LMFDB - Embedded newform 1045.6.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.31861 q^{2} +2.12368 q^{3} -30.2613 q^{4} +25.0000 q^{5} -2.80029 q^{6} -96.2869 q^{7} +82.0982 q^{8} -238.490 q^{9} +O(q^{10})$	\(q-1.31861 q^{2} +2.12368 q^{3} -30.2613 q^{4} +25.0000 q^{5} -2.80029 q^{6} -96.2869 q^{7} +82.0982 q^{8} -238.490 q^{9} -32.9652 q^{10} -121.000 q^{11} -64.2651 q^{12} +901.259 q^{13} +126.965 q^{14} +53.0919 q^{15} +860.105 q^{16} +924.084 q^{17} +314.475 q^{18} -361.000 q^{19} -756.532 q^{20} -204.482 q^{21} +159.552 q^{22} +3250.76 q^{23} +174.350 q^{24} +625.000 q^{25} -1188.41 q^{26} -1022.53 q^{27} +2913.76 q^{28} -6637.06 q^{29} -70.0074 q^{30} -1622.73 q^{31} -3761.28 q^{32} -256.965 q^{33} -1218.50 q^{34} -2407.17 q^{35} +7217.01 q^{36} -5539.28 q^{37} +476.017 q^{38} +1913.98 q^{39} +2052.45 q^{40} +5639.42 q^{41} +269.632 q^{42} -7064.91 q^{43} +3661.61 q^{44} -5962.25 q^{45} -4286.48 q^{46} -25581.3 q^{47} +1826.59 q^{48} -7535.83 q^{49} -824.130 q^{50} +1962.45 q^{51} -27273.2 q^{52} -5936.73 q^{53} +1348.31 q^{54} -3025.00 q^{55} -7904.98 q^{56} -766.647 q^{57} +8751.68 q^{58} -22312.2 q^{59} -1606.63 q^{60} +9337.37 q^{61} +2139.74 q^{62} +22963.5 q^{63} -22563.7 q^{64} +22531.5 q^{65} +338.836 q^{66} -3078.38 q^{67} -27964.0 q^{68} +6903.56 q^{69} +3174.12 q^{70} +76695.1 q^{71} -19579.6 q^{72} -25049.0 q^{73} +7304.14 q^{74} +1327.30 q^{75} +10924.3 q^{76} +11650.7 q^{77} -2523.79 q^{78} +43122.3 q^{79} +21502.6 q^{80} +55781.6 q^{81} -7436.18 q^{82} -27803.2 q^{83} +6187.89 q^{84} +23102.1 q^{85} +9315.84 q^{86} -14095.0 q^{87} -9933.88 q^{88} +28343.7 q^{89} +7861.87 q^{90} -86779.4 q^{91} -98372.1 q^{92} -3446.15 q^{93} +33731.7 q^{94} -9025.00 q^{95} -7987.75 q^{96} -14690.8 q^{97} +9936.81 q^{98} +28857.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.31861	−0.233099	−0.116550	−	0.993185i	$-0.537183\pi$
$2$	−1.31861	−0.233099	−0.116550	+	0.993185i	$0.537183\pi$
$3$	2.12368	0.136234	0.0681169	−	0.997677i	$-0.478301\pi$
$3$	2.12368	0.136234	0.0681169	+	0.997677i	$0.478301\pi$
$4$	−30.2613	−0.945665
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−2.80029	−0.0317560
$7$	−96.2869	−0.742715	−0.371357	−	0.928490i	$-0.621108\pi$
$7$	−96.2869	−0.742715	−0.371357	+	0.928490i	$0.621108\pi$
$8$	82.0982	0.453533
$9$	−238.490	−0.981440
$10$	−32.9652	−0.104245
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−64.2651	−0.128832
$13$	901.259	1.47908	0.739539	−	0.673114i	$-0.235044\pi$
$13$	901.259	1.47908	0.739539	+	0.673114i	$0.235044\pi$
$14$	126.965	0.173126
$15$	53.0919	0.0609256
$16$	860.105	0.839947
$17$	924.084	0.775513	0.387756	−	0.921762i	$-0.373250\pi$
$17$	924.084	0.775513	0.387756	+	0.921762i	$0.373250\pi$
$18$	314.475	0.228773
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−756.532	−0.422914
$21$	−204.482	−0.101183
$22$	159.552	0.0702820
$23$	3250.76	1.28134	0.640671	−	0.767815i	$-0.278656\pi$
$23$	3250.76	1.28134	0.640671	+	0.767815i	$0.278656\pi$
$24$	174.350	0.0617865
$25$	625.000	0.200000
$26$	−1188.41	−0.344772
$27$	−1022.53	−0.269939
$28$	2913.76	0.702359
$29$	−6637.06	−1.46548	−0.732741	−	0.680507i	$-0.761759\pi$
$29$	−6637.06	−1.46548	−0.732741	+	0.680507i	$0.761759\pi$
$30$	−70.0074	−0.0142017
$31$	−1622.73	−0.303279	−0.151639	−	0.988436i	$-0.548455\pi$
$31$	−1622.73	−0.303279	−0.151639	+	0.988436i	$0.548455\pi$
$32$	−3761.28	−0.649324
$33$	−256.965	−0.0410761
$34$	−1218.50	−0.180771
$35$	−2407.17	−0.332152
$36$	7217.01	0.928114
$37$	−5539.28	−0.665195	−0.332598	−	0.943069i	$-0.607925\pi$
$37$	−5539.28	−0.665195	−0.332598	+	0.943069i	$0.607925\pi$
$38$	476.017	0.0534766
$39$	1913.98	0.201500
$40$	2052.45	0.202826
$41$	5639.42	0.523932	0.261966	−	0.965077i	$-0.415629\pi$
$41$	5639.42	0.523932	0.261966	+	0.965077i	$0.415629\pi$
$42$	269.632	0.0235856
$43$	−7064.91	−0.582687	−0.291344	−	0.956618i	$-0.594102\pi$
$43$	−7064.91	−0.582687	−0.291344	+	0.956618i	$0.594102\pi$
$44$	3661.61	0.285129
$45$	−5962.25	−0.438913
$46$	−4286.48	−0.298680
$47$	−25581.3	−1.68919	−0.844593	−	0.535409i	$-0.820158\pi$
$47$	−25581.3	−1.68919	−0.844593	+	0.535409i	$0.820158\pi$
$48$	1826.59	0.114429
$49$	−7535.83	−0.448375
$50$	−824.130	−0.0466198
$51$	1962.45	0.105651
$52$	−27273.2	−1.39871
$53$	−5936.73	−0.290307	−0.145153	−	0.989409i	$-0.546368\pi$
$53$	−5936.73	−0.290307	−0.145153	+	0.989409i	$0.546368\pi$
$54$	1348.31	0.0629226
$55$	−3025.00	−0.134840
$56$	−7904.98	−0.336845
$57$	−766.647	−0.0312542
$58$	8751.68	0.341603
$59$	−22312.2	−0.834475	−0.417237	−	0.908798i	$-0.637002\pi$
$59$	−22312.2	−0.834475	−0.417237	+	0.908798i	$0.637002\pi$
$60$	−1606.63	−0.0576152
$61$	9337.37	0.321292	0.160646	−	0.987012i	$-0.448642\pi$
$61$	9337.37	0.321292	0.160646	+	0.987012i	$0.448642\pi$
$62$	2139.74	0.0706940
$63$	22963.5	0.728930
$64$	−22563.7	−0.688590
$65$	22531.5	0.661464
$66$	338.836	0.00957479
$67$	−3078.38	−0.0837789	−0.0418895	−	0.999122i	$-0.513338\pi$
$67$	−3078.38	−0.0837789	−0.0418895	+	0.999122i	$0.513338\pi$
$68$	−27964.0	−0.733375
$69$	6903.56	0.174562
$70$	3174.12	0.0774244
$71$	76695.1	1.80560	0.902800	−	0.430061i	$-0.141508\pi$
$71$	76695.1	1.80560	0.902800	+	0.430061i	$0.141508\pi$
$72$	−19579.6	−0.445115
$73$	−25049.0	−0.550152	−0.275076	−	0.961423i	$-0.588703\pi$
$73$	−25049.0	−0.550152	−0.275076	+	0.961423i	$0.588703\pi$
$74$	7304.14	0.155056
$75$	1327.30	0.0272468
$76$	10924.3	0.216950
$77$	11650.7	0.223937
$78$	−2523.79	−0.0469696
$79$	43122.3	0.777382	0.388691	−	0.921368i	$-0.372927\pi$
$79$	43122.3	0.777382	0.388691	+	0.921368i	$0.372927\pi$
$80$	21502.6	0.375636
$81$	55781.6	0.944665
$82$	−7436.18	−0.122128
$83$	−27803.2	−0.442995	−0.221498	−	0.975161i	$-0.571094\pi$
$83$	−27803.2	−0.442995	−0.221498	+	0.975161i	$0.571094\pi$
$84$	6187.89	0.0956851
$85$	23102.1	0.346820
$86$	9315.84	0.135824
$87$	−14095.0	−0.199648
$88$	−9933.88	−0.136745
$89$	28343.7	0.379299	0.189649	−	0.981852i	$-0.439265\pi$
$89$	28343.7	0.379299	0.189649	+	0.981852i	$0.439265\pi$
$90$	7861.87	0.102310
$91$	−86779.4	−1.09853
$92$	−98372.1	−1.21172
$93$	−3446.15	−0.0413168
$94$	33731.7	0.393748
$95$	−9025.00	−0.102598
$96$	−7987.75	−0.0884598
$97$	−14690.8	−0.158532	−0.0792658	−	0.996854i	$-0.525258\pi$
$97$	−14690.8	−0.158532	−0.0792658	+	0.996854i	$0.525258\pi$
$98$	9936.81	0.104516
$99$	28857.3	0.295915
$100$	−18913.3	−0.189133
$101$	−5747.12	−0.0560592	−0.0280296	−	0.999607i	$-0.508923\pi$
$101$	−5747.12	−0.0560592	−0.0280296	+	0.999607i	$0.508923\pi$
$102$	−2587.71	−0.0246272
$103$	105552.	0.980333	0.490167	−	0.871629i	$-0.336936\pi$
$103$	105552.	0.980333	0.490167	+	0.871629i	$0.336936\pi$
$104$	73991.7	0.670810
$105$	−5112.05	−0.0452504
$106$	7828.21	0.0676703
$107$	50309.6	0.424807	0.212403	−	0.977182i	$-0.431871\pi$
$107$	50309.6	0.424807	0.212403	+	0.977182i	$0.431871\pi$
$108$	30943.0	0.255272
$109$	−15017.9	−0.121072	−0.0605358	−	0.998166i	$-0.519281\pi$
$109$	−15017.9	−0.121072	−0.0605358	+	0.998166i	$0.519281\pi$
$110$	3988.79	0.0314311
$111$	−11763.6	−0.0906221
$112$	−82816.9	−0.623841
$113$	−117757.	−0.867546	−0.433773	−	0.901022i	$-0.642818\pi$
$113$	−117757.	−0.867546	−0.433773	+	0.901022i	$0.642818\pi$
$114$	1010.91	0.00728532
$115$	81269.0	0.573034
$116$	200846.	1.38586
$117$	−214941.	−1.45163
$118$	29421.1	0.194515
$119$	−88977.2	−0.575985
$120$	4358.75	0.0276318
$121$	14641.0	0.0909091
$122$	−12312.3	−0.0748929
$123$	11976.3	0.0713772
$124$	49105.8	0.286800
$125$	15625.0	0.0894427
$126$	−30279.8	−0.169913
$127$	−83704.3	−0.460509	−0.230255	−	0.973130i	$-0.573956\pi$
$127$	−83704.3	−0.460509	−0.230255	+	0.973130i	$0.573956\pi$
$128$	150114.	0.809833
$129$	−15003.6	−0.0793817
$130$	−29710.2	−0.154187
$131$	289492.	1.47387	0.736934	−	0.675965i	$-0.236273\pi$
$131$	289492.	1.47387	0.736934	+	0.675965i	$0.236273\pi$
$132$	7776.08	0.0388442
$133$	34759.6	0.170390
$134$	4059.17	0.0195288
$135$	−25563.2	−0.120721
$136$	75865.6	0.351720
$137$	204654.	0.931577	0.465789	−	0.884896i	$-0.345771\pi$
$137$	204654.	0.931577	0.465789	+	0.884896i	$0.345771\pi$
$138$	−9103.08	−0.0406903
$139$	−132468.	−0.581534	−0.290767	−	0.956794i	$-0.593910\pi$
$139$	−132468.	−0.581534	−0.290767	+	0.956794i	$0.593910\pi$
$140$	72844.1	0.314105
$141$	−54326.3	−0.230124
$142$	−101131.	−0.420884
$143$	−109052.	−0.445959
$144$	−205127.	−0.824358
$145$	−165926.	−0.655384
$146$	33029.7	0.128240
$147$	−16003.7	−0.0610838
$148$	167626.	0.629052
$149$	−169722.	−0.626287	−0.313143	−	0.949706i	$-0.601382\pi$
$149$	−169722.	−0.626287	−0.313143	+	0.949706i	$0.601382\pi$
$150$	−1750.18	−0.00635120
$151$	−97816.2	−0.349115	−0.174557	−	0.984647i	$-0.555849\pi$
$151$	−97816.2	−0.349115	−0.174557	+	0.984647i	$0.555849\pi$
$152$	−29637.4	−0.104048
$153$	−220385.	−0.761120
$154$	−15362.7	−0.0521995
$155$	−40568.2	−0.135630
$156$	−57919.5	−0.190552
$157$	−93936.7	−0.304149	−0.152074	−	0.988369i	$-0.548595\pi$
$157$	−93936.7	−0.304149	−0.152074	+	0.988369i	$0.548595\pi$
$158$	−56861.4	−0.181207
$159$	−12607.7	−0.0395496
$160$	−94032.1	−0.290386
$161$	−313006.	−0.951672
$162$	−73554.0	−0.220201
$163$	−423273.	−1.24782	−0.623910	−	0.781496i	$-0.714457\pi$
$163$	−423273.	−1.24782	−0.623910	+	0.781496i	$0.714457\pi$
$164$	−170656.	−0.495464
$165$	−6424.12	−0.0183698
$166$	36661.5	0.103262
$167$	367223.	1.01892	0.509458	−	0.860495i	$-0.329846\pi$
$167$	367223.	1.01892	0.509458	+	0.860495i	$0.329846\pi$
$168$	−16787.6	−0.0458898
$169$	440974.	1.18767
$170$	−30462.6	−0.0808434
$171$	86094.9	0.225158
$172$	213793.	0.551027
$173$	714816.	1.81584	0.907922	−	0.419138i	$-0.137668\pi$
$173$	714816.	1.81584	0.907922	+	0.419138i	$0.137668\pi$
$174$	18585.7	0.0465378
$175$	−60179.3	−0.148543
$176$	−104073.	−0.253253
$177$	−47384.0	−0.113684
$178$	−37374.2	−0.0884142
$179$	−349966.	−0.816381	−0.408191	−	0.912897i	$-0.633840\pi$
$179$	−349966.	−0.816381	−0.408191	+	0.912897i	$0.633840\pi$
$180$	180425.	0.415065
$181$	543352.	1.23278	0.616388	−	0.787442i	$-0.288595\pi$
$181$	543352.	1.23278	0.616388	+	0.787442i	$0.288595\pi$
$182$	114428.	0.256067
$183$	19829.5	0.0437708
$184$	266881.	0.581131
$185$	−138482.	−0.297484
$186$	4544.12	0.00963091
$187$	−111814.	−0.233826
$188$	774122.	1.59740
$189$	98456.1	0.200488
$190$	11900.4	0.0239155
$191$	−341895.	−0.678123	−0.339062	−	0.940764i	$-0.610110\pi$
$191$	−341895.	−0.678123	−0.339062	+	0.940764i	$0.610110\pi$
$192$	−47918.0	−0.0938093
$193$	561183.	1.08445	0.542227	−	0.840232i	$-0.317581\pi$
$193$	561183.	1.08445	0.542227	+	0.840232i	$0.317581\pi$
$194$	19371.4	0.0369536
$195$	47849.5	0.0901137
$196$	228044.	0.424012
$197$	−391268.	−0.718305	−0.359153	−	0.933279i	$-0.616934\pi$
$197$	−391268.	−0.718305	−0.359153	+	0.933279i	$0.616934\pi$
$198$	−38051.4	−0.0689776
$199$	588617.	1.05366	0.526829	−	0.849971i	$-0.323381\pi$
$199$	588617.	1.05366	0.526829	+	0.849971i	$0.323381\pi$
$200$	51311.4	0.0907065
$201$	−6537.47	−0.0114135
$202$	7578.19	0.0130673
$203$	639062.	1.08844
$204$	−59386.4	−0.0999105
$205$	140985.	0.234309
$206$	−139182.	−0.228515
$207$	−775274.	−1.25756
$208$	775177.	1.24235
$209$	43681.0	0.0691714
$210$	6740.79	0.0105478
$211$	686310.	1.06124	0.530621	−	0.847609i	$-0.321959\pi$
$211$	686310.	1.06124	0.530621	+	0.847609i	$0.321959\pi$
$212$	179653.	0.274533
$213$	162875.	0.245984
$214$	−66338.6	−0.0990221
$215$	−176623.	−0.260586
$216$	−83947.7	−0.122426
$217$	156248.	0.225249
$218$	19802.7	0.0282217
$219$	−53195.9	−0.0749493
$220$	91540.4	0.127513
$221$	832838.	1.14704
$222$	15511.6	0.0211239
$223$	−449288.	−0.605010	−0.302505	−	0.953148i	$-0.597823\pi$
$223$	−449288.	−0.605010	−0.302505	+	0.953148i	$0.597823\pi$
$224$	362162.	0.482262
$225$	−149056.	−0.196288
$226$	155276.	0.202224
$227$	1.00982e6	1.30071	0.650354	−	0.759631i	$-0.274621\pi$
$227$	1.00982e6	1.30071	0.650354	+	0.759631i	$0.274621\pi$
$228$	23199.7	0.0295560
$229$	924805.	1.16536	0.582682	−	0.812701i	$-0.302003\pi$
$229$	924805.	1.16536	0.582682	+	0.812701i	$0.302003\pi$
$230$	−107162.	−0.133574
$231$	24742.3	0.0305078
$232$	−544890.	−0.664644
$233$	−617750.	−0.745458	−0.372729	−	0.927940i	$-0.621578\pi$
$233$	−617750.	−0.745458	−0.372729	+	0.927940i	$0.621578\pi$
$234$	283423.	0.338373
$235$	−639532.	−0.755427
$236$	675197.	0.789133
$237$	91577.8	0.105906
$238$	117326.	0.134262
$239$	457418.	0.517986	0.258993	−	0.965879i	$-0.416609\pi$
$239$	457418.	0.517986	0.258993	+	0.965879i	$0.416609\pi$
$240$	45664.6	0.0511743
$241$	−915477.	−1.01532	−0.507662	−	0.861556i	$-0.669490\pi$
$241$	−915477.	−1.01532	−0.507662	+	0.861556i	$0.669490\pi$
$242$	−19305.7	−0.0211908
$243$	366936.	0.398635
$244$	−282561.	−0.303834
$245$	−188396.	−0.200519
$246$	−15792.0	−0.0166380
$247$	−325354.	−0.339324
$248$	−133223.	−0.137547
$249$	−59044.9	−0.0603509
$250$	−20603.2	−0.0208490
$251$	1.00020e6	1.00208	0.501038	−	0.865425i	$-0.332952\pi$
$251$	1.00020e6	1.00208	0.501038	+	0.865425i	$0.332952\pi$
$252$	−694904.	−0.689324
$253$	−393342.	−0.386339
$254$	110373.	0.107344
$255$	49061.4	0.0472486
$256$	524098.	0.499819
$257$	−1.85918e6	−1.75586	−0.877928	−	0.478793i	$-0.841074\pi$
$257$	−1.85918e6	−1.75586	−0.877928	+	0.478793i	$0.841074\pi$
$258$	19783.8	0.0185038
$259$	533360.	0.494051
$260$	−681831.	−0.625523
$261$	1.58287e6	1.43828
$262$	−381726.	−0.343557
$263$	410483.	0.365936	0.182968	−	0.983119i	$-0.441429\pi$
$263$	410483.	0.365936	0.182968	+	0.983119i	$0.441429\pi$
$264$	−21096.3	−0.0186293
$265$	−148418.	−0.129829
$266$	−45834.2	−0.0397179
$267$	60192.8	0.0516733
$268$	93155.6	0.0792268
$269$	−110772.	−0.0933357	−0.0466679	−	0.998910i	$-0.514860\pi$
$269$	−110772.	−0.0933357	−0.0466679	+	0.998910i	$0.514860\pi$
$270$	33707.8	0.0281398
$271$	1.67099e6	1.38214	0.691069	−	0.722788i	$-0.257140\pi$
$271$	1.67099e6	1.38214	0.691069	+	0.722788i	$0.257140\pi$
$272$	794810.	0.651390
$273$	−184291.	−0.149657
$274$	−269858.	−0.217150
$275$	−75625.0	−0.0603023
$276$	−208910.	−0.165077
$277$	604011.	0.472983	0.236491	−	0.971634i	$-0.424003\pi$
$277$	604011.	0.472983	0.236491	+	0.971634i	$0.424003\pi$
$278$	174674.	0.135555
$279$	387005.	0.297650
$280$	−197625.	−0.150642
$281$	1.12981e6	0.853568	0.426784	−	0.904354i	$-0.359647\pi$
$281$	1.12981e6	0.853568	0.426784	+	0.904354i	$0.359647\pi$
$282$	71635.1	0.0536418
$283$	1.03884e6	0.771049	0.385524	−	0.922698i	$-0.374021\pi$
$283$	1.03884e6	0.771049	0.385524	+	0.922698i	$0.374021\pi$
$284$	−2.32089e6	−1.70749
$285$	−19166.2	−0.0139773
$286$	143797.	0.103953
$287$	−543002.	−0.389132
$288$	897029.	0.637272
$289$	−565926.	−0.398580
$290$	218792.	0.152769
$291$	−31198.5	−0.0215974
$292$	758013.	0.520259
$293$	−1.48323e6	−1.00935	−0.504673	−	0.863311i	$-0.668387\pi$
$293$	−1.48323e6	−1.00935	−0.504673	+	0.863311i	$0.668387\pi$
$294$	21102.6	0.0142386
$295$	−557806.	−0.373188
$296$	−454765.	−0.301688
$297$	123726.	0.0813897
$298$	223797.	0.145987
$299$	2.92977e6	1.89520
$300$	−40165.7	−0.0257663
$301$	680258.	0.432770
$302$	128981.	0.0813784
$303$	−12205.0	−0.00763715
$304$	−310498.	−0.192697
$305$	233434.	0.143686
$306$	290601.	0.177416
$307$	221454.	0.134103	0.0670513	−	0.997750i	$-0.478641\pi$
$307$	221454.	0.134103	0.0670513	+	0.997750i	$0.478641\pi$
$308$	−352565.	−0.211769
$309$	224158.	0.133555
$310$	53493.6	0.0316153
$311$	−3.00539e6	−1.76197	−0.880986	−	0.473142i	$-0.843120\pi$
$311$	−3.00539e6	−1.76197	−0.880986	+	0.473142i	$0.843120\pi$
$312$	157134.	0.0913870
$313$	2.44641e6	1.41146	0.705729	−	0.708482i	$-0.250620\pi$
$313$	2.44641e6	1.41146	0.705729	+	0.708482i	$0.250620\pi$
$314$	123866.	0.0708969
$315$	574087.	0.325988
$316$	−1.30494e6	−0.735142
$317$	1.66430e6	0.930218	0.465109	−	0.885253i	$-0.346015\pi$
$317$	1.66430e6	0.930218	0.465109	+	0.885253i	$0.346015\pi$
$318$	16624.6	0.00921898
$319$	803084.	0.441860
$320$	−564093.	−0.307947
$321$	106841.	0.0578731
$322$	412731.	0.221834
$323$	−333594.	−0.177915
$324$	−1.68802e6	−0.893337
$325$	563287.	0.295816
$326$	558131.	0.290866
$327$	−31893.1	−0.0164941
$328$	462986.	0.237620
$329$	2.46314e6	1.25458
$330$	8470.89	0.00428198
$331$	−670756.	−0.336507	−0.168254	−	0.985744i	$-0.553813\pi$
$331$	−670756.	−0.336507	−0.168254	+	0.985744i	$0.553813\pi$
$332$	841359.	0.418925
$333$	1.32106e6	0.652850
$334$	−484223.	−0.237508
$335$	−76959.4	−0.0374671
$336$	−175876.	−0.0849883
$337$	900227.	0.431795	0.215897	−	0.976416i	$-0.430732\pi$
$337$	900227.	0.431795	0.215897	+	0.976416i	$0.430732\pi$
$338$	−581472.	−0.276845
$339$	−250079.	−0.118189
$340$	−699099.	−0.327975
$341$	196350.	0.0914419
$342$	−113525.	−0.0524841
$343$	2.34390e6	1.07573
$344$	−580016.	−0.264268
$345$	172589.	0.0780666
$346$	−942561.	−0.423272
$347$	−703529.	−0.313659	−0.156830	−	0.987626i	$-0.550127\pi$
$347$	−703529.	−0.313659	−0.156830	+	0.987626i	$0.550127\pi$
$348$	426531.	0.188800
$349$	−1.77261e6	−0.779020	−0.389510	−	0.921022i	$-0.627356\pi$
$349$	−1.77261e6	−0.779020	−0.389510	+	0.921022i	$0.627356\pi$
$350$	79352.9	0.0346252
$351$	−921563.	−0.399261
$352$	455115.	0.195778
$353$	−40019.5	−0.0170937	−0.00854683	−	0.999963i	$-0.502721\pi$
$353$	−40019.5	−0.0170937	−0.00854683	+	0.999963i	$0.502721\pi$
$354$	62480.9	0.0264996
$355$	1.91738e6	0.807489
$356$	−857716.	−0.358690
$357$	−188959.	−0.0784687
$358$	461468.	0.190298
$359$	4.04488e6	1.65642	0.828208	−	0.560421i	$-0.189361\pi$
$359$	4.04488e6	1.65642	0.828208	+	0.560421i	$0.189361\pi$
$360$	−489490.	−0.199062
$361$	130321.	0.0526316
$362$	−716467.	−0.287359
$363$	31092.7	0.0123849
$364$	2.62605e6	1.03884
$365$	−626224.	−0.246035
$366$	−26147.4	−0.0102029
$367$	2.21792e6	0.859570	0.429785	−	0.902931i	$-0.358589\pi$
$367$	2.21792e6	0.859570	0.429785	+	0.902931i	$0.358589\pi$
$368$	2.79600e6	1.07626
$369$	−1.34494e6	−0.514208
$370$	182604.	0.0693433
$371$	571629.	0.215615
$372$	104285.	0.0390719
$373$	−2.95084e6	−1.09818	−0.549091	−	0.835763i	$-0.685026\pi$
$373$	−2.95084e6	−1.09818	−0.549091	+	0.835763i	$0.685026\pi$
$374$	147439.	0.0545046
$375$	33182.4	0.0121851
$376$	−2.10018e6	−0.766101
$377$	−5.98171e6	−2.16756
$378$	−129825.	−0.0467335
$379$	−1.44783e6	−0.517748	−0.258874	−	0.965911i	$-0.583351\pi$
$379$	−1.44783e6	−0.517748	−0.258874	+	0.965911i	$0.583351\pi$
$380$	273108.	0.0970232
$381$	−177761.	−0.0627370
$382$	450825.	0.158070
$383$	−2.07980e6	−0.724477	−0.362239	−	0.932085i	$-0.617987\pi$
$383$	−2.07980e6	−0.724477	−0.362239	+	0.932085i	$0.617987\pi$
$384$	318793.	0.110327
$385$	291268.	0.100148
$386$	−739980.	−0.252785
$387$	1.68491e6	0.571873
$388$	444562.	0.149918
$389$	249239.	0.0835105	0.0417553	−	0.999128i	$-0.486705\pi$
$389$	249239.	0.0835105	0.0417553	+	0.999128i	$0.486705\pi$
$390$	−63094.7	−0.0210054
$391$	3.00397e6	0.993698
$392$	−618678.	−0.203353
$393$	614787.	0.200791
$394$	515929.	0.167436
$395$	1.07806e6	0.347656
$396$	−873258.	−0.279837
$397$	3.46227e6	1.10252	0.551258	−	0.834335i	$-0.314148\pi$
$397$	3.46227e6	1.10252	0.551258	+	0.834335i	$0.314148\pi$
$398$	−776155.	−0.245607
$399$	73818.1	0.0232130
$400$	537566.	0.167989
$401$	−379032.	−0.117710	−0.0588552	−	0.998267i	$-0.518745\pi$
$401$	−379032.	−0.117710	−0.0588552	+	0.998267i	$0.518745\pi$
$402$	8620.36	0.00266048
$403$	−1.46250e6	−0.448573
$404$	173915.	0.0530132
$405$	1.39454e6	0.422467
$406$	−842672.	−0.253713
$407$	670253.	0.200564
$408$	161114.	0.0479162
$409$	1.11474e6	0.329508	0.164754	−	0.986335i	$-0.447317\pi$
$409$	1.11474e6	0.329508	0.164754	+	0.986335i	$0.447317\pi$
$410$	−185904.	−0.0546173
$411$	434619.	0.126912
$412$	−3.19414e6	−0.927067
$413$	2.14838e6	0.619777
$414$	1.02228e6	0.293136
$415$	−695079.	−0.198113
$416$	−3.38989e6	−0.960400
$417$	−281320.	−0.0792246
$418$	−57598.1	−0.0161238
$419$	5.14607e6	1.43199	0.715997	−	0.698104i	$-0.245973\pi$
$419$	5.14607e6	1.43199	0.715997	+	0.698104i	$0.245973\pi$
$420$	154697.	0.0427917
$421$	1.12748e6	0.310029	0.155014	−	0.987912i	$-0.450458\pi$
$421$	1.12748e6	0.310029	0.155014	+	0.987912i	$0.450458\pi$
$422$	−904974.	−0.247374
$423$	6.10088e6	1.65784
$424$	−487394.	−0.131664
$425$	577552.	0.155103
$426$	−214769.	−0.0573386
$427$	−899066.	−0.238628
$428$	−1.52243e6	−0.401725
$429$	−231592.	−0.0607547
$430$	232896.	0.0607423
$431$	−1.38240e6	−0.358459	−0.179230	−	0.983807i	$-0.557360\pi$
$431$	−1.38240e6	−0.358459	−0.179230	+	0.983807i	$0.557360\pi$
$432$	−879482.	−0.226735
$433$	−828562.	−0.212376	−0.106188	−	0.994346i	$-0.533865\pi$
$433$	−828562.	−0.212376	−0.106188	+	0.994346i	$0.533865\pi$
$434$	−206029.	−0.0525055
$435$	−352374.	−0.0892855
$436$	454460.	0.114493
$437$	−1.17352e6	−0.293960
$438$	70144.5	0.0174706
$439$	6.52984e6	1.61712	0.808558	−	0.588417i	$-0.200249\pi$
$439$	6.52984e6	1.61712	0.808558	+	0.588417i	$0.200249\pi$
$440$	−248347.	−0.0611543
$441$	1.79722e6	0.440053
$442$	−1.09819e6	−0.267375
$443$	319104.	0.0772543	0.0386271	−	0.999254i	$-0.487702\pi$
$443$	319104.	0.0772543	0.0386271	+	0.999254i	$0.487702\pi$
$444$	355983.	0.0856982
$445$	708592.	0.169628
$446$	592434.	0.141027
$447$	−360435.	−0.0853215
$448$	2.17259e6	0.511426
$449$	−3.77064e6	−0.882671	−0.441336	−	0.897342i	$-0.645495\pi$
$449$	−3.77064e6	−0.882671	−0.441336	+	0.897342i	$0.645495\pi$
$450$	196547.	0.0457546
$451$	−682369.	−0.157971
$452$	3.56349e6	0.820407
$453$	−207730.	−0.0475613
$454$	−1.33156e6	−0.303194
$455$	−2.16948e6	−0.491279
$456$	−62940.3	−0.0141748
$457$	3.01341e6	0.674945	0.337472	−	0.941335i	$-0.390428\pi$
$457$	3.01341e6	0.674945	0.337472	+	0.941335i	$0.390428\pi$
$458$	−1.21945e6	−0.271645
$459$	−944902.	−0.209341
$460$	−2.45930e6	−0.541898
$461$	7.54024e6	1.65247	0.826234	−	0.563327i	$-0.190479\pi$
$461$	7.54024e6	1.65247	0.826234	+	0.563327i	$0.190479\pi$
$462$	−32625.4	−0.00711134
$463$	5.37347e6	1.16494	0.582469	−	0.812853i	$-0.302087\pi$
$463$	5.37347e6	1.16494	0.582469	+	0.812853i	$0.302087\pi$
$464$	−5.70857e6	−1.23093
$465$	−86153.7	−0.0184774
$466$	814570.	0.173766
$467$	6.20121e6	1.31578	0.657892	−	0.753112i	$-0.271448\pi$
$467$	6.20121e6	1.31578	0.657892	+	0.753112i	$0.271448\pi$
$468$	6.50439e6	1.37275
$469$	296407.	0.0622238
$470$	843292.	0.176089
$471$	−199491.	−0.0414354
$472$	−1.83179e6	−0.378462
$473$	854854.	0.175687
$474$	−120755.	−0.0246865
$475$	−225625.	−0.0458831
$476$	2.69256e6	0.544689
$477$	1.41585e6	0.284919
$478$	−603155.	−0.120742
$479$	1.48177e6	0.295081	0.147541	−	0.989056i	$-0.452864\pi$
$479$	1.48177e6	0.295081	0.147541	+	0.989056i	$0.452864\pi$
$480$	−199694.	−0.0395604
$481$	−4.99233e6	−0.983876
$482$	1.20716e6	0.236671
$483$	−664722.	−0.129650
$484$	−443055.	−0.0859695
$485$	−367270.	−0.0708974
$486$	−483845.	−0.0929214
$487$	−5.18126e6	−0.989949	−0.494974	−	0.868908i	$-0.664823\pi$
$487$	−5.18126e6	−0.989949	−0.494974	+	0.868908i	$0.664823\pi$
$488$	766581.	0.145716
$489$	−898895.	−0.169995
$490$	248420.	0.0467408
$491$	−617493.	−0.115592	−0.0577960	−	0.998328i	$-0.518407\pi$
$491$	−617493.	−0.115592	−0.0577960	+	0.998328i	$0.518407\pi$
$492$	−362418.	−0.0674989
$493$	−6.13320e6	−1.13650
$494$	429015.	0.0790960
$495$	721432.	0.132337
$496$	−1.39572e6	−0.254738
$497$	−7.38473e6	−1.34105
$498$	77857.0	0.0140677
$499$	8.05645e6	1.44841	0.724206	−	0.689583i	$-0.242206\pi$
$499$	8.05645e6	1.44841	0.724206	+	0.689583i	$0.242206\pi$
$500$	−472832.	−0.0845828
$501$	779862.	0.138811
$502$	−1.31887e6	−0.233583
$503$	−5.54222e6	−0.976706	−0.488353	−	0.872646i	$-0.662402\pi$
$503$	−5.54222e6	−0.976706	−0.488353	+	0.872646i	$0.662402\pi$
$504$	1.88526e6	0.330594
$505$	−143678.	−0.0250704
$506$	518664.	0.0900553
$507$	936486.	0.161801
$508$	2.53300e6	0.435488
$509$	−58301.6	−0.00997439	−0.00498719	−	0.999988i	$-0.501587\pi$
$509$	−58301.6	−0.00997439	−0.00498719	+	0.999988i	$0.501587\pi$
$510$	−64692.7	−0.0110136
$511$	2.41189e6	0.408606
$512$	−5.49472e6	−0.926341
$513$	369133.	0.0619283
$514$	2.45153e6	0.409288
$515$	2.63880e6	0.438418
$516$	454027.	0.0750685
$517$	3.09533e6	0.509309
$518$	−703293.	−0.115163
$519$	1.51804e6	0.247380
$520$	1.84979e6	0.299995
$521$	−5.60145e6	−0.904079	−0.452039	−	0.891998i	$-0.649303\pi$
$521$	−5.60145e6	−0.904079	−0.452039	+	0.891998i	$0.649303\pi$
$522$	−2.08719e6	−0.335263
$523$	6.48899e6	1.03734	0.518672	−	0.854973i	$-0.326427\pi$
$523$	6.48899e6	1.03734	0.518672	+	0.854973i	$0.326427\pi$
$524$	−8.76040e6	−1.39378
$525$	−127801.	−0.0202366
$526$	−541266.	−0.0852994
$527$	−1.49954e6	−0.235196
$528$	−221017.	−0.0345017
$529$	4.13109e6	0.641838
$530$	195705.	0.0302631
$531$	5.32125e6	0.818987
$532$	−1.05187e6	−0.161132
$533$	5.08257e6	0.774936
$534$	−79370.7	−0.0120450
$535$	1.25774e6	0.189979
$536$	−252729.	−0.0379965
$537$	−743214.	−0.111219
$538$	146064.	0.0217565
$539$	911836.	0.135190
$540$	773575.	0.114161
$541$	−4.26157e6	−0.626003	−0.313002	−	0.949753i	$-0.601335\pi$
$541$	−4.26157e6	−0.626003	−0.313002	+	0.949753i	$0.601335\pi$
$542$	−2.20339e6	−0.322175
$543$	1.15390e6	0.167946
$544$	−3.47574e6	−0.503559
$545$	−375447.	−0.0541449
$546$	243008.	0.0348850
$547$	1.34697e7	1.92481	0.962407	−	0.271610i	$-0.0875560\pi$
$547$	1.34697e7	1.92481	0.962407	+	0.271610i	$0.0875560\pi$
$548$	−6.19309e6	−0.880960
$549$	−2.22687e6	−0.315329
$550$	99719.7	0.0140564
$551$	2.39598e6	0.336205
$552$	566770.	0.0791697
$553$	−4.15211e6	−0.577373
$554$	−796453.	−0.110252
$555$	−294091.	−0.0405274
$556$	4.00866e6	0.549936
$557$	−5.09874e6	−0.696346	−0.348173	−	0.937430i	$-0.613198\pi$
$557$	−5.09874e6	−0.696346	−0.348173	+	0.937430i	$0.613198\pi$
$558$	−510307.	−0.0693819
$559$	−6.36731e6	−0.861840
$560$	−2.07042e6	−0.278990
$561$	−237457.	−0.0318550
$562$	−1.48977e6	−0.198966
$563$	−4.44988e6	−0.591667	−0.295834	−	0.955239i	$-0.595597\pi$
$563$	−4.44988e6	−0.591667	−0.295834	+	0.955239i	$0.595597\pi$
$564$	1.64398e6	0.217621
$565$	−2.94394e6	−0.387978
$566$	−1.36982e6	−0.179731
$567$	−5.37103e6	−0.701617
$568$	6.29652e6	0.818899
$569$	−78131.1	−0.0101168	−0.00505840	−	0.999987i	$-0.501610\pi$
$569$	−78131.1	−0.0101168	−0.00505840	+	0.999987i	$0.501610\pi$
$570$	25272.7	0.00325810
$571$	1.46583e7	1.88145	0.940726	−	0.339167i	$-0.110145\pi$
$571$	1.46583e7	1.88145	0.940726	+	0.339167i	$0.110145\pi$
$572$	3.30006e6	0.421727
$573$	−726073.	−0.0923834
$574$	716007.	0.0907063
$575$	2.03172e6	0.256268
$576$	5.38122e6	0.675810
$577$	1.04146e7	1.30227	0.651136	−	0.758961i	$-0.274293\pi$
$577$	1.04146e7	1.30227	0.651136	+	0.758961i	$0.274293\pi$
$578$	746234.	0.0929086
$579$	1.19177e6	0.147739
$580$	5.02115e6	0.619773
$581$	2.67708e6	0.329019
$582$	41138.5	0.00503432
$583$	718344.	0.0875308
$584$	−2.05647e6	−0.249512
$585$	−5.37353e6	−0.649187
$586$	1.95580e6	0.235278
$587$	−2.24594e6	−0.269032	−0.134516	−	0.990911i	$-0.542948\pi$
$587$	−2.24594e6	−0.269032	−0.134516	+	0.990911i	$0.542948\pi$
$588$	484291.	0.0577648
$589$	585805.	0.0695769
$590$	735527.	0.0869899
$591$	−830927.	−0.0978575
$592$	−4.76437e6	−0.558729
$593$	1.66575e6	0.194524	0.0972618	−	0.995259i	$-0.468992\pi$
$593$	1.66575e6	0.194524	0.0972618	+	0.995259i	$0.468992\pi$
$594$	−163146.	−0.0189719
$595$	−2.22443e6	−0.257588
$596$	5.13601e6	0.592257
$597$	1.25003e6	0.143544
$598$	−3.86322e6	−0.441771
$599$	2.93028e6	0.333689	0.166845	−	0.985983i	$-0.446642\pi$
$599$	2.93028e6	0.333689	0.166845	+	0.985983i	$0.446642\pi$
$600$	108969.	0.0123573
$601$	7.49889e6	0.846859	0.423429	−	0.905929i	$-0.360826\pi$
$601$	7.49889e6	0.846859	0.423429	+	0.905929i	$0.360826\pi$
$602$	−896994.	−0.100878
$603$	734162.	0.0822240
$604$	2.96004e6	0.330146
$605$	366025.	0.0406558
$606$	16093.6	0.00178021
$607$	−1.37640e7	−1.51626	−0.758129	−	0.652104i	$-0.773887\pi$
$607$	−1.37640e7	−1.51626	−0.758129	+	0.652104i	$0.773887\pi$
$608$	1.35782e6	0.148965
$609$	1.35716e6	0.148282
$610$	−307808.	−0.0334931
$611$	−2.30553e7	−2.49844
$612$	6.66912e6	0.719764
$613$	−204202.	−0.0219487	−0.0109743	−	0.999940i	$-0.503493\pi$
$613$	−204202.	−0.0219487	−0.0109743	+	0.999940i	$0.503493\pi$
$614$	−292011.	−0.0312592
$615$	299407.	0.0319209
$616$	956503.	0.101563
$617$	−2.62817e6	−0.277934	−0.138967	−	0.990297i	$-0.544378\pi$
$617$	−2.62817e6	−0.277934	−0.138967	+	0.990297i	$0.544378\pi$
$618$	−295577.	−0.0311315
$619$	1.48994e7	1.56294	0.781471	−	0.623942i	$-0.214470\pi$
$619$	1.48994e7	1.56294	0.781471	+	0.623942i	$0.214470\pi$
$620$	1.22765e6	0.128261
$621$	−3.32399e6	−0.345885
$622$	3.96292e6	0.410714
$623$	−2.72913e6	−0.281711
$624$	1.64623e6	0.169250
$625$	390625.	0.0400000
$626$	−3.22585e6	−0.329010
$627$	92764.3	0.00942349
$628$	2.84265e6	0.287623
$629$	−5.11876e6	−0.515868
$630$	−756995.	−0.0759874
$631$	1.06803e7	1.06785	0.533924	−	0.845532i	$-0.320717\pi$
$631$	1.06803e7	1.06785	0.533924	+	0.845532i	$0.320717\pi$
$632$	3.54026e6	0.352568
$633$	1.45750e6	0.144577
$634$	−2.19456e6	−0.216833
$635$	−2.09261e6	−0.205946
$636$	381524.	0.0374007
$637$	−6.79173e6	−0.663181
$638$	−1.05895e6	−0.102997
$639$	−1.82910e7	−1.77209
$640$	3.75284e6	0.362168
$641$	−997591.	−0.0958976	−0.0479488	−	0.998850i	$-0.515268\pi$
$641$	−997591.	−0.0958976	−0.0479488	+	0.998850i	$0.515268\pi$
$642$	−140882.	−0.0134902
$643$	−4.42182e6	−0.421768	−0.210884	−	0.977511i	$-0.567634\pi$
$643$	−4.42182e6	−0.421768	−0.210884	+	0.977511i	$0.567634\pi$
$644$	9.47195e6	0.899963
$645$	−375089.	−0.0355006
$646$	439880.	0.0414718
$647$	−1.05131e7	−0.987346	−0.493673	−	0.869648i	$-0.664346\pi$
$647$	−1.05131e7	−0.987346	−0.493673	+	0.869648i	$0.664346\pi$
$648$	4.57956e6	0.428437
$649$	2.69978e6	0.251604
$650$	−742754.	−0.0689543
$651$	331819.	0.0306866
$652$	1.28088e7	1.18002
$653$	−2.00018e6	−0.183563	−0.0917817	−	0.995779i	$-0.529256\pi$
$653$	−2.00018e6	−0.183563	−0.0917817	+	0.995779i	$0.529256\pi$
$654$	42054.5	0.00384475
$655$	7.23730e6	0.659133
$656$	4.85049e6	0.440075
$657$	5.97393e6	0.539941
$658$	−3.24792e6	−0.292442
$659$	1.84108e6	0.165142	0.0825712	−	0.996585i	$-0.473687\pi$
$659$	1.84108e6	0.165142	0.0825712	+	0.996585i	$0.473687\pi$
$660$	194402.	0.0173716
$661$	−6.33984e6	−0.564384	−0.282192	−	0.959358i	$-0.591062\pi$
$661$	−6.33984e6	−0.564384	−0.282192	+	0.959358i	$0.591062\pi$
$662$	884464.	0.0784396
$663$	1.76868e6	0.156266
$664$	−2.28259e6	−0.200913
$665$	868989.	0.0762009
$666$	−1.74196e6	−0.152179
$667$	−2.15755e7	−1.87778
$668$	−1.11126e7	−0.963553
$669$	−954141.	−0.0824228
$670$	101479.	0.00873354
$671$	−1.12982e6	−0.0968732
$672$	769115.	0.0657004
$673$	1.29584e7	1.10284	0.551420	−	0.834227i	$-0.314086\pi$
$673$	1.29584e7	1.10284	0.551420	+	0.834227i	$0.314086\pi$
$674$	−1.18705e6	−0.100651
$675$	−639080.	−0.0539879
$676$	−1.33444e7	−1.12314
$677$	−1.07517e7	−0.901585	−0.450793	−	0.892629i	$-0.648859\pi$
$677$	−1.07517e7	−0.901585	−0.450793	+	0.892629i	$0.648859\pi$
$678$	329756.	0.0275498
$679$	1.41453e6	0.117744
$680$	1.89664e6	0.157294
$681$	2.14453e6	0.177201
$682$	−258909.	−0.0213150
$683$	−7.61318e6	−0.624474	−0.312237	−	0.950004i	$-0.601078\pi$
$683$	−7.61318e6	−0.624474	−0.312237	+	0.950004i	$0.601078\pi$
$684$	−2.60534e6	−0.212924
$685$	5.11635e6	0.416614
$686$	−3.09068e6	−0.250752
$687$	1.96399e6	0.158762
$688$	−6.07657e6	−0.489426
$689$	−5.35052e6	−0.429386
$690$	−227577.	−0.0181973
$691$	−7.85487e6	−0.625812	−0.312906	−	0.949784i	$-0.601303\pi$
$691$	−7.85487e6	−0.625812	−0.312906	+	0.949784i	$0.601303\pi$
$692$	−2.16312e7	−1.71718
$693$	−2.77858e6	−0.219781
$694$	927679.	0.0731137
$695$	−3.31171e6	−0.260070
$696$	−1.15717e6	−0.0905471
$697$	5.21129e6	0.406316
$698$	2.33737e6	0.181589
$699$	−1.31190e6	−0.101557
$700$	1.82110e6	0.140472
$701$	−1.05406e7	−0.810159	−0.405079	−	0.914281i	$-0.632756\pi$
$701$	−1.05406e7	−0.810159	−0.405079	+	0.914281i	$0.632756\pi$
$702$	1.21518e6	0.0930674
$703$	1.99968e6	0.152606
$704$	2.73021e6	0.207618
$705$	−1.35816e6	−0.102915
$706$	52770.0	0.00398451
$707$	553372.	0.0416360
$708$	1.43390e6	0.107507
$709$	−3.81985e6	−0.285385	−0.142693	−	0.989767i	$-0.545576\pi$
$709$	−3.81985e6	−0.285385	−0.142693	+	0.989767i	$0.545576\pi$
$710$	−2.52827e6	−0.188225
$711$	−1.02842e7	−0.762954
$712$	2.32697e6	0.172024
$713$	−5.27510e6	−0.388604
$714$	249162.	0.0182910
$715$	−2.72631e6	−0.199439
$716$	1.05904e7	0.772023
$717$	971407.	0.0705673
$718$	−5.33361e6	−0.386109
$719$	−2.39208e7	−1.72565	−0.862827	−	0.505499i	$-0.831308\pi$
$719$	−2.39208e7	−1.72565	−0.862827	+	0.505499i	$0.831308\pi$
$720$	−5.12816e6	−0.368664
$721$	−1.01633e7	−0.728108
$722$	−171842.	−0.0122684
$723$	−1.94418e6	−0.138322
$724$	−1.64425e7	−1.16579
$725$	−4.14816e6	−0.293097
$726$	−40999.1	−0.00288691
$727$	−1.13740e6	−0.0798138	−0.0399069	−	0.999203i	$-0.512706\pi$
$727$	−1.13740e6	−0.0798138	−0.0399069	+	0.999203i	$0.512706\pi$
$728$	−7.12443e6	−0.498221
$729$	−1.27757e7	−0.890358
$730$	825744.	0.0573506
$731$	−6.52857e6	−0.451881
$732$	−600067.	−0.0413925
$733$	−7.13887e6	−0.490760	−0.245380	−	0.969427i	$-0.578913\pi$
$733$	−7.13887e6	−0.490760	−0.245380	+	0.969427i	$0.578913\pi$
$734$	−2.92457e6	−0.200365
$735$	−400092.	−0.0273175
$736$	−1.22270e7	−0.832006
$737$	372483.	0.0252603
$738$	1.77345e6	0.119861
$739$	−2.91734e6	−0.196506	−0.0982531	−	0.995161i	$-0.531325\pi$
$739$	−2.91734e6	−0.196506	−0.0982531	+	0.995161i	$0.531325\pi$
$740$	4.19064e6	0.281321
$741$	−690947.	−0.0462274
$742$	−753754.	−0.0502597
$743$	−1.26079e7	−0.837856	−0.418928	−	0.908019i	$-0.637594\pi$
$743$	−1.26079e7	−0.837856	−0.418928	+	0.908019i	$0.637594\pi$
$744$	−282923.	−0.0187385
$745$	−4.24306e6	−0.280084
$746$	3.89100e6	0.255985
$747$	6.63078e6	0.434773
$748$	3.38364e6	0.221121
$749$	−4.84416e6	−0.315510
$750$	−43754.6	−0.00284034
$751$	−5.95210e6	−0.385097	−0.192549	−	0.981287i	$-0.561675\pi$
$751$	−5.95210e6	−0.385097	−0.192549	+	0.981287i	$0.561675\pi$
$752$	−2.20026e7	−1.41883
$753$	2.12409e6	0.136517
$754$	7.88752e6	0.505257
$755$	−2.44540e6	−0.156129
$756$	−2.97941e6	−0.189594
$757$	1.29000e7	0.818183	0.409092	−	0.912493i	$-0.365846\pi$
$757$	1.29000e7	0.818183	0.409092	+	0.912493i	$0.365846\pi$
$758$	1.90912e6	0.120687
$759$	−835330.	−0.0526325
$760$	−740936.	−0.0465315
$761$	−1.37230e7	−0.858988	−0.429494	−	0.903070i	$-0.641308\pi$
$761$	−1.37230e7	−0.858988	−0.429494	+	0.903070i	$0.641308\pi$
$762$	234397.	0.0146239
$763$	1.44603e6	0.0899217
$764$	1.03462e7	0.641277
$765$	−5.50962e6	−0.340383
$766$	2.74244e6	0.168875
$767$	−2.01091e7	−1.23425
$768$	1.11301e6	0.0680922
$769$	−1.22938e7	−0.749672	−0.374836	−	0.927091i	$-0.622301\pi$
$769$	−1.22938e7	−0.749672	−0.374836	+	0.927091i	$0.622301\pi$
$770$	−384068.	−0.0233443
$771$	−3.94830e6	−0.239207
$772$	−1.69821e7	−1.02553
$773$	2.99387e7	1.80212	0.901062	−	0.433690i	$-0.142789\pi$
$773$	2.99387e7	1.80212	0.901062	+	0.433690i	$0.142789\pi$
$774$	−2.22174e6	−0.133303
$775$	−1.01421e6	−0.0606557
$776$	−1.20609e6	−0.0718992
$777$	1.13268e6	0.0673064
$778$	−328648.	−0.0194662
$779$	−2.03583e6	−0.120198
$780$	−1.44799e6	−0.0852174
$781$	−9.28010e6	−0.544409
$782$	−3.96106e6	−0.231630
$783$	6.78658e6	0.395591
$784$	−6.48161e6	−0.376611
$785$	−2.34842e6	−0.136020
$786$	−810663.	−0.0468041
$787$	9.45735e6	0.544293	0.272147	−	0.962256i	$-0.412266\pi$
$787$	9.45735e6	0.544293	0.272147	+	0.962256i	$0.412266\pi$
$788$	1.18403e7	0.679276
$789$	871732.	0.0498529
$790$	−1.42153e6	−0.0810382
$791$	1.13385e7	0.644339
$792$	2.36913e6	0.134207
$793$	8.41538e6	0.475216
$794$	−4.56538e6	−0.256995
$795$	−315192.	−0.0176871
$796$	−1.78123e7	−0.996408
$797$	2.12196e7	1.18329	0.591646	−	0.806198i	$-0.298478\pi$
$797$	2.12196e7	1.18329	0.591646	+	0.806198i	$0.298478\pi$
$798$	−97337.0	−0.00541092
$799$	−2.36392e7	−1.30999
$800$	−2.35080e6	−0.129865
$801$	−6.75969e6	−0.372259
$802$	499795.	0.0274382
$803$	3.03092e6	0.165877
$804$	197832.	0.0107934
$805$	−7.82514e6	−0.425601
$806$	1.92846e6	0.104562
$807$	−235243.	−0.0127155
$808$	−471828.	−0.0254247
$809$	3.26939e7	1.75628	0.878142	−	0.478400i	$-0.158783\pi$
$809$	3.26939e7	1.75628	0.878142	+	0.478400i	$0.158783\pi$
$810$	−1.83885e6	−0.0984767
$811$	−2.90006e7	−1.54830	−0.774149	−	0.633003i	$-0.781822\pi$
$811$	−2.90006e7	−1.54830	−0.774149	+	0.633003i	$0.781822\pi$
$812$	−1.93388e7	−1.02930
$813$	3.54865e6	0.188294
$814$	−883801.	−0.0467513
$815$	−1.05818e7	−0.558042
$816$	1.68792e6	0.0887413
$817$	2.55043e6	0.133678
$818$	−1.46991e6	−0.0768079
$819$	2.06960e7	1.07814
$820$	−4.26640e6	−0.221578
$821$	3.11215e7	1.61140	0.805699	−	0.592326i	$-0.201790\pi$
$821$	3.11215e7	1.61140	0.805699	+	0.592326i	$0.201790\pi$
$822$	−573091.	−0.0295832
$823$	−504534.	−0.0259651	−0.0129826	−	0.999916i	$-0.504133\pi$
$823$	−504534.	−0.0259651	−0.0129826	+	0.999916i	$0.504133\pi$
$824$	8.66564e6	0.444613
$825$	−160603.	−0.00821521
$826$	−2.83287e6	−0.144469
$827$	−5.78346e6	−0.294052	−0.147026	−	0.989133i	$-0.546970\pi$
$827$	−5.78346e6	−0.294052	−0.147026	+	0.989133i	$0.546970\pi$
$828$	2.34608e7	1.18923
$829$	−2.13168e7	−1.07730	−0.538650	−	0.842530i	$-0.681065\pi$
$829$	−2.13168e7	−1.07730	−0.538650	+	0.842530i	$0.681065\pi$
$830$	916536.	0.0461801
$831$	1.28272e6	0.0644362
$832$	−2.03357e7	−1.01848
$833$	−6.96374e6	−0.347720
$834$	370950.	0.0184672
$835$	9.18057e6	0.455673
$836$	−1.32184e6	−0.0654130
$837$	1.65929e6	0.0818668
$838$	−6.78565e6	−0.333796
$839$	3.16373e7	1.55165	0.775827	−	0.630946i	$-0.217333\pi$
$839$	3.16373e7	1.55165	0.775827	+	0.630946i	$0.217333\pi$
$840$	−419690.	−0.0205225
$841$	2.35394e7	1.14764
$842$	−1.48670e6	−0.0722674
$843$	2.39934e6	0.116285
$844$	−2.07686e7	−1.00358
$845$	1.10243e7	0.531143
$846$	−8.04467e6	−0.386440
$847$	−1.40974e6	−0.0675195
$848$	−5.10621e6	−0.243842
$849$	2.20616e6	0.105043
$850$	−761565.	−0.0361543
$851$	−1.80069e7	−0.852343
$852$	−4.92882e6	−0.232618
$853$	−1.77588e7	−0.835682	−0.417841	−	0.908520i	$-0.637213\pi$
$853$	−1.77588e7	−0.835682	−0.417841	+	0.908520i	$0.637213\pi$
$854$	1.18552e6	0.0556240
$855$	2.15237e6	0.100694
$856$	4.13033e6	0.192664
$857$	1.33243e7	0.619716	0.309858	−	0.950783i	$-0.399718\pi$
$857$	1.33243e7	0.619716	0.309858	+	0.950783i	$0.399718\pi$
$858$	305379.	0.0141619
$859$	2.75378e7	1.27334	0.636672	−	0.771134i	$-0.280310\pi$
$859$	2.75378e7	1.27334	0.636672	+	0.771134i	$0.280310\pi$
$860$	5.34483e6	0.246427
$861$	−1.15316e6	−0.0530129
$862$	1.82284e6	0.0835565
$863$	1.64751e7	0.753012	0.376506	−	0.926414i	$-0.377125\pi$
$863$	1.64751e7	0.753012	0.376506	+	0.926414i	$0.377125\pi$
$864$	3.84602e6	0.175278
$865$	1.78704e7	0.812071
$866$	1.09255e6	0.0495046
$867$	−1.20184e6	−0.0543000
$868$	−4.72825e6	−0.213011
$869$	−5.21780e6	−0.234389
$870$	464643.	0.0208124
$871$	−2.77441e6	−0.123916
$872$	−1.23294e6	−0.0549099
$873$	3.50360e6	0.155589
$874$	1.54742e6	0.0685218
$875$	−1.50448e6	−0.0664304
$876$	1.60977e6	0.0708769
$877$	−1.09727e7	−0.481743	−0.240871	−	0.970557i	$-0.577433\pi$
$877$	−1.09727e7	−0.481743	−0.240871	+	0.970557i	$0.577433\pi$
$878$	−8.61029e6	−0.376948
$879$	−3.14990e6	−0.137507
$880$	−2.60182e6	−0.113258
$881$	−3.51089e7	−1.52397	−0.761987	−	0.647592i	$-0.775776\pi$
$881$	−3.51089e7	−1.52397	−0.761987	+	0.647592i	$0.775776\pi$
$882$	−2.36983e6	−0.102576
$883$	−3.24936e7	−1.40248	−0.701240	−	0.712925i	$-0.747370\pi$
$883$	−3.24936e7	−1.40248	−0.701240	+	0.712925i	$0.747370\pi$
$884$	−2.52028e7	−1.08472
$885$	−1.18460e6	−0.0508409
$886$	−420772.	−0.0180079
$887$	3.60268e7	1.53750	0.768752	−	0.639547i	$-0.220878\pi$
$887$	3.60268e7	1.53750	0.768752	+	0.639547i	$0.220878\pi$
$888$	−965774.	−0.0411001
$889$	8.05963e6	0.342027
$890$	−934355.	−0.0395400
$891$	−6.74957e6	−0.284827
$892$	1.35960e7	0.572136
$893$	9.23484e6	0.387526
$894$	475272.	0.0198884
$895$	−8.74915e6	−0.365097
$896$	−1.44540e7	−0.601475
$897$	6.22189e6	0.258191
$898$	4.97199e6	0.205750
$899$	1.07701e7	0.444449
$900$	4.51063e6	0.185623
$901$	−5.48603e6	−0.225137
$902$	899778.	0.0368230
$903$	1.44465e6	0.0589580
$904$	−9.66767e6	−0.393460
$905$	1.35838e7	0.551315
$906$	273914.	0.0110865
$907$	6.55173e6	0.264447	0.132223	−	0.991220i	$-0.457788\pi$
$907$	6.55173e6	0.264447	0.132223	+	0.991220i	$0.457788\pi$
$908$	−3.05585e7	−1.23003
$909$	1.37063e6	0.0550187
$910$	2.86070e6	0.114517
$911$	2.61557e7	1.04417	0.522085	−	0.852894i	$-0.325154\pi$
$911$	2.61557e7	1.04417	0.522085	+	0.852894i	$0.325154\pi$
$912$	−659397.	−0.0262519
$913$	3.36418e6	0.133568
$914$	−3.97351e6	−0.157329
$915$	495738.	0.0195749
$916$	−2.79858e7	−1.10204
$917$	−2.78743e7	−1.09466
$918$	1.24596e6	0.0487973
$919$	7.69068e6	0.300383	0.150192	−	0.988657i	$-0.452011\pi$
$919$	7.69068e6	0.300383	0.150192	+	0.988657i	$0.452011\pi$
$920$	6.67204e6	0.259890
$921$	470296.	0.0182693
$922$	−9.94262e6	−0.385189
$923$	6.91221e7	2.67062
$924$	−748735.	−0.0288501
$925$	−3.46205e6	−0.133039
$926$	−7.08550e6	−0.271546
$927$	−2.51731e7	−0.962139
$928$	2.49639e7	0.951572
$929$	−2.57341e7	−0.978293	−0.489146	−	0.872202i	$-0.662692\pi$
$929$	−2.57341e7	−0.978293	−0.489146	+	0.872202i	$0.662692\pi$
$930$	113603.	0.00430707
$931$	2.72044e6	0.102864
$932$	1.86939e7	0.704953
$933$	−6.38246e6	−0.240040
$934$	−8.17697e6	−0.306708
$935$	−2.79535e6	−0.104570
$936$	−1.76463e7	−0.658360
$937$	−1.91075e7	−0.710977	−0.355489	−	0.934681i	$-0.615686\pi$
$937$	−1.91075e7	−0.710977	−0.355489	+	0.934681i	$0.615686\pi$
$938$	−390845.	−0.0145043
$939$	5.19538e6	0.192288
$940$	1.93531e7	0.714381
$941$	4.57102e7	1.68282	0.841412	−	0.540394i	$-0.181725\pi$
$941$	4.57102e7	1.68282	0.841412	+	0.540394i	$0.181725\pi$
$942$	263051.	0.00965855
$943$	1.83324e7	0.671336
$944$	−1.91909e7	−0.700914
$945$	2.46140e6	0.0896609
$946$	−1.12722e6	−0.0409524
$947$	4.23910e6	0.153603	0.0768013	−	0.997046i	$-0.475529\pi$
$947$	4.23910e6	0.153603	0.0768013	+	0.997046i	$0.475529\pi$
$948$	−2.77126e6	−0.100151
$949$	−2.25756e7	−0.813717
$950$	297511.	0.0106953
$951$	3.53444e6	0.126727
$952$	−7.30486e6	−0.261228
$953$	−1.15440e7	−0.411743	−0.205871	−	0.978579i	$-0.566003\pi$
$953$	−1.15440e7	−0.411743	−0.205871	+	0.978579i	$0.566003\pi$
$954$	−1.86695e6	−0.0664143
$955$	−8.54736e6	−0.303266
$956$	−1.38420e7	−0.489842
$957$	1.70549e6	0.0601962
$958$	−1.95387e6	−0.0687832
$959$	−1.97055e7	−0.691896
$960$	−1.19795e6	−0.0419528
$961$	−2.59959e7	−0.908022
$962$	6.58292e6	0.229341
$963$	−1.19983e7	−0.416923
$964$	2.77035e7	0.960157
$965$	1.40296e7	0.484983
$966$	876508.	0.0302213
$967$	5.50313e6	0.189253	0.0946267	−	0.995513i	$-0.469834\pi$
$967$	5.50313e6	0.189253	0.0946267	+	0.995513i	$0.469834\pi$
$968$	1.20200e6	0.0412302
$969$	−708446.	−0.0242380
$970$	484284.	0.0165261
$971$	3.21069e7	1.09282	0.546411	−	0.837517i	$-0.315994\pi$
$971$	3.21069e7	1.09282	0.546411	+	0.837517i	$0.315994\pi$
$972$	−1.11040e7	−0.376975
$973$	1.27550e7	0.431914
$974$	6.83205e6	0.230756
$975$	1.19624e6	0.0403001
$976$	8.03112e6	0.269868
$977$	9.49495e6	0.318241	0.159120	−	0.987259i	$-0.449134\pi$
$977$	9.49495e6	0.318241	0.159120	+	0.987259i	$0.449134\pi$
$978$	1.18529e6	0.0396257
$979$	−3.42959e6	−0.114363
$980$	5.70110e6	0.189624
$981$	3.58161e6	0.118825
$982$	814231.	0.0269444
$983$	5.96615e7	1.96929	0.984647	−	0.174558i	$-0.0558497\pi$
$983$	5.96615e7	1.96929	0.984647	+	0.174558i	$0.0558497\pi$
$984$	983232.	0.0323719
$985$	−9.78170e6	−0.321236
$986$	8.08728e6	0.264917
$987$	5.23091e6	0.170917
$988$	9.84564e6	0.320886
$989$	−2.29663e7	−0.746622
$990$	−951286.	−0.0308477
$991$	−3.55388e7	−1.14953	−0.574763	−	0.818320i	$-0.694906\pi$
$991$	−3.55388e7	−1.14953	−0.574763	+	0.818320i	$0.694906\pi$
$992$	6.10354e6	0.196926
$993$	−1.42447e6	−0.0458437
$994$	9.73756e6	0.312597
$995$	1.47154e7	0.471210
$996$	1.78677e6	0.0570718
$997$	5.59501e7	1.78264	0.891318	−	0.453378i	$-0.149781\pi$
$997$	5.59501e7	1.78264	0.891318	+	0.453378i	$0.149781\pi$
$998$	−1.06233e7	−0.337624
$999$	5.66408e6	0.179562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.17	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.31861 q^{2} +2.12368 q^{3} -30.2613 q^{4} +25.0000 q^{5} -2.80029 q^{6} -96.2869 q^{7} +82.0982 q^{8} -238.490 q^{9} +O(q^{10})\)	\(q-1.31861 q^{2} +2.12368 q^{3} -30.2613 q^{4} +25.0000 q^{5} -2.80029 q^{6} -96.2869 q^{7} +82.0982 q^{8} -238.490 q^{9} -32.9652 q^{10} -121.000 q^{11} -64.2651 q^{12} +901.259 q^{13} +126.965 q^{14} +53.0919 q^{15} +860.105 q^{16} +924.084 q^{17} +314.475 q^{18} -361.000 q^{19} -756.532 q^{20} -204.482 q^{21} +159.552 q^{22} +3250.76 q^{23} +174.350 q^{24} +625.000 q^{25} -1188.41 q^{26} -1022.53 q^{27} +2913.76 q^{28} -6637.06 q^{29} -70.0074 q^{30} -1622.73 q^{31} -3761.28 q^{32} -256.965 q^{33} -1218.50 q^{34} -2407.17 q^{35} +7217.01 q^{36} -5539.28 q^{37} +476.017 q^{38} +1913.98 q^{39} +2052.45 q^{40} +5639.42 q^{41} +269.632 q^{42} -7064.91 q^{43} +3661.61 q^{44} -5962.25 q^{45} -4286.48 q^{46} -25581.3 q^{47} +1826.59 q^{48} -7535.83 q^{49} -824.130 q^{50} +1962.45 q^{51} -27273.2 q^{52} -5936.73 q^{53} +1348.31 q^{54} -3025.00 q^{55} -7904.98 q^{56} -766.647 q^{57} +8751.68 q^{58} -22312.2 q^{59} -1606.63 q^{60} +9337.37 q^{61} +2139.74 q^{62} +22963.5 q^{63} -22563.7 q^{64} +22531.5 q^{65} +338.836 q^{66} -3078.38 q^{67} -27964.0 q^{68} +6903.56 q^{69} +3174.12 q^{70} +76695.1 q^{71} -19579.6 q^{72} -25049.0 q^{73} +7304.14 q^{74} +1327.30 q^{75} +10924.3 q^{76} +11650.7 q^{77} -2523.79 q^{78} +43122.3 q^{79} +21502.6 q^{80} +55781.6 q^{81} -7436.18 q^{82} -27803.2 q^{83} +6187.89 q^{84} +23102.1 q^{85} +9315.84 q^{86} -14095.0 q^{87} -9933.88 q^{88} +28343.7 q^{89} +7861.87 q^{90} -86779.4 q^{91} -98372.1 q^{92} -3446.15 q^{93} +33731.7 q^{94} -9025.00 q^{95} -7987.75 q^{96} -14690.8 q^{97} +9936.81 q^{98} +28857.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 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