LMFDB - Embedded newform 177.10.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} -6920.01 q^{10} +38810.0 q^{11} +36422.5 q^{12} +183461. q^{13} +9493.68 q^{14} -70992.4 q^{15} +170277. q^{16} +139737. q^{17} -51802.4 q^{18} -867454. q^{19} -394105. q^{20} +97395.7 q^{21} -306425. q^{22} +1.16660e6 q^{23} -615017. q^{24} -1.18496e6 q^{25} -1.44851e6 q^{26} -531441. q^{27} +540680. q^{28} +2.91181e6 q^{29} +560521. q^{30} +4.99286e6 q^{31} -5.23194e6 q^{32} -3.14361e6 q^{33} -1.10329e6 q^{34} -1.05386e6 q^{35} -2.95023e6 q^{36} -1.18814e6 q^{37} +6.84899e6 q^{38} -1.48603e7 q^{39} +6.65470e6 q^{40} -1.41883e7 q^{41} -768988. q^{42} -1.70225e7 q^{43} -1.74514e7 q^{44} +5.75038e6 q^{45} -9.21092e6 q^{46} +1.28461e7 q^{47} -1.37925e7 q^{48} -3.89078e7 q^{49} +9.35587e6 q^{50} -1.13187e7 q^{51} -8.24951e7 q^{52} +7.27522e7 q^{53} +4.19599e6 q^{54} +3.40150e7 q^{55} -9.12970e6 q^{56} +7.02638e7 q^{57} -2.29902e7 q^{58} +1.21174e7 q^{59} +3.19225e7 q^{60} -9.05578e7 q^{61} -3.94212e7 q^{62} -7.88905e6 q^{63} -4.58733e7 q^{64} +1.60794e8 q^{65} +2.48204e7 q^{66} -1.29418e7 q^{67} -6.28343e7 q^{68} -9.44949e7 q^{69} +8.32073e6 q^{70} +2.92250e8 q^{71} +4.98164e7 q^{72} -4.07144e8 q^{73} +9.38099e6 q^{74} +9.59819e7 q^{75} +3.90060e8 q^{76} -4.66658e7 q^{77} +1.17330e8 q^{78} +2.64575e8 q^{79} +1.49240e8 q^{80} +4.30467e7 q^{81} +1.12023e8 q^{82} -2.68636e8 q^{83} -4.37951e7 q^{84} +1.22472e8 q^{85} +1.34402e8 q^{86} -2.35857e8 q^{87} +2.94677e8 q^{88} +6.83062e8 q^{89} -4.54022e7 q^{90} -2.20596e8 q^{91} -5.24576e8 q^{92} -4.04422e8 q^{93} -1.01427e8 q^{94} -7.60280e8 q^{95} +4.23787e8 q^{96} +5.92565e8 q^{97} +3.07197e8 q^{98} +2.54633e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.89550	−0.348935	−0.174468	−	0.984663i	$-0.555820\pi$
$2$	−7.89550	−0.348935	−0.174468	+	0.984663i	$0.555820\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−449.661	−0.878244
$5$	876.449	0.627136	0.313568	−	0.949566i	$-0.398476\pi$
$5$	876.449	0.627136	0.313568	+	0.949566i	$0.398476\pi$
$6$	639.536	0.201458
$7$	−1202.42	−0.189284	−0.0946419	−	0.995511i	$-0.530171\pi$
$7$	−1202.42	−0.189284	−0.0946419	+	0.995511i	$0.530171\pi$
$8$	7592.80	0.655386
$9$	6561.00	0.333333
$10$	−6920.01	−0.218830
$11$	38810.0	0.799240	0.399620	−	0.916681i	$-0.369142\pi$
$11$	38810.0	0.799240	0.399620	+	0.916681i	$0.369142\pi$
$12$	36422.5	0.507055
$13$	183461.	1.78155	0.890774	−	0.454446i	$-0.150163\pi$
$13$	183461.	1.78155	0.890774	+	0.454446i	$0.150163\pi$
$14$	9493.68	0.0660478
$15$	−70992.4	−0.362077
$16$	170277.	0.649557
$17$	139737.	0.405781	0.202890	−	0.979201i	$-0.434967\pi$
$17$	139737.	0.405781	0.202890	+	0.979201i	$0.434967\pi$
$18$	−51802.4	−0.116312
$19$	−867454.	−1.52706	−0.763529	−	0.645774i	$-0.776535\pi$
$19$	−867454.	−1.52706	−0.763529	+	0.645774i	$0.776535\pi$
$20$	−394105.	−0.550779
$21$	97395.7	0.109283
$22$	−306425.	−0.278883
$23$	1.16660e6	0.869256	0.434628	−	0.900610i	$-0.356880\pi$
$23$	1.16660e6	0.869256	0.434628	+	0.900610i	$0.356880\pi$
$24$	−615017.	−0.378387
$25$	−1.18496e6	−0.606700
$26$	−1.44851e6	−0.621645
$27$	−531441.	−0.192450
$28$	540680.	0.166237
$29$	2.91181e6	0.764492	0.382246	−	0.924061i	$-0.375151\pi$
$29$	2.91181e6	0.764492	0.382246	+	0.924061i	$0.375151\pi$
$30$	560521.	0.126342
$31$	4.99286e6	0.971006	0.485503	−	0.874235i	$-0.338636\pi$
$31$	4.99286e6	0.971006	0.485503	+	0.874235i	$0.338636\pi$
$32$	−5.23194e6	−0.882039
$33$	−3.14361e6	−0.461441
$34$	−1.10329e6	−0.141591
$35$	−1.05386e6	−0.118707
$36$	−2.95023e6	−0.292748
$37$	−1.18814e6	−0.104222	−0.0521112	−	0.998641i	$-0.516595\pi$
$37$	−1.18814e6	−0.104222	−0.0521112	+	0.998641i	$0.516595\pi$
$38$	6.84899e6	0.532844
$39$	−1.48603e7	−1.02858
$40$	6.65470e6	0.411016
$41$	−1.41883e7	−0.784155	−0.392077	−	0.919932i	$-0.628243\pi$
$41$	−1.41883e7	−0.784155	−0.392077	+	0.919932i	$0.628243\pi$
$42$	−768988.	−0.0381327
$43$	−1.70225e7	−0.759305	−0.379653	−	0.925129i	$-0.623957\pi$
$43$	−1.70225e7	−0.759305	−0.379653	+	0.925129i	$0.623957\pi$
$44$	−1.74514e7	−0.701928
$45$	5.75038e6	0.209045
$46$	−9.21092e6	−0.303314
$47$	1.28461e7	0.384000	0.192000	−	0.981395i	$-0.438503\pi$
$47$	1.28461e7	0.384000	0.192000	+	0.981395i	$0.438503\pi$
$48$	−1.37925e7	−0.375022
$49$	−3.89078e7	−0.964172
$50$	9.35587e6	0.211699
$51$	−1.13187e7	−0.234278
$52$	−8.24951e7	−1.56463
$53$	7.27522e7	1.26650	0.633250	−	0.773948i	$-0.281721\pi$
$53$	7.27522e7	1.26650	0.633250	+	0.773948i	$0.281721\pi$
$54$	4.19599e6	0.0671526
$55$	3.40150e7	0.501232
$56$	−9.12970e6	−0.124054
$57$	7.02638e7	0.881647
$58$	−2.29902e7	−0.266758
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	3.19225e7	0.317992
$61$	−9.05578e7	−0.837417	−0.418708	−	0.908121i	$-0.637517\pi$
$61$	−9.05578e7	−0.837417	−0.418708	+	0.908121i	$0.637517\pi$
$62$	−3.94212e7	−0.338818
$63$	−7.88905e6	−0.0630946
$64$	−4.58733e7	−0.341782
$65$	1.60794e8	1.11727
$66$	2.48204e7	0.161013
$67$	−1.29418e7	−0.0784616	−0.0392308	−	0.999230i	$-0.512491\pi$
$67$	−1.29418e7	−0.0784616	−0.0392308	+	0.999230i	$0.512491\pi$
$68$	−6.28343e7	−0.356374
$69$	−9.44949e7	−0.501865
$70$	8.32073e6	0.0414210
$71$	2.92250e8	1.36487	0.682436	−	0.730945i	$-0.260921\pi$
$71$	2.92250e8	1.36487	0.682436	+	0.730945i	$0.260921\pi$
$72$	4.98164e7	0.218462
$73$	−4.07144e8	−1.67801	−0.839007	−	0.544121i	$-0.816863\pi$
$73$	−4.07144e8	−1.67801	−0.839007	+	0.544121i	$0.816863\pi$
$74$	9.38099e6	0.0363669
$75$	9.59819e7	0.350279
$76$	3.90060e8	1.34113
$77$	−4.66658e7	−0.151283
$78$	1.17330e8	0.358907
$79$	2.64575e8	0.764234	0.382117	−	0.924114i	$-0.375195\pi$
$79$	2.64575e8	0.764234	0.382117	+	0.924114i	$0.375195\pi$
$80$	1.49240e8	0.407361
$81$	4.30467e7	0.111111
$82$	1.12023e8	0.273619
$83$	−2.68636e8	−0.621317	−0.310658	−	0.950522i	$-0.600549\pi$
$83$	−2.68636e8	−0.621317	−0.310658	+	0.950522i	$0.600549\pi$
$84$	−4.37951e7	−0.0959772
$85$	1.22472e8	0.254480
$86$	1.34402e8	0.264948
$87$	−2.35857e8	−0.441379
$88$	2.94677e8	0.523810
$89$	6.83062e8	1.15400	0.576999	−	0.816745i	$-0.304224\pi$
$89$	6.83062e8	1.15400	0.576999	+	0.816745i	$0.304224\pi$
$90$	−4.54022e7	−0.0729433
$91$	−2.20596e8	−0.337218
$92$	−5.24576e8	−0.763419
$93$	−4.04422e8	−0.560611
$94$	−1.01427e8	−0.133991
$95$	−7.60280e8	−0.957673
$96$	4.23787e8	0.509245
$97$	5.92565e8	0.679615	0.339808	−	0.940495i	$-0.389638\pi$
$97$	5.92565e8	0.679615	0.339808	+	0.940495i	$0.389638\pi$
$98$	3.07197e8	0.336434
$99$	2.54633e8	0.266413
$100$	5.32831e8	0.532831
$101$	2.03064e9	1.94172	0.970862	−	0.239640i	$-0.0770295\pi$
$101$	2.03064e9	1.94172	0.970862	+	0.239640i	$0.0770295\pi$
$102$	8.93668e7	0.0817477
$103$	9.46965e8	0.829023	0.414511	−	0.910044i	$-0.363952\pi$
$103$	9.46965e8	0.829023	0.414511	+	0.910044i	$0.363952\pi$
$104$	1.39298e9	1.16760
$105$	8.53624e7	0.0685354
$106$	−5.74416e8	−0.441926
$107$	1.03749e9	0.765165	0.382582	−	0.923921i	$-0.375035\pi$
$107$	1.03749e9	0.765165	0.382582	+	0.923921i	$0.375035\pi$
$108$	2.38968e8	0.169018
$109$	−2.31698e9	−1.57219	−0.786093	−	0.618109i	$-0.787899\pi$
$109$	−2.31698e9	−1.57219	−0.786093	+	0.618109i	$0.787899\pi$
$110$	−2.68566e8	−0.174898
$111$	9.62396e7	0.0601729
$112$	−2.04744e8	−0.122951
$113$	−2.73625e9	−1.57871	−0.789355	−	0.613937i	$-0.789585\pi$
$113$	−2.73625e9	−1.57871	−0.789355	+	0.613937i	$0.789585\pi$
$114$	−5.54768e8	−0.307638
$115$	1.02247e9	0.545142
$116$	−1.30933e9	−0.671410
$117$	1.20368e9	0.593849
$118$	−9.56727e7	−0.0454275
$119$	−1.68022e8	−0.0768077
$120$	−5.39031e8	−0.237300
$121$	−8.51728e8	−0.361216
$122$	7.15000e8	0.292204
$123$	1.14925e9	0.452732
$124$	−2.24510e9	−0.852780
$125$	−2.75037e9	−1.00762
$126$	6.22881e7	0.0220159
$127$	1.54966e9	0.528591	0.264295	−	0.964442i	$-0.414861\pi$
$127$	1.54966e9	0.528591	0.264295	+	0.964442i	$0.414861\pi$
$128$	3.04095e9	1.00130
$129$	1.37883e9	0.438385
$130$	−1.26955e9	−0.389856
$131$	5.74257e9	1.70367	0.851835	−	0.523810i	$-0.175490\pi$
$131$	5.74257e9	1.70367	0.851835	+	0.523810i	$0.175490\pi$
$132$	1.41356e9	0.405258
$133$	1.04304e9	0.289047
$134$	1.02182e8	0.0273780
$135$	−4.65781e8	−0.120692
$136$	1.06099e9	0.265943
$137$	6.92192e9	1.67874	0.839371	−	0.543559i	$-0.182923\pi$
$137$	6.92192e9	1.67874	0.839371	+	0.543559i	$0.182923\pi$
$138$	7.46085e8	0.175119
$139$	5.76134e9	1.30905	0.654526	−	0.756039i	$-0.272868\pi$
$139$	5.76134e9	1.30905	0.654526	+	0.756039i	$0.272868\pi$
$140$	4.73878e8	0.104254
$141$	−1.04054e9	−0.221703
$142$	−2.30746e9	−0.476252
$143$	7.12011e9	1.42388
$144$	1.11719e9	0.216519
$145$	2.55206e9	0.479440
$146$	3.21461e9	0.585518
$147$	3.15153e9	0.556665
$148$	5.34262e8	0.0915327
$149$	−8.24091e9	−1.36974	−0.684868	−	0.728667i	$-0.740140\pi$
$149$	−8.24091e9	−1.36974	−0.684868	+	0.728667i	$0.740140\pi$
$150$	−7.57825e8	−0.122225
$151$	1.12173e10	1.75587	0.877936	−	0.478779i	$-0.158920\pi$
$151$	1.12173e10	1.75587	0.877936	+	0.478779i	$0.158920\pi$
$152$	−6.58641e9	−1.00081
$153$	9.16814e8	0.135260
$154$	3.68450e8	0.0527880
$155$	4.37599e9	0.608953
$156$	6.68210e9	0.903342
$157$	2.08610e8	0.0274023	0.0137011	−	0.999906i	$-0.495639\pi$
$157$	2.08610e8	0.0274023	0.0137011	+	0.999906i	$0.495639\pi$
$158$	−2.08895e9	−0.266668
$159$	−5.89293e9	−0.731214
$160$	−4.58553e9	−0.553159
$161$	−1.40274e9	−0.164536
$162$	−3.39876e8	−0.0387706
$163$	3.72795e9	0.413643	0.206821	−	0.978379i	$-0.433688\pi$
$163$	3.72795e9	0.413643	0.206821	+	0.978379i	$0.433688\pi$
$164$	6.37991e9	0.688679
$165$	−2.75522e9	−0.289386
$166$	2.12102e9	0.216799
$167$	−6.68944e9	−0.665527	−0.332763	−	0.943010i	$-0.607981\pi$
$167$	−6.68944e9	−0.665527	−0.332763	+	0.943010i	$0.607981\pi$
$168$	7.39506e8	0.0716226
$169$	2.30533e10	2.17391
$170$	−9.66981e8	−0.0887969
$171$	−5.69137e9	−0.509019
$172$	7.65438e9	0.666856
$173$	−8.95552e9	−0.760122	−0.380061	−	0.924961i	$-0.624097\pi$
$173$	−8.95552e9	−0.760122	−0.380061	+	0.924961i	$0.624097\pi$
$174$	1.86221e9	0.154013
$175$	1.42482e9	0.114839
$176$	6.60848e9	0.519152
$177$	−9.81506e8	−0.0751646
$178$	−5.39312e9	−0.402671
$179$	−1.53461e10	−1.11727	−0.558636	−	0.829413i	$-0.688675\pi$
$179$	−1.53461e10	−1.11727	−0.558636	+	0.829413i	$0.688675\pi$
$180$	−2.58572e9	−0.183593
$181$	1.89956e9	0.131552	0.0657762	−	0.997834i	$-0.479048\pi$
$181$	1.89956e9	0.131552	0.0657762	+	0.997834i	$0.479048\pi$
$182$	1.74172e9	0.117667
$183$	7.33518e9	0.483483
$184$	8.85778e9	0.569698
$185$	−1.04135e9	−0.0653617
$186$	3.19311e9	0.195617
$187$	5.42320e9	0.324316
$188$	−5.77640e9	−0.337246
$189$	6.39013e8	0.0364277
$190$	6.00279e9	0.334166
$191$	1.47484e10	0.801853	0.400926	−	0.916110i	$-0.368688\pi$
$191$	1.47484e10	0.801853	0.400926	+	0.916110i	$0.368688\pi$
$192$	3.71573e9	0.197328
$193$	−3.03486e10	−1.57446	−0.787229	−	0.616661i	$-0.788485\pi$
$193$	−3.03486e10	−1.57446	−0.787229	+	0.616661i	$0.788485\pi$
$194$	−4.67860e9	−0.237142
$195$	−1.30243e10	−0.645058
$196$	1.74953e10	0.846778
$197$	4.65026e9	0.219978	0.109989	−	0.993933i	$-0.464918\pi$
$197$	4.65026e9	0.219978	0.109989	+	0.993933i	$0.464918\pi$
$198$	−2.01045e9	−0.0929610
$199$	−1.09579e10	−0.495322	−0.247661	−	0.968847i	$-0.579662\pi$
$199$	−1.09579e10	−0.495322	−0.247661	+	0.968847i	$0.579662\pi$
$200$	−8.99717e9	−0.397623
$201$	1.04828e9	0.0452998
$202$	−1.60330e10	−0.677536
$203$	−3.50121e9	−0.144706
$204$	5.08958e9	0.205753
$205$	−1.24353e10	−0.491772
$206$	−7.47677e9	−0.289275
$207$	7.65408e9	0.289752
$208$	3.12392e10	1.15722
$209$	−3.36659e10	−1.22048
$210$	−6.73979e8	−0.0239144
$211$	5.11676e10	1.77715	0.888575	−	0.458731i	$-0.151696\pi$
$211$	5.11676e10	1.77715	0.888575	+	0.458731i	$0.151696\pi$
$212$	−3.27138e10	−1.11230
$213$	−2.36722e10	−0.788009
$214$	−8.19147e9	−0.266993
$215$	−1.49194e10	−0.476188
$216$	−4.03512e9	−0.126129
$217$	−6.00350e9	−0.183796
$218$	1.82938e10	0.548591
$219$	3.29787e10	0.968802
$220$	−1.52952e10	−0.440204
$221$	2.56362e10	0.722918
$222$	−7.59861e8	−0.0209964
$223$	−4.46173e10	−1.20818	−0.604090	−	0.796916i	$-0.706463\pi$
$223$	−4.46173e10	−1.20818	−0.604090	+	0.796916i	$0.706463\pi$
$224$	6.29097e9	0.166956
$225$	−7.77453e9	−0.202233
$226$	2.16041e10	0.550868
$227$	5.11536e10	1.27867	0.639336	−	0.768927i	$-0.279209\pi$
$227$	5.11536e10	1.27867	0.639336	+	0.768927i	$0.279209\pi$
$228$	−3.15949e10	−0.774301
$229$	3.14014e10	0.754553	0.377277	−	0.926101i	$-0.376861\pi$
$229$	3.14014e10	0.754553	0.377277	+	0.926101i	$0.376861\pi$
$230$	−8.07291e9	−0.190219
$231$	3.77993e9	0.0873434
$232$	2.21088e10	0.501037
$233$	2.10523e9	0.0467948	0.0233974	−	0.999726i	$-0.492552\pi$
$233$	2.10523e9	0.0467948	0.0233974	+	0.999726i	$0.492552\pi$
$234$	−9.50370e9	−0.207215
$235$	1.12590e10	0.240820
$236$	−5.44870e9	−0.114338
$237$	−2.14305e10	−0.441230
$238$	1.32662e9	0.0268009
$239$	−6.19415e10	−1.22798	−0.613989	−	0.789314i	$-0.710436\pi$
$239$	−6.19415e10	−1.22798	−0.613989	+	0.789314i	$0.710436\pi$
$240$	−1.20884e10	−0.235190
$241$	2.71277e10	0.518008	0.259004	−	0.965876i	$-0.416606\pi$
$241$	2.71277e10	0.518008	0.259004	+	0.965876i	$0.416606\pi$
$242$	6.72483e9	0.126041
$243$	−3.48678e9	−0.0641500
$244$	4.07203e10	0.735456
$245$	−3.41007e10	−0.604667
$246$	−9.07390e9	−0.157974
$247$	−1.59144e11	−2.72053
$248$	3.79098e10	0.636383
$249$	2.17595e10	0.358717
$250$	2.17156e10	0.351594
$251$	−6.17270e10	−0.981620	−0.490810	−	0.871267i	$-0.663299\pi$
$251$	−6.17270e10	−0.981620	−0.490810	+	0.871267i	$0.663299\pi$
$252$	3.54740e9	0.0554125
$253$	4.52759e10	0.694744
$254$	−1.22353e10	−0.184444
$255$	−9.92027e9	−0.146924
$256$	−5.22691e8	−0.00760615
$257$	−8.11802e9	−0.116078	−0.0580392	−	0.998314i	$-0.518485\pi$
$257$	−8.11802e9	−0.116078	−0.0580392	+	0.998314i	$0.518485\pi$
$258$	−1.08865e10	−0.152968
$259$	1.42864e9	0.0197276
$260$	−7.23027e10	−0.981239
$261$	1.91044e10	0.254831
$262$	−4.53405e10	−0.594471
$263$	−1.79341e10	−0.231142	−0.115571	−	0.993299i	$-0.536870\pi$
$263$	−1.79341e10	−0.231142	−0.115571	+	0.993299i	$0.536870\pi$
$264$	−2.38688e10	−0.302422
$265$	6.37636e10	0.794267
$266$	−8.23534e9	−0.100859
$267$	−5.53280e10	−0.666261
$268$	5.81941e9	0.0689085
$269$	−8.51762e10	−0.991821	−0.495910	−	0.868374i	$-0.665166\pi$
$269$	−8.51762e10	−0.991821	−0.495910	+	0.868374i	$0.665166\pi$
$270$	3.67758e9	0.0421138
$271$	−2.70972e10	−0.305185	−0.152592	−	0.988289i	$-0.548762\pi$
$271$	−2.70972e10	−0.305185	−0.152592	+	0.988289i	$0.548762\pi$
$272$	2.37941e10	0.263578
$273$	1.78683e10	0.194693
$274$	−5.46521e10	−0.585772
$275$	−4.59884e10	−0.484899
$276$	4.24907e10	0.440760
$277$	−7.96559e10	−0.812941	−0.406470	−	0.913664i	$-0.633241\pi$
$277$	−7.96559e10	−0.812941	−0.406470	+	0.913664i	$0.633241\pi$
$278$	−4.54887e10	−0.456775
$279$	3.27582e10	0.323669
$280$	−8.00172e9	−0.0777987
$281$	1.84846e11	1.76861	0.884305	−	0.466909i	$-0.154633\pi$
$281$	1.84846e11	1.76861	0.884305	+	0.466909i	$0.154633\pi$
$282$	8.21555e9	0.0773599
$283$	1.40912e11	1.30590	0.652951	−	0.757400i	$-0.273531\pi$
$283$	1.40912e11	1.30590	0.652951	+	0.757400i	$0.273531\pi$
$284$	−1.31413e11	−1.19869
$285$	6.15827e10	0.552913
$286$	−5.62169e10	−0.496843
$287$	1.70602e10	0.148428
$288$	−3.43268e10	−0.294013
$289$	−9.90614e10	−0.835342
$290$	−2.01498e10	−0.167294
$291$	−4.79977e10	−0.392376
$292$	1.83077e11	1.47371
$293$	−1.54732e11	−1.22652	−0.613260	−	0.789881i	$-0.710142\pi$
$293$	−1.54732e11	−1.22652	−0.613260	+	0.789881i	$0.710142\pi$
$294$	−2.48829e10	−0.194240
$295$	1.06203e10	0.0816462
$296$	−9.02134e9	−0.0683059
$297$	−2.06252e10	−0.153814
$298$	6.50661e10	0.477949
$299$	2.14026e11	1.54862
$300$	−4.31593e10	−0.307630
$301$	2.04682e10	0.143724
$302$	−8.85664e10	−0.612685
$303$	−1.64482e11	−1.12105
$304$	−1.47708e11	−0.991911
$305$	−7.93693e10	−0.525174
$306$	−7.23871e9	−0.0471971
$307$	−2.21886e10	−0.142563	−0.0712816	−	0.997456i	$-0.522709\pi$
$307$	−2.21886e10	−0.142563	−0.0712816	+	0.997456i	$0.522709\pi$
$308$	2.09838e10	0.132864
$309$	−7.67042e10	−0.478637
$310$	−3.45507e10	−0.212485
$311$	1.17393e11	0.711577	0.355789	−	0.934566i	$-0.384212\pi$
$311$	1.17393e11	0.711577	0.355789	+	0.934566i	$0.384212\pi$
$312$	−1.12831e11	−0.674115
$313$	8.69675e10	0.512162	0.256081	−	0.966655i	$-0.417569\pi$
$313$	8.69675e10	0.512162	0.256081	+	0.966655i	$0.417569\pi$
$314$	−1.64708e9	−0.00956161
$315$	−6.91436e9	−0.0395689
$316$	−1.18969e11	−0.671184
$317$	1.01021e11	0.561883	0.280941	−	0.959725i	$-0.409353\pi$
$317$	1.01021e11	0.561883	0.280941	+	0.959725i	$0.409353\pi$
$318$	4.65277e10	0.255146
$319$	1.13008e11	0.611012
$320$	−4.02056e10	−0.214344
$321$	−8.40363e10	−0.441768
$322$	1.10754e10	0.0574125
$323$	−1.21215e11	−0.619650
$324$	−1.93564e10	−0.0975827
$325$	−2.17394e11	−1.08087
$326$	−2.94340e10	−0.144335
$327$	1.87676e11	0.907702
$328$	−1.07729e11	−0.513924
$329$	−1.54464e10	−0.0726850
$330$	2.17538e10	0.100977
$331$	−2.74015e11	−1.25472	−0.627362	−	0.778728i	$-0.715865\pi$
$331$	−2.74015e11	−1.25472	−0.627362	+	0.778728i	$0.715865\pi$
$332$	1.20795e11	0.545668
$333$	−7.79541e9	−0.0347408
$334$	5.28165e10	0.232226
$335$	−1.13428e10	−0.0492061
$336$	1.65843e10	0.0709856
$337$	4.40943e11	1.86229	0.931146	−	0.364647i	$-0.118810\pi$
$337$	4.40943e11	1.86229	0.931146	+	0.364647i	$0.118810\pi$
$338$	−1.82017e11	−0.758556
$339$	2.21636e11	0.911469
$340$	−5.50711e10	−0.223495
$341$	1.93773e11	0.776066
$342$	4.49362e10	0.177615
$343$	9.53052e10	0.371786
$344$	−1.29249e11	−0.497638
$345$	−8.28200e10	−0.314738
$346$	7.07084e10	0.265234
$347$	3.61083e11	1.33698	0.668489	−	0.743722i	$-0.266941\pi$
$347$	3.61083e11	1.33698	0.668489	+	0.743722i	$0.266941\pi$
$348$	1.06056e11	0.387639
$349$	3.14559e11	1.13498	0.567490	−	0.823380i	$-0.307915\pi$
$349$	3.14559e11	1.13498	0.567490	+	0.823380i	$0.307915\pi$
$350$	−1.12496e10	−0.0400712
$351$	−9.74985e10	−0.342859
$352$	−2.03052e11	−0.704961
$353$	−2.70265e11	−0.926411	−0.463205	−	0.886251i	$-0.653301\pi$
$353$	−2.70265e11	−0.926411	−0.463205	+	0.886251i	$0.653301\pi$
$354$	7.74949e9	0.0262276
$355$	2.56142e11	0.855961
$356$	−3.07146e11	−1.01349
$357$	1.36098e10	0.0443450
$358$	1.21165e11	0.389856
$359$	5.89942e10	0.187449	0.0937247	−	0.995598i	$-0.470123\pi$
$359$	5.89942e10	0.187449	0.0937247	+	0.995598i	$0.470123\pi$
$360$	4.36615e10	0.137005
$361$	4.29789e11	1.33190
$362$	−1.49980e10	−0.0459032
$363$	6.89900e10	0.208548
$364$	9.91934e10	0.296160
$365$	−3.56841e11	−1.05234
$366$	−5.79150e10	−0.168704
$367$	2.24441e11	0.645810	0.322905	−	0.946431i	$-0.395341\pi$
$367$	2.24441e11	0.645810	0.322905	+	0.946431i	$0.395341\pi$
$368$	1.98646e11	0.564632
$369$	−9.30892e10	−0.261385
$370$	8.22197e9	0.0228070
$371$	−8.74785e10	−0.239728
$372$	1.81853e11	0.492353
$373$	−1.80422e11	−0.482615	−0.241307	−	0.970449i	$-0.577576\pi$
$373$	−1.80422e11	−0.482615	−0.241307	+	0.970449i	$0.577576\pi$
$374$	−4.28189e10	−0.113165
$375$	2.22780e11	0.581750
$376$	9.75379e10	0.251668
$377$	5.34203e11	1.36198
$378$	−5.04533e9	−0.0127109
$379$	1.57364e11	0.391767	0.195884	−	0.980627i	$-0.437243\pi$
$379$	1.57364e11	0.391767	0.195884	+	0.980627i	$0.437243\pi$
$380$	3.41868e11	0.841071
$381$	−1.25522e11	−0.305182
$382$	−1.16446e11	−0.279795
$383$	−1.42996e11	−0.339570	−0.169785	−	0.985481i	$-0.554307\pi$
$383$	−1.42996e11	−0.339570	−0.169785	+	0.985481i	$0.554307\pi$
$384$	−2.46317e11	−0.578100
$385$	−4.09002e10	−0.0948752
$386$	2.39618e11	0.549384
$387$	−1.11685e11	−0.253102
$388$	−2.66453e11	−0.596868
$389$	−5.33550e11	−1.18141	−0.590706	−	0.806887i	$-0.701151\pi$
$389$	−5.33550e11	−1.18141	−0.590706	+	0.806887i	$0.701151\pi$
$390$	1.02833e11	0.225084
$391$	1.63018e11	0.352727
$392$	−2.95419e11	−0.631904
$393$	−4.65148e11	−0.983615
$394$	−3.67161e10	−0.0767580
$395$	2.31886e11	0.479278
$396$	−1.14498e11	−0.233976
$397$	7.64619e11	1.54486	0.772428	−	0.635102i	$-0.219042\pi$
$397$	7.64619e11	1.54486	0.772428	+	0.635102i	$0.219042\pi$
$398$	8.65179e10	0.172835
$399$	−8.44863e10	−0.166882
$400$	−2.01772e11	−0.394086
$401$	4.55767e11	0.880224	0.440112	−	0.897943i	$-0.354939\pi$
$401$	4.55767e11	0.880224	0.440112	+	0.897943i	$0.354939\pi$
$402$	−8.27673e9	−0.0158067
$403$	9.15993e11	1.72989
$404$	−9.13101e11	−1.70531
$405$	3.77283e10	0.0696818
$406$	2.76438e10	0.0504930
$407$	−4.61119e10	−0.0832987
$408$	−8.59406e10	−0.153542
$409$	5.90970e11	1.04426	0.522132	−	0.852864i	$-0.325137\pi$
$409$	5.90970e11	1.04426	0.522132	+	0.852864i	$0.325137\pi$
$410$	9.81829e10	0.171597
$411$	−5.60676e11	−0.969222
$412$	−4.25813e11	−0.728085
$413$	−1.45701e10	−0.0246427
$414$	−6.04328e10	−0.101105
$415$	−2.35446e11	−0.389650
$416$	−9.59855e11	−1.57140
$417$	−4.66669e11	−0.755782
$418$	2.65810e11	0.425870
$419$	5.95379e11	0.943693	0.471846	−	0.881681i	$-0.343588\pi$
$419$	5.95379e11	0.943693	0.471846	+	0.881681i	$0.343588\pi$
$420$	−3.83841e10	−0.0601908
$421$	−1.75564e11	−0.272374	−0.136187	−	0.990683i	$-0.543485\pi$
$421$	−1.75564e11	−0.272374	−0.136187	+	0.990683i	$0.543485\pi$
$422$	−4.03994e11	−0.620111
$423$	8.42833e10	0.128000
$424$	5.52393e11	0.830045
$425$	−1.65583e11	−0.246187
$426$	1.86904e11	0.274964
$427$	1.08888e11	0.158510
$428$	−4.66517e11	−0.672002
$429$	−5.76729e11	−0.822080
$430$	1.17796e11	0.166159
$431$	9.36848e11	1.30774	0.653870	−	0.756607i	$-0.273144\pi$
$431$	9.36848e11	1.30774	0.653870	+	0.756607i	$0.273144\pi$
$432$	−9.04924e10	−0.125007
$433$	1.26449e12	1.72871	0.864353	−	0.502886i	$-0.167728\pi$
$433$	1.26449e12	1.72871	0.864353	+	0.502886i	$0.167728\pi$
$434$	4.74006e10	0.0641328
$435$	−2.06717e11	−0.276805
$436$	1.04186e12	1.38076
$437$	−1.01197e12	−1.32740
$438$	−2.60383e11	−0.338049
$439$	8.05824e11	1.03550	0.517749	−	0.855532i	$-0.326770\pi$
$439$	8.05824e11	1.03550	0.517749	+	0.855532i	$0.326770\pi$
$440$	2.58269e11	0.328500
$441$	−2.55274e11	−0.321391
$442$	−2.02411e11	−0.252252
$443$	5.61599e11	0.692802	0.346401	−	0.938086i	$-0.387404\pi$
$443$	5.61599e11	0.692802	0.346401	+	0.938086i	$0.387404\pi$
$444$	−4.32752e10	−0.0528465
$445$	5.98669e11	0.723714
$446$	3.52276e11	0.421577
$447$	6.67514e11	0.790818
$448$	5.51587e10	0.0646939
$449$	−2.97221e11	−0.345121	−0.172561	−	0.984999i	$-0.555204\pi$
$449$	−2.97221e11	−0.345121	−0.172561	+	0.984999i	$0.555204\pi$
$450$	6.13839e10	0.0705664
$451$	−5.50647e11	−0.626728
$452$	1.23038e12	1.38649
$453$	−9.08602e11	−1.01375
$454$	−4.03883e11	−0.446174
$455$	−1.93341e11	−0.211482
$456$	5.33499e11	0.577819
$457$	5.56886e11	0.597233	0.298616	−	0.954373i	$-0.403475\pi$
$457$	5.56886e11	0.597233	0.298616	+	0.954373i	$0.403475\pi$
$458$	−2.47930e11	−0.263290
$459$	−7.42620e10	−0.0780925
$460$	−4.59764e11	−0.478768
$461$	−5.80556e11	−0.598673	−0.299337	−	0.954148i	$-0.596765\pi$
$461$	−5.80556e11	−0.598673	−0.299337	+	0.954148i	$0.596765\pi$
$462$	−2.98445e10	−0.0304772
$463$	−3.71702e11	−0.375908	−0.187954	−	0.982178i	$-0.560186\pi$
$463$	−3.71702e11	−0.375908	−0.187954	+	0.982178i	$0.560186\pi$
$464$	4.95816e11	0.496581
$465$	−3.54455e11	−0.351579
$466$	−1.66218e10	−0.0163284
$467$	1.02297e12	0.995264	0.497632	−	0.867388i	$-0.334203\pi$
$467$	1.02297e12	0.995264	0.497632	+	0.867388i	$0.334203\pi$
$468$	−5.41250e11	−0.521545
$469$	1.55614e10	0.0148515
$470$	−8.88952e10	−0.0840307
$471$	−1.68974e10	−0.0158207
$472$	9.20047e10	0.0853239
$473$	−6.60646e11	−0.606867
$474$	1.69205e11	0.153961
$475$	1.02790e12	0.926466
$476$	7.55530e10	0.0674559
$477$	4.77327e11	0.422166
$478$	4.89059e11	0.428485
$479$	7.36899e11	0.639584	0.319792	−	0.947488i	$-0.396387\pi$
$479$	7.36899e11	0.639584	0.319792	+	0.947488i	$0.396387\pi$
$480$	3.71428e11	0.319366
$481$	−2.17978e11	−0.185677
$482$	−2.14187e11	−0.180751
$483$	1.13622e11	0.0949950
$484$	3.82989e11	0.317236
$485$	5.19353e11	0.426211
$486$	2.75299e10	0.0223842
$487$	−2.01369e12	−1.62223	−0.811114	−	0.584888i	$-0.801138\pi$
$487$	−2.01369e12	−1.62223	−0.811114	+	0.584888i	$0.801138\pi$
$488$	−6.87587e11	−0.548831
$489$	−3.01964e11	−0.238817
$490$	2.69242e11	0.210990
$491$	2.17028e12	1.68519	0.842595	−	0.538547i	$-0.181027\pi$
$491$	2.17028e12	1.68519	0.842595	+	0.538547i	$0.181027\pi$
$492$	−5.16772e11	−0.397609
$493$	4.06888e11	0.310216
$494$	1.25652e12	0.949288
$495$	2.23173e11	0.167077
$496$	8.50172e11	0.630724
$497$	−3.51406e11	−0.258348
$498$	−1.71802e11	−0.125169
$499$	−1.25122e12	−0.903405	−0.451702	−	0.892169i	$-0.649183\pi$
$499$	−1.25122e12	−0.903405	−0.451702	+	0.892169i	$0.649183\pi$
$500$	1.23674e12	0.884936
$501$	5.41845e11	0.384242
$502$	4.87366e11	0.342522
$503$	1.37573e12	0.958250	0.479125	−	0.877747i	$-0.340954\pi$
$503$	1.37573e12	0.958250	0.479125	+	0.877747i	$0.340954\pi$
$504$	−5.99000e10	−0.0413513
$505$	1.77976e12	1.21772
$506$	−3.57476e11	−0.242421
$507$	−1.86732e12	−1.25511
$508$	−6.96822e11	−0.464232
$509$	2.24355e12	1.48151	0.740756	−	0.671775i	$-0.234468\pi$
$509$	2.24355e12	1.48151	0.740756	+	0.671775i	$0.234468\pi$
$510$	7.83255e10	0.0512669
$511$	4.89557e11	0.317621
$512$	−1.55284e12	−0.998645
$513$	4.61001e11	0.293882
$514$	6.40959e10	0.0405038
$515$	8.29967e11	0.519910
$516$	−6.20004e11	−0.385009
$517$	4.98558e11	0.306908
$518$	−1.12799e10	−0.00688367
$519$	7.25397e11	0.438857
$520$	1.22088e12	0.732245
$521$	−1.16911e12	−0.695164	−0.347582	−	0.937650i	$-0.612997\pi$
$521$	−1.16911e12	−0.695164	−0.347582	+	0.937650i	$0.612997\pi$
$522$	−1.50839e11	−0.0889194
$523$	1.78569e12	1.04363	0.521816	−	0.853058i	$-0.325255\pi$
$523$	1.78569e12	1.04363	0.521816	+	0.853058i	$0.325255\pi$
$524$	−2.58221e12	−1.49624
$525$	−1.15410e11	−0.0663021
$526$	1.41599e11	0.0806535
$527$	6.97687e11	0.394015
$528$	−5.35286e11	−0.299732
$529$	−4.40190e11	−0.244393
$530$	−5.03446e11	−0.277148
$531$	7.95020e10	0.0433963
$532$	−4.69015e11	−0.253854
$533$	−2.60299e12	−1.39701
$534$	4.36843e11	0.232482
$535$	9.09303e11	0.479863
$536$	−9.82643e10	−0.0514226
$537$	1.24303e12	0.645057
$538$	6.72509e11	0.346081
$539$	−1.51001e12	−0.770604
$540$	2.09444e11	0.105997
$541$	1.16148e12	0.582941	0.291471	−	0.956580i	$-0.405855\pi$
$541$	1.16148e12	0.582941	0.291471	+	0.956580i	$0.405855\pi$
$542$	2.13946e11	0.106490
$543$	−1.53864e11	−0.0759518
$544$	−7.31096e11	−0.357914
$545$	−2.03072e12	−0.985974
$546$	−1.41079e11	−0.0679353
$547$	−1.01125e12	−0.482965	−0.241482	−	0.970405i	$-0.577634\pi$
$547$	−1.01125e12	−0.482965	−0.241482	+	0.970405i	$0.577634\pi$
$548$	−3.11252e12	−1.47435
$549$	−5.94150e11	−0.279139
$550$	3.63102e11	0.169198
$551$	−2.52587e12	−1.16742
$552$	−7.17480e11	−0.328915
$553$	−3.18129e11	−0.144657
$554$	6.28923e11	0.283664
$555$	8.43492e10	0.0377366
$556$	−2.59065e12	−1.14967
$557$	−8.34237e10	−0.0367232	−0.0183616	−	0.999831i	$-0.505845\pi$
$557$	−8.34237e10	−0.0367232	−0.0183616	+	0.999831i	$0.505845\pi$
$558$	−2.58642e11	−0.112939
$559$	−3.12297e12	−1.35274
$560$	−1.79448e11	−0.0771068
$561$	−4.39279e11	−0.187244
$562$	−1.45945e12	−0.617131
$563$	−1.63117e12	−0.684243	−0.342121	−	0.939656i	$-0.611145\pi$
$563$	−1.63117e12	−0.684243	−0.342121	+	0.939656i	$0.611145\pi$
$564$	4.67888e11	0.194709
$565$	−2.39818e12	−0.990067
$566$	−1.11258e12	−0.455675
$567$	−5.17601e10	−0.0210315
$568$	2.21900e12	0.894518
$569$	−2.15020e12	−0.859951	−0.429976	−	0.902840i	$-0.641478\pi$
$569$	−2.15020e12	−0.859951	−0.429976	+	0.902840i	$0.641478\pi$
$570$	−4.86226e11	−0.192931
$571$	1.46827e12	0.578021	0.289010	−	0.957326i	$-0.406674\pi$
$571$	1.46827e12	0.578021	0.289010	+	0.957326i	$0.406674\pi$
$572$	−3.20164e12	−1.25052
$573$	−1.19462e12	−0.462950
$574$	−1.34699e11	−0.0517917
$575$	−1.38238e12	−0.527378
$576$	−3.00974e11	−0.113927
$577$	4.55722e12	1.71162	0.855812	−	0.517286i	$-0.173058\pi$
$577$	4.55722e12	1.71162	0.855812	+	0.517286i	$0.173058\pi$
$578$	7.82140e11	0.291480
$579$	2.45824e12	0.909014
$580$	−1.14756e12	−0.421066
$581$	3.23012e11	0.117605
$582$	3.78966e11	0.136914
$583$	2.82352e12	1.01224
$584$	−3.09137e12	−1.09975
$585$	1.05497e12	0.372424
$586$	1.22168e12	0.427976
$587$	−1.84926e12	−0.642875	−0.321437	−	0.946931i	$-0.604166\pi$
$587$	−1.84926e12	−0.642875	−0.321437	+	0.946931i	$0.604166\pi$
$588$	−1.41712e12	−0.488888
$589$	−4.33108e12	−1.48278
$590$	−8.38523e10	−0.0284892
$591$	−3.76671e11	−0.127004
$592$	−2.02314e11	−0.0676984
$593$	1.67093e12	0.554897	0.277449	−	0.960740i	$-0.410511\pi$
$593$	1.67093e12	0.554897	0.277449	+	0.960740i	$0.410511\pi$
$594$	1.62847e11	0.0536710
$595$	−1.47263e11	−0.0481689
$596$	3.70562e12	1.20296
$597$	8.87587e11	0.285974
$598$	−1.68984e12	−0.540369
$599$	−1.82405e12	−0.578915	−0.289458	−	0.957191i	$-0.593475\pi$
$599$	−1.82405e12	−0.578915	−0.289458	+	0.957191i	$0.593475\pi$
$600$	7.28771e11	0.229568
$601$	−5.10011e12	−1.59457	−0.797286	−	0.603602i	$-0.793732\pi$
$601$	−5.10011e12	−1.59457	−0.797286	+	0.603602i	$0.793732\pi$
$602$	−1.61607e11	−0.0501505
$603$	−8.49110e10	−0.0261539
$604$	−5.04399e12	−1.54208
$605$	−7.46497e11	−0.226532
$606$	1.29867e12	0.391176
$607$	−5.91080e12	−1.76725	−0.883624	−	0.468198i	$-0.844904\pi$
$607$	−5.91080e12	−1.76725	−0.883624	+	0.468198i	$0.844904\pi$
$608$	4.53847e12	1.34692
$609$	2.83598e11	0.0835460
$610$	6.26661e11	0.183252
$611$	2.35676e12	0.684115
$612$	−4.12256e11	−0.118791
$613$	5.98563e12	1.71213	0.856066	−	0.516866i	$-0.172901\pi$
$613$	5.98563e12	1.71213	0.856066	+	0.516866i	$0.172901\pi$
$614$	1.75190e11	0.0497453
$615$	1.00726e12	0.283925
$616$	−3.54324e11	−0.0991488
$617$	2.07156e12	0.575459	0.287729	−	0.957712i	$-0.407100\pi$
$617$	2.07156e12	0.575459	0.287729	+	0.957712i	$0.407100\pi$
$618$	6.05618e11	0.167013
$619$	−2.82773e12	−0.774157	−0.387079	−	0.922047i	$-0.626516\pi$
$619$	−2.82773e12	−0.774157	−0.387079	+	0.922047i	$0.626516\pi$
$620$	−1.96771e12	−0.534809
$621$	−6.19981e11	−0.167288
$622$	−9.26880e11	−0.248294
$623$	−8.21325e11	−0.218433
$624$	−2.53038e12	−0.668120
$625$	−9.61858e10	−0.0252145
$626$	−6.86652e11	−0.178711
$627$	2.72694e12	0.704647
$628$	−9.38037e10	−0.0240659
$629$	−1.66028e11	−0.0422914
$630$	5.45923e10	0.0138070
$631$	−1.01693e12	−0.255364	−0.127682	−	0.991815i	$-0.540754\pi$
$631$	−1.01693e12	−0.255364	−0.127682	+	0.991815i	$0.540754\pi$
$632$	2.00886e12	0.500868
$633$	−4.14458e12	−1.02604
$634$	−7.97613e11	−0.196061
$635$	1.35820e12	0.331498
$636$	2.64982e12	0.642184
$637$	−7.13805e12	−1.71772
$638$	−8.92252e11	−0.213204
$639$	1.91745e12	0.454957
$640$	2.66523e12	0.627951
$641$	−5.29037e12	−1.23773	−0.618864	−	0.785498i	$-0.712407\pi$
$641$	−5.29037e12	−1.23773	−0.618864	+	0.785498i	$0.712407\pi$
$642$	6.63509e11	0.154148
$643$	3.07318e12	0.708987	0.354494	−	0.935058i	$-0.384653\pi$
$643$	3.07318e12	0.708987	0.354494	+	0.935058i	$0.384653\pi$
$644$	6.30759e11	0.144503
$645$	1.20847e12	0.274927
$646$	9.57057e11	0.216218
$647$	−6.32449e11	−0.141891	−0.0709457	−	0.997480i	$-0.522602\pi$
$647$	−6.32449e11	−0.141891	−0.0709457	+	0.997480i	$0.522602\pi$
$648$	3.26845e11	0.0728206
$649$	4.70275e11	0.104052
$650$	1.71643e12	0.377152
$651$	4.86283e11	0.106115
$652$	−1.67631e12	−0.363279
$653$	4.83475e12	1.04055	0.520277	−	0.853998i	$-0.325829\pi$
$653$	4.83475e12	1.04055	0.520277	+	0.853998i	$0.325829\pi$
$654$	−1.48179e12	−0.316729
$655$	5.03307e12	1.06843
$656$	−2.41594e12	−0.509353
$657$	−2.67127e12	−0.559338
$658$	1.21957e11	0.0253624
$659$	−1.05700e12	−0.218319	−0.109159	−	0.994024i	$-0.534816\pi$
$659$	−1.05700e12	−0.218319	−0.109159	+	0.994024i	$0.534816\pi$
$660$	1.23891e12	0.254152
$661$	7.55120e12	1.53854	0.769271	−	0.638922i	$-0.220619\pi$
$661$	7.55120e12	1.53854	0.769271	+	0.638922i	$0.220619\pi$
$662$	2.16349e12	0.437818
$663$	−2.07653e12	−0.417377
$664$	−2.03970e12	−0.407202
$665$	9.14173e11	0.181272
$666$	6.15487e10	0.0121223
$667$	3.39693e12	0.664539
$668$	3.00798e12	0.584495
$669$	3.61400e12	0.697543
$670$	8.95572e10	0.0171697
$671$	−3.51455e12	−0.669297
$672$	−5.09568e11	−0.0963920
$673$	−5.73880e12	−1.07833	−0.539167	−	0.842199i	$-0.681261\pi$
$673$	−5.73880e12	−1.07833	−0.539167	+	0.842199i	$0.681261\pi$
$674$	−3.48147e12	−0.649819
$675$	6.29737e11	0.116760
$676$	−1.03662e13	−1.90923
$677$	−4.34589e12	−0.795115	−0.397558	−	0.917577i	$-0.630142\pi$
$677$	−4.34589e12	−0.795115	−0.397558	+	0.917577i	$0.630142\pi$
$678$	−1.74993e12	−0.318044
$679$	−7.12509e11	−0.128640
$680$	9.29908e11	0.166782
$681$	−4.14344e12	−0.738242
$682$	−1.52994e12	−0.270797
$683$	3.76552e10	0.00662112	0.00331056	−	0.999995i	$-0.498946\pi$
$683$	3.76552e10	0.00662112	0.00331056	+	0.999995i	$0.498946\pi$
$684$	2.55919e12	0.447043
$685$	6.06671e12	1.05280
$686$	−7.52483e11	−0.129729
$687$	−2.54352e12	−0.435641
$688$	−2.89856e12	−0.493212
$689$	1.33472e13	2.25633
$690$	6.53905e11	0.109823
$691$	1.07494e13	1.79364	0.896819	−	0.442397i	$-0.145872\pi$
$691$	1.07494e13	1.79364	0.896819	+	0.442397i	$0.145872\pi$
$692$	4.02695e12	0.667573
$693$	−3.06174e11	−0.0504277
$694$	−2.85093e12	−0.466519
$695$	5.04952e12	0.820954
$696$	−1.79081e12	−0.289274
$697$	−1.98262e12	−0.318195
$698$	−2.48361e12	−0.396035
$699$	−1.70524e11	−0.0270170
$700$	−6.40685e11	−0.100856
$701$	−5.69152e12	−0.890220	−0.445110	−	0.895476i	$-0.646835\pi$
$701$	−5.69152e12	−0.890220	−0.445110	+	0.895476i	$0.646835\pi$
$702$	7.69800e11	0.119636
$703$	1.03066e12	0.159154
$704$	−1.78034e12	−0.273166
$705$	−9.11976e11	−0.139038
$706$	2.13388e12	0.323257
$707$	−2.44168e12	−0.367537
$708$	4.41345e11	0.0660129
$709$	1.00026e13	1.48663	0.743315	−	0.668942i	$-0.233252\pi$
$709$	1.00026e13	1.48663	0.743315	+	0.668942i	$0.233252\pi$
$710$	−2.02237e12	−0.298675
$711$	1.73587e12	0.254745
$712$	5.18635e12	0.756314
$713$	5.82469e12	0.844053
$714$	−1.07456e11	−0.0154735
$715$	6.24042e12	0.892969
$716$	6.90053e12	0.981237
$717$	5.01726e12	0.708974
$718$	−4.65789e11	−0.0654077
$719$	1.17214e13	1.63569	0.817845	−	0.575439i	$-0.195169\pi$
$719$	1.17214e13	1.63569	0.817845	+	0.575439i	$0.195169\pi$
$720$	9.79161e11	0.135787
$721$	−1.13865e12	−0.156921
$722$	−3.39340e12	−0.464749
$723$	−2.19734e12	−0.299072
$724$	−8.54156e11	−0.115535
$725$	−3.45039e12	−0.463817
$726$	−5.44711e11	−0.0727698
$727$	6.94405e11	0.0921951	0.0460976	−	0.998937i	$-0.485321\pi$
$727$	6.94405e11	0.0921951	0.0460976	+	0.998937i	$0.485321\pi$
$728$	−1.67494e12	−0.221008
$729$	2.82430e11	0.0370370
$730$	2.81744e12	0.367200
$731$	−2.37868e12	−0.308111
$732$	−3.29835e12	−0.424616
$733$	1.79471e12	0.229628	0.114814	−	0.993387i	$-0.463373\pi$
$733$	1.79471e12	0.229628	0.114814	+	0.993387i	$0.463373\pi$
$734$	−1.77207e12	−0.225346
$735$	2.76216e12	0.349105
$736$	−6.10360e12	−0.766718
$737$	−5.02271e11	−0.0627096
$738$	7.34986e11	0.0912064
$739$	1.20936e13	1.49161	0.745803	−	0.666167i	$-0.232066\pi$
$739$	1.20936e13	1.49161	0.745803	+	0.666167i	$0.232066\pi$
$740$	4.68254e11	0.0574035
$741$	1.28906e13	1.57070
$742$	6.90687e11	0.0836495
$743$	5.82688e11	0.0701434	0.0350717	−	0.999385i	$-0.488834\pi$
$743$	5.82688e11	0.0701434	0.0350717	+	0.999385i	$0.488834\pi$
$744$	−3.07069e12	−0.367416
$745$	−7.22274e12	−0.859011
$746$	1.42453e12	0.168401
$747$	−1.76252e12	−0.207106
$748$	−2.43860e12	−0.284829
$749$	−1.24749e12	−0.144833
$750$	−1.75896e12	−0.202993
$751$	9.19635e10	0.0105496	0.00527480	−	0.999986i	$-0.498321\pi$
$751$	9.19635e10	0.0105496	0.00527480	+	0.999986i	$0.498321\pi$
$752$	2.18740e12	0.249430
$753$	4.99989e12	0.566739
$754$	−4.21780e12	−0.475242
$755$	9.83141e12	1.10117
$756$	−2.87339e11	−0.0319924
$757$	−1.08916e13	−1.20548	−0.602741	−	0.797937i	$-0.705925\pi$
$757$	−1.08916e13	−1.20548	−0.602741	+	0.797937i	$0.705925\pi$
$758$	−1.24247e12	−0.136701
$759$	−3.66735e12	−0.401111
$760$	−5.77265e12	−0.627645
$761$	−6.35015e11	−0.0686362	−0.0343181	−	0.999411i	$-0.510926\pi$
$761$	−6.35015e11	−0.0686362	−0.0343181	+	0.999411i	$0.510926\pi$
$762$	9.91063e11	0.106489
$763$	2.78598e12	0.297589
$764$	−6.63178e12	−0.704222
$765$	8.03541e11	0.0848266
$766$	1.12903e12	0.118488
$767$	2.22306e12	0.231938
$768$	4.23380e10	0.00439141
$769$	−1.04080e13	−1.07324	−0.536620	−	0.843824i	$-0.680299\pi$
$769$	−1.04080e13	−1.07324	−0.536620	+	0.843824i	$0.680299\pi$
$770$	3.22928e11	0.0331053
$771$	6.57560e11	0.0670179
$772$	1.36466e13	1.38276
$773$	−7.08749e11	−0.0713978	−0.0356989	−	0.999363i	$-0.511366\pi$
$773$	−7.08749e11	−0.0713978	−0.0356989	+	0.999363i	$0.511366\pi$
$774$	8.81809e11	0.0883161
$775$	−5.91635e12	−0.589110
$776$	4.49922e12	0.445410
$777$	−1.15720e11	−0.0113898
$778$	4.21264e12	0.412237
$779$	1.23077e13	1.19745
$780$	5.85652e12	0.566519
$781$	1.13422e13	1.09086
$782$	−1.28711e12	−0.123079
$783$	−1.54746e12	−0.147126
$784$	−6.62512e12	−0.626284
$785$	1.82836e11	0.0171849
$786$	3.67258e12	0.343218
$787$	−1.88880e13	−1.75509	−0.877546	−	0.479492i	$-0.840821\pi$
$787$	−1.88880e13	−1.75509	−0.877546	+	0.479492i	$0.840821\pi$
$788$	−2.09104e12	−0.193194
$789$	1.45266e12	0.133450
$790$	−1.83086e12	−0.167237
$791$	3.29011e12	0.298825
$792$	1.93337e12	0.174603
$793$	−1.66138e13	−1.49190
$794$	−6.03705e12	−0.539055
$795$	−5.16486e12	−0.458570
$796$	4.92733e12	0.435013
$797$	2.99654e11	0.0263062	0.0131531	−	0.999913i	$-0.495813\pi$
$797$	2.99654e11	0.0263062	0.0131531	+	0.999913i	$0.495813\pi$
$798$	6.67062e11	0.0582309
$799$	1.79508e12	0.155820
$800$	6.19965e12	0.535133
$801$	4.48157e12	0.384666
$802$	−3.59851e12	−0.307141
$803$	−1.58013e13	−1.34114
$804$	−4.71372e11	−0.0397843
$805$	−1.22943e12	−0.103187
$806$	−7.23223e12	−0.603621
$807$	6.89927e12	0.572628
$808$	1.54183e13	1.27258
$809$	1.98124e13	1.62618	0.813091	−	0.582136i	$-0.197783\pi$
$809$	1.98124e13	1.62618	0.813091	+	0.582136i	$0.197783\pi$
$810$	−2.97884e11	−0.0243144
$811$	−7.08065e12	−0.574751	−0.287375	−	0.957818i	$-0.592783\pi$
$811$	−7.08065e12	−0.574751	−0.287375	+	0.957818i	$0.592783\pi$
$812$	1.57436e12	0.127087
$813$	2.19487e12	0.176198
$814$	3.64077e11	0.0290659
$815$	3.26736e12	0.259410
$816$	−1.92732e12	−0.152177
$817$	1.47663e13	1.15950
$818$	−4.66601e12	−0.364381
$819$	−1.44733e12	−0.112406
$820$	5.59167e12	0.431896
$821$	2.37038e13	1.82085	0.910423	−	0.413677i	$-0.135756\pi$
$821$	2.37038e13	1.82085	0.910423	+	0.413677i	$0.135756\pi$
$822$	4.42682e12	0.338196
$823$	−1.32450e13	−1.00636	−0.503179	−	0.864182i	$-0.667836\pi$
$823$	−1.32450e13	−1.00636	−0.503179	+	0.864182i	$0.667836\pi$
$824$	7.19012e12	0.543330
$825$	3.72506e12	0.279957
$826$	1.15038e11	0.00859869
$827$	4.25854e12	0.316582	0.158291	−	0.987392i	$-0.449402\pi$
$827$	4.25854e12	0.316582	0.158291	+	0.987392i	$0.449402\pi$
$828$	−3.44174e12	−0.254473
$829$	−7.94186e12	−0.584019	−0.292009	−	0.956415i	$-0.594324\pi$
$829$	−7.94186e12	−0.584019	−0.292009	+	0.956415i	$0.594324\pi$
$830$	1.85896e12	0.135963
$831$	6.45212e12	0.469351
$832$	−8.41593e12	−0.608902
$833$	−5.43686e12	−0.391242
$834$	3.68458e12	0.263719
$835$	−5.86295e12	−0.417376
$836$	1.51383e13	1.07188
$837$	−2.65341e12	−0.186870
$838$	−4.70082e12	−0.329288
$839$	−6.48406e12	−0.451771	−0.225885	−	0.974154i	$-0.572528\pi$
$839$	−6.48406e12	−0.451771	−0.225885	+	0.974154i	$0.572528\pi$
$840$	6.48140e11	0.0449171
$841$	−6.02848e12	−0.415553
$842$	1.38616e12	0.0950408
$843$	−1.49725e13	−1.02111
$844$	−2.30081e13	−1.56077
$845$	2.02050e13	1.36334
$846$	−6.65460e11	−0.0446637
$847$	1.02413e12	0.0683724
$848$	1.23881e13	0.822663
$849$	−1.14139e13	−0.753963
$850$	1.30736e12	0.0859034
$851$	−1.38609e12	−0.0905960
$852$	1.06445e13	0.692064
$853$	1.67071e13	1.08052	0.540258	−	0.841500i	$-0.318327\pi$
$853$	1.67071e13	1.08052	0.540258	+	0.841500i	$0.318327\pi$
$854$	−8.59727e11	−0.0553096
$855$	−4.98820e12	−0.319224
$856$	7.87742e12	0.501478
$857$	−1.85113e13	−1.17226	−0.586129	−	0.810218i	$-0.699349\pi$
$857$	−1.85113e13	−1.17226	−0.586129	+	0.810218i	$0.699349\pi$
$858$	4.55357e12	0.286853
$859$	2.23892e12	0.140304	0.0701518	−	0.997536i	$-0.477652\pi$
$859$	2.23892e12	0.140304	0.0701518	+	0.997536i	$0.477652\pi$
$860$	6.70867e12	0.418209
$861$	−1.38188e12	−0.0856949
$862$	−7.39689e12	−0.456317
$863$	1.52935e13	0.938553	0.469277	−	0.883051i	$-0.344515\pi$
$863$	1.52935e13	0.938553	0.469277	+	0.883051i	$0.344515\pi$
$864$	2.78047e12	0.169748
$865$	−7.84906e12	−0.476700
$866$	−9.98381e12	−0.603206
$867$	8.02398e12	0.482285
$868$	2.69954e12	0.161418
$869$	1.02681e13	0.610806
$870$	1.63213e12	0.0965870
$871$	−2.37431e12	−0.139783
$872$	−1.75924e13	−1.03039
$873$	3.88782e12	0.226538
$874$	7.99005e12	0.463178
$875$	3.30709e12	0.190726
$876$	−1.48292e13	−0.850845
$877$	3.67264e11	0.0209643	0.0104821	−	0.999945i	$-0.496663\pi$
$877$	3.67264e11	0.0209643	0.0104821	+	0.999945i	$0.496663\pi$
$878$	−6.36238e12	−0.361322
$879$	1.25333e13	0.708131
$880$	5.79199e12	0.325579
$881$	−1.09629e13	−0.613104	−0.306552	−	0.951854i	$-0.599175\pi$
$881$	−1.09629e13	−0.613104	−0.306552	+	0.951854i	$0.599175\pi$
$882$	2.01552e12	0.112145
$883$	7.86390e12	0.435326	0.217663	−	0.976024i	$-0.430157\pi$
$883$	7.86390e12	0.435326	0.217663	+	0.976024i	$0.430157\pi$
$884$	−1.15276e13	−0.634898
$885$	−8.60241e11	−0.0471384
$886$	−4.43411e12	−0.241743
$887$	−6.50209e12	−0.352693	−0.176347	−	0.984328i	$-0.556428\pi$
$887$	−6.50209e12	−0.352693	−0.176347	+	0.984328i	$0.556428\pi$
$888$	7.30728e11	0.0394364
$889$	−1.86334e12	−0.100054
$890$	−4.72680e12	−0.252529
$891$	1.67065e12	0.0888044
$892$	2.00627e13	1.06108
$893$	−1.11434e13	−0.586390
$894$	−5.27036e12	−0.275944
$895$	−1.34501e13	−0.700682
$896$	−3.65648e12	−0.189530
$897$	−1.73361e13	−0.894097
$898$	2.34671e12	0.120425
$899$	1.45383e13	0.742326
$900$	3.49590e12	0.177610
$901$	1.01662e13	0.513921
$902$	4.34764e12	0.218687
$903$	−1.65792e12	−0.0829792
$904$	−2.07758e13	−1.03466
$905$	1.66486e12	0.0825012
$906$	7.17387e12	0.353734
$907$	−2.74257e13	−1.34563	−0.672813	−	0.739813i	$-0.734914\pi$
$907$	−2.74257e13	−1.34563	−0.672813	+	0.739813i	$0.734914\pi$
$908$	−2.30018e13	−1.12299
$909$	1.33230e13	0.647241
$910$	1.52653e12	0.0737935
$911$	3.61196e13	1.73744	0.868720	−	0.495303i	$-0.164943\pi$
$911$	3.61196e13	1.73744	0.868720	+	0.495303i	$0.164943\pi$
$912$	1.19643e13	0.572680
$913$	−1.04258e13	−0.496581
$914$	−4.39690e12	−0.208396
$915$	6.42892e12	0.303210
$916$	−1.41200e13	−0.662682
$917$	−6.90496e12	−0.322477
$918$	5.86336e11	0.0272492
$919$	−1.70082e13	−0.786572	−0.393286	−	0.919416i	$-0.628662\pi$
$919$	−1.70082e13	−0.786572	−0.393286	+	0.919416i	$0.628662\pi$
$920$	7.76340e12	0.357278
$921$	1.79728e12	0.0823089
$922$	4.58378e12	0.208898
$923$	5.36163e13	2.43159
$924$	−1.69969e12	−0.0767088
$925$	1.40790e12	0.0632318
$926$	2.93478e12	0.131167
$927$	6.21304e12	0.276341
$928$	−1.52344e13	−0.674311
$929$	−3.02207e13	−1.33117	−0.665585	−	0.746322i	$-0.731818\pi$
$929$	−3.02207e13	−1.33117	−0.665585	+	0.746322i	$0.731818\pi$
$930$	2.79860e12	0.122678
$931$	3.37507e13	1.47235
$932$	−9.46639e11	−0.0410973
$933$	−9.50887e12	−0.410829
$934$	−8.07689e12	−0.347283
$935$	4.75316e12	0.203390
$936$	9.13934e12	0.389200
$937$	−2.32899e13	−0.987051	−0.493525	−	0.869731i	$-0.664292\pi$
$937$	−2.32899e13	−0.987051	−0.493525	+	0.869731i	$0.664292\pi$
$938$	−1.22865e11	−0.00518222
$939$	−7.04437e12	−0.295697
$940$	−5.06272e12	−0.211499
$941$	−1.92887e12	−0.0801955	−0.0400977	−	0.999196i	$-0.512767\pi$
$941$	−1.92887e12	−0.0801955	−0.0400977	+	0.999196i	$0.512767\pi$
$942$	1.33413e11	0.00552040
$943$	−1.65521e13	−0.681631
$944$	2.06331e12	0.0845651
$945$	5.60063e11	0.0228451
$946$	5.21613e12	0.211757
$947$	−1.02453e13	−0.413954	−0.206977	−	0.978346i	$-0.566362\pi$
$947$	−1.02453e13	−0.413954	−0.206977	+	0.978346i	$0.566362\pi$
$948$	9.63648e12	0.387508
$949$	−7.46949e13	−2.98946
$950$	−8.11579e12	−0.323277
$951$	−8.18272e12	−0.324403
$952$	−1.27576e12	−0.0503387
$953$	2.00482e13	0.787332	0.393666	−	0.919253i	$-0.371207\pi$
$953$	2.00482e13	0.787332	0.393666	+	0.919253i	$0.371207\pi$
$954$	−3.76874e12	−0.147309
$955$	1.29262e13	0.502871
$956$	2.78527e13	1.07847
$957$	−9.15362e12	−0.352768
$958$	−5.81819e12	−0.223174
$959$	−8.32303e12	−0.317759
$960$	3.25665e12	0.123752
$961$	−1.51096e12	−0.0571474
$962$	1.72104e12	0.0647894
$963$	6.80694e12	0.255055
$964$	−1.21983e13	−0.454937
$965$	−2.65990e13	−0.987399
$966$	−8.97104e11	−0.0331471
$967$	5.25249e12	0.193173	0.0965865	−	0.995325i	$-0.469208\pi$
$967$	5.25249e12	0.193173	0.0965865	+	0.995325i	$0.469208\pi$
$968$	−6.46700e12	−0.236736
$969$	9.81845e12	0.357755
$970$	−4.10055e12	−0.148720
$971$	−2.34931e13	−0.848114	−0.424057	−	0.905636i	$-0.639394\pi$
$971$	−2.34931e13	−0.848114	−0.424057	+	0.905636i	$0.639394\pi$
$972$	1.56787e12	0.0563394
$973$	−6.92753e12	−0.247783
$974$	1.58991e13	0.566053
$975$	1.76089e13	0.624038
$976$	−1.54200e13	−0.543950
$977$	−2.81571e13	−0.988695	−0.494347	−	0.869264i	$-0.664593\pi$
$977$	−2.81571e13	−0.988695	−0.494347	+	0.869264i	$0.664593\pi$
$978$	2.38415e12	0.0833316
$979$	2.65097e13	0.922321
$980$	1.53338e13	0.531045
$981$	−1.52017e13	−0.524062
$982$	−1.71355e13	−0.588022
$983$	−2.34417e13	−0.800754	−0.400377	−	0.916350i	$-0.631121\pi$
$983$	−2.34417e13	−0.800754	−0.400377	+	0.916350i	$0.631121\pi$
$984$	8.72602e12	0.296714
$985$	4.07572e12	0.137956
$986$	−3.21259e12	−0.108245
$987$	1.25116e12	0.0419647
$988$	7.15607e13	2.38929
$989$	−1.98586e13	−0.660031
$990$	−1.76206e12	−0.0582992
$991$	−5.51039e13	−1.81489	−0.907446	−	0.420169i	$-0.861971\pi$
$991$	−5.51039e13	−1.81489	−0.907446	+	0.420169i	$0.861971\pi$
$992$	−2.61223e13	−0.856465
$993$	2.21952e13	0.724415
$994$	2.77453e12	0.0901468
$995$	−9.60402e12	−0.310634
$996$	−9.78441e12	−0.315041
$997$	7.08244e12	0.227015	0.113508	−	0.993537i	$-0.463791\pi$
$997$	7.08244e12	0.227015	0.113508	+	0.993537i	$0.463791\pi$
$998$	9.87904e12	0.315230
$999$	6.31428e11	0.0200576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} -6920.01 q^{10} +38810.0 q^{11} +36422.5 q^{12} +183461. q^{13} +9493.68 q^{14} -70992.4 q^{15} +170277. q^{16} +139737. q^{17} -51802.4 q^{18} -867454. q^{19} -394105. q^{20} +97395.7 q^{21} -306425. q^{22} +1.16660e6 q^{23} -615017. q^{24} -1.18496e6 q^{25} -1.44851e6 q^{26} -531441. q^{27} +540680. q^{28} +2.91181e6 q^{29} +560521. q^{30} +4.99286e6 q^{31} -5.23194e6 q^{32} -3.14361e6 q^{33} -1.10329e6 q^{34} -1.05386e6 q^{35} -2.95023e6 q^{36} -1.18814e6 q^{37} +6.84899e6 q^{38} -1.48603e7 q^{39} +6.65470e6 q^{40} -1.41883e7 q^{41} -768988. q^{42} -1.70225e7 q^{43} -1.74514e7 q^{44} +5.75038e6 q^{45} -9.21092e6 q^{46} +1.28461e7 q^{47} -1.37925e7 q^{48} -3.89078e7 q^{49} +9.35587e6 q^{50} -1.13187e7 q^{51} -8.24951e7 q^{52} +7.27522e7 q^{53} +4.19599e6 q^{54} +3.40150e7 q^{55} -9.12970e6 q^{56} +7.02638e7 q^{57} -2.29902e7 q^{58} +1.21174e7 q^{59} +3.19225e7 q^{60} -9.05578e7 q^{61} -3.94212e7 q^{62} -7.88905e6 q^{63} -4.58733e7 q^{64} +1.60794e8 q^{65} +2.48204e7 q^{66} -1.29418e7 q^{67} -6.28343e7 q^{68} -9.44949e7 q^{69} +8.32073e6 q^{70} +2.92250e8 q^{71} +4.98164e7 q^{72} -4.07144e8 q^{73} +9.38099e6 q^{74} +9.59819e7 q^{75} +3.90060e8 q^{76} -4.66658e7 q^{77} +1.17330e8 q^{78} +2.64575e8 q^{79} +1.49240e8 q^{80} +4.30467e7 q^{81} +1.12023e8 q^{82} -2.68636e8 q^{83} -4.37951e7 q^{84} +1.22472e8 q^{85} +1.34402e8 q^{86} -2.35857e8 q^{87} +2.94677e8 q^{88} +6.83062e8 q^{89} -4.54022e7 q^{90} -2.20596e8 q^{91} -5.24576e8 q^{92} -4.04422e8 q^{93} -1.01427e8 q^{94} -7.60280e8 q^{95} +4.23787e8 q^{96} +5.92565e8 q^{97} +3.07197e8 q^{98} +2.54633e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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