LMFDB - Embedded newform 177.12.a.a.1.2

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-86.0142 q^{2} -243.000 q^{3} +5350.44 q^{4} +12869.1 q^{5} +20901.4 q^{6} -72810.3 q^{7} -284057. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-86.0142 q^{2} -243.000 q^{3} +5350.44 q^{4} +12869.1 q^{5} +20901.4 q^{6} -72810.3 q^{7} -284057. q^{8} +59049.0 q^{9} -1.10693e6 q^{10} -128428. q^{11} -1.30016e6 q^{12} +1.06672e6 q^{13} +6.26272e6 q^{14} -3.12720e6 q^{15} +1.34752e7 q^{16} -4.24538e6 q^{17} -5.07905e6 q^{18} +4.17284e6 q^{19} +6.88556e7 q^{20} +1.76929e7 q^{21} +1.10466e7 q^{22} -1.73947e7 q^{23} +6.90258e7 q^{24} +1.16787e8 q^{25} -9.17532e7 q^{26} -1.43489e7 q^{27} -3.89567e8 q^{28} +9.35237e7 q^{29} +2.68984e8 q^{30} +5.43406e7 q^{31} -5.77310e8 q^{32} +3.12080e7 q^{33} +3.65163e8 q^{34} -9.37006e8 q^{35} +3.15938e8 q^{36} -5.85281e7 q^{37} -3.58924e8 q^{38} -2.59214e8 q^{39} -3.65557e9 q^{40} -1.22068e9 q^{41} -1.52184e9 q^{42} -1.70364e9 q^{43} -6.87147e8 q^{44} +7.59910e8 q^{45} +1.49619e9 q^{46} +2.74021e9 q^{47} -3.27447e9 q^{48} +3.32401e9 q^{49} -1.00453e10 q^{50} +1.03163e9 q^{51} +5.70743e9 q^{52} +8.82674e8 q^{53} +1.23421e9 q^{54} -1.65276e9 q^{55} +2.06822e10 q^{56} -1.01400e9 q^{57} -8.04436e9 q^{58} +7.14924e8 q^{59} -1.67319e10 q^{60} -2.92979e9 q^{61} -4.67406e9 q^{62} -4.29937e9 q^{63} +2.20597e10 q^{64} +1.37278e10 q^{65} -2.68433e9 q^{66} +1.69588e10 q^{67} -2.27146e10 q^{68} +4.22692e9 q^{69} +8.05958e10 q^{70} -3.58652e9 q^{71} -1.67733e10 q^{72} -1.17507e10 q^{73} +5.03425e9 q^{74} -2.83792e10 q^{75} +2.23265e10 q^{76} +9.35089e9 q^{77} +2.22960e10 q^{78} -4.15998e10 q^{79} +1.73414e11 q^{80} +3.48678e9 q^{81} +1.04996e11 q^{82} -3.90038e10 q^{83} +9.46648e10 q^{84} -5.46344e10 q^{85} +1.46537e11 q^{86} -2.27263e10 q^{87} +3.64809e10 q^{88} +8.36999e10 q^{89} -6.53631e10 q^{90} -7.76684e10 q^{91} -9.30694e10 q^{92} -1.32048e10 q^{93} -2.35697e11 q^{94} +5.37009e10 q^{95} +1.40286e11 q^{96} +2.64875e10 q^{97} -2.85912e11 q^{98} -7.58355e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	−86.0142	−1.90066	−0.950331	−	0.311240i	$-0.899256\pi$
$2$	−86.0142	−1.90066	−0.950331	+	0.311240i	$0.899256\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5350.44	2.61252
$5$	12869.1	1.84168	0.920841	−	0.389938i	$-0.127503\pi$
$5$	12869.1	1.84168	0.920841	+	0.389938i	$0.127503\pi$
$6$	20901.4	1.09735
$7$	−72810.3	−1.63740	−0.818698	−	0.574225i	$-0.805304\pi$
$7$	−72810.3	−1.63740	−0.818698	+	0.574225i	$0.805304\pi$
$8$	−284057.	−3.06486
$9$	59049.0	0.333333
$10$	−1.10693e6	−3.50042
$11$	−128428.	−0.240437	−0.120218	−	0.992747i	$-0.538359\pi$
$11$	−128428.	−0.240437	−0.120218	+	0.992747i	$0.538359\pi$
$12$	−1.30016e6	−1.50834
$13$	1.06672e6	0.796825	0.398412	−	0.917206i	$-0.369561\pi$
$13$	1.06672e6	0.796825	0.398412	+	0.917206i	$0.369561\pi$
$14$	6.26272e6	3.11214
$15$	−3.12720e6	−1.06330
$16$	1.34752e7	3.21274
$17$	−4.24538e6	−0.725182	−0.362591	−	0.931948i	$-0.618108\pi$
$17$	−4.24538e6	−0.725182	−0.362591	+	0.931948i	$0.618108\pi$
$18$	−5.07905e6	−0.633554
$19$	4.17284e6	0.386623	0.193311	−	0.981137i	$-0.438077\pi$
$19$	4.17284e6	0.386623	0.193311	+	0.981137i	$0.438077\pi$
$20$	6.88556e7	4.81143
$21$	1.76929e7	0.945351
$22$	1.10466e7	0.456989
$23$	−1.73947e7	−0.563526	−0.281763	−	0.959484i	$-0.590919\pi$
$23$	−1.73947e7	−0.563526	−0.281763	+	0.959484i	$0.590919\pi$
$24$	6.90258e7	1.76950
$25$	1.16787e8	2.39179
$26$	−9.17532e7	−1.51450
$27$	−1.43489e7	−0.192450
$28$	−3.89567e8	−4.27773
$29$	9.35237e7	0.846706	0.423353	−	0.905965i	$-0.360853\pi$
$29$	9.35237e7	0.846706	0.423353	+	0.905965i	$0.360853\pi$
$30$	2.68984e8	2.02097
$31$	5.43406e7	0.340906	0.170453	−	0.985366i	$-0.445477\pi$
$31$	5.43406e7	0.340906	0.170453	+	0.985366i	$0.445477\pi$
$32$	−5.77310e8	−3.04148
$33$	3.12080e7	0.138816
$34$	3.65163e8	1.37833
$35$	−9.37006e8	−3.01556
$36$	3.15938e8	0.870840
$37$	−5.85281e7	−0.138757	−0.0693786	−	0.997590i	$-0.522102\pi$
$37$	−5.85281e7	−0.138757	−0.0693786	+	0.997590i	$0.522102\pi$
$38$	−3.58924e8	−0.734839
$39$	−2.59214e8	−0.460047
$40$	−3.65557e9	−5.64449
$41$	−1.22068e9	−1.64548	−0.822739	−	0.568419i	$-0.807555\pi$
$41$	−1.22068e9	−1.64548	−0.822739	+	0.568419i	$0.807555\pi$
$42$	−1.52184e9	−1.79679
$43$	−1.70364e9	−1.76726	−0.883630	−	0.468186i	$-0.844908\pi$
$43$	−1.70364e9	−1.76726	−0.883630	+	0.468186i	$0.844908\pi$
$44$	−6.87147e8	−0.628145
$45$	7.59910e8	0.613894
$46$	1.49619e9	1.07107
$47$	2.74021e9	1.74279	0.871395	−	0.490582i	$-0.163216\pi$
$47$	2.74021e9	1.74279	0.871395	+	0.490582i	$0.163216\pi$
$48$	−3.27447e9	−1.85488
$49$	3.32401e9	1.68106
$50$	−1.00453e10	−4.54600
$51$	1.03163e9	0.418684
$52$	5.70743e9	2.08172
$53$	8.82674e8	0.289923	0.144962	−	0.989437i	$-0.453694\pi$
$53$	8.82674e8	0.289923	0.144962	+	0.989437i	$0.453694\pi$
$54$	1.23421e9	0.365783
$55$	−1.65276e9	−0.442808
$56$	2.06822e10	5.01838
$57$	−1.01400e9	−0.223217
$58$	−8.04436e9	−1.60930
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.67319e10	−2.77788
$61$	−2.92979e9	−0.444142	−0.222071	−	0.975030i	$-0.571282\pi$
$61$	−2.92979e9	−0.444142	−0.222071	+	0.975030i	$0.571282\pi$
$62$	−4.67406e9	−0.647948
$63$	−4.29937e9	−0.545798
$64$	2.20597e10	2.56808
$65$	1.37278e10	1.46750
$66$	−2.68433e9	−0.263843
$67$	1.69588e10	1.53456	0.767281	−	0.641311i	$-0.221609\pi$
$67$	1.69588e10	1.53456	0.767281	+	0.641311i	$0.221609\pi$
$68$	−2.27146e10	−1.89455
$69$	4.22692e9	0.325352
$70$	8.05958e10	5.73157
$71$	−3.58652e9	−0.235913	−0.117957	−	0.993019i	$-0.537634\pi$
$71$	−3.58652e9	−0.235913	−0.117957	+	0.993019i	$0.537634\pi$
$72$	−1.67733e10	−1.02162
$73$	−1.17507e10	−0.663420	−0.331710	−	0.943381i	$-0.607625\pi$
$73$	−1.17507e10	−0.663420	−0.331710	+	0.943381i	$0.607625\pi$
$74$	5.03425e9	0.263731
$75$	−2.83792e10	−1.38090
$76$	2.23265e10	1.01006
$77$	9.35089e9	0.393690
$78$	2.22960e10	0.874394
$79$	−4.15998e10	−1.52104	−0.760522	−	0.649312i	$-0.775057\pi$
$79$	−4.15998e10	−1.52104	−0.760522	+	0.649312i	$0.775057\pi$
$80$	1.73414e11	5.91684
$81$	3.48678e9	0.111111
$82$	1.04996e11	3.12750
$83$	−3.90038e10	−1.08687	−0.543435	−	0.839451i	$-0.682877\pi$
$83$	−3.90038e10	−1.08687	−0.543435	+	0.839451i	$0.682877\pi$
$84$	9.46648e10	2.46975
$85$	−5.46344e10	−1.33556
$86$	1.46537e11	3.35896
$87$	−2.27263e10	−0.488846
$88$	3.64809e10	0.736903
$89$	8.36999e10	1.58884	0.794420	−	0.607369i	$-0.207775\pi$
$89$	8.36999e10	1.58884	0.794420	+	0.607369i	$0.207775\pi$
$90$	−6.53631e10	−1.16681
$91$	−7.76684e10	−1.30472
$92$	−9.30694e10	−1.47222
$93$	−1.32048e10	−0.196822
$94$	−2.35697e11	−3.31246
$95$	5.37009e10	0.712036
$96$	1.40286e11	1.75600
$97$	2.64875e10	0.313182	0.156591	−	0.987664i	$-0.449950\pi$
$97$	2.64875e10	0.313182	0.156591	+	0.987664i	$0.449950\pi$
$98$	−2.85912e11	−3.19513
$99$	−7.58355e9	−0.0801455
$100$	6.24861e11	6.24861
$101$	9.15128e10	0.866392	0.433196	−	0.901300i	$-0.357386\pi$
$101$	9.15128e10	0.866392	0.433196	+	0.901300i	$0.357386\pi$
$102$	−8.87345e10	−0.795777
$103$	−2.16558e11	−1.84064	−0.920320	−	0.391166i	$-0.872072\pi$
$103$	−2.16558e11	−1.84064	−0.920320	+	0.391166i	$0.872072\pi$
$104$	−3.03010e11	−2.44215
$105$	2.27693e11	1.74104
$106$	−7.59225e10	−0.551046
$107$	9.08001e10	0.625858	0.312929	−	0.949777i	$-0.398690\pi$
$107$	9.08001e10	0.625858	0.312929	+	0.949777i	$0.398690\pi$
$108$	−7.67730e10	−0.502780
$109$	2.83339e11	1.76385	0.881924	−	0.471392i	$-0.156248\pi$
$109$	2.83339e11	1.76385	0.881924	+	0.471392i	$0.156248\pi$
$110$	1.42161e11	0.841628
$111$	1.42223e10	0.0801115
$112$	−9.81133e11	−5.26052
$113$	−2.47545e11	−1.26393	−0.631964	−	0.774997i	$-0.717751\pi$
$113$	−2.47545e11	−1.26393	−0.631964	+	0.774997i	$0.717751\pi$
$114$	8.72184e10	0.424260
$115$	−2.23855e11	−1.03784
$116$	5.00393e11	2.21204
$117$	6.29889e10	0.265608
$118$	−6.14936e10	−0.247445
$119$	3.09107e11	1.18741
$120$	8.88303e11	3.25885
$121$	−2.68818e11	−0.942190
$122$	2.52003e11	0.844165
$123$	2.96626e11	0.950017
$124$	2.90746e11	0.890624
$125$	8.74571e11	2.56324
$126$	3.69807e11	1.03738
$127$	−2.59989e11	−0.698287	−0.349143	−	0.937069i	$-0.613527\pi$
$127$	−2.59989e11	−0.698287	−0.349143	+	0.937069i	$0.613527\pi$
$128$	−7.15113e11	−1.83958
$129$	4.13984e11	1.02033
$130$	−1.18079e12	−2.78922
$131$	−6.82477e11	−1.54560	−0.772798	−	0.634652i	$-0.781143\pi$
$131$	−6.82477e11	−1.54560	−0.772798	+	0.634652i	$0.781143\pi$
$132$	1.66977e11	0.362660
$133$	−3.03826e11	−0.633054
$134$	−1.45870e12	−2.91669
$135$	−1.84658e11	−0.354432
$136$	1.20593e12	2.22258
$137$	9.47901e10	0.167803	0.0839016	−	0.996474i	$-0.473262\pi$
$137$	9.47901e10	0.167803	0.0839016	+	0.996474i	$0.473262\pi$
$138$	−3.63575e11	−0.618385
$139$	1.07791e12	1.76197	0.880987	−	0.473140i	$-0.156880\pi$
$139$	1.07791e12	1.76197	0.880987	+	0.473140i	$0.156880\pi$
$140$	−5.01340e12	−7.87822
$141$	−6.65870e11	−1.00620
$142$	3.08491e11	0.448391
$143$	−1.36997e11	−0.191586
$144$	7.95697e11	1.07091
$145$	1.20357e12	1.55936
$146$	1.01073e12	1.26094
$147$	−8.07735e11	−0.970562
$148$	−3.13151e11	−0.362506
$149$	1.20005e12	1.33867	0.669337	−	0.742959i	$-0.266578\pi$
$149$	1.20005e12	1.33867	0.669337	+	0.742959i	$0.266578\pi$
$150$	2.44101e12	2.62463
$151$	1.89764e11	0.196716	0.0983581	−	0.995151i	$-0.468641\pi$
$151$	1.89764e11	0.196716	0.0983581	+	0.995151i	$0.468641\pi$
$152$	−1.18532e12	−1.18494
$153$	−2.50685e11	−0.241727
$154$	−8.04309e11	−0.748271
$155$	6.99317e11	0.627841
$156$	−1.38691e12	−1.20188
$157$	−1.34772e12	−1.12759	−0.563795	−	0.825915i	$-0.690659\pi$
$157$	−1.34772e12	−1.12759	−0.563795	+	0.825915i	$0.690659\pi$
$158$	3.57817e12	2.89099
$159$	−2.14490e11	−0.167387
$160$	−7.42949e12	−5.60143
$161$	1.26651e12	0.922716
$162$	−2.99913e11	−0.211185
$163$	−2.08772e10	−0.0142115	−0.00710577	−	0.999975i	$-0.502262\pi$
$163$	−2.08772e10	−0.0142115	−0.00710577	+	0.999975i	$0.502262\pi$
$164$	−6.53120e12	−4.29884
$165$	4.01621e11	0.255655
$166$	3.35488e12	2.06577
$167$	2.23710e12	1.33274	0.666368	−	0.745623i	$-0.267848\pi$
$167$	2.23710e12	1.33274	0.666368	+	0.745623i	$0.267848\pi$
$168$	−5.02579e12	−2.89736
$169$	−6.54264e11	−0.365070
$170$	4.69933e12	2.53844
$171$	2.46402e11	0.128874
$172$	−9.11520e12	−4.61700
$173$	5.09919e11	0.250177	0.125089	−	0.992146i	$-0.460078\pi$
$173$	5.09919e11	0.250177	0.125089	+	0.992146i	$0.460078\pi$
$174$	1.95478e12	0.929131
$175$	−8.50328e12	−3.91631
$176$	−1.73060e12	−0.772460
$177$	−1.73727e11	−0.0751646
$178$	−7.19938e12	−3.01985
$179$	3.36855e12	1.37010	0.685048	−	0.728498i	$-0.259781\pi$
$179$	3.36855e12	1.37010	0.685048	+	0.728498i	$0.259781\pi$
$180$	4.06585e12	1.60381
$181$	2.30258e12	0.881012	0.440506	−	0.897750i	$-0.354799\pi$
$181$	2.30258e12	0.881012	0.440506	+	0.897750i	$0.354799\pi$
$182$	6.68058e12	2.47983
$183$	7.11938e11	0.256426
$184$	4.94109e12	1.72713
$185$	−7.53207e11	−0.255547
$186$	1.13580e12	0.374093
$187$	5.45226e11	0.174360
$188$	1.46613e13	4.55307
$189$	1.04475e12	0.315117
$190$	−4.61904e12	−1.35334
$191$	6.21335e12	1.76865	0.884325	−	0.466871i	$-0.154619\pi$
$191$	6.21335e12	1.76865	0.884325	+	0.466871i	$0.154619\pi$
$192$	−5.36050e12	−1.48268
$193$	−3.55496e12	−0.955585	−0.477792	−	0.878473i	$-0.658563\pi$
$193$	−3.55496e12	−0.955585	−0.477792	+	0.878473i	$0.658563\pi$
$194$	−2.27830e12	−0.595254
$195$	−3.33586e12	−0.847261
$196$	1.77849e13	4.39181
$197$	2.48699e12	0.597186	0.298593	−	0.954380i	$-0.403483\pi$
$197$	2.48699e12	0.597186	0.298593	+	0.954380i	$0.403483\pi$
$198$	6.52293e11	0.152330
$199$	−9.47524e11	−0.215228	−0.107614	−	0.994193i	$-0.534321\pi$
$199$	−9.47524e11	−0.215228	−0.107614	+	0.994193i	$0.534321\pi$
$200$	−3.31741e13	−7.33051
$201$	−4.12100e12	−0.885980
$202$	−7.87140e12	−1.64672
$203$	−6.80949e12	−1.38639
$204$	5.51966e12	1.09382
$205$	−1.57092e13	−3.03045
$206$	1.86270e13	3.49844
$207$	−1.02714e12	−0.187842
$208$	1.43743e13	2.55999
$209$	−5.35910e11	−0.0929582
$210$	−1.95848e13	−3.30912
$211$	−8.10742e12	−1.33453	−0.667266	−	0.744819i	$-0.732536\pi$
$211$	−8.10742e12	−1.33453	−0.667266	+	0.744819i	$0.732536\pi$
$212$	4.72269e12	0.757430
$213$	8.71524e11	0.136205
$214$	−7.81010e12	−1.18954
$215$	−2.19243e13	−3.25473
$216$	4.07590e12	0.589832
$217$	−3.95655e12	−0.558198
$218$	−2.43712e13	−3.35248
$219$	2.85542e12	0.383026
$220$	−8.84300e12	−1.15684
$221$	−4.52864e12	−0.577843
$222$	−1.22332e12	−0.152265
$223$	−4.22592e12	−0.513150	−0.256575	−	0.966524i	$-0.582594\pi$
$223$	−4.22592e12	−0.513150	−0.256575	+	0.966524i	$0.582594\pi$
$224$	4.20341e13	4.98010
$225$	6.89615e12	0.797265
$226$	2.12924e13	2.40230
$227$	−6.14055e12	−0.676184	−0.338092	−	0.941113i	$-0.609782\pi$
$227$	−6.14055e12	−0.676184	−0.338092	+	0.941113i	$0.609782\pi$
$228$	−5.42535e12	−0.583158
$229$	−7.87370e12	−0.826197	−0.413099	−	0.910686i	$-0.635553\pi$
$229$	−7.87370e12	−0.826197	−0.413099	+	0.910686i	$0.635553\pi$
$230$	1.92547e13	1.97258
$231$	−2.27227e12	−0.227297
$232$	−2.65660e13	−2.59503
$233$	−9.24605e12	−0.882062	−0.441031	−	0.897492i	$-0.645387\pi$
$233$	−9.24605e12	−0.882062	−0.441031	+	0.897492i	$0.645387\pi$
$234$	−5.41794e12	−0.504832
$235$	3.52641e13	3.20967
$236$	3.82516e12	0.340121
$237$	1.01087e13	0.878176
$238$	−2.65876e13	−2.25687
$239$	7.24389e12	0.600874	0.300437	−	0.953802i	$-0.402868\pi$
$239$	7.24389e12	0.600874	0.300437	+	0.953802i	$0.402868\pi$
$240$	−4.21397e13	−3.41609
$241$	−9.26650e12	−0.734213	−0.367106	−	0.930179i	$-0.619652\pi$
$241$	−9.26650e12	−0.734213	−0.367106	+	0.930179i	$0.619652\pi$
$242$	2.31222e13	1.79079
$243$	−8.47289e11	−0.0641500
$244$	−1.56757e13	−1.16033
$245$	4.27772e13	3.09599
$246$	−2.55141e13	−1.80566
$247$	4.45126e12	0.308070
$248$	−1.54358e13	−1.04483
$249$	9.47792e12	0.627505
$250$	−7.52255e13	−4.87186
$251$	−2.37605e13	−1.50539	−0.752697	−	0.658367i	$-0.771248\pi$
$251$	−2.37605e13	−1.50539	−0.752697	+	0.658367i	$0.771248\pi$
$252$	−2.30035e13	−1.42591
$253$	2.23397e12	0.135492
$254$	2.23627e13	1.32721
$255$	1.32762e13	0.771083
$256$	1.63316e13	0.928346
$257$	8.98996e11	0.0500179	0.0250089	−	0.999687i	$-0.492039\pi$
$257$	8.98996e11	0.0500179	0.0250089	+	0.999687i	$0.492039\pi$
$258$	−3.56085e13	−1.93930
$259$	4.26145e12	0.227200
$260$	7.34498e13	3.83387
$261$	5.52248e12	0.282235
$262$	5.87027e13	2.93766
$263$	−5.82370e12	−0.285392	−0.142696	−	0.989767i	$-0.545577\pi$
$263$	−5.82370e12	−0.285392	−0.142696	+	0.989767i	$0.545577\pi$
$264$	−8.86485e12	−0.425451
$265$	1.13593e13	0.533947
$266$	2.61333e13	1.20322
$267$	−2.03391e13	−0.917317
$268$	9.07372e13	4.00907
$269$	5.34952e12	0.231567	0.115784	−	0.993274i	$-0.463062\pi$
$269$	5.34952e12	0.231567	0.115784	+	0.993274i	$0.463062\pi$
$270$	1.58832e13	0.673656
$271$	8.76617e11	0.0364316	0.0182158	−	0.999834i	$-0.494201\pi$
$271$	8.76617e11	0.0364316	0.0182158	+	0.999834i	$0.494201\pi$
$272$	−5.72073e13	−2.32982
$273$	1.88734e13	0.753279
$274$	−8.15330e12	−0.318937
$275$	−1.49987e13	−0.575075
$276$	2.26159e13	0.849989
$277$	−7.56380e11	−0.0278677	−0.0139339	−	0.999903i	$-0.504435\pi$
$277$	−7.56380e11	−0.0278677	−0.0139339	+	0.999903i	$0.504435\pi$
$278$	−9.27152e13	−3.34892
$279$	3.20876e12	0.113635
$280$	2.66163e14	9.24226
$281$	7.34680e12	0.250157	0.125079	−	0.992147i	$-0.460082\pi$
$281$	7.34680e12	0.250157	0.125079	+	0.992147i	$0.460082\pi$
$282$	5.72743e13	1.91245
$283$	2.26371e13	0.741304	0.370652	−	0.928772i	$-0.379134\pi$
$283$	2.26371e13	0.741304	0.370652	+	0.928772i	$0.379134\pi$
$284$	−1.91894e13	−0.616328
$285$	−1.30493e13	−0.411094
$286$	1.17837e13	0.364140
$287$	8.88784e13	2.69430
$288$	−3.40896e13	−1.01383
$289$	−1.62487e13	−0.474111
$290$	−1.03524e14	−2.96382
$291$	−6.43647e12	−0.180816
$292$	−6.28715e13	−1.73320
$293$	3.79170e13	1.02580	0.512899	−	0.858449i	$-0.328572\pi$
$293$	3.79170e13	1.02580	0.512899	+	0.858449i	$0.328572\pi$
$294$	6.94767e13	1.84471
$295$	9.20047e12	0.239767
$296$	1.66253e13	0.425271
$297$	1.84280e12	0.0462720
$298$	−1.03221e14	−2.54437
$299$	−1.85553e13	−0.449032
$300$	−1.51841e14	−3.60764
$301$	1.24042e14	2.89370
$302$	−1.63224e13	−0.373891
$303$	−2.22376e13	−0.500211
$304$	5.62299e13	1.24212
$305$	−3.77039e13	−0.817969
$306$	2.15625e13	0.459442
$307$	−7.27579e13	−1.52272	−0.761358	−	0.648332i	$-0.775467\pi$
$307$	−7.27579e13	−1.52272	−0.761358	+	0.648332i	$0.775467\pi$
$308$	5.00314e13	1.02852
$309$	5.26235e13	1.06269
$310$	−6.01512e13	−1.19331
$311$	−9.34073e13	−1.82053	−0.910266	−	0.414023i	$-0.864123\pi$
$311$	−9.34073e13	−1.82053	−0.910266	+	0.414023i	$0.864123\pi$
$312$	7.36313e13	1.40998
$313$	5.52589e13	1.03970	0.519850	−	0.854258i	$-0.325988\pi$
$313$	5.52589e13	1.03970	0.519850	+	0.854258i	$0.325988\pi$
$314$	1.15923e14	2.14317
$315$	−5.53293e13	−1.00519
$316$	−2.22577e14	−3.97376
$317$	−2.21602e13	−0.388820	−0.194410	−	0.980920i	$-0.562279\pi$
$317$	−2.21602e13	−0.388820	−0.194410	+	0.980920i	$0.562279\pi$
$318$	1.84492e13	0.318147
$319$	−1.20111e13	−0.203579
$320$	2.83889e14	4.72959
$321$	−2.20644e13	−0.361339
$322$	−1.08938e14	−1.75377
$323$	−1.77153e13	−0.280372
$324$	1.86558e13	0.290280
$325$	1.24579e14	1.90584
$326$	1.79574e12	0.0270114
$327$	−6.88514e13	−1.01836
$328$	3.46744e14	5.04315
$329$	−1.99515e14	−2.85364
$330$	−3.45451e13	−0.485914
$331$	−8.20321e13	−1.13483	−0.567414	−	0.823433i	$-0.692056\pi$
$331$	−8.20321e13	−1.13483	−0.567414	+	0.823433i	$0.692056\pi$
$332$	−2.08688e14	−2.83947
$333$	−3.45603e12	−0.0462524
$334$	−1.92422e14	−2.53308
$335$	2.18246e14	2.82618
$336$	2.38415e14	3.03716
$337$	−5.07694e12	−0.0636265	−0.0318132	−	0.999494i	$-0.510128\pi$
$337$	−5.07694e12	−0.0636265	−0.0318132	+	0.999494i	$0.510128\pi$
$338$	5.62760e13	0.693875
$339$	6.01534e13	0.729730
$340$	−2.92318e14	−3.48916
$341$	−6.97886e12	−0.0819663
$342$	−2.11941e13	−0.244946
$343$	−9.80525e13	−1.11517
$344$	4.83929e14	5.41640
$345$	5.43968e13	0.599195
$346$	−4.38603e13	−0.475502
$347$	−4.22761e13	−0.451110	−0.225555	−	0.974230i	$-0.572420\pi$
$347$	−4.22761e13	−0.451110	−0.225555	+	0.974230i	$0.572420\pi$
$348$	−1.21595e14	−1.27712
$349$	1.42158e14	1.46971	0.734856	−	0.678224i	$-0.237250\pi$
$349$	1.42158e14	1.46971	0.734856	+	0.678224i	$0.237250\pi$
$350$	7.31403e14	7.44359
$351$	−1.53063e13	−0.153349
$352$	7.41429e13	0.731282
$353$	−9.55970e13	−0.928290	−0.464145	−	0.885759i	$-0.653638\pi$
$353$	−9.55970e13	−0.928290	−0.464145	+	0.885759i	$0.653638\pi$
$354$	1.49430e13	0.142863
$355$	−4.61554e13	−0.434477
$356$	4.47831e14	4.15087
$357$	−7.51130e13	−0.685551
$358$	−2.89743e14	−2.60409
$359$	−1.34153e14	−1.18736	−0.593678	−	0.804703i	$-0.702325\pi$
$359$	−1.34153e14	−1.18736	−0.593678	+	0.804703i	$0.702325\pi$
$360$	−2.15858e14	−1.88150
$361$	−9.90776e13	−0.850523
$362$	−1.98054e14	−1.67451
$363$	6.53227e13	0.543974
$364$	−4.15560e14	−3.40860
$365$	−1.51222e14	−1.22181
$366$	−6.12368e13	−0.487379
$367$	−1.11235e14	−0.872121	−0.436061	−	0.899917i	$-0.643627\pi$
$367$	−1.11235e14	−0.872121	−0.436061	+	0.899917i	$0.643627\pi$
$368$	−2.34397e14	−1.81046
$369$	−7.20802e13	−0.548493
$370$	6.47865e13	0.485708
$371$	−6.42677e13	−0.474719
$372$	−7.06513e13	−0.514202
$373$	−1.25235e14	−0.898105	−0.449053	−	0.893505i	$-0.648238\pi$
$373$	−1.25235e14	−0.898105	−0.449053	+	0.893505i	$0.648238\pi$
$374$	−4.68972e13	−0.331400
$375$	−2.12521e14	−1.47989
$376$	−7.78374e14	−5.34140
$377$	9.97638e13	0.674676
$378$	−8.98632e13	−0.598931
$379$	4.79622e13	0.315053	0.157526	−	0.987515i	$-0.449648\pi$
$379$	4.79622e13	0.315053	0.157526	+	0.987515i	$0.449648\pi$
$380$	2.87324e14	1.86021
$381$	6.31772e13	0.403156
$382$	−5.34436e14	−3.36161
$383$	−2.67637e14	−1.65941	−0.829703	−	0.558206i	$-0.811490\pi$
$383$	−2.67637e14	−1.65941	−0.829703	+	0.558206i	$0.811490\pi$
$384$	1.73772e14	1.06208
$385$	1.20338e14	0.725051
$386$	3.05777e14	1.81624
$387$	−1.00598e14	−0.589087
$388$	1.41720e14	0.818195
$389$	3.46706e14	1.97351	0.986754	−	0.162225i	$-0.0518670\pi$
$389$	3.46706e14	1.97351	0.986754	+	0.162225i	$0.0518670\pi$
$390$	2.86931e14	1.61036
$391$	7.38471e13	0.408659
$392$	−9.44208e14	−5.15222
$393$	1.65842e14	0.892350
$394$	−2.13916e14	−1.13505
$395$	−5.35354e14	−2.80128
$396$	−4.05753e13	−0.209382
$397$	5.58638e13	0.284304	0.142152	−	0.989845i	$-0.454598\pi$
$397$	5.58638e13	0.284304	0.142152	+	0.989845i	$0.454598\pi$
$398$	8.15005e13	0.409076
$399$	7.38297e13	0.365494
$400$	1.57373e15	7.68421
$401$	−2.73514e14	−1.31730	−0.658651	−	0.752449i	$-0.728872\pi$
$401$	−2.73514e14	−1.31730	−0.658651	+	0.752449i	$0.728872\pi$
$402$	3.54464e14	1.68395
$403$	5.79663e13	0.271643
$404$	4.89634e14	2.26346
$405$	4.48719e13	0.204631
$406$	5.85712e14	2.63506
$407$	7.51666e12	0.0333623
$408$	−2.93040e14	−1.28321
$409$	6.33500e13	0.273696	0.136848	−	0.990592i	$-0.456303\pi$
$409$	6.33500e13	0.273696	0.136848	+	0.990592i	$0.456303\pi$
$410$	1.35121e15	5.75986
$411$	−2.30340e13	−0.0968812
$412$	−1.15868e15	−4.80871
$413$	−5.20538e13	−0.213171
$414$	8.83487e13	0.357025
$415$	−5.01946e14	−2.00167
$416$	−6.15830e14	−2.42352
$417$	−2.61931e14	−1.01728
$418$	4.60959e13	0.176682
$419$	−5.18193e13	−0.196026	−0.0980131	−	0.995185i	$-0.531249\pi$
$419$	−5.18193e13	−0.196026	−0.0980131	+	0.995185i	$0.531249\pi$
$420$	1.21826e15	4.54849
$421$	−2.44339e14	−0.900411	−0.450206	−	0.892925i	$-0.648649\pi$
$421$	−2.44339e14	−0.900411	−0.450206	+	0.892925i	$0.648649\pi$
$422$	6.97353e14	2.53650
$423$	1.61806e14	0.580930
$424$	−2.50729e14	−0.888573
$425$	−4.95804e14	−1.73449
$426$	−7.49634e13	−0.258879
$427$	2.13319e14	0.727236
$428$	4.85820e14	1.63507
$429$	3.32903e13	0.110612
$430$	1.88580e15	6.18615
$431$	−3.38705e14	−1.09698	−0.548488	−	0.836159i	$-0.684796\pi$
$431$	−3.38705e14	−1.09698	−0.548488	+	0.836159i	$0.684796\pi$
$432$	−1.93354e14	−0.618292
$433$	−2.42661e14	−0.766155	−0.383078	−	0.923716i	$-0.625136\pi$
$433$	−2.42661e14	−0.766155	−0.383078	+	0.923716i	$0.625136\pi$
$434$	3.40320e14	1.06095
$435$	−2.92467e14	−0.900299
$436$	1.51599e15	4.60809
$437$	−7.25854e13	−0.217872
$438$	−2.45607e14	−0.728002
$439$	−2.47248e14	−0.723731	−0.361865	−	0.932230i	$-0.617860\pi$
$439$	−2.47248e14	−0.723731	−0.361865	+	0.932230i	$0.617860\pi$
$440$	4.69478e14	1.35714
$441$	1.96280e14	0.560354
$442$	3.89527e14	1.09829
$443$	−1.88537e13	−0.0525019	−0.0262510	−	0.999655i	$-0.508357\pi$
$443$	−1.88537e13	−0.0525019	−0.0262510	+	0.999655i	$0.508357\pi$
$444$	7.60958e13	0.209293
$445$	1.07715e15	2.92614
$446$	3.63489e14	0.975326
$447$	−2.91612e14	−0.772883
$448$	−1.60617e15	−4.20497
$449$	2.27295e14	0.587808	0.293904	−	0.955835i	$-0.405045\pi$
$449$	2.27295e14	0.587808	0.293904	+	0.955835i	$0.405045\pi$
$450$	−5.93166e14	−1.51533
$451$	1.56770e14	0.395633
$452$	−1.32447e15	−3.30204
$453$	−4.61126e13	−0.113574
$454$	5.28174e14	1.28520
$455$	−9.99526e14	−2.40288
$456$	2.88034e14	0.684127
$457$	−1.45117e14	−0.340549	−0.170275	−	0.985397i	$-0.554465\pi$
$457$	−1.45117e14	−0.340549	−0.170275	+	0.985397i	$0.554465\pi$
$458$	6.77250e14	1.57032
$459$	6.09165e13	0.139561
$460$	−1.19772e15	−2.71137
$461$	−4.87579e14	−1.09066	−0.545330	−	0.838221i	$-0.683596\pi$
$461$	−4.87579e14	−1.09066	−0.545330	+	0.838221i	$0.683596\pi$
$462$	1.95447e14	0.432015
$463$	1.64119e14	0.358479	0.179240	−	0.983805i	$-0.442636\pi$
$463$	1.64119e14	0.358479	0.179240	+	0.983805i	$0.442636\pi$
$464$	1.26025e15	2.72024
$465$	−1.69934e14	−0.362484
$466$	7.95292e14	1.67650
$467$	−2.77889e14	−0.578934	−0.289467	−	0.957188i	$-0.593478\pi$
$467$	−2.77889e14	−0.578934	−0.289467	+	0.957188i	$0.593478\pi$
$468$	3.37018e14	0.693907
$469$	−1.23478e15	−2.51269
$470$	−3.03321e15	−6.10049
$471$	3.27495e14	0.651014
$472$	−2.03079e14	−0.399010
$473$	2.18795e14	0.424914
$474$	−8.69495e14	−1.66912
$475$	4.87333e14	0.924722
$476$	1.65386e15	3.10213
$477$	5.21210e13	0.0966411
$478$	−6.23077e14	−1.14206
$479$	8.00287e14	1.45011	0.725054	−	0.688692i	$-0.241815\pi$
$479$	8.00287e14	1.45011	0.725054	+	0.688692i	$0.241815\pi$
$480$	1.80537e15	3.23399
$481$	−6.24333e13	−0.110565
$482$	7.97050e14	1.39549
$483$	−3.07763e14	−0.532730
$484$	−1.43829e15	−2.46149
$485$	3.40872e14	0.576782
$486$	7.28788e13	0.121928
$487$	4.29990e14	0.711294	0.355647	−	0.934620i	$-0.384261\pi$
$487$	4.29990e14	0.711294	0.355647	+	0.934620i	$0.384261\pi$
$488$	8.32226e14	1.36123
$489$	5.07317e12	0.00820504
$490$	−3.67945e15	−5.88442
$491$	−1.99682e14	−0.315784	−0.157892	−	0.987456i	$-0.550470\pi$
$491$	−1.99682e14	−0.315784	−0.157892	+	0.987456i	$0.550470\pi$
$492$	1.58708e15	2.48194
$493$	−3.97043e14	−0.614016
$494$	−3.82872e14	−0.585538
$495$	−9.75939e13	−0.147603
$496$	7.32250e14	1.09524
$497$	2.61135e14	0.386283
$498$	−8.15236e14	−1.19267
$499$	−1.23903e15	−1.79278	−0.896392	−	0.443261i	$-0.853821\pi$
$499$	−1.23903e15	−1.79278	−0.896392	+	0.443261i	$0.853821\pi$
$500$	4.67934e15	6.69652
$501$	−5.43615e14	−0.769456
$502$	2.04374e15	2.86125
$503$	−1.56087e14	−0.216143	−0.108072	−	0.994143i	$-0.534468\pi$
$503$	−1.56087e14	−0.216143	−0.108072	+	0.994143i	$0.534468\pi$
$504$	1.22127e15	1.67279
$505$	1.17769e15	1.59562
$506$	−1.92153e14	−0.257525
$507$	1.58986e14	0.210773
$508$	−1.39105e15	−1.82429
$509$	−5.82804e14	−0.756092	−0.378046	−	0.925787i	$-0.623404\pi$
$509$	−5.82804e14	−0.756092	−0.378046	+	0.925787i	$0.623404\pi$
$510$	−1.14194e15	−1.46557
$511$	8.55573e14	1.08628
$512$	5.97989e13	0.0751118
$513$	−5.98757e13	−0.0744055
$514$	−7.73264e13	−0.0950671
$515$	−2.78691e15	−3.38987
$516$	2.21499e15	2.66563
$517$	−3.51920e14	−0.419030
$518$	−3.66545e14	−0.431831
$519$	−1.23910e14	−0.144440
$520$	−3.89947e15	−4.49767
$521$	7.16798e14	0.818067	0.409034	−	0.912519i	$-0.365866\pi$
$521$	7.16798e14	0.818067	0.409034	+	0.912519i	$0.365866\pi$
$522$	−4.75012e14	−0.536434
$523$	−2.01108e13	−0.0224735	−0.0112368	−	0.999937i	$-0.503577\pi$
$523$	−2.01108e13	−0.0224735	−0.0112368	+	0.999937i	$0.503577\pi$
$524$	−3.65155e15	−4.03790
$525$	2.06630e15	2.26108
$526$	5.00921e14	0.542434
$527$	−2.30696e14	−0.247219
$528$	4.20535e14	0.445980
$529$	−6.50234e14	−0.682438
$530$	−9.77058e14	−1.01485
$531$	4.22156e13	0.0433963
$532$	−1.62560e15	−1.65387
$533$	−1.30213e15	−1.31116
$534$	1.74945e15	1.74351
$535$	1.16852e15	1.15263
$536$	−4.81727e15	−4.70321
$537$	−8.18557e14	−0.791026
$538$	−4.60135e14	−0.440132
$539$	−4.26897e14	−0.404189
$540$	−9.88003e14	−0.925960
$541$	4.54140e14	0.421313	0.210657	−	0.977560i	$-0.432440\pi$
$541$	4.54140e14	0.421313	0.210657	+	0.977560i	$0.432440\pi$
$542$	−7.54015e13	−0.0692442
$543$	−5.59526e14	−0.508653
$544$	2.45090e15	2.20562
$545$	3.64633e15	3.24845
$546$	−1.62338e15	−1.43173
$547$	7.23349e14	0.631564	0.315782	−	0.948832i	$-0.397733\pi$
$547$	7.23349e14	0.631564	0.315782	+	0.948832i	$0.397733\pi$
$548$	5.07169e14	0.438389
$549$	−1.73001e14	−0.148047
$550$	1.29010e15	1.09302
$551$	3.90259e14	0.327356
$552$	−1.20068e15	−0.997157
$553$	3.02889e15	2.49055
$554$	6.50594e13	0.0529671
$555$	1.83029e14	0.147540
$556$	5.76727e15	4.60319
$557$	−1.59614e14	−0.126144	−0.0630719	−	0.998009i	$-0.520090\pi$
$557$	−1.59614e14	−0.126144	−0.0630719	+	0.998009i	$0.520090\pi$
$558$	−2.75999e14	−0.215983
$559$	−1.81731e15	−1.40820
$560$	−1.26263e16	−9.68821
$561$	−1.32490e14	−0.100667
$562$	−6.31929e14	−0.475465
$563$	−1.01573e14	−0.0756799	−0.0378399	−	0.999284i	$-0.512048\pi$
$563$	−1.01573e14	−0.0756799	−0.0378399	+	0.999284i	$0.512048\pi$
$564$	−3.56270e15	−2.62872
$565$	−3.18569e15	−2.32776
$566$	−1.94712e15	−1.40897
$567$	−2.53874e14	−0.181933
$568$	1.01877e15	0.723040
$569$	2.30804e15	1.62228	0.811139	−	0.584853i	$-0.198848\pi$
$569$	2.30804e15	1.62228	0.811139	+	0.584853i	$0.198848\pi$
$570$	1.12243e15	0.781351
$571$	4.18920e14	0.288823	0.144412	−	0.989518i	$-0.453871\pi$
$571$	4.18920e14	0.288823	0.144412	+	0.989518i	$0.453871\pi$
$572$	−7.32995e14	−0.500522
$573$	−1.50984e15	−1.02113
$574$	−7.64480e15	−5.12095
$575$	−2.03147e15	−1.34784
$576$	1.30260e15	0.856028
$577$	7.42714e14	0.483454	0.241727	−	0.970344i	$-0.422286\pi$
$577$	7.42714e14	0.483454	0.241727	+	0.970344i	$0.422286\pi$
$578$	1.39762e15	0.901125
$579$	8.63854e14	0.551707
$580$	6.43963e15	4.07387
$581$	2.83988e15	1.77964
$582$	5.53628e14	0.343670
$583$	−1.13360e14	−0.0697081
$584$	3.33787e15	2.03329
$585$	8.10613e14	0.489166
$586$	−3.26140e15	−1.94970
$587$	−2.92445e15	−1.73195	−0.865973	−	0.500091i	$-0.833300\pi$
$587$	−2.92445e15	−1.73195	−0.865973	+	0.500091i	$0.833300\pi$
$588$	−4.32174e15	−2.53561
$589$	2.26755e14	0.131802
$590$	−7.91371e14	−0.455716
$591$	−6.04339e14	−0.344786
$592$	−7.88679e14	−0.445790
$593$	−5.58726e14	−0.312895	−0.156447	−	0.987686i	$-0.550004\pi$
$593$	−5.58726e14	−0.312895	−0.156447	+	0.987686i	$0.550004\pi$
$594$	−1.58507e14	−0.0879475
$595$	3.97794e15	2.18683
$596$	6.42079e15	3.49731
$597$	2.30248e14	0.124262
$598$	1.59602e15	0.853458
$599$	−3.05362e15	−1.61796	−0.808981	−	0.587835i	$-0.799980\pi$
$599$	−3.05362e15	−1.61796	−0.808981	+	0.587835i	$0.799980\pi$
$600$	8.06130e15	4.23227
$601$	−2.62270e15	−1.36439	−0.682195	−	0.731170i	$-0.738975\pi$
$601$	−2.62270e15	−1.36439	−0.682195	+	0.731170i	$0.738975\pi$
$602$	−1.06694e16	−5.49995
$603$	1.00140e15	0.511521
$604$	1.01532e15	0.513925
$605$	−3.45946e15	−1.73522
$606$	1.91275e15	0.950733
$607$	−9.29433e14	−0.457805	−0.228902	−	0.973449i	$-0.573514\pi$
$607$	−9.29433e14	−0.457805	−0.228902	+	0.973449i	$0.573514\pi$
$608$	−2.40902e15	−1.17590
$609$	1.65470e15	0.800434
$610$	3.24307e15	1.55468
$611$	2.92304e15	1.38870
$612$	−1.34128e15	−0.631518
$613$	1.23597e15	0.576735	0.288367	−	0.957520i	$-0.406888\pi$
$613$	1.23597e15	0.576735	0.288367	+	0.957520i	$0.406888\pi$
$614$	6.25821e15	2.89417
$615$	3.81733e15	1.74963
$616$	−2.65618e15	−1.20660
$617$	3.02427e15	1.36161	0.680804	−	0.732466i	$-0.261631\pi$
$617$	3.02427e15	1.36161	0.680804	+	0.732466i	$0.261631\pi$
$618$	−4.52637e15	−2.01982
$619$	−2.25456e14	−0.0997156	−0.0498578	−	0.998756i	$-0.515877\pi$
$619$	−2.25456e14	−0.0997156	−0.0498578	+	0.998756i	$0.515877\pi$
$620$	3.74165e15	1.64025
$621$	2.49595e14	0.108451
$622$	8.03435e15	3.46022
$623$	−6.09422e15	−2.60156
$624$	−3.49295e15	−1.47801
$625$	5.55250e15	2.32889
$626$	−4.75305e15	−1.97612
$627$	1.30226e14	0.0536694
$628$	−7.21088e15	−2.94585
$629$	2.48474e14	0.100624
$630$	4.75910e15	1.91052
$631$	−3.97438e15	−1.58164	−0.790820	−	0.612049i	$-0.790346\pi$
$631$	−3.97438e15	−1.58164	−0.790820	+	0.612049i	$0.790346\pi$
$632$	1.18167e16	4.66178
$633$	1.97010e15	0.770493
$634$	1.90610e15	0.739016
$635$	−3.34583e15	−1.28602
$636$	−1.14761e15	−0.437302
$637$	3.54580e15	1.33951
$638$	1.03312e15	0.386935
$639$	−2.11780e14	−0.0786377
$640$	−9.20289e15	−3.38793
$641$	1.18795e15	0.433590	0.216795	−	0.976217i	$-0.430440\pi$
$641$	1.18795e15	0.433590	0.216795	+	0.976217i	$0.430440\pi$
$642$	1.89785e15	0.686784
$643$	−3.97154e15	−1.42495	−0.712473	−	0.701699i	$-0.752425\pi$
$643$	−3.97154e15	−1.42495	−0.712473	+	0.701699i	$0.752425\pi$
$644$	6.77641e15	2.41061
$645$	5.32762e15	1.87912
$646$	1.52377e15	0.532892
$647$	−6.53729e14	−0.226686	−0.113343	−	0.993556i	$-0.536156\pi$
$647$	−6.53729e14	−0.226686	−0.113343	+	0.993556i	$0.536156\pi$
$648$	−9.90444e14	−0.340540
$649$	−9.18164e13	−0.0313022
$650$	−1.07156e16	−3.62236
$651$	9.61442e14	0.322276
$652$	−1.11702e14	−0.0371279
$653$	2.17325e15	0.716286	0.358143	−	0.933667i	$-0.383410\pi$
$653$	2.17325e15	0.716286	0.358143	+	0.933667i	$0.383410\pi$
$654$	5.92220e15	1.93555
$655$	−8.78290e15	−2.84650
$656$	−1.64490e16	−5.28649
$657$	−6.93868e14	−0.221140
$658$	1.71611e16	5.42380
$659$	−1.49091e15	−0.467285	−0.233643	−	0.972323i	$-0.575065\pi$
$659$	−1.49091e15	−0.467285	−0.233643	+	0.972323i	$0.575065\pi$
$660$	2.14885e15	0.667904
$661$	−3.78616e15	−1.16705	−0.583527	−	0.812094i	$-0.698328\pi$
$661$	−3.78616e15	−1.16705	−0.583527	+	0.812094i	$0.698328\pi$
$662$	7.05593e15	2.15693
$663$	1.10046e15	0.333618
$664$	1.10793e16	3.33110
$665$	−3.90998e15	−1.16588
$666$	2.97267e14	0.0879102
$667$	−1.62682e15	−0.477141
$668$	1.19695e16	3.48180
$669$	1.02690e15	0.296268
$670$	−1.87722e16	−5.37161
$671$	3.76267e14	0.106788
$672$	−1.02143e16	−2.87526
$673$	−2.04085e15	−0.569809	−0.284904	−	0.958556i	$-0.591962\pi$
$673$	−2.04085e15	−0.569809	−0.284904	+	0.958556i	$0.591962\pi$
$674$	4.36689e14	0.120932
$675$	−1.67576e15	−0.460301
$676$	−3.50060e15	−0.953753
$677$	3.81365e15	1.03063	0.515316	−	0.857000i	$-0.327675\pi$
$677$	3.81365e15	1.03063	0.515316	+	0.857000i	$0.327675\pi$
$678$	−5.17405e15	−1.38697
$679$	−1.92857e15	−0.512803
$680$	1.55193e16	4.09328
$681$	1.49215e15	0.390395
$682$	6.00281e14	0.155790
$683$	−3.34357e15	−0.860789	−0.430394	−	0.902641i	$-0.641626\pi$
$683$	−3.34357e15	−0.860789	−0.430394	+	0.902641i	$0.641626\pi$
$684$	1.31836e15	0.336686
$685$	1.21987e15	0.309040
$686$	8.43391e15	2.11956
$687$	1.91331e15	0.477005
$688$	−2.29568e16	−5.67774
$689$	9.41568e14	0.231018
$690$	−4.67890e15	−1.13887
$691$	−6.30069e14	−0.152145	−0.0760727	−	0.997102i	$-0.524238\pi$
$691$	−6.30069e14	−0.152145	−0.0760727	+	0.997102i	$0.524238\pi$
$692$	2.72829e15	0.653593
$693$	5.52161e14	0.131230
$694$	3.63634e15	0.857409
$695$	1.38717e16	3.24500
$696$	6.45554e15	1.49824
$697$	5.18226e15	1.19327
$698$	−1.22276e16	−2.79343
$699$	2.24679e15	0.509258
$700$	−4.54963e16	−10.2314
$701$	−2.69170e15	−0.600589	−0.300295	−	0.953846i	$-0.597085\pi$
$701$	−2.69170e15	−0.600589	−0.300295	+	0.953846i	$0.597085\pi$
$702$	1.31656e15	0.291465
$703$	−2.44229e14	−0.0536466
$704$	−2.83308e15	−0.617461
$705$	−8.56918e15	−1.85310
$706$	8.22270e15	1.76437
$707$	−6.66307e15	−1.41863
$708$	−9.29514e14	−0.196369
$709$	−9.45615e15	−1.98226	−0.991129	−	0.132904i	$-0.957570\pi$
$709$	−9.45615e15	−1.98226	−0.991129	+	0.132904i	$0.957570\pi$
$710$	3.97002e15	0.825794
$711$	−2.45642e15	−0.507015
$712$	−2.37755e16	−4.86956
$713$	−9.45239e14	−0.192110
$714$	6.46079e15	1.30300
$715$	−1.76304e15	−0.352840
$716$	1.80232e16	3.57940
$717$	−1.76026e15	−0.346915
$718$	1.15391e16	2.25676
$719$	9.04031e15	1.75459	0.877293	−	0.479956i	$-0.159347\pi$
$719$	9.04031e15	1.75459	0.877293	+	0.479956i	$0.159347\pi$
$720$	1.02399e16	1.97228
$721$	1.57676e16	3.01386
$722$	8.52208e15	1.61656
$723$	2.25176e15	0.423898
$724$	1.23198e16	2.30166
$725$	1.09223e16	2.02515
$726$	−5.61868e15	−1.03391
$727$	4.79773e15	0.876187	0.438093	−	0.898929i	$-0.355654\pi$
$727$	4.79773e15	0.876187	0.438093	+	0.898929i	$0.355654\pi$
$728$	2.20622e16	3.99877
$729$	2.05891e14	0.0370370
$730$	1.30072e16	2.32225
$731$	7.23258e15	1.28159
$732$	3.80918e15	0.669917
$733$	−7.50700e15	−1.31037	−0.655186	−	0.755467i	$-0.727410\pi$
$733$	−7.50700e15	−1.31037	−0.655186	+	0.755467i	$0.727410\pi$
$734$	9.56776e15	1.65761
$735$	−1.03949e16	−1.78747
$736$	1.00422e16	1.71395
$737$	−2.17799e15	−0.368965
$738$	6.19992e15	1.04250
$739$	9.01567e15	1.50471	0.752356	−	0.658756i	$-0.228917\pi$
$739$	9.01567e15	1.50471	0.752356	+	0.658756i	$0.228917\pi$
$740$	−4.02999e15	−0.667620
$741$	−1.08166e15	−0.177865
$742$	5.52794e15	0.902281
$743$	6.14048e15	0.994864	0.497432	−	0.867503i	$-0.334276\pi$
$743$	6.14048e15	0.994864	0.497432	+	0.867503i	$0.334276\pi$
$744$	3.75090e15	0.603232
$745$	1.54436e16	2.46541
$746$	1.07720e16	1.70700
$747$	−2.30314e15	−0.362290
$748$	2.91720e15	0.455520
$749$	−6.61118e15	−1.02478
$750$	1.82798e16	2.81277
$751$	7.14670e15	1.09166	0.545828	−	0.837897i	$-0.316215\pi$
$751$	7.14670e15	1.09166	0.545828	+	0.837897i	$0.316215\pi$
$752$	3.69248e16	5.59913
$753$	5.77380e15	0.869140
$754$	−8.58110e15	−1.28233
$755$	2.44210e15	0.362289
$756$	5.58986e15	0.823249
$757$	−5.55750e14	−0.0812553	−0.0406277	−	0.999174i	$-0.512936\pi$
$757$	−5.55750e14	−0.0812553	−0.0406277	+	0.999174i	$0.512936\pi$
$758$	−4.12543e15	−0.598809
$759$	−5.42855e14	−0.0782265
$760$	−1.52541e16	−2.18229
$761$	−6.98562e15	−0.992177	−0.496089	−	0.868272i	$-0.665231\pi$
$761$	−6.98562e15	−0.992177	−0.496089	+	0.868272i	$0.665231\pi$
$762$	−5.43414e15	−0.766264
$763$	−2.06300e16	−2.88812
$764$	3.32441e16	4.62063
$765$	−3.22611e15	−0.445185
$766$	2.30206e16	3.15397
$767$	7.62626e14	0.103738
$768$	−3.96859e15	−0.535981
$769$	−1.23209e16	−1.65215	−0.826073	−	0.563563i	$-0.809430\pi$
$769$	−1.23209e16	−1.65215	−0.826073	+	0.563563i	$0.809430\pi$
$770$	−1.03508e16	−1.37808
$771$	−2.18456e14	−0.0288778
$772$	−1.90206e16	−2.49648
$773$	−6.39007e15	−0.832757	−0.416378	−	0.909191i	$-0.636701\pi$
$773$	−6.39007e15	−0.832757	−0.416378	+	0.909191i	$0.636701\pi$
$774$	8.65286e15	1.11965
$775$	6.34627e15	0.815378
$776$	−7.52396e15	−0.959858
$777$	−1.03553e15	−0.131174
$778$	−2.98217e16	−3.75097
$779$	−5.09372e15	−0.636179
$780$	−1.78483e16	−2.21348
$781$	4.60610e14	0.0567221
$782$	−6.35190e15	−0.776724
$783$	−1.34196e15	−0.162949
$784$	4.47917e16	5.40082
$785$	−1.73440e16	−2.07666
$786$	−1.42648e16	−1.69606
$787$	−1.64082e16	−1.93731	−0.968657	−	0.248403i	$-0.920094\pi$
$787$	−1.64082e16	−1.93731	−0.968657	+	0.248403i	$0.920094\pi$
$788$	1.33065e16	1.56016
$789$	1.41516e15	0.164771
$790$	4.60480e16	5.32429
$791$	1.80238e16	2.06955
$792$	2.15416e15	0.245634
$793$	−3.12527e15	−0.353904
$794$	−4.80508e15	−0.540366
$795$	−2.76030e15	−0.308274
$796$	−5.06967e15	−0.562287
$797$	−8.89142e15	−0.979378	−0.489689	−	0.871897i	$-0.662890\pi$
$797$	−8.89142e15	−0.979378	−0.489689	+	0.871897i	$0.662890\pi$
$798$	−6.35040e15	−0.694681
$799$	−1.16332e16	−1.26384
$800$	−6.74223e16	−7.27459
$801$	4.94240e15	0.529613
$802$	2.35261e16	2.50375
$803$	1.50912e15	0.159510
$804$	−2.20491e16	−2.31464
$805$	1.62990e16	1.69935
$806$	−4.98592e15	−0.516301
$807$	−1.29993e15	−0.133696
$808$	−2.59948e16	−2.65537
$809$	−3.54139e15	−0.359300	−0.179650	−	0.983731i	$-0.557497\pi$
$809$	−3.54139e15	−0.359300	−0.179650	+	0.983731i	$0.557497\pi$
$810$	−3.85962e15	−0.388935
$811$	−3.04072e15	−0.304342	−0.152171	−	0.988354i	$-0.548626\pi$
$811$	−3.04072e15	−0.304342	−0.152171	+	0.988354i	$0.548626\pi$
$812$	−3.64337e16	−3.62198
$813$	−2.13018e14	−0.0210338
$814$	−6.46540e14	−0.0634105
$815$	−2.68672e14	−0.0261732
$816$	1.39014e16	1.34512
$817$	−7.10901e15	−0.683262
$818$	−5.44900e15	−0.520204
$819$	−4.58624e15	−0.434906
$820$	−8.40510e16	−7.91711
$821$	1.85223e16	1.73304	0.866518	−	0.499146i	$-0.166353\pi$
$821$	1.85223e16	1.73304	0.866518	+	0.499146i	$0.166353\pi$
$822$	1.98125e15	0.184138
$823$	8.11072e15	0.748791	0.374395	−	0.927269i	$-0.377850\pi$
$823$	8.11072e15	0.748791	0.374395	+	0.927269i	$0.377850\pi$
$824$	6.15147e16	5.64130
$825$	3.64469e15	0.332020
$826$	4.47737e15	0.405166
$827$	2.56159e15	0.230266	0.115133	−	0.993350i	$-0.463271\pi$
$827$	2.56159e15	0.230266	0.115133	+	0.993350i	$0.463271\pi$
$828$	−5.49565e15	−0.490741
$829$	−1.05268e16	−0.933788	−0.466894	−	0.884313i	$-0.654627\pi$
$829$	−1.05268e16	−0.933788	−0.466894	+	0.884313i	$0.654627\pi$
$830$	4.31745e16	3.80450
$831$	1.83800e14	0.0160894
$832$	2.35315e16	2.04631
$833$	−1.41117e16	−1.21908
$834$	2.25298e16	1.93350
$835$	2.87895e16	2.45448
$836$	−2.86736e15	−0.242855
$837$	−7.79728e14	−0.0656074
$838$	4.45719e15	0.372580
$839$	−1.03348e16	−0.858242	−0.429121	−	0.903247i	$-0.641177\pi$
$839$	−1.03348e16	−0.858242	−0.429121	+	0.903247i	$0.641177\pi$
$840$	−6.46776e16	−5.33602
$841$	−3.45383e15	−0.283089
$842$	2.10166e16	1.71138
$843$	−1.78527e15	−0.144428
$844$	−4.33783e16	−3.48649
$845$	−8.41982e15	−0.672343
$846$	−1.39176e16	−1.10415
$847$	1.95727e16	1.54274
$848$	1.18942e16	0.931447
$849$	−5.50083e15	−0.427992
$850$	4.26462e16	3.29667
$851$	1.01808e15	0.0781933
$852$	4.66304e15	0.355837
$853$	−1.89957e16	−1.44024	−0.720122	−	0.693848i	$-0.755914\pi$
$853$	−1.89957e16	−1.44024	−0.720122	+	0.693848i	$0.755914\pi$
$854$	−1.83484e16	−1.38223
$855$	3.17099e15	0.237345
$856$	−2.57924e16	−1.91816
$857$	−1.71475e16	−1.26709	−0.633543	−	0.773708i	$-0.718400\pi$
$857$	−1.71475e16	−1.26709	−0.633543	+	0.773708i	$0.718400\pi$
$858$	−2.86344e15	−0.210236
$859$	−1.16779e16	−0.851930	−0.425965	−	0.904740i	$-0.640065\pi$
$859$	−1.16779e16	−0.851930	−0.425965	+	0.904740i	$0.640065\pi$
$860$	−1.17305e17	−8.50305
$861$	−2.15974e16	−1.55555
$862$	2.91335e16	2.08498
$863$	4.65167e15	0.330788	0.165394	−	0.986228i	$-0.447110\pi$
$863$	4.65167e15	0.330788	0.165394	+	0.986228i	$0.447110\pi$
$864$	8.28377e15	0.585332
$865$	6.56222e15	0.460747
$866$	2.08723e16	1.45620
$867$	3.94843e15	0.273728
$868$	−2.11693e16	−1.45830
$869$	5.34258e15	0.365715
$870$	2.51564e16	1.71116
$871$	1.80904e16	1.22278
$872$	−8.04844e16	−5.40594
$873$	1.56406e15	0.104394
$874$	6.24338e15	0.414101
$875$	−6.36778e16	−4.19704
$876$	1.52778e16	1.00066
$877$	1.09513e15	0.0712798	0.0356399	−	0.999365i	$-0.488653\pi$
$877$	1.09513e15	0.0712798	0.0356399	+	0.999365i	$0.488653\pi$
$878$	2.12668e16	1.37557
$879$	−9.21382e15	−0.592245
$880$	−2.22713e16	−1.42263
$881$	3.96514e15	0.251705	0.125852	−	0.992049i	$-0.459833\pi$
$881$	3.96514e15	0.251705	0.125852	+	0.992049i	$0.459833\pi$
$882$	−1.68828e16	−1.06504
$883$	−7.13057e15	−0.447034	−0.223517	−	0.974700i	$-0.571754\pi$
$883$	−7.13057e15	−0.447034	−0.223517	+	0.974700i	$0.571754\pi$
$884$	−2.42302e16	−1.50963
$885$	−2.23571e15	−0.138429
$886$	1.62168e15	0.0997885
$887$	−1.38631e16	−0.847772	−0.423886	−	0.905716i	$-0.639334\pi$
$887$	−1.38631e16	−0.847772	−0.423886	+	0.905716i	$0.639334\pi$
$888$	−4.03995e15	−0.245530
$889$	1.89298e16	1.14337
$890$	−9.26499e16	−5.56160
$891$	−4.47801e14	−0.0267152
$892$	−2.26105e16	−1.34062
$893$	1.14344e16	0.673802
$894$	2.50828e16	1.46899
$895$	4.33504e16	2.52328
$896$	5.20676e16	3.01213
$897$	4.50895e15	0.259249
$898$	−1.95506e16	−1.11722
$899$	5.08213e15	0.288647
$900$	3.68974e16	2.08287
$901$	−3.74728e15	−0.210247
$902$	−1.34845e16	−0.751965
$903$	−3.01423e16	−1.67068
$904$	7.03168e16	3.87376
$905$	2.96322e16	1.62254
$906$	3.96634e15	0.215866
$907$	−2.73671e16	−1.48043	−0.740216	−	0.672369i	$-0.765277\pi$
$907$	−2.73671e16	−1.48043	−0.740216	+	0.672369i	$0.765277\pi$
$908$	−3.28546e16	−1.76654
$909$	5.40374e15	0.288797
$910$	8.59734e16	4.56706
$911$	8.41323e15	0.444234	0.222117	−	0.975020i	$-0.428703\pi$
$911$	8.41323e15	0.444234	0.222117	+	0.975020i	$0.428703\pi$
$912$	−1.36639e16	−0.717137
$913$	5.00919e15	0.261323
$914$	1.24821e16	0.647269
$915$	9.16204e15	0.472255
$916$	−4.21277e16	−2.15846
$917$	4.96914e16	2.53075
$918$	−5.23968e15	−0.265259
$919$	8.20052e15	0.412673	0.206337	−	0.978481i	$-0.433846\pi$
$919$	8.20052e15	0.412673	0.206337	+	0.978481i	$0.433846\pi$
$920$	6.35876e16	3.18082
$921$	1.76802e16	0.879140
$922$	4.19387e16	2.07298
$923$	−3.82582e15	−0.187981
$924$	−1.21576e16	−0.593817
$925$	−6.83532e15	−0.331879
$926$	−1.41166e16	−0.681349
$927$	−1.27875e16	−0.613547
$928$	−5.39922e16	−2.57524
$929$	1.47434e16	0.699057	0.349528	−	0.936926i	$-0.386342\pi$
$929$	1.47434e16	0.699057	0.349528	+	0.936926i	$0.386342\pi$
$930$	1.46167e16	0.688960
$931$	1.38706e16	0.649937
$932$	−4.94705e16	−2.30440
$933$	2.26980e16	1.05109
$934$	2.39024e16	1.10036
$935$	7.01659e15	0.321116
$936$	−1.78924e16	−0.814051
$937$	1.63627e16	0.740094	0.370047	−	0.929013i	$-0.379342\pi$
$937$	1.63627e16	0.740094	0.370047	+	0.929013i	$0.379342\pi$
$938$	1.06208e17	4.77577
$939$	−1.34279e16	−0.600271
$940$	1.88679e17	8.38531
$941$	−1.85372e16	−0.819033	−0.409517	−	0.912303i	$-0.634303\pi$
$941$	−1.85372e16	−0.819033	−0.409517	+	0.912303i	$0.634303\pi$
$942$	−2.81693e16	−1.23736
$943$	2.12335e16	0.927271
$944$	9.63375e15	0.418263
$945$	1.34450e16	0.580345
$946$	−1.88195e16	−0.807618
$947$	−4.50910e16	−1.92382	−0.961912	−	0.273360i	$-0.911865\pi$
$947$	−4.50910e16	−1.92382	−0.961912	+	0.273360i	$0.911865\pi$
$948$	5.40862e16	2.29425
$949$	−1.25347e16	−0.528629
$950$	−4.19176e16	−1.75758
$951$	5.38494e15	0.224485
$952$	−8.78039e16	−3.63924
$953$	−4.10630e15	−0.169215	−0.0846077	−	0.996414i	$-0.526964\pi$
$953$	−4.10630e15	−0.169215	−0.0846077	+	0.996414i	$0.526964\pi$
$954$	−4.48315e15	−0.183682
$955$	7.99605e16	3.25729
$956$	3.87580e16	1.56979
$957$	2.91869e15	0.117536
$958$	−6.88361e16	−2.75617
$959$	−6.90170e15	−0.274760
$960$	−6.89851e16	−2.73063
$961$	−2.24556e16	−0.883783
$962$	5.37015e15	0.210147
$963$	5.36166e15	0.208619
$964$	−4.95798e16	−1.91815
$965$	−4.57493e16	−1.75988
$966$	2.64720e16	1.01254
$967$	−1.49354e16	−0.568031	−0.284016	−	0.958820i	$-0.591667\pi$
$967$	−1.49354e16	−0.568031	−0.284016	+	0.958820i	$0.591667\pi$
$968$	7.63595e16	2.88768
$969$	4.30481e15	0.161873
$970$	−2.93198e16	−1.09627
$971$	2.32789e16	0.865478	0.432739	−	0.901519i	$-0.357547\pi$
$971$	2.32789e16	0.865478	0.432739	+	0.901519i	$0.357547\pi$
$972$	−4.53337e15	−0.167593
$973$	−7.84827e16	−2.88505
$974$	−3.69852e16	−1.35193
$975$	−3.02727e16	−1.10034
$976$	−3.94795e16	−1.42691
$977$	−8.28859e15	−0.297893	−0.148947	−	0.988845i	$-0.547588\pi$
$977$	−8.28859e15	−0.297893	−0.148947	+	0.988845i	$0.547588\pi$
$978$	−4.36365e14	−0.0155950
$979$	−1.07494e16	−0.382015
$980$	2.28877e17	8.08832
$981$	1.67309e16	0.587949
$982$	1.71755e16	0.600199
$983$	3.73103e16	1.29653	0.648267	−	0.761413i	$-0.275494\pi$
$983$	3.73103e16	1.29653	0.648267	+	0.761413i	$0.275494\pi$
$984$	−8.42587e16	−2.91167
$985$	3.20055e16	1.09983
$986$	3.41513e16	1.16704
$987$	4.84822e16	1.64755
$988$	2.38162e16	0.804840
$989$	2.96343e16	0.995898
$990$	8.39446e15	0.280543
$991$	4.50911e15	0.149860	0.0749300	−	0.997189i	$-0.476127\pi$
$991$	4.50911e15	0.149860	0.0749300	+	0.997189i	$0.476127\pi$
$992$	−3.13714e16	−1.03686
$993$	1.99338e16	0.655193
$994$	−2.24613e16	−0.734194
$995$	−1.21938e16	−0.396381
$996$	5.07111e16	1.63937
$997$	3.16876e16	1.01875	0.509373	−	0.860546i	$-0.329877\pi$
$997$	3.16876e16	1.01875	0.509373	+	0.860546i	$0.329877\pi$
$998$	1.06574e17	3.40748
$999$	8.39815e14	0.0267038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.2	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.2	✓	26	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)

\(f(q)\)	\(=\)	\(q-86.0142 q^{2} -243.000 q^{3} +5350.44 q^{4} +12869.1 q^{5} +20901.4 q^{6} -72810.3 q^{7} -284057. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-86.0142 q^{2} -243.000 q^{3} +5350.44 q^{4} +12869.1 q^{5} +20901.4 q^{6} -72810.3 q^{7} -284057. q^{8} +59049.0 q^{9} -1.10693e6 q^{10} -128428. q^{11} -1.30016e6 q^{12} +1.06672e6 q^{13} +6.26272e6 q^{14} -3.12720e6 q^{15} +1.34752e7 q^{16} -4.24538e6 q^{17} -5.07905e6 q^{18} +4.17284e6 q^{19} +6.88556e7 q^{20} +1.76929e7 q^{21} +1.10466e7 q^{22} -1.73947e7 q^{23} +6.90258e7 q^{24} +1.16787e8 q^{25} -9.17532e7 q^{26} -1.43489e7 q^{27} -3.89567e8 q^{28} +9.35237e7 q^{29} +2.68984e8 q^{30} +5.43406e7 q^{31} -5.77310e8 q^{32} +3.12080e7 q^{33} +3.65163e8 q^{34} -9.37006e8 q^{35} +3.15938e8 q^{36} -5.85281e7 q^{37} -3.58924e8 q^{38} -2.59214e8 q^{39} -3.65557e9 q^{40} -1.22068e9 q^{41} -1.52184e9 q^{42} -1.70364e9 q^{43} -6.87147e8 q^{44} +7.59910e8 q^{45} +1.49619e9 q^{46} +2.74021e9 q^{47} -3.27447e9 q^{48} +3.32401e9 q^{49} -1.00453e10 q^{50} +1.03163e9 q^{51} +5.70743e9 q^{52} +8.82674e8 q^{53} +1.23421e9 q^{54} -1.65276e9 q^{55} +2.06822e10 q^{56} -1.01400e9 q^{57} -8.04436e9 q^{58} +7.14924e8 q^{59} -1.67319e10 q^{60} -2.92979e9 q^{61} -4.67406e9 q^{62} -4.29937e9 q^{63} +2.20597e10 q^{64} +1.37278e10 q^{65} -2.68433e9 q^{66} +1.69588e10 q^{67} -2.27146e10 q^{68} +4.22692e9 q^{69} +8.05958e10 q^{70} -3.58652e9 q^{71} -1.67733e10 q^{72} -1.17507e10 q^{73} +5.03425e9 q^{74} -2.83792e10 q^{75} +2.23265e10 q^{76} +9.35089e9 q^{77} +2.22960e10 q^{78} -4.15998e10 q^{79} +1.73414e11 q^{80} +3.48678e9 q^{81} +1.04996e11 q^{82} -3.90038e10 q^{83} +9.46648e10 q^{84} -5.46344e10 q^{85} +1.46537e11 q^{86} -2.27263e10 q^{87} +3.64809e10 q^{88} +8.36999e10 q^{89} -6.53631e10 q^{90} -7.76684e10 q^{91} -9.30694e10 q^{92} -1.32048e10 q^{93} -2.35697e11 q^{94} +5.37009e10 q^{95} +1.40286e11 q^{96} +2.64875e10 q^{97} -2.85912e11 q^{98} -7.58355e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

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Database

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