LMFDB - Embedded newform 177.10.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +2748.88 q^{10} +58546.2 q^{11} +40719.7 q^{12} -16581.3 q^{13} -4008.42 q^{14} +73060.1 q^{15} +247964. q^{16} -314209. q^{17} -19995.4 q^{18} -530644. q^{19} +453435. q^{20} -106537. q^{21} -178426. q^{22} -1.77605e6 q^{23} -250489. q^{24} -1.13956e6 q^{25} +50533.4 q^{26} -531441. q^{27} -661200. q^{28} -969983. q^{29} -222659. q^{30} -1.85049e6 q^{31} -2.33903e6 q^{32} -4.74224e6 q^{33} +957589. q^{34} -1.18634e6 q^{35} -3.29829e6 q^{36} -1.58532e7 q^{37} +1.61720e6 q^{38} +1.34309e6 q^{39} -2.78932e6 q^{40} +1.46562e7 q^{41} +324682. q^{42} +8.74387e6 q^{43} -2.94319e7 q^{44} -5.91787e6 q^{45} +5.41271e6 q^{46} +9.62436e6 q^{47} -2.00851e7 q^{48} -3.86237e7 q^{49} +3.47295e6 q^{50} +2.54510e7 q^{51} +8.33562e6 q^{52} +1.35914e7 q^{53} +1.61963e6 q^{54} -5.28073e7 q^{55} +4.06740e6 q^{56} +4.29821e7 q^{57} +2.95614e6 q^{58} +1.21174e7 q^{59} -3.67282e7 q^{60} +2.10664e8 q^{61} +5.63958e6 q^{62} +8.62946e6 q^{63} -1.19829e8 q^{64} +1.49560e7 q^{65} +1.44525e7 q^{66} -7.42783e7 q^{67} +1.57957e8 q^{68} +1.43860e8 q^{69} +3.61551e6 q^{70} -2.60132e8 q^{71} +2.02896e7 q^{72} +1.75339e8 q^{73} +4.83144e7 q^{74} +9.23046e7 q^{75} +2.66761e8 q^{76} +7.70038e7 q^{77} -4.09321e6 q^{78} +5.38457e6 q^{79} -2.23658e8 q^{80} +4.30467e7 q^{81} -4.46665e7 q^{82} +1.20469e8 q^{83} +5.35572e7 q^{84} +2.83410e8 q^{85} -2.66479e7 q^{86} +7.85687e7 q^{87} +1.81051e8 q^{88} -1.11762e9 q^{89} +1.80354e7 q^{90} -2.18088e7 q^{91} +8.92841e8 q^{92} +1.49890e8 q^{93} -2.93313e7 q^{94} +4.78628e8 q^{95} +1.89462e8 q^{96} -1.55196e9 q^{97} +1.17710e8 q^{98} +3.84122e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.04761	−0.134687	−0.0673434	−	0.997730i	$-0.521452\pi$
$2$	−3.04761	−0.134687	−0.0673434	+	0.997730i	$0.521452\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−502.712	−0.981859
$5$	−901.977	−0.645402	−0.322701	−	0.946501i	$-0.604591\pi$
$5$	−901.977	−0.645402	−0.322701	+	0.946501i	$0.604591\pi$
$6$	246.857	0.0777615
$7$	1315.27	0.207049	0.103524	−	0.994627i	$-0.466988\pi$
$7$	1315.27	0.207049	0.103524	+	0.994627i	$0.466988\pi$
$8$	3092.45	0.266930
$9$	6561.00	0.333333
$10$	2748.88	0.0869272
$11$	58546.2	1.20568	0.602839	−	0.797863i	$-0.294036\pi$
$11$	58546.2	1.20568	0.602839	+	0.797863i	$0.294036\pi$
$12$	40719.7	0.566877
$13$	−16581.3	−0.161018	−0.0805088	−	0.996754i	$-0.525655\pi$
$13$	−16581.3	−0.161018	−0.0805088	+	0.996754i	$0.525655\pi$
$14$	−4008.42	−0.0278867
$15$	73060.1	0.372623
$16$	247964.	0.945907
$17$	−314209.	−0.912429	−0.456214	−	0.889870i	$-0.650795\pi$
$17$	−314209.	−0.912429	−0.456214	+	0.889870i	$0.650795\pi$
$18$	−19995.4	−0.0448956
$19$	−530644.	−0.934139	−0.467070	−	0.884220i	$-0.654690\pi$
$19$	−530644.	−0.934139	−0.467070	+	0.884220i	$0.654690\pi$
$20$	453435.	0.633694
$21$	−106537.	−0.119540
$22$	−178426.	−0.162389
$23$	−1.77605e6	−1.32337	−0.661683	−	0.749784i	$-0.730157\pi$
$23$	−1.77605e6	−1.32337	−0.661683	+	0.749784i	$0.730157\pi$
$24$	−250489.	−0.154112
$25$	−1.13956e6	−0.583456
$26$	50533.4	0.0216870
$27$	−531441.	−0.192450
$28$	−661200.	−0.203293
$29$	−969983.	−0.254667	−0.127334	−	0.991860i	$-0.540642\pi$
$29$	−969983.	−0.254667	−0.127334	+	0.991860i	$0.540642\pi$
$30$	−222659.	−0.0501874
$31$	−1.85049e6	−0.359881	−0.179941	−	0.983677i	$-0.557591\pi$
$31$	−1.85049e6	−0.359881	−0.179941	+	0.983677i	$0.557591\pi$
$32$	−2.33903e6	−0.394332
$33$	−4.74224e6	−0.696099
$34$	957589.	0.122892
$35$	−1.18634e6	−0.133630
$36$	−3.29829e6	−0.327286
$37$	−1.58532e7	−1.39062	−0.695311	−	0.718709i	$-0.744733\pi$
$37$	−1.58532e7	−1.39062	−0.695311	+	0.718709i	$0.744733\pi$
$38$	1.61720e6	0.125816
$39$	1.34309e6	0.0929636
$40$	−2.78932e6	−0.172277
$41$	1.46562e7	0.810018	0.405009	−	0.914313i	$-0.367268\pi$
$41$	1.46562e7	0.810018	0.405009	+	0.914313i	$0.367268\pi$
$42$	324682.	0.0161004
$43$	8.74387e6	0.390028	0.195014	−	0.980800i	$-0.437525\pi$
$43$	8.74387e6	0.390028	0.195014	+	0.980800i	$0.437525\pi$
$44$	−2.94319e7	−1.18381
$45$	−5.91787e6	−0.215134
$46$	5.41271e6	0.178240
$47$	9.62436e6	0.287694	0.143847	−	0.989600i	$-0.454053\pi$
$47$	9.62436e6	0.287694	0.143847	+	0.989600i	$0.454053\pi$
$48$	−2.00851e7	−0.546120
$49$	−3.86237e7	−0.957131
$50$	3.47295e6	0.0785838
$51$	2.54510e7	0.526791
$52$	8.33562e6	0.158097
$53$	1.35914e7	0.236604	0.118302	−	0.992978i	$-0.462255\pi$
$53$	1.35914e7	0.236604	0.118302	+	0.992978i	$0.462255\pi$
$54$	1.61963e6	0.0259205
$55$	−5.28073e7	−0.778148
$56$	4.06740e6	0.0552676
$57$	4.29821e7	0.539326
$58$	2.95614e6	0.0343003
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−3.67282e7	−0.365864
$61$	2.10664e8	1.94807	0.974036	−	0.226393i	$-0.0726933\pi$
$61$	2.10664e8	1.94807	0.974036	+	0.226393i	$0.0726933\pi$
$62$	5.63958e6	0.0484712
$63$	8.62946e6	0.0690162
$64$	−1.19829e8	−0.892796
$65$	1.49560e7	0.103921
$66$	1.44525e7	0.0937553
$67$	−7.42783e7	−0.450324	−0.225162	−	0.974321i	$-0.572291\pi$
$67$	−7.42783e7	−0.450324	−0.225162	+	0.974321i	$0.572291\pi$
$68$	1.57957e8	0.895877
$69$	1.43860e8	0.764045
$70$	3.61551e6	0.0179982
$71$	−2.60132e8	−1.21487	−0.607436	−	0.794369i	$-0.707802\pi$
$71$	−2.60132e8	−1.21487	−0.607436	+	0.794369i	$0.707802\pi$
$72$	2.02896e7	0.0889768
$73$	1.75339e8	0.722648	0.361324	−	0.932440i	$-0.382325\pi$
$73$	1.75339e8	0.722648	0.361324	+	0.932440i	$0.382325\pi$
$74$	4.83144e7	0.187298
$75$	9.23046e7	0.336858
$76$	2.66761e8	0.917194
$77$	7.70038e7	0.249634
$78$	−4.09321e6	−0.0125210
$79$	5.38457e6	0.0155535	0.00777676	−	0.999970i	$-0.497525\pi$
$79$	5.38457e6	0.0155535	0.00777676	+	0.999970i	$0.497525\pi$
$80$	−2.23658e8	−0.610491
$81$	4.30467e7	0.111111
$82$	−4.46665e7	−0.109099
$83$	1.20469e8	0.278627	0.139314	−	0.990248i	$-0.455510\pi$
$83$	1.20469e8	0.278627	0.139314	+	0.990248i	$0.455510\pi$
$84$	5.35572e7	0.117371
$85$	2.83410e8	0.588883
$86$	−2.66479e7	−0.0525316
$87$	7.85687e7	0.147032
$88$	1.81051e8	0.321832
$89$	−1.11762e9	−1.88816	−0.944080	−	0.329717i	$-0.893047\pi$
$89$	−1.11762e9	−1.88816	−0.944080	+	0.329717i	$0.893047\pi$
$90$	1.80354e7	0.0289757
$91$	−2.18088e7	−0.0333385
$92$	8.92841e8	1.29936
$93$	1.49890e8	0.207777
$94$	−2.93313e7	−0.0387486
$95$	4.78628e8	0.602896
$96$	1.89462e8	0.227667
$97$	−1.55196e9	−1.77996	−0.889978	−	0.456004i	$-0.849280\pi$
$97$	−1.55196e9	−1.77996	−0.889978	+	0.456004i	$0.849280\pi$
$98$	1.17710e8	0.128913
$99$	3.84122e8	0.401893
$100$	5.72872e8	0.572872
$101$	−6.59584e8	−0.630702	−0.315351	−	0.948975i	$-0.602122\pi$
$101$	−6.59584e8	−0.630702	−0.315351	+	0.948975i	$0.602122\pi$
$102$	−7.75647e7	−0.0709518
$103$	−5.65496e8	−0.495065	−0.247532	−	0.968880i	$-0.579620\pi$
$103$	−5.65496e8	−0.495065	−0.247532	+	0.968880i	$0.579620\pi$
$104$	−5.12769e7	−0.0429805
$105$	9.60935e7	0.0771511
$106$	−4.14212e7	−0.0318674
$107$	2.46996e9	1.82164	0.910819	−	0.412805i	$-0.135451\pi$
$107$	2.46996e9	1.82164	0.910819	+	0.412805i	$0.135451\pi$
$108$	2.67162e8	0.188959
$109$	1.07908e7	0.00732205	0.00366103	−	0.999993i	$-0.498835\pi$
$109$	1.07908e7	0.00732205	0.00366103	+	0.999993i	$0.498835\pi$
$110$	1.60936e8	0.104806
$111$	1.28411e9	0.802875
$112$	3.26139e8	0.195849
$113$	2.28566e9	1.31874	0.659370	−	0.751819i	$-0.270823\pi$
$113$	2.28566e9	1.31874	0.659370	+	0.751819i	$0.270823\pi$
$114$	−1.30993e8	−0.0726400
$115$	1.60196e9	0.854103
$116$	4.87622e8	0.250048
$117$	−1.08790e8	−0.0536726
$118$	−3.69290e7	−0.0175347
$119$	−4.13269e8	−0.188917
$120$	2.25935e8	0.0994644
$121$	1.06971e9	0.453661
$122$	−6.42021e8	−0.262380
$123$	−1.18715e9	−0.467664
$124$	9.30263e8	0.353353
$125$	2.78953e9	1.02197
$126$	−2.62993e7	−0.00929557
$127$	−4.78876e9	−1.63345	−0.816726	−	0.577026i	$-0.804213\pi$
$127$	−4.78876e9	−1.63345	−0.816726	+	0.577026i	$0.804213\pi$
$128$	1.56278e9	0.514579
$129$	−7.08253e8	−0.225183
$130$	−4.55800e7	−0.0139968
$131$	−3.74607e9	−1.11136	−0.555680	−	0.831396i	$-0.687542\pi$
$131$	−3.74607e9	−1.11136	−0.555680	+	0.831396i	$0.687542\pi$
$132$	2.38398e9	0.683471
$133$	−6.97937e8	−0.193412
$134$	2.26372e8	0.0606528
$135$	4.79348e8	0.124208
$136$	−9.71677e8	−0.243555
$137$	6.96038e9	1.68807	0.844035	−	0.536288i	$-0.180174\pi$
$137$	6.96038e9	1.68807	0.844035	+	0.536288i	$0.180174\pi$
$138$	−4.38430e8	−0.102907
$139$	2.25010e9	0.511251	0.255626	−	0.966776i	$-0.417719\pi$
$139$	2.25010e9	0.511251	0.255626	+	0.966776i	$0.417719\pi$
$140$	5.96387e8	0.131206
$141$	−7.79573e8	−0.166100
$142$	7.92781e8	0.163627
$143$	−9.70772e8	−0.194136
$144$	1.62689e9	0.315302
$145$	8.74903e8	0.164363
$146$	−5.34367e8	−0.0973312
$147$	3.12852e9	0.552600
$148$	7.96959e9	1.36539
$149$	3.86787e9	0.642885	0.321443	−	0.946929i	$-0.395832\pi$
$149$	3.86787e9	0.642885	0.321443	+	0.946929i	$0.395832\pi$
$150$	−2.81309e8	−0.0453704
$151$	6.03451e9	0.944596	0.472298	−	0.881439i	$-0.343425\pi$
$151$	6.03451e9	0.944596	0.472298	+	0.881439i	$0.343425\pi$
$152$	−1.64099e9	−0.249350
$153$	−2.06153e9	−0.304143
$154$	−2.34678e8	−0.0336224
$155$	1.66910e9	0.232268
$156$	−6.75185e8	−0.0912772
$157$	1.04664e10	1.37483	0.687414	−	0.726266i	$-0.258746\pi$
$157$	1.04664e10	1.37483	0.687414	+	0.726266i	$0.258746\pi$
$158$	−1.64101e7	−0.00209485
$159$	−1.10090e9	−0.136603
$160$	2.10975e9	0.254502
$161$	−2.33598e9	−0.274001
$162$	−1.31190e8	−0.0149652
$163$	9.62382e9	1.06783	0.533916	−	0.845537i	$-0.320720\pi$
$163$	9.62382e9	1.06783	0.533916	+	0.845537i	$0.320720\pi$
$164$	−7.36786e9	−0.795324
$165$	4.27739e9	0.449264
$166$	−3.67143e8	−0.0375274
$167$	−7.42318e9	−0.738526	−0.369263	−	0.929325i	$-0.620390\pi$
$167$	−7.42318e9	−0.738526	−0.369263	+	0.929325i	$0.620390\pi$
$168$	−3.29459e8	−0.0319087
$169$	−1.03296e10	−0.974073
$170$	−8.63723e8	−0.0793148
$171$	−3.48155e9	−0.311380
$172$	−4.39565e9	−0.382952
$173$	1.62267e10	1.37728	0.688642	−	0.725102i	$-0.258207\pi$
$173$	1.62267e10	1.37728	0.688642	+	0.725102i	$0.258207\pi$
$174$	−2.39447e8	−0.0198033
$175$	−1.49883e9	−0.120804
$176$	1.45173e10	1.14046
$177$	−9.81506e8	−0.0751646
$178$	3.40607e9	0.254310
$179$	−5.30261e9	−0.386057	−0.193028	−	0.981193i	$-0.561831\pi$
$179$	−5.30261e9	−0.386057	−0.193028	+	0.981193i	$0.561831\pi$
$180$	2.97499e9	0.211231
$181$	−5.17037e9	−0.358070	−0.179035	−	0.983843i	$-0.557298\pi$
$181$	−5.17037e9	−0.358070	−0.179035	+	0.983843i	$0.557298\pi$
$182$	6.64649e7	0.00449025
$183$	−1.70637e10	−1.12472
$184$	−5.49235e9	−0.353246
$185$	1.42992e10	0.897510
$186$	−4.56806e8	−0.0279849
$187$	−1.83958e10	−1.10010
$188$	−4.83828e9	−0.282475
$189$	−6.98986e8	−0.0398465
$190$	−1.45867e9	−0.0812021
$191$	1.32702e10	0.721484	0.360742	−	0.932666i	$-0.382523\pi$
$191$	1.32702e10	0.721484	0.360742	+	0.932666i	$0.382523\pi$
$192$	9.70616e9	0.515456
$193$	3.53079e10	1.83174	0.915871	−	0.401473i	$-0.131502\pi$
$193$	3.53079e10	1.83174	0.915871	+	0.401473i	$0.131502\pi$
$194$	4.72979e9	0.239736
$195$	−1.21143e9	−0.0599989
$196$	1.94166e10	0.939768
$197$	−5.84038e9	−0.276276	−0.138138	−	0.990413i	$-0.544112\pi$
$197$	−5.84038e9	−0.276276	−0.138138	+	0.990413i	$0.544112\pi$
$198$	−1.17065e9	−0.0541297
$199$	2.30703e10	1.04283	0.521417	−	0.853302i	$-0.325404\pi$
$199$	2.30703e10	1.04283	0.521417	+	0.853302i	$0.325404\pi$
$200$	−3.52404e9	−0.155742
$201$	6.01654e9	0.259995
$202$	2.01016e9	0.0849472
$203$	−1.27579e9	−0.0527285
$204$	−1.27945e10	−0.517235
$205$	−1.32196e10	−0.522787
$206$	1.72341e9	0.0666787
$207$	−1.16527e10	−0.441122
$208$	−4.11157e9	−0.152308
$209$	−3.10672e10	−1.12627
$210$	−2.92856e8	−0.0103912
$211$	−9.86647e9	−0.342682	−0.171341	−	0.985212i	$-0.554810\pi$
$211$	−9.86647e9	−0.342682	−0.171341	+	0.985212i	$0.554810\pi$
$212$	−6.83254e9	−0.232312
$213$	2.10707e10	0.701407
$214$	−7.52747e9	−0.245351
$215$	−7.88677e9	−0.251725
$216$	−1.64346e9	−0.0513708
$217$	−2.43389e9	−0.0745129
$218$	−3.28861e7	−0.000986184 0
$219$	−1.42025e10	−0.417221
$220$	2.65469e10	0.764032
$221$	5.21000e9	0.146917
$222$	−3.91347e9	−0.108137
$223$	6.98728e10	1.89207	0.946033	−	0.324072i	$-0.105052\pi$
$223$	6.98728e10	1.89207	0.946033	+	0.324072i	$0.105052\pi$
$224$	−3.07645e9	−0.0816458
$225$	−7.47667e9	−0.194485
$226$	−6.96582e9	−0.177617
$227$	−5.38083e10	−1.34503	−0.672517	−	0.740082i	$-0.734787\pi$
$227$	−5.38083e10	−1.34503	−0.672517	+	0.740082i	$0.734787\pi$
$228$	−2.16076e10	−0.529542
$229$	3.90912e10	0.939333	0.469666	−	0.882844i	$-0.344374\pi$
$229$	3.90912e10	0.939333	0.469666	+	0.882844i	$0.344374\pi$
$230$	−4.88214e9	−0.115036
$231$	−6.23731e9	−0.144126
$232$	−2.99963e9	−0.0679784
$233$	−5.08792e10	−1.13094	−0.565469	−	0.824769i	$-0.691305\pi$
$233$	−5.08792e10	−1.13094	−0.565469	+	0.824769i	$0.691305\pi$
$234$	3.31550e8	0.00722898
$235$	−8.68095e9	−0.185679
$236$	−6.09154e9	−0.127827
$237$	−4.36150e8	−0.00897983
$238$	1.25948e9	0.0254446
$239$	−6.86409e10	−1.36079	−0.680397	−	0.732843i	$-0.738193\pi$
$239$	−6.86409e10	−1.36079	−0.680397	+	0.732843i	$0.738193\pi$
$240$	1.81163e10	0.352467
$241$	6.40754e10	1.22353	0.611765	−	0.791040i	$-0.290460\pi$
$241$	6.40754e10	1.22353	0.611765	+	0.791040i	$0.290460\pi$
$242$	−3.26006e9	−0.0611021
$243$	−3.48678e9	−0.0641500
$244$	−1.05903e11	−1.91273
$245$	3.48377e10	0.617734
$246$	3.61799e9	0.0629882
$247$	8.79876e9	0.150413
$248$	−5.72255e9	−0.0960632
$249$	−9.75798e9	−0.160865
$250$	−8.50142e9	−0.137645
$251$	−3.82370e10	−0.608067	−0.304034	−	0.952661i	$-0.598334\pi$
$251$	−3.82370e10	−0.608067	−0.304034	+	0.952661i	$0.598334\pi$
$252$	−4.33813e9	−0.0677642
$253$	−1.03981e11	−1.59555
$254$	1.45943e10	0.220004
$255$	−2.29562e10	−0.339992
$256$	5.65897e10	0.823489
$257$	2.41008e10	0.344613	0.172307	−	0.985043i	$-0.444878\pi$
$257$	2.41008e10	0.344613	0.172307	+	0.985043i	$0.444878\pi$
$258$	2.15848e9	0.0303291
$259$	−2.08512e10	−0.287926
$260$	−7.51854e9	−0.102036
$261$	−6.36406e9	−0.0848891
$262$	1.14166e10	0.149686
$263$	3.70783e10	0.477881	0.238940	−	0.971034i	$-0.423200\pi$
$263$	3.70783e10	0.477881	0.238940	+	0.971034i	$0.423200\pi$
$264$	−1.46651e10	−0.185810
$265$	−1.22591e10	−0.152705
$266$	2.12704e9	0.0260501
$267$	9.05271e10	1.09013
$268$	3.73406e10	0.442155
$269$	−9.07848e10	−1.05713	−0.528565	−	0.848893i	$-0.677270\pi$
$269$	−9.07848e10	−1.05713	−0.528565	+	0.848893i	$0.677270\pi$
$270$	−1.46087e9	−0.0167291
$271$	−1.00447e10	−0.113129	−0.0565647	−	0.998399i	$-0.518015\pi$
$271$	−1.00447e10	−0.113129	−0.0565647	+	0.998399i	$0.518015\pi$
$272$	−7.79126e10	−0.863073
$273$	1.76651e9	0.0192480
$274$	−2.12126e10	−0.227361
$275$	−6.67170e10	−0.703460
$276$	−7.23202e10	−0.750185
$277$	8.59336e10	0.877009	0.438505	−	0.898729i	$-0.355508\pi$
$277$	8.59336e10	0.877009	0.438505	+	0.898729i	$0.355508\pi$
$278$	−6.85742e9	−0.0688588
$279$	−1.21411e10	−0.119960
$280$	−3.66870e9	−0.0356698
$281$	−7.17150e10	−0.686169	−0.343085	−	0.939304i	$-0.611472\pi$
$281$	−7.17150e10	−0.686169	−0.343085	+	0.939304i	$0.611472\pi$
$282$	2.37584e9	0.0223715
$283$	−1.35746e11	−1.25803	−0.629013	−	0.777395i	$-0.716541\pi$
$283$	−1.35746e11	−1.25803	−0.629013	+	0.777395i	$0.716541\pi$
$284$	1.30771e11	1.19283
$285$	−3.87689e10	−0.348082
$286$	2.95854e9	0.0261475
$287$	1.92768e10	0.167713
$288$	−1.53464e10	−0.131444
$289$	−1.98604e10	−0.167474
$290$	−2.66637e9	−0.0221375
$291$	1.25709e11	1.02766
$292$	−8.81453e10	−0.709539
$293$	1.62874e10	0.129107	0.0645533	−	0.997914i	$-0.479438\pi$
$293$	1.62874e10	0.129107	0.0645533	+	0.997914i	$0.479438\pi$
$294$	−9.53452e9	−0.0744279
$295$	−1.09296e10	−0.0840242
$296$	−4.90252e10	−0.371199
$297$	−3.11138e10	−0.232033
$298$	−1.17878e10	−0.0865882
$299$	2.94492e10	0.213085
$300$	−4.64026e10	−0.330748
$301$	1.15005e10	0.0807547
$302$	−1.83909e10	−0.127225
$303$	5.34263e10	0.364136
$304$	−1.31580e11	−0.883610
$305$	−1.90014e11	−1.25729
$306$	6.28274e9	0.0409640
$307$	1.47734e11	0.949199	0.474600	−	0.880202i	$-0.342593\pi$
$307$	1.47734e11	0.949199	0.474600	+	0.880202i	$0.342593\pi$
$308$	−3.87107e10	−0.245106
$309$	4.58052e10	0.285826
$310$	−5.08677e9	−0.0312834
$311$	−1.58619e11	−0.961466	−0.480733	−	0.876867i	$-0.659629\pi$
$311$	−1.58619e11	−0.961466	−0.480733	+	0.876867i	$0.659629\pi$
$312$	4.15343e9	0.0248148
$313$	1.25095e11	0.736699	0.368350	−	0.929687i	$-0.379923\pi$
$313$	1.25095e11	0.736699	0.368350	+	0.929687i	$0.379923\pi$
$314$	−3.18975e10	−0.185171
$315$	−7.78357e9	−0.0445432
$316$	−2.70689e9	−0.0152714
$317$	−6.32118e10	−0.351586	−0.175793	−	0.984427i	$-0.556249\pi$
$317$	−6.32118e10	−0.351586	−0.175793	+	0.984427i	$0.556249\pi$
$318$	3.35512e9	0.0183987
$319$	−5.67888e10	−0.307047
$320$	1.08083e11	0.576213
$321$	−2.00066e11	−1.05172
$322$	7.11916e9	0.0369043
$323$	1.66733e11	0.852336
$324$	−2.16401e10	−0.109095
$325$	1.88954e10	0.0939467
$326$	−2.93297e10	−0.143823
$327$	−8.74052e8	−0.00422739
$328$	4.53237e10	0.216218
$329$	1.26586e10	0.0595667
$330$	−1.30358e10	−0.0605099
$331$	2.23089e11	1.02153	0.510767	−	0.859719i	$-0.329361\pi$
$331$	2.23089e11	1.02153	0.510767	+	0.859719i	$0.329361\pi$
$332$	−6.05611e10	−0.273573
$333$	−1.04013e11	−0.463540
$334$	2.26230e10	0.0994697
$335$	6.69973e10	0.290640
$336$	−2.64172e10	−0.113073
$337$	3.34285e11	1.41183	0.705914	−	0.708297i	$-0.250536\pi$
$337$	3.34285e11	1.41183	0.705914	+	0.708297i	$0.250536\pi$
$338$	3.14805e10	0.131195
$339$	−1.85139e11	−0.761375
$340$	−1.42473e11	−0.578201
$341$	−1.08339e11	−0.433901
$342$	1.06104e10	0.0419388
$343$	−1.03876e11	−0.405221
$344$	2.70400e10	0.104110
$345$	−1.29758e11	−0.493117
$346$	−4.94528e10	−0.185502
$347$	−6.46893e10	−0.239524	−0.119762	−	0.992803i	$-0.538213\pi$
$347$	−6.46893e10	−0.239524	−0.119762	+	0.992803i	$0.538213\pi$
$348$	−3.94974e10	−0.144365
$349$	8.16421e10	0.294578	0.147289	−	0.989094i	$-0.452945\pi$
$349$	8.16421e10	0.294578	0.147289	+	0.989094i	$0.452945\pi$
$350$	4.56785e9	0.0162707
$351$	8.81198e9	0.0309879
$352$	−1.36941e11	−0.475437
$353$	4.09816e11	1.40476	0.702381	−	0.711802i	$-0.252120\pi$
$353$	4.09816e11	1.40476	0.702381	+	0.711802i	$0.252120\pi$
$354$	2.99125e9	0.0101237
$355$	2.34633e11	0.784081
$356$	5.61841e11	1.85391
$357$	3.34748e10	0.109071
$358$	1.61603e10	0.0519967
$359$	5.01343e11	1.59298	0.796490	−	0.604652i	$-0.206688\pi$
$359$	5.01343e11	1.59298	0.796490	+	0.604652i	$0.206688\pi$
$360$	−1.83007e10	−0.0574258
$361$	−4.11051e10	−0.127383
$362$	1.57573e10	0.0482273
$363$	−8.66464e10	−0.261921
$364$	1.09636e10	0.0327337
$365$	−1.58152e11	−0.466399
$366$	5.20037e10	0.151485
$367$	−3.40745e11	−0.980465	−0.490233	−	0.871592i	$-0.663088\pi$
$367$	−3.40745e11	−0.980465	−0.490233	+	0.871592i	$0.663088\pi$
$368$	−4.40396e11	−1.25178
$369$	9.61595e10	0.270006
$370$	−4.35785e10	−0.120883
$371$	1.78763e10	0.0489885
$372$	−7.53513e10	−0.204008
$373$	3.56680e11	0.954088	0.477044	−	0.878879i	$-0.341708\pi$
$373$	3.56680e11	0.954088	0.477044	+	0.878879i	$0.341708\pi$
$374$	5.60632e10	0.148168
$375$	−2.25952e11	−0.590032
$376$	2.97629e10	0.0767944
$377$	1.60836e10	0.0410059
$378$	2.13024e9	0.00536680
$379$	1.35033e11	0.336174	0.168087	−	0.985772i	$-0.446241\pi$
$379$	1.35033e11	0.336174	0.168087	+	0.985772i	$0.446241\pi$
$380$	−2.40612e11	−0.591959
$381$	3.87889e11	0.943073
$382$	−4.04424e10	−0.0971744
$383$	3.10673e11	0.737749	0.368874	−	0.929479i	$-0.379743\pi$
$383$	3.10673e11	0.737749	0.368874	+	0.929479i	$0.379743\pi$
$384$	−1.26585e11	−0.297093
$385$	−6.94557e10	−0.161114
$386$	−1.07605e11	−0.246711
$387$	5.73685e10	0.130009
$388$	7.80191e11	1.74767
$389$	−2.90209e11	−0.642596	−0.321298	−	0.946978i	$-0.604119\pi$
$389$	−2.90209e11	−0.642596	−0.321298	+	0.946978i	$0.604119\pi$
$390$	3.69198e9	0.00808106
$391$	5.58051e11	1.20748
$392$	−1.19442e11	−0.255487
$393$	3.03432e11	0.641644
$394$	1.77992e10	0.0372107
$395$	−4.85675e9	−0.0100383
$396$	−1.93103e11	−0.394602
$397$	4.88071e11	0.986110	0.493055	−	0.869998i	$-0.335880\pi$
$397$	4.88071e11	0.986110	0.493055	+	0.869998i	$0.335880\pi$
$398$	−7.03095e10	−0.140456
$399$	5.65329e10	0.111667
$400$	−2.82570e11	−0.551895
$401$	−9.52691e11	−1.83993	−0.919967	−	0.391996i	$-0.871785\pi$
$401$	−9.52691e11	−1.83993	−0.919967	+	0.391996i	$0.871785\pi$
$402$	−1.83361e10	−0.0350179
$403$	3.06835e10	0.0579472
$404$	3.31581e11	0.619261
$405$	−3.88272e10	−0.0717114
$406$	3.88810e9	0.00710184
$407$	−9.28144e11	−1.67664
$408$	7.87058e10	0.140616
$409$	9.64628e11	1.70453	0.852265	−	0.523110i	$-0.175228\pi$
$409$	9.64628e11	1.70453	0.852265	+	0.523110i	$0.175228\pi$
$410$	4.02882e10	0.0704126
$411$	−5.63791e11	−0.974608
$412$	2.84282e11	0.486084
$413$	1.59376e10	0.0269554
$414$	3.55128e10	0.0594133
$415$	−1.08660e11	−0.179827
$416$	3.87842e10	0.0634943
$417$	−1.82258e11	−0.295171
$418$	9.46807e10	0.151694
$419$	4.13312e11	0.655111	0.327556	−	0.944832i	$-0.393775\pi$
$419$	4.13312e11	0.655111	0.327556	+	0.944832i	$0.393775\pi$
$420$	−4.83074e10	−0.0757516
$421$	8.80319e10	0.136575	0.0682874	−	0.997666i	$-0.478247\pi$
$421$	8.80319e10	0.136575	0.0682874	+	0.997666i	$0.478247\pi$
$422$	3.00692e10	0.0461547
$423$	6.31454e10	0.0958981
$424$	4.20306e10	0.0631567
$425$	3.58061e11	0.532362
$426$	−6.42152e10	−0.0944702
$427$	2.77079e11	0.403346
$428$	−1.24168e12	−1.78859
$429$	7.86325e10	0.112084
$430$	2.40358e10	0.0339040
$431$	1.23323e12	1.72146	0.860730	−	0.509062i	$-0.170008\pi$
$431$	1.23323e12	1.72146	0.860730	+	0.509062i	$0.170008\pi$
$432$	−1.31778e11	−0.182040
$433$	1.16757e12	1.59620	0.798098	−	0.602528i	$-0.205840\pi$
$433$	1.16757e12	1.59620	0.798098	+	0.602528i	$0.205840\pi$
$434$	7.41755e9	0.0100359
$435$	−7.08671e10	−0.0948950
$436$	−5.42465e9	−0.00718923
$437$	9.42449e11	1.23621
$438$	4.32837e10	0.0561942
$439$	8.59317e11	1.10424	0.552119	−	0.833765i	$-0.313819\pi$
$439$	8.59317e11	1.10424	0.552119	+	0.833765i	$0.313819\pi$
$440$	−1.63304e11	−0.207711
$441$	−2.53410e11	−0.319044
$442$	−1.58781e10	−0.0197878
$443$	−9.24505e11	−1.14049	−0.570246	−	0.821474i	$-0.693152\pi$
$443$	−9.24505e11	−1.14049	−0.570246	+	0.821474i	$0.693152\pi$
$444$	−6.45537e11	−0.788311
$445$	1.00807e12	1.21862
$446$	−2.12945e11	−0.254836
$447$	−3.13297e11	−0.371170
$448$	−1.57607e11	−0.184852
$449$	−2.10652e11	−0.244600	−0.122300	−	0.992493i	$-0.539027\pi$
$449$	−2.10652e11	−0.244600	−0.122300	+	0.992493i	$0.539027\pi$
$450$	2.27860e10	0.0261946
$451$	8.58066e11	0.976622
$452$	−1.14903e12	−1.29482
$453$	−4.88795e11	−0.545362
$454$	1.63987e11	0.181158
$455$	1.96711e10	0.0215167
$456$	1.32920e11	0.143962
$457$	−6.63413e11	−0.711477	−0.355738	−	0.934586i	$-0.615771\pi$
$457$	−6.63413e11	−0.711477	−0.355738	+	0.934586i	$0.615771\pi$
$458$	−1.19135e11	−0.126516
$459$	1.66984e11	0.175597
$460$	−8.05322e11	−0.838609
$461$	2.75456e11	0.284052	0.142026	−	0.989863i	$-0.454638\pi$
$461$	2.75456e11	0.284052	0.142026	+	0.989863i	$0.454638\pi$
$462$	1.90089e10	0.0194119
$463$	−1.19847e11	−0.121203	−0.0606015	−	0.998162i	$-0.519302\pi$
$463$	−1.19847e11	−0.121203	−0.0606015	+	0.998162i	$0.519302\pi$
$464$	−2.40521e11	−0.240892
$465$	−1.35197e11	−0.134100
$466$	1.55060e11	0.152322
$467$	1.61766e12	1.57384	0.786922	−	0.617052i	$-0.211673\pi$
$467$	1.61766e12	1.57384	0.786922	+	0.617052i	$0.211673\pi$
$468$	5.46900e10	0.0526989
$469$	−9.76958e10	−0.0932391
$470$	2.64562e10	0.0250085
$471$	−8.47777e11	−0.793757
$472$	3.74723e10	0.0347514
$473$	5.11920e11	0.470248
$474$	1.32922e9	0.00120946
$475$	6.04702e11	0.545029
$476$	2.07755e11	0.185490
$477$	8.91729e10	0.0788679
$478$	2.09191e11	0.183281
$479$	−1.35413e12	−1.17531	−0.587653	−	0.809113i	$-0.699948\pi$
$479$	−1.35413e12	−1.17531	−0.587653	+	0.809113i	$0.699948\pi$
$480$	−1.70890e11	−0.146937
$481$	2.62866e11	0.223915
$482$	−1.95277e11	−0.164793
$483$	1.89214e11	0.158195
$484$	−5.37755e11	−0.445431
$485$	1.39984e12	1.14879
$486$	1.06264e10	0.00864016
$487$	−3.58121e10	−0.0288502	−0.0144251	−	0.999896i	$-0.504592\pi$
$487$	−3.58121e10	−0.0288502	−0.0144251	+	0.999896i	$0.504592\pi$
$488$	6.51467e11	0.519999
$489$	−7.79529e11	−0.616514
$490$	−1.06172e11	−0.0832007
$491$	1.75049e12	1.35923	0.679616	−	0.733568i	$-0.262146\pi$
$491$	1.75049e12	1.35923	0.679616	+	0.733568i	$0.262146\pi$
$492$	5.96797e11	0.459181
$493$	3.04778e11	0.232366
$494$	−2.68152e10	−0.0202586
$495$	−3.46469e11	−0.259383
$496$	−4.58855e11	−0.340414
$497$	−3.42142e11	−0.251538
$498$	2.97385e10	0.0216664
$499$	2.12252e12	1.53250	0.766248	−	0.642545i	$-0.222121\pi$
$499$	2.12252e12	1.53250	0.766248	+	0.642545i	$0.222121\pi$
$500$	−1.40233e12	−1.00343
$501$	6.01277e11	0.426388
$502$	1.16532e11	0.0818987
$503$	−1.34616e12	−0.937651	−0.468826	−	0.883291i	$-0.655323\pi$
$503$	−1.34616e12	−0.937651	−0.468826	+	0.883291i	$0.655323\pi$
$504$	2.66862e10	0.0184225
$505$	5.94930e11	0.407056
$506$	3.16894e11	0.214900
$507$	8.36694e11	0.562381
$508$	2.40737e12	1.60382
$509$	−1.19438e12	−0.788704	−0.394352	−	0.918959i	$-0.629031\pi$
$509$	−1.19438e12	−0.788704	−0.394352	+	0.918959i	$0.629031\pi$
$510$	6.99616e10	0.0457924
$511$	2.30618e11	0.149623
$512$	−9.72606e11	−0.625493
$513$	2.82006e11	0.179775
$514$	−7.34499e10	−0.0464149
$515$	5.10064e11	0.319516
$516$	3.56047e11	0.221098
$517$	5.63469e11	0.346867
$518$	6.35463e10	0.0387799
$519$	−1.31436e12	−0.795175
$520$	4.62505e10	0.0277397
$521$	−2.86170e11	−0.170159	−0.0850795	−	0.996374i	$-0.527114\pi$
$521$	−2.86170e11	−0.170159	−0.0850795	+	0.996374i	$0.527114\pi$
$522$	1.93952e10	0.0114334
$523$	7.15569e11	0.418210	0.209105	−	0.977893i	$-0.432945\pi$
$523$	7.15569e11	0.418210	0.209105	+	0.977893i	$0.432945\pi$
$524$	1.88319e12	1.09120
$525$	1.21405e11	0.0697461
$526$	−1.13001e11	−0.0643642
$527$	5.81441e11	0.328366
$528$	−1.17590e12	−0.658445
$529$	1.35320e12	0.751296
$530$	3.73610e10	0.0205673
$531$	7.95020e10	0.0433963
$532$	3.50862e11	0.189904
$533$	−2.43019e11	−0.130427
$534$	−2.75892e11	−0.146826
$535$	−2.22784e12	−1.17569
$536$	−2.29702e11	−0.120205
$537$	4.29511e11	0.222890
$538$	2.76677e11	0.142381
$539$	−2.26127e12	−1.15399
$540$	−2.40974e11	−0.121955
$541$	−1.19257e12	−0.598546	−0.299273	−	0.954168i	$-0.596744\pi$
$541$	−1.19257e12	−0.598546	−0.299273	+	0.954168i	$0.596744\pi$
$542$	3.06124e10	0.0152370
$543$	4.18800e11	0.206732
$544$	7.34946e11	0.359799
$545$	−9.73302e9	−0.00472567
$546$	−5.38366e9	−0.00259245
$547$	−1.17324e12	−0.560329	−0.280164	−	0.959952i	$-0.590389\pi$
$547$	−1.17324e12	−0.560329	−0.280164	+	0.959952i	$0.590389\pi$
$548$	−3.49907e12	−1.65745
$549$	1.38216e12	0.649357
$550$	2.03328e11	0.0947468
$551$	5.14715e11	0.237895
$552$	4.44880e11	0.203947
$553$	7.08214e9	0.00322034
$554$	−2.61893e11	−0.118122
$555$	−1.15824e12	−0.518178
$556$	−1.13115e12	−0.501977
$557$	−3.52276e12	−1.55072	−0.775362	−	0.631517i	$-0.782433\pi$
$557$	−3.52276e12	−1.55072	−0.775362	+	0.631517i	$0.782433\pi$
$558$	3.70013e10	0.0161571
$559$	−1.44985e11	−0.0628014
$560$	−2.94170e11	−0.126401
$561$	1.49006e12	0.635141
$562$	2.18560e11	0.0924180
$563$	−2.82214e11	−0.118383	−0.0591917	−	0.998247i	$-0.518852\pi$
$563$	−2.82214e11	−0.118383	−0.0591917	+	0.998247i	$0.518852\pi$
$564$	3.91901e11	0.163087
$565$	−2.06161e12	−0.851117
$566$	4.13703e11	0.169439
$567$	5.66179e10	0.0230054
$568$	−8.04444e11	−0.324286
$569$	7.84903e11	0.313914	0.156957	−	0.987605i	$-0.449832\pi$
$569$	7.84903e11	0.313914	0.156957	+	0.987605i	$0.449832\pi$
$570$	1.18153e11	0.0468820
$571$	−4.58710e12	−1.80583	−0.902913	−	0.429824i	$-0.858575\pi$
$571$	−4.58710e12	−1.80583	−0.902913	+	0.429824i	$0.858575\pi$
$572$	4.88019e11	0.190614
$573$	−1.07488e12	−0.416549
$574$	−5.87484e10	−0.0225887
$575$	2.02392e12	0.772125
$576$	−7.86199e11	−0.297599
$577$	5.80964e11	0.218202	0.109101	−	0.994031i	$-0.465203\pi$
$577$	5.80964e11	0.218202	0.109101	+	0.994031i	$0.465203\pi$
$578$	6.05267e10	0.0225565
$579$	−2.85994e12	−1.05756
$580$	−4.39824e11	−0.161381
$581$	1.58449e11	0.0576894
$582$	−3.83113e11	−0.138412
$583$	7.95722e11	0.285268
$584$	5.42229e11	0.192897
$585$	9.81260e10	0.0346404
$586$	−4.96378e10	−0.0173890
$587$	1.82522e12	0.634518	0.317259	−	0.948339i	$-0.397238\pi$
$587$	1.82522e12	0.634518	0.317259	+	0.948339i	$0.397238\pi$
$588$	−1.57274e12	−0.542575
$589$	9.81950e11	0.336179
$590$	3.33091e10	0.0113170
$591$	4.73071e11	0.159508
$592$	−3.93102e12	−1.31540
$593$	−5.13878e12	−1.70653	−0.853265	−	0.521478i	$-0.825381\pi$
$593$	−5.13878e12	−1.70653	−0.853265	+	0.521478i	$0.825381\pi$
$594$	9.48230e10	0.0312518
$595$	3.72759e11	0.121928
$596$	−1.94442e12	−0.631223
$597$	−1.86870e12	−0.602080
$598$	−8.97498e10	−0.0286998
$599$	−1.31947e12	−0.418774	−0.209387	−	0.977833i	$-0.567147\pi$
$599$	−1.31947e12	−0.418774	−0.209387	+	0.977833i	$0.567147\pi$
$600$	2.85447e11	0.0899177
$601$	−1.88238e12	−0.588535	−0.294267	−	0.955723i	$-0.595076\pi$
$601$	−1.88238e12	−0.588535	−0.294267	+	0.955723i	$0.595076\pi$
$602$	−3.50491e10	−0.0108766
$603$	−4.87340e11	−0.150108
$604$	−3.03362e12	−0.927460
$605$	−9.64853e11	−0.292794
$606$	−1.62823e11	−0.0490443
$607$	1.29228e12	0.386372	0.193186	−	0.981162i	$-0.438118\pi$
$607$	1.29228e12	0.386372	0.193186	+	0.981162i	$0.438118\pi$
$608$	1.24119e12	0.368361
$609$	1.03339e11	0.0304428
$610$	5.79088e11	0.169340
$611$	−1.59584e11	−0.0463239
$612$	1.03635e12	0.298626
$613$	−2.00466e12	−0.573415	−0.286707	−	0.958018i	$-0.592561\pi$
$613$	−2.00466e12	−0.573415	−0.286707	+	0.958018i	$0.592561\pi$
$614$	−4.50236e11	−0.127845
$615$	1.07079e12	0.301832
$616$	2.38131e11	0.0666349
$617$	−2.59273e12	−0.720235	−0.360118	−	0.932907i	$-0.617263\pi$
$617$	−2.59273e12	−0.720235	−0.360118	+	0.932907i	$0.617263\pi$
$618$	−1.39596e11	−0.0384969
$619$	−6.08895e12	−1.66700	−0.833498	−	0.552522i	$-0.813665\pi$
$619$	−6.08895e12	−1.66700	−0.833498	+	0.552522i	$0.813665\pi$
$620$	−8.39076e11	−0.228055
$621$	9.43865e11	0.254682
$622$	4.83410e11	0.129497
$623$	−1.46997e12	−0.390941
$624$	3.33037e11	0.0879350
$625$	−2.90387e11	−0.0761231
$626$	−3.81241e11	−0.0992237
$627$	2.51644e12	0.650253
$628$	−5.26158e12	−1.34989
$629$	4.98122e12	1.26884
$630$	2.37213e10	0.00599938
$631$	2.63247e12	0.661046	0.330523	−	0.943798i	$-0.392775\pi$
$631$	2.63247e12	0.661046	0.330523	+	0.943798i	$0.392775\pi$
$632$	1.66515e10	0.00415171
$633$	7.99184e11	0.197847
$634$	1.92645e11	0.0473540
$635$	4.31935e12	1.05423
$636$	5.53436e11	0.134125
$637$	6.40431e11	0.154115
$638$	1.73070e11	0.0413552
$639$	−1.70672e12	−0.404957
$640$	−1.40959e12	−0.332111
$641$	−3.27779e12	−0.766867	−0.383434	−	0.923568i	$-0.625259\pi$
$641$	−3.27779e12	−0.766867	−0.383434	+	0.923568i	$0.625259\pi$
$642$	6.09725e11	0.141653
$643$	−1.69121e12	−0.390166	−0.195083	−	0.980787i	$-0.562498\pi$
$643$	−1.69121e12	−0.390166	−0.195083	+	0.980787i	$0.562498\pi$
$644$	1.17432e12	0.269031
$645$	6.38828e11	0.145333
$646$	−5.08138e11	−0.114798
$647$	−5.65660e11	−0.126907	−0.0634535	−	0.997985i	$-0.520211\pi$
$647$	−5.65660e11	−0.126907	−0.0634535	+	0.997985i	$0.520211\pi$
$648$	1.33120e11	0.0296589
$649$	7.09425e11	0.156966
$650$	−5.75860e10	−0.0126534
$651$	1.97145e11	0.0430200
$652$	−4.83801e12	−1.04846
$653$	−6.06730e10	−0.0130583	−0.00652914	−	0.999979i	$-0.502078\pi$
$653$	−6.06730e10	−0.0130583	−0.00652914	+	0.999979i	$0.502078\pi$
$654$	2.66377e9	0.000569374 0
$655$	3.37887e12	0.717274
$656$	3.63422e12	0.766202
$657$	1.15040e12	0.240883
$658$	−3.85785e10	−0.00802285
$659$	1.77971e12	0.367590	0.183795	−	0.982965i	$-0.441162\pi$
$659$	1.77971e12	0.367590	0.183795	+	0.982965i	$0.441162\pi$
$660$	−2.15030e12	−0.441114
$661$	4.30203e12	0.876530	0.438265	−	0.898846i	$-0.355593\pi$
$661$	4.30203e12	0.876530	0.438265	+	0.898846i	$0.355593\pi$
$662$	−6.79890e11	−0.137587
$663$	−4.22010e11	−0.0848226
$664$	3.72544e11	0.0743740
$665$	6.29524e11	0.124829
$666$	3.16991e11	0.0624328
$667$	1.72274e12	0.337018
$668$	3.73172e12	0.725128
$669$	−5.65969e12	−1.09238
$670$	−2.04182e11	−0.0391454
$671$	1.23335e13	2.34875
$672$	2.49193e11	0.0471382
$673$	4.39676e12	0.826162	0.413081	−	0.910694i	$-0.364453\pi$
$673$	4.39676e12	0.826162	0.413081	+	0.910694i	$0.364453\pi$
$674$	−1.01877e12	−0.190155
$675$	6.05610e11	0.112286
$676$	5.19279e12	0.956403
$677$	−1.43011e12	−0.261650	−0.130825	−	0.991405i	$-0.541763\pi$
$677$	−1.43011e12	−0.261650	−0.130825	+	0.991405i	$0.541763\pi$
$678$	5.64231e11	0.102547
$679$	−2.04125e12	−0.368537
$680$	8.76430e11	0.157191
$681$	4.35847e12	0.776555
$682$	3.30176e11	0.0584407
$683$	3.56294e12	0.626492	0.313246	−	0.949672i	$-0.398584\pi$
$683$	3.56294e12	0.626492	0.313246	+	0.949672i	$0.398584\pi$
$684$	1.75022e12	0.305731
$685$	−6.27811e12	−1.08948
$686$	3.16574e11	0.0545780
$687$	−3.16639e12	−0.542324
$688$	2.16816e12	0.368930
$689$	−2.25362e11	−0.0380974
$690$	3.95454e11	0.0664163
$691$	6.12100e12	1.02134	0.510671	−	0.859776i	$-0.329397\pi$
$691$	6.12100e12	1.02134	0.510671	+	0.859776i	$0.329397\pi$
$692$	−8.15737e12	−1.35230
$693$	5.05222e11	0.0832114
$694$	1.97148e11	0.0322608
$695$	−2.02953e12	−0.329963
$696$	2.42970e11	0.0392474
$697$	−4.60512e12	−0.739084
$698$	−2.48814e11	−0.0396757
$699$	4.12122e12	0.652948
$700$	7.53479e11	0.118612
$701$	−2.36726e12	−0.370266	−0.185133	−	0.982713i	$-0.559272\pi$
$701$	−2.36726e12	−0.370266	−0.185133	+	0.982713i	$0.559272\pi$
$702$	−2.68555e10	−0.00417366
$703$	8.41239e12	1.29903
$704$	−7.01554e12	−1.07643
$705$	7.03157e11	0.107202
$706$	−1.24896e12	−0.189203
$707$	−8.67529e11	−0.130586
$708$	4.93415e11	0.0738011
$709$	1.21948e13	1.81245	0.906224	−	0.422798i	$-0.138952\pi$
$709$	1.21948e13	1.81245	0.906224	+	0.422798i	$0.138952\pi$
$710$	−7.15070e11	−0.105605
$711$	3.53281e10	0.00518451
$712$	−3.45618e12	−0.504007
$713$	3.28656e12	0.476254
$714$	−1.02018e11	−0.0146905
$715$	8.75614e11	0.125296
$716$	2.66569e12	0.379053
$717$	5.55992e12	0.785655
$718$	−1.52790e12	−0.214553
$719$	2.87521e12	0.401226	0.200613	−	0.979671i	$-0.435707\pi$
$719$	2.87521e12	0.401226	0.200613	+	0.979671i	$0.435707\pi$
$720$	−1.46742e12	−0.203497
$721$	−7.43777e11	−0.102502
$722$	1.25272e11	0.0171569
$723$	−5.19010e12	−0.706405
$724$	2.59921e12	0.351574
$725$	1.10536e12	0.148587
$726$	2.64065e11	0.0352773
$727$	6.04263e12	0.802272	0.401136	−	0.916019i	$-0.368616\pi$
$727$	6.04263e12	0.802272	0.401136	+	0.916019i	$0.368616\pi$
$728$	−6.74427e10	−0.00889905
$729$	2.82430e11	0.0370370
$730$	4.81987e11	0.0628177
$731$	−2.74740e12	−0.355873
$732$	8.57815e12	1.10432
$733$	−3.93902e12	−0.503988	−0.251994	−	0.967729i	$-0.581086\pi$
$733$	−3.93902e12	−0.503988	−0.251994	+	0.967729i	$0.581086\pi$
$734$	1.03846e12	0.132056
$735$	−2.82185e12	−0.356649
$736$	4.15424e12	0.521845
$737$	−4.34871e12	−0.542946
$738$	−2.93057e11	−0.0363662
$739$	−1.10501e13	−1.36290	−0.681451	−	0.731863i	$-0.738651\pi$
$739$	−1.10501e13	−1.36290	−0.681451	+	0.731863i	$0.738651\pi$
$740$	−7.18839e12	−0.881229
$741$	−7.12700e11	−0.0868410
$742$	−5.44799e10	−0.00659810
$743$	1.30929e13	1.57611	0.788054	−	0.615606i	$-0.211089\pi$
$743$	1.30929e13	1.57611	0.788054	+	0.615606i	$0.211089\pi$
$744$	4.63526e11	0.0554621
$745$	−3.48873e12	−0.414920
$746$	−1.08702e12	−0.128503
$747$	7.90396e11	0.0928757
$748$	9.24777e12	1.08014
$749$	3.24865e12	0.377168
$750$	6.88615e11	0.0794696
$751$	−1.04795e12	−0.120216	−0.0601080	−	0.998192i	$-0.519145\pi$
$751$	−1.04795e12	−0.120216	−0.0601080	+	0.998192i	$0.519145\pi$
$752$	2.38649e12	0.272132
$753$	3.09719e12	0.351068
$754$	−4.90166e10	−0.00552296
$755$	−5.44299e12	−0.609644
$756$	3.51389e11	0.0391237
$757$	1.14401e13	1.26619	0.633094	−	0.774075i	$-0.281785\pi$
$757$	1.14401e13	1.26619	0.633094	+	0.774075i	$0.281785\pi$
$758$	−4.11529e11	−0.0452781
$759$	8.42245e12	0.921193
$760$	1.48013e12	0.160931
$761$	1.01121e13	1.09297	0.546485	−	0.837469i	$-0.315966\pi$
$761$	1.01121e13	1.09297	0.546485	+	0.837469i	$0.315966\pi$
$762$	−1.18214e12	−0.127020
$763$	1.41927e10	0.00151602
$764$	−6.67108e12	−0.708396
$765$	1.85945e12	0.196294
$766$	−9.46810e11	−0.0993650
$767$	−2.00922e11	−0.0209627
$768$	−4.58377e12	−0.475442
$769$	−5.58480e11	−0.0575890	−0.0287945	−	0.999585i	$-0.509167\pi$
$769$	−5.58480e11	−0.0575890	−0.0287945	+	0.999585i	$0.509167\pi$
$770$	2.11674e11	0.0217000
$771$	−1.95216e12	−0.198963
$772$	−1.77497e13	−1.79851
$773$	5.41948e11	0.0545946	0.0272973	−	0.999627i	$-0.491310\pi$
$773$	5.41948e11	0.0545946	0.0272973	+	0.999627i	$0.491310\pi$
$774$	−1.74837e11	−0.0175105
$775$	2.10875e12	0.209975
$776$	−4.79937e12	−0.475124
$777$	1.68894e12	0.166234
$778$	8.84445e11	0.0865491
$779$	−7.77723e12	−0.756670
$780$	6.09002e11	0.0589105
$781$	−1.52297e13	−1.46475
$782$	−1.70073e12	−0.162631
$783$	5.15489e11	0.0490108
$784$	−9.57728e12	−0.905357
$785$	−9.44044e12	−0.887317
$786$	−9.24742e11	−0.0864210
$787$	4.03856e12	0.375267	0.187633	−	0.982239i	$-0.439918\pi$
$787$	4.03856e12	0.375267	0.187633	+	0.982239i	$0.439918\pi$
$788$	2.93603e12	0.271264
$789$	−3.00335e12	−0.275905
$790$	1.48015e10	0.00135202
$791$	3.00625e12	0.273043
$792$	1.18788e12	0.107277
$793$	−3.49307e12	−0.313674
$794$	−1.48745e12	−0.132816
$795$	9.92987e11	0.0881640
$796$	−1.15977e13	−1.02392
$797$	2.35759e12	0.206969	0.103485	−	0.994631i	$-0.467001\pi$
$797$	2.35759e12	0.206969	0.103485	+	0.994631i	$0.467001\pi$
$798$	−1.72291e11	−0.0150400
$799$	−3.02406e12	−0.262501
$800$	2.66547e12	0.230075
$801$	−7.33270e12	−0.629387
$802$	2.90343e12	0.247815
$803$	1.02655e13	0.871281
$804$	−3.02459e12	−0.255278
$805$	2.10700e12	0.176841
$806$	−9.35115e10	−0.00780472
$807$	7.35357e12	0.610334
$808$	−2.03973e12	−0.168353
$809$	1.93887e13	1.59140	0.795702	−	0.605689i	$-0.207102\pi$
$809$	1.93887e13	1.59140	0.795702	+	0.605689i	$0.207102\pi$
$810$	1.18330e11	0.00965857
$811$	6.28461e12	0.510134	0.255067	−	0.966923i	$-0.417902\pi$
$811$	6.28461e12	0.510134	0.255067	+	0.966923i	$0.417902\pi$
$812$	6.41353e11	0.0517720
$813$	8.13621e11	0.0653152
$814$	2.82862e12	0.225822
$815$	−8.68046e12	−0.689182
$816$	6.31092e12	0.498296
$817$	−4.63988e12	−0.364340
$818$	−2.93981e12	−0.229578
$819$	−1.43088e11	−0.0111128
$820$	6.64564e12	0.513304
$821$	1.17775e13	0.904709	0.452355	−	0.891838i	$-0.350584\pi$
$821$	1.17775e13	0.904709	0.452355	+	0.891838i	$0.350584\pi$
$822$	1.71822e12	0.131267
$823$	7.43728e11	0.0565087	0.0282543	−	0.999601i	$-0.491005\pi$
$823$	7.43728e11	0.0565087	0.0282543	+	0.999601i	$0.491005\pi$
$824$	−1.74877e12	−0.132148
$825$	5.40408e12	0.406143
$826$	−4.85715e10	−0.00363054
$827$	−2.94757e10	−0.00219124	−0.00109562	−	0.999999i	$-0.500349\pi$
$827$	−2.94757e10	−0.00219124	−0.00109562	+	0.999999i	$0.500349\pi$
$828$	5.85793e12	0.433120
$829$	−1.09813e12	−0.0807526	−0.0403763	−	0.999185i	$-0.512856\pi$
$829$	−1.09813e12	−0.0807526	−0.0403763	+	0.999185i	$0.512856\pi$
$830$	3.31154e11	0.0242203
$831$	−6.96062e12	−0.506342
$832$	1.98692e12	0.143756
$833$	1.21359e13	0.873314
$834$	5.55451e11	0.0397556
$835$	6.69553e12	0.476646
$836$	1.56178e13	1.10584
$837$	9.83426e11	0.0692591
$838$	−1.25962e12	−0.0882348
$839$	1.55564e13	1.08388	0.541940	−	0.840417i	$-0.317690\pi$
$839$	1.55564e13	1.08388	0.541940	+	0.840417i	$0.317690\pi$
$840$	2.97164e11	0.0205940
$841$	−1.35663e13	−0.935145
$842$	−2.68287e11	−0.0183948
$843$	5.80891e12	0.396160
$844$	4.95999e12	0.336465
$845$	9.31703e12	0.628669
$846$	−1.92443e11	−0.0129162
$847$	1.40695e12	0.0939299
$848$	3.37017e12	0.223805
$849$	1.09955e13	0.726322
$850$	−1.09123e12	−0.0717021
$851$	2.81560e13	1.84030
$852$	−1.05925e13	−0.688683
$853$	−2.03753e13	−1.31775	−0.658876	−	0.752251i	$-0.728968\pi$
$853$	−2.03753e13	−1.31775	−0.658876	+	0.752251i	$0.728968\pi$
$854$	−8.44429e11	−0.0543253
$855$	3.14028e12	0.200965
$856$	7.63822e12	0.486251
$857$	−5.18994e12	−0.328661	−0.164331	−	0.986405i	$-0.552546\pi$
$857$	−5.18994e12	−0.328661	−0.164331	+	0.986405i	$0.552546\pi$
$858$	−2.39642e11	−0.0150963
$859$	1.77656e13	1.11330	0.556648	−	0.830749i	$-0.312087\pi$
$859$	1.77656e13	1.11330	0.556648	+	0.830749i	$0.312087\pi$
$860$	3.96477e12	0.247158
$861$	−1.56142e12	−0.0968292
$862$	−3.75841e12	−0.231858
$863$	1.87710e13	1.15197	0.575983	−	0.817461i	$-0.304619\pi$
$863$	1.87710e13	1.15197	0.575983	+	0.817461i	$0.304619\pi$
$864$	1.24306e12	0.0758891
$865$	−1.46361e13	−0.888902
$866$	−3.55829e12	−0.214987
$867$	1.60869e12	0.0966911
$868$	1.22354e12	0.0731612
$869$	3.15246e11	0.0187526
$870$	2.15976e11	0.0127811
$871$	1.23163e12	0.0725102
$872$	3.33699e10	0.00195448
$873$	−1.01824e13	−0.593318
$874$	−2.87222e12	−0.166501
$875$	3.66898e12	0.211597
$876$	7.13977e12	0.409652
$877$	−2.65144e13	−1.51350	−0.756752	−	0.653702i	$-0.773215\pi$
$877$	−2.65144e13	−1.51350	−0.756752	+	0.653702i	$0.773215\pi$
$878$	−2.61887e12	−0.148726
$879$	−1.31928e12	−0.0745397
$880$	−1.30943e13	−0.736056
$881$	−7.93722e12	−0.443892	−0.221946	−	0.975059i	$-0.571241\pi$
$881$	−7.93722e12	−0.443892	−0.221946	+	0.975059i	$0.571241\pi$
$882$	7.72296e11	0.0429710
$883$	6.81888e12	0.377476	0.188738	−	0.982027i	$-0.439560\pi$
$883$	6.81888e12	0.377476	0.188738	+	0.982027i	$0.439560\pi$
$884$	−2.61913e12	−0.144252
$885$	8.85296e11	0.0485114
$886$	2.81753e12	0.153609
$887$	−9.06171e12	−0.491534	−0.245767	−	0.969329i	$-0.579040\pi$
$887$	−9.06171e12	−0.491534	−0.245767	+	0.969329i	$0.579040\pi$
$888$	3.97104e12	0.214312
$889$	−6.29849e12	−0.338204
$890$	−3.07220e12	−0.164132
$891$	2.52022e12	0.133964
$892$	−3.51259e13	−1.85774
$893$	−5.10710e12	−0.268747
$894$	9.54810e11	0.0499917
$895$	4.78283e12	0.249162
$896$	2.05547e12	0.106543
$897$	−2.38539e12	−0.123025
$898$	6.41986e11	0.0329444
$899$	1.79494e12	0.0916500
$900$	3.75861e12	0.190957
$901$	−4.27053e12	−0.215884
$902$	−2.61505e12	−0.131538
$903$	−9.31541e11	−0.0466238
$904$	7.06830e12	0.352012
$905$	4.66355e12	0.231099
$906$	1.48966e12	0.0734531
$907$	−3.11139e12	−0.152659	−0.0763294	−	0.997083i	$-0.524320\pi$
$907$	−3.11139e12	−0.152659	−0.0763294	+	0.997083i	$0.524320\pi$
$908$	2.70501e13	1.32063
$909$	−4.32753e12	−0.210234
$910$	−5.99498e10	−0.00289802
$911$	−2.08740e13	−1.00409	−0.502046	−	0.864841i	$-0.667419\pi$
$911$	−2.08740e13	−1.00409	−0.502046	+	0.864841i	$0.667419\pi$
$912$	1.06580e13	0.510152
$913$	7.05299e12	0.335935
$914$	2.02183e12	0.0958265
$915$	1.53911e13	0.725897
$916$	−1.96516e13	−0.922293
$917$	−4.92708e12	−0.230106
$918$	−5.08902e11	−0.0236506
$919$	−1.30825e13	−0.605020	−0.302510	−	0.953146i	$-0.597825\pi$
$919$	−1.30825e13	−0.605020	−0.302510	+	0.953146i	$0.597825\pi$
$920$	4.95397e12	0.227986
$921$	−1.19664e13	−0.548020
$922$	−8.39484e11	−0.0382581
$923$	4.31332e12	0.195616
$924$	3.13557e12	0.141512
$925$	1.80657e13	0.811366
$926$	3.65248e11	0.0163244
$927$	−3.71022e12	−0.165022
$928$	2.26882e12	0.100423
$929$	−3.66290e13	−1.61345	−0.806723	−	0.590929i	$-0.798761\pi$
$929$	−3.66290e13	−1.61345	−0.806723	+	0.590929i	$0.798761\pi$
$930$	4.12028e11	0.0180615
$931$	2.04954e13	0.894094
$932$	2.55776e13	1.11042
$933$	1.28482e13	0.555103
$934$	−4.93001e12	−0.211976
$935$	1.65926e13	0.710004
$936$	−3.36427e11	−0.0143268
$937$	−4.16405e13	−1.76477	−0.882384	−	0.470530i	$-0.844063\pi$
$937$	−4.16405e13	−1.76477	−0.882384	+	0.470530i	$0.844063\pi$
$938$	2.97739e11	0.0125581
$939$	−1.01327e13	−0.425334
$940$	4.36402e12	0.182310
$941$	−1.28257e13	−0.533248	−0.266624	−	0.963801i	$-0.585908\pi$
$941$	−1.28257e13	−0.533248	−0.266624	+	0.963801i	$0.585908\pi$
$942$	2.58370e12	0.106909
$943$	−2.60302e13	−1.07195
$944$	3.00467e12	0.123147
$945$	6.30470e11	0.0257170
$946$	−1.56013e12	−0.0633362
$947$	−2.34295e13	−0.946648	−0.473324	−	0.880889i	$-0.656946\pi$
$947$	−2.34295e13	−0.946648	−0.473324	+	0.880889i	$0.656946\pi$
$948$	2.19258e11	0.00881693
$949$	−2.90736e12	−0.116359
$950$	−1.84290e12	−0.0734082
$951$	5.12016e12	0.202988
$952$	−1.27801e12	−0.0504277
$953$	−6.35831e12	−0.249703	−0.124852	−	0.992175i	$-0.539845\pi$
$953$	−6.35831e12	−0.249703	−0.124852	+	0.992175i	$0.539845\pi$
$954$	−2.71765e11	−0.0106225
$955$	−1.19694e13	−0.465647
$956$	3.45066e13	1.33611
$957$	4.59990e12	0.177274
$958$	4.12687e12	0.158298
$959$	9.15476e12	0.349513
$960$	−8.75473e12	−0.332677
$961$	−2.30153e13	−0.870486
$962$	−8.01116e11	−0.0301583
$963$	1.62054e13	0.607213
$964$	−3.22115e13	−1.20133
$965$	−3.18469e13	−1.18221
$966$	−5.76652e11	−0.0213067
$967$	−4.99997e13	−1.83886	−0.919430	−	0.393254i	$-0.871349\pi$
$967$	−4.99997e13	−1.83886	−0.919430	+	0.393254i	$0.871349\pi$
$968$	3.30802e12	0.121096
$969$	−1.35054e13	−0.492096
$970$	−4.26616e12	−0.154726
$971$	−3.43173e13	−1.23887	−0.619437	−	0.785046i	$-0.712639\pi$
$971$	−3.43173e13	−1.23887	−0.619437	+	0.785046i	$0.712639\pi$
$972$	1.75285e12	0.0629863
$973$	2.95947e12	0.105854
$974$	1.09141e11	0.00388574
$975$	−1.53053e12	−0.0542402
$976$	5.22370e13	1.84270
$977$	−2.71239e13	−0.952416	−0.476208	−	0.879333i	$-0.657989\pi$
$977$	−2.71239e13	−0.952416	−0.476208	+	0.879333i	$0.657989\pi$
$978$	2.37571e12	0.0830362
$979$	−6.54323e13	−2.27651
$980$	−1.75133e13	−0.606528
$981$	7.07982e10	0.00244068
$982$	−5.33483e12	−0.183071
$983$	6.56996e12	0.224425	0.112213	−	0.993684i	$-0.464206\pi$
$983$	6.56996e12	0.224425	0.112213	+	0.993684i	$0.464206\pi$
$984$	−3.67122e12	−0.124834
$985$	5.26789e12	0.178309
$986$	−9.28845e11	−0.0312966
$987$	−1.02535e12	−0.0343909
$988$	−4.42324e12	−0.147684
$989$	−1.55295e13	−0.516149
$990$	1.05590e12	0.0349354
$991$	2.02868e13	0.668162	0.334081	−	0.942544i	$-0.391574\pi$
$991$	2.02868e13	0.668162	0.334081	+	0.942544i	$0.391574\pi$
$992$	4.32836e12	0.141912
$993$	−1.80702e13	−0.589783
$994$	1.04272e12	0.0338788
$995$	−2.08089e13	−0.673047
$996$	4.90545e12	0.157947
$997$	4.84876e13	1.55418	0.777091	−	0.629388i	$-0.216694\pi$
$997$	4.84876e13	1.55418	0.777091	+	0.629388i	$0.216694\pi$
$998$	−6.46862e12	−0.206407
$999$	8.42503e12	0.267625

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-3.04761 q^{2} -81.0000 q^{3} -502.712 q^{4} -901.977 q^{5} +246.857 q^{6} +1315.27 q^{7} +3092.45 q^{8} +6561.00 q^{9} +2748.88 q^{10} +58546.2 q^{11} +40719.7 q^{12} -16581.3 q^{13} -4008.42 q^{14} +73060.1 q^{15} +247964. q^{16} -314209. q^{17} -19995.4 q^{18} -530644. q^{19} +453435. q^{20} -106537. q^{21} -178426. q^{22} -1.77605e6 q^{23} -250489. q^{24} -1.13956e6 q^{25} +50533.4 q^{26} -531441. q^{27} -661200. q^{28} -969983. q^{29} -222659. q^{30} -1.85049e6 q^{31} -2.33903e6 q^{32} -4.74224e6 q^{33} +957589. q^{34} -1.18634e6 q^{35} -3.29829e6 q^{36} -1.58532e7 q^{37} +1.61720e6 q^{38} +1.34309e6 q^{39} -2.78932e6 q^{40} +1.46562e7 q^{41} +324682. q^{42} +8.74387e6 q^{43} -2.94319e7 q^{44} -5.91787e6 q^{45} +5.41271e6 q^{46} +9.62436e6 q^{47} -2.00851e7 q^{48} -3.86237e7 q^{49} +3.47295e6 q^{50} +2.54510e7 q^{51} +8.33562e6 q^{52} +1.35914e7 q^{53} +1.61963e6 q^{54} -5.28073e7 q^{55} +4.06740e6 q^{56} +4.29821e7 q^{57} +2.95614e6 q^{58} +1.21174e7 q^{59} -3.67282e7 q^{60} +2.10664e8 q^{61} +5.63958e6 q^{62} +8.62946e6 q^{63} -1.19829e8 q^{64} +1.49560e7 q^{65} +1.44525e7 q^{66} -7.42783e7 q^{67} +1.57957e8 q^{68} +1.43860e8 q^{69} +3.61551e6 q^{70} -2.60132e8 q^{71} +2.02896e7 q^{72} +1.75339e8 q^{73} +4.83144e7 q^{74} +9.23046e7 q^{75} +2.66761e8 q^{76} +7.70038e7 q^{77} -4.09321e6 q^{78} +5.38457e6 q^{79} -2.23658e8 q^{80} +4.30467e7 q^{81} -4.46665e7 q^{82} +1.20469e8 q^{83} +5.35572e7 q^{84} +2.83410e8 q^{85} -2.66479e7 q^{86} +7.85687e7 q^{87} +1.81051e8 q^{88} -1.11762e9 q^{89} +1.80354e7 q^{90} -2.18088e7 q^{91} +8.92841e8 q^{92} +1.49890e8 q^{93} -2.93313e7 q^{94} +4.78628e8 q^{95} +1.89462e8 q^{96} -1.55196e9 q^{97} +1.17710e8 q^{98} +3.84122e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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