LMFDB - Embedded newform 165.6.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 119x^{3} + 206x^{2} + 1428x - 1320 $ x^5 - 2x^4 - 119x^3 + 206x^2 + 1428x - 1320
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-10.1900$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.1900 q^{2} +9.00000 q^{3} +71.8359 q^{4} -25.0000 q^{5} +91.7099 q^{6} +134.644 q^{7} +405.928 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+10.1900 q^{2} +9.00000 q^{3} +71.8359 q^{4} -25.0000 q^{5} +91.7099 q^{6} +134.644 q^{7} +405.928 q^{8} +81.0000 q^{9} -254.750 q^{10} -121.000 q^{11} +646.523 q^{12} +328.709 q^{13} +1372.02 q^{14} -225.000 q^{15} +1837.65 q^{16} +636.868 q^{17} +825.389 q^{18} -975.686 q^{19} -1795.90 q^{20} +1211.79 q^{21} -1232.99 q^{22} -1141.85 q^{23} +3653.35 q^{24} +625.000 q^{25} +3349.55 q^{26} +729.000 q^{27} +9672.26 q^{28} -1070.39 q^{29} -2292.75 q^{30} +8566.05 q^{31} +5735.96 q^{32} -1089.00 q^{33} +6489.68 q^{34} -3366.09 q^{35} +5818.71 q^{36} -9884.23 q^{37} -9942.23 q^{38} +2958.38 q^{39} -10148.2 q^{40} -9045.27 q^{41} +12348.2 q^{42} +14934.4 q^{43} -8692.15 q^{44} -2025.00 q^{45} -11635.4 q^{46} -25313.8 q^{47} +16538.9 q^{48} +1321.95 q^{49} +6368.74 q^{50} +5731.82 q^{51} +23613.1 q^{52} +5137.53 q^{53} +7428.50 q^{54} +3025.00 q^{55} +54655.7 q^{56} -8781.17 q^{57} -10907.3 q^{58} -23659.7 q^{59} -16163.1 q^{60} -25728.0 q^{61} +87288.0 q^{62} +10906.1 q^{63} -355.443 q^{64} -8217.73 q^{65} -11096.9 q^{66} +21264.1 q^{67} +45750.0 q^{68} -10276.6 q^{69} -34300.5 q^{70} +42804.2 q^{71} +32880.2 q^{72} -52136.5 q^{73} -100720. q^{74} +5625.00 q^{75} -70089.3 q^{76} -16291.9 q^{77} +30145.9 q^{78} -72664.1 q^{79} -45941.3 q^{80} +6561.00 q^{81} -92171.3 q^{82} -70100.2 q^{83} +87050.4 q^{84} -15921.7 q^{85} +152181. q^{86} -9633.51 q^{87} -49117.3 q^{88} +46714.1 q^{89} -20634.7 q^{90} +44258.7 q^{91} -82025.8 q^{92} +77094.5 q^{93} -257948. q^{94} +24392.1 q^{95} +51623.7 q^{96} +180979. q^{97} +13470.7 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 45 q^{3} + 82 q^{4} - 125 q^{5} - 18 q^{6} + 184 q^{7} + 24 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 45 * q^3 + 82 * q^4 - 125 * q^5 - 18 * q^6 + 184 * q^7 + 24 * q^8 + 405 * q^9	\( 5 q - 2 q^{2} + 45 q^{3} + 82 q^{4} - 125 q^{5} - 18 q^{6} + 184 q^{7} + 24 q^{8} + 405 q^{9} + 50 q^{10} - 605 q^{11} + 738 q^{12} + 1082 q^{13} + 432 q^{14} - 1125 q^{15} + 4770 q^{16} + 2174 q^{17} - 162 q^{18} + 1632 q^{19} - 2050 q^{20} + 1656 q^{21} + 242 q^{22} + 1212 q^{23} + 216 q^{24} + 3125 q^{25} + 5600 q^{26} + 3645 q^{27} + 16508 q^{28} + 82 q^{29} + 450 q^{30} + 12120 q^{31} - 4864 q^{32} - 5445 q^{33} - 4524 q^{34} - 4600 q^{35} + 6642 q^{36} - 6530 q^{37} - 15132 q^{38} + 9738 q^{39} - 600 q^{40} + 6782 q^{41} + 3888 q^{42} + 46184 q^{43} - 9922 q^{44} - 10125 q^{45} + 12048 q^{46} - 11692 q^{47} + 42930 q^{48} + 34445 q^{49} - 1250 q^{50} + 19566 q^{51} + 50020 q^{52} + 10314 q^{53} - 1458 q^{54} + 15125 q^{55} + 54928 q^{56} + 14688 q^{57} + 75048 q^{58} + 92892 q^{59} - 18450 q^{60} + 106 q^{61} + 97160 q^{62} + 14904 q^{63} + 44550 q^{64} - 27050 q^{65} + 2178 q^{66} + 100476 q^{67} + 119928 q^{68} + 10908 q^{69} - 10800 q^{70} - 13772 q^{71} + 1944 q^{72} + 94154 q^{73} - 47924 q^{74} + 28125 q^{75} - 51524 q^{76} - 22264 q^{77} + 50400 q^{78} + 178744 q^{79} - 119250 q^{80} + 32805 q^{81} - 299848 q^{82} - 100116 q^{83} + 148572 q^{84} - 54350 q^{85} - 167704 q^{86} + 738 q^{87} - 2904 q^{88} + 119410 q^{89} + 4050 q^{90} + 47536 q^{91} - 404560 q^{92} + 109080 q^{93} - 310288 q^{94} - 40800 q^{95} - 43776 q^{96} + 100682 q^{97} - 16434 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 45 * q^3 + 82 * q^4 - 125 * q^5 - 18 * q^6 + 184 * q^7 + 24 * q^8 + 405 * q^9 + 50 * q^10 - 605 * q^11 + 738 * q^12 + 1082 * q^13 + 432 * q^14 - 1125 * q^15 + 4770 * q^16 + 2174 * q^17 - 162 * q^18 + 1632 * q^19 - 2050 * q^20 + 1656 * q^21 + 242 * q^22 + 1212 * q^23 + 216 * q^24 + 3125 * q^25 + 5600 * q^26 + 3645 * q^27 + 16508 * q^28 + 82 * q^29 + 450 * q^30 + 12120 * q^31 - 4864 * q^32 - 5445 * q^33 - 4524 * q^34 - 4600 * q^35 + 6642 * q^36 - 6530 * q^37 - 15132 * q^38 + 9738 * q^39 - 600 * q^40 + 6782 * q^41 + 3888 * q^42 + 46184 * q^43 - 9922 * q^44 - 10125 * q^45 + 12048 * q^46 - 11692 * q^47 + 42930 * q^48 + 34445 * q^49 - 1250 * q^50 + 19566 * q^51 + 50020 * q^52 + 10314 * q^53 - 1458 * q^54 + 15125 * q^55 + 54928 * q^56 + 14688 * q^57 + 75048 * q^58 + 92892 * q^59 - 18450 * q^60 + 106 * q^61 + 97160 * q^62 + 14904 * q^63 + 44550 * q^64 - 27050 * q^65 + 2178 * q^66 + 100476 * q^67 + 119928 * q^68 + 10908 * q^69 - 10800 * q^70 - 13772 * q^71 + 1944 * q^72 + 94154 * q^73 - 47924 * q^74 + 28125 * q^75 - 51524 * q^76 - 22264 * q^77 + 50400 * q^78 + 178744 * q^79 - 119250 * q^80 + 32805 * q^81 - 299848 * q^82 - 100116 * q^83 + 148572 * q^84 - 54350 * q^85 - 167704 * q^86 + 738 * q^87 - 2904 * q^88 + 119410 * q^89 + 4050 * q^90 + 47536 * q^91 - 404560 * q^92 + 109080 * q^93 - 310288 * q^94 - 40800 * q^95 - 43776 * q^96 + 100682 * q^97 - 16434 * q^98 - 49005 * 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 $

$2$	10.1900	1.80135	0.900677	−	0.434490i	$-0.143071\pi$
$2$	10.1900	1.80135	0.900677	+	0.434490i	$0.143071\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	71.8359	2.24487
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	91.7099	1.04001
$7$	134.644	1.03858	0.519292	−	0.854597i	$-0.326196\pi$
$7$	134.644	1.03858	0.519292	+	0.854597i	$0.326196\pi$
$8$	405.928	2.24246
$9$	81.0000	0.333333
$10$	−254.750	−0.805590
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	646.523	1.29608
$13$	328.709	0.539453	0.269727	−	0.962937i	$-0.413067\pi$
$13$	328.709	0.539453	0.269727	+	0.962937i	$0.413067\pi$
$14$	1372.02	1.87085
$15$	−225.000	−0.258199
$16$	1837.65	1.79458
$17$	636.868	0.534475	0.267238	−	0.963631i	$-0.413889\pi$
$17$	636.868	0.534475	0.267238	+	0.963631i	$0.413889\pi$
$18$	825.389	0.600451
$19$	−975.686	−0.620049	−0.310024	−	0.950729i	$-0.600337\pi$
$19$	−975.686	−0.620049	−0.310024	+	0.950729i	$0.600337\pi$
$20$	−1795.90	−1.00394
$21$	1211.79	0.599626
$22$	−1232.99	−0.543128
$23$	−1141.85	−0.450079	−0.225040	−	0.974350i	$-0.572251\pi$
$23$	−1141.85	−0.450079	−0.225040	+	0.974350i	$0.572251\pi$
$24$	3653.35	1.29468
$25$	625.000	0.200000
$26$	3349.55	0.971746
$27$	729.000	0.192450
$28$	9672.26	2.33149
$29$	−1070.39	−0.236345	−0.118173	−	0.992993i	$-0.537704\pi$
$29$	−1070.39	−0.236345	−0.118173	+	0.992993i	$0.537704\pi$
$30$	−2292.75	−0.465107
$31$	8566.05	1.60095	0.800473	−	0.599369i	$-0.204582\pi$
$31$	8566.05	1.60095	0.800473	+	0.599369i	$0.204582\pi$
$32$	5735.96	0.990219
$33$	−1089.00	−0.174078
$34$	6489.68	0.962778
$35$	−3366.09	−0.464468
$36$	5818.71	0.748291
$37$	−9884.23	−1.18697	−0.593483	−	0.804846i	$-0.702248\pi$
$37$	−9884.23	−1.18697	−0.593483	+	0.804846i	$0.702248\pi$
$38$	−9942.23	−1.11693
$39$	2958.38	0.311453
$40$	−10148.2	−1.00286
$41$	−9045.27	−0.840354	−0.420177	−	0.907442i	$-0.638032\pi$
$41$	−9045.27	−0.840354	−0.420177	+	0.907442i	$0.638032\pi$
$42$	12348.2	1.08014
$43$	14934.4	1.23173	0.615866	−	0.787851i	$-0.288806\pi$
$43$	14934.4	1.23173	0.615866	+	0.787851i	$0.288806\pi$
$44$	−8692.15	−0.676855
$45$	−2025.00	−0.149071
$46$	−11635.4	−0.810752
$47$	−25313.8	−1.67153	−0.835763	−	0.549091i	$-0.814974\pi$
$47$	−25313.8	−1.67153	−0.835763	+	0.549091i	$0.814974\pi$
$48$	16538.9	1.03610
$49$	1321.95	0.0786547
$50$	6368.74	0.360271
$51$	5731.82	0.308579
$52$	23613.1	1.21100
$53$	5137.53	0.251226	0.125613	−	0.992079i	$-0.459910\pi$
$53$	5137.53	0.251226	0.125613	+	0.992079i	$0.459910\pi$
$54$	7428.50	0.346671
$55$	3025.00	0.134840
$56$	54655.7	2.32898
$57$	−8781.17	−0.357985
$58$	−10907.3	−0.425742
$59$	−23659.7	−0.884870	−0.442435	−	0.896801i	$-0.645885\pi$
$59$	−23659.7	−0.884870	−0.442435	+	0.896801i	$0.645885\pi$
$60$	−16163.1	−0.579624
$61$	−25728.0	−0.885280	−0.442640	−	0.896699i	$-0.645958\pi$
$61$	−25728.0	−0.885280	−0.442640	+	0.896699i	$0.645958\pi$
$62$	87288.0	2.88387
$63$	10906.1	0.346194
$64$	−355.443	−0.0108473
$65$	−8217.73	−0.241251
$66$	−11096.9	−0.313575
$67$	21264.1	0.578707	0.289354	−	0.957222i	$-0.406560\pi$
$67$	21264.1	0.578707	0.289354	+	0.957222i	$0.406560\pi$
$68$	45750.0	1.19983
$69$	−10276.6	−0.259854
$70$	−34300.5	−0.836672
$71$	42804.2	1.00772	0.503861	−	0.863785i	$-0.331912\pi$
$71$	42804.2	1.00772	0.503861	+	0.863785i	$0.331912\pi$
$72$	32880.2	0.747485
$73$	−52136.5	−1.14508	−0.572539	−	0.819878i	$-0.694041\pi$
$73$	−52136.5	−1.14508	−0.572539	+	0.819878i	$0.694041\pi$
$74$	−100720.	−2.13815
$75$	5625.00	0.115470
$76$	−70089.3	−1.39193
$77$	−16291.9	−0.313145
$78$	30145.9	0.561038
$79$	−72664.1	−1.30994	−0.654971	−	0.755654i	$-0.727319\pi$
$79$	−72664.1	−1.30994	−0.654971	+	0.755654i	$0.727319\pi$
$80$	−45941.3	−0.802561
$81$	6561.00	0.111111
$82$	−92171.3	−1.51377
$83$	−70100.2	−1.11692	−0.558462	−	0.829530i	$-0.688608\pi$
$83$	−70100.2	−1.11692	−0.558462	+	0.829530i	$0.688608\pi$
$84$	87050.4	1.34608
$85$	−15921.7	−0.239024
$86$	152181.	2.21879
$87$	−9633.51	−0.136454
$88$	−49117.3	−0.676126
$89$	46714.1	0.625134	0.312567	−	0.949896i	$-0.398811\pi$
$89$	46714.1	0.625134	0.312567	+	0.949896i	$0.398811\pi$
$90$	−20634.7	−0.268530
$91$	44258.7	0.560267
$92$	−82025.8	−1.01037
$93$	77094.5	0.924306
$94$	−257948.	−3.01101
$95$	24392.1	0.277294
$96$	51623.7	0.571703
$97$	180979.	1.95298	0.976492	−	0.215555i	$-0.0691559\pi$
$97$	180979.	1.95298	0.976492	+	0.215555i	$0.0691559\pi$
$98$	13470.7	0.141685
$99$	−9801.00	−0.100504
$100$	44897.5	0.448975
$101$	176753.	1.72411	0.862053	−	0.506819i	$-0.169179\pi$
$101$	176753.	1.72411	0.862053	+	0.506819i	$0.169179\pi$
$102$	58407.2	0.555860
$103$	−124306.	−1.15451	−0.577256	−	0.816563i	$-0.695877\pi$
$103$	−124306.	−1.15451	−0.577256	+	0.816563i	$0.695877\pi$
$104$	133432.	1.20970
$105$	−30294.9	−0.268161
$106$	52351.4	0.452547
$107$	−128872.	−1.08818	−0.544088	−	0.839028i	$-0.683124\pi$
$107$	−128872.	−1.08818	−0.544088	+	0.839028i	$0.683124\pi$
$108$	52368.4	0.432026
$109$	89843.2	0.724300	0.362150	−	0.932120i	$-0.382043\pi$
$109$	89843.2	0.724300	0.362150	+	0.932120i	$0.382043\pi$
$110$	30824.7	0.242894
$111$	−88958.1	−0.685295
$112$	247428.	1.86382
$113$	−55260.0	−0.407113	−0.203556	−	0.979063i	$-0.565250\pi$
$113$	−55260.0	−0.407113	−0.203556	+	0.979063i	$0.565250\pi$
$114$	−89480.1	−0.644858
$115$	28546.2	0.201282
$116$	−76892.5	−0.530565
$117$	26625.5	0.179818
$118$	−241092.	−1.59396
$119$	85750.4	0.555097
$120$	−91333.8	−0.579000
$121$	14641.0	0.0909091
$122$	−262168.	−1.59470
$123$	−81407.5	−0.485178
$124$	615350.	3.59392
$125$	−15625.0	−0.0894427
$126$	111134.	0.623618
$127$	−50763.1	−0.279280	−0.139640	−	0.990202i	$-0.544594\pi$
$127$	−50763.1	−0.279280	−0.139640	+	0.990202i	$0.544594\pi$
$128$	−187173.	−1.00976
$129$	134410.	0.711141
$130$	−83738.6	−0.434578
$131$	28827.5	0.146767	0.0733836	−	0.997304i	$-0.476620\pi$
$131$	28827.5	0.146767	0.0733836	+	0.997304i	$0.476620\pi$
$132$	−78229.3	−0.390782
$133$	−131370.	−0.643972
$134$	216681.	1.04246
$135$	−18225.0	−0.0860663
$136$	258523.	1.19854
$137$	−295351.	−1.34443	−0.672214	−	0.740357i	$-0.734656\pi$
$137$	−295351.	−1.34443	−0.672214	+	0.740357i	$0.734656\pi$
$138$	−104719.	−0.468088
$139$	59066.7	0.259302	0.129651	−	0.991560i	$-0.458614\pi$
$139$	59066.7	0.259302	0.129651	+	0.991560i	$0.458614\pi$
$140$	−241807.	−1.04267
$141$	−227824.	−0.965056
$142$	436175.	1.81526
$143$	−39773.8	−0.162651
$144$	148850.	0.598194
$145$	26759.8	0.105697
$146$	−531271.	−2.06269
$147$	11897.5	0.0454113
$148$	−710043.	−2.66459
$149$	248102.	0.915511	0.457756	−	0.889078i	$-0.348653\pi$
$149$	248102.	0.915511	0.457756	+	0.889078i	$0.348653\pi$
$150$	57318.7	0.208002
$151$	−156472.	−0.558462	−0.279231	−	0.960224i	$-0.590080\pi$
$151$	−156472.	−0.558462	−0.279231	+	0.960224i	$0.590080\pi$
$152$	−396058.	−1.39043
$153$	51586.3	0.178158
$154$	−166014.	−0.564084
$155$	−214151.	−0.715964
$156$	212518.	0.699173
$157$	391275.	1.26687	0.633436	−	0.773795i	$-0.281644\pi$
$157$	391275.	1.26687	0.633436	+	0.773795i	$0.281644\pi$
$158$	−740446.	−2.35967
$159$	46237.8	0.145046
$160$	−143399.	−0.442839
$161$	−153743.	−0.467445
$162$	66856.5	0.200150
$163$	−78318.8	−0.230886	−0.115443	−	0.993314i	$-0.536829\pi$
$163$	−78318.8	−0.230886	−0.115443	+	0.993314i	$0.536829\pi$
$164$	−649776.	−1.88649
$165$	27225.0	0.0778499
$166$	−714320.	−2.01198
$167$	1114.53	0.00309242	0.00154621	−	0.999999i	$-0.499508\pi$
$167$	1114.53	0.00309242	0.00154621	+	0.999999i	$0.499508\pi$
$168$	491901.	1.34464
$169$	−263243.	−0.708990
$170$	−162242.	−0.430567
$171$	−79030.5	−0.206683
$172$	1.07283e6	2.76508
$173$	−347712.	−0.883293	−0.441647	−	0.897189i	$-0.645605\pi$
$173$	−347712.	−0.883293	−0.441647	+	0.897189i	$0.645605\pi$
$174$	−98165.4	−0.245802
$175$	84152.4	0.207717
$176$	−222356.	−0.541087
$177$	−212937.	−0.510880
$178$	476017.	1.12609
$179$	226477.	0.528312	0.264156	−	0.964480i	$-0.414907\pi$
$179$	226477.	0.528312	0.264156	+	0.964480i	$0.414907\pi$
$180$	−145468.	−0.334646
$181$	472699.	1.07248	0.536239	−	0.844066i	$-0.319845\pi$
$181$	472699.	1.07248	0.536239	+	0.844066i	$0.319845\pi$
$182$	450996.	1.00924
$183$	−231552.	−0.511117
$184$	−463508.	−1.00928
$185$	247106.	0.530828
$186$	785592.	1.66500
$187$	−77061.1	−0.161150
$188$	−1.81844e6	−3.75236
$189$	98155.3	0.199875
$190$	248556.	0.499505
$191$	−360223.	−0.714477	−0.357239	−	0.934013i	$-0.616282\pi$
$191$	−360223.	−0.714477	−0.357239	+	0.934013i	$0.616282\pi$
$192$	−3198.98	−0.00626266
$193$	244438.	0.472363	0.236181	−	0.971709i	$-0.424104\pi$
$193$	244438.	0.472363	0.236181	+	0.971709i	$0.424104\pi$
$194$	1.84417e6	3.51801
$195$	−73959.6	−0.139286
$196$	94963.5	0.176570
$197$	541174.	0.993508	0.496754	−	0.867891i	$-0.334525\pi$
$197$	541174.	0.993508	0.496754	+	0.867891i	$0.334525\pi$
$198$	−99872.1	−0.181043
$199$	999402.	1.78899	0.894494	−	0.447079i	$-0.147536\pi$
$199$	999402.	1.78899	0.894494	+	0.447079i	$0.147536\pi$
$200$	253705.	0.448491
$201$	191376.	0.334117
$202$	1.80111e6	3.10572
$203$	−144121.	−0.245464
$204$	411750.	0.692721
$205$	226132.	0.375818
$206$	−1.26668e6	−2.07969
$207$	−92489.8	−0.150026
$208$	604053.	0.968093
$209$	118058.	0.186952
$210$	−308704.	−0.483053
$211$	463100.	0.716092	0.358046	−	0.933704i	$-0.383443\pi$
$211$	463100.	0.716092	0.358046	+	0.933704i	$0.383443\pi$
$212$	369060.	0.563971
$213$	385238.	0.581809
$214$	−1.31321e6	−1.96019
$215$	−373360.	−0.550848
$216$	295921.	0.431561
$217$	1.15337e6	1.66271
$218$	915501.	1.30472
$219$	−469229.	−0.661111
$220$	217304.	0.302699
$221$	209345.	0.288324
$222$	−906482.	−1.23446
$223$	1.34479e6	1.81089	0.905446	−	0.424462i	$-0.139537\pi$
$223$	1.34479e6	1.81089	0.905446	+	0.424462i	$0.139537\pi$
$224$	772312.	1.02842
$225$	50625.0	0.0666667
$226$	−563099.	−0.733354
$227$	1.28112e6	1.65016	0.825078	−	0.565019i	$-0.191131\pi$
$227$	1.28112e6	1.65016	0.825078	+	0.565019i	$0.191131\pi$
$228$	−630804.	−0.803632
$229$	293472.	0.369810	0.184905	−	0.982756i	$-0.440802\pi$
$229$	293472.	0.369810	0.184905	+	0.982756i	$0.440802\pi$
$230$	290886.	0.362579
$231$	−146627.	−0.180794
$232$	−434501.	−0.529994
$233$	−1.01992e6	−1.23077	−0.615385	−	0.788227i	$-0.710999\pi$
$233$	−1.01992e6	−1.23077	−0.615385	+	0.788227i	$0.710999\pi$
$234$	271313.	0.323915
$235$	632845.	0.747529
$236$	−1.69962e6	−1.98642
$237$	−653977.	−0.756295
$238$	873796.	0.999925
$239$	−705249.	−0.798634	−0.399317	−	0.916813i	$-0.630753\pi$
$239$	−705249.	−0.798634	−0.399317	+	0.916813i	$0.630753\pi$
$240$	−413472.	−0.463359
$241$	255105.	0.282928	0.141464	−	0.989943i	$-0.454819\pi$
$241$	255105.	0.282928	0.141464	+	0.989943i	$0.454819\pi$
$242$	149192.	0.163759
$243$	59049.0	0.0641500
$244$	−1.84819e6	−1.98734
$245$	−33048.7	−0.0351754
$246$	−829541.	−0.873978
$247$	−320717.	−0.334487
$248$	3.47720e6	3.59005
$249$	−630902.	−0.644857
$250$	−159219.	−0.161118
$251$	321566.	0.322171	0.161085	−	0.986940i	$-0.448501\pi$
$251$	321566.	0.322171	0.161085	+	0.986940i	$0.448501\pi$
$252$	783453.	0.777162
$253$	138164.	0.135704
$254$	−517276.	−0.503081
$255$	−143295.	−0.138001
$256$	−1.89591e6	−1.80808
$257$	1.37206e6	1.29580	0.647902	−	0.761723i	$-0.275646\pi$
$257$	1.37206e6	1.29580	0.647902	+	0.761723i	$0.275646\pi$
$258$	1.36963e6	1.28102
$259$	−1.33085e6	−1.23276
$260$	−590329.	−0.541577
$261$	−86701.6	−0.0787818
$262$	293752.	0.264380
$263$	1.69197e6	1.50835	0.754177	−	0.656671i	$-0.228036\pi$
$263$	1.69197e6	1.50835	0.754177	+	0.656671i	$0.228036\pi$
$264$	−442055.	−0.390361
$265$	−128438.	−0.112352
$266$	−1.33866e6	−1.16002
$267$	420427.	0.360921
$268$	1.52752e6	1.29912
$269$	1.63565e6	1.37819	0.689097	−	0.724669i	$-0.258007\pi$
$269$	1.63565e6	1.37819	0.689097	+	0.724669i	$0.258007\pi$
$270$	−185713.	−0.155036
$271$	1.37446e6	1.13687	0.568434	−	0.822729i	$-0.307550\pi$
$271$	1.37446e6	1.13687	0.568434	+	0.822729i	$0.307550\pi$
$272$	1.17034e6	0.959159
$273$	398328.	0.323470
$274$	−3.00963e6	−2.42179
$275$	−75625.0	−0.0603023
$276$	−738232.	−0.583338
$277$	−1.06340e6	−0.832714	−0.416357	−	0.909201i	$-0.636693\pi$
$277$	−1.06340e6	−0.832714	−0.416357	+	0.909201i	$0.636693\pi$
$278$	601889.	0.467094
$279$	693850.	0.533648
$280$	−1.36639e6	−1.04155
$281$	1.83504e6	1.38637	0.693186	−	0.720759i	$-0.256207\pi$
$281$	1.83504e6	1.38637	0.693186	+	0.720759i	$0.256207\pi$
$282$	−2.32153e6	−1.73841
$283$	−202576.	−0.150357	−0.0751783	−	0.997170i	$-0.523953\pi$
$283$	−202576.	−0.150357	−0.0751783	+	0.997170i	$0.523953\pi$
$284$	3.07488e6	2.26221
$285$	219529.	0.160096
$286$	−405295.	−0.292992
$287$	−1.21789e6	−0.872777
$288$	464613.	0.330073
$289$	−1.01426e6	−0.714336
$290$	272682.	0.190397
$291$	1.62881e6	1.12756
$292$	−3.74528e6	−2.57055
$293$	−205193.	−0.139634	−0.0698172	−	0.997560i	$-0.522242\pi$
$293$	−205193.	−0.139634	−0.0698172	+	0.997560i	$0.522242\pi$
$294$	121236.	0.0818018
$295$	591493.	0.395726
$296$	−4.01228e6	−2.66172
$297$	−88209.0	−0.0580259
$298$	2.52815e6	1.64916
$299$	−375337.	−0.242797
$300$	404077.	0.259216
$301$	2.01082e6	1.27926
$302$	−1.59445e6	−1.00599
$303$	1.59078e6	0.995413
$304$	−1.79297e6	−1.11273
$305$	643199.	0.395909
$306$	525664.	0.320926
$307$	1.71849e6	1.04064	0.520322	−	0.853970i	$-0.325812\pi$
$307$	1.71849e6	1.04064	0.520322	+	0.853970i	$0.325812\pi$
$308$	−1.17034e6	−0.702970
$309$	−1.11875e6	−0.666558
$310$	−2.18220e6	−1.28970
$311$	−1.87637e6	−1.10006	−0.550031	−	0.835144i	$-0.685384\pi$
$311$	−1.87637e6	−1.10006	−0.550031	+	0.835144i	$0.685384\pi$
$312$	1.20089e6	0.698420
$313$	1.84176e6	1.06261	0.531304	−	0.847181i	$-0.321702\pi$
$313$	1.84176e6	1.06261	0.531304	+	0.847181i	$0.321702\pi$
$314$	3.98709e6	2.28208
$315$	−272654.	−0.154823
$316$	−5.21989e6	−2.94065
$317$	−2.25359e6	−1.25958	−0.629791	−	0.776764i	$-0.716860\pi$
$317$	−2.25359e6	−1.25958	−0.629791	+	0.776764i	$0.716860\pi$
$318$	471163.	0.261278
$319$	129517.	0.0712608
$320$	8886.07	0.00485104
$321$	−1.15985e6	−0.628259
$322$	−1.56664e6	−0.842033
$323$	−621383.	−0.331401
$324$	471316.	0.249430
$325$	205443.	0.107891
$326$	−798068.	−0.415907
$327$	808588.	0.418175
$328$	−3.67173e6	−1.88446
$329$	−3.40835e6	−1.73602
$330$	277423.	0.140235
$331$	−372999.	−0.187128	−0.0935638	−	0.995613i	$-0.529826\pi$
$331$	−372999.	−0.187128	−0.0935638	+	0.995613i	$0.529826\pi$
$332$	−5.03571e6	−2.50735
$333$	−800623.	−0.395656
$334$	11357.0	0.00557055
$335$	−531601.	−0.258806
$336$	2.22685e6	1.07608
$337$	1.52472e6	0.731332	0.365666	−	0.930746i	$-0.380841\pi$
$337$	1.52472e6	0.731332	0.365666	+	0.930746i	$0.380841\pi$
$338$	−2.68245e6	−1.27714
$339$	−497340.	−0.235047
$340$	−1.14375e6	−0.536580
$341$	−1.03649e6	−0.482703
$342$	−805321.	−0.372309
$343$	−2.08497e6	−0.956894
$344$	6.06229e6	2.76211
$345$	256916.	0.116210
$346$	−3.54319e6	−1.59112
$347$	1.27128e6	0.566785	0.283392	−	0.959004i	$-0.408540\pi$
$347$	1.27128e6	0.566785	0.283392	+	0.959004i	$0.408540\pi$
$348$	−692032.	−0.306322
$349$	−2.76246e6	−1.21404	−0.607019	−	0.794687i	$-0.707635\pi$
$349$	−2.76246e6	−1.21404	−0.607019	+	0.794687i	$0.707635\pi$
$350$	857512.	0.374171
$351$	239629.	0.103818
$352$	−694051.	−0.298562
$353$	−2.44445e6	−1.04411	−0.522053	−	0.852913i	$-0.674834\pi$
$353$	−2.44445e6	−1.04411	−0.522053	+	0.852913i	$0.674834\pi$
$354$	−2.16983e6	−0.920275
$355$	−1.07011e6	−0.450667
$356$	3.35575e6	1.40335
$357$	771753.	0.320485
$358$	2.30779e6	0.951677
$359$	−1.86633e6	−0.764278	−0.382139	−	0.924105i	$-0.624812\pi$
$359$	−1.86633e6	−0.764278	−0.382139	+	0.924105i	$0.624812\pi$
$360$	−822004.	−0.334286
$361$	−1.52414e6	−0.615539
$362$	4.81680e6	1.93191
$363$	131769.	0.0524864
$364$	3.17936e6	1.25773
$365$	1.30341e6	0.512094
$366$	−2.35951e6	−0.920702
$367$	4.79188e6	1.85713	0.928563	−	0.371176i	$-0.121045\pi$
$367$	4.79188e6	1.85713	0.928563	+	0.371176i	$0.121045\pi$
$368$	−2.09832e6	−0.807704
$369$	−732667.	−0.280118
$370$	2.51801e6	0.956208
$371$	691737.	0.260919
$372$	5.53815e6	2.07495
$373$	−2.82793e6	−1.05244	−0.526218	−	0.850350i	$-0.676391\pi$
$373$	−2.82793e6	−1.05244	−0.526218	+	0.850350i	$0.676391\pi$
$374$	−785252.	−0.290289
$375$	−140625.	−0.0516398
$376$	−1.02756e7	−3.74832
$377$	−351847.	−0.127497
$378$	1.00020e6	0.360046
$379$	3.30279e6	1.18109	0.590545	−	0.807005i	$-0.298913\pi$
$379$	3.30279e6	1.18109	0.590545	+	0.807005i	$0.298913\pi$
$380$	1.75223e6	0.622491
$381$	−456868.	−0.161242
$382$	−3.67067e6	−1.28703
$383$	−5.55972e6	−1.93667	−0.968336	−	0.249652i	$-0.919684\pi$
$383$	−5.55972e6	−1.93667	−0.968336	+	0.249652i	$0.919684\pi$
$384$	−1.68455e6	−0.582984
$385$	407297.	0.140043
$386$	2.49082e6	0.850892
$387$	1.20969e6	0.410578
$388$	1.30008e7	4.38420
$389$	3.97769e6	1.33278	0.666388	−	0.745605i	$-0.267839\pi$
$389$	3.97769e6	1.33278	0.666388	+	0.745605i	$0.267839\pi$
$390$	−753648.	−0.250904
$391$	−727208.	−0.240556
$392$	536616.	0.176380
$393$	259448.	0.0847361
$394$	5.51456e6	1.78966
$395$	1.81660e6	0.585824
$396$	−704064.	−0.225618
$397$	3.97422e6	1.26554	0.632770	−	0.774340i	$-0.281918\pi$
$397$	3.97422e6	1.26554	0.632770	+	0.774340i	$0.281918\pi$
$398$	1.01839e7	3.22260
$399$	−1.18233e6	−0.371798
$400$	1.14853e6	0.358916
$401$	−5.52342e6	−1.71533	−0.857663	−	0.514212i	$-0.828084\pi$
$401$	−5.52342e6	−1.71533	−0.857663	+	0.514212i	$0.828084\pi$
$402$	1.95012e6	0.601862
$403$	2.81574e6	0.863635
$404$	1.26972e7	3.87040
$405$	−164025.	−0.0496904
$406$	−1.46860e6	−0.442168
$407$	1.19599e6	0.357884
$408$	2.32670e6	0.691975
$409$	−3.15672e6	−0.933099	−0.466549	−	0.884495i	$-0.654503\pi$
$409$	−3.15672e6	−0.933099	−0.466549	+	0.884495i	$0.654503\pi$
$410$	2.30428e6	0.676980
$411$	−2.65816e6	−0.776206
$412$	−8.92963e6	−2.59173
$413$	−3.18563e6	−0.919011
$414$	−942470.	−0.270251
$415$	1.75250e6	0.499504
$416$	1.88546e6	0.534177
$417$	531600.	0.149708
$418$	1.20301e6	0.336766
$419$	−5.38025e6	−1.49716	−0.748579	−	0.663045i	$-0.769264\pi$
$419$	−5.38025e6	−1.49716	−0.748579	+	0.663045i	$0.769264\pi$
$420$	−2.17626e6	−0.601987
$421$	6.14869e6	1.69074	0.845370	−	0.534181i	$-0.179380\pi$
$421$	6.14869e6	1.69074	0.845370	+	0.534181i	$0.179380\pi$
$422$	4.71898e6	1.28993
$423$	−2.05042e6	−0.557175
$424$	2.08547e6	0.563364
$425$	398043.	0.106895
$426$	3.92557e6	1.04804
$427$	−3.46411e6	−0.919437
$428$	−9.25764e6	−2.44282
$429$	−357965.	−0.0939067
$430$	−3.80453e6	−0.992271
$431$	−1.77150e6	−0.459356	−0.229678	−	0.973267i	$-0.573767\pi$
$431$	−1.77150e6	−0.459356	−0.229678	+	0.973267i	$0.573767\pi$
$432$	1.33965e6	0.345367
$433$	−639769.	−0.163985	−0.0819924	−	0.996633i	$-0.526128\pi$
$433$	−639769.	−0.163985	−0.0819924	+	0.996633i	$0.526128\pi$
$434$	1.17528e7	2.99514
$435$	240838.	0.0610241
$436$	6.45397e6	1.62596
$437$	1.11409e6	0.279071
$438$	−4.78144e6	−1.19089
$439$	−3.37312e6	−0.835353	−0.417677	−	0.908596i	$-0.637155\pi$
$439$	−3.37312e6	−0.835353	−0.417677	+	0.908596i	$0.637155\pi$
$440$	1.22793e6	0.302373
$441$	107078.	0.0262182
$442$	2.13322e6	0.519374
$443$	2.61585e6	0.633291	0.316645	−	0.948544i	$-0.397443\pi$
$443$	2.61585e6	0.633291	0.316645	+	0.948544i	$0.397443\pi$
$444$	−6.39039e6	−1.53840
$445$	−1.16785e6	−0.279569
$446$	1.37034e7	3.26205
$447$	2.23291e6	0.528571
$448$	−47858.2	−0.0112658
$449$	−6.10127e6	−1.42825	−0.714125	−	0.700018i	$-0.753175\pi$
$449$	−6.10127e6	−1.42825	−0.714125	+	0.700018i	$0.753175\pi$
$450$	515868.	0.120090
$451$	1.09448e6	0.253376
$452$	−3.96965e6	−0.913916
$453$	−1.40825e6	−0.322428
$454$	1.30546e7	2.97251
$455$	−1.10647e6	−0.250559
$456$	−3.56452e6	−0.802766
$457$	−3.44204e6	−0.770950	−0.385475	−	0.922718i	$-0.625962\pi$
$457$	−3.44204e6	−0.770950	−0.385475	+	0.922718i	$0.625962\pi$
$458$	2.99048e6	0.666158
$459$	464277.	0.102860
$460$	2.05065e6	0.451852
$461$	−1.07647e6	−0.235912	−0.117956	−	0.993019i	$-0.537634\pi$
$461$	−1.07647e6	−0.235912	−0.117956	+	0.993019i	$0.537634\pi$
$462$	−1.49413e6	−0.325674
$463$	5.81934e6	1.26160	0.630799	−	0.775946i	$-0.282727\pi$
$463$	5.81934e6	1.26160	0.630799	+	0.775946i	$0.282727\pi$
$464$	−1.96700e6	−0.424141
$465$	−1.92736e6	−0.413362
$466$	−1.03930e7	−2.21705
$467$	869141.	0.184416	0.0922078	−	0.995740i	$-0.470608\pi$
$467$	869141.	0.184416	0.0922078	+	0.995740i	$0.470608\pi$
$468$	1.91266e6	0.403668
$469$	2.86307e6	0.601036
$470$	6.44869e6	1.34656
$471$	3.52147e6	0.731429
$472$	−9.60414e6	−1.98428
$473$	−1.80706e6	−0.371381
$474$	−6.66402e6	−1.36235
$475$	−609804.	−0.124010
$476$	6.15996e6	1.24612
$477$	416140.	0.0837421
$478$	−7.18648e6	−1.43862
$479$	−2.82970e6	−0.563509	−0.281755	−	0.959487i	$-0.590916\pi$
$479$	−2.82970e6	−0.563509	−0.281755	+	0.959487i	$0.590916\pi$
$480$	−1.29059e6	−0.255673
$481$	−3.24904e6	−0.640313
$482$	2.59951e6	0.509653
$483$	−1.38369e6	−0.269879
$484$	1.05175e6	0.204079
$485$	−4.52447e6	−0.873401
$486$	601709.	0.115557
$487$	−9.69730e6	−1.85280	−0.926400	−	0.376541i	$-0.877114\pi$
$487$	−9.69730e6	−1.85280	−0.926400	+	0.376541i	$0.877114\pi$
$488$	−1.04437e7	−1.98520
$489$	−704869.	−0.133302
$490$	−336766.	−0.0633634
$491$	−5.04634e6	−0.944654	−0.472327	−	0.881423i	$-0.656586\pi$
$491$	−5.04634e6	−0.944654	−0.472327	+	0.881423i	$0.656586\pi$
$492$	−5.84798e6	−1.08916
$493$	−681698.	−0.126321
$494$	−3.26810e6	−0.602530
$495$	245025.	0.0449467
$496$	1.57414e7	2.87303
$497$	5.76333e6	1.04660
$498$	−6.42888e6	−1.16161
$499$	−8.28396e6	−1.48932	−0.744658	−	0.667446i	$-0.767387\pi$
$499$	−8.28396e6	−1.48932	−0.744658	+	0.667446i	$0.767387\pi$
$500$	−1.12244e6	−0.200788
$501$	10030.7	0.00178541
$502$	3.27676e6	0.580344
$503$	−4.33940e6	−0.764734	−0.382367	−	0.924011i	$-0.624891\pi$
$503$	−4.33940e6	−0.764734	−0.382367	+	0.924011i	$0.624891\pi$
$504$	4.42711e6	0.776325
$505$	−4.41883e6	−0.771043
$506$	1.40789e6	0.244451
$507$	−2.36919e6	−0.409336
$508$	−3.64662e6	−0.626947
$509$	−1.97982e6	−0.338712	−0.169356	−	0.985555i	$-0.554169\pi$
$509$	−1.97982e6	−0.338712	−0.169356	+	0.985555i	$0.554169\pi$
$510$	−1.46018e6	−0.248588
$511$	−7.01986e6	−1.18926
$512$	−1.33298e7	−2.24724
$513$	−711275.	−0.119328
$514$	1.39813e7	2.33420
$515$	3.10765e6	0.516314
$516$	9.65544e6	1.59642
$517$	3.06297e6	0.503984
$518$	−1.35614e7	−2.22064
$519$	−3.12941e6	−0.509970
$520$	−3.33581e6	−0.540994
$521$	−897869.	−0.144917	−0.0724584	−	0.997371i	$-0.523084\pi$
$521$	−897869.	−0.144917	−0.0724584	+	0.997371i	$0.523084\pi$
$522$	−883489.	−0.141914
$523$	5.03726e6	0.805267	0.402633	−	0.915361i	$-0.368095\pi$
$523$	5.03726e6	0.805267	0.402633	+	0.915361i	$0.368095\pi$
$524$	2.07085e6	0.329474
$525$	757371.	0.119925
$526$	1.72412e7	2.71708
$527$	5.45545e6	0.855665
$528$	−2.00120e6	−0.312397
$529$	−5.13252e6	−0.797428
$530$	−1.30879e6	−0.202385
$531$	−1.91644e6	−0.294957
$532$	−9.43709e6	−1.44564
$533$	−2.97327e6	−0.453331
$534$	4.28415e6	0.650147
$535$	3.22180e6	0.486647
$536$	8.63167e6	1.29773
$537$	2.03829e6	0.305021
$538$	1.66673e7	2.48262
$539$	−159956.	−0.0237153
$540$	−1.30921e6	−0.193208
$541$	1.34111e7	1.97003	0.985013	−	0.172483i	$-0.0551788\pi$
$541$	1.34111e7	1.97003	0.985013	+	0.172483i	$0.0551788\pi$
$542$	1.40058e7	2.04790
$543$	4.25429e6	0.619195
$544$	3.65305e6	0.529247
$545$	−2.24608e6	−0.323917
$546$	4.05896e6	0.582684
$547$	1.17349e7	1.67691	0.838456	−	0.544969i	$-0.183459\pi$
$547$	1.17349e7	1.67691	0.838456	+	0.544969i	$0.183459\pi$
$548$	−2.12168e7	−3.01807
$549$	−2.08397e6	−0.295093
$550$	−770618.	−0.108626
$551$	1.04436e6	0.146546
$552$	−4.17158e6	−0.582710
$553$	−9.78377e6	−1.36048
$554$	−1.08360e7	−1.50001
$555$	2.22395e6	0.306473
$556$	4.24311e6	0.582099
$557$	−1.15265e7	−1.57420	−0.787101	−	0.616824i	$-0.788419\pi$
$557$	−1.15265e7	−1.57420	−0.787101	+	0.616824i	$0.788419\pi$
$558$	7.07033e6	0.961289
$559$	4.90908e6	0.664462
$560$	−6.18571e6	−0.833526
$561$	−693550.	−0.0930402
$562$	1.86990e7	2.49734
$563$	7.10264e6	0.944384	0.472192	−	0.881496i	$-0.343463\pi$
$563$	7.10264e6	0.944384	0.472192	+	0.881496i	$0.343463\pi$
$564$	−1.63660e7	−2.16643
$565$	1.38150e6	0.182066
$566$	−2.06425e6	−0.270845
$567$	883398.	0.115398
$568$	1.73754e7	2.25977
$569$	1.29610e6	0.167826	0.0839128	−	0.996473i	$-0.473258\pi$
$569$	1.29610e6	0.167826	0.0839128	+	0.996473i	$0.473258\pi$
$570$	2.23700e6	0.288389
$571$	1.13637e7	1.45858	0.729290	−	0.684205i	$-0.239851\pi$
$571$	1.13637e7	1.45858	0.729290	+	0.684205i	$0.239851\pi$
$572$	−2.85719e6	−0.365131
$573$	−3.24201e6	−0.412504
$574$	−1.24103e7	−1.57218
$575$	−713656.	−0.0900159
$576$	−28790.9	−0.00361575
$577$	2.63730e6	0.329777	0.164888	−	0.986312i	$-0.447274\pi$
$577$	2.63730e6	0.329777	0.164888	+	0.986312i	$0.447274\pi$
$578$	−1.03353e7	−1.28677
$579$	2.19994e6	0.272719
$580$	1.92231e6	0.237276
$581$	−9.43855e6	−1.16002
$582$	1.65976e7	2.03113
$583$	−621642.	−0.0757476
$584$	−2.11637e7	−2.56779
$585$	−665637.	−0.0804169
$586$	−2.09091e6	−0.251531
$587$	9.19302e6	1.10119	0.550596	−	0.834772i	$-0.314401\pi$
$587$	9.19302e6	1.10119	0.550596	+	0.834772i	$0.314401\pi$
$588$	854671.	0.101943
$589$	−8.35777e6	−0.992664
$590$	6.02731e6	0.712842
$591$	4.87057e6	0.573602
$592$	−1.81638e7	−2.13011
$593$	1.36988e7	1.59973	0.799863	−	0.600183i	$-0.204905\pi$
$593$	1.36988e7	1.59973	0.799863	+	0.600183i	$0.204905\pi$
$594$	−898849.	−0.104525
$595$	−2.14376e6	−0.248247
$596$	1.78226e7	2.05521
$597$	8.99462e6	1.03287
$598$	−3.82468e6	−0.437363
$599$	−4.07920e6	−0.464524	−0.232262	−	0.972653i	$-0.574613\pi$
$599$	−4.07920e6	−0.464524	−0.232262	+	0.972653i	$0.574613\pi$
$600$	2.28334e6	0.258936
$601$	1.12151e7	1.26654	0.633269	−	0.773932i	$-0.281713\pi$
$601$	1.12151e7	1.26654	0.633269	+	0.773932i	$0.281713\pi$
$602$	2.04903e7	2.30439
$603$	1.72239e6	0.192902
$604$	−1.12403e7	−1.25368
$605$	−366025.	−0.0406558
$606$	1.62100e7	1.79309
$607$	−5.17748e6	−0.570357	−0.285179	−	0.958474i	$-0.592053\pi$
$607$	−5.17748e6	−0.570357	−0.285179	+	0.958474i	$0.592053\pi$
$608$	−5.59650e6	−0.613984
$609$	−1.29709e6	−0.141719
$610$	6.55419e6	0.713173
$611$	−8.32089e6	−0.901710
$612$	3.70575e6	0.399943
$613$	−1.47716e7	−1.58773	−0.793866	−	0.608093i	$-0.791935\pi$
$613$	−1.47716e7	−1.58773	−0.793866	+	0.608093i	$0.791935\pi$
$614$	1.75114e7	1.87457
$615$	2.03519e6	0.216978
$616$	−6.61333e6	−0.702213
$617$	5.40990e6	0.572105	0.286053	−	0.958214i	$-0.407657\pi$
$617$	5.40990e6	0.572105	0.286053	+	0.958214i	$0.407657\pi$
$618$	−1.14001e7	−1.20071
$619$	−1.06530e7	−1.11749	−0.558746	−	0.829339i	$-0.688717\pi$
$619$	−1.06530e7	−1.11749	−0.558746	+	0.829339i	$0.688717\pi$
$620$	−1.53838e7	−1.60725
$621$	−832408.	−0.0866178
$622$	−1.91202e7	−1.98160
$623$	6.28977e6	0.649254
$624$	5.43648e6	0.558928
$625$	390625.	0.0400000
$626$	1.87676e7	1.91413
$627$	1.06252e6	0.107937
$628$	2.81076e7	2.84397
$629$	−6.29495e6	−0.634404
$630$	−2.77834e6	−0.278891
$631$	−4.13999e6	−0.413929	−0.206964	−	0.978348i	$-0.566358\pi$
$631$	−4.13999e6	−0.413929	−0.206964	+	0.978348i	$0.566358\pi$
$632$	−2.94964e7	−2.93749
$633$	4.16790e6	0.413436
$634$	−2.29641e7	−2.26895
$635$	1.26908e6	0.124898
$636$	3.32154e6	0.325609
$637$	434537.	0.0424305
$638$	1.31978e6	0.128366
$639$	3.46714e6	0.335907
$640$	4.67932e6	0.451578
$641$	−8.19469e6	−0.787748	−0.393874	−	0.919164i	$-0.628865\pi$
$641$	−8.19469e6	−0.787748	−0.393874	+	0.919164i	$0.628865\pi$
$642$	−1.18188e7	−1.13172
$643$	−4.42289e6	−0.421870	−0.210935	−	0.977500i	$-0.567651\pi$
$643$	−4.42289e6	−0.421870	−0.210935	+	0.977500i	$0.567651\pi$
$644$	−1.10443e7	−1.04935
$645$	−3.36024e6	−0.318032
$646$	−6.33189e6	−0.596970
$647$	−3.31323e6	−0.311165	−0.155583	−	0.987823i	$-0.549725\pi$
$647$	−3.31323e6	−0.311165	−0.155583	+	0.987823i	$0.549725\pi$
$648$	2.66329e6	0.249162
$649$	2.86283e6	0.266798
$650$	2.09347e6	0.194349
$651$	1.03803e7	0.959969
$652$	−5.62610e6	−0.518309
$653$	−7.52954e6	−0.691011	−0.345506	−	0.938417i	$-0.612293\pi$
$653$	−7.52954e6	−0.691011	−0.345506	+	0.938417i	$0.612293\pi$
$654$	8.23951e6	0.753281
$655$	−720688.	−0.0656363
$656$	−1.66221e7	−1.50808
$657$	−4.22306e6	−0.381693
$658$	−3.47310e7	−3.12718
$659$	654806.	0.0587353	0.0293676	−	0.999569i	$-0.490651\pi$
$659$	654806.	0.0587353	0.0293676	+	0.999569i	$0.490651\pi$
$660$	1.95573e6	0.174763
$661$	−268318.	−0.0238861	−0.0119431	−	0.999929i	$-0.503802\pi$
$661$	−268318.	−0.0238861	−0.0119431	+	0.999929i	$0.503802\pi$
$662$	−3.80086e6	−0.337083
$663$	1.88410e6	0.166464
$664$	−2.84556e7	−2.50465
$665$	3.28425e6	0.287993
$666$	−8.15834e6	−0.712715
$667$	1.22222e6	0.106374
$668$	80063.0	0.00694210
$669$	1.21031e7	1.04552
$670$	−5.41701e6	−0.466201
$671$	3.11308e6	0.266922
$672$	6.95080e6	0.593761
$673$	1.09013e7	0.927773	0.463887	−	0.885895i	$-0.346455\pi$
$673$	1.09013e7	0.927773	0.463887	+	0.885895i	$0.346455\pi$
$674$	1.55369e7	1.31739
$675$	455625.	0.0384900
$676$	−1.89103e7	−1.59159
$677$	1.46402e7	1.22766	0.613828	−	0.789440i	$-0.289629\pi$
$677$	1.46402e7	1.22766	0.613828	+	0.789440i	$0.289629\pi$
$678$	−5.06789e6	−0.423402
$679$	2.43677e7	2.02834
$680$	−6.46307e6	−0.536002
$681$	1.15301e7	0.952718
$682$	−1.05618e7	−0.869519
$683$	3.65651e6	0.299927	0.149963	−	0.988692i	$-0.452084\pi$
$683$	3.65651e6	0.299927	0.149963	+	0.988692i	$0.452084\pi$
$684$	−5.67723e6	−0.463977
$685$	7.38378e6	0.601246
$686$	−2.12458e7	−1.72370
$687$	2.64125e6	0.213510
$688$	2.74442e7	2.21044
$689$	1.68876e6	0.135525
$690$	2.61797e6	0.209335
$691$	1.57863e7	1.25772	0.628862	−	0.777517i	$-0.283521\pi$
$691$	1.57863e7	1.25772	0.628862	+	0.777517i	$0.283521\pi$
$692$	−2.49782e7	−1.98288
$693$	−1.31964e6	−0.104382
$694$	1.29543e7	1.02098
$695$	−1.47667e6	−0.115963
$696$	−3.91051e6	−0.305992
$697$	−5.76065e6	−0.449148
$698$	−2.81495e7	−2.18691
$699$	−9.17929e6	−0.710585
$700$	6.04516e6	0.466297
$701$	2.47966e6	0.190589	0.0952945	−	0.995449i	$-0.469621\pi$
$701$	2.47966e6	0.190589	0.0952945	+	0.995449i	$0.469621\pi$
$702$	2.44182e6	0.187013
$703$	9.64390e6	0.735977
$704$	43008.6	0.00327057
$705$	5.69561e6	0.431586
$706$	−2.49090e7	−1.88080
$707$	2.37987e7	1.79063
$708$	−1.52966e7	−1.14686
$709$	−1.95693e7	−1.46204	−0.731021	−	0.682355i	$-0.760956\pi$
$709$	−1.95693e7	−1.46204	−0.731021	+	0.682355i	$0.760956\pi$
$710$	−1.09044e7	−0.811811
$711$	−5.88579e6	−0.436647
$712$	1.89626e7	1.40184
$713$	−9.78114e6	−0.720553
$714$	7.86416e6	0.577307
$715$	994346.	0.0727398
$716$	1.62692e7	1.18599
$717$	−6.34724e6	−0.461092
$718$	−1.90178e7	−1.37673
$719$	2.23668e7	1.61355	0.806775	−	0.590859i	$-0.201211\pi$
$719$	2.23668e7	1.61355	0.806775	+	0.590859i	$0.201211\pi$
$720$	−3.72124e6	−0.267520
$721$	−1.67370e7	−1.19906
$722$	−1.55309e7	−1.10880
$723$	2.29594e6	0.163348
$724$	3.39568e7	2.40758
$725$	−668994.	−0.0472691
$726$	1.34273e6	0.0945465
$727$	1.15759e6	0.0812301	0.0406151	−	0.999175i	$-0.487068\pi$
$727$	1.15759e6	0.0812301	0.0406151	+	0.999175i	$0.487068\pi$
$728$	1.79658e7	1.25637
$729$	531441.	0.0370370
$730$	1.32818e7	0.922463
$731$	9.51125e6	0.658330
$732$	−1.66337e7	−1.14739
$733$	−690471.	−0.0474663	−0.0237332	−	0.999718i	$-0.507555\pi$
$733$	−690471.	−0.0474663	−0.0237332	+	0.999718i	$0.507555\pi$
$734$	4.88293e7	3.34534
$735$	−297439.	−0.0203086
$736$	−6.54960e6	−0.445677
$737$	−2.57295e6	−0.174487
$738$	−7.46587e6	−0.504591
$739$	−1.97471e7	−1.33013	−0.665064	−	0.746787i	$-0.731596\pi$
$739$	−1.97471e7	−1.33013	−0.665064	+	0.746787i	$0.731596\pi$
$740$	1.77511e7	1.19164
$741$	−2.88645e6	−0.193116
$742$	7.04880e6	0.470008
$743$	2.32892e7	1.54768	0.773841	−	0.633380i	$-0.218333\pi$
$743$	2.32892e7	1.54768	0.773841	+	0.633380i	$0.218333\pi$
$744$	3.12948e7	2.07272
$745$	−6.20254e6	−0.409429
$746$	−2.88165e7	−1.89581
$747$	−5.67811e6	−0.372308
$748$	−5.53575e6	−0.361762
$749$	−1.73518e7	−1.13016
$750$	−1.43297e6	−0.0930215
$751$	−9.35160e6	−0.605043	−0.302521	−	0.953143i	$-0.597828\pi$
$751$	−9.35160e6	−0.605043	−0.302521	+	0.953143i	$0.597828\pi$
$752$	−4.65180e7	−2.99969
$753$	2.89410e6	0.186005
$754$	−3.58532e6	−0.229668
$755$	3.91179e6	0.249752
$756$	7.05108e6	0.448695
$757$	−5.83342e6	−0.369985	−0.184992	−	0.982740i	$-0.559226\pi$
$757$	−5.83342e6	−0.369985	−0.184992	+	0.982740i	$0.559226\pi$
$758$	3.36554e7	2.12756
$759$	1.24347e6	0.0783488
$760$	9.90145e6	0.621820
$761$	1.44516e7	0.904596	0.452298	−	0.891867i	$-0.350604\pi$
$761$	1.44516e7	0.904596	0.452298	+	0.891867i	$0.350604\pi$
$762$	−4.65548e6	−0.290454
$763$	1.20968e7	0.752246
$764$	−2.58770e7	−1.60391
$765$	−1.28966e6	−0.0796748
$766$	−5.66535e7	−3.48863
$767$	−7.77717e6	−0.477346
$768$	−1.70632e7	−1.04390
$769$	5.82446e6	0.355173	0.177586	−	0.984105i	$-0.443171\pi$
$769$	5.82446e6	0.355173	0.177586	+	0.984105i	$0.443171\pi$
$770$	4.15036e6	0.252266
$771$	1.23485e7	0.748133
$772$	1.75594e7	1.06039
$773$	−1.10046e7	−0.662407	−0.331204	−	0.943559i	$-0.607455\pi$
$773$	−1.10046e7	−0.662407	−0.331204	+	0.943559i	$0.607455\pi$
$774$	1.23267e7	0.739595
$775$	5.35378e6	0.320189
$776$	7.34644e7	4.37948
$777$	−1.19777e7	−0.711736
$778$	4.05326e7	2.40080
$779$	8.82535e6	0.521060
$780$	−5.31296e6	−0.312680
$781$	−5.17931e6	−0.303840
$782$	−7.41024e6	−0.433327
$783$	−780315.	−0.0454847
$784$	2.42928e6	0.141152
$785$	−9.78187e6	−0.566562
$786$	2.64377e6	0.152640
$787$	2.08102e7	1.19768	0.598839	−	0.800869i	$-0.295629\pi$
$787$	2.08102e7	1.19768	0.598839	+	0.800869i	$0.295629\pi$
$788$	3.88757e7	2.23030
$789$	1.52277e7	0.870849
$790$	1.85112e7	1.05528
$791$	−7.44041e6	−0.422820
$792$	−3.97850e6	−0.225375
$793$	−8.45702e6	−0.477567
$794$	4.04973e7	2.27969
$795$	−1.15595e6	−0.0648663
$796$	7.17930e7	4.01605
$797$	−3.43533e7	−1.91568	−0.957840	−	0.287301i	$-0.907242\pi$
$797$	−3.43533e7	−1.91568	−0.957840	+	0.287301i	$0.907242\pi$
$798$	−1.20479e7	−0.669739
$799$	−1.61216e7	−0.893389
$800$	3.58498e6	0.198044
$801$	3.78384e6	0.208378
$802$	−5.62836e7	−3.08991
$803$	6.30852e6	0.345254
$804$	1.37477e7	0.750050
$805$	3.84357e6	0.209048
$806$	2.86924e7	1.55571
$807$	1.47209e7	0.795701
$808$	7.17490e7	3.86623
$809$	−1.11150e7	−0.597086	−0.298543	−	0.954396i	$-0.596501\pi$
$809$	−1.11150e7	−0.597086	−0.298543	+	0.954396i	$0.596501\pi$
$810$	−1.67141e6	−0.0895100
$811$	−2.67488e7	−1.42808	−0.714039	−	0.700106i	$-0.753136\pi$
$811$	−2.67488e7	−1.42808	−0.714039	+	0.700106i	$0.753136\pi$
$812$	−1.03531e7	−0.551036
$813$	1.23702e7	0.656371
$814$	1.21871e7	0.644675
$815$	1.95797e6	0.103255
$816$	1.05331e7	0.553771
$817$	−1.45713e7	−0.763735
$818$	−3.21669e7	−1.68084
$819$	3.58495e6	0.186756
$820$	1.62444e7	0.843663
$821$	−1.05297e7	−0.545202	−0.272601	−	0.962127i	$-0.587884\pi$
$821$	−1.05297e7	−0.545202	−0.272601	+	0.962127i	$0.587884\pi$
$822$	−2.70866e7	−1.39822
$823$	−2.49743e7	−1.28527	−0.642633	−	0.766174i	$-0.722158\pi$
$823$	−2.49743e7	−1.28527	−0.642633	+	0.766174i	$0.722158\pi$
$824$	−5.04592e7	−2.58894
$825$	−680625.	−0.0348155
$826$	−3.24616e7	−1.65546
$827$	1.13990e7	0.579566	0.289783	−	0.957092i	$-0.406417\pi$
$827$	1.13990e7	0.579566	0.289783	+	0.957092i	$0.406417\pi$
$828$	−6.64409e6	−0.336790
$829$	−8.48674e6	−0.428899	−0.214449	−	0.976735i	$-0.568796\pi$
$829$	−8.48674e6	−0.428899	−0.214449	+	0.976735i	$0.568796\pi$
$830$	1.78580e7	0.899783
$831$	−9.57057e6	−0.480768
$832$	−116837.	−0.00585158
$833$	841908.	0.0420390
$834$	5.41700e6	0.269677
$835$	−27863.1	−0.00138297
$836$	8.48081e6	0.419683
$837$	6.24465e6	0.308102
$838$	−5.48247e7	−2.69691
$839$	−1.94174e7	−0.952329	−0.476165	−	0.879356i	$-0.657973\pi$
$839$	−1.94174e7	−0.952329	−0.476165	+	0.879356i	$0.657973\pi$
$840$	−1.22975e7	−0.601339
$841$	−1.93654e7	−0.944141
$842$	6.26551e7	3.04562
$843$	1.65154e7	0.800422
$844$	3.32672e7	1.60753
$845$	6.58108e6	0.317070
$846$	−2.08938e7	−1.00367
$847$	1.97132e6	0.0944166
$848$	9.44100e6	0.450846
$849$	−1.82319e6	−0.0868084
$850$	4.05605e6	0.192556
$851$	1.12863e7	0.534229
$852$	2.76739e7	1.30609
$853$	7.23170e6	0.340304	0.170152	−	0.985418i	$-0.445574\pi$
$853$	7.23170e6	0.340304	0.170152	+	0.985418i	$0.445574\pi$
$854$	−3.52993e7	−1.65623
$855$	1.97576e6	0.0924314
$856$	−5.23127e7	−2.44019
$857$	−2.59073e7	−1.20495	−0.602477	−	0.798136i	$-0.705820\pi$
$857$	−2.59073e7	−1.20495	−0.602477	+	0.798136i	$0.705820\pi$
$858$	−3.64766e6	−0.169159
$859$	6.83977e6	0.316270	0.158135	−	0.987417i	$-0.449452\pi$
$859$	6.83977e6	0.316270	0.158135	+	0.987417i	$0.449452\pi$
$860$	−2.68207e7	−1.23658
$861$	−1.09610e7	−0.503898
$862$	−1.80516e7	−0.827462
$863$	−1.68524e7	−0.770255	−0.385127	−	0.922863i	$-0.625843\pi$
$863$	−1.68524e7	−0.770255	−0.385127	+	0.922863i	$0.625843\pi$
$864$	4.18152e6	0.190568
$865$	8.69281e6	0.395021
$866$	−6.51925e6	−0.295395
$867$	−9.12830e6	−0.412422
$868$	8.28531e7	3.73258
$869$	8.79235e6	0.394962
$870$	2.45414e6	0.109926
$871$	6.98969e6	0.312186
$872$	3.64698e7	1.62421
$873$	1.46593e7	0.650995
$874$	1.13525e7	0.502706
$875$	−2.10381e6	−0.0928937
$876$	−3.37075e7	−1.48411
$877$	2.73229e7	1.19958	0.599788	−	0.800159i	$-0.295252\pi$
$877$	2.73229e7	1.19958	0.599788	+	0.800159i	$0.295252\pi$
$878$	−3.43720e7	−1.50477
$879$	−1.84673e6	−0.0806180
$880$	5.55890e6	0.241981
$881$	−7.68266e6	−0.333482	−0.166741	−	0.986001i	$-0.553324\pi$
$881$	−7.68266e6	−0.333482	−0.166741	+	0.986001i	$0.553324\pi$
$882$	1.09112e6	0.0472283
$883$	−4.15161e6	−0.179190	−0.0895951	−	0.995978i	$-0.528557\pi$
$883$	−4.15161e6	−0.179190	−0.0895951	+	0.995978i	$0.528557\pi$
$884$	1.50385e7	0.647251
$885$	5.32344e6	0.228473
$886$	2.66555e7	1.14078
$887$	2.13978e7	0.913190	0.456595	−	0.889675i	$-0.349069\pi$
$887$	2.13978e7	0.913190	0.456595	+	0.889675i	$0.349069\pi$
$888$	−3.61106e7	−1.53674
$889$	−6.83494e6	−0.290055
$890$	−1.19004e7	−0.503602
$891$	−793881.	−0.0335013
$892$	9.66043e7	4.06522
$893$	2.46983e7	1.03643
$894$	2.27534e7	0.952143
$895$	−5.66191e6	−0.236268
$896$	−2.52016e7	−1.04872
$897$	−3.37803e6	−0.140179
$898$	−6.21719e7	−2.57278
$899$	−9.16902e6	−0.378376
$900$	3.63669e6	0.149658
$901$	3.27193e6	0.134274
$902$	1.11527e7	0.456420
$903$	1.80974e7	0.738579
$904$	−2.24316e7	−0.912932
$905$	−1.18175e7	−0.479627
$906$	−1.43500e7	−0.580807
$907$	2.98758e7	1.20587	0.602936	−	0.797789i	$-0.293997\pi$
$907$	2.98758e7	1.20587	0.602936	+	0.797789i	$0.293997\pi$
$908$	9.20304e7	3.70439
$909$	1.43170e7	0.574702
$910$	−1.12749e7	−0.451345
$911$	1.11801e7	0.446323	0.223162	−	0.974781i	$-0.428362\pi$
$911$	1.11801e7	0.446323	0.223162	+	0.974781i	$0.428362\pi$
$912$	−1.61367e7	−0.642434
$913$	8.48212e6	0.336765
$914$	−3.50744e7	−1.38875
$915$	5.78879e6	0.228578
$916$	2.10818e7	0.830175
$917$	3.88145e6	0.152430
$918$	4.73098e6	0.185287
$919$	6.09049e6	0.237883	0.118941	−	0.992901i	$-0.462050\pi$
$919$	6.09049e6	0.237883	0.118941	+	0.992901i	$0.462050\pi$
$920$	1.15877e7	0.451365
$921$	1.54664e7	0.600816
$922$	−1.09692e7	−0.424961
$923$	1.40702e7	0.543619
$924$	−1.05331e7	−0.405860
$925$	−6.17764e6	−0.237393
$926$	5.92990e7	2.27258
$927$	−1.00688e7	−0.384838
$928$	−6.13972e6	−0.234034
$929$	−1.73381e7	−0.659118	−0.329559	−	0.944135i	$-0.606900\pi$
$929$	−1.73381e7	−0.659118	−0.329559	+	0.944135i	$0.606900\pi$
$930$	−1.96398e7	−0.744611
$931$	−1.28981e6	−0.0487698
$932$	−7.32670e7	−2.76292
$933$	−1.68873e7	−0.635121
$934$	8.85654e6	0.332198
$935$	1.92653e6	0.0720686
$936$	1.08080e7	0.403233
$937$	6.37937e6	0.237372	0.118686	−	0.992932i	$-0.462132\pi$
$937$	6.37937e6	0.237372	0.118686	+	0.992932i	$0.462132\pi$
$938$	2.91747e7	1.08268
$939$	1.65759e7	0.613497
$940$	4.54610e7	1.67811
$941$	−2.57786e7	−0.949041	−0.474521	−	0.880244i	$-0.657379\pi$
$941$	−2.57786e7	−0.949041	−0.474521	+	0.880244i	$0.657379\pi$
$942$	3.58838e7	1.31756
$943$	1.03283e7	0.378226
$944$	−4.34783e7	−1.58797
$945$	−2.45388e6	−0.0893870
$946$	−1.84139e7	−0.668989
$947$	1.57500e7	0.570696	0.285348	−	0.958424i	$-0.407891\pi$
$947$	1.57500e7	0.570696	0.285348	+	0.958424i	$0.407891\pi$
$948$	−4.69790e7	−1.69779
$949$	−1.71378e7	−0.617716
$950$	−6.21389e6	−0.223385
$951$	−2.02823e7	−0.727221
$952$	3.48085e7	1.24478
$953$	−1.94812e6	−0.0694837	−0.0347419	−	0.999396i	$-0.511061\pi$
$953$	−1.94812e6	−0.0694837	−0.0347419	+	0.999396i	$0.511061\pi$
$954$	4.24047e6	0.150849
$955$	9.00558e6	0.319524
$956$	−5.06622e7	−1.79283
$957$	1.16566e6	0.0411425
$958$	−2.88346e7	−1.01508
$959$	−3.97672e7	−1.39630
$960$	79974.6	0.00280075
$961$	4.47481e7	1.56303
$962$	−3.31077e7	−1.15343
$963$	−1.04386e7	−0.362725
$964$	1.83257e7	0.635137
$965$	−6.11095e6	−0.211247
$966$	−1.40998e7	−0.486148
$967$	4.61582e7	1.58739	0.793693	−	0.608319i	$-0.208156\pi$
$967$	4.61582e7	1.58739	0.793693	+	0.608319i	$0.208156\pi$
$968$	5.94319e6	0.203860
$969$	−5.59245e6	−0.191334
$970$	−4.61043e7	−1.57330
$971$	−3.05303e7	−1.03916	−0.519580	−	0.854422i	$-0.673912\pi$
$971$	−3.05303e7	−1.03916	−0.519580	+	0.854422i	$0.673912\pi$
$972$	4.24184e6	0.144009
$973$	7.95296e6	0.269306
$974$	−9.88154e7	−3.33755
$975$	1.84899e6	0.0622907
$976$	−4.72790e7	−1.58871
$977$	8.71629e6	0.292143	0.146072	−	0.989274i	$-0.453337\pi$
$977$	8.71629e6	0.292143	0.146072	+	0.989274i	$0.453337\pi$
$978$	−7.18261e6	−0.240124
$979$	−5.65241e6	−0.188485
$980$	−2.37409e6	−0.0789644
$981$	7.27730e6	0.241433
$982$	−5.14222e7	−1.70166
$983$	5.94838e7	1.96343	0.981714	−	0.190360i	$-0.0609656\pi$
$983$	5.94838e7	1.96343	0.981714	+	0.190360i	$0.0609656\pi$
$984$	−3.30456e7	−1.08799
$985$	−1.35294e7	−0.444310
$986$	−6.94650e6	−0.227548
$987$	−3.06751e7	−1.00229
$988$	−2.30390e7	−0.750882
$989$	−1.70528e7	−0.554378
$990$	2.49680e6	0.0809648
$991$	−2.48497e7	−0.803779	−0.401889	−	0.915688i	$-0.631646\pi$
$991$	−2.48497e7	−0.803779	−0.401889	+	0.915688i	$0.631646\pi$
$992$	4.91345e7	1.58529
$993$	−3.35699e6	−0.108038
$994$	5.87282e7	1.88530
$995$	−2.49851e7	−0.800060
$996$	−4.53214e7	−1.44762
$997$	−5.50375e7	−1.75356	−0.876781	−	0.480890i	$-0.840314\pi$
$997$	−5.50375e7	−1.75356	−0.876781	+	0.480890i	$0.840314\pi$
$998$	−8.44135e7	−2.68278
$999$	−7.20560e6	−0.228432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.f.1.5	✓	5
3.2	odd	2		495.6.a.j.1.1		5
5.4	even	2		825.6.a.l.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.f.1.5	✓	5	1.1	even	1	trivial
495.6.a.j.1.1		5	3.2	odd	2
825.6.a.l.1.1		5	5.4	even	2

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q+10.1900 q^{2} +9.00000 q^{3} +71.8359 q^{4} -25.0000 q^{5} +91.7099 q^{6} +134.644 q^{7} +405.928 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+10.1900 q^{2} +9.00000 q^{3} +71.8359 q^{4} -25.0000 q^{5} +91.7099 q^{6} +134.644 q^{7} +405.928 q^{8} +81.0000 q^{9} -254.750 q^{10} -121.000 q^{11} +646.523 q^{12} +328.709 q^{13} +1372.02 q^{14} -225.000 q^{15} +1837.65 q^{16} +636.868 q^{17} +825.389 q^{18} -975.686 q^{19} -1795.90 q^{20} +1211.79 q^{21} -1232.99 q^{22} -1141.85 q^{23} +3653.35 q^{24} +625.000 q^{25} +3349.55 q^{26} +729.000 q^{27} +9672.26 q^{28} -1070.39 q^{29} -2292.75 q^{30} +8566.05 q^{31} +5735.96 q^{32} -1089.00 q^{33} +6489.68 q^{34} -3366.09 q^{35} +5818.71 q^{36} -9884.23 q^{37} -9942.23 q^{38} +2958.38 q^{39} -10148.2 q^{40} -9045.27 q^{41} +12348.2 q^{42} +14934.4 q^{43} -8692.15 q^{44} -2025.00 q^{45} -11635.4 q^{46} -25313.8 q^{47} +16538.9 q^{48} +1321.95 q^{49} +6368.74 q^{50} +5731.82 q^{51} +23613.1 q^{52} +5137.53 q^{53} +7428.50 q^{54} +3025.00 q^{55} +54655.7 q^{56} -8781.17 q^{57} -10907.3 q^{58} -23659.7 q^{59} -16163.1 q^{60} -25728.0 q^{61} +87288.0 q^{62} +10906.1 q^{63} -355.443 q^{64} -8217.73 q^{65} -11096.9 q^{66} +21264.1 q^{67} +45750.0 q^{68} -10276.6 q^{69} -34300.5 q^{70} +42804.2 q^{71} +32880.2 q^{72} -52136.5 q^{73} -100720. q^{74} +5625.00 q^{75} -70089.3 q^{76} -16291.9 q^{77} +30145.9 q^{78} -72664.1 q^{79} -45941.3 q^{80} +6561.00 q^{81} -92171.3 q^{82} -70100.2 q^{83} +87050.4 q^{84} -15921.7 q^{85} +152181. q^{86} -9633.51 q^{87} -49117.3 q^{88} +46714.1 q^{89} -20634.7 q^{90} +44258.7 q^{91} -82025.8 q^{92} +77094.5 q^{93} -257948. q^{94} +24392.1 q^{95} +51623.7 q^{96} +180979. q^{97} +13470.7 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 45 q^{3} + 82 q^{4} - 125 q^{5} - 18 q^{6} + 184 q^{7} + 24 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 45 * q^3 + 82 * q^4 - 125 * q^5 - 18 * q^6 + 184 * q^7 + 24 * q^8 + 405 * q^9	\( 5 q - 2 q^{2} + 45 q^{3} + 82 q^{4} - 125 q^{5} - 18 q^{6} + 184 q^{7} + 24 q^{8} + 405 q^{9} + 50 q^{10} - 605 q^{11} + 738 q^{12} + 1082 q^{13} + 432 q^{14} - 1125 q^{15} + 4770 q^{16} + 2174 q^{17} - 162 q^{18} + 1632 q^{19} - 2050 q^{20} + 1656 q^{21} + 242 q^{22} + 1212 q^{23} + 216 q^{24} + 3125 q^{25} + 5600 q^{26} + 3645 q^{27} + 16508 q^{28} + 82 q^{29} + 450 q^{30} + 12120 q^{31} - 4864 q^{32} - 5445 q^{33} - 4524 q^{34} - 4600 q^{35} + 6642 q^{36} - 6530 q^{37} - 15132 q^{38} + 9738 q^{39} - 600 q^{40} + 6782 q^{41} + 3888 q^{42} + 46184 q^{43} - 9922 q^{44} - 10125 q^{45} + 12048 q^{46} - 11692 q^{47} + 42930 q^{48} + 34445 q^{49} - 1250 q^{50} + 19566 q^{51} + 50020 q^{52} + 10314 q^{53} - 1458 q^{54} + 15125 q^{55} + 54928 q^{56} + 14688 q^{57} + 75048 q^{58} + 92892 q^{59} - 18450 q^{60} + 106 q^{61} + 97160 q^{62} + 14904 q^{63} + 44550 q^{64} - 27050 q^{65} + 2178 q^{66} + 100476 q^{67} + 119928 q^{68} + 10908 q^{69} - 10800 q^{70} - 13772 q^{71} + 1944 q^{72} + 94154 q^{73} - 47924 q^{74} + 28125 q^{75} - 51524 q^{76} - 22264 q^{77} + 50400 q^{78} + 178744 q^{79} - 119250 q^{80} + 32805 q^{81} - 299848 q^{82} - 100116 q^{83} + 148572 q^{84} - 54350 q^{85} - 167704 q^{86} + 738 q^{87} - 2904 q^{88} + 119410 q^{89} + 4050 q^{90} + 47536 q^{91} - 404560 q^{92} + 109080 q^{93} - 310288 q^{94} - 40800 q^{95} - 43776 q^{96} + 100682 q^{97} - 16434 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 45 * q^3 + 82 * q^4 - 125 * q^5 - 18 * q^6 + 184 * q^7 + 24 * q^8 + 405 * q^9 + 50 * q^10 - 605 * q^11 + 738 * q^12 + 1082 * q^13 + 432 * q^14 - 1125 * q^15 + 4770 * q^16 + 2174 * q^17 - 162 * q^18 + 1632 * q^19 - 2050 * q^20 + 1656 * q^21 + 242 * q^22 + 1212 * q^23 + 216 * q^24 + 3125 * q^25 + 5600 * q^26 + 3645 * q^27 + 16508 * q^28 + 82 * q^29 + 450 * q^30 + 12120 * q^31 - 4864 * q^32 - 5445 * q^33 - 4524 * q^34 - 4600 * q^35 + 6642 * q^36 - 6530 * q^37 - 15132 * q^38 + 9738 * q^39 - 600 * q^40 + 6782 * q^41 + 3888 * q^42 + 46184 * q^43 - 9922 * q^44 - 10125 * q^45 + 12048 * q^46 - 11692 * q^47 + 42930 * q^48 + 34445 * q^49 - 1250 * q^50 + 19566 * q^51 + 50020 * q^52 + 10314 * q^53 - 1458 * q^54 + 15125 * q^55 + 54928 * q^56 + 14688 * q^57 + 75048 * q^58 + 92892 * q^59 - 18450 * q^60 + 106 * q^61 + 97160 * q^62 + 14904 * q^63 + 44550 * q^64 - 27050 * q^65 + 2178 * q^66 + 100476 * q^67 + 119928 * q^68 + 10908 * q^69 - 10800 * q^70 - 13772 * q^71 + 1944 * q^72 + 94154 * q^73 - 47924 * q^74 + 28125 * q^75 - 51524 * q^76 - 22264 * q^77 + 50400 * q^78 + 178744 * q^79 - 119250 * q^80 + 32805 * q^81 - 299848 * q^82 - 100116 * q^83 + 148572 * q^84 - 54350 * q^85 - 167704 * q^86 + 738 * q^87 - 2904 * q^88 + 119410 * q^89 + 4050 * q^90 + 47536 * q^91 - 404560 * q^92 + 109080 * q^93 - 310288 * q^94 - 40800 * q^95 - 43776 * q^96 + 100682 * q^97 - 16434 * q^98 - 49005 * q^99

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