LMFDB - Embedded newform 1045.6.a.e.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:	$1$
Dimension:	$38$
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)

$f(q)$	$=$	$q-1.87953 q^{2} +7.44103 q^{3} -28.4674 q^{4} +25.0000 q^{5} -13.9857 q^{6} +104.152 q^{7} +113.650 q^{8} -187.631 q^{9} +O(q^{10})$	\(q-1.87953 q^{2} +7.44103 q^{3} -28.4674 q^{4} +25.0000 q^{5} -13.9857 q^{6} +104.152 q^{7} +113.650 q^{8} -187.631 q^{9} -46.9883 q^{10} +121.000 q^{11} -211.826 q^{12} -401.367 q^{13} -195.758 q^{14} +186.026 q^{15} +697.346 q^{16} -1315.27 q^{17} +352.659 q^{18} -361.000 q^{19} -711.684 q^{20} +775.000 q^{21} -227.423 q^{22} +4013.91 q^{23} +845.676 q^{24} +625.000 q^{25} +754.383 q^{26} -3204.34 q^{27} -2964.94 q^{28} +8494.21 q^{29} -349.641 q^{30} -3360.42 q^{31} -4947.50 q^{32} +900.365 q^{33} +2472.09 q^{34} +2603.81 q^{35} +5341.36 q^{36} +7610.36 q^{37} +678.511 q^{38} -2986.58 q^{39} +2841.26 q^{40} -264.467 q^{41} -1456.64 q^{42} -23767.3 q^{43} -3444.55 q^{44} -4690.78 q^{45} -7544.28 q^{46} -10272.7 q^{47} +5188.97 q^{48} -5959.30 q^{49} -1174.71 q^{50} -9786.94 q^{51} +11425.9 q^{52} +8550.31 q^{53} +6022.66 q^{54} +3025.00 q^{55} +11836.9 q^{56} -2686.21 q^{57} -15965.1 q^{58} +28323.8 q^{59} -5295.66 q^{60} -47602.8 q^{61} +6316.02 q^{62} -19542.2 q^{63} -13016.1 q^{64} -10034.2 q^{65} -1692.26 q^{66} +7549.14 q^{67} +37442.2 q^{68} +29867.6 q^{69} -4893.94 q^{70} +17129.9 q^{71} -21324.3 q^{72} -65764.0 q^{73} -14303.9 q^{74} +4650.64 q^{75} +10276.7 q^{76} +12602.4 q^{77} +5613.38 q^{78} +79047.2 q^{79} +17433.6 q^{80} +21750.8 q^{81} +497.074 q^{82} -97237.4 q^{83} -22062.2 q^{84} -32881.7 q^{85} +44671.4 q^{86} +63205.6 q^{87} +13751.7 q^{88} +63294.4 q^{89} +8816.47 q^{90} -41803.3 q^{91} -114265. q^{92} -25005.0 q^{93} +19307.9 q^{94} -9025.00 q^{95} -36814.5 q^{96} +65347.7 q^{97} +11200.7 q^{98} -22703.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * 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 $

$2$	−1.87953	−0.332258	−0.166129	−	0.986104i	$-0.553127\pi$
$2$	−1.87953	−0.332258	−0.166129	+	0.986104i	$0.553127\pi$
$3$	7.44103	0.477342	0.238671	−	0.971100i	$-0.423288\pi$
$3$	7.44103	0.477342	0.238671	+	0.971100i	$0.423288\pi$
$4$	−28.4674	−0.889605
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−13.9857	−0.158601
$7$	104.152	0.803385	0.401693	−	0.915775i	$-0.368422\pi$
$7$	104.152	0.803385	0.401693	+	0.915775i	$0.368422\pi$
$8$	113.650	0.627836
$9$	−187.631	−0.772144
$10$	−46.9883	−0.148590
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−211.826	−0.424646
$13$	−401.367	−0.658694	−0.329347	−	0.944209i	$-0.606829\pi$
$13$	−401.367	−0.658694	−0.329347	+	0.944209i	$0.606829\pi$
$14$	−195.758	−0.266931
$15$	186.026	0.213474
$16$	697.346	0.681002
$17$	−1315.27	−1.10380	−0.551902	−	0.833909i	$-0.686098\pi$
$17$	−1315.27	−1.10380	−0.551902	+	0.833909i	$0.686098\pi$
$18$	352.659	0.256551
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−711.684	−0.397843
$21$	775.000	0.383490
$22$	−227.423	−0.100179
$23$	4013.91	1.58215	0.791076	−	0.611718i	$-0.209521\pi$
$23$	4013.91	1.58215	0.791076	+	0.611718i	$0.209521\pi$
$24$	845.676	0.299692
$25$	625.000	0.200000
$26$	754.383	0.218856
$27$	−3204.34	−0.845919
$28$	−2964.94	−0.714695
$29$	8494.21	1.87555	0.937773	−	0.347248i	$-0.112884\pi$
$29$	8494.21	1.87555	0.937773	+	0.347248i	$0.112884\pi$
$30$	−349.641	−0.0709283
$31$	−3360.42	−0.628043	−0.314022	−	0.949416i	$-0.601676\pi$
$31$	−3360.42	−0.628043	−0.314022	+	0.949416i	$0.601676\pi$
$32$	−4947.50	−0.854104
$33$	900.365	0.143924
$34$	2472.09	0.366747
$35$	2603.81	0.359285
$36$	5341.36	0.686903
$37$	7610.36	0.913904	0.456952	−	0.889491i	$-0.348941\pi$
$37$	7610.36	0.913904	0.456952	+	0.889491i	$0.348941\pi$
$38$	678.511	0.0762251
$39$	−2986.58	−0.314422
$40$	2841.26	0.280777
$41$	−264.467	−0.0245704	−0.0122852	−	0.999925i	$-0.503911\pi$
$41$	−264.467	−0.0245704	−0.0122852	+	0.999925i	$0.503911\pi$
$42$	−1456.64	−0.127417
$43$	−23767.3	−1.96024	−0.980118	−	0.198416i	$-0.936420\pi$
$43$	−23767.3	−1.96024	−0.980118	+	0.198416i	$0.936420\pi$
$44$	−3444.55	−0.268226
$45$	−4690.78	−0.345313
$46$	−7544.28	−0.525682
$47$	−10272.7	−0.678330	−0.339165	−	0.940727i	$-0.610144\pi$
$47$	−10272.7	−0.678330	−0.339165	+	0.940727i	$0.610144\pi$
$48$	5188.97	0.325071
$49$	−5959.30	−0.354572
$50$	−1174.71	−0.0664515
$51$	−9786.94	−0.526892
$52$	11425.9	0.585977
$53$	8550.31	0.418111	0.209056	−	0.977904i	$-0.432961\pi$
$53$	8550.31	0.418111	0.209056	+	0.977904i	$0.432961\pi$
$54$	6022.66	0.281063
$55$	3025.00	0.134840
$56$	11836.9	0.504394
$57$	−2686.21	−0.109510
$58$	−15965.1	−0.623165
$59$	28323.8	1.05931	0.529653	−	0.848214i	$-0.322322\pi$
$59$	28323.8	1.05931	0.529653	+	0.848214i	$0.322322\pi$
$60$	−5295.66	−0.189907
$61$	−47602.8	−1.63798	−0.818989	−	0.573809i	$-0.805465\pi$
$61$	−47602.8	−1.63798	−0.818989	+	0.573809i	$0.805465\pi$
$62$	6316.02	0.208672
$63$	−19542.2	−0.620329
$64$	−13016.1	−0.397219
$65$	−10034.2	−0.294577
$66$	−1692.26	−0.0478199
$67$	7549.14	0.205452	0.102726	−	0.994710i	$-0.467244\pi$
$67$	7549.14	0.205452	0.102726	+	0.994710i	$0.467244\pi$
$68$	37442.2	0.981949
$69$	29867.6	0.755228
$70$	−4893.94	−0.119375
$71$	17129.9	0.403283	0.201642	−	0.979459i	$-0.435372\pi$
$71$	17129.9	0.403283	0.201642	+	0.979459i	$0.435372\pi$
$72$	−21324.3	−0.484780
$73$	−65764.0	−1.44438	−0.722190	−	0.691695i	$-0.756864\pi$
$73$	−65764.0	−1.44438	−0.722190	+	0.691695i	$0.756864\pi$
$74$	−14303.9	−0.303652
$75$	4650.64	0.0954685
$76$	10276.7	0.204089
$77$	12602.4	0.242230
$78$	5613.38	0.104469
$79$	79047.2	1.42501	0.712506	−	0.701666i	$-0.247560\pi$
$79$	79047.2	1.42501	0.712506	+	0.701666i	$0.247560\pi$
$80$	17433.6	0.304553
$81$	21750.8	0.368351
$82$	497.074	0.00816369
$83$	−97237.4	−1.54931	−0.774655	−	0.632384i	$-0.782076\pi$
$83$	−97237.4	−1.54931	−0.774655	+	0.632384i	$0.782076\pi$
$84$	−22062.2	−0.341154
$85$	−32881.7	−0.493636
$86$	44671.4	0.651303
$87$	63205.6	0.895278
$88$	13751.7	0.189300
$89$	63294.4	0.847014	0.423507	−	0.905893i	$-0.360799\pi$
$89$	63294.4	0.847014	0.423507	+	0.905893i	$0.360799\pi$
$90$	8816.47	0.114733
$91$	−41803.3	−0.529185
$92$	−114265.	−1.40749
$93$	−25005.0	−0.299792
$94$	19307.9	0.225380
$95$	−9025.00	−0.102598
$96$	−36814.5	−0.407700
$97$	65347.7	0.705182	0.352591	−	0.935778i	$-0.385301\pi$
$97$	65347.7	0.705182	0.352591	+	0.935778i	$0.385301\pi$
$98$	11200.7	0.117809
$99$	−22703.4	−0.232810
$100$	−17792.1	−0.177921
$101$	98830.7	0.964026	0.482013	−	0.876164i	$-0.339906\pi$
$101$	98830.7	0.964026	0.482013	+	0.876164i	$0.339906\pi$
$102$	18394.9	0.175064
$103$	−29660.0	−0.275472	−0.137736	−	0.990469i	$-0.543983\pi$
$103$	−29660.0	−0.275472	−0.137736	+	0.990469i	$0.543983\pi$
$104$	−45615.5	−0.413551
$105$	19375.0	0.171502
$106$	−16070.6	−0.138921
$107$	222954.	1.88259	0.941294	−	0.337588i	$-0.109611\pi$
$107$	222954.	1.88259	0.941294	+	0.337588i	$0.109611\pi$
$108$	91219.0	0.752534
$109$	101025.	0.814445	0.407222	−	0.913329i	$-0.366497\pi$
$109$	101025.	0.814445	0.407222	+	0.913329i	$0.366497\pi$
$110$	−5685.59	−0.0448016
$111$	56628.9	0.436245
$112$	72630.2	0.547107
$113$	−50191.7	−0.369773	−0.184887	−	0.982760i	$-0.559192\pi$
$113$	−50191.7	−0.369773	−0.184887	+	0.982760i	$0.559192\pi$
$114$	5048.82	0.0363855
$115$	100348.	0.707560
$116$	−241808.	−1.66850
$117$	75308.9	0.508607
$118$	−53235.5	−0.351962
$119$	−136988.	−0.886779
$120$	21141.9	0.134027
$121$	14641.0	0.0909091
$122$	89471.1	0.544231
$123$	−1967.91	−0.0117285
$124$	95662.3	0.558710
$125$	15625.0	0.0894427
$126$	36730.2	0.206109
$127$	−124944.	−0.687396	−0.343698	−	0.939080i	$-0.611680\pi$
$127$	−124944.	−0.687396	−0.343698	+	0.939080i	$0.611680\pi$
$128$	182784.	0.986083
$129$	−176853.	−0.935703
$130$	18859.6	0.0978753
$131$	−128339.	−0.653402	−0.326701	−	0.945128i	$-0.605937\pi$
$131$	−128339.	−0.653402	−0.326701	+	0.945128i	$0.605937\pi$
$132$	−25631.0	−0.128036
$133$	−37599.0	−0.184309
$134$	−14188.9	−0.0682630
$135$	−80108.5	−0.378307
$136$	−149481.	−0.693007
$137$	150289.	0.684109	0.342055	−	0.939680i	$-0.388877\pi$
$137$	150289.	0.684109	0.342055	+	0.939680i	$0.388877\pi$
$138$	−56137.2	−0.250930
$139$	−421076.	−1.84852	−0.924259	−	0.381766i	$-0.875316\pi$
$139$	−421076.	−1.84852	−0.924259	+	0.381766i	$0.875316\pi$
$140$	−74123.5	−0.319621
$141$	−76439.6	−0.323796
$142$	−32196.3	−0.133994
$143$	−48565.4	−0.198604
$144$	−130844.	−0.525832
$145$	212355.	0.838770
$146$	123606.	0.479906
$147$	−44343.3	−0.169252
$148$	−216647.	−0.813014
$149$	−173512.	−0.640271	−0.320136	−	0.947372i	$-0.603728\pi$
$149$	−173512.	−0.640271	−0.320136	+	0.947372i	$0.603728\pi$
$150$	−8741.04	−0.0317201
$151$	331682.	1.18380	0.591901	−	0.806010i	$-0.298377\pi$
$151$	331682.	1.18380	0.591901	+	0.806010i	$0.298377\pi$
$152$	−41027.8	−0.144035
$153$	246785.	0.852295
$154$	−23686.7	−0.0804827
$155$	−84010.6	−0.280870
$156$	85020.2	0.279712
$157$	323550.	1.04759	0.523797	−	0.851843i	$-0.324515\pi$
$157$	323550.	1.04759	0.523797	+	0.851843i	$0.324515\pi$
$158$	−148572.	−0.473471
$159$	63623.1	0.199582
$160$	−123687.	−0.381967
$161$	418058.	1.27108
$162$	−40881.3	−0.122388
$163$	−220800.	−0.650925	−0.325462	−	0.945555i	$-0.605520\pi$
$163$	−220800.	−0.650925	−0.325462	+	0.945555i	$0.605520\pi$
$164$	7528.68	0.0218579
$165$	22509.1	0.0643648
$166$	182761.	0.514770
$167$	−277996.	−0.771342	−0.385671	−	0.922636i	$-0.626030\pi$
$167$	−277996.	−0.771342	−0.385671	+	0.922636i	$0.626030\pi$
$168$	88079.1	0.240768
$169$	−210197.	−0.566123
$170$	61802.2	0.164014
$171$	67734.8	0.177142
$172$	676592.	1.74384
$173$	−78638.1	−0.199764	−0.0998821	−	0.994999i	$-0.531847\pi$
$173$	−78638.1	−0.199764	−0.0998821	+	0.994999i	$0.531847\pi$
$174$	−118797.	−0.297463
$175$	65095.2	0.160677
$176$	84378.8	0.205330
$177$	210758.	0.505652
$178$	−118964.	−0.281427
$179$	−411324.	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$179$	−411324.	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$180$	133534.	0.307193
$181$	−828784.	−1.88038	−0.940188	−	0.340655i	$-0.889351\pi$
$181$	−828784.	−1.88038	−0.940188	+	0.340655i	$0.889351\pi$
$182$	78570.7	0.175826
$183$	−354214.	−0.781876
$184$	456182.	0.993331
$185$	190259.	0.408710
$186$	46997.7	0.0996081
$187$	−159147.	−0.332809
$188$	292437.	0.603446
$189$	−333739.	−0.679599
$190$	16962.8	0.0340889
$191$	−367229.	−0.728372	−0.364186	−	0.931326i	$-0.618653\pi$
$191$	−367229.	−0.728372	−0.364186	+	0.931326i	$0.618653\pi$
$192$	−96853.1	−0.189610
$193$	−764214.	−1.47680	−0.738400	−	0.674363i	$-0.764418\pi$
$193$	−764214.	−1.47680	−0.738400	+	0.674363i	$0.764418\pi$
$194$	−122823.	−0.234302
$195$	−74664.6	−0.140614
$196$	169645.	0.315429
$197$	−816660.	−1.49926	−0.749628	−	0.661860i	$-0.769767\pi$
$197$	−816660.	−1.49926	−0.749628	+	0.661860i	$0.769767\pi$
$198$	42671.7	0.0773530
$199$	−753179.	−1.34823	−0.674117	−	0.738624i	$-0.735476\pi$
$199$	−753179.	−1.34823	−0.674117	+	0.738624i	$0.735476\pi$
$200$	71031.5	0.125567
$201$	56173.4	0.0980710
$202$	−185756.	−0.320305
$203$	884691.	1.50679
$204$	278608.	0.468726
$205$	−6611.68	−0.0109882
$206$	55746.9	0.0915277
$207$	−753134.	−1.22165
$208$	−279892.	−0.448571
$209$	−43681.0	−0.0691714
$210$	−36416.0	−0.0569828
$211$	−1.02137e6	−1.57935	−0.789676	−	0.613524i	$-0.789751\pi$
$211$	−1.02137e6	−1.57935	−0.789676	+	0.613524i	$0.789751\pi$
$212$	−243405.	−0.371954
$213$	127464.	0.192504
$214$	−419049.	−0.625504
$215$	−594182.	−0.876644
$216$	−364174.	−0.531098
$217$	−349996.	−0.504561
$218$	−189879.	−0.270605
$219$	−489352.	−0.689463
$220$	−86113.8	−0.119954
$221$	527905.	0.727068
$222$	−106436.	−0.144946
$223$	825655.	1.11182	0.555912	−	0.831241i	$-0.312369\pi$
$223$	825655.	1.11182	0.555912	+	0.831241i	$0.312369\pi$
$224$	−515293.	−0.686174
$225$	−117269.	−0.154429
$226$	94336.9	0.122860
$227$	602628.	0.776219	0.388110	−	0.921613i	$-0.373128\pi$
$227$	602628.	0.776219	0.388110	+	0.921613i	$0.373128\pi$
$228$	76469.3	0.0974205
$229$	−558973.	−0.704372	−0.352186	−	0.935930i	$-0.614562\pi$
$229$	−558973.	−0.704372	−0.352186	+	0.935930i	$0.614562\pi$
$230$	−188607.	−0.235092
$231$	93775.0	0.115626
$232$	965370.	1.17753
$233$	−9582.25	−0.0115632	−0.00578160	−	0.999983i	$-0.501840\pi$
$233$	−9582.25	−0.0115632	−0.00578160	+	0.999983i	$0.501840\pi$
$234$	−141546.	−0.168988
$235$	−256818.	−0.303358
$236$	−806304.	−0.942364
$237$	588192.	0.680219
$238$	257474.	0.294639
$239$	954910.	1.08135	0.540677	−	0.841230i	$-0.318168\pi$
$239$	954910.	1.08135	0.540677	+	0.841230i	$0.318168\pi$
$240$	129724.	0.145376
$241$	−60556.1	−0.0671607	−0.0335803	−	0.999436i	$-0.510691\pi$
$241$	−60556.1	−0.0671607	−0.0335803	+	0.999436i	$0.510691\pi$
$242$	−27518.2	−0.0302052
$243$	940502.	1.02175
$244$	1.35513e6	1.45715
$245$	−148982.	−0.158570
$246$	3698.75	0.00389688
$247$	144894.	0.151115
$248$	−381913.	−0.394308
$249$	−723547.	−0.739551
$250$	−29367.7	−0.0297180
$251$	592804.	0.593918	0.296959	−	0.954890i	$-0.404028\pi$
$251$	592804.	0.593918	0.296959	+	0.954890i	$0.404028\pi$
$252$	556315.	0.551848
$253$	485683.	0.477037
$254$	234837.	0.228392
$255$	−244674.	−0.235633
$256$	72966.1	0.0695859
$257$	−810297.	−0.765265	−0.382632	−	0.923901i	$-0.624982\pi$
$257$	−810297.	−0.765265	−0.382632	+	0.923901i	$0.624982\pi$
$258$	332401.	0.310895
$259$	792636.	0.734217
$260$	285647.	0.262057
$261$	−1.59378e6	−1.44819
$262$	241217.	0.217098
$263$	−1.25616e6	−1.11983	−0.559917	−	0.828548i	$-0.689167\pi$
$263$	−1.25616e6	−1.11983	−0.559917	+	0.828548i	$0.689167\pi$
$264$	102327.	0.0903607
$265$	213758.	0.186985
$266$	70668.5	0.0612381
$267$	470976.	0.404315
$268$	−214904.	−0.182771
$269$	−858008.	−0.722954	−0.361477	−	0.932381i	$-0.617727\pi$
$269$	−858008.	−0.722954	−0.361477	+	0.932381i	$0.617727\pi$
$270$	150566.	0.125695
$271$	−2.01426e6	−1.66607	−0.833033	−	0.553224i	$-0.813397\pi$
$271$	−2.01426e6	−1.66607	−0.833033	+	0.553224i	$0.813397\pi$
$272$	−917196.	−0.751692
$273$	−311060.	−0.252602
$274$	−282473.	−0.227300
$275$	75625.0	0.0603023
$276$	−850252.	−0.671854
$277$	261524.	0.204792	0.102396	−	0.994744i	$-0.467349\pi$
$277$	261524.	0.204792	0.102396	+	0.994744i	$0.467349\pi$
$278$	791427.	0.614184
$279$	630520.	0.484940
$280$	295924.	0.225572
$281$	−263660.	−0.199195	−0.0995976	−	0.995028i	$-0.531756\pi$
$281$	−263660.	−0.199195	−0.0995976	+	0.995028i	$0.531756\pi$
$282$	143671.	0.107584
$283$	−195816.	−0.145339	−0.0726694	−	0.997356i	$-0.523152\pi$
$283$	−195816.	−0.145339	−0.0726694	+	0.997356i	$0.523152\pi$
$284$	−487644.	−0.358763
$285$	−67155.3	−0.0489743
$286$	91280.3	0.0659875
$287$	−27544.8	−0.0197395
$288$	928304.	0.659491
$289$	310071.	0.218382
$290$	−399128.	−0.278688
$291$	486254.	0.336613
$292$	1.87213e6	1.28493
$293$	28354.9	0.0192956	0.00964780	−	0.999953i	$-0.496929\pi$
$293$	28354.9	0.0192956	0.00964780	+	0.999953i	$0.496929\pi$
$294$	83344.7	0.0562354
$295$	708095.	0.473736
$296$	864920.	0.573782
$297$	−387725.	−0.255054
$298$	326122.	0.212735
$299$	−1.61105e6	−1.04215
$300$	−132392.	−0.0849292
$301$	−2.47542e6	−1.57482
$302$	−623407.	−0.393327
$303$	735402.	0.460170
$304$	−251742.	−0.156233
$305$	−1.19007e6	−0.732526
$306$	−463840.	−0.283182
$307$	2.54811e6	1.54302	0.771512	−	0.636215i	$-0.219501\pi$
$307$	2.54811e6	1.54302	0.771512	+	0.636215i	$0.219501\pi$
$308$	−358758.	−0.215489
$309$	−220701.	−0.131495
$310$	157901.	0.0933210
$311$	2.61184e6	1.53125	0.765623	−	0.643289i	$-0.222431\pi$
$311$	2.61184e6	1.53125	0.765623	+	0.643289i	$0.222431\pi$
$312$	−339426.	−0.197405
$313$	−1.20444e6	−0.694902	−0.347451	−	0.937698i	$-0.612953\pi$
$313$	−1.20444e6	−0.694902	−0.347451	+	0.937698i	$0.612953\pi$
$314$	−608124.	−0.348071
$315$	−488555.	−0.277420
$316$	−2.25026e6	−1.26770
$317$	−1.64201e6	−0.917759	−0.458879	−	0.888499i	$-0.651749\pi$
$317$	−1.64201e6	−0.917759	−0.458879	+	0.888499i	$0.651749\pi$
$318$	−119582.	−0.0663127
$319$	1.02780e6	0.565499
$320$	−325402.	−0.177642
$321$	1.65901e6	0.898639
$322$	−785754.	−0.422325
$323$	474811.	0.253230
$324$	−619187.	−0.327687
$325$	−250854.	−0.131739
$326$	415002.	0.216275
$327$	751728.	0.388769
$328$	−30056.8	−0.0154262
$329$	−1.06993e6	−0.544960
$330$	−42306.6	−0.0213857
$331$	−2.57719e6	−1.29294	−0.646468	−	0.762941i	$-0.723754\pi$
$331$	−2.57719e6	−1.29294	−0.646468	+	0.762941i	$0.723754\pi$
$332$	2.76809e6	1.37827
$333$	−1.42794e6	−0.705666
$334$	522502.	0.256284
$335$	188729.	0.0918810
$336$	540443.	0.261157
$337$	1.18493e6	0.568354	0.284177	−	0.958772i	$-0.408280\pi$
$337$	1.18493e6	0.568354	0.284177	+	0.958772i	$0.408280\pi$
$338$	395073.	0.188099
$339$	−373478.	−0.176509
$340$	936054.	0.439141
$341$	−406611.	−0.189362
$342$	−127310.	−0.0588568
$343$	−2.37116e6	−1.08824
$344$	−2.70116e6	−1.23071
$345$	746691.	0.337748
$346$	147803.	0.0663732
$347$	3.54777e6	1.58173	0.790864	−	0.611992i	$-0.209631\pi$
$347$	3.54777e6	1.58173	0.790864	+	0.611992i	$0.209631\pi$
$348$	−1.79930e6	−0.796443
$349$	−2.74285e6	−1.20542	−0.602710	−	0.797960i	$-0.705913\pi$
$349$	−2.74285e6	−1.20542	−0.602710	+	0.797960i	$0.705913\pi$
$350$	−122349.	−0.0533862
$351$	1.28612e6	0.557202
$352$	−598647.	−0.257522
$353$	−1.67999e6	−0.717578	−0.358789	−	0.933419i	$-0.616810\pi$
$353$	−1.67999e6	−0.717578	−0.358789	+	0.933419i	$0.616810\pi$
$354$	−396127.	−0.168007
$355$	428248.	0.180354
$356$	−1.80182e6	−0.753507
$357$	−1.01933e6	−0.423297
$358$	773097.	0.318806
$359$	−35890.6	−0.0146976	−0.00734878	−	0.999973i	$-0.502339\pi$
$359$	−35890.6	−0.0146976	−0.00734878	+	0.999973i	$0.502339\pi$
$360$	−533109.	−0.216800
$361$	130321.	0.0526316
$362$	1.55773e6	0.624770
$363$	108944.	0.0433948
$364$	1.19003e6	0.470765
$365$	−1.64410e6	−0.645946
$366$	665757.	0.259784
$367$	−2.45141e6	−0.950058	−0.475029	−	0.879970i	$-0.657562\pi$
$367$	−2.45141e6	−0.950058	−0.475029	+	0.879970i	$0.657562\pi$
$368$	2.79908e6	1.07745
$369$	49622.2	0.0189719
$370$	−357598.	−0.135797
$371$	890534.	0.335904
$372$	711826.	0.266696
$373$	−3.26043e6	−1.21340	−0.606698	−	0.794932i	$-0.707506\pi$
$373$	−3.26043e6	−1.21340	−0.606698	+	0.794932i	$0.707506\pi$
$374$	299123.	0.110578
$375$	116266.	0.0426948
$376$	−1.16750e6	−0.425880
$377$	−3.40930e6	−1.23541
$378$	627274.	0.225802
$379$	1.76665e6	0.631759	0.315879	−	0.948799i	$-0.397700\pi$
$379$	1.76665e6	0.631759	0.315879	+	0.948799i	$0.397700\pi$
$380$	256918.	0.0912715
$381$	−929714.	−0.328123
$382$	690218.	0.242007
$383$	−719578.	−0.250658	−0.125329	−	0.992115i	$-0.539999\pi$
$383$	−719578.	−0.250658	−0.125329	+	0.992115i	$0.539999\pi$
$384$	1.36010e6	0.470699
$385$	315061.	0.108328
$386$	1.43636e6	0.490678
$387$	4.45948e6	1.51359
$388$	−1.86028e6	−0.627333
$389$	−4.93169e6	−1.65242	−0.826212	−	0.563360i	$-0.809509\pi$
$389$	−4.93169e6	−1.65242	−0.826212	+	0.563360i	$0.809509\pi$
$390$	140335.	0.0467200
$391$	−5.27937e6	−1.74638
$392$	−677276.	−0.222613
$393$	−954974.	−0.311896
$394$	1.53494e6	0.498139
$395$	1.97618e6	0.637285
$396$	646305.	0.207109
$397$	3.37139e6	1.07358	0.536788	−	0.843717i	$-0.319637\pi$
$397$	3.37139e6	1.07358	0.536788	+	0.843717i	$0.319637\pi$
$398$	1.41562e6	0.447961
$399$	−279775.	−0.0879786
$400$	435841.	0.136200
$401$	206225.	0.0640444	0.0320222	−	0.999487i	$-0.489805\pi$
$401$	206225.	0.0640444	0.0320222	+	0.999487i	$0.489805\pi$
$402$	−105580.	−0.0325848
$403$	1.34876e6	0.413688
$404$	−2.81345e6	−0.857602
$405$	543769.	0.164732
$406$	−1.66281e6	−0.500641
$407$	920853.	0.275553
$408$	−1.11229e6	−0.330801
$409$	−5.04841e6	−1.49227	−0.746133	−	0.665796i	$-0.768092\pi$
$409$	−5.04841e6	−1.49227	−0.746133	+	0.665796i	$0.768092\pi$
$410$	12426.9	0.00365092
$411$	1.11830e6	0.326554
$412$	844341.	0.245061
$413$	2.94999e6	0.851031
$414$	1.41554e6	0.405902
$415$	−2.43094e6	−0.692872
$416$	1.98576e6	0.562593
$417$	−3.13324e6	−0.882376
$418$	82099.9	0.0229827
$419$	429336.	0.119471	0.0597355	−	0.998214i	$-0.480974\pi$
$419$	429336.	0.119471	0.0597355	+	0.998214i	$0.480974\pi$
$420$	−551555.	−0.152569
$421$	−2.89781e6	−0.796828	−0.398414	−	0.917206i	$-0.630439\pi$
$421$	−2.89781e6	−0.796828	−0.398414	+	0.917206i	$0.630439\pi$
$422$	1.91971e6	0.524752
$423$	1.92748e6	0.523769
$424$	971746.	0.262505
$425$	−822042.	−0.220761
$426$	−239573.	−0.0639609
$427$	−4.95795e6	−1.31593
$428$	−6.34690e6	−1.67476
$429$	−361377.	−0.0948019
$430$	1.11678e6	0.291272
$431$	1.21546e6	0.315171	0.157585	−	0.987505i	$-0.449629\pi$
$431$	1.21546e6	0.315171	0.157585	+	0.987505i	$0.449629\pi$
$432$	−2.23453e6	−0.576073
$433$	−4.72701e6	−1.21162	−0.605810	−	0.795609i	$-0.707151\pi$
$433$	−4.72701e6	−1.21162	−0.605810	+	0.795609i	$0.707151\pi$
$434$	657829.	0.167644
$435$	1.58014e6	0.400380
$436$	−2.87591e6	−0.724534
$437$	−1.44902e6	−0.362971
$438$	919753.	0.229079
$439$	3.01500e6	0.746667	0.373333	−	0.927697i	$-0.378215\pi$
$439$	3.01500e6	0.746667	0.373333	+	0.927697i	$0.378215\pi$
$440$	343792.	0.0846573
$441$	1.11815e6	0.273781
$442$	−992215.	−0.241574
$443$	−2.61470e6	−0.633014	−0.316507	−	0.948590i	$-0.602510\pi$
$443$	−2.61470e6	−0.633014	−0.316507	+	0.948590i	$0.602510\pi$
$444$	−1.61207e6	−0.388086
$445$	1.58236e6	0.378796
$446$	−1.55185e6	−0.369412
$447$	−1.29111e6	−0.305629
$448$	−1.35566e6	−0.319120
$449$	5.45937e6	1.27799	0.638994	−	0.769211i	$-0.279351\pi$
$449$	5.45937e6	1.27799	0.638994	+	0.769211i	$0.279351\pi$
$450$	220412.	0.0513102
$451$	−32000.5	−0.00740825
$452$	1.42882e6	0.328952
$453$	2.46805e6	0.565079
$454$	−1.13266e6	−0.257905
$455$	−1.04508e6	−0.236659
$456$	−305289.	−0.0687542
$457$	−7.38702e6	−1.65455	−0.827273	−	0.561800i	$-0.810109\pi$
$457$	−7.38702e6	−1.65455	−0.827273	+	0.561800i	$0.810109\pi$
$458$	1.05061e6	0.234033
$459$	4.21456e6	0.933729
$460$	−2.85664e6	−0.629449
$461$	765728.	0.167812	0.0839059	−	0.996474i	$-0.473260\pi$
$461$	765728.	0.167812	0.0839059	+	0.996474i	$0.473260\pi$
$462$	−176253.	−0.0384178
$463$	−4.75493e6	−1.03084	−0.515421	−	0.856937i	$-0.672364\pi$
$463$	−4.75493e6	−1.03084	−0.515421	+	0.856937i	$0.672364\pi$
$464$	5.92340e6	1.27725
$465$	−625125.	−0.134071
$466$	18010.2	0.00384196
$467$	−2.72869e6	−0.578978	−0.289489	−	0.957181i	$-0.593485\pi$
$467$	−2.72869e6	−0.578978	−0.289489	+	0.957181i	$0.593485\pi$
$468$	−2.14385e6	−0.452459
$469$	786260.	0.165057
$470$	482698.	0.100793
$471$	2.40755e6	0.500061
$472$	3.21901e6	0.665070
$473$	−2.87584e6	−0.591033
$474$	−1.10553e6	−0.226008
$475$	−225625.	−0.0458831
$476$	3.89969e6	0.788883
$477$	−1.60430e6	−0.322842
$478$	−1.79479e6	−0.359288
$479$	−5.83499e6	−1.16199	−0.580993	−	0.813908i	$-0.697336\pi$
$479$	−5.83499e6	−1.16199	−0.580993	+	0.813908i	$0.697336\pi$
$480$	−920362.	−0.182329
$481$	−3.05455e6	−0.601983
$482$	113817.	0.0223146
$483$	3.11078e6	0.606739
$484$	−416791.	−0.0808732
$485$	1.63369e6	0.315367
$486$	−1.76771e6	−0.339484
$487$	−4.62173e6	−0.883043	−0.441521	−	0.897251i	$-0.645561\pi$
$487$	−4.62173e6	−0.883043	−0.441521	+	0.897251i	$0.645561\pi$
$488$	−5.41008e6	−1.02838
$489$	−1.64298e6	−0.310714
$490$	280017.	0.0526859
$491$	4.34666e6	0.813676	0.406838	−	0.913500i	$-0.366631\pi$
$491$	4.34666e6	0.813676	0.406838	+	0.913500i	$0.366631\pi$
$492$	56021.1	0.0104337
$493$	−1.11721e7	−2.07023
$494$	−272332.	−0.0502090
$495$	−567584.	−0.104116
$496$	−2.34338e6	−0.427699
$497$	1.78412e6	0.323992
$498$	1.35993e6	0.245721
$499$	−7.41602e6	−1.33328	−0.666638	−	0.745382i	$-0.732267\pi$
$499$	−7.41602e6	−1.33328	−0.666638	+	0.745382i	$0.732267\pi$
$500$	−444802.	−0.0795687
$501$	−2.06857e6	−0.368194
$502$	−1.11419e6	−0.197334
$503$	7.01516e6	1.23628	0.618141	−	0.786067i	$-0.287886\pi$
$503$	7.01516e6	1.23628	0.618141	+	0.786067i	$0.287886\pi$
$504$	−2.22098e6	−0.389465
$505$	2.47077e6	0.431125
$506$	−912858.	−0.158499
$507$	−1.56409e6	−0.270234
$508$	3.55683e6	0.611511
$509$	−3.69181e6	−0.631605	−0.315802	−	0.948825i	$-0.602274\pi$
$509$	−3.69181e6	−0.631605	−0.315802	+	0.948825i	$0.602274\pi$
$510$	459872.	0.0782909
$511$	−6.84948e6	−1.16039
$512$	−5.98623e6	−1.00920
$513$	1.15677e6	0.194067
$514$	1.52298e6	0.254265
$515$	−741500.	−0.123195
$516$	5.03454e6	0.832406
$517$	−1.24300e6	−0.204524
$518$	−1.48979e6	−0.243949
$519$	−585148.	−0.0953559
$520$	−1.14039e6	−0.184946
$521$	2.47421e6	0.399340	0.199670	−	0.979863i	$-0.436013\pi$
$521$	2.47421e6	0.399340	0.199670	+	0.979863i	$0.436013\pi$
$522$	2.99556e6	0.481173
$523$	−3.87288e6	−0.619128	−0.309564	−	0.950879i	$-0.600183\pi$
$523$	−3.87288e6	−0.619128	−0.309564	+	0.950879i	$0.600183\pi$
$524$	3.65347e6	0.581270
$525$	484375.	0.0766979
$526$	2.36098e6	0.372074
$527$	4.41985e6	0.693236
$528$	627865.	0.0980126
$529$	9.67514e6	1.50320
$530$	−401765.	−0.0621272
$531$	−5.31442e6	−0.817937
$532$	1.07034e6	0.163962
$533$	106148.	0.0161844
$534$	−885214.	−0.134337
$535$	5.57384e6	0.841919
$536$	857963.	0.128990
$537$	−3.06067e6	−0.458017
$538$	1.61265e6	0.240207
$539$	−721075.	−0.106908
$540$	2.28048e6	0.336543
$541$	−1.67425e6	−0.245939	−0.122970	−	0.992410i	$-0.539242\pi$
$541$	−1.67425e6	−0.245939	−0.122970	+	0.992410i	$0.539242\pi$
$542$	3.78586e6	0.553563
$543$	−6.16701e6	−0.897583
$544$	6.50728e6	0.942762
$545$	2.52562e6	0.364231
$546$	584647.	0.0839290
$547$	−268757.	−0.0384053	−0.0192026	−	0.999816i	$-0.506113\pi$
$547$	−268757.	−0.0384053	−0.0192026	+	0.999816i	$0.506113\pi$
$548$	−4.27833e6	−0.608587
$549$	8.93177e6	1.26476
$550$	−142140.	−0.0200359
$551$	−3.06641e6	−0.430280
$552$	3.39447e6	0.474159
$553$	8.23295e6	1.14483
$554$	−491543.	−0.0680435
$555$	1.41572e6	0.195095
$556$	1.19869e7	1.64445
$557$	7.50823e6	1.02541	0.512707	−	0.858563i	$-0.328643\pi$
$557$	7.50823e6	1.02541	0.512707	+	0.858563i	$0.328643\pi$
$558$	−1.18508e6	−0.161125
$559$	9.53940e6	1.29119
$560$	1.81575e6	0.244674
$561$	−1.18422e6	−0.158864
$562$	495558.	0.0661841
$563$	−8.49794e6	−1.12991	−0.564954	−	0.825123i	$-0.691106\pi$
$563$	−8.49794e6	−1.12991	−0.564954	+	0.825123i	$0.691106\pi$
$564$	2.17603e6	0.288050
$565$	−1.25479e6	−0.165368
$566$	368042.	0.0482899
$567$	2.26539e6	0.295928
$568$	1.94682e6	0.253195
$569$	7.96088e6	1.03081	0.515407	−	0.856946i	$-0.327641\pi$
$569$	7.96088e6	1.03081	0.515407	+	0.856946i	$0.327641\pi$
$570$	126221.	0.0162721
$571$	8.16225e6	1.04766	0.523829	−	0.851823i	$-0.324503\pi$
$571$	8.16225e6	1.04766	0.523829	+	0.851823i	$0.324503\pi$
$572$	1.38253e6	0.176679
$573$	−2.73256e6	−0.347683
$574$	51771.4	0.00655859
$575$	2.50869e6	0.316430
$576$	2.44222e6	0.306711
$577$	−3.05810e6	−0.382395	−0.191198	−	0.981552i	$-0.561237\pi$
$577$	−3.05810e6	−0.382395	−0.191198	+	0.981552i	$0.561237\pi$
$578$	−582788.	−0.0725589
$579$	−5.68654e6	−0.704939
$580$	−6.04519e6	−0.746174
$581$	−1.01275e7	−1.24469
$582$	−913931.	−0.111842
$583$	1.03459e6	0.126065
$584$	−7.47411e6	−0.906833
$585$	1.88272e6	0.227456
$586$	−53293.9	−0.00641111
$587$	236414.	0.0283190	0.0141595	−	0.999900i	$-0.495493\pi$
$587$	236414.	0.0283190	0.0141595	+	0.999900i	$0.495493\pi$
$588$	1.26234e6	0.150568
$589$	1.21311e6	0.144083
$590$	−1.33089e6	−0.157402
$591$	−6.07679e6	−0.715658
$592$	5.30705e6	0.622370
$593$	−6.20875e6	−0.725049	−0.362524	−	0.931974i	$-0.618085\pi$
$593$	−6.20875e6	−0.725049	−0.362524	+	0.931974i	$0.618085\pi$
$594$	728742.	0.0847437
$595$	−3.42470e6	−0.396580
$596$	4.93943e6	0.569588
$597$	−5.60443e6	−0.643569
$598$	3.02802e6	0.346263
$599$	6.23915e6	0.710491	0.355246	−	0.934773i	$-0.384397\pi$
$599$	6.23915e6	0.710491	0.355246	+	0.934773i	$0.384397\pi$
$600$	528547.	0.0599385
$601$	4.12433e6	0.465765	0.232883	−	0.972505i	$-0.425184\pi$
$601$	4.12433e6	0.465765	0.232883	+	0.972505i	$0.425184\pi$
$602$	4.65263e6	0.523247
$603$	−1.41645e6	−0.158639
$604$	−9.44211e6	−1.05312
$605$	366025.	0.0406558
$606$	−1.38221e6	−0.152895
$607$	875983.	0.0964992	0.0482496	−	0.998835i	$-0.484636\pi$
$607$	875983.	0.0964992	0.0482496	+	0.998835i	$0.484636\pi$
$608$	1.78605e6	0.195945
$609$	6.58301e6	0.719253
$610$	2.23678e6	0.243387
$611$	4.12313e6	0.446812
$612$	−7.02532e6	−0.758206
$613$	5.87471e6	0.631445	0.315722	−	0.948852i	$-0.397753\pi$
$613$	5.87471e6	0.631445	0.315722	+	0.948852i	$0.397753\pi$
$614$	−4.78926e6	−0.512681
$615$	−49197.7	−0.00524514
$616$	1.43227e6	0.152080
$617$	2.10734e6	0.222854	0.111427	−	0.993773i	$-0.464458\pi$
$617$	2.10734e6	0.222854	0.111427	+	0.993773i	$0.464458\pi$
$618$	414814.	0.0436901
$619$	−18254.5	−0.00191488	−0.000957442	−	1.00000i	$-0.500305\pi$
$619$	−18254.5	−0.00191488	−0.000957442		1.00000i	$0.500305\pi$
$620$	2.39156e6	0.249863
$621$	−1.28619e7	−1.33837
$622$	−4.90903e6	−0.508768
$623$	6.59226e6	0.680478
$624$	−2.08268e6	−0.214122
$625$	390625.	0.0400000
$626$	2.26378e6	0.230887
$627$	−325032.	−0.0330185
$628$	−9.21063e6	−0.931945
$629$	−1.00097e7	−1.00877
$630$	918256.	0.0921748
$631$	4.74745e6	0.474665	0.237332	−	0.971429i	$-0.423727\pi$
$631$	4.74745e6	0.474665	0.237332	+	0.971429i	$0.423727\pi$
$632$	8.98374e6	0.894673
$633$	−7.60008e6	−0.753891
$634$	3.08622e6	0.304932
$635$	−3.12361e6	−0.307413
$636$	−1.81118e6	−0.177549
$637$	2.39187e6	0.233554
$638$	−1.93178e6	−0.187891
$639$	−3.21411e6	−0.311393
$640$	4.56960e6	0.440990
$641$	1.45767e7	1.40124	0.700621	−	0.713534i	$-0.252907\pi$
$641$	1.45767e7	1.40124	0.700621	+	0.713534i	$0.252907\pi$
$642$	−3.11815e6	−0.298580
$643$	3.84591e6	0.366836	0.183418	−	0.983035i	$-0.441284\pi$
$643$	3.84591e6	0.366836	0.183418	+	0.983035i	$0.441284\pi$
$644$	−1.19010e7	−1.13076
$645$	−4.42133e6	−0.418459
$646$	−892424.	−0.0841375
$647$	−1.55062e7	−1.45628	−0.728142	−	0.685427i	$-0.759616\pi$
$647$	−1.55062e7	−1.45628	−0.728142	+	0.685427i	$0.759616\pi$
$648$	2.47198e6	0.231264
$649$	3.42718e6	0.319393
$650$	471489.	0.0437712
$651$	−2.60433e6	−0.240848
$652$	6.28560e6	0.579066
$653$	536381.	0.0492255	0.0246127	−	0.999697i	$-0.492165\pi$
$653$	536381.	0.0492255	0.0246127	+	0.999697i	$0.492165\pi$
$654$	−1.41290e6	−0.129171
$655$	−3.20848e6	−0.292210
$656$	−184425.	−0.0167325
$657$	1.23394e7	1.11527
$658$	2.01096e6	0.181067
$659$	1.17685e7	1.05562	0.527809	−	0.849363i	$-0.323014\pi$
$659$	1.17685e7	1.05562	0.527809	+	0.849363i	$0.323014\pi$
$660$	−640775.	−0.0572593
$661$	−749207.	−0.0666958	−0.0333479	−	0.999444i	$-0.510617\pi$
$661$	−749207.	−0.0666958	−0.0333479	+	0.999444i	$0.510617\pi$
$662$	4.84392e6	0.429588
$663$	3.92816e6	0.347060
$664$	−1.10511e7	−0.972712
$665$	−939975.	−0.0824256
$666$	2.68386e6	0.234463
$667$	3.40950e7	2.96740
$668$	7.91380e6	0.686189
$669$	6.14372e6	0.530721
$670$	−354721.	−0.0305281
$671$	−5.75994e6	−0.493869
$672$	−3.83431e6	−0.327540
$673$	−1.05623e7	−0.898923	−0.449462	−	0.893300i	$-0.648384\pi$
$673$	−1.05623e7	−0.898923	−0.449462	+	0.893300i	$0.648384\pi$
$674$	−2.22712e6	−0.188840
$675$	−2.00271e6	−0.169184
$676$	5.98377e6	0.503626
$677$	1.10301e7	0.924929	0.462465	−	0.886638i	$-0.346965\pi$
$677$	1.10301e7	0.924929	0.462465	+	0.886638i	$0.346965\pi$
$678$	701964.	0.0586463
$679$	6.80612e6	0.566533
$680$	−3.73702e6	−0.309922
$681$	4.48417e6	0.370522
$682$	764239.	0.0629170
$683$	1.59564e7	1.30883	0.654414	−	0.756136i	$-0.272915\pi$
$683$	1.59564e7	1.30883	0.654414	+	0.756136i	$0.272915\pi$
$684$	−1.92823e6	−0.157586
$685$	3.75722e6	0.305943
$686$	4.45668e6	0.361577
$687$	−4.15933e6	−0.336226
$688$	−1.65740e7	−1.33492
$689$	−3.43181e6	−0.275407
$690$	−1.40343e6	−0.112219
$691$	−8.89156e6	−0.708407	−0.354204	−	0.935168i	$-0.615248\pi$
$691$	−8.89156e6	−0.708407	−0.354204	+	0.935168i	$0.615248\pi$
$692$	2.23862e6	0.177711
$693$	−2.36461e6	−0.187036
$694$	−6.66815e6	−0.525541
$695$	−1.05269e7	−0.826683
$696$	7.18334e6	0.562087
$697$	347845.	0.0271209
$698$	5.15528e6	0.400510
$699$	−71301.8	−0.00551960
$700$	−1.85309e6	−0.142939
$701$	−1.43473e7	−1.10274	−0.551372	−	0.834260i	$-0.685895\pi$
$701$	−1.43473e7	−1.10274	−0.551372	+	0.834260i	$0.685895\pi$
$702$	−2.41730e6	−0.185134
$703$	−2.74734e6	−0.209664
$704$	−1.57495e6	−0.119766
$705$	−1.91099e6	−0.144806
$706$	3.15759e6	0.238421
$707$	1.02934e7	0.774484
$708$	−5.99973e6	−0.449830
$709$	1.59762e7	1.19360	0.596799	−	0.802391i	$-0.296439\pi$
$709$	1.59762e7	1.19360	0.596799	+	0.802391i	$0.296439\pi$
$710$	−804907.	−0.0599239
$711$	−1.48317e7	−1.10032
$712$	7.19343e6	0.531785
$713$	−1.34884e7	−0.993660
$714$	1.91587e6	0.140644
$715$	−1.21414e6	−0.0888182
$716$	1.17093e7	0.853588
$717$	7.10552e6	0.516176
$718$	67457.6	0.00488337
$719$	−1.88914e6	−0.136283	−0.0681415	−	0.997676i	$-0.521707\pi$
$719$	−1.88914e6	−0.136283	−0.0681415	+	0.997676i	$0.521707\pi$
$720$	−3.27109e6	−0.235159
$721$	−3.08916e6	−0.221310
$722$	−244943.	−0.0174872
$723$	−450599.	−0.0320586
$724$	2.35933e7	1.67279
$725$	5.30888e6	0.375109
$726$	−204764.	−0.0144182
$727$	1.32841e7	0.932171	0.466086	−	0.884740i	$-0.345664\pi$
$727$	1.32841e7	0.932171	0.466086	+	0.884740i	$0.345664\pi$
$728$	−4.75096e6	−0.332241
$729$	1.71287e6	0.119373
$730$	3.09014e6	0.214621
$731$	3.12603e7	2.16371
$732$	1.00835e7	0.695561
$733$	691493.	0.0475366	0.0237683	−	0.999717i	$-0.492434\pi$
$733$	691493.	0.0475366	0.0237683	+	0.999717i	$0.492434\pi$
$734$	4.60750e6	0.315664
$735$	−1.10858e6	−0.0756919
$736$	−1.98588e7	−1.35132
$737$	913446.	0.0619461
$738$	−93266.6	−0.00630355
$739$	2.34315e7	1.57830	0.789150	−	0.614200i	$-0.210521\pi$
$739$	2.34315e7	1.57830	0.789150	+	0.614200i	$0.210521\pi$
$740$	−5.41617e6	−0.363591
$741$	1.07816e6	0.0721334
$742$	−1.67379e6	−0.111607
$743$	1.21721e7	0.808898	0.404449	−	0.914561i	$-0.367463\pi$
$743$	1.21721e7	0.808898	0.404449	+	0.914561i	$0.367463\pi$
$744$	−2.84183e6	−0.188220
$745$	−4.33780e6	−0.286338
$746$	6.12809e6	0.403160
$747$	1.82448e7	1.19629
$748$	4.53050e6	0.296069
$749$	2.32211e7	1.51244
$750$	−218526.	−0.0141857
$751$	−8.84755e6	−0.572431	−0.286216	−	0.958165i	$-0.592397\pi$
$751$	−8.84755e6	−0.572431	−0.286216	+	0.958165i	$0.592397\pi$
$752$	−7.16364e6	−0.461944
$753$	4.41107e6	0.283502
$754$	6.40788e6	0.410474
$755$	8.29205e6	0.529413
$756$	9.50067e6	0.604575
$757$	1.54196e7	0.977986	0.488993	−	0.872288i	$-0.337364\pi$
$757$	1.54196e7	0.977986	0.488993	+	0.872288i	$0.337364\pi$
$758$	−3.32047e6	−0.209907
$759$	3.61398e6	0.227710
$760$	−1.02569e6	−0.0644146
$761$	−2.02281e7	−1.26618	−0.633088	−	0.774080i	$-0.718213\pi$
$761$	−2.02281e7	−1.26618	−0.633088	+	0.774080i	$0.718213\pi$
$762$	1.74743e6	0.109021
$763$	1.05220e7	0.654313
$764$	1.04540e7	0.647963
$765$	6.16962e6	0.381158
$766$	1.35247e6	0.0832829
$767$	−1.13682e7	−0.697758
$768$	542943.	0.0332163
$769$	−1.13852e7	−0.694264	−0.347132	−	0.937816i	$-0.612844\pi$
$769$	−1.13852e7	−0.694264	−0.347132	+	0.937816i	$0.612844\pi$
$770$	−592167.	−0.0359929
$771$	−6.02945e6	−0.365293
$772$	2.17551e7	1.31377
$773$	−2.56430e7	−1.54355	−0.771775	−	0.635896i	$-0.780631\pi$
$773$	−2.56430e7	−1.54355	−0.771775	+	0.635896i	$0.780631\pi$
$774$	−8.38174e6	−0.502900
$775$	−2.10026e6	−0.125609
$776$	7.42679e6	0.442738
$777$	5.89803e6	0.350473
$778$	9.26927e6	0.549030
$779$	95472.6	0.00563683
$780$	2.12550e6	0.125091
$781$	2.07272e6	0.121594
$782$	9.92274e6	0.580249
$783$	−2.72183e7	−1.58656
$784$	−4.15569e6	−0.241464
$785$	8.08876e6	0.468498
$786$	1.79491e6	0.103630
$787$	−4.30534e6	−0.247783	−0.123891	−	0.992296i	$-0.539537\pi$
$787$	−4.30534e6	−0.247783	−0.123891	+	0.992296i	$0.539537\pi$
$788$	2.32481e7	1.33374
$789$	−9.34709e6	−0.534544
$790$	−3.71429e6	−0.211743
$791$	−5.22758e6	−0.297071
$792$	−2.58025e6	−0.146167
$793$	1.91062e7	1.07893
$794$	−6.33664e6	−0.356704
$795$	1.59058e6	0.0892559
$796$	2.14410e7	1.19940
$797$	−4.34915e6	−0.242526	−0.121263	−	0.992620i	$-0.538694\pi$
$797$	−4.34915e6	−0.242526	−0.121263	+	0.992620i	$0.538694\pi$
$798$	525847.	0.0292315
$799$	1.35114e7	0.748743
$800$	−3.09219e6	−0.170821
$801$	−1.18760e7	−0.654017
$802$	−387607.	−0.0212792
$803$	−7.95745e6	−0.435497
$804$	−1.59911e6	−0.0872444
$805$	1.04515e7	0.568443
$806$	−2.53504e6	−0.137451
$807$	−6.38446e6	−0.345096
$808$	1.12321e7	0.605250
$809$	2.00396e7	1.07651	0.538256	−	0.842782i	$-0.319083\pi$
$809$	2.00396e7	1.07651	0.538256	+	0.842782i	$0.319083\pi$
$810$	−1.02203e6	−0.0547334
$811$	−3.12222e7	−1.66691	−0.833453	−	0.552591i	$-0.813639\pi$
$811$	−3.12222e7	−1.66691	−0.833453	+	0.552591i	$0.813639\pi$
$812$	−2.51848e7	−1.34044
$813$	−1.49882e7	−0.795283
$814$	−1.73077e6	−0.0915544
$815$	−5.52001e6	−0.291102
$816$	−6.82488e6	−0.358814
$817$	8.57999e6	0.449709
$818$	9.48865e6	0.495817
$819$	7.84360e6	0.408607
$820$	188217.	0.00977516
$821$	1.33732e7	0.692433	0.346217	−	0.938155i	$-0.387466\pi$
$821$	1.33732e7	0.692433	0.346217	+	0.938155i	$0.387466\pi$
$822$	−2.10189e6	−0.108500
$823$	4.25083e6	0.218763	0.109381	−	0.994000i	$-0.465113\pi$
$823$	4.25083e6	0.218763	0.109381	+	0.994000i	$0.465113\pi$
$824$	−3.37087e6	−0.172951
$825$	562728.	0.0287848
$826$	−5.54460e6	−0.282761
$827$	−2.37646e7	−1.20828	−0.604139	−	0.796879i	$-0.706483\pi$
$827$	−2.37646e7	−1.20828	−0.604139	+	0.796879i	$0.706483\pi$
$828$	2.14397e7	1.08679
$829$	7.88930e6	0.398706	0.199353	−	0.979928i	$-0.436116\pi$
$829$	7.88930e6	0.398706	0.199353	+	0.979928i	$0.436116\pi$
$830$	4.56902e6	0.230212
$831$	1.94601e6	0.0977557
$832$	5.22423e6	0.261646
$833$	7.83807e6	0.391378
$834$	5.88903e6	0.293176
$835$	−6.94989e6	−0.344955
$836$	1.24348e6	0.0615353
$837$	1.07679e7	0.531274
$838$	−806951.	−0.0396951
$839$	1.83852e6	0.0901703	0.0450851	−	0.998983i	$-0.485644\pi$
$839$	1.83852e6	0.0901703	0.0450851	+	0.998983i	$0.485644\pi$
$840$	2.20198e6	0.107675
$841$	5.16404e7	2.51767
$842$	5.44653e6	0.264752
$843$	−1.96190e6	−0.0950843
$844$	2.90758e7	1.40500
$845$	−5.25494e6	−0.253178
$846$	−3.62277e6	−0.174026
$847$	1.52489e6	0.0730350
$848$	5.96252e6	0.284735
$849$	−1.45707e6	−0.0693763
$850$	1.54505e6	0.0733494
$851$	3.05473e7	1.44594
$852$	−3.62857e6	−0.171253
$853$	−4.96693e6	−0.233730	−0.116865	−	0.993148i	$-0.537285\pi$
$853$	−4.96693e6	−0.233730	−0.116865	+	0.993148i	$0.537285\pi$
$854$	9.31862e6	0.437227
$855$	1.69337e6	0.0792203
$856$	2.53388e7	1.18196
$857$	3.62301e7	1.68507	0.842535	−	0.538642i	$-0.181063\pi$
$857$	3.62301e7	1.68507	0.842535	+	0.538642i	$0.181063\pi$
$858$	679219.	0.0314986
$859$	2.70333e7	1.25002	0.625008	−	0.780618i	$-0.285096\pi$
$859$	2.70333e7	1.25002	0.625008	+	0.780618i	$0.285096\pi$
$860$	1.69148e7	0.779867
$861$	−204962.	−0.00942249
$862$	−2.28449e6	−0.104718
$863$	−5.84174e6	−0.267002	−0.133501	−	0.991049i	$-0.542622\pi$
$863$	−5.84174e6	−0.267002	−0.133501	+	0.991049i	$0.542622\pi$
$864$	1.58535e7	0.722503
$865$	−1.96595e6	−0.0893373
$866$	8.88457e6	0.402570
$867$	2.30724e6	0.104243
$868$	9.96345e6	0.448860
$869$	9.56471e6	0.429657
$870$	−2.96993e6	−0.133029
$871$	−3.02998e6	−0.135330
$872$	1.14815e7	0.511337
$873$	−1.22613e7	−0.544502
$874$	2.72348e6	0.120600
$875$	1.62738e6	0.0718570
$876$	1.39306e7	0.613350
$877$	−7.03950e6	−0.309060	−0.154530	−	0.987988i	$-0.549386\pi$
$877$	−7.03950e6	−0.309060	−0.154530	+	0.987988i	$0.549386\pi$
$878$	−5.66680e6	−0.248086
$879$	210989.	0.00921061
$880$	2.10947e6	0.0918263
$881$	−4.18760e7	−1.81771	−0.908856	−	0.417110i	$-0.863043\pi$
$881$	−4.18760e7	−1.81771	−0.908856	+	0.417110i	$0.863043\pi$
$882$	−2.10160e6	−0.0909658
$883$	2.73007e7	1.17834	0.589172	−	0.808008i	$-0.299454\pi$
$883$	2.73007e7	1.17834	0.589172	+	0.808008i	$0.299454\pi$
$884$	−1.50281e7	−0.646803
$885$	5.26896e6	0.226134
$886$	4.91442e6	0.210324
$887$	−2.55127e7	−1.08880	−0.544398	−	0.838827i	$-0.683242\pi$
$887$	−2.55127e7	−1.08880	−0.544398	+	0.838827i	$0.683242\pi$
$888$	6.43590e6	0.273890
$889$	−1.30132e7	−0.552244
$890$	−2.97410e6	−0.125858
$891$	2.63184e6	0.111062
$892$	−2.35042e7	−0.989085
$893$	3.70845e6	0.155620
$894$	2.42668e6	0.101547
$895$	−1.02831e7	−0.429108
$896$	1.90374e7	0.792204
$897$	−1.19879e7	−0.497464
$898$	−1.02611e7	−0.424621
$899$	−2.85441e7	−1.17792
$900$	3.33835e6	0.137381
$901$	−1.12459e7	−0.461513
$902$	60146.0	0.00246145
$903$	−1.84197e7	−0.751730
$904$	−5.70430e6	−0.232157
$905$	−2.07196e7	−0.840930
$906$	−4.63879e6	−0.187752
$907$	−1.95793e7	−0.790278	−0.395139	−	0.918621i	$-0.629304\pi$
$907$	−1.95793e7	−0.790278	−0.395139	+	0.918621i	$0.629304\pi$
$908$	−1.71552e7	−0.690529
$909$	−1.85437e7	−0.744367
$910$	1.96427e6	0.0786316
$911$	4.66822e7	1.86361	0.931806	−	0.362956i	$-0.118233\pi$
$911$	4.66822e7	1.86361	0.931806	+	0.362956i	$0.118233\pi$
$912$	−1.87322e6	−0.0745764
$913$	−1.17657e7	−0.467134
$914$	1.38841e7	0.549735
$915$	−8.85535e6	−0.349666
$916$	1.59125e7	0.626613
$917$	−1.33668e7	−0.524933
$918$	−7.92141e6	−0.310238
$919$	−3.31492e7	−1.29474	−0.647372	−	0.762174i	$-0.724132\pi$
$919$	−3.31492e7	−1.29474	−0.647372	+	0.762174i	$0.724132\pi$
$920$	1.14046e7	0.444231
$921$	1.89606e7	0.736550
$922$	−1.43921e6	−0.0557567
$923$	−6.87539e6	−0.265640
$924$	−2.66953e6	−0.102862
$925$	4.75647e6	0.182781
$926$	8.93706e6	0.342505
$927$	5.56513e6	0.212704
$928$	−4.20251e7	−1.60191
$929$	2.33506e7	0.887685	0.443842	−	0.896105i	$-0.353615\pi$
$929$	2.33506e7	0.887685	0.443842	+	0.896105i	$0.353615\pi$
$930$	1.17494e6	0.0445461
$931$	2.15131e6	0.0813445
$932$	272781.	0.0102867
$933$	1.94348e7	0.730929
$934$	5.12866e6	0.192370
$935$	−3.97868e6	−0.148837
$936$	8.55889e6	0.319321
$937$	−3.81940e7	−1.42117	−0.710586	−	0.703611i	$-0.751570\pi$
$937$	−3.81940e7	−1.42117	−0.710586	+	0.703611i	$0.751570\pi$
$938$	−1.47780e6	−0.0548415
$939$	−8.96226e6	−0.331706
$940$	7.31093e6	0.269869
$941$	−1.97398e7	−0.726724	−0.363362	−	0.931648i	$-0.618371\pi$
$941$	−1.97398e7	−0.726724	−0.363362	+	0.931648i	$0.618371\pi$
$942$	−4.52507e6	−0.166149
$943$	−1.06155e6	−0.0388741
$944$	1.97515e7	0.721389
$945$	−8.34348e6	−0.303926
$946$	5.40524e6	0.196375
$947$	2.50005e7	0.905886	0.452943	−	0.891540i	$-0.350374\pi$
$947$	2.50005e7	0.905886	0.452943	+	0.891540i	$0.350374\pi$
$948$	−1.67443e7	−0.605126
$949$	2.63955e7	0.951404
$950$	424070.	0.0152450
$951$	−1.22183e7	−0.438085
$952$	−1.55687e7	−0.556751
$953$	3.55439e7	1.26775	0.633875	−	0.773436i	$-0.281464\pi$
$953$	3.55439e7	1.26775	0.633875	+	0.773436i	$0.281464\pi$
$954$	3.01534e6	0.107267
$955$	−9.18072e6	−0.325738
$956$	−2.71838e7	−0.961978
$957$	7.64788e6	0.269936
$958$	1.09670e7	0.386079
$959$	1.56529e7	0.549603
$960$	−2.42133e6	−0.0847960
$961$	−1.73367e7	−0.605561
$962$	5.74112e6	0.200013
$963$	−4.18331e7	−1.45363
$964$	1.72387e6	0.0597465
$965$	−1.91053e7	−0.660445
$966$	−5.84682e6	−0.201594
$967$	−1.86136e7	−0.640123	−0.320062	−	0.947397i	$-0.603704\pi$
$967$	−1.86136e7	−0.640123	−0.320062	+	0.947397i	$0.603704\pi$
$968$	1.66396e6	0.0570760
$969$	3.53309e6	0.120877
$970$	−3.07058e6	−0.104783
$971$	1.46535e7	0.498764	0.249382	−	0.968405i	$-0.419773\pi$
$971$	1.46535e7	0.498764	0.249382	+	0.968405i	$0.419773\pi$
$972$	−2.67736e7	−0.908953
$973$	−4.38561e7	−1.48507
$974$	8.68668e6	0.293398
$975$	−1.86662e6	−0.0628845
$976$	−3.31956e7	−1.11547
$977$	8.92025e6	0.298979	0.149490	−	0.988763i	$-0.452237\pi$
$977$	8.92025e6	0.298979	0.149490	+	0.988763i	$0.452237\pi$
$978$	3.08804e6	0.103237
$979$	7.65862e6	0.255384
$980$	4.24114e6	0.141064
$981$	−1.89554e7	−0.628869
$982$	−8.16968e6	−0.270350
$983$	2.35300e6	0.0776673	0.0388337	−	0.999246i	$-0.487636\pi$
$983$	2.35300e6	0.0776673	0.0388337	+	0.999246i	$0.487636\pi$
$984$	−223653.	−0.00736356
$985$	−2.04165e7	−0.670487
$986$	2.09984e7	0.687851
$987$	−7.96137e6	−0.260133
$988$	−4.12474e6	−0.134432
$989$	−9.53997e7	−3.10139
$990$	1.06679e6	0.0345933
$991$	−4.42450e6	−0.143113	−0.0715567	−	0.997437i	$-0.522797\pi$
$991$	−4.42450e6	−0.143113	−0.0715567	+	0.997437i	$0.522797\pi$
$992$	1.66257e7	0.536414
$993$	−1.91770e7	−0.617173
$994$	−3.35332e6	−0.107649
$995$	−1.88295e7	−0.602949
$996$	2.05975e7	0.657908
$997$	−1.62455e7	−0.517602	−0.258801	−	0.965931i	$-0.583327\pi$
$997$	−1.62455e7	−0.517602	−0.258801	+	0.965931i	$0.583327\pi$
$998$	1.39387e7	0.442991
$999$	−2.43862e7	−0.773089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.18	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.18	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.87953 q^{2} +7.44103 q^{3} -28.4674 q^{4} +25.0000 q^{5} -13.9857 q^{6} +104.152 q^{7} +113.650 q^{8} -187.631 q^{9} +O(q^{10})\)	\(q-1.87953 q^{2} +7.44103 q^{3} -28.4674 q^{4} +25.0000 q^{5} -13.9857 q^{6} +104.152 q^{7} +113.650 q^{8} -187.631 q^{9} -46.9883 q^{10} +121.000 q^{11} -211.826 q^{12} -401.367 q^{13} -195.758 q^{14} +186.026 q^{15} +697.346 q^{16} -1315.27 q^{17} +352.659 q^{18} -361.000 q^{19} -711.684 q^{20} +775.000 q^{21} -227.423 q^{22} +4013.91 q^{23} +845.676 q^{24} +625.000 q^{25} +754.383 q^{26} -3204.34 q^{27} -2964.94 q^{28} +8494.21 q^{29} -349.641 q^{30} -3360.42 q^{31} -4947.50 q^{32} +900.365 q^{33} +2472.09 q^{34} +2603.81 q^{35} +5341.36 q^{36} +7610.36 q^{37} +678.511 q^{38} -2986.58 q^{39} +2841.26 q^{40} -264.467 q^{41} -1456.64 q^{42} -23767.3 q^{43} -3444.55 q^{44} -4690.78 q^{45} -7544.28 q^{46} -10272.7 q^{47} +5188.97 q^{48} -5959.30 q^{49} -1174.71 q^{50} -9786.94 q^{51} +11425.9 q^{52} +8550.31 q^{53} +6022.66 q^{54} +3025.00 q^{55} +11836.9 q^{56} -2686.21 q^{57} -15965.1 q^{58} +28323.8 q^{59} -5295.66 q^{60} -47602.8 q^{61} +6316.02 q^{62} -19542.2 q^{63} -13016.1 q^{64} -10034.2 q^{65} -1692.26 q^{66} +7549.14 q^{67} +37442.2 q^{68} +29867.6 q^{69} -4893.94 q^{70} +17129.9 q^{71} -21324.3 q^{72} -65764.0 q^{73} -14303.9 q^{74} +4650.64 q^{75} +10276.7 q^{76} +12602.4 q^{77} +5613.38 q^{78} +79047.2 q^{79} +17433.6 q^{80} +21750.8 q^{81} +497.074 q^{82} -97237.4 q^{83} -22062.2 q^{84} -32881.7 q^{85} +44671.4 q^{86} +63205.6 q^{87} +13751.7 q^{88} +63294.4 q^{89} +8816.47 q^{90} -41803.3 q^{91} -114265. q^{92} -25005.0 q^{93} +19307.9 q^{94} -9025.00 q^{95} -36814.5 q^{96} +65347.7 q^{97} +11200.7 q^{98} -22703.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more