LMFDB - Embedded newform 1045.6.a.d.1.14

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-3.01425 q^{2} +4.06006 q^{3} -22.9143 q^{4} -25.0000 q^{5} -12.2380 q^{6} -121.519 q^{7} +165.525 q^{8} -226.516 q^{9} +O(q^{10})$	\(q-3.01425 q^{2} +4.06006 q^{3} -22.9143 q^{4} -25.0000 q^{5} -12.2380 q^{6} -121.519 q^{7} +165.525 q^{8} -226.516 q^{9} +75.3562 q^{10} +121.000 q^{11} -93.0335 q^{12} -876.169 q^{13} +366.289 q^{14} -101.501 q^{15} +234.324 q^{16} +1811.83 q^{17} +682.775 q^{18} -361.000 q^{19} +572.858 q^{20} -493.375 q^{21} -364.724 q^{22} -315.480 q^{23} +672.042 q^{24} +625.000 q^{25} +2640.99 q^{26} -1906.26 q^{27} +2784.53 q^{28} -1796.36 q^{29} +305.950 q^{30} -10055.9 q^{31} -6003.12 q^{32} +491.267 q^{33} -5461.30 q^{34} +3037.98 q^{35} +5190.46 q^{36} -1329.12 q^{37} +1088.14 q^{38} -3557.30 q^{39} -4138.13 q^{40} -17160.0 q^{41} +1487.15 q^{42} -13674.5 q^{43} -2772.63 q^{44} +5662.90 q^{45} +950.934 q^{46} -13588.3 q^{47} +951.369 q^{48} -2040.11 q^{49} -1883.90 q^{50} +7356.14 q^{51} +20076.8 q^{52} -5192.00 q^{53} +5745.94 q^{54} -3025.00 q^{55} -20114.5 q^{56} -1465.68 q^{57} +5414.68 q^{58} -13591.2 q^{59} +2325.84 q^{60} -13386.8 q^{61} +30311.0 q^{62} +27526.0 q^{63} +10596.5 q^{64} +21904.2 q^{65} -1480.80 q^{66} +7476.22 q^{67} -41516.9 q^{68} -1280.87 q^{69} -9157.22 q^{70} -27355.9 q^{71} -37494.1 q^{72} -55495.7 q^{73} +4006.30 q^{74} +2537.54 q^{75} +8272.07 q^{76} -14703.8 q^{77} +10722.6 q^{78} +5812.67 q^{79} -5858.10 q^{80} +47303.8 q^{81} +51724.4 q^{82} +10309.2 q^{83} +11305.3 q^{84} -45295.8 q^{85} +41218.4 q^{86} -7293.34 q^{87} +20028.6 q^{88} -27485.6 q^{89} -17069.4 q^{90} +106471. q^{91} +7229.01 q^{92} -40827.6 q^{93} +40958.5 q^{94} +9025.00 q^{95} -24373.0 q^{96} -67862.9 q^{97} +6149.38 q^{98} -27408.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * 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 $

$2$	−3.01425	−0.532849	−0.266424	−	0.963856i	$-0.585842\pi$
$2$	−3.01425	−0.532849	−0.266424	+	0.963856i	$0.585842\pi$
$3$	4.06006	0.260453	0.130226	−	0.991484i	$-0.458430\pi$
$3$	4.06006	0.260453	0.130226	+	0.991484i	$0.458430\pi$
$4$	−22.9143	−0.716072
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−12.2380	−0.138782
$7$	−121.519	−0.937345	−0.468673	−	0.883372i	$-0.655268\pi$
$7$	−121.519	−0.937345	−0.468673	+	0.883372i	$0.655268\pi$
$8$	165.525	0.914407
$9$	−226.516	−0.932164
$10$	75.3562	0.238297
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−93.0335	−0.186503
$13$	−876.169	−1.43790	−0.718951	−	0.695061i	$-0.755378\pi$
$13$	−876.169	−1.43790	−0.718951	+	0.695061i	$0.755378\pi$
$14$	366.289	0.499463
$15$	−101.501	−0.116478
$16$	234.324	0.228832
$17$	1811.83	1.52053	0.760266	−	0.649612i	$-0.225069\pi$
$17$	1811.83	1.52053	0.760266	+	0.649612i	$0.225069\pi$
$18$	682.775	0.496702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	572.858	0.320237
$21$	−493.375	−0.244134
$22$	−364.724	−0.160660
$23$	−315.480	−0.124352	−0.0621759	−	0.998065i	$-0.519804\pi$
$23$	−315.480	−0.124352	−0.0621759	+	0.998065i	$0.519804\pi$
$24$	672.042	0.238160
$25$	625.000	0.200000
$26$	2640.99	0.766184
$27$	−1906.26	−0.503238
$28$	2784.53	0.671207
$29$	−1796.36	−0.396642	−0.198321	−	0.980137i	$-0.563549\pi$
$29$	−1796.36	−0.396642	−0.198321	+	0.980137i	$0.563549\pi$
$30$	305.950	0.0620652
$31$	−10055.9	−1.87939	−0.939695	−	0.342013i	$-0.888891\pi$
$31$	−10055.9	−1.87939	−0.939695	+	0.342013i	$0.888891\pi$
$32$	−6003.12	−1.03634
$33$	491.267	0.0785295
$34$	−5461.30	−0.810213
$35$	3037.98	0.419193
$36$	5190.46	0.667497
$37$	−1329.12	−0.159610	−0.0798050	−	0.996810i	$-0.525430\pi$
$37$	−1329.12	−0.159610	−0.0798050	+	0.996810i	$0.525430\pi$
$38$	1088.14	0.122244
$39$	−3557.30	−0.374506
$40$	−4138.13	−0.408935
$41$	−17160.0	−1.59425	−0.797126	−	0.603812i	$-0.793648\pi$
$41$	−17160.0	−1.59425	−0.797126	+	0.603812i	$0.793648\pi$
$42$	1487.15	0.130087
$43$	−13674.5	−1.12782	−0.563912	−	0.825835i	$-0.690704\pi$
$43$	−13674.5	−1.12782	−0.563912	+	0.825835i	$0.690704\pi$
$44$	−2772.63	−0.215904
$45$	5662.90	0.416877
$46$	950.934	0.0662607
$47$	−13588.3	−0.897265	−0.448632	−	0.893716i	$-0.648089\pi$
$47$	−13588.3	−0.897265	−0.448632	+	0.893716i	$0.648089\pi$
$48$	951.369	0.0596000
$49$	−2040.11	−0.121384
$50$	−1883.90	−0.106570
$51$	7356.14	0.396027
$52$	20076.8	1.02964
$53$	−5192.00	−0.253890	−0.126945	−	0.991910i	$-0.540517\pi$
$53$	−5192.00	−0.253890	−0.126945	+	0.991910i	$0.540517\pi$
$54$	5745.94	0.268150
$55$	−3025.00	−0.134840
$56$	−20114.5	−0.857115
$57$	−1465.68	−0.0597520
$58$	5414.68	0.211350
$59$	−13591.2	−0.508311	−0.254155	−	0.967163i	$-0.581797\pi$
$59$	−13591.2	−0.508311	−0.254155	+	0.967163i	$0.581797\pi$
$60$	2325.84	0.0834067
$61$	−13386.8	−0.460628	−0.230314	−	0.973116i	$-0.573975\pi$
$61$	−13386.8	−0.460628	−0.230314	+	0.973116i	$0.573975\pi$
$62$	30311.0	1.00143
$63$	27526.0	0.873760
$64$	10596.5	0.323380
$65$	21904.2	0.643049
$66$	−1480.80	−0.0418443
$67$	7476.22	0.203468	0.101734	−	0.994812i	$-0.467561\pi$
$67$	7476.22	0.203468	0.101734	+	0.994812i	$0.467561\pi$
$68$	−41516.9	−1.08881
$69$	−1280.87	−0.0323878
$70$	−9157.22	−0.223367
$71$	−27355.9	−0.644029	−0.322015	−	0.946735i	$-0.604360\pi$
$71$	−27355.9	−0.644029	−0.322015	+	0.946735i	$0.604360\pi$
$72$	−37494.1	−0.852377
$73$	−55495.7	−1.21885	−0.609427	−	0.792842i	$-0.708601\pi$
$73$	−55495.7	−1.21885	−0.609427	+	0.792842i	$0.708601\pi$
$74$	4006.30	0.0850479
$75$	2537.54	0.0520906
$76$	8272.07	0.164278
$77$	−14703.8	−0.282620
$78$	10722.6	0.199555
$79$	5812.67	0.104787	0.0523935	−	0.998627i	$-0.483315\pi$
$79$	5812.67	0.104787	0.0523935	+	0.998627i	$0.483315\pi$
$80$	−5858.10	−0.102337
$81$	47303.8	0.801095
$82$	51724.4	0.849495
$83$	10309.2	0.164259	0.0821297	−	0.996622i	$-0.473828\pi$
$83$	10309.2	0.164259	0.0821297	+	0.996622i	$0.473828\pi$
$84$	11305.3	0.174818
$85$	−45295.8	−0.680002
$86$	41218.4	0.600959
$87$	−7293.34	−0.103307
$88$	20028.6	0.275704
$89$	−27485.6	−0.367816	−0.183908	−	0.982943i	$-0.558875\pi$
$89$	−27485.6	−0.367816	−0.183908	+	0.982943i	$0.558875\pi$
$90$	−17069.4	−0.222132
$91$	106471.	1.34781
$92$	7229.01	0.0890449
$93$	−40827.6	−0.489493
$94$	40958.5	0.478106
$95$	9025.00	0.102598
$96$	−24373.0	−0.269918
$97$	−67862.9	−0.732324	−0.366162	−	0.930551i	$-0.619328\pi$
$97$	−67862.9	−0.732324	−0.366162	+	0.930551i	$0.619328\pi$
$98$	6149.38	0.0646794
$99$	−27408.4	−0.281058
$100$	−14321.4	−0.143214
$101$	−49663.1	−0.484429	−0.242215	−	0.970223i	$-0.577874\pi$
$101$	−49663.1	−0.484429	−0.242215	+	0.970223i	$0.577874\pi$
$102$	−22173.2	−0.211022
$103$	−71164.8	−0.660955	−0.330478	−	0.943814i	$-0.607210\pi$
$103$	−71164.8	−0.660955	−0.330478	+	0.943814i	$0.607210\pi$
$104$	−145028.	−1.31483
$105$	12334.4	0.109180
$106$	15650.0	0.135285
$107$	−114732.	−0.968782	−0.484391	−	0.874852i	$-0.660959\pi$
$107$	−114732.	−0.968782	−0.484391	+	0.874852i	$0.660959\pi$
$108$	43680.7	0.360355
$109$	−17160.9	−0.138349	−0.0691743	−	0.997605i	$-0.522036\pi$
$109$	−17160.9	−0.138349	−0.0691743	+	0.997605i	$0.522036\pi$
$110$	9118.10	0.0718493
$111$	−5396.31	−0.0415709
$112$	−28474.8	−0.214495
$113$	118336.	0.871805	0.435903	−	0.899994i	$-0.356429\pi$
$113$	118336.	0.871805	0.435903	+	0.899994i	$0.356429\pi$
$114$	4417.92	0.0318388
$115$	7887.00	0.0556118
$116$	41162.4	0.284025
$117$	198466.	1.34036
$118$	40967.4	0.270853
$119$	−220172.	−1.42526
$120$	−16801.1	−0.106508
$121$	14641.0	0.0909091
$122$	40351.0	0.245445
$123$	−69670.5	−0.415228
$124$	230424.	1.34578
$125$	−15625.0	−0.0894427
$126$	−82970.2	−0.465582
$127$	95378.0	0.524733	0.262367	−	0.964968i	$-0.415497\pi$
$127$	95378.0	0.524733	0.262367	+	0.964968i	$0.415497\pi$
$128$	160159.	0.864027
$129$	−55519.4	−0.293745
$130$	−66024.7	−0.342648
$131$	−226448.	−1.15290	−0.576449	−	0.817133i	$-0.695562\pi$
$131$	−226448.	−1.15290	−0.576449	+	0.817133i	$0.695562\pi$
$132$	−11257.0	−0.0562328
$133$	43868.4	0.215042
$134$	−22535.2	−0.108417
$135$	47656.6	0.225055
$136$	299904.	1.39038
$137$	−126473.	−0.575699	−0.287849	−	0.957676i	$-0.592940\pi$
$137$	−126473.	−0.575699	−0.287849	+	0.957676i	$0.592940\pi$
$138$	3860.85	0.0172578
$139$	245435.	1.07746	0.538728	−	0.842480i	$-0.318905\pi$
$139$	245435.	1.07746	0.538728	+	0.842480i	$0.318905\pi$
$140$	−69613.2	−0.300173
$141$	−55169.3	−0.233695
$142$	82457.5	0.343170
$143$	−106016.	−0.433544
$144$	−53078.1	−0.213309
$145$	44909.1	0.177384
$146$	167278.	0.649465
$147$	−8282.95	−0.0316149
$148$	30455.9	0.114292
$149$	−465387.	−1.71731	−0.858656	−	0.512553i	$-0.828700\pi$
$149$	−465387.	−1.71731	−0.858656	+	0.512553i	$0.828700\pi$
$150$	−7648.76	−0.0277564
$151$	273474.	0.976054	0.488027	−	0.872829i	$-0.337717\pi$
$151$	273474.	0.976054	0.488027	+	0.872829i	$0.337717\pi$
$152$	−59754.6	−0.209779
$153$	−410408.	−1.41738
$154$	44320.9	0.150594
$155$	251398.	0.840489
$156$	81513.0	0.268173
$157$	77728.5	0.251670	0.125835	−	0.992051i	$-0.459839\pi$
$157$	77728.5	0.251670	0.125835	+	0.992051i	$0.459839\pi$
$158$	−17520.8	−0.0558356
$159$	−21079.8	−0.0661263
$160$	150078.	0.463465
$161$	38336.8	0.116561
$162$	−142585.	−0.426862
$163$	128294.	0.378215	0.189108	−	0.981956i	$-0.439441\pi$
$163$	128294.	0.378215	0.189108	+	0.981956i	$0.439441\pi$
$164$	393209.	1.14160
$165$	−12281.7	−0.0351195
$166$	−31074.5	−0.0875254
$167$	695819.	1.93066	0.965328	−	0.261040i	$-0.0840653\pi$
$167$	695819.	1.93066	0.965328	+	0.261040i	$0.0840653\pi$
$168$	−81666.0	−0.223238
$169$	396379.	1.06756
$170$	136533.	0.362338
$171$	81772.2	0.213853
$172$	313342.	0.807603
$173$	−471315.	−1.19728	−0.598640	−	0.801018i	$-0.704292\pi$
$173$	−471315.	−1.19728	−0.598640	+	0.801018i	$0.704292\pi$
$174$	21983.9	0.0550468
$175$	−75949.4	−0.187469
$176$	28353.2	0.0689954
$177$	−55181.3	−0.132391
$178$	82848.4	0.195990
$179$	−67792.7	−0.158143	−0.0790715	−	0.996869i	$-0.525196\pi$
$179$	−67792.7	−0.158143	−0.0790715	+	0.996869i	$0.525196\pi$
$180$	−129761.	−0.298514
$181$	−90886.8	−0.206207	−0.103104	−	0.994671i	$-0.532877\pi$
$181$	−90886.8	−0.206207	−0.103104	+	0.994671i	$0.532877\pi$
$182$	−320931.	−0.718179
$183$	−54351.0	−0.119972
$184$	−52219.9	−0.113708
$185$	33228.0	0.0713797
$186$	123064.	0.260826
$187$	219232.	0.458457
$188$	311367.	0.642506
$189$	231647.	0.471707
$190$	−27203.6	−0.0546691
$191$	−644796.	−1.27891	−0.639454	−	0.768830i	$-0.720839\pi$
$191$	−644796.	−1.27891	−0.639454	+	0.768830i	$0.720839\pi$
$192$	43022.5	0.0842253
$193$	−108236.	−0.209160	−0.104580	−	0.994516i	$-0.533350\pi$
$193$	−108236.	−0.209160	−0.104580	+	0.994516i	$0.533350\pi$
$194$	204556.	0.390218
$195$	88932.4	0.167484
$196$	46747.6	0.0869199
$197$	−81355.3	−0.149355	−0.0746776	−	0.997208i	$-0.523793\pi$
$197$	−81355.3	−0.149355	−0.0746776	+	0.997208i	$0.523793\pi$
$198$	82615.8	0.149761
$199$	434690.	0.778120	0.389060	−	0.921212i	$-0.372800\pi$
$199$	434690.	0.778120	0.389060	+	0.921212i	$0.372800\pi$
$200$	103453.	0.182881
$201$	30353.9	0.0529937
$202$	149697.	0.258127
$203$	218292.	0.371791
$204$	−168561.	−0.283584
$205$	429000.	0.712972
$206$	214508.	0.352189
$207$	71461.2	0.115916
$208$	−205307.	−0.329038
$209$	−43681.0	−0.0691714
$210$	−37178.8	−0.0581765
$211$	−221141.	−0.341950	−0.170975	−	0.985275i	$-0.554692\pi$
$211$	−221141.	−0.341950	−0.170975	+	0.985275i	$0.554692\pi$
$212$	118971.	0.181803
$213$	−111067.	−0.167739
$214$	345831.	0.516214
$215$	341863.	0.504378
$216$	−315535.	−0.460164
$217$	1.22199e6	1.76164
$218$	51727.3	0.0737188
$219$	−225316.	−0.317454
$220$	69315.8	0.0965552
$221$	−1.58747e6	−2.18638
$222$	16265.8	0.0221510
$223$	−706969.	−0.952003	−0.476001	−	0.879444i	$-0.657914\pi$
$223$	−706969.	−0.952003	−0.476001	+	0.879444i	$0.657914\pi$
$224$	729494.	0.971408
$225$	−141572.	−0.186433
$226$	−356693.	−0.464540
$227$	250541.	0.322711	0.161356	−	0.986896i	$-0.448413\pi$
$227$	250541.	0.322711	0.161356	+	0.986896i	$0.448413\pi$
$228$	33585.1	0.0427867
$229$	−33952.0	−0.0427836	−0.0213918	−	0.999771i	$-0.506810\pi$
$229$	−33952.0	−0.0427836	−0.0213918	+	0.999771i	$0.506810\pi$
$230$	−23773.4	−0.0296327
$231$	−59698.3	−0.0736092
$232$	−297344.	−0.362692
$233$	−710050.	−0.856839	−0.428419	−	0.903580i	$-0.640929\pi$
$233$	−710050.	−0.856839	−0.428419	+	0.903580i	$0.640929\pi$
$234$	−598226.	−0.714210
$235$	339708.	0.401269
$236$	311434.	0.363987
$237$	23599.8	0.0272921
$238$	663653.	0.759449
$239$	−194978.	−0.220795	−0.110398	−	0.993887i	$-0.535212\pi$
$239$	−194978.	−0.220795	−0.110398	+	0.993887i	$0.535212\pi$
$240$	−23784.2	−0.0266539
$241$	−1.71437e6	−1.90135	−0.950673	−	0.310193i	$-0.899606\pi$
$241$	−1.71437e6	−1.90135	−0.950673	+	0.310193i	$0.899606\pi$
$242$	−44131.6	−0.0484408
$243$	655278.	0.711885
$244$	306748.	0.329843
$245$	51002.6	0.0542847
$246$	210004.	0.221254
$247$	316297.	0.329877
$248$	−1.66451e6	−1.71853
$249$	41856.0	0.0427819
$250$	47097.6	0.0476594
$251$	44486.0	0.0445697	0.0222848	−	0.999752i	$-0.492906\pi$
$251$	44486.0	0.0445697	0.0222848	+	0.999752i	$0.492906\pi$
$252$	−630740.	−0.625675
$253$	−38173.1	−0.0374935
$254$	−287493.	−0.279603
$255$	−183903.	−0.177109
$256$	−821848.	−0.783776
$257$	785456.	0.741803	0.370902	−	0.928672i	$-0.379049\pi$
$257$	785456.	0.741803	0.370902	+	0.928672i	$0.379049\pi$
$258$	167349.	0.156522
$259$	161513.	0.149610
$260$	−501920.	−0.460470
$261$	406905.	0.369736
$262$	682571.	0.614320
$263$	−1.84491e6	−1.64470	−0.822348	−	0.568985i	$-0.807336\pi$
$263$	−1.84491e6	−1.64470	−0.822348	+	0.568985i	$0.807336\pi$
$264$	81317.1	0.0718079
$265$	129800.	0.113543
$266$	−132230.	−0.114585
$267$	−111593.	−0.0957986
$268$	−171313.	−0.145698
$269$	610079.	0.514050	0.257025	−	0.966405i	$-0.417258\pi$
$269$	610079.	0.514050	0.257025	+	0.966405i	$0.417258\pi$
$270$	−143649.	−0.119920
$271$	−655774.	−0.542414	−0.271207	−	0.962521i	$-0.587423\pi$
$271$	−655774.	−0.542414	−0.271207	+	0.962521i	$0.587423\pi$
$272$	424555.	0.347946
$273$	432280.	0.351041
$274$	381220.	0.306760
$275$	75625.0	0.0603023
$276$	29350.2	0.0231920
$277$	2.16447e6	1.69493	0.847466	−	0.530850i	$-0.178127\pi$
$277$	2.16447e6	1.69493	0.847466	+	0.530850i	$0.178127\pi$
$278$	−739801.	−0.574121
$279$	2.27782e6	1.75190
$280$	502862.	0.383313
$281$	1.08050e6	0.816320	0.408160	−	0.912910i	$-0.366171\pi$
$281$	1.08050e6	0.816320	0.408160	+	0.912910i	$0.366171\pi$
$282$	166294.	0.124524
$283$	308593.	0.229045	0.114522	−	0.993421i	$-0.463466\pi$
$283$	308593.	0.229045	0.114522	+	0.993421i	$0.463466\pi$
$284$	626843.	0.461172
$285$	36642.0	0.0267219
$286$	319560.	0.231013
$287$	2.08527e6	1.49437
$288$	1.35980e6	0.966039
$289$	1.86287e6	1.31201
$290$	−135367.	−0.0945187
$291$	−275527.	−0.190736
$292$	1.27164e6	0.872788
$293$	1.71159e6	1.16474	0.582372	−	0.812922i	$-0.302125\pi$
$293$	1.71159e6	1.16474	0.582372	+	0.812922i	$0.302125\pi$
$294$	24966.8	0.0168459
$295$	339781.	0.227323
$296$	−220003.	−0.145948
$297$	−230658.	−0.151732
$298$	1.40279e6	0.915067
$299$	276414.	0.178806
$300$	−58145.9	−0.0373006
$301$	1.66172e6	1.05716
$302$	−824318.	−0.520089
$303$	−201635.	−0.126171
$304$	−84591.0	−0.0524977
$305$	334669.	0.205999
$306$	1.23707e6	0.755251
$307$	−71249.4	−0.0431455	−0.0215727	−	0.999767i	$-0.506867\pi$
$307$	−71249.4	−0.0431455	−0.0215727	+	0.999767i	$0.506867\pi$
$308$	336928.	0.202376
$309$	−288933.	−0.172148
$310$	−757775.	−0.447853
$311$	−242249.	−0.142024	−0.0710118	−	0.997475i	$-0.522623\pi$
$311$	−242249.	−0.142024	−0.0710118	+	0.997475i	$0.522623\pi$
$312$	−588823.	−0.342451
$313$	424471.	0.244899	0.122450	−	0.992475i	$-0.460925\pi$
$313$	424471.	0.244899	0.122450	+	0.992475i	$0.460925\pi$
$314$	−234293.	−0.134102
$315$	−688150.	−0.390757
$316$	−133193.	−0.0750351
$317$	1.78136e6	0.995644	0.497822	−	0.867279i	$-0.334133\pi$
$317$	1.78136e6	0.995644	0.497822	+	0.867279i	$0.334133\pi$
$318$	63539.8	0.0352353
$319$	−217360.	−0.119592
$320$	−264913.	−0.144620
$321$	−465820.	−0.252322
$322$	−115557.	−0.0621091
$323$	−654071.	−0.348834
$324$	−1.08393e6	−0.573642
$325$	−547605.	−0.287580
$326$	−386711.	−0.201531
$327$	−69674.4	−0.0360333
$328$	−2.84041e6	−1.45780
$329$	1.65124e6	0.841047
$330$	37020.0	0.0187134
$331$	−1.28935e6	−0.646845	−0.323422	−	0.946255i	$-0.604833\pi$
$331$	−1.28935e6	−0.646845	−0.323422	+	0.946255i	$0.604833\pi$
$332$	−236229.	−0.117622
$333$	301067.	0.148783
$334$	−2.09737e6	−1.02875
$335$	−186906.	−0.0909935
$336$	−115610.	−0.0558657
$337$	1.69123e6	0.811202	0.405601	−	0.914050i	$-0.367062\pi$
$337$	1.69123e6	0.811202	0.405601	+	0.914050i	$0.367062\pi$
$338$	−1.19478e6	−0.568850
$339$	480450.	0.227064
$340$	1.03792e6	0.486931
$341$	−1.21676e6	−0.566658
$342$	−246482.	−0.113951
$343$	2.29028e6	1.05112
$344$	−2.26348e6	−1.03129
$345$	32021.7	0.0144843
$346$	1.42066e6	0.637969
$347$	−3.36939e6	−1.50220	−0.751100	−	0.660189i	$-0.770476\pi$
$347$	−3.36939e6	−1.50220	−0.751100	+	0.660189i	$0.770476\pi$
$348$	167122.	0.0739750
$349$	546288.	0.240081	0.120041	−	0.992769i	$-0.461698\pi$
$349$	546288.	0.240081	0.120041	+	0.992769i	$0.461698\pi$
$350$	228930.	0.0998926
$351$	1.67021e6	0.723607
$352$	−726378.	−0.312468
$353$	504434.	0.215461	0.107730	−	0.994180i	$-0.465642\pi$
$353$	504434.	0.215461	0.107730	+	0.994180i	$0.465642\pi$
$354$	166330.	0.0705443
$355$	683898.	0.288019
$356$	629814.	0.263383
$357$	−893911.	−0.371214
$358$	204344.	0.0842663
$359$	−758494.	−0.310610	−0.155305	−	0.987867i	$-0.549636\pi$
$359$	−758494.	−0.310610	−0.155305	+	0.987867i	$0.549636\pi$
$360$	937353.	0.381195
$361$	130321.	0.0526316
$362$	273955.	0.109877
$363$	59443.3	0.0236775
$364$	−2.43972e6	−0.965130
$365$	1.38739e6	0.545088
$366$	163827.	0.0639269
$367$	2.85388e6	1.10604	0.553020	−	0.833168i	$-0.313475\pi$
$367$	2.85388e6	1.10604	0.553020	+	0.833168i	$0.313475\pi$
$368$	−73924.5	−0.0284557
$369$	3.88701e6	1.48611
$370$	−100157.	−0.0380346
$371$	630927.	0.237982
$372$	935536.	0.350512
$373$	−2.60556e6	−0.969681	−0.484841	−	0.874602i	$-0.661122\pi$
$373$	−2.60556e6	−0.969681	−0.484841	+	0.874602i	$0.661122\pi$
$374$	−660818.	−0.244288
$375$	−63438.4	−0.0232956
$376$	−2.24921e6	−0.820465
$377$	1.57392e6	0.570333
$378$	−698242.	−0.251349
$379$	2.36384e6	0.845317	0.422659	−	0.906289i	$-0.361097\pi$
$379$	2.36384e6	0.845317	0.422659	+	0.906289i	$0.361097\pi$
$380$	−206802.	−0.0734675
$381$	387240.	0.136668
$382$	1.94358e6	0.681464
$383$	948067.	0.330249	0.165125	−	0.986273i	$-0.447197\pi$
$383$	948067.	0.330249	0.165125	+	0.986273i	$0.447197\pi$
$384$	650256.	0.225038
$385$	367595.	0.126392
$386$	326251.	0.111451
$387$	3.09750e6	1.05132
$388$	1.55503e6	0.524397
$389$	−2.70733e6	−0.907125	−0.453563	−	0.891224i	$-0.649847\pi$
$389$	−2.70733e6	−0.907125	−0.453563	+	0.891224i	$0.649847\pi$
$390$	−268064.	−0.0892437
$391$	−571596.	−0.189081
$392$	−337689.	−0.110995
$393$	−919393.	−0.300276
$394$	245225.	0.0795837
$395$	−145317.	−0.0468622
$396$	628045.	0.201258
$397$	−5.09962e6	−1.62391	−0.811954	−	0.583722i	$-0.801596\pi$
$397$	−5.09962e6	−1.62391	−0.811954	+	0.583722i	$0.801596\pi$
$398$	−1.31026e6	−0.414620
$399$	178108.	0.0560082
$400$	146452.	0.0457664
$401$	−3.97793e6	−1.23537	−0.617684	−	0.786427i	$-0.711929\pi$
$401$	−3.97793e6	−1.23537	−0.617684	+	0.786427i	$0.711929\pi$
$402$	−91494.2	−0.0282376
$403$	8.81067e6	2.70238
$404$	1.13800e6	0.346886
$405$	−1.18260e6	−0.358260
$406$	−657987.	−0.198108
$407$	−160824.	−0.0481242
$408$	1.21763e6	0.362129
$409$	2.09039e6	0.617903	0.308951	−	0.951078i	$-0.400022\pi$
$409$	2.09039e6	0.617903	0.308951	+	0.951078i	$0.400022\pi$
$410$	−1.29311e6	−0.379906
$411$	−513487.	−0.149942
$412$	1.63069e6	0.473292
$413$	1.65160e6	0.476462
$414$	−215402.	−0.0617658
$415$	−257730.	−0.0734591
$416$	5.25975e6	1.49016
$417$	996480.	0.280626
$418$	131665.	0.0368579
$419$	−2.00607e6	−0.558226	−0.279113	−	0.960258i	$-0.590040\pi$
$419$	−2.00607e6	−0.558226	−0.279113	+	0.960258i	$0.590040\pi$
$420$	−282634.	−0.0781809
$421$	4.19979e6	1.15484	0.577421	−	0.816447i	$-0.304059\pi$
$421$	4.19979e6	1.15484	0.577421	+	0.816447i	$0.304059\pi$
$422$	666573.	0.182208
$423$	3.07797e6	0.836398
$424$	−859407.	−0.232158
$425$	1.13239e6	0.304106
$426$	334782.	0.0893797
$427$	1.62675e6	0.431768
$428$	2.62901e6	0.693718
$429$	−430433.	−0.112918
$430$	−1.03046e6	−0.268757
$431$	1.27147e6	0.329696	0.164848	−	0.986319i	$-0.447287\pi$
$431$	1.27147e6	0.329696	0.164848	+	0.986319i	$0.447287\pi$
$432$	−446683.	−0.115157
$433$	1.99429e6	0.511175	0.255587	−	0.966786i	$-0.417731\pi$
$433$	1.99429e6	0.511175	0.255587	+	0.966786i	$0.417731\pi$
$434$	−3.68336e6	−0.938686
$435$	182333.	0.0462001
$436$	393231.	0.0990675
$437$	113888.	0.0285283
$438$	679157.	0.169155
$439$	−688609.	−0.170534	−0.0852670	−	0.996358i	$-0.527174\pi$
$439$	−688609.	−0.170534	−0.0852670	+	0.996358i	$0.527174\pi$
$440$	−500714.	−0.123299
$441$	462116.	0.113150
$442$	4.78502e6	1.16501
$443$	2.54544e6	0.616246	0.308123	−	0.951347i	$-0.400299\pi$
$443$	2.54544e6	0.616246	0.308123	+	0.951347i	$0.400299\pi$
$444$	123653.	0.0297677
$445$	687140.	0.164492
$446$	2.13098e6	0.507273
$447$	−1.88950e6	−0.447279
$448$	−1.28768e6	−0.303119
$449$	6.60575e6	1.54634	0.773172	−	0.634196i	$-0.218669\pi$
$449$	6.60575e6	1.54634	0.773172	+	0.634196i	$0.218669\pi$
$450$	426734.	0.0993405
$451$	−2.07636e6	−0.480685
$452$	−2.71158e6	−0.624276
$453$	1.11032e6	0.254216
$454$	−755192.	−0.171956
$455$	−2.66178e6	−0.602759
$456$	−242607.	−0.0546376
$457$	2.37342e6	0.531600	0.265800	−	0.964028i	$-0.414364\pi$
$457$	2.37342e6	0.531600	0.265800	+	0.964028i	$0.414364\pi$
$458$	102340.	0.0227972
$459$	−3.45382e6	−0.765189
$460$	−180725.	−0.0398221
$461$	1.10310e6	0.241747	0.120874	−	0.992668i	$-0.461430\pi$
$461$	1.10310e6	0.241747	0.120874	+	0.992668i	$0.461430\pi$
$462$	179946.	0.0392226
$463$	−6.13151e6	−1.32927	−0.664637	−	0.747166i	$-0.731414\pi$
$463$	−6.13151e6	−1.32927	−0.664637	+	0.747166i	$0.731414\pi$
$464$	−420931.	−0.0907645
$465$	1.02069e6	0.218908
$466$	2.14027e6	0.456565
$467$	5.70833e6	1.21120	0.605601	−	0.795768i	$-0.292933\pi$
$467$	5.70833e6	1.21120	0.605601	+	0.795768i	$0.292933\pi$
$468$	−4.54772e6	−0.959796
$469$	−908504.	−0.190719
$470$	−1.02396e6	−0.213816
$471$	315582.	0.0655481
$472$	−2.24969e6	−0.464803
$473$	−1.65462e6	−0.340052
$474$	−71135.5	−0.0145426
$475$	−225625.	−0.0458831
$476$	5.04509e6	1.02059
$477$	1.17607e6	0.236667
$478$	587711.	0.117651
$479$	3.16504e6	0.630290	0.315145	−	0.949044i	$-0.397947\pi$
$479$	3.16504e6	0.630290	0.315145	+	0.949044i	$0.397947\pi$
$480$	609325.	0.120711
$481$	1.16453e6	0.229503
$482$	5.16753e6	1.01313
$483$	155650.	0.0303585
$484$	−335488.	−0.0650975
$485$	1.69657e6	0.327505
$486$	−1.97517e6	−0.379327
$487$	−7.70187e6	−1.47155	−0.735773	−	0.677228i	$-0.763181\pi$
$487$	−7.70187e6	−1.47155	−0.735773	+	0.677228i	$0.763181\pi$
$488$	−2.21585e6	−0.421202
$489$	520883.	0.0985072
$490$	−153735.	−0.0289255
$491$	−5.57840e6	−1.04425	−0.522127	−	0.852868i	$-0.674861\pi$
$491$	−5.57840e6	−1.04425	−0.522127	+	0.852868i	$0.674861\pi$
$492$	1.59645e6	0.297333
$493$	−3.25471e6	−0.603107
$494$	−953397.	−0.175775
$495$	685211.	0.125693
$496$	−2.35634e6	−0.430065
$497$	3.32427e6	0.603678
$498$	−126164.	−0.0227963
$499$	4.04605e6	0.727412	0.363706	−	0.931514i	$-0.381511\pi$
$499$	4.04605e6	0.727412	0.363706	+	0.931514i	$0.381511\pi$
$500$	358036.	0.0640475
$501$	2.82506e6	0.502845
$502$	−134092.	−0.0237489
$503$	2.44608e6	0.431073	0.215537	−	0.976496i	$-0.430850\pi$
$503$	2.44608e6	0.431073	0.215537	+	0.976496i	$0.430850\pi$
$504$	4.55625e6	0.798972
$505$	1.24158e6	0.216643
$506$	115063.	0.0199783
$507$	1.60932e6	0.278050
$508$	−2.18552e6	−0.375747
$509$	9.24842e6	1.58224	0.791121	−	0.611660i	$-0.209498\pi$
$509$	9.24842e6	1.58224	0.791121	+	0.611660i	$0.209498\pi$
$510$	554330.	0.0943720
$511$	6.74378e6	1.14249
$512$	−2.64784e6	−0.446393
$513$	688161.	0.115451
$514$	−2.36756e6	−0.395269
$515$	1.77912e6	0.295588
$516$	1.27219e6	0.210343
$517$	−1.64418e6	−0.270535
$518$	−486842.	−0.0797193
$519$	−1.91357e6	−0.311835
$520$	3.62570e6	0.588009
$521$	929908.	0.150088	0.0750440	−	0.997180i	$-0.476090\pi$
$521$	929908.	0.150088	0.0750440	+	0.997180i	$0.476090\pi$
$522$	−1.22651e6	−0.197013
$523$	−5.83699e6	−0.933113	−0.466557	−	0.884491i	$-0.654506\pi$
$523$	−5.83699e6	−0.933113	−0.466557	+	0.884491i	$0.654506\pi$
$524$	5.18891e6	0.825558
$525$	−308359.	−0.0488268
$526$	5.56101e6	0.876374
$527$	−1.82196e7	−2.85767
$528$	115116.	0.0179701
$529$	−6.33682e6	−0.984537
$530$	−391249.	−0.0605012
$531$	3.07863e6	0.473829
$532$	−1.00521e6	−0.153985
$533$	1.50350e7	2.29238
$534$	336369.	0.0510462
$535$	2.86831e6	0.433252
$536$	1.23750e6	0.186052
$537$	−275242.	−0.0411888
$538$	−1.83893e6	−0.273911
$539$	−246853.	−0.0365987
$540$	−1.09202e6	−0.161156
$541$	1.02383e7	1.50396	0.751979	−	0.659187i	$-0.229099\pi$
$541$	1.02383e7	1.50396	0.751979	+	0.659187i	$0.229099\pi$
$542$	1.97667e6	0.289025
$543$	−369006.	−0.0537073
$544$	−1.08766e7	−1.57579
$545$	429023.	0.0618713
$546$	−1.30300e6	−0.187052
$547$	−3.17294e6	−0.453413	−0.226707	−	0.973963i	$-0.572796\pi$
$547$	−3.17294e6	−0.453413	−0.226707	+	0.973963i	$0.572796\pi$
$548$	2.89804e6	0.412242
$549$	3.03231e6	0.429381
$550$	−227952.	−0.0321320
$551$	648487.	0.0909960
$552$	−212016.	−0.0296156
$553$	−706350.	−0.0982216
$554$	−6.52425e6	−0.903142
$555$	134908.	0.0185911
$556$	−5.62397e6	−0.771536
$557$	−7.41612e6	−1.01283	−0.506417	−	0.862289i	$-0.669030\pi$
$557$	−7.41612e6	−1.01283	−0.506417	+	0.862289i	$0.669030\pi$
$558$	−6.86592e6	−0.933498
$559$	1.19812e7	1.62170
$560$	711871.	0.0959249
$561$	890093.	0.119407
$562$	−3.25691e6	−0.434975
$563$	−1.23375e7	−1.64043	−0.820214	−	0.572057i	$-0.806146\pi$
$563$	−1.23375e7	−1.64043	−0.820214	+	0.572057i	$0.806146\pi$
$564$	1.26417e6	0.167343
$565$	−2.95839e6	−0.389883
$566$	−930177.	−0.122046
$567$	−5.74832e6	−0.750902
$568$	−4.52810e6	−0.588905
$569$	1.30107e7	1.68470	0.842348	−	0.538935i	$-0.181173\pi$
$569$	1.30107e7	1.68470	0.842348	+	0.538935i	$0.181173\pi$
$570$	−110448.	−0.0142387
$571$	−947375.	−0.121599	−0.0607997	−	0.998150i	$-0.519365\pi$
$571$	−947375.	−0.121599	−0.0607997	+	0.998150i	$0.519365\pi$
$572$	2.42929e6	0.310449
$573$	−2.61791e6	−0.333095
$574$	−6.28551e6	−0.796270
$575$	−197175.	−0.0248704
$576$	−2.40028e6	−0.301443
$577$	1.30083e7	1.62661	0.813303	−	0.581840i	$-0.197667\pi$
$577$	1.30083e7	1.62661	0.813303	+	0.581840i	$0.197667\pi$
$578$	−5.61516e6	−0.699105
$579$	−439445.	−0.0544764
$580$	−1.02906e6	−0.127020
$581$	−1.25277e6	−0.153968
$582$	830508.	0.101633
$583$	−628232.	−0.0765506
$584$	−9.18594e6	−1.11453
$585$	−4.96165e6	−0.599428
$586$	−5.15915e6	−0.620632
$587$	−7.56586e6	−0.906282	−0.453141	−	0.891439i	$-0.649697\pi$
$587$	−7.56586e6	−0.906282	−0.453141	+	0.891439i	$0.649697\pi$
$588$	189798.	0.0226385
$589$	3.63018e6	0.431162
$590$	−1.02418e6	−0.121129
$591$	−330307.	−0.0389000
$592$	−311445.	−0.0365239
$593$	−1.97011e6	−0.230066	−0.115033	−	0.993362i	$-0.536697\pi$
$593$	−1.97011e6	−0.230066	−0.115033	+	0.993362i	$0.536697\pi$
$594$	695259.	0.0808501
$595$	5.50430e6	0.637397
$596$	1.06640e7	1.22972
$597$	1.76487e6	0.202664
$598$	−833179.	−0.0952764
$599$	−1.16271e7	−1.32405	−0.662025	−	0.749482i	$-0.730303\pi$
$599$	−1.16271e7	−1.32405	−0.662025	+	0.749482i	$0.730303\pi$
$600$	420027.	0.0476320
$601$	−1.15739e7	−1.30705	−0.653526	−	0.756904i	$-0.726711\pi$
$601$	−1.15739e7	−1.30705	−0.653526	+	0.756904i	$0.726711\pi$
$602$	−5.00882e6	−0.563306
$603$	−1.69348e6	−0.189665
$604$	−6.26647e6	−0.698925
$605$	−366025.	−0.0406558
$606$	607778.	0.0672300
$607$	−5.78373e6	−0.637142	−0.318571	−	0.947899i	$-0.603203\pi$
$607$	−5.78373e6	−0.637142	−0.318571	+	0.947899i	$0.603203\pi$
$608$	2.16713e6	0.237753
$609$	886280.	0.0968340
$610$	−1.00877e6	−0.109766
$611$	1.19056e7	1.29018
$612$	9.40423e6	1.01495
$613$	−4.14933e6	−0.445992	−0.222996	−	0.974819i	$-0.571584\pi$
$613$	−4.14933e6	−0.445992	−0.222996	+	0.974819i	$0.571584\pi$
$614$	214763.	0.0229900
$615$	1.74176e6	0.185696
$616$	−2.43385e6	−0.258430
$617$	−810206.	−0.0856806	−0.0428403	−	0.999082i	$-0.513641\pi$
$617$	−810206.	−0.0856806	−0.0428403	+	0.999082i	$0.513641\pi$
$618$	870916.	0.0917287
$619$	5.45977e6	0.572727	0.286364	−	0.958121i	$-0.407553\pi$
$619$	5.45977e6	0.572727	0.286364	+	0.958121i	$0.407553\pi$
$620$	−5.76061e6	−0.601851
$621$	601387.	0.0625785
$622$	730197.	0.0756770
$623$	3.34003e6	0.344770
$624$	−833560.	−0.0856989
$625$	390625.	0.0400000
$626$	−1.27946e6	−0.130494
$627$	−177347.	−0.0180159
$628$	−1.78110e6	−0.180214
$629$	−2.40814e6	−0.242692
$630$	2.07426e6	0.208214
$631$	1.16325e7	1.16305	0.581525	−	0.813528i	$-0.302456\pi$
$631$	1.16325e7	1.16305	0.581525	+	0.813528i	$0.302456\pi$
$632$	962143.	0.0958180
$633$	−897845.	−0.0890619
$634$	−5.36946e6	−0.530527
$635$	−2.38445e6	−0.234668
$636$	483030.	0.0473512
$637$	1.78748e6	0.174539
$638$	655176.	0.0637245
$639$	6.19656e6	0.600341
$640$	−4.00398e6	−0.386405
$641$	−5.75632e6	−0.553350	−0.276675	−	0.960964i	$-0.589232\pi$
$641$	−5.75632e6	−0.553350	−0.276675	+	0.960964i	$0.589232\pi$
$642$	1.40409e6	0.134449
$643$	2.42551e6	0.231353	0.115676	−	0.993287i	$-0.463096\pi$
$643$	2.42551e6	0.231353	0.115676	+	0.993287i	$0.463096\pi$
$644$	−878462.	−0.0834658
$645$	1.38798e6	0.131367
$646$	1.97153e6	0.185876
$647$	1.71593e7	1.61153	0.805766	−	0.592234i	$-0.201754\pi$
$647$	1.71593e7	1.61153	0.805766	+	0.592234i	$0.201754\pi$
$648$	7.82998e6	0.732526
$649$	−1.64454e6	−0.153261
$650$	1.65062e6	0.153237
$651$	4.96133e6	0.458824
$652$	−2.93978e6	−0.270829
$653$	−1.27824e7	−1.17309	−0.586544	−	0.809918i	$-0.699512\pi$
$653$	−1.27824e7	−1.17309	−0.586544	+	0.809918i	$0.699512\pi$
$654$	210016.	0.0192003
$655$	5.66121e6	0.515592
$656$	−4.02100e6	−0.364816
$657$	1.25706e7	1.13617
$658$	−4.97724e6	−0.448151
$659$	−3.63751e6	−0.326280	−0.163140	−	0.986603i	$-0.552162\pi$
$659$	−3.63751e6	−0.326280	−0.163140	+	0.986603i	$0.552162\pi$
$660$	281426.	0.0251481
$661$	4.07407e6	0.362681	0.181340	−	0.983420i	$-0.441956\pi$
$661$	4.07407e6	0.362681	0.181340	+	0.983420i	$0.441956\pi$
$662$	3.88641e6	0.344670
$663$	−6.44522e6	−0.569448
$664$	1.70644e6	0.150200
$665$	−1.09671e6	−0.0961696
$666$	−907490.	−0.0792786
$667$	566716.	0.0493232
$668$	−1.59442e7	−1.38249
$669$	−2.87034e6	−0.247952
$670$	563380.	0.0484857
$671$	−1.61980e6	−0.138885
$672$	2.96179e6	0.253006
$673$	−8.44013e6	−0.718309	−0.359155	−	0.933278i	$-0.616935\pi$
$673$	−8.44013e6	−0.718309	−0.359155	+	0.933278i	$0.616935\pi$
$674$	−5.09779e6	−0.432248
$675$	−1.19141e6	−0.100648
$676$	−9.08275e6	−0.764452
$677$	−9.04817e6	−0.758733	−0.379367	−	0.925246i	$-0.623858\pi$
$677$	−9.04817e6	−0.758733	−0.379367	+	0.925246i	$0.623858\pi$
$678$	−1.44819e6	−0.120991
$679$	8.24664e6	0.686440
$680$	−7.49760e6	−0.621799
$681$	1.01721e6	0.0840510
$682$	3.66763e6	0.301943
$683$	1.45302e6	0.119185	0.0595923	−	0.998223i	$-0.481020\pi$
$683$	1.45302e6	0.119185	0.0595923	+	0.998223i	$0.481020\pi$
$684$	−1.87376e6	−0.153134
$685$	3.16182e6	0.257460
$686$	−6.90348e6	−0.560090
$687$	−137847.	−0.0111431
$688$	−3.20427e6	−0.258082
$689$	4.54907e6	0.365069
$690$	−96521.2	−0.00771792
$691$	−1.73982e7	−1.38614	−0.693072	−	0.720869i	$-0.743743\pi$
$691$	−1.73982e7	−1.38614	−0.693072	+	0.720869i	$0.743743\pi$
$692$	1.07999e7	0.857339
$693$	3.33065e6	0.263448
$694$	1.01562e7	0.800445
$695$	−6.13587e6	−0.481853
$696$	−1.20723e6	−0.0944643
$697$	−3.10910e7	−2.42411
$698$	−1.64665e6	−0.127927
$699$	−2.88284e6	−0.223166
$700$	1.74033e6	0.134241
$701$	−1.44628e7	−1.11163	−0.555813	−	0.831308i	$-0.687593\pi$
$701$	−1.44628e7	−1.11163	−0.555813	+	0.831308i	$0.687593\pi$
$702$	−5.03442e6	−0.385573
$703$	479812.	0.0366170
$704$	1.28218e6	0.0975028
$705$	1.37923e6	0.104512
$706$	−1.52049e6	−0.114808
$707$	6.03502e6	0.454077
$708$	1.26444e6	0.0948015
$709$	−3.75122e6	−0.280257	−0.140128	−	0.990133i	$-0.544752\pi$
$709$	−3.75122e6	−0.280257	−0.140128	+	0.990133i	$0.544752\pi$
$710$	−2.06144e6	−0.153470
$711$	−1.31666e6	−0.0976787
$712$	−4.54956e6	−0.336333
$713$	3.17244e6	0.233706
$714$	2.69447e6	0.197801
$715$	2.65041e6	0.193887
$716$	1.55342e6	0.113242
$717$	−791621.	−0.0575068
$718$	2.28629e6	0.165508
$719$	−1.09802e7	−0.792115	−0.396058	−	0.918226i	$-0.629622\pi$
$719$	−1.09802e7	−0.792115	−0.396058	+	0.918226i	$0.629622\pi$
$720$	1.32695e6	0.0953947
$721$	8.64788e6	0.619543
$722$	−392820.	−0.0280447
$723$	−6.96043e6	−0.495211
$724$	2.08261e6	0.147659
$725$	−1.12273e6	−0.0793285
$726$	−179177.	−0.0126165
$727$	−2.02022e6	−0.141763	−0.0708816	−	0.997485i	$-0.522581\pi$
$727$	−2.02022e6	−0.141763	−0.0708816	+	0.997485i	$0.522581\pi$
$728$	1.76237e7	1.23245
$729$	−8.83436e6	−0.615682
$730$	−4.18194e6	−0.290450
$731$	−2.47759e7	−1.71489
$732$	1.24542e6	0.0859086
$733$	−2.36025e7	−1.62255	−0.811274	−	0.584666i	$-0.801225\pi$
$733$	−2.36025e7	−1.62255	−0.811274	+	0.584666i	$0.801225\pi$
$734$	−8.60230e6	−0.589352
$735$	207074.	0.0141386
$736$	1.89386e6	0.128871
$737$	904623.	0.0613478
$738$	−1.17164e7	−0.791869
$739$	−1.14762e7	−0.773017	−0.386508	−	0.922286i	$-0.626319\pi$
$739$	−1.14762e7	−0.773017	−0.386508	+	0.922286i	$0.626319\pi$
$740$	−761397.	−0.0511131
$741$	1.28418e6	0.0859175
$742$	−1.90177e6	−0.126808
$743$	−1.85928e7	−1.23558	−0.617792	−	0.786341i	$-0.711973\pi$
$743$	−1.85928e7	−1.23558	−0.617792	+	0.786341i	$0.711973\pi$
$744$	−6.75800e6	−0.447595
$745$	1.16347e7	0.768005
$746$	7.85380e6	0.516693
$747$	−2.33520e6	−0.153117
$748$	−5.02354e6	−0.328289
$749$	1.39422e7	0.908083
$750$	191219.	0.0124130
$751$	−1.49341e7	−0.966226	−0.483113	−	0.875558i	$-0.660494\pi$
$751$	−1.49341e7	−0.966226	−0.483113	+	0.875558i	$0.660494\pi$
$752$	−3.18406e6	−0.205323
$753$	180616.	0.0116083
$754$	−4.74417e6	−0.303901
$755$	−6.83685e6	−0.436505
$756$	−5.30804e6	−0.337777
$757$	1.32052e7	0.837542	0.418771	−	0.908092i	$-0.362461\pi$
$757$	1.32052e7	0.837542	0.418771	+	0.908092i	$0.362461\pi$
$758$	−7.12519e6	−0.450426
$759$	−154985.	−0.00976528
$760$	1.49387e6	0.0938162
$761$	6.70796e6	0.419884	0.209942	−	0.977714i	$-0.432673\pi$
$761$	6.70796e6	0.419884	0.209942	+	0.977714i	$0.432673\pi$
$762$	−1.16724e6	−0.0728235
$763$	2.08538e6	0.129680
$764$	1.47751e7	0.915790
$765$	1.02602e7	0.633874
$766$	−2.85771e6	−0.175973
$767$	1.19082e7	0.730901
$768$	−3.33675e6	−0.204137
$769$	6.05200e6	0.369048	0.184524	−	0.982828i	$-0.440926\pi$
$769$	6.05200e6	0.369048	0.184524	+	0.982828i	$0.440926\pi$
$770$	−1.10802e6	−0.0673476
$771$	3.18900e6	0.193205
$772$	2.48016e6	0.149774
$773$	−2.75676e7	−1.65940	−0.829699	−	0.558211i	$-0.811488\pi$
$773$	−2.75676e7	−1.65940	−0.829699	+	0.558211i	$0.811488\pi$
$774$	−9.33662e6	−0.560193
$775$	−6.28494e6	−0.375878
$776$	−1.12330e7	−0.669642
$777$	655754.	0.0389662
$778$	8.16056e6	0.483360
$779$	6.19475e6	0.365747
$780$	−2.03783e6	−0.119931
$781$	−3.31007e6	−0.194182
$782$	1.72293e6	0.100751
$783$	3.42434e6	0.199605
$784$	−478046.	−0.0277766
$785$	−1.94321e6	−0.112550
$786$	2.77128e6	0.160001
$787$	2.38842e7	1.37459	0.687296	−	0.726378i	$-0.258798\pi$
$787$	2.38842e7	1.37459	0.687296	+	0.726378i	$0.258798\pi$
$788$	1.86420e6	0.106949
$789$	−7.49044e6	−0.428366
$790$	438020.	0.0249705
$791$	−1.43800e7	−0.817182
$792$	−4.53679e6	−0.257001
$793$	1.17291e7	0.662339
$794$	1.53715e7	0.865297
$795$	526996.	0.0295726
$796$	−9.96062e6	−0.557190
$797$	−2.63497e7	−1.46936	−0.734681	−	0.678412i	$-0.762668\pi$
$797$	−2.63497e7	−1.46936	−0.734681	+	0.678412i	$0.762668\pi$
$798$	−536862.	−0.0298439
$799$	−2.46197e7	−1.36432
$800$	−3.75195e6	−0.207268
$801$	6.22593e6	0.342865
$802$	1.19905e7	0.658264
$803$	−6.71497e6	−0.367498
$804$	−695539.	−0.0379473
$805$	−958421.	−0.0521275
$806$	−2.65575e7	−1.43996
$807$	2.47696e6	0.133886
$808$	−8.22050e6	−0.442965
$809$	1.62205e7	0.871352	0.435676	−	0.900104i	$-0.356509\pi$
$809$	1.62205e7	0.871352	0.435676	+	0.900104i	$0.356509\pi$
$810$	3.56464e6	0.190899
$811$	2.33019e7	1.24406	0.622028	−	0.782995i	$-0.286309\pi$
$811$	2.33019e7	1.24406	0.622028	+	0.782995i	$0.286309\pi$
$812$	−5.00202e6	−0.266229
$813$	−2.66248e6	−0.141273
$814$	484762.	0.0256429
$815$	−3.20736e6	−0.169143
$816$	1.72372e6	0.0906236
$817$	4.93650e6	0.258740
$818$	−6.30097e6	−0.329249
$819$	−2.41174e7	−1.25638
$820$	−9.83023e6	−0.510539
$821$	−2.31357e7	−1.19791	−0.598957	−	0.800781i	$-0.704418\pi$
$821$	−2.31357e7	−1.19791	−0.598957	+	0.800781i	$0.704418\pi$
$822$	1.54778e6	0.0798966
$823$	−2.80770e7	−1.44495	−0.722473	−	0.691399i	$-0.756995\pi$
$823$	−2.80770e7	−1.44495	−0.722473	+	0.691399i	$0.756995\pi$
$824$	−1.17796e7	−0.604382
$825$	307042.	0.0157059
$826$	−4.97832e6	−0.253882
$827$	2.74006e7	1.39315	0.696573	−	0.717486i	$-0.254707\pi$
$827$	2.74006e7	1.39315	0.696573	+	0.717486i	$0.254707\pi$
$828$	−1.63748e6	−0.0830045
$829$	−1.16604e7	−0.589285	−0.294642	−	0.955608i	$-0.595201\pi$
$829$	−1.16604e7	−0.589285	−0.294642	+	0.955608i	$0.595201\pi$
$830$	776863.	0.0391426
$831$	8.78787e6	0.441450
$832$	−9.28434e6	−0.464989
$833$	−3.69632e6	−0.184569
$834$	−3.00364e6	−0.149531
$835$	−1.73955e7	−0.863416
$836$	1.00092e6	0.0495318
$837$	1.91692e7	0.945780
$838$	6.04678e6	0.297450
$839$	1.79127e7	0.878531	0.439265	−	0.898357i	$-0.355239\pi$
$839$	1.79127e7	0.878531	0.439265	+	0.898357i	$0.355239\pi$
$840$	2.04165e6	0.0998351
$841$	−1.72842e7	−0.842675
$842$	−1.26592e7	−0.615356
$843$	4.38691e6	0.212613
$844$	5.06729e6	0.244861
$845$	−9.90947e6	−0.477429
$846$	−9.27775e6	−0.445674
$847$	−1.77916e6	−0.0852132
$848$	−1.21661e6	−0.0580981
$849$	1.25291e6	0.0596554
$850$	−3.41332e6	−0.162043
$851$	419311.	0.0198478
$852$	2.54502e6	0.120113
$853$	2.89265e7	1.36120	0.680602	−	0.732653i	$-0.261718\pi$
$853$	2.89265e7	1.36120	0.680602	+	0.732653i	$0.261718\pi$
$854$	−4.90342e6	−0.230067
$855$	−2.04431e6	−0.0956380
$856$	−1.89911e7	−0.885861
$857$	1.45838e7	0.678297	0.339149	−	0.940733i	$-0.389861\pi$
$857$	1.45838e7	0.678297	0.339149	+	0.940733i	$0.389861\pi$
$858$	1.29743e6	0.0601681
$859$	2.23965e7	1.03561	0.517807	−	0.855498i	$-0.326749\pi$
$859$	2.23965e7	1.03561	0.517807	+	0.855498i	$0.326749\pi$
$860$	−7.83356e6	−0.361171
$861$	8.46630e6	0.389212
$862$	−3.83253e6	−0.175678
$863$	7.68869e6	0.351419	0.175710	−	0.984442i	$-0.443778\pi$
$863$	7.68869e6	0.351419	0.175710	+	0.984442i	$0.443778\pi$
$864$	1.14435e7	0.521525
$865$	1.17829e7	0.535440
$866$	−6.01130e6	−0.272379
$867$	7.56337e6	0.341718
$868$	−2.80010e7	−1.26146
$869$	703333.	0.0315945
$870$	−549598.	−0.0246177
$871$	−6.55043e6	−0.292566
$872$	−2.84057e6	−0.126507
$873$	1.53720e7	0.682646
$874$	−343287.	−0.0152012
$875$	1.89874e6	0.0838387
$876$	5.16295e6	0.227320
$877$	−3.79122e7	−1.66449	−0.832244	−	0.554410i	$-0.812944\pi$
$877$	−3.79122e7	−1.66449	−0.832244	+	0.554410i	$0.812944\pi$
$878$	2.07564e6	0.0908688
$879$	6.94915e6	0.303361
$880$	−708830.	−0.0308557
$881$	−9.14794e6	−0.397085	−0.198543	−	0.980092i	$-0.563621\pi$
$881$	−9.14794e6	−0.397085	−0.198543	+	0.980092i	$0.563621\pi$
$882$	−1.39293e6	−0.0602919
$883$	−7.36534e6	−0.317901	−0.158950	−	0.987287i	$-0.550811\pi$
$883$	−7.36534e6	−0.317901	−0.158950	+	0.987287i	$0.550811\pi$
$884$	3.63758e7	1.56560
$885$	1.37953e6	0.0592070
$886$	−7.67259e6	−0.328366
$887$	−7.61677e6	−0.325059	−0.162529	−	0.986704i	$-0.551965\pi$
$887$	−7.61677e6	−0.325059	−0.162529	+	0.986704i	$0.551965\pi$
$888$	−893225.	−0.0380127
$889$	−1.15902e7	−0.491856
$890$	−2.07121e6	−0.0876494
$891$	5.72376e6	0.241539
$892$	1.61997e7	0.681703
$893$	4.90538e6	0.205847
$894$	5.69542e6	0.238332
$895$	1.69482e6	0.0707237
$896$	−1.94624e7	−0.809891
$897$	1.12226e6	0.0465705
$898$	−1.99114e7	−0.823967
$899$	1.80641e7	0.745446
$900$	3.24404e6	0.133499
$901$	−9.40702e6	−0.386047
$902$	6.25866e6	0.256133
$903$	6.74667e6	0.275340
$904$	1.95875e7	0.797185
$905$	2.27217e6	0.0922187
$906$	−3.34678e6	−0.135459
$907$	1.75574e7	0.708666	0.354333	−	0.935119i	$-0.384708\pi$
$907$	1.75574e7	0.708666	0.354333	+	0.935119i	$0.384708\pi$
$908$	−5.74097e6	−0.231085
$909$	1.12495e7	0.451568
$910$	8.02327e6	0.321179
$911$	−2.83482e7	−1.13170	−0.565848	−	0.824510i	$-0.691451\pi$
$911$	−2.83482e7	−1.13170	−0.565848	+	0.824510i	$0.691451\pi$
$912$	−343444.	−0.0136732
$913$	1.24742e6	0.0495261
$914$	−7.15408e6	−0.283262
$915$	1.35878e6	0.0536531
$916$	777987.	0.0306361
$917$	2.75178e7	1.08066
$918$	1.04107e7	0.407730
$919$	−4.73480e7	−1.84932	−0.924662	−	0.380789i	$-0.875653\pi$
$919$	−4.73480e7	−1.84932	−0.924662	+	0.380789i	$0.875653\pi$
$920$	1.30550e6	0.0508518
$921$	−289277.	−0.0112374
$922$	−3.32501e6	−0.128815
$923$	2.39684e7	0.926051
$924$	1.36795e6	0.0527095
$925$	−830700.	−0.0319220
$926$	1.84819e7	0.708302
$927$	1.61200e7	0.616119
$928$	1.07838e7	0.411056
$929$	−1.18062e7	−0.448818	−0.224409	−	0.974495i	$-0.572045\pi$
$929$	−1.18062e7	−0.448818	−0.224409	+	0.974495i	$0.572045\pi$
$930$	−3.07661e6	−0.116645
$931$	736478.	0.0278475
$932$	1.62703e7	0.613558
$933$	−983544.	−0.0369904
$934$	−1.72063e7	−0.645387
$935$	−5.48079e6	−0.205028
$936$	3.28512e7	1.22564
$937$	−2.07894e7	−0.773560	−0.386780	−	0.922172i	$-0.626413\pi$
$937$	−2.07894e7	−0.773560	−0.386780	+	0.922172i	$0.626413\pi$
$938$	2.73846e6	0.101625
$939$	1.72338e6	0.0637847
$940$	−7.78417e6	−0.287338
$941$	1.49762e7	0.551351	0.275675	−	0.961251i	$-0.411099\pi$
$941$	1.49762e7	0.551351	0.275675	+	0.961251i	$0.411099\pi$
$942$	−951243.	−0.0349272
$943$	5.41363e6	0.198248
$944$	−3.18475e6	−0.116318
$945$	−5.79118e6	−0.210954
$946$	4.98743e6	0.181196
$947$	1.03605e6	0.0375411	0.0187705	−	0.999824i	$-0.494025\pi$
$947$	1.03605e6	0.0375411	0.0187705	+	0.999824i	$0.494025\pi$
$948$	−540772.	−0.0195431
$949$	4.86236e7	1.75259
$950$	680089.	0.0244488
$951$	7.23243e6	0.259318
$952$	−3.64440e7	−1.30327
$953$	−3.76543e7	−1.34302	−0.671510	−	0.740995i	$-0.734354\pi$
$953$	−3.76543e7	−1.34302	−0.671510	+	0.740995i	$0.734354\pi$
$954$	−3.54497e6	−0.126108
$955$	1.61199e7	0.571945
$956$	4.46778e6	0.158105
$957$	−882494.	−0.0311481
$958$	−9.54021e6	−0.335849
$959$	1.53689e7	0.539628
$960$	−1.07556e6	−0.0376667
$961$	7.24922e7	2.53211
$962$	−3.51019e6	−0.122291
$963$	2.59887e7	0.903064
$964$	3.92836e7	1.36150
$965$	2.70591e6	0.0935393
$966$	−469167.	−0.0161765
$967$	−4.13566e7	−1.42226	−0.711129	−	0.703061i	$-0.751816\pi$
$967$	−4.13566e7	−1.42226	−0.711129	+	0.703061i	$0.751816\pi$
$968$	2.42346e6	0.0831279
$969$	−2.65557e6	−0.0908548
$970$	−5.11389e6	−0.174511
$971$	1.23367e7	0.419906	0.209953	−	0.977711i	$-0.432669\pi$
$971$	1.23367e7	0.419906	0.209953	+	0.977711i	$0.432669\pi$
$972$	−1.50152e7	−0.509761
$973$	−2.98250e7	−1.00995
$974$	2.32153e7	0.784111
$975$	−2.22331e6	−0.0749012
$976$	−3.13684e6	−0.105407
$977$	−6.06461e6	−0.203267	−0.101633	−	0.994822i	$-0.532407\pi$
$977$	−6.06461e6	−0.203267	−0.101633	+	0.994822i	$0.532407\pi$
$978$	−1.57007e6	−0.0524894
$979$	−3.32576e6	−0.110901
$980$	−1.16869e6	−0.0388718
$981$	3.88722e6	0.128964
$982$	1.68147e7	0.556429
$983$	3.65751e7	1.20726	0.603631	−	0.797264i	$-0.293720\pi$
$983$	3.65751e7	1.20726	0.603631	+	0.797264i	$0.293720\pi$
$984$	−1.15322e7	−0.379687
$985$	2.03388e6	0.0667937
$986$	9.81049e6	0.321365
$987$	6.70413e6	0.219053
$988$	−7.24773e6	−0.236216
$989$	4.31404e6	0.140247
$990$	−2.06539e6	−0.0669753
$991$	2.31266e7	0.748045	0.374022	−	0.927420i	$-0.377978\pi$
$991$	2.31266e7	0.748045	0.374022	+	0.927420i	$0.377978\pi$
$992$	6.03668e7	1.94769
$993$	−5.23483e6	−0.168473
$994$	−1.00202e7	−0.321669
$995$	−1.08672e7	−0.347986
$996$	−959102.	−0.0306349
$997$	1.64901e6	0.0525395	0.0262698	−	0.999655i	$-0.491637\pi$
$997$	1.64901e6	0.0525395	0.0262698	+	0.999655i	$0.491637\pi$
$998$	−1.21958e7	−0.387600
$999$	2.53365e6	0.0803217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.14	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.14	✓	37	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)

\(f(q)\)	\(=\)	\(q-3.01425 q^{2} +4.06006 q^{3} -22.9143 q^{4} -25.0000 q^{5} -12.2380 q^{6} -121.519 q^{7} +165.525 q^{8} -226.516 q^{9} +O(q^{10})\)	\(q-3.01425 q^{2} +4.06006 q^{3} -22.9143 q^{4} -25.0000 q^{5} -12.2380 q^{6} -121.519 q^{7} +165.525 q^{8} -226.516 q^{9} +75.3562 q^{10} +121.000 q^{11} -93.0335 q^{12} -876.169 q^{13} +366.289 q^{14} -101.501 q^{15} +234.324 q^{16} +1811.83 q^{17} +682.775 q^{18} -361.000 q^{19} +572.858 q^{20} -493.375 q^{21} -364.724 q^{22} -315.480 q^{23} +672.042 q^{24} +625.000 q^{25} +2640.99 q^{26} -1906.26 q^{27} +2784.53 q^{28} -1796.36 q^{29} +305.950 q^{30} -10055.9 q^{31} -6003.12 q^{32} +491.267 q^{33} -5461.30 q^{34} +3037.98 q^{35} +5190.46 q^{36} -1329.12 q^{37} +1088.14 q^{38} -3557.30 q^{39} -4138.13 q^{40} -17160.0 q^{41} +1487.15 q^{42} -13674.5 q^{43} -2772.63 q^{44} +5662.90 q^{45} +950.934 q^{46} -13588.3 q^{47} +951.369 q^{48} -2040.11 q^{49} -1883.90 q^{50} +7356.14 q^{51} +20076.8 q^{52} -5192.00 q^{53} +5745.94 q^{54} -3025.00 q^{55} -20114.5 q^{56} -1465.68 q^{57} +5414.68 q^{58} -13591.2 q^{59} +2325.84 q^{60} -13386.8 q^{61} +30311.0 q^{62} +27526.0 q^{63} +10596.5 q^{64} +21904.2 q^{65} -1480.80 q^{66} +7476.22 q^{67} -41516.9 q^{68} -1280.87 q^{69} -9157.22 q^{70} -27355.9 q^{71} -37494.1 q^{72} -55495.7 q^{73} +4006.30 q^{74} +2537.54 q^{75} +8272.07 q^{76} -14703.8 q^{77} +10722.6 q^{78} +5812.67 q^{79} -5858.10 q^{80} +47303.8 q^{81} +51724.4 q^{82} +10309.2 q^{83} +11305.3 q^{84} -45295.8 q^{85} +41218.4 q^{86} -7293.34 q^{87} +20028.6 q^{88} -27485.6 q^{89} -17069.4 q^{90} +106471. q^{91} +7229.01 q^{92} -40827.6 q^{93} +40958.5 q^{94} +9025.00 q^{95} -24373.0 q^{96} -67862.9 q^{97} +6149.38 q^{98} -27408.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

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