LMFDB - Embedded newform 177.6.a.d.1.4

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			1.4
Root			$-6.29094$ 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)

$f(q)$	$=$	$q-6.29094 q^{2} -9.00000 q^{3} +7.57589 q^{4} +82.0909 q^{5} +56.6184 q^{6} +51.5315 q^{7} +153.651 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.29094 q^{2} -9.00000 q^{3} +7.57589 q^{4} +82.0909 q^{5} +56.6184 q^{6} +51.5315 q^{7} +153.651 q^{8} +81.0000 q^{9} -516.429 q^{10} +677.894 q^{11} -68.1830 q^{12} +290.798 q^{13} -324.182 q^{14} -738.818 q^{15} -1209.03 q^{16} +1791.65 q^{17} -509.566 q^{18} -766.617 q^{19} +621.912 q^{20} -463.784 q^{21} -4264.59 q^{22} -3880.75 q^{23} -1382.85 q^{24} +3613.92 q^{25} -1829.39 q^{26} -729.000 q^{27} +390.397 q^{28} -4722.12 q^{29} +4647.86 q^{30} +9418.62 q^{31} +2689.14 q^{32} -6101.04 q^{33} -11271.2 q^{34} +4230.27 q^{35} +613.647 q^{36} -10201.3 q^{37} +4822.74 q^{38} -2617.19 q^{39} +12613.3 q^{40} +13038.5 q^{41} +2917.64 q^{42} +21726.5 q^{43} +5135.65 q^{44} +6649.36 q^{45} +24413.5 q^{46} +3799.78 q^{47} +10881.3 q^{48} -14151.5 q^{49} -22734.9 q^{50} -16124.9 q^{51} +2203.06 q^{52} -5749.98 q^{53} +4586.09 q^{54} +55648.9 q^{55} +7917.85 q^{56} +6899.55 q^{57} +29706.5 q^{58} +3481.00 q^{59} -5597.21 q^{60} -34546.5 q^{61} -59252.0 q^{62} +4174.06 q^{63} +21771.9 q^{64} +23871.9 q^{65} +38381.3 q^{66} +48614.6 q^{67} +13573.4 q^{68} +34926.7 q^{69} -26612.4 q^{70} +40147.1 q^{71} +12445.7 q^{72} -22800.3 q^{73} +64175.9 q^{74} -32525.2 q^{75} -5807.81 q^{76} +34932.9 q^{77} +16464.6 q^{78} -23093.2 q^{79} -99250.7 q^{80} +6561.00 q^{81} -82024.5 q^{82} -66765.7 q^{83} -3513.58 q^{84} +147079. q^{85} -136680. q^{86} +42499.0 q^{87} +104159. q^{88} -40387.5 q^{89} -41830.7 q^{90} +14985.3 q^{91} -29400.1 q^{92} -84767.6 q^{93} -23904.2 q^{94} -62932.3 q^{95} -24202.3 q^{96} +75030.3 q^{97} +89026.2 q^{98} +54909.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.29094	−1.11209	−0.556046	−	0.831152i	$-0.687682\pi$
$2$	−6.29094	−1.11209	−0.556046	+	0.831152i	$0.687682\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	7.57589	0.236747
$5$	82.0909	1.46849	0.734243	−	0.678886i	$-0.237537\pi$
$5$	82.0909	1.46849	0.734243	+	0.678886i	$0.237537\pi$
$6$	56.6184	0.642066
$7$	51.5315	0.397492	0.198746	−	0.980051i	$-0.436313\pi$
$7$	51.5315	0.397492	0.198746	+	0.980051i	$0.436313\pi$
$8$	153.651	0.848807
$9$	81.0000	0.333333
$10$	−516.429	−1.63309
$11$	677.894	1.68920	0.844598	−	0.535402i	$-0.179840\pi$
$11$	677.894	1.68920	0.844598	+	0.535402i	$0.179840\pi$
$12$	−68.1830	−0.136686
$13$	290.798	0.477236	0.238618	−	0.971113i	$-0.423306\pi$
$13$	290.798	0.477236	0.238618	+	0.971113i	$0.423306\pi$
$14$	−324.182	−0.442047
$15$	−738.818	−0.847831
$16$	−1209.03	−1.18070
$17$	1791.65	1.50360	0.751800	−	0.659392i	$-0.229186\pi$
$17$	1791.65	1.50360	0.751800	+	0.659392i	$0.229186\pi$
$18$	−509.566	−0.370697
$19$	−766.617	−0.487186	−0.243593	−	0.969878i	$-0.578326\pi$
$19$	−766.617	−0.487186	−0.243593	+	0.969878i	$0.578326\pi$
$20$	621.912	0.347659
$21$	−463.784	−0.229492
$22$	−4264.59	−1.87854
$23$	−3880.75	−1.52966	−0.764831	−	0.644231i	$-0.777178\pi$
$23$	−3880.75	−1.52966	−0.764831	+	0.644231i	$0.777178\pi$
$24$	−1382.85	−0.490059
$25$	3613.92	1.15645
$26$	−1829.39	−0.530730
$27$	−729.000	−0.192450
$28$	390.397	0.0941048
$29$	−4722.12	−1.04266	−0.521329	−	0.853356i	$-0.674563\pi$
$29$	−4722.12	−1.04266	−0.521329	+	0.853356i	$0.674563\pi$
$30$	4647.86	0.942866
$31$	9418.62	1.76029	0.880143	−	0.474709i	$-0.157447\pi$
$31$	9418.62	1.76029	0.880143	+	0.474709i	$0.157447\pi$
$32$	2689.14	0.464236
$33$	−6101.04	−0.975257
$34$	−11271.2	−1.67214
$35$	4230.27	0.583711
$36$	613.647	0.0789155
$37$	−10201.3	−1.22505	−0.612523	−	0.790453i	$-0.709845\pi$
$37$	−10201.3	−1.22505	−0.612523	+	0.790453i	$0.709845\pi$
$38$	4822.74	0.541795
$39$	−2617.19	−0.275533
$40$	12613.3	1.24646
$41$	13038.5	1.21135	0.605674	−	0.795713i	$-0.292904\pi$
$41$	13038.5	1.21135	0.605674	+	0.795713i	$0.292904\pi$
$42$	2917.64	0.255216
$43$	21726.5	1.79192	0.895961	−	0.444132i	$-0.146488\pi$
$43$	21726.5	1.79192	0.895961	+	0.444132i	$0.146488\pi$
$44$	5135.65	0.399911
$45$	6649.36	0.489496
$46$	24413.5	1.70112
$47$	3799.78	0.250908	0.125454	−	0.992099i	$-0.459961\pi$
$47$	3799.78	0.250908	0.125454	+	0.992099i	$0.459961\pi$
$48$	10881.3	0.681676
$49$	−14151.5	−0.842000
$50$	−22734.9	−1.28608
$51$	−16124.9	−0.868103
$52$	2203.06	0.112984
$53$	−5749.98	−0.281175	−0.140588	−	0.990068i	$-0.544899\pi$
$53$	−5749.98	−0.281175	−0.140588	+	0.990068i	$0.544899\pi$
$54$	4586.09	0.214022
$55$	55648.9	2.48056
$56$	7917.85	0.337394
$57$	6899.55	0.281277
$58$	29706.5	1.15953
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−5597.21	−0.200721
$61$	−34546.5	−1.18872	−0.594359	−	0.804200i	$-0.702594\pi$
$61$	−34546.5	−1.18872	−0.594359	+	0.804200i	$0.702594\pi$
$62$	−59252.0	−1.95760
$63$	4174.06	0.132497
$64$	21771.9	0.664425
$65$	23871.9	0.700815
$66$	38381.3	1.08457
$67$	48614.6	1.32306	0.661530	−	0.749919i	$-0.269908\pi$
$67$	48614.6	1.32306	0.661530	+	0.749919i	$0.269908\pi$
$68$	13573.4	0.355972
$69$	34926.7	0.883151
$70$	−26612.4	−0.649140
$71$	40147.1	0.945167	0.472583	−	0.881286i	$-0.343322\pi$
$71$	40147.1	0.945167	0.472583	+	0.881286i	$0.343322\pi$
$72$	12445.7	0.282936
$73$	−22800.3	−0.500765	−0.250382	−	0.968147i	$-0.580556\pi$
$73$	−22800.3	−0.500765	−0.250382	+	0.968147i	$0.580556\pi$
$74$	64175.9	1.36236
$75$	−32525.2	−0.667679
$76$	−5807.81	−0.115340
$77$	34932.9	0.671441
$78$	16464.6	0.306417
$79$	−23093.2	−0.416310	−0.208155	−	0.978096i	$-0.566746\pi$
$79$	−23093.2	−0.416310	−0.208155	+	0.978096i	$0.566746\pi$
$80$	−99250.7	−1.73384
$81$	6561.00	0.111111
$82$	−82024.5	−1.34713
$83$	−66765.7	−1.06380	−0.531898	−	0.846808i	$-0.678521\pi$
$83$	−66765.7	−1.06380	−0.531898	+	0.846808i	$0.678521\pi$
$84$	−3513.58	−0.0543314
$85$	147079.	2.20802
$86$	−136680.	−1.99278
$87$	42499.0	0.601978
$88$	104159.	1.43380
$89$	−40387.5	−0.540470	−0.270235	−	0.962794i	$-0.587101\pi$
$89$	−40387.5	−0.540470	−0.270235	+	0.962794i	$0.587101\pi$
$90$	−41830.7	−0.544364
$91$	14985.3	0.189698
$92$	−29400.1	−0.362142
$93$	−84767.6	−1.01630
$94$	−23904.2	−0.279032
$95$	−62932.3	−0.715426
$96$	−24202.3	−0.268027
$97$	75030.3	0.809669	0.404835	−	0.914390i	$-0.367329\pi$
$97$	75030.3	0.809669	0.404835	+	0.914390i	$0.367329\pi$
$98$	89026.2	0.936381
$99$	54909.4	0.563065
$100$	27378.6	0.273786
$101$	1376.06	0.0134225	0.00671124	−	0.999977i	$-0.497864\pi$
$101$	1376.06	0.0134225	0.00671124	+	0.999977i	$0.497864\pi$
$102$	101441.	0.965410
$103$	151296.	1.40518	0.702592	−	0.711592i	$-0.252026\pi$
$103$	151296.	1.40518	0.702592	+	0.711592i	$0.252026\pi$
$104$	44681.3	0.405082
$105$	−38072.4	−0.337006
$106$	36172.8	0.312692
$107$	−95769.2	−0.808661	−0.404331	−	0.914613i	$-0.632495\pi$
$107$	−95769.2	−0.808661	−0.404331	+	0.914613i	$0.632495\pi$
$108$	−5522.82	−0.0455619
$109$	113611.	0.915911	0.457956	−	0.888975i	$-0.348582\pi$
$109$	113611.	0.915911	0.457956	+	0.888975i	$0.348582\pi$
$110$	−350084.	−2.75861
$111$	91811.9	0.707280
$112$	−62303.4	−0.469318
$113$	−191798.	−1.41302	−0.706508	−	0.707705i	$-0.749731\pi$
$113$	−191798.	−1.41302	−0.706508	+	0.707705i	$0.749731\pi$
$114$	−43404.7	−0.312805
$115$	−318574.	−2.24629
$116$	−35774.2	−0.246846
$117$	23554.7	0.159079
$118$	−21898.8	−0.144782
$119$	92326.7	0.597668
$120$	−113520.	−0.719645
$121$	298489.	1.85338
$122$	217330.	1.32196
$123$	−117347.	−0.699372
$124$	71354.5	0.416742
$125$	40135.6	0.229750
$126$	−26258.7	−0.147349
$127$	−241164.	−1.32680	−0.663398	−	0.748267i	$-0.730886\pi$
$127$	−241164.	−1.32680	−0.663398	+	0.748267i	$0.730886\pi$
$128$	−223018.	−1.20314
$129$	−195539.	−1.03457
$130$	−150177.	−0.779371
$131$	−251589.	−1.28089	−0.640447	−	0.768002i	$-0.721251\pi$
$131$	−251589.	−1.28089	−0.640447	+	0.768002i	$0.721251\pi$
$132$	−46220.8	−0.230889
$133$	−39505.0	−0.193652
$134$	−305831.	−1.47136
$135$	−59844.3	−0.282610
$136$	275289.	1.27627
$137$	281066.	1.27940	0.639702	−	0.768623i	$-0.279058\pi$
$137$	281066.	1.27940	0.639702	+	0.768623i	$0.279058\pi$
$138$	−219722.	−0.982145
$139$	−184493.	−0.809920	−0.404960	−	0.914334i	$-0.632715\pi$
$139$	−184493.	−0.809920	−0.404960	+	0.914334i	$0.632715\pi$
$140$	32048.1	0.138192
$141$	−34198.0	−0.144862
$142$	−252563.	−1.05111
$143$	197130.	0.806146
$144$	−97931.8	−0.393566
$145$	−387643.	−1.53113
$146$	143435.	0.556896
$147$	127363.	0.486129
$148$	−77284.1	−0.290025
$149$	64871.3	0.239379	0.119690	−	0.992811i	$-0.461810\pi$
$149$	64871.3	0.239379	0.119690	+	0.992811i	$0.461810\pi$
$150$	204614.	0.742519
$151$	331835.	1.18435	0.592175	−	0.805809i	$-0.298269\pi$
$151$	331835.	1.18435	0.592175	+	0.805809i	$0.298269\pi$
$152$	−117791.	−0.413527
$153$	145124.	0.501200
$154$	−219761.	−0.746704
$155$	773183.	2.58496
$156$	−19827.5	−0.0652314
$157$	−268495.	−0.869334	−0.434667	−	0.900591i	$-0.643134\pi$
$157$	−268495.	−0.869334	−0.434667	+	0.900591i	$0.643134\pi$
$158$	145278.	0.462974
$159$	51749.8	0.162336
$160$	220754.	0.681724
$161$	−199981.	−0.608028
$162$	−41274.8	−0.123566
$163$	529252.	1.56025	0.780124	−	0.625625i	$-0.215156\pi$
$163$	529252.	1.56025	0.780124	+	0.625625i	$0.215156\pi$
$164$	98778.4	0.286782
$165$	−500840.	−1.43215
$166$	420019.	1.18304
$167$	181295.	0.503030	0.251515	−	0.967853i	$-0.419071\pi$
$167$	181295.	0.503030	0.251515	+	0.967853i	$0.419071\pi$
$168$	−71260.6	−0.194794
$169$	−286729.	−0.772245
$170$	−925262.	−2.45551
$171$	−62096.0	−0.162395
$172$	164598.	0.424231
$173$	568953.	1.44531	0.722655	−	0.691209i	$-0.242922\pi$
$173$	568953.	1.44531	0.722655	+	0.691209i	$0.242922\pi$
$174$	−267359.	−0.669455
$175$	186231.	0.459681
$176$	−819597.	−1.99443
$177$	−31329.0	−0.0751646
$178$	254075.	0.601052
$179$	474139.	1.10605	0.553023	−	0.833166i	$-0.313474\pi$
$179$	474139.	1.10605	0.553023	+	0.833166i	$0.313474\pi$
$180$	50374.8	0.115886
$181$	271053.	0.614974	0.307487	−	0.951552i	$-0.400512\pi$
$181$	271053.	0.614974	0.307487	+	0.951552i	$0.400512\pi$
$182$	−94271.5	−0.210961
$183$	310918.	0.686307
$184$	−596279.	−1.29839
$185$	−837436.	−1.79896
$186$	533268.	1.13022
$187$	1.21455e6	2.53987
$188$	28786.7	0.0594016
$189$	−37566.5	−0.0764973
$190$	395903.	0.795619
$191$	768100.	1.52347	0.761736	−	0.647888i	$-0.224348\pi$
$191$	768100.	1.52347	0.761736	+	0.647888i	$0.224348\pi$
$192$	−195947.	−0.383606
$193$	37462.7	0.0723946	0.0361973	−	0.999345i	$-0.488476\pi$
$193$	37462.7	0.0723946	0.0361973	+	0.999345i	$0.488476\pi$
$194$	−472011.	−0.900426
$195$	−214847.	−0.404616
$196$	−107210.	−0.199341
$197$	600917.	1.10319	0.551593	−	0.834113i	$-0.314020\pi$
$197$	600917.	1.10319	0.551593	+	0.834113i	$0.314020\pi$
$198$	−345431.	−0.626180
$199$	959.488	0.00171754	0.000858770	−	1.00000i	$-0.499727\pi$
$199$	959.488	0.00171754	0.000858770		1.00000i	$0.499727\pi$
$200$	555280.	0.981606
$201$	−437531.	−0.763869
$202$	−8656.69	−0.0149270
$203$	−243338.	−0.414448
$204$	−122160.	−0.205520
$205$	1.07034e6	1.77885
$206$	−951792.	−1.56269
$207$	−314340.	−0.509888
$208$	−351585.	−0.563472
$209$	−519685.	−0.822952
$210$	239511.	0.374781
$211$	−638539.	−0.987374	−0.493687	−	0.869640i	$-0.664351\pi$
$211$	−638539.	−0.987374	−0.493687	+	0.869640i	$0.664351\pi$
$212$	−43561.2	−0.0665672
$213$	−361324.	−0.545692
$214$	602478.	0.899305
$215$	1.78355e6	2.63141
$216$	−112011.	−0.163353
$217$	485356.	0.699699
$218$	−714718.	−1.01858
$219$	205203.	0.289117
$220$	421590.	0.587264
$221$	521010.	0.717572
$222$	−577583.	−0.786560
$223$	1.11924e6	1.50717	0.753584	−	0.657352i	$-0.228323\pi$
$223$	1.11924e6	1.50717	0.753584	+	0.657352i	$0.228323\pi$
$224$	138576.	0.184530
$225$	292727.	0.385484
$226$	1.20659e6	1.57140
$227$	310255.	0.399626	0.199813	−	0.979834i	$-0.435967\pi$
$227$	310255.	0.399626	0.199813	+	0.979834i	$0.435967\pi$
$228$	52270.3	0.0665913
$229$	−576057.	−0.725900	−0.362950	−	0.931809i	$-0.618230\pi$
$229$	−576057.	−0.725900	−0.362950	+	0.931809i	$0.618230\pi$
$230$	2.00413e6	2.49808
$231$	−314396.	−0.387657
$232$	−725556.	−0.885015
$233$	370645.	0.447269	0.223634	−	0.974673i	$-0.428208\pi$
$233$	370645.	0.447269	0.223634	+	0.974673i	$0.428208\pi$
$234$	−148181.	−0.176910
$235$	311928.	0.368455
$236$	26371.7	0.0308218
$237$	207839.	0.240357
$238$	−580822.	−0.664661
$239$	−457409.	−0.517977	−0.258988	−	0.965880i	$-0.583389\pi$
$239$	−457409.	−0.517977	−0.258988	+	0.965880i	$0.583389\pi$
$240$	893257.	1.00103
$241$	−1.65108e6	−1.83115	−0.915577	−	0.402143i	$-0.868266\pi$
$241$	−1.65108e6	−1.83115	−0.915577	+	0.402143i	$0.868266\pi$
$242$	−1.87777e6	−2.06113
$243$	−59049.0	−0.0641500
$244$	−261720.	−0.281425
$245$	−1.16171e6	−1.23647
$246$	738220.	0.777765
$247$	−222931.	−0.232503
$248$	1.44718e6	1.49414
$249$	600892.	0.614183
$250$	−252491.	−0.255502
$251$	−1.66249e6	−1.66562	−0.832810	−	0.553560i	$-0.813269\pi$
$251$	−1.66249e6	−1.66562	−0.832810	+	0.553560i	$0.813269\pi$
$252$	31622.2	0.0313683
$253$	−2.63073e6	−2.58390
$254$	1.51715e6	1.47552
$255$	−1.32371e6	−1.27480
$256$	706292.	0.673573
$257$	1.24468e6	1.17551	0.587753	−	0.809040i	$-0.300013\pi$
$257$	1.24468e6	1.17551	0.587753	+	0.809040i	$0.300013\pi$
$258$	1.23012e6	1.15053
$259$	−525690.	−0.486945
$260$	180851.	0.165916
$261$	−382491.	−0.347552
$262$	1.58273e6	1.42447
$263$	−1.51127e6	−1.34726	−0.673632	−	0.739067i	$-0.735267\pi$
$263$	−1.51127e6	−1.34726	−0.673632	+	0.739067i	$0.735267\pi$
$264$	−937428.	−0.827806
$265$	−472021.	−0.412902
$266$	248523.	0.215359
$267$	363487.	0.312040
$268$	368299.	0.313230
$269$	−111519.	−0.0939658	−0.0469829	−	0.998896i	$-0.514961\pi$
$269$	−111519.	−0.0939658	−0.0469829	+	0.998896i	$0.514961\pi$
$270$	376477.	0.314289
$271$	−281639.	−0.232953	−0.116477	−	0.993193i	$-0.537160\pi$
$271$	−281639.	−0.232953	−0.116477	+	0.993193i	$0.537160\pi$
$272$	−2.16617e6	−1.77530
$273$	−134868.	−0.109522
$274$	−1.76817e6	−1.42281
$275$	2.44985e6	1.95348
$276$	264601.	0.209083
$277$	2.13042e6	1.66827	0.834134	−	0.551561i	$-0.185968\pi$
$277$	2.13042e6	1.66827	0.834134	+	0.551561i	$0.185968\pi$
$278$	1.16063e6	0.900705
$279$	762909.	0.586762
$280$	649983.	0.495458
$281$	−1.74219e6	−1.31623	−0.658113	−	0.752920i	$-0.728645\pi$
$281$	−1.74219e6	−1.31623	−0.658113	+	0.752920i	$0.728645\pi$
$282$	215138.	0.161099
$283$	804963.	0.597461	0.298731	−	0.954337i	$-0.403437\pi$
$283$	804963.	0.597461	0.298731	+	0.954337i	$0.403437\pi$
$284$	304150.	0.223765
$285$	566391.	0.413051
$286$	−1.24013e6	−0.896507
$287$	671895.	0.481500
$288$	217821.	0.154745
$289$	1.79017e6	1.26081
$290$	2.43864e6	1.70275
$291$	−675273.	−0.467463
$292$	−172733.	−0.118554
$293$	404216.	0.275070	0.137535	−	0.990497i	$-0.456082\pi$
$293$	404216.	0.275070	0.137535	+	0.990497i	$0.456082\pi$
$294$	−801236.	−0.540620
$295$	285758.	0.191181
$296$	−1.56744e6	−1.03983
$297$	−494184.	−0.325086
$298$	−408101.	−0.266212
$299$	−1.12851e6	−0.730011
$300$	−246408.	−0.158071
$301$	1.11960e6	0.712274
$302$	−2.08755e6	−1.31711
$303$	−12384.5	−0.00774948
$304$	926867.	0.575219
$305$	−2.83595e6	−1.74562
$306$	−912966.	−0.557380
$307$	2.58978e6	1.56825	0.784127	−	0.620601i	$-0.213111\pi$
$307$	2.58978e6	1.56825	0.784127	+	0.620601i	$0.213111\pi$
$308$	264648.	0.158961
$309$	−1.36166e6	−0.811284
$310$	−4.86405e6	−2.87471
$311$	862615.	0.505727	0.252864	−	0.967502i	$-0.418628\pi$
$311$	862615.	0.505727	0.252864	+	0.967502i	$0.418628\pi$
$312$	−402132.	−0.233874
$313$	−1.99901e6	−1.15333	−0.576665	−	0.816981i	$-0.695646\pi$
$313$	−1.99901e6	−1.15333	−0.576665	+	0.816981i	$0.695646\pi$
$314$	1.68908e6	0.966779
$315$	342652.	0.194570
$316$	−174952.	−0.0985599
$317$	−1.20570e6	−0.673895	−0.336947	−	0.941523i	$-0.609394\pi$
$317$	−1.20570e6	−0.673895	−0.336947	+	0.941523i	$0.609394\pi$
$318$	−325555.	−0.180533
$319$	−3.20109e6	−1.76125
$320$	1.78727e6	0.975699
$321$	861923.	0.466881
$322$	1.25807e6	0.676183
$323$	−1.37351e6	−0.732532
$324$	49705.4	0.0263052
$325$	1.05092e6	0.551902
$326$	−3.32949e6	−1.73514
$327$	−1.02250e6	−0.528802
$328$	2.00338e6	1.02820
$329$	195809.	0.0997338
$330$	3.15075e6	1.59268
$331$	−332094.	−0.166606	−0.0833031	−	0.996524i	$-0.526547\pi$
$331$	−332094.	−0.166606	−0.0833031	+	0.996524i	$0.526547\pi$
$332$	−505810.	−0.251850
$333$	−826307.	−0.408348
$334$	−1.14051e6	−0.559415
$335$	3.99081e6	1.94289
$336$	560731.	0.270961
$337$	−2.07718e6	−0.996319	−0.498159	−	0.867085i	$-0.665991\pi$
$337$	−2.07718e6	−0.996319	−0.498159	+	0.867085i	$0.665991\pi$
$338$	1.80380e6	0.858807
$339$	1.72618e6	0.815805
$340$	1.11425e6	0.522740
$341$	6.38482e6	2.97347
$342$	390642.	0.180598
$343$	−1.59534e6	−0.732180
$344$	3.33829e6	1.52100
$345$	2.86717e6	1.29690
$346$	−3.57924e6	−1.60732
$347$	−2.03249e6	−0.906160	−0.453080	−	0.891470i	$-0.649675\pi$
$347$	−2.03249e6	−0.906160	−0.453080	+	0.891470i	$0.649675\pi$
$348$	321968.	0.142516
$349$	−881466.	−0.387384	−0.193692	−	0.981062i	$-0.562046\pi$
$349$	−881466.	−0.387384	−0.193692	+	0.981062i	$0.562046\pi$
$350$	−1.17157e6	−0.511207
$351$	−211992.	−0.0918442
$352$	1.82295e6	0.784185
$353$	−2.95569e6	−1.26247	−0.631237	−	0.775590i	$-0.717452\pi$
$353$	−2.95569e6	−1.26247	−0.631237	+	0.775590i	$0.717452\pi$
$354$	197089.	0.0835899
$355$	3.29571e6	1.38797
$356$	−305971.	−0.127954
$357$	−830941.	−0.345064
$358$	−2.98278e6	−1.23002
$359$	1.29738e6	0.531288	0.265644	−	0.964071i	$-0.414416\pi$
$359$	1.29738e6	0.531288	0.265644	+	0.964071i	$0.414416\pi$
$360$	1.02168e6	0.415487
$361$	−1.88840e6	−0.762650
$362$	−1.70517e6	−0.683908
$363$	−2.68640e6	−1.07005
$364$	113527.	0.0449102
$365$	−1.87170e6	−0.735366
$366$	−1.95597e6	−0.763236
$367$	1.75493e6	0.680132	0.340066	−	0.940401i	$-0.389550\pi$
$367$	1.75493e6	0.680132	0.340066	+	0.940401i	$0.389550\pi$
$368$	4.69196e6	1.80607
$369$	1.05612e6	0.403782
$370$	5.26826e6	2.00061
$371$	−296305.	−0.111765
$372$	−642190.	−0.240606
$373$	1.92485e6	0.716349	0.358175	−	0.933655i	$-0.383399\pi$
$373$	1.92485e6	0.716349	0.358175	+	0.933655i	$0.383399\pi$
$374$	−7.64067e6	−2.82457
$375$	−361220.	−0.132646
$376$	583839.	0.212972
$377$	−1.37318e6	−0.497594
$378$	236328.	0.0850720
$379$	3.48628e6	1.24671	0.623354	−	0.781940i	$-0.285770\pi$
$379$	3.48628e6	1.24671	0.623354	+	0.781940i	$0.285770\pi$
$380$	−476768.	−0.169375
$381$	2.17048e6	0.766025
$382$	−4.83207e6	−1.69424
$383$	−3.51624e6	−1.22485	−0.612423	−	0.790530i	$-0.709805\pi$
$383$	−3.51624e6	−1.22485	−0.612423	+	0.790530i	$0.709805\pi$
$384$	2.00716e6	0.694631
$385$	2.86767e6	0.986002
$386$	−235676.	−0.0805094
$387$	1.75985e6	0.597307
$388$	568422.	0.191686
$389$	−163206.	−0.0546844	−0.0273422	−	0.999626i	$-0.508704\pi$
$389$	−163206.	−0.0546844	−0.0273422	+	0.999626i	$0.508704\pi$
$390$	1.35159e6	0.449970
$391$	−6.95296e6	−2.30000
$392$	−2.17439e6	−0.714696
$393$	2.26430e6	0.739524
$394$	−3.78033e6	−1.22684
$395$	−1.89574e6	−0.611346
$396$	415987.	0.133304
$397$	−1.26098e6	−0.401544	−0.200772	−	0.979638i	$-0.564345\pi$
$397$	−1.26098e6	−0.401544	−0.200772	+	0.979638i	$0.564345\pi$
$398$	−6036.08	−0.00191006
$399$	355545.	0.111805
$400$	−4.36935e6	−1.36542
$401$	−2.88395e6	−0.895628	−0.447814	−	0.894127i	$-0.647797\pi$
$401$	−2.88395e6	−0.895628	−0.447814	+	0.894127i	$0.647797\pi$
$402$	2.75248e6	0.849491
$403$	2.73892e6	0.840073
$404$	10424.9	0.00317773
$405$	538598.	0.163165
$406$	1.53082e6	0.460904
$407$	−6.91541e6	−2.06934
$408$	−2.47760e6	−0.736852
$409$	−2.72417e6	−0.805241	−0.402621	−	0.915367i	$-0.631901\pi$
$409$	−2.72417e6	−0.805241	−0.402621	+	0.915367i	$0.631901\pi$
$410$	−6.73347e6	−1.97824
$411$	−2.52960e6	−0.738664
$412$	1.14620e6	0.332673
$413$	179381.	0.0517490
$414$	1.97750e6	0.567041
$415$	−5.48086e6	−1.56217
$416$	781998.	0.221550
$417$	1.66043e6	0.467608
$418$	3.26931e6	0.915197
$419$	−2.85576e6	−0.794669	−0.397334	−	0.917674i	$-0.630065\pi$
$419$	−2.85576e6	−0.794669	−0.397334	+	0.917674i	$0.630065\pi$
$420$	−288433.	−0.0797850
$421$	2.80641e6	0.771696	0.385848	−	0.922562i	$-0.373909\pi$
$421$	2.80641e6	0.771696	0.385848	+	0.922562i	$0.373909\pi$
$422$	4.01701e6	1.09805
$423$	307782.	0.0836359
$424$	−883488.	−0.238663
$425$	6.47489e6	1.73884
$426$	2.27307e6	0.606860
$427$	−1.78023e6	−0.472506
$428$	−725537.	−0.191448
$429$	−1.77417e6	−0.465428
$430$	−1.12202e7	−2.92637
$431$	3.86257e6	1.00157	0.500787	−	0.865571i	$-0.333044\pi$
$431$	3.86257e6	1.00157	0.500787	+	0.865571i	$0.333044\pi$
$432$	881386.	0.227225
$433$	67037.6	0.0171830	0.00859149	−	0.999963i	$-0.497265\pi$
$433$	67037.6	0.0171830	0.00859149	+	0.999963i	$0.497265\pi$
$434$	−3.05335e6	−0.778129
$435$	3.48878e6	0.883997
$436$	860703.	0.216839
$437$	2.97505e6	0.745230
$438$	−1.29092e6	−0.321524
$439$	2.63398e6	0.652305	0.326152	−	0.945317i	$-0.394248\pi$
$439$	2.63398e6	0.652305	0.326152	+	0.945317i	$0.394248\pi$
$440$	8.55048e6	2.10552
$441$	−1.14627e6	−0.280667
$442$	−3.27764e6	−0.798006
$443$	3.85966e6	0.934415	0.467208	−	0.884148i	$-0.345260\pi$
$443$	3.85966e6	0.934415	0.467208	+	0.884148i	$0.345260\pi$
$444$	695557.	0.167446
$445$	−3.31544e6	−0.793673
$446$	−7.04108e6	−1.67611
$447$	−583842.	−0.138206
$448$	1.12194e6	0.264103
$449$	−1.96762e6	−0.460602	−0.230301	−	0.973119i	$-0.573971\pi$
$449$	−1.96762e6	−0.460602	−0.230301	+	0.973119i	$0.573971\pi$
$450$	−1.84153e6	−0.428694
$451$	8.83873e6	2.04620
$452$	−1.45304e6	−0.334527
$453$	−2.98652e6	−0.683785
$454$	−1.95179e6	−0.444420
$455$	1.23016e6	0.278568
$456$	1.06012e6	0.238750
$457$	2.80506e6	0.628277	0.314139	−	0.949377i	$-0.398284\pi$
$457$	2.80506e6	0.628277	0.314139	+	0.949377i	$0.398284\pi$
$458$	3.62394e6	0.807267
$459$	−1.30612e6	−0.289368
$460$	−2.41348e6	−0.531801
$461$	−587088.	−0.128662	−0.0643311	−	0.997929i	$-0.520491\pi$
$461$	−587088.	−0.128662	−0.0643311	+	0.997929i	$0.520491\pi$
$462$	1.97785e6	0.431110
$463$	−1.11999e6	−0.242807	−0.121403	−	0.992603i	$-0.538739\pi$
$463$	−1.11999e6	−0.242807	−0.121403	+	0.992603i	$0.538739\pi$
$464$	5.70920e6	1.23106
$465$	−6.95865e6	−1.49243
$466$	−2.33171e6	−0.497404
$467$	−662714.	−0.140616	−0.0703079	−	0.997525i	$-0.522398\pi$
$467$	−662714.	−0.140616	−0.0703079	+	0.997525i	$0.522398\pi$
$468$	178448.	0.0376614
$469$	2.50518e6	0.525905
$470$	−1.96232e6	−0.409755
$471$	2.41645e6	0.501910
$472$	534858.	0.110505
$473$	1.47283e7	3.02691
$474$	−1.30750e6	−0.267298
$475$	−2.77049e6	−0.563408
$476$	699457.	0.141496
$477$	−465748.	−0.0937250
$478$	2.87753e6	0.576037
$479$	−2.14002e6	−0.426166	−0.213083	−	0.977034i	$-0.568350\pi$
$479$	−2.14002e6	−0.426166	−0.213083	+	0.977034i	$0.568350\pi$
$480$	−1.98679e6	−0.393594
$481$	−2.96653e6	−0.584636
$482$	1.03868e7	2.03641
$483$	1.79983e6	0.351045
$484$	2.26132e6	0.438781
$485$	6.15931e6	1.18899
$486$	371474.	0.0713407
$487$	8.82596e6	1.68632	0.843159	−	0.537664i	$-0.180693\pi$
$487$	8.82596e6	1.68632	0.843159	+	0.537664i	$0.180693\pi$
$488$	−5.30808e6	−1.00899
$489$	−4.76327e6	−0.900810
$490$	7.30824e6	1.37506
$491$	−338584.	−0.0633816	−0.0316908	−	0.999498i	$-0.510089\pi$
$491$	−338584.	−0.0633816	−0.0316908	+	0.999498i	$0.510089\pi$
$492$	−889005.	−0.165574
$493$	−8.46040e6	−1.56774
$494$	1.40245e6	0.258564
$495$	4.50756e6	0.826854
$496$	−1.13874e7	−2.07837
$497$	2.06884e6	0.375696
$498$	−3.78017e6	−0.683027
$499$	−4.96188e6	−0.892062	−0.446031	−	0.895018i	$-0.647163\pi$
$499$	−4.96188e6	−0.892062	−0.446031	+	0.895018i	$0.647163\pi$
$500$	304063.	0.0543924
$501$	−1.63165e6	−0.290425
$502$	1.04586e7	1.85232
$503$	−85757.8	−0.0151131	−0.00755655	−	0.999971i	$-0.502405\pi$
$503$	−85757.8	−0.0151131	−0.00755655	+	0.999971i	$0.502405\pi$
$504$	641346.	0.112465
$505$	112962.	0.0197107
$506$	1.65498e7	2.87353
$507$	2.58056e6	0.445856
$508$	−1.82703e6	−0.314114
$509$	−7.60236e6	−1.30063	−0.650315	−	0.759665i	$-0.725363\pi$
$509$	−7.60236e6	−1.30063	−0.650315	+	0.759665i	$0.725363\pi$
$510$	8.32736e6	1.41769
$511$	−1.17494e6	−0.199050
$512$	2.69334e6	0.454062
$513$	558864.	0.0937589
$514$	−7.83021e6	−1.30727
$515$	1.24200e7	2.06350
$516$	−1.48138e6	−0.244930
$517$	2.57585e6	0.423832
$518$	3.30708e6	0.541528
$519$	−5.12057e6	−0.834450
$520$	3.66793e6	0.594857
$521$	−2.25965e6	−0.364709	−0.182354	−	0.983233i	$-0.558372\pi$
$521$	−2.25965e6	−0.364709	−0.182354	+	0.983233i	$0.558372\pi$
$522$	2.40623e6	0.386510
$523$	6.30058e6	1.00722	0.503612	−	0.863930i	$-0.332004\pi$
$523$	6.30058e6	1.00722	0.503612	+	0.863930i	$0.332004\pi$
$524$	−1.90601e6	−0.303247
$525$	−1.67608e6	−0.265397
$526$	9.50730e6	1.49828
$527$	1.68749e7	2.64676
$528$	7.37637e6	1.15148
$529$	8.62385e6	1.33987
$530$	2.96946e6	0.459184
$531$	281961.	0.0433963
$532$	−299285.	−0.0458465
$533$	3.79158e6	0.578099
$534$	−2.28667e6	−0.347017
$535$	−7.86178e6	−1.18751
$536$	7.46965e6	1.12302
$537$	−4.26726e6	−0.638576
$538$	701562.	0.104499
$539$	−9.59321e6	−1.42230
$540$	−453374.	−0.0669070
$541$	−9.75064e6	−1.43232	−0.716160	−	0.697936i	$-0.754102\pi$
$541$	−9.75064e6	−1.43232	−0.716160	+	0.697936i	$0.754102\pi$
$542$	1.77177e6	0.259065
$543$	−2.43947e6	−0.355056
$544$	4.81801e6	0.698025
$545$	9.32641e6	1.34500
$546$	848444.	0.121798
$547$	6.17092e6	0.881823	0.440911	−	0.897551i	$-0.354655\pi$
$547$	6.17092e6	0.881823	0.440911	+	0.897551i	$0.354655\pi$
$548$	2.12933e6	0.302894
$549$	−2.79826e6	−0.396240
$550$	−1.54119e7	−2.17244
$551$	3.62005e6	0.507968
$552$	5.36651e6	0.749625
$553$	−1.19003e6	−0.165480
$554$	−1.34023e7	−1.85527
$555$	7.53692e6	1.03863
$556$	−1.39770e6	−0.191746
$557$	−4.46667e6	−0.610023	−0.305011	−	0.952349i	$-0.598660\pi$
$557$	−4.46667e6	−0.610023	−0.305011	+	0.952349i	$0.598660\pi$
$558$	−4.79941e6	−0.652533
$559$	6.31804e6	0.855171
$560$	−5.11454e6	−0.689187
$561$	−1.09310e7	−1.46640
$562$	1.09600e7	1.46376
$563$	−2.84216e6	−0.377901	−0.188951	−	0.981987i	$-0.560509\pi$
$563$	−2.84216e6	−0.377901	−0.188951	+	0.981987i	$0.560509\pi$
$564$	−259081.	−0.0342955
$565$	−1.57448e7	−2.07500
$566$	−5.06397e6	−0.664431
$567$	338098.	0.0441657
$568$	6.16863e6	0.802265
$569$	2.66553e6	0.345146	0.172573	−	0.984997i	$-0.444792\pi$
$569$	2.66553e6	0.345146	0.172573	+	0.984997i	$0.444792\pi$
$570$	−3.56313e6	−0.459351
$571$	−4.62842e6	−0.594076	−0.297038	−	0.954866i	$-0.595999\pi$
$571$	−4.62842e6	−0.594076	−0.297038	+	0.954866i	$0.595999\pi$
$572$	1.49344e6	0.190852
$573$	−6.91290e6	−0.879576
$574$	−4.22685e6	−0.535472
$575$	−1.40247e7	−1.76898
$576$	1.76352e6	0.221475
$577$	774192.	0.0968075	0.0484038	−	0.998828i	$-0.484587\pi$
$577$	774192.	0.0968075	0.0484038	+	0.998828i	$0.484587\pi$
$578$	−1.12618e7	−1.40214
$579$	−337165.	−0.0417971
$580$	−2.93674e6	−0.362489
$581$	−3.44054e6	−0.422850
$582$	4.24810e6	0.519861
$583$	−3.89788e6	−0.474959
$584$	−3.50328e6	−0.425053
$585$	1.93362e6	0.233605
$586$	−2.54289e6	−0.305903
$587$	−1.40973e7	−1.68865	−0.844326	−	0.535829i	$-0.819999\pi$
$587$	−1.40973e7	−1.68865	−0.844326	+	0.535829i	$0.819999\pi$
$588$	964892.	0.115089
$589$	−7.22048e6	−0.857586
$590$	−1.79769e6	−0.212610
$591$	−5.40825e6	−0.636925
$592$	1.23337e7	1.44641
$593$	4.30336e6	0.502541	0.251270	−	0.967917i	$-0.419152\pi$
$593$	4.30336e6	0.502541	0.251270	+	0.967917i	$0.419152\pi$
$594$	3.10888e6	0.361525
$595$	7.57919e6	0.877668
$596$	491458.	0.0566723
$597$	−8635.40	−0.000991623 0
$598$	7.09942e6	0.811839
$599$	−3.54981e6	−0.404238	−0.202119	−	0.979361i	$-0.564783\pi$
$599$	−3.54981e6	−0.404238	−0.202119	+	0.979361i	$0.564783\pi$
$600$	−4.99752e6	−0.566731
$601$	−6.16578e6	−0.696308	−0.348154	−	0.937437i	$-0.613191\pi$
$601$	−6.16578e6	−0.696308	−0.348154	+	0.937437i	$0.613191\pi$
$602$	−7.04334e6	−0.792114
$603$	3.93778e6	0.441020
$604$	2.51395e6	0.280391
$605$	2.45032e7	2.72166
$606$	77910.2	0.00861813
$607$	9.60415e6	1.05800	0.529002	−	0.848621i	$-0.322566\pi$
$607$	9.60415e6	1.05800	0.529002	+	0.848621i	$0.322566\pi$
$608$	−2.06154e6	−0.226169
$609$	2.19004e6	0.239281
$610$	1.78408e7	1.94129
$611$	1.10497e6	0.119742
$612$	1.09944e6	0.118657
$613$	−5.51137e6	−0.592391	−0.296195	−	0.955127i	$-0.595718\pi$
$613$	−5.51137e6	−0.592391	−0.296195	+	0.955127i	$0.595718\pi$
$614$	−1.62921e7	−1.74404
$615$	−9.63309e6	−1.02702
$616$	5.36746e6	0.569924
$617$	−8.80831e6	−0.931493	−0.465747	−	0.884918i	$-0.654214\pi$
$617$	−8.80831e6	−0.931493	−0.465747	+	0.884918i	$0.654214\pi$
$618$	8.56612e6	0.902222
$619$	3.92911e6	0.412162	0.206081	−	0.978535i	$-0.433929\pi$
$619$	3.92911e6	0.412162	0.206081	+	0.978535i	$0.433929\pi$
$620$	5.85755e6	0.611980
$621$	2.82906e6	0.294384
$622$	−5.42666e6	−0.562415
$623$	−2.08123e6	−0.214832
$624$	3.16427e6	0.325321
$625$	−7.99872e6	−0.819069
$626$	1.25756e7	1.28261
$627$	4.67716e6	0.475131
$628$	−2.03409e6	−0.205812
$629$	−1.82772e7	−1.84198
$630$	−2.15560e6	−0.216380
$631$	7.24415e6	0.724293	0.362146	−	0.932121i	$-0.382044\pi$
$631$	7.24415e6	0.724293	0.362146	+	0.932121i	$0.382044\pi$
$632$	−3.54829e6	−0.353367
$633$	5.74686e6	0.570061
$634$	7.58500e6	0.749432
$635$	−1.97974e7	−1.94838
$636$	392051.	0.0384326
$637$	−4.11523e6	−0.401833
$638$	2.01379e7	1.95867
$639$	3.25192e6	0.315056
$640$	−1.83078e7	−1.76679
$641$	−464280.	−0.0446308	−0.0223154	−	0.999751i	$-0.507104\pi$
$641$	−464280.	−0.0446308	−0.0223154	+	0.999751i	$0.507104\pi$
$642$	−5.42230e6	−0.519214
$643$	1.96736e7	1.87653	0.938265	−	0.345918i	$-0.112433\pi$
$643$	1.96736e7	1.87653	0.938265	+	0.345918i	$0.112433\pi$
$644$	−1.51503e6	−0.143949
$645$	−1.60520e7	−1.51925
$646$	8.64069e6	0.814642
$647$	−8.53718e6	−0.801777	−0.400889	−	0.916127i	$-0.631299\pi$
$647$	−8.53718e6	−0.801777	−0.400889	+	0.916127i	$0.631299\pi$
$648$	1.00810e6	0.0943119
$649$	2.35975e6	0.219914
$650$	−6.61128e6	−0.613765
$651$	−4.36821e6	−0.403971
$652$	4.00956e6	0.369383
$653$	5.29534e6	0.485971	0.242986	−	0.970030i	$-0.421873\pi$
$653$	5.29534e6	0.485971	0.242986	+	0.970030i	$0.421873\pi$
$654$	6.43246e6	0.588075
$655$	−2.06532e7	−1.88098
$656$	−1.57640e7	−1.43023
$657$	−1.84683e6	−0.166922
$658$	−1.23182e6	−0.110913
$659$	−2.00389e7	−1.79747	−0.898734	−	0.438495i	$-0.855512\pi$
$659$	−2.00389e7	−1.79747	−0.898734	+	0.438495i	$0.855512\pi$
$660$	−3.79431e6	−0.339057
$661$	1.65921e6	0.147706	0.0738530	−	0.997269i	$-0.476470\pi$
$661$	1.65921e6	0.147706	0.0738530	+	0.997269i	$0.476470\pi$
$662$	2.08918e6	0.185281
$663$	−4.68909e6	−0.414291
$664$	−1.02586e7	−0.902958
$665$	−3.24300e6	−0.284376
$666$	5.19825e6	0.454121
$667$	1.83253e7	1.59491
$668$	1.37347e6	0.119091
$669$	−1.00732e7	−0.870164
$670$	−2.51060e7	−2.16068
$671$	−2.34188e7	−2.00798
$672$	−1.24718e6	−0.106538
$673$	1.84157e7	1.56730	0.783649	−	0.621204i	$-0.213356\pi$
$673$	1.84157e7	1.56730	0.783649	+	0.621204i	$0.213356\pi$
$674$	1.30674e7	1.10800
$675$	−2.63455e6	−0.222560
$676$	−2.17223e6	−0.182826
$677$	−7.42281e6	−0.622439	−0.311219	−	0.950338i	$-0.600737\pi$
$677$	−7.42281e6	−0.622439	−0.311219	+	0.950338i	$0.600737\pi$
$678$	−1.08593e7	−0.907250
$679$	3.86643e6	0.321837
$680$	2.25987e7	1.87418
$681$	−2.79229e6	−0.230724
$682$	−4.01665e7	−3.30677
$683$	−1.19685e7	−0.981721	−0.490860	−	0.871238i	$-0.663318\pi$
$683$	−1.19685e7	−0.981721	−0.490860	+	0.871238i	$0.663318\pi$
$684$	−470432.	−0.0384465
$685$	2.30730e7	1.87879
$686$	1.00362e7	0.814251
$687$	5.18451e6	0.419099
$688$	−2.62681e7	−2.11572
$689$	−1.67209e6	−0.134187
$690$	−1.80372e7	−1.44227
$691$	−1.41570e7	−1.12791	−0.563955	−	0.825805i	$-0.690721\pi$
$691$	−1.41570e7	−1.12791	−0.563955	+	0.825805i	$0.690721\pi$
$692$	4.31032e6	0.342172
$693$	2.82957e6	0.223814
$694$	1.27863e7	1.00773
$695$	−1.51452e7	−1.18936
$696$	6.53000e6	0.510964
$697$	2.33605e7	1.82138
$698$	5.54525e6	0.430807
$699$	−3.33581e6	−0.258231
$700$	1.41086e6	0.108828
$701$	4.89919e6	0.376555	0.188278	−	0.982116i	$-0.439710\pi$
$701$	4.89919e6	0.376555	0.188278	+	0.982116i	$0.439710\pi$
$702$	1.33363e6	0.102139
$703$	7.82051e6	0.596825
$704$	1.47590e7	1.12234
$705$	−2.80735e6	−0.212727
$706$	1.85941e7	1.40399
$707$	70910.4	0.00533533
$708$	−237345.	−0.0177950
$709$	−4.60872e6	−0.344322	−0.172161	−	0.985069i	$-0.555075\pi$
$709$	−4.60872e6	−0.344322	−0.172161	+	0.985069i	$0.555075\pi$
$710$	−2.07331e7	−1.54354
$711$	−1.87055e6	−0.138770
$712$	−6.20555e6	−0.458755
$713$	−3.65513e7	−2.69264
$714$	5.22740e6	0.383742
$715$	1.61826e7	1.18381
$716$	3.59203e6	0.261853
$717$	4.11669e6	0.299054
$718$	−8.16171e6	−0.590840
$719$	2.63345e6	0.189978	0.0949890	−	0.995478i	$-0.469718\pi$
$719$	2.63345e6	0.189978	0.0949890	+	0.995478i	$0.469718\pi$
$720$	−8.03931e6	−0.577946
$721$	7.79650e6	0.558549
$722$	1.18798e7	0.848136
$723$	1.48597e7	1.05722
$724$	2.05346e6	0.145593
$725$	−1.70653e7	−1.20578
$726$	1.69000e7	1.18999
$727$	−1.62754e7	−1.14207	−0.571037	−	0.820924i	$-0.693459\pi$
$727$	−1.62754e7	−1.14207	−0.571037	+	0.820924i	$0.693459\pi$
$728$	2.30250e6	0.161017
$729$	531441.	0.0370370
$730$	1.17747e7	0.817794
$731$	3.89264e7	2.69433
$732$	2.35548e6	0.162481
$733$	−2.64491e6	−0.181824	−0.0909120	−	0.995859i	$-0.528978\pi$
$733$	−2.64491e6	−0.181824	−0.0909120	+	0.995859i	$0.528978\pi$
$734$	−1.10401e7	−0.756369
$735$	1.04554e7	0.713874
$736$	−1.04359e7	−0.710124
$737$	3.29555e7	2.23491
$738$	−6.64398e6	−0.449043
$739$	1.63591e7	1.10192	0.550959	−	0.834532i	$-0.314262\pi$
$739$	1.63591e7	1.10192	0.550959	+	0.834532i	$0.314262\pi$
$740$	−6.34432e6	−0.425898
$741$	2.00638e6	0.134236
$742$	1.86404e6	0.124293
$743$	9.62508e6	0.639635	0.319817	−	0.947479i	$-0.396378\pi$
$743$	9.62508e6	0.639635	0.319817	+	0.947479i	$0.396378\pi$
$744$	−1.30246e7	−0.862644
$745$	5.32534e6	0.351526
$746$	−1.21091e7	−0.796646
$747$	−5.40802e6	−0.354599
$748$	9.20131e6	0.601306
$749$	−4.93514e6	−0.321436
$750$	2.27242e6	0.147514
$751$	−547839.	−0.0354448	−0.0177224	−	0.999843i	$-0.505642\pi$
$751$	−547839.	−0.0354448	−0.0177224	+	0.999843i	$0.505642\pi$
$752$	−4.59407e6	−0.296246
$753$	1.49624e7	0.961646
$754$	8.63861e6	0.553370
$755$	2.72407e7	1.73920
$756$	−284600.	−0.0181105
$757$	−7.62374e6	−0.483535	−0.241768	−	0.970334i	$-0.577727\pi$
$757$	−7.62374e6	−0.483535	−0.241768	+	0.970334i	$0.577727\pi$
$758$	−2.19320e7	−1.38645
$759$	2.36766e7	1.49181
$760$	−9.66958e6	−0.607259
$761$	−2.11368e7	−1.32305	−0.661527	−	0.749922i	$-0.730091\pi$
$761$	−2.11368e7	−1.32305	−0.661527	+	0.749922i	$0.730091\pi$
$762$	−1.36543e7	−0.851890
$763$	5.85454e6	0.364067
$764$	5.81904e6	0.360677
$765$	1.19134e7	0.736005
$766$	2.21204e7	1.36214
$767$	1.01227e6	0.0621309
$768$	−6.35663e6	−0.388888
$769$	−2.53471e7	−1.54565	−0.772827	−	0.634617i	$-0.781158\pi$
$769$	−2.53471e7	−1.54565	−0.772827	+	0.634617i	$0.781158\pi$
$770$	−1.80404e7	−1.09652
$771$	−1.12021e7	−0.678679
$772$	283814.	0.0171392
$773$	−2.45392e7	−1.47711	−0.738554	−	0.674195i	$-0.764491\pi$
$773$	−2.45392e7	−1.47711	−0.738554	+	0.674195i	$0.764491\pi$
$774$	−1.10711e7	−0.664260
$775$	3.40381e7	2.03569
$776$	1.15285e7	0.687253
$777$	4.73121e6	0.281138
$778$	1.02672e6	0.0608140
$779$	−9.99555e6	−0.590151
$780$	−1.62766e6	−0.0957915
$781$	2.72155e7	1.59657
$782$	4.37406e7	2.55781
$783$	3.44242e6	0.200659
$784$	1.71096e7	0.994148
$785$	−2.20410e7	−1.27661
$786$	−1.42446e7	−0.822418
$787$	−2.27427e7	−1.30890	−0.654448	−	0.756107i	$-0.727099\pi$
$787$	−2.27427e7	−1.30890	−0.654448	+	0.756107i	$0.727099\pi$
$788$	4.55248e6	0.261176
$789$	1.36014e7	0.777843
$790$	1.19260e7	0.679872
$791$	−9.88363e6	−0.561662
$792$	8.43686e6	0.477934
$793$	−1.00461e7	−0.567300
$794$	7.93276e6	0.446553
$795$	4.24819e6	0.238389
$796$	7268.98	0.000406622 0
$797$	2.24707e7	1.25306	0.626529	−	0.779398i	$-0.284475\pi$
$797$	2.24707e7	1.25306	0.626529	+	0.779398i	$0.284475\pi$
$798$	−2.23671e6	−0.124338
$799$	6.80790e6	0.377265
$800$	9.71833e6	0.536867
$801$	−3.27138e6	−0.180157
$802$	1.81428e7	0.996020
$803$	−1.54562e7	−0.845889
$804$	−3.31469e6	−0.180843
$805$	−1.64166e7	−0.892881
$806$	−1.72304e7	−0.934237
$807$	1.00367e6	0.0542512
$808$	211432.	0.0113931
$809$	−3.57608e6	−0.192104	−0.0960519	−	0.995376i	$-0.530621\pi$
$809$	−3.57608e6	−0.192104	−0.0960519	+	0.995376i	$0.530621\pi$
$810$	−3.38829e6	−0.181455
$811$	3.19383e7	1.70514	0.852570	−	0.522613i	$-0.175043\pi$
$811$	3.19383e7	1.70514	0.852570	+	0.522613i	$0.175043\pi$
$812$	−1.84350e6	−0.0981191
$813$	2.53475e6	0.134496
$814$	4.35044e7	2.30130
$815$	4.34468e7	2.29120
$816$	1.94956e7	1.02497
$817$	−1.66559e7	−0.872999
$818$	1.71376e7	0.895501
$819$	1.21381e6	0.0632325
$820$	8.10881e6	0.421136
$821$	−3.00431e7	−1.55556	−0.777779	−	0.628538i	$-0.783654\pi$
$821$	−3.00431e7	−1.55556	−0.777779	+	0.628538i	$0.783654\pi$
$822$	1.59135e7	0.821462
$823$	−2.13843e7	−1.10051	−0.550256	−	0.834996i	$-0.685470\pi$
$823$	−2.13843e7	−1.10051	−0.550256	+	0.834996i	$0.685470\pi$
$824$	2.32467e7	1.19273
$825$	−2.20487e7	−1.12784
$826$	−1.12848e6	−0.0575496
$827$	−1.64212e7	−0.834912	−0.417456	−	0.908697i	$-0.637078\pi$
$827$	−1.64212e7	−0.834912	−0.417456	+	0.908697i	$0.637078\pi$
$828$	−2.38141e6	−0.120714
$829$	−1.98607e7	−1.00371	−0.501856	−	0.864951i	$-0.667349\pi$
$829$	−1.98607e7	−1.00371	−0.501856	+	0.864951i	$0.667349\pi$
$830$	3.44797e7	1.73728
$831$	−1.91738e7	−0.963175
$832$	6.33123e6	0.317088
$833$	−2.53546e7	−1.26603
$834$	−1.04457e7	−0.520022
$835$	1.48826e7	0.738693
$836$	−3.93708e6	−0.194831
$837$	−6.86618e6	−0.338767
$838$	1.79654e7	0.883744
$839$	2.18729e7	1.07276	0.536379	−	0.843977i	$-0.319792\pi$
$839$	2.18729e7	1.07276	0.536379	+	0.843977i	$0.319792\pi$
$840$	−5.84985e6	−0.286053
$841$	1.78722e6	0.0871342
$842$	−1.76550e7	−0.858196
$843$	1.56797e7	0.759923
$844$	−4.83751e6	−0.233757
$845$	−2.35379e7	−1.13403
$846$	−1.93624e6	−0.0930108
$847$	1.53816e7	0.736703
$848$	6.95192e6	0.331983
$849$	−7.24467e6	−0.344944
$850$	−4.07331e7	−1.93375
$851$	3.95887e7	1.87391
$852$	−2.73735e6	−0.129191
$853$	1.85070e7	0.870892	0.435446	−	0.900215i	$-0.356591\pi$
$853$	1.85070e7	0.870892	0.435446	+	0.900215i	$0.356591\pi$
$854$	1.11993e7	0.525469
$855$	−5.09752e6	−0.238475
$856$	−1.47150e7	−0.686397
$857$	−778673.	−0.0362162	−0.0181081	−	0.999836i	$-0.505764\pi$
$857$	−778673.	−0.0362162	−0.0181081	+	0.999836i	$0.505764\pi$
$858$	1.11612e7	0.517599
$859$	−2.55949e7	−1.18351	−0.591754	−	0.806119i	$-0.701564\pi$
$859$	−2.55949e7	−1.18351	−0.591754	+	0.806119i	$0.701564\pi$
$860$	1.35120e7	0.622978
$861$	−6.04705e6	−0.277994
$862$	−2.42992e7	−1.11384
$863$	−2.32218e7	−1.06137	−0.530687	−	0.847568i	$-0.678066\pi$
$863$	−2.32218e7	−1.06137	−0.530687	+	0.847568i	$0.678066\pi$
$864$	−1.96038e6	−0.0893423
$865$	4.67058e7	2.12242
$866$	−421729.	−0.0191090
$867$	−1.61115e7	−0.727929
$868$	3.67701e6	0.165651
$869$	−1.56547e7	−0.703229
$870$	−2.19477e7	−0.983086
$871$	1.41370e7	0.631412
$872$	1.74564e7	0.777432
$873$	6.07746e6	0.269890
$874$	−1.87158e7	−0.828763
$875$	2.06825e6	0.0913236
$876$	1.55459e6	0.0684474
$877$	3.47355e7	1.52502	0.762508	−	0.646979i	$-0.223968\pi$
$877$	3.47355e7	1.52502	0.762508	+	0.646979i	$0.223968\pi$
$878$	−1.65702e7	−0.725423
$879$	−3.63794e6	−0.158812
$880$	−6.72814e7	−2.92879
$881$	3.47364e7	1.50780	0.753902	−	0.656987i	$-0.228169\pi$
$881$	3.47364e7	1.50780	0.753902	+	0.656987i	$0.228169\pi$
$882$	7.21112e6	0.312127
$883$	1.73501e7	0.748859	0.374429	−	0.927255i	$-0.377839\pi$
$883$	1.73501e7	0.748859	0.374429	+	0.927255i	$0.377839\pi$
$884$	3.94712e6	0.169883
$885$	−2.57183e6	−0.110378
$886$	−2.42809e7	−1.03915
$887$	2.06179e7	0.879904	0.439952	−	0.898021i	$-0.354996\pi$
$887$	2.06179e7	0.879904	0.439952	+	0.898021i	$0.354996\pi$
$888$	1.41069e7	0.600345
$889$	−1.24276e7	−0.527390
$890$	2.08572e7	0.882636
$891$	4.44766e6	0.187688
$892$	8.47925e6	0.356817
$893$	−2.91298e6	−0.122239
$894$	3.67291e6	0.153697
$895$	3.89225e7	1.62422
$896$	−1.14925e7	−0.478237
$897$	1.01566e7	0.421472
$898$	1.23782e7	0.512232
$899$	−4.44758e7	−1.83537
$900$	2.21767e6	0.0912621
$901$	−1.03020e7	−0.422774
$902$	−5.56039e7	−2.27556
$903$	−1.00764e7	−0.411232
$904$	−2.94698e7	−1.19938
$905$	2.22509e7	0.903082
$906$	1.87880e7	0.760431
$907$	−2.03892e7	−0.822968	−0.411484	−	0.911417i	$-0.634989\pi$
$907$	−2.03892e7	−0.822968	−0.411484	+	0.911417i	$0.634989\pi$
$908$	2.35046e6	0.0946101
$909$	111461.	0.00447416
$910$	−7.73884e6	−0.309793
$911$	−8.86386e6	−0.353856	−0.176928	−	0.984224i	$-0.556616\pi$
$911$	−8.86386e6	−0.353856	−0.176928	+	0.984224i	$0.556616\pi$
$912$	−8.34180e6	−0.332103
$913$	−4.52601e7	−1.79696
$914$	−1.76464e7	−0.698701
$915$	2.55236e7	1.00783
$916$	−4.36415e6	−0.171854
$917$	−1.29648e7	−0.509145
$918$	8.21670e6	0.321803
$919$	−2.01939e7	−0.788736	−0.394368	−	0.918953i	$-0.629036\pi$
$919$	−2.01939e7	−0.788736	−0.394368	+	0.918953i	$0.629036\pi$
$920$	−4.89491e7	−1.90667
$921$	−2.33080e7	−0.905432
$922$	3.69334e6	0.143084
$923$	1.16747e7	0.451068
$924$	−2.38183e6	−0.0917764
$925$	−3.68667e7	−1.41671
$926$	7.04577e6	0.270023
$927$	1.22550e7	0.468395
$928$	−1.26984e7	−0.484039
$929$	−4.06252e7	−1.54439	−0.772194	−	0.635387i	$-0.780841\pi$
$929$	−4.06252e7	−1.54439	−0.772194	+	0.635387i	$0.780841\pi$
$930$	4.37764e7	1.65971
$931$	1.08488e7	0.410211
$932$	2.80797e6	0.105889
$933$	−7.76354e6	−0.291982
$934$	4.16909e6	0.156378
$935$	9.97036e7	3.72977
$936$	3.61919e6	0.135027
$937$	4.97755e7	1.85211	0.926054	−	0.377390i	$-0.123178\pi$
$937$	4.97755e7	1.85211	0.926054	+	0.377390i	$0.123178\pi$
$938$	−1.57599e7	−0.584854
$939$	1.79911e7	0.665875
$940$	2.36313e6	0.0872304
$941$	6.85312e6	0.252298	0.126149	−	0.992011i	$-0.459738\pi$
$941$	6.85312e6	0.252298	0.126149	+	0.992011i	$0.459738\pi$
$942$	−1.52018e7	−0.558170
$943$	−5.05992e7	−1.85295
$944$	−4.20865e6	−0.153714
$945$	−3.08387e6	−0.112335
$946$	−9.26547e7	−3.36620
$947$	2.46625e7	0.893639	0.446819	−	0.894624i	$-0.352557\pi$
$947$	2.46625e7	0.893639	0.446819	+	0.894624i	$0.352557\pi$
$948$	1.57457e6	0.0569036
$949$	−6.63029e6	−0.238983
$950$	1.74290e7	0.626560
$951$	1.08513e7	0.389073
$952$	1.41861e7	0.507305
$953$	4.33017e7	1.54444	0.772222	−	0.635352i	$-0.219145\pi$
$953$	4.33017e7	1.54444	0.772222	+	0.635352i	$0.219145\pi$
$954$	2.92999e6	0.104231
$955$	6.30540e7	2.23720
$956$	−3.46528e6	−0.122629
$957$	2.88098e7	1.01686
$958$	1.34627e7	0.473935
$959$	1.44838e7	0.508552
$960$	−1.60855e7	−0.563320
$961$	6.00813e7	2.09861
$962$	1.86622e7	0.650169
$963$	−7.75731e6	−0.269554
$964$	−1.25084e7	−0.433519
$965$	3.07535e6	0.106311
$966$	−1.13226e7	−0.390394
$967$	1.35495e7	0.465969	0.232984	−	0.972480i	$-0.425151\pi$
$967$	1.35495e7	0.465969	0.232984	+	0.972480i	$0.425151\pi$
$968$	4.58630e7	1.57316
$969$	1.23616e7	0.422928
$970$	−3.87478e7	−1.32226
$971$	2.50869e7	0.853884	0.426942	−	0.904279i	$-0.359591\pi$
$971$	2.50869e7	0.853884	0.426942	+	0.904279i	$0.359591\pi$
$972$	−447349.	−0.0151873
$973$	−9.50719e6	−0.321936
$974$	−5.55235e7	−1.87534
$975$	−9.45829e6	−0.318641
$976$	4.17679e7	1.40352
$977$	−3.14930e7	−1.05555	−0.527774	−	0.849385i	$-0.676973\pi$
$977$	−3.14930e7	−1.05555	−0.527774	+	0.849385i	$0.676973\pi$
$978$	2.99654e7	1.00178
$979$	−2.73784e7	−0.912959
$980$	−8.80098e6	−0.292729
$981$	9.20247e6	0.305304
$982$	2.13001e6	0.0704861
$983$	−3.59119e6	−0.118537	−0.0592685	−	0.998242i	$-0.518877\pi$
$983$	−3.59119e6	−0.118537	−0.0592685	+	0.998242i	$0.518877\pi$
$984$	−1.80304e7	−0.593632
$985$	4.93298e7	1.62001
$986$	5.32238e7	1.74347
$987$	−1.76228e6	−0.0575813
$988$	−1.68890e6	−0.0550442
$989$	−8.43151e7	−2.74104
$990$	−2.83568e7	−0.919536
$991$	−4.64082e6	−0.150110	−0.0750551	−	0.997179i	$-0.523913\pi$
$991$	−4.64082e6	−0.150110	−0.0750551	+	0.997179i	$0.523913\pi$
$992$	2.53280e7	0.817188
$993$	2.98885e6	0.0961901
$994$	−1.30150e7	−0.417808
$995$	78765.3	0.00252219
$996$	4.55229e6	0.145406
$997$	2.99407e7	0.953946	0.476973	−	0.878918i	$-0.341734\pi$
$997$	2.99407e7	0.953946	0.476973	+	0.878918i	$0.341734\pi$
$998$	3.12149e7	0.992054
$999$	7.43676e6	0.235760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.4	✓	13
3.2	odd	2		531.6.a.e.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.4	✓	13	1.1	even	1	trivial
531.6.a.e.1.10		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)

\(f(q)\)	\(=\)	\(q-6.29094 q^{2} -9.00000 q^{3} +7.57589 q^{4} +82.0909 q^{5} +56.6184 q^{6} +51.5315 q^{7} +153.651 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.29094 q^{2} -9.00000 q^{3} +7.57589 q^{4} +82.0909 q^{5} +56.6184 q^{6} +51.5315 q^{7} +153.651 q^{8} +81.0000 q^{9} -516.429 q^{10} +677.894 q^{11} -68.1830 q^{12} +290.798 q^{13} -324.182 q^{14} -738.818 q^{15} -1209.03 q^{16} +1791.65 q^{17} -509.566 q^{18} -766.617 q^{19} +621.912 q^{20} -463.784 q^{21} -4264.59 q^{22} -3880.75 q^{23} -1382.85 q^{24} +3613.92 q^{25} -1829.39 q^{26} -729.000 q^{27} +390.397 q^{28} -4722.12 q^{29} +4647.86 q^{30} +9418.62 q^{31} +2689.14 q^{32} -6101.04 q^{33} -11271.2 q^{34} +4230.27 q^{35} +613.647 q^{36} -10201.3 q^{37} +4822.74 q^{38} -2617.19 q^{39} +12613.3 q^{40} +13038.5 q^{41} +2917.64 q^{42} +21726.5 q^{43} +5135.65 q^{44} +6649.36 q^{45} +24413.5 q^{46} +3799.78 q^{47} +10881.3 q^{48} -14151.5 q^{49} -22734.9 q^{50} -16124.9 q^{51} +2203.06 q^{52} -5749.98 q^{53} +4586.09 q^{54} +55648.9 q^{55} +7917.85 q^{56} +6899.55 q^{57} +29706.5 q^{58} +3481.00 q^{59} -5597.21 q^{60} -34546.5 q^{61} -59252.0 q^{62} +4174.06 q^{63} +21771.9 q^{64} +23871.9 q^{65} +38381.3 q^{66} +48614.6 q^{67} +13573.4 q^{68} +34926.7 q^{69} -26612.4 q^{70} +40147.1 q^{71} +12445.7 q^{72} -22800.3 q^{73} +64175.9 q^{74} -32525.2 q^{75} -5807.81 q^{76} +34932.9 q^{77} +16464.6 q^{78} -23093.2 q^{79} -99250.7 q^{80} +6561.00 q^{81} -82024.5 q^{82} -66765.7 q^{83} -3513.58 q^{84} +147079. q^{85} -136680. q^{86} +42499.0 q^{87} +104159. q^{88} -40387.5 q^{89} -41830.7 q^{90} +14985.3 q^{91} -29400.1 q^{92} -84767.6 q^{93} -23904.2 q^{94} -62932.3 q^{95} -24202.3 q^{96} +75030.3 q^{97} +89026.2 q^{98} +54909.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 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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