LMFDB - Embedded newform 1045.6.a.g.1.11

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:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-5.04716 q^{2} +16.9331 q^{3} -6.52622 q^{4} -25.0000 q^{5} -85.4638 q^{6} +82.5359 q^{7} +194.448 q^{8} +43.7285 q^{9} +O(q^{10})$	\(q-5.04716 q^{2} +16.9331 q^{3} -6.52622 q^{4} -25.0000 q^{5} -85.4638 q^{6} +82.5359 q^{7} +194.448 q^{8} +43.7285 q^{9} +126.179 q^{10} -121.000 q^{11} -110.509 q^{12} -1096.73 q^{13} -416.571 q^{14} -423.326 q^{15} -772.570 q^{16} +1811.81 q^{17} -220.704 q^{18} +361.000 q^{19} +163.155 q^{20} +1397.58 q^{21} +610.706 q^{22} -4484.73 q^{23} +3292.60 q^{24} +625.000 q^{25} +5535.37 q^{26} -3374.28 q^{27} -538.647 q^{28} -2966.82 q^{29} +2136.59 q^{30} -1603.01 q^{31} -2323.05 q^{32} -2048.90 q^{33} -9144.51 q^{34} -2063.40 q^{35} -285.382 q^{36} +14115.5 q^{37} -1822.02 q^{38} -18571.0 q^{39} -4861.20 q^{40} +16414.9 q^{41} -7053.83 q^{42} -5473.67 q^{43} +789.672 q^{44} -1093.21 q^{45} +22635.1 q^{46} +2684.74 q^{47} -13082.0 q^{48} -9994.83 q^{49} -3154.47 q^{50} +30679.6 q^{51} +7157.51 q^{52} -7201.22 q^{53} +17030.5 q^{54} +3025.00 q^{55} +16048.9 q^{56} +6112.83 q^{57} +14974.0 q^{58} +6436.89 q^{59} +2762.72 q^{60} +22777.2 q^{61} +8090.64 q^{62} +3609.17 q^{63} +36447.0 q^{64} +27418.3 q^{65} +10341.1 q^{66} -42673.3 q^{67} -11824.3 q^{68} -75940.2 q^{69} +10414.3 q^{70} -52951.9 q^{71} +8502.91 q^{72} +10210.7 q^{73} -71243.1 q^{74} +10583.2 q^{75} -2355.96 q^{76} -9986.84 q^{77} +93730.8 q^{78} +57649.3 q^{79} +19314.2 q^{80} -67762.8 q^{81} -82848.5 q^{82} +53190.9 q^{83} -9120.94 q^{84} -45295.4 q^{85} +27626.5 q^{86} -50237.4 q^{87} -23528.2 q^{88} +104763. q^{89} +5517.61 q^{90} -90519.7 q^{91} +29268.3 q^{92} -27143.9 q^{93} -13550.3 q^{94} -9025.00 q^{95} -39336.4 q^{96} -67119.2 q^{97} +50445.5 q^{98} -5291.15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−5.04716	−0.892220	−0.446110	−	0.894978i	$-0.647191\pi$
$2$	−5.04716	−0.892220	−0.446110	+	0.894978i	$0.647191\pi$
$3$	16.9331	1.08626	0.543128	−	0.839650i	$-0.317240\pi$
$3$	16.9331	1.08626	0.543128	+	0.839650i	$0.317240\pi$
$4$	−6.52622	−0.203944
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−85.4638	−0.969179
$7$	82.5359	0.636645	0.318323	−	0.947982i	$-0.396880\pi$
$7$	82.5359	0.636645	0.318323	+	0.947982i	$0.396880\pi$
$8$	194.448	1.07418
$9$	43.7285	0.179953
$10$	126.179	0.399013
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−110.509	−0.221536
$13$	−1096.73	−1.79987	−0.899937	−	0.436021i	$-0.856387\pi$
$13$	−1096.73	−1.79987	−0.899937	+	0.436021i	$0.856387\pi$
$14$	−416.571	−0.568027
$15$	−423.326	−0.485789
$16$	−772.570	−0.754462
$17$	1811.81	1.52052	0.760259	−	0.649620i	$-0.225072\pi$
$17$	1811.81	1.52052	0.760259	+	0.649620i	$0.225072\pi$
$18$	−220.704	−0.160557
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	163.155	0.0912067
$21$	1397.58	0.691560
$22$	610.706	0.269014
$23$	−4484.73	−1.76773	−0.883867	−	0.467738i	$-0.845069\pi$
$23$	−4484.73	−1.76773	−0.883867	+	0.467738i	$0.845069\pi$
$24$	3292.60	1.16684
$25$	625.000	0.200000
$26$	5535.37	1.60588
$27$	−3374.28	−0.890782
$28$	−538.647	−0.129840
$29$	−2966.82	−0.655083	−0.327542	−	0.944837i	$-0.606220\pi$
$29$	−2966.82	−0.655083	−0.327542	+	0.944837i	$0.606220\pi$
$30$	2136.59	0.433430
$31$	−1603.01	−0.299593	−0.149797	−	0.988717i	$-0.547862\pi$
$31$	−1603.01	−0.299593	−0.149797	+	0.988717i	$0.547862\pi$
$32$	−2323.05	−0.401037
$33$	−2048.90	−0.327519
$34$	−9144.51	−1.35664
$35$	−2063.40	−0.284716
$36$	−285.382	−0.0367003
$37$	14115.5	1.69509	0.847543	−	0.530728i	$-0.178081\pi$
$37$	14115.5	1.69509	0.847543	+	0.530728i	$0.178081\pi$
$38$	−1822.02	−0.204689
$39$	−18571.0	−1.95512
$40$	−4861.20	−0.480389
$41$	16414.9	1.52503	0.762515	−	0.646971i	$-0.223964\pi$
$41$	16414.9	1.52503	0.762515	+	0.646971i	$0.223964\pi$
$42$	−7053.83	−0.617023
$43$	−5473.67	−0.451448	−0.225724	−	0.974191i	$-0.572475\pi$
$43$	−5473.67	−0.451448	−0.225724	+	0.974191i	$0.572475\pi$
$44$	789.672	0.0614915
$45$	−1093.21	−0.0804772
$46$	22635.1	1.57721
$47$	2684.74	0.177279	0.0886396	−	0.996064i	$-0.471748\pi$
$47$	2684.74	0.177279	0.0886396	+	0.996064i	$0.471748\pi$
$48$	−13082.0	−0.819539
$49$	−9994.83	−0.594683
$50$	−3154.47	−0.178444
$51$	30679.6	1.65167
$52$	7157.51	0.367074
$53$	−7201.22	−0.352141	−0.176070	−	0.984378i	$-0.556339\pi$
$53$	−7201.22	−0.352141	−0.176070	+	0.984378i	$0.556339\pi$
$54$	17030.5	0.794773
$55$	3025.00	0.134840
$56$	16048.9	0.683873
$57$	6112.83	0.249204
$58$	14974.0	0.584478
$59$	6436.89	0.240739	0.120369	−	0.992729i	$-0.461592\pi$
$59$	6436.89	0.240739	0.120369	+	0.992729i	$0.461592\pi$
$60$	2762.72	0.0990738
$61$	22777.2	0.783748	0.391874	−	0.920019i	$-0.371827\pi$
$61$	22777.2	0.783748	0.391874	+	0.920019i	$0.371827\pi$
$62$	8090.64	0.267303
$63$	3609.17	0.114566
$64$	36447.0	1.11228
$65$	27418.3	0.804928
$66$	10341.1	0.292218
$67$	−42673.3	−1.16137	−0.580683	−	0.814130i	$-0.697214\pi$
$67$	−42673.3	−1.16137	−0.580683	+	0.814130i	$0.697214\pi$
$68$	−11824.3	−0.310101
$69$	−75940.2	−1.92021
$70$	10414.3	0.254030
$71$	−52951.9	−1.24662	−0.623312	−	0.781973i	$-0.714213\pi$
$71$	−52951.9	−1.24662	−0.623312	+	0.781973i	$0.714213\pi$
$72$	8502.91	0.193302
$73$	10210.7	0.224259	0.112130	−	0.993694i	$-0.464233\pi$
$73$	10210.7	0.224259	0.112130	+	0.993694i	$0.464233\pi$
$74$	−71243.1	−1.51239
$75$	10583.2	0.217251
$76$	−2355.96	−0.0467880
$77$	−9986.84	−0.191956
$78$	93730.8	1.74440
$79$	57649.3	1.03926	0.519632	−	0.854390i	$-0.326069\pi$
$79$	57649.3	1.03926	0.519632	+	0.854390i	$0.326069\pi$
$80$	19314.2	0.337406
$81$	−67762.8	−1.14757
$82$	−82848.5	−1.36066
$83$	53190.9	0.847504	0.423752	−	0.905778i	$-0.360713\pi$
$83$	53190.9	0.847504	0.423752	+	0.905778i	$0.360713\pi$
$84$	−9120.94	−0.141040
$85$	−45295.4	−0.679996
$86$	27626.5	0.402791
$87$	−50237.4	−0.711588
$88$	−23528.2	−0.323878
$89$	104763.	1.40195	0.700977	−	0.713184i	$-0.252748\pi$
$89$	104763.	1.40195	0.700977	+	0.713184i	$0.252748\pi$
$90$	5517.61	0.0718034
$91$	−90519.7	−1.14588
$92$	29268.3	0.360519
$93$	−27143.9	−0.325435
$94$	−13550.3	−0.158172
$95$	−9025.00	−0.102598
$96$	−39336.4	−0.435628
$97$	−67119.2	−0.724299	−0.362149	−	0.932120i	$-0.617957\pi$
$97$	−67119.2	−0.724299	−0.362149	+	0.932120i	$0.617957\pi$
$98$	50445.5	0.530587
$99$	−5291.15	−0.0542577
$100$	−4078.89	−0.0407889
$101$	−103368.	−1.00828	−0.504142	−	0.863621i	$-0.668191\pi$
$101$	−103368.	−1.00828	−0.504142	+	0.863621i	$0.668191\pi$
$102$	−154845.	−1.47365
$103$	99275.3	0.922037	0.461018	−	0.887391i	$-0.347484\pi$
$103$	99275.3	0.922037	0.461018	+	0.887391i	$0.347484\pi$
$104$	−213257.	−1.93339
$105$	−34939.6	−0.309275
$106$	36345.7	0.314187
$107$	60256.3	0.508795	0.254398	−	0.967100i	$-0.418123\pi$
$107$	60256.3	0.508795	0.254398	+	0.967100i	$0.418123\pi$
$108$	22021.3	0.181670
$109$	−49008.3	−0.395097	−0.197548	−	0.980293i	$-0.563298\pi$
$109$	−49008.3	−0.395097	−0.197548	+	0.980293i	$0.563298\pi$
$110$	−15267.6	−0.120307
$111$	239018.	1.84130
$112$	−63764.7	−0.480325
$113$	−226389.	−1.66786	−0.833928	−	0.551873i	$-0.813913\pi$
$113$	−226389.	−1.66786	−0.833928	+	0.551873i	$0.813913\pi$
$114$	−30852.4	−0.222345
$115$	112118.	0.790555
$116$	19362.1	0.133600
$117$	−47958.4	−0.323892
$118$	−32488.0	−0.214792
$119$	149540.	0.968030
$120$	−82314.9	−0.521826
$121$	14641.0	0.0909091
$122$	−114960.	−0.699275
$123$	277954.	1.65657
$124$	10461.6	0.0611003
$125$	−15625.0	−0.0894427
$126$	−18216.0	−0.102218
$127$	360688.	1.98437	0.992185	−	0.124777i	$-0.0398214\pi$
$127$	360688.	1.98437	0.992185	+	0.124777i	$0.0398214\pi$
$128$	−109616.	−0.591357
$129$	−92686.0	−0.490388
$130$	−138384.	−0.718172
$131$	125015.	0.636479	0.318239	−	0.948010i	$-0.396908\pi$
$131$	125015.	0.636479	0.318239	+	0.948010i	$0.396908\pi$
$132$	13371.6	0.0667955
$133$	29795.4	0.146056
$134$	215379.	1.03619
$135$	84356.9	0.398370
$136$	352303.	1.63331
$137$	−240363.	−1.09413	−0.547063	−	0.837092i	$-0.684254\pi$
$137$	−240363.	−1.09413	−0.547063	+	0.837092i	$0.684254\pi$
$138$	383282.	1.71325
$139$	−108113.	−0.474616	−0.237308	−	0.971434i	$-0.576265\pi$
$139$	−108113.	−0.474616	−0.237308	+	0.971434i	$0.576265\pi$
$140$	13466.2	0.0580663
$141$	45460.9	0.192571
$142$	267256.	1.11226
$143$	132704.	0.542682
$144$	−33783.3	−0.135767
$145$	74170.5	0.292962
$146$	−51535.2	−0.200088
$147$	−169243.	−0.645978
$148$	−92120.7	−0.345703
$149$	−192125.	−0.708955	−0.354477	−	0.935065i	$-0.615341\pi$
$149$	−192125.	−0.708955	−0.354477	+	0.935065i	$0.615341\pi$
$150$	−53414.9	−0.193836
$151$	−152572.	−0.544542	−0.272271	−	0.962221i	$-0.587775\pi$
$151$	−152572.	−0.544542	−0.272271	+	0.962221i	$0.587775\pi$
$152$	70195.7	0.246434
$153$	79227.9	0.273621
$154$	50405.1	0.171267
$155$	40075.3	0.133982
$156$	121199.	0.398736
$157$	435497.	1.41006	0.705028	−	0.709180i	$-0.250935\pi$
$157$	435497.	1.41006	0.705028	+	0.709180i	$0.250935\pi$
$158$	−290965.	−0.927252
$159$	−121939.	−0.382515
$160$	58076.3	0.179349
$161$	−370151.	−1.12542
$162$	342010.	1.02388
$163$	551550.	1.62598	0.812992	−	0.582275i	$-0.197837\pi$
$163$	551550.	1.62598	0.812992	+	0.582275i	$0.197837\pi$
$164$	−107127.	−0.311021
$165$	51222.5	0.146471
$166$	−268463.	−0.756160
$167$	−51564.7	−0.143074	−0.0715371	−	0.997438i	$-0.522790\pi$
$167$	−51564.7	−0.143074	−0.0715371	+	0.997438i	$0.522790\pi$
$168$	271757.	0.742862
$169$	831527.	2.23954
$170$	228613.	0.606706
$171$	15786.0	0.0412840
$172$	35722.4	0.0920702
$173$	772514.	1.96242	0.981209	−	0.192950i	$-0.0618054\pi$
$173$	772514.	1.96242	0.981209	+	0.192950i	$0.0618054\pi$
$174$	253556.	0.634893
$175$	51584.9	0.127329
$176$	93480.9	0.227479
$177$	108996.	0.261504
$178$	−528756.	−1.25085
$179$	218214.	0.509037	0.254518	−	0.967068i	$-0.418083\pi$
$179$	218214.	0.509037	0.254518	+	0.967068i	$0.418083\pi$
$180$	7134.54	0.0164129
$181$	−498404.	−1.13080	−0.565399	−	0.824817i	$-0.691278\pi$
$181$	−498404.	−1.13080	−0.565399	+	0.824817i	$0.691278\pi$
$182$	456867.	1.02238
$183$	385688.	0.851351
$184$	−872046.	−1.89887
$185$	−352887.	−0.758065
$186$	136999.	0.290360
$187$	−219230.	−0.458453
$188$	−17521.2	−0.0361551
$189$	−278499.	−0.567112
$190$	45550.6	0.0915398
$191$	−399115.	−0.791617	−0.395808	−	0.918333i	$-0.629536\pi$
$191$	−399115.	−0.791617	−0.395808	+	0.918333i	$0.629536\pi$
$192$	617160.	1.20822
$193$	−314397.	−0.607554	−0.303777	−	0.952743i	$-0.598248\pi$
$193$	−314397.	−0.607554	−0.303777	+	0.952743i	$0.598248\pi$
$194$	338761.	0.646234
$195$	464275.	0.874358
$196$	65228.4	0.121282
$197$	597786.	1.09744	0.548720	−	0.836006i	$-0.315115\pi$
$197$	597786.	1.09744	0.548720	+	0.836006i	$0.315115\pi$
$198$	26705.2	0.0484098
$199$	−647832.	−1.15966	−0.579829	−	0.814739i	$-0.696880\pi$
$199$	−647832.	−1.15966	−0.579829	+	0.814739i	$0.696880\pi$
$200$	121530.	0.214837
$201$	−722589.	−1.26154
$202$	521715.	0.899611
$203$	−244869.	−0.417056
$204$	−200221.	−0.336849
$205$	−410372.	−0.682014
$206$	−501058.	−0.822659
$207$	−196111.	−0.318108
$208$	847301.	1.35794
$209$	−43681.0	−0.0691714
$210$	176346.	0.275941
$211$	−173765.	−0.268693	−0.134346	−	0.990934i	$-0.542893\pi$
$211$	−173765.	−0.268693	−0.134346	+	0.990934i	$0.542893\pi$
$212$	46996.7	0.0718171
$213$	−896637.	−1.35415
$214$	−304123.	−0.453957
$215$	136842.	0.201894
$216$	−656121.	−0.956862
$217$	−132306.	−0.190735
$218$	247353.	0.352513
$219$	172899.	0.243603
$220$	−19741.8	−0.0274998
$221$	−1.98707e6	−2.73674
$222$	−1.20636e6	−1.64284
$223$	−377400.	−0.508206	−0.254103	−	0.967177i	$-0.581780\pi$
$223$	−377400.	−0.508206	−0.254103	+	0.967177i	$0.581780\pi$
$224$	−191735.	−0.255318
$225$	27330.3	0.0359905
$226$	1.14262e6	1.48809
$227$	147934.	0.190548	0.0952739	−	0.995451i	$-0.469627\pi$
$227$	147934.	0.190548	0.0952739	+	0.995451i	$0.469627\pi$
$228$	−39893.7	−0.0508238
$229$	539551.	0.679898	0.339949	−	0.940444i	$-0.389590\pi$
$229$	539551.	0.679898	0.339949	+	0.940444i	$0.389590\pi$
$230$	−565879.	−0.705348
$231$	−169108.	−0.208513
$232$	−576892.	−0.703679
$233$	−27311.8	−0.0329580	−0.0164790	−	0.999864i	$-0.505246\pi$
$233$	−27311.8	−0.0329580	−0.0164790	+	0.999864i	$0.505246\pi$
$234$	242053.	0.288983
$235$	−67118.5	−0.0792817
$236$	−42008.5	−0.0490973
$237$	976179.	1.12891
$238$	−754750.	−0.863696
$239$	1.01593e6	1.15045	0.575226	−	0.817994i	$-0.304914\pi$
$239$	1.01593e6	1.15045	0.575226	+	0.817994i	$0.304914\pi$
$240$	327049.	0.366509
$241$	306407.	0.339826	0.169913	−	0.985459i	$-0.445651\pi$
$241$	306407.	0.339826	0.169913	+	0.985459i	$0.445651\pi$
$242$	−73895.4	−0.0811109
$243$	−327483.	−0.355773
$244$	−148649.	−0.159841
$245$	249871.	0.265950
$246$	−1.40288e6	−1.47803
$247$	−395920.	−0.412919
$248$	−311702.	−0.321818
$249$	900684.	0.920607
$250$	78861.8	0.0798025
$251$	−516200.	−0.517171	−0.258585	−	0.965988i	$-0.583256\pi$
$251$	−516200.	−0.517171	−0.258585	+	0.965988i	$0.583256\pi$
$252$	−23554.2	−0.0233651
$253$	542653.	0.532992
$254$	−1.82045e6	−1.77049
$255$	−766989.	−0.738650
$256$	−613055.	−0.584655
$257$	−750148.	−0.708458	−0.354229	−	0.935159i	$-0.615257\pi$
$257$	−750148.	−0.708458	−0.354229	+	0.935159i	$0.615257\pi$
$258$	467801.	0.437534
$259$	1.16503e6	1.07917
$260$	−178938.	−0.164160
$261$	−129735.	−0.117884
$262$	−630970.	−0.567879
$263$	111098.	0.0990411	0.0495206	−	0.998773i	$-0.484231\pi$
$263$	111098.	0.0990411	0.0495206	+	0.998773i	$0.484231\pi$
$264$	−398404.	−0.351815
$265$	180031.	0.157482
$266$	−150382.	−0.130314
$267$	1.77396e6	1.52288
$268$	278495.	0.236854
$269$	381978.	0.321853	0.160926	−	0.986966i	$-0.448552\pi$
$269$	381978.	0.321853	0.160926	+	0.986966i	$0.448552\pi$
$270$	−425762.	−0.355433
$271$	1.77422e6	1.46752	0.733758	−	0.679411i	$-0.237764\pi$
$271$	1.77422e6	1.46752	0.733758	+	0.679411i	$0.237764\pi$
$272$	−1.39975e6	−1.14717
$273$	−1.53277e6	−1.24472
$274$	1.21315e6	0.976200
$275$	−75625.0	−0.0603023
$276$	495603.	0.391616
$277$	−282101.	−0.220904	−0.110452	−	0.993881i	$-0.535230\pi$
$277$	−282101.	−0.220904	−0.110452	+	0.993881i	$0.535230\pi$
$278$	545665.	0.423462
$279$	−70097.2	−0.0539126
$280$	−401223.	−0.305837
$281$	−196639.	−0.148561	−0.0742805	−	0.997237i	$-0.523666\pi$
$281$	−196639.	−0.148561	−0.0742805	+	0.997237i	$0.523666\pi$
$282$	−229448.	−0.171815
$283$	558022.	0.414176	0.207088	−	0.978322i	$-0.433601\pi$
$283$	558022.	0.414176	0.207088	+	0.978322i	$0.433601\pi$
$284$	345576.	0.254242
$285$	−152821.	−0.111448
$286$	−669780.	−0.484192
$287$	1.35482e6	0.970903
$288$	−101584.	−0.0721676
$289$	1.86281e6	1.31197
$290$	−374350.	−0.261387
$291$	−1.13653e6	−0.786774
$292$	−66637.5	−0.0457364
$293$	675811.	0.459892	0.229946	−	0.973203i	$-0.426145\pi$
$293$	675811.	0.459892	0.229946	+	0.973203i	$0.426145\pi$
$294$	854196.	0.576354
$295$	−160922.	−0.107662
$296$	2.74473e6	1.82083
$297$	408287.	0.268581
$298$	969686.	0.632543
$299$	4.91855e6	3.18170
$300$	−69068.0	−0.0443072
$301$	−451774.	−0.287412
$302$	770052.	0.485851
$303$	−1.75034e6	−1.09526
$304$	−278898.	−0.173086
$305$	−569431.	−0.350503
$306$	−399875.	−0.244130
$307$	2.01375e6	1.21944	0.609718	−	0.792618i	$-0.291283\pi$
$307$	2.01375e6	1.21944	0.609718	+	0.792618i	$0.291283\pi$
$308$	65176.3	0.0391483
$309$	1.68104e6	1.00157
$310$	−202266.	−0.119542
$311$	2.79819e6	1.64050	0.820250	−	0.572006i	$-0.193835\pi$
$311$	2.79819e6	1.64050	0.820250	+	0.572006i	$0.193835\pi$
$312$	−3.61109e6	−2.10016
$313$	1.09994e6	0.634614	0.317307	−	0.948323i	$-0.397221\pi$
$313$	1.09994e6	0.634614	0.317307	+	0.948323i	$0.397221\pi$
$314$	−2.19802e6	−1.25808
$315$	−90229.2	−0.0512355
$316$	−376232.	−0.211952
$317$	−1.25452e6	−0.701181	−0.350590	−	0.936529i	$-0.614019\pi$
$317$	−1.25452e6	−0.701181	−0.350590	+	0.936529i	$0.614019\pi$
$318$	615444.	0.341288
$319$	358985.	0.197515
$320$	−911176.	−0.497425
$321$	1.02032e6	0.552682
$322$	1.86821e6	1.00412
$323$	654065.	0.348831
$324$	442235.	0.234040
$325$	−685457.	−0.359975
$326$	−2.78376e6	−1.45073
$327$	−829860.	−0.429176
$328$	3.19184e6	1.63816
$329$	221587.	0.112864
$330$	−258528.	−0.130684
$331$	1.76329e6	0.884611	0.442306	−	0.896864i	$-0.354161\pi$
$331$	1.76329e6	0.884611	0.442306	+	0.896864i	$0.354161\pi$
$332$	−347135.	−0.172844
$333$	617249.	0.305035
$334$	260255.	0.127654
$335$	1.06683e6	0.519378
$336$	−1.07973e6	−0.521756
$337$	3.27667e6	1.57166	0.785830	−	0.618443i	$-0.212236\pi$
$337$	3.27667e6	1.57166	0.785830	+	0.618443i	$0.212236\pi$
$338$	−4.19684e6	−1.99816
$339$	−3.83345e6	−1.81172
$340$	295607.	0.138681
$341$	193964.	0.0903308
$342$	−79674.3	−0.0368343
$343$	−2.21211e6	−1.01525
$344$	−1.06434e6	−0.484937
$345$	1.89851e6	0.858745
$346$	−3.89900e6	−1.75091
$347$	3.42677e6	1.52778	0.763891	−	0.645345i	$-0.223287\pi$
$347$	3.42677e6	1.52778	0.763891	+	0.645345i	$0.223287\pi$
$348$	327860.	0.145124
$349$	−199512.	−0.0876810	−0.0438405	−	0.999039i	$-0.513959\pi$
$349$	−199512.	−0.0876810	−0.0438405	+	0.999039i	$0.513959\pi$
$350$	−260357.	−0.113605
$351$	3.70067e6	1.60329
$352$	281089.	0.120917
$353$	3.42541e6	1.46311	0.731553	−	0.681784i	$-0.238796\pi$
$353$	3.42541e6	1.46311	0.731553	+	0.681784i	$0.238796\pi$
$354$	−550121.	−0.233319
$355$	1.32380e6	0.557507
$356$	−683708.	−0.285921
$357$	2.53216e6	1.05153
$358$	−1.10136e6	−0.454173
$359$	−1.75462e6	−0.718535	−0.359267	−	0.933235i	$-0.616973\pi$
$359$	−1.75462e6	−0.718535	−0.359267	+	0.933235i	$0.616973\pi$
$360$	−212573.	−0.0864473
$361$	130321.	0.0526316
$362$	2.51552e6	1.00892
$363$	247917.	0.0987506
$364$	590751.	0.233696
$365$	−255269.	−0.100292
$366$	−1.94663e6	−0.759592
$367$	2.58726e6	1.00271	0.501354	−	0.865242i	$-0.332836\pi$
$367$	2.58726e6	1.00271	0.501354	+	0.865242i	$0.332836\pi$
$368$	3.46477e6	1.33369
$369$	717798.	0.274433
$370$	1.78108e6	0.676360
$371$	−594359.	−0.224189
$372$	177147.	0.0663706
$373$	445613.	0.165839	0.0829193	−	0.996556i	$-0.473576\pi$
$373$	445613.	0.165839	0.0829193	+	0.996556i	$0.473576\pi$
$374$	1.10649e6	0.409041
$375$	−264579.	−0.0971577
$376$	522042.	0.190430
$377$	3.25381e6	1.17907
$378$	1.40563e6	0.505988
$379$	−2.38169e6	−0.851702	−0.425851	−	0.904793i	$-0.640025\pi$
$379$	−2.38169e6	−0.851702	−0.425851	+	0.904793i	$0.640025\pi$
$380$	58899.1	0.0209242
$381$	6.10755e6	2.15553
$382$	2.01440e6	0.706296
$383$	−1.53733e6	−0.535513	−0.267757	−	0.963487i	$-0.586282\pi$
$383$	−1.53733e6	−0.535513	−0.267757	+	0.963487i	$0.586282\pi$
$384$	−1.85614e6	−0.642365
$385$	249671.	0.0858452
$386$	1.58681e6	0.542072
$387$	−239355.	−0.0812392
$388$	438035.	0.147717
$389$	4.18410e6	1.40193	0.700967	−	0.713193i	$-0.252752\pi$
$389$	4.18410e6	1.40193	0.700967	+	0.713193i	$0.252752\pi$
$390$	−2.34327e6	−0.780119
$391$	−8.12550e6	−2.68787
$392$	−1.94347e6	−0.638798
$393$	2.11689e6	0.691379
$394$	−3.01712e6	−0.979157
$395$	−1.44123e6	−0.464773
$396$	34531.2	0.0110656
$397$	−426960.	−0.135960	−0.0679800	−	0.997687i	$-0.521655\pi$
$397$	−426960.	−0.135960	−0.0679800	+	0.997687i	$0.521655\pi$
$398$	3.26971e6	1.03467
$399$	504528.	0.158655
$400$	−482856.	−0.150892
$401$	4.57209e6	1.41989	0.709943	−	0.704259i	$-0.248721\pi$
$401$	4.57209e6	1.41989	0.709943	+	0.704259i	$0.248721\pi$
$402$	3.64702e6	1.12557
$403$	1.75807e6	0.539230
$404$	674603.	0.205634
$405$	1.69407e6	0.513209
$406$	1.23589e6	0.372105
$407$	−1.70797e6	−0.511087
$408$	5.96557e6	1.77420
$409$	1.93099e6	0.570784	0.285392	−	0.958411i	$-0.407876\pi$
$409$	1.93099e6	0.570784	0.285392	+	0.958411i	$0.407876\pi$
$410$	2.07121e6	0.608506
$411$	−4.07009e6	−1.18850
$412$	−647892.	−0.188044
$413$	531274.	0.153265
$414$	989800.	0.283822
$415$	−1.32977e6	−0.379016
$416$	2.54776e6	0.721815
$417$	−1.83069e6	−0.515555
$418$	220465.	0.0617161
$419$	4.32635e6	1.20389	0.601945	−	0.798538i	$-0.294393\pi$
$419$	4.32635e6	1.20389	0.601945	+	0.798538i	$0.294393\pi$
$420$	228024.	0.0630749
$421$	−5.04128e6	−1.38623	−0.693116	−	0.720826i	$-0.743763\pi$
$421$	−5.04128e6	−1.38623	−0.693116	+	0.720826i	$0.743763\pi$
$422$	877019.	0.239733
$423$	117400.	0.0319019
$424$	−1.40026e6	−0.378264
$425$	1.13238e6	0.304103
$426$	4.52547e6	1.20820
$427$	1.87994e6	0.498970
$428$	−393246.	−0.103766
$429$	2.24709e6	0.589492
$430$	−690662.	−0.180133
$431$	−5.27258e6	−1.36719	−0.683596	−	0.729860i	$-0.739585\pi$
$431$	−5.27258e6	−1.36719	−0.683596	+	0.729860i	$0.739585\pi$
$432$	2.60686e6	0.672061
$433$	2.73328e6	0.700590	0.350295	−	0.936640i	$-0.386081\pi$
$433$	2.73328e6	0.700590	0.350295	+	0.936640i	$0.386081\pi$
$434$	667768.	0.170177
$435$	1.25593e6	0.318232
$436$	319839.	0.0805777
$437$	−1.61899e6	−0.405546
$438$	−872649.	−0.217347
$439$	3.50324e6	0.867579	0.433789	−	0.901014i	$-0.357176\pi$
$439$	3.50324e6	0.867579	0.433789	+	0.901014i	$0.357176\pi$
$440$	588205.	0.144843
$441$	−437059.	−0.107015
$442$	1.00291e7	2.44177
$443$	7.13034e6	1.72624	0.863120	−	0.505000i	$-0.168507\pi$
$443$	7.13034e6	1.72624	0.863120	+	0.505000i	$0.168507\pi$
$444$	−1.55989e6	−0.375522
$445$	−2.61908e6	−0.626973
$446$	1.90480e6	0.453431
$447$	−3.25327e6	−0.770107
$448$	3.00819e6	0.708125
$449$	7.79699e6	1.82520	0.912602	−	0.408849i	$-0.134070\pi$
$449$	7.79699e6	1.82520	0.912602	+	0.408849i	$0.134070\pi$
$450$	−137940.	−0.0321114
$451$	−1.98620e6	−0.459814
$452$	1.47746e6	0.340150
$453$	−2.58350e6	−0.591512
$454$	−746647.	−0.170011
$455$	2.26299e6	0.512453
$456$	1.18863e6	0.267691
$457$	717341.	0.160670	0.0803351	−	0.996768i	$-0.474401\pi$
$457$	717341.	0.160670	0.0803351	+	0.996768i	$0.474401\pi$
$458$	−2.72320e6	−0.606618
$459$	−6.11356e6	−1.35445
$460$	−731708.	−0.161229
$461$	2.85030e6	0.624653	0.312326	−	0.949975i	$-0.398892\pi$
$461$	2.85030e6	0.624653	0.312326	+	0.949975i	$0.398892\pi$
$462$	853513.	0.186040
$463$	2.85481e6	0.618906	0.309453	−	0.950915i	$-0.399854\pi$
$463$	2.85481e6	0.618906	0.309453	+	0.950915i	$0.399854\pi$
$464$	2.29208e6	0.494236
$465$	678597.	0.145539
$466$	137847.	0.0294057
$467$	−8.47940e6	−1.79917	−0.899587	−	0.436742i	$-0.856132\pi$
$467$	−8.47940e6	−1.79917	−0.899587	+	0.436742i	$0.856132\pi$
$468$	312987.	0.0660559
$469$	−3.52207e6	−0.739378
$470$	338758.	0.0707367
$471$	7.37430e6	1.53168
$472$	1.25164e6	0.258597
$473$	662314.	0.136117
$474$	−4.92693e6	−1.00723
$475$	225625.	0.0458831
$476$	−975928.	−0.197424
$477$	−314898.	−0.0633687
$478$	−5.12756e6	−1.02646
$479$	−3.83041e6	−0.762792	−0.381396	−	0.924412i	$-0.624557\pi$
$479$	−3.83041e6	−0.762792	−0.381396	+	0.924412i	$0.624557\pi$
$480$	983409.	0.194819
$481$	−1.54809e7	−3.05094
$482$	−1.54649e6	−0.303199
$483$	−6.26779e6	−1.22249
$484$	−95550.4	−0.0185404
$485$	1.67798e6	0.323916
$486$	1.65286e6	0.317428
$487$	5.27248e6	1.00738	0.503689	−	0.863885i	$-0.331976\pi$
$487$	5.27248e6	1.00738	0.503689	+	0.863885i	$0.331976\pi$
$488$	4.42898e6	0.841888
$489$	9.33943e6	1.76623
$490$	−1.26114e6	−0.237286
$491$	6.74434e6	1.26251	0.631256	−	0.775574i	$-0.282540\pi$
$491$	6.74434e6	1.26251	0.631256	+	0.775574i	$0.282540\pi$
$492$	−1.81399e6	−0.337849
$493$	−5.37533e6	−0.996065
$494$	1.99827e6	0.368415
$495$	132279.	0.0242648
$496$	1.23844e6	0.226032
$497$	−4.37043e6	−0.793657
$498$	−4.54589e6	−0.821384
$499$	−5.12454e6	−0.921306	−0.460653	−	0.887580i	$-0.652385\pi$
$499$	−5.12454e6	−0.921306	−0.460653	+	0.887580i	$0.652385\pi$
$500$	101972.	0.0182413
$501$	−873148.	−0.155415
$502$	2.60534e6	0.461430
$503$	−8.59277e6	−1.51430	−0.757152	−	0.653239i	$-0.773410\pi$
$503$	−8.59277e6	−1.51430	−0.757152	+	0.653239i	$0.773410\pi$
$504$	701795.	0.123065
$505$	2.58420e6	0.450918
$506$	−2.73885e6	−0.475546
$507$	1.40803e7	2.43272
$508$	−2.35393e6	−0.404701
$509$	−996347.	−0.170457	−0.0852287	−	0.996361i	$-0.527162\pi$
$509$	−996347.	−0.170457	−0.0852287	+	0.996361i	$0.527162\pi$
$510$	3.87111e6	0.659038
$511$	842753.	0.142774
$512$	6.60190e6	1.11300
$513$	−1.21811e6	−0.204359
$514$	3.78611e6	0.632100
$515$	−2.48188e6	−0.412347
$516$	604889.	0.100012
$517$	−324854.	−0.0534517
$518$	−5.88011e6	−0.962855
$519$	1.30810e7	2.13169
$520$	5.33143e6	0.864639
$521$	4.50856e6	0.727685	0.363842	−	0.931461i	$-0.381465\pi$
$521$	4.50856e6	0.727685	0.363842	+	0.931461i	$0.381465\pi$
$522$	654791.	0.105178
$523$	510375.	0.0815896	0.0407948	−	0.999168i	$-0.487011\pi$
$523$	510375.	0.0815896	0.0407948	+	0.999168i	$0.487011\pi$
$524$	−815875.	−0.129806
$525$	873490.	0.138312
$526$	−560727.	−0.0883664
$527$	−2.90436e6	−0.455537
$528$	1.58292e6	0.247100
$529$	1.36765e7	2.12488
$530$	−908642.	−0.140509
$531$	281475.	0.0433215
$532$	−194452.	−0.0297874
$533$	−1.80027e7	−2.74486
$534$	−8.95346e6	−1.35874
$535$	−1.50641e6	−0.227540
$536$	−8.29772e6	−1.24752
$537$	3.69502e6	0.552944
$538$	−1.92790e6	−0.287163
$539$	1.20937e6	0.179304
$540$	−550532.	−0.0812452
$541$	−5.66537e6	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$541$	−5.66537e6	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$542$	−8.95474e6	−1.30935
$543$	−8.43951e6	−1.22834
$544$	−4.20894e6	−0.609783
$545$	1.22521e6	0.176693
$546$	7.73615e6	1.11056
$547$	1.01524e6	0.145077	0.0725385	−	0.997366i	$-0.476890\pi$
$547$	1.01524e6	0.145077	0.0725385	+	0.997366i	$0.476890\pi$
$548$	1.56866e6	0.223141
$549$	996014.	0.141037
$550$	381691.	0.0538029
$551$	−1.07102e6	−0.150286
$552$	−1.47664e7	−2.06266
$553$	4.75813e6	0.661643
$554$	1.42381e6	0.197095
$555$	−5.97546e6	−0.823453
$556$	705572.	0.0967953
$557$	1.10201e7	1.50504	0.752522	−	0.658567i	$-0.228837\pi$
$557$	1.10201e7	1.50504	0.752522	+	0.658567i	$0.228837\pi$
$558$	353791.	0.0481019
$559$	6.00315e6	0.812549
$560$	1.59412e6	0.214808
$561$	−3.71223e6	−0.497998
$562$	992469.	0.132549
$563$	1.23019e7	1.63569	0.817847	−	0.575435i	$-0.195167\pi$
$563$	1.23019e7	1.63569	0.817847	+	0.575435i	$0.195167\pi$
$564$	−296688.	−0.0392737
$565$	5.65972e6	0.745888
$566$	−2.81642e6	−0.369536
$567$	−5.59286e6	−0.730595
$568$	−1.02964e7	−1.33910
$569$	1.05154e7	1.36158	0.680791	−	0.732477i	$-0.261636\pi$
$569$	1.05154e7	1.36158	0.680791	+	0.732477i	$0.261636\pi$
$570$	771311.	0.0994357
$571$	−2.32130e6	−0.297949	−0.148974	−	0.988841i	$-0.547597\pi$
$571$	−2.32130e6	−0.297949	−0.148974	+	0.988841i	$0.547597\pi$
$572$	−866058.	−0.110677
$573$	−6.75824e6	−0.859899
$574$	−6.83797e6	−0.866259
$575$	−2.80296e6	−0.353547
$576$	1.59377e6	0.200157
$577$	−1.57185e7	−1.96549	−0.982747	−	0.184953i	$-0.940787\pi$
$577$	−1.57185e7	−1.96549	−0.982747	+	0.184953i	$0.940787\pi$
$578$	−9.40191e6	−1.17057
$579$	−5.32370e6	−0.659959
$580$	−484053.	−0.0597480
$581$	4.39016e6	0.539560
$582$	5.73627e6	0.701975
$583$	871348.	0.106174
$584$	1.98546e6	0.240895
$585$	1.19896e6	0.144849
$586$	−3.41092e6	−0.410325
$587$	4.09139e6	0.490090	0.245045	−	0.969512i	$-0.421197\pi$
$587$	4.09139e6	0.490090	0.245045	+	0.969512i	$0.421197\pi$
$588$	1.10452e6	0.131743
$589$	−578687.	−0.0687314
$590$	812199.	0.0960578
$591$	1.01224e7	1.19210
$592$	−1.09052e7	−1.27888
$593$	−3.56961e6	−0.416855	−0.208427	−	0.978038i	$-0.566834\pi$
$593$	−3.56961e6	−0.416855	−0.208427	+	0.978038i	$0.566834\pi$
$594$	−2.06069e6	−0.239633
$595$	−3.73849e6	−0.432916
$596$	1.25385e6	0.144587
$597$	−1.09698e7	−1.25968
$598$	−2.48247e7	−2.83877
$599$	1.49516e7	1.70263	0.851314	−	0.524656i	$-0.175806\pi$
$599$	1.49516e7	1.70263	0.851314	+	0.524656i	$0.175806\pi$
$600$	2.05787e6	0.233368
$601$	1.28617e7	1.45248	0.726242	−	0.687439i	$-0.241265\pi$
$601$	1.28617e7	1.45248	0.726242	+	0.687439i	$0.241265\pi$
$602$	2.28017e6	0.256435
$603$	−1.86604e6	−0.208991
$604$	995715.	0.111056
$605$	−366025.	−0.0406558
$606$	8.83423e6	0.977208
$607$	−1.09904e7	−1.21072	−0.605358	−	0.795953i	$-0.706970\pi$
$607$	−1.09904e7	−1.21072	−0.605358	+	0.795953i	$0.706970\pi$
$608$	−838622.	−0.0920041
$609$	−4.14638e6	−0.453029
$610$	2.87401e6	0.312725
$611$	−2.94444e6	−0.319080
$612$	−517058.	−0.0558035
$613$	5.41534e6	0.582069	0.291035	−	0.956713i	$-0.406001\pi$
$613$	5.41534e6	0.582069	0.291035	+	0.956713i	$0.406001\pi$
$614$	−1.01637e7	−1.08801
$615$	−6.94886e6	−0.740842
$616$	−1.94192e6	−0.206196
$617$	8.22203e6	0.869493	0.434747	−	0.900553i	$-0.356838\pi$
$617$	8.22203e6	0.869493	0.434747	+	0.900553i	$0.356838\pi$
$618$	−8.48445e6	−0.893619
$619$	−7.60302e6	−0.797552	−0.398776	−	0.917048i	$-0.630565\pi$
$619$	−7.60302e6	−0.797552	−0.398776	+	0.917048i	$0.630565\pi$
$620$	−261540.	−0.0273249
$621$	1.51327e7	1.57466
$622$	−1.41229e7	−1.46369
$623$	8.64672e6	0.892548
$624$	1.43474e7	1.47507
$625$	390625.	0.0400000
$626$	−5.55159e6	−0.566215
$627$	−739653.	−0.0751379
$628$	−2.84215e6	−0.287573
$629$	2.55746e7	2.57741
$630$	455401.	0.0457133
$631$	4.74638e6	0.474558	0.237279	−	0.971442i	$-0.423744\pi$
$631$	4.74638e6	0.474558	0.237279	+	0.971442i	$0.423744\pi$
$632$	1.12098e7	1.11636
$633$	−2.94237e6	−0.291869
$634$	6.33176e6	0.625607
$635$	−9.01720e6	−0.887437
$636$	795798.	0.0780118
$637$	1.09616e7	1.07035
$638$	−1.81186e6	−0.176227
$639$	−2.31551e6	−0.224333
$640$	2.74040e6	0.264463
$641$	−7.62595e6	−0.733076	−0.366538	−	0.930403i	$-0.619457\pi$
$641$	−7.62595e6	−0.733076	−0.366538	+	0.930403i	$0.619457\pi$
$642$	−5.14973e6	−0.493114
$643$	−1.62595e7	−1.55089	−0.775445	−	0.631416i	$-0.782474\pi$
$643$	−1.62595e7	−1.55089	−0.775445	+	0.631416i	$0.782474\pi$
$644$	2.41569e6	0.229523
$645$	2.31715e6	0.219308
$646$	−3.30117e6	−0.311233
$647$	1.44966e7	1.36146	0.680731	−	0.732534i	$-0.261662\pi$
$647$	1.44966e7	1.36146	0.680731	+	0.732534i	$0.261662\pi$
$648$	−1.31763e7	−1.23270
$649$	−778863.	−0.0725854
$650$	3.45961e6	0.321176
$651$	−2.24034e6	−0.207187
$652$	−3.59954e6	−0.331610
$653$	−2.49330e6	−0.228819	−0.114409	−	0.993434i	$-0.536498\pi$
$653$	−2.49330e6	−0.228819	−0.114409	+	0.993434i	$0.536498\pi$
$654$	4.18843e6	0.382919
$655$	−3.12537e6	−0.284642
$656$	−1.26816e7	−1.15058
$657$	446500.	0.0403560
$658$	−1.11839e6	−0.100699
$659$	1.46295e7	1.31225	0.656125	−	0.754652i	$-0.272194\pi$
$659$	1.46295e7	1.31225	0.656125	+	0.754652i	$0.272194\pi$
$660$	−334289.	−0.0298719
$661$	−6.42291e6	−0.571779	−0.285890	−	0.958263i	$-0.592289\pi$
$661$	−6.42291e6	−0.571779	−0.285890	+	0.958263i	$0.592289\pi$
$662$	−8.89958e6	−0.789268
$663$	−3.36472e7	−2.97280
$664$	1.03429e7	0.910375
$665$	−744886.	−0.0653184
$666$	−3.11535e6	−0.272158
$667$	1.33054e7	1.15801
$668$	336523.	0.0291792
$669$	−6.39054e6	−0.552042
$670$	−5.38446e6	−0.463399
$671$	−2.75605e6	−0.236309
$672$	−3.24666e6	−0.277341
$673$	−1.05083e7	−0.894320	−0.447160	−	0.894454i	$-0.647565\pi$
$673$	−1.05083e7	−0.894320	−0.447160	+	0.894454i	$0.647565\pi$
$674$	−1.65379e7	−1.40227
$675$	−2.10892e6	−0.178156
$676$	−5.42672e6	−0.456742
$677$	−1.88808e7	−1.58325	−0.791624	−	0.611009i	$-0.790764\pi$
$677$	−1.88808e7	−1.58325	−0.791624	+	0.611009i	$0.790764\pi$
$678$	1.93480e7	1.61645
$679$	−5.53974e6	−0.461121
$680$	−8.80758e6	−0.730440
$681$	2.50498e6	0.206984
$682$	−978968.	−0.0805949
$683$	1.21433e7	0.996063	0.498031	−	0.867159i	$-0.334056\pi$
$683$	1.21433e7	0.996063	0.498031	+	0.867159i	$0.334056\pi$
$684$	−103023.	−0.00841963
$685$	6.00909e6	0.489308
$686$	1.11649e7	0.905824
$687$	9.13624e6	0.738543
$688$	4.22879e6	0.340600
$689$	7.89780e6	0.633809
$690$	−9.58205e6	−0.766189
$691$	−1.05966e7	−0.844249	−0.422125	−	0.906538i	$-0.638715\pi$
$691$	−1.05966e7	−0.844249	−0.422125	+	0.906538i	$0.638715\pi$
$692$	−5.04160e6	−0.400224
$693$	−436709.	−0.0345429
$694$	−1.72954e7	−1.36312
$695$	2.70284e6	0.212255
$696$	−9.76855e6	−0.764376
$697$	2.97407e7	2.31883
$698$	1.00697e6	0.0782307
$699$	−462472.	−0.0358008
$700$	−336654.	−0.0259680
$701$	−2.24312e7	−1.72408	−0.862041	−	0.506839i	$-0.830814\pi$
$701$	−2.24312e7	−1.72408	−0.862041	+	0.506839i	$0.830814\pi$
$702$	−1.86779e7	−1.43049
$703$	5.09569e6	0.388879
$704$	−4.41009e6	−0.335364
$705$	−1.13652e6	−0.0861202
$706$	−1.72886e7	−1.30541
$707$	−8.53157e6	−0.641920
$708$	−711333.	−0.0533322
$709$	1.22673e7	0.916501	0.458251	−	0.888823i	$-0.348476\pi$
$709$	1.22673e7	0.916501	0.458251	+	0.888823i	$0.348476\pi$
$710$	−6.68141e6	−0.497419
$711$	2.52091e6	0.187018
$712$	2.03710e7	1.50595
$713$	7.18907e6	0.529601
$714$	−1.27802e7	−0.938195
$715$	−3.31761e6	−0.242695
$716$	−1.42411e6	−0.103815
$717$	1.72028e7	1.24969
$718$	8.85586e6	0.641091
$719$	−2.04162e7	−1.47283	−0.736414	−	0.676532i	$-0.763482\pi$
$719$	−2.04162e7	−1.47283	−0.736414	+	0.676532i	$0.763482\pi$
$720$	844582.	0.0607171
$721$	8.19378e6	0.587011
$722$	−657750.	−0.0469589
$723$	5.18841e6	0.369138
$724$	3.25269e6	0.230620
$725$	−1.85426e6	−0.131017
$726$	−1.25128e6	−0.0881072
$727$	6.34800e6	0.445452	0.222726	−	0.974881i	$-0.428504\pi$
$727$	6.34800e6	0.445452	0.222726	+	0.974881i	$0.428504\pi$
$728$	−1.76014e7	−1.23089
$729$	1.09211e7	0.761109
$730$	1.28838e6	0.0894823
$731$	−9.91728e6	−0.686434
$732$	−2.51709e6	−0.173628
$733$	−1.17266e7	−0.806144	−0.403072	−	0.915168i	$-0.632058\pi$
$733$	−1.17266e7	−0.806144	−0.403072	+	0.915168i	$0.632058\pi$
$734$	−1.30583e7	−0.894635
$735$	4.23108e6	0.288890
$736$	1.04183e7	0.708926
$737$	5.16346e6	0.350165
$738$	−3.62284e6	−0.244855
$739$	9.12030e6	0.614325	0.307162	−	0.951657i	$-0.400620\pi$
$739$	9.12030e6	0.614325	0.307162	+	0.951657i	$0.400620\pi$
$740$	2.30302e6	0.154603
$741$	−6.70414e6	−0.448536
$742$	2.99982e6	0.200026
$743$	−3.69784e6	−0.245740	−0.122870	−	0.992423i	$-0.539210\pi$
$743$	−3.69784e6	−0.245740	−0.122870	+	0.992423i	$0.539210\pi$
$744$	−5.27807e6	−0.349577
$745$	4.80313e6	0.317054
$746$	−2.24908e6	−0.147965
$747$	2.32596e6	0.152511
$748$	1.43074e6	0.0934989
$749$	4.97331e6	0.323922
$750$	1.33537e6	0.0866860
$751$	6.36907e6	0.412075	0.206037	−	0.978544i	$-0.433943\pi$
$751$	6.36907e6	0.412075	0.206037	+	0.978544i	$0.433943\pi$
$752$	−2.07415e6	−0.133750
$753$	−8.74085e6	−0.561780
$754$	−1.64225e7	−1.05199
$755$	3.81429e6	0.243526
$756$	1.81754e6	0.115659
$757$	−9.05023e6	−0.574010	−0.287005	−	0.957929i	$-0.592660\pi$
$757$	−9.05023e6	−0.574010	−0.287005	+	0.957929i	$0.592660\pi$
$758$	1.20208e7	0.759906
$759$	9.18877e6	0.578966
$760$	−1.75489e6	−0.110209
$761$	−1.96824e7	−1.23202	−0.616008	−	0.787740i	$-0.711251\pi$
$761$	−1.96824e7	−1.23202	−0.616008	+	0.787740i	$0.711251\pi$
$762$	−3.08258e7	−1.92321
$763$	−4.04494e6	−0.251536
$764$	2.60471e6	0.161446
$765$	−1.98070e6	−0.122367
$766$	7.75914e6	0.477795
$767$	−7.05954e6	−0.433299
$768$	−1.03809e7	−0.635085
$769$	−3.06851e7	−1.87116	−0.935581	−	0.353112i	$-0.885124\pi$
$769$	−3.06851e7	−1.87116	−0.935581	+	0.353112i	$0.885124\pi$
$770$	−1.26013e6	−0.0765928
$771$	−1.27023e7	−0.769567
$772$	2.05182e6	0.123907
$773$	1.96304e7	1.18163	0.590813	−	0.806809i	$-0.298807\pi$
$773$	1.96304e7	1.18163	0.590813	+	0.806809i	$0.298807\pi$
$774$	1.20806e6	0.0724832
$775$	−1.00188e6	−0.0599187
$776$	−1.30512e7	−0.778029
$777$	1.97276e7	1.17225
$778$	−2.11178e7	−1.25083
$779$	5.92578e6	0.349866
$780$	−3.02996e6	−0.178320
$781$	6.40718e6	0.375871
$782$	4.10107e7	2.39817
$783$	1.00109e7	0.583536
$784$	7.72170e6	0.448666
$785$	−1.08874e7	−0.630596
$786$	−1.06843e7	−0.616862
$787$	−9.19443e6	−0.529161	−0.264581	−	0.964364i	$-0.585234\pi$
$787$	−9.19443e6	−0.529161	−0.264581	+	0.964364i	$0.585234\pi$
$788$	−3.90128e6	−0.223816
$789$	1.88122e6	0.107584
$790$	7.27412e6	0.414680
$791$	−1.86852e7	−1.06183
$792$	−1.02885e6	−0.0582827
$793$	−2.49805e7	−1.41065
$794$	2.15493e6	0.121306
$795$	3.04847e6	0.171066
$796$	4.22789e6	0.236505
$797$	−3.23935e7	−1.80639	−0.903197	−	0.429226i	$-0.858786\pi$
$797$	−3.23935e7	−1.80639	−0.903197	+	0.429226i	$0.858786\pi$
$798$	−2.54643e6	−0.141555
$799$	4.86425e6	0.269556
$800$	−1.45191e6	−0.0802073
$801$	4.58114e6	0.252285
$802$	−2.30760e7	−1.26685
$803$	−1.23550e6	−0.0676167
$804$	4.71577e6	0.257284
$805$	9.25378e6	0.503303
$806$	−8.87326e6	−0.481111
$807$	6.46805e6	0.349614
$808$	−2.00997e7	−1.08308
$809$	1.72162e6	0.0924839	0.0462419	−	0.998930i	$-0.485275\pi$
$809$	1.72162e6	0.0924839	0.0462419	+	0.998930i	$0.485275\pi$
$810$	−8.55024e6	−0.457895
$811$	−1.08552e7	−0.579540	−0.289770	−	0.957096i	$-0.593579\pi$
$811$	−1.08552e7	−0.579540	−0.289770	+	0.957096i	$0.593579\pi$
$812$	1.59807e6	0.0850561
$813$	3.00429e7	1.59410
$814$	8.62041e6	0.456002
$815$	−1.37888e7	−0.727162
$816$	−2.37021e7	−1.24612
$817$	−1.97600e6	−0.103569
$818$	−9.74601e6	−0.509265
$819$	−3.95829e6	−0.206204
$820$	2.67818e6	0.139093
$821$	2.18432e7	1.13099	0.565494	−	0.824752i	$-0.308685\pi$
$821$	2.18432e7	1.13099	0.565494	+	0.824752i	$0.308685\pi$
$822$	2.05424e7	1.06040
$823$	−2.80055e7	−1.44126	−0.720632	−	0.693318i	$-0.756148\pi$
$823$	−2.80055e7	−1.44126	−0.720632	+	0.693318i	$0.756148\pi$
$824$	1.93039e7	0.990436
$825$	−1.28056e6	−0.0655037
$826$	−2.68142e6	−0.136746
$827$	−3.57129e7	−1.81577	−0.907886	−	0.419216i	$-0.862305\pi$
$827$	−3.57129e7	−1.81577	−0.907886	+	0.419216i	$0.862305\pi$
$828$	1.27986e6	0.0648764
$829$	7.68876e6	0.388571	0.194285	−	0.980945i	$-0.437761\pi$
$829$	7.68876e6	0.388571	0.194285	+	0.980945i	$0.437761\pi$
$830$	6.71157e6	0.338165
$831$	−4.77682e6	−0.239959
$832$	−3.99726e7	−2.00195
$833$	−1.81088e7	−0.904225
$834$	9.23979e6	0.459988
$835$	1.28912e6	0.0639847
$836$	285072.	0.0141071
$837$	5.40900e6	0.266872
$838$	−2.18358e7	−1.07413
$839$	−1.90415e7	−0.933890	−0.466945	−	0.884286i	$-0.654645\pi$
$839$	−1.90415e7	−0.933890	−0.466945	+	0.884286i	$0.654645\pi$
$840$	−6.79393e6	−0.332218
$841$	−1.17091e7	−0.570866
$842$	2.54441e7	1.23682
$843$	−3.32971e6	−0.161375
$844$	1.13403e6	0.0547984
$845$	−2.07882e7	−1.00155
$846$	−592534.	−0.0284635
$847$	1.20841e6	0.0578769
$848$	5.56344e6	0.265677
$849$	9.44901e6	0.449901
$850$	−5.71532e6	−0.271327
$851$	−6.33042e7	−2.99646
$852$	5.85165e6	0.276172
$853$	−1.00966e7	−0.475119	−0.237560	−	0.971373i	$-0.576347\pi$
$853$	−1.00966e7	−0.475119	−0.237560	+	0.971373i	$0.576347\pi$
$854$	−9.48834e6	−0.445190
$855$	−394649.	−0.0184627
$856$	1.17167e7	0.546539
$857$	1.38017e7	0.641920	0.320960	−	0.947093i	$-0.395994\pi$
$857$	1.38017e7	0.641920	0.320960	+	0.947093i	$0.395994\pi$
$858$	−1.13414e7	−0.525956
$859$	2.52073e7	1.16558	0.582792	−	0.812622i	$-0.301960\pi$
$859$	2.52073e7	1.16558	0.582792	+	0.812622i	$0.301960\pi$
$860$	−893059.	−0.0411750
$861$	2.29412e7	1.05465
$862$	2.66115e7	1.21984
$863$	−1.49138e7	−0.681651	−0.340826	−	0.940127i	$-0.610707\pi$
$863$	−1.49138e7	−0.681651	−0.340826	+	0.940127i	$0.610707\pi$
$864$	7.83862e6	0.357236
$865$	−1.93129e7	−0.877620
$866$	−1.37953e7	−0.625080
$867$	3.15431e7	1.42514
$868$	863457.	0.0388993
$869$	−6.97556e6	−0.313350
$870$	−6.33890e6	−0.283933
$871$	4.68011e7	2.09031
$872$	−9.52956e6	−0.424406
$873$	−2.93502e6	−0.130339
$874$	8.17129e6	0.361836
$875$	−1.28962e6	−0.0569433
$876$	−1.12838e6	−0.0496814
$877$	−1.14728e7	−0.503696	−0.251848	−	0.967767i	$-0.581038\pi$
$877$	−1.14728e7	−0.503696	−0.251848	+	0.967767i	$0.581038\pi$
$878$	−1.76814e7	−0.774071
$879$	1.14435e7	0.499561
$880$	−2.33702e6	−0.101732
$881$	−1.70096e7	−0.738338	−0.369169	−	0.929362i	$-0.620358\pi$
$881$	−1.70096e7	−0.738338	−0.369169	+	0.929362i	$0.620358\pi$
$882$	2.20590e6	0.0954806
$883$	1.00613e7	0.434263	0.217132	−	0.976142i	$-0.430330\pi$
$883$	1.00613e7	0.434263	0.217132	+	0.976142i	$0.430330\pi$
$884$	1.29681e7	0.558142
$885$	−2.72490e6	−0.116948
$886$	−3.59879e7	−1.54018
$887$	−4.19007e7	−1.78819	−0.894093	−	0.447881i	$-0.852179\pi$
$887$	−4.19007e7	−1.78819	−0.894093	+	0.447881i	$0.852179\pi$
$888$	4.64766e7	1.97789
$889$	2.97697e7	1.26334
$890$	1.32189e7	0.559398
$891$	8.19930e6	0.346005
$892$	2.46299e6	0.103646
$893$	969192.	0.0406706
$894$	1.64197e7	0.687104
$895$	−5.45534e6	−0.227648
$896$	−9.04727e6	−0.376485
$897$	8.32860e7	3.45614
$898$	−3.93526e7	−1.62848
$899$	4.75585e6	0.196259
$900$	−178363.	−0.00734006
$901$	−1.30473e7	−0.535436
$902$	1.00247e7	0.410255
$903$	−7.64992e6	−0.312203
$904$	−4.40208e7	−1.79158
$905$	1.24601e7	0.505708
$906$	1.30393e7	0.527758
$907$	4.66555e7	1.88315	0.941575	−	0.336804i	$-0.109346\pi$
$907$	4.66555e7	1.88315	0.941575	+	0.336804i	$0.109346\pi$
$908$	−965451.	−0.0388612
$909$	−4.52013e6	−0.181443
$910$	−1.14217e7	−0.457221
$911$	4.36719e7	1.74344	0.871718	−	0.490007i	$-0.163006\pi$
$911$	4.36719e7	1.74344	0.871718	+	0.490007i	$0.163006\pi$
$912$	−4.72259e6	−0.188015
$913$	−6.43610e6	−0.255532
$914$	−3.62053e6	−0.143353
$915$	−9.64221e6	−0.380736
$916$	−3.52123e6	−0.138661
$917$	1.03182e7	0.405211
$918$	3.08561e7	1.20847
$919$	−8.85441e6	−0.345837	−0.172918	−	0.984936i	$-0.555320\pi$
$919$	−8.85441e6	−0.345837	−0.172918	+	0.984936i	$0.555320\pi$
$920$	2.18012e7	0.849200
$921$	3.40989e7	1.32462
$922$	−1.43859e7	−0.557327
$923$	5.80740e7	2.24377
$924$	1.10363e6	0.0425251
$925$	8.82218e6	0.339017
$926$	−1.44087e7	−0.552200
$927$	4.34116e6	0.165923
$928$	6.89208e6	0.262712
$929$	6.75044e6	0.256621	0.128311	−	0.991734i	$-0.459045\pi$
$929$	6.75044e6	0.256621	0.128311	+	0.991734i	$0.459045\pi$
$930$	−3.42498e6	−0.129853
$931$	−3.60813e6	−0.136430
$932$	178243.	0.00672159
$933$	4.73819e7	1.78200
$934$	4.27969e7	1.60526
$935$	5.48074e6	0.205027
$936$	−9.32540e6	−0.347919
$937$	−2.44776e7	−0.910793	−0.455396	−	0.890289i	$-0.650502\pi$
$937$	−2.44776e7	−0.910793	−0.455396	+	0.890289i	$0.650502\pi$
$938$	1.77765e7	0.659687
$939$	1.86254e7	0.689354
$940$	438030.	0.0161690
$941$	−2.81976e7	−1.03810	−0.519048	−	0.854745i	$-0.673714\pi$
$941$	−2.81976e7	−1.03810	−0.519048	+	0.854745i	$0.673714\pi$
$942$	−3.72192e7	−1.36660
$943$	−7.36164e7	−2.69585
$944$	−4.97294e6	−0.181628
$945$	6.96247e6	0.253620
$946$	−3.34280e6	−0.121446
$947$	5.78045e6	0.209453	0.104727	−	0.994501i	$-0.466603\pi$
$947$	5.78045e6	0.209453	0.104727	+	0.994501i	$0.466603\pi$
$948$	−6.37075e6	−0.230234
$949$	−1.11984e7	−0.403638
$950$	−1.13876e6	−0.0409378
$951$	−2.12429e7	−0.761662
$952$	2.90777e7	1.03984
$953$	2.01490e7	0.718657	0.359329	−	0.933211i	$-0.383006\pi$
$953$	2.01490e7	0.718657	0.359329	+	0.933211i	$0.383006\pi$
$954$	1.58934e6	0.0565388
$955$	9.97788e6	0.354022
$956$	−6.63018e6	−0.234628
$957$	6.07872e6	0.214552
$958$	1.93327e7	0.680578
$959$	−1.98386e7	−0.696570
$960$	−1.54290e7	−0.540330
$961$	−2.60595e7	−0.910244
$962$	7.81345e7	2.72211
$963$	2.63492e6	0.0915590
$964$	−1.99968e6	−0.0693056
$965$	7.85992e6	0.271706
$966$	3.16345e7	1.09073
$967$	−8.76665e6	−0.301486	−0.150743	−	0.988573i	$-0.548167\pi$
$967$	−8.76665e6	−0.301486	−0.150743	+	0.988573i	$0.548167\pi$
$968$	2.84691e6	0.0976530
$969$	1.10753e7	0.378919
$970$	−8.46903e6	−0.289004
$971$	1.17583e7	0.400219	0.200109	−	0.979774i	$-0.435870\pi$
$971$	1.17583e7	0.400219	0.200109	+	0.979774i	$0.435870\pi$
$972$	2.13723e6	0.0725579
$973$	−8.92324e6	−0.302162
$974$	−2.66110e7	−0.898803
$975$	−1.16069e7	−0.391025
$976$	−1.75970e7	−0.591308
$977$	−2.91885e7	−0.978309	−0.489154	−	0.872197i	$-0.662695\pi$
$977$	−2.91885e7	−0.978309	−0.489154	+	0.872197i	$0.662695\pi$
$978$	−4.71376e7	−1.57587
$979$	−1.26763e7	−0.422705
$980$	−1.63071e6	−0.0542390
$981$	−2.14306e6	−0.0710987
$982$	−3.40397e7	−1.12644
$983$	−2.84911e7	−0.940429	−0.470215	−	0.882552i	$-0.655823\pi$
$983$	−2.84911e7	−0.940429	−0.470215	+	0.882552i	$0.655823\pi$
$984$	5.40476e7	1.77946
$985$	−1.49447e7	−0.490790
$986$	2.71301e7	0.888709
$987$	3.75215e6	0.122599
$988$	2.58386e6	0.0842125
$989$	2.45479e7	0.798040
$990$	−667631.	−0.0216495
$991$	3.61471e7	1.16920	0.584601	−	0.811321i	$-0.301251\pi$
$991$	3.61471e7	1.16920	0.584601	+	0.811321i	$0.301251\pi$
$992$	3.72388e6	0.120148
$993$	2.98578e7	0.960915
$994$	2.20582e7	0.708117
$995$	1.61958e7	0.518614
$996$	−5.87806e6	−0.187753
$997$	−2.59275e6	−0.0826081	−0.0413041	−	0.999147i	$-0.513151\pi$
$997$	−2.59275e6	−0.0826081	−0.0413041	+	0.999147i	$0.513151\pi$
$998$	2.58644e7	0.822007
$999$	−4.76295e7	−1.50995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.11	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.11	✓	39	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)

\(f(q)\)	\(=\)	\(q-5.04716 q^{2} +16.9331 q^{3} -6.52622 q^{4} -25.0000 q^{5} -85.4638 q^{6} +82.5359 q^{7} +194.448 q^{8} +43.7285 q^{9} +O(q^{10})\)	\(q-5.04716 q^{2} +16.9331 q^{3} -6.52622 q^{4} -25.0000 q^{5} -85.4638 q^{6} +82.5359 q^{7} +194.448 q^{8} +43.7285 q^{9} +126.179 q^{10} -121.000 q^{11} -110.509 q^{12} -1096.73 q^{13} -416.571 q^{14} -423.326 q^{15} -772.570 q^{16} +1811.81 q^{17} -220.704 q^{18} +361.000 q^{19} +163.155 q^{20} +1397.58 q^{21} +610.706 q^{22} -4484.73 q^{23} +3292.60 q^{24} +625.000 q^{25} +5535.37 q^{26} -3374.28 q^{27} -538.647 q^{28} -2966.82 q^{29} +2136.59 q^{30} -1603.01 q^{31} -2323.05 q^{32} -2048.90 q^{33} -9144.51 q^{34} -2063.40 q^{35} -285.382 q^{36} +14115.5 q^{37} -1822.02 q^{38} -18571.0 q^{39} -4861.20 q^{40} +16414.9 q^{41} -7053.83 q^{42} -5473.67 q^{43} +789.672 q^{44} -1093.21 q^{45} +22635.1 q^{46} +2684.74 q^{47} -13082.0 q^{48} -9994.83 q^{49} -3154.47 q^{50} +30679.6 q^{51} +7157.51 q^{52} -7201.22 q^{53} +17030.5 q^{54} +3025.00 q^{55} +16048.9 q^{56} +6112.83 q^{57} +14974.0 q^{58} +6436.89 q^{59} +2762.72 q^{60} +22777.2 q^{61} +8090.64 q^{62} +3609.17 q^{63} +36447.0 q^{64} +27418.3 q^{65} +10341.1 q^{66} -42673.3 q^{67} -11824.3 q^{68} -75940.2 q^{69} +10414.3 q^{70} -52951.9 q^{71} +8502.91 q^{72} +10210.7 q^{73} -71243.1 q^{74} +10583.2 q^{75} -2355.96 q^{76} -9986.84 q^{77} +93730.8 q^{78} +57649.3 q^{79} +19314.2 q^{80} -67762.8 q^{81} -82848.5 q^{82} +53190.9 q^{83} -9120.94 q^{84} -45295.4 q^{85} +27626.5 q^{86} -50237.4 q^{87} -23528.2 q^{88} +104763. q^{89} +5517.61 q^{90} -90519.7 q^{91} +29268.3 q^{92} -27143.9 q^{93} -13550.3 q^{94} -9025.00 q^{95} -39336.4 q^{96} -67119.2 q^{97} +50445.5 q^{98} -5291.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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