LMFDB - Embedded newform 983.6.a.b.1.1

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:	$0$
Dimension:	$218$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-11.2545 q^{2} +14.3637 q^{3} +94.6632 q^{4} +5.42124 q^{5} -161.655 q^{6} +48.2201 q^{7} -705.242 q^{8} -36.6855 q^{9} +O(q^{10})$	\(q-11.2545 q^{2} +14.3637 q^{3} +94.6632 q^{4} +5.42124 q^{5} -161.655 q^{6} +48.2201 q^{7} -705.242 q^{8} -36.6855 q^{9} -61.0132 q^{10} -780.764 q^{11} +1359.71 q^{12} -1161.87 q^{13} -542.692 q^{14} +77.8687 q^{15} +4907.91 q^{16} +1081.12 q^{17} +412.876 q^{18} -1155.70 q^{19} +513.192 q^{20} +692.617 q^{21} +8787.09 q^{22} -3326.75 q^{23} -10129.9 q^{24} -3095.61 q^{25} +13076.2 q^{26} -4017.31 q^{27} +4564.68 q^{28} -216.423 q^{29} -876.372 q^{30} -3947.43 q^{31} -32668.2 q^{32} -11214.6 q^{33} -12167.4 q^{34} +261.413 q^{35} -3472.77 q^{36} +13812.0 q^{37} +13006.8 q^{38} -16688.7 q^{39} -3823.28 q^{40} -2859.10 q^{41} -7795.05 q^{42} -7498.83 q^{43} -73909.7 q^{44} -198.881 q^{45} +37440.8 q^{46} -13083.1 q^{47} +70495.5 q^{48} -14481.8 q^{49} +34839.5 q^{50} +15528.8 q^{51} -109986. q^{52} -2327.78 q^{53} +45212.7 q^{54} -4232.71 q^{55} -34006.9 q^{56} -16600.1 q^{57} +2435.73 q^{58} -23448.4 q^{59} +7371.31 q^{60} -17101.2 q^{61} +44426.3 q^{62} -1768.98 q^{63} +210610. q^{64} -6298.75 q^{65} +126215. q^{66} +9518.40 q^{67} +102342. q^{68} -47784.2 q^{69} -2942.06 q^{70} +34532.0 q^{71} +25872.2 q^{72} +59589.4 q^{73} -155446. q^{74} -44464.3 q^{75} -109402. q^{76} -37648.6 q^{77} +187822. q^{78} +55423.0 q^{79} +26606.9 q^{80} -48788.6 q^{81} +32177.6 q^{82} -46568.2 q^{83} +65565.4 q^{84} +5860.98 q^{85} +84395.4 q^{86} -3108.62 q^{87} +550628. q^{88} +98725.0 q^{89} +2238.30 q^{90} -56025.4 q^{91} -314921. q^{92} -56699.5 q^{93} +147243. q^{94} -6265.32 q^{95} -469234. q^{96} +154511. q^{97} +162985. q^{98} +28642.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−11.2545	−1.98953	−0.994765	−	0.102193i	$-0.967414\pi$
$2$	−11.2545	−1.98953	−0.994765	+	0.102193i	$0.967414\pi$
$3$	14.3637	0.921429	0.460714	−	0.887548i	$-0.347593\pi$
$3$	14.3637	0.921429	0.460714	+	0.887548i	$0.347593\pi$
$4$	94.6632	2.95823
$5$	5.42124	0.0969780	0.0484890	−	0.998824i	$-0.484559\pi$
$5$	5.42124	0.0969780	0.0484890	+	0.998824i	$0.484559\pi$
$6$	−161.655	−1.83321
$7$	48.2201	0.371949	0.185974	−	0.982555i	$-0.440456\pi$
$7$	48.2201	0.371949	0.185974	+	0.982555i	$0.440456\pi$
$8$	−705.242	−3.89595
$9$	−36.6855	−0.150969
$10$	−61.0132	−0.192941
$11$	−780.764	−1.94553	−0.972765	−	0.231792i	$-0.925541\pi$
$11$	−780.764	−1.94553	−0.972765	+	0.231792i	$0.925541\pi$
$12$	1359.71	2.72579
$13$	−1161.87	−1.90677	−0.953384	−	0.301759i	$-0.902426\pi$
$13$	−1161.87	−1.90677	−0.953384	+	0.301759i	$0.902426\pi$
$14$	−542.692	−0.740003
$15$	77.8687	0.0893583
$16$	4907.91	4.79288
$17$	1081.12	0.907298	0.453649	−	0.891180i	$-0.350122\pi$
$17$	1081.12	0.907298	0.453649	+	0.891180i	$0.350122\pi$
$18$	412.876	0.300358
$19$	−1155.70	−0.734448	−0.367224	−	0.930133i	$-0.619692\pi$
$19$	−1155.70	−0.734448	−0.367224	+	0.930133i	$0.619692\pi$
$20$	513.192	0.286883
$21$	692.617	0.342724
$22$	8787.09	3.87069
$23$	−3326.75	−1.31129	−0.655647	−	0.755067i	$-0.727604\pi$
$23$	−3326.75	−1.31129	−0.655647	+	0.755067i	$0.727604\pi$
$24$	−10129.9	−3.58984
$25$	−3095.61	−0.990595
$26$	13076.2	3.79357
$27$	−4017.31	−1.06054
$28$	4564.68	1.10031
$29$	−216.423	−0.0477868	−0.0238934	−	0.999715i	$-0.507606\pi$
$29$	−216.423	−0.0477868	−0.0238934	+	0.999715i	$0.507606\pi$
$30$	−876.372	−0.177781
$31$	−3947.43	−0.737752	−0.368876	−	0.929479i	$-0.620257\pi$
$31$	−3947.43	−0.737752	−0.368876	+	0.929479i	$0.620257\pi$
$32$	−32668.2	−5.63962
$33$	−11214.6	−1.79267
$34$	−12167.4	−1.80510
$35$	261.413	0.0360709
$36$	−3472.77	−0.446601
$37$	13812.0	1.65864	0.829318	−	0.558777i	$-0.188729\pi$
$37$	13812.0	1.65864	0.829318	+	0.558777i	$0.188729\pi$
$38$	13006.8	1.46121
$39$	−16688.7	−1.75695
$40$	−3823.28	−0.377821
$41$	−2859.10	−0.265625	−0.132813	−	0.991141i	$-0.542401\pi$
$41$	−2859.10	−0.265625	−0.132813	+	0.991141i	$0.542401\pi$
$42$	−7795.05	−0.681860
$43$	−7498.83	−0.618475	−0.309237	−	0.950985i	$-0.600074\pi$
$43$	−7498.83	−0.618475	−0.309237	+	0.950985i	$0.600074\pi$
$44$	−73909.7	−5.75532
$45$	−198.881	−0.0146407
$46$	37440.8	2.60886
$47$	−13083.1	−0.863905	−0.431952	−	0.901896i	$-0.642175\pi$
$47$	−13083.1	−0.863905	−0.431952	+	0.901896i	$0.642175\pi$
$48$	70495.5	4.41629
$49$	−14481.8	−0.861654
$50$	34839.5	1.97082
$51$	15528.8	0.836010
$52$	−109986.	−5.64065
$53$	−2327.78	−0.113829	−0.0569145	−	0.998379i	$-0.518126\pi$
$53$	−2327.78	−0.113829	−0.0569145	+	0.998379i	$0.518126\pi$
$54$	45212.7	2.10997
$55$	−4232.71	−0.188674
$56$	−34006.9	−1.44909
$57$	−16600.1	−0.676742
$58$	2435.73	0.0950733
$59$	−23448.4	−0.876967	−0.438483	−	0.898739i	$-0.644484\pi$
$59$	−23448.4	−0.876967	−0.438483	+	0.898739i	$0.644484\pi$
$60$	7371.31	0.264342
$61$	−17101.2	−0.588441	−0.294220	−	0.955738i	$-0.595060\pi$
$61$	−17101.2	−0.588441	−0.294220	+	0.955738i	$0.595060\pi$
$62$	44426.3	1.46778
$63$	−1768.98	−0.0561529
$64$	210610.	6.42731
$65$	−6298.75	−0.184915
$66$	126215.	3.56656
$67$	9518.40	0.259046	0.129523	−	0.991576i	$-0.458655\pi$
$67$	9518.40	0.259046	0.129523	+	0.991576i	$0.458655\pi$
$68$	102342.	2.68399
$69$	−47784.2	−1.20826
$70$	−2942.06	−0.0717641
$71$	34532.0	0.812974	0.406487	−	0.913657i	$-0.366754\pi$
$71$	34532.0	0.812974	0.406487	+	0.913657i	$0.366754\pi$
$72$	25872.2	0.588168
$73$	59589.4	1.30876	0.654382	−	0.756164i	$-0.272929\pi$
$73$	59589.4	1.30876	0.654382	+	0.756164i	$0.272929\pi$
$74$	−155446.	−3.29991
$75$	−44464.3	−0.912763
$76$	−109402.	−2.17266
$77$	−37648.6	−0.723638
$78$	187822.	3.49551
$79$	55423.0	0.999131	0.499566	−	0.866276i	$-0.333493\pi$
$79$	55423.0	0.999131	0.499566	+	0.866276i	$0.333493\pi$
$80$	26606.9	0.464804
$81$	−48788.6	−0.826239
$82$	32177.6	0.528469
$83$	−46568.2	−0.741984	−0.370992	−	0.928636i	$-0.620982\pi$
$83$	−46568.2	−0.741984	−0.370992	+	0.928636i	$0.620982\pi$
$84$	65565.4	1.01386
$85$	5860.98	0.0879879
$86$	84395.4	1.23047
$87$	−3108.62	−0.0440322
$88$	550628.	7.57969
$89$	98725.0	1.32115	0.660575	−	0.750760i	$-0.270312\pi$
$89$	98725.0	1.32115	0.660575	+	0.750760i	$0.270312\pi$
$90$	2238.30	0.0291281
$91$	−56025.4	−0.709221
$92$	−314921.	−3.87911
$93$	−56699.5	−0.679786
$94$	147243.	1.71876
$95$	−6265.32	−0.0712253
$96$	−469234.	−5.19651
$97$	154511.	1.66736	0.833682	−	0.552245i	$-0.186229\pi$
$97$	154511.	1.66736	0.833682	+	0.552245i	$0.186229\pi$
$98$	162985.	1.71429
$99$	28642.7	0.293715
$100$	−293041.	−2.93041
$101$	129922.	1.26730	0.633649	−	0.773621i	$-0.281556\pi$
$101$	129922.	1.26730	0.633649	+	0.773621i	$0.281556\pi$
$102$	−174768.	−1.66327
$103$	−144089.	−1.33825	−0.669125	−	0.743150i	$-0.733331\pi$
$103$	−144089.	−1.33825	−0.669125	+	0.743150i	$0.733331\pi$
$104$	819397.	7.42867
$105$	3754.84	0.0332367
$106$	26198.0	0.226466
$107$	−88841.4	−0.750163	−0.375082	−	0.926992i	$-0.622385\pi$
$107$	−88841.4	−0.750163	−0.375082	+	0.926992i	$0.622385\pi$
$108$	−380291.	−3.13731
$109$	94455.5	0.761484	0.380742	−	0.924681i	$-0.375669\pi$
$109$	94455.5	0.761484	0.380742	+	0.924681i	$0.375669\pi$
$110$	47636.9	0.375372
$111$	198390.	1.52831
$112$	236660.	1.78271
$113$	−59509.3	−0.438418	−0.219209	−	0.975678i	$-0.570348\pi$
$113$	−59509.3	−0.438418	−0.219209	+	0.975678i	$0.570348\pi$
$114$	186825.	1.34640
$115$	−18035.1	−0.127167
$116$	−20487.3	−0.141364
$117$	42623.7	0.287863
$118$	263899.	1.74475
$119$	52131.6	0.337469
$120$	−54916.3	−0.348135
$121$	448542.	2.78509
$122$	192465.	1.17072
$123$	−41067.1	−0.244755
$124$	−373677.	−2.18244
$125$	−33723.4	−0.193044
$126$	19909.0	0.111718
$127$	188661.	1.03794	0.518971	−	0.854792i	$-0.326315\pi$
$127$	188661.	1.03794	0.518971	+	0.854792i	$0.326315\pi$
$128$	−1.32493e6	−7.14771
$129$	−107711.	−0.569881
$130$	70889.2	0.367893
$131$	−376007.	−1.91434	−0.957168	−	0.289535i	$-0.906499\pi$
$131$	−376007.	−1.91434	−0.957168	+	0.289535i	$0.906499\pi$
$132$	−1.06161e6	−5.30312
$133$	−55728.0	−0.273177
$134$	−107125.	−0.515380
$135$	−21778.8	−0.102849
$136$	−762448.	−3.53479
$137$	−311817.	−1.41938	−0.709689	−	0.704515i	$-0.751164\pi$
$137$	−311817.	−1.41938	−0.709689	+	0.704515i	$0.751164\pi$
$138$	537787.	2.40388
$139$	313802.	1.37759	0.688793	−	0.724958i	$-0.258141\pi$
$139$	313802.	1.37759	0.688793	+	0.724958i	$0.258141\pi$
$140$	24746.2	0.106706
$141$	−187921.	−0.796027
$142$	−388640.	−1.61743
$143$	907144.	3.70968
$144$	−180049.	−0.723577
$145$	−1173.28	−0.00463427
$146$	−670647.	−2.60383
$147$	−208012.	−0.793953
$148$	1.30749e6	4.90662
$149$	272471.	1.00544	0.502718	−	0.864451i	$-0.332333\pi$
$149$	272471.	1.00544	0.502718	+	0.864451i	$0.332333\pi$
$150$	500422.	1.81597
$151$	−191012.	−0.681738	−0.340869	−	0.940111i	$-0.610721\pi$
$151$	−191012.	−0.681738	−0.340869	+	0.940111i	$0.610721\pi$
$152$	815048.	2.86137
$153$	−39661.3	−0.136974
$154$	423715.	1.43970
$155$	−21400.0	−0.0715457
$156$	−1.57980e6	−5.19746
$157$	−126009.	−0.407993	−0.203996	−	0.978972i	$-0.565393\pi$
$157$	−126009.	−0.407993	−0.203996	+	0.978972i	$0.565393\pi$
$158$	−623757.	−1.98780
$159$	−33435.5	−0.104885
$160$	−177102.	−0.546919
$161$	−160416.	−0.487735
$162$	549090.	1.64383
$163$	39802.5	0.117339	0.0586693	−	0.998277i	$-0.481314\pi$
$163$	39802.5	0.117339	0.0586693	+	0.998277i	$0.481314\pi$
$164$	−270651.	−0.785780
$165$	−60797.1	−0.173849
$166$	524101.	1.47620
$167$	153896.	0.427010	0.213505	−	0.976942i	$-0.431512\pi$
$167$	153896.	0.427010	0.213505	+	0.976942i	$0.431512\pi$
$168$	−488463.	−1.33524
$169$	978642.	2.63577
$170$	−65962.3	−0.175055
$171$	42397.5	0.110879
$172$	−709863.	−1.82959
$173$	−174896.	−0.444287	−0.222143	−	0.975014i	$-0.571305\pi$
$173$	−174896.	−0.444287	−0.222143	+	0.975014i	$0.571305\pi$
$174$	34985.9	0.0876033
$175$	−149271.	−0.368451
$176$	−3.83192e6	−9.32469
$177$	−336805.	−0.808062
$178$	−1.11110e6	−2.62847
$179$	−473888.	−1.10546	−0.552730	−	0.833360i	$-0.686414\pi$
$179$	−473888.	−1.10546	−0.552730	+	0.833360i	$0.686414\pi$
$180$	−18826.7	−0.0433105
$181$	363137.	0.823900	0.411950	−	0.911206i	$-0.364848\pi$
$181$	363137.	0.823900	0.411950	+	0.911206i	$0.364848\pi$
$182$	630536.	1.41102
$183$	−245636.	−0.542206
$184$	2.34616e6	5.10874
$185$	74877.9	0.160851
$186$	638123.	1.35245
$187$	−844096.	−1.76518
$188$	−1.23849e6	−2.55563
$189$	−193715.	−0.394465
$190$	70512.9	0.141705
$191$	−722926.	−1.43387	−0.716936	−	0.697139i	$-0.754456\pi$
$191$	−722926.	−1.43387	−0.716936	+	0.697139i	$0.754456\pi$
$192$	3.02513e6	5.92231
$193$	517299.	0.999650	0.499825	−	0.866126i	$-0.333398\pi$
$193$	517299.	0.999650	0.499825	+	0.866126i	$0.333398\pi$
$194$	−1.73894e6	−3.31727
$195$	−90473.1	−0.170386
$196$	−1.37090e6	−2.54897
$197$	721318.	1.32422	0.662111	−	0.749405i	$-0.269661\pi$
$197$	721318.	1.32422	0.662111	+	0.749405i	$0.269661\pi$
$198$	−322359.	−0.584355
$199$	127169.	0.227640	0.113820	−	0.993501i	$-0.463691\pi$
$199$	127169.	0.227640	0.113820	+	0.993501i	$0.463691\pi$
$200$	2.18315e6	3.85931
$201$	136719.	0.238692
$202$	−1.46220e6	−2.52133
$203$	−10435.9	−0.0177743
$204$	1.47000e6	2.47311
$205$	−15499.8	−0.0257598
$206$	1.62164e6	2.66249
$207$	122043.	0.197965
$208$	−5.70233e6	−9.13891
$209$	902329.	1.42889
$210$	−42258.8	−0.0661255
$211$	−1.18689e6	−1.83529	−0.917643	−	0.397407i	$-0.869910\pi$
$211$	−1.18689e6	−1.83529	−0.917643	+	0.397407i	$0.869910\pi$
$212$	−220355.	−0.336732
$213$	496006.	0.749097
$214$	999863.	1.49247
$215$	−40652.9	−0.0599785
$216$	2.83317e6	4.13179
$217$	−190346.	−0.274406
$218$	−1.06305e6	−1.51500
$219$	855921.	1.20593
$220$	−400682.	−0.558140
$221$	−1.25611e6	−1.73001
$222$	−2.23278e6	−3.04063
$223$	−1.17859e6	−1.58709	−0.793546	−	0.608510i	$-0.791767\pi$
$223$	−1.17859e6	−1.58709	−0.793546	+	0.608510i	$0.791767\pi$
$224$	−1.57526e6	−2.09765
$225$	113564.	0.149549
$226$	669746.	0.872246
$227$	−704898.	−0.907949	−0.453975	−	0.891015i	$-0.649994\pi$
$227$	−704898.	−0.907949	−0.453975	+	0.891015i	$0.649994\pi$
$228$	−1.57142e6	−2.00195
$229$	338698.	0.426800	0.213400	−	0.976965i	$-0.431546\pi$
$229$	338698.	0.426800	0.213400	+	0.976965i	$0.431546\pi$
$230$	202975.	0.253002
$231$	−540771.	−0.666781
$232$	152631.	0.186175
$233$	307707.	0.371319	0.185660	−	0.982614i	$-0.440558\pi$
$233$	307707.	0.371319	0.185660	+	0.982614i	$0.440558\pi$
$234$	−479707.	−0.572713
$235$	−70926.6	−0.0837798
$236$	−2.21970e6	−2.59427
$237$	796077.	0.920628
$238$	−586713.	−0.671404
$239$	335238.	0.379628	0.189814	−	0.981820i	$-0.439212\pi$
$239$	335238.	0.379628	0.189814	+	0.981820i	$0.439212\pi$
$240$	382172.	0.428283
$241$	404466.	0.448580	0.224290	−	0.974522i	$-0.427994\pi$
$241$	404466.	0.448580	0.224290	+	0.974522i	$0.427994\pi$
$242$	−5.04810e6	−5.54102
$243$	275423.	0.299216
$244$	−1.61886e6	−1.74074
$245$	−78509.3	−0.0835615
$246$	462189.	0.486947
$247$	1.34277e6	1.40042
$248$	2.78389e6	2.87424
$249$	−668890.	−0.683685
$250$	379539.	0.384067
$251$	−1.58479e6	−1.58777	−0.793886	−	0.608066i	$-0.791946\pi$
$251$	−1.58479e6	−1.58777	−0.793886	+	0.608066i	$0.791946\pi$
$252$	−167457.	−0.166113
$253$	2.59741e6	2.55116
$254$	−2.12328e6	−2.06502
$255$	84185.1	0.0810746
$256$	8.17182e6	7.79326
$257$	1.04828e6	0.990021	0.495010	−	0.868887i	$-0.335164\pi$
$257$	1.04828e6	0.990021	0.495010	+	0.868887i	$0.335164\pi$
$258$	1.21223e6	1.13379
$259$	666015.	0.616928
$260$	−596260.	−0.547019
$261$	7939.59	0.00721434
$262$	4.23176e6	3.80863
$263$	1.89234e6	1.68698	0.843490	−	0.537144i	$-0.180497\pi$
$263$	1.89234e6	1.68698	0.843490	+	0.537144i	$0.180497\pi$
$264$	7.90902e6	6.98414
$265$	−12619.5	−0.0110389
$266$	627190.	0.543494
$267$	1.41805e6	1.21735
$268$	901043.	0.766317
$269$	−661976.	−0.557778	−0.278889	−	0.960323i	$-0.589966\pi$
$269$	−661976.	−0.557778	−0.278889	+	0.960323i	$0.589966\pi$
$270$	245109.	0.204620
$271$	−233491.	−0.193129	−0.0965643	−	0.995327i	$-0.530785\pi$
$271$	−233491.	−0.193129	−0.0965643	+	0.995327i	$0.530785\pi$
$272$	5.30602e6	4.34857
$273$	−804729.	−0.653496
$274$	3.50933e6	2.82389
$275$	2.41694e6	1.92723
$276$	−4.52341e6	−3.57432
$277$	596528.	0.467123	0.233562	−	0.972342i	$-0.424962\pi$
$277$	596528.	0.467123	0.233562	+	0.972342i	$0.424962\pi$
$278$	−3.53168e6	−2.74075
$279$	144814.	0.111378
$280$	−184359.	−0.140530
$281$	−1.56504e6	−1.18239	−0.591193	−	0.806530i	$-0.701343\pi$
$281$	−1.56504e6	−1.18239	−0.591193	+	0.806530i	$0.701343\pi$
$282$	2.11495e6	1.58372
$283$	1.18609e6	0.880346	0.440173	−	0.897913i	$-0.354917\pi$
$283$	1.18609e6	0.880346	0.440173	+	0.897913i	$0.354917\pi$
$284$	3.26892e6	2.40496
$285$	−89992.9	−0.0656290
$286$	−1.02094e7	−7.38051
$287$	−137866.	−0.0987990
$288$	1.19845e6	0.851409
$289$	−251046.	−0.176810
$290$	13204.7	0.00922002
$291$	2.21934e6	1.53636
$292$	5.64092e6	3.87162
$293$	77008.0	0.0524043	0.0262022	−	0.999657i	$-0.491659\pi$
$293$	77008.0	0.0524043	0.0262022	+	0.999657i	$0.491659\pi$
$294$	2.34106e6	1.57959
$295$	−127119.	−0.0850465
$296$	−9.74078e6	−6.46196
$297$	3.13657e6	2.06331
$298$	−3.06652e6	−2.00034
$299$	3.86524e6	2.50034
$300$	−4.20913e6	−2.70016
$301$	−361594.	−0.230041
$302$	2.14974e6	1.35634
$303$	1.86615e6	1.16772
$304$	−5.67207e6	−3.52012
$305$	−92709.8	−0.0570658
$306$	446367.	0.272514
$307$	116710.	0.0706746	0.0353373	−	0.999375i	$-0.488749\pi$
$307$	116710.	0.0706746	0.0353373	+	0.999375i	$0.488749\pi$
$308$	−3.56393e6	−2.14069
$309$	−2.06964e6	−1.23310
$310$	240845.	0.142342
$311$	−1.03700e6	−0.607961	−0.303981	−	0.952678i	$-0.598316\pi$
$311$	−1.03700e6	−0.607961	−0.303981	+	0.952678i	$0.598316\pi$
$312$	1.17695e7	6.84499
$313$	−19624.5	−0.0113224	−0.00566119	−	0.999984i	$-0.501802\pi$
$313$	−19624.5	−0.0113224	−0.00566119	+	0.999984i	$0.501802\pi$
$314$	1.41817e6	0.811714
$315$	−9590.06	−0.00544559
$316$	5.24652e6	2.95566
$317$	−3.17016e6	−1.77187	−0.885937	−	0.463806i	$-0.846483\pi$
$317$	−3.17016e6	−1.77187	−0.885937	+	0.463806i	$0.846483\pi$
$318$	376299.	0.208672
$319$	168975.	0.0929708
$320$	1.14177e6	0.623308
$321$	−1.27609e6	−0.691222
$322$	1.80540e6	0.970362
$323$	−1.24945e6	−0.666363
$324$	−4.61849e6	−2.44420
$325$	3.59669e6	1.88884
$326$	−447956.	−0.233449
$327$	1.35673e6	0.701653
$328$	2.01636e6	1.03486
$329$	−630869.	−0.321329
$330$	684240.	0.345878
$331$	−989027.	−0.496179	−0.248089	−	0.968737i	$-0.579803\pi$
$331$	−989027.	−0.496179	−0.248089	+	0.968737i	$0.579803\pi$
$332$	−4.40830e6	−2.19496
$333$	−506699.	−0.250403
$334$	−1.73202e6	−0.849548
$335$	51601.5	0.0251218
$336$	3.39930e6	1.64264
$337$	−354833.	−0.170196	−0.0850980	−	0.996373i	$-0.527120\pi$
$337$	−354833.	−0.170196	−0.0850980	+	0.996373i	$0.527120\pi$
$338$	−1.10141e7	−5.24393
$339$	−854770.	−0.403971
$340$	554820.	0.260288
$341$	3.08201e6	1.43532
$342$	−477161.	−0.220597
$343$	−1.50875e6	−0.692440
$344$	5.28849e6	2.40955
$345$	−259050.	−0.117175
$346$	1.96836e6	0.883922
$347$	−2.19298e6	−0.977712	−0.488856	−	0.872365i	$-0.662586\pi$
$347$	−2.19298e6	−0.977712	−0.488856	+	0.872365i	$0.662586\pi$
$348$	−294272.	−0.130257
$349$	1.46976e6	0.645926	0.322963	−	0.946412i	$-0.395321\pi$
$349$	1.46976e6	0.645926	0.322963	+	0.946412i	$0.395321\pi$
$350$	1.67996e6	0.733044
$351$	4.66757e6	2.02220
$352$	2.55061e7	10.9721
$353$	3.41981e6	1.46071	0.730357	−	0.683066i	$-0.239354\pi$
$353$	3.41981e6	1.46071	0.730357	+	0.683066i	$0.239354\pi$
$354$	3.79056e6	1.60766
$355$	187206.	0.0788406
$356$	9.34563e6	3.90826
$357$	748800.	0.310953
$358$	5.33336e6	2.19934
$359$	685308.	0.280640	0.140320	−	0.990106i	$-0.455187\pi$
$359$	685308.	0.280640	0.140320	+	0.990106i	$0.455187\pi$
$360$	140259.	0.0570394
$361$	−1.14046e6	−0.460586
$362$	−4.08692e6	−1.63917
$363$	6.44269e6	2.56626
$364$	−5.30354e6	−2.09804
$365$	323048.	0.126921
$366$	2.76451e6	1.07873
$367$	−2.32030e6	−0.899247	−0.449623	−	0.893218i	$-0.648442\pi$
$367$	−2.32030e6	−0.899247	−0.449623	+	0.893218i	$0.648442\pi$
$368$	−1.63274e7	−6.28487
$369$	104887.	0.0401012
$370$	−842712.	−0.320018
$371$	−112246.	−0.0423386
$372$	−5.36736e6	−2.01096
$373$	−586220.	−0.218167	−0.109083	−	0.994033i	$-0.534792\pi$
$373$	−586220.	−0.218167	−0.109083	+	0.994033i	$0.534792\pi$
$374$	9.49986e6	3.51187
$375$	−484391.	−0.177876
$376$	9.22675e6	3.36573
$377$	251455.	0.0911185
$378$	2.18016e6	0.784800
$379$	2.06245e6	0.737541	0.368771	−	0.929520i	$-0.379779\pi$
$379$	2.06245e6	0.737541	0.368771	+	0.929520i	$0.379779\pi$
$380$	−593096.	−0.210701
$381$	2.70986e6	0.956390
$382$	8.13615e6	2.85273
$383$	1.36911e6	0.476915	0.238458	−	0.971153i	$-0.423358\pi$
$383$	1.36911e6	0.476915	0.238458	+	0.971153i	$0.423358\pi$
$384$	−1.90308e7	−6.58610
$385$	−204102.	−0.0701770
$386$	−5.82193e6	−1.98883
$387$	275098.	0.0933707
$388$	1.46265e7	4.93244
$389$	−3.19906e6	−1.07189	−0.535944	−	0.844254i	$-0.680044\pi$
$389$	−3.19906e6	−1.07189	−0.535944	+	0.844254i	$0.680044\pi$
$390$	1.01823e6	0.338987
$391$	−3.59660e6	−1.18973
$392$	1.02132e7	3.35696
$393$	−5.40084e6	−1.76392
$394$	−8.11805e6	−2.63458
$395$	300461.	0.0968937
$396$	2.71141e6	0.868876
$397$	−1.23501e6	−0.393273	−0.196636	−	0.980476i	$-0.563002\pi$
$397$	−1.23501e6	−0.393273	−0.196636	+	0.980476i	$0.563002\pi$
$398$	−1.43122e6	−0.452896
$399$	−800458.	−0.251713
$400$	−1.51930e7	−4.74780
$401$	396126.	0.123019	0.0615095	−	0.998106i	$-0.480409\pi$
$401$	396126.	0.123019	0.0615095	+	0.998106i	$0.480409\pi$
$402$	−1.53870e6	−0.474886
$403$	4.58639e6	1.40672
$404$	1.22988e7	3.74895
$405$	−264494.	−0.0801270
$406$	117451.	0.0353624
$407$	−1.07839e7	−3.22693
$408$	−1.09515e7	−3.25705
$409$	−668768.	−0.197682	−0.0988410	−	0.995103i	$-0.531514\pi$
$409$	−668768.	−0.197682	−0.0988410	+	0.995103i	$0.531514\pi$
$410$	174443.	0.0512499
$411$	−4.47883e6	−1.30786
$412$	−1.36399e7	−3.95885
$413$	−1.13069e6	−0.326187
$414$	−1.37354e6	−0.393857
$415$	−252457.	−0.0719561
$416$	3.79561e7	10.7535
$417$	4.50734e6	1.26935
$418$	−1.01552e7	−2.84282
$419$	−5.41334e6	−1.50636	−0.753182	−	0.657812i	$-0.771482\pi$
$419$	−5.41334e6	−1.50636	−0.753182	+	0.657812i	$0.771482\pi$
$420$	355445.	0.0983218
$421$	691371.	0.190110	0.0950552	−	0.995472i	$-0.469697\pi$
$421$	691371.	0.190110	0.0950552	+	0.995472i	$0.469697\pi$
$422$	1.33578e7	3.65135
$423$	479960.	0.130423
$424$	1.64165e6	0.443472
$425$	−3.34671e6	−0.898765
$426$	−5.58229e6	−1.49035
$427$	−824624.	−0.218870
$428$	−8.41001e6	−2.21915
$429$	1.30299e7	3.41820
$430$	457527.	0.119329
$431$	2.81272e6	0.729346	0.364673	−	0.931136i	$-0.381181\pi$
$431$	2.81272e6	0.729346	0.364673	+	0.931136i	$0.381181\pi$
$432$	−1.97166e7	−5.08302
$433$	−3.46682e6	−0.888609	−0.444305	−	0.895876i	$-0.646549\pi$
$433$	−3.46682e6	−0.888609	−0.444305	+	0.895876i	$0.646549\pi$
$434$	2.14224e6	0.545939
$435$	−16852.6	−0.00427015
$436$	8.94146e6	2.25264
$437$	3.84472e6	0.963078
$438$	−9.63294e6	−2.39924
$439$	−6.92176e6	−1.71417	−0.857087	−	0.515171i	$-0.827728\pi$
$439$	−6.92176e6	−1.71417	−0.857087	+	0.515171i	$0.827728\pi$
$440$	2.98508e6	0.735063
$441$	531273.	0.130083
$442$	1.41369e7	3.44190
$443$	2.00945e6	0.486483	0.243242	−	0.969966i	$-0.421789\pi$
$443$	2.00945e6	0.486483	0.243242	+	0.969966i	$0.421789\pi$
$444$	1.87803e7	4.52110
$445$	535212.	0.128123
$446$	1.32645e7	3.15757
$447$	3.91368e6	0.926437
$448$	1.01557e7	2.39063
$449$	−443831.	−0.103897	−0.0519483	−	0.998650i	$-0.516543\pi$
$449$	−443831.	−0.103897	−0.0519483	+	0.998650i	$0.516543\pi$
$450$	−1.27810e6	−0.297533
$451$	2.23228e6	0.516782
$452$	−5.63334e6	−1.29694
$453$	−2.74363e6	−0.628173
$454$	7.93326e6	1.80639
$455$	−303727.	−0.0687788
$456$	1.17071e7	2.63655
$457$	−5.81260e6	−1.30191	−0.650953	−	0.759118i	$-0.725631\pi$
$457$	−5.81260e6	−1.30191	−0.650953	+	0.759118i	$0.725631\pi$
$458$	−3.81187e6	−0.849131
$459$	−4.34317e6	−0.962222
$460$	−1.70726e6	−0.376188
$461$	−6.98360e6	−1.53048	−0.765238	−	0.643747i	$-0.777379\pi$
$461$	−6.98360e6	−1.53048	−0.765238	+	0.643747i	$0.777379\pi$
$462$	6.08609e6	1.32658
$463$	−3.67109e6	−0.795872	−0.397936	−	0.917413i	$-0.630273\pi$
$463$	−3.67109e6	−0.795872	−0.397936	+	0.917413i	$0.630273\pi$
$464$	−1.06218e6	−0.229037
$465$	−307381.	−0.0659243
$466$	−3.46308e6	−0.738751
$467$	−3.46859e6	−0.735972	−0.367986	−	0.929831i	$-0.619953\pi$
$467$	−3.46859e6	−0.735972	−0.367986	+	0.929831i	$0.619953\pi$
$468$	4.03490e6	0.851565
$469$	458979.	0.0963519
$470$	798241.	0.166682
$471$	−1.80995e6	−0.375936
$472$	1.65368e7	3.41662
$473$	5.85481e6	1.20326
$474$	−8.95943e6	−1.83162
$475$	3.57760e6	0.727541
$476$	4.93494e6	0.998308
$477$	85395.9	0.0171847
$478$	−3.77292e6	−0.755280
$479$	3.99246e6	0.795063	0.397532	−	0.917588i	$-0.369867\pi$
$479$	3.99246e6	0.795063	0.397532	+	0.917588i	$0.369867\pi$
$480$	−2.54383e6	−0.503947
$481$	−1.60477e7	−3.16264
$482$	−4.55206e6	−0.892463
$483$	−2.30416e6	−0.449413
$484$	4.24604e7	8.23893
$485$	837641.	0.161698
$486$	−3.09974e6	−0.595298
$487$	−453768.	−0.0866985	−0.0433493	−	0.999060i	$-0.513803\pi$
$487$	−453768.	−0.0866985	−0.0433493	+	0.999060i	$0.513803\pi$
$488$	1.20605e7	2.29253
$489$	571709.	0.108119
$490$	883582.	0.166248
$491$	−3.30640e6	−0.618944	−0.309472	−	0.950909i	$-0.600152\pi$
$491$	−3.30640e6	−0.618944	−0.309472	+	0.950909i	$0.600152\pi$
$492$	−3.88754e6	−0.724040
$493$	−233978.	−0.0433569
$494$	−1.51122e7	−2.78618
$495$	155279.	0.0284839
$496$	−1.93736e7	−3.53595
$497$	1.66514e6	0.302385
$498$	7.52800e6	1.36021
$499$	385154.	0.0692441	0.0346220	−	0.999400i	$-0.488977\pi$
$499$	385154.	0.0692441	0.0346220	+	0.999400i	$0.488977\pi$
$500$	−3.19237e6	−0.571068
$501$	2.21052e6	0.393459
$502$	1.78360e7	3.15892
$503$	−5.44884e6	−0.960250	−0.480125	−	0.877200i	$-0.659409\pi$
$503$	−5.44884e6	−0.960250	−0.480125	+	0.877200i	$0.659409\pi$
$504$	1.24756e6	0.218769
$505$	704337.	0.122900
$506$	−2.92324e7	−5.07562
$507$	1.40569e7	2.42867
$508$	1.78593e7	3.07047
$509$	452110.	0.0773481	0.0386741	−	0.999252i	$-0.487687\pi$
$509$	452110.	0.0773481	0.0386741	+	0.999252i	$0.487687\pi$
$510$	−947459.	−0.161300
$511$	2.87341e6	0.486794
$512$	−4.95720e7	−8.35721
$513$	4.64280e6	0.778909
$514$	−1.17978e7	−1.96967
$515$	−781139.	−0.129781
$516$	−1.01962e7	−1.68584
$517$	1.02148e7	1.68075
$518$	−7.49565e6	−1.22740
$519$	−2.51214e6	−0.409379
$520$	4.44215e6	0.720418
$521$	−328815.	−0.0530711	−0.0265355	−	0.999648i	$-0.508448\pi$
$521$	−328815.	−0.0530711	−0.0265355	+	0.999648i	$0.508448\pi$
$522$	−89355.9	−0.0143531
$523$	−6.82979e6	−1.09183	−0.545913	−	0.837842i	$-0.683817\pi$
$523$	−6.82979e6	−1.09183	−0.545913	+	0.837842i	$0.683817\pi$
$524$	−3.55941e7	−5.66304
$525$	−2.14407e6	−0.339501
$526$	−2.12973e7	−3.35630
$527$	−4.26763e6	−0.669361
$528$	−5.50403e7	−8.59204
$529$	4.63091e6	0.719494
$530$	142025.	0.0219622
$531$	860217.	0.132395
$532$	−5.27540e6	−0.808120
$533$	3.32189e6	0.506486
$534$	−1.59594e7	−2.42195
$535$	−481630.	−0.0727493
$536$	−6.71278e6	−1.00923
$537$	−6.80676e6	−1.01860
$538$	7.45019e6	1.10972
$539$	1.13069e7	1.67637
$540$	−2.06165e6	−0.304250
$541$	−2.58492e6	−0.379712	−0.189856	−	0.981812i	$-0.560802\pi$
$541$	−2.58492e6	−0.379712	−0.189856	+	0.981812i	$0.560802\pi$
$542$	2.62782e6	0.384235
$543$	5.21598e6	0.759165
$544$	−3.53181e7	−5.11682
$545$	512065.	0.0738472
$546$	9.05680e6	1.30015
$547$	5.53872e6	0.791483	0.395741	−	0.918362i	$-0.370488\pi$
$547$	5.53872e6	0.791483	0.395741	+	0.918362i	$0.370488\pi$
$548$	−2.95176e7	−4.19884
$549$	627367.	0.0888364
$550$	−2.72014e7	−3.83429
$551$	250120.	0.0350970
$552$	3.36995e7	4.70734
$553$	2.67251e6	0.371626
$554$	−6.71361e6	−0.929356
$555$	1.07552e6	0.148213
$556$	2.97055e7	4.07521
$557$	5.26758e6	0.719405	0.359702	−	0.933067i	$-0.382878\pi$
$557$	5.26758e6	0.719405	0.359702	+	0.933067i	$0.382878\pi$
$558$	−1.62980e6	−0.221589
$559$	8.71264e6	1.17929
$560$	1.28299e6	0.172883
$561$	−1.21243e7	−1.62648
$562$	1.76137e7	2.35239
$563$	4.74388e6	0.630758	0.315379	−	0.948966i	$-0.397868\pi$
$563$	4.74388e6	0.630758	0.315379	+	0.948966i	$0.397868\pi$
$564$	−1.77892e7	−2.35483
$565$	−322614.	−0.0425169
$566$	−1.33489e7	−1.75147
$567$	−2.35259e6	−0.307319
$568$	−2.43535e7	−3.16730
$569$	1.23557e7	1.59987	0.799936	−	0.600086i	$-0.204867\pi$
$569$	1.23557e7	1.59987	0.799936	+	0.600086i	$0.204867\pi$
$570$	1.01282e6	0.130571
$571$	−4.18832e6	−0.537588	−0.268794	−	0.963198i	$-0.586625\pi$
$571$	−4.18832e6	−0.537588	−0.268794	+	0.963198i	$0.586625\pi$
$572$	8.58732e7	10.9741
$573$	−1.03839e7	−1.32121
$574$	1.55161e6	0.196564
$575$	1.02983e7	1.29896
$576$	−7.72634e6	−0.970326
$577$	−6.96205e6	−0.870558	−0.435279	−	0.900296i	$-0.643350\pi$
$577$	−6.96205e6	−0.870558	−0.435279	+	0.900296i	$0.643350\pi$
$578$	2.82539e6	0.351770
$579$	7.43030e6	0.921107
$580$	−111066.	−0.0137092
$581$	−2.24553e6	−0.275980
$582$	−2.49776e7	−3.05663
$583$	1.81745e6	0.221458
$584$	−4.20249e7	−5.09888
$585$	231073.	0.0279164
$586$	−866685.	−0.104260
$587$	−4.08048e6	−0.488783	−0.244392	−	0.969677i	$-0.578588\pi$
$587$	−4.08048e6	−0.488783	−0.244392	+	0.969677i	$0.578588\pi$
$588$	−1.96911e7	−2.34869
$589$	4.56205e6	0.541840
$590$	1.43066e6	0.169202
$591$	1.03608e7	1.22018
$592$	6.77878e7	7.94964
$593$	−1.42248e7	−1.66115	−0.830576	−	0.556905i	$-0.811989\pi$
$593$	−1.42248e7	−1.66115	−0.830576	+	0.556905i	$0.811989\pi$
$594$	−3.53004e7	−4.10501
$595$	282617.	0.0327270
$596$	2.57930e7	2.97431
$597$	1.82661e6	0.209754
$598$	−4.35012e7	−4.97449
$599$	1.06428e7	1.21197	0.605983	−	0.795478i	$-0.292780\pi$
$599$	1.06428e7	1.21197	0.605983	+	0.795478i	$0.292780\pi$
$600$	3.13581e7	3.55608
$601$	3.38307e6	0.382054	0.191027	−	0.981585i	$-0.438818\pi$
$601$	3.38307e6	0.382054	0.191027	+	0.981585i	$0.438818\pi$
$602$	4.06956e6	0.457674
$603$	−349187.	−0.0391080
$604$	−1.80818e7	−2.01674
$605$	2.43165e6	0.270092
$606$	−2.10026e7	−2.32322
$607$	4.05566e6	0.446776	0.223388	−	0.974730i	$-0.428288\pi$
$607$	4.05566e6	0.446776	0.223388	+	0.974730i	$0.428288\pi$
$608$	3.77546e7	4.14201
$609$	−149898.	−0.0163777
$610$	1.04340e6	0.113534
$611$	1.52008e7	1.64727
$612$	−3.75447e6	−0.405200
$613$	5.55142e6	0.596696	0.298348	−	0.954457i	$-0.403564\pi$
$613$	5.55142e6	0.596696	0.298348	+	0.954457i	$0.403564\pi$
$614$	−1.31351e6	−0.140609
$615$	−222634.	−0.0237358
$616$	2.65513e7	2.81926
$617$	8.23176e6	0.870522	0.435261	−	0.900304i	$-0.356656\pi$
$617$	8.23176e6	0.870522	0.435261	+	0.900304i	$0.356656\pi$
$618$	2.32927e7	2.45329
$619$	−1.10823e7	−1.16253	−0.581265	−	0.813714i	$-0.697442\pi$
$619$	−1.10823e7	−1.16253	−0.581265	+	0.813714i	$0.697442\pi$
$620$	−2.02579e6	−0.211648
$621$	1.33646e7	1.39068
$622$	1.16708e7	1.20956
$623$	4.76054e6	0.491401
$624$	−8.19063e7	−8.42085
$625$	9.49096e6	0.971874
$626$	220863.	0.0225262
$627$	1.29607e7	1.31662
$628$	−1.19284e7	−1.20694
$629$	1.49323e7	1.50488
$630$	107931.	0.0108342
$631$	−943373.	−0.0943213	−0.0471607	−	0.998887i	$-0.515017\pi$
$631$	−943373.	−0.0943213	−0.0471607	+	0.998887i	$0.515017\pi$
$632$	−3.90866e7	−3.89256
$633$	−1.70480e7	−1.69108
$634$	3.56785e7	3.52519
$635$	1.02278e6	0.100658
$636$	−3.16511e6	−0.310274
$637$	1.68259e7	1.64297
$638$	−1.90173e6	−0.184968
$639$	−1.26683e6	−0.122734
$640$	−7.18274e6	−0.693170
$641$	−3.85993e6	−0.371052	−0.185526	−	0.982639i	$-0.559399\pi$
$641$	−3.85993e6	−0.371052	−0.185526	+	0.982639i	$0.559399\pi$
$642$	1.43617e7	1.37521
$643$	−7.82784e6	−0.746645	−0.373323	−	0.927702i	$-0.621782\pi$
$643$	−7.82784e6	−0.746645	−0.373323	+	0.927702i	$0.621782\pi$
$644$	−1.51855e7	−1.44283
$645$	−583924.	−0.0552659
$646$	1.40619e7	1.32575
$647$	−1.55921e7	−1.46434	−0.732172	−	0.681119i	$-0.761494\pi$
$647$	−1.55921e7	−1.46434	−0.732172	+	0.681119i	$0.761494\pi$
$648$	3.44078e7	3.21899
$649$	1.83077e7	1.70617
$650$	−4.04788e7	−3.75789
$651$	−2.73406e6	−0.252846
$652$	3.76783e6	0.347114
$653$	1.86516e7	1.71172	0.855860	−	0.517208i	$-0.173029\pi$
$653$	1.86516e7	1.71172	0.855860	+	0.517208i	$0.173029\pi$
$654$	−1.52692e7	−1.39596
$655$	−2.03842e6	−0.185648
$656$	−1.40322e7	−1.27311
$657$	−2.18607e6	−0.197583
$658$	7.10010e6	0.639293
$659$	−9.60541e6	−0.861594	−0.430797	−	0.902449i	$-0.641767\pi$
$659$	−9.60541e6	−0.861594	−0.430797	+	0.902449i	$0.641767\pi$
$660$	−5.75525e6	−0.514286
$661$	1.26076e7	1.12235	0.561175	−	0.827697i	$-0.310349\pi$
$661$	1.26076e7	1.12235	0.561175	+	0.827697i	$0.310349\pi$
$662$	1.11310e7	0.987162
$663$	−1.80424e7	−1.59408
$664$	3.28419e7	2.89073
$665$	−302115.	−0.0264922
$666$	5.70263e6	0.498184
$667$	719985.	0.0626626
$668$	1.45683e7	1.26319
$669$	−1.69289e7	−1.46239
$670$	−580748.	−0.0499805
$671$	1.33520e7	1.14483
$672$	−2.26265e7	−1.93284
$673$	380396.	0.0323742	0.0161871	−	0.999869i	$-0.494847\pi$
$673$	380396.	0.0323742	0.0161871	+	0.999869i	$0.494847\pi$
$674$	3.99346e6	0.338610
$675$	1.24360e7	1.05056
$676$	9.26414e7	7.79719
$677$	9.88240e6	0.828687	0.414344	−	0.910121i	$-0.364011\pi$
$677$	9.88240e6	0.828687	0.414344	+	0.910121i	$0.364011\pi$
$678$	9.61999e6	0.803712
$679$	7.45055e6	0.620174
$680$	−4.13341e6	−0.342797
$681$	−1.01249e7	−0.836610
$682$	−3.46864e7	−2.85561
$683$	2.13034e7	1.74742	0.873709	−	0.486449i	$-0.161708\pi$
$683$	2.13034e7	1.74742	0.873709	+	0.486449i	$0.161708\pi$
$684$	4.01348e6	0.328005
$685$	−1.69043e6	−0.137648
$686$	1.69802e7	1.37763
$687$	4.86494e6	0.393266
$688$	−3.68035e7	−2.96427
$689$	2.70457e6	0.217045
$690$	2.91547e6	0.233123
$691$	1.67962e7	1.33818	0.669091	−	0.743181i	$-0.266684\pi$
$691$	1.67962e7	1.33818	0.669091	+	0.743181i	$0.266684\pi$
$692$	−1.65562e7	−1.31430
$693$	1.38116e6	0.109247
$694$	2.46808e7	1.94519
$695$	1.70119e6	0.133595
$696$	2.19233e6	0.171547
$697$	−3.09102e6	−0.241001
$698$	−1.65414e7	−1.28509
$699$	4.41980e6	0.342144
$700$	−1.41305e7	−1.08996
$701$	−6.79396e6	−0.522189	−0.261095	−	0.965313i	$-0.584083\pi$
$701$	−6.79396e6	−0.522189	−0.261095	+	0.965313i	$0.584083\pi$
$702$	−5.25311e7	−4.02322
$703$	−1.59625e7	−1.21818
$704$	−1.64437e8	−12.5045
$705$	−1.01876e6	−0.0771971
$706$	−3.84881e7	−2.90613
$707$	6.26485e6	0.471370
$708$	−3.18830e7	−2.39043
$709$	1.37710e7	1.02884	0.514421	−	0.857538i	$-0.328007\pi$
$709$	1.37710e7	1.02884	0.514421	+	0.857538i	$0.328007\pi$
$710$	−2.10691e6	−0.156856
$711$	−2.03322e6	−0.150838
$712$	−6.96250e7	−5.14713
$713$	1.31321e7	0.967410
$714$	−8.42735e6	−0.618650
$715$	4.91784e6	0.359757
$716$	−4.48598e7	−3.27020
$717$	4.81524e6	0.349800
$718$	−7.71279e6	−0.558342
$719$	6.67832e6	0.481776	0.240888	−	0.970553i	$-0.422561\pi$
$719$	6.67832e6	0.481776	0.240888	+	0.970553i	$0.422561\pi$
$720$	−976089.	−0.0701711
$721$	−6.94798e6	−0.497761
$722$	1.28352e7	0.916349
$723$	5.80962e6	0.413334
$724$	3.43758e7	2.43728
$725$	669961.	0.0473374
$726$	−7.25092e7	−5.10565
$727$	1.28978e7	0.905063	0.452532	−	0.891748i	$-0.350521\pi$
$727$	1.28978e7	0.905063	0.452532	+	0.891748i	$0.350521\pi$
$728$	3.95115e7	2.76309
$729$	1.58117e7	1.10194
$730$	−3.63574e6	−0.252514
$731$	−8.10710e6	−0.561141
$732$	−2.32527e7	−1.60397
$733$	−1.55858e7	−1.07145	−0.535723	−	0.844394i	$-0.679961\pi$
$733$	−1.55858e7	−1.07145	−0.535723	+	0.844394i	$0.679961\pi$
$734$	2.61138e7	1.78908
$735$	−1.12768e6	−0.0769959
$736$	1.08679e8	7.39520
$737$	−7.43162e6	−0.503982
$738$	−1.18045e6	−0.0797826
$739$	8.43453e6	0.568133	0.284066	−	0.958805i	$-0.408316\pi$
$739$	8.43453e6	0.568133	0.284066	+	0.958805i	$0.408316\pi$
$740$	7.08819e6	0.475834
$741$	1.92871e7	1.29039
$742$	1.26327e6	0.0842338
$743$	2.53347e7	1.68362	0.841809	−	0.539776i	$-0.181491\pi$
$743$	2.53347e7	1.68362	0.841809	+	0.539776i	$0.181491\pi$
$744$	3.99869e7	2.64841
$745$	1.47713e6	0.0975051
$746$	6.59760e6	0.434049
$747$	1.70838e6	0.112017
$748$	−7.99049e7	−5.22179
$749$	−4.28394e6	−0.279023
$750$	5.45157e6	0.353890
$751$	−9.91392e6	−0.641424	−0.320712	−	0.947177i	$-0.603922\pi$
$751$	−9.91392e6	−0.641424	−0.320712	+	0.947177i	$0.603922\pi$
$752$	−6.42106e7	−4.14059
$753$	−2.27634e7	−1.46302
$754$	−2.82999e6	−0.181283
$755$	−1.03552e6	−0.0661136
$756$	−1.83377e7	−1.16692
$757$	−3.74746e6	−0.237683	−0.118841	−	0.992913i	$-0.537918\pi$
$757$	−3.74746e6	−0.237683	−0.118841	+	0.992913i	$0.537918\pi$
$758$	−2.32119e7	−1.46736
$759$	3.73082e7	2.35072
$760$	4.41857e6	0.277490
$761$	4.16733e6	0.260853	0.130427	−	0.991458i	$-0.458365\pi$
$761$	4.16733e6	0.260853	0.130427	+	0.991458i	$0.458365\pi$
$762$	−3.04981e7	−1.90277
$763$	4.55466e6	0.283233
$764$	−6.84345e7	−4.24172
$765$	−215013.	−0.0132835
$766$	−1.54086e7	−0.948837
$767$	2.72439e7	1.67217
$768$	1.17377e8	7.18093
$769$	−3.11278e7	−1.89816	−0.949081	−	0.315033i	$-0.897985\pi$
$769$	−3.11278e7	−1.89816	−0.949081	+	0.315033i	$0.897985\pi$
$770$	2.29706e6	0.139619
$771$	1.50571e7	0.912233
$772$	4.89692e7	2.95719
$773$	1.31900e7	0.793956	0.396978	−	0.917828i	$-0.370059\pi$
$773$	1.31900e7	0.793956	0.396978	+	0.917828i	$0.370059\pi$
$774$	−3.09609e6	−0.185764
$775$	1.22197e7	0.730813
$776$	−1.08968e8	−6.49596
$777$	9.56641e6	0.568455
$778$	3.60038e7	2.13255
$779$	3.30426e6	0.195088
$780$	−8.56448e6	−0.504039
$781$	−2.69614e7	−1.58167
$782$	4.04778e7	2.36701
$783$	869437.	0.0506797
$784$	−7.10754e7	−4.12980
$785$	−683125.	−0.0395663
$786$	6.07836e7	3.50938
$787$	8.96730e6	0.516089	0.258045	−	0.966133i	$-0.416922\pi$
$787$	8.96730e6	0.516089	0.258045	+	0.966133i	$0.416922\pi$
$788$	6.82823e7	3.91735
$789$	2.71809e7	1.55443
$790$	−3.38153e6	−0.192773
$791$	−2.86955e6	−0.163069
$792$	−2.02001e7	−1.14430
$793$	1.98694e7	1.12202
$794$	1.38994e7	0.782428
$795$	−181261.	−0.0101716
$796$	1.20382e7	0.673410
$797$	−9.20393e6	−0.513248	−0.256624	−	0.966511i	$-0.582610\pi$
$797$	−9.20393e6	−0.513248	−0.256624	+	0.966511i	$0.582610\pi$
$798$	9.00873e6	0.500791
$799$	−1.41443e7	−0.783819
$800$	1.01128e8	5.58658
$801$	−3.62178e6	−0.199453
$802$	−4.45819e6	−0.244750
$803$	−4.65252e7	−2.54624
$804$	1.29423e7	0.706106
$805$	−869654.	−0.0472995
$806$	−5.16174e7	−2.79871
$807$	−9.50839e6	−0.513953
$808$	−9.16264e7	−4.93733
$809$	1.41633e7	0.760837	0.380419	−	0.924814i	$-0.375780\pi$
$809$	1.41633e7	0.760837	0.380419	+	0.924814i	$0.375780\pi$
$810$	2.97675e6	0.159415
$811$	6.64700e6	0.354874	0.177437	−	0.984132i	$-0.443219\pi$
$811$	6.64700e6	0.354874	0.177437	+	0.984132i	$0.443219\pi$
$812$	−987901.	−0.0525803
$813$	−3.35378e6	−0.177954
$814$	1.21367e8	6.42007
$815$	215779.	0.0113793
$816$	7.62138e7	4.00689
$817$	8.66639e6	0.454238
$818$	7.52663e6	0.393294
$819$	2.05532e6	0.107070
$820$	−1.46727e6	−0.0762033
$821$	1.61767e7	0.837590	0.418795	−	0.908081i	$-0.362453\pi$
$821$	1.61767e7	0.837590	0.418795	+	0.908081i	$0.362453\pi$
$822$	5.04068e7	2.60202
$823$	−1.29806e6	−0.0668028	−0.0334014	−	0.999442i	$-0.510634\pi$
$823$	−1.29806e6	−0.0668028	−0.0334014	+	0.999442i	$0.510634\pi$
$824$	1.01617e8	5.21375
$825$	3.47161e7	1.77581
$826$	1.27253e7	0.648958
$827$	−3.00104e7	−1.52584	−0.762918	−	0.646495i	$-0.776234\pi$
$827$	−3.00104e7	−1.52584	−0.762918	+	0.646495i	$0.776234\pi$
$828$	1.15530e7	0.585626
$829$	−3.08850e7	−1.56085	−0.780425	−	0.625250i	$-0.784997\pi$
$829$	−3.08850e7	−1.56085	−0.780425	+	0.625250i	$0.784997\pi$
$830$	2.84127e6	0.143159
$831$	8.56832e6	0.430421
$832$	−2.44701e8	−12.2554
$833$	−1.56565e7	−0.781777
$834$	−5.07278e7	−2.52540
$835$	834309.	0.0414105
$836$	8.54174e7	4.22698
$837$	1.58580e7	0.782412
$838$	6.09243e7	2.99696
$839$	−2.43025e7	−1.19192	−0.595959	−	0.803015i	$-0.703228\pi$
$839$	−2.43025e7	−1.19192	−0.595959	+	0.803015i	$0.703228\pi$
$840$	−2.64807e6	−0.129489
$841$	−2.04643e7	−0.997716
$842$	−7.78102e6	−0.378230
$843$	−2.24797e7	−1.08948
$844$	−1.12355e8	−5.42919
$845$	5.30545e6	0.255611
$846$	−5.40170e6	−0.259480
$847$	2.16287e7	1.03591
$848$	−1.14245e7	−0.545568
$849$	1.70366e7	0.811176
$850$	3.76655e7	1.78812
$851$	−4.59489e7	−2.17496
$852$	4.69536e7	2.21600
$853$	1.04321e7	0.490906	0.245453	−	0.969409i	$-0.421063\pi$
$853$	1.04321e7	0.490906	0.245453	+	0.969409i	$0.421063\pi$
$854$	9.28071e6	0.435448
$855$	229847.	0.0107528
$856$	6.26547e7	2.92260
$857$	−6.84654e6	−0.318434	−0.159217	−	0.987244i	$-0.550897\pi$
$857$	−6.84654e6	−0.318434	−0.159217	+	0.987244i	$0.550897\pi$
$858$	−1.46645e8	−6.80061
$859$	1.53863e7	0.711460	0.355730	−	0.934589i	$-0.384232\pi$
$859$	1.53863e7	0.711460	0.355730	+	0.934589i	$0.384232\pi$
$860$	−3.84834e6	−0.177430
$861$	−1.98026e6	−0.0910363
$862$	−3.16557e7	−1.45105
$863$	1.06824e7	0.488247	0.244124	−	0.969744i	$-0.421500\pi$
$863$	1.06824e7	0.488247	0.244124	+	0.969744i	$0.421500\pi$
$864$	1.31238e8	5.98102
$865$	−948150.	−0.0430861
$866$	3.90172e7	1.76791
$867$	−3.60593e6	−0.162918
$868$	−1.80187e7	−0.811755
$869$	−4.32723e7	−1.94384
$870$	189667.	0.00849559
$871$	−1.10591e7	−0.493941
$872$	−6.66140e7	−2.96670
$873$	−5.66832e6	−0.251721
$874$	−4.32703e7	−1.91607
$875$	−1.62615e6	−0.0718025
$876$	8.10242e7	3.56742
$877$	−9.03226e6	−0.396550	−0.198275	−	0.980146i	$-0.563534\pi$
$877$	−9.03226e6	−0.396550	−0.198275	+	0.980146i	$0.563534\pi$
$878$	7.79008e7	3.41040
$879$	1.10612e6	0.0482868
$880$	−2.07737e7	−0.904290
$881$	−2.05238e7	−0.890880	−0.445440	−	0.895312i	$-0.646953\pi$
$881$	−2.05238e7	−0.890880	−0.445440	+	0.895312i	$0.646953\pi$
$882$	−5.97920e6	−0.258804
$883$	4.12829e7	1.78184	0.890919	−	0.454161i	$-0.150061\pi$
$883$	4.12829e7	1.78184	0.890919	+	0.454161i	$0.150061\pi$
$884$	−1.18908e8	−5.11775
$885$	−1.82590e6	−0.0783643
$886$	−2.26153e7	−0.967872
$887$	1.19037e7	0.508009	0.254004	−	0.967203i	$-0.418252\pi$
$887$	1.19037e7	0.508009	0.254004	+	0.967203i	$0.418252\pi$
$888$	−1.39913e8	−5.95424
$889$	9.09727e6	0.386062
$890$	−6.02353e6	−0.254904
$891$	3.80924e7	1.60747
$892$	−1.11570e8	−4.69498
$893$	1.51201e7	0.634493
$894$	−4.40464e7	−1.84317
$895$	−2.56906e6	−0.107205
$896$	−6.38881e7	−2.65858
$897$	5.55189e7	2.30388
$898$	4.99508e6	0.206705
$899$	854315.	0.0352548
$900$	1.07503e7	0.442401
$901$	−2.51660e6	−0.103277
$902$	−2.51232e7	−1.02815
$903$	−5.19382e6	−0.211966
$904$	4.19684e7	1.70805
$905$	1.96865e6	0.0799002
$906$	3.08781e7	1.24977
$907$	1.65999e7	0.670020	0.335010	−	0.942215i	$-0.391260\pi$
$907$	1.65999e7	0.670020	0.335010	+	0.942215i	$0.391260\pi$
$908$	−6.67279e7	−2.68592
$909$	−4.76625e6	−0.191323
$910$	3.41829e6	0.136837
$911$	2.91511e7	1.16375	0.581873	−	0.813280i	$-0.302320\pi$
$911$	2.91511e7	1.16375	0.581873	+	0.813280i	$0.302320\pi$
$912$	−8.14716e7	−3.24354
$913$	3.63588e7	1.44355
$914$	6.54177e7	2.59018
$915$	−1.33165e6	−0.0525821
$916$	3.20623e7	1.26257
$917$	−1.81311e7	−0.712035
$918$	4.88801e7	1.91437
$919$	−1.40438e7	−0.548524	−0.274262	−	0.961655i	$-0.588433\pi$
$919$	−1.40438e7	−0.548524	−0.274262	+	0.961655i	$0.588433\pi$
$920$	1.27191e7	0.495435
$921$	1.67639e6	0.0651216
$922$	7.85967e7	3.04493
$923$	−4.01216e7	−1.55015
$924$	−5.11911e7	−1.97249
$925$	−4.27565e7	−1.64304
$926$	4.13162e7	1.58341
$927$	5.28597e6	0.202034
$928$	7.07014e6	0.269500
$929$	−3.38830e7	−1.28808	−0.644040	−	0.764992i	$-0.722743\pi$
$929$	−3.38830e7	−1.28808	−0.644040	+	0.764992i	$0.722743\pi$
$930$	3.45942e6	0.131158
$931$	1.67366e7	0.632840
$932$	2.91286e7	1.09845
$933$	−1.48950e7	−0.560193
$934$	3.90372e7	1.46424
$935$	−4.57605e6	−0.171183
$936$	−3.00600e7	−1.12150
$937$	3.87573e7	1.44213	0.721065	−	0.692868i	$-0.243653\pi$
$937$	3.87573e7	1.44213	0.721065	+	0.692868i	$0.243653\pi$
$938$	−5.16556e6	−0.191695
$939$	−281879.	−0.0104328
$940$	−6.71414e6	−0.247840
$941$	4.40128e7	1.62034	0.810168	−	0.586198i	$-0.199376\pi$
$941$	4.40128e7	1.62034	0.810168	+	0.586198i	$0.199376\pi$
$942$	2.03700e7	0.747936
$943$	9.51150e6	0.348313
$944$	−1.15083e8	−4.20319
$945$	−1.05017e6	−0.0382545
$946$	−6.58929e7	−2.39392
$947$	3.06050e7	1.10896	0.554481	−	0.832196i	$-0.312917\pi$
$947$	3.06050e7	1.10896	0.554481	+	0.832196i	$0.312917\pi$
$948$	7.53592e7	2.72343
$949$	−6.92349e7	−2.49551
$950$	−4.02640e7	−1.44746
$951$	−4.55350e7	−1.63265
$952$	−3.67654e7	−1.31476
$953$	2.34478e7	0.836314	0.418157	−	0.908375i	$-0.362676\pi$
$953$	2.34478e7	0.836314	0.418157	+	0.908375i	$0.362676\pi$
$954$	−961086.	−0.0341894
$955$	−3.91915e6	−0.139054
$956$	3.17347e7	1.12302
$957$	2.42710e6	0.0856659
$958$	−4.49330e7	−1.58180
$959$	−1.50358e7	−0.527936
$960$	1.63999e7	0.574334
$961$	−1.30469e7	−0.455722
$962$	1.80608e8	6.29216
$963$	3.25919e6	0.113252
$964$	3.82881e7	1.32700
$965$	2.80440e6	0.0969441
$966$	2.59322e7	0.894120
$967$	1.48206e7	0.509683	0.254842	−	0.966983i	$-0.417977\pi$
$967$	1.48206e7	0.509683	0.254842	+	0.966983i	$0.417977\pi$
$968$	−3.16330e8	−10.8506
$969$	−1.79466e7	−0.614006
$970$	−9.42721e6	−0.321702
$971$	2.32496e7	0.791347	0.395673	−	0.918391i	$-0.370511\pi$
$971$	2.32496e7	0.791347	0.395673	+	0.918391i	$0.370511\pi$
$972$	2.60724e7	0.885148
$973$	1.51316e7	0.512391
$974$	5.10693e6	0.172489
$975$	5.16616e7	1.74043
$976$	−8.39312e7	−2.82032
$977$	2.92954e7	0.981890	0.490945	−	0.871191i	$-0.336652\pi$
$977$	2.92954e7	0.981890	0.490945	+	0.871191i	$0.336652\pi$
$978$	−6.43429e6	−0.215106
$979$	−7.70810e7	−2.57034
$980$	−7.43195e6	−0.247194
$981$	−3.46515e6	−0.114961
$982$	3.72118e7	1.23141
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	2.89622e7	0.953552
$985$	3.91043e6	0.128420
$986$	2.63330e6	0.0862598
$987$	−9.06158e6	−0.296081
$988$	1.27111e8	4.14277
$989$	2.49467e7	0.811003
$990$	−1.74758e6	−0.0566696
$991$	−3.79491e7	−1.22749	−0.613744	−	0.789505i	$-0.710337\pi$
$991$	−3.79491e7	−1.22749	−0.613744	+	0.789505i	$0.710337\pi$
$992$	1.28955e8	4.16064
$993$	−1.42060e7	−0.457193
$994$	−1.87403e7	−0.601603
$995$	689412.	0.0220761
$996$	−6.33193e7	−2.02250
$997$	−3.96723e7	−1.26401	−0.632004	−	0.774965i	$-0.717767\pi$
$997$	−3.96723e7	−1.26401	−0.632004	+	0.774965i	$0.717767\pi$
$998$	−4.33470e6	−0.137763
$999$	−5.54869e7	−1.75904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.1	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.1	✓	218	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)

\(f(q)\)	\(=\)	\(q-11.2545 q^{2} +14.3637 q^{3} +94.6632 q^{4} +5.42124 q^{5} -161.655 q^{6} +48.2201 q^{7} -705.242 q^{8} -36.6855 q^{9} +O(q^{10})\)	\(q-11.2545 q^{2} +14.3637 q^{3} +94.6632 q^{4} +5.42124 q^{5} -161.655 q^{6} +48.2201 q^{7} -705.242 q^{8} -36.6855 q^{9} -61.0132 q^{10} -780.764 q^{11} +1359.71 q^{12} -1161.87 q^{13} -542.692 q^{14} +77.8687 q^{15} +4907.91 q^{16} +1081.12 q^{17} +412.876 q^{18} -1155.70 q^{19} +513.192 q^{20} +692.617 q^{21} +8787.09 q^{22} -3326.75 q^{23} -10129.9 q^{24} -3095.61 q^{25} +13076.2 q^{26} -4017.31 q^{27} +4564.68 q^{28} -216.423 q^{29} -876.372 q^{30} -3947.43 q^{31} -32668.2 q^{32} -11214.6 q^{33} -12167.4 q^{34} +261.413 q^{35} -3472.77 q^{36} +13812.0 q^{37} +13006.8 q^{38} -16688.7 q^{39} -3823.28 q^{40} -2859.10 q^{41} -7795.05 q^{42} -7498.83 q^{43} -73909.7 q^{44} -198.881 q^{45} +37440.8 q^{46} -13083.1 q^{47} +70495.5 q^{48} -14481.8 q^{49} +34839.5 q^{50} +15528.8 q^{51} -109986. q^{52} -2327.78 q^{53} +45212.7 q^{54} -4232.71 q^{55} -34006.9 q^{56} -16600.1 q^{57} +2435.73 q^{58} -23448.4 q^{59} +7371.31 q^{60} -17101.2 q^{61} +44426.3 q^{62} -1768.98 q^{63} +210610. q^{64} -6298.75 q^{65} +126215. q^{66} +9518.40 q^{67} +102342. q^{68} -47784.2 q^{69} -2942.06 q^{70} +34532.0 q^{71} +25872.2 q^{72} +59589.4 q^{73} -155446. q^{74} -44464.3 q^{75} -109402. q^{76} -37648.6 q^{77} +187822. q^{78} +55423.0 q^{79} +26606.9 q^{80} -48788.6 q^{81} +32177.6 q^{82} -46568.2 q^{83} +65565.4 q^{84} +5860.98 q^{85} +84395.4 q^{86} -3108.62 q^{87} +550628. q^{88} +98725.0 q^{89} +2238.30 q^{90} -56025.4 q^{91} -314921. q^{92} -56699.5 q^{93} +147243. q^{94} -6265.32 q^{95} -469234. q^{96} +154511. q^{97} +162985. q^{98} +28642.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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