LMFDB - Embedded newform 177.12.a.b.1.20

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			1.20
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)

$f(q)$	$=$	$q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +52880.9 q^{10} -336316. q^{11} -199456. q^{12} -1.03704e6 q^{13} +9126.82 q^{14} +366816. q^{15} -1.83957e6 q^{16} +1.09205e7 q^{17} +2.06857e6 q^{18} +1.71468e7 q^{19} -1.23903e6 q^{20} +63309.5 q^{21} -1.17816e7 q^{22} +5.60344e7 q^{23} -2.44210e7 q^{24} -4.65494e7 q^{25} -3.63289e7 q^{26} +1.43489e7 q^{27} -213847. q^{28} -1.56066e8 q^{29} +1.28500e7 q^{30} -1.86762e8 q^{31} +1.41377e8 q^{32} -8.17247e7 q^{33} +3.82561e8 q^{34} +393283. q^{35} -4.84677e7 q^{36} -3.36109e8 q^{37} +6.00675e8 q^{38} -2.52000e8 q^{39} -1.51705e8 q^{40} -7.88676e7 q^{41} +2.21782e6 q^{42} -6.26130e8 q^{43} +2.76050e8 q^{44} +8.91362e7 q^{45} +1.96296e9 q^{46} -1.23527e9 q^{47} -4.47016e8 q^{48} -1.97726e9 q^{49} -1.63069e9 q^{50} +2.65369e9 q^{51} +8.51207e8 q^{52} -4.49700e9 q^{53} +5.02661e8 q^{54} -5.07679e8 q^{55} -2.61831e7 q^{56} +4.16667e9 q^{57} -5.46722e9 q^{58} -7.14924e8 q^{59} -3.01084e8 q^{60} -2.43334e9 q^{61} -6.54252e9 q^{62} +1.53842e7 q^{63} +8.72008e9 q^{64} -1.56544e9 q^{65} -2.86293e9 q^{66} +1.79589e10 q^{67} -8.96364e9 q^{68} +1.36163e10 q^{69} +1.37772e7 q^{70} +2.14587e10 q^{71} -5.93431e9 q^{72} -2.60537e10 q^{73} -1.17743e10 q^{74} -1.13115e10 q^{75} -1.40742e10 q^{76} -8.76214e7 q^{77} -8.82791e9 q^{78} -1.34645e9 q^{79} -2.77689e9 q^{80} +3.48678e9 q^{81} -2.76284e9 q^{82} -4.68213e10 q^{83} -5.19648e7 q^{84} +1.64849e10 q^{85} -2.19342e10 q^{86} -3.79241e10 q^{87} +3.37991e10 q^{88} -4.74741e10 q^{89} +3.12256e9 q^{90} -2.70183e8 q^{91} -4.59933e10 q^{92} -4.53831e10 q^{93} -4.32732e10 q^{94} +2.58836e10 q^{95} +3.43547e10 q^{96} -1.01566e11 q^{97} -6.92660e10 q^{98} -1.98591e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35.0313	0.774090	0.387045	−	0.922061i	$-0.373496\pi$
$2$	35.0313	0.774090	0.387045	+	0.922061i	$0.373496\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−820.805	−0.400784
$5$	1509.53	0.216026	0.108013	−	0.994149i	$-0.465551\pi$
$5$	1509.53	0.216026	0.108013	+	0.994149i	$0.465551\pi$
$6$	8512.61	0.446921
$7$	260.533	0.00585900	0.00292950	−	0.999996i	$-0.499068\pi$
$7$	260.533	0.00585900	0.00292950	+	0.999996i	$0.499068\pi$
$8$	−100498.	−1.08433
$9$	59049.0	0.333333
$10$	52880.9	0.167224
$11$	−336316.	−0.629633	−0.314816	−	0.949153i	$-0.601943\pi$
$11$	−336316.	−0.629633	−0.314816	+	0.949153i	$0.601943\pi$
$12$	−199456.	−0.231393
$13$	−1.03704e6	−0.774652	−0.387326	−	0.921943i	$-0.626601\pi$
$13$	−1.03704e6	−0.774652	−0.387326	+	0.921943i	$0.626601\pi$
$14$	9126.82	0.00453540
$15$	366816.	0.124723
$16$	−1.83957e6	−0.438588
$17$	1.09205e7	1.86541	0.932707	−	0.360636i	$-0.117440\pi$
$17$	1.09205e7	1.86541	0.932707	+	0.360636i	$0.117440\pi$
$18$	2.06857e6	0.258030
$19$	1.71468e7	1.58869	0.794343	−	0.607469i	$-0.207815\pi$
$19$	1.71468e7	1.58869	0.794343	+	0.607469i	$0.207815\pi$
$20$	−1.23903e6	−0.0865799
$21$	63309.5	0.00338270
$22$	−1.17816e7	−0.487393
$23$	5.60344e7	1.81531	0.907656	−	0.419715i	$-0.137870\pi$
$23$	5.60344e7	1.81531	0.907656	+	0.419715i	$0.137870\pi$
$24$	−2.44210e7	−0.626040
$25$	−4.65494e7	−0.953333
$26$	−3.63289e7	−0.599651
$27$	1.43489e7	0.192450
$28$	−213847.	−0.00234819
$29$	−1.56066e8	−1.41293	−0.706465	−	0.707748i	$-0.749711\pi$
$29$	−1.56066e8	−1.41293	−0.706465	+	0.707748i	$0.749711\pi$
$30$	1.28500e7	0.0965468
$31$	−1.86762e8	−1.17165	−0.585826	−	0.810437i	$-0.699230\pi$
$31$	−1.86762e8	−1.17165	−0.585826	+	0.810437i	$0.699230\pi$
$32$	1.41377e8	0.744826
$33$	−8.17247e7	−0.363519
$34$	3.82561e8	1.44400
$35$	393283.	0.00126570
$36$	−4.84677e7	−0.133595
$37$	−3.36109e8	−0.796838	−0.398419	−	0.917203i	$-0.630441\pi$
$37$	−3.36109e8	−0.796838	−0.398419	+	0.917203i	$0.630441\pi$
$38$	6.00675e8	1.22979
$39$	−2.52000e8	−0.447246
$40$	−1.51705e8	−0.234245
$41$	−7.88676e7	−0.106313	−0.0531566	−	0.998586i	$-0.516928\pi$
$41$	−7.88676e7	−0.106313	−0.0531566	+	0.998586i	$0.516928\pi$
$42$	2.21782e6	0.00261851
$43$	−6.26130e8	−0.649513	−0.324757	−	0.945798i	$-0.605282\pi$
$43$	−6.26130e8	−0.649513	−0.324757	+	0.945798i	$0.605282\pi$
$44$	2.76050e8	0.252347
$45$	8.91362e7	0.0720088
$46$	1.96296e9	1.40522
$47$	−1.23527e9	−0.785642	−0.392821	−	0.919615i	$-0.628501\pi$
$47$	−1.23527e9	−0.785642	−0.392821	+	0.919615i	$0.628501\pi$
$48$	−4.47016e8	−0.253219
$49$	−1.97726e9	−0.999966
$50$	−1.63069e9	−0.737966
$51$	2.65369e9	1.07700
$52$	8.51207e8	0.310468
$53$	−4.49700e9	−1.47708	−0.738542	−	0.674207i	$-0.764485\pi$
$53$	−4.49700e9	−1.47708	−0.738542	+	0.674207i	$0.764485\pi$
$54$	5.02661e8	0.148974
$55$	−5.07679e8	−0.136017
$56$	−2.61831e7	−0.00635311
$57$	4.16667e9	0.917228
$58$	−5.46722e9	−1.09374
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−3.01084e8	−0.0499869
$61$	−2.43334e9	−0.368884	−0.184442	−	0.982843i	$-0.559048\pi$
$61$	−2.43334e9	−0.368884	−0.184442	+	0.982843i	$0.559048\pi$
$62$	−6.54252e9	−0.906965
$63$	1.53842e7	0.00195300
$64$	8.72008e9	1.01515
$65$	−1.56544e9	−0.167345
$66$	−2.86293e9	−0.281396
$67$	1.79589e10	1.62506	0.812530	−	0.582920i	$-0.198090\pi$
$67$	1.79589e10	1.62506	0.812530	+	0.582920i	$0.198090\pi$
$68$	−8.96364e9	−0.747628
$69$	1.36163e10	1.04807
$70$	1.37772e7	0.000979766 0
$71$	2.14587e10	1.41151	0.705753	−	0.708458i	$-0.250609\pi$
$71$	2.14587e10	1.41151	0.705753	+	0.708458i	$0.250609\pi$
$72$	−5.93431e9	−0.361445
$73$	−2.60537e10	−1.47094	−0.735469	−	0.677559i	$-0.763038\pi$
$73$	−2.60537e10	−1.47094	−0.735469	+	0.677559i	$0.763038\pi$
$74$	−1.17743e10	−0.616825
$75$	−1.13115e10	−0.550407
$76$	−1.40742e10	−0.636720
$77$	−8.76214e7	−0.00368902
$78$	−8.82791e9	−0.346209
$79$	−1.34645e9	−0.0492313	−0.0246157	−	0.999697i	$-0.507836\pi$
$79$	−1.34645e9	−0.0492313	−0.0246157	+	0.999697i	$0.507836\pi$
$80$	−2.77689e9	−0.0947466
$81$	3.48678e9	0.111111
$82$	−2.76284e9	−0.0822961
$83$	−4.68213e10	−1.30471	−0.652355	−	0.757913i	$-0.726219\pi$
$83$	−4.68213e10	−1.30471	−0.652355	+	0.757913i	$0.726219\pi$
$84$	−5.19648e7	−0.00135573
$85$	1.64849e10	0.402978
$86$	−2.19342e10	−0.502782
$87$	−3.79241e10	−0.815755
$88$	3.37991e10	0.682732
$89$	−4.74741e10	−0.901179	−0.450590	−	0.892731i	$-0.648786\pi$
$89$	−4.74741e10	−0.901179	−0.450590	+	0.892731i	$0.648786\pi$
$90$	3.12256e9	0.0557413
$91$	−2.70183e8	−0.00453869
$92$	−4.59933e10	−0.727548
$93$	−4.53831e10	−0.676454
$94$	−4.32732e10	−0.608158
$95$	2.58836e10	0.343198
$96$	3.43547e10	0.430026
$97$	−1.01566e11	−1.20090	−0.600448	−	0.799663i	$-0.705011\pi$
$97$	−1.01566e11	−1.20090	−0.600448	+	0.799663i	$0.705011\pi$
$98$	−6.92660e10	−0.774064
$99$	−1.98591e10	−0.209878
$100$	3.82080e10	0.382080
$101$	1.33164e9	0.0126072	0.00630361	−	0.999980i	$-0.497993\pi$
$101$	1.33164e9	0.0126072	0.00630361	+	0.999980i	$0.497993\pi$
$102$	9.29623e10	0.833693
$103$	−6.78644e10	−0.576816	−0.288408	−	0.957508i	$-0.593126\pi$
$103$	−6.78644e10	−0.576816	−0.288408	+	0.957508i	$0.593126\pi$
$104$	1.04220e11	0.839981
$105$	9.55677e7	0.000730752 0
$106$	−1.57536e11	−1.14340
$107$	3.57206e10	0.246211	0.123105	−	0.992394i	$-0.460715\pi$
$107$	3.57206e10	0.246211	0.123105	+	0.992394i	$0.460715\pi$
$108$	−1.17777e10	−0.0771309
$109$	−2.99734e11	−1.86591	−0.932955	−	0.359993i	$-0.882779\pi$
$109$	−2.99734e11	−1.86591	−0.932955	+	0.359993i	$0.882779\pi$
$110$	−1.77847e10	−0.105290
$111$	−8.16744e10	−0.460055
$112$	−4.79270e8	−0.00256969
$113$	2.10528e11	1.07492	0.537462	−	0.843288i	$-0.319383\pi$
$113$	2.10528e11	1.07492	0.537462	+	0.843288i	$0.319383\pi$
$114$	1.45964e11	0.710018
$115$	8.45855e10	0.392155
$116$	1.28100e11	0.566279
$117$	−6.12361e10	−0.258217
$118$	−2.50448e10	−0.100778
$119$	2.84516e9	0.0109295
$120$	−3.68643e10	−0.135241
$121$	−1.72203e11	−0.603562
$122$	−8.52433e10	−0.285549
$123$	−1.91648e10	−0.0613800
$124$	1.53295e11	0.469579
$125$	−1.43975e11	−0.421971
$126$	5.38930e8	0.00151180
$127$	4.86852e11	1.30760	0.653802	−	0.756665i	$-0.273173\pi$
$127$	4.86852e11	1.30760	0.653802	+	0.756665i	$0.273173\pi$
$128$	1.59353e10	0.0409926
$129$	−1.52150e11	−0.374997
$130$	−5.48395e10	−0.129540
$131$	5.36260e11	1.21446	0.607230	−	0.794526i	$-0.292281\pi$
$131$	5.36260e11	1.21446	0.607230	+	0.794526i	$0.292281\pi$
$132$	6.70801e10	0.145692
$133$	4.46731e9	0.00930812
$134$	6.29126e11	1.25794
$135$	2.16601e10	0.0415743
$136$	−1.09749e12	−2.02273
$137$	−7.55158e11	−1.33683	−0.668413	−	0.743790i	$-0.733026\pi$
$137$	−7.55158e11	−1.33683	−0.668413	+	0.743790i	$0.733026\pi$
$138$	4.76999e11	0.811302
$139$	−4.94454e11	−0.808248	−0.404124	−	0.914704i	$-0.632424\pi$
$139$	−4.94454e11	−0.808248	−0.404124	+	0.914704i	$0.632424\pi$
$140$	−3.22808e8	−0.000507272 0
$141$	−3.00171e11	−0.453590
$142$	7.51727e11	1.09263
$143$	3.48773e11	0.487746
$144$	−1.08625e11	−0.146196
$145$	−2.35587e11	−0.305230
$146$	−9.12697e11	−1.13864
$147$	−4.80474e11	−0.577330
$148$	2.75880e11	0.319360
$149$	−4.43350e11	−0.494564	−0.247282	−	0.968944i	$-0.579537\pi$
$149$	−4.43350e11	−0.494564	−0.247282	+	0.968944i	$0.579537\pi$
$150$	−3.96257e11	−0.426065
$151$	−6.47742e10	−0.0671473	−0.0335737	−	0.999436i	$-0.510689\pi$
$151$	−6.47742e10	−0.0671473	−0.0335737	+	0.999436i	$0.510689\pi$
$152$	−1.72322e12	−1.72267
$153$	6.44847e11	0.621804
$154$	−3.06949e9	−0.00285564
$155$	−2.81923e11	−0.253108
$156$	2.06843e11	0.179249
$157$	−1.43131e12	−1.19752	−0.598762	−	0.800927i	$-0.704341\pi$
$157$	−1.43131e12	−1.19752	−0.598762	+	0.800927i	$0.704341\pi$
$158$	−4.71680e10	−0.0381095
$159$	−1.09277e12	−0.852795
$160$	2.13413e11	0.160902
$161$	1.45988e10	0.0106359
$162$	1.22147e11	0.0860101
$163$	1.47004e12	1.00069	0.500343	−	0.865827i	$-0.333207\pi$
$163$	1.47004e12	1.00069	0.500343	+	0.865827i	$0.333207\pi$
$164$	6.47349e10	0.0426086
$165$	−1.23366e11	−0.0785296
$166$	−1.64021e12	−1.00996
$167$	2.21102e12	1.31720	0.658602	−	0.752492i	$-0.271148\pi$
$167$	2.21102e12	1.31720	0.658602	+	0.752492i	$0.271148\pi$
$168$	−6.36249e9	−0.00366797
$169$	−7.16710e11	−0.399914
$170$	5.77488e11	0.311942
$171$	1.01250e12	0.529562
$172$	5.13931e11	0.260315
$173$	2.07803e12	1.01952	0.509762	−	0.860315i	$-0.329733\pi$
$173$	2.07803e12	1.01952	0.509762	+	0.860315i	$0.329733\pi$
$174$	−1.32853e12	−0.631468
$175$	−1.21277e10	−0.00558558
$176$	6.18677e11	0.276150
$177$	−1.73727e11	−0.0751646
$178$	−1.66308e12	−0.697594
$179$	−1.83659e12	−0.747001	−0.373501	−	0.927630i	$-0.621843\pi$
$179$	−1.83659e12	−0.747001	−0.373501	+	0.927630i	$0.621843\pi$
$180$	−7.31635e10	−0.0288600
$181$	1.42224e12	0.544179	0.272089	−	0.962272i	$-0.412285\pi$
$181$	1.42224e12	0.544179	0.272089	+	0.962272i	$0.412285\pi$
$182$	−9.46487e9	−0.00351336
$183$	−5.91302e11	−0.212975
$184$	−5.63135e12	−1.96840
$185$	−5.07366e11	−0.172138
$186$	−1.58983e12	−0.523636
$187$	−3.67275e12	−1.17453
$188$	1.01392e12	0.314873
$189$	3.73836e9	0.00112757
$190$	9.06737e11	0.265666
$191$	−1.86729e12	−0.531529	−0.265765	−	0.964038i	$-0.585624\pi$
$191$	−1.86729e12	−0.531529	−0.265765	+	0.964038i	$0.585624\pi$
$192$	2.11898e12	0.586098
$193$	−4.92216e11	−0.132309	−0.0661546	−	0.997809i	$-0.521073\pi$
$193$	−4.92216e11	−0.132309	−0.0661546	+	0.997809i	$0.521073\pi$
$194$	−3.55801e12	−0.929603
$195$	−3.80402e11	−0.0966168
$196$	1.62294e12	0.400770
$197$	−2.05476e12	−0.493397	−0.246698	−	0.969092i	$-0.579346\pi$
$197$	−2.05476e12	−0.493397	−0.246698	+	0.969092i	$0.579346\pi$
$198$	−6.95691e11	−0.162464
$199$	−4.52000e11	−0.102671	−0.0513353	−	0.998681i	$-0.516348\pi$
$199$	−4.52000e11	−0.102671	−0.0513353	+	0.998681i	$0.516348\pi$
$200$	4.67813e12	1.03373
$201$	4.36402e12	0.938228
$202$	4.66491e10	0.00975913
$203$	−4.06605e10	−0.00827836
$204$	−2.17816e12	−0.431643
$205$	−1.19053e11	−0.0229665
$206$	−2.37738e12	−0.446508
$207$	3.30877e12	0.605104
$208$	1.90771e12	0.339753
$209$	−5.76674e12	−1.00029
$210$	3.34786e9	0.000565668 0
$211$	−5.87467e12	−0.967007	−0.483504	−	0.875342i	$-0.660636\pi$
$211$	−5.87467e12	−0.967007	−0.483504	+	0.875342i	$0.660636\pi$
$212$	3.69116e12	0.591992
$213$	5.21447e12	0.814933
$214$	1.25134e12	0.190590
$215$	−9.45162e11	−0.140312
$216$	−1.44204e12	−0.208680
$217$	−4.86576e10	−0.00686471
$218$	−1.05001e13	−1.44438
$219$	−6.33106e12	−0.849246
$220$	4.16706e11	0.0545136
$221$	−1.13250e13	−1.44505
$222$	−2.86116e12	−0.356124
$223$	−6.67176e12	−0.810146	−0.405073	−	0.914284i	$-0.632754\pi$
$223$	−6.67176e12	−0.810146	−0.405073	+	0.914284i	$0.632754\pi$
$224$	3.68335e10	0.00436394
$225$	−2.74870e12	−0.317778
$226$	7.37507e12	0.832089
$227$	−8.01220e12	−0.882286	−0.441143	−	0.897437i	$-0.645427\pi$
$227$	−8.01220e12	−0.882286	−0.441143	+	0.897437i	$0.645427\pi$
$228$	−3.42003e12	−0.367610
$229$	−2.34900e12	−0.246484	−0.123242	−	0.992377i	$-0.539329\pi$
$229$	−2.34900e12	−0.246484	−0.123242	+	0.992377i	$0.539329\pi$
$230$	2.96314e12	0.303564
$231$	−2.12920e10	−0.00212986
$232$	1.56844e13	1.53209
$233$	2.08431e13	1.98840	0.994201	−	0.107536i	$-0.0342962\pi$
$233$	2.08431e13	1.98840	0.994201	+	0.107536i	$0.0342962\pi$
$234$	−2.14518e12	−0.199884
$235$	−1.86468e12	−0.169719
$236$	5.86814e11	0.0521776
$237$	−3.27188e11	−0.0284237
$238$	9.96698e10	0.00846039
$239$	−1.45584e13	−1.20760	−0.603801	−	0.797135i	$-0.706348\pi$
$239$	−1.45584e13	−1.20760	−0.603801	+	0.797135i	$0.706348\pi$
$240$	−6.74784e11	−0.0547020
$241$	4.94274e12	0.391628	0.195814	−	0.980641i	$-0.437265\pi$
$241$	4.94274e12	0.391628	0.195814	+	0.980641i	$0.437265\pi$
$242$	−6.03251e12	−0.467212
$243$	8.47289e11	0.0641500
$244$	1.99730e12	0.147843
$245$	−2.98473e12	−0.216019
$246$	−6.71369e11	−0.0475137
$247$	−1.77819e13	−1.23068
$248$	1.87692e13	1.27046
$249$	−1.13776e13	−0.753275
$250$	−5.04365e12	−0.326644
$251$	3.01994e13	1.91334	0.956672	−	0.291167i	$-0.0940435\pi$
$251$	3.01994e13	1.91334	0.956672	+	0.291167i	$0.0940435\pi$
$252$	−1.26275e10	−0.000782731 0
$253$	−1.88452e13	−1.14298
$254$	1.70551e13	1.01220
$255$	4.00583e12	0.232660
$256$	−1.73005e13	−0.983419
$257$	1.73748e13	0.966688	0.483344	−	0.875430i	$-0.339422\pi$
$257$	1.73748e13	0.966688	0.483344	+	0.875430i	$0.339422\pi$
$258$	−5.33000e12	−0.290281
$259$	−8.75674e10	−0.00466868
$260$	1.28492e12	0.0670693
$261$	−9.21557e12	−0.470977
$262$	1.87859e13	0.940102
$263$	−2.89941e13	−1.42087	−0.710434	−	0.703764i	$-0.751501\pi$
$263$	−2.89941e13	−1.42087	−0.710434	+	0.703764i	$0.751501\pi$
$264$	8.21318e12	0.394176
$265$	−6.78835e12	−0.319089
$266$	1.56496e11	0.00720532
$267$	−1.15362e13	−0.520296
$268$	−1.47408e13	−0.651298
$269$	3.67415e13	1.59045	0.795224	−	0.606316i	$-0.207353\pi$
$269$	3.67415e13	1.59045	0.795224	+	0.606316i	$0.207353\pi$
$270$	7.58783e11	0.0321823
$271$	−2.77787e13	−1.15446	−0.577232	−	0.816580i	$-0.695867\pi$
$271$	−2.77787e13	−1.15446	−0.577232	+	0.816580i	$0.695867\pi$
$272$	−2.00891e13	−0.818148
$273$	−6.56545e10	−0.00262041
$274$	−2.64542e13	−1.03482
$275$	1.56553e13	0.600250
$276$	−1.11764e13	−0.420050
$277$	−3.35056e12	−0.123447	−0.0617233	−	0.998093i	$-0.519660\pi$
$277$	−3.35056e12	−0.123447	−0.0617233	+	0.998093i	$0.519660\pi$
$278$	−1.73214e13	−0.625657
$279$	−1.10281e13	−0.390551
$280$	−3.95241e10	−0.00137244
$281$	−2.49018e13	−0.847903	−0.423951	−	0.905685i	$-0.639357\pi$
$281$	−2.49018e13	−0.847903	−0.423951	+	0.905685i	$0.639357\pi$
$282$	−1.05154e13	−0.351120
$283$	1.77230e13	0.580378	0.290189	−	0.956969i	$-0.406282\pi$
$283$	1.77230e13	0.580378	0.290189	+	0.956969i	$0.406282\pi$
$284$	−1.76134e13	−0.565709
$285$	6.28971e12	0.198146
$286$	1.22180e13	0.377560
$287$	−2.05476e10	−0.000622889 0
$288$	8.34819e12	0.248275
$289$	8.49863e13	2.47977
$290$	−8.25293e12	−0.236276
$291$	−2.46806e13	−0.693338
$292$	2.13850e13	0.589528
$293$	−3.45104e13	−0.933636	−0.466818	−	0.884353i	$-0.654600\pi$
$293$	−3.45104e13	−0.933636	−0.466818	+	0.884353i	$0.654600\pi$
$294$	−1.68316e13	−0.446906
$295$	−1.07920e12	−0.0281242
$296$	3.37783e13	0.864038
$297$	−4.82576e12	−0.121173
$298$	−1.55311e13	−0.382837
$299$	−5.81098e13	−1.40624
$300$	9.28455e12	0.220594
$301$	−1.63128e11	−0.00380550
$302$	−2.26913e12	−0.0519781
$303$	3.23588e11	0.00727878
$304$	−3.15428e13	−0.696779
$305$	−3.67321e12	−0.0796886
$306$	2.25899e13	0.481333
$307$	1.44189e12	0.0301767	0.0150883	−	0.999886i	$-0.495197\pi$
$307$	1.44189e12	0.0301767	0.0150883	+	0.999886i	$0.495197\pi$
$308$	7.19201e10	0.00147850
$309$	−1.64911e13	−0.333025
$310$	−9.87613e12	−0.195928
$311$	8.31693e13	1.62099	0.810496	−	0.585744i	$-0.199198\pi$
$311$	8.31693e13	1.62099	0.810496	+	0.585744i	$0.199198\pi$
$312$	2.53256e13	0.484963
$313$	−7.11877e13	−1.33940	−0.669701	−	0.742631i	$-0.733578\pi$
$313$	−7.11877e13	−1.33940	−0.669701	+	0.742631i	$0.733578\pi$
$314$	−5.01406e13	−0.926993
$315$	2.32229e10	0.000421900 0
$316$	1.10517e12	0.0197311
$317$	−3.80953e13	−0.668413	−0.334207	−	0.942500i	$-0.608468\pi$
$317$	−3.80953e13	−0.668413	−0.334207	+	0.942500i	$0.608468\pi$
$318$	−3.82812e13	−0.660141
$319$	5.24876e13	0.889627
$320$	1.31632e13	0.219299
$321$	8.68009e12	0.142150
$322$	5.11416e11	0.00823316
$323$	1.87252e14	2.96356
$324$	−2.86197e12	−0.0445315
$325$	4.82736e13	0.738501
$326$	5.14975e13	0.774622
$327$	−7.28354e13	−1.07728
$328$	7.92604e12	0.115279
$329$	−3.21829e11	−0.00460308
$330$	−4.32167e12	−0.0607890
$331$	3.71033e13	0.513285	0.256642	−	0.966506i	$-0.417384\pi$
$331$	3.71033e13	0.513285	0.256642	+	0.966506i	$0.417384\pi$
$332$	3.84312e13	0.522907
$333$	−1.98469e13	−0.265613
$334$	7.74551e13	1.01963
$335$	2.71096e13	0.351056
$336$	−1.16463e11	−0.00148361
$337$	2.84418e13	0.356445	0.178223	−	0.983990i	$-0.442965\pi$
$337$	2.84418e13	0.356445	0.178223	+	0.983990i	$0.442965\pi$
$338$	−2.51073e13	−0.309570
$339$	5.11583e13	0.620608
$340$	−1.35309e13	−0.161507
$341$	6.28109e13	0.737711
$342$	3.54693e13	0.409929
$343$	−1.03030e12	−0.0117178
$344$	6.29249e13	0.704289
$345$	2.05543e13	0.226411
$346$	7.27961e13	0.789205
$347$	9.79399e13	1.04507	0.522537	−	0.852616i	$-0.324985\pi$
$347$	9.79399e13	1.04507	0.522537	+	0.852616i	$0.324985\pi$
$348$	3.11283e13	0.326942
$349$	−1.19120e14	−1.23153	−0.615766	−	0.787929i	$-0.711153\pi$
$349$	−1.19120e14	−1.23153	−0.615766	+	0.787929i	$0.711153\pi$
$350$	−4.24848e11	−0.00432374
$351$	−1.48804e13	−0.149082
$352$	−4.75474e13	−0.468967
$353$	1.20545e14	1.17054	0.585272	−	0.810837i	$-0.300988\pi$
$353$	1.20545e14	1.17054	0.585272	+	0.810837i	$0.300988\pi$
$354$	−6.08588e12	−0.0581842
$355$	3.23926e13	0.304922
$356$	3.89670e13	0.361178
$357$	6.91374e11	0.00631013
$358$	−6.43383e13	−0.578246
$359$	−5.83637e13	−0.516563	−0.258281	−	0.966070i	$-0.583156\pi$
$359$	−5.83637e13	−0.516563	−0.258281	+	0.966070i	$0.583156\pi$
$360$	−8.95802e12	−0.0780815
$361$	1.77522e14	1.52392
$362$	4.98231e13	0.421244
$363$	−4.18454e13	−0.348467
$364$	2.21768e11	0.00181903
$365$	−3.93289e13	−0.317761
$366$	−2.07141e13	−0.164862
$367$	−3.93716e13	−0.308688	−0.154344	−	0.988017i	$-0.549326\pi$
$367$	−3.93716e13	−0.308688	−0.154344	+	0.988017i	$0.549326\pi$
$368$	−1.03079e14	−0.796175
$369$	−4.65705e12	−0.0354377
$370$	−1.77737e13	−0.133250
$371$	−1.17162e12	−0.00865424
$372$	3.72507e13	0.271112
$373$	1.32550e14	0.950567	0.475283	−	0.879833i	$-0.342346\pi$
$373$	1.32550e14	0.950567	0.475283	+	0.879833i	$0.342346\pi$
$374$	−1.28661e14	−0.909189
$375$	−3.49860e13	−0.243625
$376$	1.24143e14	0.851898
$377$	1.61847e14	1.09453
$378$	1.30960e11	0.000872838 0
$379$	1.76578e13	0.115990	0.0579952	−	0.998317i	$-0.481529\pi$
$379$	1.76578e13	0.115990	0.0579952	+	0.998317i	$0.481529\pi$
$380$	−2.12454e13	−0.137548
$381$	1.18305e14	0.754946
$382$	−6.54135e13	−0.411452
$383$	−4.09907e13	−0.254151	−0.127075	−	0.991893i	$-0.540559\pi$
$383$	−4.09907e13	−0.254151	−0.127075	+	0.991893i	$0.540559\pi$
$384$	3.87228e12	0.0236671
$385$	−1.32267e11	−0.000796926 0
$386$	−1.72430e13	−0.102419
$387$	−3.69724e13	−0.216504
$388$	8.33663e13	0.481300
$389$	3.53527e13	0.201233	0.100617	−	0.994925i	$-0.467918\pi$
$389$	3.53527e13	0.201233	0.100617	+	0.994925i	$0.467918\pi$
$390$	−1.33260e13	−0.0747902
$391$	6.11925e14	3.38631
$392$	1.98711e14	1.08430
$393$	1.30311e14	0.701169
$394$	−7.19809e13	−0.381934
$395$	−2.03251e12	−0.0106353
$396$	1.63005e13	0.0841156
$397$	5.79838e13	0.295093	0.147546	−	0.989055i	$-0.452862\pi$
$397$	5.79838e13	0.295093	0.147546	+	0.989055i	$0.452862\pi$
$398$	−1.58342e13	−0.0794764
$399$	1.08556e12	0.00537404
$400$	8.56311e13	0.418121
$401$	1.33258e14	0.641801	0.320900	−	0.947113i	$-0.396015\pi$
$401$	1.33258e14	0.641801	0.320900	+	0.947113i	$0.396015\pi$
$402$	1.52878e14	0.726274
$403$	1.93679e14	0.907623
$404$	−1.09302e12	−0.00505277
$405$	5.26341e12	0.0240029
$406$	−1.42439e12	−0.00640820
$407$	1.13039e14	0.501716
$408$	−2.66691e14	−1.16782
$409$	−2.38767e14	−1.03156	−0.515782	−	0.856720i	$-0.672499\pi$
$409$	−2.38767e14	−1.03156	−0.515782	+	0.856720i	$0.672499\pi$
$410$	−4.17059e12	−0.0177781
$411$	−1.83503e14	−0.771817
$412$	5.57035e13	0.231179
$413$	−1.86261e11	−0.000762777 0
$414$	1.15911e14	0.468405
$415$	−7.06782e13	−0.281852
$416$	−1.46614e14	−0.576981
$417$	−1.20152e14	−0.466642
$418$	−2.02016e14	−0.774314
$419$	−2.05161e14	−0.776102	−0.388051	−	0.921638i	$-0.626852\pi$
$419$	−2.05161e14	−0.776102	−0.388051	+	0.921638i	$0.626852\pi$
$420$	−7.84425e10	−0.000292874 0
$421$	−5.23103e13	−0.192768	−0.0963842	−	0.995344i	$-0.530728\pi$
$421$	−5.23103e13	−0.192768	−0.0963842	+	0.995344i	$0.530728\pi$
$422$	−2.05797e14	−0.748551
$423$	−7.29416e13	−0.261881
$424$	4.51940e14	1.60165
$425$	−5.08345e14	−1.77836
$426$	1.82670e14	0.630832
$427$	−6.33966e11	−0.00216129
$428$	−2.93196e13	−0.0986774
$429$	8.47517e13	0.281601
$430$	−3.31103e13	−0.108614
$431$	−1.30800e14	−0.423625	−0.211813	−	0.977310i	$-0.567937\pi$
$431$	−1.30800e14	−0.423625	−0.211813	+	0.977310i	$0.567937\pi$
$432$	−2.63959e13	−0.0844064
$433$	−4.07842e14	−1.28768	−0.643841	−	0.765160i	$-0.722660\pi$
$433$	−4.07842e14	−1.28768	−0.643841	+	0.765160i	$0.722660\pi$
$434$	−1.70454e12	−0.00531391
$435$	−5.72476e13	−0.176225
$436$	2.46024e14	0.747827
$437$	9.60809e14	2.88396
$438$	−2.21785e14	−0.657393
$439$	1.90268e14	0.556943	0.278471	−	0.960445i	$-0.410172\pi$
$439$	1.90268e14	0.556943	0.278471	+	0.960445i	$0.410172\pi$
$440$	5.10207e13	0.147488
$441$	−1.16755e14	−0.333322
$442$	−3.96731e14	−1.11860
$443$	4.99000e14	1.38957	0.694784	−	0.719218i	$-0.255500\pi$
$443$	4.99000e14	1.38957	0.694784	+	0.719218i	$0.255500\pi$
$444$	6.70388e13	0.184383
$445$	−7.16635e13	−0.194679
$446$	−2.33721e14	−0.627127
$447$	−1.07734e14	−0.285537
$448$	2.27187e12	0.00594777
$449$	−7.64726e14	−1.97766	−0.988829	−	0.149054i	$-0.952377\pi$
$449$	−7.64726e14	−1.97766	−0.988829	+	0.149054i	$0.952377\pi$
$450$	−9.62906e13	−0.245989
$451$	2.65244e13	0.0669383
$452$	−1.72802e14	−0.430813
$453$	−1.57401e13	−0.0387675
$454$	−2.80678e14	−0.682969
$455$	−4.07849e11	−0.000980476 0
$456$	−4.18742e14	−0.994581
$457$	5.37215e14	1.26069	0.630346	−	0.776314i	$-0.282913\pi$
$457$	5.37215e14	1.26069	0.630346	+	0.776314i	$0.282913\pi$
$458$	−8.22886e13	−0.190801
$459$	1.56698e14	0.358999
$460$	−6.94283e13	−0.157170
$461$	−3.46322e14	−0.774684	−0.387342	−	0.921936i	$-0.626607\pi$
$461$	−3.46322e14	−0.774684	−0.387342	+	0.921936i	$0.626607\pi$
$462$	−7.45887e11	−0.00164870
$463$	−4.09490e14	−0.894434	−0.447217	−	0.894426i	$-0.647585\pi$
$463$	−4.09490e14	−0.894434	−0.447217	+	0.894426i	$0.647585\pi$
$464$	2.87096e14	0.619694
$465$	−6.85072e13	−0.146132
$466$	7.30161e14	1.53920
$467$	−2.72786e14	−0.568302	−0.284151	−	0.958779i	$-0.591712\pi$
$467$	−2.72786e14	−0.568302	−0.284151	+	0.958779i	$0.591712\pi$
$468$	5.02629e13	0.103489
$469$	4.67890e12	0.00952123
$470$	−6.53223e13	−0.131378
$471$	−3.47807e14	−0.691391
$472$	7.18485e13	0.141168
$473$	2.10577e14	0.408955
$474$	−1.14618e13	−0.0220025
$475$	−7.98174e14	−1.51455
$476$	−2.33532e12	−0.00438035
$477$	−2.65543e14	−0.492362
$478$	−5.09999e14	−0.934793
$479$	1.26905e14	0.229950	0.114975	−	0.993368i	$-0.463321\pi$
$479$	1.26905e14	0.229950	0.114975	+	0.993368i	$0.463321\pi$
$480$	5.18595e13	0.0928969
$481$	3.48558e14	0.617272
$482$	1.73151e14	0.303156
$483$	3.54751e12	0.00614065
$484$	1.41345e14	0.241898
$485$	−1.53318e14	−0.259425
$486$	2.96817e13	0.0496579
$487$	5.80668e14	0.960547	0.480274	−	0.877119i	$-0.340537\pi$
$487$	5.80668e14	0.960547	0.480274	+	0.877119i	$0.340537\pi$
$488$	2.44546e14	0.399993
$489$	3.57220e14	0.577747
$490$	−1.04559e14	−0.167218
$491$	−1.06280e15	−1.68076	−0.840378	−	0.542001i	$-0.817667\pi$
$491$	−1.06280e15	−1.68076	−0.840378	+	0.542001i	$0.817667\pi$
$492$	1.57306e13	0.0246001
$493$	−1.70433e15	−2.63570
$494$	−6.22923e14	−0.952657
$495$	−2.99779e13	−0.0453391
$496$	3.43562e14	0.513873
$497$	5.59070e12	0.00827001
$498$	−3.98572e14	−0.583103
$499$	−7.69931e14	−1.11403	−0.557017	−	0.830501i	$-0.688054\pi$
$499$	−7.69931e14	−1.11403	−0.557017	+	0.830501i	$0.688054\pi$
$500$	1.18176e14	0.169119
$501$	5.37279e14	0.760488
$502$	1.05793e15	1.48110
$503$	−1.25577e15	−1.73895	−0.869473	−	0.493980i	$-0.835542\pi$
$503$	−1.25577e15	−1.73895	−0.869473	+	0.493980i	$0.835542\pi$
$504$	−1.54608e12	−0.00211770
$505$	2.01015e12	0.00272349
$506$	−6.60174e14	−0.884770
$507$	−1.74161e14	−0.230891
$508$	−3.99611e14	−0.524067
$509$	2.94090e14	0.381534	0.190767	−	0.981635i	$-0.438903\pi$
$509$	2.94090e14	0.381534	0.190767	+	0.981635i	$0.438903\pi$
$510$	1.40329e14	0.180100
$511$	−6.78786e12	−0.00861823
$512$	−6.38695e14	−0.802248
$513$	2.46038e14	0.305743
$514$	6.08661e14	0.748304
$515$	−1.02443e14	−0.124608
$516$	1.24885e14	0.150293
$517$	4.15442e14	0.494666
$518$	−3.06760e12	−0.00361398
$519$	5.04961e14	0.588623
$520$	1.57324e14	0.181458
$521$	4.38782e14	0.500773	0.250387	−	0.968146i	$-0.419442\pi$
$521$	4.38782e14	0.500773	0.250387	+	0.968146i	$0.419442\pi$
$522$	−3.22834e14	−0.364578
$523$	1.10640e15	1.23639	0.618193	−	0.786027i	$-0.287865\pi$
$523$	1.10640e15	1.23639	0.618193	+	0.786027i	$0.287865\pi$
$524$	−4.40165e14	−0.486736
$525$	−2.94702e12	−0.00322483
$526$	−1.01570e15	−1.09988
$527$	−2.03954e15	−2.18562
$528$	1.50339e14	0.159435
$529$	2.18704e15	2.29536
$530$	−2.37805e14	−0.247004
$531$	−4.22156e13	−0.0433963
$532$	−3.66679e12	−0.00373054
$533$	8.17888e13	0.0823558
$534$	−4.04128e14	−0.402756
$535$	5.39213e13	0.0531881
$536$	−1.80484e15	−1.76211
$537$	−4.46292e14	−0.431281
$538$	1.28710e15	1.23115
$539$	6.64983e14	0.629611
$540$	−1.77787e13	−0.0166623
$541$	1.86406e15	1.72931	0.864657	−	0.502363i	$-0.167536\pi$
$541$	1.86406e15	1.72931	0.864657	+	0.502363i	$0.167536\pi$
$542$	−9.73123e14	−0.893659
$543$	3.45605e14	0.314182
$544$	1.54392e15	1.38941
$545$	−4.52458e14	−0.403086
$546$	−2.29996e12	−0.00202844
$547$	1.53114e15	1.33686	0.668429	−	0.743776i	$-0.266967\pi$
$547$	1.53114e15	1.33686	0.668429	+	0.743776i	$0.266967\pi$
$548$	6.19838e14	0.535778
$549$	−1.43686e14	−0.122961
$550$	5.48426e14	0.464648
$551$	−2.67604e15	−2.24470
$552$	−1.36842e15	−1.13646
$553$	−3.50795e11	−0.000288446 0
$554$	−1.17375e14	−0.0955588
$555$	−1.23290e14	−0.0993840
$556$	4.05851e14	0.323933
$557$	−1.89472e13	−0.0149742	−0.00748708	−	0.999972i	$-0.502383\pi$
$557$	−1.89472e13	−0.0149742	−0.00748708	+	0.999972i	$0.502383\pi$
$558$	−3.86329e14	−0.302322
$559$	6.49321e14	0.503147
$560$	−7.23472e11	−0.000555121 0
$561$	−8.92478e14	−0.678113
$562$	−8.72343e14	−0.656353
$563$	5.31050e14	0.395675	0.197838	−	0.980235i	$-0.436608\pi$
$563$	5.31050e14	0.395675	0.197838	+	0.980235i	$0.436608\pi$
$564$	2.46382e14	0.181792
$565$	3.17798e14	0.232212
$566$	6.20859e14	0.449265
$567$	9.08423e11	0.000651000 0
$568$	−2.15656e15	−1.53054
$569$	−1.05670e15	−0.742734	−0.371367	−	0.928486i	$-0.621111\pi$
$569$	−1.05670e15	−0.742734	−0.371367	+	0.928486i	$0.621111\pi$
$570$	2.20337e14	0.153383
$571$	2.39861e15	1.65372	0.826859	−	0.562409i	$-0.190125\pi$
$571$	2.39861e15	1.65372	0.826859	+	0.562409i	$0.190125\pi$
$572$	−2.86274e14	−0.195481
$573$	−4.53750e14	−0.306879
$574$	−7.19810e11	−0.000482173 0
$575$	−2.60837e15	−1.73060
$576$	5.14912e14	0.338384
$577$	−2.64391e15	−1.72100	−0.860498	−	0.509455i	$-0.829847\pi$
$577$	−2.64391e15	−1.72100	−0.860498	+	0.509455i	$0.829847\pi$
$578$	2.97718e15	1.91956
$579$	−1.19608e14	−0.0763888
$580$	1.93371e14	0.122331
$581$	−1.21985e13	−0.00764430
$582$	−8.64596e14	−0.536706
$583$	1.51241e15	0.930021
$584$	2.61835e15	1.59499
$585$	−9.24378e13	−0.0557818
$586$	−1.20894e15	−0.722719
$587$	−9.10850e14	−0.539433	−0.269716	−	0.962940i	$-0.586930\pi$
$587$	−9.10850e14	−0.539433	−0.269716	+	0.962940i	$0.586930\pi$
$588$	3.94376e14	0.231385
$589$	−3.20237e15	−1.86139
$590$	−3.78058e13	−0.0217707
$591$	−4.99306e14	−0.284863
$592$	6.18296e14	0.349484
$593$	2.44368e15	1.36850	0.684248	−	0.729249i	$-0.260130\pi$
$593$	2.44368e15	1.36850	0.684248	+	0.729249i	$0.260130\pi$
$594$	−1.69053e14	−0.0937988
$595$	4.29486e12	0.00236105
$596$	3.63904e14	0.198213
$597$	−1.09836e14	−0.0592769
$598$	−2.03566e15	−1.08855
$599$	−2.57542e15	−1.36458	−0.682292	−	0.731080i	$-0.739017\pi$
$599$	−2.57542e15	−1.36458	−0.682292	+	0.731080i	$0.739017\pi$
$600$	1.13679e15	0.596825
$601$	−1.67024e15	−0.868900	−0.434450	−	0.900696i	$-0.643057\pi$
$601$	−1.67024e15	−0.868900	−0.434450	+	0.900696i	$0.643057\pi$
$602$	−5.71458e12	−0.00294580
$603$	1.06046e15	0.541686
$604$	5.31670e13	0.0269116
$605$	−2.59946e14	−0.130385
$606$	1.13357e13	0.00563443
$607$	3.23790e15	1.59487	0.797436	−	0.603403i	$-0.206189\pi$
$607$	3.23790e15	1.59487	0.797436	+	0.603403i	$0.206189\pi$
$608$	2.42417e15	1.18330
$609$	−9.88049e12	−0.00477951
$610$	−1.28677e14	−0.0616862
$611$	1.28103e15	0.608599
$612$	−5.29294e14	−0.249209
$613$	−3.65672e15	−1.70631	−0.853157	−	0.521655i	$-0.825315\pi$
$613$	−3.65672e15	−1.70631	−0.853157	+	0.521655i	$0.825315\pi$
$614$	5.05113e13	0.0233595
$615$	−2.89299e13	−0.0132597
$616$	8.80578e12	0.00400013
$617$	−1.42899e15	−0.643369	−0.321685	−	0.946847i	$-0.604249\pi$
$617$	−1.42899e15	−0.643369	−0.321685	+	0.946847i	$0.604249\pi$
$618$	−5.77704e14	−0.257791
$619$	4.16060e15	1.84017	0.920085	−	0.391719i	$-0.128120\pi$
$619$	4.16060e15	1.84017	0.920085	+	0.391719i	$0.128120\pi$
$620$	2.31404e14	0.101442
$621$	8.04032e14	0.349357
$622$	2.91353e15	1.25479
$623$	−1.23686e13	−0.00528001
$624$	4.63573e14	0.196157
$625$	2.05559e15	0.862176
$626$	−2.49380e15	−1.03682
$627$	−1.40132e15	−0.577517
$628$	1.17482e15	0.479949
$629$	−3.67049e15	−1.48643
$630$	8.13531e11	0.000326589 0
$631$	2.74324e15	1.09170	0.545849	−	0.837883i	$-0.316207\pi$
$631$	2.74324e15	1.09170	0.545849	+	0.837883i	$0.316207\pi$
$632$	1.35316e14	0.0533832
$633$	−1.42754e15	−0.558302
$634$	−1.33453e15	−0.517412
$635$	7.34918e14	0.282477
$636$	8.96952e14	0.341787
$637$	2.05049e15	0.774625
$638$	1.83871e15	0.688652
$639$	1.26712e15	0.470502
$640$	2.40548e13	0.00885548
$641$	7.55048e14	0.275585	0.137793	−	0.990461i	$-0.455999\pi$
$641$	7.55048e14	0.275585	0.137793	+	0.990461i	$0.455999\pi$
$642$	3.04075e14	0.110037
$643$	1.51360e15	0.543064	0.271532	−	0.962429i	$-0.412470\pi$
$643$	1.51360e15	0.543064	0.271532	+	0.962429i	$0.412470\pi$
$644$	−1.19828e13	−0.00426270
$645$	−2.29674e14	−0.0810092
$646$	6.55970e15	2.29406
$647$	−2.58593e15	−0.896691	−0.448345	−	0.893860i	$-0.647987\pi$
$647$	−2.58593e15	−0.896691	−0.448345	+	0.893860i	$0.647987\pi$
$648$	−3.50415e14	−0.120482
$649$	2.40440e14	0.0819712
$650$	1.69109e15	0.571667
$651$	−1.18238e13	−0.00396334
$652$	−1.20662e15	−0.401059
$653$	−1.26468e14	−0.0416829	−0.0208415	−	0.999783i	$-0.506635\pi$
$653$	−1.26468e14	−0.0416829	−0.0208415	+	0.999783i	$0.506635\pi$
$654$	−2.55152e15	−0.833915
$655$	8.09501e14	0.262355
$656$	1.45083e14	0.0466277
$657$	−1.53845e15	−0.490313
$658$	−1.12741e13	−0.00356320
$659$	5.47257e14	0.171523	0.0857613	−	0.996316i	$-0.472668\pi$
$659$	5.47257e14	0.171523	0.0857613	+	0.996316i	$0.472668\pi$
$660$	1.01259e14	0.0314734
$661$	−1.94531e15	−0.599627	−0.299814	−	0.953998i	$-0.596924\pi$
$661$	−1.94531e15	−0.599627	−0.299814	+	0.953998i	$0.596924\pi$
$662$	1.29978e15	0.397329
$663$	−2.75198e15	−0.834298
$664$	4.70545e15	1.41474
$665$	6.74353e12	0.00201080
$666$	−6.95263e14	−0.205608
$667$	−8.74508e15	−2.56491
$668$	−1.81482e15	−0.527914
$669$	−1.62124e15	−0.467738
$670$	9.49684e14	0.271749
$671$	8.18372e14	0.232261
$672$	8.95054e12	0.00251952
$673$	−4.53850e15	−1.26715	−0.633577	−	0.773679i	$-0.718414\pi$
$673$	−4.53850e15	−1.26715	−0.633577	+	0.773679i	$0.718414\pi$
$674$	9.96354e14	0.275921
$675$	−6.67934e14	−0.183469
$676$	5.88280e14	0.160279
$677$	7.30525e15	1.97423	0.987114	−	0.160017i	$-0.0511548\pi$
$677$	7.30525e15	1.97423	0.987114	+	0.160017i	$0.0511548\pi$
$678$	1.79214e15	0.480407
$679$	−2.64614e13	−0.00703606
$680$	−1.65670e15	−0.436963
$681$	−1.94696e15	−0.509388
$682$	2.20035e15	0.571055
$683$	−4.57455e15	−1.17770	−0.588850	−	0.808243i	$-0.700419\pi$
$683$	−4.57455e15	−1.17770	−0.588850	+	0.808243i	$0.700419\pi$
$684$	−8.31066e14	−0.212240
$685$	−1.13993e15	−0.288790
$686$	−3.60928e13	−0.00907064
$687$	−5.70807e14	−0.142307
$688$	1.15181e15	0.284869
$689$	4.66356e15	1.14423
$690$	7.20044e14	0.175263
$691$	6.68207e15	1.61355	0.806774	−	0.590860i	$-0.201212\pi$
$691$	6.68207e15	1.61355	0.806774	+	0.590860i	$0.201212\pi$
$692$	−1.70566e15	−0.408609
$693$	−5.17396e12	−0.00122967
$694$	3.43096e15	0.808982
$695$	−7.46393e14	−0.174603
$696$	3.81130e15	0.884551
$697$	−8.61277e14	−0.198318
$698$	−4.17294e15	−0.953317
$699$	5.06487e15	1.14800
$700$	9.95446e12	0.00223861
$701$	−3.24290e15	−0.723576	−0.361788	−	0.932260i	$-0.617834\pi$
$701$	−3.24290e15	−0.723576	−0.361788	+	0.932260i	$0.617834\pi$
$702$	−5.21279e14	−0.115403
$703$	−5.76319e15	−1.26593
$704$	−2.93270e15	−0.639173
$705$	−4.53117e14	−0.0979875
$706$	4.22285e15	0.906107
$707$	3.46936e11	7.38657e−5 0
$708$	1.42596e14	0.0301248
$709$	−4.82624e15	−1.01171	−0.505854	−	0.862619i	$-0.668822\pi$
$709$	−4.82624e15	−1.01171	−0.505854	+	0.862619i	$0.668822\pi$
$710$	1.13475e15	0.236038
$711$	−7.95066e13	−0.0164104
$712$	4.77105e15	0.977179
$713$	−1.04651e16	−2.12691
$714$	2.42198e13	0.00488461
$715$	5.26483e14	0.105366
$716$	1.50749e15	0.299386
$717$	−3.53768e15	−0.697209
$718$	−2.04456e15	−0.399866
$719$	−2.42863e14	−0.0471360	−0.0235680	−	0.999722i	$-0.507503\pi$
$719$	−2.42863e14	−0.0471360	−0.0235680	+	0.999722i	$0.507503\pi$
$720$	−1.63973e14	−0.0315822
$721$	−1.76809e13	−0.00337957
$722$	6.21884e15	1.17965
$723$	1.20109e15	0.226107
$724$	−1.16738e15	−0.218098
$725$	7.26481e15	1.34699
$726$	−1.46590e15	−0.269745
$727$	6.24008e14	0.113960	0.0569798	−	0.998375i	$-0.481853\pi$
$727$	6.24008e14	0.113960	0.0569798	+	0.998375i	$0.481853\pi$
$728$	2.71529e13	0.00492145
$729$	2.05891e14	0.0370370
$730$	−1.37774e15	−0.245976
$731$	−6.83768e15	−1.21161
$732$	4.85344e14	0.0853570
$733$	8.38297e15	1.46327	0.731637	−	0.681694i	$-0.238757\pi$
$733$	8.38297e15	1.46327	0.731637	+	0.681694i	$0.238757\pi$
$734$	−1.37924e15	−0.238952
$735$	−7.25290e14	−0.124719
$736$	7.92199e15	1.35209
$737$	−6.03987e15	−1.02319
$738$	−1.63143e14	−0.0274320
$739$	−4.89206e15	−0.816483	−0.408242	−	0.912874i	$-0.633858\pi$
$739$	−4.89206e15	−0.816483	−0.408242	+	0.912874i	$0.633858\pi$
$740$	4.16449e14	0.0689902
$741$	−4.32100e15	−0.710533
$742$	−4.10433e13	−0.00669917
$743$	1.60463e15	0.259978	0.129989	−	0.991515i	$-0.458506\pi$
$743$	1.60463e15	0.259978	0.129989	+	0.991515i	$0.458506\pi$
$744$	4.56092e15	0.733502
$745$	−6.69250e14	−0.106839
$746$	4.64342e15	0.735825
$747$	−2.76475e15	−0.434904
$748$	3.01461e15	0.470731
$749$	9.30639e12	0.00144255
$750$	−1.22561e15	−0.188588
$751$	−6.10570e15	−0.932643	−0.466322	−	0.884615i	$-0.654421\pi$
$751$	−6.10570e15	−0.932643	−0.466322	+	0.884615i	$0.654421\pi$
$752$	2.27237e15	0.344573
$753$	7.33846e15	1.10467
$754$	5.66972e15	0.847264
$755$	−9.77786e13	−0.0145056
$756$	−3.06847e12	−0.000451910 0
$757$	−4.37120e14	−0.0639107	−0.0319553	−	0.999489i	$-0.510173\pi$
$757$	−4.37120e14	−0.0639107	−0.0319553	+	0.999489i	$0.510173\pi$
$758$	6.18578e14	0.0897871
$759$	−4.57939e15	−0.659900
$760$	−2.60125e15	−0.372141
$761$	2.99517e15	0.425409	0.212704	−	0.977117i	$-0.431773\pi$
$761$	2.99517e15	0.425409	0.212704	+	0.977117i	$0.431773\pi$
$762$	4.14438e15	0.584397
$763$	−7.80907e13	−0.0109324
$764$	1.53268e15	0.213028
$765$	9.73416e14	0.134326
$766$	−1.43596e15	−0.196736
$767$	7.41404e14	0.100851
$768$	−4.20402e15	−0.567777
$769$	4.32927e15	0.580524	0.290262	−	0.956947i	$-0.406258\pi$
$769$	4.32927e15	0.580524	0.290262	+	0.956947i	$0.406258\pi$
$770$	−4.63349e12	−0.000616893 0
$771$	4.22207e15	0.558118
$772$	4.04013e14	0.0530274
$773$	7.12088e14	0.0927997	0.0463998	−	0.998923i	$-0.485225\pi$
$773$	7.12088e14	0.0927997	0.0463998	+	0.998923i	$0.485225\pi$
$774$	−1.29519e15	−0.167594
$775$	8.69366e15	1.11697
$776$	1.02072e16	1.30217
$777$	−2.12789e13	−0.00269546
$778$	1.23845e15	0.155773
$779$	−1.35233e15	−0.168898
$780$	3.12236e14	0.0387225
$781$	−7.21690e15	−0.888730
$782$	2.14366e16	2.62131
$783$	−2.23938e15	−0.271918
$784$	3.63731e15	0.438573
$785$	−2.16060e15	−0.258697
$786$	4.56498e15	0.542768
$787$	1.24106e16	1.46531	0.732656	−	0.680599i	$-0.238280\pi$
$787$	1.24106e16	1.46531	0.732656	+	0.680599i	$0.238280\pi$
$788$	1.68656e15	0.197746
$789$	−7.04558e15	−0.820338
$790$	−7.12015e13	−0.00823266
$791$	5.48495e13	0.00629799
$792$	1.99580e15	0.227577
$793$	2.52347e15	0.285756
$794$	2.03125e15	0.228429
$795$	−1.64957e15	−0.184226
$796$	3.71004e14	0.0411487
$797$	1.39035e16	1.53145	0.765724	−	0.643170i	$-0.222381\pi$
$797$	1.39035e16	1.53145	0.765724	+	0.643170i	$0.222381\pi$
$798$	3.80285e13	0.00416000
$799$	−1.34898e16	−1.46555
$800$	−6.58104e15	−0.710067
$801$	−2.80330e15	−0.300393
$802$	4.66822e15	0.496812
$803$	8.76228e15	0.926151
$804$	−3.58201e15	−0.376027
$805$	2.20373e13	0.00229764
$806$	6.78484e15	0.702582
$807$	8.92819e15	0.918245
$808$	−1.33827e14	−0.0136704
$809$	8.18105e14	0.0830027	0.0415013	−	0.999138i	$-0.486786\pi$
$809$	8.18105e14	0.0830027	0.0415013	+	0.999138i	$0.486786\pi$
$810$	1.84384e14	0.0185804
$811$	7.48413e15	0.749077	0.374538	−	0.927211i	$-0.377801\pi$
$811$	7.48413e15	0.749077	0.374538	+	0.927211i	$0.377801\pi$
$812$	3.33743e13	0.00331783
$813$	−6.75021e15	−0.666530
$814$	3.95989e15	0.388373
$815$	2.21907e15	0.216175
$816$	−4.88166e15	−0.472358
$817$	−1.07361e16	−1.03187
$818$	−8.36434e15	−0.798525
$819$	−1.59540e13	−0.00151290
$820$	9.77194e13	0.00920459
$821$	−3.87011e15	−0.362106	−0.181053	−	0.983473i	$-0.557951\pi$
$821$	−3.87011e15	−0.362106	−0.181053	+	0.983473i	$0.557951\pi$
$822$	−6.42837e15	−0.597456
$823$	−1.03561e16	−0.956086	−0.478043	−	0.878336i	$-0.658654\pi$
$823$	−1.03561e16	−0.956086	−0.478043	+	0.878336i	$0.658654\pi$
$824$	6.82025e15	0.625461
$825$	3.80424e15	0.346554
$826$	−6.52499e12	−0.000590459 0
$827$	−7.27159e15	−0.653656	−0.326828	−	0.945084i	$-0.605980\pi$
$827$	−7.27159e15	−0.653656	−0.326828	+	0.945084i	$0.605980\pi$
$828$	−2.71586e15	−0.242516
$829$	5.68645e15	0.504419	0.252209	−	0.967673i	$-0.418843\pi$
$829$	5.68645e15	0.504419	0.252209	+	0.967673i	$0.418843\pi$
$830$	−2.47595e15	−0.218179
$831$	−8.14187e14	−0.0712719
$832$	−9.04307e15	−0.786389
$833$	−2.15927e16	−1.86535
$834$	−4.20910e15	−0.361223
$835$	3.33761e15	0.284551
$836$	4.73337e15	0.400900
$837$	−2.67983e15	−0.225485
$838$	−7.18708e15	−0.600773
$839$	−2.22324e16	−1.84627	−0.923134	−	0.384478i	$-0.874382\pi$
$839$	−2.22324e16	−1.84627	−0.923134	+	0.384478i	$0.874382\pi$
$840$	−9.60437e12	−0.000792378 0
$841$	1.21562e16	0.996370
$842$	−1.83250e15	−0.149220
$843$	−6.05114e15	−0.489537
$844$	4.82196e15	0.387561
$845$	−1.08190e15	−0.0863920
$846$	−2.55524e15	−0.202719
$847$	−4.48647e13	−0.00353627
$848$	8.27255e15	0.647832
$849$	4.30668e15	0.335081
$850$	−1.78080e16	−1.37661
$851$	−1.88336e16	−1.44651
$852$	−4.28006e15	−0.326612
$853$	1.52570e15	0.115678	0.0578388	−	0.998326i	$-0.481579\pi$
$853$	1.52570e15	0.115678	0.0578388	+	0.998326i	$0.481579\pi$
$854$	−2.22087e13	−0.00167303
$855$	1.52840e15	0.114399
$856$	−3.58985e15	−0.266975
$857$	1.81734e16	1.34290	0.671449	−	0.741051i	$-0.265672\pi$
$857$	1.81734e16	1.34290	0.671449	+	0.741051i	$0.265672\pi$
$858$	2.96897e15	0.217984
$859$	−8.59917e15	−0.627327	−0.313664	−	0.949534i	$-0.601556\pi$
$859$	−8.59917e15	−0.627327	−0.313664	+	0.949534i	$0.601556\pi$
$860$	7.75794e14	0.0562348
$861$	−4.99307e12	−0.000359625 0
$862$	−4.58209e15	−0.327924
$863$	2.56137e16	1.82143	0.910717	−	0.413031i	$-0.135530\pi$
$863$	2.56137e16	1.82143	0.910717	+	0.413031i	$0.135530\pi$
$864$	2.02861e15	0.143342
$865$	3.13685e15	0.220244
$866$	−1.42872e16	−0.996782
$867$	2.06517e16	1.43169
$868$	3.99385e13	0.00275127
$869$	4.52833e14	0.0309977
$870$	−2.00546e15	−0.136414
$871$	−1.86241e16	−1.25886
$872$	3.01227e16	2.02327
$873$	−5.99740e15	−0.400299
$874$	3.36584e16	2.23245
$875$	−3.75103e13	−0.00247233
$876$	5.19657e15	0.340364
$877$	1.07443e16	0.699327	0.349664	−	0.936875i	$-0.386296\pi$
$877$	1.07443e16	0.699327	0.349664	+	0.936875i	$0.386296\pi$
$878$	6.66534e15	0.431124
$879$	−8.38602e15	−0.539035
$880$	9.33912e14	0.0596556
$881$	−6.60441e15	−0.419244	−0.209622	−	0.977783i	$-0.567223\pi$
$881$	−6.60441e15	−0.419244	−0.209622	+	0.977783i	$0.567223\pi$
$882$	−4.09009e15	−0.258021
$883$	6.53384e15	0.409623	0.204812	−	0.978801i	$-0.434342\pi$
$883$	6.53384e15	0.409623	0.204812	+	0.978801i	$0.434342\pi$
$884$	9.29564e15	0.579151
$885$	−2.62246e14	−0.0162375
$886$	1.74806e16	1.07565
$887$	1.44562e15	0.0884044	0.0442022	−	0.999023i	$-0.485925\pi$
$887$	1.44562e15	0.0884044	0.0442022	+	0.999023i	$0.485925\pi$
$888$	8.20812e15	0.498853
$889$	1.26841e14	0.00766126
$890$	−2.51047e15	−0.150699
$891$	−1.17266e15	−0.0699592
$892$	5.47621e15	0.324694
$893$	−2.11810e16	−1.24814
$894$	−3.77407e15	−0.221031
$895$	−2.77239e15	−0.161372
$896$	4.15167e12	0.000240176 0
$897$	−1.41207e16	−0.811890
$898$	−2.67894e16	−1.53089
$899$	2.91473e16	1.65546
$900$	2.25615e15	0.127360
$901$	−4.91096e16	−2.75537
$902$	9.29186e14	0.0518163
$903$	−3.96400e13	−0.00219711
$904$	−2.11576e16	−1.16558
$905$	2.14692e15	0.117557
$906$	−5.51398e14	−0.0300096
$907$	3.18040e15	0.172045	0.0860223	−	0.996293i	$-0.472584\pi$
$907$	3.18040e15	0.172045	0.0860223	+	0.996293i	$0.472584\pi$
$908$	6.57646e15	0.353606
$909$	7.86320e13	0.00420241
$910$	−1.42875e13	−0.000758977 0
$911$	−2.72796e16	−1.44041	−0.720207	−	0.693759i	$-0.755953\pi$
$911$	−2.72796e16	−1.44041	−0.720207	+	0.693759i	$0.755953\pi$
$912$	−7.66489e15	−0.402286
$913$	1.57468e16	0.821489
$914$	1.88194e16	0.975890
$915$	−8.92589e14	−0.0460082
$916$	1.92807e15	0.0987867
$917$	1.39713e14	0.00711553
$918$	5.48933e15	0.277898
$919$	−1.45843e16	−0.733924	−0.366962	−	0.930236i	$-0.619602\pi$
$919$	−1.45843e16	−0.733924	−0.366962	+	0.930236i	$0.619602\pi$
$920$	−8.50069e15	−0.425227
$921$	3.50379e14	0.0174225
$922$	−1.21321e16	−0.599675
$923$	−2.22535e16	−1.09343
$924$	1.74766e13	0.000853613 0
$925$	1.56457e16	0.759652
$926$	−1.43450e16	−0.692373
$927$	−4.00733e15	−0.192272
$928$	−2.20643e16	−1.05239
$929$	−2.40579e16	−1.14070	−0.570349	−	0.821403i	$-0.693192\pi$
$929$	−2.40579e16	−1.14070	−0.570349	+	0.821403i	$0.693192\pi$
$930$	−2.39990e15	−0.113119
$931$	−3.39036e16	−1.58863
$932$	−1.71081e16	−0.796920
$933$	2.02101e16	0.935880
$934$	−9.55606e15	−0.439918
$935$	−5.54413e15	−0.253729
$936$	6.15411e15	0.279994
$937$	−2.42969e16	−1.09896	−0.549482	−	0.835506i	$-0.685175\pi$
$937$	−2.42969e16	−1.09896	−0.549482	+	0.835506i	$0.685175\pi$
$938$	1.63908e14	0.00737029
$939$	−1.72986e16	−0.773304
$940$	1.53054e15	0.0680208
$941$	1.97378e16	0.872081	0.436040	−	0.899927i	$-0.356380\pi$
$941$	1.97378e16	0.872081	0.436040	+	0.899927i	$0.356380\pi$
$942$	−1.21842e16	−0.535199
$943$	−4.41929e15	−0.192992
$944$	1.31516e15	0.0570993
$945$	5.64317e12	0.000243584 0
$946$	7.37681e15	0.316568
$947$	4.26802e16	1.82097	0.910483	−	0.413546i	$-0.135710\pi$
$947$	4.26802e16	1.82097	0.910483	+	0.413546i	$0.135710\pi$
$948$	2.68557e14	0.0113918
$949$	2.70187e16	1.13946
$950$	−2.79611e16	−1.17240
$951$	−9.25715e15	−0.385908
$952$	−2.85933e14	−0.0118512
$953$	−9.01467e15	−0.371483	−0.185741	−	0.982599i	$-0.559469\pi$
$953$	−9.01467e15	−0.371483	−0.185741	+	0.982599i	$0.559469\pi$
$954$	−9.30233e15	−0.381132
$955$	−2.81872e15	−0.114824
$956$	1.19496e16	0.483988
$957$	1.27545e16	0.513626
$958$	4.44566e15	0.178002
$959$	−1.96744e14	−0.00783247
$960$	3.19866e15	0.126613
$961$	9.47150e15	0.372769
$962$	1.22104e16	0.477825
$963$	2.10926e15	0.0820703
$964$	−4.05703e15	−0.156958
$965$	−7.43014e14	−0.0285823
$966$	1.24274e14	0.00475342
$967$	−6.16835e15	−0.234597	−0.117299	−	0.993097i	$-0.537423\pi$
$967$	−6.16835e15	−0.234597	−0.117299	+	0.993097i	$0.537423\pi$
$968$	1.73061e16	0.654463
$969$	4.55023e16	1.71101
$970$	−5.37092e15	−0.200819
$971$	−3.34244e16	−1.24267	−0.621337	−	0.783543i	$-0.713410\pi$
$971$	−3.34244e16	−1.24267	−0.621337	+	0.783543i	$0.713410\pi$
$972$	−6.95459e14	−0.0257103
$973$	−1.28822e14	−0.00473553
$974$	2.03416e16	0.743551
$975$	1.17305e16	0.426374
$976$	4.47631e15	0.161788
$977$	−1.05518e16	−0.379233	−0.189617	−	0.981858i	$-0.560724\pi$
$977$	−1.05518e16	−0.379233	−0.189617	+	0.981858i	$0.560724\pi$
$978$	1.25139e16	0.447228
$979$	1.59663e16	0.567412
$980$	2.44988e15	0.0865769
$981$	−1.76990e16	−0.621970
$982$	−3.72314e16	−1.30106
$983$	3.82164e16	1.32802	0.664012	−	0.747722i	$-0.268853\pi$
$983$	3.82164e16	1.32802	0.664012	+	0.747722i	$0.268853\pi$
$984$	1.92603e15	0.0665564
$985$	−3.10172e15	−0.106587
$986$	−5.97049e16	−2.04027
$987$	−7.82045e13	−0.00265759
$988$	1.45955e16	0.493236
$989$	−3.50848e16	−1.17907
$990$	−1.05017e15	−0.0350966
$991$	−2.62516e16	−0.872470	−0.436235	−	0.899833i	$-0.643688\pi$
$991$	−2.62516e16	−0.872470	−0.436235	+	0.899833i	$0.643688\pi$
$992$	−2.64039e16	−0.872678
$993$	9.01609e15	0.296345
$994$	1.95850e14	0.00640174
$995$	−6.82307e14	−0.0221796
$996$	9.33878e15	0.301901
$997$	−3.88199e16	−1.24805	−0.624024	−	0.781405i	$-0.714503\pi$
$997$	−3.88199e16	−1.24805	−0.624024	+	0.781405i	$0.714503\pi$
$998$	−2.69717e16	−0.862364
$999$	−4.82279e15	−0.153352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.20	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+35.0313 q^{2} +243.000 q^{3} -820.805 q^{4} +1509.53 q^{5} +8512.61 q^{6} +260.533 q^{7} -100498. q^{8} +59049.0 q^{9} +52880.9 q^{10} -336316. q^{11} -199456. q^{12} -1.03704e6 q^{13} +9126.82 q^{14} +366816. q^{15} -1.83957e6 q^{16} +1.09205e7 q^{17} +2.06857e6 q^{18} +1.71468e7 q^{19} -1.23903e6 q^{20} +63309.5 q^{21} -1.17816e7 q^{22} +5.60344e7 q^{23} -2.44210e7 q^{24} -4.65494e7 q^{25} -3.63289e7 q^{26} +1.43489e7 q^{27} -213847. q^{28} -1.56066e8 q^{29} +1.28500e7 q^{30} -1.86762e8 q^{31} +1.41377e8 q^{32} -8.17247e7 q^{33} +3.82561e8 q^{34} +393283. q^{35} -4.84677e7 q^{36} -3.36109e8 q^{37} +6.00675e8 q^{38} -2.52000e8 q^{39} -1.51705e8 q^{40} -7.88676e7 q^{41} +2.21782e6 q^{42} -6.26130e8 q^{43} +2.76050e8 q^{44} +8.91362e7 q^{45} +1.96296e9 q^{46} -1.23527e9 q^{47} -4.47016e8 q^{48} -1.97726e9 q^{49} -1.63069e9 q^{50} +2.65369e9 q^{51} +8.51207e8 q^{52} -4.49700e9 q^{53} +5.02661e8 q^{54} -5.07679e8 q^{55} -2.61831e7 q^{56} +4.16667e9 q^{57} -5.46722e9 q^{58} -7.14924e8 q^{59} -3.01084e8 q^{60} -2.43334e9 q^{61} -6.54252e9 q^{62} +1.53842e7 q^{63} +8.72008e9 q^{64} -1.56544e9 q^{65} -2.86293e9 q^{66} +1.79589e10 q^{67} -8.96364e9 q^{68} +1.36163e10 q^{69} +1.37772e7 q^{70} +2.14587e10 q^{71} -5.93431e9 q^{72} -2.60537e10 q^{73} -1.17743e10 q^{74} -1.13115e10 q^{75} -1.40742e10 q^{76} -8.76214e7 q^{77} -8.82791e9 q^{78} -1.34645e9 q^{79} -2.77689e9 q^{80} +3.48678e9 q^{81} -2.76284e9 q^{82} -4.68213e10 q^{83} -5.19648e7 q^{84} +1.64849e10 q^{85} -2.19342e10 q^{86} -3.79241e10 q^{87} +3.37991e10 q^{88} -4.74741e10 q^{89} +3.12256e9 q^{90} -2.70183e8 q^{91} -4.59933e10 q^{92} -4.53831e10 q^{93} -4.32732e10 q^{94} +2.58836e10 q^{95} +3.43547e10 q^{96} -1.01566e11 q^{97} -6.92660e10 q^{98} -1.98591e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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