LMFDB - Embedded newform 177.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3879361069$
Analytic rank:	$0$
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			1.2
Root			$-9.47242$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.47242 q^{2} -9.00000 q^{3} +57.7268 q^{4} -42.5216 q^{5} +85.2518 q^{6} +243.042 q^{7} -243.695 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.47242 q^{2} -9.00000 q^{3} +57.7268 q^{4} -42.5216 q^{5} +85.2518 q^{6} +243.042 q^{7} -243.695 q^{8} +81.0000 q^{9} +402.782 q^{10} +382.698 q^{11} -519.541 q^{12} +434.802 q^{13} -2302.20 q^{14} +382.694 q^{15} +461.122 q^{16} +67.7470 q^{17} -767.266 q^{18} +2843.46 q^{19} -2454.63 q^{20} -2187.38 q^{21} -3625.08 q^{22} -1477.96 q^{23} +2193.25 q^{24} -1316.92 q^{25} -4118.63 q^{26} -729.000 q^{27} +14030.0 q^{28} -413.606 q^{29} -3625.04 q^{30} -7561.45 q^{31} +3430.29 q^{32} -3444.29 q^{33} -641.728 q^{34} -10334.5 q^{35} +4675.87 q^{36} +2856.10 q^{37} -26934.4 q^{38} -3913.22 q^{39} +10362.3 q^{40} +4308.73 q^{41} +20719.8 q^{42} +991.892 q^{43} +22091.9 q^{44} -3444.25 q^{45} +13999.9 q^{46} -6818.58 q^{47} -4150.10 q^{48} +42262.4 q^{49} +12474.4 q^{50} -609.723 q^{51} +25099.7 q^{52} +27976.7 q^{53} +6905.39 q^{54} -16272.9 q^{55} -59228.0 q^{56} -25591.1 q^{57} +3917.85 q^{58} +3481.00 q^{59} +22091.7 q^{60} +32959.1 q^{61} +71625.3 q^{62} +19686.4 q^{63} -47249.0 q^{64} -18488.5 q^{65} +32625.7 q^{66} -14427.0 q^{67} +3910.81 q^{68} +13301.7 q^{69} +97893.0 q^{70} +31564.2 q^{71} -19739.3 q^{72} +21278.4 q^{73} -27054.2 q^{74} +11852.2 q^{75} +164144. q^{76} +93011.8 q^{77} +37067.7 q^{78} -51036.5 q^{79} -19607.6 q^{80} +6561.00 q^{81} -40814.1 q^{82} -17809.1 q^{83} -126270. q^{84} -2880.71 q^{85} -9395.62 q^{86} +3722.46 q^{87} -93261.6 q^{88} -38824.8 q^{89} +32625.4 q^{90} +105675. q^{91} -85318.0 q^{92} +68053.1 q^{93} +64588.5 q^{94} -120908. q^{95} -30872.6 q^{96} -83290.5 q^{97} -400327. q^{98} +30998.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.47242	−1.67450	−0.837252	−	0.546818i	$-0.815839\pi$
$2$	−9.47242	−1.67450	−0.837252	+	0.546818i	$0.815839\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	57.7268	1.80396
$5$	−42.5216	−0.760649	−0.380324	−	0.924853i	$-0.624188\pi$
$5$	−42.5216	−0.760649	−0.380324	+	0.924853i	$0.624188\pi$
$6$	85.2518	0.966775
$7$	243.042	1.87472	0.937359	−	0.348364i	$-0.113263\pi$
$7$	243.042	1.87472	0.937359	+	0.348364i	$0.113263\pi$
$8$	−243.695	−1.34624
$9$	81.0000	0.333333
$10$	402.782	1.27371
$11$	382.698	0.953619	0.476810	−	0.879007i	$-0.341793\pi$
$11$	382.698	0.953619	0.476810	+	0.879007i	$0.341793\pi$
$12$	−519.541	−1.04152
$13$	434.802	0.713565	0.356782	−	0.934188i	$-0.383874\pi$
$13$	434.802	0.713565	0.356782	+	0.934188i	$0.383874\pi$
$14$	−2302.20	−3.13922
$15$	382.694	0.439161
$16$	461.122	0.450315
$17$	67.7470	0.0568549	0.0284274	−	0.999596i	$-0.490950\pi$
$17$	67.7470	0.0568549	0.0284274	+	0.999596i	$0.490950\pi$
$18$	−767.266	−0.558168
$19$	2843.46	1.80702	0.903509	−	0.428568i	$-0.140982\pi$
$19$	2843.46	1.80702	0.903509	+	0.428568i	$0.140982\pi$
$20$	−2454.63	−1.37218
$21$	−2187.38	−1.08237
$22$	−3625.08	−1.59684
$23$	−1477.96	−0.582564	−0.291282	−	0.956637i	$-0.594082\pi$
$23$	−1477.96	−0.582564	−0.291282	+	0.956637i	$0.594082\pi$
$24$	2193.25	0.777249
$25$	−1316.92	−0.421413
$26$	−4118.63	−1.19487
$27$	−729.000	−0.192450
$28$	14030.0	3.38192
$29$	−413.606	−0.0913255	−0.0456628	−	0.998957i	$-0.514540\pi$
$29$	−413.606	−0.0913255	−0.0456628	+	0.998957i	$0.514540\pi$
$30$	−3625.04	−0.735376
$31$	−7561.45	−1.41319	−0.706596	−	0.707617i	$-0.749770\pi$
$31$	−7561.45	−1.41319	−0.706596	+	0.707617i	$0.749770\pi$
$32$	3430.29	0.592182
$33$	−3444.29	−0.550572
$34$	−641.728	−0.0952037
$35$	−10334.5	−1.42600
$36$	4675.87	0.601320
$37$	2856.10	0.342980	0.171490	−	0.985186i	$-0.445142\pi$
$37$	2856.10	0.342980	0.171490	+	0.985186i	$0.445142\pi$
$38$	−26934.4	−3.02586
$39$	−3913.22	−0.411977
$40$	10362.3	1.02401
$41$	4308.73	0.400304	0.200152	−	0.979765i	$-0.435856\pi$
$41$	4308.73	0.400304	0.200152	+	0.979765i	$0.435856\pi$
$42$	20719.8	1.81243
$43$	991.892	0.0818075	0.0409038	−	0.999163i	$-0.486976\pi$
$43$	991.892	0.0818075	0.0409038	+	0.999163i	$0.486976\pi$
$44$	22091.9	1.72029
$45$	−3444.25	−0.253550
$46$	13999.9	0.975506
$47$	−6818.58	−0.450246	−0.225123	−	0.974330i	$-0.572278\pi$
$47$	−6818.58	−0.450246	−0.225123	+	0.974330i	$0.572278\pi$
$48$	−4150.10	−0.259989
$49$	42262.4	2.51457
$50$	12474.4	0.705658
$51$	−609.723	−0.0328252
$52$	25099.7	1.28724
$53$	27976.7	1.36806	0.684032	−	0.729452i	$-0.260225\pi$
$53$	27976.7	1.36806	0.684032	+	0.729452i	$0.260225\pi$
$54$	6905.39	0.322258
$55$	−16272.9	−0.725370
$56$	−59228.0	−2.52381
$57$	−25591.1	−1.04328
$58$	3917.85	0.152925
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	22091.7	0.792229
$61$	32959.1	1.13410	0.567049	−	0.823684i	$-0.308085\pi$
$61$	32959.1	1.13410	0.567049	+	0.823684i	$0.308085\pi$
$62$	71625.3	2.36639
$63$	19686.4	0.624906
$64$	−47249.0	−1.44193
$65$	−18488.5	−0.542772
$66$	32625.7	0.921935
$67$	−14427.0	−0.392636	−0.196318	−	0.980540i	$-0.562899\pi$
$67$	−14427.0	−0.392636	−0.196318	+	0.980540i	$0.562899\pi$
$68$	3910.81	0.102564
$69$	13301.7	0.336344
$70$	97893.0	2.38785
$71$	31564.2	0.743102	0.371551	−	0.928412i	$-0.378826\pi$
$71$	31564.2	0.743102	0.371551	+	0.928412i	$0.378826\pi$
$72$	−19739.3	−0.448745
$73$	21278.4	0.467339	0.233670	−	0.972316i	$-0.424927\pi$
$73$	21278.4	0.467339	0.233670	+	0.972316i	$0.424927\pi$
$74$	−27054.2	−0.574321
$75$	11852.2	0.243303
$76$	164144.	3.25979
$77$	93011.8	1.78777
$78$	37067.7	0.689856
$79$	−51036.5	−0.920054	−0.460027	−	0.887905i	$-0.652160\pi$
$79$	−51036.5	−0.920054	−0.460027	+	0.887905i	$0.652160\pi$
$80$	−19607.6	−0.342531
$81$	6561.00	0.111111
$82$	−40814.1	−0.670310
$83$	−17809.1	−0.283757	−0.141879	−	0.989884i	$-0.545314\pi$
$83$	−17809.1	−0.283757	−0.141879	+	0.989884i	$0.545314\pi$
$84$	−126270.	−1.95255
$85$	−2880.71	−0.0432466
$86$	−9395.62	−0.136987
$87$	3722.46	0.0527268
$88$	−93261.6	−1.28380
$89$	−38824.8	−0.519559	−0.259779	−	0.965668i	$-0.583650\pi$
$89$	−38824.8	−0.519559	−0.259779	+	0.965668i	$0.583650\pi$
$90$	32625.4	0.424570
$91$	105675.	1.33773
$92$	−85318.0	−1.05092
$93$	68053.1	0.815907
$94$	64588.5	0.753938
$95$	−120908.	−1.37451
$96$	−30872.6	−0.341897
$97$	−83290.5	−0.898806	−0.449403	−	0.893329i	$-0.648363\pi$
$97$	−83290.5	−0.898806	−0.449403	+	0.893329i	$0.648363\pi$
$98$	−400327.	−4.21066
$99$	30998.6	0.317873
$100$	−76021.3	−0.760213
$101$	−151049.	−1.47338	−0.736689	−	0.676232i	$-0.763612\pi$
$101$	−151049.	−1.47338	−0.736689	+	0.676232i	$0.763612\pi$
$102$	5775.55	0.0549659
$103$	183578.	1.70501	0.852506	−	0.522718i	$-0.175082\pi$
$103$	183578.	1.70501	0.852506	+	0.522718i	$0.175082\pi$
$104$	−105959.	−0.960626
$105$	93010.7	0.823303
$106$	−265007.	−2.29083
$107$	−158219.	−1.33597	−0.667987	−	0.744173i	$-0.732844\pi$
$107$	−158219.	−1.33597	−0.667987	+	0.744173i	$0.732844\pi$
$108$	−42082.8	−0.347172
$109$	−133410.	−1.07553	−0.537766	−	0.843094i	$-0.680732\pi$
$109$	−133410.	−1.07553	−0.537766	+	0.843094i	$0.680732\pi$
$110$	154144.	1.21463
$111$	−25704.9	−0.198020
$112$	112072.	0.844213
$113$	247000.	1.81971	0.909854	−	0.414930i	$-0.136194\pi$
$113$	247000.	1.81971	0.909854	+	0.414930i	$0.136194\pi$
$114$	242410.	1.74698
$115$	62845.3	0.443127
$116$	−23876.1	−0.164748
$117$	35219.0	0.237855
$118$	−32973.5	−0.218002
$119$	16465.4	0.106587
$120$	−93260.5	−0.591214
$121$	−14592.9	−0.0906103
$122$	−312202.	−1.89905
$123$	−38778.6	−0.231115
$124$	−436498.	−2.54934
$125$	188877.	1.08120
$126$	−186478.	−1.04641
$127$	295605.	1.62631	0.813155	−	0.582048i	$-0.197748\pi$
$127$	295605.	1.62631	0.813155	+	0.582048i	$0.197748\pi$
$128$	337793.	1.82233
$129$	−8927.03	−0.0472316
$130$	175131.	0.908874
$131$	27171.8	0.138338	0.0691689	−	0.997605i	$-0.477965\pi$
$131$	27171.8	0.138338	0.0691689	+	0.997605i	$0.477965\pi$
$132$	−198827.	−0.993211
$133$	691079.	3.38765
$134$	136659.	0.657470
$135$	30998.2	0.146387
$136$	−16509.6	−0.0765401
$137$	153128.	0.697035	0.348517	−	0.937302i	$-0.386685\pi$
$137$	153128.	0.697035	0.348517	+	0.937302i	$0.386685\pi$
$138$	−125999.	−0.563209
$139$	−152753.	−0.670585	−0.335292	−	0.942114i	$-0.608835\pi$
$139$	−152753.	−0.670585	−0.335292	+	0.942114i	$0.608835\pi$
$140$	−596579.	−2.57245
$141$	61367.2	0.259949
$142$	−298989.	−1.24433
$143$	166398.	0.680469
$144$	37350.9	0.150105
$145$	17587.2	0.0694667
$146$	−201558.	−0.782561
$147$	−380361.	−1.45179
$148$	164873.	0.618722
$149$	−209034.	−0.771349	−0.385675	−	0.922635i	$-0.626031\pi$
$149$	−209034.	−0.771349	−0.385675	+	0.922635i	$0.626031\pi$
$150$	−112269.	−0.407412
$151$	468814.	1.67324	0.836620	−	0.547783i	$-0.184528\pi$
$151$	468814.	1.67324	0.836620	+	0.547783i	$0.184528\pi$
$152$	−692935.	−2.43267
$153$	5487.51	0.0189516
$154$	−881047.	−2.99362
$155$	321525.	1.07494
$156$	−225897.	−0.743190
$157$	145781.	0.472012	0.236006	−	0.971752i	$-0.424162\pi$
$157$	145781.	0.472012	0.236006	+	0.971752i	$0.424162\pi$
$158$	483439.	1.54063
$159$	−251790.	−0.789852
$160$	−145861.	−0.450443
$161$	−359207.	−1.09214
$162$	−62148.6	−0.186056
$163$	−361526.	−1.06579	−0.532894	−	0.846182i	$-0.678895\pi$
$163$	−361526.	−1.06579	−0.532894	+	0.846182i	$0.678895\pi$
$164$	248729.	0.722132
$165$	146456.	0.418792
$166$	168695.	0.475153
$167$	−405904.	−1.12624	−0.563122	−	0.826374i	$-0.690400\pi$
$167$	−405904.	−1.12624	−0.563122	+	0.826374i	$0.690400\pi$
$168$	533052.	1.45712
$169$	−182240.	−0.490826
$170$	27287.3	0.0724166
$171$	230320.	0.602340
$172$	57258.7	0.147578
$173$	184103.	0.467677	0.233839	−	0.972275i	$-0.424871\pi$
$173$	184103.	0.467677	0.233839	+	0.972275i	$0.424871\pi$
$174$	−35260.7	−0.0882912
$175$	−320066.	−0.790031
$176$	176471.	0.429429
$177$	−31329.0	−0.0751646
$178$	367765.	0.870003
$179$	636770.	1.48542	0.742711	−	0.669612i	$-0.233540\pi$
$179$	636770.	1.48542	0.742711	+	0.669612i	$0.233540\pi$
$180$	−198825.	−0.457394
$181$	543803.	1.23380	0.616901	−	0.787041i	$-0.288388\pi$
$181$	543803.	1.23380	0.616901	+	0.787041i	$0.288388\pi$
$182$	−1.00100e6	−2.24004
$183$	−296632.	−0.654771
$184$	360172.	0.784269
$185$	−121446.	−0.260887
$186$	−644627.	−1.36624
$187$	25926.7	0.0542179
$188$	−393615.	−0.812226
$189$	−177178.	−0.360790
$190$	1.14529e6	2.30162
$191$	−379624.	−0.752958	−0.376479	−	0.926425i	$-0.622865\pi$
$191$	−379624.	−0.752958	−0.376479	+	0.926425i	$0.622865\pi$
$192$	425241.	0.832496
$193$	388085.	0.749951	0.374976	−	0.927035i	$-0.377651\pi$
$193$	388085.	0.749951	0.374976	+	0.927035i	$0.377651\pi$
$194$	788962.	1.50505
$195$	166396.	0.313370
$196$	2.43967e6	4.53619
$197$	985373.	1.80899	0.904493	−	0.426489i	$-0.140250\pi$
$197$	985373.	1.80899	0.904493	+	0.426489i	$0.140250\pi$
$198$	−293632.	−0.532280
$199$	345186.	0.617903	0.308952	−	0.951078i	$-0.400022\pi$
$199$	345186.	0.617903	0.308952	+	0.951078i	$0.400022\pi$
$200$	320925.	0.567321
$201$	129843.	0.226689
$202$	1.43080e6	2.46717
$203$	−100524.	−0.171210
$204$	−35197.3	−0.0592153
$205$	−183214.	−0.304491
$206$	−1.73893e6	−2.85505
$207$	−119715.	−0.194188
$208$	200497.	0.321328
$209$	1.08819e6	1.72321
$210$	−881037.	−1.37862
$211$	−873858.	−1.35125	−0.675624	−	0.737247i	$-0.736125\pi$
$211$	−873858.	−1.35125	−0.675624	+	0.737247i	$0.736125\pi$
$212$	1.61500e6	2.46793
$213$	−284078.	−0.429030
$214$	1.49871e6	2.23709
$215$	−42176.8	−0.0622268
$216$	177653.	0.259083
$217$	−1.83775e6	−2.64934
$218$	1.26372e6	1.80098
$219$	−191506.	−0.269818
$220$	−939384.	−1.30854
$221$	29456.5	0.0405696
$222$	243487.	0.331584
$223$	−1.00517e6	−1.35356	−0.676778	−	0.736187i	$-0.736624\pi$
$223$	−1.00517e6	−1.35356	−0.676778	+	0.736187i	$0.736624\pi$
$224$	833703.	1.11018
$225$	−106670.	−0.140471
$226$	−2.33969e6	−3.04711
$227$	1.20719e6	1.55493	0.777467	−	0.628924i	$-0.216504\pi$
$227$	1.20719e6	1.55493	0.777467	+	0.628924i	$0.216504\pi$
$228$	−1.47729e6	−1.88204
$229$	−924824.	−1.16539	−0.582694	−	0.812692i	$-0.698001\pi$
$229$	−924824.	−1.16539	−0.582694	+	0.812692i	$0.698001\pi$
$230$	−595297.	−0.742018
$231$	−837106.	−1.03217
$232$	100794.	0.122946
$233$	750812.	0.906027	0.453014	−	0.891504i	$-0.350349\pi$
$233$	750812.	0.906027	0.453014	+	0.891504i	$0.350349\pi$
$234$	−333609.	−0.398289
$235$	289937.	0.342479
$236$	200947.	0.234856
$237$	459329.	0.531194
$238$	−155967.	−0.178480
$239$	1.55346e6	1.75916	0.879580	−	0.475752i	$-0.157824\pi$
$239$	1.55346e6	1.75916	0.879580	+	0.475752i	$0.157824\pi$
$240$	176469.	0.197761
$241$	571502.	0.633833	0.316917	−	0.948453i	$-0.397352\pi$
$241$	571502.	0.633833	0.316917	+	0.948453i	$0.397352\pi$
$242$	138230.	0.151727
$243$	−59049.0	−0.0641500
$244$	1.90262e6	2.04587
$245$	−1.79706e6	−1.91271
$246$	367327.	0.387004
$247$	1.23634e6	1.28942
$248$	1.84269e6	1.90249
$249$	160282.	0.163827
$250$	−1.78912e6	−1.81047
$251$	710664.	0.712000	0.356000	−	0.934486i	$-0.384140\pi$
$251$	710664.	0.712000	0.356000	+	0.934486i	$0.384140\pi$
$252$	1.13643e6	1.12731
$253$	−565614.	−0.555545
$254$	−2.80010e6	−2.72326
$255$	25926.4	0.0249684
$256$	−1.68775e6	−1.60957
$257$	1.30557e6	1.23301	0.616504	−	0.787352i	$-0.288548\pi$
$257$	1.30557e6	1.23301	0.616504	+	0.787352i	$0.288548\pi$
$258$	84560.6	0.0790895
$259$	694152.	0.642991
$260$	−1.06728e6	−0.979140
$261$	−33502.1	−0.0304418
$262$	−257383.	−0.231647
$263$	1.90024e6	1.69402	0.847012	−	0.531574i	$-0.178399\pi$
$263$	1.90024e6	1.69402	0.847012	+	0.531574i	$0.178399\pi$
$264$	839354.	0.741200
$265$	−1.18961e6	−1.04062
$266$	−6.54619e6	−5.67263
$267$	349423.	0.299967
$268$	−832826.	−0.708300
$269$	−1.46393e6	−1.23350	−0.616749	−	0.787160i	$-0.711551\pi$
$269$	−1.46393e6	−1.23350	−0.616749	+	0.787160i	$0.711551\pi$
$270$	−293628.	−0.245125
$271$	107612.	0.0890095	0.0445048	−	0.999009i	$-0.485829\pi$
$271$	107612.	0.0890095	0.0445048	+	0.999009i	$0.485829\pi$
$272$	31239.6	0.0256026
$273$	−951076.	−0.772340
$274$	−1.45050e6	−1.16719
$275$	−503982.	−0.401868
$276$	767862.	0.606751
$277$	−471552.	−0.369258	−0.184629	−	0.982808i	$-0.559108\pi$
$277$	−471552.	−0.369258	−0.184629	+	0.982808i	$0.559108\pi$
$278$	1.44694e6	1.12290
$279$	−612478.	−0.471064
$280$	2.51847e6	1.91974
$281$	−1.46229e6	−1.10476	−0.552380	−	0.833592i	$-0.686280\pi$
$281$	−1.46229e6	−1.10476	−0.552380	+	0.833592i	$0.686280\pi$
$282$	−581296.	−0.435286
$283$	−270851.	−0.201031	−0.100516	−	0.994935i	$-0.532049\pi$
$283$	−270851.	−0.201031	−0.100516	+	0.994935i	$0.532049\pi$
$284$	1.82210e6	1.34053
$285$	1.08817e6	0.793572
$286$	−1.57619e6	−1.13945
$287$	1.04720e6	0.750457
$288$	277853.	0.197394
$289$	−1.41527e6	−0.996768
$290$	−166593.	−0.116322
$291$	749614.	0.518926
$292$	1.22833e6	0.843061
$293$	−127463.	−0.0867391	−0.0433695	−	0.999059i	$-0.513809\pi$
$293$	−127463.	−0.0867391	−0.0433695	+	0.999059i	$0.513809\pi$
$294$	3.60294e6	2.43102
$295$	−148018.	−0.0990281
$296$	−696016.	−0.461732
$297$	−278987.	−0.183524
$298$	1.98006e6	1.29163
$299$	−642621.	−0.415697
$300$	684192.	0.438909
$301$	241071.	0.153366
$302$	−4.44080e6	−2.80185
$303$	1.35944e6	0.850655
$304$	1.31118e6	0.813727
$305$	−1.40147e6	−0.862650
$306$	−51980.0	−0.0317346
$307$	1.10268e6	0.667736	0.333868	−	0.942620i	$-0.391646\pi$
$307$	1.10268e6	0.667736	0.333868	+	0.942620i	$0.391646\pi$
$308$	5.36927e6	3.22506
$309$	−1.65220e6	−0.984389
$310$	−3.04562e6	−1.80000
$311$	−256033.	−0.150105	−0.0750525	−	0.997180i	$-0.523912\pi$
$311$	−256033.	−0.150105	−0.0750525	+	0.997180i	$0.523912\pi$
$312$	953631.	0.554618
$313$	1.51228e6	0.872510	0.436255	−	0.899823i	$-0.356305\pi$
$313$	1.51228e6	0.872510	0.436255	+	0.899823i	$0.356305\pi$
$314$	−1.38090e6	−0.790385
$315$	−837097.	−0.475334
$316$	−2.94617e6	−1.65974
$317$	2.98841e6	1.67029	0.835146	−	0.550028i	$-0.185383\pi$
$317$	2.98841e6	1.67029	0.835146	+	0.550028i	$0.185383\pi$
$318$	2.38506e6	1.32261
$319$	−158286.	−0.0870898
$320$	2.00910e6	1.09680
$321$	1.42397e6	0.771325
$322$	3.40256e6	1.82880
$323$	192636.	0.102738
$324$	378745.	0.200440
$325$	−572598.	−0.300705
$326$	3.42453e6	1.78466
$327$	1.20069e6	0.620959
$328$	−1.05001e6	−0.538903
$329$	−1.65720e6	−0.844084
$330$	−1.38730e6	−0.701269
$331$	−2.69754e6	−1.35331	−0.676655	−	0.736300i	$-0.736571\pi$
$331$	−2.69754e6	−1.35331	−0.676655	+	0.736300i	$0.736571\pi$
$332$	−1.02806e6	−0.511887
$333$	231344.	0.114327
$334$	3.84489e6	1.88590
$335$	613460.	0.298658
$336$	−1.00865e6	−0.487407
$337$	1.34712e6	0.646149	0.323075	−	0.946373i	$-0.395283\pi$
$337$	1.34712e6	0.646149	0.323075	+	0.946373i	$0.395283\pi$
$338$	1.72626e6	0.821889
$339$	−2.22300e6	−1.05061
$340$	−166294.	−0.0780152
$341$	−2.89376e6	−1.34765
$342$	−2.18169e6	−1.00862
$343$	6.18673e6	2.83939
$344$	−241719.	−0.110132
$345$	−565608.	−0.255840
$346$	−1.74390e6	−0.783127
$347$	−858085.	−0.382566	−0.191283	−	0.981535i	$-0.561265\pi$
$347$	−858085.	−0.382566	−0.191283	+	0.981535i	$0.561265\pi$
$348$	214885.	0.0951171
$349$	−2.15268e6	−0.946054	−0.473027	−	0.881048i	$-0.656839\pi$
$349$	−2.15268e6	−0.946054	−0.473027	+	0.881048i	$0.656839\pi$
$350$	3.03180e6	1.32291
$351$	−316971.	−0.137326
$352$	1.31277e6	0.564716
$353$	−3.43309e6	−1.46639	−0.733194	−	0.680020i	$-0.761971\pi$
$353$	−3.43309e6	−1.46639	−0.733194	+	0.680020i	$0.761971\pi$
$354$	296761.	0.125863
$355$	−1.34216e6	−0.565240
$356$	−2.24123e6	−0.937264
$357$	−148188.	−0.0615380
$358$	−6.03175e6	−2.48734
$359$	−2.78940e6	−1.14229	−0.571144	−	0.820850i	$-0.693500\pi$
$359$	−2.78940e6	−1.14229	−0.571144	+	0.820850i	$0.693500\pi$
$360$	839345.	0.341338
$361$	5.60915e6	2.26532
$362$	−5.15113e6	−2.06600
$363$	131336.	0.0523139
$364$	6.10028e6	2.41322
$365$	−904791.	−0.355481
$366$	2.80982e6	1.09642
$367$	843940.	0.327074	0.163537	−	0.986537i	$-0.447710\pi$
$367$	843940.	0.327074	0.163537	+	0.986537i	$0.447710\pi$
$368$	−681521.	−0.262337
$369$	349007.	0.133435
$370$	1.15039e6	0.436857
$371$	6.79951e6	2.56474
$372$	3.92848e6	1.47186
$373$	−4.21025e6	−1.56688	−0.783440	−	0.621467i	$-0.786537\pi$
$373$	−4.21025e6	−1.56688	−0.783440	+	0.621467i	$0.786537\pi$
$374$	−245588.	−0.0907881
$375$	−1.69990e6	−0.624229
$376$	1.66165e6	0.606137
$377$	−179837.	−0.0651666
$378$	1.67830e6	0.604144
$379$	3.19942e6	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$379$	3.19942e6	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$380$	−6.97964e6	−2.47956
$381$	−2.66045e6	−0.938950
$382$	3.59596e6	1.26083
$383$	−391078.	−0.136228	−0.0681140	−	0.997678i	$-0.521698\pi$
$383$	−391078.	−0.136228	−0.0681140	+	0.997678i	$0.521698\pi$
$384$	−3.04014e6	−1.05212
$385$	−3.95501e6	−1.35986
$386$	−3.67610e6	−1.25580
$387$	80343.3	0.0272692
$388$	−4.80809e6	−1.62141
$389$	3.96468e6	1.32841	0.664207	−	0.747548i	$-0.268769\pi$
$389$	3.96468e6	1.32841	0.664207	+	0.747548i	$0.268769\pi$
$390$	−1.57617e6	−0.524738
$391$	−100128.	−0.0331216
$392$	−1.02991e7	−3.38520
$393$	−244546.	−0.0798693
$394$	−9.33387e6	−3.02915
$395$	2.17015e6	0.699838
$396$	1.78945e6	0.573431
$397$	−4.83817e6	−1.54065	−0.770327	−	0.637649i	$-0.779907\pi$
$397$	−4.83817e6	−1.54065	−0.770327	+	0.637649i	$0.779907\pi$
$398$	−3.26975e6	−1.03468
$399$	−6.21971e6	−1.95586
$400$	−607259.	−0.189768
$401$	939464.	0.291755	0.145878	−	0.989303i	$-0.453399\pi$
$401$	939464.	0.291755	0.145878	+	0.989303i	$0.453399\pi$
$402$	−1.22993e6	−0.379591
$403$	−3.28774e6	−1.00840
$404$	−8.71956e6	−2.65791
$405$	−278984.	−0.0845166
$406$	952202.	0.286691
$407$	1.09302e6	0.327072
$408$	148586.	0.0441904
$409$	1.92053e6	0.567691	0.283846	−	0.958870i	$-0.408390\pi$
$409$	1.92053e6	0.567691	0.283846	+	0.958870i	$0.408390\pi$
$410$	1.73548e6	0.509871
$411$	−1.37816e6	−0.402433
$412$	1.05974e7	3.07577
$413$	846029.	0.244068
$414$	1.13399e6	0.325169
$415$	757272.	0.215840
$416$	1.49150e6	0.422560
$417$	1.37478e6	0.387162
$418$	−1.03078e7	−2.88552
$419$	−683307.	−0.190143	−0.0950716	−	0.995470i	$-0.530308\pi$
$419$	−683307.	−0.190143	−0.0950716	+	0.995470i	$0.530308\pi$
$420$	5.36921e6	1.48521
$421$	−645392.	−0.177467	−0.0887336	−	0.996055i	$-0.528282\pi$
$421$	−645392.	−0.177467	−0.0887336	+	0.996055i	$0.528282\pi$
$422$	8.27755e6	2.26267
$423$	−552305.	−0.150082
$424$	−6.81777e6	−1.84174
$425$	−89217.1	−0.0239594
$426$	2.69090e6	0.718413
$427$	8.01044e6	2.12611
$428$	−9.13345e6	−2.41005
$429$	−1.49758e6	−0.392869
$430$	399516.	0.104199
$431$	4.43313e6	1.14952	0.574761	−	0.818322i	$-0.305095\pi$
$431$	4.43313e6	1.14952	0.574761	+	0.818322i	$0.305095\pi$
$432$	−336158.	−0.0866631
$433$	7.41745e6	1.90123	0.950616	−	0.310371i	$-0.100453\pi$
$433$	7.41745e6	1.90123	0.950616	+	0.310371i	$0.100453\pi$
$434$	1.74079e7	4.43632
$435$	−158285.	−0.0401066
$436$	−7.70135e6	−1.94022
$437$	−4.20252e6	−1.05271
$438$	1.81402e6	0.451812
$439$	−1.71298e6	−0.424219	−0.212110	−	0.977246i	$-0.568033\pi$
$439$	−1.71298e6	−0.424219	−0.212110	+	0.977246i	$0.568033\pi$
$440$	3.96563e6	0.976518
$441$	3.42325e6	0.838190
$442$	−279025.	−0.0679340
$443$	−5.52257e6	−1.33700	−0.668501	−	0.743712i	$-0.733064\pi$
$443$	−5.52257e6	−1.33700	−0.668501	+	0.743712i	$0.733064\pi$
$444$	−1.48386e6	−0.357220
$445$	1.65089e6	0.395202
$446$	9.52137e6	2.26653
$447$	1.88131e6	0.445339
$448$	−1.14835e7	−2.70321
$449$	3.46045e6	0.810059	0.405030	−	0.914304i	$-0.367261\pi$
$449$	3.46045e6	0.810059	0.405030	+	0.914304i	$0.367261\pi$
$450$	1.01043e6	0.235219
$451$	1.64894e6	0.381737
$452$	1.42585e7	3.28268
$453$	−4.21933e6	−0.966046
$454$	−1.14350e7	−2.60374
$455$	−4.49347e6	−1.01755
$456$	6.23642e6	1.40450
$457$	−892817.	−0.199973	−0.0999866	−	0.994989i	$-0.531880\pi$
$457$	−892817.	−0.199973	−0.0999866	+	0.994989i	$0.531880\pi$
$458$	8.76032e6	1.95145
$459$	−49387.6	−0.0109417
$460$	3.62786e6	0.799384
$461$	−2.39311e6	−0.524458	−0.262229	−	0.965006i	$-0.584458\pi$
$461$	−2.39311e6	−0.524458	−0.262229	+	0.965006i	$0.584458\pi$
$462$	7.92942e6	1.72837
$463$	8.67234e6	1.88011	0.940057	−	0.341018i	$-0.110772\pi$
$463$	8.67234e6	1.88011	0.940057	+	0.341018i	$0.110772\pi$
$464$	−190723.	−0.0411252
$465$	−2.89372e6	−0.620618
$466$	−7.11201e6	−1.51715
$467$	7.47827e6	1.58675	0.793376	−	0.608732i	$-0.208321\pi$
$467$	7.47827e6	1.58675	0.793376	+	0.608732i	$0.208321\pi$
$468$	2.03308e6	0.429081
$469$	−3.50638e6	−0.736082
$470$	−2.74640e6	−0.573482
$471$	−1.31203e6	−0.272516
$472$	−848301.	−0.175265
$473$	379596.	0.0780132
$474$	−4.35096e6	−0.889485
$475$	−3.74459e6	−0.761502
$476$	950492.	0.192279
$477$	2.26611e6	0.456021
$478$	−1.47150e7	−2.94572
$479$	1.51970e6	0.302636	0.151318	−	0.988485i	$-0.451648\pi$
$479$	1.51970e6	0.302636	0.151318	+	0.988485i	$0.451648\pi$
$480$	1.31275e6	0.260063
$481$	1.24184e6	0.244738
$482$	−5.41351e6	−1.06136
$483$	3.23286e6	0.630550
$484$	−842400.	−0.163457
$485$	3.54164e6	0.683676
$486$	559337.	0.107419
$487$	−2.51702e6	−0.480910	−0.240455	−	0.970660i	$-0.577297\pi$
$487$	−2.51702e6	−0.480910	−0.240455	+	0.970660i	$0.577297\pi$
$488$	−8.03195e6	−1.52676
$489$	3.25374e6	0.615333
$490$	1.70225e7	3.20283
$491$	−5.68351e6	−1.06393	−0.531965	−	0.846767i	$-0.678546\pi$
$491$	−5.68351e6	−1.06393	−0.531965	+	0.846767i	$0.678546\pi$
$492$	−2.23856e6	−0.416923
$493$	−28020.6	−0.00519230
$494$	−1.17111e7	−2.15915
$495$	−1.31811e6	−0.241790
$496$	−3.48675e6	−0.636381
$497$	7.67142e6	1.39311
$498$	−1.51826e6	−0.274330
$499$	−2.41309e6	−0.433833	−0.216916	−	0.976190i	$-0.569600\pi$
$499$	−2.41309e6	−0.433833	−0.216916	+	0.976190i	$0.569600\pi$
$500$	1.09033e7	1.95044
$501$	3.65314e6	0.650237
$502$	−6.73171e6	−1.19225
$503$	5.40338e6	0.952237	0.476119	−	0.879381i	$-0.342043\pi$
$503$	5.40338e6	0.952237	0.476119	+	0.879381i	$0.342043\pi$
$504$	−4.79747e6	−0.841271
$505$	6.42283e6	1.12072
$506$	5.35774e6	0.930261
$507$	1.64016e6	0.283378
$508$	1.70643e7	2.93380
$509$	−4.13477e6	−0.707386	−0.353693	−	0.935362i	$-0.615074\pi$
$509$	−4.13477e6	−0.707386	−0.353693	+	0.935362i	$0.615074\pi$
$510$	−245586.	−0.0418097
$511$	5.17155e6	0.876129
$512$	5.17772e6	0.872898
$513$	−2.07288e6	−0.347761
$514$	−1.23669e7	−2.06468
$515$	−7.80602e6	−1.29692
$516$	−515328.	−0.0852040
$517$	−2.60946e6	−0.429363
$518$	−6.57530e6	−1.07669
$519$	−1.65693e6	−0.270014
$520$	4.50554e6	0.730699
$521$	3.96698e6	0.640273	0.320137	−	0.947371i	$-0.396271\pi$
$521$	3.96698e6	0.640273	0.320137	+	0.947371i	$0.396271\pi$
$522$	317346.	0.0509750
$523$	8.11326e6	1.29700	0.648502	−	0.761213i	$-0.275396\pi$
$523$	8.11326e6	1.29700	0.648502	+	0.761213i	$0.275396\pi$
$524$	1.56854e6	0.249556
$525$	2.88059e6	0.456125
$526$	−1.79999e7	−2.83665
$527$	−512266.	−0.0803468
$528$	−1.58824e6	−0.247931
$529$	−4.25197e6	−0.660619
$530$	1.12685e7	1.74252
$531$	281961.	0.0433963
$532$	3.98938e7	6.11119
$533$	1.87345e6	0.285643
$534$	−3.30989e6	−0.502296
$535$	6.72771e6	1.01621
$536$	3.51579e6	0.528581
$537$	−5.73093e6	−0.857609
$538$	1.38669e7	2.06550
$539$	1.61738e7	2.39794
$540$	1.78943e6	0.264076
$541$	−7.71908e6	−1.13389	−0.566947	−	0.823754i	$-0.691876\pi$
$541$	−7.71908e6	−1.13389	−0.566947	+	0.823754i	$0.691876\pi$
$542$	−1.01934e6	−0.149047
$543$	−4.89423e6	−0.712336
$544$	232392.	0.0336685
$545$	5.67282e6	0.818102
$546$	9.00899e6	1.29329
$547$	−147862.	−0.0211295	−0.0105647	−	0.999944i	$-0.503363\pi$
$547$	−147862.	−0.0211295	−0.0105647	+	0.999944i	$0.503363\pi$
$548$	8.83961e6	1.25742
$549$	2.66968e6	0.378032
$550$	4.77393e6	0.672929
$551$	−1.17607e6	−0.165027
$552$	−3.24155e6	−0.452798
$553$	−1.24040e7	−1.72484
$554$	4.46674e6	0.618324
$555$	1.09301e6	0.150623
$556$	−8.81796e6	−1.20971
$557$	−8.43178e6	−1.15155	−0.575773	−	0.817610i	$-0.695299\pi$
$557$	−8.43178e6	−1.15155	−0.575773	+	0.817610i	$0.695299\pi$
$558$	5.80165e6	0.788798
$559$	431277.	0.0583749
$560$	−4.76548e6	−0.642150
$561$	−233340.	−0.0313027
$562$	1.38514e7	1.84992
$563$	−1.36993e7	−1.82149	−0.910746	−	0.412966i	$-0.864493\pi$
$563$	−1.36993e7	−1.82149	−0.910746	+	0.412966i	$0.864493\pi$
$564$	3.54253e6	0.468939
$565$	−1.05028e7	−1.38416
$566$	2.56561e6	0.336628
$567$	1.59460e6	0.208302
$568$	−7.69202e6	−1.00039
$569$	3.13483e6	0.405913	0.202957	−	0.979188i	$-0.434945\pi$
$569$	3.13483e6	0.405913	0.202957	+	0.979188i	$0.434945\pi$
$570$	−1.03076e7	−1.32884
$571$	−4.13353e6	−0.530556	−0.265278	−	0.964172i	$-0.585464\pi$
$571$	−4.13353e6	−0.530556	−0.265278	+	0.964172i	$0.585464\pi$
$572$	9.60562e6	1.22754
$573$	3.41662e6	0.434720
$574$	−9.91954e6	−1.25664
$575$	1.94635e6	0.245500
$576$	−3.82717e6	−0.480642
$577$	1.21527e7	1.51961	0.759807	−	0.650149i	$-0.225293\pi$
$577$	1.21527e7	1.51961	0.759807	+	0.650149i	$0.225293\pi$
$578$	1.34060e7	1.66909
$579$	−3.49276e6	−0.432985
$580$	1.01525e6	0.125315
$581$	−4.32836e6	−0.531965
$582$	−7.10066e6	−0.868943
$583$	1.07066e7	1.30461
$584$	−5.18544e6	−0.629148
$585$	−1.49757e6	−0.180924
$586$	1.20738e6	0.145245
$587$	−2.01425e6	−0.241278	−0.120639	−	0.992696i	$-0.538494\pi$
$587$	−2.01425e6	−0.241278	−0.120639	+	0.992696i	$0.538494\pi$
$588$	−2.19570e7	−2.61897
$589$	−2.15007e7	−2.55366
$590$	1.40208e6	0.165823
$591$	−8.86836e6	−1.04442
$592$	1.31701e6	0.154449
$593$	−9.67469e6	−1.12980	−0.564899	−	0.825160i	$-0.691085\pi$
$593$	−9.67469e6	−1.12980	−0.564899	+	0.825160i	$0.691085\pi$
$594$	2.64268e6	0.307312
$595$	−700133.	−0.0810752
$596$	−1.20669e7	−1.39148
$597$	−3.10667e6	−0.356747
$598$	6.08718e6	0.696087
$599$	−3.89300e6	−0.443320	−0.221660	−	0.975124i	$-0.571148\pi$
$599$	−3.89300e6	−0.443320	−0.221660	+	0.975124i	$0.571148\pi$
$600$	−2.88833e6	−0.327543
$601$	−1.38351e6	−0.156241	−0.0781204	−	0.996944i	$-0.524892\pi$
$601$	−1.38351e6	−0.156241	−0.0781204	+	0.996944i	$0.524892\pi$
$602$	−2.28353e6	−0.256812
$603$	−1.16859e6	−0.130879
$604$	2.70631e7	3.01846
$605$	620512.	0.0689226
$606$	−1.28772e7	−1.42442
$607$	−2.91020e6	−0.320591	−0.160295	−	0.987069i	$-0.551245\pi$
$607$	−2.91020e6	−0.320591	−0.160295	+	0.987069i	$0.551245\pi$
$608$	9.75387e6	1.07008
$609$	904713.	0.0988479
$610$	1.32753e7	1.44451
$611$	−2.96473e6	−0.321279
$612$	316776.	0.0341880
$613$	7.41582e6	0.797091	0.398546	−	0.917149i	$-0.369515\pi$
$613$	7.41582e6	0.797091	0.398546	+	0.917149i	$0.369515\pi$
$614$	−1.04451e7	−1.11813
$615$	1.64893e6	0.175798
$616$	−2.26665e7	−2.40676
$617$	−532614.	−0.0563248	−0.0281624	−	0.999603i	$-0.508966\pi$
$617$	−532614.	−0.0563248	−0.0281624	+	0.999603i	$0.508966\pi$
$618$	1.56503e7	1.64836
$619$	1.74793e6	0.183357	0.0916787	−	0.995789i	$-0.470777\pi$
$619$	1.74793e6	0.183357	0.0916787	+	0.995789i	$0.470777\pi$
$620$	1.85606e7	1.93915
$621$	1.07744e6	0.112115
$622$	2.42525e6	0.251351
$623$	−9.43606e6	−0.974026
$624$	−1.80447e6	−0.185519
$625$	−3.91599e6	−0.400998
$626$	−1.43249e7	−1.46102
$627$	−9.79368e6	−0.994895
$628$	8.41548e6	0.851491
$629$	193492.	0.0195001
$630$	7.92933e6	0.795949
$631$	−2.72819e6	−0.272773	−0.136386	−	0.990656i	$-0.543549\pi$
$631$	−2.72819e6	−0.272773	−0.136386	+	0.990656i	$0.543549\pi$
$632$	1.24373e7	1.23861
$633$	7.86472e6	0.780143
$634$	−2.83075e7	−2.79691
$635$	−1.25696e7	−1.23705
$636$	−1.45350e7	−1.42486
$637$	1.83758e7	1.79431
$638$	1.49936e6	0.145832
$639$	2.55670e6	0.247701
$640$	−1.43635e7	−1.38615
$641$	−1.24990e7	−1.20152	−0.600759	−	0.799430i	$-0.705135\pi$
$641$	−1.24990e7	−1.20152	−0.600759	+	0.799430i	$0.705135\pi$
$642$	−1.34884e7	−1.29159
$643$	−1.21125e7	−1.15533	−0.577663	−	0.816275i	$-0.696035\pi$
$643$	−1.21125e7	−1.15533	−0.577663	+	0.816275i	$0.696035\pi$
$644$	−2.07359e7	−1.97019
$645$	379591.	0.0359267
$646$	−1.82473e6	−0.172035
$647$	4.87189e6	0.457548	0.228774	−	0.973480i	$-0.426528\pi$
$647$	4.87189e6	0.457548	0.228774	+	0.973480i	$0.426528\pi$
$648$	−1.59888e6	−0.149582
$649$	1.33217e6	0.124151
$650$	5.42389e6	0.503532
$651$	1.65398e7	1.52960
$652$	−2.08697e7	−1.92264
$653$	−1.94196e7	−1.78220	−0.891100	−	0.453806i	$-0.850066\pi$
$653$	−1.94196e7	−1.78220	−0.891100	+	0.453806i	$0.850066\pi$
$654$	−1.13735e7	−1.03980
$655$	−1.15539e6	−0.105226
$656$	1.98685e6	0.180263
$657$	1.72355e6	0.155780
$658$	1.56977e7	1.41342
$659$	−4.75216e6	−0.426263	−0.213132	−	0.977024i	$-0.568366\pi$
$659$	−4.75216e6	−0.426263	−0.213132	+	0.977024i	$0.568366\pi$
$660$	8.45446e6	0.755485
$661$	−548417.	−0.0488211	−0.0244105	−	0.999702i	$-0.507771\pi$
$661$	−548417.	−0.0488211	−0.0244105	+	0.999702i	$0.507771\pi$
$662$	2.55522e7	2.26612
$663$	−265109.	−0.0234229
$664$	4.33999e6	0.382004
$665$	−2.93858e7	−2.57681
$666$	−2.19139e6	−0.191440
$667$	611295.	0.0532030
$668$	−2.34315e7	−2.03170
$669$	9.04651e6	0.781476
$670$	−5.81095e6	−0.500104
$671$	1.26134e7	1.08150
$672$	−7.50333e6	−0.640960
$673$	−8.23444e6	−0.700803	−0.350402	−	0.936600i	$-0.613955\pi$
$673$	−8.23444e6	−0.700803	−0.350402	+	0.936600i	$0.613955\pi$
$674$	−1.27605e7	−1.08198
$675$	960032.	0.0811010
$676$	−1.05201e7	−0.885430
$677$	2.26732e7	1.90126	0.950630	−	0.310326i	$-0.100438\pi$
$677$	2.26732e7	1.90126	0.950630	+	0.310326i	$0.100438\pi$
$678$	2.10572e7	1.75925
$679$	−2.02431e7	−1.68501
$680$	702013.	0.0582201
$681$	−1.08647e7	−0.897741
$682$	2.74109e7	2.25664
$683$	−8.80273e6	−0.722047	−0.361024	−	0.932557i	$-0.617573\pi$
$683$	−8.80273e6	−0.722047	−0.361024	+	0.932557i	$0.617573\pi$
$684$	1.32956e7	1.08660
$685$	−6.51126e6	−0.530199
$686$	−5.86033e7	−4.75457
$687$	8.32342e6	0.672837
$688$	457383.	0.0368391
$689$	1.21643e7	0.976202
$690$	5.35768e6	0.428404
$691$	5.96759e6	0.475449	0.237724	−	0.971333i	$-0.423599\pi$
$691$	5.96759e6	0.475449	0.237724	+	0.971333i	$0.423599\pi$
$692$	1.06277e7	0.843672
$693$	7.53395e6	0.595923
$694$	8.12814e6	0.640608
$695$	6.49531e6	0.510080
$696$	−907143.	−0.0709827
$697$	291904.	0.0227592
$698$	2.03911e7	1.58417
$699$	−6.75731e6	−0.523095
$700$	−1.84764e7	−1.42519
$701$	−6.81387e6	−0.523720	−0.261860	−	0.965106i	$-0.584336\pi$
$701$	−6.81387e6	−0.523720	−0.261860	+	0.965106i	$0.584336\pi$
$702$	3.00248e6	0.229952
$703$	8.12119e6	0.619771
$704$	−1.80821e7	−1.37505
$705$	−2.60943e6	−0.197730
$706$	3.25197e7	2.45547
$707$	−3.67112e7	−2.76217
$708$	−1.80852e6	−0.135594
$709$	2.19624e7	1.64083	0.820414	−	0.571769i	$-0.193743\pi$
$709$	2.19624e7	1.64083	0.820414	+	0.571769i	$0.193743\pi$
$710$	1.27135e7	0.946496
$711$	−4.13396e6	−0.306685
$712$	9.46140e6	0.699448
$713$	1.11755e7	0.823275
$714$	1.40370e6	0.103046
$715$	−7.07551e6	−0.517598
$716$	3.67586e7	2.67964
$717$	−1.39811e7	−1.01565
$718$	2.64224e7	1.91276
$719$	4.29024e6	0.309499	0.154750	−	0.987954i	$-0.450543\pi$
$719$	4.29024e6	0.309499	0.154750	+	0.987954i	$0.450543\pi$
$720$	−1.58822e6	−0.114177
$721$	4.46171e7	3.19642
$722$	−5.31322e7	−3.79328
$723$	−5.14352e6	−0.365944
$724$	3.13920e7	2.22573
$725$	544685.	0.0384858
$726$	−1.24407e6	−0.0875998
$727$	2.05224e7	1.44010	0.720049	−	0.693923i	$-0.244119\pi$
$727$	2.05224e7	1.44010	0.720049	+	0.693923i	$0.244119\pi$
$728$	−2.57525e7	−1.80090
$729$	531441.	0.0370370
$730$	8.57057e6	0.595254
$731$	67197.7	0.00465116
$732$	−1.71236e7	−1.18118
$733$	−2.27907e7	−1.56674	−0.783372	−	0.621553i	$-0.786502\pi$
$733$	−2.27907e7	−1.56674	−0.783372	+	0.621553i	$0.786502\pi$
$734$	−7.99415e6	−0.547687
$735$	1.61736e7	1.10430
$736$	−5.06984e6	−0.344984
$737$	−5.52121e6	−0.374425
$738$	−3.30594e6	−0.223437
$739$	1.16303e7	0.783390	0.391695	−	0.920095i	$-0.371889\pi$
$739$	1.16303e7	0.783390	0.391695	+	0.920095i	$0.371889\pi$
$740$	−7.01067e6	−0.470631
$741$	−1.11271e7	−0.744450
$742$	−6.44078e7	−4.29466
$743$	−1.36248e6	−0.0905437	−0.0452718	−	0.998975i	$-0.514415\pi$
$743$	−1.36248e6	−0.0905437	−0.0452718	+	0.998975i	$0.514415\pi$
$744$	−1.65842e7	−1.09840
$745$	8.88845e6	0.586726
$746$	3.98813e7	2.62375
$747$	−1.44254e6	−0.0945858
$748$	1.49666e6	0.0978070
$749$	−3.84538e7	−2.50458
$750$	1.61021e7	1.04527
$751$	−3.68228e6	−0.238241	−0.119121	−	0.992880i	$-0.538008\pi$
$751$	−3.68228e6	−0.238241	−0.119121	+	0.992880i	$0.538008\pi$
$752$	−3.14420e6	−0.202752
$753$	−6.39597e6	−0.411073
$754$	1.70349e6	0.109122
$755$	−1.99347e7	−1.27275
$756$	−1.02279e7	−0.650851
$757$	−1.07391e7	−0.681127	−0.340563	−	0.940222i	$-0.610618\pi$
$757$	−1.07391e7	−0.681127	−0.340563	+	0.940222i	$0.610618\pi$
$758$	−3.03062e7	−1.91584
$759$	5.09053e6	0.320744
$760$	2.94647e7	1.85041
$761$	1.41023e7	0.882731	0.441366	−	0.897327i	$-0.354494\pi$
$761$	1.41023e7	0.882731	0.441366	+	0.897327i	$0.354494\pi$
$762$	2.52009e7	1.57228
$763$	−3.24243e7	−2.01632
$764$	−2.19145e7	−1.35831
$765$	−233337.	−0.0144155
$766$	3.70446e6	0.228114
$767$	1.51355e6	0.0928982
$768$	1.51898e7	0.929284
$769$	1.64536e7	1.00333	0.501665	−	0.865062i	$-0.332721\pi$
$769$	1.64536e7	1.00333	0.501665	+	0.865062i	$0.332721\pi$
$770$	3.74635e7	2.27710
$771$	−1.17501e7	−0.711878
$772$	2.24029e7	1.35288
$773$	1.13373e7	0.682433	0.341216	−	0.939985i	$-0.389161\pi$
$773$	1.13373e7	0.682433	0.341216	+	0.939985i	$0.389161\pi$
$774$	−761045.	−0.0456623
$775$	9.95780e6	0.595537
$776$	2.02974e7	1.21000
$777$	−6.24736e6	−0.371231
$778$	−3.75551e7	−2.22443
$779$	1.22517e7	0.723356
$780$	9.60551e6	0.565307
$781$	1.20796e7	0.708637
$782$	948450.	0.0554623
$783$	301519.	0.0175756
$784$	1.94881e7	1.13235
$785$	−6.19885e6	−0.359035
$786$	2.31645e6	0.133741
$787$	2.87599e7	1.65520	0.827601	−	0.561317i	$-0.189705\pi$
$787$	2.87599e7	1.65520	0.827601	+	0.561317i	$0.189705\pi$
$788$	5.68824e7	3.26334
$789$	−1.71022e7	−0.978045
$790$	−2.05566e7	−1.17188
$791$	6.00314e7	3.41144
$792$	−7.55419e6	−0.427932
$793$	1.43307e7	0.809252
$794$	4.58292e7	2.57983
$795$	1.07065e7	0.600800
$796$	1.99265e7	1.11467
$797$	−3.21674e7	−1.79378	−0.896892	−	0.442250i	$-0.854181\pi$
$797$	−3.21674e7	−1.79378	−0.896892	+	0.442250i	$0.854181\pi$
$798$	5.89158e7	3.27510
$799$	−461939.	−0.0255987
$800$	−4.51740e6	−0.249553
$801$	−3.14481e6	−0.173186
$802$	−8.89899e6	−0.488546
$803$	8.14322e6	0.445663
$804$	7.49544e6	0.408937
$805$	1.52740e7	0.830739
$806$	3.11428e7	1.68857
$807$	1.31753e7	0.712161
$808$	3.68098e7	1.98351
$809$	−1.90148e7	−1.02146	−0.510728	−	0.859742i	$-0.670624\pi$
$809$	−1.90148e7	−1.02146	−0.510728	+	0.859742i	$0.670624\pi$
$810$	2.64265e6	0.141523
$811$	−4.76970e6	−0.254647	−0.127324	−	0.991861i	$-0.540639\pi$
$811$	−4.76970e6	−0.254647	−0.127324	+	0.991861i	$0.540639\pi$
$812$	−5.80290e6	−0.308856
$813$	−968506.	−0.0513897
$814$	−1.03536e7	−0.547684
$815$	1.53727e7	0.810690
$816$	−281157.	−0.0147817
$817$	2.82040e6	0.147828
$818$	−1.81920e7	−0.950601
$819$	8.55969e6	0.445911
$820$	−1.05763e7	−0.549289
$821$	−2.63580e7	−1.36475	−0.682376	−	0.731001i	$-0.739053\pi$
$821$	−2.63580e7	−1.36475	−0.682376	+	0.731001i	$0.739053\pi$
$822$	1.30545e7	0.673875
$823$	−3.92377e6	−0.201931	−0.100966	−	0.994890i	$-0.532193\pi$
$823$	−3.92377e6	−0.201931	−0.100966	+	0.994890i	$0.532193\pi$
$824$	−4.47370e7	−2.29535
$825$	4.53584e6	0.232018
$826$	−8.01394e6	−0.408692
$827$	143623.	0.00730230	0.00365115	−	0.999993i	$-0.498838\pi$
$827$	143623.	0.00730230	0.00365115	+	0.999993i	$0.498838\pi$
$828$	−6.91076e6	−0.350308
$829$	−2.78716e6	−0.140856	−0.0704281	−	0.997517i	$-0.522437\pi$
$829$	−2.78716e6	−0.140856	−0.0704281	+	0.997517i	$0.522437\pi$
$830$	−7.17320e6	−0.361424
$831$	4.24397e6	0.213191
$832$	−2.05440e7	−1.02891
$833$	2.86315e6	0.142966
$834$	−1.30225e7	−0.648305
$835$	1.72597e7	0.856676
$836$	6.28175e7	3.10860
$837$	5.51230e6	0.271969
$838$	6.47257e6	0.318396
$839$	1.42188e7	0.697362	0.348681	−	0.937242i	$-0.386630\pi$
$839$	1.42188e7	0.697362	0.348681	+	0.937242i	$0.386630\pi$
$840$	−2.26662e7	−1.10836
$841$	−2.03401e7	−0.991660
$842$	6.11342e6	0.297169
$843$	1.31606e7	0.637833
$844$	−5.04450e7	−2.43760
$845$	7.74914e6	0.373346
$846$	5.23167e6	0.251313
$847$	−3.54668e6	−0.169869
$848$	1.29007e7	0.616059
$849$	2.43766e6	0.116065
$850$	845102.	0.0401201
$851$	−4.22121e6	−0.199808
$852$	−1.63989e7	−0.773954
$853$	3.54743e7	1.66933	0.834663	−	0.550761i	$-0.185662\pi$
$853$	3.54743e7	1.66933	0.834663	+	0.550761i	$0.185662\pi$
$854$	−7.58782e7	−3.56018
$855$	−9.79357e6	−0.458169
$856$	3.85570e7	1.79854
$857$	−6.66554e6	−0.310016	−0.155008	−	0.987913i	$-0.549540\pi$
$857$	−6.66554e6	−0.310016	−0.155008	+	0.987913i	$0.549540\pi$
$858$	1.41857e7	0.657860
$859$	−2.09784e7	−0.970038	−0.485019	−	0.874503i	$-0.661187\pi$
$859$	−2.09784e7	−0.970038	−0.485019	+	0.874503i	$0.661187\pi$
$860$	−2.43473e6	−0.112255
$861$	−9.42482e6	−0.433277
$862$	−4.19925e7	−1.92488
$863$	−3.29411e7	−1.50560	−0.752801	−	0.658248i	$-0.771298\pi$
$863$	−3.29411e7	−1.50560	−0.752801	+	0.658248i	$0.771298\pi$
$864$	−2.50068e6	−0.113966
$865$	−7.82836e6	−0.355738
$866$	−7.02612e7	−3.18362
$867$	1.27374e7	0.575484
$868$	−1.06087e8	−4.77930
$869$	−1.95316e7	−0.877381
$870$	1.49934e6	0.0671586
$871$	−6.27291e6	−0.280171
$872$	3.25114e7	1.44792
$873$	−6.74653e6	−0.299602
$874$	3.98081e7	1.76276
$875$	4.59051e7	2.02694
$876$	−1.10550e7	−0.486742
$877$	1.74947e7	0.768081	0.384041	−	0.923316i	$-0.374532\pi$
$877$	1.74947e7	0.768081	0.384041	+	0.923316i	$0.374532\pi$
$878$	1.62260e7	0.710356
$879$	1.14717e6	0.0500788
$880$	−7.50381e6	−0.326644
$881$	−2.47900e7	−1.07606	−0.538031	−	0.842925i	$-0.680832\pi$
$881$	−2.47900e7	−1.07606	−0.538031	+	0.842925i	$0.680832\pi$
$882$	−3.24265e7	−1.40355
$883$	1.85125e7	0.799028	0.399514	−	0.916727i	$-0.369179\pi$
$883$	1.85125e7	0.799028	0.399514	+	0.916727i	$0.369179\pi$
$884$	1.70043e6	0.0731860
$885$	1.33216e6	0.0571739
$886$	5.23121e7	2.23881
$887$	−3.23247e7	−1.37951	−0.689756	−	0.724042i	$-0.742282\pi$
$887$	−3.23247e7	−1.37951	−0.689756	+	0.724042i	$0.742282\pi$
$888$	6.26414e6	0.266581
$889$	7.18445e7	3.04887
$890$	−1.56380e7	−0.661767
$891$	2.51088e6	0.105958
$892$	−5.80251e7	−2.44176
$893$	−1.93883e7	−0.813602
$894$	−1.78205e7	−0.745721
$895$	−2.70764e7	−1.12988
$896$	8.20980e7	3.41635
$897$	5.78359e6	0.240003
$898$	−3.27789e7	−1.35645
$899$	3.12746e6	0.129060
$900$	−6.15772e6	−0.253404
$901$	1.89534e6	0.0777811
$902$	−1.56195e7	−0.639220
$903$	−2.16964e6	−0.0885460
$904$	−6.01927e7	−2.44975
$905$	−2.31234e7	−0.938490
$906$	3.99672e7	1.61765
$907$	5.10131e6	0.205903	0.102952	−	0.994686i	$-0.467171\pi$
$907$	5.10131e6	0.205903	0.102952	+	0.994686i	$0.467171\pi$
$908$	6.96873e7	2.80504
$909$	−1.22350e7	−0.491126
$910$	4.25641e7	1.70388
$911$	3.65998e7	1.46111	0.730555	−	0.682854i	$-0.239262\pi$
$911$	3.65998e7	1.46111	0.730555	+	0.682854i	$0.239262\pi$
$912$	−1.18006e7	−0.469805
$913$	−6.81552e6	−0.270596
$914$	8.45714e6	0.334856
$915$	1.26132e7	0.498051
$916$	−5.33871e7	−2.10231
$917$	6.60389e6	0.259344
$918$	467820.	0.0183220
$919$	−4.17959e7	−1.63247	−0.816233	−	0.577722i	$-0.803942\pi$
$919$	−4.17959e7	−1.63247	−0.816233	+	0.577722i	$0.803942\pi$
$920$	−1.53151e7	−0.596553
$921$	−9.92415e6	−0.385518
$922$	2.26686e7	0.878207
$923$	1.37242e7	0.530251
$924$	−4.83234e7	−1.86199
$925$	−3.76124e6	−0.144536
$926$	−8.21481e7	−3.14826
$927$	1.48698e7	0.568337
$928$	−1.41879e6	−0.0540813
$929$	−3.62772e6	−0.137910	−0.0689549	−	0.997620i	$-0.521966\pi$
$929$	−3.62772e6	−0.137910	−0.0689549	+	0.997620i	$0.521966\pi$
$930$	2.74106e7	1.03923
$931$	1.20171e8	4.54388
$932$	4.33419e7	1.63444
$933$	2.30430e6	0.0866631
$934$	−7.08374e7	−2.65702
$935$	−1.10244e6	−0.0412408
$936$	−8.58267e6	−0.320209
$937$	−2.61792e7	−0.974110	−0.487055	−	0.873371i	$-0.661929\pi$
$937$	−2.61792e7	−0.974110	−0.487055	+	0.873371i	$0.661929\pi$
$938$	3.32139e7	1.23257
$939$	−1.36105e7	−0.503744
$940$	1.67371e7	0.617819
$941$	2.74091e7	1.00907	0.504535	−	0.863391i	$-0.331664\pi$
$941$	2.74091e7	1.00907	0.504535	+	0.863391i	$0.331664\pi$
$942$	1.24281e7	0.456329
$943$	−6.36814e6	−0.233203
$944$	1.60517e6	0.0586260
$945$	7.53387e6	0.274434
$946$	−3.59569e6	−0.130633
$947$	−2.02712e7	−0.734523	−0.367262	−	0.930118i	$-0.619705\pi$
$947$	−2.02712e7	−0.734523	−0.367262	+	0.930118i	$0.619705\pi$
$948$	2.65156e7	0.958252
$949$	9.25190e6	0.333477
$950$	3.54704e7	1.27514
$951$	−2.68957e7	−0.964344
$952$	−4.01252e6	−0.143491
$953$	−5.47512e7	−1.95282	−0.976408	−	0.215936i	$-0.930720\pi$
$953$	−5.47512e7	−1.95282	−0.976408	+	0.215936i	$0.930720\pi$
$954$	−2.14656e7	−0.763609
$955$	1.61422e7	0.572737
$956$	8.96762e7	3.17346
$957$	1.42458e6	0.0502813
$958$	−1.43953e7	−0.506765
$959$	3.72166e7	1.30674
$960$	−1.80819e7	−0.633237
$961$	2.85464e7	0.997110
$962$	−1.17632e7	−0.409815
$963$	−1.28157e7	−0.445325
$964$	3.29909e7	1.14341
$965$	−1.65020e7	−0.570450
$966$	−3.06230e7	−1.05586
$967$	3.51750e6	0.120967	0.0604836	−	0.998169i	$-0.480736\pi$
$967$	3.51750e6	0.120967	0.0604836	+	0.998169i	$0.480736\pi$
$968$	3.55621e6	0.121983
$969$	−1.73372e6	−0.0593157
$970$	−3.35479e7	−1.14482
$971$	5.13829e7	1.74892	0.874462	−	0.485094i	$-0.161215\pi$
$971$	5.13829e7	1.74892	0.874462	+	0.485094i	$0.161215\pi$
$972$	−3.40871e6	−0.115724
$973$	−3.71255e7	−1.25716
$974$	2.38423e7	0.805286
$975$	5.15338e6	0.173612
$976$	1.51982e7	0.510701
$977$	1.29861e7	0.435253	0.217627	−	0.976032i	$-0.430169\pi$
$977$	1.29861e7	0.435253	0.217627	+	0.976032i	$0.430169\pi$
$978$	−3.08207e7	−1.03038
$979$	−1.48582e7	−0.495461
$980$	−1.03739e8	−3.45045
$981$	−1.08062e7	−0.358511
$982$	5.38366e7	1.78155
$983$	2.68171e7	0.885171	0.442586	−	0.896726i	$-0.354061\pi$
$983$	2.68171e7	0.885171	0.442586	+	0.896726i	$0.354061\pi$
$984$	9.45013e6	0.311136
$985$	−4.18996e7	−1.37600
$986$	265423.	0.00869452
$987$	1.49148e7	0.487332
$988$	7.13700e7	2.32607
$989$	−1.46598e6	−0.0476582
$990$	1.24857e7	0.404878
$991$	1.52984e7	0.494838	0.247419	−	0.968909i	$-0.420418\pi$
$991$	1.52984e7	0.494838	0.247419	+	0.968909i	$0.420418\pi$
$992$	−2.59379e7	−0.836867
$993$	2.42778e7	0.781334
$994$	−7.26669e7	−2.33276
$995$	−1.46778e7	−0.470007
$996$	9.25256e6	0.295538
$997$	5.96740e7	1.90129	0.950643	−	0.310286i	$-0.100425\pi$
$997$	5.96740e7	1.90129	0.950643	+	0.310286i	$0.100425\pi$
$998$	2.28578e7	0.726454
$999$	−2.08210e6	−0.0660065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.2	✓	13
3.2	odd	2		531.6.a.e.1.12		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.2	✓	13	1.1	even	1	trivial
531.6.a.e.1.12		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)

\(f(q)\)	\(=\)	\(q-9.47242 q^{2} -9.00000 q^{3} +57.7268 q^{4} -42.5216 q^{5} +85.2518 q^{6} +243.042 q^{7} -243.695 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.47242 q^{2} -9.00000 q^{3} +57.7268 q^{4} -42.5216 q^{5} +85.2518 q^{6} +243.042 q^{7} -243.695 q^{8} +81.0000 q^{9} +402.782 q^{10} +382.698 q^{11} -519.541 q^{12} +434.802 q^{13} -2302.20 q^{14} +382.694 q^{15} +461.122 q^{16} +67.7470 q^{17} -767.266 q^{18} +2843.46 q^{19} -2454.63 q^{20} -2187.38 q^{21} -3625.08 q^{22} -1477.96 q^{23} +2193.25 q^{24} -1316.92 q^{25} -4118.63 q^{26} -729.000 q^{27} +14030.0 q^{28} -413.606 q^{29} -3625.04 q^{30} -7561.45 q^{31} +3430.29 q^{32} -3444.29 q^{33} -641.728 q^{34} -10334.5 q^{35} +4675.87 q^{36} +2856.10 q^{37} -26934.4 q^{38} -3913.22 q^{39} +10362.3 q^{40} +4308.73 q^{41} +20719.8 q^{42} +991.892 q^{43} +22091.9 q^{44} -3444.25 q^{45} +13999.9 q^{46} -6818.58 q^{47} -4150.10 q^{48} +42262.4 q^{49} +12474.4 q^{50} -609.723 q^{51} +25099.7 q^{52} +27976.7 q^{53} +6905.39 q^{54} -16272.9 q^{55} -59228.0 q^{56} -25591.1 q^{57} +3917.85 q^{58} +3481.00 q^{59} +22091.7 q^{60} +32959.1 q^{61} +71625.3 q^{62} +19686.4 q^{63} -47249.0 q^{64} -18488.5 q^{65} +32625.7 q^{66} -14427.0 q^{67} +3910.81 q^{68} +13301.7 q^{69} +97893.0 q^{70} +31564.2 q^{71} -19739.3 q^{72} +21278.4 q^{73} -27054.2 q^{74} +11852.2 q^{75} +164144. q^{76} +93011.8 q^{77} +37067.7 q^{78} -51036.5 q^{79} -19607.6 q^{80} +6561.00 q^{81} -40814.1 q^{82} -17809.1 q^{83} -126270. q^{84} -2880.71 q^{85} -9395.62 q^{86} +3722.46 q^{87} -93261.6 q^{88} -38824.8 q^{89} +32625.4 q^{90} +105675. q^{91} -85318.0 q^{92} +68053.1 q^{93} +64588.5 q^{94} -120908. q^{95} -30872.6 q^{96} -83290.5 q^{97} -400327. q^{98} +30998.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 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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