LMFDB - Embedded newform 210.6.i.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,6,Mod(121,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("210.121");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	210.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.6806021607$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{151})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 151x^{2} + 22801 $ x^4 + 151*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$-6.14410 - 10.6419i$ of defining polynomial
Character	$\chi$	$=$	210.151
Dual form			210.6.i.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(12.5000 + 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 - 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(12.5000 + 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 - 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(50.0000 - 86.6025i) q^{10} +(188.085 - 325.773i) q^{11} +(72.0000 + 124.708i) q^{12} -444.087 q^{13} +(163.965 + 491.963i) q^{14} +225.000 q^{15} +(-128.000 - 221.703i) q^{16} +(435.207 - 753.801i) q^{17} +(-162.000 + 280.592i) q^{18} +(-131.701 - 228.113i) q^{19} -400.000 q^{20} +(-774.157 + 872.954i) q^{21} -1504.68 q^{22} +(2112.67 + 3659.26i) q^{23} +(288.000 - 498.831i) q^{24} +(-312.500 + 541.266i) q^{25} +(888.174 + 1538.36i) q^{26} -729.000 q^{27} +(1376.28 - 1551.92i) q^{28} -7291.74 q^{29} +(-450.000 - 779.423i) q^{30} +(-4352.32 + 7538.43i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1692.77 - 2931.96i) q^{33} -3481.66 q^{34} +(-1024.78 - 3074.77i) q^{35} +1296.00 q^{36} +(1384.32 + 2397.71i) q^{37} +(-526.804 + 912.451i) q^{38} +(-1998.39 + 3461.32i) q^{39} +(800.000 + 1385.64i) q^{40} +10698.1 q^{41} +(4572.31 + 935.851i) q^{42} -15869.1 q^{43} +(3009.36 + 5212.37i) q^{44} +(1012.50 - 1753.70i) q^{45} +(8450.70 - 14637.0i) q^{46} +(-579.008 - 1002.87i) q^{47} -2304.00 q^{48} +(15455.4 + 6603.40i) q^{49} +2500.00 q^{50} +(-3916.86 - 6784.21i) q^{51} +(3552.70 - 6153.45i) q^{52} +(-16139.7 + 27954.8i) q^{53} +(1458.00 + 2525.33i) q^{54} +9404.26 q^{55} +(-8128.56 - 1663.74i) q^{56} -2370.62 q^{57} +(14583.5 + 25259.3i) q^{58} +(-18252.4 + 31614.1i) q^{59} +(-1800.00 + 3117.69i) q^{60} +(20727.4 + 35900.9i) q^{61} +34818.5 q^{62} +(3320.29 + 9962.25i) q^{63} +4096.00 q^{64} +(-5551.09 - 9614.77i) q^{65} +(-6771.06 + 11727.8i) q^{66} +(15020.1 - 26015.5i) q^{67} +(6963.32 + 12060.8i) q^{68} +38028.1 q^{69} +(-8601.74 + 9699.48i) q^{70} +37623.3 q^{71} +(-2592.00 - 4489.48i) q^{72} +(16199.3 - 28058.0i) q^{73} +(5537.27 - 9590.84i) q^{74} +(2812.50 + 4871.39i) q^{75} +4214.43 q^{76} +(-32357.2 + 36486.6i) q^{77} +15987.1 q^{78} +(32339.0 + 56012.9i) q^{79} +(3200.00 - 5542.56i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-21396.1 - 37059.1i) q^{82} -105250. q^{83} +(-5902.74 - 17710.7i) q^{84} +21760.4 q^{85} +(31738.2 + 54972.1i) q^{86} +(-32812.8 + 56833.5i) q^{87} +(12037.4 - 20849.5i) q^{88} +(11195.7 + 19391.5i) q^{89} -8100.00 q^{90} +(56402.9 + 11544.4i) q^{91} -67605.6 q^{92} +(39170.8 + 67845.9i) q^{93} +(-2316.03 + 4011.49i) q^{94} +(3292.53 - 5702.82i) q^{95} +(4608.00 + 7981.29i) q^{96} +37203.1 q^{97} +(-8036.00 - 66746.0i) q^{98} -30469.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 18 * q^3 - 32 * q^4 + 50 * q^5 - 144 * q^6 - 336 * q^7 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9} + 200 q^{10} + 482 q^{11} + 288 q^{12} - 56 q^{13} + 1344 q^{14} + 900 q^{15} - 512 q^{16} - 938 q^{17} - 648 q^{18} - 2198 q^{19} - 1600 q^{20} - 3856 q^{22} - 618 q^{23} + 1152 q^{24} - 1250 q^{25} + 112 q^{26} - 2916 q^{27} - 20172 q^{29} - 1800 q^{30} - 4138 q^{31} - 2048 q^{32} - 4338 q^{33} + 7504 q^{34} - 8400 q^{35} + 5184 q^{36} + 2072 q^{37} - 8792 q^{38} - 252 q^{39} + 3200 q^{40} + 5092 q^{41} + 12096 q^{42} - 53400 q^{43} + 7712 q^{44} + 4050 q^{45} - 2472 q^{46} + 3484 q^{47} - 9216 q^{48} + 4018 q^{49} + 10000 q^{50} + 8442 q^{51} + 448 q^{52} - 316 q^{53} + 5832 q^{54} + 24100 q^{55} - 21504 q^{56} - 39564 q^{57} + 40344 q^{58} - 66202 q^{59} - 7200 q^{60} + 44472 q^{61} + 33104 q^{62} + 27216 q^{63} + 16384 q^{64} - 700 q^{65} - 17352 q^{66} + 18964 q^{67} - 15008 q^{68} - 11124 q^{69} - 68876 q^{71} - 10368 q^{72} - 34516 q^{73} + 8288 q^{74} + 11250 q^{75} + 70336 q^{76} - 46508 q^{77} + 2016 q^{78} + 121590 q^{79} + 12800 q^{80} - 13122 q^{81} - 10184 q^{82} - 221588 q^{83} - 48384 q^{84} - 46900 q^{85} + 106800 q^{86} - 90774 q^{87} + 30848 q^{88} - 94246 q^{89} - 32400 q^{90} + 78694 q^{91} + 19776 q^{92} + 37242 q^{93} + 13936 q^{94} + 54950 q^{95} + 18432 q^{96} + 143504 q^{97} - 32144 q^{98} - 78084 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 - 32 * q^4 + 50 * q^5 - 144 * q^6 - 336 * q^7 + 256 * q^8 - 162 * q^9 + 200 * q^10 + 482 * q^11 + 288 * q^12 - 56 * q^13 + 1344 * q^14 + 900 * q^15 - 512 * q^16 - 938 * q^17 - 648 * q^18 - 2198 * q^19 - 1600 * q^20 - 3856 * q^22 - 618 * q^23 + 1152 * q^24 - 1250 * q^25 + 112 * q^26 - 2916 * q^27 - 20172 * q^29 - 1800 * q^30 - 4138 * q^31 - 2048 * q^32 - 4338 * q^33 + 7504 * q^34 - 8400 * q^35 + 5184 * q^36 + 2072 * q^37 - 8792 * q^38 - 252 * q^39 + 3200 * q^40 + 5092 * q^41 + 12096 * q^42 - 53400 * q^43 + 7712 * q^44 + 4050 * q^45 - 2472 * q^46 + 3484 * q^47 - 9216 * q^48 + 4018 * q^49 + 10000 * q^50 + 8442 * q^51 + 448 * q^52 - 316 * q^53 + 5832 * q^54 + 24100 * q^55 - 21504 * q^56 - 39564 * q^57 + 40344 * q^58 - 66202 * q^59 - 7200 * q^60 + 44472 * q^61 + 33104 * q^62 + 27216 * q^63 + 16384 * q^64 - 700 * q^65 - 17352 * q^66 + 18964 * q^67 - 15008 * q^68 - 11124 * q^69 - 68876 * q^71 - 10368 * q^72 - 34516 * q^73 + 8288 * q^74 + 11250 * q^75 + 70336 * q^76 - 46508 * q^77 + 2016 * q^78 + 121590 * q^79 + 12800 * q^80 - 13122 * q^81 - 10184 * q^82 - 221588 * q^83 - 48384 * q^84 - 46900 * q^85 + 106800 * q^86 - 90774 * q^87 + 30848 * q^88 - 94246 * q^89 - 32400 * q^90 + 78694 * q^91 + 19776 * q^92 + 37242 * q^93 + 13936 * q^94 + 54950 * q^95 + 18432 * q^96 + 143504 * q^97 - 32144 * q^98 - 78084 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	12.5000	+	21.6506i	0.223607	+	0.387298i
$5$	12.5000	+	21.6506i	0.223607	+	0.387298i
$6$	−36.0000			−0.408248
$7$	−127.009	−	25.9959i	−0.979689	−	0.200521i
$7$	−127.009	−	25.9959i	−0.979689	−	0.200521i
$8$	64.0000			0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	50.0000	−	86.6025i	0.158114	−	0.273861i
$11$	188.085	−	325.773i	0.468676	−	0.811771i	−0.530683	−	0.847570i	$-0.678065\pi$
$11$	188.085	−	325.773i	0.468676	−	0.811771i	0.999359	+	0.0357997i	$0.0113978\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	−444.087			−0.728803			−0.364401	−	0.931242i	$-0.618726\pi$
$13$	−444.087			−0.728803			−0.364401	+	0.931242i	$0.618726\pi$
$14$	163.965	+	491.963i	0.223579	+	0.670830i
$15$	225.000			0.258199
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	435.207	−	753.801i	0.365236	−	0.632608i	−0.623578	−	0.781761i	$-0.714322\pi$
$17$	435.207	−	753.801i	0.365236	−	0.632608i	0.988814	+	0.149154i	$0.0476549\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	−131.701	−	228.113i	−0.0836961	−	0.144966i	0.821139	−	0.570729i	$-0.193339\pi$
$19$	−131.701	−	228.113i	−0.0836961	−	0.144966i	−0.904835	+	0.425763i	$0.860006\pi$
$20$	−400.000			−0.223607
$21$	−774.157	+	872.954i	−0.383072	+	0.431959i
$22$	−1504.68			−0.662808
$23$	2112.67	+	3659.26i	0.832747	+	1.44236i	0.895852	+	0.444353i	$0.146566\pi$
$23$	2112.67	+	3659.26i	0.832747	+	1.44236i	−0.0631053	+	0.998007i	$0.520100\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	−312.500	+	541.266i	−0.100000	+	0.173205i
$26$	888.174	+	1538.36i	0.257671	+	0.446299i
$27$	−729.000			−0.192450
$28$	1376.28	−	1551.92i	0.331750	−	0.374088i
$29$	−7291.74			−1.61004			−0.805019	−	0.593249i	$-0.797845\pi$
$29$	−7291.74			−1.61004			−0.805019	+	0.593249i	$0.797845\pi$
$30$	−450.000	−	779.423i	−0.0912871	−	0.158114i
$31$	−4352.32	+	7538.43i	−0.813422	+	1.40889i	0.0970327	+	0.995281i	$0.469065\pi$
$31$	−4352.32	+	7538.43i	−0.813422	+	1.40889i	−0.910455	+	0.413608i	$0.864268\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−1692.77	−	2931.96i	−0.270590	−	0.468676i
$34$	−3481.66			−0.516522
$35$	−1024.78	−	3074.77i	−0.141404	−	0.424270i
$36$	1296.00			0.166667
$37$	1384.32	+	2397.71i	0.166239	+	0.287934i	0.937094	−	0.349076i	$-0.113504\pi$
$37$	1384.32	+	2397.71i	0.166239	+	0.287934i	−0.770856	+	0.637010i	$0.780171\pi$
$38$	−526.804	+	912.451i	−0.0591821	+	0.102506i
$39$	−1998.39	+	3461.32i	−0.210387	+	0.364401i
$40$	800.000	+	1385.64i	0.0790569	+	0.136931i
$41$	10698.1			0.993906			0.496953	−	0.867778i	$-0.334452\pi$
$41$	10698.1			0.993906			0.496953	+	0.867778i	$0.334452\pi$
$42$	4572.31	+	935.851i	0.399957	+	0.0818622i
$43$	−15869.1			−1.30882			−0.654411	−	0.756139i	$-0.727083\pi$
$43$	−15869.1			−1.30882			−0.654411	+	0.756139i	$0.727083\pi$
$44$	3009.36	+	5212.37i	0.234338	+	0.405885i
$45$	1012.50	−	1753.70i	0.0745356	−	0.129099i
$46$	8450.70	−	14637.0i	0.588841	−	1.01990i
$47$	−579.008	−	1002.87i	−0.0382332	−	0.0662218i	0.846276	−	0.532745i	$-0.178840\pi$
$47$	−579.008	−	1002.87i	−0.0382332	−	0.0662218i	−0.884509	+	0.466524i	$0.845506\pi$
$48$	−2304.00			−0.144338
$49$	15455.4	+	6603.40i	0.919583	+	0.392896i
$50$	2500.00			0.141421
$51$	−3916.86	−	6784.21i	−0.210869	−	0.365236i
$52$	3552.70	−	6153.45i	0.182201	−	0.315581i
$53$	−16139.7	+	27954.8i	−0.789233	+	1.36699i	0.137204	+	0.990543i	$0.456188\pi$
$53$	−16139.7	+	27954.8i	−0.789233	+	1.36699i	−0.926437	+	0.376449i	$0.877145\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	9404.26			0.419197
$56$	−8128.56	−	1663.74i	−0.346373	−	0.0708948i
$57$	−2370.62			−0.0966439
$58$	14583.5	+	25259.3i	0.569235	+	0.985943i
$59$	−18252.4	+	31614.1i	−0.682638	+	1.18236i	0.291535	+	0.956560i	$0.405834\pi$
$59$	−18252.4	+	31614.1i	−0.682638	+	1.18236i	−0.974173	+	0.225803i	$0.927499\pi$
$60$	−1800.00	+	3117.69i	−0.0645497	+	0.111803i
$61$	20727.4	+	35900.9i	0.713214	+	1.23532i	0.963644	+	0.267188i	$0.0860945\pi$
$61$	20727.4	+	35900.9i	0.713214	+	1.23532i	−0.250431	+	0.968135i	$0.580572\pi$
$62$	34818.5			1.15035
$63$	3320.29	+	9962.25i	0.105396	+	0.316232i
$64$	4096.00			0.125000
$65$	−5551.09	−	9614.77i	−0.162965	−	0.282264i
$66$	−6771.06	+	11727.8i	−0.191336	+	0.331404i
$67$	15020.1	−	26015.5i	0.408776	−	0.708021i	−0.585977	−	0.810328i	$-0.699289\pi$
$67$	15020.1	−	26015.5i	0.408776	−	0.708021i	0.994753	+	0.102307i	$0.0326224\pi$
$68$	6963.32	+	12060.8i	0.182618	+	0.316304i
$69$	38028.1			0.961573
$70$	−8601.74	+	9699.48i	−0.209817	+	0.236594i
$71$	37623.3			0.885749			0.442874	−	0.896584i	$-0.353959\pi$
$71$	37623.3			0.885749			0.442874	+	0.896584i	$0.353959\pi$
$72$	−2592.00	−	4489.48i	−0.0589256	−	0.102062i
$73$	16199.3	−	28058.0i	0.355787	−	0.616241i	−0.631466	−	0.775404i	$-0.717546\pi$
$73$	16199.3	−	28058.0i	0.355787	−	0.616241i	0.987252	+	0.159163i	$0.0508797\pi$
$74$	5537.27	−	9590.84i	0.117548	−	0.203600i
$75$	2812.50	+	4871.39i	0.0577350	+	0.100000i
$76$	4214.43			0.0836961
$77$	−32357.2	+	36486.6i	−0.621934	+	0.701304i
$78$	15987.1			0.297532
$79$	32339.0	+	56012.9i	0.582988	+	1.00976i	0.995123	+	0.0986416i	$0.0314497\pi$
$79$	32339.0	+	56012.9i	0.582988	+	1.00976i	−0.412135	+	0.911123i	$0.635217\pi$
$80$	3200.00	−	5542.56i	0.0559017	−	0.0968246i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−21396.1	−	37059.1i	−0.351399	−	0.608640i
$83$	−105250.			−1.67698			−0.838490	−	0.544917i	$-0.816561\pi$
$83$	−105250.			−1.67698			−0.838490	+	0.544917i	$0.816561\pi$
$84$	−5902.74	−	17710.7i	−0.0912758	−	0.273865i
$85$	21760.4			0.326677
$86$	31738.2	+	54972.1i	0.462739	+	0.801487i
$87$	−32812.8	+	56833.5i	−0.464778	+	0.805019i
$88$	12037.4	−	20849.5i	0.165702	−	0.287004i
$89$	11195.7	+	19391.5i	0.149822	+	0.259499i	0.931162	−	0.364607i	$-0.118797\pi$
$89$	11195.7	+	19391.5i	0.149822	+	0.259499i	−0.781340	+	0.624106i	$0.785463\pi$
$90$	−8100.00			−0.105409
$91$	56402.9	+	11544.4i	0.714000	+	0.146140i
$92$	−67605.6			−0.832747
$93$	39170.8	+	67845.9i	0.469630	+	0.813422i
$94$	−2316.03	+	4011.49i	−0.0270349	+	0.0468259i
$95$	3292.53	−	5702.82i	0.0374300	−	0.0648307i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	37203.1			0.401467			0.200734	−	0.979646i	$-0.435667\pi$
$97$	37203.1			0.401467			0.200734	+	0.979646i	$0.435667\pi$
$98$	−8036.00	−	66746.0i	−0.0845230	−	0.702037i
$99$	−30469.8			−0.312451
$100$	−5000.00	−	8660.25i	−0.0500000	−	0.0866025i
$101$	−82301.6	+	142551.i	−0.802795	+	1.39048i	0.114974	+	0.993368i	$0.463321\pi$
$101$	−82301.6	+	142551.i	−0.802795	+	1.39048i	−0.917769	+	0.397114i	$0.870012\pi$
$102$	−15667.5	+	27136.8i	−0.149107	+	0.258261i
$103$	−42553.2	−	73704.3i	−0.395220	−	0.684541i	0.597909	−	0.801564i	$-0.295998\pi$
$103$	−42553.2	−	73704.3i	−0.395220	−	0.684541i	−0.993129	+	0.117023i	$0.962665\pi$
$104$	−28421.6			−0.257671
$105$	−28577.0	−	5849.07i	−0.252955	−	0.0517742i
$106$	129117.			1.11614
$107$	−25535.0	−	44227.9i	−0.215614	−	0.373454i	0.737849	−	0.674966i	$-0.235842\pi$
$107$	−25535.0	−	44227.9i	−0.215614	−	0.373454i	−0.953462	+	0.301512i	$0.902509\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	−12926.5	+	22389.4i	−0.104212	+	0.180500i	−0.913416	−	0.407028i	$-0.866565\pi$
$109$	−12926.5	+	22389.4i	−0.104212	+	0.180500i	0.809204	+	0.587527i	$0.199899\pi$
$110$	−18808.5	−	32577.3i	−0.148208	−	0.256704i
$111$	24917.7			0.191956
$112$	10493.8	+	31485.6i	0.0790472	+	0.237174i
$113$	38424.1			0.283079			0.141540	−	0.989933i	$-0.454795\pi$
$113$	38424.1			0.283079			0.141540	+	0.989933i	$0.454795\pi$
$114$	4741.24	+	8212.06i	0.0341688	+	0.0591821i
$115$	−52816.8	+	91481.5i	−0.372416	+	0.645043i
$116$	58333.9	−	101037.i	0.402510	−	0.697167i
$117$	17985.5	+	31151.9i	0.121467	+	0.210387i
$118$	146019.			0.965396
$119$	−74870.8	+	84425.7i	−0.484669	+	0.546522i
$120$	14400.0			0.0912871
$121$	9773.47	+	16928.1i	0.0606855	+	0.105110i
$122$	82909.5	−	143603.i	0.504318	−	0.873505i
$123$	48141.2	−	83383.1i	0.286916	−	0.496953i
$124$	−69637.0	−	120615.i	−0.406711	−	0.704444i
$125$	−15625.0			−0.0894427
$126$	27869.7	−	31426.3i	0.156389	−	0.176347i
$127$	−179221.			−0.986004			−0.493002	−	0.870028i	$-0.664101\pi$
$127$	−179221.			−0.986004			−0.493002	+	0.870028i	$0.664101\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−71410.9	+	123687.i	−0.377824	+	0.654411i
$130$	−22204.4	+	38459.1i	−0.115234	+	0.199591i
$131$	−117943.	−	204283.i	−0.600473	−	1.04005i	−0.992749	−	0.120202i	$-0.961646\pi$
$131$	−117943.	−	204283.i	−0.600473	−	1.04005i	0.392277	−	0.919847i	$-0.371688\pi$
$132$	54168.5			0.270590
$133$	10797.2	+	32396.0i	0.0529275	+	0.158804i
$134$	−120161.			−0.578097
$135$	−9112.50	−	15783.3i	−0.0430331	−	0.0745356i
$136$	27853.3	−	48243.3i	0.129130	−	0.223661i
$137$	60250.2	−	104356.i	0.274256	−	0.475026i	−0.695691	−	0.718341i	$-0.744902\pi$
$137$	60250.2	−	104356.i	0.274256	−	0.475026i	0.969947	+	0.243315i	$0.0782349\pi$
$138$	−76056.3	−	131733.i	−0.339967	−	0.588841i
$139$	78689.4			0.345445			0.172723	−	0.984970i	$-0.444744\pi$
$139$	78689.4			0.345445			0.172723	+	0.984970i	$0.444744\pi$
$140$	50803.5	+	10398.3i	0.219065	+	0.0448378i
$141$	−10422.1			−0.0441478
$142$	−75246.5	−	130331.i	−0.313159	−	0.542408i
$143$	−83526.2	+	144672.i	−0.341572	+	0.591621i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−91146.8	−	157871.i	−0.360016	−	0.623565i
$146$	−129595.			−0.503158
$147$	121018.	−	90747.8i	0.461909	−	0.346372i
$148$	−44298.2			−0.166239
$149$	−129970.	−	225116.i	−0.479600	−	0.830691i	0.520126	−	0.854089i	$-0.325885\pi$
$149$	−129970.	−	225116.i	−0.479600	−	0.830691i	−0.999726	+	0.0233979i	$0.992552\pi$
$150$	11250.0	−	19485.6i	0.0408248	−	0.0707107i
$151$	146790.	−	254248.i	0.523907	−	0.907434i	−0.475706	−	0.879605i	$-0.657807\pi$
$151$	146790.	−	254248.i	0.523907	−	0.907434i	0.999613	−	0.0278292i	$-0.00885947\pi$
$152$	−8428.86	−	14599.2i	−0.0295910	−	0.0512532i
$153$	−70503.6			−0.243491
$154$	191108.	+	39115.5i	0.649346	+	0.132907i
$155$	−217616.			−0.727547
$156$	−31974.3	−	55381.1i	−0.105194	−	0.182201i
$157$	194783.	−	337374.i	0.630669	−	1.09235i	−0.356747	−	0.934201i	$-0.616114\pi$
$157$	194783.	−	337374.i	0.630669	−	1.09235i	0.987415	−	0.158149i	$-0.0505526\pi$
$158$	129356.	−	224051.i	0.412235	−	0.714011i
$159$	145257.	+	251593.i	0.455664	+	0.789233i
$160$	−25600.0			−0.0790569
$161$	−173202.	−	519679.i	−0.526610	−	1.58005i
$162$	26244.0			0.0785674
$163$	−116066.	−	201033.i	−0.342166	−	0.592649i	0.642669	−	0.766144i	$-0.277827\pi$
$163$	−116066.	−	201033.i	−0.342166	−	0.592649i	−0.984835	+	0.173495i	$0.944494\pi$
$164$	−85584.4	+	148237.i	−0.248476	+	0.430374i
$165$	42319.2	−	73298.9i	0.121012	−	0.209598i
$166$	210501.	+	364598.i	0.592902	+	1.02694i
$167$	−619069.			−1.71770			−0.858851	−	0.512226i	$-0.828821\pi$
$167$	−619069.			−1.71770			−0.858851	+	0.512226i	$0.828821\pi$
$168$	−49546.0	+	55869.0i	−0.135437	+	0.152721i
$169$	−174080.			−0.468847
$170$	−43520.7	−	75380.1i	−0.115498	−	0.200048i
$171$	−10667.8	+	18477.1i	−0.0278987	+	0.0483220i
$172$	126953.	−	219888.i	0.327206	−	0.566737i
$173$	−188434.	−	326377.i	−0.478678	−	0.829095i	0.521023	−	0.853543i	$-0.325551\pi$
$173$	−188434.	−	326377.i	−0.478678	−	0.829095i	−0.999701	+	0.0244478i	$0.992217\pi$
$174$	262503.			0.657295
$175$	53760.9	−	60621.8i	0.132700	−	0.149635i
$176$	−96299.6			−0.234338
$177$	164272.	+	284527.i	0.394121	+	0.682638i
$178$	44782.8	−	77566.0i	0.105940	−	0.183494i
$179$	−334997.	+	580232.i	−0.781463	+	1.35353i	0.149626	+	0.988743i	$0.452193\pi$
$179$	−334997.	+	580232.i	−0.781463	+	1.35353i	−0.931089	+	0.364792i	$0.881140\pi$
$180$	16200.0	+	28059.2i	0.0372678	+	0.0645497i
$181$	260652.			0.591377			0.295689	−	0.955284i	$-0.404451\pi$
$181$	260652.			0.591377			0.295689	+	0.955284i	$0.404451\pi$
$182$	−72814.8	−	218474.i	−0.162945	−	0.488902i
$183$	373093.			0.823548
$184$	135211.	+	234193.i	0.294420	+	0.509951i
$185$	−34608.0	+	59942.7i	−0.0743441	+	0.128768i
$186$	156683.	−	271384.i	0.332078	−	0.575177i
$187$	−163712.	−	283558.i	−0.342355	−	0.592976i
$188$	18528.3			0.0382332
$189$	92589.4	+	18951.0i	0.188541	+	0.0385902i
$190$	−26340.2			−0.0529340
$191$	120941.	+	209476.i	0.239878	+	0.415481i	0.960679	−	0.277661i	$-0.0895592\pi$
$191$	120941.	+	209476.i	0.239878	+	0.415481i	−0.720801	+	0.693142i	$0.756226\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	−432764.	+	749569.i	−0.836292	+	1.44850i	0.0566827	+	0.998392i	$0.481948\pi$
$193$	−432764.	+	749569.i	−0.836292	+	1.44850i	−0.892974	+	0.450107i	$0.851386\pi$
$194$	−74406.3	−	128875.i	−0.141940	−	0.245847i
$195$	−99919.6			−0.188176
$196$	−215143.	+	161329.i	−0.400025	+	0.299967i
$197$	59334.4			0.108928			0.0544642	−	0.998516i	$-0.482655\pi$
$197$	59334.4			0.108928			0.0544642	+	0.998516i	$0.482655\pi$
$198$	60939.6	+	105550.i	0.110468	+	0.191336i
$199$	−454112.	+	786545.i	−0.812887	+	1.40796i	0.0979483	+	0.995192i	$0.468772\pi$
$199$	−454112.	+	786545.i	−0.812887	+	1.40796i	−0.910835	+	0.412770i	$0.864561\pi$
$200$	−20000.0	+	34641.0i	−0.0353553	+	0.0612372i
$201$	−135181.	−	234140.i	−0.236007	−	0.408776i
$202$	658413.			1.13532
$203$	926115.	+	189555.i	1.57734	+	0.322846i
$204$	125340.			0.210869
$205$	133726.	+	231620.i	0.222244	+	0.384938i
$206$	−170213.	+	294817.i	−0.279463	+	0.484044i
$207$	171127.	−	296400.i	0.277582	−	0.480786i
$208$	56843.2	+	98455.2i	0.0911003	+	0.157790i
$209$	−99084.0			−0.156905
$210$	36892.2	+	110692.i	0.0577279	+	0.173207i
$211$	−389916.			−0.602927			−0.301463	−	0.953478i	$-0.597475\pi$
$211$	−389916.			−0.602927			−0.301463	+	0.953478i	$0.597475\pi$
$212$	−258235.	−	447276.i	−0.394617	−	0.683496i
$213$	169305.	−	293244.i	0.255694	−	0.442874i
$214$	−102140.	+	176912.i	−0.152462	+	0.264072i
$215$	−198364.	−	343576.i	−0.292662	−	0.506905i
$216$	−46656.0			−0.0680414
$217$	748750.	−	844304.i	1.07941	−	1.21717i
$218$	103412.			0.147377
$219$	−145794.	−	252522.i	−0.205414	−	0.355787i
$220$	−75234.1	+	130309.i	−0.104799	+	0.181517i
$221$	−193270.	+	334753.i	−0.266185	+	0.461046i
$222$	−49835.5	−	86317.6i	−0.0678666	−	0.117548i
$223$	432482.			0.582379			0.291189	−	0.956665i	$-0.405949\pi$
$223$	432482.			0.582379			0.291189	+	0.956665i	$0.405949\pi$
$224$	88081.9	−	99322.7i	0.117291	−	0.132260i
$225$	50625.0			0.0666667
$226$	−76848.3	−	133105.i	−0.100084	−	0.173350i
$227$	−382198.	+	661987.i	−0.492294	+	0.852678i	−0.999961	−	0.00887574i	$-0.997175\pi$
$227$	−382198.	+	661987.i	−0.492294	+	0.852678i	0.507667	+	0.861553i	$0.330508\pi$
$228$	18964.9	−	32848.2i	0.0241610	−	0.0418480i
$229$	354080.	+	613284.i	0.446183	+	0.772811i	0.998134	−	0.0610656i	$-0.0194499\pi$
$229$	354080.	+	613284.i	0.446183	+	0.772811i	−0.551951	+	0.833876i	$0.686117\pi$
$230$	422535.			0.526675
$231$	138777.	+	416389.i	0.171115	+	0.513416i
$232$	−466671.			−0.569235
$233$	−635878.	−	1.10137e6i	−0.767333	−	1.32906i	−0.939004	−	0.343906i	$-0.888250\pi$
$233$	−635878.	−	1.10137e6i	−0.767333	−	1.32906i	0.171671	−	0.985154i	$-0.445083\pi$
$234$	71942.1	−	124607.i	0.0858902	−	0.148766i
$235$	14475.2	−	25071.8i	0.0170984	−	0.0296153i
$236$	−292039.	−	505826.i	−0.341319	−	0.591182i
$237$	582103.			0.673176
$238$	442201.	+	90508.7i	0.506031	+	0.103573i
$239$	−300010.			−0.339735			−0.169868	−	0.985467i	$-0.554334\pi$
$239$	−300010.			−0.339735			−0.169868	+	0.985467i	$0.554334\pi$
$240$	−28800.0	−	49883.1i	−0.0322749	−	0.0559017i
$241$	28293.5	−	49005.9i	0.0313794	−	0.0543507i	−0.849909	−	0.526929i	$-0.823343\pi$
$241$	28293.5	−	49005.9i	0.0313794	−	0.0543507i	0.881289	+	0.472578i	$0.156677\pi$
$242$	39093.9	−	67712.6i	0.0429112	−	0.0743243i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	−663276.			−0.713214
$245$	50225.0	+	417162.i	0.0534570	+	0.444007i
$246$	−385130.			−0.405760
$247$	58486.7	+	101302.i	0.0609979	+	0.105651i
$248$	−278548.	+	482460.i	−0.287588	+	0.498117i
$249$	−473626.	+	820345.i	−0.484102	+	0.838490i
$250$	31250.0	+	54126.6i	0.0316228	+	0.0547723i
$251$	1.66302e6			1.66614			0.833071	−	0.553166i	$-0.186580\pi$
$251$	1.66302e6			1.66614			0.833071	+	0.553166i	$0.186580\pi$
$252$	−164603.	−	33690.6i	−0.163282	−	0.0334201i
$253$	1.58945e6			1.56115
$254$	358441.	+	620839.i	0.348605	+	0.603802i
$255$	97921.6	−	169605.i	0.0943036	−	0.163339i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	487587.	+	844525.i	0.460489	+	0.797590i	0.998985	−	0.0450375i	$-0.0143407\pi$
$257$	487587.	+	844525.i	0.460489	+	0.797590i	−0.538496	+	0.842628i	$0.681007\pi$
$258$	571287.			0.534324
$259$	−113490.	−	340517.i	−0.105126	−	0.315420i
$260$	177635.			0.162965
$261$	295316.	+	511502.i	0.268340	+	0.464778i
$262$	−471771.	+	817132.i	−0.424598	+	0.735426i
$263$	537984.	−	931815.i	0.479601	−	0.830693i	−0.520126	−	0.854090i	$-0.674115\pi$
$263$	537984.	−	931815.i	0.479601	−	0.830693i	0.999726	+	0.0233970i	$0.00744819\pi$
$264$	−108337.	−	187645.i	−0.0956681	−	0.165702i
$265$	−806984.			−0.705912
$266$	90628.7	−	102195.i	0.0785347	−	0.0885572i
$267$	201522.			0.173000
$268$	240321.	+	416249.i	0.204388	+	0.354010i
$269$	−738079.	+	1.27839e6i	−0.621902	+	1.07717i	0.367229	+	0.930131i	$0.380307\pi$
$269$	−738079.	+	1.27839e6i	−0.621902	+	1.07717i	−0.989131	+	0.147036i	$0.953027\pi$
$270$	−36450.0	+	63133.3i	−0.0304290	+	0.0527046i
$271$	−663286.	−	1.14884e6i	−0.548627	−	0.950250i	−0.998369	−	0.0570916i	$-0.981817\pi$
$271$	−663286.	−	1.14884e6i	−0.548627	−	0.950250i	0.449742	−	0.893159i	$-0.351516\pi$
$272$	−222826.			−0.182618
$273$	343793.	−	387668.i	0.279184	−	0.314813i
$274$	−482001.			−0.387857
$275$	117553.	+	203608.i	0.0937352	+	0.162354i
$276$	−304225.	+	526933.i	−0.240393	+	0.416373i
$277$	−745269.	+	1.29084e6i	−0.583598	+	1.01082i	0.411451	+	0.911432i	$0.365022\pi$
$277$	−745269.	+	1.29084e6i	−0.583598	+	1.01082i	−0.995049	+	0.0993891i	$0.968311\pi$
$278$	−157379.	−	272588.i	−0.122133	−	0.211541i
$279$	705075.			0.542282
$280$	−65586.0	−	196785.i	−0.0499938	−	0.150002i
$281$	−1.00956e6			−0.762719			−0.381360	−	0.924427i	$-0.624544\pi$
$281$	−1.00956e6			−0.762719			−0.381360	+	0.924427i	$0.624544\pi$
$282$	20844.3	+	36103.4i	0.0156086	+	0.0270349i
$283$	497080.	−	860968.i	0.368944	−	0.639030i	−0.620457	−	0.784241i	$-0.713053\pi$
$283$	497080.	−	860968.i	0.368944	−	0.639030i	0.989401	+	0.145211i	$0.0463861\pi$
$284$	−300986.	+	521323.i	−0.221437	+	0.383540i
$285$	−29632.7	−	51325.4i	−0.0216102	−	0.0374300i
$286$	668210.			0.483056
$287$	−1.35875e6	−	278105.i	−0.973719	−	0.199299i
$288$	82944.0			0.0589256
$289$	331118.	+	573513.i	0.233205	+	0.403923i
$290$	−364587.	+	631483.i	−0.254569	+	0.440927i
$291$	167414.	−	289970.i	0.115894	−	0.200734i
$292$	259189.	+	448929.i	0.177893	+	0.308120i
$293$	1.69742e6			1.15510			0.577549	−	0.816356i	$-0.304009\pi$
$293$	1.69742e6			1.15510			0.577549	+	0.816356i	$0.304009\pi$
$294$	−556395.	−	237723.i	−0.375418	−	0.160399i
$295$	−912621.			−0.610570
$296$	88596.4	+	153453.i	0.0587742	+	0.101800i
$297$	−137114.	+	237489.i	−0.0901967	+	0.156225i
$298$	−519882.	+	900462.i	−0.339128	+	0.587388i
$299$	−938211.	−	1.62503e6i	−0.606908	−	1.05120i
$300$	−90000.0			−0.0577350
$301$	2.01551e6	+	412531.i	1.28224	+	0.262446i
$302$	−1.17432e6			−0.740917
$303$	740714.	+	1.28295e6i	0.463494	+	0.802795i
$304$	−33715.5	+	58396.9i	−0.0209240	+	0.0362415i
$305$	−518184.	+	897522.i	−0.318959	+	0.552453i
$306$	141007.	+	244232.i	0.0860870	+	0.149107i
$307$	2.95303e6			1.78822			0.894111	−	0.447846i	$-0.147809\pi$
$307$	2.95303e6			1.78822			0.894111	+	0.447846i	$0.147809\pi$
$308$	−246715.	−	740247.i	−0.148190	−	0.444631i
$309$	−765957.			−0.456361
$310$	435232.	+	753843.i	0.257227	+	0.445530i
$311$	1.06071e6	−	1.83721e6i	0.621866	−	1.07710i	−0.367272	−	0.930114i	$-0.619708\pi$
$311$	1.06071e6	−	1.83721e6i	0.621866	−	1.07710i	0.989138	−	0.146990i	$-0.0469584\pi$
$312$	−127897.	+	221524.i	−0.0743831	+	0.128835i
$313$	−192508.	−	333434.i	−0.111068	−	0.192375i	0.805133	−	0.593094i	$-0.202094\pi$
$313$	−192508.	−	333434.i	−0.111068	−	0.192375i	−0.916201	+	0.400719i	$0.868760\pi$
$314$	−1.55826e6			−0.891900
$315$	−174185.	+	196415.i	−0.0989089	+	0.111531i
$316$	−1.03485e6			−0.582988
$317$	−505089.	−	874840.i	−0.282306	−	0.488968i	0.689646	−	0.724146i	$-0.257766\pi$
$317$	−505089.	−	874840.i	−0.282306	−	0.488968i	−0.971952	+	0.235178i	$0.924433\pi$
$318$	581029.	−	1.00637e6i	0.322203	−	0.558072i
$319$	−1.37147e6	+	2.37545e6i	−0.754586	+	1.30698i
$320$	51200.0	+	88681.0i	0.0279508	+	0.0484123i
$321$	−459630.			−0.248969
$322$	−1.45381e6	+	1.63935e6i	−0.781393	+	0.881113i
$323$	−229269.			−0.122275
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	138777.	−	240369.i	0.0728803	−	0.126232i
$326$	−464265.	+	804131.i	−0.241948	+	0.419066i
$327$	116339.	+	201505.i	0.0601666	+	0.104212i
$328$	684675.			0.351399
$329$	47468.6	+	142425.i	0.0241778	+	0.0725433i
$330$	−338553.			−0.171136
$331$	−1.78311e6	−	3.08844e6i	−0.894558	−	1.54942i	−0.834350	−	0.551235i	$-0.814157\pi$
$331$	−1.78311e6	−	3.08844e6i	−0.894558	−	1.54942i	−0.0602084	−	0.998186i	$-0.519177\pi$
$332$	842002.	−	1.45839e6i	0.419245	−	0.726154i
$333$	112130.	−	194215.i	0.0554128	−	0.0959779i
$334$	1.23814e6	+	2.14452e6i	0.607299	+	1.05187i
$335$	751004.			0.365620
$336$	292628.	+	59894.5i	0.141406	+	0.0289427i
$337$	−1.16658e6			−0.559551			−0.279776	−	0.960065i	$-0.590260\pi$
$337$	−1.16658e6			−0.559551			−0.279776	+	0.960065i	$0.590260\pi$
$338$	348159.	+	603029.i	0.165762	+	0.287109i
$339$	172909.	−	299487.i	0.0817180	−	0.141540i
$340$	−174083.	+	301520.i	−0.0816693	+	0.141455i
$341$	1.63721e6	+	2.83573e6i	0.762463	+	1.32063i
$342$	85342.3			0.0394547
$343$	−1.79131e6	−	1.24047e6i	−0.822122	−	0.569311i
$344$	−1.01562e6			−0.462739
$345$	475352.	+	823333.i	0.215014	+	0.372416i
$346$	−753735.	+	1.30551e6i	−0.338477	+	0.586259i
$347$	−1.09312e6	+	1.89333e6i	−0.487351	+	0.844117i	−0.999894	−	0.0145443i	$-0.995370\pi$
$347$	−1.09312e6	+	1.89333e6i	−0.487351	+	0.844117i	0.512543	+	0.858662i	$0.328704\pi$
$348$	−525005.	−	909336.i	−0.232389	−	0.402510i
$349$	488943.			0.214880			0.107440	−	0.994212i	$-0.465735\pi$
$349$	488943.			0.214880			0.107440	+	0.994212i	$0.465735\pi$
$350$	−317522.	−	64989.7i	−0.138549	−	0.0283579i
$351$	323740.			0.140258
$352$	192599.	+	333592.i	0.0828510	+	0.143502i
$353$	−462447.	+	800981.i	−0.197526	+	0.342125i	−0.947726	−	0.319086i	$-0.896624\pi$
$353$	−462447.	+	800981.i	−0.197526	+	0.342125i	0.750200	+	0.661212i	$0.229957\pi$
$354$	657087.	−	1.13811e6i	0.278686	−	0.482698i
$355$	470291.	+	814568.i	0.198059	+	0.343049i
$356$	−358262.			−0.149822
$357$	321115.	+	963476.i	0.133349	+	0.400102i
$358$	2.67998e6			1.10516
$359$	−157198.	−	272274.i	−0.0643739	−	0.111499i	0.832042	−	0.554712i	$-0.187172\pi$
$359$	−157198.	−	272274.i	−0.0643739	−	0.111499i	−0.896416	+	0.443214i	$0.853838\pi$
$360$	64800.0	−	112237.i	0.0263523	−	0.0456435i
$361$	1.20336e6	−	2.08428e6i	0.485990	−	0.841759i
$362$	−521304.	−	902925.i	−0.209083	−	0.362143i
$363$	175922.			0.0700736
$364$	−611188.	+	689187.i	−0.241781	+	0.272636i
$365$	809966.			0.318225
$366$	−746186.	−	1.29243e6i	−0.291168	−	0.504318i
$367$	1.48827e6	−	2.57775e6i	0.576787	−	0.999024i	−0.419058	−	0.907959i	$-0.637640\pi$
$367$	1.48827e6	−	2.57775e6i	0.576787	−	0.999024i	0.995845	−	0.0910644i	$-0.0290269\pi$
$368$	540845.	−	936770.i	0.208187	−	0.360590i
$369$	−433271.	−	750448.i	−0.165651	−	0.286916i
$370$	276864.			0.105138
$371$	2.77659e6	−	3.13093e6i	1.04731	−	1.18097i
$372$	−1.25347e6			−0.469630
$373$	−1.77167e6	−	3.06862e6i	−0.659341	−	1.14201i	−0.980787	−	0.195084i	$-0.937502\pi$
$373$	−1.77167e6	−	3.06862e6i	−0.659341	−	1.14201i	0.321445	−	0.946928i	$-0.395831\pi$
$374$	−654848.	+	1.13423e6i	−0.242081	+	0.419297i
$375$	−70312.5	+	121785.i	−0.0258199	+	0.0447214i
$376$	−37056.5	−	64183.8i	−0.0135175	−	0.0234129i
$377$	3.23817e6			1.17340
$378$	−119531.	−	358641.i	−0.0430278	−	0.129101i
$379$	−2.68890e6			−0.961559			−0.480780	−	0.876842i	$-0.659646\pi$
$379$	−2.68890e6			−0.961559			−0.480780	+	0.876842i	$0.659646\pi$
$380$	52680.4	+	91245.1i	0.0187150	+	0.0324154i
$381$	−806493.	+	1.39689e6i	−0.284635	+	0.493002i
$382$	483764.	−	837905.i	0.169619	−	0.293789i
$383$	−2.30505e6	−	3.99246e6i	−0.802940	−	1.39073i	−0.917673	−	0.397336i	$-0.869935\pi$
$383$	−2.30505e6	−	3.99246e6i	−0.802940	−	1.39073i	0.114734	−	0.993396i	$-0.463399\pi$
$384$	−147456.			−0.0510310
$385$	−1.19442e6	−	244472.i	−0.410682	−	0.0840576i
$386$	3.46211e6			1.18270
$387$	642698.	+	1.11319e6i	0.218137	+	0.377824i
$388$	−297625.	+	515502.i	−0.100367	+	0.173840i
$389$	−1.41964e6	+	2.45889e6i	−0.475669	+	0.823883i	−0.999612	−	0.0278705i	$-0.991127\pi$
$389$	−1.41964e6	+	2.45889e6i	−0.475669	+	0.823883i	0.523942	+	0.851754i	$0.324461\pi$
$390$	199839.	+	346132.i	0.0665303	+	0.115234i
$391$	3.67780e6			1.21660
$392$	989148.	+	422618.i	0.325122	+	0.138910i
$393$	−2.12297e6			−0.693366
$394$	−118669.	−	205540.i	−0.0385120	−	0.0667047i
$395$	−808476.	+	1.40032e6i	−0.260720	+	0.451580i
$396$	243758.	−	422202.i	0.0781127	−	0.135295i
$397$	−148862.	−	257837.i	−0.0474033	−	0.0821049i	0.841350	−	0.540490i	$-0.181761\pi$
$397$	−148862.	−	257837.i	−0.0474033	−	0.0821049i	−0.888753	+	0.458385i	$0.848428\pi$
$398$	3.63290e6			1.14960
$399$	301089.	+	61626.3i	0.0946810	+	0.0193791i
$400$	160000.			0.0500000
$401$	2.28859e6	+	3.96396e6i	0.710734	+	1.23103i	0.964582	+	0.263784i	$0.0849705\pi$
$401$	2.28859e6	+	3.96396e6i	0.710734	+	1.23103i	−0.253847	+	0.967244i	$0.581696\pi$
$402$	−540723.	+	936560.i	−0.166882	+	0.289048i
$403$	1.93281e6	−	3.34772e6i	0.592824	−	1.02680i
$404$	−1.31683e6	−	2.28081e6i	−0.401398	−	0.695241i
$405$	−164025.			−0.0496904
$406$	−1.19559e6	−	3.58727e6i	−0.359971	−	1.08006i
$407$	1.04148e6			0.311648
$408$	−250679.	−	434189.i	−0.0745535	−	0.129130i
$409$	1.84079e6	−	3.18833e6i	0.544120	−	0.942444i	−0.454541	−	0.890726i	$-0.650197\pi$
$409$	1.84079e6	−	3.18833e6i	0.544120	−	0.942444i	0.998662	−	0.0517185i	$-0.0164699\pi$
$410$	534903.	−	926479.i	0.157150	−	0.272192i
$411$	−542252.	−	939207.i	−0.158342	−	0.274256i
$412$	1.36170e6			0.395220
$413$	3.14005e6	−	3.54078e6i	0.905861	−	1.02147i
$414$	−1.36901e6			−0.392561
$415$	−1.31563e6	−	2.27873e6i	−0.374984	−	0.649492i
$416$	227373.	−	393821.i	0.0644177	−	0.111575i
$417$	354103.	−	613324.i	0.0997215	−	0.172723i
$418$	198168.	+	343237.i	0.0554744	+	0.0960845i
$419$	−1.50062e6			−0.417576			−0.208788	−	0.977961i	$-0.566952\pi$
$419$	−1.50062e6			−0.417576			−0.208788	+	0.977961i	$0.566952\pi$
$420$	309663.	−	349181.i	0.0856576	−	0.0965891i
$421$	−2.98818e6			−0.821679			−0.410839	−	0.911708i	$-0.634764\pi$
$421$	−2.98818e6			−0.821679			−0.410839	+	0.911708i	$0.634764\pi$
$422$	779832.	+	1.35071e6i	0.213167	+	0.369216i
$423$	−46899.7	+	81232.6i	−0.0127444	+	0.0220739i
$424$	−1.03294e6	+	1.78910e6i	−0.279036	+	0.483305i
$425$	272005.	+	471126.i	0.0730472	+	0.126522i
$426$	−1.35444e6			−0.361605
$427$	−1.69928e6	−	5.09855e6i	−0.451020	−	1.35325i
$428$	817120.			0.215614
$429$	751736.	+	1.30204e6i	0.197207	+	0.341572i
$430$	−793454.	+	1.37430e6i	−0.206943	+	0.358436i
$431$	−1.51519e6	+	2.62438e6i	−0.392892	+	0.680509i	−0.992830	−	0.119538i	$-0.961859\pi$
$431$	−1.51519e6	+	2.62438e6i	−0.392892	+	0.680509i	0.599938	+	0.800047i	$0.295192\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	1.41809e6			0.363483			0.181742	−	0.983346i	$-0.441827\pi$
$433$	1.41809e6			0.363483			0.181742	+	0.983346i	$0.441827\pi$
$434$	−4.42226e6	−	905138.i	−1.12699	−	0.230670i
$435$	−1.64064e6			−0.415710
$436$	−206825.	−	358231.i	−0.0521058	−	0.0902499i
$437$	556483.	−	963856.i	0.139395	−	0.241440i
$438$	−583176.	+	1.01009e6i	−0.145249	+	0.251579i
$439$	−1.86019e6	−	3.22194e6i	−0.460676	−	0.797914i	0.538319	−	0.842741i	$-0.319060\pi$
$439$	−1.86019e6	−	3.22194e6i	−0.460676	−	0.797914i	−0.998995	+	0.0448275i	$0.985726\pi$
$440$	601872.			0.148208
$441$	−162729.	−	1.35161e6i	−0.0398445	−	0.330943i
$442$	1.54616e6			0.376443
$443$	400436.	+	693575.i	0.0969446	+	0.167913i	0.910419	−	0.413688i	$-0.135760\pi$
$443$	400436.	+	693575.i	0.0969446	+	0.167913i	−0.813474	+	0.581601i	$0.802426\pi$
$444$	−199342.	+	345270.i	−0.0479889	+	0.0831193i
$445$	−279892.	+	484788.i	−0.0670025	+	0.116052i
$446$	−864964.	−	1.49816e6i	−0.205902	−	0.356633i
$447$	−2.33947e6			−0.553794
$448$	−520228.	−	106479.i	−0.122461	−	0.0250651i
$449$	3.89383e6			0.911510			0.455755	−	0.890105i	$-0.349369\pi$
$449$	3.89383e6			0.911510			0.455755	+	0.890105i	$0.349369\pi$
$450$	−101250.	−	175370.i	−0.0235702	−	0.0408248i
$451$	2.01214e6	−	3.48514e6i	0.465820	−	0.806823i
$452$	−307393.	+	532421.i	−0.0707698	+	0.122577i
$453$	−1.32111e6	−	2.28823e6i	−0.302478	−	0.523907i
$454$	3.05759e6			0.696208
$455$	455093.	+	1.36547e6i	0.103056	+	0.309209i
$456$	−151720.			−0.0341688
$457$	1.61339e6	+	2.79447e6i	0.361367	+	0.625906i	0.988186	−	0.153259i	$-0.0489768\pi$
$457$	1.61339e6	+	2.79447e6i	0.361367	+	0.625906i	−0.626819	+	0.779165i	$0.715644\pi$
$458$	1.41632e6	−	2.45314e6i	0.315499	−	0.546460i
$459$	−317266.	+	549521.i	−0.0702897	+	0.121745i
$460$	−845070.	−	1.46370e6i	−0.186208	−	0.322521i
$461$	4.10832e6			0.900351			0.450176	−	0.892940i	$-0.351361\pi$
$461$	4.10832e6			0.900351			0.450176	+	0.892940i	$0.351361\pi$
$462$	1.16486e6	−	1.31352e6i	0.253903	−	0.286306i
$463$	−1.48281e6			−0.321465			−0.160733	−	0.986998i	$-0.551386\pi$
$463$	−1.48281e6			−0.321465			−0.160733	+	0.986998i	$0.551386\pi$
$464$	933343.	+	1.61660e6i	0.201255	+	0.348584i
$465$	−979271.	+	1.69615e6i	−0.210025	+	0.363774i
$466$	−2.54351e6	+	4.40549e6i	−0.542587	+	0.939787i
$467$	1.14431e6	+	1.98201e6i	0.242803	+	0.420546i	0.961511	−	0.274765i	$-0.0886000\pi$
$467$	1.14431e6	+	1.98201e6i	0.242803	+	0.420546i	−0.718709	+	0.695311i	$0.755267\pi$
$468$	−575537.			−0.121467
$469$	−2.58398e6	+	2.91374e6i	−0.542446	+	0.611672i
$470$	−115802.			−0.0241808
$471$	−1.75304e6	−	3.03636e6i	−0.364117	−	0.630669i
$472$	−1.16815e6	+	2.02330e6i	−0.241349	+	0.418029i
$473$	−2.98474e6	+	5.16972e6i	−0.613414	+	1.06246i
$474$	−1.16421e6	−	2.01646e6i	−0.238004	−	0.412235i
$475$	164626.			0.0334784
$476$	−570870.	−	1.71285e6i	−0.115484	−	0.346498i
$477$	2.61463e6			0.526156
$478$	600020.	+	1.03926e6i	0.120115	+	0.208045i
$479$	−252312.	+	437018.i	−0.0502458	+	0.0870283i	−0.890054	−	0.455854i	$-0.849334\pi$
$479$	−252312.	+	437018.i	−0.0502458	+	0.0870283i	0.839809	+	0.542883i	$0.182667\pi$
$480$	−115200.	+	199532.i	−0.0228218	+	0.0395285i
$481$	−614758.	−	1.06479e6i	−0.121155	−	0.209847i
$482$	−226348.			−0.0443772
$483$	−4.82990e6	−	988574.i	−0.942043	−	0.192815i
$484$	−312751.			−0.0606855
$485$	465039.	+	805471.i	0.0897708	+	0.155488i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	739529.	−	1.28090e6i	0.141297	−	0.244733i	−0.786688	−	0.617350i	$-0.788206\pi$
$487$	739529.	−	1.28090e6i	0.141297	−	0.244733i	0.927985	+	0.372617i	$0.121539\pi$
$488$	1.32655e6	+	2.29766e6i	0.252159	+	0.436752i
$489$	−2.08919e6			−0.395100
$490$	1.34464e6	−	1.00831e6i	0.252998	−	0.189716i
$491$	7.51661e6			1.40708			0.703539	−	0.710657i	$-0.251602\pi$
$491$	7.51661e6			1.40708			0.703539	+	0.710657i	$0.251602\pi$
$492$	770260.	+	1.33413e6i	0.143458	+	0.248476i
$493$	−3.17342e6	+	5.49652e6i	−0.588044	+	1.01852i
$494$	233947.	−	405208.i	0.0431320	−	0.0747069i
$495$	−380872.	−	659690.i	−0.0698661	−	0.121012i
$496$	2.22839e6			0.406711
$497$	−4.77848e6	−	978049.i	−0.867759	−	0.177611i
$498$	3.78901e6			0.684624
$499$	−1.21517e6	−	2.10474e6i	−0.218468	−	0.378397i	0.735872	−	0.677121i	$-0.236773\pi$
$499$	−1.21517e6	−	2.10474e6i	−0.218468	−	0.378397i	−0.954340	+	0.298723i	$0.903439\pi$
$500$	125000.	−	216506.i	0.0223607	−	0.0387298i
$501$	−2.78581e6	+	4.82516e6i	−0.495858	+	0.858851i
$502$	−3.32603e6	−	5.76086e6i	−0.589070	−	1.02030i
$503$	−5.24665e6			−0.924617			−0.462309	−	0.886719i	$-0.652979\pi$
$503$	−5.24665e6			−0.924617			−0.462309	+	0.886719i	$0.652979\pi$
$504$	212499.	+	637584.i	0.0372632	+	0.111805i
$505$	−4.11508e6			−0.718042
$506$	−3.17890e6	−	5.50602e6i	−0.551951	−	0.956007i
$507$	−783358.	+	1.35682e6i	−0.135344	+	0.234423i
$508$	1.43377e6	−	2.48335e6i	0.246501	−	0.426952i
$509$	−2.54111e6	−	4.40134e6i	−0.434740	−	0.752992i	0.562534	−	0.826774i	$-0.309826\pi$
$509$	−2.54111e6	−	4.40134e6i	−0.434740	−	0.752992i	−0.997274	+	0.0737822i	$0.976493\pi$
$510$	−783373.			−0.133365
$511$	−2.78685e6	+	3.14250e6i	−0.472129	+	0.532382i
$512$	262144.			0.0441942
$513$	96010.0	+	166294.i	0.0161073	+	0.0278987i
$514$	1.95035e6	−	3.37810e6i	0.325615	−	0.563982i
$515$	1.06383e6	−	1.84261e6i	0.176748	−	0.306136i
$516$	−1.14257e6	−	1.97900e6i	−0.188912	−	0.327206i
$517$	−435611.			−0.0716759
$518$	−952604.	+	1.07417e6i	−0.155987	+	0.175894i
$519$	−3.39181e6			−0.552730
$520$	−355270.	−	615345.i	−0.0576169	−	0.0997954i
$521$	−1.16985e6	+	2.02623e6i	−0.188814	+	0.327036i	−0.944855	−	0.327488i	$-0.893798\pi$
$521$	−1.16985e6	+	2.02623e6i	−0.188814	+	0.327036i	0.756041	+	0.654524i	$0.227131\pi$
$522$	1.18126e6	−	2.04601e6i	0.189745	−	0.328648i
$523$	−3.29946e6	−	5.71483e6i	−0.527459	−	0.913586i	−0.999488	−	0.0320025i	$-0.989812\pi$
$523$	−3.29946e6	−	5.71483e6i	−0.527459	−	0.913586i	0.472029	−	0.881583i	$-0.343522\pi$
$524$	3.77417e6			0.600473
$525$	−230576.	−	691823.i	−0.0365103	−	0.109546i
$526$	−4.30387e6			−0.678258
$527$	3.78832e6	+	6.56156e6i	0.594183	+	1.02915i
$528$	−433348.	+	750581.i	−0.0676476	+	0.117169i
$529$	−5.70861e6	+	9.88760e6i	−0.886934	+	1.53621i
$530$	1.61397e6	+	2.79548e6i	0.249577	+	0.432281i
$531$	2.95689e6			0.455092
$532$	−535270.	−	109558.i	−0.0819962	−	0.0167828i
$533$	−4.75087e6			−0.724361
$534$	−403045.	−	698094.i	−0.0611646	−	0.105940i
$535$	638375.	−	1.10570e6i	0.0964254	−	0.167014i
$536$	961285.	−	1.66500e6i	0.144524	−	0.250323i
$537$	3.01498e6	+	5.22209e6i	0.451178	+	0.781463i
$538$	5.90463e6			0.879502
$539$	5.05815e6	−	3.79296e6i	0.749928	−	0.562350i
$540$	291600.			0.0430331
$541$	4.18341e6	+	7.24587e6i	0.614521	+	1.06438i	0.990468	+	0.137741i	$0.0439841\pi$
$541$	4.18341e6	+	7.24587e6i	0.614521	+	1.06438i	−0.375947	+	0.926641i	$0.622683\pi$
$542$	−2.65314e6	+	4.59538e6i	−0.387938	+	0.671928i
$543$	1.17293e6	−	2.03158e6i	0.170716	−	0.295689i
$544$	445652.	+	771892.i	0.0645652	+	0.111830i
$545$	−646327.			−0.0932097
$546$	−2.03051e6	−	415600.i	−0.291489	−	0.0596614i
$547$	−1.01705e6			−0.145337			−0.0726684	−	0.997356i	$-0.523151\pi$
$547$	−1.01705e6			−0.145337			−0.0726684	+	0.997356i	$0.523151\pi$
$548$	964003.	+	1.66970e6i	0.137128	+	0.237513i
$549$	1.67892e6	−	2.90797e6i	0.237738	−	0.411774i
$550$	470213.	−	814433.i	0.0662808	−	0.114802i
$551$	960330.	+	1.66334e6i	0.134754	+	0.233401i
$552$	2.43380e6			0.339967
$553$	−2.65124e6	−	7.95480e6i	−0.368668	−	1.10616i
$554$	5.96215e6			0.825332
$555$	311472.	+	539485.i	0.0429226	+	0.0743441i
$556$	−629516.	+	1.09035e6i	−0.0863614	+	0.149582i
$557$	−4.56175e6	+	7.90117e6i	−0.623007	+	1.07908i	0.365915	+	0.930648i	$0.380756\pi$
$557$	−4.56175e6	+	7.90117e6i	−0.623007	+	1.07908i	−0.988923	+	0.148432i	$0.952577\pi$
$558$	−1.41015e6	−	2.44245e6i	−0.191726	−	0.332078i
$559$	7.04726e6			0.953873
$560$	−550512.	+	620767.i	−0.0741816	+	0.0836486i
$561$	−2.94682e6			−0.395317
$562$	2.01911e6	+	3.49721e6i	0.269662	+	0.467068i
$563$	3.19124e6	−	5.52739e6i	0.424315	−	0.734935i	−0.572041	−	0.820225i	$-0.693848\pi$
$563$	3.19124e6	−	5.52739e6i	0.424315	−	0.734935i	0.996356	+	0.0852900i	$0.0271817\pi$
$564$	83377.2	−	144414.i	0.0110370	−	0.0191166i
$565$	480302.	+	831907.i	0.0632985	+	0.109636i
$566$	−3.97664e6			−0.521765
$567$	564360.	−	636383.i	0.0737223	−	0.0831306i
$568$	2.40789e6			0.313159
$569$	4.51774e6	+	7.82496e6i	0.584980	+	1.01321i	0.994878	+	0.101083i	$0.0322309\pi$
$569$	4.51774e6	+	7.82496e6i	0.584980	+	1.01321i	−0.409898	+	0.912131i	$0.634436\pi$
$570$	−118531.	+	205302.i	−0.0152807	+	0.0264670i
$571$	−7.13771e6	+	1.23629e7i	−0.916154	+	1.58682i	−0.110950	+	0.993826i	$0.535389\pi$
$571$	−7.13771e6	+	1.23629e7i	−0.916154	+	1.58682i	−0.805203	+	0.592999i	$0.797944\pi$
$572$	−1.33642e6	−	2.31475e6i	−0.170786	−	0.295810i
$573$	2.17694e6			0.276987
$574$	1.75411e6	+	5.26304e6i	0.222217	+	0.666741i
$575$	−2.64084e6			−0.333099
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	3.94911e6	−	6.84005e6i	0.493809	−	0.855303i	−0.506165	−	0.862436i	$-0.668937\pi$
$577$	3.94911e6	−	6.84005e6i	0.493809	−	0.855303i	0.999975	+	0.00713385i	$0.00227079\pi$
$578$	1.32447e6	−	2.29405e6i	0.164901	−	0.285617i
$579$	3.89488e6	+	6.74612e6i	0.482833	+	0.836292i
$580$	2.91670e6			0.360016
$581$	1.33677e7	+	2.73607e6i	1.64292	+	0.336269i
$582$	−1.33931e6			−0.163898
$583$	6.07127e6	+	1.05157e7i	0.739789	+	1.28135i
$584$	1.03676e6	−	1.79571e6i	0.125790	−	0.217874i
$585$	−449638.	+	778796.i	−0.0543217	+	0.0940880i
$586$	−3.39483e6	−	5.88002e6i	−0.408389	−	0.707351i
$587$	−480037.			−0.0575016			−0.0287508	−	0.999587i	$-0.509153\pi$
$587$	−480037.			−0.0575016			−0.0287508	+	0.999587i	$0.509153\pi$
$588$	289296.	+	2.40286e6i	0.0345064	+	0.286605i
$589$	2.29282e6			0.272321
$590$	1.82524e6	+	3.16141e6i	0.215869	+	0.373896i
$591$	267005.	−	462466.i	0.0314449	−	0.0544642i
$592$	354386.	−	613814.i	0.0415596	−	0.0719834i
$593$	5.03687e6	+	8.72412e6i	0.588199	+	1.01879i	0.994468	+	0.105037i	$0.0334962\pi$
$593$	5.03687e6	+	8.72412e6i	0.588199	+	1.01879i	−0.406269	+	0.913753i	$0.633170\pi$
$594$	1.09691e6			0.127557
$595$	−2.76376e6	−	565679.i	−0.320042	−	0.0655055i
$596$	4.15906e6			0.479600
$597$	4.08701e6	+	7.07890e6i	0.469321	+	0.812887i
$598$	−3.75285e6	+	6.50012e6i	−0.429149	+	0.743307i
$599$	1.47865e6	−	2.56110e6i	0.168383	−	0.291649i	−0.769468	−	0.638685i	$-0.779479\pi$
$599$	1.47865e6	−	2.56110e6i	0.168383	−	0.291649i	0.937852	+	0.347036i	$0.112812\pi$
$600$	180000.	+	311769.i	0.0204124	+	0.0353553i
$601$	−1.95113e6			−0.220344			−0.110172	−	0.993913i	$-0.535140\pi$
$601$	−1.95113e6			−0.220344			−0.110172	+	0.993913i	$0.535140\pi$
$602$	−2.60198e6	−	7.80700e6i	−0.292625	−	0.877997i
$603$	−2.43325e6			−0.272517
$604$	2.34864e6	+	4.06797e6i	0.261954	+	0.453717i
$605$	−244337.	+	423204.i	−0.0271394	+	0.0470068i
$606$	2.96286e6	−	5.13182e6i	0.327740	−	0.567662i
$607$	1.00418e6	+	1.73930e6i	0.110622	+	0.191603i	0.916021	−	0.401130i	$-0.131382\pi$
$607$	1.00418e6	+	1.73930e6i	0.110622	+	0.191603i	−0.805399	+	0.592733i	$0.798049\pi$
$608$	269724.			0.0295910
$609$	5.64495e6	−	6.36535e6i	0.616761	−	0.695471i
$610$	4.14548e6			0.451076
$611$	257130.	+	445363.i	0.0278644	+	0.0482626i
$612$	564029.	−	976926.i	0.0608727	−	0.105435i
$613$	−6.88619e6	+	1.19272e7i	−0.740164	+	1.28200i	0.212257	+	0.977214i	$0.431919\pi$
$613$	−6.88619e6	+	1.19272e7i	−0.740164	+	1.28200i	−0.952420	+	0.304787i	$0.901415\pi$
$614$	−5.90605e6	−	1.02296e7i	−0.632232	−	1.09506i
$615$	2.40706e6			0.256625
$616$	−2.07086e6	+	2.33514e6i	−0.219887	+	0.247948i
$617$	5.75202e6			0.608286			0.304143	−	0.952626i	$-0.401630\pi$
$617$	5.75202e6			0.608286			0.304143	+	0.952626i	$0.401630\pi$
$618$	1.53191e6	+	2.65335e6i	0.161348	+	0.279463i
$619$	−1.63386e6	+	2.82994e6i	−0.171392	+	0.296859i	−0.938907	−	0.344172i	$-0.888160\pi$
$619$	−1.63386e6	+	2.82994e6i	−0.171392	+	0.296859i	0.767515	+	0.641031i	$0.221493\pi$
$620$	1.74093e6	−	3.01537e6i	0.181887	−	0.315037i
$621$	−1.54014e6	−	2.66760e6i	−0.160262	−	0.277582i
$622$	−8.48570e6			−0.879451
$623$	−917851.	−	2.75393e6i	−0.0947441	−	0.284271i
$624$	1.02318e6			0.105194
$625$	−195312.	−	338291.i	−0.0200000	−	0.0346410i
$626$	−770032.	+	1.33374e6i	−0.0785368	+	0.136030i
$627$	−445878.	+	772283.i	−0.0452947	+	0.0784527i
$628$	3.11652e6	+	5.39798e6i	0.315334	+	0.546175i
$629$	2.40986e6			0.242865
$630$	1.02877e6	+	210567.i	0.103268	+	0.0211367i
$631$	−4.01563e6			−0.401495			−0.200748	−	0.979643i	$-0.564337\pi$
$631$	−4.01563e6			−0.401495			−0.200748	+	0.979643i	$0.564337\pi$
$632$	2.06970e6	+	3.58482e6i	0.206117	+	0.357006i
$633$	−1.75462e6	+	3.03909e6i	−0.174050	+	0.301463i
$634$	−2.02036e6	+	3.49936e6i	−0.199620	+	0.345753i
$635$	−2.24026e6	−	3.88024e6i	−0.220477	−	0.381878i
$636$	−4.64823e6			−0.455664
$637$	−6.86356e6	−	2.93249e6i	−0.670194	−	0.286344i
$638$	1.09717e7			1.06715
$639$	−1.52374e6	−	2.63920e6i	−0.147625	−	0.255694i
$640$	204800.	−	354724.i	0.0197642	−	0.0342327i
$641$	1.62418e6	−	2.81316e6i	0.156131	−	0.270427i	−0.777339	−	0.629082i	$-0.783431\pi$
$641$	1.62418e6	−	2.81316e6i	0.156131	−	0.270427i	0.933470	+	0.358655i	$0.116764\pi$
$642$	919260.	+	1.59220e6i	0.0880239	+	0.152462i
$643$	−4.88701e6			−0.466140			−0.233070	−	0.972460i	$-0.574877\pi$
$643$	−4.88701e6			−0.466140			−0.233070	+	0.972460i	$0.574877\pi$
$644$	8.58650e6	+	1.75747e6i	0.815833	+	0.166983i
$645$	−3.57054e6			−0.337936
$646$	458538.	+	794211.i	0.0432309	+	0.0748780i
$647$	−504818.	+	874370.i	−0.0474104	+	0.0821173i	−0.888757	−	0.458379i	$-0.848430\pi$
$647$	−504818.	+	874370.i	−0.0474104	+	0.0821173i	0.841346	+	0.540496i	$0.181764\pi$
$648$	−209952.	+	363648.i	−0.0196419	+	0.0340207i
$649$	6.86602e6	+	1.18923e7i	0.639872	+	1.10829i
$650$	−1.11022e6			−0.103068
$651$	−3.21133e6	−	9.63530e6i	−0.296983	−	0.891072i
$652$	3.71412e6			0.342166
$653$	2.59693e6	+	4.49802e6i	0.238330	+	0.412799i	0.960235	−	0.279193i	$-0.0900668\pi$
$653$	2.59693e6	+	4.49802e6i	0.238330	+	0.412799i	−0.721906	+	0.691992i	$0.756733\pi$
$654$	465356.	−	806019.i	0.0425442	−	0.0736887i
$655$	2.94857e6	−	5.10707e6i	0.268540	−	0.465124i
$656$	−1.36935e6	−	2.37179e6i	−0.124238	−	0.215187i
$657$	−2.62429e6			−0.237191
$658$	398438.	−	449287.i	0.0358754	−	0.0404537i
$659$	−2.06522e7			−1.85248			−0.926240	−	0.376934i	$-0.876978\pi$
$659$	−2.06522e7			−1.85248			−0.926240	+	0.376934i	$0.876978\pi$
$660$	677106.	+	1.17278e6i	0.0605058	+	0.104799i
$661$	−219603.	+	380364.i	−0.0195495	+	0.0338607i	−0.875635	−	0.482974i	$-0.839557\pi$
$661$	−219603.	+	380364.i	−0.0195495	+	0.0338607i	0.856085	+	0.516835i	$0.172890\pi$
$662$	−7.13245e6	+	1.23538e7i	−0.632548	+	1.09561i
$663$	1.73943e6	+	3.01278e6i	0.153682	+	0.266185i
$664$	−6.73602e6			−0.592902
$665$	−566429.	+	638716.i	−0.0496697	+	0.0560085i
$666$	−897038.			−0.0783656
$667$	−1.54051e7	−	2.66824e7i	−1.34075	−	2.32225i
$668$	4.95255e6	−	8.57807e6i	0.429425	−	0.743787i
$669$	1.94617e6	−	3.37086e6i	0.168118	−	0.291189i
$670$	−1.50201e6	−	2.60155e6i	−0.129266	−	0.223896i
$671$	1.55940e7			1.33706
$672$	−377776.	−	1.13348e6i	−0.0322709	−	0.0968259i
$673$	5.73639e6			0.488204			0.244102	−	0.969750i	$-0.421507\pi$
$673$	5.73639e6			0.488204			0.244102	+	0.969750i	$0.421507\pi$
$674$	2.33316e6	+	4.04115e6i	0.197831	+	0.342654i
$675$	227812.	−	394583.i	0.0192450	−	0.0333333i
$676$	1.39264e6	−	2.41212e6i	0.117212	−	0.203017i
$677$	−223788.	−	387612.i	−0.0187657	−	0.0325031i	0.856490	−	0.516164i	$-0.172640\pi$
$677$	−223788.	−	387612.i	−0.0187657	−	0.0325031i	−0.875256	+	0.483660i	$0.839307\pi$
$678$	−1.38327e6			−0.115567
$679$	−4.72512e6	−	967127.i	−0.393313	−	0.0805025i
$680$	1.39266e6			0.115498
$681$	3.43979e6	+	5.95788e6i	0.284226	+	0.492294i
$682$	6.54885e6	−	1.13429e7i	0.539143	−	0.933823i
$683$	−8.57813e6	+	1.48578e7i	−0.703624	+	1.21871i	0.263561	+	0.964643i	$0.415103\pi$
$683$	−8.57813e6	+	1.48578e7i	−0.703624	+	1.21871i	−0.967186	+	0.254071i	$0.918230\pi$
$684$	−170685.	−	295634.i	−0.0139493	−	0.0241610i
$685$	3.01251e6			0.245302
$686$	−714478.	+	8.68623e6i	−0.0579667	+	0.704727i
$687$	6.37344e6			0.515207
$688$	2.03124e6	+	3.51822e6i	0.163603	+	0.283368i
$689$	7.16743e6	−	1.24143e7i	0.575195	−	0.996267i
$690$	1.90141e6	−	3.29333e6i	0.152038	−	0.263338i
$691$	9.83358e6	+	1.70323e7i	0.783460	+	1.35699i	0.929915	+	0.367775i	$0.119880\pi$
$691$	9.83358e6	+	1.70323e7i	0.783460	+	1.35699i	−0.146455	+	0.989217i	$0.546786\pi$
$692$	6.02988e6			0.478678
$693$	3.86993e6	+	792089.i	0.306105	+	0.0626528i
$694$	8.74492e6			0.689219
$695$	983618.	+	1.70368e6i	0.0772440	+	0.133790i
$696$	−2.10002e6	+	3.63734e6i	−0.164324	+	0.284617i
$697$	4.65587e6	−	8.06420e6i	0.363010	−	0.628752i
$698$	−977887.	−	1.69375e6i	−0.0759714	−	0.131586i
$699$	−1.14458e7			−0.886040
$700$	409913.	+	1.22991e6i	0.0316189	+	0.0948696i
$701$	−1.37912e7			−1.06000			−0.530001	−	0.847997i	$-0.677809\pi$
$701$	−1.37912e7			−1.06000			−0.530001	+	0.847997i	$0.677809\pi$
$702$	−647479.	−	1.12147e6i	−0.0495887	−	0.0858902i
$703$	364632.	−	631562.i	0.0278270	−	0.0481978i
$704$	770397.	−	1.33437e6i	0.0585845	−	0.101471i
$705$	−130277.	−	225646.i	−0.00987176	−	0.0170984i
$706$	3.69957e6			0.279344
$707$	1.41587e7	−	1.59657e7i	1.06531	−	1.20126i
$708$	−5.25670e6			−0.394121
$709$	1.17884e7	+	2.04181e7i	0.880722	+	1.52546i	0.850539	+	0.525912i	$0.176276\pi$
$709$	1.17884e7	+	2.04181e7i	0.880722	+	1.52546i	0.0301832	+	0.999544i	$0.490391\pi$
$710$	1.88116e6	−	3.25827e6i	0.140049	−	0.242572i
$711$	2.61946e6	−	4.53704e6i	0.194329	−	0.336588i
$712$	716524.	+	1.24106e6i	0.0529701	+	0.0917469i
$713$	−3.67801e7			−2.70950
$714$	2.69535e6	−	3.03933e6i	0.197865	−	0.223117i
$715$	−4.17631e6			−0.305512
$716$	−5.35996e6	−	9.28372e6i	−0.390732	−	0.676767i
$717$	−1.35004e6	+	2.33835e6i	−0.0980732	+	0.169868i
$718$	−628790.	+	1.08910e6i	−0.0455192	+	0.0788415i
$719$	−8.38687e6	−	1.45265e7i	−0.605031	−	1.04794i	−0.992047	−	0.125872i	$-0.959827\pi$
$719$	−8.38687e6	−	1.45265e7i	−0.605031	−	1.04794i	0.387015	−	0.922073i	$-0.373506\pi$
$720$	−518400.			−0.0372678
$721$	3.48862e6	+	1.04673e7i	0.249928	+	0.749888i
$722$	−9.62687e6			−0.687294
$723$	−254642.	−	441053.i	−0.0181169	−	0.0313794i
$724$	−2.08522e6	+	3.61170e6i	−0.147844	+	0.256074i
$725$	2.27867e6	−	3.94677e6i	0.161004	−	0.278867i
$726$	−351845.	−	609413.i	−0.0247748	−	0.0429112i
$727$	58043.8			0.00407305			0.00203653	−	0.999998i	$-0.499352\pi$
$727$	58043.8			0.00407305			0.00203653	+	0.999998i	$0.499352\pi$
$728$	3.60979e6	+	738844.i	0.252437	+	0.0516683i
$729$	531441.			0.0370370
$730$	−1.61993e6	−	2.80580e6i	−0.112510	−	0.194872i
$731$	−6.90634e6	+	1.19621e7i	−0.478029	+	0.827971i
$732$	−2.98474e6	+	5.16973e6i	−0.205887	+	0.356607i
$733$	2.00069e6	+	3.46530e6i	0.137537	+	0.238222i	0.926564	−	0.376137i	$-0.122748\pi$
$733$	2.00069e6	+	3.46530e6i	0.137537	+	0.238222i	−0.789026	+	0.614359i	$0.789415\pi$
$734$	−1.19061e7			−0.815699
$735$	3.47747e6	+	1.48577e6i	0.237435	+	0.101445i
$736$	−4.32676e6			−0.294420
$737$	−5.65011e6	−	9.78628e6i	−0.383167	−	0.663665i
$738$	−1.73308e6	+	3.00179e6i	−0.117133	+	0.202880i
$739$	5.24156e6	−	9.07865e6i	0.353061	−	0.611519i	−0.633723	−	0.773560i	$-0.718474\pi$
$739$	5.24156e6	−	9.07865e6i	0.353061	−	0.611519i	0.986784	+	0.162041i	$0.0518076\pi$
$740$	−553727.	−	959084.i	−0.0371721	−	0.0643839i
$741$	1.05276e6			0.0704343
$742$	−1.63990e7	−	3.35652e6i	−1.09347	−	0.223810i
$743$	−1.19520e7			−0.794269			−0.397134	−	0.917761i	$-0.629995\pi$
$743$	−1.19520e7			−0.794269			−0.397134	+	0.917761i	$0.629995\pi$
$744$	2.50693e6	+	4.34214e6i	0.166039	+	0.287588i
$745$	3.24926e6	−	5.62789e6i	0.214484	−	0.371497i
$746$	−7.08667e6	+	1.22745e7i	−0.466225	+	0.807525i
$747$	4.26264e6	+	7.38310e6i	0.279497	+	0.484102i
$748$	5.23878e6			0.342355
$749$	2.09342e6	+	6.28114e6i	0.136349	+	0.409104i
$750$	562500.			0.0365148
$751$	−1.38281e7	−	2.39510e7i	−0.894669	−	1.54961i	−0.834214	−	0.551441i	$-0.814078\pi$
$751$	−1.38281e7	−	2.39510e7i	−0.894669	−	1.54961i	−0.0604551	−	0.998171i	$-0.519255\pi$
$752$	−148226.	+	256735.i	−0.00955829	+	0.0165554i
$753$	7.48357e6	−	1.29619e7i	0.480974	−	0.833071i
$754$	−6.47634e6	−	1.12173e7i	−0.414860	−	0.718558i
$755$	7.33950e6			0.468597
$756$	−1.00331e6	+	1.13135e6i	−0.0638454	+	0.0719932i
$757$	−1.38554e7			−0.878780			−0.439390	−	0.898296i	$-0.644805\pi$
$757$	−1.38554e7			−0.878780			−0.439390	+	0.898296i	$0.644805\pi$
$758$	5.37779e6	+	9.31461e6i	0.339962	+	0.588832i
$759$	7.15253e6	−	1.23885e7i	0.450666	−	0.780577i
$760$	210722.	−	364981.i	0.0132335	−	0.0229211i
$761$	−6.29999e6	−	1.09119e7i	−0.394347	−	0.683029i	0.598671	−	0.800995i	$-0.295696\pi$
$761$	−6.29999e6	−	1.09119e7i	−0.394347	−	0.683029i	−0.993018	+	0.117967i	$0.962362\pi$
$762$	6.45195e6			0.402535
$763$	2.22382e6	−	2.50762e6i	0.138289	−	0.155937i
$764$	−3.87012e6			−0.239878
$765$	−881295.	−	1.52645e6i	−0.0544462	−	0.0943036i
$766$	−9.22019e6	+	1.59698e7i	−0.567764	+	0.983396i
$767$	8.10566e6	−	1.40394e7i	0.497508	−	0.861709i
$768$	294912.	+	510803.i	0.0180422	+	0.0312500i
$769$	2.90665e7			1.77246			0.886230	−	0.463245i	$-0.153315\pi$
$769$	2.90665e7			1.77246			0.886230	+	0.463245i	$0.153315\pi$
$770$	1.54197e6	+	4.62654e6i	0.0937236	+	0.281209i
$771$	8.77657e6			0.531727
$772$	−6.92422e6	−	1.19931e7i	−0.418146	−	0.724250i
$773$	−8.03098e6	+	1.39101e7i	−0.483415	+	0.837299i	−0.999819	−	0.0190465i	$-0.993937\pi$
$773$	−8.03098e6	+	1.39101e7i	−0.483415	+	0.837299i	0.516404	+	0.856345i	$0.327270\pi$
$774$	2.57079e6	−	4.45274e6i	0.154246	−	0.267162i
$775$	−2.72020e6	−	4.71152e6i	−0.162684	−	0.281778i
$776$	2.38100e6			0.141940
$777$	−3.16477e6	−	647758.i	−0.188057	−	0.0384911i
$778$	1.13571e7			0.672698
$779$	−1.40894e6	−	2.44036e6i	−0.0831860	−	0.144082i
$780$	799357.	−	1.38453e6i	0.0470440	−	0.0814826i
$781$	7.07638e6	−	1.22566e7i	0.415129	−	0.719025i
$782$	−7.35561e6	−	1.27403e7i	−0.430132	−	0.745010i
$783$	5.31568e6			0.309852
$784$	−514304.	−	4.27174e6i	−0.0298834	−	0.248208i
$785$	9.73913e6			0.564087
$786$	4.24594e6	+	7.35419e6i	0.245142	+	0.424598i
$787$	1.83559e6	−	3.17933e6i	0.105642	−	0.182978i	−0.808358	−	0.588691i	$-0.799643\pi$
$787$	1.83559e6	−	3.17933e6i	0.105642	−	0.182978i	0.914000	+	0.405713i	$0.132977\pi$
$788$	−474675.	+	822161.i	−0.0272321	+	0.0471674i
$789$	−4.84185e6	−	8.38634e6i	−0.276898	−	0.479601i
$790$	6.46781e6			0.368714
$791$	−4.88020e6	−	998869.i	−0.277330	−	0.0567633i
$792$	−1.95007e6			−0.110468
$793$	−9.20476e6	−	1.59431e7i	−0.519792	−	0.900306i
$794$	−595449.	+	1.03135e6i	−0.0335192	+	0.0580569i
$795$	−3.63143e6	+	6.28982e6i	−0.203779	+	0.352956i
$796$	−7.26579e6	−	1.25847e7i	−0.406443	−	0.703981i
$797$	−2.53970e7			−1.41624			−0.708121	−	0.706092i	$-0.750457\pi$
$797$	−2.53970e7			−1.41624			−0.708121	+	0.706092i	$0.750457\pi$
$798$	−388699.	−	1.16626e6i	−0.0216076	−	0.0648316i
$799$	−1.00795e6			−0.0558565
$800$	−320000.	−	554256.i	−0.0176777	−	0.0306186i
$801$	906851.	−	1.57071e6i	0.0499407	−	0.0864998i
$802$	9.15437e6	−	1.58558e7i	0.502565	−	0.870468i
$803$	−6.09370e6	−	1.05546e7i	−0.333497	−	0.577634i
$804$	4.32578e6			0.236007
$805$	9.08634e6	−	1.02459e7i	0.494196	−	0.557265i
$806$	−1.54625e7			−0.838380
$807$	6.64271e6	+	1.15055e7i	0.359055	+	0.621902i
$808$	−5.26730e6	+	9.12323e6i	−0.283831	+	0.491610i
$809$	4.93977e6	−	8.55593e6i	0.265360	−	0.459617i	−0.702298	−	0.711883i	$-0.747843\pi$
$809$	4.93977e6	−	8.55593e6i	0.265360	−	0.459617i	0.967658	+	0.252266i	$0.0811758\pi$
$810$	328050.	+	568199.i	0.0175682	+	0.0304290i
$811$	1.11209e7			0.593726			0.296863	−	0.954920i	$-0.404059\pi$
$811$	1.11209e7			0.593726			0.296863	+	0.954920i	$0.404059\pi$
$812$	−1.00355e7	+	1.13162e7i	−0.534131	+	0.602296i
$813$	−1.19391e7			−0.633500
$814$	−2.08296e6	−	3.60779e6i	−0.110184	−	0.190845i
$815$	2.90166e6	−	5.02582e6i	0.153021	−	0.265041i
$816$	−1.00272e6	+	1.73676e6i	−0.0527173	+	0.0913090i
$817$	2.08997e6	+	3.61994e6i	0.109543	+	0.189735i
$818$	−1.47263e7			−0.769502
$819$	−1.47450e6	−	4.42411e6i	−0.0768130	−	0.230471i
$820$	−4.27922e6			−0.222244
$821$	−1.29397e7	−	2.24122e7i	−0.669986	−	1.16045i	−0.977908	−	0.209038i	$-0.932967\pi$
$821$	−1.29397e7	−	2.24122e7i	−0.669986	−	1.16045i	0.307922	−	0.951412i	$-0.400366\pi$
$822$	−2.16901e6	+	3.75683e6i	−0.111965	+	0.193929i
$823$	−1.47239e7	+	2.55026e7i	−0.757747	+	1.31246i	0.186251	+	0.982502i	$0.440366\pi$
$823$	−1.47239e7	+	2.55026e7i	−0.757747	+	1.31246i	−0.943997	+	0.329953i	$0.892967\pi$
$824$	−2.72340e6	−	4.71707e6i	−0.139731	−	0.242022i
$825$	2.11596e6			0.108236
$826$	−1.85457e7	−	3.79590e6i	−0.945788	−	0.193582i
$827$	−2.61824e7			−1.33121			−0.665605	−	0.746304i	$-0.731826\pi$
$827$	−2.61824e7			−1.33121			−0.665605	+	0.746304i	$0.731826\pi$
$828$	2.73803e6	+	4.74240e6i	0.138791	+	0.240393i
$829$	1.79483e7	−	3.10874e7i	0.907063	−	1.57108i	0.0889398	−	0.996037i	$-0.471652\pi$
$829$	1.79483e7	−	3.10874e7i	0.907063	−	1.57108i	0.818123	−	0.575043i	$-0.195015\pi$
$830$	−5.26251e6	+	9.11494e6i	−0.265154	+	0.459260i
$831$	6.70742e6	+	1.16176e7i	0.336940	+	0.583598i
$832$	−1.81898e6			−0.0911003
$833$	1.17040e7	−	8.77647e6i	0.584414	−	0.438235i
$834$	−2.83282e6			−0.141028
$835$	−7.73836e6	−	1.34032e7i	−0.384090	−	0.665263i
$836$	792672.	−	1.37295e6i	0.0392263	−	0.0679420i
$837$	3.17284e6	−	5.49552e6i	0.156543	−	0.271141i
$838$	3.00124e6	+	5.19829e6i	0.147635	+	0.255712i
$839$	1.26587e7			0.620845			0.310422	−	0.950599i	$-0.399530\pi$
$839$	1.26587e7			0.620845			0.310422	+	0.950599i	$0.399530\pi$
$840$	−1.82893e6	−	374340.i	−0.0894330	−	0.0183050i
$841$	3.26583e7			1.59222
$842$	5.97637e6	+	1.03514e7i	0.290507	+	0.503173i
$843$	−4.54300e6	+	7.86871e6i	−0.220178	+	0.381360i
$844$	3.11933e6	−	5.40283e6i	0.150732	−	0.261075i
$845$	−2.17599e6	−	3.76893e6i	−0.104837	−	0.181584i
$846$	375197.			0.0180233
$847$	−801254.	−	2.40409e6i	−0.0383762	−	0.115144i
$848$	8.26352e6			0.394617
$849$	−4.47372e6	−	7.74871e6i	−0.213010	−	0.368944i
$850$	1.08802e6	−	1.88450e6i	0.0516522	−	0.0894642i
$851$	−5.84923e6	+	1.01312e7i	−0.276869	+	0.479551i
$852$	2.70887e6	+	4.69191e6i	0.127847	+	0.221437i
$853$	1.53972e6			0.0724552			0.0362276	−	0.999344i	$-0.488466\pi$
$853$	1.53972e6			0.0724552			0.0362276	+	0.999344i	$0.488466\pi$
$854$	−1.42633e7	+	1.60836e7i	−0.669231	+	0.754637i
$855$	−533389.			−0.0249533
$856$	−1.63424e6	−	2.83059e6i	−0.0762310	−	0.132036i
$857$	6.19178e6	−	1.07245e7i	0.287981	−	0.498798i	−0.685347	−	0.728217i	$-0.740349\pi$
$857$	6.19178e6	−	1.07245e7i	0.287981	−	0.498798i	0.973328	+	0.229419i	$0.0736827\pi$
$858$	3.00694e6	−	5.20818e6i	0.139446	−	0.241528i
$859$	1.67108e7	+	2.89439e7i	0.772705	+	1.33836i	0.936075	+	0.351799i	$0.114430\pi$
$859$	1.67108e7	+	2.89439e7i	0.772705	+	1.33836i	−0.163370	+	0.986565i	$0.552237\pi$
$860$	6.34763e6			0.292662
$861$	−8.28197e6	+	9.33890e6i	−0.380738	+	0.429327i
$862$	1.21215e7			0.555633
$863$	−1.73246e7	−	3.00071e7i	−0.791838	−	1.37150i	−0.924828	−	0.380386i	$-0.875791\pi$
$863$	−1.73246e7	−	3.00071e7i	−0.791838	−	1.37150i	0.132990	−	0.991117i	$-0.457542\pi$
$864$	373248.	−	646484.i	0.0170103	−	0.0294628i
$865$	4.71085e6	−	8.15942e6i	0.214071	−	0.370783i
$866$	−2.83618e6	−	4.91241e6i	−0.128511	−	0.222587i
$867$	5.96012e6			0.269282
$868$	5.70902e6	+	1.71294e7i	0.257195	+	0.771691i
$869$	2.43300e7			1.09293
$870$	3.28128e6	+	5.68335e6i	0.146976	+	0.254569i
$871$	−6.67023e6	+	1.15532e7i	−0.297917	+	0.516007i
$872$	−827299.	+	1.43292e6i	−0.0368444	+	0.0638163i
$873$	−1.50673e6	−	2.60973e6i	−0.0669112	−	0.115894i
$874$	−4.45186e6			−0.197135
$875$	1.98451e6	+	406185.i	0.0876261	+	0.0179351i
$876$	4.66540e6			0.205414
$877$	1.83963e7	+	3.18634e7i	0.807666	+	1.39892i	0.914476	+	0.404640i	$0.132603\pi$
$877$	1.83963e7	+	3.18634e7i	0.807666	+	1.39892i	−0.106810	+	0.994279i	$0.534064\pi$
$878$	−7.44075e6	+	1.28878e7i	−0.325747	+	0.564210i
$879$	7.63837e6	−	1.32300e7i	0.333448	−	0.577549i
$880$	−1.20374e6	−	2.08495e6i	−0.0523996	−	0.0907587i
$881$	−1.37404e7			−0.596432			−0.298216	−	0.954498i	$-0.596392\pi$
$881$	−1.37404e7			−0.596432			−0.298216	+	0.954498i	$0.596392\pi$
$882$	−4.35664e6	+	3.26692e6i	−0.188573	+	0.141406i
$883$	−6.26276e6			−0.270311			−0.135156	−	0.990824i	$-0.543153\pi$
$883$	−6.26276e6			−0.270311			−0.135156	+	0.990824i	$0.543153\pi$
$884$	−3.09232e6	−	5.35605e6i	−0.133093	−	0.230523i
$885$	−4.10679e6	+	7.11318e6i	−0.176256	+	0.305285i
$886$	1.60174e6	−	2.77430e6i	0.0685502	−	0.118732i
$887$	2.22623e7	+	3.85594e7i	0.950082	+	1.64559i	0.745241	+	0.666795i	$0.232334\pi$
$887$	2.22623e7	+	3.85594e7i	0.950082	+	1.64559i	0.204841	+	0.978795i	$0.434332\pi$
$888$	1.59473e6			0.0678666
$889$	2.27626e7	+	4.65900e6i	0.965978	+	0.197714i
$890$	2.23914e6			0.0947558
$891$	1.23403e6	+	2.13740e6i	0.0520751	+	0.0901967i
$892$	−3.45985e6	+	5.99264e6i	−0.145595	+	0.252178i
$893$	−152512.	+	264158.i	−0.00639993	+	0.0110850i
$894$	4.67894e6	+	8.10416e6i	0.195796	+	0.339128i
$895$	−1.67499e7			−0.698962
$896$	671601.	+	2.01508e6i	0.0279474	+	0.0838537i
$897$	−1.68878e7			−0.700797
$898$	−7.78767e6	−	1.34886e7i	−0.322268	−	0.558184i
$899$	3.17360e7	−	5.49683e7i	1.30964	−	2.26837i
$900$	−405000.	+	701481.i	−0.0166667	+	0.0288675i
$901$	1.40482e7	+	2.43322e7i	0.576513	+	0.998550i
$902$	−1.60972e7			−0.658769
$903$	1.22852e7	−	1.38530e7i	0.501374	−	0.565358i
$904$	2.45915e6			0.100084
$905$	3.25815e6	+	5.64328e6i	0.132236	+	0.229039i
$906$	−5.28444e6	+	9.15292e6i	−0.213884	+	0.370458i
$907$	1.39004e7	−	2.40762e7i	0.561060	−	0.971784i	−0.436344	−	0.899780i	$-0.643727\pi$
$907$	1.39004e7	−	2.40762e7i	0.561060	−	0.971784i	0.997404	−	0.0720046i	$-0.0229396\pi$
$908$	−6.11518e6	−	1.05918e7i	−0.246147	−	0.426339i
$909$	1.33329e7			0.535197
$910$	3.81992e6	−	4.30742e6i	0.152915	−	0.172430i
$911$	1.67045e7			0.666864			0.333432	−	0.942774i	$-0.391793\pi$
$911$	1.67045e7			0.666864			0.333432	+	0.942774i	$0.391793\pi$
$912$	303439.	+	525572.i	0.0120805	+	0.0209240i
$913$	−1.97960e7	+	3.42877e7i	−0.785960	+	1.36132i
$914$	6.45355e6	−	1.11779e7i	0.255525	−	0.442582i
$915$	4.66366e6	+	8.07770e6i	0.184151	+	0.318959i
$916$	−1.13306e7			−0.446183
$917$	9.66925e6	+	2.90117e7i	0.379725	+	1.13933i
$918$	2.53813e6			0.0994047
$919$	1.08291e7	+	1.87565e7i	0.422963	+	0.732593i	0.996228	−	0.0867770i	$-0.0276568\pi$
$919$	1.08291e7	+	1.87565e7i	0.422963	+	0.732593i	−0.573265	+	0.819370i	$0.694323\pi$
$920$	−3.38028e6	+	5.85481e6i	−0.131669	+	0.228057i
$921$	1.32886e7	−	2.30166e7i	0.516215	−	0.894111i
$922$	−8.21664e6	−	1.42316e7i	−0.318322	−	0.551350i
$923$	−1.67080e7			−0.645536
$924$	−6.87987e6	−	1.40816e6i	−0.265094	−	0.0542589i
$925$	−1.73040e6			−0.0664954
$926$	2.96563e6	+	5.13662e6i	0.113655	+	0.196856i
$927$	−3.44681e6	+	5.97005e6i	−0.131740	+	0.228180i
$928$	3.73337e6	−	6.46639e6i	0.142309	−	0.246486i
$929$	−1.15385e7	−	1.99853e7i	−0.438642	−	0.759750i	0.558943	−	0.829206i	$-0.311207\pi$
$929$	−1.15385e7	−	1.99853e7i	−0.438642	−	0.759750i	−0.997585	+	0.0694559i	$0.977874\pi$
$930$	7.83417e6			0.297020
$931$	−529175.	−	4.39526e6i	−0.0200090	−	0.166192i
$932$	2.03481e7			0.767333
$933$	−9.54641e6	−	1.65349e7i	−0.359034	−	0.621866i
$934$	4.57726e6	−	7.92804e6i	0.171687	−	0.297371i
$935$	4.09280e6	−	7.08894e6i	0.153106	−	0.265187i
$936$	1.15107e6	+	1.99372e6i	0.0429451	+	0.0743831i
$937$	2.57761e7			0.959110			0.479555	−	0.877512i	$-0.340798\pi$
$937$	2.57761e7			0.959110			0.479555	+	0.877512i	$0.340798\pi$
$938$	1.52615e7	+	3.12368e6i	0.566355	+	0.115920i
$939$	−3.46515e6			−0.128250
$940$	231603.	+	401149.i	0.00854919	+	0.0148076i
$941$	−1.53396e7	+	2.65690e7i	−0.564729	+	0.978139i	0.432346	+	0.901708i	$0.357686\pi$
$941$	−1.53396e7	+	2.65690e7i	−0.564729	+	0.978139i	−0.997075	+	0.0764314i	$0.975647\pi$
$942$	−7.01218e6	+	1.21454e7i	−0.257469	+	0.445950i
$943$	2.26015e7	+	3.91469e7i	0.827672	+	1.43357i
$944$	9.34524e6			0.341319
$945$	747066.	+	2.24151e6i	0.0272132	+	0.0816508i
$946$	2.38779e7			0.867498
$947$	1.42412e7	+	2.46666e7i	0.516028	+	0.893786i	0.999827	+	0.0186072i	$0.00592319\pi$
$947$	1.42412e7	+	2.46666e7i	0.516028	+	0.893786i	−0.483799	+	0.875179i	$0.660743\pi$
$948$	−4.65682e6	+	8.06585e6i	−0.168294	+	0.291494i
$949$	−7.19391e6	+	1.24602e7i	−0.259298	+	0.449118i
$950$	−329253.	−	570282.i	−0.0118364	−	0.0205013i
$951$	−9.09161e6			−0.325979
$952$	−4.79173e6	+	5.40325e6i	−0.171356	+	0.193225i
$953$	−2.00240e7			−0.714199			−0.357100	−	0.934066i	$-0.616234\pi$
$953$	−2.00240e7			−0.714199			−0.357100	+	0.934066i	$0.616234\pi$
$954$	−5.22926e6	−	9.05734e6i	−0.186024	−	0.322203i
$955$	−3.02353e6	+	5.23690e6i	−0.107277	+	0.185809i
$956$	2.40008e6	−	4.15706e6i	0.0849339	−	0.147110i
$957$	1.23432e7	+	2.13791e7i	0.435661	+	0.754586i
$958$	2.01850e6			0.0710583
$959$	−1.03651e7	+	1.16879e7i	−0.363939	+	0.410384i
$960$	921600.			0.0322749
$961$	−2.35707e7	−	4.08257e7i	−0.823312	−	1.42602i
$962$	−2.45903e6	+	4.25917e6i	−0.0856696	+	0.148384i
$963$	−2.06833e6	+	3.58246e6i	−0.0718712	+	0.124485i
$964$	452697.	+	784094.i	0.0156897	+	0.0271754i
$965$	−2.16382e7			−0.748002
$966$	6.23529e6	+	1.87084e7i	0.214988	+	0.645052i
$967$	1.74233e7			0.599189			0.299595	−	0.954067i	$-0.403149\pi$
$967$	1.74233e7			0.599189			0.299595	+	0.954067i	$0.403149\pi$
$968$	625502.	+	1.08340e6i	0.0214556	+	0.0371622i
$969$	−1.03171e6	+	1.78697e6i	−0.0352978	+	0.0611377i
$970$	1.86016e6	−	3.22189e6i	0.0634775	−	0.109946i
$971$	5.62603e6	+	9.74456e6i	0.191493	+	0.331676i	0.945745	−	0.324909i	$-0.105334\pi$
$971$	5.62603e6	+	9.74456e6i	0.191493	+	0.331676i	−0.754252	+	0.656585i	$0.772000\pi$
$972$	−944784.			−0.0320750
$973$	−9.99425e6	−	2.04560e6i	−0.338429	−	0.0692690i
$974$	−5.91623e6			−0.199824
$975$	−1.24900e6	−	2.16332e6i	−0.0420774	−	0.0728803i
$976$	5.30621e6	−	9.19062e6i	0.178303	−	0.308831i
$977$	−2.22637e7	+	3.85618e7i	−0.746208	+	1.29247i	0.203420	+	0.979092i	$0.434794\pi$
$977$	−2.22637e7	+	3.85618e7i	−0.746208	+	1.29247i	−0.949628	+	0.313379i	$0.898539\pi$
$978$	4.17839e6	+	7.23718e6i	0.139689	+	0.241948i
$979$	8.42297e6			0.280872
$980$	−6.18217e6	−	2.64136e6i	−0.205625	−	0.0878542i
$981$	2.09410e6			0.0694744
$982$	−1.50332e7	−	2.60383e7i	−0.497477	−	0.861656i
$983$	9.94307e6	−	1.72219e7i	0.328199	−	0.568457i	−0.653956	−	0.756533i	$-0.726892\pi$
$983$	9.94307e6	−	1.72219e7i	0.328199	−	0.568457i	0.982154	+	0.188076i	$0.0602251\pi$
$984$	3.08104e6	−	5.33652e6i	0.101440	−	0.175699i
$985$	741680.	+	1.28463e6i	0.0243571	+	0.0421878i
$986$	2.53873e7			0.831620
$987$	1.32370e6	+	270933.i	0.0432512	+	0.00885256i
$988$	−1.87158e6			−0.0609979
$989$	−3.35262e7	−	5.80691e7i	−1.08992	−	1.88779i
$990$	−1.52349e6	+	2.63876e6i	−0.0494028	+	0.0855681i
$991$	−2.46286e6	+	4.26580e6i	−0.0796628	+	0.137980i	−0.903104	−	0.429421i	$-0.858718\pi$
$991$	−2.46286e6	+	4.26580e6i	−0.0796628	+	0.137980i	0.823442	+	0.567401i	$0.192051\pi$
$992$	−4.45677e6	−	7.71935e6i	−0.143794	−	0.249059i
$993$	−3.20960e7			−1.03295
$994$	6.16890e6	+	1.85092e7i	0.198035	+	0.594187i
$995$	−2.27056e7			−0.727068
$996$	−7.57802e6	−	1.31255e7i	−0.242051	−	0.419245i
$997$	5.96238e6	−	1.03271e7i	0.189968	−	0.329035i	−0.755271	−	0.655413i	$-0.772495\pi$
$997$	5.96238e6	−	1.03271e7i	0.189968	−	0.329035i	0.945239	+	0.326378i	$0.105828\pi$
$998$	−4.86070e6	+	8.41898e6i	−0.154480	+	0.267567i
$999$	−1.00917e6	−	1.74793e6i	−0.0319926	−	0.0554128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.6.i.b.151.1	yes	4
7.2	even	3	inner	210.6.i.b.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.6.i.b.121.1	✓	4	7.2	even	3	inner
210.6.i.b.151.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	210.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(12.5000 + 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 - 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(12.5000 + 21.6506i) q^{5} -36.0000 q^{6} +(-127.009 - 25.9959i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(50.0000 - 86.6025i) q^{10} +(188.085 - 325.773i) q^{11} +(72.0000 + 124.708i) q^{12} -444.087 q^{13} +(163.965 + 491.963i) q^{14} +225.000 q^{15} +(-128.000 - 221.703i) q^{16} +(435.207 - 753.801i) q^{17} +(-162.000 + 280.592i) q^{18} +(-131.701 - 228.113i) q^{19} -400.000 q^{20} +(-774.157 + 872.954i) q^{21} -1504.68 q^{22} +(2112.67 + 3659.26i) q^{23} +(288.000 - 498.831i) q^{24} +(-312.500 + 541.266i) q^{25} +(888.174 + 1538.36i) q^{26} -729.000 q^{27} +(1376.28 - 1551.92i) q^{28} -7291.74 q^{29} +(-450.000 - 779.423i) q^{30} +(-4352.32 + 7538.43i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1692.77 - 2931.96i) q^{33} -3481.66 q^{34} +(-1024.78 - 3074.77i) q^{35} +1296.00 q^{36} +(1384.32 + 2397.71i) q^{37} +(-526.804 + 912.451i) q^{38} +(-1998.39 + 3461.32i) q^{39} +(800.000 + 1385.64i) q^{40} +10698.1 q^{41} +(4572.31 + 935.851i) q^{42} -15869.1 q^{43} +(3009.36 + 5212.37i) q^{44} +(1012.50 - 1753.70i) q^{45} +(8450.70 - 14637.0i) q^{46} +(-579.008 - 1002.87i) q^{47} -2304.00 q^{48} +(15455.4 + 6603.40i) q^{49} +2500.00 q^{50} +(-3916.86 - 6784.21i) q^{51} +(3552.70 - 6153.45i) q^{52} +(-16139.7 + 27954.8i) q^{53} +(1458.00 + 2525.33i) q^{54} +9404.26 q^{55} +(-8128.56 - 1663.74i) q^{56} -2370.62 q^{57} +(14583.5 + 25259.3i) q^{58} +(-18252.4 + 31614.1i) q^{59} +(-1800.00 + 3117.69i) q^{60} +(20727.4 + 35900.9i) q^{61} +34818.5 q^{62} +(3320.29 + 9962.25i) q^{63} +4096.00 q^{64} +(-5551.09 - 9614.77i) q^{65} +(-6771.06 + 11727.8i) q^{66} +(15020.1 - 26015.5i) q^{67} +(6963.32 + 12060.8i) q^{68} +38028.1 q^{69} +(-8601.74 + 9699.48i) q^{70} +37623.3 q^{71} +(-2592.00 - 4489.48i) q^{72} +(16199.3 - 28058.0i) q^{73} +(5537.27 - 9590.84i) q^{74} +(2812.50 + 4871.39i) q^{75} +4214.43 q^{76} +(-32357.2 + 36486.6i) q^{77} +15987.1 q^{78} +(32339.0 + 56012.9i) q^{79} +(3200.00 - 5542.56i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-21396.1 - 37059.1i) q^{82} -105250. q^{83} +(-5902.74 - 17710.7i) q^{84} +21760.4 q^{85} +(31738.2 + 54972.1i) q^{86} +(-32812.8 + 56833.5i) q^{87} +(12037.4 - 20849.5i) q^{88} +(11195.7 + 19391.5i) q^{89} -8100.00 q^{90} +(56402.9 + 11544.4i) q^{91} -67605.6 q^{92} +(39170.8 + 67845.9i) q^{93} +(-2316.03 + 4011.49i) q^{94} +(3292.53 - 5702.82i) q^{95} +(4608.00 + 7981.29i) q^{96} +37203.1 q^{97} +(-8036.00 - 66746.0i) q^{98} -30469.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 18 * q^3 - 32 * q^4 + 50 * q^5 - 144 * q^6 - 336 * q^7 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 50 q^{5} - 144 q^{6} - 336 q^{7} + 256 q^{8} - 162 q^{9} + 200 q^{10} + 482 q^{11} + 288 q^{12} - 56 q^{13} + 1344 q^{14} + 900 q^{15} - 512 q^{16} - 938 q^{17} - 648 q^{18} - 2198 q^{19} - 1600 q^{20} - 3856 q^{22} - 618 q^{23} + 1152 q^{24} - 1250 q^{25} + 112 q^{26} - 2916 q^{27} - 20172 q^{29} - 1800 q^{30} - 4138 q^{31} - 2048 q^{32} - 4338 q^{33} + 7504 q^{34} - 8400 q^{35} + 5184 q^{36} + 2072 q^{37} - 8792 q^{38} - 252 q^{39} + 3200 q^{40} + 5092 q^{41} + 12096 q^{42} - 53400 q^{43} + 7712 q^{44} + 4050 q^{45} - 2472 q^{46} + 3484 q^{47} - 9216 q^{48} + 4018 q^{49} + 10000 q^{50} + 8442 q^{51} + 448 q^{52} - 316 q^{53} + 5832 q^{54} + 24100 q^{55} - 21504 q^{56} - 39564 q^{57} + 40344 q^{58} - 66202 q^{59} - 7200 q^{60} + 44472 q^{61} + 33104 q^{62} + 27216 q^{63} + 16384 q^{64} - 700 q^{65} - 17352 q^{66} + 18964 q^{67} - 15008 q^{68} - 11124 q^{69} - 68876 q^{71} - 10368 q^{72} - 34516 q^{73} + 8288 q^{74} + 11250 q^{75} + 70336 q^{76} - 46508 q^{77} + 2016 q^{78} + 121590 q^{79} + 12800 q^{80} - 13122 q^{81} - 10184 q^{82} - 221588 q^{83} - 48384 q^{84} - 46900 q^{85} + 106800 q^{86} - 90774 q^{87} + 30848 q^{88} - 94246 q^{89} - 32400 q^{90} + 78694 q^{91} + 19776 q^{92} + 37242 q^{93} + 13936 q^{94} + 54950 q^{95} + 18432 q^{96} + 143504 q^{97} - 32144 q^{98} - 78084 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 - 32 * q^4 + 50 * q^5 - 144 * q^6 - 336 * q^7 + 256 * q^8 - 162 * q^9 + 200 * q^10 + 482 * q^11 + 288 * q^12 - 56 * q^13 + 1344 * q^14 + 900 * q^15 - 512 * q^16 - 938 * q^17 - 648 * q^18 - 2198 * q^19 - 1600 * q^20 - 3856 * q^22 - 618 * q^23 + 1152 * q^24 - 1250 * q^25 + 112 * q^26 - 2916 * q^27 - 20172 * q^29 - 1800 * q^30 - 4138 * q^31 - 2048 * q^32 - 4338 * q^33 + 7504 * q^34 - 8400 * q^35 + 5184 * q^36 + 2072 * q^37 - 8792 * q^38 - 252 * q^39 + 3200 * q^40 + 5092 * q^41 + 12096 * q^42 - 53400 * q^43 + 7712 * q^44 + 4050 * q^45 - 2472 * q^46 + 3484 * q^47 - 9216 * q^48 + 4018 * q^49 + 10000 * q^50 + 8442 * q^51 + 448 * q^52 - 316 * q^53 + 5832 * q^54 + 24100 * q^55 - 21504 * q^56 - 39564 * q^57 + 40344 * q^58 - 66202 * q^59 - 7200 * q^60 + 44472 * q^61 + 33104 * q^62 + 27216 * q^63 + 16384 * q^64 - 700 * q^65 - 17352 * q^66 + 18964 * q^67 - 15008 * q^68 - 11124 * q^69 - 68876 * q^71 - 10368 * q^72 - 34516 * q^73 + 8288 * q^74 + 11250 * q^75 + 70336 * q^76 - 46508 * q^77 + 2016 * q^78 + 121590 * q^79 + 12800 * q^80 - 13122 * q^81 - 10184 * q^82 - 221588 * q^83 - 48384 * q^84 - 46900 * q^85 + 106800 * q^86 - 90774 * q^87 + 30848 * q^88 - 94246 * q^89 - 32400 * q^90 + 78694 * q^91 + 19776 * q^92 + 37242 * q^93 + 13936 * q^94 + 54950 * q^95 + 18432 * q^96 + 143504 * q^97 - 32144 * q^98 - 78084 * q^99

Introduction

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