LMFDB - Embedded newform 177.6.a.d.1.11

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			1.11
Root			$6.57049$ 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)

$f(q)$	$=$	$q+6.57049 q^{2} -9.00000 q^{3} +11.1714 q^{4} -5.02964 q^{5} -59.1344 q^{6} -195.140 q^{7} -136.854 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.57049 q^{2} -9.00000 q^{3} +11.1714 q^{4} -5.02964 q^{5} -59.1344 q^{6} -195.140 q^{7} -136.854 q^{8} +81.0000 q^{9} -33.0472 q^{10} +615.938 q^{11} -100.542 q^{12} +601.708 q^{13} -1282.16 q^{14} +45.2668 q^{15} -1256.68 q^{16} +1581.07 q^{17} +532.210 q^{18} +1495.65 q^{19} -56.1880 q^{20} +1756.26 q^{21} +4047.01 q^{22} +4624.33 q^{23} +1231.69 q^{24} -3099.70 q^{25} +3953.52 q^{26} -729.000 q^{27} -2179.98 q^{28} -2800.56 q^{29} +297.425 q^{30} -4246.87 q^{31} -3877.70 q^{32} -5543.44 q^{33} +10388.4 q^{34} +981.482 q^{35} +904.881 q^{36} +2906.40 q^{37} +9827.15 q^{38} -5415.38 q^{39} +688.328 q^{40} +9767.23 q^{41} +11539.5 q^{42} -4044.11 q^{43} +6880.87 q^{44} -407.401 q^{45} +30384.2 q^{46} -3000.15 q^{47} +11310.2 q^{48} +21272.4 q^{49} -20366.6 q^{50} -14229.7 q^{51} +6721.91 q^{52} +35162.3 q^{53} -4789.89 q^{54} -3097.94 q^{55} +26705.7 q^{56} -13460.8 q^{57} -18401.1 q^{58} +3481.00 q^{59} +505.692 q^{60} -22123.9 q^{61} -27904.0 q^{62} -15806.3 q^{63} +14735.5 q^{64} -3026.38 q^{65} -36423.1 q^{66} +33278.2 q^{67} +17662.8 q^{68} -41619.0 q^{69} +6448.82 q^{70} +82302.6 q^{71} -11085.2 q^{72} -58773.8 q^{73} +19096.5 q^{74} +27897.3 q^{75} +16708.5 q^{76} -120194. q^{77} -35581.7 q^{78} +2387.64 q^{79} +6320.67 q^{80} +6561.00 q^{81} +64175.5 q^{82} +25112.8 q^{83} +19619.8 q^{84} -7952.24 q^{85} -26571.8 q^{86} +25205.1 q^{87} -84293.7 q^{88} +5403.27 q^{89} -2676.82 q^{90} -117417. q^{91} +51660.2 q^{92} +38221.8 q^{93} -19712.5 q^{94} -7522.58 q^{95} +34899.3 q^{96} -127853. q^{97} +139770. q^{98} +49890.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.57049	1.16151	0.580755	−	0.814078i	$-0.302757\pi$
$2$	6.57049	1.16151	0.580755	+	0.814078i	$0.302757\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	11.1714	0.349105
$5$	−5.02964	−0.0899730	−0.0449865	−	0.998988i	$-0.514324\pi$
$5$	−5.02964	−0.0899730	−0.0449865	+	0.998988i	$0.514324\pi$
$6$	−59.1344	−0.670598
$7$	−195.140	−1.50522	−0.752610	−	0.658466i	$-0.771206\pi$
$7$	−195.140	−1.50522	−0.752610	+	0.658466i	$0.771206\pi$
$8$	−136.854	−0.756021
$9$	81.0000	0.333333
$10$	−33.0472	−0.104504
$11$	615.938	1.53481	0.767406	−	0.641162i	$-0.221547\pi$
$11$	615.938	1.53481	0.767406	+	0.641162i	$0.221547\pi$
$12$	−100.542	−0.201556
$13$	601.708	0.987479	0.493739	−	0.869610i	$-0.335630\pi$
$13$	601.708	0.987479	0.493739	+	0.869610i	$0.335630\pi$
$14$	−1282.16	−1.74833
$15$	45.2668	0.0519459
$16$	−1256.68	−1.22723
$17$	1581.07	1.32688	0.663438	−	0.748232i	$-0.269097\pi$
$17$	1581.07	1.32688	0.663438	+	0.748232i	$0.269097\pi$
$18$	532.210	0.387170
$19$	1495.65	0.950486	0.475243	−	0.879855i	$-0.342360\pi$
$19$	1495.65	0.950486	0.475243	+	0.879855i	$0.342360\pi$
$20$	−56.1880	−0.0314100
$21$	1756.26	0.869040
$22$	4047.01	1.78270
$23$	4624.33	1.82276	0.911380	−	0.411565i	$-0.135018\pi$
$23$	4624.33	1.82276	0.911380	+	0.411565i	$0.135018\pi$
$24$	1231.69	0.436489
$25$	−3099.70	−0.991905
$26$	3953.52	1.14697
$27$	−729.000	−0.192450
$28$	−2179.98	−0.525481
$29$	−2800.56	−0.618373	−0.309186	−	0.951001i	$-0.600057\pi$
$29$	−2800.56	−0.618373	−0.309186	+	0.951001i	$0.600057\pi$
$30$	297.425	0.0603357
$31$	−4246.87	−0.793715	−0.396857	−	0.917880i	$-0.629899\pi$
$31$	−4246.87	−0.793715	−0.396857	+	0.917880i	$0.629899\pi$
$32$	−3877.70	−0.669420
$33$	−5543.44	−0.886124
$34$	10388.4	1.54118
$35$	981.482	0.135429
$36$	904.881	0.116368
$37$	2906.40	0.349021	0.174510	−	0.984655i	$-0.444166\pi$
$37$	2906.40	0.349021	0.174510	+	0.984655i	$0.444166\pi$
$38$	9827.15	1.10400
$39$	−5415.38	−0.570121
$40$	688.328	0.0680214
$41$	9767.23	0.907427	0.453714	−	0.891148i	$-0.350099\pi$
$41$	9767.23	0.907427	0.453714	+	0.891148i	$0.350099\pi$
$42$	11539.5	1.00940
$43$	−4044.11	−0.333543	−0.166771	−	0.985996i	$-0.553334\pi$
$43$	−4044.11	−0.333543	−0.166771	+	0.985996i	$0.553334\pi$
$44$	6880.87	0.535811
$45$	−407.401	−0.0299910
$46$	30384.2	2.11715
$47$	−3000.15	−0.198106	−0.0990532	−	0.995082i	$-0.531581\pi$
$47$	−3000.15	−0.198106	−0.0990532	+	0.995082i	$0.531581\pi$
$48$	11310.2	0.708542
$49$	21272.4	1.26569
$50$	−20366.6	−1.15211
$51$	−14229.7	−0.766072
$52$	6721.91	0.344734
$53$	35162.3	1.71944	0.859721	−	0.510764i	$-0.170638\pi$
$53$	35162.3	1.71944	0.859721	+	0.510764i	$0.170638\pi$
$54$	−4789.89	−0.223533
$55$	−3097.94	−0.138092
$56$	26705.7	1.13798
$57$	−13460.8	−0.548763
$58$	−18401.1	−0.718246
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	505.692	0.0181346
$61$	−22123.9	−0.761266	−0.380633	−	0.924726i	$-0.624294\pi$
$61$	−22123.9	−0.761266	−0.380633	+	0.924726i	$0.624294\pi$
$62$	−27904.0	−0.921908
$63$	−15806.3	−0.501740
$64$	14735.5	0.449693
$65$	−3026.38	−0.0888464
$66$	−36423.1	−1.02924
$67$	33278.2	0.905677	0.452839	−	0.891593i	$-0.350411\pi$
$67$	33278.2	0.905677	0.452839	+	0.891593i	$0.350411\pi$
$68$	17662.8	0.463219
$69$	−41619.0	−1.05237
$70$	6448.82	0.157302
$71$	82302.6	1.93762	0.968808	−	0.247814i	$-0.0797123\pi$
$71$	82302.6	1.93762	0.968808	+	0.247814i	$0.0797123\pi$
$72$	−11085.2	−0.252007
$73$	−58773.8	−1.29085	−0.645426	−	0.763823i	$-0.723320\pi$
$73$	−58773.8	−1.29085	−0.645426	+	0.763823i	$0.723320\pi$
$74$	19096.5	0.405391
$75$	27897.3	0.572677
$76$	16708.5	0.331820
$77$	−120194.	−2.31023
$78$	−35581.7	−0.662201
$79$	2387.64	0.0430428	0.0215214	−	0.999768i	$-0.493149\pi$
$79$	2387.64	0.0430428	0.0215214	+	0.999768i	$0.493149\pi$
$80$	6320.67	0.110418
$81$	6561.00	0.111111
$82$	64175.5	1.05399
$83$	25112.8	0.400128	0.200064	−	0.979783i	$-0.435885\pi$
$83$	25112.8	0.400128	0.200064	+	0.979783i	$0.435885\pi$
$84$	19619.8	0.303386
$85$	−7952.24	−0.119383
$86$	−26571.8	−0.387413
$87$	25205.1	0.357018
$88$	−84293.7	−1.16035
$89$	5403.27	0.0723072	0.0361536	−	0.999346i	$-0.488489\pi$
$89$	5403.27	0.0723072	0.0361536	+	0.999346i	$0.488489\pi$
$90$	−2676.82	−0.0348348
$91$	−117417.	−1.48637
$92$	51660.2	0.636335
$93$	38221.8	0.458251
$94$	−19712.5	−0.230103
$95$	−7522.58	−0.0855181
$96$	34899.3	0.386490
$97$	−127853.	−1.37969	−0.689843	−	0.723959i	$-0.742320\pi$
$97$	−127853.	−1.37969	−0.689843	+	0.723959i	$0.742320\pi$
$98$	139770.	1.47011
$99$	49890.9	0.511604
$100$	−34627.9	−0.346279
$101$	99497.7	0.970532	0.485266	−	0.874367i	$-0.338723\pi$
$101$	99497.7	0.970532	0.485266	+	0.874367i	$0.338723\pi$
$102$	−93495.9	−0.889800
$103$	34585.5	0.321219	0.160610	−	0.987018i	$-0.448654\pi$
$103$	34585.5	0.321219	0.160610	+	0.987018i	$0.448654\pi$
$104$	−82346.4	−0.746554
$105$	−8833.34	−0.0781901
$106$	231034.	1.99715
$107$	122866.	1.03746	0.518731	−	0.854937i	$-0.326405\pi$
$107$	122866.	1.03746	0.518731	+	0.854937i	$0.326405\pi$
$108$	−8143.93	−0.0671854
$109$	95039.0	0.766188	0.383094	−	0.923709i	$-0.374859\pi$
$109$	95039.0	0.766188	0.383094	+	0.923709i	$0.374859\pi$
$110$	−20355.0	−0.160395
$111$	−26157.6	−0.201507
$112$	245229.	1.84725
$113$	−167074.	−1.23087	−0.615437	−	0.788186i	$-0.711021\pi$
$113$	−167074.	−1.23087	−0.615437	+	0.788186i	$0.711021\pi$
$114$	−88444.4	−0.637394
$115$	−23258.7	−0.163999
$116$	−31286.1	−0.215877
$117$	48738.4	0.329160
$118$	22871.9	0.151216
$119$	−308530.	−1.99724
$120$	−6194.95	−0.0392722
$121$	218328.	1.35565
$122$	−145365.	−0.884218
$123$	−87905.1	−0.523903
$124$	−47443.3	−0.277090
$125$	31308.0	0.179218
$126$	−103855.	−0.582776
$127$	−140021.	−0.770340	−0.385170	−	0.922846i	$-0.625857\pi$
$127$	−140021.	−0.770340	−0.385170	+	0.922846i	$0.625857\pi$
$128$	220906.	1.19174
$129$	36397.0	0.192571
$130$	−19884.8	−0.103196
$131$	128630.	0.654881	0.327441	−	0.944872i	$-0.393814\pi$
$131$	128630.	0.654881	0.327441	+	0.944872i	$0.393814\pi$
$132$	−61927.8	−0.309351
$133$	−291860.	−1.43069
$134$	218654.	1.05195
$135$	3666.61	0.0173153
$136$	−216377.	−1.00314
$137$	−31223.8	−0.142130	−0.0710649	−	0.997472i	$-0.522640\pi$
$137$	−31223.8	−0.142130	−0.0710649	+	0.997472i	$0.522640\pi$
$138$	−273457.	−1.22234
$139$	293077.	1.28660	0.643302	−	0.765612i	$-0.277564\pi$
$139$	293077.	1.28660	0.643302	+	0.765612i	$0.277564\pi$
$140$	10964.5	0.0472790
$141$	27001.4	0.114377
$142$	540768.	2.25056
$143$	370615.	1.51559
$144$	−101791.	−0.409077
$145$	14085.8	0.0556368
$146$	−386173.	−1.49934
$147$	−191452.	−0.730746
$148$	32468.5	0.121845
$149$	−263246.	−0.971396	−0.485698	−	0.874127i	$-0.661434\pi$
$149$	−263246.	−0.971396	−0.485698	+	0.874127i	$0.661434\pi$
$150$	183299.	0.665170
$151$	−86212.2	−0.307699	−0.153850	−	0.988094i	$-0.549167\pi$
$151$	−86212.2	−0.307699	−0.153850	+	0.988094i	$0.549167\pi$
$152$	−204686.	−0.718587
$153$	128067.	0.442292
$154$	−789732.	−2.68335
$155$	21360.2	0.0714129
$156$	−60497.2	−0.199032
$157$	246100.	0.796823	0.398411	−	0.917207i	$-0.369562\pi$
$157$	246100.	0.796823	0.398411	+	0.917207i	$0.369562\pi$
$158$	15688.0	0.0499947
$159$	−316461.	−0.992720
$160$	19503.4	0.0602297
$161$	−902390.	−2.74366
$162$	43109.0	0.129057
$163$	69185.6	0.203961	0.101980	−	0.994786i	$-0.467482\pi$
$163$	69185.6	0.203961	0.101980	+	0.994786i	$0.467482\pi$
$164$	109113.	0.316788
$165$	27881.5	0.0797272
$166$	165003.	0.464753
$167$	142666.	0.395847	0.197924	−	0.980217i	$-0.436580\pi$
$167$	142666.	0.395847	0.197924	+	0.980217i	$0.436580\pi$
$168$	−240351.	−0.657012
$169$	−9240.04	−0.0248861
$170$	−52250.1	−0.138664
$171$	121148.	0.316829
$172$	−45178.2	−0.116442
$173$	−160819.	−0.408528	−0.204264	−	0.978916i	$-0.565480\pi$
$173$	−160819.	−0.408528	−0.204264	+	0.978916i	$0.565480\pi$
$174$	165610.	0.414680
$175$	604875.	1.49304
$176$	−774039.	−1.88357
$177$	−31329.0	−0.0751646
$178$	35502.1	0.0839856
$179$	−564558.	−1.31697	−0.658485	−	0.752593i	$-0.728803\pi$
$179$	−564558.	−1.31697	−0.658485	+	0.752593i	$0.728803\pi$
$180$	−4551.23	−0.0104700
$181$	601583.	1.36490	0.682448	−	0.730934i	$-0.260915\pi$
$181$	601583.	1.36490	0.682448	+	0.730934i	$0.260915\pi$
$182$	−771488.	−1.72644
$183$	199115.	0.439517
$184$	−632860.	−1.37804
$185$	−14618.1	−0.0314024
$186$	251136.	0.532264
$187$	973843.	2.03650
$188$	−33515.8	−0.0691600
$189$	142257.	0.289680
$190$	−49427.1	−0.0993301
$191$	−960341.	−1.90477	−0.952384	−	0.304902i	$-0.901376\pi$
$191$	−960341.	−1.90477	−0.952384	+	0.304902i	$0.901376\pi$
$192$	−132620.	−0.259630
$193$	636269.	1.22955	0.614777	−	0.788701i	$-0.289246\pi$
$193$	636269.	1.22955	0.614777	+	0.788701i	$0.289246\pi$
$194$	−840054.	−1.60252
$195$	27237.4	0.0512955
$196$	237642.	0.441859
$197$	−345122.	−0.633589	−0.316794	−	0.948494i	$-0.602607\pi$
$197$	−345122.	−0.633589	−0.316794	+	0.948494i	$0.602607\pi$
$198$	327808.	0.594233
$199$	175848.	0.314779	0.157389	−	0.987537i	$-0.449692\pi$
$199$	175848.	0.314779	0.157389	+	0.987537i	$0.449692\pi$
$200$	424208.	0.749901
$201$	−299504.	−0.522893
$202$	653749.	1.12728
$203$	546501.	0.930788
$204$	−158965.	−0.267440
$205$	−49125.7	−0.0816439
$206$	227244.	0.373099
$207$	374571.	0.607587
$208$	−756157.	−1.21186
$209$	921227.	1.45882
$210$	−58039.4	−0.0908185
$211$	−592272.	−0.915831	−0.457915	−	0.888996i	$-0.651404\pi$
$211$	−592272.	−0.915831	−0.457915	+	0.888996i	$0.651404\pi$
$212$	392811.	0.600266
$213$	−740723.	−1.11868
$214$	807290.	1.20502
$215$	20340.4	0.0300098
$216$	99766.8	0.145496
$217$	828732.	1.19472
$218$	624453.	0.889935
$219$	528964.	0.745274
$220$	−34608.3	−0.0482085
$221$	951346.	1.31026
$222$	−171868.	−0.234053
$223$	1.29732e6	1.74697	0.873486	−	0.486849i	$-0.161854\pi$
$223$	1.29732e6	1.74697	0.873486	+	0.486849i	$0.161854\pi$
$224$	756692.	1.00763
$225$	−251076.	−0.330635
$226$	−1.09776e6	−1.42967
$227$	1.21660e6	1.56705	0.783526	−	0.621359i	$-0.213419\pi$
$227$	1.21660e6	1.56705	0.783526	+	0.621359i	$0.213419\pi$
$228$	−150376.	−0.191576
$229$	−193917.	−0.244358	−0.122179	−	0.992508i	$-0.538988\pi$
$229$	−193917.	−0.244358	−0.122179	+	0.992508i	$0.538988\pi$
$230$	−152821.	−0.190487
$231$	1.08174e6	1.33381
$232$	383269.	0.467503
$233$	−842584.	−1.01677	−0.508386	−	0.861130i	$-0.669757\pi$
$233$	−842584.	−1.01677	−0.508386	+	0.861130i	$0.669757\pi$
$234$	320235.	0.382322
$235$	15089.7	0.0178242
$236$	38887.5	0.0454496
$237$	−21488.7	−0.0248508
$238$	−2.02720e6	−2.31981
$239$	728076.	0.824484	0.412242	−	0.911074i	$-0.364746\pi$
$239$	728076.	0.824484	0.412242	+	0.911074i	$0.364746\pi$
$240$	−56886.0	−0.0637496
$241$	−771205.	−0.855317	−0.427659	−	0.903940i	$-0.640661\pi$
$241$	−771205.	−0.855317	−0.427659	+	0.903940i	$0.640661\pi$
$242$	1.43452e6	1.57460
$243$	−59049.0	−0.0641500
$244$	−247154.	−0.265762
$245$	−106993.	−0.113878
$246$	−577580.	−0.608519
$247$	899945.	0.938585
$248$	581202.	0.600065
$249$	−226015.	−0.231014
$250$	205709.	0.208163
$251$	720186.	0.721540	0.360770	−	0.932655i	$-0.382514\pi$
$251$	720186.	0.721540	0.360770	+	0.932655i	$0.382514\pi$
$252$	−176578.	−0.175160
$253$	2.84830e6	2.79759
$254$	−920004.	−0.894758
$255$	71570.1	0.0689257
$256$	979924.	0.934528
$257$	−2.01626e6	−1.90420	−0.952102	−	0.305781i	$-0.901083\pi$
$257$	−2.01626e6	−1.90420	−0.952102	+	0.305781i	$0.901083\pi$
$258$	239146.	0.223673
$259$	−567154.	−0.525353
$260$	−33808.8	−0.0310167
$261$	−226846.	−0.206124
$262$	845160.	0.760651
$263$	1.17867e6	1.05076	0.525379	−	0.850868i	$-0.323924\pi$
$263$	1.17867e6	1.05076	0.525379	+	0.850868i	$0.323924\pi$
$264$	758644.	0.669928
$265$	−176854.	−0.154703
$266$	−1.91767e6	−1.66176
$267$	−48629.4	−0.0417466
$268$	371764.	0.316177
$269$	1.74125e6	1.46717	0.733586	−	0.679596i	$-0.237845\pi$
$269$	1.74125e6	1.46717	0.733586	+	0.679596i	$0.237845\pi$
$270$	24091.4	0.0201119
$271$	−498011.	−0.411923	−0.205961	−	0.978560i	$-0.566032\pi$
$271$	−498011.	−0.411923	−0.205961	+	0.978560i	$0.566032\pi$
$272$	−1.98691e6	−1.62838
$273$	1.05675e6	0.858158
$274$	−205156.	−0.165085
$275$	−1.90922e6	−1.52239
$276$	−464941.	−0.367388
$277$	1.27999e6	1.00232	0.501159	−	0.865355i	$-0.332907\pi$
$277$	1.27999e6	1.00232	0.501159	+	0.865355i	$0.332907\pi$
$278$	1.92566e6	1.49440
$279$	−343996.	−0.264572
$280$	−134320.	−0.102387
$281$	−2.01527e6	−1.52253	−0.761266	−	0.648440i	$-0.775422\pi$
$281$	−2.01527e6	−1.52253	−0.761266	+	0.648440i	$0.775422\pi$
$282$	177412.	0.132850
$283$	−2.12464e6	−1.57695	−0.788477	−	0.615065i	$-0.789130\pi$
$283$	−2.12464e6	−1.57695	−0.788477	+	0.615065i	$0.789130\pi$
$284$	919433.	0.676432
$285$	67703.2	0.0493739
$286$	2.43512e6	1.76038
$287$	−1.90597e6	−1.36588
$288$	−314093.	−0.223140
$289$	1.07994e6	0.760597
$290$	92550.8	0.0646227
$291$	1.15067e6	0.796562
$292$	−656584.	−0.450644
$293$	−390717.	−0.265885	−0.132942	−	0.991124i	$-0.542443\pi$
$293$	−390717.	−0.265885	−0.132942	+	0.991124i	$0.542443\pi$
$294$	−1.25793e6	−0.848769
$295$	−17508.2	−0.0117135
$296$	−397753.	−0.263867
$297$	−449019.	−0.295375
$298$	−1.72966e6	−1.12829
$299$	2.78250e6	1.79994
$300$	311651.	0.199924
$301$	789165.	0.502056
$302$	−566457.	−0.357396
$303$	−895480.	−0.560337
$304$	−1.87956e6	−1.16647
$305$	111275.	0.0684934
$306$	841463.	0.513726
$307$	693544.	0.419980	0.209990	−	0.977704i	$-0.432657\pi$
$307$	693544.	0.419980	0.209990	+	0.977704i	$0.432657\pi$
$308$	−1.34273e6	−0.806514
$309$	−311270.	−0.185456
$310$	140347.	0.0829467
$311$	−1.24225e6	−0.728294	−0.364147	−	0.931342i	$-0.618639\pi$
$311$	−1.24225e6	−0.728294	−0.364147	+	0.931342i	$0.618639\pi$
$312$	741118.	0.431023
$313$	2.02548e6	1.16860	0.584301	−	0.811537i	$-0.301369\pi$
$313$	2.02548e6	1.16860	0.584301	+	0.811537i	$0.301369\pi$
$314$	1.61699e6	0.925517
$315$	79500.0	0.0451431
$316$	26673.2	0.0150265
$317$	490022.	0.273884	0.136942	−	0.990579i	$-0.456273\pi$
$317$	490022.	0.273884	0.136942	+	0.990579i	$0.456273\pi$
$318$	−2.07930e6	−1.15305
$319$	−1.72497e6	−0.949086
$320$	−74114.4	−0.0404602
$321$	−1.10579e6	−0.598979
$322$	−5.92915e6	−3.18678
$323$	2.36473e6	1.26118
$324$	73295.4	0.0387895
$325$	−1.86512e6	−0.979485
$326$	454583.	0.236902
$327$	−855351.	−0.442359
$328$	−1.33669e6	−0.686034
$329$	585448.	0.298194
$330$	183195.	0.0926039
$331$	−2.66135e6	−1.33515	−0.667577	−	0.744540i	$-0.732669\pi$
$331$	−2.66135e6	−1.33515	−0.667577	+	0.744540i	$0.732669\pi$
$332$	280544.	0.139687
$333$	235418.	0.116340
$334$	937383.	0.459781
$335$	−167378.	−0.0814865
$336$	−2.20706e6	−1.06651
$337$	−3.16669e6	−1.51891	−0.759453	−	0.650562i	$-0.774533\pi$
$337$	−3.16669e6	−1.51891	−0.759453	+	0.650562i	$0.774533\pi$
$338$	−60711.6	−0.0289055
$339$	1.50367e6	0.710646
$340$	−88837.4	−0.0416772
$341$	−2.61581e6	−1.21820
$342$	795999.	0.368000
$343$	−871384.	−0.399921
$344$	553454.	0.252165
$345$	209329.	0.0946850
$346$	−1.05666e6	−0.474509
$347$	1.61569e6	0.720336	0.360168	−	0.932888i	$-0.382719\pi$
$347$	1.61569e6	0.720336	0.360168	+	0.932888i	$0.382719\pi$
$348$	281575.	0.124637
$349$	4.13215e6	1.81598	0.907992	−	0.418987i	$-0.137615\pi$
$349$	4.13215e6	1.81598	0.907992	+	0.418987i	$0.137615\pi$
$350$	3.97432e6	1.73418
$351$	−438645.	−0.190040
$352$	−2.38842e6	−1.02743
$353$	−568286.	−0.242734	−0.121367	−	0.992608i	$-0.538728\pi$
$353$	−568286.	−0.242734	−0.121367	+	0.992608i	$0.538728\pi$
$354$	−205847.	−0.0873044
$355$	−413952.	−0.174333
$356$	60361.9	0.0252428
$357$	2.77677e6	1.15311
$358$	−3.70943e6	−1.52967
$359$	2.57652e6	1.05511	0.527554	−	0.849522i	$-0.323109\pi$
$359$	2.57652e6	1.05511	0.527554	+	0.849522i	$0.323109\pi$
$360$	55754.6	0.0226738
$361$	−239132.	−0.0965760
$362$	3.95270e6	1.58534
$363$	−1.96495e6	−0.782683
$364$	−1.31171e6	−0.518901
$365$	295611.	0.116142
$366$	1.30828e6	0.510504
$367$	−2.16156e6	−0.837725	−0.418863	−	0.908050i	$-0.637571\pi$
$367$	−2.16156e6	−0.837725	−0.418863	+	0.908050i	$0.637571\pi$
$368$	−5.81133e6	−2.23695
$369$	791146.	0.302476
$370$	−96048.4	−0.0364742
$371$	−6.86155e6	−2.58814
$372$	426990.	0.159978
$373$	3.24398e6	1.20728	0.603638	−	0.797258i	$-0.293717\pi$
$373$	3.24398e6	1.20728	0.603638	+	0.797258i	$0.293717\pi$
$374$	6.39863e6	2.36542
$375$	−281772.	−0.103471
$376$	410584.	0.149773
$377$	−1.68512e6	−0.610630
$378$	934697.	0.336466
$379$	−4.30497e6	−1.53947	−0.769737	−	0.638362i	$-0.779612\pi$
$379$	−4.30497e6	−1.53947	−0.769737	+	0.638362i	$0.779612\pi$
$380$	−84037.5	−0.0298548
$381$	1.26019e6	0.444756
$382$	−6.30991e6	−2.21241
$383$	3.09889e6	1.07947	0.539733	−	0.841836i	$-0.318525\pi$
$383$	3.09889e6	1.07947	0.539733	+	0.841836i	$0.318525\pi$
$384$	−1.98815e6	−0.688053
$385$	604532.	0.207858
$386$	4.18060e6	1.42814
$387$	−327573.	−0.111181
$388$	−1.42829e6	−0.481656
$389$	1.63580e6	0.548097	0.274048	−	0.961716i	$-0.411637\pi$
$389$	1.63580e6	0.548097	0.274048	+	0.961716i	$0.411637\pi$
$390$	178963.	0.0595802
$391$	7.31142e6	2.41858
$392$	−2.91123e6	−0.956887
$393$	−1.15767e6	−0.378096
$394$	−2.26762e6	−0.735920
$395$	−12009.0	−0.00387269
$396$	557350.	0.178604
$397$	−4.43422e6	−1.41202	−0.706011	−	0.708201i	$-0.749507\pi$
$397$	−4.43422e6	−1.41202	−0.706011	+	0.708201i	$0.749507\pi$
$398$	1.15541e6	0.365619
$399$	2.62674e6	0.826010
$400$	3.89535e6	1.21730
$401$	−4.45694e6	−1.38413	−0.692063	−	0.721837i	$-0.743298\pi$
$401$	−4.45694e6	−1.38413	−0.692063	+	0.721837i	$0.743298\pi$
$402$	−1.96789e6	−0.607345
$403$	−2.55538e6	−0.783776
$404$	1.11153e6	0.338818
$405$	−32999.5	−0.00999699
$406$	3.59078e6	1.08112
$407$	1.79016e6	0.535681
$408$	1.94739e6	0.579166
$409$	−162479.	−0.0480274	−0.0240137	−	0.999712i	$-0.507645\pi$
$409$	−162479.	−0.0480274	−0.0240137	+	0.999712i	$0.507645\pi$
$410$	−322780.	−0.0948302
$411$	281015.	0.0820586
$412$	386368.	0.112139
$413$	−679281.	−0.195963
$414$	2.46112e6	0.705718
$415$	−126308.	−0.0360007
$416$	−2.33324e6	−0.661038
$417$	−2.63770e6	−0.742822
$418$	6.05291e6	1.69443
$419$	−855160.	−0.237965	−0.118982	−	0.992896i	$-0.537963\pi$
$419$	−855160.	−0.237965	−0.118982	+	0.992896i	$0.537963\pi$
$420$	−98680.5	−0.0272966
$421$	−1.16801e6	−0.321175	−0.160588	−	0.987022i	$-0.551339\pi$
$421$	−1.16801e6	−0.321175	−0.160588	+	0.987022i	$0.551339\pi$
$422$	−3.89152e6	−1.06375
$423$	−243012.	−0.0660355
$424$	−4.81211e6	−1.29993
$425$	−4.90086e6	−1.31613
$426$	−4.86692e6	−1.29936
$427$	4.31724e6	1.14587
$428$	1.37258e6	0.362184
$429$	−3.33553e6	−0.875028
$430$	133647.	0.0348567
$431$	3.14449e6	0.815374	0.407687	−	0.913122i	$-0.366335\pi$
$431$	3.14449e6	0.815374	0.407687	+	0.913122i	$0.366335\pi$
$432$	916123.	0.236181
$433$	2.87138e6	0.735987	0.367994	−	0.929828i	$-0.380045\pi$
$433$	2.87138e6	0.735987	0.367994	+	0.929828i	$0.380045\pi$
$434$	5.44518e6	1.38767
$435$	−126772.	−0.0321219
$436$	1.06172e6	0.267480
$437$	6.91638e6	1.73251
$438$	3.47556e6	0.865643
$439$	−5.45782e6	−1.35163	−0.675816	−	0.737071i	$-0.736208\pi$
$439$	−5.45782e6	−1.35163	−0.675816	+	0.737071i	$0.736208\pi$
$440$	423967.	0.104400
$441$	1.72307e6	0.421896
$442$	6.25081e6	1.52188
$443$	5.60777e6	1.35763	0.678815	−	0.734310i	$-0.262494\pi$
$443$	5.60777e6	1.35763	0.678815	+	0.734310i	$0.262494\pi$
$444$	−292216.	−0.0703472
$445$	−27176.5	−0.00650569
$446$	8.52405e6	2.02913
$447$	2.36921e6	0.560836
$448$	−2.87548e6	−0.676887
$449$	−6.77774e6	−1.58661	−0.793303	−	0.608827i	$-0.791640\pi$
$449$	−6.77774e6	−1.58661	−0.793303	+	0.608827i	$0.791640\pi$
$450$	−1.64969e6	−0.384036
$451$	6.01600e6	1.39273
$452$	−1.86645e6	−0.429705
$453$	775910.	0.177650
$454$	7.99367e6	1.82015
$455$	590566.	0.133733
$456$	1.84218e6	0.414876
$457$	−8.57672e6	−1.92102	−0.960508	−	0.278252i	$-0.910245\pi$
$457$	−8.57672e6	−1.92102	−0.960508	+	0.278252i	$0.910245\pi$
$458$	−1.27413e6	−0.283824
$459$	−1.15260e6	−0.255357
$460$	−259832.	−0.0572530
$461$	6.65721e6	1.45895	0.729474	−	0.684008i	$-0.239765\pi$
$461$	6.65721e6	1.45895	0.729474	+	0.684008i	$0.239765\pi$
$462$	7.10759e6	1.54924
$463$	3.57838e6	0.775771	0.387886	−	0.921708i	$-0.373206\pi$
$463$	3.57838e6	0.775771	0.387886	+	0.921708i	$0.373206\pi$
$464$	3.51942e6	0.758886
$465$	−192242.	−0.0412302
$466$	−5.53619e6	−1.18099
$467$	−1.64758e6	−0.349585	−0.174793	−	0.984605i	$-0.555926\pi$
$467$	−1.64758e6	−0.349585	−0.174793	+	0.984605i	$0.555926\pi$
$468$	544475.	0.114911
$469$	−6.49390e6	−1.36324
$470$	99146.7	0.0207030
$471$	−2.21490e6	−0.460046
$472$	−476390.	−0.0984255
$473$	−2.49092e6	−0.511925
$474$	−141192.	−0.0288644
$475$	−4.63607e6	−0.942792
$476$	−3.44671e6	−0.697247
$477$	2.84815e6	0.573147
$478$	4.78382e6	0.957646
$479$	−6.02191e6	−1.19921	−0.599605	−	0.800296i	$-0.704676\pi$
$479$	−6.02191e6	−1.19921	−0.599605	+	0.800296i	$0.704676\pi$
$480$	−175531.	−0.0347736
$481$	1.74881e6	0.344650
$482$	−5.06720e6	−0.993460
$483$	8.12151e6	1.58405
$484$	2.43902e6	0.473263
$485$	643052.	0.124134
$486$	−387981.	−0.0745109
$487$	−7.22031e6	−1.37954	−0.689768	−	0.724030i	$-0.742288\pi$
$487$	−7.22031e6	−1.37954	−0.689768	+	0.724030i	$0.742288\pi$
$488$	3.02775e6	0.575533
$489$	−622670.	−0.117757
$490$	−702995.	−0.132270
$491$	−2.70881e6	−0.507078	−0.253539	−	0.967325i	$-0.581595\pi$
$491$	−2.70881e6	−0.507078	−0.253539	+	0.967325i	$0.581595\pi$
$492$	−982020.	−0.182897
$493$	−4.42790e6	−0.820503
$494$	5.91308e6	1.09018
$495$	−250934.	−0.0460305
$496$	5.33697e6	0.974071
$497$	−1.60605e7	−2.91654
$498$	−1.48503e6	−0.268325
$499$	4.10648e6	0.738275	0.369137	−	0.929375i	$-0.379653\pi$
$499$	4.10648e6	0.738275	0.369137	+	0.929375i	$0.379653\pi$
$500$	349754.	0.0625658
$501$	−1.28399e6	−0.228543
$502$	4.73198e6	0.838076
$503$	3.06978e6	0.540988	0.270494	−	0.962722i	$-0.412813\pi$
$503$	3.06978e6	0.540988	0.270494	+	0.962722i	$0.412813\pi$
$504$	2.16316e6	0.379326
$505$	−500438.	−0.0873216
$506$	1.87147e7	3.24943
$507$	83160.3	0.0143680
$508$	−1.56422e6	−0.268930
$509$	−8.90675e6	−1.52379	−0.761894	−	0.647702i	$-0.775730\pi$
$509$	−8.90675e6	−1.52379	−0.761894	+	0.647702i	$0.775730\pi$
$510$	470251.	0.0800579
$511$	1.14691e7	1.94302
$512$	−630407.	−0.106279
$513$	−1.09033e6	−0.182921
$514$	−1.32478e7	−2.21175
$515$	−173953.	−0.0289010
$516$	406604.	0.0672276
$517$	−1.84791e6	−0.304056
$518$	−3.72648e6	−0.610203
$519$	1.44737e6	0.235864
$520$	414173.	0.0671697
$521$	−3.71099e6	−0.598956	−0.299478	−	0.954103i	$-0.596813\pi$
$521$	−3.71099e6	−0.598956	−0.299478	+	0.954103i	$0.596813\pi$
$522$	−1.49049e6	−0.239415
$523$	9.59008e6	1.53309	0.766545	−	0.642190i	$-0.221974\pi$
$523$	9.59008e6	1.53309	0.766545	+	0.642190i	$0.221974\pi$
$524$	1.43697e6	0.228623
$525$	−5.44387e6	−0.862005
$526$	7.74444e6	1.22047
$527$	−6.71461e6	−1.05316
$528$	6.96635e6	1.08748
$529$	1.49481e7	2.32246
$530$	−1.16202e6	−0.179689
$531$	281961.	0.0433963
$532$	−3.26048e6	−0.499462
$533$	5.87702e6	0.896065
$534$	−319519.	−0.0484891
$535$	−617972.	−0.0933436
$536$	−4.55427e6	−0.684711
$537$	5.08102e6	0.760354
$538$	1.14409e7	1.70414
$539$	1.31025e7	1.94259
$540$	40961.0	0.00604487
$541$	−5.54354e6	−0.814317	−0.407159	−	0.913357i	$-0.633480\pi$
$541$	−5.54354e6	−0.814317	−0.407159	+	0.913357i	$0.633480\pi$
$542$	−3.27218e6	−0.478453
$543$	−5.41425e6	−0.788023
$544$	−6.13093e6	−0.888237
$545$	−478012.	−0.0689362
$546$	6.94339e6	0.996759
$547$	−1.83527e6	−0.262260	−0.131130	−	0.991365i	$-0.541861\pi$
$547$	−1.83527e6	−0.262260	−0.131130	+	0.991365i	$0.541861\pi$
$548$	−348813.	−0.0496182
$549$	−1.79203e6	−0.253755
$550$	−1.25445e7	−1.76827
$551$	−4.18866e6	−0.587755
$552$	5.69574e6	0.795614
$553$	−465923.	−0.0647890
$554$	8.41014e6	1.16420
$555$	131563.	0.0181302
$556$	3.27408e6	0.449161
$557$	−3.05158e6	−0.416761	−0.208381	−	0.978048i	$-0.566819\pi$
$557$	−3.05158e6	−0.416761	−0.208381	+	0.978048i	$0.566819\pi$
$558$	−2.26022e6	−0.307303
$559$	−2.43337e6	−0.329366
$560$	−1.23341e6	−0.166203
$561$	−8.76459e6	−1.17578
$562$	−1.32413e7	−1.76844
$563$	2.01186e6	0.267502	0.133751	−	0.991015i	$-0.457298\pi$
$563$	2.01186e6	0.267502	0.133751	+	0.991015i	$0.457298\pi$
$564$	301642.	0.0399296
$565$	840325.	0.110745
$566$	−1.39599e7	−1.83165
$567$	−1.28031e6	−0.167247
$568$	−1.12635e7	−1.46488
$569$	−1.34379e7	−1.74000	−0.870001	−	0.493050i	$-0.835882\pi$
$569$	−1.34379e7	−1.74000	−0.870001	+	0.493050i	$0.835882\pi$
$570$	444843.	0.0573482
$571$	−8.45807e6	−1.08563	−0.542814	−	0.839853i	$-0.682641\pi$
$571$	−8.45807e6	−1.08563	−0.542814	+	0.839853i	$0.682641\pi$
$572$	4.14028e6	0.529102
$573$	8.64307e6	1.09972
$574$	−1.25232e7	−1.58648
$575$	−1.43341e7	−1.80801
$576$	1.19358e6	0.149898
$577$	4.56929e6	0.571360	0.285680	−	0.958325i	$-0.407781\pi$
$577$	4.56929e6	0.571360	0.285680	+	0.958325i	$0.407781\pi$
$578$	7.09573e6	0.883441
$579$	−5.72642e6	−0.709883
$580$	157358.	0.0194231
$581$	−4.90049e6	−0.602281
$582$	7.56049e6	0.925214
$583$	2.16578e7	2.63902
$584$	8.04345e6	0.975911
$585$	−245137.	−0.0296155
$586$	−2.56720e6	−0.308828
$587$	−783028.	−0.0937955	−0.0468977	−	0.998900i	$-0.514933\pi$
$587$	−783028.	−0.0937955	−0.0468977	+	0.998900i	$0.514933\pi$
$588$	−2.13878e6	−0.255107
$589$	−6.35182e6	−0.754415
$590$	−115037.	−0.0136053
$591$	3.10610e6	0.365803
$592$	−3.65243e6	−0.428329
$593$	−86034.2	−0.0100470	−0.00502348	−	0.999987i	$-0.501599\pi$
$593$	−86034.2	−0.0100470	−0.00502348	+	0.999987i	$0.501599\pi$
$594$	−2.95027e6	−0.343081
$595$	1.55180e6	0.179698
$596$	−2.94082e6	−0.339119
$597$	−1.58263e6	−0.181738
$598$	1.82824e7	2.09064
$599$	−2.62525e6	−0.298954	−0.149477	−	0.988765i	$-0.547759\pi$
$599$	−2.62525e6	−0.298954	−0.149477	+	0.988765i	$0.547759\pi$
$600$	−3.81787e6	−0.432955
$601$	−809225.	−0.0913867	−0.0456933	−	0.998956i	$-0.514550\pi$
$601$	−809225.	−0.0913867	−0.0456933	+	0.998956i	$0.514550\pi$
$602$	5.18520e6	0.583142
$603$	2.69554e6	0.301892
$604$	−963109.	−0.107419
$605$	−1.09811e6	−0.121971
$606$	−5.88374e6	−0.650837
$607$	1.68966e7	1.86135	0.930674	−	0.365850i	$-0.119222\pi$
$607$	1.68966e7	1.86135	0.930674	+	0.365850i	$0.119222\pi$
$608$	−5.79967e6	−0.636275
$609$	−4.91851e6	−0.537390
$610$	731132.	0.0795557
$611$	−1.80522e6	−0.195626
$612$	1.43068e6	0.154406
$613$	−1.59225e7	−1.71143	−0.855716	−	0.517446i	$-0.826883\pi$
$613$	−1.59225e7	−1.71143	−0.855716	+	0.517446i	$0.826883\pi$
$614$	4.55693e6	0.487810
$615$	442131.	0.0471371
$616$	1.64490e7	1.74658
$617$	1.84611e7	1.95229	0.976146	−	0.217114i	$-0.0696643\pi$
$617$	1.84611e7	1.95229	0.976146	+	0.217114i	$0.0696643\pi$
$618$	−2.04520e6	−0.215409
$619$	1.49529e7	1.56855	0.784276	−	0.620412i	$-0.213035\pi$
$619$	1.49529e7	1.56855	0.784276	+	0.620412i	$0.213035\pi$
$620$	238623.	0.0249306
$621$	−3.37114e6	−0.350790
$622$	−8.16217e6	−0.845920
$623$	−1.05439e6	−0.108838
$624$	6.80542e6	0.699670
$625$	9.52910e6	0.975780
$626$	1.33084e7	1.35734
$627$	−8.29104e6	−0.842248
$628$	2.74927e6	0.278175
$629$	4.59523e6	0.463107
$630$	522354.	0.0524341
$631$	−3.60718e6	−0.360658	−0.180329	−	0.983606i	$-0.557716\pi$
$631$	−3.60718e6	−0.360658	−0.180329	+	0.983606i	$0.557716\pi$
$632$	−326759.	−0.0325413
$633$	5.33045e6	0.528755
$634$	3.21968e6	0.318119
$635$	704253.	0.0693098
$636$	−3.53530e6	−0.346564
$637$	1.27998e7	1.24984
$638$	−1.13339e7	−1.10237
$639$	6.66651e6	0.645872
$640$	−1.11108e6	−0.107225
$641$	5.56821e6	0.535267	0.267633	−	0.963521i	$-0.413758\pi$
$641$	5.56821e6	0.535267	0.267633	+	0.963521i	$0.413758\pi$
$642$	−7.26561e6	−0.695720
$643$	4205.85	0.000401168 0	0.000200584	−	1.00000i	$-0.499936\pi$
$643$	4205.85	0.000401168 0	0.000200584		1.00000i	$0.499936\pi$
$644$	−1.00809e7	−0.957825
$645$	−183064.	−0.0173262
$646$	1.55375e7	1.46487
$647$	−9.12416e6	−0.856904	−0.428452	−	0.903565i	$-0.640941\pi$
$647$	−9.12416e6	−0.856904	−0.428452	+	0.903565i	$0.640941\pi$
$648$	−897901.	−0.0840023
$649$	2.14408e6	0.199815
$650$	−1.22547e7	−1.13768
$651$	−7.45859e6	−0.689770
$652$	772898.	0.0712038
$653$	1.43621e7	1.31806	0.659028	−	0.752119i	$-0.270968\pi$
$653$	1.43621e7	1.31806	0.659028	+	0.752119i	$0.270968\pi$
$654$	−5.62007e6	−0.513804
$655$	−646961.	−0.0589216
$656$	−1.22743e7	−1.11362
$657$	−4.76068e6	−0.430284
$658$	3.84668e6	0.346355
$659$	−6.50900e6	−0.583849	−0.291925	−	0.956441i	$-0.594296\pi$
$659$	−6.50900e6	−0.583849	−0.291925	+	0.956441i	$0.594296\pi$
$660$	311475.	0.0278332
$661$	−2.17042e7	−1.93214	−0.966072	−	0.258272i	$-0.916847\pi$
$661$	−2.17042e7	−1.93214	−0.966072	+	0.258272i	$0.916847\pi$
$662$	−1.74864e7	−1.55080
$663$	−8.56211e6	−0.756479
$664$	−3.43679e6	−0.302505
$665$	1.46795e6	0.128724
$666$	1.54681e6	0.135130
$667$	−1.29507e7	−1.12715
$668$	1.59377e6	0.138192
$669$	−1.16759e7	−1.00862
$670$	−1.09975e6	−0.0946473
$671$	−1.36269e7	−1.16840
$672$	−6.81023e6	−0.581753
$673$	−5.79203e6	−0.492939	−0.246469	−	0.969151i	$-0.579270\pi$
$673$	−5.79203e6	−0.492939	−0.246469	+	0.969151i	$0.579270\pi$
$674$	−2.08067e7	−1.76422
$675$	2.25968e6	0.190892
$676$	−103224.	−0.00868787
$677$	7.10628e6	0.595896	0.297948	−	0.954582i	$-0.403698\pi$
$677$	7.10628e6	0.595896	0.297948	+	0.954582i	$0.403698\pi$
$678$	9.87985e6	0.825422
$679$	2.49491e7	2.07673
$680$	1.08830e6	0.0902559
$681$	−1.09494e7	−0.904738
$682$	−1.71871e7	−1.41495
$683$	1.32074e7	1.08334	0.541670	−	0.840591i	$-0.317792\pi$
$683$	1.32074e7	1.08334	0.541670	+	0.840591i	$0.317792\pi$
$684$	1.35338e6	0.110607
$685$	157045.	0.0127878
$686$	−5.72542e6	−0.464513
$687$	1.74525e6	0.141080
$688$	5.08217e6	0.409334
$689$	2.11574e7	1.69791
$690$	1.37539e6	0.109978
$691$	−1.50268e7	−1.19721	−0.598605	−	0.801045i	$-0.704278\pi$
$691$	−1.50268e7	−1.19721	−0.598605	+	0.801045i	$0.704278\pi$
$692$	−1.79657e6	−0.142619
$693$	−9.73570e6	−0.770077
$694$	1.06159e7	0.836677
$695$	−1.47407e6	−0.115760
$696$	−3.44942e6	−0.269913
$697$	1.54427e7	1.20404
$698$	2.71502e7	2.10928
$699$	7.58325e6	0.587033
$700$	6.75728e6	0.521227
$701$	−4.79743e6	−0.368734	−0.184367	−	0.982857i	$-0.559024\pi$
$701$	−4.79743e6	−0.368734	−0.184367	+	0.982857i	$0.559024\pi$
$702$	−2.88212e6	−0.220734
$703$	4.34696e6	0.331739
$704$	9.07616e6	0.690193
$705$	−135807.	−0.0102908
$706$	−3.73392e6	−0.281938
$707$	−1.94159e7	−1.46086
$708$	−349988.	−0.0262404
$709$	1.37944e7	1.03060	0.515298	−	0.857011i	$-0.327681\pi$
$709$	1.37944e7	1.03060	0.515298	+	0.857011i	$0.327681\pi$
$710$	−2.71987e6	−0.202489
$711$	193399.	0.0143476
$712$	−739461.	−0.0546657
$713$	−1.96389e7	−1.44675
$714$	1.82448e7	1.33935
$715$	−1.86406e6	−0.136362
$716$	−6.30689e6	−0.459762
$717$	−6.55269e6	−0.476016
$718$	1.69290e7	1.22552
$719$	1.06010e7	0.764758	0.382379	−	0.924006i	$-0.375105\pi$
$719$	1.06010e7	0.764758	0.382379	+	0.924006i	$0.375105\pi$
$720$	511974.	0.0368059
$721$	−6.74901e6	−0.483506
$722$	−1.57121e6	−0.112174
$723$	6.94085e6	0.493818
$724$	6.72051e6	0.476492
$725$	8.68091e6	0.613367
$726$	−1.29107e7	−0.909094
$727$	−482236.	−0.0338394	−0.0169197	−	0.999857i	$-0.505386\pi$
$727$	−482236.	−0.0338394	−0.0169197	+	0.999857i	$0.505386\pi$
$728$	1.60690e7	1.12373
$729$	531441.	0.0370370
$730$	1.94231e6	0.134900
$731$	−6.39404e6	−0.442570
$732$	2.22439e6	0.153438
$733$	1.33531e6	0.0917955	0.0458977	−	0.998946i	$-0.485385\pi$
$733$	1.33531e6	0.0917955	0.0458977	+	0.998946i	$0.485385\pi$
$734$	−1.42025e7	−0.973026
$735$	962935.	0.0657474
$736$	−1.79318e7	−1.22019
$737$	2.04973e7	1.39004
$738$	5.19822e6	0.351329
$739$	−3988.00	−0.000268623 0	−0.000134312	−	1.00000i	$-0.500043\pi$
$739$	−3988.00	−0.000268623 0	−0.000134312		1.00000i	$0.500043\pi$
$740$	−163305.	−0.0109628
$741$	−8.09950e6	−0.541892
$742$	−4.50838e7	−3.00615
$743$	2.80010e7	1.86081	0.930403	−	0.366538i	$-0.119457\pi$
$743$	2.80010e7	1.86081	0.930403	+	0.366538i	$0.119457\pi$
$744$	−5.23082e6	−0.346448
$745$	1.32403e6	0.0873993
$746$	2.13146e7	1.40226
$747$	2.03413e6	0.133376
$748$	1.08792e7	0.710954
$749$	−2.39760e7	−1.56161
$750$	−1.85138e6	−0.120183
$751$	−1.88879e7	−1.22204	−0.611019	−	0.791616i	$-0.709240\pi$
$751$	−1.88879e7	−1.22204	−0.611019	+	0.791616i	$0.709240\pi$
$752$	3.77024e6	0.243122
$753$	−6.48168e6	−0.416581
$754$	−1.10721e7	−0.709253
$755$	433617.	0.0276846
$756$	1.58920e6	0.101129
$757$	−2.10079e7	−1.33242	−0.666212	−	0.745762i	$-0.732086\pi$
$757$	−2.10079e7	−1.33242	−0.666212	+	0.745762i	$0.732086\pi$
$758$	−2.82858e7	−1.78811
$759$	−2.56347e7	−1.61519
$760$	1.02950e6	0.0646534
$761$	−7.32237e6	−0.458342	−0.229171	−	0.973386i	$-0.573602\pi$
$761$	−7.32237e6	−0.458342	−0.229171	+	0.973386i	$0.573602\pi$
$762$	8.28004e6	0.516589
$763$	−1.85459e7	−1.15328
$764$	−1.07283e7	−0.664964
$765$	−644131.	−0.0397943
$766$	2.03612e7	1.25381
$767$	2.09455e6	0.128559
$768$	−8.81932e6	−0.539550
$769$	5.75082e6	0.350682	0.175341	−	0.984508i	$-0.443897\pi$
$769$	5.75082e6	0.350682	0.175341	+	0.984508i	$0.443897\pi$
$770$	3.97207e6	0.241429
$771$	1.81463e7	1.09939
$772$	7.10800e6	0.429244
$773$	−1.45427e7	−0.875376	−0.437688	−	0.899127i	$-0.644203\pi$
$773$	−1.45427e7	−0.875376	−0.437688	+	0.899127i	$0.644203\pi$
$774$	−2.15231e6	−0.129138
$775$	1.31640e7	0.787289
$776$	1.74972e7	1.04307
$777$	5.10438e6	0.303313
$778$	1.07480e7	0.636620
$779$	1.46084e7	0.862497
$780$	304279.	0.0179075
$781$	5.06932e7	2.97387
$782$	4.80396e7	2.80920
$783$	2.04161e6	0.119006
$784$	−2.67327e7	−1.55329
$785$	−1.23779e6	−0.0716925
$786$	−7.60644e6	−0.439162
$787$	5.93204e6	0.341403	0.170702	−	0.985323i	$-0.445397\pi$
$787$	5.93204e6	0.341403	0.170702	+	0.985323i	$0.445397\pi$
$788$	−3.85549e6	−0.221189
$789$	−1.06080e7	−0.606656
$790$	−78904.8	−0.00449817
$791$	3.26028e7	1.85274
$792$	−6.82779e6	−0.386783
$793$	−1.33121e7	−0.751734
$794$	−2.91350e7	−1.64008
$795$	1.59168e6	0.0893180
$796$	1.96447e6	0.109891
$797$	895889.	0.0499584	0.0249792	−	0.999688i	$-0.492048\pi$
$797$	895889.	0.0499584	0.0249792	+	0.999688i	$0.492048\pi$
$798$	1.72590e7	0.959419
$799$	−4.74346e6	−0.262862
$800$	1.20197e7	0.664001
$801$	437665.	0.0241024
$802$	−2.92843e7	−1.60768
$803$	−3.62010e7	−1.98122
$804$	−3.34587e6	−0.182545
$805$	4.53870e6	0.246855
$806$	−1.67901e7	−0.910364
$807$	−1.56713e7	−0.847073
$808$	−1.36167e7	−0.733742
$809$	2.35993e6	0.126773	0.0633865	−	0.997989i	$-0.479810\pi$
$809$	2.35993e6	0.126773	0.0633865	+	0.997989i	$0.479810\pi$
$810$	−216823.	−0.0116116
$811$	8.00417e6	0.427331	0.213665	−	0.976907i	$-0.431460\pi$
$811$	8.00417e6	0.427331	0.213665	+	0.976907i	$0.431460\pi$
$812$	6.10516e6	0.324943
$813$	4.48210e6	0.237824
$814$	1.17622e7	0.622199
$815$	−347979.	−0.0183509
$816$	1.78822e7	0.940147
$817$	−6.04857e6	−0.317028
$818$	−1.06757e6	−0.0557843
$819$	−9.51079e6	−0.495458
$820$	−548801.	−0.0285023
$821$	1.27329e7	0.659279	0.329639	−	0.944107i	$-0.393073\pi$
$821$	1.27329e7	0.659279	0.329639	+	0.944107i	$0.393073\pi$
$822$	1.84640e6	0.0953119
$823$	2.03517e7	1.04737	0.523685	−	0.851912i	$-0.324557\pi$
$823$	2.03517e7	1.04737	0.523685	+	0.851912i	$0.324557\pi$
$824$	−4.73318e6	−0.242848
$825$	1.71830e7	0.878950
$826$	−4.46321e6	−0.227613
$827$	−2.30492e7	−1.17190	−0.585952	−	0.810346i	$-0.699279\pi$
$827$	−2.30492e7	−1.17190	−0.585952	+	0.810346i	$0.699279\pi$
$828$	4.18447e6	0.212112
$829$	2.34517e7	1.18519	0.592595	−	0.805501i	$-0.298104\pi$
$829$	2.34517e7	1.18519	0.592595	+	0.805501i	$0.298104\pi$
$830$	−829907.	−0.0418152
$831$	−1.15199e7	−0.578689
$832$	8.86649e6	0.444062
$833$	3.36333e7	1.67941
$834$	−1.73310e7	−0.862795
$835$	−717556.	−0.0356156
$836$	1.02914e7	0.509281
$837$	3.09597e6	0.152750
$838$	−5.61882e6	−0.276398
$839$	−5.83510e6	−0.286183	−0.143091	−	0.989709i	$-0.545704\pi$
$839$	−5.83510e6	−0.286183	−0.143091	+	0.989709i	$0.545704\pi$
$840$	1.20888e6	0.0591133
$841$	−1.26680e7	−0.617615
$842$	−7.67441e6	−0.373048
$843$	1.81374e7	0.879034
$844$	−6.61649e6	−0.319721
$845$	46474.1	0.00223908
$846$	−1.59671e6	−0.0767009
$847$	−4.26045e7	−2.04055
$848$	−4.41879e7	−2.11015
$849$	1.91217e7	0.910454
$850$	−3.22011e7	−1.52870
$851$	1.34402e7	0.636181
$852$	−8.27489e6	−0.390538
$853$	−1.80133e7	−0.847657	−0.423829	−	0.905742i	$-0.639314\pi$
$853$	−1.80133e7	−0.847657	−0.423829	+	0.905742i	$0.639314\pi$
$854$	2.83664e7	1.33094
$855$	−609329.	−0.0285060
$856$	−1.68147e7	−0.784343
$857$	9.03246e6	0.420101	0.210051	−	0.977691i	$-0.432637\pi$
$857$	9.03246e6	0.420101	0.210051	+	0.977691i	$0.432637\pi$
$858$	−2.19161e7	−1.01635
$859$	2.29740e7	1.06232	0.531159	−	0.847272i	$-0.321757\pi$
$859$	2.29740e7	1.06232	0.531159	+	0.847272i	$0.321757\pi$
$860$	227230.	0.0104766
$861$	1.71538e7	0.788590
$862$	2.06608e7	0.947065
$863$	4.01614e7	1.83562	0.917809	−	0.397022i	$-0.129956\pi$
$863$	4.01614e7	1.83562	0.917809	+	0.397022i	$0.129956\pi$
$864$	2.82684e6	0.128830
$865$	808861.	0.0367565
$866$	1.88664e7	0.854857
$867$	−9.71946e6	−0.439131
$868$	9.25807e6	0.417082
$869$	1.47064e6	0.0660626
$870$	−832957.	−0.0373099
$871$	2.00238e7	0.894337
$872$	−1.30065e7	−0.579254
$873$	−1.03561e7	−0.459895
$874$	4.54440e7	2.01233
$875$	−6.10943e6	−0.269762
$876$	5.90926e6	0.260179
$877$	−1.11452e7	−0.489315	−0.244657	−	0.969610i	$-0.578675\pi$
$877$	−1.11452e7	−0.489315	−0.244657	+	0.969610i	$0.578675\pi$
$878$	−3.58606e7	−1.56993
$879$	3.51645e6	0.153509
$880$	3.89314e6	0.169470
$881$	2.69740e7	1.17086	0.585430	−	0.810723i	$-0.300926\pi$
$881$	2.69740e7	1.17086	0.585430	+	0.810723i	$0.300926\pi$
$882$	1.13214e7	0.490037
$883$	3.09533e7	1.33600	0.667998	−	0.744163i	$-0.267151\pi$
$883$	3.09533e7	1.33600	0.667998	+	0.744163i	$0.267151\pi$
$884$	1.06278e7	0.457419
$885$	157574.	0.00676278
$886$	3.68458e7	1.57690
$887$	4.04751e7	1.72735	0.863673	−	0.504052i	$-0.168158\pi$
$887$	4.04751e7	1.72735	0.863673	+	0.504052i	$0.168158\pi$
$888$	3.57978e6	0.152344
$889$	2.73236e7	1.15953
$890$	−178563.	−0.00755643
$891$	4.04117e6	0.170535
$892$	1.44929e7	0.609878
$893$	−4.48718e6	−0.188297
$894$	1.55669e7	0.651416
$895$	2.83953e6	0.118492
$896$	−4.31075e7	−1.79384
$897$	−2.50425e7	−1.03919
$898$	−4.45331e7	−1.84286
$899$	1.18936e7	0.490812
$900$	−2.80486e6	−0.115426
$901$	5.55942e7	2.28148
$902$	3.95281e7	1.61767
$903$	−7.10249e6	−0.289862
$904$	2.28649e7	0.930567
$905$	−3.02575e6	−0.122804
$906$	5.09811e6	0.206343
$907$	−3.00294e7	−1.21207	−0.606037	−	0.795437i	$-0.707242\pi$
$907$	−3.00294e7	−1.21207	−0.606037	+	0.795437i	$0.707242\pi$
$908$	1.35911e7	0.547066
$909$	8.05932e6	0.323511
$910$	3.88031e6	0.155333
$911$	2.23434e7	0.891975	0.445988	−	0.895039i	$-0.352853\pi$
$911$	2.23434e7	0.891975	0.445988	+	0.895039i	$0.352853\pi$
$912$	1.69160e7	0.673459
$913$	1.54679e7	0.614122
$914$	−5.63533e7	−2.23128
$915$	−1.00148e6	−0.0395447
$916$	−2.16632e6	−0.0853067
$917$	−2.51007e7	−0.985741
$918$	−7.57317e6	−0.296600
$919$	−2.16721e7	−0.846470	−0.423235	−	0.906020i	$-0.639106\pi$
$919$	−2.16721e7	−0.846470	−0.423235	+	0.906020i	$0.639106\pi$
$920$	3.18306e6	0.123987
$921$	−6.24190e6	−0.242475
$922$	4.37411e7	1.69458
$923$	4.95221e7	1.91335
$924$	1.20846e7	0.465641
$925$	−9.00898e6	−0.346195
$926$	2.35117e7	0.901066
$927$	2.80143e6	0.107073
$928$	1.08597e7	0.413951
$929$	2.99471e7	1.13845	0.569227	−	0.822181i	$-0.307243\pi$
$929$	2.99471e7	1.13845	0.569227	+	0.822181i	$0.307243\pi$
$930$	−1.26312e6	−0.0478893
$931$	3.18161e7	1.20302
$932$	−9.41281e6	−0.354960
$933$	1.11802e7	0.420481
$934$	−1.08254e7	−0.406047
$935$	−4.89808e6	−0.183230
$936$	−6.67006e6	−0.248851
$937$	−9.55526e6	−0.355544	−0.177772	−	0.984072i	$-0.556889\pi$
$937$	−9.55526e6	−0.355544	−0.177772	+	0.984072i	$0.556889\pi$
$938$	−4.26681e7	−1.58342
$939$	−1.82293e7	−0.674693
$940$	168572.	0.00622253
$941$	−3.83877e7	−1.41325	−0.706623	−	0.707591i	$-0.749782\pi$
$941$	−3.83877e7	−1.41325	−0.706623	+	0.707591i	$0.749782\pi$
$942$	−1.45530e7	−0.534348
$943$	4.51669e7	1.65402
$944$	−4.37452e6	−0.159772
$945$	−715500.	−0.0260634
$946$	−1.63666e7	−0.594606
$947$	3.04907e6	0.110482	0.0552411	−	0.998473i	$-0.482407\pi$
$947$	3.04907e6	0.110482	0.0552411	+	0.998473i	$0.482407\pi$
$948$	−240059.	−0.00867554
$949$	−3.53647e7	−1.27469
$950$	−3.04613e7	−1.09506
$951$	−4.41019e6	−0.158127
$952$	4.22237e7	1.50995
$953$	−4.29474e7	−1.53181	−0.765905	−	0.642953i	$-0.777709\pi$
$953$	−4.29474e7	−1.53181	−0.765905	+	0.642953i	$0.777709\pi$
$954$	1.87137e7	0.665716
$955$	4.83017e6	0.171378
$956$	8.13361e6	0.287832
$957$	1.55247e7	0.547955
$958$	−3.95669e7	−1.39289
$959$	6.09301e6	0.213937
$960$	667030.	0.0233597
$961$	−1.05933e7	−0.370017
$962$	1.14905e7	0.400315
$963$	9.95215e6	0.345821
$964$	−8.61542e6	−0.298596
$965$	−3.20021e6	−0.110627
$966$	5.33623e7	1.83989
$967$	1.40341e7	0.482635	0.241317	−	0.970446i	$-0.422421\pi$
$967$	1.40341e7	0.482635	0.241317	+	0.970446i	$0.422421\pi$
$968$	−2.98792e7	−1.02490
$969$	−2.12826e7	−0.728141
$970$	4.22517e6	0.144183
$971$	−2.93266e6	−0.0998190	−0.0499095	−	0.998754i	$-0.515893\pi$
$971$	−2.93266e6	−0.0998190	−0.0499095	+	0.998754i	$0.515893\pi$
$972$	−659658.	−0.0223951
$973$	−5.71910e7	−1.93662
$974$	−4.74410e7	−1.60235
$975$	1.67861e7	0.565506
$976$	2.78027e7	0.934249
$977$	−2.04075e7	−0.683995	−0.341998	−	0.939701i	$-0.611104\pi$
$977$	−2.04075e7	−0.683995	−0.341998	+	0.939701i	$0.611104\pi$
$978$	−4.09125e6	−0.136776
$979$	3.32808e6	0.110978
$980$	−1.19526e6	−0.0397554
$981$	7.69816e6	0.255396
$982$	−1.77982e7	−0.588976
$983$	1.21439e7	0.400843	0.200421	−	0.979710i	$-0.435769\pi$
$983$	1.21439e7	0.400843	0.200421	+	0.979710i	$0.435769\pi$
$984$	1.20302e7	0.396082
$985$	1.73584e6	0.0570059
$986$	−2.90935e7	−0.953023
$987$	−5.26903e6	−0.172162
$988$	1.00536e7	0.327665
$989$	−1.87013e7	−0.607969
$990$	−1.64876e6	−0.0534649
$991$	−3.41316e7	−1.10401	−0.552005	−	0.833841i	$-0.686137\pi$
$991$	−3.41316e7	−1.10401	−0.552005	+	0.833841i	$0.686137\pi$
$992$	1.64681e7	0.531329
$993$	2.39521e7	0.770852
$994$	−1.05525e8	−3.38759
$995$	−884454.	−0.0283216
$996$	−2.52490e6	−0.0806483
$997$	−3.38907e7	−1.07980	−0.539899	−	0.841730i	$-0.681538\pi$
$997$	−3.38907e7	−1.07980	−0.539899	+	0.841730i	$0.681538\pi$
$998$	2.69816e7	0.857514
$999$	−2.11877e6	−0.0671690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.11	✓	13
3.2	odd	2		531.6.a.e.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.11	✓	13	1.1	even	1	trivial
531.6.a.e.1.3		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)

\(f(q)\)	\(=\)	\(q+6.57049 q^{2} -9.00000 q^{3} +11.1714 q^{4} -5.02964 q^{5} -59.1344 q^{6} -195.140 q^{7} -136.854 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.57049 q^{2} -9.00000 q^{3} +11.1714 q^{4} -5.02964 q^{5} -59.1344 q^{6} -195.140 q^{7} -136.854 q^{8} +81.0000 q^{9} -33.0472 q^{10} +615.938 q^{11} -100.542 q^{12} +601.708 q^{13} -1282.16 q^{14} +45.2668 q^{15} -1256.68 q^{16} +1581.07 q^{17} +532.210 q^{18} +1495.65 q^{19} -56.1880 q^{20} +1756.26 q^{21} +4047.01 q^{22} +4624.33 q^{23} +1231.69 q^{24} -3099.70 q^{25} +3953.52 q^{26} -729.000 q^{27} -2179.98 q^{28} -2800.56 q^{29} +297.425 q^{30} -4246.87 q^{31} -3877.70 q^{32} -5543.44 q^{33} +10388.4 q^{34} +981.482 q^{35} +904.881 q^{36} +2906.40 q^{37} +9827.15 q^{38} -5415.38 q^{39} +688.328 q^{40} +9767.23 q^{41} +11539.5 q^{42} -4044.11 q^{43} +6880.87 q^{44} -407.401 q^{45} +30384.2 q^{46} -3000.15 q^{47} +11310.2 q^{48} +21272.4 q^{49} -20366.6 q^{50} -14229.7 q^{51} +6721.91 q^{52} +35162.3 q^{53} -4789.89 q^{54} -3097.94 q^{55} +26705.7 q^{56} -13460.8 q^{57} -18401.1 q^{58} +3481.00 q^{59} +505.692 q^{60} -22123.9 q^{61} -27904.0 q^{62} -15806.3 q^{63} +14735.5 q^{64} -3026.38 q^{65} -36423.1 q^{66} +33278.2 q^{67} +17662.8 q^{68} -41619.0 q^{69} +6448.82 q^{70} +82302.6 q^{71} -11085.2 q^{72} -58773.8 q^{73} +19096.5 q^{74} +27897.3 q^{75} +16708.5 q^{76} -120194. q^{77} -35581.7 q^{78} +2387.64 q^{79} +6320.67 q^{80} +6561.00 q^{81} +64175.5 q^{82} +25112.8 q^{83} +19619.8 q^{84} -7952.24 q^{85} -26571.8 q^{86} +25205.1 q^{87} -84293.7 q^{88} +5403.27 q^{89} -2676.82 q^{90} -117417. q^{91} +51660.2 q^{92} +38221.8 q^{93} -19712.5 q^{94} -7522.58 q^{95} +34899.3 q^{96} -127853. q^{97} +139770. q^{98} +49890.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 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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