LMFDB - Embedded newform 165.6.a.g.1.4

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:	$1$
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} - x^{4} - 143x^{3} + 71x^{2} + 4216x - 3740 $ x^5 - x^4 - 143x^3 + 71x^2 + 4216*x - 3740
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			1.4
Root			$-6.98466$ 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)

$f(q)$	$=$	$q+6.98466 q^{2} -9.00000 q^{3} +16.7854 q^{4} -25.0000 q^{5} -62.8619 q^{6} +180.375 q^{7} -106.269 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.98466 q^{2} -9.00000 q^{3} +16.7854 q^{4} -25.0000 q^{5} -62.8619 q^{6} +180.375 q^{7} -106.269 q^{8} +81.0000 q^{9} -174.616 q^{10} -121.000 q^{11} -151.069 q^{12} -723.324 q^{13} +1259.86 q^{14} +225.000 q^{15} -1279.38 q^{16} -1497.37 q^{17} +565.757 q^{18} +2597.31 q^{19} -419.636 q^{20} -1623.37 q^{21} -845.143 q^{22} -4063.64 q^{23} +956.417 q^{24} +625.000 q^{25} -5052.17 q^{26} -729.000 q^{27} +3027.67 q^{28} -7809.97 q^{29} +1571.55 q^{30} -49.3086 q^{31} -5535.46 q^{32} +1089.00 q^{33} -10458.6 q^{34} -4509.37 q^{35} +1359.62 q^{36} -7124.86 q^{37} +18141.4 q^{38} +6509.91 q^{39} +2656.71 q^{40} -11512.7 q^{41} -11338.7 q^{42} -6577.00 q^{43} -2031.04 q^{44} -2025.00 q^{45} -28383.2 q^{46} +17847.1 q^{47} +11514.4 q^{48} +15728.0 q^{49} +4365.41 q^{50} +13476.3 q^{51} -12141.3 q^{52} +6473.37 q^{53} -5091.81 q^{54} +3025.00 q^{55} -19168.2 q^{56} -23375.8 q^{57} -54550.0 q^{58} +3705.25 q^{59} +3776.72 q^{60} -29730.9 q^{61} -344.404 q^{62} +14610.4 q^{63} +2276.99 q^{64} +18083.1 q^{65} +7606.29 q^{66} +49220.1 q^{67} -25133.9 q^{68} +36572.8 q^{69} -31496.4 q^{70} +57748.6 q^{71} -8607.75 q^{72} +29536.1 q^{73} -49764.7 q^{74} -5625.00 q^{75} +43597.0 q^{76} -21825.3 q^{77} +45469.5 q^{78} +49032.1 q^{79} +31984.6 q^{80} +6561.00 q^{81} -80412.5 q^{82} +743.250 q^{83} -27249.0 q^{84} +37434.1 q^{85} -45938.1 q^{86} +70289.7 q^{87} +12858.5 q^{88} +26124.6 q^{89} -14143.9 q^{90} -130469. q^{91} -68210.0 q^{92} +443.777 q^{93} +124656. q^{94} -64932.9 q^{95} +49819.1 q^{96} -168631. q^{97} +109855. q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * 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 $

$2$	6.98466	1.23472	0.617362	−	0.786679i	$-0.288201\pi$
$2$	6.98466	1.23472	0.617362	+	0.786679i	$0.288201\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.7854	0.524545
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−62.8619	−0.712869
$7$	180.375	1.39133	0.695666	−	0.718366i	$-0.255109\pi$
$7$	180.375	1.39133	0.695666	+	0.718366i	$0.255109\pi$
$8$	−106.269	−0.587056
$9$	81.0000	0.333333
$10$	−174.616	−0.552186
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−151.069	−0.302846
$13$	−723.324	−1.18706	−0.593532	−	0.804810i	$-0.702267\pi$
$13$	−723.324	−1.18706	−0.593532	+	0.804810i	$0.702267\pi$
$14$	1259.86	1.71791
$15$	225.000	0.258199
$16$	−1279.38	−1.24940
$17$	−1497.37	−1.25662	−0.628312	−	0.777961i	$-0.716254\pi$
$17$	−1497.37	−1.25662	−0.628312	+	0.777961i	$0.716254\pi$
$18$	565.757	0.411575
$19$	2597.31	1.65060	0.825298	−	0.564698i	$-0.191007\pi$
$19$	2597.31	1.65060	0.825298	+	0.564698i	$0.191007\pi$
$20$	−419.636	−0.234583
$21$	−1623.37	−0.803286
$22$	−845.143	−0.372283
$23$	−4063.64	−1.60175	−0.800877	−	0.598828i	$-0.795633\pi$
$23$	−4063.64	−1.60175	−0.800877	+	0.598828i	$0.795633\pi$
$24$	956.417	0.338937
$25$	625.000	0.200000
$26$	−5052.17	−1.46570
$27$	−729.000	−0.192450
$28$	3027.67	0.729816
$29$	−7809.97	−1.72446	−0.862232	−	0.506513i	$-0.830934\pi$
$29$	−7809.97	−1.72446	−0.862232	+	0.506513i	$0.830934\pi$
$30$	1571.55	0.318804
$31$	−49.3086	−0.00921549	−0.00460775	−	0.999989i	$-0.501467\pi$
$31$	−49.3086	−0.00921549	−0.00460775	+	0.999989i	$0.501467\pi$
$32$	−5535.46	−0.955605
$33$	1089.00	0.174078
$34$	−10458.6	−1.55159
$35$	−4509.37	−0.622222
$36$	1359.62	0.174848
$37$	−7124.86	−0.855603	−0.427801	−	0.903873i	$-0.640712\pi$
$37$	−7124.86	−0.855603	−0.427801	+	0.903873i	$0.640712\pi$
$38$	18141.4	2.03803
$39$	6509.91	0.685352
$40$	2656.71	0.262540
$41$	−11512.7	−1.06959	−0.534797	−	0.844981i	$-0.679612\pi$
$41$	−11512.7	−1.06959	−0.534797	+	0.844981i	$0.679612\pi$
$42$	−11338.7	−0.991836
$43$	−6577.00	−0.542446	−0.271223	−	0.962516i	$-0.587428\pi$
$43$	−6577.00	−0.542446	−0.271223	+	0.962516i	$0.587428\pi$
$44$	−2031.04	−0.158156
$45$	−2025.00	−0.149071
$46$	−28383.2	−1.97773
$47$	17847.1	1.17848	0.589242	−	0.807956i	$-0.299426\pi$
$47$	17847.1	1.17848	0.589242	+	0.807956i	$0.299426\pi$
$48$	11514.4	0.721340
$49$	15728.0	0.935803
$50$	4365.41	0.246945
$51$	13476.3	0.725513
$52$	−12141.3	−0.622668
$53$	6473.37	0.316549	0.158274	−	0.987395i	$-0.449407\pi$
$53$	6473.37	0.316549	0.158274	+	0.987395i	$0.449407\pi$
$54$	−5091.81	−0.237623
$55$	3025.00	0.134840
$56$	−19168.2	−0.816790
$57$	−23375.8	−0.952972
$58$	−54550.0	−2.12924
$59$	3705.25	0.138576	0.0692879	−	0.997597i	$-0.477927\pi$
$59$	3705.25	0.138576	0.0692879	+	0.997597i	$0.477927\pi$
$60$	3776.72	0.135437
$61$	−29730.9	−1.02302	−0.511510	−	0.859277i	$-0.670914\pi$
$61$	−29730.9	−1.02302	−0.511510	+	0.859277i	$0.670914\pi$
$62$	−344.404	−0.0113786
$63$	14610.4	0.463777
$64$	2276.99	0.0694881
$65$	18083.1	0.530871
$66$	7606.29	0.214938
$67$	49220.1	1.33954	0.669770	−	0.742569i	$-0.266393\pi$
$67$	49220.1	1.33954	0.669770	+	0.742569i	$0.266393\pi$
$68$	−25133.9	−0.659156
$69$	36572.8	0.924774
$70$	−31496.4	−0.768273
$71$	57748.6	1.35955	0.679775	−	0.733421i	$-0.262077\pi$
$71$	57748.6	1.35955	0.679775	+	0.733421i	$0.262077\pi$
$72$	−8607.75	−0.195685
$73$	29536.1	0.648702	0.324351	−	0.945937i	$-0.394854\pi$
$73$	29536.1	0.648702	0.324351	+	0.945937i	$0.394854\pi$
$74$	−49764.7	−1.05643
$75$	−5625.00	−0.115470
$76$	43597.0	0.865811
$77$	−21825.3	−0.419502
$78$	45469.5	0.846221
$79$	49032.1	0.883920	0.441960	−	0.897035i	$-0.354283\pi$
$79$	49032.1	0.883920	0.441960	+	0.897035i	$0.354283\pi$
$80$	31984.6	0.558748
$81$	6561.00	0.111111
$82$	−80412.5	−1.32065
$83$	743.250	0.0118424	0.00592120	−	0.999982i	$-0.498115\pi$
$83$	743.250	0.0118424	0.00592120	+	0.999982i	$0.498115\pi$
$84$	−27249.0	−0.421359
$85$	37434.1	0.561980
$86$	−45938.1	−0.669772
$87$	70289.7	0.995620
$88$	12858.5	0.177004
$89$	26124.6	0.349602	0.174801	−	0.984604i	$-0.444072\pi$
$89$	26124.6	0.349602	0.174801	+	0.984604i	$0.444072\pi$
$90$	−14143.9	−0.184062
$91$	−130469.	−1.65160
$92$	−68210.0	−0.840192
$93$	443.777	0.00532057
$94$	124656.	1.45510
$95$	−64932.9	−0.738169
$96$	49819.1	0.551719
$97$	−168631.	−1.81973	−0.909866	−	0.414902i	$-0.863816\pi$
$97$	−168631.	−1.81973	−0.909866	+	0.414902i	$0.863816\pi$
$98$	109855.	1.15546
$99$	−9801.00	−0.100504
$100$	10490.9	0.104909
$101$	103296.	1.00758	0.503791	−	0.863826i	$-0.331938\pi$
$101$	103296.	1.00758	0.503791	+	0.863826i	$0.331938\pi$
$102$	94127.3	0.895808
$103$	−11423.2	−0.106095	−0.0530476	−	0.998592i	$-0.516893\pi$
$103$	−11423.2	−0.106095	−0.0530476	+	0.998592i	$0.516893\pi$
$104$	76866.6	0.696874
$105$	40584.3	0.359240
$106$	45214.3	0.390851
$107$	−73260.6	−0.618602	−0.309301	−	0.950964i	$-0.600095\pi$
$107$	−73260.6	−0.618602	−0.309301	+	0.950964i	$0.600095\pi$
$108$	−12236.6	−0.100949
$109$	−145295.	−1.17135	−0.585673	−	0.810547i	$-0.699170\pi$
$109$	−145295.	−1.17135	−0.585673	+	0.810547i	$0.699170\pi$
$110$	21128.6	0.166490
$111$	64123.8	0.493982
$112$	−230768.	−1.73833
$113$	−171026.	−1.25999	−0.629994	−	0.776600i	$-0.716943\pi$
$113$	−171026.	−1.25999	−0.629994	+	0.776600i	$0.716943\pi$
$114$	−163272.	−1.17666
$115$	101591.	0.716326
$116$	−131094.	−0.904559
$117$	−58589.2	−0.395688
$118$	25879.9	0.171103
$119$	−270087.	−1.74838
$120$	−23910.4	−0.151577
$121$	14641.0	0.0909091
$122$	−207660.	−1.26315
$123$	103615.	0.617530
$124$	−827.666	−0.00483394
$125$	−15625.0	−0.0894427
$126$	102048.	0.572637
$127$	212105.	1.16692	0.583461	−	0.812141i	$-0.301698\pi$
$127$	212105.	1.16692	0.583461	+	0.812141i	$0.301698\pi$
$128$	193039.	1.04140
$129$	59193.0	0.313182
$130$	126304.	0.655480
$131$	−255672.	−1.30168	−0.650841	−	0.759214i	$-0.725584\pi$
$131$	−255672.	−1.30168	−0.650841	+	0.759214i	$0.725584\pi$
$132$	18279.3	0.0913115
$133$	468490.	2.29653
$134$	343786.	1.65396
$135$	18225.0	0.0860663
$136$	159123.	0.737710
$137$	189514.	0.862661	0.431330	−	0.902194i	$-0.358044\pi$
$137$	189514.	0.862661	0.431330	+	0.902194i	$0.358044\pi$
$138$	255448.	1.14184
$139$	−169681.	−0.744896	−0.372448	−	0.928053i	$-0.621481\pi$
$139$	−169681.	−0.744896	−0.372448	+	0.928053i	$0.621481\pi$
$140$	−75691.7	−0.326383
$141$	−160624.	−0.680398
$142$	403354.	1.67867
$143$	87522.2	0.357913
$144$	−103630.	−0.416466
$145$	195249.	0.771204
$146$	206299.	0.800969
$147$	−141552.	−0.540286
$148$	−119594.	−0.448802
$149$	443084.	1.63501	0.817505	−	0.575922i	$-0.195357\pi$
$149$	443084.	1.63501	0.817505	+	0.575922i	$0.195357\pi$
$150$	−39288.7	−0.142574
$151$	293669.	1.04813	0.524067	−	0.851677i	$-0.324414\pi$
$151$	293669.	1.04813	0.524067	+	0.851677i	$0.324414\pi$
$152$	−276013.	−0.968992
$153$	−121287.	−0.418875
$154$	−152443.	−0.517970
$155$	1232.72	0.00412129
$156$	109272.	0.359498
$157$	−161893.	−0.524178	−0.262089	−	0.965044i	$-0.584411\pi$
$157$	−161893.	−0.524178	−0.262089	+	0.965044i	$0.584411\pi$
$158$	342472.	1.09140
$159$	−58260.3	−0.182760
$160$	138386.	0.427360
$161$	−732979.	−2.22857
$162$	45826.3	0.137192
$163$	522298.	1.53975	0.769873	−	0.638197i	$-0.220319\pi$
$163$	522298.	1.53975	0.769873	+	0.638197i	$0.220319\pi$
$164$	−193246.	−0.561049
$165$	−27225.0	−0.0778499
$166$	5191.35	0.0146221
$167$	−248213.	−0.688705	−0.344353	−	0.938840i	$-0.611902\pi$
$167$	−248213.	−0.688705	−0.344353	+	0.938840i	$0.611902\pi$
$168$	172513.	0.471574
$169$	151904.	0.409122
$170$	261465.	0.693890
$171$	210382.	0.550198
$172$	−110398.	−0.284537
$173$	−50068.3	−0.127188	−0.0635942	−	0.997976i	$-0.520256\pi$
$173$	−50068.3	−0.127188	−0.0635942	+	0.997976i	$0.520256\pi$
$174$	490950.	1.22932
$175$	112734.	0.278266
$176$	154805.	0.376708
$177$	−33347.3	−0.0800068
$178$	182471.	0.431662
$179$	−611282.	−1.42597	−0.712983	−	0.701182i	$-0.752656\pi$
$179$	−611282.	−1.42597	−0.712983	+	0.701182i	$0.752656\pi$
$180$	−33990.5	−0.0781945
$181$	−127969.	−0.290341	−0.145171	−	0.989407i	$-0.546373\pi$
$181$	−127969.	−0.290341	−0.145171	+	0.989407i	$0.546373\pi$
$182$	−911283.	−2.03927
$183$	267578.	0.590641
$184$	431838.	0.940320
$185$	178122.	0.382637
$186$	3099.63	0.00656943
$187$	181181.	0.378887
$188$	299572.	0.618168
$189$	−131493.	−0.267762
$190$	−453534.	−0.911435
$191$	65436.1	0.129788	0.0648939	−	0.997892i	$-0.479329\pi$
$191$	65436.1	0.129788	0.0648939	+	0.997892i	$0.479329\pi$
$192$	−20492.9	−0.0401190
$193$	−792553.	−1.53156	−0.765782	−	0.643100i	$-0.777648\pi$
$193$	−792553.	−1.53156	−0.765782	+	0.643100i	$0.777648\pi$
$194$	−1.17783e6	−2.24687
$195$	−162748.	−0.306499
$196$	264002.	0.490871
$197$	−545658.	−1.00174	−0.500870	−	0.865523i	$-0.666987\pi$
$197$	−545658.	−1.00174	−0.500870	+	0.865523i	$0.666987\pi$
$198$	−68456.6	−0.124094
$199$	−410972.	−0.735663	−0.367832	−	0.929892i	$-0.619900\pi$
$199$	−410972.	−0.735663	−0.367832	+	0.929892i	$0.619900\pi$
$200$	−66417.8	−0.117411
$201$	−442981.	−0.773384
$202$	721487.	1.24409
$203$	−1.40872e6	−2.39930
$204$	226205.	0.380564
$205$	287818.	0.478337
$206$	−79787.3	−0.130998
$207$	−329155.	−0.533918
$208$	925408.	1.48312
$209$	−314275.	−0.497673
$210$	283468.	0.443563
$211$	991401.	1.53300	0.766502	−	0.642242i	$-0.221995\pi$
$211$	991401.	1.53300	0.766502	+	0.642242i	$0.221995\pi$
$212$	108658.	0.166044
$213$	−519737.	−0.784937
$214$	−511700.	−0.763803
$215$	164425.	0.242589
$216$	77469.8	0.112979
$217$	−8894.03	−0.0128218
$218$	−1.01484e6	−1.44629
$219$	−265825.	−0.374529
$220$	50775.9	0.0707296
$221$	1.08308e6	1.49169
$222$	447882.	0.609932
$223$	−196875.	−0.265112	−0.132556	−	0.991176i	$-0.542318\pi$
$223$	−196875.	−0.265112	−0.132556	+	0.991176i	$0.542318\pi$
$224$	−998457.	−1.32956
$225$	50625.0	0.0666667
$226$	−1.19456e6	−1.55574
$227$	615049.	0.792218	0.396109	−	0.918203i	$-0.370360\pi$
$227$	615049.	0.792218	0.396109	+	0.918203i	$0.370360\pi$
$228$	−392373.	−0.499876
$229$	−1.15138e6	−1.45087	−0.725435	−	0.688291i	$-0.758361\pi$
$229$	−1.15138e6	−1.45087	−0.725435	+	0.688291i	$0.758361\pi$
$230$	709579.	0.884466
$231$	196428.	0.242200
$232$	829954.	1.01236
$233$	−731772.	−0.883051	−0.441526	−	0.897249i	$-0.645563\pi$
$233$	−731772.	−0.883051	−0.441526	+	0.897249i	$0.645563\pi$
$234$	−409226.	−0.488566
$235$	−446178.	−0.527034
$236$	62194.2	0.0726892
$237$	−441289.	−0.510331
$238$	−1.88646e6	−2.15877
$239$	1.11010e6	1.25709	0.628547	−	0.777772i	$-0.283650\pi$
$239$	1.11010e6	1.25709	0.628547	+	0.777772i	$0.283650\pi$
$240$	−287861.	−0.322593
$241$	757561.	0.840186	0.420093	−	0.907481i	$-0.361998\pi$
$241$	757561.	0.840186	0.420093	+	0.907481i	$0.361998\pi$
$242$	102262.	0.112248
$243$	−59049.0	−0.0641500
$244$	−499047.	−0.536619
$245$	−393201.	−0.418504
$246$	723712.	0.762479
$247$	−1.87870e6	−1.95936
$248$	5239.95	0.00541001
$249$	−6689.25	−0.00683721
$250$	−109135.	−0.110437
$251$	−1.46080e6	−1.46354	−0.731771	−	0.681551i	$-0.761306\pi$
$251$	−1.46080e6	−1.46354	−0.731771	+	0.681551i	$0.761306\pi$
$252$	245241.	0.243272
$253$	491701.	0.482947
$254$	1.48148e6	1.44083
$255$	−336907.	−0.324459
$256$	1.27544e6	1.21636
$257$	−1.81907e6	−1.71798	−0.858989	−	0.511994i	$-0.828907\pi$
$257$	−1.81907e6	−1.71798	−0.858989	+	0.511994i	$0.828907\pi$
$258$	413443.	0.386693
$259$	−1.28515e6	−1.19043
$260$	303532.	0.278466
$261$	−632608.	−0.574822
$262$	−1.78578e6	−1.60722
$263$	−1.57427e6	−1.40343	−0.701715	−	0.712458i	$-0.747582\pi$
$263$	−1.57427e6	−1.40343	−0.701715	+	0.712458i	$0.747582\pi$
$264$	−115726.	−0.102193
$265$	−161834.	−0.141565
$266$	3.27224e6	2.83558
$267$	−235121.	−0.201843
$268$	826181.	0.702648
$269$	1.95785e6	1.64967	0.824837	−	0.565370i	$-0.191267\pi$
$269$	1.95785e6	1.64967	0.824837	+	0.565370i	$0.191267\pi$
$270$	127295.	0.106268
$271$	879840.	0.727747	0.363873	−	0.931448i	$-0.381454\pi$
$271$	879840.	0.727747	0.363873	+	0.931448i	$0.381454\pi$
$272$	1.91570e6	1.57002
$273$	1.17422e6	0.953552
$274$	1.32369e6	1.06515
$275$	−75625.0	−0.0603023
$276$	613890.	0.485085
$277$	1.09778e6	0.859642	0.429821	−	0.902914i	$-0.358577\pi$
$277$	1.09778e6	0.859642	0.429821	+	0.902914i	$0.358577\pi$
$278$	−1.18516e6	−0.919741
$279$	−3994.00	−0.00307183
$280$	479204.	0.365280
$281$	2.09685e6	1.58417	0.792085	−	0.610411i	$-0.208996\pi$
$281$	2.09685e6	1.58417	0.792085	+	0.610411i	$0.208996\pi$
$282$	−1.12191e6	−0.840105
$283$	−1.02093e6	−0.757753	−0.378877	−	0.925447i	$-0.623690\pi$
$283$	−1.02093e6	−0.757753	−0.378877	+	0.925447i	$0.623690\pi$
$284$	969334.	0.713145
$285$	584396.	0.426182
$286$	611312.	0.441924
$287$	−2.07661e6	−1.48816
$288$	−448372.	−0.318535
$289$	822247.	0.579105
$290$	1.36375e6	0.952225
$291$	1.51768e6	1.05062
$292$	495776.	0.340273
$293$	−1.55421e6	−1.05765	−0.528823	−	0.848732i	$-0.677366\pi$
$293$	−1.55421e6	−1.05765	−0.528823	+	0.848732i	$0.677366\pi$
$294$	−988695.	−0.667105
$295$	−92631.3	−0.0619730
$296$	757149.	0.502287
$297$	88209.0	0.0580259
$298$	3.09479e6	2.01879
$299$	2.93933e6	1.90139
$300$	−94418.0	−0.0605692
$301$	−1.18633e6	−0.754723
$302$	2.05118e6	1.29416
$303$	−929664.	−0.581728
$304$	−3.32296e6	−2.06225
$305$	743273.	0.457508
$306$	−847145.	−0.517195
$307$	−597590.	−0.361874	−0.180937	−	0.983495i	$-0.557913\pi$
$307$	−597590.	−0.361874	−0.180937	+	0.983495i	$0.557913\pi$
$308$	−366348.	−0.220048
$309$	102809.	0.0612540
$310$	8610.09	0.00508866
$311$	−1.70219e6	−0.997945	−0.498973	−	0.866618i	$-0.666289\pi$
$311$	−1.70219e6	−0.997945	−0.498973	+	0.866618i	$0.666289\pi$
$312$	−691799.	−0.402340
$313$	3.21871e6	1.85704	0.928520	−	0.371283i	$-0.121082\pi$
$313$	3.21871e6	1.85704	0.928520	+	0.371283i	$0.121082\pi$
$314$	−1.13077e6	−0.647216
$315$	−365259.	−0.207407
$316$	823025.	0.463655
$317$	−567904.	−0.317415	−0.158707	−	0.987326i	$-0.550733\pi$
$317$	−567904.	−0.317415	−0.158707	+	0.987326i	$0.550733\pi$
$318$	−406928.	−0.225658
$319$	945006.	0.519946
$320$	−56924.7	−0.0310760
$321$	659346.	0.357150
$322$	−5.11960e6	−2.75167
$323$	−3.88913e6	−2.07418
$324$	110129.	0.0582827
$325$	−452077.	−0.237413
$326$	3.64807e6	1.90116
$327$	1.30766e6	0.676277
$328$	1.22344e6	0.627912
$329$	3.21917e6	1.63966
$330$	−190157.	−0.0961232
$331$	−344808.	−0.172985	−0.0864923	−	0.996253i	$-0.527566\pi$
$331$	−344808.	−0.172985	−0.0864923	+	0.996253i	$0.527566\pi$
$332$	12475.8	0.00621187
$333$	−577114.	−0.285201
$334$	−1.73368e6	−0.850362
$335$	−1.23050e6	−0.599060
$336$	2.07692e6	1.00362
$337$	2.60363e6	1.24884	0.624418	−	0.781091i	$-0.285336\pi$
$337$	2.60363e6	1.24884	0.624418	+	0.781091i	$0.285336\pi$
$338$	1.06100e6	0.505153
$339$	1.53923e6	0.727454
$340$	628348.	0.294783
$341$	5966.34	0.00277858
$342$	1.46945e6	0.679343
$343$	−194615.	−0.0893186
$344$	698929.	0.318447
$345$	−914320.	−0.413571
$346$	−349710.	−0.157043
$347$	−1.88948e6	−0.842399	−0.421199	−	0.906968i	$-0.638391\pi$
$347$	−1.88948e6	−0.842399	−0.421199	+	0.906968i	$0.638391\pi$
$348$	1.17984e6	0.522247
$349$	−3.19675e6	−1.40490	−0.702450	−	0.711733i	$-0.747911\pi$
$349$	−3.19675e6	−1.40490	−0.702450	+	0.711733i	$0.747911\pi$
$350$	787410.	0.343582
$351$	527303.	0.228451
$352$	669790.	0.288126
$353$	3.41779e6	1.45985	0.729925	−	0.683527i	$-0.239555\pi$
$353$	3.41779e6	1.45985	0.729925	+	0.683527i	$0.239555\pi$
$354$	−232919.	−0.0987864
$355$	−1.44371e6	−0.608009
$356$	438512.	0.183382
$357$	2.43078e6	1.00943
$358$	−4.26959e6	−1.76067
$359$	1.87234e6	0.766740	0.383370	−	0.923595i	$-0.374763\pi$
$359$	1.87234e6	0.766740	0.383370	+	0.923595i	$0.374763\pi$
$360$	215194.	0.0875132
$361$	4.26995e6	1.72446
$362$	−893821.	−0.358492
$363$	−131769.	−0.0524864
$364$	−2.18998e6	−0.866338
$365$	−738402.	−0.290109
$366$	1.86894e6	0.729279
$367$	−649772.	−0.251823	−0.125912	−	0.992041i	$-0.540186\pi$
$367$	−649772.	−0.251823	−0.125912	+	0.992041i	$0.540186\pi$
$368$	5.19896e6	2.00123
$369$	−932531.	−0.356531
$370$	1.24412e6	0.472452
$371$	1.16763e6	0.440424
$372$	7449.00	0.00279087
$373$	−585514.	−0.217904	−0.108952	−	0.994047i	$-0.534749\pi$
$373$	−585514.	−0.217904	−0.108952	+	0.994047i	$0.534749\pi$
$374$	1.26549e6	0.467821
$375$	140625.	0.0516398
$376$	−1.89659e6	−0.691837
$377$	5.64914e6	2.04705
$378$	−918435.	−0.330612
$379$	1.71635e6	0.613774	0.306887	−	0.951746i	$-0.400713\pi$
$379$	1.71635e6	0.613774	0.306887	+	0.951746i	$0.400713\pi$
$380$	−1.08993e6	−0.387202
$381$	−1.90895e6	−0.673723
$382$	457048.	0.160252
$383$	−523779.	−0.182453	−0.0912265	−	0.995830i	$-0.529079\pi$
$383$	−523779.	−0.182453	−0.0912265	+	0.995830i	$0.529079\pi$
$384$	−1.73735e6	−0.601255
$385$	545634.	0.187607
$386$	−5.53571e6	−1.89106
$387$	−532737.	−0.180815
$388$	−2.83054e6	−0.954531
$389$	84020.2	0.0281520	0.0140760	−	0.999901i	$-0.495519\pi$
$389$	84020.2	0.0281520	0.0140760	+	0.999901i	$0.495519\pi$
$390$	−1.13674e6	−0.378441
$391$	6.08476e6	2.01280
$392$	−1.67140e6	−0.549369
$393$	2.30105e6	0.751526
$394$	−3.81123e6	−1.23687
$395$	−1.22580e6	−0.395301
$396$	−164514.	−0.0527187
$397$	−1.97238e6	−0.628078	−0.314039	−	0.949410i	$-0.601682\pi$
$397$	−1.97238e6	−0.628078	−0.314039	+	0.949410i	$0.601682\pi$
$398$	−2.87050e6	−0.908341
$399$	−4.21641e6	−1.32590
$400$	−799614.	−0.249880
$401$	−2.34914e6	−0.729539	−0.364769	−	0.931098i	$-0.618852\pi$
$401$	−2.34914e6	−0.729539	−0.364769	+	0.931098i	$0.618852\pi$
$402$	−3.09407e6	−0.954916
$403$	35666.1	0.0109394
$404$	1.73387e6	0.528522
$405$	−164025.	−0.0496904
$406$	−9.83943e6	−2.96248
$407$	862108.	0.257974
$408$	−1.43211e6	−0.425917
$409$	859133.	0.253952	0.126976	−	0.991906i	$-0.459473\pi$
$409$	859133.	0.253952	0.126976	+	0.991906i	$0.459473\pi$
$410$	2.01031e6	0.590614
$411$	−1.70563e6	−0.498058
$412$	−191744.	−0.0556516
$413$	668334.	0.192805
$414$	−2.29904e6	−0.659242
$415$	−18581.3	−0.00529608
$416$	4.00393e6	1.13437
$417$	1.52713e6	0.430066
$418$	−2.19510e6	−0.614489
$419$	776183.	0.215988	0.107994	−	0.994152i	$-0.465557\pi$
$419$	776183.	0.215988	0.107994	+	0.994152i	$0.465557\pi$
$420$	681225.	0.188438
$421$	−456631.	−0.125563	−0.0627813	−	0.998027i	$-0.519997\pi$
$421$	−456631.	−0.125563	−0.0627813	+	0.998027i	$0.519997\pi$
$422$	6.92460e6	1.89284
$423$	1.44562e6	0.392828
$424$	−687915.	−0.185832
$425$	−935854.	−0.251325
$426$	−3.63018e6	−0.969181
$427$	−5.36271e6	−1.42336
$428$	−1.22971e6	−0.324484
$429$	−787699.	−0.206641
$430$	1.14845e6	0.299531
$431$	5.65041e6	1.46517	0.732583	−	0.680678i	$-0.238315\pi$
$431$	5.65041e6	1.46517	0.732583	+	0.680678i	$0.238315\pi$
$432$	932670.	0.240447
$433$	2.32866e6	0.596879	0.298439	−	0.954429i	$-0.403534\pi$
$433$	2.32866e6	0.596879	0.298439	+	0.954429i	$0.403534\pi$
$434$	−62121.7	−0.0158314
$435$	−1.75724e6	−0.445255
$436$	−2.43884e6	−0.614423
$437$	−1.05546e7	−2.64385
$438$	−1.85669e6	−0.462440
$439$	4.11939e6	1.02017	0.510084	−	0.860124i	$-0.329614\pi$
$439$	4.11939e6	1.02017	0.510084	+	0.860124i	$0.329614\pi$
$440$	−321462.	−0.0791587
$441$	1.27397e6	0.311934
$442$	7.56494e6	1.84183
$443$	−5.57812e6	−1.35045	−0.675225	−	0.737612i	$-0.735953\pi$
$443$	−5.57812e6	−1.35045	−0.675225	+	0.737612i	$0.735953\pi$
$444$	1.07634e6	0.259116
$445$	−653114.	−0.156347
$446$	−1.37511e6	−0.327340
$447$	−3.98776e6	−0.943973
$448$	410711.	0.0966810
$449$	−5.16659e6	−1.20945	−0.604725	−	0.796434i	$-0.706717\pi$
$449$	−5.16659e6	−1.20945	−0.604725	+	0.796434i	$0.706717\pi$
$450$	353598.	0.0823150
$451$	1.39304e6	0.322495
$452$	−2.87075e6	−0.660920
$453$	−2.64303e6	−0.605140
$454$	4.29590e6	0.978171
$455$	3.26173e6	0.738618
$456$	2.48412e6	0.559448
$457$	−6.97274e6	−1.56176	−0.780878	−	0.624684i	$-0.785228\pi$
$457$	−6.97274e6	−1.56176	−0.780878	+	0.624684i	$0.785228\pi$
$458$	−8.04196e6	−1.79142
$459$	1.09158e6	0.241838
$460$	1.70525e6	0.375745
$461$	256337.	0.0561770	0.0280885	−	0.999605i	$-0.491058\pi$
$461$	256337.	0.0561770	0.0280885	+	0.999605i	$0.491058\pi$
$462$	1.37198e6	0.299050
$463$	1.18528e6	0.256961	0.128481	−	0.991712i	$-0.458990\pi$
$463$	1.18528e6	0.256961	0.128481	+	0.991712i	$0.458990\pi$
$464$	9.99194e6	2.15454
$465$	−11094.4	−0.00237943
$466$	−5.11117e6	−1.09032
$467$	2.04974e6	0.434917	0.217458	−	0.976070i	$-0.430223\pi$
$467$	2.04974e6	0.434917	0.217458	+	0.976070i	$0.430223\pi$
$468$	−983445.	−0.207556
$469$	8.87806e6	1.86374
$470$	−3.11640e6	−0.650742
$471$	1.45704e6	0.302634
$472$	−393752.	−0.0813519
$473$	795817.	0.163554
$474$	−3.08225e6	−0.630119
$475$	1.62332e6	0.330119
$476$	−4.53353e6	−0.917104
$477$	524343.	0.105516
$478$	7.75368e6	1.55216
$479$	2.11658e6	0.421499	0.210750	−	0.977540i	$-0.432410\pi$
$479$	2.11658e6	0.421499	0.210750	+	0.977540i	$0.432410\pi$
$480$	−1.24548e6	−0.246736
$481$	5.15358e6	1.01566
$482$	5.29131e6	1.03740
$483$	6.59681e6	1.28667
$484$	245755.	0.0476859
$485$	4.21577e6	0.813809
$486$	−412437.	−0.0792076
$487$	−2.14041e6	−0.408955	−0.204477	−	0.978871i	$-0.565549\pi$
$487$	−2.14041e6	−0.408955	−0.204477	+	0.978871i	$0.565549\pi$
$488$	3.15946e6	0.600570
$489$	−4.70068e6	−0.888973
$490$	−2.74638e6	−0.516737
$491$	−3.53224e6	−0.661221	−0.330611	−	0.943767i	$-0.607255\pi$
$491$	−3.53224e6	−0.661221	−0.330611	+	0.943767i	$0.607255\pi$
$492$	1.73921e6	0.323922
$493$	1.16944e7	2.16700
$494$	−1.31221e7	−2.41927
$495$	245025.	0.0449467
$496$	63084.6	0.0115138
$497$	1.04164e7	1.89159
$498$	−46722.1	−0.00844208
$499$	−1.39307e6	−0.250451	−0.125225	−	0.992128i	$-0.539965\pi$
$499$	−1.39307e6	−0.250451	−0.125225	+	0.992128i	$0.539965\pi$
$500$	−262272.	−0.0469167
$501$	2.23392e6	0.397624
$502$	−1.02032e7	−1.80707
$503$	−1.47163e6	−0.259346	−0.129673	−	0.991557i	$-0.541393\pi$
$503$	−1.47163e6	−0.259346	−0.129673	+	0.991557i	$0.541393\pi$
$504$	−1.55262e6	−0.272263
$505$	−2.58240e6	−0.450604
$506$	3.43436e6	0.596307
$507$	−1.36714e6	−0.236207
$508$	3.56027e6	0.612103
$509$	−3.93710e6	−0.673569	−0.336785	−	0.941582i	$-0.609339\pi$
$509$	−3.93710e6	−0.673569	−0.336785	+	0.941582i	$0.609339\pi$
$510$	−2.35318e6	−0.400618
$511$	5.32756e6	0.902560
$512$	2.73131e6	0.460464
$513$	−1.89344e6	−0.317657
$514$	−1.27056e7	−2.12123
$515$	285580.	0.0474472
$516$	993580.	0.164278
$517$	−2.15950e6	−0.355327
$518$	−8.97630e6	−1.46985
$519$	450615.	0.0734323
$520$	−1.92166e6	−0.311651
$521$	−5.29757e6	−0.855033	−0.427516	−	0.904008i	$-0.640611\pi$
$521$	−5.29757e6	−0.855033	−0.427516	+	0.904008i	$0.640611\pi$
$522$	−4.41855e6	−0.709746
$523$	376869.	0.0602471	0.0301235	−	0.999546i	$-0.490410\pi$
$523$	376869.	0.0602471	0.0301235	+	0.999546i	$0.490410\pi$
$524$	−4.29156e6	−0.682790
$525$	−1.01461e6	−0.160657
$526$	−1.09958e7	−1.73285
$527$	73833.0	0.0115804
$528$	−1.39325e6	−0.217492
$529$	1.00769e7	1.56562
$530$	−1.13036e6	−0.174794
$531$	300125.	0.0461920
$532$	7.86381e6	1.20463
$533$	8.32743e6	1.26968
$534$	−1.64224e6	−0.249220
$535$	1.83152e6	0.276647
$536$	−5.23055e6	−0.786385
$537$	5.50154e6	0.823281
$538$	1.36749e7	2.03689
$539$	−1.90309e6	−0.282155
$540$	305914.	0.0451456
$541$	−1.28518e7	−1.88787	−0.943936	−	0.330129i	$-0.892908\pi$
$541$	−1.28518e7	−1.88787	−0.943936	+	0.330129i	$0.892908\pi$
$542$	6.14538e6	0.898567
$543$	1.15172e6	0.167629
$544$	8.28860e6	1.20084
$545$	3.63238e6	0.523842
$546$	8.20155e6	1.17737
$547$	−10590.3	−0.00151335	−0.000756674	−	1.00000i	$-0.500241\pi$
$547$	−10590.3	−0.00151335	−0.000756674		1.00000i	$0.500241\pi$
$548$	3.18108e6	0.452504
$549$	−2.40821e6	−0.341007
$550$	−528215.	−0.0744567
$551$	−2.02849e7	−2.84639
$552$	−3.88654e6	−0.542894
$553$	8.84415e6	1.22983
$554$	7.66764e6	1.06142
$555$	−1.60309e6	−0.220916
$556$	−2.84816e6	−0.390731
$557$	−7.71122e6	−1.05314	−0.526568	−	0.850133i	$-0.676522\pi$
$557$	−7.71122e6	−1.05314	−0.526568	+	0.850133i	$0.676522\pi$
$558$	−27896.7	−0.00379286
$559$	4.75730e6	0.643919
$560$	5.76921e6	0.777403
$561$	−1.63063e6	−0.218750
$562$	1.46458e7	1.95601
$563$	975605.	0.129719	0.0648594	−	0.997894i	$-0.479340\pi$
$563$	975605.	0.129719	0.0648594	+	0.997894i	$0.479340\pi$
$564$	−2.69615e6	−0.356899
$565$	4.27565e6	0.563484
$566$	−7.13081e6	−0.935616
$567$	1.18344e6	0.154592
$568$	−6.13686e6	−0.798133
$569$	7.76144e6	1.00499	0.502495	−	0.864580i	$-0.332415\pi$
$569$	7.76144e6	1.00499	0.502495	+	0.864580i	$0.332415\pi$
$570$	4.08180e6	0.526217
$571$	−1.19340e7	−1.53178	−0.765892	−	0.642970i	$-0.777702\pi$
$571$	−1.19340e7	−1.53178	−0.765892	+	0.642970i	$0.777702\pi$
$572$	1.46910e6	0.187742
$573$	−588925.	−0.0749330
$574$	−1.45044e7	−1.83747
$575$	−2.53978e6	−0.320351
$576$	184436.	0.0231627
$577$	9.85504e6	1.23231	0.616154	−	0.787626i	$-0.288690\pi$
$577$	9.85504e6	1.23231	0.616154	+	0.787626i	$0.288690\pi$
$578$	5.74311e6	0.715036
$579$	7.13298e6	0.884249
$580$	3.27734e6	0.404531
$581$	134064.	0.0164767
$582$	1.06005e7	1.29723
$583$	−783277.	−0.0954430
$584$	−3.13876e6	−0.380825
$585$	1.46473e6	0.176957
$586$	−1.08556e7	−1.30590
$587$	331905.	0.0397574	0.0198787	−	0.999802i	$-0.493672\pi$
$587$	331905.	0.0397574	0.0198787	+	0.999802i	$0.493672\pi$
$588$	−2.37602e6	−0.283404
$589$	−128070.	−0.0152110
$590$	−646998.	−0.0765196
$591$	4.91092e6	0.578355
$592$	9.11543e6	1.06899
$593$	−1.66994e7	−1.95013	−0.975067	−	0.221912i	$-0.928770\pi$
$593$	−1.66994e7	−1.95013	−0.975067	+	0.221912i	$0.928770\pi$
$594$	616110.	0.0716460
$595$	6.75217e6	0.781900
$596$	7.43735e6	0.857636
$597$	3.69874e6	0.424735
$598$	2.05302e7	2.34769
$599$	1.27832e7	1.45570	0.727850	−	0.685736i	$-0.240520\pi$
$599$	1.27832e7	1.45570	0.727850	+	0.685736i	$0.240520\pi$
$600$	597761.	0.0677874
$601$	−1.57381e7	−1.77732	−0.888661	−	0.458565i	$-0.848364\pi$
$601$	−1.57381e7	−1.77732	−0.888661	+	0.458565i	$0.848364\pi$
$602$	−8.28607e6	−0.931875
$603$	3.98683e6	0.446513
$604$	4.92937e6	0.549793
$605$	−366025.	−0.0406558
$606$	−6.49339e6	−0.718273
$607$	−8.51656e6	−0.938194	−0.469097	−	0.883147i	$-0.655421\pi$
$607$	−8.51656e6	−0.938194	−0.469097	+	0.883147i	$0.655421\pi$
$608$	−1.43773e7	−1.57732
$609$	1.26785e7	1.38524
$610$	5.19151e6	0.564897
$611$	−1.29093e7	−1.39894
$612$	−2.03585e6	−0.219719
$613$	−358790.	−0.0385647	−0.0192823	−	0.999814i	$-0.506138\pi$
$613$	−358790.	−0.0385647	−0.0192823	+	0.999814i	$0.506138\pi$
$614$	−4.17396e6	−0.446815
$615$	−2.59036e6	−0.276168
$616$	2.31935e6	0.246271
$617$	−1.00136e7	−1.05896	−0.529478	−	0.848324i	$-0.677612\pi$
$617$	−1.00136e7	−1.05896	−0.529478	+	0.848324i	$0.677612\pi$
$618$	718085.	0.0756319
$619$	−509128.	−0.0534072	−0.0267036	−	0.999643i	$-0.508501\pi$
$619$	−509128.	−0.0534072	−0.0267036	+	0.999643i	$0.508501\pi$
$620$	20691.7	0.00216180
$621$	2.96240e6	0.308258
$622$	−1.18892e7	−1.23219
$623$	4.71221e6	0.486413
$624$	−8.32867e6	−0.856277
$625$	390625.	0.0400000
$626$	2.24816e7	2.29293
$627$	2.82848e6	0.287332
$628$	−2.71744e6	−0.274955
$629$	1.06685e7	1.07517
$630$	−2.55121e6	−0.256091
$631$	1.28023e7	1.28002	0.640009	−	0.768367i	$-0.278931\pi$
$631$	1.28023e7	1.28002	0.640009	+	0.768367i	$0.278931\pi$
$632$	−5.21057e6	−0.518911
$633$	−8.92261e6	−0.885080
$634$	−3.96661e6	−0.391920
$635$	−5.30263e6	−0.521863
$636$	−977924.	−0.0958655
$637$	−1.13765e7	−1.11086
$638$	6.60054e6	0.641990
$639$	4.67763e6	0.453183
$640$	−4.82597e6	−0.465730
$641$	3.73732e6	0.359266	0.179633	−	0.983734i	$-0.442509\pi$
$641$	3.73732e6	0.359266	0.179633	+	0.983734i	$0.442509\pi$
$642$	4.60530e6	0.440982
$643$	−7.93526e6	−0.756892	−0.378446	−	0.925623i	$-0.623541\pi$
$643$	−7.93526e6	−0.756892	−0.378446	+	0.925623i	$0.623541\pi$
$644$	−1.23034e7	−1.16899
$645$	−1.47983e6	−0.140059
$646$	−2.71642e7	−2.56104
$647$	1.05999e6	0.0995504	0.0497752	−	0.998760i	$-0.484150\pi$
$647$	1.05999e6	0.0995504	0.0497752	+	0.998760i	$0.484150\pi$
$648$	−697228.	−0.0652285
$649$	−448335.	−0.0417822
$650$	−3.15760e6	−0.293140
$651$	80046.3	0.00740267
$652$	8.76699e6	0.807666
$653$	1.31519e7	1.20700	0.603499	−	0.797364i	$-0.293773\pi$
$653$	1.31519e7	1.20700	0.603499	+	0.797364i	$0.293773\pi$
$654$	9.13354e6	0.835016
$655$	6.39180e6	0.582130
$656$	1.47292e7	1.33635
$657$	2.39242e6	0.216234
$658$	2.24848e7	2.02453
$659$	9.08548e6	0.814956	0.407478	−	0.913215i	$-0.366408\pi$
$659$	9.08548e6	0.814956	0.407478	+	0.913215i	$0.366408\pi$
$660$	−456983.	−0.0408357
$661$	254443.	0.0226510	0.0113255	−	0.999936i	$-0.496395\pi$
$661$	254443.	0.0226510	0.0113255	+	0.999936i	$0.496395\pi$
$662$	−2.40837e6	−0.213588
$663$	−9.74772e6	−0.861230
$664$	−78984.1	−0.00695216
$665$	−1.17122e7	−1.02704
$666$	−4.03094e6	−0.352145
$667$	3.17369e7	2.76217
$668$	−4.16636e6	−0.361257
$669$	1.77188e6	0.153062
$670$	−8.59464e6	−0.739674
$671$	3.59744e6	0.308452
$672$	8.98611e6	0.767624
$673$	1.06880e6	0.0909619	0.0454809	−	0.998965i	$-0.485518\pi$
$673$	1.06880e6	0.0909619	0.0454809	+	0.998965i	$0.485518\pi$
$674$	1.81855e7	1.54197
$675$	−455625.	−0.0384900
$676$	2.54978e6	0.214603
$677$	6.40422e6	0.537025	0.268513	−	0.963276i	$-0.413468\pi$
$677$	6.40422e6	0.537025	0.268513	+	0.963276i	$0.413468\pi$
$678$	1.07510e7	0.898206
$679$	−3.04167e7	−2.53185
$680$	−3.97807e6	−0.329914
$681$	−5.53544e6	−0.457387
$682$	41672.8	0.00343078
$683$	−1.31278e7	−1.07681	−0.538405	−	0.842686i	$-0.680973\pi$
$683$	−1.31278e7	−1.07681	−0.538405	+	0.842686i	$0.680973\pi$
$684$	3.53136e6	0.288604
$685$	−4.73785e6	−0.385794
$686$	−1.35932e6	−0.110284
$687$	1.03624e7	0.837660
$688$	8.41451e6	0.677731
$689$	−4.68234e6	−0.375764
$690$	−6.38621e6	−0.510647
$691$	−1.23860e7	−0.986813	−0.493406	−	0.869799i	$-0.664248\pi$
$691$	−1.23860e7	−0.986813	−0.493406	+	0.869799i	$0.664248\pi$
$692$	−840418.	−0.0667160
$693$	−1.76785e6	−0.139834
$694$	−1.31973e7	−1.04013
$695$	4.24202e6	0.333128
$696$	−7.46959e6	−0.584485
$697$	1.72388e7	1.34408
$698$	−2.23282e7	−1.73467
$699$	6.58595e6	0.509830
$700$	1.89229e6	0.145963
$701$	−1.27932e7	−0.983294	−0.491647	−	0.870795i	$-0.663605\pi$
$701$	−1.27932e7	−0.983294	−0.491647	+	0.870795i	$0.663605\pi$
$702$	3.68303e6	0.282074
$703$	−1.85055e7	−1.41225
$704$	−275515.	−0.0209515
$705$	4.01561e6	0.304283
$706$	2.38721e7	1.80251
$707$	1.86320e7	1.40188
$708$	−559748.	−0.0419672
$709$	2.35984e7	1.76306	0.881531	−	0.472127i	$-0.156514\pi$
$709$	2.35984e7	1.76306	0.881531	+	0.472127i	$0.156514\pi$
$710$	−1.00838e7	−0.750724
$711$	3.97160e6	0.294640
$712$	−2.77622e6	−0.205236
$713$	200373.	0.0147610
$714$	1.69782e7	1.24637
$715$	−2.18805e6	−0.160064
$716$	−1.02606e7	−0.747982
$717$	−9.99091e6	−0.725784
$718$	1.30776e7	0.946713
$719$	−3.28165e6	−0.236739	−0.118369	−	0.992970i	$-0.537767\pi$
$719$	−3.28165e6	−0.236739	−0.118369	+	0.992970i	$0.537767\pi$
$720$	2.59075e6	0.186249
$721$	−2.06046e6	−0.147613
$722$	2.98241e7	2.12924
$723$	−6.81805e6	−0.485081
$724$	−2.14802e6	−0.152297
$725$	−4.88123e6	−0.344893
$726$	−920361.	−0.0648062
$727$	−2.55139e7	−1.79036	−0.895180	−	0.445704i	$-0.852953\pi$
$727$	−2.55139e7	−1.79036	−0.895180	+	0.445704i	$0.852953\pi$
$728$	1.38648e7	0.969582
$729$	531441.	0.0370370
$730$	−5.15748e6	−0.358204
$731$	9.84818e6	0.681652
$732$	4.49142e6	0.309817
$733$	265424.	0.0182465	0.00912325	−	0.999958i	$-0.497096\pi$
$733$	265424.	0.0182465	0.00912325	+	0.999958i	$0.497096\pi$
$734$	−4.53844e6	−0.310932
$735$	3.53881e6	0.241623
$736$	2.24941e7	1.53065
$737$	−5.95563e6	−0.403886
$738$	−6.51341e6	−0.440218
$739$	−7.06776e6	−0.476070	−0.238035	−	0.971257i	$-0.576503\pi$
$739$	−7.06776e6	−0.476070	−0.238035	+	0.971257i	$0.576503\pi$
$740$	2.98985e6	0.200710
$741$	1.69083e7	1.13124
$742$	8.15551e6	0.543803
$743$	−4.93136e6	−0.327714	−0.163857	−	0.986484i	$-0.552394\pi$
$743$	−4.93136e6	−0.327714	−0.163857	+	0.986484i	$0.552394\pi$
$744$	−47159.6	−0.00312347
$745$	−1.10771e7	−0.731199
$746$	−4.08962e6	−0.269052
$747$	60203.3	0.00394747
$748$	3.04120e6	0.198743
$749$	−1.32144e7	−0.860680
$750$	982217.	0.0637609
$751$	−8.00628e6	−0.518001	−0.259001	−	0.965877i	$-0.583393\pi$
$751$	−8.00628e6	−0.518001	−0.259001	+	0.965877i	$0.583393\pi$
$752$	−2.28333e7	−1.47240
$753$	1.31472e7	0.844976
$754$	3.94573e7	2.52754
$755$	−7.34174e6	−0.468739
$756$	−2.20717e6	−0.140453
$757$	−2.07218e7	−1.31428	−0.657140	−	0.753768i	$-0.728234\pi$
$757$	−2.07218e7	−1.31428	−0.657140	+	0.753768i	$0.728234\pi$
$758$	1.19881e7	0.757842
$759$	−4.42531e6	−0.278830
$760$	6.90032e6	0.433347
$761$	−6.44635e6	−0.403508	−0.201754	−	0.979436i	$-0.564664\pi$
$761$	−6.44635e6	−0.403508	−0.201754	+	0.979436i	$0.564664\pi$
$762$	−1.33333e7	−0.831862
$763$	−2.62076e7	−1.62973
$764$	1.09837e6	0.0680795
$765$	3.03217e6	0.187327
$766$	−3.65841e6	−0.225279
$767$	−2.68010e6	−0.164499
$768$	−1.14790e7	−0.702265
$769$	2.18929e7	1.33502	0.667510	−	0.744601i	$-0.267360\pi$
$769$	2.18929e7	1.33502	0.667510	+	0.744601i	$0.267360\pi$
$770$	3.81106e6	0.231643
$771$	1.63717e7	0.991875
$772$	−1.33033e7	−0.803373
$773$	2.23074e6	0.134276	0.0671381	−	0.997744i	$-0.478613\pi$
$773$	2.23074e6	0.134276	0.0671381	+	0.997744i	$0.478613\pi$
$774$	−3.72099e6	−0.223257
$775$	−30817.9	−0.00184310
$776$	1.79201e7	1.06829
$777$	1.15663e7	0.687293
$778$	586852.	0.0347600
$779$	−2.99022e7	−1.76547
$780$	−2.73179e6	−0.160772
$781$	−6.98757e6	−0.409920
$782$	4.25000e7	2.48526
$783$	5.69347e6	0.331873
$784$	−2.01222e7	−1.16919
$785$	4.04732e6	0.234420
$786$	1.60720e7	0.927928
$787$	−1.73371e7	−0.997793	−0.498897	−	0.866662i	$-0.666261\pi$
$787$	−1.73371e7	−0.997793	−0.498897	+	0.866662i	$0.666261\pi$
$788$	−9.15910e6	−0.525457
$789$	1.41685e7	0.810270
$790$	−8.56181e6	−0.488088
$791$	−3.08488e7	−1.75306
$792$	1.04154e6	0.0590014
$793$	2.15051e7	1.21439
$794$	−1.37764e7	−0.775503
$795$	1.45651e6	0.0817325
$796$	−6.89833e6	−0.385888
$797$	−2.21115e6	−0.123303	−0.0616513	−	0.998098i	$-0.519637\pi$
$797$	−2.21115e6	−0.123303	−0.0616513	+	0.998098i	$0.519637\pi$
$798$	−2.94502e7	−1.63712
$799$	−2.67237e7	−1.48091
$800$	−3.45966e6	−0.191121
$801$	2.11609e6	0.116534
$802$	−1.64080e7	−0.900780
$803$	−3.57386e6	−0.195591
$804$	−7.43563e6	−0.405674
$805$	1.83245e7	0.996648
$806$	249115.	0.0135071
$807$	−1.76206e7	−0.952440
$808$	−1.09771e7	−0.591507
$809$	9.56588e6	0.513870	0.256935	−	0.966429i	$-0.417287\pi$
$809$	9.56588e6	0.513870	0.256935	+	0.966429i	$0.417287\pi$
$810$	−1.14566e6	−0.0613540
$811$	−2.98170e7	−1.59188	−0.795942	−	0.605373i	$-0.793024\pi$
$811$	−2.98170e7	−1.59188	−0.795942	+	0.605373i	$0.793024\pi$
$812$	−2.36460e7	−1.25854
$813$	−7.91856e6	−0.420165
$814$	6.02153e6	0.318527
$815$	−1.30574e7	−0.688595
$816$	−1.72413e7	−0.906454
$817$	−1.70825e7	−0.895359
$818$	6.00075e6	0.313561
$819$	−1.05680e7	−0.550533
$820$	4.83115e6	0.250909
$821$	2.57082e7	1.33111	0.665556	−	0.746348i	$-0.268195\pi$
$821$	2.57082e7	1.33111	0.665556	+	0.746348i	$0.268195\pi$
$822$	−1.19132e7	−0.614964
$823$	7.85121e6	0.404052	0.202026	−	0.979380i	$-0.435248\pi$
$823$	7.85121e6	0.404052	0.202026	+	0.979380i	$0.435248\pi$
$824$	1.21393e6	0.0622838
$825$	680625.	0.0348155
$826$	4.66808e6	0.238061
$827$	1.94596e7	0.989395	0.494698	−	0.869065i	$-0.335279\pi$
$827$	1.94596e7	0.989395	0.494698	+	0.869065i	$0.335279\pi$
$828$	−5.52501e6	−0.280064
$829$	−7.07548e6	−0.357577	−0.178789	−	0.983888i	$-0.557218\pi$
$829$	−7.07548e6	−0.357577	−0.178789	+	0.983888i	$0.557218\pi$
$830$	−129784.	−0.00653920
$831$	−9.88006e6	−0.496314
$832$	−1.64700e6	−0.0824869
$833$	−2.35506e7	−1.17595
$834$	1.06665e7	0.531013
$835$	6.20533e6	0.307998
$836$	−5.27524e6	−0.261052
$837$	35946.0	0.00177352
$838$	5.42137e6	0.266685
$839$	3.20415e7	1.57148	0.785738	−	0.618559i	$-0.212283\pi$
$839$	3.20415e7	1.57148	0.785738	+	0.618559i	$0.212283\pi$
$840$	−4.31284e6	−0.210894
$841$	4.04845e7	1.97378
$842$	−3.18941e6	−0.155035
$843$	−1.88717e7	−0.914621
$844$	1.66411e7	0.804129
$845$	−3.79760e6	−0.182965
$846$	1.00971e7	0.485035
$847$	2.64087e6	0.126485
$848$	−8.28192e6	−0.395495
$849$	9.18833e6	0.437489
$850$	−6.53662e6	−0.310317
$851$	2.89529e7	1.37047
$852$	−8.72401e6	−0.411734
$853$	4.09405e6	0.192655	0.0963276	−	0.995350i	$-0.469290\pi$
$853$	4.09405e6	0.192655	0.0963276	+	0.995350i	$0.469290\pi$
$854$	−3.74567e7	−1.75746
$855$	−5.25956e6	−0.246056
$856$	7.78530e6	0.363154
$857$	−1.74414e7	−0.811202	−0.405601	−	0.914050i	$-0.632938\pi$
$857$	−1.74414e7	−0.811202	−0.405601	+	0.914050i	$0.632938\pi$
$858$	−5.50181e6	−0.255145
$859$	−3.19869e6	−0.147907	−0.0739537	−	0.997262i	$-0.523562\pi$
$859$	−3.19869e6	−0.147907	−0.0739537	+	0.997262i	$0.523562\pi$
$860$	2.75994e6	0.127249
$861$	1.86895e7	0.859189
$862$	3.94662e7	1.80908
$863$	−3.23839e7	−1.48014	−0.740070	−	0.672530i	$-0.765208\pi$
$863$	−3.23839e7	−1.48014	−0.740070	+	0.672530i	$0.765208\pi$
$864$	4.03535e6	0.183906
$865$	1.25171e6	0.0568804
$866$	1.62649e7	0.736981
$867$	−7.40022e6	−0.334347
$868$	−149290.	−0.00672561
$869$	−5.93289e6	−0.266512
$870$	−1.22737e7	−0.549767
$871$	−3.56021e7	−1.59012
$872$	1.54403e7	0.687646
$873$	−1.36591e7	−0.606577
$874$	−7.37200e7	−3.26442
$875$	−2.81836e6	−0.124444
$876$	−4.46198e6	−0.196457
$877$	−1.00083e7	−0.439401	−0.219701	−	0.975567i	$-0.570508\pi$
$877$	−1.00083e7	−0.439401	−0.219701	+	0.975567i	$0.570508\pi$
$878$	2.87726e7	1.25963
$879$	1.39879e7	0.610632
$880$	−3.87013e6	−0.168469
$881$	−2.66953e6	−0.115876	−0.0579382	−	0.998320i	$-0.518453\pi$
$881$	−2.66953e6	−0.115876	−0.0579382	+	0.998320i	$0.518453\pi$
$882$	8.89826e6	0.385153
$883$	−3.79635e6	−0.163857	−0.0819284	−	0.996638i	$-0.526108\pi$
$883$	−3.79635e6	−0.163857	−0.0819284	+	0.996638i	$0.526108\pi$
$884$	1.81800e7	0.782460
$885$	833682.	0.0357801
$886$	−3.89612e7	−1.66743
$887$	−8.27667e6	−0.353221	−0.176610	−	0.984281i	$-0.556513\pi$
$887$	−8.27667e6	−0.353221	−0.176610	+	0.984281i	$0.556513\pi$
$888$	−6.81434e6	−0.289996
$889$	3.82584e7	1.62358
$890$	−4.56178e6	−0.193045
$891$	−793881.	−0.0335013
$892$	−3.30463e6	−0.139063
$893$	4.63546e7	1.94520
$894$	−2.78531e7	−1.16555
$895$	1.52820e7	0.637711
$896$	3.48193e7	1.44894
$897$	−2.64540e7	−1.09777
$898$	−3.60868e7	−1.49334
$899$	385099.	0.0158918
$900$	849762.	0.0349696
$901$	−9.69300e6	−0.397783
$902$	9.72991e6	0.398192
$903$	1.06769e7	0.435739
$904$	1.81747e7	0.739684
$905$	3.19923e6	0.129845
$906$	−1.84606e7	−0.747181
$907$	4.01686e7	1.62132	0.810659	−	0.585519i	$-0.199109\pi$
$907$	4.01686e7	1.62132	0.810659	+	0.585519i	$0.199109\pi$
$908$	1.03239e7	0.415554
$909$	8.36698e6	0.335861
$910$	2.27821e7	0.911990
$911$	−6.33210e6	−0.252785	−0.126393	−	0.991980i	$-0.540340\pi$
$911$	−6.33210e6	−0.252785	−0.126393	+	0.991980i	$0.540340\pi$
$912$	2.99066e7	1.19064
$913$	−89933.3	−0.00357062
$914$	−4.87022e7	−1.92834
$915$	−6.68946e6	−0.264143
$916$	−1.93263e7	−0.761046
$917$	−4.61168e7	−1.81107
$918$	7.62431e6	0.298603
$919$	2.01159e7	0.785690	0.392845	−	0.919605i	$-0.371491\pi$
$919$	2.01159e7	0.785690	0.392845	+	0.919605i	$0.371491\pi$
$920$	−1.07959e7	−0.420524
$921$	5.37831e6	0.208928
$922$	1.79042e6	0.0693631
$923$	−4.17709e7	−1.61387
$924$	3.29713e6	0.127045
$925$	−4.45304e6	−0.171121
$926$	8.27876e6	0.317276
$927$	−925281.	−0.0353650
$928$	4.32318e7	1.64791
$929$	−5.33887e6	−0.202960	−0.101480	−	0.994838i	$-0.532358\pi$
$929$	−5.33887e6	−0.202960	−0.101480	+	0.994838i	$0.532358\pi$
$930$	−77490.8	−0.00293794
$931$	4.08507e7	1.54463
$932$	−1.22831e7	−0.463200
$933$	1.53197e7	0.576164
$934$	1.43167e7	0.537002
$935$	−4.52953e6	−0.169443
$936$	6.22619e6	0.232291
$937$	−7.81443e6	−0.290769	−0.145384	−	0.989375i	$-0.546442\pi$
$937$	−7.81443e6	−0.290769	−0.145384	+	0.989375i	$0.546442\pi$
$938$	6.20102e7	2.30121
$939$	−2.89684e7	−1.07216
$940$	−7.48930e6	−0.276453
$941$	−8.76272e6	−0.322600	−0.161300	−	0.986905i	$-0.551569\pi$
$941$	−8.76272e6	−0.322600	−0.161300	+	0.986905i	$0.551569\pi$
$942$	1.01769e7	0.373670
$943$	4.67836e7	1.71323
$944$	−4.74044e6	−0.173136
$945$	3.28733e6	0.119747
$946$	5.55851e6	0.201944
$947$	−4.90766e6	−0.177828	−0.0889139	−	0.996039i	$-0.528340\pi$
$947$	−4.90766e6	−0.177828	−0.0889139	+	0.996039i	$0.528340\pi$
$948$	−7.40722e6	−0.267692
$949$	−2.13641e7	−0.770052
$950$	1.13383e7	0.407606
$951$	5.11114e6	0.183259
$952$	2.87018e7	1.02640
$953$	−4.32026e7	−1.54091	−0.770456	−	0.637494i	$-0.779971\pi$
$953$	−4.32026e7	−1.54091	−0.770456	+	0.637494i	$0.779971\pi$
$954$	3.66235e6	0.130284
$955$	−1.63590e6	−0.0580428
$956$	1.86335e7	0.659402
$957$	−8.50506e6	−0.300191
$958$	1.47836e7	0.520435
$959$	3.41836e7	1.20025
$960$	512322.	0.0179418
$961$	−2.86267e7	−0.999915
$962$	3.59960e7	1.25405
$963$	−5.93411e6	−0.206201
$964$	1.27160e7	0.440715
$965$	1.98138e7	0.684936
$966$	4.60764e7	1.58868
$967$	1.46496e7	0.503801	0.251900	−	0.967753i	$-0.418944\pi$
$967$	1.46496e7	0.503801	0.251900	+	0.967753i	$0.418944\pi$
$968$	−1.55588e6	−0.0533688
$969$	3.50022e7	1.19753
$970$	2.94457e7	1.00483
$971$	3.81586e7	1.29881	0.649403	−	0.760445i	$-0.275019\pi$
$971$	3.81586e7	1.29881	0.649403	+	0.760445i	$0.275019\pi$
$972$	−991163.	−0.0336496
$973$	−3.06061e7	−1.03640
$974$	−1.49500e7	−0.504946
$975$	4.06870e6	0.137070
$976$	3.80373e7	1.27816
$977$	3.47084e7	1.16332	0.581659	−	0.813432i	$-0.302404\pi$
$977$	3.47084e7	1.16332	0.581659	+	0.813432i	$0.302404\pi$
$978$	−3.28326e7	−1.09764
$979$	−3.16107e6	−0.105409
$980$	−6.60005e6	−0.219524
$981$	−1.17689e7	−0.390449
$982$	−2.46715e7	−0.816426
$983$	−1.87623e7	−0.619302	−0.309651	−	0.950850i	$-0.600212\pi$
$983$	−1.87623e7	−0.619302	−0.309651	+	0.950850i	$0.600212\pi$
$984$	−1.10110e7	−0.362525
$985$	1.36415e7	0.447992
$986$	8.16812e7	2.67565
$987$	−2.89726e7	−0.946660
$988$	−3.15348e7	−1.02777
$989$	2.67266e7	0.868866
$990$	1.71142e6	0.0554967
$991$	5.23715e6	0.169399	0.0846996	−	0.996407i	$-0.473007\pi$
$991$	5.23715e6	0.169399	0.0846996	+	0.996407i	$0.473007\pi$
$992$	272946.	0.00880637
$993$	3.10327e6	0.0998728
$994$	7.27548e7	2.33559
$995$	1.02743e7	0.328999
$996$	−112282.	−0.00358642
$997$	9.03523e6	0.287873	0.143937	−	0.989587i	$-0.454024\pi$
$997$	9.03523e6	0.287873	0.143937	+	0.989587i	$0.454024\pi$
$998$	−9.73012e6	−0.309237
$999$	5.19402e6	0.164661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.g.1.4	✓	5
3.2	odd	2		495.6.a.i.1.2		5
5.4	even	2		825.6.a.k.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.g.1.4	✓	5	1.1	even	1	trivial
495.6.a.i.1.2		5	3.2	odd	2
825.6.a.k.1.2		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)

\(f(q)\)	\(=\)	\(q+6.98466 q^{2} -9.00000 q^{3} +16.7854 q^{4} -25.0000 q^{5} -62.8619 q^{6} +180.375 q^{7} -106.269 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.98466 q^{2} -9.00000 q^{3} +16.7854 q^{4} -25.0000 q^{5} -62.8619 q^{6} +180.375 q^{7} -106.269 q^{8} +81.0000 q^{9} -174.616 q^{10} -121.000 q^{11} -151.069 q^{12} -723.324 q^{13} +1259.86 q^{14} +225.000 q^{15} -1279.38 q^{16} -1497.37 q^{17} +565.757 q^{18} +2597.31 q^{19} -419.636 q^{20} -1623.37 q^{21} -845.143 q^{22} -4063.64 q^{23} +956.417 q^{24} +625.000 q^{25} -5052.17 q^{26} -729.000 q^{27} +3027.67 q^{28} -7809.97 q^{29} +1571.55 q^{30} -49.3086 q^{31} -5535.46 q^{32} +1089.00 q^{33} -10458.6 q^{34} -4509.37 q^{35} +1359.62 q^{36} -7124.86 q^{37} +18141.4 q^{38} +6509.91 q^{39} +2656.71 q^{40} -11512.7 q^{41} -11338.7 q^{42} -6577.00 q^{43} -2031.04 q^{44} -2025.00 q^{45} -28383.2 q^{46} +17847.1 q^{47} +11514.4 q^{48} +15728.0 q^{49} +4365.41 q^{50} +13476.3 q^{51} -12141.3 q^{52} +6473.37 q^{53} -5091.81 q^{54} +3025.00 q^{55} -19168.2 q^{56} -23375.8 q^{57} -54550.0 q^{58} +3705.25 q^{59} +3776.72 q^{60} -29730.9 q^{61} -344.404 q^{62} +14610.4 q^{63} +2276.99 q^{64} +18083.1 q^{65} +7606.29 q^{66} +49220.1 q^{67} -25133.9 q^{68} +36572.8 q^{69} -31496.4 q^{70} +57748.6 q^{71} -8607.75 q^{72} +29536.1 q^{73} -49764.7 q^{74} -5625.00 q^{75} +43597.0 q^{76} -21825.3 q^{77} +45469.5 q^{78} +49032.1 q^{79} +31984.6 q^{80} +6561.00 q^{81} -80412.5 q^{82} +743.250 q^{83} -27249.0 q^{84} +37434.1 q^{85} -45938.1 q^{86} +70289.7 q^{87} +12858.5 q^{88} +26124.6 q^{89} -14143.9 q^{90} -130469. q^{91} -68210.0 q^{92} +443.777 q^{93} +124656. q^{94} -64932.9 q^{95} +49819.1 q^{96} -168631. q^{97} +109855. q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * q^99

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