LMFDB - Embedded newform 177.10.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} -800.975 q^{10} +95119.1 q^{11} -41281.1 q^{12} +58936.0 q^{13} -17436.4 q^{14} +42259.1 q^{15} +258529. q^{16} -89268.2 q^{17} -10072.9 q^{18} +308991. q^{19} -265890. q^{20} +919936. q^{21} -146033. q^{22} +2.23300e6 q^{23} +127048. q^{24} -1.68094e6 q^{25} -90482.4 q^{26} +531441. q^{27} -5.78813e6 q^{28} -7.46892e6 q^{29} -64879.0 q^{30} +6.83914e6 q^{31} -1.19998e6 q^{32} +7.70465e6 q^{33} +137050. q^{34} +5.92527e6 q^{35} -3.34377e6 q^{36} -1.22568e7 q^{37} -474384. q^{38} +4.77381e6 q^{39} +818311. q^{40} +5.99927e6 q^{41} -1.41235e6 q^{42} -2.75963e7 q^{43} -4.84768e7 q^{44} +3.42299e6 q^{45} -3.42825e6 q^{46} -1.84158e6 q^{47} +2.09409e7 q^{48} +8.86331e7 q^{49} +2.58068e6 q^{50} -7.23072e6 q^{51} -3.00363e7 q^{52} +2.55383e7 q^{53} -815903. q^{54} +4.96253e7 q^{55} +1.78137e7 q^{56} +2.50283e7 q^{57} +1.14668e7 q^{58} -1.21174e7 q^{59} -2.15371e7 q^{60} +7.45458e7 q^{61} -1.04999e7 q^{62} +7.45148e7 q^{63} -1.30525e8 q^{64} +3.07479e7 q^{65} -1.18287e7 q^{66} +795340. q^{67} +4.54949e7 q^{68} +1.80873e8 q^{69} -9.09686e6 q^{70} +2.30879e8 q^{71} +1.02909e7 q^{72} +5.28924e7 q^{73} +1.88174e7 q^{74} -1.36156e8 q^{75} -1.57475e8 q^{76} +1.08029e9 q^{77} -7.32907e6 q^{78} -4.07537e8 q^{79} +1.34879e8 q^{80} +4.30467e7 q^{81} -9.21047e6 q^{82} -6.59317e8 q^{83} -4.68839e8 q^{84} -4.65728e7 q^{85} +4.23676e7 q^{86} -6.04982e8 q^{87} +1.49194e8 q^{88} -5.89798e8 q^{89} -5.25520e6 q^{90} +6.69349e8 q^{91} -1.13803e9 q^{92} +5.53971e8 q^{93} +2.82732e6 q^{94} +1.61206e8 q^{95} -9.71984e7 q^{96} +1.40309e9 q^{97} -1.36075e8 q^{98} +6.24077e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	−1.53527	−0.0678498	−0.0339249	−	0.999424i	$-0.510801\pi$
$2$	−1.53527	−0.0678498	−0.0339249	+	0.999424i	$0.510801\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−509.643	−0.995396
$5$	521.717	0.373311	0.186655	−	0.982425i	$-0.440235\pi$
$5$	521.717	0.373311	0.186655	+	0.982425i	$0.440235\pi$
$6$	−124.357	−0.0391731
$7$	11357.2	1.78785	0.893925	−	0.448216i	$-0.147940\pi$
$7$	11357.2	1.78785	0.893925	+	0.448216i	$0.147940\pi$
$8$	1568.49	0.135387
$9$	6561.00	0.333333
$10$	−800.975	−0.0253291
$11$	95119.1	1.95885	0.979424	−	0.201813i	$-0.0646832\pi$
$11$	95119.1	1.95885	0.979424	+	0.201813i	$0.0646832\pi$
$12$	−41281.1	−0.574692
$13$	58936.0	0.572315	0.286158	−	0.958183i	$-0.407622\pi$
$13$	58936.0	0.572315	0.286158	+	0.958183i	$0.407622\pi$
$14$	−17436.4	−0.121305
$15$	42259.1	0.215531
$16$	258529.	0.986210
$17$	−89268.2	−0.259225	−0.129612	−	0.991565i	$-0.541373\pi$
$17$	−89268.2	−0.259225	−0.129612	+	0.991565i	$0.541373\pi$
$18$	−10072.9	−0.0226166
$19$	308991.	0.543945	0.271973	−	0.962305i	$-0.412324\pi$
$19$	308991.	0.543945	0.271973	+	0.962305i	$0.412324\pi$
$20$	−265890.	−0.371592
$21$	919936.	1.03222
$22$	−146033.	−0.132907
$23$	2.23300e6	1.66385	0.831925	−	0.554888i	$-0.187239\pi$
$23$	2.23300e6	1.66385	0.831925	+	0.554888i	$0.187239\pi$
$24$	127048.	0.0781659
$25$	−1.68094e6	−0.860639
$26$	−90482.4	−0.0388315
$27$	531441.	0.192450
$28$	−5.78813e6	−1.77962
$29$	−7.46892e6	−1.96095	−0.980475	−	0.196643i	$-0.936996\pi$
$29$	−7.46892e6	−1.96095	−0.980475	+	0.196643i	$0.936996\pi$
$30$	−64879.0	−0.0146237
$31$	6.83914e6	1.33007	0.665034	−	0.746813i	$-0.268417\pi$
$31$	6.83914e6	1.33007	0.665034	+	0.746813i	$0.268417\pi$
$32$	−1.19998e6	−0.202301
$33$	7.70465e6	1.13094
$34$	137050.	0.0175883
$35$	5.92527e6	0.667424
$36$	−3.34377e6	−0.331799
$37$	−1.22568e7	−1.07515	−0.537574	−	0.843217i	$-0.680659\pi$
$37$	−1.22568e7	−1.07515	−0.537574	+	0.843217i	$0.680659\pi$
$38$	−474384.	−0.0369066
$39$	4.77381e6	0.330426
$40$	818311.	0.0505415
$41$	5.99927e6	0.331567	0.165783	−	0.986162i	$-0.446985\pi$
$41$	5.99927e6	0.331567	0.165783	+	0.986162i	$0.446985\pi$
$42$	−1.41235e6	−0.0700357
$43$	−2.75963e7	−1.23096	−0.615478	−	0.788154i	$-0.711037\pi$
$43$	−2.75963e7	−1.23096	−0.615478	+	0.788154i	$0.711037\pi$
$44$	−4.84768e7	−1.94983
$45$	3.42299e6	0.124437
$46$	−3.42825e6	−0.112892
$47$	−1.84158e6	−0.0550492	−0.0275246	−	0.999621i	$-0.508762\pi$
$47$	−1.84158e6	−0.0550492	−0.0275246	+	0.999621i	$0.508762\pi$
$48$	2.09409e7	0.569389
$49$	8.86331e7	2.19641
$50$	2.58068e6	0.0583942
$51$	−7.23072e6	−0.149663
$52$	−3.00363e7	−0.569681
$53$	2.55383e7	0.444581	0.222290	−	0.974981i	$-0.428647\pi$
$53$	2.55383e7	0.444581	0.222290	+	0.974981i	$0.428647\pi$
$54$	−815903.	−0.0130577
$55$	4.96253e7	0.731259
$56$	1.78137e7	0.242052
$57$	2.50283e7	0.314047
$58$	1.14668e7	0.133050
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−2.15371e7	−0.214539
$61$	7.45458e7	0.689349	0.344674	−	0.938722i	$-0.387989\pi$
$61$	7.45458e7	0.689349	0.344674	+	0.938722i	$0.387989\pi$
$62$	−1.04999e7	−0.0902449
$63$	7.45148e7	0.595950
$64$	−1.30525e8	−0.972484
$65$	3.07479e7	0.213651
$66$	−1.18287e7	−0.0767342
$67$	795340.	0.00482188	0.00241094	−	0.999997i	$-0.499233\pi$
$67$	795340.	0.00482188	0.00241094	+	0.999997i	$0.499233\pi$
$68$	4.54949e7	0.258031
$69$	1.80873e8	0.960624
$70$	−9.09686e6	−0.0452846
$71$	2.30879e8	1.07825	0.539127	−	0.842224i	$-0.318754\pi$
$71$	2.30879e8	1.07825	0.539127	+	0.842224i	$0.318754\pi$
$72$	1.02909e7	0.0451291
$73$	5.28924e7	0.217992	0.108996	−	0.994042i	$-0.465236\pi$
$73$	5.28924e7	0.217992	0.108996	+	0.994042i	$0.465236\pi$
$74$	1.88174e7	0.0729486
$75$	−1.36156e8	−0.496890
$76$	−1.57475e8	−0.541441
$77$	1.08029e9	3.50213
$78$	−7.32907e6	−0.0224194
$79$	−4.07537e8	−1.17719	−0.588593	−	0.808429i	$-0.700318\pi$
$79$	−4.07537e8	−1.17719	−0.588593	+	0.808429i	$0.700318\pi$
$80$	1.34879e8	0.368163
$81$	4.30467e7	0.111111
$82$	−9.21047e6	−0.0224967
$83$	−6.59317e8	−1.52491	−0.762453	−	0.647043i	$-0.776005\pi$
$83$	−6.59317e8	−1.52491	−0.762453	+	0.647043i	$0.776005\pi$
$84$	−4.68839e8	−1.02746
$85$	−4.65728e7	−0.0967714
$86$	4.23676e7	0.0835201
$87$	−6.04982e8	−1.13216
$88$	1.49194e8	0.265203
$89$	−5.89798e8	−0.996433	−0.498216	−	0.867053i	$-0.666011\pi$
$89$	−5.89798e8	−0.996433	−0.498216	+	0.867053i	$0.666011\pi$
$90$	−5.25520e6	−0.00844302
$91$	6.69349e8	1.02321
$92$	−1.13803e9	−1.65619
$93$	5.53971e8	0.767916
$94$	2.82732e6	0.00373508
$95$	1.61206e8	0.203061
$96$	−9.71984e7	−0.116799
$97$	1.40309e9	1.60921	0.804605	−	0.593811i	$-0.202377\pi$
$97$	1.40309e9	1.60921	0.804605	+	0.593811i	$0.202377\pi$
$98$	−1.36075e8	−0.149026
$99$	6.24077e8	0.652949
$100$	8.56677e8	0.856677
$101$	−1.10370e9	−1.05537	−0.527686	−	0.849439i	$-0.676940\pi$
$101$	−1.10370e9	−1.05537	−0.527686	+	0.849439i	$0.676940\pi$
$102$	1.11011e7	0.0101546
$103$	3.30692e8	0.289505	0.144752	−	0.989468i	$-0.453761\pi$
$103$	3.30692e8	0.289505	0.144752	+	0.989468i	$0.453761\pi$
$104$	9.24407e7	0.0774842
$105$	4.79947e8	0.385337
$106$	−3.92081e7	−0.0301647
$107$	−1.59893e9	−1.17924	−0.589621	−	0.807680i	$-0.700723\pi$
$107$	−1.59893e9	−1.17924	−0.589621	+	0.807680i	$0.700723\pi$
$108$	−2.70845e8	−0.191564
$109$	−4.91275e8	−0.333354	−0.166677	−	0.986012i	$-0.553304\pi$
$109$	−4.91275e8	−0.333354	−0.166677	+	0.986012i	$0.553304\pi$
$110$	−7.61881e7	−0.0496158
$111$	−9.92798e8	−0.620737
$112$	2.93617e9	1.76320
$113$	1.37860e9	0.795401	0.397701	−	0.917515i	$-0.369808\pi$
$113$	1.37860e9	0.795401	0.397701	+	0.917515i	$0.369808\pi$
$114$	−3.84251e7	−0.0213080
$115$	1.16500e9	0.621133
$116$	3.80648e9	1.95192
$117$	3.86679e8	0.190772
$118$	1.86034e7	0.00883329
$119$	−1.01384e9	−0.463455
$120$	6.62832e7	0.0291802
$121$	6.68970e9	2.83709
$122$	−1.14448e8	−0.0467722
$123$	4.85941e8	0.191430
$124$	−3.48552e9	−1.32395
$125$	−1.89595e9	−0.694596
$126$	−1.14400e8	−0.0404351
$127$	−9.76735e8	−0.333165	−0.166583	−	0.986027i	$-0.553273\pi$
$127$	−9.76735e8	−0.333165	−0.166583	+	0.986027i	$0.553273\pi$
$128$	8.14780e8	0.268284
$129$	−2.23530e9	−0.710692
$130$	−4.72062e7	−0.0144962
$131$	−4.62441e8	−0.137194	−0.0685970	−	0.997644i	$-0.521852\pi$
$131$	−4.62441e8	−0.137194	−0.0685970	+	0.997644i	$0.521852\pi$
$132$	−3.92662e9	−1.12574
$133$	3.50929e9	0.972493
$134$	−1.22106e6	−0.000327163 0
$135$	2.77262e8	0.0718437
$136$	−1.40017e8	−0.0350957
$137$	3.68274e9	0.893158	0.446579	−	0.894744i	$-0.352642\pi$
$137$	3.68274e9	0.893158	0.446579	+	0.894744i	$0.352642\pi$
$138$	−2.77689e8	−0.0651782
$139$	8.61871e9	1.95828	0.979142	−	0.203176i	$-0.0651265\pi$
$139$	8.61871e9	1.95828	0.979142	+	0.203176i	$0.0651265\pi$
$140$	−3.01977e9	−0.664351
$141$	−1.49168e8	−0.0317827
$142$	−3.54460e8	−0.0731593
$143$	5.60594e9	1.12108
$144$	1.69621e9	0.328737
$145$	−3.89666e9	−0.732044
$146$	−8.12039e7	−0.0147907
$147$	7.17928e9	1.26810
$148$	6.24657e9	1.07020
$149$	1.16878e9	0.194265	0.0971324	−	0.995271i	$-0.469033\pi$
$149$	1.16878e9	0.194265	0.0971324	+	0.995271i	$0.469033\pi$
$150$	2.09035e8	0.0337139
$151$	7.56814e9	1.18466	0.592329	−	0.805696i	$-0.298208\pi$
$151$	7.56814e9	1.18466	0.592329	+	0.805696i	$0.298208\pi$
$152$	4.84651e8	0.0736433
$153$	−5.85688e8	−0.0864082
$154$	−1.65853e9	−0.237619
$155$	3.56810e9	0.496529
$156$	−2.43294e9	−0.328905
$157$	−8.83066e9	−1.15996	−0.579982	−	0.814629i	$-0.696940\pi$
$157$	−8.83066e9	−1.15996	−0.579982	+	0.814629i	$0.696940\pi$
$158$	6.25678e8	0.0798719
$159$	2.06860e9	0.256679
$160$	−6.26050e8	−0.0755213
$161$	2.53607e10	2.97472
$162$	−6.60882e7	−0.00753887
$163$	−5.52494e8	−0.0613032	−0.0306516	−	0.999530i	$-0.509758\pi$
$163$	−5.52494e8	−0.0613032	−0.0306516	+	0.999530i	$0.509758\pi$
$164$	−3.05748e9	−0.330040
$165$	4.01965e9	0.422193
$166$	1.01223e9	0.103465
$167$	1.63432e10	1.62597	0.812987	−	0.582282i	$-0.197840\pi$
$167$	1.63432e10	1.62597	0.812987	+	0.582282i	$0.197840\pi$
$168$	1.44291e9	0.139749
$169$	−7.13105e9	−0.672455
$170$	7.15016e7	0.00656592
$171$	2.02729e9	0.181315
$172$	1.40642e10	1.22529
$173$	1.38478e9	0.117537	0.0587685	−	0.998272i	$-0.481283\pi$
$173$	1.38478e9	0.117537	0.0587685	+	0.998272i	$0.481283\pi$
$174$	9.28809e8	0.0768165
$175$	−1.90908e10	−1.53869
$176$	2.45911e10	1.93184
$177$	−9.81506e8	−0.0751646
$178$	9.05496e8	0.0676078
$179$	−1.93204e10	−1.40662	−0.703312	−	0.710881i	$-0.748297\pi$
$179$	−1.93204e10	−1.40662	−0.703312	+	0.710881i	$0.748297\pi$
$180$	−1.74450e9	−0.123864
$181$	−2.47164e10	−1.71171	−0.855857	−	0.517212i	$-0.826970\pi$
$181$	−2.47164e10	−1.71171	−0.855857	+	0.517212i	$0.826970\pi$
$182$	−1.02763e9	−0.0694249
$183$	6.03821e9	0.397996
$184$	3.50245e9	0.225264
$185$	−6.39457e9	−0.401364
$186$	−8.50492e8	−0.0521029
$187$	−8.49111e9	−0.507782
$188$	9.38550e8	0.0547958
$189$	6.03570e9	0.344072
$190$	−2.47494e8	−0.0137776
$191$	7.09375e9	0.385679	0.192839	−	0.981230i	$-0.438230\pi$
$191$	7.09375e9	0.385679	0.192839	+	0.981230i	$0.438230\pi$
$192$	−1.05725e10	−0.561464
$193$	1.79947e10	0.933548	0.466774	−	0.884377i	$-0.345416\pi$
$193$	1.79947e10	0.933548	0.466774	+	0.884377i	$0.345416\pi$
$194$	−2.15412e9	−0.109185
$195$	2.49058e9	0.123352
$196$	−4.51712e10	−2.18630
$197$	2.83463e10	1.34091	0.670453	−	0.741952i	$-0.266100\pi$
$197$	2.83463e10	1.34091	0.670453	+	0.741952i	$0.266100\pi$
$198$	−9.58124e8	−0.0443025
$199$	−3.68752e10	−1.66685	−0.833423	−	0.552635i	$-0.813622\pi$
$199$	−3.68752e10	−1.66685	−0.833423	+	0.552635i	$0.813622\pi$
$200$	−2.63654e9	−0.116520
$201$	6.44225e7	0.00278391
$202$	1.69448e9	0.0716068
$203$	−8.48262e10	−3.50589
$204$	3.68509e9	0.148974
$205$	3.12992e9	0.123777
$206$	−5.07700e8	−0.0196428
$207$	1.46507e10	0.554617
$208$	1.52367e10	0.564423
$209$	2.93910e10	1.06551
$210$	−7.36846e8	−0.0261451
$211$	−3.93354e10	−1.36619	−0.683097	−	0.730328i	$-0.739367\pi$
$211$	−3.93354e10	−1.36619	−0.683097	+	0.730328i	$0.739367\pi$
$212$	−1.30154e10	−0.442534
$213$	1.87012e10	0.622530
$214$	2.45478e9	0.0800113
$215$	−1.43975e10	−0.459529
$216$	8.33562e8	0.0260553
$217$	7.76737e10	2.37796
$218$	7.54239e8	0.0226180
$219$	4.28428e9	0.125858
$220$	−2.52912e10	−0.727893
$221$	−5.26110e9	−0.148358
$222$	1.52421e9	0.0421169
$223$	1.37882e10	0.373366	0.186683	−	0.982420i	$-0.440226\pi$
$223$	1.37882e10	0.373366	0.186683	+	0.982420i	$0.440226\pi$
$224$	−1.36284e10	−0.361685
$225$	−1.10286e10	−0.286880
$226$	−2.11652e9	−0.0539678
$227$	−1.75195e10	−0.437931	−0.218965	−	0.975733i	$-0.570268\pi$
$227$	−1.75195e10	−0.437931	−0.218965	+	0.975733i	$0.570268\pi$
$228$	−1.27555e10	−0.312601
$229$	−6.95923e10	−1.67225	−0.836126	−	0.548537i	$-0.815185\pi$
$229$	−6.95923e10	−1.67225	−0.836126	+	0.548537i	$0.815185\pi$
$230$	−1.78858e9	−0.0421438
$231$	8.75035e10	2.02195
$232$	−1.17149e10	−0.265488
$233$	−1.86095e10	−0.413649	−0.206825	−	0.978378i	$-0.566313\pi$
$233$	−1.86095e10	−0.413649	−0.206825	+	0.978378i	$0.566313\pi$
$234$	−5.93655e8	−0.0129438
$235$	−9.60787e8	−0.0205505
$236$	6.17553e9	0.129590
$237$	−3.30105e10	−0.679649
$238$	1.55651e9	0.0314453
$239$	8.01476e10	1.58891	0.794456	−	0.607321i	$-0.207756\pi$
$239$	8.01476e10	1.58891	0.794456	+	0.607321i	$0.207756\pi$
$240$	1.09252e10	0.212559
$241$	−4.83756e9	−0.0923739	−0.0461870	−	0.998933i	$-0.514707\pi$
$241$	−4.83756e9	−0.0923739	−0.0461870	+	0.998933i	$0.514707\pi$
$242$	−1.02705e10	−0.192496
$243$	3.48678e9	0.0641500
$244$	−3.79918e10	−0.686175
$245$	4.62414e10	0.819943
$246$	−7.46048e8	−0.0129885
$247$	1.82107e10	0.311308
$248$	1.07272e10	0.180074
$249$	−5.34047e10	−0.880405
$250$	2.91079e9	0.0471282
$251$	−7.62361e9	−0.121235	−0.0606177	−	0.998161i	$-0.519307\pi$
$251$	−7.62361e9	−0.121235	−0.0606177	+	0.998161i	$0.519307\pi$
$252$	−3.79759e10	−0.593207
$253$	2.12401e11	3.25923
$254$	1.49955e9	0.0226052
$255$	−3.77239e9	−0.0558710
$256$	6.55777e10	0.954281
$257$	5.48861e10	0.784808	0.392404	−	0.919793i	$-0.371644\pi$
$257$	5.48861e10	0.784808	0.392404	+	0.919793i	$0.371644\pi$
$258$	3.43178e9	0.0482203
$259$	−1.39203e11	−1.92220
$260$	−1.56705e10	−0.212668
$261$	−4.90036e10	−0.653650
$262$	7.09970e8	0.00930859
$263$	−9.52195e9	−0.122723	−0.0613614	−	0.998116i	$-0.519544\pi$
$263$	−9.52195e9	−0.122723	−0.0613614	+	0.998116i	$0.519544\pi$
$264$	1.20847e10	0.153115
$265$	1.33238e10	0.165967
$266$	−5.38769e9	−0.0659834
$267$	−4.77736e10	−0.575291
$268$	−4.05339e8	−0.00479968
$269$	2.50707e10	0.291932	0.145966	−	0.989290i	$-0.453371\pi$
$269$	2.50707e10	0.291932	0.145966	+	0.989290i	$0.453371\pi$
$270$	−4.25671e8	−0.00487458
$271$	5.35620e9	0.0603247	0.0301623	−	0.999545i	$-0.490398\pi$
$271$	5.35620e9	0.0603247	0.0301623	+	0.999545i	$0.490398\pi$
$272$	−2.30784e10	−0.255650
$273$	5.42173e10	0.590753
$274$	−5.65398e9	−0.0606006
$275$	−1.59889e11	−1.68586
$276$	−9.21808e10	−0.956202
$277$	−1.39810e11	−1.42685	−0.713426	−	0.700730i	$-0.752858\pi$
$277$	−1.39810e11	−1.42685	−0.713426	+	0.700730i	$0.752858\pi$
$278$	−1.32320e10	−0.132869
$279$	4.48716e10	0.443356
$280$	9.29374e9	0.0903607
$281$	5.63482e10	0.539140	0.269570	−	0.962981i	$-0.413118\pi$
$281$	5.63482e10	0.539140	0.269570	+	0.962981i	$0.413118\pi$
$282$	2.29013e8	0.00215645
$283$	−1.49244e11	−1.38312	−0.691559	−	0.722320i	$-0.743076\pi$
$283$	−1.49244e11	−1.38312	−0.691559	+	0.722320i	$0.743076\pi$
$284$	−1.17666e11	−1.07329
$285$	1.30577e10	0.117237
$286$	−8.60661e9	−0.0760650
$287$	6.81351e10	0.592792
$288$	−7.87307e9	−0.0674338
$289$	−1.10619e11	−0.932803
$290$	5.98242e9	0.0496690
$291$	1.13650e11	0.929077
$292$	−2.69562e10	−0.216988
$293$	8.99234e10	0.712801	0.356400	−	0.934333i	$-0.384004\pi$
$293$	8.99234e10	0.712801	0.356400	+	0.934333i	$0.384004\pi$
$294$	−1.10221e10	−0.0860402
$295$	−6.32184e9	−0.0486009
$296$	−1.92247e10	−0.145561
$297$	5.05502e10	0.376981
$298$	−1.79439e9	−0.0131808
$299$	1.31604e11	0.952247
$300$	6.93908e10	0.494603
$301$	−3.13417e11	−2.20076
$302$	−1.16191e10	−0.0803789
$303$	−8.93999e10	−0.609319
$304$	7.98833e10	0.536444
$305$	3.88919e10	0.257341
$306$	8.99187e8	0.00586278
$307$	−4.75255e10	−0.305354	−0.152677	−	0.988276i	$-0.548789\pi$
$307$	−4.75255e10	−0.305354	−0.152677	+	0.988276i	$0.548789\pi$
$308$	−5.50562e11	−3.48601
$309$	2.67860e10	0.167146
$310$	−5.47798e9	−0.0336894
$311$	−2.58316e11	−1.56578	−0.782888	−	0.622163i	$-0.786254\pi$
$311$	−2.58316e11	−1.56578	−0.782888	+	0.622163i	$0.786254\pi$
$312$	7.48770e9	0.0447355
$313$	1.53447e11	0.903669	0.451835	−	0.892102i	$-0.350770\pi$
$313$	1.53447e11	0.903669	0.451835	+	0.892102i	$0.350770\pi$
$314$	1.35574e10	0.0787034
$315$	3.88757e10	0.222475
$316$	2.07698e11	1.17177
$317$	6.64771e9	0.0369747	0.0184874	−	0.999829i	$-0.494115\pi$
$317$	6.64771e9	0.0369747	0.0184874	+	0.999829i	$0.494115\pi$
$318$	−3.17585e9	−0.0174156
$319$	−7.10437e11	−3.84120
$320$	−6.80970e10	−0.363039
$321$	−1.29513e11	−0.680835
$322$	−3.89355e10	−0.201834
$323$	−2.75831e10	−0.141004
$324$	−2.19385e10	−0.110600
$325$	−9.90676e10	−0.492557
$326$	8.48225e8	0.00415941
$327$	−3.97933e10	−0.192462
$328$	9.40981e9	0.0448899
$329$	−2.09153e10	−0.0984198
$330$	−6.17123e9	−0.0286457
$331$	1.80447e11	0.826272	0.413136	−	0.910669i	$-0.364433\pi$
$331$	1.80447e11	0.826272	0.413136	+	0.910669i	$0.364433\pi$
$332$	3.36017e11	1.51789
$333$	−8.04166e10	−0.358382
$334$	−2.50912e10	−0.110322
$335$	4.14943e8	0.00180006
$336$	2.37830e11	1.01798
$337$	2.39924e10	0.101330	0.0506650	−	0.998716i	$-0.483866\pi$
$337$	2.39924e10	0.101330	0.0506650	+	0.998716i	$0.483866\pi$
$338$	1.09481e10	0.0456260
$339$	1.11667e11	0.459225
$340$	2.37355e10	0.0963259
$341$	6.50533e11	2.60540
$342$	−3.11243e9	−0.0123022
$343$	5.48321e11	2.13900
$344$	−4.32846e10	−0.166656
$345$	9.43648e10	0.358611
$346$	−2.12601e9	−0.00797486
$347$	−2.11491e11	−0.783084	−0.391542	−	0.920160i	$-0.628058\pi$
$347$	−2.11491e11	−0.783084	−0.391542	+	0.920160i	$0.628058\pi$
$348$	3.08325e11	1.12694
$349$	−1.24571e11	−0.449470	−0.224735	−	0.974420i	$-0.572152\pi$
$349$	−1.24571e11	−0.449470	−0.224735	+	0.974420i	$0.572152\pi$
$350$	2.93094e10	0.104400
$351$	3.13210e10	0.110142
$352$	−1.14141e11	−0.396278
$353$	−3.97716e10	−0.136329	−0.0681644	−	0.997674i	$-0.521714\pi$
$353$	−3.97716e10	−0.136329	−0.0681644	+	0.997674i	$0.521714\pi$
$354$	1.50687e9	0.00509990
$355$	1.20453e11	0.402524
$356$	3.00586e11	0.991845
$357$	−8.21210e10	−0.267576
$358$	2.96620e10	0.0954392
$359$	9.64259e10	0.306386	0.153193	−	0.988196i	$-0.451044\pi$
$359$	9.64259e10	0.306386	0.153193	+	0.988196i	$0.451044\pi$
$360$	5.36894e9	0.0168472
$361$	−2.27212e11	−0.704124
$362$	3.79462e10	0.116140
$363$	5.41866e11	1.63799
$364$	−3.41129e11	−1.01850
$365$	2.75949e10	0.0813787
$366$	−9.27026e9	−0.0270039
$367$	−2.75007e11	−0.791308	−0.395654	−	0.918400i	$-0.629482\pi$
$367$	−2.75007e11	−0.791308	−0.395654	+	0.918400i	$0.629482\pi$
$368$	5.77296e11	1.64091
$369$	3.93612e10	0.110522
$370$	9.81736e9	0.0272325
$371$	2.90044e11	0.794844
$372$	−2.82327e11	−0.764380
$373$	−2.04623e11	−0.547348	−0.273674	−	0.961822i	$-0.588239\pi$
$373$	−2.04623e11	−0.547348	−0.273674	+	0.961822i	$0.588239\pi$
$374$	1.30361e10	0.0344529
$375$	−1.53572e11	−0.401025
$376$	−2.88851e9	−0.00745296
$377$	−4.40188e11	−1.12228
$378$	−9.26640e9	−0.0233452
$379$	1.24424e11	0.309761	0.154881	−	0.987933i	$-0.450501\pi$
$379$	1.24424e11	0.309761	0.154881	+	0.987933i	$0.450501\pi$
$380$	−8.21576e10	−0.202126
$381$	−7.91155e10	−0.192353
$382$	−1.08908e10	−0.0261682
$383$	2.31365e11	0.549418	0.274709	−	0.961527i	$-0.411418\pi$
$383$	2.31365e11	0.549418	0.274709	+	0.961527i	$0.411418\pi$
$384$	6.59972e10	0.154894
$385$	5.63606e11	1.30738
$386$	−2.76266e10	−0.0633411
$387$	−1.81059e11	−0.410318
$388$	−7.15075e11	−1.60180
$389$	5.89622e11	1.30557	0.652785	−	0.757543i	$-0.273600\pi$
$389$	5.89622e11	1.30557	0.652785	+	0.757543i	$0.273600\pi$
$390$	−3.82371e9	−0.00836939
$391$	−1.99336e11	−0.431311
$392$	1.39020e11	0.297366
$393$	−3.74577e10	−0.0792090
$394$	−4.35191e10	−0.0909802
$395$	−2.12619e11	−0.439456
$396$	−3.18056e11	−0.649944
$397$	−1.17251e11	−0.236897	−0.118448	−	0.992960i	$-0.537792\pi$
$397$	−1.17251e11	−0.236897	−0.118448	+	0.992960i	$0.537792\pi$
$398$	5.66132e10	0.113095
$399$	2.84252e11	0.561469
$400$	−4.34571e11	−0.848771
$401$	6.92604e10	0.133763	0.0668814	−	0.997761i	$-0.478695\pi$
$401$	6.92604e10	0.133763	0.0668814	+	0.997761i	$0.478695\pi$
$402$	−9.89057e7	−0.000188888 0
$403$	4.03072e11	0.761219
$404$	5.62494e11	1.05051
$405$	2.24582e10	0.0414790
$406$	1.30231e11	0.237874
$407$	−1.16585e12	−2.10605
$408$	−1.13413e10	−0.0202625
$409$	5.32844e11	0.941554	0.470777	−	0.882252i	$-0.343974\pi$
$409$	5.32844e11	0.941554	0.470777	+	0.882252i	$0.343974\pi$
$410$	−4.80526e9	−0.00839827
$411$	2.98302e11	0.515665
$412$	−1.68535e11	−0.288172
$413$	−1.37620e11	−0.232758
$414$	−2.24928e10	−0.0376306
$415$	−3.43977e11	−0.569264
$416$	−7.07220e10	−0.115780
$417$	6.98116e11	1.13062
$418$	−4.51230e10	−0.0722944
$419$	1.03837e12	1.64584	0.822920	−	0.568157i	$-0.192343\pi$
$419$	1.03837e12	1.64584	0.822920	+	0.568157i	$0.192343\pi$
$420$	−2.44601e11	−0.383563
$421$	−8.26226e11	−1.28183	−0.640914	−	0.767613i	$-0.721444\pi$
$421$	−8.26226e11	−1.28183	−0.640914	+	0.767613i	$0.721444\pi$
$422$	6.03903e10	0.0926960
$423$	−1.20826e10	−0.0183497
$424$	4.00567e10	0.0601905
$425$	1.50054e11	0.223099
$426$	−2.87113e10	−0.0422386
$427$	8.46634e11	1.23245
$428$	8.14884e11	1.17381
$429$	4.54081e11	0.647255
$430$	2.21039e10	0.0311789
$431$	5.76904e11	0.805297	0.402649	−	0.915355i	$-0.368090\pi$
$431$	5.76904e11	0.805297	0.402649	+	0.915355i	$0.368090\pi$
$432$	1.37393e11	0.189796
$433$	8.37477e11	1.14493	0.572463	−	0.819930i	$-0.305988\pi$
$433$	8.37477e11	1.14493	0.572463	+	0.819930i	$0.305988\pi$
$434$	−1.19250e11	−0.161344
$435$	−3.15630e11	−0.422646
$436$	2.50375e11	0.331820
$437$	6.89979e11	0.905043
$438$	−6.57751e9	−0.00853942
$439$	8.78080e11	1.12835	0.564175	−	0.825655i	$-0.309194\pi$
$439$	8.78080e11	1.12835	0.564175	+	0.825655i	$0.309194\pi$
$440$	7.78370e10	0.0990032
$441$	5.81522e11	0.732137
$442$	8.07720e9	0.0100661
$443$	5.02232e11	0.619566	0.309783	−	0.950807i	$-0.399744\pi$
$443$	5.02232e11	0.619566	0.309783	+	0.950807i	$0.399744\pi$
$444$	5.05972e11	0.617879
$445$	−3.07708e11	−0.371979
$446$	−2.11685e10	−0.0253328
$447$	9.46711e10	0.112159
$448$	−1.48240e12	−1.73866
$449$	1.17433e12	1.36358	0.681792	−	0.731546i	$-0.261201\pi$
$449$	1.17433e12	1.36358	0.681792	+	0.731546i	$0.261201\pi$
$450$	1.69319e10	0.0194647
$451$	5.70645e11	0.649489
$452$	−7.02595e11	−0.791739
$453$	6.13020e11	0.683963
$454$	2.68971e10	0.0297135
$455$	3.49211e11	0.381977
$456$	3.92567e10	0.0425180
$457$	−1.37774e12	−1.47755	−0.738776	−	0.673951i	$-0.764596\pi$
$457$	−1.37774e12	−1.47755	−0.738776	+	0.673951i	$0.764596\pi$
$458$	1.06843e11	0.113462
$459$	−4.74408e10	−0.0498878
$460$	−5.93733e11	−0.618273
$461$	3.12616e11	0.322372	0.161186	−	0.986924i	$-0.448468\pi$
$461$	3.12616e11	0.322372	0.161186	+	0.986924i	$0.448468\pi$
$462$	−1.34341e11	−0.137189
$463$	−3.22766e10	−0.0326417	−0.0163209	−	0.999867i	$-0.505195\pi$
$463$	−3.22766e10	−0.0326417	−0.0163209	+	0.999867i	$0.505195\pi$
$464$	−1.93093e12	−1.93391
$465$	2.89016e11	0.286671
$466$	2.85705e10	0.0280660
$467$	−1.30750e12	−1.27208	−0.636042	−	0.771654i	$-0.719429\pi$
$467$	−1.30750e12	−1.27208	−0.636042	+	0.771654i	$0.719429\pi$
$468$	−1.97068e11	−0.189894
$469$	9.03286e9	0.00862079
$470$	1.47506e9	0.00139434
$471$	−7.15283e11	−0.669706
$472$	−1.90060e10	−0.0176259
$473$	−2.62493e12	−2.41125
$474$	5.06799e10	0.0461141
$475$	−5.19395e11	−0.468140
$476$	5.16696e11	0.461322
$477$	1.67557e11	0.148194
$478$	−1.23048e11	−0.107807
$479$	1.17526e12	1.02006	0.510029	−	0.860157i	$-0.329635\pi$
$479$	1.17526e12	1.02006	0.510029	+	0.860157i	$0.329635\pi$
$480$	−5.07101e10	−0.0436022
$481$	−7.22364e11	−0.615323
$482$	7.42694e9	0.00626756
$483$	2.05422e12	1.71745
$484$	−3.40936e12	−2.82403
$485$	7.32016e11	0.600735
$486$	−5.35314e9	−0.00435257
$487$	2.59684e11	0.209201	0.104601	−	0.994514i	$-0.466644\pi$
$487$	2.59684e11	0.209201	0.104601	+	0.994514i	$0.466644\pi$
$488$	1.16925e11	0.0933291
$489$	−4.47520e10	−0.0353934
$490$	−7.09929e10	−0.0556330
$491$	−1.23696e12	−0.960484	−0.480242	−	0.877136i	$-0.659451\pi$
$491$	−1.23696e12	−0.960484	−0.480242	+	0.877136i	$0.659451\pi$
$492$	−2.47656e11	−0.190549
$493$	6.66736e11	0.508327
$494$	−2.79583e10	−0.0211222
$495$	3.25592e11	0.243753
$496$	1.76812e12	1.31173
$497$	2.62214e12	1.92776
$498$	8.19904e10	0.0597353
$499$	4.52497e10	0.0326711	0.0163355	−	0.999867i	$-0.494800\pi$
$499$	4.52497e10	0.0326711	0.0163355	+	0.999867i	$0.494800\pi$
$500$	9.66259e11	0.691399
$501$	1.32380e12	0.938756
$502$	1.17043e10	0.00822579
$503$	−2.79106e11	−0.194408	−0.0972039	−	0.995264i	$-0.530990\pi$
$503$	−2.79106e11	−0.194408	−0.0972039	+	0.995264i	$0.530990\pi$
$504$	1.16876e11	0.0806841
$505$	−5.75821e11	−0.393982
$506$	−3.26093e11	−0.221138
$507$	−5.77615e11	−0.388242
$508$	4.97786e11	0.331632
$509$	−1.97812e12	−1.30624	−0.653119	−	0.757255i	$-0.726540\pi$
$509$	−1.97812e12	−1.30624	−0.653119	+	0.757255i	$0.726540\pi$
$510$	5.79163e9	0.00379083
$511$	6.00711e11	0.389737
$512$	−5.17846e11	−0.333032
$513$	1.64211e11	0.104682
$514$	−8.42647e10	−0.0532491
$515$	1.72528e11	0.108075
$516$	1.13920e12	0.707420
$517$	−1.75170e11	−0.107833
$518$	2.13713e11	0.130421
$519$	1.12167e11	0.0678600
$520$	4.82279e10	0.0289257
$521$	−1.73104e11	−0.102929	−0.0514645	−	0.998675i	$-0.516389\pi$
$521$	−1.73104e11	−0.102929	−0.0514645	+	0.998675i	$0.516389\pi$
$522$	7.52335e10	0.0443500
$523$	−2.59134e12	−1.51449	−0.757245	−	0.653131i	$-0.773455\pi$
$523$	−2.59134e12	−1.51449	−0.757245	+	0.653131i	$0.773455\pi$
$524$	2.35680e11	0.136562
$525$	−1.54635e12	−0.888366
$526$	1.46187e10	0.00832671
$527$	−6.10518e11	−0.344787
$528$	1.99188e12	1.11535
$529$	3.18515e12	1.76840
$530$	−2.04555e10	−0.0112608
$531$	−7.95020e10	−0.0433963
$532$	−1.78848e12	−0.968016
$533$	3.53573e11	0.189761
$534$	7.33452e10	0.0390334
$535$	−8.34190e11	−0.440223
$536$	1.24749e9	0.000652821 0
$537$	−1.56496e12	−0.812115
$538$	−3.84902e10	−0.0198075
$539$	8.43070e12	4.30243
$540$	−1.41305e11	−0.0715129
$541$	8.44449e11	0.423824	0.211912	−	0.977289i	$-0.432031\pi$
$541$	8.44449e11	0.423824	0.211912	+	0.977289i	$0.432031\pi$
$542$	−8.22319e9	−0.00409302
$543$	−2.00203e12	−0.988259
$544$	1.07120e11	0.0524415
$545$	−2.56307e11	−0.124445
$546$	−8.32380e10	−0.0400825
$547$	−2.86951e12	−1.37045	−0.685227	−	0.728329i	$-0.740297\pi$
$547$	−2.86951e12	−1.37045	−0.685227	+	0.728329i	$0.740297\pi$
$548$	−1.87688e12	−0.889046
$549$	4.89095e11	0.229783
$550$	2.45472e11	0.114385
$551$	−2.30783e12	−1.06665
$552$	2.83699e11	0.130056
$553$	−4.62849e12	−2.10463
$554$	2.14645e11	0.0968117
$555$	−5.17960e11	−0.231728
$556$	−4.39247e12	−1.94927
$557$	3.23987e12	1.42619	0.713097	−	0.701065i	$-0.247292\pi$
$557$	3.23987e12	1.42619	0.713097	+	0.701065i	$0.247292\pi$
$558$	−6.88899e10	−0.0300816
$559$	−1.62641e12	−0.704494
$560$	1.53185e12	0.658220
$561$	−6.87780e11	−0.293168
$562$	−8.65095e10	−0.0365806
$563$	4.45164e11	0.186738	0.0933690	−	0.995632i	$-0.470236\pi$
$563$	4.45164e11	0.186738	0.0933690	+	0.995632i	$0.470236\pi$
$564$	7.60226e10	0.0316364
$565$	7.19241e11	0.296932
$566$	2.29130e11	0.0938443
$567$	4.88892e11	0.198650
$568$	3.62132e11	0.145982
$569$	4.19474e12	1.67764	0.838821	−	0.544407i	$-0.183245\pi$
$569$	4.19474e12	1.67764	0.838821	+	0.544407i	$0.183245\pi$
$570$	−2.00470e10	−0.00795451
$571$	3.05784e12	1.20380	0.601898	−	0.798573i	$-0.294411\pi$
$571$	3.05784e12	1.20380	0.601898	+	0.798573i	$0.294411\pi$
$572$	−2.85703e12	−1.11592
$573$	5.74594e11	0.222672
$574$	−1.04605e11	−0.0402208
$575$	−3.75354e12	−1.43197
$576$	−8.56372e11	−0.324161
$577$	−3.45286e12	−1.29684	−0.648422	−	0.761281i	$-0.724571\pi$
$577$	−3.45286e12	−1.29684	−0.648422	+	0.761281i	$0.724571\pi$
$578$	1.69830e11	0.0632905
$579$	1.45757e12	0.538984
$580$	1.98591e12	0.728674
$581$	−7.48802e12	−2.72630
$582$	−1.74483e11	−0.0630377
$583$	2.42918e12	0.870866
$584$	8.29614e10	0.0295133
$585$	2.01737e11	0.0712171
$586$	−1.38056e11	−0.0483634
$587$	7.15734e11	0.248817	0.124409	−	0.992231i	$-0.460297\pi$
$587$	7.15734e11	0.248817	0.124409	+	0.992231i	$0.460297\pi$
$588$	−3.65887e12	−1.26226
$589$	2.11324e12	0.723484
$590$	9.70571e9	0.00329756
$591$	2.29605e12	0.774173
$592$	−3.16873e12	−1.06032
$593$	−3.03726e11	−0.100864	−0.0504320	−	0.998727i	$-0.516060\pi$
$593$	−3.03726e11	−0.100864	−0.0504320	+	0.998727i	$0.516060\pi$
$594$	−7.76080e10	−0.0255781
$595$	−5.28938e11	−0.173013
$596$	−5.95660e11	−0.193371
$597$	−2.98689e12	−0.962354
$598$	−2.02047e11	−0.0646098
$599$	−2.28392e12	−0.724870	−0.362435	−	0.932009i	$-0.618055\pi$
$599$	−2.28392e12	−0.724870	−0.362435	+	0.932009i	$0.618055\pi$
$600$	−2.13560e11	−0.0672726
$601$	−1.41623e12	−0.442789	−0.221395	−	0.975184i	$-0.571061\pi$
$601$	−1.41623e12	−0.442789	−0.221395	+	0.975184i	$0.571061\pi$
$602$	4.81179e11	0.149321
$603$	5.21822e9	0.00160729
$604$	−3.85705e12	−1.17920
$605$	3.49013e12	1.05911
$606$	1.37253e11	0.0413422
$607$	6.68445e11	0.199856	0.0999278	−	0.994995i	$-0.468139\pi$
$607$	6.68445e11	0.199856	0.0999278	+	0.994995i	$0.468139\pi$
$608$	−3.70783e11	−0.110041
$609$	−6.87092e12	−2.02412
$610$	−5.97094e10	−0.0174606
$611$	−1.08536e11	−0.0315055
$612$	2.98492e11	0.0860105
$613$	3.29593e12	0.942771	0.471385	−	0.881927i	$-0.343754\pi$
$613$	3.29593e12	0.942771	0.471385	+	0.881927i	$0.343754\pi$
$614$	7.29643e10	0.0207182
$615$	2.53524e11	0.0714629
$616$	1.69443e12	0.474144
$617$	−3.51993e12	−0.977802	−0.488901	−	0.872339i	$-0.662602\pi$
$617$	−3.51993e12	−0.977802	−0.488901	+	0.872339i	$0.662602\pi$
$618$	−4.11237e10	−0.0113408
$619$	5.42052e12	1.48400	0.741998	−	0.670402i	$-0.233878\pi$
$619$	5.42052e12	1.48400	0.741998	+	0.670402i	$0.233878\pi$
$620$	−1.81846e12	−0.494243
$621$	1.18671e12	0.320208
$622$	3.96584e11	0.106238
$623$	−6.69847e12	−1.78147
$624$	1.23417e12	0.325870
$625$	2.29393e12	0.601339
$626$	−2.35582e11	−0.0613138
$627$	2.38067e12	0.615170
$628$	4.50048e12	1.15462
$629$	1.09414e12	0.278705
$630$	−5.96845e10	−0.0150949
$631$	1.04898e12	0.263413	0.131706	−	0.991289i	$-0.457954\pi$
$631$	1.04898e12	0.263413	0.131706	+	0.991289i	$0.457954\pi$
$632$	−6.39220e11	−0.159376
$633$	−3.18617e12	−0.788772
$634$	−1.02060e10	−0.00250873
$635$	−5.09580e11	−0.124374
$636$	−1.05425e12	−0.255497
$637$	5.22368e12	1.25704
$638$	1.09071e12	0.260625
$639$	1.51479e12	0.359418
$640$	4.25085e11	0.100153
$641$	2.12024e12	0.496049	0.248024	−	0.968754i	$-0.420219\pi$
$641$	2.12024e12	0.496049	0.248024	+	0.968754i	$0.420219\pi$
$642$	1.98837e11	0.0461945
$643$	1.63431e12	0.377038	0.188519	−	0.982070i	$-0.439631\pi$
$643$	1.63431e12	0.377038	0.188519	+	0.982070i	$0.439631\pi$
$644$	−1.29249e13	−2.96102
$645$	−1.16619e12	−0.265309
$646$	4.23474e10	0.00956710
$647$	−3.43085e12	−0.769719	−0.384860	−	0.922975i	$-0.625750\pi$
$647$	−3.43085e12	−0.769719	−0.384860	+	0.922975i	$0.625750\pi$
$648$	6.75185e10	0.0150430
$649$	−1.15259e12	−0.255020
$650$	1.52095e11	0.0334199
$651$	6.29157e12	1.37292
$652$	2.81575e11	0.0610210
$653$	3.32537e11	0.0715699	0.0357850	−	0.999360i	$-0.488607\pi$
$653$	3.32537e11	0.0715699	0.0357850	+	0.999360i	$0.488607\pi$
$654$	6.10933e10	0.0130585
$655$	−2.41263e11	−0.0512160
$656$	1.55099e12	0.326995
$657$	3.47027e11	0.0726640
$658$	3.21105e10	0.00667776
$659$	4.48045e11	0.0925417	0.0462709	−	0.998929i	$-0.485266\pi$
$659$	4.48045e11	0.0925417	0.0462709	+	0.998929i	$0.485266\pi$
$660$	−2.04859e12	−0.420249
$661$	−4.98017e12	−1.01470	−0.507350	−	0.861740i	$-0.669375\pi$
$661$	−4.98017e12	−1.01470	−0.507350	+	0.861740i	$0.669375\pi$
$662$	−2.77034e11	−0.0560624
$663$	−4.26149e11	−0.0856547
$664$	−1.03414e12	−0.206453
$665$	1.83086e12	0.363042
$666$	1.23461e11	0.0243162
$667$	−1.66781e13	−3.26273
$668$	−8.32920e12	−1.61849
$669$	1.11684e12	0.215563
$670$	−6.37047e8	−0.000122134 0
$671$	7.09073e12	1.35033
$672$	−1.10390e12	−0.208819
$673$	8.54363e12	1.60537	0.802684	−	0.596404i	$-0.203404\pi$
$673$	8.54363e12	1.60537	0.802684	+	0.596404i	$0.203404\pi$
$674$	−3.68347e10	−0.00687523
$675$	−8.93318e11	−0.165630
$676$	3.63429e12	0.669360
$677$	4.76231e11	0.0871301	0.0435651	−	0.999051i	$-0.486128\pi$
$677$	4.76231e11	0.0871301	0.0435651	+	0.999051i	$0.486128\pi$
$678$	−1.71438e11	−0.0311583
$679$	1.59352e13	2.87703
$680$	−7.30491e10	−0.0131016
$681$	−1.41908e12	−0.252839
$682$	−9.98742e11	−0.176776
$683$	1.00532e13	1.76771	0.883856	−	0.467759i	$-0.154938\pi$
$683$	1.00532e13	1.76771	0.883856	+	0.467759i	$0.154938\pi$
$684$	−1.03320e12	−0.180480
$685$	1.92135e12	0.333425
$686$	−8.41819e11	−0.145131
$687$	−5.63698e12	−0.965475
$688$	−7.13444e12	−1.21398
$689$	1.50512e12	0.254440
$690$	−1.44875e11	−0.0243317
$691$	−4.48639e12	−0.748594	−0.374297	−	0.927309i	$-0.622116\pi$
$691$	−4.48639e12	−0.748594	−0.374297	+	0.927309i	$0.622116\pi$
$692$	−7.05745e11	−0.116996
$693$	7.08778e12	1.16738
$694$	3.24694e11	0.0531321
$695$	4.49653e12	0.731048
$696$	−9.48911e11	−0.153279
$697$	−5.35544e11	−0.0859503
$698$	1.91249e11	0.0304965
$699$	−1.50737e12	−0.238820
$700$	9.72948e12	1.53161
$701$	7.82510e12	1.22394	0.611968	−	0.790882i	$-0.290378\pi$
$701$	7.82510e12	1.22394	0.611968	+	0.790882i	$0.290378\pi$
$702$	−4.80861e10	−0.00747312
$703$	−3.78723e12	−0.584821
$704$	−1.24154e13	−1.90495
$705$	−7.78237e10	−0.0118648
$706$	6.10601e10	0.00924988
$707$	−1.25350e13	−1.88685
$708$	5.00218e11	0.0748186
$709$	−6.85312e12	−1.01854	−0.509272	−	0.860605i	$-0.670085\pi$
$709$	−6.85312e12	−1.01854	−0.509272	+	0.860605i	$0.670085\pi$
$710$	−1.84928e11	−0.0273112
$711$	−2.67385e12	−0.392396
$712$	−9.25094e11	−0.134904
$713$	1.52718e13	2.21303
$714$	1.26078e11	0.0181550
$715$	2.92472e12	0.418511
$716$	9.84652e12	1.40015
$717$	6.49196e12	0.917359
$718$	−1.48039e11	−0.0207882
$719$	1.16115e13	1.62035	0.810174	−	0.586189i	$-0.199372\pi$
$719$	1.16115e13	1.62035	0.810174	+	0.586189i	$0.199372\pi$
$720$	8.84942e11	0.122721
$721$	3.75574e12	0.517591
$722$	3.48831e11	0.0477747
$723$	−3.91842e11	−0.0533321
$724$	1.25965e13	1.70383
$725$	1.25548e13	1.68767
$726$	−8.31908e11	−0.111138
$727$	−1.05133e13	−1.39584	−0.697920	−	0.716176i	$-0.745891\pi$
$727$	−1.05133e13	−1.39584	−0.697920	+	0.716176i	$0.745891\pi$
$728$	1.04987e12	0.138530
$729$	2.82430e11	0.0370370
$730$	−4.23655e10	−0.00552153
$731$	2.46347e12	0.319094
$732$	−3.07733e12	−0.396164
$733$	−8.91599e12	−1.14078	−0.570390	−	0.821374i	$-0.693208\pi$
$733$	−8.91599e12	−1.14078	−0.570390	+	0.821374i	$0.693208\pi$
$734$	4.22208e11	0.0536901
$735$	3.74556e12	0.473394
$736$	−2.67956e12	−0.336599
$737$	7.56520e10	0.00944532
$738$	−6.04299e10	−0.00749891
$739$	−3.97006e12	−0.489663	−0.244831	−	0.969566i	$-0.578733\pi$
$739$	−3.97006e12	−0.489663	−0.244831	+	0.969566i	$0.578733\pi$
$740$	3.25895e12	0.399516
$741$	1.47507e12	0.179734
$742$	−4.45295e11	−0.0539300
$743$	−1.12649e13	−1.35606	−0.678028	−	0.735036i	$-0.737165\pi$
$743$	−1.12649e13	−1.35606	−0.678028	+	0.735036i	$0.737165\pi$
$744$	8.68899e11	0.103966
$745$	6.09773e11	0.0725212
$746$	3.14150e11	0.0371375
$747$	−4.32578e12	−0.508302
$748$	4.32743e12	0.505444
$749$	−1.81594e13	−2.10831
$750$	2.35774e11	0.0272095
$751$	−2.00731e12	−0.230268	−0.115134	−	0.993350i	$-0.536730\pi$
$751$	−2.00731e12	−0.230268	−0.115134	+	0.993350i	$0.536730\pi$
$752$	−4.76103e11	−0.0542901
$753$	−6.17513e11	−0.0699952
$754$	6.75805e11	0.0761466
$755$	3.94843e12	0.442246
$756$	−3.07605e12	−0.342488
$757$	−2.31160e12	−0.255848	−0.127924	−	0.991784i	$-0.540831\pi$
$757$	−2.31160e12	−0.255848	−0.127924	+	0.991784i	$0.540831\pi$
$758$	−1.91024e11	−0.0210172
$759$	1.72045e13	1.88172
$760$	2.52851e11	0.0274918
$761$	−7.94917e12	−0.859193	−0.429597	−	0.903021i	$-0.641344\pi$
$761$	−7.94917e12	−0.859193	−0.429597	+	0.903021i	$0.641344\pi$
$762$	1.21463e11	0.0130511
$763$	−5.57953e12	−0.595987
$764$	−3.61528e12	−0.383903
$765$	−3.05564e11	−0.0322571
$766$	−3.55207e11	−0.0372779
$767$	−7.14148e11	−0.0745091
$768$	5.31179e12	0.550955
$769$	−9.28671e12	−0.957621	−0.478810	−	0.877918i	$-0.658932\pi$
$769$	−9.28671e12	−0.957621	−0.478810	+	0.877918i	$0.658932\pi$
$770$	−8.65285e11	−0.0887056
$771$	4.44577e12	0.453109
$772$	−9.17087e12	−0.929250
$773$	−4.08955e12	−0.411972	−0.205986	−	0.978555i	$-0.566040\pi$
$773$	−4.08955e12	−0.411972	−0.205986	+	0.978555i	$0.566040\pi$
$774$	2.77974e11	0.0278400
$775$	−1.14962e13	−1.14471
$776$	2.20074e12	0.217866
$777$	−1.12754e13	−1.10978
$778$	−9.05227e11	−0.0885828
$779$	1.85372e12	0.180354
$780$	−1.26931e12	−0.122784
$781$	2.19610e13	2.11214
$782$	3.06034e11	0.0292644
$783$	−3.96929e12	−0.377385
$784$	2.29142e13	2.16612
$785$	−4.60711e12	−0.433027
$786$	5.75075e10	0.00537432
$787$	1.69890e13	1.57864	0.789318	−	0.613985i	$-0.210434\pi$
$787$	1.69890e13	1.57864	0.789318	+	0.613985i	$0.210434\pi$
$788$	−1.44465e13	−1.33473
$789$	−7.71278e11	−0.0708540
$790$	3.26427e11	0.0298170
$791$	1.56571e13	1.42206
$792$	9.78860e11	0.0884010
$793$	4.39343e12	0.394525
$794$	1.80011e11	0.0160734
$795$	1.07923e12	0.0958209
$796$	1.87932e13	1.65917
$797$	1.39053e13	1.22072	0.610362	−	0.792123i	$-0.291024\pi$
$797$	1.39053e13	1.22072	0.610362	+	0.792123i	$0.291024\pi$
$798$	−4.36403e11	−0.0380956
$799$	1.64395e11	0.0142701
$800$	2.01709e12	0.174109
$801$	−3.86966e12	−0.332144
$802$	−1.06333e11	−0.00907578
$803$	5.03108e12	0.427013
$804$	−3.28325e10	−0.00277110
$805$	1.32311e13	1.11049
$806$	−6.18822e11	−0.0516485
$807$	2.03073e12	0.168547
$808$	−1.73115e12	−0.142884
$809$	−1.89067e12	−0.155184	−0.0775921	−	0.996985i	$-0.524723\pi$
$809$	−1.89067e12	−0.155184	−0.0775921	+	0.996985i	$0.524723\pi$
$810$	−3.44794e10	−0.00281434
$811$	−6.08028e12	−0.493548	−0.246774	−	0.969073i	$-0.579371\pi$
$811$	−6.08028e12	−0.493548	−0.246774	+	0.969073i	$0.579371\pi$
$812$	4.32311e13	3.48975
$813$	4.33852e11	0.0348285
$814$	1.78989e12	0.142895
$815$	−2.88246e11	−0.0228851
$816$	−1.86935e12	−0.147600
$817$	−8.52701e12	−0.669572
$818$	−8.18058e11	−0.0638843
$819$	4.39160e12	0.341071
$820$	−1.59514e12	−0.123208
$821$	1.01770e13	0.781768	0.390884	−	0.920440i	$-0.372169\pi$
$821$	1.01770e13	0.781768	0.390884	+	0.920440i	$0.372169\pi$
$822$	−4.57973e11	−0.0349878
$823$	1.27885e13	0.971671	0.485836	−	0.874050i	$-0.338515\pi$
$823$	1.27885e13	0.971671	0.485836	+	0.874050i	$0.338515\pi$
$824$	5.18688e11	0.0391953
$825$	−1.29510e13	−0.973333
$826$	2.11283e11	0.0157926
$827$	−1.42977e12	−0.106290	−0.0531449	−	0.998587i	$-0.516925\pi$
$827$	−1.42977e12	−0.106290	−0.0531449	+	0.998587i	$0.516925\pi$
$828$	−7.46664e12	−0.552063
$829$	−1.01993e12	−0.0750023	−0.0375011	−	0.999297i	$-0.511940\pi$
$829$	−1.01993e12	−0.0750023	−0.0375011	+	0.999297i	$0.511940\pi$
$830$	5.28097e11	0.0386244
$831$	−1.13246e13	−0.823794
$832$	−7.69259e12	−0.556568
$833$	−7.91211e12	−0.569364
$834$	−1.07179e12	−0.0767121
$835$	8.52654e12	0.606993
$836$	−1.49789e13	−1.06060
$837$	3.63460e12	0.255972
$838$	−1.59417e12	−0.111670
$839$	−2.59347e13	−1.80697	−0.903487	−	0.428616i	$-0.859001\pi$
$839$	−2.59347e13	−1.80697	−0.903487	+	0.428616i	$0.859001\pi$
$840$	7.52793e11	0.0521698
$841$	4.12776e13	2.84533
$842$	1.26848e12	0.0869718
$843$	4.56421e12	0.311273
$844$	2.00470e13	1.35990
$845$	−3.72039e12	−0.251035
$846$	1.85501e10	0.00124503
$847$	7.59765e13	5.07229
$848$	6.60239e12	0.438450
$849$	−1.20888e13	−0.798543
$850$	−2.30373e11	−0.0151372
$851$	−2.73694e13	−1.78888
$852$	−9.53092e12	−0.619664
$853$	−7.48082e12	−0.483814	−0.241907	−	0.970299i	$-0.577773\pi$
$853$	−7.48082e12	−0.483814	−0.241907	+	0.970299i	$0.577773\pi$
$854$	−1.29981e12	−0.0836217
$855$	1.05767e12	0.0676868
$856$	−2.50791e12	−0.159654
$857$	9.78179e12	0.619448	0.309724	−	0.950827i	$-0.399763\pi$
$857$	9.78179e12	0.619448	0.309724	+	0.950827i	$0.399763\pi$
$858$	−6.97135e11	−0.0439161
$859$	4.63523e12	0.290471	0.145235	−	0.989397i	$-0.453606\pi$
$859$	4.63523e12	0.290471	0.145235	+	0.989397i	$0.453606\pi$
$860$	7.33756e12	0.457413
$861$	5.51894e12	0.342248
$862$	−8.85702e11	−0.0546393
$863$	−2.36590e13	−1.45194	−0.725968	−	0.687729i	$-0.758608\pi$
$863$	−2.36590e13	−1.45194	−0.725968	+	0.687729i	$0.758608\pi$
$864$	−6.37718e11	−0.0389329
$865$	7.22466e11	0.0438778
$866$	−1.28575e12	−0.0776830
$867$	−8.96014e12	−0.538554
$868$	−3.95859e13	−2.36702
$869$	−3.87646e13	−2.30593
$870$	4.84576e11	0.0286764
$871$	4.68741e10	0.00275963
$872$	−7.70563e11	−0.0451319
$873$	9.20567e12	0.536403
$874$	−1.05930e12	−0.0614070
$875$	−2.15328e13	−1.24183
$876$	−2.18345e12	−0.125278
$877$	2.87031e13	1.63844	0.819219	−	0.573481i	$-0.194407\pi$
$877$	2.87031e13	1.63844	0.819219	+	0.573481i	$0.194407\pi$
$878$	−1.34809e12	−0.0765583
$879$	7.28379e12	0.411536
$880$	1.28296e13	0.721175
$881$	6.60321e12	0.369287	0.184643	−	0.982806i	$-0.440887\pi$
$881$	6.60321e12	0.369287	0.184643	+	0.982806i	$0.440887\pi$
$882$	−8.92790e11	−0.0496753
$883$	−3.16627e13	−1.75277	−0.876385	−	0.481611i	$-0.840052\pi$
$883$	−3.16627e13	−1.75277	−0.876385	+	0.481611i	$0.840052\pi$
$884$	2.68129e12	0.147675
$885$	−5.12069e11	−0.0280597
$886$	−7.71060e11	−0.0420374
$887$	2.15265e13	1.16766	0.583831	−	0.811875i	$-0.301553\pi$
$887$	2.15265e13	1.16766	0.583831	+	0.811875i	$0.301553\pi$
$888$	−1.55720e12	−0.0840399
$889$	−1.10930e13	−0.595650
$890$	4.72413e11	0.0252387
$891$	4.09457e12	0.217650
$892$	−7.02704e12	−0.371647
$893$	−5.69033e11	−0.0299438
$894$	−1.45345e11	−0.00760996
$895$	−1.00798e13	−0.525108
$896$	9.25364e12	0.479652
$897$	1.06599e13	0.549780
$898$	−1.80291e12	−0.0925189
$899$	−5.10810e13	−2.60820
$900$	5.62066e12	0.285559
$901$	−2.27976e12	−0.115246
$902$	−8.76092e11	−0.0440677
$903$	−2.53868e13	−1.27061
$904$	2.16233e12	0.107687
$905$	−1.28950e13	−0.639001
$906$	−9.41148e11	−0.0464068
$907$	−2.11783e13	−1.03910	−0.519550	−	0.854440i	$-0.673901\pi$
$907$	−2.11783e13	−1.03910	−0.519550	+	0.854440i	$0.673901\pi$
$908$	8.92869e12	0.435915
$909$	−7.24139e12	−0.351791
$910$	−5.36132e11	−0.0259171
$911$	1.02131e13	0.491273	0.245636	−	0.969362i	$-0.421003\pi$
$911$	1.02131e13	0.491273	0.245636	+	0.969362i	$0.421003\pi$
$912$	6.47054e12	0.309716
$913$	−6.27137e13	−2.98706
$914$	2.11519e12	0.100252
$915$	3.15024e12	0.148576
$916$	3.54672e13	1.66455
$917$	−5.25205e12	−0.245282
$918$	7.28342e10	0.00338488
$919$	−2.95207e13	−1.36523	−0.682616	−	0.730777i	$-0.739158\pi$
$919$	−2.95207e13	−1.36523	−0.682616	+	0.730777i	$0.739158\pi$
$920$	1.82729e12	0.0840935
$921$	−3.84957e12	−0.176296
$922$	−4.79949e11	−0.0218729
$923$	1.36071e13	0.617101
$924$	−4.45955e13	−2.01265
$925$	2.06028e13	0.925314
$926$	4.95532e10	0.00221474
$927$	2.16967e12	0.0965016
$928$	8.96255e12	0.396703
$929$	−1.45132e12	−0.0639280	−0.0319640	−	0.999489i	$-0.510176\pi$
$929$	−1.45132e12	−0.0639280	−0.0319640	+	0.999489i	$0.510176\pi$
$930$	−4.43717e11	−0.0194506
$931$	2.73869e13	1.19473
$932$	9.48418e12	0.411745
$933$	−2.09236e13	−0.904001
$934$	2.00736e12	0.0863107
$935$	−4.42996e12	−0.189560
$936$	6.06503e11	0.0258281
$937$	2.21200e13	0.937467	0.468734	−	0.883340i	$-0.344710\pi$
$937$	2.21200e13	0.937467	0.468734	+	0.883340i	$0.344710\pi$
$938$	−1.38678e10	−0.000584919 0
$939$	1.24292e13	0.521734
$940$	4.89658e11	0.0204559
$941$	1.25780e12	0.0522947	0.0261473	−	0.999658i	$-0.491676\pi$
$941$	1.25780e12	0.0522947	0.0261473	+	0.999658i	$0.491676\pi$
$942$	1.09815e12	0.0454394
$943$	1.33964e13	0.551677
$944$	−3.13269e12	−0.128394
$945$	3.14893e12	0.128446
$946$	4.02997e12	0.163603
$947$	2.05492e13	0.830272	0.415136	−	0.909759i	$-0.363734\pi$
$947$	2.05492e13	0.830272	0.415136	+	0.909759i	$0.363734\pi$
$948$	1.68236e13	0.676520
$949$	3.11726e12	0.124760
$950$	7.97409e11	0.0317632
$951$	5.38464e11	0.0213474
$952$	−1.59020e12	−0.0627459
$953$	−8.87114e12	−0.348387	−0.174193	−	0.984711i	$-0.555732\pi$
$953$	−8.87114e12	−0.348387	−0.174193	+	0.984711i	$0.555732\pi$
$954$	−2.57244e11	−0.0100549
$955$	3.70093e12	0.143978
$956$	−4.08467e13	−1.58160
$957$	−5.75454e13	−2.21772
$958$	−1.80434e12	−0.0692107
$959$	4.18257e13	1.59683
$960$	−5.51586e12	−0.209601
$961$	2.03343e13	0.769083
$962$	1.10902e12	0.0417496
$963$	−1.04906e13	−0.393080
$964$	2.46543e12	0.0919487
$965$	9.38815e12	0.348503
$966$	−3.15377e12	−0.116529
$967$	−3.66535e13	−1.34802	−0.674011	−	0.738722i	$-0.735430\pi$
$967$	−3.66535e13	−1.34802	−0.674011	+	0.738722i	$0.735430\pi$
$968$	1.04928e13	0.384105
$969$	−2.23423e12	−0.0814087
$970$	−1.12384e12	−0.0407598
$971$	7.42335e12	0.267987	0.133993	−	0.990982i	$-0.457220\pi$
$971$	7.42335e12	0.267987	0.133993	+	0.990982i	$0.457220\pi$
$972$	−1.77702e12	−0.0638547
$973$	9.78847e13	3.50112
$974$	−3.98683e11	−0.0141943
$975$	−8.02447e12	−0.284378
$976$	1.92723e13	0.679843
$977$	−3.60999e13	−1.26760	−0.633798	−	0.773498i	$-0.718505\pi$
$977$	−3.60999e13	−1.26760	−0.633798	+	0.773498i	$0.718505\pi$
$978$	6.87062e10	0.00240144
$979$	−5.61010e13	−1.95186
$980$	−2.35666e13	−0.816169
$981$	−3.22326e12	−0.111118
$982$	1.89907e12	0.0651687
$983$	2.65953e13	0.908479	0.454239	−	0.890880i	$-0.349911\pi$
$983$	2.65953e13	0.908479	0.454239	+	0.890880i	$0.349911\pi$
$984$	7.62195e11	0.0259172
$985$	1.47888e13	0.500575
$986$	−1.02362e12	−0.0344899
$987$	−1.69414e12	−0.0568227
$988$	−9.28096e12	−0.309875
$989$	−6.16225e13	−2.04812
$990$	−4.99870e11	−0.0165386
$991$	−4.31087e13	−1.41982	−0.709910	−	0.704292i	$-0.751264\pi$
$991$	−4.31087e13	−1.41982	−0.709910	+	0.704292i	$0.751264\pi$
$992$	−8.20683e12	−0.269075
$993$	1.46162e13	0.477048
$994$	−4.02569e12	−0.130798
$995$	−1.92384e13	−0.622251
$996$	2.72173e13	0.876352
$997$	−2.69692e13	−0.864451	−0.432226	−	0.901765i	$-0.642272\pi$
$997$	−2.69692e13	−0.864451	−0.432226	+	0.901765i	$0.642272\pi$
$998$	−6.94704e10	−0.00221673
$999$	−6.51375e12	−0.206912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.11	✓	22	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} -800.975 q^{10} +95119.1 q^{11} -41281.1 q^{12} +58936.0 q^{13} -17436.4 q^{14} +42259.1 q^{15} +258529. q^{16} -89268.2 q^{17} -10072.9 q^{18} +308991. q^{19} -265890. q^{20} +919936. q^{21} -146033. q^{22} +2.23300e6 q^{23} +127048. q^{24} -1.68094e6 q^{25} -90482.4 q^{26} +531441. q^{27} -5.78813e6 q^{28} -7.46892e6 q^{29} -64879.0 q^{30} +6.83914e6 q^{31} -1.19998e6 q^{32} +7.70465e6 q^{33} +137050. q^{34} +5.92527e6 q^{35} -3.34377e6 q^{36} -1.22568e7 q^{37} -474384. q^{38} +4.77381e6 q^{39} +818311. q^{40} +5.99927e6 q^{41} -1.41235e6 q^{42} -2.75963e7 q^{43} -4.84768e7 q^{44} +3.42299e6 q^{45} -3.42825e6 q^{46} -1.84158e6 q^{47} +2.09409e7 q^{48} +8.86331e7 q^{49} +2.58068e6 q^{50} -7.23072e6 q^{51} -3.00363e7 q^{52} +2.55383e7 q^{53} -815903. q^{54} +4.96253e7 q^{55} +1.78137e7 q^{56} +2.50283e7 q^{57} +1.14668e7 q^{58} -1.21174e7 q^{59} -2.15371e7 q^{60} +7.45458e7 q^{61} -1.04999e7 q^{62} +7.45148e7 q^{63} -1.30525e8 q^{64} +3.07479e7 q^{65} -1.18287e7 q^{66} +795340. q^{67} +4.54949e7 q^{68} +1.80873e8 q^{69} -9.09686e6 q^{70} +2.30879e8 q^{71} +1.02909e7 q^{72} +5.28924e7 q^{73} +1.88174e7 q^{74} -1.36156e8 q^{75} -1.57475e8 q^{76} +1.08029e9 q^{77} -7.32907e6 q^{78} -4.07537e8 q^{79} +1.34879e8 q^{80} +4.30467e7 q^{81} -9.21047e6 q^{82} -6.59317e8 q^{83} -4.68839e8 q^{84} -4.65728e7 q^{85} +4.23676e7 q^{86} -6.04982e8 q^{87} +1.49194e8 q^{88} -5.89798e8 q^{89} -5.25520e6 q^{90} +6.69349e8 q^{91} -1.13803e9 q^{92} +5.53971e8 q^{93} +2.82732e6 q^{94} +1.61206e8 q^{95} -9.71984e7 q^{96} +1.40309e9 q^{97} -1.36075e8 q^{98} +6.24077e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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