LMFDB - Embedded newform 177.10.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +61733.3 q^{10} -79089.2 q^{11} -39190.4 q^{12} -1847.31 q^{13} -154715. q^{14} -158457. q^{15} -275773. q^{16} +459823. q^{17} +207044. q^{18} +1.08468e6 q^{19} +946500. q^{20} +397123. q^{21} -2.49580e6 q^{22} +2.20622e6 q^{23} +72001.0 q^{24} +1.87383e6 q^{25} -58295.3 q^{26} -531441. q^{27} -2.37210e6 q^{28} -4.56225e6 q^{29} -5.00040e6 q^{30} +6.82675e6 q^{31} -8.24739e6 q^{32} +6.40623e6 q^{33} +1.45105e7 q^{34} -9.59105e6 q^{35} +3.17442e6 q^{36} +1.05656e7 q^{37} +3.42292e7 q^{38} +149632. q^{39} -1.73892e6 q^{40} -1.66901e7 q^{41} +1.25319e7 q^{42} +3.40809e7 q^{43} -3.82659e7 q^{44} +1.28350e7 q^{45} +6.96214e7 q^{46} +3.70501e6 q^{47} +2.23376e7 q^{48} -1.63167e7 q^{49} +5.91319e7 q^{50} -3.72456e7 q^{51} -893789. q^{52} -2.35435e7 q^{53} -1.67706e7 q^{54} -1.54719e8 q^{55} +4.35806e6 q^{56} -8.78594e7 q^{57} -1.43970e8 q^{58} +1.21174e7 q^{59} -7.66665e7 q^{60} +1.59558e8 q^{61} +2.15430e8 q^{62} -3.21669e7 q^{63} -1.19066e8 q^{64} -3.61383e6 q^{65} +2.02160e8 q^{66} +1.14987e8 q^{67} +2.22477e8 q^{68} -1.78704e8 q^{69} -3.02663e8 q^{70} +1.06400e8 q^{71} -5.83208e6 q^{72} +2.12864e7 q^{73} +3.33415e8 q^{74} -1.51780e8 q^{75} +5.24805e8 q^{76} +3.87755e8 q^{77} +4.72192e6 q^{78} +3.40239e8 q^{79} -5.39483e8 q^{80} +4.30467e7 q^{81} -5.26685e8 q^{82} -9.07182e7 q^{83} +1.92140e8 q^{84} +8.99532e8 q^{85} +1.07548e9 q^{86} +3.69542e8 q^{87} +7.03025e7 q^{88} +7.56249e8 q^{89} +4.05032e8 q^{90} +9.05692e6 q^{91} +1.06744e9 q^{92} -5.52966e8 q^{93} +1.16918e8 q^{94} +2.12192e9 q^{95} +6.68038e8 q^{96} +3.71927e8 q^{97} -5.14902e8 q^{98} -5.18904e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * 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 $

$2$	31.5568	1.39463	0.697313	−	0.716766i	$-0.254379\pi$
$2$	31.5568	1.39463	0.697313	+	0.716766i	$0.254379\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	483.832	0.944984
$5$	1956.26	1.39979	0.699893	−	0.714248i	$-0.253231\pi$
$5$	1956.26	1.39979	0.699893	+	0.714248i	$0.253231\pi$
$6$	−2556.10	−0.805188
$7$	−4902.75	−0.771789	−0.385894	−	0.922543i	$-0.626107\pi$
$7$	−4902.75	−0.771789	−0.385894	+	0.922543i	$0.626107\pi$
$8$	−888.901	−0.0767271
$9$	6561.00	0.333333
$10$	61733.3	1.95218
$11$	−79089.2	−1.62873	−0.814367	−	0.580350i	$-0.802916\pi$
$11$	−79089.2	−1.62873	−0.814367	+	0.580350i	$0.802916\pi$
$12$	−39190.4	−0.545587
$13$	−1847.31	−0.0179389	−0.00896945	−	0.999960i	$-0.502855\pi$
$13$	−1847.31	−0.0179389	−0.00896945	+	0.999960i	$0.502855\pi$
$14$	−154715.	−1.07636
$15$	−158457.	−0.808166
$16$	−275773.	−1.05199
$17$	459823.	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$17$	459823.	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$18$	207044.	0.464876
$19$	1.08468e6	1.90947	0.954734	−	0.297462i	$-0.0961402\pi$
$19$	1.08468e6	1.90947	0.954734	+	0.297462i	$0.0961402\pi$
$20$	946500.	1.32277
$21$	397123.	0.445592
$22$	−2.49580e6	−2.27148
$23$	2.20622e6	1.64390	0.821948	−	0.569563i	$-0.192887\pi$
$23$	2.20622e6	1.64390	0.821948	+	0.569563i	$0.192887\pi$
$24$	72001.0	0.0442984
$25$	1.87383e6	0.959399
$26$	−58295.3	−0.0250181
$27$	−531441.	−0.192450
$28$	−2.37210e6	−0.729328
$29$	−4.56225e6	−1.19781	−0.598905	−	0.800820i	$-0.704397\pi$
$29$	−4.56225e6	−1.19781	−0.598905	+	0.800820i	$0.704397\pi$
$30$	−5.00040e6	−1.12709
$31$	6.82675e6	1.32766	0.663829	−	0.747885i	$-0.268930\pi$
$31$	6.82675e6	1.32766	0.663829	+	0.747885i	$0.268930\pi$
$32$	−8.24739e6	−1.39041
$33$	6.40623e6	0.940350
$34$	1.45105e7	1.86221
$35$	−9.59105e6	−1.08034
$36$	3.17442e6	0.314995
$37$	1.05656e7	0.926797	0.463399	−	0.886150i	$-0.346630\pi$
$37$	1.05656e7	0.926797	0.463399	+	0.886150i	$0.346630\pi$
$38$	3.42292e7	2.66299
$39$	149632.	0.0103570
$40$	−1.73892e6	−0.107401
$41$	−1.66901e7	−0.922424	−0.461212	−	0.887290i	$-0.652585\pi$
$41$	−1.66901e7	−0.922424	−0.461212	+	0.887290i	$0.652585\pi$
$42$	1.25319e7	0.621435
$43$	3.40809e7	1.52021	0.760103	−	0.649802i	$-0.225148\pi$
$43$	3.40809e7	1.52021	0.760103	+	0.649802i	$0.225148\pi$
$44$	−3.82659e7	−1.53913
$45$	1.28350e7	0.466595
$46$	6.96214e7	2.29262
$47$	3.70501e6	0.110751	0.0553757	−	0.998466i	$-0.482364\pi$
$47$	3.70501e6	0.110751	0.0553757	+	0.998466i	$0.482364\pi$
$48$	2.23376e7	0.607366
$49$	−1.63167e7	−0.404342
$50$	5.91319e7	1.33800
$51$	−3.72456e7	−0.770921
$52$	−893789.	−0.0169520
$53$	−2.35435e7	−0.409855	−0.204928	−	0.978777i	$-0.565696\pi$
$53$	−2.35435e7	−0.409855	−0.204928	+	0.978777i	$0.565696\pi$
$54$	−1.67706e7	−0.268396
$55$	−1.54719e8	−2.27988
$56$	4.35806e6	0.0592171
$57$	−8.78594e7	−1.10243
$58$	−1.43970e8	−1.67050
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−7.66665e7	−0.763704
$61$	1.59558e8	1.47548	0.737741	−	0.675083i	$-0.235892\pi$
$61$	1.59558e8	1.47548	0.737741	+	0.675083i	$0.235892\pi$
$62$	2.15430e8	1.85159
$63$	−3.21669e7	−0.257263
$64$	−1.19066e8	−0.887107
$65$	−3.61383e6	−0.0251106
$66$	2.02160e8	1.31144
$67$	1.14987e8	0.697125	0.348563	−	0.937285i	$-0.386670\pi$
$67$	1.14987e8	0.697125	0.348563	+	0.937285i	$0.386670\pi$
$68$	2.22477e8	1.26181
$69$	−1.78704e8	−0.949104
$70$	−3.02663e8	−1.50667
$71$	1.06400e8	0.496911	0.248456	−	0.968643i	$-0.420077\pi$
$71$	1.06400e8	0.496911	0.248456	+	0.968643i	$0.420077\pi$
$72$	−5.83208e6	−0.0255757
$73$	2.12864e7	0.0877303	0.0438651	−	0.999037i	$-0.486033\pi$
$73$	2.12864e7	0.0877303	0.0438651	+	0.999037i	$0.486033\pi$
$74$	3.33415e8	1.29254
$75$	−1.51780e8	−0.553909
$76$	5.24805e8	1.80442
$77$	3.87755e8	1.25704
$78$	4.72192e6	0.0144442
$79$	3.40239e8	0.982794	0.491397	−	0.870936i	$-0.336486\pi$
$79$	3.40239e8	0.982794	0.491397	+	0.870936i	$0.336486\pi$
$80$	−5.39483e8	−1.47256
$81$	4.30467e7	0.111111
$82$	−5.26685e8	−1.28644
$83$	−9.07182e7	−0.209818	−0.104909	−	0.994482i	$-0.533455\pi$
$83$	−9.07182e7	−0.209818	−0.104909	+	0.994482i	$0.533455\pi$
$84$	1.92140e8	0.421078
$85$	8.99532e8	1.86910
$86$	1.07548e9	2.12012
$87$	3.69542e8	0.691556
$88$	7.03025e7	0.124968
$89$	7.56249e8	1.27764	0.638822	−	0.769355i	$-0.279422\pi$
$89$	7.56249e8	1.27764	0.638822	+	0.769355i	$0.279422\pi$
$90$	4.05032e8	0.650726
$91$	9.05692e6	0.0138450
$92$	1.06744e9	1.55345
$93$	−5.52966e8	−0.766523
$94$	1.16918e8	0.154457
$95$	2.12192e9	2.67284
$96$	6.68038e8	0.802751
$97$	3.71927e8	0.426564	0.213282	−	0.976991i	$-0.431585\pi$
$97$	3.71927e8	0.426564	0.213282	+	0.976991i	$0.431585\pi$
$98$	−5.14902e8	−0.563907
$99$	−5.18904e8	−0.542911
$100$	9.06616e8	0.906616
$101$	1.46160e8	0.139760	0.0698798	−	0.997555i	$-0.477738\pi$
$101$	1.46160e8	0.139760	0.0698798	+	0.997555i	$0.477738\pi$
$102$	−1.17535e9	−1.07515
$103$	−1.24880e9	−1.09326	−0.546632	−	0.837373i	$-0.684090\pi$
$103$	−1.24880e9	−1.09326	−0.546632	+	0.837373i	$0.684090\pi$
$104$	1.64208e6	0.00137640
$105$	7.76875e8	0.623734
$106$	−7.42959e8	−0.571595
$107$	1.73100e9	1.27664	0.638322	−	0.769770i	$-0.279629\pi$
$107$	1.73100e9	1.27664	0.638322	+	0.769770i	$0.279629\pi$
$108$	−2.57128e8	−0.181862
$109$	−1.34909e6	−0.000915426 0	−0.000457713	−	1.00000i	$-0.500146\pi$
$109$	−1.34909e6	−0.000915426 0	−0.000457713		1.00000i	$0.500146\pi$
$110$	−4.88244e9	−3.17958
$111$	−8.55810e8	−0.535087
$112$	1.35204e9	0.811913
$113$	−1.90229e9	−1.09755	−0.548775	−	0.835970i	$-0.684905\pi$
$113$	−1.90229e9	−1.09755	−0.548775	+	0.835970i	$0.684905\pi$
$114$	−2.77256e9	−1.53748
$115$	4.31595e9	2.30110
$116$	−2.20736e9	−1.13191
$117$	−1.21202e7	−0.00597963
$118$	3.82385e8	0.181565
$119$	−2.25439e9	−1.03055
$120$	1.40853e8	0.0620082
$121$	3.89716e9	1.65278
$122$	5.03514e9	2.05775
$123$	1.35189e9	0.532562
$124$	3.30300e9	1.25461
$125$	−1.55131e8	−0.0568333
$126$	−1.01509e9	−0.358786
$127$	−1.62957e9	−0.555848	−0.277924	−	0.960603i	$-0.589646\pi$
$127$	−1.62957e9	−0.555848	−0.277924	+	0.960603i	$0.589646\pi$
$128$	4.65335e8	0.153222
$129$	−2.76055e9	−0.877692
$130$	−1.14041e8	−0.0350199
$131$	−2.05451e9	−0.609519	−0.304760	−	0.952429i	$-0.598576\pi$
$131$	−2.05451e9	−0.609519	−0.304760	+	0.952429i	$0.598576\pi$
$132$	3.09954e9	0.888616
$133$	−5.31793e9	−1.47371
$134$	3.62861e9	0.972230
$135$	−1.03964e9	−0.269389
$136$	−4.08737e8	−0.102452
$137$	4.37780e9	1.06173	0.530865	−	0.847457i	$-0.321867\pi$
$137$	4.37780e9	1.06173	0.530865	+	0.847457i	$0.321867\pi$
$138$	−5.63933e9	−1.32365
$139$	−1.23302e9	−0.280157	−0.140079	−	0.990140i	$-0.544736\pi$
$139$	−1.23302e9	−0.280157	−0.140079	+	0.990140i	$0.544736\pi$
$140$	−4.64045e9	−1.02090
$141$	−3.00106e8	−0.0639423
$142$	3.35764e9	0.693005
$143$	1.46103e8	0.0292177
$144$	−1.80934e9	−0.350663
$145$	−8.92495e9	−1.67668
$146$	6.71731e8	0.122351
$147$	1.32165e9	0.233447
$148$	5.11195e9	0.875809
$149$	−6.18776e9	−1.02848	−0.514239	−	0.857647i	$-0.671926\pi$
$149$	−6.18776e9	−1.02848	−0.514239	+	0.857647i	$0.671926\pi$
$150$	−4.78969e9	−0.772496
$151$	1.21679e9	0.190467	0.0952335	−	0.995455i	$-0.469640\pi$
$151$	1.21679e9	0.190467	0.0952335	+	0.995455i	$0.469640\pi$
$152$	−9.64177e8	−0.146508
$153$	3.01690e9	0.445091
$154$	1.22363e10	1.75310
$155$	1.33549e10	1.85844
$156$	7.23969e7	0.00978722
$157$	−5.87350e9	−0.771522	−0.385761	−	0.922599i	$-0.626061\pi$
$157$	−5.87350e9	−0.771522	−0.385761	+	0.922599i	$0.626061\pi$
$158$	1.07369e10	1.37063
$159$	1.90703e9	0.236630
$160$	−1.61340e10	−1.94627
$161$	−1.08166e10	−1.26874
$162$	1.35842e9	0.154959
$163$	−2.41860e9	−0.268361	−0.134181	−	0.990957i	$-0.542840\pi$
$163$	−2.41860e9	−0.268361	−0.134181	+	0.990957i	$0.542840\pi$
$164$	−8.07518e9	−0.871676
$165$	1.25322e10	1.31629
$166$	−2.86278e9	−0.292618
$167$	−2.02117e9	−0.201085	−0.100543	−	0.994933i	$-0.532058\pi$
$167$	−2.02117e9	−0.201085	−0.100543	+	0.994933i	$0.532058\pi$
$168$	−3.53003e8	−0.0341890
$169$	−1.06011e10	−0.999678
$170$	2.83864e10	2.60669
$171$	7.11661e9	0.636489
$172$	1.64894e10	1.43657
$173$	−1.02328e10	−0.868538	−0.434269	−	0.900783i	$-0.642993\pi$
$173$	−1.02328e10	−0.868538	−0.434269	+	0.900783i	$0.642993\pi$
$174$	1.16616e10	0.964463
$175$	−9.18689e9	−0.740453
$176$	2.18107e10	1.71341
$177$	−9.81506e8	−0.0751646
$178$	2.38648e10	1.78184
$179$	1.40447e10	1.02252	0.511262	−	0.859425i	$-0.329178\pi$
$179$	1.40447e10	1.02252	0.511262	+	0.859425i	$0.329178\pi$
$180$	6.20999e9	0.440925
$181$	−1.33959e10	−0.927723	−0.463862	−	0.885908i	$-0.653536\pi$
$181$	−1.33959e10	−0.927723	−0.463862	+	0.885908i	$0.653536\pi$
$182$	2.85807e8	0.0193087
$183$	−1.29242e10	−0.851870
$184$	−1.96111e9	−0.126131
$185$	2.06690e10	1.29732
$186$	−1.74498e10	−1.06901
$187$	−3.63670e10	−2.17481
$188$	1.79260e9	0.104658
$189$	2.60552e9	0.148531
$190$	6.69611e10	3.72762
$191$	8.66978e9	0.471366	0.235683	−	0.971830i	$-0.424267\pi$
$191$	8.66978e9	0.471366	0.235683	+	0.971830i	$0.424267\pi$
$192$	9.64431e9	0.512172
$193$	−2.95756e10	−1.53436	−0.767178	−	0.641435i	$-0.778340\pi$
$193$	−2.95756e10	−1.53436	−0.767178	+	0.641435i	$0.778340\pi$
$194$	1.17368e10	0.594898
$195$	2.92720e8	0.0144976
$196$	−7.89452e9	−0.382097
$197$	2.56328e10	1.21255	0.606273	−	0.795257i	$-0.292664\pi$
$197$	2.56328e10	1.21255	0.606273	+	0.795257i	$0.292664\pi$
$198$	−1.63750e10	−0.757159
$199$	3.76194e10	1.70048	0.850242	−	0.526392i	$-0.176456\pi$
$199$	3.76194e10	1.70048	0.850242	+	0.526392i	$0.176456\pi$
$200$	−1.66565e9	−0.0736118
$201$	−9.31392e9	−0.402486
$202$	4.61233e9	0.194912
$203$	2.23676e10	0.924457
$204$	−1.80206e10	−0.728507
$205$	−3.26501e10	−1.29120
$206$	−3.94081e10	−1.52469
$207$	1.44750e10	0.547965
$208$	5.09439e8	0.0188715
$209$	−8.57868e10	−3.11001
$210$	2.45157e10	0.869876
$211$	4.47769e10	1.55519	0.777594	−	0.628767i	$-0.216440\pi$
$211$	4.47769e10	1.55519	0.777594	+	0.628767i	$0.216440\pi$
$212$	−1.13911e10	−0.387306
$213$	−8.61839e9	−0.286892
$214$	5.46248e10	1.78044
$215$	6.66710e10	2.12796
$216$	4.72399e8	0.0147661
$217$	−3.34698e10	−1.02467
$218$	−4.25731e7	−0.00127668
$219$	−1.72420e9	−0.0506511
$220$	−7.48580e10	−2.15445
$221$	−8.49437e8	−0.0239533
$222$	−2.70066e10	−0.746246
$223$	−1.95185e9	−0.0528536	−0.0264268	−	0.999651i	$-0.508413\pi$
$223$	−1.95185e9	−0.0528536	−0.0264268	+	0.999651i	$0.508413\pi$
$224$	4.04349e10	1.07310
$225$	1.22942e10	0.319800
$226$	−6.00302e10	−1.53067
$227$	−3.36446e9	−0.0841007	−0.0420503	−	0.999115i	$-0.513389\pi$
$227$	−3.36446e9	−0.0841007	−0.0420503	+	0.999115i	$0.513389\pi$
$228$	−4.25092e10	−1.04178
$229$	7.32608e10	1.76040	0.880202	−	0.474600i	$-0.157407\pi$
$229$	7.32608e10	1.76040	0.880202	+	0.474600i	$0.157407\pi$
$230$	1.36197e11	3.20918
$231$	−3.14081e10	−0.725752
$232$	4.05539e9	0.0919045
$233$	5.46189e10	1.21406	0.607032	−	0.794677i	$-0.292360\pi$
$233$	5.46189e10	1.21406	0.607032	+	0.794677i	$0.292360\pi$
$234$	−3.82476e8	−0.00833935
$235$	7.24796e9	0.155028
$236$	5.86276e9	0.123026
$237$	−2.75594e10	−0.567416
$238$	−7.11415e10	−1.43723
$239$	−1.09256e10	−0.216599	−0.108299	−	0.994118i	$-0.534541\pi$
$239$	−1.09256e10	−0.216599	−0.108299	+	0.994118i	$0.534541\pi$
$240$	4.36981e10	0.850182
$241$	−1.81118e10	−0.345847	−0.172924	−	0.984935i	$-0.555321\pi$
$241$	−1.81118e10	−0.345847	−0.172924	+	0.984935i	$0.555321\pi$
$242$	1.22982e11	2.30500
$243$	−3.48678e9	−0.0641500
$244$	7.71992e10	1.39431
$245$	−3.19196e10	−0.565992
$246$	4.26615e10	0.742725
$247$	−2.00375e9	−0.0342537
$248$	−6.06830e9	−0.101867
$249$	7.34817e9	0.121139
$250$	−4.89543e9	−0.0792613
$251$	3.71772e10	0.591214	0.295607	−	0.955310i	$-0.404478\pi$
$251$	3.71772e10	0.591214	0.295607	+	0.955310i	$0.404478\pi$
$252$	−1.55634e10	−0.243109
$253$	−1.74489e11	−2.67747
$254$	−5.14240e10	−0.775201
$255$	−7.28621e10	−1.07912
$256$	7.56460e10	1.10079
$257$	−8.72339e10	−1.24734	−0.623672	−	0.781686i	$-0.714360\pi$
$257$	−8.72339e10	−1.24734	−0.623672	+	0.781686i	$0.714360\pi$
$258$	−8.71142e10	−1.22405
$259$	−5.18003e10	−0.715292
$260$	−1.74848e9	−0.0237291
$261$	−2.99329e10	−0.399270
$262$	−6.48338e10	−0.850052
$263$	−8.87644e10	−1.14403	−0.572016	−	0.820243i	$-0.693838\pi$
$263$	−8.87644e10	−1.14403	−0.572016	+	0.820243i	$0.693838\pi$
$264$	−5.69450e9	−0.0721503
$265$	−4.60573e10	−0.573709
$266$	−1.67817e11	−2.05527
$267$	−6.12561e10	−0.737648
$268$	5.56342e10	0.658772
$269$	5.60043e9	0.0652133	0.0326067	−	0.999468i	$-0.489619\pi$
$269$	5.60043e9	0.0652133	0.0326067	+	0.999468i	$0.489619\pi$
$270$	−3.28076e10	−0.375697
$271$	1.21138e11	1.36433	0.682163	−	0.731200i	$-0.261039\pi$
$271$	1.21138e11	1.36433	0.682163	+	0.731200i	$0.261039\pi$
$272$	−1.26807e11	−1.40469
$273$	−7.33610e8	−0.00799343
$274$	1.38149e11	1.48072
$275$	−1.48199e11	−1.56261
$276$	−8.64627e10	−0.896888
$277$	−6.77355e10	−0.691286	−0.345643	−	0.938366i	$-0.612339\pi$
$277$	−6.77355e10	−0.691286	−0.345643	+	0.938366i	$0.612339\pi$
$278$	−3.89100e10	−0.390715
$279$	4.47903e10	0.442553
$280$	8.52549e9	0.0828912
$281$	1.42849e11	1.36678	0.683390	−	0.730053i	$-0.260505\pi$
$281$	1.42849e11	1.36678	0.683390	+	0.730053i	$0.260505\pi$
$282$	−9.47038e9	−0.0891757
$283$	−2.08907e11	−1.93604	−0.968020	−	0.250874i	$-0.919282\pi$
$283$	−2.08907e11	−1.93604	−0.968020	+	0.250874i	$0.919282\pi$
$284$	5.14796e10	0.469573
$285$	−1.71876e11	−1.54317
$286$	4.61053e9	0.0407478
$287$	8.18271e10	0.711916
$288$	−5.41111e10	−0.463469
$289$	9.28490e10	0.782956
$290$	−2.81643e11	−2.33834
$291$	−3.01261e10	−0.246277
$292$	1.02990e10	0.0829037
$293$	1.16872e11	0.926419	0.463209	−	0.886249i	$-0.346698\pi$
$293$	1.16872e11	0.926419	0.463209	+	0.886249i	$0.346698\pi$
$294$	4.17071e10	0.325572
$295$	2.37047e10	0.182237
$296$	−9.39174e9	−0.0711104
$297$	4.20313e10	0.313450
$298$	−1.95266e11	−1.43434
$299$	−4.07559e9	−0.0294897
$300$	−7.34359e10	−0.523435
$301$	−1.67090e11	−1.17328
$302$	3.83980e10	0.265630
$303$	−1.18389e10	−0.0806902
$304$	−2.99126e11	−2.00874
$305$	3.12137e11	2.06536
$306$	9.52036e10	0.620736
$307$	−8.34907e10	−0.536433	−0.268216	−	0.963359i	$-0.586434\pi$
$307$	−8.34907e10	−0.536433	−0.268216	+	0.963359i	$0.586434\pi$
$308$	1.87608e11	1.18788
$309$	1.01153e11	0.631196
$310$	4.21437e11	2.59182
$311$	−2.23495e11	−1.35471	−0.677356	−	0.735656i	$-0.736874\pi$
$311$	−2.23495e11	−1.35471	−0.677356	+	0.735656i	$0.736874\pi$
$312$	−1.33008e8	−0.000794664 0
$313$	−9.88835e10	−0.582337	−0.291168	−	0.956672i	$-0.594044\pi$
$313$	−9.88835e10	−0.582337	−0.291168	+	0.956672i	$0.594044\pi$
$314$	−1.85349e11	−1.07598
$315$	−6.29269e10	−0.360113
$316$	1.64619e11	0.928724
$317$	−3.06064e11	−1.70233	−0.851167	−	0.524894i	$-0.824105\pi$
$317$	−3.06064e11	−1.70233	−0.851167	+	0.524894i	$0.824105\pi$
$318$	6.01797e10	0.330010
$319$	3.60825e11	1.95092
$320$	−2.32923e11	−1.24176
$321$	−1.40211e11	−0.737070
$322$	−3.41336e11	−1.76942
$323$	4.98763e11	2.54966
$324$	2.08274e10	0.104998
$325$	−3.46154e9	−0.0172106
$326$	−7.63233e10	−0.374264
$327$	1.09277e8	0.000528521 0
$328$	1.48358e10	0.0707749
$329$	−1.81647e10	−0.0854766
$330$	3.95477e11	1.83573
$331$	−1.87985e11	−0.860788	−0.430394	−	0.902641i	$-0.641625\pi$
$331$	−1.87985e11	−0.860788	−0.430394	+	0.902641i	$0.641625\pi$
$332$	−4.38923e10	−0.198275
$333$	6.93206e10	0.308932
$334$	−6.37818e10	−0.280439
$335$	2.24944e11	0.975826
$336$	−1.09516e11	−0.468758
$337$	3.42393e11	1.44607	0.723037	−	0.690810i	$-0.242746\pi$
$337$	3.42393e11	1.44607	0.723037	+	0.690810i	$0.242746\pi$
$338$	−3.34536e11	−1.39418
$339$	1.54086e11	0.633670
$340$	4.35222e11	1.76627
$341$	−5.39922e11	−2.16240
$342$	2.24578e11	0.887665
$343$	2.77840e11	1.08386
$344$	−3.02945e10	−0.116641
$345$	−3.49592e11	−1.32854
$346$	−3.22916e11	−1.21129
$347$	−1.69656e11	−0.628182	−0.314091	−	0.949393i	$-0.601700\pi$
$347$	−1.69656e11	−0.628182	−0.314091	+	0.949393i	$0.601700\pi$
$348$	1.78796e11	0.653510
$349$	−1.32210e11	−0.477035	−0.238517	−	0.971138i	$-0.576661\pi$
$349$	−1.32210e11	−0.477035	−0.238517	+	0.971138i	$0.576661\pi$
$350$	−2.89909e11	−1.03266
$351$	9.81739e8	0.00345234
$352$	6.52279e11	2.26460
$353$	−2.27467e11	−0.779709	−0.389855	−	0.920876i	$-0.627475\pi$
$353$	−2.27467e11	−0.779709	−0.389855	+	0.920876i	$0.627475\pi$
$354$	−3.09732e10	−0.104827
$355$	2.08146e11	0.695569
$356$	3.65897e11	1.20735
$357$	1.82606e11	0.594988
$358$	4.43205e11	1.42604
$359$	2.94417e10	0.0935487	0.0467744	−	0.998905i	$-0.485106\pi$
$359$	2.94417e10	0.0935487	0.0467744	+	0.998905i	$0.485106\pi$
$360$	−1.14091e10	−0.0358005
$361$	8.53853e11	2.64606
$362$	−4.22732e11	−1.29383
$363$	−3.15670e11	−0.954230
$364$	4.38202e9	0.0130833
$365$	4.16417e10	0.122804
$366$	−4.07846e11	−1.18804
$367$	3.66167e11	1.05361	0.526807	−	0.849985i	$-0.323389\pi$
$367$	3.66167e11	1.05361	0.526807	+	0.849985i	$0.323389\pi$
$368$	−6.08416e11	−1.72936
$369$	−1.09503e11	−0.307475
$370$	6.52247e11	1.80927
$371$	1.15428e11	0.316321
$372$	−2.67543e11	−0.724352
$373$	−5.10926e11	−1.36668	−0.683342	−	0.730098i	$-0.739474\pi$
$373$	−5.10926e11	−1.36668	−0.683342	+	0.730098i	$0.739474\pi$
$374$	−1.14763e12	−3.03304
$375$	1.25656e10	0.0328127
$376$	−3.29339e9	−0.00849763
$377$	8.42791e9	0.0214874
$378$	8.22219e10	0.207145
$379$	5.37042e10	0.133700	0.0668501	−	0.997763i	$-0.478705\pi$
$379$	5.37042e10	0.133700	0.0668501	+	0.997763i	$0.478705\pi$
$380$	1.02665e12	2.52579
$381$	1.31995e11	0.320919
$382$	2.73590e11	0.657379
$383$	3.89219e11	0.924271	0.462136	−	0.886809i	$-0.347083\pi$
$383$	3.89219e11	0.924271	0.462136	+	0.886809i	$0.347083\pi$
$384$	−3.76921e10	−0.0884627
$385$	7.58548e11	1.75958
$386$	−9.33312e11	−2.13985
$387$	2.23605e11	0.506736
$388$	1.79950e11	0.403096
$389$	1.53424e11	0.339719	0.169860	−	0.985468i	$-0.445669\pi$
$389$	1.53424e11	0.339719	0.169860	+	0.985468i	$0.445669\pi$
$390$	9.23730e9	0.0202188
$391$	1.01447e12	2.19505
$392$	1.45039e10	0.0310240
$393$	1.66415e11	0.351906
$394$	8.08889e11	1.69105
$395$	6.65596e11	1.37570
$396$	−2.51062e11	−0.513043
$397$	6.24737e11	1.26223	0.631117	−	0.775687i	$-0.282597\pi$
$397$	6.24737e11	1.26223	0.631117	+	0.775687i	$0.282597\pi$
$398$	1.18715e12	2.37154
$399$	4.30753e11	0.850844
$400$	−5.16750e11	−1.00928
$401$	−2.72742e11	−0.526747	−0.263374	−	0.964694i	$-0.584835\pi$
$401$	−2.72742e11	−0.526747	−0.263374	+	0.964694i	$0.584835\pi$
$402$	−2.93918e11	−0.561317
$403$	−1.26111e10	−0.0238167
$404$	7.07167e10	0.132070
$405$	8.42105e10	0.155532
$406$	7.05849e11	1.28927
$407$	−8.35622e11	−1.50951
$408$	3.31077e10	0.0591505
$409$	−8.30315e11	−1.46720	−0.733598	−	0.679583i	$-0.762161\pi$
$409$	−8.30315e11	−1.46720	−0.733598	+	0.679583i	$0.762161\pi$
$410$	−1.03033e12	−1.80074
$411$	−3.54602e11	−0.612990
$412$	−6.04208e11	−1.03312
$413$	−5.94084e10	−0.100478
$414$	4.56786e11	0.764207
$415$	−1.77468e11	−0.293700
$416$	1.52355e10	0.0249423
$417$	9.98742e10	0.161749
$418$	−2.70716e12	−4.33731
$419$	−9.27538e11	−1.47017	−0.735087	−	0.677973i	$-0.762859\pi$
$419$	−9.27538e11	−1.47017	−0.735087	+	0.677973i	$0.762859\pi$
$420$	3.75877e11	0.589418
$421$	−7.16269e11	−1.11124	−0.555619	−	0.831437i	$-0.687519\pi$
$421$	−7.16269e11	−1.11124	−0.555619	+	0.831437i	$0.687519\pi$
$422$	1.41302e12	2.16891
$423$	2.43086e10	0.0369171
$424$	2.09279e10	0.0314470
$425$	8.61627e11	1.28106
$426$	−2.71969e11	−0.400107
$427$	−7.82272e11	−1.13876
$428$	8.37512e11	1.20641
$429$	−1.18343e10	−0.0168688
$430$	2.10392e12	2.96771
$431$	1.24444e11	0.173711	0.0868556	−	0.996221i	$-0.472318\pi$
$431$	1.24444e11	0.173711	0.0868556	+	0.996221i	$0.472318\pi$
$432$	1.46557e11	0.202455
$433$	−1.33355e12	−1.82312	−0.911560	−	0.411167i	$-0.865121\pi$
$433$	−1.33355e12	−1.82312	−0.911560	+	0.411167i	$0.865121\pi$
$434$	−1.05620e12	−1.42903
$435$	7.22921e11	0.968030
$436$	−6.52735e8	−0.000865063 0
$437$	2.39306e12	3.13896
$438$	−5.44102e10	−0.0706394
$439$	5.63941e11	0.724676	0.362338	−	0.932047i	$-0.381979\pi$
$439$	5.63941e11	0.724676	0.362338	+	0.932047i	$0.381979\pi$
$440$	1.37530e11	0.174928
$441$	−1.07054e11	−0.134781
$442$	−2.68055e10	−0.0334060
$443$	−1.49448e12	−1.84363	−0.921815	−	0.387630i	$-0.873294\pi$
$443$	−1.49448e12	−1.84363	−0.921815	+	0.387630i	$0.873294\pi$
$444$	−4.14068e11	−0.505648
$445$	1.47942e12	1.78843
$446$	−6.15941e10	−0.0737110
$447$	5.01208e11	0.593792
$448$	5.83748e11	0.684659
$449$	−3.74619e11	−0.434992	−0.217496	−	0.976061i	$-0.569789\pi$
$449$	−3.74619e11	−0.434992	−0.217496	+	0.976061i	$0.569789\pi$
$450$	3.87965e11	0.446001
$451$	1.32000e12	1.50238
$452$	−9.20389e11	−1.03717
$453$	−9.85601e10	−0.109966
$454$	−1.06172e11	−0.117289
$455$	1.77177e10	0.0193801
$456$	7.80984e10	0.0845863
$457$	−1.43898e12	−1.54323	−0.771617	−	0.636087i	$-0.780552\pi$
$457$	−1.43898e12	−1.54323	−0.771617	+	0.636087i	$0.780552\pi$
$458$	2.31188e12	2.45511
$459$	−2.44369e11	−0.256974
$460$	2.08819e12	2.17450
$461$	−4.45857e10	−0.0459771	−0.0229885	−	0.999736i	$-0.507318\pi$
$461$	−4.45857e10	−0.0459771	−0.0229885	+	0.999736i	$0.507318\pi$
$462$	−9.91140e11	−1.01215
$463$	5.37437e11	0.543517	0.271759	−	0.962365i	$-0.412395\pi$
$463$	5.37437e11	0.543517	0.271759	+	0.962365i	$0.412395\pi$
$464$	1.25814e12	1.26008
$465$	−1.08175e12	−1.07297
$466$	1.72360e12	1.69317
$467$	−2.57366e11	−0.250395	−0.125197	−	0.992132i	$-0.539956\pi$
$467$	−2.57366e11	−0.250395	−0.125197	+	0.992132i	$0.539956\pi$
$468$	−5.86415e9	−0.00565066
$469$	−5.63751e11	−0.538033
$470$	2.28722e11	0.216206
$471$	4.75753e11	0.445438
$472$	−1.07711e10	−0.00998901
$473$	−2.69543e12	−2.47601
$474$	−8.69686e11	−0.791334
$475$	2.03251e12	1.83194
$476$	−1.09075e12	−0.973852
$477$	−1.54469e11	−0.136618
$478$	−3.44778e11	−0.302074
$479$	−3.26878e11	−0.283711	−0.141855	−	0.989887i	$-0.545307\pi$
$479$	−3.26878e11	−0.283711	−0.141855	+	0.989887i	$0.545307\pi$
$480$	1.30686e12	1.12368
$481$	−1.95179e10	−0.0166257
$482$	−5.71549e11	−0.482328
$483$	8.76141e11	0.732507
$484$	1.88557e12	1.56185
$485$	7.27585e11	0.597098
$486$	−1.10032e11	−0.0894653
$487$	2.01920e12	1.62667	0.813333	−	0.581799i	$-0.197651\pi$
$487$	2.01920e12	1.62667	0.813333	+	0.581799i	$0.197651\pi$
$488$	−1.41831e11	−0.113209
$489$	1.95907e11	0.154938
$490$	−1.00728e12	−0.789348
$491$	1.19020e11	0.0924170	0.0462085	−	0.998932i	$-0.485286\pi$
$491$	1.19020e11	0.0924170	0.0462085	+	0.998932i	$0.485286\pi$
$492$	6.54090e11	0.503262
$493$	−2.09783e12	−1.59941
$494$	−6.32320e10	−0.0477712
$495$	−1.01511e12	−0.759959
$496$	−1.88263e12	−1.39668
$497$	−5.21652e11	−0.383510
$498$	2.31885e11	0.168943
$499$	−3.24580e11	−0.234352	−0.117176	−	0.993111i	$-0.537384\pi$
$499$	−3.24580e11	−0.234352	−0.117176	+	0.993111i	$0.537384\pi$
$500$	−7.50572e10	−0.0537066
$501$	1.63715e11	0.116096
$502$	1.17319e12	0.824523
$503$	−2.26643e12	−1.57865	−0.789325	−	0.613976i	$-0.789569\pi$
$503$	−2.26643e12	−1.57865	−0.789325	+	0.613976i	$0.789569\pi$
$504$	2.85932e10	0.0197390
$505$	2.85926e11	0.195633
$506$	−5.50630e12	−3.73407
$507$	8.58688e11	0.577164
$508$	−7.88438e11	−0.525268
$509$	1.77037e12	1.16905	0.584527	−	0.811374i	$-0.301280\pi$
$509$	1.77037e12	1.16905	0.584527	+	0.811374i	$0.301280\pi$
$510$	−2.29930e12	−1.50497
$511$	−1.04362e11	−0.0677092
$512$	2.14890e12	1.38198
$513$	−5.76446e11	−0.367477
$514$	−2.75282e12	−1.73958
$515$	−2.44297e12	−1.53033
$516$	−1.33564e12	−0.829405
$517$	−2.93026e11	−0.180385
$518$	−1.63465e12	−0.997565
$519$	8.28860e11	0.501451
$520$	3.21233e9	0.00192666
$521$	1.14290e11	0.0679576	0.0339788	−	0.999423i	$-0.489182\pi$
$521$	1.14290e11	0.0679576	0.0339788	+	0.999423i	$0.489182\pi$
$522$	−9.44588e11	−0.556833
$523$	5.11463e11	0.298921	0.149461	−	0.988768i	$-0.452246\pi$
$523$	5.11463e11	0.298921	0.149461	+	0.988768i	$0.452246\pi$
$524$	−9.94037e11	−0.575986
$525$	7.44138e11	0.427501
$526$	−2.80112e12	−1.59550
$527$	3.13909e12	1.77279
$528$	−1.76666e12	−0.989238
$529$	3.06627e12	1.70239
$530$	−1.45342e12	−0.800110
$531$	7.95020e10	0.0433963
$532$	−2.57299e12	−1.39263
$533$	3.08318e10	0.0165473
$534$	−1.93305e12	−1.02874
$535$	3.38628e12	1.78703
$536$	−1.02212e11	−0.0534884
$537$	−1.13762e12	−0.590354
$538$	1.76732e11	0.0909482
$539$	1.29047e12	0.658566
$540$	−5.03009e11	−0.254568
$541$	−1.19821e12	−0.601377	−0.300688	−	0.953722i	$-0.597216\pi$
$541$	−1.19821e12	−0.601377	−0.300688	+	0.953722i	$0.597216\pi$
$542$	3.82273e12	1.90273
$543$	1.08507e12	0.535621
$544$	−3.79234e12	−1.85657
$545$	−2.63918e9	−0.00128140
$546$	−2.31504e10	−0.0111479
$547$	2.72863e12	1.30317	0.651587	−	0.758574i	$-0.274104\pi$
$547$	2.72863e12	1.30317	0.651587	+	0.758574i	$0.274104\pi$
$548$	2.11812e12	1.00332
$549$	1.04686e12	0.491828
$550$	−4.67670e12	−2.17925
$551$	−4.94860e12	−2.28718
$552$	1.58850e11	0.0728219
$553$	−1.66811e12	−0.758509
$554$	−2.13752e12	−0.964086
$555$	−1.67419e12	−0.749006
$556$	−5.96572e11	−0.264744
$557$	−3.14208e12	−1.38315	−0.691573	−	0.722306i	$-0.743082\pi$
$557$	−3.14208e12	−1.38315	−0.691573	+	0.722306i	$0.743082\pi$
$558$	1.41344e12	0.617196
$559$	−6.29581e10	−0.0272708
$560$	2.64495e12	1.13650
$561$	2.94573e12	1.25562
$562$	4.50786e12	1.90615
$563$	3.69947e12	1.55186	0.775929	−	0.630820i	$-0.217281\pi$
$563$	3.69947e12	1.55186	0.775929	+	0.630820i	$0.217281\pi$
$564$	−1.45201e11	−0.0604245
$565$	−3.72137e12	−1.53633
$566$	−6.59244e12	−2.70005
$567$	−2.11047e11	−0.0857543
$568$	−9.45790e10	−0.0381265
$569$	1.93401e12	0.773489	0.386744	−	0.922187i	$-0.373600\pi$
$569$	1.93401e12	0.773489	0.386744	+	0.922187i	$0.373600\pi$
$570$	−5.42385e12	−2.15214
$571$	3.78514e12	1.49012	0.745058	−	0.667000i	$-0.232422\pi$
$571$	3.78514e12	1.49012	0.745058	+	0.667000i	$0.232422\pi$
$572$	7.06891e10	0.0276102
$573$	−7.02252e11	−0.272143
$574$	2.58220e12	0.992857
$575$	4.13408e12	1.57715
$576$	−7.81189e11	−0.295702
$577$	4.23047e12	1.58890	0.794452	−	0.607328i	$-0.207758\pi$
$577$	4.23047e12	1.58890	0.794452	+	0.607328i	$0.207758\pi$
$578$	2.93002e12	1.09193
$579$	2.39562e12	0.885860
$580$	−4.31817e12	−1.58443
$581$	4.44769e11	0.161935
$582$	−9.50682e11	−0.343465
$583$	1.86204e12	0.667545
$584$	−1.89215e10	−0.00673129
$585$	−2.37103e10	−0.00837020
$586$	3.68812e12	1.29201
$587$	1.98842e12	0.691254	0.345627	−	0.938372i	$-0.387666\pi$
$587$	1.98842e12	0.691254	0.345627	+	0.938372i	$0.387666\pi$
$588$	6.39456e11	0.220604
$589$	7.40486e12	2.53512
$590$	7.48044e11	0.254152
$591$	−2.07626e12	−0.700064
$592$	−2.91369e12	−0.974981
$593$	1.52171e12	0.505344	0.252672	−	0.967552i	$-0.418691\pi$
$593$	1.52171e12	0.505344	0.252672	+	0.967552i	$0.418691\pi$
$594$	1.32637e12	0.437146
$595$	−4.41018e12	−1.44255
$596$	−2.99383e12	−0.971895
$597$	−3.04717e12	−0.981775
$598$	−1.28613e11	−0.0411271
$599$	8.87750e11	0.281754	0.140877	−	0.990027i	$-0.455008\pi$
$599$	8.87750e11	0.281754	0.140877	+	0.990027i	$0.455008\pi$
$600$	1.34917e11	0.0424998
$601$	−4.01927e12	−1.25664	−0.628322	−	0.777954i	$-0.716258\pi$
$601$	−4.01927e12	−1.25664	−0.628322	+	0.777954i	$0.716258\pi$
$602$	−5.27282e12	−1.63629
$603$	7.54428e11	0.232375
$604$	5.88722e11	0.179988
$605$	7.62385e12	2.31353
$606$	−3.73599e11	−0.112533
$607$	6.00721e12	1.79607	0.898035	−	0.439923i	$-0.144994\pi$
$607$	6.00721e12	1.79607	0.898035	+	0.439923i	$0.144994\pi$
$608$	−8.94581e12	−2.65493
$609$	−1.81177e12	−0.533735
$610$	9.85004e12	2.88040
$611$	−6.84432e9	−0.00198676
$612$	1.45967e12	0.420604
$613$	4.90828e12	1.40397	0.701984	−	0.712193i	$-0.252298\pi$
$613$	4.90828e12	1.40397	0.701984	+	0.712193i	$0.252298\pi$
$614$	−2.63470e12	−0.748124
$615$	2.64466e12	0.745472
$616$	−3.44675e11	−0.0964489
$617$	4.52149e12	1.25603	0.628013	−	0.778203i	$-0.283868\pi$
$617$	4.52149e12	1.25603	0.628013	+	0.778203i	$0.283868\pi$
$618$	3.19206e12	0.880283
$619$	−5.02565e12	−1.37589	−0.687946	−	0.725762i	$-0.741487\pi$
$619$	−5.02565e12	−1.37589	−0.687946	+	0.725762i	$0.741487\pi$
$620$	6.46152e12	1.75619
$621$	−1.17248e12	−0.316368
$622$	−7.05280e12	−1.88932
$623$	−3.70770e12	−0.986070
$624$	−4.12645e10	−0.0108955
$625$	−3.96329e12	−1.03895
$626$	−3.12045e12	−0.812143
$627$	6.94873e12	1.79557
$628$	−2.84178e12	−0.729076
$629$	4.85828e12	1.23753
$630$	−1.98577e12	−0.502223
$631$	−3.67636e12	−0.923178	−0.461589	−	0.887094i	$-0.652721\pi$
$631$	−3.67636e12	−0.923178	−0.461589	+	0.887094i	$0.652721\pi$
$632$	−3.02439e11	−0.0754069
$633$	−3.62693e12	−0.897888
$634$	−9.65839e12	−2.37412
$635$	−3.18786e12	−0.778068
$636$	9.22680e11	0.223611
$637$	3.01420e10	0.00725345
$638$	1.13865e13	2.72080
$639$	6.98090e11	0.165637
$640$	9.10316e11	0.214478
$641$	−1.04966e12	−0.245576	−0.122788	−	0.992433i	$-0.539184\pi$
$641$	−1.04966e12	−0.245576	−0.122788	+	0.992433i	$0.539184\pi$
$642$	−4.42461e12	−1.02794
$643$	−2.71624e12	−0.626642	−0.313321	−	0.949647i	$-0.601442\pi$
$643$	−2.71624e12	−0.626642	−0.313321	+	0.949647i	$0.601442\pi$
$644$	−5.23339e12	−1.19894
$645$	−5.40035e12	−1.22858
$646$	1.57393e13	3.55583
$647$	1.92188e12	0.431179	0.215590	−	0.976484i	$-0.430833\pi$
$647$	1.92188e12	0.431179	0.215590	+	0.976484i	$0.430833\pi$
$648$	−3.82643e10	−0.00852523
$649$	−9.58353e11	−0.212043
$650$	−1.09235e11	−0.0240023
$651$	2.71105e12	0.591594
$652$	−1.17019e12	−0.253597
$653$	9.02523e11	0.194245	0.0971223	−	0.995272i	$-0.469036\pi$
$653$	9.02523e11	0.194245	0.0971223	+	0.995272i	$0.469036\pi$
$654$	3.44842e9	0.000737090 0
$655$	−4.01915e12	−0.853196
$656$	4.60266e12	0.970380
$657$	1.39660e11	0.0292434
$658$	−5.73221e11	−0.119208
$659$	2.16361e12	0.446884	0.223442	−	0.974717i	$-0.428271\pi$
$659$	2.16361e12	0.446884	0.223442	+	0.974717i	$0.428271\pi$
$660$	6.06350e12	1.24387
$661$	9.09841e12	1.85378	0.926891	−	0.375330i	$-0.122470\pi$
$661$	9.09841e12	1.85378	0.926891	+	0.375330i	$0.122470\pi$
$662$	−5.93219e12	−1.20048
$663$	6.88044e10	0.0138295
$664$	8.06395e10	0.0160987
$665$	−1.04033e13	−2.06287
$666$	2.18754e12	0.430845
$667$	−1.00653e13	−1.96908
$668$	−9.77908e11	−0.190022
$669$	1.58100e11	0.0305150
$670$	7.09851e12	1.36091
$671$	−1.26193e13	−2.40317
$672$	−3.27522e12	−0.619554
$673$	9.38452e12	1.76337	0.881687	−	0.471835i	$-0.156408\pi$
$673$	9.38452e12	1.76337	0.881687	+	0.471835i	$0.156408\pi$
$674$	1.08048e13	2.01673
$675$	−9.95828e11	−0.184636
$676$	−5.12914e12	−0.944680
$677$	−4.25164e12	−0.777871	−0.388935	−	0.921265i	$-0.627157\pi$
$677$	−4.25164e12	−0.777871	−0.388935	+	0.921265i	$0.627157\pi$
$678$	4.86245e12	0.883734
$679$	−1.82346e12	−0.329217
$680$	−7.99596e11	−0.143410
$681$	2.72522e11	0.0485555
$682$	−1.70382e13	−3.01574
$683$	7.18700e12	1.26373	0.631866	−	0.775078i	$-0.282289\pi$
$683$	7.18700e12	1.26373	0.631866	+	0.775078i	$0.282289\pi$
$684$	3.44324e12	0.601472
$685$	8.56412e12	1.48619
$686$	8.76774e12	1.51157
$687$	−5.93413e12	−1.01637
$688$	−9.39857e12	−1.59924
$689$	4.34923e10	0.00735235
$690$	−1.10320e13	−1.85282
$691$	5.15669e12	0.860438	0.430219	−	0.902725i	$-0.358436\pi$
$691$	5.15669e12	0.860438	0.430219	+	0.902725i	$0.358436\pi$
$692$	−4.95097e12	−0.820754
$693$	2.54406e12	0.419013
$694$	−5.35379e12	−0.876080
$695$	−2.41210e12	−0.392160
$696$	−3.28487e11	−0.0530611
$697$	−7.67447e12	−1.23169
$698$	−4.17212e12	−0.665285
$699$	−4.42413e12	−0.700940
$700$	−4.44491e12	−0.699716
$701$	−2.57658e12	−0.403007	−0.201503	−	0.979488i	$-0.564583\pi$
$701$	−2.57658e12	−0.403007	−0.201503	+	0.979488i	$0.564583\pi$
$702$	3.09805e10	0.00481473
$703$	1.14603e13	1.76969
$704$	9.41680e12	1.44486
$705$	−5.87085e11	−0.0895055
$706$	−7.17814e12	−1.08740
$707$	−7.16584e11	−0.107865
$708$	−4.74884e11	−0.0710293
$709$	−6.76459e12	−1.00539	−0.502694	−	0.864465i	$-0.667658\pi$
$709$	−6.76459e12	−1.00539	−0.502694	+	0.864465i	$0.667658\pi$
$710$	6.56841e12	0.970059
$711$	2.23231e12	0.327598
$712$	−6.72230e11	−0.0980298
$713$	1.50613e13	2.18253
$714$	5.76246e12	0.829786
$715$	2.85815e11	0.0408985
$716$	6.79527e12	0.966268
$717$	8.84976e11	0.125053
$718$	9.29086e11	0.130466
$719$	5.26570e10	0.00734812	0.00367406	−	0.999993i	$-0.498831\pi$
$719$	5.26570e10	0.00734812	0.00367406	+	0.999993i	$0.498831\pi$
$720$	−3.53955e12	−0.490853
$721$	6.12255e12	0.843769
$722$	2.69449e13	3.69027
$723$	1.46705e12	0.199675
$724$	−6.48136e12	−0.876683
$725$	−8.54886e12	−1.14918
$726$	−9.96153e12	−1.33080
$727$	−1.51266e12	−0.200834	−0.100417	−	0.994945i	$-0.532018\pi$
$727$	−1.51266e12	−0.200834	−0.100417	+	0.994945i	$0.532018\pi$
$728$	−8.05070e9	−0.00106229
$729$	2.82430e11	0.0370370
$730$	1.31408e12	0.171265
$731$	1.56712e13	2.02989
$732$	−6.25313e12	−0.805004
$733$	−8.43668e12	−1.07945	−0.539726	−	0.841841i	$-0.681472\pi$
$733$	−8.43668e12	−1.07945	−0.539726	+	0.841841i	$0.681472\pi$
$734$	1.15551e13	1.46940
$735$	2.58549e12	0.326776
$736$	−1.81956e13	−2.28568
$737$	−9.09421e12	−1.13543
$738$	−3.45558e12	−0.428812
$739$	6.45681e12	0.796376	0.398188	−	0.917304i	$-0.369639\pi$
$739$	6.45681e12	0.796376	0.398188	+	0.917304i	$0.369639\pi$
$740$	1.00003e13	1.22594
$741$	1.62304e11	0.0197764
$742$	3.64254e12	0.441150
$743$	−7.53304e12	−0.906819	−0.453410	−	0.891302i	$-0.649793\pi$
$743$	−7.53304e12	−0.906819	−0.453410	+	0.891302i	$0.649793\pi$
$744$	4.91532e11	0.0588131
$745$	−1.21049e13	−1.43965
$746$	−1.61232e13	−1.90602
$747$	−5.95202e11	−0.0699394
$748$	−1.75955e13	−2.05516
$749$	−8.48665e12	−0.985299
$750$	3.96530e11	0.0457615
$751$	−1.64730e12	−0.188970	−0.0944851	−	0.995526i	$-0.530120\pi$
$751$	−1.64730e12	−0.188970	−0.0944851	+	0.995526i	$0.530120\pi$
$752$	−1.02174e12	−0.116509
$753$	−3.01135e12	−0.341338
$754$	2.65958e11	0.0299669
$755$	2.38036e12	0.266613
$756$	1.26063e12	0.140359
$757$	4.40812e12	0.487890	0.243945	−	0.969789i	$-0.421558\pi$
$757$	4.40812e12	0.487890	0.243945	+	0.969789i	$0.421558\pi$
$758$	1.69473e12	0.186462
$759$	1.41336e13	1.54584
$760$	−1.88618e12	−0.205079
$761$	−9.40473e12	−1.01652	−0.508259	−	0.861204i	$-0.669711\pi$
$761$	−9.40473e12	−1.01652	−0.508259	+	0.861204i	$0.669711\pi$
$762$	4.16535e12	0.447563
$763$	6.61427e9	0.000706515 0
$764$	4.19471e12	0.445433
$765$	5.90183e12	0.623032
$766$	1.22825e13	1.28901
$767$	−2.23846e10	−0.00233545
$768$	−6.12733e12	−0.635544
$769$	4.11650e12	0.424482	0.212241	−	0.977217i	$-0.431924\pi$
$769$	4.11650e12	0.424482	0.212241	+	0.977217i	$0.431924\pi$
$770$	2.39374e13	2.45396
$771$	7.06594e12	0.720154
$772$	−1.43096e13	−1.44994
$773$	5.85547e12	0.589867	0.294933	−	0.955518i	$-0.404703\pi$
$773$	5.85547e12	0.589867	0.294933	+	0.955518i	$0.404703\pi$
$774$	7.05625e12	0.706707
$775$	1.27921e13	1.27375
$776$	−3.30606e11	−0.0327290
$777$	4.19582e12	0.412974
$778$	4.84157e12	0.473782
$779$	−1.81034e13	−1.76134
$780$	1.41627e11	0.0137000
$781$	−8.41508e12	−0.809336
$782$	3.20135e13	3.06128
$783$	2.42457e12	0.230519
$784$	4.49969e12	0.425364
$785$	−1.14901e13	−1.07996
$786$	5.25153e12	0.490778
$787$	7.07362e12	0.657288	0.328644	−	0.944454i	$-0.393408\pi$
$787$	7.07362e12	0.657288	0.328644	+	0.944454i	$0.393408\pi$
$788$	1.24020e13	1.14584
$789$	7.18991e12	0.660507
$790$	2.10041e13	1.91859
$791$	9.32645e12	0.847076
$792$	4.61255e11	0.0416560
$793$	−2.94754e11	−0.0264685
$794$	1.97147e13	1.76035
$795$	3.73064e12	0.331231
$796$	1.82014e13	1.60693
$797$	−1.28079e13	−1.12439	−0.562193	−	0.827006i	$-0.690042\pi$
$797$	−1.28079e13	−1.12439	−0.562193	+	0.827006i	$0.690042\pi$
$798$	1.35932e13	1.18661
$799$	1.70365e12	0.147883
$800$	−1.54542e13	−1.33395
$801$	4.96175e12	0.425881
$802$	−8.60686e12	−0.734616
$803$	−1.68353e12	−0.142889
$804$	−4.50637e12	−0.380342
$805$	−2.11600e13	−1.77596
$806$	−3.97967e11	−0.0332154
$807$	−4.53635e11	−0.0376509
$808$	−1.29922e11	−0.0107233
$809$	−1.83179e12	−0.150352	−0.0751758	−	0.997170i	$-0.523952\pi$
$809$	−1.83179e12	−0.150352	−0.0751758	+	0.997170i	$0.523952\pi$
$810$	2.65742e12	0.216909
$811$	−2.04629e13	−1.66102	−0.830509	−	0.557005i	$-0.811950\pi$
$811$	−2.04629e13	−1.66102	−0.830509	+	0.557005i	$0.811950\pi$
$812$	1.08221e13	0.873597
$813$	−9.81217e12	−0.787694
$814$	−2.63696e13	−2.10520
$815$	−4.73141e12	−0.375648
$816$	1.02713e13	0.811000
$817$	3.69670e13	2.90278
$818$	−2.62021e13	−2.04619
$819$	5.94224e10	0.00461501
$820$	−1.57971e13	−1.22016
$821$	1.08327e13	0.832133	0.416066	−	0.909334i	$-0.363408\pi$
$821$	1.08327e13	0.832133	0.416066	+	0.909334i	$0.363408\pi$
$822$	−1.11901e13	−0.854892
$823$	2.52645e12	0.191960	0.0959802	−	0.995383i	$-0.469401\pi$
$823$	2.52645e12	0.191960	0.0959802	+	0.995383i	$0.469401\pi$
$824$	1.11006e12	0.0838829
$825$	1.20042e13	0.902171
$826$	−1.87474e12	−0.140130
$827$	−1.26388e13	−0.939571	−0.469785	−	0.882781i	$-0.655669\pi$
$827$	−1.26388e13	−0.939571	−0.469785	+	0.882781i	$0.655669\pi$
$828$	7.00348e12	0.517818
$829$	−2.40266e12	−0.176684	−0.0883419	−	0.996090i	$-0.528157\pi$
$829$	−2.40266e12	−0.176684	−0.0883419	+	0.996090i	$0.528157\pi$
$830$	−5.60033e12	−0.409602
$831$	5.48658e12	0.399114
$832$	2.19951e11	0.0159137
$833$	−7.50278e12	−0.539908
$834$	3.15171e12	0.225579
$835$	−3.95394e12	−0.281476
$836$	−4.15064e13	−2.93891
$837$	−3.62801e12	−0.255508
$838$	−2.92701e13	−2.05034
$839$	1.42527e13	0.993045	0.496523	−	0.868024i	$-0.334610\pi$
$839$	1.42527e13	0.993045	0.496523	+	0.868024i	$0.334610\pi$
$840$	−6.90565e11	−0.0478572
$841$	6.30699e12	0.434751
$842$	−2.26032e13	−1.54976
$843$	−1.15708e13	−0.789111
$844$	2.16645e13	1.46963
$845$	−2.07385e13	−1.39933
$846$	7.67101e11	0.0514856
$847$	−1.91068e13	−1.27559
$848$	6.49267e12	0.431163
$849$	1.69215e13	1.11777
$850$	2.71902e13	1.78660
$851$	2.33100e13	1.52356
$852$	−4.16985e12	−0.271108
$853$	3.62046e12	0.234149	0.117075	−	0.993123i	$-0.462648\pi$
$853$	3.62046e12	0.234149	0.117075	+	0.993123i	$0.462648\pi$
$854$	−2.46860e13	−1.58815
$855$	1.39219e13	0.890948
$856$	−1.53869e12	−0.0979531
$857$	2.03191e13	1.28674	0.643371	−	0.765555i	$-0.277535\pi$
$857$	2.03191e13	1.28674	0.643371	+	0.765555i	$0.277535\pi$
$858$	−3.73453e11	−0.0235257
$859$	−1.37685e13	−0.862814	−0.431407	−	0.902157i	$-0.641983\pi$
$859$	−1.37685e13	−0.862814	−0.431407	+	0.902157i	$0.641983\pi$
$860$	3.22576e13	2.01089
$861$	−6.62800e12	−0.411025
$862$	3.92707e12	0.242262
$863$	−1.23986e13	−0.760894	−0.380447	−	0.924803i	$-0.624230\pi$
$863$	−1.23986e13	−0.760894	−0.380447	+	0.924803i	$0.624230\pi$
$864$	4.38300e12	0.267584
$865$	−2.00181e13	−1.21577
$866$	−4.20827e13	−2.54257
$867$	−7.52077e12	−0.452040
$868$	−1.61938e13	−0.968297
$869$	−2.69093e13	−1.60071
$870$	2.28131e13	1.35004
$871$	−2.12417e11	−0.0125057
$872$	1.19921e9	7.02379e−5 0
$873$	2.44021e12	0.142188
$874$	7.55172e13	4.37768
$875$	7.60567e11	0.0438633
$876$	−8.34222e11	−0.0478645
$877$	3.04802e13	1.73988	0.869939	−	0.493159i	$-0.164158\pi$
$877$	3.04802e13	1.73988	0.869939	+	0.493159i	$0.164158\pi$
$878$	1.77962e13	1.01065
$879$	−9.46666e12	−0.534868
$880$	4.26673e13	2.39841
$881$	2.94577e13	1.64743	0.823715	−	0.567004i	$-0.191898\pi$
$881$	2.94577e13	1.64743	0.823715	+	0.567004i	$0.191898\pi$
$882$	−3.37827e12	−0.187969
$883$	1.79573e13	0.994073	0.497036	−	0.867730i	$-0.334422\pi$
$883$	1.79573e13	0.994073	0.497036	+	0.867730i	$0.334422\pi$
$884$	−4.10985e11	−0.0226355
$885$	−1.92008e12	−0.105214
$886$	−4.71611e13	−2.57118
$887$	1.85718e12	0.100739	0.0503696	−	0.998731i	$-0.483960\pi$
$887$	1.85718e12	0.100739	0.0503696	+	0.998731i	$0.483960\pi$
$888$	7.60731e11	0.0410556
$889$	7.98937e12	0.428998
$890$	4.66857e13	2.49419
$891$	−3.40453e12	−0.180970
$892$	−9.44367e11	−0.0499458
$893$	4.01877e12	0.211476
$894$	1.58165e13	0.828118
$895$	2.74751e13	1.43131
$896$	−2.28142e12	−0.118255
$897$	3.30123e11	0.0170259
$898$	−1.18218e13	−0.606651
$899$	−3.11453e13	−1.59028
$900$	5.94831e12	0.302205
$901$	−1.08259e13	−0.547269
$902$	4.16551e13	2.09526
$903$	1.35343e13	0.677393
$904$	1.69095e12	0.0842117
$905$	−2.62059e13	−1.29861
$906$	−3.11024e12	−0.153362
$907$	2.61442e13	1.28275	0.641377	−	0.767226i	$-0.278364\pi$
$907$	2.61442e13	1.28275	0.641377	+	0.767226i	$0.278364\pi$
$908$	−1.62783e12	−0.0794738
$909$	9.58954e11	0.0465865
$910$	5.59113e11	0.0270280
$911$	−4.33892e12	−0.208713	−0.104356	−	0.994540i	$-0.533278\pi$
$911$	−4.33892e12	−0.208713	−0.104356	+	0.994540i	$0.533278\pi$
$912$	2.42292e13	1.15975
$913$	7.17483e12	0.341738
$914$	−4.54096e13	−2.15224
$915$	−2.52831e13	−1.19244
$916$	3.54459e13	1.66355
$917$	1.00727e13	0.470420
$918$	−7.71149e12	−0.358382
$919$	−3.66087e13	−1.69303	−0.846514	−	0.532366i	$-0.821303\pi$
$919$	−3.66087e13	−1.69303	−0.846514	+	0.532366i	$0.821303\pi$
$920$	−3.83645e12	−0.176557
$921$	6.76275e12	0.309710
$922$	−1.40698e12	−0.0641208
$923$	−1.96554e11	−0.00891403
$924$	−1.51962e13	−0.685823
$925$	1.97980e13	0.889168
$926$	1.69598e13	0.758004
$927$	−8.19337e12	−0.364421
$928$	3.76267e13	1.66544
$929$	−2.26411e13	−0.997304	−0.498652	−	0.866802i	$-0.666171\pi$
$929$	−2.26411e13	−0.997304	−0.498652	+	0.866802i	$0.666171\pi$
$930$	−3.41364e13	−1.49639
$931$	−1.76984e13	−0.772078
$932$	2.64264e13	1.14727
$933$	1.81031e13	0.782143
$934$	−8.12164e12	−0.349207
$935$	−7.11433e13	−3.04426
$936$	1.07737e10	0.000458800 0
$937$	4.17920e13	1.77119	0.885595	−	0.464459i	$-0.153751\pi$
$937$	4.17920e13	1.77119	0.885595	+	0.464459i	$0.153751\pi$
$938$	−1.77902e13	−0.750356
$939$	8.00956e12	0.336212
$940$	3.50679e12	0.146499
$941$	−1.33777e13	−0.556196	−0.278098	−	0.960553i	$-0.589704\pi$
$941$	−1.33777e13	−0.556196	−0.278098	+	0.960553i	$0.589704\pi$
$942$	1.50132e13	0.621220
$943$	−3.68220e13	−1.51637
$944$	−3.34164e12	−0.136957
$945$	5.09707e12	0.207911
$946$	−8.50591e13	−3.45311
$947$	−2.53638e13	−1.02480	−0.512401	−	0.858746i	$-0.671244\pi$
$947$	−2.53638e13	−1.02480	−0.512401	+	0.858746i	$0.671244\pi$
$948$	−1.33341e13	−0.536199
$949$	−3.93227e10	−0.00157378
$950$	6.41395e13	2.55487
$951$	2.47912e13	0.982844
$952$	2.00393e12	0.0790710
$953$	3.42985e13	1.34697	0.673483	−	0.739203i	$-0.264797\pi$
$953$	3.42985e13	1.34697	0.673483	+	0.739203i	$0.264797\pi$
$954$	−4.87455e12	−0.190532
$955$	1.69603e13	0.659810
$956$	−5.28617e12	−0.204682
$957$	−2.92268e13	−1.12636
$958$	−1.03152e13	−0.395670
$959$	−2.14633e13	−0.819430
$960$	1.88668e13	0.716930
$961$	2.01648e13	0.762675
$962$	−6.15923e11	−0.0231867
$963$	1.13571e13	0.425548
$964$	−8.76305e12	−0.326820
$965$	−5.78576e13	−2.14777
$966$	2.76482e13	1.02157
$967$	−4.25219e13	−1.56384	−0.781922	−	0.623376i	$-0.785760\pi$
$967$	−4.25219e13	−1.56384	−0.781922	+	0.623376i	$0.785760\pi$
$968$	−3.46419e12	−0.126813
$969$	−4.03998e13	−1.47205
$970$	2.29603e13	0.832729
$971$	4.34846e12	0.156982	0.0784908	−	0.996915i	$-0.474990\pi$
$971$	4.34846e12	0.156982	0.0784908	+	0.996915i	$0.474990\pi$
$972$	−1.68702e12	−0.0606207
$973$	6.04516e12	0.216222
$974$	6.37194e13	2.26859
$975$	2.80385e11	0.00993652
$976$	−4.40017e13	−1.55219
$977$	−3.55468e13	−1.24817	−0.624087	−	0.781355i	$-0.714529\pi$
$977$	−3.55468e13	−1.24817	−0.624087	+	0.781355i	$0.714529\pi$
$978$	6.18218e12	0.216081
$979$	−5.98111e13	−2.08094
$980$	−1.54437e13	−0.534854
$981$	−8.85141e9	−0.000305142 0
$982$	3.75588e12	0.128887
$983$	−2.05160e13	−0.700813	−0.350407	−	0.936598i	$-0.613957\pi$
$983$	−2.05160e13	−0.700813	−0.350407	+	0.936598i	$0.613957\pi$
$984$	−1.20170e12	−0.0408619
$985$	5.01444e13	1.69730
$986$	−6.62007e13	−2.23057
$987$	1.47134e12	0.0493500
$988$	−9.69479e11	−0.0323692
$989$	7.51900e13	2.49906
$990$	−3.20337e13	−1.05986
$991$	1.78616e13	0.588286	0.294143	−	0.955761i	$-0.404966\pi$
$991$	1.78616e13	0.588286	0.294143	+	0.955761i	$0.404966\pi$
$992$	−5.63028e13	−1.84598
$993$	1.52268e13	0.496976
$994$	−1.64617e13	−0.534854
$995$	7.35932e13	2.38031
$996$	3.55528e12	0.114474
$997$	−5.83450e12	−0.187015	−0.0935073	−	0.995619i	$-0.529808\pi$
$997$	−5.83450e12	−0.187015	−0.0935073	+	0.995619i	$0.529808\pi$
$998$	−1.02427e13	−0.326834
$999$	−5.61497e12	−0.178362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+31.5568 q^{2} -81.0000 q^{3} +483.832 q^{4} +1956.26 q^{5} -2556.10 q^{6} -4902.75 q^{7} -888.901 q^{8} +6561.00 q^{9} +61733.3 q^{10} -79089.2 q^{11} -39190.4 q^{12} -1847.31 q^{13} -154715. q^{14} -158457. q^{15} -275773. q^{16} +459823. q^{17} +207044. q^{18} +1.08468e6 q^{19} +946500. q^{20} +397123. q^{21} -2.49580e6 q^{22} +2.20622e6 q^{23} +72001.0 q^{24} +1.87383e6 q^{25} -58295.3 q^{26} -531441. q^{27} -2.37210e6 q^{28} -4.56225e6 q^{29} -5.00040e6 q^{30} +6.82675e6 q^{31} -8.24739e6 q^{32} +6.40623e6 q^{33} +1.45105e7 q^{34} -9.59105e6 q^{35} +3.17442e6 q^{36} +1.05656e7 q^{37} +3.42292e7 q^{38} +149632. q^{39} -1.73892e6 q^{40} -1.66901e7 q^{41} +1.25319e7 q^{42} +3.40809e7 q^{43} -3.82659e7 q^{44} +1.28350e7 q^{45} +6.96214e7 q^{46} +3.70501e6 q^{47} +2.23376e7 q^{48} -1.63167e7 q^{49} +5.91319e7 q^{50} -3.72456e7 q^{51} -893789. q^{52} -2.35435e7 q^{53} -1.67706e7 q^{54} -1.54719e8 q^{55} +4.35806e6 q^{56} -8.78594e7 q^{57} -1.43970e8 q^{58} +1.21174e7 q^{59} -7.66665e7 q^{60} +1.59558e8 q^{61} +2.15430e8 q^{62} -3.21669e7 q^{63} -1.19066e8 q^{64} -3.61383e6 q^{65} +2.02160e8 q^{66} +1.14987e8 q^{67} +2.22477e8 q^{68} -1.78704e8 q^{69} -3.02663e8 q^{70} +1.06400e8 q^{71} -5.83208e6 q^{72} +2.12864e7 q^{73} +3.33415e8 q^{74} -1.51780e8 q^{75} +5.24805e8 q^{76} +3.87755e8 q^{77} +4.72192e6 q^{78} +3.40239e8 q^{79} -5.39483e8 q^{80} +4.30467e7 q^{81} -5.26685e8 q^{82} -9.07182e7 q^{83} +1.92140e8 q^{84} +8.99532e8 q^{85} +1.07548e9 q^{86} +3.69542e8 q^{87} +7.03025e7 q^{88} +7.56249e8 q^{89} +4.05032e8 q^{90} +9.05692e6 q^{91} +1.06744e9 q^{92} -5.52966e8 q^{93} +1.16918e8 q^{94} +2.12192e9 q^{95} +6.68038e8 q^{96} +3.71927e8 q^{97} -5.14902e8 q^{98} -5.18904e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

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