LMFDB - Embedded newform 1045.6.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

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:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} +O(q^{10})$	\(q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} -15.2303 q^{10} +121.000 q^{11} -655.466 q^{12} -557.016 q^{13} +69.5563 q^{14} +518.092 q^{15} +988.508 q^{16} +1251.16 q^{17} -113.601 q^{18} +361.000 q^{19} -790.721 q^{20} -2366.10 q^{21} -73.7148 q^{22} +112.655 q^{23} +803.324 q^{24} +625.000 q^{25} +339.342 q^{26} -1171.49 q^{27} +3611.19 q^{28} +3058.85 q^{29} -315.629 q^{30} -2084.31 q^{31} -1842.65 q^{32} +2507.57 q^{33} -762.224 q^{34} -2854.35 q^{35} -5897.86 q^{36} -4134.99 q^{37} -219.926 q^{38} -11543.4 q^{39} +969.089 q^{40} +4338.04 q^{41} +1441.46 q^{42} -12533.9 q^{43} -3827.09 q^{44} +4661.77 q^{45} -68.6312 q^{46} -13727.7 q^{47} +20485.5 q^{48} -3771.31 q^{49} -380.758 q^{50} +25928.6 q^{51} +17617.8 q^{52} +2552.04 q^{53} +713.688 q^{54} +3025.00 q^{55} -4425.79 q^{56} +7481.25 q^{57} -1863.49 q^{58} +11558.1 q^{59} -16386.7 q^{60} +31983.1 q^{61} +1269.79 q^{62} -21290.1 q^{63} -30509.7 q^{64} -13925.4 q^{65} -1527.64 q^{66} +31684.8 q^{67} -39572.8 q^{68} +2334.63 q^{69} +1738.91 q^{70} +43305.0 q^{71} +7228.27 q^{72} -10784.1 q^{73} +2519.09 q^{74} +12952.3 q^{75} -11418.0 q^{76} -13815.0 q^{77} +7032.41 q^{78} -108908. q^{79} +24712.7 q^{80} -69590.0 q^{81} -2642.79 q^{82} +45563.6 q^{83} +74837.2 q^{84} +31279.0 q^{85} +7635.80 q^{86} +63390.6 q^{87} +4690.39 q^{88} +72026.0 q^{89} -2840.01 q^{90} +63596.7 q^{91} -3563.16 q^{92} -43194.7 q^{93} +8363.13 q^{94} +9025.00 q^{95} -38186.4 q^{96} +117684. q^{97} +2297.53 q^{98} +22563.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.609213	−0.107695	−0.0538474	−	0.998549i	$-0.517148\pi$
$2$	−0.609213	−0.107695	−0.0538474	+	0.998549i	$0.517148\pi$
$3$	20.7237	1.32942	0.664712	−	0.747099i	$-0.268554\pi$
$3$	20.7237	1.32942	0.664712	+	0.747099i	$0.268554\pi$
$4$	−31.6289	−0.988402
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−12.6251	−0.143172
$7$	−114.174	−0.880688	−0.440344	−	0.897829i	$-0.645143\pi$
$7$	−114.174	−0.880688	−0.440344	+	0.897829i	$0.645143\pi$
$8$	38.7636	0.214140
$9$	186.471	0.767370
$10$	−15.2303	−0.0481626
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−655.466	−1.31401
$13$	−557.016	−0.914133	−0.457066	−	0.889433i	$-0.651100\pi$
$13$	−557.016	−0.914133	−0.457066	+	0.889433i	$0.651100\pi$
$14$	69.5563	0.0948454
$15$	518.092	0.594537
$16$	988.508	0.965340
$17$	1251.16	1.05000	0.525002	−	0.851101i	$-0.324065\pi$
$17$	1251.16	1.05000	0.525002	+	0.851101i	$0.324065\pi$
$18$	−113.601	−0.0826417
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−790.721	−0.442027
$21$	−2366.10	−1.17081
$22$	−73.7148	−0.0324712
$23$	112.655	0.0444051	0.0222025	−	0.999753i	$-0.492932\pi$
$23$	112.655	0.0444051	0.0222025	+	0.999753i	$0.492932\pi$
$24$	803.324	0.284684
$25$	625.000	0.200000
$26$	339.342	0.0984473
$27$	−1171.49	−0.309264
$28$	3611.19	0.870473
$29$	3058.85	0.675404	0.337702	−	0.941253i	$-0.390350\pi$
$29$	3058.85	0.675404	0.337702	+	0.941253i	$0.390350\pi$
$30$	−315.629	−0.0640285
$31$	−2084.31	−0.389546	−0.194773	−	0.980848i	$-0.562397\pi$
$31$	−2084.31	−0.389546	−0.194773	+	0.980848i	$0.562397\pi$
$32$	−1842.65	−0.318102
$33$	2507.57	0.400837
$34$	−762.224	−0.113080
$35$	−2854.35	−0.393856
$36$	−5897.86	−0.758470
$37$	−4134.99	−0.496558	−0.248279	−	0.968689i	$-0.579865\pi$
$37$	−4134.99	−0.496558	−0.248279	+	0.968689i	$0.579865\pi$
$38$	−219.926	−0.0247069
$39$	−11543.4	−1.21527
$40$	969.089	0.0957665
$41$	4338.04	0.403027	0.201513	−	0.979486i	$-0.435414\pi$
$41$	4338.04	0.403027	0.201513	+	0.979486i	$0.435414\pi$
$42$	1441.46	0.126090
$43$	−12533.9	−1.03375	−0.516873	−	0.856062i	$-0.672904\pi$
$43$	−12533.9	−1.03375	−0.516873	+	0.856062i	$0.672904\pi$
$44$	−3827.09	−0.298014
$45$	4661.77	0.343178
$46$	−68.6312	−0.00478219
$47$	−13727.7	−0.906472	−0.453236	−	0.891390i	$-0.649731\pi$
$47$	−13727.7	−0.906472	−0.453236	+	0.891390i	$0.649731\pi$
$48$	20485.5	1.28335
$49$	−3771.31	−0.224389
$50$	−380.758	−0.0215389
$51$	25928.6	1.39590
$52$	17617.8	0.903531
$53$	2552.04	0.124795	0.0623975	−	0.998051i	$-0.480125\pi$
$53$	2552.04	0.124795	0.0623975	+	0.998051i	$0.480125\pi$
$54$	713.688	0.0333061
$55$	3025.00	0.134840
$56$	−4425.79	−0.188591
$57$	7481.25	0.304991
$58$	−1863.49	−0.0727374
$59$	11558.1	0.432272	0.216136	−	0.976363i	$-0.430654\pi$
$59$	11558.1	0.432272	0.216136	+	0.976363i	$0.430654\pi$
$60$	−16386.7	−0.587641
$61$	31983.1	1.10051	0.550257	−	0.834995i	$-0.314530\pi$
$61$	31983.1	1.10051	0.550257	+	0.834995i	$0.314530\pi$
$62$	1269.79	0.0419521
$63$	−21290.1	−0.675813
$64$	−30509.7	−0.931082
$65$	−13925.4	−0.408813
$66$	−1527.64	−0.0431680
$67$	31684.8	0.862312	0.431156	−	0.902277i	$-0.358106\pi$
$67$	31684.8	0.862312	0.431156	+	0.902277i	$0.358106\pi$
$68$	−39572.8	−1.03782
$69$	2334.63	0.0590332
$70$	1738.91	0.0424162
$71$	43305.0	1.01951	0.509755	−	0.860319i	$-0.329736\pi$
$71$	43305.0	1.01951	0.509755	+	0.860319i	$0.329736\pi$
$72$	7228.27	0.164325
$73$	−10784.1	−0.236852	−0.118426	−	0.992963i	$-0.537785\pi$
$73$	−10784.1	−0.236852	−0.118426	+	0.992963i	$0.537785\pi$
$74$	2519.09	0.0534767
$75$	12952.3	0.265885
$76$	−11418.0	−0.226755
$77$	−13815.0	−0.265537
$78$	7032.41	0.130878
$79$	−108908.	−1.96332	−0.981661	−	0.190636i	$-0.938945\pi$
$79$	−108908.	−1.96332	−0.981661	+	0.190636i	$0.938945\pi$
$80$	24712.7	0.431713
$81$	−69590.0	−1.17851
$82$	−2642.79	−0.0434039
$83$	45563.6	0.725977	0.362988	−	0.931794i	$-0.381757\pi$
$83$	45563.6	0.725977	0.362988	+	0.931794i	$0.381757\pi$
$84$	74837.2	1.15723
$85$	31279.0	0.469576
$86$	7635.80	0.111329
$87$	63390.6	0.897898
$88$	4690.39	0.0645658
$89$	72026.0	0.963860	0.481930	−	0.876210i	$-0.339936\pi$
$89$	72026.0	0.963860	0.481930	+	0.876210i	$0.339936\pi$
$90$	−2840.01	−0.0369585
$91$	63596.7	0.805066
$92$	−3563.16	−0.0438901
$93$	−43194.7	−0.517872
$94$	8363.13	0.0976223
$95$	9025.00	0.102598
$96$	−38186.4	−0.422893
$97$	117684.	1.26995	0.634977	−	0.772531i	$-0.281010\pi$
$97$	117684.	1.26995	0.634977	+	0.772531i	$0.281010\pi$
$98$	2297.53	0.0241655
$99$	22563.0	0.231371
$100$	−19768.0	−0.197680
$101$	−66340.4	−0.647105	−0.323552	−	0.946210i	$-0.604877\pi$
$101$	−66340.4	−0.647105	−0.323552	+	0.946210i	$0.604877\pi$
$102$	−15796.1	−0.150331
$103$	150322.	1.39614	0.698071	−	0.716029i	$-0.254042\pi$
$103$	150322.	1.39614	0.698071	+	0.716029i	$0.254042\pi$
$104$	−21591.9	−0.195753
$105$	−59152.6	−0.523601
$106$	−1554.74	−0.0134398
$107$	216512.	1.82820	0.914098	−	0.405493i	$-0.132900\pi$
$107$	216512.	1.82820	0.914098	+	0.405493i	$0.132900\pi$
$108$	37052.9	0.305677
$109$	41384.2	0.333633	0.166816	−	0.985988i	$-0.446651\pi$
$109$	41384.2	0.333633	0.166816	+	0.985988i	$0.446651\pi$
$110$	−1842.87	−0.0145216
$111$	−85692.2	−0.660137
$112$	−112862.	−0.850163
$113$	119837.	0.882867	0.441433	−	0.897294i	$-0.354470\pi$
$113$	119837.	0.882867	0.441433	+	0.897294i	$0.354470\pi$
$114$	−4557.68	−0.0328459
$115$	2816.39	0.0198585
$116$	−96748.0	−0.667570
$117$	−103867.	−0.701478
$118$	−7041.37	−0.0465535
$119$	−142850.	−0.924725
$120$	20083.1	0.127314
$121$	14641.0	0.0909091
$122$	−19484.5	−0.118520
$123$	89900.2	0.535794
$124$	65924.5	0.385028
$125$	15625.0	0.0894427
$126$	12970.2	0.0727815
$127$	39095.9	0.215091	0.107545	−	0.994200i	$-0.465701\pi$
$127$	39095.9	0.215091	0.107545	+	0.994200i	$0.465701\pi$
$128$	77551.6	0.418375
$129$	−259748.	−1.37429
$130$	8483.54	0.0440270
$131$	−27724.1	−0.141149	−0.0705747	−	0.997506i	$-0.522483\pi$
$131$	−27724.1	−0.141149	−0.0705747	+	0.997506i	$0.522483\pi$
$132$	−79311.4	−0.396188
$133$	−41216.8	−0.202044
$134$	−19302.8	−0.0928665
$135$	−29287.3	−0.138307
$136$	48499.4	0.224848
$137$	35413.7	0.161202	0.0806010	−	0.996746i	$-0.474316\pi$
$137$	35413.7	0.161202	0.0806010	+	0.996746i	$0.474316\pi$
$138$	−1422.29	−0.00635756
$139$	173016.	0.759535	0.379768	−	0.925082i	$-0.376004\pi$
$139$	173016.	0.759535	0.379768	+	0.925082i	$0.376004\pi$
$140$	90279.8	0.389288
$141$	−284489.	−1.20509
$142$	−26382.0	−0.109796
$143$	−67398.9	−0.275621
$144$	184328.	0.740773
$145$	76471.3	0.302050
$146$	6569.81	0.0255077
$147$	−78155.4	−0.298308
$148$	130785.	0.490799
$149$	−55220.4	−0.203767	−0.101883	−	0.994796i	$-0.532487\pi$
$149$	−55220.4	−0.203767	−0.101883	+	0.994796i	$0.532487\pi$
$150$	−7890.72	−0.0286344
$151$	446154.	1.59236	0.796182	−	0.605058i	$-0.206850\pi$
$151$	446154.	1.59236	0.796182	+	0.605058i	$0.206850\pi$
$152$	13993.6	0.0491272
$153$	233305.	0.805741
$154$	8416.31	0.0285970
$155$	−52107.9	−0.174210
$156$	365105.	1.20118
$157$	282112.	0.913424	0.456712	−	0.889615i	$-0.349027\pi$
$157$	282112.	0.913424	0.456712	+	0.889615i	$0.349027\pi$
$158$	66348.1	0.211439
$159$	52887.6	0.165906
$160$	−46066.2	−0.142260
$161$	−12862.3	−0.0391070
$162$	42395.2	0.126920
$163$	305803.	0.901515	0.450757	−	0.892647i	$-0.351154\pi$
$163$	305803.	0.901515	0.450757	+	0.892647i	$0.351154\pi$
$164$	−137207.	−0.398352
$165$	62689.1	0.179260
$166$	−27757.9	−0.0781839
$167$	156166.	0.433306	0.216653	−	0.976249i	$-0.430486\pi$
$167$	156166.	0.433306	0.216653	+	0.976249i	$0.430486\pi$
$168$	−91718.6	−0.250717
$169$	−61026.2	−0.164361
$170$	−19055.6	−0.0505708
$171$	67316.0	0.176047
$172$	396432.	1.02176
$173$	610359.	1.55050	0.775248	−	0.631657i	$-0.217625\pi$
$173$	610359.	1.55050	0.775248	+	0.631657i	$0.217625\pi$
$174$	−38618.4	−0.0966989
$175$	−71358.7	−0.176138
$176$	119609.	0.291061
$177$	239527.	0.574674
$178$	−43879.2	−0.103803
$179$	16828.2	0.0392560	0.0196280	−	0.999807i	$-0.493752\pi$
$179$	16828.2	0.0392560	0.0196280	+	0.999807i	$0.493752\pi$
$180$	−147447.	−0.339198
$181$	−417226.	−0.946618	−0.473309	−	0.880896i	$-0.656941\pi$
$181$	−417226.	−0.946618	−0.473309	+	0.880896i	$0.656941\pi$
$182$	−38744.0	−0.0867013
$183$	662807.	1.46305
$184$	4366.93	0.00950892
$185$	−103375.	−0.222068
$186$	26314.8	0.0557721
$187$	151390.	0.316588
$188$	434193.	0.895959
$189$	133754.	0.272365
$190$	−5498.15	−0.0110492
$191$	837287.	1.66070	0.830350	−	0.557242i	$-0.188141\pi$
$191$	837287.	1.66070	0.830350	+	0.557242i	$0.188141\pi$
$192$	−632273.	−1.23780
$193$	108159.	0.209010	0.104505	−	0.994524i	$-0.466674\pi$
$193$	108159.	0.209010	0.104505	+	0.994524i	$0.466674\pi$
$194$	−71694.6	−0.136767
$195$	−288586.	−0.543486
$196$	119282.	0.221787
$197$	−326694.	−0.599757	−0.299879	−	0.953977i	$-0.596946\pi$
$197$	−326694.	−0.599757	−0.299879	+	0.953977i	$0.596946\pi$
$198$	−13745.7	−0.0249174
$199$	254361.	0.455321	0.227661	−	0.973741i	$-0.426892\pi$
$199$	254361.	0.455321	0.227661	+	0.973741i	$0.426892\pi$
$200$	24227.2	0.0428281
$201$	656626.	1.14638
$202$	40415.5	0.0696898
$203$	−349241.	−0.594820
$204$	−820093.	−1.37971
$205$	108451.	0.180239
$206$	−91578.2	−0.150357
$207$	21007.0	0.0340751
$208$	−550615.	−0.882449
$209$	43681.0	0.0691714
$210$	36036.6	0.0563891
$211$	845329.	1.30713	0.653566	−	0.756869i	$-0.273272\pi$
$211$	845329.	1.30713	0.653566	+	0.756869i	$0.273272\pi$
$212$	−80718.0	−0.123348
$213$	897438.	1.35536
$214$	−131902.	−0.196887
$215$	−313347.	−0.462306
$216$	−45411.2	−0.0662260
$217$	237974.	0.343069
$218$	−25211.8	−0.0359305
$219$	−223486.	−0.314876
$220$	−95677.3	−0.133276
$221$	−696916.	−0.959842
$222$	52204.8	0.0710932
$223$	−809537.	−1.09012	−0.545060	−	0.838397i	$-0.683493\pi$
$223$	−809537.	−1.09012	−0.545060	+	0.838397i	$0.683493\pi$
$224$	210382.	0.280149
$225$	116544.	0.153474
$226$	−73006.4	−0.0950801
$227$	−309805.	−0.399047	−0.199523	−	0.979893i	$-0.563939\pi$
$227$	−309805.	−0.399047	−0.199523	+	0.979893i	$0.563939\pi$
$228$	−236623.	−0.301454
$229$	−1.19087e6	−1.50064	−0.750319	−	0.661076i	$-0.770100\pi$
$229$	−1.19087e6	−1.50064	−0.750319	+	0.661076i	$0.770100\pi$
$230$	−1715.78	−0.00213866
$231$	−286299.	−0.353012
$232$	118572.	0.144631
$233$	−60940.3	−0.0735385	−0.0367692	−	0.999324i	$-0.511707\pi$
$233$	−60940.3	−0.0735385	−0.0367692	+	0.999324i	$0.511707\pi$
$234$	63277.3	0.0755455
$235$	−343194.	−0.405387
$236$	−365570.	−0.427259
$237$	−2.25697e6	−2.61009
$238$	87026.1	0.0995880
$239$	−855678.	−0.968982	−0.484491	−	0.874796i	$-0.660995\pi$
$239$	−855678.	−0.968982	−0.484491	+	0.874796i	$0.660995\pi$
$240$	512138.	0.573930
$241$	1.55896e6	1.72898	0.864492	−	0.502646i	$-0.167640\pi$
$241$	1.55896e6	1.72898	0.864492	+	0.502646i	$0.167640\pi$
$242$	−8919.49	−0.00979043
$243$	−1.15749e6	−1.25748
$244$	−1.01159e6	−1.08775
$245$	−94282.7	−0.100350
$246$	−54768.4	−0.0577022
$247$	−201083.	−0.209716
$248$	−80795.4	−0.0834176
$249$	944245.	0.965131
$250$	−9518.96	−0.00963251
$251$	−1.64608e6	−1.64918	−0.824588	−	0.565734i	$-0.808593\pi$
$251$	−1.64608e6	−1.64918	−0.824588	+	0.565734i	$0.808593\pi$
$252$	673382.	0.667975
$253$	13631.3	0.0133886
$254$	−23817.7	−0.0231641
$255$	648216.	0.624265
$256$	929065.	0.886025
$257$	−615662.	−0.581447	−0.290723	−	0.956807i	$-0.593896\pi$
$257$	−615662.	−0.581447	−0.290723	+	0.956807i	$0.593896\pi$
$258$	158242.	0.148004
$259$	472108.	0.437313
$260$	440445.	0.404071
$261$	570387.	0.518284
$262$	16889.9	0.0152011
$263$	550187.	0.490480	0.245240	−	0.969462i	$-0.421133\pi$
$263$	550187.	0.490480	0.245240	+	0.969462i	$0.421133\pi$
$264$	97202.2	0.0858353
$265$	63800.9	0.0558100
$266$	25109.8	0.0217590
$267$	1.49264e6	1.28138
$268$	−1.00216e6	−0.852311
$269$	−187673.	−0.158132	−0.0790661	−	0.996869i	$-0.525194\pi$
$269$	−187673.	−0.158132	−0.0790661	+	0.996869i	$0.525194\pi$
$270$	17842.2	0.0148950
$271$	1.22230e6	1.01101	0.505505	−	0.862824i	$-0.331306\pi$
$271$	1.22230e6	1.01101	0.505505	+	0.862824i	$0.331306\pi$
$272$	1.23678e6	1.01361
$273$	1.31796e6	1.07027
$274$	−21574.5	−0.0173606
$275$	75625.0	0.0603023
$276$	−73841.8	−0.0583485
$277$	−838965.	−0.656968	−0.328484	−	0.944509i	$-0.606538\pi$
$277$	−838965.	−0.656968	−0.328484	+	0.944509i	$0.606538\pi$
$278$	−105403.	−0.0817980
$279$	−388664.	−0.298926
$280$	−110645.	−0.0843404
$281$	1.12952e6	0.853349	0.426675	−	0.904405i	$-0.359685\pi$
$281$	1.12952e6	0.853349	0.426675	+	0.904405i	$0.359685\pi$
$282$	173315.	0.129781
$283$	700626.	0.520020	0.260010	−	0.965606i	$-0.416274\pi$
$283$	700626.	0.520020	0.260010	+	0.965606i	$0.416274\pi$
$284$	−1.36969e6	−1.00769
$285$	187031.	0.136396
$286$	41060.3	0.0296830
$287$	−495291.	−0.354941
$288$	−343600.	−0.244102
$289$	145545.	0.102506
$290$	−46587.3	−0.0325292
$291$	2.43884e6	1.68831
$292$	341088.	0.234105
$293$	163837.	0.111492	0.0557459	−	0.998445i	$-0.482246\pi$
$293$	163837.	0.111492	0.0557459	+	0.998445i	$0.482246\pi$
$294$	47613.3	0.0321263
$295$	288953.	0.193318
$296$	−160287.	−0.106333
$297$	−141750.	−0.0932467
$298$	33641.0	0.0219446
$299$	−62750.9	−0.0405921
$300$	−409666.	−0.262801
$301$	1.43104e6	0.910408
$302$	−271803.	−0.171489
$303$	−1.37482e6	−0.860277
$304$	356851.	0.221464
$305$	799577.	0.492165
$306$	−142132.	−0.0867740
$307$	−1.46111e6	−0.884785	−0.442393	−	0.896822i	$-0.645870\pi$
$307$	−1.46111e6	−0.884785	−0.442393	+	0.896822i	$0.645870\pi$
$308$	436954.	0.262458
$309$	3.11522e6	1.85606
$310$	31744.8	0.0187615
$311$	−412561.	−0.241873	−0.120936	−	0.992660i	$-0.538590\pi$
$311$	−412561.	−0.241873	−0.120936	+	0.992660i	$0.538590\pi$
$312$	−447464.	−0.260239
$313$	2.78479e6	1.60669	0.803344	−	0.595516i	$-0.203052\pi$
$313$	2.78479e6	1.60669	0.803344	+	0.595516i	$0.203052\pi$
$314$	−171867.	−0.0983710
$315$	−532253.	−0.302233
$316$	3.44463e6	1.94055
$317$	−1.13553e6	−0.634674	−0.317337	−	0.948313i	$-0.602789\pi$
$317$	−1.13553e6	−0.634674	−0.317337	+	0.948313i	$0.602789\pi$
$318$	−32219.8	−0.0178672
$319$	370121.	0.203642
$320$	−762742.	−0.416393
$321$	4.48693e6	2.43045
$322$	7835.90	0.00421162
$323$	451669.	0.240887
$324$	2.20105e6	1.16484
$325$	−348135.	−0.182827
$326$	−186299.	−0.0970884
$327$	857633.	0.443539
$328$	168158.	0.0863043
$329$	1.56735e6	0.798319
$330$	−38191.1	−0.0193053
$331$	62356.8	0.0312834	0.0156417	−	0.999878i	$-0.495021\pi$
$331$	62356.8	0.0312834	0.0156417	+	0.999878i	$0.495021\pi$
$332$	−1.44112e6	−0.717557
$333$	−771055.	−0.381044
$334$	−95138.3	−0.0466648
$335$	792121.	0.385638
$336$	−2.33891e6	−1.13023
$337$	−1.12521e6	−0.539706	−0.269853	−	0.962902i	$-0.586975\pi$
$337$	−1.12521e6	−0.539706	−0.269853	+	0.962902i	$0.586975\pi$
$338$	37178.0	0.0177008
$339$	2.48347e6	1.17370
$340$	−989319.	−0.464129
$341$	−252202.	−0.117453
$342$	−41009.8	−0.0189593
$343$	2.34951e6	1.07830
$344$	−485858.	−0.221367
$345$	58365.9	0.0264004
$346$	−371839.	−0.166980
$347$	−122496.	−0.0546135	−0.0273067	−	0.999627i	$-0.508693\pi$
$347$	−122496.	−0.0546135	−0.0273067	+	0.999627i	$0.508693\pi$
$348$	−2.00497e6	−0.887484
$349$	3.69774e6	1.62507	0.812536	−	0.582911i	$-0.198087\pi$
$349$	3.69774e6	1.62507	0.812536	+	0.582911i	$0.198087\pi$
$350$	43472.7	0.0189691
$351$	652540.	0.282709
$352$	−222960.	−0.0959115
$353$	−2.44140e6	−1.04280	−0.521401	−	0.853312i	$-0.674590\pi$
$353$	−2.44140e6	−1.04280	−0.521401	+	0.853312i	$0.674590\pi$
$354$	−145923.	−0.0618893
$355$	1.08262e6	0.455939
$356$	−2.27810e6	−0.952681
$357$	−2.96038e6	−1.22935
$358$	−10252.0	−0.00422767
$359$	−3.74687e6	−1.53438	−0.767188	−	0.641422i	$-0.778345\pi$
$359$	−3.74687e6	−1.53438	−0.767188	+	0.641422i	$0.778345\pi$
$360$	180707.	0.0734883
$361$	130321.	0.0526316
$362$	254180.	0.101946
$363$	303415.	0.120857
$364$	−2.01149e6	−0.795728
$365$	−269602.	−0.105923
$366$	−403791.	−0.157563
$367$	−135654.	−0.0525738	−0.0262869	−	0.999654i	$-0.508368\pi$
$367$	−135654.	−0.0525738	−0.0262869	+	0.999654i	$0.508368\pi$
$368$	111361.	0.0428660
$369$	808918.	0.309271
$370$	62977.3	0.0239155
$371$	−291376.	−0.109905
$372$	1.36620e6	0.511866
$373$	3.31430e6	1.23344	0.616722	−	0.787181i	$-0.288460\pi$
$373$	3.31430e6	1.23344	0.616722	+	0.787181i	$0.288460\pi$
$374$	−92229.1	−0.0340948
$375$	323807.	0.118907
$376$	−532136.	−0.194112
$377$	−1.70383e6	−0.617409
$378$	−81484.6	−0.0293323
$379$	2.96745e6	1.06117	0.530585	−	0.847631i	$-0.321972\pi$
$379$	2.96745e6	1.06117	0.530585	+	0.847631i	$0.321972\pi$
$380$	−285450.	−0.101408
$381$	810211.	0.285947
$382$	−510087.	−0.178849
$383$	−40599.5	−0.0141424	−0.00707121	−	0.999975i	$-0.502251\pi$
$383$	−40599.5	−0.0141424	−0.00707121	+	0.999975i	$0.502251\pi$
$384$	1.60715e6	0.556198
$385$	−345376.	−0.118752
$386$	−65891.7	−0.0225093
$387$	−2.33720e6	−0.793266
$388$	−3.72221e6	−1.25522
$389$	1.75224e6	0.587109	0.293555	−	0.955942i	$-0.405162\pi$
$389$	1.75224e6	0.587109	0.293555	+	0.955942i	$0.405162\pi$
$390$	175810.	0.0585305
$391$	140950.	0.0466255
$392$	−146189.	−0.0480508
$393$	−574545.	−0.187648
$394$	199026.	0.0645907
$395$	−2.72270e6	−0.878024
$396$	−713641.	−0.228687
$397$	663352.	0.211236	0.105618	−	0.994407i	$-0.466318\pi$
$397$	663352.	0.211236	0.105618	+	0.994407i	$0.466318\pi$
$398$	−154960.	−0.0490357
$399$	−854164.	−0.268602
$400$	617818.	0.193068
$401$	−2.03063e6	−0.630624	−0.315312	−	0.948988i	$-0.602109\pi$
$401$	−2.03063e6	−0.630624	−0.315312	+	0.948988i	$0.602109\pi$
$402$	−400026.	−0.123459
$403$	1.16100e6	0.356097
$404$	2.09827e6	0.639599
$405$	−1.73975e6	−0.527047
$406$	212762.	0.0640589
$407$	−500334.	−0.149718
$408$	1.00509e6	0.298919
$409$	4.46219e6	1.31898	0.659492	−	0.751712i	$-0.270772\pi$
$409$	4.46219e6	1.31898	0.659492	+	0.751712i	$0.270772\pi$
$410$	−66069.8	−0.0194108
$411$	733903.	0.214306
$412$	−4.75451e6	−1.37995
$413$	−1.31964e6	−0.380697
$414$	−12797.7	−0.00366971
$415$	1.13909e6	0.324667
$416$	1.02638e6	0.290788
$417$	3.58552e6	1.00975
$418$	−26611.1	−0.00744940
$419$	1.44867e6	0.403121	0.201561	−	0.979476i	$-0.435399\pi$
$419$	1.44867e6	0.403121	0.201561	+	0.979476i	$0.435399\pi$
$420$	1.87093e6	0.517528
$421$	−3.16817e6	−0.871171	−0.435585	−	0.900147i	$-0.643459\pi$
$421$	−3.16817e6	−0.871171	−0.435585	+	0.900147i	$0.643459\pi$
$422$	−514986.	−0.140771
$423$	−2.55982e6	−0.695600
$424$	98926.0	0.0267237
$425$	781975.	0.210001
$426$	−546731.	−0.145965
$427$	−3.65164e6	−0.969210
$428$	−6.84803e6	−1.80699
$429$	−1.39675e6	−0.366418
$430$	190895.	0.0497879
$431$	6.58226e6	1.70680	0.853398	−	0.521260i	$-0.174538\pi$
$431$	6.58226e6	1.70680	0.853398	+	0.521260i	$0.174538\pi$
$432$	−1.15803e6	−0.298545
$433$	76748.9	0.0196722	0.00983609	−	0.999952i	$-0.496869\pi$
$433$	76748.9	0.0196722	0.00983609	+	0.999952i	$0.496869\pi$
$434$	−144977.	−0.0369467
$435$	1.58477e6	0.401552
$436$	−1.30894e6	−0.329763
$437$	40668.6	0.0101872
$438$	136151.	0.0339105
$439$	−1.53842e6	−0.380989	−0.190495	−	0.981688i	$-0.561009\pi$
$439$	−1.53842e6	−0.380989	−0.190495	+	0.981688i	$0.561009\pi$
$440$	117260.	0.0288747
$441$	−703239.	−0.172189
$442$	424571.	0.103370
$443$	7.10213e6	1.71941	0.859705	−	0.510791i	$-0.170647\pi$
$443$	7.10213e6	1.71941	0.859705	+	0.510791i	$0.170647\pi$
$444$	2.71035e6	0.652480
$445$	1.80065e6	0.431051
$446$	493181.	0.117400
$447$	−1.14437e6	−0.270893
$448$	3.48341e6	0.819993
$449$	4.40451e6	1.03105	0.515527	−	0.856873i	$-0.327596\pi$
$449$	4.40451e6	1.03105	0.515527	+	0.856873i	$0.327596\pi$
$450$	−71000.4	−0.0165283
$451$	524903.	0.121517
$452$	−3.79031e6	−0.872627
$453$	9.24595e6	2.11693
$454$	188737.	0.0429752
$455$	1.58992e6	0.360036
$456$	290000.	0.0653109
$457$	1.11602e6	0.249966	0.124983	−	0.992159i	$-0.460112\pi$
$457$	1.11602e6	0.249966	0.124983	+	0.992159i	$0.460112\pi$
$458$	725494.	0.161611
$459$	−1.46572e6	−0.324728
$460$	−89079.1	−0.0196282
$461$	6.20830e6	1.36057	0.680284	−	0.732949i	$-0.261856\pi$
$461$	6.20830e6	1.36057	0.680284	+	0.732949i	$0.261856\pi$
$462$	174417.	0.0380175
$463$	3.42480e6	0.742476	0.371238	−	0.928538i	$-0.378933\pi$
$463$	3.42480e6	0.742476	0.371238	+	0.928538i	$0.378933\pi$
$464$	3.02370e6	0.651994
$465$	−1.07987e6	−0.231600
$466$	37125.6	0.00791971
$467$	93071.3	0.0197480	0.00987401	−	0.999951i	$-0.496857\pi$
$467$	93071.3	0.0197480	0.00987401	+	0.999951i	$0.496857\pi$
$468$	3.28520e6	0.693342
$469$	−3.61758e6	−0.759428
$470$	209078.	0.0436580
$471$	5.84640e6	1.21433
$472$	448034.	0.0925670
$473$	−1.51660e6	−0.311686
$474$	1.37498e6	0.281093
$475$	225625.	0.0458831
$476$	4.51818e6	0.914000
$477$	475880.	0.0957639
$478$	521291.	0.104354
$479$	−5.98996e6	−1.19285	−0.596424	−	0.802670i	$-0.703412\pi$
$479$	−5.98996e6	−1.19285	−0.596424	+	0.802670i	$0.703412\pi$
$480$	−954660.	−0.189124
$481$	2.30326e6	0.453920
$482$	−949737.	−0.186203
$483$	−266554.	−0.0519898
$484$	−463078.	−0.0898547
$485$	2.94210e6	0.567940
$486$	705158.	0.135424
$487$	4.39175e6	0.839103	0.419551	−	0.907732i	$-0.362187\pi$
$487$	4.39175e6	0.839103	0.419551	+	0.907732i	$0.362187\pi$
$488$	1.23978e6	0.235665
$489$	6.33736e6	1.19850
$490$	57438.3	0.0108072
$491$	1.21644e6	0.227713	0.113856	−	0.993497i	$-0.463680\pi$
$491$	1.21644e6	0.227713	0.113856	+	0.993497i	$0.463680\pi$
$492$	−2.84344e6	−0.529580
$493$	3.82711e6	0.709176
$494$	122502.	0.0225854
$495$	564074.	0.103472
$496$	−2.06036e6	−0.376045
$497$	−4.94430e6	−0.897870
$498$	−575247.	−0.103940
$499$	162759.	0.0292613	0.0146307	−	0.999893i	$-0.495343\pi$
$499$	162759.	0.0292613	0.0146307	+	0.999893i	$0.495343\pi$
$500$	−494201.	−0.0884053
$501$	3.23633e6	0.576048
$502$	1.00281e6	0.177607
$503$	4.48157e6	0.789788	0.394894	−	0.918727i	$-0.370781\pi$
$503$	4.48157e6	0.789788	0.394894	+	0.918727i	$0.370781\pi$
$504$	−825281.	−0.144719
$505$	−1.65851e6	−0.289394
$506$	−8304.38	−0.00144189
$507$	−1.26469e6	−0.218506
$508$	−1.23656e6	−0.212596
$509$	−6.49298e6	−1.11084	−0.555418	−	0.831571i	$-0.687442\pi$
$509$	−6.49298e6	−1.11084	−0.555418	+	0.831571i	$0.687442\pi$
$510$	−394902.	−0.0672301
$511$	1.23126e6	0.208592
$512$	−3.04765e6	−0.513795
$513$	−422908.	−0.0709501
$514$	375070.	0.0626187
$515$	3.75805e6	0.624373
$516$	8.21553e6	1.35835
$517$	−1.66106e6	−0.273312
$518$	−287615.	−0.0470963
$519$	1.26489e7	2.06127
$520$	−539798.	−0.0875433
$521$	−3.01994e6	−0.487421	−0.243710	−	0.969848i	$-0.578365\pi$
$521$	−3.01994e6	−0.487421	−0.243710	+	0.969848i	$0.578365\pi$
$522$	−347487.	−0.0558165
$523$	661888.	0.105811	0.0529055	−	0.998600i	$-0.483152\pi$
$523$	661888.	0.105811	0.0529055	+	0.998600i	$0.483152\pi$
$524$	876881.	0.139512
$525$	−1.47882e6	−0.234162
$526$	−335181.	−0.0528221
$527$	−2.60781e6	−0.409025
$528$	2.47875e6	0.386944
$529$	−6.42365e6	−0.998028
$530$	−38868.4	−0.00601045
$531$	2.15525e6	0.331713
$532$	1.30364e6	0.199700
$533$	−2.41636e6	−0.368420
$534$	−909338.	−0.137998
$535$	5.41280e6	0.817594
$536$	1.22822e6	0.184656
$537$	348743.	0.0521879
$538$	114333.	0.0170300
$539$	−456328.	−0.0676559
$540$	926323.	0.136703
$541$	−4.71067e6	−0.691974	−0.345987	−	0.938239i	$-0.612456\pi$
$541$	−4.71067e6	−0.691974	−0.345987	+	0.938239i	$0.612456\pi$
$542$	−744643.	−0.108880
$543$	−8.64646e6	−1.25846
$544$	−2.30545e6	−0.334009
$545$	1.03461e6	0.149205
$546$	−802918.	−0.115263
$547$	7.59966e6	1.08599	0.542995	−	0.839736i	$-0.317290\pi$
$547$	7.59966e6	1.08599	0.542995	+	0.839736i	$0.317290\pi$
$548$	−1.12010e6	−0.159332
$549$	5.96392e6	0.844502
$550$	−46071.8	−0.00649424
$551$	1.10425e6	0.154948
$552$	90498.8	0.0126414
$553$	1.24344e7	1.72907
$554$	511109.	0.0707520
$555$	−2.14230e6	−0.295222
$556$	−5.47228e6	−0.750726
$557$	−1.25435e7	−1.71309	−0.856546	−	0.516070i	$-0.827394\pi$
$557$	−1.25435e7	−1.71309	−0.856546	+	0.516070i	$0.827394\pi$
$558$	236779.	0.0321928
$559$	6.98157e6	0.944982
$560$	−2.82155e6	−0.380204
$561$	3.13737e6	0.420880
$562$	−688117.	−0.0919013
$563$	1.28593e7	1.70980	0.854901	−	0.518792i	$-0.173618\pi$
$563$	1.28593e7	1.70980	0.854901	+	0.518792i	$0.173618\pi$
$564$	8.99807e6	1.19111
$565$	2.99593e6	0.394830
$566$	−426831.	−0.0560035
$567$	7.94537e6	1.03790
$568$	1.67865e6	0.218318
$569$	−9.15727e6	−1.18573	−0.592865	−	0.805302i	$-0.702003\pi$
$569$	−9.15727e6	−1.18573	−0.592865	+	0.805302i	$0.702003\pi$
$570$	−113942.	−0.0146891
$571$	−1.21179e6	−0.155538	−0.0777691	−	0.996971i	$-0.524780\pi$
$571$	−1.21179e6	−0.155538	−0.0777691	+	0.996971i	$0.524780\pi$
$572$	2.13175e6	0.272425
$573$	1.73517e7	2.20777
$574$	301738.	0.0382253
$575$	70409.6	0.00888101
$576$	−5.68917e6	−0.714484
$577$	6.20841e6	0.776321	0.388160	−	0.921592i	$-0.373111\pi$
$577$	6.20841e6	0.776321	0.388160	+	0.921592i	$0.373111\pi$
$578$	−88667.7	−0.0110394
$579$	2.24145e6	0.277864
$580$	−2.41870e6	−0.298546
$581$	−5.20217e6	−0.639359
$582$	−1.48578e6	−0.181822
$583$	308796.	0.0376271
$584$	−418030.	−0.0507195
$585$	−2.59668e6	−0.313710
$586$	−99811.6	−0.0120071
$587$	−1.08448e7	−1.29906	−0.649528	−	0.760338i	$-0.725033\pi$
$587$	−1.08448e7	−1.29906	−0.649528	+	0.760338i	$0.725033\pi$
$588$	2.47197e6	0.294849
$589$	−752437.	−0.0893680
$590$	−176034.	−0.0208193
$591$	−6.77030e6	−0.797332
$592$	−4.08747e6	−0.479347
$593$	−1.09447e7	−1.27811	−0.639054	−	0.769162i	$-0.720674\pi$
$593$	−1.09447e7	−1.27811	−0.639054	+	0.769162i	$0.720674\pi$
$594$	86356.3	0.0100422
$595$	−3.57125e6	−0.413549
$596$	1.74656e6	0.201404
$597$	5.27130e6	0.605316
$598$	38228.7	0.00437156
$599$	−1.27587e7	−1.45292	−0.726459	−	0.687210i	$-0.758835\pi$
$599$	−1.27587e7	−1.45292	−0.726459	+	0.687210i	$0.758835\pi$
$600$	502077.	0.0569367
$601$	−6.73618e6	−0.760725	−0.380363	−	0.924837i	$-0.624201\pi$
$601$	−6.73618e6	−0.760725	−0.380363	+	0.924837i	$0.624201\pi$
$602$	−871810.	−0.0980462
$603$	5.90830e6	0.661712
$604$	−1.41113e7	−1.57389
$605$	366025.	0.0406558
$606$	837557.	0.0926473
$607$	−4.75731e6	−0.524071	−0.262035	−	0.965058i	$-0.584394\pi$
$607$	−4.75731e6	−0.524071	−0.262035	+	0.965058i	$0.584394\pi$
$608$	−665195.	−0.0729777
$609$	−7.23756e6	−0.790768
$610$	−487113.	−0.0530036
$611$	7.64657e6	0.828636
$612$	−7.37917e6	−0.796396
$613$	266874.	0.0286850	0.0143425	−	0.999897i	$-0.495434\pi$
$613$	266874.	0.0286850	0.0143425	+	0.999897i	$0.495434\pi$
$614$	890130.	0.0952867
$615$	2.24750e6	0.239614
$616$	−535520.	−0.0568623
$617$	−2.11758e6	−0.223937	−0.111969	−	0.993712i	$-0.535716\pi$
$617$	−2.11758e6	−0.223937	−0.111969	+	0.993712i	$0.535716\pi$
$618$	−1.89784e6	−0.199888
$619$	1.96652e6	0.206287	0.103144	−	0.994666i	$-0.467110\pi$
$619$	1.96652e6	0.206287	0.103144	+	0.994666i	$0.467110\pi$
$620$	1.64811e6	0.172190
$621$	−131975.	−0.0137329
$622$	251338.	0.0260484
$623$	−8.22349e6	−0.848860
$624$	−1.14108e7	−1.17315
$625$	390625.	0.0400000
$626$	−1.69653e6	−0.173032
$627$	905231.	0.0919582
$628$	−8.92288e6	−0.902830
$629$	−5.17353e6	−0.521388
$630$	324256.	0.0325489
$631$	1.73409e7	1.73379	0.866896	−	0.498489i	$-0.166112\pi$
$631$	1.73409e7	1.73379	0.866896	+	0.498489i	$0.166112\pi$
$632$	−4.22166e6	−0.420427
$633$	1.75183e7	1.73773
$634$	691781.	0.0683511
$635$	977397.	0.0961915
$636$	−1.67277e6	−0.163981
$637$	2.10068e6	0.205122
$638$	−225483.	−0.0219312
$639$	8.07511e6	0.782342
$640$	1.93879e6	0.187103
$641$	−3.94482e6	−0.379212	−0.189606	−	0.981860i	$-0.560721\pi$
$641$	−3.94482e6	−0.379212	−0.189606	+	0.981860i	$0.560721\pi$
$642$	−2.73350e6	−0.261747
$643$	−1.81584e7	−1.73201	−0.866005	−	0.500035i	$-0.833321\pi$
$643$	−1.81584e7	−1.73201	−0.866005	+	0.500035i	$0.833321\pi$
$644$	406820.	0.0386534
$645$	−6.49370e6	−0.614600
$646$	−275163.	−0.0259423
$647$	1.17027e7	1.09907	0.549537	−	0.835469i	$-0.314804\pi$
$647$	1.17027e7	1.09907	0.549537	+	0.835469i	$0.314804\pi$
$648$	−2.69756e6	−0.252367
$649$	1.39853e6	0.130335
$650$	212089.	0.0196895
$651$	4.93171e6	0.456084
$652$	−9.67220e6	−0.891059
$653$	−3.95039e6	−0.362541	−0.181271	−	0.983433i	$-0.558021\pi$
$653$	−3.95039e6	−0.362541	−0.181271	+	0.983433i	$0.558021\pi$
$654$	−522482.	−0.0477669
$655$	−693102.	−0.0631239
$656$	4.28819e6	0.389058
$657$	−2.01092e6	−0.181753
$658$	−954851.	−0.0859748
$659$	1.24284e7	1.11481	0.557406	−	0.830240i	$-0.311797\pi$
$659$	1.24284e7	1.11481	0.557406	+	0.830240i	$0.311797\pi$
$660$	−1.98279e6	−0.177180
$661$	−4.42595e6	−0.394006	−0.197003	−	0.980403i	$-0.563121\pi$
$661$	−4.42595e6	−0.394006	−0.197003	+	0.980403i	$0.563121\pi$
$662$	−37988.6	−0.00336905
$663$	−1.44427e7	−1.27604
$664$	1.76621e6	0.155461
$665$	−1.03042e6	−0.0903567
$666$	469737.	0.0410364
$667$	344596.	0.0299913
$668$	−4.93935e6	−0.428281
$669$	−1.67766e7	−1.44923
$670$	−482571.	−0.0415311
$671$	3.86995e6	0.331818
$672$	4.35989e6	0.372437
$673$	1.16679e6	0.0993011	0.0496506	−	0.998767i	$-0.484189\pi$
$673$	1.16679e6	0.0993011	0.0496506	+	0.998767i	$0.484189\pi$
$674$	685491.	0.0581235
$675$	−732182.	−0.0618529
$676$	1.93019e6	0.162455
$677$	1.01941e6	0.0854822	0.0427411	−	0.999086i	$-0.486391\pi$
$677$	1.01941e6	0.0854822	0.0427411	+	0.999086i	$0.486391\pi$
$678$	−1.51296e6	−0.126402
$679$	−1.34364e7	−1.11843
$680$	1.21249e6	0.100555
$681$	−6.42030e6	−0.530503
$682$	153645.	0.0126490
$683$	−1.53024e7	−1.25519	−0.627594	−	0.778541i	$-0.715960\pi$
$683$	−1.53024e7	−1.25519	−0.627594	+	0.778541i	$0.715960\pi$
$684$	−2.12913e6	−0.174005
$685$	885344.	0.0720917
$686$	−1.43135e6	−0.116128
$687$	−2.46792e7	−1.99498
$688$	−1.23898e7	−0.997917
$689$	−1.42153e6	−0.114079
$690$	−35557.3	−0.00284319
$691$	1.44395e7	1.15042	0.575211	−	0.818005i	$-0.304920\pi$
$691$	1.44395e7	1.15042	0.575211	+	0.818005i	$0.304920\pi$
$692$	−1.93050e7	−1.53251
$693$	−2.57610e6	−0.203765
$694$	74626.5	0.00588158
$695$	4.32539e6	0.339675
$696$	2.45725e6	0.192276
$697$	5.42758e6	0.423179
$698$	−2.25271e6	−0.175012
$699$	−1.26291e6	−0.0977638
$700$	2.25699e6	0.174095
$701$	1.06826e7	0.821074	0.410537	−	0.911844i	$-0.365341\pi$
$701$	1.06826e7	0.821074	0.410537	+	0.911844i	$0.365341\pi$
$702$	−397536.	−0.0304462
$703$	−1.49273e6	−0.113918
$704$	−3.69167e6	−0.280732
$705$	−7.11223e6	−0.538931
$706$	1.48733e6	0.112304
$707$	7.57434e6	0.569897
$708$	−7.57597e6	−0.568009
$709$	−4.42131e6	−0.330321	−0.165160	−	0.986267i	$-0.552814\pi$
$709$	−4.42131e6	−0.330321	−0.165160	+	0.986267i	$0.552814\pi$
$710$	−659549.	−0.0491022
$711$	−2.03081e7	−1.50659
$712$	2.79198e6	0.206401
$713$	−234809.	−0.0172978
$714$	1.80350e6	0.132395
$715$	−1.68497e6	−0.123262
$716$	−532258.	−0.0388007
$717$	−1.77328e7	−1.28819
$718$	2.28264e6	0.165244
$719$	−1.95698e7	−1.41177	−0.705885	−	0.708326i	$-0.749451\pi$
$719$	−1.95698e7	−1.41177	−0.705885	+	0.708326i	$0.749451\pi$
$720$	4.60820e6	0.331284
$721$	−1.71629e7	−1.22956
$722$	−79393.3	−0.00566814
$723$	3.23073e7	2.29856
$724$	1.31964e7	0.935639
$725$	1.91178e6	0.135081
$726$	−184845.	−0.0130156
$727$	−2.24777e7	−1.57731	−0.788654	−	0.614837i	$-0.789222\pi$
$727$	−2.24777e7	−1.57731	−0.788654	+	0.614837i	$0.789222\pi$
$728$	2.46524e6	0.172397
$729$	−7.07705e6	−0.493212
$730$	164245.	0.0114074
$731$	−1.56819e7	−1.08544
$732$	−2.09638e7	−1.44608
$733$	−1.36016e7	−0.935040	−0.467520	−	0.883982i	$-0.654852\pi$
$733$	−1.36016e7	−0.935040	−0.467520	+	0.883982i	$0.654852\pi$
$734$	82642.5	0.00566192
$735$	−1.95388e6	−0.133408
$736$	−207584.	−0.0141254
$737$	3.83386e6	0.259997
$738$	−492804.	−0.0333068
$739$	9.16190e6	0.617127	0.308563	−	0.951204i	$-0.400152\pi$
$739$	9.16190e6	0.617127	0.308563	+	0.951204i	$0.400152\pi$
$740$	3.26962e6	0.219492
$741$	−4.16717e6	−0.278802
$742$	177510.	0.0118362
$743$	1.23617e7	0.821500	0.410750	−	0.911748i	$-0.365267\pi$
$743$	1.23617e7	0.821500	0.410750	+	0.911748i	$0.365267\pi$
$744$	−1.67438e6	−0.110897
$745$	−1.38051e6	−0.0911273
$746$	−2.01912e6	−0.132836
$747$	8.49628e6	0.557093
$748$	−4.78830e6	−0.312916
$749$	−2.47201e7	−1.61007
$750$	−197268.	−0.0128057
$751$	9.61270e6	0.621936	0.310968	−	0.950420i	$-0.399347\pi$
$751$	9.61270e6	0.621936	0.310968	+	0.950420i	$0.399347\pi$
$752$	−1.35700e7	−0.875054
$753$	−3.41128e7	−2.19245
$754$	1.03800e6	0.0664917
$755$	1.11538e7	0.712127
$756$	−4.23048e6	−0.269206
$757$	−2.55706e6	−0.162182	−0.0810908	−	0.996707i	$-0.525840\pi$
$757$	−2.55706e6	−0.162182	−0.0810908	+	0.996707i	$0.525840\pi$
$758$	−1.80781e6	−0.114283
$759$	282491.	0.0177992
$760$	349841.	0.0219703
$761$	6.00751e6	0.376039	0.188019	−	0.982165i	$-0.439793\pi$
$761$	6.00751e6	0.376039	0.188019	+	0.982165i	$0.439793\pi$
$762$	−493591.	−0.0307950
$763$	−4.72500e6	−0.293826
$764$	−2.64824e7	−1.64144
$765$	5.83262e6	0.360338
$766$	24733.8	0.00152307
$767$	−6.43806e6	−0.395154
$768$	1.92536e7	1.17790
$769$	−1.76926e7	−1.07889	−0.539443	−	0.842022i	$-0.681365\pi$
$769$	−1.76926e7	−1.07889	−0.539443	+	0.842022i	$0.681365\pi$
$770$	210408.	0.0127890
$771$	−1.27588e7	−0.772989
$772$	−3.42093e6	−0.206586
$773$	−2.65637e7	−1.59897	−0.799485	−	0.600686i	$-0.794894\pi$
$773$	−2.65637e7	−1.59897	−0.799485	+	0.600686i	$0.794894\pi$
$774$	1.42386e6	0.0854306
$775$	−1.30270e6	−0.0779092
$776$	4.56185e6	0.271948
$777$	9.78382e6	0.581374
$778$	−1.06749e6	−0.0632286
$779$	1.56603e6	0.0924607
$780$	9.12763e6	0.537182
$781$	5.23990e6	0.307394
$782$	−85868.6	−0.00502132
$783$	−3.58342e6	−0.208878
$784$	−3.72797e6	−0.216612
$785$	7.05280e6	0.408496
$786$	350021.	0.0202087
$787$	2.44560e7	1.40750	0.703751	−	0.710446i	$-0.251507\pi$
$787$	2.44560e7	1.40750	0.703751	+	0.710446i	$0.251507\pi$
$788$	1.03330e7	0.592801
$789$	1.14019e7	0.652056
$790$	1.65870e6	0.0945586
$791$	−1.36823e7	−0.777530
$792$	874621.	0.0495458
$793$	−1.78151e7	−1.00602
$794$	−404123.	−0.0227490
$795$	1.32219e6	0.0741952
$796$	−8.04515e6	−0.450041
$797$	1.74911e6	0.0975376	0.0487688	−	0.998810i	$-0.484470\pi$
$797$	1.74911e6	0.0975376	0.0487688	+	0.998810i	$0.484470\pi$
$798$	520368.	0.0289270
$799$	−1.71756e7	−0.951799
$800$	−1.15165e6	−0.0636205
$801$	1.34307e7	0.739637
$802$	1.23709e6	0.0679149
$803$	−1.30487e6	−0.0714134
$804$	−2.07683e7	−1.13308
$805$	−321558.	−0.0174892
$806$	−707295.	−0.0383498
$807$	−3.88927e6	−0.210225
$808$	−2.57159e6	−0.138571
$809$	−9.47251e6	−0.508855	−0.254427	−	0.967092i	$-0.581887\pi$
$809$	−9.47251e6	−0.508855	−0.254427	+	0.967092i	$0.581887\pi$
$810$	1.05988e6	0.0567602
$811$	−8.05797e6	−0.430203	−0.215101	−	0.976592i	$-0.569008\pi$
$811$	−8.05797e6	−0.430203	−0.215101	+	0.976592i	$0.569008\pi$
$812$	1.10461e7	0.587921
$813$	2.53306e7	1.34406
$814$	304810.	0.0161238
$815$	7.64507e6	0.403170
$816$	2.56307e7	1.34752
$817$	−4.52473e6	−0.237158
$818$	−2.71842e6	−0.142048
$819$	1.18589e7	0.617783
$820$	−3.43018e6	−0.178149
$821$	−2.53676e7	−1.31347	−0.656736	−	0.754121i	$-0.728063\pi$
$821$	−2.53676e7	−1.31347	−0.656736	+	0.754121i	$0.728063\pi$
$822$	−447104.	−0.0230796
$823$	−2.45044e7	−1.26109	−0.630544	−	0.776154i	$-0.717168\pi$
$823$	−2.45044e7	−1.26109	−0.630544	+	0.776154i	$0.717168\pi$
$824$	5.82702e6	0.298970
$825$	1.56723e6	0.0801673
$826$	803941.	0.0409991
$827$	2.50859e6	0.127546	0.0637729	−	0.997964i	$-0.479687\pi$
$827$	2.50859e6	0.127546	0.0637729	+	0.997964i	$0.479687\pi$
$828$	−664426.	−0.0336799
$829$	2.57470e7	1.30119	0.650594	−	0.759426i	$-0.274520\pi$
$829$	2.57470e7	1.30119	0.650594	+	0.759426i	$0.274520\pi$
$830$	−693949.	−0.0349649
$831$	−1.73864e7	−0.873390
$832$	1.69944e7	0.851133
$833$	−4.71851e6	−0.235609
$834$	−2.18435e6	−0.108744
$835$	3.90415e6	0.193780
$836$	−1.38158e6	−0.0683692
$837$	2.44176e6	0.120473
$838$	−882552.	−0.0434140
$839$	4.72133e6	0.231558	0.115779	−	0.993275i	$-0.463064\pi$
$839$	4.72133e6	0.231558	0.115779	+	0.993275i	$0.463064\pi$
$840$	−2.29297e6	−0.112124
$841$	−1.11546e7	−0.543830
$842$	1.93009e6	0.0938205
$843$	2.34077e7	1.13446
$844$	−2.67368e7	−1.29197
$845$	−1.52565e6	−0.0735046
$846$	1.55948e6	0.0749124
$847$	−1.67162e6	−0.0800625
$848$	2.52271e6	0.120470
$849$	1.45196e7	0.691328
$850$	−476390.	−0.0226160
$851$	−465829.	−0.0220497
$852$	−2.83849e7	−1.33964
$853$	3.31831e7	1.56151	0.780754	−	0.624839i	$-0.214835\pi$
$853$	3.31831e7	1.56151	0.780754	+	0.624839i	$0.214835\pi$
$854$	2.22463e6	0.104379
$855$	1.68290e6	0.0787305
$856$	8.39278e6	0.391491
$857$	−1.51606e7	−0.705124	−0.352562	−	0.935788i	$-0.614689\pi$
$857$	−1.51606e7	−0.705124	−0.352562	+	0.935788i	$0.614689\pi$
$858$	850921.	0.0394613
$859$	−3.64591e7	−1.68586	−0.842932	−	0.538020i	$-0.819172\pi$
$859$	−3.64591e7	−1.68586	−0.842932	+	0.538020i	$0.819172\pi$
$860$	9.91080e6	0.456944
$861$	−1.02643e7	−0.471867
$862$	−4.01000e6	−0.183813
$863$	−2.98273e7	−1.36328	−0.681642	−	0.731685i	$-0.738734\pi$
$863$	−2.98273e7	−1.36328	−0.681642	+	0.731685i	$0.738734\pi$
$864$	2.15864e6	0.0983777
$865$	1.52590e7	0.693403
$866$	−46756.5	−0.00211859
$867$	3.01622e6	0.136275
$868$	−7.52686e6	−0.339090
$869$	−1.31779e7	−0.591964
$870$	−965461.	−0.0432451
$871$	−1.76490e7	−0.788268
$872$	1.60420e6	0.0714442
$873$	2.19446e7	0.974524
$874$	−24775.9	−0.00109711
$875$	−1.78397e6	−0.0787711
$876$	7.06861e6	0.311224
$877$	−916487.	−0.0402372	−0.0201186	−	0.999798i	$-0.506404\pi$
$877$	−916487.	−0.0402372	−0.0201186	+	0.999798i	$0.506404\pi$
$878$	937225.	0.0410306
$879$	3.39530e6	0.148220
$880$	2.99024e6	0.130166
$881$	3.07967e7	1.33680	0.668398	−	0.743804i	$-0.266981\pi$
$881$	3.07967e7	1.33680	0.668398	+	0.743804i	$0.266981\pi$
$882$	428423.	0.0185439
$883$	−4.44832e6	−0.191997	−0.0959984	−	0.995381i	$-0.530604\pi$
$883$	−4.44832e6	−0.191997	−0.0959984	+	0.995381i	$0.530604\pi$
$884$	2.20427e7	0.948710
$885$	5.98817e6	0.257002
$886$	−4.32671e6	−0.185171
$887$	−2.81458e7	−1.20117	−0.600584	−	0.799561i	$-0.705065\pi$
$887$	−2.81458e7	−1.20117	−0.600584	+	0.799561i	$0.705065\pi$
$888$	−3.32173e6	−0.141362
$889$	−4.46373e6	−0.189428
$890$	−1.09698e6	−0.0464220
$891$	−8.42039e6	−0.355335
$892$	2.56047e7	1.07748
$893$	−4.95572e6	−0.207959
$894$	697165.	0.0291737
$895$	420706.	0.0175558
$896$	−8.85437e6	−0.368458
$897$	−1.30043e6	−0.0539642
$898$	−2.68329e6	−0.111039
$899$	−6.37561e6	−0.263101
$900$	−3.68616e6	−0.151694
$901$	3.19301e6	0.131035
$902$	−319778.	−0.0130868
$903$	2.96565e7	1.21032
$904$	4.64531e6	0.189057
$905$	−1.04306e7	−0.423341
$906$	−5.63276e6	−0.227982
$907$	8.55681e6	0.345377	0.172689	−	0.984976i	$-0.444755\pi$
$907$	8.55681e6	0.345377	0.172689	+	0.984976i	$0.444755\pi$
$908$	9.79878e6	0.394419
$909$	−1.23705e7	−0.496569
$910$	−968599.	−0.0387740
$911$	1.10075e7	0.439434	0.219717	−	0.975564i	$-0.429487\pi$
$911$	1.10075e7	0.439434	0.219717	+	0.975564i	$0.429487\pi$
$912$	7.39528e6	0.294420
$913$	5.51319e6	0.218890
$914$	−679893.	−0.0269200
$915$	1.65702e7	0.654297
$916$	3.76659e7	1.48323
$917$	3.16537e6	0.124309
$918$	892938.	0.0349715
$919$	2.27983e7	0.890458	0.445229	−	0.895417i	$-0.353122\pi$
$919$	2.27983e7	0.890458	0.445229	+	0.895417i	$0.353122\pi$
$920$	109173.	0.00425252
$921$	−3.02796e7	−1.17626
$922$	−3.78218e6	−0.146526
$923$	−2.41216e7	−0.931968
$924$	9.05530e6	0.348918
$925$	−2.58437e6	−0.0993116
$926$	−2.08643e6	−0.0799607
$927$	2.80307e7	1.07136
$928$	−5.63638e6	−0.214848
$929$	−1.70404e7	−0.647799	−0.323900	−	0.946091i	$-0.604994\pi$
$929$	−1.70404e7	−0.647799	−0.323900	+	0.946091i	$0.604994\pi$
$930$	657869.	0.0249421
$931$	−1.36144e6	−0.0514784
$932$	1.92747e6	0.0726855
$933$	−8.54978e6	−0.321552
$934$	−56700.3	−0.00212676
$935$	3.78476e6	0.141582
$936$	−4.02626e6	−0.150215
$937$	1.60954e7	0.598898	0.299449	−	0.954112i	$-0.403197\pi$
$937$	1.60954e7	0.598898	0.299449	+	0.954112i	$0.403197\pi$
$938$	2.20388e6	0.0817864
$939$	5.77111e7	2.13597
$940$	1.08548e7	0.400685
$941$	−4.32347e7	−1.59169	−0.795844	−	0.605501i	$-0.792973\pi$
$941$	−4.32347e7	−1.59169	−0.795844	+	0.605501i	$0.792973\pi$
$942$	−3.56171e6	−0.130777
$943$	488704.	0.0178964
$944$	1.14253e7	0.417290
$945$	3.34385e6	0.121805
$946$	923932.	0.0335670
$947$	−3.07297e7	−1.11348	−0.556741	−	0.830686i	$-0.687948\pi$
$947$	−3.07297e7	−1.11348	−0.556741	+	0.830686i	$0.687948\pi$
$948$	7.13854e7	2.57982
$949$	6.00691e6	0.216514
$950$	−137454.	−0.00494137
$951$	−2.35324e7	−0.843752
$952$	−5.53737e6	−0.198021
$953$	3.57437e7	1.27487	0.637437	−	0.770502i	$-0.279995\pi$
$953$	3.57437e7	1.27487	0.637437	+	0.770502i	$0.279995\pi$
$954$	−289913.	−0.0103133
$955$	2.09322e7	0.742687
$956$	2.70641e7	0.957744
$957$	7.67027e6	0.270726
$958$	3.64916e6	0.128463
$959$	−4.04333e6	−0.141969
$960$	−1.58068e7	−0.553563
$961$	−2.42848e7	−0.848254
$962$	−1.40317e6	−0.0488848
$963$	4.03732e7	1.40290
$964$	−4.93080e7	−1.70893
$965$	2.70397e6	0.0934723
$966$	162389.	0.00559903
$967$	−2.23534e7	−0.768738	−0.384369	−	0.923180i	$-0.625581\pi$
$967$	−2.23534e7	−0.768738	−0.384369	+	0.923180i	$0.625581\pi$
$968$	567537.	0.0194673
$969$	9.36024e6	0.320241
$970$	−1.79237e6	−0.0611642
$971$	2.85203e7	0.970747	0.485374	−	0.874307i	$-0.338684\pi$
$971$	2.85203e7	0.970747	0.485374	+	0.874307i	$0.338684\pi$
$972$	3.66101e7	1.24290
$973$	−1.97539e7	−0.668914
$974$	−2.67551e6	−0.0903670
$975$	−7.21464e6	−0.243054
$976$	3.16156e7	1.06237
$977$	−1.27850e7	−0.428514	−0.214257	−	0.976777i	$-0.568733\pi$
$977$	−1.27850e7	−0.428514	−0.214257	+	0.976777i	$0.568733\pi$
$978$	−3.86081e6	−0.129072
$979$	8.71514e6	0.290615
$980$	2.98205e6	0.0991860
$981$	7.71695e6	0.256020
$982$	−741072.	−0.0245235
$983$	3.98081e7	1.31398	0.656988	−	0.753901i	$-0.271830\pi$
$983$	3.98081e7	1.31398	0.656988	+	0.753901i	$0.271830\pi$
$984$	3.48485e6	0.114735
$985$	−8.16735e6	−0.268220
$986$	−2.33153e6	−0.0763745
$987$	3.24813e7	1.06130
$988$	6.36002e6	0.207284
$989$	−1.41201e6	−0.0459036
$990$	−343642.	−0.0111434
$991$	−1.86602e7	−0.603576	−0.301788	−	0.953375i	$-0.597583\pi$
$991$	−1.86602e7	−0.603576	−0.301788	+	0.953375i	$0.597583\pi$
$992$	3.84065e6	0.123916
$993$	1.29226e6	0.0415889
$994$	3.01213e6	0.0966959
$995$	6.35903e6	0.203626
$996$	−2.98654e7	−0.953937
$997$	4.30330e7	1.37108	0.685541	−	0.728034i	$-0.259566\pi$
$997$	4.30330e7	1.37108	0.685541	+	0.728034i	$0.259566\pi$
$998$	−99155.0	−0.00315129
$999$	4.84410e6	0.153568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.18	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.18	✓	40	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} +O(q^{10})\)	\(q-0.609213 q^{2} +20.7237 q^{3} -31.6289 q^{4} +25.0000 q^{5} -12.6251 q^{6} -114.174 q^{7} +38.7636 q^{8} +186.471 q^{9} -15.2303 q^{10} +121.000 q^{11} -655.466 q^{12} -557.016 q^{13} +69.5563 q^{14} +518.092 q^{15} +988.508 q^{16} +1251.16 q^{17} -113.601 q^{18} +361.000 q^{19} -790.721 q^{20} -2366.10 q^{21} -73.7148 q^{22} +112.655 q^{23} +803.324 q^{24} +625.000 q^{25} +339.342 q^{26} -1171.49 q^{27} +3611.19 q^{28} +3058.85 q^{29} -315.629 q^{30} -2084.31 q^{31} -1842.65 q^{32} +2507.57 q^{33} -762.224 q^{34} -2854.35 q^{35} -5897.86 q^{36} -4134.99 q^{37} -219.926 q^{38} -11543.4 q^{39} +969.089 q^{40} +4338.04 q^{41} +1441.46 q^{42} -12533.9 q^{43} -3827.09 q^{44} +4661.77 q^{45} -68.6312 q^{46} -13727.7 q^{47} +20485.5 q^{48} -3771.31 q^{49} -380.758 q^{50} +25928.6 q^{51} +17617.8 q^{52} +2552.04 q^{53} +713.688 q^{54} +3025.00 q^{55} -4425.79 q^{56} +7481.25 q^{57} -1863.49 q^{58} +11558.1 q^{59} -16386.7 q^{60} +31983.1 q^{61} +1269.79 q^{62} -21290.1 q^{63} -30509.7 q^{64} -13925.4 q^{65} -1527.64 q^{66} +31684.8 q^{67} -39572.8 q^{68} +2334.63 q^{69} +1738.91 q^{70} +43305.0 q^{71} +7228.27 q^{72} -10784.1 q^{73} +2519.09 q^{74} +12952.3 q^{75} -11418.0 q^{76} -13815.0 q^{77} +7032.41 q^{78} -108908. q^{79} +24712.7 q^{80} -69590.0 q^{81} -2642.79 q^{82} +45563.6 q^{83} +74837.2 q^{84} +31279.0 q^{85} +7635.80 q^{86} +63390.6 q^{87} +4690.39 q^{88} +72026.0 q^{89} -2840.01 q^{90} +63596.7 q^{91} -3563.16 q^{92} -43194.7 q^{93} +8363.13 q^{94} +9025.00 q^{95} -38186.4 q^{96} +117684. q^{97} +2297.53 q^{98} +22563.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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