LMFDB - Embedded newform 41.6.c.a.32.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,6,Mod(9,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("41.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	41.c (of order $4$, 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:	$6.57573661233$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.13
Character	$\chi$	$=$	41.32
Dual form			41.6.c.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.81352i q^{2} +(3.20738 - 3.20738i) q^{3} -1.79697 q^{4} +42.7691i q^{5} +(18.6461 + 18.6461i) q^{6} +(22.3392 - 22.3392i) q^{7} +175.586i q^{8} +222.425i q^{9} +O(q^{10})$	\(q+5.81352i q^{2} +(3.20738 - 3.20738i) q^{3} -1.79697 q^{4} +42.7691i q^{5} +(18.6461 + 18.6461i) q^{6} +(22.3392 - 22.3392i) q^{7} +175.586i q^{8} +222.425i q^{9} -248.639 q^{10} +(177.276 - 177.276i) q^{11} +(-5.76356 + 5.76356i) q^{12} +(-580.171 + 580.171i) q^{13} +(129.869 + 129.869i) q^{14} +(137.177 + 137.177i) q^{15} -1078.27 q^{16} +(-1112.05 - 1112.05i) q^{17} -1293.07 q^{18} +(909.297 + 909.297i) q^{19} -76.8547i q^{20} -143.300i q^{21} +(1030.60 + 1030.60i) q^{22} +4027.98 q^{23} +(563.170 + 563.170i) q^{24} +1295.81 q^{25} +(-3372.83 - 3372.83i) q^{26} +(1492.80 + 1492.80i) q^{27} +(-40.1428 + 40.1428i) q^{28} +(4259.20 - 4259.20i) q^{29} +(-797.478 + 797.478i) q^{30} +584.269 q^{31} -649.817i q^{32} -1137.18i q^{33} +(6464.91 - 6464.91i) q^{34} +(955.426 + 955.426i) q^{35} -399.692i q^{36} -6540.21 q^{37} +(-5286.21 + 5286.21i) q^{38} +3721.65i q^{39} -7509.64 q^{40} +(6314.48 - 8716.85i) q^{41} +833.079 q^{42} -19713.1i q^{43} +(-318.559 + 318.559i) q^{44} -9512.93 q^{45} +23416.7i q^{46} +(-2649.01 - 2649.01i) q^{47} +(-3458.43 + 3458.43i) q^{48} +15808.9i q^{49} +7533.19i q^{50} -7133.52 q^{51} +(1042.55 - 1042.55i) q^{52} +(12245.4 - 12245.4i) q^{53} +(-8678.39 + 8678.39i) q^{54} +(7581.93 + 7581.93i) q^{55} +(3922.44 + 3922.44i) q^{56} +5832.92 q^{57} +(24760.9 + 24760.9i) q^{58} -18496.7 q^{59} +(-246.502 - 246.502i) q^{60} +15638.9i q^{61} +3396.66i q^{62} +(4968.80 + 4968.80i) q^{63} -30727.0 q^{64} +(-24813.4 - 24813.4i) q^{65} +6611.03 q^{66} +(15672.6 + 15672.6i) q^{67} +(1998.32 + 1998.32i) q^{68} +(12919.3 - 12919.3i) q^{69} +(-5554.38 + 5554.38i) q^{70} +(32943.1 - 32943.1i) q^{71} -39054.8 q^{72} -29040.6i q^{73} -38021.6i q^{74} +(4156.14 - 4156.14i) q^{75} +(-1633.98 - 1633.98i) q^{76} -7920.40i q^{77} -21635.9 q^{78} +(12851.5 - 12851.5i) q^{79} -46116.8i q^{80} -44473.5 q^{81} +(50675.6 + 36709.3i) q^{82} -35969.0 q^{83} +257.506i q^{84} +(47561.3 - 47561.3i) q^{85} +114603. q^{86} -27321.7i q^{87} +(31127.1 + 31127.1i) q^{88} +(-25718.6 + 25718.6i) q^{89} -55303.6i q^{90} +25921.1i q^{91} -7238.16 q^{92} +(1873.97 - 1873.97i) q^{93} +(15400.1 - 15400.1i) q^{94} +(-38889.8 + 38889.8i) q^{95} +(-2084.21 - 2084.21i) q^{96} +(32563.1 + 32563.1i) q^{97} -91905.4 q^{98} +(39430.7 + 39430.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7}+O(q^{10}) $ 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7} + 1660 q^{10} + 654 q^{11} + 98 q^{12} + 854 q^{13} + 2236 q^{14} - 998 q^{15} + 8828 q^{16} + 1730 q^{17} + 2068 q^{18} + 716 q^{19} - 7750 q^{22} - 8156 q^{23} + 5496 q^{24} - 28870 q^{25} + 11470 q^{26} - 26806 q^{27} - 5942 q^{28} - 19190 q^{29} + 21430 q^{30} - 6376 q^{31} + 4228 q^{34} + 20934 q^{35} + 768 q^{37} - 6552 q^{38} - 47024 q^{40} - 9618 q^{41} + 126236 q^{42} - 57632 q^{44} + 81112 q^{45} + 2372 q^{47} + 88202 q^{48} + 24936 q^{51} + 151982 q^{52} - 94170 q^{53} - 153650 q^{54} - 105662 q^{55} + 8144 q^{56} - 69412 q^{57} - 63094 q^{58} + 87684 q^{59} + 58746 q^{60} - 76328 q^{63} - 109780 q^{64} + 88904 q^{65} - 427468 q^{66} + 212150 q^{67} - 199904 q^{68} + 125672 q^{69} + 113566 q^{70} + 189392 q^{71} + 579216 q^{72} + 199072 q^{75} + 128522 q^{76} - 327232 q^{78} - 28880 q^{79} - 557850 q^{81} - 241122 q^{82} + 384572 q^{83} - 114880 q^{85} - 453980 q^{86} + 338338 q^{88} - 391266 q^{89} + 955316 q^{92} + 394684 q^{93} - 42650 q^{94} - 404378 q^{95} - 254372 q^{96} - 324538 q^{97} - 167276 q^{98} - 685716 q^{99}+O(q^{100}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7 + 1660 * q^10 + 654 * q^11 + 98 * q^12 + 854 * q^13 + 2236 * q^14 - 998 * q^15 + 8828 * q^16 + 1730 * q^17 + 2068 * q^18 + 716 * q^19 - 7750 * q^22 - 8156 * q^23 + 5496 * q^24 - 28870 * q^25 + 11470 * q^26 - 26806 * q^27 - 5942 * q^28 - 19190 * q^29 + 21430 * q^30 - 6376 * q^31 + 4228 * q^34 + 20934 * q^35 + 768 * q^37 - 6552 * q^38 - 47024 * q^40 - 9618 * q^41 + 126236 * q^42 - 57632 * q^44 + 81112 * q^45 + 2372 * q^47 + 88202 * q^48 + 24936 * q^51 + 151982 * q^52 - 94170 * q^53 - 153650 * q^54 - 105662 * q^55 + 8144 * q^56 - 69412 * q^57 - 63094 * q^58 + 87684 * q^59 + 58746 * q^60 - 76328 * q^63 - 109780 * q^64 + 88904 * q^65 - 427468 * q^66 + 212150 * q^67 - 199904 * q^68 + 125672 * q^69 + 113566 * q^70 + 189392 * q^71 + 579216 * q^72 + 199072 * q^75 + 128522 * q^76 - 327232 * q^78 - 28880 * q^79 - 557850 * q^81 - 241122 * q^82 + 384572 * q^83 - 114880 * q^85 - 453980 * q^86 + 338338 * q^88 - 391266 * q^89 + 955316 * q^92 + 394684 * q^93 - 42650 * q^94 - 404378 * q^95 - 254372 * q^96 - 324538 * q^97 - 167276 * q^98 - 685716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			5.81352i			1.02769i	0.857882	+	0.513847i	$0.171780\pi$
$2$			5.81352i			1.02769i	−0.857882	+	0.513847i	$0.828220\pi$
$3$	3.20738	−	3.20738i	0.205753	−	0.205753i	−0.596706	−	0.802460i	$-0.703524\pi$
$3$	3.20738	−	3.20738i	0.205753	−	0.205753i	0.802460	+	0.596706i	$0.203524\pi$
$4$	−1.79697			−0.0561553
$5$			42.7691i			0.765076i	0.923940	+	0.382538i	$0.124950\pi$
$5$			42.7691i			0.765076i	−0.923940	+	0.382538i	$0.875050\pi$
$6$	18.6461	+	18.6461i	0.211452	+	0.211452i
$7$	22.3392	−	22.3392i	0.172315	−	0.172315i	−0.615681	−	0.787996i	$-0.711119\pi$
$7$	22.3392	−	22.3392i	0.172315	−	0.172315i	0.787996	+	0.615681i	$0.211119\pi$
$8$			175.586i			0.969984i
$9$			222.425i			0.915331i
$10$	−248.639			−0.786265
$11$	177.276	−	177.276i	0.441742	−	0.441742i	−0.450855	−	0.892597i	$-0.648881\pi$
$11$	177.276	−	177.276i	0.441742	−	0.441742i	0.892597	+	0.450855i	$0.148881\pi$
$12$	−5.76356	+	5.76356i	−0.0115541	+	0.0115541i
$13$	−580.171	+	580.171i	−0.952133	+	0.952133i	−0.998906	−	0.0467729i	$-0.985106\pi$
$13$	−580.171	+	580.171i	−0.952133	+	0.952133i	0.0467729	+	0.998906i	$0.485106\pi$
$14$	129.869	+	129.869i	0.177087	+	0.177087i
$15$	137.177	+	137.177i	0.157417	+	0.157417i
$16$	−1078.27			−1.05300
$17$	−1112.05	−	1112.05i	−0.933258	−	0.933258i	0.0646503	−	0.997908i	$-0.479407\pi$
$17$	−1112.05	−	1112.05i	−0.933258	−	0.933258i	−0.997908	+	0.0646503i	$0.979407\pi$
$18$	−1293.07			−0.940680
$19$	909.297	+	909.297i	0.577859	+	0.577859i	0.934313	−	0.356454i	$-0.116014\pi$
$19$	909.297	+	909.297i	0.577859	+	0.577859i	−0.356454	+	0.934313i	$0.616014\pi$
$20$		−	76.8547i		−	0.0429631i
$21$		−	143.300i		−	0.0709086i
$22$	1030.60	+	1030.60i	0.453975	+	0.453975i
$23$	4027.98			1.58770			0.793849	−	0.608115i	$-0.208074\pi$
$23$	4027.98			1.58770			0.793849	+	0.608115i	$0.208074\pi$
$24$	563.170	+	563.170i	0.199577	+	0.199577i
$25$	1295.81			0.414658
$26$	−3372.83	−	3372.83i	−0.978501	−	0.978501i
$27$	1492.80	+	1492.80i	0.394086	+	0.394086i
$28$	−40.1428	+	40.1428i	−0.00967637	+	0.00967637i
$29$	4259.20	−	4259.20i	0.940444	−	0.940444i	−0.0578799	−	0.998324i	$-0.518434\pi$
$29$	4259.20	−	4259.20i	0.940444	−	0.940444i	0.998324	+	0.0578799i	$0.0184341\pi$
$30$	−797.478	+	797.478i	−0.161777	+	0.161777i
$31$	584.269			0.109197			0.0545983	−	0.998508i	$-0.482612\pi$
$31$	584.269			0.109197			0.0545983	+	0.998508i	$0.482612\pi$
$32$		−	649.817i		−	0.112180i
$33$		−	1137.18i		−	0.181780i
$34$	6464.91	−	6464.91i	0.959103	−	0.959103i
$35$	955.426	+	955.426i	0.131834	+	0.131834i
$36$		−	399.692i		−	0.0514007i
$37$	−6540.21			−0.785393			−0.392697	−	0.919668i	$-0.628458\pi$
$37$	−6540.21			−0.785393			−0.392697	+	0.919668i	$0.628458\pi$
$38$	−5286.21	+	5286.21i	−0.593862	+	0.593862i
$39$			3721.65i			0.391809i
$40$	−7509.64			−0.742112
$41$	6314.48	−	8716.85i	0.586648	−	0.809842i
$41$	6314.48	−	8716.85i	0.586648	−	0.809842i
$42$	833.079			0.0728724
$43$		−	19713.1i		−	1.62586i	−0.582358	−	0.812932i	$-0.697870\pi$
$43$		−	19713.1i		−	1.62586i	0.582358	−	0.812932i	$-0.302130\pi$
$44$	−318.559	+	318.559i	−0.0248061	+	0.0248061i
$45$	−9512.93			−0.700298
$46$			23416.7i			1.63167i
$47$	−2649.01	−	2649.01i	−0.174920	−	0.174920i	0.614217	−	0.789137i	$-0.289472\pi$
$47$	−2649.01	−	2649.01i	−0.174920	−	0.174920i	−0.789137	+	0.614217i	$0.789472\pi$
$48$	−3458.43	+	3458.43i	−0.216659	+	0.216659i
$49$			15808.9i			0.940615i
$50$			7533.19i			0.426142i
$51$	−7133.52			−0.384042
$52$	1042.55	−	1042.55i	0.0534673	−	0.0534673i
$53$	12245.4	−	12245.4i	0.598801	−	0.598801i	−0.341192	−	0.939994i	$-0.610831\pi$
$53$	12245.4	−	12245.4i	0.598801	−	0.598801i	0.939994	+	0.341192i	$0.110831\pi$
$54$	−8678.39	+	8678.39i	−0.405000	+	0.405000i
$55$	7581.93	+	7581.93i	0.337966	+	0.337966i
$56$	3922.44	+	3922.44i	0.167142	+	0.167142i
$57$	5832.92			0.237793
$58$	24760.9	+	24760.9i	0.966488	+	0.966488i
$59$	−18496.7			−0.691775			−0.345888	−	0.938276i	$-0.612422\pi$
$59$	−18496.7			−0.691775			−0.345888	+	0.938276i	$0.612422\pi$
$60$	−246.502	−	246.502i	−0.00883980	−	0.00883980i
$61$			15638.9i			0.538124i	0.963123	+	0.269062i	$0.0867137\pi$
$61$			15638.9i			0.538124i	−0.963123	+	0.269062i	$0.913286\pi$
$62$			3396.66i			0.112221i
$63$	4968.80	+	4968.80i	0.157725	+	0.157725i
$64$	−30727.0			−0.937715
$65$	−24813.4	−	24813.4i	−0.728454	−	0.728454i
$66$	6611.03			0.186814
$67$	15672.6	+	15672.6i	0.426536	+	0.426536i	0.887446	−	0.460911i	$-0.152477\pi$
$67$	15672.6	+	15672.6i	0.426536	+	0.426536i	−0.460911	+	0.887446i	$0.652477\pi$
$68$	1998.32	+	1998.32i	0.0524073	+	0.0524073i
$69$	12919.3	−	12919.3i	0.326674	−	0.326674i
$70$	−5554.38	+	5554.38i	−0.135485	+	0.135485i
$71$	32943.1	−	32943.1i	0.775566	−	0.775566i	−0.203507	−	0.979073i	$-0.565234\pi$
$71$	32943.1	−	32943.1i	0.775566	−	0.775566i	0.979073	+	0.203507i	$0.0652341\pi$
$72$	−39054.8			−0.887856
$73$		−	29040.6i		−	0.637821i	−0.947785	−	0.318911i	$-0.896683\pi$
$73$		−	29040.6i		−	0.637821i	0.947785	−	0.318911i	$-0.103317\pi$
$74$		−	38021.6i		−	0.807144i
$75$	4156.14	−	4156.14i	0.0853173	−	0.0853173i
$76$	−1633.98	−	1633.98i	−0.0324498	−	0.0324498i
$77$		−	7920.40i		−	0.152237i
$78$	−21635.9			−0.402660
$79$	12851.5	−	12851.5i	0.231678	−	0.231678i	−0.581715	−	0.813393i	$-0.697618\pi$
$79$	12851.5	−	12851.5i	0.231678	−	0.231678i	0.813393	+	0.581715i	$0.197618\pi$
$80$		−	46116.8i		−	0.805627i
$81$	−44473.5			−0.753162
$82$	50675.6	+	36709.3i	0.832270	+	0.602895i
$83$	−35969.0			−0.573104			−0.286552	−	0.958065i	$-0.592509\pi$
$83$	−35969.0			−0.573104			−0.286552	+	0.958065i	$0.592509\pi$
$84$			257.506i			0.00398189i
$85$	47561.3	−	47561.3i	0.714013	−	0.714013i
$86$	114603.			1.67089
$87$		−	27321.7i		−	0.386999i
$88$	31127.1	+	31127.1i	0.428482	+	0.428482i
$89$	−25718.6	+	25718.6i	−0.344170	+	0.344170i	−0.857932	−	0.513763i	$-0.828251\pi$
$89$	−25718.6	+	25718.6i	−0.344170	+	0.344170i	0.513763	+	0.857932i	$0.328251\pi$
$90$		−	55303.6i		−	0.719692i
$91$			25921.1i			0.328133i
$92$	−7238.16			−0.0891577
$93$	1873.97	−	1873.97i	0.0224675	−	0.0224675i
$94$	15400.1	−	15400.1i	0.179764	−	0.179764i
$95$	−38889.8	+	38889.8i	−0.442106	+	0.442106i
$96$	−2084.21	−	2084.21i	−0.0230814	−	0.0230814i
$97$	32563.1	+	32563.1i	0.351395	+	0.351395i	0.860629	−	0.509233i	$-0.170071\pi$
$97$	32563.1	+	32563.1i	0.351395	+	0.351395i	−0.509233	+	0.860629i	$0.670071\pi$
$98$	−91905.4			−0.966665
$99$	39430.7	+	39430.7i	0.404340	+	0.404340i
$100$	−2328.52			−0.0232852
$101$	91513.8	+	91513.8i	0.892654	+	0.892654i	0.994772	−	0.102118i	$-0.0325619\pi$
$101$	91513.8	+	91513.8i	0.892654	+	0.892654i	−0.102118	+	0.994772i	$0.532562\pi$
$102$		−	41470.8i		−	0.394678i
$103$			59937.7i			0.556682i	0.960482	+	0.278341i	$0.0897846\pi$
$103$			59937.7i			0.556682i	−0.960482	+	0.278341i	$0.910215\pi$
$104$	−101870.	−	101870.i	−0.923553	−	0.923553i
$105$	6128.82			0.0542505
$106$	71188.7	+	71188.7i	0.615385	+	0.615385i
$107$	−135996.			−1.14833			−0.574164	−	0.818740i	$-0.694673\pi$
$107$	−135996.			−1.14833			−0.574164	+	0.818740i	$0.694673\pi$
$108$	−2682.51	−	2682.51i	−0.0221300	−	0.0221300i
$109$	−6503.28	−	6503.28i	−0.0524284	−	0.0524284i	0.680407	−	0.732835i	$-0.261803\pi$
$109$	−6503.28	−	6503.28i	−0.0524284	−	0.0524284i	−0.732835	+	0.680407i	$0.761803\pi$
$110$	−44077.7	+	44077.7i	−0.347326	+	0.347326i
$111$	−20976.9	+	20976.9i	−0.161597	+	0.161597i
$112$	−24087.7	+	24087.7i	−0.181448	+	0.181448i
$113$	191184.			1.40850			0.704248	−	0.709954i	$-0.251284\pi$
$113$	191184.			1.40850			0.704248	+	0.709954i	$0.251284\pi$
$114$			33909.8i			0.244378i
$115$			172273.i			1.21471i
$116$	−7653.65	+	7653.65i	−0.0528109	+	0.0528109i
$117$	−129045.	−	129045.i	−0.871517	−	0.871517i
$118$		−	107531.i		−	0.710933i
$119$	−49684.5			−0.321628
$120$	−24086.3	+	24086.3i	−0.152692	+	0.152692i
$121$			98197.4i			0.609729i
$122$	−90917.2			−0.553027
$123$	−7705.33	−	48211.2i	−0.0459228	−	0.287333i
$124$	−1049.91			−0.00613196
$125$			189074.i			1.08232i
$126$	−28886.2	+	28886.2i	−0.162093	+	0.162093i
$127$	−245230.			−1.34916			−0.674581	−	0.738201i	$-0.735676\pi$
$127$	−245230.			−1.34916			−0.674581	+	0.738201i	$0.735676\pi$
$128$		−	199426.i		−	1.07586i
$129$	−63227.4	−	63227.4i	−0.334527	−	0.334527i
$130$	144253.	−	144253.i	0.748628	−	0.748628i
$131$			40003.9i			0.203669i	0.994801	+	0.101834i	$0.0324711\pi$
$131$			40003.9i			0.203669i	−0.994801	+	0.101834i	$0.967529\pi$
$132$			2043.48i			0.0102079i
$133$	40625.9			0.199147
$134$	−91113.2	+	91113.2i	−0.438348	+	0.438348i
$135$	−63845.5	+	63845.5i	−0.301506	+	0.301506i
$136$	195260.	−	195260.i	0.905245	−	0.905245i
$137$	−204030.	−	204030.i	−0.928738	−	0.928738i	0.0688870	−	0.997624i	$-0.478055\pi$
$137$	−204030.	−	204030.i	−0.928738	−	0.928738i	−0.997624	+	0.0688870i	$0.978055\pi$
$138$	75106.3	+	75106.3i	0.335721	+	0.335721i
$139$	327570.			1.43803			0.719014	−	0.694995i	$-0.244594\pi$
$139$	327570.			1.43803			0.719014	+	0.694995i	$0.244594\pi$
$140$	−1716.87	−	1716.87i	−0.00740316	−	0.00740316i
$141$	−16992.8			−0.0719807
$142$	191515.	+	191515.i	0.797045	+	0.797045i
$143$			205701.i			0.841193i
$144$		−	239836.i		−	0.963845i
$145$	182162.	+	182162.i	0.719511	+	0.719511i
$146$	168828.			0.655485
$147$	50705.2	+	50705.2i	0.193535	+	0.193535i
$148$	11752.6			0.0441040
$149$	−194580.	−	194580.i	−0.718013	−	0.718013i	0.250185	−	0.968198i	$-0.419509\pi$
$149$	−194580.	−	194580.i	−0.718013	−	0.718013i	−0.968198	+	0.250185i	$0.919509\pi$
$150$	24161.8	+	24161.8i	0.0876801	+	0.0876801i
$151$	112834.	−	112834.i	0.402716	−	0.402716i	−0.476473	−	0.879189i	$-0.658085\pi$
$151$	112834.	−	112834.i	0.402716	−	0.402716i	0.879189	+	0.476473i	$0.158085\pi$
$152$	−159660.	+	159660.i	−0.560514	+	0.560514i
$153$	247348.	−	247348.i	0.854240	−	0.854240i
$154$	46045.4			0.156453
$155$			24988.7i			0.0835437i
$156$		−	6687.70i		−	0.0220021i
$157$	163272.	−	163272.i	0.528644	−	0.528644i	−0.391524	−	0.920168i	$-0.628052\pi$
$157$	163272.	−	163272.i	0.528644	−	0.528644i	0.920168	+	0.391524i	$0.128052\pi$
$158$	74712.3	+	74712.3i	0.238094	+	0.238094i
$159$		−	78551.1i		−	0.246411i
$160$	27792.1			0.0858264
$161$	89981.8	−	89981.8i	0.273584	−	0.273584i
$162$		−	258547.i		−	0.774020i
$163$	−457039.			−1.34736			−0.673680	−	0.739023i	$-0.735288\pi$
$163$	−457039.			−1.34736			−0.673680	+	0.739023i	$0.735288\pi$
$164$	−11346.9	+	15663.9i	−0.0329434	+	0.0454769i
$165$	48636.2			0.139075
$166$		−	209107.i		−	0.588976i
$167$	−160390.	+	160390.i	−0.445028	+	0.445028i	−0.893698	−	0.448670i	$-0.851898\pi$
$167$	−160390.	+	160390.i	−0.445028	+	0.445028i	0.448670	+	0.893698i	$0.351898\pi$
$168$	25161.5			0.0687802
$169$		−	301903.i		−	0.813113i
$170$	276498.	+	276498.i	0.733787	+	0.733787i
$171$	−202251.	+	202251.i	−0.528932	+	0.528932i
$172$			35423.9i			0.0913009i
$173$		−	30998.9i		−	0.0787466i	−0.999225	−	0.0393733i	$-0.987464\pi$
$173$		−	30998.9i		−	0.0787466i	0.999225	−	0.0393733i	$-0.0125361\pi$
$174$	158835.			0.397716
$175$	28947.3	−	28947.3i	0.0714516	−	0.0714516i
$176$	−191152.	+	191152.i	−0.465155	+	0.465155i
$177$	−59326.0	+	59326.0i	−0.142335	+	0.142335i
$178$	−149516.	−	149516.i	−0.353701	−	0.353701i
$179$	−347619.	−	347619.i	−0.810907	−	0.810907i	0.173863	−	0.984770i	$-0.444375\pi$
$179$	−347619.	−	347619.i	−0.810907	−	0.810907i	−0.984770	+	0.173863i	$0.944375\pi$
$180$	17094.4			0.0393254
$181$	20242.8	+	20242.8i	0.0459277	+	0.0459277i	0.729698	−	0.683770i	$-0.239661\pi$
$181$	20242.8	+	20242.8i	0.0459277	+	0.0459277i	−0.683770	+	0.729698i	$0.739661\pi$
$182$	−150693.			−0.337220
$183$	50160.0	+	50160.0i	0.110721	+	0.110721i
$184$			707257.i			1.54004i
$185$		−	279719.i		−	0.600886i
$186$	10894.4	+	10894.4i	0.0230898	+	0.0230898i
$187$	−394279.			−0.824517
$188$	4760.19	+	4760.19i	0.00982267	+	0.00982267i
$189$	66695.6			0.135813
$190$	−226086.	−	226086.i	−0.454350	−	0.454350i
$191$	419728.	+	419728.i	0.832501	+	0.832501i	0.987858	−	0.155357i	$-0.0496529\pi$
$191$	419728.	+	419728.i	0.832501	+	0.832501i	−0.155357	+	0.987858i	$0.549653\pi$
$192$	−98553.2	+	98553.2i	−0.192938	+	0.192938i
$193$	−285876.	+	285876.i	−0.552439	+	0.552439i	−0.927144	−	0.374705i	$-0.877744\pi$
$193$	−285876.	+	285876.i	−0.552439	+	0.552439i	0.374705	+	0.927144i	$0.377744\pi$
$194$	−189306.	+	189306.i	−0.361127	+	0.361127i
$195$	−159172.			−0.299764
$196$		−	28408.1i		−	0.0528205i
$197$		−	746196.i		−	1.36990i	−0.728592	−	0.684948i	$-0.759825\pi$
$197$		−	746196.i		−	1.36990i	0.728592	−	0.684948i	$-0.240175\pi$
$198$	−229231.	+	229231.i	−0.415538	+	0.415538i
$199$	505374.	+	505374.i	0.904650	+	0.904650i	0.995834	−	0.0911843i	$-0.0290652\pi$
$199$	505374.	+	505374.i	0.904650	+	0.904650i	−0.0911843	+	0.995834i	$0.529065\pi$
$200$			227525.i			0.402212i
$201$	100536.			0.175522
$202$	−532017.	+	532017.i	−0.917376	+	0.917376i
$203$		−	190294.i		−	0.324104i
$204$	12818.7			0.0215660
$205$	372812.	+	270064.i	0.619591	+	0.448831i
$206$	−348449.			−0.572099
$207$			895926.i			1.45327i
$208$	625583.	−	625583.i	1.00260	−	1.00260i
$209$	322393.			0.510528
$210$			35630.0i			0.0557529i
$211$	70844.0	+	70844.0i	0.109546	+	0.109546i	0.759755	−	0.650209i	$-0.225319\pi$
$211$	70844.0	+	70844.0i	0.109546	+	0.109546i	−0.650209	+	0.759755i	$0.725319\pi$
$212$	−22004.6	+	22004.6i	−0.0336259	+	0.0336259i
$213$		−	211322.i		−	0.319151i
$214$		−	790614.i		−	1.18013i
$215$	843112.			1.24391
$216$	−262114.	+	262114.i	−0.382257	+	0.382257i
$217$	13052.1	−	13052.1i	0.0188162	−	0.0188162i
$218$	37806.9	−	37806.9i	0.0538803	−	0.0538803i
$219$	−93144.3	−	93144.3i	−0.131234	−	0.131234i
$220$	−13624.5	−	13624.5i	−0.0189786	−	0.0189786i
$221$	1.29036e6			1.77717
$222$	−121950.	−	121950.i	−0.166073	−	0.166073i
$223$	−1.37201e6			−1.84754			−0.923772	−	0.382942i	$-0.874911\pi$
$223$	−1.37201e6			−1.84754			−0.923772	+	0.382942i	$0.874911\pi$
$224$	−14516.4	−	14516.4i	−0.0193303	−	0.0193303i
$225$			288220.i			0.379550i
$226$			1.11145e6i			1.44750i
$227$	184927.	+	184927.i	0.238196	+	0.238196i	0.816103	−	0.577907i	$-0.196130\pi$
$227$	184927.	+	184927.i	0.238196	+	0.238196i	−0.577907	+	0.816103i	$0.696130\pi$
$228$	−10481.6			−0.0133533
$229$	−797528.	−	797528.i	−1.00498	−	1.00498i	−0.999988	−	0.00499237i	$-0.998411\pi$
$229$	−797528.	−	797528.i	−1.00498	−	1.00498i	−0.00499237	−	0.999988i	$-0.501589\pi$
$230$	−1.00151e6			−1.24835
$231$	−25403.7	−	25403.7i	−0.0313233	−	0.0313233i
$232$	747855.	+	747855.i	0.912215	+	0.912215i
$233$	904976.	−	904976.i	1.09206	−	1.09206i	0.0967540	−	0.995308i	$-0.469154\pi$
$233$	904976.	−	904976.i	1.09206	−	1.09206i	0.995308	−	0.0967540i	$-0.0308460\pi$
$234$	750204.	−	750204.i	0.895653	−	0.895653i
$235$	113296.	−	113296.i	0.133827	−	0.133827i
$236$	33238.1			0.0388468
$237$		−	82439.1i		−	0.0953372i
$238$		−	288842.i		−	0.330535i
$239$	1.14442e6	−	1.14442e6i	1.29596	−	1.29596i	0.364916	−	0.931041i	$-0.381098\pi$
$239$	1.14442e6	−	1.14442e6i	1.29596	−	1.29596i	0.931041	−	0.364916i	$-0.118902\pi$
$240$	−147914.	−	147914.i	−0.165760	−	0.165760i
$241$		−	1.11242e6i		−	1.23374i	−0.787063	−	0.616872i	$-0.788399\pi$
$241$		−	1.11242e6i		−	1.23374i	0.787063	−	0.616872i	$-0.211601\pi$
$242$	−570872.			−0.626615
$243$	−505392.	+	505392.i	−0.549051	+	0.549051i
$244$		−	28102.7i		−	0.0302185i
$245$	−676133.			−0.719643
$246$	280276.	−	44795.0i	0.295290	−	0.0471946i
$247$	−1.05510e6			−1.10040
$248$			102589.i			0.105919i
$249$	−115366.	+	115366.i	−0.117918	+	0.117918i
$250$	−1.09918e6			−1.11230
$251$		−	680486.i		−	0.681766i	−0.940106	−	0.340883i	$-0.889274\pi$
$251$		−	680486.i		−	0.681766i	0.940106	−	0.340883i	$-0.110726\pi$
$252$	−8928.78	−	8928.78i	−0.00885709	−	0.00885709i
$253$	714065.	−	714065.i	0.701352	−	0.701352i
$254$		−	1.42565e6i		−	1.38653i
$255$		−	305094.i		−	0.293821i
$256$	176103.			0.167945
$257$	−1.12361e6	+	1.12361e6i	−1.06117	+	1.06117i	−0.0631619	+	0.998003i	$0.520118\pi$
$257$	−1.12361e6	+	1.12361e6i	−1.06117	+	1.06117i	−0.998003	+	0.0631619i	$0.979882\pi$
$258$	367574.	−	367574.i	0.343792	−	0.343792i
$259$	−146103.	+	146103.i	−0.135335	+	0.135335i
$260$	44588.8	+	44588.8i	0.0409066	+	0.0409066i
$261$	947354.	+	947354.i	0.860817	+	0.860817i
$262$	−232563.			−0.209309
$263$	1.02660e6	+	1.02660e6i	0.915191	+	0.915191i	0.996675	−	0.0814840i	$-0.0259659\pi$
$263$	1.02660e6	+	1.02660e6i	0.915191	+	0.915191i	−0.0814840	+	0.996675i	$0.525966\pi$
$264$	199673.			0.176323
$265$	523724.	+	523724.i	0.458129	+	0.458129i
$266$			236179.i			0.204662i
$267$			164979.i			0.141628i
$268$	−28163.3	−	28163.3i	−0.0239522	−	0.0239522i
$269$	1.74306e6			1.46870			0.734349	−	0.678772i	$-0.237487\pi$
$269$	1.74306e6			1.46870			0.734349	+	0.678772i	$0.237487\pi$
$270$	−371167.	−	371167.i	−0.309856	−	0.309856i
$271$	−108772.			−0.0899694			−0.0449847	−	0.998988i	$-0.514324\pi$
$271$	−108772.			−0.0899694			−0.0449847	+	0.998988i	$0.514324\pi$
$272$	1.19909e6	+	1.19909e6i	0.982722	+	0.982722i
$273$	83138.7	+	83138.7i	0.0675144	+	0.0675144i
$274$	1.18613e6	−	1.18613e6i	0.954458	−	0.954458i
$275$	229715.	−	229715.i	0.183172	−	0.183172i
$276$	−23215.5	+	23215.5i	−0.0183445	+	0.0183445i
$277$	−1.18958e6			−0.931522			−0.465761	−	0.884910i	$-0.654219\pi$
$277$	−1.18958e6			−0.931522			−0.465761	+	0.884910i	$0.654219\pi$
$278$			1.90433e6i			1.47785i
$279$			129956.i			0.0999510i
$280$	−167759.	+	167759.i	−0.127877	+	0.127877i
$281$	−871892.	−	871892.i	−0.658714	−	0.658714i	0.296362	−	0.955076i	$-0.404227\pi$
$281$	−871892.	−	871892.i	−0.658714	−	0.658714i	−0.955076	+	0.296362i	$0.904227\pi$
$282$		−	98787.6i		−	0.0739741i
$283$	−1.28153e6			−0.951178			−0.475589	−	0.879668i	$-0.657765\pi$
$283$	−1.28153e6			−0.951178			−0.475589	+	0.879668i	$0.657765\pi$
$284$	−59197.8	+	59197.8i	−0.0435521	+	0.0435521i
$285$			249468.i			0.181930i
$286$	−1.19584e6			−0.864489
$287$	−53667.1	−	335788.i	−0.0384595	−	0.240636i
$288$	144536.			0.102682
$289$			1.05345e6i			0.741940i
$290$	−1.05900e6	+	1.05900e6i	−0.739437	+	0.739437i
$291$	208884.			0.144602
$292$			52185.1i			0.0358170i
$293$	884746.	+	884746.i	0.602073	+	0.602073i	0.940862	−	0.338789i	$-0.110017\pi$
$293$	884746.	+	884746.i	0.602073	+	0.602073i	−0.338789	+	0.940862i	$0.610017\pi$
$294$	−294775.	+	294775.i	−0.198895	+	0.198895i
$295$		−	791088.i		−	0.529261i
$296$		−	1.14837e6i		−	0.761819i
$297$	529273.			0.348168
$298$	1.13119e6	−	1.13119e6i	0.737898	−	0.737898i
$299$	−2.33692e6	+	2.33692e6i	−1.51170	+	1.51170i
$300$	−7468.46	+	7468.46i	−0.00479102	+	0.00479102i
$301$	−440375.	−	440375.i	−0.280160	−	0.280160i
$302$	655965.	+	655965.i	0.413869	+	0.413869i
$303$	587039.			0.367333
$304$	−980471.	−	980471.i	−0.608486	−	0.608486i
$305$	−668863.			−0.411706
$306$	1.43796e6	+	1.43796e6i	0.877897	+	0.877897i
$307$			2.98062e6i			1.80493i	0.430759	+	0.902467i	$0.358246\pi$
$307$			2.98062e6i			1.80493i	−0.430759	+	0.902467i	$0.641754\pi$
$308$			14232.7i			0.00854891i
$309$	192243.	+	192243.i	0.114539	+	0.114539i
$310$	−145272.			−0.0858573
$311$	−1.23638e6	−	1.23638e6i	−0.724854	−	0.724854i	0.244736	−	0.969590i	$-0.421299\pi$
$311$	−1.23638e6	−	1.23638e6i	−0.724854	−	0.724854i	−0.969590	+	0.244736i	$0.921299\pi$
$312$	−653469.			−0.380048
$313$	−1.62278e6	−	1.62278e6i	−0.936267	−	0.936267i	0.0618203	−	0.998087i	$-0.480309\pi$
$313$	−1.62278e6	−	1.62278e6i	−0.936267	−	0.936267i	−0.998087	+	0.0618203i	$0.980309\pi$
$314$	949186.	+	949186.i	0.543284	+	0.543284i
$315$	−212511.	+	212511.i	−0.120672	+	0.120672i
$316$	−23093.7	+	23093.7i	−0.0130100	+	0.0130100i
$317$	−991450.	+	991450.i	−0.554144	+	0.554144i	−0.927634	−	0.373490i	$-0.878161\pi$
$317$	−991450.	+	991450.i	−0.554144	+	0.554144i	0.373490	+	0.927634i	$0.378161\pi$
$318$	456658.			0.253235
$319$		−	1.51011e6i		−	0.830866i
$320$		−	1.31417e6i		−	0.717424i
$321$	−436190.	+	436190.i	−0.236272	+	0.236272i
$322$	523111.	+	523111.i	0.281160	+	0.281160i
$323$		−	2.02237e6i		−	1.07858i
$324$	79917.5			0.0422940
$325$	−751789.	+	751789.i	−0.394810	+	0.394810i
$326$		−	2.65700e6i		−	1.38467i
$327$	−41717.0			−0.0215746
$328$	1.53056e6	+	1.10873e6i	0.785533	+	0.569039i
$329$	−118353.			−0.0602825
$330$			282747.i			0.142927i
$331$	−1.03403e6	+	1.03403e6i	−0.518756	+	0.518756i	−0.917195	−	0.398439i	$-0.869552\pi$
$331$	−1.03403e6	+	1.03403e6i	−0.518756	+	0.518756i	0.398439	+	0.917195i	$0.369552\pi$
$332$	64635.2			0.0321828
$333$		−	1.45471e6i		−	0.718895i
$334$	−932433.	−	932433.i	−0.457353	−	0.457353i
$335$	−670305.	+	670305.i	−0.326332	+	0.326332i
$336$			154517.i			0.0746669i
$337$		−	2.72705e6i		−	1.30803i	−0.756480	−	0.654016i	$-0.773083\pi$
$337$		−	2.72705e6i		−	1.30803i	0.756480	−	0.654016i	$-0.226917\pi$
$338$	1.75512e6			0.835632
$339$	613200.	−	613200.i	0.289803	−	0.289803i
$340$	−85466.2	+	85466.2i	−0.0400956	+	0.0400956i
$341$	103577.	−	103577.i	0.0482366	−	0.0482366i
$342$	−1.17579e6	−	1.17579e6i	−0.543581	−	0.543581i
$343$	728613.	+	728613.i	0.334396	+	0.334396i
$344$	3.46135e6			1.57706
$345$	552545.	+	552545.i	0.249931	+	0.249931i
$346$	180213.			0.0809274
$347$	1.94035e6	+	1.94035e6i	0.865078	+	0.865078i	0.991923	−	0.126844i	$-0.0404849\pi$
$347$	1.94035e6	+	1.94035e6i	0.865078	+	0.865078i	−0.126844	+	0.991923i	$0.540485\pi$
$348$			49096.3i			0.0217320i
$349$		−	711342.i		−	0.312619i	−0.987708	−	0.156309i	$-0.950040\pi$
$349$		−	711342.i		−	0.312619i	0.987708	−	0.156309i	$-0.0499597\pi$
$350$	168285.	+	168285.i	0.0734304	+	0.0734304i
$351$	−1.73215e6			−0.750444
$352$	−115197.	−	115197.i	−0.0495546	−	0.0495546i
$353$	−1.51777e6			−0.648291			−0.324146	−	0.946007i	$-0.605077\pi$
$353$	−1.51777e6			−0.648291			−0.324146	+	0.946007i	$0.605077\pi$
$354$	−344893.	−	344893.i	−0.146277	−	0.146277i
$355$	1.40895e6	+	1.40895e6i	0.593367	+	0.593367i
$356$	46215.6	−	46215.6i	0.0193269	−	0.0193269i
$357$	−159357.	+	159357.i	−0.0661760	+	0.0661760i
$358$	2.02089e6	−	2.02089e6i	0.833364	−	0.833364i
$359$	3.15206e6			1.29080			0.645400	−	0.763845i	$-0.276691\pi$
$359$	3.15206e6			1.29080			0.645400	+	0.763845i	$0.276691\pi$
$360$		−	1.67034e6i		−	0.679278i
$361$		−	822457.i		−	0.332158i
$362$	−117682.	+	117682.i	−0.0471996	+	0.0471996i
$363$	314956.	+	314956.i	0.125454	+	0.125454i
$364$		−	46579.4i		−	0.0184264i
$365$	1.24204e6			0.487982
$366$	−291606.	+	291606.i	−0.113787	+	0.113787i
$367$		−	430477.i		−	0.166834i	−0.996515	−	0.0834170i	$-0.973417\pi$
$367$		−	430477.i		−	0.166834i	0.996515	−	0.0834170i	$-0.0265833\pi$
$368$	−4.34327e6			−1.67185
$369$	1.93885e6	+	1.40450e6i	0.741273	+	0.536978i
$370$	1.62615e6			0.617527
$371$		−	547103.i		−	0.206364i
$372$	−3367.47	+	3367.47i	−0.00126167	+	0.00126167i
$373$	−823447.			−0.306453			−0.153226	−	0.988191i	$-0.548966\pi$
$373$	−823447.			−0.306453			−0.153226	+	0.988191i	$0.548966\pi$
$374$		−	2.29215e6i		−	0.847352i
$375$	606431.	+	606431.i	0.222691	+	0.222691i
$376$	465129.	−	465129.i	0.169669	−	0.169669i
$377$			4.94212e6i			1.79085i
$378$			387736.i			0.139575i
$379$	4.01507e6			1.43580			0.717901	−	0.696145i	$-0.245103\pi$
$379$	4.01507e6			1.43580			0.717901	+	0.696145i	$0.245103\pi$
$380$	69883.7	−	69883.7i	0.0248266	−	0.0248266i
$381$	−786544.	+	786544.i	−0.277594	+	0.277594i
$382$	−2.44010e6	+	2.44010e6i	−0.855556	+	0.855556i
$383$	−1.49548e6	−	1.49548e6i	−0.520936	−	0.520936i	0.396918	−	0.917854i	$-0.370080\pi$
$383$	−1.49548e6	−	1.49548e6i	−0.520936	−	0.520936i	−0.917854	+	0.396918i	$0.870080\pi$
$384$	−639635.	−	639635.i	−0.221363	−	0.221363i
$385$	338748.			0.116473
$386$	−1.66195e6	−	1.66195e6i	−0.567739	−	0.567739i
$387$	4.38470e6			1.48820
$388$	−58514.8	−	58514.8i	−0.0197327	−	0.0197327i
$389$		−	1.69724e6i		−	0.568681i	−0.958723	−	0.284340i	$-0.908225\pi$
$389$		−	1.69724e6i		−	0.568681i	0.958723	−	0.284340i	$-0.0917746\pi$
$390$		−	925347.i		−	0.308065i
$391$	−4.47931e6	−	4.47931e6i	−1.48173	−	1.48173i
$392$	−2.77582e6			−0.912382
$393$	128308.	+	128308.i	0.0419055	+	0.0419055i
$394$	4.33802e6			1.40783
$395$	549646.	+	549646.i	0.177252	+	0.177252i
$396$	−70855.7	−	70855.7i	−0.0227058	−	0.0227058i
$397$	−731668.	+	731668.i	−0.232990	+	0.232990i	−0.813940	−	0.580949i	$-0.802681\pi$
$397$	−731668.	+	731668.i	−0.232990	+	0.232990i	0.580949	+	0.813940i	$0.302681\pi$
$398$	−2.93800e6	+	2.93800e6i	−0.929703	+	0.929703i
$399$	130303.	−	130303.i	0.0409752	−	0.0409752i
$400$	−1.39723e6			−0.436636
$401$			4.11597e6i			1.27824i	0.769108	+	0.639118i	$0.220701\pi$
$401$			4.11597e6i			1.27824i	−0.769108	+	0.639118i	$0.779299\pi$
$402$			584469.i			0.180383i
$403$	−338976.	+	338976.i	−0.103970	+	0.103970i
$404$	−164448.	−	164448.i	−0.0501273	−	0.0501273i
$405$		−	1.90209e6i		−	0.576227i
$406$	1.10628e6			0.333080
$407$	−1.15942e6	+	1.15942e6i	−0.346941	+	0.346941i
$408$		−	1.25254e6i		−	0.372514i
$409$	−3.79128e6			−1.12067			−0.560334	−	0.828266i	$-0.689327\pi$
$409$	−3.79128e6			−1.12067			−0.560334	+	0.828266i	$0.689327\pi$
$410$	−1.57002e6	+	2.16735e6i	−0.461261	+	0.636750i
$411$	−1.30880e6			−0.382182
$412$		−	107706.i		−	0.0312606i
$413$	−413202.	+	413202.i	−0.119203	+	0.119203i
$414$	−5.20848e6			−1.49352
$415$		−	1.53836e6i		−	0.438468i
$416$	377005.	+	377005.i	0.106810	+	0.106810i
$417$	1.05064e6	−	1.05064e6i	0.295879	−	0.295879i
$418$			1.87424e6i			0.524667i
$419$		−	2.30732e6i		−	0.642057i	−0.947070	−	0.321028i	$-0.895971\pi$
$419$		−	2.30732e6i		−	0.642057i	0.947070	−	0.321028i	$-0.104029\pi$
$420$	−11013.3			−0.00304645
$421$	182088.	−	182088.i	0.0500698	−	0.0500698i	−0.681629	−	0.731698i	$-0.738728\pi$
$421$	182088.	−	182088.i	0.0500698	−	0.0500698i	0.731698	+	0.681629i	$0.238728\pi$
$422$	−411853.	+	411853.i	−0.112580	+	0.112580i
$423$	589207.	−	589207.i	0.160110	−	0.160110i
$424$	2.15012e6	+	2.15012e6i	0.580827	+	0.580827i
$425$	−1.44100e6	−	1.44100e6i	−0.386983	−	0.386983i
$426$	1.22852e6			0.327989
$427$	349361.	+	349361.i	0.0927266	+	0.0927266i
$428$	244380.			0.0644847
$429$	659760.	+	659760.i	0.173078	+	0.173078i
$430$			4.90145e6i			1.27836i
$431$			2.75129e6i			0.713417i	0.934216	+	0.356709i	$0.116101\pi$
$431$			2.75129e6i			0.713417i	−0.934216	+	0.356709i	$0.883899\pi$
$432$	−1.60964e6	−	1.60964e6i	−0.414973	−	0.414973i
$433$	6.26885e6			1.60682			0.803412	−	0.595423i	$-0.203016\pi$
$433$	6.26885e6			1.60682			0.803412	+	0.595423i	$0.203016\pi$
$434$	75878.5	+	75878.5i	0.0193372	+	0.0193372i
$435$	1.16852e6			0.296084
$436$	11686.2	+	11686.2i	0.00294413	+	0.00294413i
$437$	3.66263e6	+	3.66263e6i	0.917466	+	0.917466i
$438$	541496.	−	541496.i	0.134868	−	0.134868i
$439$	−1.04568e6	+	1.04568e6i	−0.258962	+	0.258962i	−0.824632	−	0.565670i	$-0.808618\pi$
$439$	−1.04568e6	+	1.04568e6i	−0.258962	+	0.258962i	0.565670	+	0.824632i	$0.308618\pi$
$440$	−1.33128e6	+	1.33128e6i	−0.327822	+	0.327822i
$441$	−3.51631e6			−0.860975
$442$			7.50151e6i			1.82639i
$443$		−	500255.i		−	0.121111i	−0.998165	−	0.0605553i	$-0.980713\pi$
$443$		−	500255.i		−	0.121111i	0.998165	−	0.0605553i	$-0.0192872\pi$
$444$	37694.9	−	37694.9i	0.00907454	−	0.00907454i
$445$	−1.09996e6	−	1.09996e6i	−0.263316	−	0.263316i
$446$		−	7.97620e6i		−	1.89871i
$447$	−1.24818e6			−0.295467
$448$	−686417.	+	686417.i	−0.161582	+	0.161582i
$449$			271952.i			0.0636615i	0.999493	+	0.0318307i	$0.0101337\pi$
$449$			271952.i			0.0636615i	−0.999493	+	0.0318307i	$0.989866\pi$
$450$	−1.67557e6			−0.390061
$451$	−425884.	−	2.66469e6i	−0.0985938	−	0.616888i
$452$	−343552.			−0.0790945
$453$		−	723805.i		−	0.165721i
$454$	−1.07507e6	+	1.07507e6i	−0.244793	+	0.244793i
$455$	−1.10862e6			−0.251047
$456$			1.02418e6i			0.230655i
$457$	1.97316e6	+	1.97316e6i	0.441948	+	0.441948i	0.892666	−	0.450718i	$-0.148832\pi$
$457$	1.97316e6	+	1.97316e6i	0.441948	+	0.441948i	−0.450718	+	0.892666i	$0.648832\pi$
$458$	4.63644e6	−	4.63644e6i	1.03281	−	1.03281i
$459$		−	3.32012e6i		−	0.735567i
$460$		−	309569.i		−	0.0682124i
$461$	752001.			0.164803			0.0824017	−	0.996599i	$-0.473741\pi$
$461$	752001.			0.164803			0.0824017	+	0.996599i	$0.473741\pi$
$462$	147685.	−	147685.i	0.0321907	−	0.0321907i
$463$	4.54236e6	−	4.54236e6i	0.984758	−	0.984758i	−0.0151279	−	0.999886i	$-0.504816\pi$
$463$	4.54236e6	−	4.54236e6i	0.984758	−	0.984758i	0.999886	+	0.0151279i	$0.00481555\pi$
$464$	−4.59258e6	+	4.59258e6i	−0.990289	+	0.990289i
$465$	80148.0	+	80148.0i	0.0171894	+	0.0171894i
$466$	5.26109e6	+	5.26109e6i	1.12231	+	1.12231i
$467$	−4.40683e6			−0.935049			−0.467525	−	0.883980i	$-0.654854\pi$
$467$	−4.40683e6			−0.935049			−0.467525	+	0.883980i	$0.654854\pi$
$468$	231889.	+	231889.i	0.0489403	+	0.0489403i
$469$	700228.			0.146997
$470$	658646.	+	658646.i	0.137533	+	0.137533i
$471$		−	1.04735e6i		−	0.217541i
$472$		−	3.24776e6i		−	0.671011i
$473$	−3.49466e6	−	3.49466e6i	−0.718212	−	0.718212i
$474$	479261.			0.0979774
$475$	1.17827e6	+	1.17827e6i	0.239614	+	0.239614i
$476$	89281.5			0.0180611
$477$	2.72369e6	+	2.72369e6i	0.548101	+	0.548101i
$478$	6.65310e6	+	6.65310e6i	1.33185	+	1.33185i
$479$	6.01810e6	−	6.01810e6i	1.19845	−	1.19845i	0.223823	−	0.974630i	$-0.428146\pi$
$479$	6.01810e6	−	6.01810e6i	1.19845	−	1.19845i	0.974630	−	0.223823i	$-0.0718536\pi$
$480$	89139.6	−	89139.6i	0.0176591	−	0.0176591i
$481$	3.79444e6	−	3.79444e6i	0.747799	−	0.747799i
$482$	6.46706e6			1.26791
$483$		−	577211.i		−	0.112581i
$484$		−	176458.i		−	0.0342395i
$485$	−1.39269e6	+	1.39269e6i	−0.268844	+	0.268844i
$486$	−2.93811e6	−	2.93811e6i	−0.564257	−	0.564257i
$487$		−	5.89407e6i		−	1.12614i	−0.826409	−	0.563071i	$-0.809620\pi$
$487$		−	5.89407e6i		−	1.12614i	0.826409	−	0.563071i	$-0.190380\pi$
$488$	−2.74597e6			−0.521972
$489$	−1.46590e6	+	1.46590e6i	−0.277224	+	0.277224i
$490$		−	3.93071e6i		−	0.739572i
$491$	1.65538e6			0.309881			0.154940	−	0.987924i	$-0.450481\pi$
$491$	1.65538e6			0.309881			0.154940	+	0.987924i	$0.450481\pi$
$492$	13846.2	+	86634.0i	0.00257881	+	0.0161352i
$493$	−9.47287e6			−1.75535
$494$		−	6.13381e6i		−	1.13087i
$495$	−1.68641e6	+	1.68641e6i	−0.309351	+	0.309351i
$496$	−630002.			−0.114984
$497$		−	1.47184e6i		−	0.267283i
$498$	−670683.	−	670683.i	−0.121184	−	0.121184i
$499$	−6.47246e6	+	6.47246e6i	−1.16364	+	1.16364i	−0.179966	+	0.983673i	$0.557599\pi$
$499$	−6.47246e6	+	6.47246e6i	−1.16364	+	1.16364i	−0.983673	+	0.179966i	$0.942401\pi$
$500$		−	339760.i		−	0.0607781i
$501$			1.02887e6i			0.183132i
$502$	3.95602e6			0.700647
$503$	7.76956e6	−	7.76956e6i	1.36923	−	1.36923i	0.507689	−	0.861540i	$-0.330500\pi$
$503$	7.76956e6	−	7.76956e6i	1.36923	−	1.36923i	0.861540	−	0.507689i	$-0.169500\pi$
$504$	−872451.	+	872451.i	−0.152991	+	0.152991i
$505$	−3.91396e6	+	3.91396e6i	−0.682949	+	0.682949i
$506$	4.15123e6	+	4.15123e6i	0.720776	+	0.720776i
$507$	−968317.	−	968317.i	−0.167301	−	0.167301i
$508$	440670.			0.0757625
$509$	−4.48141e6	−	4.48141e6i	−0.766691	−	0.766691i	0.210831	−	0.977522i	$-0.432383\pi$
$509$	−4.48141e6	−	4.48141e6i	−0.766691	−	0.766691i	−0.977522	+	0.210831i	$0.932383\pi$
$510$	1.77367e6			0.301958
$511$	−648744.	−	648744.i	−0.109906	−	0.109906i
$512$		−	5.35787e6i		−	0.903269i
$513$			2.71479e6i			0.455452i
$514$	−6.53213e6	−	6.53213e6i	−1.09055	−	1.09055i
$515$	−2.56348e6			−0.425904
$516$	113618.	+	113618.i	0.0187855	+	0.0187855i
$517$	−939212.			−0.154539
$518$	−849371.	−	849371.i	−0.139083	−	0.139083i
$519$	−99425.3	−	99425.3i	−0.0162024	−	0.0162024i
$520$	4.35687e6	−	4.35687e6i	0.706589	−	0.706589i
$521$	3.25748e6	−	3.25748e6i	0.525759	−	0.525759i	−0.393546	−	0.919305i	$-0.628752\pi$
$521$	3.25748e6	−	3.25748e6i	0.525759	−	0.525759i	0.919305	+	0.393546i	$0.128752\pi$
$522$	−5.50746e6	+	5.50746e6i	−0.884657	+	0.884657i
$523$	3.98076e6			0.636374			0.318187	−	0.948028i	$-0.396926\pi$
$523$	3.98076e6			0.636374			0.318187	+	0.948028i	$0.396926\pi$
$524$		−	71885.7i		−	0.0114371i
$525$		−	185690.i		−	0.0294028i
$526$	−5.96815e6	+	5.96815e6i	−0.940536	+	0.940536i
$527$	−649736.	−	649736.i	−0.101908	−	0.101908i
$528$			1.22619e6i			0.191414i
$529$	9.78830e6			1.52079
$530$	−3.04468e6	+	3.04468e6i	−0.470816	+	0.470816i
$531$		−	4.11414e6i		−	0.633203i
$532$	−73003.5			−0.0111832
$533$	1.39379e6	+	8.72074e6i	0.212510	+	1.32964i
$534$	−959106.			−0.145550
$535$		−	5.81642e6i		−	0.878559i
$536$	−2.75189e6	+	2.75189e6i	−0.413733	+	0.413733i
$537$	−2.22989e6			−0.333694
$538$			1.01333e7i			1.50937i
$539$	2.80254e6	+	2.80254e6i	0.415509	+	0.415509i
$540$	114728.	−	114728.i	0.0169311	−	0.0169311i
$541$			9.44255e6i			1.38706i	0.720427	+	0.693531i	$0.243946\pi$
$541$			9.44255e6i			1.38706i	−0.720427	+	0.693531i	$0.756054\pi$
$542$		−	632349.i		−	0.0924610i
$543$	129853.			0.0188996
$544$	−722628.	+	722628.i	−0.104693	+	0.104693i
$545$	278139.	−	278139.i	0.0401117	−	0.0401117i
$546$	−483328.	+	483328.i	−0.0693841	+	0.0693841i
$547$	−1.11156e6	−	1.11156e6i	−0.158842	−	0.158842i	0.623212	−	0.782053i	$-0.285828\pi$
$547$	−1.11156e6	−	1.11156e6i	−0.158842	−	0.158842i	−0.782053	+	0.623212i	$0.785828\pi$
$548$	366636.	+	366636.i	0.0521535	+	0.0521535i
$549$	−3.47850e6			−0.492562
$550$	1.33545e6	+	1.33545e6i	0.188245	+	0.188245i
$551$	7.74575e6			1.08689
$552$	2.26844e6	+	2.26844e6i	0.316869	+	0.316869i
$553$		−	574183.i		−	0.0798431i
$554$		−	6.91563e6i		−	0.957320i
$555$	−897163.	−	897163.i	−0.123634	−	0.123634i
$556$	−588634.			−0.0807529
$557$	−7.66574e6	−	7.66574e6i	−1.04693	−	1.04693i	−0.998843	−	0.0480829i	$-0.984689\pi$
$557$	−7.66574e6	−	7.66574e6i	−1.04693	−	1.04693i	−0.0480829	−	0.998843i	$-0.515311\pi$
$558$	−755503.			−0.102719
$559$	1.14370e7	+	1.14370e7i	1.54804	+	1.54804i
$560$	−1.03021e6	−	1.03021e6i	−0.138821	−	0.138821i
$561$	−1.26460e6	+	1.26460e6i	−0.169647	+	0.169647i
$562$	5.06876e6	−	5.06876e6i	0.676956	−	0.676956i
$563$	−9.00928e6	+	9.00928e6i	−1.19790	+	1.19790i	−0.223101	+	0.974795i	$0.571618\pi$
$563$	−9.00928e6	+	9.00928e6i	−1.19790	+	1.19790i	−0.974795	+	0.223101i	$0.928382\pi$
$564$	30535.4			0.00404210
$565$			8.17677e6i			1.07761i
$566$		−	7.45018e6i		−	0.977520i
$567$	−993501.	+	993501.i	−0.129781	+	0.129781i
$568$	5.78434e6	+	5.78434e6i	0.752286	+	0.752286i
$569$			4.87526e6i			0.631273i	0.948880	+	0.315636i	$0.102218\pi$
$569$			4.87526e6i			0.631273i	−0.948880	+	0.315636i	$0.897782\pi$
$570$	−1.45029e6			−0.186968
$571$	−4.46036e6	+	4.46036e6i	−0.572505	+	0.572505i	−0.932828	−	0.360322i	$-0.882667\pi$
$571$	−4.46036e6	+	4.46036e6i	−0.572505	+	0.572505i	0.360322	+	0.932828i	$0.382667\pi$
$572$		−	369638.i		−	0.0472374i
$573$	2.69245e6			0.342580
$574$	1.95211e6	−	311994.i	0.247300	−	0.0395246i
$575$	5.21949e6			0.658352
$576$		−	6.83448e6i		−	0.858320i
$577$	−6.40864e6	+	6.40864e6i	−0.801357	+	0.801357i	−0.983308	−	0.181951i	$-0.941759\pi$
$577$	−6.40864e6	+	6.40864e6i	−0.801357	+	0.801357i	0.181951	+	0.983308i	$0.441759\pi$
$578$	−6.12424e6			−0.762487
$579$			1.83383e6i			0.227333i
$580$	−327339.	−	327339.i	−0.0404044	−	0.0404044i
$581$	−803518.	+	803518.i	−0.0987542	+	0.0987542i
$582$			1.21435e6i			0.148606i
$583$		−	4.34163e6i		−	0.529031i
$584$	5.09912e6			0.618676
$585$	5.51912e6	−	5.51912e6i	0.666777	−	0.666777i
$586$	−5.14348e6	+	5.14348e6i	−0.618747	+	0.618747i
$587$	−7.08270e6	+	7.08270e6i	−0.848406	+	0.848406i	−0.989934	−	0.141528i	$-0.954798\pi$
$587$	−7.08270e6	+	7.08270e6i	−0.848406	+	0.848406i	0.141528	+	0.989934i	$0.454798\pi$
$588$	−91115.6	−	91115.6i	−0.0108680	−	0.0108680i
$589$	531274.	+	531274.i	0.0631002	+	0.0631002i
$590$	4.59900e6			0.543918
$591$	−2.39333e6	−	2.39333e6i	−0.281861	−	0.281861i
$592$	7.05214e6			0.827021
$593$	−2.14214e6	−	2.14214e6i	−0.250156	−	0.250156i	0.570879	−	0.821034i	$-0.306603\pi$
$593$	−2.14214e6	−	2.14214e6i	−0.250156	−	0.250156i	−0.821034	+	0.570879i	$0.806603\pi$
$594$			3.07694e6i			0.357810i
$595$		−	2.12496e6i		−	0.246070i
$596$	349654.	+	349654.i	0.0403202	+	0.0403202i
$597$	3.24185e6			0.372269
$598$	−1.35857e7	−	1.35857e7i	−1.55356	−	1.55356i
$599$	3.12893e6			0.356311			0.178156	−	0.984002i	$-0.442987\pi$
$599$	3.12893e6			0.356311			0.178156	+	0.984002i	$0.442987\pi$
$600$	729759.	+	729759.i	0.0827564	+	0.0827564i
$601$	−8.31693e6	−	8.31693e6i	−0.939240	−	0.939240i	0.0590168	−	0.998257i	$-0.481203\pi$
$601$	−8.31693e6	−	8.31693e6i	−0.939240	−	0.939240i	−0.998257	+	0.0590168i	$0.981203\pi$
$602$	2.56013e6	−	2.56013e6i	0.287919	−	0.287919i
$603$	−3.48600e6	+	3.48600e6i	−0.390421	+	0.390421i
$604$	−202760.	+	202760.i	−0.0226147	+	0.0226147i
$605$	−4.19981e6			−0.466489
$606$			3.41276e6i			0.377506i
$607$		−	1.08265e7i		−	1.19266i	−0.802741	−	0.596328i	$-0.796626\pi$
$607$		−	1.08265e7i		−	1.19266i	0.802741	−	0.596328i	$-0.203374\pi$
$608$	590877.	−	590877.i	0.0648243	−	0.0648243i
$609$	−610344.	−	610344.i	−0.0666855	−	0.0666855i
$610$		−	3.88844e6i		−	0.423108i
$611$	3.07376e6			0.333094
$612$	−444477.	+	444477.i	−0.0479701	+	0.0479701i
$613$		−	9.17949e6i		−	0.986659i	−0.869842	−	0.493330i	$-0.835780\pi$
$613$		−	9.17949e6i		−	0.986659i	0.869842	−	0.493330i	$-0.164220\pi$
$614$	−1.73279e7			−1.85492
$615$	2.06195e6	−	329550.i	0.219831	−	0.0351344i
$616$	1.39071e6			0.147667
$617$			1.17721e7i			1.24492i	0.782652	+	0.622460i	$0.213867\pi$
$617$			1.17721e7i			1.24492i	−0.782652	+	0.622460i	$0.786133\pi$
$618$	−1.11761e6	+	1.11761e6i	−0.117711	+	0.117711i
$619$	−5.19479e6			−0.544931			−0.272466	−	0.962166i	$-0.587839\pi$
$619$	−5.19479e6			−0.544931			−0.272466	+	0.962166i	$0.587839\pi$
$620$		−	44903.8i		−	0.00469142i
$621$	6.01295e6	+	6.01295e6i	0.625689	+	0.625689i
$622$	7.18771e6	−	7.18771e6i	0.744928	−	0.744928i
$623$			1.14907e6i			0.118611i
$624$		−	4.01296e6i		−	0.412576i
$625$	−4.03711e6			−0.413400
$626$	9.43408e6	−	9.43408e6i	0.962196	−	0.962196i
$627$	1.03404e6	−	1.03404e6i	0.105043	−	0.105043i
$628$	−293395.	+	293395.i	−0.0296862	+	0.0296862i
$629$	7.27303e6	+	7.27303e6i	0.732974	+	0.732974i
$630$	−1.23544e6	−	1.23544e6i	−0.124013	−	0.124013i
$631$	9.81154e6			0.980988			0.490494	−	0.871444i	$-0.336816\pi$
$631$	9.81154e6			0.980988			0.490494	+	0.871444i	$0.336816\pi$
$632$	2.25654e6	+	2.25654e6i	0.224724	+	0.224724i
$633$	454447.			0.0450790
$634$	−5.76381e6	−	5.76381e6i	−0.569491	−	0.569491i
$635$		−	1.04882e7i		−	1.03221i
$636$			141154.i			0.0138373i
$637$	−9.17187e6	−	9.17187e6i	−0.895591	−	0.895591i
$638$	8.77903e6			0.853876
$639$	7.32739e6	+	7.32739e6i	0.709900	+	0.709900i
$640$	8.52928e6			0.823118
$641$	8.18261e6	+	8.18261e6i	0.786587	+	0.786587i	0.980933	−	0.194346i	$-0.0622585\pi$
$641$	8.18261e6	+	8.18261e6i	0.786587	+	0.786587i	−0.194346	+	0.980933i	$0.562258\pi$
$642$	−2.53580e6	−	2.53580e6i	−0.242816	−	0.242816i
$643$	−7.16404e6	+	7.16404e6i	−0.683330	+	0.683330i	−0.960749	−	0.277419i	$-0.910521\pi$
$643$	−7.16404e6	+	7.16404e6i	−0.683330	+	0.683330i	0.277419	+	0.960749i	$0.410521\pi$
$644$	−161695.	+	161695.i	−0.0153632	+	0.0153632i
$645$	2.70418e6	−	2.70418e6i	0.255939	−	0.255939i
$646$	1.17571e7			1.10845
$647$		−	7.19483e6i		−	0.675709i	−0.941198	−	0.337855i	$-0.890299\pi$
$647$		−	7.19483e6i		−	0.675709i	0.941198	−	0.337855i	$-0.109701\pi$
$648$		−	7.80891e6i		−	0.730555i
$649$	−3.27903e6	+	3.27903e6i	−0.305586	+	0.305586i
$650$	−4.37054e6	−	4.37054e6i	−0.405743	−	0.405743i
$651$		−	83726.0i		−	0.00774297i
$652$	821284.			0.0756614
$653$	11077.2	−	11077.2i	0.00101660	−	0.00101660i	−0.706598	−	0.707615i	$-0.749771\pi$
$653$	11077.2	−	11077.2i	0.00101660	−	0.00101660i	0.707615	+	0.706598i	$0.249771\pi$
$654$		−	242522.i		−	0.0221721i
$655$	−1.71093e6			−0.155822
$656$	−6.80874e6	+	9.39916e6i	−0.617742	+	0.852765i
$657$	6.45938e6			0.583818
$658$		−	688049.i		−	0.0619519i
$659$	−1.19515e7	+	1.19515e7i	−1.07203	+	1.07203i	−0.0748369	+	0.997196i	$0.523844\pi$
$659$	−1.19515e7	+	1.19515e7i	−1.07203	+	1.07203i	−0.997196	+	0.0748369i	$0.976156\pi$
$660$	−87397.8			−0.00780981
$661$			1.39032e7i			1.23769i	0.785513	+	0.618845i	$0.212399\pi$
$661$			1.39032e7i			1.23769i	−0.785513	+	0.618845i	$0.787601\pi$
$662$	−6.01135e6	−	6.01135e6i	−0.533122	−	0.533122i
$663$	4.13866e6	−	4.13866e6i	0.365659	−	0.365659i
$664$		−	6.31565e6i		−	0.555902i
$665$			1.73753e6i			0.152363i
$666$	8.45697e6			0.738804
$667$	1.71560e7	−	1.71560e7i	1.49314	−	1.49314i
$668$	288217.	−	288217.i	0.0249907	−	0.0249907i
$669$	−4.40055e6	+	4.40055e6i	−0.380139	+	0.380139i
$670$	−3.89683e6	−	3.89683e6i	−0.335370	−	0.335370i
$671$	2.77241e6	+	2.77241e6i	0.237712	+	0.237712i
$672$	−93119.0			−0.00795454
$673$	−1.27602e7	−	1.27602e7i	−1.08598	−	1.08598i	−0.995938	−	0.0900380i	$-0.971301\pi$
$673$	−1.27602e7	−	1.27602e7i	−1.08598	−	1.08598i	−0.0900380	−	0.995938i	$-0.528699\pi$
$674$	1.58538e7			1.34426
$675$	1.93437e6	+	1.93437e6i	0.163411	+	0.163411i
$676$			542511.i			0.0456606i
$677$		−	1.69659e7i		−	1.42267i	−0.702853	−	0.711335i	$-0.748091\pi$
$677$		−	1.69659e7i		−	1.42267i	0.702853	−	0.711335i	$-0.251909\pi$
$678$	3.56485e6	+	3.56485e6i	0.297829	+	0.297829i
$679$	1.45486e6			0.121101
$680$	8.35109e6	+	8.35109e6i	0.692581	+	0.692581i
$681$	1.18626e6			0.0980194
$682$	602146.	+	602146.i	0.0495725	+	0.0495725i
$683$	2.53820e6	+	2.53820e6i	0.208197	+	0.208197i	0.803501	−	0.595304i	$-0.202968\pi$
$683$	2.53820e6	+	2.53820e6i	0.208197	+	0.208197i	−0.595304	+	0.803501i	$0.702968\pi$
$684$	363438.	−	363438.i	0.0297023	−	0.0297023i
$685$	8.72618e6	−	8.72618e6i	0.710555	−	0.710555i
$686$	−4.23580e6	+	4.23580e6i	−0.343657	+	0.343657i
$687$	−5.11595e6			−0.413556
$688$			2.12562e7i			1.71204i
$689$			1.42088e7i			1.14028i
$690$	−3.21223e6	+	3.21223e6i	−0.256852	+	0.256852i
$691$	7.74824e6	+	7.74824e6i	0.617317	+	0.617317i	0.944842	−	0.327526i	$-0.106215\pi$
$691$	7.74824e6	+	7.74824e6i	0.617317	+	0.617317i	−0.327526	+	0.944842i	$0.606215\pi$
$692$			55704.1i			0.00442204i
$693$	1.76170e6			0.139347
$694$	−1.12802e7	+	1.12802e7i	−0.889036	+	0.889036i
$695$			1.40099e7i			1.10020i
$696$	4.79730e6			0.375383
$697$	−1.67156e7	+	2.67156e6i	−1.30329	+	0.208297i
$698$	4.13540e6			0.321276
$699$		−	5.80520e6i		−	0.449391i
$700$	−52017.3	+	52017.3i	−0.00401239	+	0.00401239i
$701$	−1.99725e7			−1.53510			−0.767552	−	0.640987i	$-0.778525\pi$
$701$	−1.99725e7			−1.53510			−0.767552	+	0.640987i	$0.778525\pi$
$702$		−	1.00699e7i		−	0.771227i
$703$	−5.94699e6	−	5.94699e6i	−0.453846	−	0.453846i
$704$	−5.44717e6	+	5.44717e6i	−0.414228	+	0.414228i
$705$		−	726764.i		−	0.0550707i
$706$		−	8.82360e6i		−	0.666245i
$707$	4.08869e6			0.307635
$708$	106607.	−	106607.i	0.00799287	−	0.00799287i
$709$	8.66267e6	−	8.66267e6i	0.647196	−	0.647196i	−0.305118	−	0.952315i	$-0.598696\pi$
$709$	8.66267e6	−	8.66267e6i	0.647196	−	0.647196i	0.952315	+	0.305118i	$0.0986959\pi$
$710$	−8.19093e6	+	8.19093e6i	−0.609800	+	0.609800i
$711$	2.85850e6	+	2.85850e6i	0.212062	+	0.212062i
$712$	−4.51582e6	−	4.51582e6i	−0.333839	−	0.333839i
$713$	2.35343e6			0.173371
$714$	−926424.	−	926424.i	−0.0680087	−	0.0680087i
$715$	−8.79763e6			−0.643577
$716$	624661.	+	624661.i	0.0455367	+	0.0455367i
$717$		−	7.34117e6i		−	0.533295i
$718$			1.83246e7i			1.32655i
$719$	−1.30749e7	−	1.30749e7i	−0.943230	−	0.943230i	0.0552429	−	0.998473i	$-0.482407\pi$
$719$	−1.30749e7	−	1.30749e7i	−0.943230	−	0.943230i	−0.998473	+	0.0552429i	$0.982407\pi$
$720$	1.02575e7			0.737415
$721$	1.33896e6	+	1.33896e6i	0.0959245	+	0.0959245i
$722$	4.78137e6			0.341357
$723$	−3.56794e6	−	3.56794e6i	−0.253847	−	0.253847i
$724$	−36375.7	−	36375.7i	−0.00257908	−	0.00257908i
$725$	5.51910e6	−	5.51910e6i	0.389963	−	0.389963i
$726$	−1.83100e6	+	1.83100e6i	−0.128928	+	0.128928i
$727$	−1.60959e7	+	1.60959e7i	−1.12948	+	1.12948i	−0.139219	+	0.990262i	$0.544459\pi$
$727$	−1.60959e7	+	1.60959e7i	−1.12948	+	1.12948i	−0.990262	+	0.139219i	$0.955541\pi$
$728$	−4.55137e6			−0.318283
$729$		−	7.56509e6i		−	0.527224i
$730$			7.22063e6i			0.501496i
$731$	−2.19220e7	+	2.19220e7i	−1.51735	+	1.51735i
$732$	−90135.9	−	90135.9i	−0.00621756	−	0.00621756i
$733$		−	1.60770e7i		−	1.10521i	−0.833443	−	0.552605i	$-0.813634\pi$
$733$		−	1.60770e7i		−	1.10521i	0.833443	−	0.552605i	$-0.186366\pi$
$734$	2.50258e6			0.171454
$735$	−2.16861e6	+	2.16861e6i	−0.148069	+	0.148069i
$736$		−	2.61745e6i		−	0.178108i
$737$	5.55677e6			0.376837
$738$	−8.16509e6	+	1.12715e7i	−0.551849	+	0.761802i
$739$	−2.14388e7			−1.44407			−0.722037	−	0.691855i	$-0.756794\pi$
$739$	−2.14388e7			−1.44407			−0.722037	+	0.691855i	$0.756794\pi$
$740$			502646.i			0.0337429i
$741$	−3.38409e6	+	3.38409e6i	−0.226410	+	0.226410i
$742$	3.18059e6			0.212079
$743$			104279.i			0.00692989i	0.999994	+	0.00346495i	$0.00110293\pi$
$743$			104279.i			0.00692989i	−0.999994	+	0.00346495i	$0.998897\pi$
$744$	329043.	+	329043.i	0.0217932	+	0.0217932i
$745$	8.32200e6	−	8.32200e6i	0.549335	−	0.549335i
$746$		−	4.78712e6i		−	0.314940i
$747$		−	8.00043e6i		−	0.524580i
$748$	708507.			0.0463010
$749$	−3.03803e6	+	3.03803e6i	−0.197874	+	0.197874i
$750$	−3.52550e6	+	3.52550e6i	−0.228859	+	0.228859i
$751$	1.90142e7	−	1.90142e7i	1.23021	−	1.23021i	0.266323	−	0.963884i	$-0.414191\pi$
$751$	1.90142e7	−	1.90142e7i	1.23021	−	1.23021i	0.963884	−	0.266323i	$-0.0858087\pi$
$752$	2.85636e6	+	2.85636e6i	0.184191	+	0.184191i
$753$	−2.18258e6	−	2.18258e6i	−0.140276	−	0.140276i
$754$	−2.87311e7			−1.84045
$755$	4.82582e6	+	4.82582e6i	0.308109	+	0.308109i
$756$	−119850.			−0.00762664
$757$	4.23966e6	+	4.23966e6i	0.268900	+	0.268900i	0.828657	−	0.559757i	$-0.189105\pi$
$757$	4.23966e6	+	4.23966e6i	0.268900	+	0.268900i	−0.559757	+	0.828657i	$0.689105\pi$
$758$			2.33416e7i			1.47557i
$759$		−	4.58055e6i		−	0.288611i
$760$	−6.82849e6	−	6.82849e6i	−0.428836	−	0.428836i
$761$	1.28108e7			0.801889			0.400944	−	0.916102i	$-0.368682\pi$
$761$	1.28108e7			0.801889			0.400944	+	0.916102i	$0.368682\pi$
$762$	−4.57259e6	−	4.57259e6i	−0.285282	−	0.285282i
$763$	−290556.			−0.0180683
$764$	−754239.	−	754239.i	−0.0467493	−	0.0467493i
$765$	1.05788e7	+	1.05788e7i	0.653559	+	0.653559i
$766$	8.69402e6	−	8.69402e6i	0.535363	−	0.535363i
$767$	1.07313e7	−	1.07313e7i	0.658662	−	0.658662i
$768$	564828.	−	564828.i	0.0345552	−	0.0345552i
$769$	1.04373e7			0.636460			0.318230	−	0.948014i	$-0.396912\pi$
$769$	1.04373e7			0.636460			0.318230	+	0.948014i	$0.396912\pi$
$770$			1.96932e6i			0.119699i
$771$			7.20769e6i			0.436677i
$772$	513711.	−	513711.i	0.0310224	−	0.0310224i
$773$	4.38411e6	+	4.38411e6i	0.263896	+	0.263896i	0.826635	−	0.562739i	$-0.190252\pi$
$773$	4.38411e6	+	4.38411e6i	0.263896	+	0.263896i	−0.562739	+	0.826635i	$0.690252\pi$
$774$			2.54905e7i			1.52942i
$775$	757100.			0.0452792
$776$	−5.71761e6	+	5.71761e6i	−0.340848	+	0.340848i
$777$			937214.i			0.0556911i
$778$	9.86691e6			0.584430
$779$	1.36679e7	−	2.18447e6i	0.806974	−	0.128974i
$780$	286027.			0.0168333
$781$		−	1.16800e7i		−	0.685199i
$782$	2.60406e7	−	2.60406e7i	1.52277	−	1.52277i
$783$	1.27162e7			0.741231
$784$		−	1.70463e7i		−	0.990470i
$785$	6.98300e6	+	6.98300e6i	0.404453	+	0.404453i
$786$	−745918.	+	745918.i	−0.0430660	+	0.0430660i
$787$			2.13605e7i			1.22935i	0.788781	+	0.614675i	$0.210713\pi$
$787$			2.13605e7i			1.22935i	−0.788781	+	0.614675i	$0.789287\pi$
$788$			1.34089e6i			0.0769269i
$789$	6.58538e6			0.376607
$790$	−3.19537e6	+	3.19537e6i	−0.182160	+	0.182160i
$791$	4.27089e6	−	4.27089e6i	0.242704	−	0.242704i
$792$	−6.92347e6	+	6.92347e6i	−0.392203	+	0.392203i
$793$	−9.07325e6	−	9.07325e6i	−0.512366	−	0.512366i
$794$	−4.25356e6	−	4.25356e6i	−0.239443	−	0.239443i
$795$	3.35956e6			0.188523
$796$	−908142.	−	908142.i	−0.0508009	−	0.0508009i
$797$	2.36313e6			0.131778			0.0658888	−	0.997827i	$-0.479012\pi$
$797$	2.36313e6			0.131778			0.0658888	+	0.997827i	$0.479012\pi$
$798$	757516.	+	757516.i	0.0421099	+	0.0421099i
$799$			5.89166e6i			0.326490i
$800$		−	842037.i		−	0.0465164i
$801$	−5.72047e6	−	5.72047e6i	−0.315029	−	0.315029i
$802$	−2.39283e7			−1.31364
$803$	−5.14821e6	−	5.14821e6i	−0.281752	−	0.281752i
$804$	−180660.			−0.00985651
$805$	3.84844e6	+	3.84844e6i	0.209312	+	0.209312i
$806$	−1.97064e6	−	1.97064e6i	−0.106849	−	0.106849i
$807$	5.59066e6	−	5.59066e6i	0.302190	−	0.302190i
$808$	−1.60685e7	+	1.60685e7i	−0.865860	+	0.865860i
$809$	1.84991e7	−	1.84991e7i	0.993757	−	0.993757i	−0.00622355	−	0.999981i	$-0.501981\pi$
$809$	1.84991e7	−	1.84991e7i	0.993757	−	0.993757i	0.999981	+	0.00622355i	$0.00198103\pi$
$810$	1.10578e7			0.592185
$811$			1.39863e7i			0.746708i	0.927689	+	0.373354i	$0.121792\pi$
$811$			1.39863e7i			0.746708i	−0.927689	+	0.373354i	$0.878208\pi$
$812$			341952.i			0.0182002i
$813$	−348873.	+	348873.i	−0.0185115	+	0.0185115i
$814$	−6.74032e6	−	6.74032e6i	−0.356549	−	0.356549i
$815$		−	1.95471e7i		−	1.03083i
$816$	7.69189e6			0.404397
$817$	1.79251e7	−	1.79251e7i	0.939520	−	0.939520i
$818$		−	2.20407e7i		−	1.15170i
$819$	−5.76551e6			−0.300350
$820$	−669931.	−	485297.i	−0.0347933	−	0.0252042i
$821$	−616890.			−0.0319411			−0.0159705	−	0.999872i	$-0.505084\pi$
$821$	−616890.			−0.0319411			−0.0159705	+	0.999872i	$0.505084\pi$
$822$		−	7.60875e6i		−	0.392766i
$823$	−1.30109e7	+	1.30109e7i	−0.669589	+	0.669589i	−0.957621	−	0.288032i	$-0.906999\pi$
$823$	−1.30109e7	+	1.30109e7i	−0.669589	+	0.669589i	0.288032	+	0.957621i	$0.406999\pi$
$824$	−1.05242e7			−0.539973
$825$		−	1.47357e6i		−	0.0753764i
$826$	−2.40215e6	−	2.40215e6i	−0.122504	−	0.122504i
$827$	−2.66329e6	+	2.66329e6i	−0.135411	+	0.135411i	−0.771563	−	0.636152i	$-0.780525\pi$
$827$	−2.66329e6	+	2.66329e6i	−0.135411	+	0.135411i	0.636152	+	0.771563i	$0.280525\pi$
$828$		−	1.60995e6i		−	0.0816088i
$829$			3.17236e7i			1.60323i	0.597839	+	0.801616i	$0.296026\pi$
$829$			3.17236e7i			1.60323i	−0.597839	+	0.801616i	$0.703974\pi$
$830$	8.94329e6			0.450611
$831$	−3.81542e6	+	3.81542e6i	−0.191664	+	0.191664i
$832$	1.78269e7	−	1.78269e7i	0.892829	−	0.892829i
$833$	1.75803e7	−	1.75803e7i	0.877837	−	0.877837i
$834$	6.10792e6	+	6.10792e6i	0.304073	+	0.304073i
$835$	−6.85975e6	−	6.85975e6i	−0.340480	−	0.340480i
$836$	−579330.			−0.0286689
$837$	872194.	+	872194.i	0.0430328	+	0.0430328i
$838$	1.34137e7			0.659838
$839$	−8.94703e6	−	8.94703e6i	−0.438807	−	0.438807i	0.452803	−	0.891610i	$-0.350424\pi$
$839$	−8.94703e6	−	8.94703e6i	−0.438807	−	0.438807i	−0.891610	+	0.452803i	$0.850424\pi$
$840$			1.07613e6i			0.0526221i
$841$		−	1.57704e7i		−	0.768868i
$842$	1.05857e6	+	1.05857e6i	0.0514564	+	0.0514564i
$843$	−5.59297e6			−0.271065
$844$	−127305.	−	127305.i	−0.00615160	−	0.00615160i
$845$	1.29121e7			0.622094
$846$	3.42537e6	+	3.42537e6i	0.164544	+	0.164544i
$847$	2.19365e6	+	2.19365e6i	0.105065	+	0.105065i
$848$	−1.32039e7	+	1.32039e7i	−0.630539	+	0.630539i
$849$	−4.11034e6	+	4.11034e6i	−0.195708	+	0.195708i
$850$	8.37728e6	−	8.37728e6i	0.397700	−	0.397700i
$851$	−2.63438e7			−1.24697
$852$			379739.i			0.0179220i
$853$		−	1.50424e7i		−	0.707855i	−0.935273	−	0.353927i	$-0.884846\pi$
$853$		−	1.50424e7i		−	0.707855i	0.935273	−	0.353927i	$-0.115154\pi$
$854$	−2.03101e6	+	2.03101e6i	−0.0952946	+	0.0952946i
$855$	−8.65008e6	−	8.65008e6i	−0.404674	−	0.404674i
$856$		−	2.38789e7i		−	1.11386i
$857$	944309.			0.0439200			0.0219600	−	0.999759i	$-0.493009\pi$
$857$	944309.			0.0439200			0.0219600	+	0.999759i	$0.493009\pi$
$858$	−3.83552e6	+	3.83552e6i	−0.177872	+	0.177872i
$859$			1.65499e7i			0.765265i	0.923901	+	0.382633i	$0.124983\pi$
$859$			1.65499e7i			0.765265i	−0.923901	+	0.382633i	$0.875017\pi$
$860$	−1.51505e6			−0.0698522
$861$	−1.24913e6	−	904867.i	−0.0574247	−	0.0415984i
$862$	−1.59947e7			−0.733175
$863$			9.59137e6i			0.438383i	0.975682	+	0.219191i	$0.0703419\pi$
$863$			9.59137e6i			0.438383i	−0.975682	+	0.219191i	$0.929658\pi$
$864$	970044.	−	970044.i	0.0442086	−	0.0442086i
$865$	1.32580e6			0.0602471
$866$			3.64441e7i			1.65132i
$867$	3.37881e6	+	3.37881e6i	0.152657	+	0.152657i
$868$	−23454.2	+	23454.2i	−0.00105663	+	0.00105663i
$869$		−	4.55652e6i		−	0.204684i
$870$			6.79323e6i			0.304283i
$871$	−1.81856e7			−0.812237
$872$	1.14188e6	−	1.14188e6i	0.0508547	−	0.0508547i
$873$	−7.24286e6	+	7.24286e6i	−0.321643	+	0.321643i
$874$	−2.12928e7	+	2.12928e7i	−0.942874	+	0.942874i
$875$	4.22375e6	+	4.22375e6i	0.186500	+	0.186500i
$876$	167377.	+	167377.i	0.00736948	+	0.00736948i
$877$	2.51563e7			1.10446			0.552228	−	0.833693i	$-0.313778\pi$
$877$	2.51563e7			1.10446			0.552228	+	0.833693i	$0.313778\pi$
$878$	−6.07906e6	−	6.07906e6i	−0.266134	−	0.266134i
$879$	5.67543e6			0.247757
$880$	−8.17540e6	−	8.17540e6i	−0.355879	−	0.355879i
$881$		−	1.55724e7i		−	0.675950i	−0.941155	−	0.337975i	$-0.890258\pi$
$881$		−	1.55724e7i		−	0.675950i	0.941155	−	0.337975i	$-0.109742\pi$
$882$		−	2.04421e7i		−	0.884818i
$883$	2.38010e7	+	2.38010e7i	1.02729	+	1.02729i	0.999617	+	0.0276745i	$0.00881018\pi$
$883$	2.38010e7	+	2.38010e7i	1.02729	+	1.02729i	0.0276745	+	0.999617i	$0.491190\pi$
$884$	−2.31873e6			−0.0997975
$885$	−2.53732e6	−	2.53732e6i	−0.108897	−	0.108897i
$886$	2.90824e6			0.124465
$887$	−1.02362e7	−	1.02362e7i	−0.436849	−	0.436849i	0.454101	−	0.890950i	$-0.349960\pi$
$887$	−1.02362e7	−	1.02362e7i	−0.436849	−	0.436849i	−0.890950	+	0.454101i	$0.849960\pi$
$888$	−3.68325e6	−	3.68325e6i	−0.156747	−	0.156747i
$889$	−5.47823e6	+	5.47823e6i	−0.232480	+	0.232480i
$890$	6.39464e6	−	6.39464e6i	0.270608	−	0.270608i
$891$	−7.88408e6	+	7.88408e6i	−0.332703	+	0.332703i
$892$	2.46546e6			0.103749
$893$		−	4.81747e6i		−	0.202158i
$894$		−	7.25633e6i		−	0.303650i
$895$	1.48673e7	−	1.48673e7i	0.620406	−	0.620406i
$896$	−4.45502e6	−	4.45502e6i	−0.185387	−	0.185387i
$897$			1.49908e7i			0.622074i
$898$	−1.58100e6			−0.0654245
$899$	2.48852e6	−	2.48852e6i	0.102693	−	0.102693i
$900$		−	517923.i		−	0.0213137i
$901$	−2.72349e7			−1.11767
$902$	1.54912e7	−	2.47588e6i	0.633972	−	0.101324i
$903$	−2.82490e6			−0.115288
$904$			3.35692e7i			1.36622i
$905$	−865767.	+	865767.i	−0.0351382	+	0.0351382i
$906$	4.20785e6			0.170310
$907$			1.90099e7i			0.767295i	0.923480	+	0.383647i	$0.125332\pi$
$907$			1.90099e7i			0.767295i	−0.923480	+	0.383647i	$0.874668\pi$
$908$	−332308.	−	332308.i	−0.0133760	−	0.0133760i
$909$	−2.03550e7	+	2.03550e7i	−0.817074	+	0.817074i
$910$		−	6.44498e6i		−	0.257999i
$911$			4.45025e6i			0.177660i	0.996047	+	0.0888298i	$0.0283127\pi$
$911$			4.45025e6i			0.177660i	−0.996047	+	0.0888298i	$0.971687\pi$
$912$	−6.28948e6			−0.250396
$913$	−6.37644e6	+	6.37644e6i	−0.253164	+	0.253164i
$914$	−1.14710e7	+	1.14710e7i	−0.454188	+	0.454188i
$915$	−2.14529e6	+	2.14529e6i	−0.0847099	+	0.0847099i
$916$	1.43313e6	+	1.43313e6i	0.0564349	+	0.0564349i
$917$	893654.	+	893654.i	0.0350951	+	0.0350951i
$918$	1.93016e7			0.755938
$919$	2.62852e7	+	2.62852e7i	1.02665	+	1.02665i	0.999635	+	0.0270166i	$0.00860068\pi$
$919$	2.62852e7	+	2.62852e7i	1.02665	+	1.02665i	0.0270166	+	0.999635i	$0.491399\pi$
$920$	−3.02487e7			−1.17825
$921$	9.55999e6	+	9.55999e6i	0.371371	+	0.371371i
$922$			4.37177e6i			0.169368i
$923$			3.82253e7i			1.47688i
$924$	45649.7	+	45649.7i	0.00175897	+	0.00175897i
$925$	−8.47484e6			−0.325670
$926$	2.64071e7	+	2.64071e7i	1.01203	+	1.01203i
$927$	−1.33317e7			−0.509549
$928$	−2.76770e6	−	2.76770e6i	−0.105499	−	0.105499i
$929$	398304.	+	398304.i	0.0151417	+	0.0151417i	0.714637	−	0.699495i	$-0.246592\pi$
$929$	398304.	+	398304.i	0.0151417	+	0.0151417i	−0.699495	+	0.714637i	$0.746592\pi$
$930$	−465942.	+	465942.i	−0.0176654	+	0.0176654i
$931$	−1.43750e7	+	1.43750e7i	−0.543543	+	0.543543i
$932$	−1.62621e6	+	1.62621e6i	−0.0613251	+	0.0613251i
$933$	−7.93107e6			−0.298282
$934$		−	2.56192e7i		−	0.960944i
$935$		−	1.68630e7i		−	0.630819i
$936$	2.26584e7	−	2.26584e7i	0.845357	−	0.845357i
$937$	6.17562e6	+	6.17562e6i	0.229790	+	0.229790i	0.812605	−	0.582815i	$-0.198049\pi$
$937$	6.17562e6	+	6.17562e6i	0.229790	+	0.229790i	−0.582815	+	0.812605i	$0.698049\pi$
$938$			4.07079e6i			0.151068i
$939$	−1.04098e7			−0.385280
$940$	−203589.	+	203589.i	−0.00751509	+	0.00751509i
$941$		−	2.16511e7i		−	0.797087i	−0.917149	−	0.398544i	$-0.869516\pi$
$941$		−	2.16511e7i		−	0.797087i	0.917149	−	0.398544i	$-0.130484\pi$
$942$	6.08880e6			0.223565
$943$	2.54346e7	−	3.51113e7i	0.931421	−	1.28578i
$944$	1.99445e7			0.728441
$945$			2.85251e6i			0.103908i
$946$	2.03163e7	−	2.03163e7i	0.738102	−	0.738102i
$947$	1.13945e7			0.412877			0.206439	−	0.978460i	$-0.433813\pi$
$947$	1.13945e7			0.412877			0.206439	+	0.978460i	$0.433813\pi$
$948$			148140.i			0.00535369i
$949$	1.68485e7	+	1.68485e7i	0.607291	+	0.607291i
$950$	−6.84991e6	+	6.84991e6i	−0.246250	+	0.246250i
$951$			6.35991e6i			0.228034i
$952$		−	8.72389e6i		−	0.311974i
$953$	−2.22603e7			−0.793962			−0.396981	−	0.917827i	$-0.629942\pi$
$953$	−2.22603e7			−0.793962			−0.396981	+	0.917827i	$0.629942\pi$
$954$	−1.58342e7	+	1.58342e7i	−0.563281	+	0.563281i
$955$	−1.79514e7	+	1.79514e7i	−0.636927	+	0.636927i
$956$	−2.05649e6	+	2.05649e6i	−0.0727748	+	0.0727748i
$957$	−4.84348e6	−	4.84348e6i	−0.170953	−	0.170953i
$958$	3.49863e7	+	3.49863e7i	1.23164	+	1.23164i
$959$	−9.11573e6			−0.320070
$960$	−4.21503e6	−	4.21503e6i	−0.147612	−	0.147612i
$961$	−2.82878e7			−0.988076
$962$	2.20590e7	+	2.20590e7i	0.768508	+	0.768508i
$963$		−	3.02489e7i		−	1.05110i
$964$			1.99898e6i			0.0692813i
$965$	−1.22267e7	−	1.22267e7i	−0.422658	−	0.422658i
$966$	3.35563e6			0.115699
$967$	−7.61422e6	−	7.61422e6i	−0.261854	−	0.261854i	0.563953	−	0.825807i	$-0.309280\pi$
$967$	−7.61422e6	−	7.61422e6i	−0.261854	−	0.261854i	−0.825807	+	0.563953i	$0.809280\pi$
$968$	−1.72421e7			−0.591427
$969$	−6.48649e6	−	6.48649e6i	−0.221922	−	0.221922i
$970$	−8.09644e6	−	8.09644e6i	−0.276290	−	0.276290i
$971$	−1.61275e7	+	1.61275e7i	−0.548933	+	0.548933i	−0.926132	−	0.377199i	$-0.876887\pi$
$971$	−1.61275e7	+	1.61275e7i	−0.548933	+	0.548933i	0.377199	+	0.926132i	$0.376887\pi$
$972$	908175.	−	908175.i	0.0308321	−	0.0308321i
$973$	7.31765e6	−	7.31765e6i	0.247793	−	0.247793i
$974$	3.42653e7			1.15733
$975$			4.82254e6i			0.162467i
$976$		−	1.68631e7i		−	0.566646i
$977$	1.59230e7	−	1.59230e7i	0.533691	−	0.533691i	−0.387978	−	0.921669i	$-0.626826\pi$
$977$	1.59230e7	−	1.59230e7i	0.533691	−	0.533691i	0.921669	+	0.387978i	$0.126826\pi$
$978$	−8.52201e6	−	8.52201e6i	−0.284901	−	0.284901i
$979$			9.11859e6i			0.304068i
$980$	1.21499e6			0.0404117
$981$	1.44650e6	−	1.44650e6i	0.0479893	−	0.0479893i
$982$			9.62359e6i			0.318463i
$983$	−1.62120e7			−0.535121			−0.267560	−	0.963541i	$-0.586218\pi$
$983$	−1.62120e7			−0.535121			−0.267560	+	0.963541i	$0.586218\pi$
$984$	8.46520e6	−	1.35295e6i	0.278708	−	0.0445444i
$985$	3.19141e7			1.04807
$986$		−	5.50707e7i		−	1.80397i
$987$	−379604.	+	379604.i	−0.0124033	+	0.0124033i
$988$	1.89597e6			0.0617931
$989$		−	7.94041e7i		−	2.58138i
$990$	−9.80400e6	−	9.80400e6i	−0.317918	−	0.317918i
$991$	1.29471e7	−	1.29471e7i	0.418781	−	0.418781i	−0.466002	−	0.884783i	$-0.654306\pi$
$991$	1.29471e7	−	1.29471e7i	0.418781	−	0.418781i	0.884783	+	0.466002i	$0.154306\pi$
$992$		−	379668.i		−	0.0122497i
$993$			6.63305e6i			0.213471i
$994$	8.55659e6			0.274685
$995$	−2.16144e7	+	2.16144e7i	−0.692126	+	0.692126i
$996$	207310.	−	207310.i	0.00662172	−	0.00662172i
$997$	1.26639e7	−	1.26639e7i	0.403486	−	0.403486i	−0.475973	−	0.879460i	$-0.657904\pi$
$997$	1.26639e7	−	1.26639e7i	0.403486	−	0.403486i	0.879460	+	0.475973i	$0.157904\pi$
$998$	−3.76278e7	−	3.76278e7i	−1.19586	−	1.19586i
$999$	−9.76319e6	−	9.76319e6i	−0.309512	−	0.309512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.6.c.a.32.13	yes	34
41.9	even	4	inner	41.6.c.a.9.5	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.6.c.a.9.5	✓	34	41.9	even	4	inner
41.6.c.a.32.13	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	41.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+5.81352i q^{2} +(3.20738 - 3.20738i) q^{3} -1.79697 q^{4} +42.7691i q^{5} +(18.6461 + 18.6461i) q^{6} +(22.3392 - 22.3392i) q^{7} +175.586i q^{8} +222.425i q^{9} +O(q^{10})\)	\(q+5.81352i q^{2} +(3.20738 - 3.20738i) q^{3} -1.79697 q^{4} +42.7691i q^{5} +(18.6461 + 18.6461i) q^{6} +(22.3392 - 22.3392i) q^{7} +175.586i q^{8} +222.425i q^{9} -248.639 q^{10} +(177.276 - 177.276i) q^{11} +(-5.76356 + 5.76356i) q^{12} +(-580.171 + 580.171i) q^{13} +(129.869 + 129.869i) q^{14} +(137.177 + 137.177i) q^{15} -1078.27 q^{16} +(-1112.05 - 1112.05i) q^{17} -1293.07 q^{18} +(909.297 + 909.297i) q^{19} -76.8547i q^{20} -143.300i q^{21} +(1030.60 + 1030.60i) q^{22} +4027.98 q^{23} +(563.170 + 563.170i) q^{24} +1295.81 q^{25} +(-3372.83 - 3372.83i) q^{26} +(1492.80 + 1492.80i) q^{27} +(-40.1428 + 40.1428i) q^{28} +(4259.20 - 4259.20i) q^{29} +(-797.478 + 797.478i) q^{30} +584.269 q^{31} -649.817i q^{32} -1137.18i q^{33} +(6464.91 - 6464.91i) q^{34} +(955.426 + 955.426i) q^{35} -399.692i q^{36} -6540.21 q^{37} +(-5286.21 + 5286.21i) q^{38} +3721.65i q^{39} -7509.64 q^{40} +(6314.48 - 8716.85i) q^{41} +833.079 q^{42} -19713.1i q^{43} +(-318.559 + 318.559i) q^{44} -9512.93 q^{45} +23416.7i q^{46} +(-2649.01 - 2649.01i) q^{47} +(-3458.43 + 3458.43i) q^{48} +15808.9i q^{49} +7533.19i q^{50} -7133.52 q^{51} +(1042.55 - 1042.55i) q^{52} +(12245.4 - 12245.4i) q^{53} +(-8678.39 + 8678.39i) q^{54} +(7581.93 + 7581.93i) q^{55} +(3922.44 + 3922.44i) q^{56} +5832.92 q^{57} +(24760.9 + 24760.9i) q^{58} -18496.7 q^{59} +(-246.502 - 246.502i) q^{60} +15638.9i q^{61} +3396.66i q^{62} +(4968.80 + 4968.80i) q^{63} -30727.0 q^{64} +(-24813.4 - 24813.4i) q^{65} +6611.03 q^{66} +(15672.6 + 15672.6i) q^{67} +(1998.32 + 1998.32i) q^{68} +(12919.3 - 12919.3i) q^{69} +(-5554.38 + 5554.38i) q^{70} +(32943.1 - 32943.1i) q^{71} -39054.8 q^{72} -29040.6i q^{73} -38021.6i q^{74} +(4156.14 - 4156.14i) q^{75} +(-1633.98 - 1633.98i) q^{76} -7920.40i q^{77} -21635.9 q^{78} +(12851.5 - 12851.5i) q^{79} -46116.8i q^{80} -44473.5 q^{81} +(50675.6 + 36709.3i) q^{82} -35969.0 q^{83} +257.506i q^{84} +(47561.3 - 47561.3i) q^{85} +114603. q^{86} -27321.7i q^{87} +(31127.1 + 31127.1i) q^{88} +(-25718.6 + 25718.6i) q^{89} -55303.6i q^{90} +25921.1i q^{91} -7238.16 q^{92} +(1873.97 - 1873.97i) q^{93} +(15400.1 - 15400.1i) q^{94} +(-38889.8 + 38889.8i) q^{95} +(-2084.21 - 2084.21i) q^{96} +(32563.1 + 32563.1i) q^{97} -91905.4 q^{98} +(39430.7 + 39430.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7}+O(q^{10}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7} + 1660 q^{10} + 654 q^{11} + 98 q^{12} + 854 q^{13} + 2236 q^{14} - 998 q^{15} + 8828 q^{16} + 1730 q^{17} + 2068 q^{18} + 716 q^{19} - 7750 q^{22} - 8156 q^{23} + 5496 q^{24} - 28870 q^{25} + 11470 q^{26} - 26806 q^{27} - 5942 q^{28} - 19190 q^{29} + 21430 q^{30} - 6376 q^{31} + 4228 q^{34} + 20934 q^{35} + 768 q^{37} - 6552 q^{38} - 47024 q^{40} - 9618 q^{41} + 126236 q^{42} - 57632 q^{44} + 81112 q^{45} + 2372 q^{47} + 88202 q^{48} + 24936 q^{51} + 151982 q^{52} - 94170 q^{53} - 153650 q^{54} - 105662 q^{55} + 8144 q^{56} - 69412 q^{57} - 63094 q^{58} + 87684 q^{59} + 58746 q^{60} - 76328 q^{63} - 109780 q^{64} + 88904 q^{65} - 427468 q^{66} + 212150 q^{67} - 199904 q^{68} + 125672 q^{69} + 113566 q^{70} + 189392 q^{71} + 579216 q^{72} + 199072 q^{75} + 128522 q^{76} - 327232 q^{78} - 28880 q^{79} - 557850 q^{81} - 241122 q^{82} + 384572 q^{83} - 114880 q^{85} - 453980 q^{86} + 338338 q^{88} - 391266 q^{89} + 955316 q^{92} + 394684 q^{93} - 42650 q^{94} - 404378 q^{95} - 254372 q^{96} - 324538 q^{97} - 167276 q^{98} - 685716 q^{99}+O(q^{100}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7 + 1660 * q^10 + 654 * q^11 + 98 * q^12 + 854 * q^13 + 2236 * q^14 - 998 * q^15 + 8828 * q^16 + 1730 * q^17 + 2068 * q^18 + 716 * q^19 - 7750 * q^22 - 8156 * q^23 + 5496 * q^24 - 28870 * q^25 + 11470 * q^26 - 26806 * q^27 - 5942 * q^28 - 19190 * q^29 + 21430 * q^30 - 6376 * q^31 + 4228 * q^34 + 20934 * q^35 + 768 * q^37 - 6552 * q^38 - 47024 * q^40 - 9618 * q^41 + 126236 * q^42 - 57632 * q^44 + 81112 * q^45 + 2372 * q^47 + 88202 * q^48 + 24936 * q^51 + 151982 * q^52 - 94170 * q^53 - 153650 * q^54 - 105662 * q^55 + 8144 * q^56 - 69412 * q^57 - 63094 * q^58 + 87684 * q^59 + 58746 * q^60 - 76328 * q^63 - 109780 * q^64 + 88904 * q^65 - 427468 * q^66 + 212150 * q^67 - 199904 * q^68 + 125672 * q^69 + 113566 * q^70 + 189392 * q^71 + 579216 * q^72 + 199072 * q^75 + 128522 * q^76 - 327232 * q^78 - 28880 * q^79 - 557850 * q^81 - 241122 * q^82 + 384572 * q^83 - 114880 * q^85 - 453980 * q^86 + 338338 * q^88 - 391266 * q^89 + 955316 * q^92 + 394684 * q^93 - 42650 * q^94 - 404378 * q^95 - 254372 * q^96 - 324538 * q^97 - 167276 * q^98 - 685716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more