LMFDB - Embedded newform 177.6.a.d.1.10

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			1.10
Root			$6.46075$ 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)

$f(q)$	$=$	$q+6.46075 q^{2} -9.00000 q^{3} +9.74133 q^{4} -95.9365 q^{5} -58.1468 q^{6} +79.3965 q^{7} -143.808 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.46075 q^{2} -9.00000 q^{3} +9.74133 q^{4} -95.9365 q^{5} -58.1468 q^{6} +79.3965 q^{7} -143.808 q^{8} +81.0000 q^{9} -619.822 q^{10} +411.994 q^{11} -87.6720 q^{12} -318.716 q^{13} +512.961 q^{14} +863.428 q^{15} -1240.83 q^{16} +1184.02 q^{17} +523.321 q^{18} +1501.52 q^{19} -934.549 q^{20} -714.568 q^{21} +2661.79 q^{22} -2539.90 q^{23} +1294.27 q^{24} +6078.81 q^{25} -2059.14 q^{26} -729.000 q^{27} +773.427 q^{28} +6270.17 q^{29} +5578.40 q^{30} +9158.88 q^{31} -3414.84 q^{32} -3707.94 q^{33} +7649.66 q^{34} -7617.02 q^{35} +789.048 q^{36} +4023.58 q^{37} +9700.97 q^{38} +2868.44 q^{39} +13796.4 q^{40} -12707.6 q^{41} -4616.65 q^{42} +118.024 q^{43} +4013.37 q^{44} -7770.86 q^{45} -16409.6 q^{46} +17162.3 q^{47} +11167.5 q^{48} -10503.2 q^{49} +39273.7 q^{50} -10656.2 q^{51} -3104.72 q^{52} -5534.56 q^{53} -4709.89 q^{54} -39525.2 q^{55} -11417.8 q^{56} -13513.7 q^{57} +40510.0 q^{58} +3481.00 q^{59} +8410.94 q^{60} +4480.98 q^{61} +59173.3 q^{62} +6431.11 q^{63} +17644.1 q^{64} +30576.5 q^{65} -23956.1 q^{66} -8935.10 q^{67} +11533.9 q^{68} +22859.1 q^{69} -49211.7 q^{70} -71708.9 q^{71} -11648.4 q^{72} +80362.9 q^{73} +25995.4 q^{74} -54709.3 q^{75} +14626.8 q^{76} +32710.8 q^{77} +18532.3 q^{78} -15553.9 q^{79} +119041. q^{80} +6561.00 q^{81} -82100.5 q^{82} -21735.1 q^{83} -6960.84 q^{84} -113591. q^{85} +762.523 q^{86} -56431.5 q^{87} -59247.9 q^{88} +40650.9 q^{89} -50205.6 q^{90} -25304.9 q^{91} -24742.0 q^{92} -82429.9 q^{93} +110881. q^{94} -144051. q^{95} +30733.6 q^{96} +86698.9 q^{97} -67858.6 q^{98} +33371.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.46075	1.14211	0.571055	−	0.820912i	$-0.306534\pi$
$2$	6.46075	1.14211	0.571055	+	0.820912i	$0.306534\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	9.74133	0.304417
$5$	−95.9365	−1.71616	−0.858082	−	0.513513i	$-0.828344\pi$
$5$	−95.9365	−1.71616	−0.858082	+	0.513513i	$0.828344\pi$
$6$	−58.1468	−0.659398
$7$	79.3965	0.612429	0.306215	−	0.951962i	$-0.400937\pi$
$7$	79.3965	0.612429	0.306215	+	0.951962i	$0.400937\pi$
$8$	−143.808	−0.794433
$9$	81.0000	0.333333
$10$	−619.822	−1.96005
$11$	411.994	1.02662	0.513309	−	0.858204i	$-0.328420\pi$
$11$	411.994	1.02662	0.513309	+	0.858204i	$0.328420\pi$
$12$	−87.6720	−0.175755
$13$	−318.716	−0.523052	−0.261526	−	0.965196i	$-0.584226\pi$
$13$	−318.716	−0.523052	−0.261526	+	0.965196i	$0.584226\pi$
$14$	512.961	0.699462
$15$	863.428	0.990828
$16$	−1240.83	−1.21175
$17$	1184.02	0.993658	0.496829	−	0.867848i	$-0.334498\pi$
$17$	1184.02	0.993658	0.496829	+	0.867848i	$0.334498\pi$
$18$	523.321	0.380704
$19$	1501.52	0.954219	0.477109	−	0.878844i	$-0.341685\pi$
$19$	1501.52	0.954219	0.477109	+	0.878844i	$0.341685\pi$
$20$	−934.549	−0.522429
$21$	−714.568	−0.353586
$22$	2661.79	1.17251
$23$	−2539.90	−1.00114	−0.500572	−	0.865695i	$-0.666877\pi$
$23$	−2539.90	−1.00114	−0.500572	+	0.865695i	$0.666877\pi$
$24$	1294.27	0.458666
$25$	6078.81	1.94522
$26$	−2059.14	−0.597384
$27$	−729.000	−0.192450
$28$	773.427	0.186434
$29$	6270.17	1.38447	0.692236	−	0.721671i	$-0.256626\pi$
$29$	6270.17	1.38447	0.692236	+	0.721671i	$0.256626\pi$
$30$	5578.40	1.13163
$31$	9158.88	1.71174	0.855871	−	0.517190i	$-0.173022\pi$
$31$	9158.88	1.71174	0.855871	+	0.517190i	$0.173022\pi$
$32$	−3414.84	−0.589516
$33$	−3707.94	−0.592718
$34$	7649.66	1.13487
$35$	−7617.02	−1.05103
$36$	789.048	0.101472
$37$	4023.58	0.483180	0.241590	−	0.970378i	$-0.422331\pi$
$37$	4023.58	0.483180	0.241590	+	0.970378i	$0.422331\pi$
$38$	9700.97	1.08982
$39$	2868.44	0.301984
$40$	13796.4	1.36338
$41$	−12707.6	−1.18060	−0.590300	−	0.807184i	$-0.700991\pi$
$41$	−12707.6	−1.18060	−0.590300	+	0.807184i	$0.700991\pi$
$42$	−4616.65	−0.403835
$43$	118.024	0.00973417	0.00486708	−	0.999988i	$-0.498451\pi$
$43$	118.024	0.00973417	0.00486708	+	0.999988i	$0.498451\pi$
$44$	4013.37	0.312519
$45$	−7770.86	−0.572055
$46$	−16409.6	−1.14342
$47$	17162.3	1.13326	0.566632	−	0.823971i	$-0.308246\pi$
$47$	17162.3	1.13326	0.566632	+	0.823971i	$0.308246\pi$
$48$	11167.5	0.699603
$49$	−10503.2	−0.624930
$50$	39273.7	2.22166
$51$	−10656.2	−0.573689
$52$	−3104.72	−0.159226
$53$	−5534.56	−0.270641	−0.135320	−	0.990802i	$-0.543206\pi$
$53$	−5534.56	−0.270641	−0.135320	+	0.990802i	$0.543206\pi$
$54$	−4709.89	−0.219799
$55$	−39525.2	−1.76184
$56$	−11417.8	−0.486534
$57$	−13513.7	−0.550919
$58$	40510.0	1.58122
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	8410.94	0.301624
$61$	4480.98	0.154187	0.0770935	−	0.997024i	$-0.475436\pi$
$61$	4480.98	0.154187	0.0770935	+	0.997024i	$0.475436\pi$
$62$	59173.3	1.95500
$63$	6431.11	0.204143
$64$	17644.1	0.538455
$65$	30576.5	0.897644
$66$	−23956.1	−0.676950
$67$	−8935.10	−0.243171	−0.121586	−	0.992581i	$-0.538798\pi$
$67$	−8935.10	−0.243171	−0.121586	+	0.992581i	$0.538798\pi$
$68$	11533.9	0.302486
$69$	22859.1	0.578010
$70$	−49211.7	−1.20039
$71$	−71708.9	−1.68821	−0.844107	−	0.536175i	$-0.819869\pi$
$71$	−71708.9	−1.68821	−0.844107	+	0.536175i	$0.819869\pi$
$72$	−11648.4	−0.264811
$73$	80362.9	1.76502	0.882508	−	0.470298i	$-0.155853\pi$
$73$	80362.9	1.76502	0.882508	+	0.470298i	$0.155853\pi$
$74$	25995.4	0.551845
$75$	−54709.3	−1.12307
$76$	14626.8	0.290480
$77$	32710.8	0.628731
$78$	18532.3	0.344900
$79$	−15553.9	−0.280397	−0.140198	−	0.990123i	$-0.544774\pi$
$79$	−15553.9	−0.280397	−0.140198	+	0.990123i	$0.544774\pi$
$80$	119041.	2.07956
$81$	6561.00	0.111111
$82$	−82100.5	−1.34838
$83$	−21735.1	−0.346311	−0.173156	−	0.984894i	$-0.555396\pi$
$83$	−21735.1	−0.346311	−0.173156	+	0.984894i	$0.555396\pi$
$84$	−6960.84	−0.107638
$85$	−113591.	−1.70528
$86$	762.523	0.0111175
$87$	−56431.5	−0.799325
$88$	−59247.9	−0.815579
$89$	40650.9	0.543996	0.271998	−	0.962298i	$-0.412316\pi$
$89$	40650.9	0.543996	0.271998	+	0.962298i	$0.412316\pi$
$90$	−50205.6	−0.653350
$91$	−25304.9	−0.320333
$92$	−24742.0	−0.304765
$93$	−82429.9	−0.988275
$94$	110881.	1.29431
$95$	−144051.	−1.63760
$96$	30733.6	0.340357
$97$	86698.9	0.935587	0.467794	−	0.883838i	$-0.345049\pi$
$97$	86698.9	0.935587	0.467794	+	0.883838i	$0.345049\pi$
$98$	−67858.6	−0.713739
$99$	33371.5	0.342206
$100$	59215.7	0.592157
$101$	142937.	1.39425	0.697125	−	0.716950i	$-0.254462\pi$
$101$	142937.	1.39425	0.697125	+	0.716950i	$0.254462\pi$
$102$	−68847.0	−0.655216
$103$	16001.2	0.148614	0.0743068	−	0.997235i	$-0.476326\pi$
$103$	16001.2	0.148614	0.0743068	+	0.997235i	$0.476326\pi$
$104$	45833.8	0.415530
$105$	68553.2	0.606812
$106$	−35757.4	−0.309102
$107$	−16859.3	−0.142357	−0.0711785	−	0.997464i	$-0.522676\pi$
$107$	−16859.3	−0.142357	−0.0711785	+	0.997464i	$0.522676\pi$
$108$	−7101.43	−0.0585850
$109$	116486.	0.939088	0.469544	−	0.882909i	$-0.344418\pi$
$109$	116486.	0.939088	0.469544	+	0.882909i	$0.344418\pi$
$110$	−255363.	−2.01222
$111$	−36212.2	−0.278964
$112$	−98517.4	−0.742110
$113$	147797.	1.08885	0.544426	−	0.838809i	$-0.316748\pi$
$113$	147797.	1.08885	0.544426	+	0.838809i	$0.316748\pi$
$114$	−87308.7	−0.629210
$115$	243669.	1.71813
$116$	61079.8	0.421456
$117$	−25816.0	−0.174351
$118$	22489.9	0.148690
$119$	94007.0	0.608545
$120$	−124168.	−0.787146
$121$	8687.76	0.0539442
$122$	28950.5	0.176099
$123$	114368.	0.681620
$124$	89219.7	0.521083
$125$	−283378.	−1.62215
$126$	41549.8	0.233154
$127$	330232.	1.81681	0.908405	−	0.418092i	$-0.137301\pi$
$127$	330232.	1.81681	0.908405	+	0.418092i	$0.137301\pi$
$128$	223269.	1.20449
$129$	−1062.22	−0.00562003
$130$	197547.	1.02521
$131$	−206313.	−1.05038	−0.525191	−	0.850984i	$-0.676006\pi$
$131$	−206313.	−1.05038	−0.525191	+	0.850984i	$0.676006\pi$
$132$	−36120.3	−0.180433
$133$	119216.	0.584392
$134$	−57727.5	−0.277729
$135$	69937.7	0.330276
$136$	−170271.	−0.789395
$137$	87119.2	0.396563	0.198282	−	0.980145i	$-0.436464\pi$
$137$	87119.2	0.396563	0.198282	+	0.980145i	$0.436464\pi$
$138$	147687.	0.660152
$139$	−146405.	−0.642715	−0.321357	−	0.946958i	$-0.604139\pi$
$139$	−146405.	−0.642715	−0.321357	+	0.946958i	$0.604139\pi$
$140$	−74199.9	−0.319951
$141$	−154461.	−0.654290
$142$	−463294.	−1.92813
$143$	−131309.	−0.536975
$144$	−100507.	−0.403916
$145$	−601538.	−2.37598
$146$	519205.	2.01584
$147$	94528.8	0.360804
$148$	39195.1	0.147088
$149$	−191595.	−0.707000	−0.353500	−	0.935434i	$-0.615009\pi$
$149$	−191595.	−0.707000	−0.353500	+	0.935434i	$0.615009\pi$
$150$	−353463.	−1.28267
$151$	29587.2	0.105599	0.0527997	−	0.998605i	$-0.483186\pi$
$151$	29587.2	0.105599	0.0527997	+	0.998605i	$0.483186\pi$
$152$	−215931.	−0.758063
$153$	95905.7	0.331219
$154$	211337.	0.718080
$155$	−878671.	−2.93763
$156$	27942.4	0.0919291
$157$	583036.	1.88776	0.943879	−	0.330292i	$-0.107147\pi$
$157$	583036.	1.88776	0.943879	+	0.330292i	$0.107147\pi$
$158$	−100490.	−0.320244
$159$	49811.0	0.156255
$160$	327608.	1.01171
$161$	−201659.	−0.613130
$162$	42389.0	0.126901
$163$	−582152.	−1.71620	−0.858098	−	0.513485i	$-0.828354\pi$
$163$	−582152.	−1.71620	−0.858098	+	0.513485i	$0.828354\pi$
$164$	−123789.	−0.359394
$165$	355727.	1.01720
$166$	−140425.	−0.395526
$167$	37139.8	0.103050	0.0515250	−	0.998672i	$-0.483592\pi$
$167$	37139.8	0.103050	0.0515250	+	0.998672i	$0.483592\pi$
$168$	102760.	0.280901
$169$	−269713.	−0.726416
$170$	−733882.	−1.94762
$171$	121623.	0.318073
$172$	1149.71	0.00296324
$173$	−141649.	−0.359831	−0.179916	−	0.983682i	$-0.557582\pi$
$173$	−141649.	−0.359831	−0.179916	+	0.983682i	$0.557582\pi$
$174$	−364590.	−0.912918
$175$	482636.	1.19131
$176$	−511214.	−1.24400
$177$	−31329.0	−0.0751646
$178$	262636.	0.621303
$179$	−259868.	−0.606207	−0.303104	−	0.952958i	$-0.598023\pi$
$179$	−259868.	−0.606207	−0.303104	+	0.952958i	$0.598023\pi$
$180$	−75698.5	−0.174143
$181$	−5010.40	−0.0113678	−0.00568389	−	0.999984i	$-0.501809\pi$
$181$	−5010.40	−0.0113678	−0.00568389	+	0.999984i	$0.501809\pi$
$182$	−163489.	−0.365855
$183$	−40328.8	−0.0890199
$184$	365257.	0.795341
$185$	−386008.	−0.829216
$186$	−532559.	−1.12872
$187$	487809.	1.02011
$188$	167184.	0.344984
$189$	−57880.0	−0.117862
$190$	−930677.	−1.87032
$191$	810076.	1.60673	0.803364	−	0.595488i	$-0.203041\pi$
$191$	810076.	1.60673	0.803364	+	0.595488i	$0.203041\pi$
$192$	−158797.	−0.310877
$193$	736270.	1.42280	0.711400	−	0.702788i	$-0.248062\pi$
$193$	736270.	1.42280	0.711400	+	0.702788i	$0.248062\pi$
$194$	560140.	1.06854
$195$	−275188.	−0.518255
$196$	−102315.	−0.190239
$197$	−531410.	−0.975583	−0.487791	−	0.872960i	$-0.662197\pi$
$197$	−531410.	−0.975583	−0.487791	+	0.872960i	$0.662197\pi$
$198$	215605.	0.390837
$199$	63870.1	0.114331	0.0571656	−	0.998365i	$-0.481794\pi$
$199$	63870.1	0.114331	0.0571656	+	0.998365i	$0.481794\pi$
$200$	−874180.	−1.54535
$201$	80415.9	0.140395
$202$	923479.	1.59239
$203$	497829.	0.847891
$204$	−103805.	−0.174640
$205$	1.21912e6	2.02610
$206$	103380.	0.169733
$207$	−205732.	−0.333714
$208$	395472.	0.633807
$209$	618618.	0.979618
$210$	442905.	0.693047
$211$	332895.	0.514756	0.257378	−	0.966311i	$-0.417142\pi$
$211$	332895.	0.514756	0.257378	+	0.966311i	$0.417142\pi$
$212$	−53914.0	−0.0823875
$213$	645380.	0.974691
$214$	−108924.	−0.162588
$215$	−11322.8	−0.0167054
$216$	104836.	0.152889
$217$	727183.	1.04832
$218$	752586.	1.07254
$219$	−723266.	−1.01903
$220$	−385028.	−0.536335
$221$	−377366.	−0.519735
$222$	−233958.	−0.318608
$223$	1.27218e6	1.71312	0.856559	−	0.516049i	$-0.172598\pi$
$223$	1.27218e6	1.71312	0.856559	+	0.516049i	$0.172598\pi$
$224$	−271126.	−0.361037
$225$	492384.	0.648406
$226$	954878.	1.24359
$227$	804911.	1.03677	0.518386	−	0.855147i	$-0.326533\pi$
$227$	804911.	1.03677	0.518386	+	0.855147i	$0.326533\pi$
$228$	−131641.	−0.167709
$229$	1.03943e6	1.30980	0.654901	−	0.755715i	$-0.272711\pi$
$229$	1.03943e6	1.30980	0.654901	+	0.755715i	$0.272711\pi$
$230$	1.57428e6	1.96229
$231$	−294398.	−0.362998
$232$	−901699.	−1.09987
$233$	−394133.	−0.475612	−0.237806	−	0.971313i	$-0.576428\pi$
$233$	−394133.	−0.475612	−0.237806	+	0.971313i	$0.576428\pi$
$234$	−166791.	−0.199128
$235$	−1.64649e6	−1.94487
$236$	33909.6	0.0396317
$237$	139985.	0.161887
$238$	607356.	0.695026
$239$	525995.	0.595644	0.297822	−	0.954621i	$-0.403740\pi$
$239$	525995.	0.595644	0.297822	+	0.954621i	$0.403740\pi$
$240$	−1.07137e6	−1.20063
$241$	−924747.	−1.02561	−0.512803	−	0.858507i	$-0.671393\pi$
$241$	−924747.	−1.02561	−0.512803	+	0.858507i	$0.671393\pi$
$242$	56129.5	0.0616102
$243$	−59049.0	−0.0641500
$244$	43650.7	0.0469371
$245$	1.00764e6	1.07248
$246$	738904.	0.778485
$247$	−478559.	−0.499106
$248$	−1.31712e6	−1.35986
$249$	195616.	0.199943
$250$	−1.83084e6	−1.85268
$251$	−1.81104e6	−1.81444	−0.907221	−	0.420653i	$-0.861801\pi$
$251$	−1.81104e6	−1.81444	−0.907221	+	0.420653i	$0.861801\pi$
$252$	62647.6	0.0621446
$253$	−1.04642e6	−1.02779
$254$	2.13354e6	2.07500
$255$	1.02232e6	0.984544
$256$	877875.	0.837207
$257$	−479966.	−0.453292	−0.226646	−	0.973977i	$-0.572776\pi$
$257$	−479966.	−0.453292	−0.226646	+	0.973977i	$0.572776\pi$
$258$	−6862.71	−0.00641869
$259$	319458.	0.295913
$260$	297856.	0.273258
$261$	507884.	0.461491
$262$	−1.33294e6	−1.19965
$263$	1.39283e6	1.24168	0.620838	−	0.783939i	$-0.286792\pi$
$263$	1.39283e6	1.24168	0.620838	+	0.783939i	$0.286792\pi$
$264$	533231.	0.470875
$265$	530966.	0.464464
$266$	770223.	0.667440
$267$	−365858.	−0.314076
$268$	−87039.8	−0.0740254
$269$	1.73816e6	1.46457	0.732284	−	0.681000i	$-0.238455\pi$
$269$	1.73816e6	1.46457	0.732284	+	0.681000i	$0.238455\pi$
$270$	451850.	0.377212
$271$	2.20194e6	1.82130	0.910651	−	0.413176i	$-0.135581\pi$
$271$	2.20194e6	1.82130	0.910651	+	0.413176i	$0.135581\pi$
$272$	−1.46917e6	−1.20406
$273$	227744.	0.184944
$274$	562855.	0.452919
$275$	2.50443e6	1.99700
$276$	222678.	0.175956
$277$	1.04584e6	0.818968	0.409484	−	0.912317i	$-0.365709\pi$
$277$	1.04584e6	0.818968	0.409484	+	0.912317i	$0.365709\pi$
$278$	−945885.	−0.734051
$279$	741869.	0.570581
$280$	1.09539e6	0.834973
$281$	−1.99987e6	−1.51090	−0.755450	−	0.655206i	$-0.772582\pi$
$281$	−1.99987e6	−1.51090	−0.755450	+	0.655206i	$0.772582\pi$
$282$	−997932.	−0.747271
$283$	306460.	0.227461	0.113731	−	0.993512i	$-0.463720\pi$
$283$	306460.	0.227461	0.113731	+	0.993512i	$0.463720\pi$
$284$	−698540.	−0.513920
$285$	1.29646e6	0.945467
$286$	−848354.	−0.613285
$287$	−1.00894e6	−0.723034
$288$	−276602.	−0.196505
$289$	−17952.4	−0.0126438
$290$	−3.88639e6	−2.71363
$291$	−780290.	−0.540162
$292$	782842.	0.537300
$293$	−2.29345e6	−1.56070	−0.780351	−	0.625342i	$-0.784959\pi$
$293$	−2.29345e6	−1.56070	−0.780351	+	0.625342i	$0.784959\pi$
$294$	610727.	0.412078
$295$	−333955.	−0.223426
$296$	−578623.	−0.383854
$297$	−300343.	−0.197573
$298$	−1.23785e6	−0.807473
$299$	809505.	0.523650
$300$	−532941.	−0.341882
$301$	9370.68	0.00596149
$302$	191156.	0.120606
$303$	−1.28643e6	−0.804970
$304$	−1.86313e6	−1.15627
$305$	−429889.	−0.264610
$306$	619623.	0.378289
$307$	2.22160e6	1.34530	0.672650	−	0.739960i	$-0.265156\pi$
$307$	2.22160e6	1.34530	0.672650	+	0.739960i	$0.265156\pi$
$308$	318647.	0.191396
$309$	−144010.	−0.0858021
$310$	−5.67688e6	−3.35510
$311$	990599.	0.580760	0.290380	−	0.956911i	$-0.406218\pi$
$311$	990599.	0.580760	0.290380	+	0.956911i	$0.406218\pi$
$312$	−412504.	−0.239906
$313$	219330.	0.126543	0.0632713	−	0.997996i	$-0.479847\pi$
$313$	219330.	0.126543	0.0632713	+	0.997996i	$0.479847\pi$
$314$	3.76685e6	2.15603
$315$	−616978.	−0.350343
$316$	−151516.	−0.0853574
$317$	−1.77095e6	−0.989825	−0.494913	−	0.868943i	$-0.664800\pi$
$317$	−1.77095e6	−0.989825	−0.494913	+	0.868943i	$0.664800\pi$
$318$	321817.	0.178460
$319$	2.58327e6	1.42132
$320$	−1.69271e6	−0.924077
$321$	151733.	0.0821899
$322$	−1.30287e6	−0.700262
$323$	1.77783e6	0.948167
$324$	63912.9	0.0338241
$325$	−1.93741e6	−1.01745
$326$	−3.76114e6	−1.96009
$327$	−1.04837e6	−0.542183
$328$	1.82745e6	0.937908
$329$	1.36263e6	0.694044
$330$	2.29826e6	1.16176
$331$	−3.39860e6	−1.70502	−0.852511	−	0.522709i	$-0.824921\pi$
$331$	−3.39860e6	−1.70502	−0.852511	+	0.522709i	$0.824921\pi$
$332$	−211729.	−0.105423
$333$	325910.	0.161060
$334$	239951.	0.117694
$335$	857202.	0.417322
$336$	886657.	0.428457
$337$	1.02393e6	0.491129	0.245565	−	0.969380i	$-0.421027\pi$
$337$	1.02393e6	0.491129	0.245565	+	0.969380i	$0.421027\pi$
$338$	−1.74255e6	−0.829648
$339$	−1.33017e6	−0.628648
$340$	−1.10653e6	−0.519116
$341$	3.77340e6	1.75730
$342$	785779.	0.363275
$343$	−2.16833e6	−0.995155
$344$	−16972.8	−0.00773315
$345$	−2.19302e6	−0.991961
$346$	−915160.	−0.410967
$347$	−501613.	−0.223638	−0.111819	−	0.993729i	$-0.535668\pi$
$347$	−501613.	−0.223638	−0.111819	+	0.993729i	$0.535668\pi$
$348$	−549718.	−0.243328
$349$	−1.30707e6	−0.574428	−0.287214	−	0.957866i	$-0.592729\pi$
$349$	−1.30707e6	−0.574428	−0.287214	+	0.957866i	$0.592729\pi$
$350$	3.11819e6	1.36061
$351$	232344.	0.100661
$352$	−1.40689e6	−0.605208
$353$	2.37686e6	1.01523	0.507617	−	0.861583i	$-0.330526\pi$
$353$	2.37686e6	1.01523	0.507617	+	0.861583i	$0.330526\pi$
$354$	−202409.	−0.0858463
$355$	6.87950e6	2.89725
$356$	395994.	0.165601
$357$	−846063.	−0.351344
$358$	−1.67895e6	−0.692356
$359$	496562.	0.203347	0.101673	−	0.994818i	$-0.467580\pi$
$359$	496562.	0.203347	0.101673	+	0.994818i	$0.467580\pi$
$360$	1.11751e6	0.454459
$361$	−221527.	−0.0894663
$362$	−32370.9	−0.0129833
$363$	−78189.8	−0.0311447
$364$	−246503.	−0.0975146
$365$	−7.70974e6	−3.02906
$366$	−260554.	−0.101671
$367$	−2.21005e6	−0.856517	−0.428258	−	0.903656i	$-0.640873\pi$
$367$	−2.21005e6	−0.856517	−0.428258	+	0.903656i	$0.640873\pi$
$368$	3.15158e6	1.21313
$369$	−1.02931e6	−0.393533
$370$	−2.49391e6	−0.947056
$371$	−439424.	−0.165748
$372$	−802977.	−0.300847
$373$	−4.85205e6	−1.80573	−0.902866	−	0.429921i	$-0.858541\pi$
$373$	−4.85205e6	−1.80573	−0.902866	+	0.429921i	$0.858541\pi$
$374$	3.15161e6	1.16508
$375$	2.55040e6	0.936549
$376$	−2.46807e6	−0.900302
$377$	−1.99840e6	−0.724151
$378$	−373949.	−0.134612
$379$	−2.38032e6	−0.851212	−0.425606	−	0.904909i	$-0.639939\pi$
$379$	−2.38032e6	−0.851212	−0.425606	+	0.904909i	$0.639939\pi$
$380$	−1.40325e6	−0.498511
$381$	−2.97208e6	−1.04894
$382$	5.23370e6	1.83506
$383$	3.79802e6	1.32300	0.661500	−	0.749945i	$-0.269920\pi$
$383$	3.79802e6	1.32300	0.661500	+	0.749945i	$0.269920\pi$
$384$	−2.00942e6	−0.695413
$385$	−3.13816e6	−1.07901
$386$	4.75686e6	1.62499
$387$	9559.94	0.00324472
$388$	844563.	0.284808
$389$	−3.14174e6	−1.05268	−0.526339	−	0.850275i	$-0.676436\pi$
$389$	−3.14174e6	−1.05268	−0.526339	+	0.850275i	$0.676436\pi$
$390$	−1.77792e6	−0.591904
$391$	−3.00729e6	−0.994794
$392$	1.51044e6	0.496465
$393$	1.85681e6	0.606439
$394$	−3.43331e6	−1.11422
$395$	1.49219e6	0.481207
$396$	325083.	0.104173
$397$	52969.3	0.0168674	0.00843370	−	0.999964i	$-0.497315\pi$
$397$	52969.3	0.0168674	0.00843370	+	0.999964i	$0.497315\pi$
$398$	412649.	0.130579
$399$	−1.07294e6	−0.337399
$400$	−7.54276e6	−2.35711
$401$	−3.87160e6	−1.20235	−0.601173	−	0.799119i	$-0.705300\pi$
$401$	−3.87160e6	−1.20235	−0.601173	+	0.799119i	$0.705300\pi$
$402$	519547.	0.160347
$403$	−2.91908e6	−0.895331
$404$	1.39239e6	0.424433
$405$	−629439.	−0.190685
$406$	3.21635e6	0.968386
$407$	1.65769e6	0.496041
$408$	1.53244e6	0.455757
$409$	−3.15765e6	−0.933373	−0.466687	−	0.884423i	$-0.654552\pi$
$409$	−3.15765e6	−0.933373	−0.466687	+	0.884423i	$0.654552\pi$
$410$	7.87643e6	2.31403
$411$	−784073.	−0.228956
$412$	155873.	0.0452404
$413$	276379.	0.0797315
$414$	−1.32918e6	−0.381139
$415$	2.08519e6	0.594327
$416$	1.08836e6	0.308348
$417$	1.31764e6	0.371072
$418$	3.99674e6	1.11883
$419$	−1.14024e6	−0.317293	−0.158646	−	0.987335i	$-0.550713\pi$
$419$	−1.14024e6	−0.317293	−0.158646	+	0.987335i	$0.550713\pi$
$420$	667799.	0.184724
$421$	5.86685e6	1.61324	0.806622	−	0.591068i	$-0.201294\pi$
$421$	5.86685e6	1.61324	0.806622	+	0.591068i	$0.201294\pi$
$422$	2.15075e6	0.587908
$423$	1.39015e6	0.377754
$424$	795912.	0.215006
$425$	7.19744e6	1.93288
$426$	4.16964e6	1.11320
$427$	355774.	0.0944287
$428$	−164232.	−0.0433359
$429$	1.18178e6	0.310023
$430$	−73153.8	−0.0190794
$431$	−2.83424e6	−0.734925	−0.367462	−	0.930038i	$-0.619773\pi$
$431$	−2.83424e6	−0.734925	−0.367462	+	0.930038i	$0.619773\pi$
$432$	904564.	0.233201
$433$	1.57040e6	0.402522	0.201261	−	0.979538i	$-0.435496\pi$
$433$	1.57040e6	0.402522	0.201261	+	0.979538i	$0.435496\pi$
$434$	4.69815e6	1.19730
$435$	5.41384e6	1.37177
$436$	1.13473e6	0.285874
$437$	−3.81371e6	−0.955310
$438$	−4.67284e6	−1.16385
$439$	2.72637e6	0.675186	0.337593	−	0.941292i	$-0.390387\pi$
$439$	2.72637e6	0.675186	0.337593	+	0.941292i	$0.390387\pi$
$440$	5.68403e6	1.39967
$441$	−850759.	−0.208310
$442$	−2.43807e6	−0.593595
$443$	−4.86100e6	−1.17684	−0.588418	−	0.808557i	$-0.700249\pi$
$443$	−4.86100e6	−1.17684	−0.588418	+	0.808557i	$0.700249\pi$
$444$	−352755.	−0.0849212
$445$	−3.89991e6	−0.933586
$446$	8.21926e6	1.95657
$447$	1.72436e6	0.408187
$448$	1.40088e6	0.329765
$449$	−3.65621e6	−0.855884	−0.427942	−	0.903806i	$-0.640761\pi$
$449$	−3.65621e6	−0.855884	−0.427942	+	0.903806i	$0.640761\pi$
$450$	3.18117e6	0.740552
$451$	−5.23544e6	−1.21203
$452$	1.43974e6	0.331464
$453$	−266285.	−0.0609678
$454$	5.20033e6	1.18411
$455$	2.42766e6	0.549743
$456$	1.94338e6	0.437668
$457$	4.47448e6	1.00220	0.501098	−	0.865391i	$-0.332930\pi$
$457$	4.47448e6	1.00220	0.501098	+	0.865391i	$0.332930\pi$
$458$	6.71548e6	1.49594
$459$	−863151.	−0.191230
$460$	2.37366e6	0.523026
$461$	−6.47334e6	−1.41865	−0.709326	−	0.704880i	$-0.751001\pi$
$461$	−6.47334e6	−1.41865	−0.709326	+	0.704880i	$0.751001\pi$
$462$	−1.90203e6	−0.414584
$463$	−105486.	−0.0228687	−0.0114343	−	0.999935i	$-0.503640\pi$
$463$	−105486.	−0.0228687	−0.0114343	+	0.999935i	$0.503640\pi$
$464$	−7.78021e6	−1.67763
$465$	7.90804e6	1.69604
$466$	−2.54639e6	−0.543201
$467$	−1.33993e6	−0.284309	−0.142154	−	0.989844i	$-0.545403\pi$
$467$	−1.33993e6	−0.284309	−0.142154	+	0.989844i	$0.545403\pi$
$468$	−251482.	−0.0530753
$469$	−709415.	−0.148925
$470$	−1.06376e7	−2.22125
$471$	−5.24732e6	−1.08990
$472$	−500595.	−0.103426
$473$	48625.1	0.00999327
$474$	904412.	0.184893
$475$	9.12747e6	1.85616
$476$	915754.	0.185251
$477$	−448299.	−0.0902136
$478$	3.39832e6	0.680292
$479$	6.23114e6	1.24088	0.620439	−	0.784255i	$-0.286955\pi$
$479$	6.23114e6	1.24088	0.620439	+	0.784255i	$0.286955\pi$
$480$	−2.94847e6	−0.584109
$481$	−1.28238e6	−0.252728
$482$	−5.97456e6	−1.17135
$483$	1.81493e6	0.353991
$484$	84630.3	0.0164215
$485$	−8.31759e6	−1.60562
$486$	−381501.	−0.0732664
$487$	−6.06445e6	−1.15869	−0.579347	−	0.815081i	$-0.696693\pi$
$487$	−6.06445e6	−1.15869	−0.579347	+	0.815081i	$0.696693\pi$
$488$	−644399.	−0.122491
$489$	5.23936e6	0.990847
$490$	6.51012e6	1.22489
$491$	6.27890e6	1.17538	0.587692	−	0.809085i	$-0.300037\pi$
$491$	6.27890e6	1.17538	0.587692	+	0.809085i	$0.300037\pi$
$492$	1.11410e6	0.207496
$493$	7.42401e6	1.37569
$494$	−3.09185e6	−0.570035
$495$	−3.20154e6	−0.587282
$496$	−1.13646e7	−2.07420
$497$	−5.69344e6	−1.03391
$498$	1.26383e6	0.228357
$499$	7.84934e6	1.41118	0.705589	−	0.708621i	$-0.250682\pi$
$499$	7.84934e6	1.41118	0.705589	+	0.708621i	$0.250682\pi$
$500$	−2.76048e6	−0.493810
$501$	−334258.	−0.0594959
$502$	−1.17007e7	−2.07229
$503$	−85865.7	−0.0151321	−0.00756606	−	0.999971i	$-0.502408\pi$
$503$	−85865.7	−0.0151321	−0.00756606	+	0.999971i	$0.502408\pi$
$504$	−924844.	−0.162178
$505$	−1.37129e7	−2.39276
$506$	−6.76067e6	−1.17385
$507$	2.42742e6	0.419397
$508$	3.21689e6	0.553067
$509$	−8.00405e6	−1.36935	−0.684676	−	0.728847i	$-0.740056\pi$
$509$	−8.00405e6	−1.36935	−0.684676	+	0.728847i	$0.740056\pi$
$510$	6.60494e6	1.12446
$511$	6.38053e6	1.08095
$512$	−1.47287e6	−0.248308
$513$	−1.09461e6	−0.183640
$514$	−3.10094e6	−0.517709
$515$	−1.53510e6	−0.255045
$516$	−10347.4	−0.00171083
$517$	7.07076e6	1.16343
$518$	2.06394e6	0.337966
$519$	1.27484e6	0.207749
$520$	−4.39713e6	−0.713118
$521$	793103.	0.128007	0.0640037	−	0.997950i	$-0.479613\pi$
$521$	793103.	0.128007	0.0640037	+	0.997950i	$0.479613\pi$
$522$	3.28131e6	0.527073
$523$	−5.10347e6	−0.815851	−0.407926	−	0.913015i	$-0.633748\pi$
$523$	−5.10347e6	−0.815851	−0.407926	+	0.913015i	$0.633748\pi$
$524$	−2.00976e6	−0.319754
$525$	−4.34372e6	−0.687803
$526$	8.99873e6	1.41813
$527$	1.08443e7	1.70089
$528$	4.60092e6	0.718224
$529$	14724.8	0.00228775
$530$	3.43044e6	0.530469
$531$	281961.	0.0433963
$532$	1.16132e6	0.177899
$533$	4.05010e6	0.617516
$534$	−2.36372e6	−0.358710
$535$	1.61742e6	0.244308
$536$	1.28494e6	0.193183
$537$	2.33882e6	0.349994
$538$	1.12298e7	1.67270
$539$	−4.32725e6	−0.641564
$540$	681286.	0.100541
$541$	6.82517e6	1.00258	0.501291	−	0.865279i	$-0.332859\pi$
$541$	6.82517e6	1.00258	0.501291	+	0.865279i	$0.332859\pi$
$542$	1.42262e7	2.08013
$543$	45093.6	0.00656319
$544$	−4.04324e6	−0.585777
$545$	−1.11752e7	−1.61163
$546$	1.47140e6	0.211227
$547$	1.79924e6	0.257111	0.128555	−	0.991702i	$-0.458966\pi$
$547$	1.79924e6	0.257111	0.128555	+	0.991702i	$0.458966\pi$
$548$	848657.	0.120720
$549$	362959.	0.0513957
$550$	1.61805e7	2.28079
$551$	9.41480e6	1.32109
$552$	−3.28731e6	−0.459191
$553$	−1.23493e6	−0.171723
$554$	6.75693e6	0.935352
$555$	3.47408e6	0.478748
$556$	−1.42618e6	−0.195653
$557$	−9.13011e6	−1.24692	−0.623459	−	0.781856i	$-0.714273\pi$
$557$	−9.13011e6	−1.24692	−0.623459	+	0.781856i	$0.714273\pi$
$558$	4.79304e6	0.651666
$559$	−37616.1	−0.00509148
$560$	9.45142e6	1.27358
$561$	−4.39028e6	−0.588959
$562$	−1.29207e7	−1.72561
$563$	−4.93346e6	−0.655965	−0.327982	−	0.944684i	$-0.606369\pi$
$563$	−4.93346e6	−0.655965	−0.327982	+	0.944684i	$0.606369\pi$
$564$	−1.50465e6	−0.199177
$565$	−1.41791e7	−1.86865
$566$	1.97996e6	0.259786
$567$	520920.	0.0680477
$568$	1.03123e7	1.34117
$569$	−1.11137e7	−1.43906	−0.719530	−	0.694461i	$-0.755643\pi$
$569$	−1.11137e7	−1.43906	−0.719530	+	0.694461i	$0.755643\pi$
$570$	8.37609e6	1.07983
$571$	9.11226e6	1.16960	0.584798	−	0.811179i	$-0.301174\pi$
$571$	9.11226e6	1.16960	0.584798	+	0.811179i	$0.301174\pi$
$572$	−1.27912e6	−0.163464
$573$	−7.29069e6	−0.927645
$574$	−6.51849e6	−0.825785
$575$	−1.54395e7	−1.94744
$576$	1.42917e6	0.179485
$577$	−8.52668e6	−1.06620	−0.533102	−	0.846051i	$-0.678974\pi$
$577$	−8.52668e6	−1.06620	−0.533102	+	0.846051i	$0.678974\pi$
$578$	−115986.	−0.0144406
$579$	−6.62643e6	−0.821454
$580$	−5.85978e6	−0.723288
$581$	−1.72569e6	−0.212091
$582$	−5.04126e6	−0.616924
$583$	−2.28020e6	−0.277845
$584$	−1.15568e7	−1.40219
$585$	2.47669e6	0.299215
$586$	−1.48174e7	−1.78249
$587$	−1.06558e7	−1.27641	−0.638203	−	0.769868i	$-0.720322\pi$
$587$	−1.06558e7	−1.27641	−0.638203	+	0.769868i	$0.720322\pi$
$588$	920836.	0.109835
$589$	1.37523e7	1.63338
$590$	−2.15760e6	−0.255177
$591$	4.78269e6	0.563253
$592$	−4.99258e6	−0.585492
$593$	9.82138e6	1.14693	0.573463	−	0.819231i	$-0.305599\pi$
$593$	9.82138e6	1.14693	0.573463	+	0.819231i	$0.305599\pi$
$594$	−1.94044e6	−0.225650
$595$	−9.01871e6	−1.04436
$596$	−1.86639e6	−0.215223
$597$	−574831.	−0.0660092
$598$	5.23001e6	0.598067
$599$	1.52630e7	1.73809	0.869046	−	0.494731i	$-0.164733\pi$
$599$	1.52630e7	1.73809	0.869046	+	0.494731i	$0.164733\pi$
$600$	7.86762e6	0.892206
$601$	1.51746e7	1.71368	0.856840	−	0.515582i	$-0.172424\pi$
$601$	1.51746e7	1.71368	0.856840	+	0.515582i	$0.172424\pi$
$602$	60541.7	0.00680868
$603$	−723743.	−0.0810571
$604$	288219.	0.0321462
$605$	−833473.	−0.0925770
$606$	−8.31131e6	−0.919365
$607$	9.42013e6	1.03773	0.518866	−	0.854856i	$-0.326354\pi$
$607$	9.42013e6	1.03773	0.518866	+	0.854856i	$0.326354\pi$
$608$	−5.12746e6	−0.562527
$609$	−4.48046e6	−0.489530
$610$	−2.77741e6	−0.302214
$611$	−5.46989e6	−0.592756
$612$	934249.	0.100829
$613$	1.50737e7	1.62020	0.810099	−	0.586294i	$-0.199414\pi$
$613$	1.50737e7	1.62020	0.810099	+	0.586294i	$0.199414\pi$
$614$	1.43532e7	1.53648
$615$	−1.09721e7	−1.16977
$616$	−4.70407e6	−0.499485
$617$	4.49898e6	0.475774	0.237887	−	0.971293i	$-0.423545\pi$
$617$	4.49898e6	0.475774	0.237887	+	0.971293i	$0.423545\pi$
$618$	−930416.	−0.0979955
$619$	4.32828e6	0.454034	0.227017	−	0.973891i	$-0.427103\pi$
$619$	4.32828e6	0.454034	0.227017	+	0.973891i	$0.427103\pi$
$620$	−8.55942e6	−0.894263
$621$	1.85158e6	0.192670
$622$	6.40002e6	0.663293
$623$	3.22754e6	0.333159
$624$	−3.55925e6	−0.365929
$625$	8.19002e6	0.838659
$626$	1.41704e6	0.144526
$627$	−5.56756e6	−0.565583
$628$	5.67955e6	0.574665
$629$	4.76401e6	0.480115
$630$	−3.98615e6	−0.400131
$631$	−4.53423e6	−0.453346	−0.226673	−	0.973971i	$-0.572785\pi$
$631$	−4.53423e6	−0.453346	−0.226673	+	0.973971i	$0.572785\pi$
$632$	2.23678e6	0.222756
$633$	−2.99605e6	−0.297194
$634$	−1.14417e7	−1.13049
$635$	−3.16813e7	−3.11794
$636$	485226.	0.0475665
$637$	3.34754e6	0.326871
$638$	1.66899e7	1.62331
$639$	−5.80842e6	−0.562738
$640$	−2.14196e7	−2.06710
$641$	7.17166e6	0.689406	0.344703	−	0.938712i	$-0.387980\pi$
$641$	7.17166e6	0.689406	0.344703	+	0.938712i	$0.387980\pi$
$642$	980312.	0.0938700
$643$	−9.57407e6	−0.913206	−0.456603	−	0.889670i	$-0.650934\pi$
$643$	−9.57407e6	−0.913206	−0.456603	+	0.889670i	$0.650934\pi$
$644$	−1.96442e6	−0.186647
$645$	101905.	0.00964489
$646$	1.14861e7	1.08291
$647$	−8.76764e6	−0.823421	−0.411711	−	0.911315i	$-0.635069\pi$
$647$	−8.76764e6	−0.823421	−0.411711	+	0.911315i	$0.635069\pi$
$648$	−943523.	−0.0882704
$649$	1.43415e6	0.133654
$650$	−1.25171e7	−1.16204
$651$	−6.54465e6	−0.605248
$652$	−5.67093e6	−0.522439
$653$	1.68161e7	1.54327	0.771634	−	0.636067i	$-0.219440\pi$
$653$	1.68161e7	1.54327	0.771634	+	0.636067i	$0.219440\pi$
$654$	−6.77327e6	−0.619233
$655$	1.97929e7	1.80263
$656$	1.57679e7	1.43059
$657$	6.50940e6	0.588339
$658$	8.80359e6	0.792675
$659$	4.19169e6	0.375989	0.187995	−	0.982170i	$-0.439801\pi$
$659$	4.19169e6	0.375989	0.187995	+	0.982170i	$0.439801\pi$
$660$	3.46525e6	0.309653
$661$	−1.35542e7	−1.20662	−0.603309	−	0.797508i	$-0.706151\pi$
$661$	−1.35542e7	−1.20662	−0.603309	+	0.797508i	$0.706151\pi$
$662$	−2.19575e7	−1.94732
$663$	3.39629e6	0.300069
$664$	3.12568e6	0.275121
$665$	−1.14371e7	−1.00291
$666$	2.10563e6	0.183948
$667$	−1.59256e7	−1.38605
$668$	361791.	0.0313701
$669$	−1.14496e7	−0.989069
$670$	5.53817e6	0.476628
$671$	1.84613e6	0.158291
$672$	2.44014e6	0.208445
$673$	1.49534e7	1.27263	0.636316	−	0.771428i	$-0.280457\pi$
$673$	1.49534e7	1.27263	0.636316	+	0.771428i	$0.280457\pi$
$674$	6.61536e6	0.560924
$675$	−4.43145e6	−0.374358
$676$	−2.62737e6	−0.221133
$677$	2.36734e6	0.198513	0.0992564	−	0.995062i	$-0.468354\pi$
$677$	2.36734e6	0.198513	0.0992564	+	0.995062i	$0.468354\pi$
$678$	−8.59390e6	−0.717986
$679$	6.88359e6	0.572981
$680$	1.63352e7	1.35473
$681$	−7.24420e6	−0.598581
$682$	2.43790e7	2.00704
$683$	−9.65515e6	−0.791968	−0.395984	−	0.918258i	$-0.629596\pi$
$683$	−9.65515e6	−0.791968	−0.395984	+	0.918258i	$0.629596\pi$
$684$	1.18477e6	0.0968267
$685$	−8.35791e6	−0.680567
$686$	−1.40091e7	−1.13658
$687$	−9.35484e6	−0.756214
$688$	−146448.	−0.0117954
$689$	1.76395e6	0.141559
$690$	−1.41685e7	−1.13293
$691$	−1.21221e7	−0.965788	−0.482894	−	0.875679i	$-0.660414\pi$
$691$	−1.21221e7	−0.965788	−0.482894	+	0.875679i	$0.660414\pi$
$692$	−1.37985e6	−0.109539
$693$	2.64958e6	0.209577
$694$	−3.24080e6	−0.255419
$695$	1.40456e7	1.10300
$696$	8.11529e6	0.635011
$697$	−1.50460e7	−1.17311
$698$	−8.44467e6	−0.656061
$699$	3.54719e6	0.274595
$700$	4.70152e6	0.362654
$701$	−4.54661e6	−0.349456	−0.174728	−	0.984617i	$-0.555905\pi$
$701$	−4.54661e6	−0.349456	−0.174728	+	0.984617i	$0.555905\pi$
$702$	1.50112e6	0.114967
$703$	6.04150e6	0.461059
$704$	7.26925e6	0.552787
$705$	1.48184e7	1.12287
$706$	1.53563e7	1.15951
$707$	1.13487e7	0.853880
$708$	−305186.	−0.0228814
$709$	−7.39439e6	−0.552442	−0.276221	−	0.961094i	$-0.589082\pi$
$709$	−7.39439e6	−0.552442	−0.276221	+	0.961094i	$0.589082\pi$
$710$	4.44468e7	3.30898
$711$	−1.25987e6	−0.0934655
$712$	−5.84592e6	−0.432168
$713$	−2.32626e7	−1.71370
$714$	−5.46621e6	−0.401274
$715$	1.25973e7	0.921537
$716$	−2.53146e6	−0.184539
$717$	−4.73396e6	−0.343895
$718$	3.20816e6	0.232244
$719$	1.41444e7	1.02038	0.510189	−	0.860062i	$-0.329575\pi$
$719$	1.41444e7	1.02038	0.510189	+	0.860062i	$0.329575\pi$
$720$	9.64230e6	0.693186
$721$	1.27044e6	0.0910153
$722$	−1.43123e6	−0.102180
$723$	8.32272e6	0.592133
$724$	−48807.9	−0.00346054
$725$	3.81152e7	2.69310
$726$	−505165.	−0.0355707
$727$	−1.50137e7	−1.05354	−0.526771	−	0.850007i	$-0.676598\pi$
$727$	−1.50137e7	−1.05354	−0.526771	+	0.850007i	$0.676598\pi$
$728$	3.63904e6	0.254483
$729$	531441.	0.0370370
$730$	−4.98107e7	−3.45952
$731$	139743.	0.00967243
$732$	−392856.	−0.0270991
$733$	−8.67934e6	−0.596660	−0.298330	−	0.954463i	$-0.596430\pi$
$733$	−8.67934e6	−0.596660	−0.298330	+	0.954463i	$0.596430\pi$
$734$	−1.42786e7	−0.978237
$735$	−9.06876e6	−0.619198
$736$	8.67334e6	0.590190
$737$	−3.68120e6	−0.249644
$738$	−6.65014e6	−0.449459
$739$	−3.85395e6	−0.259594	−0.129797	−	0.991541i	$-0.541433\pi$
$739$	−3.85395e6	−0.259594	−0.129797	+	0.991541i	$0.541433\pi$
$740$	−3.76024e6	−0.252427
$741$	4.30703e6	0.288159
$742$	−2.83901e6	−0.189303
$743$	−1.30750e7	−0.868899	−0.434450	−	0.900696i	$-0.643057\pi$
$743$	−1.30750e7	−0.868899	−0.434450	+	0.900696i	$0.643057\pi$
$744$	1.18541e7	0.785118
$745$	1.83810e7	1.21333
$746$	−3.13479e7	−2.06235
$747$	−1.76054e6	−0.115437
$748$	4.75191e6	0.310537
$749$	−1.33857e6	−0.0871837
$750$	1.64775e7	1.06964
$751$	−2.21293e7	−1.43175	−0.715876	−	0.698227i	$-0.753973\pi$
$751$	−2.21293e7	−1.43175	−0.715876	+	0.698227i	$0.753973\pi$
$752$	−2.12955e7	−1.37323
$753$	1.62993e7	1.04757
$754$	−1.29112e7	−0.827061
$755$	−2.83849e6	−0.181226
$756$	−563828.	−0.0358792
$757$	7.15267e6	0.453658	0.226829	−	0.973935i	$-0.427164\pi$
$757$	7.15267e6	0.453658	0.226829	+	0.973935i	$0.427164\pi$
$758$	−1.53787e7	−0.972178
$759$	9.41779e6	0.593396
$760$	2.07156e7	1.30096
$761$	1.80367e7	1.12900	0.564501	−	0.825433i	$-0.309069\pi$
$761$	1.80367e7	1.12900	0.564501	+	0.825433i	$0.309069\pi$
$762$	−1.92019e7	−1.19800
$763$	9.24855e6	0.575125
$764$	7.89122e6	0.489115
$765$	−9.20085e6	−0.568427
$766$	2.45380e7	1.51101
$767$	−1.10945e6	−0.0680956
$768$	−7.90088e6	−0.483362
$769$	2.92585e6	0.178417	0.0892086	−	0.996013i	$-0.471566\pi$
$769$	2.92585e6	0.178417	0.0892086	+	0.996013i	$0.471566\pi$
$770$	−2.02749e7	−1.23234
$771$	4.31970e6	0.261708
$772$	7.17225e6	0.433124
$773$	1.03080e7	0.620477	0.310239	−	0.950659i	$-0.399591\pi$
$773$	1.03080e7	0.620477	0.310239	+	0.950659i	$0.399591\pi$
$774$	61764.4	0.00370583
$775$	5.56751e7	3.32971
$776$	−1.24680e7	−0.743262
$777$	−2.87512e6	−0.170846
$778$	−2.02980e7	−1.20228
$779$	−1.90807e7	−1.12655
$780$	−2.68070e6	−0.157765
$781$	−2.95436e7	−1.73315
$782$	−1.94293e7	−1.13616
$783$	−4.57095e6	−0.266442
$784$	1.30327e7	0.757257
$785$	−5.59344e7	−3.23970
$786$	1.19964e7	0.692620
$787$	−1.49242e7	−0.858921	−0.429461	−	0.903086i	$-0.641296\pi$
$787$	−1.49242e7	−0.858921	−0.429461	+	0.903086i	$0.641296\pi$
$788$	−5.17664e6	−0.296983
$789$	−1.25355e7	−0.716882
$790$	9.64068e6	0.549591
$791$	1.17345e7	0.666844
$792$	−4.79908e6	−0.271860
$793$	−1.42816e6	−0.0806479
$794$	342222.	0.0192644
$795$	−4.77869e6	−0.268158
$796$	622180.	0.0348043
$797$	3.02230e6	0.168536	0.0842679	−	0.996443i	$-0.473145\pi$
$797$	3.02230e6	0.168536	0.0842679	+	0.996443i	$0.473145\pi$
$798$	−6.93200e6	−0.385347
$799$	2.03205e7	1.12608
$800$	−2.07582e7	−1.14674
$801$	3.29273e6	0.181332
$802$	−2.50135e7	−1.37321
$803$	3.31090e7	1.81200
$804$	783358.	0.0427386
$805$	1.93464e7	1.05223
$806$	−1.88595e7	−1.02257
$807$	−1.56434e7	−0.845568
$808$	−2.05554e7	−1.10764
$809$	2.72990e7	1.46648	0.733239	−	0.679971i	$-0.238007\pi$
$809$	2.72990e7	1.46648	0.733239	+	0.679971i	$0.238007\pi$
$810$	−4.06665e6	−0.217783
$811$	−2.61632e6	−0.139682	−0.0698409	−	0.997558i	$-0.522249\pi$
$811$	−2.61632e6	−0.139682	−0.0698409	+	0.997558i	$0.522249\pi$
$812$	4.84952e6	0.258112
$813$	−1.98174e7	−1.05153
$814$	1.07099e7	0.566534
$815$	5.58496e7	2.94528
$816$	1.32225e7	0.695166
$817$	177216.	0.00928853
$818$	−2.04008e7	−1.06602
$819$	−2.04970e6	−0.106778
$820$	1.18758e7	0.616780
$821$	−5.80387e6	−0.300511	−0.150255	−	0.988647i	$-0.548010\pi$
$821$	−5.80387e6	−0.300511	−0.150255	+	0.988647i	$0.548010\pi$
$822$	−5.06570e6	−0.261493
$823$	−657063.	−0.0338149	−0.0169074	−	0.999857i	$-0.505382\pi$
$823$	−657063.	−0.0338149	−0.0169074	+	0.999857i	$0.505382\pi$
$824$	−2.30109e6	−0.118064
$825$	−2.25399e7	−1.15297
$826$	1.78562e6	0.0910622
$827$	3.34698e7	1.70172	0.850862	−	0.525389i	$-0.176080\pi$
$827$	3.34698e7	1.70172	0.850862	+	0.525389i	$0.176080\pi$
$828$	−2.00410e6	−0.101588
$829$	−2.97836e7	−1.50519	−0.752594	−	0.658485i	$-0.771198\pi$
$829$	−2.97836e7	−1.50519	−0.752594	+	0.658485i	$0.771198\pi$
$830$	1.34719e7	0.678787
$831$	−9.41258e6	−0.472831
$832$	−5.62345e6	−0.281640
$833$	−1.24360e7	−0.620967
$834$	8.51297e6	0.423805
$835$	−3.56306e6	−0.176851
$836$	6.02616e6	0.298212
$837$	−6.67683e6	−0.329425
$838$	−7.36679e6	−0.362383
$839$	3.20360e6	0.157121	0.0785603	−	0.996909i	$-0.474968\pi$
$839$	3.20360e6	0.157121	0.0785603	+	0.996909i	$0.474968\pi$
$840$	−9.85848e6	−0.482072
$841$	1.88039e7	0.916763
$842$	3.79043e7	1.84250
$843$	1.79988e7	0.872319
$844$	3.24284e6	0.156700
$845$	2.58753e7	1.24665
$846$	8.98139e6	0.431437
$847$	689777.	0.0330370
$848$	6.86744e6	0.327948
$849$	−2.75814e6	−0.131325
$850$	4.65009e7	2.20757
$851$	−1.02195e7	−0.483732
$852$	6.28686e6	0.296712
$853$	1.57624e7	0.741738	0.370869	−	0.928685i	$-0.379060\pi$
$853$	1.57624e7	0.741738	0.370869	+	0.928685i	$0.379060\pi$
$854$	2.29857e6	0.107848
$855$	−1.16681e7	−0.545865
$856$	2.42449e6	0.113093
$857$	3.68223e6	0.171261	0.0856306	−	0.996327i	$-0.472710\pi$
$857$	3.68223e6	0.171261	0.0856306	+	0.996327i	$0.472710\pi$
$858$	7.63519e6	0.354080
$859$	2.25206e7	1.04135	0.520676	−	0.853754i	$-0.325680\pi$
$859$	2.25206e7	1.04135	0.520676	+	0.853754i	$0.325680\pi$
$860$	−110299.	−0.00508541
$861$	9.08042e6	0.417444
$862$	−1.83113e7	−0.839366
$863$	3.01429e7	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$863$	3.01429e7	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$864$	2.48942e6	0.113452
$865$	1.35893e7	0.617529
$866$	1.01459e7	0.459724
$867$	161571.	0.00729990
$868$	7.08373e6	0.319126
$869$	−6.40813e6	−0.287860
$870$	3.49775e7	1.56672
$871$	2.84776e6	0.127191
$872$	−1.67516e7	−0.746043
$873$	7.02261e6	0.311862
$874$	−2.46394e7	−1.09107
$875$	−2.24992e7	−0.993453
$876$	−7.04558e6	−0.310210
$877$	−1.17437e7	−0.515592	−0.257796	−	0.966199i	$-0.582996\pi$
$877$	−1.17437e7	−0.515592	−0.257796	+	0.966199i	$0.582996\pi$
$878$	1.76144e7	0.771138
$879$	2.06410e7	0.901071
$880$	4.90440e7	2.13491
$881$	3.33944e7	1.44955	0.724777	−	0.688984i	$-0.241943\pi$
$881$	3.33944e7	1.44955	0.724777	+	0.688984i	$0.241943\pi$
$882$	−5.49655e6	−0.237913
$883$	−3.12269e7	−1.34780	−0.673902	−	0.738820i	$-0.735383\pi$
$883$	−3.12269e7	−1.34780	−0.673902	+	0.738820i	$0.735383\pi$
$884$	−3.67605e6	−0.158216
$885$	3.00559e6	0.128995
$886$	−3.14057e7	−1.34408
$887$	4.60083e6	0.196348	0.0981742	−	0.995169i	$-0.468700\pi$
$887$	4.60083e6	0.196348	0.0981742	+	0.995169i	$0.468700\pi$
$888$	5.20760e6	0.221618
$889$	2.62192e7	1.11267
$890$	−2.51963e7	−1.06626
$891$	2.70309e6	0.114069
$892$	1.23927e7	0.521501
$893$	2.57696e7	1.08138
$894$	1.11407e7	0.466194
$895$	2.49309e7	1.04035
$896$	1.77268e7	0.737666
$897$	−7.28554e6	−0.302330
$898$	−2.36219e7	−0.977515
$899$	5.74277e7	2.36986
$900$	4.79647e6	0.197386
$901$	−6.55303e6	−0.268924
$902$	−3.38249e7	−1.38427
$903$	−84336.1	−0.00344187
$904$	−2.12543e7	−0.865019
$905$	480680.	0.0195090
$906$	−1.72040e6	−0.0696320
$907$	2.15836e7	0.871176	0.435588	−	0.900146i	$-0.356540\pi$
$907$	2.15836e7	0.871176	0.435588	+	0.900146i	$0.356540\pi$
$908$	7.84091e6	0.315611
$909$	1.15779e7	0.464750
$910$	1.56845e7	0.627868
$911$	−6.48309e6	−0.258813	−0.129407	−	0.991592i	$-0.541307\pi$
$911$	−6.48309e6	−0.258813	−0.129407	+	0.991592i	$0.541307\pi$
$912$	1.67682e7	0.667574
$913$	−8.95472e6	−0.355529
$914$	2.89085e7	1.14462
$915$	3.86900e6	0.152773
$916$	1.01254e7	0.398725
$917$	−1.63805e7	−0.643285
$918$	−5.57661e6	−0.218405
$919$	−9.32748e6	−0.364314	−0.182157	−	0.983269i	$-0.558308\pi$
$919$	−9.32748e6	−0.364314	−0.182157	+	0.983269i	$0.558308\pi$
$920$	−3.50414e7	−1.36494
$921$	−1.99944e7	−0.776710
$922$	−4.18226e7	−1.62026
$923$	2.28548e7	0.883024
$924$	−2.86782e6	−0.110503
$925$	2.44586e7	0.939890
$926$	−681517.	−0.0261186
$927$	1.29609e6	0.0495379
$928$	−2.14116e7	−0.816169
$929$	−3.19118e7	−1.21314	−0.606571	−	0.795029i	$-0.707456\pi$
$929$	−3.19118e7	−1.21314	−0.606571	+	0.795029i	$0.707456\pi$
$930$	5.10919e7	1.93707
$931$	−1.57708e7	−0.596320
$932$	−3.83938e6	−0.144784
$933$	−8.91539e6	−0.335302
$934$	−8.65697e6	−0.324712
$935$	−4.67987e7	−1.75067
$936$	3.71254e6	0.138510
$937$	1.54673e7	0.575526	0.287763	−	0.957702i	$-0.407088\pi$
$937$	1.54673e7	0.575526	0.287763	+	0.957702i	$0.407088\pi$
$938$	−4.58336e6	−0.170089
$939$	−1.97397e6	−0.0730595
$940$	−1.60390e7	−0.592049
$941$	−4.24021e7	−1.56104	−0.780518	−	0.625133i	$-0.785045\pi$
$941$	−4.24021e7	−1.56104	−0.780518	+	0.625133i	$0.785045\pi$
$942$	−3.39017e7	−1.24478
$943$	3.22759e7	1.18195
$944$	−4.31933e6	−0.157756
$945$	5.55281e6	0.202271
$946$	314155.	0.0114134
$947$	2.75784e7	0.999295	0.499647	−	0.866229i	$-0.333463\pi$
$947$	2.75784e7	0.999295	0.499647	+	0.866229i	$0.333463\pi$
$948$	1.36364e6	0.0492811
$949$	−2.56129e7	−0.923196
$950$	5.89704e7	2.11995
$951$	1.59386e7	0.571476
$952$	−1.35189e7	−0.483449
$953$	2.72094e7	0.970482	0.485241	−	0.874380i	$-0.338732\pi$
$953$	2.72094e7	0.970482	0.485241	+	0.874380i	$0.338732\pi$
$954$	−2.89635e6	−0.103034
$955$	−7.77159e7	−2.75741
$956$	5.12389e6	0.181324
$957$	−2.32494e7	−0.820602
$958$	4.02579e7	1.41722
$959$	6.91695e6	0.242867
$960$	1.52344e7	0.533516
$961$	5.52560e7	1.93006
$962$	−8.28514e6	−0.288644
$963$	−1.36560e6	−0.0474524
$964$	−9.00826e6	−0.312211
$965$	−7.06351e7	−2.44176
$966$	1.17258e7	0.404296
$967$	−3.69486e7	−1.27067	−0.635334	−	0.772237i	$-0.719138\pi$
$967$	−3.69486e7	−1.27067	−0.635334	+	0.772237i	$0.719138\pi$
$968$	−1.24937e6	−0.0428550
$969$	−1.60005e7	−0.547425
$970$	−5.37379e7	−1.83380
$971$	−6.49752e6	−0.221156	−0.110578	−	0.993867i	$-0.535270\pi$
$971$	−6.49752e6	−0.221156	−0.110578	+	0.993867i	$0.535270\pi$
$972$	−575216.	−0.0195283
$973$	−1.16240e7	−0.393617
$974$	−3.91809e7	−1.32336
$975$	1.74367e7	0.587426
$976$	−5.56012e6	−0.186836
$977$	1.99651e7	0.669167	0.334584	−	0.942366i	$-0.391404\pi$
$977$	1.99651e7	0.669167	0.334584	+	0.942366i	$0.391404\pi$
$978$	3.38502e7	1.13166
$979$	1.67479e7	0.558476
$980$	9.81576e6	0.326482
$981$	9.43534e6	0.313029
$982$	4.05664e7	1.34242
$983$	5.41463e7	1.78725	0.893624	−	0.448817i	$-0.148155\pi$
$983$	5.41463e7	1.78725	0.893624	+	0.448817i	$0.148155\pi$
$984$	−1.64470e7	−0.541501
$985$	5.09816e7	1.67426
$986$	4.79647e7	1.57119
$987$	−1.22636e7	−0.400706
$988$	−4.66180e6	−0.151936
$989$	−299768.	−0.00974530
$990$	−2.06844e7	−0.670740
$991$	3.25133e7	1.05166	0.525831	−	0.850589i	$-0.323754\pi$
$991$	3.25133e7	1.05166	0.525831	+	0.850589i	$0.323754\pi$
$992$	−3.12761e7	−1.00910
$993$	3.05874e7	0.984395
$994$	−3.67839e7	−1.18084
$995$	−6.12748e6	−0.196211
$996$	1.90556e6	0.0608659
$997$	−9.41192e6	−0.299875	−0.149938	−	0.988695i	$-0.547907\pi$
$997$	−9.41192e6	−0.299875	−0.149938	+	0.988695i	$0.547907\pi$
$998$	5.07127e7	1.61172
$999$	−2.93319e6	−0.0929880

Twists

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

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

\(f(q)\)	\(=\)	\(q+6.46075 q^{2} -9.00000 q^{3} +9.74133 q^{4} -95.9365 q^{5} -58.1468 q^{6} +79.3965 q^{7} -143.808 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.46075 q^{2} -9.00000 q^{3} +9.74133 q^{4} -95.9365 q^{5} -58.1468 q^{6} +79.3965 q^{7} -143.808 q^{8} +81.0000 q^{9} -619.822 q^{10} +411.994 q^{11} -87.6720 q^{12} -318.716 q^{13} +512.961 q^{14} +863.428 q^{15} -1240.83 q^{16} +1184.02 q^{17} +523.321 q^{18} +1501.52 q^{19} -934.549 q^{20} -714.568 q^{21} +2661.79 q^{22} -2539.90 q^{23} +1294.27 q^{24} +6078.81 q^{25} -2059.14 q^{26} -729.000 q^{27} +773.427 q^{28} +6270.17 q^{29} +5578.40 q^{30} +9158.88 q^{31} -3414.84 q^{32} -3707.94 q^{33} +7649.66 q^{34} -7617.02 q^{35} +789.048 q^{36} +4023.58 q^{37} +9700.97 q^{38} +2868.44 q^{39} +13796.4 q^{40} -12707.6 q^{41} -4616.65 q^{42} +118.024 q^{43} +4013.37 q^{44} -7770.86 q^{45} -16409.6 q^{46} +17162.3 q^{47} +11167.5 q^{48} -10503.2 q^{49} +39273.7 q^{50} -10656.2 q^{51} -3104.72 q^{52} -5534.56 q^{53} -4709.89 q^{54} -39525.2 q^{55} -11417.8 q^{56} -13513.7 q^{57} +40510.0 q^{58} +3481.00 q^{59} +8410.94 q^{60} +4480.98 q^{61} +59173.3 q^{62} +6431.11 q^{63} +17644.1 q^{64} +30576.5 q^{65} -23956.1 q^{66} -8935.10 q^{67} +11533.9 q^{68} +22859.1 q^{69} -49211.7 q^{70} -71708.9 q^{71} -11648.4 q^{72} +80362.9 q^{73} +25995.4 q^{74} -54709.3 q^{75} +14626.8 q^{76} +32710.8 q^{77} +18532.3 q^{78} -15553.9 q^{79} +119041. q^{80} +6561.00 q^{81} -82100.5 q^{82} -21735.1 q^{83} -6960.84 q^{84} -113591. q^{85} +762.523 q^{86} -56431.5 q^{87} -59247.9 q^{88} +40650.9 q^{89} -50205.6 q^{90} -25304.9 q^{91} -24742.0 q^{92} -82429.9 q^{93} +110881. q^{94} -144051. q^{95} +30733.6 q^{96} +86698.9 q^{97} -67858.6 q^{98} +33371.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 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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