LMFDB - Embedded newform 177.6.a.a.1.9

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			1.9
Root			$7.91273$ 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)

$f(q)$	$=$	$q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} -76.9686 q^{10} -125.065 q^{11} +142.072 q^{12} +1116.22 q^{13} -1336.12 q^{14} -100.209 q^{15} -1279.95 q^{16} -1948.69 q^{17} +559.931 q^{18} -2116.73 q^{19} -175.764 q^{20} -1739.55 q^{21} -864.538 q^{22} -2537.35 q^{23} -1008.76 q^{24} -3001.03 q^{25} +7716.11 q^{26} +729.000 q^{27} -3051.13 q^{28} +4531.40 q^{29} -692.717 q^{30} -902.692 q^{31} -5261.27 q^{32} -1125.58 q^{33} -13470.8 q^{34} +2152.08 q^{35} +1278.65 q^{36} +15206.0 q^{37} -14632.4 q^{38} +10046.0 q^{39} +1247.98 q^{40} -8454.58 q^{41} -12025.0 q^{42} -9993.30 q^{43} -1974.25 q^{44} -901.881 q^{45} -17540.0 q^{46} +2702.02 q^{47} -11519.6 q^{48} +20551.5 q^{49} -20745.3 q^{50} -17538.2 q^{51} +17620.4 q^{52} +23313.3 q^{53} +5039.38 q^{54} +1392.51 q^{55} +21664.0 q^{56} -19050.6 q^{57} +31324.3 q^{58} +3481.00 q^{59} -1581.88 q^{60} -29163.2 q^{61} -6240.06 q^{62} -15656.0 q^{63} +4588.78 q^{64} -12428.3 q^{65} -7780.85 q^{66} -9692.20 q^{67} -30761.7 q^{68} -22836.2 q^{69} +14876.7 q^{70} -6707.84 q^{71} -9078.83 q^{72} +51879.5 q^{73} +105115. q^{74} -27009.2 q^{75} -33414.2 q^{76} +24172.9 q^{77} +69445.0 q^{78} -70812.0 q^{79} +14251.4 q^{80} +6561.00 q^{81} -58444.2 q^{82} +31987.2 q^{83} -27460.2 q^{84} +21697.4 q^{85} -69081.0 q^{86} +40782.6 q^{87} +14017.8 q^{88} +78629.4 q^{89} -6234.45 q^{90} -215746. q^{91} -40054.2 q^{92} -8124.23 q^{93} +18678.3 q^{94} +23568.3 q^{95} -47351.5 q^{96} +21462.8 q^{97} +142067. q^{98} -10130.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.91273	1.22201	0.611005	−	0.791627i	$-0.290766\pi$
$2$	6.91273	1.22201	0.611005	+	0.791627i	$0.290766\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	15.7858	0.493306
$5$	−11.1343	−0.199177	−0.0995885	−	0.995029i	$-0.531753\pi$
$5$	−11.1343	−0.199177	−0.0995885	+	0.995029i	$0.531753\pi$
$6$	62.2145	0.705527
$7$	−193.283	−1.49090	−0.745452	−	0.666560i	$-0.767766\pi$
$7$	−193.283	−1.49090	−0.745452	+	0.666560i	$0.767766\pi$
$8$	−112.084	−0.619185
$9$	81.0000	0.333333
$10$	−76.9686	−0.243396
$11$	−125.065	−0.311640	−0.155820	−	0.987785i	$-0.549802\pi$
$11$	−125.065	−0.311640	−0.155820	+	0.987785i	$0.549802\pi$
$12$	142.072	0.284810
$13$	1116.22	1.83185	0.915927	−	0.401346i	$-0.131457\pi$
$13$	1116.22	1.83185	0.915927	+	0.401346i	$0.131457\pi$
$14$	−1336.12	−1.82190
$15$	−100.209	−0.114995
$16$	−1279.95	−1.24996
$17$	−1948.69	−1.63539	−0.817695	−	0.575652i	$-0.804748\pi$
$17$	−1948.69	−1.63539	−0.817695	+	0.575652i	$0.804748\pi$
$18$	559.931	0.407336
$19$	−2116.73	−1.34518	−0.672591	−	0.740014i	$-0.734819\pi$
$19$	−2116.73	−1.34518	−0.672591	+	0.740014i	$0.734819\pi$
$20$	−175.764	−0.0982552
$21$	−1739.55	−0.860773
$22$	−864.538	−0.380827
$23$	−2537.35	−1.00014	−0.500071	−	0.865985i	$-0.666693\pi$
$23$	−2537.35	−1.00014	−0.500071	+	0.865985i	$0.666693\pi$
$24$	−1008.76	−0.357486
$25$	−3001.03	−0.960329
$26$	7716.11	2.23854
$27$	729.000	0.192450
$28$	−3051.13	−0.735472
$29$	4531.40	1.00055	0.500273	−	0.865867i	$-0.333233\pi$
$29$	4531.40	1.00055	0.500273	+	0.865867i	$0.333233\pi$
$30$	−692.717	−0.140525
$31$	−902.692	−0.168708	−0.0843539	−	0.996436i	$-0.526883\pi$
$31$	−902.692	−0.168708	−0.0843539	+	0.996436i	$0.526883\pi$
$32$	−5261.27	−0.908272
$33$	−1125.58	−0.179925
$34$	−13470.8	−1.99846
$35$	2152.08	0.296953
$36$	1278.65	0.164435
$37$	15206.0	1.82604	0.913020	−	0.407916i	$-0.133744\pi$
$37$	15206.0	1.82604	0.913020	+	0.407916i	$0.133744\pi$
$38$	−14632.4	−1.64382
$39$	10046.0	1.05762
$40$	1247.98	0.123327
$41$	−8454.58	−0.785475	−0.392737	−	0.919651i	$-0.628472\pi$
$41$	−8454.58	−0.785475	−0.392737	+	0.919651i	$0.628472\pi$
$42$	−12025.0	−1.05187
$43$	−9993.30	−0.824210	−0.412105	−	0.911136i	$-0.635206\pi$
$43$	−9993.30	−0.824210	−0.412105	+	0.911136i	$0.635206\pi$
$44$	−1974.25	−0.153734
$45$	−901.881	−0.0663923
$46$	−17540.0	−1.22218
$47$	2702.02	0.178420	0.0892100	−	0.996013i	$-0.471566\pi$
$47$	2702.02	0.178420	0.0892100	+	0.996013i	$0.471566\pi$
$48$	−11519.6	−0.721662
$49$	20551.5	1.22279
$50$	−20745.3	−1.17353
$51$	−17538.2	−0.944193
$52$	17620.4	0.903664
$53$	23313.3	1.14003	0.570013	−	0.821636i	$-0.306938\pi$
$53$	23313.3	1.14003	0.570013	+	0.821636i	$0.306938\pi$
$54$	5039.38	0.235176
$55$	1392.51	0.0620715
$56$	21664.0	0.923144
$57$	−19050.6	−0.776641
$58$	31324.3	1.22268
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−1581.88	−0.0567277
$61$	−29163.2	−1.00348	−0.501742	−	0.865017i	$-0.667307\pi$
$61$	−29163.2	−1.00348	−0.501742	+	0.865017i	$0.667307\pi$
$62$	−6240.06	−0.206162
$63$	−15656.0	−0.496968
$64$	4588.78	0.140039
$65$	−12428.3	−0.364863
$66$	−7780.85	−0.219870
$67$	−9692.20	−0.263776	−0.131888	−	0.991265i	$-0.542104\pi$
$67$	−9692.20	−0.263776	−0.131888	+	0.991265i	$0.542104\pi$
$68$	−30761.7	−0.806748
$69$	−22836.2	−0.577432
$70$	14876.7	0.362880
$71$	−6707.84	−0.157920	−0.0789599	−	0.996878i	$-0.525160\pi$
$71$	−6707.84	−0.157920	−0.0789599	+	0.996878i	$0.525160\pi$
$72$	−9078.83	−0.206395
$73$	51879.5	1.13943	0.569716	−	0.821841i	$-0.307053\pi$
$73$	51879.5	1.13943	0.569716	+	0.821841i	$0.307053\pi$
$74$	105115.	2.23144
$75$	−27009.2	−0.554446
$76$	−33414.2	−0.663586
$77$	24172.9	0.464625
$78$	69445.0	1.29242
$79$	−70812.0	−1.27655	−0.638277	−	0.769807i	$-0.720352\pi$
$79$	−70812.0	−1.27655	−0.638277	+	0.769807i	$0.720352\pi$
$80$	14251.4	0.248962
$81$	6561.00	0.111111
$82$	−58444.2	−0.959857
$83$	31987.2	0.509660	0.254830	−	0.966986i	$-0.417980\pi$
$83$	31987.2	0.509660	0.254830	+	0.966986i	$0.417980\pi$
$84$	−27460.2	−0.424625
$85$	21697.4	0.325732
$86$	−69081.0	−1.00719
$87$	40782.6	0.577666
$88$	14017.8	0.192963
$89$	78629.4	1.05223	0.526114	−	0.850414i	$-0.323649\pi$
$89$	78629.4	1.05223	0.526114	+	0.850414i	$0.323649\pi$
$90$	−6234.45	−0.0811320
$91$	−215746.	−2.73112
$92$	−40054.2	−0.493376
$93$	−8124.23	−0.0974035
$94$	18678.3	0.218031
$95$	23568.3	0.267929
$96$	−47351.5	−0.524391
$97$	21462.8	0.231610	0.115805	−	0.993272i	$-0.463055\pi$
$97$	21462.8	0.231610	0.115805	+	0.993272i	$0.463055\pi$
$98$	142067.	1.49426
$99$	−10130.2	−0.103880
$100$	−47373.6	−0.473736
$101$	4675.59	0.0456072	0.0228036	−	0.999740i	$-0.492741\pi$
$101$	4675.59	0.0456072	0.0228036	+	0.999740i	$0.492741\pi$
$102$	−121237.	−1.15381
$103$	71375.2	0.662909	0.331455	−	0.943471i	$-0.392461\pi$
$103$	71375.2	0.662909	0.331455	+	0.943471i	$0.392461\pi$
$104$	−125111.	−1.13426
$105$	19368.7	0.171446
$106$	161159.	1.39312
$107$	−227244.	−1.91882	−0.959409	−	0.282019i	$-0.908996\pi$
$107$	−227244.	−1.91882	−0.959409	+	0.282019i	$0.908996\pi$
$108$	11507.8	0.0949368
$109$	19845.6	0.159992	0.0799961	−	0.996795i	$-0.474509\pi$
$109$	19845.6	0.159992	0.0799961	+	0.996795i	$0.474509\pi$
$110$	9626.05	0.0758519
$111$	136854.	1.05426
$112$	247394.	1.86356
$113$	69900.0	0.514969	0.257484	−	0.966282i	$-0.417106\pi$
$113$	69900.0	0.514969	0.257484	+	0.966282i	$0.417106\pi$
$114$	−131691.	−0.949063
$115$	28251.7	0.199205
$116$	71531.8	0.493576
$117$	90413.7	0.610618
$118$	24063.2	0.159092
$119$	376650.	2.43821
$120$	11231.9	0.0712030
$121$	−145410.	−0.902881
$122$	−201597.	−1.22627
$123$	−76091.2	−0.453494
$124$	−14249.7	−0.0832246
$125$	68209.2	0.390452
$126$	−108225.	−0.607299
$127$	99756.3	0.548821	0.274411	−	0.961613i	$-0.411517\pi$
$127$	99756.3	0.548821	0.274411	+	0.961613i	$0.411517\pi$
$128$	200082.	1.07940
$129$	−89939.7	−0.475858
$130$	−85913.7	−0.445866
$131$	−197499.	−1.00551	−0.502756	−	0.864428i	$-0.667681\pi$
$131$	−197499.	−1.00551	−0.502756	+	0.864428i	$0.667681\pi$
$132$	−17768.2	−0.0887583
$133$	409128.	2.00554
$134$	−66999.6	−0.322337
$135$	−8116.92	−0.0383316
$136$	218418.	1.01261
$137$	−244667.	−1.11371	−0.556857	−	0.830608i	$-0.687993\pi$
$137$	−244667.	−1.11371	−0.556857	+	0.830608i	$0.687993\pi$
$138$	−157860.	−0.705627
$139$	−204234.	−0.896584	−0.448292	−	0.893887i	$-0.647968\pi$
$139$	−204234.	−0.896584	−0.448292	+	0.893887i	$0.647968\pi$
$140$	33972.3	0.146489
$141$	24318.2	0.103011
$142$	−46369.4	−0.192979
$143$	−139600.	−0.570879
$144$	−103676.	−0.416652
$145$	−50454.1	−0.199286
$146$	358629.	1.39240
$147$	184963.	0.705979
$148$	240038.	0.900796
$149$	−410416.	−1.51446	−0.757232	−	0.653146i	$-0.773449\pi$
$149$	−410416.	−1.51446	−0.757232	+	0.653146i	$0.773449\pi$
$150$	−186708.	−0.677538
$151$	−388786.	−1.38761	−0.693807	−	0.720161i	$-0.744068\pi$
$151$	−388786.	−1.38761	−0.693807	+	0.720161i	$0.744068\pi$
$152$	237252.	0.832916
$153$	−157844.	−0.545130
$154$	167101.	0.567776
$155$	10050.9	0.0336027
$156$	158584.	0.521731
$157$	336248.	1.08871	0.544353	−	0.838856i	$-0.316775\pi$
$157$	336248.	1.08871	0.544353	+	0.838856i	$0.316775\pi$
$158$	−489504.	−1.55996
$159$	209820.	0.658194
$160$	58580.7	0.180907
$161$	490428.	1.49111
$162$	45354.4	0.135779
$163$	299758.	0.883694	0.441847	−	0.897091i	$-0.354323\pi$
$163$	299758.	0.883694	0.441847	+	0.897091i	$0.354323\pi$
$164$	−133462.	−0.387479
$165$	12532.6	0.0358370
$166$	221119.	0.622810
$167$	263356.	0.730722	0.365361	−	0.930866i	$-0.380946\pi$
$167$	263356.	0.730722	0.365361	+	0.930866i	$0.380946\pi$
$168$	194976.	0.532978
$169$	874650.	2.35569
$170$	149988.	0.398047
$171$	−171455.	−0.448394
$172$	−157752.	−0.406588
$173$	−695281.	−1.76622	−0.883111	−	0.469164i	$-0.844555\pi$
$173$	−695281.	−1.76622	−0.883111	+	0.469164i	$0.844555\pi$
$174$	281919.	0.705913
$175$	580049.	1.43176
$176$	160077.	0.389536
$177$	31329.0	0.0751646
$178$	543543.	1.28583
$179$	450239.	1.05029	0.525147	−	0.851012i	$-0.324010\pi$
$179$	450239.	1.05029	0.525147	+	0.851012i	$0.324010\pi$
$180$	−14236.9	−0.0327517
$181$	289973.	0.657901	0.328951	−	0.944347i	$-0.393305\pi$
$181$	289973.	0.657901	0.328951	+	0.944347i	$0.393305\pi$
$182$	−1.49140e6	−3.33745
$183$	−262469.	−0.579362
$184$	284398.	0.619272
$185$	−169308.	−0.363705
$186$	−56160.6	−0.119028
$187$	243713.	0.509653
$188$	42653.5	0.0880157
$189$	−140904.	−0.286924
$190$	162922.	0.327412
$191$	−272091.	−0.539673	−0.269836	−	0.962906i	$-0.586970\pi$
$191$	−272091.	−0.539673	−0.269836	+	0.962906i	$0.586970\pi$
$192$	41299.1	0.0808513
$193$	−800409.	−1.54675	−0.773373	−	0.633951i	$-0.781432\pi$
$193$	−800409.	−1.54675	−0.773373	+	0.633951i	$0.781432\pi$
$194$	148367.	0.283030
$195$	−111855.	−0.210654
$196$	324421.	0.603211
$197$	−639502.	−1.17402	−0.587012	−	0.809579i	$-0.699696\pi$
$197$	−639502.	−1.17402	−0.587012	+	0.809579i	$0.699696\pi$
$198$	−70027.6	−0.126942
$199$	812910.	1.45516	0.727579	−	0.686024i	$-0.240646\pi$
$199$	812910.	1.45516	0.727579	+	0.686024i	$0.240646\pi$
$200$	336368.	0.594621
$201$	−87229.8	−0.152291
$202$	32321.1	0.0557324
$203$	−875845.	−1.49172
$204$	−276855.	−0.465776
$205$	94136.0	0.156448
$206$	493397.	0.810081
$207$	−205526.	−0.333381
$208$	−1.42871e6	−2.28973
$209$	264728.	0.419212
$210$	133891.	0.209509
$211$	134678.	0.208253	0.104126	−	0.994564i	$-0.466795\pi$
$211$	134678.	0.208253	0.104126	+	0.994564i	$0.466795\pi$
$212$	368019.	0.562382
$213$	−60370.5	−0.0911751
$214$	−1.57088e6	−2.34481
$215$	111269.	0.164164
$216$	−81709.5	−0.119162
$217$	174475.	0.251527
$218$	137187.	0.195512
$219$	466916.	0.657852
$220$	21981.9	0.0306202
$221$	−2.17517e6	−2.99579
$222$	946033.	1.28832
$223$	−922919.	−1.24280	−0.621401	−	0.783493i	$-0.713436\pi$
$223$	−922919.	−1.24280	−0.621401	+	0.783493i	$0.713436\pi$
$224$	1.01692e6	1.35415
$225$	−243083.	−0.320110
$226$	483200.	0.629297
$227$	−936298.	−1.20601	−0.603003	−	0.797739i	$-0.706029\pi$
$227$	−936298.	−1.20601	−0.603003	+	0.797739i	$0.706029\pi$
$228$	−300728.	−0.383122
$229$	−1.13593e6	−1.43141	−0.715706	−	0.698402i	$-0.753895\pi$
$229$	−1.13593e6	−1.43141	−0.715706	+	0.698402i	$0.753895\pi$
$230$	195297.	0.243430
$231$	217556.	0.268251
$232$	−507899.	−0.619523
$233$	−1.39667e6	−1.68540	−0.842700	−	0.538383i	$-0.819035\pi$
$233$	−1.39667e6	−1.68540	−0.842700	+	0.538383i	$0.819035\pi$
$234$	625005.	0.746180
$235$	−30085.2	−0.0355372
$236$	54950.4	0.0642230
$237$	−637308.	−0.737019
$238$	2.60368e6	2.97951
$239$	833356.	0.943704	0.471852	−	0.881678i	$-0.343586\pi$
$239$	833356.	0.943704	0.471852	+	0.881678i	$0.343586\pi$
$240$	128263.	0.143738
$241$	1.27013e6	1.40866	0.704331	−	0.709871i	$-0.251247\pi$
$241$	1.27013e6	1.40866	0.704331	+	0.709871i	$0.251247\pi$
$242$	−1.00518e6	−1.10333
$243$	59049.0	0.0641500
$244$	−460364.	−0.495025
$245$	−228827.	−0.243552
$246$	−525998.	−0.554174
$247$	−2.36273e6	−2.46418
$248$	101178.	0.104461
$249$	287885.	0.294253
$250$	471512.	0.477136
$251$	−791023.	−0.792510	−0.396255	−	0.918141i	$-0.629690\pi$
$251$	−791023.	−0.792510	−0.396255	+	0.918141i	$0.629690\pi$
$252$	−247142.	−0.245157
$253$	317334.	0.311684
$254$	689588.	0.670665
$255$	195277.	0.188061
$256$	1.23627e6	1.17900
$257$	−1.83299e6	−1.73112	−0.865559	−	0.500807i	$-0.833037\pi$
$257$	−1.83299e6	−1.73112	−0.865559	+	0.500807i	$0.833037\pi$
$258$	−621729.	−0.581502
$259$	−2.93906e6	−2.72245
$260$	−196191.	−0.179989
$261$	367043.	0.333516
$262$	−1.36526e6	−1.22874
$263$	−12651.0	−0.0112781	−0.00563905	−	0.999984i	$-0.501795\pi$
$263$	−12651.0	−0.0112781	−0.00563905	+	0.999984i	$0.501795\pi$
$264$	126160.	0.111407
$265$	−259578.	−0.227067
$266$	2.82819e6	2.45078
$267$	707664.	0.607504
$268$	−152999.	−0.130122
$269$	−148582.	−0.125195	−0.0625973	−	0.998039i	$-0.519938\pi$
$269$	−148582.	−0.125195	−0.0625973	+	0.998039i	$0.519938\pi$
$270$	−56110.1	−0.0468416
$271$	941611.	0.778840	0.389420	−	0.921060i	$-0.372675\pi$
$271$	941611.	0.778840	0.389420	+	0.921060i	$0.372675\pi$
$272$	2.49424e6	2.04416
$273$	−1.94172e6	−1.57681
$274$	−1.69131e6	−1.36097
$275$	375323.	0.299277
$276$	−360487.	−0.284851
$277$	2.13299e6	1.67028	0.835140	−	0.550038i	$-0.185387\pi$
$277$	2.13299e6	1.67028	0.835140	+	0.550038i	$0.185387\pi$
$278$	−1.41181e6	−1.09563
$279$	−73118.0	−0.0562359
$280$	−241215.	−0.183869
$281$	−890716.	−0.672935	−0.336468	−	0.941695i	$-0.609232\pi$
$281$	−890716.	−0.672935	−0.336468	+	0.941695i	$0.609232\pi$
$282$	168105.	0.125880
$283$	817581.	0.606826	0.303413	−	0.952859i	$-0.401874\pi$
$283$	817581.	0.606826	0.303413	+	0.952859i	$0.401874\pi$
$284$	−105889.	−0.0779028
$285$	212115.	0.154689
$286$	−965013.	−0.697619
$287$	1.63413e6	1.17107
$288$	−426163.	−0.302757
$289$	2.37755e6	1.67450
$290$	−348775.	−0.243529
$291$	193165.	0.133720
$292$	818959.	0.562089
$293$	610411.	0.415388	0.207694	−	0.978194i	$-0.433404\pi$
$293$	610411.	0.415388	0.207694	+	0.978194i	$0.433404\pi$
$294$	1.27860e6	0.862713
$295$	−38758.6	−0.0259306
$296$	−1.70435e6	−1.13066
$297$	−91172.2	−0.0599751
$298$	−2.83710e6	−1.85069
$299$	−2.83224e6	−1.83211
$300$	−426362.	−0.273512
$301$	1.93154e6	1.22882
$302$	−2.68757e6	−1.69568
$303$	42080.4	0.0263313
$304$	2.70931e6	1.68142
$305$	324713.	0.199871
$306$	−1.09113e6	−0.666154
$307$	−1.00422e6	−0.608112	−0.304056	−	0.952654i	$-0.598341\pi$
$307$	−1.00422e6	−0.608112	−0.304056	+	0.952654i	$0.598341\pi$
$308$	381589.	0.229202
$309$	642376.	0.382731
$310$	69478.9	0.0410628
$311$	−35455.9	−0.0207868	−0.0103934	−	0.999946i	$-0.503308\pi$
$311$	−35455.9	−0.0207868	−0.0103934	+	0.999946i	$0.503308\pi$
$312$	−1.12600e6	−0.654863
$313$	−1.63361e6	−0.942511	−0.471255	−	0.881997i	$-0.656199\pi$
$313$	−1.63361e6	−0.942511	−0.471255	+	0.881997i	$0.656199\pi$
$314$	2.32439e6	1.33041
$315$	174319.	0.0989845
$316$	−1.11782e6	−0.629732
$317$	−620992.	−0.347086	−0.173543	−	0.984826i	$-0.555522\pi$
$317$	−620992.	−0.347086	−0.173543	+	0.984826i	$0.555522\pi$
$318$	1.45043e6	0.804319
$319$	−566718.	−0.311810
$320$	−51093.0	−0.0278925
$321$	−2.04520e6	−1.10783
$322$	3.39020e6	1.82216
$323$	4.12485e6	2.19990
$324$	103571.	0.0548118
$325$	−3.34980e6	−1.75918
$326$	2.07215e6	1.07988
$327$	178611.	0.0923715
$328$	947626.	0.486354
$329$	−522255.	−0.266007
$330$	86634.5	0.0437931
$331$	2.75397e6	1.38162	0.690812	−	0.723034i	$-0.257253\pi$
$331$	2.75397e6	1.38162	0.690812	+	0.723034i	$0.257253\pi$
$332$	504943.	0.251419
$333$	1.23168e6	0.608680
$334$	1.82051e6	0.892949
$335$	107916.	0.0525381
$336$	2.22654e6	1.07593
$337$	467039.	0.224016	0.112008	−	0.993707i	$-0.464272\pi$
$337$	467039.	0.224016	0.112008	+	0.993707i	$0.464272\pi$
$338$	6.04622e6	2.87867
$339$	629100.	0.297317
$340$	342511.	0.160686
$341$	112895.	0.0525761
$342$	−1.18522e6	−0.547942
$343$	−723744.	−0.332162
$344$	1.12009e6	0.510338
$345$	254266.	0.115011
$346$	−4.80629e6	−2.15834
$347$	3.27711e6	1.46106	0.730530	−	0.682881i	$-0.239273\pi$
$347$	3.27711e6	1.46106	0.730530	+	0.682881i	$0.239273\pi$
$348$	643786.	0.284966
$349$	−3.92940e6	−1.72688	−0.863441	−	0.504450i	$-0.831695\pi$
$349$	−3.92940e6	−1.72688	−0.863441	+	0.504450i	$0.831695\pi$
$350$	4.00972e6	1.74962
$351$	813723.	0.352540
$352$	658000.	0.283054
$353$	3.34115e6	1.42712	0.713558	−	0.700597i	$-0.247083\pi$
$353$	3.34115e6	1.42712	0.713558	+	0.700597i	$0.247083\pi$
$354$	216569.	0.0918518
$355$	74687.3	0.0314540
$356$	1.24123e6	0.519070
$357$	3.38985e6	1.40770
$358$	3.11238e6	1.28347
$359$	−772755.	−0.316450	−0.158225	−	0.987403i	$-0.550577\pi$
$359$	−772755.	−0.316450	−0.158225	+	0.987403i	$0.550577\pi$
$360$	101087.	0.0411091
$361$	2.00444e6	0.809514
$362$	2.00450e6	0.803961
$363$	−1.30869e6	−0.521278
$364$	−3.40573e6	−1.34728
$365$	−577643.	−0.226949
$366$	−1.81437e6	−0.707985
$367$	−640958.	−0.248407	−0.124204	−	0.992257i	$-0.539638\pi$
$367$	−640958.	−0.248407	−0.124204	+	0.992257i	$0.539638\pi$
$368$	3.24770e6	1.25013
$369$	−684821.	−0.261825
$370$	−1.17038e6	−0.444451
$371$	−4.50608e6	−1.69967
$372$	−128247.	−0.0480497
$373$	−2.37093e6	−0.882360	−0.441180	−	0.897419i	$-0.645440\pi$
$373$	−2.37093e6	−0.882360	−0.441180	+	0.897419i	$0.645440\pi$
$374$	1.68472e6	0.622800
$375$	613883.	0.225428
$376$	−302854.	−0.110475
$377$	5.05803e6	1.83286
$378$	−974028.	−0.350624
$379$	−2.59822e6	−0.929134	−0.464567	−	0.885538i	$-0.653790\pi$
$379$	−2.59822e6	−0.929134	−0.464567	+	0.885538i	$0.653790\pi$
$380$	372045.	0.132171
$381$	897807.	0.316862
$382$	−1.88089e6	−0.659485
$383$	−2.73909e6	−0.954135	−0.477067	−	0.878867i	$-0.658300\pi$
$383$	−2.73909e6	−0.954135	−0.477067	+	0.878867i	$0.658300\pi$
$384$	1.80074e6	0.623192
$385$	−269149.	−0.0925426
$386$	−5.53301e6	−1.89014
$387$	−809457.	−0.274737
$388$	338808.	0.114255
$389$	1.26060e6	0.422381	0.211190	−	0.977445i	$-0.432266\pi$
$389$	1.26060e6	0.422381	0.211190	+	0.977445i	$0.432266\pi$
$390$	−773223.	−0.257421
$391$	4.94453e6	1.63562
$392$	−2.30350e6	−0.757134
$393$	−1.77749e6	−0.580533
$394$	−4.42071e6	−1.43467
$395$	788444.	0.254260
$396$	−159914.	−0.0512446
$397$	146031.	0.0465017	0.0232508	−	0.999730i	$-0.492598\pi$
$397$	146031.	0.0465017	0.0232508	+	0.999730i	$0.492598\pi$
$398$	5.61943e6	1.77822
$399$	3.68216e6	1.15790
$400$	3.84118e6	1.20037
$401$	−2.94941e6	−0.915956	−0.457978	−	0.888964i	$-0.651426\pi$
$401$	−2.94941e6	−0.915956	−0.457978	+	0.888964i	$0.651426\pi$
$402$	−602996.	−0.186101
$403$	−1.00760e6	−0.309048
$404$	73808.0	0.0224983
$405$	−73052.3	−0.0221308
$406$	−6.05447e6	−1.82289
$407$	−1.90173e6	−0.569067
$408$	1.96576e6	0.584630
$409$	3.43709e6	1.01597	0.507987	−	0.861365i	$-0.330390\pi$
$409$	3.43709e6	1.01597	0.507987	+	0.861365i	$0.330390\pi$
$410$	650737.	0.191181
$411$	−2.20200e6	−0.643003
$412$	1.12671e6	0.327017
$413$	−672819.	−0.194099
$414$	−1.42074e6	−0.407394
$415$	−356156.	−0.101513
$416$	−5.87273e6	−1.66382
$417$	−1.83811e6	−0.517643
$418$	1.82999e6	0.512281
$419$	−6.48770e6	−1.80533	−0.902664	−	0.430347i	$-0.858391\pi$
$419$	−6.48770e6	−1.80533	−0.902664	+	0.430347i	$0.858391\pi$
$420$	305751.	0.0845754
$421$	−3.88945e6	−1.06951	−0.534753	−	0.845008i	$-0.679595\pi$
$421$	−3.88945e6	−1.06951	−0.534753	+	0.845008i	$0.679595\pi$
$422$	930992.	0.254487
$423$	218863.	0.0594733
$424$	−2.61306e6	−0.705886
$425$	5.84808e6	1.57051
$426$	−417325.	−0.111417
$427$	5.63676e6	1.49610
$428$	−3.58723e6	−0.946565
$429$	−1.25640e6	−0.329597
$430$	769170.	0.200609
$431$	268690.	0.0696721	0.0348361	−	0.999393i	$-0.488909\pi$
$431$	268690.	0.0696721	0.0348361	+	0.999393i	$0.488909\pi$
$432$	−933087.	−0.240554
$433$	−1.71353e6	−0.439210	−0.219605	−	0.975589i	$-0.570477\pi$
$433$	−1.71353e6	−0.439210	−0.219605	+	0.975589i	$0.570477\pi$
$434$	1.20610e6	0.307368
$435$	−454087.	−0.115058
$436$	313279.	0.0789251
$437$	5.37089e6	1.34537
$438$	3.22766e6	0.803901
$439$	663061.	0.164207	0.0821035	−	0.996624i	$-0.473836\pi$
$439$	663061.	0.164207	0.0821035	+	0.996624i	$0.473836\pi$
$440$	−156079.	−0.0384337
$441$	1.66467e6	0.407597
$442$	−1.50363e7	−3.66089
$443$	−1.92044e6	−0.464934	−0.232467	−	0.972604i	$-0.574680\pi$
$443$	−1.92044e6	−0.464934	−0.232467	+	0.972604i	$0.574680\pi$
$444$	2.16035e6	0.520075
$445$	−875485.	−0.209579
$446$	−6.37989e6	−1.51871
$447$	−3.69375e6	−0.874376
$448$	−886936.	−0.208784
$449$	−641166.	−0.150091	−0.0750454	−	0.997180i	$-0.523910\pi$
$449$	−641166.	−0.150091	−0.0750454	+	0.997180i	$0.523910\pi$
$450$	−1.68037e6	−0.391177
$451$	1.05737e6	0.244785
$452$	1.10343e6	0.254037
$453$	−3.49908e6	−0.801139
$454$	−6.47237e6	−1.47375
$455$	2.40219e6	0.543975
$456$	2.13527e6	0.480884
$457$	2.82002e6	0.631629	0.315814	−	0.948821i	$-0.397722\pi$
$457$	2.82002e6	0.631629	0.315814	+	0.948821i	$0.397722\pi$
$458$	−7.85241e6	−1.74920
$459$	−1.42060e6	−0.314731
$460$	445976.	0.0982691
$461$	−4.36961e6	−0.957613	−0.478806	−	0.877920i	$-0.658930\pi$
$461$	−4.36961e6	−0.957613	−0.478806	+	0.877920i	$0.658930\pi$
$462$	1.50391e6	0.327806
$463$	712732.	0.154516	0.0772580	−	0.997011i	$-0.475383\pi$
$463$	712732.	0.154516	0.0772580	+	0.997011i	$0.475383\pi$
$464$	−5.79999e6	−1.25064
$465$	90457.8	0.0194005
$466$	−9.65478e6	−2.05957
$467$	2.02176e6	0.428981	0.214491	−	0.976726i	$-0.431191\pi$
$467$	2.02176e6	0.428981	0.214491	+	0.976726i	$0.431191\pi$
$468$	1.42725e6	0.301221
$469$	1.87334e6	0.393265
$470$	−207970.	−0.0434267
$471$	3.02623e6	0.628564
$472$	−390166.	−0.0806110
$473$	1.24981e6	0.256857
$474$	−4.40554e6	−0.900643
$475$	6.35236e6	1.29182
$476$	5.94572e6	1.20278
$477$	1.88838e6	0.380009
$478$	5.76076e6	1.15322
$479$	5.57705e6	1.11062	0.555310	−	0.831643i	$-0.312600\pi$
$479$	5.57705e6	1.11062	0.555310	+	0.831643i	$0.312600\pi$
$480$	527227.	0.104447
$481$	1.69732e7	3.34504
$482$	8.78009e6	1.72140
$483$	4.41386e6	0.860895
$484$	−2.29541e6	−0.445396
$485$	−238974.	−0.0461314
$486$	408190.	0.0783919
$487$	−1.31991e6	−0.252186	−0.126093	−	0.992018i	$-0.540244\pi$
$487$	−1.31991e6	−0.252186	−0.126093	+	0.992018i	$0.540244\pi$
$488$	3.26874e6	0.621342
$489$	2.69782e6	0.510201
$490$	−1.58182e6	−0.297623
$491$	5.36809e6	1.00488	0.502442	−	0.864611i	$-0.332435\pi$
$491$	5.36809e6	1.00488	0.502442	+	0.864611i	$0.332435\pi$
$492$	−1.20116e6	−0.223711
$493$	−8.83031e6	−1.63628
$494$	−1.63329e7	−3.01125
$495$	112793.	0.0206905
$496$	1.15540e6	0.210877
$497$	1.29651e6	0.235443
$498$	1.99007e6	0.359579
$499$	−1.33480e6	−0.239974	−0.119987	−	0.992775i	$-0.538285\pi$
$499$	−1.33480e6	−0.239974	−0.119987	+	0.992775i	$0.538285\pi$
$500$	1.07674e6	0.192612
$501$	2.37021e6	0.421883
$502$	−5.46812e6	−0.968454
$503$	−7.34574e6	−1.29454	−0.647270	−	0.762260i	$-0.724090\pi$
$503$	−7.34574e6	−1.29454	−0.647270	+	0.762260i	$0.724090\pi$
$504$	1.75479e6	0.307715
$505$	−52059.6	−0.00908390
$506$	2.19364e6	0.380881
$507$	7.87185e6	1.36006
$508$	1.57473e6	0.270737
$509$	1.37057e6	0.234480	0.117240	−	0.993104i	$-0.462595\pi$
$509$	1.37057e6	0.234480	0.117240	+	0.993104i	$0.462595\pi$
$510$	1.34989e6	0.229813
$511$	−1.00274e7	−1.69878
$512$	2.14338e6	0.361346
$513$	−1.54309e6	−0.258880
$514$	−1.26709e7	−2.11544
$515$	−794714.	−0.132036
$516$	−1.41977e6	−0.234744
$517$	−337927.	−0.0556028
$518$	−2.03169e7	−3.32686
$519$	−6.25753e6	−1.01973
$520$	1.39302e6	0.225917
$521$	−1.52552e6	−0.246220	−0.123110	−	0.992393i	$-0.539287\pi$
$521$	−1.52552e6	−0.246220	−0.123110	+	0.992393i	$0.539287\pi$
$522$	2.53727e6	0.407559
$523$	4.78382e6	0.764751	0.382376	−	0.924007i	$-0.375106\pi$
$523$	4.78382e6	0.764751	0.382376	+	0.924007i	$0.375106\pi$
$524$	−3.11768e6	−0.496025
$525$	5.22044e6	0.826625
$526$	−87452.9	−0.0137819
$527$	1.75907e6	0.275903
$528$	1.44069e6	0.224899
$529$	1823.55	0.000283320 0
$530$	−1.79439e6	−0.277478
$531$	281961.	0.0433963
$532$	6.45842e6	0.989343
$533$	−9.43715e6	−1.43887
$534$	4.89189e6	0.742375
$535$	2.53021e6	0.382184
$536$	1.08634e6	0.163326
$537$	4.05215e6	0.606387
$538$	−1.02711e6	−0.152989
$539$	−2.57026e6	−0.381071
$540$	−128132.	−0.0189092
$541$	1.22324e7	1.79688	0.898440	−	0.439096i	$-0.144701\pi$
$541$	1.22324e7	1.79688	0.898440	+	0.439096i	$0.144701\pi$
$542$	6.50910e6	0.951749
$543$	2.60975e6	0.379839
$544$	1.02526e7	1.48538
$545$	−220968.	−0.0318667
$546$	−1.34226e7	−1.92688
$547$	1.06742e7	1.52534	0.762669	−	0.646789i	$-0.223889\pi$
$547$	1.06742e7	1.52534	0.762669	+	0.646789i	$0.223889\pi$
$548$	−3.86226e6	−0.549402
$549$	−2.36222e6	−0.334495
$550$	2.59450e6	0.365719
$551$	−9.59174e6	−1.34592
$552$	2.55958e6	0.357537
$553$	1.36868e7	1.90322
$554$	1.47448e7	2.04110
$555$	−1.52378e6	−0.209985
$556$	−3.22400e6	−0.442291
$557$	5.16477e6	0.705363	0.352682	−	0.935743i	$-0.385270\pi$
$557$	5.16477e6	0.705363	0.352682	+	0.935743i	$0.385270\pi$
$558$	−505445.	−0.0687208
$559$	−1.11547e7	−1.50983
$560$	−2.75456e6	−0.371179
$561$	2.19342e6	0.294248
$562$	−6.15727e6	−0.822333
$563$	−4.48550e6	−0.596403	−0.298201	−	0.954503i	$-0.596387\pi$
$563$	−4.48550e6	−0.596403	−0.298201	+	0.954503i	$0.596387\pi$
$564$	383882.	0.0508159
$565$	−778289.	−0.102570
$566$	5.65171e6	0.741547
$567$	−1.26813e6	−0.165656
$568$	751844.	0.0977815
$569$	1.02493e7	1.32713	0.663566	−	0.748118i	$-0.269042\pi$
$569$	1.02493e7	1.32713	0.663566	+	0.748118i	$0.269042\pi$
$570$	1.46629e6	0.189031
$571$	−7.69920e6	−0.988224	−0.494112	−	0.869398i	$-0.664507\pi$
$571$	−7.69920e6	−0.988224	−0.494112	+	0.869398i	$0.664507\pi$
$572$	−2.20369e6	−0.281618
$573$	−2.44882e6	−0.311580
$574$	1.12963e7	1.43105
$575$	7.61467e6	0.960465
$576$	371692.	0.0466795
$577$	1.53456e7	1.91887	0.959435	−	0.281929i	$-0.0909743\pi$
$577$	1.53456e7	1.91887	0.959435	+	0.281929i	$0.0909743\pi$
$578$	1.64354e7	2.04625
$579$	−7.20369e6	−0.893014
$580$	−796458.	−0.0983089
$581$	−6.18259e6	−0.759854
$582$	1.33530e6	0.163407
$583$	−2.91568e6	−0.355278
$584$	−5.81488e6	−0.705519
$585$	−1.00670e6	−0.121621
$586$	4.21961e6	0.507607
$587$	−1.11377e7	−1.33413	−0.667066	−	0.744999i	$-0.732450\pi$
$587$	−1.11377e7	−1.33413	−0.667066	+	0.744999i	$0.732450\pi$
$588$	2.91979e6	0.348264
$589$	1.91075e6	0.226943
$590$	−267928.	−0.0316875
$591$	−5.75552e6	−0.677823
$592$	−1.94630e7	−2.28247
$593$	2.86489e6	0.334558	0.167279	−	0.985910i	$-0.446502\pi$
$593$	2.86489e6	0.334558	0.167279	+	0.985910i	$0.446502\pi$
$594$	−630248.	−0.0732902
$595$	−4.19375e6	−0.485635
$596$	−6.47875e6	−0.747094
$597$	7.31619e6	0.840135
$598$	−1.95785e7	−2.23886
$599$	5.10093e6	0.580874	0.290437	−	0.956894i	$-0.406199\pi$
$599$	5.10093e6	0.580874	0.290437	+	0.956894i	$0.406199\pi$
$600$	3.02731e6	0.343304
$601$	6.57438e6	0.742452	0.371226	−	0.928543i	$-0.378937\pi$
$601$	6.57438e6	0.742452	0.371226	+	0.928543i	$0.378937\pi$
$602$	1.33522e7	1.50163
$603$	−785068.	−0.0879254
$604$	−6.13730e6	−0.684518
$605$	1.61904e6	0.179833
$606$	290890.	0.0321771
$607$	−2.53033e6	−0.278744	−0.139372	−	0.990240i	$-0.544508\pi$
$607$	−2.53033e6	−0.278744	−0.139372	+	0.990240i	$0.544508\pi$
$608$	1.11367e7	1.22179
$609$	−7.88260e6	−0.861244
$610$	2.24465e6	0.244244
$611$	3.01604e6	0.326839
$612$	−2.49170e6	−0.268916
$613$	−6.47911e6	−0.696409	−0.348204	−	0.937419i	$-0.613208\pi$
$613$	−6.47911e6	−0.696409	−0.348204	+	0.937419i	$0.613208\pi$
$614$	−6.94191e6	−0.743118
$615$	847224.	0.0903255
$616$	−2.70941e6	−0.287689
$617$	499984.	0.0528741	0.0264371	−	0.999650i	$-0.491584\pi$
$617$	499984.	0.0528741	0.0264371	+	0.999650i	$0.491584\pi$
$618$	4.44057e6	0.467700
$619$	−2.37362e6	−0.248991	−0.124496	−	0.992220i	$-0.539731\pi$
$619$	−2.37362e6	−0.248991	−0.124496	+	0.992220i	$0.539731\pi$
$620$	158661.	0.0165764
$621$	−1.84973e6	−0.192477
$622$	−245097.	−0.0254016
$623$	−1.51977e7	−1.56877
$624$	−1.28584e7	−1.32198
$625$	8.61875e6	0.882560
$626$	−1.12927e7	−1.15176
$627$	2.38255e6	0.242032
$628$	5.30794e6	0.537065
$629$	−2.96318e7	−2.98629
$630$	1.20502e6	0.120960
$631$	968968.	0.0968804	0.0484402	−	0.998826i	$-0.484575\pi$
$631$	968968.	0.0968804	0.0484402	+	0.998826i	$0.484575\pi$
$632$	7.93692e6	0.790422
$633$	1.21210e6	0.120235
$634$	−4.29275e6	−0.424143
$635$	−1.11072e6	−0.109313
$636$	3.31217e6	0.324691
$637$	2.29399e7	2.23998
$638$	−3.91757e6	−0.381035
$639$	−543335.	−0.0526399
$640$	−2.22778e6	−0.214992
$641$	−1.30259e7	−1.25216	−0.626082	−	0.779757i	$-0.715343\pi$
$641$	−1.30259e7	−1.25216	−0.626082	+	0.779757i	$0.715343\pi$
$642$	−1.41379e7	−1.35378
$643$	8.48030e6	0.808879	0.404440	−	0.914565i	$-0.367467\pi$
$643$	8.48030e6	0.808879	0.404440	+	0.914565i	$0.367467\pi$
$644$	7.74180e6	0.735576
$645$	1.00142e6	0.0947799
$646$	2.85140e7	2.68829
$647$	−1.14711e7	−1.07732	−0.538660	−	0.842523i	$-0.681069\pi$
$647$	−1.14711e7	−1.07732	−0.538660	+	0.842523i	$0.681069\pi$
$648$	−735386.	−0.0687983
$649$	−435350.	−0.0405721
$650$	−2.31563e7	−2.14974
$651$	1.57028e6	0.145219
$652$	4.73192e6	0.435931
$653$	1.41233e7	1.29614	0.648072	−	0.761579i	$-0.275575\pi$
$653$	1.41233e7	1.29614	0.648072	+	0.761579i	$0.275575\pi$
$654$	1.23469e6	0.112879
$655$	2.19902e6	0.200275
$656$	1.08215e7	0.981808
$657$	4.20224e6	0.379811
$658$	−3.61021e6	−0.325063
$659$	4.29463e6	0.385223	0.192611	−	0.981275i	$-0.438304\pi$
$659$	4.29463e6	0.385223	0.192611	+	0.981275i	$0.438304\pi$
$660$	197837.	0.0176786
$661$	1.57272e7	1.40006	0.700032	−	0.714111i	$-0.253169\pi$
$661$	1.57272e7	1.40006	0.700032	+	0.714111i	$0.253169\pi$
$662$	1.90375e7	1.68836
$663$	−1.95765e7	−1.72962
$664$	−3.58526e6	−0.315574
$665$	−4.55537e6	−0.399456
$666$	8.51430e6	0.743812
$667$	−1.14978e7	−1.00069
$668$	4.15729e6	0.360470
$669$	−8.30627e6	−0.717532
$670$	745995.	0.0642020
$671$	3.64729e6	0.312726
$672$	9.15225e6	0.781816
$673$	−2.25572e6	−0.191976	−0.0959881	−	0.995382i	$-0.530601\pi$
$673$	−2.25572e6	−0.191976	−0.0959881	+	0.995382i	$0.530601\pi$
$674$	3.22851e6	0.273749
$675$	−2.18775e6	−0.184815
$676$	1.38070e7	1.16207
$677$	−1.19113e7	−0.998818	−0.499409	−	0.866366i	$-0.666449\pi$
$677$	−1.19113e7	−0.998818	−0.499409	+	0.866366i	$0.666449\pi$
$678$	4.34880e6	0.363325
$679$	−4.14841e6	−0.345308
$680$	−2.43194e6	−0.201688
$681$	−8.42668e6	−0.696288
$682$	780412.	0.0642485
$683$	2.37444e7	1.94765	0.973823	−	0.227309i	$-0.0729926\pi$
$683$	2.37444e7	1.94765	0.973823	+	0.227309i	$0.0729926\pi$
$684$	−2.70655e6	−0.221195
$685$	2.72420e6	0.221826
$686$	−5.00304e6	−0.405905
$687$	−1.02234e7	−0.826426
$688$	1.27910e7	1.03023
$689$	2.60228e7	2.08836
$690$	1.75767e6	0.140545
$691$	−671726.	−0.0535176	−0.0267588	−	0.999642i	$-0.508519\pi$
$691$	−671726.	−0.0535176	−0.0267588	+	0.999642i	$0.508519\pi$
$692$	−1.09756e7	−0.871288
$693$	1.95801e6	0.154875
$694$	2.26538e7	1.78543
$695$	2.27401e6	0.178579
$696$	−4.57109e6	−0.357682
$697$	1.64754e7	1.28456
$698$	−2.71629e7	−2.11027
$699$	−1.25700e7	−0.973067
$700$	9.15653e6	0.706294
$701$	7.09210e6	0.545105	0.272552	−	0.962141i	$-0.412132\pi$
$701$	7.09210e6	0.545105	0.272552	+	0.962141i	$0.412132\pi$
$702$	5.62505e6	0.430807
$703$	−3.21869e7	−2.45635
$704$	−573895.	−0.0436416
$705$	−270766.	−0.0205174
$706$	2.30964e7	1.74395
$707$	−903715.	−0.0679959
$708$	494553.	0.0370792
$709$	1.22100e7	0.912222	0.456111	−	0.889923i	$-0.349242\pi$
$709$	1.22100e7	0.912222	0.456111	+	0.889923i	$0.349242\pi$
$710$	516293.	0.0384371
$711$	−5.73577e6	−0.425518
$712$	−8.81312e6	−0.651523
$713$	2.29045e6	0.168732
$714$	2.34331e7	1.72022
$715$	1.55435e6	0.113706
$716$	7.10738e6	0.518116
$717$	7.50021e6	0.544848
$718$	−5.34184e6	−0.386705
$719$	−1.62202e7	−1.17013	−0.585066	−	0.810986i	$-0.698931\pi$
$719$	−1.62202e7	−1.17013	−0.585066	+	0.810986i	$0.698931\pi$
$720$	1.15437e6	0.0829874
$721$	−1.37956e7	−0.988333
$722$	1.38561e7	0.989234
$723$	1.14312e7	0.813292
$724$	4.57745e6	0.324547
$725$	−1.35989e7	−0.960854
$726$	−9.04661e6	−0.637007
$727$	2.20651e7	1.54835	0.774175	−	0.632972i	$-0.218165\pi$
$727$	2.20651e7	1.54835	0.774175	+	0.632972i	$0.218165\pi$
$728$	2.41818e7	1.69106
$729$	531441.	0.0370370
$730$	−3.99309e6	−0.277333
$731$	1.94739e7	1.34790
$732$	−4.14328e6	−0.285803
$733$	−1.13061e7	−0.777233	−0.388617	−	0.921400i	$-0.627047\pi$
$733$	−1.13061e7	−0.777233	−0.388617	+	0.921400i	$0.627047\pi$
$734$	−4.43077e6	−0.303556
$735$	−2.05944e6	−0.140615
$736$	1.33497e7	0.908401
$737$	1.21215e6	0.0822032
$738$	−4.73398e6	−0.319952
$739$	9.23997e6	0.622386	0.311193	−	0.950347i	$-0.399272\pi$
$739$	9.23997e6	0.622386	0.311193	+	0.950347i	$0.399272\pi$
$740$	−2.67267e6	−0.179418
$741$	−2.12646e7	−1.42269
$742$	−3.11493e7	−2.07701
$743$	1.10636e7	0.735233	0.367617	−	0.929977i	$-0.380174\pi$
$743$	1.10636e7	0.735233	0.367617	+	0.929977i	$0.380174\pi$
$744$	910599.	0.0603107
$745$	4.56971e6	0.301646
$746$	−1.63896e7	−1.07825
$747$	2.59096e6	0.169887
$748$	3.84720e6	0.251415
$749$	4.39226e7	2.86077
$750$	4.24360e6	0.275475
$751$	−1.63941e6	−0.106069	−0.0530343	−	0.998593i	$-0.516889\pi$
$751$	−1.63941e6	−0.106069	−0.0530343	+	0.998593i	$0.516889\pi$
$752$	−3.45846e6	−0.223017
$753$	−7.11920e6	−0.457556
$754$	3.49648e7	2.23977
$755$	4.32887e6	0.276381
$756$	−2.22428e6	−0.141542
$757$	−3.02306e7	−1.91738	−0.958688	−	0.284461i	$-0.908185\pi$
$757$	−3.02306e7	−1.91738	−0.958688	+	0.284461i	$0.908185\pi$
$758$	−1.79608e7	−1.13541
$759$	2.85600e6	0.179951
$760$	−2.64164e6	−0.165898
$761$	2.90933e7	1.82109	0.910546	−	0.413408i	$-0.135662\pi$
$761$	2.90933e7	1.82109	0.910546	+	0.413408i	$0.135662\pi$
$762$	6.20629e6	0.387208
$763$	−3.83583e6	−0.238533
$764$	−4.29517e6	−0.266224
$765$	1.75749e6	0.108577
$766$	−1.89346e7	−1.16596
$767$	3.88556e6	0.238487
$768$	1.11264e7	0.680695
$769$	−6.83882e6	−0.417028	−0.208514	−	0.978019i	$-0.566863\pi$
$769$	−6.83882e6	−0.417028	−0.208514	+	0.978019i	$0.566863\pi$
$770$	−1.86056e6	−0.113088
$771$	−1.64969e7	−0.999461
$772$	−1.26351e7	−0.763019
$773$	−2.33000e7	−1.40252	−0.701258	−	0.712907i	$-0.747378\pi$
$773$	−2.33000e7	−1.40252	−0.701258	+	0.712907i	$0.747378\pi$
$774$	−5.59556e6	−0.335731
$775$	2.70900e6	0.162015
$776$	−2.40565e6	−0.143409
$777$	−2.64516e7	−1.57181
$778$	8.71420e6	0.516153
$779$	1.78960e7	1.05661
$780$	−1.76572e6	−0.103917
$781$	838914.	0.0492141
$782$	3.41802e7	1.99874
$783$	3.30339e6	0.192555
$784$	−2.63049e7	−1.52844
$785$	−3.74389e6	−0.216845
$786$	−1.22873e7	−0.709416
$787$	−2.73298e7	−1.57290	−0.786448	−	0.617657i	$-0.788082\pi$
$787$	−2.73298e7	−1.57290	−0.786448	+	0.617657i	$0.788082\pi$
$788$	−1.00951e7	−0.579153
$789$	−113859.	−0.00651141
$790$	5.45030e6	0.310708
$791$	−1.35105e7	−0.767769
$792$	1.13544e6	0.0643209
$793$	−3.25525e7	−1.83824
$794$	1.00947e6	0.0568255
$795$	−2.33620e6	−0.131097
$796$	1.28324e7	0.717838
$797$	2.61123e7	1.45613	0.728064	−	0.685509i	$-0.240420\pi$
$797$	2.61123e7	1.45613	0.728064	+	0.685509i	$0.240420\pi$
$798$	2.54537e7	1.41496
$799$	−5.26541e6	−0.291786
$800$	1.57892e7	0.872240
$801$	6.36898e6	0.350743
$802$	−2.03885e7	−1.11931
$803$	−6.48830e6	−0.355093
$804$	−1.37699e6	−0.0751262
$805$	−5.46059e6	−0.296996
$806$	−6.96527e6	−0.377659
$807$	−1.33724e6	−0.0722812
$808$	−524061.	−0.0282393
$809$	1.70399e7	0.915369	0.457684	−	0.889115i	$-0.348679\pi$
$809$	1.70399e7	0.915369	0.457684	+	0.889115i	$0.348679\pi$
$810$	−504991.	−0.0270440
$811$	−1.19527e7	−0.638136	−0.319068	−	0.947732i	$-0.603370\pi$
$811$	−1.19527e7	−0.638136	−0.319068	+	0.947732i	$0.603370\pi$
$812$	−1.38259e7	−0.735874
$813$	8.47450e6	0.449663
$814$	−1.31462e7	−0.695405
$815$	−3.33760e6	−0.176011
$816$	2.24481e7	1.18020
$817$	2.11531e7	1.10871
$818$	2.37597e7	1.24153
$819$	−1.74755e7	−0.910372
$820$	1.48601e6	0.0771770
$821$	−2.76018e7	−1.42915	−0.714577	−	0.699556i	$-0.753381\pi$
$821$	−2.76018e7	−1.42915	−0.714577	+	0.699556i	$0.753381\pi$
$822$	−1.52218e7	−0.785755
$823$	1.60010e7	0.823472	0.411736	−	0.911303i	$-0.364923\pi$
$823$	1.60010e7	0.823472	0.411736	+	0.911303i	$0.364923\pi$
$824$	−8.00004e6	−0.410463
$825$	3.37790e6	0.172788
$826$	−4.65102e6	−0.237191
$827$	2.61565e7	1.32989	0.664945	−	0.746892i	$-0.268455\pi$
$827$	2.61565e7	1.32989	0.664945	+	0.746892i	$0.268455\pi$
$828$	−3.24439e6	−0.164459
$829$	1.29226e7	0.653076	0.326538	−	0.945184i	$-0.394118\pi$
$829$	1.29226e7	0.653076	0.326538	+	0.945184i	$0.394118\pi$
$830$	−2.46201e6	−0.124049
$831$	1.91969e7	0.964336
$832$	5.12209e6	0.256530
$833$	−4.00485e7	−1.99974
$834$	−1.27063e7	−0.632565
$835$	−2.93229e6	−0.145543
$836$	4.17894e6	0.206800
$837$	−658062.	−0.0324678
$838$	−4.48477e7	−2.20613
$839$	−2.17442e7	−1.06644	−0.533222	−	0.845975i	$-0.679019\pi$
$839$	−2.17442e7	−1.06644	−0.533222	+	0.845975i	$0.679019\pi$
$840$	−2.17093e6	−0.106157
$841$	22444.5	0.00109426
$842$	−2.68867e7	−1.30695
$843$	−8.01644e6	−0.388519
$844$	2.12600e6	0.102732
$845$	−9.73864e6	−0.469198
$846$	1.51294e6	0.0726770
$847$	2.81053e7	1.34611
$848$	−2.98400e7	−1.42498
$849$	7.35823e6	0.350351
$850$	4.04262e7	1.91918
$851$	−3.85830e7	−1.82630
$852$	−952997.	−0.0449772
$853$	−2.35835e7	−1.10978	−0.554888	−	0.831925i	$-0.687239\pi$
$853$	−2.35835e7	−1.10978	−0.554888	+	0.831925i	$0.687239\pi$
$854$	3.89654e7	1.82824
$855$	1.90904e6	0.0893097
$856$	2.54705e7	1.18810
$857$	−1.24991e7	−0.581337	−0.290668	−	0.956824i	$-0.593878\pi$
$857$	−1.24991e7	−0.581337	−0.290668	+	0.956824i	$0.593878\pi$
$858$	−8.68512e6	−0.402770
$859$	3.62400e7	1.67573	0.837867	−	0.545875i	$-0.183803\pi$
$859$	3.62400e7	1.67573	0.837867	+	0.545875i	$0.183803\pi$
$860$	1.75646e6	0.0809829
$861$	1.47072e7	0.676116
$862$	1.85738e6	0.0851400
$863$	−1.92175e7	−0.878353	−0.439177	−	0.898401i	$-0.644730\pi$
$863$	−1.92175e7	−0.878353	−0.439177	+	0.898401i	$0.644730\pi$
$864$	−3.83547e6	−0.174797
$865$	7.74149e6	0.351791
$866$	−1.18452e7	−0.536719
$867$	2.13979e7	0.966773
$868$	2.75423e6	0.124080
$869$	8.85608e6	0.397825
$870$	−3.13898e6	−0.140602
$871$	−1.08186e7	−0.483199
$872$	−2.22438e6	−0.0990646
$873$	1.73849e6	0.0772034
$874$	3.71275e7	1.64406
$875$	−1.31837e7	−0.582126
$876$	7.37063e6	0.324522
$877$	2.97880e7	1.30780	0.653901	−	0.756580i	$-0.273131\pi$
$877$	2.97880e7	1.30780	0.653901	+	0.756580i	$0.273131\pi$
$878$	4.58356e6	0.200663
$879$	5.49370e6	0.239824
$880$	−1.78235e6	−0.0775866
$881$	1.64782e7	0.715272	0.357636	−	0.933861i	$-0.383583\pi$
$881$	1.64782e7	0.715272	0.357636	+	0.933861i	$0.383583\pi$
$882$	1.15074e7	0.498088
$883$	−1.95035e7	−0.841802	−0.420901	−	0.907106i	$-0.638286\pi$
$883$	−1.95035e7	−0.841802	−0.420901	+	0.907106i	$0.638286\pi$
$884$	−3.43367e7	−1.47784
$885$	−348827.	−0.0149711
$886$	−1.32755e7	−0.568153
$887$	2.38782e7	1.01904	0.509522	−	0.860457i	$-0.329822\pi$
$887$	2.38782e7	1.01904	0.509522	+	0.860457i	$0.329822\pi$
$888$	−1.53392e7	−0.652784
$889$	−1.92812e7	−0.818240
$890$	−6.05199e6	−0.256108
$891$	−820550.	−0.0346267
$892$	−1.45690e7	−0.613081
$893$	−5.71944e6	−0.240007
$894$	−2.55339e7	−1.06850
$895$	−5.01311e6	−0.209194
$896$	−3.86725e7	−1.60928
$897$	−2.54902e7	−1.05777
$898$	−4.43220e6	−0.183412
$899$	−4.09046e6	−0.168800
$900$	−3.83726e6	−0.157912
$901$	−4.54305e7	−1.86439
$902$	7.30931e6	0.299130
$903$	1.73839e7	0.709458
$904$	−7.83470e6	−0.318861
$905$	−3.22865e6	−0.131039
$906$	−2.41882e7	−0.978999
$907$	3.15297e7	1.27263	0.636315	−	0.771429i	$-0.280458\pi$
$907$	3.15297e7	1.27263	0.636315	+	0.771429i	$0.280458\pi$
$908$	−1.47802e7	−0.594930
$909$	378723.	0.0152024
$910$	1.66057e7	0.664743
$911$	−1.40130e7	−0.559418	−0.279709	−	0.960085i	$-0.590238\pi$
$911$	−1.40130e7	−0.559418	−0.279709	+	0.960085i	$0.590238\pi$
$912$	2.43838e7	0.970767
$913$	−4.00047e6	−0.158831
$914$	1.94940e7	0.771856
$915$	2.92241e6	0.115395
$916$	−1.79316e7	−0.706124
$917$	3.81733e7	1.49912
$918$	−9.82020e6	−0.384604
$919$	−3.77111e7	−1.47293	−0.736463	−	0.676478i	$-0.763505\pi$
$919$	−3.77111e7	−1.47293	−0.736463	+	0.676478i	$0.763505\pi$
$920$	−3.16658e6	−0.123345
$921$	−9.03799e6	−0.351094
$922$	−3.02059e7	−1.17021
$923$	−7.48741e6	−0.289286
$924$	3.43430e6	0.132330
$925$	−4.56336e7	−1.75360
$926$	4.92692e6	0.188820
$927$	5.78139e6	0.220970
$928$	−2.38409e7	−0.908769
$929$	−2.22014e7	−0.843997	−0.421998	−	0.906597i	$-0.638671\pi$
$929$	−2.22014e7	−0.843997	−0.421998	+	0.906597i	$0.638671\pi$
$930$	625310.	0.0237076
$931$	−4.35019e7	−1.64488
$932$	−2.20475e7	−0.831418
$933$	−319103.	−0.0120012
$934$	1.39759e7	0.524219
$935$	−2.71358e6	−0.101511
$936$	−1.01340e7	−0.378085
$937$	3.15581e7	1.17425	0.587127	−	0.809495i	$-0.300259\pi$
$937$	3.15581e7	1.17425	0.587127	+	0.809495i	$0.300259\pi$
$938$	1.29499e7	0.480573
$939$	−1.47025e7	−0.544159
$940$	−474918.	−0.0175307
$941$	−1.61367e7	−0.594075	−0.297037	−	0.954866i	$-0.595999\pi$
$941$	−1.61367e7	−0.594075	−0.297037	+	0.954866i	$0.595999\pi$
$942$	2.09195e7	0.768111
$943$	2.14523e7	0.785586
$944$	−4.45552e6	−0.162730
$945$	1.56887e6	0.0571487
$946$	8.63959e6	0.313881
$947$	−5.18477e7	−1.87869	−0.939343	−	0.342978i	$-0.888564\pi$
$947$	−5.18477e7	−1.87869	−0.939343	+	0.342978i	$0.888564\pi$
$948$	−1.00604e7	−0.363576
$949$	5.79088e7	2.08727
$950$	4.39121e7	1.57861
$951$	−5.58893e6	−0.200390
$952$	−4.22166e7	−1.50970
$953$	3.02972e7	1.08061	0.540307	−	0.841468i	$-0.318308\pi$
$953$	3.02972e7	1.08061	0.540307	+	0.841468i	$0.318308\pi$
$954$	1.30539e7	0.464374
$955$	3.02955e6	0.107490
$956$	1.31552e7	0.465535
$957$	−5.10047e6	−0.180024
$958$	3.85526e7	1.35719
$959$	4.72900e7	1.66044
$960$	−459837.	−0.0161037
$961$	−2.78143e7	−0.971538
$962$	1.17331e8	4.08766
$963$	−1.84068e7	−0.639606
$964$	2.00501e7	0.694902
$965$	8.91202e6	0.308076
$966$	3.05118e7	1.05202
$967$	1.15030e7	0.395591	0.197795	−	0.980243i	$-0.436622\pi$
$967$	1.15030e7	0.395591	0.197795	+	0.980243i	$0.436622\pi$
$968$	1.62982e7	0.559050
$969$	3.71237e7	1.27011
$970$	−1.65196e6	−0.0563730
$971$	−1.92341e7	−0.654673	−0.327336	−	0.944908i	$-0.606151\pi$
$971$	−1.92341e7	−0.654673	−0.327336	+	0.944908i	$0.606151\pi$
$972$	932135.	0.0316456
$973$	3.94751e7	1.33672
$974$	−9.12417e6	−0.308174
$975$	−3.01482e7	−1.01566
$976$	3.73275e7	1.25431
$977$	−7.41320e6	−0.248467	−0.124234	−	0.992253i	$-0.539647\pi$
$977$	−7.41320e6	−0.248467	−0.124234	+	0.992253i	$0.539647\pi$
$978$	1.86493e7	0.623470
$979$	−9.83376e6	−0.327916
$980$	−3.61221e6	−0.120146
$981$	1.60750e6	0.0533307
$982$	3.71081e7	1.22798
$983$	−4.98279e7	−1.64471	−0.822354	−	0.568976i	$-0.807340\pi$
$983$	−4.98279e7	−1.64471	−0.822354	+	0.568976i	$0.807340\pi$
$984$	8.52863e6	0.280797
$985$	7.12043e6	0.233838
$986$	−6.10415e7	−1.99955
$987$	−4.70030e6	−0.153579
$988$	−3.72976e7	−1.21559
$989$	2.53565e7	0.824327
$990$	779710.	0.0252840
$991$	3.87158e7	1.25229	0.626144	−	0.779708i	$-0.284632\pi$
$991$	3.87158e7	1.25229	0.626144	+	0.779708i	$0.284632\pi$
$992$	4.74931e6	0.153233
$993$	2.47858e7	0.797681
$994$	8.96244e6	0.287714
$995$	−9.05121e6	−0.289834
$996$	4.54449e6	0.145157
$997$	1.92043e7	0.611873	0.305937	−	0.952052i	$-0.401030\pi$
$997$	1.92043e7	0.611873	0.305937	+	0.952052i	$0.401030\pi$
$998$	−9.22708e6	−0.293250
$999$	1.10852e7	0.351421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.9	✓	11
3.2	odd	2		531.6.a.b.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.9	✓	11	1.1	even	1	trivial
531.6.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} -76.9686 q^{10} -125.065 q^{11} +142.072 q^{12} +1116.22 q^{13} -1336.12 q^{14} -100.209 q^{15} -1279.95 q^{16} -1948.69 q^{17} +559.931 q^{18} -2116.73 q^{19} -175.764 q^{20} -1739.55 q^{21} -864.538 q^{22} -2537.35 q^{23} -1008.76 q^{24} -3001.03 q^{25} +7716.11 q^{26} +729.000 q^{27} -3051.13 q^{28} +4531.40 q^{29} -692.717 q^{30} -902.692 q^{31} -5261.27 q^{32} -1125.58 q^{33} -13470.8 q^{34} +2152.08 q^{35} +1278.65 q^{36} +15206.0 q^{37} -14632.4 q^{38} +10046.0 q^{39} +1247.98 q^{40} -8454.58 q^{41} -12025.0 q^{42} -9993.30 q^{43} -1974.25 q^{44} -901.881 q^{45} -17540.0 q^{46} +2702.02 q^{47} -11519.6 q^{48} +20551.5 q^{49} -20745.3 q^{50} -17538.2 q^{51} +17620.4 q^{52} +23313.3 q^{53} +5039.38 q^{54} +1392.51 q^{55} +21664.0 q^{56} -19050.6 q^{57} +31324.3 q^{58} +3481.00 q^{59} -1581.88 q^{60} -29163.2 q^{61} -6240.06 q^{62} -15656.0 q^{63} +4588.78 q^{64} -12428.3 q^{65} -7780.85 q^{66} -9692.20 q^{67} -30761.7 q^{68} -22836.2 q^{69} +14876.7 q^{70} -6707.84 q^{71} -9078.83 q^{72} +51879.5 q^{73} +105115. q^{74} -27009.2 q^{75} -33414.2 q^{76} +24172.9 q^{77} +69445.0 q^{78} -70812.0 q^{79} +14251.4 q^{80} +6561.00 q^{81} -58444.2 q^{82} +31987.2 q^{83} -27460.2 q^{84} +21697.4 q^{85} -69081.0 q^{86} +40782.6 q^{87} +14017.8 q^{88} +78629.4 q^{89} -6234.45 q^{90} -215746. q^{91} -40054.2 q^{92} -8124.23 q^{93} +18678.3 q^{94} +23568.3 q^{95} -47351.5 q^{96} +21462.8 q^{97} +142067. q^{98} -10130.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 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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