LMFDB - Embedded newform 177.10.a.c.1.1

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			1.1
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)

$f(q)$	$=$	$q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} -60567.9 q^{10} -91317.4 q^{11} -108630. q^{12} -95999.0 q^{13} -404316. q^{14} -113966. q^{15} +849797. q^{16} -211722. q^{17} -282437. q^{18} +541235. q^{19} +1.88694e6 q^{20} -760773. q^{21} +3.93101e6 q^{22} -1.61537e6 q^{23} +2.89102e6 q^{24} +26500.4 q^{25} +4.13255e6 q^{26} -531441. q^{27} +1.25961e7 q^{28} -791228. q^{29} +4.90600e6 q^{30} -7.46932e6 q^{31} -1.83078e7 q^{32} +7.39671e6 q^{33} +9.11416e6 q^{34} +1.32148e7 q^{35} +8.79906e6 q^{36} +8.37244e6 q^{37} -2.32990e7 q^{38} +7.77592e6 q^{39} -5.02179e7 q^{40} +1.08503e7 q^{41} +3.27496e7 q^{42} -4.24616e6 q^{43} -1.22467e8 q^{44} +9.23127e6 q^{45} +6.95381e7 q^{46} +6.51641e7 q^{47} -6.88335e7 q^{48} +4.78609e7 q^{49} -1.14078e6 q^{50} +1.71495e7 q^{51} -1.28746e8 q^{52} -3.72234e7 q^{53} +2.28774e7 q^{54} -1.28483e8 q^{55} -3.35225e8 q^{56} -4.38401e7 q^{57} +3.40607e7 q^{58} +1.21174e7 q^{59} -1.52842e8 q^{60} -1.44885e8 q^{61} +3.21538e8 q^{62} +6.16226e7 q^{63} +3.53015e8 q^{64} -1.35070e8 q^{65} -3.18412e8 q^{66} +7.39201e7 q^{67} -2.83943e8 q^{68} +1.30845e8 q^{69} -5.68870e8 q^{70} -3.81369e7 q^{71} -2.34173e8 q^{72} +3.89371e8 q^{73} -3.60415e8 q^{74} -2.14653e6 q^{75} +7.25859e8 q^{76} -8.57676e8 q^{77} -3.34737e8 q^{78} +6.34743e8 q^{79} +1.19566e9 q^{80} +4.30467e7 q^{81} -4.67081e8 q^{82} -6.48065e8 q^{83} -1.02028e9 q^{84} -2.97891e8 q^{85} +1.82788e8 q^{86} +6.40895e7 q^{87} +3.25927e9 q^{88} +9.28667e8 q^{89} -3.97386e8 q^{90} -9.01647e8 q^{91} -2.16640e9 q^{92} +6.05015e8 q^{93} -2.80517e9 q^{94} +7.61513e8 q^{95} +1.48293e9 q^{96} -2.03472e8 q^{97} -2.06031e9 q^{98} -5.99133e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−43.0478	−1.90246	−0.951232	−	0.308477i	$-0.900181\pi$
$2$	−43.0478	−1.90246	−0.951232	+	0.308477i	$0.900181\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1341.12	2.61937
$5$	1406.99	1.00676	0.503381	−	0.864065i	$-0.332089\pi$
$5$	1406.99	1.00676	0.503381	+	0.864065i	$0.332089\pi$
$6$	3486.87	1.09839
$7$	9392.26	1.47853	0.739263	−	0.673417i	$-0.235174\pi$
$7$	9392.26	1.47853	0.739263	+	0.673417i	$0.235174\pi$
$8$	−35691.7	−3.08079
$9$	6561.00	0.333333
$10$	−60567.9	−1.91533
$11$	−91317.4	−1.88056	−0.940278	−	0.340407i	$-0.889435\pi$
$11$	−91317.4	−1.88056	−0.940278	+	0.340407i	$0.889435\pi$
$12$	−108630.	−1.51229
$13$	−95999.0	−0.932227	−0.466114	−	0.884725i	$-0.654346\pi$
$13$	−95999.0	−0.932227	−0.466114	+	0.884725i	$0.654346\pi$
$14$	−404316.	−2.81284
$15$	−113966.	−0.581254
$16$	849797.	3.24172
$17$	−211722.	−0.614816	−0.307408	−	0.951578i	$-0.599462\pi$
$17$	−211722.	−0.614816	−0.307408	+	0.951578i	$0.599462\pi$
$18$	−282437.	−0.634154
$19$	541235.	0.952785	0.476392	−	0.879233i	$-0.341944\pi$
$19$	541235.	0.952785	0.476392	+	0.879233i	$0.341944\pi$
$20$	1.88694e6	2.63708
$21$	−760773.	−0.853627
$22$	3.93101e6	3.57769
$23$	−1.61537e6	−1.20364	−0.601820	−	0.798632i	$-0.705557\pi$
$23$	−1.61537e6	−1.20364	−0.601820	+	0.798632i	$0.705557\pi$
$24$	2.89102e6	1.77869
$25$	26500.4	0.0135682
$26$	4.13255e6	1.77353
$27$	−531441.	−0.192450
$28$	1.25961e7	3.87280
$29$	−791228.	−0.207736	−0.103868	−	0.994591i	$-0.533122\pi$
$29$	−791228.	−0.207736	−0.103868	+	0.994591i	$0.533122\pi$
$30$	4.90600e6	1.10581
$31$	−7.46932e6	−1.45262	−0.726312	−	0.687365i	$-0.758767\pi$
$31$	−7.46932e6	−1.45262	−0.726312	+	0.687365i	$0.758767\pi$
$32$	−1.83078e7	−3.08646
$33$	7.39671e6	1.08574
$34$	9.11416e6	1.16967
$35$	1.32148e7	1.48852
$36$	8.79906e6	0.873122
$37$	8.37244e6	0.734419	0.367210	−	0.930138i	$-0.380313\pi$
$37$	8.37244e6	0.734419	0.367210	+	0.930138i	$0.380313\pi$
$38$	−2.32990e7	−1.81264
$39$	7.77592e6	0.538222
$40$	−5.02179e7	−3.10162
$41$	1.08503e7	0.599672	0.299836	−	0.953991i	$-0.403068\pi$
$41$	1.08503e7	0.599672	0.299836	+	0.953991i	$0.403068\pi$
$42$	3.27496e7	1.62399
$43$	−4.24616e6	−0.189404	−0.0947018	−	0.995506i	$-0.530190\pi$
$43$	−4.24616e6	−0.189404	−0.0947018	+	0.995506i	$0.530190\pi$
$44$	−1.22467e8	−4.92587
$45$	9.23127e6	0.335587
$46$	6.95381e7	2.28988
$47$	6.51641e7	1.94790	0.973952	−	0.226753i	$-0.0728109\pi$
$47$	6.51641e7	1.94790	0.973952	+	0.226753i	$0.0728109\pi$
$48$	−6.88335e7	−1.87161
$49$	4.78609e7	1.18604
$50$	−1.14078e6	−0.0258130
$51$	1.71495e7	0.354964
$52$	−1.28746e8	−2.44185
$53$	−3.72234e7	−0.647999	−0.324000	−	0.946057i	$-0.605028\pi$
$53$	−3.72234e7	−0.647999	−0.324000	+	0.946057i	$0.605028\pi$
$54$	2.28774e7	0.366129
$55$	−1.28483e8	−1.89327
$56$	−3.35225e8	−4.55502
$57$	−4.38401e7	−0.550091
$58$	3.40607e7	0.395209
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.52842e8	−1.52252
$61$	−1.44885e8	−1.33980	−0.669899	−	0.742452i	$-0.733663\pi$
$61$	−1.44885e8	−1.33980	−0.669899	+	0.742452i	$0.733663\pi$
$62$	3.21538e8	2.76356
$63$	6.16226e7	0.492842
$64$	3.53015e8	2.63016
$65$	−1.35070e8	−0.938530
$66$	−3.18412e8	−2.06558
$67$	7.39201e7	0.448152	0.224076	−	0.974572i	$-0.428064\pi$
$67$	7.39201e7	0.448152	0.224076	+	0.974572i	$0.428064\pi$
$68$	−2.83943e8	−1.61043
$69$	1.30845e8	0.694922
$70$	−5.68870e8	−2.83186
$71$	−3.81369e7	−0.178108	−0.0890540	−	0.996027i	$-0.528384\pi$
$71$	−3.81369e7	−0.178108	−0.0890540	+	0.996027i	$0.528384\pi$
$72$	−2.34173e8	−1.02693
$73$	3.89371e8	1.60476	0.802381	−	0.596812i	$-0.203566\pi$
$73$	3.89371e8	1.60476	0.802381	+	0.596812i	$0.203566\pi$
$74$	−3.60415e8	−1.39721
$75$	−2.14653e6	−0.00783360
$76$	7.25859e8	2.49569
$77$	−8.57676e8	−2.78045
$78$	−3.34737e8	−1.02395
$79$	6.34743e8	1.83348	0.916740	−	0.399484i	$-0.130811\pi$
$79$	6.34743e8	1.83348	0.916740	+	0.399484i	$0.130811\pi$
$80$	1.19566e9	3.26364
$81$	4.30467e7	0.111111
$82$	−4.67081e8	−1.14085
$83$	−6.48065e8	−1.49888	−0.749440	−	0.662072i	$-0.769677\pi$
$83$	−6.48065e8	−1.49888	−0.749440	+	0.662072i	$0.769677\pi$
$84$	−1.02028e9	−2.23596
$85$	−2.97891e8	−0.618973
$86$	1.82788e8	0.360333
$87$	6.40895e7	0.119936
$88$	3.25927e9	5.79359
$89$	9.28667e8	1.56893	0.784467	−	0.620170i	$-0.212936\pi$
$89$	9.28667e8	1.56893	0.784467	+	0.620170i	$0.212936\pi$
$90$	−3.97386e8	−0.638442
$91$	−9.01647e8	−1.37832
$92$	−2.16640e9	−3.15277
$93$	6.05015e8	0.838673
$94$	−2.80517e9	−3.70582
$95$	7.61513e8	0.959227
$96$	1.48293e9	1.78197
$97$	−2.03472e8	−0.233363	−0.116681	−	0.993169i	$-0.537226\pi$
$97$	−2.03472e8	−0.233363	−0.116681	+	0.993169i	$0.537226\pi$
$98$	−2.06031e9	−2.25639
$99$	−5.99133e8	−0.626852
$100$	3.55401e7	0.0355401
$101$	9.78160e8	0.935327	0.467664	−	0.883907i	$-0.345096\pi$
$101$	9.78160e8	0.935327	0.467664	+	0.883907i	$0.345096\pi$
$102$	−7.38247e8	−0.675307
$103$	2.03791e9	1.78409	0.892046	−	0.451944i	$-0.149269\pi$
$103$	2.03791e9	1.78409	0.892046	+	0.451944i	$0.149269\pi$
$104$	3.42636e9	2.87199
$105$	−1.07040e9	−0.859398
$106$	1.60239e9	1.23279
$107$	1.58504e9	1.16900	0.584498	−	0.811395i	$-0.301291\pi$
$107$	1.58504e9	1.16900	0.584498	+	0.811395i	$0.301291\pi$
$108$	−7.12724e8	−0.504097
$109$	−2.17290e8	−0.147442	−0.0737210	−	0.997279i	$-0.523487\pi$
$109$	−2.17290e8	−0.147442	−0.0737210	+	0.997279i	$0.523487\pi$
$110$	5.53090e9	3.60188
$111$	−6.78167e8	−0.424017
$112$	7.98151e9	4.79296
$113$	−4.49722e8	−0.259472	−0.129736	−	0.991549i	$-0.541413\pi$
$113$	−4.49722e8	−0.259472	−0.129736	+	0.991549i	$0.541413\pi$
$114$	1.88722e9	1.04653
$115$	−2.27281e9	−1.21178
$116$	−1.06113e9	−0.544136
$117$	−6.29850e8	−0.310742
$118$	−5.21626e8	−0.247680
$119$	−1.98855e9	−0.909021
$120$	4.06765e9	1.79072
$121$	5.98091e9	2.53649
$122$	6.23699e9	2.54892
$123$	−8.78873e8	−0.346221
$124$	−1.00172e10	−3.80496
$125$	−2.71074e9	−0.993101
$126$	−2.65272e9	−0.937613
$127$	−1.52670e9	−0.520760	−0.260380	−	0.965506i	$-0.583848\pi$
$127$	−1.52670e9	−0.520760	−0.260380	+	0.965506i	$0.583848\pi$
$128$	−5.82293e9	−1.91733
$129$	3.43939e8	0.109352
$130$	5.81446e9	1.78552
$131$	4.32322e9	1.28259	0.641293	−	0.767296i	$-0.278398\pi$
$131$	4.32322e9	1.28259	0.641293	+	0.767296i	$0.278398\pi$
$132$	9.91984e9	2.84395
$133$	5.08342e9	1.40872
$134$	−3.18210e9	−0.852594
$135$	−7.47733e8	−0.193751
$136$	7.55670e9	1.89412
$137$	−1.97115e9	−0.478055	−0.239027	−	0.971013i	$-0.576829\pi$
$137$	−1.97115e9	−0.478055	−0.239027	+	0.971013i	$0.576829\pi$
$138$	−5.63259e9	−1.32206
$139$	−5.60538e9	−1.27362	−0.636808	−	0.771022i	$-0.719746\pi$
$139$	−5.60538e9	−1.27362	−0.636808	+	0.771022i	$0.719746\pi$
$140$	1.77226e10	3.89899
$141$	−5.27829e9	−1.12462
$142$	1.64171e9	0.338844
$143$	8.76638e9	1.75311
$144$	5.57552e9	1.08057
$145$	−1.11325e9	−0.209140
$146$	−1.67616e10	−3.05300
$147$	−3.87673e9	−0.684759
$148$	1.12284e10	1.92371
$149$	−8.07747e9	−1.34257	−0.671286	−	0.741199i	$-0.734258\pi$
$149$	−8.07747e9	−1.34257	−0.671286	+	0.741199i	$0.734258\pi$
$150$	9.24035e7	0.0149031
$151$	−1.58290e9	−0.247775	−0.123887	−	0.992296i	$-0.539536\pi$
$151$	−1.58290e9	−0.247775	−0.123887	+	0.992296i	$0.539536\pi$
$152$	−1.93176e10	−2.93533
$153$	−1.38911e9	−0.204939
$154$	3.69211e10	5.28970
$155$	−1.05093e10	−1.46245
$156$	1.04284e10	1.40980
$157$	9.59055e9	1.25978	0.629891	−	0.776684i	$-0.283100\pi$
$157$	9.59055e9	1.25978	0.629891	+	0.776684i	$0.283100\pi$
$158$	−2.73243e10	−3.48813
$159$	3.01509e9	0.374123
$160$	−2.57589e10	−3.10733
$161$	−1.51720e10	−1.77961
$162$	−1.85307e9	−0.211385
$163$	−8.10312e8	−0.0899100	−0.0449550	−	0.998989i	$-0.514314\pi$
$163$	−8.10312e8	−0.0899100	−0.0449550	+	0.998989i	$0.514314\pi$
$164$	1.45515e10	1.57076
$165$	1.04071e10	1.09308
$166$	2.78978e10	2.85156
$167$	−6.45350e9	−0.642054	−0.321027	−	0.947070i	$-0.604028\pi$
$167$	−6.45350e9	−0.642054	−0.321027	+	0.947070i	$0.604028\pi$
$168$	2.71532e10	2.62984
$169$	−1.38869e9	−0.130953
$170$	1.28236e10	1.17757
$171$	3.55104e9	0.317595
$172$	−5.69459e9	−0.496117
$173$	7.09399e9	0.602120	0.301060	−	0.953605i	$-0.402660\pi$
$173$	7.09399e9	0.602120	0.301060	+	0.953605i	$0.402660\pi$
$174$	−2.75891e9	−0.228174
$175$	2.48898e8	0.0200609
$176$	−7.76012e10	−6.09623
$177$	−9.81506e8	−0.0751646
$178$	−3.99771e10	−2.98484
$179$	−5.11714e8	−0.0372554	−0.0186277	−	0.999826i	$-0.505930\pi$
$179$	−5.11714e8	−0.0372554	−0.0186277	+	0.999826i	$0.505930\pi$
$180$	1.23802e10	0.879026
$181$	1.04870e10	0.726270	0.363135	−	0.931736i	$-0.381706\pi$
$181$	1.04870e10	0.726270	0.363135	+	0.931736i	$0.381706\pi$
$182$	3.88140e10	2.62221
$183$	1.17357e10	0.773533
$184$	5.76552e10	3.70816
$185$	1.17799e10	0.739385
$186$	−2.60446e10	−1.59554
$187$	1.93339e10	1.15620
$188$	8.73926e10	5.10228
$189$	−4.99143e9	−0.284542
$190$	−3.27815e10	−1.82489
$191$	2.74695e10	1.49348	0.746742	−	0.665113i	$-0.231617\pi$
$191$	2.74695e10	1.49348	0.746742	+	0.665113i	$0.231617\pi$
$192$	−2.85942e10	−1.51853
$193$	2.61307e10	1.35564	0.677818	−	0.735229i	$-0.262926\pi$
$193$	2.61307e10	1.35564	0.677818	+	0.735229i	$0.262926\pi$
$194$	8.75902e9	0.443964
$195$	1.09407e10	0.541861
$196$	6.41870e10	3.10667
$197$	8.12867e9	0.384522	0.192261	−	0.981344i	$-0.438418\pi$
$197$	8.12867e9	0.384522	0.192261	+	0.981344i	$0.438418\pi$
$198$	2.57914e10	1.19256
$199$	−1.27199e10	−0.574970	−0.287485	−	0.957785i	$-0.592819\pi$
$199$	−1.27199e10	−0.574970	−0.287485	+	0.957785i	$0.592819\pi$
$200$	−9.45842e8	−0.0418007
$201$	−5.98753e9	−0.258741
$202$	−4.21077e10	−1.77943
$203$	−7.43142e9	−0.307142
$204$	2.29994e10	0.929782
$205$	1.52663e10	0.603727
$206$	−8.77276e10	−3.39417
$207$	−1.05984e10	−0.401213
$208$	−8.15797e10	−3.02202
$209$	−4.94242e10	−1.79177
$210$	4.60784e10	1.63497
$211$	2.05227e10	0.712794	0.356397	−	0.934335i	$-0.384005\pi$
$211$	2.05227e10	0.712794	0.356397	+	0.934335i	$0.384005\pi$
$212$	−4.99209e10	−1.69735
$213$	3.08909e9	0.102831
$214$	−6.82325e10	−2.22397
$215$	−5.97431e9	−0.190684
$216$	1.89680e10	0.592898
$217$	−7.01537e10	−2.14774
$218$	9.35388e9	0.280503
$219$	−3.15391e10	−0.926510
$220$	−1.72310e11	−4.95917
$221$	2.03251e10	0.573149
$222$	2.91936e10	0.806677
$223$	5.32991e10	1.44327	0.721636	−	0.692272i	$-0.243390\pi$
$223$	5.32991e10	1.44327	0.721636	+	0.692272i	$0.243390\pi$
$224$	−1.71951e11	−4.56341
$225$	1.73869e8	0.00452273
$226$	1.93596e10	0.493637
$227$	5.29374e9	0.132326	0.0661631	−	0.997809i	$-0.478924\pi$
$227$	5.29374e9	0.132326	0.0661631	+	0.997809i	$0.478924\pi$
$228$	−5.87946e10	−1.44089
$229$	−5.14989e10	−1.23748	−0.618741	−	0.785595i	$-0.712357\pi$
$229$	−5.14989e10	−1.23748	−0.618741	+	0.785595i	$0.712357\pi$
$230$	9.78396e10	2.30536
$231$	6.94718e10	1.60529
$232$	2.82402e10	0.639989
$233$	−1.19187e10	−0.264927	−0.132463	−	0.991188i	$-0.542289\pi$
$233$	−1.19187e10	−0.264927	−0.132463	+	0.991188i	$0.542289\pi$
$234$	2.71137e10	0.591176
$235$	9.16853e10	1.96107
$236$	1.62508e10	0.341013
$237$	−5.14142e10	−1.05856
$238$	8.56026e10	1.72938
$239$	−1.75163e10	−0.347258	−0.173629	−	0.984811i	$-0.555549\pi$
$239$	−1.75163e10	−0.347258	−0.173629	+	0.984811i	$0.555549\pi$
$240$	−9.68482e10	−1.88426
$241$	−4.35459e10	−0.831516	−0.415758	−	0.909475i	$-0.636484\pi$
$241$	−4.35459e10	−0.831516	−0.415758	+	0.909475i	$0.636484\pi$
$242$	−2.57465e11	−4.82558
$243$	−3.48678e9	−0.0641500
$244$	−1.94308e11	−3.50942
$245$	6.73398e10	1.19406
$246$	3.78336e10	0.658672
$247$	−5.19581e10	−0.888212
$248$	2.66592e11	4.47522
$249$	5.24932e10	0.865379
$250$	1.16692e11	1.88934
$251$	−3.57888e10	−0.569136	−0.284568	−	0.958656i	$-0.591850\pi$
$251$	−3.57888e10	−0.569136	−0.284568	+	0.958656i	$0.591850\pi$
$252$	8.26430e10	1.29093
$253$	1.47511e11	2.26351
$254$	6.57212e10	0.990727
$255$	2.41292e10	0.357364
$256$	6.99210e10	1.01748
$257$	−3.73067e10	−0.533443	−0.266722	−	0.963774i	$-0.585940\pi$
$257$	−3.73067e10	−0.533443	−0.266722	+	0.963774i	$0.585940\pi$
$258$	−1.48058e10	−0.208039
$259$	7.86361e10	1.08586
$260$	−1.81144e11	−2.45836
$261$	−5.19125e9	−0.0692452
$262$	−1.86105e11	−2.44007
$263$	6.39270e10	0.823917	0.411958	−	0.911203i	$-0.364845\pi$
$263$	6.39270e10	0.823917	0.411958	+	0.911203i	$0.364845\pi$
$264$	−2.64001e11	−3.34493
$265$	−5.23730e10	−0.652380
$266$	−2.18830e11	−2.68003
$267$	−7.52220e10	−0.905825
$268$	9.91354e10	1.17388
$269$	2.59531e10	0.302206	0.151103	−	0.988518i	$-0.451717\pi$
$269$	2.59531e10	0.302206	0.151103	+	0.988518i	$0.451717\pi$
$270$	3.21883e10	0.368605
$271$	1.93051e10	0.217425	0.108713	−	0.994073i	$-0.465327\pi$
$271$	1.93051e10	0.217425	0.108713	+	0.994073i	$0.465327\pi$
$272$	−1.79921e11	−1.99306
$273$	7.30334e10	0.795774
$274$	8.48538e10	0.909482
$275$	−2.41994e9	−0.0255157
$276$	1.75478e11	1.82025
$277$	8.64529e10	0.882308	0.441154	−	0.897431i	$-0.354569\pi$
$277$	8.64529e10	0.882308	0.441154	+	0.897431i	$0.354569\pi$
$278$	2.41299e11	2.42301
$279$	−4.90062e10	−0.484208
$280$	−4.71659e11	−4.58582
$281$	1.52176e11	1.45602	0.728009	−	0.685568i	$-0.240446\pi$
$281$	1.52176e11	1.45602	0.728009	+	0.685568i	$0.240446\pi$
$282$	2.27219e11	2.13955
$283$	−3.14215e10	−0.291197	−0.145599	−	0.989344i	$-0.546511\pi$
$283$	−3.14215e10	−0.291197	−0.145599	+	0.989344i	$0.546511\pi$
$284$	−5.11461e10	−0.466530
$285$	−6.16826e10	−0.553810
$286$	−3.77374e11	−3.33522
$287$	1.01909e11	0.886630
$288$	−1.20117e11	−1.02882
$289$	−7.37618e10	−0.622001
$290$	4.79231e10	0.397881
$291$	1.64812e10	0.134732
$292$	5.22192e11	4.20346
$293$	−3.53857e10	−0.280494	−0.140247	−	0.990117i	$-0.544790\pi$
$293$	−3.53857e10	−0.280494	−0.140247	+	0.990117i	$0.544790\pi$
$294$	1.66885e11	1.30273
$295$	1.70490e10	0.131069
$296$	−2.98826e11	−2.26259
$297$	4.85298e10	0.361913
$298$	3.47718e11	2.55419
$299$	1.55074e11	1.12207
$300$	−2.87875e9	−0.0205191
$301$	−3.98810e10	−0.280038
$302$	6.81404e10	0.471382
$303$	−7.92309e10	−0.540011
$304$	4.59940e11	3.08866
$305$	−2.03852e11	−1.34886
$306$	5.97980e10	0.389889
$307$	2.21134e11	1.42080	0.710401	−	0.703797i	$-0.248514\pi$
$307$	2.21134e11	1.42080	0.710401	+	0.703797i	$0.248514\pi$
$308$	−1.15024e12	−7.28302
$309$	−1.65071e11	−1.03005
$310$	4.52401e11	2.78225
$311$	−5.85330e10	−0.354796	−0.177398	−	0.984139i	$-0.556768\pi$
$311$	−5.85330e10	−0.354796	−0.177398	+	0.984139i	$0.556768\pi$
$312$	−2.77535e11	−1.65815
$313$	2.93275e11	1.72713	0.863565	−	0.504238i	$-0.168227\pi$
$313$	2.93275e11	1.72713	0.863565	+	0.504238i	$0.168227\pi$
$314$	−4.12852e11	−2.39669
$315$	8.67025e10	0.496174
$316$	8.51265e11	4.80256
$317$	1.45588e11	0.809766	0.404883	−	0.914368i	$-0.367312\pi$
$317$	1.45588e11	0.809766	0.404883	+	0.914368i	$0.367312\pi$
$318$	−1.29793e11	−0.711754
$319$	7.22529e10	0.390658
$320$	4.96689e11	2.64795
$321$	−1.28388e11	−0.674920
$322$	6.53120e11	3.38565
$323$	−1.14591e11	−0.585788
$324$	5.77306e10	0.291041
$325$	−2.54401e9	−0.0126486
$326$	3.48822e10	0.171051
$327$	1.76005e10	0.0851256
$328$	−3.87265e11	−1.84746
$329$	6.12037e11	2.88003
$330$	−4.48003e11	−2.07955
$331$	−1.57130e11	−0.719503	−0.359752	−	0.933048i	$-0.617139\pi$
$331$	−1.57130e11	−0.719503	−0.359752	+	0.933048i	$0.617139\pi$
$332$	−8.69130e11	−3.92612
$333$	5.49316e10	0.244806
$334$	2.77809e11	1.22148
$335$	1.04005e11	0.451182
$336$	−6.46502e11	−2.76722
$337$	−8.26938e10	−0.349252	−0.174626	−	0.984635i	$-0.555872\pi$
$337$	−8.26938e10	−0.349252	−0.174626	+	0.984635i	$0.555872\pi$
$338$	5.97799e10	0.249132
$339$	3.64275e10	0.149806
$340$	−3.99506e11	−1.62132
$341$	6.82078e11	2.73174
$342$	−1.52865e11	−0.604213
$343$	7.05101e10	0.275060
$344$	1.51552e11	0.583512
$345$	1.84098e11	0.699620
$346$	−3.05381e11	−1.14551
$347$	−8.62359e10	−0.319305	−0.159652	−	0.987173i	$-0.551037\pi$
$347$	−8.62359e10	−0.319305	−0.159652	+	0.987173i	$0.551037\pi$
$348$	8.59514e10	0.314157
$349$	−1.91363e11	−0.690467	−0.345234	−	0.938517i	$-0.612200\pi$
$349$	−1.91363e11	−0.690467	−0.345234	+	0.938517i	$0.612200\pi$
$350$	−1.07145e10	−0.0381652
$351$	5.10178e10	0.179407
$352$	1.67182e12	5.80427
$353$	1.10169e11	0.377637	0.188818	−	0.982012i	$-0.439534\pi$
$353$	1.10169e11	0.377637	0.188818	+	0.982012i	$0.439534\pi$
$354$	4.22517e10	0.142998
$355$	−5.36584e10	−0.179312
$356$	1.24545e12	4.10962
$357$	1.61072e11	0.524824
$358$	2.20282e10	0.0708770
$359$	1.08108e11	0.343504	0.171752	−	0.985140i	$-0.445057\pi$
$359$	1.08108e11	0.343504	0.171752	+	0.985140i	$0.445057\pi$
$360$	−3.29479e11	−1.03387
$361$	−2.97521e10	−0.0922009
$362$	−4.51443e11	−1.38170
$363$	−4.84454e11	−1.46444
$364$	−1.20921e12	−3.61033
$365$	5.47842e11	1.61561
$366$	−5.05196e11	−1.47162
$367$	4.90550e11	1.41152	0.705758	−	0.708453i	$-0.250607\pi$
$367$	4.90550e11	1.41152	0.705758	+	0.708453i	$0.250607\pi$
$368$	−1.37274e12	−3.90186
$369$	7.11887e10	0.199891
$370$	−5.07101e11	−1.40665
$371$	−3.49612e11	−0.958083
$372$	8.11395e11	2.19679
$373$	1.38340e11	0.370049	0.185025	−	0.982734i	$-0.440764\pi$
$373$	1.38340e11	0.370049	0.185025	+	0.982734i	$0.440764\pi$
$374$	−8.32282e11	−2.19962
$375$	2.19570e11	0.573367
$376$	−2.32581e12	−6.00108
$377$	7.59571e10	0.193657
$378$	2.14870e11	0.541331
$379$	−5.56221e11	−1.38475	−0.692374	−	0.721538i	$-0.743435\pi$
$379$	−5.56221e11	−1.38475	−0.692374	+	0.721538i	$0.743435\pi$
$380$	1.02128e12	2.51257
$381$	1.23663e11	0.300661
$382$	−1.18250e12	−2.84130
$383$	4.78507e11	1.13630	0.568151	−	0.822925i	$-0.307659\pi$
$383$	4.78507e11	1.13630	0.568151	+	0.822925i	$0.307659\pi$
$384$	4.71657e11	1.10697
$385$	−1.20674e12	−2.79925
$386$	−1.12487e12	−2.57905
$387$	−2.78590e10	−0.0631345
$388$	−2.72879e11	−0.611263
$389$	7.44731e11	1.64902	0.824511	−	0.565846i	$-0.191450\pi$
$389$	7.44731e11	1.64902	0.824511	+	0.565846i	$0.191450\pi$
$390$	−4.70972e11	−1.03087
$391$	3.42009e11	0.740017
$392$	−1.70823e12	−3.65393
$393$	−3.50181e11	−0.740501
$394$	−3.49922e11	−0.731539
$395$	8.93079e11	1.84588
$396$	−8.03507e11	−1.64196
$397$	1.80985e11	0.365666	0.182833	−	0.983144i	$-0.441473\pi$
$397$	1.80985e11	0.365666	0.182833	+	0.983144i	$0.441473\pi$
$398$	5.47565e11	1.09386
$399$	−4.11757e11	−0.813323
$400$	2.25199e10	0.0439843
$401$	−1.61745e11	−0.312378	−0.156189	−	0.987727i	$-0.549921\pi$
$401$	−1.61745e11	−0.312378	−0.156189	+	0.987727i	$0.549921\pi$
$402$	2.57750e11	0.492245
$403$	7.17047e11	1.35418
$404$	1.31183e12	2.44997
$405$	6.05664e10	0.111862
$406$	3.19906e11	0.584327
$407$	−7.64549e11	−1.38112
$408$	−6.12093e11	−1.09357
$409$	−6.20792e11	−1.09696	−0.548481	−	0.836163i	$-0.684794\pi$
$409$	−6.20792e11	−1.09696	−0.548481	+	0.836163i	$0.684794\pi$
$410$	−6.57179e11	−1.14857
$411$	1.59663e11	0.276005
$412$	2.73307e12	4.67319
$413$	1.13809e11	0.192488
$414$	4.56240e11	0.763293
$415$	−9.11821e11	−1.50901
$416$	1.75753e12	2.87728
$417$	4.54036e11	0.735322
$418$	2.12760e12	3.40877
$419$	2.41725e10	0.0383141	0.0191570	−	0.999816i	$-0.493902\pi$
$419$	2.41725e10	0.0383141	0.0191570	+	0.999816i	$0.493902\pi$
$420$	−1.43553e12	−2.25108
$421$	1.42904e11	0.221705	0.110853	−	0.993837i	$-0.464642\pi$
$421$	1.42904e11	0.221705	0.110853	+	0.993837i	$0.464642\pi$
$422$	−8.83459e11	−1.35606
$423$	4.27541e11	0.649302
$424$	1.32856e12	1.99635
$425$	−5.61071e9	−0.00834195
$426$	−1.32979e11	−0.195632
$427$	−1.36080e12	−1.98092
$428$	2.12572e12	3.06203
$429$	−7.10077e11	−1.01216
$430$	2.57181e11	0.362770
$431$	3.06890e11	0.428386	0.214193	−	0.976791i	$-0.431288\pi$
$431$	3.06890e11	0.428386	0.214193	+	0.976791i	$0.431288\pi$
$432$	−4.51617e11	−0.623869
$433$	−8.43663e11	−1.15338	−0.576692	−	0.816962i	$-0.695657\pi$
$433$	−8.43663e11	−1.15338	−0.576692	+	0.816962i	$0.695657\pi$
$434$	3.01997e12	4.08600
$435$	9.01734e10	0.120747
$436$	−2.91411e11	−0.386205
$437$	−8.74294e11	−1.14681
$438$	1.35769e12	1.76265
$439$	1.15544e12	1.48476	0.742381	−	0.669978i	$-0.233697\pi$
$439$	1.15544e12	1.48476	0.742381	+	0.669978i	$0.233697\pi$
$440$	4.58576e12	5.83277
$441$	3.14015e11	0.395346
$442$	−8.74951e11	−1.09039
$443$	2.56485e11	0.316407	0.158203	−	0.987407i	$-0.449430\pi$
$443$	2.56485e11	0.316407	0.158203	+	0.987407i	$0.449430\pi$
$444$	−9.09501e11	−1.11066
$445$	1.30663e12	1.57954
$446$	−2.29441e12	−2.74577
$447$	6.54275e11	0.775134
$448$	3.31560e12	3.88876
$449$	2.28813e11	0.265688	0.132844	−	0.991137i	$-0.457589\pi$
$449$	2.28813e11	0.265688	0.132844	+	0.991137i	$0.457589\pi$
$450$	−7.48468e9	−0.00860433
$451$	−9.90819e11	−1.12772
$452$	−6.03129e11	−0.679653
$453$	1.28215e11	0.143053
$454$	−2.27884e11	−0.251746
$455$	−1.26861e12	−1.38764
$456$	1.56472e12	1.69471
$457$	−1.63048e12	−1.74860	−0.874302	−	0.485383i	$-0.838680\pi$
$457$	−1.63048e12	−1.74860	−0.874302	+	0.485383i	$0.838680\pi$
$458$	2.21692e12	2.35426
$459$	1.12518e11	0.118321
$460$	−3.04810e12	−3.17409
$461$	1.64115e12	1.69237	0.846185	−	0.532889i	$-0.178894\pi$
$461$	1.64115e12	1.69237	0.846185	+	0.532889i	$0.178894\pi$
$462$	−2.99061e12	−3.05401
$463$	5.78729e11	0.585276	0.292638	−	0.956223i	$-0.405467\pi$
$463$	5.78729e11	0.585276	0.292638	+	0.956223i	$0.405467\pi$
$464$	−6.72383e11	−0.673420
$465$	8.51250e11	0.844343
$466$	5.13073e11	0.504014
$467$	1.23952e11	0.120594	0.0602971	−	0.998180i	$-0.480795\pi$
$467$	1.23952e11	0.120594	0.0602971	+	0.998180i	$0.480795\pi$
$468$	−8.44701e11	−0.813948
$469$	6.94276e11	0.662605
$470$	−3.94685e12	−3.73087
$471$	−7.76835e11	−0.727335
$472$	−4.32489e11	−0.401084
$473$	3.87748e11	0.356184
$474$	2.21327e12	2.01387
$475$	1.43429e10	0.0129276
$476$	−2.66687e12	−2.38106
$477$	−2.44223e11	−0.216000
$478$	7.54038e11	0.660645
$479$	−1.76694e12	−1.53360	−0.766799	−	0.641888i	$-0.778152\pi$
$479$	−1.76694e12	−1.53360	−0.766799	+	0.641888i	$0.778152\pi$
$480$	2.08647e12	1.79402
$481$	−8.03746e11	−0.684646
$482$	1.87456e12	1.58193
$483$	1.22893e12	1.02746
$484$	8.02110e12	6.64400
$485$	−2.86283e11	−0.234940
$486$	1.50099e11	0.122043
$487$	−8.92659e11	−0.719126	−0.359563	−	0.933121i	$-0.617074\pi$
$487$	−8.92659e11	−0.719126	−0.359563	+	0.933121i	$0.617074\pi$
$488$	5.17119e12	4.12763
$489$	6.56353e10	0.0519096
$490$	−2.89883e12	−2.27165
$491$	1.42507e12	1.10654	0.553272	−	0.833001i	$-0.313379\pi$
$491$	1.42507e12	1.10654	0.553272	+	0.833001i	$0.313379\pi$
$492$	−1.17867e12	−0.906879
$493$	1.67520e11	0.127719
$494$	2.23668e12	1.68979
$495$	−8.42975e11	−0.631090
$496$	−6.34740e12	−4.70900
$497$	−3.58192e11	−0.263337
$498$	−2.25972e12	−1.64635
$499$	1.91332e12	1.38145	0.690724	−	0.723119i	$-0.257292\pi$
$499$	1.91332e12	1.38145	0.690724	+	0.723119i	$0.257292\pi$
$500$	−3.63542e12	−2.60130
$501$	5.22734e11	0.370690
$502$	1.54063e12	1.08276
$503$	−5.38097e11	−0.374804	−0.187402	−	0.982283i	$-0.560007\pi$
$503$	−5.38097e11	−0.374804	−0.187402	+	0.982283i	$0.560007\pi$
$504$	−2.19941e12	−1.51834
$505$	1.37626e12	0.941651
$506$	−6.35004e12	−4.30625
$507$	1.12484e11	0.0756055
$508$	−2.04748e12	−1.36406
$509$	1.31123e11	0.0865861	0.0432931	−	0.999062i	$-0.486215\pi$
$509$	1.31123e11	0.0865861	0.0432931	+	0.999062i	$0.486215\pi$
$510$	−1.03871e12	−0.679873
$511$	3.65707e12	2.37268
$512$	−2.86079e10	−0.0183980
$513$	−2.87635e11	−0.183364
$514$	1.60597e12	1.01486
$515$	2.86732e12	1.79615
$516$	4.61262e11	0.286434
$517$	−5.95061e12	−3.66314
$518$	−3.38511e12	−2.06580
$519$	−5.74613e11	−0.347634
$520$	4.82087e12	2.89141
$521$	−2.11305e12	−1.25643	−0.628217	−	0.778038i	$-0.716215\pi$
$521$	−2.11305e12	−1.25643	−0.628217	+	0.778038i	$0.716215\pi$
$522$	2.23472e11	0.131736
$523$	1.87618e12	1.09652	0.548260	−	0.836308i	$-0.315291\pi$
$523$	1.87618e12	1.09652	0.548260	+	0.836308i	$0.315291\pi$
$524$	5.79794e12	3.35956
$525$	−2.01608e10	−0.0115822
$526$	−2.75192e12	−1.56747
$527$	1.58142e12	0.893097
$528$	6.28570e12	3.51966
$529$	8.08263e11	0.448748
$530$	2.25454e12	1.24113
$531$	7.95020e10	0.0433963
$532$	6.81746e12	3.68995
$533$	−1.04162e12	−0.559031
$534$	3.23815e12	1.72330
$535$	2.23014e12	1.17690
$536$	−2.63833e12	−1.38066
$537$	4.14489e10	0.0215094
$538$	−1.11722e12	−0.574936
$539$	−4.37053e12	−2.23041
$540$	−1.00280e12	−0.507506
$541$	−3.86621e12	−1.94043	−0.970215	−	0.242245i	$-0.922116\pi$
$541$	−3.86621e12	−1.94043	−0.970215	+	0.242245i	$0.922116\pi$
$542$	−8.31041e11	−0.413643
$543$	−8.49448e11	−0.419312
$544$	3.87616e12	1.89761
$545$	−3.05726e11	−0.148439
$546$	−3.14393e12	−1.51393
$547$	1.83738e12	0.877520	0.438760	−	0.898604i	$-0.355418\pi$
$547$	1.83738e12	0.877520	0.438760	+	0.898604i	$0.355418\pi$
$548$	−2.64354e12	−1.25220
$549$	−9.50591e11	−0.446599
$550$	1.04173e11	0.0485428
$551$	−4.28241e11	−0.197927
$552$	−4.67007e12	−2.14091
$553$	5.96167e12	2.71085
$554$	−3.72161e12	−1.67856
$555$	−9.54176e11	−0.426884
$556$	−7.51747e12	−3.33607
$557$	−3.55935e12	−1.56683	−0.783416	−	0.621498i	$-0.786524\pi$
$557$	−3.55935e12	−1.56683	−0.783416	+	0.621498i	$0.786524\pi$
$558$	2.10961e12	0.921188
$559$	4.07627e11	0.176567
$560$	1.12299e13	4.82537
$561$	−1.56604e12	−0.667530
$562$	−6.55083e12	−2.77002
$563$	−8.83644e11	−0.370672	−0.185336	−	0.982675i	$-0.559337\pi$
$563$	−8.83644e11	−0.370672	−0.185336	+	0.982675i	$0.559337\pi$
$564$	−7.07880e12	−2.94580
$565$	−6.32755e11	−0.261227
$566$	1.35263e12	0.553993
$567$	4.04306e11	0.164281
$568$	1.36117e12	0.548713
$569$	2.04350e12	0.817277	0.408638	−	0.912696i	$-0.366004\pi$
$569$	2.04350e12	0.817277	0.408638	+	0.912696i	$0.366004\pi$
$570$	2.65530e12	1.05360
$571$	−4.45400e12	−1.75343	−0.876713	−	0.481013i	$-0.840269\pi$
$571$	−4.45400e12	−1.75343	−0.876713	+	0.481013i	$0.840269\pi$
$572$	1.17567e13	4.59203
$573$	−2.22503e12	−0.862264
$574$	−4.38695e12	−1.68678
$575$	−4.28079e10	−0.0163312
$576$	2.31613e12	0.876722
$577$	−2.33300e12	−0.876240	−0.438120	−	0.898916i	$-0.644356\pi$
$577$	−2.33300e12	−0.876240	−0.438120	+	0.898916i	$0.644356\pi$
$578$	3.17528e12	1.18333
$579$	−2.11659e12	−0.782677
$580$	−1.49300e12	−0.547815
$581$	−6.08679e12	−2.21613
$582$	−7.09481e11	−0.256323
$583$	3.39914e12	1.21860
$584$	−1.38973e13	−4.94393
$585$	−8.86193e11	−0.312843
$586$	1.52328e12	0.533629
$587$	5.05430e12	1.75707	0.878537	−	0.477675i	$-0.158520\pi$
$587$	5.05430e12	1.75707	0.878537	+	0.477675i	$0.158520\pi$
$588$	−5.19914e12	−1.79363
$589$	−4.04266e12	−1.38404
$590$	−7.33924e11	−0.249354
$591$	−6.58422e11	−0.222004
$592$	7.11487e12	2.38078
$593$	1.63563e12	0.543174	0.271587	−	0.962414i	$-0.412452\pi$
$593$	1.63563e12	0.543174	0.271587	+	0.962414i	$0.412452\pi$
$594$	−2.08910e12	−0.688527
$595$	−2.79787e12	−0.915168
$596$	−1.08328e13	−3.51669
$597$	1.03031e12	0.331959
$598$	−6.67559e12	−2.13469
$599$	−3.15815e12	−1.00233	−0.501166	−	0.865351i	$-0.667095\pi$
$599$	−3.15815e12	−1.00233	−0.501166	+	0.865351i	$0.667095\pi$
$600$	7.66132e10	0.0241337
$601$	−2.98906e12	−0.934542	−0.467271	−	0.884114i	$-0.654763\pi$
$601$	−2.98906e12	−0.934542	−0.467271	+	0.884114i	$0.654763\pi$
$602$	1.71679e12	0.532762
$603$	4.84990e11	0.149384
$604$	−2.12285e12	−0.649013
$605$	8.41510e12	2.55364
$606$	3.41072e12	1.02735
$607$	6.12469e12	1.83120	0.915599	−	0.402093i	$-0.131717\pi$
$607$	6.12469e12	1.83120	0.915599	+	0.402093i	$0.131717\pi$
$608$	−9.90882e12	−2.94073
$609$	6.01945e11	0.177329
$610$	8.77539e12	2.56615
$611$	−6.25569e12	−1.81589
$612$	−1.86295e12	−0.536810
$613$	6.70042e12	1.91659	0.958296	−	0.285777i	$-0.0922518\pi$
$613$	6.70042e12	1.91659	0.958296	+	0.285777i	$0.0922518\pi$
$614$	−9.51936e12	−2.70302
$615$	−1.23657e12	−0.348562
$616$	3.06119e13	8.56597
$617$	1.04834e12	0.291218	0.145609	−	0.989342i	$-0.453486\pi$
$617$	1.04834e12	0.291218	0.145609	+	0.989342i	$0.453486\pi$
$618$	7.10593e12	1.95963
$619$	−4.85801e12	−1.33000	−0.664998	−	0.746845i	$-0.731568\pi$
$619$	−4.85801e12	−1.33000	−0.664998	+	0.746845i	$0.731568\pi$
$620$	−1.40941e13	−3.83068
$621$	8.58473e11	0.231641
$622$	2.51972e12	0.674987
$623$	8.72228e12	2.31971
$624$	6.60795e12	1.74476
$625$	−3.86575e12	−1.01338
$626$	−1.26248e13	−3.28580
$627$	4.00336e12	1.03448
$628$	1.28620e13	3.29983
$629$	−1.77263e12	−0.451533
$630$	−3.73235e12	−0.943953
$631$	−1.79785e12	−0.451463	−0.225732	−	0.974190i	$-0.572477\pi$
$631$	−1.79785e12	−0.451463	−0.225732	+	0.974190i	$0.572477\pi$
$632$	−2.26550e13	−5.64856
$633$	−1.66234e12	−0.411532
$634$	−6.26726e12	−1.54055
$635$	−2.14806e12	−0.524281
$636$	4.04359e12	0.979964
$637$	−4.59460e12	−1.10566
$638$	−3.11033e12	−0.743213
$639$	−2.50217e11	−0.0593693
$640$	−8.19281e12	−1.93029
$641$	6.11084e12	1.42968	0.714841	−	0.699287i	$-0.246499\pi$
$641$	6.11084e12	1.42968	0.714841	+	0.699287i	$0.246499\pi$
$642$	5.52683e12	1.28401
$643$	4.26512e12	0.983969	0.491985	−	0.870604i	$-0.336272\pi$
$643$	4.26512e12	0.983969	0.491985	+	0.870604i	$0.336272\pi$
$644$	−2.03474e13	−4.66146
$645$	4.83919e11	0.110092
$646$	4.93291e12	1.11444
$647$	2.63397e12	0.590937	0.295468	−	0.955353i	$-0.404524\pi$
$647$	2.63397e12	0.590937	0.295468	+	0.955353i	$0.404524\pi$
$648$	−1.53641e12	−0.342310
$649$	−1.10653e12	−0.244828
$650$	1.09514e11	0.0240636
$651$	5.68245e12	1.24000
$652$	−1.08672e12	−0.235507
$653$	4.18813e11	0.0901386	0.0450693	−	0.998984i	$-0.485649\pi$
$653$	4.18813e11	0.0901386	0.0450693	+	0.998984i	$0.485649\pi$
$654$	−7.57664e11	−0.161948
$655$	6.08273e12	1.29126
$656$	9.22054e12	1.94397
$657$	2.55466e12	0.534921
$658$	−2.63469e13	−5.47914
$659$	7.75877e12	1.60254	0.801270	−	0.598303i	$-0.204158\pi$
$659$	7.75877e12	1.60254	0.801270	+	0.598303i	$0.204158\pi$
$660$	1.39571e13	2.86318
$661$	−5.87003e12	−1.19601	−0.598003	−	0.801494i	$-0.704039\pi$
$661$	−5.87003e12	−1.19601	−0.598003	+	0.801494i	$0.704039\pi$
$662$	6.76410e12	1.36883
$663$	−1.64633e12	−0.330907
$664$	2.31305e13	4.61773
$665$	7.15233e12	1.41824
$666$	−2.36468e12	−0.465735
$667$	1.27813e12	0.250039
$668$	−8.65490e12	−1.68177
$669$	−4.31723e12	−0.833274
$670$	−4.47719e12	−0.858358
$671$	1.32305e13	2.51956
$672$	1.39281e13	2.63469
$673$	−3.16408e12	−0.594537	−0.297269	−	0.954794i	$-0.596076\pi$
$673$	−3.16408e12	−0.594537	−0.297269	+	0.954794i	$0.596076\pi$
$674$	3.55979e12	0.664439
$675$	−1.40834e10	−0.00261120
$676$	−1.86239e12	−0.343013
$677$	−2.79236e12	−0.510884	−0.255442	−	0.966824i	$-0.582221\pi$
$677$	−2.79236e12	−0.510884	−0.255442	+	0.966824i	$0.582221\pi$
$678$	−1.56812e12	−0.285001
$679$	−1.91106e12	−0.345033
$680$	1.06322e13	1.90692
$681$	−4.28793e11	−0.0763986
$682$	−2.93620e13	−5.19704
$683$	−3.47599e12	−0.611203	−0.305601	−	0.952160i	$-0.598857\pi$
$683$	−3.47599e12	−0.611203	−0.305601	+	0.952160i	$0.598857\pi$
$684$	4.76236e12	0.831898
$685$	−2.77339e12	−0.481287
$686$	−3.03531e12	−0.523292
$687$	4.17141e12	0.714460
$688$	−3.60837e12	−0.613993
$689$	3.57341e12	0.604082
$690$	−7.92500e12	−1.33100
$691$	1.64952e12	0.275236	0.137618	−	0.990485i	$-0.456055\pi$
$691$	1.64952e12	0.275236	0.137618	+	0.990485i	$0.456055\pi$
$692$	9.51387e12	1.57717
$693$	−5.62721e12	−0.926817
$694$	3.71227e12	0.607466
$695$	−7.88672e12	−1.28223
$696$	−2.28746e12	−0.369498
$697$	−2.29724e12	−0.368688
$698$	8.23776e12	1.31359
$699$	9.65412e11	0.152956
$700$	3.33802e11	0.0525469
$701$	−6.16418e12	−0.964149	−0.482075	−	0.876130i	$-0.660117\pi$
$701$	−6.16418e12	−0.964149	−0.482075	+	0.876130i	$0.660117\pi$
$702$	−2.19621e12	−0.341316
$703$	4.53146e12	0.699744
$704$	−3.22364e13	−4.94617
$705$	−7.42651e12	−1.13223
$706$	−4.74255e12	−0.718440
$707$	9.18713e12	1.38290
$708$	−1.31631e12	−0.196884
$709$	−2.98907e12	−0.444251	−0.222126	−	0.975018i	$-0.571300\pi$
$709$	−2.98907e12	−0.444251	−0.222126	+	0.975018i	$0.571300\pi$
$710$	2.30988e12	0.341135
$711$	4.16455e12	0.611160
$712$	−3.31457e13	−4.83355
$713$	1.20657e13	1.74844
$714$	−6.93381e12	−0.998458
$715$	1.23342e13	1.76496
$716$	−6.86268e11	−0.0975855
$717$	1.41882e12	0.200489
$718$	−4.65381e12	−0.653504
$719$	−5.59992e12	−0.781451	−0.390725	−	0.920507i	$-0.627776\pi$
$719$	−5.59992e12	−0.781451	−0.390725	+	0.920507i	$0.627776\pi$
$720$	7.84471e12	1.08788
$721$	1.91406e13	2.63783
$722$	1.28076e12	0.175409
$723$	3.52722e12	0.480076
$724$	1.40643e13	1.90237
$725$	−2.09678e10	−0.00281860
$726$	2.08547e13	2.78605
$727$	−1.19722e13	−1.58953	−0.794766	−	0.606915i	$-0.792407\pi$
$727$	−1.19722e13	−1.58953	−0.794766	+	0.606915i	$0.792407\pi$
$728$	3.21813e13	4.24631
$729$	2.82430e11	0.0370370
$730$	−2.35834e13	−3.07364
$731$	8.99004e11	0.116448
$732$	1.57389e13	2.02617
$733$	1.91201e12	0.244637	0.122319	−	0.992491i	$-0.460967\pi$
$733$	1.91201e12	0.244637	0.122319	+	0.992491i	$0.460967\pi$
$734$	−2.11171e13	−2.68536
$735$	−5.45453e12	−0.689388
$736$	2.95738e13	3.71499
$737$	−6.75019e12	−0.842776
$738$	−3.06452e12	−0.380285
$739$	−2.40092e12	−0.296127	−0.148064	−	0.988978i	$-0.547304\pi$
$739$	−2.40092e12	−0.296127	−0.148064	+	0.988978i	$0.547304\pi$
$740$	1.57983e13	1.93672
$741$	4.20860e12	0.512809
$742$	1.50500e13	1.82272
$743$	1.35259e13	1.62823	0.814115	−	0.580704i	$-0.197223\pi$
$743$	1.35259e13	1.62823	0.814115	+	0.580704i	$0.197223\pi$
$744$	−2.15940e13	−2.58377
$745$	−1.13649e13	−1.35165
$746$	−5.95525e12	−0.704005
$747$	−4.25195e12	−0.499627
$748$	2.59290e13	3.02850
$749$	1.48871e13	1.72839
$750$	−9.45203e12	−1.09081
$751$	7.22749e11	0.0829102	0.0414551	−	0.999140i	$-0.486801\pi$
$751$	7.22749e11	0.0829102	0.0414551	+	0.999140i	$0.486801\pi$
$752$	5.53762e13	6.31456
$753$	2.89890e12	0.328591
$754$	−3.26979e12	−0.368425
$755$	−2.22713e12	−0.249450
$756$	−6.69409e12	−0.745321
$757$	3.45878e12	0.382817	0.191408	−	0.981510i	$-0.438694\pi$
$757$	3.45878e12	0.382817	0.191408	+	0.981510i	$0.438694\pi$
$758$	2.39441e13	2.63443
$759$	−1.19484e13	−1.30684
$760$	−2.71797e13	−2.95517
$761$	−5.90424e12	−0.638165	−0.319082	−	0.947727i	$-0.603375\pi$
$761$	−5.90424e12	−0.638165	−0.319082	+	0.947727i	$0.603375\pi$
$762$	−5.32342e12	−0.571996
$763$	−2.04085e12	−0.217997
$764$	3.68398e13	3.91199
$765$	−1.95446e12	−0.206324
$766$	−2.05987e13	−2.16177
$767$	−1.16325e12	−0.121366
$768$	−5.66360e12	−0.587445
$769$	5.87096e12	0.605397	0.302698	−	0.953086i	$-0.402112\pi$
$769$	5.87096e12	0.605397	0.302698	+	0.953086i	$0.402112\pi$
$770$	5.19477e13	5.32547
$771$	3.02184e12	0.307983
$772$	3.50443e13	3.55091
$773$	−5.51376e12	−0.555444	−0.277722	−	0.960661i	$-0.589579\pi$
$773$	−5.51376e12	−0.555444	−0.277722	+	0.960661i	$0.589579\pi$
$774$	1.19927e12	0.120111
$775$	−1.97940e11	−0.0197095
$776$	7.26224e12	0.718941
$777$	−6.36952e12	−0.626920
$778$	−3.20591e13	−3.13720
$779$	5.87256e12	0.571358
$780$	1.46727e13	1.41933
$781$	3.48257e12	0.334942
$782$	−1.47227e13	−1.40786
$783$	4.20491e11	0.0399787
$784$	4.06720e13	3.84480
$785$	1.34938e13	1.26830
$786$	1.50745e13	1.40878
$787$	1.26668e13	1.17701	0.588506	−	0.808493i	$-0.299716\pi$
$787$	1.26668e13	1.17701	0.588506	+	0.808493i	$0.299716\pi$
$788$	1.09015e13	1.00720
$789$	−5.17809e12	−0.475689
$790$	−3.84451e13	−3.51171
$791$	−4.22390e12	−0.383636
$792$	2.13841e13	1.93120
$793$	1.39088e13	1.24900
$794$	−7.79100e12	−0.695666
$795$	4.24221e12	0.376652
$796$	−1.70589e13	−1.50606
$797$	6.19605e12	0.543942	0.271971	−	0.962306i	$-0.412325\pi$
$797$	6.19605e12	0.543942	0.271971	+	0.962306i	$0.412325\pi$
$798$	1.77252e13	1.54732
$799$	−1.37966e13	−1.19760
$800$	−4.85163e11	−0.0418777
$801$	6.09298e12	0.522978
$802$	6.96277e12	0.594288
$803$	−3.55563e13	−3.01785
$804$	−8.02997e12	−0.677738
$805$	−2.13468e13	−1.79164
$806$	−3.08673e13	−2.57627
$807$	−2.10220e12	−0.174479
$808$	−3.49121e13	−2.88154
$809$	1.96912e13	1.61623	0.808115	−	0.589025i	$-0.200488\pi$
$809$	1.96912e13	1.61623	0.808115	+	0.589025i	$0.200488\pi$
$810$	−2.60725e12	−0.212814
$811$	1.93716e13	1.57243	0.786214	−	0.617954i	$-0.212038\pi$
$811$	1.93716e13	1.57243	0.786214	+	0.617954i	$0.212038\pi$
$812$	−9.96639e12	−0.804518
$813$	−1.56371e12	−0.125530
$814$	3.29122e13	2.62752
$815$	−1.14010e12	−0.0905179
$816$	1.45736e13	1.15069
$817$	−2.29817e12	−0.180461
$818$	2.67237e13	2.08693
$819$	−5.91571e12	−0.459440
$820$	2.04738e13	1.58138
$821$	2.11291e13	1.62307	0.811534	−	0.584306i	$-0.198633\pi$
$821$	2.11291e13	1.62307	0.811534	+	0.584306i	$0.198633\pi$
$822$	−6.87316e12	−0.525089
$823$	5.74360e12	0.436400	0.218200	−	0.975904i	$-0.429982\pi$
$823$	5.74360e12	0.436400	0.218200	+	0.975904i	$0.429982\pi$
$824$	−7.27363e13	−5.49641
$825$	1.96016e11	0.0147315
$826$	−4.89925e12	−0.366201
$827$	1.75144e13	1.30203	0.651014	−	0.759065i	$-0.274344\pi$
$827$	1.75144e13	1.30203	0.651014	+	0.759065i	$0.274344\pi$
$828$	−1.42137e13	−1.05092
$829$	−1.10876e13	−0.815346	−0.407673	−	0.913128i	$-0.633660\pi$
$829$	−1.10876e13	−0.815346	−0.407673	+	0.913128i	$0.633660\pi$
$830$	3.92519e13	2.87084
$831$	−7.00268e12	−0.509401
$832$	−3.38891e13	−2.45191
$833$	−1.01332e13	−0.729195
$834$	−1.95453e13	−1.39892
$835$	−9.08002e12	−0.646395
$836$	−6.62836e13	−4.69329
$837$	3.96950e12	0.279558
$838$	−1.04057e12	−0.0728911
$839$	−1.87455e13	−1.30607	−0.653037	−	0.757326i	$-0.726505\pi$
$839$	−1.87455e13	−1.30607	−0.653037	+	0.757326i	$0.726505\pi$
$840$	3.82044e13	2.64762
$841$	−1.38811e13	−0.956846
$842$	−6.15173e12	−0.421786
$843$	−1.23262e13	−0.840632
$844$	2.75234e13	1.86707
$845$	−1.95387e12	−0.131838
$846$	−1.84047e13	−1.23527
$847$	5.61743e13	3.75027
$848$	−3.16323e13	−2.10063
$849$	2.54514e12	0.168123
$850$	2.41529e11	0.0158702
$851$	−1.35246e13	−0.883976
$852$	4.14283e12	0.269351
$853$	−2.19866e11	−0.0142196	−0.00710979	−	0.999975i	$-0.502263\pi$
$853$	−2.19866e11	−0.0142196	−0.00710979	+	0.999975i	$0.502263\pi$
$854$	5.85794e13	3.76864
$855$	4.99629e12	0.319742
$856$	−5.65727e13	−3.60143
$857$	−6.57112e12	−0.416127	−0.208063	−	0.978115i	$-0.566716\pi$
$857$	−6.57112e12	−0.416127	−0.208063	+	0.978115i	$0.566716\pi$
$858$	3.05673e13	1.92559
$859$	7.59316e12	0.475832	0.237916	−	0.971286i	$-0.423536\pi$
$859$	7.59316e12	0.475832	0.237916	+	0.971286i	$0.423536\pi$
$860$	−8.01224e12	−0.499472
$861$	−8.25460e12	−0.511896
$862$	−1.32110e13	−0.814988
$863$	3.32127e12	0.203824	0.101912	−	0.994793i	$-0.467504\pi$
$863$	3.32127e12	0.203824	0.101912	+	0.994793i	$0.467504\pi$
$864$	9.72951e12	0.593990
$865$	9.98119e12	0.606191
$866$	3.63179e13	2.19427
$867$	5.97470e12	0.359112
$868$	−9.40843e13	−5.62572
$869$	−5.79631e13	−3.44796
$870$	−3.88177e12	−0.229717
$871$	−7.09625e12	−0.417780
$872$	7.75545e12	0.454237
$873$	−1.33498e12	−0.0777876
$874$	3.76365e13	2.18176
$875$	−2.54600e13	−1.46833
$876$	−4.22975e13	−2.42687
$877$	−1.16297e13	−0.663850	−0.331925	−	0.943306i	$-0.607698\pi$
$877$	−1.16297e13	−0.663850	−0.331925	+	0.943306i	$0.607698\pi$
$878$	−4.97391e13	−2.82470
$879$	2.86624e12	0.161943
$880$	−1.09184e14	−6.13745
$881$	−1.87746e13	−1.04998	−0.524989	−	0.851109i	$-0.675930\pi$
$881$	−1.87746e13	−1.04998	−0.524989	+	0.851109i	$0.675930\pi$
$882$	−1.35177e13	−0.752131
$883$	−2.23134e13	−1.23521	−0.617606	−	0.786487i	$-0.711897\pi$
$883$	−2.23134e13	−1.23521	−0.617606	+	0.786487i	$0.711897\pi$
$884$	2.72583e13	1.50129
$885$	−1.38097e12	−0.0756728
$886$	−1.10411e13	−0.601952
$887$	−2.09890e13	−1.13850	−0.569252	−	0.822163i	$-0.692767\pi$
$887$	−2.09890e13	−1.13850	−0.569252	+	0.822163i	$0.692767\pi$
$888$	2.42049e13	1.30631
$889$	−1.43392e13	−0.769957
$890$	−5.62474e13	−3.00502
$891$	−3.93091e12	−0.208951
$892$	7.14803e13	3.78046
$893$	3.52691e13	1.85593
$894$	−2.81651e13	−1.47466
$895$	−7.19978e11	−0.0375073
$896$	−5.46905e13	−2.83482
$897$	−1.25610e13	−0.647825
$898$	−9.84991e12	−0.505462
$899$	5.90993e12	0.301762
$900$	2.33178e11	0.0118467
$901$	7.88100e12	0.398401
$902$	4.26526e13	2.14544
$903$	3.23036e12	0.161680
$904$	1.60513e13	0.799379
$905$	1.47551e13	0.731181
$906$	−5.51937e12	−0.272153
$907$	1.25923e13	0.617837	0.308918	−	0.951089i	$-0.400033\pi$
$907$	1.25923e13	0.617837	0.308918	+	0.951089i	$0.400033\pi$
$908$	7.09951e12	0.346611
$909$	6.41771e12	0.311776
$910$	5.46109e13	2.63994
$911$	5.34987e12	0.257342	0.128671	−	0.991687i	$-0.458929\pi$
$911$	5.34987e12	0.257342	0.128671	+	0.991687i	$0.458929\pi$
$912$	−3.72551e13	−1.78324
$913$	5.91796e13	2.81873
$914$	7.01884e13	3.32665
$915$	1.65120e13	0.778763
$916$	−6.90661e13	−3.24142
$917$	4.06048e13	1.89633
$918$	−4.84364e12	−0.225102
$919$	1.31005e13	0.605855	0.302928	−	0.953014i	$-0.402036\pi$
$919$	1.31005e13	0.605855	0.302928	+	0.953014i	$0.402036\pi$
$920$	8.11203e13	3.73323
$921$	−1.79119e13	−0.820301
$922$	−7.06482e13	−3.21967
$923$	3.66111e12	0.166037
$924$	9.31697e13	4.20485
$925$	2.21873e11	0.00996474
$926$	−2.49130e13	−1.11347
$927$	1.33707e13	0.594697
$928$	1.44856e13	0.641168
$929$	3.45106e13	1.52014	0.760068	−	0.649844i	$-0.225166\pi$
$929$	3.45106e13	1.52014	0.760068	+	0.649844i	$0.225166\pi$
$930$	−3.66445e13	−1.60633
$931$	2.59040e13	1.13004
$932$	−1.59843e13	−0.693941
$933$	4.74117e12	0.204842
$934$	−5.33585e12	−0.229426
$935$	2.72026e13	1.16401
$936$	2.24804e13	0.957331
$937$	−7.78758e12	−0.330046	−0.165023	−	0.986290i	$-0.552770\pi$
$937$	−7.78758e12	−0.330046	−0.165023	+	0.986290i	$0.552770\pi$
$938$	−2.98871e13	−1.26058
$939$	−2.37552e13	−0.997159
$940$	1.22961e14	5.13678
$941$	1.47575e13	0.613565	0.306783	−	0.951780i	$-0.400748\pi$
$941$	1.47575e13	0.613565	0.306783	+	0.951780i	$0.400748\pi$
$942$	3.34410e13	1.38373
$943$	−1.75272e13	−0.721789
$944$	1.02973e13	0.422036
$945$	−7.02290e12	−0.286466
$946$	−1.66917e13	−0.677627
$947$	3.13338e12	0.126601	0.0633007	−	0.997994i	$-0.479837\pi$
$947$	3.13338e12	0.126601	0.0633007	+	0.997994i	$0.479837\pi$
$948$	−6.89524e13	−2.77276
$949$	−3.73792e13	−1.49600
$950$	−6.17432e11	−0.0245942
$951$	−1.17926e13	−0.467519
$952$	7.09745e13	2.80050
$953$	4.43314e13	1.74098	0.870489	−	0.492188i	$-0.163803\pi$
$953$	4.43314e13	1.74098	0.870489	+	0.492188i	$0.163803\pi$
$954$	1.05133e13	0.410932
$955$	3.86494e13	1.50358
$956$	−2.34914e13	−0.909595
$957$	−5.85248e12	−0.225547
$958$	7.60628e13	2.91761
$959$	−1.85136e13	−0.706816
$960$	−4.02318e13	−1.52879
$961$	2.93510e13	1.11012
$962$	3.45995e13	1.30251
$963$	1.03994e13	0.389665
$964$	−5.84001e13	−2.17804
$965$	3.67657e13	1.36480
$966$	−5.29027e13	−1.95470
$967$	1.93571e13	0.711902	0.355951	−	0.934505i	$-0.384157\pi$
$967$	1.93571e13	0.711902	0.355951	+	0.934505i	$0.384157\pi$
$968$	−2.13469e14	−7.81439
$969$	9.28190e12	0.338205
$970$	1.23239e13	0.446966
$971$	−2.51710e13	−0.908686	−0.454343	−	0.890827i	$-0.650126\pi$
$971$	−2.51710e13	−0.908686	−0.454343	+	0.890827i	$0.650126\pi$
$972$	−4.67618e12	−0.168032
$973$	−5.26472e13	−1.88307
$974$	3.84270e13	1.36811
$975$	2.06065e11	0.00730269
$976$	−1.23123e14	−4.34325
$977$	5.15806e13	1.81118	0.905589	−	0.424156i	$-0.139429\pi$
$977$	5.15806e13	1.81118	0.905589	+	0.424156i	$0.139429\pi$
$978$	−2.82546e12	−0.0987561
$979$	−8.48034e13	−2.95047
$980$	9.03105e13	3.12767
$981$	−1.42564e12	−0.0491473
$982$	−6.13461e13	−2.10516
$983$	1.68835e13	0.576730	0.288365	−	0.957521i	$-0.406888\pi$
$983$	1.68835e13	0.576730	0.288365	+	0.957521i	$0.406888\pi$
$984$	3.13684e13	1.06663
$985$	1.14370e13	0.387122
$986$	−7.21139e12	−0.242981
$987$	−4.95750e13	−1.66278
$988$	−6.96818e13	−2.32655
$989$	6.85911e12	0.227974
$990$	3.62883e13	1.20063
$991$	−5.05426e12	−0.166466	−0.0832331	−	0.996530i	$-0.526525\pi$
$991$	−5.05426e12	−0.166466	−0.0832331	+	0.996530i	$0.526525\pi$
$992$	1.36747e14	4.48347
$993$	1.27275e13	0.415406
$994$	1.54194e13	0.500989
$995$	−1.78968e13	−0.578858
$996$	7.03995e13	2.26674
$997$	−1.81696e13	−0.582394	−0.291197	−	0.956663i	$-0.594054\pi$
$997$	−1.81696e13	−0.582394	−0.291197	+	0.956663i	$0.594054\pi$
$998$	−8.23641e13	−2.62815
$999$	−4.44946e12	−0.141339

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} -60567.9 q^{10} -91317.4 q^{11} -108630. q^{12} -95999.0 q^{13} -404316. q^{14} -113966. q^{15} +849797. q^{16} -211722. q^{17} -282437. q^{18} +541235. q^{19} +1.88694e6 q^{20} -760773. q^{21} +3.93101e6 q^{22} -1.61537e6 q^{23} +2.89102e6 q^{24} +26500.4 q^{25} +4.13255e6 q^{26} -531441. q^{27} +1.25961e7 q^{28} -791228. q^{29} +4.90600e6 q^{30} -7.46932e6 q^{31} -1.83078e7 q^{32} +7.39671e6 q^{33} +9.11416e6 q^{34} +1.32148e7 q^{35} +8.79906e6 q^{36} +8.37244e6 q^{37} -2.32990e7 q^{38} +7.77592e6 q^{39} -5.02179e7 q^{40} +1.08503e7 q^{41} +3.27496e7 q^{42} -4.24616e6 q^{43} -1.22467e8 q^{44} +9.23127e6 q^{45} +6.95381e7 q^{46} +6.51641e7 q^{47} -6.88335e7 q^{48} +4.78609e7 q^{49} -1.14078e6 q^{50} +1.71495e7 q^{51} -1.28746e8 q^{52} -3.72234e7 q^{53} +2.28774e7 q^{54} -1.28483e8 q^{55} -3.35225e8 q^{56} -4.38401e7 q^{57} +3.40607e7 q^{58} +1.21174e7 q^{59} -1.52842e8 q^{60} -1.44885e8 q^{61} +3.21538e8 q^{62} +6.16226e7 q^{63} +3.53015e8 q^{64} -1.35070e8 q^{65} -3.18412e8 q^{66} +7.39201e7 q^{67} -2.83943e8 q^{68} +1.30845e8 q^{69} -5.68870e8 q^{70} -3.81369e7 q^{71} -2.34173e8 q^{72} +3.89371e8 q^{73} -3.60415e8 q^{74} -2.14653e6 q^{75} +7.25859e8 q^{76} -8.57676e8 q^{77} -3.34737e8 q^{78} +6.34743e8 q^{79} +1.19566e9 q^{80} +4.30467e7 q^{81} -4.67081e8 q^{82} -6.48065e8 q^{83} -1.02028e9 q^{84} -2.97891e8 q^{85} +1.82788e8 q^{86} +6.40895e7 q^{87} +3.25927e9 q^{88} +9.28667e8 q^{89} -3.97386e8 q^{90} -9.01647e8 q^{91} -2.16640e9 q^{92} +6.05015e8 q^{93} -2.80517e9 q^{94} +7.61513e8 q^{95} +1.48293e9 q^{96} -2.03472e8 q^{97} -2.06031e9 q^{98} -5.99133e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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

Introduction

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