LMFDB - Embedded newform 177.10.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +49254.6 q^{10} +62941.6 q^{11} -18353.4 q^{12} +89682.6 q^{13} +268587. q^{14} +146802. q^{15} -326815. q^{16} -98165.2 q^{17} -178308. q^{18} -608747. q^{19} -410657. q^{20} +800517. q^{21} -1.71056e6 q^{22} -1.34425e6 q^{23} -628291. q^{24} +1.33155e6 q^{25} -2.43730e6 q^{26} -531441. q^{27} -2.23933e6 q^{28} +1.65081e6 q^{29} -3.98962e6 q^{30} -3.82270e6 q^{31} +4.91040e6 q^{32} -5.09827e6 q^{33} +2.66783e6 q^{34} +1.79115e7 q^{35} +1.48663e6 q^{36} -243314. q^{37} +1.65439e7 q^{38} -7.26429e6 q^{39} -1.40580e7 q^{40} -3.05708e7 q^{41} -2.17556e7 q^{42} -9.67346e6 q^{43} +1.42617e7 q^{44} -1.18909e7 q^{45} +3.65327e7 q^{46} -1.94397e7 q^{47} +2.64720e7 q^{48} +5.73185e7 q^{49} -3.61875e7 q^{50} +7.95138e6 q^{51} +2.03208e7 q^{52} -6.14911e7 q^{53} +1.44429e7 q^{54} -1.14073e8 q^{55} -7.66587e7 q^{56} +4.93085e7 q^{57} -4.48639e7 q^{58} +1.21174e7 q^{59} +3.32632e7 q^{60} -1.88500e8 q^{61} +1.03889e8 q^{62} -6.48418e7 q^{63} +3.38795e7 q^{64} -1.62538e8 q^{65} +1.38555e8 q^{66} +7.34365e7 q^{67} -2.22428e7 q^{68} +1.08884e8 q^{69} -4.86779e8 q^{70} -1.30229e8 q^{71} +5.08916e7 q^{72} +3.50993e7 q^{73} +6.61254e6 q^{74} -1.07856e8 q^{75} -1.37934e8 q^{76} -6.22047e8 q^{77} +1.97421e8 q^{78} -1.62826e8 q^{79} +5.92309e8 q^{80} +4.30467e7 q^{81} +8.30822e8 q^{82} +1.68987e8 q^{83} +1.81386e8 q^{84} +1.77911e8 q^{85} +2.62895e8 q^{86} -1.33716e8 q^{87} +4.88218e8 q^{88} -9.09234e8 q^{89} +3.23159e8 q^{90} -8.86326e8 q^{91} -3.04588e8 q^{92} +3.09639e8 q^{93} +5.28311e8 q^{94} +1.10327e9 q^{95} -3.97743e8 q^{96} +2.90211e7 q^{97} -1.55774e9 q^{98} +4.12960e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−27.1769	−1.20106	−0.600531	−	0.799601i	$-0.705044\pi$
$2$	−27.1769	−1.20106	−0.600531	+	0.799601i	$0.705044\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	226.586	0.442550
$5$	−1812.37	−1.29682	−0.648412	−	0.761289i	$-0.724567\pi$
$5$	−1812.37	−1.29682	−0.648412	+	0.761289i	$0.724567\pi$
$6$	2201.33	0.693434
$7$	−9882.92	−1.55577	−0.777883	−	0.628409i	$-0.783706\pi$
$7$	−9882.92	−1.55577	−0.777883	+	0.628409i	$0.783706\pi$
$8$	7756.68	0.669532
$9$	6561.00	0.333333
$10$	49254.6	1.55757
$11$	62941.6	1.29620	0.648098	−	0.761557i	$-0.275565\pi$
$11$	62941.6	1.29620	0.648098	+	0.761557i	$0.275565\pi$
$12$	−18353.4	−0.255507
$13$	89682.6	0.870890	0.435445	−	0.900215i	$-0.356591\pi$
$13$	89682.6	0.870890	0.435445	+	0.900215i	$0.356591\pi$
$14$	268587.	1.86857
$15$	146802.	0.748722
$16$	−326815.	−1.24670
$17$	−98165.2	−0.285061	−0.142530	−	0.989790i	$-0.545524\pi$
$17$	−98165.2	−0.285061	−0.142530	+	0.989790i	$0.545524\pi$
$18$	−178308.	−0.400354
$19$	−608747.	−1.07163	−0.535816	−	0.844335i	$-0.679996\pi$
$19$	−608747.	−1.07163	−0.535816	+	0.844335i	$0.679996\pi$
$20$	−410657.	−0.573910
$21$	800517.	0.898222
$22$	−1.71056e6	−1.55681
$23$	−1.34425e6	−1.00163	−0.500813	−	0.865556i	$-0.666966\pi$
$23$	−1.34425e6	−1.00163	−0.500813	+	0.865556i	$0.666966\pi$
$24$	−628291.	−0.386554
$25$	1.33155e6	0.681755
$26$	−2.43730e6	−1.04599
$27$	−531441.	−0.192450
$28$	−2.23933e6	−0.688505
$29$	1.65081e6	0.433417	0.216708	−	0.976236i	$-0.430468\pi$
$29$	1.65081e6	0.433417	0.216708	+	0.976236i	$0.430468\pi$
$30$	−3.98962e6	−0.899262
$31$	−3.82270e6	−0.743435	−0.371718	−	0.928346i	$-0.621231\pi$
$31$	−3.82270e6	−0.743435	−0.371718	+	0.928346i	$0.621231\pi$
$32$	4.91040e6	0.827832
$33$	−5.09827e6	−0.748360
$34$	2.66783e6	0.342376
$35$	1.79115e7	2.01756
$36$	1.48663e6	0.147517
$37$	−243314.	−0.0213432	−0.0106716	−	0.999943i	$-0.503397\pi$
$37$	−243314.	−0.0213432	−0.0106716	+	0.999943i	$0.503397\pi$
$38$	1.65439e7	1.28710
$39$	−7.26429e6	−0.502808
$40$	−1.40580e7	−0.868265
$41$	−3.05708e7	−1.68959	−0.844793	−	0.535094i	$-0.820276\pi$
$41$	−3.05708e7	−1.68959	−0.844793	+	0.535094i	$0.820276\pi$
$42$	−2.17556e7	−1.07882
$43$	−9.67346e6	−0.431493	−0.215746	−	0.976449i	$-0.569218\pi$
$43$	−9.67346e6	−0.431493	−0.215746	+	0.976449i	$0.569218\pi$
$44$	1.42617e7	0.573632
$45$	−1.18909e7	−0.432275
$46$	3.65327e7	1.20301
$47$	−1.94397e7	−0.581097	−0.290549	−	0.956860i	$-0.593838\pi$
$47$	−1.94397e7	−0.581097	−0.290549	+	0.956860i	$0.593838\pi$
$48$	2.64720e7	0.719782
$49$	5.73185e7	1.42041
$50$	−3.61875e7	−0.818830
$51$	7.95138e6	0.164580
$52$	2.03208e7	0.385413
$53$	−6.14911e7	−1.07046	−0.535231	−	0.844706i	$-0.679775\pi$
$53$	−6.14911e7	−1.07046	−0.535231	+	0.844706i	$0.679775\pi$
$54$	1.44429e7	0.231145
$55$	−1.14073e8	−1.68094
$56$	−7.66587e7	−1.04163
$57$	4.93085e7	0.618707
$58$	−4.48639e7	−0.520561
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	3.32632e7	0.331347
$61$	−1.88500e8	−1.74312	−0.871558	−	0.490293i	$-0.836890\pi$
$61$	−1.88500e8	−1.74312	−0.871558	+	0.490293i	$0.836890\pi$
$62$	1.03889e8	0.892912
$63$	−6.48418e7	−0.518589
$64$	3.38795e7	0.252422
$65$	−1.62538e8	−1.12939
$66$	1.38555e8	0.898827
$67$	7.34365e7	0.445221	0.222610	−	0.974907i	$-0.428542\pi$
$67$	7.34365e7	0.445221	0.222610	+	0.974907i	$0.428542\pi$
$68$	−2.22428e7	−0.126154
$69$	1.08884e8	0.578289
$70$	−4.86779e8	−2.42321
$71$	−1.30229e8	−0.608196	−0.304098	−	0.952641i	$-0.598355\pi$
$71$	−1.30229e8	−0.608196	−0.304098	+	0.952641i	$0.598355\pi$
$72$	5.08916e7	0.223177
$73$	3.50993e7	0.144659	0.0723295	−	0.997381i	$-0.476957\pi$
$73$	3.50993e7	0.144659	0.0723295	+	0.997381i	$0.476957\pi$
$74$	6.61254e6	0.0256345
$75$	−1.07856e8	−0.393611
$76$	−1.37934e8	−0.474251
$77$	−6.22047e8	−2.01658
$78$	1.97421e8	0.603904
$79$	−1.62826e8	−0.470330	−0.235165	−	0.971955i	$-0.575563\pi$
$79$	−1.62826e8	−0.470330	−0.235165	+	0.971955i	$0.575563\pi$
$80$	5.92309e8	1.61675
$81$	4.30467e7	0.111111
$82$	8.30822e8	2.02930
$83$	1.68987e8	0.390843	0.195422	−	0.980719i	$-0.437392\pi$
$83$	1.68987e8	0.390843	0.195422	+	0.980719i	$0.437392\pi$
$84$	1.81386e8	0.397508
$85$	1.77911e8	0.369674
$86$	2.62895e8	0.518250
$87$	−1.33716e8	−0.250233
$88$	4.88218e8	0.867845
$89$	−9.09234e8	−1.53610	−0.768052	−	0.640387i	$-0.778774\pi$
$89$	−9.09234e8	−1.53610	−0.768052	+	0.640387i	$0.778774\pi$
$90$	3.23159e8	0.519189
$91$	−8.86326e8	−1.35490
$92$	−3.04588e8	−0.443270
$93$	3.09639e8	0.429223
$94$	5.28311e8	0.697934
$95$	1.10327e9	1.38972
$96$	−3.97743e8	−0.477949
$97$	2.90211e7	0.0332844	0.0166422	−	0.999862i	$-0.494702\pi$
$97$	2.90211e7	0.0332844	0.0166422	+	0.999862i	$0.494702\pi$
$98$	−1.55774e9	−1.70600
$99$	4.12960e8	0.432066
$100$	3.01711e8	0.301711
$101$	−1.28615e9	−1.22983	−0.614915	−	0.788593i	$-0.710810\pi$
$101$	−1.28615e9	−1.22983	−0.614915	+	0.788593i	$0.710810\pi$
$102$	−2.16094e8	−0.197671
$103$	6.45125e8	0.564776	0.282388	−	0.959300i	$-0.408873\pi$
$103$	6.45125e8	0.564776	0.282388	+	0.959300i	$0.408873\pi$
$104$	6.95640e8	0.583088
$105$	−1.45083e9	−1.16484
$106$	1.67114e9	1.28569
$107$	−1.70524e9	−1.25765	−0.628824	−	0.777548i	$-0.716463\pi$
$107$	−1.70524e9	−1.25765	−0.628824	+	0.777548i	$0.716463\pi$
$108$	−1.20417e8	−0.0851689
$109$	6.77929e8	0.460008	0.230004	−	0.973190i	$-0.426126\pi$
$109$	6.77929e8	0.460008	0.230004	+	0.973190i	$0.426126\pi$
$110$	3.10017e9	2.01891
$111$	1.97085e7	0.0123225
$112$	3.22988e9	1.93957
$113$	−1.94114e9	−1.11996	−0.559981	−	0.828506i	$-0.689191\pi$
$113$	−1.94114e9	−1.11996	−0.559981	+	0.828506i	$0.689191\pi$
$114$	−1.34005e9	−0.743106
$115$	2.43628e9	1.29893
$116$	3.74050e8	0.191809
$117$	5.88408e8	0.290297
$118$	−3.29313e8	−0.156365
$119$	9.70159e8	0.443487
$120$	1.13870e9	0.501293
$121$	1.60370e9	0.680127
$122$	5.12284e9	2.09359
$123$	2.47624e9	0.975483
$124$	−8.66171e8	−0.329008
$125$	1.12652e9	0.412708
$126$	1.76220e9	0.622857
$127$	3.92610e9	1.33920	0.669598	−	0.742724i	$-0.266466\pi$
$127$	3.92610e9	1.33920	0.669598	+	0.742724i	$0.266466\pi$
$128$	−3.43487e9	−1.13101
$129$	7.83550e8	0.249123
$130$	4.41728e9	1.35647
$131$	1.25295e9	0.371717	0.185859	−	0.982576i	$-0.440493\pi$
$131$	1.25295e9	0.371717	0.185859	+	0.982576i	$0.440493\pi$
$132$	−1.15520e9	−0.331187
$133$	6.01620e9	1.66721
$134$	−1.99578e9	−0.534738
$135$	9.63167e8	0.249574
$136$	−7.61436e8	−0.190857
$137$	−5.77814e9	−1.40135	−0.700674	−	0.713482i	$-0.747117\pi$
$137$	−5.77814e9	−1.40135	−0.700674	+	0.713482i	$0.747117\pi$
$138$	−2.95914e9	−0.694561
$139$	−5.20118e8	−0.118178	−0.0590888	−	0.998253i	$-0.518820\pi$
$139$	−5.20118e8	−0.118178	−0.0590888	+	0.998253i	$0.518820\pi$
$140$	4.05849e9	0.892870
$141$	1.57461e9	0.335497
$142$	3.53921e9	0.730482
$143$	5.64477e9	1.12884
$144$	−2.14423e9	−0.415567
$145$	−2.99187e9	−0.562066
$146$	−9.53892e8	−0.173745
$147$	−4.64280e9	−0.820072
$148$	−5.51316e7	−0.00944545
$149$	−2.06805e9	−0.343734	−0.171867	−	0.985120i	$-0.554980\pi$
$149$	−2.06805e9	−0.343734	−0.171867	+	0.985120i	$0.554980\pi$
$150$	2.93119e9	0.472752
$151$	−4.21433e9	−0.659678	−0.329839	−	0.944037i	$-0.606994\pi$
$151$	−4.21433e9	−0.659678	−0.329839	+	0.944037i	$0.606994\pi$
$152$	−4.72186e9	−0.717492
$153$	−6.44062e8	−0.0950202
$154$	1.69053e10	2.42204
$155$	6.92815e9	0.964105
$156$	−1.64599e9	−0.222518
$157$	−1.39983e9	−0.183876	−0.0919381	−	0.995765i	$-0.529306\pi$
$157$	−1.39983e9	−0.183876	−0.0919381	+	0.995765i	$0.529306\pi$
$158$	4.42512e9	0.564896
$159$	4.98078e9	0.618031
$160$	−8.89946e9	−1.07355
$161$	1.32851e10	1.55829
$162$	−1.16988e9	−0.133451
$163$	−1.41964e10	−1.57519	−0.787595	−	0.616193i	$-0.788674\pi$
$163$	−1.41964e10	−1.57519	−0.787595	+	0.616193i	$0.788674\pi$
$164$	−6.92692e9	−0.747727
$165$	9.23995e9	0.970492
$166$	−4.59256e9	−0.469427
$167$	8.20821e9	0.816628	0.408314	−	0.912841i	$-0.366117\pi$
$167$	8.20821e9	0.816628	0.408314	+	0.912841i	$0.366117\pi$
$168$	6.20935e9	0.601388
$169$	−2.56153e9	−0.241551
$170$	−4.83509e9	−0.444001
$171$	−3.99399e9	−0.357211
$172$	−2.19187e9	−0.190957
$173$	1.55232e10	1.31757	0.658784	−	0.752332i	$-0.271071\pi$
$173$	1.55232e10	1.31757	0.658784	+	0.752332i	$0.271071\pi$
$174$	3.63398e9	0.300546
$175$	−1.31596e10	−1.06065
$176$	−2.05703e10	−1.61597
$177$	−9.81506e8	−0.0751646
$178$	2.47102e10	1.84496
$179$	−3.36293e9	−0.244838	−0.122419	−	0.992478i	$-0.539065\pi$
$179$	−3.36293e9	−0.244838	−0.122419	+	0.992478i	$0.539065\pi$
$180$	−2.69432e9	−0.191303
$181$	1.83171e10	1.26854	0.634268	−	0.773113i	$-0.281301\pi$
$181$	1.83171e10	1.26854	0.634268	+	0.773113i	$0.281301\pi$
$182$	2.40876e10	1.62732
$183$	1.52685e10	1.00639
$184$	−1.04269e10	−0.670620
$185$	4.40975e8	0.0276784
$186$	−8.41504e9	−0.515523
$187$	−6.17868e9	−0.369495
$188$	−4.40476e9	−0.257165
$189$	5.25219e9	0.299407
$190$	−2.99836e10	−1.66914
$191$	−1.90964e10	−1.03825	−0.519125	−	0.854698i	$-0.673742\pi$
$191$	−1.90964e10	−1.03825	−0.519125	+	0.854698i	$0.673742\pi$
$192$	−2.74424e9	−0.145736
$193$	−3.18478e9	−0.165224	−0.0826118	−	0.996582i	$-0.526326\pi$
$193$	−3.18478e9	−0.165224	−0.0826118	+	0.996582i	$0.526326\pi$
$194$	−7.88705e8	−0.0399767
$195$	1.31656e10	0.652054
$196$	1.29876e10	0.628601
$197$	2.09373e10	0.990428	0.495214	−	0.868771i	$-0.335090\pi$
$197$	2.09373e10	0.990428	0.495214	+	0.868771i	$0.335090\pi$
$198$	−1.12230e10	−0.518938
$199$	−2.41219e9	−0.109037	−0.0545183	−	0.998513i	$-0.517362\pi$
$199$	−2.41219e9	−0.109037	−0.0545183	+	0.998513i	$0.517362\pi$
$200$	1.03284e10	0.456457
$201$	−5.94836e9	−0.257048
$202$	3.49536e10	1.47710
$203$	−1.63148e10	−0.674295
$204$	1.80167e9	0.0728349
$205$	5.54056e10	2.19110
$206$	−1.75325e10	−0.678331
$207$	−8.81964e9	−0.333875
$208$	−2.93096e10	−1.08574
$209$	−3.83156e10	−1.38905
$210$	3.94291e10	1.39904
$211$	−2.71223e10	−0.942011	−0.471005	−	0.882130i	$-0.656109\pi$
$211$	−2.71223e10	−0.942011	−0.471005	+	0.882130i	$0.656109\pi$
$212$	−1.39330e10	−0.473733
$213$	1.05485e10	0.351142
$214$	4.63433e10	1.51051
$215$	1.75319e10	0.559571
$216$	−4.12222e9	−0.128851
$217$	3.77795e10	1.15661
$218$	−1.84240e10	−0.552498
$219$	−2.84304e9	−0.0835190
$220$	−2.58474e10	−0.743901
$221$	−8.80371e9	−0.248256
$222$	−5.35616e8	−0.0148001
$223$	−2.52230e9	−0.0683006	−0.0341503	−	0.999417i	$-0.510872\pi$
$223$	−2.52230e9	−0.0683006	−0.0341503	+	0.999417i	$0.510872\pi$
$224$	−4.85291e10	−1.28791
$225$	8.73632e9	0.227252
$226$	5.27541e10	1.34514
$227$	5.18221e10	1.29538	0.647692	−	0.761902i	$-0.275734\pi$
$227$	5.18221e10	1.29538	0.647692	+	0.761902i	$0.275734\pi$
$228$	1.11726e10	0.273809
$229$	−3.31362e10	−0.796239	−0.398120	−	0.917334i	$-0.630337\pi$
$229$	−3.31362e10	−0.796239	−0.398120	+	0.917334i	$0.630337\pi$
$230$	−6.62106e10	−1.56010
$231$	5.03858e10	1.16427
$232$	1.28048e10	0.290186
$233$	−7.47758e10	−1.66211	−0.831054	−	0.556192i	$-0.812262\pi$
$233$	−7.47758e10	−1.66211	−0.831054	+	0.556192i	$0.812262\pi$
$234$	−1.59911e10	−0.348664
$235$	3.52319e10	0.753582
$236$	2.74562e9	0.0576152
$237$	1.31889e10	0.271545
$238$	−2.63659e10	−0.532656
$239$	−9.52011e10	−1.88735	−0.943673	−	0.330881i	$-0.892654\pi$
$239$	−9.52011e10	−1.88735	−0.943673	+	0.330881i	$0.892654\pi$
$240$	−4.79770e10	−0.933432
$241$	−5.45165e10	−1.04100	−0.520501	−	0.853861i	$-0.674255\pi$
$241$	−5.45165e10	−1.04100	−0.520501	+	0.853861i	$0.674255\pi$
$242$	−4.35837e10	−0.816874
$243$	−3.48678e9	−0.0641500
$244$	−4.27113e10	−0.771416
$245$	−1.03882e11	−1.84202
$246$	−6.72966e10	−1.17162
$247$	−5.45940e10	−0.933274
$248$	−2.96515e10	−0.497753
$249$	−1.36880e10	−0.225654
$250$	−3.06153e10	−0.495688
$251$	7.23992e10	1.15134	0.575668	−	0.817684i	$-0.304742\pi$
$251$	7.23992e10	1.15134	0.575668	+	0.817684i	$0.304742\pi$
$252$	−1.46922e10	−0.229502
$253$	−8.46094e10	−1.29830
$254$	−1.06699e11	−1.60846
$255$	−1.44108e10	−0.213431
$256$	7.60029e10	1.10599
$257$	−2.94793e10	−0.421520	−0.210760	−	0.977538i	$-0.567594\pi$
$257$	−2.94793e10	−0.421520	−0.210760	+	0.977538i	$0.567594\pi$
$258$	−2.12945e10	−0.299212
$259$	2.40466e9	0.0332051
$260$	−3.68288e10	−0.499813
$261$	1.08310e10	0.144472
$262$	−3.40513e10	−0.446456
$263$	−1.25248e11	−1.61425	−0.807125	−	0.590381i	$-0.798978\pi$
$263$	−1.25248e11	−1.61425	−0.807125	+	0.590381i	$0.798978\pi$
$264$	−3.95457e10	−0.501050
$265$	1.11445e11	1.38820
$266$	−1.63502e11	−2.00242
$267$	7.36479e10	0.886870
$268$	1.66397e10	0.197033
$269$	1.23969e11	1.44354	0.721771	−	0.692132i	$-0.243329\pi$
$269$	1.23969e11	1.44354	0.721771	+	0.692132i	$0.243329\pi$
$270$	−2.61759e10	−0.299754
$271$	1.03554e11	1.16628	0.583142	−	0.812370i	$-0.301823\pi$
$271$	1.03554e11	1.16628	0.583142	+	0.812370i	$0.301823\pi$
$272$	3.20818e10	0.355385
$273$	7.17924e10	0.782252
$274$	1.57032e11	1.68311
$275$	8.38101e10	0.883689
$276$	2.46717e10	0.255922
$277$	1.34895e11	1.37669	0.688344	−	0.725384i	$-0.258338\pi$
$277$	1.34895e11	1.37669	0.688344	+	0.725384i	$0.258338\pi$
$278$	1.41352e10	0.141939
$279$	−2.50808e10	−0.247812
$280$	1.38934e11	1.35082
$281$	−1.34882e11	−1.29055	−0.645274	−	0.763951i	$-0.723257\pi$
$281$	−1.34882e11	−1.29055	−0.645274	+	0.763951i	$0.723257\pi$
$282$	−4.27932e10	−0.402952
$283$	1.81349e11	1.68065	0.840324	−	0.542085i	$-0.182365\pi$
$283$	1.81349e11	1.68065	0.840324	+	0.542085i	$0.182365\pi$
$284$	−2.95080e10	−0.269158
$285$	−8.93652e10	−0.802355
$286$	−1.53408e11	−1.35581
$287$	3.02129e11	2.62860
$288$	3.22172e10	0.275944
$289$	−1.08951e11	−0.918740
$290$	8.13100e10	0.675076
$291$	−2.35071e9	−0.0192168
$292$	7.95301e9	0.0640189
$293$	−2.12229e11	−1.68229	−0.841145	−	0.540809i	$-0.818118\pi$
$293$	−2.12229e11	−1.68229	−0.841145	+	0.540809i	$0.818118\pi$
$294$	1.26177e11	0.984957
$295$	−2.19611e10	−0.168832
$296$	−1.88731e9	−0.0142900
$297$	−3.34498e10	−0.249453
$298$	5.62032e10	0.412845
$299$	−1.20556e11	−0.872305
$300$	−2.44386e10	−0.174193
$301$	9.56020e10	0.671302
$302$	1.14532e11	0.792314
$303$	1.04178e11	0.710043
$304$	1.98948e11	1.33600
$305$	3.41631e11	2.26052
$306$	1.75036e10	0.114125
$307$	2.37092e10	0.152333	0.0761665	−	0.997095i	$-0.475732\pi$
$307$	2.37092e10	0.152333	0.0761665	+	0.997095i	$0.475732\pi$
$308$	−1.40947e11	−0.892438
$309$	−5.22551e10	−0.326074
$310$	−1.88286e11	−1.15795
$311$	−2.29292e11	−1.38985	−0.694924	−	0.719083i	$-0.744562\pi$
$311$	−2.29292e11	−1.38985	−0.694924	+	0.719083i	$0.744562\pi$
$312$	−5.63468e10	−0.336646
$313$	−6.41849e9	−0.0377993	−0.0188996	−	0.999821i	$-0.506016\pi$
$313$	−6.41849e9	−0.0377993	−0.0188996	+	0.999821i	$0.506016\pi$
$314$	3.80430e10	0.220847
$315$	1.17517e11	0.672519
$316$	−3.68942e10	−0.208145
$317$	2.31514e11	1.28769	0.643843	−	0.765158i	$-0.277339\pi$
$317$	2.31514e11	1.28769	0.643843	+	0.765158i	$0.277339\pi$
$318$	−1.35362e11	−0.742294
$319$	1.03905e11	0.561794
$320$	−6.14021e10	−0.327347
$321$	1.38125e11	0.726103
$322$	−3.61049e11	−1.87161
$323$	5.97578e10	0.305480
$324$	9.75378e9	0.0491723
$325$	1.19417e11	0.593733
$326$	3.85814e11	1.89190
$327$	−5.49122e10	−0.265585
$328$	−2.37128e11	−1.13123
$329$	1.92121e11	0.904051
$330$	−2.51113e11	−1.16562
$331$	2.77864e11	1.27235	0.636176	−	0.771544i	$-0.280515\pi$
$331$	2.77864e11	1.27235	0.636176	+	0.771544i	$0.280515\pi$
$332$	3.82901e10	0.172968
$333$	−1.59639e9	−0.00711441
$334$	−2.23074e11	−0.980822
$335$	−1.33094e11	−0.577373
$336$	−2.61621e11	−1.11981
$337$	−4.22215e11	−1.78320	−0.891599	−	0.452826i	$-0.850416\pi$
$337$	−4.22215e11	−1.78320	−0.891599	+	0.452826i	$0.850416\pi$
$338$	6.96145e10	0.290118
$339$	1.57232e11	0.646610
$340$	4.03122e10	0.163599
$341$	−2.40607e11	−0.963638
$342$	1.08544e11	0.429032
$343$	−1.67663e11	−0.654054
$344$	−7.50339e10	−0.288898
$345$	−1.97339e11	−0.749939
$346$	−4.21873e11	−1.58248
$347$	−3.69232e11	−1.36715	−0.683575	−	0.729880i	$-0.739576\pi$
$347$	−3.69232e11	−1.36715	−0.683575	+	0.729880i	$0.739576\pi$
$348$	−3.02980e10	−0.110741
$349$	1.31293e11	0.473725	0.236863	−	0.971543i	$-0.423881\pi$
$349$	1.31293e11	0.473725	0.236863	+	0.971543i	$0.423881\pi$
$350$	3.57638e11	1.27391
$351$	−4.76610e10	−0.167603
$352$	3.09069e11	1.07303
$353$	−2.30328e11	−0.789516	−0.394758	−	0.918785i	$-0.629172\pi$
$353$	−2.30328e11	−0.789516	−0.394758	+	0.918785i	$0.629172\pi$
$354$	2.66743e10	0.0902774
$355$	2.36022e11	0.788724
$356$	−2.06020e11	−0.679803
$357$	−7.85828e10	−0.256048
$358$	9.13942e10	0.294066
$359$	−3.73488e11	−1.18673	−0.593364	−	0.804934i	$-0.702201\pi$
$359$	−3.73488e11	−1.18673	−0.593364	+	0.804934i	$0.702201\pi$
$360$	−9.22343e10	−0.289422
$361$	4.78856e10	0.148396
$362$	−4.97802e11	−1.52359
$363$	−1.29900e11	−0.392671
$364$	−2.00829e11	−0.599612
$365$	−6.36129e10	−0.187598
$366$	−4.14950e11	−1.20873
$367$	3.81640e11	1.09814	0.549069	−	0.835777i	$-0.314983\pi$
$367$	3.81640e11	1.09814	0.549069	+	0.835777i	$0.314983\pi$
$368$	4.39321e11	1.24873
$369$	−2.00575e11	−0.563195
$370$	−1.19844e10	−0.0332435
$371$	6.07712e11	1.66539
$372$	7.01598e10	0.189953
$373$	4.77457e11	1.27716	0.638579	−	0.769556i	$-0.279523\pi$
$373$	4.77457e11	1.27716	0.638579	+	0.769556i	$0.279523\pi$
$374$	1.67917e11	0.443786
$375$	−9.12479e10	−0.238277
$376$	−1.50787e11	−0.389063
$377$	1.48049e11	0.377458
$378$	−1.42738e11	−0.359607
$379$	−3.30291e11	−0.822281	−0.411141	−	0.911572i	$-0.634869\pi$
$379$	−3.30291e11	−0.822281	−0.411141	+	0.911572i	$0.634869\pi$
$380$	2.49986e11	0.615021
$381$	−3.18014e11	−0.773185
$382$	5.18982e11	1.24700
$383$	7.45540e11	1.77042	0.885210	−	0.465191i	$-0.154015\pi$
$383$	7.45540e11	1.77042	0.885210	+	0.465191i	$0.154015\pi$
$384$	2.78224e11	0.652987
$385$	1.12738e12	2.61515
$386$	8.65527e10	0.198444
$387$	−6.34675e10	−0.143831
$388$	6.57577e9	0.0147300
$389$	−3.66578e11	−0.811695	−0.405847	−	0.913941i	$-0.633024\pi$
$389$	−3.66578e11	−0.811695	−0.405847	+	0.913941i	$0.633024\pi$
$390$	−3.57800e11	−0.783158
$391$	1.31959e11	0.285524
$392$	4.44602e11	0.951007
$393$	−1.01489e11	−0.214611
$394$	−5.69012e11	−1.18957
$395$	2.95102e11	0.609936
$396$	9.35709e10	0.191211
$397$	6.83450e11	1.38086	0.690430	−	0.723399i	$-0.257421\pi$
$397$	6.83450e11	1.38086	0.690430	+	0.723399i	$0.257421\pi$
$398$	6.55558e10	0.130960
$399$	−4.87312e11	−0.962564
$400$	−4.35171e11	−0.849944
$401$	−5.64066e11	−1.08938	−0.544691	−	0.838637i	$-0.683353\pi$
$401$	−5.64066e11	−1.08938	−0.544691	+	0.838637i	$0.683353\pi$
$402$	1.61658e11	0.308731
$403$	−3.42830e11	−0.647450
$404$	−2.91423e11	−0.544262
$405$	−7.80165e10	−0.144092
$406$	4.43387e11	0.809870
$407$	−1.53146e10	−0.0276650
$408$	6.16763e10	0.110191
$409$	2.61742e11	0.462507	0.231253	−	0.972894i	$-0.425717\pi$
$409$	2.61742e11	0.462507	0.231253	+	0.972894i	$0.425717\pi$
$410$	−1.50576e12	−2.63164
$411$	4.68030e11	0.809068
$412$	1.46176e11	0.249942
$413$	−1.19755e11	−0.202543
$414$	2.39691e11	0.401005
$415$	−3.06267e11	−0.506855
$416$	4.40378e11	0.720950
$417$	4.21296e10	0.0682299
$418$	1.04130e12	1.66833
$419$	2.60416e11	0.412767	0.206384	−	0.978471i	$-0.433831\pi$
$419$	2.60416e11	0.412767	0.206384	+	0.978471i	$0.433831\pi$
$420$	−3.28738e11	−0.515499
$421$	4.17072e11	0.647056	0.323528	−	0.946219i	$-0.395131\pi$
$421$	4.17072e11	0.647056	0.323528	+	0.946219i	$0.395131\pi$
$422$	7.37102e11	1.13141
$423$	−1.27544e11	−0.193699
$424$	−4.76967e11	−0.716708
$425$	−1.30712e11	−0.194342
$426$	−2.86676e11	−0.421744
$427$	1.86293e12	2.71188
$428$	−3.86384e11	−0.556573
$429$	−4.57226e11	−0.651739
$430$	−4.76462e11	−0.672079
$431$	6.74040e11	0.940888	0.470444	−	0.882430i	$-0.344094\pi$
$431$	6.74040e11	0.940888	0.470444	+	0.882430i	$0.344094\pi$
$432$	1.73683e11	0.239927
$433$	−4.17035e11	−0.570135	−0.285067	−	0.958508i	$-0.592016\pi$
$433$	−4.17035e11	−0.570135	−0.285067	+	0.958508i	$0.592016\pi$
$434$	−1.02673e12	−1.38916
$435$	2.42342e11	0.324509
$436$	1.53609e11	0.203577
$437$	8.18310e11	1.07337
$438$	7.72652e10	0.100311
$439$	−1.26557e12	−1.62628	−0.813142	−	0.582065i	$-0.802245\pi$
$439$	−1.26557e12	−1.62628	−0.813142	+	0.582065i	$0.802245\pi$
$440$	−8.84831e11	−1.12544
$441$	3.76067e11	0.473469
$442$	2.39258e11	0.298171
$443$	−1.04011e12	−1.28310	−0.641552	−	0.767079i	$-0.721709\pi$
$443$	−1.04011e12	−1.28310	−0.641552	+	0.767079i	$0.721709\pi$
$444$	4.46566e9	0.00545333
$445$	1.64787e12	1.99206
$446$	6.85483e10	0.0820333
$447$	1.67512e11	0.198455
$448$	−3.34828e11	−0.392709
$449$	1.09333e12	1.26953	0.634766	−	0.772704i	$-0.281096\pi$
$449$	1.09333e12	1.26953	0.634766	+	0.772704i	$0.281096\pi$
$450$	−2.37426e11	−0.272943
$451$	−1.92418e12	−2.19004
$452$	−4.39834e11	−0.495639
$453$	3.41360e11	0.380865
$454$	−1.40837e12	−1.55584
$455$	1.60635e12	1.75707
$456$	3.82471e11	0.414244
$457$	6.82471e10	0.0731917	0.0365958	−	0.999330i	$-0.488349\pi$
$457$	6.82471e10	0.0731917	0.0365958	+	0.999330i	$0.488349\pi$
$458$	9.00541e11	0.956333
$459$	5.21690e10	0.0548599
$460$	5.52026e11	0.574843
$461$	3.89708e11	0.401869	0.200935	−	0.979605i	$-0.435602\pi$
$461$	3.89708e11	0.401869	0.200935	+	0.979605i	$0.435602\pi$
$462$	−1.36933e12	−1.39836
$463$	1.41589e12	1.43191	0.715953	−	0.698149i	$-0.245993\pi$
$463$	1.41589e12	1.43191	0.715953	+	0.698149i	$0.245993\pi$
$464$	−5.39509e11	−0.540341
$465$	−5.61180e11	−0.556626
$466$	2.03218e12	1.99629
$467$	9.91833e11	0.964967	0.482484	−	0.875905i	$-0.339735\pi$
$467$	9.91833e11	0.964967	0.482484	+	0.875905i	$0.339735\pi$
$468$	1.33325e11	0.128471
$469$	−7.25767e11	−0.692659
$470$	−9.57494e11	−0.905098
$471$	1.13386e11	0.106161
$472$	9.39905e10	0.0871656
$473$	−6.08863e11	−0.559300
$474$	−3.58435e11	−0.326143
$475$	−8.10579e11	−0.730591
$476$	2.19824e11	0.196266
$477$	−4.03443e11	−0.356820
$478$	2.58727e12	2.26682
$479$	8.44724e11	0.733171	0.366585	−	0.930384i	$-0.380527\pi$
$479$	8.44724e11	0.733171	0.366585	+	0.930384i	$0.380527\pi$
$480$	7.20856e11	0.619816
$481$	−2.18211e10	−0.0185876
$482$	1.48159e12	1.25031
$483$	−1.07610e12	−0.899682
$484$	3.63376e11	0.300990
$485$	−5.25969e10	−0.0431641
$486$	9.47601e10	0.0770482
$487$	−1.17244e12	−0.944521	−0.472260	−	0.881459i	$-0.656562\pi$
$487$	−1.17244e12	−0.944521	−0.472260	+	0.881459i	$0.656562\pi$
$488$	−1.46213e12	−1.16707
$489$	1.14991e12	0.909437
$490$	2.82320e12	2.21238
$491$	−2.02446e9	−0.00157196	−0.000785982	−	1.00000i	$-0.500250\pi$
$491$	−2.02446e9	−0.00157196	−0.000785982		1.00000i	$0.500250\pi$
$492$	5.61081e11	0.431700
$493$	−1.62052e11	−0.123550
$494$	1.48370e12	1.12092
$495$	−7.48436e11	−0.560314
$496$	1.24932e12	0.926840
$497$	1.28704e12	0.946211
$498$	3.71997e11	0.271024
$499$	−2.63096e12	−1.89960	−0.949799	−	0.312861i	$-0.898713\pi$
$499$	−2.63096e12	−1.89960	−0.949799	+	0.312861i	$0.898713\pi$
$500$	2.55253e11	0.182644
$501$	−6.64865e11	−0.471481
$502$	−1.96759e12	−1.38283
$503$	2.12291e11	0.147869	0.0739343	−	0.997263i	$-0.476444\pi$
$503$	2.12291e11	0.147869	0.0739343	+	0.997263i	$0.476444\pi$
$504$	−5.02958e11	−0.347211
$505$	2.33098e12	1.59487
$506$	2.29943e12	1.55934
$507$	2.07484e11	0.139460
$508$	8.89598e11	0.592662
$509$	−1.45955e12	−0.963802	−0.481901	−	0.876226i	$-0.660054\pi$
$509$	−1.45955e12	−0.963802	−0.481901	+	0.876226i	$0.660054\pi$
$510$	3.91642e11	0.256344
$511$	−3.46884e11	−0.225056
$512$	−3.06873e11	−0.197353
$513$	3.23513e11	0.206236
$514$	8.01157e11	0.506272
$515$	−1.16920e12	−0.732416
$516$	1.77541e11	0.110249
$517$	−1.22357e12	−0.753217
$518$	−6.53512e10	−0.0398813
$519$	−1.25738e12	−0.760699
$520$	−1.26075e12	−0.756163
$521$	1.80721e12	1.07458	0.537291	−	0.843397i	$-0.319448\pi$
$521$	1.80721e12	1.07458	0.537291	+	0.843397i	$0.319448\pi$
$522$	−2.94352e11	−0.173520
$523$	1.21170e12	0.708169	0.354084	−	0.935213i	$-0.384793\pi$
$523$	1.21170e12	0.708169	0.354084	+	0.935213i	$0.384793\pi$
$524$	2.83901e11	0.164504
$525$	1.06593e12	0.612367
$526$	3.40386e12	1.93881
$527$	3.75256e11	0.211924
$528$	1.66619e12	0.932980
$529$	5.86089e9	0.00325397
$530$	−3.02872e12	−1.66732
$531$	7.95020e10	0.0433963
$532$	1.36319e12	0.737824
$533$	−2.74167e12	−1.47144
$534$	−2.00153e12	−1.06519
$535$	3.09053e12	1.63095
$536$	5.69624e11	0.298089
$537$	2.72397e11	0.141357
$538$	−3.36911e12	−1.73378
$539$	3.60772e12	1.84113
$540$	2.18240e11	0.110449
$541$	−8.78587e11	−0.440958	−0.220479	−	0.975392i	$-0.570762\pi$
$541$	−8.78587e11	−0.440958	−0.220479	+	0.975392i	$0.570762\pi$
$542$	−2.81428e12	−1.40078
$543$	−1.48368e12	−0.732390
$544$	−4.82030e11	−0.235982
$545$	−1.22866e12	−0.596549
$546$	−1.95110e12	−0.939533
$547$	−5.44010e11	−0.259815	−0.129908	−	0.991526i	$-0.541468\pi$
$547$	−5.44010e11	−0.259815	−0.129908	+	0.991526i	$0.541468\pi$
$548$	−1.30925e12	−0.620167
$549$	−1.23675e12	−0.581038
$550$	−2.27770e12	−1.06137
$551$	−1.00493e12	−0.464464
$552$	8.44582e11	0.387183
$553$	1.60920e12	0.731724
$554$	−3.66602e12	−1.65349
$555$	−3.57190e10	−0.0159801
$556$	−1.17851e11	−0.0522996
$557$	2.33872e11	0.102951	0.0514754	−	0.998674i	$-0.483608\pi$
$557$	2.33872e11	0.102951	0.0514754	+	0.998674i	$0.483608\pi$
$558$	6.81618e11	0.297637
$559$	−8.67541e11	−0.375783
$560$	−5.85374e12	−2.51529
$561$	5.00473e11	0.213328
$562$	3.66567e12	1.55003
$563$	−2.84490e11	−0.119338	−0.0596691	−	0.998218i	$-0.519005\pi$
$563$	−2.84490e11	−0.119338	−0.0596691	+	0.998218i	$0.519005\pi$
$564$	3.56785e11	0.148474
$565$	3.51805e12	1.45239
$566$	−4.92851e12	−2.01856
$567$	−4.25427e11	−0.172863
$568$	−1.01014e12	−0.407207
$569$	1.45327e12	0.581219	0.290609	−	0.956842i	$-0.406142\pi$
$569$	1.45327e12	0.581219	0.290609	+	0.956842i	$0.406142\pi$
$570$	2.42867e12	0.963678
$571$	9.73987e11	0.383434	0.191717	−	0.981450i	$-0.438594\pi$
$571$	9.73987e11	0.383434	0.191717	+	0.981450i	$0.438594\pi$
$572$	1.27902e12	0.499571
$573$	1.54681e12	0.599434
$574$	−8.21095e12	−3.15711
$575$	−1.78994e12	−0.682863
$576$	2.22283e11	0.0841406
$577$	−1.87758e12	−0.705193	−0.352597	−	0.935775i	$-0.614701\pi$
$577$	−1.87758e12	−0.705193	−0.352597	+	0.935775i	$0.614701\pi$
$578$	2.96097e12	1.10346
$579$	2.57967e11	0.0953919
$580$	−6.77916e11	−0.248742
$581$	−1.67009e12	−0.608061
$582$	6.38851e10	0.0230805
$583$	−3.87035e12	−1.38753
$584$	2.72254e11	0.0968538
$585$	−1.06641e12	−0.376464
$586$	5.76774e12	2.02054
$587$	−2.01696e12	−0.701172	−0.350586	−	0.936530i	$-0.614018\pi$
$587$	−2.01696e12	−0.701172	−0.350586	+	0.936530i	$0.614018\pi$
$588$	−1.05199e12	−0.362923
$589$	2.32706e12	0.796689
$590$	5.96836e11	0.202778
$591$	−1.69592e12	−0.571824
$592$	7.95187e10	0.0266086
$593$	−2.70917e12	−0.899683	−0.449841	−	0.893108i	$-0.648520\pi$
$593$	−2.70917e12	−0.899683	−0.449841	+	0.893108i	$0.648520\pi$
$594$	9.09062e11	0.299609
$595$	−1.75828e12	−0.575126
$596$	−4.68590e11	−0.152119
$597$	1.95387e11	0.0629523
$598$	3.27634e12	1.04769
$599$	1.83662e12	0.582906	0.291453	−	0.956585i	$-0.405861\pi$
$599$	1.83662e12	0.582906	0.291453	+	0.956585i	$0.405861\pi$
$600$	−8.36603e11	−0.263535
$601$	−3.08070e12	−0.963195	−0.481598	−	0.876393i	$-0.659943\pi$
$601$	−3.08070e12	−0.963195	−0.481598	+	0.876393i	$0.659943\pi$
$602$	−2.59817e12	−0.806275
$603$	4.81817e11	0.148407
$604$	−9.54906e11	−0.291941
$605$	−2.90650e12	−0.882005
$606$	−2.83124e12	−0.852806
$607$	−8.15369e11	−0.243784	−0.121892	−	0.992543i	$-0.538896\pi$
$607$	−8.15369e11	−0.243784	−0.121892	+	0.992543i	$0.538896\pi$
$608$	−2.98919e12	−0.887132
$609$	1.32150e12	0.389304
$610$	−9.28447e12	−2.71502
$611$	−1.74340e12	−0.506072
$612$	−1.45935e11	−0.0420512
$613$	4.96108e12	1.41907	0.709535	−	0.704670i	$-0.248905\pi$
$613$	4.96108e12	1.41907	0.709535	+	0.704670i	$0.248905\pi$
$614$	−6.44343e11	−0.182961
$615$	−4.48786e12	−1.26503
$616$	−4.82502e12	−1.35016
$617$	1.62700e12	0.451965	0.225982	−	0.974131i	$-0.427441\pi$
$617$	1.62700e12	0.451965	0.225982	+	0.974131i	$0.427441\pi$
$618$	1.42013e12	0.391635
$619$	3.32891e12	0.911368	0.455684	−	0.890142i	$-0.349395\pi$
$619$	3.32891e12	0.911368	0.455684	+	0.890142i	$0.349395\pi$
$620$	1.56982e12	0.426665
$621$	7.14391e11	0.192763
$622$	6.23145e12	1.66929
$623$	8.98589e12	2.38982
$624$	2.37408e12	0.626851
$625$	−4.64235e12	−1.21697
$626$	1.74435e11	0.0453993
$627$	3.10356e12	0.801967
$628$	−3.17180e11	−0.0813744
$629$	2.38850e10	0.00608411
$630$	−3.19376e12	−0.807737
$631$	−7.18145e12	−1.80335	−0.901675	−	0.432414i	$-0.857662\pi$
$631$	−7.18145e12	−1.80335	−0.901675	+	0.432414i	$0.857662\pi$
$632$	−1.26299e12	−0.314901
$633$	2.19691e12	0.543870
$634$	−6.29183e12	−1.54659
$635$	−7.11553e12	−1.73670
$636$	1.12857e12	0.273510
$637$	5.14047e12	1.23702
$638$	−2.82381e12	−0.674749
$639$	−8.54430e11	−0.202732
$640$	6.22524e12	1.46672
$641$	7.98870e12	1.86903	0.934513	−	0.355930i	$-0.115836\pi$
$641$	7.98870e12	1.86903	0.934513	+	0.355930i	$0.115836\pi$
$642$	−3.75380e12	−0.872095
$643$	−9.48765e11	−0.218882	−0.109441	−	0.993993i	$-0.534906\pi$
$643$	−9.48765e11	−0.218882	−0.109441	+	0.993993i	$0.534906\pi$
$644$	3.01022e12	0.689624
$645$	−1.42008e12	−0.323068
$646$	−1.62403e12	−0.366901
$647$	6.80837e12	1.52747	0.763737	−	0.645527i	$-0.223362\pi$
$647$	6.80837e12	1.52747	0.763737	+	0.645527i	$0.223362\pi$
$648$	3.33900e11	0.0743924
$649$	7.62687e11	0.168750
$650$	−3.24539e12	−0.713111
$651$	−3.06014e12	−0.667770
$652$	−3.21670e12	−0.697101
$653$	−8.43389e12	−1.81518	−0.907588	−	0.419862i	$-0.862078\pi$
$653$	−8.43389e12	−1.81518	−0.907588	+	0.419862i	$0.862078\pi$
$654$	1.49235e12	0.318985
$655$	−2.27081e12	−0.482052
$656$	9.99101e12	2.10641
$657$	2.30287e11	0.0482197
$658$	−5.22126e12	−1.08582
$659$	2.96729e12	0.612880	0.306440	−	0.951890i	$-0.400862\pi$
$659$	2.96729e12	0.612880	0.306440	+	0.951890i	$0.400862\pi$
$660$	2.09364e12	0.429491
$661$	−3.53359e12	−0.719962	−0.359981	−	0.932960i	$-0.617217\pi$
$661$	−3.53359e12	−0.719962	−0.359981	+	0.932960i	$0.617217\pi$
$662$	−7.55150e12	−1.52817
$663$	7.13100e11	0.143331
$664$	1.31078e12	0.261682
$665$	−1.09036e13	−2.16208
$666$	4.33849e10	0.00854485
$667$	−2.21910e12	−0.434122
$668$	1.85986e12	0.361399
$669$	2.04306e11	0.0394334
$670$	3.61709e12	0.693461
$671$	−1.18645e13	−2.25942
$672$	3.93086e12	0.743577
$673$	6.03044e12	1.13313	0.566567	−	0.824016i	$-0.308271\pi$
$673$	6.03044e12	1.13313	0.566567	+	0.824016i	$0.308271\pi$
$674$	1.14745e13	2.14173
$675$	−7.07642e11	−0.131204
$676$	−5.80406e11	−0.106899
$677$	−6.99508e12	−1.27981	−0.639903	−	0.768456i	$-0.721025\pi$
$677$	−6.99508e12	−1.27981	−0.639903	+	0.768456i	$0.721025\pi$
$678$	−4.27309e12	−0.776619
$679$	−2.86813e11	−0.0517828
$680$	1.38000e12	0.247508
$681$	−4.19759e12	−0.747890
$682$	6.53897e12	1.15739
$683$	4.39425e11	0.0772666	0.0386333	−	0.999253i	$-0.487700\pi$
$683$	4.39425e11	0.0772666	0.0386333	+	0.999253i	$0.487700\pi$
$684$	−9.04982e11	−0.158084
$685$	1.04721e13	1.81730
$686$	4.55656e12	0.785559
$687$	2.68404e12	0.459709
$688$	3.16143e12	0.537942
$689$	−5.51468e12	−0.932254
$690$	5.36306e12	0.900724
$691$	7.79892e12	1.30132	0.650659	−	0.759370i	$-0.274493\pi$
$691$	7.79892e12	1.30132	0.650659	+	0.759370i	$0.274493\pi$
$692$	3.51733e12	0.583091
$693$	−4.08125e12	−0.672193
$694$	1.00346e13	1.64203
$695$	9.42645e11	0.153256
$696$	−1.03719e12	−0.167539
$697$	3.00099e12	0.481634
$698$	−3.56814e12	−0.568973
$699$	6.05684e12	0.959618
$700$	−2.98179e12	−0.469392
$701$	4.87558e12	0.762597	0.381299	−	0.924452i	$-0.375477\pi$
$701$	4.87558e12	0.762597	0.381299	+	0.924452i	$0.375477\pi$
$702$	1.29528e12	0.201301
$703$	1.48117e11	0.0228721
$704$	2.13243e12	0.327188
$705$	−2.85378e12	−0.435081
$706$	6.25962e12	0.948258
$707$	1.27109e13	1.91333
$708$	−2.22395e11	−0.0332641
$709$	−7.85521e12	−1.16748	−0.583740	−	0.811940i	$-0.698411\pi$
$709$	−7.85521e12	−1.16748	−0.583740	+	0.811940i	$0.698411\pi$
$710$	−6.41436e12	−0.947307
$711$	−1.06830e12	−0.156777
$712$	−7.05264e12	−1.02847
$713$	5.13868e12	0.744644
$714$	2.13564e12	0.307529
$715$	−1.02304e13	−1.46391
$716$	−7.61992e11	−0.108353
$717$	7.71129e12	1.08966
$718$	1.01503e13	1.42533
$719$	6.29800e12	0.878866	0.439433	−	0.898275i	$-0.355179\pi$
$719$	6.29800e12	0.878866	0.439433	+	0.898275i	$0.355179\pi$
$720$	3.88614e12	0.538917
$721$	−6.37572e12	−0.878659
$722$	−1.30139e12	−0.178233
$723$	4.41584e12	0.601023
$724$	4.15039e12	0.561391
$725$	2.19814e12	0.295484
$726$	3.53028e12	0.471623
$727$	3.63645e12	0.482806	0.241403	−	0.970425i	$-0.422392\pi$
$727$	3.63645e12	0.482806	0.241403	+	0.970425i	$0.422392\pi$
$728$	−6.87495e12	−0.907148
$729$	2.82430e11	0.0370370
$730$	1.72880e12	0.225316
$731$	9.49596e11	0.123002
$732$	3.45962e12	0.445377
$733$	8.12399e12	1.03945	0.519723	−	0.854335i	$-0.326035\pi$
$733$	8.12399e12	1.03945	0.519723	+	0.854335i	$0.326035\pi$
$734$	−1.03718e13	−1.31893
$735$	8.41446e12	1.06349
$736$	−6.60082e12	−0.829178
$737$	4.62221e12	0.577094
$738$	5.45102e12	0.676432
$739$	1.03954e13	1.28215	0.641076	−	0.767477i	$-0.278488\pi$
$739$	1.03954e13	1.28215	0.641076	+	0.767477i	$0.278488\pi$
$740$	9.99187e10	0.0122491
$741$	4.42212e12	0.538826
$742$	−1.65157e13	−2.00023
$743$	−1.15331e13	−1.38835	−0.694173	−	0.719808i	$-0.744230\pi$
$743$	−1.15331e13	−1.38835	−0.694173	+	0.719808i	$0.744230\pi$
$744$	2.40177e12	0.287378
$745$	3.74806e12	0.445762
$746$	−1.29758e13	−1.53395
$747$	1.10873e12	0.130281
$748$	−1.40000e12	−0.163520
$749$	1.68528e13	1.95661
$750$	2.47984e12	0.286186
$751$	−7.55764e12	−0.866975	−0.433488	−	0.901159i	$-0.642717\pi$
$751$	−7.55764e12	−0.866975	−0.433488	+	0.901159i	$0.642717\pi$
$752$	6.35318e12	0.724454
$753$	−5.86433e12	−0.664724
$754$	−4.02351e12	−0.453351
$755$	7.63791e12	0.855487
$756$	1.19007e12	0.132503
$757$	1.58446e13	1.75367	0.876836	−	0.480789i	$-0.159650\pi$
$757$	1.58446e13	1.75367	0.876836	+	0.480789i	$0.159650\pi$
$758$	8.97630e12	0.987611
$759$	6.85336e12	0.749576
$760$	8.55775e12	0.930461
$761$	7.10804e12	0.768279	0.384140	−	0.923275i	$-0.374498\pi$
$761$	7.10804e12	0.768279	0.384140	+	0.923275i	$0.374498\pi$
$762$	8.64264e12	0.928643
$763$	−6.69992e12	−0.715664
$764$	−4.32698e12	−0.459478
$765$	1.16728e12	0.123225
$766$	−2.02615e13	−2.12638
$767$	1.08672e12	0.113380
$768$	−6.15623e12	−0.638542
$769$	3.71774e12	0.383363	0.191681	−	0.981457i	$-0.438606\pi$
$769$	3.71774e12	0.383363	0.191681	+	0.981457i	$0.438606\pi$
$770$	−3.06387e13	−3.14096
$771$	2.38782e12	0.243365
$772$	−7.21627e11	−0.0731198
$773$	8.84238e12	0.890762	0.445381	−	0.895341i	$-0.353068\pi$
$773$	8.84238e12	0.890762	0.445381	+	0.895341i	$0.353068\pi$
$774$	1.72485e12	0.172750
$775$	−5.09013e12	−0.506841
$776$	2.25107e11	0.0222850
$777$	−1.94777e11	−0.0191709
$778$	9.96246e12	0.974896
$779$	1.86099e13	1.81061
$780$	2.98313e12	0.288567
$781$	−8.19680e12	−0.788342
$782$	−3.58623e12	−0.342932
$783$	−8.77308e11	−0.0834111
$784$	−1.87325e13	−1.77082
$785$	2.53700e12	0.238455
$786$	2.75816e12	0.257761
$787$	6.14962e12	0.571428	0.285714	−	0.958315i	$-0.407769\pi$
$787$	6.14962e12	0.571428	0.285714	+	0.958315i	$0.407769\pi$
$788$	4.74410e12	0.438314
$789$	1.01451e13	0.931988
$790$	−8.01995e12	−0.732571
$791$	1.91841e13	1.74240
$792$	3.20320e12	0.289282
$793$	−1.69051e13	−1.51806
$794$	−1.85741e13	−1.65850
$795$	−9.02701e12	−0.801478
$796$	−5.46567e11	−0.0482542
$797$	6.17084e11	0.0541729	0.0270864	−	0.999633i	$-0.491377\pi$
$797$	6.17084e11	0.0541729	0.0270864	+	0.999633i	$0.491377\pi$
$798$	1.32437e13	1.15610
$799$	1.90830e12	0.165648
$800$	6.53846e12	0.564379
$801$	−5.96548e12	−0.512035
$802$	1.53296e13	1.30842
$803$	2.20921e12	0.187507
$804$	−1.34781e12	−0.113757
$805$	−2.40776e13	−2.02084
$806$	9.31707e12	0.777628
$807$	−1.00415e13	−0.833429
$808$	−9.97625e12	−0.823410
$809$	1.75260e13	1.43851	0.719257	−	0.694744i	$-0.244482\pi$
$809$	1.75260e13	1.43851	0.719257	+	0.694744i	$0.244482\pi$
$810$	2.12025e12	0.173063
$811$	6.99500e11	0.0567798	0.0283899	−	0.999597i	$-0.490962\pi$
$811$	6.99500e11	0.0567798	0.0283899	+	0.999597i	$0.490962\pi$
$812$	−3.69671e12	−0.298410
$813$	−8.38786e12	−0.673354
$814$	4.16204e11	0.0332274
$815$	2.57290e13	2.04275
$816$	−2.59863e12	−0.205182
$817$	5.88869e12	0.462402
$818$	−7.11334e12	−0.555499
$819$	−5.81519e12	−0.451633
$820$	1.25541e13	0.969671
$821$	1.82627e13	1.40288	0.701440	−	0.712728i	$-0.252541\pi$
$821$	1.82627e13	1.40288	0.701440	+	0.712728i	$0.252541\pi$
$822$	−1.27196e13	−0.971741
$823$	−9.62438e12	−0.731263	−0.365631	−	0.930760i	$-0.619147\pi$
$823$	−9.62438e12	−0.731263	−0.365631	+	0.930760i	$0.619147\pi$
$824$	5.00403e12	0.378135
$825$	−6.78862e12	−0.510198
$826$	3.25457e12	0.243267
$827$	2.25132e13	1.67364	0.836819	−	0.547479i	$-0.184413\pi$
$827$	2.25132e13	1.67364	0.836819	+	0.547479i	$0.184413\pi$
$828$	−1.99840e12	−0.147757
$829$	1.77818e11	0.0130761	0.00653806	−	0.999979i	$-0.497919\pi$
$829$	1.77818e11	0.0130761	0.00653806	+	0.999979i	$0.497919\pi$
$830$	8.32340e12	0.608765
$831$	−1.09265e13	−0.794831
$832$	3.03840e12	0.219832
$833$	−5.62668e12	−0.404902
$834$	−1.14495e12	−0.0819483
$835$	−1.48763e13	−1.05902
$836$	−8.68176e12	−0.614723
$837$	2.03154e12	0.143074
$838$	−7.07732e12	−0.495759
$839$	1.57674e13	1.09858	0.549289	−	0.835633i	$-0.314899\pi$
$839$	1.57674e13	1.09858	0.549289	+	0.835633i	$0.314899\pi$
$840$	−1.12536e13	−0.779895
$841$	−1.17820e13	−0.812150
$842$	−1.13347e13	−0.777154
$843$	1.09254e13	0.745099
$844$	−6.14553e12	−0.416887
$845$	4.64244e12	0.313250
$846$	3.46625e12	0.232645
$847$	−1.58493e13	−1.05812
$848$	2.00962e13	1.33454
$849$	−1.46893e13	−0.970322
$850$	3.55235e12	0.233416
$851$	3.27076e11	0.0213779
$852$	2.39014e12	0.155398
$853$	2.28592e13	1.47839	0.739197	−	0.673489i	$-0.235205\pi$
$853$	2.28592e13	1.47839	0.739197	+	0.673489i	$0.235205\pi$
$854$	−5.06286e13	−3.25713
$855$	7.23858e12	0.463240
$856$	−1.32270e13	−0.842035
$857$	−1.78155e13	−1.12820	−0.564099	−	0.825707i	$-0.690776\pi$
$857$	−1.78155e13	−1.12820	−0.564099	+	0.825707i	$0.690776\pi$
$858$	1.24260e13	0.782779
$859$	1.32240e13	0.828691	0.414346	−	0.910120i	$-0.364010\pi$
$859$	1.32240e13	0.828691	0.414346	+	0.910120i	$0.364010\pi$
$860$	3.97247e12	0.247638
$861$	−2.44725e13	−1.51762
$862$	−1.83184e13	−1.13007
$863$	1.97202e13	1.21022	0.605108	−	0.796143i	$-0.293130\pi$
$863$	1.97202e13	1.21022	0.605108	+	0.796143i	$0.293130\pi$
$864$	−2.60959e12	−0.159316
$865$	−2.81337e13	−1.70866
$866$	1.13337e13	0.684767
$867$	8.82507e12	0.530435
$868$	8.56030e12	0.511859
$869$	−1.02486e13	−0.609641
$870$	−6.58611e12	−0.389755
$871$	6.58598e12	0.387738
$872$	5.25848e12	0.307990
$873$	1.90407e11	0.0110948
$874$	−2.22392e13	−1.28919
$875$	−1.11333e13	−0.642077
$876$	−6.44193e11	−0.0369614
$877$	−3.08255e12	−0.175959	−0.0879797	−	0.996122i	$-0.528041\pi$
$877$	−3.08255e12	−0.175959	−0.0879797	+	0.996122i	$0.528041\pi$
$878$	3.43944e13	1.95327
$879$	1.71906e13	0.971271
$880$	3.72809e13	2.09563
$881$	2.76835e12	0.154821	0.0774103	−	0.996999i	$-0.475335\pi$
$881$	2.76835e12	0.154821	0.0774103	+	0.996999i	$0.475335\pi$
$882$	−1.02203e13	−0.568665
$883$	2.65376e13	1.46906	0.734529	−	0.678577i	$-0.237403\pi$
$883$	2.65376e13	1.46906	0.734529	+	0.678577i	$0.237403\pi$
$884$	−1.99479e12	−0.109866
$885$	1.77885e12	0.0974753
$886$	2.82670e13	1.54109
$887$	1.05383e13	0.571630	0.285815	−	0.958285i	$-0.407736\pi$
$887$	1.05383e13	0.571630	0.285815	+	0.958285i	$0.407736\pi$
$888$	1.52872e11	0.00825031
$889$	−3.88013e13	−2.08347
$890$	−4.47840e13	−2.39259
$891$	2.70943e12	0.144022
$892$	−5.71517e11	−0.0302265
$893$	1.18339e13	0.622723
$894$	−4.55246e12	−0.238356
$895$	6.09487e12	0.317512
$896$	3.39465e13	1.75958
$897$	9.76504e12	0.503626
$898$	−2.97134e13	−1.52479
$899$	−6.31056e12	−0.322217
$900$	1.97953e12	0.100570
$901$	6.03629e12	0.305146
$902$	5.22933e13	2.63037
$903$	−7.74376e12	−0.387576
$904$	−1.50568e13	−0.749850
$905$	−3.31973e13	−1.64507
$906$	−9.27713e12	−0.457443
$907$	2.64723e13	1.29885	0.649425	−	0.760426i	$-0.275010\pi$
$907$	2.64723e13	1.29885	0.649425	+	0.760426i	$0.275010\pi$
$908$	1.17421e13	0.573273
$909$	−8.43843e12	−0.409943
$910$	−4.36556e13	−2.11035
$911$	1.81593e13	0.873507	0.436754	−	0.899581i	$-0.356128\pi$
$911$	1.81593e13	0.873507	0.436754	+	0.899581i	$0.356128\pi$
$912$	−1.61148e13	−0.771342
$913$	1.06363e13	0.506610
$914$	−1.85475e12	−0.0879077
$915$	−2.76721e13	−1.30511
$916$	−7.50820e12	−0.352376
$917$	−1.23828e13	−0.578305
$918$	−1.41779e12	−0.0658902
$919$	−5.97931e12	−0.276523	−0.138261	−	0.990396i	$-0.544151\pi$
$919$	−5.97931e12	−0.276523	−0.138261	+	0.990396i	$0.544151\pi$
$920$	1.88974e13	0.869677
$921$	−1.92044e12	−0.0879495
$922$	−1.05911e13	−0.482670
$923$	−1.16792e13	−0.529672
$924$	1.14167e13	0.515249
$925$	−3.23986e11	−0.0145509
$926$	−3.84795e13	−1.71981
$927$	4.23266e12	0.188259
$928$	8.10614e12	0.358796
$929$	−2.22992e13	−0.982244	−0.491122	−	0.871091i	$-0.663413\pi$
$929$	−2.22992e13	−0.982244	−0.491122	+	0.871091i	$0.663413\pi$
$930$	1.52512e13	0.668543
$931$	−3.48925e13	−1.52215
$932$	−1.69431e13	−0.735566
$933$	1.85727e13	0.802429
$934$	−2.69550e13	−1.15899
$935$	1.11980e13	0.479170
$936$	4.56409e12	0.194363
$937$	−6.70117e12	−0.284003	−0.142001	−	0.989866i	$-0.545354\pi$
$937$	−6.70117e12	−0.284003	−0.142001	+	0.989866i	$0.545354\pi$
$938$	1.97241e13	0.831927
$939$	5.19898e11	0.0218234
$940$	7.98304e12	0.333498
$941$	−3.16102e13	−1.31424	−0.657120	−	0.753786i	$-0.728225\pi$
$941$	−3.16102e13	−1.31424	−0.657120	+	0.753786i	$0.728225\pi$
$942$	−3.08148e12	−0.127506
$943$	4.10949e13	1.69233
$944$	−3.96013e12	−0.162306
$945$	−9.51890e12	−0.388279
$946$	1.65470e13	0.671754
$947$	−3.93533e13	−1.59003	−0.795016	−	0.606588i	$-0.792538\pi$
$947$	−3.93533e13	−1.59003	−0.795016	+	0.606588i	$0.792538\pi$
$948$	2.98843e12	0.120173
$949$	3.14780e12	0.125982
$950$	2.20291e13	0.877485
$951$	−1.87526e13	−0.743446
$952$	7.52521e12	0.296929
$953$	−2.79941e13	−1.09938	−0.549690	−	0.835369i	$-0.685254\pi$
$953$	−2.79941e13	−1.09938	−0.549690	+	0.835369i	$0.685254\pi$
$954$	1.09644e13	0.428564
$955$	3.46098e13	1.34643
$956$	−2.15712e13	−0.835245
$957$	−8.41628e12	−0.324352
$958$	−2.29570e13	−0.880584
$959$	5.71049e13	2.18017
$960$	4.97357e12	0.188994
$961$	−1.18266e13	−0.447304
$962$	5.93030e11	0.0223249
$963$	−1.11881e13	−0.419216
$964$	−1.23527e13	−0.460696
$965$	5.77200e12	0.214266
$966$	2.92450e13	1.08057
$967$	2.14122e13	0.787485	0.393743	−	0.919221i	$-0.371180\pi$
$967$	2.14122e13	0.787485	0.393743	+	0.919221i	$0.371180\pi$
$968$	1.24394e13	0.455366
$969$	−4.84038e12	−0.176369
$970$	1.42942e12	0.0518427
$971$	−1.75075e12	−0.0632030	−0.0316015	−	0.999501i	$-0.510061\pi$
$971$	−1.75075e12	−0.0632030	−0.0316015	+	0.999501i	$0.510061\pi$
$972$	−7.90056e11	−0.0283896
$973$	5.14028e12	0.183857
$974$	3.18634e13	1.13443
$975$	−9.67279e12	−0.342792
$976$	6.16044e13	2.17314
$977$	−5.13484e13	−1.80303	−0.901513	−	0.432753i	$-0.857542\pi$
$977$	−5.13484e13	−1.80303	−0.901513	+	0.432753i	$0.857542\pi$
$978$	−3.12509e13	−1.09229
$979$	−5.72287e13	−1.99109
$980$	−2.35382e13	−0.815186
$981$	4.44789e12	0.153336
$982$	5.50186e10	0.00188803
$983$	4.30211e12	0.146957	0.0734785	−	0.997297i	$-0.476590\pi$
$983$	4.30211e12	0.146957	0.0734785	+	0.997297i	$0.476590\pi$
$984$	1.92074e13	0.653116
$985$	−3.79461e13	−1.28441
$986$	4.40408e12	0.148391
$987$	−1.55618e13	−0.521954
$988$	−1.23702e13	−0.413021
$989$	1.30036e13	0.432194
$990$	2.03402e13	0.672971
$991$	−3.17764e13	−1.04658	−0.523291	−	0.852154i	$-0.675296\pi$
$991$	−3.17764e13	−1.04658	−0.523291	+	0.852154i	$0.675296\pi$
$992$	−1.87710e13	−0.615439
$993$	−2.25070e13	−0.734592
$994$	−3.49778e13	−1.13646
$995$	4.37177e12	0.141401
$996$	−3.10150e12	−0.0998630
$997$	−4.17148e13	−1.33709	−0.668546	−	0.743670i	$-0.733083\pi$
$997$	−4.17148e13	−1.33709	−0.668546	+	0.743670i	$0.733083\pi$
$998$	7.15014e13	2.28153
$999$	1.29307e11	0.00410751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +49254.6 q^{10} +62941.6 q^{11} -18353.4 q^{12} +89682.6 q^{13} +268587. q^{14} +146802. q^{15} -326815. q^{16} -98165.2 q^{17} -178308. q^{18} -608747. q^{19} -410657. q^{20} +800517. q^{21} -1.71056e6 q^{22} -1.34425e6 q^{23} -628291. q^{24} +1.33155e6 q^{25} -2.43730e6 q^{26} -531441. q^{27} -2.23933e6 q^{28} +1.65081e6 q^{29} -3.98962e6 q^{30} -3.82270e6 q^{31} +4.91040e6 q^{32} -5.09827e6 q^{33} +2.66783e6 q^{34} +1.79115e7 q^{35} +1.48663e6 q^{36} -243314. q^{37} +1.65439e7 q^{38} -7.26429e6 q^{39} -1.40580e7 q^{40} -3.05708e7 q^{41} -2.17556e7 q^{42} -9.67346e6 q^{43} +1.42617e7 q^{44} -1.18909e7 q^{45} +3.65327e7 q^{46} -1.94397e7 q^{47} +2.64720e7 q^{48} +5.73185e7 q^{49} -3.61875e7 q^{50} +7.95138e6 q^{51} +2.03208e7 q^{52} -6.14911e7 q^{53} +1.44429e7 q^{54} -1.14073e8 q^{55} -7.66587e7 q^{56} +4.93085e7 q^{57} -4.48639e7 q^{58} +1.21174e7 q^{59} +3.32632e7 q^{60} -1.88500e8 q^{61} +1.03889e8 q^{62} -6.48418e7 q^{63} +3.38795e7 q^{64} -1.62538e8 q^{65} +1.38555e8 q^{66} +7.34365e7 q^{67} -2.22428e7 q^{68} +1.08884e8 q^{69} -4.86779e8 q^{70} -1.30229e8 q^{71} +5.08916e7 q^{72} +3.50993e7 q^{73} +6.61254e6 q^{74} -1.07856e8 q^{75} -1.37934e8 q^{76} -6.22047e8 q^{77} +1.97421e8 q^{78} -1.62826e8 q^{79} +5.92309e8 q^{80} +4.30467e7 q^{81} +8.30822e8 q^{82} +1.68987e8 q^{83} +1.81386e8 q^{84} +1.77911e8 q^{85} +2.62895e8 q^{86} -1.33716e8 q^{87} +4.88218e8 q^{88} -9.09234e8 q^{89} +3.23159e8 q^{90} -8.86326e8 q^{91} -3.04588e8 q^{92} +3.09639e8 q^{93} +5.28311e8 q^{94} +1.10327e9 q^{95} -3.97743e8 q^{96} +2.90211e7 q^{97} -1.55774e9 q^{98} +4.12960e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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