LMFDB - Embedded newform 177.12.a.c.1.4

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:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} -215188. q^{10} +299288. q^{11} -726148. q^{12} -1.56341e6 q^{13} +4.40488e6 q^{14} -736834. q^{15} -1.38456e6 q^{16} -569100. q^{17} -4.19051e6 q^{18} -2.09189e7 q^{19} +9.06113e6 q^{20} +1.50829e7 q^{21} -2.12395e7 q^{22} +2.52186e7 q^{23} +1.62147e7 q^{24} -3.96336e7 q^{25} +1.10950e8 q^{26} -1.43489e7 q^{27} -1.85481e8 q^{28} -8.20111e7 q^{29} +5.22906e7 q^{30} -1.20933e8 q^{31} +2.34915e8 q^{32} -7.27270e7 q^{33} +4.03871e7 q^{34} -1.88210e8 q^{35} +1.76454e8 q^{36} +3.75335e8 q^{37} +1.48454e9 q^{38} +3.79908e8 q^{39} -2.02333e8 q^{40} +3.35558e8 q^{41} -1.07039e9 q^{42} +1.05595e9 q^{43} +8.94351e8 q^{44} +1.79051e8 q^{45} -1.78968e9 q^{46} -5.28373e8 q^{47} +3.36447e8 q^{48} +1.87532e9 q^{49} +2.81267e9 q^{50} +1.38291e8 q^{51} -4.67187e9 q^{52} -5.65789e9 q^{53} +1.01829e9 q^{54} +9.07513e8 q^{55} +4.14174e9 q^{56} +5.08329e9 q^{57} +5.82005e9 q^{58} -7.14924e8 q^{59} -2.20185e9 q^{60} -7.64605e9 q^{61} +8.58220e9 q^{62} -3.66516e9 q^{63} -1.38355e10 q^{64} -4.74063e9 q^{65} +5.16119e9 q^{66} -9.27226e9 q^{67} -1.70062e9 q^{68} -6.12812e9 q^{69} +1.33567e10 q^{70} -1.76284e10 q^{71} -3.94017e9 q^{72} +8.95732e8 q^{73} -2.66363e10 q^{74} +9.63098e9 q^{75} -6.25111e10 q^{76} -1.85767e10 q^{77} -2.69608e10 q^{78} +1.22188e9 q^{79} -4.19831e9 q^{80} +3.48678e9 q^{81} -2.38134e10 q^{82} -6.96998e10 q^{83} +4.50718e10 q^{84} -1.72565e9 q^{85} -7.49371e10 q^{86} +1.99287e10 q^{87} -1.99706e10 q^{88} +1.97819e10 q^{89} -1.27066e10 q^{90} +9.70403e10 q^{91} +7.53597e10 q^{92} +2.93867e10 q^{93} +3.74968e10 q^{94} -6.34310e10 q^{95} -5.70842e10 q^{96} -1.55752e11 q^{97} -1.33085e11 q^{98} +1.76727e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * 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 $

$2$	−70.9666	−1.56816	−0.784078	−	0.620663i	$-0.786864\pi$
$2$	−70.9666	−1.56816	−0.784078	+	0.620663i	$0.786864\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2988.26	1.45911
$5$	3032.24	0.433939	0.216969	−	0.976178i	$-0.430383\pi$
$5$	3032.24	0.433939	0.216969	+	0.976178i	$0.430383\pi$
$6$	17244.9	0.905375
$7$	−62069.7	−1.39586	−0.697928	−	0.716168i	$-0.745894\pi$
$7$	−62069.7	−1.39586	−0.697928	+	0.716168i	$0.745894\pi$
$8$	−66727.2	−0.719959
$9$	59049.0	0.333333
$10$	−215188.	−0.680484
$11$	299288.	0.560312	0.280156	−	0.959955i	$-0.409614\pi$
$11$	299288.	0.560312	0.280156	+	0.959955i	$0.409614\pi$
$12$	−726148.	−0.842419
$13$	−1.56341e6	−1.16784	−0.583920	−	0.811811i	$-0.698482\pi$
$13$	−1.56341e6	−1.16784	−0.583920	+	0.811811i	$0.698482\pi$
$14$	4.40488e6	2.18892
$15$	−736834.	−0.250535
$16$	−1.38456e6	−0.330104
$17$	−569100.	−0.0972119	−0.0486060	−	0.998818i	$-0.515478\pi$
$17$	−569100.	−0.0972119	−0.0486060	+	0.998818i	$0.515478\pi$
$18$	−4.19051e6	−0.522719
$19$	−2.09189e7	−1.93818	−0.969088	−	0.246714i	$-0.920649\pi$
$19$	−2.09189e7	−1.93818	−0.969088	+	0.246714i	$0.920649\pi$
$20$	9.06113e6	0.633165
$21$	1.50829e7	0.805898
$22$	−2.12395e7	−0.878656
$23$	2.52186e7	0.816992	0.408496	−	0.912760i	$-0.366053\pi$
$23$	2.52186e7	0.816992	0.408496	+	0.912760i	$0.366053\pi$
$24$	1.62147e7	0.415669
$25$	−3.96336e7	−0.811697
$26$	1.10950e8	1.83136
$27$	−1.43489e7	−0.192450
$28$	−1.85481e8	−2.03671
$29$	−8.20111e7	−0.742478	−0.371239	−	0.928537i	$-0.621067\pi$
$29$	−8.20111e7	−0.742478	−0.371239	+	0.928537i	$0.621067\pi$
$30$	5.22906e7	0.392877
$31$	−1.20933e8	−0.758674	−0.379337	−	0.925259i	$-0.623848\pi$
$31$	−1.20933e8	−0.758674	−0.379337	+	0.925259i	$0.623848\pi$
$32$	2.34915e8	1.23761
$33$	−7.27270e7	−0.323496
$34$	4.03871e7	0.152443
$35$	−1.88210e8	−0.605716
$36$	1.76454e8	0.486371
$37$	3.75335e8	0.889836	0.444918	−	0.895571i	$-0.353233\pi$
$37$	3.75335e8	0.889836	0.444918	+	0.895571i	$0.353233\pi$
$38$	1.48454e9	3.03936
$39$	3.79908e8	0.674253
$40$	−2.02333e8	−0.312418
$41$	3.35558e8	0.452331	0.226166	−	0.974089i	$-0.427381\pi$
$41$	3.35558e8	0.452331	0.226166	+	0.974089i	$0.427381\pi$
$42$	−1.07039e9	−1.26377
$43$	1.05595e9	1.09538	0.547692	−	0.836680i	$-0.315507\pi$
$43$	1.05595e9	1.09538	0.547692	+	0.836680i	$0.315507\pi$
$44$	8.94351e8	0.817557
$45$	1.79051e8	0.144646
$46$	−1.78968e9	−1.28117
$47$	−5.28373e8	−0.336049	−0.168024	−	0.985783i	$-0.553739\pi$
$47$	−5.28373e8	−0.336049	−0.168024	+	0.985783i	$0.553739\pi$
$48$	3.36447e8	0.190586
$49$	1.87532e9	0.948414
$50$	2.81267e9	1.27287
$51$	1.38291e8	0.0561253
$52$	−4.67187e9	−1.70401
$53$	−5.65789e9	−1.85839	−0.929195	−	0.369589i	$-0.879499\pi$
$53$	−5.65789e9	−1.85839	−0.929195	+	0.369589i	$0.879499\pi$
$54$	1.01829e9	0.301792
$55$	9.07513e8	0.243141
$56$	4.14174e9	1.00496
$57$	5.08329e9	1.11901
$58$	5.82005e9	1.16432
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−2.20185e9	−0.365558
$61$	−7.64605e9	−1.15911	−0.579553	−	0.814934i	$-0.696773\pi$
$61$	−7.64605e9	−1.15911	−0.579553	+	0.814934i	$0.696773\pi$
$62$	8.58220e9	1.18972
$63$	−3.66516e9	−0.465285
$64$	−1.38355e10	−1.61067
$65$	−4.74063e9	−0.506772
$66$	5.16119e9	0.507292
$67$	−9.27226e9	−0.839024	−0.419512	−	0.907750i	$-0.637799\pi$
$67$	−9.27226e9	−0.839024	−0.419512	+	0.907750i	$0.637799\pi$
$68$	−1.70062e9	−0.141843
$69$	−6.12812e9	−0.471690
$70$	1.33567e10	0.949857
$71$	−1.76284e10	−1.15956	−0.579778	−	0.814775i	$-0.696861\pi$
$71$	−1.76284e10	−1.15956	−0.579778	+	0.814775i	$0.696861\pi$
$72$	−3.94017e9	−0.239986
$73$	8.95732e8	0.0505711	0.0252856	−	0.999680i	$-0.491950\pi$
$73$	8.95732e8	0.0505711	0.0252856	+	0.999680i	$0.491950\pi$
$74$	−2.66363e10	−1.39540
$75$	9.63098e9	0.468634
$76$	−6.25111e10	−2.82802
$77$	−1.85767e10	−0.782114
$78$	−2.69608e10	−1.05733
$79$	1.22188e9	0.0446765	0.0223383	−	0.999750i	$-0.492889\pi$
$79$	1.22188e9	0.0446765	0.0223383	+	0.999750i	$0.492889\pi$
$80$	−4.19831e9	−0.143245
$81$	3.48678e9	0.111111
$82$	−2.38134e10	−0.709326
$83$	−6.96998e10	−1.94224	−0.971118	−	0.238598i	$-0.923312\pi$
$83$	−6.96998e10	−1.94224	−0.971118	+	0.238598i	$0.923312\pi$
$84$	4.50718e10	1.17590
$85$	−1.72565e9	−0.0421840
$86$	−7.49371e10	−1.71773
$87$	1.99287e10	0.428670
$88$	−1.99706e10	−0.403401
$89$	1.97819e10	0.375511	0.187755	−	0.982216i	$-0.439879\pi$
$89$	1.97819e10	0.375511	0.187755	+	0.982216i	$0.439879\pi$
$90$	−1.27066e10	−0.226828
$91$	9.70403e10	1.63014
$92$	7.53597e10	1.19208
$93$	2.93867e10	0.438021
$94$	3.74968e10	0.526977
$95$	−6.34310e10	−0.841050
$96$	−5.70842e10	−0.714537
$97$	−1.55752e11	−1.84157	−0.920784	−	0.390073i	$-0.872450\pi$
$97$	−1.55752e11	−1.84157	−0.920784	+	0.390073i	$0.872450\pi$
$98$	−1.33085e11	−1.48726
$99$	1.76727e10	0.186771
$100$	−1.18436e11	−1.18436
$101$	1.66195e11	1.57344	0.786721	−	0.617309i	$-0.211777\pi$
$101$	1.66195e11	1.57344	0.786721	+	0.617309i	$0.211777\pi$
$102$	−9.81407e9	−0.0880133
$103$	−5.38134e10	−0.457389	−0.228695	−	0.973498i	$-0.573446\pi$
$103$	−5.38134e10	−0.457389	−0.228695	+	0.973498i	$0.573446\pi$
$104$	1.04322e11	0.840798
$105$	4.57351e10	0.349710
$106$	4.01521e11	2.91425
$107$	1.15660e11	0.797211	0.398605	−	0.917123i	$-0.369494\pi$
$107$	1.15660e11	0.797211	0.398605	+	0.917123i	$0.369494\pi$
$108$	−4.28783e10	−0.280806
$109$	−2.39276e11	−1.48954	−0.744771	−	0.667320i	$-0.767441\pi$
$109$	−2.39276e11	−1.48954	−0.744771	+	0.667320i	$0.767441\pi$
$110$	−6.44031e10	−0.381283
$111$	−9.12065e10	−0.513747
$112$	8.59391e10	0.460778
$113$	−2.36020e11	−1.20508	−0.602542	−	0.798087i	$-0.705845\pi$
$113$	−2.36020e11	−1.20508	−0.602542	+	0.798087i	$0.705845\pi$
$114$	−3.60744e11	−1.75478
$115$	7.64688e10	0.354524
$116$	−2.45071e11	−1.08336
$117$	−9.23176e10	−0.389280
$118$	5.07358e10	0.204156
$119$	3.53239e10	0.135694
$120$	4.91669e10	0.180375
$121$	−1.95738e11	−0.686051
$122$	5.42615e11	1.81766
$123$	−8.15406e10	−0.261154
$124$	−3.61379e11	−1.10699
$125$	−2.68237e11	−0.786166
$126$	2.60104e11	0.729640
$127$	−9.17727e10	−0.246486	−0.123243	−	0.992376i	$-0.539330\pi$
$127$	−9.17727e10	−0.246486	−0.123243	+	0.992376i	$0.539330\pi$
$128$	5.00755e11	1.28816
$129$	−2.56595e11	−0.632420
$130$	3.36426e11	0.794697
$131$	−3.46489e11	−0.784689	−0.392344	−	0.919818i	$-0.628336\pi$
$131$	−3.46489e11	−0.784689	−0.392344	+	0.919818i	$0.628336\pi$
$132$	−2.17327e11	−0.472017
$133$	1.29843e12	2.70542
$134$	6.58021e11	1.31572
$135$	−4.35093e10	−0.0835116
$136$	3.79744e10	0.0699886
$137$	2.17262e11	0.384610	0.192305	−	0.981335i	$-0.438404\pi$
$137$	2.17262e11	0.384610	0.192305	+	0.981335i	$0.438404\pi$
$138$	4.34892e11	0.739684
$139$	2.54946e10	0.0416741	0.0208371	−	0.999783i	$-0.493367\pi$
$139$	2.54946e10	0.0416741	0.0208371	+	0.999783i	$0.493367\pi$
$140$	−5.62422e11	−0.883808
$141$	1.28395e11	0.194018
$142$	1.25103e12	1.81836
$143$	−4.67909e11	−0.654355
$144$	−8.17567e10	−0.110035
$145$	−2.48677e11	−0.322190
$146$	−6.35671e10	−0.0793034
$147$	−4.55704e11	−0.547567
$148$	1.12160e12	1.29837
$149$	4.60011e10	0.0513149	0.0256575	−	0.999671i	$-0.491832\pi$
$149$	4.60011e10	0.0513149	0.0256575	+	0.999671i	$0.491832\pi$
$150$	−6.83478e11	−0.734890
$151$	−2.82488e11	−0.292837	−0.146419	−	0.989223i	$-0.546775\pi$
$151$	−2.82488e11	−0.292837	−0.146419	+	0.989223i	$0.546775\pi$
$152$	1.39586e12	1.39541
$153$	−3.36048e10	−0.0324040
$154$	1.31833e12	1.22648
$155$	−3.66698e11	−0.329218
$156$	1.13526e12	0.983811
$157$	−1.35295e12	−1.13196	−0.565982	−	0.824417i	$-0.691503\pi$
$157$	−1.35295e12	−1.13196	−0.565982	+	0.824417i	$0.691503\pi$
$158$	−8.67127e10	−0.0700598
$159$	1.37487e12	1.07294
$160$	7.12317e11	0.537049
$161$	−1.56531e12	−1.14040
$162$	−2.47445e11	−0.174240
$163$	7.64129e11	0.520158	0.260079	−	0.965587i	$-0.416251\pi$
$163$	7.64129e11	0.520158	0.260079	+	0.965587i	$0.416251\pi$
$164$	1.00274e12	0.660002
$165$	−2.20526e11	−0.140378
$166$	4.94636e12	3.04573
$167$	2.78895e12	1.66150	0.830750	−	0.556645i	$-0.187912\pi$
$167$	2.78895e12	1.66150	0.830750	+	0.556645i	$0.187912\pi$
$168$	−1.00644e12	−0.580214
$169$	6.52081e11	0.363852
$170$	1.22463e11	0.0661511
$171$	−1.23524e12	−0.646059
$172$	3.15545e12	1.59829
$173$	−2.71827e11	−0.133364	−0.0666820	−	0.997774i	$-0.521241\pi$
$173$	−2.71827e11	−0.133364	−0.0666820	+	0.997774i	$0.521241\pi$
$174$	−1.41427e12	−0.672221
$175$	2.46005e12	1.13301
$176$	−4.14381e11	−0.184961
$177$	1.73727e11	0.0751646
$178$	−1.40385e12	−0.588860
$179$	−3.97647e12	−1.61736	−0.808680	−	0.588249i	$-0.799817\pi$
$179$	−3.97647e12	−1.61736	−0.808680	+	0.588249i	$0.799817\pi$
$180$	5.35050e11	0.211055
$181$	2.86120e12	1.09475	0.547376	−	0.836887i	$-0.315627\pi$
$181$	2.86120e12	1.09475	0.547376	+	0.836887i	$0.315627\pi$
$182$	−6.88662e12	−2.55631
$183$	1.85799e12	0.669210
$184$	−1.68276e12	−0.588201
$185$	1.13811e12	0.386135
$186$	−2.08547e12	−0.686884
$187$	−1.70325e11	−0.0544690
$188$	−1.57892e12	−0.490333
$189$	8.90633e11	0.268633
$190$	4.50149e12	1.31890
$191$	2.22610e12	0.633666	0.316833	−	0.948481i	$-0.397381\pi$
$191$	2.22610e12	0.633666	0.316833	+	0.948481i	$0.397381\pi$
$192$	3.36203e12	0.929919
$193$	5.70171e12	1.53264	0.766320	−	0.642459i	$-0.222086\pi$
$193$	5.70171e12	1.53264	0.766320	+	0.642459i	$0.222086\pi$
$194$	1.10532e13	2.88787
$195$	1.15197e12	0.292585
$196$	5.60396e12	1.38384
$197$	−5.58793e12	−1.34180	−0.670898	−	0.741550i	$-0.734091\pi$
$197$	−5.58793e12	−1.34180	−0.670898	+	0.741550i	$0.734091\pi$
$198$	−1.25417e12	−0.292885
$199$	−1.96680e12	−0.446754	−0.223377	−	0.974732i	$-0.571708\pi$
$199$	−1.96680e12	−0.446754	−0.223377	+	0.974732i	$0.571708\pi$
$200$	2.64464e12	0.584389
$201$	2.25316e12	0.484410
$202$	−1.17943e13	−2.46740
$203$	5.09041e12	1.03639
$204$	4.13251e11	0.0818931
$205$	1.01749e12	0.196284
$206$	3.81896e12	0.717258
$207$	1.48913e12	0.272331
$208$	2.16463e12	0.385509
$209$	−6.26077e12	−1.08598
$210$	−3.24567e12	−0.548400
$211$	−7.57343e12	−1.24663	−0.623317	−	0.781969i	$-0.714215\pi$
$211$	−7.57343e12	−1.24663	−0.623317	+	0.781969i	$0.714215\pi$
$212$	−1.69072e13	−2.71160
$213$	4.28370e12	0.669469
$214$	−8.20801e12	−1.25015
$215$	3.20189e12	0.475329
$216$	9.57462e11	0.138556
$217$	7.50627e12	1.05900
$218$	1.69806e13	2.33583
$219$	−2.17663e11	−0.0291972
$220$	2.71189e12	0.354770
$221$	8.89735e11	0.113528
$222$	6.47262e12	0.805636
$223$	1.44883e13	1.75930	0.879652	−	0.475619i	$-0.157776\pi$
$223$	1.44883e13	1.75930	0.879652	+	0.475619i	$0.157776\pi$
$224$	−1.45811e13	−1.72753
$225$	−2.34033e12	−0.270566
$226$	1.67495e13	1.88976
$227$	1.25150e13	1.37813	0.689063	−	0.724702i	$-0.258023\pi$
$227$	1.25150e13	1.37813	0.689063	+	0.724702i	$0.258023\pi$
$228$	1.51902e13	1.63276
$229$	−5.33646e12	−0.559962	−0.279981	−	0.960006i	$-0.590328\pi$
$229$	−5.33646e12	−0.559962	−0.279981	+	0.960006i	$0.590328\pi$
$230$	−5.42673e12	−0.555949
$231$	4.51415e12	0.451554
$232$	5.47237e12	0.534554
$233$	5.51437e12	0.526064	0.263032	−	0.964787i	$-0.415278\pi$
$233$	5.51437e12	0.526064	0.263032	+	0.964787i	$0.415278\pi$
$234$	6.55147e12	0.610452
$235$	−1.60215e12	−0.145825
$236$	−2.13638e12	−0.189960
$237$	−2.96917e11	−0.0257940
$238$	−2.50682e12	−0.212789
$239$	3.89823e12	0.323354	0.161677	−	0.986844i	$-0.448310\pi$
$239$	3.89823e12	0.323354	0.161677	+	0.986844i	$0.448310\pi$
$240$	1.02019e12	0.0827025
$241$	−1.68649e12	−0.133626	−0.0668128	−	0.997766i	$-0.521283\pi$
$241$	−1.68649e12	−0.133626	−0.0668128	+	0.997766i	$0.521283\pi$
$242$	1.38909e13	1.07583
$243$	−8.47289e11	−0.0641500
$244$	−2.28484e13	−1.69127
$245$	5.68644e12	0.411554
$246$	5.78666e12	0.409529
$247$	3.27047e13	2.26348
$248$	8.06951e12	0.546214
$249$	1.69371e13	1.12135
$250$	1.90359e13	1.23283
$251$	−1.40972e13	−0.893155	−0.446578	−	0.894745i	$-0.647357\pi$
$251$	−1.40972e13	−0.893155	−0.446578	+	0.894745i	$0.647357\pi$
$252$	−1.09524e13	−0.678903
$253$	7.54762e12	0.457770
$254$	6.51280e12	0.386529
$255$	4.19332e11	0.0243550
$256$	−7.20175e12	−0.409372
$257$	1.57343e12	0.0875417	0.0437708	−	0.999042i	$-0.486063\pi$
$257$	1.57343e12	0.0875417	0.0437708	+	0.999042i	$0.486063\pi$
$258$	1.82097e13	0.991733
$259$	−2.32970e13	−1.24208
$260$	−1.41662e13	−0.739436
$261$	−4.84268e12	−0.247493
$262$	2.45892e13	1.23051
$263$	−2.86686e13	−1.40491	−0.702457	−	0.711727i	$-0.747914\pi$
$263$	−2.86686e13	−1.40491	−0.702457	+	0.711727i	$0.747914\pi$
$264$	4.85287e12	0.232904
$265$	−1.71561e13	−0.806428
$266$	−9.21451e13	−4.24251
$267$	−4.80700e12	−0.216801
$268$	−2.77079e13	−1.22423
$269$	−1.17146e12	−0.0507095	−0.0253548	−	0.999679i	$-0.508072\pi$
$269$	−1.17146e12	−0.0507095	−0.0253548	+	0.999679i	$0.508072\pi$
$270$	3.08771e12	0.130959
$271$	−4.07109e13	−1.69192	−0.845959	−	0.533247i	$-0.820971\pi$
$271$	−4.07109e13	−1.69192	−0.845959	+	0.533247i	$0.820971\pi$
$272$	7.87951e11	0.0320901
$273$	−2.35808e13	−0.941160
$274$	−1.54183e13	−0.603128
$275$	−1.18619e13	−0.454803
$276$	−1.83124e13	−0.688249
$277$	−2.26706e12	−0.0835264	−0.0417632	−	0.999128i	$-0.513298\pi$
$277$	−2.26706e12	−0.0835264	−0.0417632	+	0.999128i	$0.513298\pi$
$278$	−1.80926e12	−0.0653515
$279$	−7.14097e12	−0.252891
$280$	1.25587e13	0.436091
$281$	1.76306e13	0.600319	0.300159	−	0.953889i	$-0.402960\pi$
$281$	1.76306e13	0.600319	0.300159	+	0.953889i	$0.402960\pi$
$282$	−9.11173e12	−0.304250
$283$	−3.71101e13	−1.21525	−0.607626	−	0.794223i	$-0.707878\pi$
$283$	−3.71101e13	−1.21525	−0.607626	+	0.794223i	$0.707878\pi$
$284$	−5.26782e13	−1.69192
$285$	1.54137e13	0.485581
$286$	3.32059e13	1.02613
$287$	−2.08280e13	−0.631389
$288$	1.38715e13	0.412538
$289$	−3.39480e13	−0.990550
$290$	1.76478e13	0.505244
$291$	3.78476e13	1.06323
$292$	2.67668e12	0.0737889
$293$	8.31149e12	0.224857	0.112429	−	0.993660i	$-0.464137\pi$
$293$	8.31149e12	0.224857	0.112429	+	0.993660i	$0.464137\pi$
$294$	3.23398e13	0.858671
$295$	−2.16782e12	−0.0564940
$296$	−2.50451e13	−0.640646
$297$	−4.29446e12	−0.107832
$298$	−3.26454e12	−0.0804698
$299$	−3.94269e13	−0.954116
$300$	2.87799e13	0.683789
$301$	−6.55424e13	−1.52900
$302$	2.00472e13	0.459215
$303$	−4.03854e13	−0.908427
$304$	2.89634e13	0.639800
$305$	−2.31847e13	−0.502981
$306$	2.38482e12	0.0508145
$307$	3.75209e13	0.785257	0.392628	−	0.919697i	$-0.371566\pi$
$307$	3.75209e13	0.785257	0.392628	+	0.919697i	$0.371566\pi$
$308$	−5.55121e13	−1.14119
$309$	1.30767e13	0.264074
$310$	2.60233e13	0.516265
$311$	5.51443e13	1.07478	0.537388	−	0.843335i	$-0.319411\pi$
$311$	5.51443e13	1.07478	0.537388	+	0.843335i	$0.319411\pi$
$312$	−2.53502e13	−0.485435
$313$	1.64291e13	0.309114	0.154557	−	0.987984i	$-0.450605\pi$
$313$	1.64291e13	0.309114	0.154557	+	0.987984i	$0.450605\pi$
$314$	9.60141e13	1.77510
$315$	−1.11136e13	−0.201905
$316$	3.65130e12	0.0651881
$317$	3.54426e13	0.621871	0.310935	−	0.950431i	$-0.399358\pi$
$317$	3.54426e13	0.621871	0.310935	+	0.950431i	$0.399358\pi$
$318$	−9.75696e13	−1.68254
$319$	−2.45450e13	−0.416019
$320$	−4.19526e13	−0.698931
$321$	−2.81054e13	−0.460270
$322$	1.11085e14	1.78833
$323$	1.19049e13	0.188414
$324$	1.04194e13	0.162124
$325$	6.19635e13	0.947933
$326$	−5.42277e13	−0.815688
$327$	5.81440e13	0.859988
$328$	−2.23908e13	−0.325660
$329$	3.27960e13	0.469076
$330$	1.56500e13	0.220134
$331$	−8.28933e13	−1.14674	−0.573371	−	0.819296i	$-0.694364\pi$
$331$	−8.28933e13	−1.14674	−0.573371	+	0.819296i	$0.694364\pi$
$332$	−2.08281e14	−2.83394
$333$	2.21632e13	0.296612
$334$	−1.97923e14	−2.60549
$335$	−2.81157e13	−0.364085
$336$	−2.08832e13	−0.266030
$337$	9.76603e13	1.22392	0.611961	−	0.790888i	$-0.290381\pi$
$337$	9.76603e13	1.22392	0.611961	+	0.790888i	$0.290381\pi$
$338$	−4.62760e13	−0.570577
$339$	5.73528e13	0.695756
$340$	−5.15669e12	−0.0615512
$341$	−3.61938e13	−0.425094
$342$	8.76607e13	1.01312
$343$	6.33122e12	0.0720062
$344$	−7.04604e13	−0.788631
$345$	−1.85819e13	−0.204685
$346$	1.92906e13	0.209135
$347$	1.34099e14	1.43091	0.715456	−	0.698658i	$-0.246219\pi$
$347$	1.34099e14	1.43091	0.715456	+	0.698658i	$0.246219\pi$
$348$	5.95522e13	0.625478
$349$	1.45916e14	1.50856	0.754281	−	0.656552i	$-0.227986\pi$
$349$	1.45916e14	1.50856	0.754281	+	0.656552i	$0.227986\pi$
$350$	−1.74581e14	−1.77674
$351$	2.24332e13	0.224751
$352$	7.03071e13	0.693449
$353$	−6.07598e13	−0.590005	−0.295003	−	0.955496i	$-0.595320\pi$
$353$	−6.07598e13	−0.590005	−0.295003	+	0.955496i	$0.595320\pi$
$354$	−1.23288e13	−0.117870
$355$	−5.34535e13	−0.503176
$356$	5.91134e13	0.547913
$357$	−8.58370e12	−0.0783429
$358$	2.82197e14	2.53627
$359$	−1.72255e14	−1.52459	−0.762295	−	0.647230i	$-0.775927\pi$
$359$	−1.72255e14	−1.52459	−0.762295	+	0.647230i	$0.775927\pi$
$360$	−1.19476e13	−0.104139
$361$	3.21109e14	2.75653
$362$	−2.03049e14	−1.71674
$363$	4.75644e13	0.396092
$364$	2.89982e14	2.37855
$365$	2.71608e12	0.0219448
$366$	−1.31855e14	−1.04943
$367$	1.04491e14	0.819247	0.409623	−	0.912255i	$-0.365660\pi$
$367$	1.04491e14	0.819247	0.409623	+	0.912255i	$0.365660\pi$
$368$	−3.49166e13	−0.269692
$369$	1.98144e13	0.150777
$370$	−8.07676e13	−0.605519
$371$	3.51184e14	2.59405
$372$	8.78151e13	0.639121
$373$	−9.84499e12	−0.0706020	−0.0353010	−	0.999377i	$-0.511239\pi$
$373$	−9.84499e12	−0.0706020	−0.0353010	+	0.999377i	$0.511239\pi$
$374$	1.20874e13	0.0854158
$375$	6.51817e13	0.453893
$376$	3.52568e13	0.241941
$377$	1.28217e14	0.867097
$378$	−6.32052e13	−0.421258
$379$	2.09842e14	1.37840	0.689201	−	0.724570i	$-0.257962\pi$
$379$	2.09842e14	1.37840	0.689201	+	0.724570i	$0.257962\pi$
$380$	−1.89549e14	−1.22719
$381$	2.23008e13	0.142309
$382$	−1.57978e14	−0.993686
$383$	2.56401e14	1.58974	0.794870	−	0.606780i	$-0.207539\pi$
$383$	2.56401e14	1.58974	0.794870	+	0.606780i	$0.207539\pi$
$384$	−1.21684e14	−0.743721
$385$	−5.63291e13	−0.339390
$386$	−4.04631e14	−2.40342
$387$	6.23527e13	0.365128
$388$	−4.65426e14	−2.68705
$389$	−1.78306e14	−1.01495	−0.507475	−	0.861667i	$-0.669421\pi$
$389$	−1.78306e14	−1.01495	−0.507475	+	0.861667i	$0.669421\pi$
$390$	−8.17516e13	−0.458818
$391$	−1.43519e13	−0.0794213
$392$	−1.25135e14	−0.682820
$393$	8.41968e13	0.453040
$394$	3.96556e14	2.10415
$395$	3.70503e12	0.0193869
$396$	5.28105e13	0.272519
$397$	−3.29642e14	−1.67762	−0.838811	−	0.544422i	$-0.816749\pi$
$397$	−3.29642e14	−1.67762	−0.838811	+	0.544422i	$0.816749\pi$
$398$	1.39577e14	0.700579
$399$	−3.15518e14	−1.56197
$400$	5.48750e13	0.267945
$401$	−3.50313e14	−1.68718	−0.843592	−	0.536985i	$-0.819563\pi$
$401$	−3.50313e14	−1.68718	−0.843592	+	0.536985i	$0.819563\pi$
$402$	−1.59899e14	−0.759631
$403$	1.89067e14	0.886010
$404$	4.96634e14	2.29583
$405$	1.05728e13	0.0482154
$406$	−3.61249e14	−1.62523
$407$	1.12333e14	0.498586
$408$	−9.22779e12	−0.0404079
$409$	−4.41416e13	−0.190709	−0.0953543	−	0.995443i	$-0.530398\pi$
$409$	−4.41416e13	−0.190709	−0.0953543	+	0.995443i	$0.530398\pi$
$410$	−7.22080e13	−0.307804
$411$	−5.27946e13	−0.222054
$412$	−1.60809e14	−0.667382
$413$	4.43752e13	0.181725
$414$	−1.05679e14	−0.427057
$415$	−2.11347e14	−0.842812
$416$	−3.67267e14	−1.44534
$417$	−6.19518e12	−0.0240606
$418$	4.44306e14	1.70299
$419$	−1.07012e14	−0.404813	−0.202407	−	0.979302i	$-0.564876\pi$
$419$	−1.07012e14	−0.404813	−0.202407	+	0.979302i	$0.564876\pi$
$420$	1.36668e14	0.510267
$421$	−3.01198e14	−1.10994	−0.554971	−	0.831870i	$-0.687271\pi$
$421$	−3.01198e14	−1.10994	−0.554971	+	0.831870i	$0.687271\pi$
$422$	5.37461e14	1.95492
$423$	−3.11999e13	−0.112016
$424$	3.77535e14	1.33797
$425$	2.25555e13	0.0789066
$426$	−3.03999e14	−1.04983
$427$	4.74589e14	1.61795
$428$	3.45623e14	1.16322
$429$	1.13702e14	0.377792
$430$	−2.27227e14	−0.745390
$431$	2.67511e14	0.866398	0.433199	−	0.901298i	$-0.357385\pi$
$431$	2.67511e14	0.866398	0.433199	+	0.901298i	$0.357385\pi$
$432$	1.98669e13	0.0635286
$433$	−3.05057e14	−0.963158	−0.481579	−	0.876403i	$-0.659937\pi$
$433$	−3.05057e14	−0.963158	−0.481579	+	0.876403i	$0.659937\pi$
$434$	−5.32695e14	−1.66068
$435$	6.04286e13	0.186017
$436$	−7.15018e14	−2.17341
$437$	−5.27544e14	−1.58347
$438$	1.54468e13	0.0457858
$439$	3.76231e14	1.10129	0.550643	−	0.834741i	$-0.314383\pi$
$439$	3.76231e14	1.10129	0.550643	+	0.834741i	$0.314383\pi$
$440$	−6.05558e13	−0.175052
$441$	1.10736e14	0.316138
$442$	−6.31415e13	−0.178030
$443$	3.92462e14	1.09289	0.546446	−	0.837494i	$-0.315980\pi$
$443$	3.92462e14	1.09289	0.546446	+	0.837494i	$0.315980\pi$
$444$	−2.72549e14	−0.749615
$445$	5.99834e13	0.162949
$446$	−1.02819e15	−2.75886
$447$	−1.11783e13	−0.0296267
$448$	8.58767e14	2.24826
$449$	−4.48564e14	−1.16003	−0.580015	−	0.814606i	$-0.696953\pi$
$449$	−4.48564e14	−1.16003	−0.580015	+	0.814606i	$0.696953\pi$
$450$	1.66085e14	0.424289
$451$	1.00429e14	0.253446
$452$	−7.05289e14	−1.75835
$453$	6.86446e13	0.169070
$454$	−8.88147e14	−2.16111
$455$	2.94249e14	0.707380
$456$	−3.39193e14	−0.805639
$457$	3.33614e14	0.782899	0.391449	−	0.920200i	$-0.371974\pi$
$457$	3.33614e14	0.782899	0.391449	+	0.920200i	$0.371974\pi$
$458$	3.78711e14	0.878107
$459$	8.16596e12	0.0187084
$460$	2.28509e14	0.517291
$461$	−3.00279e14	−0.671691	−0.335846	−	0.941917i	$-0.609022\pi$
$461$	−3.00279e14	−0.671691	−0.335846	+	0.941917i	$0.609022\pi$
$462$	−3.20354e14	−0.708107
$463$	−4.53030e14	−0.989536	−0.494768	−	0.869025i	$-0.664747\pi$
$463$	−4.53030e14	−0.989536	−0.494768	+	0.869025i	$0.664747\pi$
$464$	1.13549e14	0.245095
$465$	8.91075e13	0.190074
$466$	−3.91336e14	−0.824950
$467$	7.82679e14	1.63057	0.815287	−	0.579057i	$-0.196579\pi$
$467$	7.82679e14	1.63057	0.815287	+	0.579057i	$0.196579\pi$
$468$	−2.75869e14	−0.568004
$469$	5.75527e14	1.17116
$470$	1.13699e14	0.228676
$471$	3.28766e14	0.653540
$472$	4.77049e13	0.0937307
$473$	3.16033e14	0.613756
$474$	2.10712e13	0.0404490
$475$	8.29091e14	1.57321
$476$	1.05557e14	0.197993
$477$	−3.34093e14	−0.619464
$478$	−2.76644e14	−0.507070
$479$	3.60866e14	0.653884	0.326942	−	0.945044i	$-0.393982\pi$
$479$	3.60866e14	0.653884	0.326942	+	0.945044i	$0.393982\pi$
$480$	−1.73093e14	−0.310065
$481$	−5.86802e14	−1.03919
$482$	1.19684e14	0.209546
$483$	3.80370e14	0.658412
$484$	−5.84917e14	−1.00103
$485$	−4.72276e14	−0.799128
$486$	6.01292e13	0.100597
$487$	1.02107e15	1.68906	0.844532	−	0.535506i	$-0.179879\pi$
$487$	1.02107e15	1.68906	0.844532	+	0.535506i	$0.179879\pi$
$488$	5.10200e14	0.834509
$489$	−1.85683e14	−0.300313
$490$	−4.03547e14	−0.645380
$491$	2.63607e14	0.416878	0.208439	−	0.978035i	$-0.433162\pi$
$491$	2.63607e14	0.416878	0.208439	+	0.978035i	$0.433162\pi$
$492$	−2.43665e14	−0.381052
$493$	4.66725e13	0.0721777
$494$	−2.32094e15	−3.54949
$495$	5.35877e13	0.0810470
$496$	1.67439e14	0.250441
$497$	1.09419e15	1.61857
$498$	−1.20197e15	−1.75845
$499$	1.49421e14	0.216201	0.108100	−	0.994140i	$-0.465523\pi$
$499$	1.49421e14	0.216201	0.108100	+	0.994140i	$0.465523\pi$
$500$	−8.01563e14	−1.14710
$501$	−6.77716e14	−0.959268
$502$	1.00043e15	1.40061
$503$	6.46178e14	0.894805	0.447402	−	0.894333i	$-0.352349\pi$
$503$	6.46178e14	0.894805	0.447402	+	0.894333i	$0.352349\pi$
$504$	2.44565e14	0.334986
$505$	5.03943e14	0.682778
$506$	−5.35629e14	−0.717854
$507$	−1.58456e14	−0.210070
$508$	−2.74241e14	−0.359651
$509$	2.83806e14	0.368192	0.184096	−	0.982908i	$-0.441064\pi$
$509$	2.83806e14	0.368192	0.184096	+	0.982908i	$0.441064\pi$
$510$	−2.97586e13	−0.0381924
$511$	−5.55979e13	−0.0705900
$512$	−5.14462e14	−0.646203
$513$	3.00163e14	0.373002
$514$	−1.11661e14	−0.137279
$515$	−1.63175e14	−0.198479
$516$	−7.66774e14	−0.922771
$517$	−1.58136e14	−0.188292
$518$	1.65331e15	1.94778
$519$	6.60539e13	0.0769977
$520$	3.16329e14	0.364855
$521$	4.28729e14	0.489301	0.244650	−	0.969611i	$-0.421327\pi$
$521$	4.28729e14	0.489301	0.244650	+	0.969611i	$0.421327\pi$
$522$	3.43668e14	0.388107
$523$	−3.18577e14	−0.356005	−0.178002	−	0.984030i	$-0.556963\pi$
$523$	−3.18577e14	−0.356005	−0.178002	+	0.984030i	$0.556963\pi$
$524$	−1.03540e15	−1.14495
$525$	−5.97792e14	−0.654145
$526$	2.03451e15	2.20312
$527$	6.88229e13	0.0737522
$528$	1.00695e14	0.106787
$529$	−3.16833e14	−0.332525
$530$	1.21751e15	1.26460
$531$	−4.22156e13	−0.0433963
$532$	3.88004e15	3.94751
$533$	−5.24614e14	−0.528251
$534$	3.41136e14	0.339978
$535$	3.50709e14	0.345941
$536$	6.18712e14	0.604063
$537$	9.66283e14	0.933783
$538$	8.31345e13	0.0795204
$539$	5.61262e14	0.531408
$540$	−1.30017e14	−0.121853
$541$	−1.68448e15	−1.56272	−0.781359	−	0.624082i	$-0.785473\pi$
$541$	−1.68448e15	−1.56272	−0.781359	+	0.624082i	$0.785473\pi$
$542$	2.88911e15	2.65319
$543$	−6.95271e14	−0.632055
$544$	−1.33690e14	−0.120311
$545$	−7.25541e14	−0.646370
$546$	1.67345e15	1.47589
$547$	8.84142e13	0.0771955	0.0385977	−	0.999255i	$-0.487711\pi$
$547$	8.84142e13	0.0771955	0.0385977	+	0.999255i	$0.487711\pi$
$548$	6.49235e14	0.561188
$549$	−4.51492e14	−0.386369
$550$	8.41797e14	0.713202
$551$	1.71558e15	1.43905
$552$	4.08912e14	0.339598
$553$	−7.58418e13	−0.0623620
$554$	1.60885e14	0.130982
$555$	−2.76560e14	−0.222935
$556$	7.61845e13	0.0608072
$557$	3.30265e14	0.261011	0.130506	−	0.991448i	$-0.458340\pi$
$557$	3.30265e14	0.261011	0.130506	+	0.991448i	$0.458340\pi$
$558$	5.06770e14	0.396573
$559$	−1.65088e15	−1.27923
$560$	2.60588e14	0.199949
$561$	4.13889e13	0.0314477
$562$	−1.25118e15	−0.941394
$563$	9.30546e14	0.693333	0.346666	−	0.937988i	$-0.387314\pi$
$563$	9.30546e14	0.693333	0.346666	+	0.937988i	$0.387314\pi$
$564$	3.83677e14	0.283094
$565$	−7.15669e14	−0.522933
$566$	2.63358e15	1.90571
$567$	−2.16424e14	−0.155095
$568$	1.17629e15	0.834832
$569$	1.31150e15	0.921827	0.460913	−	0.887445i	$-0.347522\pi$
$569$	1.31150e15	0.921827	0.460913	+	0.887445i	$0.347522\pi$
$570$	−1.09386e15	−0.761466
$571$	−2.01426e15	−1.38872	−0.694362	−	0.719626i	$-0.744313\pi$
$571$	−2.01426e15	−1.38872	−0.694362	+	0.719626i	$0.744313\pi$
$572$	−1.39823e15	−0.954777
$573$	−5.40941e14	−0.365847
$574$	1.47809e15	0.990117
$575$	−9.99504e14	−0.663150
$576$	−8.16974e14	−0.536889
$577$	2.68955e14	0.175070	0.0875350	−	0.996161i	$-0.472101\pi$
$577$	2.68955e14	0.175070	0.0875350	+	0.996161i	$0.472101\pi$
$578$	2.40918e15	1.55334
$579$	−1.38552e15	−0.884870
$580$	−7.43113e14	−0.470112
$581$	4.32625e15	2.71108
$582$	−2.68592e15	−1.66731
$583$	−1.69334e15	−1.04128
$584$	−5.97697e13	−0.0364091
$585$	−2.79929e14	−0.168924
$586$	−5.89839e14	−0.352611
$587$	8.38181e14	0.496396	0.248198	−	0.968709i	$-0.420162\pi$
$587$	8.38181e14	0.496396	0.248198	+	0.968709i	$0.420162\pi$
$588$	−1.36176e15	−0.798962
$589$	2.52978e15	1.47044
$590$	1.53843e14	0.0885914
$591$	1.35787e15	0.774686
$592$	−5.19673e14	−0.293739
$593$	4.77555e14	0.267438	0.133719	−	0.991019i	$-0.457308\pi$
$593$	4.77555e14	0.267438	0.133719	+	0.991019i	$0.457308\pi$
$594$	3.04763e14	0.169097
$595$	1.07111e14	0.0588828
$596$	1.37463e14	0.0748742
$597$	4.77932e14	0.257933
$598$	2.79799e15	1.49620
$599$	3.98555e14	0.211174	0.105587	−	0.994410i	$-0.466328\pi$
$599$	3.98555e14	0.211174	0.105587	+	0.994410i	$0.466328\pi$
$600$	−6.42648e14	−0.337397
$601$	5.90443e14	0.307163	0.153581	−	0.988136i	$-0.450919\pi$
$601$	5.90443e14	0.307163	0.153581	+	0.988136i	$0.450919\pi$
$602$	4.65132e15	2.39771
$603$	−5.47518e14	−0.279675
$604$	−8.44148e14	−0.427283
$605$	−5.93526e14	−0.297704
$606$	2.86602e15	1.42456
$607$	2.99345e15	1.47447	0.737233	−	0.675638i	$-0.236132\pi$
$607$	2.99345e15	1.47447	0.737233	+	0.675638i	$0.236132\pi$
$608$	−4.91415e15	−2.39871
$609$	−1.23697e15	−0.598362
$610$	1.64534e15	0.788753
$611$	8.26062e14	0.392452
$612$	−1.00420e14	−0.0472810
$613$	1.79423e15	0.837231	0.418615	−	0.908164i	$-0.362516\pi$
$613$	1.79423e15	0.837231	0.418615	+	0.908164i	$0.362516\pi$
$614$	−2.66273e15	−1.23140
$615$	−2.47251e14	−0.113325
$616$	1.23957e15	0.563090
$617$	−1.69089e15	−0.761283	−0.380642	−	0.924723i	$-0.624297\pi$
$617$	−1.69089e15	−0.761283	−0.380642	+	0.924723i	$0.624297\pi$
$618$	−9.28007e14	−0.414109
$619$	−3.88016e15	−1.71613	−0.858067	−	0.513537i	$-0.828335\pi$
$619$	−3.88016e15	−1.71613	−0.858067	+	0.513537i	$0.828335\pi$
$620$	−1.09579e15	−0.480366
$621$	−3.61859e14	−0.157230
$622$	−3.91340e15	−1.68542
$623$	−1.22786e15	−0.524159
$624$	−5.26004e14	−0.222574
$625$	1.12188e15	0.470549
$626$	−1.16592e15	−0.484740
$627$	1.52137e15	0.626993
$628$	−4.04296e15	−1.65166
$629$	−2.13603e14	−0.0865027
$630$	7.88697e14	0.316619
$631$	2.23385e15	0.888979	0.444490	−	0.895784i	$-0.353385\pi$
$631$	2.23385e15	0.888979	0.444490	+	0.895784i	$0.353385\pi$
$632$	−8.15326e13	−0.0321653
$633$	1.84034e15	0.719745
$634$	−2.51524e15	−0.975190
$635$	−2.78277e14	−0.106960
$636$	4.10846e15	1.56554
$637$	−2.93190e15	−1.10760
$638$	1.74187e15	0.652383
$639$	−1.04094e15	−0.386518
$640$	1.51841e15	0.558984
$641$	−4.12814e15	−1.50673	−0.753365	−	0.657603i	$-0.771570\pi$
$641$	−4.12814e15	−1.50673	−0.753365	+	0.657603i	$0.771570\pi$
$642$	1.99455e15	0.721775
$643$	4.10311e15	1.47215	0.736076	−	0.676899i	$-0.236676\pi$
$643$	4.10311e15	1.47215	0.736076	+	0.676899i	$0.236676\pi$
$644$	−4.67756e15	−1.66398
$645$	−7.78059e14	−0.274431
$646$	−8.44853e14	−0.295462
$647$	−3.20964e15	−1.11297	−0.556484	−	0.830858i	$-0.687850\pi$
$647$	−3.20964e15	−1.11297	−0.556484	+	0.830858i	$0.687850\pi$
$648$	−2.32663e14	−0.0799955
$649$	−2.13968e14	−0.0729464
$650$	−4.39734e15	−1.48651
$651$	−1.82402e15	−0.611414
$652$	2.28342e15	0.758968
$653$	−3.00682e15	−0.991025	−0.495512	−	0.868601i	$-0.665020\pi$
$653$	−3.00682e15	−0.991025	−0.495512	+	0.868601i	$0.665020\pi$
$654$	−4.12628e15	−1.34859
$655$	−1.05064e15	−0.340507
$656$	−4.64599e14	−0.149316
$657$	5.28921e13	0.0168570
$658$	−2.32742e15	−0.735584
$659$	3.44573e15	1.07997	0.539984	−	0.841675i	$-0.318430\pi$
$659$	3.44573e15	1.07997	0.539984	+	0.841675i	$0.318430\pi$
$660$	−6.58988e14	−0.204827
$661$	1.31737e15	0.406070	0.203035	−	0.979171i	$-0.434919\pi$
$661$	1.31737e15	0.406070	0.203035	+	0.979171i	$0.434919\pi$
$662$	5.88266e15	1.79827
$663$	−2.16206e14	−0.0655455
$664$	4.65087e15	1.39833
$665$	3.93715e15	1.17399
$666$	−1.57285e15	−0.465134
$667$	−2.06820e15	−0.606599
$668$	8.33412e15	2.42432
$669$	−3.52066e15	−1.01573
$670$	1.99528e15	0.570942
$671$	−2.28837e15	−0.649461
$672$	3.54320e15	0.997390
$673$	3.38796e15	0.945922	0.472961	−	0.881083i	$-0.343185\pi$
$673$	3.38796e15	0.945922	0.472961	+	0.881083i	$0.343185\pi$
$674$	−6.93062e15	−1.91930
$675$	5.68699e14	0.156211
$676$	1.94859e15	0.530901
$677$	8.15250e14	0.220320	0.110160	−	0.993914i	$-0.464864\pi$
$677$	8.15250e14	0.220320	0.110160	+	0.993914i	$0.464864\pi$
$678$	−4.07014e15	−1.09105
$679$	9.66745e15	2.57056
$680$	1.15148e14	0.0303708
$681$	−3.04115e15	−0.795661
$682$	2.56855e15	0.666613
$683$	−4.51673e15	−1.16281	−0.581407	−	0.813613i	$-0.697497\pi$
$683$	−4.51673e15	−1.16281	−0.581407	+	0.813613i	$0.697497\pi$
$684$	−3.69122e15	−0.942672
$685$	6.58790e14	0.166897
$686$	−4.49305e14	−0.112917
$687$	1.29676e15	0.323294
$688$	−1.46202e15	−0.361590
$689$	8.84558e15	2.17030
$690$	1.31870e15	0.320978
$691$	7.60364e15	1.83608	0.918041	−	0.396485i	$-0.129770\pi$
$691$	7.60364e15	1.83608	0.918041	+	0.396485i	$0.129770\pi$
$692$	−8.12289e14	−0.194593
$693$	−1.09694e15	−0.260705
$694$	−9.51654e15	−2.24389
$695$	7.73057e13	0.0180840
$696$	−1.32979e15	−0.308625
$697$	−1.90966e14	−0.0439720
$698$	−1.03552e16	−2.36566
$699$	−1.33999e15	−0.303723
$700$	7.35127e15	1.65319
$701$	3.60745e14	0.0804917	0.0402458	−	0.999190i	$-0.487186\pi$
$701$	3.60745e14	0.0804917	0.0402458	+	0.999190i	$0.487186\pi$
$702$	−1.59201e15	−0.352445
$703$	−7.85159e15	−1.72466
$704$	−4.14081e15	−0.902475
$705$	3.89323e14	0.0841919
$706$	4.31192e15	0.925220
$707$	−1.03157e16	−2.19630
$708$	5.19141e14	0.109674
$709$	−6.11599e15	−1.28207	−0.641037	−	0.767510i	$-0.721495\pi$
$709$	−6.11599e15	−1.28207	−0.641037	+	0.767510i	$0.721495\pi$
$710$	3.79341e15	0.789058
$711$	7.21508e13	0.0148922
$712$	−1.31999e15	−0.270353
$713$	−3.04976e15	−0.619830
$714$	6.09157e14	0.122854
$715$	−1.41881e15	−0.283950
$716$	−1.18827e16	−2.35991
$717$	−9.47269e14	−0.186689
$718$	1.22244e16	2.39079
$719$	6.80359e15	1.32047	0.660236	−	0.751058i	$-0.270456\pi$
$719$	6.80359e15	1.32047	0.660236	+	0.751058i	$0.270456\pi$
$720$	−2.47906e14	−0.0477483
$721$	3.34019e15	0.638450
$722$	−2.27880e16	−4.32267
$723$	4.09817e14	0.0771488
$724$	8.55000e15	1.59736
$725$	3.25040e15	0.602667
$726$	−3.37549e15	−0.621133
$727$	3.38511e15	0.618206	0.309103	−	0.951029i	$-0.399971\pi$
$727$	3.38511e15	0.618206	0.309103	+	0.951029i	$0.399971\pi$
$728$	−6.47522e15	−1.17363
$729$	2.05891e14	0.0370370
$730$	−1.92751e14	−0.0344128
$731$	−6.00940e14	−0.106484
$732$	5.55216e15	0.976453
$733$	3.69274e15	0.644581	0.322290	−	0.946641i	$-0.395547\pi$
$733$	3.69274e15	0.644581	0.322290	+	0.946641i	$0.395547\pi$
$734$	−7.41536e15	−1.28471
$735$	−1.38180e15	−0.237611
$736$	5.92421e15	1.01112
$737$	−2.77508e15	−0.470115
$738$	−1.40616e15	−0.236442
$739$	−7.29990e15	−1.21835	−0.609176	−	0.793035i	$-0.708500\pi$
$739$	−7.29990e15	−1.21835	−0.609176	+	0.793035i	$0.708500\pi$
$740$	3.40096e15	0.563414
$741$	−7.94724e15	−1.30682
$742$	−2.49223e16	−4.06787
$743$	−7.54909e15	−1.22308	−0.611542	−	0.791212i	$-0.709450\pi$
$743$	−7.54909e15	−1.22308	−0.611542	+	0.791212i	$0.709450\pi$
$744$	−1.96089e15	−0.315357
$745$	1.39486e14	0.0222675
$746$	6.98666e14	0.110715
$747$	−4.11570e15	−0.647412
$748$	−5.08975e14	−0.0794763
$749$	−7.17900e15	−1.11279
$750$	−4.62572e15	−0.711775
$751$	−6.57937e15	−1.00500	−0.502498	−	0.864578i	$-0.667586\pi$
$751$	−6.57937e15	−1.00500	−0.502498	+	0.864578i	$0.667586\pi$
$752$	7.31563e14	0.110931
$753$	3.42562e15	0.515663
$754$	−9.09911e15	−1.35974
$755$	−8.56571e14	−0.127074
$756$	2.66144e15	0.391965
$757$	−5.29589e15	−0.774304	−0.387152	−	0.922016i	$-0.626541\pi$
$757$	−5.29589e15	−0.774304	−0.387152	+	0.922016i	$0.626541\pi$
$758$	−1.48917e16	−2.16155
$759$	−1.83407e15	−0.264294
$760$	4.23257e15	0.605522
$761$	−1.15832e16	−1.64518	−0.822588	−	0.568638i	$-0.807471\pi$
$761$	−1.15832e16	−1.64518	−0.822588	+	0.568638i	$0.807471\pi$
$762$	−1.58261e15	−0.223163
$763$	1.48518e16	2.07919
$764$	6.65215e15	0.924589
$765$	−1.01898e14	−0.0140613
$766$	−1.81959e16	−2.49296
$767$	1.11772e15	0.152040
$768$	1.75003e15	0.236351
$769$	7.21946e15	0.968076	0.484038	−	0.875047i	$-0.339170\pi$
$769$	7.21946e15	0.968076	0.484038	+	0.875047i	$0.339170\pi$
$770$	3.99749e15	0.532216
$771$	−3.82343e14	−0.0505422
$772$	1.70382e16	2.23629
$773$	2.28654e15	0.297983	0.148991	−	0.988838i	$-0.452397\pi$
$773$	2.28654e15	0.297983	0.148991	+	0.988838i	$0.452397\pi$
$774$	−4.42496e15	−0.572577
$775$	4.79301e15	0.615813
$776$	1.03929e16	1.32585
$777$	5.66116e15	0.717117
$778$	1.26538e16	1.59160
$779$	−7.01950e15	−0.876698
$780$	3.44239e15	0.426914
$781$	−5.27596e15	−0.649712
$782$	1.01851e15	0.124545
$783$	1.17677e15	0.142890
$784$	−2.59649e15	−0.313075
$785$	−4.10246e15	−0.491204
$786$	−5.97516e15	−0.710438
$787$	−8.50369e15	−1.00403	−0.502015	−	0.864859i	$-0.667408\pi$
$787$	−8.50369e15	−1.00403	−0.502015	+	0.864859i	$0.667408\pi$
$788$	−1.66982e16	−1.95783
$789$	6.96646e15	0.811127
$790$	−2.62934e14	−0.0304017
$791$	1.46497e16	1.68212
$792$	−1.17925e15	−0.134467
$793$	1.19539e16	1.35365
$794$	2.33936e16	2.63077
$795$	4.16893e15	0.465591
$796$	−5.87731e15	−0.651864
$797$	−4.81836e15	−0.530736	−0.265368	−	0.964147i	$-0.585493\pi$
$797$	−4.81836e15	−0.530736	−0.265368	+	0.964147i	$0.585493\pi$
$798$	2.23913e16	2.44942
$799$	3.00697e14	0.0326680
$800$	−9.31052e15	−1.00457
$801$	1.16810e15	0.125170
$802$	2.48605e16	2.64577
$803$	2.68082e14	0.0283356
$804$	6.73303e15	0.706809
$805$	−4.74640e15	−0.494865
$806$	−1.34175e16	−1.38940
$807$	2.84665e14	0.0292772
$808$	−1.10897e16	−1.13281
$809$	−6.50899e15	−0.660384	−0.330192	−	0.943914i	$-0.607114\pi$
$809$	−6.50899e15	−0.660384	−0.330192	+	0.943914i	$0.607114\pi$
$810$	−7.50314e14	−0.0756093
$811$	1.13742e16	1.13843	0.569215	−	0.822189i	$-0.307247\pi$
$811$	1.13742e16	1.13843	0.569215	+	0.822189i	$0.307247\pi$
$812$	1.52115e16	1.51221
$813$	9.89275e15	0.976830
$814$	−7.97192e15	−0.781860
$815$	2.31702e15	0.225717
$816$	−1.91472e14	−0.0185272
$817$	−2.20892e16	−2.12305
$818$	3.13258e15	0.299061
$819$	5.73013e15	0.543379
$820$	3.04053e15	0.286400
$821$	1.18256e16	1.10646	0.553230	−	0.833028i	$-0.313395\pi$
$821$	1.18256e16	1.10646	0.553230	+	0.833028i	$0.313395\pi$
$822$	3.74665e15	0.348216
$823$	−1.42822e16	−1.31854	−0.659272	−	0.751904i	$-0.729136\pi$
$823$	−1.42822e16	−1.31854	−0.659272	+	0.751904i	$0.729136\pi$
$824$	3.59082e15	0.329302
$825$	2.88244e15	0.262581
$826$	−3.14916e15	−0.284973
$827$	−6.37640e15	−0.573186	−0.286593	−	0.958052i	$-0.592523\pi$
$827$	−6.37640e15	−0.573186	−0.286593	+	0.958052i	$0.592523\pi$
$828$	4.44992e15	0.397361
$829$	9.48269e15	0.841166	0.420583	−	0.907254i	$-0.361826\pi$
$829$	9.48269e15	0.841166	0.420583	+	0.907254i	$0.361826\pi$
$830$	1.49986e16	1.32166
$831$	5.50895e14	0.0482240
$832$	2.16306e16	1.88100
$833$	−1.06725e15	−0.0921972
$834$	4.39651e14	0.0377307
$835$	8.45677e15	0.720990
$836$	−1.87088e16	−1.58457
$837$	1.73526e15	0.146007
$838$	7.59427e15	0.634811
$839$	1.13775e16	0.944835	0.472417	−	0.881375i	$-0.343382\pi$
$839$	1.13775e16	0.944835	0.472417	+	0.881375i	$0.343382\pi$
$840$	−3.05177e15	−0.251777
$841$	−5.47468e15	−0.448726
$842$	2.13750e16	1.74056
$843$	−4.28423e15	−0.346594
$844$	−2.26314e16	−1.81898
$845$	1.97727e15	0.157890
$846$	2.21415e15	0.175659
$847$	1.21494e16	0.957628
$848$	7.83367e15	0.613462
$849$	9.01775e15	0.701627
$850$	−1.60069e15	−0.123738
$851$	9.46543e15	0.726989
$852$	1.28008e16	0.976831
$853$	9.34134e15	0.708255	0.354128	−	0.935197i	$-0.384778\pi$
$853$	9.34134e15	0.708255	0.354128	+	0.935197i	$0.384778\pi$
$854$	−3.36799e16	−2.53719
$855$	−3.74554e15	−0.280350
$856$	−7.71768e15	−0.573959
$857$	2.95045e15	0.218018	0.109009	−	0.994041i	$-0.465232\pi$
$857$	2.95045e15	0.218018	0.109009	+	0.994041i	$0.465232\pi$
$858$	−8.06904e15	−0.592436
$859$	−1.13917e16	−0.831047	−0.415523	−	0.909583i	$-0.636402\pi$
$859$	−1.13917e16	−0.831047	−0.415523	+	0.909583i	$0.636402\pi$
$860$	9.56808e15	0.693559
$861$	5.06120e15	0.364533
$862$	−1.89844e16	−1.35865
$863$	7.36154e15	0.523491	0.261746	−	0.965137i	$-0.415702\pi$
$863$	7.36154e15	0.523491	0.261746	+	0.965137i	$0.415702\pi$
$864$	−3.37077e15	−0.238179
$865$	−8.24244e14	−0.0578718
$866$	2.16489e16	1.51038
$867$	8.24937e15	0.571894
$868$	2.24307e16	1.54520
$869$	3.65694e14	0.0250328
$870$	−4.28841e15	−0.291703
$871$	1.44963e16	0.979846
$872$	1.59662e16	1.07241
$873$	−9.19697e15	−0.613856
$874$	3.74380e16	2.48313
$875$	1.66494e16	1.09737
$876$	−6.50434e14	−0.0426021
$877$	−5.53741e14	−0.0360420	−0.0180210	−	0.999838i	$-0.505737\pi$
$877$	−5.53741e14	−0.0360420	−0.0180210	+	0.999838i	$0.505737\pi$
$878$	−2.66998e16	−1.72699
$879$	−2.01969e15	−0.129821
$880$	−1.25650e15	−0.0802618
$881$	3.59656e15	0.228307	0.114154	−	0.993463i	$-0.463584\pi$
$881$	3.59656e15	0.228307	0.114154	+	0.993463i	$0.463584\pi$
$882$	−7.85856e15	−0.495754
$883$	−1.07013e16	−0.670890	−0.335445	−	0.942060i	$-0.608887\pi$
$883$	−1.07013e16	−0.670890	−0.335445	+	0.942060i	$0.608887\pi$
$884$	2.65876e15	0.165650
$885$	5.26781e14	0.0326168
$886$	−2.78517e16	−1.71382
$887$	−1.84287e15	−0.112698	−0.0563488	−	0.998411i	$-0.517946\pi$
$887$	−1.84287e15	−0.112698	−0.0563488	+	0.998411i	$0.517946\pi$
$888$	6.08595e15	0.369877
$889$	5.69631e15	0.344060
$890$	−4.25682e15	−0.255529
$891$	1.04355e15	0.0622568
$892$	4.32948e16	2.56702
$893$	1.10530e16	0.651322
$894$	7.93284e14	0.0464593
$895$	−1.20576e16	−0.701835
$896$	−3.10817e16	−1.79809
$897$	9.58074e15	0.550859
$898$	3.18331e16	1.81911
$899$	9.91784e15	0.563299
$900$	−6.99351e15	−0.394786
$901$	3.21990e15	0.180658
$902$	−7.12707e15	−0.397443
$903$	1.59268e16	0.882767
$904$	1.57489e16	0.867611
$905$	8.67583e15	0.475055
$906$	−4.87147e15	−0.265128
$907$	−1.54577e16	−0.836188	−0.418094	−	0.908404i	$-0.637302\pi$
$907$	−1.54577e16	−0.836188	−0.418094	+	0.908404i	$0.637302\pi$
$908$	3.73981e16	2.01084
$909$	9.81366e15	0.524481
$910$	−2.08819e16	−1.10928
$911$	−1.52321e16	−0.804280	−0.402140	−	0.915578i	$-0.631734\pi$
$911$	−1.52321e16	−0.804280	−0.402140	+	0.915578i	$0.631734\pi$
$912$	−7.03810e15	−0.369389
$913$	−2.08603e16	−1.08826
$914$	−2.36755e16	−1.22771
$915$	5.63388e15	0.290396
$916$	−1.59468e16	−0.817047
$917$	2.15065e16	1.09531
$918$	−5.79511e14	−0.0293378
$919$	−5.82353e15	−0.293056	−0.146528	−	0.989207i	$-0.546810\pi$
$919$	−5.82353e15	−0.293056	−0.146528	+	0.989207i	$0.546810\pi$
$920$	−5.10255e15	−0.255243
$921$	−9.11757e15	−0.453368
$922$	2.13098e16	1.05332
$923$	2.75603e16	1.35418
$924$	1.34894e16	0.658868
$925$	−1.48759e16	−0.722277
$926$	3.21500e16	1.55175
$927$	−3.17763e15	−0.152463
$928$	−1.92656e16	−0.918901
$929$	1.07919e16	0.511696	0.255848	−	0.966717i	$-0.417645\pi$
$929$	1.07919e16	0.511696	0.255848	+	0.966717i	$0.417645\pi$
$930$	−6.32366e15	−0.298066
$931$	−3.92297e16	−1.83819
$932$	1.64784e16	0.767586
$933$	−1.34001e16	−0.620523
$934$	−5.55441e16	−2.55699
$935$	−5.16466e14	−0.0236362
$936$	6.16009e15	0.280266
$937$	9.99098e13	0.00451898	0.00225949	−	0.999997i	$-0.499281\pi$
$937$	9.99098e13	0.00451898	0.00225949	+	0.999997i	$0.499281\pi$
$938$	−4.08432e16	−1.83656
$939$	−3.99227e15	−0.178467
$940$	−4.78765e15	−0.212775
$941$	−1.28886e15	−0.0569458	−0.0284729	−	0.999595i	$-0.509064\pi$
$941$	−1.28886e15	−0.0569458	−0.0284729	+	0.999595i	$0.509064\pi$
$942$	−2.33314e16	−1.02485
$943$	8.46230e15	0.369551
$944$	9.89853e14	0.0429759
$945$	2.70061e15	0.116570
$946$	−2.24278e16	−0.962465
$947$	2.82850e16	1.20679	0.603395	−	0.797443i	$-0.293814\pi$
$947$	2.82850e16	1.20679	0.603395	+	0.797443i	$0.293814\pi$
$948$	−8.87265e14	−0.0376364
$949$	−1.40039e15	−0.0590590
$950$	−5.88378e16	−2.46704
$951$	−8.61256e15	−0.359037
$952$	−2.35706e15	−0.0976940
$953$	−3.20456e16	−1.32056	−0.660280	−	0.751020i	$-0.729562\pi$
$953$	−3.20456e16	−1.32056	−0.660280	+	0.751020i	$0.729562\pi$
$954$	2.37094e16	0.971415
$955$	6.75005e15	0.274972
$956$	1.16489e16	0.471810
$957$	5.96442e15	0.240189
$958$	−2.56095e16	−1.02539
$959$	−1.34854e16	−0.536860
$960$	1.01945e16	0.403528
$961$	−1.07837e16	−0.424414
$962$	4.16434e16	1.62961
$963$	6.82962e15	0.265737
$964$	−5.03967e15	−0.194975
$965$	1.72890e16	0.665072
$966$	−2.69936e16	−1.03249
$967$	5.13314e16	1.95226	0.976129	−	0.217190i	$-0.0696892\pi$
$967$	5.13314e16	1.95226	0.976129	+	0.217190i	$0.0696892\pi$
$968$	1.30611e16	0.493929
$969$	−2.89290e15	−0.108781
$970$	3.35158e16	1.25316
$971$	2.54272e16	0.945351	0.472676	−	0.881237i	$-0.343288\pi$
$971$	2.54272e16	0.945351	0.472676	+	0.881237i	$0.343288\pi$
$972$	−2.53192e15	−0.0936021
$973$	−1.58244e15	−0.0581711
$974$	−7.24618e16	−2.64871
$975$	−1.50571e16	−0.547289
$976$	1.05864e16	0.382626
$977$	1.00877e16	0.362552	0.181276	−	0.983432i	$-0.441977\pi$
$977$	1.00877e16	0.362552	0.181276	+	0.983432i	$0.441977\pi$
$978$	1.31773e16	0.470938
$979$	5.92048e15	0.210403
$980$	1.69926e16	0.600503
$981$	−1.41290e16	−0.496514
$982$	−1.87073e16	−0.653730
$983$	−5.10173e16	−1.77285	−0.886427	−	0.462868i	$-0.846820\pi$
$983$	−5.10173e16	−1.77285	−0.886427	+	0.462868i	$0.846820\pi$
$984$	5.44098e15	0.188020
$985$	−1.69439e16	−0.582257
$986$	−3.31219e15	−0.113186
$987$	−7.96942e15	−0.270821
$988$	9.77302e16	3.30267
$989$	2.66295e16	0.894919
$990$	−3.80294e15	−0.127094
$991$	−4.29328e16	−1.42687	−0.713435	−	0.700721i	$-0.752862\pi$
$991$	−4.29328e16	−1.42687	−0.713435	+	0.700721i	$0.752862\pi$
$992$	−2.84089e16	−0.938945
$993$	2.01431e16	0.662071
$994$	−7.76509e16	−2.53817
$995$	−5.96381e15	−0.193864
$996$	5.06124e16	1.63618
$997$	2.03181e16	0.653221	0.326610	−	0.945159i	$-0.394093\pi$
$997$	2.03181e16	0.653221	0.326610	+	0.945159i	$0.394093\pi$
$998$	−1.06039e16	−0.339037
$999$	−5.38565e15	−0.171249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.4	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} -215188. q^{10} +299288. q^{11} -726148. q^{12} -1.56341e6 q^{13} +4.40488e6 q^{14} -736834. q^{15} -1.38456e6 q^{16} -569100. q^{17} -4.19051e6 q^{18} -2.09189e7 q^{19} +9.06113e6 q^{20} +1.50829e7 q^{21} -2.12395e7 q^{22} +2.52186e7 q^{23} +1.62147e7 q^{24} -3.96336e7 q^{25} +1.10950e8 q^{26} -1.43489e7 q^{27} -1.85481e8 q^{28} -8.20111e7 q^{29} +5.22906e7 q^{30} -1.20933e8 q^{31} +2.34915e8 q^{32} -7.27270e7 q^{33} +4.03871e7 q^{34} -1.88210e8 q^{35} +1.76454e8 q^{36} +3.75335e8 q^{37} +1.48454e9 q^{38} +3.79908e8 q^{39} -2.02333e8 q^{40} +3.35558e8 q^{41} -1.07039e9 q^{42} +1.05595e9 q^{43} +8.94351e8 q^{44} +1.79051e8 q^{45} -1.78968e9 q^{46} -5.28373e8 q^{47} +3.36447e8 q^{48} +1.87532e9 q^{49} +2.81267e9 q^{50} +1.38291e8 q^{51} -4.67187e9 q^{52} -5.65789e9 q^{53} +1.01829e9 q^{54} +9.07513e8 q^{55} +4.14174e9 q^{56} +5.08329e9 q^{57} +5.82005e9 q^{58} -7.14924e8 q^{59} -2.20185e9 q^{60} -7.64605e9 q^{61} +8.58220e9 q^{62} -3.66516e9 q^{63} -1.38355e10 q^{64} -4.74063e9 q^{65} +5.16119e9 q^{66} -9.27226e9 q^{67} -1.70062e9 q^{68} -6.12812e9 q^{69} +1.33567e10 q^{70} -1.76284e10 q^{71} -3.94017e9 q^{72} +8.95732e8 q^{73} -2.66363e10 q^{74} +9.63098e9 q^{75} -6.25111e10 q^{76} -1.85767e10 q^{77} -2.69608e10 q^{78} +1.22188e9 q^{79} -4.19831e9 q^{80} +3.48678e9 q^{81} -2.38134e10 q^{82} -6.96998e10 q^{83} +4.50718e10 q^{84} -1.72565e9 q^{85} -7.49371e10 q^{86} +1.99287e10 q^{87} -1.99706e10 q^{88} +1.97819e10 q^{89} -1.27066e10 q^{90} +9.70403e10 q^{91} +7.53597e10 q^{92} +2.93867e10 q^{93} +3.74968e10 q^{94} -6.34310e10 q^{95} -5.70842e10 q^{96} -1.55752e11 q^{97} -1.33085e11 q^{98} +1.76727e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

Introduction

L-functions

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