LMFDB - Embedded newform 38.6.c.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, 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("38.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 386x^{6} + 3436x^{5} + 128708x^{4} + 568528x^{3} + 7340704x^{2} - 19430784x + 211527936 $ x^8 - 2x^7 + 386x^6 + 3436x^5 + 128708x^4 + 568528x^3 + 7340704x^2 - 19430784*x + 211527936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.3
Root			$-5.68703 + 9.85023i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.6.c.b.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(4.18703 + 7.25215i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.5904 - 21.8073i) q^{5} +(16.7481 - 29.0086i) q^{6} -187.086 q^{7} +64.0000 q^{8} +(86.4375 - 149.714i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(4.18703 + 7.25215i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.5904 - 21.8073i) q^{5} +(16.7481 - 29.0086i) q^{6} -187.086 q^{7} +64.0000 q^{8} +(86.4375 - 149.714i) q^{9} +(-50.3618 + 87.2292i) q^{10} -637.449 q^{11} -133.985 q^{12} +(-405.696 + 702.685i) q^{13} +(374.173 + 648.086i) q^{14} +(105.433 - 182.616i) q^{15} +(-128.000 - 221.703i) q^{16} +(238.773 + 413.567i) q^{17} -691.500 q^{18} +(-1569.76 - 109.293i) q^{19} +402.894 q^{20} +(-783.337 - 1356.78i) q^{21} +(1274.90 + 2208.19i) q^{22} +(2223.35 - 3850.96i) q^{23} +(267.970 + 464.138i) q^{24} +(1245.46 - 2157.20i) q^{25} +3245.57 q^{26} +3482.56 q^{27} +(1496.69 - 2592.35i) q^{28} +(-2325.33 + 4027.59i) q^{29} -843.466 q^{30} -574.756 q^{31} +(-512.000 + 886.810i) q^{32} +(-2669.02 - 4622.87i) q^{33} +(955.092 - 1654.27i) q^{34} +(2355.50 + 4079.85i) q^{35} +(1383.00 + 2395.43i) q^{36} +3230.02 q^{37} +(2760.92 + 5656.40i) q^{38} -6794.64 q^{39} +(-805.789 - 1395.67i) q^{40} +(6352.66 + 11003.1i) q^{41} +(-3133.35 + 5427.12i) q^{42} +(-9154.72 - 15856.4i) q^{43} +(5099.59 - 8832.75i) q^{44} -4353.15 q^{45} -17786.8 q^{46} +(-10093.2 + 17481.9i) q^{47} +(1071.88 - 1856.55i) q^{48} +18194.3 q^{49} -9963.69 q^{50} +(-1999.50 + 3463.23i) q^{51} +(-6491.13 - 11243.0i) q^{52} +(5037.17 - 8724.63i) q^{53} +(-6965.13 - 12064.0i) q^{54} +(8025.77 + 13901.0i) q^{55} -11973.5 q^{56} +(-5780.04 - 11841.8i) q^{57} +18602.6 q^{58} +(-8428.93 - 14599.3i) q^{59} +(1686.93 + 2921.85i) q^{60} +(-8278.09 + 14338.1i) q^{61} +(1149.51 + 1991.01i) q^{62} +(-16171.3 + 28009.5i) q^{63} +4096.00 q^{64} +20431.6 q^{65} +(-10676.1 + 18491.5i) q^{66} +(-2062.26 + 3571.93i) q^{67} -7640.73 q^{68} +37236.9 q^{69} +(9422.01 - 16319.4i) q^{70} +(21245.2 + 36797.8i) q^{71} +(5532.00 - 9581.71i) q^{72} +(-20762.2 - 35961.2i) q^{73} +(-6460.05 - 11189.1i) q^{74} +20859.1 q^{75} +(14072.5 - 20876.9i) q^{76} +119258. q^{77} +(13589.3 + 23537.3i) q^{78} +(-16264.6 - 28171.1i) q^{79} +(-3223.15 + 5582.67i) q^{80} +(-6422.72 - 11124.5i) q^{81} +(25410.6 - 44012.5i) q^{82} -108219. q^{83} +25066.8 q^{84} +(6012.52 - 10414.0i) q^{85} +(-36618.9 + 63425.8i) q^{86} -38944.9 q^{87} -40796.7 q^{88} +(-14269.3 + 24715.2i) q^{89} +(8706.30 + 15079.8i) q^{90} +(75900.2 - 131463. i) q^{91} +(35573.6 + 61615.3i) q^{92} +(-2406.52 - 4168.22i) q^{93} +80745.4 q^{94} +(17380.6 + 35608.3i) q^{95} -8575.04 q^{96} +(-38681.4 - 66998.1i) q^{97} +(-36388.7 - 63027.1i) q^{98} +(-55099.5 + 95435.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9}+O(q^{10}) $ 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18} + 320 q^{19} + 1152 q^{20} - 770 q^{21} - 288 q^{22} - 204 q^{23} - 896 q^{24} - 2158 q^{25} + 5392 q^{26} + 13156 q^{27} - 608 q^{28} - 5712 q^{29} + 160 q^{30} - 2324 q^{31} - 4096 q^{32} - 15650 q^{33} + 2088 q^{34} - 4188 q^{35} + 2496 q^{36} - 25508 q^{37} - 2440 q^{38} + 44156 q^{39} - 2304 q^{40} - 3480 q^{41} - 3080 q^{42} + 4066 q^{43} - 1152 q^{44} + 51560 q^{45} + 1632 q^{46} - 45768 q^{47} - 3584 q^{48} + 1416 q^{49} + 17264 q^{50} + 1506 q^{51} - 10784 q^{52} + 45654 q^{53} - 26312 q^{54} + 36570 q^{55} + 4864 q^{56} - 66702 q^{57} + 45696 q^{58} - 84006 q^{59} - 320 q^{60} - 14012 q^{61} + 4648 q^{62} - 15128 q^{63} + 32768 q^{64} - 4020 q^{65} - 62600 q^{66} - 19046 q^{67} - 16704 q^{68} + 111592 q^{69} - 16752 q^{70} - 53274 q^{71} + 9984 q^{72} - 41084 q^{73} + 51016 q^{74} + 153216 q^{75} + 4640 q^{76} + 271524 q^{77} - 88312 q^{78} - 54170 q^{79} - 9216 q^{80} - 9528 q^{81} - 13920 q^{82} + 52392 q^{83} + 24640 q^{84} - 221850 q^{85} + 16264 q^{86} - 457120 q^{87} + 9216 q^{88} - 137862 q^{89} - 103120 q^{90} + 308516 q^{91} - 3264 q^{92} + 112746 q^{93} + 366144 q^{94} + 153078 q^{95} + 28672 q^{96} - 292388 q^{97} - 2832 q^{98} - 138328 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	4.18703	+	7.25215i	0.268598	+	0.465226i	0.968500	−	0.249013i	$-0.0801063\pi$
$3$	4.18703	+	7.25215i	0.268598	+	0.465226i	−0.699902	+	0.714239i	$0.746773\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−12.5904	−	21.8073i	−0.225225	−	0.390101i	0.731162	−	0.682204i	$-0.238978\pi$
$5$	−12.5904	−	21.8073i	−0.225225	−	0.390101i	−0.956387	+	0.292103i	$0.905645\pi$
$6$	16.7481	−	29.0086i	0.189928	−	0.328964i
$7$	−187.086			−1.44310			−0.721551	−	0.692361i	$-0.756571\pi$
$7$	−187.086			−1.44310			−0.721551	+	0.692361i	$0.756571\pi$
$8$	64.0000			0.353553
$9$	86.4375	−	149.714i	0.355710	−	0.616108i
$10$	−50.3618	+	87.2292i	−0.159258	+	0.275843i
$11$	−637.449			−1.58841			−0.794207	−	0.607648i	$-0.792113\pi$
$11$	−637.449			−1.58841			−0.794207	+	0.607648i	$0.792113\pi$
$12$	−133.985			−0.268598
$13$	−405.696	+	702.685i	−0.665797	+	1.15319i	0.313271	+	0.949664i	$0.398575\pi$
$13$	−405.696	+	702.685i	−0.665797	+	1.15319i	−0.979069	+	0.203531i	$0.934758\pi$
$14$	374.173	+	648.086i	0.510214	+	0.883716i
$15$	105.433	−	182.616i	0.120990	−	0.209561i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	238.773	+	413.567i	0.200384	+	0.347075i	0.948652	−	0.316321i	$-0.102448\pi$
$17$	238.773	+	413.567i	0.200384	+	0.347075i	−0.748268	+	0.663396i	$0.769114\pi$
$18$	−691.500			−0.503050
$19$	−1569.76	−	109.293i	−0.997585	−	0.0694556i
$19$	−1569.76	−	109.293i	−0.997585	−	0.0694556i
$20$	402.894			0.225225
$21$	−783.337	−	1356.78i	−0.387615	−	0.671368i
$22$	1274.90	+	2208.19i	0.561589	+	0.972701i
$23$	2223.35	−	3850.96i	0.876372	−	1.51792i	0.0210770	−	0.999778i	$-0.493290\pi$
$23$	2223.35	−	3850.96i	0.876372	−	1.51792i	0.855295	−	0.518142i	$-0.173376\pi$
$24$	267.970	+	464.138i	0.0949638	+	0.164482i
$25$	1245.46	−	2157.20i	0.398548	−	0.690305i
$26$	3245.57			0.941579
$27$	3482.56			0.919369
$28$	1496.69	−	2592.35i	0.360776	−	0.624882i
$29$	−2325.33	+	4027.59i	−0.513440	+	0.889304i	0.486438	+	0.873715i	$0.338296\pi$
$29$	−2325.33	+	4027.59i	−0.513440	+	0.889304i	−0.999878	+	0.0155895i	$0.995038\pi$
$30$	−843.466			−0.171106
$31$	−574.756			−0.107419			−0.0537093	−	0.998557i	$-0.517104\pi$
$31$	−574.756			−0.107419			−0.0537093	+	0.998557i	$0.517104\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−2669.02	−	4622.87i	−0.426645	−	0.738971i
$34$	955.092	−	1654.27i	0.141693	−	0.245419i
$35$	2355.50	+	4079.85i	0.325023	+	0.562956i
$36$	1383.00	+	2395.43i	0.177855	+	0.308054i
$37$	3230.02			0.387884			0.193942	−	0.981013i	$-0.437873\pi$
$37$	3230.02			0.387884			0.193942	+	0.981013i	$0.437873\pi$
$38$	2760.92	+	5656.40i	0.310167	+	0.635450i
$39$	−6794.64			−0.715328
$40$	−805.789	−	1395.67i	−0.0796290	−	0.137921i
$41$	6352.66	+	11003.1i	0.590196	+	1.02225i	0.994206	+	0.107494i	$0.0342827\pi$
$41$	6352.66	+	11003.1i	0.590196	+	1.02225i	−0.404010	+	0.914754i	$0.632384\pi$
$42$	−3133.35	+	5427.12i	−0.274085	+	0.474729i
$43$	−9154.72	−	15856.4i	−0.755047	−	1.30778i	−0.945351	−	0.326055i	$-0.894281\pi$
$43$	−9154.72	−	15856.4i	−0.755047	−	1.30778i	0.190304	−	0.981725i	$-0.439053\pi$
$44$	5099.59	−	8832.75i	0.397103	−	0.687803i
$45$	−4353.15			−0.320459
$46$	−17786.8			−1.23938
$47$	−10093.2	+	17481.9i	−0.666474	+	1.15437i	0.312410	+	0.949947i	$0.398864\pi$
$47$	−10093.2	+	17481.9i	−0.666474	+	1.15437i	−0.978884	+	0.204419i	$0.934470\pi$
$48$	1071.88	−	1856.55i	0.0671495	−	0.116306i
$49$	18194.3			1.08255
$50$	−9963.69			−0.563631
$51$	−1999.50	+	3463.23i	−0.107646	+	0.186447i
$52$	−6491.13	−	11243.0i	−0.332899	−	0.576597i
$53$	5037.17	−	8724.63i	0.246318	−	0.426636i	−0.716183	−	0.697912i	$-0.754112\pi$
$53$	5037.17	−	8724.63i	0.246318	−	0.426636i	0.962501	+	0.271276i	$0.0874458\pi$
$54$	−6965.13	−	12064.0i	−0.325046	−	0.562996i
$55$	8025.77	+	13901.0i	0.357750	+	0.619641i
$56$	−11973.5			−0.510214
$57$	−5780.04	−	11841.8i	−0.235637	−	0.482758i
$58$	18602.6			0.726114
$59$	−8428.93	−	14599.3i	−0.315241	−	0.546013i	0.664248	−	0.747512i	$-0.268752\pi$
$59$	−8428.93	−	14599.3i	−0.315241	−	0.546013i	−0.979489	+	0.201499i	$0.935419\pi$
$60$	1686.93	+	2921.85i	0.0604950	+	0.104780i
$61$	−8278.09	+	14338.1i	−0.284843	+	0.493363i	−0.972571	−	0.232606i	$-0.925275\pi$
$61$	−8278.09	+	14338.1i	−0.284843	+	0.493363i	0.687728	+	0.725968i	$0.258608\pi$
$62$	1149.51	+	1991.01i	0.0379782	+	0.0657802i
$63$	−16171.3	+	28009.5i	−0.513326	+	0.889107i
$64$	4096.00			0.125000
$65$	20431.6			0.599816
$66$	−10676.1	+	18491.5i	−0.301684	+	0.522531i
$67$	−2062.26	+	3571.93i	−0.0561249	+	0.0972112i	−0.892723	−	0.450606i	$-0.851208\pi$
$67$	−2062.26	+	3571.93i	−0.0561249	+	0.0972112i	0.836598	+	0.547817i	$0.184541\pi$
$68$	−7640.73			−0.200384
$69$	37236.9			0.941567
$70$	9422.01	−	16319.4i	0.229826	−	0.398070i
$71$	21245.2	+	36797.8i	0.500167	+	0.866315i	1.00000		0.000193331i	$6.15391e-5\pi$
$71$	21245.2	+	36797.8i	0.500167	+	0.866315i	−0.499833	+	0.866122i	$0.666605\pi$
$72$	5532.00	−	9581.71i	0.125762	−	0.217827i
$73$	−20762.2	−	35961.2i	−0.456002	−	0.789818i	0.542743	−	0.839899i	$-0.317386\pi$
$73$	−20762.2	−	35961.2i	−0.456002	−	0.789818i	−0.998745	+	0.0500803i	$0.984052\pi$
$74$	−6460.05	−	11189.1i	−0.137138	−	0.237529i
$75$	20859.1			0.428197
$76$	14072.5	−	20876.9i	0.279471	−	0.414603i
$77$	119258.			2.29224
$78$	13589.3	+	23537.3i	0.252907	+	0.438047i
$79$	−16264.6	−	28171.1i	−0.293208	−	0.507851i	0.681358	−	0.731950i	$-0.261390\pi$
$79$	−16264.6	−	28171.1i	−0.293208	−	0.507851i	−0.974566	+	0.224099i	$0.928056\pi$
$80$	−3223.15	+	5582.67i	−0.0563062	+	0.0975252i
$81$	−6422.72	−	11124.5i	−0.108769	−	0.188394i
$82$	25410.6	−	44012.5i	0.417331	−	0.722839i
$83$	−108219.			−1.72428			−0.862141	−	0.506668i	$-0.830877\pi$
$83$	−108219.			−1.72428			−0.862141	+	0.506668i	$0.830877\pi$
$84$	25066.8			0.387615
$85$	6012.52	−	10414.0i	0.0902628	−	0.156340i
$86$	−36618.9	+	63425.8i	−0.533899	+	0.924740i
$87$	−38944.9			−0.551636
$88$	−40796.7			−0.561589
$89$	−14269.3	+	24715.2i	−0.190954	+	0.330742i	−0.945567	−	0.325428i	$-0.894492\pi$
$89$	−14269.3	+	24715.2i	−0.190954	+	0.330742i	0.754613	+	0.656171i	$0.227825\pi$
$90$	8706.30	+	15079.8i	0.113299	+	0.196240i
$91$	75900.2	−	131463.i	0.960814	−	1.66418i
$92$	35573.6	+	61615.3i	0.438186	+	0.758960i
$93$	−2406.52	−	4168.22i	−0.0288524	−	0.0499739i
$94$	80745.4			0.942536
$95$	17380.6	+	35608.3i	0.197586	+	0.404802i
$96$	−8575.04			−0.0949638
$97$	−38681.4	−	66998.1i	−0.417419	−	0.722992i	0.578260	−	0.815853i	$-0.303732\pi$
$97$	−38681.4	−	66998.1i	−0.417419	−	0.722992i	−0.995679	+	0.0928611i	$0.970399\pi$
$98$	−36388.7	−	63027.1i	−0.382738	−	0.662921i
$99$	−55099.5	+	95435.1i	−0.565015	+	0.978634i
$100$	19927.4	+	34515.2i	0.199274	+	0.345152i
$101$	−21950.0	+	38018.6i	−0.214107	+	0.370845i	−0.952996	−	0.302983i	$-0.902018\pi$
$101$	−21950.0	+	38018.6i	−0.214107	+	0.370845i	0.738889	+	0.673828i	$0.235351\pi$
$102$	15996.0			0.152234
$103$	−76061.9			−0.706438			−0.353219	−	0.935541i	$-0.614913\pi$
$103$	−76061.9			−0.706438			−0.353219	+	0.935541i	$0.614913\pi$
$104$	−25964.5	+	44971.9i	−0.235395	+	0.407716i
$105$	−19725.1	+	34164.9i	−0.174601	+	0.302418i
$106$	−40297.4			−0.348347
$107$	−101543.			−0.857416			−0.428708	−	0.903443i	$-0.641031\pi$
$107$	−101543.			−0.857416			−0.428708	+	0.903443i	$0.641031\pi$
$108$	−27860.5	+	48255.8i	−0.229842	+	0.398098i
$109$	−84256.0	−	145936.i	−0.679258	−	1.17651i	−0.975205	−	0.221304i	$-0.928969\pi$
$109$	−84256.0	−	145936.i	−0.679258	−	1.17651i	0.295947	−	0.955204i	$-0.404365\pi$
$110$	32103.1	−	55604.1i	0.252968	−	0.438153i
$111$	13524.2	+	23424.6i	0.104185	+	0.180453i
$112$	23947.1	+	41477.5i	0.180388	+	0.312441i
$113$	43157.0			0.317947			0.158974	−	0.987283i	$-0.449182\pi$
$113$	43157.0			0.317947			0.158974	+	0.987283i	$0.449182\pi$
$114$	−29461.0	+	43706.2i	−0.212317	+	0.314978i
$115$	−111972.			−0.789522
$116$	−37205.3	−	64441.5i	−0.256720	−	0.444652i
$117$	70134.7	+	121477.i	0.473662	+	0.820406i
$118$	−33715.7	+	58397.3i	−0.222909	+	0.386090i
$119$	−44671.2	−	77372.8i	−0.289175	−	0.500865i
$120$	6747.72	−	11687.4i	0.0427764	−	0.0740909i
$121$	245290.			1.52306
$122$	66224.7			0.402829
$123$	−53197.6	+	92140.9i	−0.317051	+	0.549148i
$124$	4598.05	−	7964.06i	0.0268547	−	0.0465136i
$125$	−141414.			−0.809501
$126$	129370.			0.725953
$127$	−95078.9	+	164682.i	−0.523088	+	0.906016i	0.476551	+	0.879147i	$0.341887\pi$
$127$	−95078.9	+	164682.i	−0.523088	+	0.906016i	−0.999639	+	0.0268686i	$0.991446\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	76662.2	−	132783.i	0.405609	−	0.702535i
$130$	−40863.1	−	70777.0i	−0.212067	−	0.367311i
$131$	39350.2	+	68156.5i	0.200340	+	0.347000i	0.948638	−	0.316363i	$-0.102462\pi$
$131$	39350.2	+	68156.5i	0.200340	+	0.347000i	−0.748298	+	0.663363i	$0.769129\pi$
$132$	85408.6			0.426645
$133$	293681.	+	20447.2i	1.43962	+	0.100232i
$134$	16498.1			0.0793726
$135$	−43847.0	−	75945.3i	−0.207065	−	0.358646i
$136$	15281.5	+	26468.3i	0.0708464	+	0.122710i
$137$	82331.8	−	142603.i	0.374771	−	0.649122i	−0.615522	−	0.788120i	$-0.711055\pi$
$137$	82331.8	−	142603.i	0.374771	−	0.649122i	0.990293	+	0.138998i	$0.0443880\pi$
$138$	−74473.9	−	128993.i	−0.332894	−	0.576590i
$139$	−3773.11	+	6535.22i	−0.0165639	+	0.0286895i	−0.874189	−	0.485587i	$-0.838606\pi$
$139$	−3773.11	+	6535.22i	−0.0165639	+	0.0286895i	0.857625	+	0.514276i	$0.171939\pi$
$140$	−75376.1			−0.325023
$141$	−169042.			−0.716054
$142$	84980.9	−	147191.i	0.353672	−	0.612577i
$143$	258610.	−	447926.i	1.05756	−	1.83175i
$144$	−44256.0			−0.177855
$145$	117108.			0.462558
$146$	−83048.9	+	143845.i	−0.322442	+	0.558486i
$147$	76180.3	+	131948.i	0.290770	+	0.503628i
$148$	−25840.2	+	44756.5i	−0.0969709	+	0.167959i
$149$	215141.	+	372636.i	0.793886	+	1.37505i	0.923544	+	0.383492i	$0.125279\pi$
$149$	215141.	+	372636.i	0.793886	+	1.37505i	−0.129658	+	0.991559i	$0.541388\pi$
$150$	−41718.3	−	72258.2i	−0.151390	−	0.262216i
$151$	512867.			1.83047			0.915234	−	0.402922i	$-0.132005\pi$
$151$	512867.			1.83047			0.915234	+	0.402922i	$0.132005\pi$
$152$	−100465.	−	6994.74i	−0.352700	−	0.0245563i
$153$	82555.8			0.285114
$154$	−238516.	−	413122.i	−0.810431	−	1.40371i
$155$	7236.44	+	12533.9i	0.0241933	+	0.0419041i
$156$	54357.1	−	94149.3i	0.178832	−	0.309746i
$157$	−95905.2	−	166113.i	−0.310522	−	0.537841i	0.667953	−	0.744203i	$-0.267171\pi$
$157$	−95905.2	−	166113.i	−0.310522	−	0.537841i	−0.978476	+	0.206363i	$0.933837\pi$
$158$	−65058.4	+	112685.i	−0.207329	+	0.359105i
$159$	84363.1			0.264643
$160$	25785.2			0.0796290
$161$	−415959.	+	720462.i	−1.26469	+	2.19051i
$162$	−25690.9	+	44497.9i	−0.0769115	+	0.133215i
$163$	−305500.			−0.900621			−0.450311	−	0.892872i	$-0.648687\pi$
$163$	−305500.			−0.900621			−0.450311	+	0.892872i	$0.648687\pi$
$164$	−203285.			−0.590196
$165$	−67208.3	+	116408.i	−0.192182	+	0.332869i
$166$	216438.	+	374882.i	0.609626	+	1.05590i
$167$	128051.	−	221791.i	0.355298	−	0.615394i	−0.631871	−	0.775074i	$-0.717713\pi$
$167$	128051.	−	221791.i	0.355298	−	0.615394i	0.987169	+	0.159679i	$0.0510461\pi$
$168$	−50133.6	−	86833.9i	−0.137043	−	0.237365i
$169$	−143531.	−	248604.i	−0.386572	−	0.669562i
$170$	−48100.1			−0.127651
$171$	−152049.	+	225569.i	−0.397643	+	0.589914i
$172$	292951.			0.755047
$173$	−204611.	−	354397.i	−0.519773	−	0.900274i	−0.999736	−	0.0229850i	$-0.992683\pi$
$173$	−204611.	−	354397.i	−0.519773	−	0.900274i	0.479962	−	0.877289i	$-0.340650\pi$
$174$	77889.9	+	134909.i	0.195033	+	0.337807i
$175$	−233009.	+	403583.i	−0.575145	+	0.996181i
$176$	81593.4	+	141324.i	0.198552	+	0.343902i
$177$	70584.4	−	122256.i	0.169346	−	0.293316i
$178$	114155.			0.270050
$179$	581658.			1.35686			0.678430	−	0.734665i	$-0.262661\pi$
$179$	581658.			1.35686			0.678430	+	0.734665i	$0.262661\pi$
$180$	34825.2	−	60319.0i	0.0801147	−	0.138763i
$181$	−337223.	+	584087.i	−0.765105	+	1.32520i	0.175087	+	0.984553i	$0.443979\pi$
$181$	−337223.	+	584087.i	−0.765105	+	1.32520i	−0.940191	+	0.340647i	$0.889354\pi$
$182$	−607201.			−1.35880
$183$	−138642.			−0.306033
$184$	142294.	−	246461.i	0.309844	−	0.536666i
$185$	−40667.5	−	70438.1i	−0.0873610	−	0.151314i
$186$	−9626.09	+	16672.9i	−0.0204018	+	0.0353369i
$187$	−152206.	−	263628.i	−0.318292	−	0.551299i
$188$	−161491.	−	279710.i	−0.333237	−	0.577183i
$189$	−651541.			−1.32674
$190$	88589.6	−	131425.i	0.178032	−	0.264115i
$191$	−173686.			−0.344494			−0.172247	−	0.985054i	$-0.555103\pi$
$191$	−173686.			−0.344494			−0.172247	+	0.985054i	$0.555103\pi$
$192$	17150.1	+	29704.8i	0.0335748	+	0.0581532i
$193$	−441373.	−	764481.i	−0.852928	−	1.47732i	−0.878554	−	0.477644i	$-0.841491\pi$
$193$	−441373.	−	764481.i	−0.852928	−	1.47732i	0.0256252	−	0.999672i	$-0.491842\pi$
$194$	−154726.	+	267993.i	−0.295160	+	0.511232i
$195$	85547.6	+	148173.i	0.161110	+	0.279050i
$196$	−145555.	+	252108.i	−0.270636	+	0.468756i
$197$	789993.			1.45030			0.725149	−	0.688592i	$-0.241771\pi$
$197$	789993.			1.45030			0.725149	+	0.688592i	$0.241771\pi$
$198$	440796.			0.799051
$199$	−320447.	+	555031.i	−0.573619	+	0.993537i	0.422571	+	0.906330i	$0.361128\pi$
$199$	−320447.	+	555031.i	−0.573619	+	0.993537i	−0.996190	+	0.0872076i	$0.972206\pi$
$200$	79709.5	−	138061.i	0.140908	−	0.244060i
$201$	−34538.9			−0.0603002
$202$	175600.			0.302794
$203$	435038.	−	753508.i	0.740947	−	1.28336i
$204$	−31992.0	−	55411.8i	−0.0538228	−	0.0932237i
$205$	159966.	−	277069.i	0.265853	−	0.460471i
$206$	152124.	+	263486.i	0.249764	+	0.432603i
$207$	−384362.	−	665734.i	−0.623468	−	1.07988i
$208$	207716.			0.332899
$209$	1.00064e6	+	69668.5i	1.58458	+	0.110324i
$210$	157801.			0.246923
$211$	−257343.	−	445732.i	−0.397930	−	0.689236i	0.595540	−	0.803326i	$-0.296938\pi$
$211$	−257343.	−	445732.i	−0.397930	−	0.689236i	−0.993470	+	0.114090i	$0.963605\pi$
$212$	80594.7	+	139594.i	0.123159	+	0.213318i
$213$	−177909.	+	308147.i	−0.268688	+	0.465381i
$214$	203086.	+	351756.i	0.303142	+	0.525058i
$215$	−230524.	+	399279.i	−0.340111	+	0.589089i
$216$	222884.			0.325046
$217$	107529.			0.155016
$218$	−337024.	+	583743.i	−0.480308	+	0.831917i
$219$	173864.	−	301141.i	0.244963	−	0.424288i
$220$	−256824.			−0.357750
$221$	−387477.			−0.533660
$222$	54096.9	−	93698.5i	0.0736698	−	0.127600i
$223$	669236.	+	1.15915e6i	0.901192	+	1.56091i	0.825949	+	0.563744i	$0.190640\pi$
$223$	669236.	+	1.15915e6i	0.901192	+	1.56091i	0.0752424	+	0.997165i	$0.476027\pi$
$224$	95788.3	−	165910.i	0.127553	−	0.220929i
$225$	−215309.	−	372926.i	−0.283535	−	0.491097i
$226$	−86314.0	−	149500.i	−0.112411	−	0.194702i
$227$	288954.			0.372190			0.186095	−	0.982532i	$-0.440417\pi$
$227$	288954.			0.372190			0.186095	+	0.982532i	$0.440417\pi$
$228$	210325.	+	14643.6i	0.267950	+	0.0186557i
$229$	−447523.			−0.563932			−0.281966	−	0.959424i	$-0.590986\pi$
$229$	−447523.			−0.563932			−0.281966	+	0.959424i	$0.590986\pi$
$230$	223944.	+	387882.i	0.279138	+	0.483482i
$231$	499337.	+	864877.i	0.615692	+	1.06641i
$232$	−148821.	+	257766.i	−0.181528	+	0.314417i
$233$	−380154.	−	658446.i	−0.458743	−	0.794566i	0.540152	−	0.841568i	$-0.318367\pi$
$233$	−380154.	−	658446.i	−0.458743	−	0.794566i	−0.998895	+	0.0470014i	$0.985033\pi$
$234$	280539.	−	485907.i	0.334929	−	0.580115i
$235$	508310.			0.600426
$236$	269726.			0.315241
$237$	136201.	−	235907.i	0.157510	−	0.272816i
$238$	−178685.	+	309491.i	−0.204477	+	0.354165i
$239$	504361.			0.571145			0.285573	−	0.958357i	$-0.407816\pi$
$239$	504361.			0.571145			0.285573	+	0.958357i	$0.407816\pi$
$240$	−53981.8			−0.0604950
$241$	−529974.	+	917942.i	−0.587776	+	1.01806i	0.406747	+	0.913541i	$0.366663\pi$
$241$	−529974.	+	917942.i	−0.587776	+	1.01806i	−0.994523	+	0.104517i	$0.966670\pi$
$242$	−490580.	−	849709.i	−0.538482	−	0.932678i
$243$	476916.	−	826042.i	0.518115	−	0.897401i
$244$	−132449.	−	229409.i	−0.142422	−	0.246681i
$245$	−229075.	−	396769.i	−0.243816	−	0.422302i
$246$	425581.			0.448378
$247$	713644.	−	1.05871e6i	0.744285	−	1.10417i
$248$	−36784.4			−0.0379782
$249$	−453116.	−	784821.i	−0.463139	−	0.802181i
$250$	282828.	+	489872.i	0.286202	+	0.495716i
$251$	452325.	−	783449.i	0.453175	−	0.784922i	−0.545406	−	0.838172i	$-0.683625\pi$
$251$	452325.	−	783449.i	0.453175	−	0.784922i	0.998581	+	0.0532496i	$0.0169579\pi$
$252$	−258741.	−	448152.i	−0.256663	−	0.444553i
$253$	−1.41727e6	+	2.45479e6i	−1.39204	+	2.41108i
$254$	760632.			0.739759
$255$	100698.			0.0969777
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	119735.	−	207388.i	0.113081	−	0.195862i	−0.803930	−	0.594724i	$-0.797261\pi$
$257$	119735.	−	207388.i	0.113081	−	0.195862i	0.917011	+	0.398862i	$0.130595\pi$
$258$	−613298.			−0.573617
$259$	−604294.			−0.559756
$260$	−163452.	+	283108.i	−0.149954	+	0.259728i
$261$	401992.	+	696270.i	0.365272	+	0.632669i
$262$	157401.	−	272626.i	0.141662	−	0.245366i
$263$	−13242.3	−	22936.4i	−0.0118052	−	0.0204473i	0.860062	−	0.510189i	$-0.170424\pi$
$263$	−13242.3	−	22936.4i	−0.0118052	−	0.0204473i	−0.871868	+	0.489742i	$0.837091\pi$
$264$	−170817.	−	295864.i	−0.150842	−	0.261266i
$265$	−253681.			−0.221908
$266$	−516531.	−	1.05824e6i	−0.447603	−	0.917019i
$267$	−238985.			−0.205160
$268$	−32996.1	−	57151.0i	−0.0280625	−	0.0486056i
$269$	132185.	+	228952.i	0.111379	+	0.192914i	0.916326	−	0.400432i	$-0.131140\pi$
$269$	132185.	+	228952.i	0.111379	+	0.192914i	−0.804948	+	0.593346i	$0.797807\pi$
$270$	−175388.	+	303781.i	−0.146417	+	0.253601i
$271$	−274366.	−	475216.i	−0.226938	−	0.393068i	0.729961	−	0.683489i	$-0.239538\pi$
$271$	−274366.	−	475216.i	−0.226938	−	0.393068i	−0.956899	+	0.290420i	$0.906205\pi$
$272$	61125.9	−	105873.i	0.0500960	−	0.0867688i
$273$	1.27119e6			1.03229
$274$	−658654.			−0.530006
$275$	−793918.	+	1.37511e6i	−0.633058	+	1.09649i
$276$	−297896.	+	515970.i	−0.235392	+	0.407711i
$277$	−1.21471e6			−0.951201			−0.475601	−	0.879661i	$-0.657769\pi$
$277$	−1.21471e6			−0.951201			−0.475601	+	0.879661i	$0.657769\pi$
$278$	30184.9			0.0234249
$279$	−49680.5	+	86049.2i	−0.0382099	+	0.0661814i
$280$	150752.	+	261110.i	0.114913	+	0.199035i
$281$	−401190.	+	694881.i	−0.303099	+	0.524982i	−0.976836	−	0.213989i	$-0.931354\pi$
$281$	−401190.	+	694881.i	−0.303099	+	0.524982i	0.673738	+	0.738971i	$0.264688\pi$
$282$	338083.	+	585578.i	0.253163	+	0.438492i
$283$	669627.	+	1.15983e6i	0.497012	+	0.860850i	0.999994	−	0.00344689i	$-0.00109718\pi$
$283$	669627.	+	1.15983e6i	0.497012	+	0.860850i	−0.502982	+	0.864297i	$0.667764\pi$
$284$	−679847.			−0.500167
$285$	−185464.	+	275140.i	−0.135253	+	0.200651i
$286$	−2.06888e6			−1.49562
$287$	−1.18850e6	−	2.05854e6i	−0.851713	−	1.47521i
$288$	88512.0	+	153307.i	0.0628812	+	0.108914i
$289$	595903.	−	1.03214e6i	0.419693	−	0.726929i
$290$	−234216.	−	405673.i	−0.163539	−	0.283258i
$291$	323920.	−	561046.i	0.224236	−	0.388389i
$292$	664391.			0.456002
$293$	1.02409e6			0.696901			0.348450	−	0.937327i	$-0.386708\pi$
$293$	1.02409e6			0.696901			0.348450	+	0.937327i	$0.386708\pi$
$294$	304721.	−	527792.i	0.205605	−	0.356119i
$295$	−212248.	+	367624.i	−0.142000	+	0.245951i
$296$	206722.			0.137138
$297$	−2.21996e6			−1.46034
$298$	860565.	−	1.49054e6i	0.561362	−	0.972308i
$299$	1.80401e6	+	3.12463e6i	1.16697	+	2.02125i
$300$	−166873.	+	289033.i	−0.107049	+	0.185415i
$301$	1.71272e6	+	2.96653e6i	1.08961	+	1.88726i
$302$	−1.02573e6	−	1.77662e6i	−0.647168	−	1.12093i
$303$	−367622.			−0.230036
$304$	176699.	+	362010.i	0.109661	+	0.224665i
$305$	416899.			0.256615
$306$	−165112.	−	285982.i	−0.100803	−	0.174596i
$307$	162112.	+	280786.i	0.0981678	+	0.170032i	0.910926	−	0.412569i	$-0.135368\pi$
$307$	162112.	+	280786.i	0.0981678	+	0.170032i	−0.812758	+	0.582601i	$0.802035\pi$
$308$	−954064.	+	1.65249e6i	−0.573061	+	0.992571i
$309$	−318474.	−	551612.i	−0.189748	−	0.328653i
$310$	28945.8	−	50135.5i	0.0171073	−	0.0296307i
$311$	−502990.			−0.294889			−0.147444	−	0.989070i	$-0.547105\pi$
$311$	−502990.			−0.294889			−0.147444	+	0.989070i	$0.547105\pi$
$312$	−434857.			−0.252907
$313$	828019.	−	1.43417e6i	0.477727	−	0.827447i	−0.521947	−	0.852978i	$-0.674794\pi$
$313$	828019.	−	1.43417e6i	0.477727	−	0.827447i	0.999674	+	0.0255308i	$0.00812758\pi$
$314$	−383621.	+	664451.i	−0.219573	+	0.380311i
$315$	814415.			0.462455
$316$	520467.			0.293208
$317$	187940.	−	325522.i	0.105044	−	0.181942i	−0.808712	−	0.588205i	$-0.799835\pi$
$317$	187940.	−	325522.i	0.105044	−	0.181942i	0.913756	+	0.406263i	$0.133168\pi$
$318$	−168726.	−	292242.i	−0.0935653	−	0.162060i
$319$	1.48228e6	−	2.56738e6i	0.815555	−	1.41258i
$320$	−51570.5	−	89322.7i	−0.0281531	−	0.0487626i
$321$	−425165.	−	736407.i	−0.230300	−	0.398892i
$322$	3.32767e6			1.78855
$323$	−329617.	−	675298.i	−0.175794	−	0.360155i
$324$	205527.			0.108769
$325$	1.01056e6	+	1.75034e6i	0.530704	+	0.919206i
$326$	611000.	+	1.05828e6i	0.318418	+	0.551516i
$327$	705565.	−	1.22207e6i	0.364895	−	0.632016i
$328$	406570.	+	704200.i	0.208666	+	0.361419i
$329$	1.88830e6	−	3.27062e6i	0.961790	−	1.66587i
$330$	537666.			0.271786
$331$	−3.20506e6			−1.60793			−0.803963	−	0.594680i	$-0.797279\pi$
$331$	−3.20506e6			−1.60793			−0.803963	+	0.594680i	$0.797279\pi$
$332$	865752.	−	1.49953e6i	0.431071	−	0.746636i
$333$	279195.	−	483581.i	0.137974	−	0.238978i
$334$	−1.02441e6			−0.502467
$335$	103859.			0.0505629
$336$	−200534.	+	347335.i	−0.0969037	+	0.167842i
$337$	284877.	+	493421.i	0.136641	+	0.236670i	0.926223	−	0.376975i	$-0.123036\pi$
$337$	284877.	+	493421.i	0.136641	+	0.236670i	−0.789582	+	0.613645i	$0.789703\pi$
$338$	−574126.	+	994415.i	−0.273348	+	0.473452i
$339$	180700.	+	312981.i	0.0854000	+	0.147917i
$340$	96200.3	+	166624.i	0.0451314	+	0.0781699i
$341$	366378.			0.170625
$342$	1.08549e6	+	75576.0i	0.501835	+	0.0349396i
$343$	−259553.			−0.119122
$344$	−585902.	−	1.01481e6i	−0.266949	−	0.462370i
$345$	−468830.	−	812037.i	−0.212064	−	0.367306i
$346$	−818445.	+	1.41759e6i	−0.367535	+	0.636590i
$347$	295269.	+	511421.i	0.131642	+	0.228011i	0.924310	−	0.381643i	$-0.124642\pi$
$347$	295269.	+	511421.i	0.131642	+	0.228011i	−0.792668	+	0.609654i	$0.791308\pi$
$348$	311559.	−	539637.i	0.137909	−	0.238866i
$349$	−1.22400e6			−0.537919			−0.268960	−	0.963151i	$-0.586680\pi$
$349$	−1.22400e6			−0.537919			−0.268960	+	0.963151i	$0.586680\pi$
$350$	1.86407e6			0.813378
$351$	−1.41286e6	+	2.44715e6i	−0.612113	+	1.06021i
$352$	326374.	−	565296.i	0.140397	−	0.243175i
$353$	−1.08998e6			−0.465568			−0.232784	−	0.972528i	$-0.574784\pi$
$353$	−1.08998e6			−0.465568			−0.232784	+	0.972528i	$0.574784\pi$
$354$	−564675.			−0.239492
$355$	534974.	−	926602.i	0.225300	−	0.390231i
$356$	−228310.	−	395444.i	−0.0954771	−	0.165371i
$357$	374079.	−	647924.i	0.155344	−	0.269063i
$358$	−1.16332e6	−	2.01492e6i	−0.479723	−	0.830904i
$359$	−1.17004e6	−	2.02656e6i	−0.479141	−	0.829897i	0.520572	−	0.853818i	$-0.325719\pi$
$359$	−1.17004e6	−	2.02656e6i	−0.479141	−	0.829897i	−0.999714	+	0.0239202i	$0.992385\pi$
$360$	−278602.			−0.113299
$361$	2.45221e6	+	343127.i	0.990352	+	0.138576i
$362$	2.69778e6			1.08202
$363$	1.02704e6	+	1.77888e6i	0.409090	+	0.708565i
$364$	1.21440e6	+	2.10341e6i	0.480407	+	0.832089i
$365$	−522811.	+	905536.i	−0.205406	+	0.355773i
$366$	277285.	+	480272.i	0.108199	+	0.187406i
$367$	−1.53524e6	+	2.65912e6i	−0.594994	+	1.03056i	0.398554	+	0.917145i	$0.369512\pi$
$367$	−1.53524e6	+	2.65912e6i	−0.594994	+	1.03056i	−0.993548	+	0.113415i	$0.963821\pi$
$368$	−1.13836e6			−0.438186
$369$	2.19643e6			0.839754
$370$	−162670.	+	281752.i	−0.0617736	+	0.106995i
$371$	−942386.	+	1.63226e6i	−0.355463	+	0.615680i
$372$	77008.7			0.0288524
$373$	921705.			0.343020			0.171510	−	0.985182i	$-0.445135\pi$
$373$	921705.			0.343020			0.171510	+	0.985182i	$0.445135\pi$
$374$	−608822.	+	1.05451e6i	−0.225067	+	0.389827i
$375$	−592105.	−	1.02556e6i	−0.217430	−	0.376601i
$376$	−645963.	+	1.11884e6i	−0.235634	+	0.408130i
$377$	−1.88675e6	−	3.26795e6i	−0.683694	−	1.18419i
$378$	1.30308e6	+	2.25700e6i	0.469075	+	0.812461i
$379$	−4.60570e6			−1.64702			−0.823508	−	0.567304i	$-0.807986\pi$
$379$	−4.60570e6			−1.64702			−0.823508	+	0.567304i	$0.807986\pi$
$380$	−632448.	−	44033.4i	−0.224681	−	0.0156431i
$381$	−1.59239e6			−0.562002
$382$	347372.	+	601667.i	0.121797	+	0.210959i
$383$	−1.76215e6	−	3.05213e6i	−0.613827	−	1.06318i	−0.990589	−	0.136870i	$-0.956296\pi$
$383$	−1.76215e6	−	3.05213e6i	−0.613827	−	1.06318i	0.376762	−	0.926310i	$-0.377038\pi$
$384$	68600.3	−	118819.i	0.0237409	−	0.0411205i
$385$	−1.50151e6	−	2.60070e6i	−0.516270	−	0.894206i
$386$	−1.76549e6	+	3.05792e6i	−0.603111	+	1.04462i
$387$	−3.16525e6			−1.07431
$388$	1.23780e6			0.417419
$389$	−1.17000e6	+	2.02651e6i	−0.392025	+	0.679007i	−0.992717	−	0.120474i	$-0.961559\pi$
$389$	−1.17000e6	+	2.02651e6i	−0.392025	+	0.679007i	0.600692	+	0.799481i	$0.294892\pi$
$390$	342190.	−	592691.i	0.113922	−	0.197318i
$391$	2.12350e6			0.702443
$392$	1.16444e6			0.382738
$393$	−329521.	+	570747.i	−0.107622	+	0.186407i
$394$	−1.57999e6	−	2.73661e6i	−0.512758	−	0.888123i
$395$	−409557.	+	709374.i	−0.132075	+	0.228761i
$396$	−881592.	−	1.52696e6i	−0.282507	−	0.489317i
$397$	487048.	+	843591.i	0.155094	+	0.268631i	0.933093	−	0.359634i	$-0.117099\pi$
$397$	487048.	+	843591.i	0.155094	+	0.268631i	−0.777999	+	0.628265i	$0.783765\pi$
$398$	2.56358e6			0.811220
$399$	1.08137e6	+	2.21543e6i	0.340048	+	0.696669i
$400$	−637676.			−0.199274
$401$	1.09485e6	+	1.89634e6i	0.340012	+	0.588919i	0.984435	−	0.175751i	$-0.0562354\pi$
$401$	1.09485e6	+	1.89634e6i	0.340012	+	0.588919i	−0.644422	+	0.764670i	$0.722902\pi$
$402$	69077.9	+	119646.i	0.0213193	+	0.0369262i
$403$	233176.	−	403873.i	0.0715190	−	0.123875i
$404$	−351201.	−	608297.i	−0.107054	−	0.185423i
$405$	−161730.	+	280124.i	−0.0489951	+	0.0848620i
$406$	−3.48030e6			−1.04786
$407$	−2.05898e6			−0.616120
$408$	−127968.	+	221647.i	−0.0380584	+	0.0659191i
$409$	2.80813e6	−	4.86383e6i	0.830060	−	1.43771i	−0.0679308	−	0.997690i	$-0.521640\pi$
$409$	2.80813e6	−	4.86383e6i	0.830060	−	1.43771i	0.897990	−	0.440015i	$-0.145027\pi$
$410$	−1.27973e6			−0.375973
$411$	1.37890e6			0.402651
$412$	608495.	−	1.05394e6i	0.176610	−	0.305897i
$413$	1.57694e6	+	2.73134e6i	0.454925	+	0.787953i
$414$	−1.53745e6	+	2.66294e6i	−0.440859	+	0.763590i
$415$	1.36253e6	+	2.35996e6i	0.388351	+	0.672644i
$416$	−415432.	−	719550.i	−0.117697	−	0.203858i
$417$	−63192.5			−0.0177961
$418$	−1.75995e6	−	3.60567e6i	−0.492673	−	1.00936i
$419$	933120.			0.259658			0.129829	−	0.991536i	$-0.458557\pi$
$419$	933120.			0.259658			0.129829	+	0.991536i	$0.458557\pi$
$420$	−315602.	−	546639.i	−0.0873005	−	0.151209i
$421$	−2.02193e6	−	3.50209e6i	−0.555984	−	0.962992i	−0.997826	−	0.0658992i	$-0.979008\pi$
$421$	−2.02193e6	−	3.50209e6i	−0.555984	−	0.962992i	0.441843	−	0.897093i	$-0.354325\pi$
$422$	−1.02937e6	+	1.78293e6i	−0.281379	+	0.487363i
$423$	1.74486e6	+	3.02218e6i	0.474143	+	0.821239i
$424$	322379.	−	558376.i	0.0870867	−	0.150839i
$425$	1.18953e6			0.319450
$426$	1.42327e6			0.379982
$427$	1.54872e6	−	2.68246e6i	0.411058	−	0.711973i
$428$	812346.	−	1.40702e6i	0.214354	−	0.371272i
$429$	4.33124e6			1.13624
$430$	1.84419e6			0.480989
$431$	−1.88347e6	+	3.26227e6i	−0.488389	+	0.845915i	−0.999911	−	0.0133555i	$-0.995749\pi$
$431$	−1.88347e6	+	3.26227e6i	−0.488389	+	0.845915i	0.511522	+	0.859270i	$0.329082\pi$
$432$	−445768.	−	772093.i	−0.114921	−	0.199049i
$433$	1.53958e6	−	2.66663e6i	0.394624	−	0.683508i	−0.598430	−	0.801175i	$-0.704208\pi$
$433$	1.53958e6	−	2.66663e6i	0.394624	−	0.683508i	0.993053	+	0.117667i	$0.0375417\pi$
$434$	−215058.	−	372492.i	−0.0548065	−	0.0949276i
$435$	490334.	+	849284.i	0.124242	+	0.215194i
$436$	2.69619e6			0.679258
$437$	−3.91101e6	+	5.80209e6i	−0.979683	+	1.45339i
$438$	−1.39091e6			−0.346429
$439$	−570810.	−	988672.i	−0.141361	−	0.244845i	0.786648	−	0.617401i	$-0.211815\pi$
$439$	−570810.	−	988672.i	−0.141361	−	0.244845i	−0.928009	+	0.372557i	$0.878481\pi$
$440$	513649.	+	889666.i	0.126484	+	0.219076i
$441$	1.57267e6	−	2.72395e6i	0.385072	−	0.666965i
$442$	774953.	+	1.34226e6i	0.188677	+	0.326799i
$443$	3.01326e6	−	5.21912e6i	0.729504	−	1.26354i	−0.227589	−	0.973757i	$-0.573084\pi$
$443$	3.01326e6	−	5.21912e6i	0.729504	−	1.26354i	0.957093	−	0.289780i	$-0.0935823\pi$
$444$	−432775.			−0.104185
$445$	718630.			0.172030
$446$	2.67694e6	−	4.63660e6i	0.637239	−	1.10373i
$447$	−1.80161e6	+	3.12047e6i	−0.426473	+	0.738672i
$448$	−766306.			−0.180388
$449$	432586.			0.101264			0.0506322	−	0.998717i	$-0.483876\pi$
$449$	432586.			0.101264			0.0506322	+	0.998717i	$0.483876\pi$
$450$	−861237.	+	1.49171e6i	−0.200489	+	0.347258i
$451$	−4.04949e6	−	7.01393e6i	−0.937474	−	1.62375i
$452$	−345256.	+	598001.i	−0.0794868	+	0.137675i
$453$	2.14739e6	+	3.71939e6i	0.491661	+	0.851581i
$454$	−577908.	−	1.00097e6i	−0.131589	−	0.227919i
$455$	−3.82247e6			−0.865596
$456$	−369922.	−	757873.i	−0.0833103	−	0.170681i
$457$	8.03079e6			1.79874			0.899369	−	0.437191i	$-0.144027\pi$
$457$	8.03079e6			1.79874			0.899369	+	0.437191i	$0.144027\pi$
$458$	895046.	+	1.55026e6i	0.199380	+	0.345336i
$459$	831542.	+	1.44027e6i	0.184227	+	0.319090i
$460$	895775.	−	1.55153e6i	0.197381	−	0.341873i
$461$	505638.	+	875790.i	0.110812	+	0.191932i	0.916098	−	0.400955i	$-0.131322\pi$
$461$	505638.	+	875790.i	0.110812	+	0.191932i	−0.805286	+	0.592887i	$0.797988\pi$
$462$	1.99735e6	−	3.45951e6i	0.435360	−	0.754066i
$463$	1.01888e6			0.220887			0.110444	−	0.993882i	$-0.464773\pi$
$463$	1.01888e6			0.220887			0.110444	+	0.993882i	$0.464773\pi$
$464$	1.19057e6			0.256720
$465$	−60598.4	+	104959.i	−0.0129966	+	0.0225107i
$466$	−1.52061e6	+	2.63378e6i	−0.324380	+	0.561843i
$467$	5.93411e6			1.25911			0.629555	−	0.776956i	$-0.283237\pi$
$467$	5.93411e6			1.25911			0.629555	+	0.776956i	$0.283237\pi$
$468$	−2.24431e6			−0.473662
$469$	385820.	−	668261.i	0.0809941	−	0.140286i
$470$	−1.01662e6	−	1.76084e6i	−0.212282	−	0.367684i
$471$	803116.	−	1.39104e6i	0.166812	−	0.288926i
$472$	−539452.	−	934358.i	−0.111454	−	0.193045i
$473$	5.83567e6	+	1.01077e7i	1.19933	+	2.07730i
$474$	−1.08961e6			−0.222753
$475$	−2.19084e6	+	3.25017e6i	−0.445531	+	0.660956i
$476$	1.42948e6			0.289175
$477$	−870801.	−	1.50827e6i	−0.175236	−	0.303517i
$478$	−1.00872e6	−	1.74716e6i	−0.201930	−	0.349754i
$479$	567539.	−	983007.i	0.113020	−	0.195757i	−0.803966	−	0.594675i	$-0.797281\pi$
$479$	567539.	−	983007.i	0.113020	−	0.195757i	0.916987	+	0.398918i	$0.130614\pi$
$480$	107964.	+	186998.i	0.0213882	+	0.0370455i
$481$	−1.31041e6	+	2.26969e6i	−0.258252	+	0.447305i
$482$	4.23979e6			0.831241
$483$	−6.96653e6			−1.35878
$484$	−1.96232e6	+	3.39884e6i	−0.380764	+	0.659503i
$485$	−974032.	+	1.68707e6i	−0.188026	+	0.325671i
$486$	−3.81533e6			−0.732725
$487$	−2.79534e6			−0.534086			−0.267043	−	0.963685i	$-0.586047\pi$
$487$	−2.79534e6			−0.534086			−0.267043	+	0.963685i	$0.586047\pi$
$488$	−529798.	+	917637.i	−0.100707	+	0.174430i
$489$	−1.27914e6	−	2.21553e6i	−0.241905	−	0.418992i
$490$	−916300.	+	1.58708e6i	−0.172404	+	0.298612i
$491$	1.13047e6	+	1.95803e6i	0.211619	+	0.366536i	0.952221	−	0.305408i	$-0.0987929\pi$
$491$	1.13047e6	+	1.95803e6i	0.211619	+	0.366536i	−0.740602	+	0.671944i	$0.765460\pi$
$492$	−851161.	−	1.47425e6i	−0.158525	−	0.274574i
$493$	−2.22090e6			−0.411541
$494$	−5.09477e6	−	354717.i	−0.939306	−	0.0653980i
$495$	2.77491e6			0.509021
$496$	73568.8	+	127425.i	0.0134273	+	0.0232568i
$497$	−3.97469e6	−	6.88437e6i	−0.721793	−	1.25018i
$498$	−1.81247e6	+	3.13928e6i	−0.327489	+	0.567227i
$499$	1.41427e6	+	2.44959e6i	0.254262	+	0.440395i	0.964695	−	0.263370i	$-0.0848341\pi$
$499$	1.41427e6	+	2.44959e6i	0.254262	+	0.440395i	−0.710433	+	0.703765i	$0.751501\pi$
$500$	1.13131e6	−	1.95949e6i	0.202375	−	0.350524i
$501$	2.14462e6			0.381730
$502$	−3.61860e6			−0.640886
$503$	1.88204e6	−	3.25979e6i	0.331673	−	0.574474i	−0.651167	−	0.758934i	$-0.725720\pi$
$503$	1.88204e6	−	3.25979e6i	0.331673	−	0.574474i	0.982840	+	0.184460i	$0.0590538\pi$
$504$	−1.03496e6	+	1.79261e6i	−0.181488	+	0.314347i
$505$	1.10544e6			0.192889
$506$	1.13382e7			1.96864
$507$	1.20194e6	−	2.08182e6i	0.207665	−	0.359686i
$508$	−1.52126e6	−	2.63490e6i	−0.261544	−	0.453008i
$509$	−3.83921e6	+	6.64970e6i	−0.656821	+	1.13765i	0.324613	+	0.945847i	$0.394766\pi$
$509$	−3.83921e6	+	6.64970e6i	−0.656821	+	1.13765i	−0.981434	+	0.191801i	$0.938567\pi$
$510$	−201397.	−	348829.i	−0.0342868	−	0.0593865i
$511$	3.88433e6	+	6.72786e6i	0.658057	+	1.13979i
$512$	262144.			0.0441942
$513$	−5.46680e6	−	380619.i	−0.917148	−	0.0638553i
$514$	−957883.			−0.159921
$515$	957653.	+	1.65870e6i	0.159107	+	0.275582i
$516$	1.22660e6	+	2.12453e6i	0.202804	+	0.351267i
$517$	6.43388e6	−	1.11438e7i	1.05864	−	1.83361i
$518$	1.20859e6	+	2.09334e6i	0.197904	+	0.342779i
$519$	1.71343e6	−	2.96774e6i	0.279220	−	0.483624i
$520$	1.30762e6			0.212067
$521$	−1.09316e7			−1.76436			−0.882182	−	0.470909i	$-0.843926\pi$
$521$	−1.09316e7			−1.76436			−0.882182	+	0.470909i	$0.843926\pi$
$522$	1.60797e6	−	2.78508e6i	0.258286	−	0.447365i
$523$	5.31960e6	−	9.21382e6i	0.850403	−	1.47294i	−0.0304415	−	0.999537i	$-0.509691\pi$
$523$	5.31960e6	−	9.21382e6i	0.850403	−	1.47294i	0.880845	−	0.473405i	$-0.156975\pi$
$524$	−1.25921e6			−0.200340
$525$	−3.90246e6			−0.617932
$526$	−52969.2	+	91745.4i	−0.00834756	+	0.0144584i
$527$	−137236.	−	237700.i	−0.0215250	−	0.0372823i
$528$	−683269.	+	1.18346e6i	−0.106661	+	0.184743i
$529$	−6.66840e6	−	1.15500e7i	−1.03605	−	1.79450i
$530$	507362.	+	878776.i	0.0784563	+	0.135890i
$531$	−2.91430e6			−0.448537
$532$	−2.63277e6	+	3.90579e6i	−0.403306	+	0.598315i
$533$	−1.03090e7			−1.57180
$534$	477970.	+	827868.i	0.0725349	+	0.125634i
$535$	1.27847e6	+	2.21438e6i	0.193111	+	0.334479i
$536$	−131984.	+	228604.i	−0.0198432	+	0.0343694i
$537$	2.43542e6	+	4.21827e6i	0.364450	+	0.631246i
$538$	528741.	−	915806.i	0.0787567	−	0.136411i
$539$	−1.15980e7			−1.71953
$540$	1.40311e6			0.207065
$541$	−754311.	+	1.30651e6i	−0.110804	+	0.191919i	−0.916095	−	0.400962i	$-0.868676\pi$
$541$	−754311.	+	1.30651e6i	−0.110804	+	0.191919i	0.805290	+	0.592881i	$0.202009\pi$
$542$	−1.09746e6	+	1.90087e6i	−0.160469	+	0.277941i
$543$	−5.64785e6			−0.822023
$544$	−489007.			−0.0708464
$545$	−2.12164e6	+	3.67479e6i	−0.305971	+	0.529958i
$546$	−2.54237e6	−	4.40352e6i	−0.364970	−	0.632147i
$547$	−3.60627e6	+	6.24625e6i	−0.515336	+	0.892588i	0.484506	+	0.874788i	$0.338999\pi$
$547$	−3.60627e6	+	6.24625e6i	−0.515336	+	0.892588i	−0.999842	+	0.0177997i	$0.994334\pi$
$548$	1.31731e6	+	2.28164e6i	0.187385	+	0.324561i
$549$	1.43108e6	+	2.47870e6i	0.202643	+	0.350988i
$550$	6.35134e6			0.895280
$551$	4.09040e6	−	6.06822e6i	0.573967	−	0.851495i
$552$	2.38316e6			0.332894
$553$	3.04289e6	+	5.27044e6i	0.423129	+	0.732882i
$554$	2.42942e6	+	4.20787e6i	0.336300	+	0.582489i
$555$	340552.	−	589853.i	0.0469300	−	0.0812852i
$556$	−60369.7	−	104563.i	−0.00828194	−	0.0143447i
$557$	−4.58311e6	+	7.93819e6i	−0.625925	+	1.08413i	0.362436	+	0.932009i	$0.381945\pi$
$557$	−4.58311e6	+	7.93819e6i	−0.625925	+	1.08413i	−0.988361	+	0.152126i	$0.951388\pi$
$558$	397444.			0.0540369
$559$	1.48561e7			2.01083
$560$	603009.	−	1.04444e6i	0.0812556	−	0.140739i
$561$	1.27458e6	−	2.20763e6i	0.170986	−	0.296156i
$562$	3.20952e6			0.428646
$563$	9.63200e6			1.28069			0.640347	−	0.768085i	$-0.278790\pi$
$563$	9.63200e6			1.28069			0.640347	+	0.768085i	$0.278790\pi$
$564$	1.35233e6	−	2.34231e6i	0.179014	−	0.310061i
$565$	−543366.	−	941137.i	−0.0716096	−	0.124031i
$566$	2.67851e6	−	4.63931e6i	0.351441	−	0.608713i
$567$	1.20160e6	+	2.08124e6i	0.156965	+	0.271872i
$568$	1.35969e6	+	2.35506e6i	0.176836	+	0.306289i
$569$	2.53662e6			0.328455			0.164227	−	0.986423i	$-0.447487\pi$
$569$	2.53662e6			0.328455			0.164227	+	0.986423i	$0.447487\pi$
$570$	1.32404e6	+	92184.7i	0.170692	+	0.0118842i
$571$	−5.11420e6			−0.656428			−0.328214	−	0.944603i	$-0.606447\pi$
$571$	−5.11420e6			−0.656428			−0.328214	+	0.944603i	$0.606447\pi$
$572$	4.13776e6	+	7.16682e6i	0.528781	+	0.915875i
$573$	−727229.	−	1.25960e6i	−0.0925305	−	0.160268i
$574$	−4.75399e6	+	8.23415e6i	−0.602252	+	1.04313i
$575$	−5.53819e6	−	9.59243e6i	−0.698552	−	1.20993i
$576$	354048.	−	613229.i	0.0444638	−	0.0770135i
$577$	−1.50712e7			−1.88455			−0.942276	−	0.334837i	$-0.891319\pi$
$577$	−1.50712e7			−1.88455			−0.942276	+	0.334837i	$0.891319\pi$
$578$	−4.76723e6			−0.593535
$579$	3.69609e6	−	6.40181e6i	0.458190	−	0.793608i
$580$	−936863.	+	1.62269e6i	−0.115639	+	0.200293i
$581$	2.02463e7			2.48832
$582$	−2.59136e6			−0.317118
$583$	−3.21094e6	+	5.56151e6i	−0.391255	+	0.677674i
$584$	−1.32878e6	−	2.30152e6i	−0.161221	−	0.279243i
$585$	1.76605e6	−	3.05890e6i	0.213361	−	0.369551i
$586$	−2.04819e6	−	3.54757e6i	−0.246392	−	0.426763i
$587$	3.08358e6	+	5.34092e6i	0.369369	+	0.639766i	0.989467	−	0.144759i	$-0.0462405\pi$
$587$	3.08358e6	+	5.34092e6i	0.369369	+	0.639766i	−0.620098	+	0.784524i	$0.712907\pi$
$588$	−2.43777e6			−0.290770
$589$	902231.	+	62816.7i	0.107159	+	0.00746082i
$590$	1.69798e6			0.200818
$591$	3.30772e6	+	5.72915e6i	0.389548	+	0.674716i
$592$	−413443.	−	716105.i	−0.0484855	−	0.0839793i
$593$	3.77017e6	−	6.53012e6i	0.440275	−	0.762579i	−0.557435	−	0.830221i	$-0.688214\pi$
$593$	3.77017e6	−	6.53012e6i	0.440275	−	0.762579i	0.997710	+	0.0676420i	$0.0215476\pi$
$594$	4.43991e6	+	7.69015e6i	0.516307	+	0.894270i
$595$	−1.12486e6	+	1.94832e6i	−0.130259	+	0.225614i
$596$	−6.88452e6			−0.793886
$597$	−5.36689e6			−0.616292
$598$	7.21603e6	−	1.24985e7i	0.825173	−	1.42924i
$599$	769104.	−	1.33213e6i	0.0875826	−	0.151698i	−0.818906	−	0.573927i	$-0.805419\pi$
$599$	769104.	−	1.33213e6i	0.0875826	−	0.151698i	0.906489	+	0.422230i	$0.138752\pi$
$600$	1.33498e6			0.151390
$601$	8.21470e6			0.927696			0.463848	−	0.885915i	$-0.346468\pi$
$601$	8.21470e6			0.927696			0.463848	+	0.885915i	$0.346468\pi$
$602$	6.85090e6	−	1.18661e7i	0.770471	−	1.33449i
$603$	356513.	+	617498.i	0.0399284	+	0.0691580i
$604$	−4.10294e6	+	7.10649e6i	−0.457617	+	0.792616i
$605$	−3.08831e6	−	5.34911e6i	−0.343030	−	0.594146i
$606$	735244.	+	1.27348e6i	0.0813298	+	0.140867i
$607$	−6.70814e6			−0.738976			−0.369488	−	0.929235i	$-0.620467\pi$
$607$	−6.70814e6			−0.738976			−0.369488	+	0.929235i	$0.620467\pi$
$608$	900640.	−	1.33612e6i	0.0988081	−	0.146584i
$609$	7.28607e6			0.796068
$610$	−833799.	−	1.44418e6i	−0.0907270	−	0.157144i
$611$	−8.18951e6	−	1.41846e7i	−0.887473	−	1.53715i
$612$	−660446.	+	1.14393e6i	−0.0712786	+	0.123458i
$613$	−44307.8	−	76743.4i	−0.00476243	−	0.00824878i	0.863634	−	0.504119i	$-0.168183\pi$
$613$	−44307.8	−	76743.4i	−0.00476243	−	0.00824878i	−0.868397	+	0.495870i	$0.834849\pi$
$614$	648448.	−	1.12314e6i	0.0694151	−	0.120231i
$615$	2.67912e6			0.285631
$616$	7.63251e6			0.810431
$617$	−4.89163e6	+	8.47256e6i	−0.517298	+	0.895987i	0.482500	+	0.875896i	$0.339729\pi$
$617$	−4.89163e6	+	8.47256e6i	−0.517298	+	0.895987i	−0.999798	+	0.0200909i	$0.993604\pi$
$618$	−1.27389e6	+	2.20645e6i	−0.134172	+	0.232393i
$619$	1.16183e7			1.21876			0.609379	−	0.792879i	$-0.291419\pi$
$619$	1.16183e7			1.21876			0.609379	+	0.792879i	$0.291419\pi$
$620$	−231566.			−0.0241933
$621$	7.74296e6	−	1.34112e7i	0.805708	−	1.39553i
$622$	1.00598e6	+	1.74241e6i	0.104259	+	0.180582i
$623$	2.66960e6	−	4.62389e6i	0.275566	−	0.477295i
$624$	869714.	+	1.50639e6i	0.0894160	+	0.154873i
$625$	−2.11160e6	−	3.65740e6i	−0.216228	−	0.374518i
$626$	−6.62415e6			−0.675608
$627$	3.68448e6	+	7.54852e6i	0.374289	+	0.766819i
$628$	3.06897e6			0.310522
$629$	771243.	+	1.33583e6i	0.0777257	+	0.134625i
$630$	−1.62883e6	−	2.82122e6i	−0.163503	−	0.283195i
$631$	−1.57051e6	+	2.72020e6i	−0.157024	+	0.271974i	−0.933794	−	0.357810i	$-0.883523\pi$
$631$	−1.57051e6	+	2.72020e6i	−0.157024	+	0.271974i	0.776770	+	0.629784i	$0.216857\pi$
$632$	−1.04093e6	−	1.80295e6i	−0.103665	−	0.179553i
$633$	2.15501e6	−	3.73259e6i	0.213767	−	0.370255i
$634$	−1.50352e6			−0.148555
$635$	4.78835e6			0.471250
$636$	−674905.	+	1.16897e6i	−0.0661607	+	0.114594i
$637$	−7.38137e6	+	1.27849e7i	−0.720756	+	1.24839i
$638$	−1.18582e7			−1.15337
$639$	7.34554e6			0.711658
$640$	−206282.	+	357291.i	−0.0199072	+	0.0344804i
$641$	1.56425e6	+	2.70936e6i	0.150370	+	0.260448i	0.931363	−	0.364091i	$-0.118620\pi$
$641$	1.56425e6	+	2.70936e6i	0.150370	+	0.260448i	−0.780994	+	0.624539i	$0.785287\pi$
$642$	−1.70066e6	+	2.94563e6i	−0.162847	+	0.282059i
$643$	488699.	+	846451.i	0.0466137	+	0.0807373i	0.888391	−	0.459088i	$-0.151824\pi$
$643$	488699.	+	846451.i	0.0466137	+	0.0807373i	−0.841777	+	0.539825i	$0.818490\pi$
$644$	−6.65534e6	−	1.15274e7i	−0.632347	−	1.09526i
$645$	−3.86085e6			−0.365412
$646$	−1.68007e6	+	2.49242e6i	−0.158396	+	0.234985i
$647$	−559451.			−0.0525413			−0.0262707	−	0.999655i	$-0.508363\pi$
$647$	−559451.			−0.0525413			−0.0262707	+	0.999655i	$0.508363\pi$
$648$	−411054.	−	711966.i	−0.0384558	−	0.0666073i
$649$	5.37301e6	+	9.30633e6i	0.500733	+	0.867295i
$650$	4.04223e6	−	7.00134e6i	0.375264	−	0.649977i
$651$	450228.	+	779817.i	0.0416370	+	0.0721175i
$652$	2.44400e6	−	4.23313e6i	0.225155	−	0.389981i
$653$	−4.20298e6			−0.385722			−0.192861	−	0.981226i	$-0.561777\pi$
$653$	−4.20298e6			−0.385722			−0.192861	+	0.981226i	$0.561777\pi$
$654$	−5.64452e6			−0.516039
$655$	990873.	−	1.71624e6i	0.0902433	−	0.156306i
$656$	1.62628e6	−	2.81680e6i	0.147549	−	0.255562i
$657$	−7.17854e6			−0.648818
$658$	−1.51064e7			−1.36018
$659$	−4.37753e6	+	7.58211e6i	−0.392659	+	0.680106i	−0.992799	−	0.119789i	$-0.961778\pi$
$659$	−4.37753e6	+	7.58211e6i	−0.392659	+	0.680106i	0.600140	+	0.799895i	$0.295112\pi$
$660$	−1.07533e6	−	1.86253e6i	−0.0960910	−	0.166435i
$661$	−1.06262e7	+	1.84051e7i	−0.945963	+	1.63846i	−0.192151	+	0.981365i	$0.561546\pi$
$661$	−1.06262e7	+	1.84051e7i	−0.945963	+	1.63846i	−0.753812	+	0.657091i	$0.771787\pi$
$662$	6.41012e6	+	1.11026e7i	0.568488	+	0.984649i
$663$	−1.62238e6	−	2.81004e6i	−0.143340	−	0.248272i
$664$	−6.92602e6			−0.609626
$665$	−3.25168e6	−	6.66183e6i	−0.285137	−	0.584171i
$666$	−2.23356e6			−0.195125
$667$	1.03400e7	+	1.79095e7i	0.899929	+	1.55872i
$668$	2.04882e6	+	3.54866e6i	0.177649	+	0.307697i
$669$	−5.60422e6	+	9.70680e6i	−0.484117	+	0.838515i
$670$	−207718.	−	359778.i	−0.0178767	−	0.0309633i
$671$	5.27686e6	−	9.13979e6i	0.452448	−	0.783664i
$672$	1.60427e6			0.137043
$673$	−1.59175e7			−1.35468			−0.677339	−	0.735671i	$-0.736867\pi$
$673$	−1.59175e7			−1.35468			−0.677339	+	0.735671i	$0.736867\pi$
$674$	1.13951e6	−	1.97368e6i	0.0966200	−	0.167351i
$675$	4.33740e6	−	7.51259e6i	0.366412	−	0.634644i
$676$	4.59301e6			0.386572
$677$	−2.05809e7			−1.72581			−0.862903	−	0.505370i	$-0.831356\pi$
$677$	−2.05809e7			−1.72581			−0.862903	+	0.505370i	$0.831356\pi$
$678$	722799.	−	1.25192e6i	0.0603870	−	0.104593i
$679$	7.23676e6	+	1.25344e7i	0.602379	+	1.04335i
$680$	384801.	−	666495.i	0.0319127	−	0.0552745i
$681$	1.20986e6	+	2.09554e6i	0.0999694	+	0.173152i
$682$	−732755.	−	1.26917e6i	−0.0603251	−	0.104486i
$683$	−6.54531e6			−0.536881			−0.268441	−	0.963296i	$-0.586508\pi$
$683$	−6.54531e6			−0.536881			−0.268441	+	0.963296i	$0.586508\pi$
$684$	−1.90918e6	−	3.91140e6i	−0.156029	−	0.319663i
$685$	−4.14637e6			−0.337631
$686$	519106.	+	899118.i	0.0421159	+	0.0729468i
$687$	−1.87379e6	−	3.24550e6i	−0.151471	−	0.262356i
$688$	−2.34361e6	+	4.05925e6i	−0.188762	+	0.326945i
$689$	4.08712e6	+	7.07909e6i	0.327996	+	0.568106i
$690$	−1.87532e6	+	3.24815e6i	−0.149952	+	0.259725i
$691$	4.63203e6			0.369042			0.184521	−	0.982829i	$-0.440927\pi$
$691$	4.63203e6			0.369042			0.184521	+	0.982829i	$0.440927\pi$
$692$	6.54756e6			0.519773
$693$	1.03084e7	−	1.78546e7i	0.815374	−	1.41227i
$694$	1.18108e6	−	2.04568e6i	0.0930849	−	0.161228i
$695$	190021.			0.0149224
$696$	−2.49248e6			−0.195033
$697$	−3.03369e6	+	5.25450e6i	−0.236531	+	0.409684i
$698$	2.44799e6	+	4.24005e6i	0.190183	+	0.329407i
$699$	3.18343e6	−	5.51386e6i	0.246435	−	0.426838i
$700$	−3.72814e6	−	6.45733e6i	−0.287573	−	0.498090i
$701$	−6.07397e6	−	1.05204e7i	−0.466850	−	0.808608i	0.532433	−	0.846472i	$-0.321278\pi$
$701$	−6.07397e6	−	1.05204e7i	−0.466850	−	0.808608i	−0.999283	+	0.0378640i	$0.987945\pi$
$702$	1.13029e7			0.865659
$703$	−5.07037e6	−	353018.i	−0.386947	−	0.0269407i
$704$	−2.61099e6			−0.198552
$705$	2.12831e6	+	3.68634e6i	0.161273	+	0.279333i
$706$	2.17997e6	+	3.77582e6i	0.164603	+	0.285101i
$707$	4.10655e6	−	7.11276e6i	0.308979	−	0.535167i
$708$	1.12935e6	+	1.95609e6i	0.0846731	+	0.146658i
$709$	6.00559e6	−	1.04020e7i	0.448684	−	0.777143i	−0.549617	−	0.835417i	$-0.685226\pi$
$709$	6.00559e6	−	1.04020e7i	0.448684	−	0.777143i	0.998301	+	0.0582740i	$0.0185597\pi$
$710$	−4.27979e6			−0.318623
$711$	−5.62349e6			−0.417188
$712$	−913238.	+	1.58177e6i	−0.0675125	+	0.116935i
$713$	−1.27788e6	+	2.21336e6i	−0.0941386	+	0.163053i
$714$	−2.99263e6			−0.219689
$715$	−1.30241e7			−0.952756
$716$	−4.65327e6	+	8.05969e6i	−0.339215	+	0.587538i
$717$	2.11177e6	+	3.65770e6i	0.153409	+	0.265711i
$718$	−4.68015e6	+	8.10626e6i	−0.338804	+	0.586826i
$719$	1.07666e7	+	1.86483e7i	0.776704	+	1.34529i	0.933832	+	0.357713i	$0.116443\pi$
$719$	1.07666e7	+	1.86483e7i	0.776704	+	1.34529i	−0.157127	+	0.987578i	$0.550223\pi$
$720$	557203.	+	965104.i	0.0400574	+	0.0693814i
$721$	1.42302e7			1.01946
$722$	−3.71579e6	−	9.18096e6i	−0.265282	−	0.655458i
$723$	−8.87607e6			−0.631502
$724$	−5.39557e6	−	9.34540e6i	−0.382552	−	0.662600i
$725$	5.79222e6	+	1.00324e7i	0.409261	+	0.708860i
$726$	4.10815e6	−	7.11552e6i	0.289271	−	0.501031i
$727$	−1.07035e7	−	1.85390e7i	−0.751085	−	1.30092i	−0.947297	−	0.320355i	$-0.896198\pi$
$727$	−1.07035e7	−	1.85390e7i	−0.751085	−	1.30092i	0.196213	−	0.980561i	$-0.437136\pi$
$728$	4.85761e6	−	8.41363e6i	0.339699	−	0.588376i
$729$	4.86600e6			0.339120
$730$	4.18249e6			0.290488
$731$	4.37180e6	−	7.57218e6i	0.302599	−	0.524116i
$732$	1.10914e6	−	1.92109e6i	0.0765083	−	0.132516i
$733$	1.73932e7			1.19569			0.597846	−	0.801611i	$-0.296024\pi$
$733$	1.73932e7			1.19569			0.597846	+	0.801611i	$0.296024\pi$
$734$	1.22820e7			0.841448
$735$	1.91829e6	−	3.32257e6i	0.130977	−	0.226859i
$736$	2.27671e6	+	3.94338e6i	0.154922	+	0.268333i
$737$	1.31458e6	−	2.27693e6i	0.0891496	−	0.154412i
$738$	−4.39287e6	−	7.60867e6i	−0.296898	−	0.514242i
$739$	−2.22732e6	−	3.85783e6i	−0.150028	−	0.259855i	0.781210	−	0.624269i	$-0.214603\pi$
$739$	−2.22732e6	−	3.85783e6i	−0.150028	−	0.259855i	−0.931237	+	0.364413i	$0.881270\pi$
$740$	1.30136e6			0.0873610
$741$	1.06660e7	+	742605.i	0.713600	+	0.0496835i
$742$	7.53909e6			0.502700
$743$	−3.38362e6	−	5.86059e6i	−0.224858	−	0.389466i	0.731419	−	0.681929i	$-0.238859\pi$
$743$	−3.38362e6	−	5.86059e6i	−0.224858	−	0.389466i	−0.956277	+	0.292463i	$0.905525\pi$
$744$	−154017.	−	266766.i	−0.0102009	−	0.0176684i
$745$	5.41745e6	−	9.38330e6i	0.357606	−	0.619391i
$746$	−1.84341e6	−	3.19288e6i	−0.121276	−	0.210056i
$747$	−9.35419e6	+	1.62019e7i	−0.613345	+	1.06234i
$748$	4.87058e6			0.318292
$749$	1.89974e7			1.23734
$750$	−2.36842e6	+	4.10222e6i	−0.153747	+	0.266297i
$751$	9.71284e6	−	1.68231e7i	0.628415	−	1.08845i	−0.359455	−	0.933163i	$-0.617037\pi$
$751$	9.71284e6	−	1.68231e7i	0.628415	−	1.08845i	0.987870	−	0.155284i	$-0.0496294\pi$
$752$	5.16770e6			0.333237
$753$	7.57559e6			0.486888
$754$	−7.54701e6	+	1.30718e7i	−0.483445	+	0.837351i
$755$	−6.45722e6	−	1.11842e7i	−0.412267	−	0.714067i
$756$	5.21232e6	−	9.02801e6i	0.331686	−	0.574497i
$757$	−4.25983e6	−	7.37825e6i	−0.270180	−	0.467965i	0.698728	−	0.715388i	$-0.253750\pi$
$757$	−4.25983e6	−	7.37825e6i	−0.270180	−	0.467965i	−0.968908	+	0.247422i	$0.920416\pi$
$758$	9.21141e6	+	1.59546e7i	0.582308	+	1.00859i
$759$	−2.37366e7			−1.49560
$760$	1.11236e6	+	2.27893e6i	0.0698573	+	0.143119i
$761$	−1.23809e7			−0.774981			−0.387490	−	0.921874i	$-0.626658\pi$
$761$	−1.23809e7			−0.774981			−0.387490	+	0.921874i	$0.626658\pi$
$762$	3.18479e6	+	5.51621e6i	0.198698	+	0.344155i
$763$	1.57632e7	+	2.73026e7i	0.980238	+	1.69782i
$764$	1.38949e6	−	2.40667e6i	0.0861235	−	0.149170i
$765$	−1.03941e6	−	1.80032e6i	−0.0642148	−	0.111223i
$766$	−7.04860e6	+	1.22085e7i	−0.434041	+	0.751782i
$767$	1.36783e7			0.839546
$768$	−548803.			−0.0335748
$769$	−9.89622e6	+	1.71407e7i	−0.603467	+	1.04523i	0.388825	+	0.921312i	$0.372881\pi$
$769$	−9.89622e6	+	1.71407e7i	−0.603467	+	1.04523i	−0.992292	+	0.123923i	$0.960452\pi$
$770$	−6.00605e6	+	1.04028e7i	−0.365058	+	0.632299i
$771$	2.00534e6			0.121493
$772$	1.41239e7			0.852928
$773$	7.75869e6	−	1.34384e7i	0.467025	−	0.808910i	−0.532266	−	0.846577i	$-0.678659\pi$
$773$	7.75869e6	−	1.34384e7i	0.467025	−	0.808910i	0.999290	+	0.0376670i	$0.0119926\pi$
$774$	6.33049e6	+	1.09647e7i	0.379826	+	0.657879i
$775$	−715837.	+	1.23987e6i	−0.0428114	+	0.0741516i
$776$	−2.47561e6	−	4.28788e6i	−0.147580	−	0.255616i
$777$	−2.53020e6	−	4.38243e6i	−0.150349	−	0.260413i
$778$	9.36004e6			0.554407
$779$	−8.76960e6	−	1.79666e7i	−0.517769	−	1.06077i
$780$	−2.73752e6			−0.161110
$781$	−1.35427e7	−	2.34567e7i	−0.794473	−	1.37607i
$782$	−4.24701e6	−	7.35603e6i	−0.248351	−	0.430157i
$783$	−8.09811e6	+	1.40263e7i	−0.472041	+	0.817599i
$784$	−2.32888e6	−	4.03373e6i	−0.135318	−	0.234378i
$785$	−2.41498e6	+	4.18287e6i	−0.139875	+	0.242270i
$786$	2.63617e6			0.152201
$787$	−6.05316e6			−0.348374			−0.174187	−	0.984713i	$-0.555730\pi$
$787$	−6.05316e6			−0.348374			−0.174187	+	0.984713i	$0.555730\pi$
$788$	−6.31994e6	+	1.09465e7i	−0.362575	+	0.627998i
$789$	110892.	−	192070.i	0.00634173	−	0.0109842i
$790$	3.27646e6			0.186783
$791$	−8.07409e6			−0.458831
$792$	−3.52637e6	+	6.10785e6i	−0.199763	+	0.345999i
$793$	−6.71677e6	−	1.16338e7i	−0.379295	−	0.656959i
$794$	1.94819e6	−	3.37437e6i	0.109668	−	0.189951i
$795$	−1.06217e6	−	1.83973e6i	−0.0596041	−	0.103237i
$796$	−5.12715e6	−	8.88049e6i	−0.286810	−	0.496769i
$797$	2.83524e7			1.58105			0.790523	−	0.612432i	$-0.209809\pi$
$797$	2.83524e7			1.58105			0.790523	+	0.612432i	$0.209809\pi$
$798$	5.51176e6	−	8.17683e6i	0.306396	−	0.454546i
$799$	−9.63991e6			−0.534202
$800$	1.27535e6	+	2.20897e6i	0.0704539	+	0.122030i
$801$	2.46681e6	+	4.27265e6i	0.135849	+	0.235297i
$802$	4.37941e6	−	7.58536e6i	0.240425	−	0.416429i
$803$	1.32348e7	+	2.29234e7i	0.724319	+	1.25456i
$804$	276312.	−	478586.i	0.0150751	−	0.0261108i
$805$	2.09484e7			1.13936
$806$	−1.86541e6			−0.101143
$807$	−1.10693e6	+	1.91725e6i	−0.0598323	+	0.103633i
$808$	−1.40480e6	+	2.43319e6i	−0.0756984	+	0.131114i
$809$	−2.53447e7			−1.36149			−0.680747	−	0.732518i	$-0.738345\pi$
$809$	−2.53447e7			−1.36149			−0.680747	+	0.732518i	$0.738345\pi$
$810$	1.29384e6			0.0692895
$811$	1.15801e7	−	2.00573e7i	0.618245	−	1.07083i	−0.371561	−	0.928408i	$-0.621177\pi$
$811$	1.15801e7	−	2.00573e7i	0.618245	−	1.07083i	0.989806	−	0.142423i	$-0.0454892\pi$
$812$	6.96061e6	+	1.20561e7i	0.370473	+	0.641679i
$813$	2.29756e6	−	3.97949e6i	0.121910	−	0.211155i
$814$	4.11795e6	+	7.13250e6i	0.217831	+	0.377295i
$815$	3.84638e6	+	6.66213e6i	0.202842	+	0.351333i
$816$	1.02374e6			0.0538228
$817$	1.26377e7	+	2.58914e7i	0.662391	+	1.35706i
$818$	−2.24651e7			−1.17388
$819$	−1.31212e7	−	2.27267e7i	−0.683542	−	1.18393i
$820$	2.55945e6	+	4.43310e6i	0.132927	+	0.230236i
$821$	173359.	−	300266.i	0.00897611	−	0.0155471i	−0.861502	−	0.507753i	$-0.830476\pi$
$821$	173359.	−	300266.i	0.00897611	−	0.0155471i	0.870479	+	0.492206i	$0.163809\pi$
$822$	−2.75780e6	−	4.77666e6i	−0.142359	−	0.246572i
$823$	−1.38880e7	+	2.40548e7i	−0.714728	+	1.23795i	0.248336	+	0.968674i	$0.420116\pi$
$823$	−1.38880e7	+	2.40548e7i	−0.714728	+	1.23795i	−0.963064	+	0.269271i	$0.913217\pi$
$824$	−4.86796e6			−0.249764
$825$	−1.32966e7			−0.680153
$826$	6.30776e6	−	1.09254e7i	0.321680	−	0.557167i
$827$	−9.95884e6	+	1.72492e7i	−0.506343	+	0.877012i	0.493630	+	0.869672i	$0.335670\pi$
$827$	−9.95884e6	+	1.72492e7i	−0.506343	+	0.877012i	−0.999973	+	0.00733995i	$0.997664\pi$
$828$	1.22996e7			0.623468
$829$	−1.41423e7			−0.714716			−0.357358	−	0.933968i	$-0.616322\pi$
$829$	−1.41423e7			−0.714716			−0.357358	+	0.933968i	$0.616322\pi$
$830$	5.45010e6	−	9.43986e6i	0.274606	−	0.475631i
$831$	−5.08602e6	−	8.80925e6i	−0.255491	−	0.442523i
$832$	−1.66173e6	+	2.87820e6i	−0.0832247	+	0.144149i
$833$	4.34432e6	+	7.52458e6i	0.216925	+	0.375725i
$834$	126385.	+	218905.i	0.00629188	+	0.0108979i
$835$	−6.44889e6			−0.320088
$836$	−8.97050e6	+	1.33080e7i	−0.443916	+	0.658561i
$837$	−2.00163e6			−0.0987573
$838$	−1.86624e6	−	3.23242e6i	−0.0918031	−	0.159008i
$839$	−7.93841e6	−	1.37497e7i	−0.389340	−	0.674356i	0.603021	−	0.797725i	$-0.293963\pi$
$839$	−7.93841e6	−	1.37497e7i	−0.389340	−	0.674356i	−0.992361	+	0.123369i	$0.960630\pi$
$840$	−1.26241e6	+	2.18655e6i	−0.0617307	+	0.106921i
$841$	−558754.	−	967790.i	−0.0272415	−	0.0471836i
$842$	−8.08774e6	+	1.40084e7i	−0.393140	+	0.680938i
$843$	−6.71917e6			−0.325647
$844$	8.23499e6			0.397930
$845$	−3.61425e6	+	6.26006e6i	−0.174131	+	0.301604i
$846$	6.97943e6	−	1.20887e7i	0.335270	−	0.580704i
$847$	−4.58904e7			−2.19793
$848$	−2.57903e6			−0.123159
$849$	−5.60750e6	+	9.71247e6i	−0.266993	+	0.462445i
$850$	−2.37906e6	−	4.12065e6i	−0.112943	−	0.195622i
$851$	7.18148e6	−	1.24387e7i	0.339930	−	0.588776i
$852$	−2.84654e6	−	4.93035e6i	−0.134344	−	0.232691i
$853$	−1.59078e7	−	2.75531e7i	−0.748578	−	1.29657i	−0.948504	−	0.316764i	$-0.897404\pi$
$853$	−1.59078e7	−	2.75531e7i	−0.748578	−	1.29657i	0.199927	−	0.979811i	$-0.435930\pi$
$854$	−1.23897e7			−0.581323
$855$	6.83341e6	+	475768.i	0.319685	+	0.0222577i
$856$	−6.49877e6			−0.303142
$857$	1.37179e7	+	2.37601e7i	0.638022	+	1.10509i	0.985866	+	0.167534i	$0.0535803\pi$
$857$	1.37179e7	+	2.37601e7i	0.638022	+	1.10509i	−0.347845	+	0.937552i	$0.613086\pi$
$858$	−8.66247e6	−	1.50038e7i	−0.401720	−	0.695800i
$859$	−5.10500e6	+	8.84211e6i	−0.236055	+	0.408859i	−0.959579	−	0.281441i	$-0.909188\pi$
$859$	−5.10500e6	+	8.84211e6i	−0.236055	+	0.408859i	0.723524	+	0.690299i	$0.242521\pi$
$860$	−3.68839e6	−	6.38847e6i	−0.170055	−	0.294544i
$861$	9.95254e6	−	1.72383e7i	0.457537	−	0.792477i
$862$	1.50678e7			0.690687
$863$	3.20983e7			1.46708			0.733541	−	0.679645i	$-0.237866\pi$
$863$	3.20983e7			1.46708			0.733541	+	0.679645i	$0.237866\pi$
$864$	−1.78307e6	+	3.08837e6i	−0.0812615	+	0.140749i
$865$	−5.15229e6	+	8.92403e6i	−0.234132	+	0.405528i
$866$	−1.23167e7			−0.558082
$867$	9.98027e6			0.450915
$868$	−860233.	+	1.48997e6i	−0.0387540	+	0.0671239i
$869$	1.03679e7	+	1.79577e7i	0.465736	+	0.806678i
$870$	1.96134e6	−	3.39713e6i	0.0878525	−	0.152165i
$871$	−1.67330e6	−	2.89824e6i	−0.0747357	−	0.129446i
$872$	−5.39238e6	−	9.33988e6i	−0.240154	−	0.415959i
$873$	−1.33741e7			−0.593921
$874$	2.79211e7	+	1.94397e6i	1.23638	+	0.0860817i
$875$	2.64566e7			1.16819
$876$	2.78183e6	+	4.81826e6i	0.122481	+	0.212144i
$877$	−1.34320e7	−	2.32649e7i	−0.589715	−	1.02142i	−0.994270	−	0.106902i	$-0.965907\pi$
$877$	−1.34320e7	−	2.32649e7i	−0.589715	−	1.02142i	0.404555	−	0.914514i	$-0.367427\pi$
$878$	−2.28324e6	+	3.95469e6i	−0.0999575	+	0.173131i
$879$	4.28791e6	+	7.42689e6i	0.187186	+	0.324216i
$880$	2.05460e6	−	3.55866e6i	0.0894375	−	0.154910i
$881$	1.36632e7			0.593080			0.296540	−	0.955021i	$-0.404167\pi$
$881$	1.36632e7			0.593080			0.296540	+	0.955021i	$0.404167\pi$
$882$	−1.25814e7			−0.544574
$883$	−1.29198e7	+	2.23778e7i	−0.557642	+	0.965864i	0.440051	+	0.897973i	$0.354960\pi$
$883$	−1.29198e7	+	2.23778e7i	−0.557642	+	0.965864i	−0.997693	+	0.0678913i	$0.978373\pi$
$884$	3.09981e6	−	5.36903e6i	0.133415	−	0.231082i
$885$	−3.55476e6			−0.152564
$886$	−2.41061e7			−1.03167
$887$	1.22757e6	−	2.12621e6i	0.0523886	−	0.0907397i	−0.838642	−	0.544683i	$-0.816650\pi$
$887$	1.22757e6	−	2.12621e6i	0.0523886	−	0.0907397i	0.891030	+	0.453944i	$0.149983\pi$
$888$	865550.	+	1.49918e6i	0.0368349	+	0.0637999i
$889$	1.77880e7	−	3.08097e7i	0.754870	−	1.30747i
$890$	−1.43726e6	−	2.48941e6i	−0.0608219	−	0.105347i
$891$	4.09415e6	+	7.09128e6i	0.172771	+	0.299247i
$892$	−2.14156e7			−0.901192
$893$	1.77545e7	−	2.63393e7i	0.745041	−	1.10529i
$894$	1.44129e7			0.603123
$895$	−7.32334e6	−	1.26844e7i	−0.305599	−	0.529312i
$896$	1.53261e6	+	2.65456e6i	0.0637767	+	0.110465i
$897$	−1.51069e7	+	2.61659e7i	−0.626893	+	1.08581i
$898$	−865173.	−	1.49852e6i	−0.0358024	−	0.0620116i
$899$	1.33650e6	−	2.31488e6i	0.0551530	−	0.0955278i
$900$	6.88989e6			0.283535
$901$	4.81096e6			0.197433
$902$	−1.61980e7	+	2.80557e7i	−0.662895	+	1.14817i
$903$	−1.43425e7	+	2.48419e7i	−0.585335	+	1.01383i
$904$	2.76205e6			0.112411
$905$	1.69832e7			0.689282
$906$	8.58956e6	−	1.48776e7i	0.347657	−	0.602159i
$907$	1.42787e7	+	2.47315e7i	0.576331	+	0.998235i	0.995896	+	0.0905091i	$0.0288494\pi$
$907$	1.42787e7	+	2.47315e7i	0.576331	+	0.998235i	−0.419565	+	0.907725i	$0.637817\pi$
$908$	−2.31163e6	+	4.00387e6i	−0.0930474	+	0.161163i
$909$	3.79461e6	+	6.57247e6i	0.152320	+	0.263827i
$910$	7.64494e6	+	1.32414e7i	0.306035	+	0.530067i
$911$	2.07947e7			0.830151			0.415076	−	0.909787i	$-0.363755\pi$
$911$	2.07947e7			0.830151			0.415076	+	0.909787i	$0.363755\pi$
$912$	−1.88550e6	+	2.79719e6i	−0.0750655	+	0.111362i
$913$	6.89841e7			2.73887
$914$	−1.60616e7	−	2.78195e7i	−0.635950	−	1.10150i
$915$	1.74557e6	+	3.02342e6i	0.0689263	+	0.119384i
$916$	3.58018e6	−	6.20106e6i	0.140983	−	0.244190i
$917$	−7.36189e6	−	1.27512e7i	−0.289112	−	0.500756i
$918$	3.32617e6	−	5.76109e6i	0.130268	−	0.225631i
$919$	2.27035e6			0.0886754			0.0443377	−	0.999017i	$-0.485882\pi$
$919$	2.27035e6			0.0886754			0.0443377	+	0.999017i	$0.485882\pi$
$920$	−7.16620e6			−0.279138
$921$	−1.35754e6	+	2.35132e6i	−0.0527354	+	0.0913404i
$922$	2.02255e6	−	3.50316e6i	0.0783560	−	0.135716i
$923$	−3.44764e7			−1.33204
$924$	−1.59788e7			−0.615692
$925$	4.02287e6	−	6.96782e6i	0.154590	−	0.267758i
$926$	−2.03776e6	−	3.52951e6i	−0.0780955	−	0.135265i
$927$	−6.57460e6	+	1.13875e7i	−0.251287	+	0.435242i
$928$	−2.38114e6	−	4.12425e6i	−0.0907642	−	0.157208i
$929$	1.54379e7	+	2.67393e7i	0.586880	+	1.01651i	0.994638	+	0.103416i	$0.0329774\pi$
$929$	1.54379e7	+	2.67393e7i	0.586880	+	1.01651i	−0.407758	+	0.913090i	$0.633689\pi$
$930$	484787.			0.0183799
$931$	−2.85608e7	−	1.98851e6i	−1.07993	−	0.0751889i
$932$	1.21649e7			0.458743
$933$	−2.10604e6	−	3.64776e6i	−0.0792066	−	0.137190i
$934$	−1.18682e7	−	2.05564e7i	−0.445163	−	0.771044i
$935$	−3.83267e6	+	6.63838e6i	−0.143375	+	0.248332i
$936$	4.48862e6	+	7.77452e6i	0.167465	+	0.290057i
$937$	2.57320e6	−	4.45692e6i	0.0957470	−	0.165839i	−0.814173	−	0.580622i	$-0.802809\pi$
$937$	2.57320e6	−	4.45692e6i	0.0957470	−	0.165839i	0.909920	+	0.414784i	$0.136143\pi$
$938$	−3.08656e6			−0.114543
$939$	1.38678e7			0.513266
$940$	−4.06648e6	+	7.04335e6i	−0.150106	+	0.259992i
$941$	4.65651e6	−	8.06530e6i	0.171430	−	0.296925i	−0.767490	−	0.641061i	$-0.778495\pi$
$941$	4.65651e6	−	8.06530e6i	0.171430	−	0.296925i	0.938920	+	0.344136i	$0.111828\pi$
$942$	−6.42493e6			−0.235907
$943$	5.64967e7			2.06892
$944$	−2.15781e6	+	3.73743e6i	−0.0788102	+	0.136503i
$945$	8.20319e6	+	1.42083e7i	0.298815	+	0.517564i
$946$	2.33427e7	−	4.04307e7i	0.848052	−	1.46887i
$947$	−1.04247e7	−	1.80561e7i	−0.377736	−	0.654258i	0.612997	−	0.790086i	$-0.289964\pi$
$947$	−1.04247e7	−	1.80561e7i	−0.377736	−	0.654258i	−0.990732	+	0.135828i	$0.956631\pi$
$948$	2.17921e6	+	3.77451e6i	0.0787551	+	0.136408i
$949$	3.36926e7			1.21442
$950$	1.56406e7	+	1.08896e6i	0.562270	+	0.0391474i
$951$	3.14764e6			0.112858
$952$	−2.85896e6	−	4.95186e6i	−0.102239	−	0.177083i
$953$	−4.80144e6	−	8.31635e6i	−0.171254	−	0.296620i	0.767605	−	0.640923i	$-0.221448\pi$
$953$	−4.80144e6	−	8.31635e6i	−0.171254	−	0.296620i	−0.938858	+	0.344304i	$0.888115\pi$
$954$	−3.48320e6	+	6.03309e6i	−0.123910	+	0.214619i
$955$	2.18679e6	+	3.78763e6i	0.0775886	+	0.134387i
$956$	−4.03489e6	+	6.98863e6i	−0.142786	+	0.247313i
$957$	2.48254e7			0.876226
$958$	−4.54031e6			−0.159835
$959$	−1.54032e7	+	2.66790e7i	−0.540833	+	0.936750i
$960$	431854.	−	747994.i	0.0151237	−	0.0261951i
$961$	−2.82988e7			−0.988461
$962$	1.04833e7			0.365223
$963$	−8.77715e6	+	1.52025e7i	−0.304991	+	0.528261i
$964$	−8.47958e6	−	1.46871e7i	−0.293888	−	0.509029i
$965$	−1.11142e7	+	1.92503e7i	−0.384201	+	0.665456i
$966$	1.39331e7	+	2.41328e7i	0.480401	+	0.832078i
$967$	−2.73128e7	−	4.73072e7i	−0.939292	−	1.62690i	−0.766796	−	0.641891i	$-0.778150\pi$
$967$	−2.73128e7	−	4.73072e7i	−0.939292	−	1.62690i	−0.172496	−	0.985010i	$-0.555183\pi$
$968$	1.56986e7			0.538482
$969$	3.51725e6	−	5.21793e6i	0.120335	−	0.178521i
$970$	7.79226e6			0.265910
$971$	−2.77128e7	−	4.80000e7i	−0.943263	−	1.63378i	−0.759193	−	0.650866i	$-0.774406\pi$
$971$	−2.77128e7	−	4.80000e7i	−0.943263	−	1.63378i	−0.184070	−	0.982913i	$-0.558927\pi$
$972$	7.63065e6	+	1.32167e7i	0.259057	+	0.448701i
$973$	705898.	−	1.22265e6i	0.0239034	−	0.0414019i
$974$	5.59067e6	+	9.68332e6i	0.188828	+	0.327060i
$975$	−8.46246e6	+	1.46574e7i	−0.285092	+	0.493794i
$976$	4.23838e6			0.142422
$977$	4.57317e7			1.53278			0.766392	−	0.642374i	$-0.222050\pi$
$977$	4.57317e7			1.53278			0.766392	+	0.642374i	$0.222050\pi$
$978$	−5.11655e6	+	8.86213e6i	−0.171053	+	0.296272i
$979$	9.09598e6	−	1.57547e7i	0.303314	−	0.525355i
$980$	7.33040e6			0.243816
$981$	−2.91315e7			−0.966475
$982$	4.52188e6	−	7.83213e6i	0.149638	−	0.259180i
$983$	−1.41535e7	−	2.45146e7i	−0.467176	−	0.809173i	0.532121	−	0.846668i	$-0.321395\pi$
$983$	−1.41535e7	−	2.45146e7i	−0.467176	−	0.809173i	−0.999297	+	0.0374959i	$0.988062\pi$
$984$	−3.40464e6	+	5.89702e6i	−0.112094	+	0.194153i
$985$	−9.94636e6	−	1.72276e7i	−0.326643	−	0.565763i
$986$	4.44181e6	+	7.69344e6i	0.145502	+	0.252016i
$987$	3.16254e7			1.03334
$988$	8.96076e6	+	1.83582e7i	0.292047	+	0.598327i
$989$	−8.14166e7			−2.64681
$990$	−5.54982e6	−	9.61257e6i	−0.179966	−	0.311711i
$991$	1.89132e7	+	3.27587e7i	0.611761	+	1.05960i	0.990944	+	0.134279i	$0.0428719\pi$
$991$	1.89132e7	+	3.27587e7i	0.611761	+	1.05960i	−0.379183	+	0.925322i	$0.623795\pi$
$992$	294275.	−	509700.i	0.00949455	−	0.0164450i
$993$	−1.34197e7	−	2.32436e7i	−0.431886	−	0.748048i
$994$	−1.58988e7	+	2.75375e7i	−0.510385	+	0.884012i
$995$	1.61383e7			0.516773
$996$	1.44997e7			0.463139
$997$	1.46045e7	−	2.52958e7i	0.465318	−	0.805955i	−0.533898	−	0.845549i	$-0.679273\pi$
$997$	1.46045e7	−	2.52958e7i	0.465318	−	0.805955i	0.999216	+	0.0395943i	$0.0126066\pi$
$998$	5.65709e6	−	9.79836e6i	0.179790	−	0.311406i
$999$	1.12488e7			0.356608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.b.7.3	✓	8
3.2	odd	2		342.6.g.d.235.2		8
4.3	odd	2		304.6.i.b.273.2		8
19.7	even	3		722.6.a.j.1.2		4
19.11	even	3	inner	38.6.c.b.11.3	yes	8
19.12	odd	6		722.6.a.g.1.3		4
57.11	odd	6		342.6.g.d.163.2		8
76.11	odd	6		304.6.i.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.3	✓	8	1.1	even	1	trivial
38.6.c.b.11.3	yes	8	19.11	even	3	inner
304.6.i.b.49.2		8	76.11	odd	6
304.6.i.b.273.2		8	4.3	odd	2
342.6.g.d.163.2		8	57.11	odd	6
342.6.g.d.235.2		8	3.2	odd	2
722.6.a.g.1.3		4	19.12	odd	6
722.6.a.j.1.2		4	19.7	even	3

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(4.18703 + 7.25215i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.5904 - 21.8073i) q^{5} +(16.7481 - 29.0086i) q^{6} -187.086 q^{7} +64.0000 q^{8} +(86.4375 - 149.714i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(4.18703 + 7.25215i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.5904 - 21.8073i) q^{5} +(16.7481 - 29.0086i) q^{6} -187.086 q^{7} +64.0000 q^{8} +(86.4375 - 149.714i) q^{9} +(-50.3618 + 87.2292i) q^{10} -637.449 q^{11} -133.985 q^{12} +(-405.696 + 702.685i) q^{13} +(374.173 + 648.086i) q^{14} +(105.433 - 182.616i) q^{15} +(-128.000 - 221.703i) q^{16} +(238.773 + 413.567i) q^{17} -691.500 q^{18} +(-1569.76 - 109.293i) q^{19} +402.894 q^{20} +(-783.337 - 1356.78i) q^{21} +(1274.90 + 2208.19i) q^{22} +(2223.35 - 3850.96i) q^{23} +(267.970 + 464.138i) q^{24} +(1245.46 - 2157.20i) q^{25} +3245.57 q^{26} +3482.56 q^{27} +(1496.69 - 2592.35i) q^{28} +(-2325.33 + 4027.59i) q^{29} -843.466 q^{30} -574.756 q^{31} +(-512.000 + 886.810i) q^{32} +(-2669.02 - 4622.87i) q^{33} +(955.092 - 1654.27i) q^{34} +(2355.50 + 4079.85i) q^{35} +(1383.00 + 2395.43i) q^{36} +3230.02 q^{37} +(2760.92 + 5656.40i) q^{38} -6794.64 q^{39} +(-805.789 - 1395.67i) q^{40} +(6352.66 + 11003.1i) q^{41} +(-3133.35 + 5427.12i) q^{42} +(-9154.72 - 15856.4i) q^{43} +(5099.59 - 8832.75i) q^{44} -4353.15 q^{45} -17786.8 q^{46} +(-10093.2 + 17481.9i) q^{47} +(1071.88 - 1856.55i) q^{48} +18194.3 q^{49} -9963.69 q^{50} +(-1999.50 + 3463.23i) q^{51} +(-6491.13 - 11243.0i) q^{52} +(5037.17 - 8724.63i) q^{53} +(-6965.13 - 12064.0i) q^{54} +(8025.77 + 13901.0i) q^{55} -11973.5 q^{56} +(-5780.04 - 11841.8i) q^{57} +18602.6 q^{58} +(-8428.93 - 14599.3i) q^{59} +(1686.93 + 2921.85i) q^{60} +(-8278.09 + 14338.1i) q^{61} +(1149.51 + 1991.01i) q^{62} +(-16171.3 + 28009.5i) q^{63} +4096.00 q^{64} +20431.6 q^{65} +(-10676.1 + 18491.5i) q^{66} +(-2062.26 + 3571.93i) q^{67} -7640.73 q^{68} +37236.9 q^{69} +(9422.01 - 16319.4i) q^{70} +(21245.2 + 36797.8i) q^{71} +(5532.00 - 9581.71i) q^{72} +(-20762.2 - 35961.2i) q^{73} +(-6460.05 - 11189.1i) q^{74} +20859.1 q^{75} +(14072.5 - 20876.9i) q^{76} +119258. q^{77} +(13589.3 + 23537.3i) q^{78} +(-16264.6 - 28171.1i) q^{79} +(-3223.15 + 5582.67i) q^{80} +(-6422.72 - 11124.5i) q^{81} +(25410.6 - 44012.5i) q^{82} -108219. q^{83} +25066.8 q^{84} +(6012.52 - 10414.0i) q^{85} +(-36618.9 + 63425.8i) q^{86} -38944.9 q^{87} -40796.7 q^{88} +(-14269.3 + 24715.2i) q^{89} +(8706.30 + 15079.8i) q^{90} +(75900.2 - 131463. i) q^{91} +(35573.6 + 61615.3i) q^{92} +(-2406.52 - 4168.22i) q^{93} +80745.4 q^{94} +(17380.6 + 35608.3i) q^{95} -8575.04 q^{96} +(-38681.4 - 66998.1i) q^{97} +(-36388.7 - 63027.1i) q^{98} +(-55099.5 + 95435.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9}+O(q^{10}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18} + 320 q^{19} + 1152 q^{20} - 770 q^{21} - 288 q^{22} - 204 q^{23} - 896 q^{24} - 2158 q^{25} + 5392 q^{26} + 13156 q^{27} - 608 q^{28} - 5712 q^{29} + 160 q^{30} - 2324 q^{31} - 4096 q^{32} - 15650 q^{33} + 2088 q^{34} - 4188 q^{35} + 2496 q^{36} - 25508 q^{37} - 2440 q^{38} + 44156 q^{39} - 2304 q^{40} - 3480 q^{41} - 3080 q^{42} + 4066 q^{43} - 1152 q^{44} + 51560 q^{45} + 1632 q^{46} - 45768 q^{47} - 3584 q^{48} + 1416 q^{49} + 17264 q^{50} + 1506 q^{51} - 10784 q^{52} + 45654 q^{53} - 26312 q^{54} + 36570 q^{55} + 4864 q^{56} - 66702 q^{57} + 45696 q^{58} - 84006 q^{59} - 320 q^{60} - 14012 q^{61} + 4648 q^{62} - 15128 q^{63} + 32768 q^{64} - 4020 q^{65} - 62600 q^{66} - 19046 q^{67} - 16704 q^{68} + 111592 q^{69} - 16752 q^{70} - 53274 q^{71} + 9984 q^{72} - 41084 q^{73} + 51016 q^{74} + 153216 q^{75} + 4640 q^{76} + 271524 q^{77} - 88312 q^{78} - 54170 q^{79} - 9216 q^{80} - 9528 q^{81} - 13920 q^{82} + 52392 q^{83} + 24640 q^{84} - 221850 q^{85} + 16264 q^{86} - 457120 q^{87} + 9216 q^{88} - 137862 q^{89} - 103120 q^{90} + 308516 q^{91} - 3264 q^{92} + 112746 q^{93} + 366144 q^{94} + 153078 q^{95} + 28672 q^{96} - 292388 q^{97} - 2832 q^{98} - 138328 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more