LMFDB - Embedded newform 21.6.g.b.5.2

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			5.2
Root			$3.57071 + 2.06155i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.6.g.b.17.2

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.973546	−	0.228493i	$-0.0733797\pi$
$2$	7.14143	+	4.12311i	1.26244	+	0.728869i	0.288892	+	0.957362i	$0.406713\pi$
$3$	−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	−0.896194	−	0.443662i	$-0.853679\pi$
$5$	−3.57071	+	6.18466i	−0.0638749	+	0.110635i	0.832319	+	0.554296i	$0.187013\pi$
$6$	−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	0.0706522	−	0.997501i	$-0.477492\pi$
$11$	389.208	−	224.709i	0.969840	−	0.559937i	0.899187	+	0.437564i	$0.144159\pi$
$12$	−560.546	−	26.7676i	−1.12372	−	0.0536607i
$13$			523.079i			0.858439i	0.903200	+	0.429219i	$0.141211\pi$
$13$			523.079i			0.858439i	−0.903200	+	0.429219i	$0.858789\pi$
$14$	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	0.502555	−	0.864545i	$-0.332393\pi$
$17$	−592.739	−	1026.65i	−0.497440	−	0.861592i	−0.999996	+	0.00295329i	$0.999060\pi$
$18$	190.941	−	1994.71i	0.138905	−	1.45110i
$19$	−471.000	−	271.932i	−0.299321	−	0.172813i	0.342817	−	0.939402i	$-0.388619\pi$
$19$	−471.000	−	271.932i	−0.299321	−	0.172813i	−0.642138	+	0.766589i	$0.721952\pi$
$20$	−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	−0.317674	−	0.948200i	$-0.602902\pi$
$23$	−3292.20	−	1900.75i	−1.29768	−	0.749214i	−0.980002	+	0.198986i	$0.936235\pi$
$24$	−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	$0.0936422\pi$
$29$			2626.42i			0.579921i	−0.957039	+	0.289961i	$0.906358\pi$
$30$	43.7872	−	916.955i	0.00888267	−	0.186014i
$31$	−7510.50	+	4336.19i	−1.40367	+	0.810409i	−0.994767	−	0.102170i	$-0.967421\pi$
$31$	−7510.50	+	4336.19i	−1.40367	+	0.810409i	−0.408902	+	0.912578i	$0.634088\pi$
$32$	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	−0.622410	−	0.782691i	$-0.713846\pi$
$37$	3053.00	−	5287.95i	0.366625	−	0.635014i	0.989036	+	0.147677i	$0.0471798\pi$
$38$	−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	−0.00609519	−	0.999981i	$-0.501940\pi$
$47$	13068.8	−	22635.8i	0.862962	−	1.49469i	0.869057	−	0.494712i	$-0.164726\pi$
$48$	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	−0.762055	−	0.647513i	$-0.775809\pi$
$53$	−11908.3	+	6875.28i	−0.582319	+	0.336202i	0.179735	+	0.983715i	$0.442476\pi$
$54$	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	−0.998738	−	0.0502156i	$-0.984009\pi$
$59$	−14515.0	−	25140.6i	−0.542857	−	0.940256i	0.455881	−	0.890041i	$-0.349324\pi$
$60$	2167.10	−	3371.20i	0.0777142	−	0.120895i
$61$	−3852.00	−	2223.95i	−0.132544	−	0.0765246i	0.432262	−	0.901748i	$-0.357716\pi$
$61$	−3852.00	−	2223.95i	−0.132544	−	0.0765246i	−0.564806	+	0.825224i	$0.691049\pi$
$62$	−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	0.856469	−	0.516198i	$-0.172653\pi$
$67$	−691.000	−	1196.85i	−0.0188058	−	0.0325725i	−0.875275	+	0.483625i	$0.839320\pi$
$68$	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	$0.435928\pi$
$71$			83237.3i			1.95962i	−0.199931	+	0.979810i	$0.564072\pi$
$72$	7291.77	−	3327.98i	0.165768	−	0.0756571i
$73$	28158.0	−	16257.0i	0.618436	−	0.357054i	−0.157824	−	0.987467i	$-0.550448\pi$
$73$	28158.0	−	16257.0i	0.618436	−	0.357054i	0.776260	+	0.630413i	$0.217115\pi$
$74$	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	−0.945280	−	0.326261i	$-0.894211\pi$
$79$	−10544.5	+	18263.6i	−0.190090	+	0.329245i	0.755190	+	0.655506i	$0.227545\pi$
$80$	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	−0.995087	−	0.0990076i	$-0.968433\pi$
$89$	−30772.4	+	53299.4i	−0.411800	+	0.713259i	0.583286	+	0.812267i	$0.301767\pi$
$90$	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	$0.224905\pi$
$97$			120324.i			1.29844i	−0.760600	+	0.649221i	$0.775095\pi$
$98$	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	0.955691	−	0.294373i	$-0.0951107\pi$
$101$	22852.6	+	39581.8i	0.222911	+	0.386093i	−0.732780	+	0.680466i	$0.761777\pi$
$102$	128187.	+	82402.1i	1.21996	+	0.784220i
$103$	−104757.	−	60481.5i	−0.972949	−	0.561732i	−0.0728149	−	0.997345i	$-0.523198\pi$
$103$	−104757.	−	60481.5i	−0.972949	−	0.561732i	−0.900134	+	0.435613i	$0.856532\pi$
$104$	−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	0.0354626	−	0.999371i	$-0.488710\pi$
$107$	−96198.6	−	55540.3i	−0.812287	−	0.468974i	−0.847749	+	0.530397i	$0.822043\pi$
$108$	50638.5	+	126617.i	0.417755	+	1.04456i
$109$	62645.0	+	108504.i	0.505033	+	0.874744i	0.999983	+	0.00582195i	$0.00185319\pi$
$109$	62645.0	+	108504.i	0.505033	+	0.874744i	−0.494950	+	0.868922i	$0.664813\pi$
$110$	−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	$0.0326804\pi$
$113$			27822.7i			0.204976i	−0.994734	+	0.102488i	$0.967320\pi$
$114$	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	−0.630832	−	0.775920i	$-0.717286\pi$
$131$	70032.4	−	121300.i	0.356550	−	0.617563i	0.987382	+	0.158356i	$0.0506195\pi$
$132$	−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	−0.700804	−	0.713354i	$-0.747175\pi$
$137$	−95216.7	+	54973.4i	−0.433423	+	0.250237i	0.267381	+	0.963591i	$0.413842\pi$
$138$	488111.	+	23308.6i	2.18183	+	0.104188i
$139$		−	99721.1i		−	0.437774i	−0.975750	−	0.218887i	$-0.929757\pi$
$139$		−	99721.1i		−	0.437774i	0.975750	−	0.218887i	$-0.0702426\pi$
$140$	−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	0.953399	−	0.301714i	$-0.0975587\pi$
$149$	316744.	+	182872.i	1.16881	+	0.674810i	0.215407	+	0.976524i	$0.430892\pi$
$150$	−332396.	−	213673.i	−1.20622	−	0.775391i
$151$	−22436.5	−	38861.2i	−0.0800779	−	0.138699i	0.823205	−	0.567744i	$-0.192184\pi$
$151$	−22436.5	−	38861.2i	−0.0800779	−	0.138699i	−0.903283	+	0.429045i	$0.858850\pi$
$152$	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	−0.373885	−	0.927475i	$-0.621975\pi$
$157$	74862.0	−	43221.6i	0.242389	−	0.139943i	0.616274	+	0.787532i	$0.288641\pi$
$158$	−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	−0.461459	−	0.887162i	$-0.652674\pi$
$163$	182351.	−	315841.i	0.537575	−	0.931107i	0.999034	−	0.0439457i	$-0.0139929\pi$
$164$	−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	−0.991571	−	0.129563i	$-0.958643\pi$
$173$	−150998.	+	261537.i	−0.383581	+	0.664382i	0.607990	+	0.793944i	$0.291976\pi$
$174$	−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	−0.0165689	−	0.999863i	$-0.505274\pi$
$179$	360542.	−	208159.i	0.841053	−	0.485582i	0.857622	+	0.514280i	$0.171941\pi$
$180$	25939.1	+	56833.7i	0.0596723	+	0.130745i
$181$		−	359595.i		−	0.815862i	−0.913013	−	0.407931i	$-0.866250\pi$
$181$		−	359595.i		−	0.815862i	0.913013	−	0.407931i	$-0.133750\pi$
$182$	−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	0.187025	−	0.982355i	$-0.440115\pi$
$191$	−287485.	−	165980.i	−0.570207	−	0.329209i	−0.757232	+	0.653146i	$0.773449\pi$
$192$	−340408.	+	529550.i	−0.666418	+	1.03670i
$193$	−3788.50	−	6561.87i	−0.00732106	−	0.0126804i	0.862342	−	0.506327i	$-0.168997\pi$
$193$	−3788.50	−	6561.87i	−0.00732106	−	0.0126804i	−0.869663	+	0.493646i	$0.835664\pi$
$194$	−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	$-0.802584\pi$
$197$		−	633169.i		−	1.16240i	0.813762	−	0.581198i	$-0.197416\pi$
$198$	−373914.	−	819264.i	−0.677812	−	1.48512i
$199$	599631.	−	346197.i	1.07337	−	0.619713i	0.144273	−	0.989538i	$-0.453916\pi$
$199$	599631.	−	346197.i	1.07337	−	0.619713i	0.929102	+	0.369825i	$0.120582\pi$
$200$	−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	$0.0327363\pi$
$223$			152478.i			0.205326i	−0.994716	+	0.102663i	$0.967264\pi$
$224$	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	0.991044	+	0.133535i	$0.0426329\pi$
$227$	474487.	+	821836.i	0.611167	+	1.05857i	−0.379877	+	0.925037i	$0.624034\pi$
$228$	256738.	+	165038.i	0.327079	+	0.210255i
$229$	−491640.	−	283848.i	−0.619525	−	0.357683i	0.157159	−	0.987573i	$-0.449766\pi$
$229$	−491640.	−	283848.i	−0.619525	−	0.357683i	−0.776684	+	0.629891i	$0.783100\pi$
$230$	223869.			0.279046
$231$	−337887.	+	843046.i	−0.416621	+	1.03949i
$232$	−86632.0			−0.105672
$233$	480211.	+	277250.i	0.579485	+	0.334566i	0.760929	−	0.648835i	$-0.224744\pi$
$233$	480211.	+	277250.i	0.579485	+	0.334566i	−0.181444	+	0.983401i	$0.558077\pi$
$234$	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	$0.0919609\pi$
$239$			503176.i			0.569803i	−0.958557	+	0.284902i	$0.908039\pi$
$240$	−97853.5	−	4672.78i	−0.109660	−	0.00523657i
$241$	−1.10136e6	+	635870.i	−1.22148	+	0.705221i	−0.965233	−	0.261390i	$-0.915819\pi$
$241$	−1.10136e6	+	635870.i	−1.22148	+	0.705221i	−0.256246	+	0.966612i	$0.582486\pi$
$242$	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	−0.728647	−	0.684890i	$-0.759850\pi$
$257$	242273.	−	419629.i	0.228808	−	0.396308i	0.957455	+	0.288582i	$0.0931837\pi$
$258$	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	−0.664686	−	0.747123i	$-0.731434\pi$
$263$	−392607.	+	226672.i	−0.350001	+	0.202073i	0.314685	+	0.949196i	$0.398101\pi$
$264$	−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	0.869826	−	0.493359i	$-0.164231\pi$
$269$	9080.33	+	15727.6i	0.00765104	+	0.0132520i	−0.862175	+	0.506611i	$0.830898\pi$
$270$	−207124.	+	82835.8i	−0.172910	+	0.0691526i
$271$	1.58848e6	+	917111.i	1.31389	+	0.758576i	0.982738	−	0.185001i	$-0.0592290\pi$
$271$	1.58848e6	+	917111.i	1.31389	+	0.758576i	0.331153	+	0.943577i	$0.392562\pi$
$272$	−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	0.991252	+	0.131983i	$0.0421346\pi$
$277$	778892.	+	1.34908e6i	0.609927	+	1.05642i	−0.381325	+	0.924441i	$0.624532\pi$
$278$	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	$0.113934\pi$
$281$			927443.i			0.700683i	−0.936622	+	0.350341i	$0.886066\pi$
$282$	−160261.	+	3.35606e6i	−0.120007	+	2.51308i
$283$	784368.	−	452855.i	0.582175	−	0.336119i	−0.179822	−	0.983699i	$-0.557552\pi$
$283$	784368.	−	452855.i	0.582175	−	0.336119i	0.761997	+	0.647580i	$0.224219\pi$
$284$	−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	$-0.778099\pi$
$307$		−	2.12041e6i		−	1.28403i	0.766692	−	0.642015i	$-0.221901\pi$
$308$	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	0.872876	−	0.487943i	$-0.162253\pi$
$311$	23652.4	+	40967.2i	0.0138667	+	0.0240179i	−0.859009	+	0.511961i	$0.828919\pi$
$312$	145436.	−	226245.i	0.0845836	−	0.131581i
$313$	330458.	+	190790.i	0.190658	+	0.110076i	0.592291	−	0.805724i	$-0.298224\pi$
$313$	330458.	+	190790.i	0.190658	+	0.110076i	−0.401633	+	0.915801i	$0.631557\pi$
$314$	712829.			0.408001
$315$	204598.	+	93562.3i	0.116178	+	0.0531281i
$316$	−759204.			−0.427702
$317$	−2.12934e6	−	1.22938e6i	−1.19014	−	0.687126i	−0.231800	−	0.972763i	$-0.574461\pi$
$317$	−2.12934e6	−	1.22938e6i	−1.19014	−	0.687126i	−0.958338	+	0.285637i	$0.907795\pi$
$318$	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	−0.709218	−	0.704989i	$-0.750952\pi$
$331$	510140.	−	883588.i	0.255929	−	0.443282i	0.965147	+	0.261707i	$0.0842854\pi$
$332$	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	0.489238	−	0.872150i	$-0.337275\pi$
$347$	3.34015e6	−	1.92843e6i	1.48916	−	0.859768i	0.999923	+	0.0123825i	$0.00394159\pi$
$348$	70302.9	−	1.47223e6i	0.0311190	−	0.651669i
$349$			1.90701e6i			0.838085i	0.907967	+	0.419043i	$0.137634\pi$
$349$			1.90701e6i			0.838085i	−0.907967	+	0.419043i	$0.862366\pi$
$350$	−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	0.854344	−	0.519708i	$-0.173959\pi$
$353$	−53632.1	−	92893.6i	−0.0229081	−	0.0396779i	−0.877252	+	0.480030i	$0.840626\pi$
$354$	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	−0.151187	−	0.988505i	$-0.548310\pi$
$359$	−2.64426e6	−	1.52667e6i	−1.08285	−	0.625184i	−0.931664	+	0.363321i	$0.881643\pi$
$360$	−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	−0.000283128	−	1.00000i	$-0.500090\pi$
$367$	2.23348e6	−	1.28950e6i	0.865601	−	0.499755i	0.865884	+	0.500245i	$0.166757\pi$
$368$	−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	−0.994586	−	0.103914i	$-0.966863\pi$
$373$	−1.09443e6	+	1.89560e6i	−0.407301	+	0.705465i	0.587286	+	0.809380i	$0.300197\pi$
$374$	−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	0.306078	+	0.952006i	$0.400983\pi$
$383$	−1.92749e6	+	3.33852e6i	−0.671422	+	1.16294i	−0.977501	+	0.210932i	$0.932350\pi$
$384$	−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	−0.550691	−	0.834709i	$-0.685636\pi$
$389$	−307874.	+	177751.i	−0.103157	+	0.0595578i	0.447534	+	0.894267i	$0.352302\pi$
$390$	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	0.949735	−	0.313055i	$-0.101352\pi$
$397$	3.62234e6	+	2.09136e6i	1.15349	+	0.665967i	0.203754	+	0.979022i	$0.434686\pi$
$398$	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	0.705132	−	0.709076i	$-0.250888\pi$
$401$	1.42847e6	+	824728.i	0.443619	+	0.256124i	−0.261512	+	0.965200i	$0.584221\pi$
$402$	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	−0.617754	−	0.786372i	$-0.711957\pi$
$409$	−830920.	+	479732.i	−0.245613	+	0.141805i	0.372141	+	0.928176i	$0.378624\pi$
$410$	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	−0.656047	−	0.754720i	$-0.727773\pi$
$431$	−1.27443e6	+	735793.i	−0.330463	+	0.190793i	0.325584	+	0.945513i	$0.394439\pi$
$432$	2.06151e6	−	2.61954e6i	0.531467	−	0.675328i
$433$		−	6.94894e6i		−	1.78114i	−0.454843	−	0.890571i	$-0.650305\pi$
$433$		−	6.94894e6i		−	1.78114i	0.454843	−	0.890571i	$-0.349695\pi$
$434$	−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	0.978644	−	0.205562i	$-0.0659021\pi$
$439$	5.20874e6	+	3.00727e6i	1.28994	+	0.744750i	0.311301	+	0.950312i	$0.399235\pi$
$440$	−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	0.127116	−	0.991888i	$-0.459428\pi$
$443$	−2.76057e6	−	1.59381e6i	−0.668327	−	0.385859i	−0.795442	+	0.606029i	$0.792761\pi$
$444$	−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	$0.203766\pi$
$449$			5.10328e6i			1.19463i	−0.802007	+	0.597315i	$0.796234\pi$
$450$	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	−0.968702	−	0.248228i	$-0.920152\pi$
$457$	−1.20269e6	+	2.08313e6i	−0.269379	+	0.466579i	0.699322	+	0.714807i	$0.253485\pi$
$458$	−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	−0.944382	−	0.328849i	$-0.893339\pi$
$467$	−883202.	+	1.52975e6i	−0.187399	+	0.324585i	0.756983	+	0.653434i	$0.226672\pi$
$468$	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	0.999332	+	0.0365433i	$0.0116347\pi$
$479$	2.66802e6	+	4.62115e6i	0.531313	+	0.920262i	−0.468019	+	0.883719i	$0.655032\pi$
$480$	−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	0.836124	−	0.548541i	$-0.184817\pi$
$487$	−298272.	−	516621.i	−0.0569888	−	0.0987075i	−0.893112	+	0.449834i	$0.851483\pi$
$488$	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	$-0.857888\pi$
$491$		−	4.61306e6i		−	0.863545i	0.901982	−	0.431773i	$-0.142112\pi$
$492$	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	−0.247658	−	0.968848i	$-0.579661\pi$
$499$	3.97823e6	−	6.89049e6i	0.715218	−	1.23879i	0.962876	−	0.269946i	$-0.0870058\pi$
$500$	−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	−0.956685	−	0.291125i	$-0.905970\pi$
$509$	−1.32229e6	+	2.29027e6i	−0.226220	+	0.391825i	0.730464	+	0.682951i	$0.239304\pi$
$510$	−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	0.609363	−	0.792891i	$-0.291425\pi$
$521$	−2.36667e6	−	4.09919e6i	−0.381982	−	0.661613i	−0.991346	+	0.131278i	$0.958092\pi$
$522$	5.23895e6	+	501492.i	0.841526	+	0.0805541i
$523$	−9.21208e6	−	5.31860e6i	−1.47266	−	0.850242i	−0.473136	−	0.880989i	$-0.656878\pi$
$523$	−9.21208e6	−	5.31860e6i	−1.47266	−	0.850242i	−0.999527	+	0.0307469i	$0.990211\pi$
$524$	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	−0.998635	−	0.0522351i	$-0.983365\pi$
$541$	−3.09119e6	+	5.35410e6i	−0.454080	+	0.786490i	0.544554	+	0.838726i	$0.316699\pi$
$542$	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	−0.180792	−	0.983521i	$-0.557866\pi$
$557$	4.25099e6	−	2.45431e6i	0.580567	−	0.335190i	0.761358	+	0.648331i	$0.224533\pi$
$558$	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	−0.849384	−	0.527776i	$-0.823026\pi$
$563$	−6.63164e6	−	1.14863e7i	−0.881759	−	1.52725i	−0.0323757	−	0.999476i	$-0.510307\pi$
$564$	−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	−0.167133	−	0.985934i	$-0.553451\pi$
$569$	−8.53029e6	−	4.92496e6i	−1.10454	−	0.637709i	−0.937411	+	0.348226i	$0.886784\pi$
$570$	−269973.	+	419979.i	−0.0348043	+	0.0541427i
$571$	90932.0	+	157499.i	0.0116715	+	0.0202156i	0.871802	−	0.489858i	$-0.162951\pi$
$571$	90932.0	+	157499.i	0.0116715	+	0.0202156i	−0.860131	+	0.510074i	$0.829618\pi$
$572$	−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	−0.583290	−	0.812264i	$-0.698235\pi$
$577$	−1.37148e6	+	791825.i	−0.171495	+	0.0990124i	0.411796	+	0.911276i	$0.364902\pi$
$578$	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	−0.485053	−	0.874485i	$-0.661200\pi$
$593$	4.40834e6	−	7.63547e6i	0.514800	−	0.891659i	0.999853	−	0.0171744i	$-0.00546705\pi$
$594$	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	−0.960224	−	0.279230i	$-0.909921\pi$
$599$	−1.05247e7	+	6.07646e6i	−1.19852	+	0.691964i	−0.238292	+	0.971194i	$0.576588\pi$
$600$	75392.0	−	1.57880e6i	0.00854963	−	0.179039i
$601$		−	8.37919e6i		−	0.946272i	−0.880990	−	0.473136i	$-0.843122\pi$
$601$		−	8.37919e6i		−	0.946272i	0.880990	−	0.473136i	$-0.156878\pi$
$602$	−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	0.995784	−	0.0917316i	$-0.0292402\pi$
$607$	1.28379e7	+	7.41195e6i	1.41423	+	0.816508i	0.418450	+	0.908240i	$0.362574\pi$
$608$	−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	0.818410	−	0.574635i	$-0.194856\pi$
$613$	−822841.	−	1.42520e6i	−0.0884433	−	0.153188i	−0.906853	+	0.421446i	$0.861523\pi$
$614$	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	$-0.937330\pi$
$617$		−	3.69950e6i		−	0.391228i	0.980681	−	0.195614i	$-0.0626700\pi$
$618$	1.55316e7	+	741676.i	1.63585	+	0.0781165i
$619$	1.51109e6	−	872431.i	0.158513	−	0.0915175i	−0.418645	−	0.908150i	$-0.637495\pi$
$619$	1.51109e6	−	872431.i	0.158513	−	0.0915175i	0.577158	+	0.816632i	$0.304162\pi$
$620$	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	−0.664153	−	0.747597i	$-0.731208\pi$
$641$	−3.62836e6	+	2.09483e6i	−0.348791	+	0.201375i	0.315362	+	0.948972i	$0.397874\pi$
$642$	1.42627e7	+	681083.i	1.36573	+	0.0652172i
$643$			1.72926e7i			1.64942i	0.565553	+	0.824712i	$0.308663\pi$
$643$			1.72926e7i			1.64942i	−0.565553	+	0.824712i	$0.691337\pi$
$644$	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	0.795444	−	0.606027i	$-0.207238\pi$
$647$	−1.35347e6	−	2.34428e6i	−0.127113	−	0.220165i	−0.922557	+	0.385861i	$0.873904\pi$
$648$	−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	0.513697	−	0.857972i	$-0.328276\pi$
$653$	299872.	+	173131.i	0.0275203	+	0.0158889i	−0.486177	+	0.873861i	$0.661609\pi$
$654$	−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	$0.292526\pi$
$659$			1.77258e7i			1.58999i	−0.606619	+	0.794993i	$0.707474\pi$
$660$	85910.4	−	1.79907e6i	0.00767690	−	0.160763i
$661$	8.33971e6	−	4.81493e6i	0.742416	−	0.428634i	−0.0805313	−	0.996752i	$-0.525662\pi$
$661$	8.33971e6	−	4.81493e6i	0.742416	−	0.428634i	0.822947	+	0.568118i	$0.192328\pi$
$662$	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	0.0377479	−	0.999287i	$-0.487982\pi$
$677$	1.05454e7	−	1.82651e7i	0.884282	−	1.53162i	0.846534	−	0.532334i	$-0.178685\pi$
$678$	−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	−0.290390	−	0.956908i	$-0.593785\pi$
$683$	4.79268e6	−	2.76706e6i	0.393121	−	0.226969i	0.683512	+	0.729940i	$0.260452\pi$
$684$	−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	0.836056	−	0.548645i	$-0.184856\pi$
$691$	9.77690e6	+	5.64469e6i	0.778944	+	0.449723i	−0.0571122	+	0.998368i	$0.518189\pi$
$692$	−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	$0.137186\pi$
$701$			1.08706e7i			0.835525i	−0.908556	+	0.417763i	$0.862814\pi$
$702$	−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	−0.605274	−	0.796017i	$-0.706936\pi$
$709$	5.17640e6	−	8.96579e6i	0.386734	−	0.669843i	0.992008	+	0.126174i	$0.0402698\pi$
$710$	−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	−0.993086	−	0.117390i	$-0.962547\pi$
$719$	−5.47378e6	+	9.48087e6i	−0.394880	+	0.683953i	0.598206	+	0.801343i	$0.295881\pi$
$720$	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	$-0.991719\pi$
$727$		−	741427.i		−	0.0520274i	0.999662	−	0.0260137i	$-0.00828136\pi$
$728$	−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	0.724047	−	0.689751i	$-0.242280\pi$
$733$	7.10931e6	+	4.10456e6i	0.488728	+	0.282167i	−0.235318	+	0.971918i	$0.575613\pi$
$734$	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	0.789957	−	0.613162i	$-0.210103\pi$
$739$	−2.01959e6	−	3.49803e6i	−0.136035	−	0.235620i	−0.925993	+	0.377542i	$0.876769\pi$
$740$	−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	$-0.860062\pi$
$743$		−	1.28088e7i		−	0.851208i	0.904909	−	0.425604i	$-0.139938\pi$
$744$	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	−0.450855	−	0.892597i	$-0.648881\pi$
$751$	8.46352e6	−	1.46593e7i	0.547585	−	0.948445i	0.998439	−	0.0558471i	$-0.0177860\pi$
$752$	−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	0.250010	+	0.968243i	$0.419566\pi$
$761$	−1.13990e7	+	1.97436e7i	−0.713518	+	1.23585i	−0.963528	+	0.267607i	$0.913767\pi$
$762$	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	$-0.846459\pi$
$769$		−	1.52141e7i		−	0.927747i	0.885901	−	0.463874i	$-0.153541\pi$
$770$	−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	0.999446	−	0.0332943i	$-0.0105999\pi$
$773$	7.82289e6	+	1.35496e7i	0.470889	+	0.815604i	−0.528557	+	0.848898i	$0.677267\pi$
$774$	−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	−0.356655	−	0.934236i	$-0.616083\pi$
$787$	4.76244e6	−	2.74960e6i	0.274090	−	0.158246i	0.630745	+	0.775990i	$0.282750\pi$
$788$	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	−0.966999	−	0.254782i	$-0.917996\pi$
$809$	−2.28941e7	+	1.32179e7i	−1.22985	+	0.710055i	−0.262852	+	0.964836i	$0.584663\pi$
$810$	659691.	−	3.41423e6i	0.0353287	−	0.182844i
$811$			3.37600e7i			1.80240i	0.433406	+	0.901199i	$0.357311\pi$
$811$			3.37600e7i			1.80240i	−0.433406	+	0.901199i	$0.642689\pi$
$812$	−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	0.386094	−	0.922459i	$-0.373824\pi$
$821$	−4.24377e6	−	2.45014e6i	−0.219732	−	0.126862i	−0.605826	+	0.795597i	$0.707157\pi$
$822$	7.64236e6	−	1.18887e7i	0.394501	−	0.613698i
$823$	−6.56892e6	−	1.13777e7i	−0.338061	−	0.585538i	0.646007	−	0.763331i	$-0.276438\pi$
$823$	−6.56892e6	−	1.13777e7i	−0.338061	−	0.585538i	−0.984068	+	0.177793i	$0.943104\pi$
$824$	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	$0.0446178\pi$
$827$			5.49577e6i			0.279424i	−0.990192	+	0.139712i	$0.955382\pi$
$828$	−3.02535e7	+	1.38078e7i	−1.53356	+	0.699920i
$829$	−1.06198e7	+	6.13134e6i	−0.536697	+	0.309862i	−0.743739	−	0.668470i	$-0.766950\pi$
$829$	−1.06198e7	+	6.13134e6i	−0.536697	+	0.309862i	0.207042	+	0.978332i	$0.433616\pi$
$830$	−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	$-0.908841\pi$
$853$		−	1.20060e7i		−	0.564970i	0.959272	−	0.282485i	$-0.0911587\pi$
$854$	−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	0.717999	−	0.696044i	$-0.245058\pi$
$857$	−5.24169e6	−	9.07888e6i	−0.243792	−	0.422260i	−0.961791	+	0.273784i	$0.911725\pi$
$858$	−2.54197e7	−	1.63404e7i	−1.17883	−	0.757784i
$859$	−1.39460e7	−	8.05175e6i	−0.644864	−	0.372312i	0.141622	−	0.989921i	$-0.454768\pi$
$859$	−1.39460e7	−	8.05175e6i	−0.644864	−	0.372312i	−0.786486	+	0.617608i	$0.788102\pi$
$860$	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	0.574393	−	0.818580i	$-0.305238\pi$
$863$	3.34044e6	+	1.92860e6i	0.152678	+	0.0881487i	−0.421715	+	0.906729i	$0.638572\pi$
$864$	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	−0.961445	−	0.274999i	$-0.911323\pi$
$877$	−5.52497e6	+	9.56952e6i	−0.242566	+	0.420137i	0.718878	+	0.695136i	$0.244656\pi$
$878$	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	−0.513942	−	0.857825i	$-0.671815\pi$
$887$	1.13862e7	−	1.97216e7i	0.485927	−	0.841651i	0.999869	+	0.0161741i	$0.00514859\pi$
$888$	−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	0.899218	−	0.437500i	$-0.144136\pi$
$907$	1.75218e6	+	3.03486e6i	0.0707229	+	0.122496i	−0.828495	+	0.559996i	$0.810803\pi$
$908$	−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	$-0.877167\pi$
$911$		−	1.88564e7i		−	0.752771i	0.926463	−	0.376386i	$-0.122833\pi$
$912$	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	−0.638528	−	0.769598i	$-0.720457\pi$
$919$	8.89002e6	−	1.53980e7i	0.347227	−	0.601416i	0.985756	+	0.168183i	$0.0537898\pi$
$920$	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	0.400259	+	0.916402i	$0.368920\pi$
$929$	−1.56120e7	+	2.70408e7i	−0.593498	+	1.02797i	−0.993757	+	0.111567i	$0.964413\pi$
$930$	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	$-0.850748\pi$
$937$		−	2.42895e7i		−	0.903793i	0.892070	−	0.451897i	$-0.149252\pi$
$938$	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	−0.995335	−	0.0964742i	$-0.969243\pi$
$941$	−1.57875e7	−	2.73447e7i	−0.581217	−	1.00670i	0.414119	−	0.910223i	$-0.364090\pi$
$942$	−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	0.166213	−	0.986090i	$-0.446846\pi$
$947$	−1.66873e7	−	9.63442e6i	−0.604660	−	0.349101i	−0.770873	+	0.636989i	$0.780180\pi$
$948$	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	$-0.957001\pi$
$953$		−	7.55185e6i		−	0.269352i	0.990890	−	0.134676i	$-0.0429994\pi$
$954$	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	−0.514858	−	0.857276i	$-0.672155\pi$
$971$	1.42490e7	−	2.46800e7i	0.484994	−	0.840034i	0.999851	+	0.0172418i	$0.00548852\pi$
$972$	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	0.242373	−	0.970183i	$-0.422074\pi$
$977$	3.59151e7	−	2.07356e7i	1.20376	−	0.694993i	0.961390	+	0.275190i	$0.0887408\pi$
$978$	−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	0.970152	+	0.242498i	$0.0779669\pi$
$983$	2.10582e7	+	3.64739e7i	0.695086	+	1.20392i	−0.275066	+	0.961425i	$0.588700\pi$
$984$	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	−0.996230	−	0.0867560i	$-0.972350\pi$
$991$	−1.77226e7	−	3.06964e7i	−0.573248	−	0.992894i	0.422982	−	0.906138i	$-0.360983\pi$
$992$	−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	−0.437398	−	0.899268i	$-0.644100\pi$
$997$	3.85085e6	−	2.22329e6i	0.122693	−	0.0708367i	0.560090	+	0.828432i	$0.310766\pi$
$998$	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.5.2	yes	4
3.2	odd	2	inner	21.6.g.b.5.1	✓	4
7.2	even	3		147.6.c.b.146.1		4
7.3	odd	6	inner	21.6.g.b.17.1	yes	4
7.5	odd	6		147.6.c.b.146.2		4
21.2	odd	6		147.6.c.b.146.4		4
21.5	even	6		147.6.c.b.146.3		4
21.17	even	6	inner	21.6.g.b.17.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.b.5.1	✓	4	3.2	odd	2	inner
21.6.g.b.5.2	yes	4	1.1	even	1	trivial
21.6.g.b.17.1	yes	4	7.3	odd	6	inner
21.6.g.b.17.2	yes	4	21.17	even	6	inner
147.6.c.b.146.1		4	7.2	even	3
147.6.c.b.146.2		4	7.5	odd	6
147.6.c.b.146.3		4	21.5	even	6
147.6.c.b.146.4		4	21.2	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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