LMFDB - Embedded newform 29.12.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	29.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:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-61.8148$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-61.8148 q^{2} +211.836 q^{3} +1773.06 q^{4} -11752.2 q^{5} -13094.6 q^{6} +18695.9 q^{7} +16995.1 q^{8} -132273. q^{9} +O(q^{10})$	\(q-61.8148 q^{2} +211.836 q^{3} +1773.06 q^{4} -11752.2 q^{5} -13094.6 q^{6} +18695.9 q^{7} +16995.1 q^{8} -132273. q^{9} +726462. q^{10} -635270. q^{11} +375598. q^{12} +25778.2 q^{13} -1.15568e6 q^{14} -2.48954e6 q^{15} -4.68178e6 q^{16} -1.02545e7 q^{17} +8.17640e6 q^{18} -1.44637e6 q^{19} -2.08375e7 q^{20} +3.96045e6 q^{21} +3.92691e7 q^{22} +4.28773e7 q^{23} +3.60017e6 q^{24} +8.92869e7 q^{25} -1.59347e6 q^{26} -6.55461e7 q^{27} +3.31490e7 q^{28} -2.05111e7 q^{29} +1.53890e8 q^{30} +1.54826e8 q^{31} +2.54597e8 q^{32} -1.34573e8 q^{33} +6.33877e8 q^{34} -2.19718e8 q^{35} -2.34528e8 q^{36} +4.92156e8 q^{37} +8.94070e7 q^{38} +5.46074e6 q^{39} -1.99731e8 q^{40} -5.59330e8 q^{41} -2.44815e8 q^{42} +7.05438e8 q^{43} -1.12637e9 q^{44} +1.55450e9 q^{45} -2.65045e9 q^{46} +1.84259e9 q^{47} -9.91769e8 q^{48} -1.62779e9 q^{49} -5.51925e9 q^{50} -2.17226e9 q^{51} +4.57064e7 q^{52} +4.62880e9 q^{53} +4.05172e9 q^{54} +7.46585e9 q^{55} +3.17739e8 q^{56} -3.06393e8 q^{57} +1.26789e9 q^{58} -1.82003e9 q^{59} -4.41412e9 q^{60} +1.03549e9 q^{61} -9.57052e9 q^{62} -2.47295e9 q^{63} -6.14958e9 q^{64} -3.02951e8 q^{65} +8.31859e9 q^{66} -6.27991e9 q^{67} -1.81818e10 q^{68} +9.08294e9 q^{69} +1.35818e10 q^{70} -2.75915e10 q^{71} -2.24799e9 q^{72} +3.06232e10 q^{73} -3.04225e10 q^{74} +1.89142e10 q^{75} -2.56450e9 q^{76} -1.18769e10 q^{77} -3.37554e8 q^{78} -4.03351e10 q^{79} +5.50214e10 q^{80} +9.54670e9 q^{81} +3.45748e10 q^{82} -5.99801e9 q^{83} +7.02214e9 q^{84} +1.20513e11 q^{85} -4.36065e10 q^{86} -4.34499e9 q^{87} -1.07965e10 q^{88} +4.30402e9 q^{89} -9.60910e10 q^{90} +4.81946e8 q^{91} +7.60242e10 q^{92} +3.27976e10 q^{93} -1.13899e11 q^{94} +1.69981e10 q^{95} +5.39328e10 q^{96} -7.40456e10 q^{97} +1.00621e11 q^{98} +8.40289e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * 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 $

$2$	−61.8148	−1.36593	−0.682963	−	0.730453i	$-0.739309\pi$
$2$	−61.8148	−1.36593	−0.682963	+	0.730453i	$0.739309\pi$
$3$	211.836	0.503306	0.251653	−	0.967818i	$-0.419026\pi$
$3$	211.836	0.503306	0.251653	+	0.967818i	$0.419026\pi$
$4$	1773.06	0.865754
$5$	−11752.2	−1.68184	−0.840922	−	0.541157i	$-0.817986\pi$
$5$	−11752.2	−1.68184	−0.840922	+	0.541157i	$0.817986\pi$
$6$	−13094.6	−0.687479
$7$	18695.9	0.420443	0.210221	−	0.977654i	$-0.432582\pi$
$7$	18695.9	0.420443	0.210221	+	0.977654i	$0.432582\pi$
$8$	16995.1	0.183370
$9$	−132273.	−0.746683
$10$	726462.	2.29727
$11$	−635270.	−1.18932	−0.594660	−	0.803977i	$-0.702713\pi$
$11$	−635270.	−1.18932	−0.594660	+	0.803977i	$0.702713\pi$
$12$	375598.	0.435739
$13$	25778.2	0.0192559	0.00962795	−	0.999954i	$-0.496935\pi$
$13$	25778.2	0.0192559	0.00962795	+	0.999954i	$0.496935\pi$
$14$	−1.15568e6	−0.574294
$15$	−2.48954e6	−0.846482
$16$	−4.68178e6	−1.11622
$17$	−1.02545e7	−1.75164	−0.875818	−	0.482642i	$-0.839677\pi$
$17$	−1.02545e7	−1.75164	−0.875818	+	0.482642i	$0.839677\pi$
$18$	8.17640e6	1.01991
$19$	−1.44637e6	−0.134009	−0.0670046	−	0.997753i	$-0.521344\pi$
$19$	−1.44637e6	−0.134009	−0.0670046	+	0.997753i	$0.521344\pi$
$20$	−2.08375e7	−1.45606
$21$	3.96045e6	0.211611
$22$	3.92691e7	1.62452
$23$	4.28773e7	1.38907	0.694535	−	0.719459i	$-0.255610\pi$
$23$	4.28773e7	1.38907	0.694535	+	0.719459i	$0.255610\pi$
$24$	3.60017e6	0.0922914
$25$	8.92869e7	1.82860
$26$	−1.59347e6	−0.0263021
$27$	−6.55461e7	−0.879116
$28$	3.31490e7	0.364000
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	1.53890e8	1.15623
$31$	1.54826e8	0.971302	0.485651	−	0.874153i	$-0.338583\pi$
$31$	1.54826e8	0.971302	0.485651	+	0.874153i	$0.338583\pi$
$32$	2.54597e8	1.34131
$33$	−1.34573e8	−0.598592
$34$	6.33877e8	2.39260
$35$	−2.19718e8	−0.707119
$36$	−2.34528e8	−0.646444
$37$	4.92156e8	1.16679	0.583396	−	0.812188i	$-0.301724\pi$
$37$	4.92156e8	1.16679	0.583396	+	0.812188i	$0.301724\pi$
$38$	8.94070e7	0.183047
$39$	5.46074e6	0.00969161
$40$	−1.99731e8	−0.308400
$41$	−5.59330e8	−0.753975	−0.376987	−	0.926218i	$-0.623040\pi$
$41$	−5.59330e8	−0.753975	−0.376987	+	0.926218i	$0.623040\pi$
$42$	−2.44815e8	−0.289045
$43$	7.05438e8	0.731783	0.365892	−	0.930658i	$-0.380764\pi$
$43$	7.05438e8	0.731783	0.365892	+	0.930658i	$0.380764\pi$
$44$	−1.12637e9	−1.02966
$45$	1.55450e9	1.25580
$46$	−2.65045e9	−1.89737
$47$	1.84259e9	1.17190	0.585950	−	0.810347i	$-0.300722\pi$
$47$	1.84259e9	1.17190	0.585950	+	0.810347i	$0.300722\pi$
$48$	−9.91769e8	−0.561802
$49$	−1.62779e9	−0.823228
$50$	−5.51925e9	−2.49773
$51$	−2.17226e9	−0.881609
$52$	4.57064e7	0.0166709
$53$	4.62880e9	1.52038	0.760188	−	0.649704i	$-0.225107\pi$
$53$	4.62880e9	1.52038	0.760188	+	0.649704i	$0.225107\pi$
$54$	4.05172e9	1.20081
$55$	7.46585e9	2.00025
$56$	3.17739e8	0.0770967
$57$	−3.06393e8	−0.0674476
$58$	1.26789e9	0.253646
$59$	−1.82003e9	−0.331431	−0.165716	−	0.986174i	$-0.552993\pi$
$59$	−1.82003e9	−0.331431	−0.165716	+	0.986174i	$0.552993\pi$
$60$	−4.41412e9	−0.732845
$61$	1.03549e9	0.156976	0.0784878	−	0.996915i	$-0.474991\pi$
$61$	1.03549e9	0.156976	0.0784878	+	0.996915i	$0.474991\pi$
$62$	−9.57052e9	−1.32673
$63$	−2.47295e9	−0.313937
$64$	−6.14958e9	−0.715905
$65$	−3.02951e8	−0.0323854
$66$	8.31859e9	0.817632
$67$	−6.27991e9	−0.568253	−0.284127	−	0.958787i	$-0.591704\pi$
$67$	−6.27991e9	−0.568253	−0.284127	+	0.958787i	$0.591704\pi$
$68$	−1.81818e10	−1.51649
$69$	9.08294e9	0.699128
$70$	1.35818e10	0.965872
$71$	−2.75915e10	−1.81491	−0.907455	−	0.420150i	$-0.861977\pi$
$71$	−2.75915e10	−1.81491	−0.907455	+	0.420150i	$0.861977\pi$
$72$	−2.24799e9	−0.136920
$73$	3.06232e10	1.72892	0.864461	−	0.502700i	$-0.167660\pi$
$73$	3.06232e10	1.72892	0.864461	+	0.502700i	$0.167660\pi$
$74$	−3.04225e10	−1.59375
$75$	1.89142e10	0.920344
$76$	−2.56450e9	−0.116019
$77$	−1.18769e10	−0.500041
$78$	−3.37554e8	−0.0132380
$79$	−4.03351e10	−1.47480	−0.737402	−	0.675454i	$-0.763948\pi$
$79$	−4.03351e10	−1.47480	−0.737402	+	0.675454i	$0.763948\pi$
$80$	5.50214e10	1.87731
$81$	9.54670e9	0.304219
$82$	3.45748e10	1.02987
$83$	−5.99801e9	−0.167139	−0.0835695	−	0.996502i	$-0.526632\pi$
$83$	−5.99801e9	−0.167139	−0.0835695	+	0.996502i	$0.526632\pi$
$84$	7.02214e9	0.183203
$85$	1.20513e11	2.94598
$86$	−4.36065e10	−0.999561
$87$	−4.34499e9	−0.0934616
$88$	−1.07965e10	−0.218086
$89$	4.30402e9	0.0817013	0.0408507	−	0.999165i	$-0.486993\pi$
$89$	4.30402e9	0.0817013	0.0408507	+	0.999165i	$0.486993\pi$
$90$	−9.60910e10	−1.71533
$91$	4.81946e8	0.00809600
$92$	7.60242e10	1.20259
$93$	3.27976e10	0.488862
$94$	−1.13899e11	−1.60073
$95$	1.69981e10	0.225382
$96$	5.39328e10	0.675089
$97$	−7.40456e10	−0.875497	−0.437748	−	0.899097i	$-0.644224\pi$
$97$	−7.40456e10	−0.875497	−0.437748	+	0.899097i	$0.644224\pi$
$98$	1.00621e11	1.12447
$99$	8.40289e10	0.888045
$100$	1.58311e11	1.58311
$101$	1.08927e11	1.03126	0.515628	−	0.856813i	$-0.327559\pi$
$101$	1.08927e11	1.03126	0.515628	+	0.856813i	$0.327559\pi$
$102$	1.34278e11	1.20421
$103$	1.03352e11	0.878446	0.439223	−	0.898378i	$-0.355254\pi$
$103$	1.03352e11	0.878446	0.439223	+	0.898378i	$0.355254\pi$
$104$	4.38103e8	0.00353096
$105$	−4.65442e10	−0.355897
$106$	−2.86128e11	−2.07672
$107$	−1.05419e11	−0.726623	−0.363312	−	0.931668i	$-0.618354\pi$
$107$	−1.05419e11	−0.726623	−0.363312	+	0.931668i	$0.618354\pi$
$108$	−1.16217e11	−0.761098
$109$	2.70757e10	0.168552	0.0842759	−	0.996442i	$-0.473142\pi$
$109$	2.70757e10	0.168552	0.0842759	+	0.996442i	$0.473142\pi$
$110$	−4.61499e11	−2.73219
$111$	1.04256e11	0.587254
$112$	−8.75301e10	−0.469308
$113$	1.16418e11	0.594411	0.297206	−	0.954814i	$-0.403945\pi$
$113$	1.16418e11	0.594411	0.297206	+	0.954814i	$0.403945\pi$
$114$	1.89396e10	0.0921284
$115$	−5.03904e11	−2.33620
$116$	−3.63676e10	−0.160766
$117$	−3.40975e9	−0.0143781
$118$	1.12505e11	0.452710
$119$	−1.91716e11	−0.736462
$120$	−4.23101e10	−0.155220
$121$	1.18257e11	0.414483
$122$	−6.40086e10	−0.214417
$123$	−1.18486e11	−0.379480
$124$	2.74516e11	0.840908
$125$	−4.75481e11	−1.39357
$126$	1.52865e11	0.428815
$127$	−1.45152e11	−0.389854	−0.194927	−	0.980818i	$-0.562447\pi$
$127$	−1.45152e11	−0.389854	−0.194927	+	0.980818i	$0.562447\pi$
$128$	−1.41281e11	−0.363436
$129$	1.49437e11	0.368311
$130$	1.87269e10	0.0442361
$131$	−1.69423e11	−0.383691	−0.191845	−	0.981425i	$-0.561447\pi$
$131$	−1.69423e11	−0.383691	−0.191845	+	0.981425i	$0.561447\pi$
$132$	−2.38606e11	−0.518233
$133$	−2.70411e10	−0.0563432
$134$	3.88191e11	0.776192
$135$	7.70313e11	1.47854
$136$	−1.74276e11	−0.321198
$137$	4.75508e11	0.841772	0.420886	−	0.907113i	$-0.361719\pi$
$137$	4.75508e11	0.841772	0.420886	+	0.907113i	$0.361719\pi$
$138$	−5.61460e11	−0.954957
$139$	7.11579e11	1.16317	0.581583	−	0.813487i	$-0.302433\pi$
$139$	7.11579e11	1.16317	0.581583	+	0.813487i	$0.302433\pi$
$140$	−3.89575e11	−0.612191
$141$	3.90326e11	0.589824
$142$	1.70556e12	2.47903
$143$	−1.63761e10	−0.0229014
$144$	6.19272e11	0.833466
$145$	2.41052e11	0.312310
$146$	−1.89297e12	−2.36158
$147$	−3.44824e11	−0.414336
$148$	8.72624e11	1.01015
$149$	4.81820e11	0.537477	0.268739	−	0.963213i	$-0.413393\pi$
$149$	4.81820e11	0.537477	0.268739	+	0.963213i	$0.413393\pi$
$150$	−1.16917e12	−1.25712
$151$	1.87140e12	1.93996	0.969979	−	0.243189i	$-0.0781935\pi$
$151$	1.87140e12	1.93996	0.969979	+	0.243189i	$0.0781935\pi$
$152$	−2.45812e10	−0.0245733
$153$	1.35638e12	1.30792
$154$	7.34170e11	0.683019
$155$	−1.81955e12	−1.63358
$156$	9.68224e9	0.00839055
$157$	−1.37006e12	−1.14629	−0.573143	−	0.819455i	$-0.694276\pi$
$157$	−1.37006e12	−1.14629	−0.573143	+	0.819455i	$0.694276\pi$
$158$	2.49330e12	2.01447
$159$	9.80544e11	0.765214
$160$	−2.99209e12	−2.25587
$161$	8.01629e11	0.584024
$162$	−5.90127e11	−0.415540
$163$	−2.60106e11	−0.177059	−0.0885295	−	0.996074i	$-0.528217\pi$
$163$	−2.60106e11	−0.177059	−0.0885295	+	0.996074i	$0.528217\pi$
$164$	−9.91727e11	−0.652756
$165$	1.58153e12	1.00674
$166$	3.70765e11	0.228299
$167$	−2.34173e12	−1.39507	−0.697537	−	0.716549i	$-0.745721\pi$
$167$	−2.34173e12	−1.39507	−0.697537	+	0.716549i	$0.745721\pi$
$168$	6.73084e10	0.0388032
$169$	−1.79150e12	−0.999629
$170$	−7.44947e12	−4.02399
$171$	1.91315e11	0.100062
$172$	1.25079e12	0.633544
$173$	2.59433e12	1.27283	0.636417	−	0.771345i	$-0.280416\pi$
$173$	2.59433e12	1.27283	0.636417	+	0.771345i	$0.280416\pi$
$174$	2.68585e11	0.127662
$175$	1.66930e12	0.768820
$176$	2.97420e12	1.32755
$177$	−3.85548e11	−0.166811
$178$	−2.66052e11	−0.111598
$179$	−8.02970e11	−0.326594	−0.163297	−	0.986577i	$-0.552213\pi$
$179$	−8.02970e11	−0.326594	−0.163297	+	0.986577i	$0.552213\pi$
$180$	2.75623e12	1.08722
$181$	2.47641e12	0.947526	0.473763	−	0.880652i	$-0.342895\pi$
$181$	2.47641e12	0.947526	0.473763	+	0.880652i	$0.342895\pi$
$182$	−2.97914e10	−0.0110585
$183$	2.19354e11	0.0790068
$184$	7.28704e11	0.254714
$185$	−5.78394e12	−1.96236
$186$	−2.02738e12	−0.667750
$187$	6.51435e12	2.08326
$188$	3.26703e12	1.01458
$189$	−1.22544e12	−0.369618
$190$	−1.05073e12	−0.307856
$191$	−2.41134e12	−0.686395	−0.343198	−	0.939263i	$-0.611510\pi$
$191$	−2.41134e12	−0.686395	−0.343198	+	0.939263i	$0.611510\pi$
$192$	−1.30270e12	−0.360319
$193$	−1.41348e12	−0.379949	−0.189974	−	0.981789i	$-0.560840\pi$
$193$	−1.41348e12	−0.379949	−0.189974	+	0.981789i	$0.560840\pi$
$194$	4.57711e12	1.19586
$195$	−6.41759e10	−0.0162998
$196$	−2.88618e12	−0.712713
$197$	−5.83336e12	−1.40073	−0.700365	−	0.713785i	$-0.746980\pi$
$197$	−5.83336e12	−1.40073	−0.700365	+	0.713785i	$0.746980\pi$
$198$	−5.19423e12	−1.21300
$199$	6.86160e12	1.55860	0.779298	−	0.626654i	$-0.215576\pi$
$199$	6.86160e12	1.55860	0.779298	+	0.626654i	$0.215576\pi$
$200$	1.51744e12	0.335310
$201$	−1.33031e12	−0.286005
$202$	−6.73327e12	−1.40862
$203$	−3.83474e11	−0.0780742
$204$	−3.85156e12	−0.763256
$205$	6.57338e12	1.26807
$206$	−6.38870e12	−1.19989
$207$	−5.67149e12	−1.03720
$208$	−1.20688e11	−0.0214939
$209$	9.18835e11	0.159380
$210$	2.87712e12	0.486129
$211$	1.88517e12	0.310310	0.155155	−	0.987890i	$-0.450412\pi$
$211$	1.88517e12	0.310310	0.155155	+	0.987890i	$0.450412\pi$
$212$	8.20715e12	1.31627
$213$	−5.84487e12	−0.913455
$214$	6.51647e12	0.992513
$215$	−8.29047e12	−1.23074
$216$	−1.11396e12	−0.161204
$217$	2.89461e12	0.408377
$218$	−1.67368e12	−0.230229
$219$	6.48709e12	0.870177
$220$	1.32374e13	1.73172
$221$	−2.64341e11	−0.0337293
$222$	−6.44457e12	−0.802145
$223$	−9.57704e12	−1.16293	−0.581466	−	0.813570i	$-0.697521\pi$
$223$	−9.57704e12	−1.16293	−0.581466	+	0.813570i	$0.697521\pi$
$224$	4.75992e12	0.563944
$225$	−1.18102e13	−1.36538
$226$	−7.19632e12	−0.811922
$227$	8.48571e12	0.934428	0.467214	−	0.884144i	$-0.345258\pi$
$227$	8.48571e12	0.934428	0.467214	+	0.884144i	$0.345258\pi$
$228$	−5.43254e11	−0.0583930
$229$	1.37794e13	1.44589	0.722945	−	0.690905i	$-0.242788\pi$
$229$	1.37794e13	1.44589	0.722945	+	0.690905i	$0.242788\pi$
$230$	3.11487e13	3.19107
$231$	−2.51596e12	−0.251674
$232$	−3.48589e11	−0.0340510
$233$	−2.88690e11	−0.0275406	−0.0137703	−	0.999905i	$-0.504383\pi$
$233$	−2.88690e11	−0.0275406	−0.0137703	+	0.999905i	$0.504383\pi$
$234$	2.10773e11	0.0196394
$235$	−2.16546e13	−1.97095
$236$	−3.22704e12	−0.286938
$237$	−8.54441e12	−0.742278
$238$	1.18509e13	1.00595
$239$	−2.14586e12	−0.177997	−0.0889986	−	0.996032i	$-0.528367\pi$
$239$	−2.14586e12	−0.177997	−0.0889986	+	0.996032i	$0.528367\pi$
$240$	1.16555e13	0.944863
$241$	−1.19776e13	−0.949024	−0.474512	−	0.880249i	$-0.657375\pi$
$241$	−1.19776e13	−0.949024	−0.474512	+	0.880249i	$0.657375\pi$
$242$	−7.31001e12	−0.566153
$243$	1.36336e13	1.03223
$244$	1.83599e12	0.135902
$245$	1.91302e13	1.38454
$246$	7.32418e12	0.518342
$247$	−3.72848e10	−0.00258047
$248$	2.63128e12	0.178108
$249$	−1.27059e12	−0.0841220
$250$	2.93918e13	1.90351
$251$	−6.88624e12	−0.436292	−0.218146	−	0.975916i	$-0.570001\pi$
$251$	−6.88624e12	−0.436292	−0.218146	+	0.975916i	$0.570001\pi$
$252$	−4.38471e12	−0.271793
$253$	−2.72387e13	−1.65205
$254$	8.97253e12	0.532512
$255$	2.55289e13	1.48273
$256$	2.13276e13	1.21233
$257$	6.69576e12	0.372536	0.186268	−	0.982499i	$-0.440361\pi$
$257$	6.69576e12	0.372536	0.186268	+	0.982499i	$0.440361\pi$
$258$	−9.23741e12	−0.503085
$259$	9.20130e12	0.490569
$260$	−5.37152e11	−0.0280378
$261$	2.71306e12	0.138656
$262$	1.04729e13	0.524093
$263$	−2.71918e13	−1.33254	−0.666271	−	0.745710i	$-0.732111\pi$
$263$	−2.71918e13	−1.33254	−0.666271	+	0.745710i	$0.732111\pi$
$264$	−2.28708e12	−0.109764
$265$	−5.43987e13	−2.55703
$266$	1.67154e12	0.0769606
$267$	9.11745e11	0.0411208
$268$	−1.11347e13	−0.491968
$269$	−6.16181e12	−0.266729	−0.133365	−	0.991067i	$-0.542578\pi$
$269$	−6.16181e12	−0.266729	−0.133365	+	0.991067i	$0.542578\pi$
$270$	−4.76167e13	−2.01957
$271$	−1.44335e13	−0.599845	−0.299923	−	0.953964i	$-0.596961\pi$
$271$	−1.44335e13	−0.599845	−0.299923	+	0.953964i	$0.596961\pi$
$272$	4.80092e13	1.95522
$273$	1.02093e11	0.00407477
$274$	−2.93934e13	−1.14980
$275$	−5.67213e13	−2.17479
$276$	1.61046e13	0.605272
$277$	1.03724e13	0.382154	0.191077	−	0.981575i	$-0.438802\pi$
$277$	1.03724e13	0.382154	0.191077	+	0.981575i	$0.438802\pi$
$278$	−4.39861e13	−1.58880
$279$	−2.04792e13	−0.725255
$280$	−3.73414e12	−0.129665
$281$	5.41769e11	0.0184471	0.00922357	−	0.999957i	$-0.497064\pi$
$281$	5.41769e11	0.0184471	0.00922357	+	0.999957i	$0.497064\pi$
$282$	−2.41279e13	−0.805656
$283$	3.09302e13	1.01288	0.506440	−	0.862275i	$-0.330961\pi$
$283$	3.09302e13	1.01288	0.506440	+	0.862275i	$0.330961\pi$
$284$	−4.89216e13	−1.57126
$285$	3.60080e12	0.113436
$286$	1.01229e12	0.0312817
$287$	−1.04572e13	−0.317003
$288$	−3.36763e13	−1.00153
$289$	7.08821e13	2.06823
$290$	−1.49006e13	−0.426593
$291$	−1.56855e13	−0.440643
$292$	5.42969e13	1.49682
$293$	5.35808e13	1.44956	0.724781	−	0.688979i	$-0.241941\pi$
$293$	5.35808e13	1.44956	0.724781	+	0.688979i	$0.241941\pi$
$294$	2.13152e13	0.565952
$295$	2.13895e13	0.557415
$296$	8.36425e12	0.213955
$297$	4.16395e13	1.04555
$298$	−2.97836e13	−0.734154
$299$	1.10530e12	0.0267478
$300$	3.35360e13	0.796791
$301$	1.31888e13	0.307673
$302$	−1.15680e14	−2.64984
$303$	2.30745e13	0.519037
$304$	6.77159e12	0.149584
$305$	−1.21693e13	−0.264008
$306$	−8.38446e13	−1.78652
$307$	2.42803e13	0.508152	0.254076	−	0.967184i	$-0.418229\pi$
$307$	2.42803e13	0.508152	0.254076	+	0.967184i	$0.418229\pi$
$308$	−2.10586e13	−0.432912
$309$	2.18937e13	0.442127
$310$	1.12475e14	2.23135
$311$	9.68530e13	1.88769	0.943846	−	0.330386i	$-0.107179\pi$
$311$	9.68530e13	1.88769	0.943846	+	0.330386i	$0.107179\pi$
$312$	9.28058e10	0.00177715
$313$	−1.16911e13	−0.219969	−0.109984	−	0.993933i	$-0.535080\pi$
$313$	−1.16911e13	−0.219969	−0.109984	+	0.993933i	$0.535080\pi$
$314$	8.46902e13	1.56574
$315$	2.90627e13	0.527993
$316$	−7.15167e13	−1.27682
$317$	−1.47397e13	−0.258620	−0.129310	−	0.991604i	$-0.541276\pi$
$317$	−1.47397e13	−0.258620	−0.129310	+	0.991604i	$0.541276\pi$
$318$	−6.06121e13	−1.04523
$319$	1.30301e13	0.220851
$320$	7.22713e13	1.20404
$321$	−2.23316e13	−0.365714
$322$	−4.95525e13	−0.797734
$323$	1.48317e13	0.234735
$324$	1.69269e13	0.263378
$325$	2.30165e12	0.0352113
$326$	1.60784e13	0.241849
$327$	5.73559e12	0.0848332
$328$	−9.50587e12	−0.138257
$329$	3.44488e13	0.492717
$330$	−9.77620e13	−1.37513
$331$	−4.31393e13	−0.596786	−0.298393	−	0.954443i	$-0.596451\pi$
$331$	−4.31393e13	−0.596786	−0.298393	+	0.954443i	$0.596451\pi$
$332$	−1.06349e13	−0.144701
$333$	−6.50988e13	−0.871224
$334$	1.44754e14	1.90557
$335$	7.38030e13	0.955713
$336$	−1.85420e13	−0.236206
$337$	9.65702e13	1.21026	0.605130	−	0.796127i	$-0.293121\pi$
$337$	9.65702e13	1.21026	0.605130	+	0.796127i	$0.293121\pi$
$338$	1.10741e14	1.36542
$339$	2.46614e13	0.299171
$340$	2.13677e14	2.55049
$341$	−9.83563e13	−1.15519
$342$	−1.18261e13	−0.136678
$343$	−6.74009e13	−0.766563
$344$	1.19890e13	0.134187
$345$	−1.06745e14	−1.17582
$346$	−1.60368e14	−1.73860
$347$	1.45227e14	1.54965	0.774826	−	0.632175i	$-0.217837\pi$
$347$	1.45227e14	1.54965	0.774826	+	0.632175i	$0.217837\pi$
$348$	−7.70395e12	−0.0809147
$349$	−1.22200e14	−1.26337	−0.631686	−	0.775225i	$-0.717637\pi$
$349$	−1.22200e14	−1.26337	−0.631686	+	0.775225i	$0.717637\pi$
$350$	−1.03187e14	−1.05015
$351$	−1.68966e12	−0.0169282
$352$	−1.61738e14	−1.59525
$353$	−5.84440e13	−0.567517	−0.283759	−	0.958896i	$-0.591581\pi$
$353$	−5.84440e13	−0.567517	−0.283759	+	0.958896i	$0.591581\pi$
$354$	2.38326e13	0.227852
$355$	3.24262e14	3.05239
$356$	7.63130e12	0.0707332
$357$	−4.06123e13	−0.370666
$358$	4.96354e13	0.446103
$359$	−6.19909e13	−0.548666	−0.274333	−	0.961635i	$-0.588457\pi$
$359$	−6.19909e13	−0.548666	−0.274333	+	0.961635i	$0.588457\pi$
$360$	2.64189e13	0.230277
$361$	−1.14398e14	−0.982042
$362$	−1.53079e14	−1.29425
$363$	2.50510e13	0.208612
$364$	8.54521e11	0.00700914
$365$	−3.59891e14	−2.90777
$366$	−1.35593e13	−0.107917
$367$	1.96835e13	0.154326	0.0771631	−	0.997018i	$-0.475414\pi$
$367$	1.96835e13	0.154326	0.0771631	+	0.997018i	$0.475414\pi$
$368$	−2.00742e14	−1.55051
$369$	7.39840e13	0.562980
$370$	3.57533e14	2.68044
$371$	8.65394e13	0.639231
$372$	5.81523e13	0.423234
$373$	−1.34822e13	−0.0966857	−0.0483429	−	0.998831i	$-0.515394\pi$
$373$	−1.34822e13	−0.0966857	−0.0483429	+	0.998831i	$0.515394\pi$
$374$	−4.02683e14	−2.84557
$375$	−1.00724e14	−0.701392
$376$	3.13150e13	0.214892
$377$	−5.28740e11	−0.00357573
$378$	7.57504e13	0.504871
$379$	−2.34627e13	−0.154121	−0.0770607	−	0.997026i	$-0.524554\pi$
$379$	−2.34627e13	−0.154121	−0.0770607	+	0.997026i	$0.524554\pi$
$380$	3.01387e13	0.195126
$381$	−3.07484e13	−0.196216
$382$	1.49056e14	0.937565
$383$	1.48367e14	0.919909	0.459955	−	0.887942i	$-0.347866\pi$
$383$	1.48367e14	0.919909	0.459955	+	0.887942i	$0.347866\pi$
$384$	−2.99283e13	−0.182920
$385$	1.39581e14	0.840990
$386$	8.73740e13	0.518982
$387$	−9.33102e13	−0.546410
$388$	−1.31288e14	−0.757965
$389$	2.73666e14	1.55775	0.778875	−	0.627179i	$-0.215791\pi$
$389$	2.73666e14	1.55775	0.778875	+	0.627179i	$0.215791\pi$
$390$	3.96702e12	0.0222643
$391$	−4.39684e14	−2.43315
$392$	−2.76645e13	−0.150956
$393$	−3.58899e13	−0.193114
$394$	3.60588e14	1.91329
$395$	4.74028e14	2.48039
$396$	1.48989e14	0.768829
$397$	2.35898e14	1.20054	0.600270	−	0.799797i	$-0.295060\pi$
$397$	2.35898e14	1.20054	0.600270	+	0.799797i	$0.295060\pi$
$398$	−4.24148e14	−2.12893
$399$	−5.72828e12	−0.0283578
$400$	−4.18022e14	−2.04112
$401$	1.07468e14	0.517591	0.258795	−	0.965932i	$-0.416674\pi$
$401$	1.07468e14	0.517591	0.258795	+	0.965932i	$0.416674\pi$
$402$	8.22327e13	0.390662
$403$	3.99113e12	0.0187033
$404$	1.93134e14	0.892813
$405$	−1.12195e14	−0.511648
$406$	2.37044e13	0.106644
$407$	−3.12652e14	−1.38769
$408$	−3.69178e13	−0.161661
$409$	4.16489e13	0.179939	0.0899695	−	0.995945i	$-0.471323\pi$
$409$	4.16489e13	0.179939	0.0899695	+	0.995945i	$0.471323\pi$
$410$	−4.06332e14	−1.73209
$411$	1.00730e14	0.423669
$412$	1.83250e14	0.760518
$413$	−3.40271e13	−0.139348
$414$	3.50582e14	1.41673
$415$	7.04900e13	0.281101
$416$	6.56305e12	0.0258281
$417$	1.50738e14	0.585429
$418$	−5.67976e13	−0.217701
$419$	−1.13847e14	−0.430670	−0.215335	−	0.976540i	$-0.569084\pi$
$419$	−1.13847e14	−0.430670	−0.215335	+	0.976540i	$0.569084\pi$
$420$	−8.25258e13	−0.308119
$421$	−1.43489e14	−0.528771	−0.264385	−	0.964417i	$-0.585169\pi$
$421$	−1.43489e14	−0.528771	−0.264385	+	0.964417i	$0.585169\pi$
$422$	−1.16531e14	−0.423861
$423$	−2.43724e14	−0.875038
$424$	7.86669e13	0.278792
$425$	−9.15589e14	−3.20303
$426$	3.61299e14	1.24771
$427$	1.93594e13	0.0659993
$428$	−1.86915e14	−0.629077
$429$	−3.46904e12	−0.0115264
$430$	5.12474e14	1.68111
$431$	2.54388e14	0.823894	0.411947	−	0.911208i	$-0.364849\pi$
$431$	2.54388e14	0.823894	0.411947	+	0.911208i	$0.364849\pi$
$432$	3.06873e14	0.981291
$433$	−6.02844e14	−1.90336	−0.951681	−	0.307087i	$-0.900646\pi$
$433$	−6.02844e14	−1.90336	−0.951681	+	0.307087i	$0.900646\pi$
$434$	−1.78929e14	−0.557813
$435$	5.10634e13	0.157188
$436$	4.80069e13	0.145924
$437$	−6.20164e13	−0.186148
$438$	−4.00998e14	−1.18860
$439$	−3.53453e12	−0.0103461	−0.00517305	−	0.999987i	$-0.501647\pi$
$439$	−3.53453e12	−0.0103461	−0.00517305	+	0.999987i	$0.501647\pi$
$440$	1.26883e14	0.366787
$441$	2.15312e14	0.614690
$442$	1.63402e13	0.0460718
$443$	6.17006e14	1.71818	0.859090	−	0.511824i	$-0.171030\pi$
$443$	6.17006e14	1.71818	0.859090	+	0.511824i	$0.171030\pi$
$444$	1.84853e14	0.508417
$445$	−5.05818e13	−0.137409
$446$	5.92002e14	1.58848
$447$	1.02067e14	0.270516
$448$	−1.14972e14	−0.300997
$449$	6.22203e14	1.60908	0.804539	−	0.593900i	$-0.202413\pi$
$449$	6.22203e14	1.60908	0.804539	+	0.593900i	$0.202413\pi$
$450$	7.30046e14	1.86501
$451$	3.55326e14	0.896717
$452$	2.06416e14	0.514614
$453$	3.96428e14	0.976393
$454$	−5.24542e14	−1.27636
$455$	−5.66394e12	−0.0136162
$456$	−5.20718e12	−0.0123679
$457$	6.88484e14	1.61568	0.807839	−	0.589403i	$-0.200637\pi$
$457$	6.88484e14	1.61568	0.807839	+	0.589403i	$0.200637\pi$
$458$	−8.51771e14	−1.97498
$459$	6.72140e14	1.53989
$460$	−8.93454e14	−2.02257
$461$	−7.14510e14	−1.59828	−0.799141	−	0.601144i	$-0.794712\pi$
$461$	−7.14510e14	−1.59828	−0.799141	+	0.601144i	$0.794712\pi$
$462$	1.55523e14	0.343768
$463$	−5.82298e14	−1.27189	−0.635945	−	0.771734i	$-0.719390\pi$
$463$	−5.82298e14	−1.27189	−0.635945	+	0.771734i	$0.719390\pi$
$464$	9.60288e13	0.207278
$465$	−3.85446e14	−0.822190
$466$	1.78453e13	0.0376184
$467$	−2.15379e12	−0.00448706	−0.00224353	−	0.999997i	$-0.500714\pi$
$467$	−2.15379e12	−0.00448706	−0.00224353	+	0.999997i	$0.500714\pi$
$468$	−6.04570e12	−0.0124479
$469$	−1.17408e14	−0.238918
$470$	1.33857e15	2.69217
$471$	−2.90229e14	−0.576933
$472$	−3.09317e13	−0.0607746
$473$	−4.48144e14	−0.870324
$474$	5.28171e14	1.01390
$475$	−1.29142e14	−0.245049
$476$	−3.39925e14	−0.637595
$477$	−6.12263e14	−1.13524
$478$	1.32646e14	0.243131
$479$	3.55936e14	0.644950	0.322475	−	0.946578i	$-0.395485\pi$
$479$	3.55936e14	0.644950	0.322475	+	0.946578i	$0.395485\pi$
$480$	−6.33831e14	−1.13539
$481$	1.26869e13	0.0224676
$482$	7.40394e14	1.29630
$483$	1.69814e14	0.293943
$484$	2.09677e14	0.358840
$485$	8.70201e14	1.47245
$486$	−8.42759e14	−1.40995
$487$	−6.22478e14	−1.02971	−0.514855	−	0.857277i	$-0.672154\pi$
$487$	−6.22478e14	−1.02971	−0.514855	+	0.857277i	$0.672154\pi$
$488$	1.75983e13	0.0287847
$489$	−5.50996e13	−0.0891148
$490$	−1.18253e15	−1.89118
$491$	4.95957e14	0.784324	0.392162	−	0.919896i	$-0.371727\pi$
$491$	4.95957e14	0.784324	0.392162	+	0.919896i	$0.371727\pi$
$492$	−2.10083e14	−0.328536
$493$	2.10331e14	0.325271
$494$	2.30475e12	0.00352473
$495$	−9.87527e14	−1.49355
$496$	−7.24861e14	−1.08419
$497$	−5.15848e14	−0.763065
$498$	7.85413e13	0.114904
$499$	5.30780e14	0.768000	0.384000	−	0.923333i	$-0.374546\pi$
$499$	5.30780e14	0.768000	0.384000	+	0.923333i	$0.374546\pi$
$500$	−8.43059e14	−1.20649
$501$	−4.96063e14	−0.702149
$502$	4.25671e14	0.595942
$503$	5.17191e14	0.716188	0.358094	−	0.933686i	$-0.383427\pi$
$503$	5.17191e14	0.716188	0.358094	+	0.933686i	$0.383427\pi$
$504$	−4.20281e13	−0.0575668
$505$	−1.28013e15	−1.73441
$506$	1.68375e15	2.25658
$507$	−3.79503e14	−0.503119
$508$	−2.57364e14	−0.337518
$509$	1.14084e15	1.48005	0.740023	−	0.672581i	$-0.234814\pi$
$509$	1.14084e15	1.48005	0.740023	+	0.672581i	$0.234814\pi$
$510$	−1.57806e15	−2.02530
$511$	5.72528e14	0.726912
$512$	−1.02902e15	−1.29252
$513$	9.48039e13	0.117810
$514$	−4.13897e14	−0.508856
$515$	−1.21462e15	−1.47741
$516$	2.64961e14	0.318867
$517$	−1.17054e15	−1.39376
$518$	−5.68776e14	−0.670081
$519$	5.49572e14	0.640626
$520$	−5.14869e12	−0.00593852
$521$	1.19750e15	1.36669	0.683343	−	0.730098i	$-0.260526\pi$
$521$	1.19750e15	1.36669	0.683343	+	0.730098i	$0.260526\pi$
$522$	−1.67707e14	−0.189393
$523$	−1.41586e15	−1.58220	−0.791098	−	0.611689i	$-0.790490\pi$
$523$	−1.41586e15	−1.58220	−0.791098	+	0.611689i	$0.790490\pi$
$524$	−3.00399e14	−0.332182
$525$	3.53617e14	0.386952
$526$	1.68085e15	1.82015
$527$	−1.58766e15	−1.70137
$528$	6.30041e14	0.668163
$529$	8.85653e14	0.929517
$530$	3.36264e15	3.49272
$531$	2.40741e14	0.247474
$532$	−4.79457e13	−0.0487793
$533$	−1.44185e13	−0.0145185
$534$	−5.63593e13	−0.0561679
$535$	1.23891e15	1.22207
$536$	−1.06728e14	−0.104201
$537$	−1.70098e14	−0.164377
$538$	3.80891e14	0.364333
$539$	1.03409e15	0.979082
$540$	1.36581e15	1.28005
$541$	−1.85539e15	−1.72128	−0.860638	−	0.509218i	$-0.829935\pi$
$541$	−1.85539e15	−1.72128	−0.860638	+	0.509218i	$0.829935\pi$
$542$	8.92201e14	0.819344
$543$	5.24593e14	0.476895
$544$	−2.61076e15	−2.34949
$545$	−3.18200e14	−0.283478
$546$	−6.31087e12	−0.00556583
$547$	−2.46210e14	−0.214969	−0.107484	−	0.994207i	$-0.534280\pi$
$547$	−2.46210e14	−0.214969	−0.107484	+	0.994207i	$0.534280\pi$
$548$	8.43106e14	0.728768
$549$	−1.36967e14	−0.117211
$550$	3.50622e15	2.97060
$551$	2.96667e13	0.0248849
$552$	1.54366e14	0.128199
$553$	−7.54101e14	−0.620070
$554$	−6.41165e14	−0.521995
$555$	−1.22524e15	−0.987668
$556$	1.26168e15	1.00702
$557$	1.49213e15	1.17924	0.589621	−	0.807680i	$-0.299277\pi$
$557$	1.49213e15	1.17924	0.589621	+	0.807680i	$0.299277\pi$
$558$	1.26592e15	0.990644
$559$	1.81849e13	0.0140911
$560$	1.02867e15	0.789303
$561$	1.37997e15	1.04852
$562$	−3.34893e13	−0.0251974
$563$	1.11751e15	0.832634	0.416317	−	0.909220i	$-0.363321\pi$
$563$	1.11751e15	0.832634	0.416317	+	0.909220i	$0.363321\pi$
$564$	6.92073e14	0.510643
$565$	−1.36817e15	−0.999706
$566$	−1.91195e15	−1.38352
$567$	1.78484e14	0.127906
$568$	−4.68921e14	−0.332801
$569$	−1.45494e15	−1.02265	−0.511325	−	0.859388i	$-0.670845\pi$
$569$	−1.45494e15	−1.02265	−0.511325	+	0.859388i	$0.670845\pi$
$570$	−2.22582e14	−0.154946
$571$	1.96264e15	1.35314	0.676570	−	0.736378i	$-0.263466\pi$
$571$	1.96264e15	1.35314	0.676570	+	0.736378i	$0.263466\pi$
$572$	−2.90359e13	−0.0198270
$573$	−5.10807e14	−0.345467
$574$	6.46407e14	0.433003
$575$	3.82838e15	2.54005
$576$	8.13421e14	0.534554
$577$	−2.62613e15	−1.70942	−0.854712	−	0.519102i	$-0.826266\pi$
$577$	−2.62613e15	−1.70942	−0.854712	+	0.519102i	$0.826266\pi$
$578$	−4.38156e15	−2.82505
$579$	−2.99426e14	−0.191230
$580$	4.27400e14	0.270384
$581$	−1.12138e14	−0.0702723
$582$	9.69595e14	0.601886
$583$	−2.94054e15	−1.80821
$584$	5.20445e14	0.317033
$585$	4.00722e13	0.0241816
$586$	−3.31208e15	−1.98000
$587$	1.51034e15	0.894467	0.447233	−	0.894417i	$-0.352409\pi$
$587$	1.51034e15	0.894467	0.447233	+	0.894417i	$0.352409\pi$
$588$	−6.11395e14	−0.358713
$589$	−2.23935e14	−0.130163
$590$	−1.32218e15	−0.761388
$591$	−1.23571e15	−0.704996
$592$	−2.30417e15	−1.30240
$593$	1.05658e15	0.591697	0.295849	−	0.955235i	$-0.404398\pi$
$593$	1.05658e15	0.591697	0.295849	+	0.955235i	$0.404398\pi$
$594$	−2.57394e15	−1.42814
$595$	2.25309e15	1.23861
$596$	8.54297e14	0.465323
$597$	1.45353e15	0.784450
$598$	−6.83238e13	−0.0365355
$599$	1.38294e15	0.732751	0.366375	−	0.930467i	$-0.380599\pi$
$599$	1.38294e15	0.732751	0.366375	+	0.930467i	$0.380599\pi$
$600$	3.21448e14	0.168764
$601$	1.50136e15	0.781046	0.390523	−	0.920593i	$-0.372294\pi$
$601$	1.50136e15	0.781046	0.390523	+	0.920593i	$0.372294\pi$
$602$	−8.15262e14	−0.420258
$603$	8.30660e14	0.424305
$604$	3.31810e15	1.67953
$605$	−1.38978e15	−0.697095
$606$	−1.42635e15	−0.708966
$607$	2.76440e15	1.36164	0.680821	−	0.732450i	$-0.261623\pi$
$607$	2.76440e15	1.36164	0.680821	+	0.732450i	$0.261623\pi$
$608$	−3.68242e14	−0.179748
$609$	−8.12335e13	−0.0392952
$610$	7.52245e14	0.360616
$611$	4.74986e13	0.0225660
$612$	2.40496e15	1.13233
$613$	−2.90567e15	−1.35586	−0.677929	−	0.735128i	$-0.737122\pi$
$613$	−2.90567e15	−1.35586	−0.677929	+	0.735128i	$0.737122\pi$
$614$	−1.50088e15	−0.694098
$615$	1.39248e15	0.638226
$616$	−2.01850e14	−0.0916927
$617$	9.26499e13	0.0417135	0.0208567	−	0.999782i	$-0.493361\pi$
$617$	9.26499e13	0.0417135	0.0208567	+	0.999782i	$0.493361\pi$
$618$	−1.35335e15	−0.603913
$619$	−2.97221e15	−1.31456	−0.657281	−	0.753646i	$-0.728293\pi$
$619$	−2.97221e15	−1.31456	−0.657281	+	0.753646i	$0.728293\pi$
$620$	−3.22618e15	−1.41428
$621$	−2.81044e15	−1.22115
$622$	−5.98695e15	−2.57845
$623$	8.04674e13	0.0343507
$624$	−2.55660e13	−0.0108180
$625$	1.22826e15	0.515168
$626$	7.22682e14	0.300461
$627$	1.94642e14	0.0802168
$628$	−2.42921e15	−0.992402
$629$	−5.04680e15	−2.04379
$630$	−1.79651e15	−0.721200
$631$	3.77072e15	1.50059	0.750295	−	0.661103i	$-0.229911\pi$
$631$	3.77072e15	1.50059	0.750295	+	0.661103i	$0.229911\pi$
$632$	−6.85500e14	−0.270435
$633$	3.99345e14	0.156181
$634$	9.11130e14	0.353256
$635$	1.70586e15	0.655674
$636$	1.73857e15	0.662487
$637$	−4.19615e13	−0.0158520
$638$	−8.05454e14	−0.301666
$639$	3.64961e15	1.35516
$640$	1.66036e15	0.611242
$641$	−3.46988e15	−1.26647	−0.633236	−	0.773959i	$-0.718274\pi$
$641$	−3.46988e15	−1.26647	−0.633236	+	0.773959i	$0.718274\pi$
$642$	1.38042e15	0.499538
$643$	2.97006e15	1.06563	0.532813	−	0.846233i	$-0.321135\pi$
$643$	2.97006e15	1.06563	0.532813	+	0.846233i	$0.321135\pi$
$644$	1.42134e15	0.505621
$645$	−1.75622e15	−0.619441
$646$	−9.16820e14	−0.320631
$647$	3.52258e15	1.22148	0.610741	−	0.791831i	$-0.290872\pi$
$647$	3.52258e15	1.22148	0.610741	+	0.791831i	$0.290872\pi$
$648$	1.62247e14	0.0557847
$649$	1.15621e15	0.394178
$650$	−1.42276e14	−0.0480960
$651$	6.13181e14	0.205539
$652$	−4.61184e14	−0.153289
$653$	5.47168e15	1.80342	0.901712	−	0.432337i	$-0.142311\pi$
$653$	5.47168e15	1.80342	0.901712	+	0.432337i	$0.142311\pi$
$654$	−3.54544e14	−0.115876
$655$	1.99110e15	0.645308
$656$	2.61866e15	0.841605
$657$	−4.05062e15	−1.29096
$658$	−2.12945e15	−0.673015
$659$	8.33296e14	0.261174	0.130587	−	0.991437i	$-0.458314\pi$
$659$	8.33296e14	0.261174	0.130587	+	0.991437i	$0.458314\pi$
$660$	2.80416e15	0.871587
$661$	4.09469e15	1.26216	0.631079	−	0.775719i	$-0.282613\pi$
$661$	4.09469e15	1.26216	0.631079	+	0.775719i	$0.282613\pi$
$662$	2.66664e15	0.815166
$663$	−5.59969e13	−0.0169762
$664$	−1.01937e14	−0.0306483
$665$	3.17794e14	0.0947603
$666$	4.02407e15	1.19003
$667$	−8.79463e14	−0.257944
$668$	−4.15204e15	−1.20779
$669$	−2.02876e15	−0.585311
$670$	−4.56211e15	−1.30543
$671$	−6.57817e14	−0.186694
$672$	1.00832e15	0.283836
$673$	5.17664e15	1.44532	0.722662	−	0.691201i	$-0.242918\pi$
$673$	5.17664e15	1.44532	0.722662	+	0.691201i	$0.242918\pi$
$674$	−5.96946e15	−1.65312
$675$	−5.85241e15	−1.60755
$676$	−3.17644e15	−0.865433
$677$	−2.10297e14	−0.0568323	−0.0284161	−	0.999596i	$-0.509046\pi$
$677$	−2.10297e14	−0.0568323	−0.0284161	+	0.999596i	$0.509046\pi$
$678$	−1.52444e15	−0.408645
$679$	−1.38435e15	−0.368096
$680$	2.04813e15	0.540205
$681$	1.79758e15	0.470303
$682$	6.07987e15	1.57790
$683$	−5.89533e15	−1.51773	−0.758865	−	0.651248i	$-0.774246\pi$
$683$	−5.89533e15	−1.51773	−0.758865	+	0.651248i	$0.774246\pi$
$684$	3.39214e14	0.0866293
$685$	−5.58828e15	−1.41573
$686$	4.16637e15	1.04707
$687$	2.91897e15	0.727726
$688$	−3.30271e15	−0.816834
$689$	1.19322e14	0.0292762
$690$	6.59841e15	1.60609
$691$	3.21649e15	0.776699	0.388350	−	0.921512i	$-0.373045\pi$
$691$	3.21649e15	0.776699	0.388350	+	0.921512i	$0.373045\pi$
$692$	4.59992e15	1.10196
$693$	1.57099e15	0.373372
$694$	−8.97715e15	−2.11671
$695$	−8.36265e15	−1.95626
$696$	−7.38436e13	−0.0171381
$697$	5.73562e15	1.32069
$698$	7.55376e15	1.72567
$699$	−6.11547e13	−0.0138614
$700$	2.95977e15	0.665609
$701$	−1.51226e15	−0.337425	−0.168712	−	0.985665i	$-0.553961\pi$
$701$	−1.51226e15	−0.337425	−0.168712	+	0.985665i	$0.553961\pi$
$702$	1.04446e14	0.0231226
$703$	−7.11840e14	−0.156361
$704$	3.90664e15	0.851440
$705$	−4.58721e15	−0.991992
$706$	3.61270e15	0.775186
$707$	2.03648e15	0.433584
$708$	−6.83601e14	−0.144418
$709$	−6.60560e15	−1.38471	−0.692354	−	0.721558i	$-0.743426\pi$
$709$	−6.60560e15	−1.38471	−0.692354	+	0.721558i	$0.743426\pi$
$710$	−2.00442e16	−4.16934
$711$	5.33523e15	1.10121
$712$	7.31473e13	0.0149816
$713$	6.63852e15	1.34921
$714$	2.51044e15	0.506302
$715$	1.92456e14	0.0385166
$716$	−1.42372e15	−0.282750
$717$	−4.54570e14	−0.0895870
$718$	3.83195e15	0.749438
$719$	3.41912e15	0.663599	0.331800	−	0.943350i	$-0.392344\pi$
$719$	3.41912e15	0.663599	0.331800	+	0.943350i	$0.392344\pi$
$720$	−7.27783e15	−1.40176
$721$	1.93226e15	0.369336
$722$	7.07150e15	1.34140
$723$	−2.53729e15	−0.477650
$724$	4.39084e15	0.820324
$725$	−1.83138e15	−0.339562
$726$	−1.54852e15	−0.284948
$727$	−6.01956e15	−1.09932	−0.549662	−	0.835387i	$-0.685243\pi$
$727$	−6.01956e15	−1.09932	−0.549662	+	0.835387i	$0.685243\pi$
$728$	8.19072e12	0.00148457
$729$	1.19692e15	0.215310
$730$	2.22466e16	3.97180
$731$	−7.23389e15	−1.28182
$732$	3.88929e14	0.0684004
$733$	6.51049e15	1.13643	0.568214	−	0.822881i	$-0.307635\pi$
$733$	6.51049e15	1.13643	0.568214	+	0.822881i	$0.307635\pi$
$734$	−1.21673e15	−0.210798
$735$	4.05245e15	0.696848
$736$	1.09164e16	1.86317
$737$	3.98944e15	0.675835
$738$	−4.57330e15	−0.768989
$739$	5.18932e15	0.866096	0.433048	−	0.901371i	$-0.357438\pi$
$739$	5.18932e15	0.866096	0.433048	+	0.901371i	$0.357438\pi$
$740$	−1.02553e16	−1.69892
$741$	−7.89824e12	−0.00129876
$742$	−5.34941e15	−0.873142
$743$	−8.50285e15	−1.37761	−0.688805	−	0.724947i	$-0.741864\pi$
$743$	−8.50285e15	−1.37761	−0.688805	+	0.724947i	$0.741864\pi$
$744$	5.57400e14	0.0896428
$745$	−5.66246e15	−0.903953
$746$	8.33399e14	0.132066
$747$	7.93373e14	0.124800
$748$	1.15504e16	1.80359
$749$	−1.97091e15	−0.305503
$750$	6.22622e15	0.958049
$751$	−3.03737e15	−0.463957	−0.231978	−	0.972721i	$-0.574520\pi$
$751$	−3.03737e15	−0.463957	−0.231978	+	0.972721i	$0.574520\pi$
$752$	−8.62661e15	−1.30810
$753$	−1.45875e15	−0.219588
$754$	3.26839e13	0.00488418
$755$	−2.19931e16	−3.26270
$756$	−2.17279e15	−0.319998
$757$	1.08942e16	1.59282	0.796410	−	0.604758i	$-0.206730\pi$
$757$	1.08942e16	1.59282	0.796410	+	0.604758i	$0.206730\pi$
$758$	1.45034e15	0.210519
$759$	−5.77012e15	−0.831487
$760$	2.88884e14	0.0413284
$761$	2.76682e15	0.392976	0.196488	−	0.980506i	$-0.437046\pi$
$761$	2.76682e15	0.392976	0.196488	+	0.980506i	$0.437046\pi$
$762$	1.90070e15	0.268017
$763$	5.06204e14	0.0708664
$764$	−4.27545e15	−0.594249
$765$	−1.59406e16	−2.19971
$766$	−9.17129e15	−1.25653
$767$	−4.69172e13	−0.00638201
$768$	4.51794e15	0.610174
$769$	−1.15516e16	−1.54898	−0.774492	−	0.632584i	$-0.781994\pi$
$769$	−1.15516e16	−1.54898	−0.774492	+	0.632584i	$0.781994\pi$
$770$	−8.62814e15	−1.14873
$771$	1.41840e15	0.187499
$772$	−2.50619e15	−0.328942
$773$	6.76729e13	0.00881917	0.00440958	−	0.999990i	$-0.498596\pi$
$773$	6.76729e13	0.00881917	0.00440958	+	0.999990i	$0.498596\pi$
$774$	5.76794e15	0.746356
$775$	1.38239e16	1.77612
$776$	−1.25841e15	−0.160540
$777$	1.94916e15	0.246906
$778$	−1.69166e16	−2.12777
$779$	8.08997e14	0.101039
$780$	−1.13788e14	−0.0141116
$781$	1.75281e16	2.15851
$782$	2.71789e16	3.32350
$783$	1.34443e15	0.163248
$784$	7.62096e15	0.918907
$785$	1.61013e16	1.92787
$786$	2.21853e15	0.263779
$787$	8.93902e15	1.05543	0.527714	−	0.849422i	$-0.323049\pi$
$787$	8.93902e15	1.05543	0.527714	+	0.849422i	$0.323049\pi$
$788$	−1.03429e16	−1.21269
$789$	−5.76019e15	−0.670676
$790$	−2.93019e16	−3.38803
$791$	2.17653e15	0.249916
$792$	1.42808e15	0.162841
$793$	2.66931e13	0.00302271
$794$	−1.45820e16	−1.63985
$795$	−1.15236e16	−1.28697
$796$	1.21661e16	1.34936
$797$	1.01444e16	1.11740	0.558698	−	0.829371i	$-0.311301\pi$
$797$	1.01444e16	1.11740	0.558698	+	0.829371i	$0.311301\pi$
$798$	3.54092e14	0.0387347
$799$	−1.88948e16	−2.05274
$800$	2.27322e16	2.45271
$801$	−5.69304e14	−0.0610050
$802$	−6.64313e15	−0.706991
$803$	−1.94540e16	−2.05624
$804$	−2.35872e15	−0.247610
$805$	−9.42093e15	−0.982238
$806$	−2.46711e14	−0.0255473
$807$	−1.30529e15	−0.134247
$808$	1.85122e15	0.189102
$809$	−1.21992e16	−1.23770	−0.618848	−	0.785511i	$-0.712400\pi$
$809$	−1.21992e16	−1.23770	−0.618848	+	0.785511i	$0.712400\pi$
$810$	6.93531e15	0.698873
$811$	−1.31219e16	−1.31336	−0.656680	−	0.754170i	$-0.728040\pi$
$811$	−1.31219e16	−1.31336	−0.656680	+	0.754170i	$0.728040\pi$
$812$	−6.79924e14	−0.0675931
$813$	−3.05752e15	−0.301906
$814$	1.93265e16	1.89548
$815$	3.05682e15	0.297785
$816$	1.01701e16	0.984073
$817$	−1.02032e15	−0.0980656
$818$	−2.57452e15	−0.245783
$819$	−6.37483e13	−0.00604515
$820$	1.16550e16	1.09783
$821$	4.21910e15	0.394759	0.197380	−	0.980327i	$-0.436757\pi$
$821$	4.21910e15	0.394759	0.197380	+	0.980327i	$0.436757\pi$
$822$	−6.22657e15	−0.578701
$823$	−1.66647e16	−1.53850	−0.769252	−	0.638946i	$-0.779371\pi$
$823$	−1.66647e16	−1.53850	−0.769252	+	0.638946i	$0.779371\pi$
$824$	1.75648e15	0.161081
$825$	−1.20156e16	−1.09458
$826$	2.10338e15	0.190339
$827$	−1.03782e16	−0.932910	−0.466455	−	0.884545i	$-0.654469\pi$
$827$	−1.03782e16	−0.932910	−0.466455	+	0.884545i	$0.654469\pi$
$828$	−1.00559e16	−0.897956
$829$	6.21380e15	0.551197	0.275599	−	0.961273i	$-0.411124\pi$
$829$	6.21380e15	0.551197	0.275599	+	0.961273i	$0.411124\pi$
$830$	−4.35732e15	−0.383964
$831$	2.19724e15	0.192341
$832$	−1.58525e14	−0.0137854
$833$	1.66921e16	1.44200
$834$	−9.31782e15	−0.799652
$835$	2.75206e16	2.34629
$836$	1.62915e15	0.137984
$837$	−1.01482e16	−0.853887
$838$	7.03742e15	0.588263
$839$	5.65518e15	0.469630	0.234815	−	0.972040i	$-0.424552\pi$
$839$	5.65518e15	0.469630	0.234815	+	0.972040i	$0.424552\pi$
$840$	−7.91024e14	−0.0652610
$841$	4.20707e14	0.0344828
$842$	8.86975e15	0.722262
$843$	1.14766e14	0.00928456
$844$	3.34252e15	0.268652
$845$	2.10541e16	1.68122
$846$	1.50658e16	1.19524
$847$	2.21091e15	0.174266
$848$	−2.16710e16	−1.69708
$849$	6.55213e15	0.509789
$850$	5.65969e16	4.37511
$851$	2.11023e16	1.62076
$852$	−1.03633e16	−0.790827
$853$	−5.40841e15	−0.410062	−0.205031	−	0.978755i	$-0.565730\pi$
$853$	−5.40841e15	−0.410062	−0.205031	+	0.978755i	$0.565730\pi$
$854$	−1.19670e15	−0.0901501
$855$	−2.24838e15	−0.168289
$856$	−1.79161e15	−0.133241
$857$	6.15040e15	0.454474	0.227237	−	0.973840i	$-0.427031\pi$
$857$	6.15040e15	0.454474	0.227237	+	0.973840i	$0.427031\pi$
$858$	2.14438e14	0.0157442
$859$	6.42630e15	0.468812	0.234406	−	0.972139i	$-0.424686\pi$
$859$	6.42630e15	0.468812	0.234406	+	0.972139i	$0.424686\pi$
$860$	−1.46995e16	−1.06552
$861$	−2.21520e15	−0.159550
$862$	−1.57249e16	−1.12538
$863$	1.63433e16	1.16220	0.581100	−	0.813832i	$-0.302623\pi$
$863$	1.63433e16	1.16220	0.581100	+	0.813832i	$0.302623\pi$
$864$	−1.66879e16	−1.17917
$865$	−3.04892e16	−2.14071
$866$	3.72647e16	2.59985
$867$	1.50154e16	1.04095
$868$	5.13232e15	0.353554
$869$	2.56237e16	1.75401
$870$	−3.15647e15	−0.214707
$871$	−1.61885e14	−0.0109422
$872$	4.60154e14	0.0309074
$873$	9.79421e15	0.653719
$874$	3.83353e15	0.254265
$875$	−8.88955e15	−0.585916
$876$	1.15020e16	0.753359
$877$	1.21939e16	0.793680	0.396840	−	0.917888i	$-0.370107\pi$
$877$	1.21939e16	0.793680	0.396840	+	0.917888i	$0.370107\pi$
$878$	2.18486e14	0.0141320
$879$	1.13503e16	0.729574
$880$	−3.49535e16	−2.23273
$881$	2.48523e16	1.57761	0.788804	−	0.614645i	$-0.210701\pi$
$881$	2.48523e16	1.57761	0.788804	+	0.614645i	$0.210701\pi$
$882$	−1.33095e16	−0.839621
$883$	1.85007e14	0.0115986	0.00579929	−	0.999983i	$-0.498154\pi$
$883$	1.85007e14	0.0115986	0.00579929	+	0.999983i	$0.498154\pi$
$884$	−4.68694e14	−0.0292013
$885$	4.53105e15	0.280550
$886$	−3.81401e16	−2.34691
$887$	2.24016e16	1.36993	0.684966	−	0.728575i	$-0.259817\pi$
$887$	2.24016e16	1.36993	0.684966	+	0.728575i	$0.259817\pi$
$888$	1.77185e15	0.107685
$889$	−2.71374e15	−0.163911
$890$	3.12670e15	0.187690
$891$	−6.06473e15	−0.361813
$892$	−1.69807e16	−1.00681
$893$	−2.66507e15	−0.157045
$894$	−6.30922e15	−0.369504
$895$	9.43670e15	0.549279
$896$	−2.64137e15	−0.152804
$897$	2.34142e14	0.0134623
$898$	−3.84613e16	−2.19788
$899$	−3.17566e15	−0.180366
$900$	−2.09403e16	−1.18208
$901$	−4.74658e16	−2.66314
$902$	−2.19644e16	−1.22485
$903$	2.79386e15	0.154854
$904$	1.97853e15	0.108997
$905$	−2.91034e16	−1.59359
$906$	−2.45051e16	−1.33368
$907$	−7.51293e15	−0.406415	−0.203207	−	0.979136i	$-0.565137\pi$
$907$	−7.51293e15	−0.406415	−0.203207	+	0.979136i	$0.565137\pi$
$908$	1.50457e16	0.808985
$909$	−1.44080e16	−0.770021
$910$	3.50115e14	0.0185987
$911$	1.10335e16	0.582591	0.291295	−	0.956633i	$-0.405914\pi$
$911$	1.10335e16	0.582591	0.291295	+	0.956633i	$0.405914\pi$
$912$	1.43446e15	0.0752866
$913$	3.81036e15	0.198782
$914$	−4.25585e16	−2.20690
$915$	−2.57790e15	−0.132877
$916$	2.44318e16	1.25179
$917$	−3.16752e15	−0.161320
$918$	−4.15482e16	−2.10338
$919$	1.53235e16	0.771119	0.385560	−	0.922683i	$-0.374008\pi$
$919$	1.53235e16	0.771119	0.385560	+	0.922683i	$0.374008\pi$
$920$	−8.56391e15	−0.428390
$921$	5.14344e15	0.255756
$922$	4.41673e16	2.18313
$923$	−7.11260e14	−0.0349477
$924$	−4.46096e15	−0.217887
$925$	4.39431e16	2.13359
$926$	3.59946e16	1.73731
$927$	−1.36707e16	−0.655921
$928$	−5.22208e15	−0.249075
$929$	−2.08784e16	−0.989944	−0.494972	−	0.868909i	$-0.664822\pi$
$929$	−2.08784e16	−0.989944	−0.494972	+	0.868909i	$0.664822\pi$
$930$	2.38262e16	1.12305
$931$	2.35439e15	0.110320
$932$	−5.11865e14	−0.0238434
$933$	2.05169e16	0.950087
$934$	1.33136e14	0.00612899
$935$	−7.65582e16	−3.50371
$936$	−5.79491e13	−0.00263651
$937$	1.32932e16	0.601257	0.300629	−	0.953741i	$-0.402804\pi$
$937$	1.32932e16	0.601257	0.300629	+	0.953741i	$0.402804\pi$
$938$	7.25758e15	0.326344
$939$	−2.47659e15	−0.110712
$940$	−3.83949e16	−1.70636
$941$	1.81715e16	0.802875	0.401438	−	0.915886i	$-0.368511\pi$
$941$	1.81715e16	0.802875	0.401438	+	0.915886i	$0.368511\pi$
$942$	1.79404e16	0.788047
$943$	−2.39825e16	−1.04732
$944$	8.52100e15	0.369951
$945$	1.44017e16	0.621639
$946$	2.77019e16	1.18880
$947$	−3.61931e16	−1.54419	−0.772094	−	0.635508i	$-0.780791\pi$
$947$	−3.61931e16	−1.54419	−0.772094	+	0.635508i	$0.780791\pi$
$948$	−1.51498e16	−0.642630
$949$	7.89411e14	0.0332919
$950$	7.98287e15	0.334718
$951$	−3.12239e15	−0.130165
$952$	−3.25824e15	−0.135045
$953$	2.88534e16	1.18901	0.594505	−	0.804092i	$-0.297348\pi$
$953$	2.88534e16	1.18901	0.594505	+	0.804092i	$0.297348\pi$
$954$	3.78469e16	1.55065
$955$	2.83386e16	1.15441
$956$	−3.80475e15	−0.154102
$957$	2.76024e15	0.111156
$958$	−2.20021e16	−0.880954
$959$	8.89004e15	0.353917
$960$	1.53096e16	0.606001
$961$	−1.43742e15	−0.0565724
$962$	−7.84237e14	−0.0306891
$963$	1.39441e16	0.542557
$964$	−2.12371e16	−0.821621
$965$	1.66116e16	0.639014
$966$	−1.04970e16	−0.401504
$967$	1.92597e16	0.732492	0.366246	−	0.930518i	$-0.380643\pi$
$967$	1.92597e16	0.732492	0.366246	+	0.930518i	$0.380643\pi$
$968$	2.00979e15	0.0760038
$969$	3.14189e15	0.118144
$970$	−5.37913e16	−2.01126
$971$	−2.81618e16	−1.04702	−0.523509	−	0.852020i	$-0.675377\pi$
$971$	−2.81618e16	−1.04702	−0.523509	+	0.852020i	$0.675377\pi$
$972$	2.41733e16	0.893658
$973$	1.33036e16	0.489045
$974$	3.84784e16	1.40651
$975$	4.87572e14	0.0177220
$976$	−4.84795e15	−0.175220
$977$	−4.14484e16	−1.48966	−0.744831	−	0.667253i	$-0.767470\pi$
$977$	−4.14484e16	−1.48966	−0.744831	+	0.667253i	$0.767470\pi$
$978$	3.40597e15	0.121724
$979$	−2.73422e15	−0.0971690
$980$	3.39190e16	1.19867
$981$	−3.58137e15	−0.125855
$982$	−3.06574e16	−1.07133
$983$	−1.72229e16	−0.598498	−0.299249	−	0.954175i	$-0.596736\pi$
$983$	−1.72229e16	−0.598498	−0.299249	+	0.954175i	$0.596736\pi$
$984$	−2.01368e15	−0.0695854
$985$	6.85550e16	2.35581
$986$	−1.30015e16	−0.444296
$987$	7.29749e15	0.247987
$988$	−6.61083e13	−0.00223405
$989$	3.02473e16	1.01650
$990$	6.10438e16	2.04008
$991$	1.94201e16	0.645425	0.322713	−	0.946497i	$-0.395405\pi$
$991$	1.94201e16	0.645425	0.322713	+	0.946497i	$0.395405\pi$
$992$	3.94183e16	1.30282
$993$	−9.13844e15	−0.300366
$994$	3.18870e16	1.04229
$995$	−8.06391e16	−2.62131
$996$	−2.25284e15	−0.0728290
$997$	−3.97113e16	−1.27670	−0.638352	−	0.769744i	$-0.720384\pi$
$997$	−3.97113e16	−1.27670	−0.638352	+	0.769744i	$0.720384\pi$
$998$	−3.28100e16	−1.04903
$999$	−3.22589e16	−1.02575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.4	✓	14
3.2	odd	2		261.12.a.e.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.4	✓	14	1.1	even	1	trivial
261.12.a.e.1.11		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-61.8148 q^{2} +211.836 q^{3} +1773.06 q^{4} -11752.2 q^{5} -13094.6 q^{6} +18695.9 q^{7} +16995.1 q^{8} -132273. q^{9} +O(q^{10})\)	\(q-61.8148 q^{2} +211.836 q^{3} +1773.06 q^{4} -11752.2 q^{5} -13094.6 q^{6} +18695.9 q^{7} +16995.1 q^{8} -132273. q^{9} +726462. q^{10} -635270. q^{11} +375598. q^{12} +25778.2 q^{13} -1.15568e6 q^{14} -2.48954e6 q^{15} -4.68178e6 q^{16} -1.02545e7 q^{17} +8.17640e6 q^{18} -1.44637e6 q^{19} -2.08375e7 q^{20} +3.96045e6 q^{21} +3.92691e7 q^{22} +4.28773e7 q^{23} +3.60017e6 q^{24} +8.92869e7 q^{25} -1.59347e6 q^{26} -6.55461e7 q^{27} +3.31490e7 q^{28} -2.05111e7 q^{29} +1.53890e8 q^{30} +1.54826e8 q^{31} +2.54597e8 q^{32} -1.34573e8 q^{33} +6.33877e8 q^{34} -2.19718e8 q^{35} -2.34528e8 q^{36} +4.92156e8 q^{37} +8.94070e7 q^{38} +5.46074e6 q^{39} -1.99731e8 q^{40} -5.59330e8 q^{41} -2.44815e8 q^{42} +7.05438e8 q^{43} -1.12637e9 q^{44} +1.55450e9 q^{45} -2.65045e9 q^{46} +1.84259e9 q^{47} -9.91769e8 q^{48} -1.62779e9 q^{49} -5.51925e9 q^{50} -2.17226e9 q^{51} +4.57064e7 q^{52} +4.62880e9 q^{53} +4.05172e9 q^{54} +7.46585e9 q^{55} +3.17739e8 q^{56} -3.06393e8 q^{57} +1.26789e9 q^{58} -1.82003e9 q^{59} -4.41412e9 q^{60} +1.03549e9 q^{61} -9.57052e9 q^{62} -2.47295e9 q^{63} -6.14958e9 q^{64} -3.02951e8 q^{65} +8.31859e9 q^{66} -6.27991e9 q^{67} -1.81818e10 q^{68} +9.08294e9 q^{69} +1.35818e10 q^{70} -2.75915e10 q^{71} -2.24799e9 q^{72} +3.06232e10 q^{73} -3.04225e10 q^{74} +1.89142e10 q^{75} -2.56450e9 q^{76} -1.18769e10 q^{77} -3.37554e8 q^{78} -4.03351e10 q^{79} +5.50214e10 q^{80} +9.54670e9 q^{81} +3.45748e10 q^{82} -5.99801e9 q^{83} +7.02214e9 q^{84} +1.20513e11 q^{85} -4.36065e10 q^{86} -4.34499e9 q^{87} -1.07965e10 q^{88} +4.30402e9 q^{89} -9.60910e10 q^{90} +4.81946e8 q^{91} +7.60242e10 q^{92} +3.27976e10 q^{93} -1.13899e11 q^{94} +1.69981e10 q^{95} +5.39328e10 q^{96} -7.40456e10 q^{97} +1.00621e11 q^{98} +8.40289e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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