LMFDB - Embedded newform 2.34.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,34,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, 34, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 34 $
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:	$13.7965657762$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 19957422 $ x^2 - x - 19957422
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4467.87$ 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)

$f(q)$	$=$	$q+65536.0 q^{2} -9.01727e7 q^{3} +4.29497e9 q^{4} -3.79693e11 q^{5} -5.90956e12 q^{6} +1.50920e14 q^{7} +2.81475e14 q^{8} +2.57205e15 q^{9} +O(q^{10})$	\(q+65536.0 q^{2} -9.01727e7 q^{3} +4.29497e9 q^{4} -3.79693e11 q^{5} -5.90956e12 q^{6} +1.50920e14 q^{7} +2.81475e14 q^{8} +2.57205e15 q^{9} -2.48835e16 q^{10} +1.29789e17 q^{11} -3.87289e17 q^{12} +1.20879e18 q^{13} +9.89072e18 q^{14} +3.42379e19 q^{15} +1.84467e19 q^{16} +7.25972e19 q^{17} +1.68562e20 q^{18} +2.41894e21 q^{19} -1.63077e21 q^{20} -1.36089e22 q^{21} +8.50583e21 q^{22} -2.97560e22 q^{23} -2.53814e22 q^{24} +2.77511e22 q^{25} +7.92194e22 q^{26} +2.69347e23 q^{27} +6.48198e23 q^{28} -1.10824e24 q^{29} +2.24381e24 q^{30} -1.95357e24 q^{31} +1.20893e24 q^{32} -1.17034e25 q^{33} +4.75773e24 q^{34} -5.73034e25 q^{35} +1.10469e25 q^{36} +1.24500e26 q^{37} +1.58528e26 q^{38} -1.09000e26 q^{39} -1.06874e26 q^{40} +3.94109e26 q^{41} -8.91873e26 q^{42} +5.67060e25 q^{43} +5.57438e26 q^{44} -9.76588e26 q^{45} -1.95009e27 q^{46} -2.69133e26 q^{47} -1.66339e27 q^{48} +1.50460e28 q^{49} +1.81869e27 q^{50} -6.54628e27 q^{51} +5.19172e27 q^{52} -9.81792e26 q^{53} +1.76519e28 q^{54} -4.92798e28 q^{55} +4.24803e28 q^{56} -2.18122e29 q^{57} -7.26299e28 q^{58} +2.39411e29 q^{59} +1.47051e29 q^{60} +1.92507e29 q^{61} -1.28029e29 q^{62} +3.88175e29 q^{63} +7.92282e28 q^{64} -4.58969e29 q^{65} -7.66993e29 q^{66} -4.67531e29 q^{67} +3.11802e29 q^{68} +2.68318e30 q^{69} -3.75543e30 q^{70} -1.71647e30 q^{71} +7.23968e29 q^{72} -3.26801e30 q^{73} +8.15925e30 q^{74} -2.50239e30 q^{75} +1.03893e31 q^{76} +1.95878e31 q^{77} -7.14342e30 q^{78} -1.85271e31 q^{79} -7.00409e30 q^{80} -3.85859e31 q^{81} +2.58283e31 q^{82} +1.46644e31 q^{83} -5.84498e31 q^{84} -2.75646e31 q^{85} +3.71629e30 q^{86} +9.99334e31 q^{87} +3.65322e31 q^{88} +1.04135e32 q^{89} -6.40017e31 q^{90} +1.82431e32 q^{91} -1.27801e32 q^{92} +1.76158e32 q^{93} -1.76379e31 q^{94} -9.18453e32 q^{95} -1.09012e32 q^{96} -1.93007e32 q^{97} +9.86053e32 q^{98} +3.33823e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 131072 q^{2} + 8356488 q^{3} + 8589934592 q^{4} - 5332476660 q^{5} + 547650797568 q^{6} + 132719095875856 q^{7} + 562949953421312 q^{8} + 67\!\cdots\!26 q^{9}+O(q^{10}) $ 2 * q + 131072 * q^2 + 8356488 * q^3 + 8589934592 * q^4 - 5332476660 * q^5 + 547650797568 * q^6 + 132719095875856 * q^7 + 562949953421312 * q^8 + 6720986327276826 * q^9	$ 2 q + 131072 q^{2} + 8356488 q^{3} + 8589934592 q^{4} - 5332476660 q^{5} + 547650797568 q^{6} + 132719095875856 q^{7} + 562949953421312 q^{8} + 67\!\cdots\!26 q^{9}+ \cdots - 86\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 131072 * q^2 + 8356488 * q^3 + 8589934592 * q^4 - 5332476660 * q^5 + 547650797568 * q^6 + 132719095875856 * q^7 + 562949953421312 * q^8 + 6720986327276826 * q^9 - 349469190389760 * q^10 - 158105471422723176 * q^11 + 35890842669416448 * q^12 + 4983398515499093788 * q^13 + 8697878667320098816 * q^14 + 71123270901495251760 * q^15 + 36893488147419103232 * q^16 + 302465632526578851876 * q^17 + 440466559944414068736 * q^18 + 2235591200465928697000 * q^19 - 22902812861383311360 * q^20 - 15402260676699297433536 * q^21 - 10361600175159586062336 * q^22 - 71424561765127117190352 * q^23 + 2352142265182876336128 * q^24 + 51481196955054820524350 * q^25 + 326592005111748610490368 * q^26 + 130408214799538026000720 * q^27 + 570024176341489996005376 * q^28 - 252883963720400854222020 * q^29 + 4661134681800392819343360 * q^30 - 4320085941116207893109696 * q^31 + 2417851639229258349412352 * q^32 - 40069350396261729983984544 * q^33 + 19822387693261871636545536 * q^34 - 64117207337688310160318880 * q^35 + 28866416472517120408682496 * q^36 + 116026284407242232995257676 * q^37 + 146511704913735103086592000 * q^38 + 262908916541617545294421872 * q^39 - 1500958743683616693288960 * q^40 - 166777326610314677606684076 * q^41 - 1009402555708165156604215296 * q^42 - 36726176847118764316966952 * q^43 - 679057829079258632181252096 * q^44 + 576607194247955860756817820 * q^45 - 4680880079839370752186908672 * q^46 + 2869532951474224704935093856 * q^47 + 154149995491024983564484608 * q^48 + 7646276407161112463093552754 * q^49 + 3373871723646472717883801600 * q^50 + 16102466566622667888770592144 * q^51 + 21403533647003556937096757248 * q^52 - 4397747242775062628314771092 * q^53 + 8546432765102524071983185920 * q^54 - 157055806778964587214335057520 * q^55 + 37357104420715888378208321536 * q^56 - 236187507701079470516663925600 * q^57 - 16573003446380190382294302720 * q^58 + 187586852967550885385845088760 * q^59 + 305472122506470543808486440960 * q^60 + 464465778169397582356016167804 * q^61 - 283121152236991800482837037056 * q^62 + 312658861452449815338473381328 * q^63 + 158456325028528675187087900672 * q^64 + 954092969996430917540586811560 * q^65 - 2625984947569408736230411075584 * q^66 - 749458286997747528573119702264 * q^67 + 1299079999865610019572648247296 * q^68 - 1422385372570989976078465505088 * q^69 - 4201985300082741094666658119680 * q^70 + 2607453085577305255019451429264 * q^71 + 1891789469942882003103416057856 * q^72 - 5204971716349166463517155924332 * q^73 + 7603898574913026981577207054336 * q^74 - 164280989427041924157498846600 * q^75 + 9601791093226543715882893312000 * q^76 + 24827809126093538111775086561472 * q^77 + 17229998754471447448415231803392 * q^78 - 26559519161049342541312928970080 * q^79 - 98366832226049503611385282560 * q^80 - 75339567615598499486481976424718 * q^81 - 10929918876733582711631647604736 * q^82 - 37062506185061977386465584779992 * q^83 - 66152205890890311703213853638656 * q^84 + 58488965180889831423090470767320 * q^85 - 2406886725852775338276746166272 * q^86 + 184211334389904891581661872551920 * q^87 - 44502733886538293718630537363456 * q^88 + 302974646079669442176749711731380 * q^89 + 37788529082234035290558812651520 * q^90 + 113728448773618228380737641674464 * q^91 - 306766156912353001615321246728192 * q^92 - 57012891826715143125581754081024 * q^93 + 188057711507814790262626310946816 * q^94 - 987091918419525594011119002435600 * q^95 + 10102374104499813322882063269888 * q^96 + 68100314316598271221487860024516 * q^97 + 501106370619710666381299073286144 * q^98 - 860631078578460214896605406940488 * 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 $

$2$	65536.0	0.707107
$2$	65536.0	0.707107
$3$	−9.01727e7	−1.20941	−0.604706	−	0.796449i	$-0.706709\pi$
$3$	−9.01727e7	−1.20941	−0.604706	+	0.796449i	$0.706709\pi$
$4$	4.29497e9	0.500000
$5$	−3.79693e11	−1.11283	−0.556413	−	0.830906i	$-0.687823\pi$
$5$	−3.79693e11	−1.11283	−0.556413	+	0.830906i	$0.687823\pi$
$6$	−5.90956e12	−0.855183
$7$	1.50920e14	1.71645	0.858223	−	0.513276i	$-0.171568\pi$
$7$	1.50920e14	1.71645	0.858223	+	0.513276i	$0.171568\pi$
$8$	2.81475e14	0.353553
$9$	2.57205e15	0.462677
$10$	−2.48835e16	−0.786886
$11$	1.29789e17	0.851642	0.425821	−	0.904807i	$-0.359985\pi$
$11$	1.29789e17	0.851642	0.425821	+	0.904807i	$0.359985\pi$
$12$	−3.87289e17	−0.604706
$13$	1.20879e18	0.503832	0.251916	−	0.967749i	$-0.418939\pi$
$13$	1.20879e18	0.503832	0.251916	+	0.967749i	$0.418939\pi$
$14$	9.89072e18	1.21371
$15$	3.42379e19	1.34586
$16$	1.84467e19	0.250000
$17$	7.25972e19	0.361837	0.180918	−	0.983498i	$-0.442093\pi$
$17$	7.25972e19	0.361837	0.180918	+	0.983498i	$0.442093\pi$
$18$	1.68562e20	0.327162
$19$	2.41894e21	1.92394	0.961968	−	0.273162i	$-0.0880694\pi$
$19$	2.41894e21	1.92394	0.961968	+	0.273162i	$0.0880694\pi$
$20$	−1.63077e21	−0.556413
$21$	−1.36089e22	−2.07589
$22$	8.50583e21	0.602202
$23$	−2.97560e22	−1.01173	−0.505866	−	0.862612i	$-0.668827\pi$
$23$	−2.97560e22	−1.01173	−0.505866	+	0.862612i	$0.668827\pi$
$24$	−2.53814e22	−0.427592
$25$	2.77511e22	0.238380
$26$	7.92194e22	0.356263
$27$	2.69347e23	0.649845
$28$	6.48198e23	0.858223
$29$	−1.10824e24	−0.822373	−0.411186	−	0.911551i	$-0.634885\pi$
$29$	−1.10824e24	−0.822373	−0.411186	+	0.911551i	$0.634885\pi$
$30$	2.24381e24	0.951670
$31$	−1.95357e24	−0.482348	−0.241174	−	0.970482i	$-0.577532\pi$
$31$	−1.95357e24	−0.482348	−0.241174	+	0.970482i	$0.577532\pi$
$32$	1.20893e24	0.176777
$33$	−1.17034e25	−1.02999
$34$	4.75773e24	0.255857
$35$	−5.73034e25	−1.91011
$36$	1.10469e25	0.231339
$37$	1.24500e26	1.65898	0.829491	−	0.558520i	$-0.188630\pi$
$37$	1.24500e26	1.65898	0.829491	+	0.558520i	$0.188630\pi$
$38$	1.58528e26	1.36043
$39$	−1.09000e26	−0.609341
$40$	−1.06874e26	−0.393443
$41$	3.94109e26	0.965345	0.482672	−	0.875801i	$-0.339666\pi$
$41$	3.94109e26	0.965345	0.482672	+	0.875801i	$0.339666\pi$
$42$	−8.91873e26	−1.46788
$43$	5.67060e25	0.0632994	0.0316497	−	0.999499i	$-0.489924\pi$
$43$	5.67060e25	0.0632994	0.0316497	+	0.999499i	$0.489924\pi$
$44$	5.57438e26	0.425821
$45$	−9.76588e26	−0.514879
$46$	−1.95009e27	−0.715403
$47$	−2.69133e26	−0.0692392	−0.0346196	−	0.999401i	$-0.511022\pi$
$47$	−2.69133e26	−0.0692392	−0.0346196	+	0.999401i	$0.511022\pi$
$48$	−1.66339e27	−0.302353
$49$	1.50460e28	1.94619
$50$	1.81869e27	0.168560
$51$	−6.54628e27	−0.437609
$52$	5.19172e27	0.251916
$53$	−9.81792e26	−0.0347911	−0.0173955	−	0.999849i	$-0.505537\pi$
$53$	−9.81792e26	−0.0347911	−0.0173955	+	0.999849i	$0.505537\pi$
$54$	1.76519e28	0.459509
$55$	−4.92798e28	−0.947729
$56$	4.24803e28	0.606856
$57$	−2.18122e29	−2.32683
$58$	−7.26299e28	−0.581505
$59$	2.39411e29	1.44573	0.722864	−	0.690991i	$-0.242825\pi$
$59$	2.39411e29	1.44573	0.722864	+	0.690991i	$0.242825\pi$
$60$	1.47051e29	0.672932
$61$	1.92507e29	0.670661	0.335331	−	0.942101i	$-0.391152\pi$
$61$	1.92507e29	0.670661	0.335331	+	0.942101i	$0.391152\pi$
$62$	−1.28029e29	−0.341071
$63$	3.88175e29	0.794161
$64$	7.92282e28	0.125000
$65$	−4.58969e29	−0.560677
$66$	−7.66993e29	−0.728310
$67$	−4.67531e29	−0.346399	−0.173199	−	0.984887i	$-0.555411\pi$
$67$	−4.67531e29	−0.346399	−0.173199	+	0.984887i	$0.555411\pi$
$68$	3.11802e29	0.180918
$69$	2.68318e30	1.22360
$70$	−3.75543e30	−1.35065
$71$	−1.71647e30	−0.488511	−0.244256	−	0.969711i	$-0.578544\pi$
$71$	−1.71647e30	−0.488511	−0.244256	+	0.969711i	$0.578544\pi$
$72$	7.23968e29	0.163581
$73$	−3.26801e30	−0.588107	−0.294053	−	0.955789i	$-0.595004\pi$
$73$	−3.26801e30	−0.588107	−0.294053	+	0.955789i	$0.595004\pi$
$74$	8.15925e30	1.17308
$75$	−2.50239e30	−0.288300
$76$	1.03893e31	0.961968
$77$	1.95878e31	1.46180
$78$	−7.14342e30	−0.430869
$79$	−1.85271e31	−0.905652	−0.452826	−	0.891599i	$-0.649584\pi$
$79$	−1.85271e31	−0.905652	−0.452826	+	0.891599i	$0.649584\pi$
$80$	−7.00409e30	−0.278206
$81$	−3.85859e31	−1.24861
$82$	2.58283e31	0.682602
$83$	1.46644e31	0.317304	0.158652	−	0.987335i	$-0.449285\pi$
$83$	1.46644e31	0.317304	0.158652	+	0.987335i	$0.449285\pi$
$84$	−5.84498e31	−1.03795
$85$	−2.75646e31	−0.402661
$86$	3.71629e30	0.0447594
$87$	9.99334e31	0.994587
$88$	3.65322e31	0.301101
$89$	1.04135e32	0.712298	0.356149	−	0.934429i	$-0.384089\pi$
$89$	1.04135e32	0.712298	0.356149	+	0.934429i	$0.384089\pi$
$90$	−6.40017e31	−0.364074
$91$	1.82431e32	0.864801
$92$	−1.27801e32	−0.505866
$93$	1.76158e32	0.583357
$94$	−1.76379e31	−0.0489595
$95$	−9.18453e32	−2.14100
$96$	−1.09012e32	−0.213796
$97$	−1.93007e32	−0.319036	−0.159518	−	0.987195i	$-0.550994\pi$
$97$	−1.93007e32	−0.319036	−0.159518	+	0.987195i	$0.550994\pi$
$98$	9.86053e32	1.37616
$99$	3.33823e32	0.394036
$100$	1.19190e32	0.119190
$101$	−1.25892e33	−1.06831	−0.534154	−	0.845387i	$-0.679370\pi$
$101$	−1.25892e33	−1.06831	−0.534154	+	0.845387i	$0.679370\pi$
$102$	−4.29017e32	−0.309437
$103$	−6.67574e32	−0.409907	−0.204953	−	0.978772i	$-0.565704\pi$
$103$	−6.67574e32	−0.409907	−0.204953	+	0.978772i	$0.565704\pi$
$104$	3.40245e32	0.178132
$105$	5.16720e33	2.31010
$106$	−6.43427e31	−0.0246010
$107$	−1.17353e33	−0.384294	−0.192147	−	0.981366i	$-0.561545\pi$
$107$	−1.17353e33	−0.384294	−0.192147	+	0.981366i	$0.561545\pi$
$108$	1.15684e33	0.324922
$109$	3.28427e33	0.792322	0.396161	−	0.918181i	$-0.370342\pi$
$109$	3.28427e33	0.792322	0.396161	+	0.918181i	$0.370342\pi$
$110$	−3.22960e33	−0.670146
$111$	−1.12265e34	−2.00639
$112$	2.78399e33	0.429112
$113$	−1.66933e31	−0.00222202	−0.00111101	−	0.999999i	$-0.500354\pi$
$113$	−1.66933e31	−0.00222202	−0.00111101	+	0.999999i	$0.500354\pi$
$114$	−1.42949e34	−1.64532
$115$	1.12981e34	1.12588
$116$	−4.75987e33	−0.411186
$117$	3.10907e33	0.233112
$118$	1.56901e34	1.02228
$119$	1.09564e34	0.621073
$120$	9.63711e33	0.475835
$121$	−6.38007e33	−0.274705
$122$	1.26161e34	0.474229
$123$	−3.55378e34	−1.16750
$124$	−8.39050e33	−0.241174
$125$	3.36651e34	0.847550
$126$	2.54394e34	0.561557
$127$	−6.28414e34	−1.21754	−0.608772	−	0.793346i	$-0.708337\pi$
$127$	−6.28414e34	−1.21754	−0.608772	+	0.793346i	$0.708337\pi$
$128$	5.19230e33	0.0883883
$129$	−5.11333e33	−0.0765550
$130$	−3.00790e34	−0.396459
$131$	−1.51502e35	−1.75971	−0.879854	−	0.475244i	$-0.842360\pi$
$131$	−1.51502e35	−1.75971	−0.879854	+	0.475244i	$0.842360\pi$
$132$	−5.02657e34	−0.514993
$133$	3.65067e35	3.30233
$134$	−3.06401e34	−0.244941
$135$	−1.02269e35	−0.723163
$136$	2.04343e34	0.127929
$137$	−3.04551e34	−0.168955	−0.0844774	−	0.996425i	$-0.526922\pi$
$137$	−3.04551e34	−0.168955	−0.0844774	+	0.996425i	$0.526922\pi$
$138$	1.75845e35	0.865217
$139$	1.82353e35	0.796467	0.398234	−	0.917284i	$-0.369623\pi$
$139$	1.82353e35	0.796467	0.398234	+	0.917284i	$0.369623\pi$
$140$	−2.46116e35	−0.955053
$141$	2.42684e34	0.0837387
$142$	−1.12491e35	−0.345430
$143$	1.56887e35	0.429085
$144$	4.74460e34	0.115669
$145$	4.20792e35	0.915157
$146$	−2.14172e35	−0.415854
$147$	−1.35674e36	−2.35375
$148$	5.34725e35	0.829491
$149$	−1.11071e36	−1.54179	−0.770896	−	0.636961i	$-0.780191\pi$
$149$	−1.11071e36	−1.54179	−0.770896	+	0.636961i	$0.780191\pi$
$150$	−1.63997e35	−0.203859
$151$	4.91876e35	0.547944	0.273972	−	0.961738i	$-0.411662\pi$
$151$	4.91876e35	0.547944	0.273972	+	0.961738i	$0.411662\pi$
$152$	6.80871e35	0.680214
$153$	1.86724e35	0.167414
$154$	1.28370e36	1.03365
$155$	7.41755e35	0.536769
$156$	−4.68151e35	−0.304670
$157$	2.84179e36	1.66436	0.832182	−	0.554503i	$-0.187092\pi$
$157$	2.84179e36	1.66436	0.832182	+	0.554503i	$0.187092\pi$
$158$	−1.21419e36	−0.640393
$159$	8.85308e34	0.0420767
$160$	−4.59020e35	−0.196722
$161$	−4.49079e36	−1.73658
$162$	−2.52877e36	−0.882898
$163$	−3.65027e35	−0.115141	−0.0575704	−	0.998341i	$-0.518335\pi$
$163$	−3.65027e35	−0.115141	−0.0575704	+	0.998341i	$0.518335\pi$
$164$	1.69268e36	0.482672
$165$	4.44369e36	1.14620
$166$	9.61045e35	0.224368
$167$	−1.54587e36	−0.326853	−0.163426	−	0.986556i	$-0.552255\pi$
$167$	−1.54587e36	−0.326853	−0.163426	+	0.986556i	$0.552255\pi$
$168$	−3.83056e36	−0.733938
$169$	−4.29495e36	−0.746153
$170$	−1.80647e36	−0.284724
$171$	6.22164e36	0.890162
$172$	2.43550e35	0.0316497
$173$	4.99584e36	0.589994	0.294997	−	0.955498i	$-0.404681\pi$
$173$	4.99584e36	0.589994	0.294997	+	0.955498i	$0.404681\pi$
$174$	6.54923e36	0.703279
$175$	4.18821e36	0.409167
$176$	2.39418e36	0.212911
$177$	−2.15884e37	−1.74848
$178$	6.82460e36	0.503671
$179$	2.06281e37	1.38799	0.693993	−	0.719982i	$-0.255850\pi$
$179$	2.06281e37	1.38799	0.693993	+	0.719982i	$0.255850\pi$
$180$	−4.19442e36	−0.257439
$181$	−9.44133e36	−0.528855	−0.264428	−	0.964406i	$-0.585183\pi$
$181$	−9.44133e36	−0.528855	−0.264428	+	0.964406i	$0.585183\pi$
$182$	1.19558e37	0.611507
$183$	−1.73588e37	−0.811106
$184$	−8.37558e36	−0.357701
$185$	−4.72718e37	−1.84616
$186$	1.15447e37	0.412496
$187$	9.42229e36	0.308155
$188$	−1.15592e36	−0.0346196
$189$	4.06499e37	1.11542
$190$	−6.01918e37	−1.51392
$191$	6.49416e37	1.49786	0.748932	−	0.662647i	$-0.230567\pi$
$191$	6.49416e37	1.49786	0.748932	+	0.662647i	$0.230567\pi$
$192$	−7.14422e36	−0.151176
$193$	−1.65250e37	−0.320956	−0.160478	−	0.987039i	$-0.551304\pi$
$193$	−1.65250e37	−0.320956	−0.160478	+	0.987039i	$0.551304\pi$
$194$	−1.26489e37	−0.225592
$195$	4.13865e37	0.678090
$196$	6.46220e37	0.973095
$197$	2.16169e37	0.299295	0.149648	−	0.988739i	$-0.452186\pi$
$197$	2.16169e37	0.299295	0.149648	+	0.988739i	$0.452186\pi$
$198$	2.18774e37	0.278625
$199$	−1.70015e37	−0.199256	−0.0996282	−	0.995025i	$-0.531765\pi$
$199$	−1.70015e37	−0.199256	−0.0996282	+	0.995025i	$0.531765\pi$
$200$	7.81124e36	0.0842801
$201$	4.21585e37	0.418939
$202$	−8.25047e37	−0.755407
$203$	−1.67257e38	−1.41156
$204$	−2.81161e37	−0.218805
$205$	−1.49640e38	−1.07426
$206$	−4.37501e37	−0.289848
$207$	−7.65340e37	−0.468106
$208$	2.22983e37	0.125958
$209$	3.13951e38	1.63851
$210$	3.38637e38	1.63349
$211$	−2.14566e38	−0.956977	−0.478488	−	0.878094i	$-0.658815\pi$
$211$	−2.14566e38	−0.956977	−0.478488	+	0.878094i	$0.658815\pi$
$212$	−4.21677e36	−0.0173955
$213$	1.54779e38	0.590811
$214$	−7.69087e37	−0.271737
$215$	−2.15308e37	−0.0704412
$216$	7.58143e37	0.229755
$217$	−2.94833e38	−0.827924
$218$	2.15238e38	0.560256
$219$	2.94685e38	0.711264
$220$	−2.11655e38	−0.473865
$221$	8.77548e37	0.182305
$222$	−7.35741e38	−1.41873
$223$	8.25144e38	1.47741	0.738703	−	0.674031i	$-0.235439\pi$
$223$	8.25144e38	1.47741	0.738703	+	0.674031i	$0.235439\pi$
$224$	1.82452e38	0.303428
$225$	7.13772e37	0.110293
$226$	−1.09401e36	−0.00157120
$227$	−9.64672e38	−1.28811	−0.644055	−	0.764979i	$-0.722749\pi$
$227$	−9.64672e38	−1.28811	−0.644055	+	0.764979i	$0.722749\pi$
$228$	−9.36828e38	−1.16342
$229$	3.69331e37	0.0426707	0.0213354	−	0.999772i	$-0.493208\pi$
$229$	3.69331e37	0.0426707	0.0213354	+	0.999772i	$0.493208\pi$
$230$	7.40435e38	0.796118
$231$	−1.76628e39	−1.76792
$232$	−3.11943e38	−0.290753
$233$	1.96773e39	1.70841	0.854206	−	0.519934i	$-0.174044\pi$
$233$	1.96773e39	1.70841	0.854206	+	0.519934i	$0.174044\pi$
$234$	2.03756e38	0.164835
$235$	1.02188e38	0.0770512
$236$	1.02826e39	0.722864
$237$	1.67064e39	1.09531
$238$	7.18038e38	0.439165
$239$	−2.33974e39	−1.33537	−0.667687	−	0.744442i	$-0.732716\pi$
$239$	−2.33974e39	−1.33537	−0.667687	+	0.744442i	$0.732716\pi$
$240$	6.31578e38	0.336466
$241$	7.21139e38	0.358705	0.179353	−	0.983785i	$-0.442600\pi$
$241$	7.21139e38	0.358705	0.179353	+	0.983785i	$0.442600\pi$
$242$	−4.18124e38	−0.194246
$243$	1.98208e39	0.860236
$244$	8.26809e38	0.335331
$245$	−5.71285e39	−2.16577
$246$	−2.32901e39	−0.825547
$247$	2.92399e39	0.969341
$248$	−5.49880e38	−0.170536
$249$	−1.32233e39	−0.383751
$250$	2.20628e39	0.599308
$251$	−3.99740e39	−1.01663	−0.508313	−	0.861172i	$-0.669731\pi$
$251$	−3.99740e39	−1.01663	−0.508313	+	0.861172i	$0.669731\pi$
$252$	1.66720e39	0.397080
$253$	−3.86199e39	−0.861634
$254$	−4.11837e39	−0.860933
$255$	2.48557e39	0.486983
$256$	3.40282e38	0.0625000
$257$	7.36087e39	1.26775	0.633874	−	0.773437i	$-0.281464\pi$
$257$	7.36087e39	1.26775	0.633874	+	0.773437i	$0.281464\pi$
$258$	−3.35107e38	−0.0541326
$259$	1.87896e40	2.84756
$260$	−1.97126e39	−0.280339
$261$	−2.85046e39	−0.380493
$262$	−9.92881e39	−1.24430
$263$	−1.68621e39	−0.198446	−0.0992232	−	0.995065i	$-0.531636\pi$
$263$	−1.68621e39	−0.198446	−0.0992232	+	0.995065i	$0.531636\pi$
$264$	−3.29421e39	−0.364155
$265$	3.72779e38	0.0387164
$266$	2.39251e40	2.33510
$267$	−9.39014e39	−0.861462
$268$	−2.00803e39	−0.173199
$269$	−2.02932e40	−1.64603	−0.823016	−	0.568019i	$-0.807710\pi$
$269$	−2.02932e40	−1.64603	−0.823016	+	0.568019i	$0.807710\pi$
$270$	−6.70230e39	−0.511354
$271$	8.11313e39	0.582364	0.291182	−	0.956668i	$-0.405951\pi$
$271$	8.11313e39	0.582364	0.291182	+	0.956668i	$0.405951\pi$
$272$	1.33918e39	0.0904591
$273$	−1.64503e40	−1.04590
$274$	−1.99590e39	−0.119469
$275$	3.60177e39	0.203015
$276$	1.15242e40	0.611801
$277$	2.06292e40	1.03173	0.515865	−	0.856670i	$-0.327470\pi$
$277$	2.06292e40	1.03173	0.515865	+	0.856670i	$0.327470\pi$
$278$	1.19507e40	0.563187
$279$	−5.02467e39	−0.223171
$280$	−1.61295e40	−0.675324
$281$	−3.02735e40	−1.19511	−0.597556	−	0.801827i	$-0.703862\pi$
$281$	−3.02735e40	−1.19511	−0.597556	+	0.801827i	$0.703862\pi$
$282$	1.59046e39	0.0592122
$283$	−3.47335e40	−1.21975	−0.609877	−	0.792496i	$-0.708781\pi$
$283$	−3.47335e40	−1.21975	−0.609877	+	0.792496i	$0.708781\pi$
$284$	−7.37220e39	−0.244256
$285$	8.28194e40	2.58936
$286$	1.02818e40	0.303409
$287$	5.94791e40	1.65696
$288$	3.10942e39	0.0817906
$289$	−3.49841e40	−0.869074
$290$	2.75770e40	0.647114
$291$	1.74040e40	0.385846
$292$	−1.40360e40	−0.294053
$293$	−7.61171e39	−0.150718	−0.0753592	−	0.997156i	$-0.524010\pi$
$293$	−7.61171e39	−0.150718	−0.0753592	+	0.997156i	$0.524010\pi$
$294$	−8.89151e40	−1.66435
$295$	−9.09027e40	−1.60884
$296$	3.50437e40	0.586539
$297$	3.49581e40	0.553435
$298$	−7.27913e40	−1.09021
$299$	−3.59688e40	−0.509744
$300$	−1.07477e40	−0.144150
$301$	8.55810e39	0.108650
$302$	3.22356e40	0.387455
$303$	1.13520e41	1.29202
$304$	4.46216e40	0.480984
$305$	−7.30933e40	−0.746329
$306$	1.22371e40	0.118379
$307$	4.73533e40	0.434077	0.217039	−	0.976163i	$-0.430360\pi$
$307$	4.73533e40	0.434077	0.217039	+	0.976163i	$0.430360\pi$
$308$	8.41288e40	0.730900
$309$	6.01969e40	0.495746
$310$	4.86116e40	0.379553
$311$	−2.41136e41	−1.78532	−0.892660	−	0.450731i	$-0.851164\pi$
$311$	−2.41136e41	−1.78532	−0.892660	+	0.450731i	$0.851164\pi$
$312$	−3.06808e40	−0.215435
$313$	1.94581e41	1.29604	0.648020	−	0.761624i	$-0.275597\pi$
$313$	1.94581e41	1.29604	0.648020	+	0.761624i	$0.275597\pi$
$314$	1.86240e41	1.17688
$315$	−1.47387e41	−0.883762
$316$	−7.95735e40	−0.452826
$317$	−3.00530e40	−0.162334	−0.0811670	−	0.996701i	$-0.525865\pi$
$317$	−3.00530e40	−0.162334	−0.0811670	+	0.996701i	$0.525865\pi$
$318$	5.80196e39	0.0297527
$319$	−1.43838e41	−0.700367
$320$	−3.00823e40	−0.139103
$321$	1.05821e41	0.464769
$322$	−2.94309e41	−1.22795
$323$	1.75608e41	0.696151
$324$	−1.65725e41	−0.624304
$325$	3.35453e40	0.120104
$326$	−2.39224e40	−0.0814168
$327$	−2.96151e41	−0.958243
$328$	1.10932e41	0.341301
$329$	−4.06177e40	−0.118845
$330$	2.91222e41	0.810482
$331$	2.92433e41	0.774219	0.387109	−	0.922034i	$-0.373474\pi$
$331$	2.92433e41	0.774219	0.387109	+	0.922034i	$0.373474\pi$
$332$	6.29830e40	0.158652
$333$	3.20221e41	0.767574
$334$	−1.01310e41	−0.231120
$335$	1.77518e41	0.385481
$336$	−2.51040e41	−0.518973
$337$	9.70728e40	0.191075	0.0955375	−	0.995426i	$-0.469543\pi$
$337$	9.70728e40	0.191075	0.0955375	+	0.995426i	$0.469543\pi$
$338$	−2.81474e41	−0.527610
$339$	1.50528e39	0.00268733
$340$	−1.18389e41	−0.201330
$341$	−2.53551e41	−0.410788
$342$	4.07741e41	0.629439
$343$	1.10398e42	1.62408
$344$	1.59613e40	0.0223797
$345$	−1.01878e42	−1.36165
$346$	3.27407e41	0.417189
$347$	−4.31667e41	−0.524460	−0.262230	−	0.965005i	$-0.584458\pi$
$347$	−4.31667e41	−0.524460	−0.262230	+	0.965005i	$0.584458\pi$
$348$	4.29211e41	0.497294
$349$	−1.73587e42	−1.91821	−0.959106	−	0.283047i	$-0.908655\pi$
$349$	−1.73587e42	−1.91821	−0.959106	+	0.283047i	$0.908655\pi$
$350$	2.74478e41	0.289324
$351$	3.25584e41	0.327413
$352$	1.56905e41	0.150551
$353$	−9.21273e41	−0.843540	−0.421770	−	0.906703i	$-0.638591\pi$
$353$	−9.21273e41	−0.843540	−0.421770	+	0.906703i	$0.638591\pi$
$354$	−1.41481e42	−1.23636
$355$	6.51733e41	0.543628
$356$	4.47257e41	0.356149
$357$	−9.87968e41	−0.751133
$358$	1.35189e42	0.981454
$359$	−3.69720e40	−0.0256339	−0.0128169	−	0.999918i	$-0.504080\pi$
$359$	−3.69720e40	−0.0256339	−0.0128169	+	0.999918i	$0.504080\pi$
$360$	−2.74885e41	−0.182037
$361$	4.27050e42	2.70153
$362$	−6.18747e41	−0.373957
$363$	5.75308e41	0.332232
$364$	7.83537e41	0.432401
$365$	1.24084e42	0.654460
$366$	−1.13763e42	−0.573538
$367$	−1.78338e41	−0.0859517	−0.0429758	−	0.999076i	$-0.513684\pi$
$367$	−1.78338e41	−0.0859517	−0.0429758	+	0.999076i	$0.513684\pi$
$368$	−5.48902e41	−0.252933
$369$	1.01367e42	0.446643
$370$	−3.09801e42	−1.30543
$371$	−1.48172e41	−0.0597170
$372$	7.56594e41	0.291679
$373$	−4.08132e42	−1.50524	−0.752619	−	0.658456i	$-0.771210\pi$
$373$	−4.08132e42	−1.50524	−0.752619	+	0.658456i	$0.771210\pi$
$374$	6.17499e41	0.217899
$375$	−3.03568e42	−1.02504
$376$	−7.57542e40	−0.0244798
$377$	−1.33964e42	−0.414338
$378$	2.66403e42	0.788724
$379$	−1.70362e41	−0.0482865	−0.0241432	−	0.999709i	$-0.507686\pi$
$379$	−1.70362e41	−0.0482865	−0.0241432	+	0.999709i	$0.507686\pi$
$380$	−3.94473e42	−1.07050
$381$	5.66658e42	1.47251
$382$	4.25601e42	1.05915
$383$	5.69071e42	1.35640	0.678198	−	0.734879i	$-0.262761\pi$
$383$	5.69071e42	1.35640	0.678198	+	0.734879i	$0.262761\pi$
$384$	−4.68203e41	−0.106898
$385$	−7.43732e42	−1.62673
$386$	−1.08298e42	−0.226950
$387$	1.45851e41	0.0292872
$388$	−8.28959e41	−0.159518
$389$	−5.79789e42	−1.06930	−0.534652	−	0.845072i	$-0.679557\pi$
$389$	−5.79789e42	−1.06930	−0.534652	+	0.845072i	$0.679557\pi$
$390$	2.71230e42	0.479482
$391$	−2.16020e42	−0.366082
$392$	4.23507e42	0.688082
$393$	1.36613e43	2.12821
$394$	1.41668e42	0.211634
$395$	7.03462e42	1.00783
$396$	1.43376e42	0.197018
$397$	1.92578e42	0.253842	0.126921	−	0.991913i	$-0.459491\pi$
$397$	1.92578e42	0.253842	0.126921	+	0.991913i	$0.459491\pi$
$398$	−1.11421e42	−0.140896
$399$	−3.29191e43	−3.99388
$400$	5.11917e41	0.0595950
$401$	3.50938e42	0.392056	0.196028	−	0.980598i	$-0.437196\pi$
$401$	3.50938e42	0.392056	0.196028	+	0.980598i	$0.437196\pi$
$402$	2.76290e42	0.296235
$403$	−2.36145e42	−0.243022
$404$	−5.40703e42	−0.534154
$405$	1.46508e43	1.38948
$406$	−1.09613e43	−0.998123
$407$	1.61587e43	1.41286
$408$	−1.84261e42	−0.154718
$409$	−2.43987e43	−1.96758	−0.983788	−	0.179336i	$-0.942605\pi$
$409$	−2.43987e43	−1.96758	−0.983788	+	0.179336i	$0.942605\pi$
$410$	−9.80682e42	−0.759616
$411$	2.74622e42	0.204336
$412$	−2.86721e42	−0.204953
$413$	3.61321e43	2.48151
$414$	−5.01573e42	−0.331001
$415$	−5.56795e42	−0.353104
$416$	1.46134e42	0.0890658
$417$	−1.64432e43	−0.963257
$418$	2.05751e43	1.15860
$419$	−2.34866e42	−0.127142	−0.0635710	−	0.997977i	$-0.520249\pi$
$419$	−2.34866e42	−0.127142	−0.0635710	+	0.997977i	$0.520249\pi$
$420$	2.21929e43	1.15505
$421$	9.88118e42	0.494486	0.247243	−	0.968953i	$-0.420475\pi$
$421$	9.88118e42	0.494486	0.247243	+	0.968953i	$0.420475\pi$
$422$	−1.40618e43	−0.676685
$423$	−6.92224e41	−0.0320354
$424$	−2.76350e41	−0.0123005
$425$	2.01465e42	0.0862546
$426$	1.01436e43	0.417767
$427$	2.90532e43	1.15115
$428$	−5.04029e42	−0.192147
$429$	−1.41470e43	−0.518941
$430$	−1.41105e42	−0.0498094
$431$	−4.62454e43	−1.57106	−0.785531	−	0.618822i	$-0.787610\pi$
$431$	−4.62454e43	−1.57106	−0.785531	+	0.618822i	$0.787610\pi$
$432$	4.96857e42	0.162461
$433$	−2.08300e42	−0.0655600	−0.0327800	−	0.999463i	$-0.510436\pi$
$433$	−2.08300e42	−0.0655600	−0.0327800	+	0.999463i	$0.510436\pi$
$434$	−1.93222e43	−0.585431
$435$	−3.79440e43	−1.10680
$436$	1.41058e43	0.396161
$437$	−7.19780e43	−1.94651
$438$	1.93125e43	0.502939
$439$	2.86420e43	0.718354	0.359177	−	0.933269i	$-0.383057\pi$
$439$	2.86420e43	0.718354	0.359177	+	0.933269i	$0.383057\pi$
$440$	−1.38710e43	−0.335073
$441$	3.86990e43	0.900458
$442$	5.75110e42	0.128909
$443$	8.73889e43	1.88710	0.943550	−	0.331231i	$-0.107464\pi$
$443$	8.73889e43	1.88710	0.943550	+	0.331231i	$0.107464\pi$
$444$	−4.82175e43	−1.00320
$445$	−3.95393e43	−0.792664
$446$	5.40767e43	1.04468
$447$	1.00155e44	1.86466
$448$	1.19571e43	0.214556
$449$	−5.44514e43	−0.941769	−0.470884	−	0.882195i	$-0.656065\pi$
$449$	−5.44514e43	−0.941769	−0.470884	+	0.882195i	$0.656065\pi$
$450$	4.67778e42	0.0779889
$451$	5.11508e43	0.822128
$452$	−7.16971e40	−0.00111101
$453$	−4.43538e43	−0.662690
$454$	−6.32207e43	−0.910831
$455$	−6.92678e43	−0.962373
$456$	−6.13960e43	−0.822659
$457$	1.06886e44	1.38135	0.690677	−	0.723163i	$-0.257312\pi$
$457$	1.06886e44	1.38135	0.690677	+	0.723163i	$0.257312\pi$
$458$	2.42044e42	0.0301727
$459$	1.95538e43	0.235138
$460$	4.85251e43	0.562941
$461$	7.60664e43	0.851388	0.425694	−	0.904867i	$-0.360030\pi$
$461$	7.60664e43	0.851388	0.425694	+	0.904867i	$0.360030\pi$
$462$	−1.15755e44	−1.25011
$463$	−7.00922e43	−0.730438	−0.365219	−	0.930922i	$-0.619006\pi$
$463$	−7.00922e43	−0.730438	−0.365219	+	0.930922i	$0.619006\pi$
$464$	−2.04435e43	−0.205593
$465$	−6.68860e43	−0.649174
$466$	1.28957e44	1.20803
$467$	1.35585e43	0.122598	0.0612988	−	0.998119i	$-0.480476\pi$
$467$	1.35585e43	0.122598	0.0612988	+	0.998119i	$0.480476\pi$
$468$	1.33534e43	0.116556
$469$	−7.05600e43	−0.594575
$470$	6.69698e42	0.0544834
$471$	−2.56252e44	−2.01290
$472$	6.73883e43	0.511142
$473$	7.35979e42	0.0539085
$474$	1.09487e44	0.774499
$475$	6.71282e43	0.458628
$476$	4.70574e43	0.310537
$477$	−2.52522e42	−0.0160970
$478$	−1.53337e44	−0.944252
$479$	−1.11161e43	−0.0661327	−0.0330663	−	0.999453i	$-0.510527\pi$
$479$	−1.11161e43	−0.0661327	−0.0330663	+	0.999453i	$0.510527\pi$
$480$	4.13911e43	0.237917
$481$	1.50495e44	0.835849
$482$	4.72606e43	0.253643
$483$	4.04947e44	2.10025
$484$	−2.74022e43	−0.137353
$485$	7.32833e43	0.355031
$486$	1.29898e44	0.608278
$487$	−3.17101e44	−1.43539	−0.717694	−	0.696359i	$-0.754802\pi$
$487$	−3.17101e44	−1.43539	−0.717694	+	0.696359i	$0.754802\pi$
$488$	5.41858e43	0.237115
$489$	3.29154e43	0.139253
$490$	−3.74397e44	−1.53143
$491$	−8.64871e43	−0.342064	−0.171032	−	0.985266i	$-0.554710\pi$
$491$	−8.64871e43	−0.342064	−0.171032	+	0.985266i	$0.554710\pi$
$492$	−1.52634e44	−0.583750
$493$	−8.04554e43	−0.297564
$494$	1.91627e44	0.685428
$495$	−1.26750e44	−0.438493
$496$	−3.60369e43	−0.120587
$497$	−2.59051e44	−0.838504
$498$	−8.66600e43	−0.271353
$499$	2.51774e44	0.762696	0.381348	−	0.924432i	$-0.375460\pi$
$499$	2.51774e44	0.762696	0.381348	+	0.924432i	$0.375460\pi$
$500$	1.44591e44	0.423775
$501$	1.39396e44	0.395300
$502$	−2.61974e44	−0.718864
$503$	−3.80947e44	−1.01156	−0.505781	−	0.862662i	$-0.668796\pi$
$503$	−3.80947e44	−1.01156	−0.505781	+	0.862662i	$0.668796\pi$
$504$	1.09262e44	0.280778
$505$	4.78003e44	1.18884
$506$	−2.53100e44	−0.609267
$507$	3.87287e44	0.902406
$508$	−2.69902e44	−0.608772
$509$	1.92280e44	0.419847	0.209923	−	0.977718i	$-0.432679\pi$
$509$	1.92280e44	0.419847	0.209923	+	0.977718i	$0.432679\pi$
$510$	1.62895e44	0.344349
$511$	−4.93210e44	−1.00945
$512$	2.23007e43	0.0441942
$513$	6.51533e44	1.25026
$514$	4.82402e44	0.896433
$515$	2.53473e44	0.456154
$516$	−2.19616e43	−0.0382775
$517$	−3.49304e43	−0.0589671
$518$	1.23140e45	2.01353
$519$	−4.50488e44	−0.713546
$520$	−1.29188e44	−0.198229
$521$	−5.38989e44	−0.801230	−0.400615	−	0.916246i	$-0.631204\pi$
$521$	−5.38989e44	−0.801230	−0.400615	+	0.916246i	$0.631204\pi$
$522$	−1.86808e44	−0.269049
$523$	−1.22241e45	−1.70585	−0.852924	−	0.522036i	$-0.825173\pi$
$523$	−1.22241e45	−1.70585	−0.852924	+	0.522036i	$0.825173\pi$
$524$	−6.50694e44	−0.879854
$525$	−3.77662e44	−0.494851
$526$	−1.10508e44	−0.140323
$527$	−1.41823e44	−0.174531
$528$	−2.15889e44	−0.257497
$529$	2.04162e43	0.0236024
$530$	2.44305e43	0.0273766
$531$	6.15778e44	0.668905
$532$	1.56795e45	1.65117
$533$	4.76395e44	0.486372
$534$	−6.15392e44	−0.609146
$535$	4.45582e44	0.427652
$536$	−1.31598e44	−0.122470
$537$	−1.86009e45	−1.67865
$538$	−1.32994e45	−1.16392
$539$	1.95280e45	1.65746
$540$	−4.39242e44	−0.361582
$541$	9.94445e44	0.794010	0.397005	−	0.917816i	$-0.370050\pi$
$541$	9.94445e44	0.794010	0.397005	+	0.917816i	$0.370050\pi$
$542$	5.31702e44	0.411794
$543$	8.51350e44	0.639604
$544$	8.77646e43	0.0639643
$545$	−1.24701e45	−0.881716
$546$	−1.07809e45	−0.739564
$547$	2.61151e45	1.73821	0.869103	−	0.494631i	$-0.164697\pi$
$547$	2.61151e45	1.73821	0.869103	+	0.494631i	$0.164697\pi$
$548$	−1.30804e44	−0.0844774
$549$	4.95137e44	0.310300
$550$	2.36046e44	0.143553
$551$	−2.68078e45	−1.58219
$552$	7.55248e44	0.432608
$553$	−2.79612e45	−1.55450
$554$	1.35196e45	0.729544
$555$	4.26263e45	2.23277
$556$	7.83199e44	0.398234
$557$	4.70313e44	0.232154	0.116077	−	0.993240i	$-0.462968\pi$
$557$	4.70313e44	0.232154	0.116077	+	0.993240i	$0.462968\pi$
$558$	−3.29297e44	−0.157806
$559$	6.85457e43	0.0318923
$560$	−1.05706e45	−0.477526
$561$	−8.49633e44	−0.372687
$562$	−1.98401e45	−0.845072
$563$	−3.98898e45	−1.64996	−0.824979	−	0.565163i	$-0.808813\pi$
$563$	−3.98898e45	−1.64996	−0.824979	+	0.565163i	$0.808813\pi$
$564$	1.04232e44	0.0418694
$565$	6.33831e42	0.00247272
$566$	−2.27629e45	−0.862496
$567$	−5.82340e45	−2.14317
$568$	−4.83145e44	−0.172715
$569$	4.06996e45	1.41331	0.706656	−	0.707557i	$-0.250203\pi$
$569$	4.06996e45	1.41331	0.706656	+	0.707557i	$0.250203\pi$
$570$	5.42765e45	1.83095
$571$	3.62519e45	1.18805	0.594026	−	0.804446i	$-0.297538\pi$
$571$	3.62519e45	1.18805	0.594026	+	0.804446i	$0.297538\pi$
$572$	6.73826e44	0.214543
$573$	−5.85595e45	−1.81153
$574$	3.89802e45	1.17165
$575$	−8.25762e44	−0.241177
$576$	2.03779e44	0.0578347
$577$	5.36110e45	1.47861	0.739303	−	0.673373i	$-0.235155\pi$
$577$	5.36110e45	1.47861	0.739303	+	0.673373i	$0.235155\pi$
$578$	−2.29272e45	−0.614528
$579$	1.49010e45	0.388168
$580$	1.80729e45	0.457578
$581$	2.21315e45	0.544635
$582$	1.14059e45	0.272834
$583$	−1.27425e44	−0.0296295
$584$	−9.19863e44	−0.207927
$585$	−1.18049e45	−0.259413
$586$	−4.98841e44	−0.106574
$587$	4.97914e45	1.03425	0.517125	−	0.855910i	$-0.327002\pi$
$587$	4.97914e45	1.03425	0.517125	+	0.855910i	$0.327002\pi$
$588$	−5.82714e45	−1.17687
$589$	−4.72556e45	−0.928006
$590$	−5.95740e45	−1.13762
$591$	−1.94925e45	−0.361971
$592$	2.29662e45	0.414746
$593$	6.77458e45	1.18982	0.594908	−	0.803794i	$-0.297188\pi$
$593$	6.77458e45	1.18982	0.594908	+	0.803794i	$0.297188\pi$
$594$	2.29102e45	0.391338
$595$	−4.16006e45	−0.691146
$596$	−4.77045e45	−0.770896
$597$	1.53307e45	0.240983
$598$	−2.35725e45	−0.360443
$599$	−3.11898e45	−0.463949	−0.231974	−	0.972722i	$-0.574519\pi$
$599$	−3.11898e45	−0.463949	−0.231974	+	0.972722i	$0.574519\pi$
$600$	−7.04360e44	−0.101929
$601$	−7.18928e44	−0.101218	−0.0506089	−	0.998719i	$-0.516116\pi$
$601$	−7.18928e44	−0.101218	−0.0506089	+	0.998719i	$0.516116\pi$
$602$	5.60863e44	0.0768272
$603$	−1.20251e45	−0.160271
$604$	2.11259e45	0.273972
$605$	2.42246e45	0.305699
$606$	7.43967e45	0.913599
$607$	−1.31379e46	−1.57005	−0.785024	−	0.619465i	$-0.787349\pi$
$607$	−1.31379e46	−1.57005	−0.785024	+	0.619465i	$0.787349\pi$
$608$	2.92432e45	0.340107
$609$	1.50820e46	1.70716
$610$	−4.79024e45	−0.527734
$611$	−3.25326e44	−0.0348850
$612$	8.01972e44	0.0837068
$613$	−2.20322e45	−0.223852	−0.111926	−	0.993717i	$-0.535702\pi$
$613$	−2.20322e45	−0.223852	−0.111926	+	0.993717i	$0.535702\pi$
$614$	3.10334e45	0.306939
$615$	1.34935e46	1.29922
$616$	5.51346e45	0.516824
$617$	−7.85262e45	−0.716654	−0.358327	−	0.933596i	$-0.616653\pi$
$617$	−7.85262e45	−0.716654	−0.358327	+	0.933596i	$0.616653\pi$
$618$	3.94506e45	0.350545
$619$	2.88009e45	0.249178	0.124589	−	0.992208i	$-0.460239\pi$
$619$	2.88009e45	0.249178	0.124589	+	0.992208i	$0.460239\pi$
$620$	3.18581e45	0.268384
$621$	−8.01469e45	−0.657469
$622$	−1.58031e46	−1.26241
$623$	1.57161e46	1.22262
$624$	−2.01069e45	−0.152335
$625$	−1.60131e46	−1.18155
$626$	1.27520e46	0.916438
$627$	−2.83098e46	−1.98163
$628$	1.22054e46	0.832182
$629$	9.03837e45	0.600281
$630$	−9.65916e45	−0.624914
$631$	−2.48664e46	−1.56722	−0.783608	−	0.621256i	$-0.786623\pi$
$631$	−2.48664e46	−1.56722	−0.783608	+	0.621256i	$0.786623\pi$
$632$	−5.21493e45	−0.320196
$633$	1.93480e46	1.15738
$634$	−1.96955e45	−0.114787
$635$	2.38604e46	1.35491
$636$	3.80237e44	0.0210384
$637$	1.81875e46	0.980553
$638$	−9.42654e45	−0.495235
$639$	−4.41486e45	−0.226023
$640$	−1.97148e45	−0.0983608
$641$	−3.83552e46	−1.86495	−0.932474	−	0.361237i	$-0.882355\pi$
$641$	−3.83552e46	−1.86495	−0.932474	+	0.361237i	$0.882355\pi$
$642$	6.93507e45	0.328642
$643$	−1.26185e46	−0.582810	−0.291405	−	0.956600i	$-0.594123\pi$
$643$	−1.26185e46	−0.582810	−0.291405	+	0.956600i	$0.594123\pi$
$644$	−1.92878e46	−0.868292
$645$	1.94149e45	0.0851924
$646$	1.15087e46	0.492253
$647$	1.84679e46	0.770012	0.385006	−	0.922914i	$-0.374199\pi$
$647$	1.84679e46	0.770012	0.385006	+	0.922914i	$0.374199\pi$
$648$	−1.08610e46	−0.441449
$649$	3.10729e46	1.23124
$650$	2.19842e45	0.0849260
$651$	2.65859e46	1.00130
$652$	−1.56778e45	−0.0575704
$653$	2.83666e46	1.01564	0.507820	−	0.861463i	$-0.330451\pi$
$653$	2.83666e46	1.01564	0.507820	+	0.861463i	$0.330451\pi$
$654$	−1.94086e46	−0.677580
$655$	5.75240e46	1.95825
$656$	7.27002e45	0.241336
$657$	−8.40549e45	−0.272104
$658$	−2.66192e45	−0.0840364
$659$	−2.92708e46	−0.901209	−0.450604	−	0.892724i	$-0.648791\pi$
$659$	−2.92708e46	−0.901209	−0.450604	+	0.892724i	$0.648791\pi$
$660$	1.90855e46	0.573098
$661$	−4.51224e46	−1.32150	−0.660751	−	0.750605i	$-0.729762\pi$
$661$	−4.51224e46	−1.32150	−0.660751	+	0.750605i	$0.729762\pi$
$662$	1.91649e46	0.547455
$663$	−7.91309e45	−0.220482
$664$	4.12766e45	0.112184
$665$	−1.38613e47	−3.67492
$666$	2.09860e46	0.542756
$667$	3.29770e46	0.832021
$668$	−6.63948e45	−0.163426
$669$	−7.44055e46	−1.78679
$670$	1.16338e46	0.272576
$671$	2.49852e46	0.571164
$672$	−1.64521e46	−0.366969
$673$	3.37681e46	0.734950	0.367475	−	0.930033i	$-0.380222\pi$
$673$	3.37681e46	0.734950	0.367475	+	0.930033i	$0.380222\pi$
$674$	6.36176e45	0.135110
$675$	7.47466e45	0.154910
$676$	−1.84467e46	−0.373076
$677$	5.90078e46	1.16465	0.582326	−	0.812955i	$-0.302143\pi$
$677$	5.90078e46	1.16465	0.582326	+	0.812955i	$0.302143\pi$
$678$	9.86498e43	0.00190023
$679$	−2.91287e46	−0.547608
$680$	−7.75875e45	−0.142362
$681$	8.69870e46	1.55786
$682$	−1.66167e46	−0.290471
$683$	−3.10555e46	−0.529904	−0.264952	−	0.964262i	$-0.585356\pi$
$683$	−3.10555e46	−0.529904	−0.264952	+	0.964262i	$0.585356\pi$
$684$	2.67217e46	0.445081
$685$	1.15636e46	0.188017
$686$	7.23505e46	1.14840
$687$	−3.33035e45	−0.0516065
$688$	1.04604e45	0.0158248
$689$	−1.18678e45	−0.0175289
$690$	−6.67670e46	−0.962835
$691$	3.01300e46	0.424240	0.212120	−	0.977244i	$-0.431963\pi$
$691$	3.01300e46	0.424240	0.212120	+	0.977244i	$0.431963\pi$
$692$	2.14570e46	0.294997
$693$	5.03807e46	0.676341
$694$	−2.82897e46	−0.370849
$695$	−6.92379e46	−0.886329
$696$	2.81287e46	0.351640
$697$	2.86112e46	0.349297
$698$	−1.13762e47	−1.35638
$699$	−1.77435e47	−2.06617
$700$	1.79882e46	0.204583
$701$	9.10970e46	1.01194	0.505972	−	0.862550i	$-0.331134\pi$
$701$	9.10970e46	1.01194	0.505972	+	0.862550i	$0.331134\pi$
$702$	2.13375e46	0.231516
$703$	3.01159e47	3.19178
$704$	1.02829e46	0.106455
$705$	−9.21454e45	−0.0931866
$706$	−6.03766e46	−0.596473
$707$	−1.89997e47	−1.83369
$708$	−9.27213e46	−0.874240
$709$	−1.72541e47	−1.58938	−0.794692	−	0.607013i	$-0.792368\pi$
$709$	−1.72541e47	−1.58938	−0.794692	+	0.607013i	$0.792368\pi$
$710$	4.27119e46	0.384403
$711$	−4.76528e46	−0.419025
$712$	2.93114e46	0.251836
$713$	5.81304e46	0.488007
$714$	−6.47474e46	−0.531132
$715$	−5.95690e46	−0.477497
$716$	8.85971e46	0.693993
$717$	2.10981e47	1.61502
$718$	−2.42299e45	−0.0181259
$719$	1.20948e47	0.884245	0.442122	−	0.896955i	$-0.354226\pi$
$719$	1.20948e47	0.884245	0.442122	+	0.896955i	$0.354226\pi$
$720$	−1.80149e46	−0.128720
$721$	−1.00750e47	−0.703583
$722$	2.79872e47	1.91027
$723$	−6.50271e46	−0.433823
$724$	−4.05502e46	−0.264428
$725$	−3.07550e46	−0.196037
$726$	3.77034e46	0.234923
$727$	−1.93796e47	−1.18040	−0.590198	−	0.807259i	$-0.700950\pi$
$727$	−1.93796e47	−1.18040	−0.590198	+	0.807259i	$0.700950\pi$
$728$	5.13499e46	0.305754
$729$	3.57720e46	0.208228
$730$	8.13196e46	0.462773
$731$	4.11670e45	0.0229040
$732$	−7.45556e46	−0.405553
$733$	−7.73101e45	−0.0411169	−0.0205585	−	0.999789i	$-0.506544\pi$
$733$	−7.73101e45	−0.0411169	−0.0205585	+	0.999789i	$0.506544\pi$
$734$	−1.16876e46	−0.0607770
$735$	5.15143e47	2.61931
$736$	−3.59728e46	−0.178851
$737$	−6.06802e46	−0.295008
$738$	6.64317e46	0.315824
$739$	−3.32807e47	−1.54724	−0.773622	−	0.633648i	$-0.781557\pi$
$739$	−3.32807e47	−1.54724	−0.773622	+	0.633648i	$0.781557\pi$
$740$	−2.03031e47	−0.923079
$741$	−2.63664e47	−1.17233
$742$	−9.71063e45	−0.0422263
$743$	−5.85910e46	−0.249181	−0.124591	−	0.992208i	$-0.539762\pi$
$743$	−5.85910e46	−0.249181	−0.124591	+	0.992208i	$0.539762\pi$
$744$	4.95842e46	0.206248
$745$	4.21727e47	1.71575
$746$	−2.67474e47	−1.06436
$747$	3.77175e46	0.146809
$748$	4.04684e46	0.154078
$749$	−1.77110e47	−0.659620
$750$	−1.98946e47	−0.724811
$751$	−1.88346e47	−0.671270	−0.335635	−	0.941992i	$-0.608951\pi$
$751$	−1.88346e47	−0.671270	−0.335635	+	0.941992i	$0.608951\pi$
$752$	−4.96463e45	−0.0173098
$753$	3.60457e47	1.22952
$754$	−8.77944e46	−0.292981
$755$	−1.86762e47	−0.609766
$756$	1.74590e47	0.557712
$757$	−4.13062e47	−1.29102	−0.645510	−	0.763752i	$-0.723355\pi$
$757$	−4.13062e47	−1.29102	−0.645510	+	0.763752i	$0.723355\pi$
$758$	−1.11648e46	−0.0341437
$759$	3.48246e47	1.04207
$760$	−2.58522e47	−0.756960
$761$	4.55231e47	1.30432	0.652162	−	0.758080i	$-0.273862\pi$
$761$	4.55231e47	1.30432	0.652162	+	0.758080i	$0.273862\pi$
$762$	3.71365e47	1.04122
$763$	4.95663e47	1.35998
$764$	2.78922e47	0.748932
$765$	−7.08976e46	−0.186302
$766$	3.72946e47	0.959117
$767$	2.89398e47	0.728404
$768$	−3.06842e46	−0.0755882
$769$	−6.33199e46	−0.152671	−0.0763354	−	0.997082i	$-0.524322\pi$
$769$	−6.33199e46	−0.152671	−0.0763354	+	0.997082i	$0.524322\pi$
$770$	−4.87412e47	−1.15027
$771$	−6.63750e47	−1.53323
$772$	−7.09742e46	−0.160478
$773$	5.70572e47	1.26284	0.631421	−	0.775441i	$-0.282472\pi$
$773$	5.70572e47	1.26284	0.631421	+	0.775441i	$0.282472\pi$
$774$	9.55847e45	0.0207092
$775$	−5.42136e46	−0.114982
$776$	−5.43266e46	−0.112796
$777$	−1.69431e48	−3.44387
$778$	−3.79970e47	−0.756112
$779$	9.53325e47	1.85726
$780$	1.77754e47	0.339045
$781$	−2.22779e47	−0.416037
$782$	−1.41571e47	−0.258859
$783$	−2.98502e47	−0.534414
$784$	2.77549e47	0.486547
$785$	−1.07901e48	−1.85215
$786$	8.95307e47	1.50487
$787$	2.70582e47	0.445365	0.222682	−	0.974891i	$-0.428519\pi$
$787$	2.70582e47	0.445365	0.222682	+	0.974891i	$0.428519\pi$
$788$	9.28437e46	0.149648
$789$	1.52051e47	0.240003
$790$	4.61021e47	0.712645
$791$	−2.51936e45	−0.00381397
$792$	9.39628e46	0.139313
$793$	2.32700e47	0.337901
$794$	1.26208e47	0.179493
$795$	−3.36145e46	−0.0468240
$796$	−7.30210e46	−0.0996282
$797$	3.10789e47	0.415339	0.207670	−	0.978199i	$-0.433412\pi$
$797$	3.10789e47	0.415339	0.207670	+	0.978199i	$0.433412\pi$
$798$	−2.15739e48	−2.82410
$799$	−1.95383e46	−0.0250533
$800$	3.35490e46	0.0421400
$801$	2.67841e47	0.329564
$802$	2.29991e47	0.277225
$803$	−4.24151e47	−0.500857
$804$	1.81070e47	0.209469
$805$	1.70512e48	1.93252
$806$	−1.54760e47	−0.171843
$807$	1.82989e48	1.99073
$808$	−3.54355e47	−0.377704
$809$	−7.05865e46	−0.0737176	−0.0368588	−	0.999320i	$-0.511735\pi$
$809$	−7.05865e46	−0.0737176	−0.0368588	+	0.999320i	$0.511735\pi$
$810$	9.60153e47	0.982512
$811$	−8.82187e47	−0.884538	−0.442269	−	0.896882i	$-0.645826\pi$
$811$	−8.82187e47	−0.884538	−0.442269	+	0.896882i	$0.645826\pi$
$812$	−7.18362e47	−0.705779
$813$	−7.31582e47	−0.704319
$814$	1.05898e48	0.999043
$815$	1.38598e47	0.128132
$816$	−1.20758e47	−0.109402
$817$	1.37168e47	0.121784
$818$	−1.59899e48	−1.39129
$819$	4.69223e47	0.400124
$820$	−6.42699e47	−0.537130
$821$	2.59890e47	0.212876	0.106438	−	0.994319i	$-0.466055\pi$
$821$	2.59890e47	0.212876	0.106438	+	0.994319i	$0.466055\pi$
$822$	1.79976e47	0.144487
$823$	−1.76844e48	−1.39153	−0.695764	−	0.718270i	$-0.744934\pi$
$823$	−1.76844e48	−1.39153	−0.695764	+	0.718270i	$0.744934\pi$
$824$	−1.87905e47	−0.144924
$825$	−3.24782e47	−0.245528
$826$	2.36795e48	1.75470
$827$	−2.01881e48	−1.46640	−0.733202	−	0.680011i	$-0.761975\pi$
$827$	−2.01881e48	−1.46640	−0.733202	+	0.680011i	$0.761975\pi$
$828$	−3.28711e47	−0.234053
$829$	8.48896e47	0.592522	0.296261	−	0.955107i	$-0.404260\pi$
$829$	8.48896e47	0.592522	0.296261	+	0.955107i	$0.404260\pi$
$830$	−3.64901e47	−0.249682
$831$	−1.86019e48	−1.24779
$832$	9.57703e46	0.0629790
$833$	1.09230e48	0.704203
$834$	−1.07762e48	−0.681125
$835$	5.86957e47	0.363730
$836$	1.34841e48	0.819253
$837$	−5.26187e47	−0.313451
$838$	−1.53922e47	−0.0899029
$839$	1.91305e47	0.109560	0.0547802	−	0.998498i	$-0.482554\pi$
$839$	1.91305e47	0.109560	0.0547802	+	0.998498i	$0.482554\pi$
$840$	1.45444e48	0.816745
$841$	−5.87870e47	−0.323703
$842$	6.47573e47	0.349655
$843$	2.72985e48	1.44538
$844$	−9.21556e47	−0.478488
$845$	1.63076e48	0.830338
$846$	−4.53656e46	−0.0226525
$847$	−9.62883e47	−0.471517
$848$	−1.81109e46	−0.00869777
$849$	3.13201e48	1.47518
$850$	1.32032e47	0.0609912
$851$	−3.70463e48	−1.67845
$852$	6.64771e47	0.295406
$853$	−1.05016e48	−0.457716	−0.228858	−	0.973460i	$-0.573499\pi$
$853$	−1.05016e48	−0.457716	−0.228858	+	0.973460i	$0.573499\pi$
$854$	1.90403e48	0.813989
$855$	−2.36231e48	−0.990594
$856$	−3.30320e47	−0.135868
$857$	3.22584e48	1.30155	0.650773	−	0.759272i	$-0.274445\pi$
$857$	3.22584e48	1.30155	0.650773	+	0.759272i	$0.274445\pi$
$858$	−9.27135e47	−0.366946
$859$	3.23235e48	1.25496	0.627482	−	0.778631i	$-0.284086\pi$
$859$	3.23235e48	1.25496	0.627482	+	0.778631i	$0.284086\pi$
$860$	−9.24743e46	−0.0352206
$861$	−5.36339e48	−2.00395
$862$	−3.03074e48	−1.11091
$863$	2.08205e47	0.0748709	0.0374355	−	0.999299i	$-0.488081\pi$
$863$	2.08205e47	0.0748709	0.0374355	+	0.999299i	$0.488081\pi$
$864$	3.25620e47	0.114877
$865$	−1.89688e48	−0.656560
$866$	−1.36512e47	−0.0463579
$867$	3.15461e48	1.05107
$868$	−1.26630e48	−0.413962
$869$	−2.40461e48	−0.771292
$870$	−2.48669e48	−0.782627
$871$	−5.65148e47	−0.174527
$872$	9.24440e47	0.280128
$873$	−4.96424e47	−0.147611
$874$	−4.71715e48	−1.37639
$875$	5.08076e48	1.45477
$876$	1.26566e48	0.355632
$877$	−4.32086e47	−0.119145	−0.0595726	−	0.998224i	$-0.518974\pi$
$877$	−4.32086e47	−0.119145	−0.0595726	+	0.998224i	$0.518974\pi$
$878$	1.87708e48	0.507953
$879$	6.86368e47	0.182281
$880$	−9.09051e47	−0.236932
$881$	1.39725e48	0.357414	0.178707	−	0.983902i	$-0.442809\pi$
$881$	1.39725e48	0.357414	0.178707	+	0.983902i	$0.442809\pi$
$882$	2.53618e48	0.636720
$883$	7.06758e48	1.74148	0.870741	−	0.491742i	$-0.163640\pi$
$883$	7.06758e48	1.74148	0.870741	+	0.491742i	$0.163640\pi$
$884$	3.76904e47	0.0911525
$885$	8.19694e48	1.94575
$886$	5.72712e48	1.33438
$887$	−4.93845e48	−1.12941	−0.564704	−	0.825293i	$-0.691010\pi$
$887$	−4.93845e48	−1.12941	−0.564704	+	0.825293i	$0.691010\pi$
$888$	−3.15999e48	−0.709367
$889$	−9.48405e48	−2.08985
$890$	−2.59125e48	−0.560498
$891$	−5.00801e48	−1.06337
$892$	3.54397e48	0.738703
$893$	−6.51016e47	−0.133212
$894$	6.56378e48	1.31852
$895$	−7.83235e48	−1.54458
$896$	7.83624e47	0.151714
$897$	3.24341e48	0.616490
$898$	−3.56853e48	−0.665931
$899$	2.16503e48	0.396670
$900$	3.06563e47	0.0551465
$901$	−7.12753e46	−0.0125887
$902$	3.35222e48	0.581333
$903$	−7.71706e47	−0.131403
$904$	−4.69874e45	−0.000785601 0
$905$	3.58480e48	0.588524
$906$	−2.90677e48	−0.468592
$907$	−4.02691e47	−0.0637458	−0.0318729	−	0.999492i	$-0.510147\pi$
$907$	−4.02691e47	−0.0637458	−0.0318729	+	0.999492i	$0.510147\pi$
$908$	−4.14323e48	−0.644055
$909$	−3.23801e48	−0.494281
$910$	−4.53954e48	−0.680500
$911$	2.39672e48	0.352829	0.176415	−	0.984316i	$-0.443550\pi$
$911$	2.39672e48	0.352829	0.176415	+	0.984316i	$0.443550\pi$
$912$	−4.02365e48	−0.581708
$913$	1.90327e48	0.270229
$914$	7.00491e48	0.976765
$915$	6.59102e48	0.902619
$916$	1.58626e47	0.0213354
$917$	−2.28647e49	−3.02045
$918$	1.28148e48	0.166267
$919$	8.18036e48	1.04248	0.521238	−	0.853411i	$-0.325470\pi$
$919$	8.18036e48	1.04248	0.521238	+	0.853411i	$0.325470\pi$
$920$	3.18014e48	0.398059
$921$	−4.26997e48	−0.524978
$922$	4.98509e48	0.602022
$923$	−2.07486e48	−0.246128
$924$	−7.58612e48	−0.883959
$925$	3.45502e48	0.395468
$926$	−4.59356e48	−0.516498
$927$	−1.71703e48	−0.189654
$928$	−1.33979e48	−0.145376
$929$	−4.85673e48	−0.517708	−0.258854	−	0.965916i	$-0.583345\pi$
$929$	−4.85673e48	−0.517708	−0.258854	+	0.965916i	$0.583345\pi$
$930$	−4.38344e48	−0.459036
$931$	3.63953e49	3.74435
$932$	8.45133e48	0.854206
$933$	2.17439e49	2.15919
$934$	8.88567e47	0.0866896
$935$	−3.57757e48	−0.342923
$936$	8.75126e47	0.0824175
$937$	9.88086e48	0.914306	0.457153	−	0.889388i	$-0.348869\pi$
$937$	9.88086e48	0.914306	0.457153	+	0.889388i	$0.348869\pi$
$938$	−4.62422e48	−0.420428
$939$	−1.75459e49	−1.56745
$940$	4.38893e47	0.0385256
$941$	2.08272e48	0.179640	0.0898198	−	0.995958i	$-0.471371\pi$
$941$	2.08272e48	0.179640	0.0898198	+	0.995958i	$0.471371\pi$
$942$	−1.67937e49	−1.42334
$943$	−1.17271e49	−0.976670
$944$	4.41636e48	0.361432
$945$	−1.54345e49	−1.24127
$946$	4.82332e47	0.0381190
$947$	−1.53943e49	−1.19560	−0.597800	−	0.801645i	$-0.703958\pi$
$947$	−1.53943e49	−1.19560	−0.597800	+	0.801645i	$0.703958\pi$
$948$	7.17535e48	0.547653
$949$	−3.95034e48	−0.296307
$950$	4.39931e48	0.324299
$951$	2.70996e48	0.196329
$952$	3.08395e48	0.219583
$953$	1.74621e49	1.22198	0.610989	−	0.791639i	$-0.290772\pi$
$953$	1.74621e49	1.22198	0.610989	+	0.791639i	$0.290772\pi$
$954$	−1.65493e47	−0.0113823
$955$	−2.46578e49	−1.66686
$956$	−1.00491e49	−0.667687
$957$	1.29702e49	0.847033
$958$	−7.28504e47	−0.0467629
$959$	−4.59630e48	−0.290002
$960$	2.71261e48	0.168233
$961$	−1.25871e49	−0.767341
$962$	9.86283e48	0.591035
$963$	−3.01839e48	−0.177804
$964$	3.09727e48	0.179353
$965$	6.27441e48	0.357168
$966$	2.65386e49	1.48510
$967$	−4.40295e48	−0.242218	−0.121109	−	0.992639i	$-0.538645\pi$
$967$	−4.40295e48	−0.242218	−0.121109	+	0.992639i	$0.538645\pi$
$968$	−1.79583e48	−0.0971229
$969$	−1.58351e49	−0.841933
$970$	4.80270e48	0.251045
$971$	3.47513e48	0.178589	0.0892943	−	0.996005i	$-0.471539\pi$
$971$	3.47513e48	0.178589	0.0892943	+	0.996005i	$0.471539\pi$
$972$	8.51296e48	0.430118
$973$	2.75207e49	1.36709
$974$	−2.07815e49	−1.01497
$975$	−3.02487e48	−0.145255
$976$	3.55112e48	0.167665
$977$	3.21627e49	1.49311	0.746556	−	0.665323i	$-0.231706\pi$
$977$	3.21627e49	1.49311	0.746556	+	0.665323i	$0.231706\pi$
$978$	2.15715e48	0.0984665
$979$	1.35156e49	0.606624
$980$	−2.45365e49	−1.08288
$981$	8.44731e48	0.366589
$982$	−5.66802e48	−0.241875
$983$	4.86681e48	0.204226	0.102113	−	0.994773i	$-0.467440\pi$
$983$	4.86681e48	0.204226	0.102113	+	0.994773i	$0.467440\pi$
$984$	−1.00030e49	−0.412773
$985$	−8.20776e48	−0.333063
$986$	−5.27273e48	−0.210410
$987$	3.66260e48	0.143733
$988$	1.25585e49	0.484671
$989$	−1.68735e48	−0.0640421
$990$	−8.30669e48	−0.310061
$991$	−4.22131e49	−1.54965	−0.774823	−	0.632178i	$-0.782161\pi$
$991$	−4.22131e49	−1.54965	−0.774823	+	0.632178i	$0.782161\pi$
$992$	−2.36172e48	−0.0852678
$993$	−2.63694e49	−0.936350
$994$	−1.69772e49	−0.592912
$995$	6.45536e48	0.221738
$996$	−5.67935e48	−0.191875
$997$	−2.50448e49	−0.832236	−0.416118	−	0.909311i	$-0.636610\pi$
$997$	−2.50448e49	−0.832236	−0.416118	+	0.909311i	$0.636610\pi$
$998$	1.65002e49	0.539307
$999$	3.35337e49	1.07808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.34.a.b.1.1	✓	2
3.2	odd	2		18.34.a.e.1.2		2
4.3	odd	2		16.34.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.34.a.b.1.1	✓	2	1.1	even	1	trivial
16.34.a.c.1.2		2	4.3	odd	2
18.34.a.e.1.2		2	3.2	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+65536.0 q^{2} -9.01727e7 q^{3} +4.29497e9 q^{4} -3.79693e11 q^{5} -5.90956e12 q^{6} +1.50920e14 q^{7} +2.81475e14 q^{8} +2.57205e15 q^{9} +O(q^{10})\)	\(q+65536.0 q^{2} -9.01727e7 q^{3} +4.29497e9 q^{4} -3.79693e11 q^{5} -5.90956e12 q^{6} +1.50920e14 q^{7} +2.81475e14 q^{8} +2.57205e15 q^{9} -2.48835e16 q^{10} +1.29789e17 q^{11} -3.87289e17 q^{12} +1.20879e18 q^{13} +9.89072e18 q^{14} +3.42379e19 q^{15} +1.84467e19 q^{16} +7.25972e19 q^{17} +1.68562e20 q^{18} +2.41894e21 q^{19} -1.63077e21 q^{20} -1.36089e22 q^{21} +8.50583e21 q^{22} -2.97560e22 q^{23} -2.53814e22 q^{24} +2.77511e22 q^{25} +7.92194e22 q^{26} +2.69347e23 q^{27} +6.48198e23 q^{28} -1.10824e24 q^{29} +2.24381e24 q^{30} -1.95357e24 q^{31} +1.20893e24 q^{32} -1.17034e25 q^{33} +4.75773e24 q^{34} -5.73034e25 q^{35} +1.10469e25 q^{36} +1.24500e26 q^{37} +1.58528e26 q^{38} -1.09000e26 q^{39} -1.06874e26 q^{40} +3.94109e26 q^{41} -8.91873e26 q^{42} +5.67060e25 q^{43} +5.57438e26 q^{44} -9.76588e26 q^{45} -1.95009e27 q^{46} -2.69133e26 q^{47} -1.66339e27 q^{48} +1.50460e28 q^{49} +1.81869e27 q^{50} -6.54628e27 q^{51} +5.19172e27 q^{52} -9.81792e26 q^{53} +1.76519e28 q^{54} -4.92798e28 q^{55} +4.24803e28 q^{56} -2.18122e29 q^{57} -7.26299e28 q^{58} +2.39411e29 q^{59} +1.47051e29 q^{60} +1.92507e29 q^{61} -1.28029e29 q^{62} +3.88175e29 q^{63} +7.92282e28 q^{64} -4.58969e29 q^{65} -7.66993e29 q^{66} -4.67531e29 q^{67} +3.11802e29 q^{68} +2.68318e30 q^{69} -3.75543e30 q^{70} -1.71647e30 q^{71} +7.23968e29 q^{72} -3.26801e30 q^{73} +8.15925e30 q^{74} -2.50239e30 q^{75} +1.03893e31 q^{76} +1.95878e31 q^{77} -7.14342e30 q^{78} -1.85271e31 q^{79} -7.00409e30 q^{80} -3.85859e31 q^{81} +2.58283e31 q^{82} +1.46644e31 q^{83} -5.84498e31 q^{84} -2.75646e31 q^{85} +3.71629e30 q^{86} +9.99334e31 q^{87} +3.65322e31 q^{88} +1.04135e32 q^{89} -6.40017e31 q^{90} +1.82431e32 q^{91} -1.27801e32 q^{92} +1.76158e32 q^{93} -1.76379e31 q^{94} -9.18453e32 q^{95} -1.09012e32 q^{96} -1.93007e32 q^{97} +9.86053e32 q^{98} +3.33823e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 131072 q^{2} + 8356488 q^{3} + 8589934592 q^{4} - 5332476660 q^{5} + 547650797568 q^{6} + 132719095875856 q^{7} + 562949953421312 q^{8} + 67\!\cdots\!26 q^{9}+O(q^{10}) \) 2 * q + 131072 * q^2 + 8356488 * q^3 + 8589934592 * q^4 - 5332476660 * q^5 + 547650797568 * q^6 + 132719095875856 * q^7 + 562949953421312 * q^8 + 6720986327276826 * q^9	\( 2 q + 131072 q^{2} + 8356488 q^{3} + 8589934592 q^{4} - 5332476660 q^{5} + 547650797568 q^{6} + 132719095875856 q^{7} + 562949953421312 q^{8} + 67\!\cdots\!26 q^{9}+ \cdots - 86\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 131072 * q^2 + 8356488 * q^3 + 8589934592 * q^4 - 5332476660 * q^5 + 547650797568 * q^6 + 132719095875856 * q^7 + 562949953421312 * q^8 + 6720986327276826 * q^9 - 349469190389760 * q^10 - 158105471422723176 * q^11 + 35890842669416448 * q^12 + 4983398515499093788 * q^13 + 8697878667320098816 * q^14 + 71123270901495251760 * q^15 + 36893488147419103232 * q^16 + 302465632526578851876 * q^17 + 440466559944414068736 * q^18 + 2235591200465928697000 * q^19 - 22902812861383311360 * q^20 - 15402260676699297433536 * q^21 - 10361600175159586062336 * q^22 - 71424561765127117190352 * q^23 + 2352142265182876336128 * q^24 + 51481196955054820524350 * q^25 + 326592005111748610490368 * q^26 + 130408214799538026000720 * q^27 + 570024176341489996005376 * q^28 - 252883963720400854222020 * q^29 + 4661134681800392819343360 * q^30 - 4320085941116207893109696 * q^31 + 2417851639229258349412352 * q^32 - 40069350396261729983984544 * q^33 + 19822387693261871636545536 * q^34 - 64117207337688310160318880 * q^35 + 28866416472517120408682496 * q^36 + 116026284407242232995257676 * q^37 + 146511704913735103086592000 * q^38 + 262908916541617545294421872 * q^39 - 1500958743683616693288960 * q^40 - 166777326610314677606684076 * q^41 - 1009402555708165156604215296 * q^42 - 36726176847118764316966952 * q^43 - 679057829079258632181252096 * q^44 + 576607194247955860756817820 * q^45 - 4680880079839370752186908672 * q^46 + 2869532951474224704935093856 * q^47 + 154149995491024983564484608 * q^48 + 7646276407161112463093552754 * q^49 + 3373871723646472717883801600 * q^50 + 16102466566622667888770592144 * q^51 + 21403533647003556937096757248 * q^52 - 4397747242775062628314771092 * q^53 + 8546432765102524071983185920 * q^54 - 157055806778964587214335057520 * q^55 + 37357104420715888378208321536 * q^56 - 236187507701079470516663925600 * q^57 - 16573003446380190382294302720 * q^58 + 187586852967550885385845088760 * q^59 + 305472122506470543808486440960 * q^60 + 464465778169397582356016167804 * q^61 - 283121152236991800482837037056 * q^62 + 312658861452449815338473381328 * q^63 + 158456325028528675187087900672 * q^64 + 954092969996430917540586811560 * q^65 - 2625984947569408736230411075584 * q^66 - 749458286997747528573119702264 * q^67 + 1299079999865610019572648247296 * q^68 - 1422385372570989976078465505088 * q^69 - 4201985300082741094666658119680 * q^70 + 2607453085577305255019451429264 * q^71 + 1891789469942882003103416057856 * q^72 - 5204971716349166463517155924332 * q^73 + 7603898574913026981577207054336 * q^74 - 164280989427041924157498846600 * q^75 + 9601791093226543715882893312000 * q^76 + 24827809126093538111775086561472 * q^77 + 17229998754471447448415231803392 * q^78 - 26559519161049342541312928970080 * q^79 - 98366832226049503611385282560 * q^80 - 75339567615598499486481976424718 * q^81 - 10929918876733582711631647604736 * q^82 - 37062506185061977386465584779992 * q^83 - 66152205890890311703213853638656 * q^84 + 58488965180889831423090470767320 * q^85 - 2406886725852775338276746166272 * q^86 + 184211334389904891581661872551920 * q^87 - 44502733886538293718630537363456 * q^88 + 302974646079669442176749711731380 * q^89 + 37788529082234035290558812651520 * q^90 + 113728448773618228380737641674464 * q^91 - 306766156912353001615321246728192 * q^92 - 57012891826715143125581754081024 * q^93 + 188057711507814790262626310946816 * q^94 - 987091918419525594011119002435600 * q^95 + 10102374104499813322882063269888 * q^96 + 68100314316598271221487860024516 * q^97 + 501106370619710666381299073286144 * q^98 - 860631078578460214896605406940488 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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