LMFDB - Embedded newform 177.10.a.c.1.12

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			1.12
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +2793.66 q^{10} -839.126 q^{11} +41327.3 q^{12} +34005.3 q^{13} +143.222 q^{14} -169321. q^{15} +259404. q^{16} -84723.3 q^{17} +8768.37 q^{18} +928571. q^{19} -1.06654e6 q^{20} -8680.50 q^{21} -1121.44 q^{22} -971930. q^{23} +110656. q^{24} +2.41656e6 q^{25} +45445.9 q^{26} -531441. q^{27} -54677.9 q^{28} +534314. q^{29} -226287. q^{30} -1.99772e6 q^{31} +1.04613e6 q^{32} +67969.2 q^{33} -113227. q^{34} +224019. q^{35} -3.34751e6 q^{36} -9.60421e6 q^{37} +1.24098e6 q^{38} -2.75443e6 q^{39} -2.85572e6 q^{40} +1.18062e7 q^{41} -11600.9 q^{42} -1.85229e7 q^{43} +428134. q^{44} +1.37150e7 q^{45} -1.29892e6 q^{46} -1.01847e7 q^{47} -2.10117e7 q^{48} -4.03421e7 q^{49} +3.22958e6 q^{50} +6.86258e6 q^{51} -1.73500e7 q^{52} -3.57403e7 q^{53} -710238. q^{54} -1.75409e6 q^{55} -146403. q^{56} -7.52143e7 q^{57} +714077. q^{58} +1.21174e7 q^{59} +8.63898e7 q^{60} -6.03548e7 q^{61} -2.66983e6 q^{62} +703120. q^{63} -1.31417e8 q^{64} +7.10839e7 q^{65} +90836.6 q^{66} +2.83501e8 q^{67} +4.32270e7 q^{68} +7.87263e7 q^{69} +299387. q^{70} +3.57688e8 q^{71} -8.96315e6 q^{72} +3.74577e8 q^{73} -1.28354e7 q^{74} -1.95741e8 q^{75} -4.73770e8 q^{76} -89926.3 q^{77} -3.68112e6 q^{78} +6.00766e7 q^{79} +5.42252e8 q^{80} +4.30467e7 q^{81} +1.57783e7 q^{82} +6.16047e8 q^{83} +4.42891e6 q^{84} -1.77104e8 q^{85} -2.47547e7 q^{86} -4.32794e7 q^{87} +1.14635e6 q^{88} +1.58856e8 q^{89} +1.83292e7 q^{90} +3.64423e6 q^{91} +4.95892e8 q^{92} +1.61815e8 q^{93} -1.36113e7 q^{94} +1.94107e9 q^{95} -8.47368e7 q^{96} +1.10346e9 q^{97} -5.39147e7 q^{98} -5.50551e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.33644	0.0590628	0.0295314	−	0.999564i	$-0.490599\pi$
$2$	1.33644	0.0590628	0.0295314	+	0.999564i	$0.490599\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−510.214	−0.996512
$5$	2090.38	1.49575	0.747877	−	0.663838i	$-0.231073\pi$
$5$	2090.38	1.49575	0.747877	+	0.663838i	$0.231073\pi$
$6$	−108.251	−0.0340999
$7$	107.167	0.0168701	0.00843506	−	0.999964i	$-0.497315\pi$
$7$	107.167	0.0168701	0.00843506	+	0.999964i	$0.497315\pi$
$8$	−1366.13	−0.117919
$9$	6561.00	0.333333
$10$	2793.66	0.0883433
$11$	−839.126	−0.0172807	−0.00864033	−	0.999963i	$-0.502750\pi$
$11$	−839.126	−0.0172807	−0.00864033	+	0.999963i	$0.502750\pi$
$12$	41327.3	0.575336
$13$	34005.3	0.330218	0.165109	−	0.986275i	$-0.447202\pi$
$13$	34005.3	0.330218	0.165109	+	0.986275i	$0.447202\pi$
$14$	143.222	0.000996396 0
$15$	−169321.	−0.863574
$16$	259404.	0.989547
$17$	−84723.3	−0.246027	−0.123013	−	0.992405i	$-0.539256\pi$
$17$	−84723.3	−0.246027	−0.123013	+	0.992405i	$0.539256\pi$
$18$	8768.37	0.0196876
$19$	928571.	1.63465	0.817323	−	0.576179i	$-0.195457\pi$
$19$	928571.	1.63465	0.817323	+	0.576179i	$0.195457\pi$
$20$	−1.06654e6	−1.49054
$21$	−8680.50	−0.00973997
$22$	−1121.44	−0.00102064
$23$	−971930.	−0.724202	−0.362101	−	0.932139i	$-0.617940\pi$
$23$	−971930.	−0.724202	−0.362101	+	0.932139i	$0.617940\pi$
$24$	110656.	0.0680808
$25$	2.41656e6	1.23728
$26$	45445.9	0.0195036
$27$	−531441.	−0.192450
$28$	−54677.9	−0.0168113
$29$	534314.	0.140283	0.0701415	−	0.997537i	$-0.477655\pi$
$29$	534314.	0.140283	0.0701415	+	0.997537i	$0.477655\pi$
$30$	−226287.	−0.0510050
$31$	−1.99772e6	−0.388514	−0.194257	−	0.980951i	$-0.562230\pi$
$31$	−1.99772e6	−0.388514	−0.194257	+	0.980951i	$0.562230\pi$
$32$	1.04613e6	0.176365
$33$	67969.2	0.00997699
$34$	−113227.	−0.0145310
$35$	224019.	0.0252335
$36$	−3.34751e6	−0.332171
$37$	−9.60421e6	−0.842469	−0.421235	−	0.906952i	$-0.638403\pi$
$37$	−9.60421e6	−0.842469	−0.421235	+	0.906952i	$0.638403\pi$
$38$	1.24098e6	0.0965468
$39$	−2.75443e6	−0.190652
$40$	−2.85572e6	−0.176378
$41$	1.18062e7	0.652506	0.326253	−	0.945283i	$-0.394214\pi$
$41$	1.18062e7	0.652506	0.326253	+	0.945283i	$0.394214\pi$
$42$	−11600.9	−0.000575270 0
$43$	−1.85229e7	−0.826230	−0.413115	−	0.910679i	$-0.635559\pi$
$43$	−1.85229e7	−0.826230	−0.413115	+	0.910679i	$0.635559\pi$
$44$	428134.	0.0172204
$45$	1.37150e7	0.498584
$46$	−1.29892e6	−0.0427734
$47$	−1.01847e7	−0.304445	−0.152223	−	0.988346i	$-0.548643\pi$
$47$	−1.01847e7	−0.304445	−0.152223	+	0.988346i	$0.548643\pi$
$48$	−2.10117e7	−0.571315
$49$	−4.03421e7	−0.999715
$50$	3.22958e6	0.0730771
$51$	6.86258e6	0.142044
$52$	−1.73500e7	−0.329066
$53$	−3.57403e7	−0.622181	−0.311090	−	0.950380i	$-0.600694\pi$
$53$	−3.57403e7	−0.622181	−0.311090	+	0.950380i	$0.600694\pi$
$54$	−710238.	−0.0113666
$55$	−1.75409e6	−0.0258476
$56$	−146403.	−0.00198932
$57$	−7.52143e7	−0.943764
$58$	714077.	0.00828551
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	8.63898e7	0.860561
$61$	−6.03548e7	−0.558120	−0.279060	−	0.960274i	$-0.590023\pi$
$61$	−6.03548e7	−0.558120	−0.279060	+	0.960274i	$0.590023\pi$
$62$	−2.66983e6	−0.0229467
$63$	703120.	0.00562338
$64$	−1.31417e8	−0.979130
$65$	7.10839e7	0.493925
$66$	90836.6	0.000589268 0
$67$	2.83501e8	1.71877	0.859386	−	0.511327i	$-0.170846\pi$
$67$	2.83501e8	1.71877	0.859386	+	0.511327i	$0.170846\pi$
$68$	4.32270e7	0.245169
$69$	7.87263e7	0.418118
$70$	299387.	0.00149036
$71$	3.57688e8	1.67048	0.835241	−	0.549884i	$-0.185328\pi$
$71$	3.57688e8	1.67048	0.835241	+	0.549884i	$0.185328\pi$
$72$	−8.96315e6	−0.0393065
$73$	3.74577e8	1.54379	0.771895	−	0.635750i	$-0.219309\pi$
$73$	3.74577e8	1.54379	0.771895	+	0.635750i	$0.219309\pi$
$74$	−1.28354e7	−0.0497585
$75$	−1.95741e8	−0.714343
$76$	−4.73770e8	−1.62894
$77$	−89926.3	−0.000291527 0
$78$	−3.68112e6	−0.0112604
$79$	6.00766e7	0.173534	0.0867668	−	0.996229i	$-0.472346\pi$
$79$	6.00766e7	0.173534	0.0867668	+	0.996229i	$0.472346\pi$
$80$	5.42252e8	1.48012
$81$	4.30467e7	0.111111
$82$	1.57783e7	0.0385388
$83$	6.16047e8	1.42483	0.712414	−	0.701759i	$-0.247602\pi$
$83$	6.16047e8	1.42483	0.712414	+	0.701759i	$0.247602\pi$
$84$	4.42891e6	0.00970599
$85$	−1.77104e8	−0.367995
$86$	−2.47547e7	−0.0487994
$87$	−4.32794e7	−0.0809925
$88$	1.14635e6	0.00203773
$89$	1.58856e8	0.268379	0.134189	−	0.990956i	$-0.457157\pi$
$89$	1.58856e8	0.268379	0.134189	+	0.990956i	$0.457157\pi$
$90$	1.83292e7	0.0294478
$91$	3.64423e6	0.00557083
$92$	4.95892e8	0.721676
$93$	1.61815e8	0.224309
$94$	−1.36113e7	−0.0179814
$95$	1.94107e9	2.44503
$96$	−8.47368e7	−0.101824
$97$	1.10346e9	1.26557	0.632784	−	0.774328i	$-0.281912\pi$
$97$	1.10346e9	1.26557	0.632784	+	0.774328i	$0.281912\pi$
$98$	−5.39147e7	−0.0590460
$99$	−5.50551e6	−0.00576022
$100$	−1.23296e9	−1.23296
$101$	−2.92749e7	−0.0279930	−0.0139965	−	0.999902i	$-0.504455\pi$
$101$	−2.92749e7	−0.0279930	−0.0139965	+	0.999902i	$0.504455\pi$
$102$	9.17142e6	0.00838949
$103$	−5.30706e8	−0.464608	−0.232304	−	0.972643i	$-0.574626\pi$
$103$	−5.30706e8	−0.464608	−0.232304	+	0.972643i	$0.574626\pi$
$104$	−4.64555e7	−0.0389392
$105$	−1.81455e7	−0.0145686
$106$	−4.77646e7	−0.0367477
$107$	−1.46128e9	−1.07772	−0.538860	−	0.842395i	$-0.681145\pi$
$107$	−1.46128e9	−1.07772	−0.538860	+	0.842395i	$0.681145\pi$
$108$	2.71149e8	0.191779
$109$	−6.89292e8	−0.467718	−0.233859	−	0.972271i	$-0.575135\pi$
$109$	−6.89292e8	−0.467718	−0.233859	+	0.972271i	$0.575135\pi$
$110$	−2.34423e6	−0.00152663
$111$	7.77941e8	0.486400
$112$	2.77994e7	0.0166938
$113$	1.55105e9	0.894899	0.447450	−	0.894309i	$-0.352332\pi$
$113$	1.55105e9	0.894899	0.447450	+	0.894309i	$0.352332\pi$
$114$	−1.00519e8	−0.0557413
$115$	−2.03170e9	−1.08323
$116$	−2.72614e8	−0.139794
$117$	2.23109e8	0.110073
$118$	1.61941e7	0.00768932
$119$	−9.07950e6	−0.00415050
$120$	2.31313e8	0.101832
$121$	−2.35724e9	−0.999701
$122$	−8.06605e7	−0.0329641
$123$	−9.56305e8	−0.376724
$124$	1.01926e9	0.387159
$125$	9.68752e8	0.354909
$126$	939676.	0.000332132 0
$127$	5.03627e9	1.71788	0.858939	−	0.512078i	$-0.171124\pi$
$127$	5.03627e9	1.71788	0.858939	+	0.512078i	$0.171124\pi$
$128$	−7.11250e8	−0.234195
$129$	1.50035e9	0.477024
$130$	9.49992e7	0.0291726
$131$	1.31283e9	0.389482	0.194741	−	0.980855i	$-0.437613\pi$
$131$	1.31283e9	0.389482	0.194741	+	0.980855i	$0.437613\pi$
$132$	−3.46788e7	−0.00994218
$133$	9.95118e7	0.0275767
$134$	3.78882e8	0.101515
$135$	−1.11091e9	−0.287858
$136$	1.15743e8	0.0290114
$137$	1.89177e9	0.458803	0.229401	−	0.973332i	$-0.426323\pi$
$137$	1.89177e9	0.458803	0.229401	+	0.973332i	$0.426323\pi$
$138$	1.05213e8	0.0246952
$139$	4.40133e9	1.00004	0.500020	−	0.866014i	$-0.333326\pi$
$139$	4.40133e9	1.00004	0.500020	+	0.866014i	$0.333326\pi$
$140$	−1.14298e8	−0.0251455
$141$	8.24963e8	0.175772
$142$	4.78028e8	0.0986632
$143$	−2.85347e7	−0.00570639
$144$	1.70195e9	0.329849
$145$	1.11692e9	0.209829
$146$	5.00599e8	0.0911805
$147$	3.26771e9	0.577186
$148$	4.90020e9	0.839530
$149$	1.12491e10	1.86973	0.934865	−	0.355002i	$-0.115520\pi$
$149$	1.12491e10	1.86973	0.934865	+	0.355002i	$0.115520\pi$
$150$	−2.61596e8	−0.0421911
$151$	−1.01153e9	−0.158337	−0.0791685	−	0.996861i	$-0.525227\pi$
$151$	−1.01153e9	−0.158337	−0.0791685	+	0.996861i	$0.525227\pi$
$152$	−1.26854e9	−0.192757
$153$	−5.55869e8	−0.0820089
$154$	−120181.	−1.72184e−5 0
$155$	−4.17599e9	−0.581121
$156$	1.40535e9	0.189987
$157$	5.95184e9	0.781813	0.390906	−	0.920430i	$-0.372162\pi$
$157$	5.95184e9	0.781813	0.390906	+	0.920430i	$0.372162\pi$
$158$	8.02887e7	0.0102494
$159$	2.89496e9	0.359216
$160$	2.18681e9	0.263798
$161$	−1.04158e8	−0.0122174
$162$	5.75293e7	0.00656253
$163$	1.40093e10	1.55443	0.777216	−	0.629233i	$-0.216631\pi$
$163$	1.40093e10	1.55443	0.777216	+	0.629233i	$0.216631\pi$
$164$	−6.02371e9	−0.650229
$165$	1.42081e8	0.0149231
$166$	8.23309e8	0.0841543
$167$	1.03853e9	0.103322	0.0516612	−	0.998665i	$-0.483548\pi$
$167$	1.03853e9	0.103322	0.0516612	+	0.998665i	$0.483548\pi$
$168$	1.18586e7	0.00114853
$169$	−9.44814e9	−0.890956
$170$	−2.36688e8	−0.0217348
$171$	6.09235e9	0.544882
$172$	9.45064e9	0.823347
$173$	1.27196e9	0.107961	0.0539804	−	0.998542i	$-0.482809\pi$
$173$	1.27196e9	0.107961	0.0539804	+	0.998542i	$0.482809\pi$
$174$	−5.78402e7	−0.00478364
$175$	2.58974e8	0.0208730
$176$	−2.17672e8	−0.0171000
$177$	−9.81506e8	−0.0751646
$178$	2.12301e8	0.0158512
$179$	4.05826e9	0.295462	0.147731	−	0.989028i	$-0.452803\pi$
$179$	4.05826e9	0.295462	0.147731	+	0.989028i	$0.452803\pi$
$180$	−6.99757e9	−0.496845
$181$	1.52164e8	0.0105380	0.00526900	−	0.999986i	$-0.498323\pi$
$181$	1.52164e8	0.0105380	0.00526900	+	0.999986i	$0.498323\pi$
$182$	4.87029e6	0.000329028 0
$183$	4.88874e9	0.322231
$184$	1.32778e9	0.0853975
$185$	−2.00764e10	−1.26013
$186$	2.16256e8	0.0132483
$187$	7.10935e7	0.00425150
$188$	5.19639e9	0.303383
$189$	−5.69527e7	−0.00324666
$190$	2.59411e9	0.144410
$191$	−1.40242e10	−0.762481	−0.381241	−	0.924476i	$-0.624503\pi$
$191$	−1.40242e10	−0.762481	−0.381241	+	0.924476i	$0.624503\pi$
$192$	1.06447e10	0.565301
$193$	8.79613e9	0.456335	0.228167	−	0.973622i	$-0.426727\pi$
$193$	8.79613e9	0.456335	0.228167	+	0.973622i	$0.426727\pi$
$194$	1.47471e9	0.0747480
$195$	−5.75780e9	−0.285168
$196$	2.05831e10	0.996228
$197$	−1.58607e10	−0.750281	−0.375140	−	0.926968i	$-0.622405\pi$
$197$	−1.58607e10	−0.750281	−0.375140	+	0.926968i	$0.622405\pi$
$198$	−7.35777e6	−0.000340214 0
$199$	1.69260e8	0.00765094	0.00382547	−	0.999993i	$-0.498782\pi$
$199$	1.69260e8	0.00765094	0.00382547	+	0.999993i	$0.498782\pi$
$200$	−3.30132e9	−0.145899
$201$	−2.29636e10	−0.992334
$202$	−3.91241e7	−0.00165334
$203$	5.72606e7	0.00236659
$204$	−3.50139e9	−0.141548
$205$	2.46795e10	0.975987
$206$	−7.09255e8	−0.0274410
$207$	−6.37683e9	−0.241401
$208$	8.82110e9	0.326767
$209$	−7.79188e8	−0.0282478
$210$	−2.42504e7	−0.000860461 0
$211$	−3.98459e10	−1.38393	−0.691963	−	0.721933i	$-0.743254\pi$
$211$	−3.98459e10	−1.38393	−0.691963	+	0.721933i	$0.743254\pi$
$212$	1.82352e10	0.620010
$213$	−2.89727e10	−0.964453
$214$	−1.95291e9	−0.0636531
$215$	−3.87199e10	−1.23584
$216$	7.26015e8	0.0226936
$217$	−2.14089e8	−0.00655428
$218$	−9.21196e8	−0.0276247
$219$	−3.03407e10	−0.891307
$220$	8.94962e8	0.0257574
$221$	−2.88104e9	−0.0812426
$222$	1.03967e9	0.0287281
$223$	3.61870e10	0.979897	0.489949	−	0.871751i	$-0.337016\pi$
$223$	3.61870e10	0.979897	0.489949	+	0.871751i	$0.337016\pi$
$224$	1.12111e8	0.00297530
$225$	1.58550e10	0.412426
$226$	2.07289e9	0.0528552
$227$	3.37796e10	0.844381	0.422191	−	0.906507i	$-0.361261\pi$
$227$	3.37796e10	0.844381	0.422191	+	0.906507i	$0.361261\pi$
$228$	3.83754e10	0.940472
$229$	−2.50877e10	−0.602838	−0.301419	−	0.953492i	$-0.597460\pi$
$229$	−2.50877e10	−0.602838	−0.301419	+	0.953492i	$0.597460\pi$
$230$	−2.71524e9	−0.0639784
$231$	7.28403e6	0.000168313 0
$232$	−7.29939e8	−0.0165421
$233$	3.91412e10	0.870027	0.435014	−	0.900424i	$-0.356744\pi$
$233$	3.91412e10	0.870027	0.435014	+	0.900424i	$0.356744\pi$
$234$	2.98171e8	0.00650120
$235$	−2.12899e10	−0.455375
$236$	−6.18245e9	−0.129735
$237$	−4.86621e9	−0.100190
$238$	−1.21342e7	−0.000245140 0
$239$	7.66958e10	1.52048	0.760241	−	0.649642i	$-0.225081\pi$
$239$	7.66958e10	1.52048	0.760241	+	0.649642i	$0.225081\pi$
$240$	−4.39224e10	−0.854547
$241$	−2.55250e10	−0.487405	−0.243702	−	0.969850i	$-0.578362\pi$
$241$	−2.55250e10	−0.487405	−0.243702	+	0.969850i	$0.578362\pi$
$242$	−3.15031e9	−0.0590451
$243$	−3.48678e9	−0.0641500
$244$	3.07939e10	0.556173
$245$	−8.43303e10	−1.49533
$246$	−1.27804e9	−0.0222504
$247$	3.15763e10	0.539790
$248$	2.72914e9	0.0458134
$249$	−4.98998e10	−0.822625
$250$	1.29468e9	0.0209619
$251$	1.01377e11	1.61215	0.806076	−	0.591811i	$-0.201587\pi$
$251$	1.01377e11	1.61215	0.806076	+	0.591811i	$0.201587\pi$
$252$	−3.58742e8	−0.00560376
$253$	8.15572e8	0.0125147
$254$	6.73066e9	0.101463
$255$	1.43454e10	0.212462
$256$	6.63348e10	0.965298
$257$	−1.07253e10	−0.153360	−0.0766799	−	0.997056i	$-0.524432\pi$
$257$	−1.07253e10	−0.153360	−0.0766799	+	0.997056i	$0.524432\pi$
$258$	2.00513e9	0.0281744
$259$	−1.02925e9	−0.0142126
$260$	−3.62680e10	−0.492202
$261$	3.50563e9	0.0467610
$262$	1.75452e9	0.0230039
$263$	−8.11509e10	−1.04591	−0.522953	−	0.852362i	$-0.675170\pi$
$263$	−8.11509e10	−1.04591	−0.522953	+	0.852362i	$0.675170\pi$
$264$	−9.28545e7	−0.00117648
$265$	−7.47107e10	−0.930629
$266$	1.32991e8	0.00162876
$267$	−1.28673e10	−0.154948
$268$	−1.44646e11	−1.71278
$269$	−1.41843e10	−0.165166	−0.0825831	−	0.996584i	$-0.526317\pi$
$269$	−1.41843e10	−0.165166	−0.0825831	+	0.996584i	$0.526317\pi$
$270$	−1.48467e9	−0.0170017
$271$	7.53268e10	0.848375	0.424188	−	0.905574i	$-0.360560\pi$
$271$	7.53268e10	0.848375	0.424188	+	0.905574i	$0.360560\pi$
$272$	−2.19775e10	−0.243455
$273$	−2.95183e8	−0.00321632
$274$	2.52824e9	0.0270982
$275$	−2.02780e9	−0.0213810
$276$	−4.01673e10	−0.416660
$277$	−2.76122e10	−0.281801	−0.140900	−	0.990024i	$-0.545000\pi$
$277$	−2.76122e10	−0.281801	−0.140900	+	0.990024i	$0.545000\pi$
$278$	5.88210e9	0.0590651
$279$	−1.31070e10	−0.129505
$280$	−3.06038e8	−0.00297553
$281$	−8.87886e10	−0.849531	−0.424765	−	0.905304i	$-0.639643\pi$
$281$	−8.87886e10	−0.849531	−0.424765	+	0.905304i	$0.639643\pi$
$282$	1.10251e9	0.0103816
$283$	−1.21939e10	−0.113006	−0.0565032	−	0.998402i	$-0.517995\pi$
$283$	−1.21939e10	−0.113006	−0.0565032	+	0.998402i	$0.517995\pi$
$284$	−1.82497e11	−1.66465
$285$	−1.57226e11	−1.41164
$286$	−3.81349e7	−0.000337035 0
$287$	1.26523e9	0.0110079
$288$	6.86368e9	0.0587883
$289$	−1.11410e11	−0.939471
$290$	1.49269e9	0.0123931
$291$	−8.93806e10	−0.730676
$292$	−1.91114e11	−1.53840
$293$	6.57189e10	0.520938	0.260469	−	0.965482i	$-0.416123\pi$
$293$	6.57189e10	0.520938	0.260469	+	0.965482i	$0.416123\pi$
$294$	4.36709e9	0.0340902
$295$	2.53299e10	0.194730
$296$	1.31206e10	0.0993435
$297$	4.45946e8	0.00332566
$298$	1.50337e10	0.110431
$299$	−3.30508e10	−0.239145
$300$	9.98699e10	0.711851
$301$	−1.98504e9	−0.0139386
$302$	−1.35185e9	−0.00935182
$303$	2.37127e9	0.0161618
$304$	2.40875e11	1.61756
$305$	−1.26164e11	−0.834810
$306$	−7.42885e8	−0.00484367
$307$	−1.26973e11	−0.815808	−0.407904	−	0.913025i	$-0.633740\pi$
$307$	−1.26973e11	−0.815808	−0.407904	+	0.913025i	$0.633740\pi$
$308$	4.58816e7	0.000290510 0
$309$	4.29872e10	0.268241
$310$	−5.58095e9	−0.0343226
$311$	−1.42906e11	−0.866220	−0.433110	−	0.901341i	$-0.642584\pi$
$311$	−1.42906e11	−0.866220	−0.433110	+	0.901341i	$0.642584\pi$
$312$	3.76289e9	0.0224815
$313$	−1.33349e11	−0.785308	−0.392654	−	0.919686i	$-0.628443\pi$
$313$	−1.33349e11	−0.785308	−0.392654	+	0.919686i	$0.628443\pi$
$314$	7.95426e9	0.0461760
$315$	1.46979e9	0.00841118
$316$	−3.06519e10	−0.172928
$317$	2.43695e11	1.35544	0.677718	−	0.735322i	$-0.262969\pi$
$317$	2.43695e11	1.35544	0.677718	+	0.735322i	$0.262969\pi$
$318$	3.86894e9	0.0212163
$319$	−4.48357e8	−0.00242418
$320$	−2.74711e11	−1.46454
$321$	1.18364e11	0.622222
$322$	−1.39201e8	−0.000721592 0
$323$	−7.86716e10	−0.402167
$324$	−2.19630e10	−0.110724
$325$	8.21757e10	0.408572
$326$	1.87225e10	0.0918091
$327$	5.58326e10	0.270037
$328$	−1.61288e10	−0.0769431
$329$	−1.09146e9	−0.00513603
$330$	1.89883e8	0.000881400 0
$331$	1.55235e11	0.710825	0.355413	−	0.934710i	$-0.384340\pi$
$331$	1.55235e11	0.710825	0.355413	+	0.934710i	$0.384340\pi$
$332$	−3.14316e11	−1.41986
$333$	−6.30132e10	−0.280823
$334$	1.38793e9	0.00610251
$335$	5.92625e11	2.57086
$336$	−2.25175e9	−0.00963816
$337$	−1.06540e11	−0.449963	−0.224981	−	0.974363i	$-0.572232\pi$
$337$	−1.06540e11	−0.449963	−0.224981	+	0.974363i	$0.572232\pi$
$338$	−1.26269e10	−0.0526223
$339$	−1.25635e11	−0.516670
$340$	9.03608e10	0.366712
$341$	1.67634e9	0.00671378
$342$	8.14205e9	0.0321823
$343$	−8.64789e9	−0.0337355
$344$	2.53046e10	0.0974286
$345$	1.64568e11	0.625402
$346$	1.69989e9	0.00637646
$347$	−3.12994e11	−1.15892	−0.579460	−	0.815001i	$-0.696736\pi$
$347$	−3.12994e11	−1.15892	−0.579460	+	0.815001i	$0.696736\pi$
$348$	2.20818e10	0.0807099
$349$	4.73312e11	1.70779	0.853893	−	0.520448i	$-0.174235\pi$
$349$	4.73312e11	1.70779	0.853893	+	0.520448i	$0.174235\pi$
$350$	3.46103e8	0.00123282
$351$	−1.80718e10	−0.0635506
$352$	−8.77838e8	−0.00304770
$353$	−6.70290e10	−0.229761	−0.114881	−	0.993379i	$-0.536649\pi$
$353$	−6.70290e10	−0.229761	−0.114881	+	0.993379i	$0.536649\pi$
$354$	−1.31172e9	−0.00443943
$355$	7.47703e11	2.49863
$356$	−8.10504e10	−0.267442
$357$	7.35440e8	0.00239629
$358$	5.42361e9	0.0174508
$359$	4.49086e10	0.142694	0.0713468	−	0.997452i	$-0.477270\pi$
$359$	4.49086e10	0.142694	0.0713468	+	0.997452i	$0.477270\pi$
$360$	−1.87364e10	−0.0587928
$361$	5.39557e11	1.67207
$362$	2.03358e8	0.000622403 0
$363$	1.90937e11	0.577178
$364$	−1.85934e9	−0.00555139
$365$	7.83008e11	2.30913
$366$	6.53350e9	0.0190318
$367$	4.86775e11	1.40065	0.700327	−	0.713822i	$-0.253037\pi$
$367$	4.86775e11	1.40065	0.700327	+	0.713822i	$0.253037\pi$
$368$	−2.52122e11	−0.716632
$369$	7.74607e10	0.217502
$370$	−2.68309e10	−0.0744265
$371$	−3.83016e9	−0.0104963
$372$	−8.25604e10	−0.223526
$373$	4.49243e11	1.20169	0.600844	−	0.799367i	$-0.294831\pi$
$373$	4.49243e11	1.20169	0.600844	+	0.799367i	$0.294831\pi$
$374$	9.50120e7	0.000251106 0
$375$	−7.84689e10	−0.204907
$376$	1.39136e10	0.0359000
$377$	1.81695e10	0.0463241
$378$	−7.61138e7	−0.000191757 0
$379$	−2.57491e11	−0.641041	−0.320520	−	0.947242i	$-0.603858\pi$
$379$	−2.57491e11	−0.641041	−0.320520	+	0.947242i	$0.603858\pi$
$380$	−9.90359e11	−2.43650
$381$	−4.07938e11	−0.991817
$382$	−1.87425e10	−0.0450342
$383$	−2.56704e11	−0.609591	−0.304796	−	0.952418i	$-0.598588\pi$
$383$	−2.56704e11	−0.609591	−0.304796	+	0.952418i	$0.598588\pi$
$384$	5.76113e10	0.135213
$385$	−1.87980e8	−0.000436052 0
$386$	1.17555e10	0.0269524
$387$	−1.21529e11	−0.275410
$388$	−5.63003e11	−1.26115
$389$	−2.78839e10	−0.0617418	−0.0308709	−	0.999523i	$-0.509828\pi$
$389$	−2.78839e10	−0.0617418	−0.0308709	+	0.999523i	$0.509828\pi$
$390$	−7.69494e9	−0.0168428
$391$	8.23451e10	0.178173
$392$	5.51124e10	0.117886
$393$	−1.06339e11	−0.224868
$394$	−2.11968e10	−0.0443136
$395$	1.25583e11	0.259563
$396$	2.80899e9	0.00574012
$397$	5.56039e10	0.112344	0.0561718	−	0.998421i	$-0.482111\pi$
$397$	5.56039e10	0.112344	0.0561718	+	0.998421i	$0.482111\pi$
$398$	2.26205e8	0.000451886 0
$399$	−8.06046e9	−0.0159214
$400$	6.26864e11	1.22434
$401$	−3.14865e11	−0.608100	−0.304050	−	0.952656i	$-0.598339\pi$
$401$	−3.14865e11	−0.608100	−0.304050	+	0.952656i	$0.598339\pi$
$402$	−3.06894e10	−0.0586100
$403$	−6.79330e10	−0.128295
$404$	1.49365e10	0.0278954
$405$	8.99840e10	0.166195
$406$	7.65252e7	0.000139778 0
$407$	8.05914e9	0.0145584
$408$	−9.37515e9	−0.0167497
$409$	−7.50752e11	−1.32660	−0.663302	−	0.748352i	$-0.730846\pi$
$409$	−7.50752e11	−1.32660	−0.663302	+	0.748352i	$0.730846\pi$
$410$	3.29826e10	0.0576445
$411$	−1.53234e11	−0.264890
$412$	2.70773e11	0.462987
$413$	1.29858e9	0.00219630
$414$	−8.52224e9	−0.0142578
$415$	1.28777e12	2.13119
$416$	3.55741e10	0.0582389
$417$	−3.56508e11	−0.577373
$418$	−1.04134e9	−0.00166839
$419$	7.08699e11	1.12331	0.561653	−	0.827373i	$-0.310165\pi$
$419$	7.08699e11	1.12331	0.561653	+	0.827373i	$0.310165\pi$
$420$	9.25810e9	0.0145178
$421$	5.65648e11	0.877560	0.438780	−	0.898594i	$-0.355411\pi$
$421$	5.65648e11	0.877560	0.438780	+	0.898594i	$0.355411\pi$
$422$	−5.32516e10	−0.0817385
$423$	−6.68220e10	−0.101482
$424$	4.88257e10	0.0733672
$425$	−2.04739e11	−0.304404
$426$	−3.87202e10	−0.0569633
$427$	−6.46802e9	−0.00941556
$428$	7.45565e11	1.07396
$429$	2.31131e9	0.00329459
$430$	−5.17467e10	−0.0729919
$431$	−3.52572e11	−0.492153	−0.246076	−	0.969250i	$-0.579141\pi$
$431$	−3.52572e11	−0.492153	−0.246076	+	0.969250i	$0.579141\pi$
$432$	−1.37858e11	−0.190438
$433$	8.77496e10	0.119964	0.0599818	−	0.998199i	$-0.480896\pi$
$433$	8.77496e10	0.119964	0.0599818	+	0.998199i	$0.480896\pi$
$434$	−2.86116e8	−0.000387114 0
$435$	−9.04704e10	−0.121145
$436$	3.51686e11	0.466086
$437$	−9.02506e11	−1.18381
$438$	−4.05485e10	−0.0526431
$439$	3.23555e11	0.415775	0.207887	−	0.978153i	$-0.433341\pi$
$439$	3.23555e11	0.415775	0.207887	+	0.978153i	$0.433341\pi$
$440$	2.39631e9	0.00304793
$441$	−2.64685e11	−0.333238
$442$	−3.85033e9	−0.00479841
$443$	1.05919e12	1.30664	0.653319	−	0.757083i	$-0.273376\pi$
$443$	1.05919e12	1.30664	0.653319	+	0.757083i	$0.273376\pi$
$444$	−3.96916e11	−0.484703
$445$	3.32069e11	0.401428
$446$	4.83616e10	0.0578754
$447$	−9.11176e11	−1.07949
$448$	−1.40835e10	−0.0165181
$449$	−4.93194e11	−0.572676	−0.286338	−	0.958129i	$-0.592438\pi$
$449$	−4.93194e11	−0.572676	−0.286338	+	0.958129i	$0.592438\pi$
$450$	2.11893e10	0.0243590
$451$	−9.90692e9	−0.0112757
$452$	−7.91370e11	−0.891777
$453$	8.19339e10	0.0914159
$454$	4.51444e10	0.0498715
$455$	7.61782e9	0.00833258
$456$	1.02752e11	0.111288
$457$	−7.63784e11	−0.819121	−0.409560	−	0.912283i	$-0.634318\pi$
$457$	−7.63784e11	−0.819121	−0.409560	+	0.912283i	$0.634318\pi$
$458$	−3.35281e10	−0.0356053
$459$	4.50254e10	0.0473479
$460$	1.03660e12	1.07945
$461$	−8.27441e11	−0.853263	−0.426631	−	0.904426i	$-0.640300\pi$
$461$	−8.27441e11	−0.853263	−0.426631	+	0.904426i	$0.640300\pi$
$462$	9.73465e6	9.94103e−6 0
$463$	1.49878e12	1.51574	0.757869	−	0.652407i	$-0.226241\pi$
$463$	1.49878e12	1.51574	0.757869	+	0.652407i	$0.226241\pi$
$464$	1.38603e11	0.138817
$465$	3.38255e11	0.335511
$466$	5.23098e10	0.0513862
$467$	4.33053e11	0.421323	0.210661	−	0.977559i	$-0.432438\pi$
$467$	4.33053e11	0.421323	0.210661	+	0.977559i	$0.432438\pi$
$468$	−1.13833e11	−0.109689
$469$	3.03819e10	0.0289959
$470$	−2.84527e10	−0.0268957
$471$	−4.82099e11	−0.451380
$472$	−1.65538e10	−0.0153518
$473$	1.55430e10	0.0142778
$474$	−6.50338e9	−0.00591748
$475$	2.24395e12	2.02251
$476$	4.63249e9	0.00413603
$477$	−2.34492e11	−0.207394
$478$	1.02499e11	0.0898038
$479$	1.89550e12	1.64518	0.822592	−	0.568631i	$-0.192527\pi$
$479$	1.89550e12	1.64518	0.822592	+	0.568631i	$0.192527\pi$
$480$	−1.77132e11	−0.152304
$481$	−3.26594e11	−0.278199
$482$	−3.41126e10	−0.0287875
$483$	8.43684e9	0.00705371
$484$	1.20270e12	0.996214
$485$	2.30666e12	1.89298
$486$	−4.65987e9	−0.00378888
$487$	2.33531e12	1.88133	0.940663	−	0.339343i	$-0.110205\pi$
$487$	2.33531e12	1.88133	0.940663	+	0.339343i	$0.110205\pi$
$488$	8.24522e10	0.0658132
$489$	−1.13475e12	−0.897452
$490$	−1.12702e11	−0.0883182
$491$	1.57618e12	1.22388	0.611942	−	0.790903i	$-0.290389\pi$
$491$	1.57618e12	1.22388	0.611942	+	0.790903i	$0.290389\pi$
$492$	4.87920e11	0.375410
$493$	−4.52688e10	−0.0345134
$494$	4.21998e10	0.0318815
$495$	−1.15086e10	−0.00861586
$496$	−5.18216e11	−0.384453
$497$	3.83322e10	0.0281812
$498$	−6.66880e10	−0.0485865
$499$	1.54552e11	0.111589	0.0557947	−	0.998442i	$-0.482231\pi$
$499$	1.54552e11	0.111589	0.0557947	+	0.998442i	$0.482231\pi$
$500$	−4.94271e11	−0.353671
$501$	−8.41208e10	−0.0596532
$502$	1.35484e11	0.0952182
$503$	−1.11366e12	−0.775708	−0.387854	−	0.921721i	$-0.626784\pi$
$503$	−1.11366e12	−0.775708	−0.387854	+	0.921721i	$0.626784\pi$
$504$	−9.60550e8	−0.000663106 0
$505$	−6.11957e10	−0.0418706
$506$	1.08996e9	0.000739152 0
$507$	7.65299e11	0.514394
$508$	−2.56958e12	−1.71189
$509$	−1.16983e12	−0.772490	−0.386245	−	0.922396i	$-0.626228\pi$
$509$	−1.16983e12	−0.772490	−0.386245	+	0.922396i	$0.626228\pi$
$510$	1.91717e10	0.0125486
$511$	4.01421e10	0.0260439
$512$	4.52812e11	0.291208
$513$	−4.93481e11	−0.314588
$514$	−1.43337e10	−0.00905785
$515$	−1.10938e12	−0.694938
$516$	−7.65502e11	−0.475360
$517$	8.54627e9	0.00526101
$518$	−1.37553e9	−0.000839433 0
$519$	−1.03029e11	−0.0623312
$520$	−9.71095e10	−0.0582434
$521$	−1.13256e12	−0.673428	−0.336714	−	0.941607i	$-0.609315\pi$
$521$	−1.13256e12	−0.673428	−0.336714	+	0.941607i	$0.609315\pi$
$522$	4.68506e9	0.00276184
$523$	1.29127e12	0.754674	0.377337	−	0.926076i	$-0.376840\pi$
$523$	1.29127e12	0.754674	0.377337	+	0.926076i	$0.376840\pi$
$524$	−6.69825e11	−0.388124
$525$	−2.09769e10	−0.0120511
$526$	−1.08453e11	−0.0617741
$527$	1.69253e11	0.0955849
$528$	1.76315e10	0.00987270
$529$	−8.56504e11	−0.475531
$530$	−9.98462e10	−0.0549655
$531$	7.95020e10	0.0433963
$532$	−5.07723e10	−0.0274805
$533$	4.01475e11	0.215469
$534$	−1.71964e10	−0.00915168
$535$	−3.05463e12	−1.61200
$536$	−3.87298e11	−0.202677
$537$	−3.28719e11	−0.170585
$538$	−1.89564e10	−0.00975518
$539$	3.38521e10	0.0172757
$540$	5.66803e11	0.286854
$541$	−1.73934e12	−0.872964	−0.436482	−	0.899713i	$-0.643776\pi$
$541$	−1.73934e12	−0.872964	−0.436482	+	0.899713i	$0.643776\pi$
$542$	1.00670e11	0.0501074
$543$	−1.23253e10	−0.00608412
$544$	−8.86318e10	−0.0433905
$545$	−1.44088e12	−0.699590
$546$	−3.94493e8	−0.000189965 0
$547$	1.01841e12	0.486385	0.243193	−	0.969978i	$-0.421805\pi$
$547$	1.01841e12	0.486385	0.243193	+	0.969978i	$0.421805\pi$
$548$	−9.65208e11	−0.457202
$549$	−3.95988e11	−0.186040
$550$	−2.71002e9	−0.00126282
$551$	4.96148e11	0.229313
$552$	−1.07550e11	−0.0493043
$553$	6.43821e9	0.00292753
$554$	−3.69020e10	−0.0166439
$555$	1.62619e12	0.727534
$556$	−2.24562e12	−0.996551
$557$	2.18895e12	0.963578	0.481789	−	0.876287i	$-0.339987\pi$
$557$	2.18895e12	0.963578	0.481789	+	0.876287i	$0.339987\pi$
$558$	−1.75167e10	−0.00764891
$559$	−6.29876e11	−0.272836
$560$	5.81113e10	0.0249698
$561$	−5.75857e9	−0.00245461
$562$	−1.18660e11	−0.0501756
$563$	−3.42758e12	−1.43780	−0.718901	−	0.695112i	$-0.755355\pi$
$563$	−3.42758e12	−1.43780	−0.718901	+	0.695112i	$0.755355\pi$
$564$	−4.20908e11	−0.175158
$565$	3.24229e12	1.33855
$566$	−1.62964e10	−0.00667447
$567$	4.61317e9	0.00187446
$568$	−4.88646e11	−0.196982
$569$	−4.02290e12	−1.60892	−0.804460	−	0.594007i	$-0.797545\pi$
$569$	−4.02290e12	−1.60892	−0.804460	+	0.594007i	$0.797545\pi$
$570$	−2.10123e11	−0.0833752
$571$	9.47651e11	0.373066	0.186533	−	0.982449i	$-0.440275\pi$
$571$	9.47651e11	0.373066	0.186533	+	0.982449i	$0.440275\pi$
$572$	1.45588e10	0.00568648
$573$	1.13596e12	0.440219
$574$	1.69091e9	0.000650154 0
$575$	−2.34873e12	−0.896039
$576$	−8.62225e11	−0.326377
$577$	−1.11164e12	−0.417517	−0.208759	−	0.977967i	$-0.566942\pi$
$577$	−1.11164e12	−0.417517	−0.208759	+	0.977967i	$0.566942\pi$
$578$	−1.48892e11	−0.0554877
$579$	−7.12486e11	−0.263465
$580$	−5.69867e11	−0.209097
$581$	6.60197e10	0.0240370
$582$	−1.19452e11	−0.0431558
$583$	2.99906e10	0.0107517
$584$	−5.11719e11	−0.182043
$585$	4.66382e11	0.164642
$586$	8.78292e10	0.0307680
$587$	−1.50367e12	−0.522735	−0.261368	−	0.965239i	$-0.584174\pi$
$587$	−1.50367e12	−0.522735	−0.261368	+	0.965239i	$0.584174\pi$
$588$	−1.66723e12	−0.575172
$589$	−1.85502e12	−0.635084
$590$	3.38518e10	0.0115013
$591$	1.28471e12	0.433175
$592$	−2.49137e12	−0.833663
$593$	−2.18166e12	−0.724504	−0.362252	−	0.932080i	$-0.617992\pi$
$593$	−2.18166e12	−0.724504	−0.362252	+	0.932080i	$0.617992\pi$
$594$	5.95979e8	0.000196423 0
$595$	−1.89796e10	−0.00620813
$596$	−5.73944e12	−1.86321
$597$	−1.37100e10	−0.00441727
$598$	−4.41703e10	−0.0141246
$599$	1.70673e12	0.541681	0.270841	−	0.962624i	$-0.412698\pi$
$599$	1.70673e12	0.541681	0.270841	+	0.962624i	$0.412698\pi$
$600$	2.67407e11	0.0842349
$601$	4.09698e12	1.28094	0.640470	−	0.767983i	$-0.278740\pi$
$601$	4.09698e12	1.28094	0.640470	+	0.767983i	$0.278740\pi$
$602$	−2.65288e9	−0.000823252 0
$603$	1.86005e12	0.572924
$604$	5.16096e11	0.157785
$605$	−4.92753e12	−1.49531
$606$	3.16905e9	0.000954559 0
$607$	−4.05392e12	−1.21206	−0.606032	−	0.795440i	$-0.707240\pi$
$607$	−4.05392e12	−1.21206	−0.606032	+	0.795440i	$0.707240\pi$
$608$	9.71409e11	0.288294
$609$	−4.63811e9	−0.00136635
$610$	−1.68611e11	−0.0493062
$611$	−3.46335e11	−0.100533
$612$	2.83612e11	0.0817229
$613$	2.62140e12	0.749828	0.374914	−	0.927060i	$-0.377672\pi$
$613$	2.62140e12	0.749828	0.374914	+	0.927060i	$0.377672\pi$
$614$	−1.69691e11	−0.0481839
$615$	−1.99904e12	−0.563487
$616$	1.22851e8	3.43767e−5 0
$617$	−1.92608e11	−0.0535046	−0.0267523	−	0.999642i	$-0.508517\pi$
$617$	−1.92608e11	−0.0535046	−0.0267523	+	0.999642i	$0.508517\pi$
$618$	5.74497e10	0.0158431
$619$	2.14110e12	0.586178	0.293089	−	0.956085i	$-0.405317\pi$
$619$	2.14110e12	0.586178	0.293089	+	0.956085i	$0.405317\pi$
$620$	2.13065e12	0.579094
$621$	5.16524e11	0.139373
$622$	−1.90985e11	−0.0511614
$623$	1.70240e10	0.00452758
$624$	−7.14509e11	−0.188659
$625$	−2.69478e12	−0.706421
$626$	−1.78213e11	−0.0463825
$627$	6.31142e10	0.0163089
$628$	−3.03671e12	−0.779085
$629$	8.13700e11	0.207270
$630$	1.96428e9	0.000496788 0
$631$	1.85087e12	0.464776	0.232388	−	0.972623i	$-0.425346\pi$
$631$	1.85087e12	0.464776	0.232388	+	0.972623i	$0.425346\pi$
$632$	−8.20722e10	−0.0204630
$633$	3.22752e12	0.799010
$634$	3.25683e11	0.0800558
$635$	1.05277e13	2.56952
$636$	−1.47705e12	−0.357963
$637$	−1.37185e12	−0.330124
$638$	−5.99201e8	−0.000143179 0
$639$	2.34679e12	0.556827
$640$	−1.48678e12	−0.350298
$641$	2.62055e12	0.613099	0.306550	−	0.951855i	$-0.400825\pi$
$641$	2.62055e12	0.613099	0.306550	+	0.951855i	$0.400825\pi$
$642$	1.58186e11	0.0367501
$643$	−2.10252e12	−0.485054	−0.242527	−	0.970145i	$-0.577976\pi$
$643$	−2.10252e12	−0.485054	−0.242527	+	0.970145i	$0.577976\pi$
$644$	5.31431e10	0.0121748
$645$	3.13631e12	0.713510
$646$	−1.05140e11	−0.0237531
$647$	8.42611e11	0.189042	0.0945209	−	0.995523i	$-0.469868\pi$
$647$	8.42611e11	0.189042	0.0945209	+	0.995523i	$0.469868\pi$
$648$	−5.88072e10	−0.0131022
$649$	−1.01680e10	−0.00224975
$650$	1.09823e11	0.0241314
$651$	1.73412e10	0.00378412
$652$	−7.14774e12	−1.54901
$653$	6.38379e12	1.37395	0.686973	−	0.726683i	$-0.258939\pi$
$653$	6.38379e12	1.37395	0.686973	+	0.726683i	$0.258939\pi$
$654$	7.46168e10	0.0159491
$655$	2.74431e12	0.582570
$656$	3.06258e12	0.645685
$657$	2.45760e12	0.514597
$658$	−1.45867e9	−0.000303348 0
$659$	−7.01173e12	−1.44824	−0.724120	−	0.689674i	$-0.757754\pi$
$659$	−7.01173e12	−1.44824	−0.724120	+	0.689674i	$0.757754\pi$
$660$	−7.24919e10	−0.0148711
$661$	−4.26630e12	−0.869250	−0.434625	−	0.900611i	$-0.643119\pi$
$661$	−4.26630e12	−0.869250	−0.434625	+	0.900611i	$0.643119\pi$
$662$	2.07461e11	0.0419833
$663$	2.33364e11	0.0469054
$664$	−8.41598e11	−0.168015
$665$	2.08017e11	0.0412479
$666$	−8.42133e10	−0.0165862
$667$	−5.19316e11	−0.101593
$668$	−5.29872e11	−0.102962
$669$	−2.93115e12	−0.565744
$670$	7.92007e11	0.151842
$671$	5.06453e10	0.00964468
$672$	−9.08095e9	−0.00171779
$673$	4.19265e12	0.787809	0.393905	−	0.919151i	$-0.371124\pi$
$673$	4.19265e12	0.787809	0.393905	+	0.919151i	$0.371124\pi$
$674$	−1.42384e11	−0.0265760
$675$	−1.28426e12	−0.238114
$676$	4.82057e12	0.887848
$677$	−4.51587e12	−0.826214	−0.413107	−	0.910682i	$-0.635557\pi$
$677$	−4.51587e12	−0.826214	−0.413107	+	0.910682i	$0.635557\pi$
$678$	−1.67904e11	−0.0305160
$679$	1.18255e11	0.0213503
$680$	2.41946e11	0.0433938
$681$	−2.73615e12	−0.487504
$682$	2.24032e9	0.000396534 0
$683$	−1.90757e12	−0.335419	−0.167709	−	0.985836i	$-0.553637\pi$
$683$	−1.90757e12	−0.335419	−0.167709	+	0.985836i	$0.553637\pi$
$684$	−3.10840e12	−0.542982
$685$	3.95452e12	0.686256
$686$	−1.15574e10	−0.00199251
$687$	2.03210e12	0.348048
$688$	−4.80491e12	−0.817593
$689$	−1.21536e12	−0.205455
$690$	2.19935e11	0.0369380
$691$	9.17365e12	1.53070	0.765352	−	0.643612i	$-0.222565\pi$
$691$	9.17365e12	1.53070	0.765352	+	0.643612i	$0.222565\pi$
$692$	−6.48971e11	−0.107584
$693$	−5.90006e8	−9.71756e−5 0
$694$	−4.18297e11	−0.0684490
$695$	9.20044e12	1.49581
$696$	5.91251e10	0.00955059
$697$	−1.00026e12	−0.160534
$698$	6.32553e11	0.100867
$699$	−3.17044e12	−0.502310
$700$	−1.32132e11	−0.0208002
$701$	7.00511e12	1.09568	0.547840	−	0.836583i	$-0.315450\pi$
$701$	7.00511e12	1.09568	0.547840	+	0.836583i	$0.315450\pi$
$702$	−2.41518e10	−0.00375347
$703$	−8.91819e12	−1.37714
$704$	1.10275e11	0.0169200
$705$	1.72449e12	0.262911
$706$	−8.95801e10	−0.0135703
$707$	−3.13729e9	−0.000472246 0
$708$	5.00778e11	0.0749024
$709$	2.04764e12	0.304331	0.152166	−	0.988355i	$-0.451375\pi$
$709$	2.04764e12	0.304331	0.152166	+	0.988355i	$0.451375\pi$
$710$	9.99259e11	0.147576
$711$	3.94163e11	0.0578445
$712$	−2.17017e11	−0.0316471
$713$	1.94164e12	0.281363
$714$	9.82870e8	0.000141532 0
$715$	−5.96484e10	−0.00853535
$716$	−2.07058e12	−0.294431
$717$	−6.21236e12	−0.877850
$718$	6.00175e10	0.00842788
$719$	−8.05377e12	−1.12388	−0.561939	−	0.827178i	$-0.689945\pi$
$719$	−8.05377e12	−1.12388	−0.561939	+	0.827178i	$0.689945\pi$
$720$	3.55772e12	0.493373
$721$	−5.68739e10	−0.00783799
$722$	7.21084e11	0.0987571
$723$	2.06753e12	0.281403
$724$	−7.76362e10	−0.0105012
$725$	1.29120e12	0.173569
$726$	2.55175e11	0.0340897
$727$	−4.54514e12	−0.603451	−0.301726	−	0.953395i	$-0.597563\pi$
$727$	−4.54514e12	−0.603451	−0.301726	+	0.953395i	$0.597563\pi$
$728$	−4.97848e9	−0.000656909 0
$729$	2.82430e11	0.0370370
$730$	1.04644e12	0.136384
$731$	1.56932e12	0.203275
$732$	−2.49430e12	−0.321107
$733$	2.35412e12	0.301204	0.150602	−	0.988594i	$-0.451879\pi$
$733$	2.35412e12	0.301204	0.150602	+	0.988594i	$0.451879\pi$
$734$	6.50545e11	0.0827266
$735$	6.83076e12	0.863328
$736$	−1.01677e12	−0.127724
$737$	−2.37893e11	−0.0297015
$738$	1.03521e11	0.0128463
$739$	−6.71592e12	−0.828335	−0.414167	−	0.910201i	$-0.635927\pi$
$739$	−6.71592e12	−0.828335	−0.414167	+	0.910201i	$0.635927\pi$
$740$	1.02433e13	1.25573
$741$	−2.55768e12	−0.311648
$742$	−5.11878e9	−0.000619938 0
$743$	4.74711e12	0.571452	0.285726	−	0.958311i	$-0.407765\pi$
$743$	4.74711e12	0.571452	0.285726	+	0.958311i	$0.407765\pi$
$744$	−2.21060e11	−0.0264504
$745$	2.35149e13	2.79666
$746$	6.00385e11	0.0709750
$747$	4.04189e12	0.474943
$748$	−3.62729e10	−0.00423667
$749$	−1.56600e11	−0.0181813
$750$	−1.04869e11	−0.0121024
$751$	3.17332e12	0.364028	0.182014	−	0.983296i	$-0.441738\pi$
$751$	3.17332e12	0.364028	0.182014	+	0.983296i	$0.441738\pi$
$752$	−2.64196e12	−0.301263
$753$	−8.21151e12	−0.930777
$754$	2.42824e10	0.00273603
$755$	−2.11448e12	−0.236833
$756$	2.90581e10	0.00323533
$757$	4.08571e12	0.452206	0.226103	−	0.974103i	$-0.427401\pi$
$757$	4.08571e12	0.452206	0.226103	+	0.974103i	$0.427401\pi$
$758$	−3.44121e11	−0.0378616
$759$	−6.60613e10	−0.00722536
$760$	−2.65174e12	−0.288317
$761$	7.13469e12	0.771159	0.385580	−	0.922675i	$-0.374002\pi$
$761$	7.13469e12	0.771159	0.385580	+	0.922675i	$0.374002\pi$
$762$	−5.45184e11	−0.0585795
$763$	−7.38691e10	−0.00789046
$764$	7.15536e12	0.759821
$765$	−1.16198e12	−0.122665
$766$	−3.43069e11	−0.0360041
$767$	4.12054e11	0.0429908
$768$	−5.37312e12	−0.557315
$769$	−1.06805e13	−1.10134	−0.550672	−	0.834722i	$-0.685628\pi$
$769$	−1.06805e13	−1.10134	−0.550672	+	0.834722i	$0.685628\pi$
$770$	−2.51224e8	−2.57544e−5 0
$771$	8.68752e11	0.0885423
$772$	−4.48791e12	−0.454743
$773$	6.56372e12	0.661214	0.330607	−	0.943768i	$-0.392747\pi$
$773$	6.56372e12	0.661214	0.330607	+	0.943768i	$0.392747\pi$
$774$	−1.62416e11	−0.0162665
$775$	−4.82761e12	−0.480700
$776$	−1.50747e12	−0.149235
$777$	8.33693e10	0.00820563
$778$	−3.72650e10	−0.00364664
$779$	1.09629e13	1.06662
$780$	2.93771e12	0.284173
$781$	−3.00145e11	−0.0288670
$782$	1.10049e11	0.0105234
$783$	−2.83956e11	−0.0269975
$784$	−1.04649e13	−0.989265
$785$	1.24416e13	1.16940
$786$	−1.42116e11	−0.0132813
$787$	1.61828e12	0.150372	0.0751860	−	0.997170i	$-0.476045\pi$
$787$	1.61828e12	0.150372	0.0751860	+	0.997170i	$0.476045\pi$
$788$	8.09234e12	0.747663
$789$	6.57322e12	0.603854
$790$	1.67834e11	0.0153305
$791$	1.66221e11	0.0150971
$792$	7.52121e9	0.000679242 0
$793$	−2.05238e12	−0.184302
$794$	7.43112e10	0.00663532
$795$	6.05157e12	0.537299
$796$	−8.63587e10	−0.00762425
$797$	−1.19360e13	−1.04784	−0.523922	−	0.851766i	$-0.675532\pi$
$797$	−1.19360e13	−1.04784	−0.523922	+	0.851766i	$0.675532\pi$
$798$	−1.07723e10	−0.000940363 0
$799$	8.62884e11	0.0749017
$800$	2.52804e12	0.218212
$801$	1.04225e12	0.0894595
$802$	−4.20798e11	−0.0359161
$803$	−3.14317e11	−0.0266777
$804$	1.17164e13	0.988872
$805$	−2.17731e11	−0.0182742
$806$	−9.07882e10	−0.00757743
$807$	1.14893e12	0.0953588
$808$	3.99932e10	0.00330092
$809$	−1.73505e13	−1.42411	−0.712054	−	0.702124i	$-0.752235\pi$
$809$	−1.73505e13	−1.42411	−0.712054	+	0.702124i	$0.752235\pi$
$810$	1.20258e11	0.00981592
$811$	8.18568e12	0.664448	0.332224	−	0.943201i	$-0.392201\pi$
$811$	8.18568e12	0.664448	0.332224	+	0.943201i	$0.392201\pi$
$812$	−2.92151e10	−0.00235834
$813$	−6.10147e12	−0.489810
$814$	1.07705e10	0.000859860 0
$815$	2.92847e13	2.32505
$816$	1.78018e12	0.140559
$817$	−1.71998e13	−1.35059
$818$	−1.00333e12	−0.0783529
$819$	2.39098e10	0.00185694
$820$	−1.25918e13	−0.972583
$821$	6.64204e12	0.510220	0.255110	−	0.966912i	$-0.417888\pi$
$821$	6.64204e12	0.510220	0.255110	+	0.966912i	$0.417888\pi$
$822$	−2.04787e11	−0.0156451
$823$	5.51708e11	0.0419189	0.0209594	−	0.999780i	$-0.493328\pi$
$823$	5.51708e11	0.0419189	0.0209594	+	0.999780i	$0.493328\pi$
$824$	7.25010e11	0.0547863
$825$	1.64252e11	0.0123443
$826$	1.73547e9	0.000129720 0
$827$	−1.63550e13	−1.21584	−0.607919	−	0.793999i	$-0.707996\pi$
$827$	−1.63550e13	−1.21584	−0.607919	+	0.793999i	$0.707996\pi$
$828$	3.25355e12	0.240559
$829$	2.05391e12	0.151038	0.0755188	−	0.997144i	$-0.475939\pi$
$829$	2.05391e12	0.151038	0.0755188	+	0.997144i	$0.475939\pi$
$830$	1.72103e12	0.125874
$831$	2.23659e12	0.162698
$832$	−4.46886e12	−0.323327
$833$	3.41792e12	0.245957
$834$	−4.76450e11	−0.0341013
$835$	2.17092e12	0.154545
$836$	3.97553e11	0.0281492
$837$	1.06167e12	0.0747696
$838$	9.47131e11	0.0663456
$839$	−9.49604e12	−0.661628	−0.330814	−	0.943696i	$-0.607323\pi$
$839$	−9.49604e12	−0.661628	−0.330814	+	0.943696i	$0.607323\pi$
$840$	2.47891e10	0.00171792
$841$	−1.42217e13	−0.980321
$842$	7.55953e11	0.0518311
$843$	7.19188e12	0.490477
$844$	2.03300e13	1.37910
$845$	−1.97502e13	−1.33265
$846$	−8.93035e10	−0.00599379
$847$	−2.52618e11	−0.0168651
$848$	−9.27116e12	−0.615677
$849$	9.87705e11	0.0652443
$850$	−2.73621e11	−0.0179789
$851$	9.33462e12	0.610118
$852$	1.47823e13	0.961089
$853$	−3.90438e12	−0.252512	−0.126256	−	0.991998i	$-0.540296\pi$
$853$	−3.90438e12	−0.252512	−0.126256	+	0.991998i	$0.540296\pi$
$854$	−8.64411e9	−0.000556109 0
$855$	1.27353e13	0.815010
$856$	1.99629e12	0.127084
$857$	−3.20675e12	−0.203073	−0.101536	−	0.994832i	$-0.532376\pi$
$857$	−3.20675e12	−0.203073	−0.101536	+	0.994832i	$0.532376\pi$
$858$	3.08892e9	0.000194587 0
$859$	−2.54347e13	−1.59389	−0.796944	−	0.604053i	$-0.793552\pi$
$859$	−2.54347e13	−1.59389	−0.796944	+	0.604053i	$0.793552\pi$
$860$	1.97554e13	1.23152
$861$	−1.02484e11	−0.00635539
$862$	−4.71190e11	−0.0290679
$863$	−6.71265e12	−0.411951	−0.205975	−	0.978557i	$-0.566037\pi$
$863$	−6.71265e12	−0.411951	−0.205975	+	0.978557i	$0.566037\pi$
$864$	−5.55958e11	−0.0339414
$865$	2.65888e12	0.161483
$866$	1.17272e11	0.00708538
$867$	9.02420e12	0.542404
$868$	1.09231e11	0.00653142
$869$	−5.04119e10	−0.00299877
$870$	−1.20908e11	−0.00715514
$871$	9.64054e12	0.567570
$872$	9.41659e11	0.0551530
$873$	7.23983e12	0.421856
$874$	−1.20614e12	−0.0699194
$875$	1.03818e11	0.00598736
$876$	1.54803e13	0.888198
$877$	−4.93714e12	−0.281823	−0.140912	−	0.990022i	$-0.545003\pi$
$877$	−4.93714e12	−0.281823	−0.140912	+	0.990022i	$0.545003\pi$
$878$	4.32412e11	0.0245568
$879$	−5.32323e12	−0.300764
$880$	−4.55018e11	−0.0255774
$881$	2.75278e13	1.53950	0.769750	−	0.638345i	$-0.220381\pi$
$881$	2.75278e13	1.53950	0.769750	+	0.638345i	$0.220381\pi$
$882$	−3.53735e11	−0.0196820
$883$	2.27999e13	1.26215	0.631073	−	0.775724i	$-0.282615\pi$
$883$	2.27999e13	1.26215	0.631073	+	0.775724i	$0.282615\pi$
$884$	1.46995e12	0.0809592
$885$	−2.05172e12	−0.112428
$886$	1.41554e12	0.0771737
$887$	−3.41001e13	−1.84969	−0.924847	−	0.380339i	$-0.875807\pi$
$887$	−3.41001e13	−1.84969	−0.924847	+	0.380339i	$0.875807\pi$
$888$	−1.06277e12	−0.0573560
$889$	5.39720e11	0.0289808
$890$	4.43789e11	0.0237095
$891$	−3.61216e10	−0.00192007
$892$	−1.84631e13	−0.976479
$893$	−9.45725e12	−0.497661
$894$	−1.21773e12	−0.0637576
$895$	8.48330e12	0.441938
$896$	−7.62223e10	−0.00395090
$897$	2.67711e12	0.138070
$898$	−6.59123e11	−0.0338239
$899$	−1.06741e12	−0.0545020
$900$	−8.08946e12	−0.410987
$901$	3.02803e12	0.153073
$902$	−1.32400e10	−0.000665975 0
$903$	1.60788e11	0.00804745
$904$	−2.11893e12	−0.105526
$905$	3.18080e11	0.0157623
$906$	1.09500e11	0.00539927
$907$	2.77919e12	0.136359	0.0681797	−	0.997673i	$-0.478281\pi$
$907$	2.77919e12	0.136359	0.0681797	+	0.997673i	$0.478281\pi$
$908$	−1.72348e13	−0.841436
$909$	−1.92073e11	−0.00933100
$910$	1.01807e10	0.000492145 0
$911$	−1.37455e13	−0.661193	−0.330596	−	0.943772i	$-0.607250\pi$
$911$	−1.37455e13	−0.661193	−0.330596	+	0.943772i	$0.607250\pi$
$912$	−1.95109e13	−0.933899
$913$	−5.16941e11	−0.0246220
$914$	−1.02075e12	−0.0483795
$915$	1.02193e13	0.481978
$916$	1.28001e13	0.600735
$917$	1.40692e11	0.00657062
$918$	6.01737e10	0.00279650
$919$	1.00087e13	0.462869	0.231435	−	0.972850i	$-0.425658\pi$
$919$	1.00087e13	0.462869	0.231435	+	0.972850i	$0.425658\pi$
$920$	2.77556e12	0.127734
$921$	1.02848e13	0.471007
$922$	−1.10582e12	−0.0503960
$923$	1.21633e13	0.551624
$924$	−3.71641e9	−0.000167726 0
$925$	−2.32091e13	−1.04237
$926$	2.00303e12	0.0895237
$927$	−3.48196e12	−0.154869
$928$	5.58963e11	0.0247410
$929$	2.63958e13	1.16269	0.581345	−	0.813657i	$-0.302527\pi$
$929$	2.63958e13	1.16269	0.581345	+	0.813657i	$0.302527\pi$
$930$	4.52057e11	0.0198162
$931$	−3.74605e13	−1.63418
$932$	−1.99704e13	−0.866992
$933$	1.15754e13	0.500113
$934$	5.78748e11	0.0248845
$935$	1.48612e11	0.00635920
$936$	−3.04794e11	−0.0129797
$937$	−3.45669e13	−1.46498	−0.732492	−	0.680776i	$-0.761643\pi$
$937$	−3.45669e13	−1.46498	−0.732492	+	0.680776i	$0.761643\pi$
$938$	4.06035e10	0.00171258
$939$	1.08013e13	0.453398
$940$	1.08624e13	0.453787
$941$	7.72112e12	0.321016	0.160508	−	0.987035i	$-0.448687\pi$
$941$	7.72112e12	0.321016	0.160508	+	0.987035i	$0.448687\pi$
$942$	−6.44295e11	−0.0266597
$943$	−1.14748e13	−0.472546
$944$	3.14329e12	0.128828
$945$	−1.19053e11	−0.00485620
$946$	2.07723e10	0.000843286 0
$947$	3.74173e13	1.51181	0.755906	−	0.654680i	$-0.227197\pi$
$947$	3.74173e13	1.51181	0.755906	+	0.654680i	$0.227197\pi$
$948$	2.48281e12	0.0998402
$949$	1.27376e13	0.509788
$950$	2.99889e12	0.119455
$951$	−1.97393e13	−0.782562
$952$	1.24037e10	0.000489425 0
$953$	1.56325e13	0.613918	0.306959	−	0.951723i	$-0.400689\pi$
$953$	1.56325e13	0.613918	0.306959	+	0.951723i	$0.400689\pi$
$954$	−3.13384e11	−0.0122492
$955$	−2.93160e13	−1.14048
$956$	−3.91313e13	−1.51518
$957$	3.63169e10	0.00139960
$958$	2.53322e12	0.0971692
$959$	2.02735e11	0.00774006
$960$	2.22516e13	0.845551
$961$	−2.24487e13	−0.849057
$962$	−4.36472e11	−0.0164312
$963$	−9.58745e12	−0.359240
$964$	1.30232e13	0.485705
$965$	1.83872e13	0.682564
$966$	1.12753e10	0.000416612 0
$967$	−1.73605e13	−0.638475	−0.319237	−	0.947675i	$-0.603427\pi$
$967$	−1.73605e13	−0.638475	−0.319237	+	0.947675i	$0.603427\pi$
$968$	3.22029e12	0.117884
$969$	6.37240e12	0.232191
$970$	3.08271e12	0.111805
$971$	−3.63320e13	−1.31161	−0.655803	−	0.754932i	$-0.727670\pi$
$971$	−3.63320e13	−1.31161	−0.655803	+	0.754932i	$0.727670\pi$
$972$	1.77901e12	0.0639262
$973$	4.71676e11	0.0168708
$974$	3.12099e12	0.111116
$975$	−6.65624e12	−0.235889
$976$	−1.56563e13	−0.552286
$977$	1.69592e13	0.595498	0.297749	−	0.954644i	$-0.403764\pi$
$977$	1.69592e13	0.595498	0.297749	+	0.954644i	$0.403764\pi$
$978$	−1.51653e12	−0.0530060
$979$	−1.33300e11	−0.00463776
$980$	4.30265e13	1.49011
$981$	−4.52244e12	−0.155906
$982$	2.10647e12	0.0722859
$983$	−4.74799e13	−1.62188	−0.810941	−	0.585128i	$-0.801044\pi$
$983$	−4.74799e13	−1.62188	−0.810941	+	0.585128i	$0.801044\pi$
$984$	1.30643e12	0.0444231
$985$	−3.31548e13	−1.12223
$986$	−6.04989e10	−0.00203846
$987$	8.84085e10	0.00296529
$988$	−1.61107e13	−0.537907
$989$	1.80030e13	0.598357
$990$	−1.53805e10	−0.000508877 0
$991$	−1.07567e13	−0.354281	−0.177141	−	0.984186i	$-0.556685\pi$
$991$	−1.07567e13	−0.354281	−0.177141	+	0.984186i	$0.556685\pi$
$992$	−2.08988e12	−0.0685203
$993$	−1.25740e13	−0.410395
$994$	5.12286e10	0.00166446
$995$	3.53817e11	0.0114439
$996$	2.54596e13	0.819755
$997$	−4.06172e13	−1.30191	−0.650956	−	0.759115i	$-0.725632\pi$
$997$	−4.06172e13	−1.30191	−0.650956	+	0.759115i	$0.725632\pi$
$998$	2.06550e11	0.00659078
$999$	5.10407e12	0.162133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.12	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.12	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +2793.66 q^{10} -839.126 q^{11} +41327.3 q^{12} +34005.3 q^{13} +143.222 q^{14} -169321. q^{15} +259404. q^{16} -84723.3 q^{17} +8768.37 q^{18} +928571. q^{19} -1.06654e6 q^{20} -8680.50 q^{21} -1121.44 q^{22} -971930. q^{23} +110656. q^{24} +2.41656e6 q^{25} +45445.9 q^{26} -531441. q^{27} -54677.9 q^{28} +534314. q^{29} -226287. q^{30} -1.99772e6 q^{31} +1.04613e6 q^{32} +67969.2 q^{33} -113227. q^{34} +224019. q^{35} -3.34751e6 q^{36} -9.60421e6 q^{37} +1.24098e6 q^{38} -2.75443e6 q^{39} -2.85572e6 q^{40} +1.18062e7 q^{41} -11600.9 q^{42} -1.85229e7 q^{43} +428134. q^{44} +1.37150e7 q^{45} -1.29892e6 q^{46} -1.01847e7 q^{47} -2.10117e7 q^{48} -4.03421e7 q^{49} +3.22958e6 q^{50} +6.86258e6 q^{51} -1.73500e7 q^{52} -3.57403e7 q^{53} -710238. q^{54} -1.75409e6 q^{55} -146403. q^{56} -7.52143e7 q^{57} +714077. q^{58} +1.21174e7 q^{59} +8.63898e7 q^{60} -6.03548e7 q^{61} -2.66983e6 q^{62} +703120. q^{63} -1.31417e8 q^{64} +7.10839e7 q^{65} +90836.6 q^{66} +2.83501e8 q^{67} +4.32270e7 q^{68} +7.87263e7 q^{69} +299387. q^{70} +3.57688e8 q^{71} -8.96315e6 q^{72} +3.74577e8 q^{73} -1.28354e7 q^{74} -1.95741e8 q^{75} -4.73770e8 q^{76} -89926.3 q^{77} -3.68112e6 q^{78} +6.00766e7 q^{79} +5.42252e8 q^{80} +4.30467e7 q^{81} +1.57783e7 q^{82} +6.16047e8 q^{83} +4.42891e6 q^{84} -1.77104e8 q^{85} -2.47547e7 q^{86} -4.32794e7 q^{87} +1.14635e6 q^{88} +1.58856e8 q^{89} +1.83292e7 q^{90} +3.64423e6 q^{91} +4.95892e8 q^{92} +1.61815e8 q^{93} -1.36113e7 q^{94} +1.94107e9 q^{95} -8.47368e7 q^{96} +1.10346e9 q^{97} -5.39147e7 q^{98} -5.50551e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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