LMFDB - Embedded newform 177.12.a.c.1.26

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			1.26
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)

$f(q)$	$=$	$q+79.4940 q^{2} -243.000 q^{3} +4271.29 q^{4} -12493.9 q^{5} -19317.0 q^{6} -4691.50 q^{7} +176738. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+79.4940 q^{2} -243.000 q^{3} +4271.29 q^{4} -12493.9 q^{5} -19317.0 q^{6} -4691.50 q^{7} +176738. q^{8} +59049.0 q^{9} -993192. q^{10} -684790. q^{11} -1.03792e6 q^{12} -807553. q^{13} -372946. q^{14} +3.03602e6 q^{15} +5.30204e6 q^{16} +2.08463e6 q^{17} +4.69404e6 q^{18} +1.99287e6 q^{19} -5.33652e7 q^{20} +1.14003e6 q^{21} -5.44367e7 q^{22} -3.43931e7 q^{23} -4.29475e7 q^{24} +1.07270e8 q^{25} -6.41956e7 q^{26} -1.43489e7 q^{27} -2.00388e7 q^{28} +5.13866e7 q^{29} +2.41346e8 q^{30} +2.77836e8 q^{31} +5.95196e7 q^{32} +1.66404e8 q^{33} +1.65716e8 q^{34} +5.86153e7 q^{35} +2.52216e8 q^{36} -1.29276e8 q^{37} +1.58421e8 q^{38} +1.96235e8 q^{39} -2.20816e9 q^{40} +4.27319e8 q^{41} +9.06259e7 q^{42} +1.12784e9 q^{43} -2.92494e9 q^{44} -7.37754e8 q^{45} -2.73404e9 q^{46} -1.50962e9 q^{47} -1.28840e9 q^{48} -1.95532e9 q^{49} +8.52733e9 q^{50} -5.06566e8 q^{51} -3.44930e9 q^{52} +3.00622e9 q^{53} -1.14065e9 q^{54} +8.55571e9 q^{55} -8.29168e8 q^{56} -4.84268e8 q^{57} +4.08493e9 q^{58} -7.14924e8 q^{59} +1.29678e10 q^{60} +5.99932e9 q^{61} +2.20863e10 q^{62} -2.77028e8 q^{63} -6.12712e9 q^{64} +1.00895e10 q^{65} +1.32281e10 q^{66} -1.44403e10 q^{67} +8.90408e9 q^{68} +8.35752e9 q^{69} +4.65956e9 q^{70} +1.55990e10 q^{71} +1.04362e10 q^{72} -2.93889e9 q^{73} -1.02767e10 q^{74} -2.60666e10 q^{75} +8.51214e9 q^{76} +3.21269e9 q^{77} +1.55995e10 q^{78} +4.42638e10 q^{79} -6.62433e10 q^{80} +3.48678e9 q^{81} +3.39693e10 q^{82} +1.50339e10 q^{83} +4.86942e9 q^{84} -2.60452e10 q^{85} +8.96569e10 q^{86} -1.24870e10 q^{87} -1.21029e11 q^{88} +5.19787e10 q^{89} -5.86470e10 q^{90} +3.78863e9 q^{91} -1.46903e11 q^{92} -6.75142e10 q^{93} -1.20006e11 q^{94} -2.48988e10 q^{95} -1.44633e10 q^{96} +1.11051e11 q^{97} -1.55436e11 q^{98} -4.04361e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	79.4940	1.75659	0.878293	−	0.478123i	$-0.158683\pi$
$2$	79.4940	1.75659	0.878293	+	0.478123i	$0.158683\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	4271.29	2.08559
$5$	−12493.9	−1.78799	−0.893993	−	0.448081i	$-0.852107\pi$
$5$	−12493.9	−1.78799	−0.893993	+	0.448081i	$0.852107\pi$
$6$	−19317.0	−1.01417
$7$	−4691.50	−0.105505	−0.0527524	−	0.998608i	$-0.516799\pi$
$7$	−4691.50	−0.105505	−0.0527524	+	0.998608i	$0.516799\pi$
$8$	176738.	1.90694
$9$	59049.0	0.333333
$10$	−993192.	−3.14075
$11$	−684790.	−1.28203	−0.641014	−	0.767529i	$-0.721486\pi$
$11$	−684790.	−1.28203	−0.641014	+	0.767529i	$0.721486\pi$
$12$	−1.03792e6	−1.20412
$13$	−807553.	−0.603229	−0.301615	−	0.953430i	$-0.597526\pi$
$13$	−807553.	−0.603229	−0.301615	+	0.953430i	$0.597526\pi$
$14$	−372946.	−0.185328
$15$	3.03602e6	1.03229
$16$	5.30204e6	1.26410
$17$	2.08463e6	0.356090	0.178045	−	0.984022i	$-0.443023\pi$
$17$	2.08463e6	0.356090	0.178045	+	0.984022i	$0.443023\pi$
$18$	4.69404e6	0.585529
$19$	1.99287e6	0.184644	0.0923218	−	0.995729i	$-0.470571\pi$
$19$	1.99287e6	0.184644	0.0923218	+	0.995729i	$0.470571\pi$
$20$	−5.33652e7	−3.72901
$21$	1.14003e6	0.0609132
$22$	−5.44367e7	−2.25199
$23$	−3.43931e7	−1.11421	−0.557106	−	0.830441i	$-0.688088\pi$
$23$	−3.43931e7	−1.11421	−0.557106	+	0.830441i	$0.688088\pi$
$24$	−4.29475e7	−1.10097
$25$	1.07270e8	2.19689
$26$	−6.41956e7	−1.05962
$27$	−1.43489e7	−0.192450
$28$	−2.00388e7	−0.220040
$29$	5.13866e7	0.465223	0.232612	−	0.972570i	$-0.425273\pi$
$29$	5.13866e7	0.465223	0.232612	+	0.972570i	$0.425273\pi$
$30$	2.41346e8	1.81331
$31$	2.77836e8	1.74301	0.871505	−	0.490387i	$-0.163145\pi$
$31$	2.77836e8	1.74301	0.871505	+	0.490387i	$0.163145\pi$
$32$	5.95196e7	0.313571
$33$	1.66404e8	0.740179
$34$	1.65716e8	0.625503
$35$	5.86153e7	0.188641
$36$	2.52216e8	0.695198
$37$	−1.29276e8	−0.306485	−0.153242	−	0.988189i	$-0.548972\pi$
$37$	−1.29276e8	−0.306485	−0.153242	+	0.988189i	$0.548972\pi$
$38$	1.58421e8	0.324342
$39$	1.96235e8	0.348275
$40$	−2.20816e9	−3.40957
$41$	4.27319e8	0.576024	0.288012	−	0.957627i	$-0.407006\pi$
$41$	4.27319e8	0.576024	0.288012	+	0.957627i	$0.407006\pi$
$42$	9.06259e7	0.106999
$43$	1.12784e9	1.16996	0.584982	−	0.811046i	$-0.301101\pi$
$43$	1.12784e9	1.16996	0.584982	+	0.811046i	$0.301101\pi$
$44$	−2.92494e9	−2.67379
$45$	−7.37754e8	−0.595995
$46$	−2.73404e9	−1.95721
$47$	−1.50962e9	−0.960131	−0.480065	−	0.877233i	$-0.659387\pi$
$47$	−1.50962e9	−0.960131	−0.480065	+	0.877233i	$0.659387\pi$
$48$	−1.28840e9	−0.729831
$49$	−1.95532e9	−0.988869
$50$	8.52733e9	3.85903
$51$	−5.06566e8	−0.205589
$52$	−3.44930e9	−1.25809
$53$	3.00622e9	0.987424	0.493712	−	0.869626i	$-0.335640\pi$
$53$	3.00622e9	0.987424	0.493712	+	0.869626i	$0.335640\pi$
$54$	−1.14065e9	−0.338055
$55$	8.55571e9	2.29225
$56$	−8.29168e8	−0.201191
$57$	−4.84268e8	−0.106604
$58$	4.08493e9	0.817204
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.29678e10	2.15294
$61$	5.99932e9	0.909469	0.454734	−	0.890627i	$-0.349734\pi$
$61$	5.99932e9	0.909469	0.454734	+	0.890627i	$0.349734\pi$
$62$	2.20863e10	3.06174
$63$	−2.77028e8	−0.0351683
$64$	−6.12712e9	−0.713290
$65$	1.00895e10	1.07857
$66$	1.32281e10	1.30019
$67$	−1.44403e10	−1.30667	−0.653334	−	0.757070i	$-0.726630\pi$
$67$	−1.44403e10	−1.30667	−0.653334	+	0.757070i	$0.726630\pi$
$68$	8.90408e9	0.742660
$69$	8.35752e9	0.643291
$70$	4.65956e9	0.331364
$71$	1.55990e10	1.02607	0.513034	−	0.858368i	$-0.328522\pi$
$71$	1.55990e10	1.02607	0.513034	+	0.858368i	$0.328522\pi$
$72$	1.04362e10	0.635645
$73$	−2.93889e9	−0.165923	−0.0829617	−	0.996553i	$-0.526438\pi$
$73$	−2.93889e9	−0.165923	−0.0829617	+	0.996553i	$0.526438\pi$
$74$	−1.02767e10	−0.538367
$75$	−2.60666e10	−1.26838
$76$	8.51214e9	0.385092
$77$	3.21269e9	0.135260
$78$	1.55995e10	0.611774
$79$	4.42638e10	1.61845	0.809225	−	0.587498i	$-0.199887\pi$
$79$	4.42638e10	1.61845	0.809225	+	0.587498i	$0.199887\pi$
$80$	−6.62433e10	−2.26020
$81$	3.48678e9	0.111111
$82$	3.39693e10	1.01184
$83$	1.50339e10	0.418932	0.209466	−	0.977816i	$-0.432828\pi$
$83$	1.50339e10	0.418932	0.209466	+	0.977816i	$0.432828\pi$
$84$	4.86942e9	0.127040
$85$	−2.60452e10	−0.636685
$86$	8.96569e10	2.05514
$87$	−1.24870e10	−0.268597
$88$	−1.21029e11	−2.44475
$89$	5.19787e10	0.986690	0.493345	−	0.869834i	$-0.335774\pi$
$89$	5.19787e10	0.986690	0.493345	+	0.869834i	$0.335774\pi$
$90$	−5.86470e10	−1.04692
$91$	3.78863e9	0.0636436
$92$	−1.46903e11	−2.32379
$93$	−6.75142e10	−1.00633
$94$	−1.20006e11	−1.68655
$95$	−2.48988e10	−0.330140
$96$	−1.44633e10	−0.181040
$97$	1.11051e11	1.31304	0.656519	−	0.754309i	$-0.272028\pi$
$97$	1.11051e11	1.31304	0.656519	+	0.754309i	$0.272028\pi$
$98$	−1.55436e11	−1.73703
$99$	−4.04361e10	−0.427343
$100$	4.58182e11	4.58182
$101$	−1.01593e11	−0.961825	−0.480913	−	0.876769i	$-0.659695\pi$
$101$	−1.01593e11	−0.961825	−0.480913	+	0.876769i	$0.659695\pi$
$102$	−4.02689e10	−0.361135
$103$	1.94290e11	1.65138	0.825688	−	0.564126i	$-0.190787\pi$
$103$	1.94290e11	1.65138	0.825688	+	0.564126i	$0.190787\pi$
$104$	−1.42726e11	−1.15032
$105$	−1.42435e10	−0.108912
$106$	2.38976e11	1.73449
$107$	−1.56118e11	−1.07608	−0.538038	−	0.842921i	$-0.680834\pi$
$107$	−1.56118e11	−1.07608	−0.538038	+	0.842921i	$0.680834\pi$
$108$	−6.12884e10	−0.401372
$109$	−4.67060e10	−0.290755	−0.145377	−	0.989376i	$-0.546440\pi$
$109$	−4.67060e10	−0.290755	−0.145377	+	0.989376i	$0.546440\pi$
$110$	6.80128e11	4.02653
$111$	3.14141e10	0.176949
$112$	−2.48745e10	−0.133369
$113$	2.25234e11	1.15001	0.575007	−	0.818148i	$-0.304999\pi$
$113$	2.25234e11	1.15001	0.575007	+	0.818148i	$0.304999\pi$
$114$	−3.84964e10	−0.187259
$115$	4.29705e11	1.99220
$116$	2.19487e11	0.970266
$117$	−4.76852e10	−0.201076
$118$	−5.68322e10	−0.228688
$119$	−9.78005e9	−0.0375693
$120$	5.36582e11	1.96852
$121$	1.83625e11	0.643595
$122$	4.76910e11	1.59756
$123$	−1.03838e11	−0.332568
$124$	1.18672e12	3.63521
$125$	−7.30170e11	−2.14003
$126$	−2.20221e10	−0.0617761
$127$	3.14209e11	0.843914	0.421957	−	0.906616i	$-0.361343\pi$
$127$	3.14209e11	0.843914	0.421957	+	0.906616i	$0.361343\pi$
$128$	−6.08965e11	−1.56653
$129$	−2.74066e11	−0.675479
$130$	8.02055e11	1.89459
$131$	−8.04859e9	−0.0182275	−0.00911376	−	0.999958i	$-0.502901\pi$
$131$	−8.04859e9	−0.0182275	−0.00911376	+	0.999958i	$0.502901\pi$
$132$	7.10760e11	1.54371
$133$	−9.34955e9	−0.0194808
$134$	−1.14792e12	−2.29527
$135$	1.79274e11	0.344098
$136$	3.68435e11	0.679042
$137$	−4.12615e11	−0.730436	−0.365218	−	0.930922i	$-0.619006\pi$
$137$	−4.12615e11	−0.730436	−0.365218	+	0.930922i	$0.619006\pi$
$138$	6.64373e11	1.13000
$139$	4.04990e11	0.662007	0.331004	−	0.943629i	$-0.392613\pi$
$139$	4.04990e11	0.662007	0.331004	+	0.943629i	$0.392613\pi$
$140$	2.50363e11	0.393429
$141$	3.66838e11	0.554332
$142$	1.24003e12	1.80238
$143$	5.53004e11	0.773357
$144$	3.13080e11	0.421368
$145$	−6.42021e11	−0.831812
$146$	−2.33624e11	−0.291459
$147$	4.75142e11	0.570924
$148$	−5.52177e11	−0.639203
$149$	−5.65880e11	−0.631248	−0.315624	−	0.948884i	$-0.602214\pi$
$149$	−5.65880e11	−0.631248	−0.315624	+	0.948884i	$0.602214\pi$
$150$	−2.07214e12	−2.22801
$151$	4.63803e11	0.480795	0.240398	−	0.970674i	$-0.422722\pi$
$151$	4.63803e11	0.480795	0.240398	+	0.970674i	$0.422722\pi$
$152$	3.52217e11	0.352104
$153$	1.23095e11	0.118697
$154$	2.55390e11	0.237596
$155$	−3.47127e12	−3.11648
$156$	8.38179e11	0.726359
$157$	−1.46330e12	−1.22429	−0.612147	−	0.790744i	$-0.709694\pi$
$157$	−1.46330e12	−1.22429	−0.612147	+	0.790744i	$0.709694\pi$
$158$	3.51870e12	2.84295
$159$	−7.30512e11	−0.570089
$160$	−7.43634e11	−0.560660
$161$	1.61355e11	0.117555
$162$	2.77178e11	0.195176
$163$	−3.02060e11	−0.205618	−0.102809	−	0.994701i	$-0.532783\pi$
$163$	−3.02060e11	−0.205618	−0.102809	+	0.994701i	$0.532783\pi$
$164$	1.82520e12	1.20135
$165$	−2.07904e12	−1.32343
$166$	1.19511e12	0.735889
$167$	1.07642e11	0.0641271	0.0320635	−	0.999486i	$-0.489792\pi$
$167$	1.07642e11	0.0641271	0.0320635	+	0.999486i	$0.489792\pi$
$168$	2.01488e11	0.116158
$169$	−1.14002e12	−0.636114
$170$	−2.07044e12	−1.11839
$171$	1.17677e11	0.0615479
$172$	4.81736e12	2.44007
$173$	2.96387e12	1.45414	0.727069	−	0.686564i	$-0.240882\pi$
$173$	2.96387e12	1.45414	0.727069	+	0.686564i	$0.240882\pi$
$174$	−9.92638e11	−0.471813
$175$	−5.03258e11	−0.231783
$176$	−3.63078e12	−1.62062
$177$	1.73727e11	0.0751646
$178$	4.13200e12	1.73321
$179$	−7.56791e11	−0.307811	−0.153906	−	0.988086i	$-0.549185\pi$
$179$	−7.56791e11	−0.307811	−0.153906	+	0.988086i	$0.549185\pi$
$180$	−3.15116e12	−1.24300
$181$	−3.30525e12	−1.26466	−0.632328	−	0.774701i	$-0.717900\pi$
$181$	−3.30525e12	−1.26466	−0.632328	+	0.774701i	$0.717900\pi$
$182$	3.01174e11	0.111795
$183$	−1.45783e12	−0.525082
$184$	−6.07858e12	−2.12473
$185$	1.61517e12	0.547991
$186$	−5.36697e12	−1.76770
$187$	−1.42753e12	−0.456518
$188$	−6.44804e12	−2.00244
$189$	6.73179e10	0.0203044
$190$	−1.97930e12	−0.579920
$191$	−2.33041e12	−0.663359	−0.331679	−	0.943392i	$-0.607615\pi$
$191$	−2.33041e12	−0.663359	−0.331679	+	0.943392i	$0.607615\pi$
$192$	1.48889e12	0.411818
$193$	3.82559e12	1.02833	0.514166	−	0.857691i	$-0.328102\pi$
$193$	3.82559e12	1.02833	0.514166	+	0.857691i	$0.328102\pi$
$194$	8.82788e12	2.30646
$195$	−2.45175e12	−0.622710
$196$	−8.35173e12	−2.06238
$197$	−5.11729e12	−1.22879	−0.614393	−	0.789001i	$-0.710599\pi$
$197$	−5.11729e12	−1.22879	−0.614393	+	0.789001i	$0.710599\pi$
$198$	−3.21443e12	−0.750664
$199$	−1.25891e12	−0.285958	−0.142979	−	0.989726i	$-0.545668\pi$
$199$	−1.25891e12	−0.285958	−0.142979	+	0.989726i	$0.545668\pi$
$200$	1.89588e13	4.18933
$201$	3.50900e12	0.754405
$202$	−8.07603e12	−1.68953
$203$	−2.41080e11	−0.0490833
$204$	−2.16369e12	−0.428775
$205$	−5.33889e12	−1.02992
$206$	1.54449e13	2.90078
$207$	−2.03088e12	−0.371404
$208$	−4.28168e12	−0.762545
$209$	−1.36470e12	−0.236718
$210$	−1.13227e12	−0.191313
$211$	3.67063e12	0.604209	0.302104	−	0.953275i	$-0.402311\pi$
$211$	3.67063e12	0.604209	0.302104	+	0.953275i	$0.402311\pi$
$212$	1.28405e13	2.05936
$213$	−3.79056e12	−0.592400
$214$	−1.24105e13	−1.89022
$215$	−1.40912e13	−2.09188
$216$	−2.53600e12	−0.366990
$217$	−1.30347e12	−0.183896
$218$	−3.71285e12	−0.510736
$219$	7.14150e11	0.0957959
$220$	3.65440e13	4.78069
$221$	−1.68345e12	−0.214804
$222$	2.49723e12	0.310826
$223$	4.24709e12	0.515720	0.257860	−	0.966182i	$-0.416983\pi$
$223$	4.24709e12	0.515720	0.257860	+	0.966182i	$0.416983\pi$
$224$	−2.79236e11	−0.0330832
$225$	6.33419e12	0.732297
$226$	1.79048e13	2.02010
$227$	1.20569e13	1.32768	0.663841	−	0.747874i	$-0.268925\pi$
$227$	1.20569e13	1.32768	0.663841	+	0.747874i	$0.268925\pi$
$228$	−2.06845e12	−0.222333
$229$	1.17629e12	0.123430	0.0617150	−	0.998094i	$-0.480343\pi$
$229$	1.17629e12	0.123430	0.0617150	+	0.998094i	$0.480343\pi$
$230$	3.41590e13	3.49946
$231$	−7.80684e11	−0.0780925
$232$	9.08200e12	0.887151
$233$	1.42987e13	1.36408	0.682040	−	0.731315i	$-0.261093\pi$
$233$	1.42987e13	1.36408	0.682040	+	0.731315i	$0.261093\pi$
$234$	−3.79069e12	−0.353208
$235$	1.88611e13	1.71670
$236$	−3.05365e12	−0.271521
$237$	−1.07561e13	−0.934413
$238$	−7.77455e11	−0.0659936
$239$	−1.91008e13	−1.58440	−0.792198	−	0.610264i	$-0.791064\pi$
$239$	−1.91008e13	−1.58440	−0.792198	+	0.610264i	$0.791064\pi$
$240$	1.60971e13	1.30493
$241$	1.15822e13	0.917693	0.458847	−	0.888515i	$-0.348263\pi$
$241$	1.15822e13	0.917693	0.458847	+	0.888515i	$0.348263\pi$
$242$	1.45971e13	1.13053
$243$	−8.47289e11	−0.0641500
$244$	2.56248e13	1.89678
$245$	2.44296e13	1.76808
$246$	−8.25453e12	−0.584183
$247$	−1.60935e12	−0.111383
$248$	4.91044e13	3.32381
$249$	−3.65325e12	−0.241870
$250$	−5.80441e13	−3.75914
$251$	1.36571e13	0.865272	0.432636	−	0.901569i	$-0.357584\pi$
$251$	1.36571e13	0.865272	0.432636	+	0.901569i	$0.357584\pi$
$252$	−1.18327e12	−0.0733467
$253$	2.35520e13	1.42845
$254$	2.49777e13	1.48241
$255$	6.32899e12	0.367590
$256$	−3.58607e13	−2.03845
$257$	1.52705e13	0.849614	0.424807	−	0.905284i	$-0.360342\pi$
$257$	1.52705e13	0.849614	0.424807	+	0.905284i	$0.360342\pi$
$258$	−2.17866e13	−1.18654
$259$	6.06499e11	0.0323356
$260$	4.30953e13	2.24945
$261$	3.03433e12	0.155074
$262$	−6.39814e11	−0.0320182
$263$	−2.29795e13	−1.12612	−0.563060	−	0.826416i	$-0.690376\pi$
$263$	−2.29795e13	−1.12612	−0.563060	+	0.826416i	$0.690376\pi$
$264$	2.94100e13	1.41147
$265$	−3.75595e13	−1.76550
$266$	−7.43233e11	−0.0342197
$267$	−1.26308e13	−0.569666
$268$	−6.16788e13	−2.72518
$269$	−2.62282e13	−1.13535	−0.567676	−	0.823252i	$-0.692157\pi$
$269$	−2.62282e13	−1.13535	−0.567676	+	0.823252i	$0.692157\pi$
$270$	1.42512e13	0.604438
$271$	2.60098e13	1.08095	0.540475	−	0.841360i	$-0.318244\pi$
$271$	2.60098e13	1.08095	0.540475	+	0.841360i	$0.318244\pi$
$272$	1.10528e13	0.450135
$273$	−9.20638e11	−0.0367447
$274$	−3.28004e13	−1.28307
$275$	−7.34575e13	−2.81648
$276$	3.56974e13	1.34164
$277$	4.36526e12	0.160832	0.0804158	−	0.996761i	$-0.474375\pi$
$277$	4.36526e12	0.160832	0.0804158	+	0.996761i	$0.474375\pi$
$278$	3.21943e13	1.16287
$279$	1.64060e13	0.581003
$280$	1.03596e13	0.359727
$281$	−5.10666e13	−1.73881	−0.869406	−	0.494099i	$-0.835498\pi$
$281$	−5.10666e13	−1.73881	−0.869406	+	0.494099i	$0.835498\pi$
$282$	2.91614e13	0.973731
$283$	−4.63457e13	−1.51769	−0.758847	−	0.651269i	$-0.774237\pi$
$283$	−4.63457e13	−1.51769	−0.758847	+	0.651269i	$0.774237\pi$
$284$	6.66279e13	2.13996
$285$	6.05041e12	0.190607
$286$	4.39605e13	1.35847
$287$	−2.00476e12	−0.0607733
$288$	3.51458e12	0.104524
$289$	−2.99262e13	−0.873200
$290$	−5.10368e13	−1.46115
$291$	−2.69854e13	−0.758083
$292$	−1.25529e13	−0.346049
$293$	6.90228e13	1.86733	0.933664	−	0.358150i	$-0.116592\pi$
$293$	6.90228e13	1.86733	0.933664	+	0.358150i	$0.116592\pi$
$294$	3.77709e13	1.00288
$295$	8.93221e12	0.232776
$296$	−2.28481e13	−0.584447
$297$	9.82598e12	0.246726
$298$	−4.49840e13	−1.10884
$299$	2.77742e13	0.672126
$300$	−1.11338e14	−2.64532
$301$	−5.29128e12	−0.123437
$302$	3.68696e13	0.844558
$303$	2.46871e13	0.555310
$304$	1.05663e13	0.233409
$305$	−7.49550e13	−1.62612
$306$	9.78535e12	0.208501
$307$	1.37933e12	0.0288673	0.0144337	−	0.999896i	$-0.495405\pi$
$307$	1.37933e12	0.0288673	0.0144337	+	0.999896i	$0.495405\pi$
$308$	1.37223e13	0.282098
$309$	−4.72125e13	−0.953423
$310$	−2.75945e14	−5.47436
$311$	−2.34303e13	−0.456662	−0.228331	−	0.973584i	$-0.573327\pi$
$311$	−2.34303e13	−0.456662	−0.228331	+	0.973584i	$0.573327\pi$
$312$	3.46823e13	0.664138
$313$	3.82607e13	0.719879	0.359939	−	0.932976i	$-0.382797\pi$
$313$	3.82607e13	0.719879	0.359939	+	0.932976i	$0.382797\pi$
$314$	−1.16324e14	−2.15058
$315$	3.46117e12	0.0628804
$316$	1.89064e14	3.37543
$317$	6.93734e12	0.121721	0.0608607	−	0.998146i	$-0.480615\pi$
$317$	6.93734e12	0.121721	0.0608607	+	0.998146i	$0.480615\pi$
$318$	−5.80713e13	−1.00141
$319$	−3.51890e13	−0.596429
$320$	7.65518e13	1.27535
$321$	3.79367e13	0.621272
$322$	1.28268e13	0.206495
$323$	4.15440e12	0.0657499
$324$	1.48931e13	0.231733
$325$	−8.66263e13	−1.32523
$326$	−2.40120e13	−0.361186
$327$	1.13496e13	0.167867
$328$	7.55236e13	1.09844
$329$	7.08239e12	0.101298
$330$	−1.65271e14	−2.32472
$331$	5.43420e13	0.751764	0.375882	−	0.926668i	$-0.377340\pi$
$331$	5.43420e13	0.751764	0.375882	+	0.926668i	$0.377340\pi$
$332$	6.42144e13	0.873721
$333$	−7.63363e12	−0.102162
$334$	8.55690e12	0.112645
$335$	1.80416e14	2.33630
$336$	6.04450e12	0.0770007
$337$	3.30920e13	0.414723	0.207362	−	0.978264i	$-0.433512\pi$
$337$	3.30920e13	0.414723	0.207362	+	0.978264i	$0.433512\pi$
$338$	−9.06246e13	−1.11739
$339$	−5.47320e13	−0.663961
$340$	−1.11247e14	−1.32786
$341$	−1.90259e14	−2.23459
$342$	9.35462e12	0.108114
$343$	1.84500e13	0.209835
$344$	1.99334e14	2.23105
$345$	−1.04418e14	−1.15020
$346$	2.35610e14	2.55432
$347$	1.53930e14	1.64252	0.821260	−	0.570554i	$-0.193271\pi$
$347$	1.53930e14	1.64252	0.821260	+	0.570554i	$0.193271\pi$
$348$	−5.33354e13	−0.560183
$349$	−6.55675e13	−0.677874	−0.338937	−	0.940809i	$-0.610067\pi$
$349$	−6.55675e13	−0.677874	−0.338937	+	0.940809i	$0.610067\pi$
$350$	−4.00060e13	−0.407146
$351$	1.15875e13	0.116092
$352$	−4.07584e13	−0.402006
$353$	−1.12454e14	−1.09198	−0.545989	−	0.837793i	$-0.683846\pi$
$353$	−1.12454e14	−1.09198	−0.545989	+	0.837793i	$0.683846\pi$
$354$	1.38102e13	0.132033
$355$	−1.94893e14	−1.83459
$356$	2.22016e14	2.05783
$357$	2.37655e12	0.0216906
$358$	−6.01603e13	−0.540697
$359$	−3.05819e13	−0.270673	−0.135336	−	0.990800i	$-0.543212\pi$
$359$	−3.05819e13	−0.270673	−0.135336	+	0.990800i	$0.543212\pi$
$360$	−1.30390e14	−1.13652
$361$	−1.12519e14	−0.965907
$362$	−2.62748e14	−2.22148
$363$	−4.46209e13	−0.371580
$364$	1.61824e13	0.132735
$365$	3.67183e13	0.296669
$366$	−1.15889e14	−0.922351
$367$	1.15511e14	0.905648	0.452824	−	0.891600i	$-0.350417\pi$
$367$	1.15511e14	0.905648	0.452824	+	0.891600i	$0.350417\pi$
$368$	−1.82353e14	−1.40848
$369$	2.52327e13	0.192008
$370$	1.28396e14	0.962593
$371$	−1.41037e13	−0.104178
$372$	−2.88373e14	−2.09879
$373$	2.39084e14	1.71456	0.857279	−	0.514852i	$-0.172153\pi$
$373$	2.39084e14	1.71456	0.857279	+	0.514852i	$0.172153\pi$
$374$	−1.13480e14	−0.801913
$375$	1.77431e14	1.23554
$376$	−2.66808e14	−1.83091
$377$	−4.14974e13	−0.280636
$378$	5.35137e12	0.0356664
$379$	1.21430e14	0.797645	0.398823	−	0.917028i	$-0.369419\pi$
$379$	1.21430e14	0.797645	0.398823	+	0.917028i	$0.369419\pi$
$380$	−1.06350e14	−0.688538
$381$	−7.63528e13	−0.487234
$382$	−1.85253e14	−1.16525
$383$	3.00914e14	1.86573	0.932866	−	0.360223i	$-0.117299\pi$
$383$	3.00914e14	1.86573	0.932866	+	0.360223i	$0.117299\pi$
$384$	1.47979e14	0.904434
$385$	−4.01391e13	−0.241843
$386$	3.04111e14	1.80635
$387$	6.65981e13	0.389988
$388$	4.74331e14	2.73846
$389$	2.81561e14	1.60269	0.801345	−	0.598203i	$-0.204118\pi$
$389$	2.81561e14	1.60269	0.801345	+	0.598203i	$0.204118\pi$
$390$	−1.94899e14	−1.09384
$391$	−7.16970e13	−0.396761
$392$	−3.45580e14	−1.88571
$393$	1.95581e12	0.0105237
$394$	−4.06794e14	−2.15847
$395$	−5.53028e14	−2.89377
$396$	−1.72715e14	−0.891263
$397$	−3.53759e13	−0.180036	−0.0900181	−	0.995940i	$-0.528692\pi$
$397$	−3.53759e13	−0.180036	−0.0900181	+	0.995940i	$0.528692\pi$
$398$	−1.00076e14	−0.502309
$399$	2.27194e12	0.0112472
$400$	5.68750e14	2.77710
$401$	−2.20852e14	−1.06367	−0.531835	−	0.846848i	$-0.678498\pi$
$401$	−2.20852e14	−1.06367	−0.531835	+	0.846848i	$0.678498\pi$
$402$	2.78944e14	1.32518
$403$	−2.24367e14	−1.05143
$404$	−4.33933e14	−2.00598
$405$	−4.35636e13	−0.198665
$406$	−1.91644e13	−0.0862190
$407$	8.85270e13	0.392922
$408$	−8.95296e13	−0.392045
$409$	2.26354e14	0.977933	0.488966	−	0.872303i	$-0.337374\pi$
$409$	2.26354e14	0.977933	0.488966	+	0.872303i	$0.337374\pi$
$410$	−4.24410e14	−1.80915
$411$	1.00266e14	0.421718
$412$	8.29871e14	3.44410
$413$	3.35407e12	0.0137356
$414$	−1.61443e14	−0.652403
$415$	−1.87833e14	−0.749044
$416$	−4.80653e13	−0.189155
$417$	−9.84126e13	−0.382210
$418$	−1.08485e14	−0.415816
$419$	−3.04567e14	−1.15214	−0.576070	−	0.817400i	$-0.695415\pi$
$419$	−3.04567e14	−1.15214	−0.576070	+	0.817400i	$0.695415\pi$
$420$	−6.08382e13	−0.227146
$421$	−2.48260e14	−0.914859	−0.457430	−	0.889246i	$-0.651230\pi$
$421$	−2.48260e14	−0.914859	−0.457430	+	0.889246i	$0.651230\pi$
$422$	2.91793e14	1.06134
$423$	−8.91417e13	−0.320044
$424$	5.31315e14	1.88295
$425$	2.23619e14	0.782292
$426$	−3.01327e14	−1.04060
$427$	−2.81458e13	−0.0959533
$428$	−6.66826e14	−2.24425
$429$	−1.34380e14	−0.446498
$430$	−1.12017e15	−3.67457
$431$	−3.46730e14	−1.12297	−0.561483	−	0.827489i	$-0.689769\pi$
$431$	−3.46730e14	−1.12297	−0.561483	+	0.827489i	$0.689769\pi$
$432$	−7.60784e13	−0.243277
$433$	−2.57409e12	−0.00812720	−0.00406360	−	0.999992i	$-0.501293\pi$
$433$	−2.57409e12	−0.00812720	−0.00406360	+	0.999992i	$0.501293\pi$
$434$	−1.03618e14	−0.323029
$435$	1.56011e14	0.480247
$436$	−1.99495e14	−0.606396
$437$	−6.85410e13	−0.205732
$438$	5.67706e13	0.168274
$439$	−1.13415e14	−0.331984	−0.165992	−	0.986127i	$-0.553083\pi$
$439$	−1.13415e14	−0.331984	−0.165992	+	0.986127i	$0.553083\pi$
$440$	1.51212e15	4.37117
$441$	−1.15459e14	−0.329623
$442$	−1.33824e14	−0.377322
$443$	−3.01735e13	−0.0840243	−0.0420122	−	0.999117i	$-0.513377\pi$
$443$	−3.01735e13	−0.0840243	−0.0420122	+	0.999117i	$0.513377\pi$
$444$	1.34179e14	0.369044
$445$	−6.49419e14	−1.76419
$446$	3.37618e14	0.905907
$447$	1.37509e14	0.364451
$448$	2.87454e13	0.0752556
$449$	3.56100e14	0.920909	0.460454	−	0.887683i	$-0.347687\pi$
$449$	3.56100e14	0.920909	0.460454	+	0.887683i	$0.347687\pi$
$450$	5.03530e14	1.28634
$451$	−2.92623e14	−0.738479
$452$	9.62042e14	2.39846
$453$	−1.12704e14	−0.277587
$454$	9.58452e14	2.33219
$455$	−4.73349e13	−0.113794
$456$	−8.55887e13	−0.203287
$457$	−3.25069e13	−0.0762845	−0.0381423	−	0.999272i	$-0.512144\pi$
$457$	−3.25069e13	−0.0762845	−0.0381423	+	0.999272i	$0.512144\pi$
$458$	9.35084e13	0.216816
$459$	−2.99122e13	−0.0685296
$460$	1.83540e15	4.15491
$461$	5.10072e14	1.14097	0.570487	−	0.821306i	$-0.306754\pi$
$461$	5.10072e14	1.14097	0.570487	+	0.821306i	$0.306754\pi$
$462$	−6.20597e13	−0.137176
$463$	−5.98857e14	−1.30806	−0.654030	−	0.756469i	$-0.726923\pi$
$463$	−5.98857e14	−1.30806	−0.654030	+	0.756469i	$0.726923\pi$
$464$	2.72454e14	0.588090
$465$	8.43518e14	1.79930
$466$	1.13666e15	2.39612
$467$	−6.63311e14	−1.38189	−0.690946	−	0.722906i	$-0.742806\pi$
$467$	−6.63311e14	−1.38189	−0.690946	+	0.722906i	$0.742806\pi$
$468$	−2.03677e14	−0.419364
$469$	6.77467e13	0.137860
$470$	1.49935e15	3.01553
$471$	3.55582e14	0.706846
$472$	−1.26355e14	−0.248262
$473$	−7.72336e14	−1.49993
$474$	−8.55045e14	−1.64138
$475$	2.13776e14	0.405642
$476$	−4.17735e13	−0.0783542
$477$	1.77514e14	0.329141
$478$	−1.51840e15	−2.78313
$479$	1.83955e14	0.333324	0.166662	−	0.986014i	$-0.446701\pi$
$479$	1.83955e14	0.333324	0.166662	+	0.986014i	$0.446701\pi$
$480$	1.80703e14	0.323697
$481$	1.04397e14	0.184881
$482$	9.20716e14	1.61201
$483$	−3.92093e13	−0.0678703
$484$	7.84317e14	1.34228
$485$	−1.38746e15	−2.34769
$486$	−6.73543e13	−0.112685
$487$	−8.78643e14	−1.45346	−0.726730	−	0.686923i	$-0.758961\pi$
$487$	−8.78643e14	−1.45346	−0.726730	+	0.686923i	$0.758961\pi$
$488$	1.06031e15	1.73430
$489$	7.34007e13	0.118714
$490$	1.94201e15	3.10579
$491$	−1.20207e15	−1.90099	−0.950496	−	0.310738i	$-0.899424\pi$
$491$	−1.20207e15	−1.90099	−0.950496	+	0.310738i	$0.899424\pi$
$492$	−4.43524e14	−0.693601
$493$	1.07122e14	0.165662
$494$	−1.27934e14	−0.195653
$495$	5.05206e14	0.764082
$496$	1.47310e15	2.20335
$497$	−7.31827e13	−0.108255
$498$	−2.90411e14	−0.424866
$499$	1.08408e15	1.56858	0.784292	−	0.620392i	$-0.213026\pi$
$499$	1.08408e15	1.56858	0.784292	+	0.620392i	$0.213026\pi$
$500$	−3.11877e15	−4.46322
$501$	−2.61570e13	−0.0370238
$502$	1.08566e15	1.51992
$503$	−8.66183e12	−0.0119946	−0.00599730	−	0.999982i	$-0.501909\pi$
$503$	−8.66183e12	−0.0119946	−0.00599730	+	0.999982i	$0.501909\pi$
$504$	−4.89616e13	−0.0670637
$505$	1.26930e15	1.71973
$506$	1.87225e15	2.50920
$507$	2.77025e14	0.367261
$508$	1.34208e15	1.76006
$509$	1.03806e15	1.34671	0.673355	−	0.739319i	$-0.264853\pi$
$509$	1.03806e15	1.34671	0.673355	+	0.739319i	$0.264853\pi$
$510$	5.03117e14	0.645703
$511$	1.37878e13	0.0175057
$512$	−1.60355e15	−2.01418
$513$	−2.85955e13	−0.0355347
$514$	1.21391e15	1.49242
$515$	−2.42745e15	−2.95264
$516$	−1.17062e15	−1.40878
$517$	1.03377e15	1.23091
$518$	4.82130e13	0.0568003
$519$	−7.20221e14	−0.839548
$520$	1.78320e15	2.05676
$521$	1.39480e15	1.59186	0.795931	−	0.605387i	$-0.206982\pi$
$521$	1.39480e15	1.59186	0.795931	+	0.605387i	$0.206982\pi$
$522$	2.41211e14	0.272401
$523$	−8.51642e14	−0.951694	−0.475847	−	0.879528i	$-0.657858\pi$
$523$	−8.51642e14	−0.951694	−0.475847	+	0.879528i	$0.657858\pi$
$524$	−3.43779e13	−0.0380152
$525$	1.22292e14	0.133820
$526$	−1.82674e15	−1.97813
$527$	5.79187e14	0.620669
$528$	8.82280e14	0.935663
$529$	2.30075e14	0.241470
$530$	−2.98575e15	−3.10125
$531$	−4.22156e13	−0.0433963
$532$	−3.99347e13	−0.0406290
$533$	−3.45082e14	−0.347475
$534$	−1.00408e15	−1.00067
$535$	1.95053e15	1.92401
$536$	−2.55216e15	−2.49173
$537$	1.83900e14	0.177715
$538$	−2.08498e15	−1.99434
$539$	1.33898e15	1.26776
$540$	7.65733e14	0.717648
$541$	1.87926e15	1.74342	0.871710	−	0.490022i	$-0.163011\pi$
$541$	1.87926e15	1.74342	0.871710	+	0.490022i	$0.163011\pi$
$542$	2.06762e15	1.89878
$543$	8.03176e14	0.730149
$544$	1.24077e14	0.111660
$545$	5.83542e14	0.519866
$546$	−7.31852e13	−0.0645451
$547$	8.87287e14	0.774700	0.387350	−	0.921933i	$-0.373390\pi$
$547$	8.87287e14	0.774700	0.387350	+	0.921933i	$0.373390\pi$
$548$	−1.76240e15	−1.52339
$549$	3.54254e14	0.303156
$550$	−5.83943e15	−4.94738
$551$	1.02407e14	0.0859005
$552$	1.47710e15	1.22672
$553$	−2.07663e14	−0.170754
$554$	3.47012e14	0.282514
$555$	−3.92486e14	−0.316383
$556$	1.72983e15	1.38068
$557$	1.29493e15	1.02339	0.511697	−	0.859166i	$-0.329017\pi$
$557$	1.29493e15	1.02339	0.511697	+	0.859166i	$0.329017\pi$
$558$	1.30417e15	1.02058
$559$	−9.10794e14	−0.705757
$560$	3.10780e14	0.238462
$561$	3.46891e14	0.263571
$562$	−4.05949e15	−3.05437
$563$	−1.62190e15	−1.20845	−0.604223	−	0.796816i	$-0.706516\pi$
$563$	−1.62190e15	−1.20845	−0.604223	+	0.796816i	$0.706516\pi$
$564$	1.56687e15	1.15611
$565$	−2.81406e15	−2.05621
$566$	−3.68420e15	−2.66596
$567$	−1.63582e13	−0.0117228
$568$	2.75694e15	1.95665
$569$	2.24550e15	1.57832	0.789159	−	0.614188i	$-0.210516\pi$
$569$	2.24550e15	1.57832	0.789159	+	0.614188i	$0.210516\pi$
$570$	4.80971e14	0.334817
$571$	−4.51235e13	−0.0311103	−0.0155552	−	0.999879i	$-0.504952\pi$
$571$	−4.51235e13	−0.0311103	−0.0155552	+	0.999879i	$0.504952\pi$
$572$	2.36204e15	1.61291
$573$	5.66289e14	0.382990
$574$	−1.59367e14	−0.106754
$575$	−3.68935e15	−2.44781
$576$	−3.61800e14	−0.237763
$577$	−5.74515e14	−0.373968	−0.186984	−	0.982363i	$-0.559871\pi$
$577$	−5.74515e14	−0.373968	−0.186984	+	0.982363i	$0.559871\pi$
$578$	−2.37895e15	−1.53385
$579$	−9.29619e14	−0.593708
$580$	−2.74226e15	−1.73482
$581$	−7.05317e13	−0.0441993
$582$	−2.14517e15	−1.33164
$583$	−2.05863e15	−1.26590
$584$	−5.19415e14	−0.316405
$585$	5.95775e14	0.359522
$586$	5.48690e15	3.28012
$587$	9.98207e14	0.591168	0.295584	−	0.955317i	$-0.404486\pi$
$587$	9.98207e14	0.591168	0.295584	+	0.955317i	$0.404486\pi$
$588$	2.02947e15	1.19071
$589$	5.53692e14	0.321836
$590$	7.10057e14	0.408891
$591$	1.24350e15	0.709439
$592$	−6.85427e14	−0.387429
$593$	1.03071e14	0.0577214	0.0288607	−	0.999583i	$-0.490812\pi$
$593$	1.03071e14	0.0577214	0.0288607	+	0.999583i	$0.490812\pi$
$594$	7.81107e14	0.433396
$595$	1.22191e14	0.0671733
$596$	−2.41704e15	−1.31653
$597$	3.05915e14	0.165098
$598$	2.20789e15	1.18065
$599$	9.24646e13	0.0489923	0.0244962	−	0.999700i	$-0.492202\pi$
$599$	9.24646e13	0.0489923	0.0244962	+	0.999700i	$0.492202\pi$
$600$	−4.60698e15	−2.41871
$601$	4.07188e13	0.0211829	0.0105915	−	0.999944i	$-0.496629\pi$
$601$	4.07188e13	0.0211829	0.0105915	+	0.999944i	$0.496629\pi$
$602$	−4.20625e14	−0.216828
$603$	−8.52686e14	−0.435556
$604$	1.98104e15	1.00274
$605$	−2.29420e15	−1.15074
$606$	1.96248e15	0.975450
$607$	1.93098e15	0.951130	0.475565	−	0.879680i	$-0.342244\pi$
$607$	1.93098e15	0.951130	0.475565	+	0.879680i	$0.342244\pi$
$608$	1.18615e14	0.0578988
$609$	5.85825e13	0.0283382
$610$	−5.95848e15	−2.85641
$611$	1.21910e15	0.579179
$612$	5.25777e14	0.247553
$613$	−6.59449e14	−0.307715	−0.153857	−	0.988093i	$-0.549170\pi$
$613$	−6.59449e14	−0.307715	−0.153857	+	0.988093i	$0.549170\pi$
$614$	1.09648e14	0.0507079
$615$	1.29735e15	0.594626
$616$	5.67806e14	0.257932
$617$	2.78902e15	1.25569	0.627846	−	0.778337i	$-0.283937\pi$
$617$	2.78902e15	1.25569	0.627846	+	0.778337i	$0.283937\pi$
$618$	−3.75311e15	−1.67477
$619$	3.98891e15	1.76423	0.882116	−	0.471033i	$-0.156119\pi$
$619$	3.98891e15	1.76423	0.882116	+	0.471033i	$0.156119\pi$
$620$	−1.48268e16	−6.49970
$621$	4.93503e14	0.214430
$622$	−1.86257e15	−0.802166
$623$	−2.43858e14	−0.104101
$624$	1.04045e15	0.440255
$625$	3.88489e15	1.62944
$626$	3.04150e15	1.26453
$627$	3.31622e14	0.136669
$628$	−6.25019e15	−2.55338
$629$	−2.69493e14	−0.109136
$630$	2.75142e14	0.110455
$631$	2.85530e15	1.13629	0.568146	−	0.822928i	$-0.307661\pi$
$631$	2.85530e15	1.13629	0.568146	+	0.822928i	$0.307661\pi$
$632$	7.82311e15	3.08628
$633$	−8.91963e14	−0.348840
$634$	5.51477e14	0.213814
$635$	−3.92570e15	−1.50891
$636$	−3.12023e15	−1.18897
$637$	1.57902e15	0.596515
$638$	−2.79732e15	−1.04768
$639$	9.21105e14	0.342022
$640$	7.60837e15	2.80093
$641$	−1.14468e15	−0.417795	−0.208897	−	0.977938i	$-0.566987\pi$
$641$	−1.14468e15	−0.417795	−0.208897	+	0.977938i	$0.566987\pi$
$642$	3.01574e15	1.09132
$643$	3.75473e15	1.34716	0.673579	−	0.739115i	$-0.264756\pi$
$643$	3.75473e15	1.34716	0.673579	+	0.739115i	$0.264756\pi$
$644$	6.89195e14	0.245172
$645$	3.42416e15	1.20775
$646$	3.30250e14	0.115495
$647$	5.48795e15	1.90299	0.951496	−	0.307661i	$-0.0995464\pi$
$647$	5.48795e15	1.90299	0.951496	+	0.307661i	$0.0995464\pi$
$648$	6.16249e14	0.211882
$649$	4.89573e14	0.166906
$650$	−6.88627e15	−2.32788
$651$	3.16743e14	0.106172
$652$	−1.29019e15	−0.428836
$653$	−1.20167e15	−0.396060	−0.198030	−	0.980196i	$-0.563454\pi$
$653$	−1.20167e15	−0.396060	−0.198030	+	0.980196i	$0.563454\pi$
$654$	9.02222e14	0.294873
$655$	1.00558e14	0.0325905
$656$	2.26566e15	0.728154
$657$	−1.73538e14	−0.0553078
$658$	5.63008e14	0.177939
$659$	−3.25679e15	−1.02075	−0.510375	−	0.859952i	$-0.670493\pi$
$659$	−3.25679e15	−1.02075	−0.510375	+	0.859952i	$0.670493\pi$
$660$	−8.88018e15	−2.76013
$661$	5.46568e15	1.68475	0.842377	−	0.538889i	$-0.181156\pi$
$661$	5.46568e15	1.68475	0.842377	+	0.538889i	$0.181156\pi$
$662$	4.31986e15	1.32054
$663$	4.09079e14	0.124017
$664$	2.65707e15	0.798876
$665$	1.16813e14	0.0348314
$666$	−6.06828e14	−0.179456
$667$	−1.76735e15	−0.518358
$668$	4.59771e14	0.133743
$669$	−1.03204e15	−0.297751
$670$	1.43420e16	4.10392
$671$	−4.10827e15	−1.16596
$672$	6.78544e13	0.0191006
$673$	5.21114e15	1.45496	0.727478	−	0.686131i	$-0.240692\pi$
$673$	5.21114e15	1.45496	0.727478	+	0.686131i	$0.240692\pi$
$674$	2.63061e15	0.728497
$675$	−1.53921e15	−0.422792
$676$	−4.86936e15	−1.32668
$677$	5.92027e15	1.59994	0.799971	−	0.600039i	$-0.204848\pi$
$677$	5.92027e15	1.59994	0.799971	+	0.600039i	$0.204848\pi$
$678$	−4.35086e15	−1.16630
$679$	−5.20995e14	−0.138532
$680$	−4.60320e15	−1.21412
$681$	−2.92983e15	−0.766537
$682$	−1.51245e16	−3.92524
$683$	3.46748e15	0.892689	0.446345	−	0.894861i	$-0.352726\pi$
$683$	3.46748e15	0.892689	0.446345	+	0.894861i	$0.352726\pi$
$684$	5.02633e14	0.128364
$685$	5.15519e15	1.30601
$686$	1.46666e15	0.368594
$687$	−2.85840e14	−0.0712624
$688$	5.97987e15	1.47896
$689$	−2.42768e15	−0.595643
$690$	−8.30063e15	−2.02042
$691$	3.88027e15	0.936986	0.468493	−	0.883467i	$-0.344797\pi$
$691$	3.88027e15	0.936986	0.468493	+	0.883467i	$0.344797\pi$
$692$	1.26596e16	3.03274
$693$	1.89706e14	0.0450867
$694$	1.22365e16	2.88523
$695$	−5.05992e15	−1.18366
$696$	−2.20693e15	−0.512197
$697$	8.90802e14	0.205117
$698$	−5.21223e15	−1.19074
$699$	−3.47459e15	−0.787552
$700$	−2.14956e15	−0.483404
$701$	7.90052e14	0.176282	0.0881408	−	0.996108i	$-0.471907\pi$
$701$	7.90052e14	0.176282	0.0881408	+	0.996108i	$0.471907\pi$
$702$	9.21137e14	0.203925
$703$	−2.57631e14	−0.0565905
$704$	4.19579e15	0.914458
$705$	−4.58325e15	−0.991137
$706$	−8.93941e15	−1.91815
$707$	4.76623e14	0.101477
$708$	7.42037e14	0.156763
$709$	−5.14116e15	−1.07772	−0.538861	−	0.842394i	$-0.681145\pi$
$709$	−5.14116e15	−1.07772	−0.538861	+	0.842394i	$0.681145\pi$
$710$	−1.54928e16	−3.22262
$711$	2.61373e15	0.539484
$712$	9.18664e15	1.88155
$713$	−9.55565e15	−1.94208
$714$	1.88922e14	0.0381014
$715$	−6.90919e15	−1.38275
$716$	−3.23248e15	−0.641969
$717$	4.64150e15	0.914752
$718$	−2.43108e15	−0.475460
$719$	7.04180e15	1.36671	0.683353	−	0.730088i	$-0.260521\pi$
$719$	7.04180e15	1.36671	0.683353	+	0.730088i	$0.260521\pi$
$720$	−3.91160e15	−0.753400
$721$	−9.11512e14	−0.174228
$722$	−8.94456e15	−1.69670
$723$	−2.81448e15	−0.529830
$724$	−1.41177e16	−2.63756
$725$	5.51225e15	1.02204
$726$	−3.54710e15	−0.652712
$727$	−6.89694e15	−1.25955	−0.629777	−	0.776776i	$-0.716854\pi$
$727$	−6.89694e15	−1.25955	−0.629777	+	0.776776i	$0.716854\pi$
$728$	6.69597e14	0.121364
$729$	2.05891e14	0.0370370
$730$	2.91888e15	0.521124
$731$	2.35114e15	0.416613
$732$	−6.22684e15	−1.09511
$733$	−3.40668e15	−0.594648	−0.297324	−	0.954777i	$-0.596094\pi$
$733$	−3.40668e15	−0.594648	−0.297324	+	0.954777i	$0.596094\pi$
$734$	9.18242e15	1.59085
$735$	−5.93639e15	−1.02080
$736$	−2.04706e15	−0.349384
$737$	9.88858e15	1.67518
$738$	2.00585e15	0.337278
$739$	8.32463e15	1.38938	0.694689	−	0.719310i	$-0.255542\pi$
$739$	8.32463e15	1.38938	0.694689	+	0.719310i	$0.255542\pi$
$740$	6.89886e15	1.14289
$741$	3.91072e14	0.0643067
$742$	−1.12116e15	−0.182998
$743$	−1.18109e15	−0.191357	−0.0956784	−	0.995412i	$-0.530502\pi$
$743$	−1.18109e15	−0.191357	−0.0956784	+	0.995412i	$0.530502\pi$
$744$	−1.19324e16	−1.91900
$745$	7.07006e15	1.12866
$746$	1.90057e16	3.01177
$747$	8.87739e14	0.139644
$748$	−6.09742e15	−0.952110
$749$	7.32428e14	0.113531
$750$	1.41047e16	2.17034
$751$	−6.90639e15	−1.05495	−0.527474	−	0.849571i	$-0.676861\pi$
$751$	−6.90639e15	−1.05495	−0.527474	+	0.849571i	$0.676861\pi$
$752$	−8.00408e15	−1.21370
$753$	−3.31867e15	−0.499565
$754$	−3.29880e15	−0.492962
$755$	−5.79472e15	−0.859655
$756$	2.87534e14	0.0423467
$757$	6.54220e15	0.956525	0.478262	−	0.878217i	$-0.341267\pi$
$757$	6.54220e15	0.956525	0.478262	+	0.878217i	$0.341267\pi$
$758$	9.65294e15	1.40113
$759$	−5.72315e15	−0.824717
$760$	−4.40057e15	−0.629556
$761$	−6.87347e15	−0.976249	−0.488124	−	0.872774i	$-0.662319\pi$
$761$	−6.87347e15	−0.976249	−0.488124	+	0.872774i	$0.662319\pi$
$762$	−6.06958e15	−0.855868
$763$	2.19121e14	0.0306760
$764$	−9.95386e15	−1.38350
$765$	−1.53795e15	−0.212228
$766$	2.39209e16	3.27732
$767$	5.77339e14	0.0785338
$768$	8.71416e15	1.17690
$769$	1.97284e15	0.264544	0.132272	−	0.991213i	$-0.457773\pi$
$769$	1.97284e15	0.264544	0.132272	+	0.991213i	$0.457773\pi$
$770$	−3.19082e15	−0.424818
$771$	−3.71073e15	−0.490525
$772$	1.63402e16	2.14468
$773$	1.12911e16	1.47146	0.735728	−	0.677277i	$-0.236840\pi$
$773$	1.12911e16	1.47146	0.735728	+	0.677277i	$0.236840\pi$
$774$	5.29415e15	0.685048
$775$	2.98035e16	3.82920
$776$	1.96270e16	2.50388
$777$	−1.47379e14	−0.0186690
$778$	2.23824e16	2.81526
$779$	8.51591e14	0.106359
$780$	−1.04721e16	−1.29872
$781$	−1.06820e16	−1.31545
$782$	−5.69948e15	−0.696944
$783$	−7.37342e14	−0.0895322
$784$	−1.03672e16	−1.25003
$785$	1.82824e16	2.18902
$786$	1.55475e14	0.0184857
$787$	−1.05190e16	−1.24198	−0.620991	−	0.783818i	$-0.713270\pi$
$787$	−1.05190e16	−1.24198	−0.620991	+	0.783818i	$0.713270\pi$
$788$	−2.18575e16	−2.56275
$789$	5.58403e15	0.650166
$790$	−4.39624e16	−5.08315
$791$	−1.05669e15	−0.121332
$792$	−7.14662e15	−0.814915
$793$	−4.84477e15	−0.548618
$794$	−2.81217e15	−0.316249
$795$	9.12696e15	1.01931
$796$	−5.37716e15	−0.596391
$797$	3.66067e15	0.403217	0.201609	−	0.979466i	$-0.435383\pi$
$797$	3.66067e15	0.403217	0.201609	+	0.979466i	$0.435383\pi$
$798$	1.80606e14	0.0197568
$799$	−3.14701e15	−0.341893
$800$	6.38468e15	0.688881
$801$	3.06929e15	0.328897
$802$	−1.75564e16	−1.86843
$803$	2.01252e15	0.212718
$804$	1.49880e16	1.57338
$805$	−2.01596e15	−0.210186
$806$	−1.78359e16	−1.84693
$807$	6.37344e15	0.655495
$808$	−1.79554e16	−1.83414
$809$	2.99370e15	0.303733	0.151866	−	0.988401i	$-0.451472\pi$
$809$	2.99370e15	0.303733	0.151866	+	0.988401i	$0.451472\pi$
$810$	−3.46305e15	−0.348972
$811$	1.00891e16	1.00980	0.504902	−	0.863177i	$-0.331529\pi$
$811$	1.00891e16	1.00980	0.504902	+	0.863177i	$0.331529\pi$
$812$	−1.02973e15	−0.102368
$813$	−6.32038e15	−0.624087
$814$	7.03737e15	0.690202
$815$	3.77392e15	0.367643
$816$	−2.68583e15	−0.259886
$817$	2.24765e15	0.216027
$818$	1.79937e16	1.71782
$819$	2.23715e14	0.0212145
$820$	−2.28040e16	−2.14800
$821$	2.88349e15	0.269794	0.134897	−	0.990860i	$-0.456930\pi$
$821$	2.88349e15	0.269794	0.134897	+	0.990860i	$0.456930\pi$
$822$	7.97051e15	0.740783
$823$	−2.30268e15	−0.212586	−0.106293	−	0.994335i	$-0.533898\pi$
$823$	−2.30268e15	−0.212586	−0.106293	+	0.994335i	$0.533898\pi$
$824$	3.43386e16	3.14907
$825$	1.78502e16	1.62609
$826$	2.66628e14	0.0241277
$827$	−1.91147e16	−1.71826	−0.859128	−	0.511760i	$-0.828994\pi$
$827$	−1.91147e16	−1.71826	−0.859128	+	0.511760i	$0.828994\pi$
$828$	−8.67448e15	−0.774598
$829$	−1.21505e16	−1.07781	−0.538906	−	0.842366i	$-0.681162\pi$
$829$	−1.21505e16	−1.07781	−0.538906	+	0.842366i	$0.681162\pi$
$830$	−1.49316e16	−1.31576
$831$	−1.06076e15	−0.0928561
$832$	4.94797e15	0.430278
$833$	−4.07612e15	−0.352127
$834$	−7.82321e15	−0.671385
$835$	−1.34487e15	−0.114658
$836$	−5.82902e15	−0.493698
$837$	−3.98665e15	−0.335442
$838$	−2.42112e16	−2.02383
$839$	2.20864e16	1.83414	0.917072	−	0.398722i	$-0.130546\pi$
$839$	2.20864e16	1.83414	0.917072	+	0.398722i	$0.130546\pi$
$840$	−2.51738e15	−0.207688
$841$	−9.55992e15	−0.783567
$842$	−1.97351e16	−1.60703
$843$	1.24092e16	1.00390
$844$	1.56783e16	1.26013
$845$	1.42433e16	1.13736
$846$	−7.08623e15	−0.562184
$847$	−8.61477e14	−0.0679024
$848$	1.59391e16	1.24821
$849$	1.12620e16	0.876241
$850$	1.77763e16	1.37416
$851$	4.44621e15	0.341490
$852$	−1.61906e16	−1.23551
$853$	−2.34442e16	−1.77753	−0.888764	−	0.458365i	$-0.848435\pi$
$853$	−2.34442e16	−1.77753	−0.888764	+	0.458365i	$0.848435\pi$
$854$	−2.23742e15	−0.168550
$855$	−1.47025e15	−0.110047
$856$	−2.75921e16	−2.05201
$857$	3.93075e15	0.290456	0.145228	−	0.989398i	$-0.453608\pi$
$857$	3.93075e15	0.290456	0.145228	+	0.989398i	$0.453608\pi$
$858$	−1.06824e16	−0.784312
$859$	1.61049e16	1.17489	0.587443	−	0.809265i	$-0.300135\pi$
$859$	1.61049e16	1.17489	0.587443	+	0.809265i	$0.300135\pi$
$860$	−6.01877e16	−4.36281
$861$	4.87158e14	0.0350875
$862$	−2.75629e16	−1.97258
$863$	2.00220e16	1.42379	0.711897	−	0.702284i	$-0.247836\pi$
$863$	2.00220e16	1.42379	0.711897	+	0.702284i	$0.247836\pi$
$864$	−8.54042e14	−0.0603467
$865$	−3.70304e16	−2.59998
$866$	−2.04625e14	−0.0142761
$867$	7.27207e15	0.504142
$868$	−5.56750e15	−0.383532
$869$	−3.03114e16	−2.07490
$870$	1.24019e16	0.843595
$871$	1.16613e16	0.788220
$872$	−8.25475e15	−0.554451
$873$	6.55744e15	0.437680
$874$	−5.44860e15	−0.361387
$875$	3.42559e15	0.225783
$876$	3.05034e15	0.199791
$877$	1.85971e15	0.121045	0.0605227	−	0.998167i	$-0.480723\pi$
$877$	1.85971e15	0.121045	0.0605227	+	0.998167i	$0.480723\pi$
$878$	−9.01585e15	−0.583159
$879$	−1.67725e16	−1.07810
$880$	4.53627e16	2.89764
$881$	8.34988e15	0.530045	0.265022	−	0.964242i	$-0.414621\pi$
$881$	8.34988e15	0.530045	0.265022	+	0.964242i	$0.414621\pi$
$882$	−9.17833e15	−0.579011
$883$	−5.67787e15	−0.355960	−0.177980	−	0.984034i	$-0.556956\pi$
$883$	−5.67787e15	−0.355960	−0.177980	+	0.984034i	$0.556956\pi$
$884$	−7.19051e15	−0.447994
$885$	−2.17053e15	−0.134393
$886$	−2.39861e15	−0.147596
$887$	1.16962e16	0.715262	0.357631	−	0.933863i	$-0.383585\pi$
$887$	1.16962e16	0.715262	0.357631	+	0.933863i	$0.383585\pi$
$888$	5.55208e15	0.337431
$889$	−1.47411e15	−0.0890370
$890$	−5.16249e16	−3.09895
$891$	−2.38771e15	−0.142448
$892$	1.81406e16	1.07558
$893$	−3.00848e15	−0.177282
$894$	1.09311e16	0.640189
$895$	9.45529e15	0.550362
$896$	2.85696e15	0.165276
$897$	−6.74914e15	−0.388052
$898$	2.83078e16	1.61765
$899$	1.42771e16	0.810888
$900$	2.70552e16	1.52727
$901$	6.26686e15	0.351612
$902$	−2.32618e16	−1.29720
$903$	1.28578e15	0.0712664
$904$	3.98076e16	2.19300
$905$	4.12956e16	2.26119
$906$	−8.95930e15	−0.487606
$907$	1.38588e16	0.749697	0.374849	−	0.927086i	$-0.377695\pi$
$907$	1.38588e16	0.749697	0.374849	+	0.927086i	$0.377695\pi$
$908$	5.14986e16	2.76900
$909$	−5.99896e15	−0.320608
$910$	−3.76284e15	−0.199889
$911$	−1.28634e16	−0.679209	−0.339605	−	0.940568i	$-0.610293\pi$
$911$	−1.28634e16	−0.679209	−0.339605	+	0.940568i	$0.610293\pi$
$912$	−2.56761e15	−0.134759
$913$	−1.02951e16	−0.537082
$914$	−2.58410e15	−0.134000
$915$	1.82141e16	0.938839
$916$	5.02430e15	0.257425
$917$	3.77599e13	0.00192309
$918$	−2.37784e15	−0.120378
$919$	5.02664e15	0.252954	0.126477	−	0.991970i	$-0.459633\pi$
$919$	5.02664e15	0.252954	0.126477	+	0.991970i	$0.459633\pi$
$920$	7.59454e16	3.79899
$921$	−3.35177e14	−0.0166665
$922$	4.05476e16	2.00422
$923$	−1.25970e16	−0.618954
$924$	−3.33453e15	−0.162869
$925$	−1.38675e16	−0.673314
$926$	−4.76055e16	−2.29772
$927$	1.14726e16	0.550459
$928$	3.05851e15	0.145880
$929$	−8.99679e15	−0.426581	−0.213290	−	0.976989i	$-0.568418\pi$
$929$	−8.99679e15	−0.426581	−0.213290	+	0.976989i	$0.568418\pi$
$930$	6.70546e16	3.16062
$931$	−3.89669e15	−0.182588
$932$	6.10741e16	2.84492
$933$	5.69355e15	0.263654
$934$	−5.27292e16	−2.42741
$935$	1.78355e16	0.816247
$936$	−8.42781e15	−0.383440
$937$	−1.14476e16	−0.517782	−0.258891	−	0.965907i	$-0.583357\pi$
$937$	−1.14476e16	−0.517782	−0.258891	+	0.965907i	$0.583357\pi$
$938$	5.38546e15	0.242162
$939$	−9.29735e15	−0.415622
$940$	8.05614e16	3.58034
$941$	1.46015e16	0.645142	0.322571	−	0.946545i	$-0.395453\pi$
$941$	1.46015e16	0.645142	0.322571	+	0.946545i	$0.395453\pi$
$942$	2.82666e16	1.24164
$943$	−1.46968e16	−0.641813
$944$	−3.79056e15	−0.164572
$945$	−8.41065e14	−0.0363040
$946$	−6.13961e16	−2.63475
$947$	1.13562e16	0.484515	0.242257	−	0.970212i	$-0.422112\pi$
$947$	1.13562e16	0.484515	0.242257	+	0.970212i	$0.422112\pi$
$948$	−4.59425e16	−1.94880
$949$	2.37331e15	0.100090
$950$	1.69939e16	0.712545
$951$	−1.68577e15	−0.0702759
$952$	−1.72851e15	−0.0716422
$953$	8.35814e14	0.0344428	0.0172214	−	0.999852i	$-0.494518\pi$
$953$	8.35814e14	0.0344428	0.0172214	+	0.999852i	$0.494518\pi$
$954$	1.41113e16	0.578165
$955$	2.91160e16	1.18608
$956$	−8.15853e16	−3.30441
$957$	8.55094e15	0.344348
$958$	1.46233e16	0.585511
$959$	1.93578e15	0.0770646
$960$	−1.86021e16	−0.736325
$961$	5.17845e16	2.03808
$962$	8.29896e15	0.324759
$963$	−9.21862e15	−0.358692
$964$	4.94710e16	1.91393
$965$	−4.77967e16	−1.83864
$966$	−3.11690e15	−0.119220
$967$	1.13496e16	0.431651	0.215826	−	0.976432i	$-0.430756\pi$
$967$	1.13496e16	0.431651	0.215826	+	0.976432i	$0.430756\pi$
$968$	3.24536e16	1.22730
$969$	−1.00952e15	−0.0379607
$970$	−1.10295e17	−4.12393
$971$	−2.31061e16	−0.859055	−0.429528	−	0.903054i	$-0.641320\pi$
$971$	−2.31061e16	−0.859055	−0.429528	+	0.903054i	$0.641320\pi$
$972$	−3.61902e15	−0.133791
$973$	−1.90001e15	−0.0698450
$974$	−6.98468e16	−2.55313
$975$	2.10502e16	0.765122
$976$	3.18086e16	1.14966
$977$	−6.97041e15	−0.250518	−0.125259	−	0.992124i	$-0.539976\pi$
$977$	−6.97041e15	−0.250518	−0.125259	+	0.992124i	$0.539976\pi$
$978$	5.83491e15	0.208531
$979$	−3.55945e16	−1.26496
$980$	1.04346e17	3.68750
$981$	−2.75794e15	−0.0969183
$982$	−9.55570e16	−3.33925
$983$	−1.67312e16	−0.581409	−0.290704	−	0.956813i	$-0.593890\pi$
$983$	−1.67312e16	−0.581409	−0.290704	+	0.956813i	$0.593890\pi$
$984$	−1.83522e16	−0.634185
$985$	6.39351e16	2.19705
$986$	8.51557e15	0.290999
$987$	−1.72102e15	−0.0584847
$988$	−6.87400e15	−0.232299
$989$	−3.87901e16	−1.30359
$990$	4.01609e16	1.34218
$991$	−3.37114e16	−1.12040	−0.560198	−	0.828359i	$-0.689275\pi$
$991$	−3.37114e16	−1.12040	−0.560198	+	0.828359i	$0.689275\pi$
$992$	1.65367e16	0.546557
$993$	−1.32051e16	−0.434031
$994$	−5.81758e15	−0.190159
$995$	1.57287e16	0.511288
$996$	−1.56041e16	−0.504443
$997$	4.90398e16	1.57661	0.788307	−	0.615282i	$-0.210958\pi$
$997$	4.90398e16	1.57661	0.788307	+	0.615282i	$0.210958\pi$
$998$	8.61777e16	2.75535
$999$	1.85497e15	0.0589831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.26	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+79.4940 q^{2} -243.000 q^{3} +4271.29 q^{4} -12493.9 q^{5} -19317.0 q^{6} -4691.50 q^{7} +176738. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+79.4940 q^{2} -243.000 q^{3} +4271.29 q^{4} -12493.9 q^{5} -19317.0 q^{6} -4691.50 q^{7} +176738. q^{8} +59049.0 q^{9} -993192. q^{10} -684790. q^{11} -1.03792e6 q^{12} -807553. q^{13} -372946. q^{14} +3.03602e6 q^{15} +5.30204e6 q^{16} +2.08463e6 q^{17} +4.69404e6 q^{18} +1.99287e6 q^{19} -5.33652e7 q^{20} +1.14003e6 q^{21} -5.44367e7 q^{22} -3.43931e7 q^{23} -4.29475e7 q^{24} +1.07270e8 q^{25} -6.41956e7 q^{26} -1.43489e7 q^{27} -2.00388e7 q^{28} +5.13866e7 q^{29} +2.41346e8 q^{30} +2.77836e8 q^{31} +5.95196e7 q^{32} +1.66404e8 q^{33} +1.65716e8 q^{34} +5.86153e7 q^{35} +2.52216e8 q^{36} -1.29276e8 q^{37} +1.58421e8 q^{38} +1.96235e8 q^{39} -2.20816e9 q^{40} +4.27319e8 q^{41} +9.06259e7 q^{42} +1.12784e9 q^{43} -2.92494e9 q^{44} -7.37754e8 q^{45} -2.73404e9 q^{46} -1.50962e9 q^{47} -1.28840e9 q^{48} -1.95532e9 q^{49} +8.52733e9 q^{50} -5.06566e8 q^{51} -3.44930e9 q^{52} +3.00622e9 q^{53} -1.14065e9 q^{54} +8.55571e9 q^{55} -8.29168e8 q^{56} -4.84268e8 q^{57} +4.08493e9 q^{58} -7.14924e8 q^{59} +1.29678e10 q^{60} +5.99932e9 q^{61} +2.20863e10 q^{62} -2.77028e8 q^{63} -6.12712e9 q^{64} +1.00895e10 q^{65} +1.32281e10 q^{66} -1.44403e10 q^{67} +8.90408e9 q^{68} +8.35752e9 q^{69} +4.65956e9 q^{70} +1.55990e10 q^{71} +1.04362e10 q^{72} -2.93889e9 q^{73} -1.02767e10 q^{74} -2.60666e10 q^{75} +8.51214e9 q^{76} +3.21269e9 q^{77} +1.55995e10 q^{78} +4.42638e10 q^{79} -6.62433e10 q^{80} +3.48678e9 q^{81} +3.39693e10 q^{82} +1.50339e10 q^{83} +4.86942e9 q^{84} -2.60452e10 q^{85} +8.96569e10 q^{86} -1.24870e10 q^{87} -1.21029e11 q^{88} +5.19787e10 q^{89} -5.86470e10 q^{90} +3.78863e9 q^{91} -1.46903e11 q^{92} -6.75142e10 q^{93} -1.20006e11 q^{94} -2.48988e10 q^{95} -1.44633e10 q^{96} +1.11051e11 q^{97} -1.55436e11 q^{98} -4.04361e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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