LMFDB - Embedded newform 1045.6.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33765 q^{2} +19.4352 q^{3} -30.2107 q^{4} +25.0000 q^{5} -25.9975 q^{6} -167.518 q^{7} +83.2162 q^{8} +134.726 q^{9} +O(q^{10})$	\(q-1.33765 q^{2} +19.4352 q^{3} -30.2107 q^{4} +25.0000 q^{5} -25.9975 q^{6} -167.518 q^{7} +83.2162 q^{8} +134.726 q^{9} -33.4413 q^{10} -121.000 q^{11} -587.150 q^{12} -163.485 q^{13} +224.081 q^{14} +485.879 q^{15} +855.428 q^{16} +685.630 q^{17} -180.216 q^{18} +361.000 q^{19} -755.267 q^{20} -3255.75 q^{21} +161.856 q^{22} +2529.24 q^{23} +1617.32 q^{24} +625.000 q^{25} +218.685 q^{26} -2104.33 q^{27} +5060.85 q^{28} -3025.55 q^{29} -649.937 q^{30} +5416.53 q^{31} -3807.18 q^{32} -2351.66 q^{33} -917.133 q^{34} -4187.96 q^{35} -4070.16 q^{36} +8017.92 q^{37} -482.892 q^{38} -3177.35 q^{39} +2080.40 q^{40} +2899.17 q^{41} +4355.05 q^{42} +6051.97 q^{43} +3655.49 q^{44} +3368.14 q^{45} -3383.24 q^{46} +15413.3 q^{47} +16625.4 q^{48} +11255.4 q^{49} -836.032 q^{50} +13325.3 q^{51} +4938.98 q^{52} -35713.2 q^{53} +2814.86 q^{54} -3025.00 q^{55} -13940.2 q^{56} +7016.09 q^{57} +4047.13 q^{58} -3251.16 q^{59} -14678.7 q^{60} -9359.04 q^{61} -7245.43 q^{62} -22569.0 q^{63} -22281.0 q^{64} -4087.11 q^{65} +3145.69 q^{66} -13987.0 q^{67} -20713.3 q^{68} +49156.2 q^{69} +5602.03 q^{70} -56846.4 q^{71} +11211.4 q^{72} +7213.03 q^{73} -10725.2 q^{74} +12147.0 q^{75} -10906.1 q^{76} +20269.7 q^{77} +4250.18 q^{78} +81416.8 q^{79} +21385.7 q^{80} -73636.3 q^{81} -3878.07 q^{82} +50778.1 q^{83} +98358.4 q^{84} +17140.7 q^{85} -8095.42 q^{86} -58802.1 q^{87} -10069.2 q^{88} -80878.4 q^{89} -4505.40 q^{90} +27386.7 q^{91} -76410.0 q^{92} +105271. q^{93} -20617.6 q^{94} +9025.00 q^{95} -73993.2 q^{96} -84013.0 q^{97} -15055.8 q^{98} -16301.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.33765	−0.236466	−0.118233	−	0.992986i	$-0.537723\pi$
$2$	−1.33765	−0.236466	−0.118233	+	0.992986i	$0.537723\pi$
$3$	19.4352	1.24677	0.623383	−	0.781916i	$-0.285758\pi$
$3$	19.4352	1.24677	0.623383	+	0.781916i	$0.285758\pi$
$4$	−30.2107	−0.944084
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−25.9975	−0.294817
$7$	−167.518	−1.29216	−0.646082	−	0.763268i	$-0.723593\pi$
$7$	−167.518	−1.29216	−0.646082	+	0.763268i	$0.723593\pi$
$8$	83.2162	0.459709
$9$	134.726	0.554427
$10$	−33.4413	−0.105751
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−587.150	−1.17705
$13$	−163.485	−0.268299	−0.134149	−	0.990961i	$-0.542830\pi$
$13$	−163.485	−0.268299	−0.134149	+	0.990961i	$0.542830\pi$
$14$	224.081	0.305552
$15$	485.879	0.557571
$16$	855.428	0.835379
$17$	685.630	0.575397	0.287698	−	0.957721i	$-0.407110\pi$
$17$	685.630	0.575397	0.287698	+	0.957721i	$0.407110\pi$
$18$	−180.216	−0.131103
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−755.267	−0.422207
$21$	−3255.75	−1.61103
$22$	161.856	0.0712970
$23$	2529.24	0.996942	0.498471	−	0.866906i	$-0.333895\pi$
$23$	2529.24	0.996942	0.498471	+	0.866906i	$0.333895\pi$
$24$	1617.32	0.573150
$25$	625.000	0.200000
$26$	218.685	0.0634433
$27$	−2104.33	−0.555526
$28$	5060.85	1.21991
$29$	−3025.55	−0.668051	−0.334026	−	0.942564i	$-0.608407\pi$
$29$	−3025.55	−0.668051	−0.334026	+	0.942564i	$0.608407\pi$
$30$	−649.937	−0.131846
$31$	5416.53	1.01232	0.506159	−	0.862440i	$-0.331065\pi$
$31$	5416.53	1.01232	0.506159	+	0.862440i	$0.331065\pi$
$32$	−3807.18	−0.657247
$33$	−2351.66	−0.375914
$34$	−917.133	−0.136061
$35$	−4187.96	−0.577873
$36$	−4070.16	−0.523425
$37$	8017.92	0.962847	0.481424	−	0.876488i	$-0.340120\pi$
$37$	8017.92	0.962847	0.481424	+	0.876488i	$0.340120\pi$
$38$	−482.892	−0.0542489
$39$	−3177.35	−0.334506
$40$	2080.40	0.205588
$41$	2899.17	0.269348	0.134674	−	0.990890i	$-0.457001\pi$
$41$	2899.17	0.269348	0.134674	+	0.990890i	$0.457001\pi$
$42$	4355.05	0.380952
$43$	6051.97	0.499144	0.249572	−	0.968356i	$-0.419710\pi$
$43$	6051.97	0.499144	0.249572	+	0.968356i	$0.419710\pi$
$44$	3655.49	0.284652
$45$	3368.14	0.247947
$46$	−3383.24	−0.235743
$47$	15413.3	1.01777	0.508887	−	0.860833i	$-0.330057\pi$
$47$	15413.3	1.01777	0.508887	+	0.860833i	$0.330057\pi$
$48$	16625.4	1.04152
$49$	11255.4	0.669686
$50$	−836.032	−0.0472931
$51$	13325.3	0.717385
$52$	4938.98	0.253296
$53$	−35713.2	−1.74638	−0.873190	−	0.487379i	$-0.837953\pi$
$53$	−35713.2	−1.74638	−0.873190	+	0.487379i	$0.837953\pi$
$54$	2814.86	0.131363
$55$	−3025.00	−0.134840
$56$	−13940.2	−0.594019
$57$	7016.09	0.286028
$58$	4047.13	0.157971
$59$	−3251.16	−0.121593	−0.0607966	−	0.998150i	$-0.519364\pi$
$59$	−3251.16	−0.121593	−0.0607966	+	0.998150i	$0.519364\pi$
$60$	−14678.7	−0.526394
$61$	−9359.04	−0.322038	−0.161019	−	0.986951i	$-0.551478\pi$
$61$	−9359.04	−0.322038	−0.161019	+	0.986951i	$0.551478\pi$
$62$	−7245.43	−0.239378
$63$	−22569.0	−0.716410
$64$	−22281.0	−0.679962
$65$	−4087.11	−0.119987
$66$	3145.69	0.0888908
$67$	−13987.0	−0.380660	−0.190330	−	0.981720i	$-0.560956\pi$
$67$	−13987.0	−0.380660	−0.190330	+	0.981720i	$0.560956\pi$
$68$	−20713.3	−0.543223
$69$	49156.2	1.24295
$70$	5602.03	0.136647
$71$	−56846.4	−1.33831	−0.669156	−	0.743122i	$-0.733344\pi$
$71$	−56846.4	−1.33831	−0.669156	+	0.743122i	$0.733344\pi$
$72$	11211.4	0.254875
$73$	7213.03	0.158420	0.0792102	−	0.996858i	$-0.474760\pi$
$73$	7213.03	0.158420	0.0792102	+	0.996858i	$0.474760\pi$
$74$	−10725.2	−0.227680
$75$	12147.0	0.249353
$76$	−10906.1	−0.216588
$77$	20269.7	0.389602
$78$	4250.18	0.0790990
$79$	81416.8	1.46773	0.733865	−	0.679295i	$-0.237714\pi$
$79$	81416.8	1.46773	0.733865	+	0.679295i	$0.237714\pi$
$80$	21385.7	0.373593
$81$	−73636.3	−1.24704
$82$	−3878.07	−0.0636915
$83$	50778.1	0.809061	0.404531	−	0.914524i	$-0.367435\pi$
$83$	50778.1	0.809061	0.404531	+	0.914524i	$0.367435\pi$
$84$	98358.4	1.52094
$85$	17140.7	0.257325
$86$	−8095.42	−0.118030
$87$	−58802.1	−0.832904
$88$	−10069.2	−0.138607
$89$	−80878.4	−1.08232	−0.541162	−	0.840918i	$-0.682016\pi$
$89$	−80878.4	−1.08232	−0.541162	+	0.840918i	$0.682016\pi$
$90$	−4505.40	−0.0586309
$91$	27386.7	0.346685
$92$	−76410.0	−0.941198
$93$	105271.	1.26212
$94$	−20617.6	−0.240668
$95$	9025.00	0.102598
$96$	−73993.2	−0.819434
$97$	−84013.0	−0.906603	−0.453301	−	0.891357i	$-0.649754\pi$
$97$	−84013.0	−0.906603	−0.453301	+	0.891357i	$0.649754\pi$
$98$	−15055.8	−0.158358
$99$	−16301.8	−0.167166
$100$	−18881.7	−0.188817
$101$	−174076.	−1.69799	−0.848994	−	0.528402i	$-0.822791\pi$
$101$	−174076.	−1.69799	−0.848994	+	0.528402i	$0.822791\pi$
$102$	−17824.6	−0.169637
$103$	−202550.	−1.88122	−0.940608	−	0.339494i	$-0.889744\pi$
$103$	−202550.	−1.88122	−0.940608	+	0.339494i	$0.889744\pi$
$104$	−13604.6	−0.123339
$105$	−81393.7	−0.720473
$106$	47771.8	0.412959
$107$	160406.	1.35445	0.677223	−	0.735778i	$-0.263183\pi$
$107$	160406.	1.35445	0.677223	+	0.735778i	$0.263183\pi$
$108$	63573.3	0.524463
$109$	163875.	1.32113	0.660565	−	0.750769i	$-0.270317\pi$
$109$	163875.	1.32113	0.660565	+	0.750769i	$0.270317\pi$
$110$	4046.39	0.0318850
$111$	155830.	1.20045
$112$	−143300.	−1.07945
$113$	−220126.	−1.62171	−0.810857	−	0.585244i	$-0.800999\pi$
$113$	−220126.	−1.62171	−0.810857	+	0.585244i	$0.800999\pi$
$114$	−9385.09	−0.0676357
$115$	63230.9	0.445846
$116$	91404.1	0.630697
$117$	−22025.6	−0.148752
$118$	4348.92	0.0287526
$119$	−114856.	−0.743506
$120$	40433.0	0.256320
$121$	14641.0	0.0909091
$122$	12519.1	0.0761508
$123$	56345.8	0.335814
$124$	−163637.	−0.955714
$125$	15625.0	0.0894427
$126$	30189.5	0.169406
$127$	−269469.	−1.48251	−0.741257	−	0.671221i	$-0.765770\pi$
$127$	−269469.	−1.48251	−0.741257	+	0.671221i	$0.765770\pi$
$128$	151634.	0.818035
$129$	117621.	0.622315
$130$	5467.13	0.0283727
$131$	−229912.	−1.17053	−0.585266	−	0.810842i	$-0.699010\pi$
$131$	−229912.	−1.17053	−0.585266	+	0.810842i	$0.699010\pi$
$132$	71045.1	0.354895
$133$	−60474.1	−0.296443
$134$	18709.7	0.0900130
$135$	−52608.2	−0.248439
$136$	57055.5	0.264515
$137$	−314366.	−1.43098	−0.715492	−	0.698621i	$-0.753797\pi$
$137$	−314366.	−1.43098	−0.715492	+	0.698621i	$0.753797\pi$
$138$	−65753.8	−0.293916
$139$	352313.	1.54665	0.773323	−	0.634012i	$-0.218593\pi$
$139$	352313.	1.54665	0.773323	+	0.634012i	$0.218593\pi$
$140$	126521.	0.545561
$141$	299560.	1.26893
$142$	76040.7	0.316464
$143$	19781.6	0.0808950
$144$	115248.	0.463156
$145$	−75638.8	−0.298762
$146$	−9648.52	−0.0374609
$147$	218751.	0.834942
$148$	−242227.	−0.909009
$149$	37405.2	0.138028	0.0690138	−	0.997616i	$-0.478015\pi$
$149$	37405.2	0.138028	0.0690138	+	0.997616i	$0.478015\pi$
$150$	−16248.4	−0.0589635
$151$	−252254.	−0.900316	−0.450158	−	0.892949i	$-0.648632\pi$
$151$	−252254.	−0.900316	−0.450158	+	0.892949i	$0.648632\pi$
$152$	30041.0	0.105464
$153$	92371.9	0.319015
$154$	−27113.8	−0.0921274
$155$	135413.	0.452723
$156$	95989.9	0.315801
$157$	304204.	0.984955	0.492477	−	0.870325i	$-0.336091\pi$
$157$	304204.	0.984955	0.492477	+	0.870325i	$0.336091\pi$
$158$	−108907.	−0.347068
$159$	−694092.	−2.17733
$160$	−95179.5	−0.293930
$161$	−423694.	−1.28821
$162$	98499.7	0.294881
$163$	−333913.	−0.984383	−0.492191	−	0.870487i	$-0.663804\pi$
$163$	−333913.	−0.984383	−0.492191	+	0.870487i	$0.663804\pi$
$164$	−87585.8	−0.254287
$165$	−58791.4	−0.168114
$166$	−67923.4	−0.191315
$167$	−376671.	−1.04513	−0.522566	−	0.852599i	$-0.675025\pi$
$167$	−376671.	−1.04513	−0.522566	+	0.852599i	$0.675025\pi$
$168$	−270931.	−0.740603
$169$	−344566.	−0.928016
$170$	−22928.3	−0.0608485
$171$	48636.0	0.127194
$172$	−182834.	−0.471233
$173$	378180.	0.960689	0.480344	−	0.877080i	$-0.340512\pi$
$173$	378180.	0.960689	0.480344	+	0.877080i	$0.340512\pi$
$174$	78656.7	0.196953
$175$	−104699.	−0.258433
$176$	−103507.	−0.251876
$177$	−63186.9	−0.151598
$178$	108187.	0.255933
$179$	694552.	1.62021	0.810107	−	0.586282i	$-0.199409\pi$
$179$	694552.	1.62021	0.810107	+	0.586282i	$0.199409\pi$
$180$	−101754.	−0.234083
$181$	−346991.	−0.787266	−0.393633	−	0.919268i	$-0.628782\pi$
$181$	−346991.	−0.787266	−0.393633	+	0.919268i	$0.628782\pi$
$182$	−36633.8	−0.0819792
$183$	−181895.	−0.401506
$184$	210474.	0.458303
$185$	200448.	0.430598
$186$	−140816.	−0.298449
$187$	−82961.2	−0.173489
$188$	−465647.	−0.960864
$189$	352514.	0.717830
$190$	−12072.3	−0.0242609
$191$	−615684.	−1.22117	−0.610583	−	0.791952i	$-0.709065\pi$
$191$	−615684.	−1.22117	−0.610583	+	0.791952i	$0.709065\pi$
$192$	−433035.	−0.847754
$193$	−834093.	−1.61184	−0.805918	−	0.592027i	$-0.798328\pi$
$193$	−834093.	−1.61184	−0.805918	+	0.592027i	$0.798328\pi$
$194$	112380.	0.214380
$195$	−79433.7	−0.149595
$196$	−340034.	−0.632240
$197$	−128117.	−0.235202	−0.117601	−	0.993061i	$-0.537520\pi$
$197$	−128117.	−0.235202	−0.117601	+	0.993061i	$0.537520\pi$
$198$	21806.1	0.0395290
$199$	882080.	1.57898	0.789488	−	0.613766i	$-0.210346\pi$
$199$	882080.	1.57898	0.789488	+	0.613766i	$0.210346\pi$
$200$	52010.1	0.0919418
$201$	−271840.	−0.474594
$202$	232853.	0.401516
$203$	506836.	0.863231
$204$	−402567.	−0.677272
$205$	72479.2	0.120456
$206$	270941.	0.444843
$207$	340753.	0.552731
$208$	−139849.	−0.224131
$209$	−43681.0	−0.0691714
$210$	108876.	0.170367
$211$	277088.	0.428462	0.214231	−	0.976783i	$-0.431276\pi$
$211$	277088.	0.428462	0.214231	+	0.976783i	$0.431276\pi$
$212$	1.07892e6	1.64873
$213$	−1.10482e6	−1.66856
$214$	−214567.	−0.320280
$215$	151299.	0.223224
$216$	−175114.	−0.255380
$217$	−907369.	−1.30808
$218$	−219207.	−0.312402
$219$	140187.	0.197513
$220$	91387.3	0.127300
$221$	−112090.	−0.154378
$222$	−208446.	−0.283864
$223$	1.37628e6	1.85329	0.926645	−	0.375937i	$-0.122679\pi$
$223$	1.37628e6	1.85329	0.926645	+	0.375937i	$0.122679\pi$
$224$	637773.	0.849271
$225$	84203.5	0.110885
$226$	294451.	0.383480
$227$	1.14126e6	1.47000	0.735002	−	0.678065i	$-0.237181\pi$
$227$	1.14126e6	1.47000	0.735002	+	0.678065i	$0.237181\pi$
$228$	−211961.	−0.270034
$229$	−1.26889e6	−1.59895	−0.799474	−	0.600700i	$-0.794889\pi$
$229$	−1.26889e6	−1.59895	−0.799474	+	0.600700i	$0.794889\pi$
$230$	−84580.9	−0.105427
$231$	393945.	0.485743
$232$	−251775.	−0.307109
$233$	−816975.	−0.985869	−0.492934	−	0.870066i	$-0.664076\pi$
$233$	−816975.	−0.985869	−0.492934	+	0.870066i	$0.664076\pi$
$234$	29462.5	0.0351747
$235$	385333.	0.455162
$236$	98219.9	0.114794
$237$	1.58235e6	1.82992
$238$	153637.	0.175814
$239$	605349.	0.685505	0.342753	−	0.939426i	$-0.388641\pi$
$239$	605349.	0.685505	0.342753	+	0.939426i	$0.388641\pi$
$240$	415635.	0.465783
$241$	101343.	0.112396	0.0561981	−	0.998420i	$-0.482102\pi$
$241$	101343.	0.112396	0.0561981	+	0.998420i	$0.482102\pi$
$242$	−19584.5	−0.0214969
$243$	−919782.	−0.999239
$244$	282743.	0.304031
$245$	281385.	0.299493
$246$	−75371.0	−0.0794084
$247$	−59017.9	−0.0615519
$248$	450743.	0.465372
$249$	986881.	1.00871
$250$	−20900.8	−0.0211501
$251$	−470173.	−0.471057	−0.235528	−	0.971867i	$-0.575682\pi$
$251$	−470173.	−0.471057	−0.235528	+	0.971867i	$0.575682\pi$
$252$	681826.	0.676351
$253$	−306038.	−0.300589
$254$	360455.	0.350563
$255$	333133.	0.320824
$256$	510159.	0.486525
$257$	1.24669e6	1.17741	0.588703	−	0.808349i	$-0.299639\pi$
$257$	1.24669e6	1.17741	0.588703	+	0.808349i	$0.299639\pi$
$258$	−157336.	−0.147156
$259$	−1.34315e6	−1.24416
$260$	123475.	0.113278
$261$	−407620.	−0.370385
$262$	307542.	0.276790
$263$	132765.	0.118357	0.0591784	−	0.998247i	$-0.481152\pi$
$263$	132765.	0.118357	0.0591784	+	0.998247i	$0.481152\pi$
$264$	−195696.	−0.172811
$265$	−892830.	−0.781005
$266$	80893.3	0.0700984
$267$	−1.57189e6	−1.34941
$268$	422557.	0.359375
$269$	1.91506e6	1.61362	0.806809	−	0.590812i	$-0.201193\pi$
$269$	1.91506e6	1.61362	0.806809	+	0.590812i	$0.201193\pi$
$270$	70371.5	0.0587472
$271$	−2.30793e6	−1.90897	−0.954487	−	0.298253i	$-0.903596\pi$
$271$	−2.30793e6	−1.90897	−0.954487	+	0.298253i	$0.903596\pi$
$272$	586507.	0.480674
$273$	532264.	0.432236
$274$	420512.	0.338378
$275$	−75625.0	−0.0603023
$276$	−1.48504e6	−1.17345
$277$	121433.	0.0950902	0.0475451	−	0.998869i	$-0.484860\pi$
$277$	121433.	0.0950902	0.0475451	+	0.998869i	$0.484860\pi$
$278$	−471271.	−0.365729
$279$	729746.	0.561256
$280$	−348506.	−0.265653
$281$	−1.66902e6	−1.26095	−0.630473	−	0.776211i	$-0.717139\pi$
$281$	−1.66902e6	−1.26095	−0.630473	+	0.776211i	$0.717139\pi$
$282$	−400707.	−0.300057
$283$	1.96868e6	1.46120	0.730600	−	0.682806i	$-0.239240\pi$
$283$	1.96868e6	1.46120	0.730600	+	0.682806i	$0.239240\pi$
$284$	1.71737e6	1.26348
$285$	175402.	0.127916
$286$	−26460.9	−0.0191289
$287$	−485664.	−0.348041
$288$	−512925.	−0.364395
$289$	−949769.	−0.668919
$290$	101178.	0.0706468
$291$	−1.63281e6	−1.13032
$292$	−217911.	−0.149562
$293$	−253219.	−0.172317	−0.0861584	−	0.996281i	$-0.527459\pi$
$293$	−253219.	−0.172317	−0.0861584	+	0.996281i	$0.527459\pi$
$294$	−292612.	−0.197435
$295$	−81279.1	−0.0543781
$296$	667221.	0.442629
$297$	254624.	0.167497
$298$	−50035.1	−0.0326388
$299$	−413491.	−0.267478
$300$	−366969.	−0.235410
$301$	−1.01382e6	−0.644975
$302$	337427.	0.212894
$303$	−3.38319e6	−2.11699
$304$	308809.	0.191649
$305$	−233976.	−0.144020
$306$	−123561.	−0.0754361
$307$	−490943.	−0.297293	−0.148647	−	0.988890i	$-0.547492\pi$
$307$	−490943.	−0.297293	−0.148647	+	0.988890i	$0.547492\pi$
$308$	−612362.	−0.367817
$309$	−3.93659e6	−2.34544
$310$	−181136.	−0.107053
$311$	−2.84292e6	−1.66672	−0.833361	−	0.552729i	$-0.813587\pi$
$311$	−2.84292e6	−1.66672	−0.833361	+	0.552729i	$0.813587\pi$
$312$	−264407.	−0.153775
$313$	−501421.	−0.289295	−0.144648	−	0.989483i	$-0.546205\pi$
$313$	−501421.	−0.289295	−0.144648	+	0.989483i	$0.546205\pi$
$314$	−406919.	−0.232908
$315$	−564226.	−0.320388
$316$	−2.45966e6	−1.38566
$317$	−303244.	−0.169490	−0.0847450	−	0.996403i	$-0.527008\pi$
$317$	−303244.	−0.169490	−0.0847450	+	0.996403i	$0.527008\pi$
$318$	928452.	0.514863
$319$	366092.	0.201425
$320$	−557025.	−0.304088
$321$	3.11752e6	1.68868
$322$	566754.	0.304618
$323$	247512.	0.132005
$324$	2.22460e6	1.17731
$325$	−102178.	−0.0536597
$326$	446659.	0.232773
$327$	3.18493e6	1.64714
$328$	241258.	0.123822
$329$	−2.58201e6	−1.31513
$330$	78642.3	0.0397532
$331$	−2.72076e6	−1.36496	−0.682480	−	0.730904i	$-0.739099\pi$
$331$	−2.72076e6	−1.36496	−0.682480	+	0.730904i	$0.739099\pi$
$332$	−1.53404e6	−0.763822
$333$	1.08022e6	0.533828
$334$	503855.	0.247138
$335$	−349675.	−0.170236
$336$	−2.78506e6	−1.34582
$337$	1.13542e6	0.544603	0.272302	−	0.962212i	$-0.412215\pi$
$337$	1.13542e6	0.544603	0.272302	+	0.962212i	$0.412215\pi$
$338$	460909.	0.219444
$339$	−4.27818e6	−2.02190
$340$	−517834.	−0.242937
$341$	−655400.	−0.305225
$342$	−65057.9	−0.0300770
$343$	929994.	0.426820
$344$	503622.	0.229461
$345$	1.22890e6	0.555866
$346$	−505872.	−0.227170
$347$	−274612.	−0.122432	−0.0612161	−	0.998125i	$-0.519498\pi$
$347$	−274612.	−0.122432	−0.0612161	+	0.998125i	$0.519498\pi$
$348$	1.77645e6	0.786331
$349$	−2.29468e6	−1.00846	−0.504231	−	0.863569i	$-0.668224\pi$
$349$	−2.29468e6	−1.00846	−0.504231	+	0.863569i	$0.668224\pi$
$350$	140051.	0.0611104
$351$	344025.	0.149047
$352$	460669.	0.198167
$353$	2.63576e6	1.12582	0.562910	−	0.826518i	$-0.309682\pi$
$353$	2.63576e6	1.12582	0.562910	+	0.826518i	$0.309682\pi$
$354$	84522.1	0.0358477
$355$	−1.42116e6	−0.598511
$356$	2.44339e6	1.02181
$357$	−2.23224e6	−0.926979
$358$	−929069.	−0.383125
$359$	−3.53919e6	−1.44933	−0.724666	−	0.689100i	$-0.758006\pi$
$359$	−3.53919e6	−1.44933	−0.724666	+	0.689100i	$0.758006\pi$
$360$	280284.	0.113983
$361$	130321.	0.0526316
$362$	464153.	0.186161
$363$	284550.	0.113342
$364$	−827370.	−0.327300
$365$	180326.	0.0708477
$366$	243311.	0.0949423
$367$	99925.3	0.0387267	0.0193633	−	0.999813i	$-0.493836\pi$
$367$	99925.3	0.0387267	0.0193633	+	0.999813i	$0.493836\pi$
$368$	2.16358e6	0.832825
$369$	390592.	0.149334
$370$	−268129.	−0.101822
$371$	5.98262e6	2.25661
$372$	−3.18032e6	−1.19155
$373$	−2.88956e6	−1.07538	−0.537688	−	0.843144i	$-0.680702\pi$
$373$	−2.88956e6	−1.07538	−0.537688	+	0.843144i	$0.680702\pi$
$374$	110973.	0.0410241
$375$	303674.	0.111514
$376$	1.28264e6	0.467880
$377$	494631.	0.179237
$378$	−471541.	−0.169742
$379$	−649914.	−0.232412	−0.116206	−	0.993225i	$-0.537073\pi$
$379$	−649914.	−0.232412	−0.116206	+	0.993225i	$0.537073\pi$
$380$	−272651.	−0.0968610
$381$	−5.23717e6	−1.84835
$382$	823571.	0.288764
$383$	334455.	0.116504	0.0582519	−	0.998302i	$-0.481447\pi$
$383$	334455.	0.116504	0.0582519	+	0.998302i	$0.481447\pi$
$384$	2.94703e6	1.01990
$385$	506743.	0.174235
$386$	1.11572e6	0.381144
$387$	815355.	0.276738
$388$	2.53809e6	0.855909
$389$	−1.61484e6	−0.541071	−0.270536	−	0.962710i	$-0.587201\pi$
$389$	−1.61484e6	−0.541071	−0.270536	+	0.962710i	$0.587201\pi$
$390$	106255.	0.0353742
$391$	1.73412e6	0.573637
$392$	936632.	0.307860
$393$	−4.46837e6	−1.45938
$394$	171376.	0.0556172
$395$	2.03542e6	0.656389
$396$	492489.	0.157819
$397$	2.70096e6	0.860086	0.430043	−	0.902808i	$-0.358498\pi$
$397$	2.70096e6	0.860086	0.430043	+	0.902808i	$0.358498\pi$
$398$	−1.17992e6	−0.373373
$399$	−1.17532e6	−0.369595
$400$	534642.	0.167076
$401$	−2.62561e6	−0.815398	−0.407699	−	0.913116i	$-0.633669\pi$
$401$	−2.62561e6	−0.815398	−0.407699	+	0.913116i	$0.633669\pi$
$402$	363627.	0.112225
$403$	−885519.	−0.271603
$404$	5.25895e6	1.60304
$405$	−1.84091e6	−0.557692
$406$	−677969.	−0.204124
$407$	−970168.	−0.290309
$408$	1.10888e6	0.329788
$409$	1.28990e6	0.381282	0.190641	−	0.981660i	$-0.438943\pi$
$409$	1.28990e6	0.381282	0.190641	+	0.981660i	$0.438943\pi$
$410$	−96951.8	−0.0284837
$411$	−6.10976e6	−1.78410
$412$	6.11917e6	1.77603
$413$	544630.	0.157118
$414$	−455809.	−0.130702
$415$	1.26945e6	0.361823
$416$	622415.	0.176338
$417$	6.84725e6	1.92831
$418$	58429.9	0.0163567
$419$	−5.72340e6	−1.59265	−0.796323	−	0.604872i	$-0.793224\pi$
$419$	−5.72340e6	−1.59265	−0.796323	+	0.604872i	$0.793224\pi$
$420$	2.45896e6	0.680187
$421$	1.33215e6	0.366309	0.183154	−	0.983084i	$-0.441369\pi$
$421$	1.33215e6	0.366309	0.183154	+	0.983084i	$0.441369\pi$
$422$	−370647.	−0.101316
$423$	2.07657e6	0.564281
$424$	−2.97192e6	−0.802827
$425$	428519.	0.115079
$426$	1.47786e6	0.394557
$427$	1.56781e6	0.416125
$428$	−4.84598e6	−1.27871
$429$	384459.	0.100857
$430$	−202385.	−0.0527847
$431$	4.01686e6	1.04158	0.520791	−	0.853684i	$-0.325637\pi$
$431$	4.01686e6	1.04158	0.520791	+	0.853684i	$0.325637\pi$
$432$	−1.80010e6	−0.464075
$433$	−7.07141e6	−1.81253	−0.906267	−	0.422705i	$-0.861081\pi$
$433$	−7.07141e6	−1.81253	−0.906267	+	0.422705i	$0.861081\pi$
$434$	1.21374e6	0.309316
$435$	−1.47005e6	−0.372486
$436$	−4.95077e6	−1.24726
$437$	913055.	0.228714
$438$	−187521.	−0.0467050
$439$	−3.17642e6	−0.786640	−0.393320	−	0.919402i	$-0.628674\pi$
$439$	−3.17642e6	−0.786640	−0.393320	+	0.919402i	$0.628674\pi$
$440$	−251729.	−0.0619871
$441$	1.51639e6	0.371292
$442$	149937.	0.0365051
$443$	−5.64812e6	−1.36740	−0.683698	−	0.729765i	$-0.739630\pi$
$443$	−5.64812e6	−1.36740	−0.683698	+	0.729765i	$0.739630\pi$
$444$	−4.70772e6	−1.13332
$445$	−2.02196e6	−0.484030
$446$	−1.84098e6	−0.438239
$447$	726976.	0.172088
$448$	3.73248e6	0.878622
$449$	3.08343e6	0.721803	0.360902	−	0.932604i	$-0.382469\pi$
$449$	3.08343e6	0.721803	0.360902	+	0.932604i	$0.382469\pi$
$450$	−112635.	−0.0262206
$451$	−350799.	−0.0812114
$452$	6.65015e6	1.53103
$453$	−4.90259e6	−1.12248
$454$	−1.52660e6	−0.347605
$455$	684667.	0.155042
$456$	583853.	0.131490
$457$	−1.69029e6	−0.378592	−0.189296	−	0.981920i	$-0.560621\pi$
$457$	−1.69029e6	−0.378592	−0.189296	+	0.981920i	$0.560621\pi$
$458$	1.69733e6	0.378096
$459$	−1.44279e6	−0.319648
$460$	−1.91025e6	−0.420916
$461$	4.68026e6	1.02569	0.512847	−	0.858480i	$-0.328591\pi$
$461$	4.68026e6	1.02569	0.512847	+	0.858480i	$0.328591\pi$
$462$	−526962.	−0.114861
$463$	−3.16586e6	−0.686341	−0.343170	−	0.939273i	$-0.611501\pi$
$463$	−3.16586e6	−0.686341	−0.343170	+	0.939273i	$0.611501\pi$
$464$	−2.58814e6	−0.558076
$465$	2.63178e6	0.564439
$466$	1.09283e6	0.233124
$467$	807069.	0.171245	0.0856227	−	0.996328i	$-0.472712\pi$
$467$	807069.	0.171245	0.0856227	+	0.996328i	$0.472712\pi$
$468$	665407.	0.140434
$469$	2.34308e6	0.491875
$470$	−515441.	−0.107630
$471$	5.91226e6	1.22801
$472$	−270550.	−0.0558974
$473$	−732288.	−0.150497
$474$	−2.11663e6	−0.432712
$475$	225625.	0.0458831
$476$	3.46987e6	0.701932
$477$	−4.81148e6	−0.968240
$478$	−809745.	−0.162098
$479$	−5.80738e6	−1.15649	−0.578244	−	0.815864i	$-0.696262\pi$
$479$	−5.80738e6	−1.15649	−0.578244	+	0.815864i	$0.696262\pi$
$480$	−1.84983e6	−0.366462
$481$	−1.31081e6	−0.258330
$482$	−135562.	−0.0265778
$483$	−8.23456e6	−1.60610
$484$	−442315.	−0.0858258
$485$	−2.10032e6	−0.405445
$486$	1.23035e6	0.236286
$487$	−1.01426e7	−1.93788	−0.968938	−	0.247304i	$-0.920456\pi$
$487$	−1.01426e7	−1.93788	−0.968938	+	0.247304i	$0.920456\pi$
$488$	−778824.	−0.148044
$489$	−6.48965e6	−1.22730
$490$	−376395.	−0.0708197
$491$	−8.55328e6	−1.60114	−0.800569	−	0.599240i	$-0.795469\pi$
$491$	−8.55328e6	−1.60114	−0.800569	+	0.599240i	$0.795469\pi$
$492$	−1.70224e6	−0.317036
$493$	−2.07441e6	−0.384394
$494$	78945.4	0.0145549
$495$	−407545.	−0.0747589
$496$	4.63345e6	0.845669
$497$	9.52282e6	1.72932
$498$	−1.32010e6	−0.238525
$499$	2.67646e6	0.481182	0.240591	−	0.970627i	$-0.422659\pi$
$499$	2.67646e6	0.481182	0.240591	+	0.970627i	$0.422659\pi$
$500$	−472042.	−0.0844414
$501$	−7.32067e6	−1.30304
$502$	628927.	0.111389
$503$	−4.28749e6	−0.755584	−0.377792	−	0.925890i	$-0.623317\pi$
$503$	−4.28749e6	−0.755584	−0.377792	+	0.925890i	$0.623317\pi$
$504$	−1.87811e6	−0.329340
$505$	−4.35189e6	−0.759363
$506$	409372.	0.0710790
$507$	−6.69669e6	−1.15702
$508$	8.14083e6	1.39962
$509$	9.44771e6	1.61634	0.808169	−	0.588951i	$-0.200459\pi$
$509$	9.44771e6	1.61634	0.808169	+	0.588951i	$0.200459\pi$
$510$	−445616.	−0.0758639
$511$	−1.20832e6	−0.204705
$512$	−5.53470e6	−0.933081
$513$	−759663.	−0.127446
$514$	−1.66764e6	−0.278416
$515$	−5.06374e6	−0.841305
$516$	−3.55341e6	−0.587518
$517$	−1.86501e6	−0.306870
$518$	1.79666e6	0.294200
$519$	7.34998e6	1.19775
$520$	−340114.	−0.0551590
$521$	−4.18363e6	−0.675241	−0.337621	−	0.941282i	$-0.609622\pi$
$521$	−4.18363e6	−0.675241	−0.337621	+	0.941282i	$0.609622\pi$
$522$	545253.	0.0875834
$523$	4.52364e6	0.723159	0.361579	−	0.932341i	$-0.382238\pi$
$523$	4.52364e6	0.723159	0.361579	+	0.932341i	$0.382238\pi$
$524$	6.94579e6	1.10508
$525$	−2.03484e6	−0.322205
$526$	−177593.	−0.0279873
$527$	3.71374e6	0.582485
$528$	−2.01167e6	−0.314031
$529$	−39298.2	−0.00610568
$530$	1.19429e6	0.184681
$531$	−438015.	−0.0674145
$532$	1.82697e6	0.279867
$533$	−473969.	−0.0722656
$534$	2.10263e6	0.319088
$535$	4.01015e6	0.605727
$536$	−1.16394e6	−0.174993
$537$	1.34987e7	2.02003
$538$	−2.56168e6	−0.381565
$539$	−1.36190e6	−0.201918
$540$	1.58933e6	0.234547
$541$	5.37064e6	0.788920	0.394460	−	0.918913i	$-0.370932\pi$
$541$	5.37064e6	0.788920	0.394460	+	0.918913i	$0.370932\pi$
$542$	3.08721e6	0.451406
$543$	−6.74382e6	−0.981537
$544$	−2.61032e6	−0.378178
$545$	4.09687e6	0.590828
$546$	−711984.	−0.102209
$547$	−1.61788e6	−0.231194	−0.115597	−	0.993296i	$-0.536878\pi$
$547$	−1.61788e6	−0.231194	−0.115597	+	0.993296i	$0.536878\pi$
$548$	9.49722e6	1.35097
$549$	−1.26090e6	−0.178546
$550$	101160.	0.0142594
$551$	−1.09222e6	−0.153261
$552$	4.09059e6	0.571397
$553$	−1.36388e7	−1.89655
$554$	−162434.	−0.0224855
$555$	3.89574e6	0.536856
$556$	−1.06436e7	−1.46016
$557$	7.38140e6	1.00809	0.504047	−	0.863676i	$-0.331844\pi$
$557$	7.38140e6	1.00809	0.504047	+	0.863676i	$0.331844\pi$
$558$	−976145.	−0.132718
$559$	−989403.	−0.133919
$560$	−3.58250e6	−0.482743
$561$	−1.61236e6	−0.216300
$562$	2.23257e6	0.298170
$563$	−2.88854e6	−0.384068	−0.192034	−	0.981388i	$-0.561508\pi$
$563$	−2.88854e6	−0.384068	−0.192034	+	0.981388i	$0.561508\pi$
$564$	−9.04992e6	−1.19797
$565$	−5.50314e6	−0.725253
$566$	−2.63341e6	−0.345523
$567$	1.23354e7	1.61138
$568$	−4.73054e6	−0.615234
$569$	6.48673e6	0.839934	0.419967	−	0.907539i	$-0.362042\pi$
$569$	6.48673e6	0.839934	0.419967	+	0.907539i	$0.362042\pi$
$570$	−234627.	−0.0302476
$571$	−7.11916e6	−0.913773	−0.456886	−	0.889525i	$-0.651035\pi$
$571$	−7.11916e6	−0.913773	−0.456886	+	0.889525i	$0.651035\pi$
$572$	−597617.	−0.0763717
$573$	−1.19659e7	−1.52251
$574$	649648.	0.0822998
$575$	1.58077e6	0.199388
$576$	−3.00182e6	−0.376989
$577$	−1.46063e7	−1.82642	−0.913208	−	0.407494i	$-0.866403\pi$
$577$	−1.46063e7	−1.82642	−0.913208	+	0.407494i	$0.866403\pi$
$578$	1.27046e6	0.158176
$579$	−1.62107e7	−2.00958
$580$	2.28510e6	0.282056
$581$	−8.50627e6	−1.04544
$582$	2.18413e6	0.267282
$583$	4.32130e6	0.526554
$584$	600241.	0.0728272
$585$	−550639.	−0.0665238
$586$	338719.	0.0407470
$587$	704037.	0.0843335	0.0421667	−	0.999111i	$-0.486574\pi$
$587$	704037.	0.0843335	0.0421667	+	0.999111i	$0.486574\pi$
$588$	−6.60861e6	−0.788255
$589$	1.95537e6	0.232242
$590$	108723.	0.0128585
$591$	−2.48998e6	−0.293242
$592$	6.85875e6	0.804342
$593$	1.59131e7	1.85831	0.929154	−	0.369693i	$-0.120537\pi$
$593$	1.59131e7	1.85831	0.929154	+	0.369693i	$0.120537\pi$
$594$	−340598.	−0.0396074
$595$	−2.87139e6	−0.332506
$596$	−1.13004e6	−0.130310
$597$	1.71434e7	1.96861
$598$	553107.	0.0632494
$599$	−7.22856e6	−0.823161	−0.411580	−	0.911373i	$-0.635023\pi$
$599$	−7.22856e6	−0.823161	−0.411580	+	0.911373i	$0.635023\pi$
$600$	1.01083e6	0.114630
$601$	−1.68898e7	−1.90738	−0.953692	−	0.300784i	$-0.902752\pi$
$601$	−1.68898e7	−1.90738	−0.953692	+	0.300784i	$0.902752\pi$
$602$	1.35613e6	0.152514
$603$	−1.88441e6	−0.211048
$604$	7.62076e6	0.849974
$605$	366025.	0.0406558
$606$	4.52553e6	0.500596
$607$	−1.62863e7	−1.79412	−0.897061	−	0.441907i	$-0.854302\pi$
$607$	−1.62863e7	−1.79412	−0.897061	+	0.441907i	$0.854302\pi$
$608$	−1.37439e6	−0.150783
$609$	9.85044e6	1.07625
$610$	312978.	0.0340557
$611$	−2.51984e6	−0.273067
$612$	−2.79062e6	−0.301177
$613$	4.87758e6	0.524268	0.262134	−	0.965032i	$-0.415574\pi$
$613$	4.87758e6	0.524268	0.262134	+	0.965032i	$0.415574\pi$
$614$	656710.	0.0702996
$615$	1.40864e6	0.150181
$616$	1.68677e6	0.179103
$617$	1.08838e6	0.115098	0.0575489	−	0.998343i	$-0.481671\pi$
$617$	1.08838e6	0.115098	0.0575489	+	0.998343i	$0.481671\pi$
$618$	5.26578e6	0.554615
$619$	1.61797e7	1.69725	0.848624	−	0.528997i	$-0.177432\pi$
$619$	1.61797e7	1.69725	0.848624	+	0.528997i	$0.177432\pi$
$620$	−4.09093e6	−0.427408
$621$	−5.32235e6	−0.553827
$622$	3.80283e6	0.394122
$623$	1.35486e7	1.39854
$624$	−2.71799e6	−0.279439
$625$	390625.	0.0400000
$626$	670726.	0.0684084
$627$	−848947.	−0.0862406
$628$	−9.19022e6	−0.929880
$629$	5.49732e6	0.554019
$630$	754737.	0.0757607
$631$	1.01928e7	1.01911	0.509556	−	0.860437i	$-0.329810\pi$
$631$	1.01928e7	1.01911	0.509556	+	0.860437i	$0.329810\pi$
$632$	6.77519e6	0.674728
$633$	5.38526e6	0.534192
$634$	405635.	0.0400785
$635$	−6.73672e6	−0.663001
$636$	2.09690e7	2.05558
$637$	−1.84008e6	−0.179676
$638$	−489703.	−0.0476301
$639$	−7.65867e6	−0.741995
$640$	3.79085e6	0.365836
$641$	1.18001e7	1.13433	0.567165	−	0.823605i	$-0.308040\pi$
$641$	1.18001e7	1.13433	0.567165	+	0.823605i	$0.308040\pi$
$642$	−4.17015e6	−0.399314
$643$	−7.34866e6	−0.700940	−0.350470	−	0.936574i	$-0.613978\pi$
$643$	−7.34866e6	−0.700940	−0.350470	+	0.936574i	$0.613978\pi$
$644$	1.28001e7	1.21618
$645$	2.94052e6	0.278308
$646$	−331085.	−0.0312146
$647$	−4.20663e6	−0.395070	−0.197535	−	0.980296i	$-0.563294\pi$
$647$	−4.20663e6	−0.395070	−0.197535	+	0.980296i	$0.563294\pi$
$648$	−6.12773e6	−0.573274
$649$	393391.	0.0366617
$650$	136678.	0.0126887
$651$	−1.76349e7	−1.63087
$652$	1.00877e7	0.929340
$653$	1.03135e7	0.946508	0.473254	−	0.880926i	$-0.343079\pi$
$653$	1.03135e7	0.946508	0.473254	+	0.880926i	$0.343079\pi$
$654$	−4.26033e6	−0.389492
$655$	−5.74779e6	−0.523477
$656$	2.48003e6	0.225007
$657$	971781.	0.0878324
$658$	3.45383e6	0.310983
$659$	−8.48692e6	−0.761266	−0.380633	−	0.924726i	$-0.624294\pi$
$659$	−8.48692e6	−0.761266	−0.380633	+	0.924726i	$0.624294\pi$
$660$	1.77613e6	0.158714
$661$	824336.	0.0733839	0.0366919	−	0.999327i	$-0.488318\pi$
$661$	824336.	0.0733839	0.0366919	+	0.999327i	$0.488318\pi$
$662$	3.63943e6	0.322766
$663$	−2.17848e6	−0.192473
$664$	4.22556e6	0.371933
$665$	−1.51185e6	−0.132573
$666$	−1.44496e6	−0.126232
$667$	−7.65234e6	−0.666009
$668$	1.13795e7	0.986693
$669$	2.67482e7	2.31062
$670$	467743.	0.0402550
$671$	1.13244e6	0.0970980
$672$	1.23952e7	1.05884
$673$	2.03130e7	1.72876	0.864382	−	0.502836i	$-0.167710\pi$
$673$	2.03130e7	1.72876	0.864382	+	0.502836i	$0.167710\pi$
$674$	−1.51879e6	−0.128780
$675$	−1.31521e6	−0.111105
$676$	1.04096e7	0.876125
$677$	1.24346e7	1.04270	0.521352	−	0.853341i	$-0.325428\pi$
$677$	1.24346e7	1.04270	0.521352	+	0.853341i	$0.325428\pi$
$678$	5.72271e6	0.478110
$679$	1.40737e7	1.17148
$680$	1.42639e6	0.118295
$681$	2.21805e7	1.83275
$682$	876697.	0.0721753
$683$	1.87070e7	1.53445	0.767225	−	0.641378i	$-0.221637\pi$
$683$	1.87070e7	1.53445	0.767225	+	0.641378i	$0.221637\pi$
$684$	−1.46933e6	−0.120082
$685$	−7.85916e6	−0.639955
$686$	−1.24401e6	−0.100928
$687$	−2.46610e7	−1.99352
$688$	5.17702e6	0.416974
$689$	5.83855e6	0.468551
$690$	−1.64384e6	−0.131443
$691$	219294.	0.0174715	0.00873577	−	0.999962i	$-0.497219\pi$
$691$	219294.	0.0174715	0.00873577	+	0.999962i	$0.497219\pi$
$692$	−1.14251e7	−0.906971
$693$	2.73085e6	0.216006
$694$	367335.	0.0289510
$695$	8.80781e6	0.691681
$696$	−4.89329e6	−0.382893
$697$	1.98775e6	0.154982
$698$	3.06949e6	0.238466
$699$	−1.58781e7	−1.22915
$700$	3.16303e6	0.243982
$701$	−3.79988e6	−0.292062	−0.146031	−	0.989280i	$-0.546650\pi$
$701$	−3.79988e6	−0.292062	−0.146031	+	0.989280i	$0.546650\pi$
$702$	−460186.	−0.0352444
$703$	2.89447e6	0.220892
$704$	2.69600e6	0.205016
$705$	7.48901e6	0.567481
$706$	−3.52573e6	−0.266218
$707$	2.91609e7	2.19408
$708$	1.90892e6	0.143121
$709$	−4.11730e6	−0.307608	−0.153804	−	0.988101i	$-0.549152\pi$
$709$	−4.11730e6	−0.307608	−0.153804	+	0.988101i	$0.549152\pi$
$710$	1.90102e6	0.141527
$711$	1.09689e7	0.813749
$712$	−6.73039e6	−0.497554
$713$	1.36997e7	1.00922
$714$	2.98595e6	0.219198
$715$	494541.	0.0361774
$716$	−2.09829e7	−1.52962
$717$	1.17651e7	0.854665
$718$	4.73420e6	0.342717
$719$	4.47422e6	0.322771	0.161386	−	0.986891i	$-0.448404\pi$
$719$	4.47422e6	0.322771	0.161386	+	0.986891i	$0.448404\pi$
$720$	2.88120e6	0.207130
$721$	3.39308e7	2.43084
$722$	−174324.	−0.0124456
$723$	1.96962e6	0.140132
$724$	1.04828e7	0.743245
$725$	−1.89097e6	−0.133610
$726$	−380629.	−0.0268016
$727$	−1.08651e7	−0.762427	−0.381214	−	0.924487i	$-0.624494\pi$
$727$	−1.08651e7	−0.762427	−0.381214	+	0.924487i	$0.624494\pi$
$728$	2.27901e6	0.159374
$729$	17509.2	0.00122025
$730$	−241213.	−0.0167530
$731$	4.14941e6	0.287205
$732$	5.49516e6	0.379055
$733$	1.67269e7	1.14989	0.574943	−	0.818193i	$-0.305024\pi$
$733$	1.67269e7	1.14989	0.574943	+	0.818193i	$0.305024\pi$
$734$	−133665.	−0.00915752
$735$	5.46877e6	0.373397
$736$	−9.62927e6	−0.655238
$737$	1.69243e6	0.114773
$738$	−522476.	−0.0353122
$739$	2.35775e7	1.58813	0.794067	−	0.607830i	$-0.207960\pi$
$739$	2.35775e7	1.58813	0.794067	+	0.607830i	$0.207960\pi$
$740$	−6.05567e6	−0.406521
$741$	−1.14702e6	−0.0767408
$742$	−8.00265e6	−0.533610
$743$	1.16893e7	0.776815	0.388407	−	0.921488i	$-0.373025\pi$
$743$	1.16893e7	0.776815	0.388407	+	0.921488i	$0.373025\pi$
$744$	8.76027e6	0.580210
$745$	935129.	0.0617278
$746$	3.86523e6	0.254289
$747$	6.84112e6	0.448565
$748$	2.50631e6	0.163788
$749$	−2.68710e7	−1.75017
$750$	−406210.	−0.0263693
$751$	−1.47305e7	−0.953053	−0.476527	−	0.879160i	$-0.658104\pi$
$751$	−1.47305e7	−0.953053	−0.476527	+	0.879160i	$0.658104\pi$
$752$	1.31850e7	0.850227
$753$	−9.13789e6	−0.587298
$754$	−661644.	−0.0423834
$755$	−6.30634e6	−0.402634
$756$	−1.06497e7	−0.677692
$757$	2.33881e7	1.48339	0.741693	−	0.670739i	$-0.234023\pi$
$757$	2.33881e7	1.48339	0.741693	+	0.670739i	$0.234023\pi$
$758$	869359.	0.0549574
$759$	−5.94790e6	−0.374765
$760$	751026.	0.0471651
$761$	1.17315e7	0.734333	0.367167	−	0.930155i	$-0.380328\pi$
$761$	1.17315e7	0.734333	0.367167	+	0.930155i	$0.380328\pi$
$762$	7.00550e6	0.437071
$763$	−2.74520e7	−1.70712
$764$	1.86002e7	1.15288
$765$	2.30930e6	0.142668
$766$	−447384.	−0.0275492
$767$	531515.	0.0326232
$768$	9.91502e6	0.606584
$769$	4.24246e6	0.258703	0.129352	−	0.991599i	$-0.458710\pi$
$769$	4.24246e6	0.258703	0.129352	+	0.991599i	$0.458710\pi$
$770$	−677845.	−0.0412006
$771$	2.42297e7	1.46795
$772$	2.51985e7	1.52171
$773$	−2.76394e7	−1.66372	−0.831858	−	0.554988i	$-0.812723\pi$
$773$	−2.76394e7	−1.66372	−0.831858	+	0.554988i	$0.812723\pi$
$774$	−1.09066e6	−0.0654391
$775$	3.38533e6	0.202464
$776$	−6.99124e6	−0.416773
$777$	−2.61043e7	−1.55117
$778$	2.16009e6	0.127945
$779$	1.04660e6	0.0617926
$780$	2.39975e6	0.141231
$781$	6.87842e6	0.403516
$782$	−2.31965e6	−0.135645
$783$	6.36676e6	0.371120
$784$	9.62819e6	0.559441
$785$	7.60511e6	0.440485
$786$	5.97712e6	0.345093
$787$	1.50812e7	0.867958	0.433979	−	0.900923i	$-0.357109\pi$
$787$	1.50812e7	0.867958	0.433979	+	0.900923i	$0.357109\pi$
$788$	3.87050e6	0.222051
$789$	2.58030e6	0.147563
$790$	−2.72268e6	−0.155213
$791$	3.68751e7	2.09552
$792$	−1.35657e6	−0.0768476
$793$	1.53006e6	0.0864023
$794$	−3.61294e6	−0.203381
$795$	−1.73523e7	−0.973731
$796$	−2.66483e7	−1.49069
$797$	−2.09030e7	−1.16564	−0.582818	−	0.812603i	$-0.698050\pi$
$797$	−2.09030e7	−1.16564	−0.582818	+	0.812603i	$0.698050\pi$
$798$	1.57217e6	0.0873964
$799$	1.05678e7	0.585624
$800$	−2.37949e6	−0.131449
$801$	−1.08964e7	−0.600070
$802$	3.51215e6	0.192814
$803$	−872777.	−0.0477655
$804$	8.21246e6	0.448057
$805$	−1.05923e7	−0.576106
$806$	1.18452e6	0.0642249
$807$	3.72194e7	2.01181
$808$	−1.44859e7	−0.780580
$809$	1.63436e7	0.877962	0.438981	−	0.898496i	$-0.355340\pi$
$809$	1.63436e7	0.877962	0.438981	+	0.898496i	$0.355340\pi$
$810$	2.46249e6	0.131875
$811$	1.75221e7	0.935477	0.467739	−	0.883867i	$-0.345069\pi$
$811$	1.75221e7	0.935477	0.467739	+	0.883867i	$0.345069\pi$
$812$	−1.53119e7	−0.814963
$813$	−4.48551e7	−2.38004
$814$	1.29775e6	0.0686481
$815$	−8.34782e6	−0.440229
$816$	1.13989e7	0.599288
$817$	2.18476e6	0.114511
$818$	−1.72543e6	−0.0901600
$819$	3.68969e6	0.192212
$820$	−2.18965e6	−0.113721
$821$	7.55411e6	0.391134	0.195567	−	0.980690i	$-0.437345\pi$
$821$	7.55411e6	0.391134	0.195567	+	0.980690i	$0.437345\pi$
$822$	8.17273e6	0.421879
$823$	−4.67937e6	−0.240817	−0.120409	−	0.992724i	$-0.538420\pi$
$823$	−4.67937e6	−0.240817	−0.120409	+	0.992724i	$0.538420\pi$
$824$	−1.68554e7	−0.864812
$825$	−1.46978e6	−0.0751828
$826$	−728525.	−0.0371530
$827$	−2.11463e7	−1.07516	−0.537578	−	0.843214i	$-0.680661\pi$
$827$	−2.11463e7	−1.07516	−0.537578	+	0.843214i	$0.680661\pi$
$828$	−1.02944e7	−0.521825
$829$	2.47632e7	1.25147	0.625735	−	0.780036i	$-0.284799\pi$
$829$	2.47632e7	1.25147	0.625735	+	0.780036i	$0.284799\pi$
$830$	−1.69808e6	−0.0855587
$831$	2.36006e6	0.118555
$832$	3.64260e6	0.182433
$833$	7.71704e6	0.385335
$834$	−9.15923e6	−0.455978
$835$	−9.41678e6	−0.467397
$836$	1.31963e6	0.0653037
$837$	−1.13982e7	−0.562369
$838$	7.65591e6	0.376606
$839$	77791.2	0.00381527	0.00190764	−	0.999998i	$-0.499393\pi$
$839$	77791.2	0.00381527	0.00190764	+	0.999998i	$0.499393\pi$
$840$	−6.77327e6	−0.331208
$841$	−1.13572e7	−0.553707
$842$	−1.78195e6	−0.0866193
$843$	−3.24378e7	−1.57211
$844$	−8.37103e6	−0.404504
$845$	−8.61415e6	−0.415021
$846$	−2.77772e6	−0.133433
$847$	−2.45264e6	−0.117469
$848$	−3.05501e7	−1.45889
$849$	3.82617e7	1.82178
$850$	−573208.	−0.0272123
$851$	2.02792e7	0.959903
$852$	3.33774e7	1.57526
$853$	1.69989e7	0.799922	0.399961	−	0.916532i	$-0.369024\pi$
$853$	1.69989e7	0.799922	0.399961	+	0.916532i	$0.369024\pi$
$854$	−2.09718e6	−0.0983993
$855$	1.21590e6	0.0568830
$856$	1.33484e7	0.622651
$857$	4.72611e6	0.219812	0.109906	−	0.993942i	$-0.464945\pi$
$857$	4.72611e6	0.219812	0.109906	+	0.993942i	$0.464945\pi$
$858$	−514272.	−0.0238493
$859$	2.45254e7	1.13405	0.567027	−	0.823699i	$-0.308093\pi$
$859$	2.45254e7	1.13405	0.567027	+	0.823699i	$0.308093\pi$
$860$	−4.57085e6	−0.210742
$861$	−9.43895e6	−0.433926
$862$	−5.37316e6	−0.246298
$863$	−5.35128e6	−0.244585	−0.122293	−	0.992494i	$-0.539025\pi$
$863$	−5.35128e6	−0.244585	−0.122293	+	0.992494i	$0.539025\pi$
$864$	8.01157e6	0.365118
$865$	9.45449e6	0.429633
$866$	9.45908e6	0.428602
$867$	−1.84589e7	−0.833985
$868$	2.74122e7	1.23494
$869$	−9.85143e6	−0.442537
$870$	1.96642e6	0.0880801
$871$	2.28666e6	0.102131
$872$	1.36370e7	0.607336
$873$	−1.13187e7	−0.502645
$874$	−1.22135e6	−0.0540830
$875$	−2.61747e6	−0.115575
$876$	−4.23513e6	−0.186469
$877$	2.00086e7	0.878453	0.439227	−	0.898376i	$-0.355253\pi$
$877$	2.00086e7	0.878453	0.439227	+	0.898376i	$0.355253\pi$
$878$	4.24894e6	0.186013
$879$	−4.92136e6	−0.214839
$880$	−2.58767e6	−0.112642
$881$	1.08538e7	0.471131	0.235566	−	0.971858i	$-0.424306\pi$
$881$	1.08538e7	0.471131	0.235566	+	0.971858i	$0.424306\pi$
$882$	−2.02840e6	−0.0877977
$883$	3.00262e7	1.29598	0.647990	−	0.761649i	$-0.275610\pi$
$883$	3.00262e7	1.29598	0.647990	+	0.761649i	$0.275610\pi$
$884$	3.38631e6	0.145746
$885$	−1.57967e6	−0.0677968
$886$	7.55521e6	0.323342
$887$	2.69438e7	1.14987	0.574937	−	0.818198i	$-0.305027\pi$
$887$	2.69438e7	1.14987	0.574937	+	0.818198i	$0.305027\pi$
$888$	1.29675e7	0.551855
$889$	4.51409e7	1.91565
$890$	2.70468e6	0.114457
$891$	8.91000e6	0.375996
$892$	−4.15783e7	−1.74966
$893$	5.56421e6	0.233493
$894$	−972440.	−0.0406929
$895$	1.73638e7	0.724582
$896$	−2.54015e7	−1.05703
$897$	−8.03627e6	−0.333483
$898$	−4.12456e6	−0.170682
$899$	−1.63880e7	−0.676281
$900$	−2.54385e6	−0.104685
$901$	−2.44860e7	−1.00486
$902$	469247.	0.0192037
$903$	−1.97037e7	−0.804133
$904$	−1.83180e7	−0.745517
$905$	−8.67477e6	−0.352076
$906$	6.55796e6	0.265429
$907$	−1.45394e7	−0.586850	−0.293425	−	0.955982i	$-0.594795\pi$
$907$	−1.45394e7	−0.586850	−0.293425	+	0.955982i	$0.594795\pi$
$908$	−3.44781e7	−1.38781
$909$	−2.34525e7	−0.941410
$910$	−915845.	−0.0366622
$911$	−3.64751e7	−1.45613	−0.728065	−	0.685508i	$-0.759580\pi$
$911$	−3.64751e7	−1.45613	−0.728065	+	0.685508i	$0.759580\pi$
$912$	6.00176e6	0.238942
$913$	−6.14415e6	−0.243941
$914$	2.26102e6	0.0895240
$915$	−4.54736e6	−0.179559
$916$	3.83340e7	1.50954
$917$	3.85144e7	1.51252
$918$	1.92995e6	0.0755857
$919$	−1.09794e7	−0.428833	−0.214416	−	0.976742i	$-0.568785\pi$
$919$	−1.09794e7	−0.428833	−0.214416	+	0.976742i	$0.568785\pi$
$920$	5.26184e6	0.204959
$921$	−9.54156e6	−0.370655
$922$	−6.26056e6	−0.242541
$923$	9.29351e6	0.359067
$924$	−1.19014e7	−0.458582
$925$	5.01120e6	0.192569
$926$	4.23482e6	0.162296
$927$	−2.72887e7	−1.04300
$928$	1.15188e7	0.439075
$929$	−4.11937e7	−1.56600	−0.783000	−	0.622022i	$-0.786311\pi$
$929$	−4.11937e7	−1.56600	−0.783000	+	0.622022i	$0.786311\pi$
$930$	−3.52040e6	−0.133470
$931$	4.06320e6	0.153636
$932$	2.46814e7	0.930743
$933$	−5.52526e7	−2.07801
$934$	−1.07958e6	−0.0404936
$935$	−2.07403e6	−0.0775865
$936$	−1.83288e6	−0.0683825
$937$	−1.92298e7	−0.715526	−0.357763	−	0.933812i	$-0.616460\pi$
$937$	−1.92298e7	−0.715526	−0.357763	+	0.933812i	$0.616460\pi$
$938$	−3.13422e6	−0.116312
$939$	−9.74519e6	−0.360684
$940$	−1.16412e7	−0.429712
$941$	−2.90218e7	−1.06844	−0.534220	−	0.845345i	$-0.679395\pi$
$941$	−2.90218e7	−1.06844	−0.534220	+	0.845345i	$0.679395\pi$
$942$	−7.90854e6	−0.290382
$943$	7.33268e6	0.268524
$944$	−2.78114e6	−0.101576
$945$	8.81285e6	0.321023
$946$	979546.	0.0355875
$947$	−4.11132e7	−1.48973	−0.744864	−	0.667217i	$-0.767486\pi$
$947$	−4.11132e7	−1.48973	−0.744864	+	0.667217i	$0.767486\pi$
$948$	−4.78038e7	−1.72759
$949$	−1.17922e6	−0.0425039
$950$	−301807.	−0.0108498
$951$	−5.89360e6	−0.211314
$952$	−9.55784e6	−0.341796
$953$	−6.02181e6	−0.214781	−0.107390	−	0.994217i	$-0.534249\pi$
$953$	−6.02181e6	−0.214781	−0.107390	+	0.994217i	$0.534249\pi$
$954$	6.43609e6	0.228955
$955$	−1.53921e7	−0.546122
$956$	−1.82880e7	−0.647175
$957$	7.11506e6	0.251130
$958$	7.76824e6	0.273470
$959$	5.26621e7	1.84906
$960$	−1.08259e7	−0.379127
$961$	709671.	0.0247884
$962$	1.75340e6	0.0610862
$963$	2.16108e7	0.750941
$964$	−3.06165e6	−0.106112
$965$	−2.08523e7	−0.720835
$966$	1.10150e7	0.379787
$967$	−3.53148e6	−0.121448	−0.0607240	−	0.998155i	$-0.519341\pi$
$967$	−3.53148e6	−0.121448	−0.0607240	+	0.998155i	$0.519341\pi$
$968$	1.21837e6	0.0417917
$969$	4.81044e6	0.164579
$970$	2.80950e6	0.0958738
$971$	1.69159e7	0.575766	0.287883	−	0.957666i	$-0.407049\pi$
$971$	1.69159e7	0.575766	0.287883	+	0.957666i	$0.407049\pi$
$972$	2.77873e7	0.943365
$973$	−5.90188e7	−1.99852
$974$	1.35672e7	0.458241
$975$	−1.98584e6	−0.0669011
$976$	−8.00599e6	−0.269024
$977$	1.33067e7	0.445998	0.222999	−	0.974819i	$-0.428415\pi$
$977$	1.33067e7	0.445998	0.222999	+	0.974819i	$0.428415\pi$
$978$	8.68089e6	0.290213
$979$	9.78629e6	0.326333
$980$	−8.50084e6	−0.282746
$981$	2.20781e7	0.732470
$982$	1.14413e7	0.378614
$983$	3.32771e7	1.09840	0.549202	−	0.835690i	$-0.314932\pi$
$983$	3.32771e7	1.09840	0.549202	+	0.835690i	$0.314932\pi$
$984$	4.68888e6	0.154377
$985$	−3.20292e6	−0.105186
$986$	2.77484e6	0.0908960
$987$	−5.01819e7	−1.63966
$988$	1.78297e6	0.0581102
$989$	1.53069e7	0.497617
$990$	545153.	0.0176779
$991$	−5.30756e6	−0.171676	−0.0858382	−	0.996309i	$-0.527357\pi$
$991$	−5.30756e6	−0.171676	−0.0858382	+	0.996309i	$0.527357\pi$
$992$	−2.06217e7	−0.665343
$993$	−5.28784e7	−1.70179
$994$	−1.27382e7	−0.408924
$995$	2.20520e7	0.706139
$996$	−2.98144e7	−0.952307
$997$	−1.85573e7	−0.591259	−0.295629	−	0.955303i	$-0.595529\pi$
$997$	−1.85573e7	−0.591259	−0.295629	+	0.955303i	$0.595529\pi$
$998$	−3.58017e6	−0.113783
$999$	−1.68723e7	−0.534887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.17	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.33765 q^{2} +19.4352 q^{3} -30.2107 q^{4} +25.0000 q^{5} -25.9975 q^{6} -167.518 q^{7} +83.2162 q^{8} +134.726 q^{9} +O(q^{10})\)	\(q-1.33765 q^{2} +19.4352 q^{3} -30.2107 q^{4} +25.0000 q^{5} -25.9975 q^{6} -167.518 q^{7} +83.2162 q^{8} +134.726 q^{9} -33.4413 q^{10} -121.000 q^{11} -587.150 q^{12} -163.485 q^{13} +224.081 q^{14} +485.879 q^{15} +855.428 q^{16} +685.630 q^{17} -180.216 q^{18} +361.000 q^{19} -755.267 q^{20} -3255.75 q^{21} +161.856 q^{22} +2529.24 q^{23} +1617.32 q^{24} +625.000 q^{25} +218.685 q^{26} -2104.33 q^{27} +5060.85 q^{28} -3025.55 q^{29} -649.937 q^{30} +5416.53 q^{31} -3807.18 q^{32} -2351.66 q^{33} -917.133 q^{34} -4187.96 q^{35} -4070.16 q^{36} +8017.92 q^{37} -482.892 q^{38} -3177.35 q^{39} +2080.40 q^{40} +2899.17 q^{41} +4355.05 q^{42} +6051.97 q^{43} +3655.49 q^{44} +3368.14 q^{45} -3383.24 q^{46} +15413.3 q^{47} +16625.4 q^{48} +11255.4 q^{49} -836.032 q^{50} +13325.3 q^{51} +4938.98 q^{52} -35713.2 q^{53} +2814.86 q^{54} -3025.00 q^{55} -13940.2 q^{56} +7016.09 q^{57} +4047.13 q^{58} -3251.16 q^{59} -14678.7 q^{60} -9359.04 q^{61} -7245.43 q^{62} -22569.0 q^{63} -22281.0 q^{64} -4087.11 q^{65} +3145.69 q^{66} -13987.0 q^{67} -20713.3 q^{68} +49156.2 q^{69} +5602.03 q^{70} -56846.4 q^{71} +11211.4 q^{72} +7213.03 q^{73} -10725.2 q^{74} +12147.0 q^{75} -10906.1 q^{76} +20269.7 q^{77} +4250.18 q^{78} +81416.8 q^{79} +21385.7 q^{80} -73636.3 q^{81} -3878.07 q^{82} +50778.1 q^{83} +98358.4 q^{84} +17140.7 q^{85} -8095.42 q^{86} -58802.1 q^{87} -10069.2 q^{88} -80878.4 q^{89} -4505.40 q^{90} +27386.7 q^{91} -76410.0 q^{92} +105271. q^{93} -20617.6 q^{94} +9025.00 q^{95} -73993.2 q^{96} -84013.0 q^{97} -15055.8 q^{98} -16301.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

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