LMFDB - Embedded newform 1045.6.a.f.1.15

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			1.15
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)

$f(q)$	$=$	$q-3.39547 q^{2} +23.0537 q^{3} -20.4708 q^{4} +25.0000 q^{5} -78.2781 q^{6} +193.366 q^{7} +178.163 q^{8} +288.472 q^{9} +O(q^{10})$	\(q-3.39547 q^{2} +23.0537 q^{3} -20.4708 q^{4} +25.0000 q^{5} -78.2781 q^{6} +193.366 q^{7} +178.163 q^{8} +288.472 q^{9} -84.8868 q^{10} -121.000 q^{11} -471.926 q^{12} -570.973 q^{13} -656.570 q^{14} +576.342 q^{15} +50.1168 q^{16} -1343.73 q^{17} -979.497 q^{18} -361.000 q^{19} -511.769 q^{20} +4457.80 q^{21} +410.852 q^{22} +1692.93 q^{23} +4107.31 q^{24} +625.000 q^{25} +1938.72 q^{26} +1048.29 q^{27} -3958.36 q^{28} -3970.27 q^{29} -1956.95 q^{30} -6878.20 q^{31} -5871.39 q^{32} -2789.49 q^{33} +4562.60 q^{34} +4834.16 q^{35} -5905.23 q^{36} +11904.4 q^{37} +1225.77 q^{38} -13163.0 q^{39} +4454.08 q^{40} +18978.9 q^{41} -15136.3 q^{42} +22560.0 q^{43} +2476.96 q^{44} +7211.79 q^{45} -5748.29 q^{46} +22385.6 q^{47} +1155.38 q^{48} +20583.5 q^{49} -2122.17 q^{50} -30977.9 q^{51} +11688.3 q^{52} -11308.2 q^{53} -3559.43 q^{54} -3025.00 q^{55} +34450.7 q^{56} -8322.37 q^{57} +13480.9 q^{58} +12744.8 q^{59} -11798.2 q^{60} -12463.0 q^{61} +23354.8 q^{62} +55780.7 q^{63} +18332.4 q^{64} -14274.3 q^{65} +9471.65 q^{66} +46695.5 q^{67} +27507.2 q^{68} +39028.2 q^{69} -16414.2 q^{70} +27439.3 q^{71} +51395.0 q^{72} +62422.8 q^{73} -40421.2 q^{74} +14408.5 q^{75} +7389.95 q^{76} -23397.3 q^{77} +44694.7 q^{78} -68279.7 q^{79} +1252.92 q^{80} -45931.7 q^{81} -64442.4 q^{82} -28008.1 q^{83} -91254.6 q^{84} -33593.3 q^{85} -76601.8 q^{86} -91529.3 q^{87} -21557.7 q^{88} +146189. q^{89} -24487.4 q^{90} -110407. q^{91} -34655.5 q^{92} -158568. q^{93} -76009.8 q^{94} -9025.00 q^{95} -135357. q^{96} -62201.3 q^{97} -69890.7 q^{98} -34905.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.39547	−0.600240	−0.300120	−	0.953901i	$-0.597027\pi$
$2$	−3.39547	−0.600240	−0.300120	+	0.953901i	$0.597027\pi$
$3$	23.0537	1.47889	0.739447	−	0.673215i	$-0.235087\pi$
$3$	23.0537	1.47889	0.739447	+	0.673215i	$0.235087\pi$
$4$	−20.4708	−0.639711
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−78.2781	−0.887692
$7$	193.366	1.49154	0.745771	−	0.666202i	$-0.232081\pi$
$7$	193.366	1.49154	0.745771	+	0.666202i	$0.232081\pi$
$8$	178.163	0.984221
$9$	288.472	1.18713
$10$	−84.8868	−0.268436
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−471.926	−0.946065
$13$	−570.973	−0.937038	−0.468519	−	0.883453i	$-0.655212\pi$
$13$	−570.973	−0.937038	−0.468519	+	0.883453i	$0.655212\pi$
$14$	−656.570	−0.895284
$15$	576.342	0.661381
$16$	50.1168	0.0489422
$17$	−1343.73	−1.12769	−0.563845	−	0.825881i	$-0.690679\pi$
$17$	−1343.73	−1.12769	−0.563845	+	0.825881i	$0.690679\pi$
$18$	−979.497	−0.712561
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−511.769	−0.286088
$21$	4457.80	2.20583
$22$	410.852	0.180979
$23$	1692.93	0.667297	0.333648	−	0.942698i	$-0.391720\pi$
$23$	1692.93	0.667297	0.333648	+	0.942698i	$0.391720\pi$
$24$	4107.31	1.45556
$25$	625.000	0.200000
$26$	1938.72	0.562448
$27$	1048.29	0.276739
$28$	−3958.36	−0.954157
$29$	−3970.27	−0.876648	−0.438324	−	0.898817i	$-0.644428\pi$
$29$	−3970.27	−0.876648	−0.438324	+	0.898817i	$0.644428\pi$
$30$	−1956.95	−0.396988
$31$	−6878.20	−1.28550	−0.642748	−	0.766078i	$-0.722206\pi$
$31$	−6878.20	−1.28550	−0.642748	+	0.766078i	$0.722206\pi$
$32$	−5871.39	−1.01360
$33$	−2789.49	−0.445903
$34$	4562.60	0.676885
$35$	4834.16	0.667038
$36$	−5905.23	−0.759418
$37$	11904.4	1.42957	0.714784	−	0.699346i	$-0.246525\pi$
$37$	11904.4	1.42957	0.714784	+	0.699346i	$0.246525\pi$
$38$	1225.77	0.137705
$39$	−13163.0	−1.38578
$40$	4454.08	0.440157
$41$	18978.9	1.76324	0.881620	−	0.471959i	$-0.156453\pi$
$41$	18978.9	1.76324	0.881620	+	0.471959i	$0.156453\pi$
$42$	−15136.3	−1.32403
$43$	22560.0	1.86066	0.930331	−	0.366722i	$-0.119520\pi$
$43$	22560.0	1.86066	0.930331	+	0.366722i	$0.119520\pi$
$44$	2476.96	0.192880
$45$	7211.79	0.530899
$46$	−5748.29	−0.400538
$47$	22385.6	1.47817	0.739086	−	0.673611i	$-0.235258\pi$
$47$	22385.6	1.47817	0.739086	+	0.673611i	$0.235258\pi$
$48$	1155.38	0.0723803
$49$	20583.5	1.22470
$50$	−2122.17	−0.120048
$51$	−30977.9	−1.66773
$52$	11688.3	0.599434
$53$	−11308.2	−0.552974	−0.276487	−	0.961018i	$-0.589170\pi$
$53$	−11308.2	−0.552974	−0.276487	+	0.961018i	$0.589170\pi$
$54$	−3559.43	−0.166110
$55$	−3025.00	−0.134840
$56$	34450.7	1.46801
$57$	−8322.37	−0.339281
$58$	13480.9	0.526199
$59$	12744.8	0.476655	0.238327	−	0.971185i	$-0.423401\pi$
$59$	12744.8	0.476655	0.238327	+	0.971185i	$0.423401\pi$
$60$	−11798.2	−0.423093
$61$	−12463.0	−0.428842	−0.214421	−	0.976741i	$-0.568786\pi$
$61$	−12463.0	−0.428842	−0.214421	+	0.976741i	$0.568786\pi$
$62$	23354.8	0.771607
$63$	55780.7	1.77065
$64$	18332.4	0.559460
$65$	−14274.3	−0.419056
$66$	9471.65	0.267649
$67$	46695.5	1.27083	0.635416	−	0.772170i	$-0.280829\pi$
$67$	46695.5	1.27083	0.635416	+	0.772170i	$0.280829\pi$
$68$	27507.2	0.721396
$69$	39028.2	0.986861
$70$	−16414.2	−0.400383
$71$	27439.3	0.645992	0.322996	−	0.946400i	$-0.395310\pi$
$71$	27439.3	0.645992	0.322996	+	0.946400i	$0.395310\pi$
$72$	51395.0	1.16839
$73$	62422.8	1.37099	0.685497	−	0.728075i	$-0.259585\pi$
$73$	62422.8	1.37099	0.685497	+	0.728075i	$0.259585\pi$
$74$	−40421.2	−0.858084
$75$	14408.5	0.295779
$76$	7389.95	0.146760
$77$	−23397.3	−0.449717
$78$	44694.7	0.831801
$79$	−68279.7	−1.23090	−0.615452	−	0.788175i	$-0.711026\pi$
$79$	−68279.7	−1.23090	−0.615452	+	0.788175i	$0.711026\pi$
$80$	1252.92	0.0218876
$81$	−45931.7	−0.777858
$82$	−64442.4	−1.05837
$83$	−28008.1	−0.446261	−0.223130	−	0.974789i	$-0.571628\pi$
$83$	−28008.1	−0.446261	−0.223130	+	0.974789i	$0.571628\pi$
$84$	−91254.6	−1.41110
$85$	−33593.3	−0.504318
$86$	−76601.8	−1.11684
$87$	−91529.3	−1.29647
$88$	−21557.7	−0.296754
$89$	146189.	1.95631	0.978157	−	0.207869i	$-0.0666526\pi$
$89$	146189.	1.95631	0.978157	+	0.207869i	$0.0666526\pi$
$90$	−24487.4	−0.318667
$91$	−110407.	−1.39763
$92$	−34655.5	−0.426877
$93$	−158568.	−1.90111
$94$	−76009.8	−0.887259
$95$	−9025.00	−0.102598
$96$	−135357.	−1.49900
$97$	−62201.3	−0.671228	−0.335614	−	0.942000i	$-0.608944\pi$
$97$	−62201.3	−0.671228	−0.335614	+	0.942000i	$0.608944\pi$
$98$	−69890.7	−0.735113
$99$	−34905.1	−0.357932
$100$	−12794.2	−0.127942
$101$	72994.0	0.712006	0.356003	−	0.934485i	$-0.384139\pi$
$101$	72994.0	0.712006	0.356003	+	0.934485i	$0.384139\pi$
$102$	105185.	1.00104
$103$	125744.	1.16787	0.583935	−	0.811800i	$-0.301512\pi$
$103$	125744.	1.16787	0.583935	+	0.811800i	$0.301512\pi$
$104$	−101726.	−0.922253
$105$	111445.	0.986478
$106$	38396.8	0.331917
$107$	110742.	0.935087	0.467543	−	0.883970i	$-0.345139\pi$
$107$	110742.	0.935087	0.467543	+	0.883970i	$0.345139\pi$
$108$	−21459.2	−0.177033
$109$	−132324.	−1.06677	−0.533387	−	0.845871i	$-0.679081\pi$
$109$	−132324.	−1.06677	−0.533387	+	0.845871i	$0.679081\pi$
$110$	10271.3	0.0809364
$111$	274441.	2.11418
$112$	9690.90	0.0729994
$113$	−122367.	−0.901507	−0.450754	−	0.892648i	$-0.648845\pi$
$113$	−122367.	−0.901507	−0.450754	+	0.892648i	$0.648845\pi$
$114$	28258.4	0.203650
$115$	42323.2	0.298424
$116$	81274.5	0.560801
$117$	−164710.	−1.11238
$118$	−43274.7	−0.286107
$119$	−259832.	−1.68200
$120$	102683.	0.650945
$121$	14641.0	0.0909091
$122$	42317.7	0.257408
$123$	437534.	2.60765
$124$	140802.	0.822347
$125$	15625.0	0.0894427
$126$	−189402.	−1.06281
$127$	24648.6	0.135607	0.0678036	−	0.997699i	$-0.478401\pi$
$127$	24648.6	0.135607	0.0678036	+	0.997699i	$0.478401\pi$
$128$	125637.	0.677787
$129$	520090.	2.75172
$130$	48468.1	0.251535
$131$	−105144.	−0.535309	−0.267654	−	0.963515i	$-0.586249\pi$
$131$	−105144.	−0.535309	−0.267654	+	0.963515i	$0.586249\pi$
$132$	57103.1	0.285249
$133$	−69805.2	−0.342183
$134$	−158553.	−0.762805
$135$	26207.2	0.123762
$136$	−239403.	−1.10990
$137$	100648.	0.458148	0.229074	−	0.973409i	$-0.426430\pi$
$137$	100648.	0.458148	0.229074	+	0.973409i	$0.426430\pi$
$138$	−132519.	−0.592354
$139$	435138.	1.91025	0.955124	−	0.296205i	$-0.0957213\pi$
$139$	435138.	1.91025	0.955124	+	0.296205i	$0.0957213\pi$
$140$	−98958.9	−0.426712
$141$	516071.	2.18606
$142$	−93169.4	−0.387751
$143$	69087.8	0.282528
$144$	14457.3	0.0581006
$145$	−99256.7	−0.392049
$146$	−211955.	−0.822926
$147$	474525.	1.81120
$148$	−243693.	−0.914511
$149$	80813.1	0.298206	0.149103	−	0.988822i	$-0.452361\pi$
$149$	80813.1	0.298206	0.149103	+	0.988822i	$0.452361\pi$
$150$	−48923.8	−0.177538
$151$	456130.	1.62797	0.813984	−	0.580887i	$-0.197294\pi$
$151$	456130.	1.62797	0.813984	+	0.580887i	$0.197294\pi$
$152$	−64316.9	−0.225796
$153$	−387628.	−1.33871
$154$	79444.9	0.269938
$155$	−171955.	−0.574891
$156$	269457.	0.886499
$157$	−76026.6	−0.246160	−0.123080	−	0.992397i	$-0.539277\pi$
$157$	−76026.6	−0.246160	−0.123080	+	0.992397i	$0.539277\pi$
$158$	231842.	0.738838
$159$	−260696.	−0.817790
$160$	−146785.	−0.453295
$161$	327355.	0.995301
$162$	155960.	0.466902
$163$	−145651.	−0.429382	−0.214691	−	0.976682i	$-0.568874\pi$
$163$	−145651.	−0.429382	−0.214691	+	0.976682i	$0.568874\pi$
$164$	−388513.	−1.12797
$165$	−69737.3	−0.199414
$166$	95100.8	0.267864
$167$	−216544.	−0.600834	−0.300417	−	0.953808i	$-0.597126\pi$
$167$	−216544.	−0.600834	−0.300417	+	0.953808i	$0.597126\pi$
$168$	794215.	2.17103
$169$	−45282.5	−0.121959
$170$	114065.	0.302712
$171$	−104138.	−0.272345
$172$	−461820.	−1.19029
$173$	−75641.1	−0.192151	−0.0960755	−	0.995374i	$-0.530629\pi$
$173$	−75641.1	−0.192151	−0.0960755	+	0.995374i	$0.530629\pi$
$174$	310785.	0.778193
$175$	120854.	0.298308
$176$	−6064.13	−0.0147566
$177$	293815.	0.704921
$178$	−496379.	−1.17426
$179$	14833.0	0.0346017	0.0173008	−	0.999850i	$-0.494493\pi$
$179$	14833.0	0.0346017	0.0173008	+	0.999850i	$0.494493\pi$
$180$	−147631.	−0.339622
$181$	382438.	0.867690	0.433845	−	0.900987i	$-0.357157\pi$
$181$	382438.	0.867690	0.433845	+	0.900987i	$0.357157\pi$
$182$	374884.	0.838916
$183$	−287317.	−0.634211
$184$	301617.	0.656767
$185$	297611.	0.639322
$186$	538413.	1.14112
$187$	162591.	0.340011
$188$	−458251.	−0.945604
$189$	202703.	0.412768
$190$	30644.1	0.0615834
$191$	415292.	0.823702	0.411851	−	0.911251i	$-0.364882\pi$
$191$	415292.	0.823702	0.411851	+	0.911251i	$0.364882\pi$
$192$	422629.	0.827382
$193$	−645455.	−1.24731	−0.623653	−	0.781701i	$-0.714352\pi$
$193$	−645455.	−1.24731	−0.623653	+	0.781701i	$0.714352\pi$
$194$	211203.	0.402898
$195$	−329076.	−0.619740
$196$	−421360.	−0.783454
$197$	−389239.	−0.714580	−0.357290	−	0.933993i	$-0.616299\pi$
$197$	−389239.	−0.714580	−0.357290	+	0.933993i	$0.616299\pi$
$198$	118519.	0.214845
$199$	−168180.	−0.301051	−0.150526	−	0.988606i	$-0.548097\pi$
$199$	−168180.	−0.301051	−0.150526	+	0.988606i	$0.548097\pi$
$200$	111352.	0.196844
$201$	1.07650e6	1.87943
$202$	−247849.	−0.427375
$203$	−767716.	−1.30756
$204$	634142.	1.06687
$205$	474473.	0.788545
$206$	−426961.	−0.701003
$207$	488362.	0.792165
$208$	−28615.4	−0.0458607
$209$	43681.0	0.0691714
$210$	−378409.	−0.592124
$211$	876566.	1.35543	0.677717	−	0.735322i	$-0.262969\pi$
$211$	876566.	1.35543	0.677717	+	0.735322i	$0.262969\pi$
$212$	231488.	0.353744
$213$	632577.	0.955354
$214$	−376021.	−0.561277
$215$	563999.	0.832113
$216$	186766.	0.272373
$217$	−1.33001e6	−1.91737
$218$	449303.	0.640321
$219$	1.43907e6	2.02756
$220$	61924.1	0.0862587
$221$	767234.	1.05669
$222$	−931857.	−1.26901
$223$	−1.46433e6	−1.97186	−0.985931	−	0.167155i	$-0.946542\pi$
$223$	−1.46433e6	−1.97186	−0.985931	+	0.167155i	$0.946542\pi$
$224$	−1.13533e6	−1.51182
$225$	180295.	0.237425
$226$	415495.	0.541121
$227$	1.37219e6	1.76747	0.883733	−	0.467991i	$-0.155022\pi$
$227$	1.37219e6	1.76747	0.883733	+	0.467991i	$0.155022\pi$
$228$	170365.	0.217042
$229$	571853.	0.720602	0.360301	−	0.932836i	$-0.382674\pi$
$229$	571853.	0.720602	0.360301	+	0.932836i	$0.382674\pi$
$230$	−143707.	−0.179126
$231$	−539394.	−0.665083
$232$	−707355.	−0.862815
$233$	−53719.6	−0.0648251	−0.0324126	−	0.999475i	$-0.510319\pi$
$233$	−53719.6	−0.0648251	−0.0324126	+	0.999475i	$0.510319\pi$
$234$	559267.	0.667697
$235$	559641.	0.661059
$236$	−260896.	−0.304921
$237$	−1.57410e6	−1.82037
$238$	882253.	1.00960
$239$	−1.59958e6	−1.81139	−0.905695	−	0.423930i	$-0.860650\pi$
$239$	−1.59958e6	−1.81139	−0.905695	+	0.423930i	$0.860650\pi$
$240$	28884.4	0.0323695
$241$	−50023.6	−0.0554795	−0.0277398	−	0.999615i	$-0.508831\pi$
$241$	−50023.6	−0.0554795	−0.0277398	+	0.999615i	$0.508831\pi$
$242$	−49713.1	−0.0545673
$243$	−1.31363e6	−1.42711
$244$	255127.	0.274335
$245$	514588.	0.547702
$246$	−1.48563e6	−1.56521
$247$	206121.	0.214971
$248$	−1.22544e6	−1.26521
$249$	−645690.	−0.659972
$250$	−53054.3	−0.0536871
$251$	−86190.5	−0.0863526	−0.0431763	−	0.999067i	$-0.513748\pi$
$251$	−86190.5	−0.0863526	−0.0431763	+	0.999067i	$0.513748\pi$
$252$	−1.14187e6	−1.13270
$253$	−204844.	−0.201198
$254$	−83693.6	−0.0813969
$255$	−774448.	−0.745833
$256$	−1.01323e6	−0.966296
$257$	600074.	0.566724	0.283362	−	0.959013i	$-0.408550\pi$
$257$	600074.	0.566724	0.283362	+	0.959013i	$0.408550\pi$
$258$	−1.76595e6	−1.65169
$259$	2.30192e6	2.13226
$260$	292207.	0.268075
$261$	−1.14531e6	−1.04069
$262$	357012.	0.321314
$263$	609595.	0.543441	0.271720	−	0.962376i	$-0.412407\pi$
$263$	609595.	0.543441	0.271720	+	0.962376i	$0.412407\pi$
$264$	−496985.	−0.438867
$265$	−282706.	−0.247297
$266$	237022.	0.205392
$267$	3.37018e6	2.89318
$268$	−955893.	−0.812966
$269$	−425812.	−0.358788	−0.179394	−	0.983777i	$-0.557414\pi$
$269$	−425812.	−0.358788	−0.179394	+	0.983777i	$0.557414\pi$
$270$	−88985.8	−0.0742867
$271$	−214608.	−0.177510	−0.0887552	−	0.996053i	$-0.528289\pi$
$271$	−214608.	−0.177510	−0.0887552	+	0.996053i	$0.528289\pi$
$272$	−67343.5	−0.0551916
$273$	−2.54529e6	−2.06695
$274$	−341749.	−0.274999
$275$	−75625.0	−0.0603023
$276$	−798937.	−0.631306
$277$	364338.	0.285302	0.142651	−	0.989773i	$-0.454437\pi$
$277$	364338.	0.285302	0.142651	+	0.989773i	$0.454437\pi$
$278$	−1.47750e6	−1.14661
$279$	−1.98417e6	−1.52605
$280$	861268.	0.656513
$281$	2.53652e6	1.91634	0.958169	−	0.286202i	$-0.0923928\pi$
$281$	2.53652e6	1.91634	0.958169	+	0.286202i	$0.0923928\pi$
$282$	−1.75231e6	−1.31216
$283$	707906.	0.525423	0.262712	−	0.964874i	$-0.415383\pi$
$283$	707906.	0.525423	0.262712	+	0.964874i	$0.415383\pi$
$284$	−561704.	−0.413249
$285$	−208059.	−0.151731
$286$	−234586.	−0.169585
$287$	3.66988e6	2.62995
$288$	−1.69373e6	−1.20327
$289$	385755.	0.271686
$290$	337024.	0.235323
$291$	−1.43397e6	−0.992675
$292$	−1.27784e6	−0.877041
$293$	−209469.	−0.142545	−0.0712724	−	0.997457i	$-0.522706\pi$
$293$	−209469.	−0.142545	−0.0712724	+	0.997457i	$0.522706\pi$
$294$	−1.61124e6	−1.08715
$295$	318621.	0.213166
$296$	2.12093e6	1.40701
$297$	−126843.	−0.0834401
$298$	−274399.	−0.178995
$299$	−966617.	−0.625283
$300$	−294954.	−0.189213
$301$	4.36234e6	2.77526
$302$	−1.54878e6	−0.977173
$303$	1.68278e6	1.05298
$304$	−18092.2	−0.0112281
$305$	−311574.	−0.191784
$306$	1.31618e6	0.803548
$307$	−482959.	−0.292459	−0.146229	−	0.989251i	$-0.546714\pi$
$307$	−482959.	−0.292459	−0.146229	+	0.989251i	$0.546714\pi$
$308$	478961.	0.287689
$309$	2.89886e6	1.72716
$310$	583869.	0.345073
$311$	−1.65108e6	−0.967984	−0.483992	−	0.875072i	$-0.660814\pi$
$311$	−1.65108e6	−0.967984	−0.483992	+	0.875072i	$0.660814\pi$
$312$	−2.34517e6	−1.36391
$313$	3.24763e6	1.87372	0.936862	−	0.349700i	$-0.113716\pi$
$313$	3.24763e6	1.87372	0.936862	+	0.349700i	$0.113716\pi$
$314$	258146.	0.147755
$315$	1.39452e6	0.791858
$316$	1.39774e6	0.787423
$317$	1.97783e6	1.10546	0.552728	−	0.833362i	$-0.313587\pi$
$317$	1.97783e6	1.10546	0.552728	+	0.833362i	$0.313587\pi$
$318$	885186.	0.490870
$319$	480403.	0.264319
$320$	458310.	0.250198
$321$	2.55300e6	1.38289
$322$	−1.11153e6	−0.597420
$323$	485087.	0.258710
$324$	940258.	0.497605
$325$	−356858.	−0.187408
$326$	494553.	0.257732
$327$	−3.05055e6	−1.57765
$328$	3.38134e6	1.73542
$329$	4.32863e6	2.20476
$330$	236791.	0.119696
$331$	−513350.	−0.257540	−0.128770	−	0.991675i	$-0.541103\pi$
$331$	−513350.	−0.257540	−0.128770	+	0.991675i	$0.541103\pi$
$332$	573348.	0.285478
$333$	3.43409e6	1.69708
$334$	735269.	0.360645
$335$	1.16739e6	0.568333
$336$	223411.	0.107958
$337$	−2.42243e6	−1.16192	−0.580959	−	0.813933i	$-0.697322\pi$
$337$	−2.42243e6	−1.16192	−0.580959	+	0.813933i	$0.697322\pi$
$338$	153755.	0.0732047
$339$	−2.82101e6	−1.33323
$340$	687680.	0.322618
$341$	832263.	0.387592
$342$	353599.	0.163473
$343$	730249.	0.335147
$344$	4.01935e6	1.83130
$345$	975705.	0.441338
$346$	256837.	0.115337
$347$	−4.19812e6	−1.87168	−0.935838	−	0.352430i	$-0.885355\pi$
$347$	−4.19812e6	−1.87168	−0.935838	+	0.352430i	$0.885355\pi$
$348$	1.87367e6	0.829366
$349$	−3.67423e6	−1.61474	−0.807369	−	0.590046i	$-0.799110\pi$
$349$	−3.67423e6	−1.61474	−0.807369	+	0.590046i	$0.799110\pi$
$350$	−410356.	−0.179057
$351$	−598544.	−0.259315
$352$	710438.	0.305611
$353$	−1.59958e6	−0.683235	−0.341618	−	0.939839i	$-0.610975\pi$
$353$	−1.59958e6	−0.683235	−0.341618	+	0.939839i	$0.610975\pi$
$354$	−997641.	−0.423122
$355$	685983.	0.288897
$356$	−2.99259e6	−1.25148
$357$	−5.99008e6	−2.48750
$358$	−50365.2	−0.0207693
$359$	2.55332e6	1.04561	0.522805	−	0.852452i	$-0.324886\pi$
$359$	2.55332e6	1.04561	0.522805	+	0.852452i	$0.324886\pi$
$360$	1.28487e6	0.522522
$361$	130321.	0.0526316
$362$	−1.29856e6	−0.520823
$363$	337529.	0.134445
$364$	2.26012e6	0.894082
$365$	1.56057e6	0.613127
$366$	975578.	0.380679
$367$	−553231.	−0.214408	−0.107204	−	0.994237i	$-0.534190\pi$
$367$	−553231.	−0.214408	−0.107204	+	0.994237i	$0.534190\pi$
$368$	84844.2	0.0326590
$369$	5.47488e6	2.09319
$370$	−1.01053e6	−0.383747
$371$	−2.18663e6	−0.824784
$372$	3.24601e6	1.21616
$373$	−197932.	−0.0736620	−0.0368310	−	0.999322i	$-0.511726\pi$
$373$	−197932.	−0.0736620	−0.0368310	+	0.999322i	$0.511726\pi$
$374$	−552075.	−0.204089
$375$	360214.	0.132276
$376$	3.98829e6	1.45485
$377$	2.26692e6	0.821452
$378$	−688274.	−0.247760
$379$	−1.29825e6	−0.464260	−0.232130	−	0.972685i	$-0.574570\pi$
$379$	−1.29825e6	−0.464260	−0.232130	+	0.972685i	$0.574570\pi$
$380$	184749.	0.0656330
$381$	568240.	0.200548
$382$	−1.41011e6	−0.494419
$383$	4.65891e6	1.62288	0.811441	−	0.584434i	$-0.198683\pi$
$383$	4.65891e6	1.62288	0.811441	+	0.584434i	$0.198683\pi$
$384$	2.89640e6	1.00238
$385$	−584933.	−0.201120
$386$	2.19163e6	0.748683
$387$	6.50791e6	2.20884
$388$	1.27331e6	0.429393
$389$	−1.53991e6	−0.515967	−0.257983	−	0.966149i	$-0.583058\pi$
$389$	−1.53991e6	−0.515967	−0.257983	+	0.966149i	$0.583058\pi$
$390$	1.11737e6	0.371993
$391$	−2.27484e6	−0.752504
$392$	3.66722e6	1.20537
$393$	−2.42394e6	−0.791664
$394$	1.32165e6	0.428920
$395$	−1.70699e6	−0.550477
$396$	714533.	0.228973
$397$	−3.63905e6	−1.15881	−0.579404	−	0.815041i	$-0.696715\pi$
$397$	−3.63905e6	−1.15881	−0.579404	+	0.815041i	$0.696715\pi$
$398$	571049.	0.180703
$399$	−1.60927e6	−0.506053
$400$	31323.0	0.00978844
$401$	686354.	0.213151	0.106575	−	0.994305i	$-0.466011\pi$
$401$	686354.	0.213151	0.106575	+	0.994305i	$0.466011\pi$
$402$	−3.65524e6	−1.12811
$403$	3.92727e6	1.20456
$404$	−1.49424e6	−0.455478
$405$	−1.14829e6	−0.347869
$406$	2.60676e6	0.784848
$407$	−1.44044e6	−0.431031
$408$	−5.51912e6	−1.64142
$409$	559464.	0.165373	0.0826863	−	0.996576i	$-0.473650\pi$
$409$	559464.	0.165373	0.0826863	+	0.996576i	$0.473650\pi$
$410$	−1.61106e6	−0.473317
$411$	2.32031e6	0.677551
$412$	−2.57408e6	−0.747100
$413$	2.46442e6	0.710951
$414$	−1.65822e6	−0.475490
$415$	−700203.	−0.199574
$416$	3.35241e6	0.949780
$417$	1.00315e7	2.82505
$418$	−148318.	−0.0415195
$419$	−2.13726e6	−0.594732	−0.297366	−	0.954763i	$-0.596108\pi$
$419$	−2.13726e6	−0.594732	−0.297366	+	0.954763i	$0.596108\pi$
$420$	−2.28137e6	−0.631061
$421$	6.48400e6	1.78294	0.891472	−	0.453076i	$-0.149673\pi$
$421$	6.48400e6	1.78294	0.891472	+	0.453076i	$0.149673\pi$
$422$	−2.97636e6	−0.813587
$423$	6.45762e6	1.75478
$424$	−2.01471e6	−0.544249
$425$	−839832.	−0.225538
$426$	−2.14790e6	−0.573442
$427$	−2.40992e6	−0.639636
$428$	−2.26697e6	−0.598186
$429$	1.59273e6	0.417828
$430$	−1.91504e6	−0.499468
$431$	−92954.0	−0.0241032	−0.0120516	−	0.999927i	$-0.503836\pi$
$431$	−92954.0	−0.0241032	−0.0120516	+	0.999927i	$0.503836\pi$
$432$	52536.8	0.0135442
$433$	3.44279e6	0.882451	0.441225	−	0.897396i	$-0.354544\pi$
$433$	3.44279e6	0.882451	0.441225	+	0.897396i	$0.354544\pi$
$434$	4.51602e6	1.15088
$435$	−2.28823e6	−0.579798
$436$	2.70877e6	0.682428
$437$	−611147.	−0.153088
$438$	−4.88633e6	−1.21702
$439$	2.72443e6	0.674705	0.337352	−	0.941378i	$-0.390469\pi$
$439$	2.72443e6	0.674705	0.337352	+	0.941378i	$0.390469\pi$
$440$	−538943.	−0.132712
$441$	5.93776e6	1.45387
$442$	−2.60512e6	−0.634268
$443$	−7.89349e6	−1.91100	−0.955498	−	0.294997i	$-0.904681\pi$
$443$	−7.89349e6	−1.91100	−0.955498	+	0.294997i	$0.904681\pi$
$444$	−5.61802e6	−1.35246
$445$	3.65471e6	0.874890
$446$	4.97209e6	1.18359
$447$	1.86304e6	0.441015
$448$	3.54487e6	0.834459
$449$	1.41220e6	0.330583	0.165291	−	0.986245i	$-0.447144\pi$
$449$	1.41220e6	0.330583	0.165291	+	0.986245i	$0.447144\pi$
$450$	−612186.	−0.142512
$451$	−2.29645e6	−0.531637
$452$	2.50495e6	0.576704
$453$	1.05155e7	2.40759
$454$	−4.65925e6	−1.06090
$455$	−2.76017e6	−0.625040
$456$	−1.48274e6	−0.333928
$457$	−2.69818e6	−0.604340	−0.302170	−	0.953254i	$-0.597711\pi$
$457$	−2.69818e6	−0.604340	−0.302170	+	0.953254i	$0.597711\pi$
$458$	−1.94171e6	−0.432535
$459$	−1.40862e6	−0.312076
$460$	−866388.	−0.190905
$461$	−7.46679e6	−1.63637	−0.818185	−	0.574955i	$-0.805020\pi$
$461$	−7.46679e6	−1.63637	−0.818185	+	0.574955i	$0.805020\pi$
$462$	1.83150e6	0.399210
$463$	4.77781e6	1.03580	0.517901	−	0.855441i	$-0.326714\pi$
$463$	4.77781e6	1.03580	0.517901	+	0.855441i	$0.326714\pi$
$464$	−198977.	−0.0429051
$465$	−3.96420e6	−0.850203
$466$	182404.	0.0389107
$467$	935728.	0.198544	0.0992722	−	0.995060i	$-0.468349\pi$
$467$	935728.	0.198544	0.0992722	+	0.995060i	$0.468349\pi$
$468$	3.37173e6	0.711604
$469$	9.02934e6	1.89550
$470$	−1.90025e6	−0.396794
$471$	−1.75269e6	−0.364044
$472$	2.27066e6	0.469134
$473$	−2.72976e6	−0.561011
$474$	5.34481e6	1.09266
$475$	−225625.	−0.0458831
$476$	5.31896e6	1.07599
$477$	−3.26210e6	−0.656450
$478$	5.43134e6	1.08727
$479$	−4.25337e6	−0.847020	−0.423510	−	0.905891i	$-0.639202\pi$
$479$	−4.25337e6	−0.847020	−0.423510	+	0.905891i	$0.639202\pi$
$480$	−3.38393e6	−0.670375
$481$	−6.79712e6	−1.33956
$482$	169854.	0.0333011
$483$	7.54674e6	1.47194
$484$	−299712.	−0.0581556
$485$	−1.55503e6	−0.300183
$486$	4.46039e6	0.856608
$487$	−1.91757e6	−0.366378	−0.183189	−	0.983078i	$-0.558642\pi$
$487$	−1.91757e6	−0.366378	−0.183189	+	0.983078i	$0.558642\pi$
$488$	−2.22044e6	−0.422075
$489$	−3.35778e6	−0.635010
$490$	−1.74727e6	−0.328753
$491$	3.59719e6	0.673379	0.336689	−	0.941616i	$-0.390693\pi$
$491$	3.59719e6	0.673379	0.336689	+	0.941616i	$0.390693\pi$
$492$	−8.95665e6	−1.66814
$493$	5.33497e6	0.988587
$494$	−699879.	−0.129035
$495$	−872627.	−0.160072
$496$	−344714.	−0.0629150
$497$	5.30584e6	0.963525
$498$	2.19242e6	0.396142
$499$	8.86016e6	1.59291	0.796453	−	0.604701i	$-0.206707\pi$
$499$	8.86016e6	1.59291	0.796453	+	0.604701i	$0.206707\pi$
$500$	−319856.	−0.0572175
$501$	−4.99213e6	−0.888570
$502$	292658.	0.0518323
$503$	1.47803e6	0.260474	0.130237	−	0.991483i	$-0.458426\pi$
$503$	1.47803e6	0.260474	0.130237	+	0.991483i	$0.458426\pi$
$504$	9.93805e6	1.74271
$505$	1.82485e6	0.318419
$506$	695543.	0.120767
$507$	−1.04393e6	−0.180364
$508$	−504575.	−0.0867494
$509$	6.65708e6	1.13891	0.569455	−	0.822023i	$-0.307154\pi$
$509$	6.65708e6	1.13891	0.569455	+	0.822023i	$0.307154\pi$
$510$	2.62962e6	0.447679
$511$	1.20705e7	2.04490
$512$	−579982.	−0.0977777
$513$	−378432.	−0.0634884
$514$	−2.03753e6	−0.340171
$515$	3.14360e6	0.522287
$516$	−1.06466e7	−1.76031
$517$	−2.70866e6	−0.445686
$518$	−7.81609e6	−1.27987
$519$	−1.74380e6	−0.284171
$520$	−2.54316e6	−0.412444
$521$	1.94795e6	0.314400	0.157200	−	0.987567i	$-0.449753\pi$
$521$	1.94795e6	0.314400	0.157200	+	0.987567i	$0.449753\pi$
$522$	3.88887e6	0.624665
$523$	5.58772e6	0.893265	0.446633	−	0.894717i	$-0.352623\pi$
$523$	5.58772e6	0.893265	0.446633	+	0.894717i	$0.352623\pi$
$524$	2.15237e6	0.342443
$525$	2.78613e6	0.441166
$526$	−2.06986e6	−0.326195
$527$	9.24245e6	1.44964
$528$	−139801.	−0.0218235
$529$	−3.57034e6	−0.554715
$530$	959919.	0.148438
$531$	3.67652e6	0.565849
$532$	1.42897e6	0.218899
$533$	−1.08365e7	−1.65222
$534$	−1.14434e7	−1.73660
$535$	2.76854e6	0.418183
$536$	8.31942e6	1.25078
$537$	341956.	0.0511722
$538$	1.44583e6	0.215359
$539$	−2.49060e6	−0.369260
$540$	−536481.	−0.0791717
$541$	8.22094e6	1.20761	0.603807	−	0.797130i	$-0.293650\pi$
$541$	8.22094e6	1.20761	0.603807	+	0.797130i	$0.293650\pi$
$542$	728697.	0.106549
$543$	8.81660e6	1.28322
$544$	7.88956e6	1.14302
$545$	−3.30810e6	−0.477076
$546$	8.64245e6	1.24067
$547$	−4.99682e6	−0.714045	−0.357023	−	0.934096i	$-0.616208\pi$
$547$	−4.99682e6	−0.714045	−0.357023	+	0.934096i	$0.616208\pi$
$548$	−2.06035e6	−0.293082
$549$	−3.59521e6	−0.509089
$550$	256783.	0.0361959
$551$	1.43327e6	0.201117
$552$	6.95338e6	0.971289
$553$	−1.32030e7	−1.83594
$554$	−1.23710e6	−0.171250
$555$	6.86102e6	0.945489
$556$	−8.90761e6	−1.22201
$557$	−9.02843e6	−1.23303	−0.616516	−	0.787343i	$-0.711456\pi$
$557$	−9.02843e6	−1.23303	−0.616516	+	0.787343i	$0.711456\pi$
$558$	6.73718e6	0.915994
$559$	−1.28811e7	−1.74351
$560$	242272.	0.0326463
$561$	3.74833e6	0.502841
$562$	−8.61268e6	−1.15026
$563$	1.56949e6	0.208683	0.104341	−	0.994542i	$-0.466727\pi$
$563$	1.56949e6	0.208683	0.104341	+	0.994542i	$0.466727\pi$
$564$	−1.05644e7	−1.39845
$565$	−3.05918e6	−0.403166
$566$	−2.40367e6	−0.315380
$567$	−8.88165e6	−1.16021
$568$	4.88867e6	0.635799
$569$	−4.52149e6	−0.585465	−0.292732	−	0.956194i	$-0.594565\pi$
$569$	−4.52149e6	−0.585465	−0.292732	+	0.956194i	$0.594565\pi$
$570$	706460.	0.0910752
$571$	1.19717e7	1.53661	0.768306	−	0.640082i	$-0.221100\pi$
$571$	1.19717e7	1.53661	0.768306	+	0.640082i	$0.221100\pi$
$572$	−1.41428e6	−0.180736
$573$	9.57400e6	1.21817
$574$	−1.24610e7	−1.57860
$575$	1.05808e6	0.133459
$576$	5.28838e6	0.664150
$577$	2.55522e6	0.319513	0.159756	−	0.987156i	$-0.448929\pi$
$577$	2.55522e6	0.319513	0.159756	+	0.987156i	$0.448929\pi$
$578$	−1.30982e6	−0.163077
$579$	−1.48801e7	−1.84463
$580$	2.03186e6	0.250798
$581$	−5.41582e6	−0.665617
$582$	4.86900e6	0.595844
$583$	1.36830e6	0.166728
$584$	1.11214e7	1.34936
$585$	−4.11774e6	−0.497473
$586$	711247.	0.0855612
$587$	−9.66827e6	−1.15812	−0.579060	−	0.815285i	$-0.696580\pi$
$587$	−9.66827e6	−1.15812	−0.579060	+	0.815285i	$0.696580\pi$
$588$	−9.71390e6	−1.15864
$589$	2.48303e6	0.294913
$590$	−1.08187e6	−0.127951
$591$	−8.97339e6	−1.05679
$592$	596612.	0.0699662
$593$	−2.19018e6	−0.255766	−0.127883	−	0.991789i	$-0.540818\pi$
$593$	−2.19018e6	−0.255766	−0.127883	+	0.991789i	$0.540818\pi$
$594$	430691.	0.0500841
$595$	−6.49580e6	−0.752212
$596$	−1.65431e6	−0.190766
$597$	−3.87716e6	−0.445223
$598$	3.28212e6	0.375320
$599$	1.23001e7	1.40069	0.700343	−	0.713807i	$-0.253031\pi$
$599$	1.23001e7	1.40069	0.700343	+	0.713807i	$0.253031\pi$
$600$	2.56707e6	0.291112
$601$	8.42005e6	0.950886	0.475443	−	0.879746i	$-0.342288\pi$
$601$	8.42005e6	0.950886	0.475443	+	0.879746i	$0.342288\pi$
$602$	−1.48122e7	−1.66582
$603$	1.34703e7	1.50864
$604$	−9.33733e6	−1.04143
$605$	366025.	0.0406558
$606$	−5.71383e6	−0.632041
$607$	−1.32299e7	−1.45742	−0.728710	−	0.684823i	$-0.759880\pi$
$607$	−1.32299e7	−1.45742	−0.728710	+	0.684823i	$0.759880\pi$
$608$	2.11957e6	0.232535
$609$	−1.76987e7	−1.93374
$610$	1.05794e6	0.115116
$611$	−1.27816e7	−1.38510
$612$	7.93504e6	0.856388
$613$	3.01071e6	0.323607	0.161803	−	0.986823i	$-0.448269\pi$
$613$	3.01071e6	0.323607	0.161803	+	0.986823i	$0.448269\pi$
$614$	1.63987e6	0.175545
$615$	1.09383e7	1.16617
$616$	−4.16854e6	−0.442621
$617$	1.60371e7	1.69595	0.847975	−	0.530037i	$-0.177822\pi$
$617$	1.60371e7	1.69595	0.847975	+	0.530037i	$0.177822\pi$
$618$	−9.84301e6	−1.03671
$619$	−6.44044e6	−0.675599	−0.337799	−	0.941218i	$-0.609683\pi$
$619$	−6.44044e6	−0.675599	−0.337799	+	0.941218i	$0.609683\pi$
$620$	3.52005e6	0.367765
$621$	1.77468e6	0.184667
$622$	5.60621e6	0.581023
$623$	2.82679e7	2.91792
$624$	−659689.	−0.0678231
$625$	390625.	0.0400000
$626$	−1.10272e7	−1.12468
$627$	1.00701e6	0.102297
$628$	1.55632e6	0.157471
$629$	−1.59964e7	−1.61211
$630$	−4.73504e6	−0.475305
$631$	−5.64501e6	−0.564406	−0.282203	−	0.959355i	$-0.591065\pi$
$631$	−5.64501e6	−0.564406	−0.282203	+	0.959355i	$0.591065\pi$
$632$	−1.21649e7	−1.21148
$633$	2.02081e7	2.00454
$634$	−6.71568e6	−0.663540
$635$	616214.	0.0606453
$636$	5.33665e6	0.523149
$637$	−1.17526e7	−1.14759
$638$	−1.63119e6	−0.158655
$639$	7.91546e6	0.766874
$640$	3.14093e6	0.303116
$641$	8.70262e6	0.836575	0.418288	−	0.908315i	$-0.362630\pi$
$641$	8.70262e6	0.836575	0.418288	+	0.908315i	$0.362630\pi$
$642$	−8.66865e6	−0.830069
$643$	−4.97276e6	−0.474318	−0.237159	−	0.971471i	$-0.576216\pi$
$643$	−4.97276e6	−0.474318	−0.237159	+	0.971471i	$0.576216\pi$
$644$	−6.70121e6	−0.636706
$645$	1.30023e7	1.23061
$646$	−1.64710e6	−0.155288
$647$	−1.28760e7	−1.20927	−0.604633	−	0.796504i	$-0.706680\pi$
$647$	−1.28760e7	−1.20927	−0.604633	+	0.796504i	$0.706680\pi$
$648$	−8.18334e6	−0.765584
$649$	−1.54212e6	−0.143717
$650$	1.21170e6	0.112490
$651$	−3.06617e7	−2.83559
$652$	2.98158e6	0.274680
$653$	1.17595e7	1.07921	0.539607	−	0.841917i	$-0.318573\pi$
$653$	1.17595e7	1.07921	0.539607	+	0.841917i	$0.318573\pi$
$654$	1.03581e7	0.946966
$655$	−2.62859e6	−0.239397
$656$	951163.	0.0862969
$657$	1.80072e7	1.62754
$658$	−1.46977e7	−1.32338
$659$	−8.41664e6	−0.754963	−0.377481	−	0.926017i	$-0.623210\pi$
$659$	−8.41664e6	−0.754963	−0.377481	+	0.926017i	$0.623210\pi$
$660$	1.42758e6	0.127567
$661$	8.08307e6	0.719569	0.359785	−	0.933035i	$-0.382850\pi$
$661$	8.08307e6	0.719569	0.359785	+	0.933035i	$0.382850\pi$
$662$	1.74307e6	0.154586
$663$	1.76876e7	1.56273
$664$	−4.99001e6	−0.439219
$665$	−1.74513e6	−0.153029
$666$	−1.16604e7	−1.01865
$667$	−6.72138e6	−0.584984
$668$	4.43282e6	0.384361
$669$	−3.37581e7	−2.91617
$670$	−3.96383e6	−0.341137
$671$	1.50802e6	0.129301
$672$	−2.61735e7	−2.23583
$673$	−1.17255e7	−0.997913	−0.498957	−	0.866627i	$-0.666283\pi$
$673$	−1.17255e7	−0.997913	−0.498957	+	0.866627i	$0.666283\pi$
$674$	8.22528e6	0.697430
$675$	655180.	0.0553479
$676$	926967.	0.0780185
$677$	−8.99430e6	−0.754216	−0.377108	−	0.926169i	$-0.623081\pi$
$677$	−8.99430e6	−0.754216	−0.377108	+	0.926169i	$0.623081\pi$
$678$	9.57868e6	0.800260
$679$	−1.20276e7	−1.00117
$680$	−5.98508e6	−0.496361
$681$	3.16341e7	2.61389
$682$	−2.82593e6	−0.232648
$683$	1.89415e7	1.55369	0.776843	−	0.629694i	$-0.216820\pi$
$683$	1.89415e7	1.55369	0.776843	+	0.629694i	$0.216820\pi$
$684$	2.13179e6	0.174222
$685$	2.51621e6	0.204890
$686$	−2.47954e6	−0.201169
$687$	1.31833e7	1.06569
$688$	1.13063e6	0.0910649
$689$	6.45669e6	0.518158
$690$	−3.31298e6	−0.264909
$691$	1.25451e7	0.999494	0.499747	−	0.866171i	$-0.333426\pi$
$691$	1.25451e7	0.999494	0.499747	+	0.866171i	$0.333426\pi$
$692$	1.54843e6	0.122921
$693$	−6.74946e6	−0.533871
$694$	1.42546e7	1.12346
$695$	1.08784e7	0.854289
$696$	−1.63071e7	−1.27601
$697$	−2.55025e7	−1.98839
$698$	1.24757e7	0.969232
$699$	−1.23843e6	−0.0958694
$700$	−2.47397e6	−0.190831
$701$	1.82197e7	1.40038	0.700190	−	0.713956i	$-0.253099\pi$
$701$	1.82197e7	1.40038	0.700190	+	0.713956i	$0.253099\pi$
$702$	2.03234e6	0.155652
$703$	−4.29750e6	−0.327965
$704$	−2.21822e6	−0.168684
$705$	1.29018e7	0.977635
$706$	5.43134e6	0.410105
$707$	1.41146e7	1.06199
$708$	−6.01462e6	−0.450946
$709$	−6.03597e6	−0.450953	−0.225476	−	0.974249i	$-0.572394\pi$
$709$	−6.03597e6	−0.450953	−0.225476	+	0.974249i	$0.572394\pi$
$710$	−2.32924e6	−0.173407
$711$	−1.96968e7	−1.46124
$712$	2.60454e7	1.92545
$713$	−1.16443e7	−0.857807
$714$	2.03392e7	1.49310
$715$	1.72719e6	0.126350
$716$	−303644.	−0.0221351
$717$	−3.68763e7	−2.67885
$718$	−8.66974e6	−0.627617
$719$	−1.32439e7	−0.955417	−0.477709	−	0.878518i	$-0.658533\pi$
$719$	−1.32439e7	−0.955417	−0.477709	+	0.878518i	$0.658533\pi$
$720$	361432.	0.0259834
$721$	2.43147e7	1.74193
$722$	−442501.	−0.0315916
$723$	−1.15323e6	−0.0820483
$724$	−7.82880e6	−0.555071
$725$	−2.48142e6	−0.175330
$726$	−1.14607e6	−0.0806992
$727$	−8.50634e6	−0.596907	−0.298453	−	0.954424i	$-0.596471\pi$
$727$	−8.50634e6	−0.596907	−0.298453	+	0.954424i	$0.596471\pi$
$728$	−1.96704e7	−1.37558
$729$	−1.91225e7	−1.33268
$730$	−5.29887e6	−0.368024
$731$	−3.03145e7	−2.09825
$732$	5.88161e6	0.405712
$733$	2.30762e7	1.58637	0.793185	−	0.608981i	$-0.208421\pi$
$733$	2.30762e7	1.58637	0.793185	+	0.608981i	$0.208421\pi$
$734$	1.87848e6	0.128696
$735$	1.18631e7	0.809993
$736$	−9.93984e6	−0.676371
$737$	−5.65016e6	−0.383170
$738$	−1.85898e7	−1.25642
$739$	−1.40421e7	−0.945844	−0.472922	−	0.881104i	$-0.656801\pi$
$739$	−1.40421e7	−0.945844	−0.472922	+	0.881104i	$0.656801\pi$
$740$	−6.09232e6	−0.408982
$741$	4.75185e6	0.317920
$742$	7.42464e6	0.495069
$743$	−2.07885e7	−1.38150	−0.690752	−	0.723092i	$-0.742720\pi$
$743$	−2.07885e7	−1.38150	−0.690752	+	0.723092i	$0.742720\pi$
$744$	−2.82509e7	−1.87111
$745$	2.02033e6	0.133362
$746$	672072.	0.0442149
$747$	−8.07955e6	−0.529768
$748$	−3.32837e6	−0.217509
$749$	2.14137e7	1.39472
$750$	−1.22310e6	−0.0793976
$751$	−597868.	−0.0386817	−0.0193408	−	0.999813i	$-0.506157\pi$
$751$	−597868.	−0.0386817	−0.0193408	+	0.999813i	$0.506157\pi$
$752$	1.12190e6	0.0723450
$753$	−1.98701e6	−0.127706
$754$	−7.69726e6	−0.493069
$755$	1.14032e7	0.728050
$756$	−4.14949e6	−0.264053
$757$	9.37643e6	0.594700	0.297350	−	0.954769i	$-0.403897\pi$
$757$	9.37643e6	0.594700	0.297350	+	0.954769i	$0.403897\pi$
$758$	4.40818e6	0.278668
$759$	−4.72241e6	−0.297550
$760$	−1.60792e6	−0.100979
$761$	−2.86057e7	−1.79057	−0.895284	−	0.445496i	$-0.853027\pi$
$761$	−2.86057e7	−1.79057	−0.895284	+	0.445496i	$0.853027\pi$
$762$	−1.92944e6	−0.120377
$763$	−2.55870e7	−1.59114
$764$	−8.50134e6	−0.526932
$765$	−9.69070e6	−0.598690
$766$	−1.58192e7	−0.974120
$767$	−7.27695e6	−0.446644
$768$	−2.33588e7	−1.42905
$769$	−7.96608e6	−0.485768	−0.242884	−	0.970055i	$-0.578093\pi$
$769$	−7.96608e6	−0.485768	−0.242884	+	0.970055i	$0.578093\pi$
$770$	1.98612e6	0.120720
$771$	1.38339e7	0.838125
$772$	1.32130e7	0.797916
$773$	−1.43550e7	−0.864080	−0.432040	−	0.901855i	$-0.642206\pi$
$773$	−1.43550e7	−0.864080	−0.432040	+	0.901855i	$0.642206\pi$
$774$	−2.20974e7	−1.32583
$775$	−4.29888e6	−0.257099
$776$	−1.10820e7	−0.660637
$777$	5.30676e7	3.15339
$778$	5.22873e6	0.309704
$779$	−6.85139e6	−0.404515
$780$	6.73643e6	0.396455
$781$	−3.32016e6	−0.194774
$782$	7.72415e6	0.451683
$783$	−4.16198e6	−0.242603
$784$	1.03158e6	0.0599394
$785$	−1.90067e6	−0.110086
$786$	8.23043e6	0.475189
$787$	−1.06584e7	−0.613416	−0.306708	−	0.951804i	$-0.599228\pi$
$787$	−1.06584e7	−0.613416	−0.306708	+	0.951804i	$0.599228\pi$
$788$	7.96802e6	0.457125
$789$	1.40534e7	0.803691
$790$	5.79605e6	0.330418
$791$	−2.36617e7	−1.34464
$792$	−6.21879e6	−0.352284
$793$	7.11603e6	0.401841
$794$	1.23563e7	0.695563
$795$	−6.51740e6	−0.365727
$796$	3.44277e6	0.192586
$797$	−3.21789e7	−1.79443	−0.897214	−	0.441597i	$-0.854412\pi$
$797$	−3.21789e7	−1.79443	−0.897214	+	0.441597i	$0.854412\pi$
$798$	5.46422e6	0.303753
$799$	−3.00803e7	−1.66692
$800$	−3.66962e6	−0.202720
$801$	4.21713e7	2.32239
$802$	−2.33050e6	−0.127942
$803$	−7.55315e6	−0.413370
$804$	−2.20368e7	−1.20229
$805$	8.18388e6	0.445112
$806$	−1.33349e7	−0.723025
$807$	−9.81654e6	−0.530609
$808$	1.30048e7	0.700771
$809$	−1.26092e7	−0.677355	−0.338678	−	0.940902i	$-0.609980\pi$
$809$	−1.26092e7	−0.677355	−0.338678	+	0.940902i	$0.609980\pi$
$810$	3.89900e6	0.208805
$811$	−1.61374e7	−0.861551	−0.430775	−	0.902459i	$-0.641760\pi$
$811$	−1.61374e7	−0.861551	−0.430775	+	0.902459i	$0.641760\pi$
$812$	1.57157e7	0.836459
$813$	−4.94751e6	−0.262519
$814$	4.89096e6	0.258722
$815$	−3.64127e6	−0.192025
$816$	−1.55251e6	−0.0816226
$817$	−8.14415e6	−0.426865
$818$	−1.89964e6	−0.0992633
$819$	−3.18493e7	−1.65917
$820$	−9.71282e6	−0.504441
$821$	−1.07737e7	−0.557837	−0.278919	−	0.960315i	$-0.589976\pi$
$821$	−1.07737e7	−0.557837	−0.278919	+	0.960315i	$0.589976\pi$
$822$	−7.87856e6	−0.406694
$823$	−2.65400e7	−1.36585	−0.682923	−	0.730490i	$-0.739292\pi$
$823$	−2.65400e7	−1.36585	−0.682923	+	0.730490i	$0.739292\pi$
$824$	2.24030e7	1.14944
$825$	−1.74343e6	−0.0891806
$826$	−8.36787e6	−0.426741
$827$	2.93658e7	1.49306	0.746530	−	0.665351i	$-0.231718\pi$
$827$	2.93658e7	1.49306	0.746530	+	0.665351i	$0.231718\pi$
$828$	−9.99714e6	−0.506757
$829$	−1.57879e7	−0.797881	−0.398940	−	0.916977i	$-0.630622\pi$
$829$	−1.57879e7	−0.797881	−0.398940	+	0.916977i	$0.630622\pi$
$830$	2.37752e6	0.119792
$831$	8.39933e6	0.421932
$832$	−1.04673e7	−0.524236
$833$	−2.76587e7	−1.38108
$834$	−3.40618e7	−1.69571
$835$	−5.41360e6	−0.268701
$836$	−894184.	−0.0442498
$837$	−7.21033e6	−0.355747
$838$	7.25700e6	0.356982
$839$	3.31591e7	1.62629	0.813144	−	0.582063i	$-0.197754\pi$
$839$	3.31591e7	1.62629	0.813144	+	0.582063i	$0.197754\pi$
$840$	1.98554e7	0.970913
$841$	−4.74811e6	−0.231489
$842$	−2.20162e7	−1.07019
$843$	5.84761e7	2.83406
$844$	−1.79440e7	−0.867087
$845$	−1.13206e6	−0.0545417
$846$	−2.19267e7	−1.05329
$847$	2.83108e6	0.135595
$848$	−566732.	−0.0270638
$849$	1.63198e7	0.777045
$850$	2.85162e6	0.135377
$851$	2.01534e7	0.953946
$852$	−1.29493e7	−0.611151
$853$	−2.60608e7	−1.22635	−0.613175	−	0.789947i	$-0.710108\pi$
$853$	−2.60608e7	−1.22635	−0.613175	+	0.789947i	$0.710108\pi$
$854$	8.18281e6	0.383935
$855$	−2.60346e6	−0.121797
$856$	1.97301e7	0.920332
$857$	2.65262e7	1.23374	0.616870	−	0.787065i	$-0.288400\pi$
$857$	2.65262e7	1.23374	0.616870	+	0.787065i	$0.288400\pi$
$858$	−5.40806e6	−0.250798
$859$	−1.07061e7	−0.495050	−0.247525	−	0.968881i	$-0.579617\pi$
$859$	−1.07061e7	−0.495050	−0.247525	+	0.968881i	$0.579617\pi$
$860$	−1.15455e7	−0.532312
$861$	8.46042e7	3.88941
$862$	315623.	0.0144677
$863$	2.26763e7	1.03644	0.518221	−	0.855247i	$-0.326595\pi$
$863$	2.26763e7	1.03644	0.518221	+	0.855247i	$0.326595\pi$
$864$	−6.15490e6	−0.280502
$865$	−1.89103e6	−0.0859325
$866$	−1.16899e7	−0.529683
$867$	8.89306e6	0.401794
$868$	2.72264e7	1.22656
$869$	8.26184e6	0.371131
$870$	7.76963e6	0.348018
$871$	−2.66619e7	−1.19082
$872$	−2.35752e7	−1.04994
$873$	−1.79433e7	−0.796833
$874$	2.07513e6	0.0918898
$875$	3.02135e6	0.133408
$876$	−2.94589e7	−1.29705
$877$	−3.36737e7	−1.47840	−0.739201	−	0.673485i	$-0.764796\pi$
$877$	−3.36737e7	−1.47840	−0.739201	+	0.673485i	$0.764796\pi$
$878$	−9.25071e6	−0.404985
$879$	−4.82904e6	−0.210809
$880$	−151603.	−0.00659936
$881$	3.75436e6	0.162966	0.0814828	−	0.996675i	$-0.474034\pi$
$881$	3.75436e6	0.162966	0.0814828	+	0.996675i	$0.474034\pi$
$882$	−2.01615e7	−0.872672
$883$	−1.04320e7	−0.450264	−0.225132	−	0.974328i	$-0.572281\pi$
$883$	−1.04320e7	−0.450264	−0.225132	+	0.974328i	$0.572281\pi$
$884$	−1.57059e7	−0.675976
$885$	7.34537e6	0.315250
$886$	2.68021e7	1.14706
$887$	−2.04659e7	−0.873417	−0.436708	−	0.899603i	$-0.643856\pi$
$887$	−2.04659e7	−0.873417	−0.436708	+	0.899603i	$0.643856\pi$
$888$	4.88952e7	2.08082
$889$	4.76620e6	0.202264
$890$	−1.24095e7	−0.525144
$891$	5.55774e6	0.234533
$892$	2.99759e7	1.26142
$893$	−8.08122e6	−0.339116
$894$	−6.32590e6	−0.264715
$895$	370826.	0.0154743
$896$	2.42940e7	1.01095
$897$	−2.22841e7	−0.924726
$898$	−4.79509e6	−0.198429
$899$	2.73083e7	1.12693
$900$	−3.69077e6	−0.151884
$901$	1.51952e7	0.623583
$902$	7.79753e6	0.319110
$903$	1.00568e8	4.10431
$904$	−2.18013e7	−0.887282
$905$	9.56095e6	0.388043
$906$	−3.57050e7	−1.44513
$907$	−4.55980e7	−1.84046	−0.920232	−	0.391374i	$-0.872000\pi$
$907$	−4.55980e7	−1.84046	−0.920232	+	0.391374i	$0.872000\pi$
$908$	−2.80899e7	−1.13067
$909$	2.10567e7	0.845240
$910$	9.37210e6	0.375174
$911$	−1.27498e6	−0.0508988	−0.0254494	−	0.999676i	$-0.508102\pi$
$911$	−1.27498e6	−0.0508988	−0.0254494	+	0.999676i	$0.508102\pi$
$912$	−417091.	−0.0166052
$913$	3.38898e6	0.134553
$914$	9.16161e6	0.362749
$915$	−7.18293e6	−0.283628
$916$	−1.17063e7	−0.460978
$917$	−2.03312e7	−0.798435
$918$	4.78292e6	0.187321
$919$	4.47506e6	0.174788	0.0873938	−	0.996174i	$-0.472146\pi$
$919$	4.47506e6	0.174788	0.0873938	+	0.996174i	$0.472146\pi$
$920$	7.54043e6	0.293715
$921$	−1.11340e7	−0.432515
$922$	2.53533e7	0.982216
$923$	−1.56671e7	−0.605320
$924$	1.10418e7	0.425461
$925$	7.44027e6	0.285913
$926$	−1.62229e7	−0.621730
$927$	3.62736e7	1.38641
$928$	2.33110e7	0.888568
$929$	−1.64772e7	−0.626387	−0.313194	−	0.949689i	$-0.601399\pi$
$929$	−1.64772e7	−0.626387	−0.313194	+	0.949689i	$0.601399\pi$
$930$	1.34603e7	0.510326
$931$	−7.43065e6	−0.280965
$932$	1.09968e6	0.0414694
$933$	−3.80635e7	−1.43155
$934$	−3.17724e6	−0.119174
$935$	4.06478e6	0.152058
$936$	−2.93452e7	−1.09483
$937$	2.25142e7	0.837736	0.418868	−	0.908047i	$-0.362427\pi$
$937$	2.25142e7	0.837736	0.418868	+	0.908047i	$0.362427\pi$
$938$	−3.06589e7	−1.13776
$939$	7.48698e7	2.77104
$940$	−1.14563e7	−0.422887
$941$	6.64021e6	0.244460	0.122230	−	0.992502i	$-0.460995\pi$
$941$	6.64021e6	0.244460	0.122230	+	0.992502i	$0.460995\pi$
$942$	5.95122e6	0.218514
$943$	3.21299e7	1.17660
$944$	638730.	0.0233285
$945$	5.06758e6	0.184596
$946$	9.26881e6	0.336741
$947$	−4.14102e7	−1.50049	−0.750245	−	0.661160i	$-0.770064\pi$
$947$	−4.14102e7	−1.50049	−0.750245	+	0.661160i	$0.770064\pi$
$948$	3.22230e7	1.16451
$949$	−3.56417e7	−1.28467
$950$	766103.	0.0275409
$951$	4.55963e7	1.63485
$952$	−4.62925e7	−1.65546
$953$	−1.86337e7	−0.664610	−0.332305	−	0.943172i	$-0.607826\pi$
$953$	−1.86337e7	−0.664610	−0.332305	+	0.943172i	$0.607826\pi$
$954$	1.10764e7	0.394028
$955$	1.03823e7	0.368371
$956$	3.27447e7	1.15877
$957$	1.10750e7	0.390900
$958$	1.44422e7	0.508416
$959$	1.94620e7	0.683347
$960$	1.05657e7	0.370017
$961$	1.86805e7	0.652501
$962$	2.30794e7	0.804058
$963$	3.19458e7	1.11007
$964$	1.02402e6	0.0354909
$965$	−1.61364e7	−0.557812
$966$	−2.56247e7	−0.883521
$967$	−3.36856e6	−0.115845	−0.0579226	−	0.998321i	$-0.518448\pi$
$967$	−3.36856e6	−0.115845	−0.0579226	+	0.998321i	$0.518448\pi$
$968$	2.60849e6	0.0894746
$969$	1.11830e7	0.382604
$970$	5.28007e6	0.180182
$971$	2.30784e7	0.785519	0.392760	−	0.919641i	$-0.371520\pi$
$971$	2.30784e7	0.785519	0.392760	+	0.919641i	$0.371520\pi$
$972$	2.68910e7	0.912938
$973$	8.41410e7	2.84922
$974$	6.51107e6	0.219915
$975$	−8.22689e6	−0.277156
$976$	−624605.	−0.0209885
$977$	−1.67793e7	−0.562389	−0.281194	−	0.959651i	$-0.590731\pi$
$977$	−1.67793e7	−0.562389	−0.281194	+	0.959651i	$0.590731\pi$
$978$	1.14013e7	0.381158
$979$	−1.76888e7	−0.589851
$980$	−1.05340e7	−0.350371
$981$	−3.81717e7	−1.26640
$982$	−1.22142e7	−0.404189
$983$	7.05173e6	0.232762	0.116381	−	0.993205i	$-0.462871\pi$
$983$	7.05173e6	0.232762	0.116381	+	0.993205i	$0.462871\pi$
$984$	7.79523e7	2.56650
$985$	−9.73098e6	−0.319570
$986$	−1.81148e7	−0.593390
$987$	9.97908e7	3.26060
$988$	−4.21946e6	−0.137520
$989$	3.81924e7	1.24161
$990$	2.96298e6	0.0960817
$991$	1.17050e7	0.378605	0.189302	−	0.981919i	$-0.439377\pi$
$991$	1.17050e7	0.378605	0.189302	+	0.981919i	$0.439377\pi$
$992$	4.03846e7	1.30298
$993$	−1.18346e7	−0.380874
$994$	−1.80158e7	−0.578347
$995$	−4.20449e6	−0.134634
$996$	1.32178e7	0.422192
$997$	−1.87984e7	−0.598940	−0.299470	−	0.954106i	$-0.596810\pi$
$997$	−1.87984e7	−0.598940	−0.299470	+	0.954106i	$0.596810\pi$
$998$	−3.00844e7	−0.956126
$999$	1.24793e7	0.395618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-3.39547 q^{2} +23.0537 q^{3} -20.4708 q^{4} +25.0000 q^{5} -78.2781 q^{6} +193.366 q^{7} +178.163 q^{8} +288.472 q^{9} +O(q^{10})\)	\(q-3.39547 q^{2} +23.0537 q^{3} -20.4708 q^{4} +25.0000 q^{5} -78.2781 q^{6} +193.366 q^{7} +178.163 q^{8} +288.472 q^{9} -84.8868 q^{10} -121.000 q^{11} -471.926 q^{12} -570.973 q^{13} -656.570 q^{14} +576.342 q^{15} +50.1168 q^{16} -1343.73 q^{17} -979.497 q^{18} -361.000 q^{19} -511.769 q^{20} +4457.80 q^{21} +410.852 q^{22} +1692.93 q^{23} +4107.31 q^{24} +625.000 q^{25} +1938.72 q^{26} +1048.29 q^{27} -3958.36 q^{28} -3970.27 q^{29} -1956.95 q^{30} -6878.20 q^{31} -5871.39 q^{32} -2789.49 q^{33} +4562.60 q^{34} +4834.16 q^{35} -5905.23 q^{36} +11904.4 q^{37} +1225.77 q^{38} -13163.0 q^{39} +4454.08 q^{40} +18978.9 q^{41} -15136.3 q^{42} +22560.0 q^{43} +2476.96 q^{44} +7211.79 q^{45} -5748.29 q^{46} +22385.6 q^{47} +1155.38 q^{48} +20583.5 q^{49} -2122.17 q^{50} -30977.9 q^{51} +11688.3 q^{52} -11308.2 q^{53} -3559.43 q^{54} -3025.00 q^{55} +34450.7 q^{56} -8322.37 q^{57} +13480.9 q^{58} +12744.8 q^{59} -11798.2 q^{60} -12463.0 q^{61} +23354.8 q^{62} +55780.7 q^{63} +18332.4 q^{64} -14274.3 q^{65} +9471.65 q^{66} +46695.5 q^{67} +27507.2 q^{68} +39028.2 q^{69} -16414.2 q^{70} +27439.3 q^{71} +51395.0 q^{72} +62422.8 q^{73} -40421.2 q^{74} +14408.5 q^{75} +7389.95 q^{76} -23397.3 q^{77} +44694.7 q^{78} -68279.7 q^{79} +1252.92 q^{80} -45931.7 q^{81} -64442.4 q^{82} -28008.1 q^{83} -91254.6 q^{84} -33593.3 q^{85} -76601.8 q^{86} -91529.3 q^{87} -21557.7 q^{88} +146189. q^{89} -24487.4 q^{90} -110407. q^{91} -34655.5 q^{92} -158568. q^{93} -76009.8 q^{94} -9025.00 q^{95} -135357. q^{96} -62201.3 q^{97} -69890.7 q^{98} -34905.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more