LMFDB - Embedded newform 177.12.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-19.9033 q^{2} +243.000 q^{3} -1651.86 q^{4} +11169.4 q^{5} -4836.50 q^{6} -27660.5 q^{7} +73639.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-19.9033 q^{2} +243.000 q^{3} -1651.86 q^{4} +11169.4 q^{5} -4836.50 q^{6} -27660.5 q^{7} +73639.4 q^{8} +59049.0 q^{9} -222307. q^{10} -1.04155e6 q^{11} -401402. q^{12} +162421. q^{13} +550535. q^{14} +2.71416e6 q^{15} +1.91734e6 q^{16} +6.41060e6 q^{17} -1.17527e6 q^{18} +1.86314e7 q^{19} -1.84502e7 q^{20} -6.72150e6 q^{21} +2.07302e7 q^{22} -5.10201e7 q^{23} +1.78944e7 q^{24} +7.59268e7 q^{25} -3.23270e6 q^{26} +1.43489e7 q^{27} +4.56912e7 q^{28} -2.37753e6 q^{29} -5.40207e7 q^{30} -2.59764e8 q^{31} -1.88975e8 q^{32} -2.53096e8 q^{33} -1.27592e8 q^{34} -3.08950e8 q^{35} -9.75406e7 q^{36} +1.23520e8 q^{37} -3.70826e8 q^{38} +3.94682e7 q^{39} +8.22506e8 q^{40} +1.74139e8 q^{41} +1.33780e8 q^{42} -1.00184e9 q^{43} +1.72049e9 q^{44} +6.59540e8 q^{45} +1.01547e9 q^{46} +1.25095e9 q^{47} +4.65914e8 q^{48} -1.21222e9 q^{49} -1.51119e9 q^{50} +1.55777e9 q^{51} -2.68296e8 q^{52} +1.52944e9 q^{53} -2.85590e8 q^{54} -1.16334e10 q^{55} -2.03690e9 q^{56} +4.52742e9 q^{57} +4.73207e7 q^{58} -7.14924e8 q^{59} -4.48341e9 q^{60} +6.43509e9 q^{61} +5.17015e9 q^{62} -1.63332e9 q^{63} -1.65494e8 q^{64} +1.81414e9 q^{65} +5.03745e9 q^{66} -1.91932e9 q^{67} -1.05894e10 q^{68} -1.23979e10 q^{69} +6.14913e9 q^{70} -1.22406e10 q^{71} +4.34833e9 q^{72} +2.33155e10 q^{73} -2.45845e9 q^{74} +1.84502e10 q^{75} -3.07764e10 q^{76} +2.88097e10 q^{77} -7.85547e8 q^{78} -1.85989e10 q^{79} +2.14155e10 q^{80} +3.48678e9 q^{81} -3.46593e9 q^{82} +3.10782e10 q^{83} +1.11030e10 q^{84} +7.16024e10 q^{85} +1.99398e10 q^{86} -5.77740e8 q^{87} -7.66989e10 q^{88} -1.78818e10 q^{89} -1.31270e10 q^{90} -4.49263e9 q^{91} +8.42781e10 q^{92} -6.31226e10 q^{93} -2.48981e10 q^{94} +2.08101e11 q^{95} -4.59209e10 q^{96} -1.24517e11 q^{97} +2.41272e10 q^{98} -6.15024e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.9033	−0.439805	−0.219902	−	0.975522i	$-0.570574\pi$
$2$	−19.9033	−0.439805	−0.219902	+	0.975522i	$0.570574\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1651.86	−0.806572
$5$	11169.4	1.59843	0.799215	−	0.601045i	$-0.205249\pi$
$5$	11169.4	1.59843	0.799215	+	0.601045i	$0.205249\pi$
$6$	−4836.50	−0.253921
$7$	−27660.5	−0.622043	−0.311022	−	0.950403i	$-0.600671\pi$
$7$	−27660.5	−0.622043	−0.311022	+	0.950403i	$0.600671\pi$
$8$	73639.4	0.794539
$9$	59049.0	0.333333
$10$	−222307.	−0.702998
$11$	−1.04155e6	−1.94993	−0.974966	−	0.222353i	$-0.928626\pi$
$11$	−1.04155e6	−1.94993	−0.974966	+	0.222353i	$0.928626\pi$
$12$	−401402.	−0.465674
$13$	162421.	0.121326	0.0606628	−	0.998158i	$-0.480679\pi$
$13$	162421.	0.121326	0.0606628	+	0.998158i	$0.480679\pi$
$14$	550535.	0.273578
$15$	2.71416e6	0.922855
$16$	1.91734e6	0.457130
$17$	6.41060e6	1.09504	0.547519	−	0.836793i	$-0.315572\pi$
$17$	6.41060e6	1.09504	0.547519	+	0.836793i	$0.315572\pi$
$18$	−1.17527e6	−0.146602
$19$	1.86314e7	1.72624	0.863118	−	0.505003i	$-0.168508\pi$
$19$	1.86314e7	1.72624	0.863118	+	0.505003i	$0.168508\pi$
$20$	−1.84502e7	−1.28925
$21$	−6.72150e6	−0.359137
$22$	2.07302e7	0.857590
$23$	−5.10201e7	−1.65287	−0.826435	−	0.563032i	$-0.809635\pi$
$23$	−5.10201e7	−1.65287	−0.826435	+	0.563032i	$0.809635\pi$
$24$	1.78944e7	0.458727
$25$	7.59268e7	1.55498
$26$	−3.23270e6	−0.0533596
$27$	1.43489e7	0.192450
$28$	4.56912e7	0.501723
$29$	−2.37753e6	−0.0215247	−0.0107623	−	0.999942i	$-0.503426\pi$
$29$	−2.37753e6	−0.0215247	−0.0107623	+	0.999942i	$0.503426\pi$
$30$	−5.40207e7	−0.405876
$31$	−2.59764e8	−1.62963	−0.814815	−	0.579721i	$-0.803162\pi$
$31$	−2.59764e8	−1.62963	−0.814815	+	0.579721i	$0.803162\pi$
$32$	−1.88975e8	−0.995587
$33$	−2.53096e8	−1.12579
$34$	−1.27592e8	−0.481603
$35$	−3.08950e8	−0.994293
$36$	−9.75406e7	−0.268857
$37$	1.23520e8	0.292838	0.146419	−	0.989223i	$-0.453225\pi$
$37$	1.23520e8	0.292838	0.146419	+	0.989223i	$0.453225\pi$
$38$	−3.70826e8	−0.759207
$39$	3.94682e7	0.0700474
$40$	8.22506e8	1.27002
$41$	1.74139e8	0.234738	0.117369	−	0.993088i	$-0.462554\pi$
$41$	1.74139e8	0.234738	0.117369	+	0.993088i	$0.462554\pi$
$42$	1.33780e8	0.157950
$43$	−1.00184e9	−1.03925	−0.519625	−	0.854394i	$-0.673928\pi$
$43$	−1.00184e9	−1.03925	−0.519625	+	0.854394i	$0.673928\pi$
$44$	1.72049e9	1.57276
$45$	6.59540e8	0.532810
$46$	1.01547e9	0.726940
$47$	1.25095e9	0.795615	0.397807	−	0.917469i	$-0.369771\pi$
$47$	1.25095e9	0.795615	0.397807	+	0.917469i	$0.369771\pi$
$48$	4.65914e8	0.263924
$49$	−1.21222e9	−0.613062
$50$	−1.51119e9	−0.683888
$51$	1.55777e9	0.632221
$52$	−2.68296e8	−0.0978578
$53$	1.52944e9	0.502361	0.251180	−	0.967940i	$-0.419181\pi$
$53$	1.52944e9	0.502361	0.251180	+	0.967940i	$0.419181\pi$
$54$	−2.85590e8	−0.0846405
$55$	−1.16334e10	−3.11683
$56$	−2.03690e9	−0.494238
$57$	4.52742e9	0.996643
$58$	4.73207e7	0.00946666
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−4.48341e9	−0.744348
$61$	6.43509e9	0.975530	0.487765	−	0.872975i	$-0.337812\pi$
$61$	6.43509e9	0.975530	0.487765	+	0.872975i	$0.337812\pi$
$62$	5.17015e9	0.716719
$63$	−1.63332e9	−0.207348
$64$	−1.65494e8	−0.0192661
$65$	1.81414e9	0.193931
$66$	5.03745e9	0.495130
$67$	−1.91932e9	−0.173674	−0.0868371	−	0.996223i	$-0.527676\pi$
$67$	−1.91932e9	−0.173674	−0.0868371	+	0.996223i	$0.527676\pi$
$68$	−1.05894e10	−0.883227
$69$	−1.23979e10	−0.954285
$70$	6.14913e9	0.437295
$71$	−1.22406e10	−0.805156	−0.402578	−	0.915386i	$-0.631886\pi$
$71$	−1.22406e10	−0.805156	−0.402578	+	0.915386i	$0.631886\pi$
$72$	4.34833e9	0.264846
$73$	2.33155e10	1.31634	0.658170	−	0.752869i	$-0.271331\pi$
$73$	2.33155e10	1.31634	0.658170	+	0.752869i	$0.271331\pi$
$74$	−2.45845e9	−0.128792
$75$	1.84502e10	0.897769
$76$	−3.07764e10	−1.39233
$77$	2.88097e10	1.21294
$78$	−7.85547e8	−0.0308072
$79$	−1.85989e10	−0.680044	−0.340022	−	0.940417i	$-0.610435\pi$
$79$	−1.85989e10	−0.680044	−0.340022	+	0.940417i	$0.610435\pi$
$80$	2.14155e10	0.730690
$81$	3.48678e9	0.111111
$82$	−3.46593e9	−0.103239
$83$	3.10782e10	0.866016	0.433008	−	0.901390i	$-0.357452\pi$
$83$	3.10782e10	0.866016	0.433008	+	0.901390i	$0.357452\pi$
$84$	1.11030e10	0.289670
$85$	7.16024e10	1.75034
$86$	1.99398e10	0.457067
$87$	−5.77740e8	−0.0124273
$88$	−7.66989e10	−1.54930
$89$	−1.78818e10	−0.339443	−0.169721	−	0.985492i	$-0.554287\pi$
$89$	−1.78818e10	−0.339443	−0.169721	+	0.985492i	$0.554287\pi$
$90$	−1.31270e10	−0.234333
$91$	−4.49263e9	−0.0754698
$92$	8.42781e10	1.33316
$93$	−6.31226e10	−0.940867
$94$	−2.48981e10	−0.349915
$95$	2.08101e11	2.75927
$96$	−4.59209e10	−0.574802
$97$	−1.24517e11	−1.47225	−0.736127	−	0.676844i	$-0.763347\pi$
$97$	−1.24517e11	−1.47225	−0.736127	+	0.676844i	$0.763347\pi$
$98$	2.41272e10	0.269628
$99$	−6.15024e10	−0.649977
$100$	−1.25420e11	−1.25420
$101$	−3.84734e10	−0.364245	−0.182122	−	0.983276i	$-0.558297\pi$
$101$	−3.84734e10	−0.364245	−0.182122	+	0.983276i	$0.558297\pi$
$102$	−3.10048e10	−0.278054
$103$	−1.97395e11	−1.67777	−0.838884	−	0.544310i	$-0.816791\pi$
$103$	−1.97395e11	−1.67777	−0.838884	+	0.544310i	$0.816791\pi$
$104$	1.19605e10	0.0963979
$105$	−7.50749e10	−0.574055
$106$	−3.04409e10	−0.220941
$107$	−3.82896e10	−0.263919	−0.131959	−	0.991255i	$-0.542127\pi$
$107$	−3.82896e10	−0.263919	−0.131959	+	0.991255i	$0.542127\pi$
$108$	−2.37024e10	−0.155225
$109$	1.87575e11	1.16770	0.583849	−	0.811862i	$-0.301546\pi$
$109$	1.87575e11	1.16770	0.583849	+	0.811862i	$0.301546\pi$
$110$	2.31544e11	1.37080
$111$	3.00154e10	0.169070
$112$	−5.30346e10	−0.284355
$113$	−2.62880e11	−1.34223	−0.671113	−	0.741355i	$-0.734183\pi$
$113$	−2.62880e11	−1.34223	−0.671113	+	0.741355i	$0.734183\pi$
$114$	−9.01106e10	−0.438328
$115$	−5.69863e11	−2.64200
$116$	3.92734e9	0.0173612
$117$	9.59077e9	0.0404419
$118$	1.42293e10	0.0572577
$119$	−1.77320e11	−0.681161
$120$	1.99869e11	0.733244
$121$	7.99511e11	2.80224
$122$	−1.28080e11	−0.429043
$123$	4.23157e10	0.135526
$124$	4.29093e11	1.31441
$125$	3.02676e11	0.887100
$126$	3.25085e10	0.0911925
$127$	−3.83464e11	−1.02992	−0.514961	−	0.857214i	$-0.672194\pi$
$127$	−3.83464e11	−1.02992	−0.514961	+	0.857214i	$0.672194\pi$
$128$	3.90314e11	1.00406
$129$	−2.43446e11	−0.600011
$130$	−3.61073e10	−0.0852916
$131$	2.09931e11	0.475428	0.237714	−	0.971335i	$-0.423602\pi$
$131$	2.09931e11	0.475428	0.237714	+	0.971335i	$0.423602\pi$
$132$	4.18079e11	0.908034
$133$	−5.15353e11	−1.07379
$134$	3.82007e10	0.0763827
$135$	1.60268e11	0.307618
$136$	4.72072e11	0.870051
$137$	2.00324e11	0.354626	0.177313	−	0.984155i	$-0.443260\pi$
$137$	2.00324e11	0.354626	0.177313	+	0.984155i	$0.443260\pi$
$138$	2.46759e11	0.419699
$139$	−2.83228e11	−0.462972	−0.231486	−	0.972838i	$-0.574359\pi$
$139$	−2.83228e11	−0.462972	−0.231486	+	0.972838i	$0.574359\pi$
$140$	5.10342e11	0.801969
$141$	3.03982e11	0.459348
$142$	2.43627e11	0.354112
$143$	−1.69169e11	−0.236577
$144$	1.13217e11	0.152377
$145$	−2.65555e10	−0.0344057
$146$	−4.64054e11	−0.578933
$147$	−2.94570e11	−0.353952
$148$	−2.04038e11	−0.236195
$149$	−1.13062e12	−1.26123	−0.630613	−	0.776097i	$-0.717196\pi$
$149$	−1.13062e12	−1.26123	−0.630613	+	0.776097i	$0.717196\pi$
$150$	−3.67220e11	−0.394843
$151$	1.43392e12	1.48645	0.743226	−	0.669041i	$-0.233295\pi$
$151$	1.43392e12	1.48645	0.743226	+	0.669041i	$0.233295\pi$
$152$	1.37200e12	1.37156
$153$	3.78539e11	0.365013
$154$	−5.73408e11	−0.533458
$155$	−2.90140e12	−2.60485
$156$	−6.51959e10	−0.0564982
$157$	−7.28991e11	−0.609922	−0.304961	−	0.952365i	$-0.598643\pi$
$157$	−7.28991e11	−0.609922	−0.304961	+	0.952365i	$0.598643\pi$
$158$	3.70178e11	0.299087
$159$	3.71654e11	0.290038
$160$	−2.11073e12	−1.59138
$161$	1.41124e12	1.02816
$162$	−6.93985e10	−0.0488672
$163$	−4.56368e11	−0.310658	−0.155329	−	0.987863i	$-0.549644\pi$
$163$	−4.56368e11	−0.310658	−0.155329	+	0.987863i	$0.549644\pi$
$164$	−2.87652e11	−0.189333
$165$	−2.82693e12	−1.79950
$166$	−6.18558e11	−0.380878
$167$	−3.91774e11	−0.233397	−0.116699	−	0.993167i	$-0.537231\pi$
$167$	−3.91774e11	−0.233397	−0.116699	+	0.993167i	$0.537231\pi$
$168$	−4.94967e11	−0.285348
$169$	−1.76578e12	−0.985280
$170$	−1.42512e12	−0.769809
$171$	1.10016e12	0.575412
$172$	1.65489e12	0.838230
$173$	−2.32022e12	−1.13835	−0.569174	−	0.822217i	$-0.692737\pi$
$173$	−2.32022e12	−1.13835	−0.569174	+	0.822217i	$0.692737\pi$
$174$	1.14989e10	0.00546558
$175$	−2.10017e12	−0.967266
$176$	−1.99700e12	−0.891372
$177$	−1.73727e11	−0.0751646
$178$	3.55907e11	0.149288
$179$	−1.20055e12	−0.488303	−0.244152	−	0.969737i	$-0.578509\pi$
$179$	−1.20055e12	−0.488303	−0.244152	+	0.969737i	$0.578509\pi$
$180$	−1.08947e12	−0.429750
$181$	−3.13673e12	−1.20018	−0.600088	−	0.799934i	$-0.704868\pi$
$181$	−3.13673e12	−1.20018	−0.600088	+	0.799934i	$0.704868\pi$
$182$	8.94181e10	0.0331920
$183$	1.56373e12	0.563223
$184$	−3.75709e12	−1.31327
$185$	1.37964e12	0.468082
$186$	1.25635e12	0.413798
$187$	−6.67694e12	−2.13525
$188$	−2.06640e12	−0.641721
$189$	−3.96898e11	−0.119712
$190$	−4.14189e12	−1.21354
$191$	−3.68407e12	−1.04868	−0.524341	−	0.851508i	$-0.675688\pi$
$191$	−3.68407e12	−1.04868	−0.524341	+	0.851508i	$0.675688\pi$
$192$	−4.02151e10	−0.0111233
$193$	1.28396e12	0.345133	0.172566	−	0.984998i	$-0.444794\pi$
$193$	1.28396e12	0.345133	0.172566	+	0.984998i	$0.444794\pi$
$194$	2.47829e12	0.647504
$195$	4.40835e11	0.111966
$196$	2.00242e12	0.494479
$197$	−3.61276e12	−0.867510	−0.433755	−	0.901031i	$-0.642812\pi$
$197$	−3.61276e12	−0.867510	−0.433755	+	0.901031i	$0.642812\pi$
$198$	1.22410e12	0.285863
$199$	−2.63629e12	−0.598827	−0.299413	−	0.954123i	$-0.596791\pi$
$199$	−2.63629e12	−0.598827	−0.299413	+	0.954123i	$0.596791\pi$
$200$	5.59120e12	1.23549
$201$	−4.66394e11	−0.100271
$202$	7.65747e11	0.160196
$203$	6.57636e10	0.0133893
$204$	−2.57322e12	−0.509931
$205$	1.94502e12	0.375213
$206$	3.92881e12	0.737890
$207$	−3.01269e12	−0.550957
$208$	3.11416e11	0.0554615
$209$	−1.94055e13	−3.36604
$210$	1.49424e12	0.252472
$211$	7.03889e11	0.115865	0.0579323	−	0.998321i	$-0.481549\pi$
$211$	7.03889e11	0.115865	0.0579323	+	0.998321i	$0.481549\pi$
$212$	−2.52642e12	−0.405190
$213$	−2.97446e12	−0.464857
$214$	7.62090e11	0.116073
$215$	−1.11899e13	−1.66117
$216$	1.05664e12	0.152909
$217$	7.18519e12	1.01370
$218$	−3.73337e12	−0.513559
$219$	5.66566e12	0.759989
$220$	1.92168e13	2.51395
$221$	1.04121e12	0.132856
$222$	−5.97405e11	−0.0743579
$223$	−1.44869e13	−1.75913	−0.879565	−	0.475778i	$-0.842166\pi$
$223$	−1.44869e13	−1.75913	−0.879565	+	0.475778i	$0.842166\pi$
$224$	5.22714e12	0.619298
$225$	4.48340e12	0.518327
$226$	5.23217e12	0.590317
$227$	9.81667e12	1.08099	0.540496	−	0.841347i	$-0.318237\pi$
$227$	9.81667e12	1.08099	0.540496	+	0.841347i	$0.318237\pi$
$228$	−7.47867e12	−0.803864
$229$	−7.88896e12	−0.827799	−0.413899	−	0.910323i	$-0.635833\pi$
$229$	−7.88896e12	−0.827799	−0.413899	+	0.910323i	$0.635833\pi$
$230$	1.13422e13	1.16196
$231$	7.00076e12	0.700293
$232$	−1.75080e11	−0.0171022
$233$	−4.80416e12	−0.458311	−0.229155	−	0.973390i	$-0.573596\pi$
$233$	−4.80416e12	−0.458311	−0.229155	+	0.973390i	$0.573596\pi$
$234$	−1.90888e11	−0.0177865
$235$	1.39724e13	1.27174
$236$	1.18095e12	0.105007
$237$	−4.51952e12	−0.392624
$238$	3.52926e12	0.299578
$239$	8.16712e12	0.677455	0.338728	−	0.940884i	$-0.390003\pi$
$239$	8.16712e12	0.677455	0.338728	+	0.940884i	$0.390003\pi$
$240$	5.20397e12	0.421864
$241$	2.05703e12	0.162984	0.0814922	−	0.996674i	$-0.474031\pi$
$241$	2.05703e12	0.162984	0.0814922	+	0.996674i	$0.474031\pi$
$242$	−1.59129e13	−1.23244
$243$	8.47289e11	0.0641500
$244$	−1.06299e13	−0.786835
$245$	−1.35398e13	−0.979938
$246$	−8.42221e11	−0.0596051
$247$	3.02612e12	0.209437
$248$	−1.91288e13	−1.29480
$249$	7.55199e12	0.499994
$250$	−6.02424e12	−0.390151
$251$	−1.86917e13	−1.18425	−0.592125	−	0.805846i	$-0.701711\pi$
$251$	−1.86917e13	−1.18425	−0.592125	+	0.805846i	$0.701711\pi$
$252$	2.69802e12	0.167241
$253$	5.31399e13	3.22298
$254$	7.63220e12	0.452965
$255$	1.73994e13	1.01056
$256$	−7.42961e12	−0.422324
$257$	2.71267e13	1.50926	0.754631	−	0.656149i	$-0.227816\pi$
$257$	2.71267e13	1.50926	0.754631	+	0.656149i	$0.227816\pi$
$258$	4.84538e12	0.263888
$259$	−3.41662e12	−0.182158
$260$	−2.99670e12	−0.156419
$261$	−1.40391e11	−0.00717490
$262$	−4.17832e12	−0.209096
$263$	−2.38754e13	−1.17002	−0.585011	−	0.811026i	$-0.698910\pi$
$263$	−2.38754e13	−1.17002	−0.585011	+	0.811026i	$0.698910\pi$
$264$	−1.86378e13	−0.894487
$265$	1.70829e13	0.802989
$266$	1.02572e13	0.472259
$267$	−4.34528e12	−0.195977
$268$	3.17044e12	0.140081
$269$	−4.08460e13	−1.76812	−0.884061	−	0.467371i	$-0.845201\pi$
$269$	−4.08460e13	−1.76812	−0.884061	+	0.467371i	$0.845201\pi$
$270$	−3.18987e12	−0.135292
$271$	1.27174e13	0.528528	0.264264	−	0.964450i	$-0.414871\pi$
$271$	1.27174e13	0.528528	0.264264	+	0.964450i	$0.414871\pi$
$272$	1.22913e13	0.500575
$273$	−1.09171e12	−0.0435725
$274$	−3.98711e12	−0.155966
$275$	−7.90815e13	−3.03211
$276$	2.04796e13	0.769699
$277$	−2.49980e13	−0.921014	−0.460507	−	0.887656i	$-0.652332\pi$
$277$	−2.49980e13	−0.921014	−0.460507	+	0.887656i	$0.652332\pi$
$278$	5.63717e12	0.203617
$279$	−1.53388e13	−0.543210
$280$	−2.27509e13	−0.790005
$281$	4.57687e13	1.55842	0.779208	−	0.626766i	$-0.215622\pi$
$281$	4.57687e13	1.55842	0.779208	+	0.626766i	$0.215622\pi$
$282$	−6.05024e12	−0.202024
$283$	−3.59305e13	−1.17662	−0.588312	−	0.808634i	$-0.700207\pi$
$283$	−3.59305e13	−1.17662	−0.588312	+	0.808634i	$0.700207\pi$
$284$	2.02197e13	0.649416
$285$	5.05685e13	1.59306
$286$	3.36702e12	0.104048
$287$	−4.81676e12	−0.146017
$288$	−1.11588e13	−0.331862
$289$	6.82384e12	0.199109
$290$	5.28542e11	0.0151318
$291$	−3.02575e13	−0.850006
$292$	−3.85138e13	−1.06172
$293$	−1.97133e13	−0.533319	−0.266660	−	0.963791i	$-0.585920\pi$
$293$	−1.97133e13	−0.533319	−0.266660	+	0.963791i	$0.585920\pi$
$294$	5.86292e12	0.155670
$295$	−7.98526e12	−0.208098
$296$	9.09594e12	0.232671
$297$	−1.49451e13	−0.375265
$298$	2.25031e13	0.554693
$299$	−8.28672e12	−0.200535
$300$	−3.04772e13	−0.724115
$301$	2.77113e13	0.646459
$302$	−2.85397e13	−0.653749
$303$	−9.34904e12	−0.210297
$304$	3.57227e13	0.789114
$305$	7.18760e13	1.55932
$306$	−7.53418e12	−0.160534
$307$	8.56709e13	1.79297	0.896483	−	0.443078i	$-0.146114\pi$
$307$	8.56709e13	1.79297	0.896483	+	0.443078i	$0.146114\pi$
$308$	−4.75896e13	−0.978325
$309$	−4.79670e13	−0.968660
$310$	5.77474e13	1.14563
$311$	−1.78231e13	−0.347376	−0.173688	−	0.984801i	$-0.555568\pi$
$311$	−1.78231e13	−0.347376	−0.173688	+	0.984801i	$0.555568\pi$
$312$	2.90641e12	0.0556554
$313$	−1.53485e13	−0.288784	−0.144392	−	0.989521i	$-0.546123\pi$
$313$	−1.53485e13	−0.288784	−0.144392	+	0.989521i	$0.546123\pi$
$314$	1.45093e13	0.268247
$315$	−1.82432e13	−0.331431
$316$	3.07227e13	0.548505
$317$	6.02868e13	1.05778	0.528891	−	0.848690i	$-0.322608\pi$
$317$	6.02868e13	1.05778	0.528891	+	0.848690i	$0.322608\pi$
$318$	−7.39714e12	−0.127560
$319$	2.47631e12	0.0419717
$320$	−1.84847e12	−0.0307955
$321$	−9.30438e12	−0.152374
$322$	−2.80884e13	−0.452188
$323$	1.19438e14	1.89029
$324$	−5.75968e12	−0.0896191
$325$	1.23321e13	0.188659
$326$	9.08322e12	0.136629
$327$	4.55808e13	0.674170
$328$	1.28235e13	0.186509
$329$	−3.46020e13	−0.494907
$330$	5.62651e13	0.791430
$331$	−9.07651e13	−1.25564	−0.627820	−	0.778359i	$-0.716053\pi$
$331$	−9.07651e13	−1.25564	−0.627820	+	0.778359i	$0.716053\pi$
$332$	−5.13367e13	−0.698504
$333$	7.29373e12	0.0976128
$334$	7.79760e12	0.102649
$335$	−2.14376e13	−0.277606
$336$	−1.28874e13	−0.164172
$337$	−7.77690e13	−0.974635	−0.487318	−	0.873225i	$-0.662025\pi$
$337$	−7.77690e13	−0.974635	−0.487318	+	0.873225i	$0.662025\pi$
$338$	3.51448e13	0.433331
$339$	−6.38797e13	−0.774934
$340$	−1.18277e14	−1.41178
$341$	2.70556e14	3.17767
$342$	−2.18969e13	−0.253069
$343$	8.82245e13	1.00339
$344$	−7.37746e13	−0.825725
$345$	−1.38477e14	−1.52536
$346$	4.61799e13	0.500651
$347$	−3.53719e13	−0.377439	−0.188719	−	0.982031i	$-0.560434\pi$
$347$	−3.53719e13	−0.377439	−0.188719	+	0.982031i	$0.560434\pi$
$348$	9.54345e11	0.0100235
$349$	1.56494e14	1.61792	0.808960	−	0.587863i	$-0.200031\pi$
$349$	1.56494e14	1.61792	0.808960	+	0.587863i	$0.200031\pi$
$350$	4.18004e13	0.425408
$351$	2.33056e12	0.0233491
$352$	1.96826e14	1.94133
$353$	7.88223e13	0.765400	0.382700	−	0.923873i	$-0.374994\pi$
$353$	7.88223e13	0.765400	0.382700	+	0.923873i	$0.374994\pi$
$354$	3.45773e12	0.0330577
$355$	−1.36719e14	−1.28699
$356$	2.95382e13	0.273785
$357$	−4.30888e13	−0.393269
$358$	2.38950e13	0.214758
$359$	−8.06824e12	−0.0714101	−0.0357050	−	0.999362i	$-0.511368\pi$
$359$	−8.06824e12	−0.0714101	−0.0357050	+	0.999362i	$0.511368\pi$
$360$	4.85681e13	0.423338
$361$	2.30638e14	1.97989
$362$	6.24313e13	0.527843
$363$	1.94281e14	1.61787
$364$	7.42119e12	0.0608718
$365$	2.60419e14	2.10408
$366$	−3.11233e13	−0.247708
$367$	−6.53952e13	−0.512723	−0.256361	−	0.966581i	$-0.582524\pi$
$367$	−6.53952e13	−0.512723	−0.256361	+	0.966581i	$0.582524\pi$
$368$	−9.78230e13	−0.755576
$369$	1.02827e13	0.0782461
$370$	−2.74594e13	−0.205865
$371$	−4.23051e13	−0.312490
$372$	1.04270e14	0.758877
$373$	−8.32583e13	−0.597075	−0.298538	−	0.954398i	$-0.596499\pi$
$373$	−8.32583e13	−0.597075	−0.298538	+	0.954398i	$0.596499\pi$
$374$	1.32893e14	0.939093
$375$	7.35502e13	0.512167
$376$	9.21194e13	0.632147
$377$	−3.86160e11	−0.00261150
$378$	7.89957e12	0.0526500
$379$	−1.64786e14	−1.08244	−0.541220	−	0.840881i	$-0.682037\pi$
$379$	−1.64786e14	−1.08244	−0.541220	+	0.840881i	$0.682037\pi$
$380$	−3.43753e14	−2.22555
$381$	−9.31818e13	−0.594626
$382$	7.33251e13	0.461216
$383$	−1.93688e14	−1.20090	−0.600452	−	0.799661i	$-0.705013\pi$
$383$	−1.93688e14	−1.20090	−0.600452	+	0.799661i	$0.705013\pi$
$384$	9.48464e13	0.579694
$385$	3.21787e14	1.93880
$386$	−2.55550e13	−0.151791
$387$	−5.91574e13	−0.346417
$388$	2.05684e14	1.18748
$389$	1.12626e14	0.641086	0.320543	−	0.947234i	$-0.396135\pi$
$389$	1.12626e14	0.641086	0.320543	+	0.947234i	$0.396135\pi$
$390$	−8.77407e12	−0.0492431
$391$	−3.27070e14	−1.80996
$392$	−8.92674e13	−0.487102
$393$	5.10133e13	0.274489
$394$	7.19058e13	0.381535
$395$	−2.07738e14	−1.08700
$396$	1.01593e14	0.524253
$397$	−1.50136e14	−0.764077	−0.382038	−	0.924146i	$-0.624778\pi$
$397$	−1.50136e14	−0.764077	−0.382038	+	0.924146i	$0.624778\pi$
$398$	5.24708e13	0.263367
$399$	−1.25231e14	−0.619955
$400$	1.45578e14	0.710828
$401$	−1.55254e14	−0.747738	−0.373869	−	0.927481i	$-0.621969\pi$
$401$	−1.55254e14	−0.747738	−0.373869	+	0.927481i	$0.621969\pi$
$402$	9.28277e12	0.0440996
$403$	−4.21909e13	−0.197716
$404$	6.35526e13	0.293789
$405$	3.89452e13	0.177603
$406$	−1.30891e12	−0.00588867
$407$	−1.28652e14	−0.571015
$408$	1.14714e14	0.502324
$409$	−3.98266e14	−1.72066	−0.860330	−	0.509737i	$-0.829743\pi$
$409$	−3.98266e14	−1.72066	−0.860330	+	0.509737i	$0.829743\pi$
$410$	−3.87123e13	−0.165020
$411$	4.86788e13	0.204743
$412$	3.26069e14	1.35324
$413$	1.97752e13	0.0809831
$414$	5.99624e13	0.242313
$415$	3.47124e14	1.38427
$416$	−3.06934e13	−0.120790
$417$	−6.88244e13	−0.267297
$418$	3.86233e14	1.48040
$419$	−1.89952e14	−0.718567	−0.359284	−	0.933228i	$-0.616979\pi$
$419$	−1.89952e14	−0.718567	−0.359284	+	0.933228i	$0.616979\pi$
$420$	1.24013e14	0.463017
$421$	−3.90610e14	−1.43943	−0.719717	−	0.694268i	$-0.755728\pi$
$421$	−3.90610e14	−1.43943	−0.719717	+	0.694268i	$0.755728\pi$
$422$	−1.40097e13	−0.0509578
$423$	7.38675e13	0.265205
$424$	1.12627e14	0.399145
$425$	4.86736e14	1.70276
$426$	5.92014e13	0.204446
$427$	−1.77998e14	−0.606822
$428$	6.32491e13	0.212870
$429$	−4.11080e13	−0.136588
$430$	2.22716e14	0.730590
$431$	−3.74617e14	−1.21328	−0.606642	−	0.794975i	$-0.707484\pi$
$431$	−3.74617e14	−1.21328	−0.606642	+	0.794975i	$0.707484\pi$
$432$	2.75118e13	0.0879747
$433$	2.01352e14	0.635729	0.317864	−	0.948136i	$-0.397034\pi$
$433$	2.01352e14	0.635729	0.317864	+	0.948136i	$0.397034\pi$
$434$	−1.43009e14	−0.445830
$435$	−6.45299e12	−0.0198642
$436$	−3.09848e14	−0.941832
$437$	−9.50575e14	−2.85324
$438$	−1.12765e14	−0.334247
$439$	−2.08787e14	−0.611150	−0.305575	−	0.952168i	$-0.598849\pi$
$439$	−2.08787e14	−0.611150	−0.305575	+	0.952168i	$0.598849\pi$
$440$	−8.56679e14	−2.47644
$441$	−7.15806e13	−0.204354
$442$	−2.07235e13	−0.0584308
$443$	6.34887e14	1.76797	0.883987	−	0.467511i	$-0.154849\pi$
$443$	6.34887e14	1.76797	0.883987	+	0.467511i	$0.154849\pi$
$444$	−4.95812e13	−0.136367
$445$	−1.99729e14	−0.542575
$446$	2.88337e14	0.773674
$447$	−2.74741e14	−0.728169
$448$	4.57765e12	0.0119843
$449$	4.50994e14	1.16631	0.583157	−	0.812359i	$-0.301817\pi$
$449$	4.50994e14	1.16631	0.583157	+	0.812359i	$0.301817\pi$
$450$	−8.92345e13	−0.227963
$451$	−1.81374e14	−0.457724
$452$	4.34240e14	1.08260
$453$	3.48442e14	0.858203
$454$	−1.95384e14	−0.475425
$455$	−5.01799e13	−0.120633
$456$	3.33397e14	0.791871
$457$	−4.41598e13	−0.103631	−0.0518153	−	0.998657i	$-0.516501\pi$
$457$	−4.41598e13	−0.103631	−0.0518153	+	0.998657i	$0.516501\pi$
$458$	1.57016e14	0.364070
$459$	9.19850e13	0.210740
$460$	9.41334e14	2.13096
$461$	−7.43702e13	−0.166358	−0.0831790	−	0.996535i	$-0.526507\pi$
$461$	−7.43702e13	−0.166358	−0.0831790	+	0.996535i	$0.526507\pi$
$462$	−1.39338e14	−0.307992
$463$	5.73448e14	1.25256	0.626280	−	0.779598i	$-0.284576\pi$
$463$	5.73448e14	1.25256	0.626280	+	0.779598i	$0.284576\pi$
$464$	−4.55854e12	−0.00983958
$465$	−7.05040e14	−1.50391
$466$	9.56186e13	0.201567
$467$	1.50443e14	0.313423	0.156711	−	0.987644i	$-0.449911\pi$
$467$	1.50443e14	0.313423	0.156711	+	0.987644i	$0.449911\pi$
$468$	−1.58426e13	−0.0326193
$469$	5.30892e13	0.108033
$470$	−2.78096e14	−0.559315
$471$	−1.77145e14	−0.352139
$472$	−5.26466e13	−0.103440
$473$	1.04346e15	2.02647
$474$	8.99534e13	0.172678
$475$	1.41462e15	2.68426
$476$	2.92908e14	0.549405
$477$	9.03120e13	0.167454
$478$	−1.62553e14	−0.297948
$479$	−1.92548e14	−0.348895	−0.174447	−	0.984666i	$-0.555814\pi$
$479$	−1.92548e14	−0.348895	−0.174447	+	0.984666i	$0.555814\pi$
$480$	−5.12908e14	−0.918782
$481$	2.00622e13	0.0355288
$482$	−4.09416e13	−0.0716813
$483$	3.42932e14	0.593606
$484$	−1.32068e15	−2.26020
$485$	−1.39077e15	−2.35330
$486$	−1.68638e13	−0.0282135
$487$	1.08217e15	1.79014	0.895072	−	0.445922i	$-0.147124\pi$
$487$	1.08217e15	1.79014	0.895072	+	0.445922i	$0.147124\pi$
$488$	4.73876e14	0.775097
$489$	−1.10897e14	−0.179359
$490$	2.69486e14	0.430981
$491$	1.12347e15	1.77670	0.888349	−	0.459168i	$-0.151852\pi$
$491$	1.12347e15	1.77670	0.888349	+	0.459168i	$0.151852\pi$
$492$	−6.98995e13	−0.109312
$493$	−1.52414e13	−0.0235704
$494$	−6.02297e13	−0.0921112
$495$	−6.86943e14	−1.03894
$496$	−4.98056e14	−0.744953
$497$	3.38580e14	0.500842
$498$	−1.50310e14	−0.219900
$499$	4.84241e14	0.700662	0.350331	−	0.936626i	$-0.386069\pi$
$499$	4.84241e14	0.700662	0.350331	+	0.936626i	$0.386069\pi$
$500$	−4.99978e14	−0.715510
$501$	−9.52012e13	−0.134752
$502$	3.72026e14	0.520838
$503$	4.09842e13	0.0567534	0.0283767	−	0.999597i	$-0.490966\pi$
$503$	4.09842e13	0.0567534	0.0283767	+	0.999597i	$0.490966\pi$
$504$	−1.20277e14	−0.164746
$505$	−4.29724e14	−0.582220
$506$	−1.05766e15	−1.41748
$507$	−4.29085e14	−0.568852
$508$	6.33429e14	0.830706
$509$	4.26043e14	0.552720	0.276360	−	0.961054i	$-0.410872\pi$
$509$	4.26043e14	0.552720	0.276360	+	0.961054i	$0.410872\pi$
$510$	−3.46305e14	−0.444450
$511$	−6.44917e14	−0.818821
$512$	−6.51490e14	−0.818320
$513$	2.67340e14	0.332214
$514$	−5.39910e14	−0.663781
$515$	−2.20478e15	−2.68180
$516$	4.02139e14	0.483952
$517$	−1.30293e15	−1.55140
$518$	6.80021e13	0.0801140
$519$	−5.63813e14	−0.657225
$520$	1.33592e14	0.154085
$521$	−7.57646e14	−0.864687	−0.432343	−	0.901709i	$-0.642313\pi$
$521$	−7.57646e14	−0.864687	−0.432343	+	0.901709i	$0.642313\pi$
$522$	2.79424e12	0.00315555
$523$	−6.73820e14	−0.752982	−0.376491	−	0.926420i	$-0.622869\pi$
$523$	−6.73820e14	−0.752982	−0.376491	+	0.926420i	$0.622869\pi$
$524$	−3.46777e14	−0.383467
$525$	−5.10342e14	−0.558451
$526$	4.75199e14	0.514581
$527$	−1.66524e15	−1.78451
$528$	−4.85272e14	−0.514634
$529$	1.65025e15	1.73198
$530$	−3.40006e14	−0.353158
$531$	−4.22156e13	−0.0433963
$532$	8.51290e14	0.866091
$533$	2.82837e13	0.0284798
$534$	8.64853e13	0.0861917
$535$	−4.27671e14	−0.421856
$536$	−1.41337e14	−0.137991
$537$	−2.91734e14	−0.281922
$538$	8.12970e14	0.777628
$539$	1.26259e15	1.19543
$540$	−2.64741e14	−0.248116
$541$	1.40310e15	1.30168	0.650838	−	0.759216i	$-0.274418\pi$
$541$	1.40310e15	1.30168	0.650838	+	0.759216i	$0.274418\pi$
$542$	−2.53119e14	−0.232449
$543$	−7.62225e14	−0.692922
$544$	−1.21144e15	−1.09021
$545$	2.09510e15	1.86648
$546$	2.17286e13	0.0191634
$547$	−2.11560e14	−0.184715	−0.0923575	−	0.995726i	$-0.529440\pi$
$547$	−2.11560e14	−0.184715	−0.0923575	+	0.995726i	$0.529440\pi$
$548$	−3.30907e14	−0.286031
$549$	3.79986e14	0.325177
$550$	1.57398e15	1.33354
$551$	−4.42966e13	−0.0371567
$552$	−9.12973e14	−0.758216
$553$	5.14453e14	0.423017
$554$	4.97542e14	0.405067
$555$	3.35253e14	0.270247
$556$	4.67853e14	0.373420
$557$	−7.06813e14	−0.558600	−0.279300	−	0.960204i	$-0.590102\pi$
$557$	−7.06813e14	−0.558600	−0.279300	+	0.960204i	$0.590102\pi$
$558$	3.05292e14	0.238906
$559$	−1.62719e14	−0.126088
$560$	−5.92363e14	−0.454521
$561$	−1.62250e15	−1.23279
$562$	−9.10947e14	−0.685399
$563$	−2.31313e15	−1.72347	−0.861736	−	0.507358i	$-0.830622\pi$
$563$	−2.31313e15	−1.72347	−0.861736	+	0.507358i	$0.830622\pi$
$564$	−5.02135e14	−0.370498
$565$	−2.93620e15	−2.14545
$566$	7.15135e14	0.517485
$567$	−9.64462e13	−0.0691159
$568$	−9.01387e14	−0.639728
$569$	5.76143e14	0.404961	0.202480	−	0.979286i	$-0.435100\pi$
$569$	5.76143e14	0.404961	0.202480	+	0.979286i	$0.435100\pi$
$570$	−1.00648e15	−0.700637
$571$	2.30158e15	1.58682	0.793408	−	0.608690i	$-0.208305\pi$
$571$	2.30158e15	1.58682	0.793408	+	0.608690i	$0.208305\pi$
$572$	2.79443e14	0.190816
$573$	−8.95229e14	−0.605457
$574$	9.58693e13	0.0642191
$575$	−3.87380e15	−2.57018
$576$	−9.77227e12	−0.00642202
$577$	2.46899e15	1.60714	0.803569	−	0.595212i	$-0.202932\pi$
$577$	2.46899e15	1.60714	0.803569	+	0.595212i	$0.202932\pi$
$578$	−1.35817e14	−0.0875691
$579$	3.12002e14	0.199263
$580$	4.38660e13	0.0277507
$581$	−8.59637e14	−0.538699
$582$	6.02224e14	0.373837
$583$	−1.59299e15	−0.979569
$584$	1.71694e15	1.04588
$585$	1.07123e14	0.0646435
$586$	3.92359e14	0.234556
$587$	2.89295e15	1.71329	0.856645	−	0.515906i	$-0.172545\pi$
$587$	2.89295e15	1.71329	0.856645	+	0.515906i	$0.172545\pi$
$588$	4.86589e14	0.285487
$589$	−4.83975e15	−2.81313
$590$	1.58933e14	0.0915225
$591$	−8.77900e14	−0.500857
$592$	2.36830e14	0.133865
$593$	1.90299e15	1.06570	0.532850	−	0.846210i	$-0.321121\pi$
$593$	1.90299e15	1.06570	0.532850	+	0.846210i	$0.321121\pi$
$594$	2.97456e14	0.165043
$595$	−1.98056e15	−1.08879
$596$	1.86763e15	1.01727
$597$	−6.40618e14	−0.345733
$598$	1.64933e14	0.0881964
$599$	−5.98455e13	−0.0317091	−0.0158545	−	0.999874i	$-0.505047\pi$
$599$	−5.98455e13	−0.0317091	−0.0158545	+	0.999874i	$0.505047\pi$
$600$	1.35866e15	0.713312
$601$	−2.02557e14	−0.105375	−0.0526875	−	0.998611i	$-0.516779\pi$
$601$	−2.02557e14	−0.105375	−0.0526875	+	0.998611i	$0.516779\pi$
$602$	−5.51546e14	−0.284316
$603$	−1.13334e14	−0.0578914
$604$	−2.36863e15	−1.19893
$605$	8.93004e15	4.47918
$606$	1.86077e14	0.0924895
$607$	2.40107e15	1.18268	0.591339	−	0.806423i	$-0.298600\pi$
$607$	2.40107e15	1.18268	0.591339	+	0.806423i	$0.298600\pi$
$608$	−3.52086e15	−1.71862
$609$	1.59806e13	0.00773031
$610$	−1.43057e15	−0.685795
$611$	2.03180e14	0.0965285
$612$	−6.25294e14	−0.294409
$613$	3.48502e15	1.62619	0.813097	−	0.582128i	$-0.197780\pi$
$613$	3.48502e15	1.62619	0.813097	+	0.582128i	$0.197780\pi$
$614$	−1.70513e15	−0.788555
$615$	4.72640e14	0.216629
$616$	2.12153e15	0.963730
$617$	−1.10199e15	−0.496144	−0.248072	−	0.968742i	$-0.579797\pi$
$617$	−1.10199e15	−0.496144	−0.248072	+	0.968742i	$0.579797\pi$
$618$	9.54702e14	0.426021
$619$	1.99223e15	0.881131	0.440566	−	0.897720i	$-0.354778\pi$
$619$	1.99223e15	0.881131	0.440566	+	0.897720i	$0.354778\pi$
$620$	4.79270e15	2.10100
$621$	−7.32083e14	−0.318095
$622$	3.54738e14	0.152778
$623$	4.94619e14	0.211148
$624$	7.56740e13	0.0320207
$625$	−3.26667e14	−0.137014
$626$	3.05486e14	0.127009
$627$	−4.71553e15	−1.94339
$628$	1.20419e15	0.491946
$629$	7.91837e14	0.320669
$630$	3.63100e14	0.145765
$631$	1.84059e15	0.732481	0.366240	−	0.930520i	$-0.380645\pi$
$631$	1.84059e15	0.732481	0.366240	+	0.930520i	$0.380645\pi$
$632$	−1.36961e15	−0.540322
$633$	1.71045e14	0.0668945
$634$	−1.19991e15	−0.465218
$635$	−4.28306e15	−1.64626
$636$	−6.13920e14	−0.233937
$637$	−1.96890e14	−0.0743801
$638$	−4.92868e13	−0.0184594
$639$	−7.22793e14	−0.268385
$640$	4.35957e15	1.60492
$641$	−3.24375e15	−1.18394	−0.591968	−	0.805961i	$-0.701649\pi$
$641$	−3.24375e15	−1.18394	−0.591968	+	0.805961i	$0.701649\pi$
$642$	1.85188e14	0.0670147
$643$	2.63199e14	0.0944329	0.0472164	−	0.998885i	$-0.484965\pi$
$643$	2.63199e14	0.0944329	0.0472164	+	0.998885i	$0.484965\pi$
$644$	−2.33117e15	−0.829282
$645$	−2.71914e15	−0.959077
$646$	−2.37721e15	−0.831360
$647$	−3.99215e15	−1.38431	−0.692156	−	0.721748i	$-0.743339\pi$
$647$	−3.99215e15	−1.38431	−0.692156	+	0.721748i	$0.743339\pi$
$648$	2.56765e14	0.0882821
$649$	7.44628e14	0.253860
$650$	−2.45449e14	−0.0829732
$651$	1.74600e15	0.585260
$652$	7.53855e14	0.250568
$653$	−3.51274e14	−0.115777	−0.0578887	−	0.998323i	$-0.518437\pi$
$653$	−3.51274e14	−0.115777	−0.0578887	+	0.998323i	$0.518437\pi$
$654$	−9.07209e14	−0.296503
$655$	2.34480e15	0.759939
$656$	3.33883e14	0.107306
$657$	1.37675e15	0.438780
$658$	6.88693e14	0.217662
$659$	−1.44034e15	−0.451435	−0.225718	−	0.974193i	$-0.572473\pi$
$659$	−1.44034e15	−0.451435	−0.225718	+	0.974193i	$0.572473\pi$
$660$	4.66968e15	1.45143
$661$	−2.84597e15	−0.877249	−0.438624	−	0.898671i	$-0.644534\pi$
$661$	−2.84597e15	−0.877249	−0.438624	+	0.898671i	$0.644534\pi$
$662$	1.80652e15	0.552236
$663$	2.53015e14	0.0767046
$664$	2.28858e15	0.688083
$665$	−5.75617e15	−1.71638
$666$	−1.45169e14	−0.0429306
$667$	1.21302e14	0.0355775
$668$	6.47156e14	0.188252
$669$	−3.52031e15	−1.01563
$670$	4.26678e14	0.122092
$671$	−6.70246e15	−1.90222
$672$	1.27019e15	0.357552
$673$	1.63336e15	0.456037	0.228019	−	0.973657i	$-0.426775\pi$
$673$	1.63336e15	0.456037	0.228019	+	0.973657i	$0.426775\pi$
$674$	1.54786e15	0.428649
$675$	1.08947e15	0.299256
$676$	2.91682e15	0.794699
$677$	−5.78179e14	−0.156252	−0.0781259	−	0.996944i	$-0.524894\pi$
$677$	−5.78179e14	−0.156252	−0.0781259	+	0.996944i	$0.524894\pi$
$678$	1.27142e15	0.340820
$679$	3.44419e15	0.915806
$680$	5.27275e15	1.39072
$681$	2.38545e15	0.624110
$682$	−5.38496e15	−1.39755
$683$	9.19834e14	0.236808	0.118404	−	0.992966i	$-0.462222\pi$
$683$	9.19834e14	0.236808	0.118404	+	0.992966i	$0.462222\pi$
$684$	−1.81732e15	−0.464111
$685$	2.23750e15	0.566845
$686$	−1.75596e15	−0.441298
$687$	−1.91702e15	−0.477930
$688$	−1.92086e15	−0.475072
$689$	2.48413e14	0.0609492
$690$	2.75614e15	0.670860
$691$	4.43480e15	1.07089	0.535445	−	0.844570i	$-0.320144\pi$
$691$	4.43480e15	1.07089	0.535445	+	0.844570i	$0.320144\pi$
$692$	3.83267e15	0.918159
$693$	1.70119e15	0.404314
$694$	7.04018e14	0.165999
$695$	−3.16348e15	−0.740029
$696$	−4.25444e13	−0.00987396
$697$	1.11633e15	0.257047
$698$	−3.11474e15	−0.711569
$699$	−1.16741e15	−0.264606
$700$	3.46919e15	0.780169
$701$	−5.48622e15	−1.22412	−0.612060	−	0.790811i	$-0.709659\pi$
$701$	−5.48622e15	−1.22412	−0.612060	+	0.790811i	$0.709659\pi$
$702$	−4.63857e13	−0.0102691
$703$	2.30135e15	0.505508
$704$	1.72370e14	0.0375675
$705$	3.39529e15	0.734237
$706$	−1.56882e15	−0.336626
$707$	1.06419e15	0.226576
$708$	2.86972e14	0.0606256
$709$	5.79662e15	1.21512	0.607562	−	0.794272i	$-0.292148\pi$
$709$	5.79662e15	1.21512	0.607562	+	0.794272i	$0.292148\pi$
$710$	2.72117e15	0.566023
$711$	−1.09824e15	−0.226681
$712$	−1.31680e15	−0.269700
$713$	1.32532e16	2.69357
$714$	8.57609e14	0.172961
$715$	−1.88951e15	−0.378152
$716$	1.98314e15	0.393852
$717$	1.98461e15	0.391129
$718$	1.60585e14	0.0314065
$719$	−6.74615e15	−1.30932	−0.654662	−	0.755922i	$-0.727189\pi$
$719$	−6.74615e15	−1.30932	−0.654662	+	0.755922i	$0.727189\pi$
$720$	1.26456e15	0.243563
$721$	5.46005e15	1.04364
$722$	−4.59045e15	−0.870765
$723$	4.99857e14	0.0940990
$724$	5.18144e15	0.968028
$725$	−1.80518e14	−0.0334705
$726$	−3.86683e15	−0.711548
$727$	6.39372e15	1.16766	0.583828	−	0.811878i	$-0.301554\pi$
$727$	6.39372e15	1.16766	0.583828	+	0.811878i	$0.301554\pi$
$728$	−3.30834e14	−0.0599637
$729$	2.05891e14	0.0370370
$730$	−5.18320e15	−0.925384
$731$	−6.42237e15	−1.13802
$732$	−2.58306e15	−0.454279
$733$	−8.08612e15	−1.41146	−0.705730	−	0.708481i	$-0.749381\pi$
$733$	−8.08612e15	−1.41146	−0.705730	+	0.708481i	$0.749381\pi$
$734$	1.30158e15	0.225498
$735$	−3.29017e15	−0.565767
$736$	9.64152e15	1.64558
$737$	1.99906e15	0.338653
$738$	−2.04660e14	−0.0344130
$739$	7.98503e15	1.33270	0.666349	−	0.745640i	$-0.267856\pi$
$739$	7.98503e15	1.33270	0.666349	+	0.745640i	$0.267856\pi$
$740$	−2.27897e15	−0.377542
$741$	7.35346e14	0.120918
$742$	8.42011e14	0.137435
$743$	6.96575e14	0.112857	0.0564286	−	0.998407i	$-0.482029\pi$
$743$	6.96575e14	0.112857	0.0564286	+	0.998407i	$0.482029\pi$
$744$	−4.64831e15	−0.747556
$745$	−1.26283e16	−2.01598
$746$	1.65711e15	0.262596
$747$	1.83513e15	0.288672
$748$	1.10294e16	1.72223
$749$	1.05911e15	0.164169
$750$	−1.46389e15	−0.225254
$751$	−7.26736e15	−1.11009	−0.555043	−	0.831822i	$-0.687298\pi$
$751$	−7.26736e15	−1.11009	−0.555043	+	0.831822i	$0.687298\pi$
$752$	2.39850e15	0.363699
$753$	−4.54208e15	−0.683727
$754$	7.68585e12	0.00114855
$755$	1.60160e16	2.37599
$756$	6.55619e14	0.0965566
$757$	6.47637e15	0.946900	0.473450	−	0.880821i	$-0.343008\pi$
$757$	6.47637e15	0.946900	0.473450	+	0.880821i	$0.343008\pi$
$758$	3.27978e15	0.476062
$759$	1.29130e16	1.86079
$760$	1.53244e16	2.19235
$761$	5.52150e14	0.0784227	0.0392113	−	0.999231i	$-0.487515\pi$
$761$	5.52150e14	0.0784227	0.0392113	+	0.999231i	$0.487515\pi$
$762$	1.85462e15	0.261519
$763$	−5.18843e15	−0.726358
$764$	6.08556e15	0.845838
$765$	4.22805e15	0.583448
$766$	3.85502e15	0.528163
$767$	−1.16118e14	−0.0157952
$768$	−1.80539e15	−0.243829
$769$	6.34106e15	0.850290	0.425145	−	0.905125i	$-0.360223\pi$
$769$	6.34106e15	0.850290	0.425145	+	0.905125i	$0.360223\pi$
$770$	−6.40461e15	−0.852696
$771$	6.59179e15	0.871373
$772$	−2.12092e15	−0.278374
$773$	−2.11511e15	−0.275642	−0.137821	−	0.990457i	$-0.544010\pi$
$773$	−2.11511e15	−0.275642	−0.137821	+	0.990457i	$0.544010\pi$
$774$	1.17743e15	0.152356
$775$	−1.97230e16	−2.53404
$776$	−9.16932e15	−1.16976
$777$	−8.30240e14	−0.105169
$778$	−2.24163e15	−0.281953
$779$	3.24444e15	0.405214
$780$	−7.28197e14	−0.0903085
$781$	1.27491e16	1.57000
$782$	6.50976e15	0.796027
$783$	−3.41150e13	−0.00414243
$784$	−2.32425e15	−0.280249
$785$	−8.14238e15	−0.974918
$786$	−1.01533e15	−0.120721
$787$	−1.46829e16	−1.73361	−0.866805	−	0.498647i	$-0.833831\pi$
$787$	−1.46829e16	−1.73361	−0.866805	+	0.498647i	$0.833831\pi$
$788$	5.96777e15	0.699709
$789$	−5.80172e15	−0.675512
$790$	4.13466e15	0.478069
$791$	7.27138e15	0.834922
$792$	−4.52900e15	−0.516432
$793$	1.04519e15	0.118357
$794$	2.98820e15	0.336045
$795$	4.15115e15	0.463606
$796$	4.35478e15	0.482997
$797$	1.64346e16	1.81025	0.905123	−	0.425150i	$-0.139779\pi$
$797$	1.64346e16	1.81025	0.905123	+	0.425150i	$0.139779\pi$
$798$	2.49250e15	0.272659
$799$	8.01936e15	0.871229
$800$	−1.43483e16	−1.54812
$801$	−1.05590e15	−0.113148
$802$	3.09007e15	0.328859
$803$	−2.42842e16	−2.56677
$804$	7.70417e14	0.0808756
$805$	1.57627e16	1.64344
$806$	8.39739e14	0.0869564
$807$	−9.92558e15	−1.02083
$808$	−2.83316e15	−0.289406
$809$	9.93747e15	1.00823	0.504114	−	0.863637i	$-0.331819\pi$
$809$	9.93747e15	1.00823	0.504114	+	0.863637i	$0.331819\pi$
$810$	−7.75138e14	−0.0781108
$811$	−1.40232e16	−1.40357	−0.701784	−	0.712390i	$-0.747613\pi$
$811$	−1.40232e16	−1.40357	−0.701784	+	0.712390i	$0.747613\pi$
$812$	−1.08632e14	−0.0107994
$813$	3.09033e15	0.305146
$814$	2.56060e15	0.251135
$815$	−5.09734e15	−0.496566
$816$	2.98679e15	0.289007
$817$	−1.86656e16	−1.79399
$818$	7.92680e15	0.756754
$819$	−2.65285e14	−0.0251566
$820$	−3.21290e15	−0.302636
$821$	−1.78706e16	−1.67206	−0.836032	−	0.548681i	$-0.815130\pi$
$821$	−1.78706e16	−1.67206	−0.836032	+	0.548681i	$0.815130\pi$
$822$	−9.68868e14	−0.0900471
$823$	1.28825e16	1.18933	0.594665	−	0.803974i	$-0.297285\pi$
$823$	1.28825e16	1.18933	0.594665	+	0.803974i	$0.297285\pi$
$824$	−1.45361e16	−1.33305
$825$	−1.92168e16	−1.75059
$826$	−3.93591e14	−0.0356168
$827$	5.58717e15	0.502240	0.251120	−	0.967956i	$-0.419201\pi$
$827$	5.58717e15	0.502240	0.251120	+	0.967956i	$0.419201\pi$
$828$	4.97654e15	0.444386
$829$	−3.13657e14	−0.0278231	−0.0139115	−	0.999903i	$-0.504428\pi$
$829$	−3.13657e14	−0.0278231	−0.0139115	+	0.999903i	$0.504428\pi$
$830$	−6.90890e15	−0.608807
$831$	−6.07451e15	−0.531748
$832$	−2.68797e13	−0.00233747
$833$	−7.77108e15	−0.671327
$834$	1.36983e15	0.117559
$835$	−4.37588e15	−0.373069
$836$	3.20551e16	2.71496
$837$	−3.72732e15	−0.313622
$838$	3.78068e15	0.316029
$839$	−6.53730e15	−0.542885	−0.271442	−	0.962455i	$-0.587501\pi$
$839$	−6.53730e15	−0.542885	−0.271442	+	0.962455i	$0.587501\pi$
$840$	−5.52847e15	−0.456109
$841$	−1.21949e16	−0.999537
$842$	7.77442e15	0.633070
$843$	1.11218e16	0.899752
$844$	−1.16273e15	−0.0934532
$845$	−1.97227e16	−1.57490
$846$	−1.47021e15	−0.116638
$847$	−2.21149e16	−1.74311
$848$	2.93246e15	0.229644
$849$	−8.73110e15	−0.679324
$850$	−9.68765e15	−0.748884
$851$	−6.30201e15	−0.484024
$852$	4.91338e15	0.374941
$853$	7.44956e15	0.564821	0.282411	−	0.959294i	$-0.408866\pi$
$853$	7.44956e15	0.564821	0.282411	+	0.959294i	$0.408866\pi$
$854$	3.54274e15	0.266883
$855$	1.22881e16	0.919756
$856$	−2.81963e15	−0.209694
$857$	−6.19950e15	−0.458102	−0.229051	−	0.973414i	$-0.573562\pi$
$857$	−6.19950e15	−0.458102	−0.229051	+	0.973414i	$0.573562\pi$
$858$	8.18185e14	0.0600719
$859$	1.44810e16	1.05642	0.528211	−	0.849113i	$-0.322863\pi$
$859$	1.44810e16	1.05642	0.528211	+	0.849113i	$0.322863\pi$
$860$	1.84841e16	1.33985
$861$	−1.17047e15	−0.0843032
$862$	7.45611e15	0.533608
$863$	1.29197e16	0.918738	0.459369	−	0.888246i	$-0.348076\pi$
$863$	1.29197e16	0.918738	0.459369	+	0.888246i	$0.348076\pi$
$864$	−2.71158e15	−0.191601
$865$	−2.59154e16	−1.81957
$866$	−4.00756e15	−0.279597
$867$	1.65819e15	0.114956
$868$	−1.18689e16	−0.817622
$869$	1.93716e16	1.32604
$870$	1.28436e14	0.00873635
$871$	−3.11736e14	−0.0210711
$872$	1.38129e16	0.927781
$873$	−7.35258e15	−0.490751
$874$	1.89196e16	1.25487
$875$	−8.37216e15	−0.551814
$876$	−9.35887e15	−0.612986
$877$	1.30252e16	0.847786	0.423893	−	0.905712i	$-0.360663\pi$
$877$	1.30252e16	0.847786	0.423893	+	0.905712i	$0.360663\pi$
$878$	4.15554e15	0.268787
$879$	−4.79033e15	−0.307912
$880$	−2.23053e16	−1.42480
$881$	−2.73110e16	−1.73368	−0.866842	−	0.498583i	$-0.833854\pi$
$881$	−2.73110e16	−1.73368	−0.866842	+	0.498583i	$0.833854\pi$
$882$	1.42469e15	0.0898759
$883$	6.04765e15	0.379143	0.189571	−	0.981867i	$-0.439290\pi$
$883$	6.04765e15	0.379143	0.189571	+	0.981867i	$0.439290\pi$
$884$	−1.71994e15	−0.107158
$885$	−1.94042e15	−0.120145
$886$	−1.26363e16	−0.777563
$887$	1.56651e16	0.957972	0.478986	−	0.877822i	$-0.341004\pi$
$887$	1.56651e16	0.957972	0.478986	+	0.877822i	$0.341004\pi$
$888$	2.21031e15	0.134333
$889$	1.06068e16	0.640656
$890$	3.97526e15	0.238627
$891$	−3.63165e15	−0.216659
$892$	2.39303e16	1.41887
$893$	2.33070e16	1.37342
$894$	5.46825e15	0.320252
$895$	−1.34094e16	−0.780519
$896$	−1.07963e16	−0.624569
$897$	−2.01367e15	−0.115779
$898$	−8.97626e15	−0.512951
$899$	6.17596e14	0.0350773
$900$	−7.40595e15	−0.418068
$901$	9.80463e15	0.550104
$902$	3.60993e15	0.201309
$903$	6.73384e15	0.373233
$904$	−1.93583e16	−1.06645
$905$	−3.50353e16	−1.91840
$906$	−6.93514e15	−0.377442
$907$	−5.54810e15	−0.300127	−0.150063	−	0.988676i	$-0.547948\pi$
$907$	−5.54810e15	−0.300127	−0.150063	+	0.988676i	$0.547948\pi$
$908$	−1.62158e16	−0.871897
$909$	−2.27182e15	−0.121415
$910$	9.98745e14	0.0530551
$911$	−1.81180e15	−0.0956662	−0.0478331	−	0.998855i	$-0.515232\pi$
$911$	−1.81180e15	−0.0956662	−0.0478331	+	0.998855i	$0.515232\pi$
$912$	8.68062e15	0.455595
$913$	−3.23694e16	−1.68867
$914$	8.78926e14	0.0455772
$915$	1.74659e16	0.900272
$916$	1.30315e16	0.667679
$917$	−5.80680e15	−0.295737
$918$	−1.83081e15	−0.0926846
$919$	2.10479e16	1.05919	0.529595	−	0.848251i	$-0.322344\pi$
$919$	2.10479e16	1.05919	0.529595	+	0.848251i	$0.322344\pi$
$920$	−4.19644e16	−2.09917
$921$	2.08180e16	1.03517
$922$	1.48021e15	0.0731651
$923$	−1.98812e15	−0.0976861
$924$	−1.15643e16	−0.564836
$925$	9.37848e15	0.455358
$926$	−1.14135e16	−0.550882
$927$	−1.16560e16	−0.559256
$928$	4.49293e14	0.0214297
$929$	2.42748e16	1.15098	0.575492	−	0.817808i	$-0.304811\pi$
$929$	2.42748e16	1.15098	0.575492	+	0.817808i	$0.304811\pi$
$930$	1.40326e16	0.661427
$931$	−2.25854e16	−1.05829
$932$	7.93579e15	0.369660
$933$	−4.33100e15	−0.200558
$934$	−2.99432e15	−0.137845
$935$	−7.45773e16	−3.41305
$936$	7.06258e14	0.0321326
$937$	1.07613e15	0.0486739	0.0243370	−	0.999704i	$-0.492253\pi$
$937$	1.07613e15	0.0486739	0.0243370	+	0.999704i	$0.492253\pi$
$938$	−1.05665e15	−0.0475134
$939$	−3.72969e15	−0.166730
$940$	−2.30804e16	−1.02575
$941$	1.33032e16	0.587780	0.293890	−	0.955839i	$-0.405050\pi$
$941$	1.33032e16	0.587780	0.293890	+	0.955839i	$0.405050\pi$
$942$	3.52577e15	0.154872
$943$	−8.88458e15	−0.387992
$944$	−1.37075e15	−0.0595132
$945$	−4.43310e15	−0.191352
$946$	−2.07683e16	−0.891250
$947$	3.09201e16	1.31922	0.659608	−	0.751610i	$-0.270722\pi$
$947$	3.09201e16	1.31922	0.659608	+	0.751610i	$0.270722\pi$
$948$	7.46561e15	0.316679
$949$	3.78691e15	0.159706
$950$	−2.81556e16	−1.18055
$951$	1.46497e16	0.610711
$952$	−1.30577e16	−0.541209
$953$	−2.13055e16	−0.877974	−0.438987	−	0.898493i	$-0.644663\pi$
$953$	−2.13055e16	−0.877974	−0.438987	+	0.898493i	$0.644663\pi$
$954$	−1.79751e15	−0.0736469
$955$	−4.11487e16	−1.67625
$956$	−1.34909e16	−0.546416
$957$	6.01744e14	0.0242324
$958$	3.83235e15	0.153446
$959$	−5.54107e15	−0.220593
$960$	−4.49178e14	−0.0177798
$961$	4.20687e16	1.65569
$962$	−3.99303e14	−0.0156257
$963$	−2.26097e15	−0.0879730
$964$	−3.39792e15	−0.131459
$965$	1.43410e16	0.551671
$966$	−6.82547e15	−0.261071
$967$	3.12915e16	1.19009	0.595046	−	0.803692i	$-0.297134\pi$
$967$	3.12915e16	1.19009	0.595046	+	0.803692i	$0.297134\pi$
$968$	5.88755e16	2.22649
$969$	2.90235e16	1.09136
$970$	2.76810e16	1.03499
$971$	−1.49974e16	−0.557584	−0.278792	−	0.960352i	$-0.589934\pi$
$971$	−1.49974e16	−0.557584	−0.278792	+	0.960352i	$0.589934\pi$
$972$	−1.39960e15	−0.0517416
$973$	7.83423e15	0.287989
$974$	−2.15388e16	−0.787314
$975$	2.99669e15	0.108922
$976$	1.23383e16	0.445944
$977$	−1.78330e16	−0.640920	−0.320460	−	0.947262i	$-0.603837\pi$
$977$	−1.78330e16	−0.640920	−0.320460	+	0.947262i	$0.603837\pi$
$978$	2.20722e15	0.0788828
$979$	1.86248e16	0.661890
$980$	2.23658e16	0.790390
$981$	1.10761e16	0.389233
$982$	−2.23608e16	−0.781401
$983$	−1.53203e16	−0.532380	−0.266190	−	0.963921i	$-0.585765\pi$
$983$	−1.53203e16	−0.532380	−0.266190	+	0.963921i	$0.585765\pi$
$984$	3.11610e15	0.107681
$985$	−4.03523e16	−1.38666
$986$	3.03354e14	0.0103664
$987$	−8.40828e15	−0.285735
$988$	−4.99872e15	−0.168926
$989$	5.11138e16	1.71775
$990$	1.36724e16	0.456933
$991$	1.56797e15	0.0521113	0.0260557	−	0.999660i	$-0.491705\pi$
$991$	1.56797e15	0.0521113	0.0260557	+	0.999660i	$0.491705\pi$
$992$	4.90888e16	1.62244
$993$	−2.20559e16	−0.724944
$994$	−6.73885e15	−0.220273
$995$	−2.94457e16	−0.957183
$996$	−1.24748e16	−0.403281
$997$	4.31229e16	1.38639	0.693193	−	0.720752i	$-0.256203\pi$
$997$	4.31229e16	1.38639	0.693193	+	0.720752i	$0.256203\pi$
$998$	−9.63799e15	−0.308155
$999$	1.77238e15	0.0563568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.11	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-19.9033 q^{2} +243.000 q^{3} -1651.86 q^{4} +11169.4 q^{5} -4836.50 q^{6} -27660.5 q^{7} +73639.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-19.9033 q^{2} +243.000 q^{3} -1651.86 q^{4} +11169.4 q^{5} -4836.50 q^{6} -27660.5 q^{7} +73639.4 q^{8} +59049.0 q^{9} -222307. q^{10} -1.04155e6 q^{11} -401402. q^{12} +162421. q^{13} +550535. q^{14} +2.71416e6 q^{15} +1.91734e6 q^{16} +6.41060e6 q^{17} -1.17527e6 q^{18} +1.86314e7 q^{19} -1.84502e7 q^{20} -6.72150e6 q^{21} +2.07302e7 q^{22} -5.10201e7 q^{23} +1.78944e7 q^{24} +7.59268e7 q^{25} -3.23270e6 q^{26} +1.43489e7 q^{27} +4.56912e7 q^{28} -2.37753e6 q^{29} -5.40207e7 q^{30} -2.59764e8 q^{31} -1.88975e8 q^{32} -2.53096e8 q^{33} -1.27592e8 q^{34} -3.08950e8 q^{35} -9.75406e7 q^{36} +1.23520e8 q^{37} -3.70826e8 q^{38} +3.94682e7 q^{39} +8.22506e8 q^{40} +1.74139e8 q^{41} +1.33780e8 q^{42} -1.00184e9 q^{43} +1.72049e9 q^{44} +6.59540e8 q^{45} +1.01547e9 q^{46} +1.25095e9 q^{47} +4.65914e8 q^{48} -1.21222e9 q^{49} -1.51119e9 q^{50} +1.55777e9 q^{51} -2.68296e8 q^{52} +1.52944e9 q^{53} -2.85590e8 q^{54} -1.16334e10 q^{55} -2.03690e9 q^{56} +4.52742e9 q^{57} +4.73207e7 q^{58} -7.14924e8 q^{59} -4.48341e9 q^{60} +6.43509e9 q^{61} +5.17015e9 q^{62} -1.63332e9 q^{63} -1.65494e8 q^{64} +1.81414e9 q^{65} +5.03745e9 q^{66} -1.91932e9 q^{67} -1.05894e10 q^{68} -1.23979e10 q^{69} +6.14913e9 q^{70} -1.22406e10 q^{71} +4.34833e9 q^{72} +2.33155e10 q^{73} -2.45845e9 q^{74} +1.84502e10 q^{75} -3.07764e10 q^{76} +2.88097e10 q^{77} -7.85547e8 q^{78} -1.85989e10 q^{79} +2.14155e10 q^{80} +3.48678e9 q^{81} -3.46593e9 q^{82} +3.10782e10 q^{83} +1.11030e10 q^{84} +7.16024e10 q^{85} +1.99398e10 q^{86} -5.77740e8 q^{87} -7.66989e10 q^{88} -1.78818e10 q^{89} -1.31270e10 q^{90} -4.49263e9 q^{91} +8.42781e10 q^{92} -6.31226e10 q^{93} -2.48981e10 q^{94} +2.08101e11 q^{95} -4.59209e10 q^{96} -1.24517e11 q^{97} +2.41272e10 q^{98} -6.15024e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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