LMFDB - Embedded newform 959.6.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,6,Mod(1,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("959.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	959.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:	$153.808083201$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	959.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.59106 q^{2} +18.0221 q^{3} +59.9885 q^{4} +20.4003 q^{5} -172.851 q^{6} +49.0000 q^{7} -268.440 q^{8} +81.7953 q^{9} +O(q^{10})$	\(q-9.59106 q^{2} +18.0221 q^{3} +59.9885 q^{4} +20.4003 q^{5} -172.851 q^{6} +49.0000 q^{7} -268.440 q^{8} +81.7953 q^{9} -195.660 q^{10} -327.400 q^{11} +1081.12 q^{12} +1009.24 q^{13} -469.962 q^{14} +367.655 q^{15} +654.990 q^{16} -1301.51 q^{17} -784.504 q^{18} -1160.10 q^{19} +1223.78 q^{20} +883.082 q^{21} +3140.12 q^{22} +3330.61 q^{23} -4837.84 q^{24} -2708.83 q^{25} -9679.69 q^{26} -2905.24 q^{27} +2939.44 q^{28} +1803.15 q^{29} -3526.20 q^{30} -5023.01 q^{31} +2308.02 q^{32} -5900.43 q^{33} +12482.9 q^{34} +999.613 q^{35} +4906.78 q^{36} +2907.95 q^{37} +11126.6 q^{38} +18188.6 q^{39} -5476.24 q^{40} -1771.23 q^{41} -8469.70 q^{42} +16633.5 q^{43} -19640.3 q^{44} +1668.65 q^{45} -31944.1 q^{46} -4342.31 q^{47} +11804.3 q^{48} +2401.00 q^{49} +25980.6 q^{50} -23455.9 q^{51} +60542.8 q^{52} +12221.8 q^{53} +27864.4 q^{54} -6679.05 q^{55} -13153.5 q^{56} -20907.4 q^{57} -17294.1 q^{58} +6323.12 q^{59} +22055.1 q^{60} -30354.0 q^{61} +48176.0 q^{62} +4007.97 q^{63} -43096.0 q^{64} +20588.8 q^{65} +56591.4 q^{66} -46703.9 q^{67} -78075.7 q^{68} +60024.5 q^{69} -9587.35 q^{70} +10845.6 q^{71} -21957.1 q^{72} -51045.6 q^{73} -27890.4 q^{74} -48818.7 q^{75} -69592.7 q^{76} -16042.6 q^{77} -174448. q^{78} -14663.0 q^{79} +13362.0 q^{80} -72234.8 q^{81} +16988.0 q^{82} -60840.0 q^{83} +52974.8 q^{84} -26551.2 q^{85} -159533. q^{86} +32496.5 q^{87} +87887.2 q^{88} +136343. q^{89} -16004.1 q^{90} +49452.8 q^{91} +199798. q^{92} -90525.0 q^{93} +41647.4 q^{94} -23666.3 q^{95} +41595.3 q^{96} -50835.8 q^{97} -23028.1 q^{98} -26779.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) $ 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * 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 $

$2$	−9.59106	−1.69548	−0.847738	−	0.530415i	$-0.822036\pi$
$2$	−9.59106	−1.69548	−0.847738	+	0.530415i	$0.822036\pi$
$3$	18.0221	1.15612	0.578058	−	0.815995i	$-0.303811\pi$
$3$	18.0221	1.15612	0.578058	+	0.815995i	$0.303811\pi$
$4$	59.9885	1.87464
$5$	20.4003	0.364931	0.182466	−	0.983212i	$-0.441592\pi$
$5$	20.4003	0.364931	0.182466	+	0.983212i	$0.441592\pi$
$6$	−172.851	−1.96017
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−268.440	−1.48293
$9$	81.7953	0.336606
$10$	−195.660	−0.618732
$11$	−327.400	−0.815825	−0.407913	−	0.913021i	$-0.633743\pi$
$11$	−327.400	−0.815825	−0.407913	+	0.913021i	$0.633743\pi$
$12$	1081.12	2.16730
$13$	1009.24	1.65629	0.828145	−	0.560514i	$-0.189396\pi$
$13$	1009.24	1.65629	0.828145	+	0.560514i	$0.189396\pi$
$14$	−469.962	−0.640830
$15$	367.655	0.421903
$16$	654.990	0.639639
$17$	−1301.51	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$17$	−1301.51	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$18$	−784.504	−0.570708
$19$	−1160.10	−0.737244	−0.368622	−	0.929579i	$-0.620170\pi$
$19$	−1160.10	−0.737244	−0.368622	+	0.929579i	$0.620170\pi$
$20$	1223.78	0.684115
$21$	883.082	0.436971
$22$	3140.12	1.38321
$23$	3330.61	1.31282	0.656408	−	0.754406i	$-0.272075\pi$
$23$	3330.61	1.31282	0.656408	+	0.754406i	$0.272075\pi$
$24$	−4837.84	−1.71445
$25$	−2708.83	−0.866825
$26$	−9679.69	−2.80820
$27$	−2905.24	−0.766961
$28$	2939.44	0.708548
$29$	1803.15	0.398140	0.199070	−	0.979985i	$-0.436208\pi$
$29$	1803.15	0.398140	0.199070	+	0.979985i	$0.436208\pi$
$30$	−3526.20	−0.715327
$31$	−5023.01	−0.938771	−0.469385	−	0.882993i	$-0.655524\pi$
$31$	−5023.01	−0.938771	−0.469385	+	0.882993i	$0.655524\pi$
$32$	2308.02	0.398441
$33$	−5900.43	−0.943189
$34$	12482.9	1.85190
$35$	999.613	0.137931
$36$	4906.78	0.631016
$37$	2907.95	0.349207	0.174603	−	0.984639i	$-0.444136\pi$
$37$	2907.95	0.349207	0.174603	+	0.984639i	$0.444136\pi$
$38$	11126.6	1.24998
$39$	18188.6	1.91486
$40$	−5476.24	−0.541169
$41$	−1771.23	−0.164557	−0.0822783	−	0.996609i	$-0.526220\pi$
$41$	−1771.23	−0.164557	−0.0822783	+	0.996609i	$0.526220\pi$
$42$	−8469.70	−0.740874
$43$	16633.5	1.37187	0.685935	−	0.727663i	$-0.259393\pi$
$43$	16633.5	1.37187	0.685935	+	0.727663i	$0.259393\pi$
$44$	−19640.3	−1.52938
$45$	1668.65	0.122838
$46$	−31944.1	−2.22585
$47$	−4342.31	−0.286732	−0.143366	−	0.989670i	$-0.545793\pi$
$47$	−4342.31	−0.286732	−0.143366	+	0.989670i	$0.545793\pi$
$48$	11804.3	0.739497
$49$	2401.00	0.142857
$50$	25980.6	1.46968
$51$	−23455.9	−1.26278
$52$	60542.8	3.10495
$53$	12221.8	0.597647	0.298823	−	0.954308i	$-0.403406\pi$
$53$	12221.8	0.597647	0.298823	+	0.954308i	$0.403406\pi$
$54$	27864.4	1.30036
$55$	−6679.05	−0.297720
$56$	−13153.5	−0.560496
$57$	−20907.4	−0.852340
$58$	−17294.1	−0.675038
$59$	6323.12	0.236484	0.118242	−	0.992985i	$-0.462274\pi$
$59$	6323.12	0.236484	0.118242	+	0.992985i	$0.462274\pi$
$60$	22055.1	0.790917
$61$	−30354.0	−1.04446	−0.522230	−	0.852805i	$-0.674900\pi$
$61$	−30354.0	−1.04446	−0.522230	+	0.852805i	$0.674900\pi$
$62$	48176.0	1.59166
$63$	4007.97	0.127225
$64$	−43096.0	−1.31519
$65$	20588.8	0.604432
$66$	56591.4	1.59916
$67$	−46703.9	−1.27106	−0.635530	−	0.772076i	$-0.719218\pi$
$67$	−46703.9	−1.27106	−0.635530	+	0.772076i	$0.719218\pi$
$68$	−78075.7	−2.04759
$69$	60024.5	1.51777
$70$	−9587.35	−0.233859
$71$	10845.6	0.255334	0.127667	−	0.991817i	$-0.459251\pi$
$71$	10845.6	0.255334	0.127667	+	0.991817i	$0.459251\pi$
$72$	−21957.1	−0.499165
$73$	−51045.6	−1.12112	−0.560559	−	0.828114i	$-0.689414\pi$
$73$	−51045.6	−1.12112	−0.560559	+	0.828114i	$0.689414\pi$
$74$	−27890.4	−0.592072
$75$	−48818.7	−1.00215
$76$	−69592.7	−1.38207
$77$	−16042.6	−0.308353
$78$	−174448.	−3.24661
$79$	−14663.0	−0.264335	−0.132168	−	0.991227i	$-0.542194\pi$
$79$	−14663.0	−0.264335	−0.132168	+	0.991227i	$0.542194\pi$
$80$	13362.0	0.233424
$81$	−72234.8	−1.22330
$82$	16988.0	0.279002
$83$	−60840.0	−0.969379	−0.484690	−	0.874686i	$-0.661067\pi$
$83$	−60840.0	−0.969379	−0.484690	+	0.874686i	$0.661067\pi$
$84$	52974.8	0.819164
$85$	−26551.2	−0.398599
$86$	−159533.	−2.32597
$87$	32496.5	0.460297
$88$	87887.2	1.20982
$89$	136343.	1.82456	0.912278	−	0.409572i	$-0.134322\pi$
$89$	136343.	1.82456	0.912278	+	0.409572i	$0.134322\pi$
$90$	−16004.1	−0.208269
$91$	49452.8	0.626019
$92$	199798.	2.46106
$93$	−90525.0	−1.08533
$94$	41647.4	0.486147
$95$	−23666.3	−0.269043
$96$	41595.3	0.460645
$97$	−50835.8	−0.548581	−0.274290	−	0.961647i	$-0.588443\pi$
$97$	−50835.8	−0.548581	−0.274290	+	0.961647i	$0.588443\pi$
$98$	−23028.1	−0.242211
$99$	−26779.8	−0.274612
$100$	−162499.	−1.62499
$101$	130633.	1.27424	0.637120	−	0.770765i	$-0.280126\pi$
$101$	130633.	1.27424	0.637120	+	0.770765i	$0.280126\pi$
$102$	224967.	2.14101
$103$	−29575.9	−0.274691	−0.137345	−	0.990523i	$-0.543857\pi$
$103$	−29575.9	−0.274691	−0.137345	+	0.990523i	$0.543857\pi$
$104$	−270920.	−2.45617
$105$	18015.1	0.159464
$106$	−117220.	−1.01330
$107$	−163639.	−1.38174	−0.690870	−	0.722979i	$-0.742772\pi$
$107$	−163639.	−1.38174	−0.690870	+	0.722979i	$0.742772\pi$
$108$	−174281.	−1.43778
$109$	−195764.	−1.57822	−0.789110	−	0.614253i	$-0.789458\pi$
$109$	−195764.	−1.57822	−0.789110	+	0.614253i	$0.789458\pi$
$110$	64059.2	0.504777
$111$	52407.3	0.403724
$112$	32094.5	0.241761
$113$	−264149.	−1.94604	−0.973021	−	0.230717i	$-0.925893\pi$
$113$	−264149.	−1.94604	−0.973021	+	0.230717i	$0.925893\pi$
$114$	200524.	1.44512
$115$	67945.3	0.479087
$116$	108168.	0.746370
$117$	82551.1	0.557517
$118$	−60645.4	−0.400953
$119$	−63774.0	−0.412835
$120$	−98693.3	−0.625654
$121$	−53860.1	−0.334429
$122$	291127.	1.77086
$123$	−31921.3	−0.190247
$124$	−301323.	−1.75986
$125$	−119012.	−0.681262
$126$	−38440.7	−0.215707
$127$	−207308.	−1.14053	−0.570266	−	0.821460i	$-0.693160\pi$
$127$	−207308.	−1.14053	−0.570266	+	0.821460i	$0.693160\pi$
$128$	339480.	1.83143
$129$	299771.	1.58604
$130$	−197468.	−1.02480
$131$	150156.	0.764479	0.382240	−	0.924063i	$-0.375153\pi$
$131$	150156.	0.764479	0.382240	+	0.924063i	$0.375153\pi$
$132$	−353958.	−1.76814
$133$	−56844.9	−0.278652
$134$	447940.	2.15505
$135$	−59267.7	−0.279888
$136$	349377.	1.61975
$137$	18769.0	0.0854358
$137$	18769.0	0.0854358
$138$	−575699.	−2.57334
$139$	−353295.	−1.55096	−0.775480	−	0.631372i	$-0.782492\pi$
$139$	−353295.	−1.55096	−0.775480	+	0.631372i	$0.782492\pi$
$140$	59965.3	0.258571
$141$	−78257.4	−0.331496
$142$	−104021.	−0.432913
$143$	−330426.	−1.35124
$144$	53575.1	0.215306
$145$	36784.7	0.145294
$146$	489582.	1.90083
$147$	43271.0	0.165160
$148$	174444.	0.654638
$149$	198403.	0.732121	0.366061	−	0.930591i	$-0.380706\pi$
$149$	198403.	0.732121	0.366061	+	0.930591i	$0.380706\pi$
$150$	468224.	1.69912
$151$	423691.	1.51219	0.756095	−	0.654462i	$-0.227105\pi$
$151$	423691.	1.51219	0.756095	+	0.654462i	$0.227105\pi$
$152$	311417.	1.09328
$153$	−106457.	−0.367661
$154$	153866.	0.522805
$155$	−102471.	−0.342587
$156$	1.09111e6	3.58968
$157$	−133996.	−0.433852	−0.216926	−	0.976188i	$-0.569603\pi$
$157$	−133996.	−0.433852	−0.216926	+	0.976188i	$0.569603\pi$
$158$	140634.	0.448174
$159$	220262.	0.690950
$160$	47084.2	0.145404
$161$	163200.	0.496198
$162$	692809.	2.07408
$163$	641074.	1.88990	0.944950	−	0.327214i	$-0.106110\pi$
$163$	641074.	1.88990	0.944950	+	0.327214i	$0.106110\pi$
$164$	−106253.	−0.308485
$165$	−120370.	−0.344199
$166$	583520.	1.64356
$167$	−42256.3	−0.117247	−0.0586233	−	0.998280i	$-0.518671\pi$
$167$	−42256.3	−0.117247	−0.0586233	+	0.998280i	$0.518671\pi$
$168$	−237054.	−0.647999
$169$	647273.	1.74330
$170$	254654.	0.675815
$171$	−94890.7	−0.248161
$172$	997820.	2.57176
$173$	592380.	1.50482	0.752411	−	0.658694i	$-0.228891\pi$
$173$	592380.	1.50482	0.752411	+	0.658694i	$0.228891\pi$
$174$	−311676.	−0.780422
$175$	−132733.	−0.327629
$176$	−214444.	−0.521834
$177$	113956.	0.273403
$178$	−1.30767e6	−3.09349
$179$	626820.	1.46221	0.731106	−	0.682264i	$-0.239005\pi$
$179$	626820.	1.46221	0.731106	+	0.682264i	$0.239005\pi$
$180$	100100.	0.230277
$181$	366431.	0.831372	0.415686	−	0.909508i	$-0.363541\pi$
$181$	366431.	0.831372	0.415686	+	0.909508i	$0.363541\pi$
$182$	−474305.	−1.06140
$183$	−547042.	−1.20752
$184$	−894068.	−1.94682
$185$	59323.0	0.127436
$186$	868231.	1.84015
$187$	426115.	0.891092
$188$	−260489.	−0.537520
$189$	−142357.	−0.289884
$190$	226985.	0.456157
$191$	−551354.	−1.09357	−0.546786	−	0.837273i	$-0.684149\pi$
$191$	−551354.	−1.09357	−0.546786	+	0.837273i	$0.684149\pi$
$192$	−776680.	−1.52051
$193$	−160362.	−0.309891	−0.154945	−	0.987923i	$-0.549520\pi$
$193$	−160362.	−0.309891	−0.154945	+	0.987923i	$0.549520\pi$
$194$	487570.	0.930106
$195$	371053.	0.698793
$196$	144032.	0.267806
$197$	−247500.	−0.454370	−0.227185	−	0.973852i	$-0.572952\pi$
$197$	−247500.	−0.454370	−0.227185	+	0.973852i	$0.572952\pi$
$198$	256847.	0.465598
$199$	−802778.	−1.43702	−0.718510	−	0.695516i	$-0.755176\pi$
$199$	−802778.	−1.43702	−0.718510	+	0.695516i	$0.755176\pi$
$200$	727157.	1.28544
$201$	−841701.	−1.46949
$202$	−1.25291e6	−2.16044
$203$	88354.2	0.150483
$204$	−1.40709e6	−2.36726
$205$	−36133.6	−0.0600518
$206$	283664.	0.465732
$207$	272428.	0.441902
$208$	661043.	1.05943
$209$	379817.	0.601463
$210$	−172784.	−0.270368
$211$	−699754.	−1.08203	−0.541015	−	0.841013i	$-0.681960\pi$
$211$	−699754.	−1.08203	−0.541015	+	0.841013i	$0.681960\pi$
$212$	733166.	1.12037
$213$	195461.	0.295196
$214$	1.56947e6	2.34271
$215$	339328.	0.500638
$216$	779883.	1.13735
$217$	−246127.	−0.354822
$218$	1.87759e6	2.67583
$219$	−919948.	−1.29614
$220$	−400666.	−0.558118
$221$	−1.31354e6	−1.80910
$222$	−502642.	−0.684505
$223$	917277.	1.23520	0.617602	−	0.786491i	$-0.288104\pi$
$223$	917277.	1.23520	0.617602	+	0.786491i	$0.288104\pi$
$224$	113093.	0.150597
$225$	−221570.	−0.291779
$226$	2.53347e6	3.29947
$227$	−1.14683e6	−1.47719	−0.738593	−	0.674152i	$-0.764509\pi$
$227$	−1.14683e6	−1.47719	−0.738593	+	0.674152i	$0.764509\pi$
$228$	−1.25420e6	−1.59783
$229$	27517.8	0.0346757	0.0173378	−	0.999850i	$-0.494481\pi$
$229$	27517.8	0.0346757	0.0173378	+	0.999850i	$0.494481\pi$
$230$	−651668.	−0.812281
$231$	−289121.	−0.356492
$232$	−484036.	−0.590416
$233$	−198786.	−0.239882	−0.119941	−	0.992781i	$-0.538270\pi$
$233$	−198786.	−0.239882	−0.119941	+	0.992781i	$0.538270\pi$
$234$	−791753.	−0.945258
$235$	−88584.3	−0.104637
$236$	379314.	0.443322
$237$	−264258.	−0.305602
$238$	611661.	0.699952
$239$	846328.	0.958394	0.479197	−	0.877707i	$-0.340928\pi$
$239$	846328.	0.958394	0.479197	+	0.877707i	$0.340928\pi$
$240$	240811.	0.269866
$241$	−227027.	−0.251788	−0.125894	−	0.992044i	$-0.540180\pi$
$241$	−227027.	−0.251788	−0.125894	+	0.992044i	$0.540180\pi$
$242$	516576.	0.567016
$243$	−595847.	−0.647320
$244$	−1.82089e6	−1.95799
$245$	48981.0	0.0521330
$246$	306159.	0.322559
$247$	−1.17082e6	−1.22109
$248$	1.34837e6	1.39213
$249$	−1.09646e6	−1.12072
$250$	1.14145e6	1.15506
$251$	1.63388e6	1.63695	0.818476	−	0.574541i	$-0.194819\pi$
$251$	1.63388e6	1.63695	0.818476	+	0.574541i	$0.194819\pi$
$252$	240432.	0.238502
$253$	−1.09044e6	−1.07103
$254$	1.98831e6	1.93374
$255$	−478507.	−0.460827
$256$	−1.87690e6	−1.78996
$257$	1.38259e6	1.30575	0.652876	−	0.757465i	$-0.273562\pi$
$257$	1.38259e6	1.30575	0.652876	+	0.757465i	$0.273562\pi$
$258$	−2.87512e6	−2.68910
$259$	142490.	0.131988
$260$	1.23509e6	1.13309
$261$	147489.	0.134017
$262$	−1.44016e6	−1.29616
$263$	−1.90293e6	−1.69642	−0.848209	−	0.529661i	$-0.822319\pi$
$263$	−1.90293e6	−1.69642	−0.848209	+	0.529661i	$0.822319\pi$
$264$	1.58391e6	1.39869
$265$	249327.	0.218100
$266$	545203.	0.472448
$267$	2.45718e6	2.10940
$268$	−2.80170e6	−2.38278
$269$	−1.62013e6	−1.36511	−0.682555	−	0.730834i	$-0.739131\pi$
$269$	−1.62013e6	−1.36511	−0.682555	+	0.730834i	$0.739131\pi$
$270$	568441.	0.474543
$271$	−1.57727e6	−1.30462	−0.652309	−	0.757953i	$-0.726199\pi$
$271$	−1.57727e6	−1.30462	−0.652309	+	0.757953i	$0.726199\pi$
$272$	−852477.	−0.698651
$273$	891242.	0.723751
$274$	−180015.	−0.144854
$275$	886871.	0.707178
$276$	3.60078e6	2.84527
$277$	67835.6	0.0531200	0.0265600	−	0.999647i	$-0.491545\pi$
$277$	67835.6	0.0531200	0.0265600	+	0.999647i	$0.491545\pi$
$278$	3.38848e6	2.62962
$279$	−410858.	−0.315996
$280$	−268336.	−0.204543
$281$	−1.88146e6	−1.42144	−0.710722	−	0.703472i	$-0.751632\pi$
$281$	−1.88146e6	−1.42144	−0.710722	+	0.703472i	$0.751632\pi$
$282$	750572.	0.562043
$283$	−1.66307e6	−1.23437	−0.617184	−	0.786819i	$-0.711727\pi$
$283$	−1.66307e6	−1.23437	−0.617184	+	0.786819i	$0.711727\pi$
$284$	650613.	0.478659
$285$	−426517.	−0.311045
$286$	3.16913e6	2.29100
$287$	−86790.3	−0.0621966
$288$	188785.	0.134118
$289$	274073.	0.193029
$290$	−352804.	−0.246342
$291$	−916167.	−0.634223
$292$	−3.06215e6	−2.10169
$293$	−2.40337e6	−1.63551	−0.817753	−	0.575569i	$-0.804781\pi$
$293$	−2.40337e6	−1.63551	−0.817753	+	0.575569i	$0.804781\pi$
$294$	−415015.	−0.280024
$295$	128993.	0.0863002
$296$	−780610.	−0.517851
$297$	951177.	0.625706
$298$	−1.90290e6	−1.24129
$299$	3.36138e6	2.17440
$300$	−2.92856e6	−1.87867
$301$	815042.	0.518518
$302$	−4.06364e6	−2.56388
$303$	2.35429e6	1.47317
$304$	−759854.	−0.471570
$305$	−619230.	−0.381156
$306$	1.02104e6	0.623361
$307$	1.08211e6	0.655280	0.327640	−	0.944803i	$-0.393747\pi$
$307$	1.08211e6	0.655280	0.327640	+	0.944803i	$0.393747\pi$
$308$	−962372.	−0.578051
$309$	−533018.	−0.317575
$310$	982803.	0.580847
$311$	1.39658e6	0.818777	0.409388	−	0.912360i	$-0.365742\pi$
$311$	1.39658e6	0.818777	0.409388	+	0.912360i	$0.365742\pi$
$312$	−4.88255e6	−2.83962
$313$	−88240.2	−0.0509103	−0.0254551	−	0.999676i	$-0.508103\pi$
$313$	−88240.2	−0.0509103	−0.0254551	+	0.999676i	$0.508103\pi$
$314$	1.28516e6	0.735586
$315$	81763.7	0.0464284
$316$	−879611.	−0.495533
$317$	−1.68298e6	−0.940653	−0.470327	−	0.882492i	$-0.655864\pi$
$317$	−1.68298e6	−0.940653	−0.470327	+	0.882492i	$0.655864\pi$
$318$	−2.11255e6	−1.17149
$319$	−590351.	−0.324813
$320$	−879171.	−0.479952
$321$	−2.94911e6	−1.59745
$322$	−1.56526e6	−0.841292
$323$	1.50988e6	0.805261
$324$	−4.33326e6	−2.29325
$325$	−2.73386e6	−1.43571
$326$	−6.14858e6	−3.20428
$327$	−3.52808e6	−1.82461
$328$	475469.	0.244027
$329$	−212773.	−0.108374
$330$	1.15448e6	0.583582
$331$	−1.54499e6	−0.775099	−0.387549	−	0.921849i	$-0.626678\pi$
$331$	−1.54499e6	−0.775099	−0.387549	+	0.921849i	$0.626678\pi$
$332$	−3.64970e6	−1.81724
$333$	237857.	0.117545
$334$	405283.	0.198789
$335$	−952771.	−0.463849
$336$	578410.	0.279504
$337$	1.74888e6	0.838852	0.419426	−	0.907790i	$-0.362231\pi$
$337$	1.74888e6	0.838852	0.419426	+	0.907790i	$0.362231\pi$
$338$	−6.20804e6	−2.95572
$339$	−4.76051e6	−2.24985
$340$	−1.59276e6	−0.747230
$341$	1.64453e6	0.765873
$342$	910103.	0.420751
$343$	117649.	0.0539949
$344$	−4.46510e6	−2.03439
$345$	1.22452e6	0.553881
$346$	−5.68155e6	−2.55139
$347$	2.52321e6	1.12494	0.562470	−	0.826818i	$-0.309851\pi$
$347$	2.52321e6	1.12494	0.562470	+	0.826818i	$0.309851\pi$
$348$	1.94941e6	0.862891
$349$	2.17217e6	0.954621	0.477311	−	0.878735i	$-0.341612\pi$
$349$	2.17217e6	0.954621	0.477311	+	0.878735i	$0.341612\pi$
$350$	1.27305e6	0.555488
$351$	−2.93209e6	−1.27031
$352$	−755646.	−0.325059
$353$	−2.73379e6	−1.16769	−0.583847	−	0.811864i	$-0.698453\pi$
$353$	−2.73379e6	−1.16769	−0.583847	+	0.811864i	$0.698453\pi$
$354$	−1.09296e6	−0.463548
$355$	221253.	0.0931792
$356$	8.17900e6	3.42039
$357$	−1.14934e6	−0.477285
$358$	−6.01187e6	−2.47914
$359$	4.13877e6	1.69487	0.847434	−	0.530902i	$-0.178147\pi$
$359$	4.13877e6	1.69487	0.847434	+	0.530902i	$0.178147\pi$
$360$	−447931.	−0.182161
$361$	−1.13027e6	−0.456471
$362$	−3.51446e6	−1.40957
$363$	−970671.	−0.386639
$364$	2.96660e6	1.17356
$365$	−1.04134e6	−0.409131
$366$	5.24672e6	2.04732
$367$	1.67813e6	0.650370	0.325185	−	0.945650i	$-0.394573\pi$
$367$	1.67813e6	0.650370	0.325185	+	0.945650i	$0.394573\pi$
$368$	2.18152e6	0.839728
$369$	−144878.	−0.0553908
$370$	−568971.	−0.216066
$371$	598867.	0.225889
$372$	−5.43046e6	−2.03460
$373$	−5.34981e6	−1.99098	−0.995488	−	0.0948846i	$-0.969752\pi$
$373$	−5.34981e6	−1.99098	−0.995488	+	0.0948846i	$0.969752\pi$
$374$	−4.08689e6	−1.51083
$375$	−2.14484e6	−0.787619
$376$	1.16565e6	0.425205
$377$	1.81981e6	0.659436
$378$	1.36535e6	0.491491
$379$	2.24164e6	0.801619	0.400810	−	0.916161i	$-0.368729\pi$
$379$	2.24164e6	0.801619	0.400810	+	0.916161i	$0.368729\pi$
$380$	−1.41971e6	−0.504360
$381$	−3.73612e6	−1.31859
$382$	5.28807e6	1.85413
$383$	−409993.	−0.142817	−0.0714085	−	0.997447i	$-0.522749\pi$
$383$	−409993.	−0.142817	−0.0714085	+	0.997447i	$0.522749\pi$
$384$	6.11814e6	2.11734
$385$	−327273.	−0.112528
$386$	1.53804e6	0.525413
$387$	1.36054e6	0.461780
$388$	−3.04957e6	−1.02839
$389$	−3.19482e6	−1.07046	−0.535232	−	0.844705i	$-0.679776\pi$
$389$	−3.19482e6	−1.07046	−0.535232	+	0.844705i	$0.679776\pi$
$390$	−3.55879e6	−1.18479
$391$	−4.33482e6	−1.43393
$392$	−644524.	−0.211848
$393$	2.70613e6	0.883827
$394$	2.37379e6	0.770373
$395$	−299129.	−0.0964641
$396$	−1.60648e6	−0.514799
$397$	3.54582e6	1.12912	0.564561	−	0.825392i	$-0.309046\pi$
$397$	3.54582e6	1.12912	0.564561	+	0.825392i	$0.309046\pi$
$398$	7.69950e6	2.43644
$399$	−1.02446e6	−0.322154
$400$	−1.77426e6	−0.554455
$401$	−1.70770e6	−0.530337	−0.265168	−	0.964202i	$-0.585428\pi$
$401$	−1.70770e6	−0.530337	−0.265168	+	0.964202i	$0.585428\pi$
$402$	8.07281e6	2.49149
$403$	−5.06942e6	−1.55488
$404$	7.83651e6	2.38874
$405$	−1.47361e6	−0.446421
$406$	−847411.	−0.255140
$407$	−952064.	−0.284892
$408$	6.29650e6	1.87262
$409$	2.79797e6	0.827057	0.413529	−	0.910491i	$-0.364296\pi$
$409$	2.79797e6	0.827057	0.413529	+	0.910491i	$0.364296\pi$
$410$	346559.	0.101816
$411$	338256.	0.0987737
$412$	−1.77421e6	−0.514947
$413$	309833.	0.0893824
$414$	−2.61288e6	−0.749235
$415$	−1.24115e6	−0.353756
$416$	2.32935e6	0.659934
$417$	−6.36711e6	−1.79309
$418$	−3.64285e6	−1.01977
$419$	−4.27077e6	−1.18842	−0.594212	−	0.804309i	$-0.702536\pi$
$419$	−4.27077e6	−1.18842	−0.594212	+	0.804309i	$0.702536\pi$
$420$	1.08070e6	0.298938
$421$	−4.70348e6	−1.29334	−0.646672	−	0.762769i	$-0.723840\pi$
$421$	−4.70348e6	−1.29334	−0.646672	+	0.762769i	$0.723840\pi$
$422$	6.71139e6	1.83456
$423$	−355181.	−0.0965158
$424$	−3.28081e6	−0.886271
$425$	3.52557e6	0.946797
$426$	−1.87467e6	−0.500498
$427$	−1.48735e6	−0.394769
$428$	−9.81644e6	−2.59027
$429$	−5.95496e6	−1.56220
$430$	−3.25452e6	−0.848820
$431$	−2.43217e6	−0.630669	−0.315335	−	0.948981i	$-0.602117\pi$
$431$	−2.43217e6	−0.630669	−0.315335	+	0.948981i	$0.602117\pi$
$432$	−1.90291e6	−0.490578
$433$	−1.77981e6	−0.456199	−0.228099	−	0.973638i	$-0.573251\pi$
$433$	−1.77981e6	−0.456199	−0.228099	+	0.973638i	$0.573251\pi$
$434$	2.36062e6	0.601592
$435$	662936.	0.167977
$436$	−1.17436e7	−2.95859
$437$	−3.86384e6	−0.967866
$438$	8.82329e6	2.19758
$439$	1.17564e6	0.291147	0.145574	−	0.989347i	$-0.453497\pi$
$439$	1.17564e6	0.291147	0.145574	+	0.989347i	$0.453497\pi$
$440$	1.79292e6	0.441499
$441$	196391.	0.0480866
$442$	1.25982e7	3.06728
$443$	3.03158e6	0.733939	0.366970	−	0.930233i	$-0.380395\pi$
$443$	3.03158e6	0.733939	0.366970	+	0.930233i	$0.380395\pi$
$444$	3.14384e6	0.756838
$445$	2.78143e6	0.665837
$446$	−8.79766e6	−2.09426
$447$	3.57564e6	0.846418
$448$	−2.11171e6	−0.497094
$449$	−1.22111e6	−0.285850	−0.142925	−	0.989733i	$-0.545651\pi$
$449$	−1.22111e6	−0.285850	−0.142925	+	0.989733i	$0.545651\pi$
$450$	2.12509e6	0.494704
$451$	579901.	0.134249
$452$	−1.58459e7	−3.64813
$453$	7.63579e6	1.74827
$454$	1.09993e7	2.50453
$455$	1.00885e6	0.228454
$456$	5.61238e6	1.26396
$457$	4.48527e6	1.00461	0.502305	−	0.864690i	$-0.332485\pi$
$457$	4.48527e6	1.00461	0.502305	+	0.864690i	$0.332485\pi$
$458$	−263925.	−0.0587918
$459$	3.78121e6	0.837719
$460$	4.07594e6	0.898117
$461$	−5.38882e6	−1.18098	−0.590488	−	0.807046i	$-0.701065\pi$
$461$	−5.38882e6	−1.18098	−0.590488	+	0.807046i	$0.701065\pi$
$462$	2.77298e6	0.604424
$463$	1.99813e6	0.433182	0.216591	−	0.976262i	$-0.430506\pi$
$463$	1.99813e6	0.433182	0.216591	+	0.976262i	$0.430506\pi$
$464$	1.18104e6	0.254666
$465$	−1.84673e6	−0.396070
$466$	1.90657e6	0.406714
$467$	−4.00805e6	−0.850435	−0.425218	−	0.905091i	$-0.639802\pi$
$467$	−4.00805e6	−0.850435	−0.425218	+	0.905091i	$0.639802\pi$
$468$	4.95212e6	1.04515
$469$	−2.28849e6	−0.480415
$470$	849617.	0.177410
$471$	−2.41488e6	−0.501584
$472$	−1.69738e6	−0.350690
$473$	−5.44582e6	−1.11921
$474$	2.53451e6	0.518141
$475$	3.14251e6	0.639062
$476$	−3.82571e6	−0.773917
$477$	999684.	0.201172
$478$	−8.11719e6	−1.62493
$479$	−4.16577e6	−0.829576	−0.414788	−	0.909918i	$-0.636144\pi$
$479$	−4.16577e6	−0.829576	−0.414788	+	0.909918i	$0.636144\pi$
$480$	848555.	0.168104
$481$	2.93482e6	0.578388
$482$	2.17743e6	0.426901
$483$	2.94120e6	0.573663
$484$	−3.23099e6	−0.626934
$485$	−1.03706e6	−0.200194
$486$	5.71481e6	1.09752
$487$	−8.46895e6	−1.61811	−0.809054	−	0.587735i	$-0.800020\pi$
$487$	−8.46895e6	−1.61811	−0.809054	+	0.587735i	$0.800020\pi$
$488$	8.14822e6	1.54886
$489$	1.15535e7	2.18495
$490$	−469780.	−0.0883903
$491$	−2.14096e6	−0.400780	−0.200390	−	0.979716i	$-0.564221\pi$
$491$	−2.14096e6	−0.400780	−0.200390	+	0.979716i	$0.564221\pi$
$492$	−1.91491e6	−0.356644
$493$	−2.34682e6	−0.434872
$494$	1.12294e7	2.07033
$495$	−546315.	−0.100214
$496$	−3.29002e6	−0.600474
$497$	531435.	0.0965071
$498$	1.05162e7	1.90015
$499$	−5.91145e6	−1.06278	−0.531389	−	0.847128i	$-0.678330\pi$
$499$	−5.91145e6	−1.06278	−0.531389	+	0.847128i	$0.678330\pi$
$500$	−7.13933e6	−1.27712
$501$	−761546.	−0.135551
$502$	−1.56706e7	−2.77541
$503$	4.03999e6	0.711968	0.355984	−	0.934492i	$-0.384146\pi$
$503$	4.03999e6	0.711968	0.355984	+	0.934492i	$0.384146\pi$
$504$	−1.07590e6	−0.188667
$505$	2.66496e6	0.465009
$506$	1.04585e7	1.81590
$507$	1.16652e7	2.01545
$508$	−1.24361e7	−2.13809
$509$	4.51086e6	0.771729	0.385865	−	0.922555i	$-0.373903\pi$
$509$	4.51086e6	0.771729	0.385865	+	0.922555i	$0.373903\pi$
$510$	4.58939e6	0.781322
$511$	−2.50124e6	−0.423743
$512$	7.13814e6	1.20340
$513$	3.37037e6	0.565437
$514$	−1.32605e7	−2.21387
$515$	−603355.	−0.100243
$516$	1.79828e7	2.97326
$517$	1.42167e6	0.233923
$518$	−1.36663e6	−0.223782
$519$	1.06759e7	1.73975
$520$	−5.52685e6	−0.896332
$521$	−5.41163e6	−0.873442	−0.436721	−	0.899597i	$-0.643860\pi$
$521$	−5.41163e6	−0.873442	−0.436721	+	0.899597i	$0.643860\pi$
$522$	−1.41458e6	−0.227222
$523$	7.85614e6	1.25590	0.627950	−	0.778254i	$-0.283894\pi$
$523$	7.85614e6	1.25590	0.627950	+	0.778254i	$0.283894\pi$
$524$	9.00766e6	1.43312
$525$	−2.39212e6	−0.378778
$526$	1.82511e7	2.87624
$527$	6.53750e6	1.02538
$528$	−3.86473e6	−0.603301
$529$	4.65661e6	0.723486
$530$	−2.39132e6	−0.369783
$531$	517201.	0.0796019
$532$	−3.41004e6	−0.522373
$533$	−1.78760e6	−0.272553
$534$	−2.35670e7	−3.57644
$535$	−3.33827e6	−0.504240
$536$	1.25372e7	1.88490
$537$	1.12966e7	1.69049
$538$	1.55387e7	2.31451
$539$	−786088.	−0.116546
$540$	−3.55538e6	−0.524689
$541$	1.17115e7	1.72036	0.860179	−	0.509993i	$-0.170352\pi$
$541$	1.17115e7	1.72036	0.860179	+	0.509993i	$0.170352\pi$
$542$	1.51277e7	2.21195
$543$	6.60385e6	0.961164
$544$	−3.00391e6	−0.435201
$545$	−3.99364e6	−0.575941
$546$	−8.54796e6	−1.22710
$547$	−7.42295e6	−1.06074	−0.530369	−	0.847767i	$-0.677947\pi$
$547$	−7.42295e6	−1.06074	−0.530369	+	0.847767i	$0.677947\pi$
$548$	1.12592e6	0.160161
$549$	−2.48282e6	−0.351572
$550$	−8.50604e6	−1.19900
$551$	−2.09183e6	−0.293527
$552$	−1.61130e7	−2.25075
$553$	−718486.	−0.0999093
$554$	−650616.	−0.0900637
$555$	1.06912e6	0.147331
$556$	−2.11937e7	−2.90750
$557$	7.00526e6	0.956723	0.478361	−	0.878163i	$-0.341231\pi$
$557$	7.00526e6	0.956723	0.478361	+	0.878163i	$0.341231\pi$
$558$	3.94057e6	0.535764
$559$	1.67872e7	2.27221
$560$	654737.	0.0882260
$561$	7.67947e6	1.03021
$562$	1.80452e7	2.41003
$563$	−1.88977e6	−0.251268	−0.125634	−	0.992077i	$-0.540096\pi$
$563$	−1.88977e6	−0.251268	−0.125634	+	0.992077i	$0.540096\pi$
$564$	−4.69455e6	−0.621435
$565$	−5.38870e6	−0.710171
$566$	1.59506e7	2.09284
$567$	−3.53950e6	−0.462365
$568$	−2.91139e6	−0.378643
$569$	−3.68472e6	−0.477116	−0.238558	−	0.971128i	$-0.576675\pi$
$569$	−3.68472e6	−0.477116	−0.238558	+	0.971128i	$0.576675\pi$
$570$	4.09075e6	0.527370
$571$	1.25029e7	1.60480	0.802399	−	0.596788i	$-0.203557\pi$
$571$	1.25029e7	1.60480	0.802399	+	0.596788i	$0.203557\pi$
$572$	−1.98217e7	−2.53310
$573$	−9.93655e6	−1.26430
$574$	832411.	0.105453
$575$	−9.02205e6	−1.13798
$576$	−3.52505e6	−0.442700
$577$	−1.44658e7	−1.80885	−0.904423	−	0.426637i	$-0.859698\pi$
$577$	−1.44658e7	−1.80885	−0.904423	+	0.426637i	$0.859698\pi$
$578$	−2.62865e6	−0.327275
$579$	−2.89006e6	−0.358270
$580$	2.20666e6	0.272374
$581$	−2.98116e6	−0.366391
$582$	8.78702e6	1.07531
$583$	−4.00141e6	−0.487575
$584$	1.37027e7	1.66254
$585$	1.68407e6	0.203455
$586$	2.30509e7	2.77296
$587$	−1.53400e7	−1.83752	−0.918758	−	0.394821i	$-0.870807\pi$
$587$	−1.53400e7	−1.83752	−0.918758	+	0.394821i	$0.870807\pi$
$588$	2.59576e6	0.309615
$589$	5.82719e6	0.692103
$590$	−1.23718e6	−0.146320
$591$	−4.46046e6	−0.525304
$592$	1.90468e6	0.223366
$593$	9.09056e6	1.06158	0.530791	−	0.847503i	$-0.321895\pi$
$593$	9.09056e6	1.06158	0.530791	+	0.847503i	$0.321895\pi$
$594$	−9.12280e6	−1.06087
$595$	−1.30101e6	−0.150656
$596$	1.19019e7	1.37246
$597$	−1.44677e7	−1.66136
$598$	−3.22393e7	−3.68665
$599$	1.22251e7	1.39215	0.696074	−	0.717970i	$-0.254929\pi$
$599$	1.22251e7	1.39215	0.696074	+	0.717970i	$0.254929\pi$
$600$	1.31049e7	1.48612
$601$	−6.03746e6	−0.681817	−0.340909	−	0.940096i	$-0.610735\pi$
$601$	−6.03746e6	−0.681817	−0.340909	+	0.940096i	$0.610735\pi$
$602$	−7.81713e6	−0.879136
$603$	−3.82016e6	−0.427846
$604$	2.54166e7	2.83481
$605$	−1.09876e6	−0.122043
$606$	−2.25801e7	−2.49772
$607$	203914.	0.0224634	0.0112317	−	0.999937i	$-0.496425\pi$
$607$	203914.	0.0224634	0.0112317	+	0.999937i	$0.496425\pi$
$608$	−2.67753e6	−0.293749
$609$	1.59233e6	0.173976
$610$	5.93907e6	0.646240
$611$	−4.38243e6	−0.474911
$612$	−6.38623e6	−0.689233
$613$	−1.06053e7	−1.13992	−0.569958	−	0.821674i	$-0.693041\pi$
$613$	−1.06053e7	−1.13992	−0.569958	+	0.821674i	$0.693041\pi$
$614$	−1.03786e7	−1.11101
$615$	−651202.	−0.0694269
$616$	4.30647e6	0.457267
$617$	−2.05591e6	−0.217416	−0.108708	−	0.994074i	$-0.534671\pi$
$617$	−2.05591e6	−0.217416	−0.108708	+	0.994074i	$0.534671\pi$
$618$	5.11221e6	0.538441
$619$	−1.03918e6	−0.109010	−0.0545049	−	0.998514i	$-0.517358\pi$
$619$	−1.03918e6	−0.109010	−0.0545049	+	0.998514i	$0.517358\pi$
$620$	−6.14706e6	−0.642227
$621$	−9.67623e6	−1.00688
$622$	−1.33947e7	−1.38822
$623$	6.68080e6	0.689617
$624$	1.19134e7	1.22482
$625$	6.03722e6	0.618212
$626$	846317.	0.0863172
$627$	6.84509e6	0.695361
$628$	−8.03820e6	−0.813317
$629$	−3.78473e6	−0.381424
$630$	−784201.	−0.0787183
$631$	−1.07167e7	−1.07149	−0.535747	−	0.844379i	$-0.679970\pi$
$631$	−1.07167e7	−1.07149	−0.535747	+	0.844379i	$0.679970\pi$
$632$	3.93613e6	0.391991
$633$	−1.26110e7	−1.25095
$634$	1.61415e7	1.59486
$635$	−4.22914e6	−0.416215
$636$	1.32132e7	1.29528
$637$	2.42319e6	0.236613
$638$	5.66209e6	0.550713
$639$	887121.	0.0859470
$640$	6.92549e6	0.668345
$641$	3.54014e6	0.340311	0.170155	−	0.985417i	$-0.445573\pi$
$641$	3.54014e6	0.340311	0.170155	+	0.985417i	$0.445573\pi$
$642$	2.82851e7	2.70845
$643$	−1.16803e6	−0.111411	−0.0557055	−	0.998447i	$-0.517741\pi$
$643$	−1.16803e6	−0.111411	−0.0557055	+	0.998447i	$0.517741\pi$
$644$	9.79011e6	0.930193
$645$	6.11540e6	0.578796
$646$	−1.44814e7	−1.36530
$647$	−1.71682e7	−1.61237	−0.806185	−	0.591663i	$-0.798472\pi$
$647$	−1.71682e7	−1.61237	−0.806185	+	0.591663i	$0.798472\pi$
$648$	1.93907e7	1.81408
$649$	−2.07019e6	−0.192929
$650$	2.62206e7	2.43422
$651$	−4.43573e6	−0.410216
$652$	3.84571e7	3.54289
$653$	−1.40074e7	−1.28551	−0.642753	−	0.766074i	$-0.722208\pi$
$653$	−1.40074e7	−1.28551	−0.642753	+	0.766074i	$0.722208\pi$
$654$	3.38380e7	3.09358
$655$	3.06323e6	0.278982
$656$	−1.16014e6	−0.105257
$657$	−4.17529e6	−0.377375
$658$	2.04072e6	0.183746
$659$	3.18361e6	0.285566	0.142783	−	0.989754i	$-0.454395\pi$
$659$	3.18361e6	0.285566	0.142783	+	0.989754i	$0.454395\pi$
$660$	−7.22084e6	−0.645250
$661$	−899188.	−0.0800473	−0.0400237	−	0.999199i	$-0.512743\pi$
$661$	−899188.	−0.0800473	−0.0400237	+	0.999199i	$0.512743\pi$
$662$	1.48181e7	1.31416
$663$	−2.36727e7	−2.09153
$664$	1.63319e7	1.43753
$665$	−1.15965e6	−0.101689
$666$	−2.28130e6	−0.199295
$667$	6.00558e6	0.522685
$668$	−2.53489e6	−0.219795
$669$	1.65312e7	1.42804
$670$	9.13809e6	0.786445
$671$	9.93791e6	0.852096
$672$	2.03817e6	0.174107
$673$	3.54145e6	0.301401	0.150700	−	0.988580i	$-0.451847\pi$
$673$	3.54145e6	0.301401	0.150700	+	0.988580i	$0.451847\pi$
$674$	−1.67736e7	−1.42225
$675$	7.86981e6	0.664821
$676$	3.88290e7	3.26805
$677$	9.25470e6	0.776052	0.388026	−	0.921649i	$-0.373157\pi$
$677$	9.25470e6	0.776052	0.388026	+	0.921649i	$0.373157\pi$
$678$	4.56583e7	3.81457
$679$	−2.49096e6	−0.207344
$680$	7.12739e6	0.591096
$681$	−2.06683e7	−1.70780
$682$	−1.57728e7	−1.29852
$683$	7.21897e6	0.592139	0.296069	−	0.955166i	$-0.404324\pi$
$683$	7.21897e6	0.592139	0.296069	+	0.955166i	$0.404324\pi$
$684$	−5.69235e6	−0.465213
$685$	382893.	0.0311782
$686$	−1.12838e6	−0.0915471
$687$	495928.	0.0400892
$688$	1.08948e7	0.877501
$689$	1.23347e7	0.989876
$690$	−1.17444e7	−0.939092
$691$	−1.11703e7	−0.889960	−0.444980	−	0.895541i	$-0.646789\pi$
$691$	−1.11703e7	−0.889960	−0.444980	+	0.895541i	$0.646789\pi$
$692$	3.55360e7	2.82100
$693$	−1.31221e6	−0.103794
$694$	−2.42003e7	−1.90731
$695$	−7.20732e6	−0.565994
$696$	−8.72334e6	−0.682590
$697$	2.30528e6	0.179738
$698$	−2.08335e7	−1.61854
$699$	−3.58255e6	−0.277331
$700$	−7.96243e6	−0.614187
$701$	−8.58771e6	−0.660058	−0.330029	−	0.943971i	$-0.607059\pi$
$701$	−8.58771e6	−0.660058	−0.330029	+	0.943971i	$0.607059\pi$
$702$	2.81219e7	2.15378
$703$	−3.37351e6	−0.257451
$704$	1.41097e7	1.07296
$705$	−1.59647e6	−0.120973
$706$	2.62200e7	1.97980
$707$	6.40104e6	0.481617
$708$	6.83603e6	0.512532
$709$	−1.51511e7	−1.13195	−0.565977	−	0.824421i	$-0.691501\pi$
$709$	−1.51511e7	−1.13195	−0.565977	+	0.824421i	$0.691501\pi$
$710$	−2.12206e6	−0.157983
$711$	−1.19936e6	−0.0889768
$712$	−3.65998e7	−2.70570
$713$	−1.67297e7	−1.23243
$714$	1.10234e7	0.809226
$715$	−6.74077e6	−0.493111
$716$	3.76020e7	2.74112
$717$	1.52526e7	1.10802
$718$	−3.96953e7	−2.87361
$719$	1.46097e7	1.05395	0.526973	−	0.849882i	$-0.323327\pi$
$719$	1.46097e7	1.05395	0.526973	+	0.849882i	$0.323327\pi$
$720$	1.09295e6	0.0785720
$721$	−1.44922e6	−0.103823
$722$	1.08405e7	0.773936
$723$	−4.09150e6	−0.291096
$724$	2.19816e7	1.55853
$725$	−4.88442e6	−0.345118
$726$	9.30977e6	0.655537
$727$	−2.62467e7	−1.84178	−0.920891	−	0.389821i	$-0.872537\pi$
$727$	−2.62467e7	−1.84178	−0.920891	+	0.389821i	$0.872537\pi$
$728$	−1.32751e7	−0.928344
$729$	6.81465e6	0.474925
$730$	9.98760e6	0.693672
$731$	−2.16487e7	−1.49844
$732$	−3.28163e7	−2.26366
$733$	−2.48002e6	−0.170489	−0.0852444	−	0.996360i	$-0.527167\pi$
$733$	−2.48002e6	−0.170489	−0.0852444	+	0.996360i	$0.527167\pi$
$734$	−1.60951e7	−1.10269
$735$	882740.	0.0602718
$736$	7.68710e6	0.523080
$737$	1.52909e7	1.03696
$738$	1.38954e6	0.0939138
$739$	8.68522e6	0.585019	0.292509	−	0.956263i	$-0.405510\pi$
$739$	8.68522e6	0.585019	0.292509	+	0.956263i	$0.405510\pi$
$740$	3.55870e6	0.238898
$741$	−2.11006e7	−1.41172
$742$	−5.74377e6	−0.382990
$743$	3.11750e6	0.207174	0.103587	−	0.994620i	$-0.466968\pi$
$743$	3.11750e6	0.207174	0.103587	+	0.994620i	$0.466968\pi$
$744$	2.43005e7	1.60947
$745$	4.04748e6	0.267174
$746$	5.13104e7	3.37565
$747$	−4.97642e6	−0.326299
$748$	2.55620e7	1.67048
$749$	−8.01830e6	−0.522249
$750$	2.05713e7	1.33539
$751$	−2.68001e7	−1.73395	−0.866975	−	0.498352i	$-0.833939\pi$
$751$	−2.68001e7	−1.73395	−0.866975	+	0.498352i	$0.833939\pi$
$752$	−2.84417e6	−0.183405
$753$	2.94459e7	1.89251
$754$	−1.74539e7	−1.11806
$755$	8.64340e6	0.551845
$756$	−8.53978e6	−0.543428
$757$	−1.47197e7	−0.933594	−0.466797	−	0.884364i	$-0.654592\pi$
$757$	−1.47197e7	−0.933594	−0.466797	+	0.884364i	$0.654592\pi$
$758$	−2.14997e7	−1.35913
$759$	−1.96520e7	−1.23823
$760$	6.35299e6	0.398973
$761$	1.36516e7	0.854520	0.427260	−	0.904129i	$-0.359479\pi$
$761$	1.36516e7	0.854520	0.427260	+	0.904129i	$0.359479\pi$
$762$	3.58334e7	2.23563
$763$	−9.59245e6	−0.596511
$764$	−3.30749e7	−2.05005
$765$	−2.17176e6	−0.134171
$766$	3.93227e6	0.242143
$767$	6.38155e6	0.391685
$768$	−3.38257e7	−2.06940
$769$	−1.71652e7	−1.04673	−0.523363	−	0.852110i	$-0.675323\pi$
$769$	−1.71652e7	−1.04673	−0.523363	+	0.852110i	$0.675323\pi$
$770$	3.13890e6	0.190788
$771$	2.49171e7	1.50960
$772$	−9.61990e6	−0.580934
$773$	5.72668e6	0.344710	0.172355	−	0.985035i	$-0.444862\pi$
$773$	5.72668e6	0.344710	0.172355	+	0.985035i	$0.444862\pi$
$774$	−1.30491e7	−0.782937
$775$	1.36065e7	0.813750
$776$	1.36464e7	0.813509
$777$	2.56796e6	0.152593
$778$	3.06417e7	1.81495
$779$	2.05480e6	0.121318
$780$	2.22589e7	1.30999
$781$	−3.55086e6	−0.208308
$782$	4.15756e7	2.43120
$783$	−5.23858e6	−0.305358
$784$	1.57263e6	0.0913770
$785$	−2.73355e6	−0.158326
$786$	−2.59547e7	−1.49851
$787$	853053.	0.0490952	0.0245476	−	0.999699i	$-0.492185\pi$
$787$	853053.	0.0490952	0.0245476	+	0.999699i	$0.492185\pi$
$788$	−1.48471e7	−0.851780
$789$	−3.42947e7	−1.96126
$790$	2.86896e6	0.163553
$791$	−1.29433e7	−0.735535
$792$	7.18876e6	0.407231
$793$	−3.06345e7	−1.72993
$794$	−3.40082e7	−1.91440
$795$	4.49340e6	0.252149
$796$	−4.81575e7	−2.69390
$797$	1.62485e6	0.0906080	0.0453040	−	0.998973i	$-0.485574\pi$
$797$	1.62485e6	0.0906080	0.0453040	+	0.998973i	$0.485574\pi$
$798$	9.82569e6	0.546205
$799$	5.65156e6	0.313185
$800$	−6.25203e6	−0.345379
$801$	1.11522e7	0.614157
$802$	1.63787e7	0.899174
$803$	1.67124e7	0.914637
$804$	−5.04924e7	−2.75477
$805$	3.32932e6	0.181078
$806$	4.86212e7	2.63626
$807$	−2.91980e7	−1.57823
$808$	−3.50672e7	−1.88961
$809$	1.32476e7	0.711650	0.355825	−	0.934553i	$-0.384200\pi$
$809$	1.32476e7	0.711650	0.355825	+	0.934553i	$0.384200\pi$
$810$	1.41335e7	0.756896
$811$	3.46880e7	1.85194	0.925971	−	0.377594i	$-0.123249\pi$
$811$	3.46880e7	1.85194	0.925971	+	0.377594i	$0.123249\pi$
$812$	5.30024e6	0.282101
$813$	−2.84257e7	−1.50829
$814$	9.13131e6	0.483028
$815$	1.30781e7	0.689683
$816$	−1.53634e7	−0.807722
$817$	−1.92965e7	−1.01140
$818$	−2.68356e7	−1.40226
$819$	4.04501e6	0.210722
$820$	−2.16760e6	−0.112576
$821$	6.32564e6	0.327527	0.163763	−	0.986500i	$-0.447637\pi$
$821$	6.32564e6	0.327527	0.163763	+	0.986500i	$0.447637\pi$
$822$	−3.24424e6	−0.167469
$823$	−8.79633e6	−0.452691	−0.226345	−	0.974047i	$-0.572678\pi$
$823$	−8.79633e6	−0.452691	−0.226345	+	0.974047i	$0.572678\pi$
$824$	7.93933e6	0.407348
$825$	1.59833e7	0.817581
$826$	−2.97163e6	−0.151546
$827$	1.94884e7	0.990860	0.495430	−	0.868648i	$-0.335011\pi$
$827$	1.94884e7	0.990860	0.495430	+	0.868648i	$0.335011\pi$
$828$	1.63426e7	0.828408
$829$	3.01558e6	0.152400	0.0762000	−	0.997093i	$-0.475721\pi$
$829$	3.01558e6	0.152400	0.0762000	+	0.997093i	$0.475721\pi$
$830$	1.19040e7	0.599786
$831$	1.22254e6	0.0614129
$832$	−4.34943e7	−2.17833
$833$	−3.12493e6	−0.156037
$834$	6.10674e7	3.04015
$835$	−862039.	−0.0427869
$836$	2.27847e7	1.12753
$837$	1.45931e7	0.720000
$838$	4.09612e7	2.01494
$839$	−1.86603e7	−0.915196	−0.457598	−	0.889159i	$-0.651290\pi$
$839$	−1.86603e7	−0.915196	−0.457598	+	0.889159i	$0.651290\pi$
$840$	−4.83597e6	−0.236475
$841$	−1.72598e7	−0.841484
$842$	4.51114e7	2.19283
$843$	−3.39079e7	−1.64336
$844$	−4.19772e7	−2.02842
$845$	1.32046e7	0.636183
$846$	3.40656e6	0.163640
$847$	−2.63915e6	−0.126402
$848$	8.00514e6	0.382278
$849$	−2.99720e7	−1.42707
$850$	−3.38140e7	−1.60527
$851$	9.68525e6	0.458445
$852$	1.17254e7	0.553386
$853$	−2.19763e7	−1.03415	−0.517074	−	0.855940i	$-0.672979\pi$
$853$	−2.19763e7	−1.03415	−0.517074	+	0.855940i	$0.672979\pi$
$854$	1.42652e7	0.669321
$855$	−1.93580e6	−0.0905616
$856$	4.39271e7	2.04903
$857$	2.83996e7	1.32087	0.660436	−	0.750882i	$-0.270372\pi$
$857$	2.83996e7	1.32087	0.660436	+	0.750882i	$0.270372\pi$
$858$	5.71144e7	2.64867
$859$	−617542.	−0.0285551	−0.0142775	−	0.999898i	$-0.504545\pi$
$859$	−617542.	−0.0285551	−0.0142775	+	0.999898i	$0.504545\pi$
$860$	2.03558e7	0.938517
$861$	−1.56414e6	−0.0719065
$862$	2.33271e7	1.06928
$863$	4.03533e7	1.84439	0.922193	−	0.386731i	$-0.126396\pi$
$863$	4.03533e7	1.84439	0.922193	+	0.386731i	$0.126396\pi$
$864$	−6.70536e6	−0.305589
$865$	1.20847e7	0.549156
$866$	1.70703e7	0.773474
$867$	4.93936e6	0.223164
$868$	−1.47648e7	−0.665164
$869$	4.80067e6	0.215651
$870$	−6.35827e6	−0.284800
$871$	−4.71354e7	−2.10524
$872$	5.25509e7	2.34039
$873$	−4.15813e6	−0.184656
$874$	3.70583e7	1.64099
$875$	−5.83157e6	−0.257493
$876$	−5.51864e7	−2.42980
$877$	2.33343e6	0.102446	0.0512231	−	0.998687i	$-0.483688\pi$
$877$	2.33343e6	0.102446	0.0512231	+	0.998687i	$0.483688\pi$
$878$	−1.12756e7	−0.493634
$879$	−4.33138e7	−1.89084
$880$	−4.37471e6	−0.190433
$881$	1.32027e7	0.573089	0.286545	−	0.958067i	$-0.407493\pi$
$881$	1.32027e7	0.573089	0.286545	+	0.958067i	$0.407493\pi$
$882$	−1.88359e6	−0.0815297
$883$	−3.25430e7	−1.40461	−0.702306	−	0.711875i	$-0.747846\pi$
$883$	−3.25430e7	−1.40461	−0.702306	+	0.711875i	$0.747846\pi$
$884$	−7.87972e7	−3.39141
$885$	2.32473e6	0.0997731
$886$	−2.90761e7	−1.24438
$887$	3.32302e7	1.41815	0.709077	−	0.705131i	$-0.249112\pi$
$887$	3.32302e7	1.41815	0.709077	+	0.705131i	$0.249112\pi$
$888$	−1.40682e7	−0.598696
$889$	−1.01581e7	−0.431080
$890$	−2.66769e7	−1.12891
$891$	2.36497e7	0.998001
$892$	5.50261e7	2.31556
$893$	5.03751e6	0.211391
$894$	−3.42942e7	−1.43508
$895$	1.27873e7	0.533606
$896$	1.66345e7	0.692214
$897$	6.05791e7	2.51387
$898$	1.17117e7	0.484653
$899$	−9.05722e6	−0.373762
$900$	−1.32916e7	−0.546981
$901$	−1.59068e7	−0.652785
$902$	−5.56187e6	−0.227617
$903$	1.46888e7	0.599468
$904$	7.09080e7	2.88585
$905$	7.47529e6	0.303394
$906$	−7.32353e7	−2.96415
$907$	−1.78747e7	−0.721474	−0.360737	−	0.932668i	$-0.617475\pi$
$907$	−1.78747e7	−0.721474	−0.360737	+	0.932668i	$0.617475\pi$
$908$	−6.87967e7	−2.76919
$909$	1.06852e7	0.428917
$910$	−9.67595e6	−0.387338
$911$	−1.71325e7	−0.683949	−0.341975	−	0.939709i	$-0.611096\pi$
$911$	−1.71325e7	−0.683949	−0.341975	+	0.939709i	$0.611096\pi$
$912$	−1.36941e7	−0.545190
$913$	1.99190e7	0.790844
$914$	−4.30185e7	−1.70329
$915$	−1.11598e7	−0.440660
$916$	1.65075e6	0.0650045
$917$	7.35766e6	0.288946
$918$	−3.62658e7	−1.42033
$919$	−1.88457e7	−0.736077	−0.368038	−	0.929811i	$-0.619971\pi$
$919$	−1.88457e7	−0.736077	−0.368038	+	0.929811i	$0.619971\pi$
$920$	−1.82392e7	−0.710455
$921$	1.95019e7	0.757580
$922$	5.16845e7	2.00232
$923$	1.09458e7	0.422907
$924$	−1.73440e7	−0.668295
$925$	−7.87714e6	−0.302701
$926$	−1.91642e7	−0.734450
$927$	−2.41917e6	−0.0924627
$928$	4.16170e6	0.158636
$929$	5.10706e6	0.194148	0.0970738	−	0.995277i	$-0.469052\pi$
$929$	5.10706e6	0.194148	0.0970738	+	0.995277i	$0.469052\pi$
$930$	1.77121e7	0.671528
$931$	−2.78540e6	−0.105321
$932$	−1.19249e7	−0.449692
$933$	2.51693e7	0.946602
$934$	3.84415e7	1.44189
$935$	8.69286e6	0.325187
$936$	−2.21600e7	−0.826762
$937$	1.43810e7	0.535106	0.267553	−	0.963543i	$-0.413785\pi$
$937$	1.43810e7	0.535106	0.267553	+	0.963543i	$0.413785\pi$
$938$	2.19490e7	0.814533
$939$	−1.59027e6	−0.0588582
$940$	−5.31404e6	−0.196158
$941$	−2.45922e7	−0.905365	−0.452682	−	0.891672i	$-0.649533\pi$
$941$	−2.45922e7	−0.905365	−0.452682	+	0.891672i	$0.649533\pi$
$942$	2.31613e7	0.850423
$943$	−5.89927e6	−0.216033
$944$	4.14158e6	0.151264
$945$	−2.90412e6	−0.105788
$946$	5.22312e7	1.89759
$947$	3.20670e7	1.16194	0.580969	−	0.813926i	$-0.302674\pi$
$947$	3.20670e7	1.16194	0.580969	+	0.813926i	$0.302674\pi$
$948$	−1.58524e7	−0.572895
$949$	−5.15173e7	−1.85690
$950$	−3.01400e7	−1.08351
$951$	−3.03307e7	−1.08751
$952$	1.71195e7	0.612207
$953$	−1.37970e6	−0.0492100	−0.0246050	−	0.999697i	$-0.507833\pi$
$953$	−1.37970e6	−0.0492100	−0.0246050	+	0.999697i	$0.507833\pi$
$954$	−9.58803e6	−0.341082
$955$	−1.12478e7	−0.399078
$956$	5.07700e7	1.79664
$957$	−1.06393e7	−0.375522
$958$	3.99541e7	1.40653
$959$	919681.	0.0322917
$960$	−1.58445e7	−0.554881
$961$	−3.39856e6	−0.118710
$962$	−2.81481e7	−0.980643
$963$	−1.33849e7	−0.465103
$964$	−1.36190e7	−0.472012
$965$	−3.27143e6	−0.113089
$966$	−2.82092e7	−0.972632
$967$	−2.46638e7	−0.848191	−0.424095	−	0.905618i	$-0.639408\pi$
$967$	−2.46638e7	−0.848191	−0.424095	+	0.905618i	$0.639408\pi$
$968$	1.44582e7	0.495936
$969$	2.72112e7	0.930976
$970$	9.94655e6	0.339424
$971$	−4.91421e7	−1.67265	−0.836326	−	0.548233i	$-0.815301\pi$
$971$	−4.91421e7	−1.67265	−0.836326	+	0.548233i	$0.815301\pi$
$972$	−3.57440e7	−1.21349
$973$	−1.73115e7	−0.586208
$974$	8.12263e7	2.74346
$975$	−4.92698e7	−1.65985
$976$	−1.98816e7	−0.668077
$977$	4.10894e7	1.37719	0.688594	−	0.725147i	$-0.258228\pi$
$977$	4.10894e7	1.37719	0.688594	+	0.725147i	$0.258228\pi$
$978$	−1.10810e8	−3.70452
$979$	−4.46387e7	−1.48852
$980$	2.93830e6	0.0977307
$981$	−1.60126e7	−0.531238
$982$	2.05341e7	0.679512
$983$	−3.52558e7	−1.16372	−0.581858	−	0.813290i	$-0.697674\pi$
$983$	−3.52558e7	−1.16372	−0.581858	+	0.813290i	$0.697674\pi$
$984$	8.56893e6	0.282123
$985$	−5.04906e6	−0.165814
$986$	2.25085e7	0.737316
$987$	−3.83461e6	−0.125294
$988$	−7.02358e7	−2.28911
$989$	5.53997e7	1.80101
$990$	5.23974e6	0.169911
$991$	2.63525e7	0.852389	0.426194	−	0.904632i	$-0.359854\pi$
$991$	2.63525e7	0.852389	0.426194	+	0.904632i	$0.359854\pi$
$992$	−1.15932e7	−0.374045
$993$	−2.78440e7	−0.896105
$994$	−5.09703e6	−0.163626
$995$	−1.63769e7	−0.524413
$996$	−6.57752e7	−2.10094
$997$	2.05815e7	0.655752	0.327876	−	0.944721i	$-0.393667\pi$
$997$	2.05815e7	0.655752	0.327876	+	0.944721i	$0.393667\pi$
$998$	5.66971e7	1.80192
$999$	−8.44831e6	−0.267828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.6.a.a.1.7	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.6.a.a.1.7	✓	74	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:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	959.a (trivial)

\(f(q)\)	\(=\)	\(q-9.59106 q^{2} +18.0221 q^{3} +59.9885 q^{4} +20.4003 q^{5} -172.851 q^{6} +49.0000 q^{7} -268.440 q^{8} +81.7953 q^{9} +O(q^{10})\)	\(q-9.59106 q^{2} +18.0221 q^{3} +59.9885 q^{4} +20.4003 q^{5} -172.851 q^{6} +49.0000 q^{7} -268.440 q^{8} +81.7953 q^{9} -195.660 q^{10} -327.400 q^{11} +1081.12 q^{12} +1009.24 q^{13} -469.962 q^{14} +367.655 q^{15} +654.990 q^{16} -1301.51 q^{17} -784.504 q^{18} -1160.10 q^{19} +1223.78 q^{20} +883.082 q^{21} +3140.12 q^{22} +3330.61 q^{23} -4837.84 q^{24} -2708.83 q^{25} -9679.69 q^{26} -2905.24 q^{27} +2939.44 q^{28} +1803.15 q^{29} -3526.20 q^{30} -5023.01 q^{31} +2308.02 q^{32} -5900.43 q^{33} +12482.9 q^{34} +999.613 q^{35} +4906.78 q^{36} +2907.95 q^{37} +11126.6 q^{38} +18188.6 q^{39} -5476.24 q^{40} -1771.23 q^{41} -8469.70 q^{42} +16633.5 q^{43} -19640.3 q^{44} +1668.65 q^{45} -31944.1 q^{46} -4342.31 q^{47} +11804.3 q^{48} +2401.00 q^{49} +25980.6 q^{50} -23455.9 q^{51} +60542.8 q^{52} +12221.8 q^{53} +27864.4 q^{54} -6679.05 q^{55} -13153.5 q^{56} -20907.4 q^{57} -17294.1 q^{58} +6323.12 q^{59} +22055.1 q^{60} -30354.0 q^{61} +48176.0 q^{62} +4007.97 q^{63} -43096.0 q^{64} +20588.8 q^{65} +56591.4 q^{66} -46703.9 q^{67} -78075.7 q^{68} +60024.5 q^{69} -9587.35 q^{70} +10845.6 q^{71} -21957.1 q^{72} -51045.6 q^{73} -27890.4 q^{74} -48818.7 q^{75} -69592.7 q^{76} -16042.6 q^{77} -174448. q^{78} -14663.0 q^{79} +13362.0 q^{80} -72234.8 q^{81} +16988.0 q^{82} -60840.0 q^{83} +52974.8 q^{84} -26551.2 q^{85} -159533. q^{86} +32496.5 q^{87} +87887.2 q^{88} +136343. q^{89} -16004.1 q^{90} +49452.8 q^{91} +199798. q^{92} -90525.0 q^{93} +41647.4 q^{94} -23666.3 q^{95} +41595.3 q^{96} -50835.8 q^{97} -23028.1 q^{98} -26779.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * q^99

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