LMFDB - Embedded newform 177.12.a.d.1.13

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:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-7.28530 q^{2} +243.000 q^{3} -1994.92 q^{4} +6136.55 q^{5} -1770.33 q^{6} -33718.8 q^{7} +29453.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-7.28530 q^{2} +243.000 q^{3} -1994.92 q^{4} +6136.55 q^{5} -1770.33 q^{6} -33718.8 q^{7} +29453.9 q^{8} +59049.0 q^{9} -44706.7 q^{10} +984083. q^{11} -484767. q^{12} -2.05640e6 q^{13} +245652. q^{14} +1.49118e6 q^{15} +3.87102e6 q^{16} +6.23478e6 q^{17} -430190. q^{18} +175904. q^{19} -1.22420e7 q^{20} -8.19368e6 q^{21} -7.16934e6 q^{22} +8.59617e6 q^{23} +7.15730e6 q^{24} -1.11708e7 q^{25} +1.49815e7 q^{26} +1.43489e7 q^{27} +6.72665e7 q^{28} -9.86614e7 q^{29} -1.08637e7 q^{30} +3.66929e7 q^{31} -8.85232e7 q^{32} +2.39132e8 q^{33} -4.54223e7 q^{34} -2.06917e8 q^{35} -1.17798e8 q^{36} +5.41747e8 q^{37} -1.28151e6 q^{38} -4.99704e8 q^{39} +1.80746e8 q^{40} -2.76260e8 q^{41} +5.96934e7 q^{42} -4.46177e8 q^{43} -1.96317e9 q^{44} +3.62357e8 q^{45} -6.26257e7 q^{46} +1.06691e8 q^{47} +9.40659e8 q^{48} -8.40367e8 q^{49} +8.13828e7 q^{50} +1.51505e9 q^{51} +4.10235e9 q^{52} -2.52362e8 q^{53} -1.04536e8 q^{54} +6.03888e9 q^{55} -9.93152e8 q^{56} +4.27446e7 q^{57} +7.18778e8 q^{58} +7.14924e8 q^{59} -2.97480e9 q^{60} +1.18084e10 q^{61} -2.67319e8 q^{62} -1.99106e9 q^{63} -7.28294e9 q^{64} -1.26192e10 q^{65} -1.74215e9 q^{66} -3.55842e9 q^{67} -1.24379e10 q^{68} +2.08887e9 q^{69} +1.50746e9 q^{70} -3.31645e9 q^{71} +1.73923e9 q^{72} -8.37143e9 q^{73} -3.94679e9 q^{74} -2.71451e9 q^{75} -3.50915e8 q^{76} -3.31821e10 q^{77} +3.64050e9 q^{78} -2.44696e9 q^{79} +2.37548e10 q^{80} +3.48678e9 q^{81} +2.01264e9 q^{82} +5.29385e10 q^{83} +1.63458e10 q^{84} +3.82601e10 q^{85} +3.25053e9 q^{86} -2.39747e10 q^{87} +2.89851e10 q^{88} +5.01235e10 q^{89} -2.63988e9 q^{90} +6.93393e10 q^{91} -1.71487e10 q^{92} +8.91637e9 q^{93} -7.77278e8 q^{94} +1.07944e9 q^{95} -2.15111e10 q^{96} -9.10022e10 q^{97} +6.12233e9 q^{98} +5.81091e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	−7.28530	−0.160984	−0.0804920	−	0.996755i	$-0.525649\pi$
$2$	−7.28530	−0.160984	−0.0804920	+	0.996755i	$0.525649\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1994.92	−0.974084
$5$	6136.55	0.878192	0.439096	−	0.898440i	$-0.355299\pi$
$5$	6136.55	0.878192	0.439096	+	0.898440i	$0.355299\pi$
$6$	−1770.33	−0.0929441
$7$	−33718.8	−0.758287	−0.379143	−	0.925338i	$-0.623781\pi$
$7$	−33718.8	−0.758287	−0.379143	+	0.925338i	$0.623781\pi$
$8$	29453.9	0.317796
$9$	59049.0	0.333333
$10$	−44706.7	−0.141375
$11$	984083.	1.84235	0.921174	−	0.389150i	$-0.127231\pi$
$11$	984083.	1.84235	0.921174	+	0.389150i	$0.127231\pi$
$12$	−484767.	−0.562388
$13$	−2.05640e6	−1.53610	−0.768048	−	0.640393i	$-0.778772\pi$
$13$	−2.05640e6	−1.53610	−0.768048	+	0.640393i	$0.778772\pi$
$14$	245652.	0.122072
$15$	1.49118e6	0.507025
$16$	3.87102e6	0.922924
$17$	6.23478e6	1.06501	0.532503	−	0.846428i	$-0.321252\pi$
$17$	6.23478e6	1.06501	0.532503	+	0.846428i	$0.321252\pi$
$18$	−430190.	−0.0536613
$19$	175904.	0.0162979	0.00814893	−	0.999967i	$-0.497406\pi$
$19$	175904.	0.0162979	0.00814893	+	0.999967i	$0.497406\pi$
$20$	−1.22420e7	−0.855433
$21$	−8.19368e6	−0.437797
$22$	−7.16934e6	−0.296589
$23$	8.59617e6	0.278485	0.139242	−	0.990258i	$-0.455533\pi$
$23$	8.59617e6	0.278485	0.139242	+	0.990258i	$0.455533\pi$
$24$	7.15730e6	0.183480
$25$	−1.11708e7	−0.228778
$26$	1.49815e7	0.247287
$27$	1.43489e7	0.192450
$28$	6.72665e7	0.738635
$29$	−9.86614e7	−0.893219	−0.446610	−	0.894729i	$-0.647369\pi$
$29$	−9.86614e7	−0.893219	−0.446610	+	0.894729i	$0.647369\pi$
$30$	−1.08637e7	−0.0816228
$31$	3.66929e7	0.230193	0.115097	−	0.993354i	$-0.463282\pi$
$31$	3.66929e7	0.230193	0.115097	+	0.993354i	$0.463282\pi$
$32$	−8.85232e7	−0.466372
$33$	2.39132e8	1.06368
$34$	−4.54223e7	−0.171449
$35$	−2.06917e8	−0.665921
$36$	−1.17798e8	−0.324695
$37$	5.41747e8	1.28436	0.642181	−	0.766553i	$-0.278030\pi$
$37$	5.41747e8	1.28436	0.642181	+	0.766553i	$0.278030\pi$
$38$	−1.28151e6	−0.00262369
$39$	−4.99704e8	−0.886865
$40$	1.80746e8	0.279086
$41$	−2.76260e8	−0.372397	−0.186199	−	0.982512i	$-0.559617\pi$
$41$	−2.76260e8	−0.372397	−0.186199	+	0.982512i	$0.559617\pi$
$42$	5.96934e7	0.0704783
$43$	−4.46177e8	−0.462839	−0.231420	−	0.972854i	$-0.574337\pi$
$43$	−4.46177e8	−0.462839	−0.231420	+	0.972854i	$0.574337\pi$
$44$	−1.96317e9	−1.79460
$45$	3.62357e8	0.292731
$46$	−6.26257e7	−0.0448316
$47$	1.06691e8	0.0678564	0.0339282	−	0.999424i	$-0.489198\pi$
$47$	1.06691e8	0.0678564	0.0339282	+	0.999424i	$0.489198\pi$
$48$	9.40659e8	0.532850
$49$	−8.40367e8	−0.425002
$50$	8.13828e7	0.0368296
$51$	1.51505e9	0.614881
$52$	4.10235e9	1.49629
$53$	−2.52362e8	−0.0828910	−0.0414455	−	0.999141i	$-0.513196\pi$
$53$	−2.52362e8	−0.0828910	−0.0414455	+	0.999141i	$0.513196\pi$
$54$	−1.04536e8	−0.0309814
$55$	6.03888e9	1.61794
$56$	−9.93152e8	−0.240980
$57$	4.27446e7	0.00940957
$58$	7.18778e8	0.143794
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−2.97480e9	−0.493885
$61$	1.18084e10	1.79009	0.895046	−	0.445974i	$-0.147143\pi$
$61$	1.18084e10	1.79009	0.895046	+	0.445974i	$0.147143\pi$
$62$	−2.67319e8	−0.0370574
$63$	−1.99106e9	−0.252762
$64$	−7.28294e9	−0.847846
$65$	−1.26192e10	−1.34899
$66$	−1.74215e9	−0.171236
$67$	−3.55842e9	−0.321992	−0.160996	−	0.986955i	$-0.551471\pi$
$67$	−3.55842e9	−0.321992	−0.160996	+	0.986955i	$0.551471\pi$
$68$	−1.24379e10	−1.03741
$69$	2.08887e9	0.160783
$70$	1.50746e9	0.107203
$71$	−3.31645e9	−0.218149	−0.109074	−	0.994034i	$-0.534789\pi$
$71$	−3.31645e9	−0.218149	−0.109074	+	0.994034i	$0.534789\pi$
$72$	1.73923e9	0.105932
$73$	−8.37143e9	−0.472633	−0.236316	−	0.971676i	$-0.575940\pi$
$73$	−8.37143e9	−0.472633	−0.236316	+	0.971676i	$0.575940\pi$
$74$	−3.94679e9	−0.206762
$75$	−2.71451e9	−0.132085
$76$	−3.50915e8	−0.0158755
$77$	−3.31821e10	−1.39703
$78$	3.64050e9	0.142771
$79$	−2.44696e9	−0.0894700	−0.0447350	−	0.998999i	$-0.514244\pi$
$79$	−2.44696e9	−0.0894700	−0.0447350	+	0.998999i	$0.514244\pi$
$80$	2.37548e10	0.810505
$81$	3.48678e9	0.111111
$82$	2.01264e9	0.0599500
$83$	5.29385e10	1.47517	0.737585	−	0.675255i	$-0.235966\pi$
$83$	5.29385e10	1.47517	0.737585	+	0.675255i	$0.235966\pi$
$84$	1.63458e10	0.426451
$85$	3.82601e10	0.935280
$86$	3.25053e9	0.0745097
$87$	−2.39747e10	−0.515700
$88$	2.89851e10	0.585491
$89$	5.01235e10	0.951473	0.475737	−	0.879588i	$-0.342182\pi$
$89$	5.01235e10	0.951473	0.475737	+	0.879588i	$0.342182\pi$
$90$	−2.63988e9	−0.0471250
$91$	6.93393e10	1.16480
$92$	−1.71487e10	−0.271268
$93$	8.91637e9	0.132902
$94$	−7.77278e8	−0.0109238
$95$	1.07944e9	0.0143126
$96$	−2.15111e10	−0.269260
$97$	−9.10022e10	−1.07599	−0.537994	−	0.842949i	$-0.680818\pi$
$97$	−9.10022e10	−1.07599	−0.537994	+	0.842949i	$0.680818\pi$
$98$	6.12233e9	0.0684184
$99$	5.81091e10	0.614116
$100$	2.22849e10	0.222849
$101$	8.70346e10	0.823995	0.411997	−	0.911185i	$-0.364831\pi$
$101$	8.70346e10	0.823995	0.411997	+	0.911185i	$0.364831\pi$
$102$	−1.10376e10	−0.0989860
$103$	7.17170e10	0.609561	0.304781	−	0.952423i	$-0.401417\pi$
$103$	7.17170e10	0.609561	0.304781	+	0.952423i	$0.401417\pi$
$104$	−6.05689e10	−0.488165
$105$	−5.02809e10	−0.384470
$106$	1.83854e9	0.0133441
$107$	−1.58378e11	−1.09165	−0.545825	−	0.837899i	$-0.683784\pi$
$107$	−1.58378e11	−1.09165	−0.545825	+	0.837899i	$0.683784\pi$
$108$	−2.86250e10	−0.187463
$109$	7.66736e10	0.477310	0.238655	−	0.971104i	$-0.423294\pi$
$109$	7.66736e10	0.477310	0.238655	+	0.971104i	$0.423294\pi$
$110$	−4.39951e10	−0.260462
$111$	1.31645e11	0.741526
$112$	−1.30526e11	−0.699841
$113$	−6.87594e10	−0.351075	−0.175538	−	0.984473i	$-0.556166\pi$
$113$	−6.87594e10	−0.351075	−0.175538	+	0.984473i	$0.556166\pi$
$114$	−3.11408e8	−0.00151479
$115$	5.27508e10	0.244563
$116$	1.96822e11	0.870071
$117$	−1.21428e11	−0.512032
$118$	−5.20844e9	−0.0209583
$119$	−2.10229e11	−0.807580
$120$	4.39212e10	0.161130
$121$	6.83107e11	2.39425
$122$	−8.60275e10	−0.288176
$123$	−6.71312e10	−0.215004
$124$	−7.31995e10	−0.224228
$125$	−3.68187e11	−1.07910
$126$	1.45055e10	0.0406907
$127$	3.88670e11	1.04390	0.521952	−	0.852975i	$-0.325204\pi$
$127$	3.88670e11	1.04390	0.521952	+	0.852975i	$0.325204\pi$
$128$	2.34354e11	0.602861
$129$	−1.08421e11	−0.267220
$130$	9.19346e10	0.217165
$131$	−4.12904e11	−0.935097	−0.467549	−	0.883967i	$-0.654863\pi$
$131$	−4.12904e11	−0.935097	−0.467549	+	0.883967i	$0.654863\pi$
$132$	−4.77050e11	−1.03611
$133$	−5.93127e9	−0.0123584
$134$	2.59242e10	0.0518356
$135$	8.80529e10	0.169008
$136$	1.83639e11	0.338454
$137$	3.63576e11	0.643624	0.321812	−	0.946804i	$-0.395708\pi$
$137$	3.63576e11	0.643624	0.321812	+	0.946804i	$0.395708\pi$
$138$	−1.52180e10	−0.0258835
$139$	1.27317e11	0.208115	0.104057	−	0.994571i	$-0.466817\pi$
$139$	1.27317e11	0.208115	0.104057	+	0.994571i	$0.466817\pi$
$140$	4.12785e11	0.648663
$141$	2.59260e10	0.0391769
$142$	2.41614e10	0.0351185
$143$	−2.02366e12	−2.83002
$144$	2.28580e11	0.307641
$145$	−6.05441e11	−0.784418
$146$	6.09884e10	0.0760863
$147$	−2.04209e11	−0.245375
$148$	−1.08074e12	−1.25108
$149$	3.81557e11	0.425633	0.212816	−	0.977092i	$-0.431736\pi$
$149$	3.81557e11	0.425633	0.212816	+	0.977092i	$0.431736\pi$
$150$	1.97760e10	0.0212636
$151$	6.92029e10	0.0717383	0.0358691	−	0.999356i	$-0.488580\pi$
$151$	6.92029e10	0.0717383	0.0358691	+	0.999356i	$0.488580\pi$
$152$	5.18106e9	0.00517939
$153$	3.68157e11	0.355002
$154$	2.41742e11	0.224899
$155$	2.25168e11	0.202154
$156$	9.96872e11	0.863881
$157$	1.78601e12	1.49429	0.747145	−	0.664661i	$-0.231424\pi$
$157$	1.78601e12	1.49429	0.747145	+	0.664661i	$0.231424\pi$
$158$	1.78268e10	0.0144032
$159$	−6.13241e10	−0.0478572
$160$	−5.43228e11	−0.409564
$161$	−2.89853e11	−0.211171
$162$	−2.54023e10	−0.0178871
$163$	1.34003e12	0.912182	0.456091	−	0.889933i	$-0.349249\pi$
$163$	1.34003e12	0.912182	0.456091	+	0.889933i	$0.349249\pi$
$164$	5.51118e11	0.362746
$165$	1.46745e12	0.934116
$166$	−3.85673e11	−0.237479
$167$	−7.41664e11	−0.441842	−0.220921	−	0.975292i	$-0.570906\pi$
$167$	−7.41664e11	−0.441842	−0.220921	+	0.975292i	$0.570906\pi$
$168$	−2.41336e11	−0.139130
$169$	2.43660e12	1.35959
$170$	−2.78736e11	−0.150565
$171$	1.03869e10	0.00543262
$172$	8.90089e11	0.450844
$173$	3.52135e12	1.72765	0.863825	−	0.503791i	$-0.168062\pi$
$173$	3.52135e12	1.72765	0.863825	+	0.503791i	$0.168062\pi$
$174$	1.74663e11	0.0830195
$175$	3.76667e11	0.173480
$176$	3.80941e12	1.70035
$177$	1.73727e11	0.0751646
$178$	−3.65165e11	−0.153172
$179$	3.10316e12	1.26215	0.631077	−	0.775720i	$-0.282613\pi$
$179$	3.10316e12	1.26215	0.631077	+	0.775720i	$0.282613\pi$
$180$	−7.22876e11	−0.285144
$181$	2.94843e12	1.12813	0.564064	−	0.825731i	$-0.309237\pi$
$181$	2.94843e12	1.12813	0.564064	+	0.825731i	$0.309237\pi$
$182$	−5.05158e11	−0.187514
$183$	2.86943e12	1.03351
$184$	2.53191e11	0.0885014
$185$	3.32446e12	1.12792
$186$	−6.49584e10	−0.0213951
$187$	6.13554e12	1.96211
$188$	−2.12841e11	−0.0660978
$189$	−4.83828e11	−0.145932
$190$	−7.86407e9	−0.00230411
$191$	1.24738e12	0.355072	0.177536	−	0.984114i	$-0.443187\pi$
$191$	1.24738e12	0.355072	0.177536	+	0.984114i	$0.443187\pi$
$192$	−1.76975e12	−0.489504
$193$	3.29097e12	0.884625	0.442313	−	0.896861i	$-0.354158\pi$
$193$	3.29097e12	0.884625	0.442313	+	0.896861i	$0.354158\pi$
$194$	6.62979e11	0.173217
$195$	−3.06646e12	−0.778838
$196$	1.67647e12	0.413987
$197$	6.40666e12	1.53839	0.769197	−	0.639012i	$-0.220657\pi$
$197$	6.40666e12	1.53839	0.769197	+	0.639012i	$0.220657\pi$
$198$	−4.23342e11	−0.0988629
$199$	−7.08530e12	−1.60941	−0.804704	−	0.593676i	$-0.797676\pi$
$199$	−7.08530e12	−1.60941	−0.804704	+	0.593676i	$0.797676\pi$
$200$	−3.29024e11	−0.0727048
$201$	−8.64695e11	−0.185902
$202$	−6.34074e11	−0.132650
$203$	3.32675e12	0.677316
$204$	−3.02241e12	−0.598946
$205$	−1.69528e12	−0.327037
$206$	−5.22480e11	−0.0981296
$207$	5.07595e11	0.0928283
$208$	−7.96036e12	−1.41770
$209$	1.73104e11	0.0300263
$210$	3.66312e11	0.0618935
$211$	7.38091e12	1.21494	0.607472	−	0.794341i	$-0.292184\pi$
$211$	7.38091e12	1.21494	0.607472	+	0.794341i	$0.292184\pi$
$212$	5.03444e11	0.0807428
$213$	−8.05898e11	−0.125948
$214$	1.15383e12	0.175738
$215$	−2.73799e12	−0.406462
$216$	4.22632e11	0.0611599
$217$	−1.23724e12	−0.174552
$218$	−5.58591e11	−0.0768392
$219$	−2.03426e12	−0.272875
$220$	−1.20471e13	−1.57601
$221$	−1.28212e13	−1.63595
$222$	−9.59071e11	−0.119374
$223$	1.50922e13	1.83263	0.916315	−	0.400459i	$-0.131149\pi$
$223$	1.50922e13	1.83263	0.916315	+	0.400459i	$0.131149\pi$
$224$	2.98490e12	0.353644
$225$	−6.59626e11	−0.0762594
$226$	5.00933e11	0.0565175
$227$	1.46411e13	1.61224	0.806121	−	0.591751i	$-0.201563\pi$
$227$	1.46411e13	1.61224	0.806121	+	0.591751i	$0.201563\pi$
$228$	−8.52723e10	−0.00916571
$229$	1.33878e13	1.40480	0.702398	−	0.711784i	$-0.252113\pi$
$229$	1.33878e13	1.40480	0.702398	+	0.711784i	$0.252113\pi$
$230$	−3.84306e11	−0.0393708
$231$	−8.06326e12	−0.806575
$232$	−2.90597e12	−0.283861
$233$	1.61708e13	1.54268	0.771339	−	0.636425i	$-0.219587\pi$
$233$	1.61708e13	1.54268	0.771339	+	0.636425i	$0.219587\pi$
$234$	8.84640e11	0.0824289
$235$	6.54717e11	0.0595910
$236$	−1.42622e12	−0.126815
$237$	−5.94611e11	−0.0516555
$238$	1.53159e12	0.130007
$239$	−3.64028e12	−0.301958	−0.150979	−	0.988537i	$-0.548243\pi$
$239$	−3.64028e12	−0.301958	−0.150979	+	0.988537i	$0.548243\pi$
$240$	5.77241e12	0.467945
$241$	2.03587e12	0.161308	0.0806540	−	0.996742i	$-0.474299\pi$
$241$	2.03587e12	0.161308	0.0806540	+	0.996742i	$0.474299\pi$
$242$	−4.97664e12	−0.385436
$243$	8.47289e11	0.0641500
$244$	−2.35568e13	−1.74370
$245$	−5.15696e12	−0.373233
$246$	4.89071e11	0.0346122
$247$	−3.61728e11	−0.0250351
$248$	1.08075e12	0.0731544
$249$	1.28640e13	0.851689
$250$	2.68235e12	0.173718
$251$	−7.68200e12	−0.486708	−0.243354	−	0.969937i	$-0.578248\pi$
$251$	−7.68200e12	−0.486708	−0.243354	+	0.969937i	$0.578248\pi$
$252$	3.97202e12	0.246212
$253$	8.45934e12	0.513066
$254$	−2.83158e12	−0.168052
$255$	9.29719e12	0.539984
$256$	1.32081e13	0.750795
$257$	−3.17374e13	−1.76579	−0.882895	−	0.469571i	$-0.844409\pi$
$257$	−3.17374e13	−1.76579	−0.882895	+	0.469571i	$0.844409\pi$
$258$	7.89879e11	0.0430182
$259$	−1.82671e13	−0.973914
$260$	2.51743e13	1.31403
$261$	−5.82586e12	−0.297740
$262$	3.00813e12	0.150536
$263$	−1.09978e13	−0.538949	−0.269474	−	0.963008i	$-0.586850\pi$
$263$	−1.09978e13	−0.538949	−0.269474	+	0.963008i	$0.586850\pi$
$264$	7.04338e12	0.338033
$265$	−1.54864e12	−0.0727943
$266$	4.32111e10	0.00198951
$267$	1.21800e13	0.549333
$268$	7.09877e12	0.313648
$269$	5.20193e12	0.225178	0.112589	−	0.993642i	$-0.464086\pi$
$269$	5.20193e12	0.225178	0.112589	+	0.993642i	$0.464086\pi$
$270$	−6.41492e11	−0.0272076
$271$	−3.29168e13	−1.36800	−0.684001	−	0.729481i	$-0.739761\pi$
$271$	−3.29168e13	−1.36800	−0.684001	+	0.729481i	$0.739761\pi$
$272$	2.41350e13	0.982919
$273$	1.68494e13	0.672498
$274$	−2.64876e12	−0.103613
$275$	−1.09930e13	−0.421489
$276$	−4.16713e12	−0.156617
$277$	−4.92559e13	−1.81476	−0.907380	−	0.420310i	$-0.861921\pi$
$277$	−4.92559e13	−1.81476	−0.907380	+	0.420310i	$0.861921\pi$
$278$	−9.27539e11	−0.0335032
$279$	2.16668e12	0.0767311
$280$	−6.09453e12	−0.211627
$281$	4.51468e13	1.53724	0.768621	−	0.639705i	$-0.220943\pi$
$281$	4.51468e13	1.53724	0.768621	+	0.639705i	$0.220943\pi$
$282$	−1.88879e11	−0.00630685
$283$	−4.94712e13	−1.62004	−0.810022	−	0.586399i	$-0.800545\pi$
$283$	−4.94712e13	−1.62004	−0.810022	+	0.586399i	$0.800545\pi$
$284$	6.61607e12	0.212495
$285$	2.62305e11	0.00826341
$286$	1.47430e13	0.455588
$287$	9.31516e12	0.282384
$288$	−5.22721e12	−0.155457
$289$	4.60057e12	0.134237
$290$	4.41082e12	0.126279
$291$	−2.21135e13	−0.621222
$292$	1.67004e13	0.460384
$293$	3.97795e13	1.07619	0.538093	−	0.842886i	$-0.319145\pi$
$293$	3.97795e13	1.07619	0.538093	+	0.842886i	$0.319145\pi$
$294$	1.48773e12	0.0395014
$295$	4.38717e12	0.114331
$296$	1.59566e13	0.408165
$297$	1.41205e13	0.354560
$298$	−2.77976e12	−0.0685200
$299$	−1.76771e13	−0.427779
$300$	5.41524e12	0.128662
$301$	1.50446e13	0.350965
$302$	−5.04164e11	−0.0115487
$303$	2.11494e13	0.475734
$304$	6.80928e11	0.0150417
$305$	7.24626e13	1.57204
$306$	−2.68214e12	−0.0571496
$307$	9.32676e12	0.195195	0.0975977	−	0.995226i	$-0.468884\pi$
$307$	9.32676e12	0.195195	0.0975977	+	0.995226i	$0.468884\pi$
$308$	6.61958e13	1.36082
$309$	1.74272e13	0.351930
$310$	−1.64042e12	−0.0325435
$311$	−4.41430e13	−0.860359	−0.430180	−	0.902743i	$-0.641550\pi$
$311$	−4.41430e13	−0.860359	−0.430180	+	0.902743i	$0.641550\pi$
$312$	−1.47182e13	−0.281842
$313$	9.01074e13	1.69538	0.847689	−	0.530494i	$-0.177993\pi$
$313$	9.01074e13	1.69538	0.847689	+	0.530494i	$0.177993\pi$
$314$	−1.30116e13	−0.240557
$315$	−1.22183e13	−0.221974
$316$	4.88150e12	0.0871513
$317$	−4.48767e13	−0.787400	−0.393700	−	0.919239i	$-0.628805\pi$
$317$	−4.48767e13	−0.787400	−0.393700	+	0.919239i	$0.628805\pi$
$318$	4.46765e11	0.00770424
$319$	−9.70909e13	−1.64562
$320$	−4.46922e13	−0.744572
$321$	−3.84858e13	−0.630265
$322$	2.11166e12	0.0339952
$323$	1.09672e12	0.0173573
$324$	−6.95587e12	−0.108232
$325$	2.29716e13	0.351425
$326$	−9.76250e12	−0.146847
$327$	1.86317e13	0.275575
$328$	−8.13694e12	−0.118346
$329$	−3.59751e12	−0.0514546
$330$	−1.06908e13	−0.150378
$331$	−4.88286e13	−0.675493	−0.337746	−	0.941237i	$-0.609665\pi$
$331$	−4.88286e13	−0.675493	−0.337746	+	0.941237i	$0.609665\pi$
$332$	−1.05608e14	−1.43694
$333$	3.19896e13	0.428120
$334$	5.40325e12	0.0711295
$335$	−2.18364e13	−0.282771
$336$	−3.17179e13	−0.404053
$337$	−7.41414e13	−0.929173	−0.464586	−	0.885528i	$-0.653797\pi$
$337$	−7.41414e13	−0.929173	−0.464586	+	0.885528i	$0.653797\pi$
$338$	−1.77514e13	−0.218872
$339$	−1.67085e13	−0.202694
$340$	−7.63259e13	−0.911041
$341$	3.61088e13	0.424096
$342$	−7.56720e10	−0.000874564 0
$343$	9.50093e13	1.08056
$344$	−1.31417e13	−0.147088
$345$	1.28185e13	0.141199
$346$	−2.56541e13	−0.278124
$347$	−2.14365e13	−0.228740	−0.114370	−	0.993438i	$-0.536485\pi$
$347$	−2.14365e13	−0.228740	−0.114370	+	0.993438i	$0.536485\pi$
$348$	4.78277e13	0.502336
$349$	−8.64032e13	−0.893285	−0.446642	−	0.894713i	$-0.647380\pi$
$349$	−8.64032e13	−0.893285	−0.446642	+	0.894713i	$0.647380\pi$
$350$	−2.74413e12	−0.0279274
$351$	−2.95070e13	−0.295622
$352$	−8.71142e13	−0.859220
$353$	−1.26783e14	−1.23112	−0.615558	−	0.788091i	$-0.711070\pi$
$353$	−1.26783e14	−1.23112	−0.615558	+	0.788091i	$0.711070\pi$
$354$	−1.26565e12	−0.0121003
$355$	−2.03516e13	−0.191577
$356$	−9.99926e13	−0.926815
$357$	−5.10858e13	−0.466256
$358$	−2.26075e13	−0.203187
$359$	−7.94965e13	−0.703604	−0.351802	−	0.936074i	$-0.614431\pi$
$359$	−7.94965e13	−0.703604	−0.351802	+	0.936074i	$0.614431\pi$
$360$	1.06729e13	0.0930286
$361$	−1.16459e14	−0.999734
$362$	−2.14802e13	−0.181610
$363$	1.65995e14	1.38232
$364$	−1.38327e14	−1.13461
$365$	−5.13717e13	−0.415062
$366$	−2.09047e13	−0.166379
$367$	1.31070e14	1.02764	0.513820	−	0.857898i	$-0.328230\pi$
$367$	1.31070e14	1.02764	0.513820	+	0.857898i	$0.328230\pi$
$368$	3.32760e13	0.257020
$369$	−1.63129e13	−0.124132
$370$	−2.42197e13	−0.181576
$371$	8.50937e12	0.0628552
$372$	−1.77875e13	−0.129458
$373$	1.07548e14	0.771264	0.385632	−	0.922653i	$-0.373983\pi$
$373$	1.07548e14	0.771264	0.385632	+	0.922653i	$0.373983\pi$
$374$	−4.46992e13	−0.315869
$375$	−8.94694e13	−0.623021
$376$	3.14248e12	0.0215645
$377$	2.02887e14	1.37207
$378$	3.52484e12	0.0234928
$379$	1.38488e14	0.909695	0.454848	−	0.890569i	$-0.349694\pi$
$379$	1.38488e14	0.909695	0.454848	+	0.890569i	$0.349694\pi$
$380$	−2.15341e12	−0.0139417
$381$	9.44469e13	0.602699
$382$	−9.08757e12	−0.0571610
$383$	−1.26680e14	−0.785445	−0.392723	−	0.919657i	$-0.628467\pi$
$383$	−1.26680e14	−0.785445	−0.392723	+	0.919657i	$0.628467\pi$
$384$	5.69480e13	0.348062
$385$	−2.03624e14	−1.22686
$386$	−2.39757e13	−0.142410
$387$	−2.63463e13	−0.154280
$388$	1.81543e14	1.04810
$389$	−9.22822e13	−0.525285	−0.262643	−	0.964893i	$-0.584594\pi$
$389$	−9.22822e13	−0.525285	−0.262643	+	0.964893i	$0.584594\pi$
$390$	2.23401e13	0.125380
$391$	5.35952e13	0.296588
$392$	−2.47521e13	−0.135064
$393$	−1.00336e14	−0.539879
$394$	−4.66745e13	−0.247657
$395$	−1.50159e13	−0.0785719
$396$	−1.15923e14	−0.598201
$397$	−1.42869e14	−0.727094	−0.363547	−	0.931576i	$-0.618434\pi$
$397$	−1.42869e14	−0.727094	−0.363547	+	0.931576i	$0.618434\pi$
$398$	5.16185e13	0.259089
$399$	−1.44130e12	−0.00713515
$400$	−4.32425e13	−0.211145
$401$	−1.62373e14	−0.782021	−0.391011	−	0.920386i	$-0.627874\pi$
$401$	−1.62373e14	−0.782021	−0.391011	+	0.920386i	$0.627874\pi$
$402$	6.29957e12	0.0299273
$403$	−7.54551e13	−0.353599
$404$	−1.73627e14	−0.802640
$405$	2.13968e13	0.0975769
$406$	−2.42364e13	−0.109037
$407$	5.33124e14	2.36624
$408$	4.46242e13	0.195407
$409$	−3.19251e14	−1.37928	−0.689642	−	0.724150i	$-0.742232\pi$
$409$	−3.19251e14	−1.37928	−0.689642	+	0.724150i	$0.742232\pi$
$410$	1.23507e13	0.0526476
$411$	8.83490e13	0.371596
$412$	−1.43070e14	−0.593764
$413$	−2.41064e13	−0.0987205
$414$	−3.69798e12	−0.0149439
$415$	3.24860e14	1.29548
$416$	1.82039e14	0.716392
$417$	3.09379e13	0.120155
$418$	−1.26111e12	−0.00483376
$419$	−1.20423e14	−0.455548	−0.227774	−	0.973714i	$-0.573145\pi$
$419$	−1.20423e14	−0.455548	−0.227774	+	0.973714i	$0.573145\pi$
$420$	1.00307e14	0.374506
$421$	3.74027e14	1.37833	0.689163	−	0.724607i	$-0.257978\pi$
$421$	3.74027e14	1.37833	0.689163	+	0.724607i	$0.257978\pi$
$422$	−5.37721e13	−0.195586
$423$	6.30001e12	0.0226188
$424$	−7.43307e12	−0.0263424
$425$	−6.96476e13	−0.243650
$426$	5.87121e12	0.0202756
$427$	−3.98164e14	−1.35740
$428$	3.15952e14	1.06336
$429$	−4.91750e14	−1.63391
$430$	1.99471e13	0.0654339
$431$	2.55097e14	0.826191	0.413096	−	0.910688i	$-0.364447\pi$
$431$	2.55097e14	0.826191	0.413096	+	0.910688i	$0.364447\pi$
$432$	5.55450e13	0.177617
$433$	−5.01589e13	−0.158367	−0.0791835	−	0.996860i	$-0.525231\pi$
$433$	−5.01589e13	−0.158367	−0.0791835	+	0.996860i	$0.525231\pi$
$434$	9.01368e12	0.0281001
$435$	−1.47122e14	−0.452884
$436$	−1.52958e14	−0.464940
$437$	1.51210e12	0.00453871
$438$	1.48202e13	0.0439284
$439$	7.04081e13	0.206095	0.103048	−	0.994676i	$-0.467141\pi$
$439$	7.04081e13	0.206095	0.103048	+	0.994676i	$0.467141\pi$
$440$	1.77869e14	0.514174
$441$	−4.96228e13	−0.141667
$442$	9.34061e13	0.263362
$443$	1.17079e14	0.326030	0.163015	−	0.986624i	$-0.447878\pi$
$443$	1.17079e14	0.326030	0.163015	+	0.986624i	$0.447878\pi$
$444$	−2.62621e14	−0.722309
$445$	3.07586e14	0.835576
$446$	−1.09951e14	−0.295024
$447$	9.27184e13	0.245739
$448$	2.45572e14	0.642910
$449$	−5.74915e13	−0.148679	−0.0743393	−	0.997233i	$-0.523685\pi$
$449$	−5.74915e13	−0.148679	−0.0743393	+	0.997233i	$0.523685\pi$
$450$	4.80557e12	0.0122765
$451$	−2.71863e14	−0.686086
$452$	1.37170e14	0.341977
$453$	1.68163e13	0.0414181
$454$	−1.06665e14	−0.259545
$455$	4.25504e14	1.02292
$456$	1.25900e12	0.00299032
$457$	2.90433e14	0.681565	0.340783	−	0.940142i	$-0.389308\pi$
$457$	2.90433e14	0.681565	0.340783	+	0.940142i	$0.389308\pi$
$458$	−9.75340e13	−0.226150
$459$	8.94623e13	0.204960
$460$	−1.05234e14	−0.238225
$461$	−4.64431e14	−1.03888	−0.519441	−	0.854506i	$-0.673860\pi$
$461$	−4.64431e14	−1.03888	−0.519441	+	0.854506i	$0.673860\pi$
$462$	5.87433e13	0.129846
$463$	1.51143e14	0.330135	0.165068	−	0.986282i	$-0.447216\pi$
$463$	1.51143e14	0.330135	0.165068	+	0.986282i	$0.447216\pi$
$464$	−3.81921e14	−0.824374
$465$	5.47158e13	0.116714
$466$	−1.17810e14	−0.248346
$467$	5.53556e14	1.15324	0.576619	−	0.817013i	$-0.304372\pi$
$467$	5.53556e14	1.15324	0.576619	+	0.817013i	$0.304372\pi$
$468$	2.42240e14	0.498762
$469$	1.19986e14	0.244162
$470$	−4.76981e12	−0.00959319
$471$	4.33999e14	0.862729
$472$	2.10573e13	0.0413735
$473$	−4.39075e14	−0.852711
$474$	4.33192e12	0.00831571
$475$	−1.96499e12	−0.00372860
$476$	4.19392e14	0.786650
$477$	−1.49018e13	−0.0276303
$478$	2.65205e13	0.0486104
$479$	9.79817e14	1.77541	0.887707	−	0.460409i	$-0.152297\pi$
$479$	9.79817e14	1.77541	0.887707	+	0.460409i	$0.152297\pi$
$480$	−1.32004e14	−0.236462
$481$	−1.11405e15	−1.97290
$482$	−1.48319e13	−0.0259680
$483$	−7.04342e13	−0.121920
$484$	−1.36275e15	−2.33220
$485$	−5.58440e14	−0.944925
$486$	−6.17275e12	−0.0103271
$487$	1.35144e14	0.223557	0.111778	−	0.993733i	$-0.464345\pi$
$487$	1.35144e14	0.223557	0.111778	+	0.993733i	$0.464345\pi$
$488$	3.47802e14	0.568884
$489$	3.25626e14	0.526648
$490$	3.75700e13	0.0600845
$491$	4.49871e14	0.711443	0.355721	−	0.934592i	$-0.384235\pi$
$491$	4.49871e14	0.711443	0.355721	+	0.934592i	$0.384235\pi$
$492$	1.33922e14	0.209432
$493$	−6.15132e14	−0.951284
$494$	2.63530e12	0.00403024
$495$	3.56590e14	0.539312
$496$	1.42039e14	0.212451
$497$	1.11827e14	0.165419
$498$	−9.37185e13	−0.137108
$499$	−7.83753e14	−1.13403	−0.567017	−	0.823706i	$-0.691903\pi$
$499$	−7.83753e14	−1.13403	−0.567017	+	0.823706i	$0.691903\pi$
$500$	7.34505e14	1.05114
$501$	−1.80224e14	−0.255098
$502$	5.59657e13	0.0783522
$503$	2.94819e14	0.408255	0.204127	−	0.978944i	$-0.434564\pi$
$503$	2.94819e14	0.408255	0.204127	+	0.978944i	$0.434564\pi$
$504$	−5.86446e13	−0.0803268
$505$	5.34093e14	0.723626
$506$	−6.16288e13	−0.0825954
$507$	5.92094e14	0.784959
$508$	−7.75368e14	−1.01685
$509$	−1.18940e15	−1.54306	−0.771528	−	0.636195i	$-0.780507\pi$
$509$	−1.18940e15	−1.54306	−0.771528	+	0.636195i	$0.780507\pi$
$510$	−6.77329e13	−0.0869288
$511$	2.82275e14	0.358391
$512$	−5.76182e14	−0.723727
$513$	2.52403e12	0.00313652
$514$	2.31216e14	0.284264
$515$	4.40095e14	0.535312
$516$	2.16292e14	0.260295
$517$	1.04993e14	0.125015
$518$	1.33081e14	0.156785
$519$	8.55689e14	0.997460
$520$	−3.71685e14	−0.428703
$521$	1.62699e15	1.85685	0.928427	−	0.371515i	$-0.121161\pi$
$521$	1.62699e15	1.85685	0.928427	+	0.371515i	$0.121161\pi$
$522$	4.24431e13	0.0479313
$523$	5.12180e14	0.572352	0.286176	−	0.958177i	$-0.407616\pi$
$523$	5.12180e14	0.572352	0.286176	+	0.958177i	$0.407616\pi$
$524$	8.23712e14	0.910864
$525$	9.15301e13	0.100158
$526$	8.01220e13	0.0867621
$527$	2.28772e14	0.245157
$528$	9.25686e14	0.981696
$529$	−8.78916e14	−0.922446
$530$	1.12823e13	0.0117187
$531$	4.22156e13	0.0433963
$532$	1.18324e13	0.0120382
$533$	5.68100e14	0.572038
$534$	−8.87351e13	−0.0884338
$535$	−9.71894e14	−0.958679
$536$	−1.04809e14	−0.102328
$537$	7.54068e14	0.728705
$538$	−3.78976e13	−0.0362501
$539$	−8.26990e14	−0.783001
$540$	−1.75659e14	−0.164628
$541$	4.66542e14	0.432819	0.216409	−	0.976303i	$-0.430565\pi$
$541$	4.66542e14	0.432819	0.216409	+	0.976303i	$0.430565\pi$
$542$	2.39809e14	0.220226
$543$	7.16468e14	0.651325
$544$	−5.51923e14	−0.496689
$545$	4.70512e14	0.419170
$546$	−1.22753e14	−0.108261
$547$	3.44855e14	0.301097	0.150548	−	0.988603i	$-0.451896\pi$
$547$	3.44855e14	0.301097	0.150548	+	0.988603i	$0.451896\pi$
$548$	−7.25307e14	−0.626944
$549$	6.97272e14	0.596697
$550$	8.00874e13	0.0678530
$551$	−1.73549e13	−0.0145576
$552$	6.15254e13	0.0510963
$553$	8.25086e13	0.0678439
$554$	3.58844e14	0.292147
$555$	8.07844e14	0.651203
$556$	−2.53987e14	−0.202721
$557$	−4.50069e14	−0.355693	−0.177846	−	0.984058i	$-0.556913\pi$
$557$	−4.50069e14	−0.355693	−0.177846	+	0.984058i	$0.556913\pi$
$558$	−1.57849e13	−0.0123525
$559$	9.17516e14	0.710965
$560$	−8.00983e14	−0.614595
$561$	1.49094e15	1.13283
$562$	−3.28908e14	−0.247471
$563$	1.65669e15	1.23437	0.617186	−	0.786817i	$-0.288273\pi$
$563$	1.65669e15	1.23437	0.617186	+	0.786817i	$0.288273\pi$
$564$	−5.17204e13	−0.0381616
$565$	−4.21946e14	−0.308312
$566$	3.60413e14	0.260801
$567$	−1.17570e14	−0.0842541
$568$	−9.76825e13	−0.0693268
$569$	−1.00863e15	−0.708946	−0.354473	−	0.935066i	$-0.615340\pi$
$569$	−1.00863e15	−0.708946	−0.354473	+	0.935066i	$0.615340\pi$
$570$	−1.91097e12	−0.00133028
$571$	1.20071e15	0.827828	0.413914	−	0.910316i	$-0.364161\pi$
$571$	1.20071e15	0.827828	0.413914	+	0.910316i	$0.364161\pi$
$572$	4.03705e15	2.75668
$573$	3.03114e14	0.205001
$574$	−6.78638e13	−0.0454593
$575$	−9.60262e13	−0.0637113
$576$	−4.30050e14	−0.282615
$577$	9.68634e14	0.630511	0.315256	−	0.949007i	$-0.397910\pi$
$577$	9.68634e14	0.630511	0.315256	+	0.949007i	$0.397910\pi$
$578$	−3.35165e13	−0.0216100
$579$	7.99707e14	0.510738
$580$	1.20781e15	0.764090
$581$	−1.78502e15	−1.11860
$582$	1.61104e14	0.100007
$583$	−2.48346e14	−0.152714
$584$	−2.46571e14	−0.150201
$585$	−7.45150e14	−0.449662
$586$	−2.89806e14	−0.173249
$587$	−2.05902e15	−1.21942	−0.609708	−	0.792626i	$-0.708713\pi$
$587$	−2.05902e15	−1.21942	−0.609708	+	0.792626i	$0.708713\pi$
$588$	4.07382e14	0.239016
$589$	6.45442e12	0.00375165
$590$	−3.19619e13	−0.0184054
$591$	1.55682e15	0.888192
$592$	2.09712e15	1.18537
$593$	−2.19888e15	−1.23140	−0.615702	−	0.787979i	$-0.711127\pi$
$593$	−2.19888e15	−1.23140	−0.615702	+	0.787979i	$0.711127\pi$
$594$	−1.02872e14	−0.0570785
$595$	−1.29008e15	−0.709210
$596$	−7.61177e14	−0.414602
$597$	−1.72173e15	−0.929192
$598$	1.28783e14	0.0688656
$599$	−1.59947e15	−0.847481	−0.423740	−	0.905784i	$-0.639283\pi$
$599$	−1.59947e15	−0.847481	−0.423740	+	0.905784i	$0.639283\pi$
$600$	−7.99529e13	−0.0419762
$601$	−2.27264e15	−1.18228	−0.591142	−	0.806568i	$-0.701323\pi$
$601$	−2.27264e15	−1.18228	−0.591142	+	0.806568i	$0.701323\pi$
$602$	−1.09604e14	−0.0564997
$603$	−2.10121e14	−0.107331
$604$	−1.38055e14	−0.0698791
$605$	4.19192e15	2.10261
$606$	−1.54080e14	−0.0765855
$607$	6.48922e14	0.319635	0.159818	−	0.987147i	$-0.448909\pi$
$607$	6.48922e14	0.319635	0.159818	+	0.987147i	$0.448909\pi$
$608$	−1.55716e13	−0.00760086
$609$	8.08399e14	0.391049
$610$	−5.27912e14	−0.253074
$611$	−2.19399e14	−0.104234
$612$	−7.34446e14	−0.345802
$613$	−2.15085e15	−1.00364	−0.501819	−	0.864973i	$-0.667336\pi$
$613$	−2.15085e15	−1.00364	−0.501819	+	0.864973i	$0.667336\pi$
$614$	−6.79483e13	−0.0314233
$615$	−4.11954e14	−0.188815
$616$	−9.77344e14	−0.443970
$617$	1.76381e15	0.794114	0.397057	−	0.917794i	$-0.370031\pi$
$617$	1.76381e15	0.794114	0.397057	+	0.917794i	$0.370031\pi$
$618$	−1.26963e14	−0.0566552
$619$	−1.42359e15	−0.629630	−0.314815	−	0.949153i	$-0.601943\pi$
$619$	−1.42359e15	−0.629630	−0.314815	+	0.949153i	$0.601943\pi$
$620$	−4.49193e14	−0.196915
$621$	1.23346e14	0.0535944
$622$	3.21595e14	0.138504
$623$	−1.69011e15	−0.721489
$624$	−1.93437e15	−0.818509
$625$	−1.71395e15	−0.718882
$626$	−6.56460e14	−0.272929
$627$	4.20642e13	0.0173357
$628$	−3.56295e15	−1.45556
$629$	3.37767e15	1.36785
$630$	8.90138e13	0.0357342
$631$	1.68693e12	0.000671327 0	0.000335664	−	1.00000i	$-0.499893\pi$
$631$	1.68693e12	0.000671327 0	0.000335664		1.00000i	$0.499893\pi$
$632$	−7.20725e13	−0.0284332
$633$	1.79356e15	0.701448
$634$	3.26941e14	0.126759
$635$	2.38510e15	0.916749
$636$	1.22337e14	0.0466169
$637$	1.72813e15	0.652843
$638$	7.07337e14	0.264919
$639$	−1.95833e14	−0.0727162
$640$	1.43813e15	0.529428
$641$	1.34445e15	0.490709	0.245355	−	0.969433i	$-0.421096\pi$
$641$	1.34445e15	0.490709	0.245355	+	0.969433i	$0.421096\pi$
$642$	2.80381e14	0.101463
$643$	−1.23473e15	−0.443008	−0.221504	−	0.975159i	$-0.571097\pi$
$643$	−1.23473e15	−0.443008	−0.221504	+	0.975159i	$0.571097\pi$
$644$	5.78234e14	0.205699
$645$	−6.65331e14	−0.234671
$646$	−7.98995e12	−0.00279425
$647$	9.70146e14	0.336406	0.168203	−	0.985752i	$-0.446204\pi$
$647$	9.70146e14	0.336406	0.168203	+	0.985752i	$0.446204\pi$
$648$	1.02700e14	0.0353107
$649$	7.03545e14	0.239853
$650$	−1.67355e14	−0.0565739
$651$	−3.00650e14	−0.100778
$652$	−2.67325e15	−0.888542
$653$	−4.52761e15	−1.49227	−0.746133	−	0.665796i	$-0.768092\pi$
$653$	−4.52761e15	−1.49227	−0.746133	+	0.665796i	$0.768092\pi$
$654$	−1.35738e14	−0.0443631
$655$	−2.53381e15	−0.821195
$656$	−1.06941e15	−0.343695
$657$	−4.94324e14	−0.157544
$658$	2.62089e13	0.00828336
$659$	3.99949e15	1.25353	0.626766	−	0.779208i	$-0.284378\pi$
$659$	3.99949e15	1.25353	0.626766	+	0.779208i	$0.284378\pi$
$660$	−2.92745e15	−0.909908
$661$	1.04030e15	0.320666	0.160333	−	0.987063i	$-0.448743\pi$
$661$	1.04030e15	0.320666	0.160333	+	0.987063i	$0.448743\pi$
$662$	3.55731e14	0.108743
$663$	−3.11554e15	−0.944516
$664$	1.55925e15	0.468803
$665$	−3.63976e13	−0.0108531
$666$	−2.33054e14	−0.0689205
$667$	−8.48110e14	−0.248748
$668$	1.47956e15	0.430391
$669$	3.66739e15	1.05807
$670$	1.59085e14	0.0455216
$671$	1.16204e16	3.29797
$672$	7.25331e14	0.204176
$673$	−3.14094e15	−0.876955	−0.438477	−	0.898742i	$-0.644482\pi$
$673$	−3.14094e15	−0.876955	−0.438477	+	0.898742i	$0.644482\pi$
$674$	5.40143e14	0.149582
$675$	−1.60289e14	−0.0440284
$676$	−4.86084e15	−1.32435
$677$	1.53188e15	0.413988	0.206994	−	0.978342i	$-0.433632\pi$
$677$	1.53188e15	0.413988	0.206994	+	0.978342i	$0.433632\pi$
$678$	1.21727e14	0.0326304
$679$	3.06849e15	0.815907
$680$	1.12691e15	0.297228
$681$	3.55778e15	0.930829
$682$	−2.63064e14	−0.0682727
$683$	−3.66393e15	−0.943264	−0.471632	−	0.881796i	$-0.656335\pi$
$683$	−3.66393e15	−0.943264	−0.471632	+	0.881796i	$0.656335\pi$
$684$	−2.07212e13	−0.00529183
$685$	2.23110e15	0.565225
$686$	−6.92172e14	−0.173953
$687$	3.25323e15	0.811060
$688$	−1.72716e15	−0.427166
$689$	5.18957e14	0.127329
$690$	−9.33863e13	−0.0227307
$691$	−6.93874e15	−1.67553	−0.837763	−	0.546034i	$-0.816137\pi$
$691$	−6.93874e15	−1.67553	−0.837763	+	0.546034i	$0.816137\pi$
$692$	−7.02483e15	−1.68288
$693$	−1.95937e15	−0.465676
$694$	1.56171e14	0.0368235
$695$	7.81285e14	0.182765
$696$	−7.06150e14	−0.163888
$697$	−1.72242e15	−0.396605
$698$	6.29474e14	0.143805
$699$	3.92952e15	0.890665
$700$	−7.51422e14	−0.168984
$701$	3.04592e15	0.679625	0.339813	−	0.940493i	$-0.389636\pi$
$701$	3.04592e15	0.679625	0.339813	+	0.940493i	$0.389636\pi$
$702$	2.14968e14	0.0475904
$703$	9.52954e13	0.0209323
$704$	−7.16701e15	−1.56203
$705$	1.59096e14	0.0344049
$706$	9.23651e14	0.198190
$707$	−2.93471e15	−0.624824
$708$	−3.46571e14	−0.0732166
$709$	3.77463e15	0.791262	0.395631	−	0.918410i	$-0.370526\pi$
$709$	3.77463e15	0.791262	0.395631	+	0.918410i	$0.370526\pi$
$710$	1.48267e14	0.0308408
$711$	−1.44490e14	−0.0298233
$712$	1.47633e15	0.302374
$713$	3.15418e14	0.0641053
$714$	3.72175e14	0.0750598
$715$	−1.24183e16	−2.48530
$716$	−6.19057e15	−1.22944
$717$	−8.84588e14	−0.174335
$718$	5.79156e14	0.113269
$719$	−1.02169e16	−1.98294	−0.991472	−	0.130321i	$-0.958399\pi$
$719$	−1.02169e16	−1.98294	−0.991472	+	0.130321i	$0.958399\pi$
$720$	1.40269e15	0.270168
$721$	−2.41821e15	−0.462222
$722$	8.48441e14	0.160941
$723$	4.94716e14	0.0931312
$724$	−5.88189e15	−1.09889
$725$	1.10213e15	0.204349
$726$	−1.20932e15	−0.222531
$727$	9.05981e15	1.65455	0.827275	−	0.561797i	$-0.189890\pi$
$727$	9.05981e15	1.65455	0.827275	+	0.561797i	$0.189890\pi$
$728$	2.04231e15	0.370169
$729$	2.05891e14	0.0370370
$730$	3.74258e14	0.0668184
$731$	−2.78181e15	−0.492927
$732$	−5.72430e15	−1.00673
$733$	5.86732e15	1.02416	0.512080	−	0.858938i	$-0.328875\pi$
$733$	5.86732e15	1.02416	0.512080	+	0.858938i	$0.328875\pi$
$734$	−9.54887e14	−0.165434
$735$	−1.25314e15	−0.215486
$736$	−7.60960e14	−0.129878
$737$	−3.50178e15	−0.593222
$738$	1.18844e14	0.0199833
$739$	−1.14387e16	−1.90912	−0.954560	−	0.298018i	$-0.903674\pi$
$739$	−1.14387e16	−1.90912	−0.954560	+	0.298018i	$0.903674\pi$
$740$	−6.63205e15	−1.09869
$741$	−8.78999e13	−0.0144540
$742$	−6.19933e13	−0.0101187
$743$	1.91244e15	0.309848	0.154924	−	0.987926i	$-0.450487\pi$
$743$	1.91244e15	0.309848	0.154924	+	0.987926i	$0.450487\pi$
$744$	2.62622e14	0.0422357
$745$	2.34145e15	0.373787
$746$	−7.83518e14	−0.124161
$747$	3.12596e15	0.491723
$748$	−1.22399e16	−1.91126
$749$	5.34032e15	0.827784
$750$	6.51812e14	0.100296
$751$	8.64165e15	1.32001	0.660005	−	0.751261i	$-0.270554\pi$
$751$	8.64165e15	1.32001	0.660005	+	0.751261i	$0.270554\pi$
$752$	4.13005e14	0.0626263
$753$	−1.86673e15	−0.281001
$754$	−1.47809e15	−0.220881
$755$	4.24667e14	0.0630000
$756$	9.65201e14	0.142150
$757$	7.45030e14	0.108930	0.0544649	−	0.998516i	$-0.482655\pi$
$757$	7.45030e14	0.108930	0.0544649	+	0.998516i	$0.482655\pi$
$758$	−1.00893e15	−0.146446
$759$	2.05562e15	0.296219
$760$	3.17938e13	0.00454850
$761$	1.21503e16	1.72573	0.862865	−	0.505434i	$-0.168668\pi$
$761$	1.21503e16	1.72573	0.862865	+	0.505434i	$0.168668\pi$
$762$	−6.88074e14	−0.0970248
$763$	−2.58535e15	−0.361938
$764$	−2.48844e15	−0.345870
$765$	2.25922e15	0.311760
$766$	9.22904e14	0.126444
$767$	−1.47017e15	−0.199983
$768$	3.20957e15	0.433472
$769$	1.05690e16	1.41723	0.708614	−	0.705596i	$-0.249321\pi$
$769$	1.05690e16	1.41723	0.708614	+	0.705596i	$0.249321\pi$
$770$	1.48346e15	0.197505
$771$	−7.71218e15	−1.01948
$772$	−6.56524e15	−0.861699
$773$	−1.01248e15	−0.131947	−0.0659736	−	0.997821i	$-0.521015\pi$
$773$	−1.01248e15	−0.131947	−0.0659736	+	0.997821i	$0.521015\pi$
$774$	1.91941e14	0.0248366
$775$	−4.09889e14	−0.0526632
$776$	−2.68037e15	−0.341945
$777$	−4.43890e15	−0.562289
$778$	6.72304e14	0.0845625
$779$	−4.85952e13	−0.00606928
$780$	6.11736e15	0.758654
$781$	−3.26366e15	−0.401906
$782$	−3.90457e14	−0.0477459
$783$	−1.41568e15	−0.171900
$784$	−3.25308e15	−0.392244
$785$	1.09599e16	1.31227
$786$	7.30976e14	0.0869118
$787$	−3.03453e14	−0.0358286	−0.0179143	−	0.999840i	$-0.505703\pi$
$787$	−3.03453e14	−0.0358286	−0.0179143	+	0.999840i	$0.505703\pi$
$788$	−1.27808e16	−1.49852
$789$	−2.67246e15	−0.311162
$790$	1.09395e14	0.0126488
$791$	2.31849e15	0.266216
$792$	1.71154e15	0.195164
$793$	−2.42827e16	−2.74975
$794$	1.04084e15	0.117050
$795$	−3.76319e14	−0.0420278
$796$	1.41346e16	1.56770
$797$	5.23026e14	0.0576106	0.0288053	−	0.999585i	$-0.490830\pi$
$797$	5.23026e14	0.0576106	0.0288053	+	0.999585i	$0.490830\pi$
$798$	1.05003e13	0.00114864
$799$	6.65196e14	0.0722674
$800$	9.88877e14	0.106696
$801$	2.95974e15	0.317158
$802$	1.18293e15	0.125893
$803$	−8.23817e15	−0.870754
$804$	1.72500e15	0.181085
$805$	−1.77870e15	−0.185449
$806$	5.49713e14	0.0569237
$807$	1.26407e15	0.130007
$808$	2.56351e15	0.261862
$809$	1.63033e16	1.65409	0.827046	−	0.562135i	$-0.190020\pi$
$809$	1.63033e16	1.65409	0.827046	+	0.562135i	$0.190020\pi$
$810$	−1.55882e14	−0.0157083
$811$	7.45401e15	0.746063	0.373031	−	0.927819i	$-0.378318\pi$
$811$	7.45401e15	0.746063	0.373031	+	0.927819i	$0.378318\pi$
$812$	−6.63661e15	−0.659763
$813$	−7.99878e15	−0.789816
$814$	−3.88397e15	−0.380927
$815$	8.22314e15	0.801071
$816$	5.86480e15	0.567489
$817$	−7.84842e13	−0.00754329
$818$	2.32584e15	0.222043
$819$	4.09441e15	0.388267
$820$	3.38196e15	0.318561
$821$	9.56085e15	0.894559	0.447280	−	0.894394i	$-0.352393\pi$
$821$	9.56085e15	0.894559	0.447280	+	0.894394i	$0.352393\pi$
$822$	−6.43649e14	−0.0598211
$823$	1.47807e15	0.136457	0.0682285	−	0.997670i	$-0.478265\pi$
$823$	1.47807e15	0.136457	0.0682285	+	0.997670i	$0.478265\pi$
$824$	2.11235e15	0.193716
$825$	−2.67130e15	−0.243347
$826$	1.75623e14	0.0158924
$827$	6.56307e14	0.0589966	0.0294983	−	0.999565i	$-0.490609\pi$
$827$	6.56307e14	0.0589966	0.0294983	+	0.999565i	$0.490609\pi$
$828$	−1.01261e15	−0.0904226
$829$	−6.73203e15	−0.597167	−0.298584	−	0.954383i	$-0.596514\pi$
$829$	−6.73203e15	−0.597167	−0.298584	+	0.954383i	$0.596514\pi$
$830$	−2.36670e15	−0.208552
$831$	−1.19692e16	−1.04775
$832$	1.49766e16	1.30237
$833$	−5.23950e15	−0.452629
$834$	−2.25392e14	−0.0193431
$835$	−4.55126e15	−0.388022
$836$	−3.45329e14	−0.0292482
$837$	5.26503e14	0.0443007
$838$	8.77321e14	0.0733359
$839$	−8.01856e15	−0.665895	−0.332947	−	0.942945i	$-0.608043\pi$
$839$	−8.01856e15	−0.665895	−0.332947	+	0.942945i	$0.608043\pi$
$840$	−1.48097e15	−0.122183
$841$	−2.46644e15	−0.202159
$842$	−2.72490e15	−0.221888
$843$	1.09707e16	0.887527
$844$	−1.47244e16	−1.18346
$845$	1.49523e16	1.19398
$846$	−4.58975e13	−0.00364126
$847$	−2.30336e16	−1.81553
$848$	−9.76901e14	−0.0765021
$849$	−1.20215e16	−0.935333
$850$	5.07404e14	0.0392238
$851$	4.65695e15	0.357675
$852$	1.60770e15	0.122684
$853$	2.59125e16	1.96467	0.982333	−	0.187139i	$-0.0599215\pi$
$853$	2.59125e16	1.96467	0.982333	+	0.187139i	$0.0599215\pi$
$854$	2.90075e15	0.218520
$855$	6.37401e13	0.00477088
$856$	−4.66485e15	−0.346922
$857$	−2.30391e16	−1.70244	−0.851218	−	0.524813i	$-0.824135\pi$
$857$	−2.30391e16	−1.70244	−0.851218	+	0.524813i	$0.824135\pi$
$858$	3.58255e15	0.263034
$859$	−9.62049e15	−0.701834	−0.350917	−	0.936406i	$-0.614130\pi$
$859$	−9.62049e15	−0.701834	−0.350917	+	0.936406i	$0.614130\pi$
$860$	5.46208e15	0.395928
$861$	2.26358e15	0.163034
$862$	−1.85846e15	−0.133004
$863$	−1.14684e16	−0.815536	−0.407768	−	0.913085i	$-0.633693\pi$
$863$	−1.14684e16	−0.815536	−0.407768	+	0.913085i	$0.633693\pi$
$864$	−1.27021e15	−0.0897533
$865$	2.16090e16	1.51721
$866$	3.65423e14	0.0254945
$867$	1.11794e15	0.0775019
$868$	2.46820e15	0.170029
$869$	−2.40801e15	−0.164835
$870$	1.07183e15	0.0729071
$871$	7.31751e15	0.494611
$872$	2.25834e15	0.151687
$873$	−5.37359e15	−0.358663
$874$	−1.10161e13	−0.000730659 0
$875$	1.24148e16	0.818270
$876$	4.05819e15	0.265803
$877$	−4.36497e15	−0.284108	−0.142054	−	0.989859i	$-0.545371\pi$
$877$	−4.36497e15	−0.284108	−0.142054	+	0.989859i	$0.545371\pi$
$878$	−5.12944e14	−0.0331780
$879$	9.66641e15	0.621336
$880$	2.33766e16	1.49323
$881$	−7.32263e15	−0.464836	−0.232418	−	0.972616i	$-0.574664\pi$
$881$	−7.32263e15	−0.464836	−0.232418	+	0.972616i	$0.574664\pi$
$882$	3.61517e14	0.0228061
$883$	9.83832e15	0.616790	0.308395	−	0.951258i	$-0.400208\pi$
$883$	9.83832e15	0.616790	0.308395	+	0.951258i	$0.400208\pi$
$884$	2.55773e16	1.59355
$885$	1.06608e15	0.0660090
$886$	−8.52954e14	−0.0524856
$887$	1.98191e16	1.21200	0.606001	−	0.795464i	$-0.292773\pi$
$887$	1.98191e16	1.21200	0.606001	+	0.795464i	$0.292773\pi$
$888$	3.87745e15	0.235654
$889$	−1.31055e16	−0.791579
$890$	−2.24086e15	−0.134514
$891$	3.43128e15	0.204705
$892$	−3.01077e16	−1.78514
$893$	1.87674e13	0.00110591
$894$	−6.75481e14	−0.0395601
$895$	1.90427e16	1.10841
$896$	−7.90214e15	−0.457142
$897$	−4.29554e15	−0.246979
$898$	4.18843e14	0.0239349
$899$	−3.62017e15	−0.205613
$900$	1.31590e15	0.0742831
$901$	−1.57342e15	−0.0882794
$902$	1.98060e15	0.110449
$903$	3.65583e15	0.202630
$904$	−2.02523e15	−0.111570
$905$	1.80932e16	0.990713
$906$	−1.22512e14	−0.00666765
$907$	2.93743e16	1.58901	0.794505	−	0.607257i	$-0.207730\pi$
$907$	2.93743e16	1.58901	0.794505	+	0.607257i	$0.207730\pi$
$908$	−2.92078e16	−1.57046
$909$	5.13931e15	0.274665
$910$	−3.09993e15	−0.164674
$911$	4.72649e15	0.249567	0.124784	−	0.992184i	$-0.460176\pi$
$911$	4.72649e15	0.249567	0.124784	+	0.992184i	$0.460176\pi$
$912$	1.65465e14	0.00868432
$913$	5.20958e16	2.71778
$914$	−2.11589e15	−0.109721
$915$	1.76084e16	0.907621
$916$	−2.67076e16	−1.36839
$917$	1.39226e16	0.709072
$918$	−6.51760e14	−0.0329953
$919$	1.45271e16	0.731046	0.365523	−	0.930802i	$-0.380890\pi$
$919$	1.45271e16	0.731046	0.365523	+	0.930802i	$0.380890\pi$
$920$	1.55372e15	0.0777212
$921$	2.26640e15	0.112696
$922$	3.38352e15	0.167243
$923$	6.81994e15	0.335097
$924$	1.60856e16	0.785671
$925$	−6.05176e15	−0.293834
$926$	−1.10112e15	−0.0531465
$927$	4.23482e15	0.203187
$928$	8.73382e15	0.416572
$929$	−2.01875e15	−0.0957185	−0.0478592	−	0.998854i	$-0.515240\pi$
$929$	−2.01875e15	−0.0957185	−0.0478592	+	0.998854i	$0.515240\pi$
$930$	−3.98621e14	−0.0187890
$931$	−1.47824e14	−0.00692661
$932$	−3.22596e16	−1.50270
$933$	−1.07268e16	−0.496729
$934$	−4.03282e15	−0.185653
$935$	3.76511e16	1.72311
$936$	−3.57653e15	−0.162722
$937$	−4.90720e15	−0.221955	−0.110978	−	0.993823i	$-0.535398\pi$
$937$	−4.90720e15	−0.221955	−0.110978	+	0.993823i	$0.535398\pi$
$938$	−8.74132e14	−0.0393062
$939$	2.18961e16	0.978827
$940$	−1.30611e15	−0.0580466
$941$	−2.30046e15	−0.101642	−0.0508208	−	0.998708i	$-0.516184\pi$
$941$	−2.30046e15	−0.101642	−0.0508208	+	0.998708i	$0.516184\pi$
$942$	−3.16182e15	−0.138885
$943$	−2.37478e15	−0.103707
$944$	2.76749e15	0.120154
$945$	−2.96904e15	−0.128157
$946$	3.19879e15	0.137273
$947$	−1.29652e16	−0.553167	−0.276583	−	0.960990i	$-0.589202\pi$
$947$	−1.29652e16	−0.553167	−0.276583	+	0.960990i	$0.589202\pi$
$948$	1.18620e15	0.0503168
$949$	1.72150e16	0.726009
$950$	1.43155e13	0.000600244 0
$951$	−1.09050e16	−0.454606
$952$	−6.19208e15	−0.256645
$953$	−3.89460e16	−1.60491	−0.802457	−	0.596710i	$-0.796474\pi$
$953$	−3.89460e16	−1.60491	−0.802457	+	0.596710i	$0.796474\pi$
$954$	1.08564e14	0.00444804
$955$	7.65464e15	0.311822
$956$	7.26208e15	0.294132
$957$	−2.35931e16	−0.950100
$958$	−7.13826e15	−0.285813
$959$	−1.22594e16	−0.488051
$960$	−1.08602e16	−0.429879
$961$	−2.40621e16	−0.947011
$962$	8.11617e15	0.317606
$963$	−9.35205e15	−0.363883
$964$	−4.06140e15	−0.157128
$965$	2.01952e16	0.776871
$966$	5.13135e14	0.0196271
$967$	−6.35337e15	−0.241634	−0.120817	−	0.992675i	$-0.538551\pi$
$967$	−6.35337e15	−0.241634	−0.120817	+	0.992675i	$0.538551\pi$
$968$	2.01202e16	0.760882
$969$	2.66503e14	0.0100212
$970$	4.06841e15	0.152118
$971$	−4.09349e16	−1.52190	−0.760952	−	0.648808i	$-0.775268\pi$
$971$	−4.09349e16	−1.52190	−0.760952	+	0.648808i	$0.775268\pi$
$972$	−1.69028e15	−0.0624875
$973$	−4.29296e15	−0.157811
$974$	−9.84566e14	−0.0359891
$975$	5.58210e15	0.202896
$976$	4.57104e16	1.65212
$977$	7.17746e14	0.0257959	0.0128980	−	0.999917i	$-0.495894\pi$
$977$	7.17746e14	0.0257959	0.0128980	+	0.999917i	$0.495894\pi$
$978$	−2.37229e15	−0.0847820
$979$	4.93257e16	1.75295
$980$	1.02877e16	0.363560
$981$	4.52750e15	0.159103
$982$	−3.27745e15	−0.114531
$983$	2.84140e16	0.987387	0.493694	−	0.869636i	$-0.335646\pi$
$983$	2.84140e16	0.987387	0.493694	+	0.869636i	$0.335646\pi$
$984$	−1.97728e15	−0.0683273
$985$	3.93148e16	1.35101
$986$	4.48142e15	0.153141
$987$	−8.74194e14	−0.0297073
$988$	7.21620e14	0.0243863
$989$	−3.83541e15	−0.128894
$990$	−2.59786e15	−0.0868206
$991$	−6.22968e15	−0.207043	−0.103522	−	0.994627i	$-0.533011\pi$
$991$	−6.22968e15	−0.207043	−0.103522	+	0.994627i	$0.533011\pi$
$992$	−3.24817e15	−0.107356
$993$	−1.18654e16	−0.389996
$994$	−8.14693e14	−0.0266298
$995$	−4.34793e16	−1.41337
$996$	−2.56628e16	−0.829617
$997$	5.19909e16	1.67149	0.835745	−	0.549118i	$-0.185036\pi$
$997$	5.19909e16	1.67149	0.835745	+	0.549118i	$0.185036\pi$
$998$	5.70988e15	0.182561
$999$	7.77348e15	0.247175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.13	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.13	✓	28	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)

\(f(q)\)	\(=\)	\(q-7.28530 q^{2} +243.000 q^{3} -1994.92 q^{4} +6136.55 q^{5} -1770.33 q^{6} -33718.8 q^{7} +29453.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-7.28530 q^{2} +243.000 q^{3} -1994.92 q^{4} +6136.55 q^{5} -1770.33 q^{6} -33718.8 q^{7} +29453.9 q^{8} +59049.0 q^{9} -44706.7 q^{10} +984083. q^{11} -484767. q^{12} -2.05640e6 q^{13} +245652. q^{14} +1.49118e6 q^{15} +3.87102e6 q^{16} +6.23478e6 q^{17} -430190. q^{18} +175904. q^{19} -1.22420e7 q^{20} -8.19368e6 q^{21} -7.16934e6 q^{22} +8.59617e6 q^{23} +7.15730e6 q^{24} -1.11708e7 q^{25} +1.49815e7 q^{26} +1.43489e7 q^{27} +6.72665e7 q^{28} -9.86614e7 q^{29} -1.08637e7 q^{30} +3.66929e7 q^{31} -8.85232e7 q^{32} +2.39132e8 q^{33} -4.54223e7 q^{34} -2.06917e8 q^{35} -1.17798e8 q^{36} +5.41747e8 q^{37} -1.28151e6 q^{38} -4.99704e8 q^{39} +1.80746e8 q^{40} -2.76260e8 q^{41} +5.96934e7 q^{42} -4.46177e8 q^{43} -1.96317e9 q^{44} +3.62357e8 q^{45} -6.26257e7 q^{46} +1.06691e8 q^{47} +9.40659e8 q^{48} -8.40367e8 q^{49} +8.13828e7 q^{50} +1.51505e9 q^{51} +4.10235e9 q^{52} -2.52362e8 q^{53} -1.04536e8 q^{54} +6.03888e9 q^{55} -9.93152e8 q^{56} +4.27446e7 q^{57} +7.18778e8 q^{58} +7.14924e8 q^{59} -2.97480e9 q^{60} +1.18084e10 q^{61} -2.67319e8 q^{62} -1.99106e9 q^{63} -7.28294e9 q^{64} -1.26192e10 q^{65} -1.74215e9 q^{66} -3.55842e9 q^{67} -1.24379e10 q^{68} +2.08887e9 q^{69} +1.50746e9 q^{70} -3.31645e9 q^{71} +1.73923e9 q^{72} -8.37143e9 q^{73} -3.94679e9 q^{74} -2.71451e9 q^{75} -3.50915e8 q^{76} -3.31821e10 q^{77} +3.64050e9 q^{78} -2.44696e9 q^{79} +2.37548e10 q^{80} +3.48678e9 q^{81} +2.01264e9 q^{82} +5.29385e10 q^{83} +1.63458e10 q^{84} +3.82601e10 q^{85} +3.25053e9 q^{86} -2.39747e10 q^{87} +2.89851e10 q^{88} +5.01235e10 q^{89} -2.63988e9 q^{90} +6.93393e10 q^{91} -1.71487e10 q^{92} +8.91637e9 q^{93} -7.77278e8 q^{94} +1.07944e9 q^{95} -2.15111e10 q^{96} -9.10022e10 q^{97} +6.12233e9 q^{98} +5.81091e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more