LMFDB - Embedded newform 177.12.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} -162297. q^{10} +275762. q^{11} -453234. q^{12} +260615. q^{13} -266242. q^{14} -2.91664e6 q^{15} +3.10438e6 q^{16} +2.78427e6 q^{17} +798447. q^{18} +1.56707e7 q^{19} +2.23868e7 q^{20} -4.78463e6 q^{21} +3.72879e6 q^{22} -5.51728e7 q^{23} -1.28578e7 q^{24} +9.52349e7 q^{25} +3.52397e6 q^{26} +1.43489e7 q^{27} +3.67247e7 q^{28} -4.30019e7 q^{29} -3.94381e7 q^{30} +1.37545e7 q^{31} +1.50342e8 q^{32} +6.70102e7 q^{33} +3.76483e7 q^{34} +2.36330e8 q^{35} -1.10136e8 q^{36} +2.61056e8 q^{37} +2.11896e8 q^{38} +6.33294e7 q^{39} +6.35094e8 q^{40} +1.38214e9 q^{41} -6.46967e7 q^{42} +4.91328e8 q^{43} -5.14341e8 q^{44} -7.08743e8 q^{45} -7.46034e8 q^{46} +9.26195e8 q^{47} +7.54363e8 q^{48} -1.58964e9 q^{49} +1.28774e9 q^{50} +6.76579e8 q^{51} -4.86089e8 q^{52} -5.11389e9 q^{53} +1.94023e8 q^{54} -3.30987e9 q^{55} +1.04185e9 q^{56} +3.80799e9 q^{57} -5.81463e8 q^{58} -7.14924e8 q^{59} +5.44000e9 q^{60} +5.97047e9 q^{61} +1.85985e8 q^{62} -1.16267e9 q^{63} -4.32487e9 q^{64} -3.12806e9 q^{65} +9.06096e8 q^{66} +1.02331e10 q^{67} -5.19312e9 q^{68} -1.34070e10 q^{69} +3.19560e9 q^{70} -2.24186e10 q^{71} -3.12445e9 q^{72} -2.72185e10 q^{73} +3.52995e9 q^{74} +2.31421e10 q^{75} -2.92285e10 q^{76} -5.42971e9 q^{77} +8.56325e8 q^{78} -2.62365e10 q^{79} -3.72607e10 q^{80} +3.48678e9 q^{81} +1.86890e10 q^{82} -4.00527e10 q^{83} +8.92411e9 q^{84} -3.34186e10 q^{85} +6.64363e9 q^{86} -1.04495e10 q^{87} -1.45914e10 q^{88} +6.06398e10 q^{89} -9.58346e9 q^{90} -5.13146e9 q^{91} +1.02906e11 q^{92} +3.34235e9 q^{93} +1.25238e10 q^{94} -1.88090e11 q^{95} +3.65332e10 q^{96} +1.53603e11 q^{97} -2.14947e10 q^{98} +1.62835e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	13.5218	0.298792	0.149396	−	0.988777i	$-0.452267\pi$
$2$	13.5218	0.298792	0.149396	+	0.988777i	$0.452267\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1865.16	−0.910723
$5$	−12002.6	−1.71768	−0.858838	−	0.512247i	$-0.828813\pi$
$5$	−12002.6	−1.71768	−0.858838	+	0.512247i	$0.828813\pi$
$6$	3285.79	0.172508
$7$	−19689.8	−0.442795	−0.221398	−	0.975184i	$-0.571062\pi$
$7$	−19689.8	−0.442795	−0.221398	+	0.975184i	$0.571062\pi$
$8$	−52912.9	−0.570908
$9$	59049.0	0.333333
$10$	−162297.	−0.513228
$11$	275762.	0.516267	0.258134	−	0.966109i	$-0.416892\pi$
$11$	275762.	0.516267	0.258134	+	0.966109i	$0.416892\pi$
$12$	−453234.	−0.525806
$13$	260615.	0.194675	0.0973376	−	0.995251i	$-0.468967\pi$
$13$	260615.	0.194675	0.0973376	+	0.995251i	$0.468967\pi$
$14$	−266242.	−0.132304
$15$	−2.91664e6	−0.991701
$16$	3.10438e6	0.740141
$17$	2.78427e6	0.475601	0.237801	−	0.971314i	$-0.423574\pi$
$17$	2.78427e6	0.475601	0.237801	+	0.971314i	$0.423574\pi$
$18$	798447.	0.0995973
$19$	1.56707e7	1.45193	0.725964	−	0.687733i	$-0.241394\pi$
$19$	1.56707e7	1.45193	0.725964	+	0.687733i	$0.241394\pi$
$20$	2.23868e7	1.56433
$21$	−4.78463e6	−0.255648
$22$	3.72879e6	0.154256
$23$	−5.51728e7	−1.78740	−0.893700	−	0.448665i	$-0.851900\pi$
$23$	−5.51728e7	−1.78740	−0.893700	+	0.448665i	$0.851900\pi$
$24$	−1.28578e7	−0.329614
$25$	9.52349e7	1.95041
$26$	3.52397e6	0.0581673
$27$	1.43489e7	0.192450
$28$	3.67247e7	0.403264
$29$	−4.30019e7	−0.389313	−0.194657	−	0.980871i	$-0.562359\pi$
$29$	−4.30019e7	−0.389313	−0.194657	+	0.980871i	$0.562359\pi$
$30$	−3.94381e7	−0.296312
$31$	1.37545e7	0.0862891	0.0431446	−	0.999069i	$-0.486262\pi$
$31$	1.37545e7	0.0862891	0.0431446	+	0.999069i	$0.486262\pi$
$32$	1.50342e8	0.792056
$33$	6.70102e7	0.298067
$34$	3.76483e7	0.142106
$35$	2.36330e8	0.760579
$36$	−1.10136e8	−0.303574
$37$	2.61056e8	0.618906	0.309453	−	0.950915i	$-0.399854\pi$
$37$	2.61056e8	0.618906	0.309453	+	0.950915i	$0.399854\pi$
$38$	2.11896e8	0.433824
$39$	6.33294e7	0.112396
$40$	6.35094e8	0.980636
$41$	1.38214e9	1.86312	0.931562	−	0.363582i	$-0.118446\pi$
$41$	1.38214e9	1.86312	0.931562	+	0.363582i	$0.118446\pi$
$42$	−6.46967e7	−0.0763855
$43$	4.91328e8	0.509677	0.254839	−	0.966984i	$-0.417978\pi$
$43$	4.91328e8	0.509677	0.254839	+	0.966984i	$0.417978\pi$
$44$	−5.14341e8	−0.470177
$45$	−7.08743e8	−0.572559
$46$	−7.46034e8	−0.534061
$47$	9.26195e8	0.589066	0.294533	−	0.955641i	$-0.404836\pi$
$47$	9.26195e8	0.589066	0.294533	+	0.955641i	$0.404836\pi$
$48$	7.54363e8	0.427320
$49$	−1.58964e9	−0.803932
$50$	1.28774e9	0.582767
$51$	6.76579e8	0.274589
$52$	−4.86089e8	−0.177295
$53$	−5.11389e9	−1.67971	−0.839855	−	0.542811i	$-0.817360\pi$
$53$	−5.11389e9	−1.67971	−0.839855	+	0.542811i	$0.817360\pi$
$54$	1.94023e8	0.0575025
$55$	−3.30987e9	−0.886780
$56$	1.04185e9	0.252796
$57$	3.80799e9	0.838271
$58$	−5.81463e8	−0.116324
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	5.44000e9	0.903165
$61$	5.97047e9	0.905096	0.452548	−	0.891740i	$-0.350515\pi$
$61$	5.97047e9	0.905096	0.452548	+	0.891740i	$0.350515\pi$
$62$	1.85985e8	0.0257825
$63$	−1.16267e9	−0.147598
$64$	−4.32487e9	−0.503481
$65$	−3.12806e9	−0.334389
$66$	9.06096e8	0.0890600
$67$	1.02331e10	0.925971	0.462985	−	0.886366i	$-0.346778\pi$
$67$	1.02331e10	0.925971	0.462985	+	0.886366i	$0.346778\pi$
$68$	−5.19312e9	−0.433141
$69$	−1.34070e10	−1.03196
$70$	3.19560e9	0.227255
$71$	−2.24186e10	−1.47464	−0.737322	−	0.675541i	$-0.763910\pi$
$71$	−2.24186e10	−1.47464	−0.737322	+	0.675541i	$0.763910\pi$
$72$	−3.12445e9	−0.190303
$73$	−2.72185e10	−1.53670	−0.768348	−	0.640032i	$-0.778921\pi$
$73$	−2.72185e10	−1.53670	−0.768348	+	0.640032i	$0.778921\pi$
$74$	3.52995e9	0.184924
$75$	2.31421e10	1.12607
$76$	−2.92285e10	−1.32230
$77$	−5.42971e9	−0.228601
$78$	8.56325e8	0.0335829
$79$	−2.62365e10	−0.959305	−0.479652	−	0.877459i	$-0.659237\pi$
$79$	−2.62365e10	−0.959305	−0.479652	+	0.877459i	$0.659237\pi$
$80$	−3.72607e10	−1.27132
$81$	3.48678e9	0.111111
$82$	1.86890e10	0.556686
$83$	−4.00527e10	−1.11610	−0.558048	−	0.829808i	$-0.688450\pi$
$83$	−4.00527e10	−1.11610	−0.558048	+	0.829808i	$0.688450\pi$
$84$	8.92411e9	0.232825
$85$	−3.34186e10	−0.816929
$86$	6.64363e9	0.152287
$87$	−1.04495e10	−0.224770
$88$	−1.45914e10	−0.294741
$89$	6.06398e10	1.15110	0.575549	−	0.817767i	$-0.304788\pi$
$89$	6.06398e10	1.15110	0.575549	+	0.817767i	$0.304788\pi$
$90$	−9.58346e9	−0.171076
$91$	−5.13146e9	−0.0862013
$92$	1.02906e11	1.62783
$93$	3.34235e9	0.0498191
$94$	1.25238e10	0.176008
$95$	−1.88090e11	−2.49394
$96$	3.65332e10	0.457294
$97$	1.53603e11	1.81617	0.908085	−	0.418786i	$-0.137544\pi$
$97$	1.53603e11	1.81617	0.908085	+	0.418786i	$0.137544\pi$
$98$	−2.14947e10	−0.240208
$99$	1.62835e10	0.172089
$100$	−1.77629e11	−1.77629
$101$	−1.19648e11	−1.13276	−0.566380	−	0.824144i	$-0.691657\pi$
$101$	−1.19648e11	−1.13276	−0.566380	+	0.824144i	$0.691657\pi$
$102$	9.14854e9	0.0820448
$103$	1.93441e10	0.164416	0.0822081	−	0.996615i	$-0.473803\pi$
$103$	1.93441e10	0.164416	0.0822081	+	0.996615i	$0.473803\pi$
$104$	−1.37899e10	−0.111142
$105$	5.74282e10	0.439121
$106$	−6.91489e10	−0.501883
$107$	−2.44523e11	−1.68543	−0.842713	−	0.538363i	$-0.819043\pi$
$107$	−2.44523e11	−1.68543	−0.842713	+	0.538363i	$0.819043\pi$
$108$	−2.67630e10	−0.175269
$109$	1.67972e11	1.04566	0.522830	−	0.852437i	$-0.324876\pi$
$109$	1.67972e11	1.04566	0.522830	+	0.852437i	$0.324876\pi$
$110$	−4.47553e10	−0.264963
$111$	6.34367e10	0.357326
$112$	−6.11247e10	−0.327731
$113$	2.72254e11	1.39009	0.695046	−	0.718966i	$-0.255384\pi$
$113$	2.72254e11	1.39009	0.695046	+	0.718966i	$0.255384\pi$
$114$	5.14908e10	0.250468
$115$	6.62218e11	3.07017
$116$	8.02056e10	0.354557
$117$	1.53890e10	0.0648917
$118$	−9.66704e9	−0.0388994
$119$	−5.48219e10	−0.210594
$120$	1.54328e11	0.566170
$121$	−2.09267e11	−0.733468
$122$	8.07314e10	0.270435
$123$	3.35861e11	1.07568
$124$	−2.56544e10	−0.0785855
$125$	−5.57003e11	−1.63250
$126$	−1.57213e10	−0.0441012
$127$	−2.86551e11	−0.769630	−0.384815	−	0.922994i	$-0.625735\pi$
$127$	−2.86551e11	−0.769630	−0.384815	+	0.922994i	$0.625735\pi$
$128$	−3.66381e11	−0.942492
$129$	1.19393e11	0.294262
$130$	−4.22969e10	−0.0999126
$131$	1.47330e11	0.333656	0.166828	−	0.985986i	$-0.446647\pi$
$131$	1.47330e11	0.333656	0.166828	+	0.985986i	$0.446647\pi$
$132$	−1.24985e11	−0.271457
$133$	−3.08555e11	−0.642907
$134$	1.38370e11	0.276673
$135$	−1.72225e11	−0.330567
$136$	−1.47324e11	−0.271525
$137$	1.04473e12	1.84945	0.924723	−	0.380641i	$-0.124297\pi$
$137$	1.04473e12	1.84945	0.924723	+	0.380641i	$0.124297\pi$
$138$	−1.81286e11	−0.308340
$139$	−6.22647e11	−1.01780	−0.508898	−	0.860827i	$-0.669947\pi$
$139$	−6.22647e11	−1.01780	−0.508898	+	0.860827i	$0.669947\pi$
$140$	−4.40793e11	−0.692677
$141$	2.25065e11	0.340098
$142$	−3.03139e11	−0.440612
$143$	7.18677e10	0.100504
$144$	1.83310e11	0.246714
$145$	5.16136e11	0.668714
$146$	−3.68042e11	−0.459152
$147$	−3.86282e11	−0.464151
$148$	−4.86912e11	−0.563652
$149$	−3.33149e10	−0.0371633	−0.0185816	−	0.999827i	$-0.505915\pi$
$149$	−3.33149e10	−0.0371633	−0.0185816	+	0.999827i	$0.505915\pi$
$150$	3.12922e11	0.336461
$151$	−1.10725e12	−1.14781	−0.573906	−	0.818921i	$-0.694573\pi$
$151$	−1.10725e12	−1.14781	−0.573906	+	0.818921i	$0.694573\pi$
$152$	−8.29184e11	−0.828918
$153$	1.64409e11	0.158534
$154$	−7.34193e10	−0.0683041
$155$	−1.65090e11	−0.148217
$156$	−1.18120e11	−0.102361
$157$	1.68694e12	1.41141	0.705703	−	0.708507i	$-0.250631\pi$
$157$	1.68694e12	1.41141	0.705703	+	0.708507i	$0.250631\pi$
$158$	−3.54764e11	−0.286632
$159$	−1.24268e12	−0.969781
$160$	−1.80450e12	−1.36050
$161$	1.08634e12	0.791453
$162$	4.71475e10	0.0331991
$163$	−7.59126e11	−0.516752	−0.258376	−	0.966044i	$-0.583187\pi$
$163$	−7.59126e11	−0.516752	−0.258376	+	0.966044i	$0.583187\pi$
$164$	−2.57792e12	−1.69679
$165$	−8.04298e11	−0.511983
$166$	−5.41583e11	−0.333481
$167$	4.25956e11	0.253761	0.126880	−	0.991918i	$-0.459504\pi$
$167$	4.25956e11	0.253761	0.126880	+	0.991918i	$0.459504\pi$
$168$	2.53169e11	0.145952
$169$	−1.72424e12	−0.962102
$170$	−4.51879e11	−0.244092
$171$	9.25342e11	0.483976
$172$	−9.16407e11	−0.464175
$173$	−2.13312e12	−1.04655	−0.523277	−	0.852163i	$-0.675291\pi$
$173$	−2.13312e12	−1.04655	−0.523277	+	0.852163i	$0.675291\pi$
$174$	−1.41295e11	−0.0671595
$175$	−1.87516e12	−0.863633
$176$	8.56069e11	0.382111
$177$	−1.73727e11	−0.0751646
$178$	8.19957e11	0.343939
$179$	2.26706e12	0.922087	0.461043	−	0.887378i	$-0.347475\pi$
$179$	2.26706e12	0.922087	0.461043	+	0.887378i	$0.347475\pi$
$180$	1.32192e12	0.521443
$181$	−3.99086e11	−0.152698	−0.0763492	−	0.997081i	$-0.524326\pi$
$181$	−3.99086e11	−0.152698	−0.0763492	+	0.997081i	$0.524326\pi$
$182$	−6.93865e10	−0.0257562
$183$	1.45083e12	0.522557
$184$	2.91935e12	1.02044
$185$	−3.13336e12	−1.06308
$186$	4.51945e10	0.0148855
$187$	7.67797e11	0.245537
$188$	−1.72750e12	−0.536476
$189$	−2.82528e11	−0.0852160
$190$	−2.54331e12	−0.745169
$191$	2.56305e12	0.729582	0.364791	−	0.931089i	$-0.381140\pi$
$191$	2.56305e12	0.729582	0.364791	+	0.931089i	$0.381140\pi$
$192$	−1.05094e12	−0.290685
$193$	1.45814e12	0.391953	0.195976	−	0.980609i	$-0.437212\pi$
$193$	1.45814e12	0.391953	0.195976	+	0.980609i	$0.437212\pi$
$194$	2.07699e12	0.542657
$195$	−7.60119e11	−0.193059
$196$	2.96493e12	0.732160
$197$	2.70562e11	0.0649684	0.0324842	−	0.999472i	$-0.489658\pi$
$197$	2.70562e11	0.0649684	0.0324842	+	0.999472i	$0.489658\pi$
$198$	2.20181e11	0.0514188
$199$	−1.19094e12	−0.270520	−0.135260	−	0.990810i	$-0.543187\pi$
$199$	−1.19094e12	−0.270520	−0.135260	+	0.990810i	$0.543187\pi$
$200$	−5.03915e12	−1.11351
$201$	2.48665e12	0.534610
$202$	−1.61785e12	−0.338460
$203$	8.46702e11	0.172386
$204$	−1.26193e12	−0.250074
$205$	−1.65894e13	−3.20024
$206$	2.61567e11	0.0491262
$207$	−3.25790e12	−0.595800
$208$	8.09046e11	0.144087
$209$	4.32140e12	0.749583
$210$	7.76530e11	0.131206
$211$	−5.22030e12	−0.859295	−0.429647	−	0.902997i	$-0.641362\pi$
$211$	−5.22030e12	−0.859295	−0.429647	+	0.902997i	$0.641362\pi$
$212$	9.53823e12	1.52975
$213$	−5.44772e12	−0.851386
$214$	−3.30639e12	−0.503591
$215$	−5.89723e12	−0.875460
$216$	−7.59242e11	−0.109871
$217$	−2.70824e11	−0.0382084
$218$	2.27128e12	0.312435
$219$	−6.61409e12	−0.887212
$220$	6.17344e12	0.807612
$221$	7.25623e11	0.0925877
$222$	8.57777e11	0.106766
$223$	−4.06546e11	−0.0493666	−0.0246833	−	0.999695i	$-0.507858\pi$
$223$	−4.06546e11	−0.0493666	−0.0246833	+	0.999695i	$0.507858\pi$
$224$	−2.96022e12	−0.350719
$225$	5.62353e12	0.650137
$226$	3.68136e12	0.415348
$227$	−4.75664e12	−0.523791	−0.261895	−	0.965096i	$-0.584348\pi$
$227$	−4.75664e12	−0.523791	−0.261895	+	0.965096i	$0.584348\pi$
$228$	−7.10252e12	−0.763433
$229$	6.57938e12	0.690383	0.345192	−	0.938532i	$-0.387814\pi$
$229$	6.57938e12	0.690383	0.345192	+	0.938532i	$0.387814\pi$
$230$	8.95437e12	0.917343
$231$	−1.31942e12	−0.131983
$232$	2.27536e12	0.222262
$233$	−1.62372e13	−1.54900	−0.774502	−	0.632571i	$-0.782000\pi$
$233$	−1.62372e13	−1.54900	−0.774502	+	0.632571i	$0.782000\pi$
$234$	2.08087e11	0.0193891
$235$	−1.11168e13	−1.01182
$236$	1.33345e12	0.118566
$237$	−6.37547e12	−0.553855
$238$	−7.41290e11	−0.0629238
$239$	3.09555e12	0.256773	0.128387	−	0.991724i	$-0.459020\pi$
$239$	3.09555e12	0.256773	0.128387	+	0.991724i	$0.459020\pi$
$240$	−9.05434e12	−0.733998
$241$	−1.74669e11	−0.0138395	−0.00691976	−	0.999976i	$-0.502203\pi$
$241$	−1.74669e11	−0.0138395	−0.00691976	+	0.999976i	$0.502203\pi$
$242$	−2.82966e12	−0.219154
$243$	8.47289e11	0.0641500
$244$	−1.11359e13	−0.824292
$245$	1.90798e13	1.38090
$246$	4.54143e12	0.321403
$247$	4.08403e12	0.282654
$248$	−7.27791e11	−0.0492632
$249$	−9.73280e12	−0.644379
$250$	−7.53167e12	−0.487777
$251$	1.34968e13	0.855119	0.427559	−	0.903987i	$-0.359373\pi$
$251$	1.34968e13	0.855119	0.427559	+	0.903987i	$0.359373\pi$
$252$	2.16856e12	0.134421
$253$	−1.52146e13	−0.922777
$254$	−3.87468e12	−0.229959
$255$	−8.12072e12	−0.471654
$256$	3.90321e12	0.221872
$257$	−2.22213e13	−1.23634	−0.618169	−	0.786045i	$-0.712125\pi$
$257$	−2.22213e13	−1.23634	−0.618169	+	0.786045i	$0.712125\pi$
$258$	1.61440e12	0.0879231
$259$	−5.14016e12	−0.274049
$260$	5.83434e12	0.304536
$261$	−2.53922e12	−0.129771
$262$	1.99216e12	0.0996938
$263$	−3.72334e13	−1.82464	−0.912318	−	0.409482i	$-0.865710\pi$
$263$	−3.72334e13	−1.82464	−0.912318	+	0.409482i	$0.865710\pi$
$264$	−3.54570e12	−0.170169
$265$	6.13801e13	2.88520
$266$	−4.17220e12	−0.192095
$267$	1.47355e13	0.664587
$268$	−1.90865e13	−0.843303
$269$	2.24861e13	0.973367	0.486683	−	0.873578i	$-0.338207\pi$
$269$	2.24861e13	0.973367	0.486683	+	0.873578i	$0.338207\pi$
$270$	−2.32878e12	−0.0987707
$271$	7.64713e12	0.317810	0.158905	−	0.987294i	$-0.449204\pi$
$271$	7.64713e12	0.317810	0.158905	+	0.987294i	$0.449204\pi$
$272$	8.64343e12	0.352012
$273$	−1.24695e12	−0.0497683
$274$	1.41266e13	0.552599
$275$	2.62622e13	1.00693
$276$	2.50062e13	0.939827
$277$	−3.50920e13	−1.29291	−0.646457	−	0.762951i	$-0.723750\pi$
$277$	−3.50920e13	−1.29291	−0.646457	+	0.762951i	$0.723750\pi$
$278$	−8.41929e12	−0.304109
$279$	8.12191e11	0.0287630
$280$	−1.25049e13	−0.434221
$281$	−1.11107e13	−0.378319	−0.189159	−	0.981946i	$-0.560576\pi$
$281$	−1.11107e13	−0.378319	−0.189159	+	0.981946i	$0.560576\pi$
$282$	3.04328e12	0.101618
$283$	2.58545e13	0.846664	0.423332	−	0.905975i	$-0.360860\pi$
$283$	2.58545e13	0.846664	0.423332	+	0.905975i	$0.360860\pi$
$284$	4.18143e13	1.34299
$285$	−4.57059e13	−1.43988
$286$	9.71778e11	0.0300299
$287$	−2.72142e13	−0.824983
$288$	8.87756e12	0.264019
$289$	−2.65197e13	−0.773803
$290$	6.97908e12	0.199806
$291$	3.73256e13	1.04857
$292$	5.07669e13	1.39951
$293$	2.80373e13	0.758514	0.379257	−	0.925291i	$-0.376180\pi$
$293$	2.80373e13	0.758514	0.379257	+	0.925291i	$0.376180\pi$
$294$	−5.22321e12	−0.138684
$295$	8.58097e12	0.223622
$296$	−1.38132e13	−0.353339
$297$	3.95688e12	0.0993557
$298$	−4.50477e11	−0.0111041
$299$	−1.43788e13	−0.347962
$300$	−4.31637e13	−1.02554
$301$	−9.67418e12	−0.225683
$302$	−1.49719e13	−0.342957
$303$	−2.90745e13	−0.654000
$304$	4.86479e13	1.07463
$305$	−7.16614e13	−1.55466
$306$	2.22310e12	0.0473686
$307$	−6.77354e13	−1.41760	−0.708802	−	0.705408i	$-0.750764\pi$
$307$	−6.77354e13	−1.41760	−0.708802	+	0.705408i	$0.750764\pi$
$308$	1.01273e13	0.208192
$309$	4.70062e12	0.0949257
$310$	−2.23231e12	−0.0442860
$311$	−7.60898e13	−1.48301	−0.741506	−	0.670947i	$-0.765888\pi$
$311$	−7.60898e13	−1.48301	−0.741506	+	0.670947i	$0.765888\pi$
$312$	−3.35094e12	−0.0641677
$313$	7.52366e13	1.41558	0.707791	−	0.706422i	$-0.249692\pi$
$313$	7.52366e13	1.41558	0.707791	+	0.706422i	$0.249692\pi$
$314$	2.28105e13	0.421717
$315$	1.39550e13	0.253526
$316$	4.89353e13	0.873661
$317$	−7.02133e13	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$317$	−7.02133e13	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$318$	−1.68032e13	−0.289762
$319$	−1.18583e13	−0.200990
$320$	5.19098e13	0.864817
$321$	−5.94192e13	−0.973081
$322$	1.46893e13	0.236480
$323$	4.36317e13	0.690538
$324$	−6.50342e12	−0.101191
$325$	2.48196e13	0.379697
$326$	−1.02647e13	−0.154401
$327$	4.08172e13	0.603713
$328$	−7.31332e13	−1.06367
$329$	−1.82366e13	−0.260836
$330$	−1.08755e13	−0.152976
$331$	1.01064e14	1.39812	0.699058	−	0.715065i	$-0.253603\pi$
$331$	1.01064e14	1.39812	0.699058	+	0.715065i	$0.253603\pi$
$332$	7.47047e13	1.01646
$333$	1.54151e13	0.206302
$334$	5.75968e12	0.0758216
$335$	−1.22825e14	−1.59052
$336$	−1.48533e13	−0.189216
$337$	−1.51730e13	−0.190155	−0.0950776	−	0.995470i	$-0.530310\pi$
$337$	−1.51730e13	−0.190155	−0.0950776	+	0.995470i	$0.530310\pi$
$338$	−2.33148e13	−0.287468
$339$	6.61578e13	0.802570
$340$	6.23311e13	0.743996
$341$	3.79297e12	0.0445483
$342$	1.25123e13	0.144608
$343$	7.02330e13	0.798773
$344$	−2.59976e13	−0.290979
$345$	1.60919e14	1.77257
$346$	−2.88436e13	−0.312702
$347$	−1.73746e14	−1.85397	−0.926985	−	0.375099i	$-0.877609\pi$
$347$	−1.73746e14	−1.85397	−0.926985	+	0.375099i	$0.877609\pi$
$348$	1.94900e13	0.204703
$349$	−1.91317e13	−0.197794	−0.0988972	−	0.995098i	$-0.531532\pi$
$349$	−1.91317e13	−0.197794	−0.0988972	+	0.995098i	$0.531532\pi$
$350$	−2.53555e13	−0.258046
$351$	3.73954e12	0.0374653
$352$	4.14587e13	0.408913
$353$	1.50374e14	1.46020	0.730098	−	0.683342i	$-0.239474\pi$
$353$	1.50374e14	1.46020	0.730098	+	0.683342i	$0.239474\pi$
$354$	−2.34909e12	−0.0224586
$355$	2.69082e14	2.53296
$356$	−1.13103e14	−1.04833
$357$	−1.33217e13	−0.121587
$358$	3.06547e13	0.275512
$359$	1.51510e14	1.34097	0.670487	−	0.741921i	$-0.266085\pi$
$359$	1.51510e14	1.34097	0.670487	+	0.741921i	$0.266085\pi$
$360$	3.75016e13	0.326879
$361$	1.29082e14	1.10809
$362$	−5.39635e12	−0.0456250
$363$	−5.08519e13	−0.423468
$364$	9.57101e12	0.0785055
$365$	3.26693e14	2.63955
$366$	1.96177e13	0.156136
$367$	−3.23653e13	−0.253756	−0.126878	−	0.991918i	$-0.540496\pi$
$367$	−3.23653e13	−0.253756	−0.126878	+	0.991918i	$0.540496\pi$
$368$	−1.71277e14	−1.32293
$369$	8.16142e13	0.621041
$370$	−4.23686e13	−0.317640
$371$	1.00692e14	0.743767
$372$	−6.23402e12	−0.0453714
$373$	−9.05386e12	−0.0649285	−0.0324642	−	0.999473i	$-0.510336\pi$
$373$	−9.05386e12	−0.0649285	−0.0324642	+	0.999473i	$0.510336\pi$
$374$	1.03820e13	0.0733646
$375$	−1.35352e14	−0.942524
$376$	−4.90076e13	−0.336303
$377$	−1.12069e13	−0.0757896
$378$	−3.82028e12	−0.0254618
$379$	−2.36249e14	−1.55186	−0.775932	−	0.630816i	$-0.782720\pi$
$379$	−2.36249e14	−1.55186	−0.775932	+	0.630816i	$0.782720\pi$
$380$	3.50818e14	2.27129
$381$	−6.96320e13	−0.444346
$382$	3.46570e13	0.217993
$383$	2.62138e13	0.162531	0.0812657	−	0.996692i	$-0.474104\pi$
$383$	2.62138e13	0.162531	0.0812657	+	0.996692i	$0.474104\pi$
$384$	−8.90305e13	−0.544148
$385$	6.51708e13	0.392662
$386$	1.97166e13	0.117112
$387$	2.90124e13	0.169892
$388$	−2.86495e14	−1.65403
$389$	1.45020e14	0.825476	0.412738	−	0.910850i	$-0.364573\pi$
$389$	1.45020e14	0.825476	0.412738	+	0.910850i	$0.364573\pi$
$390$	−1.02782e13	−0.0576846
$391$	−1.53616e14	−0.850090
$392$	8.41123e13	0.458972
$393$	3.58012e13	0.192637
$394$	3.65847e12	0.0194120
$395$	3.14907e14	1.64777
$396$	−3.03713e13	−0.156726
$397$	2.53779e14	1.29154	0.645771	−	0.763531i	$-0.276536\pi$
$397$	2.53779e14	1.29154	0.645771	+	0.763531i	$0.276536\pi$
$398$	−1.61037e13	−0.0808292
$399$	−7.49788e13	−0.371182
$400$	2.95645e14	1.44358
$401$	−1.23162e14	−0.593173	−0.296587	−	0.955006i	$-0.595848\pi$
$401$	−1.23162e14	−0.593173	−0.296587	+	0.955006i	$0.595848\pi$
$402$	3.36239e13	0.159737
$403$	3.58463e12	0.0167983
$404$	2.23163e14	1.03163
$405$	−4.18506e13	−0.190853
$406$	1.14489e13	0.0515075
$407$	7.19895e13	0.319521
$408$	−3.57997e13	−0.156765
$409$	8.02377e13	0.346657	0.173329	−	0.984864i	$-0.444548\pi$
$409$	8.02377e13	0.346657	0.173329	+	0.984864i	$0.444548\pi$
$410$	−2.24317e14	−0.956207
$411$	2.53870e14	1.06778
$412$	−3.60799e13	−0.149738
$413$	1.40767e13	0.0576470
$414$	−4.40526e13	−0.178020
$415$	4.80737e14	1.91709
$416$	3.91814e13	0.154194
$417$	−1.51303e14	−0.587624
$418$	5.84329e13	0.223969
$419$	2.61467e14	0.989099	0.494550	−	0.869149i	$-0.335333\pi$
$419$	2.61467e14	0.989099	0.494550	+	0.869149i	$0.335333\pi$
$420$	−1.07113e14	−0.399917
$421$	−1.48199e14	−0.546127	−0.273064	−	0.961996i	$-0.588037\pi$
$421$	−1.48199e14	−0.546127	−0.273064	+	0.961996i	$0.588037\pi$
$422$	−7.05877e13	−0.256750
$423$	5.46909e13	0.196355
$424$	2.70591e14	0.958960
$425$	2.65160e14	0.927618
$426$	−7.36628e13	−0.254387
$427$	−1.17558e14	−0.400772
$428$	4.56076e14	1.53496
$429$	1.74638e13	0.0580263
$430$	−7.97410e13	−0.261580
$431$	−2.49802e14	−0.809042	−0.404521	−	0.914529i	$-0.632562\pi$
$431$	−2.49802e14	−0.809042	−0.404521	+	0.914529i	$0.632562\pi$
$432$	4.45444e13	0.142440
$433$	3.87508e13	0.122348	0.0611740	−	0.998127i	$-0.480516\pi$
$433$	3.87508e13	0.122348	0.0611740	+	0.998127i	$0.480516\pi$
$434$	−3.66203e12	−0.0114164
$435$	1.25421e14	0.386082
$436$	−3.13295e14	−0.952308
$437$	−8.64599e14	−2.59518
$438$	−8.94342e13	−0.265092
$439$	−2.17907e14	−0.637847	−0.318923	−	0.947781i	$-0.603321\pi$
$439$	−2.17907e14	−0.637847	−0.318923	+	0.947781i	$0.603321\pi$
$440$	1.75135e14	0.506270
$441$	−9.38665e13	−0.267977
$442$	9.81171e12	0.0276645
$443$	−3.80522e14	−1.05964	−0.529821	−	0.848109i	$-0.677741\pi$
$443$	−3.80522e14	−1.05964	−0.529821	+	0.848109i	$0.677741\pi$
$444$	−1.18320e14	−0.325425
$445$	−7.27837e14	−1.97721
$446$	−5.49723e12	−0.0147503
$447$	−8.09552e12	−0.0214562
$448$	8.51560e13	0.222939
$449$	−2.61303e14	−0.675754	−0.337877	−	0.941190i	$-0.609709\pi$
$449$	−2.61303e14	−0.675754	−0.337877	+	0.941190i	$0.609709\pi$
$450$	7.60401e13	0.194256
$451$	3.81143e14	0.961871
$452$	−5.07798e14	−1.26599
$453$	−2.69061e14	−0.662690
$454$	−6.43182e13	−0.156504
$455$	6.15910e13	0.148066
$456$	−2.01492e14	−0.478576
$457$	−1.74585e14	−0.409702	−0.204851	−	0.978793i	$-0.565671\pi$
$457$	−1.74585e14	−0.409702	−0.204851	+	0.978793i	$0.565671\pi$
$458$	8.89649e13	0.206281
$459$	3.99513e13	0.0915295
$460$	−1.23514e15	−2.79608
$461$	−1.56304e14	−0.349636	−0.174818	−	0.984601i	$-0.555934\pi$
$461$	−1.56304e14	−0.349636	−0.174818	+	0.984601i	$0.555934\pi$
$462$	−1.78409e13	−0.0394354
$463$	−2.02023e14	−0.441272	−0.220636	−	0.975356i	$-0.570813\pi$
$463$	−2.02023e14	−0.441272	−0.220636	+	0.975356i	$0.570813\pi$
$464$	−1.33494e14	−0.288147
$465$	−4.01170e13	−0.0855730
$466$	−2.19555e14	−0.462830
$467$	5.86324e14	1.22150	0.610752	−	0.791822i	$-0.290867\pi$
$467$	5.86324e14	1.22150	0.610752	+	0.791822i	$0.290867\pi$
$468$	−2.87030e13	−0.0590984
$469$	−2.01489e14	−0.410016
$470$	−1.50318e14	−0.302325
$471$	4.09927e14	0.814876
$472$	3.78287e13	0.0743260
$473$	1.35490e14	0.263130
$474$	−8.62076e13	−0.165487
$475$	1.49240e15	2.83186
$476$	1.02252e14	0.191793
$477$	−3.01970e14	−0.559903
$478$	4.18573e13	0.0767217
$479$	2.05544e14	0.372442	0.186221	−	0.982508i	$-0.440376\pi$
$479$	2.05544e14	0.372442	0.186221	+	0.982508i	$0.440376\pi$
$480$	−4.38494e14	−0.785483
$481$	6.80351e13	0.120486
$482$	−2.36183e12	−0.00413513
$483$	2.63982e14	0.456945
$484$	3.90317e14	0.667986
$485$	−1.84364e15	−3.11959
$486$	1.14568e13	0.0191675
$487$	3.73028e14	0.617066	0.308533	−	0.951214i	$-0.400162\pi$
$487$	3.73028e14	0.617066	0.308533	+	0.951214i	$0.400162\pi$
$488$	−3.15915e14	−0.516727
$489$	−1.84468e14	−0.298347
$490$	2.57993e14	0.412600
$491$	−9.58708e14	−1.51614	−0.758068	−	0.652176i	$-0.773856\pi$
$491$	−9.58708e14	−1.51614	−0.758068	+	0.652176i	$0.773856\pi$
$492$	−6.26435e14	−0.979643
$493$	−1.19729e14	−0.185158
$494$	5.52233e13	0.0844547
$495$	−1.95444e14	−0.295593
$496$	4.26992e13	0.0638661
$497$	4.41418e14	0.652966
$498$	−1.31605e14	−0.192535
$499$	−4.42684e14	−0.640532	−0.320266	−	0.947328i	$-0.603772\pi$
$499$	−4.42684e14	−0.640532	−0.320266	+	0.947328i	$0.603772\pi$
$500$	1.03890e15	1.48675
$501$	1.03507e14	0.146509
$502$	1.82501e14	0.255502
$503$	−7.53097e14	−1.04286	−0.521431	−	0.853293i	$-0.674602\pi$
$503$	−7.53097e14	−1.04286	−0.521431	+	0.853293i	$0.674602\pi$
$504$	6.15200e13	0.0842652
$505$	1.43609e15	1.94572
$506$	−2.05728e14	−0.275718
$507$	−4.18990e14	−0.555470
$508$	5.34465e14	0.700920
$509$	8.61451e12	0.0111759	0.00558795	−	0.999984i	$-0.498221\pi$
$509$	8.61451e12	0.0111759	0.00558795	+	0.999984i	$0.498221\pi$
$510$	−1.09807e14	−0.140926
$511$	5.35928e14	0.680442
$512$	8.03126e14	1.00879
$513$	2.24858e14	0.279424
$514$	−3.00471e14	−0.369408
$515$	−2.32180e14	−0.282414
$516$	−2.22687e14	−0.267992
$517$	2.55409e14	0.304116
$518$	−6.95041e13	−0.0818835
$519$	−5.18348e14	−0.604228
$520$	1.65515e14	0.190905
$521$	−1.10177e15	−1.25743	−0.628716	−	0.777635i	$-0.716419\pi$
$521$	−1.10177e15	−1.25743	−0.628716	+	0.777635i	$0.716419\pi$
$522$	−3.43348e13	−0.0387745
$523$	−7.11378e14	−0.794952	−0.397476	−	0.917613i	$-0.630114\pi$
$523$	−7.11378e14	−0.794952	−0.397476	+	0.917613i	$0.630114\pi$
$524$	−2.74795e14	−0.303869
$525$	−4.55664e14	−0.498619
$526$	−5.03462e14	−0.545186
$527$	3.82964e13	0.0410392
$528$	2.08025e14	0.220612
$529$	2.09123e15	2.19480
$530$	8.29968e14	0.862073
$531$	−4.22156e13	−0.0433963
$532$	5.75504e14	0.585510
$533$	3.60207e14	0.362704
$534$	1.99250e14	0.198573
$535$	2.93492e15	2.89502
$536$	−5.41465e14	−0.528645
$537$	5.50896e14	0.532367
$538$	3.04052e14	0.290834
$539$	−4.38362e14	−0.415044
$540$	3.21227e14	0.301055
$541$	−1.15844e14	−0.107470	−0.0537351	−	0.998555i	$-0.517113\pi$
$541$	−1.15844e14	−0.107470	−0.0537351	+	0.998555i	$0.517113\pi$
$542$	1.03403e14	0.0949589
$543$	−9.69779e13	−0.0881604
$544$	4.18594e14	0.376703
$545$	−2.01610e15	−1.79611
$546$	−1.68609e13	−0.0148704
$547$	−3.52231e14	−0.307537	−0.153769	−	0.988107i	$-0.549141\pi$
$547$	−3.52231e14	−0.307537	−0.153769	+	0.988107i	$0.549141\pi$
$548$	−1.94859e15	−1.68433
$549$	3.52550e14	0.301699
$550$	3.55111e14	0.300864
$551$	−6.73873e14	−0.565254
$552$	7.09402e14	0.589152
$553$	5.16592e14	0.424776
$554$	−4.74506e14	−0.386312
$555$	−7.61407e14	−0.613770
$556$	1.16134e15	0.926930
$557$	−2.35408e15	−1.86045	−0.930224	−	0.366992i	$-0.880388\pi$
$557$	−2.35408e15	−1.86045	−0.930224	+	0.366992i	$0.880388\pi$
$558$	1.09823e13	0.00859416
$559$	1.28047e14	0.0992215
$560$	7.33657e14	0.562936
$561$	1.86575e14	0.141761
$562$	−1.50237e14	−0.113039
$563$	−2.47912e15	−1.84714	−0.923572	−	0.383424i	$-0.874745\pi$
$563$	−2.47912e15	−1.84714	−0.923572	+	0.383424i	$0.874745\pi$
$564$	−4.19783e14	−0.309735
$565$	−3.26777e15	−2.38773
$566$	3.49599e14	0.252976
$567$	−6.86542e13	−0.0491995
$568$	1.18623e15	0.841887
$569$	1.55307e15	1.09163	0.545814	−	0.837906i	$-0.316221\pi$
$569$	1.55307e15	1.09163	0.545814	+	0.837906i	$0.316221\pi$
$570$	−6.18025e14	−0.430224
$571$	1.84361e15	1.27107	0.635537	−	0.772071i	$-0.280779\pi$
$571$	1.84361e15	1.27107	0.635537	+	0.772071i	$0.280779\pi$
$572$	−1.34045e14	−0.0915318
$573$	6.22822e14	0.421224
$574$	−3.67984e14	−0.246498
$575$	−5.25438e15	−3.48617
$576$	−2.55379e14	−0.167827
$577$	−2.95570e15	−1.92395	−0.961973	−	0.273145i	$-0.911936\pi$
$577$	−2.95570e15	−1.92395	−0.961973	+	0.273145i	$0.911936\pi$
$578$	−3.58594e14	−0.231206
$579$	3.54328e14	0.226294
$580$	−9.62678e14	−0.609014
$581$	7.88631e14	0.494202
$582$	5.04709e14	0.313303
$583$	−1.41022e15	−0.867179
$584$	1.44021e15	0.877313
$585$	−1.84709e14	−0.111463
$586$	3.79114e14	0.226638
$587$	−1.49815e15	−0.887252	−0.443626	−	0.896212i	$-0.646308\pi$
$587$	−1.49815e15	−0.887252	−0.443626	+	0.896212i	$0.646308\pi$
$588$	7.20478e14	0.422713
$589$	2.15544e14	0.125286
$590$	1.16030e14	0.0668165
$591$	6.57465e13	0.0375095
$592$	8.10417e14	0.458078
$593$	5.87200e14	0.328841	0.164420	−	0.986390i	$-0.447425\pi$
$593$	5.87200e14	0.328841	0.164420	+	0.986390i	$0.447425\pi$
$594$	5.35041e13	0.0296867
$595$	6.58007e14	0.361732
$596$	6.21377e13	0.0338455
$597$	−2.89399e14	−0.156185
$598$	−1.94427e14	−0.103968
$599$	−1.76609e15	−0.935764	−0.467882	−	0.883791i	$-0.654983\pi$
$599$	−1.76609e15	−0.935764	−0.467882	+	0.883791i	$0.654983\pi$
$600$	−1.22451e15	−0.642883
$601$	2.22109e15	1.15546	0.577732	−	0.816226i	$-0.303938\pi$
$601$	2.22109e15	1.15546	0.577732	+	0.816226i	$0.303938\pi$
$602$	−1.30812e14	−0.0674321
$603$	6.04256e14	0.308657
$604$	2.06519e15	1.04534
$605$	2.51175e15	1.25986
$606$	−3.93138e14	−0.195410
$607$	1.63236e15	0.804042	0.402021	−	0.915630i	$-0.368308\pi$
$607$	1.63236e15	0.804042	0.402021	+	0.915630i	$0.368308\pi$
$608$	2.35597e15	1.15001
$609$	2.05749e14	0.0995272
$610$	−9.68989e14	−0.464520
$611$	2.41380e14	0.114677
$612$	−3.06649e14	−0.144380
$613$	−3.89084e15	−1.81556	−0.907779	−	0.419448i	$-0.862224\pi$
$613$	−3.89084e15	−1.81556	−0.907779	+	0.419448i	$0.862224\pi$
$614$	−9.15903e14	−0.423568
$615$	−4.03121e15	−1.84766
$616$	2.87302e14	0.130510
$617$	−9.90339e14	−0.445878	−0.222939	−	0.974832i	$-0.571565\pi$
$617$	−9.90339e14	−0.445878	−0.222939	+	0.974832i	$0.571565\pi$
$618$	6.35608e13	0.0283630
$619$	2.76711e15	1.22385	0.611925	−	0.790916i	$-0.290396\pi$
$619$	2.76711e15	1.22385	0.611925	+	0.790916i	$0.290396\pi$
$620$	3.07920e14	0.134984
$621$	−7.91669e14	−0.343985
$622$	−1.02887e15	−0.443112
$623$	−1.19399e15	−0.509701
$624$	1.96598e14	0.0831887
$625$	2.03536e15	0.853693
$626$	1.01733e15	0.422964
$627$	1.05010e15	0.432772
$628$	−3.14642e15	−1.28540
$629$	7.26853e14	0.294353
$630$	1.88697e14	0.0757516
$631$	−2.50972e14	−0.0998768	−0.0499384	−	0.998752i	$-0.515902\pi$
$631$	−2.50972e14	−0.0998768	−0.0499384	+	0.998752i	$0.515902\pi$
$632$	1.38825e15	0.547675
$633$	−1.26853e15	−0.496114
$634$	−9.49408e14	−0.368097
$635$	3.43937e15	1.32198
$636$	2.31779e15	0.883202
$637$	−4.14283e14	−0.156506
$638$	−1.60345e14	−0.0600541
$639$	−1.32379e15	−0.491548
$640$	4.39753e15	1.61890
$641$	−3.72092e15	−1.35810	−0.679049	−	0.734093i	$-0.737607\pi$
$641$	−3.72092e15	−1.35810	−0.679049	+	0.734093i	$0.737607\pi$
$642$	−8.03453e14	−0.290749
$643$	3.78590e15	1.35834	0.679171	−	0.733980i	$-0.262339\pi$
$643$	3.78590e15	1.35834	0.679171	+	0.733980i	$0.262339\pi$
$644$	−2.02621e15	−0.720794
$645$	−1.43303e15	−0.505447
$646$	5.89977e14	0.206327
$647$	9.53679e14	0.330696	0.165348	−	0.986235i	$-0.447125\pi$
$647$	9.53679e14	0.330696	0.165348	+	0.986235i	$0.447125\pi$
$648$	−1.84496e14	−0.0634343
$649$	−1.97149e14	−0.0672123
$650$	3.35605e14	0.113450
$651$	−6.58103e13	−0.0220596
$652$	1.41589e15	0.470618
$653$	−2.88986e15	−0.952477	−0.476238	−	0.879316i	$-0.658000\pi$
$653$	−2.88986e15	−0.952477	−0.476238	+	0.879316i	$0.658000\pi$
$654$	5.51921e14	0.180384
$655$	−1.76835e15	−0.573114
$656$	4.29069e15	1.37897
$657$	−1.60722e15	−0.512232
$658$	−2.46592e14	−0.0779356
$659$	−8.02108e14	−0.251399	−0.125699	−	0.992068i	$-0.540117\pi$
$659$	−8.02108e14	−0.251399	−0.125699	+	0.992068i	$0.540117\pi$
$660$	1.50015e15	0.466275
$661$	5.04397e15	1.55476	0.777381	−	0.629030i	$-0.216548\pi$
$661$	5.04397e15	1.55476	0.777381	+	0.629030i	$0.216548\pi$
$662$	1.36657e15	0.417746
$663$	1.76326e14	0.0534556
$664$	2.11930e15	0.637189
$665$	3.70347e15	1.10431
$666$	2.08440e14	0.0616414
$667$	2.37254e15	0.695859
$668$	−7.94477e14	−0.231106
$669$	−9.87907e13	−0.0285018
$670$	−1.66081e15	−0.475234
$671$	1.64643e15	0.467272
$672$	−7.19332e14	−0.202488
$673$	1.54943e15	0.432604	0.216302	−	0.976327i	$-0.430600\pi$
$673$	1.54943e15	0.432604	0.216302	+	0.976327i	$0.430600\pi$
$674$	−2.05167e14	−0.0568168
$675$	1.36652e15	0.375357
$676$	3.21599e15	0.876208
$677$	−5.29648e15	−1.43136	−0.715682	−	0.698426i	$-0.753884\pi$
$677$	−5.29648e15	−1.43136	−0.715682	+	0.698426i	$0.753884\pi$
$678$	8.94571e14	0.239801
$679$	−3.02443e15	−0.804192
$680$	1.76827e15	0.466392
$681$	−1.15586e15	−0.302411
$682$	5.12877e13	0.0133107
$683$	3.87697e14	0.0998110	0.0499055	−	0.998754i	$-0.484108\pi$
$683$	3.87697e14	0.0998110	0.0499055	+	0.998754i	$0.484108\pi$
$684$	−1.72591e15	−0.440768
$685$	−1.25395e16	−3.17675
$686$	9.49674e14	0.238667
$687$	1.59879e15	0.398593
$688$	1.52527e15	0.377233
$689$	−1.33276e15	−0.326998
$690$	2.17591e15	0.529628
$691$	4.47093e15	1.07961	0.539807	−	0.841789i	$-0.318497\pi$
$691$	4.47093e15	1.07961	0.539807	+	0.841789i	$0.318497\pi$
$692$	3.97861e15	0.953122
$693$	−3.20619e14	−0.0762003
$694$	−2.34935e15	−0.553951
$695$	7.47340e15	1.74824
$696$	5.52912e14	0.128323
$697$	3.84827e15	0.886104
$698$	−2.58695e14	−0.0590994
$699$	−3.94563e15	−0.894318
$700$	3.49748e15	0.786531
$701$	1.29897e15	0.289835	0.144918	−	0.989444i	$-0.453708\pi$
$701$	1.29897e15	0.289835	0.144918	+	0.989444i	$0.453708\pi$
$702$	5.05652e13	0.0111943
$703$	4.09095e15	0.898607
$704$	−1.19263e15	−0.259931
$705$	−2.70138e15	−0.584177
$706$	2.03332e15	0.436295
$707$	2.35585e15	0.501581
$708$	3.24028e14	0.0684542
$709$	−1.07935e15	−0.226261	−0.113130	−	0.993580i	$-0.536088\pi$
$709$	−1.07935e15	−0.226261	−0.113130	+	0.993580i	$0.536088\pi$
$710$	3.63846e15	0.756828
$711$	−1.54924e15	−0.319768
$712$	−3.20863e15	−0.657172
$713$	−7.58875e14	−0.154233
$714$	−1.80133e14	−0.0363291
$715$	−8.62601e14	−0.172634
$716$	−4.22844e15	−0.839766
$717$	7.52219e14	0.148248
$718$	2.04868e15	0.400672
$719$	−2.21158e14	−0.0429234	−0.0214617	−	0.999770i	$-0.506832\pi$
$719$	−2.21158e14	−0.0429234	−0.0214617	+	0.999770i	$0.506832\pi$
$720$	−2.20020e15	−0.423774
$721$	−3.80883e14	−0.0728027
$722$	1.74542e15	0.331089
$723$	−4.24445e13	−0.00799025
$724$	7.44360e14	0.139066
$725$	−4.09529e15	−0.759321
$726$	−6.87607e14	−0.126529
$727$	−7.51766e14	−0.137292	−0.0686458	−	0.997641i	$-0.521868\pi$
$727$	−7.51766e14	−0.137292	−0.0686458	+	0.997641i	$0.521868\pi$
$728$	2.71521e14	0.0492130
$729$	2.05891e14	0.0370370
$730$	4.41747e15	0.788675
$731$	1.36799e15	0.242403
$732$	−2.70602e15	−0.475905
$733$	8.71820e14	0.152179	0.0760895	−	0.997101i	$-0.475757\pi$
$733$	8.71820e14	0.152179	0.0760895	+	0.997101i	$0.475757\pi$
$734$	−4.37636e14	−0.0758202
$735$	4.63640e15	0.797260
$736$	−8.29480e15	−1.41572
$737$	2.82191e15	0.478049
$738$	1.10357e15	0.185562
$739$	−5.79111e15	−0.966535	−0.483267	−	0.875473i	$-0.660550\pi$
$739$	−5.79111e15	−0.966535	−0.483267	+	0.875473i	$0.660550\pi$
$740$	5.84423e15	0.968172
$741$	9.92419e14	0.163190
$742$	1.36153e15	0.222232
$743$	5.60750e15	0.908513	0.454256	−	0.890871i	$-0.349905\pi$
$743$	5.60750e15	0.908513	0.454256	+	0.890871i	$0.349905\pi$
$744$	−1.76853e14	−0.0284421
$745$	3.99866e14	0.0638345
$746$	−1.22424e14	−0.0194001
$747$	−2.36507e15	−0.372032
$748$	−1.43207e15	−0.223617
$749$	4.81463e15	0.746299
$750$	−1.83020e15	−0.281618
$751$	8.69603e15	1.32832	0.664158	−	0.747592i	$-0.268790\pi$
$751$	8.69603e15	1.32832	0.664158	+	0.747592i	$0.268790\pi$
$752$	2.87526e15	0.435992
$753$	3.27973e15	0.493703
$754$	−1.51538e14	−0.0226453
$755$	1.32899e16	1.97157
$756$	5.26960e14	0.0776082
$757$	−7.35887e15	−1.07593	−0.537965	−	0.842967i	$-0.680807\pi$
$757$	−7.35887e15	−1.07593	−0.537965	+	0.842967i	$0.680807\pi$
$758$	−3.19450e15	−0.463684
$759$	−3.69714e15	−0.532765
$760$	9.95239e15	1.42381
$761$	−1.22298e16	−1.73702	−0.868511	−	0.495670i	$-0.834923\pi$
$761$	−1.22298e16	−1.73702	−0.868511	+	0.495670i	$0.834923\pi$
$762$	−9.41548e14	−0.132767
$763$	−3.30734e15	−0.463014
$764$	−4.78051e15	−0.664448
$765$	−1.97334e15	−0.272310
$766$	3.54457e14	0.0485630
$767$	−1.86320e14	−0.0253445
$768$	9.48480e14	0.128098
$769$	8.90388e15	1.19395	0.596973	−	0.802262i	$-0.296370\pi$
$769$	8.90388e15	1.19395	0.596973	+	0.802262i	$0.296370\pi$
$770$	8.81225e14	0.117324
$771$	−5.39978e15	−0.713800
$772$	−2.71966e15	−0.356960
$773$	−1.26441e16	−1.64778	−0.823890	−	0.566749i	$-0.808201\pi$
$773$	−1.26441e16	−1.64778	−0.823890	+	0.566749i	$0.808201\pi$
$774$	3.92300e14	0.0507624
$775$	1.30991e15	0.168299
$776$	−8.12760e15	−1.03687
$777$	−1.24906e15	−0.158222
$778$	1.96092e15	0.246645
$779$	2.16592e16	2.70512
$780$	1.41774e15	0.175824
$781$	−6.18219e15	−0.761311
$782$	−2.07716e15	−0.254000
$783$	−6.17031e14	−0.0749234
$784$	−4.93483e15	−0.595023
$785$	−2.02477e16	−2.42434
$786$	4.84096e14	0.0575582
$787$	−4.60899e15	−0.544183	−0.272091	−	0.962271i	$-0.587715\pi$
$787$	−4.60899e15	−0.544183	−0.272091	+	0.962271i	$0.587715\pi$
$788$	−5.04641e14	−0.0591682
$789$	−9.04772e15	−1.05345
$790$	4.25810e15	0.492342
$791$	−5.36064e15	−0.615526
$792$	−8.61606e14	−0.0982472
$793$	1.55599e15	0.176200
$794$	3.43155e15	0.385902
$795$	1.49154e16	1.66577
$796$	2.22130e15	0.246369
$797$	−6.16784e15	−0.679379	−0.339690	−	0.940538i	$-0.610322\pi$
$797$	−6.16784e15	−0.679379	−0.339690	+	0.940538i	$0.610322\pi$
$798$	−1.01385e15	−0.110906
$799$	2.57878e15	0.280161
$800$	1.43178e16	1.54484
$801$	3.58072e15	0.383700
$802$	−1.66536e15	−0.177235
$803$	−7.50583e15	−0.793347
$804$	−4.63801e15	−0.486881
$805$	−1.30390e16	−1.35946
$806$	4.84706e13	0.00501921
$807$	5.46412e15	0.561973
$808$	6.33092e15	0.646703
$809$	7.04742e15	0.715012	0.357506	−	0.933911i	$-0.383627\pi$
$809$	7.04742e15	0.715012	0.357506	+	0.933911i	$0.383627\pi$
$810$	−5.65894e14	−0.0570253
$811$	3.60876e15	0.361196	0.180598	−	0.983557i	$-0.442197\pi$
$811$	3.60876e15	0.361196	0.180598	+	0.983557i	$0.442197\pi$
$812$	−1.57924e15	−0.156996
$813$	1.85825e15	0.183488
$814$	9.73425e14	0.0954703
$815$	9.11151e15	0.887613
$816$	2.10035e15	0.203234
$817$	7.69948e15	0.740014
$818$	1.08496e15	0.103578
$819$	−3.03008e14	−0.0287338
$820$	3.09418e16	2.91454
$821$	−1.54106e16	−1.44189	−0.720947	−	0.692990i	$-0.756293\pi$
$821$	−1.54106e16	−1.44189	−0.720947	+	0.692990i	$0.756293\pi$
$822$	3.43277e15	0.319043
$823$	1.29390e16	1.19454	0.597272	−	0.802039i	$-0.296251\pi$
$823$	1.29390e16	1.19454	0.597272	+	0.802039i	$0.296251\pi$
$824$	−1.02355e15	−0.0938666
$825$	6.38171e15	0.581354
$826$	1.90343e14	0.0172245
$827$	7.51765e15	0.675774	0.337887	−	0.941187i	$-0.390288\pi$
$827$	7.51765e15	0.675774	0.337887	+	0.941187i	$0.390288\pi$
$828$	6.07651e15	0.542609
$829$	−6.61848e15	−0.587095	−0.293547	−	0.955945i	$-0.594836\pi$
$829$	−6.61848e15	−0.587095	−0.293547	+	0.955945i	$0.594836\pi$
$830$	6.50042e15	0.572812
$831$	−8.52736e15	−0.746464
$832$	−1.12712e15	−0.0980152
$833$	−4.42599e15	−0.382351
$834$	−2.04589e15	−0.175577
$835$	−5.11259e15	−0.435879
$836$	−8.06010e15	−0.682663
$837$	1.97362e14	0.0166064
$838$	3.53550e15	0.295535
$839$	1.22395e16	1.01642	0.508210	−	0.861233i	$-0.330307\pi$
$839$	1.22395e16	1.01642	0.508210	+	0.861233i	$0.330307\pi$
$840$	−3.03869e15	−0.250698
$841$	−1.03513e16	−0.848435
$842$	−2.00391e15	−0.163178
$843$	−2.69991e15	−0.218422
$844$	9.73671e15	0.782580
$845$	2.06954e16	1.65258
$846$	7.39518e14	0.0586694
$847$	4.12043e15	0.324776
$848$	−1.58754e16	−1.24322
$849$	6.28265e15	0.488822
$850$	3.58544e15	0.277165
$851$	−1.44032e16	−1.10623
$852$	1.01609e16	0.775377
$853$	−1.16615e16	−0.884166	−0.442083	−	0.896974i	$-0.645760\pi$
$853$	−1.16615e16	−0.884166	−0.442083	+	0.896974i	$0.645760\pi$
$854$	−1.58959e15	−0.119747
$855$	−1.11065e16	−0.831314
$856$	1.29384e16	0.962224
$857$	−2.36642e16	−1.74863	−0.874313	−	0.485363i	$-0.838687\pi$
$857$	−2.36642e16	−1.74863	−0.874313	+	0.485363i	$0.838687\pi$
$858$	2.36142e14	0.0173378
$859$	−1.04372e16	−0.761415	−0.380707	−	0.924696i	$-0.624319\pi$
$859$	−1.04372e16	−0.761415	−0.380707	+	0.924696i	$0.624319\pi$
$860$	1.09993e16	0.797302
$861$	−6.61305e15	−0.476304
$862$	−3.37777e15	−0.241735
$863$	1.50730e16	1.07187	0.535933	−	0.844261i	$-0.319960\pi$
$863$	1.50730e16	1.07187	0.535933	+	0.844261i	$0.319960\pi$
$864$	2.15725e15	0.152431
$865$	2.56030e16	1.79764
$866$	5.23979e14	0.0365566
$867$	−6.44429e15	−0.446756
$868$	5.05131e14	0.0347973
$869$	−7.23503e15	−0.495258
$870$	1.69592e15	0.115358
$871$	2.66691e15	0.180264
$872$	−8.88788e15	−0.596977
$873$	9.07013e15	0.605390
$874$	−1.16909e16	−0.775417
$875$	1.09673e16	0.722863
$876$	1.23363e16	0.808005
$877$	2.11962e16	1.37962	0.689811	−	0.723989i	$-0.257693\pi$
$877$	2.11962e16	1.37962	0.689811	+	0.723989i	$0.257693\pi$
$878$	−2.94649e15	−0.190583
$879$	6.81306e15	0.437929
$880$	−1.02751e16	−0.656342
$881$	−2.88353e16	−1.83045	−0.915223	−	0.402947i	$-0.867986\pi$
$881$	−2.88353e16	−1.83045	−0.915223	+	0.402947i	$0.867986\pi$
$882$	−1.26924e15	−0.0800695
$883$	−1.45222e16	−0.910433	−0.455217	−	0.890381i	$-0.650438\pi$
$883$	−1.45222e16	−0.910433	−0.455217	+	0.890381i	$0.650438\pi$
$884$	−1.35340e15	−0.0843218
$885$	2.08518e15	0.129108
$886$	−5.14533e15	−0.316612
$887$	−1.17547e16	−0.718838	−0.359419	−	0.933176i	$-0.617025\pi$
$887$	−1.17547e16	−0.718838	−0.359419	+	0.933176i	$0.617025\pi$
$888$	−3.35662e15	−0.204000
$889$	5.64215e15	0.340789
$890$	−9.84164e15	−0.590775
$891$	9.61523e14	0.0573631
$892$	7.58274e14	0.0449593
$893$	1.45142e16	0.855281
$894$	−1.09466e14	−0.00641095
$895$	−2.72107e16	−1.58385
$896$	7.21398e15	0.417331
$897$	−3.49406e15	−0.200896
$898$	−3.53327e15	−0.201910
$899$	−5.91471e14	−0.0335935
$900$	−1.04888e16	−0.592095
$901$	−1.42385e16	−0.798872
$902$	5.15372e15	0.287399
$903$	−2.35082e15	−0.130298
$904$	−1.44058e16	−0.793615
$905$	4.79008e15	0.262286
$906$	−3.63818e15	−0.198006
$907$	−1.11488e16	−0.603100	−0.301550	−	0.953450i	$-0.597504\pi$
$907$	−1.11488e16	−0.603100	−0.301550	+	0.953450i	$0.597504\pi$
$908$	8.87190e15	0.477029
$909$	−7.06510e15	−0.377587
$910$	8.32820e14	0.0442409
$911$	2.30479e16	1.21697	0.608485	−	0.793565i	$-0.291777\pi$
$911$	2.30479e16	1.21697	0.608485	+	0.793565i	$0.291777\pi$
$912$	1.18214e16	0.620438
$913$	−1.10450e16	−0.576204
$914$	−2.36070e15	−0.122416
$915$	−1.74137e16	−0.897584
$916$	−1.22716e16	−0.628748
$917$	−2.90091e15	−0.147742
$918$	5.40212e14	0.0273483
$919$	2.16392e15	0.108895	0.0544473	−	0.998517i	$-0.482660\pi$
$919$	2.16392e15	0.108895	0.0544473	+	0.998517i	$0.482660\pi$
$920$	−3.50399e16	−1.75279
$921$	−1.64597e16	−0.818454
$922$	−2.11351e15	−0.104468
$923$	−5.84261e15	−0.287077
$924$	2.46093e15	0.120200
$925$	2.48617e16	1.20712
$926$	−2.73172e15	−0.131848
$927$	1.14225e15	0.0548054
$928$	−6.46501e15	−0.308358
$929$	8.94797e15	0.424266	0.212133	−	0.977241i	$-0.431959\pi$
$929$	8.94797e15	0.424266	0.212133	+	0.977241i	$0.431959\pi$
$930$	−5.42452e14	−0.0255685
$931$	−2.49108e16	−1.16725
$932$	3.02849e16	1.41072
$933$	−1.84898e16	−0.856217
$934$	7.92814e15	0.364975
$935$	−9.21558e15	−0.421754
$936$	−8.14278e14	−0.0370472
$937$	−3.28664e15	−0.148657	−0.0743283	−	0.997234i	$-0.523681\pi$
$937$	−3.28664e15	−0.148657	−0.0743283	+	0.997234i	$0.523681\pi$
$938$	−2.72449e15	−0.122509
$939$	1.82825e16	0.817287
$940$	2.07346e16	0.921493
$941$	−4.18818e15	−0.185047	−0.0925235	−	0.995710i	$-0.529493\pi$
$941$	−4.18818e15	−0.185047	−0.0925235	+	0.995710i	$0.529493\pi$
$942$	5.54294e15	0.243478
$943$	−7.62567e16	−3.33015
$944$	−2.21939e15	−0.0963581
$945$	3.39108e15	0.146374
$946$	1.83206e15	0.0786210
$947$	−2.66126e16	−1.13543	−0.567717	−	0.823223i	$-0.692173\pi$
$947$	−2.66126e16	−1.13543	−0.567717	+	0.823223i	$0.692173\pi$
$948$	1.18913e16	0.504409
$949$	−7.09354e15	−0.299157
$950$	2.01799e16	0.846135
$951$	−1.70618e16	−0.711267
$952$	2.90079e15	0.120230
$953$	−2.30224e16	−0.948723	−0.474362	−	0.880330i	$-0.657321\pi$
$953$	−2.30224e16	−0.948723	−0.474362	+	0.880330i	$0.657321\pi$
$954$	−4.08317e15	−0.167294
$955$	−3.07634e16	−1.25319
$956$	−5.77370e15	−0.233849
$957$	−2.88157e15	−0.116041
$958$	2.77932e15	0.111283
$959$	−2.05706e16	−0.818926
$960$	1.26141e16	0.499302
$961$	−2.52193e16	−0.992554
$962$	9.19956e14	0.0360001
$963$	−1.44389e16	−0.561809
$964$	3.25785e14	0.0126040
$965$	−1.75015e16	−0.673248
$966$	3.56950e15	0.136532
$967$	3.88914e16	1.47914	0.739568	−	0.673082i	$-0.235030\pi$
$967$	3.88914e16	1.47914	0.739568	+	0.673082i	$0.235030\pi$
$968$	1.10729e16	0.418743
$969$	1.06025e16	0.398683
$970$	−2.49293e16	−0.932108
$971$	−1.59903e16	−0.594500	−0.297250	−	0.954800i	$-0.596069\pi$
$971$	−1.59903e16	−0.594500	−0.297250	+	0.954800i	$0.596069\pi$
$972$	−1.58033e15	−0.0584229
$973$	1.22598e16	0.450675
$974$	5.04400e15	0.184374
$975$	6.03117e15	0.219218
$976$	1.85346e16	0.669898
$977$	1.52326e16	0.547461	0.273731	−	0.961806i	$-0.411742\pi$
$977$	1.52326e16	0.547461	0.273731	+	0.961806i	$0.411742\pi$
$978$	−2.49433e15	−0.0891436
$979$	1.67221e16	0.594275
$980$	−3.55869e16	−1.25761
$981$	9.91857e15	0.348554
$982$	−1.29634e16	−0.453009
$983$	1.62788e16	0.565689	0.282845	−	0.959166i	$-0.408722\pi$
$983$	1.62788e16	0.565689	0.282845	+	0.959166i	$0.408722\pi$
$984$	−1.77714e16	−0.614112
$985$	−3.24745e15	−0.111595
$986$	−1.61895e15	−0.0553236
$987$	−4.43150e15	−0.150594
$988$	−7.61737e15	−0.257420
$989$	−2.71079e16	−0.910997
$990$	−2.64276e15	−0.0883209
$991$	−4.42759e16	−1.47151	−0.735753	−	0.677250i	$-0.763171\pi$
$991$	−4.42759e16	−1.47151	−0.735753	+	0.677250i	$0.763171\pi$
$992$	2.06789e15	0.0683459
$993$	2.45586e16	0.807203
$994$	5.96876e15	0.195101
$995$	1.42945e16	0.464666
$996$	1.81532e16	0.586851
$997$	−3.68966e16	−1.18621	−0.593107	−	0.805123i	$-0.702099\pi$
$997$	−3.68966e16	−1.18621	−0.593107	+	0.805123i	$0.702099\pi$
$998$	−5.98587e15	−0.191386
$999$	3.74587e15	0.119109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.17	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.17	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} -162297. q^{10} +275762. q^{11} -453234. q^{12} +260615. q^{13} -266242. q^{14} -2.91664e6 q^{15} +3.10438e6 q^{16} +2.78427e6 q^{17} +798447. q^{18} +1.56707e7 q^{19} +2.23868e7 q^{20} -4.78463e6 q^{21} +3.72879e6 q^{22} -5.51728e7 q^{23} -1.28578e7 q^{24} +9.52349e7 q^{25} +3.52397e6 q^{26} +1.43489e7 q^{27} +3.67247e7 q^{28} -4.30019e7 q^{29} -3.94381e7 q^{30} +1.37545e7 q^{31} +1.50342e8 q^{32} +6.70102e7 q^{33} +3.76483e7 q^{34} +2.36330e8 q^{35} -1.10136e8 q^{36} +2.61056e8 q^{37} +2.11896e8 q^{38} +6.33294e7 q^{39} +6.35094e8 q^{40} +1.38214e9 q^{41} -6.46967e7 q^{42} +4.91328e8 q^{43} -5.14341e8 q^{44} -7.08743e8 q^{45} -7.46034e8 q^{46} +9.26195e8 q^{47} +7.54363e8 q^{48} -1.58964e9 q^{49} +1.28774e9 q^{50} +6.76579e8 q^{51} -4.86089e8 q^{52} -5.11389e9 q^{53} +1.94023e8 q^{54} -3.30987e9 q^{55} +1.04185e9 q^{56} +3.80799e9 q^{57} -5.81463e8 q^{58} -7.14924e8 q^{59} +5.44000e9 q^{60} +5.97047e9 q^{61} +1.85985e8 q^{62} -1.16267e9 q^{63} -4.32487e9 q^{64} -3.12806e9 q^{65} +9.06096e8 q^{66} +1.02331e10 q^{67} -5.19312e9 q^{68} -1.34070e10 q^{69} +3.19560e9 q^{70} -2.24186e10 q^{71} -3.12445e9 q^{72} -2.72185e10 q^{73} +3.52995e9 q^{74} +2.31421e10 q^{75} -2.92285e10 q^{76} -5.42971e9 q^{77} +8.56325e8 q^{78} -2.62365e10 q^{79} -3.72607e10 q^{80} +3.48678e9 q^{81} +1.86890e10 q^{82} -4.00527e10 q^{83} +8.92411e9 q^{84} -3.34186e10 q^{85} +6.64363e9 q^{86} -1.04495e10 q^{87} -1.45914e10 q^{88} +6.06398e10 q^{89} -9.58346e9 q^{90} -5.13146e9 q^{91} +1.02906e11 q^{92} +3.34235e9 q^{93} +1.25238e10 q^{94} -1.88090e11 q^{95} +3.65332e10 q^{96} +1.53603e11 q^{97} -2.14947e10 q^{98} +1.62835e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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