LMFDB - Embedded newform 273.12.a.c.1.5

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			1.5
Root			$-37.3711$ 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)

$f(q)$	$=$	$q-41.3711 q^{2} -243.000 q^{3} -336.429 q^{4} -4784.52 q^{5} +10053.2 q^{6} +16807.0 q^{7} +98646.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-41.3711 q^{2} -243.000 q^{3} -336.429 q^{4} -4784.52 q^{5} +10053.2 q^{6} +16807.0 q^{7} +98646.5 q^{8} +59049.0 q^{9} +197941. q^{10} +884509. q^{11} +81752.2 q^{12} -371293. q^{13} -695325. q^{14} +1.16264e6 q^{15} -3.39211e6 q^{16} +6.33691e6 q^{17} -2.44292e6 q^{18} -7.31264e6 q^{19} +1.60965e6 q^{20} -4.08410e6 q^{21} -3.65931e7 q^{22} -1.47316e7 q^{23} -2.39711e7 q^{24} -2.59365e7 q^{25} +1.53608e7 q^{26} -1.43489e7 q^{27} -5.65436e6 q^{28} +1.00927e8 q^{29} -4.80997e7 q^{30} -2.95315e8 q^{31} -6.16925e7 q^{32} -2.14936e8 q^{33} -2.62165e8 q^{34} -8.04135e7 q^{35} -1.98658e7 q^{36} -2.53738e8 q^{37} +3.02532e8 q^{38} +9.02242e7 q^{39} -4.71977e8 q^{40} +1.20683e9 q^{41} +1.68964e8 q^{42} +4.41770e7 q^{43} -2.97574e8 q^{44} -2.82521e8 q^{45} +6.09463e8 q^{46} -1.91405e9 q^{47} +8.24284e8 q^{48} +2.82475e8 q^{49} +1.07302e9 q^{50} -1.53987e9 q^{51} +1.24914e8 q^{52} +6.36600e8 q^{53} +5.93631e8 q^{54} -4.23195e9 q^{55} +1.65795e9 q^{56} +1.77697e9 q^{57} -4.17545e9 q^{58} +4.83453e9 q^{59} -3.91145e8 q^{60} +1.25696e10 q^{61} +1.22175e10 q^{62} +9.92437e8 q^{63} +9.49934e9 q^{64} +1.77646e9 q^{65} +8.89213e9 q^{66} -1.37371e10 q^{67} -2.13192e9 q^{68} +3.57978e9 q^{69} +3.32680e9 q^{70} -4.32356e9 q^{71} +5.82498e9 q^{72} -1.27289e10 q^{73} +1.04974e10 q^{74} +6.30256e9 q^{75} +2.46018e9 q^{76} +1.48659e10 q^{77} -3.73268e9 q^{78} -2.47713e9 q^{79} +1.62296e10 q^{80} +3.48678e9 q^{81} -4.99278e10 q^{82} -6.01852e10 q^{83} +1.37401e9 q^{84} -3.03191e10 q^{85} -1.82765e9 q^{86} -2.45251e10 q^{87} +8.72537e10 q^{88} +6.43004e10 q^{89} +1.16882e10 q^{90} -6.24032e9 q^{91} +4.95613e9 q^{92} +7.17616e10 q^{93} +7.91866e10 q^{94} +3.49875e10 q^{95} +1.49913e10 q^{96} +1.31580e11 q^{97} -1.16863e10 q^{98} +5.22294e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−41.3711	−0.914182	−0.457091	−	0.889420i	$-0.651109\pi$
$2$	−41.3711	−0.914182	−0.457091	+	0.889420i	$0.651109\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−336.429	−0.164272
$5$	−4784.52	−0.684705	−0.342353	−	0.939572i	$-0.611224\pi$
$5$	−4784.52	−0.684705	−0.342353	+	0.939572i	$0.611224\pi$
$6$	10053.2	0.527803
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	98646.5	1.06436
$9$	59049.0	0.333333
$10$	197941.	0.625945
$11$	884509.	1.65593	0.827966	−	0.560779i	$-0.189498\pi$
$11$	884509.	1.65593	0.827966	+	0.560779i	$0.189498\pi$
$12$	81752.2	0.0948424
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−695325.	−0.345528
$15$	1.16264e6	0.395315
$16$	−3.39211e6	−0.808743
$17$	6.33691e6	1.08245	0.541226	−	0.840877i	$-0.317961\pi$
$17$	6.33691e6	1.08245	0.541226	+	0.840877i	$0.317961\pi$
$18$	−2.44292e6	−0.304727
$19$	−7.31264e6	−0.677531	−0.338766	−	0.940871i	$-0.610009\pi$
$19$	−7.31264e6	−0.677531	−0.338766	+	0.940871i	$0.610009\pi$
$20$	1.60965e6	0.112478
$21$	−4.08410e6	−0.218218
$22$	−3.65931e7	−1.51382
$23$	−1.47316e7	−0.477251	−0.238626	−	0.971112i	$-0.576697\pi$
$23$	−1.47316e7	−0.477251	−0.238626	+	0.971112i	$0.576697\pi$
$24$	−2.39711e7	−0.614506
$25$	−2.59365e7	−0.531179
$26$	1.53608e7	0.253548
$27$	−1.43489e7	−0.192450
$28$	−5.65436e6	−0.0620889
$29$	1.00927e8	0.913727	0.456863	−	0.889537i	$-0.348973\pi$
$29$	1.00927e8	0.913727	0.456863	+	0.889537i	$0.348973\pi$
$30$	−4.80997e7	−0.361389
$31$	−2.95315e8	−1.85266	−0.926331	−	0.376710i	$-0.877055\pi$
$31$	−2.95315e8	−1.85266	−0.926331	+	0.376710i	$0.877055\pi$
$32$	−6.16925e7	−0.325018
$33$	−2.14936e8	−0.956052
$34$	−2.62165e8	−0.989557
$35$	−8.04135e7	−0.258794
$36$	−1.98658e7	−0.0547573
$37$	−2.53738e8	−0.601556	−0.300778	−	0.953694i	$-0.597246\pi$
$37$	−2.53738e8	−0.601556	−0.300778	+	0.953694i	$0.597246\pi$
$38$	3.02532e8	0.619387
$39$	9.02242e7	0.160128
$40$	−4.71977e8	−0.728770
$41$	1.20683e9	1.62680	0.813398	−	0.581707i	$-0.197615\pi$
$41$	1.20683e9	1.62680	0.813398	+	0.581707i	$0.197615\pi$
$42$	1.68964e8	0.199491
$43$	4.41770e7	0.0458269	0.0229134	−	0.999737i	$-0.492706\pi$
$43$	4.41770e7	0.0458269	0.0229134	+	0.999737i	$0.492706\pi$
$44$	−2.97574e8	−0.272023
$45$	−2.82521e8	−0.228235
$46$	6.09463e8	0.436294
$47$	−1.91405e9	−1.21735	−0.608676	−	0.793419i	$-0.708299\pi$
$47$	−1.91405e9	−1.21735	−0.608676	+	0.793419i	$0.708299\pi$
$48$	8.24284e8	0.466928
$49$	2.82475e8	0.142857
$50$	1.07302e9	0.485594
$51$	−1.53987e9	−0.624953
$52$	1.24914e8	0.0455608
$53$	6.36600e8	0.209098	0.104549	−	0.994520i	$-0.466660\pi$
$53$	6.36600e8	0.209098	0.104549	+	0.994520i	$0.466660\pi$
$54$	5.93631e8	0.175934
$55$	−4.23195e9	−1.13382
$56$	1.65795e9	0.402289
$57$	1.77697e9	0.391173
$58$	−4.17545e9	−0.835312
$59$	4.83453e9	0.880376	0.440188	−	0.897906i	$-0.354912\pi$
$59$	4.83453e9	0.880376	0.440188	+	0.897906i	$0.354912\pi$
$60$	−3.91145e8	−0.0649391
$61$	1.25696e10	1.90549	0.952743	−	0.303777i	$-0.0982478\pi$
$61$	1.25696e10	1.90549	0.952743	+	0.303777i	$0.0982478\pi$
$62$	1.22175e10	1.69367
$63$	9.92437e8	0.125988
$64$	9.49934e9	1.10587
$65$	1.77646e9	0.189903
$66$	8.89213e9	0.874006
$67$	−1.37371e10	−1.24303	−0.621516	−	0.783402i	$-0.713483\pi$
$67$	−1.37371e10	−1.24303	−0.621516	+	0.783402i	$0.713483\pi$
$68$	−2.13192e9	−0.177816
$69$	3.57978e9	0.275541
$70$	3.32680e9	0.236585
$71$	−4.32356e9	−0.284394	−0.142197	−	0.989838i	$-0.545417\pi$
$71$	−4.32356e9	−0.284394	−0.142197	+	0.989838i	$0.545417\pi$
$72$	5.82498e9	0.354785
$73$	−1.27289e10	−0.718648	−0.359324	−	0.933213i	$-0.616993\pi$
$73$	−1.27289e10	−0.718648	−0.359324	+	0.933213i	$0.616993\pi$
$74$	1.04974e10	0.549931
$75$	6.30256e9	0.306676
$76$	2.46018e9	0.111299
$77$	1.48659e10	0.625883
$78$	−3.73268e9	−0.146386
$79$	−2.47713e9	−0.0905731	−0.0452866	−	0.998974i	$-0.514420\pi$
$79$	−2.47713e9	−0.0905731	−0.0452866	+	0.998974i	$0.514420\pi$
$80$	1.62296e10	0.553750
$81$	3.48678e9	0.111111
$82$	−4.99278e10	−1.48719
$83$	−6.01852e10	−1.67711	−0.838553	−	0.544820i	$-0.816598\pi$
$83$	−6.01852e10	−1.67711	−0.838553	+	0.544820i	$0.816598\pi$
$84$	1.37401e9	0.0358470
$85$	−3.03191e10	−0.741160
$86$	−1.82765e9	−0.0418941
$87$	−2.45251e10	−0.527540
$88$	8.72537e10	1.76250
$89$	6.43004e10	1.22059	0.610293	−	0.792176i	$-0.291052\pi$
$89$	6.43004e10	1.22059	0.610293	+	0.792176i	$0.291052\pi$
$90$	1.16882e10	0.208648
$91$	−6.24032e9	−0.104828
$92$	4.95613e9	0.0783989
$93$	7.17616e10	1.06964
$94$	7.91866e10	1.11288
$95$	3.49875e10	0.463909
$96$	1.49913e10	0.187649
$97$	1.31580e11	1.55577	0.777885	−	0.628406i	$-0.216293\pi$
$97$	1.31580e11	1.55577	0.777885	+	0.628406i	$0.216293\pi$
$98$	−1.16863e10	−0.130597
$99$	5.22294e10	0.551977
$100$	8.72577e9	0.0872577
$101$	−1.89831e11	−1.79721	−0.898605	−	0.438759i	$-0.855418\pi$
$101$	−1.89831e11	−1.79721	−0.898605	+	0.438759i	$0.855418\pi$
$102$	6.37061e10	0.571321
$103$	−1.05355e11	−0.895465	−0.447733	−	0.894167i	$-0.647768\pi$
$103$	−1.05355e11	−0.895465	−0.447733	+	0.894167i	$0.647768\pi$
$104$	−3.66268e10	−0.295199
$105$	1.95405e10	0.149415
$106$	−2.63369e10	−0.191153
$107$	2.04540e10	0.140983	0.0704915	−	0.997512i	$-0.477543\pi$
$107$	2.04540e10	0.140983	0.0704915	+	0.997512i	$0.477543\pi$
$108$	4.82738e9	0.0316141
$109$	−1.94751e11	−1.21237	−0.606183	−	0.795325i	$-0.707300\pi$
$109$	−1.94751e11	−1.21237	−0.606183	+	0.795325i	$0.707300\pi$
$110$	1.75081e11	1.03652
$111$	6.16583e10	0.347308
$112$	−5.70113e10	−0.305676
$113$	3.68331e11	1.88064	0.940322	−	0.340285i	$-0.110524\pi$
$113$	3.68331e11	1.88064	0.940322	+	0.340285i	$0.110524\pi$
$114$	−7.35153e10	−0.357603
$115$	7.04837e10	0.326776
$116$	−3.39546e10	−0.150100
$117$	−2.19245e10	−0.0924500
$118$	−2.00010e11	−0.804823
$119$	1.06504e11	0.409128
$120$	1.14690e11	0.420756
$121$	4.97044e11	1.74211
$122$	−5.20017e11	−1.74196
$123$	−2.93259e11	−0.939232
$124$	9.93524e10	0.304340
$125$	3.57713e11	1.04841
$126$	−4.10582e10	−0.115176
$127$	−3.23542e11	−0.868980	−0.434490	−	0.900677i	$-0.643071\pi$
$127$	−3.23542e11	−0.868980	−0.434490	+	0.900677i	$0.643071\pi$
$128$	−2.66652e11	−0.685947
$129$	−1.07350e10	−0.0264582
$130$	−7.34942e10	−0.173606
$131$	−5.51792e10	−0.124964	−0.0624818	−	0.998046i	$-0.519902\pi$
$131$	−5.51792e10	−0.124964	−0.0624818	+	0.998046i	$0.519902\pi$
$132$	7.23105e10	0.157052
$133$	−1.22904e11	−0.256083
$134$	5.68318e11	1.13636
$135$	6.86527e10	0.131772
$136$	6.25114e11	1.15211
$137$	−5.47782e11	−0.969716	−0.484858	−	0.874593i	$-0.661129\pi$
$137$	−5.47782e11	−0.969716	−0.484858	+	0.874593i	$0.661129\pi$
$138$	−1.48100e11	−0.251895
$139$	3.99759e11	0.653457	0.326729	−	0.945118i	$-0.394054\pi$
$139$	3.99759e11	0.653457	0.326729	+	0.945118i	$0.394054\pi$
$140$	2.70534e10	0.0425126
$141$	4.65115e11	0.702838
$142$	1.78871e11	0.259988
$143$	−3.28412e11	−0.459273
$144$	−2.00301e11	−0.269581
$145$	−4.82885e11	−0.625633
$146$	5.26611e11	0.656975
$147$	−6.86415e10	−0.0824786
$148$	8.53647e10	0.0988186
$149$	3.17758e10	0.0354464	0.0177232	−	0.999843i	$-0.494358\pi$
$149$	3.17758e10	0.0354464	0.0177232	+	0.999843i	$0.494358\pi$
$150$	−2.60744e11	−0.280358
$151$	7.42401e11	0.769600	0.384800	−	0.923000i	$-0.374270\pi$
$151$	7.42401e11	0.769600	0.384800	+	0.923000i	$0.374270\pi$
$152$	−7.21367e11	−0.721135
$153$	3.74188e11	0.360817
$154$	−6.15021e11	−0.572171
$155$	1.41294e12	1.26853
$156$	−3.03540e10	−0.0263045
$157$	4.60184e11	0.385020	0.192510	−	0.981295i	$-0.438337\pi$
$157$	4.60184e11	0.385020	0.192510	+	0.981295i	$0.438337\pi$
$158$	1.02482e11	0.0828003
$159$	−1.54694e11	−0.120723
$160$	2.95169e11	0.222541
$161$	−2.47594e11	−0.180384
$162$	−1.44252e11	−0.101576
$163$	4.85673e11	0.330607	0.165303	−	0.986243i	$-0.447140\pi$
$163$	4.85673e11	0.330607	0.165303	+	0.986243i	$0.447140\pi$
$164$	−4.06011e11	−0.267237
$165$	1.02836e12	0.654614
$166$	2.48993e12	1.53318
$167$	1.04722e12	0.623872	0.311936	−	0.950103i	$-0.399023\pi$
$167$	1.04722e12	0.623872	0.311936	+	0.950103i	$0.399023\pi$
$168$	−4.02882e11	−0.232262
$169$	1.37858e11	0.0769231
$170$	1.25433e12	0.677555
$171$	−4.31804e11	−0.225844
$172$	−1.48624e10	−0.00752806
$173$	1.72683e12	0.847217	0.423609	−	0.905845i	$-0.360763\pi$
$173$	1.72683e12	0.847217	0.423609	+	0.905845i	$0.360763\pi$
$174$	1.01463e12	0.482268
$175$	−4.35914e11	−0.200767
$176$	−3.00035e12	−1.33922
$177$	−1.17479e12	−0.508285
$178$	−2.66018e12	−1.11584
$179$	−3.60323e11	−0.146555	−0.0732775	−	0.997312i	$-0.523346\pi$
$179$	−3.60323e11	−0.146555	−0.0732775	+	0.997312i	$0.523346\pi$
$180$	9.50482e10	0.0374926
$181$	4.36143e12	1.66877	0.834385	−	0.551182i	$-0.185823\pi$
$181$	4.36143e12	1.66877	0.834385	+	0.551182i	$0.185823\pi$
$182$	2.58169e11	0.0958323
$183$	−3.05440e12	−1.10013
$184$	−1.45322e12	−0.507965
$185$	1.21401e12	0.411888
$186$	−2.96886e12	−0.977841
$187$	5.60505e12	1.79247
$188$	6.43942e11	0.199976
$189$	−2.41162e11	−0.0727393
$190$	−1.44747e12	−0.424097
$191$	−5.06514e12	−1.44181	−0.720905	−	0.693034i	$-0.756274\pi$
$191$	−5.06514e12	−1.44181	−0.720905	+	0.693034i	$0.756274\pi$
$192$	−2.30834e12	−0.638473
$193$	1.80649e12	0.485589	0.242795	−	0.970078i	$-0.421936\pi$
$193$	1.80649e12	0.485589	0.242795	+	0.970078i	$0.421936\pi$
$194$	−5.44362e12	−1.42226
$195$	−4.31680e11	−0.109641
$196$	−9.50328e10	−0.0234674
$197$	−1.98212e12	−0.475955	−0.237978	−	0.971271i	$-0.576484\pi$
$197$	−1.98212e12	−0.475955	−0.237978	+	0.971271i	$0.576484\pi$
$198$	−2.16079e12	−0.504607
$199$	−7.04044e11	−0.159922	−0.0799609	−	0.996798i	$-0.525480\pi$
$199$	−7.04044e11	−0.159922	−0.0799609	+	0.996798i	$0.525480\pi$
$200$	−2.55854e12	−0.565363
$201$	3.33810e12	0.717665
$202$	7.85351e12	1.64298
$203$	1.69627e12	0.345356
$204$	5.18056e11	0.102662
$205$	−5.77408e12	−1.11388
$206$	4.35864e12	0.818618
$207$	−8.69886e11	−0.159084
$208$	1.25947e12	0.224305
$209$	−6.46809e12	−1.12195
$210$	−8.08412e11	−0.136592
$211$	−6.92729e12	−1.14028	−0.570138	−	0.821549i	$-0.693110\pi$
$211$	−6.92729e12	−1.14028	−0.570138	+	0.821549i	$0.693110\pi$
$212$	−2.14170e11	−0.0343489
$213$	1.05062e12	0.164195
$214$	−8.46204e11	−0.128884
$215$	−2.11366e11	−0.0313779
$216$	−1.41547e12	−0.204835
$217$	−4.96336e12	−0.700241
$218$	8.05707e12	1.10832
$219$	3.09313e12	0.414912
$220$	1.42375e12	0.186255
$221$	−2.35285e12	−0.300218
$222$	−2.55087e12	−0.317503
$223$	−1.05933e13	−1.28634	−0.643171	−	0.765723i	$-0.722381\pi$
$223$	−1.05933e13	−1.28634	−0.643171	+	0.765723i	$0.722381\pi$
$224$	−1.03687e12	−0.122845
$225$	−1.53152e12	−0.177060
$226$	−1.52383e13	−1.71925
$227$	9.52631e12	1.04902	0.524508	−	0.851405i	$-0.324249\pi$
$227$	9.52631e12	1.04902	0.524508	+	0.851405i	$0.324249\pi$
$228$	−5.97824e11	−0.0642587
$229$	1.45565e12	0.152744	0.0763718	−	0.997079i	$-0.475666\pi$
$229$	1.45565e12	0.152744	0.0763718	+	0.997079i	$0.475666\pi$
$230$	−2.91599e12	−0.298733
$231$	−3.61242e12	−0.361354
$232$	9.95605e12	0.972531
$233$	3.13813e12	0.299373	0.149687	−	0.988734i	$-0.452174\pi$
$233$	3.13813e12	0.299373	0.149687	+	0.988734i	$0.452174\pi$
$234$	9.07041e11	0.0845161
$235$	9.15783e12	0.833527
$236$	−1.62647e12	−0.144621
$237$	6.01942e11	0.0522924
$238$	−4.40621e12	−0.374017
$239$	−4.36200e12	−0.361824	−0.180912	−	0.983499i	$-0.557905\pi$
$239$	−4.36200e12	−0.361824	−0.180912	+	0.983499i	$0.557905\pi$
$240$	−3.94380e12	−0.319708
$241$	2.27001e12	0.179860	0.0899299	−	0.995948i	$-0.471336\pi$
$241$	2.27001e12	0.179860	0.0899299	+	0.995948i	$0.471336\pi$
$242$	−2.05633e13	−1.59260
$243$	−8.47289e11	−0.0641500
$244$	−4.22876e12	−0.313018
$245$	−1.35151e12	−0.0978150
$246$	1.21324e13	0.858628
$247$	2.71513e12	0.187913
$248$	−2.91318e13	−1.97189
$249$	1.46250e13	0.968277
$250$	−1.47990e13	−0.958434
$251$	6.55497e11	0.0415303	0.0207652	−	0.999784i	$-0.493390\pi$
$251$	6.55497e11	0.0415303	0.0207652	+	0.999784i	$0.493390\pi$
$252$	−3.33884e11	−0.0206963
$253$	−1.30302e13	−0.790295
$254$	1.33853e13	0.794406
$255$	7.36754e12	0.427909
$256$	−8.42293e12	−0.478788
$257$	1.53232e13	0.852545	0.426272	−	0.904595i	$-0.359826\pi$
$257$	1.53232e13	0.852545	0.426272	+	0.904595i	$0.359826\pi$
$258$	4.44120e11	0.0241876
$259$	−4.26457e12	−0.227367
$260$	−5.97652e11	−0.0311957
$261$	5.95961e12	0.304576
$262$	2.28283e12	0.114239
$263$	−1.98777e13	−0.974112	−0.487056	−	0.873371i	$-0.661929\pi$
$263$	−1.98777e13	−0.974112	−0.487056	+	0.873371i	$0.661929\pi$
$264$	−2.12027e13	−1.01758
$265$	−3.04583e12	−0.143170
$266$	5.08466e12	0.234106
$267$	−1.56250e13	−0.704706
$268$	4.62154e12	0.204195
$269$	−2.47772e13	−1.07254	−0.536272	−	0.844045i	$-0.680168\pi$
$269$	−2.47772e13	−1.07254	−0.536272	+	0.844045i	$0.680168\pi$
$270$	−2.84024e12	−0.120463
$271$	−3.90044e12	−0.162100	−0.0810500	−	0.996710i	$-0.525827\pi$
$271$	−3.90044e12	−0.162100	−0.0810500	+	0.996710i	$0.525827\pi$
$272$	−2.14955e13	−0.875425
$273$	1.51640e12	0.0605228
$274$	2.26624e13	0.886497
$275$	−2.29410e13	−0.879596
$276$	−1.20434e12	−0.0452636
$277$	−2.32051e13	−0.854957	−0.427478	−	0.904026i	$-0.640598\pi$
$277$	−2.32051e13	−0.854957	−0.427478	+	0.904026i	$0.640598\pi$
$278$	−1.65385e13	−0.597379
$279$	−1.74381e13	−0.617554
$280$	−7.93251e12	−0.275449
$281$	−4.66297e12	−0.158774	−0.0793868	−	0.996844i	$-0.525296\pi$
$281$	−4.66297e12	−0.158774	−0.0793868	+	0.996844i	$0.525296\pi$
$282$	−1.92423e13	−0.642522
$283$	−8.46371e12	−0.277163	−0.138582	−	0.990351i	$-0.544254\pi$
$283$	−8.46371e12	−0.277163	−0.138582	+	0.990351i	$0.544254\pi$
$284$	1.45457e12	0.0467179
$285$	−8.50196e12	−0.267838
$286$	1.35868e13	0.419859
$287$	2.02831e13	0.614871
$288$	−3.64288e12	−0.108339
$289$	5.88450e12	0.171701
$290$	1.99775e13	0.571943
$291$	−3.19739e13	−0.898224
$292$	4.28238e12	0.118054
$293$	6.79340e13	1.83787	0.918937	−	0.394405i	$-0.129049\pi$
$293$	6.79340e13	1.83787	0.918937	+	0.394405i	$0.129049\pi$
$294$	2.83978e12	0.0754004
$295$	−2.31309e13	−0.602798
$296$	−2.50304e13	−0.640269
$297$	−1.26917e13	−0.318684
$298$	−1.31460e12	−0.0324044
$299$	5.46974e12	0.132366
$300$	−2.12036e12	−0.0503783
$301$	7.42484e11	0.0173209
$302$	−3.07140e13	−0.703555
$303$	4.61288e13	1.03762
$304$	2.48053e13	0.547949
$305$	−6.01393e13	−1.30470
$306$	−1.54806e13	−0.329852
$307$	−6.82850e13	−1.42910	−0.714552	−	0.699582i	$-0.753370\pi$
$307$	−6.82850e13	−1.42910	−0.714552	+	0.699582i	$0.753370\pi$
$308$	−5.00133e12	−0.102815
$309$	2.56012e13	0.516997
$310$	−5.84550e13	−1.15966
$311$	9.04928e13	1.76373	0.881865	−	0.471502i	$-0.156288\pi$
$311$	9.04928e13	1.76373	0.881865	+	0.471502i	$0.156288\pi$
$312$	8.90030e12	0.170433
$313$	−9.62908e13	−1.81172	−0.905860	−	0.423577i	$-0.860774\pi$
$313$	−9.62908e13	−1.81172	−0.905860	+	0.423577i	$0.860774\pi$
$314$	−1.90383e13	−0.351978
$315$	−4.74834e12	−0.0862647
$316$	8.33377e11	0.0148786
$317$	−5.05202e13	−0.886419	−0.443210	−	0.896418i	$-0.646160\pi$
$317$	−5.05202e13	−0.886419	−0.443210	+	0.896418i	$0.646160\pi$
$318$	6.39986e12	0.110362
$319$	8.92704e13	1.51307
$320$	−4.54498e13	−0.757194
$321$	−4.97031e12	−0.0813965
$322$	1.02432e13	0.164904
$323$	−4.63395e13	−0.733395
$324$	−1.17305e12	−0.0182524
$325$	9.63003e12	0.147323
$326$	−2.00928e13	−0.302235
$327$	4.73245e13	0.699960
$328$	1.19049e14	1.73149
$329$	−3.21695e13	−0.460116
$330$	−4.25446e13	−0.598436
$331$	7.18309e12	0.0993705	0.0496853	−	0.998765i	$-0.484178\pi$
$331$	7.18309e12	0.0993705	0.0496853	+	0.998765i	$0.484178\pi$
$332$	2.02480e13	0.275501
$333$	−1.49830e13	−0.200519
$334$	−4.33245e13	−0.570333
$335$	6.57252e13	0.851110
$336$	1.38537e13	0.176482
$337$	4.46834e12	0.0559992	0.0279996	−	0.999608i	$-0.491086\pi$
$337$	4.46834e12	0.0559992	0.0279996	+	0.999608i	$0.491086\pi$
$338$	−5.70336e12	−0.0703217
$339$	−8.95044e13	−1.08579
$340$	1.02002e13	0.121752
$341$	−2.61209e14	−3.06788
$342$	1.78642e13	0.206462
$343$	4.74756e12	0.0539949
$344$	4.35791e12	0.0487761
$345$	−1.71275e13	−0.188664
$346$	−7.14407e13	−0.774511
$347$	6.77393e13	0.722817	0.361409	−	0.932408i	$-0.382296\pi$
$347$	6.77393e13	0.722817	0.361409	+	0.932408i	$0.382296\pi$
$348$	8.25096e12	0.0866600
$349$	−8.30163e12	−0.0858270	−0.0429135	−	0.999079i	$-0.513664\pi$
$349$	−8.30163e12	−0.0858270	−0.0429135	+	0.999079i	$0.513664\pi$
$350$	1.80343e13	0.183537
$351$	5.32765e12	0.0533761
$352$	−5.45675e13	−0.538207
$353$	1.95520e14	1.89859	0.949295	−	0.314386i	$-0.101799\pi$
$353$	1.95520e14	1.89859	0.949295	+	0.314386i	$0.101799\pi$
$354$	4.86024e13	0.464665
$355$	2.06862e13	0.194726
$356$	−2.16325e13	−0.200508
$357$	−2.58806e13	−0.236210
$358$	1.49070e13	0.133978
$359$	−1.70243e14	−1.50678	−0.753388	−	0.657576i	$-0.771582\pi$
$359$	−1.70243e14	−1.50678	−0.753388	+	0.657576i	$0.771582\pi$
$360$	−2.78697e13	−0.242923
$361$	−6.30156e13	−0.540951
$362$	−1.80437e14	−1.52556
$363$	−1.20782e14	−1.00581
$364$	2.09942e12	0.0172204
$365$	6.09019e13	0.492062
$366$	1.26364e14	1.00572
$367$	1.06393e14	0.834161	0.417081	−	0.908869i	$-0.363053\pi$
$367$	1.06393e14	0.834161	0.417081	+	0.908869i	$0.363053\pi$
$368$	4.99713e13	0.385973
$369$	7.12618e13	0.542266
$370$	−5.02252e13	−0.376541
$371$	1.06993e13	0.0790315
$372$	−2.41426e13	−0.175711
$373$	−2.33613e14	−1.67532	−0.837661	−	0.546191i	$-0.816077\pi$
$373$	−2.33613e14	−1.67532	−0.837661	+	0.546191i	$0.816077\pi$
$374$	−2.31887e14	−1.63864
$375$	−8.69242e13	−0.605298
$376$	−1.88815e14	−1.29570
$377$	−3.74733e13	−0.253422
$378$	9.97715e12	0.0664969
$379$	−4.56431e13	−0.299819	−0.149910	−	0.988700i	$-0.547898\pi$
$379$	−4.56431e13	−0.299819	−0.149910	+	0.988700i	$0.547898\pi$
$380$	−1.17708e13	−0.0762072
$381$	7.86207e13	0.501706
$382$	2.09551e14	1.31808
$383$	1.47555e13	0.0914872	0.0457436	−	0.998953i	$-0.485434\pi$
$383$	1.47555e13	0.0914872	0.0457436	+	0.998953i	$0.485434\pi$
$384$	6.47965e13	0.396032
$385$	−7.11264e13	−0.428545
$386$	−7.47364e13	−0.443917
$387$	2.60861e12	0.0152756
$388$	−4.42673e13	−0.255569
$389$	−1.10147e14	−0.626977	−0.313489	−	0.949592i	$-0.601498\pi$
$389$	−1.10147e14	−0.626977	−0.313489	+	0.949592i	$0.601498\pi$
$390$	1.78591e13	0.100231
$391$	−9.33528e13	−0.516601
$392$	2.78652e13	0.152051
$393$	1.34085e13	0.0721477
$394$	8.20026e13	0.435109
$395$	1.18519e13	0.0620159
$396$	−1.75715e13	−0.0906743
$397$	−2.07100e14	−1.05398	−0.526989	−	0.849872i	$-0.676679\pi$
$397$	−2.07100e14	−1.05398	−0.526989	+	0.849872i	$0.676679\pi$
$398$	2.91271e13	0.146198
$399$	2.98656e13	0.147849
$400$	8.79795e13	0.429587
$401$	1.31143e14	0.631615	0.315808	−	0.948823i	$-0.397725\pi$
$401$	1.31143e14	0.631615	0.315808	+	0.948823i	$0.397725\pi$
$402$	−1.38101e14	−0.656076
$403$	1.09648e14	0.513836
$404$	6.38645e13	0.295231
$405$	−1.66826e13	−0.0760783
$406$	−7.01767e13	−0.315718
$407$	−2.24433e14	−0.996135
$408$	−1.51903e14	−0.665173
$409$	1.18023e14	0.509902	0.254951	−	0.966954i	$-0.417941\pi$
$409$	1.18023e14	0.509902	0.254951	+	0.966954i	$0.417941\pi$
$410$	2.38880e14	1.01829
$411$	1.33111e14	0.559866
$412$	3.54443e13	0.147100
$413$	8.12539e13	0.332751
$414$	3.59882e13	0.145431
$415$	2.87958e14	1.14832
$416$	2.29060e13	0.0901438
$417$	−9.71415e13	−0.377274
$418$	2.67592e14	1.02566
$419$	1.67909e14	0.635179	0.317590	−	0.948228i	$-0.397127\pi$
$419$	1.67909e14	0.635179	0.317590	+	0.948228i	$0.397127\pi$
$420$	−6.57397e12	−0.0245447
$421$	4.39224e14	1.61858	0.809290	−	0.587409i	$-0.199852\pi$
$421$	4.39224e14	1.61858	0.809290	+	0.587409i	$0.199852\pi$
$422$	2.86590e14	1.04242
$423$	−1.13023e14	−0.405784
$424$	6.27984e13	0.222554
$425$	−1.64357e14	−0.574975
$426$	−4.34655e13	−0.150104
$427$	2.11257e14	0.720206
$428$	−6.88130e12	−0.0231595
$429$	7.98041e13	0.265161
$430$	8.74445e12	0.0286851
$431$	2.26409e13	0.0733277	0.0366639	−	0.999328i	$-0.488327\pi$
$431$	2.26409e13	0.0733277	0.0366639	+	0.999328i	$0.488327\pi$
$432$	4.86731e13	0.155643
$433$	3.58830e14	1.13294	0.566468	−	0.824084i	$-0.308310\pi$
$433$	3.58830e14	1.13294	0.566468	+	0.824084i	$0.308310\pi$
$434$	2.05340e14	0.640147
$435$	1.17341e14	0.361210
$436$	6.55198e13	0.199157
$437$	1.07727e14	0.323353
$438$	−1.27966e14	−0.379305
$439$	2.85693e14	0.836267	0.418134	−	0.908386i	$-0.362684\pi$
$439$	2.85693e14	0.836267	0.418134	+	0.908386i	$0.362684\pi$
$440$	−4.17467e14	−1.20679
$441$	1.66799e13	0.0476190
$442$	9.73401e13	0.274454
$443$	−6.68680e14	−1.86208	−0.931039	−	0.364920i	$-0.881096\pi$
$443$	−6.68680e14	−1.86208	−0.931039	+	0.364920i	$0.881096\pi$
$444$	−2.07436e13	−0.0570530
$445$	−3.07647e14	−0.835742
$446$	4.38259e14	1.17595
$447$	−7.72152e12	−0.0204650
$448$	1.59655e14	0.417979
$449$	−6.68043e13	−0.172762	−0.0863812	−	0.996262i	$-0.527530\pi$
$449$	−6.68043e13	−0.172762	−0.0863812	+	0.996262i	$0.527530\pi$
$450$	6.33608e13	0.161865
$451$	1.06745e15	2.69386
$452$	−1.23917e14	−0.308937
$453$	−1.80403e14	−0.444329
$454$	−3.94114e14	−0.958992
$455$	2.98570e13	0.0717766
$456$	1.75292e14	0.416347
$457$	1.13591e14	0.266567	0.133283	−	0.991078i	$-0.457448\pi$
$457$	1.13591e14	0.266567	0.133283	+	0.991078i	$0.457448\pi$
$458$	−6.02221e13	−0.139635
$459$	−9.09277e13	−0.208318
$460$	−2.37127e13	−0.0536801
$461$	−4.77652e14	−1.06846	−0.534228	−	0.845341i	$-0.679398\pi$
$461$	−4.77652e14	−1.06846	−0.534228	+	0.845341i	$0.679398\pi$
$462$	1.49450e14	0.330343
$463$	7.81818e14	1.70770	0.853848	−	0.520523i	$-0.174263\pi$
$463$	7.81818e14	1.70770	0.853848	+	0.520523i	$0.174263\pi$
$464$	−3.42354e14	−0.738970
$465$	−3.43345e14	−0.732385
$466$	−1.29828e14	−0.273681
$467$	2.44010e14	0.508353	0.254177	−	0.967158i	$-0.418196\pi$
$467$	2.44010e14	0.508353	0.254177	+	0.967158i	$0.418196\pi$
$468$	7.37602e12	0.0151869
$469$	−2.30879e14	−0.469822
$470$	−3.78870e14	−0.761995
$471$	−1.11825e14	−0.222291
$472$	4.76909e14	0.937033
$473$	3.90750e13	0.0758861
$474$	−2.49030e13	−0.0478048
$475$	1.89664e14	0.359890
$476$	−3.58311e13	−0.0672082
$477$	3.75906e13	0.0696992
$478$	1.80461e14	0.330773
$479$	−4.45108e14	−0.806530	−0.403265	−	0.915083i	$-0.632125\pi$
$479$	−4.45108e14	−0.806530	−0.403265	+	0.915083i	$0.632125\pi$
$480$	−7.17261e13	−0.128484
$481$	9.42111e13	0.166842
$482$	−9.39129e13	−0.164425
$483$	6.01654e13	0.104145
$484$	−1.67220e14	−0.286179
$485$	−6.29548e14	−1.06524
$486$	3.50533e13	0.0586448
$487$	2.15894e13	0.0357134	0.0178567	−	0.999841i	$-0.494316\pi$
$487$	2.15894e13	0.0357134	0.0178567	+	0.999841i	$0.494316\pi$
$488$	1.23994e15	2.02812
$489$	−1.18018e14	−0.190876
$490$	5.59135e13	0.0894207
$491$	5.13313e14	0.811772	0.405886	−	0.913924i	$-0.366963\pi$
$491$	5.13313e14	0.811772	0.405886	+	0.913924i	$0.366963\pi$
$492$	9.86606e13	0.154289
$493$	6.39562e14	0.989065
$494$	−1.12328e14	−0.171787
$495$	−2.49893e14	−0.377942
$496$	1.00174e15	1.49833
$497$	−7.26661e13	−0.107491
$498$	−6.05053e14	−0.885182
$499$	−6.42067e13	−0.0929025	−0.0464512	−	0.998921i	$-0.514791\pi$
$499$	−6.42067e13	−0.0929025	−0.0464512	+	0.998921i	$0.514791\pi$
$500$	−1.20345e14	−0.172224
$501$	−2.54473e14	−0.360193
$502$	−2.71187e13	−0.0379662
$503$	−3.93209e14	−0.544502	−0.272251	−	0.962226i	$-0.587768\pi$
$503$	−3.93209e14	−0.544502	−0.272251	+	0.962226i	$0.587768\pi$
$504$	9.79004e13	0.134096
$505$	9.08249e14	1.23056
$506$	5.39076e14	0.722473
$507$	−3.34996e13	−0.0444116
$508$	1.08849e14	0.142749
$509$	−1.94250e14	−0.252008	−0.126004	−	0.992030i	$-0.540215\pi$
$509$	−1.94250e14	−0.252008	−0.126004	+	0.992030i	$0.540215\pi$
$510$	−3.04803e14	−0.391186
$511$	−2.13935e14	−0.271624
$512$	8.94570e14	1.12365
$513$	1.04928e14	0.130391
$514$	−6.33938e14	−0.779381
$515$	5.04071e14	0.613130
$516$	3.61157e12	0.00434633
$517$	−1.69300e15	−2.01585
$518$	1.76430e14	0.207854
$519$	−4.19619e14	−0.489141
$520$	1.75242e14	0.202124
$521$	−2.73245e14	−0.311850	−0.155925	−	0.987769i	$-0.549836\pi$
$521$	−2.73245e14	−0.311850	−0.155925	+	0.987769i	$0.549836\pi$
$522$	−2.46556e14	−0.278437
$523$	1.52484e15	1.70398	0.851992	−	0.523555i	$-0.175394\pi$
$523$	1.52484e15	1.70398	0.851992	+	0.523555i	$0.175394\pi$
$524$	1.85639e13	0.0205280
$525$	1.05927e14	0.115913
$526$	8.22362e14	0.890516
$527$	−1.87138e15	−2.00542
$528$	7.29086e14	0.773201
$529$	−7.35790e14	−0.772231
$530$	1.26009e14	0.130884
$531$	2.85474e14	0.293459
$532$	4.13483e13	0.0420672
$533$	−4.48086e14	−0.451192
$534$	6.46424e14	0.644229
$535$	−9.78624e13	−0.0965317
$536$	−1.35511e15	−1.32303
$537$	8.75585e13	0.0846135
$538$	1.02506e15	0.980500
$539$	2.49852e14	0.236562
$540$	−2.30967e13	−0.0216464
$541$	−4.85484e14	−0.450391	−0.225196	−	0.974314i	$-0.572302\pi$
$541$	−4.85484e14	−0.450391	−0.225196	+	0.974314i	$0.572302\pi$
$542$	1.61366e14	0.148189
$543$	−1.05983e15	−0.963465
$544$	−3.90940e14	−0.351816
$545$	9.31790e14	0.830113
$546$	−6.27351e13	−0.0553288
$547$	−8.96399e14	−0.782656	−0.391328	−	0.920251i	$-0.627984\pi$
$547$	−8.96399e14	−0.782656	−0.391328	+	0.920251i	$0.627984\pi$
$548$	1.84290e14	0.159297
$549$	7.42220e14	0.635162
$550$	9.49097e14	0.804110
$551$	−7.38039e14	−0.619079
$552$	3.53133e14	0.293274
$553$	−4.16331e13	−0.0342334
$554$	9.60020e14	0.781586
$555$	−2.95006e14	−0.237804
$556$	−1.34491e14	−0.107345
$557$	−4.11768e14	−0.325424	−0.162712	−	0.986674i	$-0.552024\pi$
$557$	−4.11768e14	−0.325424	−0.162712	+	0.986674i	$0.552024\pi$
$558$	7.21432e14	0.564557
$559$	−1.64026e13	−0.0127101
$560$	2.72772e14	0.209298
$561$	−1.36203e15	−1.03488
$562$	1.92913e14	0.145148
$563$	−1.33565e14	−0.0995166	−0.0497583	−	0.998761i	$-0.515845\pi$
$563$	−1.33565e14	−0.0995166	−0.0497583	+	0.998761i	$0.515845\pi$
$564$	−1.56478e14	−0.115456
$565$	−1.76229e15	−1.28769
$566$	3.50154e14	0.253378
$567$	5.86024e13	0.0419961
$568$	−4.26504e14	−0.302696
$569$	1.71605e15	1.20618	0.603092	−	0.797672i	$-0.293935\pi$
$569$	1.71605e15	1.20618	0.603092	+	0.797672i	$0.293935\pi$
$570$	3.51736e14	0.244853
$571$	1.39135e15	0.959266	0.479633	−	0.877469i	$-0.340770\pi$
$571$	1.39135e15	0.959266	0.479633	+	0.877469i	$0.340770\pi$
$572$	1.10487e14	0.0754456
$573$	1.23083e15	0.832429
$574$	−8.39136e14	−0.562104
$575$	3.82086e14	0.253506
$576$	5.60926e14	0.368623
$577$	−1.34680e15	−0.876669	−0.438335	−	0.898812i	$-0.644431\pi$
$577$	−1.34680e15	−0.876669	−0.438335	+	0.898812i	$0.644431\pi$
$578$	−2.43449e14	−0.156966
$579$	−4.38976e14	−0.280355
$580$	1.62456e14	0.102774
$581$	−1.01153e15	−0.633886
$582$	1.32280e15	0.821140
$583$	5.63078e14	0.346251
$584$	−1.25567e15	−0.764898
$585$	1.04898e14	0.0633010
$586$	−2.81051e15	−1.68015
$587$	1.33148e15	0.788543	0.394272	−	0.918994i	$-0.370997\pi$
$587$	1.33148e15	0.788543	0.394272	+	0.918994i	$0.370997\pi$
$588$	2.30930e13	0.0135489
$589$	2.15953e15	1.25524
$590$	9.56952e14	0.551067
$591$	4.81655e14	0.274793
$592$	8.60708e14	0.486504
$593$	−1.37881e15	−0.772151	−0.386075	−	0.922467i	$-0.626170\pi$
$593$	−1.37881e15	−0.772151	−0.386075	+	0.922467i	$0.626170\pi$
$594$	5.25072e14	0.291335
$595$	−5.09573e14	−0.280132
$596$	−1.06903e13	−0.00582284
$597$	1.71083e14	0.0923309
$598$	−2.26289e14	−0.121006
$599$	1.75769e15	0.931310	0.465655	−	0.884966i	$-0.345819\pi$
$599$	1.75769e15	0.931310	0.465655	+	0.884966i	$0.345819\pi$
$600$	6.21726e14	0.326413
$601$	1.07241e15	0.557891	0.278946	−	0.960307i	$-0.410015\pi$
$601$	1.07241e15	0.557891	0.278946	+	0.960307i	$0.410015\pi$
$602$	−3.07174e13	−0.0158345
$603$	−8.11159e14	−0.414344
$604$	−2.49765e14	−0.126424
$605$	−2.37812e15	−1.19283
$606$	−1.90840e15	−0.948573
$607$	2.49072e15	1.22684	0.613419	−	0.789757i	$-0.289794\pi$
$607$	2.49072e15	1.22684	0.613419	+	0.789757i	$0.289794\pi$
$608$	4.51135e14	0.220210
$609$	−4.12194e14	−0.199392
$610$	2.48803e15	1.19273
$611$	7.10675e14	0.337632
$612$	−1.25888e14	−0.0592721
$613$	3.02850e15	1.41317	0.706586	−	0.707627i	$-0.250234\pi$
$613$	3.02850e15	1.41317	0.706586	+	0.707627i	$0.250234\pi$
$614$	2.82503e15	1.30646
$615$	1.40310e15	0.643097
$616$	1.46647e15	0.666163
$617$	−3.64507e15	−1.64111	−0.820555	−	0.571568i	$-0.806335\pi$
$617$	−3.64507e15	−1.64111	−0.820555	+	0.571568i	$0.806335\pi$
$618$	−1.05915e15	−0.472629
$619$	−2.76976e15	−1.22502	−0.612511	−	0.790462i	$-0.709840\pi$
$619$	−2.76976e15	−1.22502	−0.612511	+	0.790462i	$0.709840\pi$
$620$	−4.75354e14	−0.208383
$621$	2.11382e14	0.0918470
$622$	−3.74379e15	−1.61237
$623$	1.08070e15	0.461338
$624$	−3.06051e14	−0.129503
$625$	−4.45056e14	−0.186670
$626$	3.98366e15	1.65624
$627$	1.57175e15	0.647756
$628$	−1.54819e14	−0.0632479
$629$	−1.60791e15	−0.651155
$630$	1.96444e14	0.0788616
$631$	9.80104e14	0.390041	0.195021	−	0.980799i	$-0.437523\pi$
$631$	9.80104e14	0.390041	0.195021	+	0.980799i	$0.437523\pi$
$632$	−2.44360e14	−0.0964021
$633$	1.68333e15	0.658338
$634$	2.09008e15	0.810348
$635$	1.54799e15	0.594995
$636$	5.20434e13	0.0198313
$637$	−1.04881e14	−0.0396214
$638$	−3.69322e15	−1.38322
$639$	−2.55302e14	−0.0947980
$640$	1.27580e15	0.469671
$641$	−3.08449e15	−1.12581	−0.562904	−	0.826522i	$-0.690316\pi$
$641$	−3.08449e15	−1.12581	−0.562904	+	0.826522i	$0.690316\pi$
$642$	2.05627e14	0.0744112
$643$	−1.29084e15	−0.463138	−0.231569	−	0.972818i	$-0.574386\pi$
$643$	−1.29084e15	−0.463138	−0.231569	+	0.972818i	$0.574386\pi$
$644$	8.32977e13	0.0296320
$645$	5.13619e13	0.0181160
$646$	1.91712e15	0.670456
$647$	−2.69945e15	−0.936055	−0.468027	−	0.883714i	$-0.655035\pi$
$647$	−2.69945e15	−0.936055	−0.468027	+	0.883714i	$0.655035\pi$
$648$	3.43959e14	0.118262
$649$	4.27618e15	1.45784
$650$	−3.98405e14	−0.134680
$651$	1.20610e15	0.404284
$652$	−1.63394e14	−0.0543094
$653$	−3.57974e15	−1.17986	−0.589928	−	0.807456i	$-0.700844\pi$
$653$	−3.57974e15	−1.17986	−0.589928	+	0.807456i	$0.700844\pi$
$654$	−1.95787e15	−0.639890
$655$	2.64006e14	0.0855632
$656$	−4.09369e15	−1.31566
$657$	−7.51631e14	−0.239549
$658$	1.33089e15	0.420629
$659$	−4.16183e15	−1.30441	−0.652205	−	0.758043i	$-0.726156\pi$
$659$	−4.16183e15	−1.30441	−0.652205	+	0.758043i	$0.726156\pi$
$660$	−3.45971e14	−0.107535
$661$	−1.39894e15	−0.431211	−0.215606	−	0.976481i	$-0.569173\pi$
$661$	−1.39894e15	−0.431211	−0.215606	+	0.976481i	$0.569173\pi$
$662$	−2.97173e14	−0.0908427
$663$	5.71742e14	0.173331
$664$	−5.93706e15	−1.78504
$665$	5.88035e14	0.175341
$666$	6.19863e14	0.183310
$667$	−1.48681e15	−0.436077
$668$	−3.52313e14	−0.102485
$669$	2.57418e15	0.742669
$670$	−2.71913e15	−0.778069
$671$	1.11179e16	3.15535
$672$	2.51958e14	0.0709247
$673$	1.50152e15	0.419226	0.209613	−	0.977784i	$-0.432780\pi$
$673$	1.50152e15	0.419226	0.209613	+	0.977784i	$0.432780\pi$
$674$	−1.84861e14	−0.0511935
$675$	3.72160e14	0.102225
$676$	−4.63795e13	−0.0126363
$677$	1.21220e15	0.327595	0.163797	−	0.986494i	$-0.447626\pi$
$677$	1.21220e15	0.327595	0.163797	+	0.986494i	$0.447626\pi$
$678$	3.70290e15	0.992610
$679$	2.21147e15	0.588026
$680$	−2.99087e15	−0.788858
$681$	−2.31489e15	−0.605650
$682$	1.08065e16	2.80460
$683$	−2.40913e15	−0.620221	−0.310110	−	0.950701i	$-0.600366\pi$
$683$	−2.40913e15	−0.620221	−0.310110	+	0.950701i	$0.600366\pi$
$684$	1.45271e14	0.0370998
$685$	2.62088e15	0.663970
$686$	−1.96412e14	−0.0493612
$687$	−3.53724e14	−0.0881865
$688$	−1.49854e14	−0.0370622
$689$	−2.36365e14	−0.0579933
$690$	7.08586e14	0.172474
$691$	−5.51584e15	−1.33193	−0.665966	−	0.745982i	$-0.731980\pi$
$691$	−5.51584e15	−1.33193	−0.665966	+	0.745982i	$0.731980\pi$
$692$	−5.80953e14	−0.139174
$693$	8.77819e14	0.208628
$694$	−2.80245e15	−0.660786
$695$	−1.91266e15	−0.447426
$696$	−2.41932e15	−0.561491
$697$	7.64754e15	1.76093
$698$	3.43448e14	0.0784614
$699$	−7.62564e14	−0.172843
$700$	1.46654e14	0.0329803
$701$	4.04414e15	0.902355	0.451178	−	0.892434i	$-0.351004\pi$
$701$	4.04414e15	0.902355	0.451178	+	0.892434i	$0.351004\pi$
$702$	−2.20411e14	−0.0487954
$703$	1.85549e15	0.407573
$704$	8.40225e15	1.83124
$705$	−2.22535e15	−0.481237
$706$	−8.08890e15	−1.73566
$707$	−3.19048e15	−0.679281
$708$	3.95233e14	0.0834969
$709$	3.08515e15	0.646728	0.323364	−	0.946275i	$-0.395186\pi$
$709$	3.08515e15	0.646728	0.323364	+	0.946275i	$0.395186\pi$
$710$	−8.55810e14	−0.178015
$711$	−1.46272e14	−0.0301910
$712$	6.34301e15	1.29914
$713$	4.35046e15	0.884185
$714$	1.07071e15	0.215939
$715$	1.57129e15	0.314466
$716$	1.21223e14	0.0240748
$717$	1.05997e15	0.208899
$718$	7.04313e15	1.37747
$719$	−6.93720e15	−1.34640	−0.673201	−	0.739459i	$-0.735081\pi$
$719$	−6.93720e15	−1.34640	−0.673201	+	0.739459i	$0.735081\pi$
$720$	9.58344e14	0.184583
$721$	−1.77069e15	−0.338454
$722$	2.60703e15	0.494528
$723$	−5.51613e14	−0.103842
$724$	−1.46731e15	−0.274132
$725$	−2.61768e15	−0.485352
$726$	4.99688e15	0.919491
$727$	−7.17170e15	−1.30973	−0.654866	−	0.755745i	$-0.727275\pi$
$727$	−7.17170e15	−1.30973	−0.654866	+	0.755745i	$0.727275\pi$
$728$	−6.15586e14	−0.111575
$729$	2.05891e14	0.0370370
$730$	−2.51958e15	−0.449834
$731$	2.79946e14	0.0496053
$732$	1.02759e15	0.180721
$733$	−2.16288e14	−0.0377539	−0.0188769	−	0.999822i	$-0.506009\pi$
$733$	−2.16288e14	−0.0377539	−0.0188769	+	0.999822i	$0.506009\pi$
$734$	−4.40160e15	−0.762575
$735$	3.28417e14	0.0564735
$736$	9.08829e14	0.155115
$737$	−1.21505e16	−2.05837
$738$	−2.94818e15	−0.495729
$739$	9.19704e14	0.153498	0.0767492	−	0.997050i	$-0.475546\pi$
$739$	9.19704e14	0.153498	0.0767492	+	0.997050i	$0.475546\pi$
$740$	−4.08429e14	−0.0676616
$741$	−6.59777e14	−0.108492
$742$	−4.42644e14	−0.0722492
$743$	−7.53135e15	−1.22021	−0.610105	−	0.792321i	$-0.708873\pi$
$743$	−7.53135e15	−1.22021	−0.610105	+	0.792321i	$0.708873\pi$
$744$	7.07903e15	1.13847
$745$	−1.52032e14	−0.0242703
$746$	9.66483e15	1.53155
$747$	−3.55388e15	−0.559035
$748$	−1.88570e15	−0.294451
$749$	3.43770e14	0.0532865
$750$	3.59615e15	0.553352
$751$	−1.09968e16	−1.67976	−0.839879	−	0.542774i	$-0.817374\pi$
$751$	−1.09968e16	−1.67976	−0.839879	+	0.542774i	$0.817374\pi$
$752$	6.49269e15	0.984524
$753$	−1.59286e14	−0.0239775
$754$	1.55031e15	0.231674
$755$	−3.55203e15	−0.526949
$756$	8.11338e13	0.0119490
$757$	−8.13398e15	−1.18926	−0.594629	−	0.804000i	$-0.702701\pi$
$757$	−8.13398e15	−1.18926	−0.594629	+	0.804000i	$0.702701\pi$
$758$	1.88831e15	0.274089
$759$	3.16635e15	0.456277
$760$	3.45139e15	0.493765
$761$	1.85156e15	0.262980	0.131490	−	0.991317i	$-0.458024\pi$
$761$	1.85156e15	0.262980	0.131490	+	0.991317i	$0.458024\pi$
$762$	−3.25263e15	−0.458651
$763$	−3.27318e15	−0.458231
$764$	1.70406e15	0.236849
$765$	−1.79031e15	−0.247053
$766$	−6.10451e14	−0.0836359
$767$	−1.79503e15	−0.244172
$768$	2.04677e15	0.276429
$769$	5.75342e15	0.771492	0.385746	−	0.922605i	$-0.373944\pi$
$769$	5.75342e15	0.771492	0.385746	+	0.922605i	$0.373944\pi$
$770$	2.94258e15	0.391768
$771$	−3.72354e15	−0.492217
$772$	−6.07753e14	−0.0797687
$773$	−1.09432e16	−1.42613	−0.713064	−	0.701099i	$-0.752693\pi$
$773$	−1.09432e16	−1.42613	−0.713064	+	0.701099i	$0.752693\pi$
$774$	−1.07921e14	−0.0139647
$775$	7.65943e15	0.984095
$776$	1.29799e16	1.65589
$777$	1.03629e15	0.131270
$778$	4.55693e15	0.573171
$779$	−8.82508e15	−1.10221
$780$	1.45229e14	0.0180109
$781$	−3.82423e15	−0.470937
$782$	3.86211e15	0.472267
$783$	−1.44819e15	−0.175847
$784$	−9.58188e14	−0.115535
$785$	−2.20176e15	−0.263625
$786$	−5.54727e14	−0.0659561
$787$	−6.29593e13	−0.00743360	−0.00371680	−	0.999993i	$-0.501183\pi$
$787$	−6.29593e13	−0.00743360	−0.00371680	+	0.999993i	$0.501183\pi$
$788$	6.66842e14	0.0781860
$789$	4.83028e15	0.562404
$790$	−4.90326e14	−0.0566938
$791$	6.19054e15	0.710817
$792$	5.15225e15	0.587500
$793$	−4.66699e15	−0.528487
$794$	8.56795e15	0.963528
$795$	7.40136e14	0.0826594
$796$	2.36860e14	0.0262706
$797$	1.66423e16	1.83312	0.916561	−	0.399895i	$-0.130953\pi$
$797$	1.66423e16	1.83312	0.916561	+	0.399895i	$0.130953\pi$
$798$	−1.23557e15	−0.135161
$799$	−1.21292e16	−1.31772
$800$	1.60008e15	0.172643
$801$	3.79687e15	0.406862
$802$	−5.42555e15	−0.577411
$803$	−1.12589e16	−1.19003
$804$	−1.12303e15	−0.117892
$805$	1.18462e15	0.123510
$806$	−4.53628e15	−0.469740
$807$	6.02086e15	0.619233
$808$	−1.87261e16	−1.91287
$809$	−4.83065e15	−0.490104	−0.245052	−	0.969510i	$-0.578805\pi$
$809$	−4.83065e15	−0.490104	−0.245052	+	0.969510i	$0.578805\pi$
$810$	6.90178e14	0.0695494
$811$	9.33002e15	0.933830	0.466915	−	0.884302i	$-0.345365\pi$
$811$	9.33002e15	0.933830	0.466915	+	0.884302i	$0.345365\pi$
$812$	−5.70675e14	−0.0567323
$813$	9.47808e14	0.0935884
$814$	9.28507e15	0.910648
$815$	−2.32371e15	−0.226368
$816$	5.22341e15	0.505427
$817$	−3.23051e14	−0.0310491
$818$	−4.88273e15	−0.466143
$819$	−3.68485e14	−0.0349428
$820$	1.94257e15	0.182978
$821$	1.15132e16	1.07723	0.538617	−	0.842551i	$-0.318947\pi$
$821$	1.15132e16	1.07723	0.538617	+	0.842551i	$0.318947\pi$
$822$	−5.50696e15	−0.511819
$823$	1.06942e16	0.987301	0.493651	−	0.869660i	$-0.335662\pi$
$823$	1.06942e16	0.987301	0.493651	+	0.869660i	$0.335662\pi$
$824$	−1.03929e16	−0.953094
$825$	5.57467e15	0.507835
$826$	−3.36157e15	−0.304195
$827$	−1.42416e16	−1.28020	−0.640099	−	0.768292i	$-0.721107\pi$
$827$	−1.42416e16	−1.28020	−0.640099	+	0.768292i	$0.721107\pi$
$828$	2.92655e14	0.0261330
$829$	−1.56225e16	−1.38580	−0.692899	−	0.721034i	$-0.743667\pi$
$829$	−1.56225e16	−1.38580	−0.692899	+	0.721034i	$0.743667\pi$
$830$	−1.19131e16	−1.04978
$831$	5.63883e15	0.493610
$832$	−3.52704e15	−0.306713
$833$	1.79002e15	0.154636
$834$	4.01886e15	0.344897
$835$	−5.01043e15	−0.427169
$836$	2.17605e15	0.184304
$837$	4.23745e15	0.356545
$838$	−6.94658e15	−0.580669
$839$	−1.92662e16	−1.59995	−0.799975	−	0.600033i	$-0.795154\pi$
$839$	−1.92662e16	−1.59995	−0.799975	+	0.600033i	$0.795154\pi$
$840$	1.92760e15	0.159031
$841$	−2.01434e15	−0.165103
$842$	−1.81712e16	−1.47968
$843$	1.13310e15	0.0916679
$844$	2.33054e15	0.187315
$845$	−6.59587e14	−0.0526696
$846$	4.67589e15	0.370960
$847$	8.35382e15	0.658455
$848$	−2.15942e15	−0.169106
$849$	2.05668e15	0.160020
$850$	6.79964e15	0.525632
$851$	3.73797e15	0.287093
$852$	−3.53460e14	−0.0269726
$853$	−2.58227e16	−1.95786	−0.978929	−	0.204200i	$-0.934541\pi$
$853$	−2.58227e16	−1.95786	−0.978929	+	0.204200i	$0.934541\pi$
$854$	−8.73992e15	−0.658399
$855$	2.06598e15	0.154636
$856$	2.01771e15	0.150056
$857$	−1.21194e16	−0.895542	−0.447771	−	0.894148i	$-0.647782\pi$
$857$	−1.21194e16	−0.895542	−0.447771	+	0.894148i	$0.647782\pi$
$858$	−3.30159e15	−0.242406
$859$	−1.96206e16	−1.43137	−0.715683	−	0.698426i	$-0.753884\pi$
$859$	−1.96206e16	−1.43137	−0.715683	+	0.698426i	$0.753884\pi$
$860$	7.11096e13	0.00515450
$861$	−4.92880e15	−0.354996
$862$	−9.36679e14	−0.0670349
$863$	−1.94564e16	−1.38357	−0.691787	−	0.722102i	$-0.743176\pi$
$863$	−1.94564e16	−1.38357	−0.691787	+	0.722102i	$0.743176\pi$
$864$	8.85220e14	0.0625497
$865$	−8.26204e15	−0.580094
$866$	−1.48452e16	−1.03571
$867$	−1.42993e15	−0.0991314
$868$	1.66982e15	0.115030
$869$	−2.19104e15	−0.149983
$870$	−4.85454e15	−0.330211
$871$	5.10047e15	0.344755
$872$	−1.92115e16	−1.29039
$873$	7.76967e15	0.518590
$874$	−4.45679e15	−0.295603
$875$	6.01208e15	0.396260
$876$	−1.04062e15	−0.0681583
$877$	−2.63035e16	−1.71205	−0.856024	−	0.516937i	$-0.827072\pi$
$877$	−2.63035e16	−1.71205	−0.856024	+	0.516937i	$0.827072\pi$
$878$	−1.18195e16	−0.764500
$879$	−1.65080e16	−1.06110
$880$	1.43553e16	0.916973
$881$	1.47217e16	0.934525	0.467262	−	0.884119i	$-0.345240\pi$
$881$	1.47217e16	0.934525	0.467262	+	0.884119i	$0.345240\pi$
$882$	−6.90066e14	−0.0435325
$883$	−2.32000e16	−1.45447	−0.727234	−	0.686389i	$-0.759195\pi$
$883$	−2.32000e16	−1.45447	−0.727234	+	0.686389i	$0.759195\pi$
$884$	7.91566e14	0.0493173
$885$	5.62081e15	0.348025
$886$	2.76641e16	1.70228
$887$	2.26901e16	1.38758	0.693789	−	0.720178i	$-0.255940\pi$
$887$	2.26901e16	1.38758	0.693789	+	0.720178i	$0.255940\pi$
$888$	6.08238e15	0.369660
$889$	−5.43777e15	−0.328444
$890$	1.27277e16	0.764020
$891$	3.08409e15	0.183992
$892$	3.56390e15	0.211310
$893$	1.39968e16	0.824794
$894$	3.19448e14	0.0187087
$895$	1.72397e15	0.100347
$896$	−4.48162e15	−0.259264
$897$	−1.32915e15	−0.0764213
$898$	2.76377e15	0.157936
$899$	−2.98051e16	−1.69283
$900$	5.15248e14	0.0290859
$901$	4.03407e15	0.226338
$902$	−4.41615e16	−2.46268
$903$	−1.80423e14	−0.0100002
$904$	3.63346e16	2.00168
$905$	−2.08673e16	−1.14262
$906$	7.46349e15	0.406197
$907$	1.59637e16	0.863564	0.431782	−	0.901978i	$-0.357885\pi$
$907$	1.59637e16	0.863564	0.431782	+	0.901978i	$0.357885\pi$
$908$	−3.20492e15	−0.172324
$909$	−1.12093e16	−0.599070
$910$	−1.23522e15	−0.0656169
$911$	3.71587e16	1.96205	0.981023	−	0.193891i	$-0.0621107\pi$
$911$	3.71587e16	1.96205	0.981023	+	0.193891i	$0.0621107\pi$
$912$	−6.02769e15	−0.316358
$913$	−5.32344e16	−2.77717
$914$	−4.69940e15	−0.243690
$915$	1.46139e16	0.753267
$916$	−4.89724e14	−0.0250915
$917$	−9.27397e14	−0.0472318
$918$	3.76178e15	0.190440
$919$	−2.44138e16	−1.22857	−0.614286	−	0.789083i	$-0.710556\pi$
$919$	−2.44138e16	−1.22857	−0.614286	+	0.789083i	$0.710556\pi$
$920$	6.95297e15	0.347806
$921$	1.65933e16	0.825094
$922$	1.97610e16	0.976763
$923$	1.60531e15	0.0788767
$924$	1.21532e15	0.0593602
$925$	6.58107e15	0.319534
$926$	−3.23447e16	−1.56114
$927$	−6.22108e15	−0.298488
$928$	−6.22641e15	−0.296978
$929$	−3.17884e16	−1.50724	−0.753621	−	0.657309i	$-0.771694\pi$
$929$	−3.17884e16	−1.50724	−0.753621	+	0.657309i	$0.771694\pi$
$930$	1.42046e16	0.669533
$931$	−2.06564e15	−0.0967902
$932$	−1.05576e15	−0.0491785
$933$	−2.19898e16	−1.01829
$934$	−1.00950e16	−0.464727
$935$	−2.68175e16	−1.22731
$936$	−2.16277e15	−0.0983997
$937$	−2.07294e16	−0.937602	−0.468801	−	0.883304i	$-0.655314\pi$
$937$	−2.07294e16	−0.937602	−0.468801	+	0.883304i	$0.655314\pi$
$938$	9.55171e15	0.429502
$939$	2.33987e16	1.04600
$940$	−3.08096e15	−0.136925
$941$	−1.43488e16	−0.633977	−0.316988	−	0.948429i	$-0.602672\pi$
$941$	−1.43488e16	−0.633977	−0.316988	+	0.948429i	$0.602672\pi$
$942$	4.62632e15	0.203215
$943$	−1.77785e16	−0.776391
$944$	−1.63993e16	−0.711998
$945$	1.15385e15	0.0498050
$946$	−1.61658e15	−0.0693737
$947$	2.54468e15	0.108569	0.0542847	−	0.998525i	$-0.482712\pi$
$947$	2.54468e15	0.108569	0.0542847	+	0.998525i	$0.482712\pi$
$948$	−2.02511e14	−0.00859017
$949$	4.72617e15	0.199317
$950$	−7.84662e15	−0.329005
$951$	1.22764e16	0.511774
$952$	1.05063e16	0.435458
$953$	3.97221e16	1.63690	0.818449	−	0.574579i	$-0.194834\pi$
$953$	3.97221e16	1.63690	0.818449	+	0.574579i	$0.194834\pi$
$954$	−1.55517e15	−0.0637178
$955$	2.42343e16	0.987215
$956$	1.46750e15	0.0594374
$957$	−2.16927e16	−0.873571
$958$	1.84146e16	0.737315
$959$	−9.20657e15	−0.366518
$960$	1.10443e16	0.437166
$961$	6.18025e16	2.43236
$962$	−3.89762e15	−0.152523
$963$	1.20779e15	0.0469943
$964$	−7.63697e14	−0.0295459
$965$	−8.64317e15	−0.332486
$966$	−2.48911e15	−0.0952072
$967$	3.01593e16	1.14703	0.573516	−	0.819194i	$-0.305579\pi$
$967$	3.01593e16	1.14703	0.573516	+	0.819194i	$0.305579\pi$
$968$	4.90317e16	1.85422
$969$	1.12605e16	0.423426
$970$	2.60451e16	0.973826
$971$	1.45389e16	0.540536	0.270268	−	0.962785i	$-0.412888\pi$
$971$	1.45389e16	0.540536	0.270268	+	0.962785i	$0.412888\pi$
$972$	2.85052e14	0.0105380
$973$	6.71876e15	0.246984
$974$	−8.93178e14	−0.0326485
$975$	−2.34010e15	−0.0850567
$976$	−4.26374e16	−1.54105
$977$	−9.38345e15	−0.337243	−0.168621	−	0.985681i	$-0.553932\pi$
$977$	−9.38345e15	−0.337243	−0.168621	+	0.985681i	$0.553932\pi$
$978$	4.88256e15	0.174495
$979$	5.68743e16	2.02121
$980$	4.54686e14	0.0160682
$981$	−1.14998e16	−0.404122
$982$	−2.12364e16	−0.742107
$983$	−2.35900e16	−0.819753	−0.409876	−	0.912141i	$-0.634428\pi$
$983$	−2.35900e16	−0.819753	−0.409876	+	0.912141i	$0.634428\pi$
$984$	−2.89289e16	−0.999677
$985$	9.48350e15	0.325889
$986$	−2.64594e16	−0.904185
$987$	7.81719e15	0.265648
$988$	−9.13448e14	−0.0308689
$989$	−6.50799e14	−0.0218709
$990$	1.03383e16	0.345507
$991$	−1.80350e16	−0.599391	−0.299696	−	0.954035i	$-0.596885\pi$
$991$	−1.80350e16	−0.599391	−0.299696	+	0.954035i	$0.596885\pi$
$992$	1.82187e16	0.602149
$993$	−1.74549e15	−0.0573716
$994$	3.00628e15	0.0982662
$995$	3.36851e15	0.109499
$996$	−4.92027e15	−0.159061
$997$	−5.32014e16	−1.71041	−0.855203	−	0.518293i	$-0.826568\pi$
$997$	−5.32014e16	−1.71041	−0.855203	+	0.518293i	$0.826568\pi$
$998$	2.65630e15	0.0849298
$999$	3.64086e15	0.115769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-41.3711 q^{2} -243.000 q^{3} -336.429 q^{4} -4784.52 q^{5} +10053.2 q^{6} +16807.0 q^{7} +98646.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-41.3711 q^{2} -243.000 q^{3} -336.429 q^{4} -4784.52 q^{5} +10053.2 q^{6} +16807.0 q^{7} +98646.5 q^{8} +59049.0 q^{9} +197941. q^{10} +884509. q^{11} +81752.2 q^{12} -371293. q^{13} -695325. q^{14} +1.16264e6 q^{15} -3.39211e6 q^{16} +6.33691e6 q^{17} -2.44292e6 q^{18} -7.31264e6 q^{19} +1.60965e6 q^{20} -4.08410e6 q^{21} -3.65931e7 q^{22} -1.47316e7 q^{23} -2.39711e7 q^{24} -2.59365e7 q^{25} +1.53608e7 q^{26} -1.43489e7 q^{27} -5.65436e6 q^{28} +1.00927e8 q^{29} -4.80997e7 q^{30} -2.95315e8 q^{31} -6.16925e7 q^{32} -2.14936e8 q^{33} -2.62165e8 q^{34} -8.04135e7 q^{35} -1.98658e7 q^{36} -2.53738e8 q^{37} +3.02532e8 q^{38} +9.02242e7 q^{39} -4.71977e8 q^{40} +1.20683e9 q^{41} +1.68964e8 q^{42} +4.41770e7 q^{43} -2.97574e8 q^{44} -2.82521e8 q^{45} +6.09463e8 q^{46} -1.91405e9 q^{47} +8.24284e8 q^{48} +2.82475e8 q^{49} +1.07302e9 q^{50} -1.53987e9 q^{51} +1.24914e8 q^{52} +6.36600e8 q^{53} +5.93631e8 q^{54} -4.23195e9 q^{55} +1.65795e9 q^{56} +1.77697e9 q^{57} -4.17545e9 q^{58} +4.83453e9 q^{59} -3.91145e8 q^{60} +1.25696e10 q^{61} +1.22175e10 q^{62} +9.92437e8 q^{63} +9.49934e9 q^{64} +1.77646e9 q^{65} +8.89213e9 q^{66} -1.37371e10 q^{67} -2.13192e9 q^{68} +3.57978e9 q^{69} +3.32680e9 q^{70} -4.32356e9 q^{71} +5.82498e9 q^{72} -1.27289e10 q^{73} +1.04974e10 q^{74} +6.30256e9 q^{75} +2.46018e9 q^{76} +1.48659e10 q^{77} -3.73268e9 q^{78} -2.47713e9 q^{79} +1.62296e10 q^{80} +3.48678e9 q^{81} -4.99278e10 q^{82} -6.01852e10 q^{83} +1.37401e9 q^{84} -3.03191e10 q^{85} -1.82765e9 q^{86} -2.45251e10 q^{87} +8.72537e10 q^{88} +6.43004e10 q^{89} +1.16882e10 q^{90} -6.24032e9 q^{91} +4.95613e9 q^{92} +7.17616e10 q^{93} +7.91866e10 q^{94} +3.49875e10 q^{95} +1.49913e10 q^{96} +1.31580e11 q^{97} -1.16863e10 q^{98} +5.22294e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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

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