48 * q^3 + 72 * q^4 + 490 * q^7 + 282 * q^9 - 204 * q^10 - 1728 * q^12 - 204 * q^15 + 1760 * q^16 - 3264 * q^18 - 1884 * q^19 - 7056 * q^21 + 14824 * q^22 - 816 * q^24 + 6148 * q^25 + 3528 * q^28 + 1632 * q^30 - 30042 * q^31 + 11118 * q^33 + 20304 * q^36 + 12212 * q^37 - 14496 * q^39 - 816 * q^40 - 9996 * q^42 - 18976 * q^43 + 4896 * q^45 - 62696 * q^46 + 52822 * q^49 + 16932 * q^51 - 65232 * q^52 + 107100 * q^54 + 30144 * q^57 - 43316 * q^58 - 3672 * q^60 - 15408 * q^61 + 55272 * q^63 + 161536 * q^64 - 177888 * q^66 - 2764 * q^67 - 29988 * q^70 + 13056 * q^72 + 112632 * q^73 - 147552 * q^75 - 123216 * q^78 - 42178 * q^79 + 38574 * q^81 - 5712 * q^82 - 169344 * q^84 + 33864 * q^85 - 64974 * q^87 + 29648 * q^88 - 88788 * q^91 + 240336 * q^93 + 746640 * q^94 + 205632 * q^96 - 355776 * q^99

Introduction

L-functions

Modular forms

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