LMFDB - Embedded newform 35.6.e.b.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,6,Mod(11,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("35.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	35.e (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:	$5.61343369345$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 234 x^{14} - 399 x^{13} + 37070 x^{12} - 54845 x^{11} + 2990279 x^{10} + \cdots + 1025569391616 $ x^16 - 3x^15 + 234x^14 - 399x^13 + 37070x^12 - 54845x^11 + 2990279x^10 - 1696018x^9 + 168163132x^8 - 145614464x^7 + 4739118768x^6 - 5581286880x^5 + 97178302784x^4 - 96728088064x^3 + 536983468288x^2 + 469846046208*x + 1025569391616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.6
Root			$-3.31717 - 5.74550i$ of defining polynomial
Character	$\chi$	$=$	35.11
Dual form			35.6.e.b.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.31717 + 5.74550i) q^{2} +(-15.2893 + 26.4818i) q^{3} +(-6.00720 + 10.4048i) q^{4} +(-12.5000 - 21.6506i) q^{5} -202.868 q^{6} +(54.7457 + 117.516i) q^{7} +132.591 q^{8} +(-346.023 - 599.329i) q^{9} +O(q^{10})$	\(q+(3.31717 + 5.74550i) q^{2} +(-15.2893 + 26.4818i) q^{3} +(-6.00720 + 10.4048i) q^{4} +(-12.5000 - 21.6506i) q^{5} -202.868 q^{6} +(54.7457 + 117.516i) q^{7} +132.591 q^{8} +(-346.023 - 599.329i) q^{9} +(82.9292 - 143.638i) q^{10} +(-42.9017 + 74.3079i) q^{11} +(-183.691 - 318.162i) q^{12} -324.642 q^{13} +(-493.585 + 704.360i) q^{14} +764.463 q^{15} +(632.057 + 1094.76i) q^{16} +(-914.414 + 1583.81i) q^{17} +(2295.63 - 3976.15i) q^{18} +(397.081 + 687.764i) q^{19} +300.360 q^{20} +(-3949.04 - 346.963i) q^{21} -569.248 q^{22} +(-162.957 - 282.250i) q^{23} +(-2027.22 + 3511.25i) q^{24} +(-312.500 + 541.266i) q^{25} +(-1076.89 - 1865.23i) q^{26} +13731.1 q^{27} +(-1551.59 - 136.323i) q^{28} +4174.34 q^{29} +(2535.85 + 4392.22i) q^{30} +(343.203 - 594.445i) q^{31} +(-2071.82 + 3588.50i) q^{32} +(-1311.87 - 2272.22i) q^{33} -12133.1 q^{34} +(1859.97 - 2654.22i) q^{35} +8314.51 q^{36} +(1487.81 + 2576.96i) q^{37} +(-2634.37 + 4562.85i) q^{38} +(4963.53 - 8597.08i) q^{39} +(-1657.39 - 2870.68i) q^{40} +10136.9 q^{41} +(-11106.2 - 23840.2i) q^{42} -8438.98 q^{43} +(-515.438 - 892.764i) q^{44} +(-8650.57 + 14983.2i) q^{45} +(1081.11 - 1872.54i) q^{46} +(5946.22 + 10299.2i) q^{47} -38654.8 q^{48} +(-10812.8 + 12866.9i) q^{49} -4146.46 q^{50} +(-27961.4 - 48430.6i) q^{51} +(1950.19 - 3377.82i) q^{52} +(15668.4 - 27138.5i) q^{53} +(45548.5 + 78892.3i) q^{54} +2145.08 q^{55} +(7258.80 + 15581.5i) q^{56} -24284.3 q^{57} +(13847.0 + 23983.7i) q^{58} +(-521.048 + 902.482i) q^{59} +(-4592.28 + 7954.06i) q^{60} +(1000.69 + 1733.24i) q^{61} +4553.85 q^{62} +(51487.2 - 73473.7i) q^{63} +12961.4 q^{64} +(4058.02 + 7028.70i) q^{65} +(8703.38 - 15074.7i) q^{66} +(-10259.4 + 17769.7i) q^{67} +(-10986.1 - 19028.5i) q^{68} +9965.96 q^{69} +(21419.7 + 1881.93i) q^{70} +61262.0 q^{71} +(-45879.5 - 79465.7i) q^{72} +(-8863.50 + 15352.0i) q^{73} +(-9870.61 + 17096.4i) q^{74} +(-9555.78 - 16551.1i) q^{75} -9541.37 q^{76} +(-11081.0 - 973.578i) q^{77} +65859.4 q^{78} +(15130.9 + 26207.6i) q^{79} +(15801.4 - 27368.9i) q^{80} +(-125855. + 217988. i) q^{81} +(33625.9 + 58241.8i) q^{82} +41359.5 q^{83} +(27332.7 - 39004.6i) q^{84} +45720.7 q^{85} +(-27993.5 - 48486.2i) q^{86} +(-63822.6 + 110544. i) q^{87} +(-5688.38 + 9852.57i) q^{88} +(-57614.6 - 99791.5i) q^{89} -114781. q^{90} +(-17772.7 - 38150.4i) q^{91} +3915.66 q^{92} +(10494.6 + 18177.2i) q^{93} +(-39449.2 + 68328.0i) q^{94} +(9927.01 - 17194.1i) q^{95} +(-63353.2 - 109731. i) q^{96} +18962.8 q^{97} +(-109795. - 19443.3i) q^{98} +59379.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 203 q^{4} - 200 q^{5} - 112 q^{6} + 158 q^{7} + 498 q^{8} - 1218 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 203 * q^4 - 200 * q^5 - 112 * q^6 + 158 * q^7 + 498 * q^8 - 1218 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 203 q^{4} - 200 q^{5} - 112 q^{6} + 158 q^{7} + 498 q^{8} - 1218 q^{9} - 75 q^{10} - 120 q^{11} + 884 q^{12} + 3988 q^{13} - 975 q^{14} - 100 q^{15} - 6451 q^{16} - 1856 q^{17} - 2013 q^{18} + 1828 q^{19} + 10150 q^{20} - 7778 q^{21} + 4398 q^{22} - 4822 q^{23} + 2008 q^{24} - 5000 q^{25} + 7457 q^{26} + 15596 q^{27} - 4703 q^{28} + 21004 q^{29} + 1400 q^{30} - 5148 q^{31} - 12061 q^{32} + 2872 q^{33} - 81364 q^{34} + 2600 q^{35} + 81898 q^{36} - 7810 q^{37} - 18567 q^{38} + 2572 q^{39} - 6225 q^{40} - 36384 q^{41} + 70842 q^{42} + 126380 q^{43} + 4765 q^{44} - 30450 q^{45} - 6567 q^{46} - 11816 q^{47} - 214672 q^{48} - 31966 q^{49} + 3750 q^{50} - 28788 q^{51} - 167255 q^{52} + 39902 q^{53} + 126138 q^{54} + 6000 q^{55} - 11814 q^{56} + 77496 q^{57} - 67552 q^{58} - 50752 q^{59} + 22100 q^{60} + 2146 q^{61} + 203144 q^{62} - 16780 q^{63} + 540078 q^{64} - 49850 q^{65} - 164358 q^{66} - 50498 q^{67} + 125090 q^{68} - 237644 q^{69} + 65025 q^{70} + 367952 q^{71} - 522343 q^{72} - 54436 q^{73} - 228885 q^{74} + 1250 q^{75} - 131578 q^{76} + 130622 q^{77} + 783612 q^{78} - 51040 q^{79} - 161275 q^{80} - 124612 q^{81} + 195887 q^{82} + 120876 q^{83} - 570494 q^{84} + 92800 q^{85} - 260996 q^{86} - 409482 q^{87} - 205001 q^{88} + 96678 q^{89} + 100650 q^{90} - 44284 q^{91} + 349358 q^{92} + 51428 q^{93} + 139395 q^{94} + 45700 q^{95} + 587116 q^{96} - 390624 q^{97} - 887731 q^{98} + 794488 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 203 * q^4 - 200 * q^5 - 112 * q^6 + 158 * q^7 + 498 * q^8 - 1218 * q^9 - 75 * q^10 - 120 * q^11 + 884 * q^12 + 3988 * q^13 - 975 * q^14 - 100 * q^15 - 6451 * q^16 - 1856 * q^17 - 2013 * q^18 + 1828 * q^19 + 10150 * q^20 - 7778 * q^21 + 4398 * q^22 - 4822 * q^23 + 2008 * q^24 - 5000 * q^25 + 7457 * q^26 + 15596 * q^27 - 4703 * q^28 + 21004 * q^29 + 1400 * q^30 - 5148 * q^31 - 12061 * q^32 + 2872 * q^33 - 81364 * q^34 + 2600 * q^35 + 81898 * q^36 - 7810 * q^37 - 18567 * q^38 + 2572 * q^39 - 6225 * q^40 - 36384 * q^41 + 70842 * q^42 + 126380 * q^43 + 4765 * q^44 - 30450 * q^45 - 6567 * q^46 - 11816 * q^47 - 214672 * q^48 - 31966 * q^49 + 3750 * q^50 - 28788 * q^51 - 167255 * q^52 + 39902 * q^53 + 126138 * q^54 + 6000 * q^55 - 11814 * q^56 + 77496 * q^57 - 67552 * q^58 - 50752 * q^59 + 22100 * q^60 + 2146 * q^61 + 203144 * q^62 - 16780 * q^63 + 540078 * q^64 - 49850 * q^65 - 164358 * q^66 - 50498 * q^67 + 125090 * q^68 - 237644 * q^69 + 65025 * q^70 + 367952 * q^71 - 522343 * q^72 - 54436 * q^73 - 228885 * q^74 + 1250 * q^75 - 131578 * q^76 + 130622 * q^77 + 783612 * q^78 - 51040 * q^79 - 161275 * q^80 - 124612 * q^81 + 195887 * q^82 + 120876 * q^83 - 570494 * q^84 + 92800 * q^85 - 260996 * q^86 - 409482 * q^87 - 205001 * q^88 + 96678 * q^89 + 100650 * q^90 - 44284 * q^91 + 349358 * q^92 + 51428 * q^93 + 139395 * q^94 + 45700 * q^95 + 587116 * q^96 - 390624 * q^97 - 887731 * q^98 + 794488 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	3.31717	+	5.74550i	0.586398	+	1.01567i	0.994700	+	0.102824i	$0.0327878\pi$
$2$	3.31717	+	5.74550i	0.586398	+	1.01567i	−0.408302	+	0.912847i	$0.633879\pi$
$3$	−15.2893	+	26.4818i	−0.980806	+	1.69881i	−0.321541	+	0.946896i	$0.604201\pi$
$3$	−15.2893	+	26.4818i	−0.980806	+	1.69881i	−0.659265	+	0.751910i	$0.729133\pi$
$4$	−6.00720	+	10.4048i	−0.187725	+	0.325149i
$5$	−12.5000	−	21.6506i	−0.223607	−	0.387298i
$5$	−12.5000	−	21.6506i	−0.223607	−	0.387298i
$6$	−202.868			−2.30057
$7$	54.7457	+	117.516i	0.422284	+	0.906463i
$7$	54.7457	+	117.516i	0.422284	+	0.906463i
$8$	132.591			0.732470
$9$	−346.023	−	599.329i	−1.42396	−	2.46637i
$10$	82.9292	−	143.638i	0.262245	−	0.454222i
$11$	−42.9017	+	74.3079i	−0.106904	+	0.185163i	−0.914514	−	0.404553i	$-0.867427\pi$
$11$	−42.9017	+	74.3079i	−0.106904	+	0.185163i	0.807611	+	0.589716i	$0.200760\pi$
$12$	−183.691	−	318.162i	−0.368244	−	0.637817i
$13$	−324.642			−0.532777			−0.266389	−	0.963866i	$-0.585830\pi$
$13$	−324.642			−0.532777			−0.266389	+	0.963866i	$0.585830\pi$
$14$	−493.585	+	704.360i	−0.673042	+	0.960450i
$15$	764.463			0.877260
$16$	632.057	+	1094.76i	0.617244	+	1.06910i
$17$	−914.414	+	1583.81i	−0.767398	+	1.32917i	0.171572	+	0.985172i	$0.445116\pi$
$17$	−914.414	+	1583.81i	−0.767398	+	1.32917i	−0.938969	+	0.344001i	$0.888218\pi$
$18$	2295.63	−	3976.15i	1.67002	−	2.89255i
$19$	397.081	+	687.764i	0.252345	+	0.437074i	0.964171	−	0.265282i	$-0.0854649\pi$
$19$	397.081	+	687.764i	0.252345	+	0.437074i	−0.711826	+	0.702356i	$0.752132\pi$
$20$	300.360			0.167906
$21$	−3949.04	−	346.963i	−1.95408	−	0.171686i
$22$	−569.248			−0.250752
$23$	−162.957	−	282.250i	−0.0642323	−	0.111254i	0.832121	−	0.554594i	$-0.187127\pi$
$23$	−162.957	−	282.250i	−0.0642323	−	0.111254i	−0.896353	+	0.443341i	$0.853793\pi$
$24$	−2027.22	+	3511.25i	−0.718411	+	1.24432i
$25$	−312.500	+	541.266i	−0.100000	+	0.173205i
$26$	−1076.89	−	1865.23i	−0.312420	−	0.541127i
$27$	13731.1			3.62491
$28$	−1551.59	−	136.323i	−0.374009	−	0.0328604i
$29$	4174.34			0.921708			0.460854	−	0.887476i	$-0.347543\pi$
$29$	4174.34			0.921708			0.460854	+	0.887476i	$0.347543\pi$
$30$	2535.85	+	4392.22i	0.514423	+	0.891007i
$31$	343.203	−	594.445i	0.0641427	−	0.111098i	−0.832171	−	0.554520i	$-0.812902\pi$
$31$	343.203	−	594.445i	0.0641427	−	0.111098i	0.896313	+	0.443421i	$0.146235\pi$
$32$	−2071.82	+	3588.50i	−0.357666	+	0.619495i
$33$	−1311.87	−	2272.22i	−0.209703	−	0.363217i
$34$	−12133.1			−1.80000
$35$	1859.97	−	2654.22i	0.256646	−	0.366241i
$36$	8314.51			1.06925
$37$	1487.81	+	2576.96i	0.178666	+	0.309459i	0.941424	−	0.337225i	$-0.109488\pi$
$37$	1487.81	+	2576.96i	0.178666	+	0.309459i	−0.762758	+	0.646684i	$0.776155\pi$
$38$	−2634.37	+	4562.85i	−0.295949	+	0.512599i
$39$	4963.53	−	8597.08i	0.522551	−	0.905086i
$40$	−1657.39	−	2870.68i	−0.163785	−	0.283684i
$41$	10136.9			0.941774			0.470887	−	0.882193i	$-0.343934\pi$
$41$	10136.9			0.941774			0.470887	+	0.882193i	$0.343934\pi$
$42$	−11106.2	−	23840.2i	−0.971495	−	2.08538i
$43$	−8438.98			−0.696015			−0.348008	−	0.937492i	$-0.613142\pi$
$43$	−8438.98			−0.696015			−0.348008	+	0.937492i	$0.613142\pi$
$44$	−515.438	−	892.764i	−0.0401370	−	0.0695192i
$45$	−8650.57	+	14983.2i	−0.636815	+	1.10300i
$46$	1081.11	−	1872.54i	0.0753313	−	0.130478i
$47$	5946.22	+	10299.2i	0.392642	+	0.680075i	0.992797	−	0.119808i	$-0.0382280\pi$
$47$	5946.22	+	10299.2i	0.392642	+	0.680075i	−0.600155	+	0.799883i	$0.704895\pi$
$48$	−38654.8			−2.42159
$49$	−10812.8	+	12866.9i	−0.643352	+	0.765571i
$50$	−4146.46			−0.234559
$51$	−27961.4	−	48430.6i	−1.50534	−	2.60732i
$52$	1950.19	−	3377.82i	0.100016	−	0.173232i
$53$	15668.4	−	27138.5i	0.766189	−	1.32708i	−0.173427	−	0.984847i	$-0.555484\pi$
$53$	15668.4	−	27138.5i	0.766189	−	1.32708i	0.939616	−	0.342231i	$-0.111183\pi$
$54$	45548.5	+	78892.3i	2.12564	+	3.68171i
$55$	2145.08			0.0956175
$56$	7258.80	+	15581.5i	0.309310	+	0.663957i
$57$	−24284.3			−0.990006
$58$	13847.0	+	23983.7i	0.540488	+	0.936152i
$59$	−521.048	+	902.482i	−0.0194871	+	0.0337527i	−0.875605	−	0.483029i	$-0.839537\pi$
$59$	−521.048	+	902.482i	−0.0194871	+	0.0337527i	0.856117	+	0.516781i	$0.172870\pi$
$60$	−4592.28	+	7954.06i	−0.164684	+	0.285240i
$61$	1000.69	+	1733.24i	0.0344330	+	0.0596397i	0.882728	−	0.469884i	$-0.155704\pi$
$61$	1000.69	+	1733.24i	0.0344330	+	0.0596397i	−0.848295	+	0.529523i	$0.822371\pi$
$62$	4553.85			0.150452
$63$	51487.2	−	73473.7i	1.63436	−	2.33228i
$64$	12961.4			0.395549
$65$	4058.02	+	7028.70i	0.119133	+	0.206344i
$66$	8703.38	−	15074.7i	0.245939	−	0.425979i
$67$	−10259.4	+	17769.7i	−0.279211	+	0.483608i	−0.971189	−	0.238311i	$-0.923406\pi$
$67$	−10259.4	+	17769.7i	−0.279211	+	0.483608i	0.691978	+	0.721919i	$0.256740\pi$
$68$	−10986.1	−	19028.5i	−0.288119	−	0.499038i
$69$	9965.96			0.251998
$70$	21419.7	+	1881.93i	0.522477	+	0.0459049i
$71$	61262.0			1.44227			0.721133	−	0.692796i	$-0.243621\pi$
$71$	61262.0			1.44227			0.721133	+	0.692796i	$0.243621\pi$
$72$	−45879.5	−	79465.7i	−1.04301	−	1.80654i
$73$	−8863.50	+	15352.0i	−0.194670	+	0.337178i	−0.946792	−	0.321846i	$-0.895697\pi$
$73$	−8863.50	+	15352.0i	−0.194670	+	0.337178i	0.752123	+	0.659023i	$0.229030\pi$
$74$	−9870.61	+	17096.4i	−0.209539	+	0.362932i
$75$	−9555.78	−	16551.1i	−0.196161	−	0.339761i
$76$	−9541.37			−0.189486
$77$	−11081.0	−	973.578i	−0.212987	−	0.0187130i
$78$	65859.4			1.22569
$79$	15130.9	+	26207.6i	0.272771	+	0.472453i	0.969570	−	0.244813i	$-0.0787265\pi$
$79$	15130.9	+	26207.6i	0.272771	+	0.472453i	−0.696799	+	0.717266i	$0.745393\pi$
$80$	15801.4	−	27368.9i	0.276040	−	0.478115i
$81$	−125855.	+	217988.i	−2.13137	+	3.69164i
$82$	33625.9	+	58241.8i	0.552255	+	0.956533i
$83$	41359.5			0.658992			0.329496	−	0.944157i	$-0.393121\pi$
$83$	41359.5			0.658992			0.329496	+	0.944157i	$0.393121\pi$
$84$	27332.7	−	39004.6i	0.422654	−	0.603139i
$85$	45720.7			0.686382
$86$	−27993.5	−	48486.2i	−0.408142	−	0.706922i
$87$	−63822.6	+	110544.i	−0.904017	+	1.56580i
$88$	−5688.38	+	9852.57i	−0.0783037	+	0.135626i
$89$	−57614.6	−	99791.5i	−0.771006	−	1.33542i	−0.937012	−	0.349297i	$-0.886421\pi$
$89$	−57614.6	−	99791.5i	−0.771006	−	1.33542i	0.166006	−	0.986125i	$-0.446913\pi$
$90$	−114781.			−1.49371
$91$	−17772.7	−	38150.4i	−0.224984	−	0.482943i
$92$	3915.66			0.0482320
$93$	10494.6	+	18177.2i	0.125823	+	0.217932i
$94$	−39449.2	+	68328.0i	−0.460488	+	0.797589i
$95$	9927.01	−	17194.1i	0.112852	−	0.195466i
$96$	−63353.2	−	109731.i	−0.701602	−	1.21521i
$97$	18962.8			0.204632			0.102316	−	0.994752i	$-0.467375\pi$
$97$	18962.8			0.204632			0.102316	+	0.994752i	$0.467375\pi$
$98$	−109795.	−	19443.3i	−1.15483	−	0.204505i
$99$	59379.8			0.608907
$100$	−3754.50	−	6502.98i	−0.0375450	−	0.0650298i
$101$	60521.5	−	104826.i	0.590346	−	1.02251i	−0.403840	−	0.914830i	$-0.632325\pi$
$101$	60521.5	−	104826.i	0.590346	−	1.02251i	0.994186	−	0.107679i	$-0.0343419\pi$
$102$	185505.	−	321305.i	1.76545	−	3.05785i
$103$	−46556.6	−	80638.4i	−0.432402	−	0.748943i	0.564677	−	0.825312i	$-0.309001\pi$
$103$	−46556.6	−	80638.4i	−0.432402	−	0.748943i	−0.997080	+	0.0763690i	$0.975667\pi$
$104$	−43044.6			−0.390243
$105$	41851.0	+	89836.3i	0.370453	+	0.795204i
$106$	207899.			1.79717
$107$	10793.5	+	18694.8i	0.0911384	+	0.157856i	0.907990	−	0.418991i	$-0.137616\pi$
$107$	10793.5	+	18694.8i	0.0911384	+	0.157856i	−0.816852	+	0.576847i	$0.804283\pi$
$108$	−82485.7	+	142869.i	−0.680486	+	1.17864i
$109$	10949.2	−	18964.5i	0.0882705	−	0.152889i	−0.818510	−	0.574493i	$-0.805199\pi$
$109$	10949.2	−	18964.5i	0.0882705	−	0.152889i	0.906780	+	0.421604i	$0.138533\pi$
$110$	7115.60	+	12324.6i	0.0560699	+	0.0971159i
$111$	−90989.9			−0.700948
$112$	−94048.4	+	134210.i	−0.708445	+	1.01097i
$113$	−66325.7			−0.488636			−0.244318	−	0.969695i	$-0.578564\pi$
$113$	−66325.7			−0.488636			−0.244318	+	0.969695i	$0.578564\pi$
$114$	−80555.0	−	139525.i	−0.580537	−	1.00552i
$115$	−4073.92	+	7056.24i	−0.0287255	+	0.0497541i
$116$	−25076.1	+	43433.1i	−0.173028	+	0.299693i
$117$	112333.	+	194567.i	0.758655	+	1.31403i
$118$	−6913.62			−0.0457089
$119$	−236183.	−	20751.0i	−1.52891	−	0.134330i
$120$	101361.			0.642566
$121$	76844.4	+	133098.i	0.477143	+	0.826436i
$122$	−6638.90	+	11498.9i	−0.0403828	+	0.0699451i
$123$	−154986.	+	268444.i	−0.923698	+	1.59989i
$124$	4123.38	+	7141.90i	0.0240824	+	0.0417119i
$125$	15625.0			0.0894427
$126$	592935.	+	52095.3i	3.32721	+	0.292329i
$127$	224823.			1.23689			0.618446	−	0.785827i	$-0.287763\pi$
$127$	224823.			1.23689			0.618446	+	0.785827i	$0.287763\pi$
$128$	109293.	+	189302.i	0.589615	+	1.02124i
$129$	129026.	−	223479.i	0.682656	−	1.18239i
$130$	−26922.3	+	46630.7i	−0.139718	+	0.241999i
$131$	−155419.	−	269193.i	−0.791271	−	1.37052i	−0.925180	−	0.379528i	$-0.876086\pi$
$131$	−155419.	−	269193.i	−0.791271	−	1.37052i	0.133909	−	0.990994i	$-0.457247\pi$
$132$	31522.6			0.157466
$133$	−59084.5	+	84315.3i	−0.289631	+	0.413311i
$134$	−136128.			−0.654916
$135$	−171639.	−	297288.i	−0.810554	−	1.40392i
$136$	−121243.	+	209999.i	−0.562096	+	0.973578i
$137$	8532.70	−	14779.1i	0.0388405	−	0.0672738i	−0.845952	−	0.533260i	$-0.820967\pi$
$137$	8532.70	−	14779.1i	0.0388405	−	0.0672738i	0.884792	+	0.465986i	$0.154300\pi$
$138$	33058.8	+	57259.4i	0.147771	+	0.255947i
$139$	−123482.			−0.542082			−0.271041	−	0.962568i	$-0.587368\pi$
$139$	−123482.			−0.542082			−0.271041	+	0.962568i	$0.587368\pi$
$140$	16443.4	+	35297.0i	0.0709042	+	0.152201i
$141$	−363653.			−1.54042
$142$	203216.	+	351981.i	0.845742	+	1.46487i
$143$	13927.7	−	24123.4i	0.0569558	−	0.0986504i
$144$	437412.	−	757620.i	1.75786	−	3.04471i
$145$	−52179.3	−	90377.2i	−0.206100	−	0.356976i
$146$	−117607.			−0.456616
$147$	−175419.	−	483068.i	−0.669552	−	1.84381i
$148$	−35750.2			−0.134160
$149$	−16353.2	−	28324.5i	−0.0603443	−	0.104519i	0.834275	−	0.551348i	$-0.185887\pi$
$149$	−16353.2	−	28324.5i	−0.0603443	−	0.104519i	−0.894619	+	0.446829i	$0.852553\pi$
$150$	63396.3	−	109806.i	0.230057	−	0.398471i
$151$	−224544.	+	388921.i	−0.801417	+	1.38809i	0.117267	+	0.993100i	$0.462587\pi$
$151$	−224544.	+	388921.i	−0.801417	+	1.38809i	−0.918684	+	0.394994i	$0.870747\pi$
$152$	52649.4	+	91191.4i	0.184835	+	0.320144i
$153$	1.26563e6			4.37098
$154$	−31163.9	−	66895.5i	−0.105889	−	0.227298i
$155$	−17160.2			−0.0573709
$156$	59633.8	+	103289.i	0.196192	+	0.339814i
$157$	15848.4	−	27450.2i	0.0513140	−	0.0888785i	−0.839227	−	0.543781i	$-0.816992\pi$
$157$	15848.4	−	27450.2i	0.0513140	−	0.0888785i	0.890541	+	0.454902i	$0.150326\pi$
$158$	−100384.	+	173870.i	−0.319905	+	0.554091i
$159$	479117.	+	829856.i	1.50297	+	2.60321i
$160$	103591.			0.319906
$161$	24247.5	−	34601.9i	0.0737230	−	0.105205i
$162$	−1.66993e6			−4.99933
$163$	−250603.	−	434057.i	−0.738784	−	1.27961i	−0.953043	−	0.302834i	$-0.902067\pi$
$163$	−250603.	−	434057.i	−0.738784	−	1.27961i	0.214259	−	0.976777i	$-0.431266\pi$
$164$	−60894.6	+	105472.i	−0.176795	+	0.306217i
$165$	−32796.7	+	56805.6i	−0.0937822	+	0.162436i
$166$	137196.	+	237631.i	0.386432	+	0.669319i
$167$	295459.			0.819798			0.409899	−	0.912131i	$-0.365564\pi$
$167$	295459.			0.819798			0.409899	+	0.912131i	$0.365564\pi$
$168$	−523608.	−	46004.2i	−1.43131	−	0.125755i
$169$	−265901.			−0.716148
$170$	151663.	+	262688.i	0.402493	+	0.697138i
$171$	274798.	−	475964.i	0.718659	−	1.24475i
$172$	50694.6	−	87805.6i	0.130659	−	0.226309i
$173$	−27832.4	−	48207.0i	−0.0707025	−	0.122460i	0.828507	−	0.559979i	$-0.189191\pi$
$173$	−27832.4	−	48207.0i	−0.0707025	−	0.122460i	−0.899209	+	0.437519i	$0.855857\pi$
$174$	−846841.			−2.12045
$175$	−80715.2	−	7091.64i	−0.199233	−	0.0175046i
$176$	−108465.			−0.263942
$177$	−15932.9	−	27596.6i	−0.0382262	−	0.0662097i
$178$	382235.	−	662050.i	0.904232	−	1.56618i
$179$	254351.	−	440549.i	0.593336	−	1.02769i	−0.400444	−	0.916321i	$-0.631144\pi$
$179$	254351.	−	440549.i	0.593336	−	1.02769i	0.993779	−	0.111366i	$-0.0355227\pi$
$180$	−103931.	−	180014.i	−0.239092	−	0.414120i
$181$	−725751.			−1.64661			−0.823306	−	0.567598i	$-0.807873\pi$
$181$	−725751.			−1.64661			−0.823306	+	0.567598i	$0.807873\pi$
$182$	160238.	−	228665.i	0.358582	−	0.511706i
$183$	−61199.1			−0.135088
$184$	−21606.6	−	37423.8i	−0.0470482	−	0.0814898i
$185$	37195.2	−	64424.0i	0.0799020	−	0.138394i
$186$	−69624.9	+	120594.i	−0.147565	+	0.255590i
$187$	−78459.8	−	135896.i	−0.164075	−	0.284187i
$188$	−142880.			−0.294834
$189$	751721.	+	1.61362e6i	1.53074	+	3.28585i
$190$	131718.			0.264705
$191$	295104.	+	511135.i	0.585317	+	1.01380i	0.994836	+	0.101497i	$0.0323633\pi$
$191$	295104.	+	511135.i	0.585317	+	1.01380i	−0.409519	+	0.912302i	$0.634303\pi$
$192$	−198169.	+	343240.i	−0.387957	+	0.671961i
$193$	197111.	−	341405.i	0.380905	−	0.659747i	−0.610287	−	0.792180i	$-0.708946\pi$
$193$	197111.	−	341405.i	0.380905	−	0.659747i	0.991192	+	0.132434i	$0.0422792\pi$
$194$	62902.7	+	108951.i	0.119996	+	0.207838i
$195$	−248176.			−0.467384
$196$	−68922.9	−	189799.i	−0.128151	−	0.352902i
$197$	252511.			0.463569			0.231785	−	0.972767i	$-0.425544\pi$
$197$	252511.			0.463569			0.231785	+	0.972767i	$0.425544\pi$
$198$	196973.	+	341167.i	0.357062	+	0.618449i
$199$	426096.	−	738019.i	0.762736	−	1.32110i	−0.178699	−	0.983904i	$-0.557189\pi$
$199$	426096.	−	738019.i	0.762736	−	1.32110i	0.941435	−	0.337194i	$-0.109478\pi$
$200$	−41434.7	+	71767.1i	−0.0732470	+	0.126867i
$201$	−313716.	−	543372.i	−0.547704	−	0.948652i
$202$	803040.			1.38471
$203$	228527.	+	490550.i	0.389223	+	0.835494i
$204$	671879.			1.13036
$205$	−126712.	−	219471.i	−0.210587	−	0.364748i
$206$	308872.	−	534982.i	0.507120	−	0.878357i
$207$	−112774.	+	195330.i	−0.182928	+	0.316841i
$208$	−205192.	−	355403.i	−0.328853	−	0.569591i
$209$	−68141.7			−0.107906
$210$	−377328.	+	538457.i	−0.590433	+	0.842564i
$211$	452398.			0.699544			0.349772	−	0.936835i	$-0.386259\pi$
$211$	452398.			0.699544			0.349772	+	0.936835i	$0.386259\pi$
$212$	188247.	+	326053.i	0.287666	+	0.498251i
$213$	−936651.	+	1.62233e6i	−1.41458	+	2.45013i
$214$	−71607.4	+	124028.i	−0.106887	+	0.185133i
$215$	105487.	+	182709.i	0.155634	+	0.269565i
$216$	1.82063e6			2.65514
$217$	88645.4	+	7788.39i	0.127793	+	0.0112279i
$218$	145281.			0.207046
$219$	−271033.	−	469442.i	−0.381866	−	0.661412i
$220$	−12885.9	+	22319.1i	−0.0179498	+	0.0310900i
$221$	296857.	−	514171.i	0.408852	−	0.708153i
$222$	−301829.	−	522783.i	−0.411034	−	0.711932i
$223$	−812327.			−1.09388			−0.546939	−	0.837173i	$-0.684207\pi$
$223$	−812327.			−1.09388			−0.546939	+	0.837173i	$0.684207\pi$
$224$	−535128.	−	47016.4i	−0.712587	−	0.0626079i
$225$	432528.			0.569585
$226$	−220014.	−	381075.i	−0.286535	−	0.496294i
$227$	633625.	−	1.09747e6i	0.816145	−	1.41361i	−0.0923572	−	0.995726i	$-0.529440\pi$
$227$	633625.	−	1.09747e6i	0.816145	−	1.41361i	0.908503	−	0.417879i	$-0.137227\pi$
$228$	145880.	−	252672.i	0.185849	−	0.321900i
$229$	−48431.1	−	83885.2i	−0.0610290	−	0.105705i	0.833897	−	0.551921i	$-0.186105\pi$
$229$	−48431.1	−	83885.2i	−0.0610290	−	0.105705i	−0.894926	+	0.446215i	$0.852772\pi$
$230$	−54055.5			−0.0673784
$231$	195202.	−	278559.i	0.240689	−	0.343469i
$232$	553481.			0.675123
$233$	653049.	+	1.13111e6i	0.788054	+	1.36495i	0.927157	+	0.374672i	$0.122245\pi$
$233$	653049.	+	1.13111e6i	0.788054	+	1.36495i	−0.139103	+	0.990278i	$0.544422\pi$
$234$	−745257.	+	1.29082e6i	−0.889747	+	1.54109i
$235$	148655.	−	257479.i	0.175595	−	0.304139i
$236$	−6260.08	−	10842.8i	−0.00731644	−	0.0126725i
$237$	−925363.			−1.07014
$238$	−664233.	−	1.42582e6i	−0.760113	−	1.63164i
$239$	−506413.			−0.573469			−0.286734	−	0.958010i	$-0.592570\pi$
$239$	−506413.			−0.573469			−0.286734	+	0.958010i	$0.592570\pi$
$240$	483184.	+	836900.i	0.541483	+	0.937876i
$241$	−409077.	+	708543.i	−0.453694	+	0.785821i	−0.998612	−	0.0526684i	$-0.983227\pi$
$241$	−409077.	+	708543.i	−0.453694	+	0.785821i	0.544918	+	0.838489i	$0.316561\pi$
$242$	−509811.	+	883019.i	−0.559592	+	0.969241i
$243$	−2.18014e6	−	3.77611e6i	−2.36847	−	4.10231i
$244$	−24045.3			−0.0258557
$245$	413738.	+	73267.6i	0.440362	+	0.0779824i
$246$	−2.05646e6			−2.16662
$247$	−128909.	−	223277.i	−0.134444	−	0.232863i
$248$	45505.7	−	78818.2i	0.0469825	−	0.0813762i
$249$	−632356.	+	1.09527e6i	−0.646344	+	1.11950i
$250$	51830.7	+	89773.5i	0.0524490	+	0.0908444i
$251$	599979.			0.601107			0.300554	−	0.953765i	$-0.402829\pi$
$251$	599979.			0.601107			0.300554	+	0.953765i	$0.402829\pi$
$252$	455183.	+	977084.i	0.451528	+	0.969238i
$253$	27964.5			0.0274666
$254$	745776.	+	1.29172e6i	0.725311	+	1.25628i
$255$	−699036.	+	1.21077e6i	−0.673207	+	1.16603i
$256$	−517707.	+	896694.i	−0.493723	+	0.855154i
$257$	717857.	+	1.24337e6i	0.677962	+	1.17426i	0.975594	+	0.219584i	$0.0704700\pi$
$257$	717857.	+	1.24337e6i	0.677962	+	1.17426i	−0.297632	+	0.954681i	$0.596197\pi$
$258$	1.71200e6			1.60123
$259$	−221382.	+	315918.i	−0.205065	+	0.292634i
$260$	−97509.3			−0.0894567
$261$	−1.44442e6	−	2.50180e6i	−1.31248	−	2.27328i
$262$	1.03110e6	−	1.78592e6i	0.927999	−	1.60734i
$263$	−188596.	+	326658.i	−0.168129	+	0.291208i	−0.937762	−	0.347278i	$-0.887106\pi$
$263$	−188596.	+	326658.i	−0.168129	+	0.291208i	0.769633	+	0.638487i	$0.220439\pi$
$264$	−173942.	−	301277.i	−0.153601	−	0.266045i
$265$	−783422.			−0.685300
$266$	−680427.	−	59782.3i	−0.589627	−	0.0518046i
$267$	3.52354e6			3.02483
$268$	−123260.	−	213492.i	−0.104830	−	0.181571i
$269$	471907.	−	817366.i	0.397627	−	0.688709i	−0.595806	−	0.803128i	$-0.703167\pi$
$269$	471907.	−	817366.i	0.397627	−	0.688709i	0.993433	+	0.114419i	$0.0365006\pi$
$270$	1.13871e6	−	1.97231e6i	0.950614	−	1.64651i
$271$	923619.	+	1.59976e6i	0.763959	+	1.32322i	0.940795	+	0.338975i	$0.110080\pi$
$271$	923619.	+	1.59976e6i	0.763959	+	1.32322i	−0.176837	+	0.984240i	$0.556587\pi$
$272$	−2.31185e6			−1.89469
$273$	1.28202e6	+	112639.i	1.04109	+	0.0914704i
$274$	113218.			0.0911040
$275$	−26813.5	−	46442.4i	−0.0213807	−	0.0370325i
$276$	−59867.5	+	103694.i	−0.0473062	+	0.0819368i
$277$	−864787.	+	1.49786e6i	−0.677189	+	1.17293i	0.298635	+	0.954367i	$0.403469\pi$
$277$	−864787.	+	1.49786e6i	−0.677189	+	1.17293i	−0.975824	+	0.218558i	$0.929865\pi$
$278$	−409609.	−	709463.i	−0.317876	−	0.550577i
$279$	−475024.			−0.365347
$280$	246615.	−	351927.i	0.187986	−	0.268261i
$281$	−1.35071e6			−1.02046			−0.510231	−	0.860038i	$-0.670440\pi$
$281$	−1.35071e6			−1.02046			−0.510231	+	0.860038i	$0.670440\pi$
$282$	−1.20630e6	−	2.08937e6i	−0.903300	−	1.56456i
$283$	583262.	−	1.01024e6i	0.432910	−	0.749822i	−0.564213	−	0.825629i	$-0.690820\pi$
$283$	583262.	−	1.01024e6i	0.432910	−	0.749822i	0.997122	+	0.0758079i	$0.0241536\pi$
$284$	−368013.	+	637418.i	−0.270749	+	0.468952i
$285$	303553.	+	525770.i	0.221372	+	0.383428i
$286$	184802.			0.133595
$287$	554953.	+	1.19125e6i	0.397697	+	0.853684i
$288$	2.86759e6			2.03721
$289$	−962378.	−	1.66689e6i	−0.677799	−	1.17398i
$290$	346175.	−	599593.i	0.241713	−	0.418660i
$291$	−289927.	+	502168.i	−0.200704	+	0.347630i
$292$	−106490.	−	184445.i	−0.0730887	−	0.126593i
$293$	−1.21134e6			−0.824321			−0.412160	−	0.911111i	$-0.635226\pi$
$293$	−1.21134e6			−0.824321			−0.412160	+	0.911111i	$0.635226\pi$
$294$	2.19358e6	−	2.61029e6i	1.48008	−	1.76125i
$295$	26052.4			0.0174298
$296$	197270.	+	341682.i	0.130868	+	0.226669i
$297$	−589089.	+	1.02033e6i	−0.387516	+	0.671197i
$298$	108492.	−	187914.i	0.0707715	−	0.122580i
$299$	52902.6	+	91630.0i	0.0342215	+	0.0592734i
$300$	229614.			0.147297
$301$	−461998.	−	991711.i	−0.293916	−	0.630912i
$302$	−2.97939e6			−1.87980
$303$	1.85066e6	+	3.20543e6i	1.15803	+	2.00577i
$304$	−501956.	+	869412.i	−0.311517	+	0.539563i
$305$	25017.2	−	43331.1i	0.0153989	−	0.0266717i
$306$	4.19831e6	+	7.27169e6i	2.56313	+	4.43948i
$307$	−1.38256e6			−0.837220			−0.418610	−	0.908166i	$-0.637483\pi$
$307$	−1.38256e6			−0.837220			−0.418610	+	0.908166i	$0.637483\pi$
$308$	76695.7	−	109447.i	0.0460675	−	0.0657396i
$309$	2.84726e6			1.69641
$310$	−56923.1	−	98593.7i	−0.0336422	−	0.0582700i
$311$	1.44306e6	−	2.49946e6i	0.846027	−	1.46536i	−0.0386996	−	0.999251i	$-0.512322\pi$
$311$	1.44306e6	−	2.49946e6i	0.846027	−	1.46536i	0.884726	−	0.466111i	$-0.154345\pi$
$312$	658120.	−	1.13990e6i	0.382753	−	0.662948i
$313$	1.08208e6	+	1.87422e6i	0.624309	+	1.08134i	0.988674	+	0.150079i	$0.0479527\pi$
$313$	1.08208e6	+	1.87422e6i	0.624309	+	1.08134i	−0.364365	+	0.931256i	$0.618714\pi$
$314$	210287.			0.120362
$315$	−2.23434e6	−	196309.i	−1.26874	−	0.111472i
$316$	−363578.			−0.204824
$317$	−775649.	−	1.34346e6i	−0.433528	−	0.750893i	0.563646	−	0.826016i	$-0.309398\pi$
$317$	−775649.	−	1.34346e6i	−0.433528	−	0.750893i	−0.997174	+	0.0751236i	$0.976065\pi$
$318$	−3.17862e6	+	5.50554e6i	−1.76267	+	3.05304i
$319$	−179086.	+	310187.i	−0.0985339	+	0.170666i
$320$	−162017.	−	280622.i	−0.0884475	−	0.153196i
$321$	−660096.			−0.357556
$322$	279239.	+	24533.9i	0.150084	+	0.0131864i
$323$	−1.45238e6			−0.774596
$324$	−1.51208e6	−	2.61899e6i	−0.800223	−	1.38603i
$325$	101451.	−	175717.i	0.0532777	−	0.0922798i
$326$	1.66258e6	−	2.87968e6i	0.866443	−	1.50072i
$327$	334810.	+	579907.i	0.173152	+	0.299909i
$328$	1.34407e6			0.689821
$329$	−884781.	+	1.26261e6i	−0.450657	+	0.643100i
$330$	−435169.			−0.219975
$331$	991094.	+	1.71663e6i	0.497216	+	0.861203i	0.999995	−	0.00321202i	$-0.00102242\pi$
$331$	991094.	+	1.71663e6i	0.497216	+	0.861203i	−0.502779	+	0.864415i	$0.667689\pi$
$332$	−248455.	+	430336.i	−0.123709	+	0.214271i
$333$	1.02963e6	−	1.78337e6i	0.508828	−	0.881315i
$334$	980089.	+	1.69756e6i	0.480728	+	0.832645i
$335$	512968.			0.249734
$336$	−2.11618e6	−	4.54254e6i	−1.02260	−	2.19508i
$337$	727886.			0.349131			0.174565	−	0.984646i	$-0.444148\pi$
$337$	727886.			0.349131			0.174565	+	0.984646i	$0.444148\pi$
$338$	−882037.	−	1.52773e6i	−0.419948	−	0.727371i
$339$	1.01407e6	−	1.75642e6i	0.479258	−	0.830099i
$340$	−274653.	+	475714.i	−0.128851	+	0.223176i
$341$	29448.0	+	51005.4i	0.0137142	+	0.0237536i
$342$	3.64620e6			1.68568
$343$	−2.10402e6	−	566265.i	−0.965639	−	0.259887i
$344$	−1.11893e6			−0.509810
$345$	−124574.	−	215769.i	−0.0563484	−	0.0975982i
$346$	184649.	−	319822.i	0.0829196	−	0.143621i
$347$	−1.83070e6	+	3.17087e6i	−0.816194	+	1.41369i	0.0922728	+	0.995734i	$0.470587\pi$
$347$	−1.83070e6	+	3.17087e6i	−0.816194	+	1.41369i	−0.908467	+	0.417956i	$0.862747\pi$
$348$	−766790.	−	1.32812e6i	−0.339413	−	0.587881i
$349$	2.41958e6			1.06335			0.531674	−	0.846949i	$-0.321563\pi$
$349$	2.41958e6			1.06335			0.531674	+	0.846949i	$0.321563\pi$
$350$	−227001.	−	487274.i	−0.0990506	−	0.212619i
$351$	−4.45770e6			−1.93127
$352$	−177769.	−	307905.i	−0.0764716	−	0.132453i
$353$	−638842.	+	1.10651e6i	−0.272871	+	0.472626i	−0.969596	−	0.244712i	$-0.921306\pi$
$353$	−638842.	+	1.10651e6i	−0.272871	+	0.472626i	0.696725	+	0.717338i	$0.254640\pi$
$354$	105704.	−	183085.i	0.0448315	−	0.0776505i
$355$	−765776.	−	1.32636e6i	−0.322501	−	0.558588i
$356$	1.38441e6			0.578948
$357$	4.16058e6	−	5.93727e6i	1.72776	−	2.46556i
$358$	3.37490e6			1.39172
$359$	991155.	+	1.71673e6i	0.405887	+	0.703017i	0.994424	−	0.105453i	$-0.0336292\pi$
$359$	991155.	+	1.71673e6i	0.405887	+	0.703017i	−0.588537	+	0.808470i	$0.700296\pi$
$360$	−1.14699e6	+	1.98664e6i	−0.466448	+	0.807911i
$361$	922704.	−	1.59817e6i	0.372644	−	0.645438i
$362$	−2.40744e6	−	4.16980e6i	−0.965570	−	1.67242i
$363$	−4.69957e6			−1.87194
$364$	503711.	+	44256.1i	0.199264	+	0.0175073i
$365$	443175.			0.174118
$366$	−203008.	−	351620.i	−0.0792155	−	0.137205i
$367$	−1.41366e6	+	2.44854e6i	−0.547874	+	0.948945i	0.450546	+	0.892753i	$0.351229\pi$
$367$	−1.41366e6	+	2.44854e6i	−0.547874	+	0.948945i	−0.998420	+	0.0561921i	$0.982104\pi$
$368$	205996.	−	356796.i	0.0792939	−	0.137341i
$369$	−3.50761e6	−	6.07536e6i	−1.34105	−	2.32277i
$370$	493531.			0.187417
$371$	4.04698e6	+	355567.i	1.52650	+	0.134118i
$372$	−252173.			−0.0944805
$373$	−205132.	−	355299.i	−0.0763416	−	0.132228i	0.825327	−	0.564655i	$-0.190991\pi$
$373$	−205132.	−	355299.i	−0.0763416	−	0.132228i	−0.901669	+	0.432427i	$0.857657\pi$
$374$	520528.	−	901582.i	0.192427	−	0.333293i
$375$	−238895.	+	413778.i	−0.0877260	+	0.151946i
$376$	788416.	+	1.36558e6i	0.287598	+	0.498134i
$377$	−1.35517e6			−0.491065
$378$	−6.77749e6	+	9.67167e6i	−2.43972	+	3.48154i
$379$	494501.			0.176835			0.0884177	−	0.996083i	$-0.471819\pi$
$379$	494501.			0.176835			0.0884177	+	0.996083i	$0.471819\pi$
$380$	119267.	+	206577.i	0.0423703	+	0.0733875i
$381$	−3.43738e6	+	5.95372e6i	−1.21315	+	2.10124i
$382$	−1.95782e6	+	3.39104e6i	−0.686457	+	1.18898i
$383$	1.28561e6	+	2.22674e6i	0.447829	+	0.775663i	0.998244	−	0.0592278i	$-0.0188638\pi$
$383$	1.28561e6	+	2.22674e6i	0.447829	+	0.775663i	−0.550415	+	0.834891i	$0.685530\pi$
$384$	−6.68405e6			−2.31319
$385$	117434.	+	252081.i	0.0403778	+	0.0866738i
$386$	2.61539e6			0.893447
$387$	2.92008e6	+	5.05772e6i	0.991099	+	1.71663i
$388$	−113913.	+	197304.i	−0.0384145	+	0.0665358i
$389$	1.52511e6	−	2.64157e6i	0.511007	−	0.885091i	−0.488911	−	0.872334i	$-0.662606\pi$
$389$	1.52511e6	−	2.64157e6i	0.511007	−	0.885091i	0.999919	−	0.0127573i	$-0.00406088\pi$
$390$	−823243.	−	1.42590e6i	−0.274073	−	0.474709i
$391$	596040.			0.197167
$392$	−1.43368e6	+	1.70604e6i	−0.471236	+	0.560757i
$393$	9.50495e6			3.10433
$394$	837621.	+	1.45080e6i	0.271836	+	0.470834i
$395$	378273.	−	655189.i	0.121987	−	0.211287i
$396$	−356706.	+	617833.i	−0.114307	+	0.197985i
$397$	−1.73576e6	−	3.00642e6i	−0.552730	−	0.957357i	−0.998076	−	0.0619985i	$-0.980253\pi$
$397$	−1.73576e6	−	3.00642e6i	−0.552730	−	0.957357i	0.445346	−	0.895359i	$-0.353081\pi$
$398$	5.65372e6			1.78907
$399$	−1.32946e6	−	2.85378e6i	−0.418064	−	0.897404i
$400$	−790072.			−0.246897
$401$	−70459.3	−	122039.i	−0.0218815	−	0.0378999i	0.854877	−	0.518830i	$-0.173632\pi$
$401$	−70459.3	−	122039.i	−0.0218815	−	0.0378999i	−0.876759	+	0.480930i	$0.840299\pi$
$402$	2.08130e6	−	3.60491e6i	0.642345	−	1.11257i
$403$	−111418.	+	192982.i	−0.0341738	+	0.0591907i
$404$	727129.	+	1.25943e6i	0.221645	+	0.383901i
$405$	6.29277e6			1.90636
$406$	−2.06040e6	+	2.94024e6i	−0.620348	+	0.885254i
$407$	−255318.			−0.0764003
$408$	−3.70744e6	−	6.42147e6i	−1.10261	−	1.90978i
$409$	−349673.	+	605651.i	−0.103360	+	0.179025i	−0.913067	−	0.407809i	$-0.866293\pi$
$409$	−349673.	+	605651.i	−0.103360	+	0.179025i	0.809707	+	0.586835i	$0.199626\pi$
$410$	840648.	−	1.45604e6i	0.246976	−	0.427775i
$411$	260917.	+	451922.i	0.0761901	+	0.131965i
$412$	1.11870e6			0.324691
$413$	−134581.	−	11824.3i	−0.0388247	−	0.00341114i
$414$	−1.49635e6			−0.429076
$415$	−516994.	−	895460.i	−0.147355	−	0.255227i
$416$	672600.	−	1.16498e6i	0.190556	−	0.330053i
$417$	1.88794e6	−	3.27001e6i	0.531677	−	0.920892i
$418$	−226037.	−	391508.i	−0.0632761	−	0.109597i
$419$	−228295.			−0.0635274			−0.0317637	−	0.999495i	$-0.510112\pi$
$419$	−228295.			−0.0635274			−0.0317637	+	0.999495i	$0.510112\pi$
$420$	−1.18613e6	−	104214.i	−0.328103	−	0.0288271i
$421$	−2.57951e6			−0.709302			−0.354651	−	0.934999i	$-0.615400\pi$
$421$	−2.57951e6			−0.709302			−0.354651	+	0.934999i	$0.615400\pi$
$422$	1.50068e6	+	2.59926e6i	0.410211	+	0.710506i
$423$	4.11505e6	−	7.12748e6i	1.11821	−	1.93680i
$424$	2.07750e6	−	3.59833e6i	0.561210	−	0.972045i
$425$	−571509.	−	989882.i	−0.153480	−	0.265834i
$426$	−1.24281e7			−3.31804
$427$	−148900.	+	212484.i	−0.0395207	+	0.0563971i
$428$	−259354.			−0.0684358
$429$	425887.	+	737658.i	0.111725	+	0.193514i
$430$	−699837.	+	1.21215e6i	−0.182527	+	0.316145i
$431$	2.18365e6	−	3.78219e6i	0.566226	−	0.980731i	−0.430709	−	0.902491i	$-0.641736\pi$
$431$	2.18365e6	−	3.78219e6i	0.566226	−	0.980731i	0.996935	−	0.0782405i	$-0.0249302\pi$
$432$	8.67887e6	+	1.50322e7i	2.23745	+	3.87538i
$433$	−1.40410e6			−0.359896			−0.179948	−	0.983676i	$-0.557593\pi$
$433$	−1.40410e6			−0.359896			−0.179948	+	0.983676i	$0.557593\pi$
$434$	249304.	+	535148.i	0.0635337	+	0.136380i
$435$	3.19113e6			0.808577
$436$	131548.	+	227848.i	0.0331411	+	0.0574021i
$437$	129414.	−	224152.i	0.0324174	−	0.0561485i
$438$	1.79812e6	−	3.11444e6i	0.447851	−	0.775701i
$439$	2.40638e6	+	4.16797e6i	0.595940	+	1.03220i	0.993414	+	0.114584i	$0.0365536\pi$
$439$	2.40638e6	+	4.16797e6i	0.595940	+	1.03220i	−0.397474	+	0.917613i	$0.630113\pi$
$440$	284419.			0.0700369
$441$	1.14530e7	+	2.02818e6i	2.80429	+	0.496604i
$442$	3.93890e6			0.959001
$443$	1.58484e6	+	2.74502e6i	0.383686	+	0.664564i	0.991586	−	0.129450i	$-0.0413211\pi$
$443$	1.58484e6	+	2.74502e6i	0.383686	+	0.664564i	−0.607900	+	0.794014i	$0.707988\pi$
$444$	546594.	−	946729.i	0.131585	−	0.227913i
$445$	−1.44037e6	+	2.49479e6i	−0.344804	+	0.597219i
$446$	−2.69462e6	−	4.66722e6i	−0.641447	−	1.11102i
$447$	1.00011e6			0.236744
$448$	709579.	+	1.52316e6i	0.167034	+	0.358551i
$449$	−6.35197e6			−1.48694			−0.743469	−	0.668771i	$-0.766821\pi$
$449$	−6.35197e6			−1.48694			−0.743469	+	0.668771i	$0.766821\pi$
$450$	1.43477e6	+	2.48509e6i	0.334003	+	0.578510i
$451$	−434891.	+	753254.i	−0.100679	+	0.174381i
$452$	398432.	−	690104.i	0.0917293	−	0.158880i
$453$	−6.86621e6	−	1.18926e7i	−1.57207	−	2.72290i
$454$	8.40736e6			1.91434
$455$	−603822.	+	861672.i	−0.136735	+	0.195125i
$456$	−3.21988e6			−0.725149
$457$	−3.92590e6	−	6.79987e6i	−0.879325	−	1.52303i	−0.852083	−	0.523406i	$-0.824661\pi$
$457$	−3.92590e6	−	6.79987e6i	−0.879325	−	1.52303i	−0.0272411	−	0.999629i	$-0.508672\pi$
$458$	321308.	−	556522.i	0.0715745	−	0.123971i
$459$	−1.25559e7	+	2.17475e7i	−2.78175	+	4.81813i
$460$	−48945.7	−	84776.5i	−0.0107850	−	0.0186802i
$461$	−1.98815e6			−0.435710			−0.217855	−	0.975981i	$-0.569906\pi$
$461$	−1.98815e6			−0.435710			−0.217855	+	0.975981i	$0.569906\pi$
$462$	2.24798e6	+	197508.i	0.489991	+	0.0430506i
$463$	415445.			0.0900661			0.0450330	−	0.998985i	$-0.485661\pi$
$463$	415445.			0.0900661			0.0450330	+	0.998985i	$0.485661\pi$
$464$	2.63843e6	+	4.56989e6i	0.568918	+	0.985395i
$465$	262366.	−	454431.i	0.0562698	−	0.0974621i
$466$	−4.33255e6	+	7.50419e6i	−0.924227	+	1.60081i
$467$	−4.00168e6	−	6.93112e6i	−0.849083	−	1.47066i	−0.882027	−	0.471198i	$-0.843822\pi$
$467$	−4.00168e6	−	6.93112e6i	−0.849083	−	1.47066i	0.0329440	−	0.999457i	$-0.489512\pi$
$468$	−2.69924e6			−0.569674
$469$	−2.64987e6	−	232818.i	−0.556280	−	0.0488747i
$470$	1.97246e6			0.411873
$471$	484620.	+	839387.i	0.100658	+	0.174345i
$472$	−69086.4	+	119661.i	−0.0142737	+	0.0247228i
$473$	362046.	−	627082.i	0.0744065	−	0.128876i
$474$	−3.06958e6	−	5.31668e6i	−0.627529	−	1.08691i
$475$	−496351.			−0.100938
$476$	1.63471e6	−	2.33277e6i	0.330691	−	0.471906i
$477$	−2.16865e7			−4.36409
$478$	−1.67986e6	−	2.90960e6i	−0.336281	−	0.582456i
$479$	−35585.0	+	61635.0i	−0.00708644	+	0.0122741i	−0.869547	−	0.493850i	$-0.835589\pi$
$479$	−35585.0	+	61635.0i	−0.00708644	+	0.0122741i	0.862460	+	0.506124i	$0.168922\pi$
$480$	−1.58383e6	+	2.74328e6i	−0.313766	+	0.543458i
$481$	−483004.	−	836588.i	−0.0951893	−	0.164873i
$482$	−5.42791e6			−1.06418
$483$	545593.	+	1.17116e6i	0.106415	+	0.228427i
$484$	−1.84648e6			−0.358287
$485$	−237035.	−	410556.i	−0.0457570	−	0.0792535i
$486$	1.44637e7	−	2.50519e7i	2.77773	−	4.81117i
$487$	2.29111e6	−	3.96832e6i	0.437747	−	0.758200i	−0.559768	−	0.828649i	$-0.689110\pi$
$487$	2.29111e6	−	3.96832e6i	0.437747	−	0.758200i	0.997515	+	0.0704489i	$0.0224432\pi$
$488$	132683.	+	229813.i	0.0252211	+	0.0436842i
$489$	1.53261e7			2.89842
$490$	951478.	+	2.62017e6i	0.179023	+	0.492992i
$491$	5.97569e6			1.11863			0.559313	−	0.828957i	$-0.311065\pi$
$491$	5.97569e6			1.11863			0.559313	+	0.828957i	$0.311065\pi$
$492$	−1.86207e6	−	3.22519e6i	−0.346802	−	0.600679i
$493$	−3.81708e6	+	6.61138e6i	−0.707317	+	1.22511i
$494$	855225.	−	1.48129e6i	0.157675	−	0.273101i
$495$	−742247.	−	1.28561e6i	−0.136156	−	0.235828i
$496$	867696.			0.158367
$497$	3.35383e6	+	7.19924e6i	0.609047	+	1.30736i
$498$	−8.39053e6			−1.51606
$499$	−2.53107e6	−	4.38394e6i	−0.455043	−	0.788157i	0.543648	−	0.839313i	$-0.317043\pi$
$499$	−2.53107e6	−	4.38394e6i	−0.455043	−	0.788157i	−0.998691	+	0.0511562i	$0.983709\pi$
$500$	−93862.5	+	162575.i	−0.0167906	+	0.0290822i
$501$	−4.51736e6	+	7.82429e6i	−0.804063	+	1.39268i
$502$	1.99023e6	+	3.44718e6i	0.352488	+	0.610527i
$503$	−1.54242e6			−0.271820			−0.135910	−	0.990721i	$-0.543396\pi$
$503$	−1.54242e6			−0.271820			−0.135910	+	0.990721i	$0.543396\pi$
$504$	6.82675e6	−	9.74197e6i	1.19712	−	1.70832i
$505$	−3.02608e6			−0.528021
$506$	92762.9	+	160670.i	0.0161064	+	0.0278971i
$507$	4.06543e6	−	7.04152e6i	0.702403	−	1.21660i
$508$	−1.35056e6	+	2.33923e6i	−0.232196	+	0.402174i
$509$	2.10889e6	+	3.65271e6i	0.360794	+	0.624914i	0.988092	−	0.153866i	$-0.0491723\pi$
$509$	2.10889e6	+	3.65271e6i	0.360794	+	0.624914i	−0.627298	+	0.778780i	$0.715839\pi$
$510$	−9.27527e6			−1.57907
$511$	−2.28934e6	−	201142.i	−0.387845	−	0.0340761i
$512$	125493.			0.0211566
$513$	5.45237e6	+	9.44378e6i	0.914727	+	1.58435i
$514$	−4.76251e6	+	8.24890e6i	−0.795111	+	1.37717i
$515$	−1.16391e6	+	2.01596e6i	−0.193376	+	0.334937i
$516$	1.55017e6	+	2.68497e6i	0.256303	+	0.443930i
$517$	−1.02041e6			−0.167899
$518$	−2.54947e6	−	223996.i	−0.417470	−	0.0366789i
$519$	1.70214e6			0.277382
$520$	538058.	+	931943.i	0.0872611	+	0.151141i
$521$	−1.61888e6	+	2.80398e6i	−0.261289	+	0.452565i	−0.966585	−	0.256348i	$-0.917481\pi$
$521$	−1.61888e6	+	2.80398e6i	−0.261289	+	0.452565i	0.705296	+	0.708913i	$0.250814\pi$
$522$	9.58275e6	−	1.65978e7i	1.53927	−	2.66609i
$523$	4.12380e6	+	7.14263e6i	0.659240	+	1.14184i	0.980813	+	0.194952i	$0.0624550\pi$
$523$	4.12380e6	+	7.14263e6i	0.659240	+	1.14184i	−0.321573	+	0.946885i	$0.604212\pi$
$524$	3.73453e6			0.594165
$525$	1.42187e6	−	2.02906e6i	0.225145	−	0.321289i
$526$	−2.50242e6			−0.394363
$527$	627659.	+	1.08714e6i	0.0984459	+	0.170513i
$528$	1.65835e6	−	2.87235e6i	0.258876	−	0.448387i
$529$	3.16506e6	−	5.48205e6i	0.491748	−	0.851733i
$530$	−2.59874e6	−	4.50115e6i	−0.401859	−	0.696040i
$531$	721178.			0.110996
$532$	−522349.	−	1.12126e6i	−0.0800169	−	0.171762i
$533$	−3.29087e6			−0.501756
$534$	1.16882e7	+	2.02445e7i	1.77375	+	3.07223i
$535$	269837.	−	467371.i	0.0407583	−	0.0705955i
$536$	−1.36030e6	+	2.35611e6i	−0.204514	+	0.354228i
$537$	7.77767e6	+	1.34713e7i	1.16389	+	2.01592i
$538$	6.26157e6			0.932669
$539$	−492227.	−	1.35549e6i	−0.0729783	−	0.200967i
$540$	4.12428e6			0.608645
$541$	−6.50463e6	−	1.12663e7i	−0.955497	−	1.65497i	−0.733228	−	0.679983i	$-0.761987\pi$
$541$	−6.50463e6	−	1.12663e7i	−0.955497	−	1.65497i	−0.222269	−	0.974985i	$-0.571346\pi$
$542$	−6.12760e6	+	1.06133e7i	−0.895967	+	1.55186i
$543$	1.10962e7	−	1.92192e7i	1.61501	−	2.79727i
$544$	−3.78901e6	−	6.56275e6i	−0.548944	−	0.950799i
$545$	−547459.			−0.0789515
$546$	3.60552e6	+	7.73951e6i	0.517591	+	1.11105i
$547$	1.06475e7			1.52152			0.760762	−	0.649031i	$-0.224825\pi$
$547$	1.06475e7			1.52152			0.760762	+	0.649031i	$0.224825\pi$
$548$	102515.	+	177562.i	0.0145827	+	0.0252579i
$549$	692522.	−	1.19948e6i	0.0980624	−	0.169849i
$550$	177890.	−	308115.i	0.0250752	−	0.0434316i
$551$	1.65755e6	+	2.87096e6i	0.232588	+	0.402855i
$552$	1.32140e6			0.184581
$553$	−2.25144e6	+	3.21287e6i	−0.313075	+	0.446766i
$554$	−1.14746e7			−1.58841
$555$	1.13737e6	+	1.96999e6i	0.156737	+	0.271476i
$556$	741778.	−	1.28480e6i	0.101762	−	0.176258i
$557$	−1.90304e6	+	3.29616e6i	−0.259902	+	0.450163i	−0.966215	−	0.257736i	$-0.917023\pi$
$557$	−1.90304e6	+	3.29616e6i	−0.259902	+	0.450163i	0.706314	+	0.707899i	$0.250357\pi$
$558$	−1.57573e6	−	2.72925e6i	−0.214239	−	0.371072i
$559$	2.73964e6			0.370821
$560$	4.08133e6	+	358586.i	0.549961	+	0.0483196i
$561$	4.79837e6			0.643704
$562$	−4.48053e6	−	7.76051e6i	−0.598396	−	1.03645i
$563$	−3.65208e6	+	6.32559e6i	−0.485589	+	0.841066i	−0.999863	−	0.0165606i	$-0.994728\pi$
$563$	−3.65208e6	+	6.32559e6i	−0.485589	+	0.841066i	0.514273	+	0.857626i	$0.328062\pi$
$564$	2.18454e6	−	3.78373e6i	0.289175	−	0.500867i
$565$	829072.	+	1.43599e6i	0.109262	+	0.189248i
$566$	7.73911e6			1.01543
$567$	−3.25070e7	−	2.85606e6i	−4.24638	−	0.373087i
$568$	8.12281e6			1.05642
$569$	−1.45437e6	−	2.51904e6i	−0.188319	−	0.326177i	0.756371	−	0.654143i	$-0.226970\pi$
$569$	−1.45437e6	−	2.51904e6i	−0.188319	−	0.326177i	−0.944690	+	0.327965i	$0.893637\pi$
$570$	−2.01387e6	+	3.48813e6i	−0.259624	+	0.449682i
$571$	−1.34893e6	+	2.33641e6i	−0.173141	+	0.299888i	−0.939516	−	0.342504i	$-0.888725\pi$
$571$	−1.34893e6	+	2.33641e6i	−0.173141	+	0.299888i	0.766376	+	0.642393i	$0.222058\pi$
$572$	167333.	+	289828.i	0.0213841	+	0.0370383i
$573$	−1.80477e7			−2.29633
$574$	−5.00344e6	+	7.14005e6i	−0.633854	+	0.904527i
$575$	203696.			0.0256929
$576$	−4.48492e6	−	7.76811e6i	−0.563247	−	0.975572i
$577$	7.11015e6	−	1.23151e7i	0.889077	−	1.53993i	0.0481079	−	0.998842i	$-0.484681\pi$
$577$	7.11015e6	−	1.23151e7i	0.889077	−	1.53993i	0.840969	−	0.541084i	$-0.181986\pi$
$578$	6.38474e6	−	1.10587e7i	0.794920	−	1.37684i
$579$	6.02735e6	+	1.04397e7i	0.747188	+	1.29417i
$580$	1.25381e6			0.154761
$581$	2.26426e6	+	4.86039e6i	0.278282	+	0.597352i
$582$	−3.84694e6			−0.470770
$583$	1.34440e6	+	2.32858e6i	0.163817	+	0.283739i
$584$	−1.17522e6	+	2.03554e6i	−0.142590	+	0.246972i
$585$	2.80833e6	−	4.86418e6i	0.339281	−	0.587651i
$586$	−4.01821e6	−	6.95974e6i	−0.483380	−	0.837239i
$587$	115775.			0.0138682			0.00693411	−	0.999976i	$-0.497793\pi$
$587$	115775.			0.0138682			0.00693411	+	0.999976i	$0.497793\pi$
$588$	6.08000e6	+	1.07669e6i	0.725204	+	0.128424i
$589$	545117.			0.0647443
$590$	86420.2	+	149684.i	0.0102208	+	0.0177030i
$591$	−3.86070e6	+	6.68693e6i	−0.454671	+	0.787514i
$592$	−1.88076e6	+	3.25757e6i	−0.220561	+	0.382023i
$593$	−5.56845e6	−	9.64484e6i	−0.650276	−	1.12631i	−0.983056	−	0.183306i	$-0.941320\pi$
$593$	−5.56845e6	−	9.64484e6i	−0.650276	−	1.12631i	0.332780	−	0.943004i	$-0.392013\pi$
$594$	−7.81642e6			−0.908954
$595$	2.50301e6	+	5.37289e6i	0.289848	+	0.622180i
$596$	392947.			0.0453125
$597$	1.30294e7	+	2.25675e7i	1.49619	+	2.59148i
$598$	−350974.	+	607904.i	−0.0401348	+	0.0695156i
$599$	445552.	−	771718.i	0.0507377	−	0.0878803i	−0.839541	−	0.543296i	$-0.817176\pi$
$599$	445552.	−	771718.i	0.0507377	−	0.0878803i	0.890279	+	0.455416i	$0.150509\pi$
$600$	−1.26701e6	−	2.19453e6i	−0.143682	−	0.248865i
$601$	3.38207e6			0.381941			0.190971	−	0.981596i	$-0.438836\pi$
$601$	3.38207e6			0.381941			0.190971	+	0.981596i	$0.438836\pi$
$602$	4.16535e6	−	5.94408e6i	0.468447	−	0.668488i
$603$	1.41999e7			1.59034
$604$	−2.69776e6	−	4.67265e6i	−0.300892	−	0.521160i
$605$	1.92111e6	−	3.32746e6i	0.213385	−	0.369594i
$606$	−1.22779e7	+	2.12659e7i	−1.35813	+	2.35235i
$607$	−3.24412e6	−	5.61898e6i	−0.357376	−	0.618993i	0.630146	−	0.776477i	$-0.282995\pi$
$607$	−3.24412e6	−	5.61898e6i	−0.357376	−	0.618993i	−0.987522	+	0.157484i	$0.949662\pi$
$608$	−3.29072e6			−0.361021
$609$	−1.64847e7	−	1.44834e6i	−1.80110	−	0.158244i
$610$	331945.			0.0361195
$611$	−1.93039e6	−	3.34353e6i	−0.209191	−	0.362329i
$612$	−7.60290e6	+	1.31686e7i	−0.820542	+	1.42122i
$613$	2.24742e6	−	3.89264e6i	0.241564	−	0.418402i	−0.719596	−	0.694393i	$-0.755673\pi$
$613$	2.24742e6	−	3.89264e6i	0.241564	−	0.418402i	0.961160	+	0.275992i	$0.0890062\pi$
$614$	−4.58620e6	−	7.94353e6i	−0.490944	−	0.850340i
$615$	7.74931e6			0.826181
$616$	−1.46924e6	−	129088.i	−0.156006	−	0.0137067i
$617$	−3.99996e6			−0.423003			−0.211501	−	0.977378i	$-0.567835\pi$
$617$	−3.99996e6			−0.423003			−0.211501	+	0.977378i	$0.567835\pi$
$618$	9.44484e6	+	1.63589e7i	0.994772	+	1.72300i
$619$	6.31588e6	−	1.09394e7i	0.662533	−	1.14754i	−0.317415	−	0.948287i	$-0.602815\pi$
$619$	6.31588e6	−	1.09394e7i	0.662533	−	1.14754i	0.979948	−	0.199254i	$-0.0638517\pi$
$620$	103084.	−	178547.i	0.0107700	−	0.0186541i
$621$	−2.23758e6	−	3.87561e6i	−0.232836	−	0.403284i
$622$	1.91475e7			1.98443
$623$	8.57290e6	−	1.22338e7i	0.884927	−	1.26282i
$624$	1.25489e7			1.29017
$625$	−195312.	−	338291.i	−0.0200000	−	0.0346410i
$626$	−7.17890e6	+	1.24342e7i	−0.732187	+	1.26819i
$627$	1.04184e6	−	1.80451e6i	0.105835	−	0.183312i
$628$	190409.	+	329798.i	0.0192659	+	0.0333694i
$629$	−5.44189e6			−0.548432
$630$	−6.28379e6	−	1.34886e7i	−0.630769	−	1.35399i
$631$	−3.30584e6			−0.330528			−0.165264	−	0.986249i	$-0.552848\pi$
$631$	−3.30584e6			−0.330528			−0.165264	+	0.986249i	$0.552848\pi$
$632$	2.00623e6	+	3.47489e6i	0.199796	+	0.346058i
$633$	−6.91684e6	+	1.19803e7i	−0.686117	+	1.18839i
$634$	5.14592e6	−	8.91299e6i	0.508440	−	0.880644i
$635$	−2.81029e6	−	4.86757e6i	−0.276577	−	0.479046i
$636$	−1.15126e7			−1.12858
$637$	3.51029e6	−	4.17715e6i	0.342763	−	0.407879i
$638$	−2.37624e6			−0.231120
$639$	−2.11981e7	−	3.67161e7i	−2.05373	−	3.55717i
$640$	2.73233e6	−	4.73254e6i	0.263684	−	0.456714i
$641$	7.78917e6	−	1.34912e7i	0.748766	−	1.29690i	−0.199649	−	0.979868i	$-0.563980\pi$
$641$	7.78917e6	−	1.34912e7i	0.748766	−	1.29690i	0.948415	−	0.317033i	$-0.102687\pi$
$642$	−2.18965e6	−	3.79258e6i	−0.209670	−	0.363160i
$643$	504385.			0.0481100			0.0240550	−	0.999711i	$-0.492342\pi$
$643$	504385.			0.0481100			0.0240550	+	0.999711i	$0.492342\pi$
$644$	214365.	+	460151.i	0.0203676	+	0.0437205i
$645$	−6.45128e6			−0.610586
$646$	−4.81780e6	−	8.34468e6i	−0.454221	−	0.786735i
$647$	−1.84720e6	+	3.19944e6i	−0.173481	+	0.300479i	−0.939635	−	0.342179i	$-0.888835\pi$
$647$	−1.84720e6	+	3.19944e6i	−0.173481	+	0.300479i	0.766153	+	0.642658i	$0.222168\pi$
$648$	−1.66873e7	+	2.89033e7i	−1.56116	+	2.70402i
$649$	−44707.7	−	77436.0i	−0.00416649	−	0.00721657i
$650$	1.34611e6			0.124968
$651$	−1.56157e6	+	2.22841e6i	−0.144414	+	0.206083i
$652$	6.02169e6			0.554753
$653$	−5.83708e6	−	1.01101e7i	−0.535689	−	0.927840i	−0.999130	−	0.0417125i	$-0.986719\pi$
$653$	−5.83708e6	−	1.01101e7i	−0.535689	−	0.927840i	0.463441	−	0.886128i	$-0.346615\pi$
$654$	−2.22124e6	+	3.84730e6i	−0.203072	+	0.351732i
$655$	−3.88547e6	+	6.72983e6i	−0.353867	+	0.612916i
$656$	6.40712e6	+	1.10975e7i	0.581304	+	1.00685i
$657$	1.22679e7			1.10881
$658$	−1.01893e7	−	895230.i	−0.917443	−	0.0806065i
$659$	−2.88804e6			−0.259054			−0.129527	−	0.991576i	$-0.541346\pi$
$659$	−2.88804e6			−0.259054			−0.129527	+	0.991576i	$0.541346\pi$
$660$	−394033.	−	682485.i	−0.0352105	−	0.0609864i
$661$	8.46705e6	−	1.46654e7i	0.753752	−	1.30554i	−0.192240	−	0.981348i	$-0.561575\pi$
$661$	8.46705e6	−	1.46654e7i	0.753752	−	1.30554i	0.945992	−	0.324189i	$-0.105091\pi$
$662$	−6.57525e6	+	1.13887e7i	−0.583133	+	1.01002i
$663$	9.07744e6	+	1.57226e7i	0.802010	+	1.38912i
$664$	5.48391e6			0.482692
$665$	2.56404e6	+	225276.i	0.224838	+	0.0197543i
$666$	1.36618e7			1.19350
$667$	−680238.	−	1.17821e6i	−0.0592034	−	0.102543i
$668$	−1.77488e6	+	3.07419e6i	−0.153897	+	0.266557i
$669$	1.24199e7	−	2.15118e7i	1.07288	−	1.85828i
$670$	1.70160e6	+	2.94726e6i	0.146444	+	0.253648i
$671$	−171725.			−0.0147240
$672$	9.42679e6	−	1.34523e7i	0.805268	−	1.14914i
$673$	−1.63004e7			−1.38727			−0.693633	−	0.720329i	$-0.743991\pi$
$673$	−1.63004e7			−1.38727			−0.693633	+	0.720329i	$0.743991\pi$
$674$	2.41452e6	+	4.18207e6i	0.204730	+	0.354602i
$675$	−4.29098e6	+	7.43219e6i	−0.362491	+	0.627853i
$676$	1.59732e6	−	2.76664e6i	0.134439	−	0.232855i
$677$	7.29159e6	+	1.26294e7i	0.611435	+	1.05904i	0.990999	+	0.133871i	$0.0427408\pi$
$677$	7.29159e6	+	1.26294e7i	0.611435	+	1.05904i	−0.379564	+	0.925166i	$0.623926\pi$
$678$	1.34554e7			1.12414
$679$	1.03813e6	+	2.22842e6i	0.0864127	+	0.185491i
$680$	6.06216e6			0.502754
$681$	1.93753e7	+	3.35590e7i	1.60096	+	2.77295i
$682$	−195368.	+	338387.i	−0.0160839	+	0.0278582i
$683$	−5.38162e6	+	9.32124e6i	−0.441429	+	0.764578i	−0.997796	−	0.0663588i	$-0.978862\pi$
$683$	−5.38162e6	+	9.32124e6i	−0.441429	+	0.764578i	0.556366	+	0.830937i	$0.312195\pi$
$684$	3.30153e6	+	5.71842e6i	0.269820	+	0.467343i
$685$	−426635.			−0.0347400
$686$	−3.72592e6	−	1.39671e7i	−0.302289	−	1.13317i
$687$	2.96190e6			0.239430
$688$	−5.33392e6	−	9.23862e6i	−0.429611	−	0.744108i
$689$	−5.08663e6	+	8.81029e6i	−0.408208	+	0.707037i
$690$	826469.	−	1.43149e6i	0.0660851	−	0.114463i
$691$	6.55799e6	+	1.13588e7i	0.522487	+	0.904974i	0.999658	+	0.0261633i	$0.00832898\pi$
$691$	6.55799e6	+	1.13588e7i	0.522487	+	0.904974i	−0.477171	+	0.878811i	$0.658338\pi$
$692$	668778.			0.0530905
$693$	3.25079e6	+	6.97805e6i	0.257132	+	0.551952i
$694$	−2.42910e7			−1.91446
$695$	1.54352e6	+	2.67345e6i	0.121213	+	0.209947i
$696$	−8.46232e6	+	1.46572e7i	−0.662165	+	1.14690i
$697$	−9.26935e6	+	1.60550e7i	−0.722716	+	1.25178i
$698$	8.02614e6	+	1.39017e7i	0.623545	+	1.08001i
$699$	−3.99385e7			−3.09171
$700$	558659.	−	797222.i	0.0430925	−	0.0614942i
$701$	1.60167e7			1.23106			0.615528	−	0.788115i	$-0.288943\pi$
$701$	1.60167e7			1.23106			0.615528	+	0.788115i	$0.288943\pi$
$702$	−1.47869e7	−	2.56117e7i	−1.13249	−	1.96153i
$703$	−1.18156e6	+	2.04652e6i	−0.0901710	+	0.156181i
$704$	−556064.	+	963131.i	−0.0422856	+	0.0732409i
$705$	4.54566e6	+	7.87332e6i	0.344449	+	0.596603i
$706$	−8.47659e6			−0.640043
$707$	1.56320e7	+	1.37343e6i	1.17616	+	0.103337i
$708$	382848.			0.0287040
$709$	−14609.4	−	25304.2i	−0.00109148	−	0.00189050i	0.865479	−	0.500945i	$-0.167014\pi$
$709$	−14609.4	−	25304.2i	−0.00109148	−	0.00189050i	−0.866571	+	0.499054i	$0.833681\pi$
$710$	5.08041e6	−	8.79953e6i	0.378227	−	0.655109i
$711$	1.04713e7	−	1.81368e7i	0.776831	−	1.34551i
$712$	−7.63919e6	−	1.32315e7i	−0.564738	−	0.978156i
$713$	−223709.			−0.0164801
$714$	4.79139e7	+	4.20972e6i	3.51736	+	0.309035i
$715$	−696383.			−0.0509429
$716$	3.05587e6	+	5.29293e6i	0.222768	+	0.385845i
$717$	7.74267e6	−	1.34107e7i	0.562462	−	0.974213i
$718$	−6.57565e6	+	1.13894e7i	−0.476023	+	0.824496i
$719$	9.69869e6	+	1.67986e7i	0.699666	+	1.21186i	0.968582	+	0.248694i	$0.0800012\pi$
$719$	9.69869e6	+	1.67986e7i	0.699666	+	1.21186i	−0.268916	+	0.963164i	$0.586665\pi$
$720$	−2.18706e7			−1.57228
$721$	6.92749e6	−	9.88573e6i	0.496293	−	0.708224i
$722$	1.22430e7			0.874071
$723$	−1.25090e7	−	2.16662e7i	−0.889972	−	1.54148i
$724$	4.35973e6	−	7.55127e6i	0.309110	−	0.535394i
$725$	−1.30448e6	+	2.25943e6i	−0.0921708	+	0.159644i
$726$	−1.55893e7	−	2.70014e7i	−1.09770	−	1.90128i
$727$	−1.41427e7			−0.992424			−0.496212	−	0.868201i	$-0.665276\pi$
$727$	−1.41427e7			−0.992424			−0.496212	+	0.868201i	$0.665276\pi$
$728$	−2.35651e6	−	5.05841e6i	−0.164794	−	0.353741i
$729$	7.21649e7			5.02930
$730$	1.47009e6	+	2.54626e6i	0.102102	+	0.176846i
$731$	7.71672e6	−	1.33657e7i	0.534121	−	0.925124i
$732$	367635.	−	636763.i	0.0253594	−	0.0439238i
$733$	8.83743e6	+	1.53069e7i	0.607528	+	1.05227i	0.991647	+	0.128985i	$0.0411719\pi$
$733$	8.83743e6	+	1.53069e7i	0.607528	+	1.05227i	−0.384119	+	0.923284i	$0.625495\pi$
$734$	−1.87574e7			−1.28509
$735$	−8.26600e6	+	9.83630e6i	−0.564387	+	0.671604i
$736$	1.35047e6			0.0918947
$737$	−880287.	−	1.52470e6i	−0.0596974	−	0.103399i
$738$	2.32706e7	−	4.03059e7i	1.57278	−	2.72413i
$739$	−6.94529e6	+	1.20296e7i	−0.467821	+	0.810289i	−0.999324	−	0.0367670i	$-0.988294\pi$
$739$	−6.94529e6	+	1.20296e7i	−0.467821	+	0.810289i	0.531503	+	0.847056i	$0.321627\pi$
$740$	446878.	+	774015.i	0.0299992	+	0.0519601i
$741$	7.88368e6			0.527453
$742$	1.13816e7	+	2.44314e7i	0.758915	+	1.62907i
$743$	−6.42472e6			−0.426955			−0.213477	−	0.976948i	$-0.568479\pi$
$743$	−6.42472e6			−0.426955			−0.213477	+	0.976948i	$0.568479\pi$
$744$	1.39150e6	+	2.41014e6i	0.0921615	+	0.159628i
$745$	−408829.	+	708113.i	−0.0269868	+	0.0467425i
$746$	1.36091e6	−	2.35717e6i	0.0895331	−	0.155076i
$747$	−1.43113e7	−	2.47880e7i	−0.938380	−	1.62532i
$748$	1.88529e6			0.123204
$749$	−1.60604e6	+	2.29186e6i	−0.104605	+	0.149274i
$750$	−3.16981e6			−0.205769
$751$	−1.05776e7	−	1.83209e7i	−0.684364	−	1.18535i	−0.973636	−	0.228107i	$-0.926746\pi$
$751$	−1.05776e7	−	1.83209e7i	−0.684364	−	1.18535i	0.289272	−	0.957247i	$-0.406587\pi$
$752$	−7.51670e6	+	1.30193e7i	−0.484711	+	0.839544i
$753$	−9.17324e6	+	1.58885e7i	−0.589570	+	1.02116i
$754$	−4.49531e6	−	7.78611e6i	−0.287960	−	0.498761i
$755$	1.12272e7			0.716809
$756$	−2.13051e7	−	1.87187e6i	−1.35575	−	0.119116i
$757$	−7.71120e6			−0.489083			−0.244541	−	0.969639i	$-0.578637\pi$
$757$	−7.71120e6			−0.489083			−0.244541	+	0.969639i	$0.578637\pi$
$758$	1.64034e6	+	2.84116e6i	0.103696	+	0.179607i
$759$	−427556.	+	740549.i	−0.0269395	+	0.0466605i
$760$	1.31623e6	−	2.27979e6i	0.0826607	−	0.143173i
$761$	2.00832e6	+	3.47850e6i	0.125710	+	0.217736i	0.922010	−	0.387165i	$-0.126546\pi$
$761$	2.00832e6	+	3.47850e6i	0.125710	+	0.217736i	−0.796300	+	0.604902i	$0.793212\pi$
$762$	−4.56094e7			−2.84556
$763$	2.82805e6	+	248472.i	0.175863	+	0.0154514i
$764$	−7.09098e6			−0.439514
$765$	−1.58204e7	−	2.74017e7i	−0.977381	−	1.69287i
$766$	−8.52917e6	+	1.47730e7i	−0.525213	+	0.909695i
$767$	169154.	−	292983.i	0.0103823	−	0.0179827i
$768$	−1.58307e7	−	2.74196e7i	−0.968494	−	1.67748i
$769$	1.66044e7			1.01253			0.506265	−	0.862378i	$-0.331026\pi$
$769$	1.66044e7			1.01253			0.506265	+	0.862378i	$0.331026\pi$
$770$	−1.05878e6	+	1.51091e6i	−0.0643546	+	0.0918358i
$771$	−4.39020e7			−2.65980
$772$	2.36816e6	+	4.10178e6i	0.143011	+	0.247702i
$773$	−6.29598e6	+	1.09050e7i	−0.378979	+	0.656410i	−0.990914	−	0.134498i	$-0.957058\pi$
$773$	−6.29598e6	+	1.09050e7i	−0.378979	+	0.656410i	0.611935	+	0.790908i	$0.290391\pi$
$774$	−1.93728e7	+	3.35546e7i	−1.16236	+	2.01326i
$775$	214502.	+	371528.i	0.0128285	+	0.0222197i
$776$	2.51430e6			0.149887
$777$	−4.98130e6	−	1.06927e7i	−0.295999	−	0.635384i
$778$	2.02362e7			1.19861
$779$	4.02518e6	+	6.97181e6i	0.237652	+	0.411625i
$780$	1.49085e6	−	2.58222e6i	0.0877397	−	0.151970i
$781$	−2.62824e6	+	4.55225e6i	−0.154184	+	0.267054i
$782$	1.97717e6	+	3.42455e6i	0.115618	+	0.200257i
$783$	5.73185e7			3.34111
$784$	−2.09205e7	−	3.70475e6i	−1.21557	−	0.215262i
$785$	−792420.			−0.0458967
$786$	3.15295e7	+	5.46107e7i	1.82038	+	3.15298i
$787$	−1.34283e6	+	2.32585e6i	−0.0772829	+	0.133858i	−0.902077	−	0.431576i	$-0.857958\pi$
$787$	−1.34283e6	+	2.32585e6i	−0.0772829	+	0.133858i	0.824794	+	0.565434i	$0.191291\pi$
$788$	−1.51688e6	+	2.62732e6i	−0.0870235	+	0.150729i
$789$	−5.76699e6	−	9.98871e6i	−0.329804	−	0.571238i
$790$	5.01919e6			0.286131
$791$	−3.63105e6	−	7.79430e6i	−0.206343	−	0.442931i
$792$	7.87324e6			0.446006
$793$	−324865.	−	562683.i	−0.0183451	−	0.0317747i
$794$	1.15156e7	−	1.99456e7i	0.648240	−	1.12278i
$795$	1.19779e7	−	2.07464e7i	0.672147	−	1.16419i
$796$	5.11928e6	+	8.86686e6i	0.286369	+	0.496006i
$797$	−3.05957e7			−1.70614			−0.853070	−	0.521796i	$-0.825262\pi$
$797$	−3.05957e7			−1.70614			−0.853070	+	0.521796i	$0.825262\pi$
$798$	1.19864e7	−	1.71049e7i	0.666316	−	0.950851i
$799$	−2.17492e7			−1.20525
$800$	−1.29489e6	−	2.24281e6i	−0.0715332	−	0.123899i
$801$	−3.98719e7	+	6.90602e7i	−2.19577	+	3.80318i
$802$	467450.	−	809648.i	0.0256625	−	0.0444488i
$803$	−760518.	−	1.31726e6i	−0.0416218	−	0.0720910i
$804$	7.53821e6			0.411271
$805$	−1.05225e6	−	92450.5i	−0.0572306	−	0.00502828i
$806$	−1.47837e6			−0.0801577
$807$	1.44302e7	+	2.49938e7i	0.779989	+	1.35098i
$808$	8.02462e6	−	1.38990e7i	0.432410	−	0.748957i
$809$	189987.	−	329067.i	0.0102059	−	0.0176772i	−0.860877	−	0.508813i	$-0.830085\pi$
$809$	189987.	−	329067.i	0.0102059	−	0.0176772i	0.871083	+	0.491135i	$0.163418\pi$
$810$	2.08742e7	+	3.61551e7i	1.11788	+	1.93623i
$811$	2.19008e7			1.16925			0.584625	−	0.811304i	$-0.301242\pi$
$811$	2.19008e7			1.16925			0.584625	+	0.811304i	$0.301242\pi$
$812$	−6.47688e6	−	569058.i	−0.344727	−	0.0302877i
$813$	−5.64858e7			−2.99718
$814$	−846932.	−	1.46693e6i	−0.0448010	−	0.0775975i
$815$	−6.26508e6	+	1.08514e7i	−0.330394	+	0.572260i
$816$	3.53465e7	−	6.12218e7i	1.85832	−	3.21870i
$817$	−3.35095e6	−	5.80402e6i	−0.175636	−	0.304210i
$818$	−4.63969e6			−0.242441
$819$	−1.67149e7	+	2.38526e7i	−0.870751	+	1.24259i
$820$	3.04473e6			0.158130
$821$	−7.23744e6	−	1.25356e7i	−0.374737	−	0.649064i	0.615550	−	0.788098i	$-0.288934\pi$
$821$	−7.23744e6	−	1.25356e7i	−0.374737	−	0.649064i	−0.990288	+	0.139033i	$0.955600\pi$
$822$	−1.73101e6	+	2.99820e6i	−0.0893554	+	0.154768i
$823$	−3.81676e6	+	6.61082e6i	−0.196424	+	0.340217i	−0.947366	−	0.320151i	$-0.896266\pi$
$823$	−3.81676e6	+	6.61082e6i	−0.196424	+	0.340217i	0.750942	+	0.660368i	$0.229600\pi$
$824$	−6.17299e6	−	1.06919e7i	−0.316722	−	0.548578i
$825$	1.63984e6			0.0838814
$826$	−378491.	−	812458.i	−0.0193021	−	0.0414334i
$827$	2.35052e7			1.19509			0.597545	−	0.801835i	$-0.296143\pi$
$827$	2.35052e7			1.19509			0.597545	+	0.801835i	$0.296143\pi$
$828$	−1.35491e6	−	2.34677e6i	−0.0686805	−	0.118958i
$829$	−24966.6	+	43243.4i	−0.00126175	+	0.00218541i	−0.866656	−	0.498907i	$-0.833735\pi$
$829$	−24966.6	+	43243.4i	−0.00126175	+	0.00218541i	0.865394	+	0.501092i	$0.167068\pi$
$830$	3.42991e6	−	5.94078e6i	0.172817	−	0.299329i
$831$	−2.64439e7	−	4.58022e7i	−1.32838	−	2.30083i
$832$	−4.20780e6			−0.210740
$833$	−1.04914e7	−	2.88912e7i	−0.523868	−	1.44262i
$834$	2.50505e7			1.24710
$835$	−3.69324e6	−	6.39689e6i	−0.183312	−	0.317506i
$836$	409341.	−	708999.i	0.0202567	−	0.0350857i
$837$	4.71257e6	−	8.16241e6i	0.232511	−	0.402721i
$838$	−757292.	−	1.31167e6i	−0.0372523	−	0.0645229i
$839$	1.73936e7			0.853071			0.426536	−	0.904471i	$-0.359734\pi$
$839$	1.73936e7			0.853071			0.426536	+	0.904471i	$0.359734\pi$
$840$	5.54908e6	+	1.19115e7i	0.271346	+	0.582463i
$841$	−3.08600e6			−0.150455
$842$	−8.55666e6	−	1.48206e7i	−0.415933	−	0.720418i
$843$	2.06514e7	−	3.57692e7i	1.00087	−	1.73357i
$844$	−2.71765e6	+	4.70710e6i	−0.131322	+	0.227456i
$845$	3.32376e6	+	5.75692e6i	0.160136	+	0.277363i
$846$	5.46013e7			2.62287
$847$	−1.14342e7	+	1.63170e7i	−0.547644	+	0.781504i
$848$	3.96134e7			1.89170
$849$	1.78353e7	+	3.08916e7i	0.849201	+	1.47086i
$850$	3.79158e6	−	6.56721e6i	0.180000	−	0.311770i
$851$	484897.	−	839866.i	0.0229523	−	0.0397545i
$852$	−1.12533e7	−	1.94913e7i	−0.531105	−	0.919902i
$853$	1.10470e6			0.0519843			0.0259922	−	0.999662i	$-0.491726\pi$
$853$	1.10470e6			0.0519843			0.0259922	+	0.999662i	$0.491726\pi$
$854$	−1.71475e6	−	150658.i	−0.0804557	−	0.00706884i
$855$	−1.37399e7			−0.642788
$856$	1.43112e6	+	2.47877e6i	0.0667561	+	0.115625i
$857$	1.78578e7	−	3.09306e7i	0.830568	−	1.43859i	−0.0670207	−	0.997752i	$-0.521349\pi$
$857$	1.78578e7	−	3.09306e7i	0.830568	−	1.43859i	0.897589	−	0.440834i	$-0.145317\pi$
$858$	−2.82548e6	+	4.89387e6i	−0.131031	+	0.226952i
$859$	1.14999e7	+	1.99184e7i	0.531754	+	0.921025i	0.999313	+	0.0370628i	$0.0118001\pi$
$859$	1.14999e7	+	1.99184e7i	0.531754	+	0.921025i	−0.467559	+	0.883962i	$0.654867\pi$
$860$	−2.53473e6			−0.116865
$861$	−4.00312e7	−	3.51714e6i	−1.84031	−	0.161689i
$862$	2.89741e7			1.32813
$863$	−1.10481e6	−	1.91359e6i	−0.0504966	−	0.0874626i	0.839672	−	0.543093i	$-0.182747\pi$
$863$	−1.10481e6	−	1.91359e6i	−0.0504966	−	0.0874626i	−0.890169	+	0.455631i	$0.849414\pi$
$864$	−2.84485e7	+	4.92742e7i	−1.29651	+	2.24561i
$865$	−695809.	+	1.20518e6i	−0.0316191	+	0.0547659i
$866$	−4.65762e6	−	8.06724e6i	−0.211042	−	0.365536i
$867$	5.88562e7			2.65916
$868$	−613547.	+	875549.i	−0.0276407	+	0.0394440i
$869$	−2.59657e6			−0.116641
$870$	1.05855e7	+	1.83346e7i	0.474148	+	0.821248i
$871$	3.33061e6	−	5.76879e6i	0.148757	−	0.257656i
$872$	1.45177e6	−	2.51453e6i	0.0646554	−	0.111987i
$873$	−6.56155e6	−	1.13649e7i	−0.291388	−	0.504698i
$874$	1.71715e6			0.0760379
$875$	855402.	+	1.83618e6i	0.0377703	+	0.0810766i
$876$	6.51259e6			0.286743
$877$	1.15380e7	+	1.99845e7i	0.506563	+	0.877393i	0.999971	+	0.00759488i	$0.00241755\pi$
$877$	1.15380e7	+	1.99845e7i	0.506563	+	0.877393i	−0.493408	+	0.869798i	$0.664249\pi$
$878$	−1.59647e7	+	2.76517e7i	−0.698916	+	1.21056i
$879$	1.85205e7	−	3.20784e7i	0.808499	−	1.40036i
$880$	1.35582e6	+	2.34834e6i	0.0590193	+	0.102224i
$881$	−3.23900e7			−1.40596			−0.702978	−	0.711212i	$-0.748147\pi$
$881$	−3.23900e7			−1.40596			−0.702978	+	0.711212i	$0.748147\pi$
$882$	2.63386e7	+	7.25311e7i	1.14004	+	3.13944i
$883$	1.16517e7			0.502906			0.251453	−	0.967870i	$-0.419092\pi$
$883$	1.16517e7			0.502906			0.251453	+	0.967870i	$0.419092\pi$
$884$	3.56656e6	+	6.17746e6i	0.153504	+	0.265876i
$885$	−398322.	+	689914.i	−0.0170953	+	0.0296099i
$886$	−1.05144e7	+	1.82114e7i	−0.449986	+	0.779398i
$887$	−3.43202e6	−	5.94444e6i	−0.146467	−	0.253689i	0.783452	−	0.621452i	$-0.213457\pi$
$887$	−3.43202e6	−	5.94444e6i	−0.146467	−	0.253689i	−0.929919	+	0.367763i	$0.880124\pi$
$888$	−1.20645e7			−0.513423
$889$	1.23081e7	+	2.64202e7i	0.522320	+	1.12120i
$890$	−1.91117e7			−0.808770
$891$	−1.07988e7	−	1.87041e7i	−0.455703	−	0.789300i
$892$	4.87981e6	−	8.45207e6i	0.205348	−	0.355673i
$893$	−4.72226e6	+	8.17919e6i	−0.198162	+	0.343227i
$894$	3.31753e6	+	5.74614e6i	0.138826	+	0.240454i
$895$	−1.27175e7			−0.530696
$896$	−1.62625e7	+	2.32071e7i	−0.676735	+	0.965720i
$897$	−3.23536e6			−0.134259
$898$	−2.10706e7	−	3.64953e7i	−0.871937	−	1.51024i
$899$	1.43265e6	−	2.48142e6i	0.0591208	−	0.102400i
$900$	−2.59828e6	+	4.50036e6i	−0.106925	+	0.185200i
$901$	2.86549e7	+	4.96317e7i	1.17594	+	2.03679i
$902$	−5.77043e6			−0.236152
$903$	3.33259e7	+	2.92801e6i	1.36007	+	0.119496i
$904$	−8.79421e6			−0.357911
$905$	9.07189e6	+	1.57130e7i	0.368194	+	0.637730i
$906$	4.55527e7	−	7.88996e7i	1.84372	−	3.19341i
$907$	3.81778e6	−	6.61258e6i	0.154096	−	0.266903i	−0.778633	−	0.627479i	$-0.784087\pi$
$907$	3.81778e6	−	6.61258e6i	0.154096	−	0.266903i	0.932730	+	0.360577i	$0.117420\pi$
$908$	7.61262e6	+	1.31854e7i	0.306422	+	0.530738i
$909$	−8.37673e7			−3.36252
$910$	−6.95372e6	−	610953.i	−0.278364	−	0.0244571i
$911$	7.18966e6			0.287020			0.143510	−	0.989649i	$-0.454161\pi$
$911$	7.18966e6			0.287020			0.143510	+	0.989649i	$0.454161\pi$
$912$	−1.53491e7	−	2.65853e7i	−0.611075	−	1.05841i
$913$	−1.77439e6	+	3.07334e6i	−0.0704487	+	0.122021i
$914$	2.60458e7	−	4.51126e7i	1.03127	−	1.78621i
$915$	764989.	+	1.32500e6i	0.0302067	+	0.0523195i
$916$	1.16374e6			0.0458266
$917$	2.31259e7	−	3.30013e7i	0.908187	−	1.29601i
$918$	−1.66601e8			−6.52484
$919$	2.39405e7	+	4.14662e7i	0.935072	+	1.61959i	0.774506	+	0.632567i	$0.217999\pi$
$919$	2.39405e7	+	4.14662e7i	0.935072	+	1.61959i	0.160566	+	0.987025i	$0.448668\pi$
$920$	−540166.	+	935595.i	−0.0210406	+	0.0364434i
$921$	2.11384e7	−	3.66128e7i	0.821150	−	1.42227i
$922$	−6.59504e6	−	1.14229e7i	−0.255500	−	0.442538i
$923$	−1.98882e7			−0.768407
$924$	1.72573e6	+	3.70440e6i	0.0664955	+	0.142737i
$925$	−1.85976e6			−0.0714665
$926$	1.37810e6	+	2.38694e6i	0.0528145	+	0.0914775i
$927$	−3.22193e7	+	5.58054e7i	−1.23145	+	2.13293i
$928$	−8.64850e6	+	1.49796e7i	−0.329663	+	0.570994i
$929$	−4.59981e6	−	7.96710e6i	−0.174864	−	0.302873i	0.765250	−	0.643733i	$-0.222615\pi$
$929$	−4.59981e6	−	7.96710e6i	−0.174864	−	0.302873i	−0.940114	+	0.340860i	$0.889282\pi$
$930$	3.48125e6			0.131986
$931$	−1.31430e7	−	2.32745e6i	−0.496958	−	0.0880048i
$932$	−1.56920e7			−0.591750
$933$	4.41267e7	+	7.64297e7i	1.65958	+	2.87447i
$934$	2.65485e7	−	4.59833e7i	0.995801	−	1.72478i
$935$	−1.96149e6	+	3.39741e6i	−0.0733767	+	0.127092i
$936$	1.48944e7	+	2.57979e7i	0.555691	+	0.962486i
$937$	3.23616e7			1.20415			0.602076	−	0.798439i	$-0.294341\pi$
$937$	3.23616e7			1.20415			0.602076	+	0.798439i	$0.294341\pi$
$938$	−7.45242e6	−	1.59972e7i	−0.276561	−	0.593657i
$939$	−6.61770e7			−2.44930
$940$	1.78601e6	+	3.09345e6i	0.0659270	+	0.114189i
$941$	−8.04784e6	+	1.39393e7i	−0.296282	+	0.513175i	−0.975282	−	0.220963i	$-0.929080\pi$
$941$	−8.04784e6	+	1.39393e7i	−0.296282	+	0.513175i	0.679000	+	0.734138i	$0.262413\pi$
$942$	−3.21513e6	+	5.56878e6i	−0.118052	+	0.204471i
$943$	−1.65188e6	−	2.86115e6i	−0.0604923	−	0.104776i
$944$	−1.31733e6			−0.0481132
$945$	2.55394e7	−	3.64455e7i	0.930319	−	1.32759i
$946$	4.80387e6			0.174527
$947$	−1.47502e7	−	2.55481e7i	−0.534471	−	0.925730i	−0.999189	−	0.0402715i	$-0.987178\pi$
$947$	−1.47502e7	−	2.55481e7i	−0.534471	−	0.925730i	0.464718	−	0.885459i	$-0.346156\pi$
$948$	5.55884e6	−	9.62819e6i	0.200892	−	0.347956i
$949$	2.87746e6	−	4.98391e6i	0.103716	−	0.179641i
$950$	−1.64648e6	−	2.85178e6i	−0.0591898	−	0.102520i
$951$	4.74364e7			1.70083
$952$	−3.13158e7	−	2.75140e6i	−1.11988	−	0.0983924i
$953$	3.08601e7			1.10069			0.550345	−	0.834938i	$-0.314496\pi$
$953$	3.08601e7			1.10069			0.550345	+	0.834938i	$0.314496\pi$
$954$	−7.19379e7	−	1.24600e8i	−2.55910	−	4.43248i
$955$	7.37759e6	−	1.27784e7i	0.261762	−	0.453385i
$956$	3.04212e6	−	5.26911e6i	0.107654	−	0.186463i
$957$	−5.47619e6	−	9.48504e6i	−0.193285	−	0.334780i
$958$	−472165.			−0.0166219
$959$	2.20390e6	+	193635.i	0.0773830	+	0.00679887i
$960$	9.90847e6			0.346999
$961$	1.40790e7	+	2.43855e7i	0.491771	+	0.851773i
$962$	3.20441e6	−	5.55020e6i	0.111638	−	0.193362i
$963$	7.46956e6	−	1.29377e7i	0.259555	−	0.449563i
$964$	−4.91482e6	−	8.51272e6i	−0.170339	−	0.295036i
$965$	−9.85553e6			−0.340692
$966$	−4.91905e6	+	7.01963e6i	−0.169605	+	0.242031i
$967$	−5.58630e6			−0.192114			−0.0960568	−	0.995376i	$-0.530623\pi$
$967$	−5.58630e6			−0.192114			−0.0960568	+	0.995376i	$0.530623\pi$
$968$	1.01889e7	+	1.76477e7i	0.349493	+	0.605340i
$969$	2.22059e7	−	3.84617e7i	0.759729	−	1.31589i
$970$	1.57257e6	−	2.72377e6i	0.0536637	−	0.0929482i
$971$	−1.62556e7	−	2.81556e7i	−0.553294	−	0.958333i	−0.998034	−	0.0626736i	$-0.980037\pi$
$971$	−1.62556e7	−	2.81556e7i	−0.553294	−	0.958333i	0.444740	−	0.895660i	$-0.353296\pi$
$972$	5.23860e7			1.77848
$973$	−6.76008e6	−	1.45110e7i	−0.228913	−	0.491378i
$974$	3.04000e7			1.02678
$975$	3.10221e6	+	5.37318e6i	0.104510	+	0.181017i
$976$	−1.26499e6	+	2.19102e6i	−0.0425071	+	0.0736244i
$977$	−1.83732e7	+	3.18234e7i	−0.615814	+	1.06662i	0.374427	+	0.927256i	$0.377839\pi$
$977$	−1.83732e7	+	3.18234e7i	−0.615814	+	1.06662i	−0.990241	+	0.139365i	$0.955494\pi$
$978$	5.08394e7	+	8.80564e7i	1.69962	+	2.94384i
$979$	9.88705e6			0.329693
$980$	−3.24774e6	+	3.86471e6i	−0.108023	+	0.128544i
$981$	−1.51547e7			−0.502775
$982$	1.98224e7	+	3.43334e7i	0.655959	+	1.13615i
$983$	1.03283e7	−	1.78891e7i	0.340914	−	0.590480i	−0.643689	−	0.765287i	$-0.722597\pi$
$983$	1.03283e7	−	1.78891e7i	0.340914	−	0.590480i	0.984603	+	0.174807i	$0.0559303\pi$
$984$	−2.05498e7	+	3.55933e7i	−0.676581	+	1.17187i
$985$	−3.15639e6	−	5.46702e6i	−0.103657	−	0.179540i
$986$	−5.06476e7			−1.65908
$987$	−1.99084e7	−	4.27349e7i	−0.650496	−	1.39634i
$988$	3.09753e6			0.100954
$989$	1.37519e6	+	2.38190e6i	0.0447066	+	0.0774341i
$990$	4.92432e6	−	8.52917e6i	0.159683	−	0.276579i
$991$	−2.13356e7	+	3.69544e7i	−0.690115	+	1.19531i	0.281685	+	0.959507i	$0.409107\pi$
$991$	−2.13356e7	+	3.69544e7i	−0.690115	+	1.19531i	−0.971800	+	0.235807i	$0.924227\pi$
$992$	1.42211e6	+	2.46317e6i	0.0458833	+	0.0794722i
$993$	−6.06124e7			−1.95069
$994$	−3.02380e7	+	4.31506e7i	−0.970706	+	1.38523i
$995$	−2.13048e7			−0.682212
$996$	−7.59738e6	−	1.31590e7i	−0.242670	−	0.420316i
$997$	−1.53913e6	+	2.66585e6i	−0.0490385	+	0.0849372i	−0.889503	−	0.456930i	$-0.848949\pi$
$997$	−1.53913e6	+	2.66585e6i	−0.0490385	+	0.0849372i	0.840464	+	0.541867i	$0.182282\pi$
$998$	1.67919e7	−	2.90845e7i	0.533672	−	0.924347i
$999$	2.04293e7	+	3.53846e7i	0.647649	+	1.12176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.e.b.11.6	✓	16
7.2	even	3	inner	35.6.e.b.16.6	yes	16
7.3	odd	6		245.6.a.k.1.3		8
7.4	even	3		245.6.a.j.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.e.b.11.6	✓	16	1.1	even	1	trivial
35.6.e.b.16.6	yes	16	7.2	even	3	inner
245.6.a.j.1.3		8	7.4	even	3
245.6.a.k.1.3		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.31717 + 5.74550i) q^{2} +(-15.2893 + 26.4818i) q^{3} +(-6.00720 + 10.4048i) q^{4} +(-12.5000 - 21.6506i) q^{5} -202.868 q^{6} +(54.7457 + 117.516i) q^{7} +132.591 q^{8} +(-346.023 - 599.329i) q^{9} +O(q^{10})\)	\(q+(3.31717 + 5.74550i) q^{2} +(-15.2893 + 26.4818i) q^{3} +(-6.00720 + 10.4048i) q^{4} +(-12.5000 - 21.6506i) q^{5} -202.868 q^{6} +(54.7457 + 117.516i) q^{7} +132.591 q^{8} +(-346.023 - 599.329i) q^{9} +(82.9292 - 143.638i) q^{10} +(-42.9017 + 74.3079i) q^{11} +(-183.691 - 318.162i) q^{12} -324.642 q^{13} +(-493.585 + 704.360i) q^{14} +764.463 q^{15} +(632.057 + 1094.76i) q^{16} +(-914.414 + 1583.81i) q^{17} +(2295.63 - 3976.15i) q^{18} +(397.081 + 687.764i) q^{19} +300.360 q^{20} +(-3949.04 - 346.963i) q^{21} -569.248 q^{22} +(-162.957 - 282.250i) q^{23} +(-2027.22 + 3511.25i) q^{24} +(-312.500 + 541.266i) q^{25} +(-1076.89 - 1865.23i) q^{26} +13731.1 q^{27} +(-1551.59 - 136.323i) q^{28} +4174.34 q^{29} +(2535.85 + 4392.22i) q^{30} +(343.203 - 594.445i) q^{31} +(-2071.82 + 3588.50i) q^{32} +(-1311.87 - 2272.22i) q^{33} -12133.1 q^{34} +(1859.97 - 2654.22i) q^{35} +8314.51 q^{36} +(1487.81 + 2576.96i) q^{37} +(-2634.37 + 4562.85i) q^{38} +(4963.53 - 8597.08i) q^{39} +(-1657.39 - 2870.68i) q^{40} +10136.9 q^{41} +(-11106.2 - 23840.2i) q^{42} -8438.98 q^{43} +(-515.438 - 892.764i) q^{44} +(-8650.57 + 14983.2i) q^{45} +(1081.11 - 1872.54i) q^{46} +(5946.22 + 10299.2i) q^{47} -38654.8 q^{48} +(-10812.8 + 12866.9i) q^{49} -4146.46 q^{50} +(-27961.4 - 48430.6i) q^{51} +(1950.19 - 3377.82i) q^{52} +(15668.4 - 27138.5i) q^{53} +(45548.5 + 78892.3i) q^{54} +2145.08 q^{55} +(7258.80 + 15581.5i) q^{56} -24284.3 q^{57} +(13847.0 + 23983.7i) q^{58} +(-521.048 + 902.482i) q^{59} +(-4592.28 + 7954.06i) q^{60} +(1000.69 + 1733.24i) q^{61} +4553.85 q^{62} +(51487.2 - 73473.7i) q^{63} +12961.4 q^{64} +(4058.02 + 7028.70i) q^{65} +(8703.38 - 15074.7i) q^{66} +(-10259.4 + 17769.7i) q^{67} +(-10986.1 - 19028.5i) q^{68} +9965.96 q^{69} +(21419.7 + 1881.93i) q^{70} +61262.0 q^{71} +(-45879.5 - 79465.7i) q^{72} +(-8863.50 + 15352.0i) q^{73} +(-9870.61 + 17096.4i) q^{74} +(-9555.78 - 16551.1i) q^{75} -9541.37 q^{76} +(-11081.0 - 973.578i) q^{77} +65859.4 q^{78} +(15130.9 + 26207.6i) q^{79} +(15801.4 - 27368.9i) q^{80} +(-125855. + 217988. i) q^{81} +(33625.9 + 58241.8i) q^{82} +41359.5 q^{83} +(27332.7 - 39004.6i) q^{84} +45720.7 q^{85} +(-27993.5 - 48486.2i) q^{86} +(-63822.6 + 110544. i) q^{87} +(-5688.38 + 9852.57i) q^{88} +(-57614.6 - 99791.5i) q^{89} -114781. q^{90} +(-17772.7 - 38150.4i) q^{91} +3915.66 q^{92} +(10494.6 + 18177.2i) q^{93} +(-39449.2 + 68328.0i) q^{94} +(9927.01 - 17194.1i) q^{95} +(-63353.2 - 109731. i) q^{96} +18962.8 q^{97} +(-109795. - 19443.3i) q^{98} +59379.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 203 q^{4} - 200 q^{5} - 112 q^{6} + 158 q^{7} + 498 q^{8} - 1218 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 203 * q^4 - 200 * q^5 - 112 * q^6 + 158 * q^7 + 498 * q^8 - 1218 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 203 q^{4} - 200 q^{5} - 112 q^{6} + 158 q^{7} + 498 q^{8} - 1218 q^{9} - 75 q^{10} - 120 q^{11} + 884 q^{12} + 3988 q^{13} - 975 q^{14} - 100 q^{15} - 6451 q^{16} - 1856 q^{17} - 2013 q^{18} + 1828 q^{19} + 10150 q^{20} - 7778 q^{21} + 4398 q^{22} - 4822 q^{23} + 2008 q^{24} - 5000 q^{25} + 7457 q^{26} + 15596 q^{27} - 4703 q^{28} + 21004 q^{29} + 1400 q^{30} - 5148 q^{31} - 12061 q^{32} + 2872 q^{33} - 81364 q^{34} + 2600 q^{35} + 81898 q^{36} - 7810 q^{37} - 18567 q^{38} + 2572 q^{39} - 6225 q^{40} - 36384 q^{41} + 70842 q^{42} + 126380 q^{43} + 4765 q^{44} - 30450 q^{45} - 6567 q^{46} - 11816 q^{47} - 214672 q^{48} - 31966 q^{49} + 3750 q^{50} - 28788 q^{51} - 167255 q^{52} + 39902 q^{53} + 126138 q^{54} + 6000 q^{55} - 11814 q^{56} + 77496 q^{57} - 67552 q^{58} - 50752 q^{59} + 22100 q^{60} + 2146 q^{61} + 203144 q^{62} - 16780 q^{63} + 540078 q^{64} - 49850 q^{65} - 164358 q^{66} - 50498 q^{67} + 125090 q^{68} - 237644 q^{69} + 65025 q^{70} + 367952 q^{71} - 522343 q^{72} - 54436 q^{73} - 228885 q^{74} + 1250 q^{75} - 131578 q^{76} + 130622 q^{77} + 783612 q^{78} - 51040 q^{79} - 161275 q^{80} - 124612 q^{81} + 195887 q^{82} + 120876 q^{83} - 570494 q^{84} + 92800 q^{85} - 260996 q^{86} - 409482 q^{87} - 205001 q^{88} + 96678 q^{89} + 100650 q^{90} - 44284 q^{91} + 349358 q^{92} + 51428 q^{93} + 139395 q^{94} + 45700 q^{95} + 587116 q^{96} - 390624 q^{97} - 887731 q^{98} + 794488 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 203 * q^4 - 200 * q^5 - 112 * q^6 + 158 * q^7 + 498 * q^8 - 1218 * q^9 - 75 * q^10 - 120 * q^11 + 884 * q^12 + 3988 * q^13 - 975 * q^14 - 100 * q^15 - 6451 * q^16 - 1856 * q^17 - 2013 * q^18 + 1828 * q^19 + 10150 * q^20 - 7778 * q^21 + 4398 * q^22 - 4822 * q^23 + 2008 * q^24 - 5000 * q^25 + 7457 * q^26 + 15596 * q^27 - 4703 * q^28 + 21004 * q^29 + 1400 * q^30 - 5148 * q^31 - 12061 * q^32 + 2872 * q^33 - 81364 * q^34 + 2600 * q^35 + 81898 * q^36 - 7810 * q^37 - 18567 * q^38 + 2572 * q^39 - 6225 * q^40 - 36384 * q^41 + 70842 * q^42 + 126380 * q^43 + 4765 * q^44 - 30450 * q^45 - 6567 * q^46 - 11816 * q^47 - 214672 * q^48 - 31966 * q^49 + 3750 * q^50 - 28788 * q^51 - 167255 * q^52 + 39902 * q^53 + 126138 * q^54 + 6000 * q^55 - 11814 * q^56 + 77496 * q^57 - 67552 * q^58 - 50752 * q^59 + 22100 * q^60 + 2146 * q^61 + 203144 * q^62 - 16780 * q^63 + 540078 * q^64 - 49850 * q^65 - 164358 * q^66 - 50498 * q^67 + 125090 * q^68 - 237644 * q^69 + 65025 * q^70 + 367952 * q^71 - 522343 * q^72 - 54436 * q^73 - 228885 * q^74 + 1250 * q^75 - 131578 * q^76 + 130622 * q^77 + 783612 * q^78 - 51040 * q^79 - 161275 * q^80 - 124612 * q^81 + 195887 * q^82 + 120876 * q^83 - 570494 * q^84 + 92800 * q^85 - 260996 * q^86 - 409482 * q^87 - 205001 * q^88 + 96678 * q^89 + 100650 * q^90 - 44284 * q^91 + 349358 * q^92 + 51428 * q^93 + 139395 * q^94 + 45700 * q^95 + 587116 * q^96 - 390624 * q^97 - 887731 * q^98 + 794488 * q^99

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