LMFDB - Embedded newform 1045.6.a.d.1.20

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			1.20
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.872903 q^{2} -19.2132 q^{3} -31.2380 q^{4} -25.0000 q^{5} -16.7713 q^{6} +14.4713 q^{7} -55.2007 q^{8} +126.149 q^{9} +O(q^{10})$	\(q+0.872903 q^{2} -19.2132 q^{3} -31.2380 q^{4} -25.0000 q^{5} -16.7713 q^{6} +14.4713 q^{7} -55.2007 q^{8} +126.149 q^{9} -21.8226 q^{10} +121.000 q^{11} +600.184 q^{12} +515.646 q^{13} +12.6320 q^{14} +480.331 q^{15} +951.433 q^{16} +1425.39 q^{17} +110.116 q^{18} -361.000 q^{19} +780.951 q^{20} -278.040 q^{21} +105.621 q^{22} +4707.83 q^{23} +1060.58 q^{24} +625.000 q^{25} +450.109 q^{26} +2245.09 q^{27} -452.055 q^{28} -8515.91 q^{29} +419.282 q^{30} -2847.13 q^{31} +2596.93 q^{32} -2324.80 q^{33} +1244.23 q^{34} -361.782 q^{35} -3940.64 q^{36} +6525.55 q^{37} -315.118 q^{38} -9907.23 q^{39} +1380.02 q^{40} -7395.63 q^{41} -242.702 q^{42} -1596.99 q^{43} -3779.80 q^{44} -3153.72 q^{45} +4109.48 q^{46} -5138.00 q^{47} -18280.1 q^{48} -16597.6 q^{49} +545.564 q^{50} -27386.4 q^{51} -16107.8 q^{52} +27130.0 q^{53} +1959.75 q^{54} -3025.00 q^{55} -798.824 q^{56} +6935.98 q^{57} -7433.56 q^{58} +7068.94 q^{59} -15004.6 q^{60} +352.855 q^{61} -2485.27 q^{62} +1825.53 q^{63} -28179.0 q^{64} -12891.1 q^{65} -2029.33 q^{66} +2457.20 q^{67} -44526.4 q^{68} -90452.7 q^{69} -315.801 q^{70} +16351.3 q^{71} -6963.49 q^{72} +72447.8 q^{73} +5696.17 q^{74} -12008.3 q^{75} +11276.9 q^{76} +1751.03 q^{77} -8648.05 q^{78} -4870.40 q^{79} -23785.8 q^{80} -73789.6 q^{81} -6455.66 q^{82} -45833.5 q^{83} +8685.43 q^{84} -35634.8 q^{85} -1394.02 q^{86} +163618. q^{87} -6679.28 q^{88} -32895.4 q^{89} -2752.89 q^{90} +7462.06 q^{91} -147063. q^{92} +54702.7 q^{93} -4484.97 q^{94} +9025.00 q^{95} -49895.4 q^{96} +114728. q^{97} -14488.1 q^{98} +15264.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.872903	0.154309	0.0771544	−	0.997019i	$-0.475417\pi$
$2$	0.872903	0.154309	0.0771544	+	0.997019i	$0.475417\pi$
$3$	−19.2132	−1.23253	−0.616265	−	0.787539i	$-0.711355\pi$
$3$	−19.2132	−1.23253	−0.616265	+	0.787539i	$0.711355\pi$
$4$	−31.2380	−0.976189
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−16.7713	−0.190190
$7$	14.4713	0.111625	0.0558126	−	0.998441i	$-0.482225\pi$
$7$	14.4713	0.111625	0.0558126	+	0.998441i	$0.482225\pi$
$8$	−55.2007	−0.304943
$9$	126.149	0.519130
$10$	−21.8226	−0.0690090
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	600.184	1.20318
$13$	515.646	0.846239	0.423120	−	0.906074i	$-0.360935\pi$
$13$	515.646	0.846239	0.423120	+	0.906074i	$0.360935\pi$
$14$	12.6320	0.0172247
$15$	480.331	0.551204
$16$	951.433	0.929133
$17$	1425.39	1.19622	0.598111	−	0.801413i	$-0.295918\pi$
$17$	1425.39	1.19622	0.598111	+	0.801413i	$0.295918\pi$
$18$	110.116	0.0801064
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	780.951	0.436565
$21$	−278.040	−0.137581
$22$	105.621	0.0465259
$23$	4707.83	1.85567	0.927837	−	0.372987i	$-0.121666\pi$
$23$	4707.83	1.85567	0.927837	+	0.372987i	$0.121666\pi$
$24$	1060.58	0.375852
$25$	625.000	0.200000
$26$	450.109	0.130582
$27$	2245.09	0.592686
$28$	−452.055	−0.108967
$29$	−8515.91	−1.88034	−0.940169	−	0.340709i	$-0.889333\pi$
$29$	−8515.91	−1.88034	−0.940169	+	0.340709i	$0.889333\pi$
$30$	419.282	0.0850557
$31$	−2847.13	−0.532113	−0.266056	−	0.963957i	$-0.585721\pi$
$31$	−2847.13	−0.532113	−0.266056	+	0.963957i	$0.585721\pi$
$32$	2596.93	0.448317
$33$	−2324.80	−0.371622
$34$	1244.23	0.184588
$35$	−361.782	−0.0499203
$36$	−3940.64	−0.506769
$37$	6525.55	0.783633	0.391817	−	0.920043i	$-0.371847\pi$
$37$	6525.55	0.783633	0.391817	+	0.920043i	$0.371847\pi$
$38$	−315.118	−0.0354009
$39$	−9907.23	−1.04302
$40$	1380.02	0.136375
$41$	−7395.63	−0.687093	−0.343546	−	0.939136i	$-0.611628\pi$
$41$	−7395.63	−0.687093	−0.343546	+	0.939136i	$0.611628\pi$
$42$	−242.702	−0.0212300
$43$	−1596.99	−0.131714	−0.0658568	−	0.997829i	$-0.520978\pi$
$43$	−1596.99	−0.131714	−0.0658568	+	0.997829i	$0.520978\pi$
$44$	−3779.80	−0.294332
$45$	−3153.72	−0.232162
$46$	4109.48	0.286347
$47$	−5138.00	−0.339273	−0.169637	−	0.985507i	$-0.554259\pi$
$47$	−5138.00	−0.339273	−0.169637	+	0.985507i	$0.554259\pi$
$48$	−18280.1	−1.14518
$49$	−16597.6	−0.987540
$50$	545.564	0.0308618
$51$	−27386.4	−1.47438
$52$	−16107.8	−0.826089
$53$	27130.0	1.32666	0.663330	−	0.748327i	$-0.269143\pi$
$53$	27130.0	1.32666	0.663330	+	0.748327i	$0.269143\pi$
$54$	1959.75	0.0914567
$55$	−3025.00	−0.134840
$56$	−798.824	−0.0340393
$57$	6935.98	0.282762
$58$	−7433.56	−0.290153
$59$	7068.94	0.264377	0.132189	−	0.991225i	$-0.457800\pi$
$59$	7068.94	0.264377	0.132189	+	0.991225i	$0.457800\pi$
$60$	−15004.6	−0.538079
$61$	352.855	0.0121415	0.00607075	−	0.999982i	$-0.498068\pi$
$61$	352.855	0.0121415	0.00607075	+	0.999982i	$0.498068\pi$
$62$	−2485.27	−0.0821097
$63$	1825.53	0.0579480
$64$	−28179.0	−0.859954
$65$	−12891.1	−0.378450
$66$	−2029.33	−0.0573445
$67$	2457.20	0.0668735	0.0334367	−	0.999441i	$-0.489355\pi$
$67$	2457.20	0.0668735	0.0334367	+	0.999441i	$0.489355\pi$
$68$	−44526.4	−1.16774
$69$	−90452.7	−2.28717
$70$	−315.801	−0.00770314
$71$	16351.3	0.384951	0.192476	−	0.981302i	$-0.438348\pi$
$71$	16351.3	0.384951	0.192476	+	0.981302i	$0.438348\pi$
$72$	−6963.49	−0.158305
$73$	72447.8	1.59118	0.795588	−	0.605838i	$-0.207162\pi$
$73$	72447.8	1.59118	0.795588	+	0.605838i	$0.207162\pi$
$74$	5696.17	0.120922
$75$	−12008.3	−0.246506
$76$	11276.9	0.223953
$77$	1751.03	0.0336562
$78$	−8648.05	−0.160946
$79$	−4870.40	−0.0878005	−0.0439003	−	0.999036i	$-0.513978\pi$
$79$	−4870.40	−0.0878005	−0.0439003	+	0.999036i	$0.513978\pi$
$80$	−23785.8	−0.415521
$81$	−73789.6	−1.24963
$82$	−6455.66	−0.106025
$83$	−45833.5	−0.730278	−0.365139	−	0.930953i	$-0.618979\pi$
$83$	−45833.5	−0.730278	−0.365139	+	0.930953i	$0.618979\pi$
$84$	8685.43	0.134305
$85$	−35634.8	−0.534967
$86$	−1394.02	−0.0203246
$87$	163618.	2.31757
$88$	−6679.28	−0.0919439
$89$	−32895.4	−0.440211	−0.220105	−	0.975476i	$-0.570640\pi$
$89$	−32895.4	−0.440211	−0.220105	+	0.975476i	$0.570640\pi$
$90$	−2752.89	−0.0358247
$91$	7462.06	0.0944616
$92$	−147063.	−1.81149
$93$	54702.7	0.655845
$94$	−4484.97	−0.0523529
$95$	9025.00	0.102598
$96$	−49895.4	−0.552564
$97$	114728.	1.23805	0.619025	−	0.785371i	$-0.287528\pi$
$97$	114728.	1.23805	0.619025	+	0.785371i	$0.287528\pi$
$98$	−14488.1	−0.152386
$99$	15264.0	0.156524
$100$	−19523.8	−0.195238
$101$	15074.2	0.147039	0.0735194	−	0.997294i	$-0.476577\pi$
$101$	15074.2	0.147039	0.0735194	+	0.997294i	$0.476577\pi$
$102$	−23905.6	−0.227510
$103$	−180855.	−1.67972	−0.839861	−	0.542802i	$-0.817363\pi$
$103$	−180855.	−1.67972	−0.839861	+	0.542802i	$0.817363\pi$
$104$	−28464.0	−0.258055
$105$	6951.01	0.0615282
$106$	23681.8	0.204715
$107$	−102033.	−0.861554	−0.430777	−	0.902459i	$-0.641760\pi$
$107$	−102033.	−0.861554	−0.430777	+	0.902459i	$0.641760\pi$
$108$	−70132.3	−0.578574
$109$	−53954.6	−0.434973	−0.217487	−	0.976063i	$-0.569786\pi$
$109$	−53954.6	−0.434973	−0.217487	+	0.976063i	$0.569786\pi$
$110$	−2640.53	−0.0208070
$111$	−125377.	−0.965851
$112$	13768.5	0.103715
$113$	208157.	1.53354	0.766771	−	0.641921i	$-0.221862\pi$
$113$	208157.	1.53354	0.766771	+	0.641921i	$0.221862\pi$
$114$	6054.44	0.0436326
$115$	−117696.	−0.829882
$116$	266020.	1.83556
$117$	65048.1	0.439309
$118$	6170.50	0.0407958
$119$	20627.2	0.133528
$120$	−26514.6	−0.168086
$121$	14641.0	0.0909091
$122$	308.008	0.00187354
$123$	142094.	0.846863
$124$	88938.9	0.519442
$125$	−15625.0	−0.0894427
$126$	1593.51	0.00894189
$127$	52309.8	0.287789	0.143894	−	0.989593i	$-0.454037\pi$
$127$	52309.8	0.287789	0.143894	+	0.989593i	$0.454037\pi$
$128$	−107699.	−0.581015
$129$	30683.3	0.162341
$130$	−11252.7	−0.0583981
$131$	72705.2	0.370158	0.185079	−	0.982724i	$-0.440746\pi$
$131$	72705.2	0.370158	0.185079	+	0.982724i	$0.440746\pi$
$132$	72622.3	0.362773
$133$	−5224.13	−0.0256086
$134$	2144.90	0.0103192
$135$	−56127.3	−0.265057
$136$	−78682.5	−0.364780
$137$	−292914.	−1.33333	−0.666666	−	0.745356i	$-0.732279\pi$
$137$	−292914.	−1.33333	−0.666666	+	0.745356i	$0.732279\pi$
$138$	−78956.4	−0.352931
$139$	272051.	1.19430	0.597151	−	0.802129i	$-0.296299\pi$
$139$	272051.	1.19430	0.597151	+	0.802129i	$0.296299\pi$
$140$	11301.4	0.0487316
$141$	98717.7	0.418164
$142$	14273.1	0.0594014
$143$	62393.2	0.255151
$144$	120022.	0.482341
$145$	212898.	0.840913
$146$	63239.9	0.245533
$147$	318893.	1.21717
$148$	−203845.	−0.764974
$149$	−356568.	−1.31576	−0.657880	−	0.753123i	$-0.728547\pi$
$149$	−356568.	−1.31576	−0.657880	+	0.753123i	$0.728547\pi$
$150$	−10482.1	−0.0380381
$151$	−247819.	−0.884488	−0.442244	−	0.896895i	$-0.645818\pi$
$151$	−247819.	−0.884488	−0.442244	+	0.896895i	$0.645818\pi$
$152$	19927.4	0.0699588
$153$	179811.	0.620995
$154$	1528.47	0.00519346
$155$	71178.3	0.237968
$156$	309482.	1.01818
$157$	−483290.	−1.56480	−0.782399	−	0.622777i	$-0.786004\pi$
$157$	−483290.	−1.56480	−0.782399	+	0.622777i	$0.786004\pi$
$158$	−4251.39	−0.0135484
$159$	−521255.	−1.63515
$160$	−64923.2	−0.200493
$161$	68128.4	0.207140
$162$	−64411.2	−0.192830
$163$	248693.	0.733152	0.366576	−	0.930388i	$-0.380530\pi$
$163$	248693.	0.733152	0.366576	+	0.930388i	$0.380530\pi$
$164$	231025.	0.670732
$165$	58120.1	0.166194
$166$	−40008.2	−0.112688
$167$	−407497.	−1.13066	−0.565332	−	0.824864i	$-0.691252\pi$
$167$	−407497.	−1.13066	−0.565332	+	0.824864i	$0.691252\pi$
$168$	15348.0	0.0419545
$169$	−105402.	−0.283879
$170$	−31105.7	−0.0825501
$171$	−45539.7	−0.119097
$172$	49886.8	0.128577
$173$	352168.	0.894611	0.447305	−	0.894381i	$-0.352384\pi$
$173$	352168.	0.894611	0.447305	+	0.894381i	$0.352384\pi$
$174$	142823.	0.357622
$175$	9044.55	0.0223250
$176$	115123.	0.280144
$177$	−135817.	−0.325853
$178$	−28714.5	−0.0679284
$179$	−222100.	−0.518103	−0.259052	−	0.965863i	$-0.583410\pi$
$179$	−222100.	−0.518103	−0.259052	+	0.965863i	$0.583410\pi$
$180$	98516.0	0.226634
$181$	419707.	0.952247	0.476124	−	0.879378i	$-0.342041\pi$
$181$	419707.	0.952247	0.476124	+	0.879378i	$0.342041\pi$
$182$	6513.65	0.0145763
$183$	−6779.50	−0.0149648
$184$	−259875.	−0.565875
$185$	−163139.	−0.350451
$186$	47750.1	0.101203
$187$	172472.	0.360674
$188$	160501.	0.331195
$189$	32489.4	0.0661587
$190$	7877.95	0.0158318
$191$	742870.	1.47343	0.736715	−	0.676203i	$-0.236376\pi$
$191$	742870.	1.47343	0.736715	+	0.676203i	$0.236376\pi$
$192$	541409.	1.05992
$193$	629696.	1.21685	0.608426	−	0.793611i	$-0.291801\pi$
$193$	629696.	1.21685	0.608426	+	0.793611i	$0.291801\pi$
$194$	100146.	0.191042
$195$	247681.	0.466451
$196$	518476.	0.964025
$197$	662082.	1.21548	0.607738	−	0.794138i	$-0.292077\pi$
$197$	662082.	1.21548	0.607738	+	0.794138i	$0.292077\pi$
$198$	13324.0	0.0241530
$199$	263963.	0.472509	0.236254	−	0.971691i	$-0.424080\pi$
$199$	263963.	0.472509	0.236254	+	0.971691i	$0.424080\pi$
$200$	−34500.4	−0.0609887
$201$	−47210.8	−0.0824236
$202$	13158.3	0.0226894
$203$	−123236.	−0.209893
$204$	855497.	1.43927
$205$	184891.	0.307277
$206$	−157869.	−0.259196
$207$	593887.	0.963336
$208$	490602.	0.786269
$209$	−43681.0	−0.0691714
$210$	6067.55	0.00949435
$211$	52871.6	0.0817554	0.0408777	−	0.999164i	$-0.486985\pi$
$211$	52871.6	0.0817554	0.0408777	+	0.999164i	$0.486985\pi$
$212$	−847487.	−1.29507
$213$	−314161.	−0.474464
$214$	−89065.1	−0.132945
$215$	39924.7	0.0589041
$216$	−123931.	−0.180736
$217$	−41201.7	−0.0593971
$218$	−47097.1	−0.0671202
$219$	−1.39196e6	−1.96117
$220$	94495.1	0.131629
$221$	734997.	1.01229
$222$	−109442.	−0.149039
$223$	454961.	0.612650	0.306325	−	0.951927i	$-0.400901\pi$
$223$	454961.	0.612650	0.306325	+	0.951927i	$0.400901\pi$
$224$	37580.9	0.0500434
$225$	78842.9	0.103826
$226$	181701.	0.236639
$227$	1.43197e6	1.84446	0.922231	−	0.386639i	$-0.126364\pi$
$227$	1.43197e6	1.84446	0.922231	+	0.386639i	$0.126364\pi$
$228$	−216666.	−0.276029
$229$	644820.	0.812549	0.406275	−	0.913751i	$-0.366828\pi$
$229$	644820.	0.812549	0.406275	+	0.913751i	$0.366828\pi$
$230$	−102737.	−0.128058
$231$	−33642.9	−0.0414823
$232$	470084.	0.573397
$233$	−954427.	−1.15174	−0.575868	−	0.817543i	$-0.695336\pi$
$233$	−954427.	−1.15174	−0.575868	+	0.817543i	$0.695336\pi$
$234$	56780.6	0.0677892
$235$	128450.	0.151728
$236$	−220820.	−0.258082
$237$	93576.2	0.108217
$238$	18005.6	0.0206046
$239$	532720.	0.603260	0.301630	−	0.953425i	$-0.402469\pi$
$239$	532720.	0.603260	0.301630	+	0.953425i	$0.402469\pi$
$240$	457003.	0.512142
$241$	1.59598e6	1.77005	0.885026	−	0.465542i	$-0.154140\pi$
$241$	1.59598e6	1.77005	0.885026	+	0.465542i	$0.154140\pi$
$242$	12780.2	0.0140281
$243$	872181.	0.947525
$244$	−11022.5	−0.0118524
$245$	414940.	0.441641
$246$	124034.	0.130678
$247$	−186148.	−0.194141
$248$	157164.	0.162264
$249$	880611.	0.900089
$250$	−13639.1	−0.0138018
$251$	−1.52806e6	−1.53093	−0.765467	−	0.643476i	$-0.777492\pi$
$251$	−1.52806e6	−1.53093	−0.765467	+	0.643476i	$0.777492\pi$
$252$	−57026.1	−0.0565682
$253$	569648.	0.559506
$254$	45661.3	0.0444083
$255$	684659.	0.659362
$256$	807716.	0.770298
$257$	−1.50277e6	−1.41926	−0.709629	−	0.704576i	$-0.751137\pi$
$257$	−1.50277e6	−1.41926	−0.709629	+	0.704576i	$0.751137\pi$
$258$	26783.6	0.0250506
$259$	94433.1	0.0874731
$260$	402694.	0.369438
$261$	−1.07427e6	−0.976140
$262$	63464.6	0.0571187
$263$	−552669.	−0.492693	−0.246346	−	0.969182i	$-0.579230\pi$
$263$	−552669.	−0.492693	−0.246346	+	0.969182i	$0.579230\pi$
$264$	128331.	0.113324
$265$	−678249.	−0.593300
$266$	−4560.16	−0.00395163
$267$	632028.	0.542573
$268$	−76758.2	−0.0652811
$269$	−577587.	−0.486673	−0.243336	−	0.969942i	$-0.578242\pi$
$269$	−577587.	−0.486673	−0.243336	+	0.969942i	$0.578242\pi$
$270$	−48993.7	−0.0409007
$271$	−2.10898e6	−1.74441	−0.872207	−	0.489137i	$-0.837312\pi$
$271$	−2.10898e6	−1.74441	−0.872207	+	0.489137i	$0.837312\pi$
$272$	1.35616e6	1.11145
$273$	−143370.	−0.116427
$274$	−255685.	−0.205745
$275$	75625.0	0.0603023
$276$	2.82557e6	2.23271
$277$	−1.35845e6	−1.06376	−0.531882	−	0.846818i	$-0.678515\pi$
$277$	−1.35845e6	−1.06376	−0.531882	+	0.846818i	$0.678515\pi$
$278$	237474.	0.184291
$279$	−359162.	−0.276236
$280$	19970.6	0.0152229
$281$	2.30339e6	1.74021	0.870105	−	0.492866i	$-0.164051\pi$
$281$	2.30339e6	1.74021	0.870105	+	0.492866i	$0.164051\pi$
$282$	86170.9	0.0645265
$283$	353653.	0.262489	0.131245	−	0.991350i	$-0.458103\pi$
$283$	353653.	0.262489	0.131245	+	0.991350i	$0.458103\pi$
$284$	−510782.	−0.375785
$285$	−173400.	−0.126455
$286$	54463.1	0.0393720
$287$	−107024.	−0.0766968
$288$	327599.	0.232735
$289$	611882.	0.430946
$290$	185839.	0.129760
$291$	−2.20429e6	−1.52594
$292$	−2.26313e6	−1.55329
$293$	2.30159e6	1.56625	0.783123	−	0.621867i	$-0.213626\pi$
$293$	2.30159e6	1.56625	0.783123	+	0.621867i	$0.213626\pi$
$294$	278363.	0.187820
$295$	−176724.	−0.118233
$296$	−360215.	−0.238964
$297$	271656.	0.178702
$298$	−311249.	−0.203033
$299$	2.42757e6	1.57034
$300$	375115.	0.240636
$301$	−23110.5	−0.0147025
$302$	−216322.	−0.136484
$303$	−289625.	−0.181230
$304$	−343467.	−0.213158
$305$	−8821.39	−0.00542984
$306$	156958.	0.0958250
$307$	1.97784e6	1.19769	0.598847	−	0.800863i	$-0.295626\pi$
$307$	1.97784e6	1.19769	0.598847	+	0.800863i	$0.295626\pi$
$308$	−54698.6	−0.0328548
$309$	3.47481e6	2.07031
$310$	62131.8	0.0367206
$311$	4797.46	0.00281262	0.00140631	−	0.999999i	$-0.499552\pi$
$311$	4797.46	0.00281262	0.00140631	+	0.999999i	$0.499552\pi$
$312$	546886.	0.318061
$313$	−621572.	−0.358617	−0.179309	−	0.983793i	$-0.557386\pi$
$313$	−621572.	−0.358617	−0.179309	+	0.983793i	$0.557386\pi$
$314$	−421865.	−0.241462
$315$	−45638.3	−0.0259151
$316$	152142.	0.0857099
$317$	2.87495e6	1.60687	0.803437	−	0.595390i	$-0.203003\pi$
$317$	2.87495e6	1.60687	0.803437	+	0.595390i	$0.203003\pi$
$318$	−455005.	−0.252318
$319$	−1.03042e6	−0.566943
$320$	704474.	0.384583
$321$	1.96039e6	1.06189
$322$	59469.4	0.0319635
$323$	−514566.	−0.274432
$324$	2.30504e6	1.21988
$325$	322279.	0.169248
$326$	217085.	0.113132
$327$	1.03664e6	0.536117
$328$	408244.	0.209524
$329$	−74353.5	−0.0378714
$330$	50733.2	0.0256453
$331$	−970007.	−0.486636	−0.243318	−	0.969947i	$-0.578236\pi$
$331$	−970007.	−0.486636	−0.243318	+	0.969947i	$0.578236\pi$
$332$	1.43175e6	0.712889
$333$	823190.	0.406808
$334$	−355705.	−0.174471
$335$	−61430.0	−0.0299067
$336$	−264537.	−0.127831
$337$	−3.35539e6	−1.60941	−0.804707	−	0.593672i	$-0.797678\pi$
$337$	−3.35539e6	−1.60941	−0.804707	+	0.593672i	$0.797678\pi$
$338$	−92006.0	−0.0438051
$339$	−3.99938e6	−1.89014
$340$	1.11316e6	0.522228
$341$	−344503.	−0.160438
$342$	−39751.7	−0.0183777
$343$	−483407.	−0.221859
$344$	88154.8	0.0401652
$345$	2.26132e6	1.02285
$346$	307408.	0.138046
$347$	3.83159e6	1.70827	0.854133	−	0.520054i	$-0.174088\pi$
$347$	3.83159e6	1.70827	0.854133	+	0.520054i	$0.174088\pi$
$348$	−5.11111e6	−2.26239
$349$	−1.83501e6	−0.806446	−0.403223	−	0.915102i	$-0.632110\pi$
$349$	−1.83501e6	−0.806446	−0.403223	+	0.915102i	$0.632110\pi$
$350$	7895.01	0.00344495
$351$	1.15767e6	0.501554
$352$	314228.	0.135173
$353$	−1.60883e6	−0.687183	−0.343592	−	0.939119i	$-0.611644\pi$
$353$	−1.60883e6	−0.687183	−0.343592	+	0.939119i	$0.611644\pi$
$354$	−118555.	−0.0502820
$355$	−408782.	−0.172155
$356$	1.02759e6	0.429729
$357$	−396316.	−0.164578
$358$	−193872.	−0.0799479
$359$	−2.70386e6	−1.10726	−0.553628	−	0.832764i	$-0.686757\pi$
$359$	−2.70386e6	−1.10726	−0.553628	+	0.832764i	$0.686757\pi$
$360$	174087.	0.0707963
$361$	130321.	0.0526316
$362$	366363.	0.146940
$363$	−281301.	−0.112048
$364$	−233100.	−0.0922123
$365$	−1.81120e6	−0.711595
$366$	−5917.84	−0.00230919
$367$	−3.46229e6	−1.34183	−0.670915	−	0.741534i	$-0.734099\pi$
$367$	−3.46229e6	−1.34183	−0.670915	+	0.741534i	$0.734099\pi$
$368$	4.47919e6	1.72417
$369$	−932949.	−0.356691
$370$	−142404.	−0.0540777
$371$	392606.	0.148089
$372$	−1.70880e6	−0.640228
$373$	−1.66846e6	−0.620931	−0.310465	−	0.950585i	$-0.600485\pi$
$373$	−1.66846e6	−0.620931	−0.310465	+	0.950585i	$0.600485\pi$
$374$	150552.	0.0556552
$375$	300207.	0.110241
$376$	283621.	0.103459
$377$	−4.39119e6	−1.59122
$378$	28360.1	0.0102089
$379$	62465.3	0.0223378	0.0111689	−	0.999938i	$-0.496445\pi$
$379$	62465.3	0.0223378	0.0111689	+	0.999938i	$0.496445\pi$
$380$	−281923.	−0.100155
$381$	−1.00504e6	−0.354708
$382$	648453.	0.227363
$383$	2.78813e6	0.971217	0.485609	−	0.874176i	$-0.338598\pi$
$383$	2.78813e6	0.971217	0.485609	+	0.874176i	$0.338598\pi$
$384$	2.06925e6	0.716119
$385$	−43775.6	−0.0150515
$386$	549663.	0.187771
$387$	−201458.	−0.0683765
$388$	−3.58387e6	−1.20857
$389$	−2.62099e6	−0.878197	−0.439098	−	0.898439i	$-0.644702\pi$
$389$	−2.62099e6	−0.878197	−0.439098	+	0.898439i	$0.644702\pi$
$390$	216201.	0.0719775
$391$	6.71050e6	2.21980
$392$	916197.	0.301144
$393$	−1.39690e6	−0.456231
$394$	577933.	0.187559
$395$	121760.	0.0392656
$396$	−476817.	−0.152797
$397$	3.40604e6	1.08461	0.542304	−	0.840182i	$-0.317552\pi$
$397$	3.40604e6	1.08461	0.542304	+	0.840182i	$0.317552\pi$
$398$	230414.	0.0729123
$399$	100373.	0.0315633
$400$	594645.	0.185827
$401$	−1.68971e6	−0.524748	−0.262374	−	0.964966i	$-0.584505\pi$
$401$	−1.68971e6	−0.524748	−0.262374	+	0.964966i	$0.584505\pi$
$402$	−41210.4	−0.0127187
$403$	−1.46811e6	−0.450295
$404$	−470890.	−0.143538
$405$	1.84474e6	0.558853
$406$	−107573.	−0.0323883
$407$	789592.	0.236274
$408$	1.51175e6	0.449602
$409$	−6.42803e6	−1.90007	−0.950035	−	0.312145i	$-0.898953\pi$
$409$	−6.42803e6	−1.90007	−0.950035	+	0.312145i	$0.898953\pi$
$410$	161392.	0.0474156
$411$	5.62782e6	1.64337
$412$	5.64955e6	1.63973
$413$	102297.	0.0295112
$414$	518406.	0.148651
$415$	1.14584e6	0.326590
$416$	1.33910e6	0.379383
$417$	−5.22699e6	−1.47201
$418$	−38129.3	−0.0106738
$419$	−2.37424e6	−0.660677	−0.330338	−	0.943863i	$-0.607163\pi$
$419$	−2.37424e6	−0.660677	−0.330338	+	0.943863i	$0.607163\pi$
$420$	−217136.	−0.0600632
$421$	1.45966e6	0.401372	0.200686	−	0.979656i	$-0.435683\pi$
$421$	1.45966e6	0.401372	0.200686	+	0.979656i	$0.435683\pi$
$422$	46151.7	0.0126156
$423$	−648152.	−0.176127
$424$	−1.49759e6	−0.404556
$425$	890869.	0.239244
$426$	−274232.	−0.0732140
$427$	5106.27	0.00135530
$428$	3.18732e6	0.841039
$429$	−1.19877e6	−0.314481
$430$	34850.4	0.00908943
$431$	1.08944e6	0.282496	0.141248	−	0.989974i	$-0.454889\pi$
$431$	1.08944e6	0.282496	0.141248	+	0.989974i	$0.454889\pi$
$432$	2.13605e6	0.550685
$433$	1.06858e6	0.273897	0.136949	−	0.990578i	$-0.456271\pi$
$433$	1.06858e6	0.273897	0.136949	+	0.990578i	$0.456271\pi$
$434$	−35965.0	−0.00916550
$435$	−4.09045e6	−1.03645
$436$	1.68544e6	0.424616
$437$	−1.69953e6	−0.425721
$438$	−1.21504e6	−0.302626
$439$	5.16409e6	1.27889	0.639444	−	0.768838i	$-0.279165\pi$
$439$	5.16409e6	1.27889	0.639444	+	0.768838i	$0.279165\pi$
$440$	166982.	0.0411186
$441$	−2.09376e6	−0.512662
$442$	641581.	0.156205
$443$	1.80010e6	0.435801	0.217900	−	0.975971i	$-0.430079\pi$
$443$	1.80010e6	0.435801	0.217900	+	0.975971i	$0.430079\pi$
$444$	3.91653e6	0.942853
$445$	822386.	0.196868
$446$	397137.	0.0945373
$447$	6.85083e6	1.62171
$448$	−407786.	−0.0959925
$449$	−4.12315e6	−0.965191	−0.482596	−	0.875843i	$-0.660306\pi$
$449$	−4.12315e6	−0.965191	−0.482596	+	0.875843i	$0.660306\pi$
$450$	68822.2	0.0160213
$451$	−894871.	−0.207166
$452$	−6.50243e6	−1.49703
$453$	4.76141e6	1.09016
$454$	1.24997e6	0.284617
$455$	−186551.	−0.0422445
$456$	−382871.	−0.0862263
$457$	−2.74851e6	−0.615613	−0.307806	−	0.951449i	$-0.599595\pi$
$457$	−2.74851e6	−0.615613	−0.307806	+	0.951449i	$0.599595\pi$
$458$	562865.	0.125384
$459$	3.20013e6	0.708984
$460$	3.67659e6	0.810122
$461$	−4.38391e6	−0.960747	−0.480374	−	0.877064i	$-0.659499\pi$
$461$	−4.38391e6	−0.960747	−0.480374	+	0.877064i	$0.659499\pi$
$462$	−29367.0	−0.00640109
$463$	1.36621e6	0.296186	0.148093	−	0.988973i	$-0.452687\pi$
$463$	1.36621e6	0.296186	0.148093	+	0.988973i	$0.452687\pi$
$464$	−8.10231e6	−1.74708
$465$	−1.36757e6	−0.293303
$466$	−833122.	−0.177723
$467$	4.20093e6	0.891360	0.445680	−	0.895192i	$-0.352962\pi$
$467$	4.20093e6	0.891360	0.445680	+	0.895192i	$0.352962\pi$
$468$	−2.03197e6	−0.428848
$469$	35558.9	0.00746476
$470$	112124.	0.0234129
$471$	9.28556e6	1.92866
$472$	−390210.	−0.0806201
$473$	−193236.	−0.0397131
$474$	81682.9	0.0166988
$475$	−225625.	−0.0458831
$476$	−644354.	−0.130349
$477$	3.42241e6	0.688710
$478$	465013.	0.0930883
$479$	1.49255e6	0.297229	0.148615	−	0.988895i	$-0.452519\pi$
$479$	1.49255e6	0.297229	0.148615	+	0.988895i	$0.452519\pi$
$480$	1.24739e6	0.247114
$481$	3.36487e6	0.663141
$482$	1.39314e6	0.273135
$483$	−1.30897e6	−0.255306
$484$	−457356.	−0.0887444
$485$	−2.86819e6	−0.553673
$486$	761329.	0.146212
$487$	−107855.	−0.0206071	−0.0103036	−	0.999947i	$-0.503280\pi$
$487$	−107855.	−0.0206071	−0.0103036	+	0.999947i	$0.503280\pi$
$488$	−19477.9	−0.00370247
$489$	−4.77819e6	−0.903632
$490$	362202.	0.0681491
$491$	−1.46118e6	−0.273526	−0.136763	−	0.990604i	$-0.543670\pi$
$491$	−1.46118e6	−0.273526	−0.136763	+	0.990604i	$0.543670\pi$
$492$	−4.43874e6	−0.826698
$493$	−1.21385e7	−2.24930
$494$	−162489.	−0.0299576
$495$	−381600.	−0.0699995
$496$	−2.70886e6	−0.494404
$497$	236624.	0.0429702
$498$	768687.	0.138892
$499$	−7.93664e6	−1.42687	−0.713436	−	0.700720i	$-0.752862\pi$
$499$	−7.93664e6	−1.42687	−0.713436	+	0.700720i	$0.752862\pi$
$500$	488094.	0.0873130
$501$	7.82934e6	1.39358
$502$	−1.33385e6	−0.236237
$503$	429860.	0.0757542	0.0378771	−	0.999282i	$-0.487940\pi$
$503$	429860.	0.0757542	0.0378771	+	0.999282i	$0.487940\pi$
$504$	−100771.	−0.0176709
$505$	−376856.	−0.0657578
$506$	497247.	0.0863368
$507$	2.02512e6	0.349890
$508$	−1.63405e6	−0.280936
$509$	−8.50960e6	−1.45584	−0.727921	−	0.685661i	$-0.759513\pi$
$509$	−8.50960e6	−1.45584	−0.727921	+	0.685661i	$0.759513\pi$
$510$	597641.	0.101745
$511$	1.04841e6	0.177615
$512$	4.15143e6	0.699879
$513$	−810478.	−0.135972
$514$	−1.31178e6	−0.219004
$515$	4.52137e6	0.751194
$516$	−958487.	−0.158475
$517$	−621698.	−0.102295
$518$	82430.9	0.0134979
$519$	−6.76628e6	−1.10263
$520$	711600.	0.115406
$521$	−1.42439e6	−0.229898	−0.114949	−	0.993371i	$-0.536670\pi$
$521$	−1.42439e6	−0.229898	−0.114949	+	0.993371i	$0.536670\pi$
$522$	−937733.	−0.150627
$523$	−1.97327e6	−0.315451	−0.157726	−	0.987483i	$-0.550416\pi$
$523$	−1.97327e6	−0.315451	−0.157726	+	0.987483i	$0.550416\pi$
$524$	−2.27117e6	−0.361344
$525$	−173775.	−0.0275163
$526$	−482427.	−0.0760268
$527$	−4.05828e6	−0.636525
$528$	−2.21189e6	−0.345286
$529$	1.57273e7	2.44352
$530$	−592046.	−0.0915515
$531$	891738.	0.137246
$532$	163192.	0.0249988
$533$	−3.81353e6	−0.581445
$534$	551699.	0.0837238
$535$	2.55083e6	0.385298
$536$	−135639.	−0.0203926
$537$	4.26726e6	0.638578
$538$	−504178.	−0.0750979
$539$	−2.00831e6	−0.297754
$540$	1.75331e6	0.258746
$541$	8.59715e6	1.26288	0.631439	−	0.775425i	$-0.282465\pi$
$541$	8.59715e6	1.26288	0.631439	+	0.775425i	$0.282465\pi$
$542$	−1.84094e6	−0.269178
$543$	−8.06393e6	−1.17367
$544$	3.70164e6	0.536286
$545$	1.34887e6	0.194526
$546$	−125148.	−0.0179657
$547$	6.20346e6	0.886473	0.443236	−	0.896405i	$-0.353830\pi$
$547$	6.20346e6	0.886473	0.443236	+	0.896405i	$0.353830\pi$
$548$	9.15005e6	1.30158
$549$	44512.3	0.00630302
$550$	66013.3	0.00930517
$551$	3.07424e6	0.431379
$552$	4.99305e6	0.697458
$553$	−70481.0	−0.00980075
$554$	−1.18580e6	−0.164148
$555$	3.13442e6	0.431942
$556$	−8.49835e6	−1.16586
$557$	−9.45629e6	−1.29147	−0.645733	−	0.763564i	$-0.723448\pi$
$557$	−9.45629e6	−1.29147	−0.645733	+	0.763564i	$0.723448\pi$
$558$	−313514.	−0.0426256
$559$	−823480.	−0.111461
$560$	−344211.	−0.0463826
$561$	−3.31375e6	−0.444542
$562$	2.01064e6	0.268530
$563$	3.70113e6	0.492112	0.246056	−	0.969256i	$-0.420865\pi$
$563$	3.70113e6	0.492112	0.246056	+	0.969256i	$0.420865\pi$
$564$	−3.08375e6	−0.408207
$565$	−5.20393e6	−0.685821
$566$	308705.	0.0405044
$567$	−1.06783e6	−0.139491
$568$	−902601.	−0.117388
$569$	7.93015e6	1.02684	0.513418	−	0.858139i	$-0.328379\pi$
$569$	7.93015e6	1.02684	0.513418	+	0.858139i	$0.328379\pi$
$570$	−151361.	−0.0195131
$571$	8.46182e6	1.08611	0.543055	−	0.839697i	$-0.317268\pi$
$571$	8.46182e6	1.08611	0.543055	+	0.839697i	$0.317268\pi$
$572$	−1.94904e6	−0.249075
$573$	−1.42729e7	−1.81605
$574$	−93421.8	−0.0118350
$575$	2.94240e6	0.371135
$576$	−3.55474e6	−0.446428
$577$	8.67543e6	1.08480	0.542402	−	0.840119i	$-0.317515\pi$
$577$	8.67543e6	1.08480	0.542402	+	0.840119i	$0.317515\pi$
$578$	534113.	0.0664988
$579$	−1.20985e7	−1.49981
$580$	−6.65050e6	−0.820889
$581$	−663270.	−0.0815174
$582$	−1.92413e6	−0.235465
$583$	3.28273e6	0.400003
$584$	−3.99917e6	−0.485219
$585$	−1.62620e6	−0.196465
$586$	2.00907e6	0.241685
$587$	−6.53706e6	−0.783046	−0.391523	−	0.920168i	$-0.628052\pi$
$587$	−6.53706e6	−0.783046	−0.391523	+	0.920168i	$0.628052\pi$
$588$	−9.96160e6	−1.18819
$589$	1.02782e6	0.122075
$590$	−154262.	−0.0182444
$591$	−1.27207e7	−1.49811
$592$	6.20862e6	0.728100
$593$	−820529.	−0.0958202	−0.0479101	−	0.998852i	$-0.515256\pi$
$593$	−820529.	−0.0958202	−0.0479101	+	0.998852i	$0.515256\pi$
$594$	237129.	0.0275752
$595$	−515681.	−0.0597157
$596$	1.11385e7	1.28443
$597$	−5.07158e6	−0.582382
$598$	2.11904e6	0.242318
$599$	−1.56520e7	−1.78239	−0.891197	−	0.453616i	$-0.850134\pi$
$599$	−1.56520e7	−1.78239	−0.891197	+	0.453616i	$0.850134\pi$
$600$	662865.	0.0751704
$601$	9.43040e6	1.06499	0.532493	−	0.846434i	$-0.321255\pi$
$601$	9.43040e6	1.06499	0.532493	+	0.846434i	$0.321255\pi$
$602$	−20173.2	−0.00226873
$603$	309973.	0.0347160
$604$	7.74138e6	0.863428
$605$	−366025.	−0.0406558
$606$	−252814.	−0.0279654
$607$	1.36172e7	1.50008	0.750042	−	0.661391i	$-0.230033\pi$
$607$	1.36172e7	1.50008	0.750042	+	0.661391i	$0.230033\pi$
$608$	−937491.	−0.102851
$609$	2.36776e6	0.258699
$610$	−7700.21	−0.000837873 0
$611$	−2.64939e6	−0.287106
$612$	−5.61695e6	−0.606208
$613$	1.02492e7	1.10163	0.550817	−	0.834626i	$-0.314316\pi$
$613$	1.02492e7	1.10163	0.550817	+	0.834626i	$0.314316\pi$
$614$	1.72646e6	0.184815
$615$	−3.55235e6	−0.378729
$616$	−96657.7	−0.0102632
$617$	1.71156e7	1.81000	0.905002	−	0.425407i	$-0.139869\pi$
$617$	1.71156e7	1.81000	0.905002	+	0.425407i	$0.139869\pi$
$618$	3.03317e6	0.319467
$619$	5.75198e6	0.603380	0.301690	−	0.953406i	$-0.402449\pi$
$619$	5.75198e6	0.603380	0.301690	+	0.953406i	$0.402449\pi$
$620$	−2.22347e6	−0.232302
$621$	1.05695e7	1.09983
$622$	4187.72	0.000434012 0
$623$	−476039.	−0.0491386
$624$	−9.42606e6	−0.969100
$625$	390625.	0.0400000
$626$	−542572.	−0.0553378
$627$	839254.	0.0852559
$628$	1.50970e7	1.52754
$629$	9.30146e6	0.937399
$630$	−39837.8	−0.00399893
$631$	4.22232e6	0.422161	0.211081	−	0.977469i	$-0.432302\pi$
$631$	4.22232e6	0.422161	0.211081	+	0.977469i	$0.432302\pi$
$632$	268849.	0.0267742
$633$	−1.01583e6	−0.100766
$634$	2.50955e6	0.247955
$635$	−1.30774e6	−0.128703
$636$	1.62830e7	1.59621
$637$	−8.55847e6	−0.835695
$638$	−899460.	−0.0874843
$639$	2.06269e6	0.199840
$640$	2.69248e6	0.259838
$641$	5.62914e6	0.541124	0.270562	−	0.962703i	$-0.412791\pi$
$641$	5.62914e6	0.541124	0.270562	+	0.962703i	$0.412791\pi$
$642$	1.71123e6	0.163859
$643$	1.45021e6	0.138325	0.0691627	−	0.997605i	$-0.477967\pi$
$643$	1.45021e6	0.138325	0.0691627	+	0.997605i	$0.477967\pi$
$644$	−2.12820e6	−0.202207
$645$	−767083.	−0.0726011
$646$	−449166.	−0.0423473
$647$	−1.74997e6	−0.164350	−0.0821749	−	0.996618i	$-0.526187\pi$
$647$	−1.74997e6	−0.164350	−0.0821749	+	0.996618i	$0.526187\pi$
$648$	4.07324e6	0.381068
$649$	855342.	0.0797128
$650$	281318.	0.0261164
$651$	791618.	0.0732088
$652$	−7.76867e6	−0.715695
$653$	2.18372e6	0.200408	0.100204	−	0.994967i	$-0.468051\pi$
$653$	2.18372e6	0.200408	0.100204	+	0.994967i	$0.468051\pi$
$654$	904888.	0.0827276
$655$	−1.81763e6	−0.165540
$656$	−7.03644e6	−0.638401
$657$	9.13920e6	0.826028
$658$	−64903.3	−0.00584389
$659$	1.12388e7	1.00811	0.504055	−	0.863671i	$-0.331841\pi$
$659$	1.12388e7	1.00811	0.504055	+	0.863671i	$0.331841\pi$
$660$	−1.81556e6	−0.162237
$661$	−1.99507e7	−1.77605	−0.888024	−	0.459796i	$-0.847922\pi$
$661$	−1.99507e7	−1.77605	−0.888024	+	0.459796i	$0.847922\pi$
$662$	−846721.	−0.0750923
$663$	−1.41217e7	−1.24768
$664$	2.53004e6	0.222693
$665$	130603.	0.0114525
$666$	718564.	0.0627740
$667$	−4.00915e7	−3.48929
$668$	1.27294e7	1.10374
$669$	−8.74128e6	−0.755109
$670$	−53622.4	−0.00461487
$671$	42695.5	0.00366080
$672$	−722051.	−0.0616800
$673$	−9.67137e6	−0.823096	−0.411548	−	0.911388i	$-0.635012\pi$
$673$	−9.67137e6	−0.823096	−0.411548	+	0.911388i	$0.635012\pi$
$674$	−2.92893e6	−0.248347
$675$	1.40318e6	0.118537
$676$	3.29256e6	0.277120
$677$	−1.94877e6	−0.163414	−0.0817068	−	0.996656i	$-0.526037\pi$
$677$	−1.94877e6	−0.163414	−0.0817068	+	0.996656i	$0.526037\pi$
$678$	−3.49107e6	−0.291665
$679$	1.66026e6	0.138198
$680$	1.96706e6	0.163135
$681$	−2.75128e7	−2.27335
$682$	−300718.	−0.0247570
$683$	2.01947e7	1.65648	0.828238	−	0.560376i	$-0.189343\pi$
$683$	2.01947e7	1.65648	0.828238	+	0.560376i	$0.189343\pi$
$684$	1.42257e6	0.116261
$685$	7.32284e6	0.596284
$686$	−421967.	−0.0342349
$687$	−1.23891e7	−1.00149
$688$	−1.51943e6	−0.122379
$689$	1.39895e7	1.12267
$690$	1.97391e6	0.157836
$691$	2.00644e7	1.59857	0.799284	−	0.600954i	$-0.205213\pi$
$691$	2.00644e7	1.59857	0.799284	+	0.600954i	$0.205213\pi$
$692$	−1.10010e7	−0.873309
$693$	220890.	0.0174720
$694$	3.34461e6	0.263601
$695$	−6.80129e6	−0.534108
$696$	−9.03183e6	−0.706728
$697$	−1.05417e7	−0.821915
$698$	−1.60179e6	−0.124442
$699$	1.83376e7	1.41955
$700$	−282534.	−0.0217934
$701$	−811483.	−0.0623713	−0.0311856	−	0.999514i	$-0.509928\pi$
$701$	−811483.	−0.0623713	−0.0311856	+	0.999514i	$0.509928\pi$
$702$	1.01054e6	0.0773943
$703$	−2.35572e6	−0.179778
$704$	−3.40966e6	−0.259286
$705$	−2.46794e6	−0.187009
$706$	−1.40435e6	−0.106038
$707$	218144.	0.0164132
$708$	4.24267e6	0.318094
$709$	−4.02841e6	−0.300966	−0.150483	−	0.988613i	$-0.548083\pi$
$709$	−4.02841e6	−0.300966	−0.150483	+	0.988613i	$0.548083\pi$
$710$	−356827.	−0.0265651
$711$	−614395.	−0.0455799
$712$	1.81585e6	0.134239
$713$	−1.34038e7	−0.987427
$714$	−345945.	−0.0253958
$715$	−1.55983e6	−0.114107
$716$	6.93797e6	0.505766
$717$	−1.02353e7	−0.743536
$718$	−2.36021e6	−0.170859
$719$	1.89234e7	1.36514	0.682571	−	0.730819i	$-0.260862\pi$
$719$	1.89234e7	1.36514	0.682571	+	0.730819i	$0.260862\pi$
$720$	−3.00055e6	−0.215710
$721$	−2.61720e6	−0.187499
$722$	113758.	0.00812152
$723$	−3.06640e7	−2.18164
$724$	−1.31108e7	−0.929573
$725$	−5.32244e6	−0.376068
$726$	−245548.	−0.0172900
$727$	1.45216e7	1.01901	0.509504	−	0.860468i	$-0.329829\pi$
$727$	1.45216e7	1.01901	0.509504	+	0.860468i	$0.329829\pi$
$728$	−411910.	−0.0288054
$729$	1.17346e6	0.0817805
$730$	−1.58100e6	−0.109805
$731$	−2.27633e6	−0.157559
$732$	211778.	0.0146084
$733$	9.67628e6	0.665194	0.332597	−	0.943069i	$-0.392075\pi$
$733$	9.67628e6	0.665194	0.332597	+	0.943069i	$0.392075\pi$
$734$	−3.02224e6	−0.207056
$735$	−7.97233e6	−0.544336
$736$	1.22259e7	0.831930
$737$	297321.	0.0201631
$738$	−814374.	−0.0550406
$739$	−4.65079e6	−0.313268	−0.156634	−	0.987657i	$-0.550064\pi$
$739$	−4.65079e6	−0.313268	−0.156634	+	0.987657i	$0.550064\pi$
$740$	5.09613e6	0.342107
$741$	3.57651e6	0.239284
$742$	342706.	0.0228514
$743$	3.37717e6	0.224430	0.112215	−	0.993684i	$-0.464206\pi$
$743$	3.37717e6	0.224430	0.112215	+	0.993684i	$0.464206\pi$
$744$	−3.01962e6	−0.199996
$745$	8.91420e6	0.588426
$746$	−1.45640e6	−0.0958151
$747$	−5.78184e6	−0.379109
$748$	−5.38770e6	−0.352086
$749$	−1.47655e6	−0.0961710
$750$	262051.	0.0170111
$751$	2.07936e7	1.34533	0.672666	−	0.739946i	$-0.265149\pi$
$751$	2.07936e7	1.34533	0.672666	+	0.739946i	$0.265149\pi$
$752$	−4.88846e6	−0.315230
$753$	2.93590e7	1.88692
$754$	−3.83308e6	−0.245539
$755$	6.19547e6	0.395555
$756$	−1.01490e6	−0.0645834
$757$	2.05798e7	1.30527	0.652637	−	0.757671i	$-0.273663\pi$
$757$	2.05798e7	1.30527	0.652637	+	0.757671i	$0.273663\pi$
$758$	54526.1	0.00344692
$759$	−1.09448e7	−0.689609
$760$	−498186.	−0.0312865
$761$	−9.58126e6	−0.599737	−0.299869	−	0.953980i	$-0.596943\pi$
$761$	−9.58126e6	−0.599737	−0.299869	+	0.953980i	$0.596943\pi$
$762$	−877302.	−0.0547346
$763$	−780793.	−0.0485539
$764$	−2.32058e7	−1.43835
$765$	−4.49528e6	−0.277717
$766$	2.43377e6	0.149867
$767$	3.64507e6	0.223727
$768$	−1.55188e7	−0.949416
$769$	−2.54251e7	−1.55041	−0.775206	−	0.631708i	$-0.782354\pi$
$769$	−2.54251e7	−1.55041	−0.775206	+	0.631708i	$0.782354\pi$
$770$	−38211.9	−0.00232258
$771$	2.88732e7	1.74928
$772$	−1.96705e7	−1.18788
$773$	−2.77857e7	−1.67252	−0.836261	−	0.548331i	$-0.815263\pi$
$773$	−2.77857e7	−1.67252	−0.836261	+	0.548331i	$0.815263\pi$
$774$	−175853.	−0.0105511
$775$	−1.77946e6	−0.106423
$776$	−6.33304e6	−0.377535
$777$	−1.81437e6	−0.107813
$778$	−2.28787e6	−0.135514
$779$	2.66982e6	0.157630
$780$	−7.73706e6	−0.455344
$781$	1.97850e6	0.116067
$782$	5.85761e6	0.342534
$783$	−1.91190e7	−1.11445
$784$	−1.57915e7	−0.917556
$785$	1.20822e7	0.699799
$786$	−1.21936e6	−0.0704005
$787$	−1.13153e7	−0.651224	−0.325612	−	0.945503i	$-0.605570\pi$
$787$	−1.13153e7	−0.651224	−0.325612	+	0.945503i	$0.605570\pi$
$788$	−2.06821e7	−1.18653
$789$	1.06186e7	0.607258
$790$	106285.	0.00605903
$791$	3.01230e6	0.171182
$792$	−842582.	−0.0477309
$793$	181948.	0.0102746
$794$	2.97314e6	0.167365
$795$	1.30314e7	0.731261
$796$	−8.24568e6	−0.461258
$797$	−1.60747e7	−0.896389	−0.448194	−	0.893936i	$-0.647933\pi$
$797$	−1.60747e7	−0.896389	−0.448194	+	0.893936i	$0.647933\pi$
$798$	87615.5	0.00487050
$799$	−7.32366e6	−0.405846
$800$	1.62308e6	0.0896634
$801$	−4.14972e6	−0.228527
$802$	−1.47495e6	−0.0809732
$803$	8.76619e6	0.479758
$804$	1.47477e6	0.0804609
$805$	−1.70321e6	−0.0926357
$806$	−1.28152e6	−0.0694844
$807$	1.10973e7	0.599839
$808$	−832108.	−0.0448385
$809$	1.55281e7	0.834157	0.417078	−	0.908871i	$-0.363054\pi$
$809$	1.55281e7	0.834157	0.417078	+	0.908871i	$0.363054\pi$
$810$	1.61028e6	0.0862360
$811$	−1.02642e7	−0.547992	−0.273996	−	0.961731i	$-0.588346\pi$
$811$	−1.02642e7	−0.547992	−0.273996	+	0.961731i	$0.588346\pi$
$812$	3.84965e6	0.204895
$813$	4.05204e7	2.15004
$814$	689237.	0.0364592
$815$	−6.21732e6	−0.327876
$816$	−2.60563e7	−1.36989
$817$	576513.	0.0302172
$818$	−5.61104e6	−0.293197
$819$	941329.	0.0490379
$820$	−5.77562e6	−0.299961
$821$	2.88354e7	1.49303	0.746513	−	0.665371i	$-0.231727\pi$
$821$	2.88354e7	1.49303	0.746513	+	0.665371i	$0.231727\pi$
$822$	4.91254e6	0.253587
$823$	−2.27784e6	−0.117226	−0.0586130	−	0.998281i	$-0.518668\pi$
$823$	−2.27784e6	−0.117226	−0.0586130	+	0.998281i	$0.518668\pi$
$824$	9.98331e6	0.512220
$825$	−1.45300e6	−0.0743244
$826$	89295.0	0.00455383
$827$	−2.80391e7	−1.42561	−0.712805	−	0.701362i	$-0.752575\pi$
$827$	−2.80391e7	−1.42561	−0.712805	+	0.701362i	$0.752575\pi$
$828$	−1.85519e7	−0.940398
$829$	3.30425e7	1.66988	0.834942	−	0.550338i	$-0.185501\pi$
$829$	3.30425e7	1.66988	0.834942	+	0.550338i	$0.185501\pi$
$830$	1.00021e6	0.0503958
$831$	2.61003e7	1.31112
$832$	−1.45304e7	−0.727727
$833$	−2.36580e7	−1.18132
$834$	−4.56265e6	−0.227145
$835$	1.01874e7	0.505648
$836$	1.36451e6	0.0675244
$837$	−6.39208e6	−0.315376
$838$	−2.07248e6	−0.101948
$839$	−3.85966e7	−1.89297	−0.946485	−	0.322747i	$-0.895394\pi$
$839$	−3.85966e7	−1.89297	−0.946485	+	0.322747i	$0.895394\pi$
$840$	−383700.	−0.0187626
$841$	5.20095e7	2.53567
$842$	1.27414e6	0.0619353
$843$	−4.42556e7	−2.14486
$844$	−1.65160e6	−0.0798087
$845$	2.63506e6	0.126955
$846$	−565774.	−0.0271780
$847$	211874.	0.0101477
$848$	2.58123e7	1.23264
$849$	−6.79482e6	−0.323526
$850$	777642.	0.0369175
$851$	3.07212e7	1.45417
$852$	9.81378e6	0.463167
$853$	4.90013e6	0.230587	0.115294	−	0.993331i	$-0.463219\pi$
$853$	4.90013e6	0.230587	0.115294	+	0.993331i	$0.463219\pi$
$854$	4457.28	0.000209134 0
$855$	1.13849e6	0.0532617
$856$	5.63230e6	0.262725
$857$	−2.88163e7	−1.34025	−0.670127	−	0.742247i	$-0.733760\pi$
$857$	−2.88163e7	−1.34025	−0.670127	+	0.742247i	$0.733760\pi$
$858$	−1.04641e6	−0.0485272
$859$	1.12165e7	0.518652	0.259326	−	0.965790i	$-0.416500\pi$
$859$	1.12165e7	0.518652	0.259326	+	0.965790i	$0.416500\pi$
$860$	−1.24717e6	−0.0575015
$861$	2.05628e6	0.0945312
$862$	950979.	0.0435916
$863$	−1.83352e7	−0.838027	−0.419013	−	0.907980i	$-0.637624\pi$
$863$	−1.83352e7	−0.838027	−0.419013	+	0.907980i	$0.637624\pi$
$864$	5.83035e6	0.265711
$865$	−8.80419e6	−0.400082
$866$	932766.	0.0422647
$867$	−1.17562e7	−0.531154
$868$	1.28706e6	0.0579828
$869$	−589319.	−0.0264729
$870$	−3.57057e6	−0.159933
$871$	1.26705e6	0.0565909
$872$	2.97833e6	0.132642
$873$	1.44727e7	0.642710
$874$	−1.48352e6	−0.0656925
$875$	−226114.	−0.00998405
$876$	4.34820e7	1.91447
$877$	1.61290e7	0.708125	0.354062	−	0.935222i	$-0.384800\pi$
$877$	1.61290e7	0.708125	0.354062	+	0.935222i	$0.384800\pi$
$878$	4.50775e6	0.197344
$879$	−4.42211e7	−1.93044
$880$	−2.87808e6	−0.125284
$881$	−2.08699e7	−0.905899	−0.452950	−	0.891536i	$-0.649628\pi$
$881$	−2.08699e7	−0.905899	−0.452950	+	0.891536i	$0.649628\pi$
$882$	−1.82765e6	−0.0791083
$883$	3.34070e7	1.44190	0.720951	−	0.692986i	$-0.243705\pi$
$883$	3.34070e7	1.44190	0.720951	+	0.692986i	$0.243705\pi$
$884$	−2.29599e7	−0.988186
$885$	3.39543e6	0.145726
$886$	1.57131e6	0.0672479
$887$	2.98683e7	1.27468	0.637340	−	0.770583i	$-0.280035\pi$
$887$	2.98683e7	1.27468	0.637340	+	0.770583i	$0.280035\pi$
$888$	6.92089e6	0.294530
$889$	756990.	0.0321244
$890$	717863.	0.0303785
$891$	−8.92855e6	−0.376779
$892$	−1.42121e7	−0.598062
$893$	1.85482e6	0.0778346
$894$	5.98010e6	0.250245
$895$	5.55250e6	0.231703
$896$	−1.55855e6	−0.0648559
$897$	−4.66416e7	−1.93550
$898$	−3.59911e6	−0.148938
$899$	2.42459e7	1.00055
$900$	−2.46290e6	−0.101354
$901$	3.86708e7	1.58698
$902$	−781135.	−0.0319676
$903$	444027.	0.0181213
$904$	−1.14904e7	−0.467644
$905$	−1.04927e7	−0.425858
$906$	4.15624e6	0.168221
$907$	−3.38423e7	−1.36597	−0.682987	−	0.730431i	$-0.739319\pi$
$907$	−3.38423e7	−1.36597	−0.682987	+	0.730431i	$0.739319\pi$
$908$	−4.47320e7	−1.80054
$909$	1.90160e6	0.0763323
$910$	−162841.	−0.00651870
$911$	3.50632e7	1.39977	0.699883	−	0.714257i	$-0.253235\pi$
$911$	3.50632e7	1.39977	0.699883	+	0.714257i	$0.253235\pi$
$912$	6.59912e6	0.262723
$913$	−5.54586e6	−0.220187
$914$	−2.39919e6	−0.0949945
$915$	169487.	0.00669244
$916$	−2.01429e7	−0.793202
$917$	1.05214e6	0.0413190
$918$	2.79341e6	0.109403
$919$	−2.41846e7	−0.944604	−0.472302	−	0.881437i	$-0.656577\pi$
$919$	−2.41846e7	−0.944604	−0.472302	+	0.881437i	$0.656577\pi$
$920$	6.49689e6	0.253067
$921$	−3.80008e7	−1.47619
$922$	−3.82673e6	−0.148252
$923$	8.43147e6	0.325761
$924$	1.05094e6	0.0404946
$925$	4.07847e6	0.156727
$926$	1.19257e6	0.0457041
$927$	−2.28146e7	−0.871994
$928$	−2.21152e7	−0.842987
$929$	4.73906e7	1.80158	0.900790	−	0.434256i	$-0.142989\pi$
$929$	4.73906e7	1.80158	0.900790	+	0.434256i	$0.142989\pi$
$930$	−1.19375e6	−0.0452592
$931$	5.99173e6	0.226557
$932$	2.98144e7	1.12431
$933$	−92174.8	−0.00346663
$934$	3.66700e6	0.137545
$935$	−4.31181e6	−0.161298
$936$	−3.59069e6	−0.133964
$937$	2.29147e7	0.852639	0.426319	−	0.904573i	$-0.359810\pi$
$937$	2.29147e7	0.852639	0.426319	+	0.904573i	$0.359810\pi$
$938$	31039.4	0.00115188
$939$	1.19424e7	0.442006
$940$	−4.01253e6	−0.148115
$941$	−1.02808e7	−0.378487	−0.189244	−	0.981930i	$-0.560604\pi$
$941$	−1.02808e7	−0.378487	−0.189244	+	0.981930i	$0.560604\pi$
$942$	8.10539e6	0.297609
$943$	−3.48174e7	−1.27502
$944$	6.72562e6	0.245642
$945$	−812234.	−0.0295871
$946$	−168676.	−0.00612809
$947$	2.17758e7	0.789041	0.394521	−	0.918887i	$-0.370911\pi$
$947$	2.17758e7	0.789041	0.394521	+	0.918887i	$0.370911\pi$
$948$	−2.92314e6	−0.105640
$949$	3.73574e7	1.34652
$950$	−196949.	−0.00708018
$951$	−5.52370e7	−1.98052
$952$	−1.13864e6	−0.0407186
$953$	−1.70938e7	−0.609686	−0.304843	−	0.952403i	$-0.598604\pi$
$953$	−1.70938e7	−0.609686	−0.304843	+	0.952403i	$0.598604\pi$
$954$	2.98743e6	0.106274
$955$	−1.85718e7	−0.658938
$956$	−1.66411e7	−0.588895
$957$	1.97978e7	0.698774
$958$	1.30286e6	0.0458651
$959$	−4.23884e6	−0.148833
$960$	−1.35352e7	−0.474010
$961$	−2.05230e7	−0.716856
$962$	2.93721e6	0.102329
$963$	−1.28714e7	−0.447259
$964$	−4.98554e7	−1.72790
$965$	−1.57424e7	−0.544192
$966$	−1.14260e6	−0.0393960
$967$	−3.06692e7	−1.05472	−0.527359	−	0.849643i	$-0.676818\pi$
$967$	−3.06692e7	−1.05472	−0.527359	+	0.849643i	$0.676818\pi$
$968$	−808193.	−0.0277221
$969$	9.88648e6	0.338246
$970$	−2.50365e6	−0.0854367
$971$	−4.65159e7	−1.58326	−0.791632	−	0.610998i	$-0.790768\pi$
$971$	−4.65159e7	−1.58326	−0.791632	+	0.610998i	$0.790768\pi$
$972$	−2.72452e7	−0.924964
$973$	3.93693e6	0.133314
$974$	−94146.9	−0.00317986
$975$	−6.19202e6	−0.208603
$976$	335718.	0.0112811
$977$	4.18693e7	1.40333	0.701663	−	0.712509i	$-0.252441\pi$
$977$	4.18693e7	1.40333	0.701663	+	0.712509i	$0.252441\pi$
$978$	−4.17090e6	−0.139438
$979$	−3.98035e6	−0.132728
$980$	−1.29619e7	−0.431125
$981$	−6.80630e6	−0.225808
$982$	−1.27546e6	−0.0422075
$983$	−1.05239e7	−0.347371	−0.173685	−	0.984801i	$-0.555568\pi$
$983$	−1.05239e7	−0.347371	−0.173685	+	0.984801i	$0.555568\pi$
$984$	−7.84368e6	−0.258245
$985$	−1.65521e7	−0.543577
$986$	−1.05957e7	−0.347087
$987$	1.42857e6	0.0466777
$988$	5.81490e6	0.189518
$989$	−7.51835e6	−0.244417
$990$	−333099.	−0.0108015
$991$	4.99776e7	1.61656	0.808279	−	0.588800i	$-0.200399\pi$
$991$	4.99776e7	1.61656	0.808279	+	0.588800i	$0.200399\pi$
$992$	−7.39380e6	−0.238555
$993$	1.86370e7	0.599794
$994$	206550.	0.00663069
$995$	−6.59907e6	−0.211312
$996$	−2.75086e7	−0.878657
$997$	−3.58643e7	−1.14268	−0.571341	−	0.820713i	$-0.693576\pi$
$997$	−3.58643e7	−1.14268	−0.571341	+	0.820713i	$0.693576\pi$
$998$	−6.92791e6	−0.220179
$999$	1.46505e7	0.464449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.20	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+0.872903 q^{2} -19.2132 q^{3} -31.2380 q^{4} -25.0000 q^{5} -16.7713 q^{6} +14.4713 q^{7} -55.2007 q^{8} +126.149 q^{9} +O(q^{10})\)	\(q+0.872903 q^{2} -19.2132 q^{3} -31.2380 q^{4} -25.0000 q^{5} -16.7713 q^{6} +14.4713 q^{7} -55.2007 q^{8} +126.149 q^{9} -21.8226 q^{10} +121.000 q^{11} +600.184 q^{12} +515.646 q^{13} +12.6320 q^{14} +480.331 q^{15} +951.433 q^{16} +1425.39 q^{17} +110.116 q^{18} -361.000 q^{19} +780.951 q^{20} -278.040 q^{21} +105.621 q^{22} +4707.83 q^{23} +1060.58 q^{24} +625.000 q^{25} +450.109 q^{26} +2245.09 q^{27} -452.055 q^{28} -8515.91 q^{29} +419.282 q^{30} -2847.13 q^{31} +2596.93 q^{32} -2324.80 q^{33} +1244.23 q^{34} -361.782 q^{35} -3940.64 q^{36} +6525.55 q^{37} -315.118 q^{38} -9907.23 q^{39} +1380.02 q^{40} -7395.63 q^{41} -242.702 q^{42} -1596.99 q^{43} -3779.80 q^{44} -3153.72 q^{45} +4109.48 q^{46} -5138.00 q^{47} -18280.1 q^{48} -16597.6 q^{49} +545.564 q^{50} -27386.4 q^{51} -16107.8 q^{52} +27130.0 q^{53} +1959.75 q^{54} -3025.00 q^{55} -798.824 q^{56} +6935.98 q^{57} -7433.56 q^{58} +7068.94 q^{59} -15004.6 q^{60} +352.855 q^{61} -2485.27 q^{62} +1825.53 q^{63} -28179.0 q^{64} -12891.1 q^{65} -2029.33 q^{66} +2457.20 q^{67} -44526.4 q^{68} -90452.7 q^{69} -315.801 q^{70} +16351.3 q^{71} -6963.49 q^{72} +72447.8 q^{73} +5696.17 q^{74} -12008.3 q^{75} +11276.9 q^{76} +1751.03 q^{77} -8648.05 q^{78} -4870.40 q^{79} -23785.8 q^{80} -73789.6 q^{81} -6455.66 q^{82} -45833.5 q^{83} +8685.43 q^{84} -35634.8 q^{85} -1394.02 q^{86} +163618. q^{87} -6679.28 q^{88} -32895.4 q^{89} -2752.89 q^{90} +7462.06 q^{91} -147063. q^{92} +54702.7 q^{93} -4484.97 q^{94} +9025.00 q^{95} -49895.4 q^{96} +114728. q^{97} -14488.1 q^{98} +15264.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 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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