LMFDB - Embedded newform 1045.6.a.a.1.1

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:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-11.2768 q^{2} +20.0827 q^{3} +95.1666 q^{4} -25.0000 q^{5} -226.469 q^{6} -33.0605 q^{7} -712.318 q^{8} +160.315 q^{9} +O(q^{10})$	\(q-11.2768 q^{2} +20.0827 q^{3} +95.1666 q^{4} -25.0000 q^{5} -226.469 q^{6} -33.0605 q^{7} -712.318 q^{8} +160.315 q^{9} +281.920 q^{10} +121.000 q^{11} +1911.20 q^{12} +134.380 q^{13} +372.817 q^{14} -502.068 q^{15} +4987.35 q^{16} -121.767 q^{17} -1807.85 q^{18} +361.000 q^{19} -2379.16 q^{20} -663.945 q^{21} -1364.49 q^{22} -163.868 q^{23} -14305.3 q^{24} +625.000 q^{25} -1515.37 q^{26} -1660.53 q^{27} -3146.26 q^{28} -3853.45 q^{29} +5661.73 q^{30} +447.330 q^{31} -33447.2 q^{32} +2430.01 q^{33} +1373.15 q^{34} +826.513 q^{35} +15256.7 q^{36} +8459.29 q^{37} -4070.93 q^{38} +2698.71 q^{39} +17807.9 q^{40} -12114.6 q^{41} +7487.18 q^{42} +17292.9 q^{43} +11515.2 q^{44} -4007.88 q^{45} +1847.91 q^{46} +2270.81 q^{47} +100159. q^{48} -15714.0 q^{49} -7048.01 q^{50} -2445.41 q^{51} +12788.4 q^{52} +33016.4 q^{53} +18725.5 q^{54} -3025.00 q^{55} +23549.6 q^{56} +7249.86 q^{57} +43454.7 q^{58} -345.219 q^{59} -47780.1 q^{60} -23114.7 q^{61} -5044.46 q^{62} -5300.10 q^{63} +217583. q^{64} -3359.49 q^{65} -27402.8 q^{66} +7507.08 q^{67} -11588.2 q^{68} -3290.92 q^{69} -9320.43 q^{70} -3884.91 q^{71} -114195. q^{72} -52254.6 q^{73} -95393.8 q^{74} +12551.7 q^{75} +34355.1 q^{76} -4000.32 q^{77} -30432.8 q^{78} +92757.0 q^{79} -124684. q^{80} -72304.6 q^{81} +136614. q^{82} +1429.78 q^{83} -63185.3 q^{84} +3044.18 q^{85} -195009. q^{86} -77387.7 q^{87} -86190.5 q^{88} -40090.6 q^{89} +45196.2 q^{90} -4442.66 q^{91} -15594.8 q^{92} +8983.60 q^{93} -25607.5 q^{94} -9025.00 q^{95} -671711. q^{96} -6282.18 q^{97} +177204. q^{98} +19398.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−11.2768	−1.99348	−0.996739	−	0.0806912i	$-0.974287\pi$
$2$	−11.2768	−1.99348	−0.996739	+	0.0806912i	$0.974287\pi$
$3$	20.0827	1.28831	0.644153	−	0.764896i	$-0.277210\pi$
$3$	20.0827	1.28831	0.644153	+	0.764896i	$0.277210\pi$
$4$	95.1666	2.97396
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−226.469	−2.56821
$7$	−33.0605	−0.255014	−0.127507	−	0.991838i	$-0.540698\pi$
$7$	−33.0605	−0.255014	−0.127507	+	0.991838i	$0.540698\pi$
$8$	−712.318	−3.93504
$9$	160.315	0.659734
$10$	281.920	0.891511
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	1911.20	3.83137
$13$	134.380	0.220534	0.110267	−	0.993902i	$-0.464829\pi$
$13$	134.380	0.220534	0.110267	+	0.993902i	$0.464829\pi$
$14$	372.817	0.508365
$15$	−502.068	−0.576148
$16$	4987.35	4.87046
$17$	−121.767	−0.102190	−0.0510949	−	0.998694i	$-0.516271\pi$
$17$	−121.767	−0.102190	−0.0510949	+	0.998694i	$0.516271\pi$
$18$	−1807.85	−1.31516
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−2379.16	−1.32999
$21$	−663.945	−0.328536
$22$	−1364.49	−0.601056
$23$	−163.868	−0.0645914	−0.0322957	−	0.999478i	$-0.510282\pi$
$23$	−163.868	−0.0645914	−0.0322957	+	0.999478i	$0.510282\pi$
$24$	−14305.3	−5.06954
$25$	625.000	0.200000
$26$	−1515.37	−0.439629
$27$	−1660.53	−0.438367
$28$	−3146.26	−0.758401
$29$	−3853.45	−0.850854	−0.425427	−	0.904993i	$-0.639876\pi$
$29$	−3853.45	−0.850854	−0.425427	+	0.904993i	$0.639876\pi$
$30$	5661.73	1.14854
$31$	447.330	0.0836034	0.0418017	−	0.999126i	$-0.486690\pi$
$31$	447.330	0.0836034	0.0418017	+	0.999126i	$0.486690\pi$
$32$	−33447.2	−5.77411
$33$	2430.01	0.388439
$34$	1373.15	0.203713
$35$	826.513	0.114046
$36$	15256.7	1.96202
$37$	8459.29	1.01585	0.507925	−	0.861401i	$-0.330413\pi$
$37$	8459.29	1.01585	0.507925	+	0.861401i	$0.330413\pi$
$38$	−4070.93	−0.457335
$39$	2698.71	0.284115
$40$	17807.9	1.75980
$41$	−12114.6	−1.12551	−0.562755	−	0.826624i	$-0.690259\pi$
$41$	−12114.6	−1.12551	−0.562755	+	0.826624i	$0.690259\pi$
$42$	7487.18	0.654930
$43$	17292.9	1.42626	0.713128	−	0.701033i	$-0.247278\pi$
$43$	17292.9	1.42626	0.713128	+	0.701033i	$0.247278\pi$
$44$	11515.2	0.896681
$45$	−4007.88	−0.295042
$46$	1847.91	0.128762
$47$	2270.81	0.149946	0.0749732	−	0.997186i	$-0.476113\pi$
$47$	2270.81	0.149946	0.0749732	+	0.997186i	$0.476113\pi$
$48$	100159.	6.27464
$49$	−15714.0	−0.934968
$50$	−7048.01	−0.398696
$51$	−2445.41	−0.131652
$52$	12788.4	0.655857
$53$	33016.4	1.61451	0.807253	−	0.590205i	$-0.200953\pi$
$53$	33016.4	1.61451	0.807253	+	0.590205i	$0.200953\pi$
$54$	18725.5	0.873876
$55$	−3025.00	−0.134840
$56$	23549.6	1.00349
$57$	7249.86	0.295558
$58$	43454.7	1.69616
$59$	−345.219	−0.0129111	−0.00645557	−	0.999979i	$-0.502055\pi$
$59$	−345.219	−0.0129111	−0.00645557	+	0.999979i	$0.502055\pi$
$60$	−47780.1	−1.71344
$61$	−23114.7	−0.795360	−0.397680	−	0.917524i	$-0.630185\pi$
$61$	−23114.7	−0.795360	−0.397680	+	0.917524i	$0.630185\pi$
$62$	−5044.46	−0.166662
$63$	−5300.10	−0.168241
$64$	217583.	6.64011
$65$	−3359.49	−0.0986256
$66$	−27402.8	−0.774345
$67$	7507.08	0.204307	0.102154	−	0.994769i	$-0.467427\pi$
$67$	7507.08	0.204307	0.102154	+	0.994769i	$0.467427\pi$
$68$	−11588.2	−0.303908
$69$	−3290.92	−0.0832135
$70$	−9320.43	−0.227348
$71$	−3884.91	−0.0914609	−0.0457304	−	0.998954i	$-0.514562\pi$
$71$	−3884.91	−0.0914609	−0.0457304	+	0.998954i	$0.514562\pi$
$72$	−114195.	−2.59608
$73$	−52254.6	−1.14767	−0.573836	−	0.818970i	$-0.694545\pi$
$73$	−52254.6	−1.14767	−0.573836	+	0.818970i	$0.694545\pi$
$74$	−95393.8	−2.02507
$75$	12551.7	0.257661
$76$	34355.1	0.682272
$77$	−4000.32	−0.0768897
$78$	−30432.8	−0.566377
$79$	92757.0	1.67216	0.836082	−	0.548604i	$-0.184841\pi$
$79$	92757.0	1.67216	0.836082	+	0.548604i	$0.184841\pi$
$80$	−124684.	−2.17813
$81$	−72304.6	−1.22449
$82$	136614.	2.24368
$83$	1429.78	0.0227810	0.0113905	−	0.999935i	$-0.496374\pi$
$83$	1429.78	0.0227810	0.0113905	+	0.999935i	$0.496374\pi$
$84$	−63185.3	−0.977053
$85$	3044.18	0.0457007
$86$	−195009.	−2.84321
$87$	−77387.7	−1.09616
$88$	−86190.5	−1.18646
$89$	−40090.6	−0.536497	−0.268249	−	0.963350i	$-0.586445\pi$
$89$	−40090.6	−0.536497	−0.268249	+	0.963350i	$0.586445\pi$
$90$	45196.2	0.588160
$91$	−4442.66	−0.0562392
$92$	−15594.8	−0.192092
$93$	8983.60	0.107707
$94$	−25607.5	−0.298915
$95$	−9025.00	−0.102598
$96$	−671711.	−7.43883
$97$	−6282.18	−0.0677924	−0.0338962	−	0.999425i	$-0.510792\pi$
$97$	−6282.18	−0.0677924	−0.0338962	+	0.999425i	$0.510792\pi$
$98$	177204.	1.86384
$99$	19398.2	0.198917
$100$	59479.1	0.594791
$101$	−102898.	−1.00370	−0.501850	−	0.864954i	$-0.667347\pi$
$101$	−102898.	−1.00370	−0.501850	+	0.864954i	$0.667347\pi$
$102$	27576.5	0.262445
$103$	43545.1	0.404432	0.202216	−	0.979341i	$-0.435186\pi$
$103$	43545.1	0.404432	0.202216	+	0.979341i	$0.435186\pi$
$104$	−95721.0	−0.867808
$105$	16598.6	0.146926
$106$	−372320.	−3.21848
$107$	20491.6	0.173028	0.0865141	−	0.996251i	$-0.472427\pi$
$107$	20491.6	0.173028	0.0865141	+	0.996251i	$0.472427\pi$
$108$	−158027.	−1.30368
$109$	−127871.	−1.03087	−0.515437	−	0.856927i	$-0.672370\pi$
$109$	−127871.	−1.03087	−0.515437	+	0.856927i	$0.672370\pi$
$110$	34112.4	0.268801
$111$	169885.	1.30873
$112$	−164884.	−1.24204
$113$	−17708.4	−0.130462	−0.0652309	−	0.997870i	$-0.520778\pi$
$113$	−17708.4	−0.130462	−0.0652309	+	0.997870i	$0.520778\pi$
$114$	−81755.3	−0.589188
$115$	4096.70	0.0288862
$116$	−366720.	−2.53040
$117$	21543.1	0.145493
$118$	3892.97	0.0257381
$119$	4025.68	0.0260599
$120$	357632.	2.26717
$121$	14641.0	0.0909091
$122$	260660.	1.58553
$123$	−243294.	−1.45000
$124$	42570.9	0.248633
$125$	−15625.0	−0.0894427
$126$	59768.3	0.335386
$127$	−140597.	−0.773510	−0.386755	−	0.922183i	$-0.626404\pi$
$127$	−140597.	−0.773510	−0.386755	+	0.922183i	$0.626404\pi$
$128$	−1.38333e6	−7.46280
$129$	347289.	1.83746
$130$	37884.3	0.196608
$131$	−97181.1	−0.494770	−0.247385	−	0.968917i	$-0.579571\pi$
$131$	−97181.1	−0.494770	−0.247385	+	0.968917i	$0.579571\pi$
$132$	231256.	1.15520
$133$	−11934.8	−0.0585043
$134$	−84656.0	−0.407282
$135$	41513.3	0.196044
$136$	86736.9	0.402121
$137$	301263.	1.37134	0.685668	−	0.727915i	$-0.259510\pi$
$137$	301263.	1.37134	0.685668	+	0.727915i	$0.259510\pi$
$138$	37111.0	0.165884
$139$	66319.1	0.291140	0.145570	−	0.989348i	$-0.453498\pi$
$139$	66319.1	0.291140	0.145570	+	0.989348i	$0.453498\pi$
$140$	78656.4	0.339167
$141$	45604.0	0.193177
$142$	43809.4	0.182325
$143$	16259.9	0.0664934
$144$	799548.	3.21320
$145$	96336.3	0.380513
$146$	589266.	2.28786
$147$	−315580.	−1.20453
$148$	805041.	3.02109
$149$	−143103.	−0.528059	−0.264029	−	0.964515i	$-0.585052\pi$
$149$	−143103.	−0.528059	−0.264029	+	0.964515i	$0.585052\pi$
$150$	−141543.	−0.513642
$151$	−95323.2	−0.340217	−0.170109	−	0.985425i	$-0.554412\pi$
$151$	−95323.2	−0.340217	−0.170109	+	0.985425i	$0.554412\pi$
$152$	−257147.	−0.902760
$153$	−19521.1	−0.0674181
$154$	45110.9	0.153278
$155$	−11183.3	−0.0373886
$156$	256827.	0.844945
$157$	64828.5	0.209902	0.104951	−	0.994477i	$-0.466531\pi$
$157$	64828.5	0.209902	0.104951	+	0.994477i	$0.466531\pi$
$158$	−1.04600e6	−3.33342
$159$	663059.	2.07998
$160$	836181.	2.58226
$161$	5417.56	0.0164717
$162$	815366.	2.44098
$163$	−204985.	−0.604302	−0.302151	−	0.953260i	$-0.597705\pi$
$163$	−204985.	−0.604302	−0.302151	+	0.953260i	$0.597705\pi$
$164$	−1.15291e6	−3.34722
$165$	−60750.2	−0.173715
$166$	−16123.3	−0.0454134
$167$	−148530.	−0.412119	−0.206059	−	0.978539i	$-0.566064\pi$
$167$	−148530.	−0.412119	−0.206059	+	0.978539i	$0.566064\pi$
$168$	472940.	1.29280
$169$	−353235.	−0.951365
$170$	−34328.6	−0.0911033
$171$	57873.8	0.151353
$172$	1.64571e6	4.24162
$173$	−291290.	−0.739964	−0.369982	−	0.929039i	$-0.620636\pi$
$173$	−291290.	−0.739964	−0.369982	+	0.929039i	$0.620636\pi$
$174$	872687.	2.18517
$175$	−20662.8	−0.0510028
$176$	603469.	1.46850
$177$	−6932.93	−0.0166335
$178$	452094.	1.06950
$179$	745459.	1.73897	0.869483	−	0.493962i	$-0.164452\pi$
$179$	745459.	1.73897	0.869483	+	0.493962i	$0.164452\pi$
$180$	−381416.	−0.877442
$181$	99376.3	0.225469	0.112734	−	0.993625i	$-0.464039\pi$
$181$	99376.3	0.225469	0.112734	+	0.993625i	$0.464039\pi$
$182$	50099.0	0.112112
$183$	−464206.	−1.02467
$184$	116726.	0.254170
$185$	−211482.	−0.454302
$186$	−101306.	−0.214711
$187$	−14733.8	−0.0308114
$188$	216105.	0.445934
$189$	54898.1	0.111790
$190$	101773.	0.204527
$191$	−873366.	−1.73226	−0.866130	−	0.499819i	$-0.833400\pi$
$191$	−873366.	−1.73226	−0.866130	+	0.499819i	$0.833400\pi$
$192$	4.36966e6	8.55450
$193$	425420.	0.822099	0.411050	−	0.911613i	$-0.365162\pi$
$193$	425420.	0.822099	0.411050	+	0.911613i	$0.365162\pi$
$194$	70843.0	0.135143
$195$	−67467.7	−0.127060
$196$	−1.49545e6	−2.78055
$197$	−93814.4	−0.172228	−0.0861140	−	0.996285i	$-0.527445\pi$
$197$	−93814.4	−0.172228	−0.0861140	+	0.996285i	$0.527445\pi$
$198$	−218749.	−0.396537
$199$	398760.	0.713804	0.356902	−	0.934142i	$-0.383833\pi$
$199$	398760.	0.713804	0.356902	+	0.934142i	$0.383833\pi$
$200$	−445199.	−0.787008
$201$	150763.	0.263211
$202$	1.16036e6	2.00086
$203$	127397.	0.216980
$204$	−232722.	−0.391527
$205$	302865.	0.503344
$206$	−491050.	−0.806227
$207$	−26270.6	−0.0426131
$208$	670198.	1.07410
$209$	43681.0	0.0691714
$210$	−187180.	−0.292894
$211$	563219.	0.870906	0.435453	−	0.900211i	$-0.356588\pi$
$211$	563219.	0.870906	0.435453	+	0.900211i	$0.356588\pi$
$212$	3.14206e6	4.80147
$213$	−78019.6	−0.117830
$214$	−231080.	−0.344928
$215$	−432323.	−0.637841
$216$	1.18283e6	1.72499
$217$	−14789.0	−0.0213201
$218$	1.44198e6	2.05503
$219$	−1.04941e6	−1.47855
$220$	−287879.	−0.401008
$221$	−16363.0	−0.0225363
$222$	−1.91577e6	−2.60892
$223$	−403301.	−0.543084	−0.271542	−	0.962427i	$-0.587534\pi$
$223$	−403301.	−0.543084	−0.271542	+	0.962427i	$0.587534\pi$
$224$	1.10578e6	1.47248
$225$	100197.	0.131947
$226$	199695.	0.260073
$227$	155836.	0.200726	0.100363	−	0.994951i	$-0.468000\pi$
$227$	155836.	0.200726	0.100363	+	0.994951i	$0.468000\pi$
$228$	689944.	0.878976
$229$	−1.30621e6	−1.64597	−0.822987	−	0.568060i	$-0.807694\pi$
$229$	−1.30621e6	−1.64597	−0.822987	+	0.568060i	$0.807694\pi$
$230$	−46197.8	−0.0575839
$231$	−80337.3	−0.0990575
$232$	2.74488e6	3.34814
$233$	−610951.	−0.737253	−0.368626	−	0.929578i	$-0.620172\pi$
$233$	−610951.	−0.737253	−0.368626	+	0.929578i	$0.620172\pi$
$234$	−242938.	−0.290038
$235$	−56770.2	−0.0670581
$236$	−32853.3	−0.0383971
$237$	1.86281e6	2.15426
$238$	−45396.9	−0.0519498
$239$	659741.	0.747099	0.373550	−	0.927610i	$-0.378141\pi$
$239$	659741.	0.747099	0.373550	+	0.927610i	$0.378141\pi$
$240$	−2.50399e6	−2.80610
$241$	−726300.	−0.805515	−0.402757	−	0.915307i	$-0.631948\pi$
$241$	−726300.	−0.805515	−0.402757	+	0.915307i	$0.631948\pi$
$242$	−165104.	−0.181225
$243$	−1.04856e6	−1.13914
$244$	−2.19975e6	−2.36536
$245$	392850.	0.418130
$246$	2.74358e6	2.89055
$247$	48511.0	0.0505939
$248$	−318641.	−0.328983
$249$	28713.8	0.0293489
$250$	176200.	0.178302
$251$	1.16619e6	1.16838	0.584190	−	0.811617i	$-0.301412\pi$
$251$	1.16619e6	1.16838	0.584190	+	0.811617i	$0.301412\pi$
$252$	−504393.	−0.500343
$253$	−19828.0	−0.0194750
$254$	1.58548e6	1.54198
$255$	61135.4	0.0588765
$256$	8.63694e6	8.23683
$257$	−343030.	−0.323966	−0.161983	−	0.986794i	$-0.551789\pi$
$257$	−343030.	−0.323966	−0.161983	+	0.986794i	$0.551789\pi$
$258$	−3.91632e6	−3.66293
$259$	−279668.	−0.259056
$260$	−319711.	−0.293308
$261$	−617767.	−0.561337
$262$	1.09589e6	0.986314
$263$	−971692.	−0.866242	−0.433121	−	0.901336i	$-0.642588\pi$
$263$	−971692.	−0.866242	−0.433121	+	0.901336i	$0.642588\pi$
$264$	−1.73094e6	−1.52852
$265$	−825410.	−0.722029
$266$	134587.	0.116627
$267$	−805128.	−0.691173
$268$	714423.	0.607601
$269$	−1.30488e6	−1.09949	−0.549744	−	0.835333i	$-0.685275\pi$
$269$	−1.30488e6	−1.09949	−0.549744	+	0.835333i	$0.685275\pi$
$270$	−468138.	−0.390809
$271$	−913066.	−0.755230	−0.377615	−	0.925963i	$-0.623256\pi$
$271$	−913066.	−0.755230	−0.377615	+	0.925963i	$0.623256\pi$
$272$	−607295.	−0.497711
$273$	−89220.6	−0.0724533
$274$	−3.39728e6	−2.73373
$275$	75625.0	0.0603023
$276$	−313185.	−0.247473
$277$	−2.05507e6	−1.60927	−0.804633	−	0.593773i	$-0.797638\pi$
$277$	−2.05507e6	−1.60927	−0.804633	+	0.593773i	$0.797638\pi$
$278$	−747868.	−0.580381
$279$	71713.9	0.0551560
$280$	−588740.	−0.448775
$281$	−1.51745e6	−1.14643	−0.573217	−	0.819404i	$-0.694305\pi$
$281$	−1.51745e6	−1.14643	−0.573217	+	0.819404i	$0.694305\pi$
$282$	−514268.	−0.385094
$283$	−127889.	−0.0949222	−0.0474611	−	0.998873i	$-0.515113\pi$
$283$	−127889.	−0.0949222	−0.0474611	+	0.998873i	$0.515113\pi$
$284$	−369714.	−0.272001
$285$	−181246.	−0.132177
$286$	−183360.	−0.132553
$287$	400515.	0.287021
$288$	−5.36210e6	−3.80938
$289$	−1.40503e6	−0.989557
$290$	−1.08637e6	−0.758545
$291$	−126163.	−0.0873374
$292$	−4.97289e6	−3.41312
$293$	−2.62100e6	−1.78360	−0.891799	−	0.452431i	$-0.850557\pi$
$293$	−2.62100e6	−1.78360	−0.891799	+	0.452431i	$0.850557\pi$
$294$	3.55874e6	2.40119
$295$	8630.47	0.00577403
$296$	−6.02570e6	−3.99741
$297$	−200924.	−0.132173
$298$	1.61374e6	1.05267
$299$	−22020.5	−0.0142446
$300$	1.19450e6	0.766273
$301$	−571713.	−0.363716
$302$	1.07494e6	0.678215
$303$	−2.06647e6	−1.29307
$304$	1.80043e6	1.11736
$305$	577867.	0.355696
$306$	220136.	0.134396
$307$	3.07359e6	1.86123	0.930616	−	0.365997i	$-0.119272\pi$
$307$	3.07359e6	1.86123	0.930616	+	0.365997i	$0.119272\pi$
$308$	−380697.	−0.228667
$309$	874503.	0.521033
$310$	126112.	0.0745333
$311$	297056.	0.174156	0.0870779	−	0.996202i	$-0.472247\pi$
$311$	297056.	0.174156	0.0870779	+	0.996202i	$0.472247\pi$
$312$	−1.92234e6	−1.11800
$313$	2.19740e6	1.26779	0.633896	−	0.773418i	$-0.281455\pi$
$313$	2.19740e6	1.26779	0.633896	+	0.773418i	$0.281455\pi$
$314$	−731059.	−0.418435
$315$	132503.	0.0752399
$316$	8.82737e6	4.97294
$317$	1.07101e6	0.598614	0.299307	−	0.954157i	$-0.403245\pi$
$317$	1.07101e6	0.598614	0.299307	+	0.954157i	$0.403245\pi$
$318$	−7.47719e6	−4.14639
$319$	−466268.	−0.256542
$320$	−5.43958e6	−2.96955
$321$	411527.	0.222913
$322$	−61092.8	−0.0328360
$323$	−43957.9	−0.0234440
$324$	−6.88098e6	−3.64156
$325$	83987.2	0.0441067
$326$	2.31158e6	1.20466
$327$	−2.56800e6	−1.32808
$328$	8.62945e6	4.42893
$329$	−75074.1	−0.0382385
$330$	685069.	0.346298
$331$	−3.80099e6	−1.90690	−0.953448	−	0.301557i	$-0.902494\pi$
$331$	−3.80099e6	−1.90690	−0.953448	+	0.301557i	$0.902494\pi$
$332$	136067.	0.0677496
$333$	1.35615e6	0.670190
$334$	1.67494e6	0.821550
$335$	−187677.	−0.0913691
$336$	−3.31132e6	−1.60012
$337$	1.35183e6	0.648404	0.324202	−	0.945988i	$-0.394904\pi$
$337$	1.35183e6	0.648404	0.324202	+	0.945988i	$0.394904\pi$
$338$	3.98337e6	1.89653
$339$	−355633.	−0.168075
$340$	289704.	0.135912
$341$	54127.0	0.0252074
$342$	−652632.	−0.301720
$343$	1.07516e6	0.493444
$344$	−1.23181e7	−5.61237
$345$	82272.9	0.0372142
$346$	3.28483e6	1.47510
$347$	65855.7	0.0293609	0.0146804	−	0.999892i	$-0.495327\pi$
$347$	65855.7	0.0293609	0.0146804	+	0.999892i	$0.495327\pi$
$348$	−7.36473e6	−3.25993
$349$	4.24211e6	1.86431	0.932155	−	0.362061i	$-0.117927\pi$
$349$	4.24211e6	1.86431	0.932155	+	0.362061i	$0.117927\pi$
$350$	233011.	0.101673
$351$	−223142.	−0.0966747
$352$	−4.04712e6	−1.74096
$353$	2.47380e6	1.05664	0.528322	−	0.849044i	$-0.322822\pi$
$353$	2.47380e6	1.05664	0.528322	+	0.849044i	$0.322822\pi$
$354$	78181.4	0.0331585
$355$	97122.8	0.0409025
$356$	−3.81529e6	−1.59552
$357$	80846.6	0.0335731
$358$	−8.40641e6	−3.46659
$359$	−3.65348e6	−1.49614	−0.748068	−	0.663622i	$-0.769018\pi$
$359$	−3.65348e6	−1.49614	−0.748068	+	0.663622i	$0.769018\pi$
$360$	2.85489e6	1.16100
$361$	130321.	0.0526316
$362$	−1.12065e6	−0.449467
$363$	294031.	0.117119
$364$	−422792.	−0.167253
$365$	1.30637e6	0.513254
$366$	5.23476e6	2.04265
$367$	−1.42550e6	−0.552461	−0.276231	−	0.961091i	$-0.589085\pi$
$367$	−1.42550e6	−0.552461	−0.276231	+	0.961091i	$0.589085\pi$
$368$	−817267.	−0.314590
$369$	−1.94216e6	−0.742537
$370$	2.38485e6	0.905641
$371$	−1.09154e6	−0.411722
$372$	854939.	0.320315
$373$	2.95500e6	1.09973	0.549864	−	0.835254i	$-0.314680\pi$
$373$	2.95500e6	1.09973	0.549864	+	0.835254i	$0.314680\pi$
$374$	166151.	0.0614219
$375$	−313792.	−0.115230
$376$	−1.61754e6	−0.590045
$377$	−517825.	−0.187642
$378$	−619075.	−0.222851
$379$	91110.0	0.0325813	0.0162906	−	0.999867i	$-0.494814\pi$
$379$	91110.0	0.0325813	0.0162906	+	0.999867i	$0.494814\pi$
$380$	−858878.	−0.305121
$381$	−2.82356e6	−0.996518
$382$	9.84879e6	3.45322
$383$	−4.14722e6	−1.44464	−0.722321	−	0.691558i	$-0.756925\pi$
$383$	−4.14722e6	−1.44464	−0.722321	+	0.691558i	$0.756925\pi$
$384$	−2.77811e7	−9.61438
$385$	100008.	0.0343861
$386$	−4.79738e6	−1.63884
$387$	2.77232e6	0.940950
$388$	−597853.	−0.201612
$389$	−2.98761e6	−1.00104	−0.500518	−	0.865726i	$-0.666857\pi$
$389$	−2.98761e6	−1.00104	−0.500518	+	0.865726i	$0.666857\pi$
$390$	760820.	0.253291
$391$	19953.7	0.00660059
$392$	1.11934e7	3.67913
$393$	−1.95166e6	−0.637416
$394$	1.05793e6	0.343333
$395$	−2.31892e6	−0.747815
$396$	1.84606e6	0.591571
$397$	1.77299e6	0.564587	0.282293	−	0.959328i	$-0.408905\pi$
$397$	1.77299e6	0.564587	0.282293	+	0.959328i	$0.408905\pi$
$398$	−4.49674e6	−1.42295
$399$	−239684.	−0.0753714
$400$	3.11709e6	0.974091
$401$	−3.23770e6	−1.00549	−0.502743	−	0.864436i	$-0.667676\pi$
$401$	−3.23770e6	−1.00549	−0.502743	+	0.864436i	$0.667676\pi$
$402$	−1.70012e6	−0.524705
$403$	60112.0	0.0184374
$404$	−9.79247e6	−2.98496
$405$	1.80762e6	0.547606
$406$	−1.43663e6	−0.432544
$407$	1.02357e6	0.306290
$408$	1.74191e6	0.518055
$409$	1.91089e6	0.564843	0.282421	−	0.959290i	$-0.408862\pi$
$409$	1.91089e6	0.564843	0.282421	+	0.959290i	$0.408862\pi$
$410$	−3.41535e6	−1.00340
$411$	6.05017e6	1.76670
$412$	4.14404e6	1.20276
$413$	11413.1	0.00329252
$414$	296248.	0.0849484
$415$	−35744.4	−0.0101880
$416$	−4.49462e6	−1.27339
$417$	1.33187e6	0.375077
$418$	−492583.	−0.137892
$419$	3.80102e6	1.05771	0.528853	−	0.848713i	$-0.322622\pi$
$419$	3.80102e6	1.05771	0.528853	+	0.848713i	$0.322622\pi$
$420$	1.57963e6	0.436951
$421$	3.39145e6	0.932568	0.466284	−	0.884635i	$-0.345592\pi$
$421$	3.39145e6	0.932568	0.466284	+	0.884635i	$0.345592\pi$
$422$	−6.35132e6	−1.73613
$423$	364046.	0.0989247
$424$	−2.35182e7	−6.35315
$425$	−76104.5	−0.0204380
$426$	879812.	0.234891
$427$	764184.	0.202828
$428$	1.95012e6	0.514578
$429$	326543.	0.0856639
$430$	4.87523e6	1.27152
$431$	−4.33803e6	−1.12486	−0.562431	−	0.826845i	$-0.690134\pi$
$431$	−4.33803e6	−1.12486	−0.562431	+	0.826845i	$0.690134\pi$
$432$	−8.28166e6	−2.13505
$433$	743867.	0.190667	0.0953335	−	0.995445i	$-0.469608\pi$
$433$	743867.	0.190667	0.0953335	+	0.995445i	$0.469608\pi$
$434$	166772.	0.0425011
$435$	1.93469e6	0.490218
$436$	−1.21690e7	−3.06577
$437$	−59156.4	−0.0148183
$438$	1.18341e7	2.94746
$439$	−1.71249e6	−0.424099	−0.212049	−	0.977259i	$-0.568014\pi$
$439$	−1.71249e6	−0.424099	−0.212049	+	0.977259i	$0.568014\pi$
$440$	2.15476e6	0.530600
$441$	−2.51920e6	−0.616830
$442$	184523.	0.0449256
$443$	5.99398e6	1.45113	0.725564	−	0.688154i	$-0.241579\pi$
$443$	5.99398e6	1.45113	0.725564	+	0.688154i	$0.241579\pi$
$444$	1.61674e7	3.89209
$445$	1.00227e6	0.239929
$446$	4.54795e6	1.08263
$447$	−2.87389e6	−0.680302
$448$	−7.19341e6	−1.69332
$449$	−6.56209e6	−1.53612	−0.768062	−	0.640375i	$-0.778779\pi$
$449$	−6.56209e6	−1.53612	−0.768062	+	0.640375i	$0.778779\pi$
$450$	−1.12990e6	−0.263033
$451$	−1.46587e6	−0.339354
$452$	−1.68525e6	−0.387988
$453$	−1.91435e6	−0.438304
$454$	−1.75734e6	−0.400143
$455$	111066.	0.0251509
$456$	−5.16420e6	−1.16303
$457$	−7.94094e6	−1.77861	−0.889306	−	0.457313i	$-0.848812\pi$
$457$	−7.94094e6	−1.77861	−0.889306	+	0.457313i	$0.848812\pi$
$458$	1.47298e7	3.28121
$459$	202198.	0.0447967
$460$	389869.	0.0859061
$461$	556671.	0.121996	0.0609980	−	0.998138i	$-0.480572\pi$
$461$	556671.	0.121996	0.0609980	+	0.998138i	$0.480572\pi$
$462$	905949.	0.197469
$463$	1.57647e6	0.341769	0.170884	−	0.985291i	$-0.445338\pi$
$463$	1.57647e6	0.341769	0.170884	+	0.985291i	$0.445338\pi$
$464$	−1.92185e7	−4.14405
$465$	−224590.	−0.0481680
$466$	6.88958e6	1.46970
$467$	−4.00819e6	−0.850465	−0.425232	−	0.905084i	$-0.639808\pi$
$467$	−4.00819e6	−0.850465	−0.425232	+	0.905084i	$0.639808\pi$
$468$	2.05018e6	0.432691
$469$	−248188.	−0.0521013
$470$	640188.	0.133679
$471$	1.30193e6	0.270418
$472$	245906.	0.0508058
$473$	2.09245e6	0.430033
$474$	−2.10066e7	−4.29447
$475$	225625.	0.0458831
$476$	383110.	0.0775009
$477$	5.29303e6	1.06514
$478$	−7.43977e6	−1.48933
$479$	1.01467e6	0.202062	0.101031	−	0.994883i	$-0.467786\pi$
$479$	1.01467e6	0.202062	0.101031	+	0.994883i	$0.467786\pi$
$480$	1.67928e7	3.32674
$481$	1.13676e6	0.224029
$482$	8.19035e6	1.60578
$483$	108799.	0.0212206
$484$	1.39333e6	0.270360
$485$	157054.	0.0303177
$486$	1.18245e7	2.27086
$487$	7.06812e6	1.35046	0.675230	−	0.737607i	$-0.264044\pi$
$487$	7.06812e6	1.35046	0.675230	+	0.737607i	$0.264044\pi$
$488$	1.64650e7	3.12977
$489$	−4.11666e6	−0.778526
$490$	−4.43010e6	−0.833534
$491$	8.20749e6	1.53641	0.768204	−	0.640205i	$-0.221150\pi$
$491$	8.20749e6	1.53641	0.768204	+	0.640205i	$0.221150\pi$
$492$	−2.31535e7	−4.31224
$493$	469224.	0.0869486
$494$	−547050.	−0.100858
$495$	−484954.	−0.0889585
$496$	2.23099e6	0.407187
$497$	128437.	0.0233238
$498$	−323800.	−0.0585064
$499$	1.21499e6	0.218435	0.109218	−	0.994018i	$-0.465165\pi$
$499$	1.21499e6	0.218435	0.109218	+	0.994018i	$0.465165\pi$
$500$	−1.48698e6	−0.265999
$501$	−2.98288e6	−0.530935
$502$	−1.31509e7	−2.32914
$503$	−8.25962e6	−1.45559	−0.727797	−	0.685793i	$-0.759456\pi$
$503$	−8.25962e6	−1.45559	−0.727797	+	0.685793i	$0.759456\pi$
$504$	3.77536e6	0.662037
$505$	2.57246e6	0.448869
$506$	223597.	0.0388231
$507$	−7.09392e6	−1.22565
$508$	−1.33801e7	−2.30038
$509$	−8.95947e6	−1.53281	−0.766404	−	0.642359i	$-0.777956\pi$
$509$	−8.95947e6	−1.53281	−0.766404	+	0.642359i	$0.777956\pi$
$510$	−689412.	−0.117369
$511$	1.72756e6	0.292673
$512$	−5.31305e7	−8.95713
$513$	−599452.	−0.100568
$514$	3.86829e6	0.645819
$515$	−1.08863e6	−0.180868
$516$	3.30503e7	5.46451
$517$	274768.	0.0452105
$518$	3.15377e6	0.516423
$519$	−5.84990e6	−0.953300
$520$	2.39302e6	0.388096
$521$	−9.52874e6	−1.53795	−0.768974	−	0.639281i	$-0.779232\pi$
$521$	−9.52874e6	−1.53795	−0.768974	+	0.639281i	$0.779232\pi$
$522$	6.96645e6	1.11901
$523$	−1.03798e7	−1.65935	−0.829673	−	0.558250i	$-0.811473\pi$
$523$	−1.03798e7	−1.65935	−0.829673	+	0.558250i	$0.811473\pi$
$524$	−9.24840e6	−1.47143
$525$	−414965.	−0.0657073
$526$	1.09576e7	1.72684
$527$	−54470.1	−0.00854342
$528$	1.21193e7	1.89188
$529$	−6.40949e6	−0.995828
$530$	9.30799e6	1.43935
$531$	−55343.9	−0.00851791
$532$	−1.13580e6	−0.173989
$533$	−1.62796e6	−0.248213
$534$	9.07928e6	1.37784
$535$	−512290.	−0.0773805
$536$	−5.34743e6	−0.803958
$537$	1.49708e7	2.24032
$538$	1.47149e7	2.19181
$539$	−1.90139e6	−0.281903
$540$	3.95068e6	0.583026
$541$	1.02187e7	1.50108	0.750539	−	0.660826i	$-0.229794\pi$
$541$	1.02187e7	1.50108	0.750539	+	0.660826i	$0.229794\pi$
$542$	1.02965e7	1.50553
$543$	1.99575e6	0.290473
$544$	4.07277e6	0.590056
$545$	3.19677e6	0.461021
$546$	1.00612e6	0.144434
$547$	1.05442e7	1.50676	0.753382	−	0.657583i	$-0.228421\pi$
$547$	1.05442e7	1.50676	0.753382	+	0.657583i	$0.228421\pi$
$548$	2.86701e7	4.07829
$549$	−3.70564e6	−0.524726
$550$	−852809.	−0.120211
$551$	−1.39110e6	−0.195199
$552$	2.34418e6	0.327448
$553$	−3.06659e6	−0.426426
$554$	2.31747e7	3.20804
$555$	−4.24714e6	−0.585280
$556$	6.31136e6	0.865837
$557$	−482527.	−0.0658997	−0.0329498	−	0.999457i	$-0.510490\pi$
$557$	−482527.	−0.0658997	−0.0329498	+	0.999457i	$0.510490\pi$
$558$	−808704.	−0.109952
$559$	2.32382e6	0.314538
$560$	4.12211e6	0.555455
$561$	−295895.	−0.0396945
$562$	1.71120e7	2.28539
$563$	−8.21336e6	−1.09207	−0.546034	−	0.837763i	$-0.683863\pi$
$563$	−8.21336e6	−1.09207	−0.546034	+	0.837763i	$0.683863\pi$
$564$	4.33998e6	0.574500
$565$	442710.	0.0583443
$566$	1.44218e6	0.189225
$567$	2.39043e6	0.312261
$568$	2.76729e6	0.359902
$569$	1.51180e7	1.95755	0.978775	−	0.204940i	$-0.0656999\pi$
$569$	1.51180e7	1.95755	0.978775	+	0.204940i	$0.0656999\pi$
$570$	2.04388e6	0.263493
$571$	−5.41498e6	−0.695034	−0.347517	−	0.937674i	$-0.612975\pi$
$571$	−5.41498e6	−0.695034	−0.347517	+	0.937674i	$0.612975\pi$
$572$	1.54740e6	0.197748
$573$	−1.75396e7	−2.23168
$574$	−4.51653e6	−0.572170
$575$	−102418.	−0.0129183
$576$	3.48819e7	4.38070
$577$	−6.30163e6	−0.787977	−0.393988	−	0.919115i	$-0.628905\pi$
$577$	−6.30163e6	−0.787977	−0.393988	+	0.919115i	$0.628905\pi$
$578$	1.58443e7	1.97266
$579$	8.54358e6	1.05912
$580$	9.16799e6	1.13163
$581$	−47269.1	−0.00580947
$582$	1.42272e6	0.174105
$583$	3.99498e6	0.486792
$584$	3.72219e7	4.51613
$585$	−538577.	−0.0650667
$586$	2.95565e7	3.55557
$587$	−1.21372e7	−1.45386	−0.726929	−	0.686713i	$-0.759053\pi$
$587$	−1.21372e7	−1.45386	−0.726929	+	0.686713i	$0.759053\pi$
$588$	−3.00327e7	−3.58220
$589$	161486.	0.0191799
$590$	−97324.2	−0.0115104
$591$	−1.88405e6	−0.221883
$592$	4.21894e7	4.94765
$593$	−1.65428e7	−1.93185	−0.965923	−	0.258829i	$-0.916663\pi$
$593$	−1.65428e7	−1.93185	−0.965923	+	0.258829i	$0.916663\pi$
$594$	2.26579e6	0.263483
$595$	−100642.	−0.0116543
$596$	−1.36186e7	−1.57042
$597$	8.00818e6	0.919598
$598$	248321.	0.0283963
$599$	1.32995e7	1.51450	0.757250	−	0.653125i	$-0.226543\pi$
$599$	1.32995e7	1.51450	0.757250	+	0.653125i	$0.226543\pi$
$600$	−8.94080e6	−1.01391
$601$	−1.39035e7	−1.57014	−0.785072	−	0.619405i	$-0.787374\pi$
$601$	−1.39035e7	−1.57014	−0.785072	+	0.619405i	$0.787374\pi$
$602$	6.44711e6	0.725059
$603$	1.20350e6	0.134789
$604$	−9.07158e6	−1.01179
$605$	−366025.	−0.0406558
$606$	2.33033e7	2.57772
$607$	−1.05201e7	−1.15891	−0.579455	−	0.815004i	$-0.696734\pi$
$607$	−1.05201e7	−1.15891	−0.579455	+	0.815004i	$0.696734\pi$
$608$	−1.20745e7	−1.32467
$609$	2.55848e6	0.279536
$610$	−6.51650e6	−0.709072
$611$	305150.	0.0330682
$612$	−1.85776e6	−0.200498
$613$	2.53352e6	0.272316	0.136158	−	0.990687i	$-0.456524\pi$
$613$	2.53352e6	0.272316	0.136158	+	0.990687i	$0.456524\pi$
$614$	−3.46604e7	−3.71033
$615$	6.08235e6	0.648461
$616$	2.84950e6	0.302564
$617$	2.30971e6	0.244255	0.122128	−	0.992514i	$-0.461028\pi$
$617$	2.30971e6	0.244255	0.122128	+	0.992514i	$0.461028\pi$
$618$	−9.86161e6	−1.03867
$619$	−1.05536e7	−1.10707	−0.553533	−	0.832827i	$-0.686721\pi$
$619$	−1.05536e7	−1.10707	−0.553533	+	0.832827i	$0.686721\pi$
$620$	−1.06427e6	−0.111192
$621$	272108.	0.0283148
$622$	−3.34985e6	−0.347176
$623$	1.32542e6	0.136814
$624$	1.34594e7	1.38377
$625$	390625.	0.0400000
$626$	−2.47797e7	−2.52732
$627$	877233.	0.0891140
$628$	6.16951e6	0.624240
$629$	−1.03006e6	−0.103810
$630$	−1.49421e6	−0.149989
$631$	−1.97249e7	−1.97216	−0.986079	−	0.166276i	$-0.946826\pi$
$631$	−1.97249e7	−1.97216	−0.986079	+	0.166276i	$0.946826\pi$
$632$	−6.60725e7	−6.58003
$633$	1.13110e7	1.12199
$634$	−1.20776e7	−1.19332
$635$	3.51492e6	0.345924
$636$	6.31010e7	6.18577
$637$	−2.11164e6	−0.206192
$638$	5.25801e6	0.511411
$639$	−622811.	−0.0603398
$640$	3.45833e7	3.33747
$641$	4.66760e6	0.448692	0.224346	−	0.974510i	$-0.427975\pi$
$641$	4.66760e6	0.448692	0.224346	+	0.974510i	$0.427975\pi$
$642$	−4.64072e6	−0.444373
$643$	−1.41681e7	−1.35140	−0.675699	−	0.737177i	$-0.736158\pi$
$643$	−1.41681e7	−1.35140	−0.675699	+	0.737177i	$0.736158\pi$
$644$	515571.	0.0489862
$645$	−8.68223e6	−0.821735
$646$	495706.	0.0467350
$647$	1.46011e7	1.37127	0.685637	−	0.727944i	$-0.259524\pi$
$647$	1.46011e7	1.37127	0.685637	+	0.727944i	$0.259524\pi$
$648$	5.15039e7	4.81840
$649$	−41771.5	−0.00389285
$650$	−947109.	−0.0879258
$651$	−297002.	−0.0274668
$652$	−1.95078e7	−1.79717
$653$	−3.08478e6	−0.283101	−0.141550	−	0.989931i	$-0.545209\pi$
$653$	−3.08478e6	−0.283101	−0.141550	+	0.989931i	$0.545209\pi$
$654$	2.89588e7	2.64750
$655$	2.42953e6	0.221268
$656$	−6.04197e7	−5.48175
$657$	−8.37721e6	−0.757157
$658$	846597.	0.0762276
$659$	−2.45303e6	−0.220034	−0.110017	−	0.993930i	$-0.535091\pi$
$659$	−2.45303e6	−0.220034	−0.110017	+	0.993930i	$0.535091\pi$
$660$	−5.78139e6	−0.516621
$661$	8.55200e6	0.761315	0.380657	−	0.924716i	$-0.375698\pi$
$661$	8.55200e6	0.761315	0.380657	+	0.924716i	$0.375698\pi$
$662$	4.28631e7	3.80136
$663$	−328614.	−0.0290337
$664$	−1.01845e6	−0.0896440
$665$	298371.	0.0261639
$666$	−1.52931e7	−1.33601
$667$	631458.	0.0549578
$668$	−1.41351e7	−1.22562
$669$	−8.09937e6	−0.699658
$670$	2.11640e6	0.182142
$671$	−2.79688e6	−0.239810
$672$	2.22071e7	1.89701
$673$	−1.06188e7	−0.903729	−0.451864	−	0.892087i	$-0.649241\pi$
$673$	−1.06188e7	−0.903729	−0.451864	+	0.892087i	$0.649241\pi$
$674$	−1.52443e7	−1.29258
$675$	−1.03783e6	−0.0876735
$676$	−3.36162e7	−2.82932
$677$	−1.29477e7	−1.08572	−0.542862	−	0.839822i	$-0.682659\pi$
$677$	−1.29477e7	−1.08572	−0.542862	+	0.839822i	$0.682659\pi$
$678$	4.01041e6	0.335054
$679$	207692.	0.0172880
$680$	−2.16842e6	−0.179834
$681$	3.12961e6	0.258597
$682$	−610380.	−0.0502504
$683$	−2.58029e6	−0.211649	−0.105825	−	0.994385i	$-0.533748\pi$
$683$	−2.58029e6	−0.211649	−0.105825	+	0.994385i	$0.533748\pi$
$684$	5.50765e6	0.450118
$685$	−7.53156e6	−0.613280
$686$	−1.21244e7	−0.983670
$687$	−2.62322e7	−2.12052
$688$	8.62459e7	6.94652
$689$	4.43673e6	0.356053
$690$	−927776.	−0.0741857
$691$	−1.82324e7	−1.45261	−0.726305	−	0.687373i	$-0.758764\pi$
$691$	−1.82324e7	−1.45261	−0.726305	+	0.687373i	$0.758764\pi$
$692$	−2.77211e7	−2.20062
$693$	−641313.	−0.0507267
$694$	−742642.	−0.0585303
$695$	−1.65798e6	−0.130202
$696$	5.51247e7	4.31343
$697$	1.47516e6	0.115016
$698$	−4.78374e7	−3.71646
$699$	−1.22695e7	−0.949808
$700$	−1.96641e6	−0.151680
$701$	−1.96041e7	−1.50679	−0.753394	−	0.657570i	$-0.771584\pi$
$701$	−1.96041e7	−1.50679	−0.753394	+	0.657570i	$0.771584\pi$
$702$	2.51633e6	0.192719
$703$	3.05380e6	0.233052
$704$	2.63276e7	2.00207
$705$	−1.14010e6	−0.0863914
$706$	−2.78966e7	−2.10640
$707$	3.40187e6	0.255958
$708$	−659783.	−0.0494673
$709$	−7.86037e6	−0.587256	−0.293628	−	0.955920i	$-0.594863\pi$
$709$	−7.86037e6	−0.587256	−0.293628	+	0.955920i	$0.594863\pi$
$710$	−1.09524e6	−0.0815383
$711$	1.48704e7	1.10318
$712$	2.85573e7	2.11114
$713$	−73303.1	−0.00540006
$714$	−911693.	−0.0669272
$715$	−406498.	−0.0297368
$716$	7.09428e7	5.17161
$717$	1.32494e7	0.962493
$718$	4.11997e7	2.98251
$719$	1.91561e6	0.138192	0.0690961	−	0.997610i	$-0.477988\pi$
$719$	1.91561e6	0.138192	0.0690961	+	0.997610i	$0.477988\pi$
$720$	−1.99887e7	−1.43699
$721$	−1.43962e6	−0.103136
$722$	−1.46961e6	−0.104920
$723$	−1.45861e7	−1.03775
$724$	9.45730e6	0.670534
$725$	−2.40841e6	−0.170171
$726$	−3.31573e6	−0.233474
$727$	680694.	0.0477657	0.0238829	−	0.999715i	$-0.492397\pi$
$727$	680694.	0.0477657	0.0238829	+	0.999715i	$0.492397\pi$
$728$	3.16458e6	0.221303
$729$	−3.48797e6	−0.243083
$730$	−1.47316e7	−1.02316
$731$	−2.10571e6	−0.145749
$732$	−4.41769e7	−3.04731
$733$	−1.49937e7	−1.03074	−0.515371	−	0.856967i	$-0.672346\pi$
$733$	−1.49937e7	−1.03074	−0.515371	+	0.856967i	$0.672346\pi$
$734$	1.60751e7	1.10132
$735$	7.88949e6	0.538680
$736$	5.48093e6	0.372958
$737$	908357.	0.0616010
$738$	2.19013e7	1.48023
$739$	9.91587e6	0.667913	0.333956	−	0.942589i	$-0.391616\pi$
$739$	9.91587e6	0.667913	0.333956	+	0.942589i	$0.391616\pi$
$740$	−2.01260e7	−1.35107
$741$	974233.	0.0651804
$742$	1.23091e7	0.820759
$743$	1.96869e7	1.30829	0.654146	−	0.756369i	$-0.273028\pi$
$743$	1.96869e7	1.30829	0.654146	+	0.756369i	$0.273028\pi$
$744$	−6.39918e6	−0.423830
$745$	3.57757e6	0.236155
$746$	−3.33230e7	−2.19228
$747$	229215.	0.0150294
$748$	−1.40217e6	−0.0916317
$749$	−677463.	−0.0441246
$750$	3.53858e6	0.229708
$751$	1.21758e6	0.0787766	0.0393883	−	0.999224i	$-0.487459\pi$
$751$	1.21758e6	0.0787766	0.0393883	+	0.999224i	$0.487459\pi$
$752$	1.13253e7	0.730308
$753$	2.34202e7	1.50523
$754$	5.83942e6	0.374060
$755$	2.38308e6	0.152150
$756$	5.22446e6	0.332458
$757$	1.65823e7	1.05173	0.525867	−	0.850567i	$-0.323741\pi$
$757$	1.65823e7	1.05173	0.525867	+	0.850567i	$0.323741\pi$
$758$	−1.02743e6	−0.0649501
$759$	−398201.	−0.0250898
$760$	6.42867e6	0.403726
$761$	−2.92543e7	−1.83117	−0.915585	−	0.402124i	$-0.868272\pi$
$761$	−2.92543e7	−1.83117	−0.915585	+	0.402124i	$0.868272\pi$
$762$	3.18408e7	1.98654
$763$	4.22748e6	0.262888
$764$	−8.31153e7	−5.15166
$765$	488028.	0.0301503
$766$	4.67674e7	2.87986
$767$	−46390.3	−0.00284734
$768$	1.73453e8	10.6116
$769$	−2.26727e7	−1.38257	−0.691284	−	0.722583i	$-0.742955\pi$
$769$	−2.26727e7	−1.38257	−0.691284	+	0.722583i	$0.742955\pi$
$770$	−1.12777e6	−0.0685480
$771$	−6.88897e6	−0.417367
$772$	4.04857e7	2.44489
$773$	1.11171e7	0.669181	0.334591	−	0.942364i	$-0.391402\pi$
$773$	1.11171e7	0.669181	0.334591	+	0.942364i	$0.391402\pi$
$774$	−3.12630e7	−1.87576
$775$	279581.	0.0167207
$776$	4.47491e6	0.266766
$777$	−5.61650e6	−0.333744
$778$	3.36907e7	1.99554
$779$	−4.37337e6	−0.258210
$780$	−6.42067e6	−0.377871
$781$	−470074.	−0.0275765
$782$	−225015.	−0.0131581
$783$	6.39878e6	0.372986
$784$	−7.83712e7	−4.55372
$785$	−1.62071e6	−0.0938711
$786$	2.20085e7	1.27067
$787$	1.81954e7	1.04719	0.523594	−	0.851968i	$-0.324591\pi$
$787$	1.81954e7	1.04719	0.523594	+	0.851968i	$0.324591\pi$
$788$	−8.92800e6	−0.512199
$789$	−1.95142e7	−1.11599
$790$	2.61501e7	1.49075
$791$	585449.	0.0332696
$792$	−1.38177e7	−0.782747
$793$	−3.10614e6	−0.175404
$794$	−1.99937e7	−1.12549
$795$	−1.65765e7	−0.930195
$796$	3.79486e7	2.12282
$797$	−3.97807e6	−0.221833	−0.110917	−	0.993830i	$-0.535379\pi$
$797$	−3.97807e6	−0.221833	−0.110917	+	0.993830i	$0.535379\pi$
$798$	2.70287e6	0.150251
$799$	−276510.	−0.0153230
$800$	−2.09045e7	−1.15482
$801$	−6.42714e6	−0.353945
$802$	3.65110e7	2.00441
$803$	−6.32281e6	−0.346036
$804$	1.43476e7	0.782777
$805$	−135439.	−0.00736638
$806$	−677872.	−0.0367545
$807$	−2.62056e7	−1.41648
$808$	7.32962e7	3.94960
$809$	−7.98316e6	−0.428848	−0.214424	−	0.976741i	$-0.568787\pi$
$809$	−7.98316e6	−0.428848	−0.214424	+	0.976741i	$0.568787\pi$
$810$	−2.03841e7	−1.09164
$811$	3.22960e6	0.172424	0.0862119	−	0.996277i	$-0.472524\pi$
$811$	3.22960e6	0.172424	0.0862119	+	0.996277i	$0.472524\pi$
$812$	1.21239e7	0.645288
$813$	−1.83368e7	−0.972967
$814$	−1.15427e7	−0.610583
$815$	5.12464e6	0.270252
$816$	−1.21961e7	−0.641205
$817$	6.24275e6	0.327206
$818$	−2.15488e7	−1.12600
$819$	−712226.	−0.0371029
$820$	2.88226e7	1.49692
$821$	−1.19968e7	−0.621167	−0.310583	−	0.950546i	$-0.600524\pi$
$821$	−1.19968e7	−0.621167	−0.310583	+	0.950546i	$0.600524\pi$
$822$	−6.82266e7	−3.52188
$823$	−1.66747e7	−0.858138	−0.429069	−	0.903272i	$-0.641158\pi$
$823$	−1.66747e7	−0.858138	−0.429069	+	0.903272i	$0.641158\pi$
$824$	−3.10179e7	−1.59146
$825$	1.51876e6	0.0776878
$826$	−128704.	−0.00656357
$827$	1.57659e7	0.801595	0.400797	−	0.916167i	$-0.368733\pi$
$827$	1.57659e7	0.801595	0.400797	+	0.916167i	$0.368733\pi$
$828$	−2.50008e6	−0.126730
$829$	−1.31348e7	−0.663799	−0.331900	−	0.943315i	$-0.607690\pi$
$829$	−1.31348e7	−0.663799	−0.331900	+	0.943315i	$0.607690\pi$
$830$	403083.	0.0203095
$831$	−4.12714e7	−2.07323
$832$	2.92387e7	1.46437
$833$	1.91345e6	0.0955442
$834$	−1.50192e7	−0.747708
$835$	3.71325e6	0.184305
$836$	4.15697e6	0.205713
$837$	−742807.	−0.0366490
$838$	−4.28634e7	−2.10852
$839$	−1.80414e7	−0.884841	−0.442421	−	0.896808i	$-0.645880\pi$
$839$	−1.80414e7	−0.884841	−0.442421	+	0.896808i	$0.645880\pi$
$840$	−1.18235e7	−0.578159
$841$	−5.66207e6	−0.276048
$842$	−3.82448e7	−1.85905
$843$	−3.04745e7	−1.47696
$844$	5.35997e7	2.59004
$845$	8.83088e6	0.425463
$846$	−4.10527e6	−0.197204
$847$	−484039.	−0.0231831
$848$	1.64664e8	7.86339
$849$	−2.56836e6	−0.122289
$850$	858216.	0.0407426
$851$	−1.38621e6	−0.0656152
$852$	−7.42485e6	−0.350420
$853$	2.66030e7	1.25187	0.625933	−	0.779877i	$-0.284718\pi$
$853$	2.66030e7	1.25187	0.625933	+	0.779877i	$0.284718\pi$
$854$	−8.61756e6	−0.404333
$855$	−1.44685e6	−0.0676873
$856$	−1.45965e7	−0.680872
$857$	−1.29754e7	−0.603490	−0.301745	−	0.953389i	$-0.597569\pi$
$857$	−1.29754e7	−0.603490	−0.301745	+	0.953389i	$0.597569\pi$
$858$	−3.68237e6	−0.170769
$859$	−2.63991e7	−1.22069	−0.610346	−	0.792135i	$-0.708970\pi$
$859$	−2.63991e7	−1.22069	−0.610346	+	0.792135i	$0.708970\pi$
$860$	−4.11428e7	−1.89691
$861$	8.04343e6	0.369771
$862$	4.89191e7	2.24239
$863$	1.91343e7	0.874550	0.437275	−	0.899328i	$-0.355944\pi$
$863$	1.91343e7	0.874550	0.437275	+	0.899328i	$0.355944\pi$
$864$	5.55402e7	2.53118
$865$	7.28225e6	0.330922
$866$	−8.38846e6	−0.380091
$867$	−2.82168e7	−1.27485
$868$	−1.40742e6	−0.0634049
$869$	1.12236e7	0.504176
$870$	−2.18172e7	−0.977238
$871$	1.00880e6	0.0450567
$872$	9.10848e7	4.05653
$873$	−1.00713e6	−0.0447249
$874$	667096.	0.0295399
$875$	516570.	0.0228092
$876$	−9.98692e7	−4.39715
$877$	7.36431e6	0.323320	0.161660	−	0.986846i	$-0.448315\pi$
$877$	7.36431e6	0.323320	0.161660	+	0.986846i	$0.448315\pi$
$878$	1.93114e7	0.845432
$879$	−5.26367e7	−2.29782
$880$	−1.50867e7	−0.656732
$881$	−1.65721e7	−0.719345	−0.359673	−	0.933079i	$-0.617112\pi$
$881$	−1.65721e7	−0.719345	−0.359673	+	0.933079i	$0.617112\pi$
$882$	2.84085e7	1.22964
$883$	−3.12589e7	−1.34918	−0.674592	−	0.738191i	$-0.735680\pi$
$883$	−3.12589e7	−1.34918	−0.674592	+	0.738191i	$0.735680\pi$
$884$	−1.55721e6	−0.0670220
$885$	173323.	0.00743873
$886$	−6.75930e7	−2.89279
$887$	3.48961e7	1.48925	0.744626	−	0.667482i	$-0.232628\pi$
$887$	3.48961e7	1.48925	0.744626	+	0.667482i	$0.232628\pi$
$888$	−1.21012e8	−5.14989
$889$	4.64820e6	0.197256
$890$	−1.13024e7	−0.478293
$891$	−8.74886e6	−0.369196
$892$	−3.83808e7	−1.61511
$893$	819762.	0.0344001
$894$	3.24083e7	1.35617
$895$	−1.86365e7	−0.777690
$896$	4.57337e7	1.90312
$897$	−442232.	−0.0183514
$898$	7.39995e7	3.06223
$899$	−1.72376e6	−0.0711343
$900$	9.53541e6	0.392404
$901$	−4.02031e6	−0.164986
$902$	1.65303e7	0.676495
$903$	−1.14816e7	−0.468577
$904$	1.26140e7	0.513372
$905$	−2.48441e6	−0.100833
$906$	2.15877e7	0.873749
$907$	9.13004e6	0.368515	0.184257	−	0.982878i	$-0.441012\pi$
$907$	9.13004e6	0.368515	0.184257	+	0.982878i	$0.441012\pi$
$908$	1.48304e7	0.596950
$909$	−1.64962e7	−0.662175
$910$	−1.25248e6	−0.0501379
$911$	2.88247e7	1.15072	0.575359	−	0.817901i	$-0.304862\pi$
$911$	2.88247e7	1.15072	0.575359	+	0.817901i	$0.304862\pi$
$912$	3.61576e7	1.43950
$913$	173003.	0.00686873
$914$	8.95485e7	3.54562
$915$	1.16051e7	0.458245
$916$	−1.24307e8	−4.89505
$917$	3.21286e6	0.126173
$918$	−2.28015e6	−0.0893012
$919$	3.24309e7	1.26669	0.633346	−	0.773869i	$-0.281681\pi$
$919$	3.24309e7	1.26669	0.633346	+	0.773869i	$0.281681\pi$
$920$	−2.91815e6	−0.113668
$921$	6.17261e7	2.39784
$922$	−6.27747e6	−0.243197
$923$	−522053.	−0.0201702
$924$	−7.64543e6	−0.294593
$925$	5.28705e6	0.203170
$926$	−1.77775e7	−0.681308
$927$	6.98094e6	0.266818
$928$	1.28887e8	4.91292
$929$	−2.30382e7	−0.875810	−0.437905	−	0.899021i	$-0.644279\pi$
$929$	−2.30382e7	−0.875810	−0.437905	+	0.899021i	$0.644279\pi$
$930$	2.53266e6	0.0960218
$931$	−5.67276e6	−0.214496
$932$	−5.81421e7	−2.19256
$933$	5.96569e6	0.224366
$934$	4.51997e7	1.69538
$935$	368346.	0.0137793
$936$	−1.53455e7	−0.572522
$937$	1.94485e7	0.723665	0.361832	−	0.932243i	$-0.382151\pi$
$937$	1.94485e7	0.723665	0.361832	+	0.932243i	$0.382151\pi$
$938$	2.79877e6	0.103863
$939$	4.41297e7	1.63331
$940$	−5.40263e6	−0.199428
$941$	1.52859e7	0.562752	0.281376	−	0.959598i	$-0.409209\pi$
$941$	1.52859e7	0.562752	0.281376	+	0.959598i	$0.409209\pi$
$942$	−1.46816e7	−0.539073
$943$	1.98520e6	0.0726983
$944$	−1.72173e6	−0.0628831
$945$	−1.37245e6	−0.0499940
$946$	−2.35961e7	−0.857261
$947$	−1.90130e7	−0.688930	−0.344465	−	0.938799i	$-0.611940\pi$
$947$	−1.90130e7	−0.688930	−0.344465	+	0.938799i	$0.611940\pi$
$948$	1.77277e8	6.40667
$949$	−7.02195e6	−0.253100
$950$	−2.54433e6	−0.0914671
$951$	2.15089e7	0.771199
$952$	−2.86757e6	−0.102547
$953$	3.31467e7	1.18225	0.591123	−	0.806581i	$-0.298685\pi$
$953$	3.31467e7	1.18225	0.591123	+	0.806581i	$0.298685\pi$
$954$	−5.96886e7	−2.12334
$955$	2.18342e7	0.774690
$956$	6.27853e7	2.22184
$957$	−9.36392e6	−0.330505
$958$	−1.14422e7	−0.402807
$959$	−9.95989e6	−0.349710
$960$	−1.09241e8	−3.82569
$961$	−2.84290e7	−0.993010
$962$	−1.28190e7	−0.446597
$963$	3.28512e6	0.114152
$964$	−6.91195e7	−2.39557
$965$	−1.06355e7	−0.367654
$966$	−1.22691e6	−0.0423029
$967$	2.69917e7	0.928248	0.464124	−	0.885770i	$-0.346369\pi$
$967$	2.69917e7	0.928248	0.464124	+	0.885770i	$0.346369\pi$
$968$	−1.04290e7	−0.357731
$969$	−882794.	−0.0302030
$970$	−1.77107e6	−0.0604376
$971$	−2.18430e7	−0.743472	−0.371736	−	0.928338i	$-0.621237\pi$
$971$	−2.18430e7	−0.743472	−0.371736	+	0.928338i	$0.621237\pi$
$972$	−9.97882e7	−3.38777
$973$	−2.19254e6	−0.0742448
$974$	−7.97059e7	−2.69211
$975$	1.68669e6	0.0568230
$976$	−1.15281e8	−3.87377
$977$	−1.25312e7	−0.420006	−0.210003	−	0.977701i	$-0.567347\pi$
$977$	−1.25312e7	−0.420006	−0.210003	+	0.977701i	$0.567347\pi$
$978$	4.64229e7	1.55198
$979$	−4.85096e6	−0.161760
$980$	3.73862e7	1.24350
$981$	−2.04997e7	−0.680103
$982$	−9.25544e7	−3.06280
$983$	−1.33719e7	−0.441377	−0.220688	−	0.975344i	$-0.570830\pi$
$983$	−1.33719e7	−0.441377	−0.220688	+	0.975344i	$0.570830\pi$
$984$	1.73303e8	5.70581
$985$	2.34536e6	0.0770227
$986$	−5.29135e6	−0.173330
$987$	−1.50769e6	−0.0492629
$988$	4.61663e6	0.150464
$989$	−2.83376e6	−0.0921239
$990$	5.46873e6	0.177337
$991$	3.91120e7	1.26510	0.632552	−	0.774518i	$-0.282007\pi$
$991$	3.91120e7	1.26510	0.632552	+	0.774518i	$0.282007\pi$
$992$	−1.49620e7	−0.482735
$993$	−7.63342e7	−2.45667
$994$	−1.44836e6	−0.0464955
$995$	−9.96900e6	−0.319223
$996$	2.73259e6	0.0872823
$997$	−1.37428e6	−0.0437862	−0.0218931	−	0.999760i	$-0.506969\pi$
$997$	−1.37428e6	−0.0437862	−0.0218931	+	0.999760i	$0.506969\pi$
$998$	−1.37013e7	−0.435446
$999$	−1.40469e7	−0.445315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.1	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.1	✓	35	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)

\(f(q)\)	\(=\)	\(q-11.2768 q^{2} +20.0827 q^{3} +95.1666 q^{4} -25.0000 q^{5} -226.469 q^{6} -33.0605 q^{7} -712.318 q^{8} +160.315 q^{9} +O(q^{10})\)	\(q-11.2768 q^{2} +20.0827 q^{3} +95.1666 q^{4} -25.0000 q^{5} -226.469 q^{6} -33.0605 q^{7} -712.318 q^{8} +160.315 q^{9} +281.920 q^{10} +121.000 q^{11} +1911.20 q^{12} +134.380 q^{13} +372.817 q^{14} -502.068 q^{15} +4987.35 q^{16} -121.767 q^{17} -1807.85 q^{18} +361.000 q^{19} -2379.16 q^{20} -663.945 q^{21} -1364.49 q^{22} -163.868 q^{23} -14305.3 q^{24} +625.000 q^{25} -1515.37 q^{26} -1660.53 q^{27} -3146.26 q^{28} -3853.45 q^{29} +5661.73 q^{30} +447.330 q^{31} -33447.2 q^{32} +2430.01 q^{33} +1373.15 q^{34} +826.513 q^{35} +15256.7 q^{36} +8459.29 q^{37} -4070.93 q^{38} +2698.71 q^{39} +17807.9 q^{40} -12114.6 q^{41} +7487.18 q^{42} +17292.9 q^{43} +11515.2 q^{44} -4007.88 q^{45} +1847.91 q^{46} +2270.81 q^{47} +100159. q^{48} -15714.0 q^{49} -7048.01 q^{50} -2445.41 q^{51} +12788.4 q^{52} +33016.4 q^{53} +18725.5 q^{54} -3025.00 q^{55} +23549.6 q^{56} +7249.86 q^{57} +43454.7 q^{58} -345.219 q^{59} -47780.1 q^{60} -23114.7 q^{61} -5044.46 q^{62} -5300.10 q^{63} +217583. q^{64} -3359.49 q^{65} -27402.8 q^{66} +7507.08 q^{67} -11588.2 q^{68} -3290.92 q^{69} -9320.43 q^{70} -3884.91 q^{71} -114195. q^{72} -52254.6 q^{73} -95393.8 q^{74} +12551.7 q^{75} +34355.1 q^{76} -4000.32 q^{77} -30432.8 q^{78} +92757.0 q^{79} -124684. q^{80} -72304.6 q^{81} +136614. q^{82} +1429.78 q^{83} -63185.3 q^{84} +3044.18 q^{85} -195009. q^{86} -77387.7 q^{87} -86190.5 q^{88} -40090.6 q^{89} +45196.2 q^{90} -4442.66 q^{91} -15594.8 q^{92} +8983.60 q^{93} -25607.5 q^{94} -9025.00 q^{95} -671711. q^{96} -6282.18 q^{97} +177204. q^{98} +19398.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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