LMFDB - Embedded newform 177.6.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 $ x^11 - 5x^10 - 238x^9 + 1067x^8 + 20782x^7 - 79077x^6 - 813818x^5 + 2364885x^4 + 13849341x^3 - 23890558x^2 - 74443300x - 14846072
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			1.2
Root			$-8.44473$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} -130.245 q^{10} -138.804 q^{11} +514.827 q^{12} -485.356 q^{13} -637.385 q^{14} +124.112 q^{15} +417.688 q^{16} -2224.39 q^{17} -765.023 q^{18} +1850.55 q^{19} +788.844 q^{20} +607.372 q^{21} +1310.97 q^{22} -1008.66 q^{23} -2142.32 q^{24} -2934.83 q^{25} +4584.06 q^{26} +729.000 q^{27} +3860.39 q^{28} +1534.86 q^{29} -1172.21 q^{30} +5924.08 q^{31} +3672.19 q^{32} -1249.24 q^{33} +21008.8 q^{34} +930.646 q^{35} +4633.44 q^{36} +1074.65 q^{37} -17477.9 q^{38} -4368.21 q^{39} -3282.57 q^{40} -10573.5 q^{41} -5736.47 q^{42} +15070.3 q^{43} -7940.01 q^{44} +1117.01 q^{45} +9526.48 q^{46} -14991.6 q^{47} +3759.19 q^{48} -12252.7 q^{49} +27718.7 q^{50} -20019.6 q^{51} -27763.8 q^{52} -40821.3 q^{53} -6885.21 q^{54} -1914.14 q^{55} -16064.0 q^{56} +16654.9 q^{57} -14496.4 q^{58} +3481.00 q^{59} +7099.60 q^{60} -34218.1 q^{61} -55951.4 q^{62} +5466.35 q^{63} -48048.9 q^{64} -6693.19 q^{65} +11798.7 q^{66} +18426.3 q^{67} -127242. q^{68} -9077.90 q^{69} -8789.71 q^{70} +17658.3 q^{71} -19280.9 q^{72} -25695.8 q^{73} -10149.8 q^{74} -26413.5 q^{75} +105857. q^{76} -9367.30 q^{77} +41256.6 q^{78} -13512.5 q^{79} +5760.02 q^{80} +6561.00 q^{81} +99863.6 q^{82} -80373.4 q^{83} +34743.5 q^{84} -30675.0 q^{85} -142335. q^{86} +13813.8 q^{87} +33040.3 q^{88} +43704.2 q^{89} -10549.9 q^{90} -32754.7 q^{91} -57698.1 q^{92} +53316.7 q^{93} +141591. q^{94} +25519.5 q^{95} +33049.7 q^{96} +67602.6 q^{97} +115723. q^{98} -11243.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * 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 $

$2$	−9.44473	−1.66961	−0.834804	−	0.550547i	$-0.814419\pi$
$2$	−9.44473	−1.66961	−0.834804	+	0.550547i	$0.814419\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	57.2030	1.78759
$5$	13.7903	0.246688	0.123344	−	0.992364i	$-0.460638\pi$
$5$	13.7903	0.246688	0.123344	+	0.992364i	$0.460638\pi$
$6$	−85.0026	−0.963949
$7$	67.4858	0.520556	0.260278	−	0.965534i	$-0.416186\pi$
$7$	67.4858	0.520556	0.260278	+	0.965534i	$0.416186\pi$
$8$	−238.036	−1.31497
$9$	81.0000	0.333333
$10$	−130.245	−0.411872
$11$	−138.804	−0.345876	−0.172938	−	0.984933i	$-0.555326\pi$
$11$	−138.804	−0.345876	−0.172938	+	0.984933i	$0.555326\pi$
$12$	514.827	1.03207
$13$	−485.356	−0.796530	−0.398265	−	0.917270i	$-0.630388\pi$
$13$	−485.356	−0.796530	−0.398265	+	0.917270i	$0.630388\pi$
$14$	−637.385	−0.869125
$15$	124.112	0.142425
$16$	417.688	0.407898
$17$	−2224.39	−1.86676	−0.933382	−	0.358884i	$-0.883157\pi$
$17$	−2224.39	−1.86676	−0.933382	+	0.358884i	$0.883157\pi$
$18$	−765.023	−0.556536
$19$	1850.55	1.17602	0.588012	−	0.808852i	$-0.299911\pi$
$19$	1850.55	1.17602	0.588012	+	0.808852i	$0.299911\pi$
$20$	788.844	0.440977
$21$	607.372	0.300543
$22$	1310.97	0.577478
$23$	−1008.66	−0.397579	−0.198789	−	0.980042i	$-0.563701\pi$
$23$	−1008.66	−0.397579	−0.198789	+	0.980042i	$0.563701\pi$
$24$	−2142.32	−0.759201
$25$	−2934.83	−0.939145
$26$	4584.06	1.32989
$27$	729.000	0.192450
$28$	3860.39	0.930542
$29$	1534.86	0.338902	0.169451	−	0.985539i	$-0.445800\pi$
$29$	1534.86	0.338902	0.169451	+	0.985539i	$0.445800\pi$
$30$	−1172.21	−0.237794
$31$	5924.08	1.10718	0.553588	−	0.832790i	$-0.313258\pi$
$31$	5924.08	1.10718	0.553588	+	0.832790i	$0.313258\pi$
$32$	3672.19	0.633943
$33$	−1249.24	−0.199692
$34$	21008.8	3.11677
$35$	930.646	0.128415
$36$	4633.44	0.595865
$37$	1074.65	0.129051	0.0645257	−	0.997916i	$-0.479447\pi$
$37$	1074.65	0.129051	0.0645257	+	0.997916i	$0.479447\pi$
$38$	−17477.9	−1.96350
$39$	−4368.21	−0.459877
$40$	−3282.57	−0.324388
$41$	−10573.5	−0.982331	−0.491165	−	0.871066i	$-0.663429\pi$
$41$	−10573.5	−0.982331	−0.491165	+	0.871066i	$0.663429\pi$
$42$	−5736.47	−0.501789
$43$	15070.3	1.24294	0.621470	−	0.783438i	$-0.286536\pi$
$43$	15070.3	1.24294	0.621470	+	0.783438i	$0.286536\pi$
$44$	−7940.01	−0.618286
$45$	1117.01	0.0822292
$46$	9526.48	0.663801
$47$	−14991.6	−0.989924	−0.494962	−	0.868915i	$-0.664818\pi$
$47$	−14991.6	−0.989924	−0.494962	+	0.868915i	$0.664818\pi$
$48$	3759.19	0.235500
$49$	−12252.7	−0.729022
$50$	27718.7	1.56801
$51$	−20019.6	−1.07778
$52$	−27763.8	−1.42387
$53$	−40821.3	−1.99617	−0.998084	−	0.0618654i	$-0.980295\pi$
$53$	−40821.3	−1.99617	−0.998084	+	0.0618654i	$0.980295\pi$
$54$	−6885.21	−0.321316
$55$	−1914.14	−0.0853233
$56$	−16064.0	−0.684517
$57$	16654.9	0.678977
$58$	−14496.4	−0.565835
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	7099.60	0.254598
$61$	−34218.1	−1.17742	−0.588710	−	0.808345i	$-0.700364\pi$
$61$	−34218.1	−1.17742	−0.588710	+	0.808345i	$0.700364\pi$
$62$	−55951.4	−1.84855
$63$	5466.35	0.173519
$64$	−48048.9	−1.46634
$65$	−6693.19	−0.196494
$66$	11798.7	0.333407
$67$	18426.3	0.501478	0.250739	−	0.968055i	$-0.419326\pi$
$67$	18426.3	0.501478	0.250739	+	0.968055i	$0.419326\pi$
$68$	−127242.	−3.33702
$69$	−9077.90	−0.229542
$70$	−8789.71	−0.214402
$71$	17658.3	0.415723	0.207861	−	0.978158i	$-0.433350\pi$
$71$	17658.3	0.415723	0.207861	+	0.978158i	$0.433350\pi$
$72$	−19280.9	−0.438325
$73$	−25695.8	−0.564357	−0.282179	−	0.959362i	$-0.591057\pi$
$73$	−25695.8	−0.564357	−0.282179	+	0.959362i	$0.591057\pi$
$74$	−10149.8	−0.215465
$75$	−26413.5	−0.542216
$76$	105857.	2.10225
$77$	−9367.30	−0.180048
$78$	41256.6	0.767815
$79$	−13512.5	−0.243594	−0.121797	−	0.992555i	$-0.538866\pi$
$79$	−13512.5	−0.243594	−0.121797	+	0.992555i	$0.538866\pi$
$80$	5760.02	0.100623
$81$	6561.00	0.111111
$82$	99863.6	1.64011
$83$	−80373.4	−1.28061	−0.640306	−	0.768120i	$-0.721192\pi$
$83$	−80373.4	−1.28061	−0.640306	+	0.768120i	$0.721192\pi$
$84$	34743.5	0.537249
$85$	−30675.0	−0.460508
$86$	−142335.	−2.07522
$87$	13813.8	0.195665
$88$	33040.3	0.454818
$89$	43704.2	0.584855	0.292427	−	0.956288i	$-0.405537\pi$
$89$	43704.2	0.584855	0.292427	+	0.956288i	$0.405537\pi$
$90$	−10549.9	−0.137291
$91$	−32754.7	−0.414638
$92$	−57698.1	−0.710710
$93$	53316.7	0.639229
$94$	141591.	1.65279
$95$	25519.5	0.290110
$96$	33049.7	0.366007
$97$	67602.6	0.729515	0.364757	−	0.931103i	$-0.381152\pi$
$97$	67602.6	0.729515	0.364757	+	0.931103i	$0.381152\pi$
$98$	115723.	1.21718
$99$	−11243.1	−0.115292
$100$	−167881.	−1.67881
$101$	21691.1	0.211582	0.105791	−	0.994388i	$-0.466263\pi$
$101$	21691.1	0.211582	0.105791	+	0.994388i	$0.466263\pi$
$102$	189079.	1.79947
$103$	35953.6	0.333926	0.166963	−	0.985963i	$-0.446604\pi$
$103$	35953.6	0.333926	0.166963	+	0.985963i	$0.446604\pi$
$104$	115532.	1.04742
$105$	8375.82	0.0741402
$106$	385546.	3.33282
$107$	−120880.	−1.02069	−0.510347	−	0.859969i	$-0.670483\pi$
$107$	−120880.	−1.02069	−0.510347	+	0.859969i	$0.670483\pi$
$108$	41701.0	0.344023
$109$	−183993.	−1.48332	−0.741661	−	0.670775i	$-0.765962\pi$
$109$	−183993.	−1.48332	−0.741661	+	0.670775i	$0.765962\pi$
$110$	18078.6	0.142457
$111$	9671.85	0.0745079
$112$	28188.0	0.212334
$113$	−68654.1	−0.505790	−0.252895	−	0.967494i	$-0.581383\pi$
$113$	−68654.1	−0.505790	−0.252895	+	0.967494i	$0.581383\pi$
$114$	−157301.	−1.13363
$115$	−13909.6	−0.0980778
$116$	87798.8	0.605820
$117$	−39313.9	−0.265510
$118$	−32877.1	−0.217365
$119$	−150115.	−0.971755
$120$	−29543.2	−0.187285
$121$	−141784.	−0.880370
$122$	323181.	1.96583
$123$	−95161.2	−0.567149
$124$	338875.	1.97918
$125$	−83566.6	−0.478363
$126$	−51628.2	−0.289708
$127$	139438.	0.767136	0.383568	−	0.923513i	$-0.374695\pi$
$127$	139438.	0.767136	0.383568	+	0.923513i	$0.374695\pi$
$128$	336299.	1.81426
$129$	135632.	0.717612
$130$	63215.4	0.328068
$131$	−45314.3	−0.230705	−0.115353	−	0.993325i	$-0.536800\pi$
$131$	−45314.3	−0.230705	−0.115353	+	0.993325i	$0.536800\pi$
$132$	−71460.1	−0.356968
$133$	124886.	0.612186
$134$	−174032.	−0.837272
$135$	10053.1	0.0474750
$136$	529485.	2.45475
$137$	72094.5	0.328171	0.164086	−	0.986446i	$-0.447533\pi$
$137$	72094.5	0.328171	0.164086	+	0.986446i	$0.447533\pi$
$138$	85738.3	0.383246
$139$	−437395.	−1.92016	−0.960078	−	0.279732i	$-0.909754\pi$
$139$	−437395.	−1.92016	−0.960078	+	0.279732i	$0.909754\pi$
$140$	53235.8	0.229553
$141$	−134924.	−0.571533
$142$	−166778.	−0.694094
$143$	67369.4	0.275501
$144$	33832.7	0.135966
$145$	21166.2	0.0836030
$146$	242690.	0.942256
$147$	−110274.	−0.420901
$148$	61473.2	0.230692
$149$	236655.	0.873271	0.436636	−	0.899638i	$-0.356170\pi$
$149$	236655.	0.873271	0.436636	+	0.899638i	$0.356170\pi$
$150$	249468.	0.905288
$151$	378542.	1.35105	0.675526	−	0.737336i	$-0.263917\pi$
$151$	378542.	1.35105	0.675526	+	0.737336i	$0.263917\pi$
$152$	−440496.	−1.54644
$153$	−180176.	−0.622255
$154$	88471.7	0.300609
$155$	81694.6	0.273127
$156$	−249875.	−0.822073
$157$	103612.	0.335475	0.167738	−	0.985832i	$-0.446354\pi$
$157$	103612.	0.335475	0.167738	+	0.985832i	$0.446354\pi$
$158$	127622.	0.406707
$159$	−367392.	−1.15249
$160$	50640.5	0.156386
$161$	−68069.9	−0.206962
$162$	−61966.9	−0.185512
$163$	−318233.	−0.938160	−0.469080	−	0.883156i	$-0.655414\pi$
$163$	−318233.	−0.938160	−0.469080	+	0.883156i	$0.655414\pi$
$164$	−604834.	−1.75601
$165$	−17227.3	−0.0492614
$166$	759106.	2.13812
$167$	−24793.8	−0.0687942	−0.0343971	−	0.999408i	$-0.510951\pi$
$167$	−24793.8	−0.0687942	−0.0343971	+	0.999408i	$0.510951\pi$
$168$	−144576.	−0.395206
$169$	−135722.	−0.365539
$170$	289717.	0.768868
$171$	149894.	0.392008
$172$	862065.	2.22187
$173$	−313813.	−0.797178	−0.398589	−	0.917130i	$-0.630500\pi$
$173$	−313813.	−0.797178	−0.398589	+	0.917130i	$0.630500\pi$
$174$	−130467.	−0.326685
$175$	−198059.	−0.488877
$176$	−57976.8	−0.141082
$177$	31329.0	0.0751646
$178$	−412774.	−0.976478
$179$	−313044.	−0.730253	−0.365126	−	0.930958i	$-0.618974\pi$
$179$	−313044.	−0.730253	−0.365126	+	0.930958i	$0.618974\pi$
$180$	63896.4	0.146992
$181$	−240755.	−0.546235	−0.273117	−	0.961981i	$-0.588055\pi$
$181$	−240755.	−0.546235	−0.273117	+	0.961981i	$0.588055\pi$
$182$	309359.	0.692284
$183$	−307963.	−0.679783
$184$	240096.	0.522806
$185$	14819.7	0.0318354
$186$	−503563.	−1.06726
$187$	308755.	0.645669
$188$	−857562.	−1.76958
$189$	49197.1	0.100181
$190$	−241025.	−0.484371
$191$	804807.	1.59628	0.798139	−	0.602474i	$-0.205818\pi$
$191$	804807.	1.59628	0.798139	+	0.602474i	$0.205818\pi$
$192$	−432440.	−0.846589
$193$	−724642.	−1.40033	−0.700164	−	0.713982i	$-0.746890\pi$
$193$	−724642.	−1.40033	−0.700164	+	0.713982i	$0.746890\pi$
$194$	−638489.	−1.21800
$195$	−60238.7	−0.113446
$196$	−700889.	−1.30319
$197$	−483578.	−0.887771	−0.443886	−	0.896083i	$-0.646400\pi$
$197$	−483578.	−0.887771	−0.443886	+	0.896083i	$0.646400\pi$
$198$	106188.	0.192493
$199$	356378.	0.637937	0.318968	−	0.947765i	$-0.396664\pi$
$199$	356378.	0.637937	0.318968	+	0.947765i	$0.396664\pi$
$200$	698594.	1.23495
$201$	165837.	0.289528
$202$	−204866.	−0.353258
$203$	103581.	0.176418
$204$	−1.14518e6	−1.92663
$205$	−145811.	−0.242329
$206$	−339573.	−0.557525
$207$	−81701.1	−0.132526
$208$	−202727.	−0.324903
$209$	−256863.	−0.406758
$210$	−79107.4	−0.123785
$211$	64318.7	0.0994561	0.0497280	−	0.998763i	$-0.484165\pi$
$211$	64318.7	0.0994561	0.0497280	+	0.998763i	$0.484165\pi$
$212$	−2.33510e6	−3.56834
$213$	158925.	0.240018
$214$	1.14168e6	1.70416
$215$	207823.	0.306618
$216$	−173528.	−0.253067
$217$	399791.	0.576347
$218$	1.73777e6	2.47657
$219$	−231262.	−0.325832
$220$	−109495.	−0.152523
$221$	1.07962e6	1.48693
$222$	−91348.1	−0.124399
$223$	359718.	0.484396	0.242198	−	0.970227i	$-0.422132\pi$
$223$	359718.	0.484396	0.242198	+	0.970227i	$0.422132\pi$
$224$	247821.	0.330003
$225$	−237721.	−0.313048
$226$	648420.	0.844472
$227$	628492.	0.809533	0.404767	−	0.914420i	$-0.367353\pi$
$227$	628492.	0.809533	0.404767	+	0.914420i	$0.367353\pi$
$228$	952711.	1.21374
$229$	−712809.	−0.898223	−0.449112	−	0.893476i	$-0.648259\pi$
$229$	−712809.	−0.898223	−0.449112	+	0.893476i	$0.648259\pi$
$230$	131373.	0.163751
$231$	−84305.7	−0.103951
$232$	−365352.	−0.445648
$233$	451301.	0.544598	0.272299	−	0.962213i	$-0.412216\pi$
$233$	451301.	0.544598	0.272299	+	0.962213i	$0.412216\pi$
$234$	371309.	0.443298
$235$	−206737.	−0.244202
$236$	199124.	0.232725
$237$	−121612.	−0.140639
$238$	1.41780e6	1.62245
$239$	479799.	0.543331	0.271665	−	0.962392i	$-0.412426\pi$
$239$	479799.	0.543331	0.271665	+	0.962392i	$0.412426\pi$
$240$	51840.2	0.0580950
$241$	−165266.	−0.183291	−0.0916456	−	0.995792i	$-0.529213\pi$
$241$	−165266.	−0.183291	−0.0916456	+	0.995792i	$0.529213\pi$
$242$	1.33912e6	1.46987
$243$	59049.0	0.0641500
$244$	−1.95738e6	−2.10475
$245$	−168967.	−0.179841
$246$	898772.	0.946917
$247$	−898174.	−0.936738
$248$	−1.41014e6	−1.45591
$249$	−723361.	−0.739361
$250$	789264.	0.798679
$251$	1.49986e6	1.50268	0.751340	−	0.659915i	$-0.229408\pi$
$251$	1.49986e6	1.50268	0.751340	+	0.659915i	$0.229408\pi$
$252$	312692.	0.310181
$253$	140005.	0.137513
$254$	−1.31696e6	−1.28082
$255$	−276075.	−0.265874
$256$	−1.63869e6	−1.56278
$257$	−602030.	−0.568572	−0.284286	−	0.958739i	$-0.591757\pi$
$257$	−602030.	−0.568572	−0.284286	+	0.958739i	$0.591757\pi$
$258$	−1.28101e6	−1.19813
$259$	72523.6	0.0671785
$260$	−382870.	−0.351252
$261$	124324.	0.112967
$262$	427982.	0.385187
$263$	−136455.	−0.121647	−0.0608233	−	0.998149i	$-0.519373\pi$
$263$	−136455.	−0.121647	−0.0608233	+	0.998149i	$0.519373\pi$
$264$	297363.	0.262589
$265$	−562936.	−0.492430
$266$	−1.17951e6	−1.02211
$267$	393338.	0.337666
$268$	1.05404e6	0.896439
$269$	1.68628e6	1.42085	0.710425	−	0.703773i	$-0.248503\pi$
$269$	1.68628e6	1.42085	0.710425	+	0.703773i	$0.248503\pi$
$270$	−94948.8	−0.0792648
$271$	−459713.	−0.380245	−0.190123	−	0.981760i	$-0.560889\pi$
$271$	−459713.	−0.380245	−0.190123	+	0.981760i	$0.560889\pi$
$272$	−929103.	−0.761450
$273$	−294792.	−0.239392
$274$	−680913.	−0.547918
$275$	407366.	0.324828
$276$	−519283.	−0.410328
$277$	−2.13458e6	−1.67152	−0.835761	−	0.549093i	$-0.814973\pi$
$277$	−2.13458e6	−1.67152	−0.835761	+	0.549093i	$0.814973\pi$
$278$	4.13108e6	3.20591
$279$	479851.	0.369059
$280$	−221527.	−0.168862
$281$	2.25092e6	1.70057	0.850284	−	0.526325i	$-0.176430\pi$
$281$	2.25092e6	1.70057	0.850284	+	0.526325i	$0.176430\pi$
$282$	1.27432e6	0.954237
$283$	−5499.56	−0.00408189	−0.00204095	−	0.999998i	$-0.500650\pi$
$283$	−5499.56	−0.00408189	−0.00204095	+	0.999998i	$0.500650\pi$
$284$	1.01011e6	0.743143
$285$	229676.	0.167495
$286$	−636286.	−0.459978
$287$	−713559.	−0.511358
$288$	297448.	0.211314
$289$	3.52808e6	2.48481
$290$	−199909.	−0.139584
$291$	608424.	0.421186
$292$	−1.46987e6	−1.00884
$293$	−902523.	−0.614171	−0.307085	−	0.951682i	$-0.599354\pi$
$293$	−902523.	−0.614171	−0.307085	+	0.951682i	$0.599354\pi$
$294$	1.04151e6	0.702740
$295$	48003.9	0.0321160
$296$	−255805.	−0.169699
$297$	−101188.	−0.0665639
$298$	−2.23514e6	−1.45802
$299$	489557.	0.316684
$300$	−1.51093e6	−0.969262
$301$	1.01703e6	0.647019
$302$	−3.57523e6	−2.25573
$303$	195220.	0.122157
$304$	772951.	0.479698
$305$	−471876.	−0.290455
$306$	1.70171e6	1.03892
$307$	500034.	0.302798	0.151399	−	0.988473i	$-0.451622\pi$
$307$	500034.	0.302798	0.151399	+	0.988473i	$0.451622\pi$
$308$	−535838.	−0.321852
$309$	323583.	0.192792
$310$	−771584.	−0.456015
$311$	−1.44596e6	−0.847728	−0.423864	−	0.905726i	$-0.639327\pi$
$311$	−1.44596e6	−0.847728	−0.423864	+	0.905726i	$0.639327\pi$
$312$	1.03979e6	0.604726
$313$	−1.78320e6	−1.02882	−0.514410	−	0.857544i	$-0.671989\pi$
$313$	−1.78320e6	−1.02882	−0.514410	+	0.857544i	$0.671989\pi$
$314$	−978587.	−0.560113
$315$	75382.3	0.0428049
$316$	−772953.	−0.435447
$317$	−1.43302e6	−0.800948	−0.400474	−	0.916308i	$-0.631154\pi$
$317$	−1.43302e6	−0.800948	−0.400474	+	0.916308i	$0.631154\pi$
$318$	3.46992e6	1.92421
$319$	−213045.	−0.117218
$320$	−662606.	−0.361727
$321$	−1.08792e6	−0.589298
$322$	642902.	0.345545
$323$	−4.11634e6	−2.19536
$324$	375309.	0.198622
$325$	1.42444e6	0.748058
$326$	3.00563e6	1.56636
$327$	−1.65594e6	−0.856396
$328$	2.51686e6	1.29174
$329$	−1.01172e6	−0.515311
$330$	162707.	0.0822473
$331$	2.77285e6	1.39109	0.695547	−	0.718481i	$-0.255162\pi$
$331$	2.77285e6	1.39109	0.695547	+	0.718481i	$0.255162\pi$
$332$	−4.59760e6	−2.28921
$333$	87046.7	0.0430171
$334$	234171.	0.114859
$335$	254104.	0.123708
$336$	253692.	0.122591
$337$	−1.39166e6	−0.667509	−0.333754	−	0.942660i	$-0.608316\pi$
$337$	−1.39166e6	−0.667509	−0.333754	+	0.942660i	$0.608316\pi$
$338$	1.28186e6	0.610308
$339$	−617887.	−0.292018
$340$	−1.75470e6	−0.823201
$341$	−822287.	−0.382946
$342$	−1.41571e6	−0.654500
$343$	−1.96111e6	−0.900052
$344$	−3.58726e6	−1.63443
$345$	−125187.	−0.0566252
$346$	2.96388e6	1.33098
$347$	−3.44484e6	−1.53584	−0.767918	−	0.640548i	$-0.778707\pi$
$347$	−3.44484e6	−1.53584	−0.767918	+	0.640548i	$0.778707\pi$
$348$	790189.	0.349770
$349$	−1.33302e6	−0.585833	−0.292917	−	0.956138i	$-0.594626\pi$
$349$	−1.33302e6	−0.585833	−0.292917	+	0.956138i	$0.594626\pi$
$350$	1.87062e6	0.816234
$351$	−353825.	−0.153292
$352$	−509715.	−0.219266
$353$	3.77713e6	1.61334	0.806669	−	0.591003i	$-0.201268\pi$
$353$	3.77713e6	1.61334	0.806669	+	0.591003i	$0.201268\pi$
$354$	−295894.	−0.125495
$355$	243513.	0.102554
$356$	2.50001e6	1.04548
$357$	−1.35104e6	−0.561043
$358$	2.95662e6	1.21924
$359$	331917.	0.135923	0.0679616	−	0.997688i	$-0.478350\pi$
$359$	331917.	0.135923	0.0679616	+	0.997688i	$0.478350\pi$
$360$	−265888.	−0.108129
$361$	948422.	0.383031
$362$	2.27387e6	0.911998
$363$	−1.27606e6	−0.508282
$364$	−1.87366e6	−0.741205
$365$	−354351.	−0.139220
$366$	2.90863e6	1.13497
$367$	−1.30195e6	−0.504578	−0.252289	−	0.967652i	$-0.581183\pi$
$367$	−1.30195e6	−0.504578	−0.252289	+	0.967652i	$0.581183\pi$
$368$	−421303.	−0.162172
$369$	−856451.	−0.327444
$370$	−139968.	−0.0531526
$371$	−2.75486e6	−1.03912
$372$	3.04988e6	1.14268
$373$	5.01394e6	1.86598	0.932990	−	0.359903i	$-0.117190\pi$
$373$	5.01394e6	1.86598	0.932990	+	0.359903i	$0.117190\pi$
$374$	−2.91611e6	−1.07801
$375$	−752099.	−0.276183
$376$	3.56852e6	1.30172
$377$	−744956.	−0.269946
$378$	−464654.	−0.167263
$379$	4.28983e6	1.53406	0.767030	−	0.641611i	$-0.221734\pi$
$379$	4.28983e6	1.53406	0.767030	+	0.641611i	$0.221734\pi$
$380$	1.45979e6	0.518599
$381$	1.25494e6	0.442906
$382$	−7.60119e6	−2.66516
$383$	2.99051e6	1.04171	0.520856	−	0.853645i	$-0.325613\pi$
$383$	2.99051e6	1.04171	0.520856	+	0.853645i	$0.325613\pi$
$384$	3.02669e6	1.04747
$385$	−129177.	−0.0444155
$386$	6.84405e6	2.33800
$387$	1.22069e6	0.414313
$388$	3.86707e6	1.30408
$389$	5.18724e6	1.73805	0.869026	−	0.494767i	$-0.164746\pi$
$389$	5.18724e6	1.73805	0.869026	+	0.494767i	$0.164746\pi$
$390$	568938.	0.189410
$391$	2.24365e6	0.742186
$392$	2.91657e6	0.958645
$393$	−407829.	−0.133198
$394$	4.56727e6	1.48223
$395$	−186340.	−0.0600916
$396$	−643141.	−0.206095
$397$	2.45853e6	0.782887	0.391443	−	0.920202i	$-0.371976\pi$
$397$	2.45853e6	0.782887	0.391443	+	0.920202i	$0.371976\pi$
$398$	−3.36589e6	−1.06511
$399$	1.12397e6	0.353446
$400$	−1.22584e6	−0.383076
$401$	−1.41766e6	−0.440261	−0.220130	−	0.975470i	$-0.570648\pi$
$401$	−1.41766e6	−0.440261	−0.220130	+	0.975470i	$0.570648\pi$
$402$	−1.56629e6	−0.483399
$403$	−2.87529e6	−0.881900
$404$	1.24079e6	0.378222
$405$	90477.9	0.0274097
$406$	−978300.	−0.294548
$407$	−149166.	−0.0446358
$408$	4.76537e6	1.41725
$409$	−2.35592e6	−0.696391	−0.348195	−	0.937422i	$-0.613205\pi$
$409$	−2.35592e6	−0.696391	−0.348195	+	0.937422i	$0.613205\pi$
$410$	1.37714e6	0.404594
$411$	648850.	0.189470
$412$	2.05666e6	0.596924
$413$	234918.	0.0677706
$414$	771645.	0.221267
$415$	−1.10837e6	−0.315911
$416$	−1.78232e6	−0.504955
$417$	−3.93655e6	−1.10860
$418$	2.42601e6	0.679127
$419$	4.25487e6	1.18400	0.592000	−	0.805938i	$-0.298339\pi$
$419$	4.25487e6	1.18400	0.592000	+	0.805938i	$0.298339\pi$
$420$	479122.	0.132533
$421$	−1.91147e6	−0.525607	−0.262804	−	0.964849i	$-0.584647\pi$
$421$	−1.91147e6	−0.525607	−0.262804	+	0.964849i	$0.584647\pi$
$422$	−607473.	−0.166053
$423$	−1.21432e6	−0.329975
$424$	9.71693e6	2.62491
$425$	6.52822e6	1.75316
$426$	−1.50100e6	−0.400736
$427$	−2.30923e6	−0.612912
$428$	−6.91471e6	−1.82459
$429$	606325.	0.159060
$430$	−1.96283e6	−0.511932
$431$	−5.28060e6	−1.36927	−0.684637	−	0.728885i	$-0.740039\pi$
$431$	−5.28060e6	−1.36927	−0.684637	+	0.728885i	$0.740039\pi$
$432$	304494.	0.0785001
$433$	−3.92135e6	−1.00512	−0.502558	−	0.864543i	$-0.667608\pi$
$433$	−3.92135e6	−1.00512	−0.502558	+	0.864543i	$0.667608\pi$
$434$	−3.77592e6	−0.962274
$435$	190495.	0.0482682
$436$	−1.05250e7	−2.65158
$437$	−1.86656e6	−0.467562
$438$	2.18421e6	0.544012
$439$	3.26904e6	0.809578	0.404789	−	0.914410i	$-0.367345\pi$
$439$	3.26904e6	0.809578	0.404789	+	0.914410i	$0.367345\pi$
$440$	455634.	0.112198
$441$	−992466.	−0.243007
$442$	−1.01968e7	−2.48260
$443$	6.03039e6	1.45994	0.729972	−	0.683477i	$-0.239533\pi$
$443$	6.03039e6	1.45994	0.729972	+	0.683477i	$0.239533\pi$
$444$	553259.	0.133190
$445$	602692.	0.144276
$446$	−3.39745e6	−0.808752
$447$	2.12989e6	0.504183
$448$	−3.24262e6	−0.763309
$449$	5.58738e6	1.30795	0.653976	−	0.756515i	$-0.273100\pi$
$449$	5.58738e6	1.30795	0.653976	+	0.756515i	$0.273100\pi$
$450$	2.24521e6	0.522668
$451$	1.46764e6	0.339765
$452$	−3.92722e6	−0.904148
$453$	3.40688e6	0.780030
$454$	−5.93594e6	−1.35160
$455$	−451695.	−0.102286
$456$	−3.96446e6	−0.892838
$457$	−2.59965e6	−0.582270	−0.291135	−	0.956682i	$-0.594033\pi$
$457$	−2.59965e6	−0.582270	−0.291135	+	0.956682i	$0.594033\pi$
$458$	6.73229e6	1.49968
$459$	−1.62158e6	−0.359259
$460$	−795672.	−0.175323
$461$	−4.29896e6	−0.942130	−0.471065	−	0.882099i	$-0.656130\pi$
$461$	−4.29896e6	−0.942130	−0.471065	+	0.882099i	$0.656130\pi$
$462$	796245.	0.173557
$463$	−4.21015e6	−0.912735	−0.456367	−	0.889791i	$-0.650850\pi$
$463$	−4.21015e6	−0.912735	−0.456367	+	0.889791i	$0.650850\pi$
$464$	641094.	0.138238
$465$	735251.	0.157690
$466$	−4.26242e6	−0.909266
$467$	5.46044e6	1.15860	0.579302	−	0.815113i	$-0.303325\pi$
$467$	5.46044e6	1.15860	0.579302	+	0.815113i	$0.303325\pi$
$468$	−2.24887e6	−0.474624
$469$	1.24352e6	0.261047
$470$	1.95258e6	0.407722
$471$	932508.	0.193687
$472$	−828602.	−0.171195
$473$	−2.09182e6	−0.429903
$474$	1.14859e6	0.234812
$475$	−5.43104e6	−1.10446
$476$	−8.58703e6	−1.73710
$477$	−3.30653e6	−0.665390
$478$	−4.53157e6	−0.907150
$479$	−692304.	−0.137866	−0.0689331	−	0.997621i	$-0.521960\pi$
$479$	−692304.	−0.137866	−0.0689331	+	0.997621i	$0.521960\pi$
$480$	455764.	0.0902895
$481$	−521588.	−0.102793
$482$	1.56090e6	0.306025
$483$	−612629.	−0.119490
$484$	−8.11050e6	−1.57374
$485$	932257.	0.179962
$486$	−557702.	−0.107105
$487$	9.19622e6	1.75706	0.878530	−	0.477686i	$-0.158524\pi$
$487$	9.19622e6	1.75706	0.878530	+	0.477686i	$0.158524\pi$
$488$	8.14513e6	1.54828
$489$	−2.86410e6	−0.541647
$490$	1.59585e6	0.300263
$491$	454736.	0.0851247	0.0425623	−	0.999094i	$-0.486448\pi$
$491$	454736.	0.0851247	0.0425623	+	0.999094i	$0.486448\pi$
$492$	−5.44351e6	−1.01383
$493$	−3.41414e6	−0.632651
$494$	8.48302e6	1.56399
$495$	−155046.	−0.0284411
$496$	2.47442e6	0.451615
$497$	1.19169e6	0.216407
$498$	6.83195e6	1.23444
$499$	−4.56440e6	−0.820601	−0.410301	−	0.911950i	$-0.634576\pi$
$499$	−4.56440e6	−0.820601	−0.410301	+	0.911950i	$0.634576\pi$
$500$	−4.78026e6	−0.855119
$501$	−223144.	−0.0397184
$502$	−1.41658e7	−2.50889
$503$	−1.87618e6	−0.330639	−0.165320	−	0.986240i	$-0.552866\pi$
$503$	−1.87618e6	−0.330639	−0.165320	+	0.986240i	$0.552866\pi$
$504$	−1.30119e6	−0.228172
$505$	299125.	0.0521945
$506$	−1.32231e6	−0.229593
$507$	−1.22150e6	−0.211044
$508$	7.97629e6	1.37133
$509$	2.91027e6	0.497897	0.248948	−	0.968517i	$-0.419915\pi$
$509$	2.91027e6	0.497897	0.248948	+	0.968517i	$0.419915\pi$
$510$	2.60745e6	0.443906
$511$	−1.73410e6	−0.293779
$512$	4.71542e6	0.794960
$513$	1.34905e6	0.226326
$514$	5.68602e6	0.949293
$515$	495810.	0.0823753
$516$	7.75859e6	1.28280
$517$	2.08089e6	0.342391
$518$	−684966.	−0.112162
$519$	−2.82431e6	−0.460251
$520$	1.59322e6	0.258385
$521$	−6.05299e6	−0.976958	−0.488479	−	0.872576i	$-0.662448\pi$
$521$	−6.05299e6	−0.976958	−0.488479	+	0.872576i	$0.662448\pi$
$522$	−1.17421e6	−0.188612
$523$	4.76464e6	0.761685	0.380843	−	0.924640i	$-0.375634\pi$
$523$	4.76464e6	0.761685	0.380843	+	0.924640i	$0.375634\pi$
$524$	−2.59212e6	−0.412407
$525$	−1.78253e6	−0.282254
$526$	1.28878e6	0.203102
$527$	−1.31775e7	−2.06684
$528$	−521791.	−0.0814539
$529$	−5.41896e6	−0.841931
$530$	5.31678e6	0.822166
$531$	281961.	0.0433963
$532$	7.14383e6	1.09434
$533$	5.13190e6	0.782456
$534$	−3.71497e6	−0.563770
$535$	−1.66697e6	−0.251792
$536$	−4.38613e6	−0.659431
$537$	−2.81740e6	−0.421612
$538$	−1.59264e7	−2.37226
$539$	1.70072e6	0.252151
$540$	575067.	0.0848661
$541$	1.03136e7	1.51502	0.757511	−	0.652822i	$-0.226415\pi$
$541$	1.03136e7	1.51502	0.757511	+	0.652822i	$0.226415\pi$
$542$	4.34187e6	0.634861
$543$	−2.16680e6	−0.315369
$544$	−8.16840e6	−1.18342
$545$	−2.53731e6	−0.365917
$546$	2.78423e6	0.399690
$547$	9.32864e6	1.33306	0.666530	−	0.745478i	$-0.267779\pi$
$547$	9.32864e6	1.33306	0.666530	+	0.745478i	$0.267779\pi$
$548$	4.12402e6	0.586637
$549$	−2.77166e6	−0.392473
$550$	−3.84746e6	−0.542335
$551$	2.84034e6	0.398557
$552$	2.16086e6	0.301842
$553$	−911899.	−0.126804
$554$	2.01605e7	2.79079
$555$	133377.	0.0183802
$556$	−2.50203e7	−3.43246
$557$	1.72698e6	0.235857	0.117929	−	0.993022i	$-0.462375\pi$
$557$	1.72698e6	0.235857	0.117929	+	0.993022i	$0.462375\pi$
$558$	−4.53206e6	−0.616184
$559$	−7.31445e6	−0.990039
$560$	388720.	0.0523801
$561$	2.77879e6	0.372777
$562$	−2.12593e7	−2.83928
$563$	−2.82325e6	−0.375386	−0.187693	−	0.982228i	$-0.560101\pi$
$563$	−2.82325e6	−0.375386	−0.187693	+	0.982228i	$0.560101\pi$
$564$	−7.71806e6	−1.02167
$565$	−946758.	−0.124772
$566$	51941.9	0.00681517
$567$	442774.	0.0578395
$568$	−4.20331e6	−0.546664
$569$	1.12737e7	1.45978	0.729888	−	0.683567i	$-0.239572\pi$
$569$	1.12737e7	1.45978	0.729888	+	0.683567i	$0.239572\pi$
$570$	−2.16922e6	−0.279652
$571$	7.15556e6	0.918445	0.459223	−	0.888321i	$-0.348128\pi$
$571$	7.15556e6	0.918445	0.459223	+	0.888321i	$0.348128\pi$
$572$	3.85373e6	0.492483
$573$	7.24326e6	0.921611
$574$	6.73937e6	0.853768
$575$	2.96023e6	0.373384
$576$	−3.89196e6	−0.488779
$577$	6.00795e6	0.751254	0.375627	−	0.926771i	$-0.377427\pi$
$577$	6.00795e6	0.751254	0.375627	+	0.926771i	$0.377427\pi$
$578$	−3.33217e7	−4.14866
$579$	−6.52178e6	−0.808480
$580$	1.21077e6	0.149448
$581$	−5.42406e6	−0.666629
$582$	−5.74640e6	−0.703215
$583$	5.66616e6	0.690427
$584$	6.11651e6	0.742115
$585$	−542148.	−0.0654980
$586$	8.52409e6	1.02542
$587$	−6.67034e6	−0.799011	−0.399505	−	0.916731i	$-0.630818\pi$
$587$	−6.67034e6	−0.799011	−0.399505	+	0.916731i	$0.630818\pi$
$588$	−6.30801e6	−0.752400
$589$	1.09628e7	1.30207
$590$	−453384.	−0.0536211
$591$	−4.35220e6	−0.512555
$592$	448868.	0.0526399
$593$	1.86332e6	0.217596	0.108798	−	0.994064i	$-0.465300\pi$
$593$	1.86332e6	0.217596	0.108798	+	0.994064i	$0.465300\pi$
$594$	955695.	0.111136
$595$	−2.07012e6	−0.239720
$596$	1.35374e7	1.56105
$597$	3.20740e6	0.368313
$598$	−4.62374e6	−0.528738
$599$	1.74289e6	0.198474	0.0992369	−	0.995064i	$-0.468360\pi$
$599$	1.74289e6	0.198474	0.0992369	+	0.995064i	$0.468360\pi$
$600$	6.28735e6	0.713000
$601$	4.23218e6	0.477945	0.238972	−	0.971026i	$-0.423189\pi$
$601$	4.23218e6	0.477945	0.238972	+	0.971026i	$0.423189\pi$
$602$	−9.60557e6	−1.08027
$603$	1.49253e6	0.167159
$604$	2.16538e7	2.41513
$605$	−1.95524e6	−0.217176
$606$	−1.84380e6	−0.203954
$607$	−1.13339e7	−1.24856	−0.624279	−	0.781201i	$-0.714607\pi$
$607$	−1.13339e7	−1.24856	−0.624279	+	0.781201i	$0.714607\pi$
$608$	6.79556e6	0.745532
$609$	932233.	0.101855
$610$	4.45674e6	0.484946
$611$	7.27624e6	0.788505
$612$	−1.03066e7	−1.11234
$613$	1.16293e7	1.24997	0.624987	−	0.780635i	$-0.285104\pi$
$613$	1.16293e7	1.24997	0.624987	+	0.780635i	$0.285104\pi$
$614$	−4.72269e6	−0.505555
$615$	−1.31230e6	−0.139909
$616$	2.22975e6	0.236758
$617$	−1.03462e7	−1.09413	−0.547066	−	0.837090i	$-0.684255\pi$
$617$	−1.03462e7	−1.09413	−0.547066	+	0.837090i	$0.684255\pi$
$618$	−3.05615e6	−0.321887
$619$	−1.09852e7	−1.15234	−0.576169	−	0.817331i	$-0.695453\pi$
$619$	−1.09852e7	−1.15234	−0.576169	+	0.817331i	$0.695453\pi$
$620$	4.67318e6	0.488240
$621$	−735310.	−0.0765141
$622$	1.36568e7	1.41537
$623$	2.94941e6	0.304449
$624$	−1.82455e6	−0.187583
$625$	8.01894e6	0.821139
$626$	1.68419e7	1.71773
$627$	−2.31177e6	−0.234842
$628$	5.92692e6	0.599694
$629$	−2.39045e6	−0.240909
$630$	−711966.	−0.0714674
$631$	1.54733e7	1.54707	0.773535	−	0.633753i	$-0.218487\pi$
$631$	1.54733e7	1.54707	0.773535	+	0.633753i	$0.218487\pi$
$632$	3.21645e6	0.320320
$633$	578868.	0.0574210
$634$	1.35345e7	1.33727
$635$	1.92289e6	0.189243
$636$	−2.10159e7	−2.06018
$637$	5.94691e6	0.580688
$638$	2.01216e6	0.195709
$639$	1.43032e6	0.138574
$640$	4.63765e6	0.447556
$641$	1.22578e7	1.17833	0.589166	−	0.808012i	$-0.299456\pi$
$641$	1.22578e7	1.17833	0.589166	+	0.808012i	$0.299456\pi$
$642$	1.02751e7	0.983897
$643$	−1.32338e7	−1.26228	−0.631141	−	0.775668i	$-0.717413\pi$
$643$	−1.32338e7	−1.26228	−0.631141	+	0.775668i	$0.717413\pi$
$644$	−3.89380e6	−0.369964
$645$	1.87041e6	0.177026
$646$	3.88778e7	3.66539
$647$	−1.49533e7	−1.40436	−0.702178	−	0.712002i	$-0.747789\pi$
$647$	−1.49533e7	−1.40436	−0.702178	+	0.712002i	$0.747789\pi$
$648$	−1.56175e6	−0.146108
$649$	−483177.	−0.0450292
$650$	−1.34534e7	−1.24896
$651$	3.59812e6	0.332754
$652$	−1.82039e7	−1.67705
$653$	−1.46185e7	−1.34159	−0.670794	−	0.741643i	$-0.734047\pi$
$653$	−1.46185e7	−1.34159	−0.670794	+	0.741643i	$0.734047\pi$
$654$	1.56399e7	1.42985
$655$	−624896.	−0.0569121
$656$	−4.41641e6	−0.400691
$657$	−2.08136e6	−0.188119
$658$	9.55539e6	0.860367
$659$	−7.89681e6	−0.708334	−0.354167	−	0.935182i	$-0.615236\pi$
$659$	−7.89681e6	−0.708334	−0.354167	+	0.935182i	$0.615236\pi$
$660$	−985453.	−0.0880594
$661$	2.56132e6	0.228013	0.114007	−	0.993480i	$-0.463631\pi$
$661$	2.56132e6	0.228013	0.114007	+	0.993480i	$0.463631\pi$
$662$	−2.61888e7	−2.32258
$663$	9.71662e6	0.858482
$664$	1.91317e7	1.68397
$665$	1.72220e6	0.151019
$666$	−822133.	−0.0718218
$667$	−1.54815e6	−0.134740
$668$	−1.41828e6	−0.122976
$669$	3.23747e6	0.279666
$670$	−2.39994e6	−0.206545
$671$	4.74961e6	0.407241
$672$	2.23039e6	0.190527
$673$	1.96637e7	1.67351	0.836754	−	0.547578i	$-0.184450\pi$
$673$	1.96637e7	1.67351	0.836754	+	0.547578i	$0.184450\pi$
$674$	1.31438e7	1.11448
$675$	−2.13949e6	−0.180739
$676$	−7.76372e6	−0.653436
$677$	2.65672e6	0.222779	0.111389	−	0.993777i	$-0.464470\pi$
$677$	2.65672e6	0.222779	0.111389	+	0.993777i	$0.464470\pi$
$678$	5.83578e6	0.487556
$679$	4.56222e6	0.379753
$680$	7.30174e6	0.605556
$681$	5.65642e6	0.467384
$682$	7.76628e6	0.639370
$683$	−360849.	−0.0295988	−0.0147994	−	0.999890i	$-0.504711\pi$
$683$	−360849.	−0.0295988	−0.0147994	+	0.999890i	$0.504711\pi$
$684$	8.57440e6	0.700751
$685$	994201.	0.0809558
$686$	1.85222e7	1.50274
$687$	−6.41528e6	−0.518589
$688$	6.29467e6	0.506993
$689$	1.98129e7	1.59001
$690$	1.18235e6	0.0945420
$691$	1.57193e7	1.25238	0.626191	−	0.779670i	$-0.284613\pi$
$691$	1.57193e7	1.25238	0.626191	+	0.779670i	$0.284613\pi$
$692$	−1.79510e7	−1.42503
$693$	−758751.	−0.0600159
$694$	3.25356e7	2.56425
$695$	−6.03179e6	−0.473679
$696$	−3.28817e6	−0.257295
$697$	2.35196e7	1.83378
$698$	1.25901e7	0.978113
$699$	4.06171e6	0.314424
$700$	−1.13296e7	−0.873914
$701$	−2.32970e7	−1.79062	−0.895312	−	0.445440i	$-0.853047\pi$
$701$	−2.32970e7	−1.79062	−0.895312	+	0.445440i	$0.853047\pi$
$702$	3.34178e6	0.255938
$703$	1.98869e6	0.151767
$704$	6.66938e6	0.507170
$705$	−1.86064e6	−0.140990
$706$	−3.56740e7	−2.69364
$707$	1.46384e6	0.110140
$708$	1.79211e6	0.134364
$709$	5.36409e6	0.400756	0.200378	−	0.979719i	$-0.435783\pi$
$709$	5.36409e6	0.400756	0.200378	+	0.979719i	$0.435783\pi$
$710$	−2.29991e6	−0.171224
$711$	−1.09451e6	−0.0811980
$712$	−1.04032e7	−0.769069
$713$	−5.97536e6	−0.440190
$714$	1.27602e7	0.936722
$715$	929041.	0.0679626
$716$	−1.79071e7	−1.30540
$717$	4.31819e6	0.313692
$718$	−3.13487e6	−0.226939
$719$	2.10973e7	1.52196	0.760981	−	0.648774i	$-0.224718\pi$
$719$	2.10973e7	1.52196	0.760981	+	0.648774i	$0.224718\pi$
$720$	466562.	0.0335411
$721$	2.42636e6	0.173827
$722$	−8.95759e6	−0.639511
$723$	−1.48740e6	−0.105823
$724$	−1.37719e7	−0.976446
$725$	−4.50456e6	−0.318279
$726$	1.20520e7	0.848632
$727$	1.02219e7	0.717291	0.358646	−	0.933474i	$-0.383239\pi$
$727$	1.02219e7	0.717291	0.358646	+	0.933474i	$0.383239\pi$
$728$	7.79678e6	0.545239
$729$	531441.	0.0370370
$730$	3.34675e6	0.232443
$731$	−3.35222e7	−2.32028
$732$	−1.76164e7	−1.21518
$733$	1.18831e7	0.816900	0.408450	−	0.912781i	$-0.366069\pi$
$733$	1.18831e7	0.816900	0.408450	+	0.912781i	$0.366069\pi$
$734$	1.22965e7	0.842447
$735$	−1.52071e6	−0.103831
$736$	−3.70398e6	−0.252042
$737$	−2.55765e6	−0.173449
$738$	8.08895e6	0.546703
$739$	−7.32133e6	−0.493150	−0.246575	−	0.969124i	$-0.579305\pi$
$739$	−7.32133e6	−0.493150	−0.246575	+	0.969124i	$0.579305\pi$
$740$	847731.	0.0569087
$741$	−8.08357e6	−0.540826
$742$	2.60189e7	1.73492
$743$	1.09019e7	0.724484	0.362242	−	0.932084i	$-0.382011\pi$
$743$	1.09019e7	0.724484	0.362242	+	0.932084i	$0.382011\pi$
$744$	−1.26913e7	−0.840569
$745$	3.26353e6	0.215425
$746$	−4.73553e7	−3.11546
$747$	−6.51025e6	−0.426870
$748$	1.76617e7	1.15419
$749$	−8.15769e6	−0.531328
$750$	7.10338e6	0.461118
$751$	−3.73740e6	−0.241808	−0.120904	−	0.992664i	$-0.538579\pi$
$751$	−3.73740e6	−0.241808	−0.120904	+	0.992664i	$0.538579\pi$
$752$	−6.26179e6	−0.403788
$753$	1.34987e7	0.867573
$754$	7.03591e6	0.450704
$755$	5.22019e6	0.333288
$756$	2.81422e6	0.179083
$757$	−1.93400e7	−1.22664	−0.613319	−	0.789835i	$-0.710166\pi$
$757$	−1.93400e7	−1.22664	−0.613319	+	0.789835i	$0.710166\pi$
$758$	−4.05163e7	−2.56128
$759$	1.26005e6	0.0793931
$760$	−6.07455e6	−0.381488
$761$	1.32949e7	0.832190	0.416095	−	0.909321i	$-0.363398\pi$
$761$	1.32949e7	0.832190	0.416095	+	0.909321i	$0.363398\pi$
$762$	−1.18526e7	−0.739481
$763$	−1.24169e7	−0.772152
$764$	4.60374e7	2.85350
$765$	−2.48467e6	−0.153503
$766$	−2.82445e7	−1.73925
$767$	−1.68953e6	−0.103699
$768$	−1.47482e7	−0.902269
$769$	−1.41450e7	−0.862555	−0.431277	−	0.902219i	$-0.641937\pi$
$769$	−1.41450e7	−0.862555	−0.431277	+	0.902219i	$0.641937\pi$
$770$	1.22005e6	0.0741566
$771$	−5.41827e6	−0.328265
$772$	−4.14517e7	−2.50322
$773$	1.48281e7	0.892557	0.446278	−	0.894894i	$-0.352749\pi$
$773$	1.48281e7	0.892557	0.446278	+	0.894894i	$0.352749\pi$
$774$	−1.15291e7	−0.691741
$775$	−1.73862e7	−1.03980
$776$	−1.60918e7	−0.959293
$777$	652713.	0.0387855
$778$	−4.89921e7	−2.90187
$779$	−1.95667e7	−1.15524
$780$	−3.44583e6	−0.202795
$781$	−2.45105e6	−0.143788
$782$	−2.11907e7	−1.23916
$783$	1.11892e6	0.0652218
$784$	−5.11779e6	−0.297367
$785$	1.42884e6	0.0827576
$786$	3.85184e6	0.222388
$787$	−3.31567e7	−1.90825	−0.954123	−	0.299414i	$-0.903209\pi$
$787$	−3.31567e7	−1.90825	−0.954123	+	0.299414i	$0.903209\pi$
$788$	−2.76621e7	−1.58697
$789$	−1.22809e6	−0.0702326
$790$	1.75993e6	0.100330
$791$	−4.63318e6	−0.263292
$792$	2.67627e6	0.151606
$793$	1.66080e7	0.937850
$794$	−2.32202e7	−1.30712
$795$	−5.06643e6	−0.284305
$796$	2.03859e7	1.14037
$797$	2.23535e7	1.24652	0.623261	−	0.782014i	$-0.285808\pi$
$797$	2.23535e7	1.24652	0.623261	+	0.782014i	$0.285808\pi$
$798$	−1.06156e7	−0.590116
$799$	3.33471e7	1.84796
$800$	−1.07773e7	−0.595365
$801$	3.54004e6	0.194952
$802$	1.33894e7	0.735063
$803$	3.56667e6	0.195198
$804$	9.48638e6	0.517559
$805$	−938701.	−0.0510549
$806$	2.71564e7	1.47243
$807$	1.51765e7	0.820328
$808$	−5.16325e6	−0.278224
$809$	−1.54732e6	−0.0831206	−0.0415603	−	0.999136i	$-0.513233\pi$
$809$	−1.54732e6	−0.0831206	−0.0415603	+	0.999136i	$0.513233\pi$
$810$	−854539.	−0.0457635
$811$	−2.84004e7	−1.51625	−0.758127	−	0.652107i	$-0.773885\pi$
$811$	−2.84004e7	−1.51625	−0.758127	+	0.652107i	$0.773885\pi$
$812$	5.92517e6	0.315363
$813$	−4.13742e6	−0.219535
$814$	1.40883e6	0.0745243
$815$	−4.38852e6	−0.231432
$816$	−8.36192e6	−0.439623
$817$	2.78882e7	1.46173
$818$	2.22511e7	1.16270
$819$	−2.65313e6	−0.138213
$820$	−8.34082e6	−0.433186
$821$	−3.12187e7	−1.61643	−0.808216	−	0.588886i	$-0.799567\pi$
$821$	−3.12187e7	−1.61643	−0.808216	+	0.588886i	$0.799567\pi$
$822$	−6.12822e6	−0.316340
$823$	4.30753e6	0.221681	0.110841	−	0.993838i	$-0.464646\pi$
$823$	4.30753e6	0.221681	0.110841	+	0.993838i	$0.464646\pi$
$824$	−8.55825e6	−0.439104
$825$	3.66630e6	0.187539
$826$	−2.21874e6	−0.113150
$827$	−3.37874e7	−1.71787	−0.858937	−	0.512081i	$-0.828875\pi$
$827$	−3.37874e7	−1.71787	−0.858937	+	0.512081i	$0.828875\pi$
$828$	−4.67355e6	−0.236903
$829$	2.32056e7	1.17275	0.586377	−	0.810038i	$-0.300554\pi$
$829$	2.32056e7	1.17275	0.586377	+	0.810038i	$0.300554\pi$
$830$	1.04683e7	0.527448
$831$	−1.92112e7	−0.965054
$832$	2.33208e7	1.16798
$833$	2.72548e7	1.36091
$834$	3.71797e7	1.85093
$835$	−341913.	−0.0169707
$836$	−1.46934e7	−0.727119
$837$	4.31866e6	0.213076
$838$	−4.01861e7	−1.97682
$839$	−3.03381e7	−1.48794	−0.743968	−	0.668216i	$-0.767058\pi$
$839$	−3.03381e7	−1.48794	−0.743968	+	0.668216i	$0.767058\pi$
$840$	−1.99374e6	−0.0974925
$841$	−1.81553e7	−0.885145
$842$	1.80533e7	0.877559
$843$	2.02583e7	0.981823
$844$	3.67922e6	0.177787
$845$	−1.87164e6	−0.0901740
$846$	1.14689e7	0.550929
$847$	−9.56843e6	−0.458282
$848$	−1.70506e7	−0.814234
$849$	−49496.0	−0.00235668
$850$	−6.16573e7	−2.92710
$851$	−1.08395e6	−0.0513081
$852$	9.09098e6	0.429054
$853$	−2.55496e7	−1.20230	−0.601149	−	0.799137i	$-0.705290\pi$
$853$	−2.55496e7	−1.20230	−0.601149	+	0.799137i	$0.705290\pi$
$854$	2.18101e7	1.02332
$855$	2.06708e6	0.0967034
$856$	2.87738e7	1.34219
$857$	−3.85037e7	−1.79081	−0.895407	−	0.445250i	$-0.853115\pi$
$857$	−3.85037e7	−1.79081	−0.895407	+	0.445250i	$0.853115\pi$
$858$	−5.72658e6	−0.265569
$859$	2.49038e7	1.15155	0.575774	−	0.817609i	$-0.304701\pi$
$859$	2.49038e7	1.15155	0.575774	+	0.817609i	$0.304701\pi$
$860$	1.18881e7	0.548108
$861$	−6.42203e6	−0.295233
$862$	4.98739e7	2.28615
$863$	−3.38580e7	−1.54751	−0.773756	−	0.633483i	$-0.781625\pi$
$863$	−3.38580e7	−1.54751	−0.773756	+	0.633483i	$0.781625\pi$
$864$	2.67703e6	0.122002
$865$	−4.32756e6	−0.196654
$866$	3.70361e7	1.67815
$867$	3.17527e7	1.43461
$868$	2.28693e7	1.03027
$869$	1.87558e6	0.0842533
$870$	−1.79918e6	−0.0805891
$871$	−8.94334e6	−0.399442
$872$	4.37969e7	1.95053
$873$	5.47581e6	0.243172
$874$	1.76292e7	0.780646
$875$	−5.63956e6	−0.249015
$876$	−1.32289e7	−0.582455
$877$	4.91457e6	0.215768	0.107884	−	0.994163i	$-0.465593\pi$
$877$	4.91457e6	0.215768	0.107884	+	0.994163i	$0.465593\pi$
$878$	−3.08752e7	−1.35168
$879$	−8.12270e6	−0.354592
$880$	−799514.	−0.0348032
$881$	3.12482e7	1.35639	0.678196	−	0.734881i	$-0.262762\pi$
$881$	3.12482e7	1.35639	0.678196	+	0.734881i	$0.262762\pi$
$882$	9.37358e6	0.405727
$883$	2.31563e7	0.999466	0.499733	−	0.866179i	$-0.333431\pi$
$883$	2.31563e7	0.999466	0.499733	+	0.866179i	$0.333431\pi$
$884$	6.17577e7	2.65804
$885$	432035.	0.0185422
$886$	−5.69555e7	−2.43754
$887$	−1.87182e6	−0.0798832	−0.0399416	−	0.999202i	$-0.512717\pi$
$887$	−1.87182e6	−0.0798832	−0.0399416	+	0.999202i	$0.512717\pi$
$888$	−2.30225e6	−0.0979759
$889$	9.41010e6	0.399337
$890$	−5.69226e6	−0.240885
$891$	−910693.	−0.0384307
$892$	2.05770e7	0.865903
$893$	−2.77426e7	−1.16417
$894$	−2.01163e7	−0.841789
$895$	−4.31696e6	−0.180144
$896$	2.26954e7	0.944426
$897$	4.40602e6	0.182837
$898$	−5.27713e7	−2.18377
$899$	9.09266e6	0.375225
$900$	−1.35984e7	−0.559603
$901$	9.08027e7	3.72638
$902$	−1.38615e7	−0.567274
$903$	9.15327e6	0.373557
$904$	1.63421e7	0.665101
$905$	−3.32008e6	−0.134749
$906$	−3.21771e7	−1.30235
$907$	−1.61068e7	−0.650117	−0.325059	−	0.945694i	$-0.605384\pi$
$907$	−1.61068e7	−0.650117	−0.325059	+	0.945694i	$0.605384\pi$
$908$	3.59516e7	1.44712
$909$	1.75698e6	0.0705272
$910$	4.26614e6	0.170778
$911$	−2.80661e7	−1.12043	−0.560217	−	0.828346i	$-0.689282\pi$
$911$	−2.80661e7	−1.12043	−0.560217	+	0.828346i	$0.689282\pi$
$912$	6.95656e6	0.276954
$913$	1.11562e7	0.442933
$914$	2.45530e7	0.972163
$915$	−4.24688e6	−0.167694
$916$	−4.07748e7	−1.60566
$917$	−3.05807e6	−0.120095
$918$	1.53154e7	0.599822
$919$	1.01464e7	0.396301	0.198150	−	0.980172i	$-0.436507\pi$
$919$	1.01464e7	0.396301	0.198150	+	0.980172i	$0.436507\pi$
$920$	3.31099e6	0.128970
$921$	4.50031e6	0.174821
$922$	4.06025e7	1.57299
$923$	−8.57058e6	−0.331136
$924$	−4.82254e6	−0.185821
$925$	−3.15391e6	−0.121198
$926$	3.97637e7	1.52391
$927$	2.91224e6	0.111309
$928$	5.63631e6	0.214845
$929$	−1.17387e6	−0.0446254	−0.0223127	−	0.999751i	$-0.507103\pi$
$929$	−1.17387e6	−0.0446254	−0.0223127	+	0.999751i	$0.507103\pi$
$930$	−6.94425e6	−0.263280
$931$	−2.26741e7	−0.857346
$932$	2.58158e7	0.973521
$933$	−1.30137e7	−0.489436
$934$	−5.15724e7	−1.93442
$935$	4.25781e6	0.159279
$936$	9.35810e6	0.349139
$937$	−1.37307e7	−0.510908	−0.255454	−	0.966821i	$-0.582225\pi$
$937$	−1.37307e7	−0.510908	−0.255454	+	0.966821i	$0.582225\pi$
$938$	−1.17447e7	−0.435847
$939$	−1.60488e7	−0.593990
$940$	−1.18260e7	−0.436534
$941$	8.16579e6	0.300624	0.150312	−	0.988639i	$-0.451972\pi$
$941$	8.16579e6	0.300624	0.150312	+	0.988639i	$0.451972\pi$
$942$	−8.80729e6	−0.323381
$943$	1.06650e7	0.390554
$944$	1.45397e6	0.0531038
$945$	678441.	0.0247134
$946$	1.97566e7	0.717770
$947$	−1.84586e6	−0.0668844	−0.0334422	−	0.999441i	$-0.510647\pi$
$947$	−1.84586e6	−0.0668844	−0.0334422	+	0.999441i	$0.510647\pi$
$948$	−6.95658e6	−0.251406
$949$	1.24716e7	0.449528
$950$	5.12947e7	1.84401
$951$	−1.28972e7	−0.462427
$952$	3.57327e7	1.27783
$953$	2.06466e7	0.736403	0.368201	−	0.929746i	$-0.379974\pi$
$953$	2.06466e7	0.736403	0.368201	+	0.929746i	$0.379974\pi$
$954$	3.12293e7	1.11094
$955$	1.10985e7	0.393782
$956$	2.74459e7	0.971255
$957$	−1.91741e6	−0.0676760
$958$	6.53862e6	0.230183
$959$	4.86535e6	0.170831
$960$	−5.96346e6	−0.208843
$961$	6.46561e6	0.225840
$962$	4.92626e6	0.171625
$963$	−9.79129e6	−0.340231
$964$	−9.45373e6	−0.327650
$965$	−9.99299e6	−0.345444
$966$	5.78612e6	0.199501
$967$	259971.	0.00894044	0.00447022	−	0.999990i	$-0.498577\pi$
$967$	259971.	0.00894044	0.00447022	+	0.999990i	$0.498577\pi$
$968$	3.37498e7	1.15766
$969$	−3.70471e7	−1.26749
$970$	−8.80492e6	−0.300467
$971$	−4.97402e7	−1.69301	−0.846505	−	0.532380i	$-0.821298\pi$
$971$	−4.97402e7	−1.69301	−0.846505	+	0.532380i	$0.821298\pi$
$972$	3.37778e6	0.114674
$973$	−2.95179e7	−0.999548
$974$	−8.68558e7	−2.93360
$975$	1.28199e7	0.431891
$976$	−1.42925e7	−0.480267
$977$	−3.30137e6	−0.110652	−0.0553259	−	0.998468i	$-0.517620\pi$
$977$	−3.30137e6	−0.110652	−0.0553259	+	0.998468i	$0.517620\pi$
$978$	2.70507e7	0.904338
$979$	−6.06632e6	−0.202287
$980$	−9.66544e6	−0.321482
$981$	−1.49034e7	−0.494441
$982$	−4.29486e6	−0.142125
$983$	1.02213e7	0.337383	0.168692	−	0.985669i	$-0.446046\pi$
$983$	1.02213e7	0.337383	0.168692	+	0.985669i	$0.446046\pi$
$984$	2.26518e7	0.745786
$985$	−6.66866e6	−0.219002
$986$	3.22457e7	1.05628
$987$	−9.10545e6	−0.297515
$988$	−5.13783e7	−1.67451
$989$	−1.52007e7	−0.494167
$990$	1.46436e6	0.0474855
$991$	−1.38660e7	−0.448506	−0.224253	−	0.974531i	$-0.571994\pi$
$991$	−1.38660e7	−0.448506	−0.224253	+	0.974531i	$0.571994\pi$
$992$	2.17544e7	0.701887
$993$	2.49556e7	0.803148
$994$	−1.12552e7	−0.361315
$995$	4.91454e6	0.157371
$996$	−4.13784e7	−1.32168
$997$	−2.38978e7	−0.761412	−0.380706	−	0.924696i	$-0.624319\pi$
$997$	−2.38978e7	−0.761412	−0.380706	+	0.924696i	$0.624319\pi$
$998$	4.31095e7	1.37008
$999$	783420.	0.0248360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.2	✓	11
3.2	odd	2		531.6.a.b.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.2	✓	11	1.1	even	1	trivial
531.6.a.b.1.10		11	3.2	odd	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} -130.245 q^{10} -138.804 q^{11} +514.827 q^{12} -485.356 q^{13} -637.385 q^{14} +124.112 q^{15} +417.688 q^{16} -2224.39 q^{17} -765.023 q^{18} +1850.55 q^{19} +788.844 q^{20} +607.372 q^{21} +1310.97 q^{22} -1008.66 q^{23} -2142.32 q^{24} -2934.83 q^{25} +4584.06 q^{26} +729.000 q^{27} +3860.39 q^{28} +1534.86 q^{29} -1172.21 q^{30} +5924.08 q^{31} +3672.19 q^{32} -1249.24 q^{33} +21008.8 q^{34} +930.646 q^{35} +4633.44 q^{36} +1074.65 q^{37} -17477.9 q^{38} -4368.21 q^{39} -3282.57 q^{40} -10573.5 q^{41} -5736.47 q^{42} +15070.3 q^{43} -7940.01 q^{44} +1117.01 q^{45} +9526.48 q^{46} -14991.6 q^{47} +3759.19 q^{48} -12252.7 q^{49} +27718.7 q^{50} -20019.6 q^{51} -27763.8 q^{52} -40821.3 q^{53} -6885.21 q^{54} -1914.14 q^{55} -16064.0 q^{56} +16654.9 q^{57} -14496.4 q^{58} +3481.00 q^{59} +7099.60 q^{60} -34218.1 q^{61} -55951.4 q^{62} +5466.35 q^{63} -48048.9 q^{64} -6693.19 q^{65} +11798.7 q^{66} +18426.3 q^{67} -127242. q^{68} -9077.90 q^{69} -8789.71 q^{70} +17658.3 q^{71} -19280.9 q^{72} -25695.8 q^{73} -10149.8 q^{74} -26413.5 q^{75} +105857. q^{76} -9367.30 q^{77} +41256.6 q^{78} -13512.5 q^{79} +5760.02 q^{80} +6561.00 q^{81} +99863.6 q^{82} -80373.4 q^{83} +34743.5 q^{84} -30675.0 q^{85} -142335. q^{86} +13813.8 q^{87} +33040.3 q^{88} +43704.2 q^{89} -10549.9 q^{90} -32754.7 q^{91} -57698.1 q^{92} +53316.7 q^{93} +141591. q^{94} +25519.5 q^{95} +33049.7 q^{96} +67602.6 q^{97} +115723. q^{98} -11243.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * q^99

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