LMFDB - Embedded newform 2.26.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,26,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	2.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:	$7.91993559904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{106705}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 26676 $ x^2 - x - 26676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$163.829$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00 q^{2} -1.37803e6 q^{3} +1.67772e7 q^{4} +8.78994e8 q^{5} -5.64442e9 q^{6} +3.00388e10 q^{7} +6.87195e10 q^{8} +1.05168e12 q^{9} +3.60036e12 q^{10} +5.73599e12 q^{11} -2.31195e13 q^{12} -1.07343e13 q^{13} +1.23039e14 q^{14} -1.21128e15 q^{15} +2.81475e14 q^{16} +2.97473e15 q^{17} +4.30769e15 q^{18} -5.42738e15 q^{19} +1.47471e16 q^{20} -4.13944e16 q^{21} +2.34946e16 q^{22} -1.04540e17 q^{23} -9.46976e16 q^{24} +4.74607e17 q^{25} -4.39677e16 q^{26} -2.81659e17 q^{27} +5.03967e17 q^{28} +3.09182e18 q^{29} -4.96141e18 q^{30} -4.26809e18 q^{31} +1.15292e18 q^{32} -7.90437e18 q^{33} +1.21845e19 q^{34} +2.64039e19 q^{35} +1.76443e19 q^{36} -4.51028e19 q^{37} -2.22305e19 q^{38} +1.47922e19 q^{39} +6.04040e19 q^{40} -7.56724e19 q^{41} -1.69551e20 q^{42} -1.39036e20 q^{43} +9.62339e19 q^{44} +9.24421e20 q^{45} -4.28196e20 q^{46} +4.67328e20 q^{47} -3.87881e20 q^{48} -4.38741e20 q^{49} +1.94399e21 q^{50} -4.09927e21 q^{51} -1.80092e20 q^{52} -1.24315e21 q^{53} -1.15368e21 q^{54} +5.04190e21 q^{55} +2.06425e21 q^{56} +7.47909e21 q^{57} +1.26641e22 q^{58} -1.32468e22 q^{59} -2.03219e22 q^{60} -2.36984e20 q^{61} -1.74821e22 q^{62} +3.15912e22 q^{63} +4.72237e21 q^{64} -9.43539e21 q^{65} -3.23763e22 q^{66} -5.36922e22 q^{67} +4.99076e22 q^{68} +1.44059e23 q^{69} +1.08150e23 q^{70} -2.27032e23 q^{71} +7.22710e22 q^{72} +2.78528e23 q^{73} -1.84741e23 q^{74} -6.54024e23 q^{75} -9.10563e22 q^{76} +1.72302e23 q^{77} +6.05889e22 q^{78} +6.36958e23 q^{79} +2.47415e23 q^{80} -5.02942e23 q^{81} -3.09954e23 q^{82} +1.19662e24 q^{83} -6.94482e23 q^{84} +2.61477e24 q^{85} -5.69491e23 q^{86} -4.26063e24 q^{87} +3.94174e23 q^{88} -3.22134e24 q^{89} +3.78643e24 q^{90} -3.22445e23 q^{91} -1.75389e24 q^{92} +5.88156e24 q^{93} +1.91418e24 q^{94} -4.77063e24 q^{95} -1.58876e24 q^{96} +3.58465e24 q^{97} -1.79708e24 q^{98} +6.03243e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8192 q^{2} + 379848 q^{3} + 33554432 q^{4} + 741953100 q^{5} + 1555857408 q^{6} - 376536944 q^{7} + 137438953472 q^{8} + 3294531432666 q^{9} + 3039039897600 q^{10} + 8323034610264 q^{11} + 6372791943168 q^{12}+ \cdots + 11\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 8192 * q^2 + 379848 * q^3 + 33554432 * q^4 + 741953100 * q^5 + 1555857408 * q^6 - 376536944 * q^7 + 137438953472 * q^8 + 3294531432666 * q^9 + 3039039897600 * q^10 + 8323034610264 * q^11 + 6372791943168 * q^12 - 106467053152292 * q^13 - 1542295322624 * q^14 - 1452182413035600 * q^15 + 562949953421312 * q^16 + 1327878920113956 * q^17 + 13494400748199936 * q^18 - 477079242949400 * q^19 + 12447907420569600 * q^20 - 94860791661752256 * q^21 + 34091149763641344 * q^22 - 115305025781473872 * q^23 + 26102955799216128 * q^24 + 195364218352298750 * q^25 - 436089049711788032 * q^26 + 2171569557205152720 * q^27 - 6317241641467904 * q^28 + 1724412645206435580 * q^29 - 5948139163793817600 * q^30 - 8688082288351126976 * q^31 + 2305843009213693952 * q^32 - 3356662204005020064 * q^33 + 5438992056786763776 * q^34 + 30572039779548136800 * q^35 + 55273065464626937856 * q^36 - 34908364049750170484 * q^37 - 1954116579120742400 * q^38 - 153494373835331105808 * q^39 + 50986628794653081600 * q^40 + 83014324355953468884 * q^41 - 388549802646537240576 * q^42 + 44539608583471901848 * q^43 + 139637349431874945024 * q^44 + 617059152350257182300 * q^45 - 472289385600916979712 * q^46 + 1869360732054674599776 * q^47 + 106917706953589260288 * q^48 - 854718643011973772046 * q^49 + 800211838371015680000 * q^50 - 6994225992587553820656 * q^51 - 1786220747619483779072 * q^52 - 3242170458210097794132 * q^53 + 8894748906312305541120 * q^54 + 4687370283547568509200 * q^55 - 25875421763452534784 * q^56 + 16181115057055601354400 * q^57 + 7063194194765560135680 * q^58 - 17413675430632049453640 * q^59 - 24363578014899476889600 * q^60 + 33975859953090212810044 * q^61 - 35586385053086216093696 * q^62 - 36625774166984600306352 * q^63 + 9444732965739290427392 * q^64 + 3683906908205094047400 * q^65 - 13748888387604562182144 * q^66 + 33012908196969622380616 * q^67 + 22278111464598584426496 * q^68 + 125135868082548386734272 * q^69 + 125223074937029168332800 * q^70 - 278348008145600813615856 * q^71 + 226398476143111937458176 * q^72 + 313442631796571689392148 * q^73 - 142984659147776698302464 * q^74 - 1144898988230230172205000 * q^75 - 8004061508078560870400 * q^76 + 93616352280445975603392 * q^77 - 628712955229516209389568 * q^78 + 928546182288781647817120 * q^79 + 208841231542899022233600 * q^80 + 1909195802481672047728242 * q^81 + 340026672561985408548864 * q^82 - 452542629950725008985752 * q^83 - 1591499991640216537399296 * q^84 + 2840452690831654686931800 * q^85 + 182434236757900909969408 * q^86 - 6664364855011895770504080 * q^87 + 571954583272959774818304 * q^88 - 2346904179674200701244620 * q^89 + 2527474288026653418700800 * q^90 + 2589295264446210583737824 * q^91 - 1934497323421355948900352 * q^92 - 1888263951389289833389824 * q^93 + 7656901558495947160682496 * q^94 - 5449023740708681753370000 * q^95 + 437934927681901610139648 * q^96 + 13645482361777595497674436 * q^97 - 3500927561777044570300416 * q^98 + 11834785687944312803841912 * q^99

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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	−1.37803e6	−1.49707	−0.748537	−	0.663093i	$-0.769243\pi$
$3$	−1.37803e6	−1.49707	−0.748537	+	0.663093i	$0.769243\pi$
$4$	1.67772e7	0.500000
$5$	8.78994e8	1.61013	0.805065	−	0.593187i	$-0.202130\pi$
$5$	8.78994e8	1.61013	0.805065	+	0.593187i	$0.202130\pi$
$6$	−5.64442e9	−1.05859
$7$	3.00388e10	0.820270	0.410135	−	0.912025i	$-0.365482\pi$
$7$	3.00388e10	0.820270	0.410135	+	0.912025i	$0.365482\pi$
$8$	6.87195e10	0.353553
$9$	1.05168e12	1.24123
$10$	3.60036e12	1.13853
$11$	5.73599e12	0.551061	0.275531	−	0.961292i	$-0.411146\pi$
$11$	5.73599e12	0.551061	0.275531	+	0.961292i	$0.411146\pi$
$12$	−2.31195e13	−0.748537
$13$	−1.07343e13	−0.127786	−0.0638928	−	0.997957i	$-0.520352\pi$
$13$	−1.07343e13	−0.127786	−0.0638928	+	0.997957i	$0.520352\pi$
$14$	1.23039e14	0.580018
$15$	−1.21128e15	−2.41048
$16$	2.81475e14	0.250000
$17$	2.97473e15	1.23833	0.619164	−	0.785262i	$-0.287472\pi$
$17$	2.97473e15	1.23833	0.619164	+	0.785262i	$0.287472\pi$
$18$	4.30769e15	0.877683
$19$	−5.42738e15	−0.562561	−0.281281	−	0.959626i	$-0.590759\pi$
$19$	−5.42738e15	−0.562561	−0.281281	+	0.959626i	$0.590759\pi$
$20$	1.47471e16	0.805065
$21$	−4.13944e16	−1.22800
$22$	2.34946e16	0.389659
$23$	−1.04540e17	−0.994683	−0.497341	−	0.867555i	$-0.665690\pi$
$23$	−1.04540e17	−0.994683	−0.497341	+	0.867555i	$0.665690\pi$
$24$	−9.46976e16	−0.529296
$25$	4.74607e17	1.59252
$26$	−4.39677e16	−0.0903581
$27$	−2.81659e17	−0.361141
$28$	5.03967e17	0.410135
$29$	3.09182e18	1.62270	0.811352	−	0.584558i	$-0.198732\pi$
$29$	3.09182e18	1.62270	0.811352	+	0.584558i	$0.198732\pi$
$30$	−4.96141e18	−1.70447
$31$	−4.26809e18	−0.973222	−0.486611	−	0.873619i	$-0.661767\pi$
$31$	−4.26809e18	−0.973222	−0.486611	+	0.873619i	$0.661767\pi$
$32$	1.15292e18	0.176777
$33$	−7.90437e18	−0.824980
$34$	1.21845e19	0.875630
$35$	2.64039e19	1.32074
$36$	1.76443e19	0.620616
$37$	−4.51028e19	−1.12637	−0.563186	−	0.826330i	$-0.690424\pi$
$37$	−4.51028e19	−1.12637	−0.563186	+	0.826330i	$0.690424\pi$
$38$	−2.22305e19	−0.397791
$39$	1.47922e19	0.191305
$40$	6.04040e19	0.569267
$41$	−7.56724e19	−0.523769	−0.261884	−	0.965099i	$-0.584344\pi$
$41$	−7.56724e19	−0.523769	−0.261884	+	0.965099i	$0.584344\pi$
$42$	−1.69551e20	−0.868330
$43$	−1.39036e20	−0.530605	−0.265302	−	0.964165i	$-0.585472\pi$
$43$	−1.39036e20	−0.530605	−0.265302	+	0.964165i	$0.585472\pi$
$44$	9.62339e19	0.275531
$45$	9.24421e20	1.99854
$46$	−4.28196e20	−0.703347
$47$	4.67328e20	0.586676	0.293338	−	0.956009i	$-0.405234\pi$
$47$	4.67328e20	0.586676	0.293338	+	0.956009i	$0.405234\pi$
$48$	−3.87881e20	−0.374269
$49$	−4.38741e20	−0.327158
$50$	1.94399e21	1.12608
$51$	−4.09927e21	−1.85387
$52$	−1.80092e20	−0.0638928
$53$	−1.24315e21	−0.347595	−0.173797	−	0.984781i	$-0.555604\pi$
$53$	−1.24315e21	−0.347595	−0.173797	+	0.984781i	$0.555604\pi$
$54$	−1.15368e21	−0.255365
$55$	5.04190e21	0.887280
$56$	2.06425e21	0.290009
$57$	7.47909e21	0.842196
$58$	1.26641e22	1.14743
$59$	−1.32468e22	−0.969303	−0.484652	−	0.874707i	$-0.661054\pi$
$59$	−1.32468e22	−0.969303	−0.484652	+	0.874707i	$0.661054\pi$
$60$	−2.03219e22	−1.20524
$61$	−2.36984e20	−0.0114313	−0.00571565	−	0.999984i	$-0.501819\pi$
$61$	−2.36984e20	−0.0114313	−0.00571565	+	0.999984i	$0.501819\pi$
$62$	−1.74821e22	−0.688172
$63$	3.15912e22	1.01814
$64$	4.72237e21	0.125000
$65$	−9.43539e21	−0.205752
$66$	−3.23763e22	−0.583349
$67$	−5.36922e22	−0.801634	−0.400817	−	0.916158i	$-0.631274\pi$
$67$	−5.36922e22	−0.801634	−0.400817	+	0.916158i	$0.631274\pi$
$68$	4.99076e22	0.619164
$69$	1.44059e23	1.48911
$70$	1.08150e23	0.933905
$71$	−2.27032e23	−1.64194	−0.820971	−	0.570970i	$-0.806567\pi$
$71$	−2.27032e23	−1.64194	−0.820971	+	0.570970i	$0.806567\pi$
$72$	7.22710e22	0.438842
$73$	2.78528e23	1.42342	0.711710	−	0.702473i	$-0.247921\pi$
$73$	2.78528e23	1.42342	0.711710	+	0.702473i	$0.247921\pi$
$74$	−1.84741e23	−0.796465
$75$	−6.54024e23	−2.38412
$76$	−9.10563e22	−0.281281
$77$	1.72302e23	0.452019
$78$	6.05889e22	0.135273
$79$	6.36958e23	1.21275	0.606376	−	0.795178i	$-0.292622\pi$
$79$	6.36958e23	1.21275	0.606376	+	0.795178i	$0.292622\pi$
$80$	2.47415e23	0.402532
$81$	−5.02942e23	−0.700576
$82$	−3.09954e23	−0.370360
$83$	1.19662e24	1.22880	0.614398	−	0.788996i	$-0.289399\pi$
$83$	1.19662e24	1.22880	0.614398	+	0.788996i	$0.289399\pi$
$84$	−6.94482e23	−0.614002
$85$	2.61477e24	1.99387
$86$	−5.69491e23	−0.375194
$87$	−4.26063e24	−2.42931
$88$	3.94174e23	0.194830
$89$	−3.22134e24	−1.38249	−0.691244	−	0.722621i	$-0.742937\pi$
$89$	−3.22134e24	−1.38249	−0.691244	+	0.722621i	$0.742937\pi$
$90$	3.78643e24	1.41318
$91$	−3.22445e23	−0.104819
$92$	−1.75389e24	−0.497341
$93$	5.88156e24	1.45699
$94$	1.91418e24	0.414843
$95$	−4.77063e24	−0.905797
$96$	−1.58876e24	−0.264648
$97$	3.58465e24	0.524566	0.262283	−	0.964991i	$-0.415525\pi$
$97$	3.58465e24	0.524566	0.262283	+	0.964991i	$0.415525\pi$
$98$	−1.79708e24	−0.231335
$99$	6.03243e24	0.683994
$100$	7.96259e24	0.796259
$101$	−3.40630e24	−0.300792	−0.150396	−	0.988626i	$-0.548055\pi$
$101$	−3.40630e24	−0.300792	−0.150396	+	0.988626i	$0.548055\pi$
$102$	−1.67906e25	−1.31088
$103$	8.27075e24	0.571583	0.285792	−	0.958292i	$-0.407743\pi$
$103$	8.27075e24	0.571583	0.285792	+	0.958292i	$0.407743\pi$
$104$	−7.37656e23	−0.0451791
$105$	−3.63854e25	−1.97725
$106$	−5.09192e24	−0.245787
$107$	1.57986e25	0.678142	0.339071	−	0.940761i	$-0.389887\pi$
$107$	1.57986e25	0.678142	0.339071	+	0.940761i	$0.389887\pi$
$108$	−4.72546e24	−0.180571
$109$	3.00869e25	1.02458	0.512290	−	0.858813i	$-0.328797\pi$
$109$	3.00869e25	1.02458	0.512290	+	0.858813i	$0.328797\pi$
$110$	2.06516e25	0.627402
$111$	6.21530e25	1.68626
$112$	8.45516e24	0.205067
$113$	−8.06745e25	−1.75088	−0.875439	−	0.483329i	$-0.839428\pi$
$113$	−8.06745e25	−1.75088	−0.875439	+	0.483329i	$0.839428\pi$
$114$	3.06344e25	0.595523
$115$	−9.18901e25	−1.60157
$116$	5.18722e25	0.811352
$117$	−1.12891e25	−0.158612
$118$	−5.42587e25	−0.685401
$119$	8.93571e25	1.01576
$120$	−8.32386e25	−0.852235
$121$	−7.54455e25	−0.696332
$122$	−9.70685e23	−0.00808315
$123$	1.04279e26	0.784121
$124$	−7.16066e25	−0.486611
$125$	1.55216e26	0.954030
$126$	1.29398e26	0.719937
$127$	−1.32973e26	−0.670221	−0.335111	−	0.942179i	$-0.608774\pi$
$127$	−1.32973e26	−0.670221	−0.335111	+	0.942179i	$0.608774\pi$
$128$	1.93428e25	0.0883883
$129$	1.91596e26	0.794355
$130$	−3.86474e25	−0.145488
$131$	6.73908e25	0.230520	0.115260	−	0.993335i	$-0.463230\pi$
$131$	6.73908e25	0.230520	0.115260	+	0.993335i	$0.463230\pi$
$132$	−1.32613e26	−0.412490
$133$	−1.63032e26	−0.461452
$134$	−2.19923e26	−0.566841
$135$	−2.47577e26	−0.581484
$136$	2.04422e26	0.437815
$137$	−3.22963e26	−0.631170	−0.315585	−	0.948897i	$-0.602201\pi$
$137$	−3.22963e26	−0.631170	−0.315585	+	0.948897i	$0.602201\pi$
$138$	5.90067e26	1.05296
$139$	−9.21581e25	−0.150262	−0.0751309	−	0.997174i	$-0.523937\pi$
$139$	−9.21581e25	−0.150262	−0.0751309	+	0.997174i	$0.523937\pi$
$140$	4.42984e26	0.660370
$141$	−6.43992e26	−0.878298
$142$	−9.29923e26	−1.16103
$143$	−6.15719e25	−0.0704177
$144$	2.96022e26	0.310308
$145$	2.71769e27	2.61276
$146$	1.14085e27	1.00651
$147$	6.04599e26	0.489779
$148$	−7.56699e26	−0.563186
$149$	−7.12667e26	−0.487594	−0.243797	−	0.969826i	$-0.578393\pi$
$149$	−7.12667e26	−0.487594	−0.243797	+	0.969826i	$0.578393\pi$
$150$	−2.67888e27	−1.68583
$151$	−3.06161e27	−1.77312	−0.886559	−	0.462616i	$-0.846911\pi$
$151$	−3.06161e27	−1.77312	−0.886559	+	0.462616i	$0.846911\pi$
$152$	−3.72966e26	−0.198895
$153$	3.12846e27	1.53705
$154$	7.05749e26	0.319626
$155$	−3.75162e27	−1.56701
$156$	2.48172e26	0.0956523
$157$	2.38960e27	0.850315	0.425157	−	0.905119i	$-0.360219\pi$
$157$	2.38960e27	0.850315	0.425157	+	0.905119i	$0.360219\pi$
$158$	2.60898e27	0.857546
$159$	1.71309e27	0.520375
$160$	1.01341e27	0.284633
$161$	−3.14025e27	−0.815908
$162$	−2.06005e27	−0.495382
$163$	6.63092e27	1.47648	0.738242	−	0.674536i	$-0.235656\pi$
$163$	6.63092e27	1.47648	0.738242	+	0.674536i	$0.235656\pi$
$164$	−1.26957e27	−0.261884
$165$	−6.94790e27	−1.32832
$166$	4.90135e27	0.868890
$167$	4.06997e27	0.669323	0.334662	−	0.942338i	$-0.391378\pi$
$167$	4.06997e27	0.669323	0.334662	+	0.942338i	$0.391378\pi$
$168$	−2.84460e27	−0.434165
$169$	−6.94118e27	−0.983671
$170$	1.07101e28	1.40988
$171$	−5.70787e27	−0.698269
$172$	−2.33263e27	−0.265302
$173$	−8.68916e27	−0.919182	−0.459591	−	0.888131i	$-0.652004\pi$
$173$	−8.68916e27	−0.919182	−0.459591	+	0.888131i	$0.652004\pi$
$174$	−1.74515e28	−1.71778
$175$	1.42566e28	1.30629
$176$	1.61454e27	0.137765
$177$	1.82545e28	1.45112
$178$	−1.31946e28	−0.977567
$179$	−4.31406e27	−0.298005	−0.149002	−	0.988837i	$-0.547606\pi$
$179$	−4.31406e27	−0.298005	−0.149002	+	0.988837i	$0.547606\pi$
$180$	1.55092e28	0.999272
$181$	2.22969e28	1.34049	0.670243	−	0.742142i	$-0.266190\pi$
$181$	2.22969e28	1.34049	0.670243	+	0.742142i	$0.266190\pi$
$182$	−1.32074e27	−0.0741180
$183$	3.26571e26	0.0171135
$184$	−7.18394e27	−0.351674
$185$	−3.96451e28	−1.81360
$186$	2.40909e28	1.03024
$187$	1.70630e28	0.682394
$188$	7.84046e27	0.293338
$189$	−8.46070e27	−0.296233
$190$	−1.95405e28	−0.640495
$191$	−1.91337e28	−0.587329	−0.293665	−	0.955908i	$-0.594875\pi$
$191$	−1.91337e28	−0.587329	−0.293665	+	0.955908i	$0.594875\pi$
$192$	−6.50757e27	−0.187134
$193$	−5.96748e28	−1.60814	−0.804071	−	0.594533i	$-0.797337\pi$
$193$	−5.96748e28	−1.60814	−0.804071	+	0.594533i	$0.797337\pi$
$194$	1.46827e28	0.370924
$195$	1.30023e28	0.308025
$196$	−7.36085e27	−0.163579
$197$	6.24204e28	1.30166	0.650832	−	0.759222i	$-0.274420\pi$
$197$	6.24204e28	1.30166	0.650832	+	0.759222i	$0.274420\pi$
$198$	2.47088e28	0.483657
$199$	−3.24229e28	−0.595921	−0.297960	−	0.954578i	$-0.596306\pi$
$199$	−3.24229e28	−0.595921	−0.297960	+	0.954578i	$0.596306\pi$
$200$	3.26148e28	0.563040
$201$	7.39895e28	1.20011
$202$	−1.39522e28	−0.212692
$203$	9.28745e28	1.33106
$204$	−6.87743e28	−0.926934
$205$	−6.65156e28	−0.843335
$206$	3.38770e28	0.404171
$207$	−1.09943e29	−1.23463
$208$	−3.02144e27	−0.0319464
$209$	−3.11314e28	−0.310006
$210$	−1.49035e29	−1.39812
$211$	3.82197e28	0.337875	0.168938	−	0.985627i	$-0.445966\pi$
$211$	3.82197e28	0.337875	0.168938	+	0.985627i	$0.445966\pi$
$212$	−2.08565e28	−0.173797
$213$	3.12857e29	2.45811
$214$	6.47109e28	0.479519
$215$	−1.22212e29	−0.854342
$216$	−1.93555e28	−0.127683
$217$	−1.28208e29	−0.798305
$218$	1.23236e29	0.724487
$219$	−3.83820e29	−2.13097
$220$	8.45891e28	0.443640
$221$	−3.19316e28	−0.158241
$222$	2.54579e29	1.19237
$223$	3.11100e29	1.37749	0.688746	−	0.725003i	$-0.258161\pi$
$223$	3.11100e29	1.37749	0.688746	+	0.725003i	$0.258161\pi$
$224$	3.46323e28	0.145005
$225$	4.99135e29	1.97668
$226$	−3.30443e29	−1.23806
$227$	−1.05572e29	−0.374304	−0.187152	−	0.982331i	$-0.559926\pi$
$227$	−1.05572e29	−0.374304	−0.187152	+	0.982331i	$0.559926\pi$
$228$	1.25478e29	0.421098
$229$	−3.70322e29	−1.17662	−0.588310	−	0.808635i	$-0.700207\pi$
$229$	−3.70322e29	−1.17662	−0.588310	+	0.808635i	$0.700207\pi$
$230$	−3.76382e29	−1.13248
$231$	−2.37438e29	−0.676706
$232$	2.12468e29	0.573713
$233$	−6.84781e28	−0.175228	−0.0876138	−	0.996155i	$-0.527924\pi$
$233$	−6.84781e28	−0.175228	−0.0876138	+	0.996155i	$0.527924\pi$
$234$	−4.62400e28	−0.112155
$235$	4.10778e29	0.944625
$236$	−2.22244e29	−0.484652
$237$	−8.77748e29	−1.81558
$238$	3.66007e29	0.718253
$239$	3.87773e29	0.722111	0.361055	−	0.932544i	$-0.382417\pi$
$239$	3.87773e29	0.722111	0.361055	+	0.932544i	$0.382417\pi$
$240$	−3.40945e29	−0.602621
$241$	1.03723e30	1.74046	0.870230	−	0.492646i	$-0.163970\pi$
$241$	1.03723e30	1.74046	0.870230	+	0.492646i	$0.163970\pi$
$242$	−3.09025e29	−0.492381
$243$	9.31717e29	1.40996
$244$	−3.97593e27	−0.00571565
$245$	−3.85651e29	−0.526766
$246$	4.27127e29	0.554457
$247$	5.82591e28	0.0718873
$248$	−2.93301e29	−0.344086
$249$	−1.64898e30	−1.83960
$250$	6.35766e29	0.674601
$251$	1.47990e30	1.49386	0.746930	−	0.664903i	$-0.231527\pi$
$251$	1.47990e30	1.49386	0.746930	+	0.664903i	$0.231527\pi$
$252$	5.30013e29	0.509072
$253$	−5.99641e29	−0.548131
$254$	−5.44659e29	−0.473918
$255$	−3.60323e30	−2.98497
$256$	7.92282e28	0.0625000
$257$	6.75384e29	0.507442	0.253721	−	0.967277i	$-0.418345\pi$
$257$	6.75384e29	0.507442	0.253721	+	0.967277i	$0.418345\pi$
$258$	7.84776e29	0.561694
$259$	−1.35483e30	−0.923929
$260$	−1.58300e29	−0.102876
$261$	3.25161e30	2.01415
$262$	2.76033e29	0.163003
$263$	1.42102e30	0.800119	0.400059	−	0.916489i	$-0.368989\pi$
$263$	1.42102e30	0.800119	0.400059	+	0.916489i	$0.368989\pi$
$264$	−5.43184e29	−0.291674
$265$	−1.09272e30	−0.559673
$266$	−6.67778e29	−0.326296
$267$	4.43911e30	2.06969
$268$	−9.00805e29	−0.400817
$269$	−1.90129e30	−0.807504	−0.403752	−	0.914868i	$-0.632294\pi$
$269$	−1.90129e30	−0.807504	−0.403752	+	0.914868i	$0.632294\pi$
$270$	−1.01407e30	−0.411171
$271$	−1.45800e30	−0.564471	−0.282236	−	0.959345i	$-0.591076\pi$
$271$	−1.45800e30	−0.564471	−0.282236	+	0.959345i	$0.591076\pi$
$272$	8.37311e29	0.309582
$273$	4.44340e29	0.156921
$274$	−1.32286e30	−0.446304
$275$	2.72234e30	0.877575
$276$	2.41692e30	0.744557
$277$	−5.31088e29	−0.156376	−0.0781879	−	0.996939i	$-0.524913\pi$
$277$	−5.31088e29	−0.156376	−0.0781879	+	0.996939i	$0.524913\pi$
$278$	−3.77479e29	−0.106251
$279$	−4.48867e30	−1.20799
$280$	1.81446e30	0.466952
$281$	−3.64974e30	−0.898323	−0.449161	−	0.893451i	$-0.648277\pi$
$281$	−3.64974e30	−0.898323	−0.449161	+	0.893451i	$0.648277\pi$
$282$	−2.63779e30	−0.621050
$283$	−1.43965e30	−0.324285	−0.162143	−	0.986767i	$-0.551840\pi$
$283$	−1.43965e30	−0.324285	−0.162143	+	0.986767i	$0.551840\pi$
$284$	−3.80897e30	−0.820971
$285$	6.57408e30	1.35604
$286$	−2.52199e29	−0.0497929
$287$	−2.27311e30	−0.429632
$288$	1.21251e30	0.219421
$289$	3.07837e30	0.533456
$290$	1.11317e31	1.84750
$291$	−4.93976e30	−0.785315
$292$	4.67292e30	0.711710
$293$	1.24504e31	1.81692	0.908462	−	0.417967i	$-0.137257\pi$
$293$	1.24504e31	1.81692	0.908462	+	0.417967i	$0.137257\pi$
$294$	2.47644e30	0.346326
$295$	−1.16438e31	−1.56070
$296$	−3.09944e30	−0.398233
$297$	−1.61559e30	−0.199011
$298$	−2.91909e30	−0.344781
$299$	1.12217e30	0.127106
$300$	−1.09727e31	−1.19206
$301$	−4.17647e30	−0.435239
$302$	−1.25403e31	−1.25378
$303$	4.69399e30	0.450307
$304$	−1.52767e30	−0.140640
$305$	−2.08307e29	−0.0184059
$306$	1.28142e31	1.08686
$307$	2.27193e31	1.84997	0.924986	−	0.380001i	$-0.124076\pi$
$307$	2.27193e31	1.84997	0.924986	+	0.380001i	$0.124076\pi$
$308$	2.89075e30	0.226009
$309$	−1.13974e31	−0.855703
$310$	−1.53666e31	−1.10805
$311$	−1.84336e31	−1.27675	−0.638374	−	0.769726i	$-0.720393\pi$
$311$	−1.84336e31	−1.27675	−0.638374	+	0.769726i	$0.720393\pi$
$312$	1.01651e30	0.0676364
$313$	4.98693e30	0.318808	0.159404	−	0.987213i	$-0.449043\pi$
$313$	4.98693e30	0.318808	0.159404	+	0.987213i	$0.449043\pi$
$314$	9.78780e30	0.601263
$315$	2.77685e31	1.63934
$316$	1.06864e31	0.606376
$317$	−8.79478e30	−0.479716	−0.239858	−	0.970808i	$-0.577101\pi$
$317$	−8.79478e30	−0.479716	−0.239858	+	0.970808i	$0.577101\pi$
$318$	7.01683e30	0.367961
$319$	1.77347e31	0.894209
$320$	4.15093e30	0.201266
$321$	−2.17709e31	−1.01523
$322$	−1.28625e31	−0.576934
$323$	−1.61450e31	−0.696635
$324$	−8.43797e30	−0.350288
$325$	−5.09458e30	−0.203501
$326$	2.71602e31	1.04403
$327$	−4.14606e31	−1.53387
$328$	−5.20017e30	−0.185180
$329$	1.40380e31	0.481233
$330$	−2.84586e31	−0.939267
$331$	5.97122e31	1.89764	0.948818	−	0.315822i	$-0.102280\pi$
$331$	5.97122e31	1.89764	0.948818	+	0.315822i	$0.102280\pi$
$332$	2.00759e31	0.614398
$333$	−4.74337e31	−1.39809
$334$	1.66706e31	0.473283
$335$	−4.71951e31	−1.29073
$336$	−1.16515e31	−0.307001
$337$	1.08428e31	0.275275	0.137638	−	0.990483i	$-0.456049\pi$
$337$	1.08428e31	0.275275	0.137638	+	0.990483i	$0.456049\pi$
$338$	−2.84311e31	−0.695560
$339$	1.11172e32	2.62119
$340$	4.38685e31	0.996934
$341$	−2.44817e31	−0.536305
$342$	−2.33794e31	−0.493751
$343$	−5.34633e31	−1.08863
$344$	−9.55447e30	−0.187597
$345$	1.26627e32	2.39767
$346$	−3.55908e31	−0.649960
$347$	7.20193e30	0.126862	0.0634308	−	0.997986i	$-0.479796\pi$
$347$	7.20193e30	0.126862	0.0634308	+	0.997986i	$0.479796\pi$
$348$	−7.14814e31	−1.21465
$349$	5.27779e31	0.865235	0.432618	−	0.901577i	$-0.357590\pi$
$349$	5.27779e31	0.865235	0.432618	+	0.901577i	$0.357590\pi$
$350$	5.83951e31	0.923689
$351$	3.02342e30	0.0461487
$352$	6.61315e30	0.0974148
$353$	−5.67715e31	−0.807135	−0.403567	−	0.914950i	$-0.632230\pi$
$353$	−5.67715e31	−0.807135	−0.403567	+	0.914950i	$0.632230\pi$
$354$	7.47702e31	1.02610
$355$	−1.99560e32	−2.64374
$356$	−5.40451e31	−0.691244
$357$	−1.23137e32	−1.52067
$358$	−1.76704e31	−0.210721
$359$	2.18925e31	0.252125	0.126062	−	0.992022i	$-0.459766\pi$
$359$	2.18925e31	0.252125	0.126062	+	0.992022i	$0.459766\pi$
$360$	6.35258e31	0.706592
$361$	−6.36201e31	−0.683525
$362$	9.13280e31	0.947866
$363$	1.03966e32	1.04246
$364$	−5.40974e30	−0.0524094
$365$	2.44824e32	2.29189
$366$	1.33763e30	0.0121011
$367$	1.00500e32	0.878699	0.439349	−	0.898316i	$-0.355209\pi$
$367$	1.00500e32	0.878699	0.439349	+	0.898316i	$0.355209\pi$
$368$	−2.94254e31	−0.248671
$369$	−7.95833e31	−0.650118
$370$	−1.62386e32	−1.28241
$371$	−3.73425e31	−0.285122
$372$	9.86761e31	0.728493
$373$	6.31052e31	0.450510	0.225255	−	0.974300i	$-0.427678\pi$
$373$	6.31052e31	0.450510	0.225255	+	0.974300i	$0.427678\pi$
$374$	6.98901e31	0.482526
$375$	−2.13893e32	−1.42825
$376$	3.21145e31	0.207421
$377$	−3.31886e31	−0.207358
$378$	−3.46550e31	−0.209468
$379$	−8.85755e31	−0.517993	−0.258996	−	0.965878i	$-0.583392\pi$
$379$	−8.85755e31	−0.517993	−0.258996	+	0.965878i	$0.583392\pi$
$380$	−8.00379e31	−0.452898
$381$	1.83241e32	1.00337
$382$	−7.83716e31	−0.415305
$383$	9.08315e31	0.465856	0.232928	−	0.972494i	$-0.425169\pi$
$383$	9.08315e31	0.465856	0.232928	+	0.972494i	$0.425169\pi$
$384$	−2.66550e31	−0.132324
$385$	1.51453e32	0.727809
$386$	−2.44428e32	−1.13713
$387$	−1.46221e32	−0.658603
$388$	6.01405e31	0.262283
$389$	7.13043e31	0.301124	0.150562	−	0.988601i	$-0.451892\pi$
$389$	7.13043e31	0.301124	0.150562	+	0.988601i	$0.451892\pi$
$390$	5.32573e31	0.217807
$391$	−3.10978e32	−1.23174
$392$	−3.01500e31	−0.115668
$393$	−9.28666e31	−0.345106
$394$	2.55674e32	0.920416
$395$	5.59883e32	1.95269
$396$	1.01207e32	0.341997
$397$	2.99427e31	0.0980413	0.0490206	−	0.998798i	$-0.484390\pi$
$397$	2.99427e31	0.0980413	0.0490206	+	0.998798i	$0.484390\pi$
$398$	−1.32804e32	−0.421380
$399$	2.24663e32	0.690828
$400$	1.33590e32	0.398129
$401$	−5.00588e32	−1.44603	−0.723013	−	0.690835i	$-0.757243\pi$
$401$	−5.00588e32	−1.44603	−0.723013	+	0.690835i	$0.757243\pi$
$402$	3.03061e32	0.848603
$403$	4.58150e31	0.124364
$404$	−5.71482e31	−0.150396
$405$	−4.42083e32	−1.12802
$406$	3.80414e32	0.941198
$407$	−2.58709e32	−0.620700
$408$	−2.81699e32	−0.655441
$409$	−2.78379e32	−0.628195	−0.314097	−	0.949391i	$-0.601702\pi$
$409$	−2.78379e32	−0.628195	−0.314097	+	0.949391i	$0.601702\pi$
$410$	−2.72448e32	−0.596328
$411$	4.45054e32	0.944908
$412$	1.38760e32	0.285792
$413$	−3.97916e32	−0.795090
$414$	−4.50326e32	−0.873016
$415$	1.05182e33	1.97852
$416$	−1.23758e31	−0.0225895
$417$	1.26997e32	0.224953
$418$	−1.27514e32	−0.219207
$419$	−6.36828e32	−1.06254	−0.531272	−	0.847201i	$-0.678286\pi$
$419$	−6.36828e32	−1.06254	−0.531272	+	0.847201i	$0.678286\pi$
$420$	−6.10446e32	−0.988623
$421$	−3.92275e32	−0.616686	−0.308343	−	0.951275i	$-0.599775\pi$
$421$	−3.92275e32	−0.616686	−0.308343	+	0.951275i	$0.599775\pi$
$422$	1.56548e32	0.238914
$423$	4.91480e32	0.728201
$424$	−8.54283e31	−0.122893
$425$	1.41183e33	1.97206
$426$	1.28146e33	1.73815
$427$	−7.11870e30	−0.00937675
$428$	2.65056e32	0.339071
$429$	8.48480e31	0.105421
$430$	−5.00579e32	−0.604111
$431$	2.44178e32	0.286247	0.143124	−	0.989705i	$-0.454285\pi$
$431$	2.44178e32	0.286247	0.143124	+	0.989705i	$0.454285\pi$
$432$	−7.92800e31	−0.0902853
$433$	9.12872e32	1.00998	0.504988	−	0.863126i	$-0.331497\pi$
$433$	9.12872e32	1.00998	0.504988	+	0.863126i	$0.331497\pi$
$434$	−5.25140e32	−0.564487
$435$	−3.74506e33	−3.91150
$436$	5.04774e32	0.512290
$437$	5.67378e32	0.559570
$438$	−1.57213e33	−1.50682
$439$	6.07601e32	0.565995	0.282997	−	0.959121i	$-0.408671\pi$
$439$	6.07601e32	0.565995	0.282997	+	0.959121i	$0.408671\pi$
$440$	3.46477e32	0.313701
$441$	−4.61416e32	−0.406078
$442$	−1.30792e32	−0.111893
$443$	9.06289e32	0.753737	0.376869	−	0.926267i	$-0.377001\pi$
$443$	9.06289e32	0.753737	0.376869	+	0.926267i	$0.377001\pi$
$444$	1.04275e33	0.843131
$445$	−2.83154e33	−2.22598
$446$	1.27427e33	0.974034
$447$	9.82078e32	0.729965
$448$	1.41854e32	0.102534
$449$	−1.21579e33	−0.854630	−0.427315	−	0.904103i	$-0.640540\pi$
$449$	−1.21579e33	−0.854630	−0.427315	+	0.904103i	$0.640540\pi$
$450$	2.04446e33	1.39773
$451$	−4.34056e32	−0.288629
$452$	−1.35349e33	−0.875439
$453$	4.21899e33	2.65449
$454$	−4.32422e32	−0.264673
$455$	−2.83428e32	−0.168772
$456$	5.13959e32	0.297761
$457$	−5.59530e32	−0.315407	−0.157703	−	0.987487i	$-0.550409\pi$
$457$	−5.59530e32	−0.315407	−0.157703	+	0.987487i	$0.550409\pi$
$458$	−1.51684e33	−0.831997
$459$	−8.37859e32	−0.447211
$460$	−1.54166e33	−0.800784
$461$	−3.78592e32	−0.191386	−0.0956930	−	0.995411i	$-0.530507\pi$
$461$	−3.78592e32	−0.191386	−0.0956930	+	0.995411i	$0.530507\pi$
$462$	−9.72545e32	−0.478503
$463$	2.77039e33	1.32672	0.663359	−	0.748301i	$-0.269130\pi$
$463$	2.77039e33	1.32672	0.663359	+	0.748301i	$0.269130\pi$
$464$	8.70270e32	0.405676
$465$	5.16985e33	2.34594
$466$	−2.80486e32	−0.123905
$467$	−2.31922e33	−0.997428	−0.498714	−	0.866767i	$-0.666194\pi$
$467$	−2.31922e33	−0.997428	−0.498714	+	0.866767i	$0.666194\pi$
$468$	−1.89399e32	−0.0793058
$469$	−1.61285e33	−0.657556
$470$	1.68255e33	0.667951
$471$	−3.29294e33	−1.27298
$472$	−9.10311e32	−0.342700
$473$	−7.97508e32	−0.292396
$474$	−3.59526e33	−1.28381
$475$	−2.57587e33	−0.895889
$476$	1.49916e33	0.507881
$477$	−1.30739e33	−0.431446
$478$	1.58832e33	0.510609
$479$	2.24376e33	0.702720	0.351360	−	0.936240i	$-0.385719\pi$
$479$	2.24376e33	0.702720	0.351360	+	0.936240i	$0.385719\pi$
$480$	−1.39651e33	−0.426117
$481$	4.84147e32	0.143934
$482$	4.24851e33	1.23069
$483$	4.32737e33	1.22148
$484$	−1.26577e33	−0.348166
$485$	3.15089e33	0.844620
$486$	3.81631e33	0.996989
$487$	3.71393e32	0.0945632	0.0472816	−	0.998882i	$-0.484944\pi$
$487$	3.71393e32	0.0945632	0.0472816	+	0.998882i	$0.484944\pi$
$488$	−1.62854e31	−0.00404157
$489$	−9.13761e33	−2.21041
$490$	−1.57963e33	−0.372480
$491$	−2.65508e33	−0.610323	−0.305161	−	0.952301i	$-0.598710\pi$
$491$	−2.65508e33	−0.610323	−0.305161	+	0.952301i	$0.598710\pi$
$492$	1.74951e33	0.392060
$493$	9.19732e33	2.00944
$494$	2.38629e32	0.0508320
$495$	5.30247e33	1.10132
$496$	−1.20136e33	−0.243306
$497$	−6.81976e33	−1.34684
$498$	−6.75421e33	−1.30079
$499$	−2.39117e33	−0.449111	−0.224556	−	0.974461i	$-0.572093\pi$
$499$	−2.39117e33	−0.449111	−0.224556	+	0.974461i	$0.572093\pi$
$500$	2.60410e33	0.477015
$501$	−5.60855e33	−1.00203
$502$	6.06166e33	1.05632
$503$	−6.34146e33	−1.07793	−0.538964	−	0.842329i	$-0.681184\pi$
$503$	−6.34146e33	−1.07793	−0.538964	+	0.842329i	$0.681184\pi$
$504$	2.17093e33	0.359968
$505$	−2.99412e33	−0.484314
$506$	−2.45613e33	−0.387587
$507$	9.56517e33	1.47263
$508$	−2.23092e33	−0.335111
$509$	−3.62528e32	−0.0531337	−0.0265668	−	0.999647i	$-0.508457\pi$
$509$	−3.62528e32	−0.0531337	−0.0265668	+	0.999647i	$0.508457\pi$
$510$	−1.47588e34	−2.11069
$511$	8.36664e33	1.16759
$512$	3.24519e32	0.0441942
$513$	1.52867e33	0.203164
$514$	2.76637e33	0.358816
$515$	7.26994e33	0.920323
$516$	3.21444e33	0.397177
$517$	2.68059e33	0.323295
$518$	−5.54939e33	−0.653316
$519$	1.19739e34	1.37608
$520$	−6.48395e32	−0.0727442
$521$	8.23573e33	0.902050	0.451025	−	0.892511i	$-0.351058\pi$
$521$	8.23573e33	0.902050	0.451025	+	0.892511i	$0.351058\pi$
$522$	1.33186e34	1.42422
$523$	−1.20443e34	−1.25750	−0.628752	−	0.777606i	$-0.716434\pi$
$523$	−1.20443e34	−1.25750	−0.628752	+	0.777606i	$0.716434\pi$
$524$	1.13063e33	0.115260
$525$	−1.96461e34	−1.95562
$526$	5.82051e33	0.565770
$527$	−1.26964e34	−1.20517
$528$	−2.22488e33	−0.206245
$529$	−1.17149e32	−0.0106057
$530$	−4.47577e33	−0.395749
$531$	−1.39314e34	−1.20313
$532$	−2.73522e33	−0.230726
$533$	8.12291e32	0.0669301
$534$	1.81826e34	1.46349
$535$	1.38868e34	1.09190
$536$	−3.68970e33	−0.283420
$537$	5.94490e33	0.446135
$538$	−7.78769e33	−0.570992
$539$	−2.51661e33	−0.180284
$540$	−4.15365e33	−0.290742
$541$	1.30366e34	0.891657	0.445829	−	0.895118i	$-0.352909\pi$
$541$	1.30366e34	0.891657	0.445829	+	0.895118i	$0.352909\pi$
$542$	−5.97197e33	−0.399141
$543$	−3.07258e34	−2.00681
$544$	3.42963e33	0.218907
$545$	2.64462e34	1.64971
$546$	1.82002e33	0.110960
$547$	−1.78334e34	−1.06266	−0.531328	−	0.847166i	$-0.678307\pi$
$547$	−1.78334e34	−1.06266	−0.531328	+	0.847166i	$0.678307\pi$
$548$	−5.41843e33	−0.315585
$549$	−2.49231e32	−0.0141889
$550$	1.11507e34	0.620539
$551$	−1.67805e34	−0.912871
$552$	9.89969e33	0.526481
$553$	1.91334e34	0.994784
$554$	−2.17534e33	−0.110574
$555$	5.46321e34	2.71510
$556$	−1.54616e33	−0.0751309
$557$	8.73339e33	0.414947	0.207474	−	0.978241i	$-0.433476\pi$
$557$	8.73339e33	0.414947	0.207474	+	0.978241i	$0.433476\pi$
$558$	−1.83856e34	−0.854181
$559$	1.49245e33	0.0678037
$560$	7.43204e33	0.330185
$561$	−2.35134e34	−1.02160
$562$	−1.49493e34	−0.635210
$563$	3.82416e34	1.58921	0.794606	−	0.607126i	$-0.207678\pi$
$563$	3.82416e34	1.58921	0.794606	+	0.607126i	$0.207678\pi$
$564$	−1.08044e34	−0.439149
$565$	−7.09124e34	−2.81914
$566$	−5.89682e33	−0.229304
$567$	−1.51078e34	−0.574661
$568$	−1.56015e34	−0.580514
$569$	3.49591e34	1.27250	0.636248	−	0.771484i	$-0.280485\pi$
$569$	3.49591e34	1.27250	0.636248	+	0.771484i	$0.280485\pi$
$570$	2.69274e34	0.958869
$571$	−3.60524e34	−1.25598	−0.627989	−	0.778222i	$-0.716122\pi$
$571$	−3.60524e34	−1.25598	−0.627989	+	0.778222i	$0.716122\pi$
$572$	−1.03301e33	−0.0352089
$573$	2.63668e34	0.879276
$574$	−9.31065e33	−0.303795
$575$	−4.96155e34	−1.58405
$576$	4.96642e33	0.155154
$577$	−4.45926e34	−1.36322	−0.681609	−	0.731717i	$-0.738719\pi$
$577$	−4.45926e34	−1.36322	−0.681609	+	0.731717i	$0.738719\pi$
$578$	1.26090e34	0.377210
$579$	8.22337e34	2.40751
$580$	4.55953e34	1.30638
$581$	3.59450e34	1.00794
$582$	−2.02333e34	−0.555301
$583$	−7.13067e33	−0.191546
$584$	1.91403e34	0.503255
$585$	−9.92303e33	−0.255385
$586$	5.09967e34	1.28476
$587$	−2.50958e34	−0.618905	−0.309452	−	0.950915i	$-0.600146\pi$
$587$	−2.50958e34	−0.618905	−0.309452	+	0.950915i	$0.600146\pi$
$588$	1.01435e34	0.244890
$589$	2.31645e34	0.547497
$590$	−4.76931e34	−1.10358
$591$	−8.60173e34	−1.94869
$592$	−1.26953e34	−0.281593
$593$	−4.88078e33	−0.106000	−0.0530000	−	0.998595i	$-0.516878\pi$
$593$	−4.88078e33	−0.106000	−0.0530000	+	0.998595i	$0.516878\pi$
$594$	−6.61748e33	−0.140722
$595$	7.85444e34	1.63551
$596$	−1.19566e34	−0.243797
$597$	4.46798e34	0.892138
$598$	4.59639e33	0.0898777
$599$	4.61838e34	0.884412	0.442206	−	0.896914i	$-0.354196\pi$
$599$	4.61838e34	0.884412	0.442206	+	0.896914i	$0.354196\pi$
$600$	−4.49442e34	−0.842913
$601$	−3.07405e34	−0.564651	−0.282325	−	0.959319i	$-0.591106\pi$
$601$	−3.07405e34	−0.564651	−0.282325	+	0.959319i	$0.591106\pi$
$602$	−1.71068e34	−0.307760
$603$	−5.64671e34	−0.995013
$604$	−5.13652e34	−0.886559
$605$	−6.63161e34	−1.12118
$606$	1.92266e34	0.318415
$607$	1.03737e35	1.68297	0.841484	−	0.540282i	$-0.181682\pi$
$607$	1.03737e35	1.68297	0.841484	+	0.540282i	$0.181682\pi$
$608$	−6.25734e33	−0.0994477
$609$	−1.27984e35	−1.99269
$610$	−8.53226e32	−0.0130149
$611$	−5.01644e33	−0.0749688
$612$	5.24869e34	0.768526
$613$	2.85744e34	0.409941	0.204970	−	0.978768i	$-0.434290\pi$
$613$	2.85744e34	0.409941	0.204970	+	0.978768i	$0.434290\pi$
$614$	9.30582e34	1.30813
$615$	9.16606e34	1.26254
$616$	1.18405e34	0.159813
$617$	5.36336e34	0.709370	0.354685	−	0.934986i	$-0.384588\pi$
$617$	5.36336e34	0.709370	0.354685	+	0.934986i	$0.384588\pi$
$618$	−4.66836e34	−0.605073
$619$	6.60909e34	0.839477	0.419738	−	0.907645i	$-0.362122\pi$
$619$	6.60909e34	0.839477	0.419738	+	0.907645i	$0.362122\pi$
$620$	−6.29418e34	−0.783507
$621$	2.94447e34	0.359221
$622$	−7.55041e34	−0.902798
$623$	−9.67651e34	−1.13401
$624$	4.16364e33	0.0478262
$625$	−5.00979e33	−0.0564053
$626$	2.04264e34	0.225431
$627$	4.29000e34	0.464102
$628$	4.00908e34	0.425157
$629$	−1.34168e35	−1.39482
$630$	1.13740e35	1.15919
$631$	8.62816e34	0.862087	0.431043	−	0.902331i	$-0.358146\pi$
$631$	8.62816e34	0.862087	0.431043	+	0.902331i	$0.358146\pi$
$632$	4.37714e34	0.428773
$633$	−5.26679e34	−0.505824
$634$	−3.60234e34	−0.339210
$635$	−1.16883e35	−1.07914
$636$	2.87409e34	0.260188
$637$	4.70958e33	0.0418061
$638$	7.26412e34	0.632302
$639$	−2.38765e35	−2.03803
$640$	1.70022e34	0.142317
$641$	1.77093e35	1.45370	0.726850	−	0.686796i	$-0.240983\pi$
$641$	1.77093e35	1.45370	0.726850	+	0.686796i	$0.240983\pi$
$642$	−8.91737e34	−0.717875
$643$	−7.98617e34	−0.630524	−0.315262	−	0.949005i	$-0.602092\pi$
$643$	−7.98617e34	−0.630524	−0.315262	+	0.949005i	$0.602092\pi$
$644$	−5.26847e34	−0.407954
$645$	1.68412e35	1.27901
$646$	−6.61298e34	−0.492596
$647$	−2.16671e35	−1.58306	−0.791530	−	0.611130i	$-0.790715\pi$
$647$	−2.16671e35	−1.58306	−0.791530	+	0.611130i	$0.790715\pi$
$648$	−3.45619e34	−0.247691
$649$	−7.59833e34	−0.534145
$650$	−2.08674e34	−0.143897
$651$	1.76675e35	1.19512
$652$	1.11248e35	0.738242
$653$	2.41184e35	1.57013	0.785063	−	0.619416i	$-0.212631\pi$
$653$	2.41184e35	1.57013	0.785063	+	0.619416i	$0.212631\pi$
$654$	−1.69823e35	−1.08461
$655$	5.92361e34	0.371168
$656$	−2.12999e34	−0.130942
$657$	2.92923e35	1.76679
$658$	5.74995e34	0.340283
$659$	2.18788e35	1.27045	0.635223	−	0.772329i	$-0.280908\pi$
$659$	2.18788e35	1.27045	0.635223	+	0.772329i	$0.280908\pi$
$660$	−1.16566e35	−0.664162
$661$	−8.90411e34	−0.497820	−0.248910	−	0.968527i	$-0.580072\pi$
$661$	−8.90411e34	−0.497820	−0.248910	+	0.968527i	$0.580072\pi$
$662$	2.44581e35	1.34183
$663$	4.40028e34	0.236898
$664$	8.22310e34	0.434445
$665$	−1.43304e35	−0.742998
$666$	−1.94289e35	−0.988597
$667$	−3.23219e35	−1.61408
$668$	6.82828e34	0.334662
$669$	−4.28705e35	−2.06221
$670$	−1.93311e35	−0.912687
$671$	−1.35934e33	−0.00629934
$672$	−4.77244e34	−0.217083
$673$	2.39665e35	1.07008	0.535040	−	0.844827i	$-0.320297\pi$
$673$	2.39665e35	1.07008	0.535040	+	0.844827i	$0.320297\pi$
$674$	4.44120e34	0.194649
$675$	−1.33678e35	−0.575124
$676$	−1.16454e35	−0.491835
$677$	−3.79216e34	−0.157227	−0.0786137	−	0.996905i	$-0.525049\pi$
$677$	−3.79216e34	−0.157227	−0.0786137	+	0.996905i	$0.525049\pi$
$678$	4.55360e35	1.85346
$679$	1.07679e35	0.430286
$680$	1.79685e35	0.704939
$681$	1.45481e35	0.560361
$682$	−1.00277e35	−0.379225
$683$	−3.21208e35	−1.19269	−0.596345	−	0.802729i	$-0.703381\pi$
$683$	−3.21208e35	−1.19269	−0.596345	+	0.802729i	$0.703381\pi$
$684$	−9.57621e34	−0.349134
$685$	−2.83883e35	−1.01627
$686$	−2.18986e35	−0.769776
$687$	5.10316e35	1.76149
$688$	−3.91351e34	−0.132651
$689$	1.33443e34	0.0444177
$690$	5.18666e35	1.69541
$691$	8.34540e34	0.267899	0.133950	−	0.990988i	$-0.457234\pi$
$691$	8.34540e34	0.267899	0.133950	+	0.990988i	$0.457234\pi$
$692$	−1.45780e35	−0.459591
$693$	1.81207e35	0.561060
$694$	2.94991e34	0.0897047
$695$	−8.10064e34	−0.241941
$696$	−2.92788e35	−0.858890
$697$	−2.25105e35	−0.648597
$698$	2.16178e35	0.611814
$699$	9.43649e34	0.262329
$700$	2.39186e35	0.653147
$701$	1.50008e35	0.402383	0.201191	−	0.979552i	$-0.435519\pi$
$701$	1.50008e35	0.402383	0.201191	+	0.979552i	$0.435519\pi$
$702$	1.23839e34	0.0326320
$703$	2.44790e35	0.633653
$704$	2.70874e34	0.0688827
$705$	−5.66066e35	−1.41417
$706$	−2.32536e35	−0.570731
$707$	−1.02321e35	−0.246730
$708$	3.06259e35	0.725559
$709$	−2.12042e35	−0.493564	−0.246782	−	0.969071i	$-0.579373\pi$
$709$	−2.12042e35	−0.493564	−0.246782	+	0.969071i	$0.579373\pi$
$710$	−8.17397e35	−1.86941
$711$	6.69877e35	1.50531
$712$	−2.21369e35	−0.488783
$713$	4.46186e35	0.968048
$714$	−5.04369e35	−1.07528
$715$	−5.41213e34	−0.113382
$716$	−7.23778e34	−0.149002
$717$	−5.34363e35	−1.08105
$718$	8.96718e34	0.178279
$719$	3.27911e35	0.640686	0.320343	−	0.947302i	$-0.396202\pi$
$719$	3.27911e35	0.640686	0.320343	+	0.947302i	$0.396202\pi$
$720$	2.60201e35	0.499636
$721$	2.48443e35	0.468853
$722$	−2.60588e35	−0.483325
$723$	−1.42934e36	−2.60560
$724$	3.74080e35	0.670243
$725$	1.46740e36	2.58419
$726$	4.25846e35	0.737131
$727$	2.40795e35	0.409701	0.204850	−	0.978793i	$-0.434329\pi$
$727$	2.40795e35	0.409701	0.204850	+	0.978793i	$0.434329\pi$
$728$	−2.21583e34	−0.0370590
$729$	−8.57797e35	−1.41023
$730$	1.00280e36	1.62061
$731$	−4.13594e35	−0.657063
$732$	5.47895e33	0.00855675
$733$	−3.39196e35	−0.520776	−0.260388	−	0.965504i	$-0.583850\pi$
$733$	−3.39196e35	−0.520776	−0.260388	+	0.965504i	$0.583850\pi$
$734$	4.11648e35	0.621334
$735$	5.31439e35	0.788608
$736$	−1.20526e35	−0.175837
$737$	−3.07978e35	−0.441749
$738$	−3.25973e35	−0.459703
$739$	1.23366e36	1.71057	0.855284	−	0.518159i	$-0.173383\pi$
$739$	1.23366e36	1.71057	0.855284	+	0.518159i	$0.173383\pi$
$740$	−6.65134e35	−0.906802
$741$	−8.02829e34	−0.107621
$742$	−1.52955e35	−0.201611
$743$	−6.24478e35	−0.809389	−0.404694	−	0.914452i	$-0.632622\pi$
$743$	−6.24478e35	−0.809389	−0.404694	+	0.914452i	$0.632622\pi$
$744$	4.04177e35	0.515122
$745$	−6.26430e35	−0.785090
$746$	2.58479e35	0.318559
$747$	1.25846e36	1.52522
$748$	2.86270e35	0.341197
$749$	4.74570e35	0.556259
$750$	−8.76105e35	−1.00993
$751$	−4.41291e35	−0.500294	−0.250147	−	0.968208i	$-0.580479\pi$
$751$	−4.41291e35	−0.500294	−0.250147	+	0.968208i	$0.580479\pi$
$752$	1.31541e35	0.146669
$753$	−2.03934e36	−2.23642
$754$	−1.35940e35	−0.146625
$755$	−2.69113e36	−2.85495
$756$	−1.41947e35	−0.148117
$757$	1.83266e35	0.188098	0.0940489	−	0.995568i	$-0.470019\pi$
$757$	1.83266e35	0.188098	0.0940489	+	0.995568i	$0.470019\pi$
$758$	−3.62805e35	−0.366276
$759$	8.26323e35	0.820593
$760$	−3.27835e35	−0.320247
$761$	1.88027e36	1.80681	0.903406	−	0.428787i	$-0.141059\pi$
$761$	1.88027e36	1.80681	0.903406	+	0.428787i	$0.141059\pi$
$762$	7.50557e35	0.709490
$763$	9.03772e35	0.840431
$764$	−3.21010e35	−0.293665
$765$	2.74990e36	2.47485
$766$	3.72046e35	0.329410
$767$	1.42195e35	0.123863
$768$	−1.09179e35	−0.0935671
$769$	1.28453e36	1.08309	0.541546	−	0.840671i	$-0.317839\pi$
$769$	1.28453e36	1.08309	0.541546	+	0.840671i	$0.317839\pi$
$770$	6.20349e35	0.514639
$771$	−9.30700e35	−0.759679
$772$	−1.00118e36	−0.804071
$773$	−1.04808e36	−0.828226	−0.414113	−	0.910225i	$-0.635908\pi$
$773$	−1.04808e36	−0.828226	−0.414113	+	0.910225i	$0.635908\pi$
$774$	−5.98923e35	−0.465703
$775$	−2.02566e36	−1.54987
$776$	2.46335e35	0.185462
$777$	1.86700e36	1.38319
$778$	2.92063e35	0.212927
$779$	4.10703e35	0.294652
$780$	2.18142e35	0.154013
$781$	−1.30225e36	−0.904811
$782$	−1.27377e36	−0.870974
$783$	−8.70840e35	−0.586025
$784$	−1.23495e35	−0.0817894
$785$	2.10044e36	1.36912
$786$	−3.80382e35	−0.244027
$787$	−8.93146e35	−0.563947	−0.281974	−	0.959422i	$-0.590989\pi$
$787$	−8.93146e35	−0.563947	−0.281974	+	0.959422i	$0.590989\pi$
$788$	1.04724e36	0.650832
$789$	−1.95822e36	−1.19784
$790$	2.29328e36	1.38076
$791$	−2.42336e36	−1.43619
$792$	4.14546e35	0.241829
$793$	2.54386e33	0.00146076
$794$	1.22645e35	0.0693257
$795$	1.50580e36	0.837872
$796$	−5.43966e35	−0.297960
$797$	−1.02840e36	−0.554540	−0.277270	−	0.960792i	$-0.589430\pi$
$797$	−1.02840e36	−0.554540	−0.277270	+	0.960792i	$0.589430\pi$
$798$	9.20219e35	0.488489
$799$	1.39017e36	0.726498
$800$	5.47185e35	0.281520
$801$	−3.38782e36	−1.71599
$802$	−2.05041e36	−1.02249
$803$	1.59763e36	0.784392
$804$	1.24134e36	0.600053
$805$	−2.76026e36	−1.31372
$806$	1.87658e35	0.0879385
$807$	2.62004e36	1.20889
$808$	−2.34079e35	−0.106346
$809$	1.33897e36	0.598981	0.299490	−	0.954099i	$-0.403183\pi$
$809$	1.33897e36	0.598981	0.299490	+	0.954099i	$0.403183\pi$
$810$	−1.81077e36	−0.797630
$811$	1.29485e36	0.561643	0.280821	−	0.959760i	$-0.409393\pi$
$811$	1.29485e36	0.561643	0.280821	+	0.959760i	$0.409393\pi$
$812$	1.55818e36	0.665528
$813$	2.00917e36	0.845055
$814$	−1.05967e36	−0.438901
$815$	5.82854e36	2.37733
$816$	−1.15384e36	−0.463467
$817$	7.54600e35	0.298498
$818$	−1.14024e36	−0.444201
$819$	−3.39110e35	−0.130104
$820$	−1.11595e36	−0.421668
$821$	3.91664e34	0.0145755	0.00728777	−	0.999973i	$-0.497680\pi$
$821$	3.91664e34	0.0145755	0.00728777	+	0.999973i	$0.497680\pi$
$822$	1.82294e36	0.668151
$823$	−3.40400e36	−1.22883	−0.614414	−	0.788984i	$-0.710608\pi$
$823$	−3.40400e36	−1.22883	−0.614414	+	0.788984i	$0.710608\pi$
$824$	5.68362e35	0.202085
$825$	−3.75147e36	−1.31379
$826$	−1.62987e36	−0.562213
$827$	−5.02186e36	−1.70626	−0.853132	−	0.521696i	$-0.825300\pi$
$827$	−5.02186e36	−1.70626	−0.853132	+	0.521696i	$0.825300\pi$
$828$	−1.84453e36	−0.617316
$829$	8.20485e35	0.270482	0.135241	−	0.990813i	$-0.456819\pi$
$829$	8.20485e35	0.270482	0.135241	+	0.990813i	$0.456819\pi$
$830$	4.30826e36	1.39902
$831$	7.31856e35	0.234106
$832$	−5.06913e34	−0.0159732
$833$	−1.30513e36	−0.405128
$834$	5.20178e35	0.159066
$835$	3.57748e36	1.07770
$836$	−5.22298e35	−0.155003
$837$	1.20215e36	0.351471
$838$	−2.60845e36	−0.751332
$839$	−5.38664e36	−1.52860	−0.764300	−	0.644861i	$-0.776915\pi$
$839$	−5.38664e36	−1.52860	−0.764300	+	0.644861i	$0.776915\pi$
$840$	−2.50039e36	−0.699062
$841$	5.92900e36	1.63317
$842$	−1.60676e36	−0.436063
$843$	5.02945e36	1.34486
$844$	6.41220e35	0.168938
$845$	−6.10126e36	−1.58384
$846$	2.01310e36	0.514916
$847$	−2.26629e36	−0.571180
$848$	−3.49914e35	−0.0868987
$849$	1.98389e36	0.485479
$850$	5.78284e36	1.39446
$851$	4.71505e36	1.12038
$852$	5.24887e36	1.22905
$853$	9.55369e35	0.220449	0.110225	−	0.993907i	$-0.464843\pi$
$853$	9.55369e35	0.220449	0.110225	+	0.993907i	$0.464843\pi$
$854$	−2.91582e34	−0.00663036
$855$	−5.01718e36	−1.12430
$856$	1.08567e36	0.239759
$857$	−5.39118e36	−1.17334	−0.586669	−	0.809827i	$-0.699561\pi$
$857$	−5.39118e36	−1.17334	−0.586669	+	0.809827i	$0.699561\pi$
$858$	3.47537e35	0.0745436
$859$	5.48992e36	1.16052	0.580258	−	0.814432i	$-0.302952\pi$
$859$	5.48992e36	1.16052	0.580258	+	0.814432i	$0.302952\pi$
$860$	−2.05037e36	−0.427171
$861$	3.13241e36	0.643190
$862$	1.00016e36	0.202407
$863$	−2.89510e36	−0.577469	−0.288735	−	0.957409i	$-0.593234\pi$
$863$	−2.89510e36	−0.577469	−0.288735	+	0.957409i	$0.593234\pi$
$864$	−3.24731e35	−0.0638413
$865$	−7.63772e36	−1.48000
$866$	3.73912e36	0.714161
$867$	−4.24209e36	−0.798623
$868$	−2.15097e36	−0.399152
$869$	3.65359e36	0.668301
$870$	−1.53398e37	−2.76585
$871$	5.76349e35	0.102437
$872$	2.06755e36	0.362244
$873$	3.76991e36	0.651108
$874$	2.32398e36	0.395676
$875$	4.66251e36	0.782562
$876$	−6.43943e36	−1.06548
$877$	2.04429e36	0.333463	0.166731	−	0.986002i	$-0.446679\pi$
$877$	2.04429e36	0.333463	0.166731	+	0.986002i	$0.446679\pi$
$878$	2.48874e36	0.400219
$879$	−1.71570e37	−2.72007
$880$	1.41917e36	0.221820
$881$	−1.76163e36	−0.271466	−0.135733	−	0.990745i	$-0.543339\pi$
$881$	−1.76163e36	−0.271466	−0.135733	+	0.990745i	$0.543339\pi$
$882$	−1.88996e36	−0.287141
$883$	1.25672e37	1.88248	0.941240	−	0.337738i	$-0.109662\pi$
$883$	1.25672e37	1.88248	0.941240	+	0.337738i	$0.109662\pi$
$884$	−5.35724e35	−0.0791203
$885$	1.60456e37	2.33649
$886$	3.71216e36	0.532973
$887$	8.81003e36	1.24719	0.623595	−	0.781748i	$-0.285672\pi$
$887$	8.81003e36	1.24719	0.623595	+	0.781748i	$0.285672\pi$
$888$	4.27112e36	0.596184
$889$	−3.99436e36	−0.549762
$890$	−1.15980e37	−1.57401
$891$	−2.88487e36	−0.386060
$892$	5.21939e36	0.688746
$893$	−2.53636e36	−0.330041
$894$	4.02259e36	0.516163
$895$	−3.79203e36	−0.479826
$896$	5.81034e35	0.0725023
$897$	−1.54638e36	−0.190288
$898$	−4.97986e36	−0.604315
$899$	−1.31962e37	−1.57925
$900$	8.37410e36	0.988341
$901$	−3.69802e36	−0.430436
$902$	−1.77789e36	−0.204091
$903$	5.75530e36	0.651585
$904$	−5.54391e36	−0.619029
$905$	1.95988e37	2.15835
$906$	1.72810e37	1.87701
$907$	−1.59523e37	−1.70896	−0.854482	−	0.519481i	$-0.826125\pi$
$907$	−1.59523e37	−1.70896	−0.854482	+	0.519481i	$0.826125\pi$
$908$	−1.77120e36	−0.187152
$909$	−3.58234e36	−0.373352
$910$	−1.16092e36	−0.119340
$911$	−1.71775e36	−0.174172	−0.0870862	−	0.996201i	$-0.527756\pi$
$911$	−1.71775e36	−0.174172	−0.0870862	+	0.996201i	$0.527756\pi$
$912$	2.10518e36	0.210549
$913$	6.86379e36	0.677142
$914$	−2.29183e36	−0.223026
$915$	2.87054e35	0.0275550
$916$	−6.21298e36	−0.588310
$917$	2.02434e36	0.189089
$918$	−3.43187e36	−0.316226
$919$	−7.70373e35	−0.0700256	−0.0350128	−	0.999387i	$-0.511147\pi$
$919$	−7.70373e35	−0.0700256	−0.0350128	+	0.999387i	$0.511147\pi$
$920$	−6.31464e36	−0.566240
$921$	−3.13079e37	−2.76955
$922$	−1.55071e36	−0.135330
$923$	2.43703e36	0.209817
$924$	−3.98354e36	−0.338353
$925$	−2.14061e37	−1.79377
$926$	1.13475e37	0.938132
$927$	8.69819e36	0.709467
$928$	3.56463e36	0.286856
$929$	1.66420e37	1.32132	0.660662	−	0.750684i	$-0.270276\pi$
$929$	1.66420e37	1.32132	0.660662	+	0.750684i	$0.270276\pi$
$930$	2.11757e37	1.65883
$931$	2.38121e36	0.184046
$932$	−1.14887e36	−0.0876138
$933$	2.54021e37	1.91139
$934$	−9.49954e36	−0.705288
$935$	1.49983e37	1.09874
$936$	−7.75779e35	−0.0560777
$937$	9.66427e36	0.689325	0.344663	−	0.938727i	$-0.387993\pi$
$937$	9.66427e36	0.689325	0.344663	+	0.938727i	$0.387993\pi$
$938$	−6.60622e36	−0.464962
$939$	−6.87214e36	−0.477279
$940$	6.89172e36	0.472312
$941$	−1.33808e37	−0.904923	−0.452461	−	0.891784i	$-0.649454\pi$
$941$	−1.33808e37	−0.904923	−0.452461	+	0.891784i	$0.649454\pi$
$942$	−1.34879e37	−0.900136
$943$	7.91080e36	0.520984
$944$	−3.72863e36	−0.242326
$945$	−7.43690e36	−0.476974
$946$	−3.26659e36	−0.206755
$947$	2.63078e37	1.64328	0.821638	−	0.570010i	$-0.193061\pi$
$947$	2.63078e37	1.64328	0.821638	+	0.570010i	$0.193061\pi$
$948$	−1.47262e37	−0.907791
$949$	−2.98981e36	−0.181893
$950$	−1.05508e37	−0.633489
$951$	1.21195e37	0.718170
$952$	6.14058e36	0.359126
$953$	−9.10378e36	−0.525485	−0.262742	−	0.964866i	$-0.584627\pi$
$953$	−9.10378e36	−0.525485	−0.262742	+	0.964866i	$0.584627\pi$
$954$	−5.35508e36	−0.305078
$955$	−1.68184e37	−0.945677
$956$	6.50575e36	0.361055
$957$	−2.44389e37	−1.33870
$958$	9.19044e36	0.496898
$959$	−9.70142e36	−0.517729
$960$	−5.72011e36	−0.301310
$961$	−1.01623e36	−0.0528386
$962$	1.98307e36	0.101777
$963$	1.66151e37	0.841731
$964$	1.74019e37	0.870230
$965$	−5.24538e37	−2.58932
$966$	1.77249e37	0.863713
$967$	−1.34794e36	−0.0648394	−0.0324197	−	0.999474i	$-0.510321\pi$
$967$	−1.34794e36	−0.0648394	−0.0324197	+	0.999474i	$0.510321\pi$
$968$	−5.18457e36	−0.246190
$969$	2.22483e37	1.04291
$970$	1.29060e37	0.597236
$971$	3.82504e36	0.174741	0.0873707	−	0.996176i	$-0.472154\pi$
$971$	3.82504e36	0.174741	0.0873707	+	0.996176i	$0.472154\pi$
$972$	1.56316e37	0.704978
$973$	−2.76831e36	−0.123255
$974$	1.52123e36	0.0668663
$975$	7.02049e36	0.304656
$976$	−6.67050e34	−0.00285782
$977$	1.16914e37	0.494522	0.247261	−	0.968949i	$-0.420470\pi$
$977$	1.16914e37	0.494522	0.247261	+	0.968949i	$0.420470\pi$
$978$	−3.74277e37	−1.56299
$979$	−1.84776e37	−0.761835
$980$	−6.47014e36	−0.263383
$981$	3.16418e37	1.27174
$982$	−1.08752e37	−0.431563
$983$	1.38138e37	0.541244	0.270622	−	0.962686i	$-0.412771\pi$
$983$	1.38138e37	0.541244	0.270622	+	0.962686i	$0.412771\pi$
$984$	7.16600e36	0.277228
$985$	5.48672e37	2.09585
$986$	3.76722e37	1.42089
$987$	−1.93447e37	−0.720441
$988$	9.77426e35	0.0359436
$989$	1.45348e37	0.527784
$990$	2.17189e37	0.778751
$991$	−3.79186e37	−1.34255	−0.671276	−	0.741207i	$-0.734254\pi$
$991$	−3.79186e37	−1.34255	−0.671276	+	0.741207i	$0.734254\pi$
$992$	−4.92077e36	−0.172043
$993$	−8.22853e37	−2.84090
$994$	−2.79338e37	−0.952356
$995$	−2.84995e37	−0.959510
$996$	−2.76653e37	−0.919799
$997$	5.34619e37	1.75531	0.877657	−	0.479289i	$-0.159106\pi$
$997$	5.34619e37	1.75531	0.877657	+	0.479289i	$0.159106\pi$
$998$	−9.79424e36	−0.317570
$999$	1.27036e37	0.406779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.26.a.b.1.1	✓	2
3.2	odd	2		18.26.a.e.1.1		2
4.3	odd	2		16.26.a.c.1.2		2
5.2	odd	4		50.26.b.e.49.4		4
5.3	odd	4		50.26.b.e.49.1		4
5.4	even	2		50.26.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.b.1.1	✓	2	1.1	even	1	trivial
16.26.a.c.1.2		2	4.3	odd	2
18.26.a.e.1.1		2	3.2	odd	2
50.26.a.c.1.2		2	5.4	even	2
50.26.b.e.49.1		4	5.3	odd	4
50.26.b.e.49.4		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+4096.00 q^{2} -1.37803e6 q^{3} +1.67772e7 q^{4} +8.78994e8 q^{5} -5.64442e9 q^{6} +3.00388e10 q^{7} +6.87195e10 q^{8} +1.05168e12 q^{9} +3.60036e12 q^{10} +5.73599e12 q^{11} -2.31195e13 q^{12} -1.07343e13 q^{13} +1.23039e14 q^{14} -1.21128e15 q^{15} +2.81475e14 q^{16} +2.97473e15 q^{17} +4.30769e15 q^{18} -5.42738e15 q^{19} +1.47471e16 q^{20} -4.13944e16 q^{21} +2.34946e16 q^{22} -1.04540e17 q^{23} -9.46976e16 q^{24} +4.74607e17 q^{25} -4.39677e16 q^{26} -2.81659e17 q^{27} +5.03967e17 q^{28} +3.09182e18 q^{29} -4.96141e18 q^{30} -4.26809e18 q^{31} +1.15292e18 q^{32} -7.90437e18 q^{33} +1.21845e19 q^{34} +2.64039e19 q^{35} +1.76443e19 q^{36} -4.51028e19 q^{37} -2.22305e19 q^{38} +1.47922e19 q^{39} +6.04040e19 q^{40} -7.56724e19 q^{41} -1.69551e20 q^{42} -1.39036e20 q^{43} +9.62339e19 q^{44} +9.24421e20 q^{45} -4.28196e20 q^{46} +4.67328e20 q^{47} -3.87881e20 q^{48} -4.38741e20 q^{49} +1.94399e21 q^{50} -4.09927e21 q^{51} -1.80092e20 q^{52} -1.24315e21 q^{53} -1.15368e21 q^{54} +5.04190e21 q^{55} +2.06425e21 q^{56} +7.47909e21 q^{57} +1.26641e22 q^{58} -1.32468e22 q^{59} -2.03219e22 q^{60} -2.36984e20 q^{61} -1.74821e22 q^{62} +3.15912e22 q^{63} +4.72237e21 q^{64} -9.43539e21 q^{65} -3.23763e22 q^{66} -5.36922e22 q^{67} +4.99076e22 q^{68} +1.44059e23 q^{69} +1.08150e23 q^{70} -2.27032e23 q^{71} +7.22710e22 q^{72} +2.78528e23 q^{73} -1.84741e23 q^{74} -6.54024e23 q^{75} -9.10563e22 q^{76} +1.72302e23 q^{77} +6.05889e22 q^{78} +6.36958e23 q^{79} +2.47415e23 q^{80} -5.02942e23 q^{81} -3.09954e23 q^{82} +1.19662e24 q^{83} -6.94482e23 q^{84} +2.61477e24 q^{85} -5.69491e23 q^{86} -4.26063e24 q^{87} +3.94174e23 q^{88} -3.22134e24 q^{89} +3.78643e24 q^{90} -3.22445e23 q^{91} -1.75389e24 q^{92} +5.88156e24 q^{93} +1.91418e24 q^{94} -4.77063e24 q^{95} -1.58876e24 q^{96} +3.58465e24 q^{97} -1.79708e24 q^{98} +6.03243e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8192 q^{2} + 379848 q^{3} + 33554432 q^{4} + 741953100 q^{5} + 1555857408 q^{6} - 376536944 q^{7} + 137438953472 q^{8} + 3294531432666 q^{9} + 3039039897600 q^{10} + 8323034610264 q^{11} + 6372791943168 q^{12}+ \cdots + 11\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 8192 * q^2 + 379848 * q^3 + 33554432 * q^4 + 741953100 * q^5 + 1555857408 * q^6 - 376536944 * q^7 + 137438953472 * q^8 + 3294531432666 * q^9 + 3039039897600 * q^10 + 8323034610264 * q^11 + 6372791943168 * q^12 - 106467053152292 * q^13 - 1542295322624 * q^14 - 1452182413035600 * q^15 + 562949953421312 * q^16 + 1327878920113956 * q^17 + 13494400748199936 * q^18 - 477079242949400 * q^19 + 12447907420569600 * q^20 - 94860791661752256 * q^21 + 34091149763641344 * q^22 - 115305025781473872 * q^23 + 26102955799216128 * q^24 + 195364218352298750 * q^25 - 436089049711788032 * q^26 + 2171569557205152720 * q^27 - 6317241641467904 * q^28 + 1724412645206435580 * q^29 - 5948139163793817600 * q^30 - 8688082288351126976 * q^31 + 2305843009213693952 * q^32 - 3356662204005020064 * q^33 + 5438992056786763776 * q^34 + 30572039779548136800 * q^35 + 55273065464626937856 * q^36 - 34908364049750170484 * q^37 - 1954116579120742400 * q^38 - 153494373835331105808 * q^39 + 50986628794653081600 * q^40 + 83014324355953468884 * q^41 - 388549802646537240576 * q^42 + 44539608583471901848 * q^43 + 139637349431874945024 * q^44 + 617059152350257182300 * q^45 - 472289385600916979712 * q^46 + 1869360732054674599776 * q^47 + 106917706953589260288 * q^48 - 854718643011973772046 * q^49 + 800211838371015680000 * q^50 - 6994225992587553820656 * q^51 - 1786220747619483779072 * q^52 - 3242170458210097794132 * q^53 + 8894748906312305541120 * q^54 + 4687370283547568509200 * q^55 - 25875421763452534784 * q^56 + 16181115057055601354400 * q^57 + 7063194194765560135680 * q^58 - 17413675430632049453640 * q^59 - 24363578014899476889600 * q^60 + 33975859953090212810044 * q^61 - 35586385053086216093696 * q^62 - 36625774166984600306352 * q^63 + 9444732965739290427392 * q^64 + 3683906908205094047400 * q^65 - 13748888387604562182144 * q^66 + 33012908196969622380616 * q^67 + 22278111464598584426496 * q^68 + 125135868082548386734272 * q^69 + 125223074937029168332800 * q^70 - 278348008145600813615856 * q^71 + 226398476143111937458176 * q^72 + 313442631796571689392148 * q^73 - 142984659147776698302464 * q^74 - 1144898988230230172205000 * q^75 - 8004061508078560870400 * q^76 + 93616352280445975603392 * q^77 - 628712955229516209389568 * q^78 + 928546182288781647817120 * q^79 + 208841231542899022233600 * q^80 + 1909195802481672047728242 * q^81 + 340026672561985408548864 * q^82 - 452542629950725008985752 * q^83 - 1591499991640216537399296 * q^84 + 2840452690831654686931800 * q^85 + 182434236757900909969408 * q^86 - 6664364855011895770504080 * q^87 + 571954583272959774818304 * q^88 - 2346904179674200701244620 * q^89 + 2527474288026653418700800 * q^90 + 2589295264446210583737824 * q^91 - 1934497323421355948900352 * q^92 - 1888263951389289833389824 * q^93 + 7656901558495947160682496 * q^94 - 5449023740708681753370000 * q^95 + 437934927681901610139648 * q^96 + 13645482361777595497674436 * q^97 - 3500927561777044570300416 * q^98 + 11834785687944312803841912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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