LMFDB - Embedded newform 273.12.a.c.1.11

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			1.11
Root			$25.8857$ 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)

$f(q)$	$=$	$q+21.8857 q^{2} -243.000 q^{3} -1569.02 q^{4} -9779.77 q^{5} -5318.23 q^{6} +16807.0 q^{7} -79161.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+21.8857 q^{2} -243.000 q^{3} -1569.02 q^{4} -9779.77 q^{5} -5318.23 q^{6} +16807.0 q^{7} -79161.0 q^{8} +59049.0 q^{9} -214037. q^{10} -283765. q^{11} +381271. q^{12} -371293. q^{13} +367833. q^{14} +2.37648e6 q^{15} +1.48085e6 q^{16} -6.90608e6 q^{17} +1.29233e6 q^{18} +3.16398e6 q^{19} +1.53446e7 q^{20} -4.08410e6 q^{21} -6.21039e6 q^{22} -4.57705e7 q^{23} +1.92361e7 q^{24} +4.68158e7 q^{25} -8.12601e6 q^{26} -1.43489e7 q^{27} -2.63704e7 q^{28} -3.23441e7 q^{29} +5.20110e7 q^{30} +2.87505e8 q^{31} +1.94531e8 q^{32} +6.89548e7 q^{33} -1.51144e8 q^{34} -1.64369e8 q^{35} -9.26488e7 q^{36} +2.00433e8 q^{37} +6.92460e7 q^{38} +9.02242e7 q^{39} +7.74176e8 q^{40} +4.97616e8 q^{41} -8.93835e7 q^{42} +1.18136e9 q^{43} +4.45231e8 q^{44} -5.77486e8 q^{45} -1.00172e9 q^{46} -1.39480e9 q^{47} -3.59847e8 q^{48} +2.82475e8 q^{49} +1.02460e9 q^{50} +1.67818e9 q^{51} +5.82565e8 q^{52} +3.13354e9 q^{53} -3.14036e8 q^{54} +2.77515e9 q^{55} -1.33046e9 q^{56} -7.68847e8 q^{57} -7.07874e8 q^{58} -2.04183e9 q^{59} -3.72874e9 q^{60} +1.08050e10 q^{61} +6.29226e9 q^{62} +9.92437e8 q^{63} +1.22467e9 q^{64} +3.63116e9 q^{65} +1.50913e9 q^{66} +1.02912e8 q^{67} +1.08357e10 q^{68} +1.11222e10 q^{69} -3.59732e9 q^{70} +5.85845e9 q^{71} -4.67438e9 q^{72} -5.19073e9 q^{73} +4.38662e9 q^{74} -1.13762e10 q^{75} -4.96434e9 q^{76} -4.76923e9 q^{77} +1.97462e9 q^{78} +4.54124e10 q^{79} -1.44824e10 q^{80} +3.48678e9 q^{81} +1.08907e10 q^{82} -4.50938e9 q^{83} +6.40802e9 q^{84} +6.75399e10 q^{85} +2.58549e10 q^{86} +7.85962e9 q^{87} +2.24631e10 q^{88} +6.08111e10 q^{89} -1.26387e10 q^{90} -6.24032e9 q^{91} +7.18146e10 q^{92} -6.98638e10 q^{93} -3.05262e10 q^{94} -3.09430e10 q^{95} -4.72711e10 q^{96} -3.24724e10 q^{97} +6.18217e9 q^{98} -1.67560e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.8857	0.483610	0.241805	−	0.970325i	$-0.422260\pi$
$2$	21.8857	0.483610	0.241805	+	0.970325i	$0.422260\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1569.02	−0.766121
$5$	−9779.77	−1.39957	−0.699783	−	0.714355i	$-0.746720\pi$
$5$	−9779.77	−1.39957	−0.699783	+	0.714355i	$0.746720\pi$
$6$	−5318.23	−0.279213
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−79161.0	−0.854115
$9$	59049.0	0.333333
$10$	−214037.	−0.676845
$11$	−283765.	−0.531250	−0.265625	−	0.964076i	$-0.585578\pi$
$11$	−283765.	−0.531250	−0.265625	+	0.964076i	$0.585578\pi$
$12$	381271.	0.442320
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	367833.	0.182788
$15$	2.37648e6	0.808040
$16$	1.48085e6	0.353062
$17$	−6.90608e6	−1.17968	−0.589838	−	0.807522i	$-0.700808\pi$
$17$	−6.90608e6	−1.17968	−0.589838	+	0.807522i	$0.700808\pi$
$18$	1.29233e6	0.161203
$19$	3.16398e6	0.293149	0.146575	−	0.989200i	$-0.453175\pi$
$19$	3.16398e6	0.293149	0.146575	+	0.989200i	$0.453175\pi$
$20$	1.53446e7	1.07224
$21$	−4.08410e6	−0.218218
$22$	−6.21039e6	−0.256918
$23$	−4.57705e7	−1.48280	−0.741400	−	0.671063i	$-0.765838\pi$
$23$	−4.57705e7	−1.48280	−0.741400	+	0.671063i	$0.765838\pi$
$24$	1.92361e7	0.493123
$25$	4.68158e7	0.958787
$26$	−8.12601e6	−0.134129
$27$	−1.43489e7	−0.192450
$28$	−2.63704e7	−0.289566
$29$	−3.23441e7	−0.292824	−0.146412	−	0.989224i	$-0.546772\pi$
$29$	−3.23441e7	−0.292824	−0.146412	+	0.989224i	$0.546772\pi$
$30$	5.20110e7	0.390777
$31$	2.87505e8	1.80367	0.901834	−	0.432084i	$-0.142221\pi$
$31$	2.87505e8	1.80367	0.901834	+	0.432084i	$0.142221\pi$
$32$	1.94531e8	1.02486
$33$	6.89548e7	0.306717
$34$	−1.51144e8	−0.570503
$35$	−1.64369e8	−0.528987
$36$	−9.26488e7	−0.255374
$37$	2.00433e8	0.475182	0.237591	−	0.971365i	$-0.423642\pi$
$37$	2.00433e8	0.475182	0.237591	+	0.971365i	$0.423642\pi$
$38$	6.92460e7	0.141770
$39$	9.02242e7	0.160128
$40$	7.74176e8	1.19539
$41$	4.97616e8	0.670784	0.335392	−	0.942079i	$-0.391131\pi$
$41$	4.97616e8	0.670784	0.335392	+	0.942079i	$0.391131\pi$
$42$	−8.93835e7	−0.105532
$43$	1.18136e9	1.22548	0.612739	−	0.790285i	$-0.290068\pi$
$43$	1.18136e9	1.22548	0.612739	+	0.790285i	$0.290068\pi$
$44$	4.45231e8	0.407001
$45$	−5.77486e8	−0.466522
$46$	−1.00172e9	−0.717098
$47$	−1.39480e9	−0.887104	−0.443552	−	0.896249i	$-0.646282\pi$
$47$	−1.39480e9	−0.887104	−0.443552	+	0.896249i	$0.646282\pi$
$48$	−3.59847e8	−0.203841
$49$	2.82475e8	0.142857
$50$	1.02460e9	0.463680
$51$	1.67818e9	0.681086
$52$	5.82565e8	0.212484
$53$	3.13354e9	1.02924	0.514621	−	0.857418i	$-0.327933\pi$
$53$	3.13354e9	1.02924	0.514621	+	0.857418i	$0.327933\pi$
$54$	−3.14036e8	−0.0930709
$55$	2.77515e9	0.743519
$56$	−1.33046e9	−0.322825
$57$	−7.68847e8	−0.169250
$58$	−7.07874e8	−0.141613
$59$	−2.04183e9	−0.371821	−0.185911	−	0.982567i	$-0.559523\pi$
$59$	−2.04183e9	−0.371821	−0.185911	+	0.982567i	$0.559523\pi$
$60$	−3.72874e9	−0.619057
$61$	1.08050e10	1.63798	0.818991	−	0.573807i	$-0.194534\pi$
$61$	1.08050e10	1.63798	0.818991	+	0.573807i	$0.194534\pi$
$62$	6.29226e9	0.872272
$63$	9.92437e8	0.125988
$64$	1.22467e9	0.142570
$65$	3.63116e9	0.388170
$66$	1.50913e9	0.148332
$67$	1.02912e8	0.00931226	0.00465613	−	0.999989i	$-0.498518\pi$
$67$	1.02912e8	0.00931226	0.00465613	+	0.999989i	$0.498518\pi$
$68$	1.08357e10	0.903774
$69$	1.11222e10	0.856095
$70$	−3.59732e9	−0.255823
$71$	5.85845e9	0.385356	0.192678	−	0.981262i	$-0.438283\pi$
$71$	5.85845e9	0.385356	0.192678	+	0.981262i	$0.438283\pi$
$72$	−4.67438e9	−0.284705
$73$	−5.19073e9	−0.293057	−0.146529	−	0.989206i	$-0.546810\pi$
$73$	−5.19073e9	−0.293057	−0.146529	+	0.989206i	$0.546810\pi$
$74$	4.38662e9	0.229803
$75$	−1.13762e10	−0.553556
$76$	−4.96434e9	−0.224588
$77$	−4.76923e9	−0.200793
$78$	1.97462e9	0.0774396
$79$	4.54124e10	1.66045	0.830224	−	0.557430i	$-0.188213\pi$
$79$	4.54124e10	1.66045	0.830224	+	0.557430i	$0.188213\pi$
$80$	−1.44824e10	−0.494134
$81$	3.48678e9	0.111111
$82$	1.08907e10	0.324398
$83$	−4.50938e9	−0.125657	−0.0628285	−	0.998024i	$-0.520012\pi$
$83$	−4.50938e9	−0.125657	−0.0628285	+	0.998024i	$0.520012\pi$
$84$	6.40802e9	0.167181
$85$	6.75399e10	1.65103
$86$	2.58549e10	0.592654
$87$	7.85962e9	0.169062
$88$	2.24631e10	0.453748
$89$	6.08111e10	1.15435	0.577176	−	0.816620i	$-0.304155\pi$
$89$	6.08111e10	1.15435	0.577176	+	0.816620i	$0.304155\pi$
$90$	−1.26387e10	−0.225615
$91$	−6.24032e9	−0.104828
$92$	7.18146e10	1.13600
$93$	−6.98638e10	−1.04135
$94$	−3.05262e10	−0.429013
$95$	−3.09430e10	−0.410282
$96$	−4.72711e10	−0.591703
$97$	−3.24724e10	−0.383946	−0.191973	−	0.981400i	$-0.561489\pi$
$97$	−3.24724e10	−0.383946	−0.191973	+	0.981400i	$0.561489\pi$
$98$	6.18217e9	0.0690872
$99$	−1.67560e10	−0.177083
$100$	−7.34547e10	−0.734547
$101$	−1.67825e11	−1.58887	−0.794437	−	0.607347i	$-0.792234\pi$
$101$	−1.67825e11	−1.58887	−0.794437	+	0.607347i	$0.792234\pi$
$102$	3.67281e10	0.329380
$103$	−5.94753e10	−0.505513	−0.252756	−	0.967530i	$-0.581337\pi$
$103$	−5.94753e10	−0.505513	−0.252756	+	0.967530i	$0.581337\pi$
$104$	2.93919e10	0.236889
$105$	3.99416e10	0.305411
$106$	6.85797e10	0.497752
$107$	−2.44715e11	−1.68675	−0.843373	−	0.537329i	$-0.819433\pi$
$107$	−2.44715e11	−1.68675	−0.843373	+	0.537329i	$0.819433\pi$
$108$	2.25137e10	0.147440
$109$	1.09563e11	0.682052	0.341026	−	0.940054i	$-0.389226\pi$
$109$	1.09563e11	0.682052	0.341026	+	0.940054i	$0.389226\pi$
$110$	6.07362e10	0.359574
$111$	−4.87053e10	−0.274347
$112$	2.48887e10	0.133445
$113$	−2.10119e11	−1.07284	−0.536420	−	0.843951i	$-0.680224\pi$
$113$	−2.10119e11	−1.07284	−0.536420	+	0.843951i	$0.680224\pi$
$114$	−1.68268e10	−0.0818510
$115$	4.47625e11	2.07528
$116$	5.07484e10	0.224338
$117$	−2.19245e10	−0.0924500
$118$	−4.46870e10	−0.179817
$119$	−1.16071e11	−0.445875
$120$	−1.88125e11	−0.690159
$121$	−2.04789e11	−0.717774
$122$	2.36474e11	0.792145
$123$	−1.20921e11	−0.387277
$124$	−4.51100e11	−1.38183
$125$	1.96803e10	0.0576800
$126$	2.17202e10	0.0609292
$127$	−2.84958e11	−0.765351	−0.382676	−	0.923883i	$-0.624997\pi$
$127$	−2.84958e11	−0.765351	−0.382676	+	0.923883i	$0.624997\pi$
$128$	−3.71597e11	−0.955911
$129$	−2.87071e11	−0.707531
$130$	7.94705e10	0.187723
$131$	6.79653e10	0.153920	0.0769600	−	0.997034i	$-0.475479\pi$
$131$	6.79653e10	0.153920	0.0769600	+	0.997034i	$0.475479\pi$
$132$	−1.08191e11	−0.234982
$133$	5.31770e10	0.110800
$134$	2.25230e9	0.00450350
$135$	1.40329e11	0.269347
$136$	5.46692e11	1.00758
$137$	−6.77457e10	−0.119927	−0.0599637	−	0.998201i	$-0.519099\pi$
$137$	−6.77457e10	−0.119927	−0.0599637	+	0.998201i	$0.519099\pi$
$138$	2.43418e11	0.414017
$139$	−4.30199e11	−0.703215	−0.351607	−	0.936148i	$-0.614365\pi$
$139$	−4.30199e11	−0.703215	−0.351607	+	0.936148i	$0.614365\pi$
$140$	2.57897e11	0.405268
$141$	3.38937e11	0.512169
$142$	1.28216e11	0.186362
$143$	1.05360e11	0.147342
$144$	8.74427e10	0.117687
$145$	3.16318e11	0.409826
$146$	−1.13603e11	−0.141726
$147$	−6.86415e10	−0.0824786
$148$	−3.14483e11	−0.364047
$149$	−1.49124e12	−1.66350	−0.831751	−	0.555149i	$-0.812661\pi$
$149$	−1.49124e12	−1.66350	−0.831751	+	0.555149i	$0.812661\pi$
$150$	−2.48977e11	−0.267705
$151$	1.80919e12	1.87547	0.937735	−	0.347353i	$-0.112919\pi$
$151$	1.80919e12	1.87547	0.937735	+	0.347353i	$0.112919\pi$
$152$	−2.50464e11	−0.250383
$153$	−4.07797e11	−0.393225
$154$	−1.04378e11	−0.0971058
$155$	−2.81173e12	−2.52435
$156$	−1.41563e11	−0.122678
$157$	9.91186e11	0.829291	0.414645	−	0.909983i	$-0.363906\pi$
$157$	9.91186e11	0.829291	0.414645	+	0.909983i	$0.363906\pi$
$158$	9.93882e11	0.803010
$159$	−7.61450e11	−0.594233
$160$	−1.90247e12	−1.43436
$161$	−7.69265e11	−0.560446
$162$	7.63108e10	0.0537345
$163$	3.67789e11	0.250361	0.125181	−	0.992134i	$-0.460049\pi$
$163$	3.67789e11	0.250361	0.125181	+	0.992134i	$0.460049\pi$
$164$	−7.80767e11	−0.513902
$165$	−6.74362e11	−0.429271
$166$	−9.86909e10	−0.0607691
$167$	−2.08355e11	−0.124126	−0.0620630	−	0.998072i	$-0.519768\pi$
$167$	−2.08355e11	−0.124126	−0.0620630	+	0.998072i	$0.519768\pi$
$168$	3.23301e11	0.186383
$169$	1.37858e11	0.0769231
$170$	1.47816e12	0.798458
$171$	1.86830e11	0.0977165
$172$	−1.85357e12	−0.938865
$173$	1.50544e12	0.738602	0.369301	−	0.929310i	$-0.379597\pi$
$173$	1.50544e12	0.738602	0.369301	+	0.929310i	$0.379597\pi$
$174$	1.72013e11	0.0817601
$175$	7.86833e11	0.362388
$176$	−4.20213e11	−0.187564
$177$	4.96165e11	0.214671
$178$	1.33090e12	0.558257
$179$	7.43638e11	0.302461	0.151231	−	0.988499i	$-0.451676\pi$
$179$	7.43638e11	0.302461	0.151231	+	0.988499i	$0.451676\pi$
$180$	9.06084e11	0.357412
$181$	9.93438e11	0.380109	0.190055	−	0.981774i	$-0.439133\pi$
$181$	9.93438e11	0.380109	0.190055	+	0.981774i	$0.439133\pi$
$182$	−1.36574e11	−0.0506961
$183$	−2.62560e12	−0.945689
$184$	3.62324e12	1.26648
$185$	−1.96019e12	−0.665049
$186$	−1.52902e12	−0.503607
$187$	1.95970e12	0.626702
$188$	2.18847e12	0.679629
$189$	−2.41162e11	−0.0727393
$190$	−6.77210e11	−0.198417
$191$	2.16981e12	0.617645	0.308822	−	0.951120i	$-0.400065\pi$
$191$	2.16981e12	0.617645	0.308822	+	0.951120i	$0.400065\pi$
$192$	−2.97595e11	−0.0823130
$193$	−5.83725e12	−1.56907	−0.784536	−	0.620083i	$-0.787099\pi$
$193$	−5.83725e12	−1.56907	−0.784536	+	0.620083i	$0.787099\pi$
$194$	−7.10682e11	−0.185680
$195$	−8.82372e11	−0.224110
$196$	−4.43208e11	−0.109446
$197$	2.43781e12	0.585376	0.292688	−	0.956208i	$-0.405450\pi$
$197$	2.43781e12	0.585376	0.292688	+	0.956208i	$0.405450\pi$
$198$	−3.66717e11	−0.0856393
$199$	1.73852e12	0.394902	0.197451	−	0.980313i	$-0.436734\pi$
$199$	1.73852e12	0.394902	0.197451	+	0.980313i	$0.436734\pi$
$200$	−3.70598e12	−0.818914
$201$	−2.50076e10	−0.00537643
$202$	−3.67297e12	−0.768396
$203$	−5.43607e11	−0.110677
$204$	−2.63309e12	−0.521794
$205$	−4.86657e12	−0.938807
$206$	−1.30166e12	−0.244471
$207$	−2.70270e12	−0.494267
$208$	−5.49829e11	−0.0979218
$209$	−8.97826e11	−0.155736
$210$	8.74150e11	0.147700
$211$	−9.72206e12	−1.60031	−0.800156	−	0.599791i	$-0.795250\pi$
$211$	−9.72206e12	−1.60031	−0.800156	+	0.599791i	$0.795250\pi$
$212$	−4.91657e12	−0.788524
$213$	−1.42360e12	−0.222485
$214$	−5.35576e12	−0.815728
$215$	−1.15534e13	−1.71514
$216$	1.13587e12	0.164374
$217$	4.83210e12	0.681722
$218$	2.39786e12	0.329847
$219$	1.26135e12	0.169197
$220$	−4.35426e12	−0.569626
$221$	2.56418e12	0.327183
$222$	−1.06595e12	−0.132677
$223$	−2.17933e12	−0.264634	−0.132317	−	0.991207i	$-0.542242\pi$
$223$	−2.17933e12	−0.264634	−0.132317	+	0.991207i	$0.542242\pi$
$224$	3.26948e12	0.387360
$225$	2.76443e12	0.319596
$226$	−4.59861e12	−0.518836
$227$	3.41956e12	0.376554	0.188277	−	0.982116i	$-0.439710\pi$
$227$	3.41956e12	0.376554	0.188277	+	0.982116i	$0.439710\pi$
$228$	1.20633e12	0.129666
$229$	−9.10469e11	−0.0955367	−0.0477683	−	0.998858i	$-0.515211\pi$
$229$	−9.10469e11	−0.0955367	−0.0477683	+	0.998858i	$0.515211\pi$
$230$	9.79659e12	1.00363
$231$	1.15892e12	0.115928
$232$	2.56039e12	0.250105
$233$	1.11498e13	1.06368	0.531838	−	0.846846i	$-0.321501\pi$
$233$	1.11498e13	1.06368	0.531838	+	0.846846i	$0.321501\pi$
$234$	−4.79833e11	−0.0447098
$235$	1.36408e13	1.24156
$236$	3.20367e12	0.284860
$237$	−1.10352e13	−0.958660
$238$	−2.54029e12	−0.215630
$239$	7.11989e12	0.590589	0.295294	−	0.955406i	$-0.404582\pi$
$239$	7.11989e12	0.590589	0.295294	+	0.955406i	$0.404582\pi$
$240$	3.51922e12	0.285288
$241$	4.43366e12	0.351292	0.175646	−	0.984453i	$-0.443799\pi$
$241$	4.43366e12	0.351292	0.175646	+	0.984453i	$0.443799\pi$
$242$	−4.48196e12	−0.347123
$243$	−8.47289e11	−0.0641500
$244$	−1.69531e13	−1.25489
$245$	−2.76254e12	−0.199938
$246$	−2.64643e12	−0.187291
$247$	−1.17476e12	−0.0813050
$248$	−2.27592e13	−1.54054
$249$	1.09578e12	0.0725481
$250$	4.30716e11	0.0278947
$251$	−1.96830e12	−0.124706	−0.0623528	−	0.998054i	$-0.519860\pi$
$251$	−1.96830e12	−0.124706	−0.0623528	+	0.998054i	$0.519860\pi$
$252$	−1.55715e12	−0.0965222
$253$	1.29881e13	0.787737
$254$	−6.23652e12	−0.370132
$255$	−1.64122e13	−0.953225
$256$	−1.06408e13	−0.604859
$257$	−2.07984e13	−1.15717	−0.578585	−	0.815622i	$-0.696395\pi$
$257$	−2.07984e13	−1.15717	−0.578585	+	0.815622i	$0.696395\pi$
$258$	−6.28274e12	−0.342169
$259$	3.36868e12	0.179602
$260$	−5.69735e12	−0.297385
$261$	−1.90989e12	−0.0976079
$262$	1.48747e12	0.0744373
$263$	1.93266e13	0.947104	0.473552	−	0.880766i	$-0.342972\pi$
$263$	1.93266e13	0.947104	0.473552	+	0.880766i	$0.342972\pi$
$264$	−5.45853e12	−0.261972
$265$	−3.06453e13	−1.44049
$266$	1.16382e12	0.0535841
$267$	−1.47771e13	−0.666465
$268$	−1.61471e11	−0.00713431
$269$	3.75229e13	1.62427	0.812135	−	0.583469i	$-0.198305\pi$
$269$	3.75229e13	1.62427	0.812135	+	0.583469i	$0.198305\pi$
$270$	3.07120e12	0.130259
$271$	3.43312e13	1.42678	0.713391	−	0.700766i	$-0.247158\pi$
$271$	3.43312e13	1.42678	0.713391	+	0.700766i	$0.247158\pi$
$272$	−1.02269e13	−0.416499
$273$	1.51640e12	0.0605228
$274$	−1.48266e12	−0.0579982
$275$	−1.32847e13	−0.509355
$276$	−1.74510e13	−0.655872
$277$	−4.19044e13	−1.54391	−0.771953	−	0.635679i	$-0.780720\pi$
$277$	−4.19044e13	−1.54391	−0.771953	+	0.635679i	$0.780720\pi$
$278$	−9.41521e12	−0.340082
$279$	1.69769e13	0.601222
$280$	1.30116e13	0.451815
$281$	4.63073e13	1.57676	0.788378	−	0.615191i	$-0.210921\pi$
$281$	4.63073e13	1.57676	0.788378	+	0.615191i	$0.210921\pi$
$282$	7.41787e12	0.247691
$283$	2.20904e13	0.723398	0.361699	−	0.932295i	$-0.382197\pi$
$283$	2.20904e13	0.723398	0.361699	+	0.932295i	$0.382197\pi$
$284$	−9.19200e12	−0.295229
$285$	7.51915e12	0.236877
$286$	2.30588e12	0.0712562
$287$	8.36343e12	0.253533
$288$	1.14869e13	0.341620
$289$	1.34221e13	0.391635
$290$	6.92284e12	0.198196
$291$	7.89079e12	0.221671
$292$	8.14434e12	0.224517
$293$	−2.63632e12	−0.0713224	−0.0356612	−	0.999364i	$-0.511354\pi$
$293$	−2.63632e12	−0.0713224	−0.0356612	+	0.999364i	$0.511354\pi$
$294$	−1.50227e12	−0.0398875
$295$	1.99687e13	0.520389
$296$	−1.58665e13	−0.405860
$297$	4.07171e12	0.102239
$298$	−3.26369e13	−0.804487
$299$	1.69943e13	0.411255
$300$	1.78495e13	0.424091
$301$	1.98551e13	0.463187
$302$	3.95953e13	0.906996
$303$	4.07815e13	0.917336
$304$	4.68538e12	0.103500
$305$	−1.05670e14	−2.29246
$306$	−8.92493e12	−0.190168
$307$	−6.77279e13	−1.41745	−0.708723	−	0.705487i	$-0.750728\pi$
$307$	−6.77279e13	−1.41745	−0.708723	+	0.705487i	$0.750728\pi$
$308$	7.48300e12	0.153832
$309$	1.44525e13	0.291858
$310$	−6.15368e13	−1.22080
$311$	1.16463e13	0.226990	0.113495	−	0.993539i	$-0.463795\pi$
$311$	1.16463e13	0.226990	0.113495	+	0.993539i	$0.463795\pi$
$312$	−7.14223e12	−0.136768
$313$	−6.16780e13	−1.16048	−0.580238	−	0.814447i	$-0.697041\pi$
$313$	−6.16780e13	−1.16048	−0.580238	+	0.814447i	$0.697041\pi$
$314$	2.16928e13	0.401054
$315$	−9.70580e12	−0.176329
$316$	−7.12527e13	−1.27210
$317$	3.42859e13	0.601575	0.300787	−	0.953691i	$-0.402751\pi$
$317$	3.42859e13	0.601575	0.300787	+	0.953691i	$0.402751\pi$
$318$	−1.66649e13	−0.287377
$319$	9.17812e12	0.155562
$320$	−1.19770e13	−0.199537
$321$	5.94657e13	0.973843
$322$	−1.68359e13	−0.271037
$323$	−2.18507e13	−0.345821
$324$	−5.47082e12	−0.0851245
$325$	−1.73824e13	−0.265920
$326$	8.04933e12	0.121077
$327$	−2.66238e13	−0.393783
$328$	−3.93917e13	−0.572927
$329$	−2.34424e13	−0.335294
$330$	−1.47589e13	−0.207600
$331$	4.77027e13	0.659917	0.329958	−	0.943995i	$-0.392965\pi$
$331$	4.77027e13	0.659917	0.329958	+	0.943995i	$0.392965\pi$
$332$	7.07528e12	0.0962685
$333$	1.18354e13	0.158394
$334$	−4.55999e12	−0.0600286
$335$	−1.00646e12	−0.0130331
$336$	−6.04794e12	−0.0770445
$337$	−1.43193e14	−1.79456	−0.897278	−	0.441467i	$-0.854458\pi$
$337$	−1.43193e14	−1.79456	−0.897278	+	0.441467i	$0.854458\pi$
$338$	3.01713e12	0.0372008
$339$	5.10590e13	0.619404
$340$	−1.05971e14	−1.26489
$341$	−8.15838e13	−0.958197
$342$	4.08891e12	0.0472567
$343$	4.74756e12	0.0539949
$344$	−9.35176e13	−1.04670
$345$	−1.08773e14	−1.19816
$346$	3.29477e13	0.357196
$347$	−6.91011e13	−0.737349	−0.368674	−	0.929559i	$-0.620188\pi$
$347$	−6.91011e13	−0.737349	−0.368674	+	0.929559i	$0.620188\pi$
$348$	−1.23319e13	−0.129522
$349$	−1.52003e13	−0.157150	−0.0785749	−	0.996908i	$-0.525037\pi$
$349$	−1.52003e13	−0.157150	−0.0785749	+	0.996908i	$0.525037\pi$
$350$	1.72204e13	0.175254
$351$	5.32765e12	0.0533761
$352$	−5.52011e13	−0.544456
$353$	5.34353e13	0.518880	0.259440	−	0.965759i	$-0.416462\pi$
$353$	5.34353e13	0.518880	0.259440	+	0.965759i	$0.416462\pi$
$354$	1.08589e13	0.103817
$355$	−5.72943e13	−0.539331
$356$	−9.54136e13	−0.884373
$357$	2.82051e13	0.257426
$358$	1.62750e13	0.146273
$359$	−6.97131e13	−0.617014	−0.308507	−	0.951222i	$-0.599829\pi$
$359$	−6.97131e13	−0.617014	−0.308507	+	0.951222i	$0.599829\pi$
$360$	4.57143e13	0.398463
$361$	−1.06479e14	−0.914063
$362$	2.17421e13	0.183825
$363$	4.97638e13	0.414407
$364$	9.79116e12	0.0803113
$365$	5.07641e13	0.410153
$366$	−5.74632e13	−0.457345
$367$	−2.41976e12	−0.0189718	−0.00948591	−	0.999955i	$-0.503020\pi$
$367$	−2.41976e12	−0.0189718	−0.00948591	+	0.999955i	$0.503020\pi$
$368$	−6.77793e13	−0.523521
$369$	2.93837e13	0.223595
$370$	−4.29002e13	−0.321625
$371$	5.26654e13	0.389017
$372$	1.09617e14	0.797798
$373$	−9.79695e13	−0.702575	−0.351287	−	0.936268i	$-0.614256\pi$
$373$	−9.79695e13	−0.702575	−0.351287	+	0.936268i	$0.614256\pi$
$374$	4.28895e13	0.303080
$375$	−4.78230e12	−0.0333016
$376$	1.10414e14	0.757688
$377$	1.20091e13	0.0812147
$378$	−5.27800e12	−0.0351775
$379$	−5.12632e13	−0.336737	−0.168368	−	0.985724i	$-0.553850\pi$
$379$	−5.12632e13	−0.336737	−0.168368	+	0.985724i	$0.553850\pi$
$380$	4.85501e13	0.314326
$381$	6.92449e13	0.441876
$382$	4.74879e13	0.298699
$383$	−1.85494e14	−1.15011	−0.575053	−	0.818116i	$-0.695018\pi$
$383$	−1.85494e14	−1.15011	−0.575053	+	0.818116i	$0.695018\pi$
$384$	9.02981e13	0.551895
$385$	4.66420e13	0.281024
$386$	−1.27752e14	−0.758820
$387$	6.97581e13	0.408493
$388$	5.09497e13	0.294149
$389$	−7.66769e13	−0.436457	−0.218229	−	0.975898i	$-0.570028\pi$
$389$	−7.66769e13	−0.436457	−0.218229	+	0.975898i	$0.570028\pi$
$390$	−1.93113e13	−0.108382
$391$	3.16095e14	1.74922
$392$	−2.23610e13	−0.122016
$393$	−1.65156e13	−0.0888657
$394$	5.33531e13	0.283094
$395$	−4.44123e14	−2.32391
$396$	2.62905e13	0.135667
$397$	−2.92212e14	−1.48714	−0.743568	−	0.668661i	$-0.766868\pi$
$397$	−2.92212e14	−1.48714	−0.743568	+	0.668661i	$0.766868\pi$
$398$	3.80488e13	0.190979
$399$	−1.29220e13	−0.0639704
$400$	6.93272e13	0.338512
$401$	7.58782e13	0.365446	0.182723	−	0.983164i	$-0.441509\pi$
$401$	7.58782e13	0.365446	0.182723	+	0.983164i	$0.441509\pi$
$402$	−5.47310e11	−0.00260010
$403$	−1.06749e14	−0.500247
$404$	2.63320e14	1.21727
$405$	−3.41000e13	−0.155507
$406$	−1.18972e13	−0.0535245
$407$	−5.68759e13	−0.252440
$408$	−1.32846e14	−0.581725
$409$	3.04971e14	1.31759	0.658794	−	0.752323i	$-0.271067\pi$
$409$	3.04971e14	1.31759	0.658794	+	0.752323i	$0.271067\pi$
$410$	−1.06508e14	−0.454017
$411$	1.64622e13	0.0692401
$412$	9.33177e13	0.387284
$413$	−3.43171e13	−0.140535
$414$	−5.91506e13	−0.239033
$415$	4.41007e13	0.175865
$416$	−7.22280e13	−0.284245
$417$	1.04538e14	0.406001
$418$	−1.96496e13	−0.0753153
$419$	4.17152e14	1.57804	0.789019	−	0.614369i	$-0.210589\pi$
$419$	4.17152e14	1.57804	0.789019	+	0.614369i	$0.210589\pi$
$420$	−6.26689e13	−0.233981
$421$	−2.13188e14	−0.785616	−0.392808	−	0.919620i	$-0.628496\pi$
$421$	−2.13188e14	−0.785616	−0.392808	+	0.919620i	$0.628496\pi$
$422$	−2.12774e14	−0.773928
$423$	−8.23617e13	−0.295701
$424$	−2.48054e14	−0.879091
$425$	−3.23314e14	−1.13106
$426$	−3.11566e13	−0.107596
$427$	1.81599e14	0.619099
$428$	3.83961e14	1.29225
$429$	−2.56024e13	−0.0850680
$430$	−2.52855e14	−0.829459
$431$	−4.47181e13	−0.144830	−0.0724149	−	0.997375i	$-0.523071\pi$
$431$	−4.47181e13	−0.144830	−0.0724149	+	0.997375i	$0.523071\pi$
$432$	−2.12486e13	−0.0679469
$433$	−1.01322e14	−0.319905	−0.159953	−	0.987125i	$-0.551134\pi$
$433$	−1.01322e14	−0.319905	−0.159953	+	0.987125i	$0.551134\pi$
$434$	1.05754e14	0.329688
$435$	−7.68652e13	−0.236613
$436$	−1.71906e14	−0.522534
$437$	−1.44817e14	−0.434682
$438$	2.76055e13	0.0818253
$439$	1.56730e14	0.458772	0.229386	−	0.973336i	$-0.426328\pi$
$439$	1.56730e14	0.458772	0.229386	+	0.973336i	$0.426328\pi$
$440$	−2.19684e14	−0.635051
$441$	1.66799e13	0.0476190
$442$	5.61189e13	0.158229
$443$	1.38339e13	0.0385234	0.0192617	−	0.999814i	$-0.493868\pi$
$443$	1.38339e13	0.0385234	0.0192617	+	0.999814i	$0.493868\pi$
$444$	7.64193e13	0.210183
$445$	−5.94719e14	−1.61559
$446$	−4.76961e13	−0.127980
$447$	3.62371e14	0.960423
$448$	2.05830e13	0.0538865
$449$	−2.89775e13	−0.0749388	−0.0374694	−	0.999298i	$-0.511930\pi$
$449$	−2.89775e13	−0.0749388	−0.0374694	+	0.999298i	$0.511930\pi$
$450$	6.05014e13	0.154560
$451$	−1.41206e14	−0.356354
$452$	3.29681e14	0.821925
$453$	−4.39632e14	−1.08280
$454$	7.48395e13	0.182106
$455$	6.10289e13	0.146714
$456$	6.08627e13	0.144559
$457$	4.89758e14	1.14932	0.574662	−	0.818391i	$-0.305134\pi$
$457$	4.89758e14	1.14932	0.574662	+	0.818391i	$0.305134\pi$
$458$	−1.99263e13	−0.0462025
$459$	9.90947e13	0.227029
$460$	−7.02331e14	−1.58991
$461$	4.22198e14	0.944411	0.472205	−	0.881489i	$-0.343458\pi$
$461$	4.22198e14	0.944411	0.472205	+	0.881489i	$0.343458\pi$
$462$	2.53639e13	0.0560641
$463$	−7.82063e14	−1.70823	−0.854115	−	0.520085i	$-0.825900\pi$
$463$	−7.82063e14	−1.70823	−0.854115	+	0.520085i	$0.825900\pi$
$464$	−4.78968e13	−0.103385
$465$	6.83252e14	1.45744
$466$	2.44021e14	0.514405
$467$	7.47623e13	0.155754	0.0778772	−	0.996963i	$-0.475186\pi$
$467$	7.47623e13	0.155754	0.0778772	+	0.996963i	$0.475186\pi$
$468$	3.43999e13	0.0708279
$469$	1.72964e12	0.00351970
$470$	2.98540e14	0.600432
$471$	−2.40858e14	−0.478791
$472$	1.61633e14	0.317578
$473$	−3.35228e14	−0.651035
$474$	−2.41513e14	−0.463618
$475$	1.48124e14	0.281068
$476$	1.82116e14	0.341595
$477$	1.85032e14	0.343081
$478$	1.55824e14	0.285615
$479$	5.07102e14	0.918861	0.459431	−	0.888214i	$-0.348053\pi$
$479$	5.07102e14	0.918861	0.459431	+	0.888214i	$0.348053\pi$
$480$	4.62300e14	0.828127
$481$	−7.44195e13	−0.131792
$482$	9.70337e13	0.169889
$483$	1.86931e14	0.323574
$484$	3.21318e14	0.549902
$485$	3.17573e14	0.537358
$486$	−1.85435e13	−0.0310236
$487$	1.91965e14	0.317551	0.158775	−	0.987315i	$-0.449245\pi$
$487$	1.91965e14	0.317551	0.158775	+	0.987315i	$0.449245\pi$
$488$	−8.55331e14	−1.39902
$489$	−8.93728e13	−0.144546
$490$	−6.04602e13	−0.0966922
$491$	−6.93371e14	−1.09652	−0.548261	−	0.836307i	$-0.684710\pi$
$491$	−6.93371e14	−1.09652	−0.548261	+	0.836307i	$0.684710\pi$
$492$	1.89726e14	0.296701
$493$	2.23371e14	0.345437
$494$	−2.57105e13	−0.0393200
$495$	1.63870e14	0.247840
$496$	4.25752e14	0.636807
$497$	9.84629e13	0.145651
$498$	2.39819e13	0.0350850
$499$	9.88588e14	1.43042	0.715208	−	0.698912i	$-0.246332\pi$
$499$	9.88588e14	1.43042	0.715208	+	0.698912i	$0.246332\pi$
$500$	−3.08786e13	−0.0441899
$501$	5.06302e13	0.0716642
$502$	−4.30776e13	−0.0603089
$503$	−1.25055e14	−0.173172	−0.0865858	−	0.996244i	$-0.527596\pi$
$503$	−1.25055e14	−0.173172	−0.0865858	+	0.996244i	$0.527596\pi$
$504$	−7.85622e13	−0.107608
$505$	1.64129e15	2.22373
$506$	2.84253e14	0.380958
$507$	−3.34996e13	−0.0444116
$508$	4.47104e14	0.586352
$509$	6.93927e14	0.900256	0.450128	−	0.892964i	$-0.351378\pi$
$509$	6.93927e14	0.900256	0.450128	+	0.892964i	$0.351378\pi$
$510$	−3.59192e14	−0.460990
$511$	−8.72406e13	−0.110765
$512$	5.28149e14	0.663395
$513$	−4.53997e13	−0.0564166
$514$	−4.55187e14	−0.559619
$515$	5.81655e14	0.707499
$516$	4.50418e14	0.542054
$517$	3.95796e14	0.471273
$518$	7.37260e13	0.0868574
$519$	−3.65822e14	−0.426432
$520$	−2.87446e14	−0.331542
$521$	3.10634e14	0.354520	0.177260	−	0.984164i	$-0.443277\pi$
$521$	3.10634e14	0.354520	0.177260	+	0.984164i	$0.443277\pi$
$522$	−4.17992e13	−0.0472042
$523$	−4.25447e12	−0.00475430	−0.00237715	−	0.999997i	$-0.500757\pi$
$523$	−4.25447e12	−0.00475430	−0.00237715	+	0.999997i	$0.500757\pi$
$524$	−1.06639e14	−0.117921
$525$	−1.91200e14	−0.209225
$526$	4.22975e14	0.458030
$527$	−1.98553e15	−2.12774
$528$	1.02112e14	0.108290
$529$	1.14213e15	1.19870
$530$	−6.70694e14	−0.696638
$531$	−1.20568e14	−0.123940
$532$	−8.34356e13	−0.0848863
$533$	−1.84761e14	−0.186042
$534$	−3.23408e14	−0.322310
$535$	2.39325e15	2.36071
$536$	−8.14662e12	−0.00795373
$537$	−1.80704e14	−0.174626
$538$	8.21214e14	0.785514
$539$	−8.01565e13	−0.0758928
$540$	−2.20178e14	−0.206352
$541$	−4.29590e14	−0.398538	−0.199269	−	0.979945i	$-0.563857\pi$
$541$	−4.29590e14	−0.398538	−0.199269	+	0.979945i	$0.563857\pi$
$542$	7.51362e14	0.690006
$543$	−2.41405e14	−0.219456
$544$	−1.34345e15	−1.20900
$545$	−1.07150e15	−0.954577
$546$	3.31875e13	0.0292694
$547$	2.15979e14	0.188574	0.0942870	−	0.995545i	$-0.469943\pi$
$547$	2.15979e14	0.188574	0.0942870	+	0.995545i	$0.469943\pi$
$548$	1.06294e14	0.0918789
$549$	6.38022e14	0.545994
$550$	−2.90744e14	−0.246330
$551$	−1.02336e14	−0.0858411
$552$	−8.80447e14	−0.731203
$553$	7.63246e14	0.627590
$554$	−9.17108e14	−0.746649
$555$	4.76326e14	0.383966
$556$	6.74989e14	0.538748
$557$	1.73656e15	1.37242	0.686209	−	0.727404i	$-0.259273\pi$
$557$	1.73656e15	1.37242	0.686209	+	0.727404i	$0.259273\pi$
$558$	3.71551e14	0.290757
$559$	−4.38631e14	−0.339887
$560$	−2.43405e14	−0.186765
$561$	−4.76208e14	−0.361827
$562$	1.01347e15	0.762536
$563$	2.26184e15	1.68525	0.842626	−	0.538499i	$-0.181008\pi$
$563$	2.26184e15	1.68525	0.842626	+	0.538499i	$0.181008\pi$
$564$	−5.31797e14	−0.392384
$565$	2.05492e15	1.50151
$566$	4.83463e14	0.349843
$567$	5.86024e13	0.0419961
$568$	−4.63760e14	−0.329138
$569$	1.48563e15	1.04422	0.522111	−	0.852878i	$-0.325145\pi$
$569$	1.48563e15	1.04422	0.522111	+	0.852878i	$0.325145\pi$
$570$	1.64562e14	0.114556
$571$	−1.51335e15	−1.04338	−0.521689	−	0.853135i	$-0.674698\pi$
$571$	−1.51335e15	−1.04338	−0.521689	+	0.853135i	$0.674698\pi$
$572$	−1.65311e14	−0.112882
$573$	−5.27264e14	−0.356597
$574$	1.83040e14	0.122611
$575$	−2.14278e15	−1.42169
$576$	7.23155e13	0.0475234
$577$	1.31871e15	0.858384	0.429192	−	0.903213i	$-0.358798\pi$
$577$	1.31871e15	0.858384	0.429192	+	0.903213i	$0.358798\pi$
$578$	2.93751e14	0.189399
$579$	1.41845e15	0.905905
$580$	−4.96308e14	−0.313976
$581$	−7.57891e13	−0.0474939
$582$	1.72696e14	0.107202
$583$	−8.89188e14	−0.546785
$584$	4.10903e14	0.250305
$585$	2.14416e14	0.129390
$586$	−5.76977e13	−0.0344922
$587$	−8.63297e14	−0.511271	−0.255635	−	0.966773i	$-0.582285\pi$
$587$	−8.63297e14	−0.511271	−0.255635	+	0.966773i	$0.582285\pi$
$588$	1.07700e14	0.0631886
$589$	9.09661e14	0.528744
$590$	4.37028e14	0.251665
$591$	−5.92387e14	−0.337967
$592$	2.96812e14	0.167769
$593$	1.15510e15	0.646874	0.323437	−	0.946250i	$-0.395162\pi$
$593$	1.15510e15	0.646874	0.323437	+	0.946250i	$0.395162\pi$
$594$	8.91123e13	0.0494439
$595$	1.13514e15	0.624032
$596$	2.33978e15	1.27444
$597$	−4.22461e14	−0.227997
$598$	3.71932e14	0.198887
$599$	−2.89946e15	−1.53628	−0.768139	−	0.640283i	$-0.778817\pi$
$599$	−2.89946e15	−1.53628	−0.768139	+	0.640283i	$0.778817\pi$
$600$	9.00554e14	0.472800
$601$	−5.95706e14	−0.309900	−0.154950	−	0.987922i	$-0.549522\pi$
$601$	−5.95706e14	−0.309900	−0.154950	+	0.987922i	$0.549522\pi$
$602$	4.34543e14	0.224002
$603$	6.07685e12	0.00310409
$604$	−2.83864e15	−1.43684
$605$	2.00279e15	1.00457
$606$	8.92532e14	0.443633
$607$	−1.97325e15	−0.971953	−0.485976	−	0.873972i	$-0.661536\pi$
$607$	−1.97325e15	−0.971953	−0.485976	+	0.873972i	$0.661536\pi$
$608$	6.15493e14	0.300437
$609$	1.32097e14	0.0638994
$610$	−2.31266e15	−1.10866
$611$	5.17880e14	0.246038
$612$	6.39840e14	0.301258
$613$	2.78976e15	1.30177	0.650885	−	0.759176i	$-0.274398\pi$
$613$	2.78976e15	1.30177	0.650885	+	0.759176i	$0.274398\pi$
$614$	−1.48227e15	−0.685492
$615$	1.18258e15	0.542021
$616$	3.77537e14	0.171501
$617$	−3.22395e15	−1.45151	−0.725755	−	0.687954i	$-0.758509\pi$
$617$	−3.22395e15	−1.45151	−0.725755	+	0.687954i	$0.758509\pi$
$618$	3.16303e14	0.141145
$619$	−2.20820e15	−0.976653	−0.488327	−	0.872661i	$-0.662392\pi$
$619$	−2.20820e15	−0.976653	−0.488327	+	0.872661i	$0.662392\pi$
$620$	4.41166e15	1.93396
$621$	6.56757e14	0.285365
$622$	2.54888e14	0.109775
$623$	1.02205e15	0.436304
$624$	1.33609e14	0.0565352
$625$	−2.47840e15	−1.03951
$626$	−1.34987e15	−0.561219
$627$	2.18172e14	0.0899139
$628$	−1.55519e15	−0.635337
$629$	−1.38421e15	−0.560561
$630$	−2.12418e14	−0.0852745
$631$	−5.48130e14	−0.218133	−0.109067	−	0.994034i	$-0.534786\pi$
$631$	−5.48130e14	−0.218133	−0.109067	+	0.994034i	$0.534786\pi$
$632$	−3.59489e15	−1.41821
$633$	2.36246e15	0.923941
$634$	7.50371e14	0.290928
$635$	2.78683e15	1.07116
$636$	1.19473e15	0.455255
$637$	−1.04881e14	−0.0396214
$638$	2.00870e14	0.0752316
$639$	3.45936e14	0.128452
$640$	3.63413e15	1.33786
$641$	−2.82097e15	−1.02963	−0.514813	−	0.857302i	$-0.672139\pi$
$641$	−2.82097e15	−1.02963	−0.514813	+	0.857302i	$0.672139\pi$
$642$	1.30145e15	0.470961
$643$	3.33485e15	1.19651	0.598254	−	0.801307i	$-0.295862\pi$
$643$	3.33485e15	1.19651	0.598254	+	0.801307i	$0.295862\pi$
$644$	1.20699e15	0.429369
$645$	2.80748e15	0.990236
$646$	−4.78218e14	−0.167243
$647$	1.57721e15	0.546910	0.273455	−	0.961885i	$-0.411833\pi$
$647$	1.57721e15	0.546910	0.273455	+	0.961885i	$0.411833\pi$
$648$	−2.76017e14	−0.0949016
$649$	5.79400e14	0.197530
$650$	−3.80426e14	−0.128602
$651$	−1.17420e15	−0.393592
$652$	−5.77067e14	−0.191807
$653$	3.39544e15	1.11911	0.559556	−	0.828793i	$-0.310972\pi$
$653$	3.39544e15	1.11911	0.559556	+	0.828793i	$0.310972\pi$
$654$	−5.82680e14	−0.190437
$655$	−6.64685e14	−0.215421
$656$	7.36894e14	0.236829
$657$	−3.06507e14	−0.0976858
$658$	−5.13054e14	−0.162152
$659$	5.32478e15	1.66891	0.834453	−	0.551078i	$-0.185784\pi$
$659$	5.32478e15	1.66891	0.834453	+	0.551078i	$0.185784\pi$
$660$	1.05809e15	0.328874
$661$	−4.11455e15	−1.26828	−0.634138	−	0.773219i	$-0.718645\pi$
$661$	−4.11455e15	−1.26828	−0.634138	+	0.773219i	$0.718645\pi$
$662$	1.04401e15	0.319143
$663$	−6.23096e14	−0.188899
$664$	3.56966e14	0.107326
$665$	−5.20059e14	−0.155072
$666$	2.59026e14	0.0766010
$667$	1.48041e15	0.434199
$668$	3.26912e14	0.0950955
$669$	5.29576e14	0.152786
$670$	−2.20270e13	−0.00630295
$671$	−3.06607e15	−0.870177
$672$	−7.94485e14	−0.223643
$673$	−2.92145e15	−0.815671	−0.407835	−	0.913055i	$-0.633716\pi$
$673$	−2.92145e15	−0.815671	−0.407835	+	0.913055i	$0.633716\pi$
$674$	−3.13388e15	−0.867866
$675$	−6.71755e14	−0.184519
$676$	−2.16302e14	−0.0589324
$677$	−2.94339e15	−0.795444	−0.397722	−	0.917506i	$-0.630199\pi$
$677$	−2.94339e15	−0.795444	−0.397722	+	0.917506i	$0.630199\pi$
$678$	1.11746e15	0.299550
$679$	−5.45764e14	−0.145118
$680$	−5.34652e15	−1.41017
$681$	−8.30953e14	−0.217404
$682$	−1.78552e15	−0.463394
$683$	2.70431e15	0.696213	0.348106	−	0.937455i	$-0.386825\pi$
$683$	2.70431e15	0.696213	0.348106	+	0.937455i	$0.386825\pi$
$684$	−2.93139e14	−0.0748626
$685$	6.62537e14	0.167846
$686$	1.03904e14	0.0261125
$687$	2.21244e14	0.0551581
$688$	1.74942e15	0.432670
$689$	−1.16346e15	−0.285460
$690$	−2.38057e15	−0.579444
$691$	4.62350e15	1.11646	0.558228	−	0.829687i	$-0.311481\pi$
$691$	4.62350e15	1.11646	0.558228	+	0.829687i	$0.311481\pi$
$692$	−2.36206e15	−0.565858
$693$	−2.81618e14	−0.0669312
$694$	−1.51233e15	−0.356590
$695$	4.20725e15	0.984196
$696$	−6.22175e14	−0.144398
$697$	−3.43657e15	−0.791308
$698$	−3.32670e14	−0.0759993
$699$	−2.70940e15	−0.614114
$700$	−1.23455e15	−0.277633
$701$	8.27761e15	1.84695	0.923477	−	0.383654i	$-0.125335\pi$
$701$	8.27761e15	1.84695	0.923477	+	0.383654i	$0.125335\pi$
$702$	1.16599e14	0.0258132
$703$	6.34167e14	0.139299
$704$	−3.47518e14	−0.0757404
$705$	−3.31472e15	−0.716815
$706$	1.16947e15	0.250936
$707$	−2.82064e15	−0.600538
$708$	−7.78491e14	−0.164464
$709$	−2.83243e14	−0.0593751	−0.0296875	−	0.999559i	$-0.509451\pi$
$709$	−2.83243e14	−0.0593751	−0.0296875	+	0.999559i	$0.509451\pi$
$710$	−1.25393e15	−0.260826
$711$	2.68156e15	0.553483
$712$	−4.81387e15	−0.985949
$713$	−1.31593e16	−2.67448
$714$	6.17289e14	0.124494
$715$	−1.03040e15	−0.206215
$716$	−1.16678e15	−0.231722
$717$	−1.73013e15	−0.340976
$718$	−1.52572e15	−0.298394
$719$	8.78763e15	1.70554	0.852772	−	0.522284i	$-0.174920\pi$
$719$	8.78763e15	1.70554	0.852772	+	0.522284i	$0.174920\pi$
$720$	−8.55170e14	−0.164711
$721$	−9.99601e14	−0.191066
$722$	−2.33038e15	−0.442051
$723$	−1.07738e15	−0.202819
$724$	−1.55872e15	−0.291210
$725$	−1.51421e15	−0.280756
$726$	1.08912e15	0.200412
$727$	3.97720e15	0.726338	0.363169	−	0.931723i	$-0.381695\pi$
$727$	3.97720e15	0.726338	0.363169	+	0.931723i	$0.381695\pi$
$728$	4.93990e14	0.0895355
$729$	2.05891e14	0.0370370
$730$	1.11101e15	0.198354
$731$	−8.15857e15	−1.44567
$732$	4.11961e15	0.724512
$733$	−1.00761e16	−1.75881	−0.879406	−	0.476073i	$-0.842060\pi$
$733$	−1.00761e16	−1.75881	−0.879406	+	0.476073i	$0.842060\pi$
$734$	−5.29581e13	−0.00917497
$735$	6.71298e14	0.115434
$736$	−8.90379e15	−1.51966
$737$	−2.92028e13	−0.00494713
$738$	6.43083e14	0.108133
$739$	5.26696e15	0.879055	0.439527	−	0.898229i	$-0.355146\pi$
$739$	5.26696e15	0.879055	0.439527	+	0.898229i	$0.355146\pi$
$740$	3.07557e15	0.509508
$741$	2.85468e14	0.0469415
$742$	1.15262e15	0.188133
$743$	7.53304e15	1.22048	0.610242	−	0.792215i	$-0.291072\pi$
$743$	7.53304e15	1.22048	0.610242	+	0.792215i	$0.291072\pi$
$744$	5.53048e15	0.889430
$745$	1.45840e16	2.32818
$746$	−2.14413e15	−0.339772
$747$	−2.66274e14	−0.0418857
$748$	−3.07480e15	−0.480130
$749$	−4.11292e15	−0.637530
$750$	−1.04664e14	−0.0161050
$751$	−5.49459e15	−0.839297	−0.419649	−	0.907687i	$-0.637847\pi$
$751$	−5.49459e15	−0.839297	−0.419649	+	0.907687i	$0.637847\pi$
$752$	−2.06549e15	−0.313203
$753$	4.78297e14	0.0719988
$754$	2.62829e14	0.0392763
$755$	−1.76934e16	−2.62484
$756$	3.78387e14	0.0557271
$757$	−6.42408e15	−0.939255	−0.469627	−	0.882865i	$-0.655612\pi$
$757$	−6.42408e15	−0.939255	−0.469627	+	0.882865i	$0.655612\pi$
$758$	−1.12193e15	−0.162849
$759$	−3.15610e15	−0.454800
$760$	2.44948e15	0.350428
$761$	−1.03588e16	−1.47127	−0.735636	−	0.677377i	$-0.763117\pi$
$761$	−1.03588e16	−1.47127	−0.735636	+	0.677377i	$0.763117\pi$
$762$	1.51547e15	0.213696
$763$	1.84142e15	0.257791
$764$	−3.40447e15	−0.473191
$765$	3.98816e15	0.550345
$766$	−4.05968e15	−0.556203
$767$	7.58118e14	0.103125
$768$	2.58571e15	0.349215
$769$	5.10813e15	0.684963	0.342481	−	0.939525i	$-0.388733\pi$
$769$	5.10813e15	0.684963	0.342481	+	0.939525i	$0.388733\pi$
$770$	1.02079e15	0.135906
$771$	5.05400e15	0.668092
$772$	9.15874e15	1.20210
$773$	−4.90543e15	−0.639278	−0.319639	−	0.947539i	$-0.603562\pi$
$773$	−4.90543e15	−0.639278	−0.319639	+	0.947539i	$0.603562\pi$
$774$	1.52671e15	0.197551
$775$	1.34598e16	1.72933
$776$	2.57055e15	0.327934
$777$	−8.18590e14	−0.103693
$778$	−1.67813e15	−0.211075
$779$	1.57445e15	0.196640
$780$	1.38446e15	0.171695
$781$	−1.66242e15	−0.204720
$782$	6.91796e15	0.845943
$783$	4.64103e14	0.0563539
$784$	4.18304e14	0.0504375
$785$	−9.69357e15	−1.16065
$786$	−3.61455e14	−0.0429764
$787$	7.70251e15	0.909434	0.454717	−	0.890636i	$-0.349740\pi$
$787$	7.70251e15	0.909434	0.454717	+	0.890636i	$0.349740\pi$
$788$	−3.82496e15	−0.448469
$789$	−4.69635e15	−0.546811
$790$	−9.71994e15	−1.12387
$791$	−3.53148e15	−0.405495
$792$	1.32642e15	0.151249
$793$	−4.01180e15	−0.454294
$794$	−6.39527e15	−0.719194
$795$	7.44680e15	0.831669
$796$	−2.72777e15	−0.302542
$797$	−1.51815e16	−1.67222	−0.836111	−	0.548561i	$-0.815176\pi$
$797$	−1.51815e16	−1.67222	−0.836111	+	0.548561i	$0.815176\pi$
$798$	−2.82808e14	−0.0309368
$799$	9.63262e15	1.04649
$800$	9.10713e15	0.982622
$801$	3.59084e15	0.384784
$802$	1.66065e15	0.176733
$803$	1.47295e15	0.155687
$804$	3.92374e13	0.00411900
$805$	7.52323e15	0.784381
$806$	−2.33627e15	−0.241925
$807$	−9.11805e15	−0.937773
$808$	1.32852e16	1.35708
$809$	−9.55183e15	−0.969102	−0.484551	−	0.874763i	$-0.661017\pi$
$809$	−9.55183e15	−0.969102	−0.484551	+	0.874763i	$0.661017\pi$
$810$	−7.46302e14	−0.0752050
$811$	−6.32875e15	−0.633437	−0.316718	−	0.948520i	$-0.602581\pi$
$811$	−6.32875e15	−0.633437	−0.316718	+	0.948520i	$0.602581\pi$
$812$	8.52928e14	0.0847919
$813$	−8.34247e15	−0.823753
$814$	−1.24477e15	−0.122083
$815$	−3.59690e15	−0.350397
$816$	2.48513e15	0.240466
$817$	3.73780e15	0.359248
$818$	6.67450e15	0.637200
$819$	−3.68485e14	−0.0349428
$820$	7.63572e15	0.719240
$821$	−1.94938e16	−1.82394	−0.911968	−	0.410262i	$-0.865437\pi$
$821$	−1.94938e16	−1.82394	−0.911968	+	0.410262i	$0.865437\pi$
$822$	3.60287e14	0.0334853
$823$	1.51114e16	1.39510	0.697549	−	0.716537i	$-0.254274\pi$
$823$	1.51114e16	1.39510	0.697549	+	0.716537i	$0.254274\pi$
$824$	4.70812e15	0.431766
$825$	3.22817e15	0.294076
$826$	−7.51054e14	−0.0679643
$827$	−8.49094e15	−0.763265	−0.381633	−	0.924314i	$-0.624638\pi$
$827$	−8.49094e15	−0.763265	−0.381633	+	0.924314i	$0.624638\pi$
$828$	4.24058e15	0.378668
$829$	1.42149e16	1.26094	0.630469	−	0.776215i	$-0.282863\pi$
$829$	1.42149e16	1.26094	0.630469	+	0.776215i	$0.282863\pi$
$830$	9.65174e14	0.0850504
$831$	1.01828e16	0.891375
$832$	−4.54711e14	−0.0395419
$833$	−1.95080e15	−0.168525
$834$	2.28790e15	0.196346
$835$	2.03766e15	0.173723
$836$	1.40870e15	0.119312
$837$	−4.12539e15	−0.347116
$838$	9.12967e15	0.763155
$839$	−1.12382e16	−0.933266	−0.466633	−	0.884451i	$-0.654533\pi$
$839$	−1.12382e16	−0.933266	−0.466633	+	0.884451i	$0.654533\pi$
$840$	−3.16181e15	−0.260856
$841$	−1.11544e16	−0.914254
$842$	−4.66576e15	−0.379932
$843$	−1.12527e16	−0.910340
$844$	1.52541e16	1.22603
$845$	−1.34822e15	−0.107659
$846$	−1.80254e15	−0.143004
$847$	−3.44189e15	−0.271293
$848$	4.64030e15	0.363387
$849$	−5.36796e15	−0.417654
$850$	−7.07595e15	−0.546991
$851$	−9.17393e15	−0.704600
$852$	2.23366e15	0.170451
$853$	1.09814e16	0.832606	0.416303	−	0.909226i	$-0.363326\pi$
$853$	1.09814e16	0.832606	0.416303	+	0.909226i	$0.363326\pi$
$854$	3.97442e15	0.299403
$855$	−1.82715e15	−0.136761
$856$	1.93719e16	1.44067
$857$	−1.95017e16	−1.44105	−0.720523	−	0.693431i	$-0.756098\pi$
$857$	−1.95017e16	−1.44105	−0.720523	+	0.693431i	$0.756098\pi$
$858$	−5.60328e14	−0.0411398
$859$	1.69074e16	1.23343	0.616717	−	0.787185i	$-0.288462\pi$
$859$	1.69074e16	1.23343	0.616717	+	0.787185i	$0.288462\pi$
$860$	1.81275e16	1.31400
$861$	−2.03231e15	−0.146377
$862$	−9.78687e14	−0.0700412
$863$	−2.37131e15	−0.168628	−0.0843138	−	0.996439i	$-0.526870\pi$
$863$	−2.37131e15	−0.168628	−0.0843138	+	0.996439i	$0.526870\pi$
$864$	−2.79131e15	−0.197234
$865$	−1.47229e16	−1.03372
$866$	−2.21751e15	−0.154709
$867$	−3.26156e15	−0.226110
$868$	−7.58164e15	−0.522282
$869$	−1.28864e16	−0.882112
$870$	−1.68225e15	−0.114429
$871$	−3.82105e13	−0.00258275
$872$	−8.67309e15	−0.582550
$873$	−1.91746e15	−0.127982
$874$	−3.16942e15	−0.210217
$875$	3.30766e14	0.0218010
$876$	−1.97907e15	−0.129625
$877$	−2.88500e16	−1.87780	−0.938899	−	0.344193i	$-0.888152\pi$
$877$	−2.88500e16	−1.87780	−0.938899	+	0.344193i	$0.888152\pi$
$878$	3.43015e15	0.221867
$879$	6.40625e14	0.0411780
$880$	4.10959e15	0.262509
$881$	−1.27629e16	−0.810179	−0.405090	−	0.914277i	$-0.632760\pi$
$881$	−1.27629e16	−0.810179	−0.405090	+	0.914277i	$0.632760\pi$
$882$	3.65051e14	0.0230291
$883$	3.88144e15	0.243337	0.121669	−	0.992571i	$-0.461175\pi$
$883$	3.88144e15	0.243337	0.121669	+	0.992571i	$0.461175\pi$
$884$	−4.02324e15	−0.250662
$885$	−4.85238e15	−0.300447
$886$	3.02765e14	0.0186303
$887$	−4.00116e13	−0.00244684	−0.00122342	−	0.999999i	$-0.500389\pi$
$887$	−4.00116e13	−0.00244684	−0.00122342	+	0.999999i	$0.500389\pi$
$888$	3.85556e15	0.234323
$889$	−4.78929e15	−0.289276
$890$	−1.30158e16	−0.781317
$891$	−9.89426e14	−0.0590277
$892$	3.41940e15	0.202742
$893$	−4.41313e15	−0.260054
$894$	7.93076e15	0.464471
$895$	−7.27261e15	−0.423315
$896$	−6.24543e15	−0.361300
$897$	−4.12961e15	−0.237438
$898$	−6.34194e14	−0.0362412
$899$	−9.29910e15	−0.528156
$900$	−4.33743e15	−0.244849
$901$	−2.16405e16	−1.21417
$902$	−3.09039e15	−0.172336
$903$	−4.82479e15	−0.267421
$904$	1.66333e16	0.916328
$905$	−9.71559e15	−0.531988
$906$	−9.62166e15	−0.523655
$907$	2.62902e16	1.42218	0.711088	−	0.703103i	$-0.248203\pi$
$907$	2.62902e16	1.42218	0.711088	+	0.703103i	$0.248203\pi$
$908$	−5.36534e15	−0.288486
$909$	−9.90990e15	−0.529624
$910$	1.33566e15	0.0709526
$911$	−2.93657e16	−1.55056	−0.775282	−	0.631615i	$-0.782392\pi$
$911$	−2.93657e16	−1.55056	−0.775282	+	0.631615i	$0.782392\pi$
$912$	−1.13855e15	−0.0597557
$913$	1.27960e15	0.0667553
$914$	1.07187e16	0.555825
$915$	2.56778e16	1.32355
$916$	1.42854e15	0.0731927
$917$	1.14229e15	0.0581763
$918$	2.16876e15	0.109793
$919$	1.30984e16	0.659148	0.329574	−	0.944130i	$-0.393095\pi$
$919$	1.30984e16	0.659148	0.329574	+	0.944130i	$0.393095\pi$
$920$	−3.54344e16	−1.77253
$921$	1.64579e16	0.818363
$922$	9.24010e15	0.456727
$923$	−2.17520e15	−0.106878
$924$	−1.81837e15	−0.0888150
$925$	9.38344e15	0.455599
$926$	−1.71160e16	−0.826117
$927$	−3.51196e15	−0.168504
$928$	−6.29193e15	−0.300103
$929$	1.02576e16	0.486359	0.243180	−	0.969981i	$-0.421810\pi$
$929$	1.02576e16	0.486359	0.243180	+	0.969981i	$0.421810\pi$
$930$	1.49534e16	0.704831
$931$	8.93746e14	0.0418785
$932$	−1.74942e16	−0.814905
$933$	−2.83005e15	−0.131053
$934$	1.63623e15	0.0753244
$935$	−1.91654e16	−0.877112
$936$	1.73556e15	0.0789629
$937$	−8.89305e15	−0.402238	−0.201119	−	0.979567i	$-0.564458\pi$
$937$	−8.89305e15	−0.402238	−0.201119	+	0.979567i	$0.564458\pi$
$938$	3.78545e13	0.00170216
$939$	1.49878e16	0.670001
$940$	−2.14027e16	−0.951186
$941$	2.80186e16	1.23795	0.618976	−	0.785410i	$-0.287548\pi$
$941$	2.80186e16	1.23795	0.618976	+	0.785410i	$0.287548\pi$
$942$	−5.27135e15	−0.231548
$943$	−2.27761e16	−0.994639
$944$	−3.02365e15	−0.131276
$945$	2.35851e15	0.101804
$946$	−7.33671e15	−0.314847
$947$	−2.40794e16	−1.02736	−0.513678	−	0.857983i	$-0.671718\pi$
$947$	−2.40794e16	−1.02736	−0.513678	+	0.857983i	$0.671718\pi$
$948$	1.73144e16	0.734449
$949$	1.92728e15	0.0812795
$950$	3.24180e15	0.135927
$951$	−8.33148e15	−0.347319
$952$	9.18825e15	0.380829
$953$	−3.14022e16	−1.29405	−0.647023	−	0.762471i	$-0.723986\pi$
$953$	−3.14022e16	−1.29405	−0.647023	+	0.762471i	$0.723986\pi$
$954$	4.04956e15	0.165917
$955$	−2.12203e16	−0.864435
$956$	−1.11712e16	−0.452462
$957$	−2.23028e15	−0.0898140
$958$	1.10983e16	0.444371
$959$	−1.13860e15	−0.0453283
$960$	2.91041e15	0.115203
$961$	5.72508e16	2.25321
$962$	−1.62872e15	−0.0637359
$963$	−1.44502e16	−0.562248
$964$	−6.95648e15	−0.269132
$965$	5.70870e16	2.19602
$966$	4.09113e15	0.156484
$967$	−2.74495e15	−0.104397	−0.0521986	−	0.998637i	$-0.516623\pi$
$967$	−2.74495e15	−0.104397	−0.0521986	+	0.998637i	$0.516623\pi$
$968$	1.62113e16	0.613061
$969$	5.30972e15	0.199660
$970$	6.95030e15	0.259872
$971$	−4.84584e16	−1.80162	−0.900811	−	0.434211i	$-0.857027\pi$
$971$	−4.84584e16	−1.80162	−0.900811	+	0.434211i	$0.857027\pi$
$972$	1.32941e15	0.0491467
$973$	−7.23035e15	−0.265790
$974$	4.20130e15	0.153571
$975$	4.22392e15	0.153529
$976$	1.60005e16	0.578309
$977$	2.29689e16	0.825505	0.412752	−	0.910843i	$-0.364568\pi$
$977$	2.29689e16	0.825505	0.412752	+	0.910843i	$0.364568\pi$
$978$	−1.95599e15	−0.0699041
$979$	−1.72561e16	−0.613249
$980$	4.33447e15	0.153177
$981$	6.46957e15	0.227351
$982$	−1.51749e16	−0.530290
$983$	3.71855e16	1.29220	0.646100	−	0.763253i	$-0.276399\pi$
$983$	3.71855e16	1.29220	0.646100	+	0.763253i	$0.276399\pi$
$984$	9.57219e15	0.330779
$985$	−2.38412e16	−0.819273
$986$	4.88863e15	0.167057
$987$	5.69651e15	0.193582
$988$	1.84322e15	0.0622895
$989$	−5.40715e16	−1.81714
$990$	3.58641e15	0.119858
$991$	−4.21708e16	−1.40154	−0.700771	−	0.713386i	$-0.747161\pi$
$991$	−4.21708e16	−1.40154	−0.700771	+	0.713386i	$0.747161\pi$
$992$	5.59287e16	1.84850
$993$	−1.15918e16	−0.381003
$994$	2.15493e15	0.0704382
$995$	−1.70024e16	−0.552691
$996$	−1.71929e15	−0.0555806
$997$	4.68309e16	1.50560	0.752799	−	0.658251i	$-0.228703\pi$
$997$	4.68309e16	1.50560	0.752799	+	0.658251i	$0.228703\pi$
$998$	2.16359e16	0.691764
$999$	−2.87600e15	−0.0914489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+21.8857 q^{2} -243.000 q^{3} -1569.02 q^{4} -9779.77 q^{5} -5318.23 q^{6} +16807.0 q^{7} -79161.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+21.8857 q^{2} -243.000 q^{3} -1569.02 q^{4} -9779.77 q^{5} -5318.23 q^{6} +16807.0 q^{7} -79161.0 q^{8} +59049.0 q^{9} -214037. q^{10} -283765. q^{11} +381271. q^{12} -371293. q^{13} +367833. q^{14} +2.37648e6 q^{15} +1.48085e6 q^{16} -6.90608e6 q^{17} +1.29233e6 q^{18} +3.16398e6 q^{19} +1.53446e7 q^{20} -4.08410e6 q^{21} -6.21039e6 q^{22} -4.57705e7 q^{23} +1.92361e7 q^{24} +4.68158e7 q^{25} -8.12601e6 q^{26} -1.43489e7 q^{27} -2.63704e7 q^{28} -3.23441e7 q^{29} +5.20110e7 q^{30} +2.87505e8 q^{31} +1.94531e8 q^{32} +6.89548e7 q^{33} -1.51144e8 q^{34} -1.64369e8 q^{35} -9.26488e7 q^{36} +2.00433e8 q^{37} +6.92460e7 q^{38} +9.02242e7 q^{39} +7.74176e8 q^{40} +4.97616e8 q^{41} -8.93835e7 q^{42} +1.18136e9 q^{43} +4.45231e8 q^{44} -5.77486e8 q^{45} -1.00172e9 q^{46} -1.39480e9 q^{47} -3.59847e8 q^{48} +2.82475e8 q^{49} +1.02460e9 q^{50} +1.67818e9 q^{51} +5.82565e8 q^{52} +3.13354e9 q^{53} -3.14036e8 q^{54} +2.77515e9 q^{55} -1.33046e9 q^{56} -7.68847e8 q^{57} -7.07874e8 q^{58} -2.04183e9 q^{59} -3.72874e9 q^{60} +1.08050e10 q^{61} +6.29226e9 q^{62} +9.92437e8 q^{63} +1.22467e9 q^{64} +3.63116e9 q^{65} +1.50913e9 q^{66} +1.02912e8 q^{67} +1.08357e10 q^{68} +1.11222e10 q^{69} -3.59732e9 q^{70} +5.85845e9 q^{71} -4.67438e9 q^{72} -5.19073e9 q^{73} +4.38662e9 q^{74} -1.13762e10 q^{75} -4.96434e9 q^{76} -4.76923e9 q^{77} +1.97462e9 q^{78} +4.54124e10 q^{79} -1.44824e10 q^{80} +3.48678e9 q^{81} +1.08907e10 q^{82} -4.50938e9 q^{83} +6.40802e9 q^{84} +6.75399e10 q^{85} +2.58549e10 q^{86} +7.85962e9 q^{87} +2.24631e10 q^{88} +6.08111e10 q^{89} -1.26387e10 q^{90} -6.24032e9 q^{91} +7.18146e10 q^{92} -6.98638e10 q^{93} -3.05262e10 q^{94} -3.09430e10 q^{95} -4.72711e10 q^{96} -3.24724e10 q^{97} +6.18217e9 q^{98} -1.67560e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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