LMFDB - Embedded newform 1045.6.a.b.1.2

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:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-10.6840 q^{2} +22.9747 q^{3} +82.1485 q^{4} +25.0000 q^{5} -245.462 q^{6} +48.0772 q^{7} -535.788 q^{8} +284.836 q^{9} +O(q^{10})$	\(q-10.6840 q^{2} +22.9747 q^{3} +82.1485 q^{4} +25.0000 q^{5} -245.462 q^{6} +48.0772 q^{7} -535.788 q^{8} +284.836 q^{9} -267.101 q^{10} -121.000 q^{11} +1887.34 q^{12} +1196.89 q^{13} -513.658 q^{14} +574.367 q^{15} +3095.63 q^{16} -718.671 q^{17} -3043.19 q^{18} +361.000 q^{19} +2053.71 q^{20} +1104.56 q^{21} +1292.77 q^{22} -4603.77 q^{23} -12309.6 q^{24} +625.000 q^{25} -12787.6 q^{26} +961.158 q^{27} +3949.47 q^{28} -4889.79 q^{29} -6136.55 q^{30} -4290.56 q^{31} -15928.6 q^{32} -2779.94 q^{33} +7678.30 q^{34} +1201.93 q^{35} +23398.8 q^{36} +1247.77 q^{37} -3856.94 q^{38} +27498.1 q^{39} -13394.7 q^{40} +5473.03 q^{41} -11801.1 q^{42} -15497.8 q^{43} -9939.97 q^{44} +7120.89 q^{45} +49186.8 q^{46} +7929.87 q^{47} +71121.0 q^{48} -14495.6 q^{49} -6677.52 q^{50} -16511.2 q^{51} +98322.4 q^{52} -39954.8 q^{53} -10269.0 q^{54} -3025.00 q^{55} -25759.2 q^{56} +8293.86 q^{57} +52242.7 q^{58} -33729.9 q^{59} +47183.4 q^{60} -880.624 q^{61} +45840.5 q^{62} +13694.1 q^{63} +71121.1 q^{64} +29922.1 q^{65} +29700.9 q^{66} +33235.9 q^{67} -59037.7 q^{68} -105770. q^{69} -12841.4 q^{70} -41370.5 q^{71} -152612. q^{72} +28084.7 q^{73} -13331.3 q^{74} +14359.2 q^{75} +29655.6 q^{76} -5817.34 q^{77} -293790. q^{78} -9112.05 q^{79} +77390.7 q^{80} -47132.8 q^{81} -58474.0 q^{82} -22730.5 q^{83} +90737.7 q^{84} -17966.8 q^{85} +165579. q^{86} -112341. q^{87} +64830.4 q^{88} -89504.8 q^{89} -76079.8 q^{90} +57542.9 q^{91} -378193. q^{92} -98574.2 q^{93} -84723.0 q^{94} +9025.00 q^{95} -365953. q^{96} -110733. q^{97} +154871. q^{98} -34465.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * 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 $

$2$	−10.6840	−1.88869	−0.944344	−	0.328960i	$-0.893302\pi$
$2$	−10.6840	−1.88869	−0.944344	+	0.328960i	$0.893302\pi$
$3$	22.9747	1.47383	0.736913	−	0.675988i	$-0.236283\pi$
$3$	22.9747	1.47383	0.736913	+	0.675988i	$0.236283\pi$
$4$	82.1485	2.56714
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−245.462	−2.78360
$7$	48.0772	0.370846	0.185423	−	0.982659i	$-0.440634\pi$
$7$	48.0772	0.370846	0.185423	+	0.982659i	$0.440634\pi$
$8$	−535.788	−2.95984
$9$	284.836	1.17216
$10$	−267.101	−0.844647
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	1887.34	3.78352
$13$	1196.89	1.96424	0.982119	−	0.188260i	$-0.0602847\pi$
$13$	1196.89	1.96424	0.982119	+	0.188260i	$0.0602847\pi$
$14$	−513.658	−0.700412
$15$	574.367	0.659115
$16$	3095.63	3.02307
$17$	−718.671	−0.603125	−0.301563	−	0.953446i	$-0.597508\pi$
$17$	−718.671	−0.603125	−0.301563	+	0.953446i	$0.597508\pi$
$18$	−3043.19	−2.21385
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	2053.71	1.14806
$21$	1104.56	0.546563
$22$	1292.77	0.569461
$23$	−4603.77	−1.81465	−0.907327	−	0.420425i	$-0.861881\pi$
$23$	−4603.77	−1.81465	−0.907327	+	0.420425i	$0.861881\pi$
$24$	−12309.6	−4.36229
$25$	625.000	0.200000
$26$	−12787.6	−3.70983
$27$	961.158	0.253738
$28$	3949.47	0.952014
$29$	−4889.79	−1.07968	−0.539840	−	0.841767i	$-0.681515\pi$
$29$	−4889.79	−1.07968	−0.539840	+	0.841767i	$0.681515\pi$
$30$	−6136.55	−1.24486
$31$	−4290.56	−0.801881	−0.400940	−	0.916104i	$-0.631317\pi$
$31$	−4290.56	−0.801881	−0.400940	+	0.916104i	$0.631317\pi$
$32$	−15928.6	−2.74980
$33$	−2779.94	−0.444375
$34$	7678.30	1.13912
$35$	1201.93	0.165847
$36$	23398.8	3.00911
$37$	1247.77	0.149841	0.0749207	−	0.997189i	$-0.476130\pi$
$37$	1247.77	0.149841	0.0749207	+	0.997189i	$0.476130\pi$
$38$	−3856.94	−0.433295
$39$	27498.1	2.89495
$40$	−13394.7	−1.32368
$41$	5473.03	0.508473	0.254237	−	0.967142i	$-0.418176\pi$
$41$	5473.03	0.508473	0.254237	+	0.967142i	$0.418176\pi$
$42$	−11801.1	−1.03229
$43$	−15497.8	−1.27820	−0.639100	−	0.769124i	$-0.720693\pi$
$43$	−15497.8	−1.27820	−0.639100	+	0.769124i	$0.720693\pi$
$44$	−9939.97	−0.774022
$45$	7120.89	0.524207
$46$	49186.8	3.42732
$47$	7929.87	0.523626	0.261813	−	0.965119i	$-0.415680\pi$
$47$	7929.87	0.523626	0.261813	+	0.965119i	$0.415680\pi$
$48$	71121.0	4.45549
$49$	−14495.6	−0.862473
$50$	−6677.52	−0.377738
$51$	−16511.2	−0.888902
$52$	98322.4	5.04248
$53$	−39954.8	−1.95380	−0.976898	−	0.213708i	$-0.931446\pi$
$53$	−39954.8	−1.95380	−0.976898	+	0.213708i	$0.931446\pi$
$54$	−10269.0	−0.479231
$55$	−3025.00	−0.134840
$56$	−25759.2	−1.09765
$57$	8293.86	0.338119
$58$	52242.7	2.03918
$59$	−33729.9	−1.26149	−0.630747	−	0.775989i	$-0.717251\pi$
$59$	−33729.9	−1.26149	−0.630747	+	0.775989i	$0.717251\pi$
$60$	47183.4	1.69204
$61$	−880.624	−0.0303016	−0.0151508	−	0.999885i	$-0.504823\pi$
$61$	−880.624	−0.0303016	−0.0151508	+	0.999885i	$0.504823\pi$
$62$	45840.5	1.51450
$63$	13694.1	0.434692
$64$	71121.1	2.17044
$65$	29922.1	0.878434
$66$	29700.9	0.839286
$67$	33235.9	0.904525	0.452262	−	0.891885i	$-0.350617\pi$
$67$	33235.9	0.904525	0.452262	+	0.891885i	$0.350617\pi$
$68$	−59037.7	−1.54831
$69$	−105770.	−2.67448
$70$	−12841.4	−0.313234
$71$	−41370.5	−0.973968	−0.486984	−	0.873411i	$-0.661903\pi$
$71$	−41370.5	−0.973968	−0.486984	+	0.873411i	$0.661903\pi$
$72$	−152612.	−3.46942
$73$	28084.7	0.616827	0.308413	−	0.951252i	$-0.400202\pi$
$73$	28084.7	0.616827	0.308413	+	0.951252i	$0.400202\pi$
$74$	−13331.3	−0.283004
$75$	14359.2	0.294765
$76$	29655.6	0.588943
$77$	−5817.34	−0.111814
$78$	−293790.	−5.46765
$79$	−9112.05	−0.164266	−0.0821332	−	0.996621i	$-0.526173\pi$
$79$	−9112.05	−0.164266	−0.0821332	+	0.996621i	$0.526173\pi$
$80$	77390.7	1.35196
$81$	−47132.8	−0.798197
$82$	−58474.0	−0.960347
$83$	−22730.5	−0.362171	−0.181085	−	0.983467i	$-0.557961\pi$
$83$	−22730.5	−0.362171	−0.181085	+	0.983467i	$0.557961\pi$
$84$	90737.7	1.40310
$85$	−17966.8	−0.269726
$86$	165579.	2.41412
$87$	−112341.	−1.59126
$88$	64830.4	0.892426
$89$	−89504.8	−1.19776	−0.598882	−	0.800837i	$-0.704388\pi$
$89$	−89504.8	−1.19776	−0.598882	+	0.800837i	$0.704388\pi$
$90$	−76079.8	−0.990064
$91$	57542.9	0.728430
$92$	−378193.	−4.65848
$93$	−98574.2	−1.18183
$94$	−84723.0	−0.988967
$95$	9025.00	0.102598
$96$	−365953.	−4.05273
$97$	−110733.	−1.19494	−0.597471	−	0.801891i	$-0.703828\pi$
$97$	−110733.	−1.19494	−0.597471	+	0.801891i	$0.703828\pi$
$98$	154871.	1.62894
$99$	−34465.1	−0.353420
$100$	51342.8	0.513428
$101$	30335.1	0.295898	0.147949	−	0.988995i	$-0.452733\pi$
$101$	30335.1	0.295898	0.147949	+	0.988995i	$0.452733\pi$
$102$	176406.	1.67886
$103$	49499.3	0.459733	0.229867	−	0.973222i	$-0.426171\pi$
$103$	49499.3	0.459733	0.229867	+	0.973222i	$0.426171\pi$
$104$	−641277.	−5.81383
$105$	27613.9	0.244430
$106$	426878.	3.69011
$107$	38482.5	0.324941	0.162470	−	0.986713i	$-0.448054\pi$
$107$	38482.5	0.324941	0.162470	+	0.986713i	$0.448054\pi$
$108$	78957.7	0.651381
$109$	−118333.	−0.953980	−0.476990	−	0.878909i	$-0.658272\pi$
$109$	−118333.	−0.953980	−0.476990	+	0.878909i	$0.658272\pi$
$110$	32319.2	0.254671
$111$	28667.2	0.220840
$112$	148829.	1.12110
$113$	−61916.5	−0.456153	−0.228076	−	0.973643i	$-0.573244\pi$
$113$	−61916.5	−0.456153	−0.228076	+	0.973643i	$0.573244\pi$
$114$	−88611.8	−0.638601
$115$	−115094.	−0.811538
$116$	−401689.	−2.77169
$117$	340916.	2.30241
$118$	360371.	2.38257
$119$	−34551.6	−0.223667
$120$	−307739.	−1.95088
$121$	14641.0	0.0909091
$122$	9408.61	0.0572303
$123$	125741.	0.749401
$124$	−352463.	−2.05854
$125$	15625.0	0.0894427
$126$	−146308.	−0.820997
$127$	−113135.	−0.622428	−0.311214	−	0.950340i	$-0.600736\pi$
$127$	−113135.	−0.622428	−0.311214	+	0.950340i	$0.600736\pi$
$128$	−250146.	−1.34949
$129$	−356057.	−1.88384
$130$	−319689.	−1.65909
$131$	−92488.3	−0.470878	−0.235439	−	0.971889i	$-0.575653\pi$
$131$	−92488.3	−0.470878	−0.235439	+	0.971889i	$0.575653\pi$
$132$	−228368.	−1.14077
$133$	17355.9	0.0850779
$134$	−355093.	−1.70836
$135$	24028.9	0.113475
$136$	385056.	1.78516
$137$	−106531.	−0.484925	−0.242462	−	0.970161i	$-0.577955\pi$
$137$	−106531.	−0.484925	−0.242462	+	0.970161i	$0.577955\pi$
$138$	1.13005e6	5.05127
$139$	−7691.12	−0.0337639	−0.0168819	−	0.999857i	$-0.505374\pi$
$139$	−7691.12	−0.0337639	−0.0168819	+	0.999857i	$0.505374\pi$
$140$	98736.7	0.425754
$141$	182186.	0.771734
$142$	442004.	1.83952
$143$	−144823.	−0.592240
$144$	881745.	3.54353
$145$	−122245.	−0.482848
$146$	−300058.	−1.16499
$147$	−333031.	−1.27114
$148$	102503.	0.384664
$149$	479237.	1.76842	0.884209	−	0.467092i	$-0.154698\pi$
$149$	479237.	1.76842	0.884209	+	0.467092i	$0.154698\pi$
$150$	−153414.	−0.556719
$151$	−310087.	−1.10673	−0.553364	−	0.832940i	$-0.686656\pi$
$151$	−310087.	−1.10673	−0.553364	+	0.832940i	$0.686656\pi$
$152$	−193420.	−0.679034
$153$	−204703.	−0.706961
$154$	62152.6	0.211182
$155$	−107264.	−0.358612
$156$	2.25892e6	7.43174
$157$	−273925.	−0.886917	−0.443458	−	0.896295i	$-0.646249\pi$
$157$	−273925.	−0.886917	−0.443458	+	0.896295i	$0.646249\pi$
$158$	97353.5	0.310248
$159$	−917948.	−2.87955
$160$	−398214.	−1.22975
$161$	−221336.	−0.672958
$162$	503568.	1.50755
$163$	−271154.	−0.799368	−0.399684	−	0.916653i	$-0.630880\pi$
$163$	−271154.	−0.799368	−0.399684	+	0.916653i	$0.630880\pi$
$164$	449601.	1.30532
$165$	−69498.4	−0.198731
$166$	242853.	0.684028
$167$	343951.	0.954344	0.477172	−	0.878810i	$-0.341662\pi$
$167$	343951.	0.954344	0.477172	+	0.878810i	$0.341662\pi$
$168$	−591809.	−1.61774
$169$	1.06124e6	2.85823
$170$	191958.	0.509428
$171$	102826.	0.268913
$172$	−1.27312e6	−3.28132
$173$	−1766.78	−0.00448815	−0.00224407	−	0.999997i	$-0.500714\pi$
$173$	−1766.78	−0.00448815	−0.00224407	+	0.999997i	$0.500714\pi$
$174$	1.20026e6	3.00540
$175$	30048.2	0.0741692
$176$	−374571.	−0.911491
$177$	−774933.	−1.85922
$178$	956272.	2.26220
$179$	10882.8	0.0253867	0.0126934	−	0.999919i	$-0.495959\pi$
$179$	10882.8	0.0253867	0.0126934	+	0.999919i	$0.495959\pi$
$180$	584971.	1.34571
$181$	−88954.5	−0.201823	−0.100912	−	0.994895i	$-0.532176\pi$
$181$	−88954.5	−0.201823	−0.100912	+	0.994895i	$0.532176\pi$
$182$	−614790.	−1.37578
$183$	−20232.0	−0.0446593
$184$	2.46665e6	5.37109
$185$	31194.4	0.0670111
$186$	1.05317e6	2.23211
$187$	86959.2	0.181849
$188$	651427.	1.34422
$189$	46209.7	0.0940977
$190$	−96423.4	−0.193775
$191$	846475.	1.67892	0.839462	−	0.543419i	$-0.182870\pi$
$191$	846475.	1.67892	0.839462	+	0.543419i	$0.182870\pi$
$192$	1.63398e6	3.19886
$193$	882099.	1.70461	0.852303	−	0.523049i	$-0.175205\pi$
$193$	882099.	1.70461	0.852303	+	0.523049i	$0.175205\pi$
$194$	1.18307e6	2.25687
$195$	687451.	1.29466
$196$	−1.19079e6	−2.21409
$197$	−99633.2	−0.182910	−0.0914552	−	0.995809i	$-0.529152\pi$
$197$	−99633.2	−0.182910	−0.0914552	+	0.995809i	$0.529152\pi$
$198$	368226.	0.667501
$199$	992471.	1.77658	0.888291	−	0.459282i	$-0.151893\pi$
$199$	992471.	1.77658	0.888291	+	0.459282i	$0.151893\pi$
$200$	−334868.	−0.591968
$201$	763584.	1.33311
$202$	−324101.	−0.558859
$203$	−235087.	−0.400395
$204$	−1.35637e6	−2.28194
$205$	136826.	0.227396
$206$	−528852.	−0.868293
$207$	−1.31132e6	−2.12707
$208$	3.70511e6	5.93804
$209$	−43681.0	−0.0691714
$210$	−295028.	−0.461652
$211$	277332.	0.428838	0.214419	−	0.976742i	$-0.431214\pi$
$211$	277332.	0.428838	0.214419	+	0.976742i	$0.431214\pi$
$212$	−3.28223e6	−5.01567
$213$	−950474.	−1.43546
$214$	−411148.	−0.613711
$215$	−387445.	−0.571628
$216$	−514977.	−0.751024
$217$	−206278.	−0.297374
$218$	1.26427e6	1.80177
$219$	645238.	0.909095
$220$	−248499.	−0.346153
$221$	−860167.	−1.18468
$222$	−306281.	−0.417098
$223$	−169780.	−0.228625	−0.114313	−	0.993445i	$-0.536467\pi$
$223$	−169780.	−0.228625	−0.114313	+	0.993445i	$0.536467\pi$
$224$	−765800.	−1.01975
$225$	178022.	0.234433
$226$	661518.	0.861530
$227$	−547362.	−0.705034	−0.352517	−	0.935805i	$-0.614674\pi$
$227$	−547362.	−0.705034	−0.352517	+	0.935805i	$0.614674\pi$
$228$	681328.	0.867999
$229$	603208.	0.760114	0.380057	−	0.924963i	$-0.375904\pi$
$229$	603208.	0.760114	0.380057	+	0.924963i	$0.375904\pi$
$230$	1.22967e6	1.53274
$231$	−133651.	−0.164795
$232$	2.61989e6	3.19568
$233$	136416.	0.164617	0.0823084	−	0.996607i	$-0.473771\pi$
$233$	136416.	0.164617	0.0823084	+	0.996607i	$0.473771\pi$
$234$	−3.64235e6	−4.34853
$235$	198247.	0.234173
$236$	−2.77086e6	−3.23843
$237$	−209346.	−0.242100
$238$	369151.	0.422437
$239$	−32920.4	−0.0372795	−0.0186398	−	0.999826i	$-0.505934\pi$
$239$	−32920.4	−0.0372795	−0.0186398	+	0.999826i	$0.505934\pi$
$240$	1.77803e6	1.99255
$241$	−608404.	−0.674760	−0.337380	−	0.941368i	$-0.609541\pi$
$241$	−608404.	−0.674760	−0.337380	+	0.941368i	$0.609541\pi$
$242$	−156425.	−0.171699
$243$	−1.31642e6	−1.43014
$244$	−72342.0	−0.0777886
$245$	−362390.	−0.385710
$246$	−1.34342e6	−1.41538
$247$	432076.	0.450627
$248$	2.29883e6	2.37344
$249$	−522226.	−0.533777
$250$	−166938.	−0.168929
$251$	1.00648e6	1.00837	0.504185	−	0.863596i	$-0.331793\pi$
$251$	1.00648e6	1.00837	0.504185	+	0.863596i	$0.331793\pi$
$252$	1.12495e6	1.11592
$253$	557056.	0.547139
$254$	1.20874e6	1.17557
$255$	−412781.	−0.397529
$256$	396696.	0.378318
$257$	−312158.	−0.294809	−0.147405	−	0.989076i	$-0.547092\pi$
$257$	−312158.	−0.294809	−0.147405	+	0.989076i	$0.547092\pi$
$258$	3.80412e6	3.55799
$259$	59989.4	0.0555681
$260$	2.45806e6	2.25506
$261$	−1.39279e6	−1.26556
$262$	988148.	0.889342
$263$	283526.	0.252757	0.126378	−	0.991982i	$-0.459665\pi$
$263$	283526.	0.252757	0.126378	+	0.991982i	$0.459665\pi$
$264$	1.48946e6	1.31528
$265$	−998869.	−0.873764
$266$	−185430.	−0.160686
$267$	−2.05634e6	−1.76530
$268$	2.73028e6	2.32204
$269$	1.01581e6	0.855918	0.427959	−	0.903798i	$-0.359233\pi$
$269$	1.01581e6	0.855918	0.427959	+	0.903798i	$0.359233\pi$
$270$	−256726.	−0.214319
$271$	−1.62100e6	−1.34079	−0.670394	−	0.742005i	$-0.733875\pi$
$271$	−1.62100e6	−1.34079	−0.670394	+	0.742005i	$0.733875\pi$
$272$	−2.22474e6	−1.82329
$273$	1.32203e6	1.07358
$274$	1.13818e6	0.915872
$275$	−75625.0	−0.0603023
$276$	−8.68886e6	−6.86578
$277$	−2.35185e6	−1.84166	−0.920832	−	0.389960i	$-0.872489\pi$
$277$	−2.35185e6	−1.84166	−0.920832	+	0.389960i	$0.872489\pi$
$278$	82172.1	0.0637694
$279$	−1.22210e6	−0.939935
$280$	−643980.	−0.490882
$281$	1.73994e6	1.31452	0.657261	−	0.753663i	$-0.271715\pi$
$281$	1.73994e6	1.31452	0.657261	+	0.753663i	$0.271715\pi$
$282$	−1.94648e6	−1.45756
$283$	48802.6	0.0362224	0.0181112	−	0.999836i	$-0.494235\pi$
$283$	48802.6	0.0362224	0.0181112	+	0.999836i	$0.494235\pi$
$284$	−3.39853e6	−2.50031
$285$	207346.	0.151211
$286$	1.54730e6	1.11856
$287$	263128.	0.188565
$288$	−4.53702e6	−3.22322
$289$	−903369.	−0.636240
$290$	1.30607e6	0.911949
$291$	−2.54405e6	−1.76114
$292$	2.30712e6	1.58348
$293$	1.40622e6	0.956937	0.478468	−	0.878105i	$-0.341192\pi$
$293$	1.40622e6	0.956937	0.478468	+	0.878105i	$0.341192\pi$
$294$	3.55812e6	2.40078
$295$	−843248.	−0.564157
$296$	−668543.	−0.443507
$297$	−116300.	−0.0765048
$298$	−5.12018e6	−3.33999
$299$	−5.51019e6	−3.56441
$300$	1.17958e6	0.756704
$301$	−745089.	−0.474015
$302$	3.31298e6	2.09026
$303$	696939.	0.436102
$304$	1.11752e6	0.693541
$305$	−22015.6	−0.0135513
$306$	2.18705e6	1.33523
$307$	201068.	0.121758	0.0608790	−	0.998145i	$-0.480610\pi$
$307$	201068.	0.121758	0.0608790	+	0.998145i	$0.480610\pi$
$308$	−477886.	−0.287043
$309$	1.13723e6	0.677567
$310$	1.14601e6	0.677306
$311$	2.02858e6	1.18930	0.594651	−	0.803984i	$-0.297290\pi$
$311$	2.02858e6	1.18930	0.594651	+	0.803984i	$0.297290\pi$
$312$	−1.47331e7	−8.56858
$313$	1.16161e6	0.670193	0.335096	−	0.942184i	$-0.391231\pi$
$313$	1.16161e6	0.670193	0.335096	+	0.942184i	$0.391231\pi$
$314$	2.92663e6	1.67511
$315$	342352.	0.194400
$316$	−748542.	−0.421695
$317$	130008.	0.0726646	0.0363323	−	0.999340i	$-0.488433\pi$
$317$	130008.	0.0726646	0.0363323	+	0.999340i	$0.488433\pi$
$318$	9.80738e6	5.43858
$319$	591665.	0.325536
$320$	1.77803e6	0.970652
$321$	884123.	0.478906
$322$	2.36476e6	1.27101
$323$	−259440.	−0.138366
$324$	−3.87189e6	−2.04909
$325$	748053.	0.392848
$326$	2.89702e6	1.50976
$327$	−2.71866e6	−1.40600
$328$	−2.93239e6	−1.50500
$329$	381246.	0.194185
$330$	742523.	0.375340
$331$	742912.	0.372707	0.186353	−	0.982483i	$-0.440333\pi$
$331$	742912.	0.372707	0.186353	+	0.982483i	$0.440333\pi$
$332$	−1.86728e6	−0.929744
$333$	355410.	0.175638
$334$	−3.67478e6	−1.80246
$335$	830897.	0.404516
$336$	3.41930e6	1.65230
$337$	−781130.	−0.374670	−0.187335	−	0.982296i	$-0.559985\pi$
$337$	−781130.	−0.374670	−0.187335	+	0.982296i	$0.559985\pi$
$338$	−1.13383e7	−5.39831
$339$	−1.42251e6	−0.672290
$340$	−1.47594e6	−0.692425
$341$	519158.	0.241776
$342$	−1.09859e6	−0.507892
$343$	−1.50494e6	−0.690691
$344$	8.30353e6	3.78327
$345$	−2.64425e6	−1.19607
$346$	18876.3	0.00847671
$347$	3.57465e6	1.59371	0.796856	−	0.604169i	$-0.206495\pi$
$347$	3.57465e6	1.59371	0.796856	+	0.604169i	$0.206495\pi$
$348$	−9.22867e6	−4.08499
$349$	−1.90925e6	−0.839073	−0.419536	−	0.907738i	$-0.637807\pi$
$349$	−1.90925e6	−0.839073	−0.419536	+	0.907738i	$0.637807\pi$
$350$	−321036.	−0.140082
$351$	1.15040e6	0.498402
$352$	1.92736e6	0.829097
$353$	1.98358e6	0.847252	0.423626	−	0.905837i	$-0.360757\pi$
$353$	1.98358e6	0.847252	0.423626	+	0.905837i	$0.360757\pi$
$354$	8.27941e6	3.51149
$355$	−1.03426e6	−0.435572
$356$	−7.35268e6	−3.07483
$357$	−793813.	−0.329646
$358$	−116272.	−0.0479476
$359$	−1.61741e6	−0.662343	−0.331172	−	0.943571i	$-0.607444\pi$
$359$	−1.61741e6	−0.662343	−0.331172	+	0.943571i	$0.607444\pi$
$360$	−3.81529e6	−1.55157
$361$	130321.	0.0526316
$362$	950393.	0.381182
$363$	336372.	0.133984
$364$	4.72706e6	1.86998
$365$	702119.	0.275853
$366$	216160.	0.0843475
$367$	−2.61060e6	−1.01175	−0.505877	−	0.862606i	$-0.668831\pi$
$367$	−2.61060e6	−1.01175	−0.505877	+	0.862606i	$0.668831\pi$
$368$	−1.42516e7	−5.48584
$369$	1.55891e6	0.596013
$370$	−333282.	−0.126563
$371$	−1.92091e6	−0.724557
$372$	−8.09773e6	−3.03393
$373$	4.28244e6	1.59375	0.796873	−	0.604147i	$-0.206486\pi$
$373$	4.28244e6	1.59375	0.796873	+	0.604147i	$0.206486\pi$
$374$	−929074.	−0.343456
$375$	358979.	0.131823
$376$	−4.24873e6	−1.54985
$377$	−5.85252e6	−2.12075
$378$	−493706.	−0.177721
$379$	−4.19328e6	−1.49953	−0.749767	−	0.661702i	$-0.769834\pi$
$379$	−4.19328e6	−1.49953	−0.749767	+	0.661702i	$0.769834\pi$
$380$	741390.	0.263383
$381$	−2.59925e6	−0.917351
$382$	−9.04377e6	−3.17096
$383$	1.41524e6	0.492983	0.246491	−	0.969145i	$-0.420722\pi$
$383$	1.41524e6	0.492983	0.246491	+	0.969145i	$0.420722\pi$
$384$	−5.74703e6	−1.98891
$385$	−145433.	−0.0500049
$386$	−9.42437e6	−3.21947
$387$	−4.41432e6	−1.49826
$388$	−9.09653e6	−3.06758
$389$	3.74205e6	1.25382	0.626911	−	0.779091i	$-0.284319\pi$
$389$	3.74205e6	1.25382	0.626911	+	0.779091i	$0.284319\pi$
$390$	−7.34475e6	−2.44521
$391$	3.30859e6	1.09446
$392$	7.76657e6	2.55278
$393$	−2.12489e6	−0.693992
$394$	1.06448e6	0.345461
$395$	−227801.	−0.0734621
$396$	−2.83126e6	−0.907280
$397$	−6.07866e6	−1.93567	−0.967835	−	0.251586i	$-0.919048\pi$
$397$	−6.07866e6	−1.93567	−0.967835	+	0.251586i	$0.919048\pi$
$398$	−1.06036e7	−3.35541
$399$	398745.	0.125390
$400$	1.93477e6	0.604615
$401$	6.16658e6	1.91506	0.957532	−	0.288327i	$-0.0930991\pi$
$401$	6.16658e6	1.91506	0.957532	+	0.288327i	$0.0930991\pi$
$402$	−8.15815e6	−2.51783
$403$	−5.13531e6	−1.57509
$404$	2.49198e6	0.759612
$405$	−1.17832e6	−0.356965
$406$	2.51168e6	0.756222
$407$	−150981.	−0.0451789
$408$	8.84652e6	2.63101
$409$	4.78136e6	1.41333	0.706664	−	0.707549i	$-0.250199\pi$
$409$	4.78136e6	1.41333	0.706664	+	0.707549i	$0.250199\pi$
$410$	−1.46185e6	−0.429480
$411$	−2.44751e6	−0.714695
$412$	4.06629e6	1.18020
$413$	−1.62164e6	−0.467820
$414$	1.40102e7	4.01737
$415$	−568262.	−0.161968
$416$	−1.90647e7	−5.40127
$417$	−176701.	−0.0497621
$418$	466689.	0.130643
$419$	−827219.	−0.230189	−0.115095	−	0.993355i	$-0.536717\pi$
$419$	−827219.	−0.230189	−0.115095	+	0.993355i	$0.536717\pi$
$420$	2.26844e6	0.627487
$421$	1.51386e6	0.416276	0.208138	−	0.978099i	$-0.433260\pi$
$421$	1.51386e6	0.416276	0.208138	+	0.978099i	$0.433260\pi$
$422$	−2.96302e6	−0.809941
$423$	2.25871e6	0.613775
$424$	2.14073e7	5.78292
$425$	−449169.	−0.120625
$426$	1.01549e7	2.71114
$427$	−42337.9	−0.0112372
$428$	3.16128e6	0.834169
$429$	−3.32726e6	−0.872859
$430$	4.13947e6	1.07963
$431$	6.41423e6	1.66323	0.831614	−	0.555355i	$-0.187417\pi$
$431$	6.41423e6	1.66323	0.831614	+	0.555355i	$0.187417\pi$
$432$	2.97539e6	0.767068
$433$	4.99383e6	1.28001	0.640006	−	0.768370i	$-0.278932\pi$
$433$	4.99383e6	1.28001	0.640006	+	0.768370i	$0.278932\pi$
$434$	2.20388e6	0.561647
$435$	−2.80853e6	−0.711634
$436$	−9.72088e6	−2.44900
$437$	−1.66196e6	−0.416310
$438$	−6.89374e6	−1.71700
$439$	4.09820e6	1.01492	0.507460	−	0.861675i	$-0.330584\pi$
$439$	4.09820e6	1.01492	0.507460	+	0.861675i	$0.330584\pi$
$440$	1.62076e6	0.399105
$441$	−4.12886e6	−1.01096
$442$	9.19005e6	2.23750
$443$	−7.82139e6	−1.89354	−0.946771	−	0.321908i	$-0.895676\pi$
$443$	−7.82139e6	−1.89354	−0.946771	+	0.321908i	$0.895676\pi$
$444$	2.35497e6	0.566928
$445$	−2.23762e6	−0.535656
$446$	1.81394e6	0.431802
$447$	1.10103e7	2.60634
$448$	3.41930e6	0.804901
$449$	6.72878e6	1.57514	0.787572	−	0.616222i	$-0.211338\pi$
$449$	6.72878e6	1.57514	0.787572	+	0.616222i	$0.211338\pi$
$450$	−1.90199e6	−0.442770
$451$	−662237.	−0.153310
$452$	−5.08635e6	−1.17101
$453$	−7.12414e6	−1.63112
$454$	5.84804e6	1.33159
$455$	1.43857e6	0.325764
$456$	−4.44375e6	−1.00078
$457$	3.20278e6	0.717359	0.358679	−	0.933461i	$-0.383227\pi$
$457$	3.20278e6	0.717359	0.358679	+	0.933461i	$0.383227\pi$
$458$	−6.44470e6	−1.43562
$459$	−690756.	−0.153036
$460$	−9.45482e6	−2.08333
$461$	2.94421e6	0.645233	0.322617	−	0.946530i	$-0.395438\pi$
$461$	2.94421e6	0.645233	0.322617	+	0.946530i	$0.395438\pi$
$462$	1.42794e6	0.311246
$463$	426460.	0.0924541	0.0462270	−	0.998931i	$-0.485280\pi$
$463$	426460.	0.0924541	0.0462270	+	0.998931i	$0.485280\pi$
$464$	−1.51370e7	−3.26395
$465$	−2.46436e6	−0.528532
$466$	−1.45747e6	−0.310910
$467$	−7.23779e6	−1.53573	−0.767863	−	0.640614i	$-0.778680\pi$
$467$	−7.23779e6	−1.53573	−0.767863	+	0.640614i	$0.778680\pi$
$468$	2.80057e7	5.91060
$469$	1.59789e6	0.335439
$470$	−2.11808e6	−0.442279
$471$	−6.29334e6	−1.30716
$472$	1.80721e7	3.73382
$473$	1.87523e6	0.385392
$474$	2.23666e6	0.457251
$475$	225625.	0.0458831
$476$	−2.83837e6	−0.574184
$477$	−1.13805e7	−2.29017
$478$	351723.	0.0704094
$479$	−6.73006e6	−1.34023	−0.670116	−	0.742257i	$-0.733756\pi$
$479$	−6.73006e6	−1.34023	−0.670116	+	0.742257i	$0.733756\pi$
$480$	−9.14883e6	−1.81244
$481$	1.49344e6	0.294324
$482$	6.50021e6	1.27441
$483$	−5.08513e6	−0.991822
$484$	1.20274e6	0.233377
$485$	−2.76832e6	−0.534394
$486$	1.40647e7	2.70109
$487$	−9.08609e6	−1.73602	−0.868010	−	0.496546i	$-0.834601\pi$
$487$	−9.08609e6	−1.73602	−0.868010	+	0.496546i	$0.834601\pi$
$488$	471828.	0.0896880
$489$	−6.22967e6	−1.17813
$490$	3.87178e6	0.728485
$491$	−4.94322e6	−0.925351	−0.462676	−	0.886528i	$-0.653111\pi$
$491$	−4.94322e6	−0.925351	−0.462676	+	0.886528i	$0.653111\pi$
$492$	1.03294e7	1.92382
$493$	3.51415e6	0.651183
$494$	−4.61631e6	−0.851094
$495$	−861627.	−0.158054
$496$	−1.32820e7	−2.42415
$497$	−1.98898e6	−0.361192
$498$	5.57947e6	1.00814
$499$	5.12433e6	0.921268	0.460634	−	0.887590i	$-0.347622\pi$
$499$	5.12433e6	0.921268	0.460634	+	0.887590i	$0.347622\pi$
$500$	1.28357e6	0.229612
$501$	7.90216e6	1.40654
$502$	−1.07532e7	−1.90449
$503$	92190.4	0.0162467	0.00812336	−	0.999967i	$-0.497414\pi$
$503$	92190.4	0.0162467	0.00812336	+	0.999967i	$0.497414\pi$
$504$	−7.33713e6	−1.28662
$505$	758377.	0.132330
$506$	−5.95161e6	−1.03337
$507$	2.43817e7	4.21254
$508$	−9.29391e6	−1.59786
$509$	−7.05594e6	−1.20715	−0.603574	−	0.797307i	$-0.706257\pi$
$509$	−7.05594e6	−1.20715	−0.603574	+	0.797307i	$0.706257\pi$
$510$	4.41016e6	0.750808
$511$	1.35023e6	0.228748
$512$	3.76637e6	0.634963
$513$	346978.	0.0582114
$514$	3.33510e6	0.556803
$515$	1.23748e6	0.205599
$516$	−2.92495e7	−4.83609
$517$	−959515.	−0.157879
$518$	−640929.	−0.104951
$519$	−40591.2	−0.00661475
$520$	−1.60319e7	−2.60003
$521$	−6.68245e6	−1.07855	−0.539276	−	0.842129i	$-0.681302\pi$
$521$	−6.68245e6	−1.07855	−0.539276	+	0.842129i	$0.681302\pi$
$522$	1.48806e7	2.39025
$523$	2.31636e6	0.370298	0.185149	−	0.982710i	$-0.440723\pi$
$523$	2.31636e6	0.370298	0.185149	+	0.982710i	$0.440723\pi$
$524$	−7.59778e6	−1.20881
$525$	690348.	0.109313
$526$	−3.02920e6	−0.477379
$527$	3.08350e6	0.483635
$528$	−8.60565e6	−1.34338
$529$	1.47584e7	2.29297
$530$	1.06720e7	1.65027
$531$	−9.60747e6	−1.47868
$532$	1.42576e6	0.218407
$533$	6.55059e6	0.998763
$534$	2.19700e7	3.33409
$535$	962063.	0.145318
$536$	−1.78074e7	−2.67725
$537$	250028.	0.0374156
$538$	−1.08530e7	−1.61656
$539$	1.75397e6	0.260045
$540$	1.97394e6	0.291306
$541$	−5.76655e6	−0.847078	−0.423539	−	0.905878i	$-0.639212\pi$
$541$	−5.76655e6	−0.847078	−0.423539	+	0.905878i	$0.639212\pi$
$542$	1.73188e7	2.53233
$543$	−2.04370e6	−0.297453
$544$	1.14474e7	1.65848
$545$	−2.95832e6	−0.426633
$546$	−1.41246e7	−2.02766
$547$	7.58049e6	1.08325	0.541625	−	0.840620i	$-0.317809\pi$
$547$	7.58049e6	1.08325	0.541625	+	0.840620i	$0.317809\pi$
$548$	−8.75136e6	−1.24487
$549$	−250833.	−0.0355184
$550$	807980.	0.113892
$551$	−1.76521e6	−0.247696
$552$	5.66704e7	7.91605
$553$	−438082.	−0.0609175
$554$	2.51272e7	3.47833
$555$	716680.	0.0987627
$556$	−631814.	−0.0866767
$557$	−706759.	−0.0965236	−0.0482618	−	0.998835i	$-0.515368\pi$
$557$	−706759.	−0.0965236	−0.0482618	+	0.998835i	$0.515368\pi$
$558$	1.30570e7	1.77524
$559$	−1.85491e7	−2.51069
$560$	3.72072e6	0.501369
$561$	1.99786e6	0.268014
$562$	−1.85895e7	−2.48272
$563$	−1.45412e7	−1.93343	−0.966714	−	0.255860i	$-0.917641\pi$
$563$	−1.45412e7	−1.93343	−0.966714	+	0.255860i	$0.917641\pi$
$564$	1.49663e7	1.98115
$565$	−1.54791e6	−0.203998
$566$	−521409.	−0.0684128
$567$	−2.26601e6	−0.296008
$568$	2.21658e7	2.88279
$569$	−1.33676e7	−1.73090	−0.865450	−	0.500996i	$-0.832967\pi$
$569$	−1.33676e7	−1.73090	−0.865450	+	0.500996i	$0.832967\pi$
$570$	−2.21530e6	−0.285591
$571$	9.71231e6	1.24661	0.623307	−	0.781977i	$-0.285789\pi$
$571$	9.71231e6	1.24661	0.623307	+	0.781977i	$0.285789\pi$
$572$	−1.18970e7	−1.52036
$573$	1.94475e7	2.47444
$574$	−2.81126e6	−0.356141
$575$	−2.87736e6	−0.362931
$576$	2.02578e7	2.54411
$577$	8.06882e6	1.00895	0.504476	−	0.863426i	$-0.331686\pi$
$577$	8.06882e6	1.00895	0.504476	+	0.863426i	$0.331686\pi$
$578$	9.65163e6	1.20166
$579$	2.02659e7	2.51229
$580$	−1.00422e7	−1.23954
$581$	−1.09282e6	−0.134310
$582$	2.71807e7	3.32624
$583$	4.83453e6	0.589091
$584$	−1.50475e7	−1.82571
$585$	8.52289e6	1.02967
$586$	−1.50241e7	−1.80735
$587$	−2.37384e6	−0.284352	−0.142176	−	0.989841i	$-0.545410\pi$
$587$	−2.37384e6	−0.284352	−0.142176	+	0.989841i	$0.545410\pi$
$588$	−2.73580e7	−3.26318
$589$	−1.54889e6	−0.183964
$590$	9.00928e6	1.06552
$591$	−2.28904e6	−0.269578
$592$	3.86265e6	0.452982
$593$	−1.01833e7	−1.18919	−0.594596	−	0.804025i	$-0.702688\pi$
$593$	−1.01833e7	−1.18919	−0.594596	+	0.804025i	$0.702688\pi$
$594$	1.24255e6	0.144494
$595$	−863791.	−0.100027
$596$	3.93686e7	4.53978
$597$	2.28017e7	2.61837
$598$	5.88710e7	6.73207
$599$	6.49029e6	0.739090	0.369545	−	0.929213i	$-0.379514\pi$
$599$	6.49029e6	0.739090	0.369545	+	0.929213i	$0.379514\pi$
$600$	−7.69348e6	−0.872458
$601$	1.10109e7	1.24348	0.621739	−	0.783224i	$-0.286426\pi$
$601$	1.10109e7	1.24348	0.621739	+	0.783224i	$0.286426\pi$
$602$	7.96056e6	0.895267
$603$	9.46676e6	1.06025
$604$	−2.54732e7	−2.84113
$605$	366025.	0.0406558
$606$	−7.44611e6	−0.823660
$607$	3.02295e6	0.333012	0.166506	−	0.986040i	$-0.446752\pi$
$607$	3.02295e6	0.333012	0.166506	+	0.986040i	$0.446752\pi$
$608$	−5.75021e6	−0.630848
$609$	−5.40105e6	−0.590113
$610$	235215.	0.0255942
$611$	9.49115e6	1.02853
$612$	−1.68160e7	−1.81487
$613$	−1.60671e7	−1.72698	−0.863489	−	0.504367i	$-0.831726\pi$
$613$	−1.60671e7	−1.72698	−0.863489	+	0.504367i	$0.831726\pi$
$614$	−2.14822e6	−0.229963
$615$	3.14353e6	0.335142
$616$	3.11686e6	0.330953
$617$	−1.00757e7	−1.06553	−0.532763	−	0.846264i	$-0.678846\pi$
$617$	−1.00757e7	−1.06553	−0.532763	+	0.846264i	$0.678846\pi$
$618$	−1.21502e7	−1.27971
$619$	−1.44053e7	−1.51111	−0.755555	−	0.655086i	$-0.772633\pi$
$619$	−1.44053e7	−1.51111	−0.755555	+	0.655086i	$0.772633\pi$
$620$	−8.81158e6	−0.920608
$621$	−4.42495e6	−0.460446
$622$	−2.16735e7	−2.24622
$623$	−4.30313e6	−0.444186
$624$	8.51237e7	8.75164
$625$	390625.	0.0400000
$626$	−1.24107e7	−1.26578
$627$	−1.00356e6	−0.101947
$628$	−2.25026e7	−2.27684
$629$	−896739.	−0.0903731
$630$	−3.65770e6	−0.367161
$631$	−817563.	−0.0817425	−0.0408712	−	0.999164i	$-0.513013\pi$
$631$	−817563.	−0.0817425	−0.0408712	+	0.999164i	$0.513013\pi$
$632$	4.88213e6	0.486202
$633$	6.37160e6	0.632032
$634$	−1.38901e6	−0.137241
$635$	−2.82839e6	−0.278358
$636$	−7.54081e7	−7.39222
$637$	−1.73496e7	−1.69410
$638$	−6.32136e6	−0.614836
$639$	−1.17838e7	−1.14165
$640$	−6.25366e6	−0.603510
$641$	1.60253e7	1.54050	0.770251	−	0.637741i	$-0.220131\pi$
$641$	1.60253e7	1.54050	0.770251	+	0.637741i	$0.220131\pi$
$642$	−9.44600e6	−0.904504
$643$	477621.	0.0455571	0.0227785	−	0.999741i	$-0.492749\pi$
$643$	477621.	0.0455571	0.0227785	+	0.999741i	$0.492749\pi$
$644$	−1.81824e7	−1.72758
$645$	−8.90141e6	−0.842480
$646$	2.77187e6	0.261331
$647$	−5.53554e6	−0.519875	−0.259938	−	0.965625i	$-0.583702\pi$
$647$	−5.53554e6	−0.519875	−0.259938	+	0.965625i	$0.583702\pi$
$648$	2.52532e7	2.36254
$649$	4.08132e6	0.380355
$650$	−7.99223e6	−0.741967
$651$	−4.73917e6	−0.438278
$652$	−2.22749e7	−2.05209
$653$	−1.83804e7	−1.68683	−0.843417	−	0.537260i	$-0.819459\pi$
$653$	−1.83804e7	−1.68683	−0.843417	+	0.537260i	$0.819459\pi$
$654$	2.90463e7	2.65550
$655$	−2.31221e6	−0.210583
$656$	1.69425e7	1.53715
$657$	7.99953e6	0.723021
$658$	−4.07324e6	−0.366754
$659$	1.09017e7	0.977868	0.488934	−	0.872321i	$-0.337386\pi$
$659$	1.09017e7	0.977868	0.488934	+	0.872321i	$0.337386\pi$
$660$	−5.70919e6	−0.510170
$661$	1.40578e7	1.25145	0.625727	−	0.780043i	$-0.284803\pi$
$661$	1.40578e7	1.25145	0.625727	+	0.780043i	$0.284803\pi$
$662$	−7.93730e6	−0.703927
$663$	−1.97620e7	−1.74602
$664$	1.21787e7	1.07197
$665$	433896.	0.0380480
$666$	−3.79722e6	−0.331726
$667$	2.25115e7	1.95925
$668$	2.82551e7	2.44994
$669$	−3.90064e6	−0.336954
$670$	−8.87733e6	−0.764004
$671$	106555.	0.00913628
$672$	−1.75940e7	−1.50294
$673$	−5.39685e6	−0.459306	−0.229653	−	0.973273i	$-0.573759\pi$
$673$	−5.39685e6	−0.459306	−0.229653	+	0.973273i	$0.573759\pi$
$674$	8.34562e6	0.707634
$675$	600723.	0.0507476
$676$	8.71795e7	7.33749
$677$	−7.43017e6	−0.623056	−0.311528	−	0.950237i	$-0.600841\pi$
$677$	−7.43017e6	−0.623056	−0.311528	+	0.950237i	$0.600841\pi$
$678$	1.51982e7	1.26975
$679$	−5.32371e6	−0.443139
$680$	9.62639e6	0.798346
$681$	−1.25755e7	−1.03910
$682$	−5.54670e6	−0.456640
$683$	−8.61066e6	−0.706293	−0.353146	−	0.935568i	$-0.614888\pi$
$683$	−8.61066e6	−0.706293	−0.353146	+	0.935568i	$0.614888\pi$
$684$	8.44697e6	0.690337
$685$	−2.66327e6	−0.216865
$686$	1.60788e7	1.30450
$687$	1.38585e7	1.12028
$688$	−4.79754e7	−3.86409
$689$	−4.78213e7	−3.83772
$690$	2.82513e7	2.25900
$691$	−2.10326e6	−0.167571	−0.0837854	−	0.996484i	$-0.526701\pi$
$691$	−2.10326e6	−0.167571	−0.0837854	+	0.996484i	$0.526701\pi$
$692$	−145138.	−0.0115217
$693$	−1.65698e6	−0.131065
$694$	−3.81917e7	−3.01002
$695$	−192278.	−0.0150997
$696$	6.01912e7	4.70988
$697$	−3.93331e6	−0.306673
$698$	2.03985e7	1.58475
$699$	3.13410e6	0.242616
$700$	2.46842e6	0.190403
$701$	−1.93542e7	−1.48758	−0.743789	−	0.668415i	$-0.766973\pi$
$701$	−1.93542e7	−1.48758	−0.743789	+	0.668415i	$0.766973\pi$
$702$	−1.22909e7	−0.941325
$703$	450447.	0.0343760
$704$	−8.60565e6	−0.654413
$705$	4.55466e6	0.345130
$706$	−2.11926e7	−1.60019
$707$	1.45842e6	0.109733
$708$	−6.36596e7	−4.77289
$709$	−794057.	−0.0593247	−0.0296624	−	0.999560i	$-0.509443\pi$
$709$	−794057.	−0.0593247	−0.0296624	+	0.999560i	$0.509443\pi$
$710$	1.10501e7	0.822659
$711$	−2.59544e6	−0.192547
$712$	4.79556e7	3.54519
$713$	1.97528e7	1.45514
$714$	8.48112e6	0.622598
$715$	−3.62058e6	−0.264858
$716$	894004.	0.0651713
$717$	−756335.	−0.0549435
$718$	1.72804e7	1.25096
$719$	−1.65348e7	−1.19283	−0.596414	−	0.802677i	$-0.703408\pi$
$719$	−1.65348e7	−1.19283	−0.596414	+	0.802677i	$0.703408\pi$
$720$	2.20436e7	1.58472
$721$	2.37979e6	0.170490
$722$	−1.39235e6	−0.0994046
$723$	−1.39779e7	−0.994479
$724$	−7.30748e6	−0.518109
$725$	−3.05612e6	−0.215936
$726$	−3.59381e6	−0.253054
$727$	−2.26593e7	−1.59005	−0.795025	−	0.606576i	$-0.792542\pi$
$727$	−2.26593e7	−1.59005	−0.795025	+	0.606576i	$0.792542\pi$
$728$	−3.08308e7	−2.15604
$729$	−1.87911e7	−1.30958
$730$	−7.50146e6	−0.521001
$731$	1.11378e7	0.770914
$732$	−1.66203e6	−0.114647
$733$	5.60066e6	0.385017	0.192508	−	0.981295i	$-0.438338\pi$
$733$	5.60066e6	0.385017	0.192508	+	0.981295i	$0.438338\pi$
$734$	2.78917e7	1.91089
$735$	−8.32578e6	−0.568469
$736$	7.33314e7	4.98994
$737$	−4.02154e6	−0.272724
$738$	−1.66555e7	−1.12568
$739$	1.00819e7	0.679098	0.339549	−	0.940588i	$-0.389726\pi$
$739$	1.00819e7	0.679098	0.339549	+	0.940588i	$0.389726\pi$
$740$	2.56257e6	0.172027
$741$	9.92680e6	0.664146
$742$	2.05231e7	1.36846
$743$	−2.46888e7	−1.64069	−0.820347	−	0.571866i	$-0.806220\pi$
$743$	−2.46888e7	−1.64069	−0.820347	+	0.571866i	$0.806220\pi$
$744$	5.28149e7	3.49804
$745$	1.19809e7	0.790860
$746$	−4.57537e7	−3.01009
$747$	−6.47445e6	−0.424523
$748$	7.14357e6	0.466833
$749$	1.85013e6	0.120503
$750$	−3.83535e6	−0.248972
$751$	5.40927e6	0.349977	0.174988	−	0.984571i	$-0.444011\pi$
$751$	5.40927e6	0.349977	0.174988	+	0.984571i	$0.444011\pi$
$752$	2.45479e7	1.58296
$753$	2.31235e7	1.48616
$754$	6.25285e7	4.00543
$755$	−7.75217e6	−0.494944
$756$	3.79606e6	0.241562
$757$	−1.57067e7	−0.996196	−0.498098	−	0.867121i	$-0.665968\pi$
$757$	−1.57067e7	−0.996196	−0.498098	+	0.867121i	$0.665968\pi$
$758$	4.48012e7	2.83215
$759$	1.27982e7	0.806388
$760$	−4.83549e6	−0.303673
$761$	−1.99642e7	−1.24965	−0.624827	−	0.780763i	$-0.714831\pi$
$761$	−1.99642e7	−1.24965	−0.624827	+	0.780763i	$0.714831\pi$
$762$	2.77705e7	1.73259
$763$	−5.68911e6	−0.353780
$764$	6.95367e7	4.31003
$765$	−5.11757e6	−0.316163
$766$	−1.51204e7	−0.931091
$767$	−4.03708e7	−2.47787
$768$	9.11395e6	0.557576
$769$	3.17133e6	0.193386	0.0966932	−	0.995314i	$-0.469173\pi$
$769$	3.17133e6	0.193386	0.0966932	+	0.995314i	$0.469173\pi$
$770$	1.55382e6	0.0944436
$771$	−7.17172e6	−0.434498
$772$	7.24631e7	4.37596
$773$	4.39117e6	0.264321	0.132160	−	0.991228i	$-0.457809\pi$
$773$	4.39117e6	0.264321	0.132160	+	0.991228i	$0.457809\pi$
$774$	4.71627e7	2.82974
$775$	−2.68160e6	−0.160376
$776$	5.93293e7	3.53684
$777$	1.37824e6	0.0818977
$778$	−3.99802e7	−2.36808
$779$	1.97576e6	0.116652
$780$	5.64731e7	3.32357
$781$	5.00583e6	0.293663
$782$	−3.53491e7	−2.06710
$783$	−4.69986e6	−0.273956
$784$	−4.48729e7	−2.60732
$785$	−6.84813e6	−0.396641
$786$	2.27024e7	1.31074
$787$	−2.34632e7	−1.35037	−0.675183	−	0.737651i	$-0.735935\pi$
$787$	−2.34632e7	−1.35037	−0.675183	+	0.737651i	$0.735935\pi$
$788$	−8.18472e6	−0.469557
$789$	6.51391e6	0.372520
$790$	2.43384e6	0.138747
$791$	−2.97677e6	−0.169162
$792$	1.84660e7	1.04607
$793$	−1.05401e6	−0.0595196
$794$	6.49445e7	3.65588
$795$	−2.29487e7	−1.28778
$796$	8.15300e7	4.56074
$797$	−2.77883e7	−1.54959	−0.774794	−	0.632214i	$-0.782146\pi$
$797$	−2.77883e7	−1.54959	−0.774794	+	0.632214i	$0.782146\pi$
$798$	−4.26020e6	−0.236823
$799$	−5.69897e6	−0.315812
$800$	−9.95535e6	−0.549960
$801$	−2.54941e7	−1.40397
$802$	−6.58839e7	−3.61696
$803$	−3.39825e6	−0.185980
$804$	6.27273e7	3.42229
$805$	−5.53340e6	−0.300956
$806$	5.48658e7	2.97484
$807$	2.33379e7	1.26147
$808$	−1.62532e7	−0.875811
$809$	2.55828e7	1.37429	0.687143	−	0.726522i	$-0.258865\pi$
$809$	2.55828e7	1.37429	0.687143	+	0.726522i	$0.258865\pi$
$810$	1.25892e7	0.674195
$811$	−1.63557e7	−0.873205	−0.436603	−	0.899655i	$-0.643818\pi$
$811$	−1.63557e7	−0.873205	−0.436603	+	0.899655i	$0.643818\pi$
$812$	−1.93121e7	−1.02787
$813$	−3.72420e7	−1.97609
$814$	1.61308e6	0.0853288
$815$	−6.77885e6	−0.357488
$816$	−5.11126e7	−2.68722
$817$	−5.59470e6	−0.293239
$818$	−5.10842e7	−2.66934
$819$	1.63902e7	0.853839
$820$	1.12400e7	0.583758
$821$	−3.64912e6	−0.188943	−0.0944715	−	0.995528i	$-0.530116\pi$
$821$	−3.64912e6	−0.188943	−0.0944715	+	0.995528i	$0.530116\pi$
$822$	2.61493e7	1.34984
$823$	1.13491e7	0.584066	0.292033	−	0.956408i	$-0.405668\pi$
$823$	1.13491e7	0.584066	0.292033	+	0.956408i	$0.405668\pi$
$824$	−2.65211e7	−1.36074
$825$	−1.73746e6	−0.0888750
$826$	1.73256e7	0.883566
$827$	3.74128e7	1.90220	0.951099	−	0.308885i	$-0.0999557\pi$
$827$	3.74128e7	1.90220	0.951099	+	0.308885i	$0.0999557\pi$
$828$	−1.07723e8	−5.46049
$829$	1.28301e7	0.648401	0.324200	−	0.945988i	$-0.394905\pi$
$829$	1.28301e7	0.648401	0.324200	+	0.945988i	$0.394905\pi$
$830$	6.07133e6	0.305907
$831$	−5.40330e7	−2.71429
$832$	8.51238e7	4.26327
$833$	1.04176e7	0.520180
$834$	1.88788e6	0.0939850
$835$	8.59877e6	0.426796
$836$	−3.58833e6	−0.177573
$837$	−4.12390e6	−0.203467
$838$	8.83803e6	0.434756
$839$	−3.13429e7	−1.53721	−0.768607	−	0.639721i	$-0.779050\pi$
$839$	−3.13429e7	−1.53721	−0.768607	+	0.639721i	$0.779050\pi$
$840$	−1.47952e7	−0.723475
$841$	3.39890e6	0.165710
$842$	−1.61742e7	−0.786215
$843$	3.99745e7	1.93738
$844$	2.27824e7	1.10089
$845$	2.65310e7	1.27824
$846$	−2.41321e7	−1.15923
$847$	703898.	0.0337133
$848$	−1.23685e8	−5.90647
$849$	1.12122e6	0.0533855
$850$	4.79894e6	0.227823
$851$	−5.74447e6	−0.271910
$852$	−7.80800e7	−3.68503
$853$	2.67448e7	1.25854	0.629270	−	0.777187i	$-0.283354\pi$
$853$	2.67448e7	1.25854	0.629270	+	0.777187i	$0.283354\pi$
$854$	452339.	0.0212236
$855$	2.57064e6	0.120261
$856$	−2.06185e7	−0.961773
$857$	3.83692e6	0.178456	0.0892278	−	0.996011i	$-0.471560\pi$
$857$	3.83692e6	0.178456	0.0892278	+	0.996011i	$0.471560\pi$
$858$	3.55486e7	1.64856
$859$	−131321.	−0.00607227	−0.00303614	−	0.999995i	$-0.500966\pi$
$859$	−131321.	−0.00607227	−0.00303614	+	0.999995i	$0.500966\pi$
$860$	−3.18280e7	−1.46745
$861$	6.04527e6	0.277912
$862$	−6.85299e7	−3.14132
$863$	−3.80638e7	−1.73974	−0.869872	−	0.493278i	$-0.835798\pi$
$863$	−3.80638e7	−1.73974	−0.869872	+	0.493278i	$0.835798\pi$
$864$	−1.53099e7	−0.697729
$865$	−44169.5	−0.00200716
$866$	−5.33543e7	−2.41754
$867$	−2.07546e7	−0.937706
$868$	−1.69454e7	−0.763402
$869$	1.10256e6	0.0495282
$870$	3.00065e7	1.34405
$871$	3.97796e7	1.77670
$872$	6.34014e7	2.82363
$873$	−3.15406e7	−1.40067
$874$	1.77564e7	0.786280
$875$	751206.	0.0331695
$876$	5.30053e7	2.33378
$877$	3.98300e7	1.74869	0.874343	−	0.485309i	$-0.161293\pi$
$877$	3.98300e7	1.74869	0.874343	+	0.485309i	$0.161293\pi$
$878$	−4.37853e7	−1.91687
$879$	3.23074e7	1.41036
$880$	−9.36427e6	−0.407631
$881$	−5.11624e6	−0.222081	−0.111040	−	0.993816i	$-0.535418\pi$
$881$	−5.11624e6	−0.222081	−0.111040	+	0.993816i	$0.535418\pi$
$882$	4.41129e7	1.90939
$883$	3.97119e7	1.71403	0.857016	−	0.515290i	$-0.172316\pi$
$883$	3.97119e7	1.71403	0.857016	+	0.515290i	$0.172316\pi$
$884$	−7.06614e7	−3.04125
$885$	−1.93733e7	−0.831469
$886$	8.35640e7	3.57631
$887$	4.46705e7	1.90639	0.953195	−	0.302355i	$-0.0977729\pi$
$887$	4.46705e7	1.90639	0.953195	+	0.302355i	$0.0977729\pi$
$888$	−1.53596e7	−0.653652
$889$	−5.43923e6	−0.230825
$890$	2.39068e7	1.01169
$891$	5.70306e6	0.240666
$892$	−1.39472e7	−0.586914
$893$	2.86268e6	0.120128
$894$	−1.17635e8	−4.92256
$895$	272069.	0.0113533
$896$	−1.20263e7	−0.500452
$897$	−1.26595e8	−5.25333
$898$	−7.18905e7	−2.97496
$899$	2.09799e7	0.865775
$900$	1.46243e7	0.601822
$901$	2.87143e7	1.17838
$902$	7.07536e6	0.289556
$903$	−1.71182e7	−0.698616
$904$	3.31741e7	1.35014
$905$	−2.22386e6	−0.0902582
$906$	7.61145e7	3.08068
$907$	6.60084e6	0.266429	0.133214	−	0.991087i	$-0.457470\pi$
$907$	6.60084e6	0.266429	0.133214	+	0.991087i	$0.457470\pi$
$908$	−4.49650e7	−1.80992
$909$	8.64051e6	0.346840
$910$	−1.53697e7	−0.615266
$911$	1.77264e7	0.707659	0.353830	−	0.935310i	$-0.384879\pi$
$911$	1.77264e7	0.707659	0.353830	+	0.935310i	$0.384879\pi$
$912$	2.56747e7	1.02216
$913$	2.75039e6	0.109199
$914$	−3.42186e7	−1.35487
$915$	−505801.	−0.0199723
$916$	4.95527e7	1.95132
$917$	−4.44657e6	−0.174623
$918$	7.38006e6	0.289037
$919$	−2.93723e7	−1.14723	−0.573614	−	0.819126i	$-0.694459\pi$
$919$	−2.93723e7	−1.14723	−0.573614	+	0.819126i	$0.694459\pi$
$920$	6.16662e7	2.40202
$921$	4.61948e6	0.179450
$922$	−3.14561e7	−1.21864
$923$	−4.95157e7	−1.91311
$924$	−1.09793e7	−0.423052
$925$	779859.	0.0299683
$926$	−4.55631e6	−0.174617
$927$	1.40992e7	0.538882
$928$	7.78873e7	2.96891
$929$	1.65223e6	0.0628105	0.0314052	−	0.999507i	$-0.490002\pi$
$929$	1.65223e6	0.0628105	0.0314052	+	0.999507i	$0.490002\pi$
$930$	2.63293e7	0.998231
$931$	−5.23291e6	−0.197865
$932$	1.12063e7	0.422595
$933$	4.66060e7	1.75282
$934$	7.73288e7	2.90051
$935$	2.17398e6	0.0813254
$936$	−1.82659e8	−6.81476
$937$	−2.93354e7	−1.09155	−0.545774	−	0.837932i	$-0.683764\pi$
$937$	−2.93354e7	−1.09155	−0.545774	+	0.837932i	$0.683764\pi$
$938$	−1.70719e7	−0.633540
$939$	2.66876e7	0.987747
$940$	1.62857e7	0.601155
$941$	−2.02276e7	−0.744679	−0.372340	−	0.928097i	$-0.621444\pi$
$941$	−2.02276e7	−0.744679	−0.372340	+	0.928097i	$0.621444\pi$
$942$	6.72383e7	2.46882
$943$	−2.51966e7	−0.922703
$944$	−1.04415e8	−3.81359
$945$	1.15524e6	0.0420818
$946$	−2.00350e7	−0.727884
$947$	−1.60973e7	−0.583283	−0.291641	−	0.956528i	$-0.594201\pi$
$947$	−1.60973e7	−0.583283	−0.291641	+	0.956528i	$0.594201\pi$
$948$	−1.71975e7	−0.621505
$949$	3.36142e7	1.21160
$950$	−2.41058e6	−0.0866589
$951$	2.98690e6	0.107095
$952$	1.85124e7	0.662018
$953$	−2.52749e7	−0.901483	−0.450742	−	0.892654i	$-0.648840\pi$
$953$	−2.52749e7	−0.901483	−0.450742	+	0.892654i	$0.648840\pi$
$954$	1.21590e8	4.32541
$955$	2.11619e7	0.750837
$956$	−2.70436e6	−0.0957018
$957$	1.35933e7	0.479783
$958$	7.19041e7	2.53128
$959$	−5.12171e6	−0.179833
$960$	4.08496e7	1.43057
$961$	−1.02202e7	−0.356987
$962$	−1.59560e7	−0.555887
$963$	1.09612e7	0.380883
$964$	−4.99795e7	−1.73221
$965$	2.20525e7	0.762323
$966$	5.43296e7	1.87324
$967$	7.85008e6	0.269965	0.134983	−	0.990848i	$-0.456902\pi$
$967$	7.85008e6	0.269965	0.134983	+	0.990848i	$0.456902\pi$
$968$	−7.84448e6	−0.269076
$969$	−5.96055e6	−0.203928
$970$	2.95768e7	1.00930
$971$	−4.26310e7	−1.45103	−0.725517	−	0.688204i	$-0.758399\pi$
$971$	−4.26310e7	−1.45103	−0.725517	+	0.688204i	$0.758399\pi$
$972$	−1.08142e8	−3.67138
$973$	−369767.	−0.0125212
$974$	9.70761e7	3.27880
$975$	1.71863e7	0.578989
$976$	−2.72608e6	−0.0916041
$977$	5.18690e6	0.173849	0.0869243	−	0.996215i	$-0.472296\pi$
$977$	5.18690e6	0.173849	0.0869243	+	0.996215i	$0.472296\pi$
$978$	6.65580e7	2.22512
$979$	1.08301e7	0.361139
$980$	−2.97698e7	−0.990172
$981$	−3.37054e7	−1.11822
$982$	5.28136e7	1.74770
$983$	−1.12541e7	−0.371471	−0.185736	−	0.982600i	$-0.559467\pi$
$983$	−1.12541e7	−0.371471	−0.185736	+	0.982600i	$0.559467\pi$
$984$	−6.73706e7	−2.21811
$985$	−2.49083e6	−0.0818000
$986$	−3.75453e7	−1.22988
$987$	8.75899e6	0.286195
$988$	3.54944e7	1.15682
$989$	7.13482e7	2.31949
$990$	9.20566e6	0.298515
$991$	−1.38691e7	−0.448606	−0.224303	−	0.974520i	$-0.572010\pi$
$991$	−1.38691e7	−0.448606	−0.224303	+	0.974520i	$0.572010\pi$
$992$	6.83424e7	2.20501
$993$	1.70682e7	0.549305
$994$	2.12503e7	0.682180
$995$	2.48118e7	0.794511
$996$	−4.29001e7	−1.37028
$997$	−2.25434e7	−0.718261	−0.359130	−	0.933287i	$-0.616927\pi$
$997$	−2.25434e7	−0.718261	−0.359130	+	0.933287i	$0.616927\pi$
$998$	−5.47485e7	−1.73999
$999$	1.19931e6	0.0380204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.2	✓	36	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)

\(f(q)\)	\(=\)	\(q-10.6840 q^{2} +22.9747 q^{3} +82.1485 q^{4} +25.0000 q^{5} -245.462 q^{6} +48.0772 q^{7} -535.788 q^{8} +284.836 q^{9} +O(q^{10})\)	\(q-10.6840 q^{2} +22.9747 q^{3} +82.1485 q^{4} +25.0000 q^{5} -245.462 q^{6} +48.0772 q^{7} -535.788 q^{8} +284.836 q^{9} -267.101 q^{10} -121.000 q^{11} +1887.34 q^{12} +1196.89 q^{13} -513.658 q^{14} +574.367 q^{15} +3095.63 q^{16} -718.671 q^{17} -3043.19 q^{18} +361.000 q^{19} +2053.71 q^{20} +1104.56 q^{21} +1292.77 q^{22} -4603.77 q^{23} -12309.6 q^{24} +625.000 q^{25} -12787.6 q^{26} +961.158 q^{27} +3949.47 q^{28} -4889.79 q^{29} -6136.55 q^{30} -4290.56 q^{31} -15928.6 q^{32} -2779.94 q^{33} +7678.30 q^{34} +1201.93 q^{35} +23398.8 q^{36} +1247.77 q^{37} -3856.94 q^{38} +27498.1 q^{39} -13394.7 q^{40} +5473.03 q^{41} -11801.1 q^{42} -15497.8 q^{43} -9939.97 q^{44} +7120.89 q^{45} +49186.8 q^{46} +7929.87 q^{47} +71121.0 q^{48} -14495.6 q^{49} -6677.52 q^{50} -16511.2 q^{51} +98322.4 q^{52} -39954.8 q^{53} -10269.0 q^{54} -3025.00 q^{55} -25759.2 q^{56} +8293.86 q^{57} +52242.7 q^{58} -33729.9 q^{59} +47183.4 q^{60} -880.624 q^{61} +45840.5 q^{62} +13694.1 q^{63} +71121.1 q^{64} +29922.1 q^{65} +29700.9 q^{66} +33235.9 q^{67} -59037.7 q^{68} -105770. q^{69} -12841.4 q^{70} -41370.5 q^{71} -152612. q^{72} +28084.7 q^{73} -13331.3 q^{74} +14359.2 q^{75} +29655.6 q^{76} -5817.34 q^{77} -293790. q^{78} -9112.05 q^{79} +77390.7 q^{80} -47132.8 q^{81} -58474.0 q^{82} -22730.5 q^{83} +90737.7 q^{84} -17966.8 q^{85} +165579. q^{86} -112341. q^{87} +64830.4 q^{88} -89504.8 q^{89} -76079.8 q^{90} +57542.9 q^{91} -378193. q^{92} -98574.2 q^{93} -84723.0 q^{94} +9025.00 q^{95} -365953. q^{96} -110733. q^{97} +154871. q^{98} -34465.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

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