LMFDB - Embedded newform 177.12.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +283528. q^{10} -158942. q^{11} +345938. q^{12} -2.30733e6 q^{13} -1.15210e6 q^{14} -2.75724e6 q^{15} +747929. q^{16} -3.64274e6 q^{17} +1.47550e6 q^{18} +8.79583e6 q^{19} -1.61533e7 q^{20} +1.12039e7 q^{21} -3.97161e6 q^{22} -4.28026e6 q^{23} +2.10797e7 q^{24} +7.99192e7 q^{25} -5.76548e7 q^{26} -1.43489e7 q^{27} +6.56381e7 q^{28} -9.38699e7 q^{29} -6.88973e7 q^{30} -1.47835e8 q^{31} +1.96348e8 q^{32} +3.86230e7 q^{33} -9.10238e7 q^{34} -5.23159e8 q^{35} -8.40629e7 q^{36} +3.64192e8 q^{37} +2.19788e8 q^{38} +5.60680e8 q^{39} -9.84300e8 q^{40} -1.41920e8 q^{41} +2.79961e8 q^{42} +2.12648e7 q^{43} +2.26272e8 q^{44} +6.70011e8 q^{45} -1.06954e8 q^{46} -9.13862e7 q^{47} -1.81747e8 q^{48} +1.48504e8 q^{49} +1.99700e9 q^{50} +8.85186e8 q^{51} +3.28474e9 q^{52} +2.00062e9 q^{53} -3.58547e8 q^{54} -1.80347e9 q^{55} +3.99966e9 q^{56} -2.13739e9 q^{57} -2.34560e9 q^{58} -7.14924e8 q^{59} +3.92525e9 q^{60} -3.63962e9 q^{61} -3.69407e9 q^{62} -2.72256e9 q^{63} +3.37455e9 q^{64} -2.61805e10 q^{65} +9.65101e8 q^{66} +7.77012e8 q^{67} +5.18585e9 q^{68} +1.04010e9 q^{69} -1.30725e10 q^{70} -2.23660e10 q^{71} -5.12237e9 q^{72} -2.80490e10 q^{73} +9.10033e9 q^{74} -1.94204e10 q^{75} -1.25219e10 q^{76} +7.32831e9 q^{77} +1.40101e10 q^{78} +4.41096e10 q^{79} +8.48652e9 q^{80} +3.48678e9 q^{81} -3.54626e9 q^{82} +2.91614e10 q^{83} -1.59501e10 q^{84} -4.13330e10 q^{85} +5.31358e8 q^{86} +2.28104e10 q^{87} +1.37879e10 q^{88} +2.60526e10 q^{89} +1.67420e10 q^{90} +1.06383e11 q^{91} +6.09343e9 q^{92} +3.59240e10 q^{93} -2.28354e9 q^{94} +9.98035e10 q^{95} -4.77127e10 q^{96} +4.00595e9 q^{97} +3.71077e9 q^{98} -9.38539e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	24.9877	0.552156	0.276078	−	0.961135i	$-0.410965\pi$
$2$	24.9877	0.552156	0.276078	+	0.961135i	$0.410965\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1423.61	−0.695124
$5$	11346.7	1.62381	0.811903	−	0.583793i	$-0.198432\pi$
$5$	11346.7	1.62381	0.811903	+	0.583793i	$0.198432\pi$
$6$	−6072.02	−0.318788
$7$	−46106.7	−1.03687	−0.518436	−	0.855116i	$-0.673486\pi$
$7$	−46106.7	−1.03687	−0.518436	+	0.855116i	$0.673486\pi$
$8$	−86747.8	−0.935973
$9$	59049.0	0.333333
$10$	283528.	0.896594
$11$	−158942.	−0.297564	−0.148782	−	0.988870i	$-0.547535\pi$
$11$	−158942.	−0.297564	−0.148782	+	0.988870i	$0.547535\pi$
$12$	345938.	0.401330
$13$	−2.30733e6	−1.72354	−0.861768	−	0.507302i	$-0.830643\pi$
$13$	−2.30733e6	−1.72354	−0.861768	+	0.507302i	$0.830643\pi$
$14$	−1.15210e6	−0.572515
$15$	−2.75724e6	−0.937505
$16$	747929.	0.178320
$17$	−3.64274e6	−0.622242	−0.311121	−	0.950370i	$-0.600704\pi$
$17$	−3.64274e6	−0.622242	−0.311121	+	0.950370i	$0.600704\pi$
$18$	1.47550e6	0.184052
$19$	8.79583e6	0.814952	0.407476	−	0.913216i	$-0.366409\pi$
$19$	8.79583e6	0.814952	0.407476	+	0.913216i	$0.366409\pi$
$20$	−1.61533e7	−1.12875
$21$	1.12039e7	0.598638
$22$	−3.97161e6	−0.164302
$23$	−4.28026e6	−0.138665	−0.0693325	−	0.997594i	$-0.522087\pi$
$23$	−4.28026e6	−0.138665	−0.0693325	+	0.997594i	$0.522087\pi$
$24$	2.10797e7	0.540384
$25$	7.99192e7	1.63674
$26$	−5.76548e7	−0.951661
$27$	−1.43489e7	−0.192450
$28$	6.56381e7	0.720754
$29$	−9.38699e7	−0.849840	−0.424920	−	0.905231i	$-0.639698\pi$
$29$	−9.38699e7	−0.849840	−0.424920	+	0.905231i	$0.639698\pi$
$30$	−6.88973e7	−0.517649
$31$	−1.47835e8	−0.927447	−0.463723	−	0.885980i	$-0.653487\pi$
$31$	−1.47835e8	−0.927447	−0.463723	+	0.885980i	$0.653487\pi$
$32$	1.96348e8	1.03443
$33$	3.86230e7	0.171798
$34$	−9.10238e7	−0.343575
$35$	−5.23159e8	−1.68368
$36$	−8.40629e7	−0.231708
$37$	3.64192e8	0.863417	0.431709	−	0.902013i	$-0.357911\pi$
$37$	3.64192e8	0.863417	0.431709	+	0.902013i	$0.357911\pi$
$38$	2.19788e8	0.449981
$39$	5.60680e8	0.995084
$40$	−9.84300e8	−1.51984
$41$	−1.41920e8	−0.191308	−0.0956538	−	0.995415i	$-0.530494\pi$
$41$	−1.41920e8	−0.191308	−0.0956538	+	0.995415i	$0.530494\pi$
$42$	2.79961e8	0.330542
$43$	2.12648e7	0.0220589	0.0110295	−	0.999939i	$-0.496489\pi$
$43$	2.12648e7	0.0220589	0.0110295	+	0.999939i	$0.496489\pi$
$44$	2.26272e8	0.206843
$45$	6.70011e8	0.541269
$46$	−1.06954e8	−0.0765647
$47$	−9.13862e7	−0.0581223	−0.0290611	−	0.999578i	$-0.509252\pi$
$47$	−9.13862e7	−0.0581223	−0.0290611	+	0.999578i	$0.509252\pi$
$48$	−1.81747e8	−0.102953
$49$	1.48504e8	0.0751032
$50$	1.99700e9	0.903739
$51$	8.85186e8	0.359251
$52$	3.28474e9	1.19807
$53$	2.00062e9	0.657124	0.328562	−	0.944482i	$-0.393436\pi$
$53$	2.00062e9	0.657124	0.328562	+	0.944482i	$0.393436\pi$
$54$	−3.58547e8	−0.106263
$55$	−1.80347e9	−0.483186
$56$	3.99966e9	0.970484
$57$	−2.13739e9	−0.470513
$58$	−2.34560e9	−0.469245
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	3.92525e9	0.651681
$61$	−3.63962e9	−0.551750	−0.275875	−	0.961194i	$-0.588968\pi$
$61$	−3.63962e9	−0.551750	−0.275875	+	0.961194i	$0.588968\pi$
$62$	−3.69407e9	−0.512095
$63$	−2.72256e9	−0.345624
$64$	3.37455e9	0.392849
$65$	−2.61805e10	−2.79869
$66$	9.65101e8	0.0948596
$67$	7.77012e8	0.0703099	0.0351549	−	0.999382i	$-0.488808\pi$
$67$	7.77012e8	0.0703099	0.0351549	+	0.999382i	$0.488808\pi$
$68$	5.18585e9	0.432535
$69$	1.04010e9	0.0800583
$70$	−1.30725e10	−0.929653
$71$	−2.23660e10	−1.47119	−0.735594	−	0.677422i	$-0.763097\pi$
$71$	−2.23660e10	−1.47119	−0.735594	+	0.677422i	$0.763097\pi$
$72$	−5.12237e9	−0.311991
$73$	−2.80490e10	−1.58359	−0.791794	−	0.610788i	$-0.790853\pi$
$73$	−2.80490e10	−1.58359	−0.791794	+	0.610788i	$0.790853\pi$
$74$	9.10033e9	0.476741
$75$	−1.94204e10	−0.944975
$76$	−1.25219e10	−0.566492
$77$	7.32831e9	0.308535
$78$	1.40101e10	0.549442
$79$	4.41096e10	1.61281	0.806406	−	0.591362i	$-0.201410\pi$
$79$	4.41096e10	1.61281	0.806406	+	0.591362i	$0.201410\pi$
$80$	8.48652e9	0.289557
$81$	3.48678e9	0.111111
$82$	−3.54626e9	−0.105632
$83$	2.91614e10	0.812602	0.406301	−	0.913739i	$-0.366818\pi$
$83$	2.91614e10	0.812602	0.406301	+	0.913739i	$0.366818\pi$
$84$	−1.59501e10	−0.416127
$85$	−4.13330e10	−1.01040
$86$	5.31358e8	0.0121800
$87$	2.28104e10	0.490656
$88$	1.37879e10	0.278512
$89$	2.60526e10	0.494545	0.247272	−	0.968946i	$-0.420466\pi$
$89$	2.60526e10	0.494545	0.247272	+	0.968946i	$0.420466\pi$
$90$	1.67420e10	0.298865
$91$	1.06383e11	1.78709
$92$	6.09343e9	0.0963893
$93$	3.59240e10	0.535462
$94$	−2.28354e9	−0.0320926
$95$	9.98035e10	1.32332
$96$	−4.77127e10	−0.597231
$97$	4.00595e9	0.0473653	0.0236827	−	0.999720i	$-0.492461\pi$
$97$	4.00595e9	0.0473653	0.0236827	+	0.999720i	$0.492461\pi$
$98$	3.71077e9	0.0414687
$99$	−9.38539e9	−0.0991879
$100$	−1.13774e11	−1.13774
$101$	1.36683e11	1.29404	0.647020	−	0.762473i	$-0.276015\pi$
$101$	1.36683e11	1.29404	0.647020	+	0.762473i	$0.276015\pi$
$102$	2.21188e10	0.198363
$103$	3.32592e10	0.282688	0.141344	−	0.989961i	$-0.454858\pi$
$103$	3.32592e10	0.282688	0.141344	+	0.989961i	$0.454858\pi$
$104$	2.00155e11	1.61318
$105$	1.27128e11	0.972072
$106$	4.99910e10	0.362835
$107$	2.20332e11	1.51868	0.759340	−	0.650694i	$-0.225522\pi$
$107$	2.20332e11	1.51868	0.759340	+	0.650694i	$0.225522\pi$
$108$	2.04273e10	0.133777
$109$	3.41039e10	0.212304	0.106152	−	0.994350i	$-0.466147\pi$
$109$	3.41039e10	0.212304	0.106152	+	0.994350i	$0.466147\pi$
$110$	−4.50646e10	−0.266794
$111$	−8.84986e10	−0.498494
$112$	−3.44846e10	−0.184895
$113$	1.78537e11	0.911582	0.455791	−	0.890087i	$-0.349356\pi$
$113$	1.78537e11	0.911582	0.455791	+	0.890087i	$0.349356\pi$
$114$	−5.34084e10	−0.259796
$115$	−4.85667e10	−0.225165
$116$	1.33634e11	0.590744
$117$	−1.36245e11	−0.574512
$118$	−1.78643e10	−0.0718846
$119$	1.67955e11	0.645185
$120$	2.39185e11	0.877479
$121$	−2.60049e11	−0.911456
$122$	−9.09460e10	−0.304652
$123$	3.44865e10	0.110451
$124$	2.10460e11	0.644690
$125$	3.52780e11	1.03395
$126$	−6.80305e10	−0.190838
$127$	−3.67519e11	−0.987095	−0.493547	−	0.869719i	$-0.664300\pi$
$127$	−3.67519e11	−0.987095	−0.493547	+	0.869719i	$0.664300\pi$
$128$	−3.17799e11	−0.817520
$129$	−5.16734e9	−0.0127357
$130$	−6.54191e11	−1.54531
$131$	8.20347e11	1.85783	0.928914	−	0.370296i	$-0.120744\pi$
$131$	8.20347e11	1.85783	0.928914	+	0.370296i	$0.120744\pi$
$132$	−5.49842e10	−0.119421
$133$	−4.05547e11	−0.845001
$134$	1.94158e10	0.0388220
$135$	−1.62813e11	−0.312502
$136$	3.16000e11	0.582402
$137$	4.76223e11	0.843038	0.421519	−	0.906820i	$-0.361497\pi$
$137$	4.76223e11	0.843038	0.421519	+	0.906820i	$0.361497\pi$
$138$	2.59898e10	0.0442047
$139$	5.05261e11	0.825913	0.412957	−	0.910751i	$-0.364496\pi$
$139$	5.05261e11	0.825913	0.412957	+	0.910751i	$0.364496\pi$
$140$	7.44775e11	1.17036
$141$	2.22069e10	0.0335569
$142$	−5.58877e11	−0.812326
$143$	3.66732e11	0.512862
$144$	4.41645e10	0.0594401
$145$	−1.06511e12	−1.37998
$146$	−7.00882e11	−0.874388
$147$	−3.60864e10	−0.0433608
$148$	−5.18468e11	−0.600181
$149$	4.01963e11	0.448396	0.224198	−	0.974544i	$-0.428024\pi$
$149$	4.01963e11	0.448396	0.224198	+	0.974544i	$0.428024\pi$
$150$	−4.85271e11	−0.521774
$151$	7.98467e11	0.827720	0.413860	−	0.910340i	$-0.364180\pi$
$151$	7.98467e11	0.827720	0.413860	+	0.910340i	$0.364180\pi$
$152$	−7.63018e11	−0.762773
$153$	−2.15100e11	−0.207414
$154$	1.83118e11	0.170360
$155$	−1.67744e12	−1.50599
$156$	−7.98191e11	−0.691706
$157$	1.89568e12	1.58605	0.793023	−	0.609191i	$-0.208506\pi$
$157$	1.89568e12	1.58605	0.793023	+	0.609191i	$0.208506\pi$
$158$	1.10220e12	0.890524
$159$	−4.86151e11	−0.379391
$160$	2.22790e12	1.67972
$161$	1.97349e11	0.143778
$162$	8.71269e10	0.0613507
$163$	5.31502e11	0.361804	0.180902	−	0.983501i	$-0.442098\pi$
$163$	5.31502e11	0.361804	0.180902	+	0.983501i	$0.442098\pi$
$164$	2.02039e11	0.132982
$165$	4.38243e11	0.278967
$166$	7.28676e11	0.448684
$167$	7.57455e10	0.0451249	0.0225625	−	0.999745i	$-0.492818\pi$
$167$	7.57455e10	0.0451249	0.0225625	+	0.999745i	$0.492818\pi$
$168$	−9.71916e11	−0.560309
$169$	3.53159e12	1.97058
$170$	−1.03282e12	−0.557899
$171$	5.19385e11	0.271651
$172$	−3.02728e10	−0.0153337
$173$	−1.34894e12	−0.661821	−0.330911	−	0.943662i	$-0.607356\pi$
$173$	−1.34894e12	−0.661821	−0.330911	+	0.943662i	$0.607356\pi$
$174$	5.69980e11	0.270919
$175$	−3.68481e12	−1.69709
$176$	−1.18878e11	−0.0530616
$177$	1.73727e11	0.0751646
$178$	6.50995e11	0.273066
$179$	2.42722e12	0.987229	0.493614	−	0.869681i	$-0.335675\pi$
$179$	2.42722e12	0.987229	0.493614	+	0.869681i	$0.335675\pi$
$180$	−9.53836e11	−0.376248
$181$	−4.50546e11	−0.172388	−0.0861940	−	0.996278i	$-0.527470\pi$
$181$	−4.50546e11	−0.172388	−0.0861940	+	0.996278i	$0.527470\pi$
$182$	2.65828e12	0.986751
$183$	8.84428e11	0.318553
$184$	3.71303e11	0.129787
$185$	4.13237e12	1.40202
$186$	8.97659e11	0.295658
$187$	5.78986e11	0.185157
$188$	1.30099e11	0.0404022
$189$	6.61581e11	0.199546
$190$	2.49386e12	0.730681
$191$	−7.48171e11	−0.212970	−0.106485	−	0.994314i	$-0.533960\pi$
$191$	−7.48171e11	−0.212970	−0.106485	+	0.994314i	$0.533960\pi$
$192$	−8.20014e11	−0.226811
$193$	−1.99875e12	−0.537272	−0.268636	−	0.963242i	$-0.586573\pi$
$193$	−1.99875e12	−0.537272	−0.268636	+	0.963242i	$0.586573\pi$
$194$	1.00100e11	0.0261531
$195$	6.36186e12	1.61582
$196$	−2.11412e11	−0.0522060
$197$	2.36660e12	0.568279	0.284139	−	0.958783i	$-0.408292\pi$
$197$	2.36660e12	0.568279	0.284139	+	0.958783i	$0.408292\pi$
$198$	−2.34520e11	−0.0547672
$199$	−8.64639e11	−0.196401	−0.0982004	−	0.995167i	$-0.531309\pi$
$199$	−8.64639e11	−0.196401	−0.0982004	+	0.995167i	$0.531309\pi$
$200$	−6.93281e12	−1.53195
$201$	−1.88814e11	−0.0405934
$202$	3.41541e12	0.714513
$203$	4.32803e12	0.881176
$204$	−1.26016e12	−0.249724
$205$	−1.61032e12	−0.310646
$206$	8.31072e11	0.156088
$207$	−2.52745e11	−0.0462217
$208$	−1.72572e12	−0.307341
$209$	−1.39803e12	−0.242500
$210$	3.17663e12	0.536736
$211$	−9.33836e12	−1.53715	−0.768577	−	0.639758i	$-0.779035\pi$
$211$	−9.33836e12	−1.53715	−0.768577	+	0.639758i	$0.779035\pi$
$212$	−2.84811e12	−0.456782
$213$	5.43495e12	0.849391
$214$	5.50559e12	0.838549
$215$	2.41285e11	0.0358194
$216$	1.24474e12	0.180128
$217$	6.81620e12	0.961643
$218$	8.52178e11	0.117225
$219$	6.81592e12	0.914285
$220$	2.56744e12	0.335874
$221$	8.40499e12	1.07246
$222$	−2.21138e12	−0.275247
$223$	−2.98323e12	−0.362251	−0.181125	−	0.983460i	$-0.557974\pi$
$223$	−2.98323e12	−0.362251	−0.181125	+	0.983460i	$0.557974\pi$
$224$	−9.05298e12	−1.07258
$225$	4.71915e12	0.545582
$226$	4.46122e12	0.503336
$227$	5.65977e12	0.623241	0.311621	−	0.950207i	$-0.399128\pi$
$227$	5.65977e12	0.623241	0.311621	+	0.950207i	$0.399128\pi$
$228$	3.04281e12	0.327064
$229$	5.53904e11	0.0581218	0.0290609	−	0.999578i	$-0.490748\pi$
$229$	5.53904e11	0.0581218	0.0290609	+	0.999578i	$0.490748\pi$
$230$	−1.21357e12	−0.124326
$231$	−1.78078e12	−0.178133
$232$	8.14300e12	0.795428
$233$	−6.26960e12	−0.598111	−0.299056	−	0.954236i	$-0.596672\pi$
$233$	−6.26960e12	−0.598111	−0.299056	+	0.954236i	$0.596672\pi$
$234$	−3.40446e12	−0.317220
$235$	−1.03693e12	−0.0943793
$236$	1.01778e12	0.0904974
$237$	−1.07186e13	−0.931158
$238$	4.19681e12	0.356243
$239$	−1.63168e13	−1.35347	−0.676733	−	0.736228i	$-0.736605\pi$
$239$	−1.63168e13	−1.35347	−0.676733	+	0.736228i	$0.736605\pi$
$240$	−2.06222e12	−0.167176
$241$	6.93338e10	0.00549353	0.00274676	−	0.999996i	$-0.499126\pi$
$241$	6.93338e10	0.00549353	0.00274676	+	0.999996i	$0.499126\pi$
$242$	−6.49804e12	−0.503266
$243$	−8.47289e11	−0.0641500
$244$	5.18141e12	0.383534
$245$	1.68502e12	0.121953
$246$	8.61741e11	0.0609865
$247$	−2.02948e13	−1.40460
$248$	1.28244e13	0.868065
$249$	−7.08621e12	−0.469156
$250$	8.81519e12	0.570902
$251$	1.77996e13	1.12773	0.563866	−	0.825866i	$-0.309314\pi$
$251$	1.77996e13	1.12773	0.563866	+	0.825866i	$0.309314\pi$
$252$	3.87587e12	0.240251
$253$	6.80314e11	0.0412617
$254$	−9.18346e12	−0.545030
$255$	1.00439e13	0.583355
$256$	−1.48522e13	−0.844247
$257$	2.62327e13	1.45952	0.729762	−	0.683701i	$-0.239631\pi$
$257$	2.62327e13	1.45952	0.729762	+	0.683701i	$0.239631\pi$
$258$	−1.29120e11	−0.00703211
$259$	−1.67917e13	−0.895253
$260$	3.72709e13	1.94543
$261$	−5.54292e12	−0.283280
$262$	2.04986e13	1.02581
$263$	3.26150e13	1.59831	0.799154	−	0.601127i	$-0.205281\pi$
$263$	3.26150e13	1.59831	0.799154	+	0.601127i	$0.205281\pi$
$264$	−3.35046e12	−0.160799
$265$	2.27004e13	1.06704
$266$	−1.01337e13	−0.466572
$267$	−6.33078e12	−0.285526
$268$	−1.10616e12	−0.0488740
$269$	−2.34861e13	−1.01665	−0.508327	−	0.861164i	$-0.669736\pi$
$269$	−2.34861e13	−1.01665	−0.508327	+	0.861164i	$0.669736\pi$
$270$	−4.06832e12	−0.172550
$271$	5.02136e12	0.208685	0.104342	−	0.994541i	$-0.466726\pi$
$271$	5.02136e12	0.208685	0.104342	+	0.994541i	$0.466726\pi$
$272$	−2.72451e12	−0.110958
$273$	−2.58511e13	−1.03177
$274$	1.18997e13	0.465489
$275$	−1.27025e13	−0.487036
$276$	−1.48070e12	−0.0556504
$277$	1.70115e13	0.626764	0.313382	−	0.949627i	$-0.398538\pi$
$277$	1.70115e13	0.626764	0.313382	+	0.949627i	$0.398538\pi$
$278$	1.26253e13	0.456033
$279$	−8.72953e12	−0.309149
$280$	4.53828e13	1.57588
$281$	−1.28857e13	−0.438756	−0.219378	−	0.975640i	$-0.570403\pi$
$281$	−1.28857e13	−0.438756	−0.219378	+	0.975640i	$0.570403\pi$
$282$	5.54899e11	0.0185287
$283$	4.68660e13	1.53473	0.767366	−	0.641210i	$-0.221567\pi$
$283$	4.68660e13	1.53473	0.767366	+	0.641210i	$0.221567\pi$
$284$	3.18406e13	1.02266
$285$	−2.42523e13	−0.764021
$286$	9.16380e12	0.283180
$287$	6.54346e12	0.198361
$288$	1.15942e13	0.344811
$289$	−2.10023e13	−0.612815
$290$	−2.66147e13	−0.761962
$291$	−9.73445e11	−0.0273464
$292$	3.99310e13	1.10079
$293$	7.34035e13	1.98584	0.992922	−	0.118769i	$-0.0378947\pi$
$293$	7.34035e13	1.98584	0.992922	+	0.118769i	$0.0378947\pi$
$294$	−9.01716e11	−0.0239420
$295$	−8.11202e12	−0.211401
$296$	−3.15928e13	−0.808135
$297$	2.28065e12	0.0572662
$298$	1.00441e13	0.247585
$299$	9.87595e12	0.238994
$300$	2.76471e13	0.656874
$301$	−9.80449e11	−0.0228723
$302$	1.99519e13	0.457031
$303$	−3.32140e13	−0.747115
$304$	6.57866e12	0.145322
$305$	−4.12977e13	−0.895935
$306$	−5.37487e12	−0.114525
$307$	3.58069e13	0.749386	0.374693	−	0.927149i	$-0.377748\pi$
$307$	3.58069e13	0.749386	0.374693	+	0.927149i	$0.377748\pi$
$308$	−1.04327e13	−0.214470
$309$	−8.08198e12	−0.163210
$310$	−4.19155e13	−0.831544
$311$	−1.02620e13	−0.200009	−0.100004	−	0.994987i	$-0.531886\pi$
$311$	−1.02620e13	−0.200009	−0.100004	+	0.994987i	$0.531886\pi$
$312$	−4.86377e13	−0.931372
$313$	−9.38393e13	−1.76559	−0.882797	−	0.469754i	$-0.844343\pi$
$313$	−9.38393e13	−1.76559	−0.882797	+	0.469754i	$0.844343\pi$
$314$	4.73686e13	0.875745
$315$	−3.08920e13	−0.561226
$316$	−6.27950e13	−1.12110
$317$	−7.53558e13	−1.32218	−0.661090	−	0.750306i	$-0.729906\pi$
$317$	−7.53558e13	−1.32218	−0.661090	+	0.750306i	$0.729906\pi$
$318$	−1.21478e13	−0.209483
$319$	1.49199e13	0.252882
$320$	3.82899e13	0.637910
$321$	−5.35406e13	−0.876810
$322$	4.93130e12	0.0793878
$323$	−3.20409e13	−0.507097
$324$	−4.96383e12	−0.0772359
$325$	−1.84400e14	−2.82099
$326$	1.32810e13	0.199772
$327$	−8.28724e12	−0.122574
$328$	1.23112e13	0.179059
$329$	4.21352e12	0.0602653
$330$	1.09507e13	0.154034
$331$	−1.30987e14	−1.81207	−0.906035	−	0.423202i	$-0.860906\pi$
$331$	−1.30987e14	−1.81207	−0.906035	+	0.423202i	$0.860906\pi$
$332$	−4.15145e13	−0.564859
$333$	2.15052e13	0.287806
$334$	1.89271e12	0.0249160
$335$	8.81651e12	0.114170
$336$	8.37975e12	0.106749
$337$	3.42343e13	0.429039	0.214520	−	0.976720i	$-0.431181\pi$
$337$	3.42343e13	0.429039	0.214520	+	0.976720i	$0.431181\pi$
$338$	8.82465e13	1.08807
$339$	−4.33844e13	−0.526302
$340$	5.88422e13	0.702353
$341$	2.34973e13	0.275974
$342$	1.29783e13	0.149994
$343$	8.43211e13	0.958999
$344$	−1.84467e12	−0.0206466
$345$	1.18017e13	0.129999
$346$	−3.37071e13	−0.365429
$347$	−7.09428e13	−0.757001	−0.378500	−	0.925601i	$-0.623560\pi$
$347$	−7.09428e13	−0.757001	−0.378500	+	0.925601i	$0.623560\pi$
$348$	−3.24732e13	−0.341066
$349$	−7.61162e13	−0.786932	−0.393466	−	0.919339i	$-0.628724\pi$
$349$	−7.61162e13	−0.786932	−0.393466	+	0.919339i	$0.628724\pi$
$350$	−9.20751e13	−0.937061
$351$	3.31076e13	0.331695
$352$	−3.12081e13	−0.307810
$353$	−3.44627e13	−0.334648	−0.167324	−	0.985902i	$-0.553513\pi$
$353$	−3.44627e13	−0.334648	−0.167324	+	0.985902i	$0.553513\pi$
$354$	4.34103e12	0.0415026
$355$	−2.53781e14	−2.38892
$356$	−3.70888e13	−0.343770
$357$	−4.08130e13	−0.372498
$358$	6.06508e13	0.545105
$359$	1.32771e14	1.17512	0.587561	−	0.809180i	$-0.300088\pi$
$359$	1.32771e14	1.17512	0.587561	+	0.809180i	$0.300088\pi$
$360$	−5.81219e13	−0.506613
$361$	−3.91237e13	−0.335853
$362$	−1.12581e13	−0.0951851
$363$	6.31919e13	0.526229
$364$	−1.51449e14	−1.24225
$365$	−3.18264e14	−2.57144
$366$	2.20999e13	0.175891
$367$	−4.06463e13	−0.318682	−0.159341	−	0.987224i	$-0.550937\pi$
$367$	−4.06463e13	−0.318682	−0.159341	+	0.987224i	$0.550937\pi$
$368$	−3.20133e12	−0.0247268
$369$	−8.38023e12	−0.0637692
$370$	1.03259e14	0.774135
$371$	−9.22421e13	−0.681353
$372$	−5.11419e13	−0.372212
$373$	1.60092e14	1.14808	0.574038	−	0.818828i	$-0.305376\pi$
$373$	1.60092e14	1.14808	0.574038	+	0.818828i	$0.305376\pi$
$374$	1.44675e13	0.102235
$375$	−8.57256e13	−0.596951
$376$	7.92755e12	0.0544009
$377$	2.16588e14	1.46473
$378$	1.65314e13	0.110181
$379$	−6.88174e13	−0.452046	−0.226023	−	0.974122i	$-0.572572\pi$
$379$	−6.88174e13	−0.452046	−0.226023	+	0.974122i	$0.572572\pi$
$380$	−1.42082e14	−0.919873
$381$	8.93070e13	0.569899
$382$	−1.86951e13	−0.117592
$383$	1.17164e14	0.726444	0.363222	−	0.931703i	$-0.381677\pi$
$383$	1.17164e14	0.726444	0.363222	+	0.931703i	$0.381677\pi$
$384$	7.72253e13	0.471995
$385$	8.31521e13	0.501001
$386$	−4.99443e13	−0.296658
$387$	1.25566e12	0.00735297
$388$	−5.70292e12	−0.0329248
$389$	−2.48888e14	−1.41671	−0.708355	−	0.705856i	$-0.750562\pi$
$389$	−2.48888e14	−1.41671	−0.708355	+	0.705856i	$0.750562\pi$
$390$	1.58969e14	0.892187
$391$	1.55919e13	0.0862831
$392$	−1.28823e13	−0.0702945
$393$	−1.99344e14	−1.07262
$394$	5.91361e13	0.313779
$395$	5.00498e14	2.61889
$396$	1.33612e13	0.0689478
$397$	−3.77720e14	−1.92230	−0.961151	−	0.276023i	$-0.910983\pi$
$397$	−3.77720e14	−1.92230	−0.961151	+	0.276023i	$0.910983\pi$
$398$	−2.16054e13	−0.108444
$399$	9.85479e13	0.487861
$400$	5.97739e13	0.291865
$401$	1.13652e14	0.547371	0.273686	−	0.961819i	$-0.411757\pi$
$401$	1.13652e14	0.547371	0.273686	+	0.961819i	$0.411757\pi$
$402$	−4.71803e12	−0.0224139
$403$	3.41104e14	1.59849
$404$	−1.94584e14	−0.899518
$405$	3.95635e13	0.180423
$406$	1.08148e14	0.486547
$407$	−5.78855e13	−0.256922
$408$	−7.67879e13	−0.336250
$409$	1.19370e14	0.515724	0.257862	−	0.966182i	$-0.416982\pi$
$409$	1.19370e14	0.515724	0.257862	+	0.966182i	$0.416982\pi$
$410$	−4.02383e13	−0.171525
$411$	−1.15722e14	−0.486728
$412$	−4.73482e13	−0.196503
$413$	3.29628e13	0.134989
$414$	−6.31552e12	−0.0255216
$415$	3.30885e14	1.31951
$416$	−4.53040e14	−1.78288
$417$	−1.22778e14	−0.476841
$418$	−3.49336e13	−0.133898
$419$	2.87309e14	1.08686	0.543428	−	0.839456i	$-0.317126\pi$
$419$	2.87309e14	1.08686	0.543428	+	0.839456i	$0.317126\pi$
$420$	−1.80980e14	−0.675710
$421$	3.25120e14	1.19810	0.599049	−	0.800712i	$-0.295545\pi$
$421$	3.25120e14	1.19810	0.599049	+	0.800712i	$0.295545\pi$
$422$	−2.33344e14	−0.848749
$423$	−5.39627e12	−0.0193741
$424$	−1.73549e14	−0.615050
$425$	−2.91125e14	−1.01845
$426$	1.35807e14	0.468997
$427$	1.67811e14	0.572094
$428$	−3.13667e14	−1.05567
$429$	−8.91158e13	−0.296101
$430$	6.02916e12	0.0197779
$431$	4.11329e14	1.33219	0.666093	−	0.745869i	$-0.267966\pi$
$431$	4.11329e14	1.33219	0.666093	+	0.745869i	$0.267966\pi$
$432$	−1.07320e13	−0.0343177
$433$	2.50637e13	0.0791337	0.0395669	−	0.999217i	$-0.487402\pi$
$433$	2.50637e13	0.0791337	0.0395669	+	0.999217i	$0.487402\pi$
$434$	1.70322e14	0.530977
$435$	2.58822e14	0.796729
$436$	−4.85507e13	−0.147577
$437$	−3.76484e13	−0.113005
$438$	1.70314e14	0.504828
$439$	9.80836e13	0.287106	0.143553	−	0.989643i	$-0.454147\pi$
$439$	9.80836e13	0.287106	0.143553	+	0.989643i	$0.454147\pi$
$440$	1.56447e14	0.452249
$441$	8.76898e12	0.0250344
$442$	2.10022e14	0.592163
$443$	−2.21763e14	−0.617546	−0.308773	−	0.951136i	$-0.599918\pi$
$443$	−2.21763e14	−0.617546	−0.308773	+	0.951136i	$0.599918\pi$
$444$	1.25988e14	0.346515
$445$	2.95610e14	0.803045
$446$	−7.45441e13	−0.200019
$447$	−9.76770e13	−0.258881
$448$	−1.55589e14	−0.407334
$449$	−1.67607e14	−0.433448	−0.216724	−	0.976233i	$-0.569537\pi$
$449$	−1.67607e14	−0.433448	−0.216724	+	0.976233i	$0.569537\pi$
$450$	1.17921e14	0.301246
$451$	2.25571e13	0.0569262
$452$	−2.54167e14	−0.633662
$453$	−1.94027e14	−0.477885
$454$	1.41425e14	0.344127
$455$	1.20710e15	2.90188
$456$	1.85413e14	0.440387
$457$	−6.66669e14	−1.56448	−0.782242	−	0.622974i	$-0.785924\pi$
$457$	−6.66669e14	−1.56448	−0.782242	+	0.622974i	$0.785924\pi$
$458$	1.38408e13	0.0320923
$459$	5.22693e13	0.119750
$460$	6.91402e13	0.156517
$461$	−5.09805e14	−1.14038	−0.570189	−	0.821513i	$-0.693130\pi$
$461$	−5.09805e14	−1.14038	−0.570189	+	0.821513i	$0.693130\pi$
$462$	−4.44977e13	−0.0983572
$463$	1.18421e13	0.0258662	0.0129331	−	0.999916i	$-0.495883\pi$
$463$	1.18421e13	0.0258662	0.0129331	+	0.999916i	$0.495883\pi$
$464$	−7.02080e13	−0.151544
$465$	4.07618e14	0.869486
$466$	−1.56663e14	−0.330251
$467$	−7.86087e14	−1.63767	−0.818837	−	0.574026i	$-0.805381\pi$
$467$	−7.86087e14	−1.63767	−0.818837	+	0.574026i	$0.805381\pi$
$468$	1.93961e14	0.399357
$469$	−3.58255e13	−0.0729023
$470$	−2.59106e13	−0.0521121
$471$	−4.60649e14	−0.915704
$472$	6.20181e13	0.121853
$473$	−3.37987e12	−0.00656393
$474$	−2.67834e14	−0.514144
$475$	7.02955e14	1.33387
$476$	−2.39103e14	−0.448483
$477$	1.18135e14	0.219041
$478$	−4.07721e14	−0.747325
$479$	−3.44582e14	−0.624377	−0.312188	−	0.950020i	$-0.601062\pi$
$479$	−3.44582e14	−0.624377	−0.312188	+	0.950020i	$0.601062\pi$
$480$	−5.41381e14	−0.969786
$481$	−8.40309e14	−1.48813
$482$	1.73250e12	0.00303329
$483$	−4.79557e13	−0.0830102
$484$	3.70209e14	0.633574
$485$	4.54542e13	0.0769121
$486$	−2.11718e13	−0.0354208
$487$	−6.12126e14	−1.01259	−0.506293	−	0.862362i	$-0.668984\pi$
$487$	−6.12126e14	−1.01259	−0.506293	+	0.862362i	$0.668984\pi$
$488$	3.15729e14	0.516423
$489$	−1.29155e14	−0.208887
$490$	4.21049e13	0.0673371
$491$	−8.24882e14	−1.30450	−0.652249	−	0.758005i	$-0.726174\pi$
$491$	−8.24882e14	−1.30450	−0.652249	+	0.758005i	$0.726174\pi$
$492$	−4.90955e13	−0.0767774
$493$	3.41944e14	0.528806
$494$	−5.07122e14	−0.775558
$495$	−1.06493e14	−0.161062
$496$	−1.10570e14	−0.165382
$497$	1.03123e15	1.52543
$498$	−1.77068e14	−0.259048
$499$	1.05005e15	1.51934	0.759670	−	0.650308i	$-0.225360\pi$
$499$	1.05005e15	1.51934	0.759670	+	0.650308i	$0.225360\pi$
$500$	−5.02223e14	−0.718723
$501$	−1.84062e13	−0.0260529
$502$	4.44773e14	0.622684
$503$	7.43308e14	1.02931	0.514653	−	0.857398i	$-0.327921\pi$
$503$	7.43308e14	1.02931	0.514653	+	0.857398i	$0.327921\pi$
$504$	2.36176e14	0.323495
$505$	1.55090e15	2.10127
$506$	1.69995e13	0.0227829
$507$	−8.58177e14	−1.13771
$508$	5.23204e14	0.686153
$509$	4.36328e14	0.566063	0.283032	−	0.959111i	$-0.408660\pi$
$509$	4.36328e14	0.566063	0.283032	+	0.959111i	$0.408660\pi$
$510$	2.50975e14	0.322103
$511$	1.29325e15	1.64198
$512$	2.79731e14	0.351363
$513$	−1.26211e14	−0.156838
$514$	6.55496e14	0.805885
$515$	3.77382e14	0.459030
$516$	7.35629e12	0.00885290
$517$	1.45251e13	0.0172951
$518$	−4.19586e14	−0.494319
$519$	3.27794e14	0.382103
$520$	2.27110e15	2.61950
$521$	−1.34886e15	−1.53942	−0.769712	−	0.638392i	$-0.779600\pi$
$521$	−1.34886e15	−1.53942	−0.769712	+	0.638392i	$0.779600\pi$
$522$	−1.38505e14	−0.156415
$523$	2.29606e14	0.256580	0.128290	−	0.991737i	$-0.459051\pi$
$523$	2.29606e14	0.256580	0.128290	+	0.991737i	$0.459051\pi$
$524$	−1.16786e15	−1.29142
$525$	8.95409e14	0.979818
$526$	8.14974e14	0.882516
$527$	5.38526e14	0.577096
$528$	2.88873e13	0.0306351
$529$	−9.34489e14	−0.980772
$530$	5.67232e14	0.589174
$531$	−4.22156e13	−0.0433963
$532$	5.77342e14	0.587380
$533$	3.27456e14	0.329726
$534$	−1.58192e14	−0.157655
$535$	2.50004e15	2.46604
$536$	−6.74040e13	−0.0658081
$537$	−5.89815e14	−0.569977
$538$	−5.86864e14	−0.561352
$539$	−2.36035e13	−0.0223480
$540$	2.31782e14	0.217227
$541$	1.15412e15	1.07069	0.535347	−	0.844632i	$-0.320181\pi$
$541$	1.15412e15	1.07069	0.535347	+	0.844632i	$0.320181\pi$
$542$	1.25472e14	0.115226
$543$	1.09483e14	0.0995282
$544$	−7.15247e14	−0.643668
$545$	3.86966e14	0.344740
$546$	−6.45961e14	−0.569701
$547$	2.08672e15	1.82194	0.910970	−	0.412472i	$-0.135335\pi$
$547$	2.08672e15	1.82194	0.910970	+	0.412472i	$0.135335\pi$
$548$	−6.77957e14	−0.586016
$549$	−2.14916e14	−0.183917
$550$	−3.17408e14	−0.268920
$551$	−8.25664e14	−0.692579
$552$	−9.02266e13	−0.0749324
$553$	−2.03375e15	−1.67228
$554$	4.25079e14	0.346071
$555$	−1.00417e15	−0.809457
$556$	−7.19296e14	−0.574112
$557$	5.49786e14	0.434500	0.217250	−	0.976116i	$-0.430291\pi$
$557$	5.49786e14	0.434500	0.217250	+	0.976116i	$0.430291\pi$
$558$	−2.18131e14	−0.170698
$559$	−4.90647e13	−0.0380193
$560$	−3.91286e14	−0.300234
$561$	−1.40694e14	−0.106900
$562$	−3.21985e14	−0.242262
$563$	1.07926e15	0.804134	0.402067	−	0.915610i	$-0.368292\pi$
$563$	1.07926e15	0.804134	0.402067	+	0.915610i	$0.368292\pi$
$564$	−3.16140e13	−0.0233262
$565$	2.02580e15	1.48023
$566$	1.17107e15	0.847411
$567$	−1.60764e14	−0.115208
$568$	1.94020e15	1.37699
$569$	1.60362e14	0.112716	0.0563578	−	0.998411i	$-0.482051\pi$
$569$	1.60362e14	0.112716	0.0563578	+	0.998411i	$0.482051\pi$
$570$	−6.06009e14	−0.421859
$571$	−2.36698e15	−1.63191	−0.815956	−	0.578115i	$-0.803789\pi$
$571$	−2.36698e15	−1.63191	−0.815956	+	0.578115i	$0.803789\pi$
$572$	−5.22084e14	−0.356502
$573$	1.81806e14	0.122958
$574$	1.63506e14	0.109527
$575$	−3.42075e14	−0.226959
$576$	1.99264e14	0.130950
$577$	−1.07977e15	−0.702854	−0.351427	−	0.936215i	$-0.614304\pi$
$577$	−1.07977e15	−0.702854	−0.351427	+	0.936215i	$0.614304\pi$
$578$	−5.24801e14	−0.338370
$579$	4.85697e14	0.310194
$580$	1.51631e15	0.959253
$581$	−1.34453e15	−0.842565
$582$	−2.43242e13	−0.0150995
$583$	−3.17983e14	−0.195536
$584$	2.43319e15	1.48220
$585$	−1.54593e15	−0.932896
$586$	1.83419e15	1.09650
$587$	2.34278e15	1.38746	0.693732	−	0.720233i	$-0.255965\pi$
$587$	2.34278e15	1.38746	0.693732	+	0.720233i	$0.255965\pi$
$588$	5.13730e13	0.0301411
$589$	−1.30033e15	−0.755824
$590$	−2.02701e14	−0.116727
$591$	−5.75085e14	−0.328096
$592$	2.72390e14	0.153965
$593$	−1.16395e14	−0.0651829	−0.0325915	−	0.999469i	$-0.510376\pi$
$593$	−1.16395e14	−0.0651829	−0.0325915	+	0.999469i	$0.510376\pi$
$594$	5.69883e13	0.0316199
$595$	1.90573e15	1.04766
$596$	−5.72240e14	−0.311690
$597$	2.10107e14	0.113392
$598$	2.46778e14	0.131962
$599$	−2.24089e15	−1.18734	−0.593668	−	0.804710i	$-0.702321\pi$
$599$	−2.24089e15	−1.18734	−0.593668	+	0.804710i	$0.702321\pi$
$600$	1.68467e15	0.884471
$601$	−1.18510e15	−0.616520	−0.308260	−	0.951302i	$-0.599747\pi$
$601$	−1.18510e15	−0.616520	−0.308260	+	0.951302i	$0.599747\pi$
$602$	−2.44992e13	−0.0126291
$603$	4.58818e13	0.0234366
$604$	−1.13671e15	−0.575368
$605$	−2.95069e15	−1.48003
$606$	−8.29944e14	−0.412524
$607$	3.64904e15	1.79738	0.898692	−	0.438581i	$-0.144519\pi$
$607$	3.64904e15	1.79738	0.898692	+	0.438581i	$0.144519\pi$
$608$	1.72705e15	0.843014
$609$	−1.05171e15	−0.508747
$610$	−1.03194e15	−0.494696
$611$	2.10858e14	0.100176
$612$	3.06219e14	0.144178
$613$	−2.47416e15	−1.15450	−0.577251	−	0.816566i	$-0.695875\pi$
$613$	−2.47416e15	−1.15450	−0.577251	+	0.816566i	$0.695875\pi$
$614$	8.94734e14	0.413778
$615$	3.91308e14	0.179352
$616$	−6.35715e14	−0.288781
$617$	2.04469e15	0.920577	0.460288	−	0.887769i	$-0.347746\pi$
$617$	2.04469e15	0.920577	0.460288	+	0.887769i	$0.347746\pi$
$618$	−2.01950e14	−0.0901173
$619$	1.43884e15	0.636374	0.318187	−	0.948028i	$-0.396926\pi$
$619$	1.43884e15	0.636374	0.318187	+	0.948028i	$0.396926\pi$
$620$	2.38803e15	1.04685
$621$	6.14170e13	0.0266861
$622$	−2.56424e14	−0.110436
$623$	−1.20120e15	−0.512780
$624$	4.19349e14	0.177444
$625$	1.00586e14	0.0421887
$626$	−2.34483e15	−0.974884
$627$	3.39721e14	0.140007
$628$	−2.69871e15	−1.10250
$629$	−1.32666e15	−0.537254
$630$	−7.71921e14	−0.309884
$631$	1.86730e15	0.743108	0.371554	−	0.928411i	$-0.378825\pi$
$631$	1.86730e15	0.743108	0.371554	+	0.928411i	$0.378825\pi$
$632$	−3.82641e15	−1.50955
$633$	2.26922e15	0.887476
$634$	−1.88297e15	−0.730050
$635$	−4.17012e15	−1.60285
$636$	6.92090e14	0.263723
$637$	−3.42646e14	−0.129443
$638$	3.72815e14	0.139630
$639$	−1.32069e15	−0.490396
$640$	−3.60597e15	−1.32749
$641$	−2.42900e15	−0.886561	−0.443281	−	0.896383i	$-0.646185\pi$
$641$	−2.42900e15	−0.886561	−0.443281	+	0.896383i	$0.646185\pi$
$642$	−1.33786e15	−0.484136
$643$	1.94259e15	0.696980	0.348490	−	0.937313i	$-0.386695\pi$
$643$	1.94259e15	0.696980	0.348490	+	0.937313i	$0.386695\pi$
$644$	−2.80948e14	−0.0999433
$645$	−5.86322e13	−0.0206803
$646$	−8.00630e14	−0.279997
$647$	2.89049e15	1.00230	0.501150	−	0.865360i	$-0.332910\pi$
$647$	2.89049e15	1.00230	0.501150	+	0.865360i	$0.332910\pi$
$648$	−3.02471e14	−0.103997
$649$	1.13632e14	0.0387395
$650$	−4.60773e15	−1.55763
$651$	−1.65634e15	−0.555205
$652$	−7.56653e14	−0.251498
$653$	4.48440e15	1.47803	0.739013	−	0.673691i	$-0.235292\pi$
$653$	4.48440e15	1.47803	0.739013	+	0.673691i	$0.235292\pi$
$654$	−2.07079e14	−0.0676798
$655$	9.30822e15	3.01675
$656$	−1.06146e14	−0.0341140
$657$	−1.65627e15	−0.527863
$658$	1.05286e14	0.0332759
$659$	6.73335e14	0.211038	0.105519	−	0.994417i	$-0.466350\pi$
$659$	6.73335e14	0.211038	0.105519	+	0.994417i	$0.466350\pi$
$660$	−6.23888e14	−0.193917
$661$	−2.74625e14	−0.0846508	−0.0423254	−	0.999104i	$-0.513477\pi$
$661$	−2.74625e14	−0.0846508	−0.0423254	+	0.999104i	$0.513477\pi$
$662$	−3.27308e15	−1.00055
$663$	−2.04241e15	−0.619183
$664$	−2.52968e15	−0.760574
$665$	−4.60161e15	−1.37212
$666$	5.37365e14	0.158914
$667$	4.01787e14	0.117843
$668$	−1.07832e14	−0.0313674
$669$	7.24924e14	0.209146
$670$	2.20305e14	0.0630394
$671$	5.78490e14	0.164181
$672$	2.19988e15	0.619251
$673$	−8.34894e14	−0.233103	−0.116552	−	0.993185i	$-0.537184\pi$
$673$	−8.34894e14	−0.233103	−0.116552	+	0.993185i	$0.537184\pi$
$674$	8.55438e14	0.236897
$675$	−1.14675e15	−0.314992
$676$	−5.02762e15	−1.36979
$677$	3.97083e15	1.07311	0.536554	−	0.843866i	$-0.319726\pi$
$677$	3.97083e15	1.07311	0.536554	+	0.843866i	$0.319726\pi$
$678$	−1.08408e15	−0.290601
$679$	−1.84701e14	−0.0491118
$680$	3.58555e15	0.945707
$681$	−1.37532e15	−0.359829
$682$	5.87144e14	0.152381
$683$	−1.11756e15	−0.287711	−0.143856	−	0.989599i	$-0.545950\pi$
$683$	−1.11756e15	−0.287711	−0.143856	+	0.989599i	$0.545950\pi$
$684$	−7.39403e14	−0.188831
$685$	5.40355e15	1.36893
$686$	2.10699e15	0.529518
$687$	−1.34599e14	−0.0335566
$688$	1.59045e13	0.00393355
$689$	−4.61608e15	−1.13258
$690$	2.94898e14	0.0717798
$691$	1.51192e15	0.365089	0.182545	−	0.983198i	$-0.441567\pi$
$691$	1.51192e15	0.365089	0.182545	+	0.983198i	$0.441567\pi$
$692$	1.92038e15	0.460047
$693$	4.32730e14	0.102845
$694$	−1.77270e15	−0.417983
$695$	5.73304e15	1.34112
$696$	−1.97875e15	−0.459240
$697$	5.16978e14	0.119040
$698$	−1.90197e15	−0.434509
$699$	1.52351e15	0.345320
$700$	5.24575e15	1.17969
$701$	7.06634e15	1.57669	0.788343	−	0.615236i	$-0.210939\pi$
$701$	7.06634e15	1.57669	0.788343	+	0.615236i	$0.210939\pi$
$702$	8.27284e14	0.183147
$703$	3.20337e15	0.703643
$704$	−5.36358e14	−0.116898
$705$	2.51974e14	0.0544899
$706$	−8.61144e14	−0.184778
$707$	−6.30202e15	−1.34175
$708$	−2.47319e14	−0.0522487
$709$	8.67632e15	1.81878	0.909392	−	0.415939i	$-0.136547\pi$
$709$	8.67632e15	1.81878	0.909392	+	0.415939i	$0.136547\pi$
$710$	−6.34140e15	−1.31906
$711$	2.60463e15	0.537604
$712$	−2.26000e15	−0.462881
$713$	6.32773e14	0.128604
$714$	−1.01983e15	−0.205677
$715$	4.16119e15	0.832788
$716$	−3.45543e15	−0.686246
$717$	3.96499e15	0.781424
$718$	3.31764e15	0.648851
$719$	−2.70240e15	−0.524495	−0.262247	−	0.965001i	$-0.584464\pi$
$719$	−2.70240e15	−0.524495	−0.262247	+	0.965001i	$0.584464\pi$
$720$	5.01120e14	0.0965191
$721$	−1.53347e15	−0.293111
$722$	−9.77612e14	−0.185444
$723$	−1.68481e13	−0.00317169
$724$	6.41403e14	0.119831
$725$	−7.50201e15	−1.39097
$726$	1.57902e15	0.290561
$727$	3.41265e15	0.623236	0.311618	−	0.950207i	$-0.399129\pi$
$727$	3.41265e15	0.623236	0.311618	+	0.950207i	$0.399129\pi$
$728$	−9.22851e15	−1.67266
$729$	2.05891e14	0.0370370
$730$	−7.95269e15	−1.41984
$731$	−7.74620e13	−0.0137260
$732$	−1.25908e15	−0.221434
$733$	−9.45746e15	−1.65083	−0.825416	−	0.564525i	$-0.809059\pi$
$733$	−9.45746e15	−1.65083	−0.825416	+	0.564525i	$0.809059\pi$
$734$	−1.01566e15	−0.175962
$735$	−4.09461e14	−0.0704096
$736$	−8.40422e14	−0.143440
$737$	−1.23500e14	−0.0209217
$738$	−2.09403e14	−0.0352106
$739$	2.54064e14	0.0424033	0.0212016	−	0.999775i	$-0.493251\pi$
$739$	2.54064e14	0.0424033	0.0212016	+	0.999775i	$0.493251\pi$
$740$	−5.88289e15	−0.974578
$741$	4.93165e15	0.810946
$742$	−2.30492e15	−0.376214
$743$	−8.07197e15	−1.30780	−0.653900	−	0.756581i	$-0.726868\pi$
$743$	−8.07197e15	−1.30780	−0.653900	+	0.756581i	$0.726868\pi$
$744$	−3.11633e15	−0.501178
$745$	4.56095e15	0.728108
$746$	4.00034e15	0.633918
$747$	1.72195e15	0.270867
$748$	−8.24252e14	−0.128707
$749$	−1.01588e16	−1.57468
$750$	−2.14209e15	−0.329610
$751$	4.23375e15	0.646705	0.323352	−	0.946279i	$-0.395190\pi$
$751$	4.23375e15	0.646705	0.323352	+	0.946279i	$0.395190\pi$
$752$	−6.83504e13	−0.0103644
$753$	−4.32531e15	−0.651096
$754$	5.41205e15	0.808760
$755$	9.05995e15	1.34406
$756$	−9.41835e14	−0.138709
$757$	8.54159e15	1.24885	0.624427	−	0.781083i	$-0.285333\pi$
$757$	8.54159e15	1.24885	0.624427	+	0.781083i	$0.285333\pi$
$758$	−1.71959e15	−0.249600
$759$	−1.65316e14	−0.0238224
$760$	−8.65773e15	−1.23859
$761$	−7.25893e15	−1.03100	−0.515498	−	0.856891i	$-0.672393\pi$
$761$	−7.25893e15	−1.03100	−0.515498	+	0.856891i	$0.672393\pi$
$762$	2.23158e15	0.314673
$763$	−1.57242e15	−0.220132
$764$	1.06511e15	0.148040
$765$	−2.44067e15	−0.336800
$766$	2.92767e15	0.401110
$767$	1.64956e15	0.224385
$768$	3.60907e15	0.487426
$769$	−9.20046e15	−1.23371	−0.616857	−	0.787075i	$-0.711595\pi$
$769$	−9.20046e15	−1.23371	−0.616857	+	0.787075i	$0.711595\pi$
$770$	2.07778e15	0.276631
$771$	−6.37455e15	−0.842656
$772$	2.84545e15	0.373470
$773$	1.01836e16	1.32713	0.663565	−	0.748118i	$-0.269043\pi$
$773$	1.01836e16	1.32713	0.663565	+	0.748118i	$0.269043\pi$
$774$	3.13762e13	0.00405999
$775$	−1.18149e16	−1.51799
$776$	−3.47507e14	−0.0443327
$777$	4.08038e15	0.516874
$778$	−6.21915e15	−0.782245
$779$	−1.24830e15	−0.155906
$780$	−9.05683e15	−1.12320
$781$	3.55491e15	0.437772
$782$	3.89606e14	0.0476418
$783$	1.34693e15	0.163552
$784$	1.11070e14	0.0133924
$785$	2.15096e16	2.57543
$786$	−4.98116e15	−0.592252
$787$	−1.49460e16	−1.76467	−0.882336	−	0.470620i	$-0.844030\pi$
$787$	−1.49460e16	−1.76467	−0.882336	+	0.470620i	$0.844030\pi$
$788$	−3.36913e15	−0.395024
$789$	−7.92544e15	−0.922783
$790$	1.25063e16	1.44604
$791$	−8.23174e15	−0.945194
$792$	8.14161e14	0.0928372
$793$	8.39780e15	0.950961
$794$	−9.43836e15	−1.06141
$795$	−5.51620e15	−0.616057
$796$	1.23091e15	0.136523
$797$	−1.60985e16	−1.77323	−0.886613	−	0.462512i	$-0.846948\pi$
$797$	−1.60985e16	−1.77323	−0.886613	+	0.462512i	$0.846948\pi$
$798$	2.46249e15	0.269376
$799$	3.32896e14	0.0361661
$800$	1.56920e16	1.69310
$801$	1.53838e15	0.164848
$802$	2.83990e15	0.302234
$803$	4.45818e15	0.471218
$804$	2.68798e14	0.0282174
$805$	2.23925e15	0.233467
$806$	8.52342e15	0.882615
$807$	5.70712e15	0.586965
$808$	−1.18570e16	−1.21119
$809$	1.31507e16	1.33424	0.667119	−	0.744951i	$-0.267527\pi$
$809$	1.31507e16	1.33424	0.667119	+	0.744951i	$0.267527\pi$
$810$	9.88601e14	0.0996216
$811$	1.83930e16	1.84093	0.920466	−	0.390823i	$-0.127809\pi$
$811$	1.83930e16	1.84093	0.920466	+	0.390823i	$0.127809\pi$
$812$	−6.16144e15	−0.612526
$813$	−1.22019e15	−0.120484
$814$	−1.44643e15	−0.141861
$815$	6.03078e15	0.587499
$816$	6.62056e14	0.0640618
$817$	1.87041e14	0.0179770
$818$	2.98279e15	0.284760
$819$	6.28182e15	0.595695
$820$	2.29247e15	0.215938
$821$	2.16713e15	0.202768	0.101384	−	0.994847i	$-0.467673\pi$
$821$	2.16713e15	0.202768	0.101384	+	0.994847i	$0.467673\pi$
$822$	−2.89164e15	−0.268750
$823$	−1.42522e16	−1.31578	−0.657891	−	0.753113i	$-0.728551\pi$
$823$	−1.42522e16	−1.31578	−0.657891	+	0.753113i	$0.728551\pi$
$824$	−2.88516e15	−0.264588
$825$	3.08672e15	0.281190
$826$	8.23666e14	0.0745351
$827$	1.02767e16	0.923789	0.461894	−	0.886935i	$-0.347170\pi$
$827$	1.02767e16	0.923789	0.461894	+	0.886935i	$0.347170\pi$
$828$	3.59811e14	0.0321298
$829$	−1.09609e16	−0.972290	−0.486145	−	0.873878i	$-0.661597\pi$
$829$	−1.09609e16	−0.972290	−0.486145	+	0.873878i	$0.661597\pi$
$830$	8.26806e15	0.728575
$831$	−4.13379e15	−0.361862
$832$	−7.78617e15	−0.677089
$833$	−5.40960e14	−0.0467323
$834$	−3.06796e15	−0.263291
$835$	8.59461e14	0.0732741
$836$	1.99025e15	0.168567
$837$	2.12128e15	0.178487
$838$	7.17920e15	0.600115
$839$	−3.71803e15	−0.308761	−0.154380	−	0.988011i	$-0.549338\pi$
$839$	−3.71803e15	−0.308761	−0.154380	+	0.988011i	$0.549338\pi$
$840$	−1.10280e16	−0.909833
$841$	−3.38895e15	−0.277771
$842$	8.12402e15	0.661537
$843$	3.13123e15	0.253316
$844$	1.32942e16	1.06851
$845$	4.00719e16	3.19983
$846$	−1.34840e14	−0.0106975
$847$	1.19900e16	0.945063
$848$	1.49632e15	0.117178
$849$	−1.13884e16	−0.886077
$850$	−7.27455e15	−0.562344
$851$	−1.55883e15	−0.119726
$852$	−7.73726e15	−0.590432
$853$	−1.95258e16	−1.48043	−0.740216	−	0.672370i	$-0.765277\pi$
$853$	−1.95258e16	−1.48043	−0.740216	+	0.672370i	$0.765277\pi$
$854$	4.19322e15	0.315885
$855$	5.89330e15	0.441108
$856$	−1.91133e16	−1.42144
$857$	2.10648e16	1.55655	0.778275	−	0.627924i	$-0.216095\pi$
$857$	2.10648e16	1.55655	0.778275	+	0.627924i	$0.216095\pi$
$858$	−2.22680e15	−0.163494
$859$	4.27980e15	0.312220	0.156110	−	0.987740i	$-0.450105\pi$
$859$	4.27980e15	0.312220	0.156110	+	0.987740i	$0.450105\pi$
$860$	−3.43496e14	−0.0248989
$861$	−1.59006e15	−0.114524
$862$	1.02782e16	0.735574
$863$	−1.94699e16	−1.38454	−0.692270	−	0.721639i	$-0.743389\pi$
$863$	−1.94699e16	−1.38454	−0.692270	+	0.721639i	$0.743389\pi$
$864$	−2.81739e15	−0.199077
$865$	−1.53061e16	−1.07467
$866$	6.26285e14	0.0436942
$867$	5.10357e15	0.353809
$868$	−9.70364e15	−0.668461
$869$	−7.01088e15	−0.479914
$870$	6.46738e15	0.439919
$871$	−1.79282e15	−0.121182
$872$	−2.95843e15	−0.198711
$873$	2.36547e14	0.0157884
$874$	−9.40749e14	−0.0623966
$875$	−1.62656e16	−1.07207
$876$	−9.70323e15	−0.635541
$877$	−1.03948e16	−0.676580	−0.338290	−	0.941042i	$-0.609849\pi$
$877$	−1.03948e16	−0.676580	−0.338290	+	0.941042i	$0.609849\pi$
$878$	2.45089e15	0.158527
$879$	−1.78371e16	−1.14653
$880$	−1.34887e15	−0.0861617
$881$	−1.97751e16	−1.25531	−0.627654	−	0.778492i	$-0.715985\pi$
$881$	−1.97751e16	−1.25531	−0.627654	+	0.778492i	$0.715985\pi$
$882$	2.19117e14	0.0138229
$883$	9.09389e15	0.570120	0.285060	−	0.958510i	$-0.407987\pi$
$883$	9.09389e15	0.570120	0.285060	+	0.958510i	$0.407987\pi$
$884$	−1.19654e16	−0.745490
$885$	1.97122e15	0.122053
$886$	−5.54136e15	−0.340982
$887$	−2.81999e15	−0.172452	−0.0862259	−	0.996276i	$-0.527481\pi$
$887$	−2.81999e15	−0.172452	−0.0862259	+	0.996276i	$0.527481\pi$
$888$	7.67705e15	0.466577
$889$	1.69451e16	1.02349
$890$	7.38664e15	0.443406
$891$	−5.54198e14	−0.0330626
$892$	4.24696e15	0.251809
$893$	−8.03818e14	−0.0473669
$894$	−2.44073e15	−0.142943
$895$	2.75409e16	1.60307
$896$	1.46527e16	0.847663
$897$	−2.39986e15	−0.137983
$898$	−4.18812e15	−0.239331
$899$	1.38773e16	0.788182
$900$	−6.71824e15	−0.379247
$901$	−7.28774e15	−0.408890
$902$	5.63651e14	0.0314321
$903$	2.38249e14	0.0132053
$904$	−1.54876e16	−0.853216
$905$	−5.11220e15	−0.279924
$906$	−4.84831e15	−0.263867
$907$	4.87855e15	0.263907	0.131953	−	0.991256i	$-0.457875\pi$
$907$	4.87855e15	0.263907	0.131953	+	0.991256i	$0.457875\pi$
$908$	−8.05732e15	−0.433230
$909$	8.07101e15	0.431347
$910$	3.01626e16	1.60229
$911$	2.85112e16	1.50545	0.752723	−	0.658337i	$-0.228740\pi$
$911$	2.85112e16	1.50545	0.752723	+	0.658337i	$0.228740\pi$
$912$	−1.59861e15	−0.0839019
$913$	−4.63497e15	−0.241801
$914$	−1.66586e16	−0.863840
$915$	1.00353e16	0.517268
$916$	−7.88545e14	−0.0404018
$917$	−3.78235e16	−1.92633
$918$	1.30609e15	0.0661210
$919$	−1.16794e16	−0.587741	−0.293870	−	0.955845i	$-0.594943\pi$
$919$	−1.16794e16	−0.587741	−0.293870	+	0.955845i	$0.594943\pi$
$920$	4.21306e15	0.210748
$921$	−8.70108e15	−0.432658
$922$	−1.27389e16	−0.629667
$923$	5.16058e16	2.53565
$924$	2.53514e15	0.123824
$925$	2.91059e16	1.41319
$926$	2.95907e14	0.0142822
$927$	1.96392e15	0.0942292
$928$	−1.84312e16	−0.879103
$929$	−9.14172e14	−0.0433453	−0.0216726	−	0.999765i	$-0.506899\pi$
$929$	−9.14172e14	−0.0433453	−0.0216726	+	0.999765i	$0.506899\pi$
$930$	1.01855e16	0.480092
$931$	1.30621e15	0.0612055
$932$	8.92548e15	0.415761
$933$	2.49366e15	0.115475
$934$	−1.96425e16	−0.904252
$935$	6.56957e15	0.300658
$936$	1.18190e16	0.537728
$937$	−3.46960e16	−1.56932	−0.784661	−	0.619925i	$-0.787163\pi$
$937$	−3.46960e16	−1.56932	−0.784661	+	0.619925i	$0.787163\pi$
$938$	−8.95198e14	−0.0402535
$939$	2.28030e16	1.01937
$940$	1.47619e15	0.0656053
$941$	1.95869e16	0.865413	0.432707	−	0.901535i	$-0.357559\pi$
$941$	1.95869e16	0.865413	0.432707	+	0.901535i	$0.357559\pi$
$942$	−1.15106e16	−0.505612
$943$	6.07454e14	0.0265277
$944$	−5.34713e14	−0.0232153
$945$	7.50675e15	0.324024
$946$	−8.44554e13	−0.00362432
$947$	1.54606e16	0.659631	0.329816	−	0.944045i	$-0.393013\pi$
$947$	1.54606e16	0.659631	0.329816	+	0.944045i	$0.393013\pi$
$948$	1.52592e16	0.647270
$949$	6.47183e16	2.72937
$950$	1.75653e16	0.736504
$951$	1.83115e16	0.763361
$952$	−1.45697e16	−0.603876
$953$	−2.84619e16	−1.17288	−0.586439	−	0.809994i	$-0.699470\pi$
$953$	−2.84619e16	−1.17288	−0.586439	+	0.809994i	$0.699470\pi$
$954$	2.95192e15	0.120945
$955$	−8.48927e15	−0.345821
$956$	2.32289e16	0.940826
$957$	−3.62554e15	−0.146001
$958$	−8.61031e15	−0.344754
$959$	−2.19571e16	−0.874123
$960$	−9.30445e15	−0.368298
$961$	−3.55319e15	−0.139843
$962$	−2.09974e16	−0.821681
$963$	1.30104e16	0.506227
$964$	−9.87045e13	−0.00381868
$965$	−2.26792e16	−0.872425
$966$	−1.19831e15	−0.0458346
$967$	3.63956e16	1.38421	0.692106	−	0.721796i	$-0.256683\pi$
$967$	3.63956e16	1.38421	0.692106	+	0.721796i	$0.256683\pi$
$968$	2.25587e16	0.853098
$969$	7.78594e15	0.292773
$970$	1.13580e15	0.0424675
$971$	−4.89750e15	−0.182083	−0.0910414	−	0.995847i	$-0.529020\pi$
$971$	−4.89750e15	−0.182083	−0.0910414	+	0.995847i	$0.529020\pi$
$972$	1.20621e15	0.0445922
$973$	−2.32959e16	−0.856366
$974$	−1.52956e16	−0.559105
$975$	4.48091e16	1.62870
$976$	−2.72218e15	−0.0983882
$977$	−7.30223e15	−0.262443	−0.131222	−	0.991353i	$-0.541890\pi$
$977$	−7.30223e15	−0.262443	−0.131222	+	0.991353i	$0.541890\pi$
$978$	−3.22729e15	−0.115338
$979$	−4.14086e15	−0.147159
$980$	−2.39882e15	−0.0847724
$981$	2.01380e15	0.0707679
$982$	−2.06119e16	−0.720287
$983$	2.87349e16	0.998541	0.499271	−	0.866446i	$-0.333601\pi$
$983$	2.87349e16	0.998541	0.499271	+	0.866446i	$0.333601\pi$
$984$	−2.99163e15	−0.103380
$985$	2.68531e16	0.922774
$986$	8.54440e15	0.291984
$987$	−1.02389e15	−0.0347942
$988$	2.88920e16	0.976370
$989$	−9.10187e13	−0.00305880
$990$	−2.66102e15	−0.0889313
$991$	4.57403e16	1.52018	0.760089	−	0.649820i	$-0.225156\pi$
$991$	4.57403e16	1.52018	0.760089	+	0.649820i	$0.225156\pi$
$992$	−2.90272e16	−0.959382
$993$	3.18299e16	1.04620
$994$	2.57680e16	0.842278
$995$	−9.81079e15	−0.318917
$996$	1.00880e16	0.326122
$997$	5.16771e16	1.66140	0.830701	−	0.556719i	$-0.187940\pi$
$997$	5.16771e16	1.66140	0.830701	+	0.556719i	$0.187940\pi$
$998$	2.62383e16	0.838914
$999$	−5.22575e15	−0.166165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.18	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +283528. q^{10} -158942. q^{11} +345938. q^{12} -2.30733e6 q^{13} -1.15210e6 q^{14} -2.75724e6 q^{15} +747929. q^{16} -3.64274e6 q^{17} +1.47550e6 q^{18} +8.79583e6 q^{19} -1.61533e7 q^{20} +1.12039e7 q^{21} -3.97161e6 q^{22} -4.28026e6 q^{23} +2.10797e7 q^{24} +7.99192e7 q^{25} -5.76548e7 q^{26} -1.43489e7 q^{27} +6.56381e7 q^{28} -9.38699e7 q^{29} -6.88973e7 q^{30} -1.47835e8 q^{31} +1.96348e8 q^{32} +3.86230e7 q^{33} -9.10238e7 q^{34} -5.23159e8 q^{35} -8.40629e7 q^{36} +3.64192e8 q^{37} +2.19788e8 q^{38} +5.60680e8 q^{39} -9.84300e8 q^{40} -1.41920e8 q^{41} +2.79961e8 q^{42} +2.12648e7 q^{43} +2.26272e8 q^{44} +6.70011e8 q^{45} -1.06954e8 q^{46} -9.13862e7 q^{47} -1.81747e8 q^{48} +1.48504e8 q^{49} +1.99700e9 q^{50} +8.85186e8 q^{51} +3.28474e9 q^{52} +2.00062e9 q^{53} -3.58547e8 q^{54} -1.80347e9 q^{55} +3.99966e9 q^{56} -2.13739e9 q^{57} -2.34560e9 q^{58} -7.14924e8 q^{59} +3.92525e9 q^{60} -3.63962e9 q^{61} -3.69407e9 q^{62} -2.72256e9 q^{63} +3.37455e9 q^{64} -2.61805e10 q^{65} +9.65101e8 q^{66} +7.77012e8 q^{67} +5.18585e9 q^{68} +1.04010e9 q^{69} -1.30725e10 q^{70} -2.23660e10 q^{71} -5.12237e9 q^{72} -2.80490e10 q^{73} +9.10033e9 q^{74} -1.94204e10 q^{75} -1.25219e10 q^{76} +7.32831e9 q^{77} +1.40101e10 q^{78} +4.41096e10 q^{79} +8.48652e9 q^{80} +3.48678e9 q^{81} -3.54626e9 q^{82} +2.91614e10 q^{83} -1.59501e10 q^{84} -4.13330e10 q^{85} +5.31358e8 q^{86} +2.28104e10 q^{87} +1.37879e10 q^{88} +2.60526e10 q^{89} +1.67420e10 q^{90} +1.06383e11 q^{91} +6.09343e9 q^{92} +3.59240e10 q^{93} -2.28354e9 q^{94} +9.98035e10 q^{95} -4.77127e10 q^{96} +4.00595e9 q^{97} +3.71077e9 q^{98} -9.38539e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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