LMFDB - Embedded newform 177.6.a.d.1.13

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 $ x^13 - 331x^11 - 41x^10 + 41990x^9 + 7229x^8 - 2592364x^7 - 312100x^6 + 81977088x^5 - 3773728x^4 - 1245415104x^3 + 453320896x^2 + 6872784896*x - 6400833792
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$10.6702$ 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)

$f(q)$	$=$	$q+10.6702 q^{2} -9.00000 q^{3} +81.8525 q^{4} -61.2778 q^{5} -96.0315 q^{6} +186.685 q^{7} +531.935 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+10.6702 q^{2} -9.00000 q^{3} +81.8525 q^{4} -61.2778 q^{5} -96.0315 q^{6} +186.685 q^{7} +531.935 q^{8} +81.0000 q^{9} -653.844 q^{10} -424.892 q^{11} -736.673 q^{12} +983.052 q^{13} +1991.96 q^{14} +551.500 q^{15} +3056.56 q^{16} +1043.17 q^{17} +864.284 q^{18} -302.603 q^{19} -5015.74 q^{20} -1680.17 q^{21} -4533.67 q^{22} +4122.49 q^{23} -4787.42 q^{24} +629.966 q^{25} +10489.3 q^{26} -729.000 q^{27} +15280.7 q^{28} -8426.58 q^{29} +5884.60 q^{30} +10049.9 q^{31} +15592.1 q^{32} +3824.03 q^{33} +11130.8 q^{34} -11439.6 q^{35} +6630.06 q^{36} +10289.5 q^{37} -3228.83 q^{38} -8847.47 q^{39} -32595.8 q^{40} +1605.50 q^{41} -17927.7 q^{42} -4917.05 q^{43} -34778.5 q^{44} -4963.50 q^{45} +43987.7 q^{46} -24046.6 q^{47} -27509.0 q^{48} +18044.3 q^{49} +6721.85 q^{50} -9388.55 q^{51} +80465.3 q^{52} -6856.60 q^{53} -7778.55 q^{54} +26036.4 q^{55} +99304.4 q^{56} +2723.43 q^{57} -89913.0 q^{58} +3481.00 q^{59} +45141.7 q^{60} -31403.4 q^{61} +107234. q^{62} +15121.5 q^{63} +68560.1 q^{64} -60239.3 q^{65} +40803.0 q^{66} -61147.0 q^{67} +85386.3 q^{68} -37102.4 q^{69} -122063. q^{70} -7454.90 q^{71} +43086.7 q^{72} -4324.62 q^{73} +109790. q^{74} -5669.70 q^{75} -24768.9 q^{76} -79321.0 q^{77} -94404.0 q^{78} -30676.1 q^{79} -187299. q^{80} +6561.00 q^{81} +17130.9 q^{82} -29240.6 q^{83} -137526. q^{84} -63923.3 q^{85} -52465.8 q^{86} +75839.2 q^{87} -226015. q^{88} +23916.5 q^{89} -52961.4 q^{90} +183521. q^{91} +337436. q^{92} -90449.4 q^{93} -256582. q^{94} +18542.9 q^{95} -140329. q^{96} +31653.6 q^{97} +192536. q^{98} -34416.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) $ 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	10.6702	1.88624	0.943119	−	0.332456i	$-0.107877\pi$
$2$	10.6702	1.88624	0.943119	+	0.332456i	$0.107877\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	81.8525	2.55789
$5$	−61.2778	−1.09617	−0.548085	−	0.836423i	$-0.684643\pi$
$5$	−61.2778	−1.09617	−0.548085	+	0.836423i	$0.684643\pi$
$6$	−96.0315	−1.08902
$7$	186.685	1.44001	0.720004	−	0.693970i	$-0.244140\pi$
$7$	186.685	1.44001	0.720004	+	0.693970i	$0.244140\pi$
$8$	531.935	2.93855
$9$	81.0000	0.333333
$10$	−653.844	−2.06764
$11$	−424.892	−1.05876	−0.529379	−	0.848385i	$-0.677575\pi$
$11$	−424.892	−1.05876	−0.529379	+	0.848385i	$0.677575\pi$
$12$	−736.673	−1.47680
$13$	983.052	1.61331	0.806656	−	0.591021i	$-0.201275\pi$
$13$	983.052	1.61331	0.806656	+	0.591021i	$0.201275\pi$
$14$	1991.96	2.71620
$15$	551.500	0.632874
$16$	3056.56	2.98492
$17$	1043.17	0.875455	0.437727	−	0.899108i	$-0.355783\pi$
$17$	1043.17	0.875455	0.437727	+	0.899108i	$0.355783\pi$
$18$	864.284	0.628746
$19$	−302.603	−0.192305	−0.0961523	−	0.995367i	$-0.530654\pi$
$19$	−302.603	−0.192305	−0.0961523	+	0.995367i	$0.530654\pi$
$20$	−5015.74	−2.80389
$21$	−1680.17	−0.831388
$22$	−4533.67	−1.99707
$23$	4122.49	1.62495	0.812475	−	0.582996i	$-0.198120\pi$
$23$	4122.49	1.62495	0.812475	+	0.582996i	$0.198120\pi$
$24$	−4787.42	−1.69658
$25$	629.966	0.201589
$26$	10489.3	3.04309
$27$	−729.000	−0.192450
$28$	15280.7	3.68338
$29$	−8426.58	−1.86061	−0.930307	−	0.366782i	$-0.880460\pi$
$29$	−8426.58	−1.86061	−0.930307	+	0.366782i	$0.880460\pi$
$30$	5884.60	1.19375
$31$	10049.9	1.87827	0.939137	−	0.343544i	$-0.111628\pi$
$31$	10049.9	1.87827	0.939137	+	0.343544i	$0.111628\pi$
$32$	15592.1	2.69171
$33$	3824.03	0.611274
$34$	11130.8	1.65132
$35$	−11439.6	−1.57849
$36$	6630.06	0.852631
$37$	10289.5	1.23563	0.617815	−	0.786323i	$-0.288018\pi$
$37$	10289.5	1.23563	0.617815	+	0.786323i	$0.288018\pi$
$38$	−3228.83	−0.362732
$39$	−8847.47	−0.931446
$40$	−32595.8	−3.22116
$41$	1605.50	0.149159	0.0745796	−	0.997215i	$-0.476239\pi$
$41$	1605.50	0.149159	0.0745796	+	0.997215i	$0.476239\pi$
$42$	−17927.7	−1.56820
$43$	−4917.05	−0.405540	−0.202770	−	0.979226i	$-0.564994\pi$
$43$	−4917.05	−0.405540	−0.202770	+	0.979226i	$0.564994\pi$
$44$	−34778.5	−2.70819
$45$	−4963.50	−0.365390
$46$	43987.7	3.06504
$47$	−24046.6	−1.58785	−0.793926	−	0.608015i	$-0.791966\pi$
$47$	−24046.6	−1.58785	−0.793926	+	0.608015i	$0.791966\pi$
$48$	−27509.0	−1.72334
$49$	18044.3	1.07362
$50$	6721.85	0.380245
$51$	−9388.55	−0.505444
$52$	80465.3	4.12668
$53$	−6856.60	−0.335289	−0.167644	−	0.985848i	$-0.553616\pi$
$53$	−6856.60	−0.335289	−0.167644	+	0.985848i	$0.553616\pi$
$54$	−7778.55	−0.363007
$55$	26036.4	1.16058
$56$	99304.4	4.23154
$57$	2723.43	0.111027
$58$	−89913.0	−3.50956
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	45141.7	1.61882
$61$	−31403.4	−1.08057	−0.540283	−	0.841483i	$-0.681683\pi$
$61$	−31403.4	−1.08057	−0.540283	+	0.841483i	$0.681683\pi$
$62$	107234.	3.54287
$63$	15121.5	0.480002
$64$	68560.1	2.09229
$65$	−60239.3	−1.76846
$66$	40803.0	1.15301
$67$	−61147.0	−1.66413	−0.832066	−	0.554676i	$-0.812842\pi$
$67$	−61147.0	−1.66413	−0.832066	+	0.554676i	$0.812842\pi$
$68$	85386.3	2.23932
$69$	−37102.4	−0.938166
$70$	−122063.	−2.97741
$71$	−7454.90	−0.175508	−0.0877538	−	0.996142i	$-0.527969\pi$
$71$	−7454.90	−0.175508	−0.0877538	+	0.996142i	$0.527969\pi$
$72$	43086.7	0.979518
$73$	−4324.62	−0.0949820	−0.0474910	−	0.998872i	$-0.515123\pi$
$73$	−4324.62	−0.0949820	−0.0474910	+	0.998872i	$0.515123\pi$
$74$	109790.	2.33069
$75$	−5669.70	−0.116388
$76$	−24768.9	−0.491894
$77$	−79321.0	−1.52462
$78$	−94404.0	−1.75693
$79$	−30676.1	−0.553010	−0.276505	−	0.961013i	$-0.589176\pi$
$79$	−30676.1	−0.553010	−0.276505	+	0.961013i	$0.589176\pi$
$80$	−187299.	−3.27198
$81$	6561.00	0.111111
$82$	17130.9	0.281350
$83$	−29240.6	−0.465898	−0.232949	−	0.972489i	$-0.574837\pi$
$83$	−29240.6	−0.465898	−0.232949	+	0.972489i	$0.574837\pi$
$84$	−137526.	−2.12660
$85$	−63923.3	−0.959648
$86$	−52465.8	−0.764944
$87$	75839.2	1.07423
$88$	−226015.	−3.11122
$89$	23916.5	0.320053	0.160027	−	0.987113i	$-0.448842\pi$
$89$	23916.5	0.320053	0.160027	+	0.987113i	$0.448842\pi$
$90$	−52961.4	−0.689212
$91$	183521.	2.32318
$92$	337436.	4.15645
$93$	−90449.4	−1.08442
$94$	−256582.	−2.99506
$95$	18542.9	0.210799
$96$	−140329.	−1.55406
$97$	31653.6	0.341581	0.170790	−	0.985307i	$-0.445368\pi$
$97$	31653.6	0.341581	0.170790	+	0.985307i	$0.445368\pi$
$98$	192536.	2.02510
$99$	−34416.2	−0.352919
$100$	51564.3	0.515643
$101$	−90035.5	−0.878234	−0.439117	−	0.898430i	$-0.644709\pi$
$101$	−90035.5	−0.878234	−0.439117	+	0.898430i	$0.644709\pi$
$102$	−100177.	−0.953388
$103$	98739.3	0.917059	0.458529	−	0.888679i	$-0.348376\pi$
$103$	98739.3	0.917059	0.458529	+	0.888679i	$0.348376\pi$
$104$	522920.	4.74080
$105$	102957.	0.911343
$106$	−73161.1	−0.632435
$107$	−98628.3	−0.832803	−0.416401	−	0.909181i	$-0.636709\pi$
$107$	−98628.3	−0.832803	−0.416401	+	0.909181i	$0.636709\pi$
$108$	−59670.5	−0.492267
$109$	57081.3	0.460180	0.230090	−	0.973169i	$-0.426098\pi$
$109$	57081.3	0.460180	0.230090	+	0.973169i	$0.426098\pi$
$110$	277813.	2.18913
$111$	−92605.2	−0.713392
$112$	570614.	4.29830
$113$	70846.0	0.521938	0.260969	−	0.965347i	$-0.415958\pi$
$113$	70846.0	0.521938	0.260969	+	0.965347i	$0.415958\pi$
$114$	29059.5	0.209424
$115$	−252617.	−1.78122
$116$	−689737.	−4.75925
$117$	79627.2	0.537771
$118$	37142.9	0.245567
$119$	194745.	1.26066
$120$	293362.	1.85974
$121$	19482.1	0.120969
$122$	−335079.	−2.03821
$123$	−14449.5	−0.0861172
$124$	822612.	4.80442
$125$	152890.	0.875194
$126$	161349.	0.905398
$127$	−347695.	−1.91289	−0.956444	−	0.291916i	$-0.905707\pi$
$127$	−347695.	−1.91289	−0.956444	+	0.291916i	$0.905707\pi$
$128$	232602.	1.25484
$129$	44253.4	0.234138
$130$	−642763.	−3.33574
$131$	107422.	0.546909	0.273455	−	0.961885i	$-0.411834\pi$
$131$	107422.	0.546909	0.273455	+	0.961885i	$0.411834\pi$
$132$	313006.	1.56357
$133$	−56491.5	−0.276920
$134$	−652449.	−3.13895
$135$	44671.5	0.210958
$136$	554900.	2.57257
$137$	191277.	0.870686	0.435343	−	0.900265i	$-0.356627\pi$
$137$	191277.	0.870686	0.435343	+	0.900265i	$0.356627\pi$
$138$	−395889.	−1.76960
$139$	23303.1	0.102300	0.0511502	−	0.998691i	$-0.483711\pi$
$139$	23303.1	0.102300	0.0511502	+	0.998691i	$0.483711\pi$
$140$	−936364.	−4.03761
$141$	216420.	0.916746
$142$	−79545.1	−0.331049
$143$	−417691.	−1.70811
$144$	247581.	0.994973
$145$	516362.	2.03955
$146$	−46144.5	−0.179159
$147$	−162399.	−0.619855
$148$	842219.	3.16061
$149$	−16697.0	−0.0616132	−0.0308066	−	0.999525i	$-0.509808\pi$
$149$	−16697.0	−0.0616132	−0.0308066	+	0.999525i	$0.509808\pi$
$150$	−60496.6	−0.219535
$151$	−141376.	−0.504583	−0.252291	−	0.967651i	$-0.581184\pi$
$151$	−141376.	−0.504583	−0.252291	+	0.967651i	$0.581184\pi$
$152$	−160965.	−0.565097
$153$	84497.0	0.291818
$154$	−846369.	−2.87579
$155$	−615837.	−2.05891
$156$	−724188.	−2.38254
$157$	−6851.37	−0.0221834	−0.0110917	−	0.999938i	$-0.503531\pi$
$157$	−6851.37	−0.0221834	−0.0110917	+	0.999938i	$0.503531\pi$
$158$	−327319.	−1.04311
$159$	61709.4	0.193579
$160$	−955447.	−2.95057
$161$	769608.	2.33994
$162$	70007.0	0.209582
$163$	−275831.	−0.813158	−0.406579	−	0.913616i	$-0.633278\pi$
$163$	−275831.	−0.813158	−0.406579	+	0.913616i	$0.633278\pi$
$164$	131414.	0.381533
$165$	−234328.	−0.670061
$166$	−312002.	−0.878794
$167$	546461.	1.51624	0.758120	−	0.652115i	$-0.226118\pi$
$167$	546461.	1.51624	0.758120	+	0.652115i	$0.226118\pi$
$168$	−893739.	−2.44308
$169$	595099.	1.60277
$170$	−682072.	−1.81012
$171$	−24510.9	−0.0641015
$172$	−402473.	−1.03733
$173$	−563301.	−1.43095	−0.715476	−	0.698637i	$-0.753790\pi$
$173$	−563301.	−1.43095	−0.715476	+	0.698637i	$0.753790\pi$
$174$	809217.	2.02625
$175$	117605.	0.290290
$176$	−1.29871e6	−3.16031
$177$	−31329.0	−0.0751646
$178$	255193.	0.603696
$179$	603180.	1.40707	0.703533	−	0.710663i	$-0.251605\pi$
$179$	603180.	1.40707	0.703533	+	0.710663i	$0.251605\pi$
$180$	−406275.	−0.934628
$181$	158219.	0.358973	0.179487	−	0.983760i	$-0.442556\pi$
$181$	158219.	0.358973	0.179487	+	0.983760i	$0.442556\pi$
$182$	1.95820e6	4.38207
$183$	282630.	0.623865
$184$	2.19290e6	4.77501
$185$	−630516.	−1.35446
$186$	−965110.	−2.04548
$187$	−443235.	−0.926895
$188$	−1.96828e6	−4.06155
$189$	−136093.	−0.277129
$190$	197855.	0.397616
$191$	−512314.	−1.01614	−0.508070	−	0.861316i	$-0.669641\pi$
$191$	−512314.	−1.01614	−0.508070	+	0.861316i	$0.669641\pi$
$192$	−617041.	−1.20798
$193$	−779315.	−1.50598	−0.752991	−	0.658030i	$-0.771390\pi$
$193$	−779315.	−1.50598	−0.752991	+	0.658030i	$0.771390\pi$
$194$	337749.	0.644302
$195$	542153.	1.02102
$196$	1.47697e6	2.74620
$197$	−375338.	−0.689059	−0.344530	−	0.938775i	$-0.611962\pi$
$197$	−375338.	−0.689059	−0.344530	+	0.938775i	$0.611962\pi$
$198$	−367227.	−0.665690
$199$	373163.	0.667984	0.333992	−	0.942576i	$-0.391604\pi$
$199$	373163.	0.667984	0.333992	+	0.942576i	$0.391604\pi$
$200$	335101.	0.592381
$201$	550323.	0.960788
$202$	−960694.	−1.65656
$203$	−1.57312e6	−2.67930
$204$	−768477.	−1.29287
$205$	−98381.4	−0.163504
$206$	1.05357e6	1.72979
$207$	333922.	0.541650
$208$	3.00476e6	4.81560
$209$	128574.	0.203604
$210$	1.09857e6	1.71901
$211$	968282.	1.49725	0.748627	−	0.662991i	$-0.230713\pi$
$211$	968282.	1.49725	0.748627	+	0.662991i	$0.230713\pi$
$212$	−561230.	−0.857633
$213$	67094.1	0.101329
$214$	−1.05238e6	−1.57086
$215$	301306.	0.444541
$216$	−387781.	−0.565525
$217$	1.87617e6	2.70473
$218$	609068.	0.868009
$219$	38921.6	0.0548379
$220$	2.13115e6	2.96864
$221$	1.02549e6	1.41238
$222$	−988113.	−1.34563
$223$	−423194.	−0.569872	−0.284936	−	0.958547i	$-0.591972\pi$
$223$	−423194.	−0.569872	−0.284936	+	0.958547i	$0.591972\pi$
$224$	2.91081e6	3.87608
$225$	51027.3	0.0671964
$226$	755939.	0.984500
$227$	185430.	0.238845	0.119423	−	0.992844i	$-0.461896\pi$
$227$	185430.	0.238845	0.119423	+	0.992844i	$0.461896\pi$
$228$	222920.	0.283995
$229$	418097.	0.526851	0.263426	−	0.964680i	$-0.415148\pi$
$229$	418097.	0.526851	0.263426	+	0.964680i	$0.415148\pi$
$230$	−2.69547e6	−3.35981
$231$	713889.	0.880239
$232$	−4.48239e6	−5.46751
$233$	137239.	0.165611	0.0828055	−	0.996566i	$-0.473612\pi$
$233$	137239.	0.165611	0.0828055	+	0.996566i	$0.473612\pi$
$234$	849636.	1.01436
$235$	1.47352e6	1.74056
$236$	284929.	0.333009
$237$	276085.	0.319280
$238$	2.07796e6	2.37791
$239$	−207578.	−0.235064	−0.117532	−	0.993069i	$-0.537498\pi$
$239$	−207578.	−0.235064	−0.117532	+	0.993069i	$0.537498\pi$
$240$	1.68569e6	1.88908
$241$	−507933.	−0.563331	−0.281666	−	0.959513i	$-0.590887\pi$
$241$	−507933.	−0.563331	−0.281666	+	0.959513i	$0.590887\pi$
$242$	207877.	0.228176
$243$	−59049.0	−0.0641500
$244$	−2.57044e6	−2.76397
$245$	−1.10572e6	−1.17687
$246$	−154178.	−0.162437
$247$	−297475.	−0.310247
$248$	5.34591e6	5.51941
$249$	263165.	0.268986
$250$	1.63136e6	1.65082
$251$	−58645.3	−0.0587556	−0.0293778	−	0.999568i	$-0.509353\pi$
$251$	−58645.3	−0.0587556	−0.0293778	+	0.999568i	$0.509353\pi$
$252$	1.23773e6	1.22779
$253$	−1.75161e6	−1.72043
$254$	−3.70997e6	−3.60816
$255$	575310.	0.554053
$256$	287983.	0.274642
$257$	1586.01	0.00149787	0.000748935	−	1.00000i	$-0.499762\pi$
$257$	1586.01	0.00149787	0.000748935		1.00000i	$0.499762\pi$
$258$	472192.	0.441641
$259$	1.92089e6	1.77932
$260$	−4.93074e6	−4.52354
$261$	−682553.	−0.620205
$262$	1.14621e6	1.03160
$263$	−1.39407e6	−1.24278	−0.621391	−	0.783501i	$-0.713432\pi$
$263$	−1.39407e6	−1.24278	−0.621391	+	0.783501i	$0.713432\pi$
$264$	2.03413e6	1.79626
$265$	420157.	0.367534
$266$	−602774.	−0.522337
$267$	−215248.	−0.184783
$268$	−5.00504e6	−4.25667
$269$	749950.	0.631904	0.315952	−	0.948775i	$-0.397676\pi$
$269$	749950.	0.631904	0.315952	+	0.948775i	$0.397676\pi$
$270$	476653.	0.397917
$271$	66861.0	0.0553031	0.0276516	−	0.999618i	$-0.491197\pi$
$271$	66861.0	0.0553031	0.0276516	+	0.999618i	$0.491197\pi$
$272$	3.18852e6	2.61316
$273$	−1.65169e6	−1.34129
$274$	2.04096e6	1.64232
$275$	−267668.	−0.213434
$276$	−3.03693e6	−2.39973
$277$	−398436.	−0.312003	−0.156002	−	0.987757i	$-0.549860\pi$
$277$	−398436.	−0.312003	−0.156002	+	0.987757i	$0.549860\pi$
$278$	248649.	0.192963
$279$	814044.	0.626091
$280$	−6.08515e6	−4.63849
$281$	406894.	0.307408	0.153704	−	0.988117i	$-0.450880\pi$
$281$	406894.	0.307408	0.153704	+	0.988117i	$0.450880\pi$
$282$	2.30924e6	1.72920
$283$	2.31675e6	1.71954	0.859772	−	0.510678i	$-0.170605\pi$
$283$	2.31675e6	1.71954	0.859772	+	0.510678i	$0.170605\pi$
$284$	−610203.	−0.448930
$285$	−166886.	−0.121705
$286$	−4.45683e6	−3.22189
$287$	299723.	0.214790
$288$	1.26296e6	0.897237
$289$	−331649.	−0.233579
$290$	5.50967e6	3.84707
$291$	−284882.	−0.197212
$292$	−353981.	−0.242954
$293$	1.71243e6	1.16531	0.582657	−	0.812718i	$-0.302013\pi$
$293$	1.71243e6	1.16531	0.582657	+	0.812718i	$0.302013\pi$
$294$	−1.73283e6	−1.16919
$295$	−213308.	−0.142709
$296$	5.47333e6	3.63097
$297$	309746.	0.203758
$298$	−178160.	−0.116217
$299$	4.05263e6	2.62155
$300$	−464079.	−0.297707
$301$	−917940.	−0.583980
$302$	−1.50850e6	−0.951763
$303$	810319.	0.507048
$304$	−924924.	−0.574014
$305$	1.92433e6	1.18448
$306$	901597.	0.550439
$307$	518531.	0.313999	0.157000	−	0.987599i	$-0.449818\pi$
$307$	518531.	0.313999	0.157000	+	0.987599i	$0.449818\pi$
$308$	−6.49262e6	−3.89981
$309$	−888654.	−0.529464
$310$	−6.57109e6	−3.88359
$311$	−50432.7	−0.0295673	−0.0147836	−	0.999891i	$-0.504706\pi$
$311$	−50432.7	−0.0295673	−0.0147836	+	0.999891i	$0.504706\pi$
$312$	−4.70628e6	−2.73710
$313$	2.84888e6	1.64366	0.821832	−	0.569730i	$-0.192952\pi$
$313$	2.84888e6	1.64366	0.821832	+	0.569730i	$0.192952\pi$
$314$	−73105.2	−0.0418432
$315$	−926612.	−0.526164
$316$	−2.51092e6	−1.41454
$317$	1.74502e6	0.975331	0.487666	−	0.873031i	$-0.337849\pi$
$317$	1.74502e6	0.975331	0.487666	+	0.873031i	$0.337849\pi$
$318$	658450.	0.365136
$319$	3.58038e6	1.96994
$320$	−4.20121e6	−2.29351
$321$	887655.	0.480819
$322$	8.21185e6	4.41368
$323$	−315667.	−0.168354
$324$	537035.	0.284210
$325$	619290.	0.325226
$326$	−2.94317e6	−1.53381
$327$	−513732.	−0.265685
$328$	854021.	0.438313
$329$	−4.48915e6	−2.28652
$330$	−2.50032e6	−1.26389
$331$	−515970.	−0.258854	−0.129427	−	0.991589i	$-0.541314\pi$
$331$	−515970.	−0.258854	−0.129427	+	0.991589i	$0.541314\pi$
$332$	−2.39341e6	−1.19172
$333$	833447.	0.411877
$334$	5.83083e6	2.85999
$335$	3.74695e6	1.82417
$336$	−5.13552e6	−2.48163
$337$	−2.01691e6	−0.967414	−0.483707	−	0.875230i	$-0.660710\pi$
$337$	−2.01691e6	−0.967414	−0.483707	+	0.875230i	$0.660710\pi$
$338$	6.34981e6	3.02321
$339$	−637614.	−0.301341
$340$	−5.23228e6	−2.45467
$341$	−4.27013e6	−1.98864
$342$	−261535.	−0.120911
$343$	230992.	0.106014
$344$	−2.61555e6	−1.19170
$345$	2.27355e6	1.02839
$346$	−6.01052e6	−2.69912
$347$	1.32354e6	0.590084	0.295042	−	0.955484i	$-0.404666\pi$
$347$	1.32354e6	0.590084	0.295042	+	0.955484i	$0.404666\pi$
$348$	6.20763e6	2.74775
$349$	−1.20078e6	−0.527714	−0.263857	−	0.964562i	$-0.584995\pi$
$349$	−1.20078e6	−0.527714	−0.263857	+	0.964562i	$0.584995\pi$
$350$	1.25487e6	0.547556
$351$	−716645.	−0.310482
$352$	−6.62494e6	−2.84987
$353$	−2.56612e6	−1.09607	−0.548037	−	0.836454i	$-0.684625\pi$
$353$	−2.56612e6	−1.09607	−0.548037	+	0.836454i	$0.684625\pi$
$354$	−334286.	−0.141778
$355$	456820.	0.192386
$356$	1.95762e6	0.818661
$357$	−1.75270e6	−0.727843
$358$	6.43603e6	2.65406
$359$	1.98664e6	0.813547	0.406773	−	0.913529i	$-0.366654\pi$
$359$	1.98664e6	0.813547	0.406773	+	0.913529i	$0.366654\pi$
$360$	−2.64026e6	−1.07372
$361$	−2.38453e6	−0.963019
$362$	1.68822e6	0.677109
$363$	−175339.	−0.0698413
$364$	1.50217e7	5.94244
$365$	265003.	0.104116
$366$	3.01571e6	1.17676
$367$	−1.10023e6	−0.426400	−0.213200	−	0.977009i	$-0.568389\pi$
$367$	−1.10023e6	−0.426400	−0.213200	+	0.977009i	$0.568389\pi$
$368$	1.26006e7	4.85035
$369$	130045.	0.0497198
$370$	−6.72771e6	−2.55484
$371$	−1.28003e6	−0.482818
$372$	−7.40351e6	−2.77383
$373$	−2.20944e6	−0.822263	−0.411131	−	0.911576i	$-0.634866\pi$
$373$	−2.20944e6	−0.822263	−0.411131	+	0.911576i	$0.634866\pi$
$374$	−4.72940e6	−1.74834
$375$	−1.37601e6	−0.505294
$376$	−1.27913e7	−4.66599
$377$	−8.28377e6	−3.00175
$378$	−1.45214e6	−0.522732
$379$	−560573.	−0.200463	−0.100231	−	0.994964i	$-0.531958\pi$
$379$	−560573.	−0.200463	−0.100231	+	0.994964i	$0.531958\pi$
$380$	1.51778e6	0.539200
$381$	3.12926e6	1.10441
$382$	−5.46648e6	−1.91668
$383$	−3.40354e6	−1.18559	−0.592795	−	0.805354i	$-0.701975\pi$
$383$	−3.40354e6	−1.18559	−0.592795	+	0.805354i	$0.701975\pi$
$384$	−2.09342e6	−0.724484
$385$	4.86061e6	1.67124
$386$	−8.31543e6	−2.84064
$387$	−398281.	−0.135180
$388$	2.59092e6	0.873726
$389$	−3.10419e6	−1.04010	−0.520048	−	0.854137i	$-0.674086\pi$
$389$	−3.10419e6	−1.04010	−0.520048	+	0.854137i	$0.674086\pi$
$390$	5.78487e6	1.92589
$391$	4.30047e6	1.42257
$392$	9.59842e6	3.15489
$393$	−966798.	−0.315758
$394$	−4.00492e6	−1.29973
$395$	1.87976e6	0.606193
$396$	−2.81706e6	−0.902730
$397$	−3.18351e6	−1.01375	−0.506875	−	0.862020i	$-0.669199\pi$
$397$	−3.18351e6	−1.01375	−0.506875	+	0.862020i	$0.669199\pi$
$398$	3.98171e6	1.25998
$399$	508424.	0.159880
$400$	1.92553e6	0.601728
$401$	311471.	0.0967289	0.0483644	−	0.998830i	$-0.484599\pi$
$401$	311471.	0.0967289	0.0483644	+	0.998830i	$0.484599\pi$
$402$	5.87204e6	1.81227
$403$	9.87961e6	3.03024
$404$	−7.36963e6	−2.24643
$405$	−402044.	−0.121797
$406$	−1.67854e7	−5.05379
$407$	−4.37191e6	−1.30823
$408$	−4.99410e6	−1.48527
$409$	−559438.	−0.165365	−0.0826825	−	0.996576i	$-0.526349\pi$
$409$	−559438.	−0.165365	−0.0826825	+	0.996576i	$0.526349\pi$
$410$	−1.04975e6	−0.308407
$411$	−1.72149e6	−0.502691
$412$	8.08206e6	2.34574
$413$	649851.	0.187473
$414$	3.56300e6	1.02168
$415$	1.79180e6	0.510703
$416$	1.53278e7	4.34257
$417$	−209728.	−0.0590632
$418$	1.37190e6	0.384046
$419$	142773.	0.0397294	0.0198647	−	0.999803i	$-0.493676\pi$
$419$	142773.	0.0397294	0.0198647	+	0.999803i	$0.493676\pi$
$420$	8.42728e6	2.33112
$421$	−3.82502e6	−1.05179	−0.525895	−	0.850550i	$-0.676270\pi$
$421$	−3.82502e6	−1.05179	−0.525895	+	0.850550i	$0.676270\pi$
$422$	1.03317e7	2.82418
$423$	−1.94778e6	−0.529284
$424$	−3.64727e6	−0.985265
$425$	657163.	0.176482
$426$	715906.	0.191131
$427$	−5.86254e6	−1.55602
$428$	−8.07298e6	−2.13022
$429$	3.75922e6	0.986176
$430$	3.21499e6	0.838509
$431$	−4.27196e6	−1.10773	−0.553865	−	0.832606i	$-0.686848\pi$
$431$	−4.27196e6	−1.10773	−0.553865	+	0.832606i	$0.686848\pi$
$432$	−2.22823e6	−0.574448
$433$	−3.40429e6	−0.872583	−0.436292	−	0.899805i	$-0.643708\pi$
$433$	−3.40429e6	−0.872583	−0.436292	+	0.899805i	$0.643708\pi$
$434$	2.00191e7	5.10176
$435$	−4.64726e6	−1.17753
$436$	4.67225e6	1.17709
$437$	−1.24748e6	−0.312486
$438$	415300.	0.103437
$439$	6.97376e6	1.72705	0.863527	−	0.504303i	$-0.168250\pi$
$439$	6.97376e6	1.72705	0.863527	+	0.504303i	$0.168250\pi$
$440$	1.38497e7	3.41042
$441$	1.46159e6	0.357873
$442$	1.09422e7	2.66409
$443$	4.62500e6	1.11970	0.559851	−	0.828593i	$-0.310858\pi$
$443$	4.62500e6	1.11970	0.559851	+	0.828593i	$0.310858\pi$
$444$	−7.57997e6	−1.82478
$445$	−1.46555e6	−0.350833
$446$	−4.51555e6	−1.07491
$447$	150273.	0.0355724
$448$	1.27992e7	3.01291
$449$	−4.22998e6	−0.990199	−0.495100	−	0.868836i	$-0.664868\pi$
$449$	−4.22998e6	−0.990199	−0.495100	+	0.868836i	$0.664868\pi$
$450$	544470.	0.126748
$451$	−682163.	−0.157924
$452$	5.79893e6	1.33506
$453$	1.27238e6	0.291321
$454$	1.97857e6	0.450519
$455$	−1.12458e7	−2.54660
$456$	1.44869e6	0.326259
$457$	8.46533e6	1.89607	0.948033	−	0.318173i	$-0.103069\pi$
$457$	8.46533e6	1.89607	0.948033	+	0.318173i	$0.103069\pi$
$458$	4.46116e6	0.993767
$459$	−760473.	−0.168481
$460$	−2.06774e7	−4.55617
$461$	−5.61651e6	−1.23088	−0.615438	−	0.788185i	$-0.711021\pi$
$461$	−5.61651e6	−1.23088	−0.615438	+	0.788185i	$0.711021\pi$
$462$	7.61732e6	1.66034
$463$	692123.	0.150048	0.0750241	−	0.997182i	$-0.476097\pi$
$463$	692123.	0.150048	0.0750241	+	0.997182i	$0.476097\pi$
$464$	−2.57563e7	−5.55378
$465$	5.54254e6	1.18871
$466$	1.46437e6	0.312382
$467$	6.20510e6	1.31661	0.658304	−	0.752752i	$-0.271274\pi$
$467$	6.20510e6	1.31661	0.658304	+	0.752752i	$0.271274\pi$
$468$	6.51769e6	1.37556
$469$	−1.14152e7	−2.39636
$470$	1.57228e7	3.28310
$471$	61662.3	0.0128076
$472$	1.85167e6	0.382567
$473$	2.08921e6	0.429368
$474$	2.94588e6	0.602238
$475$	−190630.	−0.0387665
$476$	1.59404e7	3.22463
$477$	−555385.	−0.111763
$478$	−2.21489e6	−0.443387
$479$	−4.54829e6	−0.905752	−0.452876	−	0.891573i	$-0.649602\pi$
$479$	−4.54829e6	−0.905752	−0.452876	+	0.891573i	$0.649602\pi$
$480$	8.59902e6	1.70352
$481$	1.01151e7	1.99346
$482$	−5.41973e6	−1.06258
$483$	−6.92647e6	−1.35097
$484$	1.59466e6	0.309425
$485$	−1.93966e6	−0.374430
$486$	−630063.	−0.121002
$487$	−3.94237e6	−0.753242	−0.376621	−	0.926367i	$-0.622914\pi$
$487$	−3.94237e6	−0.753242	−0.376621	+	0.926367i	$0.622914\pi$
$488$	−1.67045e7	−3.17530
$489$	2.48248e6	0.469477
$490$	−1.17982e7	−2.21986
$491$	557676.	0.104395	0.0521973	−	0.998637i	$-0.483378\pi$
$491$	557676.	0.104395	0.0521973	+	0.998637i	$0.483378\pi$
$492$	−1.18273e6	−0.220278
$493$	−8.79037e6	−1.62888
$494$	−3.17411e6	−0.585200
$495$	2.10895e6	0.386860
$496$	3.07182e7	5.60649
$497$	−1.39172e6	−0.252732
$498$	2.80802e6	0.507372
$499$	−4.02783e6	−0.724136	−0.362068	−	0.932152i	$-0.617929\pi$
$499$	−4.02783e6	−0.724136	−0.362068	+	0.932152i	$0.617929\pi$
$500$	1.25144e7	2.23865
$501$	−4.91815e6	−0.875402
$502$	−625755.	−0.110827
$503$	9.17895e6	1.61761	0.808803	−	0.588079i	$-0.200116\pi$
$503$	9.17895e6	1.61761	0.808803	+	0.588079i	$0.200116\pi$
$504$	8.04365e6	1.41051
$505$	5.51717e6	0.962694
$506$	−1.86900e7	−3.24514
$507$	−5.35589e6	−0.925362
$508$	−2.84597e7	−4.89296
$509$	−8.23834e6	−1.40944	−0.704718	−	0.709487i	$-0.748927\pi$
$509$	−8.23834e6	−1.40944	−0.704718	+	0.709487i	$0.748927\pi$
$510$	6.13865e6	1.04508
$511$	−807343.	−0.136775
$512$	−4.37045e6	−0.736803
$513$	220598.	0.0370090
$514$	16923.0	0.00282534
$515$	−6.05053e6	−1.00525
$516$	3.62226e6	0.598901
$517$	1.02172e7	1.68115
$518$	2.04962e7	3.35621
$519$	5.06971e6	0.826161
$520$	−3.20434e7	−5.19673
$521$	−4.78219e6	−0.771850	−0.385925	−	0.922530i	$-0.626118\pi$
$521$	−4.78219e6	−0.771850	−0.385925	+	0.922530i	$0.626118\pi$
$522$	−7.28296e6	−1.16985
$523$	−1.22841e7	−1.96376	−0.981881	−	0.189501i	$-0.939313\pi$
$523$	−1.22841e7	−1.96376	−0.981881	+	0.189501i	$0.939313\pi$
$524$	8.79277e6	1.39893
$525$	−1.05845e6	−0.167599
$526$	−1.48749e7	−2.34418
$527$	1.04838e7	1.64434
$528$	1.16884e7	1.82460
$529$	1.05586e7	1.64046
$530$	4.48315e6	0.693256
$531$	281961.	0.0433963
$532$	−4.62398e6	−0.708331
$533$	1.57829e6	0.240640
$534$	−2.29674e6	−0.348544
$535$	6.04373e6	0.912894
$536$	−3.25262e7	−4.89014
$537$	−5.42862e6	−0.812370
$538$	8.00209e6	1.19192
$539$	−7.66689e6	−1.13670
$540$	3.65648e6	0.539608
$541$	−7.08864e6	−1.04128	−0.520642	−	0.853775i	$-0.674307\pi$
$541$	−7.08864e6	−1.04128	−0.520642	+	0.853775i	$0.674307\pi$
$542$	713418.	0.104315
$543$	−1.42397e6	−0.207253
$544$	1.62652e7	2.35647
$545$	−3.49782e6	−0.504436
$546$	−1.76238e7	−2.52999
$547$	1.55919e6	0.222807	0.111404	−	0.993775i	$-0.464465\pi$
$547$	1.55919e6	0.222807	0.111404	+	0.993775i	$0.464465\pi$
$548$	1.56565e7	2.22712
$549$	−2.54367e6	−0.360189
$550$	−2.85606e6	−0.402588
$551$	2.54991e6	0.357805
$552$	−1.97361e7	−2.75685
$553$	−5.72678e6	−0.796338
$554$	−4.25138e6	−0.588512
$555$	5.67464e6	0.781999
$556$	1.90742e6	0.261674
$557$	2.40850e6	0.328934	0.164467	−	0.986383i	$-0.447410\pi$
$557$	2.40850e6	0.328934	0.164467	+	0.986383i	$0.447410\pi$
$558$	8.68599e6	1.18096
$559$	−4.83372e6	−0.654262
$560$	−3.49659e7	−4.71167
$561$	3.98912e6	0.535143
$562$	4.34163e6	0.579845
$563$	−1.96787e6	−0.261652	−0.130826	−	0.991405i	$-0.541763\pi$
$563$	−1.96787e6	−0.261652	−0.130826	+	0.991405i	$0.541763\pi$
$564$	1.77145e7	2.34494
$565$	−4.34129e6	−0.572133
$566$	2.47201e7	3.24347
$567$	1.22484e6	0.160001
$568$	−3.96552e6	−0.515739
$569$	5.44328e6	0.704823	0.352411	−	0.935845i	$-0.385362\pi$
$569$	5.44328e6	0.704823	0.352411	+	0.935845i	$0.385362\pi$
$570$	−1.78070e6	−0.229564
$571$	1.26908e7	1.62892	0.814461	−	0.580218i	$-0.197033\pi$
$571$	1.26908e7	1.62892	0.814461	+	0.580218i	$0.197033\pi$
$572$	−3.41891e7	−4.36915
$573$	4.61083e6	0.586668
$574$	3.19809e6	0.405146
$575$	2.59703e6	0.327573
$576$	5.55337e6	0.697430
$577$	4.17811e6	0.522445	0.261222	−	0.965279i	$-0.415874\pi$
$577$	4.17811e6	0.522445	0.261222	+	0.965279i	$0.415874\pi$
$578$	−3.53875e6	−0.440585
$579$	7.01384e6	0.869480
$580$	4.22655e7	5.21695
$581$	−5.45878e6	−0.670896
$582$	−3.03974e6	−0.371988
$583$	2.91331e6	0.354990
$584$	−2.30042e6	−0.279110
$585$	−4.87938e6	−0.589488
$586$	1.82719e7	2.19806
$587$	1.07114e6	0.128307	0.0641537	−	0.997940i	$-0.479565\pi$
$587$	1.07114e6	0.128307	0.0641537	+	0.997940i	$0.479565\pi$
$588$	−1.32928e7	−1.58552
$589$	−3.04114e6	−0.361201
$590$	−2.27603e6	−0.269183
$591$	3.37804e6	0.397828
$592$	3.14503e7	3.68826
$593$	−7.74188e6	−0.904085	−0.452043	−	0.891996i	$-0.649305\pi$
$593$	−7.74188e6	−0.904085	−0.452043	+	0.891996i	$0.649305\pi$
$594$	3.30504e6	0.384336
$595$	−1.19335e7	−1.38190
$596$	−1.36670e6	−0.157600
$597$	−3.35847e6	−0.385661
$598$	4.32422e7	4.94487
$599$	3.00377e6	0.342058	0.171029	−	0.985266i	$-0.445291\pi$
$599$	3.00377e6	0.342058	0.171029	+	0.985266i	$0.445291\pi$
$600$	−3.01591e6	−0.342011
$601$	5.32845e6	0.601748	0.300874	−	0.953664i	$-0.402722\pi$
$601$	5.32845e6	0.601748	0.300874	+	0.953664i	$0.402722\pi$
$602$	−9.79458e6	−1.10153
$603$	−4.95291e6	−0.554711
$604$	−1.15720e7	−1.29067
$605$	−1.19382e6	−0.132602
$606$	8.64624e6	0.956414
$607$	1.59774e7	1.76009	0.880046	−	0.474888i	$-0.157512\pi$
$607$	1.59774e7	1.76009	0.880046	+	0.474888i	$0.157512\pi$
$608$	−4.71821e6	−0.517629
$609$	1.41581e7	1.54689
$610$	2.05329e7	2.23422
$611$	−2.36391e7	−2.56170
$612$	6.91629e6	0.746440
$613$	8.04897e6	0.865145	0.432573	−	0.901599i	$-0.357606\pi$
$613$	8.04897e6	0.865145	0.432573	+	0.901599i	$0.357606\pi$
$614$	5.53281e6	0.592277
$615$	885433.	0.0943991
$616$	−4.21936e7	−4.48018
$617$	−1.00376e7	−1.06150	−0.530748	−	0.847529i	$-0.678089\pi$
$617$	−1.00376e7	−1.06150	−0.530748	+	0.847529i	$0.678089\pi$
$618$	−9.48209e6	−0.998695
$619$	−3.31323e6	−0.347556	−0.173778	−	0.984785i	$-0.555598\pi$
$619$	−3.31323e6	−0.347556	−0.173778	+	0.984785i	$0.555598\pi$
$620$	−5.04078e7	−5.26646
$621$	−3.00530e6	−0.312722
$622$	−538126.	−0.0557709
$623$	4.46485e6	0.460879
$624$	−2.70428e7	−2.78029
$625$	−1.13374e7	−1.16095
$626$	3.03980e7	3.10034
$627$	−1.15716e6	−0.117551
$628$	−560802.	−0.0567427
$629$	1.07337e7	1.08174
$630$	−9.88710e6	−0.992471
$631$	1.30632e7	1.30610	0.653048	−	0.757316i	$-0.273490\pi$
$631$	1.30632e7	1.30610	0.653048	+	0.757316i	$0.273490\pi$
$632$	−1.63177e7	−1.62505
$633$	−8.71454e6	−0.864441
$634$	1.86197e7	1.83971
$635$	2.13060e7	2.09685
$636$	5.05107e6	0.495155
$637$	1.77385e7	1.73208
$638$	3.82033e7	3.71577
$639$	−603847.	−0.0585025
$640$	−1.42534e7	−1.37552
$641$	−3.24010e6	−0.311468	−0.155734	−	0.987799i	$-0.549774\pi$
$641$	−3.24010e6	−0.311468	−0.155734	+	0.987799i	$0.549774\pi$
$642$	9.47143e6	0.906939
$643$	−1.43038e7	−1.36435	−0.682174	−	0.731189i	$-0.738966\pi$
$643$	−1.43038e7	−1.36435	−0.682174	+	0.731189i	$0.738966\pi$
$644$	6.29944e7	5.98531
$645$	−2.71175e6	−0.256656
$646$	−3.36823e6	−0.317556
$647$	−1.69491e7	−1.59179	−0.795896	−	0.605434i	$-0.793000\pi$
$647$	−1.69491e7	−1.59179	−0.795896	+	0.605434i	$0.793000\pi$
$648$	3.49003e6	0.326506
$649$	−1.47905e6	−0.137839
$650$	6.60793e6	0.613454
$651$	−1.68855e7	−1.56157
$652$	−2.25775e7	−2.07997
$653$	4.66123e6	0.427777	0.213889	−	0.976858i	$-0.431387\pi$
$653$	4.66123e6	0.427777	0.213889	+	0.976858i	$0.431387\pi$
$654$	−5.48161e6	−0.501145
$655$	−6.58258e6	−0.599506
$656$	4.90730e6	0.445228
$657$	−350295.	−0.0316607
$658$	−4.79000e7	−4.31291
$659$	1.84395e7	1.65400	0.827001	−	0.562201i	$-0.190045\pi$
$659$	1.84395e7	1.65400	0.827001	+	0.562201i	$0.190045\pi$
$660$	−1.91803e7	−1.71394
$661$	−1.59041e6	−0.141581	−0.0707905	−	0.997491i	$-0.522552\pi$
$661$	−1.59041e6	−0.141581	−0.0707905	+	0.997491i	$0.522552\pi$
$662$	−5.50549e6	−0.488260
$663$	−9.22944e6	−0.815439
$664$	−1.55541e7	−1.36907
$665$	3.46168e6	0.303551
$666$	8.89302e6	0.776897
$667$	−3.47385e7	−3.02341
$668$	4.47292e7	3.87838
$669$	3.80875e6	0.329016
$670$	3.99806e7	3.44082
$671$	1.33430e7	1.14406
$672$	−2.61973e7	−2.23786
$673$	−1.37250e7	−1.16809	−0.584044	−	0.811722i	$-0.698530\pi$
$673$	−1.37250e7	−1.16809	−0.584044	+	0.811722i	$0.698530\pi$
$674$	−2.15208e7	−1.82477
$675$	−459245.	−0.0387959
$676$	4.87104e7	4.09972
$677$	1.55559e7	1.30444	0.652219	−	0.758031i	$-0.273838\pi$
$677$	1.55559e7	1.30444	0.652219	+	0.758031i	$0.273838\pi$
$678$	−6.80345e6	−0.568401
$679$	5.90925e6	0.491878
$680$	−3.40030e7	−2.81998
$681$	−1.66887e6	−0.137897
$682$	−4.55630e7	−3.75104
$683$	−1.03021e7	−0.845033	−0.422517	−	0.906355i	$-0.638853\pi$
$683$	−1.03021e7	−0.845033	−0.422517	+	0.906355i	$0.638853\pi$
$684$	−2.00628e6	−0.163965
$685$	−1.17210e7	−0.954420
$686$	2.46472e6	0.199967
$687$	−3.76287e6	−0.304178
$688$	−1.50292e7	−1.21050
$689$	−6.74040e6	−0.540926
$690$	2.42592e7	1.93979
$691$	5.02324e6	0.400211	0.200106	−	0.979774i	$-0.435871\pi$
$691$	5.02324e6	0.400211	0.200106	+	0.979774i	$0.435871\pi$
$692$	−4.61076e7	−3.66022
$693$	−6.42500e6	−0.508206
$694$	1.41224e7	1.11304
$695$	−1.42797e6	−0.112139
$696$	4.03415e7	3.15667
$697$	1.67481e6	0.130582
$698$	−1.28125e7	−0.995393
$699$	−1.23515e6	−0.0956155
$700$	9.62630e6	0.742530
$701$	−1.22395e7	−0.940739	−0.470370	−	0.882469i	$-0.655879\pi$
$701$	−1.22395e7	−0.940739	−0.470370	+	0.882469i	$0.655879\pi$
$702$	−7.64673e6	−0.585643
$703$	−3.11363e6	−0.237617
$704$	−2.91306e7	−2.21523
$705$	−1.32617e7	−1.00491
$706$	−2.73809e7	−2.06745
$707$	−1.68083e7	−1.26466
$708$	−2.56436e6	−0.192263
$709$	3.66774e6	0.274021	0.137010	−	0.990570i	$-0.456251\pi$
$709$	3.66774e6	0.274021	0.137010	+	0.990570i	$0.456251\pi$
$710$	4.87435e6	0.362886
$711$	−2.48477e6	−0.184337
$712$	1.27220e7	0.940493
$713$	4.14307e7	3.05210
$714$	−1.87016e7	−1.37288
$715$	2.55952e7	1.87238
$716$	4.93718e7	3.59912
$717$	1.86820e6	0.135714
$718$	2.11978e7	1.53454
$719$	1.96481e7	1.41742	0.708709	−	0.705501i	$-0.249278\pi$
$719$	1.96481e7	1.41742	0.708709	+	0.705501i	$0.249278\pi$
$720$	−1.51712e7	−1.09066
$721$	1.84332e7	1.32057
$722$	−2.54433e7	−1.81648
$723$	4.57140e6	0.325240
$724$	1.29506e7	0.918215
$725$	−5.30846e6	−0.375080
$726$	−1.87090e6	−0.131737
$727$	1.64307e6	0.115297	0.0576486	−	0.998337i	$-0.481640\pi$
$727$	1.64307e6	0.115297	0.0576486	+	0.998337i	$0.481640\pi$
$728$	9.76214e7	6.82679
$729$	531441.	0.0370370
$730$	2.82763e6	0.196388
$731$	−5.12933e6	−0.355032
$732$	2.31340e7	1.59578
$733$	−4.63590e6	−0.318694	−0.159347	−	0.987223i	$-0.550939\pi$
$733$	−4.63590e6	−0.318694	−0.159347	+	0.987223i	$0.550939\pi$
$734$	−1.17396e7	−0.804291
$735$	9.95145e6	0.679467
$736$	6.42781e7	4.37390
$737$	2.59809e7	1.76191
$738$	1.38761e6	0.0937833
$739$	2.52043e7	1.69771	0.848855	−	0.528625i	$-0.177292\pi$
$739$	2.52043e7	1.69771	0.848855	+	0.528625i	$0.177292\pi$
$740$	−5.16093e7	−3.46457
$741$	2.67727e6	0.179121
$742$	−1.36581e7	−0.910710
$743$	2.59323e7	1.72333	0.861666	−	0.507475i	$-0.169421\pi$
$743$	2.59323e7	1.72333	0.861666	+	0.507475i	$0.169421\pi$
$744$	−4.81132e7	−3.18663
$745$	1.02316e6	0.0675386
$746$	−2.35751e7	−1.55098
$747$	−2.36849e6	−0.155299
$748$	−3.62799e7	−2.37090
$749$	−1.84124e7	−1.19924
$750$	−1.46823e7	−0.953104
$751$	2.11649e7	1.36936	0.684678	−	0.728846i	$-0.259943\pi$
$751$	2.11649e7	1.36936	0.684678	+	0.728846i	$0.259943\pi$
$752$	−7.34999e7	−4.73961
$753$	527808.	0.0339225
$754$	−8.83892e7	−5.66201
$755$	8.66319e6	0.553109
$756$	−1.11396e7	−0.708867
$757$	1.49940e7	0.950992	0.475496	−	0.879718i	$-0.342269\pi$
$757$	1.49940e7	0.950992	0.475496	+	0.879718i	$0.342269\pi$
$758$	−5.98140e6	−0.378120
$759$	1.57645e7	0.993291
$760$	9.86360e6	0.619443
$761$	−2.32932e7	−1.45803	−0.729015	−	0.684497i	$-0.760022\pi$
$761$	−2.32932e7	−1.45803	−0.729015	+	0.684497i	$0.760022\pi$
$762$	3.33897e7	2.08317
$763$	1.06562e7	0.662663
$764$	−4.19342e7	−2.59917
$765$	−5.17779e6	−0.319883
$766$	−3.63164e7	−2.23630
$767$	3.42201e6	0.210035
$768$	−2.59185e6	−0.158565
$769$	−5.03552e6	−0.307064	−0.153532	−	0.988144i	$-0.549065\pi$
$769$	−5.03552e6	−0.307064	−0.153532	+	0.988144i	$0.549065\pi$
$770$	5.18636e7	3.15236
$771$	−14274.1	−0.000864795 0
$772$	−6.37890e7	−3.85214
$773$	−1.34665e7	−0.810599	−0.405300	−	0.914184i	$-0.632833\pi$
$773$	−1.34665e7	−0.810599	−0.405300	+	0.914184i	$0.632833\pi$
$774$	−4.24973e6	−0.254981
$775$	6.33112e6	0.378640
$776$	1.68376e7	1.00375
$777$	−1.72880e7	−1.02729
$778$	−3.31222e7	−1.96187
$779$	−485829.	−0.0286840
$780$	4.43766e7	2.61167
$781$	3.16753e6	0.185820
$782$	4.58867e7	2.68331
$783$	6.14298e6	0.358075
$784$	5.51535e7	3.20467
$785$	419837.	0.0243168
$786$	−1.03159e7	−0.595595
$787$	6.43085e6	0.370111	0.185055	−	0.982728i	$-0.440754\pi$
$787$	6.43085e6	0.370111	0.185055	+	0.982728i	$0.440754\pi$
$788$	−3.07223e7	−1.76254
$789$	1.25466e7	0.717520
$790$	2.00574e7	1.14342
$791$	1.32259e7	0.751595
$792$	−1.83072e7	−1.03707
$793$	−3.08711e7	−1.74329
$794$	−3.39686e7	−1.91217
$795$	−3.78142e6	−0.212196
$796$	3.05444e7	1.70863
$797$	2.19054e7	1.22153	0.610765	−	0.791812i	$-0.290862\pi$
$797$	2.19054e7	1.22153	0.610765	+	0.791812i	$0.290862\pi$
$798$	5.42497e6	0.301571
$799$	−2.50848e7	−1.39009
$800$	9.82247e6	0.542620
$801$	1.93723e6	0.106684
$802$	3.32344e6	0.182454
$803$	1.83750e6	0.100563
$804$	4.50453e7	2.45759
$805$	−4.71599e7	−2.56497
$806$	1.05417e8	5.71575
$807$	−6.74955e6	−0.364830
$808$	−4.78930e7	−2.58074
$809$	−3.19147e7	−1.71443	−0.857214	−	0.514961i	$-0.827806\pi$
$809$	−3.19147e7	−1.71443	−0.857214	+	0.514961i	$0.827806\pi$
$810$	−4.28987e6	−0.229737
$811$	7.21928e6	0.385426	0.192713	−	0.981255i	$-0.438271\pi$
$811$	7.21928e6	0.385426	0.192713	+	0.981255i	$0.438271\pi$
$812$	−1.28764e8	−6.85335
$813$	−601749.	−0.0319293
$814$	−4.66490e7	−2.46764
$815$	1.69023e7	0.891359
$816$	−2.86966e7	−1.50871
$817$	1.48792e6	0.0779872
$818$	−5.96930e6	−0.311918
$819$	1.48652e7	0.774393
$820$	−8.05277e6	−0.418225
$821$	1.80572e7	0.934958	0.467479	−	0.884004i	$-0.345162\pi$
$821$	1.80572e7	0.934958	0.467479	+	0.884004i	$0.345162\pi$
$822$	−1.83686e7	−0.948194
$823$	−4.54084e6	−0.233688	−0.116844	−	0.993150i	$-0.537278\pi$
$823$	−4.54084e6	−0.233688	−0.116844	+	0.993150i	$0.537278\pi$
$824$	5.25229e7	2.69483
$825$	2.40901e6	0.123226
$826$	6.93402e6	0.353619
$827$	2.72523e7	1.38561	0.692803	−	0.721127i	$-0.256376\pi$
$827$	2.72523e7	1.38561	0.692803	+	0.721127i	$0.256376\pi$
$828$	2.73323e7	1.38548
$829$	1.54051e7	0.778537	0.389269	−	0.921124i	$-0.372728\pi$
$829$	1.54051e7	0.778537	0.389269	+	0.921124i	$0.372728\pi$
$830$	1.91188e7	0.963308
$831$	3.58592e6	0.180135
$832$	6.73982e7	3.37552
$833$	1.88234e7	0.939906
$834$	−2.23784e6	−0.111407
$835$	−3.34859e7	−1.66206
$836$	1.05241e7	0.520797
$837$	−7.32640e6	−0.361474
$838$	1.52341e6	0.0749390
$839$	1.50266e7	0.736979	0.368489	−	0.929632i	$-0.379875\pi$
$839$	1.50266e7	0.736979	0.368489	+	0.929632i	$0.379875\pi$
$840$	5.47664e7	2.67803
$841$	5.04961e7	2.46188
$842$	−4.08137e7	−1.98393
$843$	−3.66204e6	−0.177482
$844$	7.92564e7	3.82982
$845$	−3.64663e7	−1.75691
$846$	−2.07831e7	−0.998355
$847$	3.63702e6	0.174196
$848$	−2.09576e7	−1.00081
$849$	−2.08508e7	−0.992780
$850$	7.01205e6	0.332887
$851$	4.24182e7	2.00784
$852$	5.49182e6	0.259190
$853$	3.68547e7	1.73428	0.867142	−	0.498060i	$-0.165954\pi$
$853$	3.68547e7	1.73428	0.867142	+	0.498060i	$0.165954\pi$
$854$	−6.25543e7	−2.93503
$855$	1.50197e6	0.0702662
$856$	−5.24639e7	−2.44724
$857$	−3.27506e7	−1.52324	−0.761618	−	0.648026i	$-0.775595\pi$
$857$	−3.27506e7	−1.52324	−0.761618	+	0.648026i	$0.775595\pi$
$858$	4.01115e7	1.86016
$859$	3.34950e7	1.54881	0.774403	−	0.632693i	$-0.218050\pi$
$859$	3.34950e7	1.54881	0.774403	+	0.632693i	$0.218050\pi$
$860$	2.46627e7	1.13709
$861$	−2.69750e6	−0.124009
$862$	−4.55826e7	−2.08944
$863$	1.12755e7	0.515358	0.257679	−	0.966231i	$-0.417042\pi$
$863$	1.12755e7	0.515358	0.257679	+	0.966231i	$0.417042\pi$
$864$	−1.13666e7	−0.518020
$865$	3.45178e7	1.56857
$866$	−3.63244e7	−1.64590
$867$	2.98484e6	0.134857
$868$	1.53569e8	6.91840
$869$	1.30340e7	0.585503
$870$	−4.95870e7	−2.22111
$871$	−6.01107e7	−2.68476
$872$	3.03636e7	1.35226
$873$	2.56394e6	0.113860
$874$	−1.33108e7	−0.589422
$875$	2.85423e7	1.26029
$876$	3.18583e6	0.140269
$877$	−3.74225e6	−0.164299	−0.0821493	−	0.996620i	$-0.526178\pi$
$877$	−3.74225e6	−0.164299	−0.0821493	+	0.996620i	$0.526178\pi$
$878$	7.44112e7	3.25763
$879$	−1.54118e7	−0.672794
$880$	7.95818e7	3.46423
$881$	1.20043e7	0.521073	0.260537	−	0.965464i	$-0.416101\pi$
$881$	1.20043e7	0.521073	0.260537	+	0.965464i	$0.416101\pi$
$882$	1.55954e7	0.675034
$883$	−1.38235e7	−0.596647	−0.298324	−	0.954465i	$-0.596427\pi$
$883$	−1.38235e7	−0.596647	−0.298324	+	0.954465i	$0.596427\pi$
$884$	8.39392e7	3.61272
$885$	1.91977e6	0.0823932
$886$	4.93495e7	2.11202
$887$	1.58414e7	0.676059	0.338030	−	0.941135i	$-0.390240\pi$
$887$	1.58414e7	0.676059	0.338030	+	0.941135i	$0.390240\pi$
$888$	−4.92600e7	−2.09634
$889$	−6.49095e7	−2.75457
$890$	−1.56376e7	−0.661754
$891$	−2.78772e6	−0.117640
$892$	−3.46395e7	−1.45767
$893$	7.27659e6	0.305351
$894$	1.60344e6	0.0670980
$895$	−3.69615e7	−1.54238
$896$	4.34234e7	1.80698
$897$	−3.64736e7	−1.51355
$898$	−4.51346e7	−1.86775
$899$	−8.46865e7	−3.49474
$900$	4.17671e6	0.171881
$901$	−7.15262e6	−0.293530
$902$	−7.27880e6	−0.297881
$903$	8.26146e6	0.337161
$904$	3.76855e7	1.53374
$905$	−9.69531e6	−0.393496
$906$	1.35765e7	0.549501
$907$	−3.64791e7	−1.47240	−0.736200	−	0.676764i	$-0.763382\pi$
$907$	−3.64791e7	−1.47240	−0.736200	+	0.676764i	$0.763382\pi$
$908$	1.51780e7	0.610940
$909$	−7.29287e6	−0.292745
$910$	−1.19994e8	−4.80349
$911$	−3.55848e7	−1.42059	−0.710294	−	0.703905i	$-0.751438\pi$
$911$	−3.55848e7	−1.42059	−0.710294	+	0.703905i	$0.751438\pi$
$912$	8.32432e6	0.331407
$913$	1.24241e7	0.493273
$914$	9.03265e7	3.57643
$915$	−1.73190e7	−0.683863
$916$	3.42223e7	1.34763
$917$	2.00541e7	0.787553
$918$	−8.11437e6	−0.317796
$919$	3.19136e7	1.24649	0.623243	−	0.782028i	$-0.285815\pi$
$919$	3.19136e7	1.24649	0.623243	+	0.782028i	$0.285815\pi$
$920$	−1.34376e8	−5.23422
$921$	−4.66678e6	−0.181288
$922$	−5.99291e7	−2.32172
$923$	−7.32856e6	−0.283149
$924$	5.84336e7	2.25156
$925$	6.48202e6	0.249090
$926$	7.38507e6	0.283026
$927$	7.99788e6	0.305686
$928$	−1.31388e8	−5.00824
$929$	−3.37958e6	−0.128477	−0.0642383	−	0.997935i	$-0.520462\pi$
$929$	−3.37958e6	−0.128477	−0.0642383	+	0.997935i	$0.520462\pi$
$930$	5.91398e7	2.24219
$931$	−5.46028e6	−0.206462
$932$	1.12334e7	0.423615
$933$	453894.	0.0170707
$934$	6.62095e7	2.48344
$935$	2.71605e7	1.01603
$936$	4.23565e7	1.58027
$937$	3.48856e7	1.29807	0.649034	−	0.760760i	$-0.275173\pi$
$937$	3.48856e7	1.29807	0.649034	+	0.760760i	$0.275173\pi$
$938$	−1.21802e8	−4.52011
$939$	−2.56399e7	−0.948970
$940$	1.20612e8	4.45215
$941$	−4.74186e7	−1.74572	−0.872859	−	0.487972i	$-0.837737\pi$
$941$	−4.74186e7	−1.74572	−0.872859	+	0.487972i	$0.837737\pi$
$942$	657947.	0.0241582
$943$	6.61865e6	0.242376
$944$	1.06399e7	0.388603
$945$	8.33950e6	0.303781
$946$	2.22923e7	0.809891
$947$	3.31556e7	1.20139	0.600693	−	0.799480i	$-0.294892\pi$
$947$	3.31556e7	1.20139	0.600693	+	0.799480i	$0.294892\pi$
$948$	2.25983e7	0.816684
$949$	−4.25133e6	−0.153236
$950$	−2.03405e6	−0.0731229
$951$	−1.57052e7	−0.563108
$952$	1.03592e8	3.70452
$953$	4.68158e7	1.66978	0.834892	−	0.550413i	$-0.185530\pi$
$953$	4.68158e7	1.66978	0.834892	+	0.550413i	$0.185530\pi$
$954$	−5.92605e6	−0.210812
$955$	3.13935e7	1.11386
$956$	−1.69908e7	−0.601269
$957$	−3.22235e7	−1.13735
$958$	−4.85310e7	−1.70846
$959$	3.57086e7	1.25379
$960$	3.78109e7	1.32416
$961$	7.23719e7	2.52791
$962$	1.07930e8	3.76013
$963$	−7.98890e6	−0.277601
$964$	−4.15756e7	−1.44094
$965$	4.77547e7	1.65081
$966$	−7.39066e7	−2.54824
$967$	−3.49546e7	−1.20209	−0.601047	−	0.799214i	$-0.705250\pi$
$967$	−3.49546e7	−1.20209	−0.601047	+	0.799214i	$0.705250\pi$
$968$	1.03632e7	0.355473
$969$	2.84101e6	0.0971992
$970$	−2.06965e7	−0.706265
$971$	5.44571e6	0.185356	0.0926780	−	0.995696i	$-0.470457\pi$
$971$	5.44571e6	0.185356	0.0926780	+	0.995696i	$0.470457\pi$
$972$	−4.83331e6	−0.164089
$973$	4.35035e6	0.147313
$974$	−4.20657e7	−1.42079
$975$	−5.57361e6	−0.187769
$976$	−9.59862e7	−3.22540
$977$	2.76151e7	0.925573	0.462786	−	0.886470i	$-0.346850\pi$
$977$	2.76151e7	0.925573	0.462786	+	0.886470i	$0.346850\pi$
$978$	2.64885e7	0.885545
$979$	−1.01619e7	−0.338859
$980$	−9.05057e7	−3.01031
$981$	4.62359e6	0.153393
$982$	5.95050e6	0.196913
$983$	−8.85517e6	−0.292289	−0.146145	−	0.989263i	$-0.546687\pi$
$983$	−8.85517e6	−0.292289	−0.146145	+	0.989263i	$0.546687\pi$
$984$	−7.68619e6	−0.253060
$985$	2.29999e7	0.755326
$986$	−9.37948e7	−3.07246
$987$	4.04024e7	1.32012
$988$	−2.43491e7	−0.793579
$989$	−2.02705e7	−0.658982
$990$	2.25029e7	0.729709
$991$	3.63535e7	1.17588	0.587938	−	0.808906i	$-0.299940\pi$
$991$	3.63535e7	1.17588	0.587938	+	0.808906i	$0.299940\pi$
$992$	1.56699e8	5.05577
$993$	4.64373e6	0.149449
$994$	−1.48499e7	−0.476713
$995$	−2.28666e7	−0.732224
$996$	2.15407e7	0.688038
$997$	3.59054e6	0.114399	0.0571994	−	0.998363i	$-0.481783\pi$
$997$	3.59054e6	0.114399	0.0571994	+	0.998363i	$0.481783\pi$
$998$	−4.29777e7	−1.36589
$999$	−7.50102e6	−0.237797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.13	✓	13
3.2	odd	2		531.6.a.e.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.13	✓	13	1.1	even	1	trivial
531.6.a.e.1.1		13	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)

\(f(q)\)	\(=\)	\(q+10.6702 q^{2} -9.00000 q^{3} +81.8525 q^{4} -61.2778 q^{5} -96.0315 q^{6} +186.685 q^{7} +531.935 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+10.6702 q^{2} -9.00000 q^{3} +81.8525 q^{4} -61.2778 q^{5} -96.0315 q^{6} +186.685 q^{7} +531.935 q^{8} +81.0000 q^{9} -653.844 q^{10} -424.892 q^{11} -736.673 q^{12} +983.052 q^{13} +1991.96 q^{14} +551.500 q^{15} +3056.56 q^{16} +1043.17 q^{17} +864.284 q^{18} -302.603 q^{19} -5015.74 q^{20} -1680.17 q^{21} -4533.67 q^{22} +4122.49 q^{23} -4787.42 q^{24} +629.966 q^{25} +10489.3 q^{26} -729.000 q^{27} +15280.7 q^{28} -8426.58 q^{29} +5884.60 q^{30} +10049.9 q^{31} +15592.1 q^{32} +3824.03 q^{33} +11130.8 q^{34} -11439.6 q^{35} +6630.06 q^{36} +10289.5 q^{37} -3228.83 q^{38} -8847.47 q^{39} -32595.8 q^{40} +1605.50 q^{41} -17927.7 q^{42} -4917.05 q^{43} -34778.5 q^{44} -4963.50 q^{45} +43987.7 q^{46} -24046.6 q^{47} -27509.0 q^{48} +18044.3 q^{49} +6721.85 q^{50} -9388.55 q^{51} +80465.3 q^{52} -6856.60 q^{53} -7778.55 q^{54} +26036.4 q^{55} +99304.4 q^{56} +2723.43 q^{57} -89913.0 q^{58} +3481.00 q^{59} +45141.7 q^{60} -31403.4 q^{61} +107234. q^{62} +15121.5 q^{63} +68560.1 q^{64} -60239.3 q^{65} +40803.0 q^{66} -61147.0 q^{67} +85386.3 q^{68} -37102.4 q^{69} -122063. q^{70} -7454.90 q^{71} +43086.7 q^{72} -4324.62 q^{73} +109790. q^{74} -5669.70 q^{75} -24768.9 q^{76} -79321.0 q^{77} -94404.0 q^{78} -30676.1 q^{79} -187299. q^{80} +6561.00 q^{81} +17130.9 q^{82} -29240.6 q^{83} -137526. q^{84} -63923.3 q^{85} -52465.8 q^{86} +75839.2 q^{87} -226015. q^{88} +23916.5 q^{89} -52961.4 q^{90} +183521. q^{91} +337436. q^{92} -90449.4 q^{93} -256582. q^{94} +18542.9 q^{95} -140329. q^{96} +31653.6 q^{97} +192536. q^{98} -34416.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * q^99

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