LMFDB - Embedded newform 983.6.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.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:	$157.657294876$
Analytic rank:	$1$
Dimension:	$191$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.88271 q^{2} -13.0845 q^{3} +65.6680 q^{4} -13.4569 q^{5} +129.310 q^{6} -107.789 q^{7} -332.731 q^{8} -71.7966 q^{9} +O(q^{10})$	\(q-9.88271 q^{2} -13.0845 q^{3} +65.6680 q^{4} -13.4569 q^{5} +129.310 q^{6} -107.789 q^{7} -332.731 q^{8} -71.7966 q^{9} +132.990 q^{10} +680.193 q^{11} -859.231 q^{12} +495.261 q^{13} +1065.25 q^{14} +176.076 q^{15} +1186.91 q^{16} -1710.33 q^{17} +709.545 q^{18} +999.216 q^{19} -883.685 q^{20} +1410.36 q^{21} -6722.15 q^{22} -2230.95 q^{23} +4353.61 q^{24} -2943.91 q^{25} -4894.53 q^{26} +4118.95 q^{27} -7078.29 q^{28} +3951.68 q^{29} -1740.11 q^{30} +3448.32 q^{31} -1082.51 q^{32} -8899.96 q^{33} +16902.7 q^{34} +1450.50 q^{35} -4714.74 q^{36} -5484.80 q^{37} -9874.97 q^{38} -6480.23 q^{39} +4477.52 q^{40} +5512.17 q^{41} -13938.2 q^{42} -1326.15 q^{43} +44666.9 q^{44} +966.157 q^{45} +22047.8 q^{46} -15853.8 q^{47} -15530.1 q^{48} -5188.52 q^{49} +29093.8 q^{50} +22378.7 q^{51} +32522.8 q^{52} +3632.76 q^{53} -40706.4 q^{54} -9153.26 q^{55} +35864.8 q^{56} -13074.2 q^{57} -39053.3 q^{58} -11122.5 q^{59} +11562.6 q^{60} +15416.1 q^{61} -34078.7 q^{62} +7738.89 q^{63} -27283.1 q^{64} -6664.66 q^{65} +87955.8 q^{66} -18647.0 q^{67} -112314. q^{68} +29190.8 q^{69} -14334.9 q^{70} -14092.4 q^{71} +23889.0 q^{72} -5458.20 q^{73} +54204.7 q^{74} +38519.5 q^{75} +65616.6 q^{76} -73317.3 q^{77} +64042.3 q^{78} -31343.2 q^{79} -15972.1 q^{80} -36447.7 q^{81} -54475.2 q^{82} -37066.3 q^{83} +92615.7 q^{84} +23015.6 q^{85} +13105.9 q^{86} -51705.6 q^{87} -226322. q^{88} -81930.7 q^{89} -9548.25 q^{90} -53383.7 q^{91} -146502. q^{92} -45119.4 q^{93} +156679. q^{94} -13446.3 q^{95} +14164.1 q^{96} +116430. q^{97} +51276.7 q^{98} -48835.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) $ 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * 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 $

$2$	−9.88271	−1.74703	−0.873517	−	0.486794i	$-0.838166\pi$
$2$	−9.88271	−1.74703	−0.873517	+	0.486794i	$0.838166\pi$
$3$	−13.0845	−0.839369	−0.419685	−	0.907670i	$-0.637859\pi$
$3$	−13.0845	−0.839369	−0.419685	+	0.907670i	$0.637859\pi$
$4$	65.6680	2.05213
$5$	−13.4569	−0.240724	−0.120362	−	0.992730i	$-0.538405\pi$
$5$	−13.4569	−0.240724	−0.120362	+	0.992730i	$0.538405\pi$
$6$	129.310	1.46641
$7$	−107.789	−0.831437	−0.415719	−	0.909493i	$-0.636470\pi$
$7$	−107.789	−0.831437	−0.415719	+	0.909493i	$0.636470\pi$
$8$	−332.731	−1.83810
$9$	−71.7966	−0.295459
$10$	132.990	0.420552
$11$	680.193	1.69492	0.847462	−	0.530856i	$-0.178129\pi$
$11$	680.193	1.69492	0.847462	+	0.530856i	$0.178129\pi$
$12$	−859.231	−1.72249
$13$	495.261	0.812786	0.406393	−	0.913698i	$-0.366786\pi$
$13$	495.261	0.812786	0.406393	+	0.913698i	$0.366786\pi$
$14$	1065.25	1.45255
$15$	176.076	0.202056
$16$	1186.91	1.15909
$17$	−1710.33	−1.43535	−0.717674	−	0.696380i	$-0.754793\pi$
$17$	−1710.33	−1.43535	−0.717674	+	0.696380i	$0.754793\pi$
$18$	709.545	0.516177
$19$	999.216	0.635003	0.317501	−	0.948258i	$-0.397156\pi$
$19$	999.216	0.635003	0.317501	+	0.948258i	$0.397156\pi$
$20$	−883.685	−0.493995
$21$	1410.36	0.697883
$22$	−6722.15	−2.96109
$23$	−2230.95	−0.879367	−0.439683	−	0.898153i	$-0.644909\pi$
$23$	−2230.95	−0.879367	−0.439683	+	0.898153i	$0.644909\pi$
$24$	4353.61	1.54284
$25$	−2943.91	−0.942052
$26$	−4894.53	−1.41996
$27$	4118.95	1.08737
$28$	−7078.29	−1.70621
$29$	3951.68	0.872543	0.436271	−	0.899815i	$-0.356299\pi$
$29$	3951.68	0.872543	0.436271	+	0.899815i	$0.356299\pi$
$30$	−1740.11	−0.352999
$31$	3448.32	0.644471	0.322235	−	0.946660i	$-0.395566\pi$
$31$	3448.32	0.644471	0.322235	+	0.946660i	$0.395566\pi$
$32$	−1082.51	−0.186878
$33$	−8899.96	−1.42267
$34$	16902.7	2.50760
$35$	1450.50	0.200147
$36$	−4714.74	−0.606320
$37$	−5484.80	−0.658652	−0.329326	−	0.944216i	$-0.606822\pi$
$37$	−5484.80	−0.658652	−0.329326	+	0.944216i	$0.606822\pi$
$38$	−9874.97	−1.10937
$39$	−6480.23	−0.682227
$40$	4477.52	0.442474
$41$	5512.17	0.512110	0.256055	−	0.966662i	$-0.417577\pi$
$41$	5512.17	0.512110	0.256055	+	0.966662i	$0.417577\pi$
$42$	−13938.2	−1.21922
$43$	−1326.15	−0.109376	−0.0546879	−	0.998503i	$-0.517416\pi$
$43$	−1326.15	−0.109376	−0.0546879	+	0.998503i	$0.517416\pi$
$44$	44666.9	3.47820
$45$	966.157	0.0711240
$46$	22047.8	1.53628
$47$	−15853.8	−1.04686	−0.523431	−	0.852068i	$-0.675348\pi$
$47$	−15853.8	−1.04686	−0.523431	+	0.852068i	$0.675348\pi$
$48$	−15530.1	−0.972908
$49$	−5188.52	−0.308712
$50$	29093.8	1.64580
$51$	22378.7	1.20479
$52$	32522.8	1.66794
$53$	3632.76	0.177643	0.0888214	−	0.996048i	$-0.471690\pi$
$53$	3632.76	0.177643	0.0888214	+	0.996048i	$0.471690\pi$
$54$	−40706.4	−1.89967
$55$	−9153.26	−0.408008
$56$	35864.8	1.52826
$57$	−13074.2	−0.533002
$58$	−39053.3	−1.52436
$59$	−11122.5	−0.415979	−0.207990	−	0.978131i	$-0.566692\pi$
$59$	−11122.5	−0.415979	−0.207990	+	0.978131i	$0.566692\pi$
$60$	11562.6	0.414644
$61$	15416.1	0.530458	0.265229	−	0.964185i	$-0.414552\pi$
$61$	15416.1	0.530458	0.265229	+	0.964185i	$0.414552\pi$
$62$	−34078.7	−1.12591
$63$	7738.89	0.245656
$64$	−27283.1	−0.832613
$65$	−6664.66	−0.195657
$66$	87955.8	2.48545
$67$	−18647.0	−0.507483	−0.253741	−	0.967272i	$-0.581661\pi$
$67$	−18647.0	−0.507483	−0.253741	+	0.967272i	$0.581661\pi$
$68$	−112314.	−2.94551
$69$	29190.8	0.738113
$70$	−14334.9	−0.349663
$71$	−14092.4	−0.331772	−0.165886	−	0.986145i	$-0.553048\pi$
$71$	−14092.4	−0.331772	−0.165886	+	0.986145i	$0.553048\pi$
$72$	23889.0	0.543083
$73$	−5458.20	−0.119879	−0.0599394	−	0.998202i	$-0.519091\pi$
$73$	−5458.20	−0.119879	−0.0599394	+	0.998202i	$0.519091\pi$
$74$	54204.7	1.15069
$75$	38519.5	0.790730
$76$	65616.6	1.30311
$77$	−73317.3	−1.40922
$78$	64042.3	1.19187
$79$	−31343.2	−0.565036	−0.282518	−	0.959262i	$-0.591170\pi$
$79$	−31343.2	−0.565036	−0.282518	+	0.959262i	$0.591170\pi$
$80$	−15972.1	−0.279021
$81$	−36447.7	−0.617245
$82$	−54475.2	−0.894673
$83$	−37066.3	−0.590587	−0.295294	−	0.955407i	$-0.595417\pi$
$83$	−37066.3	−0.590587	−0.295294	+	0.955407i	$0.595417\pi$
$84$	92615.7	1.43214
$85$	23015.6	0.345522
$86$	13105.9	0.191083
$87$	−51705.6	−0.732385
$88$	−226322.	−3.11544
$89$	−81930.7	−1.09641	−0.548204	−	0.836345i	$-0.684688\pi$
$89$	−81930.7	−1.09641	−0.548204	+	0.836345i	$0.684688\pi$
$90$	−9548.25	−0.124256
$91$	−53383.7	−0.675780
$92$	−146502.	−1.80457
$93$	−45119.4	−0.540949
$94$	156679.	1.82890
$95$	−13446.3	−0.152860
$96$	14164.1	0.156859
$97$	116430.	1.25642	0.628211	−	0.778043i	$-0.283787\pi$
$97$	116430.	1.25642	0.628211	+	0.778043i	$0.283787\pi$
$98$	51276.7	0.539330
$99$	−48835.5	−0.500781
$100$	−193321.	−1.93321
$101$	121821.	1.18828	0.594139	−	0.804363i	$-0.297493\pi$
$101$	121821.	1.18828	0.594139	+	0.804363i	$0.297493\pi$
$102$	−221163.	−2.10480
$103$	−30737.7	−0.285482	−0.142741	−	0.989760i	$-0.545592\pi$
$103$	−30737.7	−0.285482	−0.142741	+	0.989760i	$0.545592\pi$
$104$	−164789.	−1.49398
$105$	−18979.1	−0.167997
$106$	−35901.6	−0.310348
$107$	154341.	1.30323	0.651616	−	0.758549i	$-0.274091\pi$
$107$	154341.	1.30323	0.651616	+	0.758549i	$0.274091\pi$
$108$	270483.	2.23142
$109$	204920.	1.65203	0.826017	−	0.563645i	$-0.190601\pi$
$109$	204920.	1.65203	0.826017	+	0.563645i	$0.190601\pi$
$110$	90459.1	0.712804
$111$	71765.7	0.552852
$112$	−127936.	−0.963714
$113$	−89093.6	−0.656373	−0.328186	−	0.944613i	$-0.606437\pi$
$113$	−89093.6	−0.656373	−0.328186	+	0.944613i	$0.606437\pi$
$114$	129209.	0.931172
$115$	30021.6	0.211684
$116$	259499.	1.79057
$117$	−35558.1	−0.240145
$118$	109920.	0.726730
$119$	184355.	1.19340
$120$	−58586.0	−0.371399
$121$	301611.	1.87277
$122$	−152353.	−0.926728
$123$	−72123.9	−0.429849
$124$	226444.	1.32253
$125$	81668.5	0.467498
$126$	−76481.2	−0.429169
$127$	−121327.	−0.667498	−0.333749	−	0.942662i	$-0.608314\pi$
$127$	−121327.	−0.667498	−0.333749	+	0.942662i	$0.608314\pi$
$128$	304271.	1.64148
$129$	17352.0	0.0918067
$130$	65864.9	0.341819
$131$	187011.	0.952115	0.476057	−	0.879414i	$-0.342065\pi$
$131$	187011.	0.952115	0.476057	+	0.879414i	$0.342065\pi$
$132$	−584443.	−2.91949
$133$	−107705.	−0.527965
$134$	184283.	0.886589
$135$	−55428.1	−0.261755
$136$	569080.	2.63831
$137$	268552.	1.22244	0.611220	−	0.791461i	$-0.290679\pi$
$137$	268552.	1.22244	0.611220	+	0.791461i	$0.290679\pi$
$138$	−288484.	−1.28951
$139$	134085.	0.588631	0.294315	−	0.955708i	$-0.404908\pi$
$139$	134085.	0.588631	0.294315	+	0.955708i	$0.404908\pi$
$140$	95251.6	0.410726
$141$	207439.	0.878703
$142$	139271.	0.579617
$143$	336873.	1.37761
$144$	−85216.3	−0.342465
$145$	−53177.2	−0.210042
$146$	53941.8	0.209432
$147$	67889.0	0.259123
$148$	−360176.	−1.35164
$149$	444067.	1.63864	0.819319	−	0.573338i	$-0.194352\pi$
$149$	444067.	1.63864	0.819319	+	0.573338i	$0.194352\pi$
$150$	−380678.	−1.38143
$151$	−130825.	−0.466928	−0.233464	−	0.972365i	$-0.575006\pi$
$151$	−130825.	−0.466928	−0.233464	+	0.972365i	$0.575006\pi$
$152$	−332471.	−1.16720
$153$	122796.	0.424087
$154$	724574.	2.46196
$155$	−46403.5	−0.155139
$156$	−425544.	−1.40002
$157$	−1649.19	−0.00533977	−0.00266988	−	0.999996i	$-0.500850\pi$
$157$	−1649.19	−0.00533977	−0.00266988	+	0.999996i	$0.500850\pi$
$158$	309756.	0.987136
$159$	−47532.8	−0.149108
$160$	14567.2	0.0449859
$161$	240472.	0.731138
$162$	360202.	1.07835
$163$	−679.400	−0.00200289	−0.00100144	−	0.999999i	$-0.500319\pi$
$163$	−679.400	−0.00200289	−0.00100144	+	0.999999i	$0.500319\pi$
$164$	361974.	1.05091
$165$	119766.	0.342470
$166$	366316.	1.03178
$167$	245611.	0.681485	0.340742	−	0.940157i	$-0.389322\pi$
$167$	245611.	0.681485	0.340742	+	0.940157i	$0.389322\pi$
$168$	−469272.	−1.28278
$169$	−126009.	−0.339380
$170$	−227457.	−0.603639
$171$	−71740.3	−0.187617
$172$	−87085.6	−0.224453
$173$	−223053.	−0.566622	−0.283311	−	0.959028i	$-0.591433\pi$
$173$	−223053.	−0.566622	−0.283311	+	0.959028i	$0.591433\pi$
$174$	510992.	1.27950
$175$	317322.	0.783257
$176$	807329.	1.96458
$177$	145532.	0.349160
$178$	809698.	1.91546
$179$	−44182.7	−0.103067	−0.0515335	−	0.998671i	$-0.516411\pi$
$179$	−44182.7	−0.103067	−0.0515335	+	0.998671i	$0.516411\pi$
$180$	63445.6	0.145955
$181$	−558434.	−1.26700	−0.633499	−	0.773744i	$-0.718382\pi$
$181$	−558434.	−1.26700	−0.633499	+	0.773744i	$0.718382\pi$
$182$	527576.	1.18061
$183$	−201712.	−0.445250
$184$	742307.	1.61636
$185$	73808.1	0.158553
$186$	445902.	0.945056
$187$	−1.16335e6	−2.43281
$188$	−1.04109e6	−2.14829
$189$	−443977.	−0.904079
$190$	132886.	0.267052
$191$	−65270.0	−0.129458	−0.0647292	−	0.997903i	$-0.520618\pi$
$191$	−65270.0	−0.129458	−0.0647292	+	0.997903i	$0.520618\pi$
$192$	356984.	0.698870
$193$	919499.	1.77688	0.888440	−	0.458993i	$-0.151790\pi$
$193$	919499.	1.77688	0.888440	+	0.458993i	$0.151790\pi$
$194$	−1.15064e6	−2.19501
$195$	87203.6	0.164228
$196$	−340720.	−0.633516
$197$	426267.	0.782558	0.391279	−	0.920272i	$-0.372033\pi$
$197$	426267.	0.782558	0.391279	+	0.920272i	$0.372033\pi$
$198$	482628.	0.874881
$199$	282122.	0.505015	0.252507	−	0.967595i	$-0.418745\pi$
$199$	282122.	0.505015	0.252507	+	0.967595i	$0.418745\pi$
$200$	979532.	1.73158
$201$	243986.	0.425965
$202$	−1.20392e6	−2.07596
$203$	−425948.	−0.725465
$204$	1.46957e6	2.47237
$205$	−74176.5	−0.123277
$206$	303772.	0.498746
$207$	160175.	0.259817
$208$	587832.	0.942095
$209$	679660.	1.07628
$210$	187565.	0.293496
$211$	−39365.3	−0.0608706	−0.0304353	−	0.999537i	$-0.509689\pi$
$211$	−39365.3	−0.0608706	−0.0304353	+	0.999537i	$0.509689\pi$
$212$	238556.	0.364545
$213$	184392.	0.278479
$214$	−1.52531e6	−2.27679
$215$	17845.8	0.0263293
$216$	−1.37050e6	−1.99869
$217$	−371691.	−0.535837
$218$	−2.02517e6	−2.88616
$219$	71417.7	0.100623
$220$	−601077.	−0.837285
$221$	−847059.	−1.16663
$222$	−709239.	−0.965852
$223$	−355202.	−0.478314	−0.239157	−	0.970981i	$-0.576871\pi$
$223$	−355202.	−0.478314	−0.239157	+	0.970981i	$0.576871\pi$
$224$	116683.	0.155377
$225$	211363.	0.278338
$226$	880487.	1.14670
$227$	−99207.4	−0.127785	−0.0638924	−	0.997957i	$-0.520351\pi$
$227$	−99207.4	−0.127785	−0.0638924	+	0.997957i	$0.520351\pi$
$228$	−858558.	−1.09379
$229$	1.01011e6	1.27286	0.636429	−	0.771335i	$-0.280411\pi$
$229$	1.01011e6	1.27286	0.636429	+	0.771335i	$0.280411\pi$
$230$	−296695.	−0.369820
$231$	959319.	1.18286
$232$	−1.31485e6	−1.60382
$233$	294526.	0.355414	0.177707	−	0.984083i	$-0.443132\pi$
$233$	294526.	0.355414	0.177707	+	0.984083i	$0.443132\pi$
$234$	351410.	0.419541
$235$	213343.	0.252004
$236$	−730391.	−0.853642
$237$	410109.	0.474273
$238$	−1.82192e6	−2.08491
$239$	244277.	0.276623	0.138311	−	0.990389i	$-0.455833\pi$
$239$	244277.	0.276623	0.138311	+	0.990389i	$0.455833\pi$
$240$	208987.	0.234202
$241$	34363.7	0.0381116	0.0190558	−	0.999818i	$-0.493934\pi$
$241$	34363.7	0.0381116	0.0190558	+	0.999818i	$0.493934\pi$
$242$	−2.98074e6	−3.27179
$243$	−524006.	−0.569273
$244$	1.01235e6	1.08857
$245$	69821.2	0.0743142
$246$	712780.	0.750961
$247$	494873.	0.516121
$248$	−1.14736e6	−1.18460
$249$	484993.	0.495721
$250$	−807107.	−0.816734
$251$	421134.	0.421926	0.210963	−	0.977494i	$-0.432340\pi$
$251$	421134.	0.421926	0.210963	+	0.977494i	$0.432340\pi$
$252$	508197.	0.504117
$253$	−1.51748e6	−1.49046
$254$	1.19904e6	1.16614
$255$	−301148.	−0.290021
$256$	−2.13397e6	−2.03511
$257$	1.12539e6	1.06285	0.531423	−	0.847106i	$-0.321657\pi$
$257$	1.12539e6	1.06285	0.531423	+	0.847106i	$0.321657\pi$
$258$	−171484.	−0.160389
$259$	591201.	0.547628
$260$	−437655.	−0.401512
$261$	−283717.	−0.257801
$262$	−1.84818e6	−1.66338
$263$	−1.27822e6	−1.13951	−0.569755	−	0.821815i	$-0.692962\pi$
$263$	−1.27822e6	−1.13951	−0.569755	+	0.821815i	$0.692962\pi$
$264$	2.96130e6	2.61500
$265$	−48885.6	−0.0427628
$266$	1.06441e6	0.922372
$267$	1.07202e6	0.920291
$268$	−1.22451e6	−1.04142
$269$	−1.30816e6	−1.10225	−0.551124	−	0.834423i	$-0.685801\pi$
$269$	−1.30816e6	−1.10225	−0.551124	+	0.834423i	$0.685801\pi$
$270$	547780.	0.457295
$271$	1.30650e6	1.08066	0.540328	−	0.841455i	$-0.318300\pi$
$271$	1.30650e6	1.08066	0.540328	+	0.841455i	$0.318300\pi$
$272$	−2.03001e6	−1.66370
$273$	698498.	0.567229
$274$	−2.65402e6	−2.13564
$275$	−2.00243e6	−1.59671
$276$	1.91690e6	1.51470
$277$	−579411.	−0.453720	−0.226860	−	0.973927i	$-0.572846\pi$
$277$	−579411.	−0.453720	−0.226860	+	0.973927i	$0.572846\pi$
$278$	−1.32512e6	−1.02836
$279$	−247578.	−0.190415
$280$	−482628.	−0.367889
$281$	−1.01675e6	−0.768152	−0.384076	−	0.923302i	$-0.625480\pi$
$281$	−1.01675e6	−0.768152	−0.384076	+	0.923302i	$0.625480\pi$
$282$	−2.05006e6	−1.53512
$283$	−1.72481e6	−1.28019	−0.640096	−	0.768295i	$-0.721105\pi$
$283$	−1.72481e6	−1.28019	−0.640096	+	0.768295i	$0.721105\pi$
$284$	−925421.	−0.680838
$285$	175938.	0.128306
$286$	−3.32922e6	−2.40673
$287$	−594152.	−0.425787
$288$	77720.6	0.0552147
$289$	1.50536e6	1.06022
$290$	525535.	0.366950
$291$	−1.52342e6	−1.05460
$292$	−358429.	−0.246006
$293$	316425.	0.215329	0.107664	−	0.994187i	$-0.465663\pi$
$293$	316425.	0.215329	0.107664	+	0.994187i	$0.465663\pi$
$294$	−670928.	−0.452697
$295$	149674.	0.100136
$296$	1.82496e6	1.21067
$297$	2.80168e6	1.84301
$298$	−4.38859e6	−2.86275
$299$	−1.10490e6	−0.714737
$300$	2.52950e6	1.62268
$301$	142944.	0.0909391
$302$	1.29291e6	0.815739
$303$	−1.59396e6	−0.997403
$304$	1.18598e6	0.736028
$305$	−207453.	−0.127694
$306$	−1.21355e6	−0.740894
$307$	1.90543e6	1.15384	0.576922	−	0.816800i	$-0.304254\pi$
$307$	1.90543e6	1.15384	0.576922	+	0.816800i	$0.304254\pi$
$308$	−4.81461e6	−2.89190
$309$	402186.	0.239625
$310$	458593.	0.271034
$311$	643835.	0.377462	0.188731	−	0.982029i	$-0.439562\pi$
$311$	643835.	0.377462	0.188731	+	0.982029i	$0.439562\pi$
$312$	2.15618e6	1.25400
$313$	−2.27810e6	−1.31435	−0.657177	−	0.753736i	$-0.728250\pi$
$313$	−2.27810e6	−1.31435	−0.657177	+	0.753736i	$0.728250\pi$
$314$	16298.5	0.00932875
$315$	−104141.	−0.0591352
$316$	−2.05825e6	−1.15952
$317$	2.60541e6	1.45622	0.728112	−	0.685458i	$-0.240398\pi$
$317$	2.60541e6	1.45622	0.728112	+	0.685458i	$0.240398\pi$
$318$	469753.	0.260496
$319$	2.68790e6	1.47889
$320$	367144.	0.200430
$321$	−2.01947e6	−1.09389
$322$	−2.37651e6	−1.27732
$323$	−1.70899e6	−0.911449
$324$	−2.39345e6	−1.26666
$325$	−1.45801e6	−0.765686
$326$	6714.32	0.00349911
$327$	−2.68128e6	−1.38667
$328$	−1.83407e6	−0.941309
$329$	1.70887e6	0.870400
$330$	−1.18361e6	−0.598306
$331$	−1.22901e6	−0.616575	−0.308287	−	0.951293i	$-0.599756\pi$
$331$	−1.22901e6	−0.616575	−0.308287	+	0.951293i	$0.599756\pi$
$332$	−2.43407e6	−1.21196
$333$	393790.	0.194605
$334$	−2.42730e6	−1.19058
$335$	250930.	0.122163
$336$	1.67398e6	0.808912
$337$	−107228.	−0.0514318	−0.0257159	−	0.999669i	$-0.508187\pi$
$337$	−107228.	−0.0514318	−0.0257159	+	0.999669i	$0.508187\pi$
$338$	1.24531e6	0.592907
$339$	1.16574e6	0.550939
$340$	1.51139e6	0.709055
$341$	2.34552e6	1.09233
$342$	708989.	0.327774
$343$	2.37088e6	1.08811
$344$	441251.	0.201043
$345$	−392816.	−0.177681
$346$	2.20437e6	0.989907
$347$	2.51358e6	1.12065	0.560324	−	0.828273i	$-0.310676\pi$
$347$	2.51358e6	1.12065	0.560324	+	0.828273i	$0.310676\pi$
$348$	−3.39541e6	−1.50295
$349$	183112.	0.0804737	0.0402368	−	0.999190i	$-0.487189\pi$
$349$	183112.	0.0804737	0.0402368	+	0.999190i	$0.487189\pi$
$350$	−3.13600e6	−1.36838
$351$	2.03996e6	0.883798
$352$	−736316.	−0.316743
$353$	3.02739e6	1.29310	0.646549	−	0.762873i	$-0.276212\pi$
$353$	3.02739e6	1.29310	0.646549	+	0.762873i	$0.276212\pi$
$354$	−1.43825e6	−0.609995
$355$	189640.	0.0798654
$356$	−5.38023e6	−2.24997
$357$	−2.41218e6	−1.00170
$358$	436645.	0.180061
$359$	4.10666e6	1.68172	0.840858	−	0.541255i	$-0.182051\pi$
$359$	4.10666e6	1.68172	0.840858	+	0.541255i	$0.182051\pi$
$360$	−321471.	−0.130733
$361$	−1.47767e6	−0.596772
$362$	5.51885e6	2.21349
$363$	−3.94643e6	−1.57194
$364$	−3.50561e6	−1.38679
$365$	73450.3	0.0288577
$366$	1.99346e6	0.777867
$367$	−3.59290e6	−1.39245	−0.696225	−	0.717824i	$-0.745138\pi$
$367$	−3.59290e6	−1.39245	−0.696225	+	0.717824i	$0.745138\pi$
$368$	−2.64794e6	−1.01927
$369$	−395755.	−0.151308
$370$	−729425.	−0.276998
$371$	−391572.	−0.147699
$372$	−2.96290e6	−1.11010
$373$	−4.70158e6	−1.74973	−0.874866	−	0.484365i	$-0.839051\pi$
$373$	−4.70158e6	−1.74973	−0.874866	+	0.484365i	$0.839051\pi$
$374$	1.14971e7	4.25019
$375$	−1.06859e6	−0.392403
$376$	5.27506e6	1.92423
$377$	1.95711e6	0.709190
$378$	4.38770e6	1.57946
$379$	−375819.	−0.134394	−0.0671971	−	0.997740i	$-0.521406\pi$
$379$	−375819.	−0.134394	−0.0671971	+	0.997740i	$0.521406\pi$
$380$	−882993.	−0.313688
$381$	1.58751e6	0.560277
$382$	645045.	0.226168
$383$	−1.37839e6	−0.480149	−0.240074	−	0.970755i	$-0.577172\pi$
$383$	−1.37839e6	−0.480149	−0.240074	+	0.970755i	$0.577172\pi$
$384$	−3.98123e6	−1.37781
$385$	986621.	0.339233
$386$	−9.08715e6	−3.10427
$387$	95213.0	0.0323161
$388$	7.64573e6	2.57834
$389$	−1.58274e6	−0.530317	−0.265159	−	0.964205i	$-0.585424\pi$
$389$	−1.58274e6	−0.530317	−0.265159	+	0.964205i	$0.585424\pi$
$390$	−861808.	−0.286912
$391$	3.81565e6	1.26220
$392$	1.72638e6	0.567443
$393$	−2.44694e6	−0.799176
$394$	−4.21268e6	−1.36715
$395$	421781.	0.136017
$396$	−3.20693e6	−1.02767
$397$	−1.44774e6	−0.461014	−0.230507	−	0.973071i	$-0.574039\pi$
$397$	−1.44774e6	−0.461014	−0.230507	+	0.973071i	$0.574039\pi$
$398$	−2.78813e6	−0.882278
$399$	1.40926e6	0.443158
$400$	−3.49417e6	−1.09193
$401$	−3.65140e6	−1.13396	−0.566982	−	0.823731i	$-0.691889\pi$
$401$	−3.65140e6	−1.13396	−0.566982	+	0.823731i	$0.691889\pi$
$402$	−2.41124e6	−0.744175
$403$	1.70782e6	0.523816
$404$	7.99973e6	2.43849
$405$	490471.	0.148585
$406$	4.20952e6	1.26741
$407$	−3.73072e6	−1.11637
$408$	−7.44611e6	−2.21452
$409$	−2.44561e6	−0.722900	−0.361450	−	0.932391i	$-0.617718\pi$
$409$	−2.44561e6	−0.722900	−0.361450	+	0.932391i	$0.617718\pi$
$410$	733066.	0.215369
$411$	−3.51386e6	−1.02608
$412$	−2.01848e6	−0.585844
$413$	1.19888e6	0.345861
$414$	−1.58296e6	−0.453909
$415$	498796.	0.142168
$416$	−536126.	−0.151891
$417$	−1.75443e6	−0.494078
$418$	−6.71688e6	−1.88030
$419$	−3.01034e6	−0.837685	−0.418843	−	0.908059i	$-0.637564\pi$
$419$	−3.01034e6	−0.837685	−0.418843	+	0.908059i	$0.637564\pi$
$420$	−1.24632e6	−0.344751
$421$	−3.22541e6	−0.886909	−0.443454	−	0.896297i	$-0.646247\pi$
$421$	−3.22541e6	−0.886909	−0.443454	+	0.896297i	$0.646247\pi$
$422$	389036.	0.106343
$423$	1.13825e6	0.309305
$424$	−1.20873e6	−0.326525
$425$	5.03506e6	1.35217
$426$	−1.82229e6	−0.486512
$427$	−1.66169e6	−0.441043
$428$	1.01353e7	2.67440
$429$	−4.40781e6	−1.15632
$430$	−176365.	−0.0459982
$431$	−968548.	−0.251147	−0.125573	−	0.992084i	$-0.540077\pi$
$431$	−968548.	−0.251147	−0.125573	+	0.992084i	$0.540077\pi$
$432$	4.88883e6	1.26036
$433$	−3.04394e6	−0.780219	−0.390110	−	0.920768i	$-0.627563\pi$
$433$	−3.04394e6	−0.780219	−0.390110	+	0.920768i	$0.627563\pi$
$434$	3.67332e6	0.936125
$435$	695795.	0.176303
$436$	1.34567e7	3.39018
$437$	−2.22920e6	−0.558400
$438$	−705801.	−0.175791
$439$	−3.30522e6	−0.818539	−0.409269	−	0.912414i	$-0.634216\pi$
$439$	−3.30522e6	−0.818539	−0.409269	+	0.912414i	$0.634216\pi$
$440$	3.04558e6	0.749960
$441$	372518.	0.0912118
$442$	8.37124e6	2.03814
$443$	−5.92639e6	−1.43476	−0.717382	−	0.696680i	$-0.754660\pi$
$443$	−5.92639e6	−1.43476	−0.717382	+	0.696680i	$0.754660\pi$
$444$	4.71271e6	1.13452
$445$	1.10253e6	0.263931
$446$	3.51036e6	0.835630
$447$	−5.81038e6	−1.37542
$448$	2.94081e6	0.692265
$449$	−3.36874e6	−0.788590	−0.394295	−	0.918984i	$-0.629011\pi$
$449$	−3.36874e6	−0.788590	−0.394295	+	0.918984i	$0.629011\pi$
$450$	−2.08884e6	−0.486266
$451$	3.74934e6	0.867988
$452$	−5.85060e6	−1.34696
$453$	1.71178e6	0.391925
$454$	980438.	0.223244
$455$	718378.	0.162676
$456$	4.35020e6	0.979710
$457$	1.74926e6	0.391800	0.195900	−	0.980624i	$-0.437237\pi$
$457$	1.74926e6	0.391800	0.195900	+	0.980624i	$0.437237\pi$
$458$	−9.98263e6	−2.22372
$459$	−7.04475e6	−1.56075
$460$	1.97146e6	0.434403
$461$	−3.02078e6	−0.662014	−0.331007	−	0.943628i	$-0.607388\pi$
$461$	−3.02078e6	−0.662014	−0.331007	+	0.943628i	$0.607388\pi$
$462$	−9.48067e6	−2.06649
$463$	−1.51452e6	−0.328339	−0.164170	−	0.986432i	$-0.552494\pi$
$463$	−1.51452e6	−0.328339	−0.164170	+	0.986432i	$0.552494\pi$
$464$	4.69030e6	1.01136
$465$	607166.	0.130219
$466$	−2.91072e6	−0.620919
$467$	4.77493e6	1.01315	0.506576	−	0.862195i	$-0.330911\pi$
$467$	4.77493e6	1.01315	0.506576	+	0.862195i	$0.330911\pi$
$468$	−2.33503e6	−0.492808
$469$	2.00994e6	0.421940
$470$	−2.10840e6	−0.440260
$471$	21578.8	0.00448204
$472$	3.70080e6	0.764611
$473$	−902037.	−0.185384
$474$	−4.05299e6	−0.828572
$475$	−2.94161e6	−0.598206
$476$	1.21062e7	2.44901
$477$	−260820.	−0.0524862
$478$	−2.41412e6	−0.483269
$479$	213780.	0.0425724	0.0212862	−	0.999773i	$-0.493224\pi$
$479$	213780.	0.0425724	0.0212862	+	0.999773i	$0.493224\pi$
$480$	−190604.	−0.0377597
$481$	−2.71641e6	−0.535343
$482$	−339607.	−0.0665823
$483$	−3.14645e6	−0.613695
$484$	1.98062e7	3.84316
$485$	−1.56678e6	−0.302450
$486$	5.17860e6	0.994538
$487$	−2.71191e6	−0.518148	−0.259074	−	0.965858i	$-0.583417\pi$
$487$	−2.71191e6	−0.518148	−0.259074	+	0.965858i	$0.583417\pi$
$488$	−5.12944e6	−0.975035
$489$	8889.59	0.00168116
$490$	−690023.	−0.129829
$491$	234230.	0.0438468	0.0219234	−	0.999760i	$-0.493021\pi$
$491$	234230.	0.0438468	0.0219234	+	0.999760i	$0.493021\pi$
$492$	−4.73623e6	−0.882105
$493$	−6.75867e6	−1.25240
$494$	−4.89069e6	−0.901681
$495$	657173.	0.120550
$496$	4.09285e6	0.747002
$497$	1.51901e6	0.275848
$498$	−4.79305e6	−0.866041
$499$	−2.52460e6	−0.453881	−0.226940	−	0.973909i	$-0.572872\pi$
$499$	−2.52460e6	−0.453881	−0.226940	+	0.973909i	$0.572872\pi$
$500$	5.36301e6	0.959364
$501$	−3.21369e6	−0.572017
$502$	−4.16195e6	−0.737119
$503$	−263576.	−0.0464500	−0.0232250	−	0.999730i	$-0.507393\pi$
$503$	−263576.	−0.0464500	−0.0232250	+	0.999730i	$0.507393\pi$
$504$	−2.57497e6	−0.451540
$505$	−1.63932e6	−0.286046
$506$	1.49968e7	2.60388
$507$	1.64876e6	0.284865
$508$	−7.96734e6	−1.36979
$509$	−8.72460e6	−1.49263	−0.746313	−	0.665595i	$-0.768178\pi$
$509$	−8.72460e6	−1.49263	−0.746313	+	0.665595i	$0.768178\pi$
$510$	2.97615e6	0.506676
$511$	588334.	0.0996717
$512$	1.13527e7	1.91392
$513$	4.11572e6	0.690482
$514$	−1.11219e7	−1.85683
$515$	413633.	0.0687222
$516$	1.13947e6	0.188399
$517$	−1.07837e7	−1.77435
$518$	−5.84267e6	−0.956724
$519$	2.91853e6	0.475605
$520$	2.21754e6	0.359636
$521$	1.62545e6	0.262349	0.131174	−	0.991359i	$-0.458125\pi$
$521$	1.62545e6	0.262349	0.131174	+	0.991359i	$0.458125\pi$
$522$	2.80389e6	0.450387
$523$	−1.02405e7	−1.63707	−0.818533	−	0.574460i	$-0.805212\pi$
$523$	−1.02405e7	−1.63707	−0.818533	+	0.574460i	$0.805212\pi$
$524$	1.22807e7	1.95386
$525$	−4.15199e6	−0.657442
$526$	1.26323e7	1.99076
$527$	−5.89775e6	−0.925039
$528$	−1.05635e7	−1.64901
$529$	−1.45921e6	−0.226714
$530$	483122.	0.0747081
$531$	798556.	0.122905
$532$	−7.07275e6	−1.08345
$533$	2.72997e6	0.416236
$534$	−1.05945e7	−1.60778
$535$	−2.07695e6	−0.313719
$536$	6.20443e6	0.932803
$537$	578107.	0.0865112
$538$	1.29281e7	1.92566
$539$	−3.52919e6	−0.523243
$540$	−3.63985e6	−0.537155
$541$	7.74653e6	1.13793	0.568963	−	0.822363i	$-0.307345\pi$
$541$	7.74653e6	1.13793	0.568963	+	0.822363i	$0.307345\pi$
$542$	−1.29118e7	−1.88794
$543$	7.30682e6	1.06348
$544$	1.85145e6	0.268234
$545$	−2.75759e6	−0.397684
$546$	−6.90306e6	−0.990968
$547$	2.31282e6	0.330502	0.165251	−	0.986252i	$-0.447157\pi$
$547$	2.31282e6	0.330502	0.165251	+	0.986252i	$0.447157\pi$
$548$	1.76353e7	2.50860
$549$	−1.10683e6	−0.156729
$550$	1.97894e7	2.78950
$551$	3.94858e6	0.554067
$552$	−9.71269e6	−1.35673
$553$	3.37845e6	0.469792
$554$	5.72615e6	0.792663
$555$	−965740.	−0.133085
$556$	8.80509e6	1.20794
$557$	1.02500e7	1.39987	0.699933	−	0.714208i	$-0.253213\pi$
$557$	1.02500e7	1.39987	0.699933	+	0.714208i	$0.253213\pi$
$558$	2.44674e6	0.332661
$559$	−656790.	−0.0888991
$560$	1.72162e6	0.231989
$561$	1.52219e7	2.04202
$562$	1.00482e7	1.34199
$563$	1.30091e7	1.72973	0.864863	−	0.502008i	$-0.167405\pi$
$563$	1.30091e7	1.72973	0.864863	+	0.502008i	$0.167405\pi$
$564$	1.36221e7	1.80321
$565$	1.19892e6	0.158004
$566$	1.70458e7	2.23654
$567$	3.92866e6	0.513200
$568$	4.68899e6	0.609830
$569$	−6.11783e6	−0.792167	−0.396084	−	0.918214i	$-0.629631\pi$
$569$	−6.11783e6	−0.792167	−0.396084	+	0.918214i	$0.629631\pi$
$570$	−1.73874e6	−0.224155
$571$	6.34781e6	0.814767	0.407384	−	0.913257i	$-0.366441\pi$
$571$	6.34781e6	0.814767	0.407384	+	0.913257i	$0.366441\pi$
$572$	2.21218e7	2.82703
$573$	854024.	0.108663
$574$	5.87183e6	0.743865
$575$	6.56772e6	0.828409
$576$	1.95883e6	0.246003
$577$	−3.88404e6	−0.485674	−0.242837	−	0.970067i	$-0.578078\pi$
$577$	−3.88404e6	−0.485674	−0.242837	+	0.970067i	$0.578078\pi$
$578$	−1.48771e7	−1.85224
$579$	−1.20312e7	−1.49146
$580$	−3.49204e6	−0.431032
$581$	3.99534e6	0.491036
$582$	1.50556e7	1.84242
$583$	2.47098e6	0.301091
$584$	1.81612e6	0.220349
$585$	478500.	0.0578086
$586$	−3.12714e6	−0.376186
$587$	2.29433e6	0.274828	0.137414	−	0.990514i	$-0.456121\pi$
$587$	2.29433e6	0.274828	0.137414	+	0.990514i	$0.456121\pi$
$588$	4.45814e6	0.531753
$589$	3.44562e6	0.409241
$590$	−1.47918e6	−0.174941
$591$	−5.57748e6	−0.656855
$592$	−6.50997e6	−0.763440
$593$	8.88309e6	1.03736	0.518678	−	0.854970i	$-0.326424\pi$
$593$	8.88309e6	1.03736	0.518678	+	0.854970i	$0.326424\pi$
$594$	−2.76882e7	−3.21980
$595$	−2.48083e6	−0.287280
$596$	2.91610e7	3.36269
$597$	−3.69142e6	−0.423894
$598$	1.09194e7	1.24867
$599$	8.71980e6	0.992978	0.496489	−	0.868043i	$-0.334622\pi$
$599$	8.71980e6	0.992978	0.496489	+	0.868043i	$0.334622\pi$
$600$	−1.28167e7	−1.45344
$601$	−9.82734e6	−1.10981	−0.554906	−	0.831913i	$-0.687246\pi$
$601$	−9.82734e6	−1.10981	−0.554906	+	0.831913i	$0.687246\pi$
$602$	−1.41268e6	−0.158874
$603$	1.33879e6	0.149940
$604$	−8.59105e6	−0.958195
$605$	−4.05874e6	−0.450820
$606$	1.57526e7	1.74250
$607$	1.52445e6	0.167935	0.0839673	−	0.996469i	$-0.473241\pi$
$607$	1.52445e6	0.167935	0.0839673	+	0.996469i	$0.473241\pi$
$608$	−1.08166e6	−0.118668
$609$	5.57330e6	0.608933
$610$	2.05020e6	0.223085
$611$	−7.85178e6	−0.850874
$612$	8.06375e6	0.870279
$613$	−9.12714e6	−0.981032	−0.490516	−	0.871432i	$-0.663192\pi$
$613$	−9.12714e6	−0.981032	−0.490516	+	0.871432i	$0.663192\pi$
$614$	−1.88308e7	−2.01580
$615$	970561.	0.103475
$616$	2.43950e7	2.59029
$617$	1.55732e7	1.64689	0.823446	−	0.567394i	$-0.192048\pi$
$617$	1.55732e7	1.64689	0.823446	+	0.567394i	$0.192048\pi$
$618$	−3.97469e6	−0.418632
$619$	2.07705e6	0.217882	0.108941	−	0.994048i	$-0.465254\pi$
$619$	2.07705e6	0.217882	0.108941	+	0.994048i	$0.465254\pi$
$620$	−3.04723e6	−0.318365
$621$	−9.18916e6	−0.956196
$622$	−6.36284e6	−0.659440
$623$	8.83124e6	0.911594
$624$	−7.69147e6	−0.790766
$625$	8.10073e6	0.829514
$626$	2.25138e7	2.29622
$627$	−8.89299e6	−0.903398
$628$	−108299.	−0.0109579
$629$	9.38080e6	0.945395
$630$	1.02920e6	0.103311
$631$	−4.67475e6	−0.467396	−0.233698	−	0.972309i	$-0.575083\pi$
$631$	−4.67475e6	−0.467396	−0.233698	+	0.972309i	$0.575083\pi$
$632$	1.04289e7	1.03859
$633$	515075.	0.0510929
$634$	−2.57485e7	−2.54407
$635$	1.63269e6	0.160683
$636$	−3.12138e6	−0.305988
$637$	−2.56967e6	−0.250917
$638$	−2.65638e7	−2.58368
$639$	1.01179e6	0.0980251
$640$	−4.09453e6	−0.395143
$641$	9.73129e6	0.935461	0.467730	−	0.883871i	$-0.345072\pi$
$641$	9.73129e6	0.935461	0.467730	+	0.883871i	$0.345072\pi$
$642$	1.99578e7	1.91107
$643$	−1.56325e7	−1.49108	−0.745539	−	0.666462i	$-0.767808\pi$
$643$	−1.56325e7	−1.49108	−0.745539	+	0.666462i	$0.767808\pi$
$644$	1.57913e7	1.50039
$645$	−233503.	−0.0221000
$646$	1.68894e7	1.59233
$647$	2.17979e6	0.204717	0.102358	−	0.994748i	$-0.467361\pi$
$647$	2.17979e6	0.204717	0.102358	+	0.994748i	$0.467361\pi$
$648$	1.21273e7	1.13456
$649$	−7.56543e6	−0.705053
$650$	1.44091e7	1.33768
$651$	4.86338e6	0.449765
$652$	−44614.9	−0.00411018
$653$	1.88716e6	0.173191	0.0865954	−	0.996244i	$-0.472401\pi$
$653$	1.88716e6	0.173191	0.0865954	+	0.996244i	$0.472401\pi$
$654$	2.64983e7	2.42255
$655$	−2.51658e6	−0.229197
$656$	6.54247e6	0.593584
$657$	391880.	0.0354193
$658$	−1.68883e7	−1.52062
$659$	−8.08845e6	−0.725524	−0.362762	−	0.931882i	$-0.618166\pi$
$659$	−8.08845e6	−0.725524	−0.362762	+	0.931882i	$0.618166\pi$
$660$	7.86477e6	0.702791
$661$	−6.56117e6	−0.584088	−0.292044	−	0.956405i	$-0.594335\pi$
$661$	−6.56117e6	−0.584088	−0.292044	+	0.956405i	$0.594335\pi$
$662$	1.21460e7	1.07718
$663$	1.10833e7	0.979233
$664$	1.23331e7	1.08556
$665$	1.44937e6	0.127094
$666$	−3.89171e6	−0.339981
$667$	−8.81599e6	−0.767285
$668$	1.61288e7	1.39849
$669$	4.64762e6	0.401482
$670$	−2.47986e6	−0.213423
$671$	1.04860e7	0.899087
$672$	−1.52673e6	−0.130419
$673$	−1.71265e6	−0.145758	−0.0728789	−	0.997341i	$-0.523219\pi$
$673$	−1.71265e6	−0.145758	−0.0728789	+	0.997341i	$0.523219\pi$
$674$	1.05970e6	0.0898531
$675$	−1.21258e7	−1.02436
$676$	−8.27478e6	−0.696449
$677$	−1.74218e7	−1.46090	−0.730450	−	0.682966i	$-0.760690\pi$
$677$	−1.74218e7	−1.46090	−0.730450	+	0.682966i	$0.760690\pi$
$678$	−1.15207e7	−0.962509
$679$	−1.25499e7	−1.04464
$680$	−7.65803e6	−0.635104
$681$	1.29808e6	0.107259
$682$	−2.31801e7	−1.90834
$683$	8.35972e6	0.685709	0.342855	−	0.939388i	$-0.388606\pi$
$683$	8.35972e6	0.685709	0.342855	+	0.939388i	$0.388606\pi$
$684$	−4.71105e6	−0.385014
$685$	−3.61387e6	−0.294270
$686$	−2.34307e7	−1.90097
$687$	−1.32168e7	−1.06840
$688$	−1.57402e6	−0.126777
$689$	1.79917e6	0.144385
$690$	3.88209e6	0.310415
$691$	−6.60853e6	−0.526514	−0.263257	−	0.964726i	$-0.584797\pi$
$691$	−6.60853e6	−0.526514	−0.263257	+	0.964726i	$0.584797\pi$
$692$	−1.46475e7	−1.16278
$693$	5.26394e6	0.416368
$694$	−2.48410e7	−1.95781
$695$	−1.80436e6	−0.141697
$696$	1.72041e7	1.34620
$697$	−9.42762e6	−0.735056
$698$	−1.80965e6	−0.140590
$699$	−3.85372e6	−0.298323
$700$	2.08379e7	1.60734
$701$	−1.06575e7	−0.819146	−0.409573	−	0.912277i	$-0.634322\pi$
$701$	−1.06575e7	−0.819146	−0.409573	+	0.912277i	$0.634322\pi$
$702$	−2.01603e7	−1.54402
$703$	−5.48050e6	−0.418246
$704$	−1.85577e7	−1.41122
$705$	−2.79148e6	−0.211525
$706$	−2.99188e7	−2.25908
$707$	−1.31309e7	−0.987978
$708$	9.55679e6	0.716521
$709$	4.85502e6	0.362724	0.181362	−	0.983416i	$-0.441950\pi$
$709$	4.85502e6	0.362724	0.181362	+	0.983416i	$0.441950\pi$
$710$	−1.87416e6	−0.139527
$711$	2.25034e6	0.166945
$712$	2.72609e7	2.01530
$713$	−7.69302e6	−0.566726
$714$	2.38389e7	1.75001
$715$	−4.53326e6	−0.331623
$716$	−2.90139e6	−0.211506
$717$	−3.19624e6	−0.232189
$718$	−4.05850e7	−2.93802
$719$	1.34645e6	0.0971330	0.0485665	−	0.998820i	$-0.484535\pi$
$719$	1.34645e6	0.0971330	0.0485665	+	0.998820i	$0.484535\pi$
$720$	1.14674e6	0.0824394
$721$	3.31319e6	0.237360
$722$	1.46033e7	1.04258
$723$	−449631.	−0.0319897
$724$	−3.66713e7	−2.60004
$725$	−1.16334e7	−0.821981
$726$	3.90014e7	2.74624
$727$	−347808.	−0.0244064	−0.0122032	−	0.999926i	$-0.503884\pi$
$727$	−347808.	−0.0244064	−0.0122032	+	0.999926i	$0.503884\pi$
$728$	1.77625e7	1.24215
$729$	1.57131e7	1.09507
$730$	−725888.	−0.0504153
$731$	2.26815e6	0.156992
$732$	−1.32460e7	−0.913710
$733$	−1.50471e7	−1.03441	−0.517204	−	0.855862i	$-0.673027\pi$
$733$	−1.50471e7	−1.03441	−0.517204	+	0.855862i	$0.673027\pi$
$734$	3.55076e7	2.43266
$735$	−913573.	−0.0623771
$736$	2.41503e6	0.164334
$737$	−1.26835e7	−0.860145
$738$	3.91114e6	0.264339
$739$	2.57267e7	1.73290	0.866449	−	0.499265i	$-0.166397\pi$
$739$	2.57267e7	1.73290	0.866449	+	0.499265i	$0.166397\pi$
$740$	4.84683e6	0.325371
$741$	−6.47515e6	−0.433216
$742$	3.86980e6	0.258035
$743$	7.95497e6	0.528648	0.264324	−	0.964434i	$-0.414851\pi$
$743$	7.95497e6	0.528648	0.264324	+	0.964434i	$0.414851\pi$
$744$	1.50127e7	0.994317
$745$	−5.97575e6	−0.394459
$746$	4.64644e7	3.05684
$747$	2.66123e6	0.174494
$748$	−7.63951e7	−4.99242
$749$	−1.66363e7	−1.08356
$750$	1.05606e7	0.685542
$751$	−8.90155e6	−0.575925	−0.287962	−	0.957642i	$-0.592978\pi$
$751$	−8.90155e6	−0.575925	−0.287962	+	0.957642i	$0.592978\pi$
$752$	−1.88171e7	−1.21341
$753$	−5.51032e6	−0.354152
$754$	−1.93416e7	−1.23898
$755$	1.76050e6	0.112401
$756$	−2.91551e7	−1.85528
$757$	−1.13685e7	−0.721048	−0.360524	−	0.932750i	$-0.617402\pi$
$757$	−1.13685e7	−0.721048	−0.360524	+	0.932750i	$0.617402\pi$
$758$	3.71411e6	0.234791
$759$	1.98554e7	1.25105
$760$	4.47401e6	0.280972
$761$	4.30228e6	0.269300	0.134650	−	0.990893i	$-0.457009\pi$
$761$	4.30228e6	0.269300	0.134650	+	0.990893i	$0.457009\pi$
$762$	−1.56889e7	−0.978823
$763$	−2.20882e7	−1.37356
$764$	−4.28615e6	−0.265665
$765$	−1.65244e6	−0.102088
$766$	1.36222e7	0.838836
$767$	−5.50853e6	−0.338102
$768$	2.79218e7	1.70821
$769$	−1.72965e7	−1.05473	−0.527365	−	0.849639i	$-0.676820\pi$
$769$	−1.72965e7	−1.05473	−0.527365	+	0.849639i	$0.676820\pi$
$770$	−9.75050e6	−0.592652
$771$	−1.47251e7	−0.892121
$772$	6.03817e7	3.64638
$773$	1.78750e7	1.07597	0.537983	−	0.842956i	$-0.319186\pi$
$773$	1.78750e7	1.07597	0.537983	+	0.842956i	$0.319186\pi$
$774$	−940963.	−0.0564573
$775$	−1.01515e7	−0.607125
$776$	−3.87399e7	−2.30943
$777$	−7.73555e6	−0.459662
$778$	1.56418e7	0.926482
$779$	5.50785e6	0.325191
$780$	5.72649e6	0.337017
$781$	−9.58556e6	−0.562328
$782$	−3.77090e7	−2.20510
$783$	1.62768e7	0.948776
$784$	−6.15832e6	−0.357826
$785$	22193.0	0.00128541
$786$	2.41824e7	1.39619
$787$	1.28564e7	0.739916	0.369958	−	0.929049i	$-0.379372\pi$
$787$	1.28564e7	0.739916	0.369958	+	0.929049i	$0.379372\pi$
$788$	2.79921e7	1.60591
$789$	1.67249e7	0.956469
$790$	−4.16834e6	−0.237627
$791$	9.60332e6	0.545733
$792$	1.62491e7	0.920485
$793$	7.63502e6	0.431149
$794$	1.43076e7	0.805408
$795$	639642.	0.0358938
$796$	1.85264e7	1.03635
$797$	−7.65415e6	−0.426826	−0.213413	−	0.976962i	$-0.568458\pi$
$797$	−7.65415e6	−0.426826	−0.213413	+	0.976962i	$0.568458\pi$
$798$	−1.39273e7	−0.774211
$799$	2.71152e7	1.50261
$800$	3.18682e6	0.176048
$801$	5.88235e6	0.323944
$802$	3.60858e7	1.98107
$803$	−3.71263e6	−0.203186
$804$	1.60221e7	0.874134
$805$	−3.23600e6	−0.176002
$806$	−1.68779e7	−0.915125
$807$	1.71165e7	0.925193
$808$	−4.05336e7	−2.18417
$809$	1.12760e7	0.605736	0.302868	−	0.953033i	$-0.402056\pi$
$809$	1.12760e7	0.605736	0.302868	+	0.953033i	$0.402056\pi$
$810$	−4.84719e6	−0.259584
$811$	1.94655e7	1.03923	0.519617	−	0.854399i	$-0.326075\pi$
$811$	1.94655e7	1.03923	0.519617	+	0.854399i	$0.326075\pi$
$812$	−2.79711e7	−1.48874
$813$	−1.70949e7	−0.907069
$814$	3.68696e7	1.95033
$815$	9142.59	0.000482142 0
$816$	2.65616e7	1.39646
$817$	−1.32511e6	−0.0694539
$818$	2.41692e7	1.26293
$819$	3.83277e6	0.199666
$820$	−4.87103e6	−0.252980
$821$	−1.65808e7	−0.858516	−0.429258	−	0.903182i	$-0.641225\pi$
$821$	−1.65808e7	−0.858516	−0.429258	+	0.903182i	$0.641225\pi$
$822$	3.47265e7	1.79259
$823$	−1.08232e7	−0.557000	−0.278500	−	0.960436i	$-0.589837\pi$
$823$	−1.08232e7	−0.557000	−0.278500	+	0.960436i	$0.589837\pi$
$824$	1.02274e7	0.524743
$825$	2.62007e7	1.34023
$826$	−1.18482e7	−0.604230
$827$	1.72273e7	0.875900	0.437950	−	0.898999i	$-0.355705\pi$
$827$	1.72273e7	0.875900	0.437950	+	0.898999i	$0.355705\pi$
$828$	1.05183e7	0.533177
$829$	1.72592e7	0.872235	0.436118	−	0.899890i	$-0.356353\pi$
$829$	1.72592e7	0.872235	0.436118	+	0.899890i	$0.356353\pi$
$830$	−4.92946e6	−0.248373
$831$	7.58129e6	0.380838
$832$	−1.35122e7	−0.676736
$833$	8.87407e6	0.443109
$834$	1.73385e7	0.863171
$835$	−3.30515e6	−0.164049
$836$	4.46319e7	2.20866
$837$	1.42034e7	0.700777
$838$	2.97503e7	1.46346
$839$	1.81679e7	0.891044	0.445522	−	0.895271i	$-0.353018\pi$
$839$	1.81679e7	0.891044	0.445522	+	0.895271i	$0.353018\pi$
$840$	6.31493e6	0.308795
$841$	−4.89538e6	−0.238669
$842$	3.18758e7	1.54946
$843$	1.33036e7	0.644763
$844$	−2.58504e6	−0.124914
$845$	1.69569e6	0.0816967
$846$	−1.12490e7	−0.540366
$847$	−3.25104e7	−1.55709
$848$	4.31177e6	0.205905
$849$	2.25682e7	1.07455
$850$	−4.97600e7	−2.36229
$851$	1.22363e7	0.579197
$852$	1.21086e7	0.571474
$853$	−2.73727e7	−1.28809	−0.644044	−	0.764988i	$-0.722745\pi$
$853$	−2.73727e7	−1.28809	−0.644044	+	0.764988i	$0.722745\pi$
$854$	1.64220e7	0.770517
$855$	965400.	0.0451639
$856$	−5.13541e7	−2.39547
$857$	−1.97356e7	−0.917906	−0.458953	−	0.888460i	$-0.651775\pi$
$857$	−1.97356e7	−0.917906	−0.458953	+	0.888460i	$0.651775\pi$
$858$	4.35611e7	2.02014
$859$	−1.64807e7	−0.762068	−0.381034	−	0.924561i	$-0.624432\pi$
$859$	−1.64807e7	−0.762068	−0.381034	+	0.924561i	$0.624432\pi$
$860$	1.17190e6	0.0540311
$861$	7.77416e6	0.357393
$862$	9.57188e6	0.438762
$863$	−4.23583e6	−0.193603	−0.0968013	−	0.995304i	$-0.530861\pi$
$863$	−4.23583e6	−0.193603	−0.0968013	+	0.995304i	$0.530861\pi$
$864$	−4.45880e6	−0.203205
$865$	3.00160e6	0.136399
$866$	3.00824e7	1.36307
$867$	−1.96969e7	−0.889918
$868$	−2.44082e7	−1.09960
$869$	−2.13194e7	−0.957693
$870$	−6.87635e6	−0.308006
$871$	−9.23512e6	−0.412474
$872$	−6.81835e7	−3.03660
$873$	−8.35928e6	−0.371222
$874$	2.20305e7	0.975544
$875$	−8.80297e6	−0.388695
$876$	4.68986e6	0.206490
$877$	−3.23081e7	−1.41844	−0.709222	−	0.704985i	$-0.750954\pi$
$877$	−3.23081e7	−1.41844	−0.709222	+	0.704985i	$0.750954\pi$
$878$	3.26646e7	1.43001
$879$	−4.14025e6	−0.180740
$880$	−1.08641e7	−0.472920
$881$	2.23632e7	0.970721	0.485360	−	0.874314i	$-0.338688\pi$
$881$	2.23632e7	0.970721	0.485360	+	0.874314i	$0.338688\pi$
$882$	−3.68149e6	−0.159350
$883$	−3.98231e7	−1.71883	−0.859416	−	0.511277i	$-0.829173\pi$
$883$	−3.98231e7	−1.71883	−0.859416	+	0.511277i	$0.829173\pi$
$884$	−5.56247e7	−2.39407
$885$	−1.95840e6	−0.0840511
$886$	5.85688e7	2.50658
$887$	2.61558e6	0.111625	0.0558123	−	0.998441i	$-0.482225\pi$
$887$	2.61558e6	0.111625	0.0558123	+	0.998441i	$0.482225\pi$
$888$	−2.38787e7	−1.01620
$889$	1.30778e7	0.554983
$890$	−1.08960e7	−0.461097
$891$	−2.47915e7	−1.04618
$892$	−2.33254e7	−0.981560
$893$	−1.58414e7	−0.664760
$894$	5.74224e7	2.40291
$895$	594560.	0.0248106
$896$	−3.27971e7	−1.36479
$897$	1.44571e7	0.599928
$898$	3.32923e7	1.37769
$899$	1.36266e7	0.562328
$900$	1.38798e7	0.571185
$901$	−6.21322e6	−0.254979
$902$	−3.70537e7	−1.51640
$903$	−1.87035e6	−0.0763315
$904$	2.96442e7	1.20648
$905$	7.51477e6	0.304996
$906$	−1.69170e7	−0.684706
$907$	4.75736e7	1.92021	0.960103	−	0.279648i	$-0.0902178\pi$
$907$	4.75736e7	1.92021	0.960103	+	0.279648i	$0.0902178\pi$
$908$	−6.51475e6	−0.262231
$909$	−8.74631e6	−0.351088
$910$	−7.09952e6	−0.284201
$911$	1.61853e7	0.646137	0.323068	−	0.946376i	$-0.395286\pi$
$911$	1.61853e7	0.646137	0.323068	+	0.946376i	$0.395286\pi$
$912$	−1.55180e7	−0.617799
$913$	−2.52122e7	−1.00100
$914$	−1.72875e7	−0.684488
$915$	2.71441e6	0.107182
$916$	6.63319e7	2.61206
$917$	−2.01578e7	−0.791624
$918$	6.96212e7	2.72669
$919$	−1.41251e7	−0.551698	−0.275849	−	0.961201i	$-0.588959\pi$
$919$	−1.41251e7	−0.551698	−0.275849	+	0.961201i	$0.588959\pi$
$920$	−9.98912e6	−0.389097
$921$	−2.49315e7	−0.968500
$922$	2.98535e7	1.15656
$923$	−6.97943e6	−0.269659
$924$	6.29966e7	2.42738
$925$	1.61468e7	0.620485
$926$	1.49676e7	0.573619
$927$	2.20686e6	0.0843482
$928$	−4.27774e6	−0.163059
$929$	1.67879e7	0.638200	0.319100	−	0.947721i	$-0.396619\pi$
$929$	1.67879e7	0.638200	0.319100	+	0.947721i	$0.396619\pi$
$930$	−6.00045e6	−0.227497
$931$	−5.18445e6	−0.196033
$932$	1.93409e7	0.729353
$933$	−8.42424e6	−0.316830
$934$	−4.71893e7	−1.77001
$935$	1.56551e7	0.585634
$936$	1.18313e7	0.441410
$937$	157201.	0.00584934	0.00292467	−	0.999996i	$-0.499069\pi$
$937$	157201.	0.00584934	0.00292467	+	0.999996i	$0.499069\pi$
$938$	−1.98636e7	−0.737143
$939$	2.98078e7	1.10323
$940$	1.40098e7	0.517145
$941$	1.80150e7	0.663223	0.331612	−	0.943416i	$-0.392408\pi$
$941$	1.80150e7	0.663223	0.331612	+	0.943416i	$0.392408\pi$
$942$	−213257.	−0.00783027
$943$	−1.22974e7	−0.450332
$944$	−1.32014e7	−0.482159
$945$	5.97454e6	0.217633
$946$	8.91457e6	0.323871
$947$	4.21095e7	1.52582	0.762912	−	0.646502i	$-0.223769\pi$
$947$	4.21095e7	1.52582	0.762912	+	0.646502i	$0.223769\pi$
$948$	2.69311e7	0.973269
$949$	−2.70324e6	−0.0974358
$950$	2.90710e7	1.04509
$951$	−3.40904e7	−1.22231
$952$	−6.13406e7	−2.19359
$953$	−4.00499e7	−1.42846	−0.714232	−	0.699909i	$-0.753224\pi$
$953$	−4.00499e7	−1.42846	−0.714232	+	0.699909i	$0.753224\pi$
$954$	2.57761e6	0.0916951
$955$	878330.	0.0311637
$956$	1.60412e7	0.567665
$957$	−3.51698e7	−1.24134
$958$	−2.11273e6	−0.0743754
$959$	−2.89470e7	−1.01638
$960$	−4.80389e6	−0.168234
$961$	−1.67382e7	−0.584658
$962$	2.68455e7	0.935262
$963$	−1.10812e7	−0.385052
$964$	2.25660e6	0.0782099
$965$	−1.23736e7	−0.427737
$966$	3.10954e7	1.07215
$967$	4.96687e7	1.70811	0.854057	−	0.520179i	$-0.174135\pi$
$967$	4.96687e7	1.70811	0.854057	+	0.520179i	$0.174135\pi$
$968$	−1.00356e8	−3.44234
$969$	2.23612e7	0.765043
$970$	1.54841e7	0.528391
$971$	−3.45382e7	−1.17558	−0.587789	−	0.809014i	$-0.700002\pi$
$971$	−3.45382e7	−1.17558	−0.587789	+	0.809014i	$0.700002\pi$
$972$	−3.44104e7	−1.16822
$973$	−1.44529e7	−0.489409
$974$	2.68011e7	0.905221
$975$	1.90772e7	0.642694
$976$	1.82976e7	0.614851
$977$	−4.06098e7	−1.36111	−0.680557	−	0.732695i	$-0.738262\pi$
$977$	−4.06098e7	−1.36111	−0.680557	+	0.732695i	$0.738262\pi$
$978$	−87853.3	−0.00293705
$979$	−5.57287e7	−1.85833
$980$	4.58502e6	0.152502
$981$	−1.47126e7	−0.488109
$982$	−2.31482e6	−0.0766018
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	2.39979e7	0.790106
$985$	−5.73622e6	−0.188380
$986$	6.67940e7	2.18799
$987$	−2.23596e7	−0.730587
$988$	3.24973e7	1.05915
$989$	2.95857e6	0.0961814
$990$	−6.49465e6	−0.210605
$991$	−4.14683e6	−0.134132	−0.0670660	−	0.997749i	$-0.521364\pi$
$991$	−4.14683e6	−0.134132	−0.0670660	+	0.997749i	$0.521364\pi$
$992$	−3.73284e6	−0.120437
$993$	1.60810e7	0.517534
$994$	−1.50119e7	−0.481915
$995$	−3.79647e6	−0.121569
$996$	3.18485e7	1.01728
$997$	3.02594e7	0.964101	0.482051	−	0.876143i	$-0.339892\pi$
$997$	3.02594e7	0.964101	0.482051	+	0.876143i	$0.339892\pi$
$998$	2.49499e7	0.792945
$999$	−2.25916e7	−0.716198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.13	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.13	✓	191	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-9.88271 q^{2} -13.0845 q^{3} +65.6680 q^{4} -13.4569 q^{5} +129.310 q^{6} -107.789 q^{7} -332.731 q^{8} -71.7966 q^{9} +O(q^{10})\)	\(q-9.88271 q^{2} -13.0845 q^{3} +65.6680 q^{4} -13.4569 q^{5} +129.310 q^{6} -107.789 q^{7} -332.731 q^{8} -71.7966 q^{9} +132.990 q^{10} +680.193 q^{11} -859.231 q^{12} +495.261 q^{13} +1065.25 q^{14} +176.076 q^{15} +1186.91 q^{16} -1710.33 q^{17} +709.545 q^{18} +999.216 q^{19} -883.685 q^{20} +1410.36 q^{21} -6722.15 q^{22} -2230.95 q^{23} +4353.61 q^{24} -2943.91 q^{25} -4894.53 q^{26} +4118.95 q^{27} -7078.29 q^{28} +3951.68 q^{29} -1740.11 q^{30} +3448.32 q^{31} -1082.51 q^{32} -8899.96 q^{33} +16902.7 q^{34} +1450.50 q^{35} -4714.74 q^{36} -5484.80 q^{37} -9874.97 q^{38} -6480.23 q^{39} +4477.52 q^{40} +5512.17 q^{41} -13938.2 q^{42} -1326.15 q^{43} +44666.9 q^{44} +966.157 q^{45} +22047.8 q^{46} -15853.8 q^{47} -15530.1 q^{48} -5188.52 q^{49} +29093.8 q^{50} +22378.7 q^{51} +32522.8 q^{52} +3632.76 q^{53} -40706.4 q^{54} -9153.26 q^{55} +35864.8 q^{56} -13074.2 q^{57} -39053.3 q^{58} -11122.5 q^{59} +11562.6 q^{60} +15416.1 q^{61} -34078.7 q^{62} +7738.89 q^{63} -27283.1 q^{64} -6664.66 q^{65} +87955.8 q^{66} -18647.0 q^{67} -112314. q^{68} +29190.8 q^{69} -14334.9 q^{70} -14092.4 q^{71} +23889.0 q^{72} -5458.20 q^{73} +54204.7 q^{74} +38519.5 q^{75} +65616.6 q^{76} -73317.3 q^{77} +64042.3 q^{78} -31343.2 q^{79} -15972.1 q^{80} -36447.7 q^{81} -54475.2 q^{82} -37066.3 q^{83} +92615.7 q^{84} +23015.6 q^{85} +13105.9 q^{86} -51705.6 q^{87} -226322. q^{88} -81930.7 q^{89} -9548.25 q^{90} -53383.7 q^{91} -146502. q^{92} -45119.4 q^{93} +156679. q^{94} -13446.3 q^{95} +14164.1 q^{96} +116430. q^{97} +51276.7 q^{98} -48835.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * q^99

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