LMFDB - Embedded newform 177.6.a.d.1.3

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			1.3
Root			$-6.40804$ 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)

$f(q)$	$=$	$q-6.40804 q^{2} -9.00000 q^{3} +9.06300 q^{4} -77.9071 q^{5} +57.6724 q^{6} +112.353 q^{7} +146.981 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.40804 q^{2} -9.00000 q^{3} +9.06300 q^{4} -77.9071 q^{5} +57.6724 q^{6} +112.353 q^{7} +146.981 q^{8} +81.0000 q^{9} +499.232 q^{10} -791.290 q^{11} -81.5670 q^{12} -741.012 q^{13} -719.963 q^{14} +701.163 q^{15} -1231.88 q^{16} -1119.21 q^{17} -519.051 q^{18} -1177.03 q^{19} -706.072 q^{20} -1011.18 q^{21} +5070.62 q^{22} -3483.97 q^{23} -1322.83 q^{24} +2944.51 q^{25} +4748.44 q^{26} -729.000 q^{27} +1018.26 q^{28} -4197.07 q^{29} -4493.09 q^{30} +6822.15 q^{31} +3190.53 q^{32} +7121.61 q^{33} +7171.97 q^{34} -8753.09 q^{35} +734.103 q^{36} -11247.3 q^{37} +7542.43 q^{38} +6669.11 q^{39} -11450.9 q^{40} +2867.88 q^{41} +6479.67 q^{42} -8326.13 q^{43} -7171.46 q^{44} -6310.47 q^{45} +22325.5 q^{46} -10172.3 q^{47} +11086.9 q^{48} -4183.80 q^{49} -18868.5 q^{50} +10072.9 q^{51} -6715.79 q^{52} +27469.2 q^{53} +4671.46 q^{54} +61647.0 q^{55} +16513.8 q^{56} +10593.2 q^{57} +26895.0 q^{58} +3481.00 q^{59} +6354.65 q^{60} -9702.92 q^{61} -43716.6 q^{62} +9100.60 q^{63} +18975.1 q^{64} +57730.1 q^{65} -45635.5 q^{66} +19207.6 q^{67} -10143.4 q^{68} +31355.8 q^{69} +56090.2 q^{70} -55295.1 q^{71} +11905.5 q^{72} +64498.9 q^{73} +72073.1 q^{74} -26500.6 q^{75} -10667.4 q^{76} -88903.8 q^{77} -42735.9 q^{78} +41735.8 q^{79} +95972.0 q^{80} +6561.00 q^{81} -18377.5 q^{82} -83035.3 q^{83} -9164.30 q^{84} +87194.7 q^{85} +53354.2 q^{86} +37773.6 q^{87} -116305. q^{88} +31732.9 q^{89} +40437.8 q^{90} -83255.0 q^{91} -31575.3 q^{92} -61399.4 q^{93} +65184.3 q^{94} +91698.6 q^{95} -28714.7 q^{96} -137590. q^{97} +26809.9 q^{98} -64094.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.40804	−1.13279	−0.566396	−	0.824133i	$-0.691663\pi$
$2$	−6.40804	−1.13279	−0.566396	+	0.824133i	$0.691663\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	9.06300	0.283219
$5$	−77.9071	−1.39364	−0.696822	−	0.717244i	$-0.745403\pi$
$5$	−77.9071	−1.39364	−0.696822	+	0.717244i	$0.745403\pi$
$6$	57.6724	0.654018
$7$	112.353	0.866642	0.433321	−	0.901240i	$-0.357342\pi$
$7$	112.353	0.866642	0.433321	+	0.901240i	$0.357342\pi$
$8$	146.981	0.811964
$9$	81.0000	0.333333
$10$	499.232	1.57871
$11$	−791.290	−1.97176	−0.985879	−	0.167458i	$-0.946444\pi$
$11$	−791.290	−1.97176	−0.985879	+	0.167458i	$0.946444\pi$
$12$	−81.5670	−0.163516
$13$	−741.012	−1.21609	−0.608047	−	0.793901i	$-0.708047\pi$
$13$	−741.012	−1.21609	−0.608047	+	0.793901i	$0.708047\pi$
$14$	−719.963	−0.981725
$15$	701.163	0.804621
$16$	−1231.88	−1.20301
$17$	−1119.21	−0.939271	−0.469636	−	0.882860i	$-0.655615\pi$
$17$	−1119.21	−0.939271	−0.469636	+	0.882860i	$0.655615\pi$
$18$	−519.051	−0.377597
$19$	−1177.03	−0.748001	−0.374000	−	0.927429i	$-0.622014\pi$
$19$	−1177.03	−0.748001	−0.374000	+	0.927429i	$0.622014\pi$
$20$	−706.072	−0.394706
$21$	−1011.18	−0.500356
$22$	5070.62	2.23359
$23$	−3483.97	−1.37327	−0.686634	−	0.727003i	$-0.740913\pi$
$23$	−3483.97	−1.37327	−0.686634	+	0.727003i	$0.740913\pi$
$24$	−1322.83	−0.468788
$25$	2944.51	0.942243
$26$	4748.44	1.37758
$27$	−729.000	−0.192450
$28$	1018.26	0.245449
$29$	−4197.07	−0.926725	−0.463363	−	0.886169i	$-0.653357\pi$
$29$	−4197.07	−0.926725	−0.463363	+	0.886169i	$0.653357\pi$
$30$	−4493.09	−0.911468
$31$	6822.15	1.27502	0.637510	−	0.770442i	$-0.279964\pi$
$31$	6822.15	1.27502	0.637510	+	0.770442i	$0.279964\pi$
$32$	3190.53	0.550792
$33$	7121.61	1.13840
$34$	7171.97	1.06400
$35$	−8753.09	−1.20779
$36$	734.103	0.0944063
$37$	−11247.3	−1.35065	−0.675326	−	0.737519i	$-0.735997\pi$
$37$	−11247.3	−1.35065	−0.675326	+	0.737519i	$0.735997\pi$
$38$	7542.43	0.847330
$39$	6669.11	0.702112
$40$	−11450.9	−1.13159
$41$	2867.88	0.266442	0.133221	−	0.991086i	$-0.457468\pi$
$41$	2867.88	0.266442	0.133221	+	0.991086i	$0.457468\pi$
$42$	6479.67	0.566799
$43$	−8326.13	−0.686708	−0.343354	−	0.939206i	$-0.611563\pi$
$43$	−8326.13	−0.686708	−0.343354	+	0.939206i	$0.611563\pi$
$44$	−7171.46	−0.558439
$45$	−6310.47	−0.464548
$46$	22325.5	1.55563
$47$	−10172.3	−0.671696	−0.335848	−	0.941916i	$-0.609023\pi$
$47$	−10172.3	−0.671696	−0.335848	+	0.941916i	$0.609023\pi$
$48$	11086.9	0.694556
$49$	−4183.80	−0.248932
$50$	−18868.5	−1.06737
$51$	10072.9	0.542288
$52$	−6715.79	−0.344420
$53$	27469.2	1.34325	0.671624	−	0.740892i	$-0.265597\pi$
$53$	27469.2	1.34325	0.671624	+	0.740892i	$0.265597\pi$
$54$	4671.46	0.218006
$55$	61647.0	2.74793
$56$	16513.8	0.703682
$57$	10593.2	0.431859
$58$	26895.0	1.04979
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	6354.65	0.227884
$61$	−9702.92	−0.333870	−0.166935	−	0.985968i	$-0.553387\pi$
$61$	−9702.92	−0.333870	−0.166935	+	0.985968i	$0.553387\pi$
$62$	−43716.6	−1.44433
$63$	9100.60	0.288881
$64$	18975.1	0.579073
$65$	57730.1	1.69480
$66$	−45635.5	−1.28957
$67$	19207.6	0.522742	0.261371	−	0.965238i	$-0.415825\pi$
$67$	19207.6	0.522742	0.261371	+	0.965238i	$0.415825\pi$
$68$	−10143.4	−0.266019
$69$	31355.8	0.792857
$70$	56090.2	1.36818
$71$	−55295.1	−1.30179	−0.650895	−	0.759168i	$-0.725606\pi$
$71$	−55295.1	−1.30179	−0.650895	+	0.759168i	$0.725606\pi$
$72$	11905.5	0.270655
$73$	64498.9	1.41659	0.708297	−	0.705914i	$-0.249464\pi$
$73$	64498.9	1.41659	0.708297	+	0.705914i	$0.249464\pi$
$74$	72073.1	1.53001
$75$	−26500.6	−0.544004
$76$	−10667.4	−0.211848
$77$	−88903.8	−1.70881
$78$	−42735.9	−0.795347
$79$	41735.8	0.752387	0.376194	−	0.926541i	$-0.377233\pi$
$79$	41735.8	0.752387	0.376194	+	0.926541i	$0.377233\pi$
$80$	95972.0	1.67656
$81$	6561.00	0.111111
$82$	−18377.5	−0.301823
$83$	−83035.3	−1.32302	−0.661512	−	0.749935i	$-0.730085\pi$
$83$	−83035.3	−1.32302	−0.661512	+	0.749935i	$0.730085\pi$
$84$	−9164.30	−0.141710
$85$	87194.7	1.30901
$86$	53354.2	0.777897
$87$	37773.6	0.535045
$88$	−116305.	−1.60100
$89$	31732.9	0.424653	0.212327	−	0.977199i	$-0.431896\pi$
$89$	31732.9	0.424653	0.212327	+	0.977199i	$0.431896\pi$
$90$	40437.8	0.526236
$91$	−83255.0	−1.05392
$92$	−31575.3	−0.388935
$93$	−61399.4	−0.736134
$94$	65184.3	0.760892
$95$	91698.6	1.04245
$96$	−28714.7	−0.318000
$97$	−137590.	−1.48477	−0.742383	−	0.669976i	$-0.766304\pi$
$97$	−137590.	−1.48477	−0.742383	+	0.669976i	$0.766304\pi$
$98$	26809.9	0.281988
$99$	−64094.5	−0.657253
$100$	26686.1	0.266861
$101$	−81837.9	−0.798272	−0.399136	−	0.916892i	$-0.630690\pi$
$101$	−81837.9	−0.798272	−0.399136	+	0.916892i	$0.630690\pi$
$102$	−64547.7	−0.614300
$103$	−71474.1	−0.663828	−0.331914	−	0.943310i	$-0.607694\pi$
$103$	−71474.1	−0.663828	−0.331914	+	0.943310i	$0.607694\pi$
$104$	−108915.	−0.987425
$105$	78777.8	0.697318
$106$	−176024.	−1.52162
$107$	−14058.6	−0.118709	−0.0593544	−	0.998237i	$-0.518904\pi$
$107$	−14058.6	−0.118709	−0.0593544	+	0.998237i	$0.518904\pi$
$108$	−6606.93	−0.0545055
$109$	106429.	0.858013	0.429007	−	0.903301i	$-0.358864\pi$
$109$	106429.	0.858013	0.429007	+	0.903301i	$0.358864\pi$
$110$	−395037.	−3.11283
$111$	101226.	0.779799
$112$	−138405.	−1.04258
$113$	−35251.8	−0.259708	−0.129854	−	0.991533i	$-0.541451\pi$
$113$	−35251.8	−0.259708	−0.129854	+	0.991533i	$0.541451\pi$
$114$	−67881.9	−0.489206
$115$	271426.	1.91385
$116$	−38038.0	−0.262466
$117$	−60022.0	−0.405364
$118$	−22306.4	−0.147477
$119$	−125747.	−0.814012
$120$	103058.	0.653323
$121$	465088.	2.88783
$122$	62176.7	0.378206
$123$	−25811.0	−0.153830
$124$	61829.2	0.361110
$125$	14061.5	0.0804928
$126$	−58317.0	−0.327242
$127$	313489.	1.72470	0.862348	−	0.506316i	$-0.168993\pi$
$127$	313489.	1.72470	0.862348	+	0.506316i	$0.168993\pi$
$128$	−223690.	−1.20676
$129$	74935.1	0.396471
$130$	−369937.	−1.91986
$131$	−157920.	−0.804003	−0.402002	−	0.915639i	$-0.631685\pi$
$131$	−157920.	−0.804003	−0.402002	+	0.915639i	$0.631685\pi$
$132$	64543.1	0.322415
$133$	−132242.	−0.648249
$134$	−123083.	−0.592158
$135$	56794.2	0.268207
$136$	−164504.	−0.762655
$137$	−88237.1	−0.401652	−0.200826	−	0.979627i	$-0.564363\pi$
$137$	−88237.1	−0.401652	−0.200826	+	0.979627i	$0.564363\pi$
$138$	−200929.	−0.898142
$139$	−54487.9	−0.239201	−0.119601	−	0.992822i	$-0.538161\pi$
$139$	−54487.9	−0.239201	−0.119601	+	0.992822i	$0.538161\pi$
$140$	−79329.3	−0.342069
$141$	91550.3	0.387804
$142$	354334.	1.47466
$143$	586355.	2.39784
$144$	−99782.1	−0.401002
$145$	326981.	1.29152
$146$	−413312.	−1.60471
$147$	37654.2	0.143721
$148$	−101934.	−0.382530
$149$	279909.	1.03288	0.516442	−	0.856322i	$-0.327256\pi$
$149$	279909.	1.03288	0.516442	+	0.856322i	$0.327256\pi$
$150$	169817.	0.616244
$151$	−526579.	−1.87941	−0.939704	−	0.341989i	$-0.888899\pi$
$151$	−526579.	−1.87941	−0.939704	+	0.341989i	$0.888899\pi$
$152$	−173001.	−0.607350
$153$	−90656.4	−0.313090
$154$	569699.	1.93573
$155$	−531494.	−1.77692
$156$	60442.1	0.198851
$157$	−133800.	−0.433219	−0.216609	−	0.976258i	$-0.569500\pi$
$157$	−133800.	−0.433219	−0.216609	+	0.976258i	$0.569500\pi$
$158$	−267445.	−0.852299
$159$	−247223.	−0.775524
$160$	−248564.	−0.767607
$161$	−391435.	−1.19013
$162$	−42043.2	−0.125866
$163$	121943.	0.359489	0.179745	−	0.983713i	$-0.442473\pi$
$163$	121943.	0.359489	0.179745	+	0.983713i	$0.442473\pi$
$164$	25991.6	0.0754613
$165$	−554823.	−1.58652
$166$	532094.	1.49871
$167$	163269.	0.453014	0.226507	−	0.974010i	$-0.427269\pi$
$167$	163269.	0.453014	0.226507	+	0.974010i	$0.427269\pi$
$168$	−148624.	−0.406271
$169$	177806.	0.478883
$170$	−558747.	−1.48284
$171$	−95339.1	−0.249334
$172$	−75459.7	−0.194488
$173$	357919.	0.909220	0.454610	−	0.890691i	$-0.349779\pi$
$173$	357919.	0.909220	0.454610	+	0.890691i	$0.349779\pi$
$174$	−242055.	−0.606095
$175$	330825.	0.816587
$176$	974772.	2.37204
$177$	−31329.0	−0.0751646
$178$	−203346.	−0.481044
$179$	−99379.8	−0.231828	−0.115914	−	0.993259i	$-0.536980\pi$
$179$	−99379.8	−0.231828	−0.115914	+	0.993259i	$0.536980\pi$
$180$	−57191.8	−0.131569
$181$	−251935.	−0.571601	−0.285800	−	0.958289i	$-0.592259\pi$
$181$	−251935.	−0.571601	−0.285800	+	0.958289i	$0.592259\pi$
$182$	533501.	1.19387
$183$	87326.3	0.192760
$184$	−512079.	−1.11505
$185$	876243.	1.88233
$186$	393450.	0.833887
$187$	885623.	1.85202
$188$	−92191.2	−0.190237
$189$	−81905.4	−0.166785
$190$	−587609.	−1.18088
$191$	92165.2	0.182803	0.0914015	−	0.995814i	$-0.470865\pi$
$191$	92165.2	0.182803	0.0914015	+	0.995814i	$0.470865\pi$
$192$	−170776.	−0.334328
$193$	−199542.	−0.385603	−0.192801	−	0.981238i	$-0.561757\pi$
$193$	−199542.	−0.385603	−0.192801	+	0.981238i	$0.561757\pi$
$194$	881683.	1.68193
$195$	−519571.	−0.978494
$196$	−37917.7	−0.0705021
$197$	−35347.2	−0.0648918	−0.0324459	−	0.999473i	$-0.510330\pi$
$197$	−35347.2	−0.0648918	−0.0324459	+	0.999473i	$0.510330\pi$
$198$	410720.	0.744531
$199$	−93366.9	−0.167132	−0.0835661	−	0.996502i	$-0.526631\pi$
$199$	−93366.9	−0.167132	−0.0835661	+	0.996502i	$0.526631\pi$
$200$	432788.	0.765068
$201$	−172869.	−0.301805
$202$	524420.	0.904276
$203$	−471553.	−0.803139
$204$	91291.0	0.153586
$205$	−223428.	−0.371325
$206$	458009.	0.751980
$207$	−282202.	−0.457756
$208$	912837.	1.46297
$209$	931368.	1.47488
$210$	−504812.	−0.789917
$211$	−1036.79	−0.00160319	−0.000801593	−	1.00000i	$-0.500255\pi$
$211$	−1036.79	−0.00160319	−0.000801593		1.00000i	$0.500255\pi$
$212$	248953.	0.380433
$213$	497656.	0.751589
$214$	90088.2	0.134472
$215$	648664.	0.957026
$216$	−107149.	−0.156263
$217$	766490.	1.10499
$218$	−682002.	−0.971951
$219$	−580490.	−0.817871
$220$	558707.	0.778265
$221$	829351.	1.14224
$222$	−648658.	−0.883351
$223$	−688653.	−0.927339	−0.463669	−	0.886008i	$-0.653467\pi$
$223$	−688653.	−0.927339	−0.463669	+	0.886008i	$0.653467\pi$
$224$	358465.	0.477339
$225$	238505.	0.314081
$226$	225895.	0.294195
$227$	7219.24	0.00929880	0.00464940	−	0.999989i	$-0.498520\pi$
$227$	7219.24	0.00929880	0.00464940	+	0.999989i	$0.498520\pi$
$228$	96006.5	0.122310
$229$	−106116.	−0.133719	−0.0668594	−	0.997762i	$-0.521298\pi$
$229$	−106116.	−0.133719	−0.0668594	+	0.997762i	$0.521298\pi$
$230$	−1.73931e6	−2.16799
$231$	800134.	0.986581
$232$	−616890.	−0.752468
$233$	1.48504e6	1.79204	0.896021	−	0.444012i	$-0.146445\pi$
$233$	1.48504e6	1.79204	0.896021	+	0.444012i	$0.146445\pi$
$234$	384623.	0.459194
$235$	792491.	0.936105
$236$	31548.3	0.0368719
$237$	−375623.	−0.434391
$238$	805793.	0.922106
$239$	−1.67141e6	−1.89273	−0.946363	−	0.323106i	$-0.895273\pi$
$239$	−1.67141e6	−1.89273	−0.946363	+	0.323106i	$0.895273\pi$
$240$	−863748.	−0.967963
$241$	−1.00362e6	−1.11308	−0.556538	−	0.830822i	$-0.687871\pi$
$241$	−1.00362e6	−1.11308	−0.556538	+	0.830822i	$0.687871\pi$
$242$	−2.98030e6	−3.27131
$243$	−59049.0	−0.0641500
$244$	−87937.6	−0.0945584
$245$	325947.	0.346922
$246$	165398.	0.174258
$247$	872191.	0.909639
$248$	1.00273e6	1.03527
$249$	747318.	0.763848
$250$	−90106.7	−0.0911816
$251$	784031.	0.785505	0.392752	−	0.919644i	$-0.371523\pi$
$251$	784031.	0.785505	0.392752	+	0.919644i	$0.371523\pi$
$252$	82478.7	0.0818164
$253$	2.75683e6	2.70775
$254$	−2.00885e6	−1.95372
$255$	−784752.	−0.755757
$256$	826212.	0.787937
$257$	−578684.	−0.546523	−0.273261	−	0.961940i	$-0.588102\pi$
$257$	−578684.	−0.546523	−0.273261	+	0.961940i	$0.588102\pi$
$258$	−480188.	−0.449119
$259$	−1.26367e6	−1.17053
$260$	523208.	0.479999
$261$	−339963.	−0.308908
$262$	1.01196e6	0.910769
$263$	1.51077e6	1.34682	0.673408	−	0.739271i	$-0.264830\pi$
$263$	1.51077e6	1.34682	0.673408	+	0.739271i	$0.264830\pi$
$264$	1.04674e6	0.924336
$265$	−2.14004e6	−1.87201
$266$	847415.	0.734332
$267$	−285596.	−0.245174
$268$	174079.	0.148050
$269$	−1.87261e6	−1.57785	−0.788925	−	0.614489i	$-0.789362\pi$
$269$	−1.87261e6	−1.57785	−0.788925	+	0.614489i	$0.789362\pi$
$270$	−363940.	−0.303823
$271$	−1.90549e6	−1.57610	−0.788049	−	0.615613i	$-0.788908\pi$
$271$	−1.90549e6	−1.57610	−0.788049	+	0.615613i	$0.788908\pi$
$272$	1.37874e6	1.12995
$273$	749295.	0.608480
$274$	565427.	0.454988
$275$	−2.32996e6	−1.85788
$276$	284177.	0.224552
$277$	−1.41618e6	−1.10897	−0.554483	−	0.832195i	$-0.687084\pi$
$277$	−1.41618e6	−1.10897	−0.554483	+	0.832195i	$0.687084\pi$
$278$	349161.	0.270965
$279$	552594.	0.425007
$280$	−1.28654e6	−0.980683
$281$	2.40331e6	1.81570	0.907848	−	0.419299i	$-0.137724\pi$
$281$	2.40331e6	1.81570	0.907848	+	0.419299i	$0.137724\pi$
$282$	−586658.	−0.439301
$283$	1.22675e6	0.910524	0.455262	−	0.890357i	$-0.349546\pi$
$283$	1.22675e6	0.910524	0.455262	+	0.890357i	$0.349546\pi$
$284$	−501140.	−0.368692
$285$	−825288.	−0.601857
$286$	−3.75739e6	−2.71626
$287$	322216.	0.230909
$288$	258433.	0.183597
$289$	−167216.	−0.117770
$290$	−2.09531e6	−1.46303
$291$	1.23831e6	0.857230
$292$	584554.	0.401206
$293$	−2.15295e6	−1.46509	−0.732545	−	0.680719i	$-0.761668\pi$
$293$	−2.15295e6	−1.46509	−0.732545	+	0.680719i	$0.761668\pi$
$294$	−241289.	−0.162806
$295$	−271194.	−0.181437
$296$	−1.65314e6	−1.09668
$297$	576850.	0.379465
$298$	−1.79367e6	−1.17004
$299$	2.58167e6	1.67002
$300$	−240175.	−0.154072
$301$	−935466.	−0.595130
$302$	3.37434e6	2.12898
$303$	736541.	0.460882
$304$	1.44995e6	0.899850
$305$	755926.	0.465296
$306$	580930.	0.354666
$307$	691785.	0.418914	0.209457	−	0.977818i	$-0.432830\pi$
$307$	691785.	0.418914	0.209457	+	0.977818i	$0.432830\pi$
$308$	−805735.	−0.483967
$309$	643267.	0.383261
$310$	3.40584e6	2.01289
$311$	2.23606e6	1.31094	0.655470	−	0.755221i	$-0.272470\pi$
$311$	2.23606e6	1.31094	0.655470	+	0.755221i	$0.272470\pi$
$312$	980234.	0.570090
$313$	−793499.	−0.457810	−0.228905	−	0.973449i	$-0.573515\pi$
$313$	−793499.	−0.457810	−0.228905	+	0.973449i	$0.573515\pi$
$314$	857396.	0.490747
$315$	−709001.	−0.402597
$316$	378252.	0.213090
$317$	825754.	0.461533	0.230766	−	0.973009i	$-0.425877\pi$
$317$	825754.	0.461533	0.230766	+	0.973009i	$0.425877\pi$
$318$	1.58421e6	0.878508
$319$	3.32110e6	1.82728
$320$	−1.47829e6	−0.807022
$321$	126527.	0.0685366
$322$	2.50833e6	1.34817
$323$	1.31734e6	0.702576
$324$	59462.3	0.0314688
$325$	−2.18192e6	−1.14586
$326$	−781413.	−0.407227
$327$	−957861.	−0.495374
$328$	421525.	0.216341
$329$	−1.14288e6	−0.582120
$330$	3.55533e6	1.79719
$331$	2.70727e6	1.35819	0.679097	−	0.734049i	$-0.262372\pi$
$331$	2.70727e6	1.35819	0.679097	+	0.734049i	$0.262372\pi$
$332$	−752549.	−0.374705
$333$	−911030.	−0.450217
$334$	−1.04623e6	−0.513171
$335$	−1.49641e6	−0.728516
$336$	1.24565e6	0.601931
$337$	−3.16111e6	−1.51623	−0.758114	−	0.652122i	$-0.773879\pi$
$337$	−3.16111e6	−1.51623	−0.758114	+	0.652122i	$0.773879\pi$
$338$	−1.13939e6	−0.542475
$339$	317266.	0.149942
$340$	790246.	0.370736
$341$	−5.39830e6	−2.51403
$342$	610937.	0.282443
$343$	−2.35838e6	−1.08238
$344$	−1.22378e6	−0.557582
$345$	−2.44284e6	−1.10496
$346$	−2.29356e6	−1.02996
$347$	353187.	0.157464	0.0787320	−	0.996896i	$-0.474913\pi$
$347$	353187.	0.157464	0.0787320	+	0.996896i	$0.474913\pi$
$348$	342342.	0.151535
$349$	−2.04245e6	−0.897609	−0.448804	−	0.893630i	$-0.648150\pi$
$349$	−2.04245e6	−0.897609	−0.448804	+	0.893630i	$0.648150\pi$
$350$	−2.11994e6	−0.925024
$351$	540198.	0.234037
$352$	−2.52463e6	−1.08603
$353$	3.90565e6	1.66823	0.834116	−	0.551589i	$-0.185978\pi$
$353$	3.90565e6	1.66823	0.834116	+	0.551589i	$0.185978\pi$
$354$	200758.	0.0851459
$355$	4.30788e6	1.81423
$356$	287595.	0.120270
$357$	1.13172e6	0.469970
$358$	636830.	0.262613
$359$	−4.27616e6	−1.75113	−0.875565	−	0.483101i	$-0.839511\pi$
$359$	−4.27616e6	−1.75113	−0.875565	+	0.483101i	$0.839511\pi$
$360$	−927521.	−0.377196
$361$	−1.09071e6	−0.440495
$362$	1.61441e6	0.647505
$363$	−4.18579e6	−1.66729
$364$	−754540.	−0.298489
$365$	−5.02492e6	−1.97423
$366$	−559590.	−0.218357
$367$	4.97282e6	1.92725	0.963623	−	0.267263i	$-0.0861194\pi$
$367$	4.97282e6	1.92725	0.963623	+	0.267263i	$0.0861194\pi$
$368$	4.29183e6	1.65205
$369$	232299.	0.0888139
$370$	−5.61500e6	−2.13229
$371$	3.08625e6	1.16411
$372$	−556463.	−0.208487
$373$	−1.58522e6	−0.589955	−0.294977	−	0.955504i	$-0.595312\pi$
$373$	−1.58522e6	−0.589955	−0.294977	+	0.955504i	$0.595312\pi$
$374$	−5.67511e6	−2.09795
$375$	−126554.	−0.0464725
$376$	−1.49513e6	−0.545393
$377$	3.11008e6	1.12698
$378$	524853.	0.188933
$379$	−1.21636e6	−0.434975	−0.217487	−	0.976063i	$-0.569786\pi$
$379$	−1.21636e6	−0.434975	−0.217487	+	0.976063i	$0.569786\pi$
$380$	831065.	0.295241
$381$	−2.82140e6	−0.995753
$382$	−590598.	−0.207078
$383$	3.08220e6	1.07365	0.536826	−	0.843693i	$-0.319623\pi$
$383$	3.08220e6	1.07365	0.536826	+	0.843693i	$0.319623\pi$
$384$	2.01321e6	0.696724
$385$	6.92623e6	2.38147
$386$	1.27867e6	0.436808
$387$	−674416.	−0.228903
$388$	−1.24698e6	−0.420514
$389$	−5.31319e6	−1.78025	−0.890125	−	0.455716i	$-0.849383\pi$
$389$	−5.31319e6	−1.78025	−0.890125	+	0.455716i	$0.849383\pi$
$390$	3.32943e6	1.10843
$391$	3.89931e6	1.28987
$392$	−614939.	−0.202124
$393$	1.42128e6	0.464191
$394$	226506.	0.0735089
$395$	−3.25152e6	−1.04856
$396$	−580888.	−0.186146
$397$	−2.02282e6	−0.644140	−0.322070	−	0.946716i	$-0.604379\pi$
$397$	−2.02282e6	−0.644140	−0.322070	+	0.946716i	$0.604379\pi$
$398$	598299.	0.189326
$399$	1.19018e6	0.374267
$400$	−3.62728e6	−1.13352
$401$	−3.06176e6	−0.950846	−0.475423	−	0.879757i	$-0.657705\pi$
$401$	−3.06176e6	−0.950846	−0.475423	+	0.879757i	$0.657705\pi$
$402$	1.10775e6	0.341882
$403$	−5.05530e6	−1.55054
$404$	−741697.	−0.226086
$405$	−511148.	−0.154849
$406$	3.02173e6	0.909790
$407$	8.89986e6	2.66316
$408$	1.48053e6	0.440319
$409$	−2.12583e6	−0.628377	−0.314189	−	0.949361i	$-0.601732\pi$
$409$	−2.12583e6	−0.628377	−0.314189	+	0.949361i	$0.601732\pi$
$410$	1.43174e6	0.420634
$411$	794134.	0.231894
$412$	−647770.	−0.188009
$413$	391101.	0.112827
$414$	1.80836e6	0.518543
$415$	6.46904e6	1.84382
$416$	−2.36422e6	−0.669814
$417$	490391.	0.138103
$418$	−5.96825e6	−1.67073
$419$	−2.23813e6	−0.622802	−0.311401	−	0.950279i	$-0.600798\pi$
$419$	−2.23813e6	−0.622802	−0.311401	+	0.950279i	$0.600798\pi$
$420$	713964.	0.197494
$421$	−4.39012e6	−1.20718	−0.603589	−	0.797296i	$-0.706263\pi$
$421$	−4.39012e6	−1.20718	−0.603589	+	0.797296i	$0.706263\pi$
$422$	6643.78	0.00181608
$423$	−823953.	−0.223899
$424$	4.03745e6	1.09067
$425$	−3.29554e6	−0.885022
$426$	−3.18900e6	−0.851394
$427$	−1.09015e6	−0.289346
$428$	−127413.	−0.0336206
$429$	−5.27720e6	−1.38439
$430$	−4.15667e6	−1.08411
$431$	5.73593e6	1.48734	0.743671	−	0.668546i	$-0.233083\pi$
$431$	5.73593e6	1.48734	0.743671	+	0.668546i	$0.233083\pi$
$432$	898039.	0.231519
$433$	−638791.	−0.163734	−0.0818670	−	0.996643i	$-0.526088\pi$
$433$	−638791.	−0.163734	−0.0818670	+	0.996643i	$0.526088\pi$
$434$	−4.91170e6	−1.25172
$435$	−2.94283e6	−0.745662
$436$	964567.	0.243005
$437$	4.10073e6	1.02721
$438$	3.71981e6	0.926478
$439$	−4.97543e6	−1.23217	−0.616084	−	0.787681i	$-0.711282\pi$
$439$	−4.97543e6	−1.23217	−0.616084	+	0.787681i	$0.711282\pi$
$440$	9.06096e6	2.23122
$441$	−338887.	−0.0829772
$442$	−5.31452e6	−1.29392
$443$	−1.77072e6	−0.428686	−0.214343	−	0.976758i	$-0.568761\pi$
$443$	−1.77072e6	−0.428686	−0.214343	+	0.976758i	$0.568761\pi$
$444$	917408.	0.220854
$445$	−2.47222e6	−0.591815
$446$	4.41292e6	1.05048
$447$	−2.51918e6	−0.596336
$448$	2.13191e6	0.501849
$449$	−4.31307e6	−1.00965	−0.504825	−	0.863222i	$-0.668443\pi$
$449$	−4.31307e6	−1.00965	−0.504825	+	0.863222i	$0.668443\pi$
$450$	−1.52835e6	−0.355789
$451$	−2.26933e6	−0.525358
$452$	−319487.	−0.0735541
$453$	4.73921e6	1.08508
$454$	−46261.2	−0.0105336
$455$	6.48615e6	1.46879
$456$	1.55701e6	0.350654
$457$	−5.37134e6	−1.20307	−0.601537	−	0.798845i	$-0.705445\pi$
$457$	−5.37134e6	−1.20307	−0.601537	+	0.798845i	$0.705445\pi$
$458$	679996.	0.151476
$459$	815907.	0.180763
$460$	2.45994e6	0.542037
$461$	888496.	0.194717	0.0973583	−	0.995249i	$-0.468961\pi$
$461$	888496.	0.194717	0.0973583	+	0.995249i	$0.468961\pi$
$462$	−5.12729e6	−1.11759
$463$	−6.92120e6	−1.50048	−0.750238	−	0.661168i	$-0.770061\pi$
$463$	−6.92120e6	−1.50048	−0.750238	+	0.661168i	$0.770061\pi$
$464$	5.17028e6	1.11486
$465$	4.78345e6	1.02591
$466$	−9.51620e6	−2.03001
$467$	4.60279e6	0.976627	0.488314	−	0.872668i	$-0.337612\pi$
$467$	4.60279e6	0.976627	0.488314	+	0.872668i	$0.337612\pi$
$468$	−543979.	−0.114807
$469$	2.15804e6	0.453030
$470$	−5.07831e6	−1.06041
$471$	1.20420e6	0.250119
$472$	511642.	0.105709
$473$	6.58838e6	1.35402
$474$	2.40701e6	0.492075
$475$	−3.46576e6	−0.704799
$476$	−1.13965e6	−0.230543
$477$	2.22500e6	0.447749
$478$	1.07105e7	2.14407
$479$	6.55474e6	1.30532	0.652660	−	0.757651i	$-0.273653\pi$
$479$	6.55474e6	1.30532	0.652660	+	0.757651i	$0.273653\pi$
$480$	2.23708e6	0.443178
$481$	8.33438e6	1.64252
$482$	6.43121e6	1.26088
$483$	3.52292e6	0.687123
$484$	4.21509e6	0.817888
$485$	1.07192e7	2.06923
$486$	378388.	0.0726687
$487$	5.44521e6	1.04038	0.520190	−	0.854050i	$-0.325861\pi$
$487$	5.44521e6	1.04038	0.520190	+	0.854050i	$0.325861\pi$
$488$	−1.42615e6	−0.271091
$489$	−1.09748e6	−0.207551
$490$	−2.08868e6	−0.392991
$491$	−8.17373e6	−1.53009	−0.765044	−	0.643978i	$-0.777283\pi$
$491$	−8.17373e6	−1.53009	−0.765044	+	0.643978i	$0.777283\pi$
$492$	−233925.	−0.0435676
$493$	4.69742e6	0.870446
$494$	−5.58903e6	−1.03043
$495$	4.99341e6	0.915976
$496$	−8.40406e6	−1.53386
$497$	−6.21258e6	−1.12819
$498$	−4.78885e6	−0.865282
$499$	−3.11680e6	−0.560347	−0.280173	−	0.959949i	$-0.590392\pi$
$499$	−3.11680e6	−0.560347	−0.280173	+	0.959949i	$0.590392\pi$
$500$	127439.	0.0227971
$501$	−1.46942e6	−0.261548
$502$	−5.02410e6	−0.889814
$503$	−2.18435e6	−0.384948	−0.192474	−	0.981302i	$-0.561651\pi$
$503$	−2.18435e6	−0.384948	−0.192474	+	0.981302i	$0.561651\pi$
$504$	1.33762e6	0.234561
$505$	6.37575e6	1.11251
$506$	−1.76659e7	−3.06732
$507$	−1.60025e6	−0.276483
$508$	2.84115e6	0.488466
$509$	−9.83203e6	−1.68209	−0.841044	−	0.540966i	$-0.818059\pi$
$509$	−9.83203e6	−1.68209	−0.841044	+	0.540966i	$0.818059\pi$
$510$	5.02873e6	0.856116
$511$	7.24665e6	1.22768
$512$	1.86368e6	0.314192
$513$	858052.	0.143953
$514$	3.70823e6	0.619097
$515$	5.56834e6	0.925140
$516$	679137.	0.112288
$517$	8.04920e6	1.32442
$518$	8.09763e6	1.32597
$519$	−3.22127e6	−0.524939
$520$	8.48524e6	1.37612
$521$	5.86736e6	0.946997	0.473498	−	0.880795i	$-0.342991\pi$
$521$	5.86736e6	0.946997	0.473498	+	0.880795i	$0.342991\pi$
$522$	2.17849e6	0.349929
$523$	−3.20838e6	−0.512898	−0.256449	−	0.966558i	$-0.582553\pi$
$523$	−3.20838e6	−0.512898	−0.256449	+	0.966558i	$0.582553\pi$
$524$	−1.43123e6	−0.227709
$525$	−2.97742e6	−0.471457
$526$	−9.68107e6	−1.52566
$527$	−7.63545e6	−1.19759
$528$	−8.77295e6	−1.36950
$529$	5.70174e6	0.885866
$530$	1.37135e7	2.12060
$531$	281961.	0.0433963
$532$	−1.19851e6	−0.183596
$533$	−2.12514e6	−0.324018
$534$	1.83011e6	0.277731
$535$	1.09526e6	0.165438
$536$	2.82316e6	0.424448
$537$	894418.	0.133846
$538$	1.19997e7	1.78738
$539$	3.31059e6	0.490833
$540$	514726.	0.0759612
$541$	1.00581e7	1.47748	0.738740	−	0.673990i	$-0.235421\pi$
$541$	1.00581e7	1.47748	0.738740	+	0.673990i	$0.235421\pi$
$542$	1.22104e7	1.78539
$543$	2.26742e6	0.330014
$544$	−3.57088e6	−0.517343
$545$	−8.29157e6	−1.19576
$546$	−4.80151e6	−0.689281
$547$	−1.05803e7	−1.51193	−0.755963	−	0.654615i	$-0.772831\pi$
$547$	−1.05803e7	−1.51193	−0.755963	+	0.654615i	$0.772831\pi$
$548$	−799693.	−0.113755
$549$	−785937.	−0.111290
$550$	1.49305e7	2.10459
$551$	4.94006e6	0.693191
$552$	4.60871e6	0.643772
$553$	4.68915e6	0.652050
$554$	9.07492e6	1.25623
$555$	−7.88619e6	−1.08676
$556$	−493824.	−0.0677462
$557$	2.00697e6	0.274097	0.137048	−	0.990564i	$-0.456238\pi$
$557$	2.00697e6	0.274097	0.137048	+	0.990564i	$0.456238\pi$
$558$	−3.54105e6	−0.481445
$559$	6.16976e6	0.835101
$560$	1.07827e7	1.45298
$561$	−7.97060e6	−1.06926
$562$	−1.54005e7	−2.05681
$563$	9.10656e6	1.21083	0.605415	−	0.795910i	$-0.293007\pi$
$563$	9.10656e6	1.21083	0.605415	+	0.795910i	$0.293007\pi$
$564$	829721.	0.109833
$565$	2.74636e6	0.361940
$566$	−7.86109e6	−1.03144
$567$	737148.	0.0962936
$568$	−8.12735e6	−1.05701
$569$	−8.89813e6	−1.15217	−0.576087	−	0.817388i	$-0.695421\pi$
$569$	−8.89813e6	−1.15217	−0.576087	+	0.817388i	$0.695421\pi$
$570$	5.28848e6	0.681779
$571$	−2.49080e6	−0.319704	−0.159852	−	0.987141i	$-0.551102\pi$
$571$	−2.49080e6	−0.319704	−0.159852	+	0.987141i	$0.551102\pi$
$572$	5.31414e6	0.679114
$573$	−829486.	−0.105541
$574$	−2.06477e6	−0.261572
$575$	−1.02586e7	−1.29395
$576$	1.53698e6	0.193024
$577$	1.14355e7	1.42993	0.714967	−	0.699158i	$-0.246442\pi$
$577$	1.14355e7	1.42993	0.714967	+	0.699158i	$0.246442\pi$
$578$	1.07153e6	0.133409
$579$	1.79588e6	0.222628
$580$	2.96343e6	0.365784
$581$	−9.32927e6	−1.14659
$582$	−7.93515e6	−0.971064
$583$	−2.17361e7	−2.64856
$584$	9.48014e6	1.15022
$585$	4.67614e6	0.564934
$586$	1.37962e7	1.65964
$587$	1.17932e7	1.41266	0.706330	−	0.707882i	$-0.250349\pi$
$587$	1.17932e7	1.41266	0.706330	+	0.707882i	$0.250349\pi$
$588$	341260.	0.0407044
$589$	−8.02985e6	−0.953717
$590$	1.73783e6	0.205530
$591$	318125.	0.0374653
$592$	1.38553e7	1.62484
$593$	−5.74068e6	−0.670388	−0.335194	−	0.942149i	$-0.608802\pi$
$593$	−5.74068e6	−0.670388	−0.335194	+	0.942149i	$0.608802\pi$
$594$	−3.69648e6	−0.429855
$595$	9.79659e6	1.13444
$596$	2.53682e6	0.292532
$597$	840302.	0.0964939
$598$	−1.65434e7	−1.89179
$599$	4.08541e6	0.465231	0.232616	−	0.972569i	$-0.425272\pi$
$599$	4.08541e6	0.465231	0.232616	+	0.972569i	$0.425272\pi$
$600$	−3.89509e6	−0.441712
$601$	−8.71853e6	−0.984593	−0.492297	−	0.870427i	$-0.663842\pi$
$601$	−8.71853e6	−0.984593	−0.492297	+	0.870427i	$0.663842\pi$
$602$	5.99450e6	0.674158
$603$	1.55582e6	0.174247
$604$	−4.77238e6	−0.532284
$605$	−3.62336e7	−4.02461
$606$	−4.71978e6	−0.522084
$607$	5.80502e6	0.639488	0.319744	−	0.947504i	$-0.396403\pi$
$607$	5.80502e6	0.639488	0.319744	+	0.947504i	$0.396403\pi$
$608$	−3.75533e6	−0.411993
$609$	4.24398e6	0.463693
$610$	−4.84401e6	−0.527084
$611$	7.53777e6	0.816845
$612$	−821619.	−0.0886731
$613$	−6.95328e6	−0.747375	−0.373687	−	0.927555i	$-0.621907\pi$
$613$	−6.95328e6	−0.747375	−0.373687	+	0.927555i	$0.621907\pi$
$614$	−4.43299e6	−0.474543
$615$	2.01086e6	0.214384
$616$	−1.30672e7	−1.38749
$617$	3.37898e6	0.357333	0.178667	−	0.983910i	$-0.442822\pi$
$617$	3.37898e6	0.357333	0.178667	+	0.983910i	$0.442822\pi$
$618$	−4.12208e6	−0.434156
$619$	−3.45946e6	−0.362896	−0.181448	−	0.983401i	$-0.558078\pi$
$619$	−3.45946e6	−0.362896	−0.181448	+	0.983401i	$0.558078\pi$
$620$	−4.81693e6	−0.503258
$621$	2.53982e6	0.264286
$622$	−1.43288e7	−1.48502
$623$	3.56529e6	0.368022
$624$	−8.21553e6	−0.844645
$625$	−1.02971e7	−1.05442
$626$	5.08478e6	0.518604
$627$	−8.38232e6	−0.851521
$628$	−1.21263e6	−0.122696
$629$	1.25881e7	1.26863
$630$	4.54331e6	0.456059
$631$	−1.43190e7	−1.43166	−0.715830	−	0.698275i	$-0.753951\pi$
$631$	−1.43190e7	−1.43166	−0.715830	+	0.698275i	$0.753951\pi$
$632$	6.13439e6	0.610912
$633$	9331.09	0.000925600 0
$634$	−5.29147e6	−0.522821
$635$	−2.44230e7	−2.40361
$636$	−2.24058e6	−0.219643
$637$	3.10024e6	0.302724
$638$	−2.12817e7	−2.06993
$639$	−4.47891e6	−0.433930
$640$	1.74270e7	1.68180
$641$	−1.51966e7	−1.46083	−0.730417	−	0.683002i	$-0.760674\pi$
$641$	−1.51966e7	−1.46083	−0.730417	+	0.683002i	$0.760674\pi$
$642$	−810793.	−0.0776377
$643$	−453468.	−0.0432533	−0.0216267	−	0.999766i	$-0.506885\pi$
$643$	−453468.	−0.0432533	−0.0216267	+	0.999766i	$0.506885\pi$
$644$	−3.54758e6	−0.337068
$645$	−5.83798e6	−0.552539
$646$	−8.44160e6	−0.795872
$647$	−1.54955e7	−1.45527	−0.727637	−	0.685962i	$-0.759381\pi$
$647$	−1.54955e7	−1.45527	−0.727637	+	0.685962i	$0.759381\pi$
$648$	964344.	0.0902183
$649$	−2.75448e6	−0.256701
$650$	1.39818e7	1.29802
$651$	−6.89841e6	−0.637964
$652$	1.10517e6	0.101814
$653$	−1.29624e6	−0.118960	−0.0594802	−	0.998229i	$-0.518944\pi$
$653$	−1.29624e6	−0.118960	−0.0594802	+	0.998229i	$0.518944\pi$
$654$	6.13802e6	0.561156
$655$	1.23030e7	1.12049
$656$	−3.53288e6	−0.320531
$657$	5.22441e6	0.472198
$658$	7.32365e6	0.659421
$659$	−2.00979e7	−1.80275	−0.901376	−	0.433037i	$-0.857442\pi$
$659$	−2.00979e7	−1.80275	−0.901376	+	0.433037i	$0.857442\pi$
$660$	−5.02836e6	−0.449332
$661$	1.96942e7	1.75321	0.876606	−	0.481208i	$-0.159802\pi$
$661$	1.96942e7	1.75321	0.876606	+	0.481208i	$0.159802\pi$
$662$	−1.73483e7	−1.53855
$663$	−7.46416e6	−0.659473
$664$	−1.22046e7	−1.07425
$665$	1.03026e7	0.903428
$666$	5.83792e6	0.510003
$667$	1.46225e7	1.27264
$668$	1.47970e6	0.128302
$669$	6.19788e6	0.535399
$670$	9.58906e6	0.825257
$671$	7.67782e6	0.658312
$672$	−3.22619e6	−0.275592
$673$	−1.40959e7	−1.19965	−0.599826	−	0.800130i	$-0.704764\pi$
$673$	−1.40959e7	−1.19965	−0.599826	+	0.800130i	$0.704764\pi$
$674$	2.02565e7	1.71757
$675$	−2.14655e6	−0.181335
$676$	1.61146e6	0.135629
$677$	−9.59108e6	−0.804259	−0.402130	−	0.915583i	$-0.631730\pi$
$677$	−9.59108e6	−0.804259	−0.402130	+	0.915583i	$0.631730\pi$
$678$	−2.03305e6	−0.169853
$679$	−1.54587e7	−1.28676
$680$	1.28160e7	1.06287
$681$	−64973.2	−0.00536867
$682$	3.45925e7	2.84788
$683$	−4.16302e6	−0.341473	−0.170737	−	0.985317i	$-0.554615\pi$
$683$	−4.16302e6	−0.341473	−0.170737	+	0.985317i	$0.554615\pi$
$684$	−864059.	−0.0706160
$685$	6.87430e6	0.559760
$686$	1.51126e7	1.22611
$687$	955044.	0.0772025
$688$	1.02568e7	0.826113
$689$	−2.03550e7	−1.63351
$690$	1.56538e7	1.25169
$691$	2.14081e7	1.70562	0.852810	−	0.522221i	$-0.174896\pi$
$691$	2.14081e7	1.70562	0.852810	+	0.522221i	$0.174896\pi$
$692$	3.24382e6	0.257508
$693$	−7.20121e6	−0.569603
$694$	−2.26324e6	−0.178374
$695$	4.24499e6	0.333361
$696$	5.55201e6	0.434438
$697$	−3.20978e6	−0.250261
$698$	1.30881e7	1.01680
$699$	−1.33654e7	−1.03464
$700$	2.99826e6	0.231273
$701$	1.08299e7	0.832396	0.416198	−	0.909274i	$-0.363362\pi$
$701$	1.08299e7	0.832396	0.416198	+	0.909274i	$0.363362\pi$
$702$	−3.46161e6	−0.265116
$703$	1.32384e7	1.01029
$704$	−1.50148e7	−1.14179
$705$	−7.13242e6	−0.540460
$706$	−2.50276e7	−1.88976
$707$	−9.19473e6	−0.691816
$708$	−283935.	−0.0212880
$709$	1.98972e7	1.48654	0.743268	−	0.668993i	$-0.233275\pi$
$709$	1.98972e7	1.48654	0.743268	+	0.668993i	$0.233275\pi$
$710$	−2.76051e7	−2.05515
$711$	3.38060e6	0.250796
$712$	4.66414e6	0.344803
$713$	−2.37682e7	−1.75095
$714$	−7.25214e6	−0.532378
$715$	−4.56812e7	−3.34174
$716$	−900679.	−0.0656580
$717$	1.50427e7	1.09277
$718$	2.74018e7	1.98367
$719$	4.44979e6	0.321009	0.160504	−	0.987035i	$-0.448688\pi$
$719$	4.44979e6	0.321009	0.160504	+	0.987035i	$0.448688\pi$
$720$	7.77373e6	0.558854
$721$	−8.03033e6	−0.575301
$722$	6.98930e6	0.498989
$723$	9.03254e6	0.642635
$724$	−2.28329e6	−0.161888
$725$	−1.23583e7	−0.873200
$726$	2.68227e7	1.88869
$727$	2.41778e7	1.69661	0.848304	−	0.529510i	$-0.177624\pi$
$727$	2.41778e7	1.69661	0.848304	+	0.529510i	$0.177624\pi$
$728$	−1.22369e7	−0.855744
$729$	531441.	0.0370370
$730$	3.21999e7	2.23639
$731$	9.31872e6	0.645005
$732$	791438.	0.0545933
$733$	−1.45075e7	−0.997318	−0.498659	−	0.866798i	$-0.666174\pi$
$733$	−1.45075e7	−0.997318	−0.498659	+	0.866798i	$0.666174\pi$
$734$	−3.18660e7	−2.18317
$735$	−2.93352e6	−0.200296
$736$	−1.11157e7	−0.756385
$737$	−1.51988e7	−1.03072
$738$	−1.48858e6	−0.100608
$739$	9.82939e6	0.662087	0.331044	−	0.943615i	$-0.392599\pi$
$739$	9.82939e6	0.662087	0.331044	+	0.943615i	$0.392599\pi$
$740$	7.94139e6	0.533111
$741$	−7.84972e6	−0.525180
$742$	−1.97768e7	−1.31870
$743$	1.48739e7	0.988447	0.494223	−	0.869335i	$-0.335452\pi$
$743$	1.48739e7	0.988447	0.494223	+	0.869335i	$0.335452\pi$
$744$	−9.02456e6	−0.597714
$745$	−2.18069e7	−1.43947
$746$	1.01582e7	0.668296
$747$	−6.72586e6	−0.441008
$748$	8.02640e6	0.524526
$749$	−1.57953e6	−0.102878
$750$	810960.	0.0526437
$751$	−9.91059e6	−0.641209	−0.320605	−	0.947213i	$-0.603886\pi$
$751$	−9.91059e6	−0.641209	−0.320605	+	0.947213i	$0.603886\pi$
$752$	1.25310e7	0.808054
$753$	−7.05628e6	−0.453511
$754$	−1.99295e7	−1.27664
$755$	4.10242e7	2.61922
$756$	−742308.	−0.0472367
$757$	4.84319e6	0.307179	0.153590	−	0.988135i	$-0.450917\pi$
$757$	4.84319e6	0.307179	0.153590	+	0.988135i	$0.450917\pi$
$758$	7.79449e6	0.492736
$759$	−2.48115e7	−1.56332
$760$	1.34780e7	0.846430
$761$	2.91931e7	1.82734	0.913668	−	0.406462i	$-0.133237\pi$
$761$	2.91931e7	1.82734	0.913668	+	0.406462i	$0.133237\pi$
$762$	1.80796e7	1.12798
$763$	1.19576e7	0.743590
$764$	835293.	0.0517732
$765$	7.06277e6	0.436336
$766$	−1.97508e7	−1.21622
$767$	−2.57946e6	−0.158322
$768$	−7.43591e6	−0.454916
$769$	−2.52988e6	−0.154271	−0.0771355	−	0.997021i	$-0.524577\pi$
$769$	−2.52988e6	−0.154271	−0.0771355	+	0.997021i	$0.524577\pi$
$770$	−4.43836e7	−2.69771
$771$	5.20815e6	0.315535
$772$	−1.80845e6	−0.109210
$773$	5.94551e6	0.357882	0.178941	−	0.983860i	$-0.442733\pi$
$773$	5.94551e6	0.357882	0.178941	+	0.983860i	$0.442733\pi$
$774$	4.32169e6	0.259299
$775$	2.00879e7	1.20138
$776$	−2.02232e7	−1.20558
$777$	1.13730e7	0.675807
$778$	3.40471e7	2.01665
$779$	−3.37558e6	−0.199299
$780$	−4.70887e6	−0.277128
$781$	4.37545e7	2.56682
$782$	−2.49870e7	−1.46116
$783$	3.05966e6	0.178348
$784$	5.15393e6	0.299466
$785$	1.04240e7	0.603752
$786$	−9.10760e6	−0.525833
$787$	2.81502e7	1.62011	0.810055	−	0.586354i	$-0.199437\pi$
$787$	2.81502e7	1.62011	0.810055	+	0.586354i	$0.199437\pi$
$788$	−320352.	−0.0183786
$789$	−1.35969e7	−0.777585
$790$	2.08359e7	1.18780
$791$	−3.96064e6	−0.225073
$792$	−9.42068e6	−0.533666
$793$	7.18998e6	0.406018
$794$	1.29623e7	0.729677
$795$	1.92604e7	1.08080
$796$	−846185.	−0.0473350
$797$	−1.13649e7	−0.633754	−0.316877	−	0.948467i	$-0.602634\pi$
$797$	−1.13649e7	−0.633754	−0.316877	+	0.948467i	$0.602634\pi$
$798$	−7.62674e6	−0.423967
$799$	1.13849e7	0.630905
$800$	9.39453e6	0.518980
$801$	2.57036e6	0.141551
$802$	1.96199e7	1.07711
$803$	−5.10373e7	−2.79318
$804$	−1.56671e6	−0.0854768
$805$	3.04956e7	1.65862
$806$	3.23946e7	1.75645
$807$	1.68535e7	0.910972
$808$	−1.20286e7	−0.648168
$809$	−7.77539e6	−0.417687	−0.208844	−	0.977949i	$-0.566970\pi$
$809$	−7.77539e6	−0.417687	−0.208844	+	0.977949i	$0.566970\pi$
$810$	3.27546e6	0.175412
$811$	2.24931e7	1.20087	0.600436	−	0.799672i	$-0.294994\pi$
$811$	2.24931e7	1.20087	0.600436	+	0.799672i	$0.294994\pi$
$812$	−4.27369e6	−0.227464
$813$	1.71494e7	0.909960
$814$	−5.70307e7	−3.01681
$815$	−9.50018e6	−0.501000
$816$	−1.24086e7	−0.652376
$817$	9.80007e6	0.513658
$818$	1.36224e7	0.711821
$819$	−6.74365e6	−0.351306
$820$	−2.02493e6	−0.105166
$821$	−2.02402e7	−1.04799	−0.523994	−	0.851722i	$-0.675559\pi$
$821$	−2.02402e7	−1.04799	−0.523994	+	0.851722i	$0.675559\pi$
$822$	−5.08885e6	−0.262688
$823$	−1.76518e7	−0.908427	−0.454214	−	0.890893i	$-0.650080\pi$
$823$	−1.76518e7	−0.908427	−0.454214	+	0.890893i	$0.650080\pi$
$824$	−1.05054e7	−0.539005
$825$	2.09696e7	1.07264
$826$	−2.50619e6	−0.127810
$827$	2.34135e7	1.19042	0.595212	−	0.803568i	$-0.297068\pi$
$827$	2.34135e7	1.19042	0.595212	+	0.803568i	$0.297068\pi$
$828$	−2.55760e6	−0.129645
$829$	−2.17139e7	−1.09736	−0.548682	−	0.836031i	$-0.684870\pi$
$829$	−2.17139e7	−1.09736	−0.548682	+	0.836031i	$0.684870\pi$
$830$	−4.14539e7	−2.08867
$831$	1.27456e7	0.640262
$832$	−1.40608e7	−0.704207
$833$	4.68256e6	0.233814
$834$	−3.14245e6	−0.156442
$835$	−1.27198e7	−0.631340
$836$	8.44099e6	0.417713
$837$	−4.97335e6	−0.245378
$838$	1.43420e7	0.705505
$839$	3.27814e7	1.60776	0.803882	−	0.594789i	$-0.202764\pi$
$839$	3.27814e7	1.60776	0.803882	+	0.594789i	$0.202764\pi$
$840$	1.15789e7	0.566197
$841$	−2.89577e6	−0.141180
$842$	2.81321e7	1.36748
$843$	−2.16298e7	−1.04829
$844$	−9396.41	−0.000454052 0
$845$	−1.38523e7	−0.667393
$846$	5.27993e6	0.253631
$847$	5.22541e7	2.50272
$848$	−3.38387e7	−1.61593
$849$	−1.10408e7	−0.525691
$850$	2.11179e7	1.00255
$851$	3.91853e7	1.85481
$852$	4.51026e6	0.212864
$853$	1.33583e7	0.628606	0.314303	−	0.949323i	$-0.398229\pi$
$853$	1.33583e7	0.628606	0.314303	+	0.949323i	$0.398229\pi$
$854$	6.98574e6	0.327769
$855$	7.42759e6	0.347482
$856$	−2.06635e6	−0.0963873
$857$	−2.16518e7	−1.00703	−0.503513	−	0.863987i	$-0.667960\pi$
$857$	−2.16518e7	−1.00703	−0.503513	+	0.863987i	$0.667960\pi$
$858$	3.38165e7	1.56823
$859$	1.28214e7	0.592859	0.296429	−	0.955055i	$-0.404204\pi$
$859$	1.28214e7	0.592859	0.296429	+	0.955055i	$0.404204\pi$
$860$	5.87884e6	0.271048
$861$	−2.89994e6	−0.133316
$862$	−3.67561e7	−1.68485
$863$	4.17964e6	0.191035	0.0955173	−	0.995428i	$-0.469549\pi$
$863$	4.17964e6	0.191035	0.0955173	+	0.995428i	$0.469549\pi$
$864$	−2.32589e6	−0.106000
$865$	−2.78844e7	−1.26713
$866$	4.09340e6	0.185477
$867$	1.50495e6	0.0679944
$868$	6.94670e6	0.312953
$869$	−3.30251e7	−1.48353
$870$	1.88578e7	0.844681
$871$	−1.42331e7	−0.635703
$872$	1.56431e7	0.696676
$873$	−1.11448e7	−0.494922
$874$	−2.62776e7	−1.16361
$875$	1.57985e6	0.0697584
$876$	−5.26099e6	−0.231636
$877$	−1.69571e7	−0.744481	−0.372240	−	0.928136i	$-0.621410\pi$
$877$	−1.69571e7	−0.744481	−0.372240	+	0.928136i	$0.621410\pi$
$878$	3.18828e7	1.39579
$879$	1.93765e7	0.845870
$880$	−7.59416e7	−3.30577
$881$	3.38299e6	0.146846	0.0734229	−	0.997301i	$-0.476608\pi$
$881$	3.38299e6	0.146846	0.0734229	+	0.997301i	$0.476608\pi$
$882$	2.17160e6	0.0939960
$883$	−9.00396e6	−0.388626	−0.194313	−	0.980940i	$-0.562248\pi$
$883$	−9.00396e6	−0.388626	−0.194313	+	0.980940i	$0.562248\pi$
$884$	7.51641e6	0.323504
$885$	2.44075e6	0.104753
$886$	1.13468e7	0.485612
$887$	−5.68826e6	−0.242756	−0.121378	−	0.992606i	$-0.538731\pi$
$887$	−5.68826e6	−0.242756	−0.121378	+	0.992606i	$0.538731\pi$
$888$	1.48783e7	0.633169
$889$	3.52214e7	1.49469
$890$	1.58421e7	0.670404
$891$	−5.19165e6	−0.219084
$892$	−6.24126e6	−0.262640
$893$	1.19730e7	0.502429
$894$	1.61430e7	0.675525
$895$	7.74239e6	0.323085
$896$	−2.51322e7	−1.04583
$897$	−2.32350e7	−0.964188
$898$	2.76383e7	1.14372
$899$	−2.86330e7	−1.18159
$900$	2.16157e6	0.0889536
$901$	−3.07439e7	−1.26167
$902$	1.45419e7	0.595122
$903$	8.41919e6	0.343598
$904$	−5.18135e6	−0.210873
$905$	1.96275e7	0.796608
$906$	−3.03691e7	−1.22917
$907$	−6.31035e6	−0.254704	−0.127352	−	0.991858i	$-0.540648\pi$
$907$	−6.31035e6	−0.254704	−0.127352	+	0.991858i	$0.540648\pi$
$908$	65428.0	0.00263360
$909$	−6.62887e6	−0.266091
$910$	−4.15635e7	−1.66383
$911$	4.64931e7	1.85606	0.928031	−	0.372504i	$-0.121501\pi$
$911$	4.64931e7	1.85606	0.928031	+	0.372504i	$0.121501\pi$
$912$	−1.30496e7	−0.519528
$913$	6.57050e7	2.60868
$914$	3.44198e7	1.36283
$915$	−6.80333e6	−0.268639
$916$	−961730.	−0.0378717
$917$	−1.77427e7	−0.696783
$918$	−5.22837e6	−0.204767
$919$	6.67252e6	0.260616	0.130308	−	0.991474i	$-0.458403\pi$
$919$	6.67252e6	0.260616	0.130308	+	0.991474i	$0.458403\pi$
$920$	3.98946e7	1.55398
$921$	−6.22606e6	−0.241860
$922$	−5.69352e6	−0.220573
$923$	4.09744e7	1.58310
$924$	7.25162e6	0.279418
$925$	−3.31177e7	−1.27264
$926$	4.43513e7	1.69973
$927$	−5.78940e6	−0.221276
$928$	−1.33909e7	−0.510433
$929$	2.72214e7	1.03483	0.517417	−	0.855734i	$-0.326894\pi$
$929$	2.72214e7	1.03483	0.517417	+	0.855734i	$0.326894\pi$
$930$	−3.06525e7	−1.16214
$931$	4.92444e6	0.186201
$932$	1.34589e7	0.507540
$933$	−2.01246e7	−0.756872
$934$	−2.94949e7	−1.10632
$935$	−6.89962e7	−2.58105
$936$	−8.82211e6	−0.329142
$937$	4.62771e7	1.72194	0.860969	−	0.508658i	$-0.169858\pi$
$937$	4.62771e7	1.72194	0.860969	+	0.508658i	$0.169858\pi$
$938$	−1.38288e7	−0.513189
$939$	7.14149e6	0.264317
$940$	7.18234e6	0.265123
$941$	3.52404e7	1.29738	0.648689	−	0.761054i	$-0.275318\pi$
$941$	3.52404e7	1.29738	0.648689	+	0.761054i	$0.275318\pi$
$942$	−7.71657e6	−0.283333
$943$	−9.99164e6	−0.365896
$944$	−4.28817e6	−0.156618
$945$	6.38101e6	0.232439
$946$	−4.22186e7	−1.53383
$947$	−2.39436e7	−0.867589	−0.433795	−	0.901012i	$-0.642826\pi$
$947$	−2.39436e7	−0.867589	−0.433795	+	0.901012i	$0.642826\pi$
$948$	−3.40427e6	−0.123028
$949$	−4.77945e7	−1.72271
$950$	2.22088e7	0.798391
$951$	−7.43179e6	−0.266466
$952$	−1.84825e7	−0.660949
$953$	3.30839e7	1.18000	0.590002	−	0.807401i	$-0.299127\pi$
$953$	3.30839e7	1.18000	0.590002	+	0.807401i	$0.299127\pi$
$954$	−1.42579e7	−0.507207
$955$	−7.18032e6	−0.254762
$956$	−1.51480e7	−0.536055
$957$	−2.98899e7	−1.05498
$958$	−4.20031e7	−1.47866
$959$	−9.91371e6	−0.348089
$960$	1.33046e7	0.465934
$961$	1.79126e7	0.625678
$962$	−5.34070e7	−1.86063
$963$	−1.13875e6	−0.0395696
$964$	−9.09577e6	−0.315244
$965$	1.55457e7	0.537393
$966$	−2.25750e7	−0.778368
$967$	−2.27815e6	−0.0783459	−0.0391729	−	0.999232i	$-0.512472\pi$
$967$	−2.27815e6	−0.0783459	−0.0391729	+	0.999232i	$0.512472\pi$
$968$	6.83592e7	2.34482
$969$	−1.18561e7	−0.405632
$970$	−6.86894e7	−2.34401
$971$	321611.	0.0109467	0.00547334	−	0.999985i	$-0.498258\pi$
$971$	321611.	0.0109467	0.00547334	+	0.999985i	$0.498258\pi$
$972$	−535161.	−0.0181685
$973$	−6.12188e6	−0.207302
$974$	−3.48931e7	−1.17854
$975$	1.96373e7	0.661560
$976$	1.19528e7	0.401648
$977$	−1.30739e7	−0.438195	−0.219098	−	0.975703i	$-0.570311\pi$
$977$	−1.30739e7	−0.438195	−0.219098	+	0.975703i	$0.570311\pi$
$978$	7.03272e6	0.235113
$979$	−2.51099e7	−0.837314
$980$	2.95406e6	0.0982549
$981$	8.62075e6	0.286004
$982$	5.23776e7	1.73327
$983$	−1.97078e7	−0.650509	−0.325255	−	0.945626i	$-0.605450\pi$
$983$	−1.97078e7	−0.650509	−0.325255	+	0.945626i	$0.605450\pi$
$984$	−3.79373e6	−0.124905
$985$	2.75380e6	0.0904360
$986$	−3.01013e7	−0.986035
$987$	1.02860e7	0.336087
$988$	7.90467e6	0.257627
$989$	2.90080e7	0.943034
$990$	−3.19980e7	−1.03761
$991$	−1.51237e7	−0.489185	−0.244592	−	0.969626i	$-0.578654\pi$
$991$	−1.51237e7	−0.489185	−0.244592	+	0.969626i	$0.578654\pi$
$992$	2.17663e7	0.702271
$993$	−2.43654e7	−0.784154
$994$	3.98105e7	1.27800
$995$	7.27394e6	0.232923
$996$	6.77294e6	0.216336
$997$	4.33699e7	1.38182	0.690908	−	0.722943i	$-0.257211\pi$
$997$	4.33699e7	1.38182	0.690908	+	0.722943i	$0.257211\pi$
$998$	1.99726e7	0.634757
$999$	8.19927e6	0.259933

Twists

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

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

\(f(q)\)	\(=\)	\(q-6.40804 q^{2} -9.00000 q^{3} +9.06300 q^{4} -77.9071 q^{5} +57.6724 q^{6} +112.353 q^{7} +146.981 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.40804 q^{2} -9.00000 q^{3} +9.06300 q^{4} -77.9071 q^{5} +57.6724 q^{6} +112.353 q^{7} +146.981 q^{8} +81.0000 q^{9} +499.232 q^{10} -791.290 q^{11} -81.5670 q^{12} -741.012 q^{13} -719.963 q^{14} +701.163 q^{15} -1231.88 q^{16} -1119.21 q^{17} -519.051 q^{18} -1177.03 q^{19} -706.072 q^{20} -1011.18 q^{21} +5070.62 q^{22} -3483.97 q^{23} -1322.83 q^{24} +2944.51 q^{25} +4748.44 q^{26} -729.000 q^{27} +1018.26 q^{28} -4197.07 q^{29} -4493.09 q^{30} +6822.15 q^{31} +3190.53 q^{32} +7121.61 q^{33} +7171.97 q^{34} -8753.09 q^{35} +734.103 q^{36} -11247.3 q^{37} +7542.43 q^{38} +6669.11 q^{39} -11450.9 q^{40} +2867.88 q^{41} +6479.67 q^{42} -8326.13 q^{43} -7171.46 q^{44} -6310.47 q^{45} +22325.5 q^{46} -10172.3 q^{47} +11086.9 q^{48} -4183.80 q^{49} -18868.5 q^{50} +10072.9 q^{51} -6715.79 q^{52} +27469.2 q^{53} +4671.46 q^{54} +61647.0 q^{55} +16513.8 q^{56} +10593.2 q^{57} +26895.0 q^{58} +3481.00 q^{59} +6354.65 q^{60} -9702.92 q^{61} -43716.6 q^{62} +9100.60 q^{63} +18975.1 q^{64} +57730.1 q^{65} -45635.5 q^{66} +19207.6 q^{67} -10143.4 q^{68} +31355.8 q^{69} +56090.2 q^{70} -55295.1 q^{71} +11905.5 q^{72} +64498.9 q^{73} +72073.1 q^{74} -26500.6 q^{75} -10667.4 q^{76} -88903.8 q^{77} -42735.9 q^{78} +41735.8 q^{79} +95972.0 q^{80} +6561.00 q^{81} -18377.5 q^{82} -83035.3 q^{83} -9164.30 q^{84} +87194.7 q^{85} +53354.2 q^{86} +37773.6 q^{87} -116305. q^{88} +31732.9 q^{89} +40437.8 q^{90} -83255.0 q^{91} -31575.3 q^{92} -61399.4 q^{93} +65184.3 q^{94} +91698.6 q^{95} -28714.7 q^{96} -137590. q^{97} +26809.9 q^{98} -64094.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 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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