LMFDB - Embedded newform 1045.6.a.f.1.1

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			1.1
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)

$f(q)$	$=$	$q-11.0683 q^{2} +7.73173 q^{3} +90.5062 q^{4} +25.0000 q^{5} -85.5768 q^{6} +83.0891 q^{7} -647.562 q^{8} -183.220 q^{9} +O(q^{10})$	\(q-11.0683 q^{2} +7.73173 q^{3} +90.5062 q^{4} +25.0000 q^{5} -85.5768 q^{6} +83.0891 q^{7} -647.562 q^{8} -183.220 q^{9} -276.706 q^{10} -121.000 q^{11} +699.770 q^{12} -427.952 q^{13} -919.651 q^{14} +193.293 q^{15} +4271.18 q^{16} +1541.30 q^{17} +2027.93 q^{18} -361.000 q^{19} +2262.66 q^{20} +642.423 q^{21} +1339.26 q^{22} +339.911 q^{23} -5006.78 q^{24} +625.000 q^{25} +4736.68 q^{26} -3295.42 q^{27} +7520.08 q^{28} -1889.21 q^{29} -2139.42 q^{30} +3887.11 q^{31} -26552.5 q^{32} -935.540 q^{33} -17059.5 q^{34} +2077.23 q^{35} -16582.6 q^{36} +3721.25 q^{37} +3995.64 q^{38} -3308.81 q^{39} -16189.0 q^{40} +8557.31 q^{41} -7110.50 q^{42} -19397.4 q^{43} -10951.3 q^{44} -4580.51 q^{45} -3762.23 q^{46} -17572.1 q^{47} +33023.6 q^{48} -9903.20 q^{49} -6917.66 q^{50} +11916.9 q^{51} -38732.3 q^{52} +22186.7 q^{53} +36474.6 q^{54} -3025.00 q^{55} -53805.3 q^{56} -2791.16 q^{57} +20910.3 q^{58} +36201.5 q^{59} +17494.3 q^{60} -22394.4 q^{61} -43023.5 q^{62} -15223.6 q^{63} +157212. q^{64} -10698.8 q^{65} +10354.8 q^{66} -8867.03 q^{67} +139497. q^{68} +2628.11 q^{69} -22991.3 q^{70} +9773.16 q^{71} +118646. q^{72} +14057.2 q^{73} -41187.7 q^{74} +4832.33 q^{75} -32672.7 q^{76} -10053.8 q^{77} +36622.8 q^{78} +16057.0 q^{79} +106779. q^{80} +19043.2 q^{81} -94714.5 q^{82} +28732.9 q^{83} +58143.3 q^{84} +38532.4 q^{85} +214696. q^{86} -14606.9 q^{87} +78355.0 q^{88} -31454.3 q^{89} +50698.2 q^{90} -35558.2 q^{91} +30764.1 q^{92} +30054.1 q^{93} +194493. q^{94} -9025.00 q^{95} -205297. q^{96} -76485.4 q^{97} +109611. q^{98} +22169.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.0683	−1.95661	−0.978305	−	0.207172i	$-0.933574\pi$
$2$	−11.0683	−1.95661	−0.978305	+	0.207172i	$0.933574\pi$
$3$	7.73173	0.495991	0.247995	−	0.968761i	$-0.420228\pi$
$3$	7.73173	0.495991	0.247995	+	0.968761i	$0.420228\pi$
$4$	90.5062	2.82832
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−85.5768	−0.970461
$7$	83.0891	0.640913	0.320456	−	0.947263i	$-0.396164\pi$
$7$	83.0891	0.640913	0.320456	+	0.947263i	$0.396164\pi$
$8$	−647.562	−3.57731
$9$	−183.220	−0.753993
$10$	−276.706	−0.875022
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	699.770	1.40282
$13$	−427.952	−0.702323	−0.351161	−	0.936315i	$-0.614213\pi$
$13$	−427.952	−0.702323	−0.351161	+	0.936315i	$0.614213\pi$
$14$	−919.651	−1.25402
$15$	193.293	0.221814
$16$	4271.18	4.17107
$17$	1541.30	1.29349	0.646747	−	0.762705i	$-0.276129\pi$
$17$	1541.30	1.29349	0.646747	+	0.762705i	$0.276129\pi$
$18$	2027.93	1.47527
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	2262.66	1.26486
$21$	642.423	0.317887
$22$	1339.26	0.589940
$23$	339.911	0.133982	0.0669910	−	0.997754i	$-0.478660\pi$
$23$	339.911	0.133982	0.0669910	+	0.997754i	$0.478660\pi$
$24$	−5006.78	−1.77431
$25$	625.000	0.200000
$26$	4736.68	1.37417
$27$	−3295.42	−0.869965
$28$	7520.08	1.81271
$29$	−1889.21	−0.417144	−0.208572	−	0.978007i	$-0.566881\pi$
$29$	−1889.21	−0.417144	−0.208572	+	0.978007i	$0.566881\pi$
$30$	−2139.42	−0.434003
$31$	3887.11	0.726477	0.363239	−	0.931696i	$-0.381671\pi$
$31$	3887.11	0.726477	0.363239	+	0.931696i	$0.381671\pi$
$32$	−26552.5	−4.58385
$33$	−935.540	−0.149547
$34$	−17059.5	−2.53086
$35$	2077.23	0.286625
$36$	−16582.6	−2.13253
$37$	3721.25	0.446873	0.223437	−	0.974718i	$-0.428272\pi$
$37$	3721.25	0.446873	0.223437	+	0.974718i	$0.428272\pi$
$38$	3995.64	0.448877
$39$	−3308.81	−0.348346
$40$	−16189.0	−1.59982
$41$	8557.31	0.795019	0.397510	−	0.917598i	$-0.369875\pi$
$41$	8557.31	0.795019	0.397510	+	0.917598i	$0.369875\pi$
$42$	−7110.50	−0.621981
$43$	−19397.4	−1.59983	−0.799914	−	0.600115i	$-0.795122\pi$
$43$	−19397.4	−1.59983	−0.799914	+	0.600115i	$0.795122\pi$
$44$	−10951.3	−0.852770
$45$	−4580.51	−0.337196
$46$	−3762.23	−0.262150
$47$	−17572.1	−1.16032	−0.580162	−	0.814501i	$-0.697011\pi$
$47$	−17572.1	−1.16032	−0.580162	+	0.814501i	$0.697011\pi$
$48$	33023.6	2.06881
$49$	−9903.20	−0.589231
$50$	−6917.66	−0.391322
$51$	11916.9	0.641561
$52$	−38732.3	−1.98639
$53$	22186.7	1.08493	0.542466	−	0.840078i	$-0.317491\pi$
$53$	22186.7	1.08493	0.542466	+	0.840078i	$0.317491\pi$
$54$	36474.6	1.70218
$55$	−3025.00	−0.134840
$56$	−53805.3	−2.29274
$57$	−2791.16	−0.113788
$58$	20910.3	0.816187
$59$	36201.5	1.35393	0.676966	−	0.736014i	$-0.263294\pi$
$59$	36201.5	1.35393	0.676966	+	0.736014i	$0.263294\pi$
$60$	17494.3	0.627361
$61$	−22394.4	−0.770574	−0.385287	−	0.922797i	$-0.625898\pi$
$61$	−22394.4	−0.770574	−0.385287	+	0.922797i	$0.625898\pi$
$62$	−43023.5	−1.42143
$63$	−15223.6	−0.483244
$64$	157212.	4.79773
$65$	−10698.8	−0.314088
$66$	10354.8	0.292605
$67$	−8867.03	−0.241319	−0.120659	−	0.992694i	$-0.538501\pi$
$67$	−8867.03	−0.241319	−0.120659	+	0.992694i	$0.538501\pi$
$68$	139497.	3.65841
$69$	2628.11	0.0664538
$70$	−22991.3	−0.560813
$71$	9773.16	0.230086	0.115043	−	0.993361i	$-0.463299\pi$
$71$	9773.16	0.230086	0.115043	+	0.993361i	$0.463299\pi$
$72$	118646.	2.69726
$73$	14057.2	0.308738	0.154369	−	0.988013i	$-0.450666\pi$
$73$	14057.2	0.308738	0.154369	+	0.988013i	$0.450666\pi$
$74$	−41187.7	−0.874356
$75$	4832.33	0.0991982
$76$	−32672.7	−0.648861
$77$	−10053.8	−0.193243
$78$	36622.8	0.681577
$79$	16057.0	0.289465	0.144732	−	0.989471i	$-0.453768\pi$
$79$	16057.0	0.289465	0.144732	+	0.989471i	$0.453768\pi$
$80$	106779.	1.86536
$81$	19043.2	0.322498
$82$	−94714.5	−1.55554
$83$	28732.9	0.457809	0.228905	−	0.973449i	$-0.426486\pi$
$83$	28732.9	0.457809	0.228905	+	0.973449i	$0.426486\pi$
$84$	58143.3	0.899086
$85$	38532.4	0.578468
$86$	214696.	3.13024
$87$	−14606.9	−0.206899
$88$	78355.0	1.07860
$89$	−31454.3	−0.420925	−0.210463	−	0.977602i	$-0.567497\pi$
$89$	−31454.3	−0.420925	−0.210463	+	0.977602i	$0.567497\pi$
$90$	50698.2	0.659761
$91$	−35558.2	−0.450128
$92$	30764.1	0.378944
$93$	30054.1	0.360326
$94$	194493.	2.27030
$95$	−9025.00	−0.102598
$96$	−205297.	−2.27355
$97$	−76485.4	−0.825371	−0.412686	−	0.910874i	$-0.635409\pi$
$97$	−76485.4	−0.825371	−0.412686	+	0.910874i	$0.635409\pi$
$98$	109611.	1.15289
$99$	22169.7	0.227337
$100$	56566.4	0.565664
$101$	−37505.0	−0.365835	−0.182918	−	0.983128i	$-0.558554\pi$
$101$	−37505.0	−0.365835	−0.182918	+	0.983128i	$0.558554\pi$
$102$	−131899.	−1.25528
$103$	156903.	1.45726	0.728632	−	0.684905i	$-0.240156\pi$
$103$	156903.	1.45726	0.728632	+	0.684905i	$0.240156\pi$
$104$	277125.	2.51242
$105$	16060.6	0.142163
$106$	−245568.	−2.12279
$107$	144776.	1.22247	0.611235	−	0.791449i	$-0.290673\pi$
$107$	144776.	1.22247	0.611235	+	0.791449i	$0.290673\pi$
$108$	−298256.	−2.46054
$109$	−102352.	−0.825143	−0.412571	−	0.910925i	$-0.635369\pi$
$109$	−102352.	−0.825143	−0.412571	+	0.910925i	$0.635369\pi$
$110$	33481.5	0.263829
$111$	28771.7	0.221645
$112$	354888.	2.67329
$113$	148776.	1.09607	0.548033	−	0.836457i	$-0.315377\pi$
$113$	148776.	1.09607	0.548033	+	0.836457i	$0.315377\pi$
$114$	30893.2	0.222639
$115$	8497.79	0.0599185
$116$	−170985.	−1.17982
$117$	78409.5	0.529546
$118$	−400688.	−2.64912
$119$	128065.	0.829017
$120$	−125169.	−0.793496
$121$	14641.0	0.0909091
$122$	247867.	1.50771
$123$	66162.8	0.394322
$124$	351807.	2.05471
$125$	15625.0	0.0894427
$126$	168499.	0.945519
$127$	30487.1	0.167729	0.0838643	−	0.996477i	$-0.473274\pi$
$127$	30487.1	0.167729	0.0838643	+	0.996477i	$0.473274\pi$
$128$	−890383.	−4.80344
$129$	−149976.	−0.793500
$130$	118417.	0.614548
$131$	−237936.	−1.21139	−0.605693	−	0.795698i	$-0.707104\pi$
$131$	−237936.	−1.21139	−0.605693	+	0.795698i	$0.707104\pi$
$132$	−84672.2	−0.422966
$133$	−29995.2	−0.147036
$134$	98142.6	0.472167
$135$	−82385.6	−0.389060
$136$	−998085.	−4.62722
$137$	138707.	0.631388	0.315694	−	0.948861i	$-0.397763\pi$
$137$	138707.	0.631388	0.315694	+	0.948861i	$0.397763\pi$
$138$	−29088.5	−0.130024
$139$	−139820.	−0.613806	−0.306903	−	0.951741i	$-0.599293\pi$
$139$	−139820.	−0.613806	−0.306903	+	0.951741i	$0.599293\pi$
$140$	188002.	0.810667
$141$	−135863.	−0.575510
$142$	−108172.	−0.450187
$143$	51782.2	0.211758
$144$	−782566.	−3.14496
$145$	−47230.3	−0.186552
$146$	−155588.	−0.604080
$147$	−76568.9	−0.292253
$148$	336796.	1.26390
$149$	−224988.	−0.830222	−0.415111	−	0.909771i	$-0.636257\pi$
$149$	−224988.	−0.830222	−0.415111	+	0.909771i	$0.636257\pi$
$150$	−53485.5	−0.194092
$151$	234876.	0.838296	0.419148	−	0.907918i	$-0.362329\pi$
$151$	234876.	0.838296	0.419148	+	0.907918i	$0.362329\pi$
$152$	233770.	0.820690
$153$	−282397.	−0.975285
$154$	111278.	0.378100
$155$	97177.6	0.324891
$156$	−299468.	−0.985233
$157$	190472.	0.616711	0.308356	−	0.951271i	$-0.400221\pi$
$157$	190472.	0.616711	0.308356	+	0.951271i	$0.400221\pi$
$158$	−177722.	−0.566369
$159$	171541.	0.538117
$160$	−663813.	−2.04996
$161$	28242.9	0.0858708
$162$	−210775.	−0.631003
$163$	308905.	0.910660	0.455330	−	0.890323i	$-0.349521\pi$
$163$	308905.	0.910660	0.455330	+	0.890323i	$0.349521\pi$
$164$	774490.	2.24857
$165$	−23388.5	−0.0668794
$166$	−318023.	−0.895754
$167$	315220.	0.874628	0.437314	−	0.899309i	$-0.355930\pi$
$167$	315220.	0.874628	0.437314	+	0.899309i	$0.355930\pi$
$168$	−416009.	−1.13718
$169$	−188150.	−0.506743
$170$	−426487.	−1.13184
$171$	66142.5	0.172978
$172$	−1.75559e6	−4.52482
$173$	561729.	1.42696	0.713480	−	0.700676i	$-0.247118\pi$
$173$	561729.	1.42696	0.713480	+	0.700676i	$0.247118\pi$
$174$	161673.	0.404821
$175$	51930.7	0.128183
$176$	−516813.	−1.25763
$177$	279901.	0.671538
$178$	348144.	0.823586
$179$	563279.	1.31399	0.656994	−	0.753896i	$-0.271828\pi$
$179$	563279.	1.31399	0.656994	+	0.753896i	$0.271828\pi$
$180$	−414564.	−0.953698
$181$	221995.	0.503671	0.251836	−	0.967770i	$-0.418966\pi$
$181$	221995.	0.503671	0.251836	+	0.967770i	$0.418966\pi$
$182$	393567.	0.880724
$183$	−173147.	−0.382198
$184$	−220114.	−0.479295
$185$	93031.2	0.199848
$186$	−332646.	−0.705018
$187$	−186497.	−0.390003
$188$	−1.59039e6	−3.28177
$189$	−273814.	−0.557572
$190$	99891.0	0.200744
$191$	−168405.	−0.334020	−0.167010	−	0.985955i	$-0.553411\pi$
$191$	−168405.	−0.334020	−0.167010	+	0.985955i	$0.553411\pi$
$192$	1.21552e6	2.37963
$193$	−111003.	−0.214507	−0.107253	−	0.994232i	$-0.534206\pi$
$193$	−111003.	−0.214507	−0.107253	+	0.994232i	$0.534206\pi$
$194$	846560.	1.61493
$195$	−82720.3	−0.155785
$196$	−896301.	−1.66653
$197$	137308.	0.252074	0.126037	−	0.992026i	$-0.459774\pi$
$197$	137308.	0.252074	0.126037	+	0.992026i	$0.459774\pi$
$198$	−245379.	−0.444810
$199$	−686649.	−1.22914	−0.614571	−	0.788861i	$-0.710671\pi$
$199$	−686649.	−1.22914	−0.614571	+	0.788861i	$0.710671\pi$
$200$	−404726.	−0.715461
$201$	−68557.6	−0.119692
$202$	415115.	0.715797
$203$	−156973.	−0.267353
$204$	1.07855e6	1.81454
$205$	213933.	0.355543
$206$	−1.73664e6	−2.85130
$207$	−62278.7	−0.101021
$208$	−1.82786e6	−2.92944
$209$	43681.0	0.0691714
$210$	−177763.	−0.278158
$211$	−640373.	−0.990210	−0.495105	−	0.868833i	$-0.664870\pi$
$211$	−640373.	−0.990210	−0.495105	+	0.868833i	$0.664870\pi$
$212$	2.00803e6	3.06853
$213$	75563.5	0.114120
$214$	−1.60242e6	−2.39189
$215$	−484936.	−0.715465
$216$	2.13399e6	3.11213
$217$	322976.	0.465609
$218$	1.13286e6	1.61448
$219$	108686.	0.153131
$220$	−273781.	−0.381371
$221$	−659602.	−0.908450
$222$	−318452.	−0.433673
$223$	241531.	0.325245	0.162623	−	0.986688i	$-0.448005\pi$
$223$	241531.	0.325245	0.162623	+	0.986688i	$0.448005\pi$
$224$	−2.20622e6	−2.93785
$225$	−114513.	−0.150799
$226$	−1.64669e6	−2.14457
$227$	23785.2	0.0306368	0.0153184	−	0.999883i	$-0.495124\pi$
$227$	23785.2	0.0306368	0.0153184	+	0.999883i	$0.495124\pi$
$228$	−252617.	−0.321829
$229$	−896428.	−1.12960	−0.564802	−	0.825226i	$-0.691048\pi$
$229$	−896428.	−1.12960	−0.564802	+	0.825226i	$0.691048\pi$
$230$	−94055.7	−0.117237
$231$	−77733.2	−0.0958466
$232$	1.22338e6	1.49225
$233$	−1.48092e6	−1.78707	−0.893536	−	0.448991i	$-0.851783\pi$
$233$	−1.48092e6	−1.78707	−0.893536	+	0.448991i	$0.851783\pi$
$234$	−867856.	−1.03612
$235$	−439303.	−0.518913
$236$	3.27646e6	3.82935
$237$	124148.	0.143572
$238$	−1.41746e6	−1.62206
$239$	−74625.8	−0.0845074	−0.0422537	−	0.999107i	$-0.513454\pi$
$239$	−74625.8	−0.0845074	−0.0422537	+	0.999107i	$0.513454\pi$
$240$	825590.	0.925202
$241$	−587279.	−0.651331	−0.325665	−	0.945485i	$-0.605588\pi$
$241$	−587279.	−0.651331	−0.325665	+	0.945485i	$0.605588\pi$
$242$	−162050.	−0.177874
$243$	948025.	1.02992
$244$	−2.02683e6	−2.17943
$245$	−247580.	−0.263512
$246$	−732307.	−0.771535
$247$	154491.	0.161124
$248$	−2.51714e6	−2.59883
$249$	222155.	0.227069
$250$	−172941.	−0.175004
$251$	934516.	0.936273	0.468136	−	0.883656i	$-0.344926\pi$
$251$	934516.	0.936273	0.468136	+	0.883656i	$0.344926\pi$
$252$	−1.37783e6	−1.36677
$253$	−41129.3	−0.0403971
$254$	−337439.	−0.328179
$255$	297923.	0.286915
$256$	4.82420e6	4.60072
$257$	1.27625e6	1.20532	0.602661	−	0.797998i	$-0.294107\pi$
$257$	1.27625e6	1.20532	0.602661	+	0.797998i	$0.294107\pi$
$258$	1.65997e6	1.55257
$259$	309195.	0.286407
$260$	−968308.	−0.888342
$261$	346142.	0.314523
$262$	2.63354e6	2.37021
$263$	−480108.	−0.428006	−0.214003	−	0.976833i	$-0.568650\pi$
$263$	−480108.	−0.428006	−0.214003	+	0.976833i	$0.568650\pi$
$264$	605820.	0.534975
$265$	554667.	0.485196
$266$	331994.	0.287691
$267$	−243196.	−0.208775
$268$	−802522.	−0.682527
$269$	1.12517e6	0.948063	0.474032	−	0.880508i	$-0.342798\pi$
$269$	1.12517e6	0.948063	0.474032	+	0.880508i	$0.342798\pi$
$270$	911864.	0.761238
$271$	1.67935e6	1.38905	0.694523	−	0.719470i	$-0.255615\pi$
$271$	1.67935e6	1.38905	0.694523	+	0.719470i	$0.255615\pi$
$272$	6.58316e6	5.39525
$273$	−274926.	−0.223259
$274$	−1.53524e6	−1.23538
$275$	−75625.0	−0.0603023
$276$	237860.	0.187953
$277$	1.13300e6	0.887221	0.443611	−	0.896220i	$-0.353697\pi$
$277$	1.13300e6	0.887221	0.443611	+	0.896220i	$0.353697\pi$
$278$	1.54756e6	1.20098
$279$	−712197.	−0.547759
$280$	−1.34513e6	−1.02535
$281$	679244.	0.513169	0.256584	−	0.966522i	$-0.417403\pi$
$281$	679244.	0.513169	0.256584	+	0.966522i	$0.417403\pi$
$282$	1.50377e6	1.12605
$283$	2.01319e6	1.49423	0.747116	−	0.664693i	$-0.231438\pi$
$283$	2.01319e6	1.49423	0.747116	+	0.664693i	$0.231438\pi$
$284$	884532.	0.650755
$285$	−69778.9	−0.0508876
$286$	−573139.	−0.414328
$287$	711019.	0.509538
$288$	4.86496e6	3.45619
$289$	955742.	0.673125
$290$	522757.	0.365010
$291$	−591365.	−0.409377
$292$	1.27226e6	0.873210
$293$	32788.7	0.0223128	0.0111564	−	0.999938i	$-0.496449\pi$
$293$	32788.7	0.0223128	0.0111564	+	0.999938i	$0.496449\pi$
$294$	847484.	0.571825
$295$	905038.	0.605497
$296$	−2.40974e6	−1.59860
$297$	398746.	0.262304
$298$	2.49023e6	1.62442
$299$	−145466.	−0.0940986
$300$	437356.	0.280564
$301$	−1.61172e6	−1.02535
$302$	−2.59967e6	−1.64022
$303$	−289979.	−0.181451
$304$	−1.54190e6	−0.956910
$305$	−559859.	−0.344611
$306$	3.12564e6	1.90825
$307$	−3.14159e6	−1.90241	−0.951205	−	0.308559i	$-0.900153\pi$
$307$	−3.14159e6	−1.90241	−0.951205	+	0.308559i	$0.900153\pi$
$308$	−909930.	−0.546552
$309$	1.21313e6	0.722790
$310$	−1.07559e6	−0.635684
$311$	376629.	0.220807	0.110403	−	0.993887i	$-0.464786\pi$
$311$	376629.	0.220807	0.110403	+	0.993887i	$0.464786\pi$
$312$	2.14266e6	1.24614
$313$	3.10298e6	1.79027	0.895134	−	0.445797i	$-0.147080\pi$
$313$	3.10298e6	1.79027	0.895134	+	0.445797i	$0.147080\pi$
$314$	−2.10819e6	−1.20666
$315$	−380590.	−0.216113
$316$	1.45325e6	0.818699
$317$	1.27872e6	0.714708	0.357354	−	0.933969i	$-0.383679\pi$
$317$	1.27872e6	0.714708	0.357354	+	0.933969i	$0.383679\pi$
$318$	−1.89866e6	−1.05288
$319$	228595.	0.125774
$320$	3.93030e6	2.14561
$321$	1.11937e6	0.606334
$322$	−312600.	−0.168016
$323$	−556408.	−0.296748
$324$	1.72353e6	0.912128
$325$	−267470.	−0.140465
$326$	−3.41904e6	−1.78180
$327$	−791357.	−0.409263
$328$	−5.54139e6	−2.84403
$329$	−1.46005e6	−0.743667
$330$	258870.	0.130857
$331$	718851.	0.360636	0.180318	−	0.983608i	$-0.442287\pi$
$331$	718851.	0.360636	0.180318	+	0.983608i	$0.442287\pi$
$332$	2.60051e6	1.29483
$333$	−681808.	−0.336939
$334$	−3.48894e6	−1.71130
$335$	−221676.	−0.107921
$336$	2.74390e6	1.32593
$337$	360905.	0.173109	0.0865543	−	0.996247i	$-0.472414\pi$
$337$	360905.	0.173109	0.0865543	+	0.996247i	$0.472414\pi$
$338$	2.08249e6	0.991497
$339$	1.15030e6	0.543639
$340$	3.48743e6	1.63609
$341$	−470340.	−0.219041
$342$	−732082.	−0.338450
$343$	−2.21933e6	−1.01856
$344$	1.25610e7	5.72308
$345$	65702.6	0.0297191
$346$	−6.21736e6	−2.79200
$347$	−249644.	−0.111300	−0.0556502	−	0.998450i	$-0.517723\pi$
$347$	−249644.	−0.111300	−0.0556502	+	0.998450i	$0.517723\pi$
$348$	−1.32201e6	−0.585178
$349$	687900.	0.302316	0.151158	−	0.988510i	$-0.451700\pi$
$349$	687900.	0.302316	0.151158	+	0.988510i	$0.451700\pi$
$350$	−574782.	−0.250803
$351$	1.41028e6	0.610996
$352$	3.21285e6	1.38208
$353$	3.24880e6	1.38767	0.693836	−	0.720133i	$-0.255919\pi$
$353$	3.24880e6	1.38767	0.693836	+	0.720133i	$0.255919\pi$
$354$	−3.09801e6	−1.31394
$355$	244329.	0.102897
$356$	−2.84681e6	−1.19051
$357$	990165.	0.411185
$358$	−6.23452e6	−2.57096
$359$	190459.	0.0779948	0.0389974	−	0.999239i	$-0.487584\pi$
$359$	190459.	0.0779948	0.0389974	+	0.999239i	$0.487584\pi$
$360$	2.96616e6	1.20625
$361$	130321.	0.0526316
$362$	−2.45710e6	−0.985488
$363$	113200.	0.0450901
$364$	−3.21824e6	−1.27311
$365$	351429.	0.138072
$366$	1.91644e6	0.747811
$367$	624456.	0.242012	0.121006	−	0.992652i	$-0.461388\pi$
$367$	624456.	0.242012	0.121006	+	0.992652i	$0.461388\pi$
$368$	1.45182e6	0.558848
$369$	−1.56787e6	−0.599439
$370$	−1.02969e6	−0.391024
$371$	1.84347e6	0.695347
$372$	2.72008e6	1.01912
$373$	3.23596e6	1.20429	0.602144	−	0.798387i	$-0.294313\pi$
$373$	3.23596e6	1.20429	0.602144	+	0.798387i	$0.294313\pi$
$374$	2.06420e6	0.763083
$375$	120808.	0.0443628
$376$	1.13790e7	4.15084
$377$	808492.	0.292969
$378$	3.03064e6	1.09095
$379$	2.09470e6	0.749074	0.374537	−	0.927212i	$-0.377802\pi$
$379$	2.09470e6	0.749074	0.374537	+	0.927212i	$0.377802\pi$
$380$	−816819.	−0.290179
$381$	235718.	0.0831918
$382$	1.86395e6	0.653547
$383$	4.15433e6	1.44712	0.723559	−	0.690263i	$-0.242505\pi$
$383$	4.15433e6	1.44712	0.723559	+	0.690263i	$0.242505\pi$
$384$	−6.88421e6	−2.38246
$385$	−251345.	−0.0864207
$386$	1.22861e6	0.419706
$387$	3.55400e6	1.20626
$388$	−6.92241e6	−2.33441
$389$	−2.10465e6	−0.705190	−0.352595	−	0.935776i	$-0.614701\pi$
$389$	−2.10465e6	−0.705190	−0.352595	+	0.935776i	$0.614701\pi$
$390$	915569.	0.304810
$391$	523905.	0.173305
$392$	6.41293e6	2.10786
$393$	−1.83966e6	−0.600836
$394$	−1.51975e6	−0.493211
$395$	401424.	0.129453
$396$	2.00649e6	0.642983
$397$	−3.73507e6	−1.18938	−0.594692	−	0.803953i	$-0.702726\pi$
$397$	−3.73507e6	−1.18938	−0.594692	+	0.803953i	$0.702726\pi$
$398$	7.60001e6	2.40495
$399$	−231915.	−0.0729283
$400$	2.66949e6	0.834214
$401$	5.05052e6	1.56847	0.784234	−	0.620466i	$-0.213056\pi$
$401$	5.05052e6	1.56847	0.784234	+	0.620466i	$0.213056\pi$
$402$	758812.	0.234190
$403$	−1.66349e6	−0.510222
$404$	−3.39443e6	−1.03470
$405$	476080.	0.144226
$406$	1.73742e6	0.523105
$407$	−450271.	−0.134737
$408$	−7.71693e6	−2.29506
$409$	−5.53496e6	−1.63609	−0.818043	−	0.575157i	$-0.804941\pi$
$409$	−5.53496e6	−1.63609	−0.818043	+	0.575157i	$0.804941\pi$
$410$	−2.36786e6	−0.695659
$411$	1.07244e6	0.313163
$412$	1.42007e7	4.12161
$413$	3.00795e6	0.867753
$414$	689316.	0.197659
$415$	718323.	0.204739
$416$	1.13632e7	3.21934
$417$	−1.08105e6	−0.304442
$418$	−483472.	−0.135341
$419$	−217859.	−0.0606233	−0.0303117	−	0.999540i	$-0.509650\pi$
$419$	−217859.	−0.0606233	−0.0303117	+	0.999540i	$0.509650\pi$
$420$	1.45358e6	0.402084
$421$	−3.50086e6	−0.962653	−0.481327	−	0.876541i	$-0.659845\pi$
$421$	−3.50086e6	−0.962653	−0.481327	+	0.876541i	$0.659845\pi$
$422$	7.08782e6	1.93745
$423$	3.21957e6	0.874876
$424$	−1.43672e7	−3.88113
$425$	963311.	0.258699
$426$	−836356.	−0.223289
$427$	−1.86073e6	−0.493871
$428$	1.31032e7	3.45753
$429$	400366.	0.105030
$430$	5.36739e6	1.39988
$431$	−3.01181e6	−0.780970	−0.390485	−	0.920609i	$-0.627693\pi$
$431$	−3.01181e6	−0.780970	−0.390485	+	0.920609i	$0.627693\pi$
$432$	−1.40753e7	−3.62869
$433$	2.67877e6	0.686619	0.343310	−	0.939222i	$-0.388452\pi$
$433$	2.67877e6	0.686619	0.343310	+	0.939222i	$0.388452\pi$
$434$	−3.57478e6	−0.911014
$435$	−365172.	−0.0925282
$436$	−9.26347e6	−2.33377
$437$	−122708.	−0.0307376
$438$	−1.20297e6	−0.299618
$439$	−1.02783e6	−0.254543	−0.127272	−	0.991868i	$-0.540622\pi$
$439$	−1.02783e6	−0.254543	−0.127272	+	0.991868i	$0.540622\pi$
$440$	1.95887e6	0.482364
$441$	1.81447e6	0.444276
$442$	7.30064e6	1.77748
$443$	−4.76229e6	−1.15294	−0.576470	−	0.817119i	$-0.695570\pi$
$443$	−4.76229e6	−1.15294	−0.576470	+	0.817119i	$0.695570\pi$
$444$	2.60402e6	0.626883
$445$	−786357.	−0.188243
$446$	−2.67333e6	−0.636377
$447$	−1.73955e6	−0.411783
$448$	1.30626e7	3.07493
$449$	1.97926e6	0.463327	0.231663	−	0.972796i	$-0.425583\pi$
$449$	1.97926e6	0.463327	0.231663	+	0.972796i	$0.425583\pi$
$450$	1.26746e6	0.295054
$451$	−1.03543e6	−0.239707
$452$	1.34652e7	3.10003
$453$	1.81600e6	0.415787
$454$	−263261.	−0.0599442
$455$	−888954.	−0.201303
$456$	1.80745e6	0.407055
$457$	4.18483e6	0.937319	0.468659	−	0.883379i	$-0.344737\pi$
$457$	4.18483e6	0.937319	0.468659	+	0.883379i	$0.344737\pi$
$458$	9.92189e6	2.21020
$459$	−5.07923e6	−1.12529
$460$	769103.	0.169469
$461$	−2.59174e6	−0.567987	−0.283994	−	0.958826i	$-0.591659\pi$
$461$	−2.59174e6	−0.567987	−0.283994	+	0.958826i	$0.591659\pi$
$462$	860371.	0.187534
$463$	−6.96758e6	−1.51053	−0.755265	−	0.655419i	$-0.772492\pi$
$463$	−6.96758e6	−1.51053	−0.755265	+	0.655419i	$0.772492\pi$
$464$	−8.06916e6	−1.73994
$465$	751352.	0.161143
$466$	1.63912e7	3.49660
$467$	1.94429e6	0.412542	0.206271	−	0.978495i	$-0.433867\pi$
$467$	1.94429e6	0.412542	0.206271	+	0.978495i	$0.433867\pi$
$468$	7.09655e6	1.49773
$469$	−736754.	−0.154664
$470$	4.86232e6	1.01531
$471$	1.47268e6	0.305883
$472$	−2.34427e7	−4.84343
$473$	2.34709e6	0.482366
$474$	−1.37410e6	−0.280914
$475$	−225625.	−0.0458831
$476$	1.15907e7	2.34472
$477$	−4.06505e6	−0.818031
$478$	825978.	0.165348
$479$	−7.53241e6	−1.50001	−0.750007	−	0.661430i	$-0.769950\pi$
$479$	−7.53241e6	−1.50001	−0.750007	+	0.661430i	$0.769950\pi$
$480$	−5.13242e6	−1.01676
$481$	−1.59252e6	−0.313849
$482$	6.50015e6	1.27440
$483$	218367.	0.0425911
$484$	1.32510e6	0.257120
$485$	−1.91214e6	−0.369117
$486$	−1.04930e7	−2.01515
$487$	−2.72112e6	−0.519906	−0.259953	−	0.965621i	$-0.583707\pi$
$487$	−2.72112e6	−0.519906	−0.259953	+	0.965621i	$0.583707\pi$
$488$	1.45017e7	2.75658
$489$	2.38837e6	0.451679
$490$	2.74028e6	0.515590
$491$	8.81170e6	1.64951	0.824757	−	0.565488i	$-0.191312\pi$
$491$	8.81170e6	1.64951	0.824757	+	0.565488i	$0.191312\pi$
$492$	5.98815e6	1.11527
$493$	−2.91184e6	−0.539572
$494$	−1.70994e6	−0.315257
$495$	554241.	0.101668
$496$	1.66025e7	3.03019
$497$	812044.	0.147465
$498$	−2.45887e6	−0.444286
$499$	3.51153e6	0.631314	0.315657	−	0.948873i	$-0.397775\pi$
$499$	3.51153e6	0.631314	0.315657	+	0.948873i	$0.397775\pi$
$500$	1.41416e6	0.252973
$501$	2.43720e6	0.433807
$502$	−1.03435e7	−1.83192
$503$	8.09638e6	1.42683	0.713413	−	0.700744i	$-0.247148\pi$
$503$	8.09638e6	1.42683	0.713413	+	0.700744i	$0.247148\pi$
$504$	9.85823e6	1.72871
$505$	−937625.	−0.163607
$506$	455229.	0.0790413
$507$	−1.45473e6	−0.251340
$508$	2.75927e6	0.474390
$509$	5.31928e6	0.910035	0.455018	−	0.890482i	$-0.349633\pi$
$509$	5.31928e6	0.910035	0.455018	+	0.890482i	$0.349633\pi$
$510$	−3.29748e6	−0.561380
$511$	1.16800e6	0.197874
$512$	−2.49032e7	−4.19837
$513$	1.18965e6	0.199584
$514$	−1.41259e7	−2.35834
$515$	3.92258e6	0.651709
$516$	−1.35737e7	−2.24427
$517$	2.12623e6	0.349851
$518$	−3.42225e6	−0.560386
$519$	4.34314e6	0.707759
$520$	6.92813e6	1.12359
$521$	3.15860e6	0.509801	0.254901	−	0.966967i	$-0.417957\pi$
$521$	3.15860e6	0.509801	0.254901	+	0.966967i	$0.417957\pi$
$522$	−3.83118e6	−0.615399
$523$	−6.59646e6	−1.05453	−0.527263	−	0.849702i	$-0.676782\pi$
$523$	−6.59646e6	−1.05453	−0.527263	+	0.849702i	$0.676782\pi$
$524$	−2.15347e7	−3.42619
$525$	401514.	0.0635774
$526$	5.31396e6	0.837440
$527$	5.99119e6	0.939694
$528$	−3.99586e6	−0.623771
$529$	−6.32080e6	−0.982049
$530$	−6.13919e6	−0.949340
$531$	−6.63285e6	−1.02086
$532$	−2.71475e6	−0.415863
$533$	−3.66212e6	−0.558360
$534$	2.69176e6	0.408491
$535$	3.61941e6	0.546705
$536$	5.74195e6	0.863272
$537$	4.35513e6	0.651726
$538$	−1.24537e7	−1.85499
$539$	1.19829e6	0.177660
$540$	−7.45641e6	−1.10039
$541$	8.79878e6	1.29250	0.646248	−	0.763127i	$-0.276337\pi$
$541$	8.79878e6	1.29250	0.646248	+	0.763127i	$0.276337\pi$
$542$	−1.85874e7	−2.71782
$543$	1.71641e6	0.249817
$544$	−4.09253e7	−5.92918
$545$	−2.55879e6	−0.369015
$546$	3.04295e6	0.436831
$547$	−6.43283e6	−0.919250	−0.459625	−	0.888113i	$-0.652016\pi$
$547$	−6.43283e6	−0.919250	−0.459625	+	0.888113i	$0.652016\pi$
$548$	1.25538e7	1.78577
$549$	4.10310e6	0.581007
$550$	837037.	0.117988
$551$	682005.	0.0956993
$552$	−1.70186e6	−0.237726
$553$	1.33416e6	0.185522
$554$	−1.25404e7	−1.73595
$555$	719292.	0.0991227
$556$	−1.26545e7	−1.73604
$557$	9.29892e6	1.26997	0.634986	−	0.772523i	$-0.281006\pi$
$557$	9.29892e6	1.26997	0.634986	+	0.772523i	$0.281006\pi$
$558$	7.88277e6	1.07175
$559$	8.30117e6	1.12360
$560$	8.87221e6	1.19553
$561$	−1.44195e6	−0.193438
$562$	−7.51805e6	−1.00407
$563$	−9.44255e6	−1.25550	−0.627752	−	0.778413i	$-0.716025\pi$
$563$	−9.44255e6	−1.25550	−0.627752	+	0.778413i	$0.716025\pi$
$564$	−1.22964e7	−1.62773
$565$	3.71940e6	0.490176
$566$	−2.22825e7	−2.92363
$567$	1.58228e6	0.206693
$568$	−6.32873e6	−0.823086
$569$	−1.37768e7	−1.78389	−0.891943	−	0.452149i	$-0.850658\pi$
$569$	−1.37768e7	−1.78389	−0.891943	+	0.452149i	$0.850658\pi$
$570$	772331.	0.0995672
$571$	1.06264e7	1.36394	0.681969	−	0.731381i	$-0.261124\pi$
$571$	1.06264e7	1.36394	0.681969	+	0.731381i	$0.261124\pi$
$572$	4.68661e6	0.598920
$573$	−1.30207e6	−0.165671
$574$	−7.86974e6	−0.996967
$575$	212445.	0.0267964
$576$	−2.88044e7	−3.61746
$577$	2.36122e6	0.295255	0.147628	−	0.989043i	$-0.452836\pi$
$577$	2.36122e6	0.295255	0.147628	+	0.989043i	$0.452836\pi$
$578$	−1.05784e7	−1.31704
$579$	−858246.	−0.106394
$580$	−4.27463e6	−0.527629
$581$	2.38739e6	0.293416
$582$	6.54538e6	0.800990
$583$	−2.68459e6	−0.327119
$584$	−9.10288e6	−1.10445
$585$	1.96024e6	0.236820
$586$	−362913.	−0.0436575
$587$	−2.07602e6	−0.248678	−0.124339	−	0.992240i	$-0.539681\pi$
$587$	−2.07602e6	−0.248678	−0.124339	+	0.992240i	$0.539681\pi$
$588$	−6.92996e6	−0.826585
$589$	−1.40325e6	−0.166665
$590$	−1.00172e7	−1.18472
$591$	1.06163e6	0.125027
$592$	1.58941e7	1.86394
$593$	−1.10478e7	−1.29015	−0.645075	−	0.764119i	$-0.723174\pi$
$593$	−1.10478e7	−1.29015	−0.645075	+	0.764119i	$0.723174\pi$
$594$	−4.41342e6	−0.513227
$595$	3.20163e6	0.370748
$596$	−2.03628e7	−2.34813
$597$	−5.30899e6	−0.609644
$598$	1.61005e6	0.184114
$599$	−1.56569e7	−1.78295	−0.891476	−	0.453069i	$-0.850329\pi$
$599$	−1.56569e7	−1.78295	−0.891476	+	0.453069i	$0.850329\pi$
$600$	−3.12923e6	−0.354862
$601$	−3.00197e6	−0.339016	−0.169508	−	0.985529i	$-0.554218\pi$
$601$	−3.00197e6	−0.339016	−0.169508	+	0.985529i	$0.554218\pi$
$602$	1.78389e7	2.00621
$603$	1.62462e6	0.181953
$604$	2.12578e7	2.37097
$605$	366025.	0.0406558
$606$	3.20956e6	0.355029
$607$	−5.30403e6	−0.584298	−0.292149	−	0.956373i	$-0.594370\pi$
$607$	−5.30403e6	−0.584298	−0.292149	+	0.956373i	$0.594370\pi$
$608$	9.58545e6	1.05161
$609$	−1.21367e6	−0.132605
$610$	6.19666e6	0.674269
$611$	7.52002e6	0.814922
$612$	−2.55587e7	−2.75842
$613$	2.05652e6	0.221046	0.110523	−	0.993874i	$-0.464747\pi$
$613$	2.05652e6	0.221046	0.110523	+	0.993874i	$0.464747\pi$
$614$	3.47720e7	3.72227
$615$	1.65407e6	0.176346
$616$	6.51045e6	0.691288
$617$	1.32563e7	1.40188	0.700938	−	0.713222i	$-0.252765\pi$
$617$	1.32563e7	1.40188	0.700938	+	0.713222i	$0.252765\pi$
$618$	−1.34273e7	−1.41422
$619$	1.48765e7	1.56054	0.780270	−	0.625442i	$-0.215081\pi$
$619$	1.48765e7	1.56054	0.780270	+	0.625442i	$0.215081\pi$
$620$	8.79518e6	0.918894
$621$	−1.12015e6	−0.116560
$622$	−4.16863e6	−0.432033
$623$	−2.61351e6	−0.269776
$624$	−1.41325e7	−1.45298
$625$	390625.	0.0400000
$626$	−3.43446e7	−3.50285
$627$	337730.	0.0343084
$628$	1.72389e7	1.74426
$629$	5.73555e6	0.578027
$630$	4.21247e6	0.422849
$631$	9.92296e6	0.992129	0.496064	−	0.868286i	$-0.334778\pi$
$631$	9.92296e6	0.992129	0.496064	+	0.868286i	$0.334778\pi$
$632$	−1.03979e7	−1.03550
$633$	−4.95120e6	−0.491135
$634$	−1.41532e7	−1.39840
$635$	762178.	0.0750105
$636$	1.55256e7	1.52197
$637$	4.23809e6	0.413830
$638$	−2.53014e6	−0.246090
$639$	−1.79064e6	−0.173483
$640$	−2.22596e7	−2.14816
$641$	−8.91690e6	−0.857173	−0.428587	−	0.903501i	$-0.640988\pi$
$641$	−8.91690e6	−0.857173	−0.428587	+	0.903501i	$0.640988\pi$
$642$	−1.23895e7	−1.18636
$643$	1.54401e6	0.147273	0.0736365	−	0.997285i	$-0.476540\pi$
$643$	1.54401e6	0.147273	0.0736365	+	0.997285i	$0.476540\pi$
$644$	2.55616e6	0.242870
$645$	−3.74940e6	−0.354864
$646$	6.15847e6	0.580619
$647$	1.32729e6	0.124653	0.0623267	−	0.998056i	$-0.480148\pi$
$647$	1.32729e6	0.124653	0.0623267	+	0.998056i	$0.480148\pi$
$648$	−1.23316e7	−1.15368
$649$	−4.38038e6	−0.408226
$650$	2.96043e6	0.274834
$651$	2.49717e6	0.230938
$652$	2.79578e7	2.57564
$653$	1.71030e7	1.56960	0.784800	−	0.619749i	$-0.212766\pi$
$653$	1.71030e7	1.56960	0.784800	+	0.619749i	$0.212766\pi$
$654$	8.75894e6	0.800769
$655$	−5.94841e6	−0.541748
$656$	3.65498e7	3.31608
$657$	−2.57556e6	−0.232786
$658$	1.61602e7	1.45507
$659$	1.93440e7	1.73513	0.867566	−	0.497322i	$-0.165683\pi$
$659$	1.93440e7	1.73513	0.867566	+	0.497322i	$0.165683\pi$
$660$	−2.11680e6	−0.189156
$661$	2.72152e6	0.242274	0.121137	−	0.992636i	$-0.461346\pi$
$661$	2.72152e6	0.242274	0.121137	+	0.992636i	$0.461346\pi$
$662$	−7.95642e6	−0.705623
$663$	−5.09986e6	−0.450583
$664$	−1.86063e7	−1.63772
$665$	−749879.	−0.0657563
$666$	7.54642e6	0.659258
$667$	−642165.	−0.0558897
$668$	2.85294e7	2.47373
$669$	1.86745e6	0.161319
$670$	2.45356e6	0.211159
$671$	2.70972e6	0.232337
$672$	−1.70579e7	−1.45715
$673$	1.38162e7	1.17585	0.587925	−	0.808916i	$-0.299945\pi$
$673$	1.38162e7	1.17585	0.587925	+	0.808916i	$0.299945\pi$
$674$	−3.99459e6	−0.338706
$675$	−2.05964e6	−0.173993
$676$	−1.70287e7	−1.43323
$677$	1.79534e7	1.50548	0.752742	−	0.658316i	$-0.228731\pi$
$677$	1.79534e7	1.50548	0.752742	+	0.658316i	$0.228731\pi$
$678$	−1.27318e7	−1.06369
$679$	−6.35510e6	−0.528991
$680$	−2.49521e7	−2.06936
$681$	183901.	0.0151956
$682$	5.20584e6	0.428578
$683$	116133.	0.00952587	0.00476293	−	0.999989i	$-0.498484\pi$
$683$	116133.	0.00952587	0.00476293	+	0.999989i	$0.498484\pi$
$684$	5.98631e6	0.489237
$685$	3.46767e6	0.282365
$686$	2.45641e7	1.99292
$687$	−6.93094e6	−0.560274
$688$	−8.28499e7	−6.67300
$689$	−9.49483e6	−0.761973
$690$	−727213.	−0.0581486
$691$	1.70093e7	1.35516	0.677581	−	0.735448i	$-0.263028\pi$
$691$	1.70093e7	1.35516	0.677581	+	0.735448i	$0.263028\pi$
$692$	5.08400e7	4.03590
$693$	1.84206e6	0.145704
$694$	2.76312e6	0.217771
$695$	−3.49549e6	−0.274502
$696$	9.45886e6	0.740143
$697$	1.31894e7	1.02835
$698$	−7.61385e6	−0.591515
$699$	−1.14501e7	−0.886372
$700$	4.70005e6	0.362541
$701$	2.03895e7	1.56716	0.783578	−	0.621294i	$-0.213393\pi$
$701$	2.03895e7	1.56716	0.783578	+	0.621294i	$0.213393\pi$
$702$	−1.56094e7	−1.19548
$703$	−1.34337e6	−0.102520
$704$	−1.90227e7	−1.44657
$705$	−3.39657e6	−0.257376
$706$	−3.59586e7	−2.71513
$707$	−3.11626e6	−0.234469
$708$	2.53327e7	1.89932
$709$	−3.58252e6	−0.267653	−0.133827	−	0.991005i	$-0.542727\pi$
$709$	−3.58252e6	−0.267653	−0.133827	+	0.991005i	$0.542727\pi$
$710$	−2.70430e6	−0.201330
$711$	−2.94196e6	−0.218254
$712$	2.03686e7	1.50578
$713$	1.32127e6	0.0973348
$714$	−1.09594e7	−0.804528
$715$	1.29456e6	0.0947012
$716$	5.09803e7	3.71638
$717$	−576987.	−0.0419149
$718$	−2.10805e6	−0.152605
$719$	1.72752e7	1.24624	0.623120	−	0.782126i	$-0.285865\pi$
$719$	1.72752e7	1.24624	0.623120	+	0.782126i	$0.285865\pi$
$720$	−1.95642e7	−1.40647
$721$	1.30369e7	0.933980
$722$	−1.44243e6	−0.102979
$723$	−4.54068e6	−0.323054
$724$	2.00920e7	1.42454
$725$	−1.18076e6	−0.0834287
$726$	−1.25293e6	−0.0882237
$727$	−3.34257e6	−0.234555	−0.117277	−	0.993099i	$-0.537417\pi$
$727$	−3.34257e6	−0.234555	−0.117277	+	0.993099i	$0.537417\pi$
$728$	2.30261e7	1.61025
$729$	2.70238e6	0.188333
$730$	−3.88971e6	−0.270153
$731$	−2.98972e7	−2.06937
$732$	−1.56709e7	−1.08098
$733$	1.79657e7	1.23505	0.617523	−	0.786553i	$-0.288136\pi$
$733$	1.79657e7	1.23505	0.617523	+	0.786553i	$0.288136\pi$
$734$	−6.91164e6	−0.473523
$735$	−1.91422e6	−0.130700
$736$	−9.02550e6	−0.614153
$737$	1.07291e6	0.0727604
$738$	1.73536e7	1.17287
$739$	−352939.	−0.0237732	−0.0118866	−	0.999929i	$-0.503784\pi$
$739$	−352939.	−0.0237732	−0.0118866	+	0.999929i	$0.503784\pi$
$740$	8.41990e6	0.565233
$741$	1.19448e6	0.0799160
$742$	−2.04040e7	−1.36052
$743$	−1.04928e7	−0.697299	−0.348649	−	0.937253i	$-0.613360\pi$
$743$	−1.04928e7	−0.697299	−0.348649	+	0.937253i	$0.613360\pi$
$744$	−1.94619e7	−1.28900
$745$	−5.62471e6	−0.371287
$746$	−3.58164e7	−2.35632
$747$	−5.26446e6	−0.345185
$748$	−1.68791e7	−1.10305
$749$	1.20293e7	0.783496
$750$	−1.33714e6	−0.0868006
$751$	−2.61556e7	−1.69225	−0.846125	−	0.532984i	$-0.821071\pi$
$751$	−2.61556e7	−1.69225	−0.846125	+	0.532984i	$0.821071\pi$
$752$	−7.50536e7	−4.83980
$753$	7.22543e6	0.464383
$754$	−8.94859e6	−0.573227
$755$	5.87191e6	0.374897
$756$	−2.47818e7	−1.57699
$757$	1.45496e7	0.922809	0.461404	−	0.887190i	$-0.347346\pi$
$757$	1.45496e7	0.922809	0.461404	+	0.887190i	$0.347346\pi$
$758$	−2.31847e7	−1.46565
$759$	−318001.	−0.0200366
$760$	5.84424e6	0.367024
$761$	2.24946e7	1.40804	0.704022	−	0.710178i	$-0.251386\pi$
$761$	2.24946e7	1.40804	0.704022	+	0.710178i	$0.251386\pi$
$762$	−2.60899e6	−0.162774
$763$	−8.50432e6	−0.528845
$764$	−1.52417e7	−0.944716
$765$	−7.05993e6	−0.436161
$766$	−4.59812e7	−2.83144
$767$	−1.54925e7	−0.950897
$768$	3.72994e7	2.28191
$769$	2.47757e7	1.51081	0.755405	−	0.655258i	$-0.227440\pi$
$769$	2.47757e7	1.51081	0.755405	+	0.655258i	$0.227440\pi$
$770$	2.78195e6	0.169092
$771$	9.86762e6	0.597828
$772$	−1.00465e7	−0.606694
$773$	2.98097e7	1.79436	0.897178	−	0.441669i	$-0.145614\pi$
$773$	2.98097e7	1.79436	0.897178	+	0.441669i	$0.145614\pi$
$774$	−3.93366e7	−2.36018
$775$	2.42944e6	0.145295
$776$	4.95290e7	2.95261
$777$	2.39061e6	0.142055
$778$	2.32948e7	1.37978
$779$	−3.08919e6	−0.182390
$780$	−7.48670e6	−0.440610
$781$	−1.18255e6	−0.0693734
$782$	−5.79871e6	−0.339090
$783$	6.22575e6	0.362900
$784$	−4.22983e7	−2.45772
$785$	4.76180e6	0.275802
$786$	2.03618e7	1.17560
$787$	2.43455e7	1.40114	0.700570	−	0.713583i	$-0.252929\pi$
$787$	2.43455e7	1.40114	0.700570	+	0.713583i	$0.252929\pi$
$788$	1.24272e7	0.712947
$789$	−3.71207e6	−0.212287
$790$	−4.44306e6	−0.253288
$791$	1.23617e7	0.702483
$792$	−1.43562e7	−0.813256
$793$	9.58372e6	0.541192
$794$	4.13407e7	2.32716
$795$	4.28854e6	0.240653
$796$	−6.21460e7	−3.47641
$797$	1.02852e7	0.573545	0.286772	−	0.957999i	$-0.407418\pi$
$797$	1.02852e7	0.573545	0.286772	+	0.957999i	$0.407418\pi$
$798$	2.56689e6	0.142692
$799$	−2.70839e7	−1.50087
$800$	−1.65953e7	−0.916770
$801$	5.76307e6	0.317375
$802$	−5.59005e7	−3.06888
$803$	−1.70092e6	−0.0930881
$804$	−6.20489e6	−0.338527
$805$	706074.	0.0384026
$806$	1.84120e7	0.998304
$807$	8.69951e6	0.470231
$808$	2.42868e7	1.30870
$809$	−1.95608e7	−1.05079	−0.525394	−	0.850859i	$-0.676082\pi$
$809$	−1.95608e7	−1.05079	−0.525394	+	0.850859i	$0.676082\pi$
$810$	−5.26937e6	−0.282193
$811$	−2.18947e7	−1.16892	−0.584462	−	0.811421i	$-0.698694\pi$
$811$	−2.18947e7	−1.16892	−0.584462	+	0.811421i	$0.698694\pi$
$812$	−1.42070e7	−0.756159
$813$	1.29843e7	0.688955
$814$	4.98371e6	0.263628
$815$	7.72263e6	0.407259
$816$	5.08992e7	2.67600
$817$	7.00248e6	0.367026
$818$	6.12623e7	3.20118
$819$	6.51498e6	0.339393
$820$	1.93622e7	1.00559
$821$	7.52525e6	0.389639	0.194820	−	0.980839i	$-0.437588\pi$
$821$	7.52525e6	0.389639	0.194820	+	0.980839i	$0.437588\pi$
$822$	−1.18701e7	−0.612737
$823$	7.56802e6	0.389478	0.194739	−	0.980855i	$-0.437614\pi$
$823$	7.56802e6	0.389478	0.194739	+	0.980855i	$0.437614\pi$
$824$	−1.01604e8	−5.21308
$825$	−584712.	−0.0299094
$826$	−3.32928e7	−1.69785
$827$	1.99915e7	1.01644	0.508220	−	0.861227i	$-0.330304\pi$
$827$	1.99915e7	1.01644	0.508220	+	0.861227i	$0.330304\pi$
$828$	−5.63661e6	−0.285721
$829$	−5.77787e6	−0.291999	−0.146000	−	0.989285i	$-0.546640\pi$
$829$	−5.77787e6	−0.291999	−0.146000	+	0.989285i	$0.546640\pi$
$830$	−7.95059e6	−0.400593
$831$	8.76009e6	0.440054
$832$	−6.72793e7	−3.36956
$833$	−1.52638e7	−0.762166
$834$	1.19653e7	0.595674
$835$	7.88051e6	0.391145
$836$	3.95340e6	0.195639
$837$	−1.28097e7	−0.632010
$838$	2.41131e6	0.118616
$839$	2.70118e7	1.32479	0.662397	−	0.749153i	$-0.269539\pi$
$839$	2.70118e7	1.32479	0.662397	+	0.749153i	$0.269539\pi$
$840$	−1.04002e7	−0.508562
$841$	−1.69420e7	−0.825991
$842$	3.87484e7	1.88354
$843$	5.25174e6	0.254527
$844$	−5.79578e7	−2.80063
$845$	−4.70375e6	−0.226622
$846$	−3.56350e7	−1.71179
$847$	1.21651e6	0.0582648
$848$	9.47632e7	4.52533
$849$	1.55654e7	0.741126
$850$	−1.06622e7	−0.506172
$851$	1.26489e6	0.0598729
$852$	6.83897e6	0.322769
$853$	9.98506e6	0.469871	0.234935	−	0.972011i	$-0.424512\pi$
$853$	9.98506e6	0.469871	0.234935	+	0.972011i	$0.424512\pi$
$854$	2.05950e7	0.966312
$855$	1.65356e6	0.0773580
$856$	−9.37516e7	−4.37315
$857$	−3.21841e7	−1.49689	−0.748444	−	0.663198i	$-0.769199\pi$
$857$	−3.21841e7	−1.49689	−0.748444	+	0.663198i	$0.769199\pi$
$858$	−4.43135e6	−0.205503
$859$	1.20224e7	0.555914	0.277957	−	0.960593i	$-0.410343\pi$
$859$	1.20224e7	0.555914	0.277957	+	0.960593i	$0.410343\pi$
$860$	−4.38897e7	−2.02356
$861$	5.49741e6	0.252726
$862$	3.33355e7	1.52805
$863$	−1.52389e6	−0.0696507	−0.0348254	−	0.999393i	$-0.511088\pi$
$863$	−1.52389e6	−0.0696507	−0.0348254	+	0.999393i	$0.511088\pi$
$864$	8.75017e7	3.98779
$865$	1.40432e7	0.638155
$866$	−2.96493e7	−1.34345
$867$	7.38954e6	0.333864
$868$	2.92314e7	1.31689
$869$	−1.94289e6	−0.0872769
$870$	4.04182e6	0.181042
$871$	3.79467e6	0.169484
$872$	6.62791e7	2.95179
$873$	1.40137e7	0.622324
$874$	1.35816e6	0.0601414
$875$	1.29827e6	0.0573250
$876$	9.83678e6	0.433105
$877$	3.25864e7	1.43066	0.715331	−	0.698786i	$-0.246276\pi$
$877$	3.25864e7	1.43066	0.715331	+	0.698786i	$0.246276\pi$
$878$	1.13763e7	0.498041
$879$	253513.	0.0110670
$880$	−1.29203e7	−0.562427
$881$	−6.81305e6	−0.295734	−0.147867	−	0.989007i	$-0.547241\pi$
$881$	−6.81305e6	−0.295734	−0.147867	+	0.989007i	$0.547241\pi$
$882$	−2.00830e7	−0.869274
$883$	3.92024e7	1.69204	0.846020	−	0.533151i	$-0.178992\pi$
$883$	3.92024e7	1.69204	0.846020	+	0.533151i	$0.178992\pi$
$884$	−5.96980e7	−2.56939
$885$	6.99751e6	0.300321
$886$	5.27102e7	2.25585
$887$	3.50360e7	1.49522	0.747610	−	0.664138i	$-0.231201\pi$
$887$	3.50360e7	1.49522	0.747610	+	0.664138i	$0.231201\pi$
$888$	−1.86314e7	−0.792892
$889$	2.53315e6	0.107499
$890$	8.70360e6	0.368319
$891$	−2.30423e6	−0.0972369
$892$	2.18601e7	0.919897
$893$	6.34353e6	0.266197
$894$	1.92538e7	0.805698
$895$	1.40820e7	0.587633
$896$	−7.39812e7	−3.07859
$897$	−1.12470e6	−0.0466720
$898$	−2.19070e7	−0.906550
$899$	−7.34356e6	−0.303045
$900$	−1.03641e7	−0.426507
$901$	3.41963e7	1.40335
$902$	1.14605e7	0.469014
$903$	−1.24614e7	−0.508565
$904$	−9.63416e7	−3.92096
$905$	5.54988e6	0.225249
$906$	−2.01000e7	−0.813533
$907$	−5.14628e6	−0.207719	−0.103859	−	0.994592i	$-0.533119\pi$
$907$	−5.14628e6	−0.207719	−0.103859	+	0.994592i	$0.533119\pi$
$908$	2.15271e6	0.0866506
$909$	6.87167e6	0.275837
$910$	9.83917e6	0.393872
$911$	−4.05847e7	−1.62019	−0.810097	−	0.586296i	$-0.800585\pi$
$911$	−4.05847e7	−1.62019	−0.810097	+	0.586296i	$0.800585\pi$
$912$	−1.19215e7	−0.474619
$913$	−3.47669e6	−0.138035
$914$	−4.63188e7	−1.83397
$915$	−4.32868e6	−0.170924
$916$	−8.11323e7	−3.19488
$917$	−1.97699e7	−0.776393
$918$	5.62182e7	2.20176
$919$	3.38656e7	1.32273	0.661363	−	0.750066i	$-0.269978\pi$
$919$	3.38656e7	1.32273	0.661363	+	0.750066i	$0.269978\pi$
$920$	−5.50284e6	−0.214347
$921$	−2.42900e7	−0.943578
$922$	2.86860e7	1.11133
$923$	−4.18245e6	−0.161594
$924$	−7.03534e6	−0.271085
$925$	2.32578e6	0.0893746
$926$	7.71189e7	2.95552
$927$	−2.87478e7	−1.09877
$928$	5.01633e7	1.91212
$929$	1.15180e7	0.437863	0.218932	−	0.975740i	$-0.429743\pi$
$929$	1.15180e7	0.437863	0.218932	+	0.975740i	$0.429743\pi$
$930$	−8.31615e6	−0.315293
$931$	3.57505e6	0.135179
$932$	−1.34033e8	−5.05441
$933$	2.91200e6	0.109518
$934$	−2.15198e7	−0.807183
$935$	−4.66243e6	−0.174415
$936$	−5.07750e7	−1.89435
$937$	8.92614e6	0.332135	0.166067	−	0.986114i	$-0.446893\pi$
$937$	8.92614e6	0.332135	0.166067	+	0.986114i	$0.446893\pi$
$938$	8.15458e6	0.302618
$939$	2.39914e7	0.887957
$940$	−3.97596e7	−1.46765
$941$	−5.46597e6	−0.201230	−0.100615	−	0.994925i	$-0.532081\pi$
$941$	−5.46597e6	−0.201230	−0.100615	+	0.994925i	$0.532081\pi$
$942$	−1.63000e7	−0.598494
$943$	2.90873e6	0.106518
$944$	1.54623e8	5.64735
$945$	−6.84534e6	−0.249354
$946$	−2.59782e7	−0.943802
$947$	9.40563e6	0.340811	0.170405	−	0.985374i	$-0.445492\pi$
$947$	9.40563e6	0.340811	0.170405	+	0.985374i	$0.445492\pi$
$948$	1.12362e7	0.406067
$949$	−6.01579e6	−0.216834
$950$	2.49727e6	0.0897754
$951$	9.88675e6	0.354489
$952$	−8.29300e7	−2.96565
$953$	−2.85000e7	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$953$	−2.85000e7	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$954$	4.49930e7	1.60057
$955$	−4.21014e6	−0.149378
$956$	−6.75410e6	−0.239014
$957$	1.76743e6	0.0623825
$958$	8.33707e7	2.93494
$959$	1.15250e7	0.404665
$960$	3.03881e7	1.06420
$961$	−1.35196e7	−0.472231
$962$	1.76264e7	0.614080
$963$	−2.65259e7	−0.921733
$964$	−5.31524e7	−1.84217
$965$	−2.77507e6	−0.0959304
$966$	−2.41694e6	−0.0833342
$967$	5.51080e7	1.89517	0.947585	−	0.319504i	$-0.103516\pi$
$967$	5.51080e7	1.89517	0.947585	+	0.319504i	$0.103516\pi$
$968$	−9.48095e6	−0.325210
$969$	−4.30200e6	−0.147184
$970$	2.11640e7	0.722218
$971$	4.08244e7	1.38954	0.694770	−	0.719232i	$-0.255506\pi$
$971$	4.08244e7	1.38954	0.694770	+	0.719232i	$0.255506\pi$
$972$	8.58021e7	2.91295
$973$	−1.16175e7	−0.393396
$974$	3.01180e7	1.01725
$975$	−2.06801e6	−0.0696692
$976$	−9.56503e7	−3.21412
$977$	−1.55554e6	−0.0521368	−0.0260684	−	0.999660i	$-0.508299\pi$
$977$	−1.55554e6	−0.0521368	−0.0260684	+	0.999660i	$0.508299\pi$
$978$	−2.64351e7	−0.883759
$979$	3.80597e6	0.126914
$980$	−2.24075e7	−0.745296
$981$	1.87529e7	0.622152
$982$	−9.75301e7	−3.22745
$983$	−3.38379e7	−1.11691	−0.558457	−	0.829533i	$-0.688607\pi$
$983$	−3.38379e7	−1.11691	−0.558457	+	0.829533i	$0.688607\pi$
$984$	−4.28445e7	−1.41061
$985$	3.43269e6	0.112731
$986$	3.22289e7	1.05573
$987$	−1.12887e7	−0.368852
$988$	1.39824e7	0.455710
$989$	−6.59341e6	−0.214348
$990$	−6.13448e6	−0.198925
$991$	2.68427e7	0.868245	0.434122	−	0.900854i	$-0.357059\pi$
$991$	2.68427e7	0.868245	0.434122	+	0.900854i	$0.357059\pi$
$992$	−1.03212e8	−3.33006
$993$	5.55796e6	0.178872
$994$	−8.98790e6	−0.288531
$995$	−1.71662e7	−0.549689
$996$	2.01064e7	0.642225
$997$	−5.53320e7	−1.76294	−0.881471	−	0.472237i	$-0.843446\pi$
$997$	−5.53320e7	−1.76294	−0.881471	+	0.472237i	$0.843446\pi$
$998$	−3.88665e7	−1.23523
$999$	−1.22631e7	−0.388764

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-11.0683 q^{2} +7.73173 q^{3} +90.5062 q^{4} +25.0000 q^{5} -85.5768 q^{6} +83.0891 q^{7} -647.562 q^{8} -183.220 q^{9} +O(q^{10})\)	\(q-11.0683 q^{2} +7.73173 q^{3} +90.5062 q^{4} +25.0000 q^{5} -85.5768 q^{6} +83.0891 q^{7} -647.562 q^{8} -183.220 q^{9} -276.706 q^{10} -121.000 q^{11} +699.770 q^{12} -427.952 q^{13} -919.651 q^{14} +193.293 q^{15} +4271.18 q^{16} +1541.30 q^{17} +2027.93 q^{18} -361.000 q^{19} +2262.66 q^{20} +642.423 q^{21} +1339.26 q^{22} +339.911 q^{23} -5006.78 q^{24} +625.000 q^{25} +4736.68 q^{26} -3295.42 q^{27} +7520.08 q^{28} -1889.21 q^{29} -2139.42 q^{30} +3887.11 q^{31} -26552.5 q^{32} -935.540 q^{33} -17059.5 q^{34} +2077.23 q^{35} -16582.6 q^{36} +3721.25 q^{37} +3995.64 q^{38} -3308.81 q^{39} -16189.0 q^{40} +8557.31 q^{41} -7110.50 q^{42} -19397.4 q^{43} -10951.3 q^{44} -4580.51 q^{45} -3762.23 q^{46} -17572.1 q^{47} +33023.6 q^{48} -9903.20 q^{49} -6917.66 q^{50} +11916.9 q^{51} -38732.3 q^{52} +22186.7 q^{53} +36474.6 q^{54} -3025.00 q^{55} -53805.3 q^{56} -2791.16 q^{57} +20910.3 q^{58} +36201.5 q^{59} +17494.3 q^{60} -22394.4 q^{61} -43023.5 q^{62} -15223.6 q^{63} +157212. q^{64} -10698.8 q^{65} +10354.8 q^{66} -8867.03 q^{67} +139497. q^{68} +2628.11 q^{69} -22991.3 q^{70} +9773.16 q^{71} +118646. q^{72} +14057.2 q^{73} -41187.7 q^{74} +4832.33 q^{75} -32672.7 q^{76} -10053.8 q^{77} +36622.8 q^{78} +16057.0 q^{79} +106779. q^{80} +19043.2 q^{81} -94714.5 q^{82} +28732.9 q^{83} +58143.3 q^{84} +38532.4 q^{85} +214696. q^{86} -14606.9 q^{87} +78355.0 q^{88} -31454.3 q^{89} +50698.2 q^{90} -35558.2 q^{91} +30764.1 q^{92} +30054.1 q^{93} +194493. q^{94} -9025.00 q^{95} -205297. q^{96} -76485.4 q^{97} +109611. q^{98} +22169.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 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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