LMFDB - Embedded newform 1045.6.a.a.1.9

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			1.9
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)

$f(q)$	$=$	$q-6.89804 q^{2} +25.8209 q^{3} +15.5830 q^{4} -25.0000 q^{5} -178.113 q^{6} +221.117 q^{7} +113.245 q^{8} +423.717 q^{9} +O(q^{10})$	\(q-6.89804 q^{2} +25.8209 q^{3} +15.5830 q^{4} -25.0000 q^{5} -178.113 q^{6} +221.117 q^{7} +113.245 q^{8} +423.717 q^{9} +172.451 q^{10} +121.000 q^{11} +402.366 q^{12} -1057.63 q^{13} -1525.27 q^{14} -645.522 q^{15} -1279.83 q^{16} -1490.08 q^{17} -2922.82 q^{18} +361.000 q^{19} -389.574 q^{20} +5709.42 q^{21} -834.663 q^{22} +4345.86 q^{23} +2924.09 q^{24} +625.000 q^{25} +7295.59 q^{26} +4666.27 q^{27} +3445.65 q^{28} -4705.89 q^{29} +4452.83 q^{30} -3143.17 q^{31} +5204.44 q^{32} +3124.32 q^{33} +10278.6 q^{34} -5527.91 q^{35} +6602.77 q^{36} +11120.9 q^{37} -2490.19 q^{38} -27309.0 q^{39} -2831.13 q^{40} -13570.7 q^{41} -39383.8 q^{42} -1878.40 q^{43} +1885.54 q^{44} -10592.9 q^{45} -29977.9 q^{46} -28209.3 q^{47} -33046.2 q^{48} +32085.5 q^{49} -4311.28 q^{50} -38475.1 q^{51} -16481.0 q^{52} -18123.0 q^{53} -32188.1 q^{54} -3025.00 q^{55} +25040.4 q^{56} +9321.33 q^{57} +32461.4 q^{58} -44805.2 q^{59} -10059.1 q^{60} -27256.7 q^{61} +21681.7 q^{62} +93690.8 q^{63} +5053.99 q^{64} +26440.8 q^{65} -21551.7 q^{66} -31037.6 q^{67} -23219.8 q^{68} +112214. q^{69} +38131.8 q^{70} -38945.9 q^{71} +47984.0 q^{72} -64978.7 q^{73} -76712.4 q^{74} +16138.0 q^{75} +5625.45 q^{76} +26755.1 q^{77} +188378. q^{78} -14484.0 q^{79} +31995.7 q^{80} +17523.9 q^{81} +93611.0 q^{82} +38156.9 q^{83} +88969.7 q^{84} +37252.0 q^{85} +12957.3 q^{86} -121510. q^{87} +13702.7 q^{88} +76016.7 q^{89} +73070.4 q^{90} -233860. q^{91} +67721.4 q^{92} -81159.4 q^{93} +194589. q^{94} -9025.00 q^{95} +134383. q^{96} -3703.93 q^{97} -221327. q^{98} +51269.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.89804	−1.21941	−0.609706	−	0.792627i	$-0.708713\pi$
$2$	−6.89804	−1.21941	−0.609706	+	0.792627i	$0.708713\pi$
$3$	25.8209	1.65641	0.828205	−	0.560426i	$-0.189363\pi$
$3$	25.8209	1.65641	0.828205	+	0.560426i	$0.189363\pi$
$4$	15.5830	0.486968
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−178.113	−2.01985
$7$	221.117	1.70560	0.852798	−	0.522241i	$-0.174904\pi$
$7$	221.117	1.70560	0.852798	+	0.522241i	$0.174904\pi$
$8$	113.245	0.625598
$9$	423.717	1.74369
$10$	172.451	0.545338
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	402.366	0.806618
$13$	−1057.63	−1.73571	−0.867853	−	0.496822i	$-0.834500\pi$
$13$	−1057.63	−1.73571	−0.867853	+	0.496822i	$0.834500\pi$
$14$	−1525.27	−2.07983
$15$	−645.522	−0.740769
$16$	−1279.83	−1.24983
$17$	−1490.08	−1.25051	−0.625254	−	0.780421i	$-0.715005\pi$
$17$	−1490.08	−1.25051	−0.625254	+	0.780421i	$0.715005\pi$
$18$	−2922.82	−2.12628
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−389.574	−0.217779
$21$	5709.42	2.82516
$22$	−834.663	−0.367667
$23$	4345.86	1.71300	0.856498	−	0.516151i	$-0.172635\pi$
$23$	4345.86	1.71300	0.856498	+	0.516151i	$0.172635\pi$
$24$	2924.09	1.03625
$25$	625.000	0.200000
$26$	7295.59	2.11654
$27$	4666.27	1.23186
$28$	3445.65	0.830570
$29$	−4705.89	−1.03907	−0.519537	−	0.854448i	$-0.673896\pi$
$29$	−4705.89	−1.03907	−0.519537	+	0.854448i	$0.673896\pi$
$30$	4452.83	0.903303
$31$	−3143.17	−0.587440	−0.293720	−	0.955891i	$-0.594893\pi$
$31$	−3143.17	−0.587440	−0.293720	+	0.955891i	$0.594893\pi$
$32$	5204.44	0.898461
$33$	3124.32	0.499426
$34$	10278.6	1.52489
$35$	−5527.91	−0.762766
$36$	6602.77	0.849121
$37$	11120.9	1.33547	0.667737	−	0.744397i	$-0.267263\pi$
$37$	11120.9	1.33547	0.667737	+	0.744397i	$0.267263\pi$
$38$	−2490.19	−0.279752
$39$	−27309.0	−2.87504
$40$	−2831.13	−0.279776
$41$	−13570.7	−1.26079	−0.630393	−	0.776276i	$-0.717106\pi$
$41$	−13570.7	−1.26079	−0.630393	+	0.776276i	$0.717106\pi$
$42$	−39383.8	−3.44504
$43$	−1878.40	−0.154923	−0.0774616	−	0.996995i	$-0.524682\pi$
$43$	−1878.40	−0.154923	−0.0774616	+	0.996995i	$0.524682\pi$
$44$	1885.54	0.146826
$45$	−10592.9	−0.779802
$46$	−29977.9	−2.08885
$47$	−28209.3	−1.86272	−0.931361	−	0.364097i	$-0.881378\pi$
$47$	−28209.3	−1.86272	−0.931361	+	0.364097i	$0.881378\pi$
$48$	−33046.2	−2.07023
$49$	32085.5	1.90906
$50$	−4311.28	−0.243883
$51$	−38475.1	−2.07135
$52$	−16481.0	−0.845232
$53$	−18123.0	−0.886216	−0.443108	−	0.896468i	$-0.646124\pi$
$53$	−18123.0	−0.886216	−0.443108	+	0.896468i	$0.646124\pi$
$54$	−32188.1	−1.50214
$55$	−3025.00	−0.134840
$56$	25040.4	1.06702
$57$	9321.33	0.380006
$58$	32461.4	1.26706
$59$	−44805.2	−1.67571	−0.837855	−	0.545893i	$-0.816190\pi$
$59$	−44805.2	−1.67571	−0.837855	+	0.545893i	$0.816190\pi$
$60$	−10059.1	−0.360730
$61$	−27256.7	−0.937884	−0.468942	−	0.883229i	$-0.655365\pi$
$61$	−27256.7	−0.937884	−0.468942	+	0.883229i	$0.655365\pi$
$62$	21681.7	0.716332
$63$	93690.8	2.97403
$64$	5053.99	0.154236
$65$	26440.8	0.776231
$66$	−21551.7	−0.609007
$67$	−31037.6	−0.844697	−0.422349	−	0.906433i	$-0.638794\pi$
$67$	−31037.6	−0.844697	−0.422349	+	0.906433i	$0.638794\pi$
$68$	−23219.8	−0.608957
$69$	112214.	2.83742
$70$	38131.8	0.930126
$71$	−38945.9	−0.916886	−0.458443	−	0.888724i	$-0.651593\pi$
$71$	−38945.9	−0.916886	−0.458443	+	0.888724i	$0.651593\pi$
$72$	47984.0	1.09085
$73$	−64978.7	−1.42713	−0.713565	−	0.700589i	$-0.752921\pi$
$73$	−64978.7	−1.42713	−0.713565	+	0.700589i	$0.752921\pi$
$74$	−76712.4	−1.62849
$75$	16138.0	0.331282
$76$	5625.45	0.111718
$77$	26755.1	0.514256
$78$	188378.	3.50586
$79$	−14484.0	−0.261108	−0.130554	−	0.991441i	$-0.541676\pi$
$79$	−14484.0	−0.261108	−0.130554	+	0.991441i	$0.541676\pi$
$80$	31995.7	0.558941
$81$	17523.9	0.296768
$82$	93611.0	1.53742
$83$	38156.9	0.607964	0.303982	−	0.952678i	$-0.401684\pi$
$83$	38156.9	0.607964	0.303982	+	0.952678i	$0.401684\pi$
$84$	88969.7	1.37576
$85$	37252.0	0.559244
$86$	12957.3	0.188915
$87$	−121510.	−1.72113
$88$	13702.7	0.188625
$89$	76016.7	1.01727	0.508633	−	0.860984i	$-0.330151\pi$
$89$	76016.7	1.01727	0.508633	+	0.860984i	$0.330151\pi$
$90$	73070.4	0.950901
$91$	−233860.	−2.96041
$92$	67721.4	0.834174
$93$	−81159.4	−0.973042
$94$	194589.	2.27143
$95$	−9025.00	−0.102598
$96$	134383.	1.48822
$97$	−3703.93	−0.0399699	−0.0199850	−	0.999800i	$-0.506362\pi$
$97$	−3703.93	−0.0399699	−0.0199850	+	0.999800i	$0.506362\pi$
$98$	−221327.	−2.32793
$99$	51269.8	0.525743
$100$	9739.35	0.0973935
$101$	36971.8	0.360634	0.180317	−	0.983609i	$-0.442288\pi$
$101$	36971.8	0.360634	0.180317	+	0.983609i	$0.442288\pi$
$102$	265403.	2.52584
$103$	−131318.	−1.21964	−0.609821	−	0.792539i	$-0.708759\pi$
$103$	−131318.	−1.21964	−0.609821	+	0.792539i	$0.708759\pi$
$104$	−119772.	−1.08585
$105$	−142735.	−1.26345
$106$	125013.	1.08066
$107$	78327.2	0.661383	0.330692	−	0.943739i	$-0.392718\pi$
$107$	78327.2	0.661383	0.330692	+	0.943739i	$0.392718\pi$
$108$	72714.3	0.599875
$109$	155570.	1.25418	0.627091	−	0.778946i	$-0.284245\pi$
$109$	155570.	1.25418	0.627091	+	0.778946i	$0.284245\pi$
$110$	20866.6	0.164426
$111$	287151.	2.21209
$112$	−282991.	−2.13170
$113$	232439.	1.71243	0.856214	−	0.516621i	$-0.172810\pi$
$113$	232439.	1.71243	0.856214	+	0.516621i	$0.172810\pi$
$114$	−64298.9	−0.463385
$115$	−108647.	−0.766075
$116$	−73331.7	−0.505996
$117$	−448136.	−3.02653
$118$	309068.	2.04338
$119$	−329481.	−2.13286
$120$	−73102.3	−0.463424
$121$	14641.0	0.0909091
$122$	188018.	1.14367
$123$	−350406.	−2.08838
$124$	−48979.9	−0.286064
$125$	−15625.0	−0.0894427
$126$	−646283.	−3.62657
$127$	−41375.3	−0.227631	−0.113816	−	0.993502i	$-0.536307\pi$
$127$	−41375.3	−0.227631	−0.113816	+	0.993502i	$0.536307\pi$
$128$	−201405.	−1.08654
$129$	−48501.9	−0.256616
$130$	−182390.	−0.946546
$131$	20724.4	0.105512	0.0527562	−	0.998607i	$-0.483199\pi$
$131$	20724.4	0.105512	0.0527562	+	0.998607i	$0.483199\pi$
$132$	48686.2	0.243204
$133$	79823.1	0.391290
$134$	214099.	1.03003
$135$	−116657.	−0.550903
$136$	−168744.	−0.782316
$137$	−150322.	−0.684258	−0.342129	−	0.939653i	$-0.611148\pi$
$137$	−150322.	−0.684258	−0.342129	+	0.939653i	$0.611148\pi$
$138$	−774056.	−3.45999
$139$	−309477.	−1.35860	−0.679301	−	0.733860i	$-0.737717\pi$
$139$	−309477.	−1.35860	−0.679301	+	0.733860i	$0.737717\pi$
$140$	−86141.3	−0.371442
$141$	−728389.	−3.08543
$142$	268650.	1.11806
$143$	−127973.	−0.523335
$144$	−542284.	−2.17932
$145$	117647.	0.464688
$146$	448225.	1.74026
$147$	828476.	3.16218
$148$	173296.	0.650333
$149$	340887.	1.25789	0.628947	−	0.777448i	$-0.283486\pi$
$149$	340887.	1.25789	0.628947	+	0.777448i	$0.283486\pi$
$150$	−111321.	−0.403969
$151$	15991.2	0.0570739	0.0285369	−	0.999593i	$-0.490915\pi$
$151$	15991.2	0.0570739	0.0285369	+	0.999593i	$0.490915\pi$
$152$	40881.6	0.143522
$153$	−631371.	−2.18050
$154$	−184558.	−0.627091
$155$	78579.3	0.262711
$156$	−425555.	−1.40005
$157$	169672.	0.549366	0.274683	−	0.961535i	$-0.411427\pi$
$157$	169672.	0.549366	0.274683	+	0.961535i	$0.411427\pi$
$158$	99911.1	0.318398
$159$	−467951.	−1.46794
$160$	−130111.	−0.401804
$161$	960942.	2.92168
$162$	−120880.	−0.361883
$163$	−355709.	−1.04864	−0.524320	−	0.851521i	$-0.675680\pi$
$163$	−355709.	−1.04864	−0.524320	+	0.851521i	$0.675680\pi$
$164$	−211471.	−0.613962
$165$	−78108.1	−0.223350
$166$	−263208.	−0.741360
$167$	325947.	0.904390	0.452195	−	0.891919i	$-0.350641\pi$
$167$	325947.	0.904390	0.452195	+	0.891919i	$0.350641\pi$
$168$	646565.	1.76742
$169$	747291.	2.01267
$170$	−256965.	−0.681950
$171$	152962.	0.400030
$172$	−29271.0	−0.0754426
$173$	−614098.	−1.55999	−0.779996	−	0.625785i	$-0.784779\pi$
$173$	−614098.	−1.55999	−0.779996	+	0.625785i	$0.784779\pi$
$174$	838182.	2.09877
$175$	138198.	0.341119
$176$	−154859.	−0.376838
$177$	−1.15691e6	−2.77566
$178$	−524367.	−1.24047
$179$	416252.	0.971011	0.485505	−	0.874234i	$-0.338636\pi$
$179$	416252.	0.971011	0.485505	+	0.874234i	$0.338636\pi$
$180$	−165069.	−0.379739
$181$	650357.	1.47555	0.737777	−	0.675045i	$-0.235876\pi$
$181$	650357.	1.47555	0.737777	+	0.675045i	$0.235876\pi$
$182$	1.61317e6	3.60996
$183$	−703792.	−1.55352
$184$	492149.	1.07165
$185$	−278022.	−0.597242
$186$	559841.	1.18654
$187$	−180299.	−0.377043
$188$	−439585.	−0.907086
$189$	1.03179e6	2.10105
$190$	62254.8	0.125109
$191$	650761.	1.29074	0.645369	−	0.763871i	$-0.276703\pi$
$191$	650761.	1.29074	0.645369	+	0.763871i	$0.276703\pi$
$192$	130498.	0.255477
$193$	168400.	0.325424	0.162712	−	0.986674i	$-0.447976\pi$
$193$	168400.	0.325424	0.162712	+	0.986674i	$0.447976\pi$
$194$	25549.9	0.0487398
$195$	682724.	1.28576
$196$	499988.	0.929649
$197$	−267148.	−0.490441	−0.245221	−	0.969467i	$-0.578860\pi$
$197$	−267148.	−0.490441	−0.245221	+	0.969467i	$0.578860\pi$
$198$	−353661.	−0.641097
$199$	−112902.	−0.202101	−0.101050	−	0.994881i	$-0.532220\pi$
$199$	−112902.	−0.202101	−0.101050	+	0.994881i	$0.532220\pi$
$200$	70778.4	0.125120
$201$	−801418.	−1.39916
$202$	−255033.	−0.439762
$203$	−1.04055e6	−1.77224
$204$	−599556.	−1.00868
$205$	339267.	0.563841
$206$	905839.	1.48725
$207$	1.84142e6	2.98694
$208$	1.35358e6	2.16934
$209$	43681.0	0.0691714
$210$	984595.	1.54067
$211$	497547.	0.769357	0.384679	−	0.923051i	$-0.374312\pi$
$211$	497547.	0.769357	0.384679	+	0.923051i	$0.374312\pi$
$212$	−282410.	−0.431559
$213$	−1.00562e6	−1.51874
$214$	−540304.	−0.806499
$215$	46960.0	0.0692838
$216$	528433.	0.770648
$217$	−695007.	−1.00194
$218$	−1.07313e6	−1.52937
$219$	−1.67780e6	−2.36391
$220$	−47138.5	−0.0656627
$221$	1.57595e6	2.17051
$222$	−1.98078e6	−2.69745
$223$	223888.	0.301488	0.150744	−	0.988573i	$-0.451833\pi$
$223$	223888.	0.301488	0.150744	+	0.988573i	$0.451833\pi$
$224$	1.15079e6	1.53241
$225$	264823.	0.348738
$226$	−1.60337e6	−2.08816
$227$	−718886.	−0.925967	−0.462983	−	0.886367i	$-0.653221\pi$
$227$	−718886.	−0.925967	−0.462983	+	0.886367i	$0.653221\pi$
$228$	145254.	0.185051
$229$	−930650.	−1.17273	−0.586365	−	0.810047i	$-0.699441\pi$
$229$	−930650.	−1.17273	−0.586365	+	0.810047i	$0.699441\pi$
$230$	749448.	0.934162
$231$	690840.	0.851819
$232$	−532920.	−0.650043
$233$	−951144.	−1.14777	−0.573887	−	0.818934i	$-0.694565\pi$
$233$	−951144.	−1.14777	−0.573887	+	0.818934i	$0.694565\pi$
$234$	3.09126e6	3.69059
$235$	705233.	0.833035
$236$	−698198.	−0.816016
$237$	−373989.	−0.432502
$238$	2.27277e6	2.60084
$239$	−643582.	−0.728801	−0.364401	−	0.931242i	$-0.618726\pi$
$239$	−643582.	−0.728801	−0.364401	+	0.931242i	$0.618726\pi$
$240$	826155.	0.925835
$241$	846889.	0.939255	0.469628	−	0.882865i	$-0.344388\pi$
$241$	846889.	0.939255	0.469628	+	0.882865i	$0.344388\pi$
$242$	−100994.	−0.110856
$243$	−681422.	−0.740288
$244$	−424741.	−0.456719
$245$	−802138.	−0.853756
$246$	2.41712e6	2.54660
$247$	−381805.	−0.398198
$248$	−355950.	−0.367502
$249$	985245.	1.00704
$250$	107782.	0.109068
$251$	−1.32059e6	−1.32307	−0.661537	−	0.749913i	$-0.730095\pi$
$251$	−1.32059e6	−1.32307	−0.661537	+	0.749913i	$0.730095\pi$
$252$	1.45998e6	1.44826
$253$	525849.	0.516488
$254$	285408.	0.277576
$255$	961878.	0.926338
$256$	1.22757e6	1.17070
$257$	95208.4	0.0899171	0.0449586	−	0.998989i	$-0.485684\pi$
$257$	95208.4	0.0899171	0.0449586	+	0.998989i	$0.485684\pi$
$258$	334568.	0.312921
$259$	2.45901e6	2.27778
$260$	412026.	0.377999
$261$	−1.99397e6	−1.81183
$262$	−142958.	−0.128663
$263$	−364932.	−0.325329	−0.162665	−	0.986681i	$-0.552009\pi$
$263$	−364932.	−0.325329	−0.162665	+	0.986681i	$0.552009\pi$
$264$	353815.	0.312440
$265$	453074.	0.396328
$266$	−550623.	−0.477145
$267$	1.96282e6	1.68501
$268$	−483658.	−0.411340
$269$	−1.26049e6	−1.06208	−0.531041	−	0.847346i	$-0.678199\pi$
$269$	−1.26049e6	−1.06208	−0.531041	+	0.847346i	$0.678199\pi$
$270$	804703.	0.671779
$271$	−282493.	−0.233660	−0.116830	−	0.993152i	$-0.537273\pi$
$271$	−282493.	−0.233660	−0.116830	+	0.993152i	$0.537273\pi$
$272$	1.90704e6	1.56292
$273$	−6.03846e6	−4.90365
$274$	1.03692e6	0.834393
$275$	75625.0	0.0603023
$276$	1.74863e6	1.38173
$277$	−878043.	−0.687569	−0.343785	−	0.939049i	$-0.611709\pi$
$277$	−878043.	−0.687569	−0.343785	+	0.939049i	$0.611709\pi$
$278$	2.13479e6	1.65670
$279$	−1.33181e6	−1.02431
$280$	−626011.	−0.477185
$281$	511901.	0.386741	0.193370	−	0.981126i	$-0.438058\pi$
$281$	511901.	0.386741	0.193370	+	0.981126i	$0.438058\pi$
$282$	5.02446e6	3.76241
$283$	−2.39158e6	−1.77508	−0.887540	−	0.460730i	$-0.847588\pi$
$283$	−2.39158e6	−1.77508	−0.887540	+	0.460730i	$0.847588\pi$
$284$	−606892.	−0.446494
$285$	−233033.	−0.169944
$286$	882766.	0.638161
$287$	−3.00070e6	−2.15039
$288$	2.20521e6	1.56664
$289$	800476.	0.563772
$290$	−811536.	−0.566647
$291$	−95638.7	−0.0662066
$292$	−1.01256e6	−0.694966
$293$	−784028.	−0.533535	−0.266767	−	0.963761i	$-0.585956\pi$
$293$	−784028.	−0.533535	−0.266767	+	0.963761i	$0.585956\pi$
$294$	−5.71486e6	−3.85600
$295$	1.12013e6	0.749400
$296$	1.25939e6	0.835470
$297$	564619.	0.371419
$298$	−2.35145e6	−1.53389
$299$	−4.59632e6	−2.97326
$300$	251479.	0.161324
$301$	−415345.	−0.264236
$302$	−110308.	−0.0695966
$303$	954643.	0.597357
$304$	−462017.	−0.286731
$305$	681418.	0.419435
$306$	4.35523e6	2.65893
$307$	2.00619e6	1.21486	0.607431	−	0.794372i	$-0.292200\pi$
$307$	2.00619e6	1.21486	0.607431	+	0.794372i	$0.292200\pi$
$308$	416924.	0.250426
$309$	−3.39075e6	−2.02023
$310$	−542043.	−0.320354
$311$	−1.50345e6	−0.881431	−0.440715	−	0.897647i	$-0.645275\pi$
$311$	−1.50345e6	−0.881431	−0.440715	+	0.897647i	$0.645275\pi$
$312$	−3.09261e6	−1.79862
$313$	1.56549e6	0.903213	0.451607	−	0.892217i	$-0.350851\pi$
$313$	1.56549e6	0.903213	0.451607	+	0.892217i	$0.350851\pi$
$314$	−1.17041e6	−0.669904
$315$	−2.34227e6	−1.33003
$316$	−225703.	−0.127151
$317$	−1.16388e6	−0.650520	−0.325260	−	0.945625i	$-0.605452\pi$
$317$	−1.16388e6	−0.650520	−0.325260	+	0.945625i	$0.605452\pi$
$318$	3.22794e6	1.79002
$319$	−569413.	−0.313293
$320$	−126350.	−0.0689762
$321$	2.02248e6	1.09552
$322$	−6.62862e6	−3.56273
$323$	−537918.	−0.286886
$324$	273074.	0.144517
$325$	−661020.	−0.347141
$326$	2.45370e6	1.27873
$327$	4.01696e6	2.07744
$328$	−1.53682e6	−0.788746
$329$	−6.23755e6	−3.17705
$330$	538793.	0.272356
$331$	1.85989e6	0.933075	0.466537	−	0.884502i	$-0.345501\pi$
$331$	1.85989e6	0.933075	0.466537	+	0.884502i	$0.345501\pi$
$332$	594598.	0.296059
$333$	4.71211e6	2.32865
$334$	−2.24840e6	−1.10282
$335$	775940.	0.377760
$336$	−7.30706e6	−3.53098
$337$	131384.	0.0630183	0.0315091	−	0.999503i	$-0.489969\pi$
$337$	131384.	0.0630183	0.0315091	+	0.999503i	$0.489969\pi$
$338$	−5.15485e6	−2.45428
$339$	6.00177e6	2.83648
$340$	580496.	0.272334
$341$	−380324.	−0.177120
$342$	−1.05514e6	−0.487802
$343$	3.37833e6	1.55048
$344$	−212720.	−0.0969197
$345$	−2.80535e6	−1.26893
$346$	4.23607e6	1.90227
$347$	829180.	0.369679	0.184840	−	0.982769i	$-0.440823\pi$
$347$	829180.	0.369679	0.184840	+	0.982769i	$0.440823\pi$
$348$	−1.89349e6	−0.838136
$349$	−3.51764e6	−1.54592	−0.772961	−	0.634454i	$-0.781225\pi$
$349$	−3.51764e6	−1.54592	−0.772961	+	0.634454i	$0.781225\pi$
$350$	−953294.	−0.415965
$351$	−4.93519e6	−2.13814
$352$	629737.	0.270896
$353$	825671.	0.352671	0.176336	−	0.984330i	$-0.443576\pi$
$353$	825671.	0.352671	0.176336	+	0.984330i	$0.443576\pi$
$354$	7.98041e6	3.38468
$355$	973647.	0.410044
$356$	1.18457e6	0.495375
$357$	−8.50748e6	−3.53289
$358$	−2.87133e6	−1.18406
$359$	−3.89592e6	−1.59542	−0.797708	−	0.603044i	$-0.793954\pi$
$359$	−3.89592e6	−1.59542	−0.797708	+	0.603044i	$0.793954\pi$
$360$	−1.19960e6	−0.487843
$361$	130321.	0.0526316
$362$	−4.48619e6	−1.79931
$363$	378043.	0.150583
$364$	−3.64423e6	−1.44162
$365$	1.62447e6	0.638232
$366$	4.85479e6	1.89438
$367$	2.80411e6	1.08675	0.543374	−	0.839490i	$-0.317146\pi$
$367$	2.80411e6	1.08675	0.543374	+	0.839490i	$0.317146\pi$
$368$	−5.56195e6	−2.14095
$369$	−5.75012e6	−2.19842
$370$	1.91781e6	0.728285
$371$	−4.00729e6	−1.51153
$372$	−1.26470e6	−0.473840
$373$	5.30698e6	1.97504	0.987519	−	0.157498i	$-0.0503427\pi$
$373$	5.30698e6	1.97504	0.987519	+	0.157498i	$0.0503427\pi$
$374$	1.24371e6	0.459771
$375$	−403451.	−0.148154
$376$	−3.19458e6	−1.16532
$377$	4.97710e6	1.80353
$378$	−7.11732e6	−2.56205
$379$	5.01135e6	1.79208	0.896039	−	0.443975i	$-0.146432\pi$
$379$	5.01135e6	1.79208	0.896039	+	0.443975i	$0.146432\pi$
$380$	−140636.	−0.0499618
$381$	−1.06835e6	−0.377050
$382$	−4.48898e6	−1.57394
$383$	1.55211e6	0.540661	0.270331	−	0.962768i	$-0.412867\pi$
$383$	1.55211e6	0.540661	0.270331	+	0.962768i	$0.412867\pi$
$384$	−5.20044e6	−1.79975
$385$	−668877.	−0.229982
$386$	−1.16163e6	−0.396827
$387$	−795910.	−0.270138
$388$	−57718.2	−0.0194641
$389$	62589.5	0.0209714	0.0104857	−	0.999945i	$-0.496662\pi$
$389$	62589.5	0.0209714	0.0104857	+	0.999945i	$0.496662\pi$
$390$	−4.70946e6	−1.56787
$391$	−6.47567e6	−2.14212
$392$	3.63354e6	1.19430
$393$	535122.	0.174772
$394$	1.84280e6	0.598050
$395$	362099.	0.116771
$396$	798935.	0.256020
$397$	1.95993e6	0.624113	0.312057	−	0.950064i	$-0.398982\pi$
$397$	1.95993e6	0.624113	0.312057	+	0.950064i	$0.398982\pi$
$398$	778800.	0.246444
$399$	2.06110e6	0.648137
$400$	−799891.	−0.249966
$401$	2.38764e6	0.741494	0.370747	−	0.928734i	$-0.379102\pi$
$401$	2.38764e6	0.741494	0.370747	+	0.928734i	$0.379102\pi$
$402$	5.52821e6	1.70616
$403$	3.32432e6	1.01962
$404$	576130.	0.175617
$405$	−438097.	−0.132719
$406$	7.17776e6	2.16109
$407$	1.34563e6	0.402660
$408$	−4.35713e6	−1.29584
$409$	−90325.8	−0.0266995	−0.0133498	−	0.999911i	$-0.504249\pi$
$409$	−90325.8	−0.0266995	−0.0133498	+	0.999911i	$0.504249\pi$
$410$	−2.34028e6	−0.687555
$411$	−3.88143e6	−1.13341
$412$	−2.04633e6	−0.593926
$413$	−9.90718e6	−2.85808
$414$	−1.27022e7	−3.64231
$415$	−953923.	−0.271890
$416$	−5.50438e6	−1.55946
$417$	−7.99098e6	−2.25040
$418$	−301313.	−0.0843486
$419$	−2.14441e6	−0.596722	−0.298361	−	0.954453i	$-0.596440\pi$
$419$	−2.14441e6	−0.596722	−0.298361	+	0.954453i	$0.596440\pi$
$420$	−2.22424e6	−0.615260
$421$	−1.76362e6	−0.484954	−0.242477	−	0.970157i	$-0.577960\pi$
$421$	−1.76362e6	−0.484954	−0.242477	+	0.970157i	$0.577960\pi$
$422$	−3.43210e6	−0.938164
$423$	−1.19528e7	−3.24801
$424$	−2.05234e6	−0.554415
$425$	−931299.	−0.250102
$426$	6.93678e6	1.85197
$427$	−6.02691e6	−1.59965
$428$	1.22057e6	0.322072
$429$	−3.30438e6	−0.866857
$430$	−323932.	−0.0844856
$431$	−2.95116e6	−0.765244	−0.382622	−	0.923905i	$-0.624979\pi$
$431$	−2.95116e6	−0.765244	−0.382622	+	0.923905i	$0.624979\pi$
$432$	−5.97201e6	−1.53961
$433$	4.15079e6	1.06393	0.531963	−	0.846768i	$-0.321455\pi$
$433$	4.15079e6	1.06393	0.531963	+	0.846768i	$0.321455\pi$
$434$	4.79419e6	1.22177
$435$	3.03775e6	0.769714
$436$	2.42425e6	0.610746
$437$	1.56886e6	0.392988
$438$	1.15736e7	2.88258
$439$	3.27073e6	0.809998	0.404999	−	0.914317i	$-0.367272\pi$
$439$	3.27073e6	0.809998	0.404999	+	0.914317i	$0.367272\pi$
$440$	−342567.	−0.0843556
$441$	1.35952e7	3.32881
$442$	−1.08710e7	−2.64675
$443$	−3.23062e6	−0.782125	−0.391063	−	0.920364i	$-0.627892\pi$
$443$	−3.23062e6	−0.782125	−0.391063	+	0.920364i	$0.627892\pi$
$444$	4.47467e6	1.07722
$445$	−1.90042e6	−0.454935
$446$	−1.54439e6	−0.367638
$447$	8.80198e6	2.08359
$448$	1.11752e6	0.263063
$449$	7.75890e6	1.81629	0.908143	−	0.418661i	$-0.137500\pi$
$449$	7.75890e6	1.81629	0.908143	+	0.418661i	$0.137500\pi$
$450$	−1.82676e6	−0.425256
$451$	−1.64205e6	−0.380142
$452$	3.62208e6	0.833897
$453$	412905.	0.0945377
$454$	4.95890e6	1.12914
$455$	5.84650e6	1.32394
$456$	1.05560e6	0.237731
$457$	−5.86566e6	−1.31379	−0.656895	−	0.753982i	$-0.728131\pi$
$457$	−5.86566e6	−1.31379	−0.656895	+	0.753982i	$0.728131\pi$
$458$	6.41966e6	1.43004
$459$	−6.95310e6	−1.54045
$460$	−1.69304e6	−0.373054
$461$	6.10842e6	1.33868	0.669339	−	0.742957i	$-0.266577\pi$
$461$	6.10842e6	1.33868	0.669339	+	0.742957i	$0.266577\pi$
$462$	−4.76544e6	−1.03872
$463$	−4.98288e6	−1.08026	−0.540129	−	0.841582i	$-0.681625\pi$
$463$	−4.98288e6	−1.08026	−0.540129	+	0.841582i	$0.681625\pi$
$464$	6.02272e6	1.29867
$465$	2.02898e6	0.435157
$466$	6.56103e6	1.39961
$467$	−3.41906e6	−0.725463	−0.362731	−	0.931894i	$-0.618156\pi$
$467$	−3.41906e6	−0.725463	−0.362731	+	0.931894i	$0.618156\pi$
$468$	−6.98330e6	−1.47382
$469$	−6.86293e6	−1.44071
$470$	−4.86473e6	−1.01581
$471$	4.38109e6	0.909975
$472$	−5.07398e6	−1.04832
$473$	−227286.	−0.0467111
$474$	2.57979e6	0.527398
$475$	225625.	0.0458831
$476$	−5.13429e6	−1.03864
$477$	−7.67901e6	−1.54529
$478$	4.43946e6	0.888710
$479$	−4.25452e6	−0.847250	−0.423625	−	0.905838i	$-0.639243\pi$
$479$	−4.25452e6	−0.847250	−0.423625	+	0.905838i	$0.639243\pi$
$480$	−3.35958e6	−0.665552
$481$	−1.17618e7	−2.31799
$482$	−5.84187e6	−1.14534
$483$	2.48123e7	4.83949
$484$	228150.	0.0442698
$485$	92598.2	0.0178751
$486$	4.70048e6	0.902716
$487$	4.64342e6	0.887188	0.443594	−	0.896228i	$-0.353703\pi$
$487$	4.64342e6	0.887188	0.443594	+	0.896228i	$0.353703\pi$
$488$	−3.08670e6	−0.586739
$489$	−9.18473e6	−1.73698
$490$	5.53318e6	1.04108
$491$	−6.48784e6	−1.21450	−0.607249	−	0.794512i	$-0.707727\pi$
$491$	−6.48784e6	−1.21450	−0.607249	+	0.794512i	$0.707727\pi$
$492$	−5.46037e6	−1.01697
$493$	7.01214e6	1.29937
$494$	2.63371e6	0.485568
$495$	−1.28174e6	−0.235119
$496$	4.02271e6	0.734201
$497$	−8.61158e6	−1.56384
$498$	−6.79626e6	−1.22799
$499$	−1.36519e6	−0.245439	−0.122719	−	0.992441i	$-0.539161\pi$
$499$	−1.36519e6	−0.245439	−0.122719	+	0.992441i	$0.539161\pi$
$500$	−243484.	−0.0435557
$501$	8.41623e6	1.49804
$502$	9.10949e6	1.61337
$503$	−6.72089e6	−1.18442	−0.592212	−	0.805782i	$-0.701745\pi$
$503$	−6.72089e6	−1.18442	−0.592212	+	0.805782i	$0.701745\pi$
$504$	1.06101e7	1.86055
$505$	−924294.	−0.161280
$506$	−3.62733e6	−0.629812
$507$	1.92957e7	3.33381
$508$	−644750.	−0.110849
$509$	8.32811e6	1.42479	0.712397	−	0.701777i	$-0.247610\pi$
$509$	8.32811e6	1.42479	0.712397	+	0.701777i	$0.247610\pi$
$510$	−6.63507e6	−1.12959
$511$	−1.43679e7	−2.43411
$512$	−2.02288e6	−0.341032
$513$	1.68452e6	0.282607
$514$	−656751.	−0.109646
$515$	3.28296e6	0.545440
$516$	−755803.	−0.124964
$517$	−3.41333e6	−0.561632
$518$	−1.69624e7	−2.77755
$519$	−1.58565e7	−2.58398
$520$	2.99430e6	0.485609
$521$	−6.49446e6	−1.04821	−0.524106	−	0.851653i	$-0.675600\pi$
$521$	−6.49446e6	−1.04821	−0.524106	+	0.851653i	$0.675600\pi$
$522$	1.37545e7	2.20936
$523$	−9.88499e6	−1.58024	−0.790118	−	0.612954i	$-0.789981\pi$
$523$	−9.88499e6	−1.58024	−0.790118	+	0.612954i	$0.789981\pi$
$524$	322947.	0.0513811
$525$	3.56839e6	0.565033
$526$	2.51732e6	0.396711
$527$	4.68357e6	0.734599
$528$	−3.99859e6	−0.624198
$529$	1.24502e7	1.93435
$530$	−3.12532e6	−0.483287
$531$	−1.89847e7	−2.92192
$532$	1.24388e6	0.190546
$533$	1.43528e7	2.18835
$534$	−1.35396e7	−2.05472
$535$	−1.95818e6	−0.295779
$536$	−3.51486e6	−0.528441
$537$	1.07480e7	1.60839
$538$	8.69490e6	1.29512
$539$	3.88235e6	0.575602
$540$	−1.81786e6	−0.268272
$541$	5.62394e6	0.826129	0.413064	−	0.910702i	$-0.364458\pi$
$541$	5.62394e6	0.826129	0.413064	+	0.910702i	$0.364458\pi$
$542$	1.94865e6	0.284928
$543$	1.67928e7	2.44412
$544$	−7.75502e6	−1.12353
$545$	−3.88926e6	−0.560888
$546$	4.16536e7	5.97958
$547$	−1.13354e7	−1.61983	−0.809913	−	0.586549i	$-0.800486\pi$
$547$	−1.13354e7	−1.61983	−0.809913	+	0.586549i	$0.800486\pi$
$548$	−2.34246e6	−0.333212
$549$	−1.15491e7	−1.63538
$550$	−521664.	−0.0735334
$551$	−1.69883e6	−0.238380
$552$	1.27077e7	1.77509
$553$	−3.20265e6	−0.445345
$554$	6.05678e6	0.838431
$555$	−7.17878e6	−0.989277
$556$	−4.82258e6	−0.661595
$557$	−3.98560e6	−0.544322	−0.272161	−	0.962252i	$-0.587738\pi$
$557$	−3.98560e6	−0.544322	−0.272161	+	0.962252i	$0.587738\pi$
$558$	9.18691e6	1.24906
$559$	1.98665e6	0.268901
$560$	7.07477e6	0.953327
$561$	−4.65549e6	−0.624537
$562$	−3.53111e6	−0.471597
$563$	1.13149e7	1.50446	0.752231	−	0.658899i	$-0.228978\pi$
$563$	1.13149e7	1.50446	0.752231	+	0.658899i	$0.228978\pi$
$564$	−1.13505e7	−1.50251
$565$	−5.81097e6	−0.765821
$566$	1.64972e7	2.16456
$567$	3.87482e6	0.506167
$568$	−4.41044e6	−0.573602
$569$	−6.67303e6	−0.864058	−0.432029	−	0.901860i	$-0.642202\pi$
$569$	−6.67303e6	−0.864058	−0.432029	+	0.901860i	$0.642202\pi$
$570$	1.60747e6	0.207232
$571$	−6.63350e6	−0.851436	−0.425718	−	0.904856i	$-0.639979\pi$
$571$	−6.63350e6	−0.851436	−0.425718	+	0.904856i	$0.639979\pi$
$572$	−1.99421e6	−0.254847
$573$	1.68032e7	2.13799
$574$	2.06989e7	2.62222
$575$	2.71616e6	0.342599
$576$	2.14146e6	0.268939
$577$	1.18234e6	0.147844	0.0739219	−	0.997264i	$-0.476448\pi$
$577$	1.18234e6	0.147844	0.0739219	+	0.997264i	$0.476448\pi$
$578$	−5.52171e6	−0.687471
$579$	4.34824e6	0.539036
$580$	1.83329e6	0.226288
$581$	8.43713e6	1.03694
$582$	659719.	0.0807331
$583$	−2.19288e6	−0.267204
$584$	−7.35853e6	−0.892810
$585$	1.12034e7	1.35351
$586$	5.40826e6	0.650599
$587$	−7.00770e6	−0.839421	−0.419711	−	0.907658i	$-0.637868\pi$
$587$	−7.00770e6	−0.839421	−0.419711	+	0.907658i	$0.637868\pi$
$588$	1.29101e7	1.53988
$589$	−1.13468e6	−0.134768
$590$	−7.72671e6	−0.913828
$591$	−6.89800e6	−0.812371
$592$	−1.42328e7	−1.66912
$593$	−7.25399e6	−0.847111	−0.423556	−	0.905870i	$-0.639218\pi$
$593$	−7.25399e6	−0.847111	−0.423556	+	0.905870i	$0.639218\pi$
$594$	−3.89476e6	−0.452913
$595$	8.23702e6	0.953845
$596$	5.31202e6	0.612554
$597$	−2.91522e6	−0.334761
$598$	3.17056e7	3.62563
$599$	−8.70375e6	−0.991149	−0.495575	−	0.868565i	$-0.665043\pi$
$599$	−8.70375e6	−0.991149	−0.495575	+	0.868565i	$0.665043\pi$
$600$	1.82756e6	0.207249
$601$	6.97192e6	0.787347	0.393674	−	0.919250i	$-0.371204\pi$
$601$	6.97192e6	0.787347	0.393674	+	0.919250i	$0.371204\pi$
$602$	2.86507e6	0.322213
$603$	−1.31512e7	−1.47289
$604$	249190.	0.0277931
$605$	−366025.	−0.0406558
$606$	−6.58516e6	−0.728425
$607$	1.51167e6	0.166527	0.0832637	−	0.996528i	$-0.473466\pi$
$607$	1.51167e6	0.166527	0.0832637	+	0.996528i	$0.473466\pi$
$608$	1.87880e6	0.206121
$609$	−2.68679e7	−2.93556
$610$	−4.70045e6	−0.511464
$611$	2.98351e7	3.23314
$612$	−9.83864e6	−1.06183
$613$	1.77875e6	0.191189	0.0955945	−	0.995420i	$-0.469525\pi$
$613$	1.77875e6	0.191189	0.0955945	+	0.995420i	$0.469525\pi$
$614$	−1.38388e7	−1.48142
$615$	8.76016e6	0.933951
$616$	3.02989e6	0.321718
$617$	−1.06900e6	−0.113049	−0.0565243	−	0.998401i	$-0.518002\pi$
$617$	−1.06900e6	−0.113049	−0.0565243	+	0.998401i	$0.518002\pi$
$618$	2.33896e7	2.46349
$619$	−1.17071e7	−1.22807	−0.614037	−	0.789277i	$-0.710455\pi$
$619$	−1.17071e7	−1.22807	−0.614037	+	0.789277i	$0.710455\pi$
$620$	1.22450e6	0.127932
$621$	2.02790e7	2.11017
$622$	1.03709e7	1.07483
$623$	1.68086e7	1.73504
$624$	3.49507e7	3.59331
$625$	390625.	0.0400000
$626$	−1.07988e7	−1.10139
$627$	1.12788e6	0.114576
$628$	2.64400e6	0.267524
$629$	−1.65710e7	−1.67002
$630$	1.61571e7	1.62185
$631$	1.59388e7	1.59361	0.796806	−	0.604235i	$-0.206521\pi$
$631$	1.59388e7	1.59361	0.796806	+	0.604235i	$0.206521\pi$
$632$	−1.64024e6	−0.163349
$633$	1.28471e7	1.27437
$634$	8.02850e6	0.793252
$635$	1.03438e6	0.101800
$636$	−7.29206e6	−0.714838
$637$	−3.39347e7	−3.31356
$638$	3.92783e6	0.382033
$639$	−1.65020e7	−1.59877
$640$	5.03512e6	0.485914
$641$	−2.05286e7	−1.97339	−0.986696	−	0.162574i	$-0.948020\pi$
$641$	−2.05286e7	−1.97339	−0.986696	+	0.162574i	$0.948020\pi$
$642$	−1.39511e7	−1.33589
$643$	9.72012e6	0.927138	0.463569	−	0.886061i	$-0.346569\pi$
$643$	9.72012e6	0.927138	0.463569	+	0.886061i	$0.346569\pi$
$644$	1.49743e7	1.42276
$645$	1.21255e6	0.114762
$646$	3.71058e6	0.349833
$647$	−1.02851e7	−0.965933	−0.482966	−	0.875639i	$-0.660441\pi$
$647$	−1.02851e7	−0.965933	−0.482966	+	0.875639i	$0.660441\pi$
$648$	1.98450e6	0.185658
$649$	−5.42143e6	−0.505245
$650$	4.55974e6	0.423308
$651$	−1.79457e7	−1.65962
$652$	−5.54301e6	−0.510654
$653$	−3.54137e6	−0.325004	−0.162502	−	0.986708i	$-0.551956\pi$
$653$	−3.54137e6	−0.325004	−0.162502	+	0.986708i	$0.551956\pi$
$654$	−2.77092e7	−2.53326
$655$	−518110.	−0.0471866
$656$	1.73681e7	1.57577
$657$	−2.75326e7	−2.48847
$658$	4.30269e7	3.87414
$659$	−4.59875e6	−0.412502	−0.206251	−	0.978499i	$-0.566126\pi$
$659$	−4.59875e6	−0.412502	−0.206251	+	0.978499i	$0.566126\pi$
$660$	−1.21716e6	−0.108764
$661$	1.46896e7	1.30770	0.653849	−	0.756625i	$-0.273153\pi$
$661$	1.46896e7	1.30770	0.653849	+	0.756625i	$0.273153\pi$
$662$	−1.28296e7	−1.13780
$663$	4.06925e7	3.59526
$664$	4.32110e6	0.380341
$665$	−1.99558e6	−0.174990
$666$	−3.25043e7	−2.83959
$667$	−2.04511e7	−1.77993
$668$	5.07922e6	0.440409
$669$	5.78099e6	0.499387
$670$	−5.35247e6	−0.460646
$671$	−3.29806e6	−0.282783
$672$	2.97143e7	2.53830
$673$	−1.51328e7	−1.28790	−0.643948	−	0.765069i	$-0.722705\pi$
$673$	−1.51328e7	−1.28790	−0.643948	+	0.765069i	$0.722705\pi$
$674$	−906290.	−0.0768453
$675$	2.91642e6	0.246371
$676$	1.16450e7	0.980107
$677$	−5.16041e6	−0.432726	−0.216363	−	0.976313i	$-0.569419\pi$
$677$	−5.16041e6	−0.432726	−0.216363	+	0.976313i	$0.569419\pi$
$678$	−4.14004e7	−3.45884
$679$	−819000.	−0.0681725
$680$	4.21861e6	0.349862
$681$	−1.85623e7	−1.53378
$682$	2.62349e6	0.215982
$683$	−1.84101e7	−1.51010	−0.755048	−	0.655669i	$-0.772387\pi$
$683$	−1.84101e7	−1.51010	−0.755048	+	0.655669i	$0.772387\pi$
$684$	2.38360e6	0.194802
$685$	3.75804e6	0.306010
$686$	−2.33039e7	−1.89068
$687$	−2.40302e7	−1.94252
$688$	2.40402e6	0.193628
$689$	1.91674e7	1.53821
$690$	1.93514e7	1.54735
$691$	1.95778e7	1.55980	0.779899	−	0.625906i	$-0.215271\pi$
$691$	1.95778e7	1.55980	0.779899	+	0.625906i	$0.215271\pi$
$692$	−9.56946e6	−0.759665
$693$	1.13366e7	0.896705
$694$	−5.71972e6	−0.450792
$695$	7.73694e6	0.607585
$696$	−1.37605e7	−1.07674
$697$	2.02214e7	1.57662
$698$	2.42648e7	1.88512
$699$	−2.45594e7	−1.90118
$700$	2.15353e6	0.166114
$701$	4.73604e6	0.364016	0.182008	−	0.983297i	$-0.441740\pi$
$701$	4.73604e6	0.364016	0.182008	+	0.983297i	$0.441740\pi$
$702$	3.40432e7	2.60728
$703$	4.01464e6	0.306379
$704$	611533.	0.0465038
$705$	1.82097e7	1.37985
$706$	−5.69551e6	−0.430052
$707$	8.17507e6	0.615096
$708$	−1.80281e7	−1.35166
$709$	−1.33217e7	−0.995278	−0.497639	−	0.867384i	$-0.665799\pi$
$709$	−1.33217e7	−0.995278	−0.497639	+	0.867384i	$0.665799\pi$
$710$	−6.71625e6	−0.500013
$711$	−6.13711e6	−0.455292
$712$	8.60854e6	0.636399
$713$	−1.36598e7	−1.00628
$714$	5.86849e7	4.30805
$715$	3.19934e6	0.234042
$716$	6.48645e6	0.472851
$717$	−1.66178e7	−1.20719
$718$	2.68742e7	1.94547
$719$	−7.02316e6	−0.506653	−0.253326	−	0.967381i	$-0.581525\pi$
$719$	−7.02316e6	−0.506653	−0.253326	+	0.967381i	$0.581525\pi$
$720$	1.35571e7	0.974621
$721$	−2.90367e7	−2.08022
$722$	−898960.	−0.0641796
$723$	2.18674e7	1.55579
$724$	1.01345e7	0.718547
$725$	−2.94118e6	−0.207815
$726$	−2.60776e6	−0.183622
$727$	1.67149e7	1.17292	0.586458	−	0.809980i	$-0.300522\pi$
$727$	1.67149e7	1.17292	0.586458	+	0.809980i	$0.300522\pi$
$728$	−2.64835e7	−1.85203
$729$	−2.18532e7	−1.52299
$730$	−1.12056e7	−0.778268
$731$	2.79896e6	0.193733
$732$	−1.09672e7	−0.756514
$733$	2.55098e7	1.75367	0.876834	−	0.480793i	$-0.159651\pi$
$733$	2.55098e7	1.75367	0.876834	+	0.480793i	$0.159651\pi$
$734$	−1.93428e7	−1.32520
$735$	−2.07119e7	−1.41417
$736$	2.26178e7	1.53906
$737$	−3.75555e6	−0.254686
$738$	3.96646e7	2.68079
$739$	−1.70957e7	−1.15153	−0.575767	−	0.817614i	$-0.695296\pi$
$739$	−1.70957e7	−1.15153	−0.575767	+	0.817614i	$0.695296\pi$
$740$	−4.33241e6	−0.290838
$741$	−9.85853e6	−0.659579
$742$	2.76424e7	1.84317
$743$	−1.76269e6	−0.117139	−0.0585697	−	0.998283i	$-0.518654\pi$
$743$	−1.76269e6	−0.117139	−0.0585697	+	0.998283i	$0.518654\pi$
$744$	−9.19092e6	−0.608733
$745$	−8.52216e6	−0.562547
$746$	−3.66078e7	−2.40839
$747$	1.61677e7	1.06010
$748$	−2.80960e6	−0.183608
$749$	1.73194e7	1.12805
$750$	2.78302e6	0.180661
$751$	8.68021e6	0.561604	0.280802	−	0.959766i	$-0.409400\pi$
$751$	8.68021e6	0.561604	0.280802	+	0.959766i	$0.409400\pi$
$752$	3.61030e7	2.32809
$753$	−3.40988e7	−2.19155
$754$	−3.43322e7	−2.19925
$755$	−399779.	−0.0255242
$756$	1.60783e7	1.02314
$757$	1.61098e7	1.02177	0.510883	−	0.859650i	$-0.329319\pi$
$757$	1.61098e7	1.02177	0.510883	+	0.859650i	$0.329319\pi$
$758$	−3.45685e7	−2.18528
$759$	1.35779e7	0.855515
$760$	−1.02204e6	−0.0641850
$761$	1.85091e7	1.15857	0.579286	−	0.815124i	$-0.303331\pi$
$761$	1.85091e7	1.15857	0.579286	+	0.815124i	$0.303331\pi$
$762$	7.36949e6	0.459780
$763$	3.43992e7	2.13913
$764$	1.01408e7	0.628548
$765$	1.57843e7	0.975150
$766$	−1.07065e7	−0.659289
$767$	4.73874e7	2.90854
$768$	3.16969e7	1.93916
$769$	−4.37027e6	−0.266497	−0.133249	−	0.991083i	$-0.542541\pi$
$769$	−4.37027e6	−0.266497	−0.133249	+	0.991083i	$0.542541\pi$
$770$	4.61394e6	0.280444
$771$	2.45836e6	0.148940
$772$	2.62418e6	0.158471
$773$	1.09433e7	0.658719	0.329359	−	0.944205i	$-0.393167\pi$
$773$	1.09433e7	0.658719	0.329359	+	0.944205i	$0.393167\pi$
$774$	5.49022e6	0.329410
$775$	−1.96448e6	−0.117488
$776$	−419453.	−0.0250051
$777$	6.34938e7	3.77293
$778$	−431745.	−0.0255728
$779$	−4.89901e6	−0.289244
$780$	1.06389e7	0.626122
$781$	−4.71245e6	−0.276452
$782$	4.46695e7	2.61212
$783$	−2.19590e7	−1.27999
$784$	−4.10639e7	−2.38600
$785$	−4.24181e6	−0.245684
$786$	−3.69129e6	−0.213119
$787$	3.02319e7	1.73992	0.869959	−	0.493125i	$-0.164145\pi$
$787$	3.02319e7	1.73992	0.869959	+	0.493125i	$0.164145\pi$
$788$	−4.16296e6	−0.238829
$789$	−9.42287e6	−0.538878
$790$	−2.49778e6	−0.142392
$791$	5.13960e7	2.92071
$792$	5.80606e6	0.328904
$793$	2.88276e7	1.62789
$794$	−1.35196e7	−0.761052
$795$	1.16988e7	0.656481
$796$	−1.75934e6	−0.0984165
$797$	−1.53852e7	−0.857943	−0.428971	−	0.903318i	$-0.641124\pi$
$797$	−1.53852e7	−0.857943	−0.428971	+	0.903318i	$0.641124\pi$
$798$	−1.42176e7	−0.790347
$799$	4.20341e7	2.32935
$800$	3.25278e6	0.179692
$801$	3.22096e7	1.77380
$802$	−1.64700e7	−0.904187
$803$	−7.86242e6	−0.430296
$804$	−1.24885e7	−0.681348
$805$	−2.40235e7	−1.30661
$806$	−2.29313e7	−1.24334
$807$	−3.25469e7	−1.75924
$808$	4.18688e6	0.225612
$809$	−513318.	−0.0275750	−0.0137875	−	0.999905i	$-0.504389\pi$
$809$	−513318.	−0.0275750	−0.0137875	+	0.999905i	$0.504389\pi$
$810$	3.02201e6	0.161839
$811$	−5.62414e6	−0.300264	−0.150132	−	0.988666i	$-0.547970\pi$
$811$	−5.62414e6	−0.300264	−0.150132	+	0.988666i	$0.547970\pi$
$812$	−1.62149e7	−0.863024
$813$	−7.29421e6	−0.387036
$814$	−9.28220e6	−0.491009
$815$	8.89274e6	0.468966
$816$	4.92414e7	2.58884
$817$	−678102.	−0.0355418
$818$	623071.	0.0325577
$819$	−9.90904e7	−5.16204
$820$	5.28678e6	0.274572
$821$	−7.76101e6	−0.401847	−0.200923	−	0.979607i	$-0.564394\pi$
$821$	−7.76101e6	−0.401847	−0.200923	+	0.979607i	$0.564394\pi$
$822$	2.67743e7	1.38210
$823$	2.89763e7	1.49123	0.745614	−	0.666378i	$-0.232156\pi$
$823$	2.89763e7	1.49123	0.745614	+	0.666378i	$0.232156\pi$
$824$	−1.48712e7	−0.763006
$825$	1.95270e6	0.0998852
$826$	6.83401e7	3.48518
$827$	9.46810e6	0.481392	0.240696	−	0.970601i	$-0.422624\pi$
$827$	9.46810e6	0.481392	0.240696	+	0.970601i	$0.422624\pi$
$828$	2.86947e7	1.45454
$829$	−1.28655e7	−0.650190	−0.325095	−	0.945681i	$-0.605396\pi$
$829$	−1.28655e7	−0.650190	−0.325095	+	0.945681i	$0.605396\pi$
$830$	6.58020e6	0.331546
$831$	−2.26718e7	−1.13890
$832$	−5.34526e6	−0.267707
$833$	−4.78099e7	−2.38729
$834$	5.51221e7	2.74417
$835$	−8.14867e6	−0.404455
$836$	680680.	0.0336843
$837$	−1.46669e7	−0.723643
$838$	1.47922e7	0.727651
$839$	−2.82029e7	−1.38321	−0.691606	−	0.722275i	$-0.743097\pi$
$839$	−2.82029e7	−1.38321	−0.691606	+	0.722275i	$0.743097\pi$
$840$	−1.61641e7	−0.790413
$841$	1.63426e6	0.0796766
$842$	1.21656e7	0.591360
$843$	1.32177e7	0.640601
$844$	7.75326e6	0.374652
$845$	−1.86823e7	−0.900095
$846$	8.24507e7	3.96067
$847$	3.23737e6	0.155054
$848$	2.31942e7	1.10762
$849$	−6.17525e7	−2.94026
$850$	6.42414e6	0.304977
$851$	4.83299e7	2.28766
$852$	−1.56705e7	−0.739577
$853$	2.34337e7	1.10273	0.551364	−	0.834265i	$-0.314108\pi$
$853$	2.34337e7	1.10273	0.551364	+	0.834265i	$0.314108\pi$
$854$	4.15739e7	1.95064
$855$	−3.82405e6	−0.178899
$856$	8.87019e6	0.413760
$857$	−7.22968e6	−0.336253	−0.168127	−	0.985765i	$-0.553772\pi$
$857$	−7.22968e6	−0.336253	−0.168127	+	0.985765i	$0.553772\pi$
$858$	2.27938e7	1.05706
$859$	2.76883e7	1.28030	0.640152	−	0.768248i	$-0.278871\pi$
$859$	2.76883e7	1.28030	0.640152	+	0.768248i	$0.278871\pi$
$860$	731776.	0.0337390
$861$	−7.74806e7	−3.56193
$862$	2.03572e7	0.933149
$863$	−2.77410e7	−1.26793	−0.633964	−	0.773362i	$-0.718573\pi$
$863$	−2.77410e7	−1.26793	−0.633964	+	0.773362i	$0.718573\pi$
$864$	2.42853e7	1.10678
$865$	1.53524e7	0.697649
$866$	−2.86323e7	−1.29736
$867$	2.06690e7	0.933837
$868$	−1.08303e7	−0.487910
$869$	−1.75256e6	−0.0787270
$870$	−2.09546e7	−0.938599
$871$	3.28263e7	1.46615
$872$	1.76176e7	0.784614
$873$	−1.56942e6	−0.0696952
$874$	−1.08220e7	−0.479215
$875$	−3.45495e6	−0.152553
$876$	−2.61452e7	−1.15115
$877$	−1.87255e6	−0.0822120	−0.0411060	−	0.999155i	$-0.513088\pi$
$877$	−1.87255e6	−0.0822120	−0.0411060	+	0.999155i	$0.513088\pi$
$878$	−2.25617e7	−0.987722
$879$	−2.02443e7	−0.883752
$880$	3.87147e6	0.168527
$881$	5.98948e6	0.259986	0.129993	−	0.991515i	$-0.458505\pi$
$881$	5.98948e6	0.259986	0.129993	+	0.991515i	$0.458505\pi$
$882$	−9.37801e7	−4.05919
$883$	4.90555e6	0.211732	0.105866	−	0.994380i	$-0.466239\pi$
$883$	4.90555e6	0.211732	0.105866	+	0.994380i	$0.466239\pi$
$884$	2.45580e7	1.05697
$885$	2.89227e7	1.24131
$886$	2.22849e7	0.953734
$887$	81383.6	0.00347318	0.00173659	−	0.999998i	$-0.499447\pi$
$887$	81383.6	0.00347318	0.00173659	+	0.999998i	$0.499447\pi$
$888$	3.25185e7	1.38388
$889$	−9.14876e6	−0.388247
$890$	1.31092e7	0.554753
$891$	2.12039e6	0.0894790
$892$	3.48884e6	0.146815
$893$	−1.01836e7	−0.427338
$894$	−6.07164e7	−2.54075
$895$	−1.04063e7	−0.434249
$896$	−4.45339e7	−1.85319
$897$	−1.18681e8	−4.92493
$898$	−5.35212e7	−2.21480
$899$	1.47914e7	0.610395
$900$	4.12673e6	0.169824
$901$	2.70046e7	1.10822
$902$	1.13269e7	0.463549
$903$	−1.07246e7	−0.437684
$904$	2.63226e7	1.07129
$905$	−1.62589e7	−0.659888
$906$	−2.84824e6	−0.115280
$907$	4.33092e6	0.174808	0.0874040	−	0.996173i	$-0.472143\pi$
$907$	4.33092e6	0.174808	0.0874040	+	0.996173i	$0.472143\pi$
$908$	−1.12024e7	−0.450916
$909$	1.56656e7	0.628834
$910$	−4.03294e7	−1.61442
$911$	−1.98058e7	−0.790672	−0.395336	−	0.918537i	$-0.629372\pi$
$911$	−1.98058e7	−0.790672	−0.395336	+	0.918537i	$0.629372\pi$
$912$	−1.19297e7	−0.474943
$913$	4.61699e6	0.183308
$914$	4.04615e7	1.60205
$915$	1.75948e7	0.694755
$916$	−1.45023e7	−0.571081
$917$	4.58250e6	0.179961
$918$	4.79628e7	1.87844
$919$	−3.59571e7	−1.40442	−0.702208	−	0.711972i	$-0.747802\pi$
$919$	−3.59571e7	−1.40442	−0.702208	+	0.711972i	$0.747802\pi$
$920$	−1.23037e7	−0.479255
$921$	5.18017e7	2.01231
$922$	−4.21361e7	−1.63240
$923$	4.11904e7	1.59144
$924$	1.07653e7	0.414808
$925$	6.95056e6	0.267095
$926$	3.43721e7	1.31728
$927$	−5.56418e7	−2.12668
$928$	−2.44915e7	−0.933568
$929$	2.62857e7	0.999265	0.499632	−	0.866238i	$-0.333468\pi$
$929$	2.62857e7	0.999265	0.499632	+	0.866238i	$0.333468\pi$
$930$	−1.39960e7	−0.530637
$931$	1.15829e7	0.437968
$932$	−1.48216e7	−0.558929
$933$	−3.88204e7	−1.46001
$934$	2.35848e7	0.884638
$935$	4.50749e6	0.168619
$936$	−5.07494e7	−1.89339
$937$	1.35704e7	0.504943	0.252472	−	0.967604i	$-0.418757\pi$
$937$	1.35704e7	0.504943	0.252472	+	0.967604i	$0.418757\pi$
$938$	4.73408e7	1.75682
$939$	4.04224e7	1.49609
$940$	1.09896e7	0.405661
$941$	−9.23782e6	−0.340091	−0.170046	−	0.985436i	$-0.554392\pi$
$941$	−9.23782e6	−0.340091	−0.170046	+	0.985436i	$0.554392\pi$
$942$	−3.02209e7	−1.10964
$943$	−5.89763e7	−2.15972
$944$	5.73429e7	2.09435
$945$	−2.57947e7	−0.939618
$946$	1.56783e6	0.0569602
$947$	−2.81701e7	−1.02073	−0.510367	−	0.859957i	$-0.670491\pi$
$947$	−2.81701e7	−1.02073	−0.510367	+	0.859957i	$0.670491\pi$
$948$	−5.82785e6	−0.210614
$949$	6.87235e7	2.47708
$950$	−1.55637e6	−0.0559505
$951$	−3.00524e7	−1.07753
$952$	−3.73122e7	−1.33431
$953$	1.90675e7	0.680083	0.340042	−	0.940410i	$-0.389559\pi$
$953$	1.90675e7	0.680083	0.340042	+	0.940410i	$0.389559\pi$
$954$	5.29701e7	1.88434
$955$	−1.62690e7	−0.577236
$956$	−1.00289e7	−0.354903
$957$	−1.47027e7	−0.518941
$958$	2.93478e7	1.03315
$959$	−3.32386e7	−1.16707
$960$	−3.26246e6	−0.114253
$961$	−1.87496e7	−0.654914
$962$	8.11334e7	2.82659
$963$	3.31886e7	1.15325
$964$	1.31970e7	0.457387
$965$	−4.21001e6	−0.145534
$966$	−1.71157e8	−5.90134
$967$	1.79405e7	0.616977	0.308488	−	0.951228i	$-0.400177\pi$
$967$	1.79405e7	0.616977	0.308488	+	0.951228i	$0.400177\pi$
$968$	1.65803e6	0.0568726
$969$	−1.38895e7	−0.475201
$970$	−638746.	−0.0217971
$971$	1.81795e7	0.618776	0.309388	−	0.950936i	$-0.399876\pi$
$971$	1.81795e7	0.618776	0.309388	+	0.950936i	$0.399876\pi$
$972$	−1.06186e7	−0.360496
$973$	−6.84306e7	−2.31722
$974$	−3.20305e7	−1.08185
$975$	−1.70681e7	−0.575008
$976$	3.48839e7	1.17220
$977$	2.58272e7	0.865648	0.432824	−	0.901478i	$-0.357517\pi$
$977$	2.58272e7	0.865648	0.432824	+	0.901478i	$0.357517\pi$
$978$	6.33566e7	2.11809
$979$	9.19803e6	0.306717
$980$	−1.24997e7	−0.415752
$981$	6.59178e7	2.18691
$982$	4.47534e7	1.48097
$983$	−4.20582e7	−1.38825	−0.694124	−	0.719856i	$-0.744208\pi$
$983$	−4.20582e7	−1.38825	−0.694124	+	0.719856i	$0.744208\pi$
$984$	−3.96819e7	−1.30649
$985$	6.67871e6	0.219332
$986$	−4.83701e7	−1.58447
$987$	−1.61059e8	−5.26250
$988$	−5.94965e6	−0.193910
$989$	−8.16326e6	−0.265383
$990$	8.84152e6	0.286707
$991$	3.87533e7	1.25350	0.626750	−	0.779220i	$-0.284385\pi$
$991$	3.87533e7	1.25350	0.626750	+	0.779220i	$0.284385\pi$
$992$	−1.63584e7	−0.527792
$993$	4.80239e7	1.54555
$994$	5.94030e7	1.90696
$995$	2.82254e6	0.0903821
$996$	1.53530e7	0.490395
$997$	−2.23369e7	−0.711681	−0.355840	−	0.934547i	$-0.615805\pi$
$997$	−2.23369e7	−0.711681	−0.355840	+	0.934547i	$0.615805\pi$
$998$	9.41716e6	0.299291
$999$	5.18931e7	1.64511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.9	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-6.89804 q^{2} +25.8209 q^{3} +15.5830 q^{4} -25.0000 q^{5} -178.113 q^{6} +221.117 q^{7} +113.245 q^{8} +423.717 q^{9} +O(q^{10})\)	\(q-6.89804 q^{2} +25.8209 q^{3} +15.5830 q^{4} -25.0000 q^{5} -178.113 q^{6} +221.117 q^{7} +113.245 q^{8} +423.717 q^{9} +172.451 q^{10} +121.000 q^{11} +402.366 q^{12} -1057.63 q^{13} -1525.27 q^{14} -645.522 q^{15} -1279.83 q^{16} -1490.08 q^{17} -2922.82 q^{18} +361.000 q^{19} -389.574 q^{20} +5709.42 q^{21} -834.663 q^{22} +4345.86 q^{23} +2924.09 q^{24} +625.000 q^{25} +7295.59 q^{26} +4666.27 q^{27} +3445.65 q^{28} -4705.89 q^{29} +4452.83 q^{30} -3143.17 q^{31} +5204.44 q^{32} +3124.32 q^{33} +10278.6 q^{34} -5527.91 q^{35} +6602.77 q^{36} +11120.9 q^{37} -2490.19 q^{38} -27309.0 q^{39} -2831.13 q^{40} -13570.7 q^{41} -39383.8 q^{42} -1878.40 q^{43} +1885.54 q^{44} -10592.9 q^{45} -29977.9 q^{46} -28209.3 q^{47} -33046.2 q^{48} +32085.5 q^{49} -4311.28 q^{50} -38475.1 q^{51} -16481.0 q^{52} -18123.0 q^{53} -32188.1 q^{54} -3025.00 q^{55} +25040.4 q^{56} +9321.33 q^{57} +32461.4 q^{58} -44805.2 q^{59} -10059.1 q^{60} -27256.7 q^{61} +21681.7 q^{62} +93690.8 q^{63} +5053.99 q^{64} +26440.8 q^{65} -21551.7 q^{66} -31037.6 q^{67} -23219.8 q^{68} +112214. q^{69} +38131.8 q^{70} -38945.9 q^{71} +47984.0 q^{72} -64978.7 q^{73} -76712.4 q^{74} +16138.0 q^{75} +5625.45 q^{76} +26755.1 q^{77} +188378. q^{78} -14484.0 q^{79} +31995.7 q^{80} +17523.9 q^{81} +93611.0 q^{82} +38156.9 q^{83} +88969.7 q^{84} +37252.0 q^{85} +12957.3 q^{86} -121510. q^{87} +13702.7 q^{88} +76016.7 q^{89} +73070.4 q^{90} -233860. q^{91} +67721.4 q^{92} -81159.4 q^{93} +194589. q^{94} -9025.00 q^{95} +134383. q^{96} -3703.93 q^{97} -221327. q^{98} +51269.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 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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