LMFDB - Embedded newform 177.10.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q+18.6113 q^{2} -81.0000 q^{3} -165.619 q^{4} +1492.75 q^{5} -1507.52 q^{6} +11801.9 q^{7} -12611.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+18.6113 q^{2} -81.0000 q^{3} -165.619 q^{4} +1492.75 q^{5} -1507.52 q^{6} +11801.9 q^{7} -12611.4 q^{8} +6561.00 q^{9} +27782.1 q^{10} +54115.8 q^{11} +13415.1 q^{12} +176081. q^{13} +219649. q^{14} -120913. q^{15} -149917. q^{16} +108748. q^{17} +122109. q^{18} +54464.9 q^{19} -247228. q^{20} -955953. q^{21} +1.00717e6 q^{22} -2.05205e6 q^{23} +1.02152e6 q^{24} +275183. q^{25} +3.27711e6 q^{26} -531441. q^{27} -1.95462e6 q^{28} -3.15094e6 q^{29} -2.25035e6 q^{30} +5.67861e6 q^{31} +3.66687e6 q^{32} -4.38338e6 q^{33} +2.02394e6 q^{34} +1.76173e7 q^{35} -1.08663e6 q^{36} +1.48233e7 q^{37} +1.01366e6 q^{38} -1.42626e7 q^{39} -1.88257e7 q^{40} -2.73520e7 q^{41} -1.77915e7 q^{42} +1.96666e7 q^{43} -8.96260e6 q^{44} +9.79394e6 q^{45} -3.81914e7 q^{46} -1.60710e7 q^{47} +1.21433e7 q^{48} +9.89308e7 q^{49} +5.12152e6 q^{50} -8.80857e6 q^{51} -2.91624e7 q^{52} -4.91083e7 q^{53} -9.89081e6 q^{54} +8.07814e7 q^{55} -1.48838e8 q^{56} -4.41166e6 q^{57} -5.86430e7 q^{58} +1.21174e7 q^{59} +2.00255e7 q^{60} +9.09669e7 q^{61} +1.05686e8 q^{62} +7.74322e7 q^{63} +1.45003e8 q^{64} +2.62846e8 q^{65} -8.15804e7 q^{66} -1.83319e7 q^{67} -1.80107e7 q^{68} +1.66216e8 q^{69} +3.27881e8 q^{70} -3.08979e8 q^{71} -8.27433e7 q^{72} +1.21812e7 q^{73} +2.75880e8 q^{74} -2.22898e7 q^{75} -9.02043e6 q^{76} +6.38668e8 q^{77} -2.65446e8 q^{78} -2.20744e8 q^{79} -2.23789e8 q^{80} +4.30467e7 q^{81} -5.09056e8 q^{82} +4.48981e8 q^{83} +1.58324e8 q^{84} +1.62333e8 q^{85} +3.66022e8 q^{86} +2.55226e8 q^{87} -6.82475e8 q^{88} +7.18855e8 q^{89} +1.82278e8 q^{90} +2.07809e9 q^{91} +3.39859e8 q^{92} -4.59968e8 q^{93} -2.99103e8 q^{94} +8.13026e7 q^{95} -2.97016e8 q^{96} -1.57982e9 q^{97} +1.84123e9 q^{98} +3.55054e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.6113	0.822512	0.411256	−	0.911520i	$-0.365090\pi$
$2$	18.6113	0.822512	0.411256	+	0.911520i	$0.365090\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−165.619	−0.323475
$5$	1492.75	1.06813	0.534063	−	0.845445i	$-0.320664\pi$
$5$	1492.75	1.06813	0.534063	+	0.845445i	$0.320664\pi$
$6$	−1507.52	−0.474877
$7$	11801.9	1.85785	0.928924	−	0.370271i	$-0.120735\pi$
$7$	11801.9	1.85785	0.928924	+	0.370271i	$0.120735\pi$
$8$	−12611.4	−1.08857
$9$	6561.00	0.333333
$10$	27782.1	0.878546
$11$	54115.8	1.11444	0.557220	−	0.830365i	$-0.311868\pi$
$11$	54115.8	1.11444	0.557220	+	0.830365i	$0.311868\pi$
$12$	13415.1	0.186758
$13$	176081.	1.70989	0.854945	−	0.518718i	$-0.173591\pi$
$13$	176081.	1.70989	0.854945	+	0.518718i	$0.173591\pi$
$14$	219649.	1.52810
$15$	−120913.	−0.616683
$16$	−149917.	−0.571889
$17$	108748.	0.315791	0.157896	−	0.987456i	$-0.449529\pi$
$17$	108748.	0.315791	0.157896	+	0.987456i	$0.449529\pi$
$18$	122109.	0.274171
$19$	54464.9	0.0958795	0.0479397	−	0.998850i	$-0.484734\pi$
$19$	54464.9	0.0958795	0.0479397	+	0.998850i	$0.484734\pi$
$20$	−247228.	−0.345512
$21$	−955953.	−1.07263
$22$	1.00717e6	0.916640
$23$	−2.05205e6	−1.52902	−0.764511	−	0.644611i	$-0.777019\pi$
$23$	−2.05205e6	−1.52902	−0.764511	+	0.644611i	$0.777019\pi$
$24$	1.02152e6	0.628488
$25$	275183.	0.140894
$26$	3.27711e6	1.40640
$27$	−531441.	−0.192450
$28$	−1.95462e6	−0.600967
$29$	−3.15094e6	−0.827272	−0.413636	−	0.910442i	$-0.635741\pi$
$29$	−3.15094e6	−0.827272	−0.413636	+	0.910442i	$0.635741\pi$
$30$	−2.25035e6	−0.507229
$31$	5.67861e6	1.10437	0.552185	−	0.833722i	$-0.313794\pi$
$31$	5.67861e6	1.10437	0.552185	+	0.833722i	$0.313794\pi$
$32$	3.66687e6	0.618188
$33$	−4.38338e6	−0.643422
$34$	2.02394e6	0.259742
$35$	1.76173e7	1.98442
$36$	−1.08663e6	−0.107825
$37$	1.48233e7	1.30028	0.650139	−	0.759815i	$-0.274711\pi$
$37$	1.48233e7	1.30028	0.650139	+	0.759815i	$0.274711\pi$
$38$	1.01366e6	0.0788620
$39$	−1.42626e7	−0.987206
$40$	−1.88257e7	−1.16273
$41$	−2.73520e7	−1.51168	−0.755842	−	0.654754i	$-0.772772\pi$
$41$	−2.73520e7	−1.51168	−0.755842	+	0.654754i	$0.772772\pi$
$42$	−1.77915e7	−0.882250
$43$	1.96666e7	0.877247	0.438623	−	0.898671i	$-0.355466\pi$
$43$	1.96666e7	0.877247	0.438623	+	0.898671i	$0.355466\pi$
$44$	−8.96260e6	−0.360493
$45$	9.79394e6	0.356042
$46$	−3.81914e7	−1.25764
$47$	−1.60710e7	−0.480400	−0.240200	−	0.970723i	$-0.577213\pi$
$47$	−1.60710e7	−0.480400	−0.240200	+	0.970723i	$0.577213\pi$
$48$	1.21433e7	0.330181
$49$	9.89308e7	2.45160
$50$	5.12152e6	0.115887
$51$	−8.80857e6	−0.182322
$52$	−2.91624e7	−0.553106
$53$	−4.91083e7	−0.854896	−0.427448	−	0.904040i	$-0.640587\pi$
$53$	−4.91083e7	−0.854896	−0.427448	+	0.904040i	$0.640587\pi$
$54$	−9.89081e6	−0.158292
$55$	8.07814e7	1.19036
$56$	−1.48838e8	−2.02240
$57$	−4.41166e6	−0.0553561
$58$	−5.86430e7	−0.680441
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	2.00255e7	0.199481
$61$	9.09669e7	0.841200	0.420600	−	0.907246i	$-0.361820\pi$
$61$	9.09669e7	0.841200	0.420600	+	0.907246i	$0.361820\pi$
$62$	1.05686e8	0.908357
$63$	7.74322e7	0.619283
$64$	1.45003e8	1.08036
$65$	2.62846e8	1.82638
$66$	−8.15804e7	−0.529222
$67$	−1.83319e7	−0.111140	−0.0555700	−	0.998455i	$-0.517698\pi$
$67$	−1.83319e7	−0.111140	−0.0555700	+	0.998455i	$0.517698\pi$
$68$	−1.80107e7	−0.102150
$69$	1.66216e8	0.882781
$70$	3.27881e8	1.63221
$71$	−3.08979e8	−1.44300	−0.721500	−	0.692414i	$-0.756547\pi$
$71$	−3.08979e8	−1.44300	−0.721500	+	0.692414i	$0.756547\pi$
$72$	−8.27433e7	−0.362858
$73$	1.21812e7	0.0502039	0.0251019	−	0.999685i	$-0.492009\pi$
$73$	1.21812e7	0.0502039	0.0251019	+	0.999685i	$0.492009\pi$
$74$	2.75880e8	1.06949
$75$	−2.22898e7	−0.0813451
$76$	−9.02043e6	−0.0310146
$77$	6.38668e8	2.07046
$78$	−2.65446e8	−0.811988
$79$	−2.20744e8	−0.637626	−0.318813	−	0.947818i	$-0.603284\pi$
$79$	−2.20744e8	−0.637626	−0.318813	+	0.947818i	$0.603284\pi$
$80$	−2.23789e8	−0.610850
$81$	4.30467e7	0.111111
$82$	−5.09056e8	−1.24338
$83$	4.48981e8	1.03843	0.519215	−	0.854644i	$-0.326224\pi$
$83$	4.48981e8	1.03843	0.519215	+	0.854644i	$0.326224\pi$
$84$	1.58324e8	0.346968
$85$	1.62333e8	0.337305
$86$	3.66022e8	0.721546
$87$	2.55226e8	0.477626
$88$	−6.82475e8	−1.21315
$89$	7.18855e8	1.21447	0.607234	−	0.794523i	$-0.292279\pi$
$89$	7.18855e8	1.21447	0.607234	+	0.794523i	$0.292279\pi$
$90$	1.82278e8	0.292849
$91$	2.07809e9	3.17672
$92$	3.39859e8	0.494600
$93$	−4.59968e8	−0.637608
$94$	−2.99103e8	−0.395134
$95$	8.13026e7	0.102411
$96$	−2.97016e8	−0.356911
$97$	−1.57982e9	−1.81191	−0.905953	−	0.423378i	$-0.860844\pi$
$97$	−1.57982e9	−1.81191	−0.905953	+	0.423378i	$0.860844\pi$
$98$	1.84123e9	2.01647
$99$	3.55054e8	0.371480
$100$	−4.55756e7	−0.0455756
$101$	4.78446e8	0.457495	0.228748	−	0.973486i	$-0.426537\pi$
$101$	4.78446e8	0.457495	0.228748	+	0.973486i	$0.426537\pi$
$102$	−1.63939e8	−0.149962
$103$	1.88156e9	1.64722	0.823608	−	0.567160i	$-0.191958\pi$
$103$	1.88156e9	1.64722	0.823608	+	0.567160i	$0.191958\pi$
$104$	−2.22063e9	−1.86134
$105$	−1.42700e9	−1.14570
$106$	−9.13970e8	−0.703162
$107$	1.55230e9	1.14485	0.572426	−	0.819956i	$-0.306002\pi$
$107$	1.55230e9	1.14485	0.572426	+	0.819956i	$0.306002\pi$
$108$	8.80167e7	0.0622527
$109$	2.26041e9	1.53380	0.766898	−	0.641769i	$-0.221799\pi$
$109$	2.26041e9	1.53380	0.766898	+	0.641769i	$0.221799\pi$
$110$	1.50345e9	0.979087
$111$	−1.20068e9	−0.750716
$112$	−1.76931e9	−1.06248
$113$	5.97898e8	0.344964	0.172482	−	0.985013i	$-0.444821\pi$
$113$	5.97898e8	0.344964	0.172482	+	0.985013i	$0.444821\pi$
$114$	−8.21068e7	−0.0455310
$115$	−3.06321e9	−1.63319
$116$	5.21855e8	0.267602
$117$	1.15527e9	0.569964
$118$	2.25520e8	0.107082
$119$	1.28343e9	0.586692
$120$	1.52488e9	0.671305
$121$	5.70570e8	0.241977
$122$	1.69301e9	0.691897
$123$	2.21551e9	0.872771
$124$	−9.40486e8	−0.357236
$125$	−2.50475e9	−0.917634
$126$	1.44111e9	0.509367
$127$	−1.45243e9	−0.495425	−0.247712	−	0.968834i	$-0.579679\pi$
$127$	−1.45243e9	−0.495425	−0.247712	+	0.968834i	$0.579679\pi$
$128$	8.21259e8	0.270418
$129$	−1.59300e9	−0.506479
$130$	4.89191e9	1.50222
$131$	6.58148e8	0.195255	0.0976276	−	0.995223i	$-0.468875\pi$
$131$	6.58148e8	0.195255	0.0976276	+	0.995223i	$0.468875\pi$
$132$	7.25971e8	0.208131
$133$	6.42789e8	0.178129
$134$	−3.41180e8	−0.0914139
$135$	−7.93310e8	−0.205561
$136$	−1.37146e9	−0.343762
$137$	−2.80147e9	−0.679429	−0.339714	−	0.940529i	$-0.610330\pi$
$137$	−2.80147e9	−0.679429	−0.339714	+	0.940529i	$0.610330\pi$
$138$	3.09351e9	0.726098
$139$	−8.04977e9	−1.82901	−0.914507	−	0.404571i	$-0.867421\pi$
$139$	−8.04977e9	−1.82901	−0.914507	+	0.404571i	$0.867421\pi$
$140$	−2.91776e9	−0.641908
$141$	1.30175e9	0.277359
$142$	−5.75051e9	−1.18688
$143$	9.52878e9	1.90557
$144$	−9.83608e8	−0.190630
$145$	−4.70356e9	−0.883631
$146$	2.26708e8	0.0412933
$147$	−8.01340e9	−1.41543
$148$	−2.45501e9	−0.420607
$149$	−1.17236e9	−0.194861	−0.0974304	−	0.995242i	$-0.531062\pi$
$149$	−1.17236e9	−0.194861	−0.0974304	+	0.995242i	$0.531062\pi$
$150$	−4.14843e8	−0.0669072
$151$	1.25208e9	0.195991	0.0979954	−	0.995187i	$-0.468757\pi$
$151$	1.25208e9	0.195991	0.0979954	+	0.995187i	$0.468757\pi$
$152$	−6.86878e8	−0.104372
$153$	7.13494e8	0.105264
$154$	1.18865e10	1.70298
$155$	8.47676e9	1.17961
$156$	2.36216e9	0.319336
$157$	6.13909e9	0.806410	0.403205	−	0.915110i	$-0.367896\pi$
$157$	6.13909e9	0.806410	0.403205	+	0.915110i	$0.367896\pi$
$158$	−4.10833e9	−0.524455
$159$	3.97777e9	0.493575
$160$	5.47372e9	0.660302
$161$	−2.42181e10	−2.84069
$162$	8.01156e8	0.0913902
$163$	1.04317e10	1.15748	0.578738	−	0.815513i	$-0.303545\pi$
$163$	1.04317e10	1.15748	0.578738	+	0.815513i	$0.303545\pi$
$164$	4.53000e9	0.488992
$165$	−6.54330e9	−0.687256
$166$	8.35613e9	0.854120
$167$	6.18162e9	0.615004	0.307502	−	0.951547i	$-0.400507\pi$
$167$	6.18162e9	0.615004	0.307502	+	0.951547i	$0.400507\pi$
$168$	1.20559e10	1.16764
$169$	2.04002e10	1.92373
$170$	3.02124e9	0.277437
$171$	3.57344e8	0.0319598
$172$	−3.25717e9	−0.283767
$173$	−1.19474e10	−1.01407	−0.507033	−	0.861927i	$-0.669258\pi$
$173$	−1.19474e10	−1.01407	−0.507033	+	0.861927i	$0.669258\pi$
$174$	4.75009e9	0.392853
$175$	3.24768e9	0.261759
$176$	−8.11290e9	−0.637337
$177$	−9.81506e8	−0.0751646
$178$	1.33788e10	0.998914
$179$	1.17881e10	0.858230	0.429115	−	0.903250i	$-0.358826\pi$
$179$	1.17881e10	0.858230	0.429115	+	0.903250i	$0.358826\pi$
$180$	−1.62206e9	−0.115171
$181$	1.59490e10	1.10453	0.552266	−	0.833668i	$-0.313763\pi$
$181$	1.59490e10	1.10453	0.552266	+	0.833668i	$0.313763\pi$
$182$	3.86760e10	2.61289
$183$	−7.36832e9	−0.485667
$184$	2.58792e10	1.66445
$185$	2.21275e10	1.38886
$186$	−8.56060e9	−0.524440
$187$	5.88497e9	0.351931
$188$	2.66166e9	0.155397
$189$	−6.27200e9	−0.357543
$190$	1.51315e9	0.0842346
$191$	−2.20091e10	−1.19661	−0.598305	−	0.801269i	$-0.704159\pi$
$191$	−2.20091e10	−1.19661	−0.598305	+	0.801269i	$0.704159\pi$
$192$	−1.17452e10	−0.623744
$193$	−2.16486e10	−1.12311	−0.561556	−	0.827439i	$-0.689797\pi$
$193$	−2.16486e10	−1.12311	−0.561556	+	0.827439i	$0.689797\pi$
$194$	−2.94026e10	−1.49031
$195$	−2.12905e10	−1.05446
$196$	−1.63848e10	−0.793030
$197$	1.45366e10	0.687647	0.343823	−	0.939034i	$-0.388278\pi$
$197$	1.45366e10	0.687647	0.343823	+	0.939034i	$0.388278\pi$
$198$	6.60801e9	0.305547
$199$	−2.43774e10	−1.10192	−0.550958	−	0.834533i	$-0.685737\pi$
$199$	−2.43774e10	−1.10192	−0.550958	+	0.834533i	$0.685737\pi$
$200$	−3.47044e9	−0.153373
$201$	1.48488e9	0.0641667
$202$	8.90450e9	0.376295
$203$	−3.71870e10	−1.53695
$204$	1.45887e9	0.0589766
$205$	−4.08297e10	−1.61467
$206$	3.50183e10	1.35485
$207$	−1.34635e10	−0.509674
$208$	−2.63977e10	−0.977868
$209$	2.94741e9	0.106852
$210$	−2.65583e10	−0.942354
$211$	−1.54719e10	−0.537370	−0.268685	−	0.963228i	$-0.586589\pi$
$211$	−1.54719e10	−0.537370	−0.268685	+	0.963228i	$0.586589\pi$
$212$	8.13327e9	0.276537
$213$	2.50273e10	0.833117
$214$	2.88904e10	0.941655
$215$	2.93574e10	0.937010
$216$	6.70220e9	0.209496
$217$	6.70183e10	2.05175
$218$	4.20691e10	1.26156
$219$	−9.86678e8	−0.0289852
$220$	−1.33789e10	−0.385052
$221$	1.91485e10	0.539969
$222$	−2.23463e10	−0.617472
$223$	−2.66817e10	−0.722505	−0.361253	−	0.932468i	$-0.617651\pi$
$223$	−2.66817e10	−0.722505	−0.361253	+	0.932468i	$0.617651\pi$
$224$	4.32759e10	1.14850
$225$	1.80548e9	0.0469646
$226$	1.11277e10	0.283737
$227$	−2.11753e10	−0.529315	−0.264657	−	0.964343i	$-0.585259\pi$
$227$	−2.11753e10	−0.529315	−0.264657	+	0.964343i	$0.585259\pi$
$228$	7.30655e8	0.0179063
$229$	−3.86876e10	−0.929634	−0.464817	−	0.885407i	$-0.653880\pi$
$229$	−3.86876e10	−0.929634	−0.464817	+	0.885407i	$0.653880\pi$
$230$	−5.70103e10	−1.34332
$231$	−5.17321e10	−1.19538
$232$	3.97376e10	0.900547
$233$	−2.74168e10	−0.609418	−0.304709	−	0.952446i	$-0.598559\pi$
$233$	−2.74168e10	−0.609418	−0.304709	+	0.952446i	$0.598559\pi$
$234$	2.15011e10	0.468802
$235$	−2.39900e10	−0.513128
$236$	−2.00687e9	−0.0421128
$237$	1.78802e10	0.368134
$238$	2.38863e10	0.482561
$239$	7.19297e10	1.42599	0.712997	−	0.701167i	$-0.247337\pi$
$239$	7.19297e10	1.42599	0.712997	+	0.701167i	$0.247337\pi$
$240$	1.81269e10	0.352675
$241$	1.36309e10	0.260283	0.130142	−	0.991495i	$-0.458457\pi$
$241$	1.36309e10	0.260283	0.130142	+	0.991495i	$0.458457\pi$
$242$	1.06191e10	0.199029
$243$	−3.48678e9	−0.0641500
$244$	−1.50658e10	−0.272107
$245$	1.47679e11	2.61862
$246$	4.12335e10	0.717864
$247$	9.59026e9	0.163943
$248$	−7.16151e10	−1.20219
$249$	−3.63675e10	−0.599538
$250$	−4.66167e10	−0.754765
$251$	2.60960e10	0.414994	0.207497	−	0.978236i	$-0.433468\pi$
$251$	2.60960e10	0.414994	0.207497	+	0.978236i	$0.433468\pi$
$252$	−1.28242e10	−0.200322
$253$	−1.11049e11	−1.70400
$254$	−2.70316e10	−0.407493
$255$	−1.31490e10	−0.194743
$256$	−5.89568e10	−0.857934
$257$	−7.00925e10	−1.00224	−0.501121	−	0.865377i	$-0.667079\pi$
$257$	−7.00925e10	−1.00224	−0.501121	+	0.865377i	$0.667079\pi$
$258$	−2.96478e10	−0.416585
$259$	1.74942e11	2.41572
$260$	−4.35323e10	−0.590787
$261$	−2.06733e10	−0.275757
$262$	1.22490e10	0.160600
$263$	1.15879e11	1.49350	0.746750	−	0.665105i	$-0.231613\pi$
$263$	1.15879e11	1.49350	0.746750	+	0.665105i	$0.231613\pi$
$264$	5.52804e10	0.700413
$265$	−7.33065e10	−0.913137
$266$	1.19631e10	0.146514
$267$	−5.82272e10	−0.701173
$268$	3.03611e9	0.0359510
$269$	1.49016e11	1.73519	0.867597	−	0.497268i	$-0.165663\pi$
$269$	1.49016e11	1.73519	0.867597	+	0.497268i	$0.165663\pi$
$270$	−1.47645e10	−0.169076
$271$	−1.47037e11	−1.65602	−0.828009	−	0.560715i	$-0.810526\pi$
$271$	−1.47037e11	−1.65602	−0.828009	+	0.560715i	$0.810526\pi$
$272$	−1.63032e10	−0.180598
$273$	−1.68325e11	−1.83408
$274$	−5.21391e10	−0.558838
$275$	1.48918e10	0.157018
$276$	−2.75286e10	−0.285557
$277$	1.15628e11	1.18006	0.590032	−	0.807380i	$-0.299115\pi$
$277$	1.15628e11	1.18006	0.590032	+	0.807380i	$0.299115\pi$
$278$	−1.49817e11	−1.50438
$279$	3.72574e10	0.368123
$280$	−2.22178e11	−2.16018
$281$	−1.10467e11	−1.05695	−0.528476	−	0.848948i	$-0.677236\pi$
$281$	−1.10467e11	−1.05695	−0.528476	+	0.848948i	$0.677236\pi$
$282$	2.42273e10	0.228131
$283$	−1.39797e11	−1.29557	−0.647783	−	0.761825i	$-0.724303\pi$
$283$	−1.39797e11	−1.29557	−0.647783	+	0.761825i	$0.724303\pi$
$284$	5.11728e10	0.466774
$285$	−6.58551e9	−0.0591273
$286$	1.77343e11	1.56735
$287$	−3.22805e11	−2.80848
$288$	2.40583e10	0.206063
$289$	−1.06762e11	−0.900276
$290$	−8.75395e10	−0.726797
$291$	1.27966e11	1.04610
$292$	−2.01744e9	−0.0162397
$293$	−2.95432e10	−0.234182	−0.117091	−	0.993121i	$-0.537357\pi$
$293$	−2.95432e10	−0.234182	−0.117091	+	0.993121i	$0.537357\pi$
$294$	−1.49140e11	−1.16421
$295$	1.80882e10	0.139058
$296$	−1.86942e11	−1.41545
$297$	−2.87593e10	−0.214474
$298$	−2.18192e10	−0.160275
$299$	−3.61329e11	−2.61446
$300$	3.69162e9	0.0263131
$301$	2.32103e11	1.62979
$302$	2.33029e10	0.161205
$303$	−3.87541e10	−0.264135
$304$	−8.16524e9	−0.0548325
$305$	1.35791e11	0.898508
$306$	1.32791e10	0.0865807
$307$	−5.96724e9	−0.0383399	−0.0191700	−	0.999816i	$-0.506102\pi$
$307$	−5.96724e9	−0.0383399	−0.0191700	+	0.999816i	$0.506102\pi$
$308$	−1.05776e11	−0.669742
$309$	−1.52406e11	−0.951021
$310$	1.57764e11	0.970240
$311$	−2.69967e11	−1.63640	−0.818199	−	0.574934i	$-0.805028\pi$
$311$	−2.69967e11	−1.63640	−0.818199	+	0.574934i	$0.805028\pi$
$312$	1.79871e11	1.07465
$313$	−3.88607e10	−0.228855	−0.114428	−	0.993432i	$-0.536503\pi$
$313$	−3.88607e10	−0.228855	−0.114428	+	0.993432i	$0.536503\pi$
$314$	1.14257e11	0.663281
$315$	1.15587e11	0.661472
$316$	3.65593e10	0.206256
$317$	−2.23628e11	−1.24383	−0.621913	−	0.783086i	$-0.713644\pi$
$317$	−2.23628e11	−1.24383	−0.621913	+	0.783086i	$0.713644\pi$
$318$	7.40316e10	0.405971
$319$	−1.70515e11	−0.921946
$320$	2.16453e11	1.15396
$321$	−1.25737e11	−0.660981
$322$	−4.50731e11	−2.33650
$323$	5.92294e9	0.0302779
$324$	−7.12936e9	−0.0359416
$325$	4.84546e10	0.240913
$326$	1.94148e11	0.952038
$327$	−1.83093e11	−0.885537
$328$	3.44946e11	1.64558
$329$	−1.89668e11	−0.892510
$330$	−1.21779e11	−0.565276
$331$	3.56601e11	1.63289	0.816444	−	0.577425i	$-0.195942\pi$
$331$	3.56601e11	1.63289	0.816444	+	0.577425i	$0.195942\pi$
$332$	−7.43599e10	−0.335906
$333$	9.72554e10	0.433426
$334$	1.15048e11	0.505848
$335$	−2.73649e10	−0.118712
$336$	1.43314e11	0.613425
$337$	4.09649e11	1.73012	0.865061	−	0.501666i	$-0.167279\pi$
$337$	4.09649e11	1.73012	0.865061	+	0.501666i	$0.167279\pi$
$338$	3.79674e11	1.58229
$339$	−4.84298e10	−0.199165
$340$	−2.68855e10	−0.109110
$341$	3.07303e11	1.23075
$342$	6.65065e9	0.0262873
$343$	6.91322e11	2.69685
$344$	−2.48023e11	−0.954947
$345$	2.48120e11	0.942922
$346$	−2.22357e11	−0.834081
$347$	2.00285e11	0.741595	0.370797	−	0.928714i	$-0.379084\pi$
$347$	2.00285e11	0.741595	0.370797	+	0.928714i	$0.379084\pi$
$348$	−4.22702e10	−0.154500
$349$	4.58740e11	1.65521	0.827603	−	0.561314i	$-0.189704\pi$
$349$	4.58740e11	1.65521	0.827603	+	0.561314i	$0.189704\pi$
$350$	6.04436e10	0.215300
$351$	−9.35769e10	−0.329069
$352$	1.98435e11	0.688933
$353$	2.90410e11	0.995463	0.497732	−	0.867331i	$-0.334166\pi$
$353$	2.90410e11	0.995463	0.497732	+	0.867331i	$0.334166\pi$
$354$	−1.82671e10	−0.0618238
$355$	−4.61229e11	−1.54131
$356$	−1.19056e11	−0.392850
$357$	−1.03958e11	−0.338727
$358$	2.19391e11	0.705904
$359$	8.27981e10	0.263084	0.131542	−	0.991311i	$-0.458007\pi$
$359$	8.27981e10	0.263084	0.131542	+	0.991311i	$0.458007\pi$
$360$	−1.23515e11	−0.387578
$361$	−3.19721e11	−0.990807
$362$	2.96831e11	0.908491
$363$	−4.62162e10	−0.139706
$364$	−3.44172e11	−1.02759
$365$	1.81835e10	0.0536241
$366$	−1.37134e11	−0.399467
$367$	3.34608e11	0.962808	0.481404	−	0.876499i	$-0.340127\pi$
$367$	3.34608e11	0.962808	0.481404	+	0.876499i	$0.340127\pi$
$368$	3.07639e11	0.874431
$369$	−1.79456e11	−0.503895
$370$	4.11821e11	1.14235
$371$	−5.79570e11	−1.58827
$372$	7.61794e10	0.206250
$373$	4.59899e11	1.23019	0.615096	−	0.788453i	$-0.289117\pi$
$373$	4.59899e11	1.23019	0.615096	+	0.788453i	$0.289117\pi$
$374$	1.09527e11	0.289467
$375$	2.02885e11	0.529796
$376$	2.02678e11	0.522950
$377$	−5.54821e11	−1.41455
$378$	−1.16730e11	−0.294083
$379$	−4.64799e10	−0.115715	−0.0578574	−	0.998325i	$-0.518427\pi$
$379$	−4.64799e10	−0.115715	−0.0578574	+	0.998325i	$0.518427\pi$
$380$	−1.34653e10	−0.0331275
$381$	1.17647e11	0.286034
$382$	−4.09618e11	−0.984225
$383$	−3.29063e11	−0.781419	−0.390710	−	0.920514i	$-0.627770\pi$
$383$	−3.29063e11	−0.781419	−0.390710	+	0.920514i	$0.627770\pi$
$384$	−6.65220e10	−0.156126
$385$	9.53373e11	2.21151
$386$	−4.02910e11	−0.923772
$387$	1.29033e11	0.292416
$388$	2.61649e11	0.586106
$389$	−1.15550e11	−0.255857	−0.127929	−	0.991783i	$-0.540833\pi$
$389$	−1.15550e11	−0.255857	−0.127929	+	0.991783i	$0.540833\pi$
$390$	−3.96244e11	−0.867306
$391$	−2.23156e11	−0.482852
$392$	−1.24765e12	−2.66874
$393$	−5.33100e10	−0.112731
$394$	2.70546e11	0.565598
$395$	−3.29515e11	−0.681065
$396$	−5.88036e10	−0.120164
$397$	−3.49147e11	−0.705425	−0.352713	−	0.935732i	$-0.614741\pi$
$397$	−3.49147e11	−0.705425	−0.352713	+	0.935732i	$0.614741\pi$
$398$	−4.53695e11	−0.906338
$399$	−5.20659e10	−0.102843
$400$	−4.12547e10	−0.0805757
$401$	5.89365e11	1.13824	0.569122	−	0.822253i	$-0.307283\pi$
$401$	5.89365e11	1.13824	0.569122	+	0.822253i	$0.307283\pi$
$402$	2.76356e10	0.0527778
$403$	9.99898e11	1.88835
$404$	−7.92397e10	−0.147988
$405$	6.42581e10	0.118681
$406$	−6.92098e11	−1.26416
$407$	8.02173e11	1.44908
$408$	1.11088e11	0.198471
$409$	3.27083e11	0.577967	0.288983	−	0.957334i	$-0.406683\pi$
$409$	3.27083e11	0.577967	0.288983	+	0.957334i	$0.406683\pi$
$410$	−7.59894e11	−1.32808
$411$	2.26919e11	0.392268
$412$	−3.11622e11	−0.532833
$413$	1.43008e11	0.241871
$414$	−2.50574e11	−0.419213
$415$	6.70218e11	1.10917
$416$	6.45667e11	1.05703
$417$	6.52031e11	1.05598
$418$	5.48552e10	0.0878870
$419$	4.85479e11	0.769497	0.384749	−	0.923021i	$-0.374288\pi$
$419$	4.85479e11	0.769497	0.384749	+	0.923021i	$0.374288\pi$
$420$	2.36338e11	0.370606
$421$	−6.01168e9	−0.00932667	−0.00466333	−	0.999989i	$-0.501484\pi$
$421$	−6.01168e9	−0.00932667	−0.00466333	+	0.999989i	$0.501484\pi$
$422$	−2.87953e11	−0.441993
$423$	−1.05442e11	−0.160133
$424$	6.19323e11	0.930617
$425$	2.99255e10	0.0444930
$426$	4.65791e11	0.685248
$427$	1.07358e12	1.56282
$428$	−2.57091e11	−0.370331
$429$	−7.71831e11	−1.10018
$430$	5.46379e11	0.770702
$431$	2.61315e11	0.364768	0.182384	−	0.983227i	$-0.441619\pi$
$431$	2.61315e11	0.364768	0.182384	+	0.983227i	$0.441619\pi$
$432$	7.96722e10	0.110060
$433$	−1.12179e12	−1.53361	−0.766805	−	0.641881i	$-0.778154\pi$
$433$	−1.12179e12	−1.53361	−0.766805	+	0.641881i	$0.778154\pi$
$434$	1.24730e12	1.68759
$435$	3.80989e11	0.510165
$436$	−3.74366e11	−0.496144
$437$	−1.11765e11	−0.146602
$438$	−1.83634e10	−0.0238407
$439$	2.31501e11	0.297483	0.148742	−	0.988876i	$-0.452478\pi$
$439$	2.31501e11	0.297483	0.148742	+	0.988876i	$0.452478\pi$
$440$	−1.01877e12	−1.29580
$441$	6.49085e11	0.817199
$442$	3.56378e11	0.444130
$443$	2.00771e11	0.247676	0.123838	−	0.992302i	$-0.460480\pi$
$443$	2.00771e11	0.247676	0.123838	+	0.992302i	$0.460480\pi$
$444$	1.98856e11	0.242837
$445$	1.07307e12	1.29721
$446$	−4.96581e11	−0.594269
$447$	9.49615e10	0.112503
$448$	1.71131e12	2.00714
$449$	−3.68935e11	−0.428392	−0.214196	−	0.976791i	$-0.568713\pi$
$449$	−3.68935e11	−0.428392	−0.214196	+	0.976791i	$0.568713\pi$
$450$	3.36023e10	0.0386289
$451$	−1.48017e12	−1.68468
$452$	−9.90233e10	−0.111587
$453$	−1.01418e11	−0.113155
$454$	−3.94101e11	−0.435368
$455$	3.10208e12	3.39313
$456$	5.56371e10	0.0602591
$457$	−1.37268e12	−1.47213	−0.736066	−	0.676910i	$-0.763319\pi$
$457$	−1.37268e12	−1.47213	−0.736066	+	0.676910i	$0.763319\pi$
$458$	−7.20027e11	−0.764634
$459$	−5.77930e10	−0.0607741
$460$	5.07326e11	0.528295
$461$	4.80655e11	0.495654	0.247827	−	0.968804i	$-0.420283\pi$
$461$	4.80655e11	0.495654	0.247827	+	0.968804i	$0.420283\pi$
$462$	−9.62803e11	−0.983215
$463$	2.39475e11	0.242185	0.121092	−	0.992641i	$-0.461360\pi$
$463$	2.39475e11	0.242185	0.121092	+	0.992641i	$0.461360\pi$
$464$	4.72380e11	0.473108
$465$	−6.86617e11	−0.681046
$466$	−5.10263e11	−0.501253
$467$	−1.22103e12	−1.18796	−0.593980	−	0.804480i	$-0.702444\pi$
$467$	−1.22103e12	−1.18796	−0.593980	+	0.804480i	$0.702444\pi$
$468$	−1.91335e11	−0.184369
$469$	−2.16351e11	−0.206481
$470$	−4.46486e11	−0.422053
$471$	−4.97266e11	−0.465581
$472$	−1.52817e11	−0.141720
$473$	1.06427e12	0.977639
$474$	3.32775e11	0.302794
$475$	1.49878e10	0.0135088
$476$	−2.12560e11	−0.189780
$477$	−3.22199e11	−0.284965
$478$	1.33871e12	1.17290
$479$	1.73521e12	1.50606	0.753028	−	0.657988i	$-0.228592\pi$
$479$	1.73521e12	1.50606	0.753028	+	0.657988i	$0.228592\pi$
$480$	−4.43372e11	−0.381226
$481$	2.61010e12	2.22333
$482$	2.53688e11	0.214086
$483$	1.96167e12	1.64007
$484$	−9.44973e10	−0.0782736
$485$	−2.35828e12	−1.93534
$486$	−6.48936e10	−0.0527641
$487$	−1.80440e12	−1.45363	−0.726815	−	0.686834i	$-0.759000\pi$
$487$	−1.80440e12	−1.45363	−0.726815	+	0.686834i	$0.759000\pi$
$488$	−1.14722e12	−0.915708
$489$	−8.44970e11	−0.668269
$490$	2.74850e12	2.15384
$491$	−1.81935e12	−1.41270	−0.706351	−	0.707862i	$-0.749660\pi$
$491$	−1.81935e12	−1.41270	−0.706351	+	0.707862i	$0.749660\pi$
$492$	−3.66930e11	−0.282319
$493$	−3.42657e11	−0.261245
$494$	1.78487e11	0.134845
$495$	5.30007e11	0.396788
$496$	−8.51323e11	−0.631578
$497$	−3.64653e12	−2.68088
$498$	−6.76847e11	−0.493127
$499$	−3.19828e11	−0.230921	−0.115461	−	0.993312i	$-0.536834\pi$
$499$	−3.19828e11	−0.230921	−0.115461	+	0.993312i	$0.536834\pi$
$500$	4.14834e11	0.296831
$501$	−5.00711e11	−0.355073
$502$	4.85680e11	0.341337
$503$	8.65153e11	0.602611	0.301305	−	0.953528i	$-0.402578\pi$
$503$	8.65153e11	0.602611	0.301305	+	0.953528i	$0.402578\pi$
$504$	−9.76526e11	−0.674134
$505$	7.14201e11	0.488663
$506$	−2.06676e12	−1.40156
$507$	−1.65241e12	−1.11066
$508$	2.40550e11	0.160257
$509$	1.81057e12	1.19560	0.597798	−	0.801647i	$-0.296042\pi$
$509$	1.81057e12	1.19560	0.597798	+	0.801647i	$0.296042\pi$
$510$	−2.44720e11	−0.160178
$511$	1.43761e11	0.0932712
$512$	−1.51775e12	−0.976079
$513$	−2.89449e10	−0.0184520
$514$	−1.30451e12	−0.824356
$515$	2.80870e12	1.75943
$516$	2.63831e11	0.163833
$517$	−8.69695e11	−0.535377
$518$	3.25591e12	1.98696
$519$	9.67740e11	0.585471
$520$	−3.31485e12	−1.98815
$521$	−2.25238e12	−1.33928	−0.669640	−	0.742686i	$-0.733552\pi$
$521$	−2.25238e12	−1.33928	−0.669640	+	0.742686i	$0.733552\pi$
$522$	−3.84757e11	−0.226814
$523$	−3.18471e11	−0.186128	−0.0930640	−	0.995660i	$-0.529666\pi$
$523$	−3.18471e11	−0.186128	−0.0930640	+	0.995660i	$0.529666\pi$
$524$	−1.09002e11	−0.0631601
$525$	−2.63062e11	−0.151127
$526$	2.15667e12	1.22842
$527$	6.17536e11	0.348750
$528$	6.57145e11	0.367967
$529$	2.40978e12	1.33791
$530$	−1.36433e12	−0.751066
$531$	7.95020e10	0.0433963
$532$	−1.06458e11	−0.0576204
$533$	−4.81617e12	−2.58481
$534$	−1.08369e12	−0.576723
$535$	2.31720e12	1.22285
$536$	2.31190e11	0.120984
$537$	−9.54833e11	−0.495499
$538$	2.77339e12	1.42722
$539$	5.35372e12	2.73216
$540$	1.31387e11	0.0664938
$541$	−1.83667e11	−0.0921816	−0.0460908	−	0.998937i	$-0.514676\pi$
$541$	−1.83667e11	−0.0921816	−0.0460908	+	0.998937i	$0.514676\pi$
$542$	−2.73655e12	−1.36209
$543$	−1.29187e12	−0.637702
$544$	3.98764e11	0.195218
$545$	3.37423e12	1.63829
$546$	−3.13276e12	−1.50855
$547$	1.87270e12	0.894386	0.447193	−	0.894437i	$-0.352424\pi$
$547$	1.87270e12	0.894386	0.447193	+	0.894437i	$0.352424\pi$
$548$	4.63977e11	0.219778
$549$	5.96834e11	0.280400
$550$	2.77155e11	0.129149
$551$	−1.71615e11	−0.0793185
$552$	−2.09622e12	−0.960972
$553$	−2.60519e12	−1.18461
$554$	2.15200e12	0.970617
$555$	−1.79232e12	−0.801859
$556$	1.33320e12	0.591640
$557$	−3.46768e12	−1.52648	−0.763239	−	0.646116i	$-0.776392\pi$
$557$	−3.46768e12	−1.52648	−0.763239	+	0.646116i	$0.776392\pi$
$558$	6.93409e11	0.302786
$559$	3.46293e12	1.50000
$560$	−2.64114e12	−1.13487
$561$	−4.76683e11	−0.203187
$562$	−2.05594e12	−0.869355
$563$	−1.63273e12	−0.684898	−0.342449	−	0.939536i	$-0.611256\pi$
$563$	−1.63273e12	−0.684898	−0.342449	+	0.939536i	$0.611256\pi$
$564$	−2.15595e11	−0.0897186
$565$	8.92514e11	0.368466
$566$	−2.60181e12	−1.06562
$567$	5.08032e11	0.206428
$568$	3.89665e12	1.57081
$569$	−2.02549e12	−0.810075	−0.405038	−	0.914300i	$-0.632742\pi$
$569$	−2.02549e12	−0.810075	−0.405038	+	0.914300i	$0.632742\pi$
$570$	−1.22565e11	−0.0486329
$571$	1.28759e12	0.506893	0.253447	−	0.967349i	$-0.418436\pi$
$571$	1.28759e12	0.506893	0.253447	+	0.967349i	$0.418436\pi$
$572$	−1.57815e12	−0.616404
$573$	1.78274e12	0.690863
$574$	−6.00782e12	−2.31001
$575$	−5.64691e11	−0.215430
$576$	9.51364e11	0.360119
$577$	−4.89310e12	−1.83778	−0.918889	−	0.394515i	$-0.870913\pi$
$577$	−4.89310e12	−1.83778	−0.918889	+	0.394515i	$0.870913\pi$
$578$	−1.98698e12	−0.740487
$579$	1.75354e12	0.648429
$580$	7.79000e11	0.285832
$581$	5.29883e12	1.92924
$582$	2.38161e12	0.860433
$583$	−2.65753e12	−0.952731
$584$	−1.53622e11	−0.0546506
$585$	1.72453e12	0.608793
$586$	−5.49838e11	−0.192617
$587$	−1.75813e12	−0.611195	−0.305598	−	0.952161i	$-0.598856\pi$
$587$	−1.75813e12	−0.611195	−0.305598	+	0.952161i	$0.598856\pi$
$588$	1.32717e12	0.457856
$589$	3.09285e11	0.105886
$590$	3.36645e11	0.114377
$591$	−1.17747e12	−0.397013
$592$	−2.22226e12	−0.743615
$593$	−1.62832e12	−0.540745	−0.270372	−	0.962756i	$-0.587147\pi$
$593$	−1.62832e12	−0.540745	−0.270372	+	0.962756i	$0.587147\pi$
$594$	−5.35249e11	−0.176407
$595$	1.91584e12	0.626661
$596$	1.94166e11	0.0630325
$597$	1.97457e12	0.636191
$598$	−6.72480e12	−2.15042
$599$	2.05355e12	0.651754	0.325877	−	0.945412i	$-0.394340\pi$
$599$	2.05355e12	0.651754	0.325877	+	0.945412i	$0.394340\pi$
$600$	2.81106e11	0.0885500
$601$	−4.87509e12	−1.52422	−0.762110	−	0.647448i	$-0.775836\pi$
$601$	−4.87509e12	−1.52422	−0.762110	+	0.647448i	$0.775836\pi$
$602$	4.31974e12	1.34052
$603$	−1.20275e11	−0.0370467
$604$	−2.07368e11	−0.0633981
$605$	8.51720e11	0.258462
$606$	−7.21265e11	−0.217254
$607$	−3.47527e12	−1.03906	−0.519528	−	0.854453i	$-0.673892\pi$
$607$	−3.47527e12	−1.03906	−0.519528	+	0.854453i	$0.673892\pi$
$608$	1.99716e11	0.0592715
$609$	3.01214e12	0.887356
$610$	2.52725e12	0.739033
$611$	−2.82981e12	−0.821431
$612$	−1.18168e11	−0.0340502
$613$	2.62214e12	0.750038	0.375019	−	0.927017i	$-0.377636\pi$
$613$	2.62214e12	0.750038	0.375019	+	0.927017i	$0.377636\pi$
$614$	−1.11058e11	−0.0315350
$615$	3.30720e12	0.932230
$616$	−8.05449e12	−2.25385
$617$	−3.35752e12	−0.932685	−0.466342	−	0.884604i	$-0.654429\pi$
$617$	−3.35752e12	−0.932685	−0.466342	+	0.884604i	$0.654429\pi$
$618$	−2.83648e12	−0.782225
$619$	3.47281e12	0.950766	0.475383	−	0.879779i	$-0.342309\pi$
$619$	3.47281e12	0.950766	0.475383	+	0.879779i	$0.342309\pi$
$620$	−1.40391e12	−0.381573
$621$	1.09055e12	0.294260
$622$	−5.02444e12	−1.34596
$623$	8.48384e12	2.25630
$624$	2.13821e12	0.564573
$625$	−4.27644e12	−1.12104
$626$	−7.23249e11	−0.188236
$627$	−2.38740e11	−0.0616910
$628$	−1.01675e12	−0.260853
$629$	1.61200e12	0.410616
$630$	2.15123e12	0.544068
$631$	−2.45725e12	−0.617045	−0.308523	−	0.951217i	$-0.599835\pi$
$631$	−2.45725e12	−0.617045	−0.308523	+	0.951217i	$0.599835\pi$
$632$	2.78388e12	0.694103
$633$	1.25323e12	0.310251
$634$	−4.16201e12	−1.02306
$635$	−2.16811e12	−0.529176
$636$	−6.58795e11	−0.159659
$637$	1.74199e13	4.19197
$638$	−3.17351e12	−0.758311
$639$	−2.02721e12	−0.481000
$640$	1.22594e12	0.288840
$641$	5.98365e12	1.39992	0.699962	−	0.714180i	$-0.253200\pi$
$641$	5.98365e12	1.39992	0.699962	+	0.714180i	$0.253200\pi$
$642$	−2.34012e12	−0.543665
$643$	4.95464e12	1.14304	0.571522	−	0.820587i	$-0.306353\pi$
$643$	4.95464e12	1.14304	0.571522	+	0.820587i	$0.306353\pi$
$644$	4.01098e12	0.918891
$645$	−2.37795e12	−0.540983
$646$	1.10234e11	0.0249039
$647$	−7.46826e12	−1.67552	−0.837761	−	0.546037i	$-0.816136\pi$
$647$	−7.46826e12	−1.67552	−0.837761	+	0.546037i	$0.816136\pi$
$648$	−5.42879e11	−0.120953
$649$	6.55740e11	0.145088
$650$	9.01804e11	0.198154
$651$	−5.42848e12	−1.18458
$652$	−1.72769e12	−0.374414
$653$	−5.31545e12	−1.14401	−0.572007	−	0.820249i	$-0.693835\pi$
$653$	−5.31545e12	−1.14401	−0.572007	+	0.820249i	$0.693835\pi$
$654$	−3.40760e12	−0.728365
$655$	9.82452e11	0.208557
$656$	4.10053e12	0.864516
$657$	7.99209e10	0.0167346
$658$	−3.52997e12	−0.734099
$659$	3.34203e12	0.690282	0.345141	−	0.938551i	$-0.387831\pi$
$659$	3.34203e12	0.690282	0.345141	+	0.938551i	$0.387831\pi$
$660$	1.08369e12	0.222310
$661$	−1.03490e12	−0.210859	−0.105430	−	0.994427i	$-0.533622\pi$
$661$	−1.03490e12	−0.210859	−0.105430	+	0.994427i	$0.533622\pi$
$662$	6.63681e12	1.34307
$663$	−1.55102e12	−0.311751
$664$	−5.66228e12	−1.13041
$665$	9.59524e11	0.190265
$666$	1.81005e12	0.356498
$667$	6.46589e12	1.26492
$668$	−1.02379e12	−0.198938
$669$	2.16121e12	0.417138
$670$	−5.09297e11	−0.0976416
$671$	4.92274e12	0.937467
$672$	−3.50535e12	−0.663086
$673$	2.81027e12	0.528056	0.264028	−	0.964515i	$-0.414949\pi$
$673$	2.81027e12	0.528056	0.264028	+	0.964515i	$0.414949\pi$
$674$	7.62410e12	1.42305
$675$	−1.46244e11	−0.0271150
$676$	−3.37865e12	−0.622277
$677$	3.12734e12	0.572172	0.286086	−	0.958204i	$-0.407646\pi$
$677$	3.12734e12	0.572172	0.286086	+	0.958204i	$0.407646\pi$
$678$	−9.01341e11	−0.163816
$679$	−1.86449e13	−3.36625
$680$	−2.04725e12	−0.367181
$681$	1.71520e12	0.305600
$682$	5.71930e12	1.01231
$683$	8.96063e12	1.57560	0.787799	−	0.615933i	$-0.211221\pi$
$683$	8.96063e12	1.57560	0.787799	+	0.615933i	$0.211221\pi$
$684$	−5.91830e10	−0.0103382
$685$	−4.18190e12	−0.725715
$686$	1.28664e13	2.21819
$687$	3.13369e12	0.536724
$688$	−2.94837e12	−0.501688
$689$	−8.64706e12	−1.46178
$690$	4.61784e12	0.775564
$691$	3.78288e11	0.0631206	0.0315603	−	0.999502i	$-0.489952\pi$
$691$	3.78288e11	0.0631206	0.0315603	+	0.999502i	$0.489952\pi$
$692$	1.97872e12	0.328025
$693$	4.19030e12	0.690154
$694$	3.72757e12	0.609970
$695$	−1.20163e13	−1.95362
$696$	−3.21875e12	−0.519931
$697$	−2.97446e12	−0.477377
$698$	8.53775e12	1.36143
$699$	2.22076e12	0.351848
$700$	−5.37877e11	−0.0846725
$701$	−5.57092e12	−0.871356	−0.435678	−	0.900103i	$-0.643491\pi$
$701$	−5.57092e12	−0.871356	−0.435678	+	0.900103i	$0.643491\pi$
$702$	−1.74159e12	−0.270663
$703$	8.07348e11	0.124670
$704$	7.84695e12	1.20399
$705$	1.94319e12	0.296254
$706$	5.40491e12	0.818780
$707$	5.64656e12	0.849956
$708$	1.62556e11	0.0243138
$709$	4.49290e12	0.667757	0.333879	−	0.942616i	$-0.391642\pi$
$709$	4.49290e12	0.667757	0.333879	+	0.942616i	$0.391642\pi$
$710$	−8.58408e12	−1.26774
$711$	−1.44830e12	−0.212542
$712$	−9.06575e12	−1.32204
$713$	−1.16528e13	−1.68861
$714$	−1.93479e12	−0.278607
$715$	1.42241e13	2.03539
$716$	−1.95233e12	−0.277616
$717$	−5.82631e12	−0.823298
$718$	1.54098e12	0.216390
$719$	−3.51348e12	−0.490295	−0.245148	−	0.969486i	$-0.578836\pi$
$719$	−3.51348e12	−0.490295	−0.245148	+	0.969486i	$0.578836\pi$
$720$	−1.46828e12	−0.203617
$721$	2.22059e13	3.06028
$722$	−5.95043e12	−0.814950
$723$	−1.10410e12	−0.150275
$724$	−2.64145e12	−0.357288
$725$	−8.67084e11	−0.116558
$726$	−8.60144e11	−0.114910
$727$	2.85192e12	0.378646	0.189323	−	0.981915i	$-0.439371\pi$
$727$	2.85192e12	0.378646	0.189323	+	0.981915i	$0.439371\pi$
$728$	−2.62076e13	−3.45809
$729$	2.82430e11	0.0370370
$730$	3.38419e11	0.0441064
$731$	2.13870e12	0.277027
$732$	1.22033e12	0.157101
$733$	−6.61645e12	−0.846559	−0.423279	−	0.905999i	$-0.639121\pi$
$733$	−6.61645e12	−0.846559	−0.423279	+	0.905999i	$0.639121\pi$
$734$	6.22750e12	0.791921
$735$	−1.19620e13	−1.51186
$736$	−7.52461e12	−0.945222
$737$	−9.92044e11	−0.123859
$738$	−3.33992e12	−0.414459
$739$	6.98786e12	0.861875	0.430937	−	0.902382i	$-0.358183\pi$
$739$	6.98786e12	0.861875	0.430937	+	0.902382i	$0.358183\pi$
$740$	−3.66473e12	−0.449261
$741$	−7.76811e11	−0.0946528
$742$	−1.07866e13	−1.30637
$743$	−1.02827e13	−1.23783	−0.618913	−	0.785460i	$-0.712427\pi$
$743$	−1.02827e13	−1.23783	−0.618913	+	0.785460i	$0.712427\pi$
$744$	5.80083e12	0.694083
$745$	−1.75005e12	−0.208136
$746$	8.55932e12	1.01185
$747$	2.94577e12	0.346143
$748$	−9.74663e11	−0.113841
$749$	1.83201e13	2.12696
$750$	3.77595e12	0.435764
$751$	6.20048e12	0.711289	0.355644	−	0.934621i	$-0.384261\pi$
$751$	6.20048e12	0.711289	0.355644	+	0.934621i	$0.384261\pi$
$752$	2.40932e12	0.274736
$753$	−2.11377e12	−0.239597
$754$	−1.03259e13	−1.16348
$755$	1.86904e12	0.209343
$756$	1.03876e12	0.115656
$757$	−8.98211e10	−0.00994139	−0.00497069	−	0.999988i	$-0.501582\pi$
$757$	−8.98211e10	−0.00994139	−0.00497069	+	0.999988i	$0.501582\pi$
$758$	−8.65052e11	−0.0951767
$759$	8.99493e12	0.983807
$760$	−1.02534e12	−0.111482
$761$	−8.53129e12	−0.922112	−0.461056	−	0.887371i	$-0.652529\pi$
$761$	−8.53129e12	−0.922112	−0.461056	+	0.887371i	$0.652529\pi$
$762$	2.18956e12	0.235266
$763$	2.66771e13	2.84956
$764$	3.64513e12	0.387073
$765$	1.06507e12	0.112435
$766$	−6.12429e12	−0.642726
$767$	2.13364e12	0.222609
$768$	4.77550e12	0.495329
$769$	−1.33335e13	−1.37492	−0.687458	−	0.726224i	$-0.741274\pi$
$769$	−1.33335e13	−1.37492	−0.687458	+	0.726224i	$0.741274\pi$
$770$	1.77435e13	1.81900
$771$	5.67750e12	0.578645
$772$	3.58543e12	0.363298
$773$	−9.54484e12	−0.961525	−0.480763	−	0.876851i	$-0.659640\pi$
$773$	−9.54484e12	−0.961525	−0.480763	+	0.876851i	$0.659640\pi$
$774$	2.40147e12	0.240515
$775$	1.56266e12	0.155599
$776$	1.99238e13	1.97239
$777$	−1.41703e13	−1.39472
$778$	−2.15054e12	−0.210445
$779$	−1.48972e12	−0.144940
$780$	3.52611e12	0.341091
$781$	−1.67206e13	−1.60814
$782$	−4.15323e12	−0.397151
$783$	1.67454e12	0.159209
$784$	−1.48315e13	−1.40204
$785$	9.16414e12	0.861347
$786$	−9.92169e11	−0.0927223
$787$	7.44479e12	0.691777	0.345888	−	0.938276i	$-0.387578\pi$
$787$	7.44479e12	0.691777	0.345888	+	0.938276i	$0.387578\pi$
$788$	−2.40754e12	−0.222436
$789$	−9.38622e12	−0.862272
$790$	−6.13271e12	−0.560184
$791$	7.05633e12	0.640891
$792$	−4.47772e12	−0.404383
$793$	1.60176e13	1.43836
$794$	−6.49808e12	−0.580220
$795$	5.93783e12	0.527200
$796$	4.03736e12	0.356442
$797$	1.74579e13	1.53260	0.766301	−	0.642482i	$-0.222095\pi$
$797$	1.74579e13	1.53260	0.766301	+	0.642482i	$0.222095\pi$
$798$	−9.69014e11	−0.0845897
$799$	−1.74769e12	−0.151706
$800$	1.00906e12	0.0870988
$801$	4.71641e12	0.404823
$802$	1.09689e13	0.936218
$803$	6.59195e11	0.0559492
$804$	−2.45925e11	−0.0207563
$805$	−3.61516e13	−3.03422
$806$	1.86094e13	1.55319
$807$	−1.20703e13	−1.00181
$808$	−6.03386e12	−0.498017
$809$	7.20004e12	0.590971	0.295486	−	0.955347i	$-0.404519\pi$
$809$	7.20004e12	0.590971	0.295486	+	0.955347i	$0.404519\pi$
$810$	1.19593e12	0.0976163
$811$	−1.08968e13	−0.884517	−0.442259	−	0.896888i	$-0.645823\pi$
$811$	−1.08968e13	−0.884517	−0.442259	+	0.896888i	$0.645823\pi$
$812$	6.15887e12	0.497163
$813$	1.19100e13	0.956102
$814$	1.49295e13	1.19189
$815$	1.55720e13	1.23633
$816$	1.32056e12	0.104268
$817$	1.07114e12	0.0841100
$818$	6.08744e12	0.475384
$819$	1.36344e13	1.05891
$820$	6.76217e12	0.522305
$821$	−2.50890e13	−1.92726	−0.963629	−	0.267242i	$-0.913888\pi$
$821$	−2.50890e13	−1.92726	−0.963629	+	0.267242i	$0.913888\pi$
$822$	4.22327e12	0.322645
$823$	−1.83804e13	−1.39655	−0.698274	−	0.715831i	$-0.746048\pi$
$823$	−1.83804e13	−1.39655	−0.698274	+	0.715831i	$0.746048\pi$
$824$	−2.37291e13	−1.79312
$825$	−1.20623e12	−0.0906542
$826$	2.66156e12	0.198942
$827$	−5.81755e12	−0.432480	−0.216240	−	0.976340i	$-0.569379\pi$
$827$	−5.81755e12	−0.432480	−0.216240	+	0.976340i	$0.569379\pi$
$828$	2.22982e12	0.164867
$829$	−7.71834e12	−0.567582	−0.283791	−	0.958886i	$-0.591592\pi$
$829$	−7.71834e12	−0.567582	−0.283791	+	0.958886i	$0.591592\pi$
$830$	1.24736e13	0.912308
$831$	−9.36590e12	−0.681311
$832$	2.55323e13	1.84729
$833$	1.07585e13	0.774193
$834$	1.21352e13	0.868557
$835$	9.22762e12	0.656902
$836$	−4.88148e11	−0.0345639
$837$	−3.01785e12	−0.212536
$838$	9.03540e12	0.632920
$839$	9.00347e12	0.627308	0.313654	−	0.949537i	$-0.398447\pi$
$839$	9.00347e12	0.627308	0.313654	+	0.949537i	$0.398447\pi$
$840$	1.79964e13	1.24718
$841$	−4.57875e12	−0.315620
$842$	−1.11885e11	−0.00767129
$843$	8.94785e12	0.610232
$844$	2.56245e12	0.173826
$845$	3.04524e13	2.05478
$846$	−1.96241e12	−0.131711
$847$	6.73380e12	0.449557
$848$	7.36219e12	0.488906
$849$	1.13236e13	0.747995
$850$	5.56954e11	0.0365960
$851$	−3.04181e13	−1.98815
$852$	−4.14500e12	−0.269492
$853$	−3.36589e11	−0.0217685	−0.0108843	−	0.999941i	$-0.503465\pi$
$853$	−3.36589e11	−0.0217685	−0.0108843	+	0.999941i	$0.503465\pi$
$854$	1.99807e13	1.28544
$855$	5.33427e11	0.0341371
$856$	−1.95767e13	−1.24626
$857$	−2.49442e12	−0.157963	−0.0789816	−	0.996876i	$-0.525167\pi$
$857$	−2.49442e12	−0.157963	−0.0789816	+	0.996876i	$0.525167\pi$
$858$	−1.43648e13	−0.904913
$859$	−2.48059e13	−1.55448	−0.777242	−	0.629202i	$-0.783382\pi$
$859$	−2.48059e13	−1.55448	−0.777242	+	0.629202i	$0.783382\pi$
$860$	−4.86214e12	−0.303099
$861$	2.61472e13	1.62148
$862$	4.86341e12	0.300026
$863$	−1.49580e13	−0.917962	−0.458981	−	0.888446i	$-0.651785\pi$
$863$	−1.49580e13	−0.917962	−0.458981	+	0.888446i	$0.651785\pi$
$864$	−1.94872e12	−0.118970
$865$	−1.78345e13	−1.08315
$866$	−2.08779e13	−1.26141
$867$	8.64771e12	0.519775
$868$	−1.10995e13	−0.663690
$869$	−1.19457e13	−0.710596
$870$	7.09070e12	0.419616
$871$	−3.22790e12	−0.190037
$872$	−2.85069e13	−1.66965
$873$	−1.03652e13	−0.603969
$874$	−2.08009e12	−0.120582
$875$	−2.95608e13	−1.70482
$876$	1.63413e11	0.00937599
$877$	−6.24566e12	−0.356517	−0.178258	−	0.983984i	$-0.557046\pi$
$877$	−6.24566e12	−0.356517	−0.178258	+	0.983984i	$0.557046\pi$
$878$	4.30854e12	0.244684
$879$	2.39300e12	0.135205
$880$	−1.21105e13	−0.680756
$881$	2.33730e13	1.30714	0.653572	−	0.756864i	$-0.273270\pi$
$881$	2.33730e13	1.30714	0.653572	+	0.756864i	$0.273270\pi$
$882$	1.20803e13	0.672156
$883$	5.34930e12	0.296124	0.148062	−	0.988978i	$-0.452696\pi$
$883$	5.34930e12	0.296124	0.148062	+	0.988978i	$0.452696\pi$
$884$	−3.17135e12	−0.174666
$885$	−1.46515e12	−0.0802853
$886$	3.73661e12	0.203716
$887$	−2.76665e12	−0.150071	−0.0750357	−	0.997181i	$-0.523907\pi$
$887$	−2.76665e12	−0.150071	−0.0750357	+	0.997181i	$0.523907\pi$
$888$	1.51423e13	0.817209
$889$	−1.71414e13	−0.920424
$890$	1.99713e13	1.06697
$891$	2.32951e12	0.123827
$892$	4.41899e12	0.233712
$893$	−8.75306e11	−0.0460605
$894$	1.76736e12	0.0925349
$895$	1.75966e13	0.916698
$896$	9.69240e12	0.502395
$897$	2.92676e13	1.50946
$898$	−6.86636e12	−0.352357
$899$	−1.78929e13	−0.913615
$900$	−2.99021e11	−0.0151919
$901$	−5.34042e12	−0.269969
$902$	−2.75480e13	−1.38567
$903$	−1.88004e13	−0.940960
$904$	−7.54032e12	−0.375519
$905$	2.38078e13	1.17978
$906$	−1.88753e12	−0.0930716
$907$	−5.41718e12	−0.265791	−0.132896	−	0.991130i	$-0.542428\pi$
$907$	−5.41718e12	−0.265791	−0.132896	+	0.991130i	$0.542428\pi$
$908$	3.50704e12	0.171220
$909$	3.13908e12	0.152498
$910$	5.77337e13	2.79089
$911$	−3.39211e13	−1.63169	−0.815844	−	0.578272i	$-0.803727\pi$
$911$	−3.39211e13	−1.63169	−0.815844	+	0.578272i	$0.803727\pi$
$912$	6.61384e11	0.0316575
$913$	2.42970e13	1.15727
$914$	−2.55474e13	−1.21085
$915$	−1.09991e13	−0.518754
$916$	6.40740e12	0.300713
$917$	7.76739e12	0.362755
$918$	−1.07560e12	−0.0499874
$919$	3.66041e13	1.69282	0.846409	−	0.532534i	$-0.178760\pi$
$919$	3.66041e13	1.69282	0.846409	+	0.532534i	$0.178760\pi$
$920$	3.86313e13	1.77785
$921$	4.83347e11	0.0221356
$922$	8.94561e12	0.407682
$923$	−5.44055e13	−2.46737
$924$	8.56782e12	0.386675
$925$	4.07911e12	0.183201
$926$	4.45695e12	0.199200
$927$	1.23449e13	0.549072
$928$	−1.15541e13	−0.511409
$929$	1.54600e13	0.680989	0.340494	−	0.940247i	$-0.389406\pi$
$929$	1.54600e13	0.680989	0.340494	+	0.940247i	$0.389406\pi$
$930$	−1.27789e13	−0.560168
$931$	5.38826e12	0.235058
$932$	4.54075e12	0.197131
$933$	2.18673e13	0.944775
$934$	−2.27251e13	−0.977111
$935$	8.78480e12	0.375906
$936$	−1.45695e13	−0.620447
$937$	−3.37491e13	−1.43032	−0.715161	−	0.698960i	$-0.753646\pi$
$937$	−3.37491e13	−1.43032	−0.715161	+	0.698960i	$0.753646\pi$
$938$	−4.02657e12	−0.169833
$939$	3.14772e12	0.132130
$940$	3.97321e12	0.165984
$941$	−2.38639e12	−0.0992175	−0.0496087	−	0.998769i	$-0.515797\pi$
$941$	−2.38639e12	−0.0992175	−0.0496087	+	0.998769i	$0.515797\pi$
$942$	−9.25478e12	−0.382946
$943$	5.61277e13	2.31140
$944$	−1.81660e12	−0.0744537
$945$	−9.36255e12	−0.381901
$946$	1.98075e13	0.804120
$947$	1.40787e13	0.568837	0.284419	−	0.958700i	$-0.408199\pi$
$947$	1.40787e13	0.568837	0.284419	+	0.958700i	$0.408199\pi$
$948$	−2.96131e12	−0.119082
$949$	2.14488e12	0.0858432
$950$	2.78943e11	0.0111112
$951$	1.81139e13	0.718124
$952$	−1.61858e13	−0.638657
$953$	4.17831e12	0.164090	0.0820452	−	0.996629i	$-0.473855\pi$
$953$	4.17831e12	0.164090	0.0820452	+	0.996629i	$0.473855\pi$
$954$	−5.99656e12	−0.234387
$955$	−3.28541e13	−1.27813
$956$	−1.19129e13	−0.461273
$957$	1.38117e13	0.532286
$958$	3.22945e13	1.23875
$959$	−3.30626e13	−1.26227
$960$	−1.75327e13	−0.666237
$961$	5.80701e12	0.219633
$962$	4.85774e13	1.82872
$963$	1.01847e13	0.381618
$964$	−2.25753e12	−0.0841951
$965$	−3.23161e13	−1.19963
$966$	3.65092e13	1.34898
$967$	−2.15220e13	−0.791521	−0.395761	−	0.918354i	$-0.629519\pi$
$967$	−2.15220e13	−0.791521	−0.395761	+	0.918354i	$0.629519\pi$
$968$	−7.19568e12	−0.263410
$969$	−4.79758e11	−0.0174810
$970$	−4.38908e13	−1.59184
$971$	3.09036e13	1.11564	0.557818	−	0.829963i	$-0.311639\pi$
$971$	3.09036e13	1.11564	0.557818	+	0.829963i	$0.311639\pi$
$972$	5.77478e11	0.0207509
$973$	−9.50025e13	−3.39803
$974$	−3.35823e13	−1.19563
$975$	−3.92482e12	−0.139091
$976$	−1.36375e13	−0.481073
$977$	−4.38260e13	−1.53889	−0.769443	−	0.638715i	$-0.779466\pi$
$977$	−4.38260e13	−1.53889	−0.769443	+	0.638715i	$0.779466\pi$
$978$	−1.57260e13	−0.549659
$979$	3.89014e13	1.35345
$980$	−2.44585e13	−0.847056
$981$	1.48305e13	0.511265
$982$	−3.38606e13	−1.16196
$983$	1.32092e13	0.451219	0.225609	−	0.974218i	$-0.427563\pi$
$983$	1.32092e13	0.451219	0.225609	+	0.974218i	$0.427563\pi$
$984$	−2.79406e13	−0.950075
$985$	2.16996e13	0.734494
$986$	−6.37730e12	−0.214877
$987$	1.53631e13	0.515291
$988$	−1.58833e12	−0.0530316
$989$	−4.03570e13	−1.34133
$990$	9.86413e12	0.326362
$991$	−4.72326e13	−1.55565	−0.777823	−	0.628483i	$-0.783676\pi$
$991$	−4.72326e13	−1.55565	−0.777823	+	0.628483i	$0.783676\pi$
$992$	2.08227e13	0.682708
$993$	−2.88847e13	−0.942748
$994$	−6.78668e13	−2.20505
$995$	−3.63894e13	−1.17699
$996$	6.02315e12	0.193935
$997$	−1.97696e13	−0.633681	−0.316840	−	0.948479i	$-0.602622\pi$
$997$	−1.97696e13	−0.633681	−0.316840	+	0.948479i	$0.602622\pi$
$998$	−5.95242e12	−0.189936
$999$	−7.87769e12	−0.250239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.15	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+18.6113 q^{2} -81.0000 q^{3} -165.619 q^{4} +1492.75 q^{5} -1507.52 q^{6} +11801.9 q^{7} -12611.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+18.6113 q^{2} -81.0000 q^{3} -165.619 q^{4} +1492.75 q^{5} -1507.52 q^{6} +11801.9 q^{7} -12611.4 q^{8} +6561.00 q^{9} +27782.1 q^{10} +54115.8 q^{11} +13415.1 q^{12} +176081. q^{13} +219649. q^{14} -120913. q^{15} -149917. q^{16} +108748. q^{17} +122109. q^{18} +54464.9 q^{19} -247228. q^{20} -955953. q^{21} +1.00717e6 q^{22} -2.05205e6 q^{23} +1.02152e6 q^{24} +275183. q^{25} +3.27711e6 q^{26} -531441. q^{27} -1.95462e6 q^{28} -3.15094e6 q^{29} -2.25035e6 q^{30} +5.67861e6 q^{31} +3.66687e6 q^{32} -4.38338e6 q^{33} +2.02394e6 q^{34} +1.76173e7 q^{35} -1.08663e6 q^{36} +1.48233e7 q^{37} +1.01366e6 q^{38} -1.42626e7 q^{39} -1.88257e7 q^{40} -2.73520e7 q^{41} -1.77915e7 q^{42} +1.96666e7 q^{43} -8.96260e6 q^{44} +9.79394e6 q^{45} -3.81914e7 q^{46} -1.60710e7 q^{47} +1.21433e7 q^{48} +9.89308e7 q^{49} +5.12152e6 q^{50} -8.80857e6 q^{51} -2.91624e7 q^{52} -4.91083e7 q^{53} -9.89081e6 q^{54} +8.07814e7 q^{55} -1.48838e8 q^{56} -4.41166e6 q^{57} -5.86430e7 q^{58} +1.21174e7 q^{59} +2.00255e7 q^{60} +9.09669e7 q^{61} +1.05686e8 q^{62} +7.74322e7 q^{63} +1.45003e8 q^{64} +2.62846e8 q^{65} -8.15804e7 q^{66} -1.83319e7 q^{67} -1.80107e7 q^{68} +1.66216e8 q^{69} +3.27881e8 q^{70} -3.08979e8 q^{71} -8.27433e7 q^{72} +1.21812e7 q^{73} +2.75880e8 q^{74} -2.22898e7 q^{75} -9.02043e6 q^{76} +6.38668e8 q^{77} -2.65446e8 q^{78} -2.20744e8 q^{79} -2.23789e8 q^{80} +4.30467e7 q^{81} -5.09056e8 q^{82} +4.48981e8 q^{83} +1.58324e8 q^{84} +1.62333e8 q^{85} +3.66022e8 q^{86} +2.55226e8 q^{87} -6.82475e8 q^{88} +7.18855e8 q^{89} +1.82278e8 q^{90} +2.07809e9 q^{91} +3.39859e8 q^{92} -4.59968e8 q^{93} -2.99103e8 q^{94} +8.13026e7 q^{95} -2.97016e8 q^{96} -1.57982e9 q^{97} +1.84123e9 q^{98} +3.55054e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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