LMFDB - Embedded newform 210.6.i.b.121.2

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			121.2
Root			$6.14410 - 10.6419i$ of defining polynomial
Character	$\chi$	$=$	210.121
Dual form			210.6.i.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(12.5000 - 21.6506i) q^{5} -36.0000 q^{6} +(-40.9913 - 122.991i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(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} +(-40.9913 - 122.991i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(50.0000 + 86.6025i) q^{10} +(52.9149 + 91.6512i) q^{11} +(72.0000 - 124.708i) q^{12} +416.087 q^{13} +(508.035 + 103.983i) q^{14} +225.000 q^{15} +(-128.000 + 221.703i) q^{16} +(-904.207 - 1566.13i) q^{17} +(-162.000 - 280.592i) q^{18} +(-967.299 + 1675.41i) q^{19} -400.000 q^{20} +(774.157 - 872.954i) q^{21} -423.319 q^{22} +(-2421.67 + 4194.46i) q^{23} +(288.000 + 498.831i) q^{24} +(-312.500 - 541.266i) q^{25} +(-832.174 + 1441.37i) q^{26} -729.000 q^{27} +(-1376.28 + 1551.92i) q^{28} -2794.26 q^{29} +(-450.000 + 779.423i) q^{30} +(2283.32 + 3954.82i) q^{31} +(-512.000 - 886.810i) q^{32} +(-476.234 + 824.861i) q^{33} +7233.66 q^{34} +(-3175.22 - 649.897i) q^{35} +1296.00 q^{36} +(-348.319 + 603.305i) q^{37} +(-3869.20 - 6701.64i) q^{38} +(1872.39 + 3243.08i) q^{39} +(800.000 - 1385.64i) q^{40} -8152.05 q^{41} +(1475.69 + 4427.67i) q^{42} -10830.9 q^{43} +(846.638 - 1466.42i) q^{44} +(1012.50 + 1753.70i) q^{45} +(-9686.70 - 16777.8i) q^{46} +(2321.01 - 4020.10i) q^{47} -2304.00 q^{48} +(-13446.4 + 10083.1i) q^{49} +2500.00 q^{50} +(8137.86 - 14095.2i) q^{51} +(-3328.70 - 5765.47i) q^{52} +(15981.7 + 27681.1i) q^{53} +(1458.00 - 2525.33i) q^{54} +2645.74 q^{55} +(-2623.44 - 7871.41i) q^{56} -17411.4 q^{57} +(5588.52 - 9679.59i) q^{58} +(-14848.6 - 25718.5i) q^{59} +(-1800.00 - 3117.69i) q^{60} +(1508.62 - 2613.01i) q^{61} -18266.5 q^{62} +(10287.7 + 2105.67i) q^{63} +4096.00 q^{64} +(5201.09 - 9008.55i) q^{65} +(-1904.94 - 3299.44i) q^{66} +(-5538.08 - 9592.24i) q^{67} +(-14467.3 + 25058.1i) q^{68} -43590.1 q^{69} +(8601.74 - 9699.48i) q^{70} -72061.3 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-33457.3 - 57949.8i) q^{73} +(-1393.27 - 2413.22i) q^{74} +(2812.50 - 4871.39i) q^{75} +30953.6 q^{76} +(9103.20 - 10264.9i) q^{77} -14979.1 q^{78} +(28456.0 - 49287.2i) q^{79} +(3200.00 + 5542.56i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16304.1 - 28239.5i) q^{82} -5543.75 q^{83} +(-18289.3 - 3743.40i) q^{84} -45210.4 q^{85} +(21661.8 - 37519.4i) q^{86} +(-12574.2 - 21779.1i) q^{87} +(3386.55 + 5865.68i) q^{88} +(-58318.7 + 101011. i) q^{89} -8100.00 q^{90} +(-17055.9 - 51174.9i) q^{91} +77493.6 q^{92} +(-20549.8 + 35593.4i) q^{93} +(9284.03 + 16080.4i) q^{94} +(24182.5 + 41885.3i) q^{95} +(4608.00 - 7981.29i) q^{96} +34548.9 q^{97} +(-8036.00 - 66746.0i) q^{98} -8572.21 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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
$7$	−40.9913	−	122.991i	−0.316189	−	0.948696i
$7$	−40.9913	−	122.991i	−0.316189	−	0.948696i
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	50.0000	+	86.6025i	0.158114	+	0.273861i
$11$	52.9149	+	91.6512i	0.131855	+	0.228379i	0.924392	−	0.381445i	$-0.124573\pi$
$11$	52.9149	+	91.6512i	0.131855	+	0.228379i	−0.792537	+	0.609824i	$0.791240\pi$
$12$	72.0000	−	124.708i	0.144338	−	0.250000i
$13$	416.087			0.682851			0.341426	−	0.939909i	$-0.389090\pi$
$13$	416.087			0.682851			0.341426	+	0.939909i	$0.389090\pi$
$14$	508.035	+	103.983i	0.692745	+	0.141790i
$15$	225.000			0.258199
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−904.207	−	1566.13i	−0.758832	−	1.31434i	−0.943447	−	0.331525i	$-0.892437\pi$
$17$	−904.207	−	1566.13i	−0.758832	−	1.31434i	0.184615	−	0.982811i	$-0.440896\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	−967.299	+	1675.41i	−0.614719	+	1.06472i	0.375715	+	0.926735i	$0.377397\pi$
$19$	−967.299	+	1675.41i	−0.614719	+	1.06472i	−0.990434	+	0.137989i	$0.955936\pi$
$20$	−400.000			−0.223607
$21$	774.157	−	872.954i	0.383072	−	0.431959i
$22$	−423.319			−0.186471
$23$	−2421.67	+	4194.46i	−0.954544	+	1.65332i	−0.219137	+	0.975694i	$0.570324\pi$
$23$	−2421.67	+	4194.46i	−0.954544	+	1.65332i	−0.735408	+	0.677625i	$0.763009\pi$
$24$	288.000	+	498.831i	0.102062	+	0.176777i
$25$	−312.500	−	541.266i	−0.100000	−	0.173205i
$26$	−832.174	+	1441.37i	−0.241424	+	0.418159i
$27$	−729.000			−0.192450
$28$	−1376.28	+	1551.92i	−0.331750	+	0.374088i
$29$	−2794.26			−0.616981			−0.308490	−	0.951227i	$-0.599824\pi$
$29$	−2794.26			−0.616981			−0.308490	+	0.951227i	$0.599824\pi$
$30$	−450.000	+	779.423i	−0.0912871	+	0.158114i
$31$	2283.32	+	3954.82i	0.426738	+	0.739133i	0.996581	−	0.0826213i	$-0.0263292\pi$
$31$	2283.32	+	3954.82i	0.426738	+	0.739133i	−0.569843	+	0.821754i	$0.692996\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−476.234	+	824.861i	−0.0761264	+	0.131855i
$34$	7233.66			1.07315
$35$	−3175.22	−	649.897i	−0.438130	−	0.0896756i
$36$	1296.00			0.166667
$37$	−348.319	+	603.305i	−0.0418285	+	0.0724491i	−0.886182	−	0.463338i	$-0.846652\pi$
$37$	−348.319	+	603.305i	−0.0418285	+	0.0724491i	0.844353	+	0.535787i	$0.179985\pi$
$38$	−3869.20	−	6701.64i	−0.434672	−	0.752874i
$39$	1872.39	+	3243.08i	0.197122	+	0.341426i
$40$	800.000	−	1385.64i	0.0790569	−	0.136931i
$41$	−8152.05			−0.757369			−0.378684	−	0.925526i	$-0.623623\pi$
$41$	−8152.05			−0.757369			−0.378684	+	0.925526i	$0.623623\pi$
$42$	1475.69	+	4427.67i	0.129084	+	0.387304i
$43$	−10830.9			−0.893293			−0.446647	−	0.894710i	$-0.647382\pi$
$43$	−10830.9			−0.893293			−0.446647	+	0.894710i	$0.647382\pi$
$44$	846.638	−	1466.42i	0.0659274	−	0.114190i
$45$	1012.50	+	1753.70i	0.0745356	+	0.129099i
$46$	−9686.70	−	16777.8i	−0.674965	−	1.16907i
$47$	2321.01	−	4020.10i	0.153261	−	0.265456i	−0.779163	−	0.626821i	$-0.784356\pi$
$47$	2321.01	−	4020.10i	0.153261	−	0.265456i	0.932425	+	0.361365i	$0.117689\pi$
$48$	−2304.00			−0.144338
$49$	−13446.4	+	10083.1i	−0.800049	+	0.599934i
$50$	2500.00			0.141421
$51$	8137.86	−	14095.2i	0.438112	−	0.758832i
$52$	−3328.70	−	5765.47i	−0.170713	−	0.295683i
$53$	15981.7	+	27681.1i	0.781507	+	1.35361i	0.931064	+	0.364857i	$0.118882\pi$
$53$	15981.7	+	27681.1i	0.781507	+	1.35361i	−0.149557	+	0.988753i	$0.547785\pi$
$54$	1458.00	−	2525.33i	0.0680414	−	0.117851i
$55$	2645.74			0.117935
$56$	−2623.44	−	7871.41i	−0.111790	−	0.335415i
$57$	−17411.4			−0.709817
$58$	5588.52	−	9679.59i	0.218136	−	0.377822i
$59$	−14848.6	−	25718.5i	−0.555335	−	0.961868i	−0.997877	−	0.0651208i	$-0.979257\pi$
$59$	−14848.6	−	25718.5i	−0.555335	−	0.961868i	0.442542	−	0.896748i	$-0.354077\pi$
$60$	−1800.00	−	3117.69i	−0.0645497	−	0.111803i
$61$	1508.62	−	2613.01i	0.0519106	−	0.0899118i	−0.838902	−	0.544282i	$-0.816802\pi$
$61$	1508.62	−	2613.01i	0.0519106	−	0.0899118i	0.890813	+	0.454370i	$0.150136\pi$
$62$	−18266.5			−0.603499
$63$	10287.7	+	2105.67i	0.326563	+	0.0668402i
$64$	4096.00			0.125000
$65$	5201.09	−	9008.55i	0.152690	−	0.264467i
$66$	−1904.94	−	3299.44i	−0.0538295	−	0.0932354i
$67$	−5538.08	−	9592.24i	−0.150721	−	0.261056i	0.780772	−	0.624816i	$-0.214826\pi$
$67$	−5538.08	−	9592.24i	−0.150721	−	0.261056i	−0.931493	+	0.363760i	$0.881493\pi$
$68$	−14467.3	+	25058.1i	−0.379416	+	0.657168i
$69$	−43590.1			−1.10221
$70$	8601.74	−	9699.48i	0.209817	−	0.236594i
$71$	−72061.3			−1.69651			−0.848254	−	0.529589i	$-0.822346\pi$
$71$	−72061.3			−1.69651			−0.848254	+	0.529589i	$0.822346\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	−33457.3	−	57949.8i	−0.734825	−	1.27275i	−0.954800	−	0.297249i	$-0.903931\pi$
$73$	−33457.3	−	57949.8i	−0.734825	−	1.27275i	0.219975	−	0.975506i	$-0.429402\pi$
$74$	−1393.27	−	2413.22i	−0.0295772	−	0.0512292i
$75$	2812.50	−	4871.39i	0.0577350	−	0.100000i
$76$	30953.6			0.614719
$77$	9103.20	−	10264.9i	0.174972	−	0.197301i
$78$	−14979.1			−0.278773
$79$	28456.0	−	49287.2i	0.512986	−	0.888518i	−0.486901	−	0.873457i	$-0.661873\pi$
$79$	28456.0	−	49287.2i	0.512986	−	0.888518i	0.999887	−	0.0150605i	$-0.00479409\pi$
$80$	3200.00	+	5542.56i	0.0559017	+	0.0968246i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	16304.1	−	28239.5i	0.267770	−	0.463792i
$83$	−5543.75			−0.0883300			−0.0441650	−	0.999024i	$-0.514063\pi$
$83$	−5543.75			−0.0883300			−0.0441650	+	0.999024i	$0.514063\pi$
$84$	−18289.3	−	3743.40i	−0.282812	−	0.0578853i
$85$	−45210.4			−0.678720
$86$	21661.8	−	37519.4i	0.315827	−	0.547028i
$87$	−12574.2	−	21779.1i	−0.178107	−	0.308490i
$88$	3386.55	+	5865.68i	0.0466177	+	0.0807443i
$89$	−58318.7	+	101011.i	−0.780428	+	1.35174i	0.151265	+	0.988493i	$0.451665\pi$
$89$	−58318.7	+	101011.i	−0.780428	+	1.35174i	−0.931693	+	0.363247i	$0.881668\pi$
$90$	−8100.00			−0.105409
$91$	−17055.9	−	51174.9i	−0.215910	−	0.647818i
$92$	77493.6			0.954544
$93$	−20549.8	+	35593.4i	−0.246378	+	0.426738i
$94$	9284.03	+	16080.4i	0.108372	+	0.187706i
$95$	24182.5	+	41885.3i	0.274911	+	0.476159i
$96$	4608.00	−	7981.29i	0.0510310	−	0.0883883i
$97$	34548.9			0.372825			0.186412	−	0.982472i	$-0.440314\pi$
$97$	34548.9			0.372825			0.186412	+	0.982472i	$0.440314\pi$
$98$	−8036.00	−	66746.0i	−0.0845230	−	0.702037i
$99$	−8572.21			−0.0879032
$100$	−5000.00	+	8660.25i	−0.0500000	+	0.0866025i
$101$	−29253.4	−	50668.4i	−0.285347	−	0.494235i	0.687346	−	0.726330i	$-0.258775\pi$
$101$	−29253.4	−	50668.4i	−0.285347	−	0.494235i	−0.972693	+	0.232095i	$0.925442\pi$
$102$	32551.5	+	56380.8i	0.309792	+	0.536575i
$103$	−54730.8	+	94796.5i	−0.508322	+	0.880439i	0.491632	+	0.870803i	$0.336401\pi$
$103$	−54730.8	+	94796.5i	−0.508322	+	0.880439i	−0.999954	+	0.00963605i	$0.996933\pi$
$104$	26629.6			0.241424
$105$	−9223.04	−	27672.9i	−0.0816396	−	0.244952i
$106$	−127853.			−1.10522
$107$	−109402.	+	189490.i	−0.923774	+	1.60002i	−0.130253	+	0.991481i	$0.541579\pi$
$107$	−109402.	+	189490.i	−0.923774	+	1.60002i	−0.793521	+	0.608543i	$0.791754\pi$
$108$	5832.00	+	10101.3i	0.0481125	+	0.0833333i
$109$	−87196.5	−	151029.i	−0.702963	−	1.21757i	−0.967422	−	0.253171i	$-0.918527\pi$
$109$	−87196.5	−	151029.i	−0.702963	−	1.21757i	0.264458	−	0.964397i	$-0.414807\pi$
$110$	−5291.49	+	9165.12i	−0.0416962	+	0.0722199i
$111$	−6269.73			−0.0482994
$112$	32514.2	+	6654.94i	0.244922	+	0.0501302i
$113$	22891.9			0.168649			0.0843247	−	0.996438i	$-0.473127\pi$
$113$	22891.9			0.168649			0.0843247	+	0.996438i	$0.473127\pi$
$114$	34822.8	−	60314.8i	0.250958	−	0.434672i
$115$	60541.8	+	104862.i	0.426885	+	0.739387i
$116$	22354.1	+	38718.4i	0.154245	+	0.267160i
$117$	−16851.5	+	29187.7i	−0.113809	+	0.197122i
$118$	118789.			0.785362
$119$	−155555.	+	175407.i	−1.00697	+	1.13548i
$120$	14400.0			0.0912871
$121$	74925.5	−	129775.i	0.465229	−	0.805800i
$122$	6034.49	+	10452.0i	0.0367063	+	0.0635773i
$123$	−36684.2	−	63539.0i	−0.218634	−	0.378684i
$124$	36533.0	−	63277.1i	0.213369	−	0.369566i
$125$	−15625.0			−0.0894427
$126$	−27869.7	+	31426.3i	−0.156389	+	0.176347i
$127$	323785.			1.78134			0.890670	−	0.454650i	$-0.150235\pi$
$127$	323785.			1.78134			0.890670	+	0.454650i	$0.150235\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	−48739.1	−	84418.6i	−0.257872	−	0.446647i
$130$	20804.4	+	36034.2i	0.107968	+	0.187006i
$131$	45170.8	−	78238.2i	0.229975	−	0.398328i	−0.727826	−	0.685762i	$-0.759469\pi$
$131$	45170.8	−	78238.2i	0.229975	−	0.398328i	0.957800	+	0.287435i	$0.0928024\pi$
$132$	15239.5			0.0761264
$133$	245711.	+	50291.5i	1.20447	+	0.246528i
$134$	44304.7			0.213151
$135$	−9112.50	+	15783.3i	−0.0430331	+	0.0745356i
$136$	−57869.3	−	100233.i	−0.268288	−	0.464688i
$137$	181793.	+	314874.i	0.827514	+	1.43330i	0.899983	+	0.435925i	$0.143579\pi$
$137$	181793.	+	314874.i	0.827514	+	1.43330i	−0.0724688	+	0.997371i	$0.523088\pi$
$138$	87180.3	−	151001.i	0.389691	−	0.674965i
$139$	−185015.			−0.812215			−0.406107	−	0.913825i	$-0.633114\pi$
$139$	−185015.			−0.812215			−0.406107	+	0.913825i	$0.633114\pi$
$140$	16396.5	+	49196.3i	0.0707019	+	0.212135i
$141$	41778.1			0.176971
$142$	144123.	−	249628.i	0.599806	−	1.03889i
$143$	22017.2	+	38134.9i	0.0900372	+	0.155949i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	−34928.2	+	60497.5i	−0.137961	+	0.238956i
$146$	267659.			1.03920
$147$	−139099.	−	59430.6i	−0.530921	−	0.226839i
$148$	11146.2			0.0418285
$149$	−85585.5	+	148238.i	−0.315816	+	0.547010i	−0.979611	−	0.200905i	$-0.935612\pi$
$149$	−85585.5	+	148238.i	−0.315816	+	0.547010i	0.663794	+	0.747915i	$0.268945\pi$
$150$	11250.0	+	19485.6i	0.0408248	+	0.0707107i
$151$	195304.	+	338276.i	0.697057	+	1.20734i	0.969482	+	0.245162i	$0.0788411\pi$
$151$	195304.	+	338276.i	0.697057	+	1.20734i	−0.272425	+	0.962177i	$0.587826\pi$
$152$	−61907.1	+	107226.i	−0.217336	+	0.376437i
$153$	146482.			0.505888
$154$	17352.4	+	52064.3i	0.0589600	+	0.176904i
$155$	114166.			0.381686
$156$	29958.3	−	51889.3i	0.0985611	−	0.170713i
$157$	−91114.7	−	157815.i	−0.295012	−	0.510975i	0.679976	−	0.733234i	$-0.261990\pi$
$157$	−91114.7	−	157815.i	−0.295012	−	0.510975i	−0.974988	+	0.222259i	$0.928657\pi$
$158$	113824.	+	197149.i	0.362736	+	0.628277i
$159$	−143835.	+	249130.i	−0.451203	+	0.781507i
$160$	−25600.0			−0.0790569
$161$	615147.	+	125907.i	1.87031	+	0.382812i
$162$	26244.0			0.0785674
$163$	2490.30	−	4313.33i	0.00734148	−	0.0127158i	−0.862331	−	0.506344i	$-0.830996\pi$
$163$	2490.30	−	4313.33i	0.00734148	−	0.0127158i	0.869673	+	0.493629i	$0.164330\pi$
$164$	65216.4	+	112958.i	0.189342	+	0.327950i
$165$	11905.8	+	20621.5i	0.0340448	+	0.0589673i
$166$	11087.5	−	19204.1i	0.0312294	−	0.0540909i
$167$	238771.			0.662506			0.331253	−	0.943542i	$-0.392529\pi$
$167$	238771.			0.662506			0.331253	+	0.943542i	$0.392529\pi$
$168$	49546.0	−	55869.0i	0.135437	−	0.152721i
$169$	−198164.			−0.533714
$170$	90420.7	−	156613.i	0.239964	−	0.415629i
$171$	−78351.2	−	135708.i	−0.204906	−	0.354908i
$172$	86647.3	+	150078.i	0.223323	+	0.386807i
$173$	−92856.2	+	160832.i	−0.235882	+	0.408560i	−0.959529	−	0.281611i	$-0.909131\pi$
$173$	−92856.2	+	160832.i	−0.235882	+	0.408560i	0.723646	+	0.690171i	$0.242465\pi$
$174$	100593.			0.251881
$175$	−53760.9	+	60621.8i	−0.132700	+	0.149635i
$176$	−27092.4			−0.0659274
$177$	133637.	−	231467.i	0.320623	−	0.555335i
$178$	−233275.	−	404044.i	−0.551846	−	0.955825i
$179$	67859.3	+	117536.i	0.158298	+	0.274181i	0.934255	−	0.356605i	$-0.116066\pi$
$179$	67859.3	+	117536.i	0.158298	+	0.274181i	−0.775957	+	0.630786i	$0.782733\pi$
$180$	16200.0	−	28059.2i	0.0372678	−	0.0645497i
$181$	−151986.			−0.344832			−0.172416	−	0.985024i	$-0.555157\pi$
$181$	−151986.			−0.344832			−0.172416	+	0.985024i	$0.555157\pi$
$182$	211387.	+	43266.2i	0.473042	+	0.0968211i
$183$	27155.2			0.0599412
$184$	−154987.	+	268446.i	−0.337482	+	0.584537i
$185$	8707.96	+	15082.6i	0.0187063	+	0.0324002i
$186$	−82199.4	−	142373.i	−0.174215	−	0.301750i
$187$	95692.0	−	165743.i	0.200111	−	0.346603i
$188$	−74272.3			−0.153261
$189$	29882.6	+	89660.2i	0.0608505	+	0.182577i
$190$	−193460.			−0.388783
$191$	−441023.	+	763874.i	−0.874738	+	1.51509i	−0.0176962	+	0.999843i	$0.505633\pi$
$191$	−441023.	+	763874.i	−0.874738	+	1.51509i	−0.857042	+	0.515247i	$0.827700\pi$
$192$	18432.0	+	31925.2i	0.0360844	+	0.0625000i
$193$	−98070.1	−	169862.i	−0.189515	−	0.328249i	0.755574	−	0.655064i	$-0.227358\pi$
$193$	−98070.1	−	169862.i	−0.189515	−	0.328249i	−0.945089	+	0.326814i	$0.894025\pi$
$194$	−69097.7	+	119681.i	−0.131813	+	0.228308i
$195$	93619.6			0.176311
$196$	247287.	+	105654.i	0.459791	+	0.196448i
$197$	−360160.			−0.661196			−0.330598	−	0.943772i	$-0.607250\pi$
$197$	−360160.			−0.661196			−0.330598	+	0.943772i	$0.607250\pi$
$198$	17144.4	−	29695.0i	0.0310785	−	0.0538295i
$199$	−39606.1	−	68599.8i	−0.0708973	−	0.122798i	0.828398	−	0.560141i	$-0.189253\pi$
$199$	−39606.1	−	68599.8i	−0.0708973	−	0.122798i	−0.899295	+	0.437343i	$0.855920\pi$
$200$	−20000.0	−	34641.0i	−0.0353553	−	0.0612372i
$201$	49842.8	−	86330.2i	0.0870186	−	0.150721i
$202$	234027.			0.403541
$203$	114540.	+	343668.i	0.195082	+	0.585327i
$204$	−260412.			−0.438112
$205$	−101901.	+	176497.i	−0.169353	+	0.293328i
$206$	−218923.	−	379186.i	−0.359438	−	0.622565i
$207$	−196156.	−	339751.i	−0.318181	−	0.551106i
$208$	−53259.2	+	92247.6i	−0.0853564	+	0.147842i
$209$	−204738.			−0.324215
$210$	114308.	+	23396.3i	0.178866	+	0.0366099i
$211$	−39456.2			−0.0610111			−0.0305056	−	0.999535i	$-0.509712\pi$
$211$	−39456.2			−0.0610111			−0.0305056	+	0.999535i	$0.509712\pi$
$212$	255707.	−	442897.i	0.390754	−	0.676805i
$213$	−324276.	−	561662.i	−0.489740	−	0.848254i
$214$	−437608.	−	757959.i	−0.653207	−	1.13139i
$215$	−135386.	+	234496.i	−0.199746	+	0.345971i
$216$	−46656.0			−0.0680414
$217$	392810.	−	442940.i	0.566282	−	0.638550i
$218$	697572.			0.994140
$219$	301116.	−	521548.i	0.424251	−	0.734825i
$220$	−21165.9	−	36660.5i	−0.0294836	−	0.0510672i
$221$	−376229.	−	651648.i	−0.518169	−	0.897495i
$222$	12539.5	−	21719.0i	0.0170764	−	0.0295772i
$223$	530050.			0.713764			0.356882	−	0.934149i	$-0.383840\pi$
$223$	530050.			0.713764			0.356882	+	0.934149i	$0.383840\pi$
$224$	−88081.9	+	99322.7i	−0.117291	+	0.132260i
$225$	50625.0			0.0666667
$226$	−45783.7	+	79299.7i	−0.0596266	+	0.103276i
$227$	68127.4	+	118000.i	0.0877521	+	0.151991i	0.906561	−	0.422076i	$-0.138698\pi$
$227$	68127.4	+	118000.i	0.0877521	+	0.151991i	−0.818809	+	0.574067i	$0.805365\pi$
$228$	139291.	+	241259.i	0.177454	+	0.307360i
$229$	−439001.	+	760372.i	−0.553193	+	0.958158i	0.444849	+	0.895606i	$0.353257\pi$
$229$	−439001.	+	760372.i	−0.553193	+	0.958158i	−0.998042	+	0.0625527i	$0.980076\pi$
$230$	−484335.			−0.603707
$231$	120972.	+	24760.2i	0.149160	+	0.0305298i
$232$	−178833.			−0.218136
$233$	511570.	−	886065.i	0.617327	−	1.06924i	−0.372644	−	0.927974i	$-0.621549\pi$
$233$	511570.	−	886065.i	0.617327	−	1.06924i	0.989971	−	0.141268i	$-0.0451178\pi$
$234$	−67406.1	−	116751.i	−0.0804748	−	0.139386i
$235$	−58025.2	−	100503.i	−0.0685405	−	0.118716i
$236$	−237577.	+	411496.i	−0.277667	+	0.480934i
$237$	512207.			0.592345
$238$	−296517.	−	889673.i	−0.339318	−	1.01809i
$239$	−492394.			−0.557594			−0.278797	−	0.960350i	$-0.589936\pi$
$239$	−492394.			−0.557594			−0.278797	+	0.960350i	$0.589936\pi$
$240$	−28800.0	+	49883.1i	−0.0322749	+	0.0559017i
$241$	163832.	+	283766.i	0.181701	+	0.314715i	0.942460	−	0.334319i	$-0.108506\pi$
$241$	163832.	+	283766.i	0.181701	+	0.314715i	−0.760759	+	0.649035i	$0.775173\pi$
$242$	299702.	+	519099.i	0.328966	+	0.569786i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−48275.9			−0.0519106
$245$	50225.0	+	417162.i	0.0534570	+	0.444007i
$246$	293474.			0.309195
$247$	−402481.	+	697117.i	−0.419762	+	0.727048i
$248$	146132.	+	253108.i	0.150875	+	0.261323i
$249$	−24946.9	−	43209.3i	−0.0254987	−	0.0441650i
$250$	31250.0	−	54126.6i	0.0316228	−	0.0547723i
$251$	826558.			0.828112			0.414056	−	0.910251i	$-0.364112\pi$
$251$	826558.			0.828112			0.414056	+	0.910251i	$0.364112\pi$
$252$	−53124.7	−	159396.i	−0.0526981	−	0.158116i
$253$	−512570.			−0.503445
$254$	−647569.	+	1.12162e6i	−0.629799	+	1.09084i
$255$	−203447.	−	352380.i	−0.195930	−	0.339360i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−454390.	+	787027.i	−0.429137	+	0.743287i	−0.996797	−	0.0799762i	$-0.974516\pi$
$257$	−454390.	+	787027.i	−0.429137	+	0.743287i	0.567660	+	0.823263i	$0.307849\pi$
$258$	389913.			0.364686
$259$	88479.0	+	18109.7i	0.0819579	+	0.0167750i
$260$	−166435.			−0.152690
$261$	113167.	−	196012.i	0.102830	−	0.178107i
$262$	180683.	+	312953.i	0.162617	+	0.281660i
$263$	−949258.	−	1.64416e6i	−0.846242	−	1.46573i	−0.884538	−	0.466468i	$-0.845526\pi$
$263$	−949258.	−	1.64416e6i	−0.846242	−	1.46573i	0.0382954	−	0.999266i	$-0.487807\pi$
$264$	−30479.0	+	52791.1i	−0.0269148	+	0.0466177i
$265$	799084.			0.699001
$266$	−665637.	+	750584.i	−0.576810	+	0.650422i
$267$	−1.04974e6			−0.901160
$268$	−88609.3	+	153476.i	−0.0753603	+	0.130528i
$269$	−450461.	−	780222.i	−0.379557	−	0.657411i	0.611441	−	0.791290i	$-0.290590\pi$
$269$	−450461.	−	780222.i	−0.379557	−	0.657411i	−0.990998	+	0.133879i	$0.957257\pi$
$270$	−36450.0	−	63133.3i	−0.0304290	−	0.0527046i
$271$	1.08488e6	−	1.87907e6i	0.897346	−	1.55425i	0.0664720	−	0.997788i	$-0.478826\pi$
$271$	1.08488e6	−	1.87907e6i	0.897346	−	1.55425i	0.830874	−	0.556461i	$-0.187841\pi$
$272$	462954.			0.379416
$273$	322117.	−	363225.i	0.261581	−	0.294964i
$274$	−1.45434e6			−1.17028
$275$	33071.8	−	57282.0i	0.0263710	−	0.0456758i
$276$	348721.	+	604003.i	0.275553	+	0.477272i
$277$	−1.21845e6	−	2.11042e6i	−0.954132	−	1.65261i	−0.736341	−	0.676610i	$-0.763448\pi$
$277$	−1.21845e6	−	2.11042e6i	−0.954132	−	1.65261i	−0.217791	−	0.975995i	$-0.569885\pi$
$278$	370031.	−	640912.i	0.287161	−	0.497378i
$279$	−369897.			−0.284492
$280$	−203214.	−	41593.4i	−0.154903	−	0.0317051i
$281$	130396.			0.0985142			0.0492571	−	0.998786i	$-0.484315\pi$
$281$	130396.			0.0985142			0.0492571	+	0.998786i	$0.484315\pi$
$282$	−83556.3	+	144724.i	−0.0625686	+	0.108372i
$283$	−289500.	−	501429.i	−0.214873	−	0.372172i	0.738360	−	0.674407i	$-0.235601\pi$
$283$	−289500.	−	501429.i	−0.214873	−	0.372172i	−0.953233	+	0.302235i	$0.902267\pi$
$284$	576490.	+	998510.i	0.424127	+	0.734610i
$285$	−217642.	+	376967.i	−0.158720	+	0.274911i
$286$	−176138.			−0.127332
$287$	334163.	+	1.00263e6i	0.239471	+	0.718513i
$288$	82944.0			0.0589256
$289$	−925253.	+	1.60258e6i	−0.651652	+	1.12869i
$290$	−139713.	−	241990.i	−0.0975532	−	0.168967i
$291$	155470.	+	269282.i	0.107625	+	0.186412i
$292$	−535317.	+	927196.i	−0.367413	+	0.636377i
$293$	927289.			0.631024			0.315512	−	0.948922i	$-0.397824\pi$
$293$	927289.			0.631024			0.315512	+	0.948922i	$0.397824\pi$
$294$	484071.	−	362991.i	0.326619	−	0.244922i
$295$	−742429.			−0.496707
$296$	−22292.4	+	38611.5i	−0.0147886	+	0.0256146i
$297$	−38574.9	−	66813.8i	−0.0253755	−	0.0439516i
$298$	−342342.	−	592954.i	−0.223316	−	0.386794i
$299$	−1.00763e6	+	1.74526e6i	−0.651812	+	1.12897i
$300$	−90000.0			−0.0577350
$301$	443973.	+	1.33210e6i	0.282449	+	0.847464i
$302$	−1.56243e6			−0.985788
$303$	263281.	−	456015.i	0.164745	−	0.285347i
$304$	−247629.	−	428905.i	−0.153680	−	0.266181i
$305$	−37715.6	−	65325.3i	−0.0232151	−	0.0402098i
$306$	−292963.	+	507427.i	−0.178858	+	0.309792i
$307$	2.72021e6			1.64724			0.823620	−	0.567141i	$-0.191951\pi$
$307$	2.72021e6			1.64724			0.823620	+	0.567141i	$0.191951\pi$
$308$	−215061.	−	44018.2i	−0.129177	−	0.0264396i
$309$	−985155.			−0.586960
$310$	−228332.	+	395482.i	−0.134947	+	0.233734i
$311$	−1.05808e6	−	1.83265e6i	−0.620323	−	1.07443i	−0.989425	−	0.145043i	$-0.953668\pi$
$311$	−1.05808e6	−	1.83265e6i	−0.620323	−	1.07443i	0.369102	−	0.929389i	$-0.379665\pi$
$312$	119833.	+	207557.i	0.0696932	+	0.120712i
$313$	87626.1	−	151773.i	0.0505560	−	0.0875656i	−0.839640	−	0.543143i	$-0.817234\pi$
$313$	87626.1	−	151773.i	0.0505560	−	0.0875656i	0.890196	+	0.455578i	$0.150567\pi$
$314$	728918.			0.417210
$315$	174185.	−	196415.i	0.0989089	−	0.111531i
$316$	−910591.			−0.512986
$317$	321796.	−	557368.i	0.179859	−	0.311525i	−0.761973	−	0.647609i	$-0.775769\pi$
$317$	321796.	−	557368.i	0.179859	−	0.311525i	0.941832	+	0.336083i	$0.109102\pi$
$318$	−575341.	−	996519.i	−0.319049	−	0.552609i
$319$	−147858.	−	256097.i	−0.0813519	−	0.140906i
$320$	51200.0	−	88681.0i	0.0279508	−	0.0484123i
$321$	−1.96924e6			−1.06668
$322$	−1.66645e6	+	1.87912e6i	−0.895679	+	1.00998i
$323$	3.49855e6			1.86587
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	−130027.	−	225214.i	−0.0682851	−	0.118273i
$326$	9961.22	+	17253.3i	0.00519121	+	0.00899144i
$327$	784768.	−	1.35926e6i	0.405856	−	0.702963i
$328$	−521731.			−0.267770
$329$	−589577.	−	120673.i	−0.300297	−	0.0614641i
$330$	−95246.8			−0.0481466
$331$	1.11875e6	−	1.93773e6i	0.561257	−	0.972126i	−0.436130	−	0.899884i	$-0.643651\pi$
$331$	1.11875e6	−	1.93773e6i	0.561257	−	0.972126i	0.997387	−	0.0722425i	$-0.0230155\pi$
$332$	44350.0	+	76816.4i	0.0220825	+	0.0382480i
$333$	−28213.8	−	48867.7i	−0.0139428	−	0.0241497i
$334$	−477542.	+	827126.i	−0.234231	+	0.405701i
$335$	−276904.			−0.134809
$336$	94443.9	+	283371.i	0.0456379	+	0.136933i
$337$	−1.19266e6			−0.572058			−0.286029	−	0.958221i	$-0.592335\pi$
$337$	−1.19266e6			−0.572058			−0.286029	+	0.958221i	$0.592335\pi$
$338$	396329.	−	686462.i	0.188697	−	0.326832i
$339$	103013.	+	178424.i	0.0486849	+	0.0843247i
$340$	361683.	+	626453.i	0.169680	+	0.293894i
$341$	−241643.	+	418537.i	−0.112535	+	0.194916i
$342$	626810.			0.289781
$343$	1.79131e6	+	1.24047e6i	0.822122	+	0.569311i
$344$	−693179.			−0.315827
$345$	−544877.	+	943754.i	−0.246462	+	0.426885i
$346$	−371425.	−	643326.i	−0.166794	−	0.288896i
$347$	493587.	+	854918.i	0.220060	+	0.381154i	0.954826	−	0.297166i	$-0.0960415\pi$
$347$	493587.	+	854918.i	0.220060	+	0.381154i	−0.734766	+	0.678320i	$0.762708\pi$
$348$	−201187.	+	348465.i	−0.0890535	+	0.154245i
$349$	−866691.			−0.380891			−0.190446	−	0.981698i	$-0.560993\pi$
$349$	−866691.			−0.380891			−0.190446	+	0.981698i	$0.560993\pi$
$350$	−102478.	−	307477.i	−0.0447158	−	0.134166i
$351$	−303328.			−0.131415
$352$	54184.8	−	93850.9i	0.0233089	−	0.0403721i
$353$	1.39107e6	+	2.40940e6i	0.594172	+	1.02914i	0.993663	+	0.112399i	$0.0358534\pi$
$353$	1.39107e6	+	2.40940e6i	0.594172	+	1.02914i	−0.399491	+	0.916737i	$0.630813\pi$
$354$	534549.	+	925866.i	0.226715	+	0.392681i
$355$	−900766.	+	1.56017e6i	−0.379351	+	0.657055i
$356$	1.86620e6			0.780428
$357$	−2.06716e6	−	423102.i	−0.858427	−	0.175701i
$358$	−542874.			−0.223868
$359$	−1.81722e6	+	3.14752e6i	−0.744170	+	1.28894i	0.206411	+	0.978465i	$0.433821\pi$
$359$	−1.81722e6	+	3.14752e6i	−0.744170	+	1.28894i	−0.950581	+	0.310475i	$0.899512\pi$
$360$	64800.0	+	112237.i	0.0263523	+	0.0456435i
$361$	−633285.	−	1.09688e6i	−0.255759	−	0.442988i
$362$	303972.	−	526495.i	0.121916	−	0.211165i
$363$	1.34866e6			0.537200
$364$	−572652.	+	645733.i	−0.226536	+	0.255446i
$365$	−1.67287e6			−0.657248
$366$	−54310.4	+	94068.4i	−0.0211924	+	0.0367063i
$367$	1.72787e6	+	2.99276e6i	0.669648	+	1.15986i	0.978003	+	0.208593i	$0.0668884\pi$
$367$	1.72787e6	+	2.99276e6i	0.669648	+	1.15986i	−0.308354	+	0.951272i	$0.599778\pi$
$368$	−619949.	−	1.07378e6i	−0.238636	−	0.413330i
$369$	330158.	−	571851.i	0.126228	−	0.218634i
$370$	−69663.7			−0.0264547
$371$	2.74941e6	−	3.10028e6i	1.03706	−	1.16941i
$372$	657595.			0.246378
$373$	1.30421e6	−	2.25895e6i	0.485371	−	0.840687i	−0.514488	−	0.857498i	$-0.672018\pi$
$373$	1.30421e6	−	2.25895e6i	0.485371	−	0.840687i	0.999859	+	0.0168104i	$0.00535116\pi$
$374$	382768.	+	662974.i	0.141500	+	0.245085i
$375$	−70312.5	−	121785.i	−0.0258199	−	0.0447214i
$376$	148545.	−	257287.i	0.0541860	−	0.0938529i
$377$	−1.16266e6			−0.421306
$378$	−370357.	−	75803.9i	−0.133319	−	0.0272874i
$379$	1.17324e6			0.419554			0.209777	−	0.977749i	$-0.432726\pi$
$379$	1.17324e6			0.419554			0.209777	+	0.977749i	$0.432726\pi$
$380$	386920.	−	670164.i	0.137455	−	0.238080i
$381$	1.45703e6	+	2.52365e6i	0.514229	+	0.890670i
$382$	−1.76409e6	−	3.05550e6i	−0.618533	−	1.07133i
$383$	1.07183e6	−	1.85646e6i	0.373359	−	0.646677i	−0.616721	−	0.787182i	$-0.711539\pi$
$383$	1.07183e6	−	1.85646e6i	0.373359	−	0.646677i	0.990080	+	0.140505i	$0.0448725\pi$
$384$	−147456.			−0.0510310
$385$	−108452.	−	325402.i	−0.0372896	−	0.111884i
$386$	784561.			0.268014
$387$	438652.	−	759768.i	0.148882	−	0.257872i
$388$	−276391.	−	478723.i	−0.0932061	−	0.161438i
$389$	−2.24542e6	−	3.88919e6i	−0.752357	−	1.30312i	−0.946678	−	0.322183i	$-0.895583\pi$
$389$	−2.24542e6	−	3.88919e6i	−0.752357	−	1.30312i	0.194320	−	0.980938i	$-0.437750\pi$
$390$	−187239.	+	324308.i	−0.0623355	+	0.107968i
$391$	8.75878e6			2.89736
$392$	−860572.	+	645318.i	−0.282860	+	0.212109i
$393$	813075.			0.265552
$394$	720321.	−	1.24763e6i	0.233768	−	0.404898i
$395$	−711399.	−	1.23218e6i	−0.229414	−	0.397357i
$396$	68577.7	+	118780.i	0.0219758	+	0.0380632i
$397$	2.11535e6	−	3.66389e6i	0.673606	−	1.16672i	−0.303268	−	0.952905i	$-0.598078\pi$
$397$	2.11535e6	−	3.66389e6i	0.673606	−	1.16672i	0.976874	−	0.213815i	$-0.0685889\pi$
$398$	316849.			0.100264
$399$	713715.	+	2.14144e6i	0.224436	+	0.673400i
$400$	160000.			0.0500000
$401$	2.00102e6	−	3.46587e6i	0.621428	−	1.07635i	−0.367792	−	0.929908i	$-0.619886\pi$
$401$	2.00102e6	−	3.46587e6i	0.621428	−	1.07635i	0.989220	−	0.146437i	$-0.0467807\pi$
$402$	199371.	+	345321.i	0.0615314	+	0.106576i
$403$	950058.	+	1.64555e6i	0.291399	+	0.504717i
$404$	−468055.	+	810694.i	−0.142673	+	0.247118i
$405$	−164025.			−0.0496904
$406$	−1.41958e6	−	290557.i	−0.427410	−	0.0874814i
$407$	−73724.9			−0.0220612
$408$	520823.	−	902093.i	0.154896	−	0.268288i
$409$	1.84349e6	+	3.19302e6i	0.544919	+	0.943828i	0.998612	+	0.0526699i	$0.0167731\pi$
$409$	1.84349e6	+	3.19302e6i	0.544919	+	0.943828i	−0.453693	+	0.891158i	$0.649894\pi$
$410$	−407603.	−	705989.i	−0.119751	−	0.207414i
$411$	−1.63614e6	+	2.83387e6i	−0.477765	+	0.827514i
$412$	1.75139e6			0.508322
$413$	−2.55447e6	+	2.88047e6i	−0.736930	+	0.830976i
$414$	1.56924e6			0.449976
$415$	−69296.9	+	120026.i	−0.0197512	+	0.0342101i
$416$	−213037.	−	368990.i	−0.0603561	−	0.104540i
$417$	−832570.	−	1.44205e6i	−0.234466	−	0.406107i
$418$	409476.	−	709233.i	0.114627	−	0.198540i
$419$	5.64655e6			1.57126			0.785630	−	0.618697i	$-0.212339\pi$
$419$	5.64655e6			1.57126			0.785630	+	0.618697i	$0.212339\pi$
$420$	−309663.	+	349181.i	−0.0856576	+	0.0965891i
$421$	−896338.			−0.246471			−0.123236	−	0.992377i	$-0.539327\pi$
$421$	−896338.			−0.246471			−0.123236	+	0.992377i	$0.539327\pi$
$422$	78912.4	−	136680.i	0.0215707	−	0.0373615i
$423$	188002.	+	325628.i	0.0510870	+	0.0884854i
$424$	1.02283e6	+	1.77159e6i	0.276304	+	0.478573i
$425$	−565130.	+	978833.i	−0.151766	+	0.262867i
$426$	2.59421e6			0.692597
$427$	−383217.	−	78435.9i	−0.101713	−	0.0208183i
$428$	3.50086e6			0.923774
$429$	−198155.	+	343214.i	−0.0519830	+	0.0900372i
$430$	−541546.	−	937985.i	−0.141242	−	0.244638i
$431$	−3.64913e6	−	6.32048e6i	−0.946229	−	1.63892i	−0.753271	−	0.657711i	$-0.771525\pi$
$431$	−3.64913e6	−	6.32048e6i	−0.946229	−	1.63892i	−0.192959	−	0.981207i	$-0.561808\pi$
$432$	93312.0	−	161621.i	0.0240563	−	0.0416667i
$433$	7.04459e6			1.80566			0.902830	−	0.429998i	$-0.141486\pi$
$433$	7.04459e6			1.80566			0.902830	+	0.429998i	$0.141486\pi$
$434$	748768.	+	2.24661e6i	0.190820	+	0.572537i
$435$	−628708.			−0.159304
$436$	−1.39514e6	+	2.41646e6i	−0.351482	+	0.608784i
$437$	−4.68497e6	−	8.11460e6i	−1.17355	−	2.03265i
$438$	1.20446e6	+	2.08619e6i	0.299991	+	0.519600i
$439$	−1.90823e6	+	3.30516e6i	−0.472574	+	0.818523i	−0.999507	−	0.0313839i	$-0.990009\pi$
$439$	−1.90823e6	+	3.30516e6i	−0.472574	+	0.818523i	0.526933	+	0.849907i	$0.323342\pi$
$440$	169328.			0.0416962
$441$	−162729.	−	1.35161e6i	−0.0398445	−	0.330943i
$442$	3.00983e6			0.732802
$443$	−876874.	+	1.51879e6i	−0.212289	+	0.367696i	−0.952431	−	0.304756i	$-0.901425\pi$
$443$	−876874.	+	1.51879e6i	−0.212289	+	0.367696i	0.740141	+	0.672451i	$0.234759\pi$
$444$	50157.9	+	86876.0i	0.0120748	+	0.0209142i
$445$	1.45797e6	+	2.52527e6i	0.349018	+	0.604517i
$446$	−1.06010e6	+	1.83615e6i	−0.252354	+	0.437090i
$447$	−1.54054e6			−0.364673
$448$	−167900.	−	503770.i	−0.0395236	−	0.118587i
$449$	−1.36660e6			−0.319908			−0.159954	−	0.987124i	$-0.551135\pi$
$449$	−1.36660e6			−0.319908			−0.159954	+	0.987124i	$0.551135\pi$
$450$	−101250.	+	175370.i	−0.0235702	+	0.0408248i
$451$	−431365.	−	747146.i	−0.0998627	−	0.172967i
$452$	−183135.	−	317199.i	−0.0421624	−	0.0730273i
$453$	−1.75774e6	+	3.04449e6i	−0.402446	+	0.697057i
$454$	−545020.			−0.124100
$455$	−1.32117e6	−	270414.i	−0.299178	−	0.0612351i
$456$	−1.11433e6			−0.250958
$457$	−423246.	+	733084.i	−0.0947988	+	0.164196i	−0.909525	−	0.415650i	$-0.863554\pi$
$457$	−423246.	+	733084.i	−0.0947988	+	0.164196i	0.814726	+	0.579846i	$0.196887\pi$
$458$	−1.75600e6	−	3.04149e6i	−0.391167	−	0.677520i
$459$	659167.	+	1.14171e6i	0.146037	+	0.252944i
$460$	968670.	−	1.67778e6i	0.213443	−	0.369693i
$461$	−1.43688e6			−0.314897			−0.157449	−	0.987527i	$-0.550327\pi$
$461$	−1.43688e6			−0.314897			−0.157449	+	0.987527i	$0.550327\pi$
$462$	−327715.	+	369538.i	−0.0714318	+	0.0805478i
$463$	2.98938e6			0.648080			0.324040	−	0.946043i	$-0.394959\pi$
$463$	2.98938e6			0.648080			0.324040	+	0.946043i	$0.394959\pi$
$464$	357665.	−	619494.i	0.0771226	−	0.133580i
$465$	513746.	+	889834.i	0.110183	+	0.190843i
$466$	2.04628e6	+	3.54426e6i	0.436516	+	0.756068i
$467$	−359369.	+	622445.i	−0.0762514	+	0.132071i	−0.901630	−	0.432509i	$-0.857628\pi$
$467$	−359369.	+	622445.i	−0.0762514	+	0.132071i	0.825378	+	0.564580i	$0.190962\pi$
$468$	539249.			0.113809
$469$	−952744.	+	1.07433e6i	−0.200006	+	0.225531i
$470$	464202.			0.0969309
$471$	820032.	−	1.42034e6i	0.170325	−	0.295012i
$472$	−950309.	−	1.64598e6i	−0.196341	−	0.340072i
$473$	−573117.	−	992667.i	−0.117785	−	0.204010i
$474$	−1.02441e6	+	1.77434e6i	−0.209426	+	0.362736i
$475$	1.20912e6			0.245888
$476$	3.67495e6	+	752181.i	0.743420	+	0.152162i
$477$	−2.58903e6			−0.521005
$478$	984788.	−	1.70570e6i	0.197139	−	0.341455i
$479$	4.63903e6	+	8.03504e6i	0.923823	+	1.60011i	0.793444	+	0.608644i	$0.208286\pi$
$479$	4.63903e6	+	8.03504e6i	0.923823	+	1.60011i	0.130379	+	0.991464i	$0.458381\pi$
$480$	−115200.	−	199532.i	−0.0228218	−	0.0395285i
$481$	−144931.	+	251028.i	−0.0285626	+	0.0494719i
$482$	−1.31066e6			−0.256964
$483$	1.78682e6	+	5.36118e6i	0.348507	+	1.04567i
$484$	−2.39762e6			−0.465229
$485$	431861.	−	748005.i	0.0833661	−	0.144394i
$486$	118098.	+	204552.i	0.0226805	+	0.0392837i
$487$	1.83319e6	+	3.17518e6i	0.350256	+	0.606661i	0.986294	−	0.164997i	$-0.0527613\pi$
$487$	1.83319e6	+	3.17518e6i	0.350256	+	0.606661i	−0.636038	+	0.771657i	$0.719428\pi$
$488$	96551.9	−	167233.i	0.0183532	−	0.0317886i
$489$	44825.5			0.00847721
$490$	−1.54554e6	−	660340.i	−0.290798	−	0.124245i
$491$	−5.08357e6			−0.951624			−0.475812	−	0.879547i	$-0.657846\pi$
$491$	−5.08357e6			−0.951624			−0.475812	+	0.879547i	$0.657846\pi$
$492$	−586948.	+	1.01662e6i	−0.109317	+	0.189342i
$493$	2.52659e6	+	4.37618e6i	0.468185	+	0.810920i
$494$	−1.60992e6	−	2.78847e6i	−0.296816	−	0.514101i
$495$	−107153.	+	185594.i	−0.0196558	+	0.0340448i
$496$	−1.16906e6			−0.213369
$497$	2.95388e6	+	8.86287e6i	0.536417	+	1.60947i
$498$	199575.			0.0360606
$499$	1.41008e6	−	2.44233e6i	0.253508	−	0.439089i	−0.710981	−	0.703211i	$-0.751749\pi$
$499$	1.41008e6	−	2.44233e6i	0.253508	−	0.439089i	0.964489	+	0.264122i	$0.0850823\pi$
$500$	125000.	+	216506.i	0.0223607	+	0.0387298i
$501$	1.07447e6	+	1.86103e6i	0.191249	+	0.331253i
$502$	−1.65312e6	+	2.86328e6i	−0.292782	+	0.507113i
$503$	1.45136e6			0.255773			0.127887	−	0.991789i	$-0.459181\pi$
$503$	1.45136e6			0.255773			0.127887	+	0.991789i	$0.459181\pi$
$504$	658413.	+	134763.i	0.115458	+	0.0236316i
$505$	−1.46267e6			−0.255222
$506$	1.02514e6	−	1.77560e6i	0.177995	−	0.308296i
$507$	−891740.	−	1.54454e6i	−0.154070	−	0.266857i
$508$	−2.59028e6	−	4.48649e6i	−0.445335	−	0.771343i
$509$	−57494.8	+	99583.9i	−0.00983635	+	0.0170371i	−0.870902	−	0.491457i	$-0.836464\pi$
$509$	−57494.8	+	99583.9i	−0.00983635	+	0.0170371i	0.861065	+	0.508494i	$0.169798\pi$
$510$	1.62757e6			0.277086
$511$	−5.75583e6	+	6.49038e6i	−0.975114	+	1.09956i
$512$	262144.			0.0441942
$513$	705161.	−	1.22137e6i	0.118303	−	0.204906i
$514$	−1.81756e6	−	3.14811e6i	−0.303446	−	0.525583i
$515$	1.36827e6	+	2.36991e6i	0.227328	+	0.393744i
$516$	−779826.	+	1.35070e6i	−0.128936	+	0.223323i
$517$	491263.			0.0808329
$518$	−239692.	+	270281.i	−0.0392490	+	0.0442579i
$519$	−1.67141e6			−0.272374
$520$	332870.	−	576547.i	0.0539841	−	0.0935032i
$521$	−3.88940e6	−	6.73664e6i	−0.627752	−	1.08730i	−0.988002	−	0.154443i	$-0.950642\pi$
$521$	−3.88940e6	−	6.73664e6i	−0.627752	−	1.08730i	0.360250	−	0.932856i	$-0.382692\pi$
$522$	452670.	+	784047.i	0.0727119	+	0.125941i
$523$	−3.96539e6	+	6.86826e6i	−0.633917	+	1.09798i	0.352827	+	0.935689i	$0.385220\pi$
$523$	−3.96539e6	+	6.86826e6i	−0.633917	+	1.09798i	−0.986744	+	0.162287i	$0.948113\pi$
$524$	−1.44547e6			−0.229975
$525$	−714424.	−	146227.i	−0.113125	−	0.0231541i
$526$	7.59406e6			1.19677
$527$	4.12918e6	−	7.15195e6i	0.647646	−	1.12175i
$528$	−121916.	−	211164.i	−0.0190316	−	0.0329637i
$529$	−8.51084e6	−	1.47412e7i	−1.32231	−	2.29031i
$530$	−1.59817e6	+	2.76811e6i	−0.247134	+	0.428049i
$531$	2.40547e6			0.370223
$532$	−1.26883e6	−	3.80700e6i	−0.194367	−	0.583182i
$533$	−3.39197e6			−0.517170
$534$	2.09947e6	−	3.63639e6i	0.318608	−	0.551846i
$535$	2.73505e6	+	4.73725e6i	0.413124	+	0.715552i
$536$	−354437.	−	613904.i	−0.0532878	−	0.0922971i
$537$	−610733.	+	1.05782e6i	−0.0913936	+	0.158298i
$538$	3.60369e6			0.536774
$539$	−1.63564e6	−	698836.i	−0.242503	−	0.103610i
$540$	291600.			0.0430331
$541$	−5.57225e6	+	9.65142e6i	−0.818535	+	1.41774i	0.0882259	+	0.996100i	$0.471880\pi$
$541$	−5.57225e6	+	9.65142e6i	−0.818535	+	1.41774i	−0.906761	+	0.421644i	$0.861453\pi$
$542$	4.33953e6	+	7.51629e6i	0.634519	+	1.09902i
$543$	−683937.	−	1.18461e6i	−0.0995443	−	0.172416i
$544$	−925908.	+	1.60372e6i	−0.134144	+	0.232344i
$545$	−4.35982e6			−0.628749
$546$	614014.	+	1.84229e6i	0.0881448	+	0.264471i
$547$	5.22226e6			0.746260			0.373130	−	0.927779i	$-0.378285\pi$
$547$	5.22226e6			0.746260			0.373130	+	0.927779i	$0.378285\pi$
$548$	2.90869e6	−	5.03799e6i	0.413757	−	0.716648i
$549$	122198.	+	211654.i	0.0173035	+	0.0299706i
$550$	132287.	+	229128.i	0.0186471	+	0.0322977i
$551$	2.70288e6	−	4.68153e6i	0.379270	−	0.656915i
$552$	−2.78977e6			−0.389691
$553$	−7.22831e6	−	1.47947e6i	−1.00513	−	0.205729i
$554$	9.74761e6			1.34935
$555$	−78371.7	+	135744.i	−0.0108001	+	0.0187063i
$556$	1.48012e6	+	2.56365e6i	0.203054	+	0.351699i
$557$	−4.13466e6	−	7.16144e6i	−0.564679	−	0.978052i	−0.997079	−	0.0763708i	$-0.975667\pi$
$557$	−4.13466e6	−	7.16144e6i	−0.564679	−	0.978052i	0.432401	−	0.901682i	$-0.357667\pi$
$558$	739794.	−	1.28136e6i	0.100583	−	0.174215i
$559$	−4.50661e6			−0.609986
$560$	550512.	−	620767.i	0.0741816	−	0.0836486i
$561$	1.72246e6			0.231069
$562$	−260792.	+	451705.i	−0.0348300	+	0.0603274i
$563$	−4.22848e6	−	7.32394e6i	−0.562229	−	0.973809i	−0.997302	−	0.0734138i	$-0.976611\pi$
$563$	−4.22848e6	−	7.32394e6i	−0.562229	−	0.973809i	0.435073	−	0.900395i	$-0.356723\pi$
$564$	−334225.	−	578895.i	−0.0442427	−	0.0766306i
$565$	286148.	−	495623.i	0.0377112	−	0.0653176i
$566$	2.31600e6			0.303877
$567$	−564360.	+	636383.i	−0.0737223	+	0.0831306i
$568$	−4.61192e6			−0.599806
$569$	5.51113e6	−	9.54556e6i	0.713609	−	1.23601i	−0.249885	−	0.968276i	$-0.580393\pi$
$569$	5.51113e6	−	9.54556e6i	0.713609	−	1.23601i	0.963494	−	0.267731i	$-0.0862740\pi$
$570$	−870569.	−	1.50787e6i	−0.112232	−	0.194391i
$571$	−3.72045e6	−	6.44401e6i	−0.477535	−	0.827116i	0.522133	−	0.852864i	$-0.325136\pi$
$571$	−3.72045e6	−	6.44401e6i	−0.477535	−	0.827116i	−0.999668	+	0.0257484i	$0.991803\pi$
$572$	352275.	−	610159.i	0.0450186	−	0.0779745i
$573$	−7.93842e6			−1.01006
$574$	−4.14153e6	−	847679.i	−0.524663	−	0.107387i
$575$	3.02709e6			0.381818
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	4.07871e6	+	7.06453e6i	0.510015	+	0.883372i	0.999933	+	0.0116035i	$0.00369359\pi$
$577$	4.07871e6	+	7.06453e6i	0.510015	+	0.883372i	−0.489917	+	0.871769i	$0.662973\pi$
$578$	−3.70101e6	−	6.41034e6i	−0.460788	−	0.798108i
$579$	882631.	−	1.52876e6i	0.109416	−	0.189515i
$580$	1.11770e6			0.137961
$581$	227245.	+	681830.i	0.0279290	+	0.0837984i
$582$	−1.24376e6			−0.152205
$583$	−1.69134e6	+	2.92948e6i	−0.206091	+	0.356960i
$584$	−2.14127e6	−	3.70879e6i	−0.259800	−	0.449987i
$585$	421288.	+	729693.i	0.0508967	+	0.0881557i
$586$	−1.85458e6	+	3.21222e6i	−0.223101	+	0.386422i
$587$	−1.01228e7			−1.21256			−0.606281	−	0.795251i	$-0.707339\pi$
$587$	−1.01228e7			−1.21256			−0.606281	+	0.795251i	$0.707339\pi$
$588$	289296.	+	2.40286e6i	0.0345064	+	0.286605i
$589$	−8.83460e6			−1.04930
$590$	1.48486e6	−	2.57185e6i	0.175612	−	0.304169i
$591$	−1.62072e6	−	2.80717e6i	−0.190871	−	0.330598i
$592$	−89169.5	−	154446.i	−0.0104571	−	0.0181123i
$593$	−7.15009e6	+	1.23843e7i	−0.834977	+	1.44622i	0.0590714	+	0.998254i	$0.481186\pi$
$593$	−7.15009e6	+	1.23843e7i	−0.834977	+	1.44622i	−0.894049	+	0.447970i	$0.852147\pi$
$594$	308600.			0.0358863
$595$	1.85323e6	+	5.56045e6i	0.214604	+	0.643899i
$596$	2.73874e6			0.315816
$597$	356455.	−	617398.i	0.0409326	−	0.0708973i
$598$	−4.03051e6	−	6.98105e6i	−0.460900	−	0.798303i
$599$	−1.74000e6	−	3.01376e6i	−0.198144	−	0.343196i	0.749783	−	0.661684i	$-0.230158\pi$
$599$	−1.74000e6	−	3.01376e6i	−0.198144	−	0.343196i	−0.947927	+	0.318489i	$0.896825\pi$
$600$	180000.	−	311769.i	0.0204124	−	0.0353553i
$601$	−2.54608e6			−0.287532			−0.143766	−	0.989612i	$-0.545921\pi$
$601$	−2.54608e6			−0.287532			−0.143766	+	0.989612i	$0.545921\pi$
$602$	−5.50248e6	−	1.12624e6i	−0.618825	−	0.126660i
$603$	897170.			0.100480
$604$	3.12486e6	−	5.41242e6i	0.348529	−	0.603669i
$605$	−1.87314e6	−	3.24437e6i	−0.208057	−	0.360365i
$606$	1.05312e6	+	1.82406e6i	0.116492	+	0.201771i
$607$	4.51118e6	−	7.81359e6i	0.496956	−	0.860753i	−0.503038	−	0.864265i	$-0.667784\pi$
$607$	4.51118e6	−	7.81359e6i	0.496956	−	0.860753i	0.999994	+	0.00351105i	$0.00111761\pi$
$608$	1.98103e6			0.217336
$609$	−2.16319e6	+	2.43926e6i	−0.236348	+	0.266511i
$610$	301725.			0.0328312
$611$	965742.	−	1.67271e6i	0.104655	−	0.181267i
$612$	−1.17185e6	−	2.02971e6i	−0.126472	−	0.219056i
$613$	−1.69147e6	−	2.92972e6i	−0.181808	−	0.314902i	0.760688	−	0.649118i	$-0.224862\pi$
$613$	−1.69147e6	−	2.92972e6i	−0.181808	−	0.314902i	−0.942496	+	0.334216i	$0.891528\pi$
$614$	−5.44043e6	+	9.42310e6i	−0.582388	+	1.00872i
$615$	−1.83421e6			−0.195552
$616$	582605.	−	656956.i	0.0618618	−	0.0697565i
$617$	−7.69772e6			−0.814046			−0.407023	−	0.913418i	$-0.633433\pi$
$617$	−7.69772e6			−0.814046			−0.407023	+	0.913418i	$0.633433\pi$
$618$	1.97031e6	−	3.41268e6i	0.207522	−	0.359438i
$619$	4.87591e6	+	8.44533e6i	0.511481	+	0.885910i	0.999911	+	0.0133078i	$0.00423612\pi$
$619$	4.87591e6	+	8.44533e6i	0.511481	+	0.885910i	−0.488431	+	0.872603i	$0.662431\pi$
$620$	−913326.	−	1.58193e6i	−0.0954216	−	0.165275i
$621$	1.76540e6	−	3.05776e6i	0.183702	−	0.318181i
$622$	8.46465e6			0.877270
$623$	1.48140e7	+	3.03209e6i	1.52915	+	0.312984i
$624$	−958665.			−0.0985611
$625$	−195312.	+	338291.i	−0.0200000	+	0.0346410i
$626$	350504.	+	607092.i	0.0357485	+	0.0619182i
$627$	−921321.	−	1.59577e6i	−0.0935927	−	0.162107i
$628$	−1.45784e6	+	2.52504e6i	−0.147506	+	0.255488i
$629$	1.25981e6			0.126963
$630$	332029.	+	996225.i	0.0333292	+	0.100001i
$631$	−9.00267e6			−0.900115			−0.450058	−	0.892999i	$-0.648597\pi$
$631$	−9.00267e6			−0.900115			−0.450058	+	0.892999i	$0.648597\pi$
$632$	1.82118e6	−	3.15438e6i	0.181368	−	0.314139i
$633$	−177553.	−	307531.i	−0.0176124	−	0.0305056i
$634$	1.28719e6	+	2.22947e6i	0.127180	+	0.220282i
$635$	4.04731e6	−	7.01014e6i	0.398320	−	0.689910i
$636$	4.60273e6			0.451203
$637$	−5.59489e6	+	4.19545e6i	−0.546315	+	0.409666i
$638$	1.18286e6			0.115049
$639$	2.91848e6	−	5.05496e6i	0.282751	−	0.489740i
$640$	204800.	+	354724.i	0.0197642	+	0.0342327i
$641$	−6.86686e6	−	1.18938e7i	−0.660105	−	1.14334i	−0.980588	−	0.196081i	$-0.937178\pi$
$641$	−6.86686e6	−	1.18938e7i	−0.660105	−	1.14334i	0.320482	−	0.947254i	$-0.396155\pi$
$642$	3.93847e6	−	6.82163e6i	0.377129	−	0.653207i
$643$	−6.64838e6			−0.634145			−0.317072	−	0.948401i	$-0.602700\pi$
$643$	−6.64838e6			−0.634145			−0.317072	+	0.948401i	$0.602700\pi$
$644$	−3.17656e6	−	9.53099e6i	−0.301816	−	0.905573i
$645$	−2.43696e6			−0.230647
$646$	−6.99711e6	+	1.21193e7i	−0.659686	+	1.14261i
$647$	7.71364e6	+	1.33604e7i	0.724434	+	1.25476i	0.959206	+	0.282706i	$0.0912322\pi$
$647$	7.71364e6	+	1.33604e7i	0.724434	+	1.25476i	−0.234772	+	0.972050i	$0.575434\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	1.57142e6	−	2.72178e6i	0.146447	−	0.253654i
$650$	1.04022e6			0.0965697
$651$	5.22002e6	+	1.06842e6i	0.482747	+	0.0988076i
$652$	−79689.7			−0.00734148
$653$	−4.59315e6	+	7.95557e6i	−0.421529	+	0.730111i	−0.996089	−	0.0883521i	$-0.971840\pi$
$653$	−4.59315e6	+	7.95557e6i	−0.421529	+	0.730111i	0.574560	+	0.818463i	$0.305173\pi$
$654$	3.13907e6	+	5.43703e6i	0.286984	+	0.497070i
$655$	−1.12927e6	−	1.95595e6i	−0.102848	−	0.178138i
$656$	1.04346e6	−	1.80733e6i	0.0946711	−	0.163975i
$657$	5.42009e6			0.489883
$658$	1.59718e6	−	1.80101e6i	0.143810	−	0.162163i
$659$	−5.01908e6			−0.450206			−0.225103	−	0.974335i	$-0.572272\pi$
$659$	−5.01908e6			−0.450206			−0.225103	+	0.974335i	$0.572272\pi$
$660$	190494.	−	329944.i	0.0170224	−	0.0294836i
$661$	−9.91202e6	−	1.71681e7i	−0.882386	−	1.52834i	−0.848681	−	0.528906i	$-0.822602\pi$
$661$	−9.91202e6	−	1.71681e7i	−0.882386	−	1.52834i	−0.0337057	−	0.999432i	$-0.510731\pi$
$662$	4.47499e6	+	7.75091e6i	0.396869	+	0.687397i
$663$	3.38606e6	−	5.86483e6i	0.299165	−	0.518169i
$664$	−354800.			−0.0312294
$665$	4.16023e6	−	4.69115e6i	0.364807	−	0.411363i
$666$	225710.			0.0197181
$667$	6.76678e6	−	1.17204e7i	0.588935	−	1.02007i
$668$	−1.91017e6	−	3.30851e6i	−0.165627	−	0.286874i
$669$	2.38523e6	+	4.13133e6i	0.206046	+	0.356882i
$670$	553808.	−	959224.i	0.0476620	−	0.0825531i
$671$	319314.			0.0273787
$672$	−1.17051e6	−	239578.i	−0.0999891	−	0.0204656i
$673$	−1.06167e7			−0.903552			−0.451776	−	0.892131i	$-0.649209\pi$
$673$	−1.06167e7			−0.903552			−0.451776	+	0.892131i	$0.649209\pi$
$674$	2.38531e6	−	4.13148e6i	0.202253	−	0.350313i
$675$	227812.	+	394583.i	0.0192450	+	0.0333333i
$676$	1.58532e6	+	2.74585e6i	0.133429	+	0.231105i
$677$	−2.85891e6	+	4.95177e6i	−0.239733	+	0.415230i	−0.960638	−	0.277804i	$-0.910393\pi$
$677$	−2.85891e6	+	4.95177e6i	−0.239733	+	0.415230i	0.720904	+	0.693035i	$0.243727\pi$
$678$	−824107.			−0.0688508
$679$	−1.41620e6	−	4.24919e6i	−0.117883	−	0.353697i
$680$	−2.89346e6			−0.239964
$681$	−613147.	+	1.06200e6i	−0.0506637	+	0.0877521i
$682$	−966571.	−	1.67415e6i	−0.0795743	−	0.137827i
$683$	8.46562e6	+	1.46629e7i	0.694396	+	1.20273i	0.970384	+	0.241568i	$0.0776617\pi$
$683$	8.46562e6	+	1.46629e7i	0.694396	+	1.20273i	−0.275988	+	0.961161i	$0.589005\pi$
$684$	−1.25362e6	+	2.17133e6i	−0.102453	+	0.177454i
$685$	9.08964e6			0.740151
$686$	−7.87973e6	+	3.72436e6i	−0.639295	+	0.302163i
$687$	−7.90202e6			−0.638772
$688$	1.38636e6	−	2.40124e6i	0.111662	−	0.193404i
$689$	6.64977e6	+	1.15177e7i	0.533653	+	0.924314i
$690$	−2.17951e6	−	3.77502e6i	−0.174275	−	0.301853i
$691$	−4.54123e6	+	7.86565e6i	−0.361808	+	0.626671i	−0.988259	−	0.152791i	$-0.951174\pi$
$691$	−4.54123e6	+	7.86565e6i	−0.361808	+	0.626671i	0.626450	+	0.779462i	$0.284507\pi$
$692$	2.97140e6			0.235882
$693$	351386.	+	1.05430e6i	0.0277940	+	0.0833935i
$694$	−3.94870e6			−0.311211
$695$	−2.31269e6	+	4.00570e6i	−0.181617	+	0.314570i
$696$	−804746.	−	1.39386e6i	−0.0629703	−	0.109068i
$697$	7.37115e6	+	1.27672e7i	0.574716	+	0.995437i
$698$	1.73338e6	−	3.00231e6i	0.134665	−	0.233247i
$699$	9.20826e6			0.712828
$700$	1.27009e6	+	259959.i	0.0979689	+	0.0200521i
$701$	7.08079e6			0.544235			0.272118	−	0.962264i	$-0.412276\pi$
$701$	7.08079e6			0.544235			0.272118	+	0.962264i	$0.412276\pi$
$702$	606655.	−	1.05076e6i	0.0464621	−	0.0804748i
$703$	−673856.	−	1.16715e6i	−0.0514256	−	0.0890717i
$704$	216739.	+	375403.i	0.0164819	+	0.0285474i
$705$	522227.	−	904523.i	0.0395719	−	0.0685405i
$706$	−1.11286e7			−0.840286
$707$	−5.03261e6	+	5.67486e6i	−0.378656	+	0.426979i
$708$	−4.27639e6			−0.320623
$709$	6.17652e6	−	1.06980e7i	0.461454	−	0.799261i	−0.537580	−	0.843213i	$-0.680661\pi$
$709$	6.17652e6	−	1.06980e7i	0.461454	−	0.799261i	0.999034	+	0.0439515i	$0.0139947\pi$
$710$	−3.60306e6	−	6.24069e6i	−0.268242	−	0.464608i
$711$	2.30493e6	+	3.99226e6i	0.170995	+	0.296173i
$712$	−3.73240e6	+	6.46470e6i	−0.275923	+	0.477912i
$713$	−2.21178e7			−1.62936
$714$	5.59999e6	−	6.31465e6i	0.411094	−	0.463557i
$715$	1.10086e6			0.0805317
$716$	1.08575e6	−	1.88057e6i	0.0791492	−	0.137090i
$717$	−2.21577e6	−	3.83783e6i	−0.160964	−	0.278797i
$718$	−7.26889e6	−	1.25901e7i	−0.526208	−	0.911419i
$719$	−1.76105e6	+	3.05022e6i	−0.127042	+	0.220044i	−0.922529	−	0.385927i	$-0.873882\pi$
$719$	−1.76105e6	+	3.05022e6i	−0.127042	+	0.220044i	0.795487	+	0.605971i	$0.207215\pi$
$720$	−518400.			−0.0372678
$721$	1.39026e7	+	2.84555e6i	0.995995	+	0.203858i
$722$	5.06628e6			0.361698
$723$	−1.47449e6	+	2.55390e6i	−0.104905	+	0.181701i
$724$	1.21589e6	+	2.10598e6i	0.0862079	+	0.149316i
$725$	873206.	+	1.51244e6i	0.0616981	+	0.106864i
$726$	−2.69732e6	+	4.67189e6i	−0.189929	+	0.328966i
$727$	2.05553e7			1.44241			0.721205	−	0.692722i	$-0.243589\pi$
$727$	2.05553e7			1.44241			0.721205	+	0.692722i	$0.243589\pi$
$728$	−1.09158e6	−	3.27519e6i	−0.0763356	−	0.229038i
$729$	531441.			0.0370370
$730$	3.34573e6	−	5.79498e6i	0.232372	−	0.402480i
$731$	9.79339e6	+	1.69627e7i	0.677860	+	1.17409i
$732$	−217242.	−	376274.i	−0.0149853	−	0.0259553i
$733$	5.16617e6	−	8.94807e6i	0.355148	−	0.615134i	−0.631996	−	0.774972i	$-0.717764\pi$
$733$	5.16617e6	−	8.94807e6i	0.355148	−	0.615134i	0.987143	+	0.159838i	$0.0510972\pi$
$734$	−1.38230e7			−0.947025
$735$	−3.02545e6	+	2.26870e6i	−0.206572	+	0.154902i
$736$	4.95959e6			0.337482
$737$	586094.	−	1.01514e6i	0.0397465	−	0.0688429i
$738$	1.32063e6	+	2.28740e6i	0.0892568	+	0.154597i
$739$	−1.43224e6	−	2.48071e6i	−0.0964727	−	0.167096i	0.813750	−	0.581216i	$-0.197423\pi$
$739$	−1.43224e6	−	2.48071e6i	−0.0964727	−	0.167096i	−0.910222	+	0.414120i	$0.864089\pi$
$740$	139327.	−	241322.i	0.00935314	−	0.0162001i
$741$	−7.24465e6			−0.484699
$742$	5.24088e6	+	1.57248e7i	0.349457	+	1.04852i
$743$	−7.63461e6			−0.507358			−0.253679	−	0.967288i	$-0.581641\pi$
$743$	−7.63461e6			−0.507358			−0.253679	+	0.967288i	$0.581641\pi$
$744$	−1.31519e6	+	2.27798e6i	−0.0871076	+	0.150875i
$745$	2.13964e6	+	3.70596e6i	0.141237	+	0.244630i
$746$	5.21682e6	+	9.03580e6i	0.343209	+	0.594456i
$747$	224522.	−	388883.i	0.0147217	−	0.0254987i
$748$	−3.06214e6			−0.200111
$749$	2.77900e7	+	5.68800e6i	1.81002	+	0.370472i
$750$	562500.			0.0365148
$751$	−5.84712e6	+	1.01275e7i	−0.378305	+	0.655244i	−0.990816	−	0.135219i	$-0.956826\pi$
$751$	−5.84712e6	+	1.01275e7i	−0.378305	+	0.655244i	0.612511	+	0.790462i	$0.290160\pi$
$752$	594178.	+	1.02915e6i	0.0383153	+	0.0663640i
$753$	3.71951e6	+	6.44238e6i	0.239055	+	0.414056i
$754$	2.32531e6	−	4.02756e6i	0.148954	−	0.257996i
$755$	9.76520e6			0.623467
$756$	1.00331e6	−	1.13135e6i	0.0638454	−	0.0719932i
$757$	1.96685e7			1.24747			0.623736	−	0.781635i	$-0.285614\pi$
$757$	1.96685e7			1.24747			0.623736	+	0.781635i	$0.285614\pi$
$758$	−2.34648e6	+	4.06422e6i	−0.148335	+	0.256923i
$759$	−2.30657e6	−	3.99509e6i	−0.145332	−	0.251723i
$760$	1.54768e6	+	2.68066e6i	0.0971956	+	0.168348i
$761$	1.50185e6	−	2.60129e6i	0.0940082	−	0.162827i	−0.815186	−	0.579199i	$-0.803365\pi$
$761$	1.50185e6	−	2.60129e6i	0.0940082	−	0.162827i	0.909194	+	0.416372i	$0.136699\pi$
$762$	−1.16562e7			−0.727229
$763$	−1.50008e7	+	1.69152e7i	−0.932833	+	1.05188i
$764$	1.41127e7			0.874738
$765$	1.83102e6	−	3.17142e6i	0.113120	−	0.195930i
$766$	4.28730e6	+	7.42582e6i	0.264005	+	0.457270i
$767$	−6.17831e6	−	1.07011e7i	−0.379211	−	0.656813i
$768$	294912.	−	510803.i	0.0180422	−	0.0312500i
$769$	−1.12834e6			−0.0688057			−0.0344029	−	0.999408i	$-0.510953\pi$
$769$	−1.12834e6			−0.0688057			−0.0344029	+	0.999408i	$0.510953\pi$
$770$	1.34413e6	+	275114.i	0.0816986	+	0.0167219i
$771$	−8.17902e6			−0.495525
$772$	−1.56912e6	+	2.71780e6i	−0.0947574	+	0.164125i
$773$	1.19372e7	+	2.06759e7i	0.718546	+	1.24456i	0.961576	+	0.274539i	$0.0885253\pi$
$773$	1.19372e7	+	2.06759e7i	0.718546	+	1.24456i	−0.243030	+	0.970019i	$0.578141\pi$
$774$	1.75461e6	+	3.03907e6i	0.105276	+	0.182343i
$775$	1.42707e6	−	2.47176e6i	0.0853477	−	0.147827i
$776$	2.21113e6			0.131813
$777$	257004.	+	771119.i	0.0152717	+	0.0458214i
$778$	1.79634e7			1.06399
$779$	7.88547e6	−	1.36580e7i	0.465569	−	0.806389i
$780$	−748957.	−	1.29723e6i	−0.0440778	−	0.0763451i
$781$	−3.81311e6	−	6.60450e6i	−0.223693	−	0.387447i
$782$	−1.75176e7	+	3.03413e7i	−1.02437	+	1.77426i
$783$	2.03701e6			0.118738
$784$	−514304.	−	4.27174e6i	−0.0298834	−	0.248208i
$785$	−4.55573e6			−0.263867
$786$	−1.62615e6	+	2.81657e6i	−0.0938867	+	0.162617i
$787$	3.25446e6	+	5.63689e6i	0.187302	+	0.324416i	0.944350	−	0.328943i	$-0.106692\pi$
$787$	3.25446e6	+	5.63689e6i	0.187302	+	0.324416i	−0.757048	+	0.653359i	$0.773359\pi$
$788$	2.88128e6	+	4.99053e6i	0.165299	+	0.286306i
$789$	8.54332e6	−	1.47975e7i	0.488578	−	0.846242i
$790$	5.69119e6			0.324441
$791$	−938366.	−	2.81549e6i	−0.0533250	−	0.159997i
$792$	−548621.			−0.0310785
$793$	627719.	−	1.08724e6i	0.0354472	−	0.0613964i
$794$	8.46140e6	+	1.46556e7i	0.476311	+	0.824996i
$795$	3.59588e6	+	6.22825e6i	0.201784	+	0.349501i
$796$	−633698.	+	1.09760e6i	−0.0354486	+	0.0613989i
$797$	4.59772e6			0.256387			0.128194	−	0.991749i	$-0.459082\pi$
$797$	4.59772e6			0.256387			0.128194	+	0.991749i	$0.459082\pi$
$798$	−8.84559e6	−	1.81050e6i	−0.491722	−	0.100645i
$799$	−8.39469e6			−0.465198
$800$	−320000.	+	554256.i	−0.0176777	+	0.0306186i
$801$	−4.72381e6	−	8.18189e6i	−0.260143	−	0.450580i
$802$	8.00409e6	+	1.38635e7i	0.439416	+	0.761091i
$803$	3.54078e6	−	6.13281e6i	0.193780	−	0.335638i
$804$	−1.59497e6			−0.0870186
$805$	1.04153e7	−	1.17445e7i	0.566477	−	0.638770i
$806$	−7.60047e6			−0.412100
$807$	4.05415e6	−	7.02199e6i	0.219137	−	0.379557i
$808$	−1.87222e6	−	3.24278e6i	−0.100885	−	0.174739i
$809$	5.17069e6	+	8.95590e6i	0.277765	+	0.481103i	0.970829	−	0.239773i	$-0.0770731\pi$
$809$	5.17069e6	+	8.95590e6i	0.277765	+	0.481103i	−0.693064	+	0.720876i	$0.743740\pi$
$810$	328050.	−	568199.i	0.0175682	−	0.0304290i
$811$	3.40251e7			1.81655			0.908276	−	0.418371i	$-0.137399\pi$
$811$	3.40251e7			1.81655			0.908276	+	0.418371i	$0.137399\pi$
$812$	3.84568e6	−	4.33646e6i	0.204684	−	0.230805i
$813$	1.95279e7			1.03617
$814$	147450.	−	255391.i	0.00779980	−	0.0135096i
$815$	−62257.6	−	107833.i	−0.00328321	−	0.00568668i
$816$	2.08329e6	+	3.60837e6i	0.109528	+	0.189708i
$817$	1.04767e7	−	1.81462e7i	0.549125	−	0.951112i
$818$	−1.47479e7			−0.770633
$819$	4.28058e6	+	876140.i	0.222994	+	0.0456419i
$820$	3.26082e6			0.169353
$821$	−1.34698e7	+	2.33303e7i	−0.697432	+	1.20799i	0.271922	+	0.962319i	$0.412341\pi$
$821$	−1.34698e7	+	2.33303e7i	−0.697432	+	1.20799i	−0.969354	+	0.245668i	$0.920993\pi$
$822$	−6.54454e6	−	1.13355e7i	−0.337831	−	0.585141i
$823$	1.63087e6	+	2.82475e6i	0.0839304	+	0.145372i	0.904935	−	0.425550i	$-0.139919\pi$
$823$	1.63087e6	+	2.82475e6i	0.0839304	+	0.145372i	−0.821005	+	0.570922i	$0.806586\pi$
$824$	−3.50277e6	+	6.06698e6i	−0.179719	+	0.311282i
$825$	595292.			0.0304506
$826$	−4.86930e6	−	1.46099e7i	−0.248323	−	0.745070i
$827$	1.25867e7			0.639953			0.319976	−	0.947426i	$-0.396325\pi$
$827$	1.25867e7			0.639953			0.319976	+	0.947426i	$0.396325\pi$
$828$	−3.13849e6	+	5.43602e6i	−0.159091	+	0.275553i
$829$	−1.92874e7	−	3.34067e7i	−0.974735	−	1.68829i	−0.680805	−	0.732464i	$-0.738370\pi$
$829$	−1.92874e7	−	3.34067e7i	−0.974735	−	1.68829i	−0.293930	−	0.955827i	$-0.594963\pi$
$830$	−277187.	−	480103.i	−0.0139662	−	0.0241902i
$831$	1.09661e7	−	1.89938e7i	0.550869	−	0.954132i
$832$	1.70429e6			0.0853564
$833$	2.79498e7	+	1.19417e7i	1.39562	+	0.596284i
$834$	6.66056e6			0.331585
$835$	2.98464e6	−	5.16954e6i	0.148141	−	0.256588i
$836$	1.63790e6	+	2.83693e6i	0.0810537	+	0.140389i
$837$	−1.66454e6	−	2.88306e6i	−0.0821258	−	0.142246i
$838$	−1.12931e7	+	1.95602e7i	−0.555524	+	0.962196i
$839$	2.69514e7			1.32183			0.660916	−	0.750460i	$-0.270168\pi$
$839$	2.69514e7			1.32183			0.660916	+	0.750460i	$0.270168\pi$
$840$	−590274.	−	1.77107e6i	−0.0288639	−	0.0866037i
$841$	−1.27033e7			−0.619335
$842$	1.79268e6	−	3.10501e6i	0.0871408	−	0.150932i
$843$	586783.	+	1.01634e6i	0.0284386	+	0.0492571i
$844$	315649.	+	546721.i	0.0152528	+	0.0264186i
$845$	−2.47706e6	+	4.29039e6i	−0.119342	+	0.206707i
$846$	−1.50401e6			−0.0722480
$847$	−1.90324e7	−	3.89551e6i	−0.911559	−	0.186576i
$848$	−8.18262e6			−0.390754
$849$	2.60550e6	−	4.51286e6i	0.124057	−	0.214873i
$850$	−2.26052e6	−	3.91533e6i	−0.107315	−	0.185875i
$851$	−1.68703e6	−	2.92202e6i	−0.0798543	−	0.138312i
$852$	−5.18841e6	+	8.98659e6i	−0.244870	+	0.424127i
$853$	−2.66594e7			−1.25452			−0.627261	−	0.778809i	$-0.715824\pi$
$853$	−2.66594e7			−1.25452			−0.627261	+	0.778809i	$0.715824\pi$
$854$	1.03814e6	−	1.17063e6i	0.0487094	−	0.0549256i
$855$	−3.91756e6			−0.183274
$856$	−7.00173e6	+	1.21273e7i	−0.326603	+	0.565694i
$857$	1.20433e6	+	2.08597e6i	0.0560138	+	0.0970187i	0.892673	−	0.450706i	$-0.148828\pi$
$857$	1.20433e6	+	2.08597e6i	0.0560138	+	0.0970187i	−0.836659	+	0.547724i	$0.815494\pi$
$858$	−792619.	−	1.37286e6i	−0.0367575	−	0.0636659i
$859$	1.27488e7	−	2.20816e7i	0.589505	−	1.02105i	−0.404792	−	0.914409i	$-0.632656\pi$
$859$	1.27488e7	−	2.20816e7i	0.589505	−	1.02105i	0.994297	−	0.106644i	$-0.0340106\pi$
$860$	4.33237e6			0.199746
$861$	−6.31097e6	+	7.11636e6i	−0.290127	+	0.327153i
$862$	2.91931e7			1.33817
$863$	−1.53111e7	+	2.65196e7i	−0.699808	+	1.21210i	0.268725	+	0.963217i	$0.413398\pi$
$863$	−1.53111e7	+	2.65196e7i	−0.699808	+	1.21210i	−0.968533	+	0.248886i	$0.919936\pi$
$864$	373248.	+	646484.i	0.0170103	+	0.0294628i
$865$	2.32140e6	+	4.02079e6i	0.105490	+	0.182714i
$866$	−1.40892e7	+	2.44032e7i	−0.638397	+	1.10574i
$867$	−1.66546e7			−0.752463
$868$	−9.28003e6	−	1.89942e6i	−0.418071	−	0.0855699i
$869$	6.02297e6			0.270559
$870$	1.25742e6	−	2.17791e6i	0.0563224	−	0.0975532i
$871$	−2.30433e6	−	3.99121e6i	−0.102920	−	0.178262i
$872$	−5.58057e6	−	9.66584e6i	−0.248535	−	0.430475i
$873$	−1.39923e6	+	2.42354e6i	−0.0621374	+	0.107625i
$874$	3.74797e7			1.65965
$875$	640489.	+	1.92173e6i	0.0282808	+	0.0848540i
$876$	−9.63571e6			−0.424251
$877$	−1.70039e7	+	2.94516e7i	−0.746533	+	1.29303i	0.202941	+	0.979191i	$0.434950\pi$
$877$	−1.70039e7	+	2.94516e7i	−0.746533	+	1.29303i	−0.949475	+	0.313843i	$0.898383\pi$
$878$	−7.63293e6	−	1.32206e7i	−0.334161	−	0.578783i
$879$	4.17280e6	+	7.22750e6i	0.182161	+	0.315512i
$880$	−338655.	+	586568.i	−0.0147418	+	0.0255336i
$881$	1.08690e7			0.471792			0.235896	−	0.971778i	$-0.424198\pi$
$881$	1.08690e7			0.471792			0.235896	+	0.971778i	$0.424198\pi$
$882$	5.00756e6	+	2.13950e6i	0.216748	+	0.0926065i
$883$	−6.50846e6			−0.280916			−0.140458	−	0.990087i	$-0.544857\pi$
$883$	−6.50846e6			−0.280916			−0.140458	+	0.990087i	$0.544857\pi$
$884$	−6.01966e6	+	1.04264e7i	−0.259085	+	0.448748i
$885$	−3.34093e6	−	5.78666e6i	−0.143387	−	0.248353i
$886$	−3.50750e6	−	6.07516e6i	−0.150111	−	0.260000i
$887$	1.96291e7	−	3.39985e7i	0.837704	−	1.45095i	−0.0541065	−	0.998535i	$-0.517231\pi$
$887$	1.96291e7	−	3.39985e7i	0.837704	−	1.45095i	0.891810	−	0.452410i	$-0.149436\pi$
$888$	−401263.			−0.0170764
$889$	−1.32723e7	−	3.98225e7i	−0.563240	−	1.68995i
$890$	−1.16637e7			−0.493586
$891$	347174.	−	601324.i	0.0146505	−	0.0253755i
$892$	−4.24040e6	−	7.34459e6i	−0.178441	−	0.309069i
$893$	4.49022e6	+	7.77729e6i	0.188425	+	0.326362i
$894$	3.08108e6	−	5.33658e6i	0.128931	−	0.223316i
$895$	3.39296e6			0.141586
$896$	2.08091e6	+	425916.i	0.0865931	+	0.0177237i
$897$	−1.81373e7			−0.752647
$898$	2.73320e6	−	4.73404e6i	0.113105	−	0.195903i
$899$	−6.38017e6	−	1.10508e7i	−0.263289	−	0.456030i
$900$	−405000.	−	701481.i	−0.0166667	−	0.0288675i
$901$	2.89015e7	−	5.00589e7i	1.18607	−	2.05433i
$902$	3.45092e6			0.141227
$903$	−8.38483e6	+	9.45489e6i	−0.342196	+	0.385866i
$904$	1.46508e6			0.0596266
$905$	−1.89982e6	+	3.29059e6i	−0.0771067	+	0.133553i
$906$	−7.03094e6	−	1.21779e7i	−0.284573	−	0.492894i
$907$	1.13302e7	+	1.96244e7i	0.457318	+	0.792098i	0.998818	−	0.0486028i	$-0.0154769\pi$
$907$	1.13302e7	+	1.96244e7i	0.457318	+	0.792098i	−0.541500	+	0.840701i	$0.682144\pi$
$908$	1.09004e6	−	1.88800e6i	0.0438760	−	0.0759955i
$909$	4.73905e6			0.190231
$910$	3.57908e6	−	4.03583e6i	0.143274	−	0.161558i
$911$	−3.38061e6			−0.134958			−0.0674791	−	0.997721i	$-0.521496\pi$
$911$	−3.38061e6			−0.134958			−0.0674791	+	0.997721i	$0.521496\pi$
$912$	2.22866e6	−	3.86015e6i	0.0887271	−	0.153680i
$913$	−293347.	−	508092.i	−0.0116467	−	0.0201727i
$914$	−1.69299e6	−	2.93234e6i	−0.0670329	−	0.116104i
$915$	339440.	−	587928.i	0.0134033	−	0.0232151i
$916$	1.40480e7			0.553193
$917$	−1.14742e7	−	2.34851e6i	−0.450607	−	0.0922293i
$918$	−5.27334e6			−0.206528
$919$	−2.43139e7	+	4.21129e7i	−0.949655	+	1.64485i	−0.203504	+	0.979074i	$0.565233\pi$
$919$	−2.43139e7	+	4.21129e7i	−0.949655	+	1.64485i	−0.746151	+	0.665777i	$0.768100\pi$
$920$	3.87468e6	+	6.71114e6i	0.150927	+	0.261413i
$921$	1.22410e7	+	2.12020e7i	0.475517	+	0.823620i
$922$	2.87376e6	−	4.97750e6i	0.111333	−	0.192834i
$923$	−2.99838e7			−1.15846
$924$	−624686.	−	1.87431e6i	−0.0240703	−	0.0722208i
$925$	435398.			0.0167314
$926$	−5.97876e6	+	1.03555e7i	−0.229131	+	0.396866i
$927$	−4.43320e6	−	7.67852e6i	−0.169441	−	0.293480i
$928$	1.43066e6	+	2.47798e6i	0.0545339	+	0.0944555i
$929$	−426978.	+	739548.i	−0.0162318	+	0.0281143i	−0.874027	−	0.485877i	$-0.838500\pi$
$929$	−426978.	+	739548.i	−0.0162318	+	0.0281143i	0.857795	+	0.513991i	$0.171834\pi$
$930$	−4.10997e6			−0.155823
$931$	−3.88661e6	−	3.22817e7i	−0.146959	−	1.22062i
$932$	−1.63702e7			−0.617327
$933$	9.52273e6	−	1.64939e7i	0.358144	−	0.620323i
$934$	−1.43747e6	−	2.48978e6i	−0.0539179	−	0.0933885i
$935$	−2.39230e6	−	4.14359e6i	−0.0894925	−	0.155006i
$936$	−1.07850e6	+	1.86801e6i	−0.0402374	+	0.0696932i
$937$	−8.79766e6			−0.327354			−0.163677	−	0.986514i	$-0.552336\pi$
$937$	−8.79766e6			−0.327354			−0.163677	+	0.986514i	$0.552336\pi$
$938$	−1.81611e6	−	5.44906e6i	−0.0673960	−	0.202216i
$939$	1.57727e6			0.0583770
$940$	−928403.	+	1.60804e6i	−0.0342702	+	0.0593578i
$941$	−2.31247e6	−	4.00532e6i	−0.0851338	−	0.147456i	0.820314	−	0.571913i	$-0.193798\pi$
$941$	−2.31247e6	−	4.00532e6i	−0.0851338	−	0.147456i	−0.905448	+	0.424457i	$0.860465\pi$
$942$	3.28013e6	+	5.68135e6i	0.120438	+	0.208605i
$943$	1.97416e7	−	3.41935e7i	0.722942	−	1.25217i
$944$	7.60247e6			0.277667
$945$	2.31473e6	+	473775.i	0.0843182	+	0.0172581i
$946$	4.58493e6			0.166573
$947$	−1.69831e7	+	2.94156e7i	−0.615378	+	1.06587i	0.374940	+	0.927049i	$0.377663\pi$
$947$	−1.69831e7	+	2.94156e7i	−0.615378	+	1.06587i	−0.990318	+	0.138817i	$0.955670\pi$
$948$	−4.09766e6	−	7.09735e6i	−0.148086	−	0.256493i
$949$	−1.39212e7	−	2.41122e7i	−0.501776	−	0.869102i
$950$	−2.41825e6	+	4.18853e6i	−0.0869344	+	0.150575i
$951$	5.79233e6			0.207684
$952$	−9.95553e6	+	1.12260e7i	−0.356018	+	0.401453i
$953$	2.05449e7			0.732777			0.366388	−	0.930462i	$-0.380594\pi$
$953$	2.05449e7			0.732777			0.366388	+	0.930462i	$0.380594\pi$
$954$	5.17807e6	−	8.96867e6i	0.184203	−	0.319049i
$955$	1.10256e7	+	1.90969e7i	0.391195	+	0.677569i
$956$	3.93915e6	+	6.82281e6i	0.139398	+	0.241445i
$957$	1.33072e6	−	2.30488e6i	0.0469685	−	0.0813519i
$958$	−3.71123e7			−1.30648
$959$	3.12747e7	−	3.52659e7i	1.09811	−	1.23825i
$960$	921600.			0.0322749
$961$	3.88752e6	−	6.73337e6i	0.135789	−	0.235193i
$962$	−579723.	−	1.00411e6i	−0.0201968	−	0.0349819i
$963$	−8.86156e6	−	1.53487e7i	−0.307925	−	0.533341i
$964$	2.62132e6	−	4.54026e6i	0.0908505	−	0.157358i
$965$	−4.90350e6			−0.169507
$966$	−2.21453e7	−	4.53265e6i	−0.763552	−	0.156282i
$967$	−1.16164e7			−0.399490			−0.199745	−	0.979848i	$-0.564011\pi$
$967$	−1.16164e7			−0.399490			−0.199745	+	0.979848i	$0.564011\pi$
$968$	4.79523e6	−	8.30559e6i	0.164483	−	0.284893i
$969$	1.57435e7	+	2.72685e7i	0.538632	+	0.932937i
$970$	1.72744e6	+	2.99202e6i	0.0589487	+	0.102102i
$971$	−2.54983e7	+	4.41644e7i	−0.867888	+	1.50323i	−0.00373700	+	0.999993i	$0.501190\pi$
$971$	−2.54983e7	+	4.41644e7i	−0.867888	+	1.50323i	−0.864151	+	0.503233i	$0.832144\pi$
$972$	−944784.			−0.0320750
$973$	7.58402e6	+	2.27552e7i	0.256813	+	0.770545i
$974$	−1.46655e7			−0.495337
$975$	1.17025e6	−	2.02692e6i	0.0394244	−	0.0682851i
$976$	386208.	+	668931.i	0.0129777	+	0.0224780i
$977$	−1.99572e7	−	3.45669e7i	−0.668904	−	1.15858i	−0.978211	−	0.207613i	$-0.933430\pi$
$977$	−1.99572e7	−	3.45669e7i	−0.668904	−	1.15858i	0.309307	−	0.950962i	$-0.399903\pi$
$978$	−89651.0	+	155280.i	−0.00299715	+	0.00519121i
$979$	−1.23437e7			−0.411613
$980$	5.37857e6	−	4.03324e6i	0.178896	−	0.134149i
$981$	1.41258e7			0.468642
$982$	1.01671e7	−	1.76100e7i	0.336450	−	0.582748i
$983$	−1.79058e6	−	3.10137e6i	−0.0591030	−	0.102369i	0.834960	−	0.550311i	$-0.185491\pi$
$983$	−1.79058e6	−	3.10137e6i	−0.0591030	−	0.102369i	−0.894063	+	0.447941i	$0.852157\pi$
$984$	−2.34779e6	−	4.06649e6i	−0.0772986	−	0.133885i
$985$	−4.50200e6	+	7.79770e6i	−0.147848	+	0.256080i
$986$	−2.02127e7			−0.662113
$987$	−1.71254e6	−	5.13832e6i	−0.0559561	−	0.167891i
$988$	1.28794e7			0.419762
$989$	2.62290e7	−	4.54299e7i	0.852688	−	1.47690i
$990$	−428610.	−	742375.i	−0.0138987	−	0.0240733i
$991$	−9.02348e6	−	1.56291e7i	−0.291870	−	0.505534i	0.682382	−	0.730996i	$-0.260944\pi$
$991$	−9.02348e6	−	1.56291e7i	−0.291870	−	0.505534i	−0.974252	+	0.225462i	$0.927611\pi$
$992$	2.33812e6	−	4.04973e6i	0.0754374	−	0.130661i
$993$	2.01375e7			0.648084
$994$	−3.66096e7	−	7.49318e6i	−1.17525	−	0.240547i
$995$	−1.98031e6			−0.0634125
$996$	−399150.	+	691348.i	−0.0127493	+	0.0220825i
$997$	−3.86319e6	−	6.69124e6i	−0.123086	−	0.213191i	0.797897	−	0.602793i	$-0.205946\pi$
$997$	−3.86319e6	−	6.69124e6i	−0.123086	−	0.213191i	−0.920983	+	0.389603i	$0.872612\pi$
$998$	5.64031e6	+	9.76930e6i	0.179257	+	0.310483i
$999$	253924.	−	439810.i	0.00804990	−	0.0139428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.6.i.b.121.2	✓	4
7.4	even	3	inner	210.6.i.b.151.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.6.i.b.121.2	✓	4	1.1	even	1	trivial
210.6.i.b.151.2	yes	4	7.4	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(12.5000 - 21.6506i) q^{5} -36.0000 q^{6} +(-40.9913 - 122.991i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(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} +(-40.9913 - 122.991i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(50.0000 + 86.6025i) q^{10} +(52.9149 + 91.6512i) q^{11} +(72.0000 - 124.708i) q^{12} +416.087 q^{13} +(508.035 + 103.983i) q^{14} +225.000 q^{15} +(-128.000 + 221.703i) q^{16} +(-904.207 - 1566.13i) q^{17} +(-162.000 - 280.592i) q^{18} +(-967.299 + 1675.41i) q^{19} -400.000 q^{20} +(774.157 - 872.954i) q^{21} -423.319 q^{22} +(-2421.67 + 4194.46i) q^{23} +(288.000 + 498.831i) q^{24} +(-312.500 - 541.266i) q^{25} +(-832.174 + 1441.37i) q^{26} -729.000 q^{27} +(-1376.28 + 1551.92i) q^{28} -2794.26 q^{29} +(-450.000 + 779.423i) q^{30} +(2283.32 + 3954.82i) q^{31} +(-512.000 - 886.810i) q^{32} +(-476.234 + 824.861i) q^{33} +7233.66 q^{34} +(-3175.22 - 649.897i) q^{35} +1296.00 q^{36} +(-348.319 + 603.305i) q^{37} +(-3869.20 - 6701.64i) q^{38} +(1872.39 + 3243.08i) q^{39} +(800.000 - 1385.64i) q^{40} -8152.05 q^{41} +(1475.69 + 4427.67i) q^{42} -10830.9 q^{43} +(846.638 - 1466.42i) q^{44} +(1012.50 + 1753.70i) q^{45} +(-9686.70 - 16777.8i) q^{46} +(2321.01 - 4020.10i) q^{47} -2304.00 q^{48} +(-13446.4 + 10083.1i) q^{49} +2500.00 q^{50} +(8137.86 - 14095.2i) q^{51} +(-3328.70 - 5765.47i) q^{52} +(15981.7 + 27681.1i) q^{53} +(1458.00 - 2525.33i) q^{54} +2645.74 q^{55} +(-2623.44 - 7871.41i) q^{56} -17411.4 q^{57} +(5588.52 - 9679.59i) q^{58} +(-14848.6 - 25718.5i) q^{59} +(-1800.00 - 3117.69i) q^{60} +(1508.62 - 2613.01i) q^{61} -18266.5 q^{62} +(10287.7 + 2105.67i) q^{63} +4096.00 q^{64} +(5201.09 - 9008.55i) q^{65} +(-1904.94 - 3299.44i) q^{66} +(-5538.08 - 9592.24i) q^{67} +(-14467.3 + 25058.1i) q^{68} -43590.1 q^{69} +(8601.74 - 9699.48i) q^{70} -72061.3 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-33457.3 - 57949.8i) q^{73} +(-1393.27 - 2413.22i) q^{74} +(2812.50 - 4871.39i) q^{75} +30953.6 q^{76} +(9103.20 - 10264.9i) q^{77} -14979.1 q^{78} +(28456.0 - 49287.2i) q^{79} +(3200.00 + 5542.56i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16304.1 - 28239.5i) q^{82} -5543.75 q^{83} +(-18289.3 - 3743.40i) q^{84} -45210.4 q^{85} +(21661.8 - 37519.4i) q^{86} +(-12574.2 - 21779.1i) q^{87} +(3386.55 + 5865.68i) q^{88} +(-58318.7 + 101011. i) q^{89} -8100.00 q^{90} +(-17055.9 - 51174.9i) q^{91} +77493.6 q^{92} +(-20549.8 + 35593.4i) q^{93} +(9284.03 + 16080.4i) q^{94} +(24182.5 + 41885.3i) q^{95} +(4608.00 - 7981.29i) q^{96} +34548.9 q^{97} +(-8036.00 - 66746.0i) q^{98} -8572.21 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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