LMFDB - Embedded newform 273.12.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,12,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("273.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	273.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:	$209.757688293$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} + \cdots + 45\!\cdots\!68 $ x^16 - x^15 - 26640x^14 - 38138x^13 + 279954048x^12 + 940095168x^11 - 1473489774048x^10 - 6951601887328x^9 + 4072481535854976x^8 + 21355761647276288x^7 - 5703452025696599040x^6 - 25041700255043457024x^5 + 3737994671267475603456x^4 + 6711995200063092490240x^3 - 963518272786595267739648x^2 + 1287697466669064032092160x + 45555354651594891689197568
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$18.3601$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.3601 q^{2} -243.000 q^{3} -1841.79 q^{4} +4424.64 q^{5} -3489.51 q^{6} +16807.0 q^{7} -55857.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+14.3601 q^{2} -243.000 q^{3} -1841.79 q^{4} +4424.64 q^{5} -3489.51 q^{6} +16807.0 q^{7} -55857.8 q^{8} +59049.0 q^{9} +63538.3 q^{10} +338272. q^{11} +447554. q^{12} -371293. q^{13} +241350. q^{14} -1.07519e6 q^{15} +2.96986e6 q^{16} -3.75161e6 q^{17} +847950. q^{18} -1.16379e7 q^{19} -8.14925e6 q^{20} -4.08410e6 q^{21} +4.85763e6 q^{22} +5.77416e7 q^{23} +1.35734e7 q^{24} -2.92507e7 q^{25} -5.33181e6 q^{26} -1.43489e7 q^{27} -3.09549e7 q^{28} -1.08561e8 q^{29} -1.54398e7 q^{30} -9.12180e7 q^{31} +1.57044e8 q^{32} -8.22002e7 q^{33} -5.38735e7 q^{34} +7.43650e7 q^{35} -1.08756e8 q^{36} -5.76597e8 q^{37} -1.67122e8 q^{38} +9.02242e7 q^{39} -2.47151e8 q^{40} +1.17326e9 q^{41} -5.86481e7 q^{42} +1.62472e9 q^{43} -6.23026e8 q^{44} +2.61271e8 q^{45} +8.29176e8 q^{46} +7.56156e8 q^{47} -7.21675e8 q^{48} +2.82475e8 q^{49} -4.20043e8 q^{50} +9.11641e8 q^{51} +6.83843e8 q^{52} -2.53658e9 q^{53} -2.06052e8 q^{54} +1.49673e9 q^{55} -9.38802e8 q^{56} +2.82802e9 q^{57} -1.55895e9 q^{58} +1.62567e9 q^{59} +1.98027e9 q^{60} +1.26515e8 q^{61} -1.30990e9 q^{62} +9.92437e8 q^{63} -3.82709e9 q^{64} -1.64284e9 q^{65} -1.18040e9 q^{66} -1.00750e10 q^{67} +6.90967e9 q^{68} -1.40312e10 q^{69} +1.06789e9 q^{70} +1.02472e10 q^{71} -3.29835e9 q^{72} +1.14591e10 q^{73} -8.28000e9 q^{74} +7.10791e9 q^{75} +2.14346e10 q^{76} +5.68534e9 q^{77} +1.29563e9 q^{78} +2.44618e10 q^{79} +1.31406e10 q^{80} +3.48678e9 q^{81} +1.68481e10 q^{82} -1.15405e10 q^{83} +7.52205e9 q^{84} -1.65995e10 q^{85} +2.33311e10 q^{86} +2.63803e10 q^{87} -1.88951e10 q^{88} +2.29828e10 q^{89} +3.75188e9 q^{90} -6.24032e9 q^{91} -1.06348e11 q^{92} +2.21660e10 q^{93} +1.08585e10 q^{94} -5.14937e10 q^{95} -3.81617e10 q^{96} -5.73728e10 q^{97} +4.05638e9 q^{98} +1.99746e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) $ 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9 + 1056711 * q^10 - 466884 * q^11 - 5044923 * q^12 - 5940688 * q^13 - 1058841 * q^14 + 769824 * q^15 + 40058265 * q^16 + 1753452 * q^17 - 3720087 * q^18 + 4237800 * q^19 - 20710503 * q^20 - 65345616 * q^21 - 37479661 * q^22 - 150481440 * q^23 + 45675495 * q^24 + 150983176 * q^25 + 23391459 * q^26 - 229582512 * q^27 + 348930127 * q^28 - 111411432 * q^29 - 256780773 * q^30 - 90536236 * q^31 - 609941313 * q^32 + 113452812 * q^33 + 443745577 * q^34 - 53244576 * q^35 + 1225916289 * q^36 - 1756337900 * q^37 - 4378868973 * q^38 + 1443587184 * q^39 + 57535383 * q^40 + 649575720 * q^41 + 257298363 * q^42 - 1889554520 * q^43 - 4979587689 * q^44 - 187067232 * q^45 - 3204000867 * q^46 - 4036082940 * q^47 - 9734158395 * q^48 + 4519603984 * q^49 - 15928886862 * q^50 - 426088836 * q^51 - 7708413973 * q^52 + 511144020 * q^53 + 903981141 * q^54 - 8519365572 * q^55 - 3159127755 * q^56 - 1029785400 * q^57 - 7851149577 * q^58 + 3728287296 * q^59 + 5032652229 * q^60 + 26227205052 * q^61 + 2996618490 * q^62 + 15878984688 * q^63 + 51104408465 * q^64 + 1176256224 * q^65 + 9107557623 * q^66 - 5295680024 * q^67 + 7919540325 * q^68 + 36566989920 * q^69 + 17760141777 * q^70 + 17082800928 * q^71 - 11099145285 * q^72 + 21076301488 * q^73 + 52794333675 * q^74 - 36688911768 * q^75 + 81459179177 * q^76 - 7846919388 * q^77 - 5684124537 * q^78 - 83677977852 * q^79 - 163988465427 * q^80 + 55788550416 * q^81 - 61543728760 * q^82 - 72857072340 * q^83 - 84790020861 * q^84 - 12608565060 * q^85 - 20177818011 * q^86 + 27072977976 * q^87 - 202213679643 * q^88 + 32238476676 * q^89 + 62397727839 * q^90 - 99845143216 * q^91 - 487057197033 * q^92 + 22000305348 * q^93 + 183904776602 * q^94 - 143022915504 * q^95 + 148215739059 * q^96 + 6973535140 * q^97 - 17795940687 * q^98 - 27569033316 * 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 $

$2$	14.3601	0.317317	0.158658	−	0.987334i	$-0.449283\pi$
$2$	14.3601	0.317317	0.158658	+	0.987334i	$0.449283\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1841.79	−0.899310
$5$	4424.64	0.633203	0.316602	−	0.948559i	$-0.397458\pi$
$5$	4424.64	0.633203	0.316602	+	0.948559i	$0.397458\pi$
$6$	−3489.51	−0.183203
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−55857.8	−0.602683
$9$	59049.0	0.333333
$10$	63538.3	0.200926
$11$	338272.	0.633296	0.316648	−	0.948543i	$-0.397443\pi$
$11$	338272.	0.633296	0.316648	+	0.948543i	$0.397443\pi$
$12$	447554.	0.519217
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	241350.	0.119934
$15$	−1.07519e6	−0.365580
$16$	2.96986e6	0.708069
$17$	−3.75161e6	−0.640838	−0.320419	−	0.947276i	$-0.603824\pi$
$17$	−3.75161e6	−0.640838	−0.320419	+	0.947276i	$0.603824\pi$
$18$	847950.	0.105772
$19$	−1.16379e7	−1.07828	−0.539139	−	0.842217i	$-0.681250\pi$
$19$	−1.16379e7	−1.07828	−0.539139	+	0.842217i	$0.681250\pi$
$20$	−8.14925e6	−0.569446
$21$	−4.08410e6	−0.218218
$22$	4.85763e6	0.200955
$23$	5.77416e7	1.87062	0.935311	−	0.353827i	$-0.115120\pi$
$23$	5.77416e7	1.87062	0.935311	+	0.353827i	$0.115120\pi$
$24$	1.35734e7	0.347959
$25$	−2.92507e7	−0.599054
$26$	−5.33181e6	−0.0880078
$27$	−1.43489e7	−0.192450
$28$	−3.09549e7	−0.339907
$29$	−1.08561e8	−0.982843	−0.491422	−	0.870922i	$-0.663523\pi$
$29$	−1.08561e8	−0.982843	−0.491422	+	0.870922i	$0.663523\pi$
$30$	−1.54398e7	−0.116005
$31$	−9.12180e7	−0.572257	−0.286128	−	0.958191i	$-0.592368\pi$
$31$	−9.12180e7	−0.572257	−0.286128	+	0.958191i	$0.592368\pi$
$32$	1.57044e8	0.827365
$33$	−8.22002e7	−0.365634
$34$	−5.38735e7	−0.203349
$35$	7.43650e7	0.239328
$36$	−1.08756e8	−0.299770
$37$	−5.76597e8	−1.36698	−0.683492	−	0.729958i	$-0.739539\pi$
$37$	−5.76597e8	−1.36698	−0.683492	+	0.729958i	$0.739539\pi$
$38$	−1.67122e8	−0.342156
$39$	9.02242e7	0.160128
$40$	−2.47151e8	−0.381621
$41$	1.17326e9	1.58154	0.790772	−	0.612111i	$-0.209679\pi$
$41$	1.17326e9	1.58154	0.790772	+	0.612111i	$0.209679\pi$
$42$	−5.86481e7	−0.0692442
$43$	1.62472e9	1.68539	0.842697	−	0.538387i	$-0.180966\pi$
$43$	1.62472e9	1.68539	0.842697	+	0.538387i	$0.180966\pi$
$44$	−6.23026e8	−0.569530
$45$	2.61271e8	0.211068
$46$	8.29176e8	0.593579
$47$	7.56156e8	0.480920	0.240460	−	0.970659i	$-0.422702\pi$
$47$	7.56156e8	0.480920	0.240460	+	0.970659i	$0.422702\pi$
$48$	−7.21675e8	−0.408804
$49$	2.82475e8	0.142857
$50$	−4.20043e8	−0.190090
$51$	9.11641e8	0.369988
$52$	6.83843e8	0.249424
$53$	−2.53658e9	−0.833164	−0.416582	−	0.909098i	$-0.636772\pi$
$53$	−2.53658e9	−0.833164	−0.416582	+	0.909098i	$0.636772\pi$
$54$	−2.06052e8	−0.0610676
$55$	1.49673e9	0.401005
$56$	−9.38802e8	−0.227793
$57$	2.82802e9	0.622544
$58$	−1.55895e9	−0.311873
$59$	1.62567e9	0.296038	0.148019	−	0.988985i	$-0.452710\pi$
$59$	1.62567e9	0.296038	0.148019	+	0.988985i	$0.452710\pi$
$60$	1.98027e9	0.328770
$61$	1.26515e8	0.0191790	0.00958951	−	0.999954i	$-0.496948\pi$
$61$	1.26515e8	0.0191790	0.00958951	+	0.999954i	$0.496948\pi$
$62$	−1.30990e9	−0.181587
$63$	9.92437e8	0.125988
$64$	−3.82709e9	−0.445532
$65$	−1.64284e9	−0.175619
$66$	−1.18040e9	−0.116022
$67$	−1.00750e10	−0.911664	−0.455832	−	0.890066i	$-0.650658\pi$
$67$	−1.00750e10	−0.911664	−0.455832	+	0.890066i	$0.650658\pi$
$68$	6.90967e9	0.576313
$69$	−1.40312e10	−1.08000
$70$	1.06789e9	0.0759428
$71$	1.02472e10	0.674036	0.337018	−	0.941498i	$-0.390582\pi$
$71$	1.02472e10	0.674036	0.337018	+	0.941498i	$0.390582\pi$
$72$	−3.29835e9	−0.200894
$73$	1.14591e10	0.646956	0.323478	−	0.946236i	$-0.395148\pi$
$73$	1.14591e10	0.646956	0.323478	+	0.946236i	$0.395148\pi$
$74$	−8.28000e9	−0.433767
$75$	7.10791e9	0.345864
$76$	2.14346e10	0.969707
$77$	5.68534e9	0.239363
$78$	1.29563e9	0.0508113
$79$	2.44618e10	0.894417	0.447208	−	0.894430i	$-0.352418\pi$
$79$	2.44618e10	0.894417	0.447208	+	0.894430i	$0.352418\pi$
$80$	1.31406e10	0.448352
$81$	3.48678e9	0.111111
$82$	1.68481e10	0.501850
$83$	−1.15405e10	−0.321585	−0.160793	−	0.986988i	$-0.551405\pi$
$83$	−1.15405e10	−0.321585	−0.160793	+	0.986988i	$0.551405\pi$
$84$	7.52205e9	0.196246
$85$	−1.65995e10	−0.405781
$86$	2.33311e10	0.534804
$87$	2.63803e10	0.567445
$88$	−1.88951e10	−0.381677
$89$	2.29828e10	0.436273	0.218136	−	0.975918i	$-0.430002\pi$
$89$	2.29828e10	0.436273	0.218136	+	0.975918i	$0.430002\pi$
$90$	3.75188e9	0.0669753
$91$	−6.24032e9	−0.104828
$92$	−1.06348e11	−1.68227
$93$	2.21660e10	0.330393
$94$	1.08585e10	0.152604
$95$	−5.14937e10	−0.682769
$96$	−3.81617e10	−0.477679
$97$	−5.73728e10	−0.678362	−0.339181	−	0.940721i	$-0.610150\pi$
$97$	−5.73728e10	−0.678362	−0.339181	+	0.940721i	$0.610150\pi$
$98$	4.05638e9	0.0453309
$99$	1.99746e10	0.211099
$100$	5.38735e10	0.538735
$101$	1.65759e11	1.56931	0.784655	−	0.619933i	$-0.212840\pi$
$101$	1.65759e11	1.56931	0.784655	+	0.619933i	$0.212840\pi$
$102$	1.30913e10	0.117403
$103$	1.25356e11	1.06547	0.532736	−	0.846282i	$-0.321164\pi$
$103$	1.25356e11	1.06547	0.532736	+	0.846282i	$0.321164\pi$
$104$	2.07396e10	0.167154
$105$	−1.80707e10	−0.138176
$106$	−3.64255e10	−0.264377
$107$	2.37292e11	1.63558	0.817791	−	0.575516i	$-0.195199\pi$
$107$	2.37292e11	1.63558	0.817791	+	0.575516i	$0.195199\pi$
$108$	2.64276e10	0.173072
$109$	−2.15796e11	−1.34338	−0.671688	−	0.740834i	$-0.734431\pi$
$109$	−2.15796e11	−1.34338	−0.671688	+	0.740834i	$0.734431\pi$
$110$	2.14933e10	0.127246
$111$	1.40113e11	0.789228
$112$	4.99144e10	0.267625
$113$	−2.51250e10	−0.128285	−0.0641423	−	0.997941i	$-0.520431\pi$
$113$	−2.51250e10	−0.128285	−0.0641423	+	0.997941i	$0.520431\pi$
$114$	4.06106e10	0.197544
$115$	2.55486e11	1.18448
$116$	1.99946e11	0.883881
$117$	−2.19245e10	−0.0924500
$118$	2.33449e10	0.0939378
$119$	−6.30533e10	−0.242214
$120$	6.00576e10	0.220329
$121$	−1.70883e11	−0.598936
$122$	1.81676e9	0.00608582
$123$	−2.85101e11	−0.913105
$124$	1.68004e11	0.514636
$125$	−3.45471e11	−1.01253
$126$	1.42515e10	0.0399781
$127$	−4.50271e11	−1.20936	−0.604678	−	0.796470i	$-0.706698\pi$
$127$	−4.50271e11	−1.20936	−0.604678	+	0.796470i	$0.706698\pi$
$128$	−3.76584e11	−0.968739
$129$	−3.94807e11	−0.973063
$130$	−2.35913e10	−0.0557268
$131$	−2.39336e11	−0.542022	−0.271011	−	0.962576i	$-0.587358\pi$
$131$	−2.39336e11	−0.542022	−0.271011	+	0.962576i	$0.587358\pi$
$132$	1.51395e11	0.328818
$133$	−1.95599e11	−0.407551
$134$	−1.44678e11	−0.289286
$135$	−6.34888e10	−0.121860
$136$	2.09557e11	0.386222
$137$	1.02628e11	0.181678	0.0908388	−	0.995866i	$-0.471045\pi$
$137$	1.02628e11	0.181678	0.0908388	+	0.995866i	$0.471045\pi$
$138$	−2.01490e11	−0.342703
$139$	−5.39795e10	−0.0882363	−0.0441181	−	0.999026i	$-0.514048\pi$
$139$	−5.39795e10	−0.0882363	−0.0441181	+	0.999026i	$0.514048\pi$
$140$	−1.36964e11	−0.215230
$141$	−1.83746e11	−0.277659
$142$	1.47151e11	0.213883
$143$	−1.25598e11	−0.175645
$144$	1.75367e11	0.236023
$145$	−4.80343e11	−0.622340
$146$	1.64554e11	0.205290
$147$	−6.86415e10	−0.0824786
$148$	1.06197e12	1.22934
$149$	−1.61055e12	−1.79659	−0.898294	−	0.439394i	$-0.855193\pi$
$149$	−1.61055e12	−1.79659	−0.898294	+	0.439394i	$0.855193\pi$
$150$	1.02070e11	0.109748
$151$	−6.54417e11	−0.678393	−0.339197	−	0.940715i	$-0.610155\pi$
$151$	−6.54417e11	−0.678393	−0.339197	+	0.940715i	$0.610155\pi$
$152$	6.50069e11	0.649860
$153$	−2.21529e11	−0.213613
$154$	8.16422e10	0.0759540
$155$	−4.03607e11	−0.362355
$156$	−1.66174e11	−0.144005
$157$	−9.44292e11	−0.790056	−0.395028	−	0.918669i	$-0.629265\pi$
$157$	−9.44292e11	−0.790056	−0.395028	+	0.918669i	$0.629265\pi$
$158$	3.51275e11	0.283813
$159$	6.16388e11	0.481028
$160$	6.94864e11	0.523890
$161$	9.70464e11	0.707029
$162$	5.00706e10	0.0352574
$163$	6.94267e11	0.472601	0.236301	−	0.971680i	$-0.424065\pi$
$163$	6.94267e11	0.472601	0.236301	+	0.971680i	$0.424065\pi$
$164$	−2.16089e12	−1.42230
$165$	−3.63706e11	−0.231520
$166$	−1.65723e11	−0.102044
$167$	−2.56300e12	−1.52689	−0.763444	−	0.645874i	$-0.776493\pi$
$167$	−2.56300e12	−1.52689	−0.763444	+	0.645874i	$0.776493\pi$
$168$	2.28129e11	0.131516
$169$	1.37858e11	0.0769231
$170$	−2.38371e11	−0.128761
$171$	−6.87208e11	−0.359426
$172$	−2.99239e12	−1.51569
$173$	3.50023e12	1.71729	0.858645	−	0.512571i	$-0.171307\pi$
$173$	3.50023e12	1.71729	0.858645	+	0.512571i	$0.171307\pi$
$174$	3.78824e11	0.180060
$175$	−4.91616e11	−0.226421
$176$	1.00462e12	0.448417
$177$	−3.95039e11	−0.170918
$178$	3.30036e11	0.138437
$179$	3.94665e12	1.60523	0.802615	−	0.596497i	$-0.203441\pi$
$179$	3.94665e12	1.60523	0.802615	+	0.596497i	$0.203441\pi$
$180$	−4.81205e11	−0.189815
$181$	−4.53603e12	−1.73558	−0.867788	−	0.496934i	$-0.834459\pi$
$181$	−4.53603e12	−1.73558	−0.867788	+	0.496934i	$0.834459\pi$
$182$	−8.96117e10	−0.0332638
$183$	−3.07430e10	−0.0110730
$184$	−3.22532e12	−1.12739
$185$	−2.55124e12	−0.865578
$186$	3.18306e11	0.104839
$187$	−1.26907e12	−0.405840
$188$	−1.39268e12	−0.432496
$189$	−2.41162e11	−0.0727393
$190$	−7.39455e11	−0.216654
$191$	4.14824e12	1.18081	0.590405	−	0.807107i	$-0.298968\pi$
$191$	4.14824e12	1.18081	0.590405	+	0.807107i	$0.298968\pi$
$192$	9.29984e11	0.257228
$193$	−7.06168e12	−1.89820	−0.949102	−	0.314970i	$-0.898005\pi$
$193$	−7.06168e12	−1.89820	−0.949102	+	0.314970i	$0.898005\pi$
$194$	−8.23880e11	−0.215256
$195$	3.99210e11	0.101394
$196$	−5.20259e11	−0.128473
$197$	3.37833e11	0.0811219	0.0405610	−	0.999177i	$-0.487085\pi$
$197$	3.37833e11	0.0811219	0.0405610	+	0.999177i	$0.487085\pi$
$198$	2.86838e11	0.0669851
$199$	−3.00148e12	−0.681780	−0.340890	−	0.940103i	$-0.610728\pi$
$199$	−3.00148e12	−0.681780	−0.340890	+	0.940103i	$0.610728\pi$
$200$	1.63388e12	0.361039
$201$	2.44823e12	0.526349
$202$	2.38031e12	0.497968
$203$	−1.82458e12	−0.371480
$204$	−1.67905e12	−0.332734
$205$	5.19123e12	1.00144
$206$	1.80013e12	0.338092
$207$	3.40959e12	0.623541
$208$	−1.10269e12	−0.196383
$209$	−3.93679e12	−0.682870
$210$	−2.59497e11	−0.0438456
$211$	−3.07714e12	−0.506516	−0.253258	−	0.967399i	$-0.581502\pi$
$211$	−3.07714e12	−0.506516	−0.253258	+	0.967399i	$0.581502\pi$
$212$	4.67183e12	0.749273
$213$	−2.49006e12	−0.389155
$214$	3.40754e12	0.518997
$215$	7.18880e12	1.06720
$216$	8.01498e11	0.115986
$217$	−1.53310e12	−0.216293
$218$	−3.09885e12	−0.426276
$219$	−2.78456e12	−0.373520
$220$	−2.75667e12	−0.360628
$221$	1.39295e12	0.177737
$222$	2.01204e12	0.250435
$223$	−8.21247e12	−0.997234	−0.498617	−	0.866823i	$-0.666159\pi$
$223$	−8.21247e12	−0.997234	−0.498617	+	0.866823i	$0.666159\pi$
$224$	2.63944e12	0.312714
$225$	−1.72722e12	−0.199685
$226$	−3.60798e11	−0.0407068
$227$	2.91907e12	0.321442	0.160721	−	0.987000i	$-0.448618\pi$
$227$	2.91907e12	0.321442	0.160721	+	0.987000i	$0.448618\pi$
$228$	−5.20861e12	−0.559861
$229$	−9.73078e12	−1.02106	−0.510531	−	0.859859i	$-0.670551\pi$
$229$	−9.73078e12	−1.02106	−0.510531	+	0.859859i	$0.670551\pi$
$230$	3.66881e12	0.375856
$231$	−1.38154e12	−0.138197
$232$	6.06397e12	0.592343
$233$	7.20907e12	0.687735	0.343868	−	0.939018i	$-0.388263\pi$
$233$	7.20907e12	0.687735	0.343868	+	0.939018i	$0.388263\pi$
$234$	−3.14838e11	−0.0293359
$235$	3.34572e12	0.304520
$236$	−2.99415e12	−0.266230
$237$	−5.94422e12	−0.516392
$238$	−9.05452e11	−0.0768586
$239$	−1.17393e13	−0.973762	−0.486881	−	0.873468i	$-0.661865\pi$
$239$	−1.17393e13	−0.973762	−0.486881	+	0.873468i	$0.661865\pi$
$240$	−3.19315e12	−0.258856
$241$	−1.26058e13	−0.998798	−0.499399	−	0.866372i	$-0.666446\pi$
$241$	−1.26058e13	−0.998798	−0.499399	+	0.866372i	$0.666446\pi$
$242$	−2.45391e12	−0.190052
$243$	−8.47289e11	−0.0641500
$244$	−2.33013e11	−0.0172479
$245$	1.24985e12	0.0904576
$246$	−4.09408e12	−0.289743
$247$	4.32108e12	0.299061
$248$	5.09523e12	0.344889
$249$	2.80435e12	0.185667
$250$	−4.96100e12	−0.321291
$251$	2.08449e13	1.32067	0.660334	−	0.750972i	$-0.270415\pi$
$251$	2.08449e13	1.32067	0.660334	+	0.750972i	$0.270415\pi$
$252$	−1.82786e12	−0.113302
$253$	1.95324e13	1.18466
$254$	−6.46595e12	−0.383749
$255$	4.03369e12	0.234278
$256$	2.43010e12	0.138135
$257$	−2.39536e12	−0.133272	−0.0666361	−	0.997777i	$-0.521227\pi$
$257$	−2.39536e12	−0.133272	−0.0666361	+	0.997777i	$0.521227\pi$
$258$	−5.66947e12	−0.308769
$259$	−9.69087e12	−0.516671
$260$	3.02576e12	0.157936
$261$	−6.41041e12	−0.327614
$262$	−3.43690e12	−0.171993
$263$	−1.40462e13	−0.688340	−0.344170	−	0.938907i	$-0.611840\pi$
$263$	−1.40462e13	−0.688340	−0.344170	+	0.938907i	$0.611840\pi$
$264$	4.59152e12	0.220361
$265$	−1.12234e13	−0.527562
$266$	−2.80882e12	−0.129323
$267$	−5.58482e12	−0.251882
$268$	1.85561e13	0.819869
$269$	1.56369e13	0.676884	0.338442	−	0.940987i	$-0.390100\pi$
$269$	1.56369e13	0.676884	0.338442	+	0.940987i	$0.390100\pi$
$270$	−9.11706e11	−0.0386682
$271$	−2.91728e13	−1.21240	−0.606202	−	0.795311i	$-0.707308\pi$
$271$	−2.91728e13	−1.21240	−0.606202	+	0.795311i	$0.707308\pi$
$272$	−1.11417e13	−0.453758
$273$	1.51640e12	0.0605228
$274$	1.47375e12	0.0576493
$275$	−9.89469e12	−0.379378
$276$	2.58425e13	0.971259
$277$	−1.45533e13	−0.536193	−0.268097	−	0.963392i	$-0.586395\pi$
$277$	−1.45533e13	−0.536193	−0.268097	+	0.963392i	$0.586395\pi$
$278$	−7.75151e11	−0.0279988
$279$	−5.38633e12	−0.190752
$280$	−4.15386e12	−0.144239
$281$	−4.74697e13	−1.61634	−0.808168	−	0.588952i	$-0.799541\pi$
$281$	−4.74697e13	−1.61634	−0.808168	+	0.588952i	$0.799541\pi$
$282$	−2.63861e12	−0.0881059
$283$	−2.66240e13	−0.871864	−0.435932	−	0.899980i	$-0.643581\pi$
$283$	−2.66240e13	−0.871864	−0.435932	+	0.899980i	$0.643581\pi$
$284$	−1.88731e13	−0.606168
$285$	1.25130e13	0.394197
$286$	−1.80360e12	−0.0557350
$287$	1.97189e13	0.597768
$288$	9.27330e12	0.275788
$289$	−2.01973e13	−0.589326
$290$	−6.89778e12	−0.197479
$291$	1.39416e13	0.391653
$292$	−2.11052e13	−0.581814
$293$	−3.08487e13	−0.834574	−0.417287	−	0.908775i	$-0.637019\pi$
$293$	−3.08487e13	−0.834574	−0.417287	+	0.908775i	$0.637019\pi$
$294$	−9.85699e11	−0.0261718
$295$	7.19303e12	0.187452
$296$	3.22075e13	0.823857
$297$	−4.85384e12	−0.121878
$298$	−2.31276e13	−0.570087
$299$	−2.14391e13	−0.518817
$300$	−1.30913e13	−0.311039
$301$	2.73066e13	0.637019
$302$	−9.39750e12	−0.215265
$303$	−4.02793e13	−0.906041
$304$	−3.45630e13	−0.763496
$305$	5.59782e11	0.0121442
$306$	−3.18118e12	−0.0677829
$307$	7.57475e13	1.58528	0.792642	−	0.609687i	$-0.208705\pi$
$307$	7.57475e13	1.58528	0.792642	+	0.609687i	$0.208705\pi$
$308$	−1.04712e13	−0.215262
$309$	−3.04616e13	−0.615150
$310$	−5.79584e12	−0.114981
$311$	−5.43810e13	−1.05990	−0.529950	−	0.848029i	$-0.677789\pi$
$311$	−5.43810e13	−1.05990	−0.529950	+	0.848029i	$0.677789\pi$
$312$	−5.03972e12	−0.0965065
$313$	7.63285e13	1.43613	0.718064	−	0.695977i	$-0.245029\pi$
$313$	7.63285e13	1.43613	0.718064	+	0.695977i	$0.245029\pi$
$314$	−1.35601e13	−0.250698
$315$	4.39118e12	0.0797761
$316$	−4.50535e13	−0.804358
$317$	1.24347e13	0.218178	0.109089	−	0.994032i	$-0.465207\pi$
$317$	1.24347e13	0.218178	0.109089	+	0.994032i	$0.465207\pi$
$318$	8.85140e12	0.152638
$319$	−3.67231e13	−0.622431
$320$	−1.69335e13	−0.282113
$321$	−5.76619e13	−0.944303
$322$	1.39360e13	0.224352
$323$	4.36610e13	0.691002
$324$	−6.42192e12	−0.0999234
$325$	1.08606e13	0.166148
$326$	9.96975e12	0.149964
$327$	5.24384e13	0.775599
$328$	−6.55354e13	−0.953169
$329$	1.27087e13	0.181771
$330$	−5.22286e12	−0.0734653
$331$	2.35824e12	0.0326238	0.0163119	−	0.999867i	$-0.494808\pi$
$331$	2.35824e12	0.0326238	0.0163119	+	0.999867i	$0.494808\pi$
$332$	2.12552e13	0.289205
$333$	−3.40475e13	−0.455661
$334$	−3.68049e13	−0.484507
$335$	−4.45784e13	−0.577268
$336$	−1.21292e13	−0.154513
$337$	−1.18171e13	−0.148097	−0.0740487	−	0.997255i	$-0.523592\pi$
$337$	−1.18171e13	−0.148097	−0.0740487	+	0.997255i	$0.523592\pi$
$338$	1.97966e12	0.0244090
$339$	6.10537e12	0.0740652
$340$	3.05728e13	0.364923
$341$	−3.08565e13	−0.362408
$342$	−9.86838e12	−0.114052
$343$	4.74756e12	0.0539949
$344$	−9.07532e13	−1.01576
$345$	−6.20831e13	−0.683862
$346$	5.02638e13	0.544925
$347$	−6.85979e11	−0.00731980	−0.00365990	−	0.999993i	$-0.501165\pi$
$347$	−6.85979e11	−0.00731980	−0.00365990	+	0.999993i	$0.501165\pi$
$348$	−4.85869e13	−0.510309
$349$	−3.85641e13	−0.398697	−0.199349	−	0.979929i	$-0.563883\pi$
$349$	−3.85641e13	−0.398697	−0.199349	+	0.979929i	$0.563883\pi$
$350$	−7.05966e12	−0.0718471
$351$	5.32765e12	0.0533761
$352$	5.31237e13	0.523967
$353$	2.41846e13	0.234843	0.117422	−	0.993082i	$-0.462537\pi$
$353$	2.41846e13	0.234843	0.117422	+	0.993082i	$0.462537\pi$
$354$	−5.67280e12	−0.0542350
$355$	4.53401e13	0.426802
$356$	−4.23295e13	−0.392345
$357$	1.53220e13	0.139842
$358$	5.66744e13	0.509366
$359$	−1.30749e14	−1.15723	−0.578615	−	0.815601i	$-0.696407\pi$
$359$	−1.30749e14	−1.15723	−0.578615	+	0.815601i	$0.696407\pi$
$360$	−1.45940e13	−0.127207
$361$	1.89512e13	0.162685
$362$	−6.51379e13	−0.550727
$363$	4.15247e13	0.345796
$364$	1.14933e13	0.0942733
$365$	5.07024e13	0.409655
$366$	−4.41473e11	−0.00351365
$367$	−1.88991e14	−1.48176	−0.740882	−	0.671636i	$-0.765592\pi$
$367$	−1.88991e14	−1.48176	−0.740882	+	0.671636i	$0.765592\pi$
$368$	1.71484e14	1.32453
$369$	6.92796e13	0.527181
$370$	−3.66360e13	−0.274662
$371$	−4.26322e13	−0.314906
$372$	−4.08250e13	−0.297125
$373$	−6.86251e13	−0.492135	−0.246068	−	0.969253i	$-0.579139\pi$
$373$	−6.86251e13	−0.492135	−0.246068	+	0.969253i	$0.579139\pi$
$374$	−1.82239e13	−0.128780
$375$	8.39494e13	0.584582
$376$	−4.22372e13	−0.289842
$377$	4.03079e13	0.272592
$378$	−3.46311e12	−0.0230814
$379$	8.54281e13	0.561158	0.280579	−	0.959831i	$-0.409474\pi$
$379$	8.54281e13	0.561158	0.280579	+	0.959831i	$0.409474\pi$
$380$	9.48404e13	0.614021
$381$	1.09416e14	0.698222
$382$	5.95692e13	0.374691
$383$	−2.73679e14	−1.69687	−0.848433	−	0.529303i	$-0.822454\pi$
$383$	−2.73679e14	−1.69687	−0.848433	+	0.529303i	$0.822454\pi$
$384$	9.15099e13	0.559302
$385$	2.51556e13	0.151566
$386$	−1.01406e14	−0.602331
$387$	9.59380e13	0.561798
$388$	1.05669e14	0.610058
$389$	9.67709e13	0.550835	0.275418	−	0.961325i	$-0.411184\pi$
$389$	9.67709e13	0.550835	0.275418	+	0.961325i	$0.411184\pi$
$390$	5.73270e12	0.0321739
$391$	−2.16624e14	−1.19877
$392$	−1.57784e13	−0.0860975
$393$	5.81588e13	0.312936
$394$	4.85132e12	0.0257413
$395$	1.08235e14	0.566347
$396$	−3.67890e13	−0.189843
$397$	−4.26925e13	−0.217272	−0.108636	−	0.994082i	$-0.534648\pi$
$397$	−4.26925e13	−0.217272	−0.108636	+	0.994082i	$0.534648\pi$
$398$	−4.31016e13	−0.216340
$399$	4.75305e13	0.235300
$400$	−8.68703e13	−0.424171
$401$	2.31618e14	1.11552	0.557762	−	0.830001i	$-0.311660\pi$
$401$	2.31618e14	1.11552	0.557762	+	0.830001i	$0.311660\pi$
$402$	3.51569e13	0.167019
$403$	3.38686e13	0.158716
$404$	−3.05292e14	−1.41130
$405$	1.54278e13	0.0703559
$406$	−2.62012e13	−0.117877
$407$	−1.95047e14	−0.865705
$408$	−5.09222e13	−0.222985
$409$	−1.08333e14	−0.468039	−0.234019	−	0.972232i	$-0.575188\pi$
$409$	−1.08333e14	−0.468039	−0.234019	+	0.972232i	$0.575188\pi$
$410$	7.45467e13	0.317773
$411$	−2.49385e13	−0.104892
$412$	−2.30880e14	−0.958189
$413$	2.73227e13	0.111892
$414$	4.89620e13	0.197860
$415$	−5.10627e13	−0.203629
$416$	−5.83094e13	−0.229470
$417$	1.31170e13	0.0509433
$418$	−5.65327e13	−0.216686
$419$	−2.76667e14	−1.04660	−0.523299	−	0.852149i	$-0.675299\pi$
$419$	−2.76667e14	−1.04660	−0.523299	+	0.852149i	$0.675299\pi$
$420$	3.32824e13	0.124263
$421$	−4.58583e14	−1.68992	−0.844960	−	0.534830i	$-0.820376\pi$
$421$	−4.58583e14	−1.68992	−0.844960	+	0.534830i	$0.820376\pi$
$422$	−4.41880e13	−0.160726
$423$	4.46502e13	0.160307
$424$	1.41687e14	0.502134
$425$	1.09737e14	0.383897
$426$	−3.57576e13	−0.123485
$427$	2.12633e12	0.00724899
$428$	−4.37041e14	−1.47089
$429$	3.05204e13	0.101409
$430$	1.03232e14	0.338639
$431$	1.04507e14	0.338470	0.169235	−	0.985576i	$-0.445870\pi$
$431$	1.04507e14	0.338470	0.169235	+	0.985576i	$0.445870\pi$
$432$	−4.26142e13	−0.136268
$433$	−3.84367e14	−1.21357	−0.606783	−	0.794868i	$-0.707540\pi$
$433$	−3.84367e14	−1.21357	−0.606783	+	0.794868i	$0.707540\pi$
$434$	−2.20155e13	−0.0686333
$435$	1.16723e14	0.359308
$436$	3.97450e14	1.20811
$437$	−6.71993e14	−2.01705
$438$	−3.99866e13	−0.118524
$439$	5.48221e14	1.60473	0.802363	−	0.596837i	$-0.203576\pi$
$439$	5.48221e14	1.60473	0.802363	+	0.596837i	$0.203576\pi$
$440$	−8.36042e13	−0.241679
$441$	1.66799e13	0.0476190
$442$	2.00029e13	0.0563988
$443$	1.57696e14	0.439138	0.219569	−	0.975597i	$-0.429535\pi$
$443$	1.57696e14	0.439138	0.219569	+	0.975597i	$0.429535\pi$
$444$	−2.58059e14	−0.709761
$445$	1.01691e14	0.276249
$446$	−1.17932e14	−0.316439
$447$	3.91363e14	1.03726
$448$	−6.43220e13	−0.168395
$449$	−3.11807e14	−0.806365	−0.403182	−	0.915120i	$-0.632096\pi$
$449$	−3.11807e14	−0.806365	−0.403182	+	0.915120i	$0.632096\pi$
$450$	−2.48031e13	−0.0633632
$451$	3.96880e14	1.00159
$452$	4.62749e13	0.115368
$453$	1.59023e14	0.391671
$454$	4.19182e13	0.101999
$455$	−2.76112e13	−0.0663777
$456$	−1.57967e14	−0.375197
$457$	−1.77079e14	−0.415554	−0.207777	−	0.978176i	$-0.566623\pi$
$457$	−1.77079e14	−0.415554	−0.207777	+	0.978176i	$0.566623\pi$
$458$	−1.39735e14	−0.324000
$459$	5.38315e13	0.123329
$460$	−4.70551e14	−1.06522
$461$	5.44865e14	1.21880	0.609401	−	0.792862i	$-0.291410\pi$
$461$	5.44865e14	1.21880	0.609401	+	0.792862i	$0.291410\pi$
$462$	−1.98390e13	−0.0438521
$463$	−4.79572e14	−1.04751	−0.523755	−	0.851869i	$-0.675469\pi$
$463$	−4.79572e14	−1.04751	−0.523755	+	0.851869i	$0.675469\pi$
$464$	−3.22410e14	−0.695921
$465$	9.80764e13	0.209206
$466$	1.03523e14	0.218230
$467$	3.66938e14	0.764452	0.382226	−	0.924069i	$-0.375158\pi$
$467$	3.66938e14	0.764452	0.382226	+	0.924069i	$0.375158\pi$
$468$	4.03802e13	0.0831413
$469$	−1.69331e14	−0.344577
$470$	4.80449e13	0.0966293
$471$	2.29463e14	0.456139
$472$	−9.08066e13	−0.178417
$473$	5.49597e14	1.06735
$474$	−8.53597e13	−0.163860
$475$	3.40417e14	0.645947
$476$	1.16131e14	0.217826
$477$	−1.49782e14	−0.277721
$478$	−1.68577e14	−0.308991
$479$	−6.21358e13	−0.112589	−0.0562945	−	0.998414i	$-0.517929\pi$
$479$	−6.21358e13	−0.112589	−0.0562945	+	0.998414i	$0.517929\pi$
$480$	−1.68852e14	−0.302468
$481$	2.14087e14	0.379133
$482$	−1.81021e14	−0.316935
$483$	−2.35823e14	−0.408203
$484$	3.14731e14	0.538629
$485$	−2.53854e14	−0.429541
$486$	−1.21672e13	−0.0203559
$487$	−5.76505e14	−0.953661	−0.476831	−	0.878995i	$-0.658215\pi$
$487$	−5.76505e14	−0.953661	−0.476831	+	0.878995i	$0.658215\pi$
$488$	−7.06682e12	−0.0115589
$489$	−1.68707e14	−0.272856
$490$	1.79480e13	0.0287037
$491$	7.52984e14	1.19080	0.595398	−	0.803431i	$-0.296994\pi$
$491$	7.52984e14	1.19080	0.595398	+	0.803431i	$0.296994\pi$
$492$	5.25095e14	0.821165
$493$	4.07278e14	0.629844
$494$	6.20512e13	0.0948969
$495$	8.83807e13	0.133668
$496$	−2.70904e14	−0.405197
$497$	1.72224e14	0.254762
$498$	4.02707e13	0.0589153
$499$	−1.17700e15	−1.70303	−0.851516	−	0.524329i	$-0.824316\pi$
$499$	−1.17700e15	−1.70303	−0.851516	+	0.524329i	$0.824316\pi$
$500$	6.36284e14	0.910575
$501$	6.22808e14	0.881549
$502$	2.99335e14	0.419070
$503$	1.40677e15	1.94805	0.974023	−	0.226451i	$-0.0727122\pi$
$503$	1.40677e15	1.94805	0.974023	+	0.226451i	$0.0727122\pi$
$504$	−5.54353e13	−0.0759309
$505$	7.33423e14	0.993692
$506$	2.80487e14	0.375911
$507$	−3.34996e13	−0.0444116
$508$	8.29304e14	1.08759
$509$	−2.38636e14	−0.309590	−0.154795	−	0.987947i	$-0.549472\pi$
$509$	−2.38636e14	−0.309590	−0.154795	+	0.987947i	$0.549472\pi$
$510$	5.79242e13	0.0743402
$511$	1.92593e14	0.244527
$512$	8.06141e14	1.01257
$513$	1.66992e14	0.207515
$514$	−3.43977e13	−0.0422895
$515$	5.54657e14	0.674660
$516$	7.27150e14	0.875086
$517$	2.55787e14	0.304565
$518$	−1.39162e14	−0.163948
$519$	−8.50557e14	−0.991478
$520$	9.17653e13	0.105842
$521$	7.26317e14	0.828932	0.414466	−	0.910065i	$-0.363968\pi$
$521$	7.26317e14	0.828932	0.414466	+	0.910065i	$0.363968\pi$
$522$	−9.20542e13	−0.103958
$523$	−3.93852e14	−0.440123	−0.220061	−	0.975486i	$-0.570626\pi$
$523$	−3.93852e14	−0.440123	−0.220061	+	0.975486i	$0.570626\pi$
$524$	4.40807e14	0.487446
$525$	1.19463e14	0.130724
$526$	−2.01705e14	−0.218422
$527$	3.42214e14	0.366724
$528$	−2.44123e14	−0.258894
$529$	2.38129e15	2.49923
$530$	−1.61170e14	−0.167404
$531$	9.59945e13	0.0986794
$532$	3.60251e14	0.366515
$533$	−4.35622e14	−0.438641
$534$	−8.01987e13	−0.0799264
$535$	1.04993e15	1.03566
$536$	5.62768e14	0.549444
$537$	−9.59037e14	−0.926780
$538$	2.24548e14	0.214786
$539$	9.55536e13	0.0904709
$540$	1.16933e14	0.109590
$541$	6.71611e14	0.623064	0.311532	−	0.950236i	$-0.399158\pi$
$541$	6.71611e14	0.623064	0.311532	+	0.950236i	$0.399158\pi$
$542$	−4.18925e14	−0.384716
$543$	1.10226e15	1.00204
$544$	−5.89168e14	−0.530207
$545$	−9.54820e14	−0.850630
$546$	2.17756e13	0.0192049
$547$	1.41217e15	1.23298	0.616491	−	0.787362i	$-0.288554\pi$
$547$	1.41217e15	1.23298	0.616491	+	0.787362i	$0.288554\pi$
$548$	−1.89018e14	−0.163385
$549$	7.47056e12	0.00639301
$550$	−1.42089e14	−0.120383
$551$	1.26342e15	1.05978
$552$	7.83752e14	0.650900
$553$	4.11130e14	0.338058
$554$	−2.08986e14	−0.170143
$555$	6.19951e14	0.499742
$556$	9.94187e13	0.0793518
$557$	−2.05467e15	−1.62382	−0.811909	−	0.583783i	$-0.801572\pi$
$557$	−2.05467e15	−1.62382	−0.811909	+	0.583783i	$0.801572\pi$
$558$	−7.73483e13	−0.0605289
$559$	−6.03247e14	−0.467444
$560$	2.20853e14	0.169461
$561$	3.08383e14	0.234312
$562$	−6.81670e14	−0.512890
$563$	2.82561e14	0.210531	0.105266	−	0.994444i	$-0.466431\pi$
$563$	2.82561e14	0.210531	0.105266	+	0.994444i	$0.466431\pi$
$564$	3.38421e14	0.249702
$565$	−1.11169e14	−0.0812302
$566$	−3.82324e14	−0.276657
$567$	5.86024e13	0.0419961
$568$	−5.72385e14	−0.406230
$569$	4.92020e14	0.345832	0.172916	−	0.984937i	$-0.444681\pi$
$569$	4.92020e14	0.345832	0.172916	+	0.984937i	$0.444681\pi$
$570$	1.79688e14	0.125085
$571$	−3.14202e14	−0.216626	−0.108313	−	0.994117i	$-0.534545\pi$
$571$	−3.14202e14	−0.216626	−0.108313	+	0.994117i	$0.534545\pi$
$572$	2.31325e14	0.157959
$573$	−1.00802e15	−0.681741
$574$	2.83166e14	0.189682
$575$	−1.68898e15	−1.12060
$576$	−2.25986e14	−0.148511
$577$	1.24691e15	0.811649	0.405824	−	0.913951i	$-0.366984\pi$
$577$	1.24691e15	0.811649	0.405824	+	0.913951i	$0.366984\pi$
$578$	−2.90036e14	−0.187003
$579$	1.71599e15	1.09593
$580$	8.84690e14	0.559676
$581$	−1.93962e14	−0.121548
$582$	2.00203e14	0.124278
$583$	−8.58054e14	−0.527640
$584$	−6.40080e14	−0.389909
$585$	−9.70080e13	−0.0585397
$586$	−4.42990e14	−0.264824
$587$	1.13347e14	0.0671276	0.0335638	−	0.999437i	$-0.489314\pi$
$587$	1.13347e14	0.0671276	0.0335638	+	0.999437i	$0.489314\pi$
$588$	1.26423e14	0.0741739
$589$	1.06159e15	0.617052
$590$	1.03293e14	0.0594817
$591$	−8.20935e13	−0.0468358
$592$	−1.71241e15	−0.967919
$593$	−1.19853e15	−0.671196	−0.335598	−	0.942005i	$-0.608938\pi$
$593$	−1.19853e15	−0.671196	−0.335598	+	0.942005i	$0.608938\pi$
$594$	−6.97017e13	−0.0386739
$595$	−2.78988e14	−0.153371
$596$	2.96628e15	1.61569
$597$	7.29361e14	0.393626
$598$	−3.07867e14	−0.164629
$599$	2.49233e15	1.32056	0.660280	−	0.751020i	$-0.270438\pi$
$599$	2.49233e15	1.32056	0.660280	+	0.751020i	$0.270438\pi$
$600$	−3.97032e14	−0.208446
$601$	−1.73260e15	−0.901341	−0.450670	−	0.892690i	$-0.648815\pi$
$601$	−1.73260e15	−0.901341	−0.450670	+	0.892690i	$0.648815\pi$
$602$	3.92126e14	0.202137
$603$	−5.94920e14	−0.303888
$604$	1.20530e15	0.610086
$605$	−7.56098e14	−0.379248
$606$	−5.78416e14	−0.287502
$607$	−2.42676e15	−1.19533	−0.597666	−	0.801746i	$-0.703905\pi$
$607$	−2.42676e15	−1.19533	−0.597666	+	0.801746i	$0.703905\pi$
$608$	−1.82767e15	−0.892130
$609$	4.43374e14	0.214474
$610$	8.03853e12	0.00385356
$611$	−2.80755e14	−0.133383
$612$	4.08009e14	0.192104
$613$	2.24780e15	1.04888	0.524439	−	0.851448i	$-0.324275\pi$
$613$	2.24780e15	1.04888	0.524439	+	0.851448i	$0.324275\pi$
$614$	1.08774e15	0.503037
$615$	−1.26147e15	−0.578181
$616$	−3.17571e14	−0.144260
$617$	−2.85833e15	−1.28690	−0.643450	−	0.765488i	$-0.722497\pi$
$617$	−2.85833e15	−1.28690	−0.643450	+	0.765488i	$0.722497\pi$
$618$	−4.37432e14	−0.195197
$619$	4.48909e15	1.98545	0.992727	−	0.120384i	$-0.0384126\pi$
$619$	4.48909e15	1.98545	0.992727	+	0.120384i	$0.0384126\pi$
$620$	7.43358e14	0.325869
$621$	−8.28529e14	−0.360001
$622$	−7.80917e14	−0.336324
$623$	3.86272e14	0.164896
$624$	2.67953e14	0.113382
$625$	−1.00329e14	−0.0420809
$626$	1.09609e15	0.455707
$627$	9.56640e14	0.394255
$628$	1.73918e15	0.710506
$629$	2.16317e15	0.876016
$630$	6.30578e13	0.0253143
$631$	−3.15742e15	−1.25652	−0.628261	−	0.778002i	$-0.716233\pi$
$631$	−3.15742e15	−1.25652	−0.628261	+	0.778002i	$0.716233\pi$
$632$	−1.36638e15	−0.539049
$633$	7.47745e14	0.292437
$634$	1.78564e14	0.0692314
$635$	−1.99229e15	−0.765768
$636$	−1.13526e15	−0.432593
$637$	−1.04881e14	−0.0396214
$638$	−5.27348e14	−0.197508
$639$	6.05086e14	0.224679
$640$	−1.66625e15	−0.613409
$641$	−3.46542e15	−1.26484	−0.632422	−	0.774624i	$-0.717939\pi$
$641$	−3.46542e15	−1.26484	−0.632422	+	0.774624i	$0.717939\pi$
$642$	−8.28032e14	−0.299643
$643$	2.12153e15	0.761183	0.380592	−	0.924743i	$-0.375720\pi$
$643$	2.12153e15	0.761183	0.380592	+	0.924743i	$0.375720\pi$
$644$	−1.78739e15	−0.635838
$645$	−1.74688e15	−0.616147
$646$	6.26976e14	0.219266
$647$	−7.97510e14	−0.276543	−0.138271	−	0.990394i	$-0.544155\pi$
$647$	−7.97510e14	−0.276543	−0.138271	+	0.990394i	$0.544155\pi$
$648$	−1.94764e14	−0.0669647
$649$	5.49921e14	0.187480
$650$	1.55959e14	0.0527214
$651$	3.72543e14	0.124877
$652$	−1.27869e15	−0.425015
$653$	3.52532e15	1.16192	0.580960	−	0.813932i	$-0.302677\pi$
$653$	3.52532e15	1.16192	0.580960	+	0.813932i	$0.302677\pi$
$654$	7.53022e14	0.246110
$655$	−1.05898e15	−0.343210
$656$	3.48440e15	1.11984
$657$	6.76649e14	0.215652
$658$	1.82498e14	0.0576789
$659$	−5.45502e13	−0.0170973	−0.00854863	−	0.999963i	$-0.502721\pi$
$659$	−5.45502e13	−0.0170973	−0.00854863	+	0.999963i	$0.502721\pi$
$660$	6.69870e14	0.208209
$661$	5.37751e15	1.65758	0.828788	−	0.559563i	$-0.189031\pi$
$661$	5.37751e15	1.65758	0.828788	+	0.559563i	$0.189031\pi$
$662$	3.38646e13	0.0103521
$663$	−3.38486e14	−0.102616
$664$	6.44628e14	0.193814
$665$	−8.65454e14	−0.258063
$666$	−4.88926e14	−0.144589
$667$	−6.26848e15	−1.83853
$668$	4.72049e15	1.37315
$669$	1.99563e15	0.575753
$670$	−6.40150e14	−0.183177
$671$	4.27964e13	0.0121460
$672$	−6.41384e14	−0.180546
$673$	2.35400e15	0.657240	0.328620	−	0.944462i	$-0.393416\pi$
$673$	2.35400e15	0.657240	0.328620	+	0.944462i	$0.393416\pi$
$674$	−1.69695e14	−0.0469938
$675$	4.19715e14	0.115288
$676$	−2.53906e14	−0.0691777
$677$	−1.68449e15	−0.455230	−0.227615	−	0.973751i	$-0.573093\pi$
$677$	−1.68449e15	−0.455230	−0.227615	+	0.973751i	$0.573093\pi$
$678$	8.76738e13	0.0235021
$679$	−9.64265e14	−0.256397
$680$	9.27213e14	0.244557
$681$	−7.09334e14	−0.185585
$682$	−4.43103e14	−0.114998
$683$	2.86844e15	0.738467	0.369234	−	0.929337i	$-0.379620\pi$
$683$	2.86844e15	0.738467	0.369234	+	0.929337i	$0.379620\pi$
$684$	1.26569e15	0.323236
$685$	4.54091e14	0.115039
$686$	6.81755e13	0.0171335
$687$	2.36458e15	0.589511
$688$	4.82518e15	1.19338
$689$	9.41813e14	0.231078
$690$	−8.91520e14	−0.217001
$691$	−5.57355e15	−1.34587	−0.672934	−	0.739703i	$-0.734966\pi$
$691$	−5.57355e15	−1.34587	−0.672934	+	0.739703i	$0.734966\pi$
$692$	−6.44669e15	−1.54438
$693$	3.35714e14	0.0797878
$694$	−9.85074e12	−0.00232269
$695$	−2.38840e14	−0.0558715
$696$	−1.47354e15	−0.341989
$697$	−4.40160e15	−1.01351
$698$	−5.53785e14	−0.126513
$699$	−1.75180e15	−0.397064
$700$	9.05452e14	0.203623
$701$	−7.00824e15	−1.56372	−0.781861	−	0.623452i	$-0.785729\pi$
$701$	−7.00824e15	−1.56372	−0.781861	+	0.623452i	$0.785729\pi$
$702$	7.65056e13	0.0169371
$703$	6.71040e15	1.47399
$704$	−1.29460e15	−0.282154
$705$	−8.13009e14	−0.175815
$706$	3.47294e14	0.0745197
$707$	2.78591e15	0.593143
$708$	7.27578e14	0.153708
$709$	4.11385e15	0.862371	0.431185	−	0.902263i	$-0.358095\pi$
$709$	4.11385e15	0.862371	0.431185	+	0.902263i	$0.358095\pi$
$710$	6.51089e14	0.135431
$711$	1.44445e15	0.298139
$712$	−1.28377e15	−0.262934
$713$	−5.26707e15	−1.07048
$714$	2.20025e14	0.0443743
$715$	−5.55727e14	−0.111219
$716$	−7.26890e15	−1.44360
$717$	2.85264e15	0.562202
$718$	−1.87757e15	−0.367208
$719$	−9.76609e14	−0.189545	−0.0947724	−	0.995499i	$-0.530212\pi$
$719$	−9.76609e14	−0.189545	−0.0947724	+	0.995499i	$0.530212\pi$
$720$	7.75936e14	0.149451
$721$	2.10686e15	0.402710
$722$	2.72141e14	0.0516225
$723$	3.06322e15	0.576656
$724$	8.35440e15	1.56082
$725$	3.17548e15	0.588776
$726$	5.96299e14	0.109727
$727$	−8.85628e15	−1.61738	−0.808690	−	0.588235i	$-0.799823\pi$
$727$	−8.85628e15	−1.61738	−0.808690	+	0.588235i	$0.799823\pi$
$728$	3.48570e14	0.0631783
$729$	2.05891e14	0.0370370
$730$	7.28092e14	0.129990
$731$	−6.09531e15	−1.08007
$732$	5.66221e13	0.00995807
$733$	4.63449e15	0.808965	0.404483	−	0.914546i	$-0.367452\pi$
$733$	4.63449e15	0.808965	0.404483	+	0.914546i	$0.367452\pi$
$734$	−2.71394e15	−0.470188
$735$	−3.03714e14	−0.0522257
$736$	9.06799e15	1.54769
$737$	−3.40810e15	−0.577353
$738$	9.94862e14	0.167283
$739$	−7.36735e15	−1.22961	−0.614804	−	0.788680i	$-0.710765\pi$
$739$	−7.36735e15	−1.22961	−0.614804	+	0.788680i	$0.710765\pi$
$740$	4.69884e15	0.778423
$741$	−1.05002e15	−0.172663
$742$	−6.12204e14	−0.0999250
$743$	−2.70268e15	−0.437882	−0.218941	−	0.975738i	$-0.570260\pi$
$743$	−2.70268e15	−0.437882	−0.218941	+	0.975738i	$0.570260\pi$
$744$	−1.23814e15	−0.199122
$745$	−7.12609e15	−1.13761
$746$	−9.85464e14	−0.156163
$747$	−6.81456e14	−0.107195
$748$	2.33735e15	0.364976
$749$	3.98816e15	0.618192
$750$	1.20552e15	0.185498
$751$	−3.02136e15	−0.461512	−0.230756	−	0.973012i	$-0.574120\pi$
$751$	−3.02136e15	−0.461512	−0.230756	+	0.973012i	$0.574120\pi$
$752$	2.24567e15	0.340525
$753$	−5.06530e15	−0.762488
$754$	5.78826e14	0.0864979
$755$	−2.89556e15	−0.429561
$756$	4.44169e14	0.0654152
$757$	8.01585e15	1.17199	0.585993	−	0.810316i	$-0.300705\pi$
$757$	8.01585e15	1.17199	0.585993	+	0.810316i	$0.300705\pi$
$758$	1.22676e15	0.178065
$759$	−4.74637e15	−0.683962
$760$	2.87632e15	0.411493
$761$	−1.34585e15	−0.191153	−0.0955763	−	0.995422i	$-0.530469\pi$
$761$	−1.34585e15	−0.191153	−0.0955763	+	0.995422i	$0.530469\pi$
$762$	1.57123e15	0.221557
$763$	−3.62688e15	−0.507749
$764$	−7.64017e15	−1.06191
$765$	−9.80186e14	−0.135260
$766$	−3.93005e15	−0.538444
$767$	−6.03602e14	−0.0821062
$768$	−5.90515e14	−0.0797525
$769$	9.79480e15	1.31341	0.656706	−	0.754147i	$-0.271949\pi$
$769$	9.79480e15	1.31341	0.656706	+	0.754147i	$0.271949\pi$
$770$	3.61237e14	0.0480943
$771$	5.82073e14	0.0769447
$772$	1.30061e16	1.70707
$773$	−1.30070e16	−1.69508	−0.847542	−	0.530729i	$-0.821918\pi$
$773$	−1.30070e16	−1.69508	−0.847542	+	0.530729i	$0.821918\pi$
$774$	1.37768e15	0.178268
$775$	2.66819e15	0.342813
$776$	3.20472e15	0.408837
$777$	2.35488e15	0.298300
$778$	1.38964e15	0.174789
$779$	−1.36543e16	−1.70535
$780$	−7.35259e14	−0.0911843
$781$	3.46634e15	0.426865
$782$	−3.11075e15	−0.380388
$783$	1.55773e15	0.189148
$784$	8.38911e14	0.101153
$785$	−4.17815e15	−0.500266
$786$	8.35166e14	0.0992999
$787$	−4.70397e15	−0.555397	−0.277699	−	0.960668i	$-0.589572\pi$
$787$	−4.70397e15	−0.555397	−0.277699	+	0.960668i	$0.589572\pi$
$788$	−6.22217e14	−0.0729538
$789$	3.41323e15	0.397413
$790$	1.55426e15	0.179711
$791$	−4.22276e14	−0.0484870
$792$	−1.11574e15	−0.127226
$793$	−4.69740e13	−0.00531930
$794$	−6.13069e14	−0.0689440
$795$	2.72730e15	0.304588
$796$	5.52809e15	0.613131
$797$	4.79116e15	0.527740	0.263870	−	0.964558i	$-0.415001\pi$
$797$	4.79116e15	0.527740	0.263870	+	0.964558i	$0.415001\pi$
$798$	6.82543e14	0.0746645
$799$	−2.83680e15	−0.308192
$800$	−4.59365e15	−0.495636
$801$	1.35711e15	0.145424
$802$	3.32606e15	0.353974
$803$	3.87630e15	0.409715
$804$	−4.50912e15	−0.473351
$805$	4.29395e15	0.447693
$806$	4.86357e14	0.0503631
$807$	−3.79977e15	−0.390799
$808$	−9.25891e15	−0.945796
$809$	−4.14348e15	−0.420386	−0.210193	−	0.977660i	$-0.567409\pi$
$809$	−4.14348e15	−0.420386	−0.210193	+	0.977660i	$0.567409\pi$
$810$	2.21544e14	0.0223251
$811$	1.70586e16	1.70738	0.853689	−	0.520783i	$-0.174360\pi$
$811$	1.70586e16	1.70738	0.853689	+	0.520783i	$0.174360\pi$
$812$	3.36049e15	0.334076
$813$	7.08899e15	0.699981
$814$	−2.80090e15	−0.274703
$815$	3.07188e15	0.299253
$816$	2.70744e15	0.261977
$817$	−1.89084e16	−1.81732
$818$	−1.55567e15	−0.148516
$819$	−3.68485e14	−0.0349428
$820$	−9.56115e15	−0.900604
$821$	−9.45209e15	−0.884383	−0.442191	−	0.896921i	$-0.645799\pi$
$821$	−9.45209e15	−0.884383	−0.442191	+	0.896921i	$0.645799\pi$
$822$	−3.58120e14	−0.0332839
$823$	−1.45167e16	−1.34019	−0.670097	−	0.742274i	$-0.733747\pi$
$823$	−1.45167e16	−1.34019	−0.670097	+	0.742274i	$0.733747\pi$
$824$	−7.00213e15	−0.642141
$825$	2.40441e15	0.219034
$826$	3.92357e14	0.0355051
$827$	−1.13804e16	−1.02301	−0.511504	−	0.859281i	$-0.670911\pi$
$827$	−1.13804e16	−1.02301	−0.511504	+	0.859281i	$0.670911\pi$
$828$	−6.27973e15	−0.560756
$829$	−1.11977e16	−0.993297	−0.496649	−	0.867952i	$-0.665436\pi$
$829$	−1.11977e16	−0.993297	−0.496649	+	0.867952i	$0.665436\pi$
$830$	−7.33266e14	−0.0646148
$831$	3.53644e15	0.309571
$832$	1.42097e15	0.123568
$833$	−1.05974e15	−0.0915484
$834$	1.88362e14	0.0161651
$835$	−1.13403e16	−0.966831
$836$	7.25073e15	0.614112
$837$	1.30888e15	0.110131
$838$	−3.97297e15	−0.332103
$839$	−4.70211e15	−0.390483	−0.195242	−	0.980755i	$-0.562549\pi$
$839$	−4.70211e15	−0.390483	−0.195242	+	0.980755i	$0.562549\pi$
$840$	1.00939e15	0.0832764
$841$	−4.15045e14	−0.0340187
$842$	−6.58530e15	−0.536240
$843$	1.15351e16	0.933192
$844$	5.66743e15	0.455515
$845$	6.09974e14	0.0487079
$846$	6.41182e14	0.0508680
$847$	−2.87204e15	−0.226377
$848$	−7.53327e15	−0.589938
$849$	6.46964e15	0.503371
$850$	1.57584e15	0.121817
$851$	−3.32937e16	−2.55711
$852$	4.58617e15	0.349971
$853$	−7.88595e15	−0.597908	−0.298954	−	0.954268i	$-0.596638\pi$
$853$	−7.88595e15	−0.597908	−0.298954	+	0.954268i	$0.596638\pi$
$854$	3.05343e13	0.00230022
$855$	−3.04065e15	−0.227590
$856$	−1.32546e16	−0.985736
$857$	1.22466e16	0.904941	0.452471	−	0.891779i	$-0.350543\pi$
$857$	1.22466e16	0.904941	0.452471	+	0.891779i	$0.350543\pi$
$858$	4.38276e14	0.0321786
$859$	9.72186e15	0.709230	0.354615	−	0.935012i	$-0.384612\pi$
$859$	9.72186e15	0.709230	0.354615	+	0.935012i	$0.384612\pi$
$860$	−1.32402e16	−0.959741
$861$	−4.79169e15	−0.345121
$862$	1.50073e15	0.107402
$863$	−1.71694e15	−0.122094	−0.0610471	−	0.998135i	$-0.519444\pi$
$863$	−1.71694e15	−0.122094	−0.0610471	+	0.998135i	$0.519444\pi$
$864$	−2.25341e15	−0.159226
$865$	1.54873e16	1.08739
$866$	−5.51956e15	−0.385084
$867$	4.90795e15	0.340248
$868$	2.82364e15	0.194514
$869$	8.27476e15	0.566431
$870$	1.67616e15	0.114014
$871$	3.74079e15	0.252850
$872$	1.20539e16	0.809630
$873$	−3.38781e15	−0.226121
$874$	−9.64989e15	−0.640044
$875$	−5.80633e15	−0.382699
$876$	5.12857e15	0.335911
$877$	9.93119e15	0.646403	0.323202	−	0.946330i	$-0.395241\pi$
$877$	9.93119e15	0.646403	0.323202	+	0.946330i	$0.395241\pi$
$878$	7.87251e15	0.509206
$879$	7.49623e15	0.481841
$880$	4.44509e15	0.283939
$881$	−1.03838e16	−0.659160	−0.329580	−	0.944128i	$-0.606907\pi$
$881$	−1.03838e16	−0.659160	−0.329580	+	0.944128i	$0.606907\pi$
$882$	2.39525e14	0.0151103
$883$	−4.58291e14	−0.0287315	−0.0143657	−	0.999897i	$-0.504573\pi$
$883$	−4.58291e14	−0.0287315	−0.0143657	+	0.999897i	$0.504573\pi$
$884$	−2.56551e15	−0.159840
$885$	−1.74791e15	−0.108226
$886$	2.26454e15	0.139346
$887$	−1.51623e16	−0.927224	−0.463612	−	0.886038i	$-0.653447\pi$
$887$	−1.51623e16	−0.927224	−0.463612	+	0.886038i	$0.653447\pi$
$888$	−7.82641e15	−0.475654
$889$	−7.56771e15	−0.457093
$890$	1.46029e15	0.0876585
$891$	1.17948e15	0.0703662
$892$	1.51256e16	0.896822
$893$	−8.80009e15	−0.518566
$894$	5.62001e15	0.329140
$895$	1.74625e16	1.01644
$896$	−6.32925e15	−0.366149
$897$	5.20969e15	0.299539
$898$	−4.47759e15	−0.255873
$899$	9.90270e15	0.562439
$900$	3.18118e15	0.179578
$901$	9.51624e15	0.533924
$902$	5.69924e15	0.317820
$903$	−6.63551e15	−0.367783
$904$	1.40343e15	0.0773149
$905$	−2.00703e16	−1.09897
$906$	2.28359e15	0.124284
$907$	−3.65610e16	−1.97778	−0.988891	−	0.148640i	$-0.952510\pi$
$907$	−3.65610e16	−1.97778	−0.988891	+	0.148640i	$0.952510\pi$
$908$	−5.37631e15	−0.289076
$909$	9.78788e15	0.523103
$910$	−3.96500e14	−0.0210628
$911$	−1.72118e16	−0.908814	−0.454407	−	0.890794i	$-0.650149\pi$
$911$	−1.72118e16	−0.908814	−0.454407	+	0.890794i	$0.650149\pi$
$912$	8.39881e15	0.440804
$913$	−3.90384e15	−0.203659
$914$	−2.54287e15	−0.131862
$915$	−1.36027e14	−0.00701147
$916$	1.79220e16	0.918252
$917$	−4.02253e15	−0.204865
$918$	7.73026e14	0.0391345
$919$	−3.23789e16	−1.62940	−0.814699	−	0.579884i	$-0.803098\pi$
$919$	−3.23789e16	−1.62940	−0.814699	+	0.579884i	$0.803098\pi$
$920$	−1.42709e16	−0.713868
$921$	−1.84066e16	−0.915264
$922$	7.82431e15	0.386746
$923$	−3.80471e15	−0.186944
$924$	2.54450e15	0.124282
$925$	1.68659e16	0.818897
$926$	−6.88671e15	−0.332392
$927$	7.40217e15	0.355157
$928$	−1.70489e16	−0.813170
$929$	−3.06416e15	−0.145286	−0.0726431	−	0.997358i	$-0.523143\pi$
$929$	−3.06416e15	−0.145286	−0.0726431	+	0.997358i	$0.523143\pi$
$930$	1.40839e15	0.0663844
$931$	−3.28743e15	−0.154040
$932$	−1.32776e16	−0.618488
$933$	1.32146e16	0.611933
$934$	5.26927e15	0.242573
$935$	−5.61516e15	−0.256979
$936$	1.22465e15	0.0557180
$937$	−2.98777e16	−1.35138	−0.675692	−	0.737184i	$-0.736155\pi$
$937$	−2.98777e16	−1.35138	−0.675692	+	0.737184i	$0.736155\pi$
$938$	−2.43161e15	−0.109340
$939$	−1.85478e16	−0.829148
$940$	−6.16210e15	−0.273858
$941$	−2.65487e16	−1.17300	−0.586502	−	0.809947i	$-0.699496\pi$
$941$	−2.65487e16	−1.17300	−0.586502	+	0.809947i	$0.699496\pi$
$942$	3.29511e15	0.144741
$943$	6.77457e16	2.95847
$944$	4.82802e15	0.209615
$945$	−1.06706e15	−0.0460588
$946$	7.89228e15	0.338689
$947$	−9.07376e15	−0.387135	−0.193568	−	0.981087i	$-0.562006\pi$
$947$	−9.07376e15	−0.387135	−0.193568	+	0.981087i	$0.562006\pi$
$948$	1.09480e16	0.464396
$949$	−4.25469e15	−0.179433
$950$	4.88843e15	0.204970
$951$	−3.02164e15	−0.125965
$952$	3.52202e15	0.145978
$953$	−3.04447e16	−1.25459	−0.627293	−	0.778783i	$-0.715837\pi$
$953$	−3.04447e16	−1.25459	−0.627293	+	0.778783i	$0.715837\pi$
$954$	−2.15089e15	−0.0881256
$955$	1.83545e16	0.747693
$956$	2.16212e16	0.875714
$957$	8.92373e15	0.359361
$958$	−8.92276e14	−0.0357264
$959$	1.72486e15	0.0686677
$960$	4.11485e15	0.162878
$961$	−1.70878e16	−0.672522
$962$	3.07431e15	0.120305
$963$	1.40118e16	0.545194
$964$	2.32173e16	0.898229
$965$	−3.12454e16	−1.20195
$966$	−3.38644e15	−0.129530
$967$	3.12630e16	1.18901	0.594504	−	0.804093i	$-0.297348\pi$
$967$	3.12630e16	1.18901	0.594504	+	0.804093i	$0.297348\pi$
$968$	9.54517e15	0.360968
$969$	−1.06096e16	−0.398950
$970$	−3.64537e15	−0.136301
$971$	7.64208e15	0.284123	0.142061	−	0.989858i	$-0.454627\pi$
$971$	7.64208e15	0.284123	0.142061	+	0.989858i	$0.454627\pi$
$972$	1.56053e15	0.0576908
$973$	−9.07233e14	−0.0333502
$974$	−8.27868e15	−0.302613
$975$	−2.63912e15	−0.0959254
$976$	3.75730e14	0.0135801
$977$	−1.47644e16	−0.530634	−0.265317	−	0.964161i	$-0.585477\pi$
$977$	−1.47644e16	−0.530634	−0.265317	+	0.964161i	$0.585477\pi$
$978$	−2.42265e15	−0.0865819
$979$	7.77445e15	0.276290
$980$	−2.30196e15	−0.0813494
$981$	−1.27425e16	−0.447792
$982$	1.08129e16	0.377859
$983$	3.40812e16	1.18432	0.592162	−	0.805819i	$-0.298274\pi$
$983$	3.40812e16	1.18432	0.592162	+	0.805819i	$0.298274\pi$
$984$	1.59251e16	0.550313
$985$	1.49479e15	0.0513667
$986$	5.84856e15	0.199860
$987$	−3.08822e15	−0.104945
$988$	−7.95851e15	−0.268948
$989$	9.38139e16	3.15274
$990$	1.26916e15	0.0424152
$991$	5.15004e16	1.71161	0.855806	−	0.517297i	$-0.173062\pi$
$991$	5.15004e16	1.71161	0.855806	+	0.517297i	$0.173062\pi$
$992$	−1.43252e16	−0.473465
$993$	−5.73052e14	−0.0188353
$994$	2.47316e15	0.0808402
$995$	−1.32805e16	−0.431705
$996$	−5.16501e15	−0.166972
$997$	2.96920e16	0.954588	0.477294	−	0.878744i	$-0.341618\pi$
$997$	2.96920e16	0.954588	0.477294	+	0.878744i	$0.341618\pi$
$998$	−1.69018e16	−0.540400
$999$	8.27354e15	0.263076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.10	✓	16	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q+14.3601 q^{2} -243.000 q^{3} -1841.79 q^{4} +4424.64 q^{5} -3489.51 q^{6} +16807.0 q^{7} -55857.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+14.3601 q^{2} -243.000 q^{3} -1841.79 q^{4} +4424.64 q^{5} -3489.51 q^{6} +16807.0 q^{7} -55857.8 q^{8} +59049.0 q^{9} +63538.3 q^{10} +338272. q^{11} +447554. q^{12} -371293. q^{13} +241350. q^{14} -1.07519e6 q^{15} +2.96986e6 q^{16} -3.75161e6 q^{17} +847950. q^{18} -1.16379e7 q^{19} -8.14925e6 q^{20} -4.08410e6 q^{21} +4.85763e6 q^{22} +5.77416e7 q^{23} +1.35734e7 q^{24} -2.92507e7 q^{25} -5.33181e6 q^{26} -1.43489e7 q^{27} -3.09549e7 q^{28} -1.08561e8 q^{29} -1.54398e7 q^{30} -9.12180e7 q^{31} +1.57044e8 q^{32} -8.22002e7 q^{33} -5.38735e7 q^{34} +7.43650e7 q^{35} -1.08756e8 q^{36} -5.76597e8 q^{37} -1.67122e8 q^{38} +9.02242e7 q^{39} -2.47151e8 q^{40} +1.17326e9 q^{41} -5.86481e7 q^{42} +1.62472e9 q^{43} -6.23026e8 q^{44} +2.61271e8 q^{45} +8.29176e8 q^{46} +7.56156e8 q^{47} -7.21675e8 q^{48} +2.82475e8 q^{49} -4.20043e8 q^{50} +9.11641e8 q^{51} +6.83843e8 q^{52} -2.53658e9 q^{53} -2.06052e8 q^{54} +1.49673e9 q^{55} -9.38802e8 q^{56} +2.82802e9 q^{57} -1.55895e9 q^{58} +1.62567e9 q^{59} +1.98027e9 q^{60} +1.26515e8 q^{61} -1.30990e9 q^{62} +9.92437e8 q^{63} -3.82709e9 q^{64} -1.64284e9 q^{65} -1.18040e9 q^{66} -1.00750e10 q^{67} +6.90967e9 q^{68} -1.40312e10 q^{69} +1.06789e9 q^{70} +1.02472e10 q^{71} -3.29835e9 q^{72} +1.14591e10 q^{73} -8.28000e9 q^{74} +7.10791e9 q^{75} +2.14346e10 q^{76} +5.68534e9 q^{77} +1.29563e9 q^{78} +2.44618e10 q^{79} +1.31406e10 q^{80} +3.48678e9 q^{81} +1.68481e10 q^{82} -1.15405e10 q^{83} +7.52205e9 q^{84} -1.65995e10 q^{85} +2.33311e10 q^{86} +2.63803e10 q^{87} -1.88951e10 q^{88} +2.29828e10 q^{89} +3.75188e9 q^{90} -6.24032e9 q^{91} -1.06348e11 q^{92} +2.21660e10 q^{93} +1.08585e10 q^{94} -5.14937e10 q^{95} -3.81617e10 q^{96} -5.73728e10 q^{97} +4.05638e9 q^{98} +1.99746e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9 + 1056711 * q^10 - 466884 * q^11 - 5044923 * q^12 - 5940688 * q^13 - 1058841 * q^14 + 769824 * q^15 + 40058265 * q^16 + 1753452 * q^17 - 3720087 * q^18 + 4237800 * q^19 - 20710503 * q^20 - 65345616 * q^21 - 37479661 * q^22 - 150481440 * q^23 + 45675495 * q^24 + 150983176 * q^25 + 23391459 * q^26 - 229582512 * q^27 + 348930127 * q^28 - 111411432 * q^29 - 256780773 * q^30 - 90536236 * q^31 - 609941313 * q^32 + 113452812 * q^33 + 443745577 * q^34 - 53244576 * q^35 + 1225916289 * q^36 - 1756337900 * q^37 - 4378868973 * q^38 + 1443587184 * q^39 + 57535383 * q^40 + 649575720 * q^41 + 257298363 * q^42 - 1889554520 * q^43 - 4979587689 * q^44 - 187067232 * q^45 - 3204000867 * q^46 - 4036082940 * q^47 - 9734158395 * q^48 + 4519603984 * q^49 - 15928886862 * q^50 - 426088836 * q^51 - 7708413973 * q^52 + 511144020 * q^53 + 903981141 * q^54 - 8519365572 * q^55 - 3159127755 * q^56 - 1029785400 * q^57 - 7851149577 * q^58 + 3728287296 * q^59 + 5032652229 * q^60 + 26227205052 * q^61 + 2996618490 * q^62 + 15878984688 * q^63 + 51104408465 * q^64 + 1176256224 * q^65 + 9107557623 * q^66 - 5295680024 * q^67 + 7919540325 * q^68 + 36566989920 * q^69 + 17760141777 * q^70 + 17082800928 * q^71 - 11099145285 * q^72 + 21076301488 * q^73 + 52794333675 * q^74 - 36688911768 * q^75 + 81459179177 * q^76 - 7846919388 * q^77 - 5684124537 * q^78 - 83677977852 * q^79 - 163988465427 * q^80 + 55788550416 * q^81 - 61543728760 * q^82 - 72857072340 * q^83 - 84790020861 * q^84 - 12608565060 * q^85 - 20177818011 * q^86 + 27072977976 * q^87 - 202213679643 * q^88 + 32238476676 * q^89 + 62397727839 * q^90 - 99845143216 * q^91 - 487057197033 * q^92 + 22000305348 * q^93 + 183904776602 * q^94 - 143022915504 * q^95 + 148215739059 * q^96 + 6973535140 * q^97 - 17795940687 * q^98 - 27569033316 * q^99

Introduction

L-functions

Modular forms

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