LMFDB - Embedded newform 14.6.c.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,6,Mod(9,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	14.c (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:	$2.24537347738$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{79})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 79x^{2} + 6241 $ x^4 + 79*x^2 + 6241
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$4.44410 - 7.69740i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.6.c.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-12.3882 + 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(18.0528 + 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 + 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-12.3882 + 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(18.0528 + 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 + 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +(72.2111 - 125.073i) q^{10} +(-77.7174 + 134.610i) q^{11} +(-198.211 - 343.312i) q^{12} +1158.87 q^{13} +(374.869 + 358.308i) q^{14} -894.565 q^{15} +(-128.000 - 221.703i) q^{16} +(-619.040 + 1072.21i) q^{17} +(-741.739 + 1284.73i) q^{18} +(140.140 + 242.729i) q^{19} -577.689 q^{20} +(761.065 - 3120.59i) q^{21} +621.739 q^{22} +(1741.20 + 3015.84i) q^{23} +(-792.844 + 1373.25i) q^{24} +(910.694 - 1577.37i) q^{25} +(-2317.74 - 4014.44i) q^{26} +3168.14 q^{27} +(491.478 - 2015.20i) q^{28} -5656.78 q^{29} +(1789.13 + 3098.87i) q^{30} +(1157.35 - 2004.59i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1925.56 - 3335.16i) q^{33} +4952.32 q^{34} +(-3383.72 - 3234.23i) q^{35} +5933.91 q^{36} +(1166.59 + 2020.59i) q^{37} +(560.558 - 970.916i) q^{38} +(-14356.3 + 24865.8i) q^{39} +(1155.38 + 2001.17i) q^{40} +3812.61 q^{41} +(-12332.2 + 3604.77i) q^{42} +3925.73 q^{43} +(-1243.48 - 2153.77i) q^{44} +(6695.22 - 11596.5i) q^{45} +(6964.78 - 12063.4i) q^{46} +(5558.23 + 9627.13i) q^{47} +6342.76 q^{48} +(14161.0 - 9052.14i) q^{49} -7285.56 q^{50} +(-15337.6 - 26565.5i) q^{51} +(-9270.96 + 16057.8i) q^{52} +(5593.10 - 9687.54i) q^{53} +(-6336.29 - 10974.8i) q^{54} -5612.06 q^{55} +(-7963.82 + 2327.88i) q^{56} -6944.31 q^{57} +(11313.6 + 19595.7i) q^{58} +(3005.18 - 5205.12i) q^{59} +(7156.52 - 12395.5i) q^{60} +(7419.36 + 12850.7i) q^{61} -9258.81 q^{62} +(34756.9 + 33221.4i) q^{63} +4096.00 q^{64} +(20920.8 + 36235.9i) q^{65} +(-7702.22 + 13340.6i) q^{66} +(21491.9 - 37225.1i) q^{67} +(-9904.64 - 17155.3i) q^{68} -86281.1 q^{69} +(-4436.27 + 18190.0i) q^{70} -19962.4 q^{71} +(-11867.8 - 20555.7i) q^{72} +(-22775.3 + 39448.0i) q^{73} +(4666.35 - 8082.36i) q^{74} +(22563.7 + 39081.5i) q^{75} -4484.47 q^{76} +(4774.54 - 19577.0i) q^{77} +114850. q^{78} +(-54496.0 - 94389.9i) q^{79} +(4621.51 - 8004.69i) q^{80} +(5813.07 - 10068.5i) q^{81} +(-7625.22 - 13207.3i) q^{82} +55829.0 q^{83} +(37151.6 + 35510.4i) q^{84} -44701.6 q^{85} +(-7851.47 - 13599.1i) q^{86} +(70077.3 - 121377. i) q^{87} +(-4973.91 + 8615.07i) q^{88} +(47772.9 + 82745.1i) q^{89} -53561.8 q^{90} +(-144204. + 42151.6i) q^{91} -55718.2 q^{92} +(28675.0 + 49666.5i) q^{93} +(22232.9 - 38508.5i) q^{94} +(-5059.82 + 8763.86i) q^{95} +(-12685.5 - 21971.9i) q^{96} +15004.9 q^{97} +(-59679.5 - 30950.9i) q^{98} +57646.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 14 * q^3 - 32 * q^4 - 70 * q^5 + 112 * q^6 + 256 * q^8 - 244 * q^9	\( 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9} - 280 q^{10} - 62 q^{11} - 224 q^{12} + 3640 q^{13} + 504 q^{14} - 4076 q^{15} - 512 q^{16} - 1694 q^{17} - 976 q^{18} - 826 q^{19} + 2240 q^{20} + 3542 q^{21} + 496 q^{22} + 2734 q^{23} - 896 q^{24} - 6312 q^{25} - 7280 q^{26} + 14308 q^{27} - 2016 q^{28} - 5704 q^{29} + 8152 q^{30} + 2674 q^{31} - 2048 q^{32} - 4858 q^{33} + 13552 q^{34} - 13286 q^{35} + 7808 q^{36} + 9146 q^{37} - 3304 q^{38} - 21588 q^{39} - 4480 q^{40} + 12264 q^{41} - 35392 q^{42} - 32080 q^{43} - 992 q^{44} + 26852 q^{45} + 10936 q^{46} + 25326 q^{47} + 7168 q^{48} + 56644 q^{49} + 50496 q^{50} - 25762 q^{51} - 29120 q^{52} - 14958 q^{53} - 28616 q^{54} - 31052 q^{55} - 37732 q^{57} + 11408 q^{58} + 1106 q^{59} + 32608 q^{60} + 28042 q^{61} - 21392 q^{62} + 77308 q^{63} + 16384 q^{64} - 28308 q^{65} - 19432 q^{66} + 102642 q^{67} - 27104 q^{68} - 188692 q^{69} - 88424 q^{70} - 22112 q^{71} - 15616 q^{72} - 35070 q^{73} + 36584 q^{74} + 132776 q^{75} + 26432 q^{76} + 27062 q^{77} + 172704 q^{78} - 101762 q^{79} - 17920 q^{80} + 23750 q^{81} - 24528 q^{82} - 89264 q^{83} + 84896 q^{84} + 7348 q^{85} + 64160 q^{86} + 170380 q^{87} - 3968 q^{88} + 75474 q^{89} - 214816 q^{90} - 123872 q^{91} - 87488 q^{92} + 53478 q^{93} + 101304 q^{94} - 127502 q^{95} - 14336 q^{96} - 16632 q^{97} - 113288 q^{98} + 139000 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 14 * q^3 - 32 * q^4 - 70 * q^5 + 112 * q^6 + 256 * q^8 - 244 * q^9 - 280 * q^10 - 62 * q^11 - 224 * q^12 + 3640 * q^13 + 504 * q^14 - 4076 * q^15 - 512 * q^16 - 1694 * q^17 - 976 * q^18 - 826 * q^19 + 2240 * q^20 + 3542 * q^21 + 496 * q^22 + 2734 * q^23 - 896 * q^24 - 6312 * q^25 - 7280 * q^26 + 14308 * q^27 - 2016 * q^28 - 5704 * q^29 + 8152 * q^30 + 2674 * q^31 - 2048 * q^32 - 4858 * q^33 + 13552 * q^34 - 13286 * q^35 + 7808 * q^36 + 9146 * q^37 - 3304 * q^38 - 21588 * q^39 - 4480 * q^40 + 12264 * q^41 - 35392 * q^42 - 32080 * q^43 - 992 * q^44 + 26852 * q^45 + 10936 * q^46 + 25326 * q^47 + 7168 * q^48 + 56644 * q^49 + 50496 * q^50 - 25762 * q^51 - 29120 * q^52 - 14958 * q^53 - 28616 * q^54 - 31052 * q^55 - 37732 * q^57 + 11408 * q^58 + 1106 * q^59 + 32608 * q^60 + 28042 * q^61 - 21392 * q^62 + 77308 * q^63 + 16384 * q^64 - 28308 * q^65 - 19432 * q^66 + 102642 * q^67 - 27104 * q^68 - 188692 * q^69 - 88424 * q^70 - 22112 * q^71 - 15616 * q^72 - 35070 * q^73 + 36584 * q^74 + 132776 * q^75 + 26432 * q^76 + 27062 * q^77 + 172704 * q^78 - 101762 * q^79 - 17920 * q^80 + 23750 * q^81 - 24528 * q^82 - 89264 * q^83 + 84896 * q^84 + 7348 * q^85 + 64160 * q^86 + 170380 * q^87 - 3968 * q^88 + 75474 * q^89 - 214816 * q^90 - 123872 * q^91 - 87488 * q^92 + 53478 * q^93 + 101304 * q^94 - 127502 * q^95 - 14336 * q^96 - 16632 * q^97 - 113288 * q^98 + 139000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	−12.3882	+	21.4570i	−0.794703	+	1.37647i	0.128325	+	0.991732i	$0.459040\pi$
$3$	−12.3882	+	21.4570i	−0.794703	+	1.37647i	−0.923028	+	0.384734i	$0.874293\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	18.0528	+	31.2683i	0.322938	+	0.559345i	0.981093	−	0.193538i	$-0.0619962\pi$
$5$	18.0528	+	31.2683i	0.322938	+	0.559345i	−0.658155	+	0.752883i	$0.728663\pi$
$6$	99.1056			1.12388
$7$	−124.435	+	36.3731i	−0.959835	+	0.280566i
$7$	−124.435	+	36.3731i	−0.959835	+	0.280566i
$8$	64.0000			0.353553
$9$	−185.435	−	321.182i	−0.763106	−	1.32174i
$10$	72.2111	−	125.073i	0.228352	−	0.395517i
$11$	−77.7174	+	134.610i	−0.193658	+	0.335426i	−0.946460	−	0.322821i	$-0.895369\pi$
$11$	−77.7174	+	134.610i	−0.193658	+	0.335426i	0.752801	+	0.658248i	$0.228702\pi$
$12$	−198.211	−	343.312i	−0.397352	−	0.688233i
$13$	1158.87			1.90185			0.950925	−	0.309422i	$-0.100136\pi$
$13$	1158.87			1.90185			0.950925	+	0.309422i	$0.100136\pi$
$14$	374.869	+	358.308i	0.511164	+	0.488581i
$15$	−894.565			−1.02656
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−619.040	+	1072.21i	−0.519513	+	0.899823i	0.480230	+	0.877143i	$0.340553\pi$
$17$	−619.040	+	1072.21i	−0.519513	+	0.899823i	−0.999743	+	0.0226804i	$0.992780\pi$
$18$	−741.739	+	1284.73i	−0.539597	+	0.934610i
$19$	140.140	+	242.729i	0.0890588	+	0.154254i	0.907114	−	0.420886i	$-0.138281\pi$
$19$	140.140	+	242.729i	0.0890588	+	0.154254i	−0.818055	+	0.575140i	$0.804947\pi$
$20$	−577.689			−0.322938
$21$	761.065	−	3120.59i	0.376594	−	1.54415i
$22$	621.739			0.273874
$23$	1741.20	+	3015.84i	0.686322	+	1.18874i	0.973019	+	0.230723i	$0.0741092\pi$
$23$	1741.20	+	3015.84i	0.686322	+	1.18874i	−0.286698	+	0.958021i	$0.592557\pi$
$24$	−792.844	+	1373.25i	−0.280970	+	0.486654i
$25$	910.694	−	1577.37i	0.291422	−	0.504758i
$26$	−2317.74	−	4014.44i	−0.672405	−	1.16464i
$27$	3168.14			0.836364
$28$	491.478	−	2015.20i	0.118470	−	0.485762i
$29$	−5656.78			−1.24903			−0.624517	−	0.781011i	$-0.714704\pi$
$29$	−5656.78			−1.24903			−0.624517	+	0.781011i	$0.714704\pi$
$30$	1789.13	+	3098.87i	0.362943	+	0.628636i
$31$	1157.35	−	2004.59i	0.216302	−	0.374646i	−0.737372	−	0.675486i	$-0.763934\pi$
$31$	1157.35	−	2004.59i	0.216302	−	0.374646i	0.953675	+	0.300840i	$0.0972671\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−1925.56	−	3335.16i	−0.307802	−	0.533128i
$34$	4952.32			0.734703
$35$	−3383.72	−	3234.23i	−0.466900	−	0.446273i
$36$	5933.91			0.763106
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	0.927531	−	0.373746i	$-0.121927\pi$
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	−0.787439	+	0.616392i	$0.788594\pi$
$38$	560.558	−	970.916i	0.0629741	−	0.109074i
$39$	−14356.3	+	24865.8i	−1.51141	+	2.61783i
$40$	1155.38	+	2001.17i	0.114176	+	0.197758i
$41$	3812.61			0.354211			0.177106	−	0.984192i	$-0.443327\pi$
$41$	3812.61			0.354211			0.177106	+	0.984192i	$0.443327\pi$
$42$	−12332.2	+	3604.77i	−1.07874	+	0.315322i
$43$	3925.73			0.323780			0.161890	−	0.986809i	$-0.448241\pi$
$43$	3925.73			0.323780			0.161890	+	0.986809i	$0.448241\pi$
$44$	−1243.48	−	2153.77i	−0.0968292	−	0.167713i
$45$	6695.22	−	11596.5i	0.492872	−	0.853679i
$46$	6964.78	−	12063.4i	0.485303	−	0.840569i
$47$	5558.23	+	9627.13i	0.367022	+	0.635700i	0.989098	−	0.147256i	$-0.0470442\pi$
$47$	5558.23	+	9627.13i	0.367022	+	0.635700i	−0.622077	+	0.782956i	$0.713711\pi$
$48$	6342.76			0.397352
$49$	14161.0	−	9052.14i	0.842566	−	0.538594i
$50$	−7285.56			−0.412133
$51$	−15337.6	−	26565.5i	−0.825717	−	1.43018i
$52$	−9270.96	+	16057.8i	−0.475462	+	0.823525i
$53$	5593.10	−	9687.54i	0.273504	−	0.473722i	−0.696253	−	0.717797i	$-0.745151\pi$
$53$	5593.10	−	9687.54i	0.273504	−	0.473722i	0.969757	+	0.244074i	$0.0784841\pi$
$54$	−6336.29	−	10974.8i	−0.295699	−	0.512166i
$55$	−5612.06			−0.250159
$56$	−7963.82	+	2327.88i	−0.339353	+	0.0991950i
$57$	−6944.31			−0.283101
$58$	11313.6	+	19595.7i	0.441600	+	0.764874i
$59$	3005.18	−	5205.12i	0.112393	−	0.194671i	−0.804342	−	0.594167i	$-0.797482\pi$
$59$	3005.18	−	5205.12i	0.112393	−	0.194671i	0.916735	+	0.399497i	$0.130815\pi$
$60$	7156.52	−	12395.5i	0.256640	−	0.444513i
$61$	7419.36	+	12850.7i	0.255295	+	0.442183i	0.964975	−	0.262340i	$-0.0844942\pi$
$61$	7419.36	+	12850.7i	0.255295	+	0.442183i	−0.709681	+	0.704523i	$0.751161\pi$
$62$	−9258.81			−0.305897
$63$	34756.9	+	33221.4i	1.10329	+	1.05455i
$64$	4096.00			0.125000
$65$	20920.8	+	36235.9i	0.614179	+	1.06379i
$66$	−7702.22	+	13340.6i	−0.217649	+	0.376979i
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	−0.409977	−	0.912096i	$-0.634463\pi$
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	0.994887	−	0.100997i	$-0.0322032\pi$
$68$	−9904.64	−	17155.3i	−0.259757	−	0.449912i
$69$	−86281.1			−2.18169
$70$	−4436.27	+	18190.0i	−0.108211	+	0.443698i
$71$	−19962.4			−0.469967			−0.234984	−	0.971999i	$-0.575504\pi$
$71$	−19962.4			−0.469967			−0.234984	+	0.971999i	$0.575504\pi$
$72$	−11867.8	−	20555.7i	−0.269799	−	0.467305i
$73$	−22775.3	+	39448.0i	−0.500215	+	0.866398i	0.499785	+	0.866150i	$0.333412\pi$
$73$	−22775.3	+	39448.0i	−0.500215	+	0.866398i	−1.00000		0.000248463i	$0.999921\pi$
$74$	4666.35	−	8082.36i	0.0990599	−	0.171577i
$75$	22563.7	+	39081.5i	0.463188	+	0.802266i
$76$	−4484.47			−0.0890588
$77$	4774.54	−	19577.0i	0.0917709	−	0.376288i
$78$	114850.			2.13745
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.652885	−	0.757457i	$-0.726442\pi$
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.329534	−	0.944144i	$-0.606892\pi$
$80$	4621.51	−	8004.69i	0.0807345	−	0.139836i
$81$	5813.07	−	10068.5i	0.0984448	−	0.170511i
$82$	−7625.22	−	13207.3i	−0.125233	−	0.216909i
$83$	55829.0			0.889538			0.444769	−	0.895645i	$-0.353286\pi$
$83$	55829.0			0.889538			0.444769	+	0.895645i	$0.353286\pi$
$84$	37151.6	+	35510.4i	0.574486	+	0.549107i
$85$	−44701.6			−0.671082
$86$	−7851.47	−	13599.1i	−0.114473	−	0.198274i
$87$	70077.3	−	121377.i	0.992611	−	1.71925i
$88$	−4973.91	+	8615.07i	−0.0684686	+	0.118591i
$89$	47772.9	+	82745.1i	0.639303	+	1.10731i	0.985586	+	0.169175i	$0.0541103\pi$
$89$	47772.9	+	82745.1i	0.639303	+	1.10731i	−0.346283	+	0.938130i	$0.612556\pi$
$90$	−53561.8			−0.697026
$91$	−144204.	+	42151.6i	−1.82546	+	0.533594i
$92$	−55718.2			−0.686322
$93$	28675.0	+	49666.5i	0.343792	+	0.595465i
$94$	22232.9	−	38508.5i	0.259523	−	0.449508i
$95$	−5059.82	+	8763.86i	−0.0575209	+	0.0996292i
$96$	−12685.5	−	21971.9i	−0.140485	−	0.243327i
$97$	15004.9			0.161922			0.0809609	−	0.996717i	$-0.474201\pi$
$97$	15004.9			0.161922			0.0809609	+	0.996717i	$0.474201\pi$
$98$	−59679.5	−	30950.9i	−0.627712	−	0.325542i
$99$	57646.0			0.591127
$100$	14571.1	+	25237.9i	0.145711	+	0.252379i
$101$	−13438.1	+	23275.4i	−0.131079	+	0.227036i	−0.924093	−	0.382168i	$-0.875178\pi$
$101$	−13438.1	+	23275.4i	−0.131079	+	0.227036i	0.793014	+	0.609204i	$0.208511\pi$
$102$	−61350.3	+	106262.i	−0.583870	+	1.01129i
$103$	25957.6	+	44959.9i	0.241086	+	0.417573i	0.961024	−	0.276466i	$-0.0891632\pi$
$103$	25957.6	+	44959.9i	0.241086	+	0.417573i	−0.719938	+	0.694038i	$0.755830\pi$
$104$	74167.6			0.672405
$105$	111315.	−	32538.1i	0.985327	−	0.288017i
$106$	−44744.8			−0.386793
$107$	12487.4	+	21628.8i	0.105442	+	0.182630i	0.913919	−	0.405898i	$-0.133041\pi$
$107$	12487.4	+	21628.8i	0.105442	+	0.182630i	−0.808477	+	0.588528i	$0.799708\pi$
$108$	−25345.1	+	43899.1i	−0.209091	+	0.362156i
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	−0.858604	−	0.512640i	$-0.828668\pi$
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	0.873261	+	0.487253i	$0.162001\pi$
$110$	11224.1	+	19440.7i	0.0884444	+	0.153190i
$111$	−57807.7			−0.445326
$112$	23991.6	+	22931.7i	0.180724	+	0.172740i
$113$	62175.0			0.458057			0.229028	−	0.973420i	$-0.426445\pi$
$113$	62175.0			0.458057			0.229028	+	0.973420i	$0.426445\pi$
$114$	13888.6	+	24055.8i	0.100091	+	0.173363i
$115$	−62866.8	+	108889.i	−0.443279	+	0.767781i
$116$	45254.2	−	78382.7i	0.312259	−	0.540848i
$117$	−214895.	−	372208.i	−1.45131	−	2.51375i
$118$	−24041.4			−0.158948
$119$	38030.6	−	155936.i	0.246187	−	1.00944i
$120$	−57252.2			−0.362943
$121$	68445.5	+	118551.i	0.424993	+	0.736109i
$122$	29677.4	−	51402.8i	0.180521	−	0.312671i
$123$	−47231.3	+	81807.1i	−0.281493	+	0.487560i
$124$	18517.6	+	32073.4i	0.108151	+	0.187323i
$125$	178592.			1.02232
$126$	45568.5	−	186844.i	0.255705	−	1.04846i
$127$	63550.3			0.349630			0.174815	−	0.984601i	$-0.444067\pi$
$127$	63550.3			0.349630			0.174815	+	0.984601i	$0.444067\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−48632.7	+	84234.4i	−0.257309	+	0.445672i
$130$	83683.2	−	144944.i	0.434290	−	0.752213i
$131$	−68148.5	−	118037.i	−0.346959	−	0.600950i	0.638749	−	0.769415i	$-0.279452\pi$
$131$	−68148.5	−	118037.i	−0.346959	−	0.600950i	−0.985708	+	0.168465i	$0.946119\pi$
$132$	61617.8			0.307802
$133$	−26267.0	−	25106.6i	−0.128760	−	0.123072i
$134$	−171935.			−0.827187
$135$	57193.8	+	99062.5i	0.270094	+	0.467816i
$136$	−39618.6	+	68621.4i	−0.183676	+	0.318136i
$137$	−167652.	+	290381.i	−0.763144	+	1.32180i	0.178078	+	0.984016i	$0.443012\pi$
$137$	−167652.	+	290381.i	−0.763144	+	1.32180i	−0.941222	+	0.337788i	$0.890321\pi$
$138$	172562.	+	298886.i	0.771343	+	1.33601i
$139$	58195.2			0.255476			0.127738	−	0.991808i	$-0.459228\pi$
$139$	58195.2			0.255476			0.127738	+	0.991808i	$0.459228\pi$
$140$	71884.6	−	21012.3i	0.309967	−	0.0906054i
$141$	−275426.			−1.16669
$142$	39924.9	+	69151.9i	0.166158	+	0.287795i
$143$	−90064.3	+	155996.i	−0.368309	+	0.637930i
$144$	−47471.3	+	82222.7i	−0.190776	+	0.330435i
$145$	−102121.	−	176878.i	−0.403360	−	0.698641i
$146$	182202.			0.707411
$147$	18802.5	+	415992.i	0.0717665	+	1.58779i
$148$	−37330.8			−0.140092
$149$	−141529.	−	245135.i	−0.522251	−	0.904566i	−0.999665	−	0.0258870i	$-0.991759\pi$
$149$	−141529.	−	245135.i	−0.522251	−	0.904566i	0.477414	−	0.878679i	$-0.341574\pi$
$150$	90254.9	−	156326.i	0.327524	−	0.567287i
$151$	120779.	−	209195.i	0.431071	−	0.746637i	−0.565895	−	0.824477i	$-0.691469\pi$
$151$	120779.	−	209195.i	0.431071	−	0.746637i	0.996966	+	0.0778407i	$0.0248026\pi$
$152$	8968.93	+	15534.6i	0.0314870	+	0.0545372i
$153$	459166.			1.58577
$154$	−77365.9	+	22614.6i	−0.262874	+	0.0768398i
$155$	83573.6			0.279409
$156$	−229701.	−	397853.i	−0.755703	−	1.30892i
$157$	107014.	−	185354.i	0.346492	−	0.600142i	−0.639132	−	0.769097i	$-0.720706\pi$
$157$	107014.	−	185354.i	0.346492	−	0.600142i	0.985624	+	0.168956i	$0.0540394\pi$
$158$	−217984.	+	377559.i	−0.694675	+	1.20321i
$159$	138577.	+	240022.i	0.434708	+	0.752937i
$160$	−36972.1			−0.114176
$161$	−326360.	−	311942.i	−0.992277	−	0.948440i
$162$	−46504.5			−0.139222
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	0.814595	−	0.580030i	$-0.196959\pi$
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	−0.909619	+	0.415445i	$0.863626\pi$
$164$	−30500.9	+	52829.1i	−0.0885529	+	0.153378i
$165$	69523.3	−	120418.i	0.198802	−	0.344335i
$166$	−111658.	−	193397.i	−0.314499	−	0.544729i
$167$	−442694.			−1.22832			−0.614162	−	0.789180i	$-0.710506\pi$
$167$	−442694.			−1.22832			−0.614162	+	0.789180i	$0.710506\pi$
$168$	48708.2	−	199718.i	0.133146	−	0.545938i
$169$	971685.			2.61703
$170$	89403.2	+	154851.i	0.237263	+	0.410952i
$171$	51973.5	−	90020.7i	0.135923	−	0.235425i
$172$	−31405.9	+	54396.6i	−0.0809449	+	0.140201i
$173$	39299.5	+	68068.8i	0.0998325	+	0.172915i	0.911615	−	0.411045i	$-0.134836\pi$
$173$	39299.5	+	68068.8i	0.0998325	+	0.172915i	−0.811783	+	0.583960i	$0.801503\pi$
$174$	−560618.			−1.40376
$175$	−55948.3	+	229404.i	−0.138099	+	0.566247i
$176$	39791.3			0.0968292
$177$	74457.4	+	128964.i	0.178638	+	0.309411i
$178$	191092.	−	330980.i	0.452055	−	0.782983i
$179$	255214.	−	442043.i	0.595348	−	1.03117i	−0.398149	−	0.917321i	$-0.630347\pi$
$179$	255214.	−	442043.i	0.595348	−	1.03117i	0.993498	−	0.113853i	$-0.0363193\pi$
$180$	107124.	+	185543.i	0.246436	+	0.426839i
$181$	−22051.8			−0.0500319			−0.0250160	−	0.999687i	$-0.507964\pi$
$181$	−22051.8			−0.0500319			−0.0250160	+	0.999687i	$0.507964\pi$
$182$	434425.	+	415233.i	0.972156	+	0.929208i
$183$	−367650.			−0.811534
$184$	111436.	+	193014.i	0.242651	+	0.420285i
$185$	−42120.3	+	72954.5i	−0.0904820	+	0.156719i
$186$	114700.	−	198666.i	0.243098	−	0.421057i
$187$	−96220.4	−	166659.i	−0.201216	−	0.348517i
$188$	−177863.			−0.367022
$189$	−394227.	+	115235.i	−0.802771	+	0.234655i
$190$	40478.5			0.0813469
$191$	279076.	+	483374.i	0.553528	+	0.958738i	0.998016	+	0.0629535i	$0.0200520\pi$
$191$	279076.	+	483374.i	0.553528	+	0.958738i	−0.444489	+	0.895784i	$0.646615\pi$
$192$	−50742.0	+	87887.8i	−0.0993379	+	0.172058i
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	−0.841216	−	0.540699i	$-0.818160\pi$
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	0.888867	+	0.458166i	$0.151493\pi$
$194$	−30009.9	−	51978.7i	−0.0572480	−	0.0991564i
$195$	−1.03668e6			−1.95236
$196$	12142.2	+	268638.i	0.0225765	+	0.499490i
$197$	−941509.			−1.72846			−0.864229	−	0.503099i	$-0.832193\pi$
$197$	−941509.			−1.72846			−0.864229	+	0.503099i	$0.832193\pi$
$198$	−115292.	−	199692.i	−0.208995	−	0.361990i
$199$	−320006.	+	554267.i	−0.572830	+	0.992170i	0.423444	+	0.905922i	$0.360821\pi$
$199$	−320006.	+	554267.i	−0.572830	+	0.992170i	−0.996274	+	0.0862477i	$0.972512\pi$
$200$	58284.4	−	100952.i	0.103033	−	0.178459i
$201$	532493.	+	922304.i	0.929658	+	1.61022i
$202$	107505.			0.185374
$203$	703900.	−	205754.i	1.19887	−	0.350436i
$204$	490803.			0.825717
$205$	68828.2	+	119214.i	0.114388	+	0.198126i
$206$	103830.	−	179840.i	0.170473	−	0.295268i
$207$	645756.	−	1.11848e6i	1.04747	−	1.81428i
$208$	−148335.	−	256924.i	−0.237731	−	0.411762i
$209$	−43565.1			−0.0689879
$210$	−335345.	−	320530.i	−0.524740	−	0.501558i
$211$	921869.			1.42549			0.712743	−	0.701425i	$-0.247452\pi$
$211$	921869.			1.42549			0.712743	+	0.701425i	$0.247452\pi$
$212$	89489.7	+	155001.i	0.136752	+	0.236861i
$213$	247298.	−	428333.i	0.373484	−	0.646894i
$214$	49949.5	−	86515.1i	0.0745585	−	0.129139i
$215$	70870.4	+	122751.i	0.104561	+	0.181105i
$216$	202761.			0.295699
$217$	−71101.5	+	291537.i	−0.102501	+	0.420285i
$218$	−14544.6			−0.0207281
$219$	−564290.	−	977378.i	−0.795045	−	1.37706i
$220$	44896.5	−	77762.9i	0.0625396	−	0.108322i
$221$	−717387.	+	1.24255e6i	−0.988036	+	1.71133i
$222$	115615.	+	200252.i	0.157446	+	0.272705i
$223$	−837700.			−1.12805			−0.564023	−	0.825759i	$-0.690747\pi$
$223$	−837700.			−1.12805			−0.564023	+	0.825759i	$0.690747\pi$
$224$	31454.6	−	128973.i	0.0418855	−	0.171743i
$225$	−675497.			−0.889544
$226$	−124350.	−	215380.i	−0.161948	−	0.280501i
$227$	665344.	−	1.15241e6i	0.857002	−	1.48437i	−0.0177731	−	0.999842i	$-0.505658\pi$
$227$	665344.	−	1.15241e6i	0.857002	−	1.48437i	0.874775	−	0.484529i	$-0.161009\pi$
$228$	55554.4	−	96223.1i	0.0707753	−	0.122586i
$229$	−505317.	−	875234.i	−0.636759	−	1.10290i	−0.986140	−	0.165918i	$-0.946941\pi$
$229$	−505317.	−	875234.i	−0.636759	−	1.10290i	0.349381	−	0.936981i	$-0.386392\pi$
$230$	502935.			0.626891
$231$	360916.	+	344971.i	0.445017	+	0.425357i
$232$	−362034.			−0.441600
$233$	−743050.	−	1.28700e6i	−0.896661	−	1.55306i	−0.831736	−	0.555172i	$-0.812653\pi$
$233$	−743050.	−	1.28700e6i	−0.896661	−	1.55306i	−0.0649249	−	0.997890i	$-0.520681\pi$
$234$	−859579.	+	1.48883e6i	−1.02623	+	1.77749i
$235$	−200683.	+	347593.i	−0.237050	+	0.410583i
$236$	48082.8	+	83281.9i	0.0561966	+	0.0973353i
$237$	2.70043e6			3.12293
$238$	−616241.	+	180131.i	−0.705193	+	0.206132i
$239$	875637.			0.991584			0.495792	−	0.868441i	$-0.334878\pi$
$239$	875637.			0.991584			0.495792	+	0.868441i	$0.334878\pi$
$240$	114504.	+	198327.i	0.128320	+	0.222257i
$241$	−726472.	+	1.25829e6i	−0.805706	+	1.39552i	0.110108	+	0.993920i	$0.464880\pi$
$241$	−726472.	+	1.25829e6i	−0.805706	+	1.39552i	−0.915814	+	0.401604i	$0.868453\pi$
$242$	273782.	−	474204.i	0.300515	−	0.520508i
$243$	528956.	+	916179.i	0.574651	+	0.995324i
$244$	−237419.			−0.255295
$245$	538691.	+	279374.i	0.573356	+	0.297352i
$246$	377851.			0.398091
$247$	162403.	+	281291.i	0.169376	+	0.293369i
$248$	74070.4	−	128294.i	0.0764743	−	0.132457i
$249$	−691621.	+	1.19792e6i	−0.706919	+	1.22442i
$250$	−357184.	−	618661.i	−0.361445	−	0.626041i
$251$	−198384.			−0.198757			−0.0993786	−	0.995050i	$-0.531685\pi$
$251$	−198384.			−0.198757			−0.0993786	+	0.995050i	$0.531685\pi$
$252$	−738385.	+	215835.i	−0.732456	+	0.214101i
$253$	−541284.			−0.531648
$254$	−127101.	−	220145.i	−0.123613	−	0.214104i
$255$	553772.	−	959161.i	0.533311	−	0.923722i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−239786.	−	415321.i	−0.226460	−	0.392240i	0.730297	−	0.683130i	$-0.239382\pi$
$257$	−239786.	−	415321.i	−0.226460	−	0.392240i	−0.956756	+	0.290890i	$0.906048\pi$
$258$	389062.			0.363890
$259$	−218659.	−	208999.i	−0.202543	−	0.193595i
$260$	−669466.			−0.614179
$261$	1.04896e6	+	1.81686e6i	0.953145	+	1.65090i
$262$	−272594.	+	472147.i	−0.245337	+	0.424936i
$263$	−227471.	+	393992.i	−0.202786	+	0.351235i	−0.949425	−	0.313994i	$-0.898333\pi$
$263$	−227471.	+	393992.i	−0.202786	+	0.351235i	0.746639	+	0.665229i	$0.231666\pi$
$264$	−123236.	−	213450.i	−0.108824	−	0.188489i
$265$	403884.			0.353299
$266$	−34437.7	+	141205.i	−0.0298422	+	0.122362i
$267$	−2.36728e6			−2.03222
$268$	343871.	+	595602.i	0.292455	+	0.506546i
$269$	430068.	−	744900.i	0.362374	−	0.627650i	−0.625977	−	0.779841i	$-0.715300\pi$
$269$	430068.	−	744900.i	0.362374	−	0.627650i	0.988351	+	0.152192i	$0.0486331\pi$
$270$	228775.	−	396250.i	0.190985	−	0.330796i
$271$	−652790.	−	1.13067e6i	−0.539946	−	0.935214i	−0.998906	−	0.0467569i	$-0.985111\pi$
$271$	−652790.	−	1.13067e6i	−0.539946	−	0.935214i	0.458960	−	0.888457i	$-0.348222\pi$
$272$	316949.			0.259757
$273$	881975.	−	3.61636e6i	0.716226	−	2.93673i
$274$	1.34121e6			1.07925
$275$	141554.	+	245178.i	0.112873	+	0.195501i
$276$	690248.	−	1.19555e6i	0.545422	−	0.944699i
$277$	271554.	−	470346.i	0.212646	−	0.368314i	−0.739896	−	0.672721i	$-0.765125\pi$
$277$	271554.	−	470346.i	0.212646	−	0.368314i	0.952542	+	0.304408i	$0.0984586\pi$
$278$	−116390.	−	201594.i	−0.0903245	−	0.156447i
$279$	−858452.			−0.660246
$280$	−216558.	−	206991.i	−0.165074	−	0.157781i
$281$	998089.			0.754055			0.377028	−	0.926202i	$-0.376946\pi$
$281$	998089.			0.754055			0.377028	+	0.926202i	$0.376946\pi$
$282$	550851.	+	954102.i	0.412488	+	0.714450i
$283$	−888660.	+	1.53920e6i	−0.659583	+	1.14243i	0.321140	+	0.947032i	$0.395934\pi$
$283$	−888660.	+	1.53920e6i	−0.659583	+	1.14243i	−0.980724	+	0.195400i	$0.937399\pi$
$284$	159699.	−	276608.i	0.117492	−	0.203502i
$285$	−125364.	−	217137.i	−0.0914241	−	0.158351i
$286$	720514.			0.520868
$287$	−474421.	+	138676.i	−0.339984	+	0.0993796i
$288$	379770.			0.269799
$289$	−56493.2	−	97849.1i	−0.0397880	−	0.0689148i
$290$	−408482.	+	707512.i	−0.285219	+	0.494014i
$291$	−185884.	+	321961.i	−0.128680	+	0.222880i
$292$	−364405.	−	631167.i	−0.250108	−	0.433199i
$293$	−1.63987e6			−1.11594			−0.557969	−	0.829862i	$-0.688419\pi$
$293$	−1.63987e6			−1.11594			−0.557969	+	0.829862i	$0.688419\pi$
$294$	1.40343e6	−	897118.i	0.946942	−	0.605315i
$295$	217007.			0.145184
$296$	74661.6	+	129318.i	0.0495300	+	0.0857884i
$297$	−246220.	+	426465.i	−0.161969	+	0.280538i
$298$	−566116.	+	980541.i	−0.369287	+	0.639625i
$299$	2.01782e6	+	3.49496e6i	1.30528	+	2.26081i
$300$	−722039.			−0.463188
$301$	−488498.	+	142791.i	−0.310775	+	0.0908415i
$302$	−966231.			−0.609626
$303$	−332947.	−	576681.i	−0.208338	−	0.360852i
$304$	35875.7	−	62138.6i	0.0222647	−	0.0385636i
$305$	−267880.	+	463982.i	−0.164889	+	0.285595i
$306$	−918332.	−	1.59060e6i	−0.560656	−	0.971084i
$307$	2.38130e6			1.44201			0.721006	−	0.692928i	$-0.243680\pi$
$307$	2.38130e6			1.44201			0.721006	+	0.692928i	$0.243680\pi$
$308$	233071.	+	222774.i	0.139995	+	0.133810i
$309$	−1.28627e6			−0.766366
$310$	−167147.	−	289507.i	−0.0987859	−	0.171102i
$311$	622564.	−	1.07831e6i	0.364992	−	0.632184i	−0.623783	−	0.781597i	$-0.714405\pi$
$311$	622564.	−	1.07831e6i	0.364992	−	0.632184i	0.988775	+	0.149413i	$0.0477385\pi$
$312$	−918803.	+	1.59141e6i	−0.534363	+	0.925543i
$313$	−831495.	−	1.44019e6i	−0.479732	−	0.830921i	0.519997	−	0.854168i	$-0.325933\pi$
$313$	−831495.	−	1.44019e6i	−0.479732	−	0.830921i	−0.999730	+	0.0232470i	$0.992600\pi$
$314$	−856115.			−0.490014
$315$	−411319.	+	1.68653e6i	−0.233562	+	0.957673i
$316$	1.74387e6			0.982419
$317$	1.31243e6	+	2.27319e6i	0.733547	+	1.27054i	0.955358	+	0.295450i	$0.0954697\pi$
$317$	1.31243e6	+	2.27319e6i	0.733547	+	1.27054i	−0.221812	+	0.975090i	$0.571197\pi$
$318$	554308.	−	960089.i	0.307385	−	0.532407i
$319$	439630.	−	761462.i	0.241886	−	0.418959i
$320$	73944.2	+	128075.i	0.0403672	+	0.0699181i
$321$	−618784.			−0.335179
$322$	−427879.	+	1.75443e6i	−0.229976	+	0.942967i
$323$	−347008.			−0.185069
$324$	93009.0	+	161096.i	0.0492224	+	0.0852557i
$325$	1.05538e6	−	1.82796e6i	0.554241	−	0.959974i
$326$	−128932.	+	223317.i	−0.0671919	+	0.116380i
$327$	45045.3	+	78020.7i	0.0232959	+	0.0403497i
$328$	244007.			0.125233
$329$	−1.04180e6	−	995780.i	−0.530636	−	0.507193i
$330$	−556186.			−0.281148
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	0.561213	−	0.827671i	$-0.310335\pi$
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	−0.997391	+	0.0721894i	$0.977001\pi$
$332$	−446632.	+	773589.i	−0.222385	+	0.385181i
$333$	432652.	−	749375.i	0.213810	−	0.370330i
$334$	885389.	+	1.53354e6i	0.434278	+	0.752191i
$335$	1.55196e6			0.755558
$336$	−789259.	+	230705.i	−0.381392	+	0.111483i
$337$	853564.			0.409413			0.204706	−	0.978823i	$-0.434376\pi$
$337$	853564.			0.409413			0.204706	+	0.978823i	$0.434376\pi$
$338$	−1.94337e6	−	3.36602e6i	−0.925260	−	1.60260i
$339$	−770236.	+	1.33409e6i	−0.364019	+	0.630500i
$340$	357613.	−	619403.i	0.167771	−	0.290587i
$341$	179892.	+	311583.i	0.0837774	+	0.145107i
$342$	−415788.			−0.192224
$343$	−1.43287e6	+	1.64148e6i	−0.657613	+	0.753356i
$344$	251247.			0.114473
$345$	−1.55761e6	−	2.69786e6i	−0.704550	−	1.22032i
$346$	157198.	−	272275.i	0.0705922	−	0.122269i
$347$	1.49250e6	−	2.58508e6i	0.665411	−	1.15253i	−0.313763	−	0.949501i	$-0.601590\pi$
$347$	1.49250e6	−	2.58508e6i	0.665411	−	1.15253i	0.979174	−	0.203024i	$-0.0650770\pi$
$348$	1.12124e6	+	1.94204e6i	0.496306	+	0.859627i
$349$	2.87467e6			1.26335			0.631676	−	0.775233i	$-0.282367\pi$
$349$	2.87467e6			1.26335			0.631676	+	0.775233i	$0.282367\pi$
$350$	906576.	−	264998.i	0.395580	−	0.115631i
$351$	3.67146e6			1.59064
$352$	−79582.6	−	137841.i	−0.0342343	−	0.0592955i
$353$	−735546.	+	1.27400e6i	−0.314176	+	0.544169i	−0.979262	−	0.202598i	$-0.935062\pi$
$353$	−735546.	+	1.27400e6i	−0.314176	+	0.544169i	0.665086	+	0.746767i	$0.268395\pi$
$354$	297830.	−	515856.i	0.126316	−	0.218786i
$355$	−360377.	−	624192.i	−0.151770	−	0.262874i
$356$	−1.52873e6			−0.639303
$357$	2.87480e6	+	2.74779e6i	1.19381	+	1.14107i
$358$	−2.04171e6			−0.841950
$359$	−1.53900e6	−	2.66562e6i	−0.630233	−	1.09160i	−0.987504	−	0.157595i	$-0.949626\pi$
$359$	−1.53900e6	−	2.66562e6i	−0.630233	−	1.09160i	0.357270	−	0.934001i	$-0.383707\pi$
$360$	428494.	−	742174.i	0.174256	−	0.301821i
$361$	1.19877e6	−	2.07633e6i	0.484137	−	0.838550i
$362$	44103.6	+	76389.6i	0.0176890	+	0.0306382i
$363$	−3.39167e6			−1.35097
$364$	569559.	−	2.33536e6i	0.225312	−	0.923846i
$365$	−1.64463e6			−0.646154
$366$	735299.	+	1.27358e6i	0.286920	+	0.496961i
$367$	−808349.	+	1.40010e6i	−0.313281	+	0.542618i	−0.979071	−	0.203521i	$-0.934761\pi$
$367$	−808349.	+	1.40010e6i	−0.313281	+	0.542618i	0.665790	+	0.746139i	$0.268095\pi$
$368$	445746.	−	772055.i	0.171580	−	0.297186i
$369$	−706990.	−	1.22454e6i	−0.270301	−	0.468175i
$370$	336962.			0.127961
$371$	−343611.	+	1.40890e6i	−0.129608	+	0.531431i
$372$	−917599.			−0.343792
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.844612	+	0.535379i	$0.179831\pi$
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.0413462	+	0.999145i	$0.486835\pi$
$374$	−384881.	+	666634.i	−0.142281	+	0.246439i
$375$	−2.21243e6	+	3.83205e6i	−0.812442	+	1.40719i
$376$	355727.	+	616136.i	0.129762	+	0.224754i
$377$	−6.55547e6			−2.37548
$378$	1.18764e6	+	1.13517e6i	0.427519	+	0.408632i
$379$	1.00193e6			0.358294			0.179147	−	0.983822i	$-0.442666\pi$
$379$	1.00193e6			0.358294			0.179147	+	0.983822i	$0.442666\pi$
$380$	−80957.1	−	140222.i	−0.0287605	−	0.0498146i
$381$	−787273.	+	1.36360e6i	−0.277852	+	0.481253i
$382$	1.11630e6	−	1.93350e6i	0.391403	−	0.677930i
$383$	1.41076e6	+	2.44351e6i	0.491424	+	0.851172i	0.999951	−	0.00987425i	$-0.00314312\pi$
$383$	1.41076e6	+	2.44351e6i	0.491424	+	0.851172i	−0.508527	+	0.861046i	$0.669810\pi$
$384$	405936.			0.140485
$385$	698335.	−	204128.i	0.240111	−	0.0701859i
$386$	−197265.			−0.0673879
$387$	−727967.	−	1.26088e6i	−0.247078	−	0.427952i
$388$	−120040.	+	207915.i	−0.0404804	+	0.0701142i
$389$	621198.	−	1.07595e6i	0.208140	−	0.360510i	−0.742988	−	0.669304i	$-0.766592\pi$
$389$	621198.	−	1.07595e6i	0.208140	−	0.360510i	0.951129	+	0.308795i	$0.0999256\pi$
$390$	2.07337e6	+	3.59118e6i	0.690264	+	1.19557i
$391$	−4.31148e6			−1.42621
$392$	906304.	−	579337.i	0.297892	−	0.190422i
$393$	3.37695e6			1.10292
$394$	1.88302e6	+	3.26148e6i	0.611102	+	1.05846i
$395$	1.96761e6	−	3.40800e6i	0.634521	−	1.09902i
$396$	−461168.	+	798766.i	−0.147782	+	0.255966i
$397$	−1.37281e6	−	2.37778e6i	−0.437154	−	0.757173i	0.560315	−	0.828280i	$-0.310680\pi$
$397$	−1.37281e6	−	2.37778e6i	−0.437154	−	0.757173i	−0.997469	+	0.0711068i	$0.977347\pi$
$398$	2.56005e6			0.810103
$399$	864113.	−	252586.i	0.271730	−	0.0794285i
$400$	−466276.			−0.145711
$401$	1.85668e6	+	3.21586e6i	0.576601	+	0.998702i	0.995866	+	0.0908378i	$0.0289545\pi$
$401$	1.85668e6	+	3.21586e6i	0.576601	+	0.998702i	−0.419265	+	0.907864i	$0.637712\pi$
$402$	2.12997e6	−	3.68922e6i	0.657368	−	1.13859i
$403$	1.34122e6	−	2.32306e6i	0.411374	−	0.712521i
$404$	−215009.	−	372407.i	−0.0655396	−	0.113518i
$405$	419768.			0.127166
$406$	−2.12055e6	−	2.02687e6i	−0.638461	−	0.610255i
$407$	−362656.			−0.108520
$408$	−981605.	−	1.70019e6i	−0.291935	−	0.505647i
$409$	−1.87970e6	+	3.25574e6i	−0.555623	+	0.962367i	0.442232	+	0.896901i	$0.354187\pi$
$409$	−1.87970e6	+	3.25574e6i	−0.555623	+	0.962367i	−0.997855	+	0.0654664i	$0.979146\pi$
$410$	275313.	−	476856.i	0.0808847	−	0.140096i
$411$	−4.15380e6	−	7.19460e6i	−1.21295	−	2.10088i
$412$	−830643.			−0.241086
$413$	−184622.	+	757005.i	−0.0532609	+	0.218385i
$414$	−5.16605e6			−1.48135
$415$	1.00787e6	+	1.74568e6i	0.287266	+	0.497559i
$416$	−593341.	+	1.02770e6i	−0.168101	+	0.291160i
$417$	−720934.	+	1.24869e6i	−0.203028	+	0.351654i
$418$	87130.2	+	150914.i	0.0243909	+	0.0422463i
$419$	4.60027e6			1.28011			0.640056	−	0.768328i	$-0.278911\pi$
$419$	4.60027e6			1.28011			0.640056	+	0.768328i	$0.278911\pi$
$420$	−439659.	+	1.80273e6i	−0.121617	+	0.498663i
$421$	−404864.			−0.111328			−0.0556639	−	0.998450i	$-0.517728\pi$
$421$	−404864.			−0.111328			−0.0556639	+	0.998450i	$0.517728\pi$
$422$	−1.84374e6	−	3.19345e6i	−0.503986	−	0.872929i
$423$	2.06138e6	−	3.57041e6i	0.560153	−	0.970213i
$424$	357959.	−	620003.i	0.0966982	−	0.167486i
$425$	1.12751e6	+	1.95291e6i	0.302795	+	0.524457i
$426$	−1.97839e6			−0.528187
$427$	−1.39065e6	−	1.32921e6i	−0.369102	−	0.352796i
$428$	−399596.			−0.105442
$429$	−2.23147e6	−	3.86502e6i	−0.585393	−	1.01393i
$430$	283482.	−	491004.i	0.0739356	−	0.128060i
$431$	−47379.2	+	82063.2i	−0.0122856	+	0.0212792i	−0.872103	−	0.489323i	$-0.837244\pi$
$431$	−47379.2	+	82063.2i	−0.0122856	+	0.0212792i	0.859817	+	0.510602i	$0.170577\pi$
$432$	−405522.	−	702385.i	−0.104546	−	0.181078i
$433$	4.31727e6			1.10660			0.553298	−	0.832983i	$-0.313369\pi$
$433$	4.31727e6			1.10660			0.553298	+	0.832983i	$0.313369\pi$
$434$	1.15212e6	−	336771.i	0.293611	−	0.0858244i
$435$	5.06036e6			1.28221
$436$	29089.2	+	50383.9i	0.00732850	+	0.0126933i
$437$	−488021.	+	845277.i	−0.122246	+	0.211736i
$438$	−2.25716e6	+	3.90951e6i	−0.562182	+	0.973727i
$439$	1.11184e6	+	1.92576e6i	0.275346	+	0.476914i	0.970222	−	0.242216i	$-0.0778741\pi$
$439$	1.11184e6	+	1.92576e6i	0.275346	+	0.476914i	−0.694876	+	0.719130i	$0.744541\pi$
$440$	−359172.			−0.0884444
$441$	−5.53333e6	−	2.86968e6i	−1.35485	−	0.702647i
$442$	5.73909e6			1.39729
$443$	2.34213e6	+	4.05668e6i	0.567024	+	0.982114i	0.996858	+	0.0792062i	$0.0252386\pi$
$443$	2.34213e6	+	4.05668e6i	0.567024	+	0.982114i	−0.429835	+	0.902908i	$0.641428\pi$
$444$	462461.	−	801006.i	0.111331	−	0.192832i
$445$	−1.72487e6	+	2.98756e6i	−0.412910	+	0.715182i
$446$	1.67540e6	+	2.90188e6i	0.398824	+	0.690784i
$447$	7.01315e6			1.66014
$448$	−509685.	+	148984.i	−0.119979	+	0.0350707i
$449$	897932.			0.210198			0.105099	−	0.994462i	$-0.466484\pi$
$449$	897932.			0.210198			0.105099	+	0.994462i	$0.466484\pi$
$450$	1.35099e6	+	2.33999e6i	0.314501	+	0.544732i
$451$	−296306.	+	513217.i	−0.0685960	+	0.118812i
$452$	−497400.	+	861522.i	−0.114514	+	0.198344i
$453$	2.99246e6	+	5.18310e6i	0.685147	+	1.18671i
$454$	−5.32276e6			−1.21198
$455$	−3.92129e6	−	3.74805e6i	−0.887974	−	0.848745i
$456$	−444436.			−0.100091
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	−0.977931	−	0.208929i	$-0.933002\pi$
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	0.308027	−	0.951377i	$-0.400331\pi$
$458$	−2.02127e6	+	3.50094e6i	−0.450256	+	0.779867i
$459$	−1.96121e6	+	3.39691e6i	−0.434502	+	0.752580i
$460$	−1.00587e6	−	1.74222e6i	−0.221639	−	0.383891i
$461$	1.62507e6			0.356138			0.178069	−	0.984018i	$-0.443015\pi$
$461$	1.62507e6			0.356138			0.178069	+	0.984018i	$0.443015\pi$
$462$	473184.	−	1.94019e6i	0.103139	−	0.422902i
$463$	−8.46295e6			−1.83472			−0.917359	−	0.398060i	$-0.869683\pi$
$463$	−8.46295e6			−1.83472			−0.917359	+	0.398060i	$0.869683\pi$
$464$	724068.	+	1.25412e6i	0.156129	+	0.270424i
$465$	−1.03533e6	+	1.79324e6i	−0.222047	+	0.384596i
$466$	−2.97220e6	+	5.14800e6i	−0.634035	+	1.09818i
$467$	−3.83297e6	−	6.63890e6i	−0.813286	−	1.40865i	−0.910552	−	0.413395i	$-0.864343\pi$
$467$	−3.83297e6	−	6.63890e6i	−0.813286	−	1.40865i	0.0972658	−	0.995258i	$-0.468990\pi$
$468$	6.87663e6			1.45131
$469$	−1.32035e6	+	5.41383e6i	−0.277177	+	1.13651i
$470$	1.60546e6			0.335240
$471$	2.65143e6	+	4.59241e6i	0.550717	+	0.953869i
$472$	192331.	−	333127.i	0.0397370	−	0.0688265i
$473$	−305098.	+	528445.i	−0.0627027	+	0.108604i
$474$	−5.40086e6	−	9.35456e6i	−1.10412	−	1.91239i
$475$	510497.			0.103815
$476$	1.85647e6	+	1.77446e6i	0.375553	+	0.358962i
$477$	−4.14862e6			−0.834849
$478$	−1.75127e6	−	3.03330e6i	−0.350578	−	0.607219i
$479$	1.20146e6	−	2.08099e6i	0.239261	−	0.414412i	−0.721242	−	0.692683i	$-0.756428\pi$
$479$	1.20146e6	−	2.08099e6i	0.239261	−	0.414412i	0.960502	+	0.278272i	$0.0897616\pi$
$480$	458017.	−	793309.i	0.0907358	−	0.157159i
$481$	1.35192e6	+	2.34160e6i	0.266434	+	0.461477i
$482$	5.81178e6			1.13944
$483$	1.07364e7	−	3.13831e6i	2.09406	−	0.612107i
$484$	−2.19026e6			−0.424993
$485$	270881.	+	469180.i	0.0522907	+	0.0905701i
$486$	2.11582e6	−	3.66472e6i	0.406339	−	0.703801i
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	−0.857776	−	0.514023i	$-0.828154\pi$
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	0.874045	+	0.485844i	$0.161488\pi$
$488$	474839.	+	822445.i	0.0902603	+	0.156335i
$489$	1.59724e6			0.302063
$490$	−109600.	−	2.42483e6i	−0.0206215	−	0.456237i
$491$	−5.77628e6			−1.08130			−0.540648	−	0.841249i	$-0.681821\pi$
$491$	−5.77628e6			−1.08130			−0.540648	+	0.841249i	$0.681821\pi$
$492$	−755701.	−	1.30891e6i	−0.140746	−	0.243780i
$493$	3.50177e6	−	6.06525e6i	0.648890	−	1.12391i
$494$	649614.	−	1.12516e6i	0.119767	−	0.207443i
$495$	1.04067e6	+	1.80249e6i	0.190897	+	0.330644i
$496$	−592564.			−0.108151
$497$	2.48402e6	−	726095.i	0.451091	−	0.131857i
$498$	5.53296e6			0.999734
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	0.840558	−	0.541721i	$-0.182227\pi$
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	−0.889423	+	0.457084i	$0.848894\pi$
$500$	−1.42874e6	+	2.47464e6i	−0.255580	+	0.442678i
$501$	5.48418e6	−	9.49888e6i	0.976152	−	1.69075i
$502$	396769.	+	687223.i	0.0702713	+	0.121713i
$503$	−5.40086e6			−0.951794			−0.475897	−	0.879501i	$-0.657876\pi$
$503$	−5.40086e6			−0.951794			−0.475897	+	0.879501i	$0.657876\pi$
$504$	2.22444e6	+	2.12617e6i	0.390072	+	0.372839i
$505$	−970378.			−0.169322
$506$	1.08257e6	+	1.87506e6i	0.187966	+	0.325567i
$507$	−1.20374e7	+	2.08494e7i	−2.07976	+	3.60225i
$508$	−508402.	+	880579.i	−0.0874074	+	0.151394i
$509$	−4.17209e6	−	7.22628e6i	−0.713772	−	1.23629i	−0.963431	−	0.267955i	$-0.913652\pi$
$509$	−4.17209e6	−	7.22628e6i	−0.713772	−	1.23629i	0.249659	−	0.968334i	$-0.419681\pi$
$510$	−4.43018e6			−0.754216
$511$	1.39919e6	−	5.73710e6i	0.237042	−	0.971942i
$512$	262144.			0.0441942
$513$	443982.	+	769000.i	0.0744856	+	0.129013i
$514$	−959144.	+	1.66129e6i	−0.160131	+	0.277355i
$515$	−937213.	+	1.62330e6i	−0.155711	+	0.269700i
$516$	−778124.	−	1.34775e6i	−0.128654	−	0.222836i
$517$	−1.72788e6			−0.284307
$518$	−286676.	+	1.17546e6i	−0.0469426	+	0.192478i
$519$	−1.94740e6			−0.317349
$520$	1.33893e6	+	2.31910e6i	0.217145	+	0.376106i
$521$	5.73919e6	−	9.94057e6i	0.926310	−	1.60442i	0.136870	−	0.990589i	$-0.456296\pi$
$521$	5.73919e6	−	9.94057e6i	0.926310	−	1.60442i	0.789441	−	0.613827i	$-0.210371\pi$
$522$	4.19585e6	−	7.26743e6i	0.673976	−	1.16736i
$523$	2.19367e6	+	3.79955e6i	0.350685	+	0.607404i	0.986370	−	0.164545i	$-0.0526155\pi$
$523$	2.19367e6	+	3.79955e6i	0.350685	+	0.607404i	−0.635685	+	0.771949i	$0.719282\pi$
$524$	2.18075e6			0.346959
$525$	−4.22922e6	−	4.04238e6i	−0.669673	−	0.640088i
$526$	1.81977e6			0.286782
$527$	1.43289e6	+	2.48184e6i	0.224744	+	0.389267i
$528$	−492942.	+	853801.i	−0.0769505	+	0.133282i
$529$	−2.84535e6	+	4.92829e6i	−0.442075	+	0.765697i
$530$	−807769.	−	1.39910e6i	−0.124910	−	0.216350i
$531$	−2.22906e6			−0.343071
$532$	558023.	−	163114.i	0.0854817	−	0.0249869i
$533$	4.41832e6			0.673657
$534$	4.73456e6	+	8.20050e6i	0.718500	+	1.24448i
$535$	−450864.	+	780919.i	−0.0681022	+	0.117956i
$536$	1.37548e6	−	2.38241e6i	0.206797	−	0.358182i
$537$	6.32327e6	+	1.09522e7i	0.946250	+	1.63895i
$538$	−3.44055e6			−0.512474
$539$	117957.	+	2.60973e6i	0.0174885	+	0.386922i
$540$	−1.83020e6			−0.270094
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	−0.999366	−	0.0356020i	$-0.988665\pi$
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	0.468851	−	0.883277i	$-0.344668\pi$
$542$	−2.61116e6	+	4.52266e6i	−0.381799	+	0.661296i
$543$	273182.	−	473165.i	0.0397605	−	0.0688673i
$544$	−633897.	−	1.09794e6i	−0.0918378	−	0.159068i
$545$	131285.			0.0189332
$546$	−1.42914e7	+	4.17746e6i	−2.05160	+	0.599696i
$547$	3.54529e6			0.506622			0.253311	−	0.967385i	$-0.418480\pi$
$547$	3.54529e6			0.506622			0.253311	+	0.967385i	$0.418480\pi$
$548$	−2.68243e6	−	4.64610e6i	−0.381572	−	0.660902i
$549$	2.75161e6	−	4.76593e6i	0.389634	−	0.674865i
$550$	566214.	−	980712.i	0.0798131	−	0.138240i
$551$	−792739.	−	1.37306e6i	−0.111237	−	0.192669i
$552$	−5.52199e6			−0.771343
$553$	1.02144e7	+	9.76319e6i	1.42037	+	1.35762i
$554$	−2.17243e6			−0.300727
$555$	−1.04359e6	−	1.80755e6i	−0.143813	−	0.249091i
$556$	−465562.	+	806377.i	−0.0638691	+	0.110624i
$557$	−5.18314e6	+	8.97747e6i	−0.707873	+	1.22607i	0.257772	+	0.966206i	$0.417012\pi$
$557$	−5.18314e6	+	8.97747e6i	−0.707873	+	1.22607i	−0.965645	+	0.259866i	$0.916322\pi$
$558$	1.71690e6	+	2.97377e6i	0.233432	+	0.404316i
$559$	4.54941e6			0.615780
$560$	−283921.	+	1.16416e6i	−0.0382585	+	0.156871i
$561$	4.76799e6			0.639628
$562$	−1.99618e6	−	3.45748e6i	−0.266599	−	0.461763i
$563$	2.24141e6	−	3.88223e6i	0.298023	−	0.516191i	−0.677660	−	0.735375i	$-0.737006\pi$
$563$	2.24141e6	−	3.88223e6i	0.298023	−	0.516191i	0.975684	+	0.219184i	$0.0703394\pi$
$564$	2.20340e6	−	3.81641e6i	0.291673	−	0.505193i
$565$	1.12243e6	+	1.94411e6i	0.147924	+	0.256212i
$566$	7.10928e6			0.932792
$567$	−357124.	+	1.46431e6i	−0.0466511	+	0.191283i
$568$	−1.27760e6			−0.166158
$569$	−3.24668e6	−	5.62341e6i	−0.420396	−	0.728147i	0.575582	−	0.817744i	$-0.304775\pi$
$569$	−3.24668e6	−	5.62341e6i	−0.420396	−	0.728147i	−0.995978	+	0.0895969i	$0.971442\pi$
$570$	−501456.	+	868547.i	−0.0646466	+	0.111971i
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	−0.849620	−	0.527396i	$-0.823168\pi$
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	0.881548	+	0.472094i	$0.156502\pi$
$572$	−1.44103e6	−	2.49593e6i	−0.184155	−	0.318965i
$573$	−1.38290e7			−1.75956
$574$	1.42923e6	+	1.36609e6i	0.181060	+	0.173061i
$575$	6.34279e6			0.800038
$576$	−759541.	−	1.31556e6i	−0.0953882	−	0.165217i
$577$	3.27561e6	−	5.67353e6i	0.409594	−	0.709437i	−0.585250	−	0.810853i	$-0.699004\pi$
$577$	3.27561e6	−	5.67353e6i	0.409594	−	0.709437i	0.994844	+	0.101416i	$0.0323372\pi$
$578$	−225973.	+	391397.i	−0.0281343	+	0.0487301i
$579$	610939.	+	1.05818e6i	0.0757359	+	0.131178i
$580$	3.26786e6			0.403360
$581$	−6.94707e6	+	2.03067e6i	−0.853810	+	0.249574i
$582$	1.48707e6			0.181981
$583$	869363.	+	1.50578e6i	0.105933	+	0.183481i
$584$	−1.45762e6	+	2.52467e6i	−0.176853	+	0.306318i
$585$	7.75889e6	−	1.34388e7i	0.937368	−	1.62357i
$586$	3.27974e6	+	5.68067e6i	0.394543	+	0.683369i
$587$	−30793.5			−0.00368862			−0.00184431	−	0.999998i	$-0.500587\pi$
$587$	−30793.5			−0.00368862			−0.00184431	+	0.999998i	$0.500587\pi$
$588$	−5.91457e6	−	3.06740e6i	−0.705473	−	0.365870i
$589$	648763.			0.0770544
$590$	−434014.	−	751735.i	−0.0513303	−	0.0889067i
$591$	1.16636e7	−	2.02019e7i	1.37361	−	2.37916i
$592$	298646.	−	517271.i	0.0350230	−	0.0606616i
$593$	−285468.	−	494446.i	−0.0333366	−	0.0577407i	0.848876	−	0.528592i	$-0.177280\pi$
$593$	−285468.	−	494446.i	−0.0333366	−	0.0577407i	−0.882212	+	0.470852i	$0.843947\pi$
$594$	1.96976e6			0.229059
$595$	5.56243e6	−	1.62593e6i	0.644128	−	0.188283i
$596$	4.52893e6			0.522251
$597$	−7.92859e6	−	1.37327e7i	−0.910459	−	1.57696i
$598$	8.07127e6	−	1.39799e7i	0.922973	−	1.59864i
$599$	−4.53555e6	+	7.85581e6i	−0.516492	+	0.894590i	0.483325	+	0.875441i	$0.339429\pi$
$599$	−4.53555e6	+	7.85581e6i	−0.516492	+	0.894590i	−0.999817	+	0.0191488i	$0.993904\pi$
$600$	1.44408e6	+	2.50122e6i	0.163762	+	0.283644i
$601$	−1.36309e7			−1.53936			−0.769679	−	0.638431i	$-0.779584\pi$
$601$	−1.36309e7			−1.53936			−0.769679	+	0.638431i	$0.779584\pi$
$602$	1.47164e6	+	1.40662e6i	0.165504	+	0.158193i
$603$	−1.59414e7			−1.78539
$604$	1.93246e6	+	3.34712e6i	0.215535	+	0.373318i
$605$	−2.47126e6	+	4.28035e6i	−0.274493	+	0.475435i
$606$	−1.33179e6	+	2.30672e6i	−0.147317	+	0.255161i
$607$	1.97825e6	+	3.42644e6i	0.217927	+	0.377460i	0.954174	−	0.299253i	$-0.0967373\pi$
$607$	1.97825e6	+	3.42644e6i	0.217927	+	0.377460i	−0.736247	+	0.676713i	$0.763404\pi$
$608$	−287006.			−0.0314870
$609$	−4.30518e6	+	1.76525e7i	−0.470379	+	1.92869i
$610$	2.14304e6			0.233188
$611$	6.44126e6	+	1.11566e7i	0.698020	+	1.20901i
$612$	−3.67333e6	+	6.36239e6i	−0.396444	+	0.686660i
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	−0.899387	−	0.437154i	$-0.855987\pi$
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	0.828280	+	0.560315i	$0.189320\pi$
$614$	−4.76261e6	−	8.24908e6i	−0.509828	−	0.883049i
$615$	−3.41063e6			−0.363619
$616$	305571.	−	1.25293e6i	0.0324459	−	0.133038i
$617$	9.26370e6			0.979651			0.489826	−	0.871820i	$-0.337060\pi$
$617$	9.26370e6			0.979651			0.489826	+	0.871820i	$0.337060\pi$
$618$	2.57254e6	+	4.45577e6i	0.270951	+	0.469301i
$619$	−334693.	+	579705.i	−0.0351091	+	0.0608107i	−0.883046	−	0.469286i	$-0.844511\pi$
$619$	−334693.	+	579705.i	−0.0351091	+	0.0608107i	0.847937	+	0.530097i	$0.177845\pi$
$620$	−668589.	+	1.15803e6i	−0.0698521	+	0.120987i
$621$	5.51636e6	+	9.55461e6i	0.574015	+	0.994223i
$622$	−4.98051e6			−0.516176
$623$	−8.95430e6	−	8.55872e6i	−0.924297	−	0.883463i
$624$	7.35043e6			0.755703
$625$	378164.	+	654999.i	0.0387240	+	0.0670719i
$626$	−3.32598e6	+	5.76077e6i	−0.339222	+	0.587550i
$627$	539693.	−	934776.i	0.0548249	−	0.0949595i
$628$	1.71223e6	+	2.96567e6i	0.173246	+	0.300071i
$629$	−2.88866e6			−0.291118
$630$	6.66495e6	−	1.94821e6i	0.669030	−	0.195562i
$631$	−666246.			−0.0666133			−0.0333067	−	0.999445i	$-0.510604\pi$
$631$	−666246.			−0.0666133			−0.0333067	+	0.999445i	$0.510604\pi$
$632$	−3.48774e6	−	6.04095e6i	−0.347338	−	0.601607i
$633$	−1.14203e7	+	1.97805e7i	−1.13284	+	1.96213i
$634$	5.24972e6	−	9.09277e6i	0.518696	−	0.898407i
$635$	1.14726e6	+	1.98711e6i	0.112909	+	0.195564i
$636$	−4.43446e6			−0.434708
$637$	1.64108e7	−	1.04903e7i	1.60243	−	1.02432i
$638$	−3.51704e6			−0.342078
$639$	3.70173e6	+	6.41158e6i	0.358635	+	0.621173i
$640$	295777.	−	512300.i	0.0285439	−	0.0494396i
$641$	1.05439e6	−	1.82625e6i	0.101357	−	0.175556i	−0.810887	−	0.585203i	$-0.801015\pi$
$641$	1.05439e6	−	1.82625e6i	0.101357	−	0.175556i	0.912244	+	0.409647i	$0.134348\pi$
$642$	1.23757e6	+	2.14353e6i	0.118504	+	0.205254i
$643$	1.25977e7			1.20161			0.600806	−	0.799395i	$-0.294846\pi$
$643$	1.25977e7			1.20161			0.600806	+	0.799395i	$0.294846\pi$
$644$	6.93328e6	−	2.02664e6i	0.658756	−	0.192558i
$645$	−3.51182e6			−0.332379
$646$	694016.	+	1.20207e6i	0.0654317	+	0.113331i
$647$	−8.56496e6	+	1.48349e7i	−0.804386	+	1.39324i	0.112319	+	0.993672i	$0.464172\pi$
$647$	−8.56496e6	+	1.48349e7i	−0.804386	+	1.39324i	−0.916705	+	0.399565i	$0.869161\pi$
$648$	372036.	−	644386.i	0.0348055	−	0.0602849i
$649$	467109.	+	809056.i	0.0435318	+	0.0753992i
$650$	−8.44301e6			−0.783815
$651$	−5.37469e6	−	5.13724e6i	−0.497051	−	0.475092i
$652$	1.03146e6			0.0950237
$653$	4.12762e6	+	7.14925e6i	0.378806	+	0.656112i	0.990889	−	0.134682i	$-0.0430013\pi$
$653$	4.12762e6	+	7.14925e6i	0.378806	+	0.656112i	−0.612083	+	0.790794i	$0.709668\pi$
$654$	180181.	−	312083.i	0.0164727	−	0.0285316i
$655$	2.46054e6	−	4.26178e6i	0.224092	−	0.388139i
$656$	−488014.	−	845265.i	−0.0442764	−	0.0766890i
$657$	1.68933e7			1.52687
$658$	−1.36587e6	+	5.60048e6i	−0.122983	+	0.504267i
$659$	−1.05417e7			−0.945581			−0.472790	−	0.881175i	$-0.656753\pi$
$659$	−1.05417e7			−0.945581			−0.472790	+	0.881175i	$0.656753\pi$
$660$	1.11237e6	+	1.92668e6i	0.0994009	+	0.172167i
$661$	−2.23820e6	+	3.87668e6i	−0.199249	+	0.345109i	−0.948285	−	0.317420i	$-0.897184\pi$
$661$	−2.23820e6	+	3.87668e6i	−0.199249	+	0.345109i	0.749036	+	0.662529i	$0.230517\pi$
$662$	−3.47771e6	+	6.02357e6i	−0.308424	+	0.534206i
$663$	−1.77743e7	−	3.07859e7i	−1.57039	−	2.72000i
$664$	3.57306e6			0.314499
$665$	310848.	−	1.27457e6i	0.0272580	−	0.111766i
$666$	−3.46121e6			−0.302373
$667$	−9.84956e6	−	1.70599e7i	−0.857240	−	1.48478i
$668$	3.54155e6	−	6.13415e6i	0.307081	−	0.531880i
$669$	1.03776e7	−	1.79745e7i	0.896461	−	1.55272i
$670$	−3.10391e6	−	5.37614e6i	−0.267130	−	0.462683i
$671$	−2.30645e6			−0.197760
$672$	2.37771e6	+	2.27266e6i	0.203112	+	0.194139i
$673$	−1.87165e7			−1.59289			−0.796447	−	0.604708i	$-0.793290\pi$
$673$	−1.87165e7			−1.59289			−0.796447	+	0.604708i	$0.793290\pi$
$674$	−1.70713e6	−	2.95683e6i	−0.144749	−	0.250713i
$675$	2.88521e6	−	4.99733e6i	0.243735	−	0.422162i
$676$	−7.77348e6	+	1.34641e7i	−0.654258	+	1.13321i
$677$	−2.08116e6	−	3.60467e6i	−0.174515	−	0.302270i	0.765478	−	0.643462i	$-0.222503\pi$
$677$	−2.08116e6	−	3.60467e6i	−0.174515	−	0.302270i	−0.939993	+	0.341192i	$0.889169\pi$
$678$	6.16188e6			0.514801
$679$	−1.86714e6	+	545776.i	−0.155418	+	0.0454297i
$680$	−2.86090e6			−0.237263
$681$	1.64848e7	+	2.85526e7i	1.36212	+	2.35927i
$682$	719570.	−	1.24633e6i	0.0592396	−	0.102606i
$683$	6.43455e6	−	1.11450e7i	0.527796	−	0.914170i	−0.471679	−	0.881770i	$-0.656352\pi$
$683$	6.43455e6	−	1.11450e7i	0.527796	−	0.914170i	0.999475	−	0.0323992i	$-0.0103148\pi$
$684$	831576.	+	1.44033e6i	0.0679613	+	0.117712i
$685$	−1.21063e7			−0.985793
$686$	8.55199e6	+	1.68063e6i	0.693836	+	0.136352i
$687$	2.50398e7			2.02414
$688$	−502494.	−	870345.i	−0.0404725	−	0.0701004i
$689$	6.48168e6	−	1.12266e7i	0.520163	−	0.900949i
$690$	−6.23045e6	+	1.07915e7i	−0.498192	+	0.862894i
$691$	4.64518e6	+	8.04569e6i	0.370090	+	0.641015i	0.989579	−	0.143990i	$-0.0459934\pi$
$691$	4.64518e6	+	8.04569e6i	0.370090	+	0.641015i	−0.619489	+	0.785006i	$0.712660\pi$
$692$	−1.25758e6			−0.0998325
$693$	−7.17316e6	+	2.09676e6i	−0.567385	+	0.165850i
$694$	−1.19400e7			−0.941033
$695$	1.05059e6	+	1.81967e6i	0.0825029	+	0.142899i
$696$	4.48495e6	−	7.76816e6i	0.350941	−	0.607848i
$697$	−2.36016e6	+	4.08791e6i	−0.184018	+	0.318728i
$698$	−5.74934e6	−	9.95815e6i	−0.446662	−	0.773642i
$699$	3.68202e7			2.85032
$700$	−2.73113e6	−	2.61048e6i	−0.210668	−	0.201361i
$701$	2.50809e7			1.92774			0.963870	−	0.266375i	$-0.0858258\pi$
$701$	2.50809e7			1.92774			0.963870	+	0.266375i	$0.0858258\pi$
$702$	−7.34293e6	−	1.27183e7i	−0.562376	−	0.974063i
$703$	−326970.	+	566329.i	−0.0249528	+	0.0432196i
$704$	−318330.	+	551364.i	−0.0242073	+	0.0419283i
$705$	−4.97220e6	−	8.61210e6i	−0.376769	−	0.652584i
$706$	5.88437e6			0.444312
$707$	825564.	−	3.38505e6i	0.0621158	−	0.254693i
$708$	−2.38264e6			−0.178638
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	0.618524	−	0.785766i	$-0.287731\pi$
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	−0.989755	+	0.142774i	$0.954398\pi$
$710$	−1.44151e6	+	2.49677e6i	−0.107318	+	0.185880i
$711$	−2.02109e7	+	3.50063e7i	−1.49938	+	2.59700i
$712$	3.05747e6	+	5.29569e6i	0.226028	+	0.391491i
$713$	8.06069e6			0.593811
$714$	3.76904e6	−	1.54542e7i	0.276685	−	1.13449i
$715$	−6.50364e6			−0.475764
$716$	4.08342e6	+	7.07269e6i	0.297674	+	0.515587i
$717$	−1.08476e7	+	1.87885e7i	−0.788015	+	1.36488i
$718$	−6.15598e6	+	1.06625e7i	−0.445642	+	0.771875i
$719$	7.00047e6	+	1.21252e7i	0.505016	+	0.874713i	0.999983	+	0.00580117i	$0.00184658\pi$
$719$	7.00047e6	+	1.21252e7i	0.505016	+	0.874713i	−0.494968	+	0.868911i	$0.664820\pi$
$720$	−3.42795e6			−0.246436
$721$	−4.86536e6	−	4.65041e6i	−0.348559	−	0.333160i
$722$	−9.59017e6			−0.684673
$723$	−1.79994e7	−	3.11758e7i	−1.28059	−	2.21805i
$724$	176414.	−	305559.i	0.0125080	−	0.0216645i
$725$	−5.15160e6	+	8.92283e6i	−0.363996	+	0.630460i
$726$	6.78333e6	+	1.17491e7i	0.477641	+	0.827298i
$727$	8.27315e6			0.580544			0.290272	−	0.956944i	$-0.406254\pi$
$727$	8.27315e6			0.580544			0.290272	+	0.956944i	$0.406254\pi$
$728$	−9.22903e6	+	2.69770e6i	−0.645398	+	0.188654i
$729$	−2.33861e7			−1.62982
$730$	3.28926e6	+	5.69716e6i	0.228450	+	0.395687i
$731$	−2.43019e6	+	4.20921e6i	−0.168208	+	0.291345i
$732$	2.94120e6	−	5.09430e6i	0.202883	−	0.351404i
$733$	1.64295e6	+	2.84568e6i	0.112945	+	0.195626i	0.916956	−	0.398988i	$-0.130638\pi$
$733$	1.64295e6	+	2.84568e6i	0.112945	+	0.195626i	−0.804012	+	0.594614i	$0.797305\pi$
$734$	6.46679e6			0.443046
$735$	−1.26679e7	+	8.09773e6i	−0.864943	+	0.552898i
$736$	−3.56597e6			−0.242651
$737$	3.34059e6	+	5.78608e6i	0.226545	+	0.392388i
$738$	−2.82796e6	+	4.89817e6i	−0.191132	+	0.331050i
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	−0.984407	−	0.175907i	$-0.943714\pi$
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	0.644543	+	0.764568i	$0.277048\pi$
$740$	−673925.	−	1.16727e6i	−0.0452410	−	0.0783597i
$741$	−8.04754e6			−0.538416
$742$	5.56781e6	−	1.62751e6i	0.371257	−	0.108521i
$743$	1.73443e7			1.15261			0.576307	−	0.817233i	$-0.304493\pi$
$743$	1.73443e7			1.15261			0.576307	+	0.817233i	$0.304493\pi$
$744$	1.83520e6	+	3.17866e6i	0.121549	+	0.210529i
$745$	5.10998e6	−	8.85074e6i	0.337309	−	0.584237i
$746$	9.52237e6	−	1.64932e7i	0.626467	−	1.08507i
$747$	−1.03526e7	−	1.79313e7i	−0.678812	−	1.17574i
$748$	3.07905e6			0.201216
$749$	−2.34057e6	−	2.23717e6i	−0.152446	−	0.145711i
$750$	1.76995e7			1.14897
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	0.996639	+	0.0819170i	$0.0261042\pi$
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	−0.427377	+	0.904073i	$0.640562\pi$
$752$	1.42291e6	−	2.46455e6i	0.0917554	−	0.158925i
$753$	2.45762e6	−	4.25673e6i	0.157953	−	0.273583i
$754$	1.31109e7	+	2.27088e7i	0.839857	+	1.45468i
$755$	8.72158e6			0.556836
$756$	1.55707e6	−	6.38445e6i	0.0990841	−	0.406274i
$757$	−4.66480e6			−0.295865			−0.147932	−	0.988997i	$-0.547262\pi$
$757$	−4.66480e6			−0.295865			−0.147932	+	0.988997i	$0.547262\pi$
$758$	−2.00386e6	−	3.47079e6i	−0.126676	−	0.219409i
$759$	6.70554e6	−	1.16143e7i	0.422502	−	0.731795i
$760$	−323828.	+	560887.i	−0.0203367	+	0.0352242i
$761$	−9.13585e6	−	1.58238e7i	−0.571857	−	0.990485i	−0.996375	−	0.0850658i	$-0.972890\pi$
$761$	−9.13585e6	−	1.58238e7i	−0.571857	−	0.990485i	0.424518	−	0.905419i	$-0.360443\pi$
$762$	6.29819e6			0.392942
$763$	−111693.	+	457973.i	−0.00694566	+	0.0284792i
$764$	−8.93044e6			−0.553528
$765$	8.28923e6	+	1.43574e7i	0.512107	+	0.886995i
$766$	5.64305e6	−	9.77404e6i	0.347489	−	0.601869i
$767$	3.48261e6	−	6.03205e6i	0.213755	−	0.370234i
$768$	−811873.	−	1.40620e6i	−0.0496689	−	0.0860291i
$769$	−2.31895e7			−1.41409			−0.707043	−	0.707171i	$-0.749971\pi$
$769$	−2.31895e7			−1.41409			−0.707043	+	0.707171i	$0.749971\pi$
$770$	−2.10379e6	−	2.01085e6i	−0.127872	−	0.122223i
$771$	1.18821e7			0.719873
$772$	394530.	+	683346.i	0.0238252	+	0.0412665i
$773$	−1.01074e6	+	1.75066e6i	−0.0608405	+	0.105379i	−0.894841	−	0.446384i	$-0.852711\pi$
$773$	−1.01074e6	+	1.75066e6i	−0.0608405	+	0.105379i	0.834001	+	0.551763i	$0.186045\pi$
$774$	−2.91187e6	+	5.04351e6i	−0.174711	+	0.302608i
$775$	−2.10799e6	−	3.65114e6i	−0.126070	−	0.218360i
$776$	960317.			0.0572480
$777$	7.19328e6	−	2.10264e6i	0.427439	−	0.124943i
$778$	−4.96959e6			−0.294355
$779$	534297.	+	925430.i	0.0315456	+	0.0546387i
$780$	8.29347e6	−	1.43647e7i	0.488090	−	0.845397i
$781$	1.55143e6	−	2.68715e6i	0.0910131	−	0.157639i
$782$	8.62296e6	+	1.49354e7i	0.504243	+	0.873374i
$783$	−1.79215e7			−1.04465
$784$	−3.81949e6	−	1.98085e6i	−0.221930	−	0.115097i
$785$	7.72763e6			0.447582
$786$	−6.75389e6	−	1.16981e7i	−0.389940	−	0.675396i
$787$	−7.88722e6	+	1.36611e7i	−0.453928	+	0.786227i	−0.998626	−	0.0524059i	$-0.983311\pi$
$787$	−7.88722e6	+	1.36611e7i	−0.453928	+	0.786227i	0.544698	+	0.838632i	$0.316644\pi$
$788$	7.53207e6	−	1.30459e7i	0.432114	−	0.748444i
$789$	−5.63592e6	−	9.76170e6i	−0.322309	−	0.558255i
$790$	−1.57409e7			−0.897348
$791$	−7.73672e6	+	2.26149e6i	−0.439659	+	0.128515i
$792$	3.68934e6			0.208995
$793$	8.59807e6	+	1.48923e7i	0.485532	+	0.840966i
$794$	−5.49124e6	+	9.51111e6i	−0.309115	+	0.535402i
$795$	−5.00340e6	+	8.66614e6i	−0.280768	+	0.486304i
$796$	−5.12010e6	−	8.86827e6i	−0.286415	−	0.496085i
$797$	1.22436e6			0.0682750			0.0341375	−	0.999417i	$-0.489132\pi$
$797$	1.22436e6			0.0682750			0.0341375	+	0.999417i	$0.489132\pi$
$798$	−2.60321e6	−	2.48820e6i	−0.144711	−	0.138318i
$799$	−1.37631e7			−0.762690
$800$	932551.	+	1.61523e6i	0.0515167	+	0.0892295i
$801$	1.77175e7	−	3.06876e7i	0.975712	−	1.68998i
$802$	7.42670e6	−	1.28634e7i	0.407718	−	0.706189i
$803$	−3.54007e6	−	6.13158e6i	−0.193742	−	0.335571i
$804$	−1.70398e7			−0.929658
$805$	3.86221e6	−	1.58362e7i	0.210061	−	0.861312i
$806$	−1.07297e7			−0.581771
$807$	1.06555e7	+	1.84559e7i	0.575959	+	0.997590i
$808$	−860037.	+	1.48963e6i	−0.0463435	+	0.0802692i
$809$	1.38662e7	−	2.40170e7i	0.744882	−	1.29017i	−0.205368	−	0.978685i	$-0.565839\pi$
$809$	1.38662e7	−	2.40170e7i	0.744882	−	1.29017i	0.950250	−	0.311489i	$-0.100828\pi$
$810$	−839536.	−	1.45412e6i	−0.0449600	−	0.0778731i
$811$	−1.19246e7			−0.636636			−0.318318	−	0.947984i	$-0.603118\pi$
$811$	−1.19246e7			−0.636636			−0.318318	+	0.947984i	$0.603118\pi$
$812$	−2.78018e6	+	1.13996e7i	−0.147973	+	0.606734i
$813$	3.23476e7			1.71639
$814$	725313.	+	1.25628e6i	0.0383676	+	0.0664546i
$815$	1.16379e6	−	2.01575e6i	0.0613735	−	0.106302i
$816$	−3.92642e6	+	6.80076e6i	−0.206429	+	0.357546i
$817$	550151.	+	952889.i	0.0288354	+	0.0499444i
$818$	1.50376e7			0.785770
$819$	4.02787e7	+	3.84993e7i	2.09829	+	2.00559i
$820$	−2.20250e6			−0.114388
$821$	−8.02312e6	−	1.38965e7i	−0.415418	−	0.719525i	0.580054	−	0.814578i	$-0.303031\pi$
$821$	−8.02312e6	−	1.38965e7i	−0.415418	−	0.719525i	−0.995472	+	0.0950526i	$0.969698\pi$
$822$	−1.66152e7	+	2.87784e7i	−0.857682	+	1.48555i
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	−0.684583	−	0.728935i	$-0.740016\pi$
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	0.973568	+	0.228398i	$0.0733489\pi$
$824$	1.66129e6	+	2.87743e6i	0.0852367	+	0.147634i
$825$	−7.01437e6			−0.358801
$826$	2.99159e6	−	874460.i	0.152564	−	0.0445954i
$827$	−2.68427e7			−1.36478			−0.682389	−	0.730989i	$-0.739059\pi$
$827$	−2.68427e7			−1.36478			−0.682389	+	0.730989i	$0.739059\pi$
$828$	1.03321e7	+	1.78957e7i	0.523736	+	0.907138i
$829$	−1.40210e7	+	2.42850e7i	−0.708584	+	1.22730i	0.256798	+	0.966465i	$0.417332\pi$
$829$	−1.40210e7	+	2.42850e7i	−0.708584	+	1.22730i	−0.965382	+	0.260839i	$0.916001\pi$
$830$	4.03147e6	−	6.98272e6i	0.203127	−	0.351827i
$831$	6.72813e6	+	1.16535e7i	0.337981	+	0.585400i
$832$	4.74673e6			0.237731
$833$	939564.	+	2.07872e7i	0.0469152	+	1.03797i
$834$	5.76747e6			0.287125
$835$	−7.99186e6	−	1.38423e7i	−0.396672	−	0.687056i
$836$	348521.	−	603656.i	0.0172470	−	0.0298727i
$837$	3.66665e6	−	6.35083e6i	0.180907	−	0.313341i
$838$	−9.20054e6	−	1.59358e7i	−0.452588	−	0.783905i
$839$	−3.30603e7			−1.62145			−0.810723	−	0.585430i	$-0.800926\pi$
$839$	−3.30603e7			−1.62145			−0.810723	+	0.585430i	$0.800926\pi$
$840$	7.12416e6	−	2.08244e6i	0.348366	−	0.101830i
$841$	1.14880e7			0.560086
$842$	809728.	+	1.40249e6i	0.0393604	+	0.0681741i
$843$	−1.23645e7	+	2.14160e7i	−0.599250	+	1.03793i
$844$	−7.37495e6	+	1.27738e7i	−0.356372	+	0.617254i
$845$	1.75416e7	+	3.03830e7i	0.845139	+	1.46382i
$846$	−1.64910e7			−0.792176
$847$	−1.28291e7	−	1.22623e7i	−0.614450	−	0.587305i
$848$	−2.86367e6			−0.136752
$849$	−2.20178e7	−	3.81359e7i	−1.04835	−	1.81579i
$850$	4.51005e6	−	7.81164e6i	0.214109	−	0.370847i
$851$	−4.06251e6	+	7.03648e6i	−0.192296	+	0.333067i
$852$	3.95677e6	+	6.85334e6i	0.186742	+	0.323447i
$853$	2.73897e7			1.28889			0.644444	−	0.764652i	$-0.277089\pi$
$853$	2.73897e7			1.28889			0.644444	+	0.764652i	$0.277089\pi$
$854$	−1.82322e6	+	7.47575e6i	−0.0855452	+	0.350760i
$855$	3.75306e6			0.175578
$856$	799192.	+	1.38424e6i	0.0372792	+	0.0645695i
$857$	1.48360e6	−	2.56968e6i	0.0690027	−	0.119516i	−0.829460	−	0.558566i	$-0.811352\pi$
$857$	1.48360e6	−	2.56968e6i	0.0690027	−	0.119516i	0.898463	+	0.439050i	$0.144685\pi$
$858$	−8.92587e6	+	1.54601e7i	−0.413935	+	0.716957i
$859$	1.98980e7	+	3.44643e7i	0.920081	+	1.59363i	0.799287	+	0.600949i	$0.205211\pi$
$859$	1.98980e7	+	3.44643e7i	0.920081	+	1.59363i	0.120794	+	0.992678i	$0.461456\pi$
$860$	−2.26785e6			−0.104561
$861$	2.90164e6	−	1.18976e7i	0.133394	−	0.546954i
$862$	379034.			0.0173744
$863$	−3.59799e6	−	6.23190e6i	−0.164450	−	0.284835i	0.772010	−	0.635610i	$-0.219251\pi$
$863$	−3.59799e6	−	6.23190e6i	−0.164450	−	0.284835i	−0.936460	+	0.350775i	$0.885918\pi$
$864$	−1.62209e6	+	2.80954e6i	−0.0739248	+	0.128042i
$865$	−1.41893e6	+	2.45766e6i	−0.0644794	+	0.111682i
$866$	−8.63453e6	−	1.49554e7i	−0.391241	−	0.677649i
$867$	2.79940e6			0.126478
$868$	−3.47084e6	−	3.31751e6i	−0.156364	−	0.149456i
$869$	1.69411e7			0.761015
$870$	−1.01207e7	−	1.75296e7i	−0.453329	−	0.785188i
$871$	2.49063e7	−	4.31391e7i	1.11241	−	1.92675i
$872$	116357.	−	201536.i	0.00518203	−	0.00897554i
$873$	−2.78244e6	−	4.81932e6i	−0.123563	−	0.214018i
$874$	3.90417e6			0.172882
$875$	−2.22231e7	+	6.49594e6i	−0.981259	+	0.286828i
$876$	1.80573e7			0.795045
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	−0.998165	−	0.0605532i	$-0.980714\pi$
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	0.446642	−	0.894713i	$-0.352620\pi$
$878$	4.44734e6	−	7.70303e6i	0.194699	−	0.337229i
$879$	2.03150e7	−	3.51866e7i	0.886839	−	1.53605i
$880$	718343.	+	1.24421e6i	0.0312698	+	0.0541609i
$881$	120262.			0.00522022			0.00261011	−	0.999997i	$-0.499169\pi$
$881$	120262.			0.00522022			0.00261011	+	0.999997i	$0.499169\pi$
$882$	1.12579e6	+	2.49074e7i	0.0487289	+	1.07809i
$883$	2.43497e7			1.05097			0.525487	−	0.850802i	$-0.323883\pi$
$883$	2.43497e7			1.05097			0.525487	+	0.850802i	$0.323883\pi$
$884$	−1.14782e7	−	1.98808e7i	−0.494018	−	0.855664i
$885$	−2.68833e6	+	4.65632e6i	−0.115378	+	0.199841i
$886$	9.36851e6	−	1.62267e7i	0.400946	−	0.694459i
$887$	1.41383e7	+	2.44883e7i	0.603377	+	1.04508i	0.992306	+	0.123812i	$0.0395120\pi$
$887$	1.41383e7	+	2.44883e7i	0.603377	+	1.04508i	−0.388929	+	0.921268i	$0.627155\pi$
$888$	−3.69969e6			−0.157446
$889$	−7.90786e6	+	2.31152e6i	−0.335587	+	0.0980941i
$890$	1.37989e7			0.583943
$891$	903552.	+	1.56500e6i	0.0381293	+	0.0660419i
$892$	6.70160e6	−	1.16075e7i	0.282011	−	0.488458i
$893$	−1.55786e6	+	2.69828e6i	−0.0653730	+	0.113229i
$894$	−1.40263e7	−	2.42943e7i	−0.586948	−	1.01662i
$895$	1.84293e7			0.769042
$896$	1.53547e6	+	1.46763e6i	0.0638955	+	0.0610727i
$897$	−9.99885e7			−4.14924
$898$	−1.79586e6	−	3.11053e6i	−0.0743161	−	0.128719i
$899$	−6.54688e6	+	1.13395e7i	−0.270169	+	0.467946i
$900$	5.40398e6	−	9.35997e6i	0.222386	−	0.385184i
$901$	6.92471e6	+	1.19940e7i	0.284178	+	0.492210i
$902$	2.37045e6			0.0970094
$903$	2.98774e6	−	1.22506e7i	0.121934	−	0.499963i
$904$	3.97920e6			0.161948
$905$	−398096.	−	689523.i	−0.0161572	−	0.0279851i
$906$	1.19699e7	−	2.07324e7i	0.484472	−	0.839130i
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	−0.509195	−	0.860651i	$-0.670057\pi$
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	0.999943	+	0.0106507i	$0.00339029\pi$
$908$	1.06455e7	+	1.84386e7i	0.428501	+	0.742186i
$909$	9.96754e6			0.400109
$910$	−5.14106e6	+	2.10798e7i	−0.205802	+	0.843847i
$911$	−3.36224e7			−1.34225			−0.671123	−	0.741346i	$-0.734188\pi$
$911$	−3.36224e7			−1.34225			−0.671123	+	0.741346i	$0.734188\pi$
$912$	888871.	+	1.53957e6i	0.0353876	+	0.0612932i
$913$	−4.33888e6	+	7.51517e6i	−0.172267	+	0.298374i
$914$	−1.19636e7	+	2.07216e7i	−0.473693	+	0.820461i
$915$	−6.63710e6	−	1.14958e7i	−0.262075	−	0.453927i
$916$	1.61701e7			0.636759
$917$	1.27734e7	+	1.22091e7i	0.501629	+	0.479468i
$918$	1.56897e7			0.614479
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	0.934479	−	0.356019i	$-0.115866\pi$
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	−0.775561	+	0.631272i	$0.782533\pi$
$920$	−4.02348e6	+	6.96887e6i	−0.156723	+	0.271452i
$921$	−2.95001e7	+	5.10956e7i	−1.14597	+	1.98488i
$922$	−3.25013e6	−	5.62939e6i	−0.125914	−	0.218089i
$923$	−2.31338e7			−0.893807
$924$	−7.66739e6	+	2.24123e6i	−0.295439	+	0.0863587i
$925$	4.24962e6			0.163304
$926$	1.69259e7	+	2.93165e7i	0.648671	+	1.12353i
$927$	9.62688e6	−	1.66742e7i	0.367948	−	0.637304i
$928$	2.89627e6	−	5.01649e6i	0.110400	−	0.191219i
$929$	−1.79027e7	−	3.10084e7i	−0.680580	−	1.17880i	−0.974804	−	0.223063i	$-0.928395\pi$
$929$	−1.79027e7	−	3.10084e7i	−0.680580	−	1.17880i	0.294224	−	0.955736i	$-0.404939\pi$
$930$	8.28261e6			0.314022
$931$	4.18173e6	+	2.16872e6i	0.158118	+	0.0820029i
$932$	2.37776e7			0.896661
$933$	1.54249e7	+	2.67167e7i	0.580120	+	1.00480i
$934$	−1.53319e7	+	2.65556e7i	−0.575080	+	0.996068i
$935$	3.47409e6	−	6.01730e6i	0.129961	−	0.225098i
$936$	−1.37533e7	−	2.38213e7i	−0.513116	−	0.888744i
$937$	4.65849e7			1.73339			0.866694	−	0.498840i	$-0.166241\pi$
$937$	4.65849e7			1.73339			0.866694	+	0.498840i	$0.166241\pi$
$938$	2.13947e7	−	6.25382e6i	0.793963	−	0.232080i
$939$	4.12029e7			1.52498
$940$	−3.21093e6	−	5.56149e6i	−0.118525	−	0.205292i
$941$	1.03362e6	−	1.79029e6i	0.0380529	−	0.0659096i	−0.846372	−	0.532593i	$-0.821218\pi$
$941$	1.03362e6	−	1.79029e6i	0.0380529	−	0.0659096i	0.884425	+	0.466683i	$0.154551\pi$
$942$	1.06057e7	−	1.83697e7i	0.389415	−	0.674487i
$943$	6.63850e6	+	1.14982e7i	0.243103	+	0.421067i
$944$	−1.53865e6			−0.0561966
$945$	−1.07201e7	−	1.02465e7i	−0.390498	−	0.373247i
$946$	2.44078e6			0.0886750
$947$	−1.18386e7	−	2.05051e7i	−0.428970	−	0.742998i	0.567812	−	0.823158i	$-0.307790\pi$
$947$	−1.18386e7	−	2.05051e7i	−0.428970	−	0.742998i	−0.996782	+	0.0801602i	$0.974457\pi$
$948$	−2.16034e7	+	3.74182e7i	−0.780732	+	1.35227i
$949$	−2.63936e7	+	4.57150e7i	−0.951334	+	1.64776i
$950$	−1.02099e6	−	1.76841e6i	−0.0367041	−	0.0635734i
$951$	−6.50345e7			−2.33181
$952$	2.43396e6	−	9.97993e6i	0.0870403	−	0.356891i
$953$	−3.40521e6			−0.121454			−0.0607270	−	0.998154i	$-0.519342\pi$
$953$	−3.40521e6			−0.121454			−0.0607270	+	0.998154i	$0.519342\pi$
$954$	8.29725e6	+	1.43713e7i	0.295164	+	0.511239i
$955$	−1.00762e7	+	1.74525e7i	−0.357510	+	0.619226i
$956$	−7.00510e6	+	1.21332e7i	−0.247896	+	0.429368i
$957$	1.08924e7	+	1.88663e7i	0.384455	+	0.665896i
$958$	−9.61170e6			−0.338366
$959$	1.02996e7	−	4.22315e7i	0.361639	−	1.48283i
$960$	−3.66414e6			−0.128320
$961$	1.16357e7	+	2.01535e7i	0.406427	+	0.703952i
$962$	5.40769e6	−	9.36639e6i	0.188397	−	0.326313i
$963$	4.63119e6	−	8.02145e6i	0.160926	−	0.278732i
$964$	−1.16236e7	−	2.01326e7i	−0.402853	−	0.697762i
$965$	1.78059e6			0.0615525
$966$	−3.23441e7	−	3.09152e7i	−1.11520	−	1.06593i
$967$	1.44238e6			0.0496036			0.0248018	−	0.999692i	$-0.492105\pi$
$967$	1.44238e6			0.0496036			0.0248018	+	0.999692i	$0.492105\pi$
$968$	4.38051e6	+	7.58727e6i	0.150258	+	0.260254i
$969$	4.29880e6	−	7.44575e6i	0.147075	−	0.254741i
$970$	1.08352e6	−	1.87672e6i	0.0369751	−	0.0640427i
$971$	2.57977e6	+	4.46830e6i	0.0878078	+	0.152088i	0.906584	−	0.422025i	$-0.138681\pi$
$971$	2.57977e6	+	4.46830e6i	0.0878078	+	0.152088i	−0.818776	+	0.574113i	$0.805347\pi$
$972$	−1.69266e7			−0.574651
$973$	−7.24151e6	+	2.11674e6i	−0.245215	+	0.0716779i
$974$	−681206.			−0.0230081
$975$	2.61484e7	+	4.52904e7i	0.880914	+	1.52579i
$976$	1.89936e6	−	3.28978e6i	0.0638237	−	0.110546i
$977$	3.48825e6	−	6.04183e6i	0.116915	−	0.202503i	−0.801628	−	0.597823i	$-0.796033\pi$
$977$	3.48825e6	−	6.04183e6i	0.116915	−	0.202503i	0.918544	+	0.395319i	$0.129366\pi$
$978$	−3.19447e6	−	5.53299e6i	−0.106795	−	0.184975i
$979$	−1.48511e7			−0.495225
$980$	−8.18065e6	+	5.22932e6i	−0.272096	+	0.173932i
$981$	−1.34853e6			−0.0447394
$982$	1.15526e7	+	2.00096e7i	0.382296	+	0.662156i
$983$	1.40784e7	−	2.43845e7i	0.464696	−	0.804878i	−0.534491	−	0.845174i	$-0.679497\pi$
$983$	1.40784e7	−	2.43845e7i	0.464696	−	0.804878i	0.999188	+	0.0402961i	$0.0128301\pi$
$984$	−3.02281e6	+	5.23565e6i	−0.0995228	+	0.172378i
$985$	−1.69968e7	−	2.94394e7i	−0.558184	−	0.966804i
$986$	−2.80142e7			−0.917669
$987$	3.42725e7	−	1.00181e7i	1.11983	−	0.327334i
$988$	−5.19691e6			−0.169376
$989$	6.83547e6	+	1.18394e7i	0.222217	+	0.384891i
$990$	4.16268e6	−	7.20997e6i	0.134985	−	0.233801i
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	−0.612332	−	0.790601i	$-0.709768\pi$
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	0.990846	+	0.134995i	$0.0431018\pi$
$992$	1.18513e6	+	2.05270e6i	0.0382372	+	0.0662287i
$993$	4.30825e7			1.38653
$994$	−7.48330e6	−	7.15271e6i	−0.240230	−	0.229617i
$995$	−2.31080e7			−0.739954
$996$	−1.10659e7	−	1.91668e7i	−0.353459	−	0.612210i
$997$	2.15142e7	−	3.72637e7i	0.685468	−	1.18727i	−0.287822	−	0.957684i	$-0.592931\pi$
$997$	2.15142e7	−	3.72637e7i	0.685468	−	1.18727i	0.973290	−	0.229581i	$-0.0737356\pi$
$998$	−1.08720e6	+	1.88309e6i	−0.0345529	+	0.0598474i
$999$	3.69592e6	+	6.40151e6i	0.117168	+	0.202941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.6.c.a.11.1	yes	4
3.2	odd	2		126.6.g.j.109.1		4
4.3	odd	2		112.6.i.d.81.2		4
7.2	even	3	inner	14.6.c.a.9.1	✓	4
7.3	odd	6		98.6.a.g.1.1		2
7.4	even	3		98.6.a.h.1.2		2
7.5	odd	6		98.6.c.e.79.2		4
7.6	odd	2		98.6.c.e.67.2		4
21.2	odd	6		126.6.g.j.37.1		4
21.11	odd	6		882.6.a.ba.1.2		2
21.17	even	6		882.6.a.bi.1.1		2
28.3	even	6		784.6.a.bb.1.2		2
28.11	odd	6		784.6.a.s.1.1		2
28.23	odd	6		112.6.i.d.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.1	✓	4	7.2	even	3	inner
14.6.c.a.11.1	yes	4	1.1	even	1	trivial
98.6.a.g.1.1		2	7.3	odd	6
98.6.a.h.1.2		2	7.4	even	3
98.6.c.e.67.2		4	7.6	odd	2
98.6.c.e.79.2		4	7.5	odd	6
112.6.i.d.65.2		4	28.23	odd	6
112.6.i.d.81.2		4	4.3	odd	2
126.6.g.j.37.1		4	21.2	odd	6
126.6.g.j.109.1		4	3.2	odd	2
784.6.a.s.1.1		2	28.11	odd	6
784.6.a.bb.1.2		2	28.3	even	6
882.6.a.ba.1.2		2	21.11	odd	6
882.6.a.bi.1.1		2	21.17	even	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-12.3882 + 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(18.0528 + 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 + 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-12.3882 + 21.4570i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(18.0528 + 31.2683i) q^{5} +99.1056 q^{6} +(-124.435 + 36.3731i) q^{7} +64.0000 q^{8} +(-185.435 - 321.182i) q^{9} +(72.2111 - 125.073i) q^{10} +(-77.7174 + 134.610i) q^{11} +(-198.211 - 343.312i) q^{12} +1158.87 q^{13} +(374.869 + 358.308i) q^{14} -894.565 q^{15} +(-128.000 - 221.703i) q^{16} +(-619.040 + 1072.21i) q^{17} +(-741.739 + 1284.73i) q^{18} +(140.140 + 242.729i) q^{19} -577.689 q^{20} +(761.065 - 3120.59i) q^{21} +621.739 q^{22} +(1741.20 + 3015.84i) q^{23} +(-792.844 + 1373.25i) q^{24} +(910.694 - 1577.37i) q^{25} +(-2317.74 - 4014.44i) q^{26} +3168.14 q^{27} +(491.478 - 2015.20i) q^{28} -5656.78 q^{29} +(1789.13 + 3098.87i) q^{30} +(1157.35 - 2004.59i) q^{31} +(-512.000 + 886.810i) q^{32} +(-1925.56 - 3335.16i) q^{33} +4952.32 q^{34} +(-3383.72 - 3234.23i) q^{35} +5933.91 q^{36} +(1166.59 + 2020.59i) q^{37} +(560.558 - 970.916i) q^{38} +(-14356.3 + 24865.8i) q^{39} +(1155.38 + 2001.17i) q^{40} +3812.61 q^{41} +(-12332.2 + 3604.77i) q^{42} +3925.73 q^{43} +(-1243.48 - 2153.77i) q^{44} +(6695.22 - 11596.5i) q^{45} +(6964.78 - 12063.4i) q^{46} +(5558.23 + 9627.13i) q^{47} +6342.76 q^{48} +(14161.0 - 9052.14i) q^{49} -7285.56 q^{50} +(-15337.6 - 26565.5i) q^{51} +(-9270.96 + 16057.8i) q^{52} +(5593.10 - 9687.54i) q^{53} +(-6336.29 - 10974.8i) q^{54} -5612.06 q^{55} +(-7963.82 + 2327.88i) q^{56} -6944.31 q^{57} +(11313.6 + 19595.7i) q^{58} +(3005.18 - 5205.12i) q^{59} +(7156.52 - 12395.5i) q^{60} +(7419.36 + 12850.7i) q^{61} -9258.81 q^{62} +(34756.9 + 33221.4i) q^{63} +4096.00 q^{64} +(20920.8 + 36235.9i) q^{65} +(-7702.22 + 13340.6i) q^{66} +(21491.9 - 37225.1i) q^{67} +(-9904.64 - 17155.3i) q^{68} -86281.1 q^{69} +(-4436.27 + 18190.0i) q^{70} -19962.4 q^{71} +(-11867.8 - 20555.7i) q^{72} +(-22775.3 + 39448.0i) q^{73} +(4666.35 - 8082.36i) q^{74} +(22563.7 + 39081.5i) q^{75} -4484.47 q^{76} +(4774.54 - 19577.0i) q^{77} +114850. q^{78} +(-54496.0 - 94389.9i) q^{79} +(4621.51 - 8004.69i) q^{80} +(5813.07 - 10068.5i) q^{81} +(-7625.22 - 13207.3i) q^{82} +55829.0 q^{83} +(37151.6 + 35510.4i) q^{84} -44701.6 q^{85} +(-7851.47 - 13599.1i) q^{86} +(70077.3 - 121377. i) q^{87} +(-4973.91 + 8615.07i) q^{88} +(47772.9 + 82745.1i) q^{89} -53561.8 q^{90} +(-144204. + 42151.6i) q^{91} -55718.2 q^{92} +(28675.0 + 49666.5i) q^{93} +(22232.9 - 38508.5i) q^{94} +(-5059.82 + 8763.86i) q^{95} +(-12685.5 - 21971.9i) q^{96} +15004.9 q^{97} +(-59679.5 - 30950.9i) q^{98} +57646.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 14 * q^3 - 32 * q^4 - 70 * q^5 + 112 * q^6 + 256 * q^8 - 244 * q^9	\( 4 q - 8 q^{2} - 14 q^{3} - 32 q^{4} - 70 q^{5} + 112 q^{6} + 256 q^{8} - 244 q^{9} - 280 q^{10} - 62 q^{11} - 224 q^{12} + 3640 q^{13} + 504 q^{14} - 4076 q^{15} - 512 q^{16} - 1694 q^{17} - 976 q^{18} - 826 q^{19} + 2240 q^{20} + 3542 q^{21} + 496 q^{22} + 2734 q^{23} - 896 q^{24} - 6312 q^{25} - 7280 q^{26} + 14308 q^{27} - 2016 q^{28} - 5704 q^{29} + 8152 q^{30} + 2674 q^{31} - 2048 q^{32} - 4858 q^{33} + 13552 q^{34} - 13286 q^{35} + 7808 q^{36} + 9146 q^{37} - 3304 q^{38} - 21588 q^{39} - 4480 q^{40} + 12264 q^{41} - 35392 q^{42} - 32080 q^{43} - 992 q^{44} + 26852 q^{45} + 10936 q^{46} + 25326 q^{47} + 7168 q^{48} + 56644 q^{49} + 50496 q^{50} - 25762 q^{51} - 29120 q^{52} - 14958 q^{53} - 28616 q^{54} - 31052 q^{55} - 37732 q^{57} + 11408 q^{58} + 1106 q^{59} + 32608 q^{60} + 28042 q^{61} - 21392 q^{62} + 77308 q^{63} + 16384 q^{64} - 28308 q^{65} - 19432 q^{66} + 102642 q^{67} - 27104 q^{68} - 188692 q^{69} - 88424 q^{70} - 22112 q^{71} - 15616 q^{72} - 35070 q^{73} + 36584 q^{74} + 132776 q^{75} + 26432 q^{76} + 27062 q^{77} + 172704 q^{78} - 101762 q^{79} - 17920 q^{80} + 23750 q^{81} - 24528 q^{82} - 89264 q^{83} + 84896 q^{84} + 7348 q^{85} + 64160 q^{86} + 170380 q^{87} - 3968 q^{88} + 75474 q^{89} - 214816 q^{90} - 123872 q^{91} - 87488 q^{92} + 53478 q^{93} + 101304 q^{94} - 127502 q^{95} - 14336 q^{96} - 16632 q^{97} - 113288 q^{98} + 139000 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 14 * q^3 - 32 * q^4 - 70 * q^5 + 112 * q^6 + 256 * q^8 - 244 * q^9 - 280 * q^10 - 62 * q^11 - 224 * q^12 + 3640 * q^13 + 504 * q^14 - 4076 * q^15 - 512 * q^16 - 1694 * q^17 - 976 * q^18 - 826 * q^19 + 2240 * q^20 + 3542 * q^21 + 496 * q^22 + 2734 * q^23 - 896 * q^24 - 6312 * q^25 - 7280 * q^26 + 14308 * q^27 - 2016 * q^28 - 5704 * q^29 + 8152 * q^30 + 2674 * q^31 - 2048 * q^32 - 4858 * q^33 + 13552 * q^34 - 13286 * q^35 + 7808 * q^36 + 9146 * q^37 - 3304 * q^38 - 21588 * q^39 - 4480 * q^40 + 12264 * q^41 - 35392 * q^42 - 32080 * q^43 - 992 * q^44 + 26852 * q^45 + 10936 * q^46 + 25326 * q^47 + 7168 * q^48 + 56644 * q^49 + 50496 * q^50 - 25762 * q^51 - 29120 * q^52 - 14958 * q^53 - 28616 * q^54 - 31052 * q^55 - 37732 * q^57 + 11408 * q^58 + 1106 * q^59 + 32608 * q^60 + 28042 * q^61 - 21392 * q^62 + 77308 * q^63 + 16384 * q^64 - 28308 * q^65 - 19432 * q^66 + 102642 * q^67 - 27104 * q^68 - 188692 * q^69 - 88424 * q^70 - 22112 * q^71 - 15616 * q^72 - 35070 * q^73 + 36584 * q^74 + 132776 * q^75 + 26432 * q^76 + 27062 * q^77 + 172704 * q^78 - 101762 * q^79 - 17920 * q^80 + 23750 * q^81 - 24528 * q^82 - 89264 * q^83 + 84896 * q^84 + 7348 * q^85 + 64160 * q^86 + 170380 * q^87 - 3968 * q^88 + 75474 * q^89 - 214816 * q^90 - 123872 * q^91 - 87488 * q^92 + 53478 * q^93 + 101304 * q^94 - 127502 * q^95 - 14336 * q^96 - 16632 * q^97 - 113288 * q^98 + 139000 * q^99

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