LMFDB - Embedded newform 1.28.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,28,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	1.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:	$4.61855574838$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{18209}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4552 $ x^2 - x - 4552
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$67.9704$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} +O(q^{10})$	\(q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} -1.07895e13 q^{10} +2.06714e14 q^{11} -7.43249e14 q^{12} -1.66656e14 q^{13} +3.68421e15 q^{14} -1.98410e15 q^{15} -3.55072e14 q^{16} -5.47219e15 q^{17} -7.89105e16 q^{18} +1.61471e17 q^{19} +1.24526e17 q^{20} +6.77495e17 q^{21} -3.86837e18 q^{22} +2.80341e18 q^{23} +5.26544e18 q^{24} -7.11816e18 q^{25} +3.11874e18 q^{26} +1.17308e19 q^{27} -4.25209e19 q^{28} -2.99842e18 q^{29} +3.71297e19 q^{30} +9.09190e19 q^{31} +2.12009e20 q^{32} -7.11360e20 q^{33} +1.02404e20 q^{34} -1.13509e20 q^{35} +9.10738e20 q^{36} +1.50001e21 q^{37} -3.02171e21 q^{38} +5.73510e20 q^{39} -8.82187e20 q^{40} +5.47146e21 q^{41} -1.26784e22 q^{42} -6.81035e21 q^{43} +4.46463e22 q^{44} +2.43121e21 q^{45} -5.24619e22 q^{46} -9.41657e21 q^{47} +1.22190e21 q^{48} -2.69532e22 q^{49} +1.33206e23 q^{50} +1.88313e22 q^{51} -3.59946e22 q^{52} -5.35936e22 q^{53} -2.19525e23 q^{54} +1.19183e23 q^{55} +3.01233e23 q^{56} -5.55667e23 q^{57} +5.61113e22 q^{58} +9.16258e23 q^{59} -4.28528e23 q^{60} +1.47362e24 q^{61} -1.70142e24 q^{62} -8.30166e23 q^{63} -3.91980e24 q^{64} -9.60874e22 q^{65} +1.33121e25 q^{66} -3.21915e24 q^{67} -1.18189e24 q^{68} -9.64729e24 q^{69} +2.12417e24 q^{70} +3.38255e24 q^{71} -6.45199e24 q^{72} +1.32172e25 q^{73} -2.80705e25 q^{74} +2.44955e25 q^{75} +3.48748e25 q^{76} -4.06965e25 q^{77} -1.07324e25 q^{78} +4.66230e25 q^{79} -2.04720e23 q^{80} -7.25240e25 q^{81} -1.02391e26 q^{82} +7.14690e25 q^{83} +1.46326e26 q^{84} -3.15505e24 q^{85} +1.27446e26 q^{86} +1.03184e25 q^{87} -3.16290e26 q^{88} -1.40708e26 q^{89} -4.54967e25 q^{90} +3.28102e25 q^{91} +6.05484e26 q^{92} -3.12877e26 q^{93} +1.76218e26 q^{94} +9.30980e25 q^{95} -7.29582e26 q^{96} +3.77568e26 q^{97} +5.04391e26 q^{98} +8.71662e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8280 q^{2} - 1286280 q^{3} + 190623296 q^{4} + 5443587900 q^{5} + 86882873184 q^{6} - 175391963600 q^{7} - 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) $ 2 * q - 8280 * q^2 - 1286280 * q^3 + 190623296 * q^4 + 5443587900 * q^5 + 86882873184 * q^6 - 175391963600 * q^7 - 3195032348160 * q^8 + 1235136554154 * q^9	$ 2 q - 8280 q^{2} - 1286280 q^{3} + 190623296 q^{4} + 5443587900 q^{5} + 86882873184 q^{6} - 175391963600 q^{7} - 3195032348160 q^{8} + 1235136554154 q^{9} + 39991096148400 q^{10} + 138167337691944 q^{11} - 797895007176960 q^{12} - 753433801271060 q^{13} + 39\!\cdots\!12 q^{14}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 8280 * q^2 - 1286280 * q^3 + 190623296 * q^4 + 5443587900 * q^5 + 86882873184 * q^6 - 175391963600 * q^7 - 3195032348160 * q^8 + 1235136554154 * q^9 + 39991096148400 * q^10 + 138167337691944 * q^11 - 797895007176960 * q^12 - 753433801271060 * q^13 + 3908340052811712 * q^14 + 8504300488438800 * q^15 - 14322995785166848 * q^16 - 29753620331011740 * q^17 - 110019470226337080 * q^18 + 404565810372684760 * q^19 + 1109219331427200 * q^20 + 723787313583184704 * q^21 - 4583556785578779360 * q^22 + 2929078923121218960 * q^23 + 1677495533792532480 * q^24 + 9119218786673228750 * q^25 - 3003459254146640016 * q^26 - 11127665129740313040 * q^27 - 43065656535315868160 * q^28 - 15546679995448558260 * q^29 + 146561411061600148800 * q^30 + 28544554594467385024 * q^31 + 289738949030869893120 * q^32 - 859077391009750054560 * q^33 - 150938335185934859568 * q^34 - 8958395384765013600 * q^35 + 986344620988374211392 * q^36 + 1867697204682824566780 * q^37 - 485361223888169521440 * q^38 - 690990221801025527472 * q^39 - 8985527186071883904000 * q^40 + 9081343698046512254964 * q^41 - 12195371021026332061440 * q^42 + 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 - 12080376719602732775700 * q^45 - 51150723570313970279616 * q^46 - 1150251488862201070560 * q^47 - 28878849836569912688640 * q^48 - 92204113217840907690414 * q^49 + 302620649115949014735000 * q^50 - 33494974704727214464656 * q^51 - 21115266673184124022400 * q^52 + 106953735591470060758620 * q^53 - 458020779785618027135040 * q^54 - 214436254091483969701200 * q^55 + 265467760964859260989440 * q^56 - 31800538920577362634080 * q^57 - 74812163717162466470160 * q^58 + 2009620977624026488631880 * q^59 - 694490206253033569881600 * q^60 + 147857426692448940370444 * q^61 - 2352212714010270811080960 * q^62 - 894215232558851858338320 * q^63 - 1234057803938137445761024 * q^64 - 2951949350200452960922200 * q^65 + 11770868153144268253438848 * q^66 + 3051578535738098902157560 * q^67 - 566166870324676171716480 * q^68 - 9376480489705868528695872 * q^69 + 3215012724032159046326400 * q^70 - 13175198820369338598286416 * q^71 - 1487763126543110308830720 * q^72 + 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 + 59486914888952006559645000 * q^75 + 28710432717942786872615680 * q^76 - 42169025756092787413646400 * q^77 - 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 - 68186991639088251432345600 * q^80 - 99047155826597708238103278 * q^81 - 64726649726985190956760560 * q^82 + 171806873410054757883176280 * q^83 + 145152183633423443589998592 * q^84 - 121333441005595565089302600 * q^85 + 252189883901197432712215584 * q^86 - 16722988656204557792643120 * q^87 - 202163623954874235550955520 * q^88 - 313473438761105539763494380 * q^89 - 196904738457998748777517200 * q^90 + 20205365125040878536694304 * q^91 + 602296848225491467788034560 * q^92 - 447293490375807514724002560 * q^93 + 262465434750720041893579392 * q^94 + 1276245244260479145691314000 * q^95 - 562074901098402916384505856 * q^96 - 653202933397052842883888060 * q^97 - 176410316250092689584969240 * q^98 + 1076041779280842335610479688 * 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 $

$2$	−18713.6	−1.61530	−0.807648	−	0.589664i	$-0.799260\pi$
$2$	−18713.6	−1.61530	−0.807648	+	0.589664i	$0.799260\pi$
$3$	−3.44127e6	−1.24618	−0.623092	−	0.782149i	$-0.714124\pi$
$3$	−3.44127e6	−1.24618	−0.623092	+	0.782149i	$0.714124\pi$
$4$	2.15981e8	1.60918
$5$	5.76560e8	0.211227	0.105614	−	0.994407i	$-0.466319\pi$
$5$	5.76560e8	0.211227	0.105614	+	0.994407i	$0.466319\pi$
$6$	6.43986e10	2.01296
$7$	−1.96873e11	−0.768004	−0.384002	−	0.923332i	$-0.625454\pi$
$7$	−1.96873e11	−0.768004	−0.384002	+	0.923332i	$0.625454\pi$
$8$	−1.53009e12	−0.984013
$9$	4.21675e12	0.552973
$10$	−1.07895e13	−0.341194
$11$	2.06714e14	1.80538	0.902691	−	0.430290i	$-0.141589\pi$
$11$	2.06714e14	1.80538	0.902691	+	0.430290i	$0.141589\pi$
$12$	−7.43249e14	−2.00534
$13$	−1.66656e14	−0.152611	−0.0763057	−	0.997084i	$-0.524312\pi$
$13$	−1.66656e14	−0.152611	−0.0763057	+	0.997084i	$0.524312\pi$
$14$	3.68421e15	1.24055
$15$	−1.98410e15	−0.263228
$16$	−3.55072e14	−0.0197105
$17$	−5.47219e15	−0.133999	−0.0669994	−	0.997753i	$-0.521343\pi$
$17$	−5.47219e15	−0.133999	−0.0669994	+	0.997753i	$0.521343\pi$
$18$	−7.89105e16	−0.893215
$19$	1.61471e17	0.880891	0.440445	−	0.897779i	$-0.354821\pi$
$19$	1.61471e17	0.880891	0.440445	+	0.897779i	$0.354821\pi$
$20$	1.24526e17	0.339903
$21$	6.77495e17	0.957074
$22$	−3.86837e18	−2.91623
$23$	2.80341e18	1.15974	0.579870	−	0.814709i	$-0.303103\pi$
$23$	2.80341e18	1.15974	0.579870	+	0.814709i	$0.303103\pi$
$24$	5.26544e18	1.22626
$25$	−7.11816e18	−0.955383
$26$	3.11874e18	0.246513
$27$	1.17308e19	0.557078
$28$	−4.25209e19	−1.23586
$29$	−2.99842e18	−0.0542650	−0.0271325	−	0.999632i	$-0.508638\pi$
$29$	−2.99842e18	−0.0542650	−0.0271325	+	0.999632i	$0.508638\pi$
$30$	3.71297e19	0.425191
$31$	9.09190e19	0.668763	0.334381	−	0.942438i	$-0.391473\pi$
$31$	9.09190e19	0.668763	0.334381	+	0.942438i	$0.391473\pi$
$32$	2.12009e20	1.01585
$33$	−7.11360e20	−2.24984
$34$	1.02404e20	0.216448
$35$	−1.13509e20	−0.162223
$36$	9.10738e20	0.889835
$37$	1.50001e21	1.01244	0.506220	−	0.862404i	$-0.331042\pi$
$37$	1.50001e21	1.01244	0.506220	+	0.862404i	$0.331042\pi$
$38$	−3.02171e21	−1.42290
$39$	5.73510e20	0.190182
$40$	−8.82187e20	−0.207850
$41$	5.47146e21	0.923679	0.461840	−	0.886963i	$-0.347190\pi$
$41$	5.47146e21	0.923679	0.461840	+	0.886963i	$0.347190\pi$
$42$	−1.26784e22	−1.54596
$43$	−6.81035e21	−0.604429	−0.302215	−	0.953240i	$-0.597726\pi$
$43$	−6.81035e21	−0.604429	−0.302215	+	0.953240i	$0.597726\pi$
$44$	4.46463e22	2.90519
$45$	2.43121e21	0.116803
$46$	−5.24619e22	−1.87333
$47$	−9.41657e21	−0.251520	−0.125760	−	0.992061i	$-0.540137\pi$
$47$	−9.41657e21	−0.251520	−0.125760	+	0.992061i	$0.540137\pi$
$48$	1.22190e21	0.0245628
$49$	−2.69532e22	−0.410169
$50$	1.33206e23	1.54323
$51$	1.88313e22	0.166987
$52$	−3.59946e22	−0.245580
$53$	−5.35936e22	−0.282741	−0.141370	−	0.989957i	$-0.545151\pi$
$53$	−5.35936e22	−0.282741	−0.141370	+	0.989957i	$0.545151\pi$
$54$	−2.19525e23	−0.899846
$55$	1.19183e23	0.381346
$56$	3.01233e23	0.755726
$57$	−5.55667e23	−1.09775
$58$	5.61113e22	0.0876541
$59$	9.16258e23	1.13636	0.568180	−	0.822904i	$-0.307648\pi$
$59$	9.16258e23	1.13636	0.568180	+	0.822904i	$0.307648\pi$
$60$	−4.28528e23	−0.423582
$61$	1.47362e24	1.16529	0.582643	−	0.812728i	$-0.302019\pi$
$61$	1.47362e24	1.16529	0.582643	+	0.812728i	$0.302019\pi$
$62$	−1.70142e24	−1.08025
$63$	−8.30166e23	−0.424685
$64$	−3.91980e24	−1.62119
$65$	−9.60874e22	−0.0322356
$66$	1.33121e25	3.63415
$67$	−3.21915e24	−0.717349	−0.358675	−	0.933463i	$-0.616771\pi$
$67$	−3.21915e24	−0.717349	−0.358675	+	0.933463i	$0.616771\pi$
$68$	−1.18189e24	−0.215629
$69$	−9.64729e24	−1.44525
$70$	2.12417e24	0.262039
$71$	3.38255e24	0.344554	0.172277	−	0.985049i	$-0.444888\pi$
$71$	3.38255e24	0.344554	0.172277	+	0.985049i	$0.444888\pi$
$72$	−6.45199e24	−0.544133
$73$	1.32172e25	0.925295	0.462648	−	0.886542i	$-0.346900\pi$
$73$	1.32172e25	0.925295	0.462648	+	0.886542i	$0.346900\pi$
$74$	−2.80705e25	−1.63539
$75$	2.44955e25	1.19058
$76$	3.48748e25	1.41752
$77$	−4.06965e25	−1.38654
$78$	−1.07324e25	−0.307200
$79$	4.66230e25	1.12366	0.561830	−	0.827253i	$-0.310098\pi$
$79$	4.66230e25	1.12366	0.561830	+	0.827253i	$0.310098\pi$
$80$	−2.04720e23	−0.00416338
$81$	−7.25240e25	−1.24719
$82$	−1.02391e26	−1.49202
$83$	7.14690e25	0.884226	0.442113	−	0.896959i	$-0.354229\pi$
$83$	7.14690e25	0.884226	0.442113	+	0.896959i	$0.354229\pi$
$84$	1.46326e26	1.54011
$85$	−3.15505e24	−0.0283042
$86$	1.27446e26	0.976332
$87$	1.03184e25	0.0676242
$88$	−3.16290e26	−1.77652
$89$	−1.40708e26	−0.678504	−0.339252	−	0.940696i	$-0.610174\pi$
$89$	−1.40708e26	−0.678504	−0.339252	+	0.940696i	$0.610174\pi$
$90$	−4.54967e25	−0.188671
$91$	3.28102e25	0.117206
$92$	6.05484e26	1.86624
$93$	−3.12877e26	−0.833401
$94$	1.76218e26	0.406279
$95$	9.30980e25	0.186068
$96$	−7.29582e26	−1.26594
$97$	3.77568e26	0.569609	0.284805	−	0.958586i	$-0.408071\pi$
$97$	3.77568e26	0.569609	0.284805	+	0.958586i	$0.408071\pi$
$98$	5.04391e26	0.662545
$99$	8.71662e26	0.998327
$100$	−1.53739e27	−1.53739
$101$	−1.82546e27	−1.59600	−0.798002	−	0.602654i	$-0.794110\pi$
$101$	−1.82546e27	−1.59600	−0.798002	+	0.602654i	$0.794110\pi$
$102$	−3.52401e26	−0.269734
$103$	2.87048e27	1.92598	0.962991	−	0.269534i	$-0.0868695\pi$
$103$	2.87048e27	1.92598	0.962991	+	0.269534i	$0.0868695\pi$
$104$	2.54999e26	0.150172
$105$	3.90617e26	0.202160
$106$	1.00293e27	0.456710
$107$	−1.31331e27	−0.526849	−0.263425	−	0.964680i	$-0.584852\pi$
$107$	−1.31331e27	−0.526849	−0.263425	+	0.964680i	$0.584852\pi$
$108$	2.53362e27	0.896441
$109$	−3.16013e27	−0.987296	−0.493648	−	0.869662i	$-0.664337\pi$
$109$	−3.16013e27	−0.987296	−0.493648	+	0.869662i	$0.664337\pi$
$110$	−2.23035e27	−0.615986
$111$	−5.16192e27	−1.26169
$112$	6.99043e25	0.0151377
$113$	3.68033e27	0.706851	0.353425	−	0.935463i	$-0.385017\pi$
$113$	3.68033e27	0.706851	0.353425	+	0.935463i	$0.385017\pi$
$114$	1.03985e28	1.77319
$115$	1.61633e27	0.244969
$116$	−6.47603e26	−0.0873224
$117$	−7.02748e26	−0.0843899
$118$	−1.71465e28	−1.83556
$119$	1.07733e27	0.102912
$120$	3.03584e27	0.259020
$121$	2.96208e28	2.25940
$122$	−2.75767e28	−1.88228
$123$	−1.88288e28	−1.15107
$124$	1.96368e28	1.07616
$125$	−8.39976e27	−0.413030
$126$	1.55354e28	0.685993
$127$	−2.69227e28	−1.06849	−0.534243	−	0.845331i	$-0.679403\pi$
$127$	−2.69227e28	−1.06849	−0.534243	+	0.845331i	$0.679403\pi$
$128$	4.48982e28	1.60285
$129$	2.34363e28	0.753229
$130$	1.79814e27	0.0520701
$131$	3.17810e28	0.829860	0.414930	−	0.909853i	$-0.363806\pi$
$131$	3.17810e28	0.829860	0.414930	+	0.909853i	$0.363806\pi$
$132$	−1.53640e29	−3.62040
$133$	−3.17894e28	−0.676528
$134$	6.02418e28	1.15873
$135$	6.76350e27	0.117670
$136$	8.37292e27	0.131857
$137$	2.13194e28	0.304122	0.152061	−	0.988371i	$-0.451409\pi$
$137$	2.13194e28	0.304122	0.152061	+	0.988371i	$0.451409\pi$
$138$	1.80536e29	2.33451
$139$	−1.15969e29	−1.36032	−0.680161	−	0.733062i	$-0.738090\pi$
$139$	−1.15969e29	−1.36032	−0.680161	+	0.733062i	$0.738090\pi$
$140$	−2.45159e28	−0.261047
$141$	3.24050e28	0.313439
$142$	−6.32998e28	−0.556557
$143$	−3.44502e28	−0.275522
$144$	−1.49725e27	−0.0108993
$145$	−1.72877e27	−0.0114622
$146$	−2.47341e29	−1.49463
$147$	9.27533e28	0.511146
$148$	3.23973e29	1.62920
$149$	2.70481e29	1.24200	0.621000	−	0.783810i	$-0.286727\pi$
$149$	2.70481e29	1.24200	0.621000	+	0.783810i	$0.286727\pi$
$150$	−4.58399e29	−1.92314
$151$	6.43669e28	0.246873	0.123437	−	0.992352i	$-0.460608\pi$
$151$	6.43669e28	0.246873	0.123437	+	0.992352i	$0.460608\pi$
$152$	−2.47065e29	−0.866808
$153$	−2.30748e28	−0.0740977
$154$	7.61579e29	2.23968
$155$	5.24203e28	0.141261
$156$	1.23867e29	0.306037
$157$	−7.36476e29	−1.66922	−0.834609	−	0.550842i	$-0.814307\pi$
$157$	−7.36476e29	−1.66922	−0.834609	+	0.550842i	$0.814307\pi$
$158$	−8.72484e29	−1.81504
$159$	1.84430e29	0.352347
$160$	1.22236e29	0.214575
$161$	−5.51917e29	−0.890686
$162$	1.35718e30	2.01459
$163$	4.91659e29	0.671632	0.335816	−	0.941928i	$-0.390988\pi$
$163$	4.91659e29	0.671632	0.335816	+	0.941928i	$0.390988\pi$
$164$	1.18173e30	1.48637
$165$	−4.10142e29	−0.475226
$166$	−1.33744e30	−1.42829
$167$	6.37427e29	0.627709	0.313854	−	0.949471i	$-0.398380\pi$
$167$	6.37427e29	0.627709	0.313854	+	0.949471i	$0.398380\pi$
$168$	−1.03663e30	−0.941774
$169$	−1.16476e30	−0.976710
$170$	5.90423e28	0.0457196
$171$	6.80884e29	0.487109
$172$	−1.47091e30	−0.972638
$173$	2.71145e30	1.65798	0.828989	−	0.559265i	$-0.188917\pi$
$173$	2.71145e30	1.65798	0.828989	+	0.559265i	$0.188917\pi$
$174$	−1.93094e29	−0.109233
$175$	1.40138e30	0.733738
$176$	−7.33984e28	−0.0355849
$177$	−3.15309e30	−1.41611
$178$	2.63315e30	1.09599
$179$	−1.65055e30	−0.636961	−0.318481	−	0.947929i	$-0.603173\pi$
$179$	−1.65055e30	−0.636961	−0.318481	+	0.947929i	$0.603173\pi$
$180$	5.25095e29	0.187957
$181$	4.30260e30	1.42913	0.714563	−	0.699571i	$-0.246626\pi$
$181$	4.30260e30	1.42913	0.714563	+	0.699571i	$0.246626\pi$
$182$	−6.13997e29	−0.189323
$183$	−5.07112e30	−1.45216
$184$	−4.28946e30	−1.14120
$185$	8.64843e29	0.213855
$186$	5.85506e30	1.34619
$187$	−1.13118e30	−0.241919
$188$	−2.03380e30	−0.404741
$189$	−2.30948e30	−0.427838
$190$	−1.74220e30	−0.300555
$191$	5.35850e30	0.861177	0.430589	−	0.902548i	$-0.358306\pi$
$191$	5.35850e30	0.861177	0.430589	+	0.902548i	$0.358306\pi$
$192$	1.34891e31	2.02030
$193$	2.47114e30	0.345044	0.172522	−	0.985006i	$-0.444808\pi$
$193$	2.47114e30	0.345044	0.172522	+	0.985006i	$0.444808\pi$
$194$	−7.06566e30	−0.920088
$195$	3.30663e29	0.0401715
$196$	−5.82138e30	−0.660038
$197$	−4.41349e30	−0.467185	−0.233592	−	0.972335i	$-0.575048\pi$
$197$	−4.41349e30	−0.467185	−0.233592	+	0.972335i	$0.575048\pi$
$198$	−1.63119e31	−1.61259
$199$	−1.58034e31	−1.45960	−0.729802	−	0.683658i	$-0.760388\pi$
$199$	−1.58034e31	−1.45960	−0.729802	+	0.683658i	$0.760388\pi$
$200$	1.08914e31	0.940110
$201$	1.10780e31	0.893949
$202$	3.41610e31	2.57802
$203$	5.90310e29	0.0416758
$204$	4.06720e30	0.268713
$205$	3.15463e30	0.195106
$206$	−5.37170e31	−3.11103
$207$	1.18213e31	0.641305
$208$	5.91750e28	0.00300804
$209$	3.33784e31	1.59034
$210$	−7.30984e30	−0.326548
$211$	−1.50086e31	−0.628820	−0.314410	−	0.949287i	$-0.601807\pi$
$211$	−1.50086e31	−0.628820	−0.314410	+	0.949287i	$0.601807\pi$
$212$	−1.15752e31	−0.454982
$213$	−1.16403e31	−0.429377
$214$	2.45768e31	0.851018
$215$	−3.92658e30	−0.127672
$216$	−1.79491e31	−0.548172
$217$	−1.78995e31	−0.513613
$218$	5.91374e31	1.59478
$219$	−4.54839e31	−1.15309
$220$	2.57413e31	0.613655
$221$	9.11975e29	0.0204497
$222$	9.65982e31	2.03800
$223$	−1.04534e31	−0.207559	−0.103779	−	0.994600i	$-0.533094\pi$
$223$	−1.04534e31	−0.207559	−0.103779	+	0.994600i	$0.533094\pi$
$224$	−4.17390e31	−0.780178
$225$	−3.00155e31	−0.528301
$226$	−6.88722e31	−1.14177
$227$	9.45028e31	1.47603	0.738016	−	0.674783i	$-0.235763\pi$
$227$	9.45028e31	1.47603	0.738016	+	0.674783i	$0.235763\pi$
$228$	−1.20013e32	−1.76648
$229$	−6.26689e31	−0.869508	−0.434754	−	0.900549i	$-0.643165\pi$
$229$	−6.26689e31	−0.869508	−0.434754	+	0.900549i	$0.643165\pi$
$230$	−3.02474e31	−0.395697
$231$	1.40048e32	1.72788
$232$	4.58785e30	0.0533975
$233$	7.87335e31	0.864678	0.432339	−	0.901711i	$-0.357688\pi$
$233$	7.87335e31	0.864678	0.432339	+	0.901711i	$0.357688\pi$
$234$	1.31509e31	0.136315
$235$	−5.42922e30	−0.0531277
$236$	1.97894e32	1.82861
$237$	−1.60442e32	−1.40029
$238$	−2.01607e31	−0.166233
$239$	−5.65108e30	−0.0440311	−0.0220156	−	0.999758i	$-0.507008\pi$
$239$	−5.65108e30	−0.0440311	−0.0220156	+	0.999758i	$0.507008\pi$
$240$	7.04498e29	0.00518834
$241$	−4.42939e31	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$241$	−4.42939e31	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$242$	−5.54311e32	−3.64961
$243$	1.60121e32	0.997154
$244$	3.18274e32	1.87516
$245$	−1.55401e31	−0.0866389
$246$	3.52354e32	1.85933
$247$	−2.69102e31	−0.134434
$248$	−1.39114e32	−0.658071
$249$	−2.45944e32	−1.10191
$250$	1.57190e32	0.667166
$251$	−3.28116e32	−1.31957	−0.659785	−	0.751454i	$-0.729353\pi$
$251$	−3.28116e32	−1.31957	−0.659785	+	0.751454i	$0.729353\pi$
$252$	−1.79300e32	−0.683397
$253$	5.79505e32	2.09377
$254$	5.03822e32	1.72592
$255$	1.08574e31	0.0352722
$256$	−3.14099e32	−0.967894
$257$	3.48288e31	0.101822	0.0509109	−	0.998703i	$-0.483788\pi$
$257$	3.48288e31	0.101822	0.0509109	+	0.998703i	$0.483788\pi$
$258$	−4.38577e32	−1.21669
$259$	−2.95311e32	−0.777559
$260$	−2.07531e31	−0.0518731
$261$	−1.26436e31	−0.0300071
$262$	−5.94736e32	−1.34047
$263$	3.82694e31	0.0819311	0.0409656	−	0.999161i	$-0.486957\pi$
$263$	3.82694e31	0.0819311	0.0409656	+	0.999161i	$0.486957\pi$
$264$	1.08844e33	2.21387
$265$	−3.08999e31	−0.0597225
$266$	5.94895e32	1.09279
$267$	4.84213e32	0.845541
$268$	−6.95274e32	−1.15435
$269$	−4.44965e31	−0.0702539	−0.0351269	−	0.999383i	$-0.511184\pi$
$269$	−4.44965e31	−0.0702539	−0.0351269	+	0.999383i	$0.511184\pi$
$270$	−1.26569e32	−0.190072
$271$	3.62870e32	0.518401	0.259200	−	0.965824i	$-0.416541\pi$
$271$	3.62870e32	0.518401	0.259200	+	0.965824i	$0.416541\pi$
$272$	1.94302e30	0.00264118
$273$	−1.12909e32	−0.146060
$274$	−3.98963e32	−0.491247
$275$	−1.47142e33	−1.72483
$276$	−2.08363e33	−2.32567
$277$	1.40758e33	1.49622	0.748111	−	0.663574i	$-0.230961\pi$
$277$	1.40758e33	1.49622	0.748111	+	0.663574i	$0.230961\pi$
$278$	2.17020e33	2.19733
$279$	3.83383e32	0.369808
$280$	1.73679e32	0.159630
$281$	3.59534e32	0.314924	0.157462	−	0.987525i	$-0.449669\pi$
$281$	3.59534e32	0.314924	0.157462	+	0.987525i	$0.449669\pi$
$282$	−6.06414e32	−0.506298
$283$	−3.59177e32	−0.285885	−0.142943	−	0.989731i	$-0.545656\pi$
$283$	−3.59177e32	−0.285885	−0.142943	+	0.989731i	$0.545656\pi$
$284$	7.30568e32	0.554451
$285$	−3.20375e32	−0.231875
$286$	6.44688e32	0.445049
$287$	−1.07719e33	−0.709390
$288$	8.93990e32	0.561738
$289$	−1.63777e33	−0.982044
$290$	3.23515e31	0.0185149
$291$	−1.29931e33	−0.709838
$292$	2.85466e33	1.48897
$293$	3.51312e32	0.174976	0.0874882	−	0.996166i	$-0.472116\pi$
$293$	3.51312e32	0.174976	0.0874882	+	0.996166i	$0.472116\pi$
$294$	−1.73575e33	−0.825653
$295$	5.28278e32	0.240030
$296$	−2.29514e33	−0.996255
$297$	2.42492e33	1.00574
$298$	−5.06167e33	−2.00620
$299$	−4.67206e32	−0.176990
$300$	5.29057e33	1.91587
$301$	1.34078e33	0.464204
$302$	−1.20454e33	−0.398773
$303$	6.28191e33	1.98891
$304$	−5.73340e31	−0.0173628
$305$	8.49630e32	0.246140
$306$	4.31813e32	0.119690
$307$	−6.75654e32	−0.179208	−0.0896038	−	0.995977i	$-0.528560\pi$
$307$	−6.75654e32	−0.179208	−0.0896038	+	0.995977i	$0.528560\pi$
$308$	−8.78968e33	−2.23120
$309$	−9.87810e33	−2.40013
$310$	−9.80972e32	−0.228178
$311$	5.16690e33	1.15071	0.575354	−	0.817905i	$-0.304864\pi$
$311$	5.16690e33	1.15071	0.575354	+	0.817905i	$0.304864\pi$
$312$	−8.77519e32	−0.187141
$313$	−1.10679e33	−0.226056	−0.113028	−	0.993592i	$-0.536055\pi$
$313$	−1.10679e33	−0.226056	−0.113028	+	0.993592i	$0.536055\pi$
$314$	1.37821e34	2.69628
$315$	−4.78641e32	−0.0897051
$316$	1.00697e34	1.80817
$317$	−9.49991e33	−1.63463	−0.817315	−	0.576191i	$-0.804539\pi$
$317$	−9.49991e33	−1.63463	−0.817315	+	0.576191i	$0.804539\pi$
$318$	−3.45135e33	−0.569145
$319$	−6.19817e32	−0.0979691
$320$	−2.26000e33	−0.342440
$321$	4.51946e33	0.656551
$322$	1.03284e34	1.43872
$323$	−8.83602e32	−0.118038
$324$	−1.56638e34	−2.00696
$325$	1.18629e33	0.145802
$326$	−9.20072e33	−1.08489
$327$	1.08749e34	1.23035
$328$	−8.37180e33	−0.908913
$329$	1.85387e33	0.193168
$330$	7.67523e33	0.767632
$331$	−1.25351e34	−1.20351	−0.601757	−	0.798679i	$-0.705533\pi$
$331$	−1.25351e34	−1.20351	−0.601757	+	0.798679i	$0.705533\pi$
$332$	1.54359e34	1.42288
$333$	6.32514e33	0.559852
$334$	−1.19286e34	−1.01394
$335$	−1.85603e33	−0.151524
$336$	−2.40560e32	−0.0188644
$337$	−3.36740e33	−0.253683	−0.126842	−	0.991923i	$-0.540484\pi$
$337$	−3.36740e33	−0.253683	−0.126842	+	0.991923i	$0.540484\pi$
$338$	2.17968e34	1.57768
$339$	−1.26650e34	−0.880865
$340$	−6.81430e32	−0.0455466
$341$	1.87943e34	1.20737
$342$	−1.27418e34	−0.786825
$343$	1.82434e34	1.08302
$344$	1.04204e34	0.594766
$345$	−5.56225e33	−0.305276
$346$	−5.07409e34	−2.67813
$347$	−1.91545e34	−0.972353	−0.486177	−	0.873861i	$-0.661609\pi$
$347$	−1.91545e34	−0.972353	−0.486177	+	0.873861i	$0.661609\pi$
$348$	2.22858e33	0.108820
$349$	1.45433e34	0.683158	0.341579	−	0.939853i	$-0.389038\pi$
$349$	1.45433e34	0.683158	0.341579	+	0.939853i	$0.389038\pi$
$350$	−2.62248e34	−1.18521
$351$	−1.95501e33	−0.0850164
$352$	4.38253e34	1.83400
$353$	−4.39359e33	−0.176954	−0.0884772	−	0.996078i	$-0.528200\pi$
$353$	−4.39359e33	−0.176954	−0.0884772	+	0.996078i	$0.528200\pi$
$354$	5.90057e34	2.28744
$355$	1.95025e33	0.0727791
$356$	−3.03902e34	−1.09184
$357$	−3.70738e33	−0.128247
$358$	3.08877e34	1.02888
$359$	2.60550e34	0.835828	0.417914	−	0.908487i	$-0.362761\pi$
$359$	2.60550e34	0.835828	0.417914	+	0.908487i	$0.362761\pi$
$360$	−3.71996e33	−0.114936
$361$	−7.52760e33	−0.224032
$362$	−8.05172e34	−2.30846
$363$	−1.01933e35	−2.81563
$364$	7.08639e33	0.188606
$365$	7.62050e33	0.195447
$366$	9.48990e34	2.34567
$367$	3.50053e34	0.833953	0.416977	−	0.908917i	$-0.363090\pi$
$367$	3.50053e34	0.833953	0.416977	+	0.908917i	$0.363090\pi$
$368$	−9.95413e32	−0.0228590
$369$	2.30718e34	0.510770
$370$	−1.61843e34	−0.345439
$371$	1.05512e34	0.217146
$372$	−6.75755e34	−1.34110
$373$	−2.06100e34	−0.394464	−0.197232	−	0.980357i	$-0.563195\pi$
$373$	−2.06100e34	−0.394464	−0.197232	+	0.980357i	$0.563195\pi$
$374$	2.11684e34	0.390771
$375$	2.89058e34	0.514711
$376$	1.44082e34	0.247499
$377$	4.99707e32	0.00828146
$378$	4.32186e34	0.691086
$379$	−3.69120e34	−0.569559	−0.284779	−	0.958593i	$-0.591920\pi$
$379$	−3.69120e34	−0.569559	−0.284779	+	0.958593i	$0.591920\pi$
$380$	2.01074e34	0.299418
$381$	9.26485e34	1.33153
$382$	−1.00277e35	−1.39106
$383$	6.12833e34	0.820652	0.410326	−	0.911939i	$-0.365415\pi$
$383$	6.12833e34	0.820652	0.410326	+	0.911939i	$0.365415\pi$
$384$	−1.54507e35	−1.99745
$385$	−2.34640e34	−0.292875
$386$	−4.62439e34	−0.557348
$387$	−2.87175e34	−0.334233
$388$	8.15476e34	0.916606
$389$	5.65060e34	0.613444	0.306722	−	0.951799i	$-0.400768\pi$
$389$	5.65060e34	0.613444	0.306722	+	0.951799i	$0.400768\pi$
$390$	−6.18789e33	−0.0648889
$391$	−1.53408e34	−0.155404
$392$	4.12407e34	0.403612
$393$	−1.09367e35	−1.03416
$394$	8.25924e34	0.754642
$395$	2.68810e34	0.237347
$396$	1.88262e35	1.60649
$397$	−2.20649e35	−1.81983	−0.909915	−	0.414794i	$-0.863854\pi$
$397$	−2.20649e35	−1.81983	−0.909915	+	0.414794i	$0.863854\pi$
$398$	2.95739e35	2.35769
$399$	1.09396e35	0.843078
$400$	2.52746e33	0.0188310
$401$	−1.87612e35	−1.35148	−0.675741	−	0.737139i	$-0.736176\pi$
$401$	−1.87612e35	−1.35148	−0.675741	+	0.737139i	$0.736176\pi$
$402$	−2.07308e35	−1.44399
$403$	−1.51522e34	−0.102061
$404$	−3.94265e35	−2.56827
$405$	−4.18145e34	−0.263441
$406$	−1.10468e34	−0.0673188
$407$	3.10072e35	1.82784
$408$	−2.88135e34	−0.164317
$409$	2.22853e35	1.22957	0.614786	−	0.788694i	$-0.289242\pi$
$409$	2.22853e35	1.22957	0.614786	+	0.788694i	$0.289242\pi$
$410$	−5.90344e34	−0.315154
$411$	−7.33658e34	−0.378991
$412$	6.19970e35	3.09926
$413$	−1.80387e35	−0.872729
$414$	−2.21219e35	−1.03590
$415$	4.12062e34	0.186773
$416$	−3.53327e34	−0.155030
$417$	3.99081e35	1.69521
$418$	−6.24631e35	−2.56888
$419$	−5.47879e34	−0.218170	−0.109085	−	0.994032i	$-0.534792\pi$
$419$	−5.47879e34	−0.218170	−0.109085	+	0.994032i	$0.534792\pi$
$420$	8.43658e34	0.325313
$421$	−1.97758e35	−0.738458	−0.369229	−	0.929338i	$-0.620378\pi$
$421$	−1.97758e35	−0.738458	−0.369229	+	0.929338i	$0.620378\pi$
$422$	2.80864e35	1.01573
$423$	−3.97073e34	−0.139083
$424$	8.20028e34	0.278221
$425$	3.89519e34	0.128020
$426$	2.17832e35	0.693572
$427$	−2.90116e35	−0.894945
$428$	−2.83650e35	−0.847798
$429$	1.18553e35	0.343350
$430$	7.34804e34	0.206228
$431$	−4.94928e35	−1.34617	−0.673083	−	0.739567i	$-0.735030\pi$
$431$	−4.94928e35	−1.34617	−0.673083	+	0.739567i	$0.735030\pi$
$432$	−4.16527e33	−0.0109803
$433$	3.12882e35	0.799454	0.399727	−	0.916634i	$-0.369105\pi$
$433$	3.12882e35	0.799454	0.399727	+	0.916634i	$0.369105\pi$
$434$	3.34965e35	0.829637
$435$	5.94917e33	0.0142841
$436$	−6.82528e35	−1.58874
$437$	4.52671e35	1.02160
$438$	8.51168e35	1.86258
$439$	7.22790e35	1.53370	0.766852	−	0.641824i	$-0.221822\pi$
$439$	7.22790e35	1.53370	0.766852	+	0.641824i	$0.221822\pi$
$440$	−1.82361e35	−0.375249
$441$	−1.13655e35	−0.226813
$442$	−1.70663e34	−0.0330324
$443$	−7.68142e35	−1.44209	−0.721043	−	0.692891i	$-0.756337\pi$
$443$	−7.68142e35	−1.44209	−0.721043	+	0.692891i	$0.756337\pi$
$444$	−1.11488e36	−2.03029
$445$	−8.11264e34	−0.143318
$446$	1.95620e35	0.335269
$447$	−9.30798e35	−1.54776
$448$	7.71705e35	1.24508
$449$	−6.52536e35	−1.02160	−0.510798	−	0.859701i	$-0.670650\pi$
$449$	−6.52536e35	−1.02160	−0.510798	+	0.859701i	$0.670650\pi$
$450$	5.61698e35	0.853363
$451$	1.13103e36	1.66759
$452$	7.94881e35	1.13745
$453$	−2.21504e35	−0.307649
$454$	−1.76849e36	−2.38423
$455$	1.89171e34	0.0247571
$456$	8.50218e35	1.08020
$457$	6.21081e35	0.766090	0.383045	−	0.923730i	$-0.374875\pi$
$457$	6.21081e35	0.766090	0.383045	+	0.923730i	$0.374875\pi$
$458$	1.17276e36	1.40451
$459$	−6.41930e34	−0.0746477
$460$	3.49098e35	0.394200
$461$	1.02161e36	1.12027	0.560133	−	0.828402i	$-0.310750\pi$
$461$	1.02161e36	1.12027	0.560133	+	0.828402i	$0.310750\pi$
$462$	−2.62080e36	−2.79105
$463$	−1.10341e36	−1.14129	−0.570643	−	0.821199i	$-0.693306\pi$
$463$	−1.10341e36	−1.14129	−0.570643	+	0.821199i	$0.693306\pi$
$464$	1.06466e33	0.00106959
$465$	−1.80392e35	−0.176037
$466$	−1.47339e36	−1.39671
$467$	8.66440e35	0.797922	0.398961	−	0.916968i	$-0.369371\pi$
$467$	8.66440e35	0.797922	0.398961	+	0.916968i	$0.369371\pi$
$468$	−1.51780e35	−0.135799
$469$	6.33764e35	0.550927
$470$	1.01600e35	0.0858171
$471$	2.53441e36	2.08015
$472$	−1.40195e36	−1.11819
$473$	−1.40780e36	−1.09123
$474$	3.00246e36	2.26188
$475$	−1.14938e36	−0.841588
$476$	2.32683e35	0.165604
$477$	−2.25991e35	−0.156348
$478$	1.05752e35	0.0711234
$479$	−2.57345e36	−1.68262	−0.841311	−	0.540552i	$-0.818215\pi$
$479$	−2.57345e36	−1.68262	−0.841311	+	0.540552i	$0.818215\pi$
$480$	−4.20648e35	−0.267400
$481$	−2.49985e35	−0.154510
$482$	8.28899e35	0.498157
$483$	1.89930e36	1.10996
$484$	6.39752e36	3.63580
$485$	2.17691e35	0.120317
$486$	−2.99643e36	−1.61070
$487$	−2.28927e36	−1.19690	−0.598448	−	0.801162i	$-0.704216\pi$
$487$	−2.28927e36	−1.19690	−0.598448	+	0.801162i	$0.704216\pi$
$488$	−2.25476e36	−1.14666
$489$	−1.69193e36	−0.836977
$490$	2.90812e35	0.139948
$491$	1.74114e36	0.815142	0.407571	−	0.913174i	$-0.366376\pi$
$491$	1.74114e36	0.815142	0.407571	+	0.913174i	$0.366376\pi$
$492$	−4.06666e36	−1.85229
$493$	1.64079e34	0.00727145
$494$	5.03587e35	0.217151
$495$	5.02565e35	0.210874
$496$	−3.22828e34	−0.0131816
$497$	−6.65935e35	−0.264619
$498$	4.60250e36	1.77991
$499$	2.80174e36	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$499$	2.80174e36	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$500$	−1.81419e36	−0.664641
$501$	−2.19356e36	−0.782240
$502$	6.14024e36	2.13150
$503$	3.44032e36	1.16260	0.581301	−	0.813688i	$-0.302544\pi$
$503$	3.44032e36	1.16260	0.581301	+	0.813688i	$0.302544\pi$
$504$	1.27022e36	0.417896
$505$	−1.05249e36	−0.337119
$506$	−1.08446e37	−3.38207
$507$	4.00825e36	1.21716
$508$	−5.81480e36	−1.71939
$509$	1.50719e35	0.0433989	0.0216995	−	0.999765i	$-0.493092\pi$
$509$	1.50719e35	0.0433989	0.0216995	+	0.999765i	$0.493092\pi$
$510$	−2.03180e35	−0.0569750
$511$	−2.60211e36	−0.710631
$512$	−1.48198e35	−0.0394183
$513$	1.89418e36	0.490725
$514$	−6.51772e35	−0.164473
$515$	1.65501e36	0.406820
$516$	5.06179e36	1.21208
$517$	−1.94654e36	−0.454089
$518$	5.52634e36	1.25599
$519$	−9.33082e36	−2.06614
$520$	1.47022e35	0.0317203
$521$	8.14778e36	1.71289	0.856446	−	0.516236i	$-0.172667\pi$
$521$	8.14778e36	1.71289	0.856446	+	0.516236i	$0.172667\pi$
$522$	2.36607e35	0.0484704
$523$	−4.14380e36	−0.827229	−0.413615	−	0.910452i	$-0.635734\pi$
$523$	−4.14380e36	−0.827229	−0.413615	+	0.910452i	$0.635734\pi$
$524$	6.86409e36	1.33540
$525$	−4.82252e36	−0.914372
$526$	−7.16158e35	−0.132343
$527$	−4.97526e35	−0.0896133
$528$	2.52584e35	0.0443453
$529$	2.01590e36	0.344999
$530$	5.78249e35	0.0964696
$531$	3.86363e36	0.628376
$532$	−6.86591e36	−1.08866
$533$	−9.11854e35	−0.140964
$534$	−9.06137e36	−1.36580
$535$	−7.57203e35	−0.111285
$536$	4.92557e36	0.705881
$537$	5.67999e36	0.793770
$538$	8.32690e35	0.113481
$539$	−5.57161e36	−0.740512
$540$	1.46079e36	0.189353
$541$	1.06017e37	1.34033	0.670163	−	0.742214i	$-0.266224\pi$
$541$	1.06017e37	1.34033	0.670163	+	0.742214i	$0.266224\pi$
$542$	−6.79060e36	−0.837371
$543$	−1.48064e37	−1.78095
$544$	−1.16016e36	−0.136123
$545$	−1.82201e36	−0.208544
$546$	2.11293e36	0.235931
$547$	8.42305e36	0.917573	0.458786	−	0.888547i	$-0.348284\pi$
$547$	8.42305e36	0.917573	0.458786	+	0.888547i	$0.348284\pi$
$548$	4.60459e36	0.489388
$549$	6.21388e36	0.644371
$550$	2.75356e37	2.78611
$551$	−4.84160e35	−0.0478016
$552$	1.47612e37	1.42214
$553$	−9.17883e36	−0.862975
$554$	−2.63409e37	−2.41684
$555$	−2.97616e36	−0.266502
$556$	−2.50471e37	−2.18901
$557$	−5.59363e36	−0.477143	−0.238571	−	0.971125i	$-0.576679\pi$
$557$	−5.59363e36	−0.477143	−0.238571	+	0.971125i	$0.576679\pi$
$558$	−7.17447e36	−0.597349
$559$	1.13499e36	0.0922427
$560$	4.03040e34	0.00319750
$561$	3.89269e36	0.301475
$562$	−6.72818e36	−0.508695
$563$	2.06136e37	1.52157	0.760783	−	0.649006i	$-0.224815\pi$
$563$	2.06136e37	1.52157	0.760783	+	0.649006i	$0.224815\pi$
$564$	6.99886e36	0.504382
$565$	2.12193e36	0.149306
$566$	6.72150e36	0.461790
$567$	1.42780e37	0.957850
$568$	−5.17560e36	−0.339046
$569$	4.96854e36	0.317844	0.158922	−	0.987291i	$-0.449198\pi$
$569$	4.96854e36	0.317844	0.158922	+	0.987291i	$0.449198\pi$
$570$	5.99538e36	0.374547
$571$	1.02940e36	0.0628055	0.0314028	−	0.999507i	$-0.490003\pi$
$571$	1.02940e36	0.0628055	0.0314028	+	0.999507i	$0.490003\pi$
$572$	−7.44060e36	−0.443365
$573$	−1.84400e37	−1.07318
$574$	2.01580e37	1.14587
$575$	−1.99551e37	−1.10800
$576$	−1.65288e37	−0.896475
$577$	−4.63258e36	−0.245442	−0.122721	−	0.992441i	$-0.539162\pi$
$577$	−4.63258e36	−0.245442	−0.122721	+	0.992441i	$0.539162\pi$
$578$	3.06485e37	1.58629
$579$	−8.50387e36	−0.429987
$580$	−3.73382e35	−0.0184449
$581$	−1.40703e37	−0.679090
$582$	2.43149e37	1.14660
$583$	−1.10786e37	−0.510455
$584$	−2.02234e37	−0.910503
$585$	−4.05177e35	−0.0178254
$586$	−6.57430e36	−0.282639
$587$	2.64137e36	0.110972	0.0554862	−	0.998459i	$-0.482329\pi$
$587$	2.64137e36	0.110972	0.0554862	+	0.998459i	$0.482329\pi$
$588$	2.00330e37	0.822529
$589$	1.46808e37	0.589107
$590$	−9.88599e36	−0.387720
$591$	1.51880e37	0.582198
$592$	−5.32610e35	−0.0199557
$593$	−3.52090e37	−1.28948	−0.644741	−	0.764401i	$-0.723035\pi$
$593$	−3.52090e37	−1.28948	−0.644741	+	0.764401i	$0.723035\pi$
$594$	−4.53789e37	−1.62457
$595$	6.21145e35	0.0217377
$596$	5.84187e37	1.99861
$597$	5.43839e37	1.81893
$598$	8.74311e36	0.285891
$599$	4.76915e37	1.52468	0.762341	−	0.647176i	$-0.224050\pi$
$599$	4.76915e37	1.52468	0.762341	+	0.647176i	$0.224050\pi$
$600$	−3.74802e37	−1.17155
$601$	−2.39124e37	−0.730831	−0.365416	−	0.930844i	$-0.619073\pi$
$601$	−2.39124e37	−0.730831	−0.365416	+	0.930844i	$0.619073\pi$
$602$	−2.50908e37	−0.749827
$603$	−1.35743e37	−0.396675
$604$	1.39020e37	0.397264
$605$	1.70782e37	0.477247
$606$	−1.17557e38	−3.21269
$607$	3.35424e37	0.896493	0.448246	−	0.893910i	$-0.352049\pi$
$607$	3.35424e37	0.896493	0.448246	+	0.893910i	$0.352049\pi$
$608$	3.42334e37	0.894854
$609$	−2.03142e36	−0.0519357
$610$	−1.58996e37	−0.397589
$611$	1.56933e36	0.0383847
$612$	−4.98373e36	−0.119237
$613$	−6.25036e37	−1.46281	−0.731407	−	0.681942i	$-0.761136\pi$
$613$	−6.25036e37	−1.46281	−0.731407	+	0.681942i	$0.761136\pi$
$614$	1.26439e37	0.289474
$615$	−1.08559e37	−0.243138
$616$	6.22692e37	1.36437
$617$	−6.57455e37	−1.40934	−0.704671	−	0.709534i	$-0.748906\pi$
$617$	−6.57455e37	−1.40934	−0.704671	+	0.709534i	$0.748906\pi$
$618$	1.84855e38	3.87692
$619$	2.39694e37	0.491851	0.245926	−	0.969289i	$-0.420908\pi$
$619$	2.39694e37	0.491851	0.245926	+	0.969289i	$0.420908\pi$
$620$	1.13218e37	0.227315
$621$	3.28862e37	0.646066
$622$	−9.66913e37	−1.85873
$623$	2.77016e37	0.521094
$624$	−2.03637e35	−0.00374857
$625$	4.81915e37	0.868140
$626$	2.07120e37	0.365148
$627$	−1.14864e38	−1.98186
$628$	−1.59065e38	−2.68608
$629$	−8.20831e36	−0.135666
$630$	8.95709e36	0.144900
$631$	−2.72032e37	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$631$	−2.72032e37	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$632$	−7.13372e37	−1.10570
$633$	5.16486e37	0.783625
$634$	1.77778e38	2.64041
$635$	−1.55226e37	−0.225693
$636$	3.98334e37	0.566991
$637$	4.49192e36	0.0625965
$638$	1.15990e37	0.158249
$639$	1.42634e37	0.190529
$640$	2.58865e37	0.338566
$641$	6.03099e37	0.772334	0.386167	−	0.922429i	$-0.373799\pi$
$641$	6.03099e37	0.772334	0.386167	+	0.922429i	$0.373799\pi$
$642$	−8.45753e37	−1.06052
$643$	−1.01937e38	−1.25165	−0.625823	−	0.779965i	$-0.715237\pi$
$643$	−1.01937e38	−1.25165	−0.625823	+	0.779965i	$0.715237\pi$
$644$	−1.19204e38	−1.43328
$645$	1.35124e37	0.159102
$646$	1.65354e37	0.190667
$647$	1.38190e36	0.0156052	0.00780260	−	0.999970i	$-0.497516\pi$
$647$	1.38190e36	0.0156052	0.00780260	+	0.999970i	$0.497516\pi$
$648$	1.10968e38	1.22726
$649$	1.89404e38	2.05156
$650$	−2.21997e37	−0.235514
$651$	6.15972e37	0.640055
$652$	1.06189e38	1.08078
$653$	−1.67383e38	−1.66872	−0.834358	−	0.551224i	$-0.814161\pi$
$653$	−1.67383e38	−1.66872	−0.834358	+	0.551224i	$0.814161\pi$
$654$	−2.03508e38	−1.98738
$655$	1.83236e37	0.175289
$656$	−1.94276e36	−0.0182061
$657$	5.57335e37	0.511663
$658$	−3.46926e37	−0.312024
$659$	−1.83021e38	−1.61268	−0.806339	−	0.591454i	$-0.798554\pi$
$659$	−1.83021e38	−1.61268	−0.806339	+	0.591454i	$0.798554\pi$
$660$	−8.85828e37	−0.764727
$661$	6.09366e37	0.515417	0.257708	−	0.966223i	$-0.417033\pi$
$661$	6.09366e37	0.515417	0.257708	+	0.966223i	$0.417033\pi$
$662$	2.34578e38	1.94403
$663$	−3.13835e36	−0.0254841
$664$	−1.09354e38	−0.870090
$665$	−1.83285e37	−0.142901
$666$	−1.18366e38	−0.904327
$667$	−8.40581e36	−0.0629334
$668$	1.37672e38	1.01010
$669$	3.59729e37	0.258656
$670$	3.47330e37	0.244756
$671$	3.04618e38	2.10379
$672$	1.43635e38	0.972245
$673$	−6.36340e37	−0.422168	−0.211084	−	0.977468i	$-0.567699\pi$
$673$	−6.36340e37	−0.422168	−0.211084	+	0.977468i	$0.567699\pi$
$674$	6.30163e37	0.409774
$675$	−8.35015e37	−0.532223
$676$	−2.51566e38	−1.57171
$677$	−5.37104e37	−0.328936	−0.164468	−	0.986382i	$-0.552591\pi$
$677$	−5.37104e37	−0.328936	−0.164468	+	0.986382i	$0.552591\pi$
$678$	2.37008e38	1.42286
$679$	−7.43332e37	−0.437462
$680$	4.82749e36	0.0278517
$681$	−3.25210e38	−1.83941
$682$	−3.51708e38	−1.95026
$683$	1.59190e38	0.865437	0.432718	−	0.901529i	$-0.357554\pi$
$683$	1.59190e38	0.865437	0.432718	+	0.901529i	$0.357554\pi$
$684$	1.47058e38	0.783847
$685$	1.22919e37	0.0642387
$686$	−3.41399e38	−1.74939
$687$	2.15661e38	1.08357
$688$	2.41817e36	0.0119136
$689$	8.93171e36	0.0431495
$690$	1.04090e38	0.493111
$691$	−1.11503e38	−0.518006	−0.259003	−	0.965877i	$-0.583394\pi$
$691$	−1.11503e38	−0.518006	−0.259003	+	0.965877i	$0.583394\pi$
$692$	5.85621e38	2.66799
$693$	−1.71607e38	−0.766719
$694$	3.58451e38	1.57064
$695$	−6.68631e37	−0.287337
$696$	−1.57880e37	−0.0665431
$697$	−2.99409e37	−0.123772
$698$	−2.72158e38	−1.10350
$699$	−2.70943e38	−1.07755
$700$	3.02671e38	1.18072
$701$	9.04824e37	0.346235	0.173117	−	0.984901i	$-0.444616\pi$
$701$	9.04824e37	0.346235	0.173117	+	0.984901i	$0.444616\pi$
$702$	3.65852e37	0.137327
$703$	2.42208e38	0.891849
$704$	−8.10278e38	−2.92687
$705$	1.86834e37	0.0662069
$706$	8.22199e37	0.285834
$707$	3.59385e38	1.22574
$708$	−6.81008e38	−2.27879
$709$	2.52263e38	0.828190	0.414095	−	0.910234i	$-0.364098\pi$
$709$	2.52263e38	0.828190	0.414095	+	0.910234i	$0.364098\pi$
$710$	−3.64961e37	−0.117560
$711$	1.96598e38	0.621353
$712$	2.15295e38	0.667657
$713$	2.54883e38	0.775591
$714$	6.93784e37	0.207157
$715$	−1.98626e37	−0.0581976
$716$	−3.56488e38	−1.02499
$717$	1.94469e37	0.0548709
$718$	−4.87584e38	−1.35011
$719$	−2.15368e38	−0.585249	−0.292624	−	0.956227i	$-0.594529\pi$
$719$	−2.15368e38	−0.585249	−0.292624	+	0.956227i	$0.594529\pi$
$720$	−8.63254e35	−0.00230224
$721$	−5.65122e38	−1.47916
$722$	1.40869e38	0.361878
$723$	1.52427e38	0.384323
$724$	9.29280e38	2.29973
$725$	2.13433e37	0.0518439
$726$	1.90753e39	4.54808
$727$	−6.18554e38	−1.44765	−0.723824	−	0.689985i	$-0.757617\pi$
$727$	−6.18554e38	−1.44765	−0.723824	+	0.689985i	$0.757617\pi$
$728$	−5.02025e37	−0.115332
$729$	2.02058e36	0.00455675
$730$	−1.42607e38	−0.315706
$731$	3.72675e37	0.0809927
$732$	−1.09527e39	−2.33679
$733$	−5.13013e36	−0.0107455	−0.00537273	−	0.999986i	$-0.501710\pi$
$733$	−5.13013e36	−0.0107455	−0.00537273	+	0.999986i	$0.501710\pi$
$734$	−6.55075e38	−1.34708
$735$	5.34779e37	0.107968
$736$	5.94349e38	1.17812
$737$	−6.65443e38	−1.29509
$738$	−4.31756e38	−0.825044
$739$	−5.22466e38	−0.980298	−0.490149	−	0.871639i	$-0.663058\pi$
$739$	−5.22466e38	−0.980298	−0.490149	+	0.871639i	$0.663058\pi$
$740$	1.86790e38	0.344132
$741$	9.26054e37	0.167529
$742$	−1.97450e38	−0.350756
$743$	1.00984e39	1.76158	0.880789	−	0.473509i	$-0.157013\pi$
$743$	1.00984e39	1.76158	0.880789	+	0.473509i	$0.157013\pi$
$744$	4.78729e38	0.820077
$745$	1.55948e38	0.262344
$746$	3.85686e38	0.637177
$747$	3.01367e38	0.488953
$748$	−2.44313e38	−0.389292
$749$	2.58556e38	0.404622
$750$	−5.40932e38	−0.831411
$751$	−4.44629e38	−0.671210	−0.335605	−	0.942003i	$-0.608941\pi$
$751$	−4.44629e38	−0.671210	−0.335605	+	0.942003i	$0.608941\pi$
$752$	3.34356e36	0.00495757
$753$	1.12914e39	1.64443
$754$	−9.35131e36	−0.0133770
$755$	3.71114e37	0.0521463
$756$	−4.98803e38	−0.688470
$757$	8.24934e38	1.11847	0.559235	−	0.829009i	$-0.311095\pi$
$757$	8.24934e38	1.11847	0.559235	+	0.829009i	$0.311095\pi$
$758$	6.90757e38	0.920007
$759$	−1.99423e39	−2.60923
$760$	−1.42448e38	−0.183093
$761$	−5.69669e38	−0.719333	−0.359666	−	0.933081i	$-0.617109\pi$
$761$	−5.69669e38	−0.719333	−0.359666	+	0.933081i	$0.617109\pi$
$762$	−1.73379e39	−2.15082
$763$	6.22146e38	0.758248
$764$	1.15733e39	1.38579
$765$	−1.33040e37	−0.0156514
$766$	−1.14683e39	−1.32560
$767$	−1.52700e38	−0.173421
$768$	1.08090e39	1.20617
$769$	1.47938e39	1.62209	0.811043	−	0.584986i	$-0.198900\pi$
$769$	1.47938e39	1.62209	0.811043	+	0.584986i	$0.198900\pi$
$770$	4.39096e38	0.473080
$771$	−1.19855e38	−0.126889
$772$	5.33720e38	0.555239
$773$	−1.83758e39	−1.87855	−0.939277	−	0.343160i	$-0.888503\pi$
$773$	−1.83758e39	−1.87855	−0.939277	+	0.343160i	$0.888503\pi$
$774$	5.37408e38	0.539885
$775$	−6.47176e38	−0.638924
$776$	−5.77712e38	−0.560503
$777$	1.01625e39	0.968981
$778$	−1.05743e39	−0.990894
$779$	8.83484e38	0.813660
$780$	7.14169e37	0.0646434
$781$	6.99222e38	0.622051
$782$	2.87081e38	0.251023
$783$	−3.51738e37	−0.0302298
$784$	9.57033e36	0.00808463
$785$	−4.24623e38	−0.352584
$786$	2.04665e39	1.67047
$787$	−3.93218e38	−0.315482	−0.157741	−	0.987481i	$-0.550421\pi$
$787$	−3.93218e38	−0.315482	−0.157741	+	0.987481i	$0.550421\pi$
$788$	−9.53231e38	−0.751786
$789$	−1.31695e38	−0.102101
$790$	−5.03040e38	−0.383386
$791$	−7.24559e38	−0.542864
$792$	−1.33372e39	−0.982367
$793$	−2.45588e38	−0.177836
$794$	4.12914e39	2.93957
$795$	1.06335e38	0.0744252
$796$	−3.41324e39	−2.34877
$797$	−1.32458e39	−0.896168	−0.448084	−	0.893991i	$-0.647893\pi$
$797$	−1.32458e39	−0.896168	−0.448084	+	0.893991i	$0.647893\pi$
$798$	−2.04719e39	−1.36182
$799$	5.15293e37	0.0337033
$800$	−1.50912e39	−0.970527
$801$	−5.93329e38	−0.375194
$802$	3.51089e39	2.18305
$803$	2.73218e39	1.67051
$804$	2.39263e39	1.43853
$805$	−3.18213e38	−0.188137
$806$	2.83553e38	0.164858
$807$	1.53125e38	0.0875492
$808$	2.79311e39	1.57049
$809$	−2.19258e39	−1.21241	−0.606206	−	0.795308i	$-0.707309\pi$
$809$	−2.19258e39	−1.21241	−0.606206	+	0.795308i	$0.707309\pi$
$810$	7.82499e38	0.425536
$811$	2.76373e39	1.47813	0.739066	−	0.673633i	$-0.235267\pi$
$811$	2.76373e39	1.47813	0.739066	+	0.673633i	$0.235267\pi$
$812$	1.27496e38	0.0670640
$813$	−1.24873e39	−0.646022
$814$	−5.80257e39	−2.95251
$815$	2.83471e38	0.141867
$816$	−6.68646e36	−0.00329139
$817$	−1.09968e39	−0.532436
$818$	−4.17038e39	−1.98612
$819$	1.38352e38	0.0648118
$820$	6.81340e38	0.313962
$821$	−9.42212e38	−0.427087	−0.213543	−	0.976934i	$-0.568500\pi$
$821$	−9.42212e38	−0.427087	−0.213543	+	0.976934i	$0.568500\pi$
$822$	1.37294e39	0.612183
$823$	2.17900e39	0.955782	0.477891	−	0.878419i	$-0.341401\pi$
$823$	2.17900e39	0.955782	0.477891	+	0.878419i	$0.341401\pi$
$824$	−4.39208e39	−1.89519
$825$	5.06357e39	2.14946
$826$	3.37569e39	1.40972
$827$	−8.15484e38	−0.335036	−0.167518	−	0.985869i	$-0.553575\pi$
$827$	−8.15484e38	−0.335036	−0.167518	+	0.985869i	$0.553575\pi$
$828$	2.55317e39	1.03198
$829$	1.51577e39	0.602763	0.301382	−	0.953504i	$-0.402552\pi$
$829$	1.51577e39	0.602763	0.301382	+	0.953504i	$0.402552\pi$
$830$	−7.71116e38	−0.301693
$831$	−4.84386e39	−1.86457
$832$	6.53260e38	0.247412
$833$	1.47493e38	0.0549622
$834$	−7.46823e39	−2.73827
$835$	3.67515e38	0.132589
$836$	7.20911e39	2.55916
$837$	1.06655e39	0.372553
$838$	1.02528e39	0.352409
$839$	3.04177e39	1.02882	0.514410	−	0.857544i	$-0.328011\pi$
$839$	3.04177e39	1.02882	0.514410	+	0.857544i	$0.328011\pi$
$840$	−5.97677e38	−0.198928
$841$	−3.04414e39	−0.997055
$842$	3.70077e39	1.19283
$843$	−1.23726e39	−0.392453
$844$	−3.24157e39	−1.01189
$845$	−6.71554e38	−0.206308
$846$	7.43067e38	0.224661
$847$	−5.83154e39	−1.73523
$848$	1.90296e37	0.00557295
$849$	1.23603e39	0.356266
$850$	−7.28931e38	−0.206791
$851$	4.20513e39	1.17417
$852$	−2.51408e39	−0.690947
$853$	−9.78044e38	−0.264574	−0.132287	−	0.991211i	$-0.542232\pi$
$853$	−9.78044e38	−0.264574	−0.132287	+	0.991211i	$0.542232\pi$
$854$	5.42912e39	1.44560
$855$	3.92571e38	0.102891
$856$	2.00948e39	0.518427
$857$	−6.93851e39	−1.76208	−0.881039	−	0.473044i	$-0.843155\pi$
$857$	−6.93851e39	−1.76208	−0.881039	+	0.473044i	$0.843155\pi$
$858$	−2.21855e39	−0.554613
$859$	−6.79141e39	−1.67129	−0.835646	−	0.549268i	$-0.814907\pi$
$859$	−6.79141e39	−1.67129	−0.835646	+	0.549268i	$0.814907\pi$
$860$	−8.48066e38	−0.205447
$861$	3.70689e39	0.884030
$862$	9.26188e39	2.17446
$863$	−5.27048e38	−0.121816	−0.0609080	−	0.998143i	$-0.519400\pi$
$863$	−5.27048e38	−0.121816	−0.0609080	+	0.998143i	$0.519400\pi$
$864$	2.48703e39	0.565908
$865$	1.56331e39	0.350210
$866$	−5.85514e39	−1.29136
$867$	5.63600e39	1.22381
$868$	−3.86596e39	−0.826497
$869$	9.63764e39	2.02863
$870$	−1.11330e38	−0.0230730
$871$	5.36491e38	0.109476
$872$	4.83527e39	0.971512
$873$	1.59211e39	0.314978
$874$	−8.47110e39	−1.65019
$875$	1.65369e39	0.317209
$876$	−9.82366e39	−1.85553
$877$	3.42049e39	0.636200	0.318100	−	0.948057i	$-0.396955\pi$
$877$	3.42049e39	0.636200	0.318100	+	0.948057i	$0.396955\pi$
$878$	−1.35260e40	−2.47739
$879$	−1.20896e39	−0.218053
$880$	−4.23186e37	−0.00751650
$881$	−7.31752e39	−1.27994	−0.639969	−	0.768401i	$-0.721053\pi$
$881$	−7.31752e39	−1.27994	−0.639969	+	0.768401i	$0.721053\pi$
$882$	2.12689e39	0.366370
$883$	−2.06213e39	−0.349821	−0.174910	−	0.984584i	$-0.555964\pi$
$883$	−2.06213e39	−0.349821	−0.174910	+	0.984584i	$0.555964\pi$
$884$	1.96969e38	0.0329074
$885$	−1.81795e39	−0.299121
$886$	1.43747e40	2.32940
$887$	6.98969e39	1.11555	0.557775	−	0.829992i	$-0.311655\pi$
$887$	6.98969e39	1.11555	0.557775	+	0.829992i	$0.311655\pi$
$888$	7.89819e39	1.24152
$889$	5.30037e39	0.820602
$890$	1.51817e39	0.231502
$891$	−1.49917e40	−2.25166
$892$	−2.25773e39	−0.334000
$893$	−1.52051e39	−0.221561
$894$	1.74186e40	2.50009
$895$	−9.51642e38	−0.134543
$896$	−8.83926e39	−1.23100
$897$	1.60778e39	0.220561
$898$	1.22113e40	1.65018
$899$	−2.72614e38	−0.0362904
$900$	−6.48278e39	−0.850133
$901$	2.93274e38	0.0378869
$902$	−2.11656e40	−2.69366
$903$	−4.61398e39	−0.578483
$904$	−5.63122e39	−0.695550
$905$	2.48071e39	0.301870
$906$	4.14514e39	0.496945
$907$	−2.28488e39	−0.269876	−0.134938	−	0.990854i	$-0.543084\pi$
$907$	−2.28488e39	−0.269876	−0.134938	+	0.990854i	$0.543084\pi$
$908$	2.04108e40	2.37521
$909$	−7.69751e39	−0.882547
$910$	−3.54006e38	−0.0399901
$911$	7.51662e39	0.836612	0.418306	−	0.908306i	$-0.362624\pi$
$911$	7.51662e39	0.836612	0.418306	+	0.908306i	$0.362624\pi$
$912$	1.97302e38	0.0216372
$913$	1.47737e40	1.59637
$914$	−1.16227e40	−1.23746
$915$	−2.92381e39	−0.306736
$916$	−1.35353e40	−1.39920
$917$	−6.25683e39	−0.637336
$918$	1.20128e39	0.120578
$919$	5.26405e39	0.520668	0.260334	−	0.965519i	$-0.416167\pi$
$919$	5.26405e39	0.520668	0.260334	+	0.965519i	$0.416167\pi$
$920$	−2.47313e39	−0.241052
$921$	2.32511e39	0.223326
$922$	−1.91179e40	−1.80956
$923$	−5.63724e38	−0.0525828
$924$	3.02477e40	2.78048
$925$	−1.06773e40	−0.967269
$926$	2.06488e40	1.84351
$927$	1.21041e40	1.06502
$928$	−6.35694e38	−0.0551252
$929$	−2.48177e39	−0.212104	−0.106052	−	0.994361i	$-0.533821\pi$
$929$	−2.48177e39	−0.212104	−0.106052	+	0.994361i	$0.533821\pi$
$930$	3.37579e39	0.284352
$931$	−4.35217e39	−0.361314
$932$	1.70049e40	1.39143
$933$	−1.77807e40	−1.43399
$934$	−1.62142e40	−1.28888
$935$	−6.52193e38	−0.0510998
$936$	1.07526e39	0.0830408
$937$	−2.96211e39	−0.225485	−0.112742	−	0.993624i	$-0.535963\pi$
$937$	−2.96211e39	−0.225485	−0.112742	+	0.993624i	$0.535963\pi$
$938$	−1.18600e40	−0.889911
$939$	3.80877e39	0.281708
$940$	−1.17261e39	−0.0854923
$941$	1.23582e40	0.888168	0.444084	−	0.895985i	$-0.353529\pi$
$941$	1.23582e40	0.888168	0.444084	+	0.895985i	$0.353529\pi$
$942$	−4.74280e40	−3.36006
$943$	1.53388e40	1.07123
$944$	−3.25338e38	−0.0223982
$945$	−1.33155e39	−0.0903710
$946$	2.63449e40	1.76265
$947$	3.62546e39	0.239132	0.119566	−	0.992826i	$-0.461850\pi$
$947$	3.62546e39	0.239132	0.119566	+	0.992826i	$0.461850\pi$
$948$	−3.46525e40	−2.25332
$949$	−2.20273e39	−0.141210
$950$	2.15090e40	1.35941
$951$	3.26918e40	2.03705
$952$	−1.64841e39	−0.101266
$953$	−2.05559e40	−1.24504	−0.622519	−	0.782605i	$-0.713891\pi$
$953$	−2.05559e40	−1.24504	−0.622519	+	0.782605i	$0.713891\pi$
$954$	4.22910e39	0.252548
$955$	3.08950e39	0.181904
$956$	−1.22053e39	−0.0708542
$957$	2.13296e39	0.122087
$958$	4.81585e40	2.71793
$959$	−4.19722e39	−0.233567
$960$	7.77728e39	0.426742
$961$	−1.02164e40	−0.552757
$962$	4.67813e39	0.249579
$963$	−5.53790e39	−0.291333
$964$	−9.56665e39	−0.496272
$965$	1.42476e39	0.0728825
$966$	−3.55427e40	−1.79291
$967$	−2.81961e40	−1.40259	−0.701296	−	0.712871i	$-0.747395\pi$
$967$	−2.81961e40	−1.40259	−0.701296	+	0.712871i	$0.747395\pi$
$968$	−4.53223e40	−2.22328
$969$	3.04071e39	0.147097
$970$	−4.07378e39	−0.194348
$971$	−1.81766e40	−0.855170	−0.427585	−	0.903975i	$-0.640636\pi$
$971$	−1.81766e40	−0.855170	−0.427585	+	0.903975i	$0.640636\pi$
$972$	3.45830e40	1.60461
$973$	2.28312e40	1.04473
$974$	4.28405e40	1.93334
$975$	−4.08233e39	−0.181696
$976$	−5.23241e38	−0.0229683
$977$	2.03258e40	0.879974	0.439987	−	0.898004i	$-0.354983\pi$
$977$	2.03258e40	0.879974	0.439987	+	0.898004i	$0.354983\pi$
$978$	3.16622e40	1.35197
$979$	−2.90863e40	−1.22496
$980$	−3.35638e39	−0.139418
$981$	−1.33255e40	−0.545948
$982$	−3.25830e40	−1.31670
$983$	7.72807e39	0.308034	0.154017	−	0.988068i	$-0.450779\pi$
$983$	7.72807e39	0.308034	0.154017	+	0.988068i	$0.450779\pi$
$984$	2.88096e40	1.13267
$985$	−2.54465e39	−0.0986820
$986$	−3.07052e38	−0.0117455
$987$	−6.37968e39	−0.240723
$988$	−5.81210e39	−0.216329
$989$	−1.90922e40	−0.700981
$990$	−9.40481e39	−0.340624
$991$	1.25885e40	0.449758	0.224879	−	0.974387i	$-0.427801\pi$
$991$	1.25885e40	0.449758	0.224879	+	0.974387i	$0.427801\pi$
$992$	1.92757e40	0.679364
$993$	4.31368e40	1.49980
$994$	1.24620e40	0.427438
$995$	−9.11164e39	−0.308308
$996$	−5.31193e40	−1.77317
$997$	4.50833e40	1.48467	0.742336	−	0.670028i	$-0.233718\pi$
$997$	4.50833e40	1.48467	0.742336	+	0.670028i	$0.233718\pi$
$998$	−5.24306e40	−1.70342
$999$	1.75962e40	0.564008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.28.a.a.1.1	✓	2
3.2	odd	2		9.28.a.d.1.2		2
4.3	odd	2		16.28.a.d.1.2		2
5.2	odd	4		25.28.b.a.24.1		4
5.3	odd	4		25.28.b.a.24.4		4
5.4	even	2		25.28.a.a.1.2		2
7.6	odd	2		49.28.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.28.a.a.1.1	✓	2	1.1	even	1	trivial
9.28.a.d.1.2		2	3.2	odd	2
16.28.a.d.1.2		2	4.3	odd	2
25.28.a.a.1.2		2	5.4	even	2
25.28.b.a.24.1		4	5.2	odd	4
25.28.b.a.24.4		4	5.3	odd	4
49.28.a.b.1.1		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} +O(q^{10})\)	\(q-18713.6 q^{2} -3.44127e6 q^{3} +2.15981e8 q^{4} +5.76560e8 q^{5} +6.43986e10 q^{6} -1.96873e11 q^{7} -1.53009e12 q^{8} +4.21675e12 q^{9} -1.07895e13 q^{10} +2.06714e14 q^{11} -7.43249e14 q^{12} -1.66656e14 q^{13} +3.68421e15 q^{14} -1.98410e15 q^{15} -3.55072e14 q^{16} -5.47219e15 q^{17} -7.89105e16 q^{18} +1.61471e17 q^{19} +1.24526e17 q^{20} +6.77495e17 q^{21} -3.86837e18 q^{22} +2.80341e18 q^{23} +5.26544e18 q^{24} -7.11816e18 q^{25} +3.11874e18 q^{26} +1.17308e19 q^{27} -4.25209e19 q^{28} -2.99842e18 q^{29} +3.71297e19 q^{30} +9.09190e19 q^{31} +2.12009e20 q^{32} -7.11360e20 q^{33} +1.02404e20 q^{34} -1.13509e20 q^{35} +9.10738e20 q^{36} +1.50001e21 q^{37} -3.02171e21 q^{38} +5.73510e20 q^{39} -8.82187e20 q^{40} +5.47146e21 q^{41} -1.26784e22 q^{42} -6.81035e21 q^{43} +4.46463e22 q^{44} +2.43121e21 q^{45} -5.24619e22 q^{46} -9.41657e21 q^{47} +1.22190e21 q^{48} -2.69532e22 q^{49} +1.33206e23 q^{50} +1.88313e22 q^{51} -3.59946e22 q^{52} -5.35936e22 q^{53} -2.19525e23 q^{54} +1.19183e23 q^{55} +3.01233e23 q^{56} -5.55667e23 q^{57} +5.61113e22 q^{58} +9.16258e23 q^{59} -4.28528e23 q^{60} +1.47362e24 q^{61} -1.70142e24 q^{62} -8.30166e23 q^{63} -3.91980e24 q^{64} -9.60874e22 q^{65} +1.33121e25 q^{66} -3.21915e24 q^{67} -1.18189e24 q^{68} -9.64729e24 q^{69} +2.12417e24 q^{70} +3.38255e24 q^{71} -6.45199e24 q^{72} +1.32172e25 q^{73} -2.80705e25 q^{74} +2.44955e25 q^{75} +3.48748e25 q^{76} -4.06965e25 q^{77} -1.07324e25 q^{78} +4.66230e25 q^{79} -2.04720e23 q^{80} -7.25240e25 q^{81} -1.02391e26 q^{82} +7.14690e25 q^{83} +1.46326e26 q^{84} -3.15505e24 q^{85} +1.27446e26 q^{86} +1.03184e25 q^{87} -3.16290e26 q^{88} -1.40708e26 q^{89} -4.54967e25 q^{90} +3.28102e25 q^{91} +6.05484e26 q^{92} -3.12877e26 q^{93} +1.76218e26 q^{94} +9.30980e25 q^{95} -7.29582e26 q^{96} +3.77568e26 q^{97} +5.04391e26 q^{98} +8.71662e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8280 q^{2} - 1286280 q^{3} + 190623296 q^{4} + 5443587900 q^{5} + 86882873184 q^{6} - 175391963600 q^{7} - 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) \) 2 * q - 8280 * q^2 - 1286280 * q^3 + 190623296 * q^4 + 5443587900 * q^5 + 86882873184 * q^6 - 175391963600 * q^7 - 3195032348160 * q^8 + 1235136554154 * q^9	\( 2 q - 8280 q^{2} - 1286280 q^{3} + 190623296 q^{4} + 5443587900 q^{5} + 86882873184 q^{6} - 175391963600 q^{7} - 3195032348160 q^{8} + 1235136554154 q^{9} + 39991096148400 q^{10} + 138167337691944 q^{11} - 797895007176960 q^{12} - 753433801271060 q^{13} + 39\!\cdots\!12 q^{14}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 8280 * q^2 - 1286280 * q^3 + 190623296 * q^4 + 5443587900 * q^5 + 86882873184 * q^6 - 175391963600 * q^7 - 3195032348160 * q^8 + 1235136554154 * q^9 + 39991096148400 * q^10 + 138167337691944 * q^11 - 797895007176960 * q^12 - 753433801271060 * q^13 + 3908340052811712 * q^14 + 8504300488438800 * q^15 - 14322995785166848 * q^16 - 29753620331011740 * q^17 - 110019470226337080 * q^18 + 404565810372684760 * q^19 + 1109219331427200 * q^20 + 723787313583184704 * q^21 - 4583556785578779360 * q^22 + 2929078923121218960 * q^23 + 1677495533792532480 * q^24 + 9119218786673228750 * q^25 - 3003459254146640016 * q^26 - 11127665129740313040 * q^27 - 43065656535315868160 * q^28 - 15546679995448558260 * q^29 + 146561411061600148800 * q^30 + 28544554594467385024 * q^31 + 289738949030869893120 * q^32 - 859077391009750054560 * q^33 - 150938335185934859568 * q^34 - 8958395384765013600 * q^35 + 986344620988374211392 * q^36 + 1867697204682824566780 * q^37 - 485361223888169521440 * q^38 - 690990221801025527472 * q^39 - 8985527186071883904000 * q^40 + 9081343698046512254964 * q^41 - 12195371021026332061440 * q^42 + 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 - 12080376719602732775700 * q^45 - 51150723570313970279616 * q^46 - 1150251488862201070560 * q^47 - 28878849836569912688640 * q^48 - 92204113217840907690414 * q^49 + 302620649115949014735000 * q^50 - 33494974704727214464656 * q^51 - 21115266673184124022400 * q^52 + 106953735591470060758620 * q^53 - 458020779785618027135040 * q^54 - 214436254091483969701200 * q^55 + 265467760964859260989440 * q^56 - 31800538920577362634080 * q^57 - 74812163717162466470160 * q^58 + 2009620977624026488631880 * q^59 - 694490206253033569881600 * q^60 + 147857426692448940370444 * q^61 - 2352212714010270811080960 * q^62 - 894215232558851858338320 * q^63 - 1234057803938137445761024 * q^64 - 2951949350200452960922200 * q^65 + 11770868153144268253438848 * q^66 + 3051578535738098902157560 * q^67 - 566166870324676171716480 * q^68 - 9376480489705868528695872 * q^69 + 3215012724032159046326400 * q^70 - 13175198820369338598286416 * q^71 - 1487763126543110308830720 * q^72 + 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 + 59486914888952006559645000 * q^75 + 28710432717942786872615680 * q^76 - 42169025756092787413646400 * q^77 - 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 - 68186991639088251432345600 * q^80 - 99047155826597708238103278 * q^81 - 64726649726985190956760560 * q^82 + 171806873410054757883176280 * q^83 + 145152183633423443589998592 * q^84 - 121333441005595565089302600 * q^85 + 252189883901197432712215584 * q^86 - 16722988656204557792643120 * q^87 - 202163623954874235550955520 * q^88 - 313473438761105539763494380 * q^89 - 196904738457998748777517200 * q^90 + 20205365125040878536694304 * q^91 + 602296848225491467788034560 * q^92 - 447293490375807514724002560 * q^93 + 262465434750720041893579392 * q^94 + 1276245244260479145691314000 * q^95 - 562074901098402916384505856 * q^96 - 653202933397052842883888060 * q^97 - 176410316250092689584969240 * q^98 + 1076041779280842335610479688 * q^99

Introduction

L-functions

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