LMFDB - Embedded newform 1045.6.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.39231 q^{2} -29.7744 q^{3} -20.4922 q^{4} +25.0000 q^{5} +101.004 q^{6} +10.0128 q^{7} +178.070 q^{8} +643.513 q^{9} +O(q^{10})$	\(q-3.39231 q^{2} -29.7744 q^{3} -20.4922 q^{4} +25.0000 q^{5} +101.004 q^{6} +10.0128 q^{7} +178.070 q^{8} +643.513 q^{9} -84.8078 q^{10} +121.000 q^{11} +610.143 q^{12} -206.781 q^{13} -33.9665 q^{14} -744.359 q^{15} +51.6816 q^{16} +1912.33 q^{17} -2183.00 q^{18} -361.000 q^{19} -512.305 q^{20} -298.124 q^{21} -410.470 q^{22} +1214.00 q^{23} -5301.92 q^{24} +625.000 q^{25} +701.467 q^{26} -11925.0 q^{27} -205.184 q^{28} -6133.15 q^{29} +2525.10 q^{30} -4166.25 q^{31} -5873.56 q^{32} -3602.70 q^{33} -6487.23 q^{34} +250.319 q^{35} -13187.0 q^{36} +505.924 q^{37} +1224.62 q^{38} +6156.78 q^{39} +4451.75 q^{40} +4220.39 q^{41} +1011.33 q^{42} +4168.16 q^{43} -2479.56 q^{44} +16087.8 q^{45} -4118.26 q^{46} +9448.90 q^{47} -1538.79 q^{48} -16706.7 q^{49} -2120.20 q^{50} -56938.5 q^{51} +4237.41 q^{52} -17414.4 q^{53} +40453.3 q^{54} +3025.00 q^{55} +1782.98 q^{56} +10748.5 q^{57} +20805.6 q^{58} +4557.96 q^{59} +15253.6 q^{60} +42065.0 q^{61} +14133.2 q^{62} +6443.35 q^{63} +18271.1 q^{64} -5169.53 q^{65} +12221.5 q^{66} -52232.4 q^{67} -39187.9 q^{68} -36146.0 q^{69} -849.162 q^{70} +7175.10 q^{71} +114590. q^{72} -28411.3 q^{73} -1716.25 q^{74} -18609.0 q^{75} +7397.69 q^{76} +1211.55 q^{77} -20885.7 q^{78} -27724.6 q^{79} +1292.04 q^{80} +198686. q^{81} -14316.9 q^{82} -23497.6 q^{83} +6109.22 q^{84} +47808.3 q^{85} -14139.7 q^{86} +182611. q^{87} +21546.5 q^{88} +92660.5 q^{89} -54574.9 q^{90} -2070.46 q^{91} -24877.5 q^{92} +124048. q^{93} -32053.6 q^{94} -9025.00 q^{95} +174882. q^{96} -160708. q^{97} +56674.5 q^{98} +77865.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.39231	−0.599682	−0.299841	−	0.953989i	$-0.596934\pi$
$2$	−3.39231	−0.599682	−0.299841	+	0.953989i	$0.596934\pi$
$3$	−29.7744	−1.91003	−0.955013	−	0.296564i	$-0.904159\pi$
$3$	−29.7744	−1.91003	−0.955013	+	0.296564i	$0.904159\pi$
$4$	−20.4922	−0.640382
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	101.004	1.14541
$7$	10.0128	0.0772342	0.0386171	−	0.999254i	$-0.487705\pi$
$7$	10.0128	0.0772342	0.0386171	+	0.999254i	$0.487705\pi$
$8$	178.070	0.983707
$9$	643.513	2.64820
$10$	−84.8078	−0.268186
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	610.143	1.22315
$13$	−206.781	−0.339354	−0.169677	−	0.985500i	$-0.554272\pi$
$13$	−206.781	−0.339354	−0.169677	+	0.985500i	$0.554272\pi$
$14$	−33.9665	−0.0463159
$15$	−744.359	−0.854190
$16$	51.6816	0.0504703
$17$	1912.33	1.60488	0.802438	−	0.596736i	$-0.203536\pi$
$17$	1912.33	1.60488	0.802438	+	0.596736i	$0.203536\pi$
$18$	−2183.00	−1.58808
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−512.305	−0.286387
$21$	−298.124	−0.147519
$22$	−410.470	−0.180811
$23$	1214.00	0.478518	0.239259	−	0.970956i	$-0.423095\pi$
$23$	1214.00	0.478518	0.239259	+	0.970956i	$0.423095\pi$
$24$	−5301.92	−1.87891
$25$	625.000	0.200000
$26$	701.467	0.203504
$27$	−11925.0	−3.14810
$28$	−205.184	−0.0494593
$29$	−6133.15	−1.35422	−0.677109	−	0.735882i	$-0.736768\pi$
$29$	−6133.15	−1.35422	−0.677109	+	0.735882i	$0.736768\pi$
$30$	2525.10	0.512242
$31$	−4166.25	−0.778648	−0.389324	−	0.921101i	$-0.627291\pi$
$31$	−4166.25	−0.778648	−0.389324	+	0.921101i	$0.627291\pi$
$32$	−5873.56	−1.01397
$33$	−3602.70	−0.575895
$34$	−6487.23	−0.962415
$35$	250.319	0.0345402
$36$	−13187.0	−1.69586
$37$	505.924	0.0607549	0.0303774	−	0.999538i	$-0.490329\pi$
$37$	505.924	0.0607549	0.0303774	+	0.999538i	$0.490329\pi$
$38$	1224.62	0.137576
$39$	6156.78	0.648175
$40$	4451.75	0.439927
$41$	4220.39	0.392096	0.196048	−	0.980594i	$-0.437189\pi$
$41$	4220.39	0.392096	0.196048	+	0.980594i	$0.437189\pi$
$42$	1011.33	0.0884646
$43$	4168.16	0.343774	0.171887	−	0.985117i	$-0.445014\pi$
$43$	4168.16	0.343774	0.171887	+	0.985117i	$0.445014\pi$
$44$	−2479.56	−0.193082
$45$	16087.8	1.18431
$46$	−4118.26	−0.286959
$47$	9448.90	0.623931	0.311965	−	0.950093i	$-0.399013\pi$
$47$	9448.90	0.623931	0.311965	+	0.950093i	$0.399013\pi$
$48$	−1538.79	−0.0963997
$49$	−16706.7	−0.994035
$50$	−2120.20	−0.119936
$51$	−56938.5	−3.06535
$52$	4237.41	0.217316
$53$	−17414.4	−0.851565	−0.425783	−	0.904825i	$-0.640001\pi$
$53$	−17414.4	−0.851565	−0.425783	+	0.904825i	$0.640001\pi$
$54$	40453.3	1.88786
$55$	3025.00	0.134840
$56$	1782.98	0.0759758
$57$	10748.5	0.438190
$58$	20805.6	0.812100
$59$	4557.96	0.170467	0.0852335	−	0.996361i	$-0.472836\pi$
$59$	4557.96	0.170467	0.0852335	+	0.996361i	$0.472836\pi$
$60$	15253.6	0.547007
$61$	42065.0	1.44743	0.723714	−	0.690100i	$-0.242434\pi$
$61$	42065.0	1.44743	0.723714	+	0.690100i	$0.242434\pi$
$62$	14133.2	0.466941
$63$	6443.35	0.204531
$64$	18271.1	0.557591
$65$	−5169.53	−0.151764
$66$	12221.5	0.345354
$67$	−52232.4	−1.42152	−0.710760	−	0.703435i	$-0.751649\pi$
$67$	−52232.4	−1.42152	−0.710760	+	0.703435i	$0.751649\pi$
$68$	−39187.9	−1.02773
$69$	−36146.0	−0.913983
$70$	−849.162	−0.0207131
$71$	7175.10	0.168920	0.0844602	−	0.996427i	$-0.473083\pi$
$71$	7175.10	0.168920	0.0844602	+	0.996427i	$0.473083\pi$
$72$	114590.	2.60505
$73$	−28411.3	−0.623999	−0.312000	−	0.950082i	$-0.600999\pi$
$73$	−28411.3	−0.623999	−0.312000	+	0.950082i	$0.600999\pi$
$74$	−1716.25	−0.0364336
$75$	−18609.0	−0.382005
$76$	7397.69	0.146914
$77$	1211.55	0.0232870
$78$	−20885.7	−0.388699
$79$	−27724.6	−0.499801	−0.249900	−	0.968272i	$-0.580398\pi$
$79$	−27724.6	−0.499801	−0.249900	+	0.968272i	$0.580398\pi$
$80$	1292.04	0.0225710
$81$	198686.	3.36476
$82$	−14316.9	−0.235133
$83$	−23497.6	−0.374394	−0.187197	−	0.982322i	$-0.559940\pi$
$83$	−23497.6	−0.374394	−0.187197	+	0.982322i	$0.559940\pi$
$84$	6109.22	0.0944686
$85$	47808.3	0.717722
$86$	−14139.7	−0.206155
$87$	182611.	2.58659
$88$	21546.5	0.296599
$89$	92660.5	1.23999	0.619997	−	0.784604i	$-0.287134\pi$
$89$	92660.5	1.23999	0.619997	+	0.784604i	$0.287134\pi$
$90$	−54574.9	−0.710210
$91$	−2070.46	−0.0262097
$92$	−24877.5	−0.306434
$93$	124048.	1.48724
$94$	−32053.6	−0.374160
$95$	−9025.00	−0.102598
$96$	174882.	1.93672
$97$	−160708.	−1.73424	−0.867120	−	0.498100i	$-0.834031\pi$
$97$	−160708.	−1.73424	−0.867120	+	0.498100i	$0.834031\pi$
$98$	56674.5	0.596105
$99$	77865.0	0.798462
$100$	−12807.6	−0.128076
$101$	200357.	1.95435	0.977173	−	0.212447i	$-0.0681433\pi$
$101$	200357.	1.95435	0.977173	+	0.212447i	$0.0681433\pi$
$102$	193153.	1.83824
$103$	122142.	1.13442	0.567209	−	0.823574i	$-0.308023\pi$
$103$	122142.	1.13442	0.567209	+	0.823574i	$0.308023\pi$
$104$	−36821.6	−0.333825
$105$	−7453.10	−0.0659726
$106$	59075.0	0.510668
$107$	−9270.69	−0.0782803	−0.0391402	−	0.999234i	$-0.512462\pi$
$107$	−9270.69	−0.0782803	−0.0391402	+	0.999234i	$0.512462\pi$
$108$	244370.	2.01599
$109$	40027.5	0.322695	0.161347	−	0.986898i	$-0.448416\pi$
$109$	40027.5	0.322695	0.161347	+	0.986898i	$0.448416\pi$
$110$	−10261.7	−0.0808611
$111$	−15063.6	−0.116043
$112$	517.477	0.00389803
$113$	61686.2	0.454456	0.227228	−	0.973842i	$-0.427034\pi$
$113$	61686.2	0.454456	0.227228	+	0.973842i	$0.427034\pi$
$114$	−36462.4	−0.262775
$115$	30350.0	0.214000
$116$	125682.	0.867217
$117$	−133066.	−0.898677
$118$	−15462.0	−0.102226
$119$	19147.8	0.123951
$120$	−132548.	−0.840272
$121$	14641.0	0.0909091
$122$	−142698.	−0.867996
$123$	−125659.	−0.748914
$124$	85375.7	0.498632
$125$	15625.0	0.0894427
$126$	−21857.8	−0.122654
$127$	−310734.	−1.70954	−0.854771	−	0.519005i	$-0.826303\pi$
$127$	−310734.	−1.70954	−0.854771	+	0.519005i	$0.826303\pi$
$128$	125973.	0.679596
$129$	−124104.	−0.656617
$130$	17536.7	0.0910100
$131$	89438.3	0.455350	0.227675	−	0.973737i	$-0.426888\pi$
$131$	89438.3	0.455350	0.227675	+	0.973737i	$0.426888\pi$
$132$	73827.2	0.368792
$133$	−3614.61	−0.0177187
$134$	177189.	0.852459
$135$	−298125.	−1.40788
$136$	340529.	1.57873
$137$	−90979.6	−0.414135	−0.207068	−	0.978327i	$-0.566392\pi$
$137$	−90979.6	−0.414135	−0.207068	+	0.978327i	$0.566392\pi$
$138$	122619.	0.548099
$139$	−190292.	−0.835381	−0.417691	−	0.908589i	$-0.637160\pi$
$139$	−190292.	−0.835381	−0.417691	+	0.908589i	$0.637160\pi$
$140$	−5129.60	−0.0221189
$141$	−281335.	−1.19172
$142$	−24340.2	−0.101298
$143$	−25020.5	−0.102319
$144$	33257.8	0.133656
$145$	−153329.	−0.605625
$146$	96380.0	0.374201
$147$	497433.	1.89863
$148$	−10367.5	−0.0389063
$149$	180484.	0.665998	0.332999	−	0.942927i	$-0.391939\pi$
$149$	180484.	0.665998	0.332999	+	0.942927i	$0.391939\pi$
$150$	63127.5	0.229082
$151$	−91260.1	−0.325715	−0.162858	−	0.986650i	$-0.552071\pi$
$151$	−91260.1	−0.325715	−0.162858	+	0.986650i	$0.552071\pi$
$152$	−64283.3	−0.225678
$153$	1.23061e6	4.25003
$154$	−4109.94	−0.0139648
$155$	−104156.	−0.348222
$156$	−126166.	−0.415079
$157$	−180845.	−0.585541	−0.292770	−	0.956183i	$-0.594577\pi$
$157$	−180845.	−0.585541	−0.292770	+	0.956183i	$0.594577\pi$
$158$	94050.4	0.299721
$159$	518502.	1.62651
$160$	−146839.	−0.453463
$161$	12155.5	0.0369580
$162$	−674005.	−2.01779
$163$	66742.5	0.196758	0.0983792	−	0.995149i	$-0.468634\pi$
$163$	66742.5	0.196758	0.0983792	+	0.995149i	$0.468634\pi$
$164$	−86485.1	−0.251091
$165$	−90067.4	−0.257548
$166$	79711.4	0.224517
$167$	−79869.3	−0.221610	−0.110805	−	0.993842i	$-0.535343\pi$
$167$	−79869.3	−0.221610	−0.110805	+	0.993842i	$0.535343\pi$
$168$	−53086.9	−0.145116
$169$	−328534.	−0.884839
$170$	−162181.	−0.430405
$171$	−232308.	−0.607539
$172$	−85414.8	−0.220147
$173$	274054.	0.696180	0.348090	−	0.937461i	$-0.386830\pi$
$173$	274054.	0.696180	0.348090	+	0.937461i	$0.386830\pi$
$174$	−619473.	−1.55113
$175$	6257.98	0.0154468
$176$	6253.48	0.0152174
$177$	−135710.	−0.325597
$178$	−314333.	−0.743602
$179$	24150.2	0.0563364	0.0281682	−	0.999603i	$-0.491033\pi$
$179$	24150.2	0.0563364	0.0281682	+	0.999603i	$0.491033\pi$
$180$	−329675.	−0.758411
$181$	280071.	0.635437	0.317718	−	0.948185i	$-0.397083\pi$
$181$	280071.	0.635437	0.317718	+	0.948185i	$0.397083\pi$
$182$	7023.63	0.0157175
$183$	−1.25246e6	−2.76462
$184$	216177.	0.470722
$185$	12648.1	0.0271704
$186$	−420808.	−0.891870
$187$	231392.	0.483888
$188$	−193629.	−0.399554
$189$	−119402.	−0.243141
$190$	30615.6	0.0615261
$191$	424742.	0.842446	0.421223	−	0.906957i	$-0.361601\pi$
$191$	424742.	0.842446	0.421223	+	0.906957i	$0.361601\pi$
$192$	−544012.	−1.06501
$193$	−97074.2	−0.187590	−0.0937952	−	0.995592i	$-0.529900\pi$
$193$	−97074.2	−0.187590	−0.0937952	+	0.995592i	$0.529900\pi$
$194$	545173.	1.03999
$195$	153920.	0.289873
$196$	342358.	0.636562
$197$	−390049.	−0.716066	−0.358033	−	0.933709i	$-0.616552\pi$
$197$	−390049.	−0.716066	−0.358033	+	0.933709i	$0.616552\pi$
$198$	−264143.	−0.478823
$199$	−649393.	−1.16245	−0.581225	−	0.813743i	$-0.697427\pi$
$199$	−649393.	−1.16245	−0.581225	+	0.813743i	$0.697427\pi$
$200$	111294.	0.196741
$201$	1.55519e6	2.71514
$202$	−679674.	−1.17199
$203$	−61409.9	−0.104592
$204$	1.16680e6	1.96300
$205$	105510.	0.175351
$206$	−414345.	−0.680290
$207$	781224.	1.26721
$208$	−10686.8	−0.0171273
$209$	−43681.0	−0.0691714
$210$	25283.2	0.0395626
$211$	126419.	0.195482	0.0977411	−	0.995212i	$-0.468838\pi$
$211$	126419.	0.195482	0.0977411	+	0.995212i	$0.468838\pi$
$212$	356859.	0.545327
$213$	−213634.	−0.322642
$214$	31449.1	0.0469433
$215$	104204.	0.153740
$216$	−2.12349e6	−3.09681
$217$	−41715.8	−0.0601383
$218$	−135786.	−0.193514
$219$	845928.	1.19185
$220$	−61988.9	−0.0863490
$221$	−395435.	−0.544621
$222$	51100.3	0.0695891
$223$	−389424.	−0.524397	−0.262199	−	0.965014i	$-0.584448\pi$
$223$	−389424.	−0.524397	−0.262199	+	0.965014i	$0.584448\pi$
$224$	−58810.6	−0.0783134
$225$	402195.	0.529640
$226$	−209259.	−0.272529
$227$	−416951.	−0.537057	−0.268529	−	0.963272i	$-0.586537\pi$
$227$	−416951.	−0.537057	−0.268529	+	0.963272i	$0.586537\pi$
$228$	−220261.	−0.280609
$229$	−392403.	−0.494474	−0.247237	−	0.968955i	$-0.579523\pi$
$229$	−392403.	−0.494474	−0.247237	+	0.968955i	$0.579523\pi$
$230$	−102957.	−0.128332
$231$	−36073.0	−0.0444787
$232$	−1.09213e6	−1.33215
$233$	−1.33481e6	−1.61075	−0.805375	−	0.592766i	$-0.798036\pi$
$233$	−1.33481e6	−1.61075	−0.805375	+	0.592766i	$0.798036\pi$
$234$	451403.	0.538921
$235$	236222.	0.279030
$236$	−93402.7	−0.109164
$237$	825481.	0.954632
$238$	−64955.2	−0.0743313
$239$	1.18580e6	1.34282	0.671408	−	0.741088i	$-0.265690\pi$
$239$	1.18580e6	1.34282	0.671408	+	0.741088i	$0.265690\pi$
$240$	−38469.7	−0.0431112
$241$	−304701.	−0.337933	−0.168967	−	0.985622i	$-0.554043\pi$
$241$	−304701.	−0.337933	−0.168967	+	0.985622i	$0.554043\pi$
$242$	−49666.9	−0.0545165
$243$	−3.01797e6	−3.27868
$244$	−862006.	−0.926906
$245$	−417669.	−0.444546
$246$	426276.	0.449110
$247$	74648.1	0.0778532
$248$	−741885.	−0.765962
$249$	699627.	0.715103
$250$	−53004.9	−0.0536372
$251$	−790127.	−0.791612	−0.395806	−	0.918334i	$-0.629535\pi$
$251$	−790127.	−0.791612	−0.395806	+	0.918334i	$0.629535\pi$
$252$	−132038.	−0.130978
$253$	146894.	0.144279
$254$	1.05411e6	1.02518
$255$	−1.42346e6	−1.37087
$256$	−1.01201e6	−0.965132
$257$	1.79744e6	1.69754	0.848772	−	0.528759i	$-0.177342\pi$
$257$	1.79744e6	1.69754	0.848772	+	0.528759i	$0.177342\pi$
$258$	421000.	0.393762
$259$	5065.70	0.00469235
$260$	105935.	0.0971867
$261$	−3.94676e6	−3.58624
$262$	−303403.	−0.273065
$263$	−596175.	−0.531477	−0.265738	−	0.964045i	$-0.585616\pi$
$263$	−596175.	−0.531477	−0.265738	+	0.964045i	$0.585616\pi$
$264$	−641532.	−0.566512
$265$	−435359.	−0.380832
$266$	12261.9	0.0106256
$267$	−2.75891e6	−2.36842
$268$	1.07036e6	0.910315
$269$	1.12707e6	0.949665	0.474833	−	0.880076i	$-0.342509\pi$
$269$	1.12707e6	0.949665	0.474833	+	0.880076i	$0.342509\pi$
$270$	1.01133e6	0.844277
$271$	−56505.4	−0.0467376	−0.0233688	−	0.999727i	$-0.507439\pi$
$271$	−56505.4	−0.0467376	−0.0233688	+	0.999727i	$0.507439\pi$
$272$	98832.5	0.0809986
$273$	61646.5	0.0500613
$274$	308631.	0.248350
$275$	75625.0	0.0603023
$276$	740712.	0.585298
$277$	−289130.	−0.226409	−0.113205	−	0.993572i	$-0.536112\pi$
$277$	−289130.	−0.226409	−0.113205	+	0.993572i	$0.536112\pi$
$278$	645532.	0.500963
$279$	−2.68104e6	−2.06202
$280$	44574.4	0.0339774
$281$	1.13670e6	0.858773	0.429387	−	0.903121i	$-0.358730\pi$
$281$	1.13670e6	0.858773	0.429387	+	0.903121i	$0.358730\pi$
$282$	954376.	0.714655
$283$	−1.64342e6	−1.21978	−0.609890	−	0.792486i	$-0.708787\pi$
$283$	−1.64342e6	−1.21978	−0.609890	+	0.792486i	$0.708787\pi$
$284$	−147034.	−0.108173
$285$	268714.	0.195965
$286$	84877.5	0.0613589
$287$	42257.8	0.0302832
$288$	−3.77971e6	−2.68520
$289$	2.23716e6	1.57562
$290$	520139.	0.363182
$291$	4.78499e6	3.31244
$292$	582211.	0.399598
$293$	2.21459e6	1.50704	0.753518	−	0.657427i	$-0.228355\pi$
$293$	2.21459e6	1.50704	0.753518	+	0.657427i	$0.228355\pi$
$294$	−1.68745e6	−1.13858
$295$	113949.	0.0762352
$296$	90089.9	0.0597650
$297$	−1.44293e6	−0.949189
$298$	−612258.	−0.399387
$299$	−251032.	−0.162387
$300$	381339.	0.244629
$301$	41734.8	0.0265511
$302$	309583.	0.195326
$303$	−5.96550e6	−3.73285
$304$	−18657.1	−0.0115787
$305$	1.05163e6	0.647309
$306$	−4.17462e6	−2.54867
$307$	−2.11429e6	−1.28032	−0.640159	−	0.768243i	$-0.721131\pi$
$307$	−2.11429e6	−1.28032	−0.640159	+	0.768243i	$0.721131\pi$
$308$	−24827.3	−0.0149126
$309$	−3.63671e6	−2.16677
$310$	353331.	0.208823
$311$	1.57518e6	0.923484	0.461742	−	0.887014i	$-0.347225\pi$
$311$	1.57518e6	0.923484	0.461742	+	0.887014i	$0.347225\pi$
$312$	1.09634e6	0.637615
$313$	2.13366e6	1.23102	0.615510	−	0.788129i	$-0.288950\pi$
$313$	2.13366e6	1.23102	0.615510	+	0.788129i	$0.288950\pi$
$314$	613482.	0.351138
$315$	161084.	0.0914693
$316$	568137.	0.320063
$317$	−2.61837e6	−1.46347	−0.731734	−	0.681590i	$-0.761289\pi$
$317$	−2.61837e6	−1.46347	−0.731734	+	0.681590i	$0.761289\pi$
$318$	−1.75892e6	−0.975390
$319$	−742111.	−0.408312
$320$	456779.	0.249362
$321$	276029.	0.149517
$322$	−41235.3	−0.0221630
$323$	−690352.	−0.368184
$324$	−4.07151e6	−2.15473
$325$	−129238.	−0.0678708
$326$	−226411.	−0.117992
$327$	−1.19179e6	−0.616355
$328$	751524.	0.385708
$329$	94609.7	0.0481888
$330$	305537.	0.154447
$331$	−1.03899e6	−0.521244	−0.260622	−	0.965441i	$-0.583928\pi$
$331$	−1.03899e6	−0.521244	−0.260622	+	0.965441i	$0.583928\pi$
$332$	481519.	0.239755
$333$	325568.	0.160891
$334$	270942.	0.132895
$335$	−1.30581e6	−0.635723
$336$	−15407.5	−0.00744535
$337$	1.86434e6	0.894234	0.447117	−	0.894476i	$-0.352451\pi$
$337$	1.86434e6	0.894234	0.447117	+	0.894476i	$0.352451\pi$
$338$	1.11449e6	0.530622
$339$	−1.83667e6	−0.868024
$340$	−979699.	−0.459616
$341$	−504117.	−0.234771
$342$	788062.	0.364330
$343$	−335566.	−0.154008
$344$	742224.	0.338173
$345$	−903651.	−0.408746
$346$	−929679.	−0.417487
$347$	3.11417e6	1.38841	0.694207	−	0.719776i	$-0.255755\pi$
$347$	3.11417e6	1.38841	0.694207	+	0.719776i	$0.255755\pi$
$348$	−3.74210e6	−1.65641
$349$	−2.83448e6	−1.24569	−0.622845	−	0.782345i	$-0.714023\pi$
$349$	−2.83448e6	−1.24569	−0.622845	+	0.782345i	$0.714023\pi$
$350$	−21229.0	−0.00926318
$351$	2.46587e6	1.06832
$352$	−710701.	−0.305724
$353$	2.11759e6	0.904491	0.452245	−	0.891894i	$-0.350623\pi$
$353$	2.11759e6	0.904491	0.452245	+	0.891894i	$0.350623\pi$
$354$	460372.	0.195254
$355$	179377.	0.0755435
$356$	−1.89882e6	−0.794070
$357$	−570112.	−0.236750
$358$	−81925.2	−0.0337839
$359$	−1.22797e6	−0.502865	−0.251432	−	0.967875i	$-0.580902\pi$
$359$	−1.22797e6	−0.502865	−0.251432	+	0.967875i	$0.580902\pi$
$360$	2.86476e6	1.16502
$361$	130321.	0.0526316
$362$	−950090.	−0.381060
$363$	−435926.	−0.173639
$364$	42428.2	0.0167842
$365$	−710283.	−0.279061
$366$	4.24873e6	1.65789
$367$	3.25358e6	1.26094	0.630472	−	0.776212i	$-0.282861\pi$
$367$	3.25358e6	1.26094	0.630472	+	0.776212i	$0.282861\pi$
$368$	62741.4	0.0241510
$369$	2.71587e6	1.03835
$370$	−42906.3	−0.0162936
$371$	−174366.	−0.0657699
$372$	−2.54201e6	−0.952401
$373$	−2.26158e6	−0.841664	−0.420832	−	0.907139i	$-0.638262\pi$
$373$	−2.26158e6	−0.841664	−0.420832	+	0.907139i	$0.638262\pi$
$374$	−784955.	−0.290179
$375$	−465224.	−0.170838
$376$	1.68257e6	0.613765
$377$	1.26822e6	0.459560
$378$	405050.	0.145807
$379$	−4.17744e6	−1.49387	−0.746933	−	0.664899i	$-0.768475\pi$
$379$	−4.17744e6	−1.49387	−0.746933	+	0.664899i	$0.768475\pi$
$380$	184942.	0.0657018
$381$	9.25192e6	3.26527
$382$	−1.44086e6	−0.505199
$383$	−753292.	−0.262401	−0.131201	−	0.991356i	$-0.541883\pi$
$383$	−753292.	−0.262401	−0.131201	+	0.991356i	$0.541883\pi$
$384$	−3.75075e6	−1.29805
$385$	30288.6	0.0104143
$386$	329306.	0.112495
$387$	2.68226e6	0.910382
$388$	3.29327e6	1.11058
$389$	−3.23188e6	−1.08288	−0.541441	−	0.840739i	$-0.682121\pi$
$389$	−3.23188e6	−1.08288	−0.541441	+	0.840739i	$0.682121\pi$
$390$	−522143.	−0.173831
$391$	2.32157e6	0.767962
$392$	−2.97497e6	−0.977839
$393$	−2.66297e6	−0.869731
$394$	1.32317e6	0.429412
$395$	−693114.	−0.223518
$396$	−1.59563e6	−0.511321
$397$	310747.	0.0989535	0.0494767	−	0.998775i	$-0.484245\pi$
$397$	310747.	0.0989535	0.0494767	+	0.998775i	$0.484245\pi$
$398$	2.20294e6	0.697101
$399$	107623.	0.0338432
$400$	32301.0	0.0100941
$401$	5.11082e6	1.58719	0.793597	−	0.608444i	$-0.208206\pi$
$401$	5.11082e6	1.58719	0.793597	+	0.608444i	$0.208206\pi$
$402$	−5.27568e6	−1.62822
$403$	861504.	0.264238
$404$	−4.10576e6	−1.25153
$405$	4.96715e6	1.50477
$406$	208322.	0.0627219
$407$	61216.8	0.0183183
$408$	−1.01390e7	−3.01541
$409$	5.87477e6	1.73653	0.868266	−	0.496099i	$-0.165235\pi$
$409$	5.87477e6	1.73653	0.868266	+	0.496099i	$0.165235\pi$
$410$	−357922.	−0.105155
$411$	2.70886e6	0.791010
$412$	−2.50297e6	−0.726460
$413$	45637.8	0.0131659
$414$	−2.65015e6	−0.759924
$415$	−587441.	−0.167434
$416$	1.21454e6	0.344096
$417$	5.66584e6	1.59560
$418$	148180.	0.0414809
$419$	−157330.	−0.0437799	−0.0218900	−	0.999760i	$-0.506968\pi$
$419$	−157330.	−0.0437799	−0.0218900	+	0.999760i	$0.506968\pi$
$420$	152731.	0.0422477
$421$	−1.06276e6	−0.292233	−0.146117	−	0.989267i	$-0.546677\pi$
$421$	−1.06276e6	−0.292233	−0.146117	+	0.989267i	$0.546677\pi$
$422$	−428854.	−0.117227
$423$	6.08048e6	1.65229
$424$	−3.10098e6	−0.837691
$425$	1.19521e6	0.320975
$426$	724713.	0.193483
$427$	421188.	0.111791
$428$	189977.	0.0501293
$429$	744971.	0.195432
$430$	−353492.	−0.0921953
$431$	5.41016e6	1.40287	0.701434	−	0.712735i	$-0.252544\pi$
$431$	5.41016e6	1.40287	0.701434	+	0.712735i	$0.252544\pi$
$432$	−616304.	−0.158886
$433$	5.85943e6	1.50188	0.750941	−	0.660369i	$-0.229600\pi$
$433$	5.85943e6	1.50188	0.750941	+	0.660369i	$0.229600\pi$
$434$	141513.	0.0360638
$435$	4.56527e6	1.15676
$436$	−820251.	−0.206648
$437$	−438254.	−0.109780
$438$	−2.86965e6	−0.714734
$439$	6.18208e6	1.53099	0.765497	−	0.643440i	$-0.222493\pi$
$439$	6.18208e6	1.53099	0.765497	+	0.643440i	$0.222493\pi$
$440$	538662.	0.132643
$441$	−1.07510e7	−2.63240
$442$	1.34144e6	0.326599
$443$	467820.	0.113258	0.0566291	−	0.998395i	$-0.481965\pi$
$443$	467820.	0.113258	0.0566291	+	0.998395i	$0.481965\pi$
$444$	308686.	0.0743120
$445$	2.31651e6	0.554542
$446$	1.32105e6	0.314471
$447$	−5.37380e6	−1.27207
$448$	182945.	0.0430651
$449$	7.22928e6	1.69231	0.846153	−	0.532940i	$-0.178913\pi$
$449$	7.22928e6	1.69231	0.846153	+	0.532940i	$0.178913\pi$
$450$	−1.36437e6	−0.317615
$451$	510667.	0.118221
$452$	−1.26409e6	−0.291026
$453$	2.71721e6	0.622125
$454$	1.41443e6	0.322063
$455$	−51761.4	−0.0117213
$456$	1.91399e6	0.431051
$457$	3.94054e6	0.882603	0.441301	−	0.897359i	$-0.354517\pi$
$457$	3.94054e6	0.882603	0.441301	+	0.897359i	$0.354517\pi$
$458$	1.33115e6	0.296527
$459$	−2.28046e7	−5.05232
$460$	−621938.	−0.137042
$461$	−3.37162e6	−0.738902	−0.369451	−	0.929250i	$-0.620454\pi$
$461$	−3.37162e6	−0.738902	−0.369451	+	0.929250i	$0.620454\pi$
$462$	122371.	0.0266731
$463$	−7.94245e6	−1.72188	−0.860939	−	0.508709i	$-0.830123\pi$
$463$	−7.94245e6	−1.72188	−0.860939	+	0.508709i	$0.830123\pi$
$464$	−316971.	−0.0683479
$465$	3.10119e6	0.665113
$466$	4.52808e6	0.965937
$467$	−5.42647e6	−1.15140	−0.575699	−	0.817662i	$-0.695270\pi$
$467$	−5.42647e6	−1.15140	−0.575699	+	0.817662i	$0.695270\pi$
$468$	2.72683e6	0.575497
$469$	−522991.	−0.109790
$470$	−801340.	−0.167329
$471$	5.38454e6	1.11840
$472$	811636.	0.167690
$473$	504347.	0.103652
$474$	−2.80029e6	−0.572476
$475$	−225625.	−0.0458831
$476$	−392380.	−0.0793761
$477$	−1.12064e7	−2.25512
$478$	−4.02260e6	−0.805262
$479$	−785273.	−0.156380	−0.0781901	−	0.996938i	$-0.524914\pi$
$479$	−785273.	−0.156380	−0.0781901	+	0.996938i	$0.524914\pi$
$480$	4.37204e6	0.866125
$481$	−104616.	−0.0206174
$482$	1.03364e6	0.202653
$483$	−361922.	−0.0705907
$484$	−300026.	−0.0582165
$485$	−4.01771e6	−0.775576
$486$	1.02379e7	1.96616
$487$	−3.41167e6	−0.651845	−0.325922	−	0.945397i	$-0.605675\pi$
$487$	−3.41167e6	−0.651845	−0.325922	+	0.945397i	$0.605675\pi$
$488$	7.49052e6	1.42384
$489$	−1.98721e6	−0.375814
$490$	1.41686e6	0.266586
$491$	6.93803e6	1.29877	0.649386	−	0.760459i	$-0.275026\pi$
$491$	6.93803e6	1.29877	0.649386	+	0.760459i	$0.275026\pi$
$492$	2.57504e6	0.479591
$493$	−1.17286e7	−2.17335
$494$	−253230.	−0.0466871
$495$	1.94663e6	0.357083
$496$	−215319.	−0.0392987
$497$	71842.6	0.0130464
$498$	−2.37335e6	−0.428834
$499$	−2.18852e6	−0.393458	−0.196729	−	0.980458i	$-0.563032\pi$
$499$	−2.18852e6	−0.393458	−0.196729	+	0.980458i	$0.563032\pi$
$500$	−320191.	−0.0572775
$501$	2.37806e6	0.423280
$502$	2.68036e6	0.474715
$503$	−1.98859e6	−0.350450	−0.175225	−	0.984528i	$-0.556065\pi$
$503$	−1.98859e6	−0.350450	−0.175225	+	0.984528i	$0.556065\pi$
$504$	1.14737e6	0.201199
$505$	5.00893e6	0.874010
$506$	−498310.	−0.0865213
$507$	9.78190e6	1.69007
$508$	6.36763e6	1.09476
$509$	−3.89749e6	−0.666792	−0.333396	−	0.942787i	$-0.608195\pi$
$509$	−3.89749e6	−0.666792	−0.333396	+	0.942787i	$0.608195\pi$
$510$	4.82883e6	0.822085
$511$	−284476.	−0.0481940
$512$	−598050.	−0.100824
$513$	4.30493e6	0.722225
$514$	−6.09747e6	−1.01799
$515$	3.05356e6	0.507327
$516$	2.54317e6	0.420486
$517$	1.14332e6	0.188122
$518$	−17184.5	−0.00281392
$519$	−8.15980e6	−1.32972
$520$	−920539.	−0.149291
$521$	−4.70056e6	−0.758674	−0.379337	−	0.925259i	$-0.623848\pi$
$521$	−4.70056e6	−0.758674	−0.379337	+	0.925259i	$0.623848\pi$
$522$	1.33886e7	2.15060
$523$	−6.03809e6	−0.965263	−0.482631	−	0.875824i	$-0.660319\pi$
$523$	−6.03809e6	−0.965263	−0.482631	+	0.875824i	$0.660319\pi$
$524$	−1.83279e6	−0.291598
$525$	−186327.	−0.0295038
$526$	2.02241e6	0.318717
$527$	−7.96727e6	−1.24963
$528$	−186193.	−0.0290656
$529$	−4.96255e6	−0.771020
$530$	1.47687e6	0.228378
$531$	2.93310e6	0.451431
$532$	74071.4	0.0113467
$533$	−872698.	−0.133059
$534$	9.35908e6	1.42030
$535$	−231767.	−0.0350080
$536$	−9.30102e6	−1.39836
$537$	−719058.	−0.107604
$538$	−3.82338e6	−0.569497
$539$	−2.02152e6	−0.299713
$540$	6.10924e6	0.901577
$541$	−3.81177e6	−0.559930	−0.279965	−	0.960010i	$-0.590323\pi$
$541$	−3.81177e6	−0.559930	−0.279965	+	0.960010i	$0.590323\pi$
$542$	191684.	0.0280277
$543$	−8.33895e6	−1.21370
$544$	−1.12322e7	−1.62730
$545$	1.00069e6	0.144313
$546$	−209124.	−0.0300208
$547$	8.65563e6	1.23689	0.618444	−	0.785829i	$-0.287763\pi$
$547$	8.65563e6	1.23689	0.618444	+	0.785829i	$0.287763\pi$
$548$	1.86437e6	0.265205
$549$	2.70694e7	3.83308
$550$	−256544.	−0.0361622
$551$	2.21407e6	0.310679
$552$	−6.43653e6	−0.899091
$553$	−277600.	−0.0386017
$554$	980821.	0.135774
$555$	−376589.	−0.0518962
$556$	3.89951e6	0.534963
$557$	2.75620e6	0.376420	0.188210	−	0.982129i	$-0.439731\pi$
$557$	2.75620e6	0.376420	0.188210	+	0.982129i	$0.439731\pi$
$558$	9.09491e6	1.23655
$559$	−861898.	−0.116661
$560$	12936.9	0.00174325
$561$	−6.88956e6	−0.924239
$562$	−3.85603e6	−0.514991
$563$	−1.21838e7	−1.61999	−0.809993	−	0.586440i	$-0.800529\pi$
$563$	−1.21838e7	−1.61999	−0.809993	+	0.586440i	$0.800529\pi$
$564$	5.76517e6	0.763158
$565$	1.54216e6	0.203239
$566$	5.57499e6	0.731480
$567$	1.98940e6	0.259875
$568$	1.27767e6	0.166168
$569$	−961249.	−0.124467	−0.0622336	−	0.998062i	$-0.519822\pi$
$569$	−961249.	−0.124467	−0.0622336	+	0.998062i	$0.519822\pi$
$570$	−911561.	−0.117516
$571$	156259.	0.0200565	0.0100283	−	0.999950i	$-0.496808\pi$
$571$	156259.	0.0200565	0.0100283	+	0.999950i	$0.496808\pi$
$572$	512726.	0.0655233
$573$	−1.26464e7	−1.60909
$574$	−143352.	−0.0181603
$575$	758749.	0.0957037
$576$	1.17577e7	1.47661
$577$	−1.04493e7	−1.30662	−0.653310	−	0.757090i	$-0.726620\pi$
$577$	−1.04493e7	−1.30662	−0.653310	+	0.757090i	$0.726620\pi$
$578$	−7.58915e6	−0.944874
$579$	2.89032e6	0.358303
$580$	3.14205e6	0.387831
$581$	−235277.	−0.0289160
$582$	−1.62322e7	−1.98641
$583$	−2.10714e6	−0.256757
$584$	−5.05920e6	−0.613832
$585$	−3.32666e6	−0.401901
$586$	−7.51257e6	−0.903743
$587$	6.31995e6	0.757040	0.378520	−	0.925593i	$-0.376433\pi$
$587$	6.31995e6	0.757040	0.378520	+	0.925593i	$0.376433\pi$
$588$	−1.01935e7	−1.21585
$589$	1.50402e6	0.178634
$590$	−386551.	−0.0457169
$591$	1.16134e7	1.36770
$592$	26147.0	0.00306632
$593$	5.06664e6	0.591675	0.295838	−	0.955238i	$-0.404401\pi$
$593$	5.06664e6	0.591675	0.295838	+	0.955238i	$0.404401\pi$
$594$	4.89486e6	0.569212
$595$	478694.	0.0554327
$596$	−3.69852e6	−0.426493
$597$	1.93352e7	2.22031
$598$	851580.	0.0973807
$599$	2.93113e6	0.333786	0.166893	−	0.985975i	$-0.446627\pi$
$599$	2.93113e6	0.333786	0.166893	+	0.985975i	$0.446627\pi$
$600$	−3.31370e6	−0.375781
$601$	−8.89825e6	−1.00489	−0.502445	−	0.864609i	$-0.667566\pi$
$601$	−8.89825e6	−1.00489	−0.502445	+	0.864609i	$0.667566\pi$
$602$	−141578.	−0.0159222
$603$	−3.36122e7	−3.76447
$604$	1.87012e6	0.208582
$605$	366025.	0.0406558
$606$	2.02369e7	2.23852
$607$	50397.7	0.00555186	0.00277593	−	0.999996i	$-0.499116\pi$
$607$	50397.7	0.00555186	0.00277593	+	0.999996i	$0.499116\pi$
$608$	2.12036e6	0.232621
$609$	1.82844e6	0.199773
$610$	−3.56744e6	−0.388180
$611$	−1.95386e6	−0.211733
$612$	−2.52179e7	−2.72164
$613$	1.14242e6	0.122794	0.0613968	−	0.998113i	$-0.480444\pi$
$613$	1.14242e6	0.122794	0.0613968	+	0.998113i	$0.480444\pi$
$614$	7.17232e6	0.767783
$615$	−3.14148e6	−0.334925
$616$	215740.	0.0229076
$617$	110199.	0.0116537	0.00582687	−	0.999983i	$-0.498145\pi$
$617$	110199.	0.0116537	0.00582687	+	0.999983i	$0.498145\pi$
$618$	1.23369e7	1.29937
$619$	−1.79086e7	−1.87860	−0.939300	−	0.343097i	$-0.888524\pi$
$619$	−1.79086e7	−1.87860	−0.939300	+	0.343097i	$0.888524\pi$
$620$	2.13439e6	0.222995
$621$	−1.44769e7	−1.50643
$622$	−5.34350e6	−0.553796
$623$	927789.	0.0957699
$624$	318193.	0.0327136
$625$	390625.	0.0400000
$626$	−7.23806e6	−0.738221
$627$	1.30057e6	0.132119
$628$	3.70591e6	0.374970
$629$	967495.	0.0975040
$630$	−546446.	−0.0548525
$631$	−1.69206e6	−0.169177	−0.0845887	−	0.996416i	$-0.526958\pi$
$631$	−1.69206e6	−0.169177	−0.0845887	+	0.996416i	$0.526958\pi$
$632$	−4.93691e6	−0.491658
$633$	−3.76405e6	−0.373376
$634$	8.88234e6	0.877616
$635$	−7.76836e6	−0.764531
$636$	−1.06252e7	−1.04159
$637$	3.45464e6	0.337330
$638$	2.51747e6	0.244857
$639$	4.61727e6	0.447335
$640$	3.14931e6	0.303925
$641$	7.60772e6	0.731324	0.365662	−	0.930748i	$-0.380843\pi$
$641$	7.60772e6	0.731324	0.365662	+	0.930748i	$0.380843\pi$
$642$	−936376.	−0.0896629
$643$	−1.70872e7	−1.62983	−0.814916	−	0.579579i	$-0.803217\pi$
$643$	−1.70872e7	−1.62983	−0.814916	+	0.579579i	$0.803217\pi$
$644$	−249093.	−0.0236672
$645$	−3.10261e6	−0.293648
$646$	2.34189e6	0.220793
$647$	3.50243e6	0.328934	0.164467	−	0.986383i	$-0.447410\pi$
$647$	3.50243e6	0.328934	0.164467	+	0.986383i	$0.447410\pi$
$648$	3.53800e7	3.30994
$649$	551513.	0.0513978
$650$	438417.	0.0407009
$651$	1.24206e6	0.114866
$652$	−1.36770e6	−0.126000
$653$	5.87657e6	0.539313	0.269656	−	0.962957i	$-0.413090\pi$
$653$	5.87657e6	0.539313	0.269656	+	0.962957i	$0.413090\pi$
$654$	4.04293e6	0.369617
$655$	2.23596e6	0.203639
$656$	218116.	0.0197892
$657$	−1.82830e7	−1.65247
$658$	−320946.	−0.0288979
$659$	−2.05209e7	−1.84070	−0.920350	−	0.391095i	$-0.872096\pi$
$659$	−2.05209e7	−1.84070	−0.920350	+	0.391095i	$0.872096\pi$
$660$	1.84568e6	0.164929
$661$	8.76978e6	0.780702	0.390351	−	0.920666i	$-0.372354\pi$
$661$	8.76978e6	0.780702	0.390351	+	0.920666i	$0.372354\pi$
$662$	3.52457e6	0.312580
$663$	1.17738e7	1.04024
$664$	−4.18423e6	−0.368294
$665$	−90365.3	−0.00792406
$666$	−1.10443e6	−0.0964834
$667$	−7.44564e6	−0.648019
$668$	1.63670e6	0.141915
$669$	1.15948e7	1.00161
$670$	4.42971e6	0.381231
$671$	5.08987e6	0.436416
$672$	1.75105e6	0.149581
$673$	−2.66920e6	−0.227166	−0.113583	−	0.993528i	$-0.536233\pi$
$673$	−2.66920e6	−0.227166	−0.113583	+	0.993528i	$0.536233\pi$
$674$	−6.32443e6	−0.536256
$675$	−7.45313e6	−0.629621
$676$	6.73240e6	0.566635
$677$	−2.69018e6	−0.225585	−0.112792	−	0.993619i	$-0.535980\pi$
$677$	−2.69018e6	−0.225585	−0.112792	+	0.993619i	$0.535980\pi$
$678$	6.23055e6	0.520538
$679$	−1.60914e6	−0.133943
$680$	8.51323e6	0.706028
$681$	1.24145e7	1.02579
$682$	1.71012e6	0.140788
$683$	1.33156e7	1.09222	0.546108	−	0.837715i	$-0.316109\pi$
$683$	1.33156e7	1.09222	0.546108	+	0.837715i	$0.316109\pi$
$684$	4.76051e6	0.389057
$685$	−2.27449e6	−0.185207
$686$	1.13834e6	0.0923556
$687$	1.16835e7	0.944458
$688$	215417.	0.0173504
$689$	3.60097e6	0.288982
$690$	3.06547e6	0.245117
$691$	3.07998e6	0.245388	0.122694	−	0.992445i	$-0.460847\pi$
$691$	3.07998e6	0.245388	0.122694	+	0.992445i	$0.460847\pi$
$692$	−5.61598e6	−0.445821
$693$	779645.	0.0616686
$694$	−1.05642e7	−0.832606
$695$	−4.75731e6	−0.373594
$696$	3.25175e7	2.54445
$697$	8.07079e6	0.629266
$698$	9.61544e6	0.747018
$699$	3.97430e7	3.07657
$700$	−128240.	−0.00989187
$701$	2.19754e7	1.68904	0.844522	−	0.535520i	$-0.179884\pi$
$701$	2.19754e7	1.68904	0.844522	+	0.535520i	$0.179884\pi$
$702$	−8.36500e6	−0.640653
$703$	−182639.	−0.0139381
$704$	2.21081e6	0.168120
$705$	−7.03337e6	−0.532955
$706$	−7.18351e6	−0.542407
$707$	2.00613e6	0.150942
$708$	2.78101e6	0.208506
$709$	1.58641e7	1.18522	0.592612	−	0.805488i	$-0.298097\pi$
$709$	1.58641e7	1.18522	0.592612	+	0.805488i	$0.298097\pi$
$710$	−608504.	−0.0453021
$711$	−1.78411e7	−1.32357
$712$	1.65001e7	1.21979
$713$	−5.05783e6	−0.372598
$714$	1.93400e6	0.141975
$715$	−625514.	−0.0457585
$716$	−494892.	−0.0360768
$717$	−3.53064e7	−2.56481
$718$	4.16565e6	0.301559
$719$	−1.70821e7	−1.23231	−0.616154	−	0.787626i	$-0.711310\pi$
$719$	−1.70821e7	−1.23231	−0.616154	+	0.787626i	$0.711310\pi$
$720$	831444.	0.0597726
$721$	1.22298e6	0.0876158
$722$	−442090.	−0.0315622
$723$	9.07227e6	0.645462
$724$	−5.73928e6	−0.406922
$725$	−3.83322e6	−0.270844
$726$	1.47880e6	0.104128
$727$	−2.11140e7	−1.48161	−0.740806	−	0.671719i	$-0.765556\pi$
$727$	−2.11140e7	−1.48161	−0.740806	+	0.671719i	$0.765556\pi$
$728$	−368686.	−0.0257827
$729$	4.15774e7	2.89760
$730$	2.40950e6	0.167348
$731$	7.97091e6	0.551714
$732$	2.56657e7	1.77041
$733$	−2.14902e7	−1.47734	−0.738670	−	0.674067i	$-0.764546\pi$
$733$	−2.14902e7	−1.47734	−0.738670	+	0.674067i	$0.764546\pi$
$734$	−1.10371e7	−0.756165
$735$	1.24358e7	0.849094
$736$	−7.13050e6	−0.485205
$737$	−6.32012e6	−0.428604
$738$	−9.21309e6	−0.622679
$739$	1.82570e7	1.22975	0.614877	−	0.788623i	$-0.289206\pi$
$739$	1.82570e7	1.22975	0.614877	+	0.788623i	$0.289206\pi$
$740$	−259188.	−0.0173994
$741$	−2.22260e6	−0.148702
$742$	591504.	0.0394410
$743$	6.94009e6	0.461204	0.230602	−	0.973048i	$-0.425930\pi$
$743$	6.94009e6	0.461204	0.230602	+	0.973048i	$0.425930\pi$
$744$	2.20891e7	1.46301
$745$	4.51210e6	0.297843
$746$	7.67197e6	0.504731
$747$	−1.51210e7	−0.991471
$748$	−4.74174e6	−0.309873
$749$	−92825.3	−0.00604591
$750$	1.57819e6	0.102448
$751$	1.13560e7	0.734729	0.367364	−	0.930077i	$-0.380260\pi$
$751$	1.13560e7	0.734729	0.367364	+	0.930077i	$0.380260\pi$
$752$	488334.	0.0314900
$753$	2.35255e7	1.51200
$754$	−4.30221e6	−0.275590
$755$	−2.28150e6	−0.145664
$756$	2.44682e6	0.155703
$757$	−2.50618e7	−1.58955	−0.794773	−	0.606907i	$-0.792410\pi$
$757$	−2.50618e7	−1.58955	−0.794773	+	0.606907i	$0.792410\pi$
$758$	1.41712e7	0.895845
$759$	−4.37367e6	−0.275576
$760$	−1.60708e6	−0.100926
$761$	3.14112e6	0.196618	0.0983090	−	0.995156i	$-0.468657\pi$
$761$	3.14112e6	0.196618	0.0983090	+	0.995156i	$0.468657\pi$
$762$	−3.13854e7	−1.95812
$763$	400786.	0.0249230
$764$	−8.70391e6	−0.539487
$765$	3.07653e7	1.90067
$766$	2.55540e6	0.157357
$767$	−942501.	−0.0578487
$768$	3.01321e7	1.84343
$769$	−680343.	−0.0414870	−0.0207435	−	0.999785i	$-0.506603\pi$
$769$	−680343.	−0.0414870	−0.0207435	+	0.999785i	$0.506603\pi$
$770$	−102749.	−0.00624524
$771$	−5.35176e7	−3.24235
$772$	1.98927e6	0.120129
$773$	−1.07219e7	−0.645391	−0.322696	−	0.946503i	$-0.604589\pi$
$773$	−1.07219e7	−0.645391	−0.322696	+	0.946503i	$0.604589\pi$
$774$	−9.09907e6	−0.545940
$775$	−2.60391e6	−0.155730
$776$	−2.86173e7	−1.70598
$777$	−150828.	−0.00896251
$778$	1.09635e7	0.649384
$779$	−1.52356e6	−0.0899531
$780$	−3.15415e6	−0.185629
$781$	868187.	0.0509314
$782$	−7.87549e6	−0.460533
$783$	7.31379e7	4.26322
$784$	−863432.	−0.0501693
$785$	−4.52112e6	−0.261862
$786$	9.03363e6	0.521562
$787$	2.46881e7	1.42086	0.710429	−	0.703769i	$-0.248501\pi$
$787$	2.46881e7	1.42086	0.710429	+	0.703769i	$0.248501\pi$
$788$	7.99296e6	0.458556
$789$	1.77507e7	1.01513
$790$	2.35126e6	0.134039
$791$	617650.	0.0350996
$792$	1.38654e7	0.785453
$793$	−8.69827e6	−0.491190
$794$	−1.05415e6	−0.0593406
$795$	1.29625e7	0.727398
$796$	1.33075e7	0.744412
$797$	−6.34060e6	−0.353577	−0.176789	−	0.984249i	$-0.556571\pi$
$797$	−6.34060e6	−0.353577	−0.176789	+	0.984249i	$0.556571\pi$
$798$	−365090.	−0.0202952
$799$	1.80694e7	1.00133
$800$	−3.67098e6	−0.202795
$801$	5.96282e7	3.28375
$802$	−1.73375e7	−0.951812
$803$	−3.43777e6	−0.188143
$804$	−3.18692e7	−1.73873
$805$	303887.	0.0165281
$806$	−2.92249e6	−0.158458
$807$	−3.35578e7	−1.81389
$808$	3.56776e7	1.92250
$809$	2.80304e7	1.50577	0.752884	−	0.658153i	$-0.228662\pi$
$809$	2.80304e7	1.50577	0.752884	+	0.658153i	$0.228662\pi$
$810$	−1.68501e7	−0.902382
$811$	3.13330e7	1.67282	0.836410	−	0.548104i	$-0.184650\pi$
$811$	3.13330e7	1.67282	0.836410	+	0.548104i	$0.184650\pi$
$812$	1.25842e6	0.0669788
$813$	1.68241e6	0.0892701
$814$	−207667.	−0.0109851
$815$	1.66856e6	0.0879930
$816$	−2.94267e6	−0.154709
$817$	−1.50471e6	−0.0788672
$818$	−1.99291e7	−1.04137
$819$	−1.33236e6	−0.0694086
$820$	−2.16213e6	−0.112291
$821$	−7.08543e6	−0.366867	−0.183433	−	0.983032i	$-0.558721\pi$
$821$	−7.08543e6	−0.366867	−0.183433	+	0.983032i	$0.558721\pi$
$822$	−9.18929e6	−0.474354
$823$	−3.31679e7	−1.70694	−0.853471	−	0.521141i	$-0.825507\pi$
$823$	−3.31679e7	−1.70694	−0.853471	+	0.521141i	$0.825507\pi$
$824$	2.17499e7	1.11593
$825$	−2.25169e6	−0.115179
$826$	−154818.	−0.00789534
$827$	2.05544e7	1.04506	0.522530	−	0.852621i	$-0.324988\pi$
$827$	2.05544e7	1.04506	0.522530	+	0.852621i	$0.324988\pi$
$828$	−1.60090e7	−0.811500
$829$	−2.86510e7	−1.44795	−0.723976	−	0.689825i	$-0.757687\pi$
$829$	−2.86510e7	−1.44795	−0.723976	+	0.689825i	$0.757687\pi$
$830$	1.99278e6	0.100407
$831$	8.60867e6	0.432448
$832$	−3.77813e6	−0.189221
$833$	−3.19489e7	−1.59530
$834$	−1.92203e7	−0.956852
$835$	−1.99673e6	−0.0991069
$836$	895120.	0.0442961
$837$	4.96826e7	2.45127
$838$	533711.	0.0262540
$839$	−1.87915e7	−0.921628	−0.460814	−	0.887497i	$-0.652442\pi$
$839$	−1.87915e7	−0.921628	−0.460814	+	0.887497i	$0.652442\pi$
$840$	−1.32717e6	−0.0648977
$841$	1.71044e7	0.833908
$842$	3.60521e6	0.175247
$843$	−3.38444e7	−1.64028
$844$	−2.59061e6	−0.125183
$845$	−8.21336e6	−0.395712
$846$	−2.06269e7	−0.990851
$847$	146597.	0.00702129
$848$	−900003.	−0.0429788
$849$	4.89317e7	2.32981
$850$	−4.05452e6	−0.192483
$851$	614191.	0.0290723
$852$	4.37783e6	0.206614
$853$	−2.15364e7	−1.01345	−0.506724	−	0.862109i	$-0.669144\pi$
$853$	−2.15364e7	−1.01345	−0.506724	+	0.862109i	$0.669144\pi$
$854$	−1.42880e6	−0.0670389
$855$	−5.80770e6	−0.271700
$856$	−1.65083e6	−0.0770049
$857$	1.12893e7	0.525069	0.262534	−	0.964923i	$-0.415442\pi$
$857$	1.12893e7	0.525069	0.262534	+	0.964923i	$0.415442\pi$
$858$	−2.52717e6	−0.117197
$859$	5.50058e6	0.254346	0.127173	−	0.991881i	$-0.459410\pi$
$859$	5.50058e6	0.254346	0.127173	+	0.991881i	$0.459410\pi$
$860$	−2.13537e6	−0.0984525
$861$	−1.25820e6	−0.0578417
$862$	−1.83529e7	−0.841274
$863$	−4.85257e6	−0.221792	−0.110896	−	0.993832i	$-0.535372\pi$
$863$	−4.85257e6	−0.221792	−0.110896	+	0.993832i	$0.535372\pi$
$864$	7.00422e7	3.19209
$865$	6.85136e6	0.311341
$866$	−1.98770e7	−0.900652
$867$	−6.66101e7	−3.00948
$868$	854848.	0.0385114
$869$	−3.35467e6	−0.150696
$870$	−1.54868e7	−0.693688
$871$	1.08007e7	0.482398
$872$	7.12769e6	0.317437
$873$	−1.03418e8	−4.59261
$874$	1.48669e6	0.0658329
$875$	156450.	0.00690803
$876$	−1.73349e7	−0.763242
$877$	1.99867e6	0.0877492	0.0438746	−	0.999037i	$-0.486030\pi$
$877$	1.99867e6	0.0877492	0.0438746	+	0.999037i	$0.486030\pi$
$878$	−2.09716e7	−0.918109
$879$	−6.59379e7	−2.87848
$880$	156337.	0.00680542
$881$	−1.47320e7	−0.639473	−0.319736	−	0.947507i	$-0.603594\pi$
$881$	−1.47320e7	−0.639473	−0.319736	+	0.947507i	$0.603594\pi$
$882$	3.64708e7	1.57860
$883$	−1.87599e7	−0.809709	−0.404855	−	0.914381i	$-0.632678\pi$
$883$	−1.87599e7	−0.809709	−0.404855	+	0.914381i	$0.632678\pi$
$884$	8.10334e6	0.348765
$885$	−3.39276e6	−0.145611
$886$	−1.58699e6	−0.0679189
$887$	−3.39862e7	−1.45042	−0.725210	−	0.688527i	$-0.758257\pi$
$887$	−3.39862e7	−1.45042	−0.725210	+	0.688527i	$0.758257\pi$
$888$	−2.68237e6	−0.114153
$889$	−3.11131e6	−0.132035
$890$	−7.85834e6	−0.332549
$891$	2.40410e7	1.01451
$892$	7.98016e6	0.335814
$893$	−3.41105e6	−0.143140
$894$	1.82296e7	0.762840
$895$	603756.	0.0251944
$896$	1.26133e6	0.0524880
$897$	7.47433e6	0.310164
$898$	−2.45240e7	−1.01485
$899$	2.55523e7	1.05446
$900$	−8.24187e6	−0.339172
$901$	−3.33021e7	−1.36666
$902$	−1.73234e6	−0.0708953
$903$	−1.24263e6	−0.0507133
$904$	1.09845e7	0.447052
$905$	7.00179e6	0.284176
$906$	−9.21763e6	−0.373077
$907$	−3.17242e7	−1.28048	−0.640240	−	0.768175i	$-0.721165\pi$
$907$	−3.17242e7	−1.28048	−0.640240	+	0.768175i	$0.721165\pi$
$908$	8.54425e6	0.343921
$909$	1.28932e8	5.17550
$910$	175591.	0.00702908
$911$	−4.15820e7	−1.66001	−0.830003	−	0.557759i	$-0.811661\pi$
$911$	−4.15820e7	−1.66001	−0.830003	+	0.557759i	$0.811661\pi$
$912$	555502.	0.0221156
$913$	−2.84322e6	−0.112884
$914$	−1.33675e7	−0.529281
$915$	−3.13115e7	−1.23638
$916$	8.04120e6	0.316652
$917$	895526.	0.0351686
$918$	7.73603e7	3.02978
$919$	3.34522e7	1.30658	0.653290	−	0.757108i	$-0.273388\pi$
$919$	3.34522e7	1.30658	0.653290	+	0.757108i	$0.273388\pi$
$920$	5.40442e6	0.210513
$921$	6.29515e7	2.44544
$922$	1.14376e7	0.443106
$923$	−1.48368e6	−0.0573238
$924$	739216.	0.0284834
$925$	316202.	0.0121510
$926$	2.69433e7	1.03258
$927$	7.86001e7	3.00416
$928$	3.60234e7	1.37314
$929$	−3.39463e7	−1.29049	−0.645243	−	0.763977i	$-0.723244\pi$
$929$	−3.39463e7	−1.29049	−0.645243	+	0.763977i	$0.723244\pi$
$930$	−1.05202e7	−0.398856
$931$	6.03113e6	0.228047
$932$	2.73531e7	1.03149
$933$	−4.69000e7	−1.76388
$934$	1.84083e7	0.690472
$935$	5.78481e6	0.216401
$936$	−2.36951e7	−0.884035
$937$	−9.27824e6	−0.345237	−0.172618	−	0.984989i	$-0.555223\pi$
$937$	−9.27824e6	−0.345237	−0.172618	+	0.984989i	$0.555223\pi$
$938$	1.77415e6	0.0658390
$939$	−6.35285e7	−2.35128
$940$	−4.84072e6	−0.178686
$941$	2.40439e7	0.885180	0.442590	−	0.896724i	$-0.354060\pi$
$941$	2.40439e7	0.885180	0.442590	+	0.896724i	$0.354060\pi$
$942$	−1.82660e7	−0.670683
$943$	5.12355e6	0.187625
$944$	235563.	0.00860353
$945$	−2.98506e6	−0.108736
$946$	−1.71090e6	−0.0621581
$947$	−1.51122e7	−0.547586	−0.273793	−	0.961789i	$-0.588278\pi$
$947$	−1.51122e7	−0.547586	−0.273793	+	0.961789i	$0.588278\pi$
$948$	−1.69159e7	−0.611329
$949$	5.87493e6	0.211757
$950$	765391.	0.0275153
$951$	7.79604e7	2.79526
$952$	3.40964e6	0.121932
$953$	−2.99992e7	−1.06998	−0.534992	−	0.844857i	$-0.679685\pi$
$953$	−2.99992e7	−1.06998	−0.534992	+	0.844857i	$0.679685\pi$
$954$	3.80155e7	1.35235
$955$	1.06186e7	0.376753
$956$	−2.42996e7	−0.859914
$957$	2.20959e7	0.779887
$958$	2.66389e6	0.0937784
$959$	−910958.	−0.0319854
$960$	−1.36003e7	−0.476289
$961$	−1.12715e7	−0.393707
$962$	354889.	0.0123639
$963$	−5.96581e6	−0.207302
$964$	6.24400e6	0.216406
$965$	−2.42686e6	−0.0838930
$966$	1.22775e6	0.0423320
$967$	−3.60659e7	−1.24031	−0.620155	−	0.784480i	$-0.712930\pi$
$967$	−3.60659e7	−1.24031	−0.620155	+	0.784480i	$0.712930\pi$
$968$	2.60712e6	0.0894279
$969$	2.05548e7	0.703240
$970$	1.36293e7	0.465099
$971$	−2.03990e7	−0.694321	−0.347161	−	0.937806i	$-0.612854\pi$
$971$	−2.03990e7	−0.694321	−0.347161	+	0.937806i	$0.612854\pi$
$972$	6.18448e7	2.09961
$973$	−1.90536e6	−0.0645200
$974$	1.15734e7	0.390899
$975$	3.84799e6	0.129635
$976$	2.17399e6	0.0730521
$977$	3.43448e7	1.15113	0.575565	−	0.817756i	$-0.304782\pi$
$977$	3.43448e7	1.15113	0.575565	+	0.817756i	$0.304782\pi$
$978$	6.74125e6	0.225369
$979$	1.12119e7	0.373872
$980$	8.55895e6	0.284679
$981$	2.57582e7	0.854560
$982$	−2.35360e7	−0.778849
$983$	−3.14271e7	−1.03734	−0.518670	−	0.854975i	$-0.673573\pi$
$983$	−3.14271e7	−1.03734	−0.518670	+	0.854975i	$0.673573\pi$
$984$	−2.23762e7	−0.736712
$985$	−9.75121e6	−0.320234
$986$	3.97872e7	1.30332
$987$	−2.81694e6	−0.0920418
$988$	−1.52970e6	−0.0498557
$989$	5.06014e6	0.164502
$990$	−6.60356e6	−0.214136
$991$	−3.06614e7	−0.991763	−0.495881	−	0.868390i	$-0.665155\pi$
$991$	−3.06614e7	−0.991763	−0.495881	+	0.868390i	$0.665155\pi$
$992$	2.44707e7	0.789529
$993$	3.09352e7	0.995589
$994$	−243713.	−0.00782370
$995$	−1.62348e7	−0.519864
$996$	−1.43369e7	−0.457939
$997$	−2.47970e7	−0.790062	−0.395031	−	0.918668i	$-0.629266\pi$
$997$	−2.47970e7	−0.790062	−0.395031	+	0.918668i	$0.629266\pi$
$998$	7.42414e6	0.235950
$999$	−6.03315e6	−0.191263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.15	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.39231 q^{2} -29.7744 q^{3} -20.4922 q^{4} +25.0000 q^{5} +101.004 q^{6} +10.0128 q^{7} +178.070 q^{8} +643.513 q^{9} +O(q^{10})\)	\(q-3.39231 q^{2} -29.7744 q^{3} -20.4922 q^{4} +25.0000 q^{5} +101.004 q^{6} +10.0128 q^{7} +178.070 q^{8} +643.513 q^{9} -84.8078 q^{10} +121.000 q^{11} +610.143 q^{12} -206.781 q^{13} -33.9665 q^{14} -744.359 q^{15} +51.6816 q^{16} +1912.33 q^{17} -2183.00 q^{18} -361.000 q^{19} -512.305 q^{20} -298.124 q^{21} -410.470 q^{22} +1214.00 q^{23} -5301.92 q^{24} +625.000 q^{25} +701.467 q^{26} -11925.0 q^{27} -205.184 q^{28} -6133.15 q^{29} +2525.10 q^{30} -4166.25 q^{31} -5873.56 q^{32} -3602.70 q^{33} -6487.23 q^{34} +250.319 q^{35} -13187.0 q^{36} +505.924 q^{37} +1224.62 q^{38} +6156.78 q^{39} +4451.75 q^{40} +4220.39 q^{41} +1011.33 q^{42} +4168.16 q^{43} -2479.56 q^{44} +16087.8 q^{45} -4118.26 q^{46} +9448.90 q^{47} -1538.79 q^{48} -16706.7 q^{49} -2120.20 q^{50} -56938.5 q^{51} +4237.41 q^{52} -17414.4 q^{53} +40453.3 q^{54} +3025.00 q^{55} +1782.98 q^{56} +10748.5 q^{57} +20805.6 q^{58} +4557.96 q^{59} +15253.6 q^{60} +42065.0 q^{61} +14133.2 q^{62} +6443.35 q^{63} +18271.1 q^{64} -5169.53 q^{65} +12221.5 q^{66} -52232.4 q^{67} -39187.9 q^{68} -36146.0 q^{69} -849.162 q^{70} +7175.10 q^{71} +114590. q^{72} -28411.3 q^{73} -1716.25 q^{74} -18609.0 q^{75} +7397.69 q^{76} +1211.55 q^{77} -20885.7 q^{78} -27724.6 q^{79} +1292.04 q^{80} +198686. q^{81} -14316.9 q^{82} -23497.6 q^{83} +6109.22 q^{84} +47808.3 q^{85} -14139.7 q^{86} +182611. q^{87} +21546.5 q^{88} +92660.5 q^{89} -54574.9 q^{90} -2070.46 q^{91} -24877.5 q^{92} +124048. q^{93} -32053.6 q^{94} -9025.00 q^{95} +174882. q^{96} -160708. q^{97} +56674.5 q^{98} +77865.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

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