LMFDB - Embedded newform 285.10.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4398 x^{10} + 11376 x^{9} + 7070146 x^{8} - 15274638 x^{7} - 5114407260 x^{6} + \cdots + 43\!\cdots\!00 $ x^12 - 3x^11 - 4398x^10 + 11376x^9 + 7070146x^8 - 15274638x^7 - 5114407260x^6 + 8284970600x^5 + 1621868619141x^4 - 1541179405015x^3 - 176385539891230x^2 + 130401229370000*x + 4344410152258400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$33.7980$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+30.7980 q^{2} +81.0000 q^{3} +436.517 q^{4} +625.000 q^{5} +2494.64 q^{6} -2782.02 q^{7} -2324.71 q^{8} +6561.00 q^{9} +19248.8 q^{10} +1151.71 q^{11} +35357.9 q^{12} +39804.6 q^{13} -85680.5 q^{14} +50625.0 q^{15} -295093. q^{16} -175791. q^{17} +202066. q^{18} -130321. q^{19} +272823. q^{20} -225343. q^{21} +35470.4 q^{22} -2.33041e6 q^{23} -188302. q^{24} +390625. q^{25} +1.22590e6 q^{26} +531441. q^{27} -1.21440e6 q^{28} -1.00066e6 q^{29} +1.55915e6 q^{30} -4.83994e6 q^{31} -7.89804e6 q^{32} +93288.5 q^{33} -5.41402e6 q^{34} -1.73876e6 q^{35} +2.86399e6 q^{36} +9.22167e6 q^{37} -4.01363e6 q^{38} +3.22417e6 q^{39} -1.45294e6 q^{40} +1.49454e7 q^{41} -6.94012e6 q^{42} +3.22833e7 q^{43} +502742. q^{44} +4.10062e6 q^{45} -7.17720e7 q^{46} -5.41216e7 q^{47} -2.39026e7 q^{48} -3.26140e7 q^{49} +1.20305e7 q^{50} -1.42391e7 q^{51} +1.73754e7 q^{52} -5.17654e7 q^{53} +1.63673e7 q^{54} +719819. q^{55} +6.46738e6 q^{56} -1.05560e7 q^{57} -3.08184e7 q^{58} -3.49621e7 q^{59} +2.20987e7 q^{60} +1.98210e7 q^{61} -1.49061e8 q^{62} -1.82528e7 q^{63} -9.21560e7 q^{64} +2.48778e7 q^{65} +2.87310e6 q^{66} -7.44306e7 q^{67} -7.67359e7 q^{68} -1.88763e8 q^{69} -5.35503e7 q^{70} -3.42811e8 q^{71} -1.52524e7 q^{72} -3.02412e8 q^{73} +2.84009e8 q^{74} +3.16406e7 q^{75} -5.68874e7 q^{76} -3.20408e6 q^{77} +9.92980e7 q^{78} +3.94342e8 q^{79} -1.84433e8 q^{80} +4.30467e7 q^{81} +4.60288e8 q^{82} -4.79544e8 q^{83} -9.83663e7 q^{84} -1.09869e8 q^{85} +9.94260e8 q^{86} -8.10535e7 q^{87} -2.67739e6 q^{88} +5.64393e8 q^{89} +1.26291e8 q^{90} -1.10737e8 q^{91} -1.01727e9 q^{92} -3.92035e8 q^{93} -1.66684e9 q^{94} -8.14506e7 q^{95} -6.39741e8 q^{96} +1.27447e9 q^{97} -1.00445e9 q^{98} +7.55637e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 33 q^{2} + 972 q^{3} + 2751 q^{4} + 7500 q^{5} - 2673 q^{6} - 5100 q^{7} - 40215 q^{8} + 78732 q^{9} - 20625 q^{10} - 60416 q^{11} + 222831 q^{12} - 164042 q^{13} - 444762 q^{14} + 607500 q^{15}+ \cdots - 396389376 q^{99}+O(q^{100}) $ 12 * q - 33 * q^2 + 972 * q^3 + 2751 * q^4 + 7500 * q^5 - 2673 * q^6 - 5100 * q^7 - 40215 * q^8 + 78732 * q^9 - 20625 * q^10 - 60416 * q^11 + 222831 * q^12 - 164042 * q^13 - 444762 * q^14 + 607500 * q^15 + 319475 * q^16 - 552834 * q^17 - 216513 * q^18 - 1563852 * q^19 + 1719375 * q^20 - 413100 * q^21 + 708846 * q^22 - 2749174 * q^23 - 3257415 * q^24 + 4687500 * q^25 - 5159376 * q^26 + 6377292 * q^27 - 2379170 * q^28 - 3415632 * q^29 - 1670625 * q^30 - 9822574 * q^31 - 22282623 * q^32 - 4893696 * q^33 + 5214442 * q^34 - 3187500 * q^35 + 18049311 * q^36 - 24559054 * q^37 + 4300593 * q^38 - 13287402 * q^39 - 25134375 * q^40 - 35856950 * q^41 - 36025722 * q^42 - 73839462 * q^43 - 88153054 * q^44 + 49207500 * q^45 - 19966000 * q^46 - 134699358 * q^47 + 25877475 * q^48 - 64331236 * q^49 - 12890625 * q^50 - 44779554 * q^51 - 290325860 * q^52 - 74807846 * q^53 - 17537553 * q^54 - 37760000 * q^55 - 403278618 * q^56 - 126672012 * q^57 - 377474064 * q^58 - 294192102 * q^59 + 139269375 * q^60 - 184407884 * q^61 - 356900784 * q^62 - 33461100 * q^63 + 169573219 * q^64 - 102526250 * q^65 + 57416526 * q^66 - 427627864 * q^67 - 56755242 * q^68 - 222683094 * q^69 - 277976250 * q^70 - 488904216 * q^71 - 263850615 * q^72 - 184702472 * q^73 - 1424419204 * q^74 + 379687500 * q^75 - 358513071 * q^76 - 827371672 * q^77 - 417909456 * q^78 - 620531838 * q^79 + 199671875 * q^80 + 516560652 * q^81 + 100137664 * q^82 - 32273124 * q^83 - 192712770 * q^84 - 345521250 * q^85 + 1147824298 * q^86 - 276666192 * q^87 + 2717542210 * q^88 + 473499162 * q^89 - 135320625 * q^90 - 1430236924 * q^91 + 1920565904 * q^92 - 795628494 * q^93 + 2483643504 * q^94 - 977407500 * q^95 - 1804892463 * q^96 + 318965234 * q^97 + 2863543931 * q^98 - 396389376 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	30.7980	1.36109	0.680546	−	0.732705i	$-0.261743\pi$
$2$	30.7980	1.36109	0.680546	+	0.732705i	$0.261743\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	436.517	0.852573
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2494.64	0.785827
$7$	−2782.02	−0.437944	−0.218972	−	0.975731i	$-0.570270\pi$
$7$	−2782.02	−0.437944	−0.218972	+	0.975731i	$0.570270\pi$
$8$	−2324.71	−0.200662
$9$	6561.00	0.333333
$10$	19248.8	0.608699
$11$	1151.71	0.0237179	0.0118589	−	0.999930i	$-0.496225\pi$
$11$	1151.71	0.0237179	0.0118589	+	0.999930i	$0.496225\pi$
$12$	35357.9	0.492233
$13$	39804.6	0.386534	0.193267	−	0.981146i	$-0.438092\pi$
$13$	39804.6	0.386534	0.193267	+	0.981146i	$0.438092\pi$
$14$	−85680.5	−0.596082
$15$	50625.0	0.258199
$16$	−295093.	−1.12569
$17$	−175791.	−0.510478	−0.255239	−	0.966878i	$-0.582154\pi$
$17$	−175791.	−0.510478	−0.255239	+	0.966878i	$0.582154\pi$
$18$	202066.	0.453698
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	272823.	0.381282
$21$	−225343.	−0.252847
$22$	35470.4	0.0322823
$23$	−2.33041e6	−1.73643	−0.868215	−	0.496188i	$-0.834733\pi$
$23$	−2.33041e6	−1.73643	−0.868215	+	0.496188i	$0.834733\pi$
$24$	−188302.	−0.115852
$25$	390625.	0.200000
$26$	1.22590e6	0.526109
$27$	531441.	0.192450
$28$	−1.21440e6	−0.373379
$29$	−1.00066e6	−0.262722	−0.131361	−	0.991335i	$-0.541935\pi$
$29$	−1.00066e6	−0.262722	−0.131361	+	0.991335i	$0.541935\pi$
$30$	1.55915e6	0.351433
$31$	−4.83994e6	−0.941266	−0.470633	−	0.882329i	$-0.655974\pi$
$31$	−4.83994e6	−0.941266	−0.470633	+	0.882329i	$0.655974\pi$
$32$	−7.89804e6	−1.33151
$33$	93288.5	0.0136935
$34$	−5.41402e6	−0.694807
$35$	−1.73876e6	−0.195854
$36$	2.86399e6	0.284191
$37$	9.22167e6	0.808913	0.404456	−	0.914557i	$-0.367461\pi$
$37$	9.22167e6	0.808913	0.404456	+	0.914557i	$0.367461\pi$
$38$	−4.01363e6	−0.312256
$39$	3.22417e6	0.223165
$40$	−1.45294e6	−0.0897386
$41$	1.49454e7	0.825999	0.412999	−	0.910731i	$-0.364481\pi$
$41$	1.49454e7	0.825999	0.412999	+	0.910731i	$0.364481\pi$
$42$	−6.94012e6	−0.344148
$43$	3.22833e7	1.44002	0.720011	−	0.693962i	$-0.244137\pi$
$43$	3.22833e7	1.44002	0.720011	+	0.693962i	$0.244137\pi$
$44$	502742.	0.0202212
$45$	4.10062e6	0.149071
$46$	−7.17720e7	−2.36344
$47$	−5.41216e7	−1.61782	−0.808910	−	0.587932i	$-0.799942\pi$
$47$	−5.41216e7	−1.61782	−0.808910	+	0.587932i	$0.799942\pi$
$48$	−2.39026e7	−0.649919
$49$	−3.26140e7	−0.808205
$50$	1.20305e7	0.272219
$51$	−1.42391e7	−0.294724
$52$	1.73754e7	0.329548
$53$	−5.17654e7	−0.901153	−0.450576	−	0.892738i	$-0.648781\pi$
$53$	−5.17654e7	−0.901153	−0.450576	+	0.892738i	$0.648781\pi$
$54$	1.63673e7	0.261942
$55$	719819.	0.0106070
$56$	6.46738e6	0.0878785
$57$	−1.05560e7	−0.132453
$58$	−3.08184e7	−0.357588
$59$	−3.49621e7	−0.375632	−0.187816	−	0.982204i	$-0.560141\pi$
$59$	−3.49621e7	−0.375632	−0.187816	+	0.982204i	$0.560141\pi$
$60$	2.20987e7	0.220133
$61$	1.98210e7	0.183291	0.0916454	−	0.995792i	$-0.470787\pi$
$61$	1.98210e7	0.183291	0.0916454	+	0.995792i	$0.470787\pi$
$62$	−1.49061e8	−1.28115
$63$	−1.82528e7	−0.145981
$64$	−9.21560e7	−0.686616
$65$	2.48778e7	0.172863
$66$	2.87310e6	0.0186382
$67$	−7.44306e7	−0.451248	−0.225624	−	0.974214i	$-0.572442\pi$
$67$	−7.44306e7	−0.451248	−0.225624	+	0.974214i	$0.572442\pi$
$68$	−7.67359e7	−0.435220
$69$	−1.88763e8	−1.00253
$70$	−5.35503e7	−0.266576
$71$	−3.42811e8	−1.60100	−0.800502	−	0.599330i	$-0.795434\pi$
$71$	−3.42811e8	−1.60100	−0.800502	+	0.599330i	$0.795434\pi$
$72$	−1.52524e7	−0.0668872
$73$	−3.02412e8	−1.24637	−0.623185	−	0.782075i	$-0.714162\pi$
$73$	−3.02412e8	−1.24637	−0.623185	+	0.782075i	$0.714162\pi$
$74$	2.84009e8	1.10101
$75$	3.16406e7	0.115470
$76$	−5.68874e7	−0.195594
$77$	−3.20408e6	−0.0103871
$78$	9.92980e7	0.303749
$79$	3.94342e8	1.13907	0.569536	−	0.821966i	$-0.307123\pi$
$79$	3.94342e8	1.13907	0.569536	+	0.821966i	$0.307123\pi$
$80$	−1.84433e8	−0.503425
$81$	4.30467e7	0.111111
$82$	4.60288e8	1.12426
$83$	−4.79544e8	−1.10912	−0.554558	−	0.832145i	$-0.687112\pi$
$83$	−4.79544e8	−1.10912	−0.554558	+	0.832145i	$0.687112\pi$
$84$	−9.83663e7	−0.215571
$85$	−1.09869e8	−0.228293
$86$	9.94260e8	1.96000
$87$	−8.10535e7	−0.151682
$88$	−2.67739e6	−0.00475927
$89$	5.64393e8	0.953514	0.476757	−	0.879035i	$-0.341812\pi$
$89$	5.64393e8	0.953514	0.476757	+	0.879035i	$0.341812\pi$
$90$	1.26291e8	0.202900
$91$	−1.10737e8	−0.169280
$92$	−1.01727e9	−1.48043
$93$	−3.92035e8	−0.543440
$94$	−1.66684e9	−2.20200
$95$	−8.14506e7	−0.102598
$96$	−6.39741e8	−0.768748
$97$	1.27447e9	1.46169	0.730845	−	0.682543i	$-0.239126\pi$
$97$	1.27447e9	1.46169	0.730845	+	0.682543i	$0.239126\pi$
$98$	−1.00445e9	−1.10004
$99$	7.55637e6	0.00790597
$100$	1.70515e8	0.170515
$101$	7.95234e8	0.760412	0.380206	−	0.924902i	$-0.375853\pi$
$101$	7.95234e8	0.760412	0.380206	+	0.924902i	$0.375853\pi$
$102$	−4.38535e8	−0.401147
$103$	5.01052e8	0.438647	0.219323	−	0.975652i	$-0.429615\pi$
$103$	5.01052e8	0.438647	0.219323	+	0.975652i	$0.429615\pi$
$104$	−9.25341e7	−0.0775625
$105$	−1.40840e8	−0.113077
$106$	−1.59427e9	−1.22655
$107$	−2.61865e9	−1.93130	−0.965652	−	0.259837i	$-0.916331\pi$
$107$	−2.61865e9	−1.93130	−0.965652	+	0.259837i	$0.916331\pi$
$108$	2.31983e8	0.164078
$109$	−1.65433e9	−1.12254	−0.561270	−	0.827632i	$-0.689687\pi$
$109$	−1.65433e9	−1.12254	−0.561270	+	0.827632i	$0.689687\pi$
$110$	2.21690e7	0.0144371
$111$	7.46955e8	0.467026
$112$	8.20954e8	0.492990
$113$	1.26156e9	0.727873	0.363937	−	0.931424i	$-0.381432\pi$
$113$	1.26156e9	0.727873	0.363937	+	0.931424i	$0.381432\pi$
$114$	−3.25104e8	−0.180281
$115$	−1.45651e9	−0.776555
$116$	−4.36806e8	−0.223989
$117$	2.61158e8	0.128845
$118$	−1.07676e9	−0.511270
$119$	4.89054e8	0.223560
$120$	−1.17689e8	−0.0518106
$121$	−2.35662e9	−0.999437
$122$	6.10447e8	0.249476
$123$	1.21057e9	0.476891
$124$	−2.11272e9	−0.802498
$125$	2.44141e8	0.0894427
$126$	−5.62150e8	−0.198694
$127$	−1.46488e9	−0.499671	−0.249836	−	0.968288i	$-0.580377\pi$
$127$	−1.46488e9	−0.499671	−0.249836	+	0.968288i	$0.580377\pi$
$128$	1.20557e9	0.396962
$129$	2.61494e9	0.831397
$130$	7.66188e8	0.235283
$131$	−3.71095e9	−1.10094	−0.550471	−	0.834855i	$-0.685552\pi$
$131$	−3.71095e9	−1.10094	−0.550471	+	0.834855i	$0.685552\pi$
$132$	4.07221e7	0.0116747
$133$	3.62555e8	0.100471
$134$	−2.29231e9	−0.614190
$135$	3.32151e8	0.0860663
$136$	4.08664e8	0.102433
$137$	6.10071e9	1.47958	0.739788	−	0.672840i	$-0.234926\pi$
$137$	6.10071e9	1.47958	0.739788	+	0.672840i	$0.234926\pi$
$138$	−5.81353e9	−1.36453
$139$	−4.69271e8	−0.106625	−0.0533123	−	0.998578i	$-0.516978\pi$
$139$	−4.69271e8	−0.106625	−0.0533123	+	0.998578i	$0.516978\pi$
$140$	−7.58999e8	−0.166980
$141$	−4.38385e9	−0.934049
$142$	−1.05579e10	−2.17911
$143$	4.58433e7	0.00916777
$144$	−1.93611e9	−0.375231
$145$	−6.25413e8	−0.117493
$146$	−9.31370e9	−1.69642
$147$	−2.64173e9	−0.466618
$148$	4.02542e9	0.689657
$149$	−1.09108e10	−1.81350	−0.906750	−	0.421669i	$-0.861444\pi$
$149$	−1.09108e10	−1.81350	−0.906750	+	0.421669i	$0.861444\pi$
$150$	9.74468e8	0.157165
$151$	1.01608e10	1.59050	0.795249	−	0.606282i	$-0.207340\pi$
$151$	1.01608e10	1.59050	0.795249	+	0.606282i	$0.207340\pi$
$152$	3.02959e8	0.0460349
$153$	−1.15337e9	−0.170159
$154$	−9.86792e7	−0.0141378
$155$	−3.02496e9	−0.420947
$156$	1.40741e9	0.190265
$157$	1.19097e10	1.56442	0.782211	−	0.623013i	$-0.214092\pi$
$157$	1.19097e10	1.56442	0.782211	+	0.623013i	$0.214092\pi$
$158$	1.21450e10	1.55038
$159$	−4.19300e9	−0.520281
$160$	−4.93627e9	−0.595469
$161$	6.48324e9	0.760459
$162$	1.32575e9	0.151233
$163$	4.00627e9	0.444524	0.222262	−	0.974987i	$-0.428656\pi$
$163$	4.00627e9	0.444524	0.222262	+	0.974987i	$0.428656\pi$
$164$	6.52391e9	0.704224
$165$	5.83053e7	0.00612393
$166$	−1.47690e10	−1.50961
$167$	−5.78334e9	−0.575380	−0.287690	−	0.957724i	$-0.592887\pi$
$167$	−5.78334e9	−0.575380	−0.287690	+	0.957724i	$0.592887\pi$
$168$	5.23858e8	0.0507367
$169$	−9.02010e9	−0.850591
$170$	−3.38376e9	−0.310727
$171$	−8.55036e8	−0.0764719
$172$	1.40922e10	1.22772
$173$	−4.11606e9	−0.349361	−0.174680	−	0.984625i	$-0.555889\pi$
$173$	−4.11606e9	−0.349361	−0.174680	+	0.984625i	$0.555889\pi$
$174$	−2.49629e9	−0.206454
$175$	−1.08672e9	−0.0875887
$176$	−3.39862e8	−0.0266991
$177$	−2.83193e9	−0.216871
$178$	1.73822e10	1.29782
$179$	−1.32967e10	−0.968070	−0.484035	−	0.875049i	$-0.660829\pi$
$179$	−1.32967e10	−0.968070	−0.484035	+	0.875049i	$0.660829\pi$
$180$	1.78999e9	0.127094
$181$	6.54575e9	0.453321	0.226661	−	0.973974i	$-0.427219\pi$
$181$	6.54575e9	0.453321	0.226661	+	0.973974i	$0.427219\pi$
$182$	−3.41048e9	−0.230406
$183$	1.60550e9	0.105823
$184$	5.41753e9	0.348435
$185$	5.76354e9	0.361757
$186$	−1.20739e10	−0.739672
$187$	−2.02460e8	−0.0121075
$188$	−2.36250e10	−1.37931
$189$	−1.47848e9	−0.0842823
$190$	−2.50852e9	−0.139645
$191$	−1.15900e10	−0.630137	−0.315069	−	0.949069i	$-0.602028\pi$
$191$	−1.15900e10	−0.630137	−0.315069	+	0.949069i	$0.602028\pi$
$192$	−7.46464e9	−0.396418
$193$	−3.40240e10	−1.76514	−0.882568	−	0.470185i	$-0.844187\pi$
$193$	−3.40240e10	−1.76514	−0.882568	+	0.470185i	$0.844187\pi$
$194$	3.92510e10	1.98950
$195$	2.01511e9	0.0998026
$196$	−1.42366e10	−0.689054
$197$	1.70734e10	0.807648	0.403824	−	0.914837i	$-0.367681\pi$
$197$	1.70734e10	0.807648	0.403824	+	0.914837i	$0.367681\pi$
$198$	2.32721e8	0.0107608
$199$	−4.29428e9	−0.194112	−0.0970558	−	0.995279i	$-0.530943\pi$
$199$	−4.29428e9	−0.194112	−0.0970558	+	0.995279i	$0.530943\pi$
$200$	−9.08091e8	−0.0401323
$201$	−6.02888e9	−0.260528
$202$	2.44916e10	1.03499
$203$	2.78385e9	0.115057
$204$	−6.21561e9	−0.251274
$205$	9.34086e9	0.369398
$206$	1.54314e10	0.597039
$207$	−1.52898e10	−0.578810
$208$	−1.17461e10	−0.435118
$209$	−1.50092e8	−0.00544126
$210$	−4.33758e9	−0.153908
$211$	3.13775e10	1.08980	0.544901	−	0.838500i	$-0.316567\pi$
$211$	3.13775e10	1.08980	0.544901	+	0.838500i	$0.316567\pi$
$212$	−2.25965e10	−0.768299
$213$	−2.77677e10	−0.924340
$214$	−8.06493e10	−2.62868
$215$	2.01770e10	0.643998
$216$	−1.23545e9	−0.0386173
$217$	1.34648e10	0.412221
$218$	−5.09500e10	−1.52788
$219$	−2.44954e10	−0.719592
$220$	3.14214e8	0.00904321
$221$	−6.99729e9	−0.197317
$222$	2.30047e10	0.635666
$223$	−4.74070e9	−0.128372	−0.0641861	−	0.997938i	$-0.520445\pi$
$223$	−4.74070e9	−0.128372	−0.0641861	+	0.997938i	$0.520445\pi$
$224$	2.19725e10	0.583126
$225$	2.56289e9	0.0666667
$226$	3.88536e10	0.990703
$227$	4.48664e10	1.12152	0.560758	−	0.827980i	$-0.310510\pi$
$227$	4.48664e10	1.12152	0.560758	+	0.827980i	$0.310510\pi$
$228$	−4.60788e9	−0.112926
$229$	4.34555e10	1.04420	0.522102	−	0.852883i	$-0.325148\pi$
$229$	4.34555e10	1.04420	0.522102	+	0.852883i	$0.325148\pi$
$230$	−4.48575e10	−1.05696
$231$	−2.59530e8	−0.00599700
$232$	2.32625e9	0.0527181
$233$	7.61271e10	1.69214	0.846072	−	0.533068i	$-0.178961\pi$
$233$	7.61271e10	1.69214	0.846072	+	0.533068i	$0.178961\pi$
$234$	8.04314e9	0.175370
$235$	−3.38260e10	−0.723511
$236$	−1.52615e10	−0.320254
$237$	3.19417e10	0.657644
$238$	1.50619e10	0.304287
$239$	3.59080e10	0.711870	0.355935	−	0.934511i	$-0.384162\pi$
$239$	3.59080e10	0.711870	0.355935	+	0.934511i	$0.384162\pi$
$240$	−1.49391e10	−0.290652
$241$	−9.27673e10	−1.77141	−0.885703	−	0.464252i	$-0.846323\pi$
$241$	−9.27673e10	−1.77141	−0.885703	+	0.464252i	$0.846323\pi$
$242$	−7.25792e10	−1.36033
$243$	3.48678e9	0.0641500
$244$	8.65220e9	0.156269
$245$	−2.03837e10	−0.361440
$246$	3.72833e10	0.649092
$247$	−5.18737e9	−0.0886770
$248$	1.12515e10	0.188876
$249$	−3.88430e10	−0.640348
$250$	7.51905e9	0.121740
$251$	−8.41177e9	−0.133769	−0.0668845	−	0.997761i	$-0.521306\pi$
$251$	−8.41177e9	−0.133769	−0.0668845	+	0.997761i	$0.521306\pi$
$252$	−7.96767e9	−0.124460
$253$	−2.68396e9	−0.0411845
$254$	−4.51153e10	−0.680099
$255$	−8.89942e9	−0.131805
$256$	8.43131e10	1.22692
$257$	−8.98210e10	−1.28434	−0.642168	−	0.766564i	$-0.721965\pi$
$257$	−8.98210e10	−1.28434	−0.642168	+	0.766564i	$0.721965\pi$
$258$	8.05351e10	1.13161
$259$	−2.56548e10	−0.354258
$260$	1.08596e10	0.147379
$261$	−6.56533e9	−0.0875739
$262$	−1.14290e11	−1.49848
$263$	9.35545e10	1.20577	0.602884	−	0.797829i	$-0.294018\pi$
$263$	9.35545e10	1.20577	0.602884	+	0.797829i	$0.294018\pi$
$264$	−2.16869e8	−0.00274777
$265$	−3.23534e10	−0.403008
$266$	1.11660e10	0.136751
$267$	4.57159e10	0.550511
$268$	−3.24903e10	−0.384722
$269$	1.52794e11	1.77919	0.889594	−	0.456752i	$-0.150987\pi$
$269$	1.52794e11	1.77919	0.889594	+	0.456752i	$0.150987\pi$
$270$	1.02296e10	0.117144
$271$	−1.37162e11	−1.54480	−0.772399	−	0.635138i	$-0.780943\pi$
$271$	−1.37162e11	−1.54480	−0.772399	+	0.635138i	$0.780943\pi$
$272$	5.18748e10	0.574641
$273$	−8.96969e9	−0.0977339
$274$	1.87890e11	2.01384
$275$	4.49887e8	0.00474358
$276$	−8.23985e10	−0.854729
$277$	8.40167e10	0.857445	0.428723	−	0.903436i	$-0.358964\pi$
$277$	8.40167e10	0.857445	0.428723	+	0.903436i	$0.358964\pi$
$278$	−1.44526e10	−0.145126
$279$	−3.17548e10	−0.313755
$280$	4.04211e9	0.0393004
$281$	5.98704e10	0.572840	0.286420	−	0.958104i	$-0.407535\pi$
$281$	5.98704e10	0.572840	0.286420	+	0.958104i	$0.407535\pi$
$282$	−1.35014e11	−1.27133
$283$	1.64644e11	1.52583	0.762915	−	0.646499i	$-0.223768\pi$
$283$	1.64644e11	1.52583	0.762915	+	0.646499i	$0.223768\pi$
$284$	−1.49643e11	−1.36497
$285$	−6.59750e9	−0.0592349
$286$	1.41188e9	0.0124782
$287$	−4.15782e10	−0.361741
$288$	−5.18190e10	−0.443837
$289$	−8.76854e10	−0.739413
$290$	−1.92615e10	−0.159918
$291$	1.03232e11	0.843907
$292$	−1.32008e11	−1.06262
$293$	−7.35831e10	−0.583275	−0.291638	−	0.956529i	$-0.594200\pi$
$293$	−7.35831e10	−0.583275	−0.291638	+	0.956529i	$0.594200\pi$
$294$	−8.13601e10	−0.635110
$295$	−2.18513e10	−0.167988
$296$	−2.14377e10	−0.162318
$297$	6.12066e8	0.00456451
$298$	−3.36030e11	−2.46834
$299$	−9.27610e10	−0.671189
$300$	1.38117e10	0.0984467
$301$	−8.98125e10	−0.630649
$302$	3.12934e11	2.16482
$303$	6.44140e10	0.439024
$304$	3.84569e10	0.258251
$305$	1.23881e10	0.0819702
$306$	−3.55214e10	−0.231602
$307$	−2.40045e11	−1.54230	−0.771151	−	0.636652i	$-0.780319\pi$
$307$	−2.40045e11	−1.54230	−0.771151	+	0.636652i	$0.780319\pi$
$308$	−1.39863e9	−0.00885577
$309$	4.05852e10	0.253253
$310$	−9.31628e10	−0.572948
$311$	−1.14775e11	−0.695708	−0.347854	−	0.937549i	$-0.613090\pi$
$311$	−1.14775e11	−0.695708	−0.347854	+	0.937549i	$0.613090\pi$
$312$	−7.49526e9	−0.0447807
$313$	−3.24935e11	−1.91358	−0.956789	−	0.290782i	$-0.906085\pi$
$313$	−3.24935e11	−1.91358	−0.956789	+	0.290782i	$0.906085\pi$
$314$	3.66796e11	2.12932
$315$	−1.14080e10	−0.0652848
$316$	1.72137e11	0.971143
$317$	1.06700e11	0.593468	0.296734	−	0.954960i	$-0.404103\pi$
$317$	1.06700e11	0.593468	0.296734	+	0.954960i	$0.404103\pi$
$318$	−1.29136e11	−0.708150
$319$	−1.15247e9	−0.00623120
$320$	−5.75975e10	−0.307064
$321$	−2.12111e11	−1.11504
$322$	1.99671e11	1.03505
$323$	2.29093e10	0.117112
$324$	1.87906e10	0.0947304
$325$	1.55487e10	0.0773068
$326$	1.23385e11	0.605039
$327$	−1.34000e11	−0.648099
$328$	−3.47437e10	−0.165746
$329$	1.50567e11	0.708514
$330$	1.79569e9	0.00833524
$331$	−3.46295e11	−1.58570	−0.792850	−	0.609417i	$-0.791403\pi$
$331$	−3.46295e11	−1.58570	−0.792850	+	0.609417i	$0.791403\pi$
$332$	−2.09329e11	−0.945602
$333$	6.05034e10	0.269638
$334$	−1.78115e11	−0.783145
$335$	−4.65191e10	−0.201804
$336$	6.64973e10	0.284628
$337$	1.45369e11	0.613954	0.306977	−	0.951717i	$-0.400683\pi$
$337$	1.45369e11	0.613954	0.306977	+	0.951717i	$0.400683\pi$
$338$	−2.77801e11	−1.15773
$339$	1.02187e11	0.420238
$340$	−4.79599e10	−0.194636
$341$	−5.57421e9	−0.0223248
$342$	−2.63334e10	−0.104085
$343$	2.02997e11	0.791892
$344$	−7.50493e10	−0.288957
$345$	−1.17977e11	−0.448344
$346$	−1.26766e11	−0.475512
$347$	−8.39537e10	−0.310854	−0.155427	−	0.987847i	$-0.549675\pi$
$347$	−8.39537e10	−0.310854	−0.155427	+	0.987847i	$0.549675\pi$
$348$	−3.53813e10	−0.129320
$349$	2.87506e11	1.03737	0.518684	−	0.854966i	$-0.326422\pi$
$349$	2.87506e11	1.03737	0.518684	+	0.854966i	$0.326422\pi$
$350$	−3.34690e10	−0.119216
$351$	2.11538e10	0.0743885
$352$	−9.09625e9	−0.0315806
$353$	1.61913e11	0.555005	0.277502	−	0.960725i	$-0.410493\pi$
$353$	1.61913e11	0.555005	0.277502	+	0.960725i	$0.410493\pi$
$354$	−8.72177e10	−0.295182
$355$	−2.14257e11	−0.715991
$356$	2.46368e11	0.812940
$357$	3.96133e10	0.129073
$358$	−4.09513e11	−1.31763
$359$	4.41518e10	0.140289	0.0701445	−	0.997537i	$-0.477654\pi$
$359$	4.41518e10	0.140289	0.0701445	+	0.997537i	$0.477654\pi$
$360$	−9.53277e9	−0.0299129
$361$	1.69836e10	0.0526316
$362$	2.01596e11	0.617012
$363$	−1.90886e11	−0.577025
$364$	−4.83386e10	−0.144324
$365$	−1.89008e11	−0.557393
$366$	4.94462e10	0.144035
$367$	−2.25970e11	−0.650210	−0.325105	−	0.945678i	$-0.605400\pi$
$367$	−2.25970e11	−0.650210	−0.325105	+	0.945678i	$0.605400\pi$
$368$	6.87689e11	1.95469
$369$	9.80566e10	0.275333
$370$	1.77506e11	0.492385
$371$	1.44012e11	0.394654
$372$	−1.71130e11	−0.463322
$373$	−2.52590e10	−0.0675658	−0.0337829	−	0.999429i	$-0.510755\pi$
$373$	−2.52590e10	−0.0675658	−0.0337829	+	0.999429i	$0.510755\pi$
$374$	−6.23538e9	−0.0164794
$375$	1.97754e10	0.0516398
$376$	1.25817e11	0.324634
$377$	−3.98308e10	−0.101551
$378$	−4.55341e10	−0.114716
$379$	1.92804e11	0.479999	0.240000	−	0.970773i	$-0.422853\pi$
$379$	1.92804e11	0.479999	0.240000	+	0.970773i	$0.422853\pi$
$380$	−3.55546e10	−0.0874722
$381$	−1.18655e11	−0.288485
$382$	−3.56950e11	−0.857675
$383$	3.29359e11	0.782123	0.391061	−	0.920365i	$-0.372108\pi$
$383$	3.29359e11	0.782123	0.391061	+	0.920365i	$0.372108\pi$
$384$	9.76514e10	0.229186
$385$	−2.00255e9	−0.00464525
$386$	−1.04787e12	−2.40251
$387$	2.11810e11	0.480007
$388$	5.56326e11	1.24620
$389$	6.86136e11	1.51928	0.759638	−	0.650346i	$-0.225376\pi$
$389$	6.86136e11	1.51928	0.759638	+	0.650346i	$0.225376\pi$
$390$	6.20612e10	0.135841
$391$	4.09665e11	0.886409
$392$	7.58182e10	0.162176
$393$	−3.00587e11	−0.635629
$394$	5.25827e11	1.09928
$395$	2.46464e11	0.509409
$396$	3.29849e9	0.00674041
$397$	−1.25923e11	−0.254418	−0.127209	−	0.991876i	$-0.540602\pi$
$397$	−1.25923e11	−0.254418	−0.127209	+	0.991876i	$0.540602\pi$
$398$	−1.32255e11	−0.264204
$399$	2.93670e10	0.0580071
$400$	−1.15271e11	−0.225138
$401$	3.47020e11	0.670200	0.335100	−	0.942183i	$-0.391230\pi$
$401$	3.47020e11	0.670200	0.335100	+	0.942183i	$0.391230\pi$
$402$	−1.85677e11	−0.354603
$403$	−1.92652e11	−0.363831
$404$	3.47134e11	0.648307
$405$	2.69042e10	0.0496904
$406$	8.57371e10	0.156604
$407$	1.06207e10	0.0191857
$408$	3.31018e10	0.0591399
$409$	−4.90257e11	−0.866300	−0.433150	−	0.901322i	$-0.642598\pi$
$409$	−4.90257e11	−0.866300	−0.433150	+	0.901322i	$0.642598\pi$
$410$	2.87680e11	0.502785
$411$	4.94157e11	0.854234
$412$	2.18718e11	0.373979
$413$	9.72650e10	0.164506
$414$	−4.70896e11	−0.787814
$415$	−2.99715e11	−0.496011
$416$	−3.14378e11	−0.514674
$417$	−3.80109e10	−0.0615597
$418$	−4.62254e9	−0.00740606
$419$	9.03886e11	1.43268	0.716342	−	0.697749i	$-0.245815\pi$
$419$	9.03886e11	1.43268	0.716342	+	0.697749i	$0.245815\pi$
$420$	−6.14789e10	−0.0964061
$421$	1.19112e12	1.84793	0.923967	−	0.382473i	$-0.124927\pi$
$421$	1.19112e12	1.84793	0.923967	+	0.382473i	$0.124927\pi$
$422$	9.66366e11	1.48332
$423$	−3.55092e11	−0.539273
$424$	1.20340e11	0.180827
$425$	−6.86684e10	−0.102096
$426$	−8.55190e11	−1.25811
$427$	−5.51423e10	−0.0802711
$428$	−1.14309e12	−1.64658
$429$	3.71331e9	0.00529302
$430$	6.21412e11	0.876540
$431$	5.73251e11	0.800197	0.400098	−	0.916472i	$-0.368976\pi$
$431$	5.73251e11	0.800197	0.400098	+	0.916472i	$0.368976\pi$
$432$	−1.56825e11	−0.216640
$433$	1.09093e12	1.49143	0.745714	−	0.666266i	$-0.232109\pi$
$433$	1.09093e12	1.49143	0.745714	+	0.666266i	$0.232109\pi$
$434$	4.14689e11	0.561072
$435$	−5.06584e10	−0.0678344
$436$	−7.22143e11	−0.957048
$437$	3.03701e11	0.398364
$438$	−7.54410e11	−0.979431
$439$	−2.73492e11	−0.351443	−0.175721	−	0.984440i	$-0.556226\pi$
$439$	−2.73492e11	−0.351443	−0.175721	+	0.984440i	$0.556226\pi$
$440$	−1.67337e9	−0.00212841
$441$	−2.13980e11	−0.269402
$442$	−2.15503e11	−0.268567
$443$	−7.49545e10	−0.0924658	−0.0462329	−	0.998931i	$-0.514722\pi$
$443$	−7.49545e10	−0.0924658	−0.0462329	+	0.998931i	$0.514722\pi$
$444$	3.26059e11	0.398174
$445$	3.52746e11	0.426424
$446$	−1.46004e11	−0.174726
$447$	−8.83773e11	−1.04702
$448$	2.56379e11	0.300699
$449$	−3.55853e10	−0.0413202	−0.0206601	−	0.999787i	$-0.506577\pi$
$449$	−3.55853e10	−0.0413202	−0.0206601	+	0.999787i	$0.506577\pi$
$450$	7.89319e10	0.0907395
$451$	1.72127e10	0.0195909
$452$	5.50694e11	0.620565
$453$	8.23028e11	0.918275
$454$	1.38180e12	1.52649
$455$	−6.92105e10	−0.0757044
$456$	2.45397e10	0.0265783
$457$	3.36805e11	0.361207	0.180603	−	0.983556i	$-0.442195\pi$
$457$	3.36805e11	0.361207	0.180603	+	0.983556i	$0.442195\pi$
$458$	1.33834e12	1.42126
$459$	−9.34226e10	−0.0982415
$460$	−6.35791e11	−0.662070
$461$	1.71990e12	1.77357	0.886785	−	0.462182i	$-0.152933\pi$
$461$	1.71990e12	1.77357	0.886785	+	0.462182i	$0.152933\pi$
$462$	−7.99301e9	−0.00816247
$463$	1.28766e12	1.30222	0.651112	−	0.758982i	$-0.274303\pi$
$463$	1.28766e12	1.30222	0.651112	+	0.758982i	$0.274303\pi$
$464$	2.95288e11	0.295744
$465$	−2.45022e11	−0.243034
$466$	2.34456e12	2.30317
$467$	−9.12843e11	−0.888117	−0.444058	−	0.895998i	$-0.646462\pi$
$467$	−9.12843e11	−0.888117	−0.444058	+	0.895998i	$0.646462\pi$
$468$	1.14000e11	0.109849
$469$	2.07067e11	0.197621
$470$	−1.04177e12	−0.984766
$471$	9.64689e11	0.903220
$472$	8.12767e10	0.0753750
$473$	3.71810e10	0.0341543
$474$	9.83742e11	0.895114
$475$	−5.09066e10	−0.0458831
$476$	2.13480e11	0.190602
$477$	−3.39633e11	−0.300384
$478$	1.10590e12	0.968921
$479$	−3.70513e11	−0.321584	−0.160792	−	0.986988i	$-0.551405\pi$
$479$	−3.70513e11	−0.321584	−0.160792	+	0.986988i	$0.551405\pi$
$480$	−3.99838e11	−0.343794
$481$	3.67064e11	0.312672
$482$	−2.85705e12	−2.41105
$483$	5.25142e11	0.439051
$484$	−1.02871e12	−0.852094
$485$	7.96541e11	0.653688
$486$	1.07386e11	0.0873141
$487$	−1.09971e12	−0.885929	−0.442965	−	0.896539i	$-0.646073\pi$
$487$	−1.09971e12	−0.885929	−0.442965	+	0.896539i	$0.646073\pi$
$488$	−4.60781e10	−0.0367794
$489$	3.24507e11	0.256646
$490$	−6.27779e11	−0.491954
$491$	−1.16248e12	−0.902648	−0.451324	−	0.892360i	$-0.649048\pi$
$491$	−1.16248e12	−0.902648	−0.451324	+	0.892360i	$0.649048\pi$
$492$	5.28437e11	0.406584
$493$	1.75907e11	0.134114
$494$	−1.59761e11	−0.120698
$495$	4.72273e9	0.00353566
$496$	1.42823e12	1.05958
$497$	9.53706e11	0.701150
$498$	−1.19629e12	−0.871573
$499$	1.89801e12	1.37040	0.685198	−	0.728357i	$-0.259716\pi$
$499$	1.89801e12	1.37040	0.685198	+	0.728357i	$0.259716\pi$
$500$	1.06572e11	0.0762565
$501$	−4.68450e11	−0.332196
$502$	−2.59066e11	−0.182072
$503$	6.71585e11	0.467784	0.233892	−	0.972263i	$-0.424854\pi$
$503$	6.71585e11	0.467784	0.233892	+	0.972263i	$0.424854\pi$
$504$	4.24325e10	0.0292928
$505$	4.97021e11	0.340067
$506$	−8.26606e10	−0.0560559
$507$	−7.30628e11	−0.491089
$508$	−6.39444e11	−0.426006
$509$	−6.25114e11	−0.412790	−0.206395	−	0.978469i	$-0.566173\pi$
$509$	−6.25114e11	−0.412790	−0.206395	+	0.978469i	$0.566173\pi$
$510$	−2.74085e11	−0.179399
$511$	8.41316e11	0.545840
$512$	1.97942e12	1.27299
$513$	−6.92579e10	−0.0441511
$514$	−2.76631e12	−1.74810
$515$	3.13157e11	0.196169
$516$	1.14147e12	0.708827
$517$	−6.23324e10	−0.0383713
$518$	−7.90117e11	−0.482178
$519$	−3.33401e11	−0.201703
$520$	−5.78338e10	−0.0346870
$521$	1.53513e11	0.0912801	0.0456401	−	0.998958i	$-0.485467\pi$
$521$	1.53513e11	0.0912801	0.0456401	+	0.998958i	$0.485467\pi$
$522$	−2.02199e11	−0.119196
$523$	3.35387e10	0.0196015	0.00980074	−	0.999952i	$-0.496880\pi$
$523$	3.35387e10	0.0196015	0.00980074	+	0.999952i	$0.496880\pi$
$524$	−1.61989e12	−0.938633
$525$	−8.80247e10	−0.0505694
$526$	2.88129e12	1.64116
$527$	8.50818e11	0.480495
$528$	−2.75288e10	−0.0154147
$529$	3.62966e12	2.01519
$530$	−9.96420e11	−0.548531
$531$	−2.29386e11	−0.125211
$532$	1.58262e11	0.0856590
$533$	5.94894e11	0.319277
$534$	1.40796e12	0.749297
$535$	−1.63666e12	−0.863706
$536$	1.73030e11	0.0905481
$537$	−1.07704e12	−0.558915
$538$	4.70576e12	2.42164
$539$	−3.75619e10	−0.0191689
$540$	1.44990e11	0.0733778
$541$	1.21969e12	0.612156	0.306078	−	0.952006i	$-0.400983\pi$
$541$	1.21969e12	0.612156	0.306078	+	0.952006i	$0.400983\pi$
$542$	−4.22431e12	−2.10261
$543$	5.30206e11	0.261725
$544$	1.38840e12	0.679706
$545$	−1.03395e12	−0.502016
$546$	−2.76248e11	−0.133025
$547$	−2.58499e12	−1.23457	−0.617284	−	0.786740i	$-0.711767\pi$
$547$	−2.58499e12	−1.23457	−0.617284	+	0.786740i	$0.711767\pi$
$548$	2.66306e12	1.26145
$549$	1.30045e11	0.0610969
$550$	1.38556e10	0.00645645
$551$	1.30407e11	0.0602725
$552$	4.38820e11	0.201169
$553$	−1.09707e12	−0.498850
$554$	2.58755e12	1.16706
$555$	4.66847e11	0.208860
$556$	−2.04845e11	−0.0909052
$557$	−2.79411e12	−1.22997	−0.614985	−	0.788539i	$-0.710838\pi$
$557$	−2.79411e12	−1.22997	−0.614985	+	0.788539i	$0.710838\pi$
$558$	−9.77986e11	−0.427050
$559$	1.28502e12	0.556618
$560$	5.13097e11	0.220472
$561$	−1.63993e10	−0.00699024
$562$	1.84389e12	0.779688
$563$	1.75088e12	0.734463	0.367231	−	0.930130i	$-0.380306\pi$
$563$	1.75088e12	0.734463	0.367231	+	0.930130i	$0.380306\pi$
$564$	−1.91363e12	−0.796345
$565$	7.88477e11	0.325515
$566$	5.07070e12	2.07680
$567$	−1.19757e11	−0.0486604
$568$	7.96937e11	0.321260
$569$	−2.15562e12	−0.862119	−0.431060	−	0.902323i	$-0.641860\pi$
$569$	−2.15562e12	−0.862119	−0.431060	+	0.902323i	$0.641860\pi$
$570$	−2.03190e11	−0.0806242
$571$	1.35671e12	0.534101	0.267050	−	0.963683i	$-0.413951\pi$
$571$	1.35671e12	0.534101	0.267050	+	0.963683i	$0.413951\pi$
$572$	2.00114e10	0.00781620
$573$	−9.38794e11	−0.363810
$574$	−1.28053e12	−0.492363
$575$	−9.10317e11	−0.347286
$576$	−6.04636e11	−0.228872
$577$	−2.81402e10	−0.0105690	−0.00528452	−	0.999986i	$-0.501682\pi$
$577$	−2.81402e10	−0.0105690	−0.00528452	+	0.999986i	$0.501682\pi$
$578$	−2.70053e12	−1.00641
$579$	−2.75595e12	−1.01910
$580$	−2.73004e11	−0.100171
$581$	1.33410e12	0.485730
$582$	3.17933e12	1.14864
$583$	−5.96188e10	−0.0213734
$584$	7.03022e11	0.250098
$585$	1.63224e11	0.0576211
$586$	−2.26621e12	−0.793892
$587$	−2.10751e12	−0.732653	−0.366326	−	0.930486i	$-0.619385\pi$
$587$	−2.10751e12	−0.732653	−0.366326	+	0.930486i	$0.619385\pi$
$588$	−1.15316e12	−0.397826
$589$	6.30746e11	0.215941
$590$	−6.72976e11	−0.228647
$591$	1.38295e12	0.466296
$592$	−2.72125e12	−0.910587
$593$	−5.28692e11	−0.175573	−0.0877863	−	0.996139i	$-0.527979\pi$
$593$	−5.28692e11	−0.175573	−0.0877863	+	0.996139i	$0.527979\pi$
$594$	1.88504e10	0.00621272
$595$	3.05658e11	0.0999793
$596$	−4.76275e12	−1.54614
$597$	−3.47837e11	−0.112070
$598$	−2.85685e12	−0.913551
$599$	−4.36326e12	−1.38481	−0.692406	−	0.721508i	$-0.743449\pi$
$599$	−4.36326e12	−1.38481	−0.692406	+	0.721508i	$0.743449\pi$
$600$	−7.35553e10	−0.0231704
$601$	−4.12015e12	−1.28818	−0.644092	−	0.764948i	$-0.722765\pi$
$601$	−4.12015e12	−1.28818	−0.644092	+	0.764948i	$0.722765\pi$
$602$	−2.76605e12	−0.858371
$603$	−4.88339e11	−0.150416
$604$	4.43538e12	1.35602
$605$	−1.47289e12	−0.446962
$606$	1.98382e12	0.597552
$607$	3.04102e12	0.909224	0.454612	−	0.890690i	$-0.349778\pi$
$607$	3.04102e12	0.909224	0.454612	+	0.890690i	$0.349778\pi$
$608$	1.02928e12	0.305469
$609$	2.25492e11	0.0664284
$610$	3.81529e11	0.111569
$611$	−2.15429e12	−0.625343
$612$	−5.03464e11	−0.145073
$613$	5.17191e12	1.47938	0.739689	−	0.672949i	$-0.234973\pi$
$613$	5.17191e12	1.47938	0.739689	+	0.672949i	$0.234973\pi$
$614$	−7.39290e12	−2.09922
$615$	7.56609e11	0.213272
$616$	7.44855e9	0.00208429
$617$	−5.29471e12	−1.47082	−0.735409	−	0.677623i	$-0.763010\pi$
$617$	−5.29471e12	−1.47082	−0.735409	+	0.677623i	$0.763010\pi$
$618$	1.24994e12	0.344701
$619$	−8.50875e10	−0.0232947	−0.0116474	−	0.999932i	$-0.503708\pi$
$619$	−8.50875e10	−0.0232947	−0.0116474	+	0.999932i	$0.503708\pi$
$620$	−1.32045e12	−0.358888
$621$	−1.23848e12	−0.334176
$622$	−3.53486e12	−0.946924
$623$	−1.57015e12	−0.417585
$624$	−9.51431e11	−0.251216
$625$	1.52588e11	0.0400000
$626$	−1.00073e13	−2.60456
$627$	−1.21575e10	−0.00314151
$628$	5.19881e12	1.33378
$629$	−1.62109e12	−0.412932
$630$	−3.51344e11	−0.0888587
$631$	3.70696e12	0.930862	0.465431	−	0.885084i	$-0.345899\pi$
$631$	3.70696e12	0.930862	0.465431	+	0.885084i	$0.345899\pi$
$632$	−9.16732e11	−0.228568
$633$	2.54158e12	0.629198
$634$	3.28614e12	0.807765
$635$	−9.15548e11	−0.223460
$636$	−1.83032e12	−0.443577
$637$	−1.29819e12	−0.312399
$638$	−3.54938e10	−0.00848125
$639$	−2.24918e12	−0.533668
$640$	7.53483e11	0.177527
$641$	−2.42257e12	−0.566781	−0.283391	−	0.959005i	$-0.591459\pi$
$641$	−2.42257e12	−0.566781	−0.283391	+	0.959005i	$0.591459\pi$
$642$	−6.53259e12	−1.51767
$643$	−5.39995e12	−1.24578	−0.622889	−	0.782311i	$-0.714041\pi$
$643$	−5.39995e12	−1.24578	−0.622889	+	0.782311i	$0.714041\pi$
$644$	2.83005e12	0.648347
$645$	1.63434e12	0.371812
$646$	7.05560e11	0.159400
$647$	−7.72344e12	−1.73277	−0.866386	−	0.499375i	$-0.833563\pi$
$647$	−7.72344e12	−1.73277	−0.866386	+	0.499375i	$0.833563\pi$
$648$	−1.00071e11	−0.0222957
$649$	−4.02662e10	−0.00890921
$650$	4.78868e11	0.105222
$651$	1.09065e12	0.237996
$652$	1.74880e12	0.378989
$653$	2.40816e12	0.518293	0.259146	−	0.965838i	$-0.416559\pi$
$653$	2.40816e12	0.518293	0.259146	+	0.965838i	$0.416559\pi$
$654$	−4.12695e12	−0.882123
$655$	−2.31934e12	−0.492356
$656$	−4.41028e12	−0.929820
$657$	−1.98413e12	−0.415456
$658$	4.63717e12	0.964354
$659$	8.31254e12	1.71692	0.858459	−	0.512883i	$-0.171422\pi$
$659$	8.31254e12	1.71692	0.858459	+	0.512883i	$0.171422\pi$
$660$	2.54513e10	0.00522110
$661$	−2.38376e12	−0.485686	−0.242843	−	0.970066i	$-0.578080\pi$
$661$	−2.38376e12	−0.485686	−0.242843	+	0.970066i	$0.578080\pi$
$662$	−1.06652e13	−2.15828
$663$	−5.66780e11	−0.113921
$664$	1.11480e12	0.222557
$665$	2.26597e11	0.0449321
$666$	1.86338e12	0.367002
$667$	2.33195e12	0.456198
$668$	−2.52453e12	−0.490553
$669$	−3.83997e11	−0.0741157
$670$	−1.43270e12	−0.274674
$671$	2.28280e10	0.00434727
$672$	1.77977e12	0.336668
$673$	−5.22205e12	−0.981236	−0.490618	−	0.871375i	$-0.663229\pi$
$673$	−5.22205e12	−0.981236	−0.490618	+	0.871375i	$0.663229\pi$
$674$	4.47706e12	0.835648
$675$	2.07594e11	0.0384900
$676$	−3.93743e12	−0.725191
$677$	−9.27082e12	−1.69617	−0.848085	−	0.529860i	$-0.822244\pi$
$677$	−9.27082e12	−1.69617	−0.848085	+	0.529860i	$0.822244\pi$
$678$	3.14714e12	0.571983
$679$	−3.54558e12	−0.640138
$680$	2.55415e11	0.0458095
$681$	3.63418e12	0.647507
$682$	−1.71675e11	−0.0303862
$683$	1.03618e12	0.182197	0.0910985	−	0.995842i	$-0.470962\pi$
$683$	1.03618e12	0.182197	0.0910985	+	0.995842i	$0.470962\pi$
$684$	−3.73238e11	−0.0651979
$685$	3.81294e12	0.661687
$686$	6.25190e12	1.07784
$687$	3.51990e12	0.602871
$688$	−9.52658e12	−1.62102
$689$	−2.06050e12	−0.348326
$690$	−3.63346e12	−0.610238
$691$	6.02122e12	1.00469	0.502346	−	0.864667i	$-0.332470\pi$
$691$	6.02122e12	1.00469	0.502346	+	0.864667i	$0.332470\pi$
$692$	−1.79673e12	−0.297855
$693$	−2.10219e10	−0.00346237
$694$	−2.58561e12	−0.423102
$695$	−2.93294e11	−0.0476839
$696$	1.88426e11	0.0304368
$697$	−2.62726e12	−0.421654
$698$	8.85462e12	1.41195
$699$	6.16629e12	0.976960
$700$	−4.74374e11	−0.0746758
$701$	−1.02410e13	−1.60181	−0.800903	−	0.598794i	$-0.795647\pi$
$701$	−1.02410e13	−1.60181	−0.800903	+	0.598794i	$0.795647\pi$
$702$	6.51494e11	0.101250
$703$	−1.20178e12	−0.185577
$704$	−1.06137e11	−0.0162851
$705$	−2.73991e12	−0.417719
$706$	4.98661e12	0.755413
$707$	−2.21235e12	−0.333018
$708$	−1.23619e12	−0.184899
$709$	−4.01293e12	−0.596422	−0.298211	−	0.954500i	$-0.596390\pi$
$709$	−4.01293e12	−0.596422	−0.298211	+	0.954500i	$0.596390\pi$
$710$	−6.59869e12	−0.974530
$711$	2.58728e12	0.379691
$712$	−1.31205e12	−0.191334
$713$	1.12790e13	1.63444
$714$	1.22001e12	0.175680
$715$	2.86521e10	0.00409995
$716$	−5.80426e12	−0.825350
$717$	2.90855e12	0.410998
$718$	1.35979e12	0.190946
$719$	−1.02819e13	−1.43481	−0.717406	−	0.696655i	$-0.754671\pi$
$719$	−1.02819e13	−1.43481	−0.717406	+	0.696655i	$0.754671\pi$
$720$	−1.21007e12	−0.167808
$721$	−1.39393e12	−0.192103
$722$	5.23060e11	0.0716365
$723$	−7.51415e12	−1.02272
$724$	2.85734e12	0.386489
$725$	−3.90883e11	−0.0525443
$726$	−5.87892e12	−0.785385
$727$	3.68797e11	0.0489646	0.0244823	−	0.999700i	$-0.492206\pi$
$727$	3.68797e11	0.0489646	0.0244823	+	0.999700i	$0.492206\pi$
$728$	2.57431e11	0.0339680
$729$	2.82430e11	0.0370370
$730$	−5.82106e12	−0.758664
$731$	−5.67511e12	−0.735099
$732$	7.00828e11	0.0902219
$733$	6.45808e12	0.826295	0.413148	−	0.910664i	$-0.364429\pi$
$733$	6.45808e12	0.826295	0.413148	+	0.910664i	$0.364429\pi$
$734$	−6.95943e12	−0.884996
$735$	−1.65108e12	−0.208678
$736$	1.84057e13	2.31207
$737$	−8.57225e10	−0.0107026
$738$	3.01995e12	0.374754
$739$	−5.44774e12	−0.671919	−0.335959	−	0.941876i	$-0.609060\pi$
$739$	−5.44774e12	−0.671919	−0.335959	+	0.941876i	$0.609060\pi$
$740$	2.51589e12	0.308424
$741$	−4.20177e11	−0.0511977
$742$	4.43529e12	0.537161
$743$	−5.12022e12	−0.616366	−0.308183	−	0.951327i	$-0.599721\pi$
$743$	−5.12022e12	−0.616366	−0.308183	+	0.951327i	$0.599721\pi$
$744$	9.11369e11	0.109048
$745$	−6.81924e12	−0.811022
$746$	−7.77928e11	−0.0919633
$747$	−3.14629e12	−0.369705
$748$	−8.83775e10	−0.0103225
$749$	7.28513e12	0.845803
$750$	6.09043e11	0.0702865
$751$	6.79016e12	0.778934	0.389467	−	0.921040i	$-0.372659\pi$
$751$	6.79016e12	0.778934	0.389467	+	0.921040i	$0.372659\pi$
$752$	1.59709e13	1.82117
$753$	−6.81353e11	−0.0772316
$754$	−1.22671e12	−0.138220
$755$	6.35052e12	0.711293
$756$	−6.45381e11	−0.0718568
$757$	−8.06088e12	−0.892177	−0.446088	−	0.894989i	$-0.647183\pi$
$757$	−8.06088e12	−0.892177	−0.446088	+	0.894989i	$0.647183\pi$
$758$	5.93799e12	0.653323
$759$	−2.17401e11	−0.0237779
$760$	1.89349e11	0.0205874
$761$	8.37191e12	0.904886	0.452443	−	0.891793i	$-0.350553\pi$
$761$	8.37191e12	0.904886	0.452443	+	0.891793i	$0.350553\pi$
$762$	−3.65434e12	−0.392655
$763$	4.60236e12	0.491610
$764$	−5.05926e12	−0.537238
$765$	−7.20853e11	−0.0760975
$766$	1.01436e13	1.06454
$767$	−1.39165e12	−0.145195
$768$	6.82936e12	0.708361
$769$	−4.89308e12	−0.504561	−0.252280	−	0.967654i	$-0.581181\pi$
$769$	−4.89308e12	−0.504561	−0.252280	+	0.967654i	$0.581181\pi$
$770$	−6.16745e10	−0.00632262
$771$	−7.27550e12	−0.741512
$772$	−1.48521e13	−1.50491
$773$	−1.21911e11	−0.0122811	−0.00614054	−	0.999981i	$-0.501955\pi$
$773$	−1.21911e11	−0.0122811	−0.00614054	+	0.999981i	$0.501955\pi$
$774$	6.52334e12	0.653335
$775$	−1.89060e12	−0.188253
$776$	−2.96277e12	−0.293305
$777$	−2.07804e12	−0.204531
$778$	2.11316e13	2.06788
$779$	−1.94770e12	−0.189497
$780$	8.79629e11	0.0850891
$781$	−3.94819e11	−0.0379725
$782$	1.26169e13	1.20648
$783$	−5.31792e11	−0.0505608
$784$	9.62418e12	0.909790
$785$	7.44359e12	0.699631
$786$	−9.25748e12	−0.865150
$787$	9.93051e12	0.922753	0.461376	−	0.887205i	$-0.347356\pi$
$787$	9.93051e12	0.922753	0.461376	+	0.887205i	$0.347356\pi$
$788$	7.45284e12	0.688579
$789$	7.57791e12	0.696150
$790$	7.59060e12	0.693353
$791$	−3.50969e12	−0.318768
$792$	−1.75664e10	−0.00158642
$793$	7.88965e11	0.0708481
$794$	−3.87818e12	−0.346287
$795$	−2.62062e12	−0.232677
$796$	−1.87453e12	−0.165494
$797$	−7.87450e12	−0.691291	−0.345645	−	0.938365i	$-0.612340\pi$
$797$	−7.87450e12	−0.691291	−0.345645	+	0.938365i	$0.612340\pi$
$798$	9.04444e11	0.0789530
$799$	9.51410e12	0.825861
$800$	−3.08517e12	−0.266302
$801$	3.70299e12	0.317838
$802$	1.06875e13	0.912205
$803$	−3.48292e11	−0.0295613
$804$	−2.63171e12	−0.222119
$805$	4.05202e12	0.340087
$806$	−5.93329e12	−0.495208
$807$	1.23763e13	1.02721
$808$	−1.84869e12	−0.152585
$809$	−4.03673e12	−0.331330	−0.165665	−	0.986182i	$-0.552977\pi$
$809$	−4.03673e12	−0.331330	−0.165665	+	0.986182i	$0.552977\pi$
$810$	8.28596e11	0.0676332
$811$	1.51544e12	0.123011	0.0615056	−	0.998107i	$-0.480410\pi$
$811$	1.51544e12	0.123011	0.0615056	+	0.998107i	$0.480410\pi$
$812$	1.21520e12	0.0980948
$813$	−1.11101e13	−0.891889
$814$	3.27096e11	0.0261135
$815$	2.50392e12	0.198797
$816$	4.20186e12	0.331769
$817$	−4.20719e12	−0.330364
$818$	−1.50989e13	−1.17912
$819$	−7.26545e11	−0.0564267
$820$	4.07745e12	0.314939
$821$	−2.26437e13	−1.73941	−0.869707	−	0.493568i	$-0.835693\pi$
$821$	−2.26437e13	−1.73941	−0.869707	+	0.493568i	$0.835693\pi$
$822$	1.52191e13	1.16269
$823$	−4.04735e11	−0.0307519	−0.0153759	−	0.999882i	$-0.504895\pi$
$823$	−4.04735e11	−0.0307519	−0.0153759	+	0.999882i	$0.504895\pi$
$824$	−1.16480e12	−0.0880196
$825$	3.64408e10	0.00273871
$826$	2.99557e12	0.223908
$827$	6.96675e12	0.517911	0.258956	−	0.965889i	$-0.416622\pi$
$827$	6.96675e12	0.517911	0.258956	+	0.965889i	$0.416622\pi$
$828$	−6.67428e12	−0.493478
$829$	9.54746e12	0.702090	0.351045	−	0.936359i	$-0.385826\pi$
$829$	9.54746e12	0.702090	0.351045	+	0.936359i	$0.385826\pi$
$830$	−9.23062e12	−0.675117
$831$	6.80535e12	0.495046
$832$	−3.66823e12	−0.265400
$833$	5.73325e12	0.412571
$834$	−1.17066e12	−0.0837884
$835$	−3.61459e12	−0.257318
$836$	−6.55178e10	−0.00463907
$837$	−2.57214e12	−0.181147
$838$	2.78379e13	1.95002
$839$	1.19112e13	0.829902	0.414951	−	0.909844i	$-0.363799\pi$
$839$	1.19112e13	0.829902	0.414951	+	0.909844i	$0.363799\pi$
$840$	3.27411e11	0.0226901
$841$	−1.35058e13	−0.930977
$842$	3.66841e13	2.51521
$843$	4.84950e12	0.330729
$844$	1.36968e13	0.929137
$845$	−5.63756e12	−0.380396
$846$	−1.09361e13	−0.734001
$847$	6.55616e12	0.437697
$848$	1.52756e13	1.01442
$849$	1.33361e13	0.880938
$850$	−2.11485e12	−0.138961
$851$	−2.14903e13	−1.40462
$852$	−1.21211e13	−0.788068
$853$	2.54020e13	1.64284	0.821422	−	0.570320i	$-0.193181\pi$
$853$	2.54020e13	1.64284	0.821422	+	0.570320i	$0.193181\pi$
$854$	−1.69827e12	−0.109256
$855$	−5.34398e11	−0.0341993
$856$	6.08761e12	0.387539
$857$	−2.56377e13	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$857$	−2.56377e13	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$858$	1.14363e11	0.00720429
$859$	−2.10765e13	−1.32077	−0.660387	−	0.750926i	$-0.729608\pi$
$859$	−2.10765e13	−1.32077	−0.660387	+	0.750926i	$0.729608\pi$
$860$	8.80763e12	0.549055
$861$	−3.36784e12	−0.208851
$862$	1.76550e13	1.08914
$863$	9.48317e12	0.581976	0.290988	−	0.956727i	$-0.406016\pi$
$863$	9.48317e12	0.581976	0.290988	+	0.956727i	$0.406016\pi$
$864$	−4.19734e12	−0.256249
$865$	−2.57254e12	−0.156239
$866$	3.35985e13	2.02997
$867$	−7.10251e12	−0.426900
$868$	5.87761e12	0.351449
$869$	4.54168e11	0.0270164
$870$	−1.56018e12	−0.0923289
$871$	−2.96268e12	−0.174423
$872$	3.84583e12	0.225251
$873$	8.36177e12	0.487230
$874$	9.35340e12	0.542211
$875$	−6.79203e11	−0.0391709
$876$	−1.06927e13	−0.613505
$877$	8.55003e12	0.488056	0.244028	−	0.969768i	$-0.421531\pi$
$877$	8.55003e12	0.488056	0.244028	+	0.969768i	$0.421531\pi$
$878$	−8.42301e12	−0.478346
$879$	−5.96023e12	−0.336754
$880$	−2.12414e11	−0.0119402
$881$	9.61493e12	0.537718	0.268859	−	0.963180i	$-0.413353\pi$
$881$	9.61493e12	0.537718	0.268859	+	0.963180i	$0.413353\pi$
$882$	−6.59017e12	−0.366681
$883$	−1.80164e13	−0.997341	−0.498671	−	0.866792i	$-0.666178\pi$
$883$	−1.80164e13	−0.997341	−0.498671	+	0.866792i	$0.666178\pi$
$884$	−3.05444e12	−0.168227
$885$	−1.76995e12	−0.0969878
$886$	−2.30845e12	−0.125854
$887$	−3.05992e13	−1.65979	−0.829897	−	0.557917i	$-0.811601\pi$
$887$	−3.05992e13	−1.65979	−0.829897	+	0.557917i	$0.811601\pi$
$888$	−1.73646e12	−0.0937142
$889$	4.07531e12	0.218828
$890$	1.08639e13	0.580403
$891$	4.95774e10	0.00263532
$892$	−2.06940e12	−0.109447
$893$	7.05318e12	0.371153
$894$	−2.72185e13	−1.42510
$895$	−8.31046e12	−0.432934
$896$	−3.35392e12	−0.173847
$897$	−7.51364e12	−0.387511
$898$	−1.09596e12	−0.0562406
$899$	4.84314e12	0.247291
$900$	1.11875e12	0.0568382
$901$	9.09990e12	0.460018
$902$	5.30118e11	0.0266651
$903$	−7.27481e12	−0.364105
$904$	−2.93277e12	−0.146056
$905$	4.09110e12	0.202731
$906$	2.53476e13	1.24986
$907$	1.30788e13	0.641703	0.320852	−	0.947129i	$-0.396031\pi$
$907$	1.30788e13	0.641703	0.320852	+	0.947129i	$0.396031\pi$
$908$	1.95850e13	0.956174
$909$	5.21753e12	0.253471
$910$	−2.13155e12	−0.103041
$911$	−8.21342e12	−0.395086	−0.197543	−	0.980294i	$-0.563296\pi$
$911$	−8.21342e12	−0.395086	−0.197543	+	0.980294i	$0.563296\pi$
$912$	3.11501e12	0.149102
$913$	−5.52295e11	−0.0263059
$914$	1.03729e13	0.491636
$915$	1.00344e12	0.0473255
$916$	1.89691e13	0.890260
$917$	1.03239e13	0.482150
$918$	−2.87723e12	−0.133716
$919$	−2.09082e13	−0.966936	−0.483468	−	0.875362i	$-0.660623\pi$
$919$	−2.09082e13	−0.966936	−0.483468	+	0.875362i	$0.660623\pi$
$920$	3.38596e12	0.155825
$921$	−1.94436e13	−0.890449
$922$	5.29694e13	2.41399
$923$	−1.36454e13	−0.618842
$924$	−1.13289e11	−0.00511288
$925$	3.60221e12	0.161783
$926$	3.96573e13	1.77245
$927$	3.28740e12	0.146216
$928$	7.90326e12	0.349816
$929$	−3.77790e13	−1.66410	−0.832051	−	0.554699i	$-0.812833\pi$
$929$	−3.77790e13	−1.66410	−0.832051	+	0.554699i	$0.812833\pi$
$930$	−7.54619e12	−0.330792
$931$	4.25029e12	0.185415
$932$	3.32308e13	1.44268
$933$	−9.29681e12	−0.401667
$934$	−2.81138e13	−1.20881
$935$	−1.26538e11	−0.00541462
$936$	−6.07116e11	−0.0258542
$937$	−7.01705e12	−0.297390	−0.148695	−	0.988883i	$-0.547507\pi$
$937$	−7.01705e12	−0.297390	−0.148695	+	0.988883i	$0.547507\pi$
$938$	6.37725e12	0.268981
$939$	−2.63197e13	−1.10481
$940$	−1.47656e13	−0.616846
$941$	−3.74660e13	−1.55770	−0.778850	−	0.627210i	$-0.784197\pi$
$941$	−3.74660e13	−1.55770	−0.778850	+	0.627210i	$0.784197\pi$
$942$	2.97105e13	1.22937
$943$	−3.48289e13	−1.43429
$944$	1.03171e13	0.422846
$945$	−9.24048e11	−0.0376922
$946$	1.14510e12	0.0464872
$947$	1.45907e13	0.589524	0.294762	−	0.955571i	$-0.404760\pi$
$947$	1.45907e13	0.589524	0.294762	+	0.955571i	$0.404760\pi$
$948$	1.39431e13	0.560690
$949$	−1.20374e13	−0.481764
$950$	−1.56782e12	−0.0624512
$951$	8.64269e12	0.342639
$952$	−1.13691e12	−0.0448600
$953$	4.45651e13	1.75016	0.875078	−	0.483982i	$-0.160810\pi$
$953$	4.45651e13	1.75016	0.875078	+	0.483982i	$0.160810\pi$
$954$	−1.04600e13	−0.408851
$955$	−7.24378e12	−0.281806
$956$	1.56745e13	0.606921
$957$	−9.33502e10	−0.00359759
$958$	−1.14111e13	−0.437705
$959$	−1.69723e13	−0.647971
$960$	−4.66540e12	−0.177283
$961$	−3.01461e12	−0.114019
$962$	1.13049e13	0.425576
$963$	−1.71810e13	−0.643768
$964$	−4.04945e13	−1.51025
$965$	−2.12650e13	−0.789393
$966$	1.61733e13	0.597589
$967$	−3.76646e13	−1.38520	−0.692602	−	0.721320i	$-0.743536\pi$
$967$	−3.76646e13	−1.38520	−0.692602	+	0.721320i	$0.743536\pi$
$968$	5.47847e12	0.200549
$969$	1.85565e12	0.0676144
$970$	2.45319e13	0.889729
$971$	−1.31198e13	−0.473631	−0.236816	−	0.971555i	$-0.576104\pi$
$971$	−1.31198e13	−0.473631	−0.236816	+	0.971555i	$0.576104\pi$
$972$	1.52204e12	0.0546926
$973$	1.30552e12	0.0466955
$974$	−3.38690e13	−1.20583
$975$	1.25944e12	0.0446331
$976$	−5.84904e12	−0.206329
$977$	−3.02751e13	−1.06306	−0.531532	−	0.847038i	$-0.678384\pi$
$977$	−3.02751e13	−1.06306	−0.531532	+	0.847038i	$0.678384\pi$
$978$	9.99418e12	0.349319
$979$	6.50018e11	0.0226153
$980$	−8.89786e12	−0.308154
$981$	−1.08540e13	−0.374180
$982$	−3.58020e13	−1.22859
$983$	−1.79214e13	−0.612181	−0.306091	−	0.952002i	$-0.599021\pi$
$983$	−1.79214e13	−0.612181	−0.306091	+	0.952002i	$0.599021\pi$
$984$	−2.81424e12	−0.0956936
$985$	1.06709e13	0.361191
$986$	5.41759e12	0.182541
$987$	1.21959e13	0.409061
$988$	−2.26438e12	−0.0756036
$989$	−7.52332e13	−2.50050
$990$	1.45451e11	0.00481235
$991$	−2.22633e13	−0.733259	−0.366630	−	0.930367i	$-0.619488\pi$
$991$	−2.22633e13	−0.733259	−0.366630	+	0.930367i	$0.619488\pi$
$992$	3.82260e13	1.25330
$993$	−2.80499e13	−0.915504
$994$	2.93722e13	0.954330
$995$	−2.68393e12	−0.0868094
$996$	−1.69557e13	−0.545943
$997$	3.89578e13	1.24872	0.624362	−	0.781135i	$-0.285359\pi$
$997$	3.89578e13	1.24872	0.624362	+	0.781135i	$0.285359\pi$
$998$	5.84549e13	1.86524
$999$	4.90077e12	0.155675

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.d.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.d.1.11	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q+30.7980 q^{2} +81.0000 q^{3} +436.517 q^{4} +625.000 q^{5} +2494.64 q^{6} -2782.02 q^{7} -2324.71 q^{8} +6561.00 q^{9} +19248.8 q^{10} +1151.71 q^{11} +35357.9 q^{12} +39804.6 q^{13} -85680.5 q^{14} +50625.0 q^{15} -295093. q^{16} -175791. q^{17} +202066. q^{18} -130321. q^{19} +272823. q^{20} -225343. q^{21} +35470.4 q^{22} -2.33041e6 q^{23} -188302. q^{24} +390625. q^{25} +1.22590e6 q^{26} +531441. q^{27} -1.21440e6 q^{28} -1.00066e6 q^{29} +1.55915e6 q^{30} -4.83994e6 q^{31} -7.89804e6 q^{32} +93288.5 q^{33} -5.41402e6 q^{34} -1.73876e6 q^{35} +2.86399e6 q^{36} +9.22167e6 q^{37} -4.01363e6 q^{38} +3.22417e6 q^{39} -1.45294e6 q^{40} +1.49454e7 q^{41} -6.94012e6 q^{42} +3.22833e7 q^{43} +502742. q^{44} +4.10062e6 q^{45} -7.17720e7 q^{46} -5.41216e7 q^{47} -2.39026e7 q^{48} -3.26140e7 q^{49} +1.20305e7 q^{50} -1.42391e7 q^{51} +1.73754e7 q^{52} -5.17654e7 q^{53} +1.63673e7 q^{54} +719819. q^{55} +6.46738e6 q^{56} -1.05560e7 q^{57} -3.08184e7 q^{58} -3.49621e7 q^{59} +2.20987e7 q^{60} +1.98210e7 q^{61} -1.49061e8 q^{62} -1.82528e7 q^{63} -9.21560e7 q^{64} +2.48778e7 q^{65} +2.87310e6 q^{66} -7.44306e7 q^{67} -7.67359e7 q^{68} -1.88763e8 q^{69} -5.35503e7 q^{70} -3.42811e8 q^{71} -1.52524e7 q^{72} -3.02412e8 q^{73} +2.84009e8 q^{74} +3.16406e7 q^{75} -5.68874e7 q^{76} -3.20408e6 q^{77} +9.92980e7 q^{78} +3.94342e8 q^{79} -1.84433e8 q^{80} +4.30467e7 q^{81} +4.60288e8 q^{82} -4.79544e8 q^{83} -9.83663e7 q^{84} -1.09869e8 q^{85} +9.94260e8 q^{86} -8.10535e7 q^{87} -2.67739e6 q^{88} +5.64393e8 q^{89} +1.26291e8 q^{90} -1.10737e8 q^{91} -1.01727e9 q^{92} -3.92035e8 q^{93} -1.66684e9 q^{94} -8.14506e7 q^{95} -6.39741e8 q^{96} +1.27447e9 q^{97} -1.00445e9 q^{98} +7.55637e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 33 q^{2} + 972 q^{3} + 2751 q^{4} + 7500 q^{5} - 2673 q^{6} - 5100 q^{7} - 40215 q^{8} + 78732 q^{9} - 20625 q^{10} - 60416 q^{11} + 222831 q^{12} - 164042 q^{13} - 444762 q^{14} + 607500 q^{15}+ \cdots - 396389376 q^{99}+O(q^{100}) \) 12 * q - 33 * q^2 + 972 * q^3 + 2751 * q^4 + 7500 * q^5 - 2673 * q^6 - 5100 * q^7 - 40215 * q^8 + 78732 * q^9 - 20625 * q^10 - 60416 * q^11 + 222831 * q^12 - 164042 * q^13 - 444762 * q^14 + 607500 * q^15 + 319475 * q^16 - 552834 * q^17 - 216513 * q^18 - 1563852 * q^19 + 1719375 * q^20 - 413100 * q^21 + 708846 * q^22 - 2749174 * q^23 - 3257415 * q^24 + 4687500 * q^25 - 5159376 * q^26 + 6377292 * q^27 - 2379170 * q^28 - 3415632 * q^29 - 1670625 * q^30 - 9822574 * q^31 - 22282623 * q^32 - 4893696 * q^33 + 5214442 * q^34 - 3187500 * q^35 + 18049311 * q^36 - 24559054 * q^37 + 4300593 * q^38 - 13287402 * q^39 - 25134375 * q^40 - 35856950 * q^41 - 36025722 * q^42 - 73839462 * q^43 - 88153054 * q^44 + 49207500 * q^45 - 19966000 * q^46 - 134699358 * q^47 + 25877475 * q^48 - 64331236 * q^49 - 12890625 * q^50 - 44779554 * q^51 - 290325860 * q^52 - 74807846 * q^53 - 17537553 * q^54 - 37760000 * q^55 - 403278618 * q^56 - 126672012 * q^57 - 377474064 * q^58 - 294192102 * q^59 + 139269375 * q^60 - 184407884 * q^61 - 356900784 * q^62 - 33461100 * q^63 + 169573219 * q^64 - 102526250 * q^65 + 57416526 * q^66 - 427627864 * q^67 - 56755242 * q^68 - 222683094 * q^69 - 277976250 * q^70 - 488904216 * q^71 - 263850615 * q^72 - 184702472 * q^73 - 1424419204 * q^74 + 379687500 * q^75 - 358513071 * q^76 - 827371672 * q^77 - 417909456 * q^78 - 620531838 * q^79 + 199671875 * q^80 + 516560652 * q^81 + 100137664 * q^82 - 32273124 * q^83 - 192712770 * q^84 - 345521250 * q^85 + 1147824298 * q^86 - 276666192 * q^87 + 2717542210 * q^88 + 473499162 * q^89 - 135320625 * q^90 - 1430236924 * q^91 + 1920565904 * q^92 - 795628494 * q^93 + 2483643504 * q^94 - 977407500 * q^95 - 1804892463 * q^96 + 318965234 * q^97 + 2863543931 * q^98 - 396389376 * q^99

Introduction

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