LMFDB - Embedded newform 1045.6.a.f.1.20

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			1.20
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)

$f(q)$	$=$	$q+0.514635 q^{2} -15.6824 q^{3} -31.7352 q^{4} +25.0000 q^{5} -8.07072 q^{6} +177.020 q^{7} -32.8003 q^{8} +2.93807 q^{9} +O(q^{10})$	\(q+0.514635 q^{2} -15.6824 q^{3} -31.7352 q^{4} +25.0000 q^{5} -8.07072 q^{6} +177.020 q^{7} -32.8003 q^{8} +2.93807 q^{9} +12.8659 q^{10} -121.000 q^{11} +497.684 q^{12} -253.519 q^{13} +91.1008 q^{14} -392.060 q^{15} +998.645 q^{16} +1422.16 q^{17} +1.51203 q^{18} -361.000 q^{19} -793.379 q^{20} -2776.10 q^{21} -62.2708 q^{22} +1259.36 q^{23} +514.389 q^{24} +625.000 q^{25} -130.470 q^{26} +3764.75 q^{27} -5617.76 q^{28} +5122.69 q^{29} -201.768 q^{30} -3221.17 q^{31} +1563.55 q^{32} +1897.57 q^{33} +731.893 q^{34} +4425.51 q^{35} -93.2401 q^{36} +1761.26 q^{37} -185.783 q^{38} +3975.79 q^{39} -820.009 q^{40} +3745.08 q^{41} -1428.68 q^{42} -838.553 q^{43} +3839.95 q^{44} +73.4517 q^{45} +648.113 q^{46} -1076.89 q^{47} -15661.2 q^{48} +14529.2 q^{49} +321.647 q^{50} -22302.9 q^{51} +8045.47 q^{52} -23028.1 q^{53} +1937.47 q^{54} -3025.00 q^{55} -5806.33 q^{56} +5661.35 q^{57} +2636.32 q^{58} -16062.8 q^{59} +12442.1 q^{60} +21615.4 q^{61} -1657.73 q^{62} +520.098 q^{63} -31152.0 q^{64} -6337.98 q^{65} +976.557 q^{66} +34355.7 q^{67} -45132.4 q^{68} -19749.9 q^{69} +2277.52 q^{70} +11202.2 q^{71} -96.3697 q^{72} -68701.0 q^{73} +906.408 q^{74} -9801.51 q^{75} +11456.4 q^{76} -21419.5 q^{77} +2046.08 q^{78} +37311.5 q^{79} +24966.1 q^{80} -59754.3 q^{81} +1927.35 q^{82} +1115.08 q^{83} +88100.1 q^{84} +35554.0 q^{85} -431.549 q^{86} -80336.2 q^{87} +3968.84 q^{88} +37899.8 q^{89} +37.8008 q^{90} -44878.0 q^{91} -39966.1 q^{92} +50515.8 q^{93} -554.205 q^{94} -9025.00 q^{95} -24520.2 q^{96} -47346.1 q^{97} +7477.22 q^{98} -355.506 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.514635	0.0909755	0.0454877	−	0.998965i	$-0.485516\pi$
$2$	0.514635	0.0909755	0.0454877	+	0.998965i	$0.485516\pi$
$3$	−15.6824	−1.00603	−0.503014	−	0.864278i	$-0.667775\pi$
$3$	−15.6824	−1.00603	−0.503014	+	0.864278i	$0.667775\pi$
$4$	−31.7352	−0.991723
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−8.07072	−0.0915238
$7$	177.020	1.36546	0.682728	−	0.730672i	$-0.260793\pi$
$7$	177.020	1.36546	0.682728	+	0.730672i	$0.260793\pi$
$8$	−32.8003	−0.181198
$9$	2.93807	0.0120908
$10$	12.8659	0.0406855
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	497.684	0.997701
$13$	−253.519	−0.416057	−0.208028	−	0.978123i	$-0.566705\pi$
$13$	−253.519	−0.416057	−0.208028	+	0.978123i	$0.566705\pi$
$14$	91.1008	0.124223
$15$	−392.060	−0.449909
$16$	998.645	0.975239
$17$	1422.16	1.19351	0.596754	−	0.802424i	$-0.296457\pi$
$17$	1422.16	1.19351	0.596754	+	0.802424i	$0.296457\pi$
$18$	1.51203	0.00109997
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−793.379	−0.443512
$21$	−2776.10	−1.37369
$22$	−62.2708	−0.0274301
$23$	1259.36	0.496400	0.248200	−	0.968709i	$-0.420161\pi$
$23$	1259.36	0.496400	0.248200	+	0.968709i	$0.420161\pi$
$24$	514.389	0.182290
$25$	625.000	0.200000
$26$	−130.470	−0.0378510
$27$	3764.75	0.993864
$28$	−5617.76	−1.35416
$29$	5122.69	1.13111	0.565553	−	0.824712i	$-0.308663\pi$
$29$	5122.69	1.13111	0.565553	+	0.824712i	$0.308663\pi$
$30$	−201.768	−0.0409307
$31$	−3221.17	−0.602019	−0.301009	−	0.953621i	$-0.597324\pi$
$31$	−3221.17	−0.602019	−0.301009	+	0.953621i	$0.597324\pi$
$32$	1563.55	0.269921
$33$	1897.57	0.303329
$34$	731.893	0.108580
$35$	4425.51	0.610651
$36$	−93.2401	−0.0119908
$37$	1761.26	0.211505	0.105752	−	0.994392i	$-0.466275\pi$
$37$	1761.26	0.211505	0.105752	+	0.994392i	$0.466275\pi$
$38$	−185.783	−0.0208712
$39$	3975.79	0.418564
$40$	−820.009	−0.0810342
$41$	3745.08	0.347938	0.173969	−	0.984751i	$-0.444341\pi$
$41$	3745.08	0.347938	0.173969	+	0.984751i	$0.444341\pi$
$42$	−1428.68	−0.124972
$43$	−838.553	−0.0691607	−0.0345804	−	0.999402i	$-0.511009\pi$
$43$	−838.553	−0.0691607	−0.0345804	+	0.999402i	$0.511009\pi$
$44$	3839.95	0.299016
$45$	73.4517	0.00540718
$46$	648.113	0.0451603
$47$	−1076.89	−0.0711093	−0.0355547	−	0.999368i	$-0.511320\pi$
$47$	−1076.89	−0.0711093	−0.0355547	+	0.999368i	$0.511320\pi$
$48$	−15661.2	−0.981117
$49$	14529.2	0.864471
$50$	321.647	0.0181951
$51$	−22302.9	−1.20070
$52$	8045.47	0.412613
$53$	−23028.1	−1.12608	−0.563039	−	0.826430i	$-0.690368\pi$
$53$	−23028.1	−1.12608	−0.563039	+	0.826430i	$0.690368\pi$
$54$	1937.47	0.0904172
$55$	−3025.00	−0.134840
$56$	−5806.33	−0.247418
$57$	5661.35	0.230798
$58$	2636.32	0.102903
$59$	−16062.8	−0.600747	−0.300373	−	0.953822i	$-0.597111\pi$
$59$	−16062.8	−0.600747	−0.300373	+	0.953822i	$0.597111\pi$
$60$	12442.1	0.446185
$61$	21615.4	0.743769	0.371884	−	0.928279i	$-0.378712\pi$
$61$	21615.4	0.743769	0.371884	+	0.928279i	$0.378712\pi$
$62$	−1657.73	−0.0547689
$63$	520.098	0.0165095
$64$	−31152.0	−0.950683
$65$	−6337.98	−0.186066
$66$	976.557	0.0275955
$67$	34355.7	0.935000	0.467500	−	0.883993i	$-0.345155\pi$
$67$	34355.7	0.935000	0.467500	+	0.883993i	$0.345155\pi$
$68$	−45132.4	−1.18363
$69$	−19749.9	−0.499392
$70$	2277.52	0.0555542
$71$	11202.2	0.263728	0.131864	−	0.991268i	$-0.457904\pi$
$71$	11202.2	0.263728	0.131864	+	0.991268i	$0.457904\pi$
$72$	−96.3697	−0.00219083
$73$	−68701.0	−1.50888	−0.754442	−	0.656366i	$-0.772093\pi$
$73$	−68701.0	−1.50888	−0.754442	+	0.656366i	$0.772093\pi$
$74$	906.408	0.0192418
$75$	−9801.51	−0.201205
$76$	11456.4	0.227517
$77$	−21419.5	−0.411701
$78$	2046.08	0.0380791
$79$	37311.5	0.672628	0.336314	−	0.941750i	$-0.390820\pi$
$79$	37311.5	0.672628	0.336314	+	0.941750i	$0.390820\pi$
$80$	24966.1	0.436140
$81$	−59754.3	−1.01194
$82$	1927.35	0.0316538
$83$	1115.08	0.0177669	0.00888344	−	0.999961i	$-0.497172\pi$
$83$	1115.08	0.0177669	0.00888344	+	0.999961i	$0.497172\pi$
$84$	88100.1	1.36232
$85$	35554.0	0.533753
$86$	−431.549	−0.00629193
$87$	−80336.2	−1.13792
$88$	3968.84	0.0546333
$89$	37899.8	0.507179	0.253590	−	0.967312i	$-0.418389\pi$
$89$	37899.8	0.507179	0.253590	+	0.967312i	$0.418389\pi$
$90$	37.8008	0.000491921 0
$91$	−44878.0	−0.568107
$92$	−39966.1	−0.492292
$93$	50515.8	0.605647
$94$	−554.205	−0.00646921
$95$	−9025.00	−0.102598
$96$	−24520.2	−0.271548
$97$	−47346.1	−0.510922	−0.255461	−	0.966819i	$-0.582227\pi$
$97$	−47346.1	−0.510922	−0.255461	+	0.966819i	$0.582227\pi$
$98$	7477.22	0.0786457
$99$	−355.506	−0.00364552
$100$	−19834.5	−0.198345
$101$	−35789.5	−0.349101	−0.174551	−	0.984648i	$-0.555847\pi$
$101$	−35789.5	−0.349101	−0.174551	+	0.984648i	$0.555847\pi$
$102$	−11477.8	−0.109234
$103$	−6437.15	−0.0597861	−0.0298931	−	0.999553i	$-0.509517\pi$
$103$	−6437.15	−0.0597861	−0.0298931	+	0.999553i	$0.509517\pi$
$104$	8315.52	0.0753887
$105$	−69402.6	−0.614331
$106$	−11851.1	−0.102446
$107$	−148424.	−1.25327	−0.626635	−	0.779313i	$-0.715568\pi$
$107$	−148424.	−1.25327	−0.626635	+	0.779313i	$0.715568\pi$
$108$	−119475.	−0.985638
$109$	32929.6	0.265473	0.132737	−	0.991151i	$-0.457624\pi$
$109$	32929.6	0.265473	0.132737	+	0.991151i	$0.457624\pi$
$110$	−1556.77	−0.0122671
$111$	−27620.9	−0.212780
$112$	176780.	1.33165
$113$	−139537.	−1.02800	−0.514001	−	0.857790i	$-0.671837\pi$
$113$	−139537.	−1.02800	−0.514001	+	0.857790i	$0.671837\pi$
$114$	2913.53	0.0209970
$115$	31484.1	0.221997
$116$	−162569.	−1.12174
$117$	−744.857	−0.00503047
$118$	−8266.48	−0.0546532
$119$	251751.	1.62968
$120$	12859.7	0.0815226
$121$	14641.0	0.0909091
$122$	11124.0	0.0676647
$123$	−58731.9	−0.350035
$124$	102224.	0.597036
$125$	15625.0	0.0894427
$126$	267.661	0.00150196
$127$	−72819.8	−0.400627	−0.200313	−	0.979732i	$-0.564196\pi$
$127$	−72819.8	−0.400627	−0.200313	+	0.979732i	$0.564196\pi$
$128$	−66065.4	−0.356410
$129$	13150.5	0.0695776
$130$	−3261.75	−0.0169275
$131$	−319250.	−1.62537	−0.812686	−	0.582702i	$-0.801995\pi$
$131$	−319250.	−1.62537	−0.812686	+	0.582702i	$0.801995\pi$
$132$	−60219.7	−0.300818
$133$	−63904.3	−0.313257
$134$	17680.6	0.0850621
$135$	94118.8	0.444469
$136$	−46647.3	−0.216261
$137$	−67862.8	−0.308909	−0.154454	−	0.988000i	$-0.549362\pi$
$137$	−67862.8	−0.308909	−0.154454	+	0.988000i	$0.549362\pi$
$138$	−10164.0	−0.0454324
$139$	81405.5	0.357369	0.178685	−	0.983906i	$-0.442816\pi$
$139$	81405.5	0.357369	0.178685	+	0.983906i	$0.442816\pi$
$140$	−140444.	−0.605597
$141$	16888.2	0.0715379
$142$	5765.04	0.0239928
$143$	30675.8	0.125446
$144$	2934.09	0.0117914
$145$	128067.	0.505846
$146$	−35356.0	−0.137271
$147$	−227852.	−0.869682
$148$	−55894.0	−0.209754
$149$	−338896.	−1.25055	−0.625275	−	0.780404i	$-0.715013\pi$
$149$	−338896.	−1.25055	−0.625275	+	0.780404i	$0.715013\pi$
$150$	−5044.20	−0.0183048
$151$	202939.	0.724308	0.362154	−	0.932118i	$-0.382041\pi$
$151$	202939.	0.724308	0.362154	+	0.932118i	$0.382041\pi$
$152$	11840.9	0.0415697
$153$	4178.40	0.0144305
$154$	−11023.2	−0.0374547
$155$	−80529.3	−0.269231
$156$	−126172.	−0.415100
$157$	1534.22	0.00496751	0.00248376	−	0.999997i	$-0.499209\pi$
$157$	1534.22	0.00496751	0.00248376	+	0.999997i	$0.499209\pi$
$158$	19201.8	0.0611927
$159$	361136.	1.13287
$160$	39088.7	0.120712
$161$	222933.	0.677813
$162$	−30751.7	−0.0920622
$163$	250993.	0.739932	0.369966	−	0.929045i	$-0.379369\pi$
$163$	250993.	0.739932	0.369966	+	0.929045i	$0.379369\pi$
$164$	−118851.	−0.345058
$165$	47439.3	0.135653
$166$	573.860	0.00161635
$167$	412638.	1.14493	0.572463	−	0.819930i	$-0.305988\pi$
$167$	412638.	1.14493	0.572463	+	0.819930i	$0.305988\pi$
$168$	91057.2	0.248909
$169$	−307021.	−0.826897
$170$	18297.3	0.0485585
$171$	−1060.64	−0.00277382
$172$	26611.6	0.0685883
$173$	416244.	1.05738	0.528692	−	0.848813i	$-0.322683\pi$
$173$	416244.	1.05738	0.528692	+	0.848813i	$0.322683\pi$
$174$	−41343.8	−0.103523
$175$	110638.	0.273091
$176$	−120836.	−0.294046
$177$	251904.	0.604368
$178$	19504.6	0.0461409
$179$	712483.	1.66204	0.831020	−	0.556242i	$-0.187757\pi$
$179$	712483.	1.66204	0.831020	+	0.556242i	$0.187757\pi$
$180$	−2331.00	−0.00536243
$181$	797992.	1.81051	0.905257	−	0.424864i	$-0.139678\pi$
$181$	797992.	1.81051	0.905257	+	0.424864i	$0.139678\pi$
$182$	−23095.8	−0.0516839
$183$	−338981.	−0.748252
$184$	−41307.6	−0.0899467
$185$	44031.6	0.0945878
$186$	25997.2	0.0550990
$187$	−172081.	−0.359856
$188$	34175.3	0.0705208
$189$	666437.	1.35708
$190$	−4644.58	−0.00933389
$191$	307371.	0.609649	0.304825	−	0.952409i	$-0.401402\pi$
$191$	307371.	0.609649	0.304825	+	0.952409i	$0.401402\pi$
$192$	488538.	0.956413
$193$	−206103.	−0.398281	−0.199141	−	0.979971i	$-0.563815\pi$
$193$	−206103.	−0.398281	−0.199141	+	0.979971i	$0.563815\pi$
$194$	−24366.0	−0.0464814
$195$	99394.8	0.187188
$196$	−461085.	−0.857317
$197$	953423.	1.75033	0.875165	−	0.483825i	$-0.160753\pi$
$197$	953423.	1.75033	0.875165	+	0.483825i	$0.160753\pi$
$198$	−182.956	−0.000331653 0
$199$	243088.	0.435142	0.217571	−	0.976045i	$-0.430187\pi$
$199$	243088.	0.435142	0.217571	+	0.976045i	$0.430187\pi$
$200$	−20500.2	−0.0362396
$201$	−538780.	−0.940636
$202$	−18418.5	−0.0317597
$203$	906821.	1.54448
$204$	707785.	1.19076
$205$	93627.0	0.155602
$206$	−3312.78	−0.00543907
$207$	3700.10	0.00600189
$208$	−253176.	−0.405755
$209$	43681.0	0.0691714
$210$	−35717.0	−0.0558891
$211$	−291532.	−0.450796	−0.225398	−	0.974267i	$-0.572368\pi$
$211$	−291532.	−0.450796	−0.225398	+	0.974267i	$0.572368\pi$
$212$	730801.	1.11676
$213$	−175677.	−0.265318
$214$	−76384.2	−0.114017
$215$	−20963.8	−0.0309296
$216$	−123485.	−0.180086
$217$	−570213.	−0.822030
$218$	16946.7	0.0241515
$219$	1.07740e6	1.51798
$220$	95998.8	0.133724
$221$	−360545.	−0.496567
$222$	−14214.7	−0.0193577
$223$	405782.	0.546425	0.273212	−	0.961954i	$-0.411914\pi$
$223$	405782.	0.546425	0.273212	+	0.961954i	$0.411914\pi$
$224$	276780.	0.368565
$225$	1836.29	0.00241816
$226$	−71810.7	−0.0935230
$227$	−330795.	−0.426083	−0.213041	−	0.977043i	$-0.568337\pi$
$227$	−330795.	−0.426083	−0.213041	+	0.977043i	$0.568337\pi$
$228$	−179664.	−0.228888
$229$	1.35233e6	1.70410	0.852050	−	0.523461i	$-0.175359\pi$
$229$	1.35233e6	1.70410	0.852050	+	0.523461i	$0.175359\pi$
$230$	16202.8	0.0201963
$231$	335909.	0.414182
$232$	−168026.	−0.204954
$233$	685375.	0.827063	0.413531	−	0.910490i	$-0.364295\pi$
$233$	685375.	0.827063	0.413531	+	0.910490i	$0.364295\pi$
$234$	−383.330	−0.000457649 0
$235$	−26922.2	−0.0318011
$236$	509756.	0.595775
$237$	−585135.	−0.676682
$238$	129560.	0.148261
$239$	632601.	0.716366	0.358183	−	0.933651i	$-0.383396\pi$
$239$	632601.	0.716366	0.358183	+	0.933651i	$0.383396\pi$
$240$	−391529.	−0.438769
$241$	549358.	0.609275	0.304637	−	0.952468i	$-0.401465\pi$
$241$	549358.	0.609275	0.304637	+	0.952468i	$0.401465\pi$
$242$	7534.77	0.00827050
$243$	22257.6	0.0241803
$244$	−685967.	−0.737613
$245$	363229.	0.386603
$246$	−30225.5	−0.0318446
$247$	91520.5	0.0954500
$248$	105656.	0.109085
$249$	−17487.2	−0.0178740
$250$	8041.17	0.00813709
$251$	−140249.	−0.140513	−0.0702563	−	0.997529i	$-0.522382\pi$
$251$	−140249.	−0.140513	−0.0702563	+	0.997529i	$0.522382\pi$
$252$	−16505.4	−0.0163729
$253$	−152383.	−0.149670
$254$	−37475.6	−0.0364472
$255$	−557572.	−0.536970
$256$	962863.	0.918258
$257$	832435.	0.786172	0.393086	−	0.919502i	$-0.371407\pi$
$257$	832435.	0.786172	0.393086	+	0.919502i	$0.371407\pi$
$258$	6767.73	0.00632985
$259$	311780.	0.288801
$260$	201137.	0.184526
$261$	15050.8	0.0136760
$262$	−164297.	−0.147869
$263$	−1.44263e6	−1.28607	−0.643037	−	0.765835i	$-0.722326\pi$
$263$	−1.44263e6	−1.28607	−0.643037	+	0.765835i	$0.722326\pi$
$264$	−62241.0	−0.0549625
$265$	−575703.	−0.503598
$266$	−32887.4	−0.0284987
$267$	−594360.	−0.510236
$268$	−1.09028e6	−0.927262
$269$	1.84973e6	1.55858	0.779289	−	0.626665i	$-0.215580\pi$
$269$	1.84973e6	1.55858	0.779289	+	0.626665i	$0.215580\pi$
$270$	48436.8	0.0404358
$271$	−766206.	−0.633757	−0.316878	−	0.948466i	$-0.602635\pi$
$271$	−766206.	−0.633757	−0.316878	+	0.948466i	$0.602635\pi$
$272$	1.42023e6	1.16396
$273$	703796.	0.571532
$274$	−34924.6	−0.0281031
$275$	−75625.0	−0.0603023
$276$	626765.	0.495259
$277$	165607.	0.129682	0.0648408	−	0.997896i	$-0.479346\pi$
$277$	165607.	0.129682	0.0648408	+	0.997896i	$0.479346\pi$
$278$	41894.2	0.0325118
$279$	−9464.03	−0.00727890
$280$	−145158.	−0.110649
$281$	1.68579e6	1.27361	0.636807	−	0.771023i	$-0.280255\pi$
$281$	1.68579e6	1.27361	0.636807	+	0.771023i	$0.280255\pi$
$282$	8691.28	0.00650820
$283$	1.61651e6	1.19981	0.599904	−	0.800072i	$-0.295205\pi$
$283$	1.61651e6	1.19981	0.599904	+	0.800072i	$0.295205\pi$
$284$	−355503.	−0.261546
$285$	141534.	0.103216
$286$	15786.9	0.0114125
$287$	662955.	0.475094
$288$	4593.81	0.00326356
$289$	602677.	0.424463
$290$	65907.9	0.0460196
$291$	742501.	0.514002
$292$	2.18024e6	1.49640
$293$	−429908.	−0.292554	−0.146277	−	0.989244i	$-0.546729\pi$
$293$	−429908.	−0.292554	−0.146277	+	0.989244i	$0.546729\pi$
$294$	−117261.	−0.0791197
$295$	−401570.	−0.268662
$296$	−57770.1	−0.0383243
$297$	−455535.	−0.299661
$298$	−174408.	−0.113769
$299$	−319273.	−0.206531
$300$	311052.	0.199540
$301$	−148441.	−0.0944359
$302$	104440.	0.0658943
$303$	561265.	0.351206
$304$	−360511.	−0.223735
$305$	540384.	0.332623
$306$	2150.35	0.00131282
$307$	2.69327e6	1.63093	0.815463	−	0.578809i	$-0.196482\pi$
$307$	2.69327e6	1.63093	0.815463	+	0.578809i	$0.196482\pi$
$308$	679750.	0.408293
$309$	100950.	0.0601465
$310$	−41443.2	−0.0244934
$311$	1.07356e6	0.629400	0.314700	−	0.949191i	$-0.398096\pi$
$311$	1.07356e6	0.629400	0.314700	+	0.949191i	$0.398096\pi$
$312$	−130407.	−0.0758430
$313$	−635066.	−0.366402	−0.183201	−	0.983075i	$-0.558646\pi$
$313$	−635066.	−0.366402	−0.183201	+	0.983075i	$0.558646\pi$
$314$	789.564	0.000451922 0
$315$	13002.4	0.00738327
$316$	−1.18409e6	−0.667061
$317$	−2.33465e6	−1.30489	−0.652445	−	0.757836i	$-0.726257\pi$
$317$	−2.33465e6	−1.30489	−0.652445	+	0.757836i	$0.726257\pi$
$318$	185853.	0.103063
$319$	−619846.	−0.341041
$320$	−778799.	−0.425158
$321$	2.32765e6	1.26082
$322$	114729.	0.0616644
$323$	−513399.	−0.273810
$324$	1.89631e6	1.00357
$325$	−158450.	−0.0832114
$326$	129170.	0.0673157
$327$	−516416.	−0.267073
$328$	−122840.	−0.0630456
$329$	−190631.	−0.0970967
$330$	24413.9	0.0123411
$331$	−1.94526e6	−0.975906	−0.487953	−	0.872870i	$-0.662256\pi$
$331$	−1.94526e6	−0.975906	−0.487953	+	0.872870i	$0.662256\pi$
$332$	−35387.3	−0.0176198
$333$	5174.72	0.00255727
$334$	212358.	0.104160
$335$	858892.	0.418145
$336$	−2.77234e6	−1.33967
$337$	2.61284e6	1.25325	0.626626	−	0.779320i	$-0.284435\pi$
$337$	2.61284e6	1.25325	0.626626	+	0.779320i	$0.284435\pi$
$338$	−158004.	−0.0752273
$339$	2.18828e6	1.03420
$340$	−1.12831e6	−0.529336
$341$	389762.	0.181515
$342$	−545.844	−0.000252350 0
$343$	−403222.	−0.185058
$344$	27504.8	0.0125318
$345$	−493747.	−0.223335
$346$	214214.	0.0961961
$347$	−1.90333e6	−0.848575	−0.424287	−	0.905528i	$-0.639475\pi$
$347$	−1.90333e6	−0.848575	−0.424287	+	0.905528i	$0.639475\pi$
$348$	2.54948e6	1.12851
$349$	764573.	0.336013	0.168006	−	0.985786i	$-0.446267\pi$
$349$	764573.	0.336013	0.168006	+	0.985786i	$0.446267\pi$
$350$	56938.0	0.0248446
$351$	−954437.	−0.413504
$352$	−189189.	−0.0813842
$353$	−2.00305e6	−0.855568	−0.427784	−	0.903881i	$-0.640706\pi$
$353$	−2.00305e6	−0.855568	−0.427784	+	0.903881i	$0.640706\pi$
$354$	129638.	0.0549826
$355$	280055.	0.117943
$356$	−1.20276e6	−0.502982
$357$	−3.94806e6	−1.63951
$358$	366669.	0.151205
$359$	−316948.	−0.129793	−0.0648965	−	0.997892i	$-0.520672\pi$
$359$	−316948.	−0.129793	−0.0648965	+	0.997892i	$0.520672\pi$
$360$	−2409.24	−0.000979770 0
$361$	130321.	0.0526316
$362$	410675.	0.164712
$363$	−229606.	−0.0914570
$364$	1.42421e6	0.563405
$365$	−1.71753e6	−0.674794
$366$	−174452.	−0.0680726
$367$	−4.44808e6	−1.72388	−0.861942	−	0.507008i	$-0.830752\pi$
$367$	−4.44808e6	−1.72388	−0.861942	+	0.507008i	$0.830752\pi$
$368$	1.25766e6	0.484109
$369$	11003.3	0.00420685
$370$	22660.2	0.00860517
$371$	−4.07644e6	−1.53761
$372$	−1.60313e6	−0.600634
$373$	2.95114e6	1.09829	0.549146	−	0.835726i	$-0.314953\pi$
$373$	2.95114e6	1.09829	0.549146	+	0.835726i	$0.314953\pi$
$374$	−88559.0	−0.0327381
$375$	−245038.	−0.0899818
$376$	35322.4	0.0128849
$377$	−1.29870e6	−0.470604
$378$	342972.	0.123461
$379$	−2.80023e6	−1.00137	−0.500687	−	0.865629i	$-0.666919\pi$
$379$	−2.80023e6	−1.00137	−0.500687	+	0.865629i	$0.666919\pi$
$380$	286410.	0.101749
$381$	1.14199e6	0.403041
$382$	158184.	0.0554631
$383$	958082.	0.333738	0.166869	−	0.985979i	$-0.446634\pi$
$383$	958082.	0.333738	0.166869	+	0.985979i	$0.446634\pi$
$384$	1.03607e6	0.358558
$385$	−535486.	−0.184118
$386$	−106068.	−0.0362338
$387$	−2463.73	−0.000836210 0
$388$	1.50254e6	0.506694
$389$	2.86031e6	0.958384	0.479192	−	0.877710i	$-0.340930\pi$
$389$	2.86031e6	0.958384	0.479192	+	0.877710i	$0.340930\pi$
$390$	51152.1	0.0170295
$391$	1.79102e6	0.592458
$392$	−476562.	−0.156641
$393$	5.00661e6	1.63517
$394$	490665.	0.159237
$395$	932788.	0.300809
$396$	11282.1	0.00361535
$397$	−4.62889e6	−1.47401	−0.737006	−	0.675887i	$-0.763761\pi$
$397$	−4.62889e6	−1.47401	−0.737006	+	0.675887i	$0.763761\pi$
$398$	125102.	0.0395872
$399$	1.00217e6	0.315145
$400$	624153.	0.195048
$401$	261324.	0.0811556	0.0405778	−	0.999176i	$-0.487080\pi$
$401$	261324.	0.0811556	0.0405778	+	0.999176i	$0.487080\pi$
$402$	−277275.	−0.0855748
$403$	816630.	0.250474
$404$	1.13578e6	0.346212
$405$	−1.49386e6	−0.452555
$406$	466682.	0.140509
$407$	−213113.	−0.0637711
$408$	731542.	0.217565
$409$	198430.	0.0586541	0.0293270	−	0.999570i	$-0.490664\pi$
$409$	198430.	0.0586541	0.0293270	+	0.999570i	$0.490664\pi$
$410$	48183.7	0.0141560
$411$	1.06425e6	0.310771
$412$	204284.	0.0592913
$413$	−2.84344e6	−0.820294
$414$	1904.20	0.000546025 0
$415$	27877.0	0.00794559
$416$	−396390.	−0.112302
$417$	−1.27664e6	−0.359523
$418$	22479.8	0.00629291
$419$	−1.15720e6	−0.322013	−0.161006	−	0.986953i	$-0.551474\pi$
$419$	−1.15720e6	−0.322013	−0.161006	+	0.986953i	$0.551474\pi$
$420$	2.20250e6	0.609247
$421$	877816.	0.241378	0.120689	−	0.992690i	$-0.461490\pi$
$421$	877816.	0.241378	0.120689	+	0.992690i	$0.461490\pi$
$422$	−150033.	−0.0410114
$423$	−3163.98	−0.000859770 0
$424$	755330.	0.204043
$425$	888849.	0.238702
$426$	−90409.7	−0.0241374
$427$	3.82636e6	1.01558
$428$	4.71026e6	1.24290
$429$	−481071.	−0.126202
$430$	−10788.7	−0.00281384
$431$	3.97072e6	1.02962	0.514809	−	0.857305i	$-0.327863\pi$
$431$	3.97072e6	1.02962	0.514809	+	0.857305i	$0.327863\pi$
$432$	3.75965e6	0.969254
$433$	−1.99678e6	−0.511812	−0.255906	−	0.966702i	$-0.582374\pi$
$433$	−1.99678e6	−0.511812	−0.255906	+	0.966702i	$0.582374\pi$
$434$	−293452.	−0.0747846
$435$	−2.00840e6	−0.508895
$436$	−1.04503e6	−0.263276
$437$	−454631.	−0.113882
$438$	554467.	0.138099
$439$	106456.	0.0263637	0.0131819	−	0.999913i	$-0.495804\pi$
$439$	106456.	0.0263637	0.0131819	+	0.999913i	$0.495804\pi$
$440$	99221.0	0.0244327
$441$	42687.7	0.0104522
$442$	−185549.	−0.0451755
$443$	5.38198e6	1.30297	0.651483	−	0.758663i	$-0.274147\pi$
$443$	5.38198e6	1.30297	0.651483	+	0.758663i	$0.274147\pi$
$444$	876553.	0.211019
$445$	947494.	0.226818
$446$	208829.	0.0497112
$447$	5.31471e6	1.25809
$448$	−5.51453e6	−1.29812
$449$	−867532.	−0.203081	−0.101541	−	0.994831i	$-0.532377\pi$
$449$	−867532.	−0.203081	−0.101541	+	0.994831i	$0.532377\pi$
$450$	945.021	0.000219994 0
$451$	−453154.	−0.104907
$452$	4.42823e6	1.01949
$453$	−3.18258e6	−0.728674
$454$	−170239.	−0.0387631
$455$	−1.12195e6	−0.254065
$456$	−185694.	−0.0418202
$457$	−3.86867e6	−0.866505	−0.433253	−	0.901273i	$-0.642634\pi$
$457$	−3.86867e6	−0.866505	−0.433253	+	0.901273i	$0.642634\pi$
$458$	695958.	0.155031
$459$	5.35407e6	1.18618
$460$	−999153.	−0.220160
$461$	−5.59760e6	−1.22673	−0.613366	−	0.789799i	$-0.710185\pi$
$461$	−5.59760e6	−1.22673	−0.613366	+	0.789799i	$0.710185\pi$
$462$	172870.	0.0376804
$463$	4.69091e6	1.01696	0.508480	−	0.861074i	$-0.330207\pi$
$463$	4.69091e6	1.01696	0.508480	+	0.861074i	$0.330207\pi$
$464$	5.11575e6	1.10310
$465$	1.26289e6	0.270854
$466$	352718.	0.0752425
$467$	−2.98539e6	−0.633445	−0.316722	−	0.948518i	$-0.602582\pi$
$467$	−2.98539e6	−0.633445	−0.316722	+	0.948518i	$0.602582\pi$
$468$	23638.2	0.00498883
$469$	6.08165e6	1.27670
$470$	−13855.1	−0.00289312
$471$	−24060.3	−0.00499745
$472$	526866.	0.108854
$473$	101465.	0.0208527
$474$	−301131.	−0.0615615
$475$	−225625.	−0.0458831
$476$	−7.98935e6	−1.61620
$477$	−67658.2	−0.0136152
$478$	325559.	0.0651718
$479$	−3.40896e6	−0.678865	−0.339433	−	0.940630i	$-0.610235\pi$
$479$	−3.40896e6	−0.678865	−0.339433	+	0.940630i	$0.610235\pi$
$480$	−613005.	−0.121440
$481$	−446515.	−0.0879980
$482$	282719.	0.0554291
$483$	−3.49613e6	−0.681898
$484$	−464634.	−0.0901567
$485$	−1.18365e6	−0.228491
$486$	11454.5	0.00219982
$487$	8.59383e6	1.64197	0.820984	−	0.570952i	$-0.193426\pi$
$487$	8.59383e6	1.64197	0.820984	+	0.570952i	$0.193426\pi$
$488$	−708991.	−0.134769
$489$	−3.93617e6	−0.744392
$490$	186931.	0.0351714
$491$	2.22731e6	0.416942	0.208471	−	0.978029i	$-0.433151\pi$
$491$	2.22731e6	0.416942	0.208471	+	0.978029i	$0.433151\pi$
$492$	1.86386e6	0.347138
$493$	7.28528e6	1.34999
$494$	47099.6	0.00868361
$495$	−8887.66	−0.00163033
$496$	−3.21681e6	−0.587112
$497$	1.98301e6	0.360110
$498$	−8999.50	−0.00162609
$499$	−3.86437e6	−0.694748	−0.347374	−	0.937727i	$-0.612927\pi$
$499$	−3.86437e6	−0.694748	−0.347374	+	0.937727i	$0.612927\pi$
$500$	−495862.	−0.0887024
$501$	−6.47115e6	−1.15183
$502$	−72177.0	−0.0127832
$503$	440689.	0.0776626	0.0388313	−	0.999246i	$-0.487637\pi$
$503$	440689.	0.0776626	0.0388313	+	0.999246i	$0.487637\pi$
$504$	−17059.4	−0.00299149
$505$	−894737.	−0.156123
$506$	−78421.7	−0.0136163
$507$	4.81483e6	0.831881
$508$	2.31095e6	0.397311
$509$	451107.	0.0771765	0.0385883	−	0.999255i	$-0.487714\pi$
$509$	451107.	0.0771765	0.0385883	+	0.999255i	$0.487714\pi$
$510$	−286946.	−0.0488511
$511$	−1.21615e7	−2.06032
$512$	2.60962e6	0.439949
$513$	−1.35907e6	−0.228008
$514$	428400.	0.0715224
$515$	−160929.	−0.0267372
$516$	−417334.	−0.0690017
$517$	130304.	0.0214403
$518$	160453.	0.0262738
$519$	−6.52772e6	−1.06376
$520$	207888.	0.0337148
$521$	−7.62688e6	−1.23098	−0.615492	−	0.788143i	$-0.711043\pi$
$521$	−7.62688e6	−1.23098	−0.615492	+	0.788143i	$0.711043\pi$
$522$	7745.69	0.00124418
$523$	−1.10337e6	−0.176387	−0.0881936	−	0.996103i	$-0.528109\pi$
$523$	−1.10337e6	−0.176387	−0.0881936	+	0.996103i	$0.528109\pi$
$524$	1.01314e7	1.61192
$525$	−1.73507e6	−0.274737
$526$	−742429.	−0.117001
$527$	−4.58102e6	−0.718515
$528$	1.89500e6	0.295818
$529$	−4.85034e6	−0.753587
$530$	−296277.	−0.0458150
$531$	−47193.6	−0.00726352
$532$	2.02801e6	0.310665
$533$	−949450.	−0.144762
$534$	−305878.	−0.0464190
$535$	−3.71060e6	−0.560480
$536$	−1.12688e6	−0.169420
$537$	−1.11734e7	−1.67206
$538$	951938.	0.141792
$539$	−1.75803e6	−0.260648
$540$	−2.98687e6	−0.440791
$541$	3.05113e6	0.448195	0.224097	−	0.974567i	$-0.428057\pi$
$541$	3.05113e6	0.448195	0.224097	+	0.974567i	$0.428057\pi$
$542$	−394317.	−0.0576563
$543$	−1.25144e7	−1.82143
$544$	2.22361e6	0.322153
$545$	823240.	0.118723
$546$	362198.	0.0519954
$547$	6.93538e6	0.991064	0.495532	−	0.868590i	$-0.334973\pi$
$547$	6.93538e6	0.991064	0.495532	+	0.868590i	$0.334973\pi$
$548$	2.15364e6	0.306352
$549$	63507.4	0.00899277
$550$	−38919.3	−0.00548603
$551$	−1.84929e6	−0.259494
$552$	647803.	0.0904889
$553$	6.60489e6	0.918445
$554$	85227.0	0.0117978
$555$	−690522.	−0.0951579
$556$	−2.58342e6	−0.354411
$557$	741145.	0.101220	0.0506099	−	0.998719i	$-0.483883\pi$
$557$	741145.	0.101220	0.0506099	+	0.998719i	$0.483883\pi$
$558$	−4870.52	−0.000662201 0
$559$	212589.	0.0287748
$560$	4.41951e6	0.595530
$561$	2.69865e6	0.362025
$562$	867567.	0.115868
$563$	8.74451e6	1.16269	0.581346	−	0.813657i	$-0.302526\pi$
$563$	8.74451e6	1.16269	0.581346	+	0.813657i	$0.302526\pi$
$564$	−535951.	−0.0709459
$565$	−3.48843e6	−0.459736
$566$	831912.	0.109153
$567$	−1.05777e7	−1.38177
$568$	−367436.	−0.0477871
$569$	5.58681e6	0.723408	0.361704	−	0.932293i	$-0.382195\pi$
$569$	5.58681e6	0.723408	0.361704	+	0.932293i	$0.382195\pi$
$570$	72838.2	0.00939015
$571$	−4.08088e6	−0.523798	−0.261899	−	0.965095i	$-0.584349\pi$
$571$	−4.08088e6	−0.523798	−0.261899	+	0.965095i	$0.584349\pi$
$572$	−973502.	−0.124408
$573$	−4.82032e6	−0.613324
$574$	341180.	0.0432219
$575$	787103.	0.0992801
$576$	−91526.7	−0.0114945
$577$	8.15572e6	1.01982	0.509909	−	0.860228i	$-0.329679\pi$
$577$	8.15572e6	1.01982	0.509909	+	0.860228i	$0.329679\pi$
$578$	310159.	0.0386158
$579$	3.23219e6	0.400682
$580$	−4.06424e6	−0.501659
$581$	197392.	0.0242599
$582$	382117.	0.0467616
$583$	2.78640e6	0.339525
$584$	2.25342e6	0.273407
$585$	−18621.4	−0.00224969
$586$	−221246.	−0.0266153
$587$	−7.39511e6	−0.885828	−0.442914	−	0.896564i	$-0.646055\pi$
$587$	−7.39511e6	−0.885828	−0.442914	+	0.896564i	$0.646055\pi$
$588$	7.23093e6	0.862484
$589$	1.16284e6	0.138113
$590$	−206662.	−0.0244417
$591$	−1.49520e7	−1.76088
$592$	1.75888e6	0.206268
$593$	5.69079e6	0.664562	0.332281	−	0.943180i	$-0.392182\pi$
$593$	5.69079e6	0.664562	0.332281	+	0.943180i	$0.392182\pi$
$594$	−234434.	−0.0272618
$595$	6.29377e6	0.728817
$596$	1.07549e7	1.24020
$597$	−3.81221e6	−0.437764
$598$	−164309.	−0.0187892
$599$	−4.40676e6	−0.501826	−0.250913	−	0.968010i	$-0.580731\pi$
$599$	−4.40676e6	−0.501826	−0.250913	+	0.968010i	$0.580731\pi$
$600$	321493.	0.0364580
$601$	1.33125e7	1.50340	0.751699	−	0.659506i	$-0.229235\pi$
$601$	1.33125e7	1.50340	0.751699	+	0.659506i	$0.229235\pi$
$602$	−76392.9	−0.00859136
$603$	100939.	0.0113049
$604$	−6.44031e6	−0.718314
$605$	366025.	0.0406558
$606$	288847.	0.0319511
$607$	8.45511e6	0.931424	0.465712	−	0.884936i	$-0.345798\pi$
$607$	8.45511e6	0.931424	0.465712	+	0.884936i	$0.345798\pi$
$608$	−564441.	−0.0619241
$609$	−1.42211e7	−1.55379
$610$	278101.	0.0302606
$611$	273012.	0.0295855
$612$	−132602.	−0.0143111
$613$	−3.47467e6	−0.373476	−0.186738	−	0.982410i	$-0.559791\pi$
$613$	−3.47467e6	−0.373476	−0.186738	+	0.982410i	$0.559791\pi$
$614$	1.38605e6	0.148374
$615$	−1.46830e6	−0.156540
$616$	702565.	0.0745993
$617$	5.69590e6	0.602351	0.301175	−	0.953569i	$-0.402621\pi$
$617$	5.69590e6	0.602351	0.301175	+	0.953569i	$0.402621\pi$
$618$	51952.4	0.00547185
$619$	4.75766e6	0.499076	0.249538	−	0.968365i	$-0.419721\pi$
$619$	4.75766e6	0.499076	0.249538	+	0.968365i	$0.419721\pi$
$620$	2.55561e6	0.267003
$621$	4.74119e6	0.493354
$622$	552493.	0.0572600
$623$	6.70903e6	0.692531
$624$	3.97041e6	0.408200
$625$	390625.	0.0400000
$626$	−326827.	−0.0333336
$627$	−685023.	−0.0695884
$628$	−48688.8	−0.00492640
$629$	2.50480e6	0.252433
$630$	6691.51	0.000671696 0
$631$	7.64382e6	0.764253	0.382126	−	0.924110i	$-0.375192\pi$
$631$	7.64382e6	0.764253	0.382126	+	0.924110i	$0.375192\pi$
$632$	−1.22383e6	−0.121879
$633$	4.57192e6	0.453513
$634$	−1.20149e6	−0.118713
$635$	−1.82049e6	−0.179166
$636$	−1.14607e7	−1.12349
$637$	−3.68343e6	−0.359669
$638$	−318994.	−0.0310264
$639$	32912.8	0.00318869
$640$	−1.65164e6	−0.159391
$641$	−1.01511e7	−0.975815	−0.487907	−	0.872895i	$-0.662240\pi$
$641$	−1.01511e7	−0.975815	−0.487907	+	0.872895i	$0.662240\pi$
$642$	1.19789e6	0.114704
$643$	1.69084e7	1.61278	0.806390	−	0.591385i	$-0.201418\pi$
$643$	1.69084e7	1.61278	0.806390	+	0.591385i	$0.201418\pi$
$644$	−7.07482e6	−0.672203
$645$	328763.	0.0311160
$646$	−264213.	−0.0249100
$647$	6.70048e6	0.629282	0.314641	−	0.949211i	$-0.398116\pi$
$647$	6.70048e6	0.629282	0.314641	+	0.949211i	$0.398116\pi$
$648$	1.95996e6	0.183362
$649$	1.94360e6	0.181132
$650$	−81543.7	−0.00757019
$651$	8.94232e6	0.826985
$652$	−7.96529e6	−0.733808
$653$	3.91830e6	0.359596	0.179798	−	0.983704i	$-0.442456\pi$
$653$	3.91830e6	0.359596	0.179798	+	0.983704i	$0.442456\pi$
$654$	−265766.	−0.0242971
$655$	−7.98125e6	−0.726888
$656$	3.74000e6	0.339322
$657$	−201848.	−0.0182437
$658$	−98105.6	−0.00883342
$659$	6.73067e6	0.603733	0.301866	−	0.953350i	$-0.402390\pi$
$659$	6.73067e6	0.603733	0.301866	+	0.953350i	$0.402390\pi$
$660$	−1.50549e6	−0.134530
$661$	4.44568e6	0.395763	0.197881	−	0.980226i	$-0.436594\pi$
$661$	4.44568e6	0.395763	0.197881	+	0.980226i	$0.436594\pi$
$662$	−1.00110e6	−0.0887835
$663$	5.65421e6	0.499560
$664$	−36575.0	−0.00321932
$665$	−1.59761e6	−0.140093
$666$	2663.09	0.000232649 0
$667$	6.45134e6	0.561481
$668$	−1.30951e7	−1.13545
$669$	−6.36364e6	−0.549718
$670$	442016.	0.0380409
$671$	−2.61546e6	−0.224255
$672$	−4.34057e6	−0.370787
$673$	−8.35171e6	−0.710784	−0.355392	−	0.934717i	$-0.615653\pi$
$673$	−8.35171e6	−0.710784	−0.355392	+	0.934717i	$0.615653\pi$
$674$	1.34466e6	0.114015
$675$	2.35297e6	0.198773
$676$	9.74336e6	0.820053
$677$	2.32530e7	1.94988	0.974938	−	0.222479i	$-0.0714149\pi$
$677$	2.32530e7	1.94988	0.974938	+	0.222479i	$0.0714149\pi$
$678$	1.12617e6	0.0940866
$679$	−8.38122e6	−0.697642
$680$	−1.16618e6	−0.0967151
$681$	5.18766e6	0.428651
$682$	200585.	0.0165135
$683$	−1.35599e7	−1.11226	−0.556130	−	0.831095i	$-0.687714\pi$
$683$	−1.35599e7	−1.11226	−0.556130	+	0.831095i	$0.687714\pi$
$684$	33659.7	0.00275087
$685$	−1.69657e6	−0.138148
$686$	−207512.	−0.0168358
$687$	−2.12078e7	−1.71437
$688$	−837417.	−0.0674482
$689$	5.83807e6	0.468513
$690$	−254100.	−0.0203180
$691$	6.34420e6	0.505454	0.252727	−	0.967538i	$-0.418673\pi$
$691$	6.34420e6	0.505454	0.252727	+	0.967538i	$0.418673\pi$
$692$	−1.32096e7	−1.04863
$693$	−62931.8	−0.00497780
$694$	−979520.	−0.0771995
$695$	2.03514e6	0.159820
$696$	2.63505e6	0.206190
$697$	5.32609e6	0.415267
$698$	393476.	0.0305689
$699$	−1.07483e7	−0.832048
$700$	−3.51110e6	−0.270831
$701$	9.65419e6	0.742029	0.371014	−	0.928627i	$-0.379010\pi$
$701$	9.65419e6	0.742029	0.371014	+	0.928627i	$0.379010\pi$
$702$	−491187.	−0.0376187
$703$	−635816.	−0.0485225
$704$	3.76939e6	0.286642
$705$	422206.	0.0319927
$706$	−1.03084e6	−0.0778357
$707$	−6.33546e6	−0.476683
$708$	−7.99420e6	−0.599366
$709$	2.43844e7	1.82178	0.910891	−	0.412648i	$-0.135396\pi$
$709$	2.43844e7	1.82178	0.910891	+	0.412648i	$0.135396\pi$
$710$	144126.	0.0107299
$711$	109624.	0.00813263
$712$	−1.24313e6	−0.0918999
$713$	−4.05663e6	−0.298842
$714$	−2.03181e6	−0.149155
$715$	766896.	0.0561011
$716$	−2.26107e7	−1.64828
$717$	−9.92071e6	−0.720684
$718$	−163112.	−0.0118080
$719$	−601814.	−0.0434150	−0.0217075	−	0.999764i	$-0.506910\pi$
$719$	−601814.	−0.0434150	−0.0217075	+	0.999764i	$0.506910\pi$
$720$	73352.2	0.00527329
$721$	−1.13951e6	−0.0816353
$722$	67067.8	0.00478818
$723$	−8.61526e6	−0.612947
$724$	−2.53244e7	−1.79553
$725$	3.20168e6	0.226221
$726$	−118163.	−0.00832035
$727$	−17901.4	−0.00125618	−0.000628090	−	1.00000i	$-0.500200\pi$
$727$	−17901.4	−0.00125618	−0.000628090		1.00000i	$0.500200\pi$
$728$	1.47202e6	0.102940
$729$	1.41712e7	0.987619
$730$	−883899.	−0.0613897
$731$	−1.19256e6	−0.0825439
$732$	1.07576e7	0.742059
$733$	2.27280e6	0.156243	0.0781216	−	0.996944i	$-0.475108\pi$
$733$	2.27280e6	0.156243	0.0781216	+	0.996944i	$0.475108\pi$
$734$	−2.28914e6	−0.156831
$735$	−5.69631e6	−0.388934
$736$	1.96908e6	0.133989
$737$	−4.15704e6	−0.281913
$738$	5662.68	0.000382720 0
$739$	−3.00268e6	−0.202254	−0.101127	−	0.994874i	$-0.532245\pi$
$739$	−3.00268e6	−0.202254	−0.101127	+	0.994874i	$0.532245\pi$
$740$	−1.39735e6	−0.0938050
$741$	−1.43526e6	−0.0960253
$742$	−2.09788e6	−0.139885
$743$	−1.11055e6	−0.0738020	−0.0369010	−	0.999319i	$-0.511749\pi$
$743$	−1.11055e6	−0.0738020	−0.0369010	+	0.999319i	$0.511749\pi$
$744$	−1.65693e6	−0.109742
$745$	−8.47241e6	−0.559263
$746$	1.51876e6	0.0999176
$747$	3276.18	0.000214816 0
$748$	5.46102e6	0.356878
$749$	−2.62741e7	−1.71129
$750$	−126105.	−0.00818614
$751$	−1.70861e7	−1.10546	−0.552730	−	0.833360i	$-0.686414\pi$
$751$	−1.70861e7	−1.10546	−0.552730	+	0.833360i	$0.686414\pi$
$752$	−1.07543e6	−0.0693486
$753$	2.19944e6	0.141359
$754$	−668357.	−0.0428135
$755$	5.07348e6	0.323921
$756$	−2.11495e7	−1.34585
$757$	2.66939e7	1.69306	0.846531	−	0.532339i	$-0.178687\pi$
$757$	2.66939e7	1.69306	0.846531	+	0.532339i	$0.178687\pi$
$758$	−1.44110e6	−0.0911004
$759$	2.38974e6	0.150572
$760$	296023.	0.0185905
$761$	6.76491e6	0.423449	0.211724	−	0.977329i	$-0.432092\pi$
$761$	6.76491e6	0.423449	0.211724	+	0.977329i	$0.432092\pi$
$762$	587708.	0.0366669
$763$	5.82921e6	0.362492
$764$	−9.75448e6	−0.604603
$765$	104460.	0.00645352
$766$	493063.	0.0303620
$767$	4.07223e6	0.249945
$768$	−1.51000e7	−0.923793
$769$	−2.22112e7	−1.35443	−0.677215	−	0.735786i	$-0.736813\pi$
$769$	−2.22112e7	−1.35443	−0.677215	+	0.735786i	$0.736813\pi$
$770$	−275580.	−0.0167502
$771$	−1.30546e7	−0.790911
$772$	6.54070e6	0.394985
$773$	−7.27891e6	−0.438144	−0.219072	−	0.975709i	$-0.570303\pi$
$773$	−7.27891e6	−0.438144	−0.219072	+	0.975709i	$0.570303\pi$
$774$	−1267.92	−7.60746e−5 0
$775$	−2.01323e6	−0.120404
$776$	1.55297e6	0.0925781
$777$	−4.88945e6	−0.290541
$778$	1.47202e6	0.0871895
$779$	−1.35197e6	−0.0798223
$780$	−3.15431e6	−0.185638
$781$	−1.35546e6	−0.0795171
$782$	921720.	0.0538992
$783$	1.92857e7	1.12417
$784$	1.45095e7	0.843066
$785$	38355.5	0.00222154
$786$	2.57658e6	0.148760
$787$	2.16138e7	1.24393	0.621964	−	0.783046i	$-0.286335\pi$
$787$	2.16138e7	1.24393	0.621964	+	0.783046i	$0.286335\pi$
$788$	−3.02570e7	−1.73584
$789$	2.26240e7	1.29383
$790$	480045.	0.0273662
$791$	−2.47009e7	−1.40369
$792$	11660.7	0.000660561 0
$793$	−5.47991e6	−0.309450
$794$	−2.38219e6	−0.134099
$795$	9.02841e6	0.506633
$796$	−7.71443e6	−0.431540
$797$	−7.47335e6	−0.416744	−0.208372	−	0.978050i	$-0.566817\pi$
$797$	−7.47335e6	−0.416744	−0.208372	+	0.978050i	$0.566817\pi$
$798$	515754.	0.0286705
$799$	−1.53151e6	−0.0848696
$800$	977218.	0.0539842
$801$	111352.	0.00613222
$802$	134487.	0.00738317
$803$	8.31282e6	0.454946
$804$	1.70983e7	0.932851
$805$	5.57333e6	0.303127
$806$	420266.	0.0227870
$807$	−2.90083e7	−1.56797
$808$	1.17391e6	0.0632565
$809$	2.03885e7	1.09525	0.547625	−	0.836724i	$-0.315532\pi$
$809$	2.03885e7	1.09525	0.547625	+	0.836724i	$0.315532\pi$
$810$	−768792.	−0.0411714
$811$	1.85503e7	0.990373	0.495187	−	0.868787i	$-0.335100\pi$
$811$	1.85503e7	0.990373	0.495187	+	0.868787i	$0.335100\pi$
$812$	−2.87781e7	−1.53169
$813$	1.20160e7	0.637577
$814$	−109675.	−0.00580161
$815$	6.27482e6	0.330908
$816$	−2.22726e7	−1.17097
$817$	302718.	0.0158666
$818$	102119.	0.00533608
$819$	−131855.	−0.00686889
$820$	−2.97127e6	−0.154315
$821$	−1.95910e7	−1.01437	−0.507187	−	0.861836i	$-0.669315\pi$
$821$	−1.95910e7	−1.01437	−0.507187	+	0.861836i	$0.669315\pi$
$822$	547702.	0.0282725
$823$	3.09176e6	0.159113	0.0795566	−	0.996830i	$-0.474650\pi$
$823$	3.09176e6	0.159113	0.0795566	+	0.996830i	$0.474650\pi$
$824$	211141.	0.0108331
$825$	1.18598e6	0.0606657
$826$	−1.46334e6	−0.0746266
$827$	1.41760e7	0.720760	0.360380	−	0.932806i	$-0.382647\pi$
$827$	1.41760e7	0.720760	0.360380	+	0.932806i	$0.382647\pi$
$828$	−117423.	−0.00595221
$829$	−1.11797e7	−0.564994	−0.282497	−	0.959268i	$-0.591163\pi$
$829$	−1.11797e7	−0.564994	−0.282497	+	0.959268i	$0.591163\pi$
$830$	14346.5	0.000722854 0
$831$	−2.59711e6	−0.130463
$832$	7.89763e6	0.395538
$833$	2.06628e7	1.03175
$834$	−657001.	−0.0327078
$835$	1.03159e7	0.512027
$836$	−1.38622e6	−0.0685989
$837$	−1.21269e7	−0.598324
$838$	−595535.	−0.0292953
$839$	−9.95198e6	−0.488095	−0.244048	−	0.969763i	$-0.578475\pi$
$839$	−9.95198e6	−0.488095	−0.244048	+	0.969763i	$0.578475\pi$
$840$	2.27643e6	0.111316
$841$	5.73084e6	0.279401
$842$	451755.	0.0219595
$843$	−2.64373e7	−1.28129
$844$	9.25181e6	0.447065
$845$	−7.67552e6	−0.369799
$846$	−1628.29	−7.82180e−5 0
$847$	2.59175e6	0.124132
$848$	−2.29969e7	−1.09820
$849$	−2.53508e7	−1.20704
$850$	457433.	0.0217160
$851$	2.21807e6	0.104991
$852$	5.57515e6	0.263122
$853$	−1.35979e7	−0.639883	−0.319942	−	0.947437i	$-0.603663\pi$
$853$	−1.35979e7	−0.639883	−0.319942	+	0.947437i	$0.603663\pi$
$854$	1.96918e6	0.0923932
$855$	−26516.1	−0.00124049
$856$	4.86836e6	0.227090
$857$	3.22769e6	0.150120	0.0750602	−	0.997179i	$-0.476085\pi$
$857$	3.22769e6	0.150120	0.0750602	+	0.997179i	$0.476085\pi$
$858$	−247576.	−0.0114813
$859$	−3.21374e7	−1.48603	−0.743015	−	0.669275i	$-0.766605\pi$
$859$	−3.21374e7	−1.48603	−0.743015	+	0.669275i	$0.766605\pi$
$860$	665290.	0.0306736
$861$	−1.03967e7	−0.477957
$862$	2.04347e6	0.0936700
$863$	2.65080e7	1.21157	0.605786	−	0.795627i	$-0.292859\pi$
$863$	2.65080e7	1.21157	0.605786	+	0.795627i	$0.292859\pi$
$864$	5.88637e6	0.268264
$865$	1.04061e7	0.472877
$866$	−1.02761e6	−0.0465624
$867$	−9.45144e6	−0.427022
$868$	1.80958e7	0.815227
$869$	−4.51469e6	−0.202805
$870$	−1.03360e6	−0.0462970
$871$	−8.70983e6	−0.389013
$872$	−1.08010e6	−0.0481032
$873$	−139106.	−0.00617747
$874$	−233969.	−0.0103605
$875$	2.76594e6	0.122130
$876$	−3.41914e7	−1.50542
$877$	−1.20742e7	−0.530103	−0.265052	−	0.964234i	$-0.585389\pi$
$877$	−1.20742e7	−0.530103	−0.265052	+	0.964234i	$0.585389\pi$
$878$	54785.8	0.00239845
$879$	6.74200e6	0.294318
$880$	−3.02090e6	−0.131501
$881$	−1.21966e7	−0.529418	−0.264709	−	0.964328i	$-0.585276\pi$
$881$	−1.21966e7	−0.529418	−0.264709	+	0.964328i	$0.585276\pi$
$882$	21968.6	0.000950891 0
$883$	−2.81630e6	−0.121556	−0.0607782	−	0.998151i	$-0.519358\pi$
$883$	−2.81630e6	−0.121556	−0.0607782	+	0.998151i	$0.519358\pi$
$884$	1.14419e7	0.492458
$885$	6.29759e6	0.270281
$886$	2.76976e6	0.118538
$887$	2.89931e7	1.23733	0.618665	−	0.785655i	$-0.287674\pi$
$887$	2.89931e7	1.23733	0.618665	+	0.785655i	$0.287674\pi$
$888$	905974.	0.0385552
$889$	−1.28906e7	−0.547038
$890$	487614.	0.0206348
$891$	7.23027e6	0.305113
$892$	−1.28775e7	−0.541902
$893$	388757.	0.0163136
$894$	2.73514e6	0.114455
$895$	1.78121e7	0.743287
$896$	−1.16949e7	−0.486662
$897$	5.00698e6	0.207776
$898$	−446463.	−0.0184754
$899$	−1.65011e7	−0.680947
$900$	−58275.1	−0.00239815
$901$	−3.27496e7	−1.34398
$902$	−233209.	−0.00954398
$903$	2.32791e6	0.0950051
$904$	4.57687e6	0.186272
$905$	1.99498e7	0.809687
$906$	−1.63787e6	−0.0662915
$907$	1.65999e7	0.670021	0.335011	−	0.942214i	$-0.391260\pi$
$907$	1.65999e7	0.670021	0.335011	+	0.942214i	$0.391260\pi$
$908$	1.04978e7	0.422556
$909$	−105152.	−0.00422092
$910$	−577395.	−0.0231137
$911$	1.04797e7	0.418361	0.209181	−	0.977877i	$-0.432920\pi$
$911$	1.04797e7	0.418361	0.209181	+	0.977877i	$0.432920\pi$
$912$	5.65368e6	0.225084
$913$	−134925.	−0.00535691
$914$	−1.99095e6	−0.0788307
$915$	−8.47453e6	−0.334628
$916$	−4.29165e7	−1.69000
$917$	−5.65137e7	−2.21937
$918$	2.75539e6	0.107914
$919$	1.88786e7	0.737362	0.368681	−	0.929556i	$-0.379809\pi$
$919$	1.88786e7	0.737362	0.368681	+	0.929556i	$0.379809\pi$
$920$	−1.03269e6	−0.0402254
$921$	−4.22370e7	−1.64076
$922$	−2.88072e6	−0.111603
$923$	−2.83997e6	−0.109726
$924$	−1.06601e7	−0.410754
$925$	1.10079e6	0.0423010
$926$	2.41410e6	0.0925185
$927$	−18912.8	−0.000722863 0
$928$	8.00958e6	0.305309
$929$	−2.53916e7	−0.965273	−0.482637	−	0.875821i	$-0.660321\pi$
$929$	−2.53916e7	−0.965273	−0.482637	+	0.875821i	$0.660321\pi$
$930$	649930.	0.0246410
$931$	−5.24503e6	−0.198323
$932$	−2.17505e7	−0.820218
$933$	−1.68361e7	−0.633194
$934$	−1.53639e6	−0.0576280
$935$	−4.30203e6	−0.160933
$936$	24431.6	0.000911511 0
$937$	4.35718e7	1.62127	0.810637	−	0.585549i	$-0.199121\pi$
$937$	4.35718e7	1.62127	0.810637	+	0.585549i	$0.199121\pi$
$938$	3.12983e6	0.116149
$939$	9.95936e6	0.368610
$940$	854382.	0.0315379
$941$	1.65347e6	0.0608728	0.0304364	−	0.999537i	$-0.490310\pi$
$941$	1.65347e6	0.0608728	0.0304364	+	0.999537i	$0.490310\pi$
$942$	−12382.3	−0.000454646 0
$943$	4.71642e6	0.172716
$944$	−1.60410e7	−0.585872
$945$	1.66609e7	0.606903
$946$	52217.4	0.00189709
$947$	−2.72154e7	−0.986144	−0.493072	−	0.869988i	$-0.664126\pi$
$947$	−2.72154e7	−0.986144	−0.493072	+	0.869988i	$0.664126\pi$
$948$	1.85693e7	0.671082
$949$	1.74170e7	0.627782
$950$	−116115.	−0.00417424
$951$	3.66130e7	1.31275
$952$	−8.25751e6	−0.295296
$953$	2.52748e7	0.901477	0.450739	−	0.892656i	$-0.351161\pi$
$953$	2.52748e7	0.901477	0.450739	+	0.892656i	$0.351161\pi$
$954$	−34819.3	−0.00123865
$955$	7.68428e6	0.272643
$956$	−2.00757e7	−0.710437
$957$	9.72068e6	0.343097
$958$	−1.75437e6	−0.0617601
$959$	−1.20131e7	−0.421802
$960$	1.22135e7	0.427721
$961$	−1.82532e7	−0.637574
$962$	−229792.	−0.00800566
$963$	−436080.	−0.0151531
$964$	−1.74340e7	−0.604232
$965$	−5.15256e6	−0.178117
$966$	−1.79923e6	−0.0620360
$967$	3.26403e7	1.12251	0.561253	−	0.827645i	$-0.310320\pi$
$967$	3.26403e7	1.12251	0.561253	+	0.827645i	$0.310320\pi$
$968$	−480230.	−0.0164725
$969$	8.05134e6	0.275460
$970$	−609149.	−0.0207871
$971$	−3.84502e7	−1.30873	−0.654365	−	0.756179i	$-0.727064\pi$
$971$	−3.84502e7	−1.30873	−0.654365	+	0.756179i	$0.727064\pi$
$972$	−706347.	−0.0239802
$973$	1.44104e7	0.487972
$974$	4.42269e6	0.149379
$975$	2.48487e6	0.0837129
$976$	2.15861e7	0.725352
$977$	−5.85125e7	−1.96116	−0.980578	−	0.196127i	$-0.937163\pi$
$977$	−5.85125e7	−1.96116	−0.980578	+	0.196127i	$0.937163\pi$
$978$	−2.02569e6	−0.0677214
$979$	−4.58587e6	−0.152920
$980$	−1.15271e7	−0.383404
$981$	96749.5	0.00320979
$982$	1.14625e6	0.0379315
$983$	−3.46871e7	−1.14494	−0.572471	−	0.819925i	$-0.694015\pi$
$983$	−3.46871e7	−1.14494	−0.572471	+	0.819925i	$0.694015\pi$
$984$	1.92643e6	0.0634256
$985$	2.38356e7	0.782771
$986$	3.74926e6	0.122816
$987$	2.98956e6	0.0976819
$988$	−2.90442e6	−0.0946600
$989$	−1.05604e6	−0.0343314
$990$	−4573.90	−0.000148320 0
$991$	−3.06000e7	−0.989778	−0.494889	−	0.868956i	$-0.664791\pi$
$991$	−3.06000e7	−0.989778	−0.494889	+	0.868956i	$0.664791\pi$
$992$	−5.03646e6	−0.162497
$993$	3.05064e7	0.981788
$994$	1.02053e6	0.0327612
$995$	6.07720e6	0.194601
$996$	554957.	0.0177260
$997$	2.15852e6	0.0687731	0.0343866	−	0.999409i	$-0.489052\pi$
$997$	2.15852e6	0.0687731	0.0343866	+	0.999409i	$0.489052\pi$
$998$	−1.98874e6	−0.0632051
$999$	6.63072e6	0.210207

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.20	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+0.514635 q^{2} -15.6824 q^{3} -31.7352 q^{4} +25.0000 q^{5} -8.07072 q^{6} +177.020 q^{7} -32.8003 q^{8} +2.93807 q^{9} +O(q^{10})\)	\(q+0.514635 q^{2} -15.6824 q^{3} -31.7352 q^{4} +25.0000 q^{5} -8.07072 q^{6} +177.020 q^{7} -32.8003 q^{8} +2.93807 q^{9} +12.8659 q^{10} -121.000 q^{11} +497.684 q^{12} -253.519 q^{13} +91.1008 q^{14} -392.060 q^{15} +998.645 q^{16} +1422.16 q^{17} +1.51203 q^{18} -361.000 q^{19} -793.379 q^{20} -2776.10 q^{21} -62.2708 q^{22} +1259.36 q^{23} +514.389 q^{24} +625.000 q^{25} -130.470 q^{26} +3764.75 q^{27} -5617.76 q^{28} +5122.69 q^{29} -201.768 q^{30} -3221.17 q^{31} +1563.55 q^{32} +1897.57 q^{33} +731.893 q^{34} +4425.51 q^{35} -93.2401 q^{36} +1761.26 q^{37} -185.783 q^{38} +3975.79 q^{39} -820.009 q^{40} +3745.08 q^{41} -1428.68 q^{42} -838.553 q^{43} +3839.95 q^{44} +73.4517 q^{45} +648.113 q^{46} -1076.89 q^{47} -15661.2 q^{48} +14529.2 q^{49} +321.647 q^{50} -22302.9 q^{51} +8045.47 q^{52} -23028.1 q^{53} +1937.47 q^{54} -3025.00 q^{55} -5806.33 q^{56} +5661.35 q^{57} +2636.32 q^{58} -16062.8 q^{59} +12442.1 q^{60} +21615.4 q^{61} -1657.73 q^{62} +520.098 q^{63} -31152.0 q^{64} -6337.98 q^{65} +976.557 q^{66} +34355.7 q^{67} -45132.4 q^{68} -19749.9 q^{69} +2277.52 q^{70} +11202.2 q^{71} -96.3697 q^{72} -68701.0 q^{73} +906.408 q^{74} -9801.51 q^{75} +11456.4 q^{76} -21419.5 q^{77} +2046.08 q^{78} +37311.5 q^{79} +24966.1 q^{80} -59754.3 q^{81} +1927.35 q^{82} +1115.08 q^{83} +88100.1 q^{84} +35554.0 q^{85} -431.549 q^{86} -80336.2 q^{87} +3968.84 q^{88} +37899.8 q^{89} +37.8008 q^{90} -44878.0 q^{91} -39966.1 q^{92} +50515.8 q^{93} -554.205 q^{94} -9025.00 q^{95} -24520.2 q^{96} -47346.1 q^{97} +7477.22 q^{98} -355.506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 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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