LMFDB - Embedded newform 1045.6.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.07979 q^{2} -6.58287 q^{3} -15.3553 q^{4} +25.0000 q^{5} +26.8567 q^{6} +210.046 q^{7} +193.200 q^{8} -199.666 q^{9} +O(q^{10})$	\(q-4.07979 q^{2} -6.58287 q^{3} -15.3553 q^{4} +25.0000 q^{5} +26.8567 q^{6} +210.046 q^{7} +193.200 q^{8} -199.666 q^{9} -101.995 q^{10} -121.000 q^{11} +101.082 q^{12} +824.427 q^{13} -856.945 q^{14} -164.572 q^{15} -296.842 q^{16} -522.410 q^{17} +814.594 q^{18} -361.000 q^{19} -383.884 q^{20} -1382.71 q^{21} +493.654 q^{22} +2478.67 q^{23} -1271.81 q^{24} +625.000 q^{25} -3363.48 q^{26} +2914.01 q^{27} -3225.34 q^{28} +1492.41 q^{29} +671.418 q^{30} +9861.52 q^{31} -4971.34 q^{32} +796.528 q^{33} +2131.32 q^{34} +5251.16 q^{35} +3065.94 q^{36} +4567.40 q^{37} +1472.80 q^{38} -5427.09 q^{39} +4829.99 q^{40} +1819.60 q^{41} +5641.16 q^{42} -6681.64 q^{43} +1858.00 q^{44} -4991.64 q^{45} -10112.4 q^{46} +13547.9 q^{47} +1954.08 q^{48} +27312.5 q^{49} -2549.87 q^{50} +3438.96 q^{51} -12659.4 q^{52} +5880.71 q^{53} -11888.5 q^{54} -3025.00 q^{55} +40580.9 q^{56} +2376.42 q^{57} -6088.70 q^{58} +49713.7 q^{59} +2527.06 q^{60} -2199.67 q^{61} -40232.9 q^{62} -41939.1 q^{63} +29780.9 q^{64} +20610.7 q^{65} -3249.66 q^{66} -47860.8 q^{67} +8021.79 q^{68} -16316.8 q^{69} -21423.6 q^{70} -26499.9 q^{71} -38575.4 q^{72} +66922.9 q^{73} -18634.0 q^{74} -4114.30 q^{75} +5543.28 q^{76} -25415.6 q^{77} +22141.4 q^{78} +4448.81 q^{79} -7421.06 q^{80} +29336.2 q^{81} -7423.58 q^{82} -20094.8 q^{83} +21232.0 q^{84} -13060.3 q^{85} +27259.7 q^{86} -9824.32 q^{87} -23377.2 q^{88} -72607.5 q^{89} +20364.8 q^{90} +173168. q^{91} -38060.8 q^{92} -64917.1 q^{93} -55272.7 q^{94} -9025.00 q^{95} +32725.7 q^{96} -89655.8 q^{97} -111429. q^{98} +24159.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−4.07979	−0.721211	−0.360606	−	0.932718i	$-0.617430\pi$
$2$	−4.07979	−0.721211	−0.360606	+	0.932718i	$0.617430\pi$
$3$	−6.58287	−0.422291	−0.211146	−	0.977455i	$-0.567719\pi$
$3$	−6.58287	−0.422291	−0.211146	+	0.977455i	$0.567719\pi$
$4$	−15.3553	−0.479855
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	26.8567	0.304561
$7$	210.046	1.62021	0.810103	−	0.586288i	$-0.199411\pi$
$7$	210.046	1.62021	0.810103	+	0.586288i	$0.199411\pi$
$8$	193.200	1.06729
$9$	−199.666	−0.821670
$10$	−101.995	−0.322535
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	101.082	0.202638
$13$	824.427	1.35299	0.676493	−	0.736449i	$-0.263499\pi$
$13$	824.427	1.35299	0.676493	+	0.736449i	$0.263499\pi$
$14$	−856.945	−1.16851
$15$	−164.572	−0.188854
$16$	−296.842	−0.289885
$17$	−522.410	−0.438419	−0.219209	−	0.975678i	$-0.570348\pi$
$17$	−522.410	−0.438419	−0.219209	+	0.975678i	$0.570348\pi$
$18$	814.594	0.592597
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−383.884	−0.214597
$21$	−1382.71	−0.684199
$22$	493.654	0.217453
$23$	2478.67	0.977009	0.488505	−	0.872561i	$-0.337543\pi$
$23$	2478.67	0.977009	0.488505	+	0.872561i	$0.337543\pi$
$24$	−1271.81	−0.450706
$25$	625.000	0.200000
$26$	−3363.48	−0.975789
$27$	2914.01	0.769276
$28$	−3225.34	−0.777463
$29$	1492.41	0.329528	0.164764	−	0.986333i	$-0.447314\pi$
$29$	1492.41	0.329528	0.164764	+	0.986333i	$0.447314\pi$
$30$	671.418	0.136204
$31$	9861.52	1.84306	0.921530	−	0.388307i	$-0.126940\pi$
$31$	9861.52	1.84306	0.921530	+	0.388307i	$0.126940\pi$
$32$	−4971.34	−0.858219
$33$	796.528	0.127326
$34$	2131.32	0.316193
$35$	5251.16	0.724578
$36$	3065.94	0.394282
$37$	4567.40	0.548485	0.274242	−	0.961661i	$-0.411573\pi$
$37$	4567.40	0.548485	0.274242	+	0.961661i	$0.411573\pi$
$38$	1472.80	0.165457
$39$	−5427.09	−0.571355
$40$	4829.99	0.477305
$41$	1819.60	0.169050	0.0845252	−	0.996421i	$-0.473063\pi$
$41$	1819.60	0.169050	0.0845252	+	0.996421i	$0.473063\pi$
$42$	5641.16	0.493452
$43$	−6681.64	−0.551077	−0.275538	−	0.961290i	$-0.588856\pi$
$43$	−6681.64	−0.551077	−0.275538	+	0.961290i	$0.588856\pi$
$44$	1858.00	0.144682
$45$	−4991.64	−0.367462
$46$	−10112.4	−0.704630
$47$	13547.9	0.894599	0.447300	−	0.894384i	$-0.352386\pi$
$47$	13547.9	0.894599	0.447300	+	0.894384i	$0.352386\pi$
$48$	1954.08	0.122416
$49$	27312.5	1.62507
$50$	−2549.87	−0.144242
$51$	3438.96	0.185141
$52$	−12659.4	−0.649237
$53$	5880.71	0.287568	0.143784	−	0.989609i	$-0.454073\pi$
$53$	5880.71	0.287568	0.143784	+	0.989609i	$0.454073\pi$
$54$	−11888.5	−0.554810
$55$	−3025.00	−0.134840
$56$	40580.9	1.72923
$57$	2376.42	0.0968803
$58$	−6088.70	−0.237659
$59$	49713.7	1.85928	0.929642	−	0.368464i	$-0.120116\pi$
$59$	49713.7	1.85928	0.929642	+	0.368464i	$0.120116\pi$
$60$	2527.06	0.0906227
$61$	−2199.67	−0.0756890	−0.0378445	−	0.999284i	$-0.512049\pi$
$61$	−2199.67	−0.0756890	−0.0378445	+	0.999284i	$0.512049\pi$
$62$	−40232.9	−1.32924
$63$	−41939.1	−1.33127
$64$	29780.9	0.908842
$65$	20610.7	0.605074
$66$	−3249.66	−0.0918287
$67$	−47860.8	−1.30255	−0.651273	−	0.758843i	$-0.725765\pi$
$67$	−47860.8	−1.30255	−0.651273	+	0.758843i	$0.725765\pi$
$68$	8021.79	0.210377
$69$	−16316.8	−0.412583
$70$	−21423.6	−0.522574
$71$	−26499.9	−0.623875	−0.311938	−	0.950103i	$-0.600978\pi$
$71$	−26499.9	−0.623875	−0.311938	+	0.950103i	$0.600978\pi$
$72$	−38575.4	−0.876958
$73$	66922.9	1.46983	0.734916	−	0.678158i	$-0.237221\pi$
$73$	66922.9	1.46983	0.734916	+	0.678158i	$0.237221\pi$
$74$	−18634.0	−0.395573
$75$	−4114.30	−0.0844583
$76$	5543.28	0.110086
$77$	−25415.6	−0.488511
$78$	22141.4	0.412067
$79$	4448.81	0.0802003	0.0401001	−	0.999196i	$-0.487232\pi$
$79$	4448.81	0.0802003	0.0401001	+	0.999196i	$0.487232\pi$
$80$	−7421.06	−0.129641
$81$	29336.2	0.496811
$82$	−7423.58	−0.121921
$83$	−20094.8	−0.320176	−0.160088	−	0.987103i	$-0.551178\pi$
$83$	−20094.8	−0.320176	−0.160088	+	0.987103i	$0.551178\pi$
$84$	21232.0	0.328316
$85$	−13060.3	−0.196067
$86$	27259.7	0.397443
$87$	−9824.32	−0.139157
$88$	−23377.2	−0.321799
$89$	−72607.5	−0.971642	−0.485821	−	0.874058i	$-0.661479\pi$
$89$	−72607.5	−0.971642	−0.485821	+	0.874058i	$0.661479\pi$
$90$	20364.8	0.265018
$91$	173168.	2.19212
$92$	−38060.8	−0.468822
$93$	−64917.1	−0.778308
$94$	−55272.7	−0.645195
$95$	−9025.00	−0.102598
$96$	32725.7	0.362419
$97$	−89655.8	−0.967496	−0.483748	−	0.875207i	$-0.660725\pi$
$97$	−89655.8	−0.967496	−0.483748	+	0.875207i	$0.660725\pi$
$98$	−111429.	−1.17202
$99$	24159.6	0.247743
$100$	−9597.09	−0.0959709
$101$	28789.3	0.280820	0.140410	−	0.990093i	$-0.455158\pi$
$101$	28789.3	0.280820	0.140410	+	0.990093i	$0.455158\pi$
$102$	−14030.2	−0.133525
$103$	−52822.0	−0.490593	−0.245297	−	0.969448i	$-0.578885\pi$
$103$	−52822.0	−0.490593	−0.245297	+	0.969448i	$0.578885\pi$
$104$	159279.	1.44403
$105$	−34567.7	−0.305983
$106$	−23992.1	−0.207397
$107$	−99926.4	−0.843764	−0.421882	−	0.906651i	$-0.638630\pi$
$107$	−99926.4	−0.843764	−0.421882	+	0.906651i	$0.638630\pi$
$108$	−44745.7	−0.369140
$109$	−194331.	−1.56666	−0.783332	−	0.621603i	$-0.786482\pi$
$109$	−194331.	−1.56666	−0.783332	+	0.621603i	$0.786482\pi$
$110$	12341.4	0.0972481
$111$	−30066.6	−0.231620
$112$	−62350.7	−0.469674
$113$	73256.7	0.539699	0.269849	−	0.962903i	$-0.413026\pi$
$113$	73256.7	0.539699	0.269849	+	0.962903i	$0.413026\pi$
$114$	−9695.27	−0.0698712
$115$	61966.7	0.436932
$116$	−22916.4	−0.158125
$117$	−164610.	−1.11171
$118$	−202821.	−1.34094
$119$	−109730.	−0.710329
$120$	−31795.2	−0.201562
$121$	14641.0	0.0909091
$122$	8974.18	0.0545878
$123$	−11978.2	−0.0713885
$124$	−151427.	−0.884401
$125$	15625.0	0.0894427
$126$	171103.	0.960130
$127$	−285442.	−1.57040	−0.785198	−	0.619245i	$-0.787439\pi$
$127$	−285442.	−1.57040	−0.785198	+	0.619245i	$0.787439\pi$
$128$	37582.9	0.202752
$129$	43984.4	0.232715
$130$	−84087.1	−0.436386
$131$	165942.	0.844846	0.422423	−	0.906399i	$-0.361180\pi$
$131$	165942.	0.844846	0.422423	+	0.906399i	$0.361180\pi$
$132$	−12231.0	−0.0610978
$133$	−75826.8	−0.371701
$134$	195262.	0.939411
$135$	72850.3	0.344031
$136$	−100929.	−0.467919
$137$	210065.	0.956206	0.478103	−	0.878304i	$-0.341325\pi$
$137$	210065.	0.956206	0.478103	+	0.878304i	$0.341325\pi$
$138$	66568.9	0.297559
$139$	207496.	0.910904	0.455452	−	0.890260i	$-0.349478\pi$
$139$	207496.	0.910904	0.455452	+	0.890260i	$0.349478\pi$
$140$	−80633.4	−0.347692
$141$	−89184.3	−0.377782
$142$	108114.	0.449946
$143$	−99755.6	−0.407941
$144$	59269.3	0.238190
$145$	37310.2	0.147369
$146$	−273031.	−1.06006
$147$	−179795.	−0.686252
$148$	−70134.0	−0.263193
$149$	27962.2	0.103182	0.0515912	−	0.998668i	$-0.483571\pi$
$149$	27962.2	0.103182	0.0515912	+	0.998668i	$0.483571\pi$
$150$	16785.4	0.0609123
$151$	−412951.	−1.47386	−0.736929	−	0.675970i	$-0.763725\pi$
$151$	−412951.	−1.47386	−0.736929	+	0.675970i	$0.763725\pi$
$152$	−69745.1	−0.244853
$153$	104307.	0.360236
$154$	103690.	0.352319
$155$	246538.	0.824241
$156$	83334.9	0.274167
$157$	−301129.	−0.974996	−0.487498	−	0.873124i	$-0.662090\pi$
$157$	−301129.	−0.974996	−0.487498	+	0.873124i	$0.662090\pi$
$158$	−18150.2	−0.0578413
$159$	−38712.0	−0.121437
$160$	−124283.	−0.383807
$161$	520635.	1.58296
$162$	−119685.	−0.358306
$163$	−237225.	−0.699344	−0.349672	−	0.936872i	$-0.613707\pi$
$163$	−237225.	−0.699344	−0.349672	+	0.936872i	$0.613707\pi$
$164$	−27940.6	−0.0811196
$165$	19913.2	0.0569418
$166$	81982.6	0.230915
$167$	−164664.	−0.456886	−0.228443	−	0.973557i	$-0.573363\pi$
$167$	−164664.	−0.456886	−0.228443	+	0.973557i	$0.573363\pi$
$168$	−267139.	−0.730237
$169$	308386.	0.830574
$170$	53283.0	0.141406
$171$	72079.4	0.188504
$172$	102599.	0.264437
$173$	300909.	0.764399	0.382200	−	0.924080i	$-0.375167\pi$
$173$	300909.	0.764399	0.382200	+	0.924080i	$0.375167\pi$
$174$	40081.1	0.100361
$175$	131279.	0.324041
$176$	35917.9	0.0874037
$177$	−327259.	−0.785160
$178$	296223.	0.700759
$179$	499496.	1.16520	0.582599	−	0.812760i	$-0.302036\pi$
$179$	499496.	1.16520	0.582599	+	0.812760i	$0.302036\pi$
$180$	76648.4	0.176328
$181$	−537706.	−1.21997	−0.609984	−	0.792413i	$-0.708824\pi$
$181$	−537706.	−1.21997	−0.609984	+	0.792413i	$0.708824\pi$
$182$	−706488.	−1.58098
$183$	14480.1	0.0319628
$184$	478878.	1.04275
$185$	114185.	0.245290
$186$	264848.	0.561325
$187$	63211.6	0.132188
$188$	−208033.	−0.429277
$189$	612078.	1.24639
$190$	36820.1	0.0739947
$191$	8045.09	0.0159569	0.00797843	−	0.999968i	$-0.497460\pi$
$191$	8045.09	0.0159569	0.00797843	+	0.999968i	$0.497460\pi$
$192$	−196044.	−0.383796
$193$	385672.	0.745289	0.372644	−	0.927974i	$-0.378451\pi$
$193$	385672.	0.745289	0.372644	+	0.927974i	$0.378451\pi$
$194$	365777.	0.697769
$195$	−135677.	−0.255518
$196$	−419393.	−0.779796
$197$	643448.	1.18127	0.590633	−	0.806940i	$-0.298878\pi$
$197$	643448.	1.18127	0.590633	+	0.806940i	$0.298878\pi$
$198$	−98565.8	−0.178675
$199$	−512157.	−0.916790	−0.458395	−	0.888748i	$-0.651576\pi$
$199$	−512157.	−0.916790	−0.458395	+	0.888748i	$0.651576\pi$
$200$	120750.	0.213458
$201$	315062.	0.550054
$202$	−117454.	−0.202530
$203$	313475.	0.533903
$204$	−52806.4	−0.0888405
$205$	45490.0	0.0756016
$206$	215502.	0.353821
$207$	−494905.	−0.802779
$208$	−244725.	−0.392211
$209$	43681.0	0.0691714
$210$	141029.	0.220678
$211$	1.16484e6	1.80120	0.900599	−	0.434651i	$-0.143128\pi$
$211$	1.16484e6	1.80120	0.900599	+	0.434651i	$0.143128\pi$
$212$	−90300.4	−0.137991
$213$	174445.	0.263457
$214$	407678.	0.608532
$215$	−167041.	−0.246449
$216$	562986.	0.821038
$217$	2.07138e6	2.98614
$218$	792829.	1.12990
$219$	−440545.	−0.620698
$220$	46449.9	0.0647036
$221$	−430689.	−0.593175
$222$	122665.	0.167047
$223$	706823.	0.951806	0.475903	−	0.879498i	$-0.342121\pi$
$223$	706823.	0.951806	0.475903	+	0.879498i	$0.342121\pi$
$224$	−1.04421e6	−1.39049
$225$	−124791.	−0.164334
$226$	−298872.	−0.389237
$227$	−383598.	−0.494096	−0.247048	−	0.969003i	$-0.579461\pi$
$227$	−383598.	−0.494096	−0.247048	+	0.969003i	$0.579461\pi$
$228$	−36490.7	−0.0464885
$229$	462421.	0.582705	0.291353	−	0.956616i	$-0.405895\pi$
$229$	462421.	0.582705	0.291353	+	0.956616i	$0.405895\pi$
$230$	−252811.	−0.315120
$231$	167308.	0.206294
$232$	288332.	0.351701
$233$	416402.	0.502485	0.251243	−	0.967924i	$-0.419161\pi$
$233$	416402.	0.502485	0.251243	+	0.967924i	$0.419161\pi$
$234$	671573.	0.801777
$235$	338698.	0.400077
$236$	−763370.	−0.892186
$237$	−29285.9	−0.0338679
$238$	447677.	0.512297
$239$	1.01075e6	1.14458	0.572292	−	0.820050i	$-0.306054\pi$
$239$	1.01075e6	1.14458	0.572292	+	0.820050i	$0.306054\pi$
$240$	48851.9	0.0547461
$241$	473813.	0.525489	0.262745	−	0.964865i	$-0.415372\pi$
$241$	473813.	0.525489	0.262745	+	0.964865i	$0.415372\pi$
$242$	−59732.1	−0.0655646
$243$	−901222.	−0.979075
$244$	33776.7	0.0363197
$245$	682813.	0.726752
$246$	48868.5	0.0514862
$247$	−297618.	−0.310396
$248$	1.90524e6	1.96707
$249$	132282.	0.135208
$250$	−63746.7	−0.0645071
$251$	−1.21435e6	−1.21663	−0.608316	−	0.793695i	$-0.708155\pi$
$251$	−1.21435e6	−1.21663	−0.608316	+	0.793695i	$0.708155\pi$
$252$	643989.	0.638818
$253$	−299919.	−0.294579
$254$	1.16454e6	1.13259
$255$	85974.0	0.0827974
$256$	−1.10632e6	−1.05507
$257$	1.18063e6	1.11502	0.557509	−	0.830171i	$-0.311757\pi$
$257$	1.18063e6	1.11502	0.557509	+	0.830171i	$0.311757\pi$
$258$	−179447.	−0.167837
$259$	959366.	0.888658
$260$	−316484.	−0.290348
$261$	−297982.	−0.270763
$262$	−677007.	−0.609312
$263$	−1.55725e6	−1.38826	−0.694129	−	0.719851i	$-0.744210\pi$
$263$	−1.55725e6	−1.38826	−0.694129	+	0.719851i	$0.744210\pi$
$264$	153889.	0.135893
$265$	147018.	0.128604
$266$	309357.	0.268075
$267$	477966.	0.410316
$268$	734920.	0.625033
$269$	668686.	0.563432	0.281716	−	0.959498i	$-0.409096\pi$
$269$	668686.	0.563432	0.281716	+	0.959498i	$0.409096\pi$
$270$	−297214.	−0.248119
$271$	−781169.	−0.646133	−0.323067	−	0.946376i	$-0.604714\pi$
$271$	−781169.	−0.646133	−0.323067	+	0.946376i	$0.604714\pi$
$272$	155073.	0.127091
$273$	−1.13994e6	−0.925713
$274$	−857019.	−0.689626
$275$	−75625.0	−0.0603023
$276$	250549.	0.197980
$277$	998429.	0.781840	0.390920	−	0.920425i	$-0.372157\pi$
$277$	998429.	0.781840	0.390920	+	0.920425i	$0.372157\pi$
$278$	−846539.	−0.656954
$279$	−1.96901e6	−1.51439
$280$	1.01452e6	0.773333
$281$	−1.38996e6	−1.05011	−0.525056	−	0.851067i	$-0.675956\pi$
$281$	−1.38996e6	−1.05011	−0.525056	+	0.851067i	$0.675956\pi$
$282$	363853.	0.272460
$283$	−101065.	−0.0750125	−0.0375063	−	0.999296i	$-0.511941\pi$
$283$	−101065.	−0.0750125	−0.0375063	+	0.999296i	$0.511941\pi$
$284$	406915.	0.299369
$285$	59410.4	0.0433262
$286$	406982.	0.294212
$287$	382200.	0.273897
$288$	992606.	0.705173
$289$	−1.14694e6	−0.807789
$290$	−152217.	−0.106284
$291$	590193.	0.408565
$292$	−1.02762e6	−0.705306
$293$	−1.37838e6	−0.937994	−0.468997	−	0.883200i	$-0.655385\pi$
$293$	−1.37838e6	−0.937994	−0.468997	+	0.883200i	$0.655385\pi$
$294$	733524.	0.494933
$295$	1.24284e6	0.831497
$296$	882420.	0.585391
$297$	−352596.	−0.231945
$298$	−114080.	−0.0744163
$299$	2.04348e6	1.32188
$300$	63176.4	0.0405277
$301$	−1.40345e6	−0.892858
$302$	1.68475e6	1.06296
$303$	−189516.	−0.118588
$304$	107160.	0.0665042
$305$	−54991.7	−0.0338492
$306$	−425552.	−0.259806
$307$	−2.05887e6	−1.24676	−0.623381	−	0.781919i	$-0.714241\pi$
$307$	−2.05887e6	−1.24676	−0.623381	+	0.781919i	$0.714241\pi$
$308$	390266.	0.234414
$309$	347720.	0.207173
$310$	−1.00582e6	−0.594452
$311$	1.34917e6	0.790978	0.395489	−	0.918471i	$-0.370575\pi$
$311$	1.34917e6	0.790978	0.395489	+	0.918471i	$0.370575\pi$
$312$	−1.04851e6	−0.609800
$313$	−989820.	−0.571078	−0.285539	−	0.958367i	$-0.592173\pi$
$313$	−989820.	−0.571078	−0.285539	+	0.958367i	$0.592173\pi$
$314$	1.22854e6	0.703178
$315$	−1.04848e6	−0.595364
$316$	−68313.0	−0.0384845
$317$	−289994.	−0.162084	−0.0810421	−	0.996711i	$-0.525825\pi$
$317$	−289994.	−0.162084	−0.0810421	+	0.996711i	$0.525825\pi$
$318$	157937.	0.0875820
$319$	−180581.	−0.0993564
$320$	744524.	0.406447
$321$	657803.	0.356314
$322$	−2.12408e6	−1.14165
$323$	188590.	0.100580
$324$	−450468.	−0.238397
$325$	515267.	0.270597
$326$	967826.	0.504375
$327$	1.27926e6	0.661589
$328$	351546.	0.180425
$329$	2.84570e6	1.44943
$330$	−81241.6	−0.0410670
$331$	2.30154e6	1.15464	0.577322	−	0.816516i	$-0.304098\pi$
$331$	2.30154e6	1.15464	0.577322	+	0.816516i	$0.304098\pi$
$332$	308563.	0.153638
$333$	−911953.	−0.450673
$334$	671795.	0.329511
$335$	−1.19652e6	−0.582517
$336$	410447.	0.198339
$337$	−2.05828e6	−0.987256	−0.493628	−	0.869673i	$-0.664330\pi$
$337$	−2.05828e6	−0.987256	−0.493628	+	0.869673i	$0.664330\pi$
$338$	−1.25815e6	−0.599019
$339$	−482240.	−0.227910
$340$	200545.	0.0940836
$341$	−1.19324e6	−0.555703
$342$	−294068.	−0.135951
$343$	2.20665e6	1.01274
$344$	−1.29089e6	−0.588157
$345$	−407919.	−0.184513
$346$	−1.22765e6	−0.551293
$347$	1.18072e6	0.526408	0.263204	−	0.964740i	$-0.415221\pi$
$347$	1.18072e6	0.526408	0.263204	+	0.964740i	$0.415221\pi$
$348$	150856.	0.0667750
$349$	1.22096e6	0.536586	0.268293	−	0.963337i	$-0.413540\pi$
$349$	1.22096e6	0.536586	0.268293	+	0.963337i	$0.413540\pi$
$350$	−535590.	−0.233702
$351$	2.40239e6	1.04082
$352$	601532.	0.258763
$353$	−1.18419e6	−0.505806	−0.252903	−	0.967492i	$-0.581385\pi$
$353$	−1.18419e6	−0.505806	−0.252903	+	0.967492i	$0.581385\pi$
$354$	1.33515e6	0.566266
$355$	−662497.	−0.279006
$356$	1.11491e6	0.466247
$357$	722341.	0.299966
$358$	−2.03784e6	−0.840353
$359$	1.83490e6	0.751410	0.375705	−	0.926739i	$-0.377401\pi$
$359$	1.83490e6	0.751410	0.375705	+	0.926739i	$0.377401\pi$
$360$	−964384.	−0.392188
$361$	130321.	0.0526316
$362$	2.19373e6	0.879855
$363$	−96379.8	−0.0383901
$364$	−2.65905e6	−1.05190
$365$	1.67307e6	0.657329
$366$	−59075.9	−0.0230519
$367$	1.79623e6	0.696140	0.348070	−	0.937468i	$-0.386837\pi$
$367$	1.79623e6	0.696140	0.348070	+	0.937468i	$0.386837\pi$
$368$	−735773.	−0.283220
$369$	−363312.	−0.138904
$370$	−465850.	−0.176906
$371$	1.23522e6	0.465919
$372$	996824.	0.373475
$373$	4.87345e6	1.81369	0.906847	−	0.421460i	$-0.138482\pi$
$373$	4.87345e6	1.81369	0.906847	+	0.421460i	$0.138482\pi$
$374$	−257890.	−0.0953357
$375$	−102857.	−0.0377709
$376$	2.61746e6	0.954794
$377$	1.23038e6	0.445847
$378$	−2.49715e6	−0.898907
$379$	3.61238e6	1.29180	0.645900	−	0.763422i	$-0.276482\pi$
$379$	3.61238e6	1.29180	0.645900	+	0.763422i	$0.276482\pi$
$380$	138582.	0.0492320
$381$	1.87903e6	0.663165
$382$	−32822.2	−0.0115083
$383$	2.06581e6	0.719603	0.359802	−	0.933029i	$-0.382844\pi$
$383$	2.06581e6	0.719603	0.359802	+	0.933029i	$0.382844\pi$
$384$	−247403.	−0.0856204
$385$	−635391.	−0.218469
$386$	−1.57346e6	−0.537511
$387$	1.33409e6	0.452803
$388$	1.37670e6	0.464257
$389$	−4.82210e6	−1.61571	−0.807853	−	0.589384i	$-0.799370\pi$
$389$	−4.82210e6	−1.61571	−0.807853	+	0.589384i	$0.799370\pi$
$390$	553535.	0.184282
$391$	−1.29488e6	−0.428339
$392$	5.27677e6	1.73441
$393$	−1.09237e6	−0.356771
$394$	−2.62513e6	−0.851942
$395$	111220.	0.0358667
$396$	−370978.	−0.118881
$397$	4.99448e6	1.59043	0.795213	−	0.606330i	$-0.207359\pi$
$397$	4.99448e6	1.59043	0.795213	+	0.606330i	$0.207359\pi$
$398$	2.08949e6	0.661199
$399$	499158.	0.156966
$400$	−185526.	−0.0579770
$401$	1.99618e6	0.619924	0.309962	−	0.950749i	$-0.399684\pi$
$401$	1.99618e6	0.619924	0.309962	+	0.950749i	$0.399684\pi$
$402$	−1.28538e6	−0.396705
$403$	8.13010e6	2.49364
$404$	−442070.	−0.134753
$405$	733405.	0.222181
$406$	−1.27891e6	−0.385057
$407$	−552655.	−0.165374
$408$	664406.	0.197598
$409$	2.13418e6	0.630846	0.315423	−	0.948951i	$-0.397854\pi$
$409$	2.13418e6	0.630846	0.315423	+	0.948951i	$0.397854\pi$
$410$	−185589.	−0.0545247
$411$	−1.38283e6	−0.403798
$412$	811100.	0.235413
$413$	1.04422e7	3.01242
$414$	2.01911e6	0.578973
$415$	−502371.	−0.143187
$416$	−4.09850e6	−1.16116
$417$	−1.36592e6	−0.384667
$418$	−178209.	−0.0498872
$419$	4.37416e6	1.21719	0.608596	−	0.793480i	$-0.291733\pi$
$419$	4.37416e6	1.21719	0.608596	+	0.793480i	$0.291733\pi$
$420$	530799.	0.146827
$421$	−4.70073e6	−1.29259	−0.646293	−	0.763089i	$-0.723682\pi$
$421$	−4.70073e6	−1.29259	−0.646293	+	0.763089i	$0.723682\pi$
$422$	−4.75231e6	−1.29904
$423$	−2.70506e6	−0.735065
$424$	1.13615e6	0.306918
$425$	−326506.	−0.0876838
$426$	−711699.	−0.190008
$427$	−462033.	−0.122632
$428$	1.53440e6	0.404884
$429$	656678.	0.172270
$430$	681492.	0.177742
$431$	273519.	0.0709243	0.0354622	−	0.999371i	$-0.488710\pi$
$431$	273519.	0.0709243	0.0354622	+	0.999371i	$0.488710\pi$
$432$	−865002.	−0.223002
$433$	6.79343e6	1.74128	0.870641	−	0.491918i	$-0.163704\pi$
$433$	6.79343e6	1.74128	0.870641	+	0.491918i	$0.163704\pi$
$434$	−8.45077e6	−2.15364
$435$	−245608.	−0.0622328
$436$	2.98402e6	0.751771
$437$	−894799.	−0.224141
$438$	1.79733e6	0.447654
$439$	−2.58069e6	−0.639108	−0.319554	−	0.947568i	$-0.603533\pi$
$439$	−2.58069e6	−0.639108	−0.319554	+	0.947568i	$0.603533\pi$
$440$	−584429.	−0.143913
$441$	−5.45337e6	−1.33527
$442$	1.75712e6	0.427804
$443$	5.16396e6	1.25018	0.625091	−	0.780552i	$-0.285062\pi$
$443$	5.16396e6	1.25018	0.625091	+	0.780552i	$0.285062\pi$
$444$	461683.	0.111144
$445$	−1.81519e6	−0.434532
$446$	−2.88369e6	−0.686453
$447$	−184072.	−0.0435731
$448$	6.25538e6	1.47251
$449$	7.77346e6	1.81969	0.909847	−	0.414944i	$-0.136199\pi$
$449$	7.77346e6	1.81969	0.909847	+	0.414944i	$0.136199\pi$
$450$	509121.	0.118519
$451$	−220172.	−0.0509706
$452$	−1.12488e6	−0.258977
$453$	2.71840e6	0.622398
$454$	1.56500e6	0.356348
$455$	4.32920e6	0.980345
$456$	459123.	0.103399
$457$	1.00940e6	0.226085	0.113043	−	0.993590i	$-0.463940\pi$
$457$	1.00940e6	0.226085	0.113043	+	0.993590i	$0.463940\pi$
$458$	−1.88658e6	−0.420254
$459$	−1.52231e6	−0.337265
$460$	−951520.	−0.209664
$461$	1.67857e6	0.367865	0.183932	−	0.982939i	$-0.441117\pi$
$461$	1.67857e6	0.367865	0.183932	+	0.982939i	$0.441117\pi$
$462$	−682580.	−0.148781
$463$	2.10152e6	0.455598	0.227799	−	0.973708i	$-0.426847\pi$
$463$	2.10152e6	0.455598	0.227799	+	0.973708i	$0.426847\pi$
$464$	−443009.	−0.0955252
$465$	−1.62293e6	−0.348070
$466$	−1.69883e6	−0.362398
$467$	1.55158e6	0.329218	0.164609	−	0.986359i	$-0.447364\pi$
$467$	1.55158e6	0.329218	0.164609	+	0.986359i	$0.447364\pi$
$468$	2.52764e6	0.533458
$469$	−1.00530e7	−2.11039
$470$	−1.38182e6	−0.288540
$471$	1.98229e6	0.411733
$472$	9.60466e6	1.98439
$473$	808478.	0.166156
$474$	119480.	0.0244259
$475$	−225625.	−0.0458831
$476$	1.68495e6	0.340855
$477$	−1.17418e6	−0.236286
$478$	−4.12363e6	−0.825487
$479$	−3.09269e6	−0.615881	−0.307941	−	0.951406i	$-0.599640\pi$
$479$	−3.09269e6	−0.615881	−0.307941	+	0.951406i	$0.599640\pi$
$480$	818142.	0.162079
$481$	3.76548e6	0.742093
$482$	−1.93305e6	−0.378989
$483$	−3.42728e6	−0.668469
$484$	−224818.	−0.0436231
$485$	−2.24140e6	−0.432677
$486$	3.67679e6	0.706120
$487$	−2.82670e6	−0.540079	−0.270040	−	0.962849i	$-0.587037\pi$
$487$	−2.82670e6	−0.540079	−0.270040	+	0.962849i	$0.587037\pi$
$488$	−424975.	−0.0807819
$489$	1.56162e6	0.295327
$490$	−2.78573e6	−0.524142
$491$	−1.77530e6	−0.332330	−0.166165	−	0.986098i	$-0.553138\pi$
$491$	−1.77530e6	−0.332330	−0.166165	+	0.986098i	$0.553138\pi$
$492$	183929.	0.0342561
$493$	−779648.	−0.144471
$494$	1.21422e6	0.223861
$495$	603989.	0.110794
$496$	−2.92732e6	−0.534276
$497$	−5.56620e6	−1.01081
$498$	−539681.	−0.0975133
$499$	−3.08761e6	−0.555100	−0.277550	−	0.960711i	$-0.589522\pi$
$499$	−3.08761e6	−0.555100	−0.277550	+	0.960711i	$0.589522\pi$
$500$	−239927.	−0.0429195
$501$	1.08396e6	0.192939
$502$	4.95429e6	0.877449
$503$	−9.56933e6	−1.68640	−0.843202	−	0.537597i	$-0.819332\pi$
$503$	−9.56933e6	−1.68640	−0.843202	+	0.537597i	$0.819332\pi$
$504$	−8.10262e6	−1.42085
$505$	719733.	0.125587
$506$	1.22360e6	0.212454
$507$	−2.03007e6	−0.350744
$508$	4.38306e6	0.753561
$509$	9.03618e6	1.54593	0.772966	−	0.634447i	$-0.218772\pi$
$509$	9.03618e6	1.54593	0.772966	+	0.634447i	$0.218772\pi$
$510$	−350755.	−0.0597144
$511$	1.40569e7	2.38143
$512$	3.31090e6	0.558176
$513$	−1.05196e6	−0.176484
$514$	−4.81673e6	−0.804163
$515$	−1.32055e6	−0.219400
$516$	−675395.	−0.111669
$517$	−1.63930e6	−0.269732
$518$	−3.91401e6	−0.640910
$519$	−1.98085e6	−0.322799
$520$	3.98197e6	0.645788
$521$	−9.36886e6	−1.51214	−0.756071	−	0.654490i	$-0.772883\pi$
$521$	−9.36886e6	−1.51214	−0.756071	+	0.654490i	$0.772883\pi$
$522$	1.21570e6	0.195277
$523$	−4.95845e6	−0.792668	−0.396334	−	0.918106i	$-0.629718\pi$
$523$	−4.95845e6	−0.792668	−0.396334	+	0.918106i	$0.629718\pi$
$524$	−2.54809e6	−0.405403
$525$	−864193.	−0.136840
$526$	6.35327e6	1.00123
$527$	−5.15176e6	−0.808032
$528$	−236443.	−0.0369098
$529$	−292551.	−0.0454530
$530$	−599801.	−0.0927508
$531$	−9.92612e6	−1.52772
$532$	1.16435e6	0.178362
$533$	1.50013e6	0.228723
$534$	−1.95000e6	−0.295925
$535$	−2.49816e6	−0.377343
$536$	−9.24670e6	−1.39019
$537$	−3.28812e6	−0.492053
$538$	−2.72810e6	−0.406354
$539$	−3.30481e6	−0.489976
$540$	−1.11864e6	−0.165085
$541$	−6.96808e6	−1.02358	−0.511788	−	0.859112i	$-0.671017\pi$
$541$	−6.96808e6	−1.02358	−0.511788	+	0.859112i	$0.671017\pi$
$542$	3.18700e6	0.465998
$543$	3.53965e6	0.515182
$544$	2.59708e6	0.376260
$545$	−4.85828e6	−0.700634
$546$	4.65072e6	0.667634
$547$	−5.04978e6	−0.721613	−0.360806	−	0.932641i	$-0.617498\pi$
$547$	−5.04978e6	−0.721613	−0.360806	+	0.932641i	$0.617498\pi$
$548$	−3.22561e6	−0.458840
$549$	439199.	0.0621914
$550$	308534.	0.0434907
$551$	−538759.	−0.0755989
$552$	−3.15239e6	−0.440344
$553$	934456.	0.129941
$554$	−4.07338e6	−0.563872
$555$	−751665.	−0.103584
$556$	−3.18617e6	−0.437101
$557$	360695.	0.0492609	0.0246304	−	0.999697i	$-0.492159\pi$
$557$	360695.	0.0492609	0.0246304	+	0.999697i	$0.492159\pi$
$558$	8.03313e6	1.09219
$559$	−5.50852e6	−0.745599
$560$	−1.55877e6	−0.210044
$561$	−416114.	−0.0558220
$562$	5.67073e6	0.757353
$563$	7.71842e6	1.02626	0.513130	−	0.858311i	$-0.328486\pi$
$563$	7.71842e6	1.02626	0.513130	+	0.858311i	$0.328486\pi$
$564$	1.36946e6	0.181280
$565$	1.83142e6	0.241361
$566$	412323.	0.0540999
$567$	6.16197e6	0.804937
$568$	−5.11977e6	−0.665854
$569$	−331544.	−0.0429300	−0.0214650	−	0.999770i	$-0.506833\pi$
$569$	−331544.	−0.0429300	−0.0214650	+	0.999770i	$0.506833\pi$
$570$	−242382.	−0.0312473
$571$	8.11674e6	1.04182	0.520908	−	0.853613i	$-0.325593\pi$
$571$	8.11674e6	1.04182	0.520908	+	0.853613i	$0.325593\pi$
$572$	1.53178e6	0.195752
$573$	−52959.8	−0.00673844
$574$	−1.55930e6	−0.197537
$575$	1.54917e6	0.195402
$576$	−5.94624e6	−0.746768
$577$	−793812.	−0.0992609	−0.0496304	−	0.998768i	$-0.515804\pi$
$577$	−793812.	−0.0992609	−0.0496304	+	0.998768i	$0.515804\pi$
$578$	4.67929e6	0.582586
$579$	−2.53883e6	−0.314729
$580$	−572910.	−0.0707158
$581$	−4.22085e6	−0.518752
$582$	−2.40786e6	−0.294662
$583$	−711566.	−0.0867050
$584$	1.29295e7	1.56873
$585$	−4.11524e6	−0.497171
$586$	5.62350e6	0.676492
$587$	−1.37887e6	−0.165168	−0.0825842	−	0.996584i	$-0.526317\pi$
$587$	−1.37887e6	−0.165168	−0.0825842	+	0.996584i	$0.526317\pi$
$588$	2.76081e6	0.329301
$589$	−3.56001e6	−0.422827
$590$	−5.07053e6	−0.599685
$591$	−4.23573e6	−0.498839
$592$	−1.35580e6	−0.158998
$593$	3.60434e6	0.420910	0.210455	−	0.977604i	$-0.432506\pi$
$593$	3.60434e6	0.420910	0.210455	+	0.977604i	$0.432506\pi$
$594$	1.43851e6	0.167282
$595$	−2.74326e6	−0.317669
$596$	−429369.	−0.0495126
$597$	3.37146e6	0.387153
$598$	−8.33696e6	−0.953355
$599$	1.13719e7	1.29499	0.647493	−	0.762072i	$-0.275818\pi$
$599$	1.13719e7	1.29499	0.647493	+	0.762072i	$0.275818\pi$
$600$	−794881.	−0.0901413
$601$	7.20675e6	0.813866	0.406933	−	0.913458i	$-0.366598\pi$
$601$	7.20675e6	0.813866	0.406933	+	0.913458i	$0.366598\pi$
$602$	5.72580e6	0.643939
$603$	9.55617e6	1.07026
$604$	6.34100e6	0.707238
$605$	366025.	0.0406558
$606$	773187.	0.0855269
$607$	1.05596e7	1.16325	0.581626	−	0.813456i	$-0.302417\pi$
$607$	1.05596e7	1.16325	0.581626	+	0.813456i	$0.302417\pi$
$608$	1.79465e6	0.196889
$609$	−2.06356e6	−0.225463
$610$	224355.	0.0244124
$611$	1.11693e7	1.21038
$612$	−1.60168e6	−0.172861
$613$	1.64229e7	1.76522	0.882611	−	0.470105i	$-0.155784\pi$
$613$	1.64229e7	1.76522	0.882611	+	0.470105i	$0.155784\pi$
$614$	8.39975e6	0.899178
$615$	−299455.	−0.0319259
$616$	−4.91029e6	−0.521381
$617$	−1.27230e7	−1.34548	−0.672741	−	0.739878i	$-0.734883\pi$
$617$	−1.27230e7	−1.34548	−0.672741	+	0.739878i	$0.734883\pi$
$618$	−1.41862e6	−0.149416
$619$	−1.19071e7	−1.24905	−0.624527	−	0.781003i	$-0.714708\pi$
$619$	−1.19071e7	−1.24905	−0.624527	+	0.781003i	$0.714708\pi$
$620$	−3.78567e6	−0.395516
$621$	7.22287e6	0.751589
$622$	−5.50431e6	−0.570462
$623$	−1.52509e7	−1.57426
$624$	1.61099e6	0.165627
$625$	390625.	0.0400000
$626$	4.03825e6	0.411868
$627$	−287546.	−0.0292105
$628$	4.62393e6	0.467856
$629$	−2.38605e6	−0.240466
$630$	4.27756e6	0.429383
$631$	−6.08545e6	−0.608442	−0.304221	−	0.952601i	$-0.598396\pi$
$631$	−6.08545e6	−0.608442	−0.304221	+	0.952601i	$0.598396\pi$
$632$	859508.	0.0855968
$633$	−7.66802e6	−0.760631
$634$	1.18311e6	0.116897
$635$	−7.13606e6	−0.702302
$636$	594436.	0.0582723
$637$	2.25172e7	2.19870
$638$	736733.	0.0716569
$639$	5.29112e6	0.512620
$640$	939572.	0.0906734
$641$	4.98030e6	0.478751	0.239376	−	0.970927i	$-0.423057\pi$
$641$	4.98030e6	0.478751	0.239376	+	0.970927i	$0.423057\pi$
$642$	−2.68370e6	−0.256978
$643$	3.24420e6	0.309442	0.154721	−	0.987958i	$-0.450552\pi$
$643$	3.24420e6	0.309442	0.154721	+	0.987958i	$0.450552\pi$
$644$	−7.99453e6	−0.759589
$645$	1.09961e6	0.104073
$646$	−769407.	−0.0725396
$647$	−1.80368e6	−0.169395	−0.0846973	−	0.996407i	$-0.526992\pi$
$647$	−1.80368e6	−0.169395	−0.0846973	+	0.996407i	$0.526992\pi$
$648$	5.66775e6	0.530241
$649$	−6.01535e6	−0.560595
$650$	−2.10218e6	−0.195158
$651$	−1.36356e7	−1.26102
$652$	3.64267e6	0.335583
$653$	−2.03558e7	−1.86812	−0.934060	−	0.357116i	$-0.883760\pi$
$653$	−2.03558e7	−1.86812	−0.934060	+	0.357116i	$0.883760\pi$
$654$	−5.21909e6	−0.477145
$655$	4.14854e6	0.377827
$656$	−540134.	−0.0490052
$657$	−1.33622e7	−1.20772
$658$	−1.16098e7	−1.04535
$659$	−165550.	−0.0148496	−0.00742482	−	0.999972i	$-0.502363\pi$
$659$	−165550.	−0.0148496	−0.00742482	+	0.999972i	$0.502363\pi$
$660$	−305774.	−0.0273238
$661$	8.30638e6	0.739449	0.369725	−	0.929141i	$-0.379452\pi$
$661$	8.30638e6	0.739449	0.369725	+	0.929141i	$0.379452\pi$
$662$	−9.38979e6	−0.832743
$663$	2.83517e6	0.250493
$664$	−3.88232e6	−0.341720
$665$	−1.89567e6	−0.166230
$666$	3.72057e6	0.325031
$667$	3.69918e6	0.321952
$668$	2.52847e6	0.219239
$669$	−4.65292e6	−0.401940
$670$	4.88155e6	0.420117
$671$	266160.	0.0228211
$672$	6.87391e6	0.587193
$673$	−7.51559e6	−0.639625	−0.319813	−	0.947481i	$-0.603620\pi$
$673$	−7.51559e6	−0.639625	−0.319813	+	0.947481i	$0.603620\pi$
$674$	8.39734e6	0.712020
$675$	1.82126e6	0.153855
$676$	−4.73538e6	−0.398554
$677$	−9.91813e6	−0.831683	−0.415842	−	0.909437i	$-0.636513\pi$
$677$	−9.91813e6	−0.831683	−0.415842	+	0.909437i	$0.636513\pi$
$678$	1.96743e6	0.164371
$679$	−1.88319e7	−1.56754
$680$	−2.52324e6	−0.209260
$681$	2.52517e6	0.208653
$682$	4.86818e6	0.400780
$683$	1.89165e7	1.55164	0.775818	−	0.630956i	$-0.217337\pi$
$683$	1.89165e7	1.55164	0.775818	+	0.630956i	$0.217337\pi$
$684$	−1.10680e6	−0.0904545
$685$	5.25161e6	0.427628
$686$	−9.00264e6	−0.730398
$687$	−3.04406e6	−0.246072
$688$	1.98339e6	0.159749
$689$	4.84822e6	0.389076
$690$	1.66422e6	0.133073
$691$	1.32732e7	1.05750	0.528751	−	0.848777i	$-0.322660\pi$
$691$	1.32732e7	1.05750	0.528751	+	0.848777i	$0.322660\pi$
$692$	−4.62056e6	−0.366800
$693$	5.07463e6	0.401394
$694$	−4.81708e6	−0.379651
$695$	5.18740e6	0.407368
$696$	−1.89806e6	−0.148520
$697$	−950577.	−0.0741149
$698$	−4.98127e6	−0.386992
$699$	−2.74112e6	−0.212195
$700$	−2.01583e6	−0.155493
$701$	−1.09126e7	−0.838749	−0.419375	−	0.907813i	$-0.637751\pi$
$701$	−1.09126e7	−0.838749	−0.419375	+	0.907813i	$0.637751\pi$
$702$	−9.80123e6	−0.750651
$703$	−1.64883e6	−0.125831
$704$	−3.60349e6	−0.274026
$705$	−2.22961e6	−0.168949
$706$	4.83123e6	0.364793
$707$	6.04710e6	0.454986
$708$	5.02517e6	0.376762
$709$	5.10024e6	0.381044	0.190522	−	0.981683i	$-0.438982\pi$
$709$	5.10024e6	0.381044	0.190522	+	0.981683i	$0.438982\pi$
$710$	2.70284e6	0.201222
$711$	−888275.	−0.0658982
$712$	−1.40277e7	−1.03702
$713$	2.44434e7	1.80069
$714$	−2.94700e6	−0.216339
$715$	−2.49389e6	−0.182437
$716$	−7.66993e6	−0.559125
$717$	−6.65362e6	−0.483348
$718$	−7.48601e6	−0.541925
$719$	−2.63201e7	−1.89874	−0.949368	−	0.314165i	$-0.898275\pi$
$719$	−2.63201e7	−1.89874	−0.949368	+	0.314165i	$0.898275\pi$
$720$	1.48173e6	0.106522
$721$	−1.10951e7	−0.794862
$722$	−531682.	−0.0379585
$723$	−3.11905e6	−0.221910
$724$	8.25666e6	0.585407
$725$	932754.	0.0659056
$726$	393209.	0.0276874
$727$	−2.25871e7	−1.58498	−0.792490	−	0.609885i	$-0.791216\pi$
$727$	−2.25871e7	−1.58498	−0.792490	+	0.609885i	$0.791216\pi$
$728$	3.34560e7	2.33962
$729$	−1.19607e6	−0.0833564
$730$	−6.82578e6	−0.474073
$731$	3.49056e6	0.241602
$732$	−222348.	−0.0153375
$733$	−3.75956e6	−0.258450	−0.129225	−	0.991615i	$-0.541249\pi$
$733$	−3.75956e6	−0.258450	−0.129225	+	0.991615i	$0.541249\pi$
$734$	−7.32823e6	−0.502064
$735$	−4.49487e6	−0.306901
$736$	−1.23223e7	−0.838488
$737$	5.79116e6	0.392733
$738$	1.48223e6	0.100179
$739$	−2.58034e7	−1.73807	−0.869033	−	0.494753i	$-0.835258\pi$
$739$	−2.58034e7	−1.73807	−0.869033	+	0.494753i	$0.835258\pi$
$740$	−1.75335e6	−0.117703
$741$	1.95918e6	0.131078
$742$	−5.03945e6	−0.336026
$743$	−4.76898e6	−0.316923	−0.158461	−	0.987365i	$-0.550653\pi$
$743$	−4.76898e6	−0.316923	−0.158461	+	0.987365i	$0.550653\pi$
$744$	−1.25420e7	−0.830679
$745$	699055.	0.0461446
$746$	−1.98826e7	−1.30806
$747$	4.01225e6	0.263079
$748$	−970636.	−0.0634311
$749$	−2.09892e7	−1.36707
$750$	419636.	0.0272408
$751$	2.19021e7	1.41705	0.708526	−	0.705685i	$-0.249360\pi$
$751$	2.19021e7	1.41705	0.708526	+	0.705685i	$0.249360\pi$
$752$	−4.02160e6	−0.259331
$753$	7.99391e6	0.513774
$754$	−5.01969e6	−0.321550
$755$	−1.03238e7	−0.659130
$756$	−9.39867e6	−0.598084
$757$	−2.52354e7	−1.60055	−0.800277	−	0.599630i	$-0.795314\pi$
$757$	−2.52354e7	−1.60055	−0.800277	+	0.599630i	$0.795314\pi$
$758$	−1.47377e7	−0.931661
$759$	1.97433e6	0.124398
$760$	−1.74363e6	−0.109501
$761$	2.08823e7	1.30712	0.653562	−	0.756873i	$-0.273274\pi$
$761$	2.08823e7	1.30712	0.653562	+	0.756873i	$0.273274\pi$
$762$	−7.66604e6	−0.478282
$763$	−4.08186e7	−2.53832
$764$	−123535.	−0.00765697
$765$	2.60769e6	0.161102
$766$	−8.42806e6	−0.518986
$767$	4.09853e7	2.51559
$768$	7.28277e6	0.445547
$769$	1.75713e7	1.07149	0.535744	−	0.844380i	$-0.320031\pi$
$769$	1.75713e7	1.07149	0.535744	+	0.844380i	$0.320031\pi$
$770$	2.59226e6	0.157562
$771$	−7.77195e6	−0.470863
$772$	−5.92212e6	−0.357630
$773$	2.31530e7	1.39367	0.696833	−	0.717233i	$-0.254592\pi$
$773$	2.31530e7	1.39367	0.696833	+	0.717233i	$0.254592\pi$
$774$	−5.44282e6	−0.326567
$775$	6.16345e6	0.368612
$776$	−1.73215e7	−1.03260
$777$	−6.31538e6	−0.375273
$778$	1.96731e7	1.16526
$779$	−656876.	−0.0387828
$780$	2.08337e6	0.122611
$781$	3.20648e6	0.188105
$782$	5.28284e6	0.308923
$783$	4.34889e6	0.253498
$784$	−8.10751e6	−0.471083
$785$	−7.52822e6	−0.436032
$786$	4.45665e6	0.257307
$787$	−297704.	−0.0171336	−0.00856680	−	0.999963i	$-0.502727\pi$
$787$	−297704.	−0.0171336	−0.00856680	+	0.999963i	$0.502727\pi$
$788$	−9.88036e6	−0.566836
$789$	1.02512e7	0.586250
$790$	−453755.	−0.0258674
$791$	1.53873e7	0.874423
$792$	4.66762e6	0.264413
$793$	−1.81347e6	−0.102406
$794$	−2.03764e7	−1.14703
$795$	−967800.	−0.0543085
$796$	7.86434e6	0.439926
$797$	4.21104e6	0.234824	0.117412	−	0.993083i	$-0.462540\pi$
$797$	4.21104e6	0.234824	0.117412	+	0.993083i	$0.462540\pi$
$798$	−2.03646e6	−0.113206
$799$	−7.07758e6	−0.392209
$800$	−3.10709e6	−0.171644
$801$	1.44972e7	0.798369
$802$	−8.14399e6	−0.447096
$803$	−8.09768e6	−0.443171
$804$	−4.83788e6	−0.263946
$805$	1.30159e7	0.707920
$806$	−3.31691e7	−1.79844
$807$	−4.40188e6	−0.237933
$808$	5.56209e6	0.299716
$809$	2.37005e7	1.27317	0.636584	−	0.771207i	$-0.280347\pi$
$809$	2.37005e7	1.27317	0.636584	+	0.771207i	$0.280347\pi$
$810$	−2.99214e6	−0.160239
$811$	−8.11912e6	−0.433468	−0.216734	−	0.976231i	$-0.569540\pi$
$811$	−8.11912e6	−0.433468	−0.216734	+	0.976231i	$0.569540\pi$
$812$	−4.81351e6	−0.256196
$813$	5.14234e6	0.272856
$814$	2.25471e6	0.119270
$815$	−5.93062e6	−0.312756
$816$	−1.02083e6	−0.0536695
$817$	2.41207e6	0.126426
$818$	−8.70701e6	−0.454973
$819$	−3.45757e7	−1.80120
$820$	−698515.	−0.0362778
$821$	2.34342e7	1.21336	0.606682	−	0.794944i	$-0.292500\pi$
$821$	2.34342e7	1.21336	0.606682	+	0.794944i	$0.292500\pi$
$822$	5.64164e6	0.291223
$823$	3.23077e7	1.66267	0.831336	−	0.555771i	$-0.187577\pi$
$823$	3.23077e7	1.66267	0.831336	+	0.555771i	$0.187577\pi$
$824$	−1.02052e7	−0.523604
$825$	497830.	0.0254651
$826$	−4.26019e7	−2.17259
$827$	−1.41621e7	−0.720050	−0.360025	−	0.932943i	$-0.617232\pi$
$827$	−1.41621e7	−0.720050	−0.360025	+	0.932943i	$0.617232\pi$
$828$	7.59944e6	0.385217
$829$	2.99595e7	1.51408	0.757040	−	0.653369i	$-0.226645\pi$
$829$	2.99595e7	1.51408	0.757040	+	0.653369i	$0.226645\pi$
$830$	2.04957e6	0.103268
$831$	−6.57253e6	−0.330164
$832$	2.45522e7	1.22965
$833$	−1.42683e7	−0.712460
$834$	5.57266e6	0.277426
$835$	−4.11660e6	−0.204326
$836$	−670737.	−0.0331922
$837$	2.87366e7	1.41782
$838$	−1.78456e7	−0.877853
$839$	2.02332e6	0.0992336	0.0496168	−	0.998768i	$-0.484200\pi$
$839$	2.02332e6	0.0992336	0.0496168	+	0.998768i	$0.484200\pi$
$840$	−6.67847e6	−0.326572
$841$	−1.82839e7	−0.891411
$842$	1.91780e7	0.932228
$843$	9.14992e6	0.443454
$844$	−1.78866e7	−0.864313
$845$	7.70965e6	0.371444
$846$	1.10361e7	0.530137
$847$	3.07529e6	0.147291
$848$	−1.74564e6	−0.0833616
$849$	665297.	0.0316772
$850$	1.33208e6	0.0632385
$851$	1.13211e7	0.535875
$852$	−2.67867e6	−0.126421
$853$	3.03778e7	1.42950	0.714749	−	0.699381i	$-0.246541\pi$
$853$	3.03778e7	1.42950	0.714749	+	0.699381i	$0.246541\pi$
$854$	1.88499e6	0.0884434
$855$	1.80198e6	0.0843016
$856$	−1.93058e7	−0.900539
$857$	−1.20348e7	−0.559742	−0.279871	−	0.960038i	$-0.590292\pi$
$857$	−1.20348e7	−0.559742	−0.279871	+	0.960038i	$0.590292\pi$
$858$	−2.67911e6	−0.124243
$859$	1.93337e6	0.0893987	0.0446994	−	0.999000i	$-0.485767\pi$
$859$	1.93337e6	0.0893987	0.0446994	+	0.999000i	$0.485767\pi$
$860$	2.56497e6	0.118260
$861$	−2.51598e6	−0.115664
$862$	−1.11590e6	−0.0511514
$863$	−3.29690e7	−1.50688	−0.753440	−	0.657516i	$-0.771607\pi$
$863$	−3.29690e7	−1.50688	−0.753440	+	0.657516i	$0.771607\pi$
$864$	−1.44865e7	−0.660207
$865$	7.52273e6	0.341850
$866$	−2.77157e7	−1.25583
$867$	7.55019e6	0.341122
$868$	−3.18067e7	−1.43291
$869$	−538306.	−0.0241813
$870$	1.00203e6	0.0448830
$871$	−3.94577e7	−1.76233
$872$	−3.75447e7	−1.67208
$873$	1.79012e7	0.794962
$874$	3.65059e6	0.161653
$875$	3.28198e6	0.144916
$876$	6.76472e6	0.297845
$877$	1.21352e7	0.532779	0.266390	−	0.963865i	$-0.414169\pi$
$877$	1.21352e7	0.532779	0.266390	+	0.963865i	$0.414169\pi$
$878$	1.05287e7	0.460932
$879$	9.07370e6	0.396107
$880$	897948.	0.0390881
$881$	−9.17426e6	−0.398227	−0.199114	−	0.979976i	$-0.563806\pi$
$881$	−9.17426e6	−0.398227	−0.199114	+	0.979976i	$0.563806\pi$
$882$	2.22486e7	0.963011
$883$	−96425.4	−0.00416188	−0.00208094	−	0.999998i	$-0.500662\pi$
$883$	−96425.4	−0.00416188	−0.00208094	+	0.999998i	$0.500662\pi$
$884$	6.61337e6	0.284638
$885$	−8.18147e6	−0.351134
$886$	−2.10678e7	−0.901646
$887$	1.11743e7	0.476882	0.238441	−	0.971157i	$-0.423364\pi$
$887$	1.11743e7	0.476882	0.238441	+	0.971157i	$0.423364\pi$
$888$	−5.80886e6	−0.247206
$889$	−5.99561e7	−2.54436
$890$	7.40558e6	0.313389
$891$	−3.54968e6	−0.149794
$892$	−1.08535e7	−0.456728
$893$	−4.89080e6	−0.205235
$894$	750973.	0.0314254
$895$	1.24874e7	0.521092
$896$	7.89415e6	0.328500
$897$	−1.34520e7	−0.558219
$898$	−3.17140e7	−1.31238
$899$	1.47174e7	0.607340
$900$	1.91621e6	0.0788564
$901$	−3.07214e6	−0.126075
$902$	898253.	0.0367606
$903$	9.23876e6	0.377046
$904$	1.41532e7	0.576014
$905$	−1.34427e7	−0.545587
$906$	−1.10905e7	−0.448880
$907$	−4.01600e7	−1.62097	−0.810485	−	0.585759i	$-0.800796\pi$
$907$	−4.01600e7	−1.62097	−0.810485	+	0.585759i	$0.800796\pi$
$908$	5.89028e6	0.237094
$909$	−5.74824e6	−0.230741
$910$	−1.76622e7	−0.707036
$911$	2.13383e7	0.851853	0.425927	−	0.904758i	$-0.359948\pi$
$911$	2.13383e7	0.851853	0.425927	+	0.904758i	$0.359948\pi$
$912$	−705421.	−0.0280842
$913$	2.43148e6	0.0965368
$914$	−4.11813e6	−0.163055
$915$	362004.	0.0142942
$916$	−7.10064e6	−0.279614
$917$	3.48555e7	1.36882
$918$	6.21070e6	0.243239
$919$	−3.05750e7	−1.19420	−0.597100	−	0.802167i	$-0.703681\pi$
$919$	−3.05750e7	−1.19420	−0.597100	+	0.802167i	$0.703681\pi$
$920$	1.19719e7	0.466332
$921$	1.35533e7	0.526497
$922$	−6.84822e6	−0.265308
$923$	−2.18472e7	−0.844095
$924$	−2.56907e6	−0.0989910
$925$	2.85462e6	0.109697
$926$	−8.57377e6	−0.328583
$927$	1.05467e7	0.403106
$928$	−7.41925e6	−0.282807
$929$	2.38811e7	0.907852	0.453926	−	0.891039i	$-0.350023\pi$
$929$	2.38811e7	0.907852	0.453926	+	0.891039i	$0.350023\pi$
$930$	6.62120e6	0.251032
$931$	−9.85982e6	−0.372816
$932$	−6.39400e6	−0.241120
$933$	−8.88138e6	−0.334023
$934$	−6.33013e6	−0.237435
$935$	1.58029e6	0.0591164
$936$	−3.18026e7	−1.18651
$937$	−1.42477e7	−0.530147	−0.265073	−	0.964228i	$-0.585396\pi$
$937$	−1.42477e7	−0.530147	−0.265073	+	0.964228i	$0.585396\pi$
$938$	4.10141e7	1.52204
$939$	6.51586e6	0.241161
$940$	−5.20083e6	−0.191979
$941$	2.75426e7	1.01398	0.506991	−	0.861951i	$-0.330758\pi$
$941$	2.75426e7	1.01398	0.506991	+	0.861951i	$0.330758\pi$
$942$	−8.08733e6	−0.296946
$943$	4.51018e6	0.165164
$944$	−1.47571e7	−0.538979
$945$	1.53019e7	0.557400
$946$	−3.29842e6	−0.119833
$947$	2.51094e7	0.909833	0.454916	−	0.890534i	$-0.349669\pi$
$947$	2.51094e7	0.909833	0.454916	+	0.890534i	$0.349669\pi$
$948$	449696.	0.0162517
$949$	5.51730e7	1.98866
$950$	920502.	0.0330914
$951$	1.90899e6	0.0684468
$952$	−2.11999e7	−0.758125
$953$	1.97941e7	0.705997	0.352999	−	0.935624i	$-0.385162\pi$
$953$	1.97941e7	0.705997	0.352999	+	0.935624i	$0.385162\pi$
$954$	4.79039e6	0.170412
$955$	201127.	0.00713612
$956$	−1.55204e7	−0.549234
$957$	1.18874e6	0.0419573
$958$	1.26175e7	0.444181
$959$	4.41233e7	1.54925
$960$	−4.90110e6	−0.171639
$961$	6.86203e7	2.39687
$962$	−1.53624e7	−0.535205
$963$	1.99519e7	0.693295
$964$	−7.27556e6	−0.252158
$965$	9.64179e6	0.333303
$966$	1.39826e7	0.482107
$967$	−4.27567e7	−1.47041	−0.735205	−	0.677845i	$-0.762914\pi$
$967$	−4.27567e7	−1.47041	−0.735205	+	0.677845i	$0.762914\pi$
$968$	2.82864e6	0.0970261
$969$	−1.24146e6	−0.0424742
$970$	9.14441e6	0.312052
$971$	1.77494e7	0.604136	0.302068	−	0.953286i	$-0.402323\pi$
$971$	1.77494e7	0.604136	0.302068	+	0.953286i	$0.402323\pi$
$972$	1.38386e7	0.469813
$973$	4.35838e7	1.47585
$974$	1.15323e7	0.389511
$975$	−3.39193e6	−0.114271
$976$	652955.	0.0219411
$977$	3.20453e7	1.07406	0.537029	−	0.843564i	$-0.319547\pi$
$977$	3.20453e7	1.07406	0.537029	+	0.843564i	$0.319547\pi$
$978$	−6.37107e6	−0.212993
$979$	8.78551e6	0.292961
$980$	−1.04848e7	−0.348735
$981$	3.88013e7	1.28728
$982$	7.24286e6	0.239680
$983$	1.16575e7	0.384787	0.192393	−	0.981318i	$-0.438375\pi$
$983$	1.16575e7	0.384787	0.192393	+	0.981318i	$0.438375\pi$
$984$	−2.31418e6	−0.0761921
$985$	1.60862e7	0.528278
$986$	3.18080e6	0.104194
$987$	−1.87329e7	−0.612084
$988$	4.57003e6	0.148945
$989$	−1.65616e7	−0.538407
$990$	−2.46415e6	−0.0799058
$991$	−3.86468e7	−1.25005	−0.625027	−	0.780603i	$-0.714912\pi$
$991$	−3.86468e7	−1.25005	−0.625027	+	0.780603i	$0.714912\pi$
$992$	−4.90249e7	−1.58175
$993$	−1.51507e7	−0.487597
$994$	2.27089e7	0.729005
$995$	−1.28039e7	−0.410001
$996$	−2.03123e6	−0.0648800
$997$	−4.05654e7	−1.29246	−0.646231	−	0.763142i	$-0.723656\pi$
$997$	−4.05654e7	−1.29246	−0.646231	+	0.763142i	$0.723656\pi$
$998$	1.25968e7	0.400344
$999$	1.33095e7	0.421936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.14	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.14	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-4.07979 q^{2} -6.58287 q^{3} -15.3553 q^{4} +25.0000 q^{5} +26.8567 q^{6} +210.046 q^{7} +193.200 q^{8} -199.666 q^{9} +O(q^{10})\)	\(q-4.07979 q^{2} -6.58287 q^{3} -15.3553 q^{4} +25.0000 q^{5} +26.8567 q^{6} +210.046 q^{7} +193.200 q^{8} -199.666 q^{9} -101.995 q^{10} -121.000 q^{11} +101.082 q^{12} +824.427 q^{13} -856.945 q^{14} -164.572 q^{15} -296.842 q^{16} -522.410 q^{17} +814.594 q^{18} -361.000 q^{19} -383.884 q^{20} -1382.71 q^{21} +493.654 q^{22} +2478.67 q^{23} -1271.81 q^{24} +625.000 q^{25} -3363.48 q^{26} +2914.01 q^{27} -3225.34 q^{28} +1492.41 q^{29} +671.418 q^{30} +9861.52 q^{31} -4971.34 q^{32} +796.528 q^{33} +2131.32 q^{34} +5251.16 q^{35} +3065.94 q^{36} +4567.40 q^{37} +1472.80 q^{38} -5427.09 q^{39} +4829.99 q^{40} +1819.60 q^{41} +5641.16 q^{42} -6681.64 q^{43} +1858.00 q^{44} -4991.64 q^{45} -10112.4 q^{46} +13547.9 q^{47} +1954.08 q^{48} +27312.5 q^{49} -2549.87 q^{50} +3438.96 q^{51} -12659.4 q^{52} +5880.71 q^{53} -11888.5 q^{54} -3025.00 q^{55} +40580.9 q^{56} +2376.42 q^{57} -6088.70 q^{58} +49713.7 q^{59} +2527.06 q^{60} -2199.67 q^{61} -40232.9 q^{62} -41939.1 q^{63} +29780.9 q^{64} +20610.7 q^{65} -3249.66 q^{66} -47860.8 q^{67} +8021.79 q^{68} -16316.8 q^{69} -21423.6 q^{70} -26499.9 q^{71} -38575.4 q^{72} +66922.9 q^{73} -18634.0 q^{74} -4114.30 q^{75} +5543.28 q^{76} -25415.6 q^{77} +22141.4 q^{78} +4448.81 q^{79} -7421.06 q^{80} +29336.2 q^{81} -7423.58 q^{82} -20094.8 q^{83} +21232.0 q^{84} -13060.3 q^{85} +27259.7 q^{86} -9824.32 q^{87} -23377.2 q^{88} -72607.5 q^{89} +20364.8 q^{90} +173168. q^{91} -38060.8 q^{92} -64917.1 q^{93} -55272.7 q^{94} -9025.00 q^{95} +32725.7 q^{96} -89655.8 q^{97} -111429. q^{98} +24159.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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